LMFDB - Embedded newform 180.7.c.b.91.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,7,Mod(91,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("180.91");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	180.c (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:	$41.4097350516$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.11
Character	$\chi$	$=$	180.91
Dual form			180.7.c.b.91.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59351 - 7.56794i) q^{2} +(-50.5474 + 39.2551i) q^{4} +55.9017 q^{5} -671.100i q^{7} +(428.176 + 280.731i) q^{8} +O(q^{10})$	\(q+(-2.59351 - 7.56794i) q^{2} +(-50.5474 + 39.2551i) q^{4} +55.9017 q^{5} -671.100i q^{7} +(428.176 + 280.731i) q^{8} +(-144.982 - 423.061i) q^{10} -199.628i q^{11} +2041.73 q^{13} +(-5078.84 + 1740.51i) q^{14} +(1014.07 - 3968.49i) q^{16} +8219.18 q^{17} +5147.13i q^{19} +(-2825.68 + 2194.43i) q^{20} +(-1510.77 + 517.738i) q^{22} +14631.4i q^{23} +3125.00 q^{25} +(-5295.27 - 15451.7i) q^{26} +(26344.1 + 33922.3i) q^{28} +12573.4 q^{29} -54422.8i q^{31} +(-32663.3 + 2617.90i) q^{32} +(-21316.6 - 62202.2i) q^{34} -37515.6i q^{35} -11.6361 q^{37} +(38953.1 - 13349.2i) q^{38} +(23935.7 + 15693.3i) q^{40} +67862.4 q^{41} -105037. i q^{43} +(7836.42 + 10090.7i) q^{44} +(110729. - 37946.7i) q^{46} -89660.8i q^{47} -332726. q^{49} +(-8104.73 - 23649.8i) q^{50} +(-103204. + 80148.5i) q^{52} +1369.17 q^{53} -11159.5i q^{55} +(188398. - 287349. i) q^{56} +(-32609.2 - 95154.5i) q^{58} +5601.86i q^{59} -132681. q^{61} +(-411868. + 141146. i) q^{62} +(104525. + 240404. i) q^{64} +114136. q^{65} +325492. i q^{67} +(-415458. + 322645. i) q^{68} +(-283916. + 97297.4i) q^{70} -303340. i q^{71} -247561. q^{73} +(30.1783 + 88.0611i) q^{74} +(-202051. - 260174. i) q^{76} -133970. q^{77} -389964. i q^{79} +(56688.3 - 221845. i) q^{80} +(-176002. - 513578. i) q^{82} +215366. i q^{83} +459466. q^{85} +(-794916. + 272416. i) q^{86} +(56041.7 - 85475.8i) q^{88} -46200.5 q^{89} -1.37021e6i q^{91} +(-574357. - 739578. i) q^{92} +(-678547. + 232537. i) q^{94} +287733. i q^{95} +800223. q^{97} +(862931. + 2.51805e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8}+O(q^{10}) $ 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8	$ 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8} - 750 q^{10} + 5040 q^{13} + 2596 q^{14} + 4194 q^{16} - 7000 q^{20} + 45780 q^{22} + 75000 q^{25} - 75852 q^{26} + 54300 q^{28} - 132800 q^{29} + 10700 q^{32} - 173484 q^{34} - 69840 q^{37} - 215800 q^{38} - 14250 q^{40} + 70448 q^{41} + 395668 q^{44} - 158760 q^{46} - 642984 q^{49} - 62500 q^{50} - 210240 q^{52} + 644320 q^{53} + 917708 q^{56} - 1345020 q^{58} - 222864 q^{61} - 1948520 q^{62} + 935922 q^{64} - 266000 q^{65} - 572680 q^{68} + 220500 q^{70} + 771120 q^{73} + 589164 q^{74} - 191544 q^{76} - 1383840 q^{77} + 946000 q^{80} + 2672520 q^{82} - 372000 q^{85} - 1781528 q^{86} + 956940 q^{88} + 1566224 q^{89} + 3040560 q^{92} - 3788352 q^{94} - 1666800 q^{97} + 2709660 q^{98}+O(q^{100}) $ 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8 - 750 * q^10 + 5040 * q^13 + 2596 * q^14 + 4194 * q^16 - 7000 * q^20 + 45780 * q^22 + 75000 * q^25 - 75852 * q^26 + 54300 * q^28 - 132800 * q^29 + 10700 * q^32 - 173484 * q^34 - 69840 * q^37 - 215800 * q^38 - 14250 * q^40 + 70448 * q^41 + 395668 * q^44 - 158760 * q^46 - 642984 * q^49 - 62500 * q^50 - 210240 * q^52 + 644320 * q^53 + 917708 * q^56 - 1345020 * q^58 - 222864 * q^61 - 1948520 * q^62 + 935922 * q^64 - 266000 * q^65 - 572680 * q^68 + 220500 * q^70 + 771120 * q^73 + 589164 * q^74 - 191544 * q^76 - 1383840 * q^77 + 946000 * q^80 + 2672520 * q^82 - 372000 * q^85 - 1781528 * q^86 + 956940 * q^88 + 1566224 * q^89 + 3040560 * q^92 - 3788352 * q^94 - 1666800 * q^97 + 2709660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−2.59351	−	7.56794i	−0.324189	−	0.945992i
$2$	−2.59351	−	7.56794i	−0.324189	−	0.945992i
$3$		0			0
$3$		0			0
$4$	−50.5474	+	39.2551i	−0.789803	+	0.613361i
$5$	55.9017			0.447214
$5$	55.9017			0.447214
$6$		0			0
$7$		−	671.100i		−	1.95656i	−0.207288	−	0.978280i	$-0.566464\pi$
$7$		−	671.100i		−	1.95656i	0.207288	−	0.978280i	$-0.433536\pi$
$8$	428.176	+	280.731i	0.836281	+	0.548302i
$9$		0			0
$10$	−144.982	−	423.061i	−0.144982	−	0.423061i
$11$		−	199.628i		−	0.149983i	−0.997184	−	0.0749917i	$-0.976107\pi$
$11$		−	199.628i		−	0.149983i	0.997184	−	0.0749917i	$-0.0238930\pi$
$12$		0			0
$13$	2041.73			0.929328			0.464664	−	0.885487i	$-0.346175\pi$
$13$	2041.73			0.929328			0.464664	+	0.885487i	$0.346175\pi$
$14$	−5078.84	+	1740.51i	−1.85089	+	0.634296i
$15$		0			0
$16$	1014.07	−	3968.49i	0.247576	−	0.968868i
$17$	8219.18			1.67294			0.836472	−	0.548009i	$-0.184614\pi$
$17$	8219.18			1.67294			0.836472	+	0.548009i	$0.184614\pi$
$18$		0			0
$19$			5147.13i			0.750420i	0.926940	+	0.375210i	$0.122429\pi$
$19$			5147.13i			0.750420i	−0.926940	+	0.375210i	$0.877571\pi$
$20$	−2825.68	+	2194.43i	−0.353210	+	0.274303i
$21$		0			0
$22$	−1510.77	+	517.738i	−0.141883	+	0.0486230i
$23$			14631.4i			1.20255i	0.799044	+	0.601273i	$0.205340\pi$
$23$			14631.4i			1.20255i	−0.799044	+	0.601273i	$0.794660\pi$
$24$		0			0
$25$	3125.00			0.200000
$26$	−5295.27	−	15451.7i	−0.301278	−	0.879137i
$27$		0			0
$28$	26344.1	+	33922.3i	1.20008	+	1.54530i
$29$	12573.4			0.515534			0.257767	−	0.966207i	$-0.417013\pi$
$29$	12573.4			0.515534			0.257767	+	0.966207i	$0.417013\pi$
$30$		0			0
$31$		−	54422.8i		−	1.82682i	−0.407041	−	0.913410i	$-0.633439\pi$
$31$		−	54422.8i		−	1.82682i	0.407041	−	0.913410i	$-0.366561\pi$
$32$	−32663.3	+	2617.90i	−0.996804	+	0.0798919i
$33$		0			0
$34$	−21316.6	−	62202.2i	−0.542351	−	1.58259i
$35$		−	37515.6i		−	0.875000i
$36$		0			0
$37$	−11.6361			−0.000229721			−0.000114861	−	1.00000i	$-0.500037\pi$
$37$	−11.6361			−0.000229721			−0.000114861		1.00000i	$0.500037\pi$
$38$	38953.1	−	13349.2i	0.709891	−	0.243278i
$39$		0			0
$40$	23935.7	+	15693.3i	0.373996	+	0.245208i
$41$	67862.4			0.984640			0.492320	−	0.870414i	$-0.336149\pi$
$41$	67862.4			0.984640			0.492320	+	0.870414i	$0.336149\pi$
$42$		0			0
$43$		−	105037.i		−	1.32111i	−0.750778	−	0.660554i	$-0.770321\pi$
$43$		−	105037.i		−	1.32111i	0.750778	−	0.660554i	$-0.229679\pi$
$44$	7836.42	+	10090.7i	0.0919940	+	0.118457i
$45$		0			0
$46$	110729.	−	37946.7i	1.13760	−	0.389853i
$47$		−	89660.8i		−	0.863592i	−0.901971	−	0.431796i	$-0.857880\pi$
$47$		−	89660.8i		−	0.863592i	0.901971	−	0.431796i	$-0.142120\pi$
$48$		0			0
$49$	−332726.			−2.82813
$50$	−8104.73	−	23649.8i	−0.0648379	−	0.189198i
$51$		0			0
$52$	−103204.	+	80148.5i	−0.733985	+	0.570014i
$53$	1369.17			0.00919668			0.00459834	−	0.999989i	$-0.498536\pi$
$53$	1369.17			0.00919668			0.00459834	+	0.999989i	$0.498536\pi$
$54$		0			0
$55$		−	11159.5i		−	0.0670746i
$56$	188398.	−	287349.i	1.07279	−	1.63623i
$57$		0			0
$58$	−32609.2	−	95154.5i	−0.167131	−	0.487691i
$59$			5601.86i			0.0272757i	0.999907	+	0.0136379i	$0.00434120\pi$
$59$			5601.86i			0.0272757i	−0.999907	+	0.0136379i	$0.995659\pi$
$60$		0			0
