LMFDB - Embedded newform 60.7.f.a.19.13

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			19.13
Character	$\chi$	$=$	60.19
Dual form			60.7.f.a.19.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.70638 - 7.08962i) q^{2} +15.5885 q^{3} +(-36.5255 + 52.5537i) q^{4} +(108.680 + 61.7555i) q^{5} +(-57.7768 - 110.516i) q^{6} -629.059 q^{7} +(507.963 + 64.1675i) q^{8} +243.000 q^{9} +O(q^{10})$	\(q+(-3.70638 - 7.08962i) q^{2} +15.5885 q^{3} +(-36.5255 + 52.5537i) q^{4} +(108.680 + 61.7555i) q^{5} +(-57.7768 - 110.516i) q^{6} -629.059 q^{7} +(507.963 + 64.1675i) q^{8} +243.000 q^{9} +(35.0151 - 999.387i) q^{10} -1255.72i q^{11} +(-569.375 + 819.231i) q^{12} -3334.77i q^{13} +(2331.53 + 4459.79i) q^{14} +(1694.15 + 962.673i) q^{15} +(-1427.78 - 3839.10i) q^{16} -7637.86i q^{17} +(-900.651 - 1722.78i) q^{18} +1250.64i q^{19} +(-7215.05 + 3455.87i) q^{20} -9806.06 q^{21} +(-8902.61 + 4654.19i) q^{22} -14407.2 q^{23} +(7918.36 + 1000.27i) q^{24} +(7997.51 + 13423.1i) q^{25} +(-23642.3 + 12359.9i) q^{26} +3788.00 q^{27} +(22976.7 - 33059.4i) q^{28} -7208.72 q^{29} +(545.832 - 15578.9i) q^{30} -3243.73i q^{31} +(-21925.8 + 24351.6i) q^{32} -19574.8i q^{33} +(-54149.5 + 28308.8i) q^{34} +(-68365.9 - 38847.9i) q^{35} +(-8875.69 + 12770.5i) q^{36} -54841.3i q^{37} +(8866.54 - 4635.34i) q^{38} -51984.0i q^{39} +(51242.5 + 38343.2i) q^{40} +29113.1 q^{41} +(36345.0 + 69521.3i) q^{42} -12739.1 q^{43} +(65992.9 + 45865.9i) q^{44} +(26409.1 + 15006.6i) q^{45} +(53398.7 + 102142. i) q^{46} +15012.6 q^{47} +(-22256.9 - 59845.6i) q^{48} +278067. q^{49} +(65523.1 - 106451. i) q^{50} -119062. i q^{51} +(175255. + 121804. i) q^{52} +203806. i q^{53} +(-14039.8 - 26855.4i) q^{54} +(77547.9 - 136472. i) q^{55} +(-319539. - 40365.2i) q^{56} +19495.5i q^{57} +(26718.3 + 51107.1i) q^{58} +14568.1i q^{59} +(-112472. + 53871.6i) q^{60} -311116. q^{61} +(-22996.8 + 12022.5i) q^{62} -152861. q^{63} +(253909. + 65189.5i) q^{64} +(205941. - 362422. i) q^{65} +(-138778. + 72551.7i) q^{66} +101935. q^{67} +(401398. + 278976. i) q^{68} -224586. q^{69} +(-22026.6 + 628674. i) q^{70} -530826. i q^{71} +(123435. + 15592.7i) q^{72} -224270. i q^{73} +(-388804. + 203263. i) q^{74} +(124669. + 209246. i) q^{75} +(-65725.6 - 45680.1i) q^{76} +789925. i q^{77} +(-368547. + 192672. i) q^{78} -13747.8i q^{79} +(81914.6 - 505405. i) q^{80} +59049.0 q^{81} +(-107904. - 206401. i) q^{82} -632021. q^{83} +(358171. - 515345. i) q^{84} +(471680. - 830079. i) q^{85} +(47215.9 + 90315.3i) q^{86} -112373. q^{87} +(80576.7 - 637861. i) q^{88} -303793. q^{89} +(8508.68 - 242851. i) q^{90} +2.09777e6i q^{91} +(526231. - 757153. i) q^{92} -50564.7i q^{93} +(-55642.3 - 106433. i) q^{94} +(-77233.7 + 135919. i) q^{95} +(-341790. + 379604. i) q^{96} +625514. i q^{97} +(-1.03062e6 - 1.97139e6i) q^{98} -305141. 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 $

$2$	−3.70638	−	7.08962i	−0.463298	−	0.886203i
$2$	−3.70638	−	7.08962i	−0.463298	−	0.886203i
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	−36.5255	+	52.5537i	−0.570710	+	0.821152i
$5$	108.680	+	61.7555i	0.869437	+	0.494044i
$5$	108.680	+	61.7555i	0.869437	+	0.494044i
$6$	−57.7768	−	110.516i	−0.267485	−	0.511649i
$7$	−629.059			−1.83399			−0.916996	−	0.398896i	$-0.869393\pi$
$7$	−629.059			−1.83399			−0.916996	+	0.398896i	$0.869393\pi$
$8$	507.963	+	64.1675i	0.992115	+	0.125327i
$9$	243.000			0.333333
$10$	35.0151	−	999.387i	0.0350151	−	0.999387i
$11$		−	1255.72i		−	0.943444i	−0.881747	−	0.471722i	$-0.843633\pi$
$11$		−	1255.72i		−	0.943444i	0.881747	−	0.471722i	$-0.156367\pi$
$12$	−569.375	+	819.231i	−0.329500	+	0.474092i
$13$		−	3334.77i		−	1.51788i	−0.651163	−	0.758938i	$-0.725719\pi$
$13$		−	3334.77i		−	1.51788i	0.651163	−	0.758938i	$-0.274281\pi$
$14$	2331.53	+	4459.79i	0.849685	+	1.62529i
$15$	1694.15	+	962.673i	0.501970	+	0.285237i
$16$	−1427.78	−	3839.10i	−0.348580	−	0.937279i
$17$		−	7637.86i		−	1.55462i	−0.629117	−	0.777311i	$-0.716583\pi$
$17$		−	7637.86i		−	1.55462i	0.629117	−	0.777311i	$-0.283417\pi$
$18$	−900.651	−	1722.78i	−0.154433	−	0.295401i
$19$			1250.64i			0.182335i	0.995836	+	0.0911675i	$0.0290599\pi$
$19$			1250.64i			0.182335i	−0.995836	+	0.0911675i	$0.970940\pi$
$20$	−7215.05	+	3455.87i	−0.901882	+	0.431983i
$21$	−9806.06			−1.05886
$22$	−8902.61	+	4654.19i	−0.836083	+	0.437096i
$23$	−14407.2			−1.18412			−0.592062	−	0.805893i	$-0.701686\pi$
$23$	−14407.2			−1.18412			−0.592062	+	0.805893i	$0.701686\pi$
$24$	7918.36	+	1000.27i	0.572798	+	0.0723577i
$25$	7997.51	+	13423.1i	0.511841	+	0.859080i
$26$	−23642.3	+	12359.9i	−1.34515	+	0.703228i
$27$	3788.00			0.192450
$28$	22976.7	−	33059.4i	1.04668	−	1.50599i
$29$	−7208.72			−0.295573			−0.147786	−	0.989019i	$-0.547215\pi$
$29$	−7208.72			−0.295573			−0.147786	+	0.989019i	$0.547215\pi$
$30$	545.832	−	15578.9i	0.0202160	−	0.576996i
$31$		−	3243.73i		−	0.108883i	−0.998517	−	0.0544414i	$-0.982662\pi$
$31$		−	3243.73i		−	0.108883i	0.998517	−	0.0544414i	$-0.0173378\pi$
$32$	−21925.8	+	24351.6i	−0.669123	+	0.743152i
$33$		−	19574.8i		−	0.544698i
$34$	−54149.5	+	28308.8i	−1.37771	+	0.720253i
$35$	−68365.9	−	38847.9i	−1.59454	−	0.906073i
$36$	−8875.69	+	12770.5i	−0.190237	+	0.273717i
$37$		−	54841.3i		−	1.08269i	−0.840802	−	0.541343i	$-0.817916\pi$
$37$		−	54841.3i		−	1.08269i	0.840802	−	0.541343i	$-0.182084\pi$
$38$	8866.54	−	4635.34i	0.161586	−	0.0844755i
$39$		−	51984.0i		−	0.876346i
$40$	51242.5	+	38343.2i	0.800664	+	0.599113i
$41$	29113.1			0.422412			0.211206	−	0.977442i	$-0.432261\pi$
$41$	29113.1			0.422412			0.211206	+	0.977442i	$0.432261\pi$
$42$	36345.0	+	69521.3i	0.490566	+	0.938361i
$43$	−12739.1			−0.160226			−0.0801129	−	0.996786i	$-0.525528\pi$
$43$	−12739.1			−0.160226			−0.0801129	+	0.996786i	$0.525528\pi$
$44$	65992.9	+	45865.9i	0.774711	+	0.538433i
$45$	26409.1	+	15006.6i	0.289812	+	0.164681i
$46$	53398.7	+	102142.i	0.548602	+	1.04937i
$47$	15012.6			0.144598			0.0722988	−	0.997383i	$-0.476966\pi$
$47$	15012.6			0.144598			0.0722988	+	0.997383i	$0.476966\pi$
$48$	−22256.9	−	59845.6i	−0.201253	−	0.541138i
$49$	278067.			2.36353
$50$	65523.1	−	106451.i	0.524185	−	0.851605i
$51$		−	119062.i		−	0.897561i
$52$	175255.	+	121804.i	1.24641	+	0.866267i
$53$			203806.i			1.36895i	0.729035	+	0.684476i	$0.239969\pi$
$53$			203806.i			1.36895i	−0.729035	+	0.684476i	$0.760031\pi$
$54$	−14039.8	−	26855.4i	−0.0891617	−	0.170550i
$55$	77547.9	−	136472.i	0.466103	−	0.820265i
$56$	−319539.	−	40365.2i	−1.81953	−	0.229849i
$57$			19495.5i			0.105271i
$58$	26718.3	+	51107.1i	0.136938	+	0.261937i
$59$			14568.1i			0.0709328i	0.999371	+	0.0354664i	$0.0112917\pi$
$59$			14568.1i			0.0709328i	−0.999371	+	0.0354664i	$0.988708\pi$
$60$	−112472.	+	53871.6i	−0.520702	+	0.249406i
$61$	−311116.			−1.37067			−0.685335	−	0.728228i	$-0.740344\pi$
$61$	−311116.			−1.37067			−0.685335	+	0.728228i	$0.740344\pi$
$62$	−22996.8	+	12022.5i	−0.0964922	+	0.0504452i
$63$	−152861.			−0.611331
$64$	253909.	+	65189.5i	0.968586	+	0.248678i
$65$	205941.	−	362422.i	0.749898	−	1.31970i
$66$	−138778.	+	72551.7i	−0.482712	+	0.252357i
$67$	101935.			0.338921			0.169461	−	0.985537i	$-0.445797\pi$
$67$	101935.			0.338921			0.169461	+	0.985537i	$0.445797\pi$
$68$	401398.	+	278976.i	1.27658	+	0.887239i
$69$	−224586.			−0.683654
$70$	−22026.6	+	628674.i	−0.0642175	+	1.83287i
$71$		−	530826.i		−	1.48312i	−0.670885	−	0.741561i	$-0.734086\pi$
$71$		−	530826.i		−	1.48312i	0.670885	−	0.741561i	$-0.265914\pi$
$72$	123435.	+	15592.7i	0.330705	+	0.0417757i
$73$		−	224270.i		−	0.576504i	−0.957555	−	0.288252i	$-0.906926\pi$
$73$		−	224270.i		−	0.576504i	0.957555	−	0.288252i	$-0.0930741\pi$
$74$	−388804.	+	203263.i	−0.959480	+	0.501606i
$75$	124669.	+	209246.i	0.295511	+	0.495990i
$76$	−65725.6	−	45680.1i	−0.149725	−	0.104061i
$77$			789925.i			1.73027i
$78$	−368547.	+	192672.i	−0.776620	+	0.406009i
$79$		−	13747.8i		−	0.0278837i	−0.999903	−	0.0139419i	$-0.995562\pi$
$79$		−	13747.8i		−	0.0278837i	0.999903	−	0.0139419i	$-0.00443797\pi$
$80$	81914.6	−	505405.i	0.159989	−	0.987119i
$81$	59049.0			0.111111
$82$	−107904.	−	206401.i	−0.195703	−	0.374343i
$83$	−632021.			−1.10534			−0.552671	−	0.833399i	$-0.686392\pi$
$83$	−632021.			−1.10534			−0.552671	+	0.833399i	$0.686392\pi$
$84$	358171.	−	515345.i	0.604300	−	0.869481i
