LMFDB - Embedded newform 570.8.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,8,Mod(1,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	570.a (trivial)

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:	yes
Analytic conductor:	$178.059464526$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4122x^{2} - 49773x + 620550 $ x^4 - 2x^3 - 4122x^2 - 49773*x + 620550
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$69.6283$ of defining polynomial
Character	$\chi$	$=$	570.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} -216.000 q^{6} +366.713 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} -216.000 q^{6} +366.713 q^{7} +512.000 q^{8} +729.000 q^{9} +1000.00 q^{10} +245.228 q^{11} -1728.00 q^{12} -5603.82 q^{13} +2933.70 q^{14} -3375.00 q^{15} +4096.00 q^{16} +11610.8 q^{17} +5832.00 q^{18} +6859.00 q^{19} +8000.00 q^{20} -9901.24 q^{21} +1961.83 q^{22} -93785.8 q^{23} -13824.0 q^{24} +15625.0 q^{25} -44830.6 q^{26} -19683.0 q^{27} +23469.6 q^{28} -139019. q^{29} -27000.0 q^{30} -35437.3 q^{31} +32768.0 q^{32} -6621.17 q^{33} +92886.5 q^{34} +45839.1 q^{35} +46656.0 q^{36} -2194.07 q^{37} +54872.0 q^{38} +151303. q^{39} +64000.0 q^{40} -94052.2 q^{41} -79210.0 q^{42} +558954. q^{43} +15694.6 q^{44} +91125.0 q^{45} -750286. q^{46} -400292. q^{47} -110592. q^{48} -689065. q^{49} +125000. q^{50} -313492. q^{51} -358645. q^{52} +376602. q^{53} -157464. q^{54} +30653.6 q^{55} +187757. q^{56} -185193. q^{57} -1.11215e6 q^{58} -2.19517e6 q^{59} -216000. q^{60} +1.41806e6 q^{61} -283498. q^{62} +267334. q^{63} +262144. q^{64} -700478. q^{65} -52969.3 q^{66} -2.08078e6 q^{67} +743092. q^{68} +2.53222e6 q^{69} +366713. q^{70} +5.55873e6 q^{71} +373248. q^{72} -3.62494e6 q^{73} -17552.5 q^{74} -421875. q^{75} +438976. q^{76} +89928.4 q^{77} +1.21043e6 q^{78} -2.45264e6 q^{79} +512000. q^{80} +531441. q^{81} -752418. q^{82} +1.88156e6 q^{83} -633680. q^{84} +1.45135e6 q^{85} +4.47163e6 q^{86} +3.75351e6 q^{87} +125557. q^{88} +1.28712e6 q^{89} +729000. q^{90} -2.05499e6 q^{91} -6.00229e6 q^{92} +956807. q^{93} -3.20233e6 q^{94} +857375. q^{95} -884736. q^{96} +1.52941e6 q^{97} -5.51252e6 q^{98} +178772. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} - 108 q^{3} + 256 q^{4} + 500 q^{5} - 864 q^{6} - 1496 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) $ 4 * q + 32 * q^2 - 108 * q^3 + 256 * q^4 + 500 * q^5 - 864 * q^6 - 1496 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} - 108 q^{3} + 256 q^{4} + 500 q^{5} - 864 q^{6} - 1496 q^{7} + 2048 q^{8} + 2916 q^{9} + 4000 q^{10} - 2912 q^{11} - 6912 q^{12} - 3696 q^{13} - 11968 q^{14} - 13500 q^{15} + 16384 q^{16} + 16 q^{17} + 23328 q^{18} + 27436 q^{19} + 32000 q^{20} + 40392 q^{21} - 23296 q^{22} - 73016 q^{23} - 55296 q^{24} + 