$61$	−132681.			−0.584548			−0.292274	−	0.956335i	$-0.594412\pi$
$61$	−132681.			−0.584548			−0.292274	+	0.956335i	$0.594412\pi$
$62$	−411868.	+	141146.i	−1.72816	+	0.592235i
$63$		0			0
$64$	104525.	+	240404.i	0.398730	+	0.917068i
$65$	114136.			0.415608
$66$		0			0
$67$			325492.i			1.08222i	0.840951	+	0.541111i	$0.181996\pi$
$67$			325492.i			1.08222i	−0.840951	+	0.541111i	$0.818004\pi$
$68$	−415458.	+	322645.i	−1.32130	+	1.02612i
$69$		0			0
$70$	−283916.	+	97297.4i	−0.827743	+	0.283666i
$71$		−	303340.i		−	0.847529i	−0.905772	−	0.423764i	$-0.860708\pi$
$71$		−	303340.i		−	0.847529i	0.905772	−	0.423764i	$-0.139292\pi$
$72$		0			0
$73$	−247561.			−0.636376			−0.318188	−	0.948028i	$-0.603074\pi$
$73$	−247561.			−0.636376			−0.318188	+	0.948028i	$0.603074\pi$
$74$	30.1783	+	88.0611i	7.44732e−5	+	0.000217315i
$75$		0			0
$76$	−202051.	−	260174.i	−0.460278	−	0.592683i
$77$	−133970.			−0.293452
$78$		0			0
$79$		−	389964.i		−	0.790939i	−0.918479	−	0.395470i	$-0.870582\pi$
$79$		−	389964.i		−	0.790939i	0.918479	−	0.395470i	$-0.129418\pi$
$80$	56688.3	−	221845.i	0.110719	−	0.433291i
$81$		0			0
$82$	−176002.	−	513578.i	−0.319210	−	0.931462i
$83$			215366.i			0.376654i	0.982106	+	0.188327i	$0.0603065\pi$
$83$			215366.i			0.376654i	−0.982106	+	0.188327i	$0.939694\pi$
$84$		0			0
$85$	459466.			0.748164
$86$	−794916.	+	272416.i	−1.24976	+	0.428289i
$87$		0			0
$88$	56041.7	−	85475.8i	0.0822362	−	0.125428i
$89$	−46200.5			−0.0655355			−0.0327677	−	0.999463i	$-0.510432\pi$
$89$	−46200.5			−0.0655355			−0.0327677	+	0.999463i	$0.510432\pi$
$90$		0			0
$91$		−	1.37021e6i		−	1.81829i
$92$	−574357.	−	739578.i	−0.737595	−	0.949774i
$93$		0			0
$94$	−678547.	+	232537.i	−0.816952	+	0.279968i
$95$			287733.i			0.335598i
$96$		0			0
$97$	800223.			0.876791			0.438396	−	0.898782i	$-0.355547\pi$
$97$	800223.			0.876791			0.438396	+	0.898782i	$0.355547\pi$
$98$	862931.	+	2.51805e6i	0.916849	+	2.67539i
$99$		0			0
$100$	−157961.	+	122672.i	−0.157961	+	0.122672i
$101$	−850500.			−0.825487			−0.412743	−	0.910847i	$-0.635429\pi$
$101$	−850500.			−0.825487			−0.412743	+	0.910847i	$0.635429\pi$
$102$		0			0
$103$		−	591093.i		−	0.540934i	−0.962729	−	0.270467i	$-0.912822\pi$
$103$		−	591093.i		−	0.540934i	0.962729	−	0.270467i	$-0.0871781\pi$
$104$	874220.	+	573177.i	0.777179	+	0.509552i
$105$		0			0
$106$	−3550.97	−	10361.8i	−0.00298147	−	0.00869999i
$107$		−	1.02379e6i		−	0.835718i	−0.908512	−	0.417859i	$-0.862781\pi$
$107$		−	1.02379e6i		−	0.835718i	0.908512	−	0.417859i	$-0.137219\pi$
$108$		0			0
$109$	−1.78875e6			−1.38125			−0.690623	−	0.723215i	$-0.742663\pi$
$109$	−1.78875e6			−1.38125			−0.690623	+	0.723215i	$0.742663\pi$
$110$	−84454.7	+	28942.4i	−0.0634521	+	0.0217449i
$111$		0			0
$112$	−2.66325e6	−	680543.i	−1.89565	−	0.484397i
$113$	−2.22824e6			−1.54428			−0.772142	−	0.635450i	$-0.780814\pi$
$113$	−2.22824e6			−1.54428			−0.772142	+	0.635450i	$0.780814\pi$
$114$		0			0
$115$			817919.i			0.537795i
$116$	−635551.	+	493569.i	−0.407170	+	0.316209i
$117$		0			0
$118$	42394.5	−	14528.5i	0.0258026	−	0.00884250i
$119$		−	5.51589e6i		−	3.27322i
$120$		0			0
$121$	1.73171e6			0.977505
$122$	344111.	+	1.00412e6i	0.189504	+	0.552978i
$123$		0			0
$124$	2.13637e6	+	2.75093e6i	1.12050	+	1.44283i
$125$	174693.			0.0894427
$126$		0			0
$127$		−	1.20836e6i		−	0.589908i	−0.955511	−	0.294954i	$-0.904696\pi$
$127$		−	1.20836e6i		−	0.589908i	0.955511	−	0.294954i	$-0.0953043\pi$
$128$	1.54828e6	−	1.41453e6i	0.738275	−	0.674499i
$129$		0			0
$130$	−296014.	−	863777.i	−0.134736	−	0.393162i
$131$		−	283537.i		−	0.126123i	−0.998010	−	0.0630616i	$-0.979914\pi$
$131$		−	283537.i		−	0.126123i	0.998010	−	0.0630616i	$-0.0200865\pi$
$132$		0			0
$133$	3.45424e6			1.46824
$134$	2.46331e6	−	844169.i	1.02377	−	0.350845i
$135$		0			0
$136$	3.51925e6	+	2.30737e6i	1.39905	+	0.917279i
$137$	4.15204e6			1.61473			0.807364	−	0.590053i	$-0.200893\pi$
$137$	4.15204e6			1.61473			0.807364	+	0.590053i	$0.200893\pi$
$138$		0			0
$139$			3.85092e6i			1.43391i	0.697122	+	0.716953i	$0.254464\pi$
$139$			3.85092e6i			1.43391i	−0.697122	+	0.716953i	$0.745536\pi$
$140$	1.47268e6	+	1.89632e6i	0.536691	+	0.691077i
$141$		0			0
$142$	−2.29566e6	+	786716.i	−0.801756	+	0.274760i
$143$		−	407587.i		−	0.139384i
$144$		0			0
$145$	702873.			0.230554
$146$	642054.	+	1.87353e6i	0.206306	+	0.602007i
$147$		0			0
$148$	588.173	−	456.776i	0.000181435	−	0.000140902i
$149$	3.30508e6			0.999132			0.499566	−	0.866276i	$-0.333493\pi$
$149$	3.30508e6			0.999132			0.499566	+	0.866276i	$0.333493\pi$
$150$		0			0
$151$		−	2.96350e6i		−	0.860743i	−0.902652	−	0.430371i	$-0.858383\pi$
$151$		−	2.96350e6i		−	0.860743i	0.902652	−	0.430371i	$-0.141617\pi$
$152$	−1.44496e6	+	2.20387e6i	−0.411456	+	0.627561i
$153$		0			0
$154$	347454.	+	1.01388e6i	0.0951339	+	0.277603i
$155$		−	3.04233e6i		−	0.816979i
$156$		0			0
$157$	3010.29			0.000777874			0.000388937	−	1.00000i	$-0.499876\pi$
$157$	3010.29			0.000777874			0.000388937		1.00000i	$0.499876\pi$
$158$	−2.95122e6	+	1.01138e6i	−0.748222	+	0.256414i
$159$		0			0
$160$	−1.82593e6	+	146345.i	−0.445784	+	0.0357287i
$161$	9.81912e6			2.35285
$162$		0			0
$163$			1.03461e6i			0.238899i	0.992840	+	0.119449i	$0.0381129\pi$
$163$			1.03461e6i			0.238899i	−0.992840	+	0.119449i	$0.961887\pi$
$164$	−3.43026e6	+	2.66395e6i	−0.777671	+	0.603940i
$165$		0			0
$166$	1.62988e6	−	558555.i	0.356312	−	0.122107i
$167$			593738.i			0.127481i	0.997967	+	0.0637405i	$0.0203030\pi$
$167$			593738.i			0.127481i	−0.997967	+	0.0637405i	$0.979697\pi$
$168$		0			0
$169$	−658135.			−0.136350
$170$	−1.19163e6	−	3.47721e6i	−0.242547	−	0.707757i
$171$		0			0
$172$	4.12325e6	+	5.30936e6i	0.810317	+	1.04341i
$173$	−1.01324e6			−0.195692			−0.0978458	−	0.995202i	$-0.531195\pi$
$173$	−1.01324e6			−0.195692			−0.0978458	+	0.995202i	$0.531195\pi$
$174$		0			0
$175$		−	2.09719e6i		−	0.391312i
$176$	−792221.	−	202437.i	−0.145314	−	0.0371323i
$177$		0			0
$178$	119822.	+	349642.i	0.0212459	+	0.0619960i
$179$			1.05856e7i			1.84569i	0.385176	+	0.922843i	$0.374141\pi$
$179$			1.05856e7i			1.84569i	−0.385176	+	0.922843i	$0.625859\pi$
$180$		0			0
$181$	−2.44921e6			−0.413038			−0.206519	−	0.978443i	$-0.566214\pi$
$181$	−2.44921e6			−0.413038			−0.206519	+	0.978443i	$0.566214\pi$
$182$	−1.03696e7	+	3.55365e6i	−1.72008	+	0.589469i
$183$		0			0
$184$	−4.10748e6	+	6.26480e6i	−0.659358	+	1.00567i
$185$	−650.477			−0.000102735
$186$		0			0
$187$		−	1.64078e6i		−	0.250914i
$188$	3.51964e6	+	4.53212e6i	0.529694	+	0.682068i
$189$		0			0
$190$	2.17755e6	−	746240.i	0.317473	−	0.108797i
$191$		−	5.41860e6i		−	0.777655i	−0.921311	−	0.388827i	$-0.872880\pi$
$191$		−	5.41860e6i		−	0.777655i	0.921311	−	0.388827i	$-0.127120\pi$
$192$		0			0
$193$	9.97092e6			1.38696			0.693479	−	0.720477i	$-0.256077\pi$
$193$	9.97092e6			1.38696			0.693479	+	0.720477i	$0.256077\pi$
$194$	−2.07539e6	−	6.05604e6i	−0.284246	−	0.829437i
$195$		0			0
$196$	1.68184e7	−	1.30612e7i	2.23366	−	1.73466i
$197$	−1.33406e7			−1.74492			−0.872459	−	0.488687i	$-0.837476\pi$