$85$	471680.	−	830079.i	0.768052	−	1.35165i
$86$	47215.9	+	90315.3i	0.0742323	+	0.141993i
$87$	−112373.			−0.170649
$88$	80576.7	−	637861.i	0.118239	−	0.936005i
$89$	−303793.			−0.430931			−0.215465	−	0.976512i	$-0.569127\pi$
$89$	−303793.			−0.430931			−0.215465	+	0.976512i	$0.569127\pi$
$90$	8508.68	−	242851.i	0.0116717	−	0.333129i
$91$			2.09777e6i			2.78377i
$92$	526231.	−	757153.i	0.675791	−	0.972345i
$93$		−	50564.7i		−	0.0628635i
$94$	−55642.3	−	106433.i	−0.0669917	−	0.128143i
$95$	−77233.7	+	135919.i	−0.0900816	+	0.158529i
$96$	−341790.	+	379604.i	−0.386318	+	0.429059i
$97$			625514.i			0.685364i	0.939451	+	0.342682i	$0.111335\pi$
$97$			625514.i			0.685364i	−0.939451	+	0.342682i	$0.888665\pi$
$98$	−1.03062e6	−	1.97139e6i	−1.09502	−	2.09456i
$99$		−	305141.i		−	0.314481i
$100$	−997548.	−	69987.3i	−0.997548	−	0.0699873i
$101$	70748.0			0.0686673			0.0343336	−	0.999410i	$-0.489069\pi$
$101$	70748.0			0.0686673			0.0343336	+	0.999410i	$0.489069\pi$
$102$	−844107.	+	441291.i	−0.795421	+	0.415838i
$103$	1.12706e6			1.03142			0.515709	−	0.856764i	$-0.327529\pi$
$103$	1.12706e6			1.03142			0.515709	+	0.856764i	$0.327529\pi$
$104$	213984.	−	1.69394e6i	0.190231	−	1.50591i
$105$	−1.06572e6	−	605579.i	−0.920608	−	0.523122i
$106$	1.44490e6	−	755381.i	1.21317	−	0.634233i
$107$	1.13145e6			0.923599			0.461800	−	0.886984i	$-0.347204\pi$
$107$	1.13145e6			0.923599			0.461800	+	0.886984i	$0.347204\pi$
$108$	−138358.	+	199073.i	−0.109833	+	0.158031i
$109$	−1.24198e6			−0.959034			−0.479517	−	0.877533i	$-0.659188\pi$
$109$	−1.24198e6			−0.959034			−0.479517	+	0.877533i	$0.659188\pi$
$110$	−1.25495e6	−	43969.4i	−0.942865	−	0.0330348i
$111$		−	854892.i		−	0.625089i
$112$	898160.	+	2.41502e6i	0.639292	+	1.71896i
$113$			439583.i			0.304653i	0.988330	+	0.152327i	$0.0486766\pi$
$113$			439583.i			0.304653i	−0.988330	+	0.152327i	$0.951323\pi$
$114$	138216.	−	72257.8i	0.0932916	−	0.0487719i
$115$	−1.56577e6	−	889726.i	−1.02952	−	0.585009i
$116$	263302.	−	378845.i	0.168686	−	0.242710i
$117$		−	810350.i		−	0.505959i
$118$	103282.	−	53995.0i	0.0628608	−	0.0328630i
$119$			4.80467e6i			2.85116i
$120$	798792.	+	597712.i	0.462264	+	0.345898i
$121$	194718.			0.109913
$122$	1.15311e6	+	2.20569e6i	0.635028	+	1.21469i
$123$	453828.			0.243880
$124$	170470.	+	118479.i	0.0894092	+	0.0621405i
$125$	40213.3	+	1.95271e6i	0.0205892	+	0.999788i
$126$	566563.	+	1.08373e6i	0.283228	+	0.541763i
$127$	2.74141e6			1.33833			0.669164	−	0.743115i	$-0.266652\pi$
$127$	2.74141e6			1.33833			0.669164	+	0.743115i	$0.266652\pi$
$128$	−478916.	−	2.04174e6i	−0.228365	−	0.973576i
$129$	−198583.			−0.0925065
$130$	−3.33273e6	−	116768.i	−1.51694	−	0.0531486i
$131$		−	1.16176e6i		−	0.516777i	−0.966041	−	0.258388i	$-0.916809\pi$
$131$		−	1.16176e6i		−	0.516777i	0.966041	−	0.258388i	$-0.0831914\pi$
$132$	1.02873e6	+	714978.i	0.447279	+	0.310865i
$133$		−	786725.i		−	0.334401i
$134$	−377810.	−	722680.i	−0.157021	−	0.300353i
$135$	411678.	+	233930.i	0.167323	+	0.0950789i
$136$	490102.	−	3.87975e6i	0.194836	−	1.54236i
$137$			4.10213e6i			1.59532i	0.603108	+	0.797660i	$0.293929\pi$
$137$			4.10213e6i			1.59532i	−0.603108	+	0.797660i	$0.706071\pi$
$138$	832403.	+	1.59223e6i	0.316735	+	0.605856i
$139$		−	1.18125e6i		−	0.439842i	−0.975518	−	0.219921i	$-0.929420\pi$
$139$		−	1.18125e6i		−	0.439842i	0.975518	−	0.219921i	$-0.0705799\pi$
$140$	4.53870e6	−	2.17394e6i	1.65404	−	0.792254i
$141$	234023.			0.0834834
$142$	−3.76335e6	+	1.96744e6i	−1.31435	+	0.687127i
$143$	−4.18755e6			−1.43203
$144$	−346951.	−	932900.i	−0.116193	−	0.312426i
$145$	−783441.	−	445178.i	−0.256982	−	0.146026i
$146$	−1.58999e6	+	831230.i	−0.510899	+	0.267093i
$147$	4.33463e6			1.36458
$148$	2.88211e6	+	2.00310e6i	0.889050	+	0.617900i
$149$	1.36642e6			0.413073			0.206536	−	0.978439i	$-0.433781\pi$
$149$	1.36642e6			0.413073			0.206536	+	0.978439i	$0.433781\pi$
$150$	1.02140e6	−	1.65940e6i	0.302638	−	0.491674i
$151$		−	3.24068e6i		−	0.941251i	−0.882333	−	0.470626i	$-0.844028\pi$
$151$		−	3.24068e6i		−	0.941251i	0.882333	−	0.470626i	$-0.155972\pi$
$152$	−80250.2	+	635277.i	−0.0228515	+	0.180897i
$153$		−	1.85600e6i		−	0.518207i
$154$	5.60027e6	−	2.92776e6i	1.53337	−	0.801630i
$155$	200318.	−	352527.i	0.0537929	−	0.0946667i
$156$	2.73195e6	+	1.89874e6i	0.719613	+	0.500140i
$157$		−	533613.i		−	0.137888i	−0.997621	−	0.0689442i	$-0.978037\pi$
$157$		−	533613.i		−	0.137888i	0.997621	−	0.0689442i	$-0.0219630\pi$
$158$	−97466.4	+	50954.4i	−0.0247106	+	0.0129185i
$159$			3.17701e6i			0.790365i
$160$	−3.88674e6	+	1.29248e6i	−0.948910	+	0.315547i
$161$	9.06300e6			2.17167
$162$	−218858.	−	418635.i	−0.0514775	−	0.0984670i
$163$	3.68844e6			0.851686			0.425843	−	0.904797i	$-0.359978\pi$
$163$	3.68844e6			0.851686			0.425843	+	0.904797i	$0.359978\pi$
$164$	−1.06337e6	+	1.53000e6i	−0.241075	+	0.346864i
$165$	1.20885e6	−	2.12738e6i	0.269105	−	0.473580i
$166$	2.34251e6	+	4.48079e6i	0.512103	+	0.979558i
$167$	−5.03742e6			−1.08158			−0.540790	−	0.841157i	$-0.681875\pi$
$167$	−5.03742e6			−1.08158			−0.540790	+	0.841157i	$0.681875\pi$
$168$	−4.98112e6	−	629231.i	−1.05051	−	0.132703i
$169$	−6.29390e6			−1.30395
$170$	−7.63317e6	−	267441.i	−1.55367	−	0.0544353i
$171$			303905.i			0.0607784i
$172$	465301.	−	669486.i	0.0914426	−	0.131570i
$173$			3.35046e6i			0.647092i	0.946212	+	0.323546i	$0.104875\pi$
$173$			3.35046e6i			0.647092i	−0.946212	+	0.323546i	$0.895125\pi$
$174$	416497.	+	796681.i	0.0790613	+	0.151230i
$175$	−5.03091e6	−	8.44395e6i	−0.938712	−	1.57555i
$176$	−4.82084e6	+	1.79290e6i	−0.884270	+	0.328865i
$177$			227094.i			0.0409530i
$178$	1.12597e6	+	2.15377e6i	0.199649	+	0.381892i
$179$		−	497081.i		−	0.0866699i	−0.999061	−	0.0433349i	$-0.986202\pi$
$179$		−	497081.i		−	0.0866699i	0.999061	−	0.0433349i	$-0.0137983\pi$
$180$	−1.75326e6	+	839775.i	−0.300627	+	0.143994i
$181$	−2.46770e6			−0.416157			−0.208079	−	0.978112i	$-0.566721\pi$
$181$	−2.46770e6			−0.416157			−0.208079	+	0.978112i	$0.566721\pi$
$182$	1.48724e7	−	7.77514e6i	2.46699	−	1.28972i
$183$	−4.84982e6			−0.791356
$184$	−7.31834e6	−	924476.i	−1.17479	−	0.148403i
$185$	3.38676e6	−	5.96013e6i	0.534895	−	0.941328i
$186$	−358484.	+	187412.i	−0.0557098	+	0.0291245i
$187$	−9.59104e6			−1.46670
$188$	−548340.	+	788965.i	−0.0825233	+	0.118736i
$189$	−2.38287e6			−0.352952
$190$	1.24987e6	+	43791.2i	0.182223	+	0.00638449i
$191$		−	1.52891e6i		−	0.219423i	−0.993963	−	0.109711i	$-0.965007\pi$
$191$		−	1.52891e6i		−	0.219423i	0.993963	−	0.109711i	$-0.0349926\pi$
$192$	3.95805e6	+	1.01620e6i	0.559214	+	0.143574i
$193$		−	9.85234e6i		−	1.37046i	−0.728325	−	0.685232i	$-0.759701\pi$
$193$		−	9.85234e6i		−	1.37046i	0.728325	−	0.685232i	$-0.240299\pi$
$194$	4.43465e6	−	2.31839e6i	0.607372	−	0.317528i
$195$	3.21030e6	−	5.64960e6i	0.432954	−	0.761927i
$196$	−1.01565e7	+	1.46134e7i	−1.34889	+	1.94081i
$197$			2.71648e6i			0.355310i	0.984093	+	0.177655i	$0.0568511\pi$
$197$			2.71648e6i			0.355310i	−0.984093	+	0.177655i	$0.943149\pi$
$198$	−2.16333e6	+	1.13097e6i	−0.278694	+	0.145699i
$199$			1.14524e7i			1.45324i	0.687042	+	0.726618i	$0.258909\pi$
$199$			1.14524e7i			1.45324i	−0.687042	+	0.726618i	$0.741091\pi$
$200$	3.20111e6	+	7.33164e6i	0.400139	+	0.916455i
$201$	1.58901e6			0.195676
$202$	−262219.	−	501576.i	−0.0318134	−	0.0608531i
$203$	4.53471e6			0.542078
$204$	6.25717e6	+	4.34881e6i	0.737034	+	0.512247i
$205$	3.16400e6	+	1.79789e6i	0.367261	+	0.208690i
$206$	−4.17731e6	−	7.99041e6i	−0.477853	−	0.914045i
$207$	−3.50096e6			−0.394708
$208$	−1.28025e7	+	4.76133e6i	−1.42267	+	0.529101i
$209$	1.57045e6			0.172023
$210$	−343361.	+	9.80005e6i	−0.0370760	+	1.05821i
$211$		−	1.59562e7i		−	1.69857i	−0.527936	−	0.849284i	$-0.677034\pi$
$211$		−	1.59562e7i		−	1.69857i	0.527936	−	0.849284i	$-0.322966\pi$
$212$	−1.07107e7	−	7.44409e6i	−1.12412	−	0.781275i
$213$		−	8.27475e6i		−	0.856281i
$214$	−4.19358e6	−	8.02154e6i	−0.427901	−	0.818496i
$215$	−1.38448e6	−	786709.i	−0.139306	−	0.0791587i
$216$	1.92416e6	+	243066.i	0.190933	+	0.0241192i
$217$			2.04050e6i			0.199690i
$218$	4.60324e6	+	8.80515e6i	0.444318	+	0.849899i
$219$		−	3.49602e6i		−	0.332845i
$220$	4.33961e6	+	9.06012e6i	0.407552	+	0.850875i
$221$	−2.54705e7			−2.35972
$222$	−6.06086e6	+	3.16856e6i	−0.553956	+	0.289603i