62500 q^{25} - 29568 q^{26} - 78732 q^{27} - 95744 q^{28} - 137784 q^{29} - 108000 q^{30} + 198072 q^{31} + 131072 q^{32} + 78624 q^{33} + 128 q^{34} - 187000 q^{35} + 186624 q^{36} + 207256 q^{37} + 219488 q^{38} + 99792 q^{39} + 256000 q^{40} - 504056 q^{41} + 323136 q^{42} - 250368 q^{43} - 186368 q^{44} + 364500 q^{45} - 584128 q^{46} - 1000376 q^{47} - 442368 q^{48} - 940908 q^{49} + 500000 q^{50} - 432 q^{51} - 236544 q^{52} - 2178688 q^{53} - 629856 q^{54} - 364000 q^{55} - 765952 q^{56} - 740772 q^{57} - 1102272 q^{58} + 327976 q^{59} - 864000 q^{60} + 572936 q^{61} + 1584576 q^{62} - 1090584 q^{63} + 1048576 q^{64} - 462000 q^{65} + 628992 q^{66} + 2017152 q^{67} + 1024 q^{68} + 1971432 q^{69} - 1496000 q^{70} + 2828960 q^{71} + 1492992 q^{72} - 132392 q^{73} + 1658048 q^{74} - 1687500 q^{75} + 1755904 q^{76} - 2304704 q^{77} + 798336 q^{78} + 3418408 q^{79} + 2048000 q^{80} + 2125764 q^{81} - 4032448 q^{82} - 3201760 q^{83} + 2585088 q^{84} + 2000 q^{85} - 2002944 q^{86} + 3720168 q^{87} - 1490944 q^{88} - 1389392 q^{89} + 2916000 q^{90} - 7865280 q^{91} - 4673024 q^{92} - 5347944 q^{93} - 8003008 q^{94} + 3429500 q^{95} - 3538944 q^{96} - 21061144 q^{97} - 7527264 q^{98} - 2122848 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 - 108 * q^3 + 256 * q^4 + 500 * q^5 - 864 * q^6 - 1496 * q^7 + 2048 * q^8 + 2916 * q^9 + 4000 * q^10 - 2912 * q^11 - 6912 * q^12 - 3696 * q^13 - 11968 * q^14 - 13500 * q^15 + 16384 * q^16 + 16 * q^17 + 23328 * q^18 + 27436 * q^19 + 32000 * q^20 + 40392 * q^21 - 23296 * q^22 - 73016 * q^23 - 55296 * q^24 + 62500 * q^25 - 29568 * q^26 - 78732 * q^27 - 95744 * q^28 - 137784 * q^29 - 108000 * q^30 + 198072 * q^31 + 131072 * q^32 + 78624 * q^33 + 128 * q^34 - 187000 * q^35 + 186624 * q^36 + 207256 * q^37 + 219488 * q^38 + 99792 * q^39 + 256000 * q^40 - 504056 * q^41 + 323136 * q^42 - 250368 * q^43 - 186368 * q^44 + 364500 * q^45 - 584128 * q^46 - 1000376 * q^47 - 442368 * q^48 - 940908 * q^49 + 500000 * q^50 - 432 * q^51 - 236544 * q^52 - 2178688 * q^53 - 629856 * q^54 - 364000 * q^55 - 765952 * q^56 - 740772 * q^57 - 1102272 * q^58 + 327976 * q^59 - 864000 * q^60 + 572936 * q^61 + 1584576 * q^62 - 1090584 * q^63 + 1048576 * q^64 - 462000 * q^65 + 628992 * q^66 + 2017152 * q^67 + 1024 * q^68 + 1971432 * q^69 - 1496000 * q^70 + 2828960 * q^71 + 1492992 * q^72 - 132392 * q^73 + 1658048 * q^74 - 1687500 * q^75 + 1755904 * q^76 - 2304704 * q^77 + 798336 * q^78 + 3418408 * q^79 + 2048000 * q^80 + 2125764 * q^81 - 4032448 * q^82 - 3201760 * q^83 + 2585088 * q^84 + 2000 * q^85 - 2002944 * q^86 + 3720168 * q^87 - 1490944 * q^88 - 1389392 * q^89 + 2916000 * q^90 - 7865280 * q^91 - 4673024 * q^92 - 5347944 * q^93 - 8003008 * q^94 + 3429500 * q^95 - 3538944 * q^96 - 21061144 * q^97 - 7527264 * q^98 - 2122848 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	64.0000	0.500000