$197$	−1.33406e7			−1.74492			−0.872459	+	0.488687i	$0.837476\pi$
$198$		0			0
$199$		−	6.57996e6i		−	0.834957i	−0.908687	−	0.417479i	$-0.862914\pi$
$199$		−	6.57996e6i		−	0.834957i	0.908687	−	0.417479i	$-0.137086\pi$
$200$	1.33805e6	+	877283.i	0.167256	+	0.109660i
$201$		0			0
$202$	2.20578e6	+	6.43653e6i	0.267614	+	0.780904i
$203$		−	8.43799e6i		−	1.00867i
$204$		0			0
$205$	3.79362e6			0.440344
$206$	−4.47336e6	+	1.53301e6i	−0.511719	+	0.175365i
$207$		0			0
$208$	2.07046e6	−	8.10259e6i	0.230079	−	0.900396i
$209$	1.02751e6			0.112551
$210$		0			0
$211$			870512.i			0.0926675i	0.998926	+	0.0463337i	$0.0147538\pi$
$211$			870512.i			0.0926675i	−0.998926	+	0.0463337i	$0.985246\pi$
$212$	−69208.1	+	53747.1i	−0.00726356	+	0.00564089i
$213$		0			0
$214$	−7.74798e6	+	2.65521e6i	−0.790582	+	0.270931i
$215$		−	5.87177e6i		−	0.590818i
$216$		0			0
$217$	−3.65231e7			−3.57428
$218$	4.63916e6	+	1.35372e7i	0.447785	+	1.30665i
$219$		0			0
$220$	438069.	+	564086.i	0.0411410	+	0.0529757i
$221$	1.67814e7			1.55471
$222$		0			0
$223$			5.16242e6i			0.465521i	0.972534	+	0.232760i	$0.0747758\pi$
$223$			5.16242e6i			0.465521i	−0.972534	+	0.232760i	$0.925224\pi$
$224$	1.75687e6	+	2.19203e7i	0.156313	+	1.95031i
$225$		0			0
$226$	5.77898e6	+	1.68632e7i	0.500640	+	1.46088i
$227$			3.88936e6i			0.332506i	0.986083	+	0.166253i	$0.0531669\pi$
$227$			3.88936e6i			0.332506i	−0.986083	+	0.166253i	$0.946833\pi$
$228$		0			0
$229$	1.00633e7			0.837978			0.418989	−	0.907991i	$-0.362385\pi$
$229$	1.00633e7			0.837978			0.418989	+	0.907991i	$0.362385\pi$
$230$	6.18996e6	−	2.12129e6i	0.508750	−	0.174347i
$231$		0			0
$232$	5.38361e6	+	3.52973e6i	0.431131	+	0.282668i
$233$	−6.03617e6			−0.477192			−0.238596	−	0.971119i	$-0.576687\pi$
$233$	−6.03617e6			−0.477192			−0.238596	+	0.971119i	$0.576687\pi$
$234$		0			0
$235$		−	5.01219e6i		−	0.386210i
$236$	−219902.	−	283159.i	−0.0167299	−	0.0215424i
$237$		0			0
$238$	−4.17439e7	+	1.43055e7i	−3.09644	+	1.06114i
$239$			1.34966e6i			0.0988621i	0.998778	+	0.0494311i	$0.0157408\pi$
$239$			1.34966e6i			0.0988621i	−0.998778	+	0.0494311i	$0.984259\pi$
$240$		0			0
$241$	7.74261e6			0.553141			0.276571	−	0.960994i	$-0.410802\pi$
$241$	7.74261e6			0.553141			0.276571	+	0.960994i	$0.410802\pi$
$242$	−4.49121e6	−	1.31055e7i	−0.316897	−	0.924712i
$243$		0			0
$244$	6.70669e6	−	5.20842e6i	0.461677	−	0.358539i
$245$	−1.86000e7			−1.26478
$246$		0			0
$247$			1.05091e7i			0.697386i
$248$	1.52781e7	−	2.33025e7i	1.00165	−	1.52773i
$249$		0			0
$250$	−453068.	−	1.32206e6i	−0.0289964	−	0.0846121i
$251$			1.64750e7i			1.04185i	0.853603	+	0.520924i	$0.174413\pi$
$251$			1.64750e7i			1.04185i	−0.853603	+	0.520924i	$0.825587\pi$
$252$		0			0
$253$	2.92083e6			0.180362
$254$	−9.14477e6	+	3.13389e6i	−0.558048	+	0.191242i
$255$		0			0
$256$	−1.47205e7	−	8.04865e6i	−0.877412	−	0.479737i
$257$	−1.38542e7			−0.816175			−0.408088	−	0.912943i	$-0.633804\pi$
$257$	−1.38542e7			−0.816175			−0.408088	+	0.912943i	$0.633804\pi$
$258$		0			0
$259$			7808.97i			0.000449464i
$260$	−5.76929e6	+	4.48044e6i	−0.328248	+	0.254918i
$261$		0			0
$262$	−2.14579e6	+	735356.i	−0.119312	+	0.0408878i
$263$		−	7.65702e6i		−	0.420913i	−0.977603	−	0.210457i	$-0.932505\pi$
$263$		−	7.65702e6i		−	0.420913i	0.977603	−	0.210457i	$-0.0674950\pi$
$264$		0			0
$265$	76539.2			0.00411288
$266$	−8.95862e6	−	2.61415e7i	−0.475988	−	1.38894i
$267$		0			0
$268$	−1.27772e7	−	1.64528e7i	−0.663793	−	0.854742i
$269$	3.63062e7			1.86520			0.932598	−	0.360917i	$-0.117536\pi$
$269$	3.63062e7			1.86520			0.932598	+	0.360917i	$0.117536\pi$
$270$		0			0
$271$		−	144294.i		−	0.00725002i	−0.999993	−	0.00362501i	$-0.998846\pi$
$271$		−	144294.i		−	0.00725002i	0.999993	−	0.00362501i	$-0.00115388\pi$
$272$	8.33483e6	−	3.26177e7i	0.414181	−	1.62086i
$273$		0			0
$274$	−1.07684e7	−	3.14224e7i	−0.523478	−	1.52752i
$275$		−	623838.i		−	0.0299967i
$276$		0			0
$277$	4.74727e6			0.223360			0.111680	−	0.993744i	$-0.464377\pi$
$277$	4.74727e6			0.223360			0.111680	+	0.993744i	$0.464377\pi$
$278$	2.91436e7	−	9.98743e6i	1.35646	−	0.464857i
$279$		0			0
$280$	1.05318e7	−	1.60633e7i	0.479764	−	0.731746i
$281$	−4.52651e6			−0.204007			−0.102003	−	0.994784i	$-0.532525\pi$
$281$	−4.52651e6			−0.204007			−0.102003	+	0.994784i	$0.532525\pi$
$282$		0			0
$283$			1.07319e7i			0.473497i	0.971571	+	0.236749i	$0.0760818\pi$
$283$			1.07319e7i			0.473497i	−0.971571	+	0.236749i	$0.923918\pi$
$284$	1.19076e7	+	1.53330e7i	0.519841	+	0.669380i
$285$		0			0
$286$	−3.08459e6	+	1.05708e6i	−0.131856	+	0.0451867i
$287$		−	4.55424e7i		−	1.92651i
$288$		0			0
$289$	4.34173e7			1.79874
$290$	−1.82291e6	−	5.31930e6i	−0.0747431	−	0.218102i
$291$		0			0
$292$	1.25136e7	−	9.71804e6i	0.502612	−	0.390328i
$293$	−2.88844e7			−1.14831			−0.574157	−	0.818745i	$-0.694670\pi$
$293$	−2.88844e7			−1.14831			−0.574157	+	0.818745i	$0.694670\pi$
$294$		0			0
$295$			313153.i			0.0121981i
$296$	−4982.29	−	3266.60i	−0.000192112	−	0.000125957i
$297$		0			0
$298$	−8.57177e6	−	2.50126e7i	−0.323908	−	0.945171i
$299$			2.98734e7i			1.11756i
$300$		0			0
$301$	−7.04906e7			−2.58483
$302$	−2.24275e7	+	7.68587e6i	−0.814256	+	0.279044i
$303$		0			0
$304$	2.04263e7	+	5.21956e6i	0.727058	+	0.185786i
$305$	−7.41711e6			−0.261418
$306$		0			0
$307$		−	4.55936e7i		−	1.57575i	−0.615833	−	0.787877i	$-0.711180\pi$
$307$		−	4.55936e7i		−	1.57575i	0.615833	−	0.787877i	$-0.288820\pi$
$308$	6.77185e6	−	5.25902e6i	0.231769	−	0.179992i
$309$		0			0
$310$	−2.30241e7	+	7.89032e6i	−0.772855	+	0.264856i
$311$			2.33624e7i			0.776670i	0.921518	+	0.388335i	$0.126950\pi$
$311$			2.33624e7i			0.776670i	−0.921518	+	0.388335i	$0.873050\pi$
$312$		0			0
$313$	2.77900e7			0.906266			0.453133	−	0.891443i	$-0.350306\pi$
$313$	2.77900e7			0.906266			0.453133	+	0.891443i	$0.350306\pi$
$314$	−7807.23	−	22781.7i	−0.000252179	−	0.000735863i
$315$		0			0
$316$	1.53081e7	+	1.97116e7i	0.485131	+	0.624686i
$317$	−7.68469e6			−0.241239			−0.120620	−	0.992699i	$-0.538488\pi$
$317$	−7.68469e6			−0.241239			−0.120620	+	0.992699i	$0.538488\pi$
$318$		0			0
$319$		−	2.51000e6i		−	0.0773216i
$320$	5.84311e6	+	1.34390e7i	0.178318	+	0.410125i
$321$		0			0
$322$	−2.54660e7	−	7.43105e7i	−0.762770	−	2.22578i
$323$			4.23052e7i			1.25541i
$324$		0			0
$325$	6.38042e6			0.185866
$326$	7.82987e6	−	2.68328e6i	0.225996	−	0.0774484i
$327$		0			0
$328$	2.90570e7	+	1.90510e7i	0.823435	+	0.539880i
$329$	−6.01713e7			−1.68967
$330$		0			0
$331$		−	2.26621e7i		−	0.624907i	−0.949933	−	0.312453i	$-0.898849\pi$
$331$		−	2.26621e7i		−	0.624907i	0.949933	−	0.312453i	$-0.101151\pi$
$332$	−8.45421e6	−	1.08862e7i	−0.231025	−	0.297482i
$333$		0			0
$334$	4.49338e6	−	1.53987e6i	0.120596	−	0.0413280i
$335$			1.81956e7i			0.483984i
$336$		0			0
$337$	−5.15429e7			−1.34673			−0.673363	−	0.739312i	$-0.735151\pi$
$337$	−5.15429e7			−1.34673			−0.673363	+	0.739312i	$0.735151\pi$
$338$	1.70688e6	+	4.98073e6i	0.0442032	+	0.128986i
$339$		0			0
$340$	−2.32248e7	+	1.80364e7i	−0.590901	+	0.458895i
$341$	−1.08643e7			−0.273993