$223$	4.91870e6			0.443543			0.221771	−	0.975099i	$-0.428816\pi$
$223$	4.91870e6			0.443543			0.221771	+	0.975099i	$0.428816\pi$
$224$	1.37926e7	−	1.53186e7i	1.22717	−	1.36293i
$225$	1.94339e6	+	3.26182e6i	0.170614	+	0.286360i
$226$	3.11648e6	−	1.62926e6i	0.269985	−	0.141145i
$227$	9.26812e6			0.792344			0.396172	−	0.918176i	$-0.370338\pi$
$227$	9.26812e6			0.792344			0.396172	+	0.918176i	$0.370338\pi$
$228$	−1.02456e6	−	712082.i	−0.0864436	−	0.0600794i
$229$	4.35025e6			0.362249			0.181125	−	0.983460i	$-0.442026\pi$
$229$	4.35025e6			0.362249			0.181125	+	0.983460i	$0.442026\pi$
$230$	−504471.	+	1.43984e7i	−0.0414623	+	1.18340i
$231$			1.23137e7i			0.998971i
$232$	−3.66177e6	−	462566.i	−0.293242	−	0.0370433i
$233$			151080.i			0.0119437i	0.999982	+	0.00597185i	$0.00190091\pi$
$233$			151080.i			0.0119437i	−0.999982	+	0.00597185i	$0.998099\pi$
$234$	−5.74507e6	+	3.00347e6i	−0.448382	+	0.234409i
$235$	1.63156e6	+	927108.i	0.125718	+	0.0714376i
$236$	−765608.	−	532106.i	−0.0582465	−	0.0404821i
$237$		−	214306.i		−	0.0160987i
$238$	3.40633e7	−	1.78079e7i	2.52671	−	1.32094i
$239$			1.10896e7i			0.812313i	0.913804	+	0.406156i	$0.133131\pi$
$239$			1.10896e7i			0.812313i	−0.913804	+	0.406156i	$0.866869\pi$
$240$	1.27692e6	−	7.87848e6i	0.0923699	−	0.569913i
$241$	2.28233e7			1.63053			0.815264	−	0.579090i	$-0.196592\pi$
$241$	2.28233e7			1.63053			0.815264	+	0.579090i	$0.196592\pi$
$242$	−721700.	−	1.38048e6i	−0.0509226	−	0.0974055i
$243$	920483.			0.0641500
$244$	1.13636e7	−	1.63503e7i	0.782255	−	1.12553i
$245$	3.02202e7	+	1.71722e7i	2.05494	+	1.16769i
$246$	−1.68206e6	−	3.21747e6i	−0.112989	−	0.216127i
$247$	4.17059e6			0.276762
$248$	208142.	−	1.64769e6i	0.0136460	−	0.108024i
$249$	−9.85223e6			−0.638170
$250$	1.36949e7	−	7.52259e6i	0.876476	−	0.481446i
$251$		−	1.40380e7i		−	0.887737i	−0.896092	−	0.443868i	$-0.853606\pi$
$251$		−	1.40380e7i		−	0.887737i	0.896092	−	0.443868i	$-0.146394\pi$
$252$	5.58333e6	−	8.03343e6i	0.348893	−	0.501995i
$253$			1.80915e7i			1.11715i
$254$	−1.01607e7	−	1.94356e7i	−0.620045	−	1.18603i
$255$	7.35276e6	−	1.29397e7i	0.443435	−	0.780373i
$256$	−1.27001e7	+	1.09628e7i	−0.756984	+	0.653433i
$257$		−	1.36204e7i		−	0.802401i	−0.915990	−	0.401200i	$-0.868593\pi$
$257$		−	1.36204e7i		−	0.802401i	0.915990	−	0.401200i	$-0.131407\pi$
$258$	736023.	+	1.40788e6i	0.0428580	+	0.0819795i
$259$			3.44985e7i			1.98564i
$260$	1.15245e7	+	2.40606e7i	0.655697	+	1.36894i
$261$	−1.75172e6			−0.0985242
$262$	−8.23644e6	+	4.30593e6i	−0.457969	+	0.239421i
$263$	−1.24080e7			−0.682081			−0.341041	−	0.940049i	$-0.610779\pi$
$263$	−1.24080e7			−0.682081			−0.341041	+	0.940049i	$0.610779\pi$
$264$	1.25607e6	−	9.94328e6i	0.0682654	−	0.540403i
$265$	−1.25861e7	+	2.21495e7i	−0.676323	+	1.19022i
$266$	−5.57758e6	+	2.91590e6i	−0.296347	+	0.154927i
$267$	−4.73566e6			−0.248798
$268$	−3.72322e6	+	5.35706e6i	−0.193426	+	0.278306i
$269$	−1.82099e7			−0.935513			−0.467756	−	0.883857i	$-0.654938\pi$
$269$	−1.82099e7			−0.935513			−0.467756	+	0.883857i	$0.654938\pi$
$270$	132637.	−	3.78567e6i	0.00673867	−	0.192332i
$271$			2.00391e7i			1.00686i	0.864036	+	0.503430i	$0.167929\pi$
$271$			2.00391e7i			1.00686i	−0.864036	+	0.503430i	$0.832071\pi$
$272$	−2.93225e7	+	1.09052e7i	−1.45711	+	0.541910i
$273$			3.27010e7i			1.60721i
$274$	2.90825e7	−	1.52041e7i	1.41378	−	0.739108i
$275$	1.68557e7	−	1.00427e7i	0.810494	−	0.482893i
$276$	8.20312e6	−	1.18028e7i	0.390168	−	0.561383i
$277$		−	4.03922e7i		−	1.90046i	−0.311552	−	0.950229i	$-0.600849\pi$
$277$		−	4.03922e7i		−	1.90046i	0.311552	−	0.950229i	$-0.399151\pi$
$278$	−8.37459e6	+	4.37815e6i	−0.389789	+	0.203778i
$279$		−	788226.i		−	0.0362943i
$280$	−3.22346e7	−	2.41202e7i	−1.46841	−	1.09877i
$281$	−1.17723e7			−0.530570			−0.265285	−	0.964170i	$-0.585466\pi$
$281$	−1.17723e7			−0.530570			−0.265285	+	0.964170i	$0.585466\pi$
$282$	−867377.	−	1.65913e6i	−0.0386777	−	0.0739832i
$283$	3.11617e7			1.37487			0.687435	−	0.726246i	$-0.258737\pi$
$283$	3.11617e7			1.37487			0.687435	+	0.726246i	$0.258737\pi$
$284$	2.78969e7	+	1.93887e7i	1.21787	+	0.846433i
$285$	−1.20395e6	+	2.11876e6i	−0.0520086	+	0.0915267i
$286$	1.55207e7	+	2.96882e7i	0.663457	+	1.26907i
$287$	−1.83138e7			−0.774701
$288$	−5.32798e6	+	5.91744e6i	−0.223041	+	0.247717i
$289$	−3.41993e7			−1.41685
$290$	−252414.	+	7.20430e6i	−0.0103495	+	0.295391i
$291$			9.75079e6i			0.395695i
$292$	1.17862e7	+	8.19156e6i	0.473397	+	0.329017i
$293$		−	4.74720e6i		−	0.188727i	−0.995538	−	0.0943637i	$-0.969918\pi$
$293$		−	4.74720e6i		−	0.188727i	0.995538	−	0.0943637i	$-0.0300817\pi$
$294$	−1.60658e7	−	3.07309e7i	−0.632209	−	1.20930i
$295$	−899661.	+	1.58326e6i	−0.0350439	+	0.0616715i
$296$	3.51903e6	−	2.78574e7i	0.135690	−	1.07415i
$297$		−	4.75668e6i		−	0.181566i
$298$	−5.06449e6	−	9.68743e6i	−0.191376	−	0.366066i
$299$			4.80448e7i			1.79735i
$300$	−1.55502e7	−	1.09099e6i	−0.575935	−	0.0404072i
$301$	8.01364e6			0.293853
$302$	−2.29752e7	+	1.20112e7i	−0.834140	+	0.436080i
$303$	1.10285e6			0.0396451
$304$	4.80131e6	−	1.78564e6i	0.170899	−	0.0635583i
$305$	−3.38119e7	−	1.92131e7i	−1.19171	−	0.677171i
$306$	−1.31583e7	+	6.87904e6i	−0.459237	+	0.240084i
$307$	1.59064e7			0.549739			0.274870	−	0.961482i	$-0.411365\pi$
$307$	1.59064e7			0.549739			0.274870	+	0.961482i	$0.411365\pi$
$308$	−4.15135e7	−	2.88524e7i	−1.42081	−	0.987482i
$309$	1.75691e7			0.595489
$310$	−3.24174e6	−	113580.i	−0.108816	−	0.00381255i
$311$		−	3.14540e7i		−	1.04567i	−0.852433	−	0.522836i	$-0.824874\pi$
$311$		−	3.14540e7i		−	1.04567i	0.852433	−	0.522836i	$-0.175126\pi$
$312$	3.33568e6	−	2.64059e7i	0.109830	−	0.869436i
$313$			3.36787e7i			1.09830i	0.835722	+	0.549152i	$0.185049\pi$
$313$			3.36787e7i			1.09830i	−0.835722	+	0.549152i	$0.814951\pi$
$314$	−3.78311e6	+	1.97777e6i	−0.122197	+	0.0638834i
$315$	−1.66129e7	−	9.44004e6i	−0.531513	−	0.302024i
$316$	722495.	+	502143.i	0.0228968	+	0.0159135i
$317$		−	3.04193e7i		−	0.954931i	−0.878650	−	0.477466i	$-0.841556\pi$
$317$		−	3.04193e7i		−	0.954931i	0.878650	−	0.477466i	$-0.158444\pi$
$318$	2.25238e7	−	1.17752e7i	0.700424	−	0.366174i
$319$			9.05217e6i			0.278856i
$320$	2.35689e7	+	2.27651e7i	0.719267	+	0.694734i
$321$	1.76375e7			0.533240
$322$	−3.35910e7	−	6.42533e7i	−1.00613	−	1.92454i
$323$	9.55218e6			0.283462
$324$	−2.15679e6	+	3.10324e6i	−0.0634122	+	0.0912391i
$325$	4.47631e7	−	2.66699e7i	1.30398	−	0.776910i
$326$	−1.36708e7	−	2.61496e7i	−0.394584	−	0.754766i
$327$	−1.93605e7			−0.553699
$328$	1.47884e7	+	1.86811e6i	0.419082	+	0.0529397i
$329$	−9.44379e6			−0.265191
$330$	−1.95628e7	−	685414.i	−0.544364	−	0.0190727i
$331$			632136.i			0.0174312i	0.999962	+	0.00871559i	$0.00277429\pi$
$331$			632136.i			0.0174312i	−0.999962	+	0.00871559i	$0.997226\pi$
$332$	2.30848e7	−	3.32150e7i	0.630830	−	0.907654i
$333$		−	1.33264e7i		−	0.360896i
$334$	1.86706e7	+	3.57134e7i	0.501094	+	0.958499i
$335$	1.10783e7	+	6.29505e6i	0.294671	+	0.167442i
$336$	1.40009e7	+	3.76464e7i	0.369096	+	0.992444i
$337$		−	9.03413e6i		−	0.236046i	−0.993011	−	0.118023i	$-0.962344\pi$
$337$		−	9.03413e6i		−	0.236046i	0.993011	−	0.118023i	$-0.0376557\pi$
$338$	2.33276e7	+	4.46214e7i	0.604116	+	1.15556i
$339$			6.85243e6i			0.175892i
$340$	2.63954e7	+	5.51075e7i	0.671571	+	1.40208i
$341$	−4.07323e6			−0.102725
$342$	2.15457e6	−	1.12639e6i	0.0538619	−	0.0281585i
$343$	−1.00912e8			−2.50070
$344$	−6.47098e6	−	817435.i	−0.158963	−	0.0200807i
$345$	−2.44080e7	−	1.38695e7i	−0.594394	−	0.337755i
$346$	2.37535e7	−	1.24181e7i	0.573455	−	0.299796i
$347$	2.44261e7			0.584610			0.292305	−	0.956325i	$-0.405578\pi$
$347$	2.44261e7			0.584610			0.292305	+	0.956325i	$0.405578\pi$
$348$	4.10447e6	−	5.90561e6i	0.0973911	−	0.140129i
$349$	4.73481e6			0.111385			0.0556924	−	0.998448i	$-0.482263\pi$
$349$	4.73481e6			0.111385			0.0556924	+	0.998448i	$0.482263\pi$
$350$	−4.12179e7	+	6.69637e7i	−0.961351	+	1.56184i
$351$		−	1.26321e7i		−	0.292115i
$352$	3.05789e7	+	2.75328e7i	0.701122	+	0.631280i
$353$		−	4.56869e7i		−	1.03865i	−0.854578	−	0.519323i	$-0.826184\pi$
$353$		−	4.56869e7i		−	1.03865i	0.854578	−	0.519323i	$-0.173816\pi$
$354$	1.61001e6	−	841698.i	0.0362927	−	0.0189735i
$355$	3.27814e7	−	5.76899e7i	0.732728	−	1.28948i
$356$	1.10962e7	−	1.59654e7i	0.245936	−	0.353859i
$357$			7.48973e7i			1.64612i