$5$	125.000	0.447214
$5$	125.000	0.447214
$6$	−216.000	−0.408248
$7$	366.713	0.404094	0.202047	−	0.979376i	$-0.435241\pi$
$7$	366.713	0.404094	0.202047	+	0.979376i	$0.435241\pi$
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	1000.00	0.316228
$11$	245.228	0.0555516	0.0277758	−	0.999614i	$-0.491158\pi$
$11$	245.228	0.0555516	0.0277758	+	0.999614i	$0.491158\pi$
$12$	−1728.00	−0.288675
$13$	−5603.82	−0.707429	−0.353714	−	0.935353i	$-0.615082\pi$
$13$	−5603.82	−0.707429	−0.353714	+	0.935353i	$0.615082\pi$
$14$	2933.70	0.285738
$15$	−3375.00	−0.258199
$16$	4096.00	0.250000
$17$	11610.8	0.573181	0.286590	−	0.958053i	$-0.407478\pi$
$17$	11610.8	0.573181	0.286590	+	0.958053i	$0.407478\pi$
$18$	5832.00	0.235702
$19$	6859.00	0.229416
$19$	6859.00	0.229416
$20$	8000.00	0.223607
$21$	−9901.24	−0.233304
$22$	1961.83	0.0392809
$23$	−93785.8	−1.60727	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−93785.8	−1.60727	−0.803636	+	0.595121i	$0.797104\pi$
$24$	−13824.0	−0.204124
$25$	15625.0	0.200000
$26$	−44830.6	−0.500228
$27$	−19683.0	−0.192450
$28$	23469.6	0.202047
$29$	−139019.	−1.05847	−0.529237	−	0.848474i	$-0.677522\pi$
$29$	−139019.	−1.05847	−0.529237	+	0.848474i	$0.677522\pi$
$30$	−27000.0	−0.182574
$31$	−35437.3	−0.213646	−0.106823	−	0.994278i	$-0.534068\pi$
$31$	−35437.3	−0.213646	−0.106823	+	0.994278i	$0.534068\pi$
$32$	32768.0	0.176777
$33$	−6621.17	−0.0320727
$34$	92886.5	0.405300
$35$	45839.1	0.180717
$36$	46656.0	0.166667
$37$	−2194.07	−0.00712105	−0.00356053	−	0.999994i	$-0.501133\pi$
$37$	−2194.07	−0.00712105	−0.00356053	+	0.999994i	$0.501133\pi$
$38$	54872.0	0.162221
$39$	151303.	0.408434
$40$	64000.0	0.158114
$41$	−94052.2	−0.213121	−0.106560	−	0.994306i	$-0.533984\pi$
$41$	−94052.2	−0.213121	−0.106560	+	0.994306i	$0.533984\pi$
$42$	−79210.0	−0.164971
$43$	558954.	1.07210	0.536051	−	0.844185i	$-0.319915\pi$
$43$	558954.	1.07210	0.536051	+	0.844185i	$0.319915\pi$
$44$	15694.6	0.0277758
$45$	91125.0	0.149071
$46$	−750286.	−1.13651
$47$	−400292.	−0.562385	−0.281193	−	0.959651i	$-0.590730\pi$
$47$	−400292.	−0.562385	−0.281193	+	0.959651i	$0.590730\pi$
$48$	−110592.	−0.144338
$49$	−689065.	−0.836708
$50$	125000.	0.141421
$51$	−313492.	−0.330926
$52$	−358645.	−0.353714
$53$	376602.	0.347470	0.173735	−	0.984792i	$-0.444416\pi$
$53$	376602.	0.347470	0.173735	+	0.984792i	$0.444416\pi$
$54$	−157464.	−0.136083
$55$	30653.6	0.0248434
$56$	187757.	0.142869
$57$	−185193.	−0.132453
$58$	−1.11215e6	−0.748455
$59$	−2.19517e6	−1.39151	−0.695756	−	0.718279i	$-0.744930\pi$
$59$	−2.19517e6	−1.39151	−0.695756	+	0.718279i	$0.744930\pi$
$60$	−216000.	−0.129099
$61$	1.41806e6	0.799907	0.399954	−	0.916535i	$-0.369026\pi$