$342$		0			0
$343$			1.44338e8i			3.57684i
$344$	2.94872e7	−	4.49744e7i	0.724366	−	1.10482i
$345$		0			0
$346$	2.62784e6	+	7.66811e6i	0.0634411	+	0.185123i
$347$			2.69989e7i			0.646186i	0.946367	+	0.323093i	$0.104723\pi$
$347$			2.69989e7i			0.646186i	−0.946367	+	0.323093i	$0.895277\pi$
$348$		0			0
$349$	−3.98391e7			−0.937201			−0.468601	−	0.883410i	$-0.655242\pi$
$349$	−3.98391e7			−0.937201			−0.468601	+	0.883410i	$0.655242\pi$
$350$	−1.58714e7	+	5.43909e6i	−0.370178	+	0.126859i
$351$		0			0
$352$	522605.	+	6.52050e6i	0.0119825	+	0.149504i
$353$	3.70984e7			0.843395			0.421697	−	0.906737i	$-0.361434\pi$
$353$	3.70984e7			0.843395			0.421697	+	0.906737i	$0.361434\pi$
$354$		0			0
$355$		−	1.69572e7i		−	0.379026i
$356$	2.33531e6	−	1.81360e6i	0.0517601	−	0.0401969i
$357$		0			0
$358$	8.01114e7	−	2.74540e7i	1.74600	−	0.598352i
$359$			3.23502e7i			0.699186i	0.936902	+	0.349593i	$0.113680\pi$
$359$			3.23502e7i			0.699186i	−0.936902	+	0.349593i	$0.886320\pi$
$360$		0			0
$361$	2.05530e7			0.436870
$362$	6.35206e6	+	1.85355e7i	0.133903	+	0.390731i
$363$		0			0
$364$	5.37876e7	+	6.92604e7i	1.11527	+	1.43609i
$365$	−1.38391e7			−0.284596
$366$		0			0
$367$			5.83482e6i			0.118040i	0.998257	+	0.0590200i	$0.0187976\pi$
$367$			5.83482e6i			0.118040i	−0.998257	+	0.0590200i	$0.981202\pi$
$368$	5.80644e7	+	1.48373e7i	1.16511	+	0.297722i
$369$		0			0
$370$	1687.02	+	4922.77i	3.33054e−5	+	9.71861e-5i
$371$		−	918853.i		−	0.0179939i
$372$		0			0
$373$	−1.63274e7			−0.314623			−0.157311	−	0.987549i	$-0.550283\pi$
$373$	−1.63274e7			−0.314623			−0.157311	+	0.987549i	$0.550283\pi$
$374$	−1.24173e7	+	4.25538e6i	−0.237363	+	0.0813437i
$375$		0			0
$376$	2.51705e7	−	3.83906e7i	0.473509	−	0.722206i
$377$	2.56715e7			0.479100
$378$		0			0
$379$		−	6.49860e7i		−	1.19372i	−0.802346	−	0.596859i	$-0.796415\pi$
$379$		−	6.49860e7i		−	1.19372i	0.802346	−	0.596859i	$-0.203585\pi$
$380$	−1.12950e7	−	1.45442e7i	−0.205843	−	0.265056i
$381$		0			0
$382$	−4.10076e7	+	1.40532e7i	−0.735656	+	0.252107i
$383$			5.64474e7i			1.00473i	0.864657	+	0.502363i	$0.167536\pi$
$383$			5.64474e7i			1.00473i	−0.864657	+	0.502363i	$0.832464\pi$
$384$		0			0
$385$	−7.48917e6			−0.131236
$386$	−2.58597e7	−	7.54593e7i	−0.449637	−	1.31205i
$387$		0			0
$388$	−4.04492e7	+	3.14129e7i	−0.692492	+	0.537790i
$389$	8.66539e7			1.47211			0.736053	−	0.676924i	$-0.236687\pi$
$389$	8.66539e7			1.47211			0.736053	+	0.676924i	$0.236687\pi$
$390$		0			0
$391$			1.20258e8i			2.01179i
$392$	−1.42465e8	−	9.34064e7i	−2.36511	−	1.55067i
$393$		0			0
$394$	3.45989e7	+	1.00960e8i	0.565684	+	1.65068i
$395$		−	2.17996e7i		−	0.353719i
$396$		0			0
$397$	1.11044e8			1.77469			0.887346	−	0.461105i	$-0.152547\pi$
$397$	1.11044e8			1.77469			0.887346	+	0.461105i	$0.152547\pi$
$398$	−4.97968e7	+	1.70652e7i	−0.789863	+	0.270684i
$399$		0			0
$400$	3.16897e6	−	1.24015e7i	0.0495152	−	0.193774i
$401$	5.61325e7			0.870525			0.435262	−	0.900304i	$-0.356656\pi$
$401$	5.61325e7			0.870525			0.435262	+	0.900304i	$0.356656\pi$
$402$		0			0
$403$		−	1.11117e8i		−	1.69771i
$404$	4.29905e7	−	3.33865e7i	0.651971	−	0.506321i
$405$		0			0
$406$	−6.38582e7	+	2.18840e7i	−0.954198	+	0.327001i
$407$			2322.89i			3.44544e-5i
$408$		0			0
$409$	−5.17276e7			−0.756053			−0.378026	−	0.925795i	$-0.623397\pi$
$409$	−5.17276e7			−0.756053			−0.378026	+	0.925795i	$0.623397\pi$
$410$	−9.83881e6	−	2.87099e7i	−0.142755	−	0.416562i
$411$		0			0
$412$	2.32034e7	+	2.98782e7i	0.331788	+	0.427231i
$413$	3.75941e6			0.0533666
$414$		0			0
$415$			1.20393e7i			0.168445i
$416$	−6.66897e7	+	5.34505e6i	−0.926357	+	0.0742457i
$417$		0			0
$418$	−2.66486e6	−	7.77614e6i	−0.0364877	−	0.106472i
$419$		−	2.85658e7i		−	0.388333i	−0.980969	−	0.194167i	$-0.937800\pi$
$419$		−	2.85658e7i		−	0.388333i	0.980969	−	0.194167i	$-0.0622002\pi$
$420$		0			0
$421$	−1.03346e7			−0.138499			−0.0692496	−	0.997599i	$-0.522060\pi$
$421$	−1.03346e7			−0.138499			−0.0692496	+	0.997599i	$0.522060\pi$
$422$	6.58798e6	−	2.25769e6i	0.0876627	−	0.0300418i
$423$		0			0
$424$	586247.	+	384369.i	0.00769101	+	0.00504256i
$425$	2.56849e7			0.334589
$426$		0			0
$427$			8.90424e7i			1.14370i
$428$	4.01890e7	+	5.17499e7i	0.512597	+	0.660052i
$429$		0			0
$430$	−4.44372e7	+	1.52285e7i	−0.558909	+	0.191537i
$431$			3.74717e7i			0.468027i	0.972233	+	0.234014i	$0.0751860\pi$
$431$			3.74717e7i			0.468027i	−0.972233	+	0.234014i	$0.924814\pi$
$432$		0			0
$433$	−7.74967e7			−0.954595			−0.477298	−	0.878742i	$-0.658384\pi$
$433$	−7.74967e7			−0.954595			−0.477298	+	0.878742i	$0.658384\pi$
$434$	9.47233e7	+	2.76405e8i	1.15874	+	3.38124i
$435$		0			0
$436$	9.04167e7	−	7.02177e7i	1.09091	−	0.847202i
$437$	−7.53096e7			−0.902414
$438$		0			0
$439$			1.06961e8i			1.26425i	0.774868	+	0.632124i	$0.217817\pi$
$439$			1.06961e8i			1.26425i	−0.774868	+	0.632124i	$0.782183\pi$
$440$	3.13283e6	−	4.77824e6i	0.0367772	−	0.0560932i
$441$		0			0
$442$	−4.35227e7	−	1.27000e8i	−0.504022	−	1.47075i
$443$			6.93528e7i			0.797724i	0.917011	+	0.398862i	$0.130595\pi$
$443$			6.93528e7i			0.797724i	−0.917011	+	0.398862i	$0.869405\pi$
$444$		0			0
$445$	−2.58268e6			−0.0293083
$446$	3.90689e7	−	1.33888e7i	0.440379	−	0.150917i
$447$		0			0
$448$	1.61335e8	−	7.01466e7i	1.79430	−	0.780140i
$449$	1.10854e8			1.22465			0.612327	−	0.790605i	$-0.290234\pi$
$449$	1.10854e8			1.22465			0.612327	+	0.790605i	$0.290234\pi$
$450$		0			0
$451$		−	1.35472e7i		−	0.147680i
$452$	1.12632e8	−	8.74699e7i	1.21968	−	0.947204i
$453$		0			0
$454$	2.94344e7	−	1.00871e7i	0.314548	−	0.107795i
$455$		−	7.65969e7i		−	0.813162i
$456$		0			0
$457$	1.12207e8			1.17564			0.587818	−	0.808993i	$-0.299987\pi$
$457$	1.12207e8			1.17564			0.587818	+	0.808993i	$0.299987\pi$
$458$	−2.60992e7	−	7.61582e7i	−0.271664	−	0.792721i
$459$		0			0
$460$	−3.21075e7	−	4.13436e7i	−0.329863	−	0.424752i
$461$	−1.44607e8			−1.47600			−0.737998	−	0.674803i	$-0.764229\pi$
$461$	−1.44607e8			−1.47600			−0.737998	+	0.674803i	$0.764229\pi$
$462$		0			0
$463$		−	9.36261e7i		−	0.943309i	−0.881783	−	0.471655i	$-0.843657\pi$
$463$		−	9.36261e7i		−	0.943309i	0.881783	−	0.471655i	$-0.156343\pi$
$464$	1.27503e7	−	4.98972e7i	0.127634	−	0.499485i
$465$		0			0
$466$	1.56549e7	+	4.56813e7i	0.154701	+	0.451420i
$467$			5.11897e7i			0.502611i	0.967908	+	0.251305i	$0.0808598\pi$
$467$			5.11897e7i			0.502611i	−0.967908	+	0.251305i	$0.919140\pi$
$468$		0			0
$469$	2.18438e8			2.11743
$470$	−3.79319e7	+	1.29992e7i	−0.365352	+	0.125205i
$471$		0			0
$472$	−1.57261e6	+	2.39858e6i	−0.0149553	+	0.0228101i
$473$	−2.09684e7			−0.198144
$474$		0			0
$475$			1.60848e7i			0.150084i
$476$	2.16527e8	+	2.78814e8i	2.00766	+	2.58519i
$477$		0			0
$478$	1.02141e7	−	3.50036e6i	0.0935228	−	0.0320500i
$479$		−	1.88871e8i		−	1.71854i	−0.511525	−	0.859269i	$-0.670919\pi$
$479$		−	1.88871e8i		−	1.71854i	0.511525	−	0.859269i	$-0.329081\pi$
$480$		0			0
$481$	−23757.8			−0.000213487
$482$	−2.00806e7	−	5.85956e7i	−0.179323	−	0.523267i
$483$		0			0
$484$	−8.75334e7	+	6.79785e7i	−0.772036	+	0.599564i