$358$	−3.52412e6	+	1.84237e6i	−0.0768071	+	0.0401540i
$359$			2.01055e7i			0.434542i	0.976111	+	0.217271i	$0.0697155\pi$
$359$			2.01055e7i			0.434542i	−0.976111	+	0.217271i	$0.930285\pi$
$360$	1.24519e7	+	9.31741e6i	0.266888	+	0.199704i
$361$	4.54818e7			0.966754
$362$	9.14626e6	+	1.74951e7i	0.192805	+	0.368800i
$363$	3.03536e6			0.0634585
$364$	−1.10246e8	−	7.66220e7i	−2.28590	−	1.58873i
$365$	1.38499e7	−	2.43736e7i	0.284818	−	0.501234i
$366$	1.79753e7	+	3.43834e7i	0.366634	+	0.701302i
$367$	−6.85183e7			−1.38614			−0.693072	−	0.720868i	$-0.743743\pi$
$367$	−6.85183e7			−1.38614			−0.693072	+	0.720868i	$0.743743\pi$
$368$	2.05704e7	+	5.53107e7i	0.412761	+	1.10985i
$369$	7.07447e6			0.140804
$370$	−5.48077e7	−	1.92028e6i	−1.08202	−	0.0379104i
$371$		−	1.28206e8i		−	2.51065i
$372$	2.65736e6	+	1.84690e6i	0.0516205	+	0.0358768i
$373$			1.07141e7i			0.206457i	0.994658	+	0.103229i	$0.0329173\pi$
$373$			1.07141e7i			0.206457i	−0.994658	+	0.103229i	$0.967083\pi$
$374$	3.55481e7	+	6.79968e7i	0.679518	+	1.29979i
$375$	626863.	+	3.04398e7i	0.0118872	+	0.577228i
$376$	7.62582e6	+	963318.i	0.143457	+	0.0181220i
$377$			2.40395e7i			0.448643i
$378$	8.83184e6	+	1.68937e7i	0.163522	+	0.312787i
$379$		−	9.89266e7i		−	1.81717i	−0.417701	−	0.908585i	$-0.637164\pi$
$379$		−	9.89266e7i		−	1.81717i	0.417701	−	0.908585i	$-0.362836\pi$
$380$	−4.32203e6	−	9.02341e6i	−0.0787657	−	0.164445i
$381$	4.27343e7			0.772684
$382$	−1.08394e7	+	5.66672e6i	−0.194453	+	0.101658i
$383$	9.90039e7			1.76220			0.881102	−	0.472927i	$-0.156802\pi$
$383$	9.90039e7			1.76220			0.881102	+	0.472927i	$0.156802\pi$
$384$	−7.46556e6	−	3.18275e7i	−0.131846	−	0.562094i
$385$	−4.87822e7	+	8.58487e7i	−0.854829	+	1.50436i
$386$	−6.98494e7	+	3.65166e7i	−1.21451	+	0.634933i
$387$	−3.09560e6			−0.0534086
$388$	−3.28731e7	−	2.28472e7i	−0.562788	−	0.391145i
$389$	−1.22554e7			−0.208199			−0.104099	−	0.994567i	$-0.533196\pi$
$389$	−1.22554e7			−0.208199			−0.104099	+	0.994567i	$0.533196\pi$
$390$	−5.19521e7	−	1.82023e6i	−0.875808	−	0.0306854i
$391$			1.10040e8i			1.84086i
$392$	1.41248e8	+	1.78428e7i	2.34489	+	0.296214i
$393$		−	1.81101e7i		−	0.298361i
$394$	1.92588e7	−	1.00683e7i	0.314877	−	0.164614i
$395$	849000.	−	1.49410e6i	0.0137758	−	0.0242431i
$396$	1.60363e7	+	1.11454e7i	0.258237	+	0.179478i
$397$			7.48415e7i			1.19611i	0.801455	+	0.598055i	$0.204060\pi$
$397$			7.48415e7i			1.19611i	−0.801455	+	0.598055i	$0.795940\pi$
$398$	8.11929e7	−	4.24469e7i	1.28786	−	0.673281i
$399$		−	1.22638e7i		−	0.193067i
$400$	4.01140e7	−	4.98685e7i	0.626781	−	0.779195i
$401$	1.45370e7			0.225446			0.112723	−	0.993626i	$-0.464043\pi$
$401$	1.45370e7			0.225446			0.112723	+	0.993626i	$0.464043\pi$
$402$	−5.88948e6	−	1.12655e7i	−0.0906564	−	0.173409i
$403$	−1.08171e7			−0.165270
$404$	−2.58410e6	+	3.71807e6i	−0.0391891	+	0.0563862i
$405$	6.41742e6	+	3.64660e6i	0.0966041	+	0.0548938i
$406$	−1.68074e7	−	3.21494e7i	−0.251144	−	0.480391i
$407$	−6.88656e7			−1.02145
$408$	7.63994e6	−	6.04793e7i	0.112489	−	0.890485i
$409$	7.39246e7			1.08049			0.540243	−	0.841509i	$-0.318332\pi$
$409$	7.39246e7			1.08049			0.540243	+	0.841509i	$0.318332\pi$
$410$	1.01940e6	−	2.90952e7i	0.0147908	−	0.422153i
$411$			6.39459e7i			0.921058i
$412$	−4.11663e7	+	5.92310e7i	−0.588640	+	0.846950i
$413$		−	9.16420e6i		−	0.130090i
$414$	1.29759e7	+	2.48205e7i	0.182867	+	0.349791i
$415$	−6.86878e7	−	3.90308e7i	−0.961026	−	0.546088i
$416$	8.12070e7	+	7.31176e7i	1.12801	+	1.01565i
$417$		−	1.84138e7i		−	0.253943i
$418$	−5.82070e6	−	1.11339e7i	−0.0796979	−	0.152447i
$419$		−	3.43347e7i		−	0.466757i	−0.972386	−	0.233379i	$-0.925022\pi$
$419$		−	3.43347e7i		−	0.466757i	0.972386	−	0.233379i	$-0.0749782\pi$
$420$	7.07513e7	−	3.38884e7i	0.954963	−	0.457408i
$421$	−5.83664e7			−0.782198			−0.391099	−	0.920349i	$-0.627905\pi$
$421$	−5.83664e7			−0.782198			−0.391099	+	0.920349i	$0.627905\pi$
$422$	−1.13124e8	+	5.91399e7i	−1.50528	+	0.786943i
$423$	3.64805e6			0.0481992
$424$	−1.30777e7	+	1.03526e8i	−0.171567	+	1.35816i
$425$	1.02524e8	−	6.10838e7i	1.33555	−	0.795719i
$426$	−5.86649e7	+	3.06694e7i	−0.758839	+	0.396713i
$427$	1.95710e8			2.51380
$428$	−4.13267e7	+	5.94618e7i	−0.527107	+	0.758415i
$429$	−6.52775e7			−0.826783
$430$	−446061.	+	1.27313e7i	−0.00561033	+	0.160128i
$431$		−	5.13527e7i		−	0.641404i	−0.947180	−	0.320702i	$-0.896081\pi$
$431$		−	5.13527e7i		−	0.641404i	0.947180	−	0.320702i	$-0.103919\pi$
$432$	−5.40843e6	−	1.45425e7i	−0.0670842	−	0.180379i
$433$		−	4.34673e7i		−	0.535425i	−0.963499	−	0.267713i	$-0.913732\pi$
$433$		−	4.34673e7i		−	0.535425i	0.963499	−	0.267713i	$-0.0862678\pi$
$434$	1.44663e7	−	7.56286e6i	0.176966	−	0.0925160i
$435$	−1.22126e7	−	6.93965e6i	−0.148368	−	0.0843081i
$436$	4.53638e7	−	6.52705e7i	0.547331	−	0.787512i
$437$		−	1.80182e7i		−	0.215907i
$438$	−2.47855e7	+	1.29576e7i	−0.294968	+	0.154206i
$439$		−	5.32902e7i		−	0.629875i	−0.949112	−	0.314937i	$-0.898016\pi$
$439$		−	5.32902e7i		−	0.629875i	0.949112	−	0.314937i	$-0.101984\pi$
$440$	4.81485e7	−	6.43465e7i	0.565230	−	0.755382i
$441$	6.75702e7			0.787843
$442$	9.44035e7	+	1.80576e8i	1.09325	+	2.09119i
$443$	−1.63589e6			−0.0188167			−0.00940834	−	0.999956i	$-0.502995\pi$
$443$	−1.63589e6			−0.0188167			−0.00940834	+	0.999956i	$0.502995\pi$
$444$	4.49277e7	+	3.12253e7i	0.513293	+	0.356745i
$445$	−3.30161e7	−	1.87609e7i	−0.374667	−	0.212899i
$446$	−1.82306e7	−	3.48717e7i	−0.205492	−	0.393069i
$447$	2.13004e7			0.238488
$448$	−1.59724e8	−	4.10080e7i	−1.77638	−	0.456074i
$449$	3.93808e7			0.435056			0.217528	−	0.976054i	$-0.430201\pi$
$449$	3.93808e7			0.435056			0.217528	+	0.976054i	$0.430201\pi$
$450$	1.59221e7	−	2.58675e7i	0.174728	−	0.283868i
$451$		−	3.65580e7i		−	0.398522i
$452$	−2.31017e7	−	1.60560e7i	−0.250167	−	0.173869i
$453$		−	5.05172e7i		−	0.543432i
$454$	−3.43512e7	−	6.57074e7i	−0.367091	−	0.702178i
$455$	−1.29549e8	+	2.27985e8i	−1.37531	+	2.42031i
$456$	−1.25098e6	+	9.90299e6i	−0.0131933	+	0.104441i
$457$		−	1.72529e8i		−	1.80765i	−0.427901	−	0.903826i	$-0.640747\pi$
$457$		−	1.72529e8i		−	1.80765i	0.427901	−	0.903826i	$-0.359253\pi$
$458$	−1.61237e7	−	3.08416e7i	−0.167829	−	0.321026i
$459$		−	2.89322e7i		−	0.299187i
$460$	1.03949e8	−	4.97895e7i	1.06794	−	0.511521i
$461$	−1.57854e8			−1.61122			−0.805608	−	0.592449i	$-0.798161\pi$
$461$	−1.57854e8			−1.61122			−0.805608	+	0.592449i	$0.798161\pi$
$462$	8.72995e7	−	4.56393e7i	0.885291	−	0.462821i
$463$	−1.65529e8			−1.66775			−0.833876	−	0.551951i	$-0.813883\pi$
$463$	−1.65529e8			−1.66775			−0.833876	+	0.551951i	$0.813883\pi$
$464$	1.02925e7	+	2.76750e7i	0.103031	+	0.277034i
$465$	3.12265e6	−	5.49535e6i	0.0310573	−	0.0546558i
$466$	1.07110e6	−	559960.i	0.0105845	−	0.00553349i
$467$	6.51048e7			0.639238			0.319619	−	0.947546i	$-0.396445\pi$
$467$	6.51048e7			0.639238			0.319619	+	0.947546i	$0.396445\pi$
$468$	4.25869e7	+	2.95984e7i	0.415469	+	0.288756i
$469$	−6.41231e7			−0.621579
$470$	525667.	−	1.50033e7i	0.00506310	−	0.144509i
$471$		−	8.31820e6i		−	0.0796099i
$472$	−934799.	+	7.40006e6i	−0.00888980	+	0.0703735i
$473$			1.59968e7i			0.151164i
$474$	−1.51935e6	+	794301.i	−0.0142667	+	0.00745848i
$475$	−1.67875e7	+	1.00020e7i	−0.156641	+	0.0933265i
$476$	−2.52503e8	−	1.75493e8i	−2.34124	−	1.62719i
$477$			4.95247e7i			0.456317i
$478$	7.86212e7	−	4.11024e7i	0.719874	−	0.376343i
$479$			7.59285e7i			0.690873i	0.938442	+	0.345436i	$0.112269\pi$
$479$			7.59285e7i			0.690873i	−0.938442	+	0.345436i	$0.887731\pi$
$480$	−6.05882e7	+	2.01478e7i	−0.547853	+	0.182181i
$481$	−1.82883e8			−1.64338
$482$	−8.45920e7	−	1.61809e8i	−0.755420	−	1.44498i
$483$	1.41278e8			1.25382
$484$	−7.11217e6	+	1.02332e7i	−0.0627287	+	0.0902555i
$485$	−3.86289e7	+	6.79806e7i	−0.338600	+	0.595881i
$486$	−3.41166e6	−	6.52587e6i	−0.0297206	−	0.0568499i
$487$	1.07212e8			0.928235			0.464118	−	0.885774i	$-0.346372\pi$
$487$	1.07212e8			0.928235			0.464118	+	0.885774i	$0.346372\pi$
$488$	−1.58035e8	−	1.99635e7i	−1.35986	−	0.171782i
$489$	5.74970e7			0.491721
$490$	9.73654e6	−	2.77896e8i	0.0827593	−	2.36208i
$491$			2.26135e8i			1.91040i	0.295967	+	0.955198i	$0.404358\pi$
$491$			2.26135e8i			1.91040i	−0.295967	+	0.955198i	$0.595642\pi$
$492$	−1.65763e7	+	2.38503e7i	−0.139185	+	0.200262i
$493$			5.50592e7i			0.459504i