$61$	1.41806e6	0.799907	0.399954	+	0.916535i	$0.369026\pi$
$62$	−283498.	−0.151071
$63$	267334.	0.134698
$64$	262144.	0.125000
$65$	−700478.	−0.316372
$66$	−52969.3	−0.0226788
$67$	−2.08078e6	−0.845210	−0.422605	−	0.906314i	$-0.638884\pi$
$67$	−2.08078e6	−0.845210	−0.422605	+	0.906314i	$0.638884\pi$
$68$	743092.	0.286590
$69$	2.53222e6	0.927959
$70$	366713.	0.127786
$71$	5.55873e6	1.84319	0.921597	−	0.388147i	$-0.126885\pi$
$71$	5.55873e6	1.84319	0.921597	+	0.388147i	$0.126885\pi$
$72$	373248.	0.117851
$73$	−3.62494e6	−1.09061	−0.545306	−	0.838237i	$-0.683587\pi$
$73$	−3.62494e6	−1.09061	−0.545306	+	0.838237i	$0.683587\pi$
$74$	−17552.5	−0.00503534
$75$	−421875.	−0.115470
$76$	438976.	0.114708
$77$	89928.4	0.0224481
$78$	1.21043e6	0.288807
$79$	−2.45264e6	−0.559680	−0.279840	−	0.960047i	$-0.590281\pi$
$79$	−2.45264e6	−0.559680	−0.279840	+	0.960047i	$0.590281\pi$
$80$	512000.	0.111803
$81$	531441.	0.111111
$82$	−752418.	−0.150699
$83$	1.88156e6	0.361197	0.180598	−	0.983557i	$-0.442197\pi$
$83$	1.88156e6	0.361197	0.180598	+	0.983557i	$0.442197\pi$
$84$	−633680.	−0.116652
$85$	1.45135e6	0.256334
$86$	4.47163e6	0.758091
$87$	3.75351e6	0.611111
$88$	125557.	0.0196404
$89$	1.28712e6	0.193533	0.0967664	−	0.995307i	$-0.469150\pi$
$89$	1.28712e6	0.193533	0.0967664	+	0.995307i	$0.469150\pi$
$90$	729000.	0.105409
$91$	−2.05499e6	−0.285868
$92$	−6.00229e6	−0.803636
$93$	956807.	0.123349
$94$	−3.20233e6	−0.397666
$95$	857375.	0.102598
$96$	−884736.	−0.102062
$97$	1.52941e6	0.170146	0.0850731	−	0.996375i	$-0.472888\pi$
$97$	1.52941e6	0.170146	0.0850731	+	0.996375i	$0.472888\pi$
$98$	−5.51252e6	−0.591642
$99$	178772.	0.0185172
$100$	1.00000e6	0.100000
$101$	−9.90300e6	−0.956405	−0.478202	−	0.878250i	$-0.658711\pi$
$101$	−9.90300e6	−0.956405	−0.478202	+	0.878250i	$0.658711\pi$
$102$	−2.50794e6	−0.234000
$103$	1.01246e7	0.912953	0.456476	−	0.889736i	$-0.349111\pi$
$103$	1.01246e7	0.912953	0.456476	+	0.889736i	$0.349111\pi$
$104$	−2.86916e6	−0.250114
$105$	−1.23766e6	−0.104337
$106$	3.01282e6	0.245698
$107$	−1.37634e7	−1.08613	−0.543064	−	0.839691i	$-0.682736\pi$
$107$	−1.37634e7	−1.08613	−0.543064	+	0.839691i	$0.682736\pi$
$108$	−1.25971e6	−0.0962250
$109$	8.07116e6	0.596957	0.298478	−	0.954416i	$-0.403521\pi$
$109$	8.07116e6	0.596957	0.298478	+	0.954416i	$0.403521\pi$
$110$	245228.	0.0175670
$111$	59239.8	0.00411134
$112$	1.50206e6	0.101024
$113$	2.40979e6	0.157110	0.0785552	−	0.996910i	$-0.474969\pi$
$113$	2.40979e6	0.157110	0.0785552	+	0.996910i	$0.474969\pi$
$114$	−1.48154e6	−0.0936586
$115$	−1.17232e7	−0.718794
$116$	−8.89720e6	−0.529237
$117$	−4.08519e6	−0.235810
$118$	−1.75614e7	−0.983947
$119$	4.25783e6	0.231619
$120$	−1.72800e6	−0.0912871
$121$	−1.94270e7	−0.996914
$122$	1.13445e7	0.565620
$123$	2.53941e6	0.123045