$485$	4.47339e7			0.392113
$486$		0			0
$487$		−	1.41791e8i		−	1.22761i	−0.789456	−	0.613807i	$-0.789637\pi$
$487$		−	1.41791e8i		−	1.22761i	0.789456	−	0.613807i	$-0.210363\pi$
$488$	−5.68109e7	−	3.72477e7i	−0.488846	−	0.320509i
$489$		0			0
$490$	4.82393e7	+	1.40763e8i	0.410027	+	1.19647i
$491$		−	1.73081e7i		−	0.146219i	−0.997324	−	0.0731095i	$-0.976708\pi$
$491$		−	1.73081e7i		−	0.146219i	0.997324	−	0.0731095i	$-0.0232923\pi$
$492$		0			0
$493$	1.03343e8			0.862460
$494$	7.95319e7	−	2.72554e7i	0.659721	−	0.226085i
$495$		0			0
$496$	−2.15976e8	−	5.51886e7i	−1.76995	−	0.452277i
$497$	−2.03571e8			−1.65824
$498$		0			0
$499$		−	2.37084e8i		−	1.90810i	−0.299655	−	0.954048i	$-0.596872\pi$
$499$		−	2.37084e8i		−	1.90810i	0.299655	−	0.954048i	$-0.403128\pi$
$500$	−8.83026e6	+	6.85759e6i	−0.0706421	+	0.0548607i
$501$		0			0
$502$	1.24682e8	−	4.27282e7i	0.985580	−	0.337756i
$503$			2.25165e7i			0.176928i	0.996079	+	0.0884640i	$0.0281958\pi$
$503$			2.25165e7i			0.176928i	−0.996079	+	0.0884640i	$0.971804\pi$
$504$		0			0
$505$	−4.75444e7			−0.369169
$506$	−7.57522e6	−	2.21047e7i	−0.0584715	−	0.170621i
$507$		0			0
$508$	4.74342e7	+	6.10793e7i	0.361827	+	0.465911i
$509$	9.38014e7			0.711305			0.355653	−	0.934618i	$-0.384259\pi$
$509$	9.38014e7			0.711305			0.355653	+	0.934618i	$0.384259\pi$
$510$		0			0
$511$			1.66138e8i			1.24511i
$512$	−2.27338e7	+	1.32278e8i	−0.169380	+	0.985551i
$513$		0			0
$514$	3.59312e7	+	1.04848e8i	0.264595	+	0.772095i
$515$		−	3.30431e7i		−	0.241913i
$516$		0			0
$517$	−1.78988e7			−0.129525
$518$	59097.8	−	20252.7i	0.000425189	−	0.000145711i
$519$		0			0
$520$	4.88704e7	+	3.20416e7i	0.347565	+	0.227879i
$521$	−1.78407e8			−1.26153			−0.630765	−	0.775974i	$-0.717259\pi$
$521$	−1.78407e8			−1.26153			−0.630765	+	0.775974i	$0.717259\pi$
$522$		0			0
$523$			2.26348e8i			1.58224i	0.611662	+	0.791119i	$0.290501\pi$
$523$			2.26348e8i			1.58224i	−0.611662	+	0.791119i	$0.709499\pi$
$524$	1.11303e7	+	1.43320e7i	0.0773591	+	0.0996125i
$525$		0			0
$526$	−5.79478e7	+	1.98586e7i	−0.398180	+	0.136456i
$527$		−	4.47310e8i		−	3.05617i
$528$		0			0
$529$	−6.60414e7			−0.446118
$530$	−198505.	−	579244.i	−0.00133335	−	0.00389075i
$531$		0			0
$532$	−1.74603e8	+	1.35597e8i	−1.15962	+	0.900562i
$533$	1.38557e8			0.915053
$534$		0			0
$535$		−	5.72316e7i		−	0.373744i
$536$	−9.13757e7	+	1.39368e8i	−0.593384	+	0.905041i
$537$		0			0
$538$	−9.41608e7	−	2.74763e8i	−0.604677	−	1.76446i
$539$			6.64215e7i			0.424172i
$540$		0			0
$541$	5.52591e7			0.348990			0.174495	−	0.984658i	$-0.444171\pi$
$541$	5.52591e7			0.348990			0.174495	+	0.984658i	$0.444171\pi$
$542$	−1.09201e6	+	374228.i	−0.00685847	+	0.00235038i
$543$		0			0
$544$	−2.68465e8	+	2.15170e7i	−1.66760	+	0.133655i
$545$	−9.99943e7			−0.617712
$546$		0			0
$547$		−	5.20328e7i		−	0.317918i	−0.987285	−	0.158959i	$-0.949186\pi$
$547$		−	5.20328e7i		−	0.317918i	0.987285	−	0.158959i	$-0.0508137\pi$
$548$	−2.09875e8	+	1.62989e8i	−1.27532	+	0.990412i
$549$		0			0
$550$	−4.72116e6	+	1.61793e6i	−0.0283766	+	0.00972461i
$551$			6.47167e7i			0.386867i
$552$		0			0
$553$	−2.61705e8			−1.54752
$554$	−1.23121e7	−	3.59271e7i	−0.0724109	−	0.211297i
$555$		0			0
$556$	−1.51168e8	−	1.94654e8i	−0.879502	−	1.13250i
$557$	2.24751e8			1.30058			0.650289	−	0.759687i	$-0.274648\pi$
$557$	2.24751e8			1.30058			0.650289	+	0.759687i	$0.274648\pi$
$558$		0			0
$559$		−	2.14458e8i		−	1.22774i
$560$	−1.48880e8	−	3.80435e7i	−0.847760	−	0.216629i
$561$		0			0
$562$	1.17396e7	+	3.42563e7i	0.0661367	+	0.192989i
$563$		−	1.16024e8i		−	0.650165i	−0.945686	−	0.325083i	$-0.894608\pi$
$563$		−	1.16024e8i		−	0.650165i	0.945686	−	0.325083i	$-0.105392\pi$
$564$		0			0
$565$	−1.24563e8			−0.690625
$566$	8.12184e7	−	2.78334e7i	0.447925	−	0.153503i
$567$		0			0
$568$	8.51568e7	−	1.29883e8i	0.464702	−	0.708772i
$569$	−6.45365e7			−0.350323			−0.175161	−	0.984540i	$-0.556045\pi$
$569$	−6.45365e7			−0.350323			−0.175161	+	0.984540i	$0.556045\pi$
$570$		0			0
$571$		−	5.29903e7i		−	0.284635i	−0.989821	−	0.142317i	$-0.954545\pi$
$571$		−	5.29903e7i		−	0.284635i	0.989821	−	0.142317i	$-0.0454553\pi$
$572$	1.59999e7	+	2.06025e7i	0.0854926	+	0.110086i
$573$		0			0
$574$	−3.44662e8	+	1.18115e8i	−1.82246	+	0.624553i
$575$			4.57231e7i			0.240509i
$576$		0			0
$577$	−1.97923e8			−1.03031			−0.515155	−	0.857097i	$-0.672266\pi$
$577$	−1.97923e8			−1.03031			−0.515155	+	0.857097i	$0.672266\pi$
$578$	−1.12603e8	−	3.28579e8i	−0.583134	−	1.70160i
$579$		0			0
$580$	−3.55284e7	+	2.75913e7i	−0.182092	+	0.141413i
$581$	1.44532e8			0.736946
$582$		0			0
$583$		−	273326.i		−	0.00137935i
$584$	−1.06000e8	−	6.94980e7i	−0.532189	−	0.348926i
$585$		0			0
$586$	7.49122e7	+	2.18596e8i	0.372271	+	1.08630i
$587$			6.20004e7i			0.306535i	0.988185	+	0.153268i	$0.0489796\pi$
$587$			6.20004e7i			0.306535i	−0.988185	+	0.153268i	$0.951020\pi$
$588$		0			0
$589$	2.80121e8			1.37088
$590$	2.36993e6	−	812168.i	0.0115393	−	0.00395448i
$591$		0			0
$592$	−11799.8	+	46177.6i	−5.68735e−5	+	0.000222570i
$593$	3.48324e8			1.67039			0.835197	−	0.549950i	$-0.185353\pi$
$593$	3.48324e8			1.67039			0.835197	+	0.549950i	$0.185353\pi$
$594$		0			0
$595$		−	3.08348e8i		−	1.46383i
$596$	−1.67063e8	+	1.29741e8i	−0.789117	+	0.612829i
$597$		0			0
$598$	2.26080e8	−	7.74770e7i	1.05720	−	0.362301i
$599$		−	2.16010e8i		−	1.00506i	−0.864559	−	0.502531i	$-0.832402\pi$
$599$		−	2.16010e8i		−	1.00506i	0.864559	−	0.502531i	$-0.167598\pi$
$600$		0			0
$601$	2.07109e8			0.954058			0.477029	−	0.878888i	$-0.341714\pi$
$601$	2.07109e8			0.954058			0.477029	+	0.878888i	$0.341714\pi$
$602$	1.82818e8	+	5.33468e8i	0.837974	+	2.44523i
$603$		0			0
$604$	1.16332e8	+	1.49797e8i	0.527946	+	0.679817i
$605$	9.68055e7			0.437154
$606$		0			0
$607$		−	7.87805e7i		−	0.352251i	−0.984368	−	0.176126i	$-0.943644\pi$
$607$		−	7.87805e7i		−	0.352251i	0.984368	−	0.176126i	$-0.0563565\pi$
$608$	−1.34746e7	−	1.68122e8i	−0.0599524	−	0.748021i
$609$		0			0
$610$	1.92364e7	+	5.61322e7i	0.0847489	+	0.247299i
$611$		−	1.83063e8i		−	0.802560i
$612$		0			0
$613$	−2.49628e8			−1.08371			−0.541853	−	0.840473i	$-0.682277\pi$
$613$	−2.49628e8			−1.08371			−0.541853	+	0.840473i	$0.682277\pi$
$614$	−3.45049e8	+	1.18248e8i	−1.49065	+	0.510843i
$615$		0			0
$616$	−5.73628e7	−	3.76096e7i	−0.245408	−	0.160900i
$617$	−2.37350e8			−1.01049			−0.505247	−	0.862975i	$-0.668599\pi$
$617$	−2.37350e8			−1.01049			−0.505247	+	0.862975i	$0.668599\pi$
$618$		0			0
$619$			5.81494e7i			0.245173i	0.992458	+	0.122587i	$0.0391190\pi$
$619$			5.81494e7i			0.245173i	−0.992458	+	0.122587i	$0.960881\pi$
$620$	1.19427e8	+	1.53782e8i	0.501103	+	0.645252i
$621$		0			0
$622$	1.76805e8	−	6.05908e7i	0.734724	−	0.251788i
$623$			3.10051e7i			0.128224i
$624$		0			0
$625$	9.76562e6			0.0400000
$626$	−7.20738e7	−	2.10313e8i	−0.293802	−	0.857320i
$627$		0			0
$628$	−152162.	+	118169.i	−0.000614367	+	0.000477118i
$629$	−95639.0			−0.000384311
$630$		0			0
$631$		−	1.07588e8i		−	0.428227i	−0.976809	−	0.214114i	$-0.931314\pi$