$494$	−1.54578e7	−	2.95679e7i	−0.128223	−	0.245267i
$495$	1.88441e7	−	3.31626e7i	0.155368	−	0.273422i
$496$	−1.24530e7	+	4.63134e6i	−0.102054	+	0.0379543i
$497$			3.33921e8i			2.72003i
$498$	3.65161e7	+	6.98486e7i	0.295663	+	0.565548i
$499$			2.26180e7i			0.182034i	0.995849	+	0.0910172i	$0.0290118\pi$
$499$			2.26180e7i			0.182034i	−0.995849	+	0.0910172i	$0.970988\pi$
$500$	−1.04091e8	−	6.92103e7i	−0.832728	−	0.553682i
$501$	−7.85256e7			−0.624451
$502$	−9.95241e7	+	5.20302e7i	−0.786715	+	0.411287i
$503$	−8.37768e7			−0.658294			−0.329147	−	0.944279i	$-0.606761\pi$
$503$	−8.37768e7			−0.658294			−0.329147	+	0.944279i	$0.606761\pi$
$504$	−7.76480e7	−	9.80874e6i	−0.606511	−	0.0766163i
$505$	7.68886e6	+	4.36908e6i	0.0597019	+	0.0339247i
$506$	1.28262e8	−	6.70540e7i	0.990025	−	0.517575i
$507$	−9.81122e7			−0.752834
$508$	−1.00131e8	+	1.44071e8i	−0.763798	+	1.09897i
$509$	2.00831e8			1.52292			0.761461	−	0.648211i	$-0.224483\pi$
$509$	2.00831e8			1.52292			0.761461	+	0.648211i	$0.224483\pi$
$510$	−1.18989e8	−	4.16899e6i	−0.897011	−	0.0314282i
$511$			1.41079e8i			1.05730i
$512$	1.24793e8	+	4.94065e7i	0.929783	+	0.368107i
$513$			4.73740e6i			0.0350904i
$514$	−9.65636e7	+	5.04825e7i	−0.711090	+	0.371750i
$515$	1.22488e8	+	6.96020e7i	0.896752	+	0.509566i
$516$	7.25332e6	−	1.04363e7i	0.0527944	−	0.0759618i
$517$		−	1.88516e7i		−	0.136420i
$518$	2.44581e8	−	1.27864e8i	1.75968	−	0.919942i
$519$			5.22285e7i			0.373599i
$520$	1.27866e8	−	1.70882e8i	0.909379	−	1.21531i
$521$	−1.16604e8			−0.824518			−0.412259	−	0.911067i	$-0.635260\pi$
$521$	−1.16604e8			−0.824518			−0.412259	+	0.911067i	$0.635260\pi$
$522$	6.49254e6	+	1.24190e7i	0.0456461	+	0.0873124i
$523$	1.50247e8			1.05027			0.525134	−	0.851020i	$-0.324015\pi$
$523$	1.50247e8			1.05027			0.525134	+	0.851020i	$0.324015\pi$
$524$	6.10548e7	+	4.24338e7i	0.424352	+	0.294930i
$525$	−7.84241e7	−	1.31628e8i	−0.541965	−	0.909642i
$526$	4.59889e7	+	8.79683e7i	0.316007	+	0.604462i
$527$	−2.47751e7			−0.169272
$528$	−7.51495e7	+	2.79486e7i	−0.510534	+	0.189871i
$529$	5.95324e7			0.402148
$530$	2.03681e8	+	7.13628e6i	1.36811	+	0.0479341i
$531$			3.54005e6i			0.0236443i
$532$	4.13453e7	+	2.87355e7i	0.274594	+	0.190846i
$533$		−	9.70855e7i		−	0.641169i
$534$	1.75522e7	+	3.35740e7i	0.115268	+	0.220485i
$535$	1.22965e8	+	6.98732e7i	0.803011	+	0.456299i
$536$	5.17792e7	+	6.54091e6i	0.336249	+	0.0424760i
$537$		−	7.74873e6i		−	0.0500389i
$538$	6.74927e7	+	1.29101e8i	0.433421	+	0.829054i
$539$		−	3.49175e8i		−	2.22986i
$540$	−2.73306e7	+	1.30908e7i	−0.173567	+	0.0831352i
$541$	2.98826e8			1.88724			0.943618	−	0.331036i	$-0.107398\pi$
$541$	2.98826e8			1.88724			0.943618	+	0.331036i	$0.107398\pi$
$542$	1.42069e8	−	7.42724e7i	0.892282	−	0.466476i
$543$	−3.84677e7			−0.240268
$544$	1.85994e8	+	1.67466e8i	1.15532	+	1.04023i
$545$	−1.34978e8	−	7.66990e7i	−0.833820	−	0.473805i
$546$	2.31838e8	−	1.21202e8i	1.42432	−	0.744618i
$547$	−430499.			−0.00263033			−0.00131517	−	0.999999i	$-0.500419\pi$
$547$	−430499.			−0.00263033			−0.00131517	+	0.999999i	$0.500419\pi$
$548$	−2.15582e8	−	1.49832e8i	−1.31000	−	0.910465i
$549$	−7.56011e7			−0.456890
$550$	−1.33673e8	−	8.22789e7i	−0.803441	−	0.494539i
$551$		−	9.01549e6i		−	0.0538933i
$552$	−1.14082e8	−	1.44112e7i	−0.678264	−	0.0856804i
$553$			8.64815e6i			0.0511385i
$554$	−2.86365e8	+	1.49709e8i	−1.68419	+	0.880478i
$555$	5.27943e7	−	9.29093e7i	0.308822	−	0.543476i
$556$	6.20789e7	+	4.31456e7i	0.361177	+	0.251022i
$557$			2.29944e8i			1.33063i	0.746563	+	0.665314i	$0.231702\pi$
$557$			2.29944e8i			1.33063i	−0.746563	+	0.665314i	$0.768298\pi$
$558$	−5.58822e6	+	2.92147e6i	−0.0321641	+	0.0168151i
$559$			4.24819e7i			0.243203i
$560$	−5.15291e7	+	3.17930e8i	−0.293419	+	1.81037i
$561$	−1.49510e8			−0.846799
$562$	4.36327e7	+	8.34613e7i	0.245812	+	0.470193i
$563$	−1.37064e8			−0.768068			−0.384034	−	0.923319i	$-0.625465\pi$
$563$	−1.37064e8			−0.768068			−0.384034	+	0.923319i	$0.625465\pi$
$564$	−8.54778e6	+	1.22987e7i	−0.0476448	+	0.0685525i
$565$	−2.71467e7	+	4.77737e7i	−0.150512	+	0.264877i
$566$	−1.15497e8	−	2.20925e8i	−0.636974	−	1.21841i
$567$	−3.71453e7			−0.203777
$568$	3.40618e7	−	2.69640e8i	0.185875	−	1.47143i
$569$	1.95327e8			1.06029			0.530147	−	0.847906i	$-0.322137\pi$
$569$	1.95327e8			1.06029			0.530147	+	0.847906i	$0.322137\pi$
$570$	1.94835e7	+	682637.i	0.105207	+	0.00368609i
$571$		−	6.46592e7i		−	0.347314i	−0.984806	−	0.173657i	$-0.944442\pi$
$571$		−	6.46592e7i		−	0.347314i	0.984806	−	0.173657i	$-0.0555584\pi$
$572$	1.52952e8	−	2.20071e8i	0.817275	−	1.17591i
$573$		−	2.38333e7i		−	0.126684i
$574$	6.78781e7	+	1.29838e8i	0.358917	+	0.686542i
$575$	−1.15222e8	−	1.93390e8i	−0.606082	−	1.01726i
$576$	6.16999e7	+	1.58410e7i	0.322862	+	0.0828927i
$577$		−	1.40370e8i		−	0.730714i	−0.930867	−	0.365357i	$-0.880947\pi$
$577$		−	1.40370e8i		−	0.730714i	0.930867	−	0.365357i	$-0.119053\pi$
$578$	1.26756e8	+	2.42460e8i	0.656423	+	1.25562i
$579$		−	1.53583e8i		−	0.791238i
$580$	5.20113e7	−	2.49124e7i	0.266572	−	0.127682i
$581$	3.97579e8			2.02719
$582$	6.91294e7	−	3.61402e7i	0.350666	−	0.183325i
$583$	2.55923e8			1.29153
$584$	1.43908e7	−	1.13921e8i	0.0722516	−	0.571958i
$585$	5.00436e7	−	8.80685e7i	0.249966	−	0.439899i
$586$	−3.36559e7	+	1.75950e7i	−0.167251	+	0.0874370i
$587$	−1.73258e7			−0.0856603			−0.0428301	−	0.999082i	$-0.513637\pi$
$587$	−1.73258e7			−0.0856603			−0.0428301	+	0.999082i	$0.513637\pi$
$588$	−1.58324e8	+	2.27801e8i	−0.778782	+	1.12053i
$589$	4.05672e6			0.0198531
$590$	1.45592e7	+	510104.i	0.0708893	+	0.00248372i
$591$			4.23457e7i			0.205138i
$592$	−2.10541e8	+	7.83015e7i	−1.01478	+	0.377403i
$593$			1.03223e8i			0.495008i	0.968887	+	0.247504i	$0.0796104\pi$
$593$			1.03223e8i			0.495008i	−0.968887	+	0.247504i	$0.920390\pi$
$594$	−3.37230e7	+	1.76301e7i	−0.160904	+	0.0841191i
$595$	−2.96715e8	+	5.22169e8i	−1.40860	+	2.47891i
$596$	−4.99093e7	+	7.18106e7i	−0.235745	+	0.339195i
$597$			1.78525e8i			0.839026i
$598$	3.40620e8	−	1.78073e8i	1.59282	−	0.832709i
$599$		−	2.33746e8i		−	1.08759i	−0.839219	−	0.543794i	$-0.816987\pi$
$599$		−	2.33746e8i		−	1.08759i	0.839219	−	0.543794i	$-0.183013\pi$
$600$	4.99004e7	+	1.14289e8i	0.231020	+	0.529115i
$601$	−3.82158e7			−0.176043			−0.0880216	−	0.996119i	$-0.528054\pi$
$601$	−3.82158e7			−0.176043			−0.0880216	+	0.996119i	$0.528054\pi$
$602$	−2.97016e7	−	5.68137e7i	−0.136141	−	0.260413i
$603$	2.47702e7			0.112974
$604$	1.70310e8	+	1.18367e8i	0.772910	+	0.537182i
$605$	2.11619e7	+	1.20249e7i	0.0955627	+	0.0543021i
$606$	−4.08759e6	−	7.81880e6i	−0.0183675	−	0.0351336i
$607$	−7.16449e6			−0.0320346			−0.0160173	−	0.999872i	$-0.505099\pi$
$607$	−7.16449e6			−0.0320346			−0.0160173	+	0.999872i	$0.505099\pi$
$608$	−3.04550e7	−	2.74212e7i	−0.135503	−	0.122005i
$609$	7.06892e7			0.312969
$610$	−1.08938e7	+	3.10925e8i	−0.0479942	+	1.36983i
$611$		−	5.00634e7i		−	0.219481i
$612$	9.75396e7	+	6.77912e7i	0.425527	+	0.295746i
$613$			6.22401e6i			0.0270202i	0.999909	+	0.0135101i	$0.00430053\pi$
$613$			6.22401e6i			0.0270202i	−0.999909	+	0.0135101i	$0.995699\pi$
$614$	−5.89552e7	−	1.12770e8i	−0.254693	−	0.487180i
$615$	4.93218e7	+	2.80264e7i	0.212038	+	0.120487i
$616$	−5.06875e7	+	4.01253e8i	−0.216850	+	1.71663i
$617$			5.77344e7i			0.245799i	0.992419	+	0.122899i	$0.0392192\pi$
$617$			5.77344e7i			0.245799i	−0.992419	+	0.122899i	$0.960781\pi$
$618$	−6.51178e7	−	1.24558e8i	−0.275889	−	0.527724i
$619$		−	2.83393e8i		−	1.19486i	−0.801920	−	0.597431i	$-0.796188\pi$
$619$		−	2.83393e8i		−	1.19486i	0.801920	−	0.597431i	$-0.203812\pi$
$620$	1.12099e7	+	2.34037e7i	0.0470355	+	0.0981994i
$621$	−5.45745e7			−0.227885
$622$	−2.22997e8	+	1.16581e8i	−0.926677	+	0.484457i
$623$	1.91104e8			0.790323
$624$	−1.99571e8	+	7.42218e7i	−0.821381	+	0.305476i
$625$	−1.16220e8	+	2.14703e8i	−0.476039	+	0.879424i
$626$	2.38769e8	−	1.24826e8i	0.973320	−	0.508842i
$627$	2.44810e7			0.0993175
$628$	2.80433e7	+	1.94905e7i	0.113227	+	0.0786943i
$629$	−4.18870e8			−1.68317
$630$	−5.35246e6	+	1.52768e8i	−0.0214058	+	0.610956i
$631$		−	3.72306e8i		−	1.48187i	−0.671574	−	0.740937i	$-0.734382\pi$
$631$		−	3.72306e8i		−	1.48187i	0.671574	−	0.740937i	$-0.265618\pi$
$632$	882159.	−	6.98335e6i	0.00349459	−	0.0276639i
$633$		−	2.48733e8i		−	0.980669i