$124$	−2.26799e6	−0.106823
$125$	1.95312e6	0.0894427
$126$	2.13867e6	0.0952460
$127$	−9.84110e6	−0.426315	−0.213158	−	0.977018i	$-0.568375\pi$
$127$	−9.84110e6	−0.426315	−0.213158	+	0.977018i	$0.568375\pi$
$128$	2.09715e6	0.0883883
$129$	−1.50918e7	−0.618979
$130$	−5.60382e6	−0.223709
$131$	−240802.	−0.00935861	−0.00467931	−	0.999989i	$-0.501489\pi$
$131$	−240802.	−0.00935861	−0.00467931	+	0.999989i	$0.501489\pi$
$132$	−423755.	−0.0160364
$133$	2.51528e6	0.0927056
$134$	−1.66462e7	−0.597653
$135$	−2.46038e6	−0.0860663
$136$	5.94474e6	0.202650
$137$	−5.27477e7	−1.75259	−0.876297	−	0.481770i	$-0.839994\pi$
$137$	−5.27477e7	−1.75259	−0.876297	+	0.481770i	$0.839994\pi$
$138$	2.02577e7	0.656166
$139$	3.98649e7	1.25904	0.629519	−	0.776985i	$-0.283252\pi$
$139$	3.98649e7	1.25904	0.629519	+	0.776985i	$0.283252\pi$
$140$	2.93370e6	0.0903583
$141$	1.08079e7	0.324693
$142$	4.44698e7	1.30334
$143$	−1.37422e6	−0.0392988
$144$	2.98598e6	0.0833333
$145$	−1.73773e7	−0.473364
$146$	−2.89995e7	−0.771179
$147$	1.86047e7	0.483073
$148$	−140420.	−0.00356053
$149$	4.44972e7	1.10200	0.550999	−	0.834506i	$-0.314247\pi$
$149$	4.44972e7	1.10200	0.550999	+	0.834506i	$0.314247\pi$
$150$	−3.37500e6	−0.0816497
$151$	5.27728e7	1.24736	0.623679	−	0.781681i	$-0.285637\pi$
$151$	5.27728e7	1.24736	0.623679	+	0.781681i	$0.285637\pi$
$152$	3.51181e6	0.0811107
$153$	8.46429e6	0.191060
$154$	719427.	0.0158732
$155$	−4.42966e6	−0.0955454
$156$	9.68341e6	0.204217
$157$	−8.04223e7	−1.65855	−0.829274	−	0.558843i	$-0.811246\pi$
$157$	−8.04223e7	−1.65855	−0.829274	+	0.558843i	$0.811246\pi$
$158$	−1.96212e7	−0.395754
$159$	−1.01683e7	−0.200612
$160$	4.09600e6	0.0790569
$161$	−3.43924e7	−0.649490
$162$	4.25153e6	0.0785674
$163$	−9.11530e7	−1.64860	−0.824298	−	0.566156i	$-0.808430\pi$
$163$	−9.11530e7	−1.64860	−0.824298	+	0.566156i	$0.808430\pi$
$164$	−6.01934e6	−0.106560
$165$	−827646.	−0.0143434
$166$	1.50525e7	0.255405
$167$	−1.26702e7	−0.210511	−0.105256	−	0.994445i	$-0.533566\pi$
$167$	−1.26702e7	−0.210511	−0.105256	+	0.994445i	$0.533566\pi$
$168$	−5.06944e6	−0.0824854
$169$	−3.13457e7	−0.499544
$170$	1.16108e7	0.181256
$171$	5.00021e6	0.0764719
$172$	3.57730e7	0.536051
$173$	8.70136e7	1.27769	0.638846	−	0.769335i	$-0.279412\pi$
$173$	8.70136e7	1.27769	0.638846	+	0.769335i	$0.279412\pi$
$174$	3.00281e7	0.432120
$175$	5.72989e6	0.0808189
$176$	1.00446e6	0.0138879
$177$	5.92697e7	0.803389
$178$	1.02970e7	0.136848
$179$	−9.43684e7	−1.22982	−0.614909	−	0.788598i	$-0.710807\pi$
$179$	−9.43684e7	−1.22982	−0.614909	+	0.788598i	$0.710807\pi$
$180$	5.83200e6	0.0745356
$181$	−1.37434e8	−1.72274	−0.861371	−	0.507977i	$-0.830394\pi$
$181$	−1.37434e8	−1.72274	−0.861371	+	0.507977i	$0.830394\pi$
$182$	−1.64400e7	−0.202139
$183$	−3.82876e7	−0.461827
$184$	−4.80183e7	−0.568257