$631$		−	1.07588e8i		−	0.428227i	0.976809	−	0.214114i	$-0.0686863\pi$
$632$	1.09475e8	−	1.66973e8i	0.433673	−	0.661447i
$633$		0			0
$634$	1.99304e7	+	5.81572e7i	0.0782073	+	0.228211i
$635$		−	6.75492e7i		−	0.263815i
$636$		0			0
$637$	−6.79338e8			−2.62826
$638$	−1.89955e7	+	6.50971e6i	−0.0731457	+	0.0250668i
$639$		0			0
$640$	8.65512e7	−	7.90745e7i	0.330167	−	0.301645i
$641$	−2.45332e8			−0.931492			−0.465746	−	0.884918i	$-0.654214\pi$
$641$	−2.45332e8			−0.931492			−0.465746	+	0.884918i	$0.654214\pi$
$642$		0			0
$643$			3.42151e8i			1.28702i	0.765439	+	0.643509i	$0.222522\pi$
$643$			3.42151e8i			1.28702i	−0.765439	+	0.643509i	$0.777478\pi$
$644$	−4.96331e8	+	3.85451e8i	−1.85829	+	1.44315i
$645$		0			0
$646$	3.20163e8	−	1.09719e8i	1.18761	−	0.406991i
$647$			2.08510e8i			0.769862i	0.922945	+	0.384931i	$0.125775\pi$
$647$			2.08510e8i			0.769862i	−0.922945	+	0.384931i	$0.874225\pi$
$648$		0			0
$649$	1.11829e6			0.00409091
$650$	−1.65477e7	−	4.82866e7i	−0.0602556	−	0.175827i
$651$		0			0
$652$	−4.06137e7	−	5.22968e7i	−0.146531	−	0.188683i
$653$	−4.76031e8			−1.70960			−0.854802	−	0.518954i	$-0.826322\pi$
$653$	−4.76031e8			−1.70960			−0.854802	+	0.518954i	$0.826322\pi$
$654$		0			0
$655$		−	1.58502e7i		−	0.0564040i
$656$	6.88173e7	−	2.69311e8i	0.243773	−	0.953987i
$657$		0			0
$658$	1.56055e8	+	4.55373e8i	0.547773	+	1.59842i
$659$		−	1.75876e8i		−	0.614540i	−0.951622	−	0.307270i	$-0.900584\pi$
$659$		−	1.75876e8i		−	0.614540i	0.951622	−	0.307270i	$-0.0994155\pi$
$660$		0			0
$661$	3.80396e8			1.31714			0.658570	−	0.752520i	$-0.271162\pi$
$661$	3.80396e8			1.31714			0.658570	+	0.752520i	$0.271162\pi$
$662$	−1.71505e8	+	5.87744e7i	−0.591157	+	0.202588i
$663$		0			0
$664$	−6.04598e7	+	9.22144e7i	−0.206520	+	0.314988i
$665$	1.93098e8			0.656617
$666$		0			0
$667$			1.83966e8i			0.619954i
$668$	−2.33073e7	−	3.00119e7i	−0.0781920	−	0.100685i
$669$		0			0
$670$	1.37703e8	−	4.71905e7i	0.457846	−	0.156903i
$671$			2.64869e7i			0.0876725i
$672$		0			0
$673$	−3.67932e8			−1.20704			−0.603521	−	0.797347i	$-0.706236\pi$
$673$	−3.67932e8			−1.20704			−0.603521	+	0.797347i	$0.706236\pi$
$674$	1.33677e8	+	3.90074e8i	0.436594	+	1.27399i
$675$		0			0
$676$	3.32670e7	−	2.58352e7i	0.107690	−	0.0836318i
$677$	−4.64821e7			−0.149803			−0.0749014	−	0.997191i	$-0.523864\pi$
$677$	−4.64821e7			−0.149803			−0.0749014	+	0.997191i	$0.523864\pi$
$678$		0			0
$679$		−	5.37030e8i		−	1.71549i
$680$	1.96732e8	+	1.28986e8i	0.625675	+	0.410219i
$681$		0			0
$682$	2.81768e7	+	8.22204e7i	0.0888255	+	0.259195i
$683$			6.18385e8i			1.94087i	0.241361	+	0.970435i	$0.422406\pi$
$683$			6.18385e8i			1.94087i	−0.241361	+	0.970435i	$0.577594\pi$
$684$		0			0
$685$	2.32106e8			0.722129
$686$	1.09234e9	−	3.74344e8i	3.38366	−	1.15957i
$687$		0			0
$688$	−4.16839e8	−	1.06515e8i	−1.27998	−	0.327075i
$689$	2.79549e6			0.00854673
$690$		0			0
$691$			5.57874e7i			0.169084i	0.996420	+	0.0845419i	$0.0269427\pi$
$691$			5.57874e7i			0.169084i	−0.996420	+	0.0845419i	$0.973057\pi$
$692$	5.12164e7	−	3.97747e7i	0.154558	−	0.120030i
$693$		0			0
$694$	2.04326e8	−	7.00221e7i	0.611287	−	0.209487i
$695$			2.15273e8i			0.641262i
$696$		0			0
$697$	5.57773e8			1.64725
$698$	1.03323e8	+	3.01500e8i	0.303831	+	0.886585i
$699$		0			0
$700$	8.23254e7	+	1.06007e8i	0.240016	+	0.309059i
$701$	5.45837e8			1.58456			0.792280	−	0.610158i	$-0.208894\pi$
$701$	5.45837e8			1.58456			0.792280	+	0.610158i	$0.208894\pi$
$702$		0			0
$703$		−	59892.4i		−	0.000172387i
$704$	4.79914e7	−	2.08661e7i	0.137545	−	0.0598029i
$705$		0			0
$706$	−9.62152e7	−	2.80758e8i	−0.273420	−	0.797845i
$707$			5.70770e8i			1.61511i
$708$		0			0
$709$	2.11110e8			0.592339			0.296170	−	0.955135i	$-0.404291\pi$
$709$	2.11110e8			0.592339			0.296170	+	0.955135i	$0.404291\pi$
$710$	−1.28331e8	+	4.39788e7i	−0.358556	+	0.122876i
$711$		0			0
$712$	−1.97819e7	−	1.29699e7i	−0.0548060	−	0.0359332i
$713$	7.96280e8			2.19684
$714$		0			0
$715$		−	2.27848e7i		−	0.0623343i
$716$	−4.15540e8	−	5.35076e8i	−1.13207	−	1.45773i
$717$		0			0
$718$	2.44824e8	−	8.39006e7i	0.661425	−	0.226669i
$719$		−	2.73670e8i		−	0.736276i	−0.929771	−	0.368138i	$-0.879995\pi$
$719$		−	2.73670e8i		−	0.736276i	0.929771	−	0.368138i	$-0.120005\pi$
$720$		0			0
$721$	−3.96683e8			−1.05837
$722$	−5.33044e7	−	1.55543e8i	−0.141629	−	0.413276i
$723$		0			0
$724$	1.23801e8	−	9.61440e7i	0.326219	−	0.253342i
$725$	3.92918e7			0.103107
$726$		0			0
$727$			6.77998e8i			1.76451i	0.470768	+	0.882257i	$0.343977\pi$
$727$			6.77998e8i			1.76451i	−0.470768	+	0.882257i	$0.656023\pi$
$728$	3.84659e8	−	5.86689e8i	0.996969	−	1.52060i
$729$		0			0
$730$	3.58919e7	+	1.04733e8i	0.0922630	+	0.269226i
$731$		−	8.63321e8i		−	2.21014i
$732$		0			0
$733$	4.75863e8			1.20829			0.604143	−	0.796876i	$-0.293516\pi$
$733$	4.75863e8			1.20829			0.604143	+	0.796876i	$0.293516\pi$
$734$	4.41575e7	−	1.51327e7i	0.111665	−	0.0382673i
$735$		0			0
$736$	−3.83034e7	−	4.77909e8i	−0.0960737	−	1.19870i
$737$	6.49774e7			0.162315
$738$		0			0
$739$		−	4.04862e8i		−	1.00317i	−0.865109	−	0.501584i	$-0.832751\pi$
$739$		−	4.04862e8i		−	1.00317i	0.865109	−	0.501584i	$-0.167249\pi$
$740$	32879.9	−	25534.5i	8.11400e−5	−	6.30134e-5i
$741$		0			0
$742$	−6.95382e6	+	2.38306e6i	−0.0170221	+	0.00583342i
$743$		−	3.57127e8i		−	0.870676i	−0.900267	−	0.435338i	$-0.856629\pi$
$743$		−	3.57127e8i		−	0.870676i	0.900267	−	0.435338i	$-0.143371\pi$
$744$		0			0
$745$	1.84759e8			0.446825
$746$	4.23453e7	+	1.23565e8i	0.101997	+	0.297631i
$747$		0			0
$748$	6.44089e7	+	8.29370e7i	0.153901	+	0.198173i
$749$	−6.87066e8			−1.63513
$750$		0			0
$751$			1.02196e8i			0.241275i	0.992697	+	0.120637i	$0.0384938\pi$
$751$			1.02196e8i			0.241275i	−0.992697	+	0.120637i	$0.961506\pi$
$752$	−3.55817e8	−	9.09224e7i	−0.836708	−	0.213805i
$753$		0			0
$754$	−6.65793e7	−	1.94280e8i	−0.155319	−	0.453225i
$755$		−	1.65664e8i		−	0.384936i
$756$		0			0
$757$	4.38046e8			1.00979			0.504896	−	0.863180i	$-0.331531\pi$
$757$	4.38046e8			1.00979			0.504896	+	0.863180i	$0.331531\pi$
$758$	−4.91810e8	+	1.68542e8i	−1.12925	+	0.386991i
$759$		0			0
$760$	−8.07755e7	+	1.23200e8i	−0.184009	+	0.280654i
$761$	−1.40458e8			−0.318708			−0.159354	−	0.987222i	$-0.550941\pi$
$761$	−1.40458e8			−0.318708			−0.159354	+	0.987222i	$0.550941\pi$
$762$		0			0
$763$			1.20043e9i			2.70249i
$764$	2.12708e8	+	2.73896e8i	0.476983	+	0.614194i
$765$		0			0
$766$	4.27191e8	−	1.46397e8i	0.950464	−	0.325722i
$767$			1.14375e7i			0.0253481i
$768$		0			0
$769$	2.32792e7			0.0511905			0.0255952	−	0.999672i	$-0.491852\pi$
$769$	2.32792e7			0.0511905			0.0255952	+	0.999672i	$0.491852\pi$
$770$	1.94233e7	+	5.66776e7i	0.0425452	+	0.124148i
$771$		0			0
$772$	−5.04004e8	+	3.91410e8i	−1.09542	+	0.850706i
$773$	−1.98042e8			−0.428763			−0.214382	−	0.976750i	$-0.568774\pi$
$773$	−1.98042e8			−0.428763			−0.214382	+	0.976750i	$0.568774\pi$
$774$		0			0
$775$		−	1.70071e8i		−	0.365364i
$776$	3.42636e8	+	2.24647e8i	0.733243	+	0.480746i
$777$		0			0
$778$	−2.24738e8	−	6.55791e8i	−0.477241	−	1.39260i
$779$			3.49296e8i			0.738893i