$634$	−2.15662e8	+	1.12746e8i	−0.846262	+	0.442417i
$635$	2.97935e8	+	1.69297e8i	1.16359	+	0.661193i
$636$	−1.66964e8	−	1.16042e8i	−0.649009	−	0.451069i
$637$		−	9.27289e8i		−	3.58754i
$638$	6.41764e7	−	3.35508e7i	0.247123	−	0.129194i
$639$		−	1.28991e8i		−	0.494374i
$640$	7.40401e7	−	2.51471e8i	0.282441	−	0.959285i
$641$	−1.96445e8			−0.745876			−0.372938	−	0.927856i	$-0.621650\pi$
$641$	−1.96445e8			−0.745876			−0.372938	+	0.927856i	$0.621650\pi$
$642$	−6.53715e7	−	1.25043e8i	−0.247049	−	0.472559i
$643$	−3.91175e8			−1.47142			−0.735712	−	0.677295i	$-0.763152\pi$
$643$	−3.91175e8			−1.47142			−0.735712	+	0.677295i	$0.763152\pi$
$644$	−3.31030e8	+	4.76294e8i	−1.23940	+	1.78327i
$645$	−2.15819e7	−	1.22636e7i	−0.0804285	−	0.0457023i
$646$	−3.54040e7	−	6.77214e7i	−0.131327	−	0.251205i
$647$	−5.32848e8			−1.96739			−0.983694	−	0.179848i	$-0.942439\pi$
$647$	−5.32848e8			−1.96739			−0.983694	+	0.179848i	$0.942439\pi$
$648$	2.99947e7	+	3.78903e6i	0.110235	+	0.0139252i
$649$	1.82935e7			0.0669211
$650$	−3.54988e8	−	2.18505e8i	−1.29263	−	0.795647i
$651$			3.18082e7i			0.115291i
$652$	−1.34722e8	+	1.93841e8i	−0.486066	+	0.699363i
$653$			3.49177e8i			1.25402i	0.779009	+	0.627012i	$0.215723\pi$
$653$			3.49177e8i			1.25402i	−0.779009	+	0.627012i	$0.784277\pi$
$654$	7.17574e7	+	1.37259e8i	0.256527	+	0.490689i
$655$	7.17452e7	−	1.26260e8i	0.255311	−	0.449305i
$656$	−4.15671e7	−	1.11768e8i	−0.147244	−	0.395918i
$657$		−	5.44976e7i		−	0.192168i
$658$	3.50023e7	+	6.69529e7i	0.122862	+	0.235013i
$659$			2.26836e8i			0.792602i	0.918121	+	0.396301i	$0.129706\pi$
$659$			2.26836e8i			0.792602i	−0.918121	+	0.396301i	$0.870294\pi$
$660$	6.76479e7	+	1.41233e8i	0.235300	+	0.491253i
$661$	3.94230e8			1.36504			0.682521	−	0.730866i	$-0.260884\pi$
$661$	3.94230e8			1.36504			0.682521	+	0.730866i	$0.260884\pi$
$662$	4.48161e6	−	2.34294e6i	0.0154476	−	0.00807583i
$663$	−3.97046e8			−1.36239
$664$	−3.21043e8	−	4.05552e7i	−1.09663	−	0.138529i
$665$	4.85846e7	−	8.55009e7i	0.165209	−	0.290741i
$666$	−9.44794e7	+	4.93929e7i	−0.319827	+	0.167202i
$667$	1.03858e8			0.349995
$668$	1.83994e8	−	2.64735e8i	0.617269	−	0.888141i
$669$	7.66749e7			0.256080
$670$	3.56927e6	−	1.01872e8i	0.0118674	−	0.338713i
$671$			3.90676e8i			1.29315i
$672$	2.15006e8	−	2.38793e8i	0.708505	−	0.786891i
$673$			3.10414e8i			1.01835i	0.860664	+	0.509174i	$0.170049\pi$
$673$			3.10414e8i			1.01835i	−0.860664	+	0.509174i	$0.829951\pi$
$674$	−6.40486e7	+	3.34839e7i	−0.209185	+	0.109360i
$675$	3.02945e7	+	5.08468e7i	0.0985038	+	0.165330i
$676$	2.29888e8	−	3.30768e8i	0.744176	−	1.07074i
$677$		−	5.73658e8i		−	1.84879i	−0.381439	−	0.924394i	$-0.624571\pi$
$677$		−	5.73658e8i		−	1.84879i	0.381439	−	0.924394i	$-0.375429\pi$
$678$	4.85811e7	−	2.53977e7i	0.155876	−	0.0814902i
$679$		−	3.93485e8i		−	1.25695i
$680$	2.92860e8	−	3.91383e8i	0.931394	−	1.24473i
$681$	1.44476e8			0.457460
$682$	1.50969e7	+	2.88776e7i	0.0475922	+	0.0910350i
$683$	−4.50762e8			−1.41477			−0.707384	−	0.706830i	$-0.750125\pi$
$683$	−4.50762e8			−1.41477			−0.707384	+	0.706830i	$0.750125\pi$
$684$	−1.59713e7	−	1.11003e7i	−0.0499082	−	0.0346868i
$685$	−2.53329e8	+	4.45818e8i	−0.788158	+	1.38703i
$686$	3.74019e8	+	7.15430e8i	1.15857	+	2.21613i
$687$	6.78137e7			0.209145
$688$	1.81886e7	+	4.89065e7i	0.0558515	+	0.150176i
$689$	6.79645e8			2.07790
$690$	−7.86393e6	+	2.24449e8i	−0.0239382	+	0.683235i
$691$		−	1.07184e8i		−	0.324859i	−0.986720	−	0.162430i	$-0.948067\pi$
$691$		−	1.07184e8i		−	0.324859i	0.986720	−	0.162430i	$-0.0519330\pi$
$692$	−1.76079e8	−	1.22377e8i	−0.531361	−	0.369302i
$693$			1.91952e8i			0.576756i
$694$	−9.05325e7	−	1.73172e8i	−0.270848	−	0.518083i
$695$	7.29485e7	−	1.28377e8i	0.217301	−	0.382414i
$696$	−5.70813e7	−	7.21069e6i	−0.169303	−	0.0213870i
$697$		−	2.22361e8i		−	0.656691i
$698$	−1.75490e7	−	3.35680e7i	−0.0516044	−	0.0987096i
$699$			2.35510e6i			0.00689570i
$700$	6.27517e8	+	4.40262e7i	1.82950	+	0.128356i
$701$	1.74408e8			0.506305			0.253153	−	0.967426i	$-0.418533\pi$
$701$	1.74408e8			0.506305			0.253153	+	0.967426i	$0.418533\pi$
$702$	−8.95568e7	+	4.68194e7i	−0.258873	+	0.135336i
$703$	6.85866e7			0.197412
$704$	8.18600e7	−	3.18840e8i	0.234614	−	0.913807i
$705$	2.54335e7	+	1.44522e7i	0.0725836	+	0.0412445i
$706$	−3.23903e8	+	1.69333e8i	−0.920450	+	0.481202i
$707$	−4.45047e7			−0.125935
$708$	−1.19346e7	−	8.29472e6i	−0.0336287	−	0.0233723i
$709$	−3.49999e7			−0.0982038			−0.0491019	−	0.998794i	$-0.515636\pi$
$709$	−3.49999e7			−0.0982038			−0.0491019	+	0.998794i	$0.515636\pi$
$710$	−5.30500e8	−	1.85869e7i	−1.48221	−	0.0519317i
$711$		−	3.34070e6i		−	0.00929457i
$712$	−1.54315e8	−	1.94936e7i	−0.427533	−	0.0540073i
$713$			4.67331e7i			0.128931i
$714$	5.30994e8	−	2.77598e8i	1.45880	−	0.762644i
$715$	−4.55102e8	−	2.58605e8i	−1.24506	−	0.707487i
$716$	2.61235e7	+	1.81561e7i	0.0711691	+	0.0494634i
$717$			1.72870e8i			0.468989i
$718$	1.42540e8	−	7.45187e7i	0.385092	−	0.201322i
$719$			2.53393e6i			0.00681722i	0.999994	+	0.00340861i	$0.00108500\pi$
$719$			2.53393e6i			0.00681722i	−0.999994	+	0.00340861i	$0.998915\pi$
$720$	1.99052e7	−	1.22813e8i	0.0533298	−	0.329040i
$721$	−7.08986e8			−1.89161
$722$	−1.68573e8	−	3.22449e8i	−0.447895	−	0.856740i
$723$	3.55781e8			0.941385
$724$	9.01340e7	−	1.29687e8i	0.237505	−	0.341728i
$725$	−5.76518e7	−	9.67636e7i	−0.151286	−	0.253921i
$726$	−1.12502e7	−	2.15195e7i	−0.0294002	−	0.0562371i
$727$	3.79075e8			0.986555			0.493278	−	0.869872i	$-0.335799\pi$
$727$	3.79075e8			0.986555			0.493278	+	0.869872i	$0.335799\pi$
$728$	−1.34609e8	+	1.06559e9i	−0.348882	+	2.76182i
$729$	1.43489e7			0.0370370
$730$	−2.24132e8	−	7.85284e6i	−0.576150	−	0.0201864i
$731$			9.72993e7i			0.249091i
$732$	1.77142e8	−	2.54876e8i	0.451635	−	0.649823i
$733$		−	5.64609e7i		−	0.143363i	−0.997428	−	0.0716813i	$-0.977164\pi$
$733$		−	5.64609e7i		−	0.143363i	0.997428	−	0.0716813i	$-0.0228364\pi$
$734$	2.53955e8	+	4.85769e8i	0.642198	+	1.22841i
$735$	4.71086e8	+	2.67687e8i	1.18642	+	0.674165i
$736$	3.15890e8	−	3.50839e8i	0.792324	−	0.879983i
$737$		−	1.28002e8i		−	0.319753i
$738$	−2.62207e7	−	5.01553e7i	−0.0652342	−	0.124781i
$739$			6.72986e8i			1.66753i	0.552122	+	0.833763i	$0.313818\pi$
$739$			6.72986e8i			1.66753i	−0.552122	+	0.833763i	$0.686182\pi$
$740$	1.89524e8	+	3.95683e8i	0.467703	+	0.976455i
$741$	6.50130e7			0.159789
$742$	−9.08930e8	+	4.75180e8i	−2.22494	+	1.16318i
$743$	7.85948e8			1.91614			0.958070	−	0.286533i	$-0.0925027\pi$
$743$	7.85948e8			1.91614			0.958070	+	0.286533i	$0.0925027\pi$
$744$	3.24461e6	−	2.56850e7i	0.00787850	−	0.0623678i
$745$	1.48502e8	+	8.43842e7i	0.359141	+	0.204076i
$746$	7.59591e7	−	3.97107e7i	0.182963	−	0.0956512i
$747$	−1.53581e8			−0.368448
$748$	3.50317e8	−	5.04045e8i	0.837060	−	1.20438i
$749$	−7.11748e8			−1.69387
$750$	2.13483e8	−	1.17266e8i	0.506034	−	0.277963i
$751$			5.89245e8i			1.39116i	0.718451	+	0.695578i	$0.244852\pi$
$751$			5.89245e8i			1.39116i	−0.718451	+	0.695578i	$0.755148\pi$
$752$	−2.14347e7	−	5.76346e7i	−0.0504038	−	0.135528i
$753$		−	2.18831e8i		−	0.512535i
$754$	1.70431e8	−	8.90994e7i	0.397588	−	0.207855i
$755$	2.00130e8	−	3.52196e8i	0.465020	−	0.818359i
$756$	8.70355e7	−	1.25229e8i	0.201433	−	0.289827i
$757$			3.30745e8i			0.762440i	0.924484	+	0.381220i	$0.124496\pi$
$757$			3.30745e8i			0.762440i	−0.924484	+	0.381220i	$0.875504\pi$
$758$	−7.01352e8	+	3.66660e8i	−1.61038	+	0.841891i
$759$			2.82019e8i			0.644989i
$760$	−4.79534e7	+	6.40858e7i	−0.109239	+	0.145989i
$761$	−5.22089e7			−0.118465			−0.0592325	−	0.998244i	$-0.518865\pi$
$761$	−5.22089e7			−0.118465			−0.0592325	+	0.998244i	$0.518865\pi$
$762$	−1.58390e8	−	3.02970e8i	−0.357983	−	0.684755i
$763$	7.81277e8			1.75886
$764$	8.03498e7	+	5.58441e7i	0.180179	+	0.125227i
$765$	1.14618e8	−	2.01709e8i	0.256017	−	0.450548i
$766$	−3.66946e8	−	7.01900e8i	−0.816425	−	1.56167i
$767$	4.85813e7			0.107667
$768$	−1.97975e8	+	1.70893e8i	−0.437045	+	0.377260i
$769$	2.35312e8			0.517446			0.258723	−	0.965952i	$-0.416698\pi$
$769$	2.35312e8			0.517446			0.258723	+	0.965952i	$0.416698\pi$
$770$	7.89441e8	+	2.76593e7i	1.72921	+	0.0605856i
$771$		−	2.12321e8i		−	0.463266i
$772$	5.17777e8	+	3.59861e8i	1.12536	+	0.782138i
$773$		−	2.53680e8i		−	0.549221i	−0.961556	−	0.274611i	$-0.911451\pi$