$780$		0			0
$781$	−6.05551e7			−0.127115
$782$	9.10104e8	−	3.11891e8i	1.90314	−	0.652202i
$783$		0			0
$784$	−3.37408e8	+	1.32042e9i	−0.700176	+	2.74008i
$785$	168280.			0.000347876
$786$		0			0
$787$			8.67740e8i			1.78019i	0.455778	+	0.890093i	$0.349361\pi$
$787$			8.67740e8i			1.78019i	−0.455778	+	0.890093i	$0.650639\pi$
$788$	6.74330e8	−	5.23685e8i	1.37814	−	1.07027i
$789$		0			0
$790$	−1.64978e8	+	5.65377e7i	−0.334615	+	0.114672i
$791$			1.49537e9i			3.02148i
$792$		0			0
$793$	−2.70900e8			−0.543237
$794$	−2.87994e8	−	8.40372e8i	−0.575336	−	1.67884i
$795$		0			0
$796$	2.58297e8	+	3.32600e8i	0.512130	+	0.659451i
$797$	9.81006e8			1.93775			0.968873	−	0.247558i	$-0.0796282\pi$
$797$	9.81006e8			1.93775			0.968873	+	0.247558i	$0.0796282\pi$
$798$		0			0
$799$		−	7.36938e8i		−	1.44474i
$800$	−1.02073e8	+	8.18093e6i	−0.199361	+	0.0159784i
$801$		0			0
$802$	−1.45580e8	−	4.24807e8i	−0.282215	−	0.823509i
$803$			4.94201e7i			0.0954459i
$804$		0			0
$805$	5.48906e8			1.05223
$806$	−8.40925e8	+	2.88183e8i	−1.60602	+	0.550381i
$807$		0			0
$808$	−3.64163e8	−	2.38761e8i	−0.690338	−	0.452616i
$809$	−1.28177e8			−0.242084			−0.121042	−	0.992647i	$-0.538624\pi$
$809$	−1.28177e8			−0.242084			−0.121042	+	0.992647i	$0.538624\pi$
$810$		0			0
$811$			7.64793e8i			1.43378i	0.697189	+	0.716888i	$0.254434\pi$
$811$			7.64793e8i			1.43378i	−0.697189	+	0.716888i	$0.745566\pi$
$812$	3.31234e8	+	4.26518e8i	0.618681	+	0.796653i
$813$		0			0
$814$	17579.5	−	6024.44i	3.25936e−5	−	1.11698e-5i
$815$			5.78365e7i			0.106839i
$816$		0			0
$817$	5.40641e8			0.991386
$818$	1.34156e8	+	3.91471e8i	0.245104	+	0.715220i
$819$		0			0
$820$	−1.91758e8	+	1.48919e8i	−0.347785	+	0.270090i
$821$	−5.85652e8			−1.05830			−0.529152	−	0.848527i	$-0.677490\pi$
$821$	−5.85652e8			−1.05830			−0.529152	+	0.848527i	$0.677490\pi$
$822$		0			0
$823$			2.85566e8i			0.512280i	0.966640	+	0.256140i	$0.0824508\pi$
$823$			2.85566e8i			0.512280i	−0.966640	+	0.256140i	$0.917549\pi$
$824$	1.65938e8	−	2.53092e8i	0.296595	−	0.452372i
$825$		0			0
$826$	−9.75008e6	−	2.84510e7i	−0.0173009	−	0.0504844i
$827$		−	8.74738e7i		−	0.154654i	−0.997006	−	0.0773271i	$-0.975361\pi$
$827$		−	8.74738e7i		−	0.154654i	0.997006	−	0.0773271i	$-0.0246386\pi$
$828$		0			0
$829$	−6.72359e8			−1.18015			−0.590076	−	0.807348i	$-0.700902\pi$
$829$	−6.72359e8			−1.18015			−0.590076	+	0.807348i	$0.700902\pi$
$830$	9.11128e7	−	3.12242e7i	0.159348	−	0.0546080i
$831$		0			0
$832$	2.13412e8	+	4.90841e8i	0.370551	+	0.852257i
$833$	−2.73474e9			−4.73130
$834$		0			0
$835$			3.31910e7i			0.0570113i
$836$	−5.19380e7	+	4.03351e7i	−0.0888927	+	0.0690341i
$837$		0			0
$838$	−2.16184e8	+	7.40859e7i	−0.367360	+	0.125893i
$839$			1.71003e8i			0.289547i	0.989465	+	0.144773i	$0.0462453\pi$
$839$			1.71003e8i			0.289547i	−0.989465	+	0.144773i	$0.953755\pi$
$840$		0			0
$841$	−4.36734e8			−0.734224
$842$	2.68029e7	+	7.82116e7i	0.0449000	+	0.131019i
$843$		0			0
$844$	−3.41720e7	−	4.40021e7i	−0.0568386	−	0.0731890i
$845$	−3.67909e7			−0.0609775
$846$		0			0
$847$		−	1.16215e9i		−	1.91255i
$848$	1.38844e6	−	5.43355e6i	0.00227688	−	0.00891037i
$849$		0			0
$850$	−6.66142e7	−	1.94382e8i	−0.108470	−	0.316519i
$851$		−	170252.i		−	0.000276251i
$852$		0			0
$853$	−4.85282e8			−0.781892			−0.390946	−	0.920414i	$-0.627852\pi$
$853$	−4.85282e8			−0.781892			−0.390946	+	0.920414i	$0.627852\pi$
$854$	6.73867e8	−	2.30933e8i	1.08193	−	0.370776i
$855$		0			0
$856$	2.87409e8	−	4.38362e8i	0.458226	−	0.698894i
$857$	3.49086e8			0.554612			0.277306	−	0.960782i	$-0.410558\pi$
$857$	3.49086e8			0.554612			0.277306	+	0.960782i	$0.410558\pi$
$858$		0			0
$859$		−	7.34854e8i		−	1.15937i	−0.814841	−	0.579684i	$-0.803176\pi$
$859$		−	7.34854e8i		−	1.15937i	0.814841	−	0.579684i	$-0.196824\pi$
$860$	2.30497e8	+	2.96802e8i	0.362385	+	0.466629i
$861$		0			0
$862$	2.83583e8	−	9.71833e7i	0.442750	−	0.151729i
$863$			8.76714e8i			1.36403i	0.731336	+	0.682017i	$0.238897\pi$
$863$			8.76714e8i			1.36403i	−0.731336	+	0.682017i	$0.761103\pi$
$864$		0			0
$865$	−5.66416e7			−0.0875160
$866$	2.00989e8	+	5.86490e8i	0.309470	+	0.903040i
$867$		0			0
$868$	1.84615e9	−	1.43372e9i	2.82298	−	2.19233i
$869$	−7.78477e7			−0.118628
$870$		0			0
$871$			6.64569e8i			1.00574i
$872$	−7.65900e8	−	5.02158e8i	−1.15511	−	0.757339i
$873$		0			0
$874$	1.95317e8	+	5.69938e8i	0.292553	+	0.853677i
$875$		−	1.17236e8i		−	0.175000i
$876$		0			0
$877$	4.38615e8			0.650256			0.325128	−	0.945670i	$-0.394593\pi$
$877$	4.38615e8			0.650256			0.325128	+	0.945670i	$0.394593\pi$
$878$	8.09474e8	−	2.77405e8i	1.19597	−	0.409856i
$879$		0			0
$880$	−4.42865e7	−	1.13166e7i	−0.0649865	−	0.0166061i
$881$	9.05059e7			0.132358			0.0661788	−	0.997808i	$-0.478919\pi$
$881$	9.05059e7			0.132358			0.0661788	+	0.997808i	$0.478919\pi$
$882$		0			0
$883$		−	8.35267e8i		−	1.21323i	−0.794995	−	0.606615i	$-0.792527\pi$
$883$		−	8.35267e8i		−	1.21323i	0.794995	−	0.606615i	$-0.207473\pi$
$884$	−8.48254e8	+	6.58754e8i	−1.22792	+	0.953601i
$885$		0			0
$886$	5.24858e8	−	1.79868e8i	0.754641	−	0.258614i
$887$			9.00078e8i			1.28976i	0.764283	+	0.644881i	$0.223093\pi$
$887$			9.00078e8i			1.28976i	−0.764283	+	0.644881i	$0.776907\pi$
$888$		0			0
$889$	−8.10928e8			−1.15419
$890$	6.69823e6	+	1.95456e7i	0.00950145	+	0.0277255i
$891$		0			0
$892$	−2.02652e8	−	2.60947e8i	−0.285532	−	0.367669i
$893$	4.61495e8			0.648057
$894$		0			0
$895$			5.91755e8i			0.825416i
$896$	−9.49290e8	−	1.03905e9i	−1.31970	−	1.44448i
$897$		0			0
$898$	−2.87502e8	−	8.38938e8i	−0.397020	−	1.15851i
$899$		−	6.84278e8i		−	0.941788i
$900$		0			0
$901$	1.12535e7			0.0153855
$902$	−1.02525e8	+	3.51349e7i	−0.139704	+	0.0478762i
$903$		0			0
$904$	−9.54079e8	−	6.25536e8i	−1.29145	−	0.846733i
$905$	−1.36915e8			−0.184716
$906$		0			0
$907$			5.63841e8i			0.755675i	0.925872	+	0.377838i	$0.123332\pi$
$907$			5.63841e8i			0.755675i	−0.925872	+	0.377838i	$0.876668\pi$
$908$	−1.52677e8	−	1.96597e8i	−0.203947	−	0.262614i
$909$		0			0
$910$	−5.79681e8	+	1.98655e8i	−0.769245	+	0.263618i
$911$			1.25733e9i			1.66301i	0.555517	+	0.831505i	$0.312520\pi$
$911$			1.25733e9i			1.66301i	−0.555517	+	0.831505i	$0.687480\pi$
$912$		0			0
$913$	4.29931e7			0.0564919
$914$	−2.91012e8	−	8.49178e8i	−0.381129	−	1.11214i
$915$		0			0
$916$	−5.08672e8	+	3.95035e8i	−0.661837	+	0.513983i
$917$	−1.90281e8			−0.246768
$918$		0			0
$919$			6.09120e8i			0.784796i	0.919796	+	0.392398i	$0.128354\pi$
$919$			6.09120e8i			0.784796i	−0.919796	+	0.392398i	$0.871646\pi$
$920$	−2.29615e8	+	3.50213e8i	−0.294874	+	0.449748i
$921$		0			0
$922$	3.75039e8	+	1.09437e9i	0.478502	+	1.39628i
$923$		−	6.19339e8i		−	0.787632i
$924$		0			0
$925$	−36362.8			−4.59443e−5
$926$	−7.08557e8	+	2.42821e8i	−0.892363	+	0.305811i
$927$		0			0
$928$	−4.10687e8	+	3.29158e7i	−0.513886	+	0.0411870i
$929$	−1.98668e8			−0.247788			−0.123894	−	0.992295i	$-0.539538\pi$
$929$	−1.98668e8			−0.247788			−0.123894	+	0.992295i	$0.539538\pi$
$930$		0			0
$931$		−	1.71259e9i		−	2.12228i
$932$	3.05112e8	−	2.36951e8i	0.376888	−	0.292691i