$773$		−	2.53680e8i		−	0.549221i	0.961556	−	0.274611i	$-0.0885489\pi$
$774$	1.14735e7	+	2.19466e7i	0.0247441	+	0.0473309i
$775$	4.35410e7	−	2.59417e7i	0.0935391	−	0.0557306i
$776$	−4.01377e7	+	3.17738e8i	−0.0858948	+	0.679961i
$777$			5.37778e8i			1.14641i
$778$	4.54231e7	+	8.68860e7i	0.0964580	+	0.184506i
$779$			3.64099e7i			0.0770206i
$780$	1.79650e8	+	3.75067e8i	0.378567	+	0.790360i
$781$	−6.66571e8			−1.39924
$782$	7.80144e8	−	4.07852e8i	1.63138	−	0.852868i
$783$	−2.73066e7			−0.0568830
$784$	−3.97019e8	−	1.06752e9i	−0.823878	−	2.21529i
$785$	3.29536e7	−	5.79928e7i	0.0681229	−	0.119885i
$786$	−1.28393e8	+	6.71228e7i	−0.264408	+	0.138230i
$787$	−5.60356e8			−1.14958			−0.574791	−	0.818300i	$-0.694917\pi$
$787$	−5.60356e8			−1.14958			−0.574791	+	0.818300i	$0.694917\pi$
$788$	−1.42761e8	−	9.92206e7i	−0.291763	−	0.202779i
$789$	−1.93422e8			−0.393800
$790$	−1.37393e7	−	481380.i	−0.0278666	−	0.000976352i
$791$		−	2.76524e8i		−	0.558732i
$792$	1.95801e7	−	1.55000e8i	0.0394131	−	0.312002i
$793$			1.03750e9i			2.08051i
$794$	5.30598e8	−	2.77391e8i	1.06000	−	0.554155i
$795$	−1.96198e8	+	3.45277e8i	−0.390475	+	0.687172i
$796$	−6.01864e8	−	4.18303e8i	−1.19333	−	0.829376i
$797$			8.17996e8i			1.61576i	0.589349	+	0.807879i	$0.299384\pi$
$797$			8.17996e8i			1.61576i	−0.589349	+	0.807879i	$0.700616\pi$
$798$	−8.69458e7	+	4.54544e7i	−0.171096	+	0.0894473i
$799$		−	1.14664e8i		−	0.224795i
$800$	−5.02227e8	−	9.95611e7i	−0.980911	−	0.194455i
$801$	−7.38216e7			−0.143644
$802$	−5.38797e7	−	1.03062e8i	−0.104449	−	0.199791i
$803$	−2.81621e8			−0.543899
$804$	−5.80393e7	+	8.35083e7i	−0.111674	+	0.160680i
$805$	9.84963e8	+	5.59691e8i	1.88813	+	1.07290i
$806$	4.00923e7	+	7.66891e7i	0.0765695	+	0.146463i
$807$	−2.83864e8			−0.540119
$808$	3.59374e7	+	4.53972e6i	0.0681259	+	0.00860588i
$809$	−8.25351e8			−1.55881			−0.779405	−	0.626520i	$-0.784479\pi$
$809$	−8.25351e8			−1.55881			−0.779405	+	0.626520i	$0.784479\pi$
$810$	2.06761e6	−	5.90128e7i	0.00389057	−	0.111043i
$811$		−	4.97694e7i		−	0.0933039i	−0.998911	−	0.0466520i	$-0.985145\pi$
$811$		−	4.97694e7i		−	0.0933039i	0.998911	−	0.0466520i	$-0.0148552\pi$
$812$	−1.65632e8	+	2.38316e8i	−0.309369	+	0.445128i
$813$			3.12378e8i			0.581311i
$814$	2.55242e8	+	4.88231e8i	0.473238	+	0.905216i
$815$	4.00858e8	+	2.27781e8i	0.740487	+	0.420771i
$816$	−4.57092e8	+	1.69995e8i	−0.841266	+	0.312872i
$817$		−	1.59320e7i		−	0.0292148i
$818$	−2.73993e8	−	5.24098e8i	−0.500587	−	0.957530i
$819$			5.09758e8i			0.927924i
$820$	−2.10052e8	+	1.00611e8i	−0.380966	+	0.182475i
$821$	3.24281e8			0.585993			0.292997	−	0.956113i	$-0.405348\pi$
$821$	3.24281e8			0.585993			0.292997	+	0.956113i	$0.405348\pi$
$822$	4.53352e8	−	2.37008e8i	0.816244	−	0.426724i
$823$	−5.16871e8			−0.927219			−0.463610	−	0.886040i	$-0.653446\pi$
$823$	−5.16871e8			−0.927219			−0.463610	+	0.886040i	$0.653446\pi$
$824$	5.72504e8	+	7.23205e7i	1.02328	+	0.129265i
$825$	2.62755e8	−	1.56550e8i	0.467939	−	0.278798i
$826$	−6.49707e7	+	3.39660e7i	−0.115286	+	0.0602705i
$827$	7.27572e8			1.28635			0.643175	−	0.765719i	$-0.277617\pi$
$827$	7.27572e8			1.28635			0.643175	+	0.765719i	$0.277617\pi$
$828$	1.27874e8	−	1.83988e8i	0.225264	−	0.324115i
$829$	9.40548e8			1.65089			0.825444	−	0.564484i	$-0.190925\pi$
$829$	9.40548e8			1.65089			0.825444	+	0.564484i	$0.190925\pi$
$830$	−2.21303e7	+	6.31633e8i	−0.0387037	+	1.10467i
$831$		−	6.29652e8i		−	1.09723i
$832$	2.17392e8	−	8.46729e8i	0.377462	−	1.47019i
$833$		−	2.12383e9i		−	3.67439i
$834$	−1.30547e8	+	6.82486e7i	−0.225045	+	0.117651i
$835$	−5.47465e8	−	3.11089e8i	−0.940366	−	0.534349i
$836$	−5.73615e7	+	8.25332e7i	−0.0981753	+	0.141257i
$837$		−	1.22872e7i		−	0.0209545i
$838$	−2.43420e8	+	1.27258e8i	−0.413642	+	0.216248i
$839$			7.65799e8i			1.29667i	0.761356	+	0.648334i	$0.224534\pi$
$839$			7.65799e8i			1.29667i	−0.761356	+	0.648334i	$0.775466\pi$
$840$	−5.02488e8	−	3.75996e8i	−0.847788	−	0.634374i
$841$	−5.42858e8			−0.912637
$842$	2.16328e8	+	4.13796e8i	0.362391	+	0.693186i
$843$	−1.83512e8			−0.306325
$844$	8.38559e8	+	5.82809e8i	1.39478	+	0.969391i
$845$	−6.84018e8	−	3.88683e8i	−1.13370	−	0.644207i
$846$	−1.35211e7	−	2.58633e7i	−0.0223306	−	0.0427142i
$847$	−1.22489e8			−0.201580
$848$	7.82429e8	−	2.90990e8i	1.28309	−	0.477189i
$849$	4.85763e8			0.793782
$850$	−8.13054e8	−	5.00456e8i	−1.32392	−	0.814909i
$851$			7.90112e8i			1.28203i
$852$	4.34869e8	+	3.02239e8i	0.703137	+	0.488688i
$853$		−	1.03777e9i		−	1.67206i	−0.548681	−	0.836032i	$-0.684870\pi$
$853$		−	1.03777e9i		−	1.67206i	0.548681	−	0.836032i	$-0.315130\pi$
$854$	−7.25377e8	−	1.38751e9i	−1.16464	−	2.22773i
$855$	−1.87678e7	+	3.30282e7i	−0.0300272	+	0.0528429i
$856$	5.74734e8	+	7.26022e7i	0.916317	+	0.115752i
$857$			2.57612e8i			0.409283i	0.978837	+	0.204641i	$0.0656028\pi$
$857$			2.57612e8i			0.409283i	−0.978837	+	0.204641i	$0.934397\pi$
$858$	2.41943e8	+	4.62793e8i	0.383047	+	0.732698i
$859$			4.00986e8i			0.632630i	0.948654	+	0.316315i	$0.102446\pi$
$859$			4.00986e8i			0.632630i	−0.948654	+	0.316315i	$0.897554\pi$
$860$	9.19131e7	−	4.40246e7i	0.144505	−	0.0692149i
$861$	−2.85485e8			−0.447274
$862$	−3.64071e8	+	1.90333e8i	−0.568414	+	0.297161i
$863$	8.41242e8			1.30885			0.654423	−	0.756129i	$-0.272912\pi$
$863$	8.41242e8			1.30885			0.654423	+	0.756129i	$0.272912\pi$
$864$	−8.30549e7	+	9.22437e7i	−0.128773	+	0.143020i
$865$	−2.06909e8	+	3.64127e8i	−0.319692	+	0.562605i
$866$	−3.08167e8	+	1.61106e8i	−0.474495	+	0.248061i
$867$	−5.33114e8			−0.818018
$868$	−1.07236e8	−	7.45301e7i	−0.163976	−	0.113965i
$869$	−1.72634e7			−0.0263067
$870$	−3.93475e6	+	1.12304e8i	−0.00597530	+	0.170544i
$871$		−	3.39930e8i		−	0.514440i
$872$	−6.30879e8	−	7.96946e7i	−0.951473	−	0.120193i
$873$			1.52000e8i			0.228455i
$874$	−1.27742e8	+	6.67824e7i	−0.191338	+	0.100029i
$875$	−2.52966e7	−	1.22837e9i	−0.0377605	−	1.83360i
$876$	1.83729e8	+	1.27694e8i	0.273316	+	0.189958i
$877$		−	1.05281e9i		−	1.56081i	−0.625276	−	0.780404i	$-0.715014\pi$
$877$		−	1.05281e9i		−	1.56081i	0.625276	−	0.780404i	$-0.284986\pi$
$878$	−3.77808e8	+	1.97514e8i	−0.558197	+	0.291820i
$879$		−	7.40016e7i		−	0.108962i
$880$	−6.34649e8	−	1.02862e8i	−0.931291	−	0.150941i
$881$	7.73565e8			1.13128			0.565639	−	0.824653i	$-0.308630\pi$
$881$	7.73565e8			1.13128			0.565639	+	0.824653i	$0.308630\pi$
$882$	−2.50441e8	−	4.79047e8i	−0.365006	−	0.698188i
$883$	−5.23480e8			−0.760358			−0.380179	−	0.924913i	$-0.624138\pi$
$883$	−5.23480e8			−0.760358			−0.380179	+	0.924913i	$0.624138\pi$
$884$	9.30322e8	−	1.33857e9i	1.34672	−	1.93769i
$885$	−1.40243e7	+	2.46805e7i	−0.0202326	+	0.0356061i
$886$	6.06324e6	+	1.15978e7i	0.00871773	+	0.0166754i
$887$	3.93574e8			0.563969			0.281984	−	0.959419i	$-0.409007\pi$
$887$	3.93574e8			0.563969			0.281984	+	0.959419i	$0.409007\pi$
$888$	5.48563e7	−	4.34253e8i	0.0783407	−	0.620161i
$889$	−1.72451e9			−2.45448
$890$	−1.06373e7	+	3.03606e8i	−0.0150891	+	0.430666i
$891$		−	7.41492e7i		−	0.104827i
$892$	−1.79658e8	+	2.58496e8i	−0.253134	+	0.364216i
$893$			1.87752e7i			0.0263652i
$894$	−7.89476e7	−	1.51012e8i	−0.110491	−	0.211348i
$895$	3.06975e7	−	5.40226e7i	0.0428188	−	0.0753540i
$896$	3.01266e8	+	1.28437e9i	0.418819	+	1.78553i
$897$			7.48945e8i			1.03770i
$898$	−1.45960e8	−	2.79195e8i	−0.201561	−	0.385548i
$899$			2.33831e7i			0.0321828i
$900$	−2.42404e8	−	1.70069e7i	−0.332516	−	0.0233291i
$901$	1.55664e9			2.12820
$902$	−2.59182e8	+	1.35498e8i	−0.353171	+	0.184634i
$903$	1.24920e8			0.169656
$904$	−2.82070e7	+	2.23292e8i	−0.0381813	+	0.302251i
$905$	−2.68189e8	−	1.52394e8i	−0.361822	−	0.205600i
$906$	−3.58148e8	+	1.87236e8i	−0.481591	+	0.251771i
$907$	1.14062e9			1.52868			0.764342	−	0.644811i	$-0.223064\pi$
$907$	1.14062e9			1.52868			0.764342	+	0.644811i	$0.223064\pi$
$908$	−3.38522e8	+	4.87074e8i	−0.452199	+	0.650635i
$909$	1.71918e7			0.0228891
$910$	2.09648e9	+	7.34537e7i	2.78207	+	0.0974742i
$911$		−	6.75025e8i		−	0.892821i	−0.894828	−	0.446411i	$-0.852702\pi$
$911$		−	6.75025e8i		−	0.892821i	0.894828	−	0.446411i	$-0.147298\pi$
$912$	7.48451e7	−	2.78353e7i	0.0986685	−	0.0366954i
$913$			7.93644e8i			1.04283i
$914$	−1.22317e9	+	6.39460e8i	−1.60195	+	0.837481i
$915$	−5.27076e8	−	2.99503e8i	−0.688034	−	0.390965i
$916$	−1.58895e8	+	2.28622e8i	−0.206739	+	0.297462i
$917$			7.30816e8i			0.947764i
$918$	−2.05118e8	+	1.07234e8i	−0.265140	+	0.138613i
$919$			8.33732e8i			1.07419i	0.843523	+	0.537094i	$0.180478\pi$
$919$			8.33732e8i			1.07419i	−0.843523	+	0.537094i	$0.819522\pi$
$920$	−7.38263e8	−	5.52420e8i	−0.948086	−	0.709424i
$921$	2.47956e8			0.317392
$922$	5.85069e8	+	1.11913e9i	0.746473	+	1.42786i
$923$	−1.77018e9			−2.25120
$924$	−6.47131e8	−	4.49764e8i	−0.820307	−	0.570123i
$925$	7.36142e8	−	4.38594e8i	0.930115	−	0.554163i
$926$	6.13514e8	+	1.17354e9i	0.772666	+	1.47797i
$927$	2.73875e8			0.343806
$928$	1.58057e8	−	1.75544e8i	0.197774	−	0.219655i
$929$	1.25073e8			0.155997			0.0779986	−	0.996953i	$-0.475147\pi$
$929$	1.25073e8			0.155997			0.0779986	+	0.996953i	$0.475147\pi$
$930$	−5.05337e7	−	1.77053e6i	−0.0628249	−	0.00220117i
$931$			3.47760e8i			0.430954i
$932$	−7.93980e6	−	5.51826e6i	−0.00980759	−	0.00681639i
$933$		−	4.90320e8i		−	0.603719i
$934$	−2.41303e8	−	4.61569e8i	−0.296158	−	0.566494i
$935$	−1.04235e9	−	5.92300e8i	−1.27520	−	0.724614i
$936$	5.19981e7	−	4.11628e8i	0.0634103	−	0.501969i
$937$		−	7.76885e8i		−	0.944361i	−0.881502	−	0.472181i	$-0.843467\pi$
$937$		−	7.76885e8i		−	0.944361i	0.881502	−	0.472181i	$-0.156533\pi$
$938$	2.37665e8	+	4.54609e8i	0.287976	+	0.550845i
$939$			5.24999e8i			0.634106i
$940$	−1.08316e8	+	5.18814e7i	−0.130410	+	0.0624637i
$941$	−1.33114e9			−1.59756			−0.798778	−	0.601626i	$-0.794520\pi$
$941$	−1.33114e9			−1.59756			−0.798778	+	0.601626i	$0.794520\pi$
$942$	−5.89729e7	+	3.08304e7i	−0.0705505	+	0.0368831i
$943$	−4.19439e8			−0.500188
$944$	5.59283e7	−	2.08001e7i	0.0664838	−	0.0247257i
$945$	−2.58970e8	−	1.47156e8i	−0.306869	−	0.174374i
$946$	1.13411e8	−	5.92901e7i	0.133962	−	0.0700340i
$947$	−1.12323e9			−1.32257			−0.661284	−	0.750136i	$-0.729988\pi$
$947$	−1.12323e9			−1.32257			−0.661284	+	0.750136i	$0.729988\pi$
$948$	1.12626e7	+	7.82764e6i	0.0132194	+	0.00918767i
$949$	−7.47889e8			−0.875061
$950$	1.33131e8	+	8.19456e7i	0.155277	+	0.0955773i
$951$		−	4.74191e8i		−	0.551330i
$952$	−3.08303e8	+	2.44059e9i	−0.357328	+	2.82868i
$953$			1.15890e9i			1.33895i	0.742833	+	0.669477i	$0.233482\pi$
$953$			1.15890e9i			1.33895i	−0.742833	+	0.669477i	$0.766518\pi$
$954$	3.51112e8	−	1.83558e8i	0.404390	−	0.211411i
$955$	9.44186e7	−	1.66161e8i	0.108404	−	0.190774i
$956$	−5.82801e8	−	4.05054e8i	−0.667032	−	0.463595i
$957$			1.41109e8i			0.160998i
$958$	5.38304e8	−	2.81420e8i	0.612253	−	0.320080i
$959$		−	2.58048e9i		−	2.92580i
$960$	3.67403e8	+	3.54872e8i	0.415269	+	0.401105i
$961$	8.76982e8			0.988145
$962$	6.77836e8	+	1.29657e9i	0.761376	+	1.45637i
$963$	2.74942e8			0.307866
$964$	−8.33633e8	+	1.19945e9i	−0.930559	+	1.33891i
$965$	6.08437e8	−	1.07075e9i	0.677070	−	1.19153i
$966$	−5.23631e8	−	1.00161e9i	−0.580890	−	1.11114i
$967$	1.31608e9			1.45547			0.727737	−	0.685857i	$-0.240572\pi$
$967$	1.31608e9			1.45547			0.727737	+	0.685857i	$0.240572\pi$
$968$	9.89097e7	+	1.24946e7i	0.109047	+	0.0137751i
$969$	1.48904e8			0.163657
$970$	6.25130e8	+	2.19025e7i	0.684944	+	0.0239981i
$971$		−	3.94143e8i		−	0.430523i	−0.976556	−	0.215261i	$-0.930940\pi$
$971$		−	3.94143e8i		−	0.430523i	0.976556	−	0.215261i	$-0.0690604\pi$
$972$	−3.36211e7	+	4.83748e7i	−0.0366111	+	0.0526769i
$973$			7.43074e8i			0.806666i
$974$	−3.97370e8	−	7.60095e8i	−0.430049	−	0.822604i
$975$	6.97788e8	−	4.15742e8i	0.752852	−	0.448549i
$976$	4.44206e8	+	1.19440e9i	0.477787	+	1.28470i
$977$		−	1.51060e9i		−	1.61982i	−0.586553	−	0.809911i	$-0.699516\pi$
$977$		−	1.51060e9i		−	1.61982i	0.586553	−	0.809911i	$-0.300484\pi$
$978$	−2.13106e8	−	4.07632e8i	−0.227813	−	0.435765i
$979$			3.81480e8i			0.406559i
$980$	−2.00627e9	+	9.60961e8i	−2.13162	+	1.02100i
$981$	−3.01800e8			−0.319678
$982$	1.60321e9	−	8.38143e8i	1.69300	−	0.885083i
$983$	1.64220e9			1.72888			0.864440	−	0.502736i	$-0.167673\pi$
$983$	1.64220e9			1.72888			0.864440	+	0.502736i	$0.167673\pi$
$984$	2.30528e8	+	2.91210e7i	0.241957	+	0.0305648i
$985$	−1.67757e8	+	2.95226e8i	−0.175539	+	0.308920i
$986$	3.90349e8	−	2.04070e8i	0.407213	−	0.212887i
$987$	−1.47214e8			−0.153108
$988$	−1.52333e8	+	2.19180e8i	−0.157951	+	0.227264i
$989$	1.83535e8			0.189727
$990$	−3.04954e8	−	1.06846e7i	−0.314288	−	0.0110116i
$991$		−	1.90807e9i		−	1.96053i	−0.197680	−	0.980267i	$-0.563341\pi$
$991$		−	1.90807e9i		−	1.96053i	0.197680	−	0.980267i	$-0.436659\pi$
$992$	7.89899e7	+	7.11214e7i	0.0809164	+	0.0728560i
$993$			9.85403e6i			0.0100639i
$994$	2.36737e9	−	1.23764e9i	2.41050	−	1.26019i
$995$	−7.07247e8	+	1.24464e9i	−0.717963	+	1.26350i
$996$	3.59857e8	−	5.17771e8i	0.364210	−	0.524034i
$997$			7.29485e7i			0.0736090i	0.999322	+	0.0368045i	$0.0117179\pi$
$997$			7.29485e7i			0.0736090i	−0.999322	+	0.0368045i	$0.988282\pi$
$998$	1.60353e8	−	8.38311e7i	0.161319	−	0.0843361i
$999$		−	2.07739e8i		−	0.208363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.f.a.19.13	✓	36
3.2	odd	2		180.7.f.g.19.24		36
4.3	odd	2	inner	60.7.f.a.19.23	yes	36
5.4	even	2	inner	60.7.f.a.19.24	yes	36
12.11	even	2		180.7.f.g.19.14		36
15.14	odd	2		180.7.f.g.19.13		36
20.19	odd	2	inner	60.7.f.a.19.14	yes	36
60.59	even	2		180.7.f.g.19.23		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.f.a.19.13	✓	36	1.1	even	1	trivial
60.7.f.a.19.14	yes	36	20.19	odd	2	inner
60.7.f.a.19.23	yes	36	4.3	odd	2	inner
60.7.f.a.19.24	yes	36	5.4	even	2	inner
180.7.f.g.19.13		36	15.14	odd	2
180.7.f.g.19.14		36	12.11	even	2
180.7.f.g.19.23		36	60.59	even	2
180.7.f.g.19.24		36	3.2	odd	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)

\(f(q)\)	\(=\)	\(q+(-3.70638 - 7.08962i) q^{2} +15.5885 q^{3} +(-36.5255 + 52.5537i) q^{4} +(108.680 + 61.7555i) q^{5} +(-57.7768 - 110.516i) q^{6} -629.059 q^{7} +(507.963 + 64.1675i) q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+(-3.70638 - 7.08962i) q^{2} +15.5885 q^{3} +(-36.5255 + 52.5537i) q^{4} +(108.680 + 61.7555i) q^{5} +(-57.7768 - 110.516i) q^{6} -629.059 q^{7} +(507.963 + 64.1675i) q^{8} +243.000 q^{9} +(35.0151 - 999.387i) q^{10} -1255.72i q^{11} +(-569.375 + 819.231i) q^{12} -3334.77i q^{13} +(2331.53 + 4459.79i) q^{14} +(1694.15 + 962.673i) q^{15} +(-1427.78 - 3839.10i) q^{16} -7637.86i q^{17} +(-900.651 - 1722.78i) q^{18} +1250.64i q^{19} +(-7215.05 + 3455.87i) q^{20} -9806.06 q^{21} +(-8902.61 + 4654.19i) q^{22} -14407.2 q^{23} +(7918.36 + 1000.27i) q^{24} +(7997.51 + 13423.1i) q^{25} +(-23642.3 + 12359.9i) q^{26} +3788.00 q^{27} +(22976.7 - 33059.4i) q^{28} -7208.72 q^{29} +(545.832 - 15578.9i) q^{30} -3243.73i q^{31} +(-21925.8 + 24351.6i) q^{32} -19574.8i q^{33} +(-54149.5 + 28308.8i) q^{34} +(-68365.9 - 38847.9i) q^{35} +(-8875.69 + 12770.5i) q^{36} -54841.3i q^{37} +(8866.54 - 4635.34i) q^{38} -51984.0i q^{39} +(51242.5 + 38343.2i) q^{40} +29113.1 q^{41} +(36345.0 + 69521.3i) q^{42} -12739.1 q^{43} +(65992.9 + 45865.9i) q^{44} +(26409.1 + 15006.6i) q^{45} +(53398.7 + 102142. i) q^{46} +15012.6 q^{47} +(-22256.9 - 59845.6i) q^{48} +278067. q^{49} +(65523.1 - 106451. i) q^{50} -119062. i q^{51} +(175255. + 121804. i) q^{52} +203806. i q^{53} +(-14039.8 - 26855.4i) q^{54} +(77547.9 - 136472. i) q^{55} +(-319539. - 40365.2i) q^{56} +19495.5i q^{57} +(26718.3 + 51107.1i) q^{58} +14568.1i q^{59} +(-112472. + 53871.6i) q^{60} -311116. q^{61} +(-22996.8 + 12022.5i) q^{62} -152861. q^{63} +(253909. + 65189.5i) q^{64} +(205941. - 362422. i) q^{65} +(-138778. + 72551.7i) q^{66} +101935. q^{67} +(401398. + 278976. i) q^{68} -224586. q^{69} +(-22026.6 + 628674. i) q^{70} -530826. i q^{71} +(123435. + 15592.7i) q^{72} -224270. i q^{73} +(-388804. + 203263. i) q^{74} +(124669. + 209246. i) q^{75} +(-65725.6 - 45680.1i) q^{76} +789925. i q^{77} +(-368547. + 192672. i) q^{78} -13747.8i q^{79} +(81914.6 - 505405. i) q^{80} +59049.0 q^{81} +(-107904. - 206401. i) q^{82} -632021. q^{83} +(358171. - 515345. i) q^{84} +(471680. - 830079. i) q^{85} +(47215.9 + 90315.3i) q^{86} -112373. q^{87} +(80576.7 - 637861. i) q^{88} -303793. q^{89} +(8508.68 - 242851. i) q^{90} +2.09777e6i q^{91} +(526231. - 757153. i) q^{92} -50564.7i q^{93} +(-55642.3 - 106433. i) q^{94} +(-77233.7 + 135919. i) q^{95} +(-341790. + 379604. i) q^{96} +625514. i q^{97} +(-1.03062e6 - 1.97139e6i) q^{98} -305141. 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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