$933$		0			0
$934$	3.87400e8	−	1.32761e8i	0.475466	−	0.162941i
$935$		−	9.17223e7i		−	0.112212i
$936$		0			0
$937$	−1.36957e9			−1.66481			−0.832404	−	0.554169i	$-0.813036\pi$
$937$	−1.36957e9			−1.66481			−0.832404	+	0.554169i	$0.813036\pi$
$938$	−5.66522e8	−	1.65312e9i	−0.686449	−	2.00307i
$939$		0			0
$940$	1.96754e8	+	2.53353e8i	0.236886	+	0.305030i
$941$	1.54960e9			1.85974			0.929869	−	0.367890i	$-0.119920\pi$
$941$	1.54960e9			1.85974			0.929869	+	0.367890i	$0.119920\pi$
$942$		0			0
$943$			9.92920e8i			1.18408i
$944$	2.22309e7	+	5.68068e6i	0.0264266	+	0.00675281i
$945$		0			0
$946$	5.43819e7	+	1.58688e8i	0.0642363	+	0.187443i
$947$			1.24286e9i			1.46343i	0.681613	+	0.731713i	$0.261279\pi$
$947$			1.24286e9i			1.46343i	−0.681613	+	0.731713i	$0.738721\pi$
$948$		0			0
$949$	−5.05454e8			−0.591402
$950$	1.21729e8	−	4.17161e7i	0.141978	−	0.0486556i
$951$		0			0
$952$	1.54848e9	−	2.36177e9i	1.79471	−	2.73733i
$953$	−1.19499e8			−0.138066			−0.0690331	−	0.997614i	$-0.521991\pi$
$953$	−1.19499e8			−0.138066			−0.0690331	+	0.997614i	$0.521991\pi$
$954$		0			0
$955$		−	3.02909e8i		−	0.347778i
$956$	−5.29810e7	−	6.82216e7i	−0.0606382	−	0.0780815i
$957$		0			0
$958$	−1.42936e9	+	4.89840e8i	−1.62572	+	0.557131i
$959$		−	2.78643e9i		−	3.15931i
$960$		0			0
$961$	−2.07434e9			−2.33727
$962$	61616.1	+	179797.i	6.92101e−5	+	0.000201957i
$963$		0			0
$964$	−3.91368e8	+	3.03937e8i	−0.436872	+	0.339276i
$965$	5.57391e8			0.620266
$966$		0			0
$967$		−	5.80070e8i		−	0.641506i	−0.947163	−	0.320753i	$-0.896064\pi$
$967$		−	5.80070e8i		−	0.641506i	0.947163	−	0.320753i	$-0.103936\pi$
$968$	7.41476e8	+	4.86144e8i	0.817468	+	0.535968i
$969$		0			0
$970$	−1.16018e8	−	3.38543e8i	−0.127119	−	0.370936i
$971$		−	1.33064e9i		−	1.45346i	−0.686925	−	0.726729i	$-0.741040\pi$
$971$		−	1.33064e9i		−	1.45346i	0.686925	−	0.726729i	$-0.258960\pi$
$972$		0			0
$973$	2.58436e9			2.80552
$974$	−1.07306e9	+	3.67737e8i	−1.16131	+	0.397979i
$975$		0			0
$976$	−1.34548e8	+	5.26544e8i	−0.144720	+	0.566350i
$977$	1.81751e9			1.94891			0.974456	−	0.224577i	$-0.0721001\pi$
$977$	1.81751e9			1.94891			0.974456	+	0.224577i	$0.0721001\pi$
$978$		0			0
$979$			9.22291e6i			0.00982923i
$980$	9.40179e8	−	7.30144e8i	0.998924	−	0.775765i
$981$		0			0
$982$	−1.30986e8	+	4.48887e7i	−0.138322	+	0.0474027i
$983$			9.05360e8i			0.953149i	0.879134	+	0.476575i	$0.158122\pi$
$983$			9.05360e8i			0.953149i	−0.879134	+	0.476575i	$0.841878\pi$
$984$		0			0
$985$	−7.45760e8			−0.780351
$986$	−2.68021e8	−	7.82091e8i	−0.279600	−	0.815881i
$987$		0			0
$988$	−4.12534e8	−	5.31205e8i	−0.427749	−	0.550797i
$989$	1.53684e9			1.58869
$990$		0			0
$991$			1.75428e6i			0.00180251i	1.00000		0.000901257i	$0.000286879\pi$
$991$			1.75428e6i			0.00180251i	−1.00000		0.000901257i	$0.999713\pi$
$992$	1.42473e8	+	1.77763e9i	0.145948	+	1.82098i
$993$		0			0
$994$	5.27965e8	+	1.54062e9i	0.537584	+	1.56868i
$995$		−	3.67831e8i		−	0.373404i
$996$		0			0
$997$	2.07639e8			0.209519			0.104759	−	0.994498i	$-0.466593\pi$
$997$	2.07639e8			0.209519			0.104759	+	0.994498i	$0.466593\pi$
$998$	−1.79423e9	+	6.14880e8i	−1.80504	+	0.618584i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.7.c.b.91.11		24
3.2	odd	2		60.7.c.a.31.14	yes	24
4.3	odd	2	inner	180.7.c.b.91.12		24
12.11	even	2		60.7.c.a.31.13	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.13	✓	24	12.11	even	2
60.7.c.a.31.14	yes	24	3.2	odd	2
180.7.c.b.91.11		24	1.1	even	1	trivial
180.7.c.b.91.12		24	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.59351 - 7.56794i) q^{2} +(-50.5474 + 39.2551i) q^{4} +55.9017 q^{5} -671.100i q^{7} +(428.176 + 280.731i) q^{8} +O(q^{10})\)	\(q+(-2.59351 - 7.56794i) q^{2} +(-50.5474 + 39.2551i) q^{4} +55.9017 q^{5} -671.100i q^{7} +(428.176 + 280.731i) q^{8} +(-144.982 - 423.061i) q^{10} -199.628i q^{11} +2041.73 q^{13} +(-5078.84 + 1740.51i) q^{14} +(1014.07 - 3968.49i) q^{16} +8219.18 q^{17} +5147.13i q^{19} +(-2825.68 + 2194.43i) q^{20} +(-1510.77 + 517.738i) q^{22} +14631.4i q^{23} +3125.00 q^{25} +(-5295.27 - 15451.7i) q^{26} +(26344.1 + 33922.3i) q^{28} +12573.4 q^{29} -54422.8i q^{31} +(-32663.3 + 2617.90i) q^{32} +(-21316.6 - 62202.2i) q^{34} -37515.6i q^{35} -11.6361 q^{37} +(38953.1 - 13349.2i) q^{38} +(23935.7 + 15693.3i) q^{40} +67862.4 q^{41} -105037. i q^{43} +(7836.42 + 10090.7i) q^{44} +(110729. - 37946.7i) q^{46} -89660.8i q^{47} -332726. q^{49} +(-8104.73 - 23649.8i) q^{50} +(-103204. + 80148.5i) q^{52} +1369.17 q^{53} -11159.5i q^{55} +(188398. - 287349. i) q^{56} +(-32609.2 - 95154.5i) q^{58} +5601.86i q^{59} -132681. q^{61} +(-411868. + 141146. i) q^{62} +(104525. + 240404. i) q^{64} +114136. q^{65} +325492. i q^{67} +(-415458. + 322645. i) q^{68} +(-283916. + 97297.4i) q^{70} -303340. i q^{71} -247561. q^{73} +(30.1783 + 88.0611i) q^{74} +(-202051. - 260174. i) q^{76} -133970. q^{77} -389964. i q^{79} +(56688.3 - 221845. i) q^{80} +(-176002. - 513578. i) q^{82} +215366. i q^{83} +459466. q^{85} +(-794916. + 272416. i) q^{86} +(56041.7 - 85475.8i) q^{88} -46200.5 q^{89} -1.37021e6i q^{91} +(-574357. - 739578. i) q^{92} +(-678547. + 232537. i) q^{94} +287733. i q^{95} +800223. q^{97} +(862931. + 2.51805e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8}+O(q^{10}) \) 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8	\( 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8} - 750 q^{10} + 5040 q^{13} + 2596 q^{14} + 4194 q^{16} - 7000 q^{20} + 45780 q^{22} + 75000 q^{25} - 75852 q^{26} + 54300 q^{28} - 132800 q^{29} + 10700 q^{32} - 173484 q^{34} - 69840 q^{37} - 215800 q^{38} - 14250 q^{40} + 70448 q^{41} + 395668 q^{44} - 158760 q^{46} - 642984 q^{49} - 62500 q^{50} - 210240 q^{52} + 644320 q^{53} + 917708 q^{56} - 1345020 q^{58} - 222864 q^{61} - 1948520 q^{62} + 935922 q^{64} - 266000 q^{65} - 572680 q^{68} + 220500 q^{70} + 771120 q^{73} + 589164 q^{74} - 191544 q^{76} - 1383840 q^{77} + 946000 q^{80} + 2672520 q^{82} - 372000 q^{85} - 1781528 q^{86} + 956940 q^{88} + 1566224 q^{89} + 3040560 q^{92} - 3788352 q^{94} - 1666800 q^{97} + 2709660 q^{98}+O(q^{100}) \) 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8 - 750 * q^10 + 5040 * q^13 + 2596 * q^14 + 4194 * q^16 - 7000 * q^20 + 45780 * q^22 + 75000 * q^25 - 75852 * q^26 + 54300 * q^28 - 132800 * q^29 + 10700 * q^32 - 173484 * q^34 - 69840 * q^37 - 215800 * q^38 - 14250 * q^40 + 70448 * q^41 + 395668 * q^44 - 158760 * q^46 - 642984 * q^49 - 62500 * q^50 - 210240 * q^52 + 644320 * q^53 + 917708 * q^56 - 1345020 * q^58 - 222864 * q^61 - 1948520 * q^62 + 935922 * q^64 - 266000 * q^65 - 572680 * q^68 + 220500 * q^70 + 771120 * q^73 + 589164 * q^74 - 191544 * q^76 - 1383840 * q^77 + 946000 * q^80 + 2672520 * q^82 - 372000 * q^85 - 1781528 * q^86 + 956940 * q^88 + 1566224 * q^89 + 3040560 * q^92 - 3788352 * q^94 - 1666800 * q^97 + 2709660 * q^98

Introduction

L-functions

Modular forms

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Database

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