$185$	−274259.	−0.00318463
$186$	7.65446e6	0.0872206
$187$	2.84730e6	0.0318411
$188$	−2.56187e7	−0.281193
$189$	−7.21801e6	−0.0777680
$190$	6.85900e6	0.0725476
$191$	−7.82237e7	−0.812310	−0.406155	−	0.913804i	$-0.633131\pi$
$191$	−7.82237e7	−0.812310	−0.406155	+	0.913804i	$0.633131\pi$
$192$	−7.07789e6	−0.0721688
$193$	6.13504e7	0.614281	0.307140	−	0.951664i	$-0.400628\pi$
$193$	6.13504e7	0.614281	0.307140	+	0.951664i	$0.400628\pi$
$194$	1.22353e7	0.120311
$195$	1.89129e7	0.182657
$196$	−4.41001e7	−0.418354
$197$	−6.28987e7	−0.586152	−0.293076	−	0.956089i	$-0.594679\pi$
$197$	−6.28987e7	−0.586152	−0.293076	+	0.956089i	$0.594679\pi$
$198$	1.43017e6	0.0130936
$199$	−1.83990e8	−1.65504	−0.827522	−	0.561434i	$-0.810250\pi$
$199$	−1.83990e8	−1.65504	−0.827522	+	0.561434i	$0.810250\pi$
$200$	8.00000e6	0.0707107
$201$	5.61811e7	0.487982
$202$	−7.92240e7	−0.676280
$203$	−5.09800e7	−0.427724
$204$	−2.00635e7	−0.165463
$205$	−1.17565e7	−0.0953105
$206$	8.09969e7	0.645555
$207$	−6.83698e7	−0.535757
$208$	−2.29533e7	−0.176857
$209$	1.68202e6	0.0127444
$210$	−9.90124e6	−0.0737772
$211$	−1.69597e8	−1.24288	−0.621441	−	0.783461i	$-0.713453\pi$
$211$	−1.69597e8	−1.24288	−0.621441	+	0.783461i	$0.713453\pi$
$212$	2.41025e7	0.173735
$213$	−1.50086e8	−1.06417
$214$	−1.10107e8	−0.768008
$215$	6.98692e7	0.479459
$216$	−1.00777e7	−0.0680414
$217$	−1.29953e7	−0.0863332
$218$	6.45693e7	0.422112
$219$	9.78733e7	0.629665
$220$	1.96183e6	0.0124217
$221$	−6.50650e7	−0.405485
$222$	473919.	0.00290716
$223$	1.50891e8	0.911164	0.455582	−	0.890194i	$-0.349431\pi$
$223$	1.50891e8	0.911164	0.455582	+	0.890194i	$0.349431\pi$
$224$	1.20164e7	0.0714345
$225$	1.13906e7	0.0666667
$226$	1.92783e7	0.111094
$227$	−2.71149e8	−1.53857	−0.769284	−	0.638907i	$-0.779387\pi$
$227$	−2.71149e8	−1.53857	−0.769284	+	0.638907i	$0.779387\pi$
$228$	−1.18524e7	−0.0662266
$229$	9.61047e7	0.528835	0.264418	−	0.964408i	$-0.414820\pi$
$229$	9.61047e7	0.528835	0.264418	+	0.964408i	$0.414820\pi$
$230$	−9.37858e7	−0.508264
$231$	−2.42807e6	−0.0129604
$232$	−7.11776e7	−0.374227
$233$	4.28832e7	0.222096	0.111048	−	0.993815i	$-0.464579\pi$
$233$	4.28832e7	0.222096	0.111048	+	0.993815i	$0.464579\pi$
$234$	−3.26815e7	−0.166743
$235$	−5.00364e7	−0.251506
$236$	−1.40491e8	−0.695756
$237$	6.62214e7	0.323131
$238$	3.40627e7	0.163779
$239$	−6.97352e7	−0.330415	−0.165207	−	0.986259i	$-0.552829\pi$
$239$	−6.97352e7	−0.330415	−0.165207	+	0.986259i	$0.552829\pi$
$240$	−1.38240e7	−0.0645497
$241$	−7.56406e7	−0.348093	−0.174046	−	0.984737i	$-0.555684\pi$
$241$	−7.56406e7	−0.348093	−0.174046	+	0.984737i	$0.555684\pi$
$242$	−1.55416e8	−0.704925
$243$	−1.43489e7	−0.0641500
$244$	9.07557e7	0.399954
$245$	−8.61331e7	−0.374187
$246$	2.03153e7	0.0870062
$247$	−3.84366e7	−0.162295
$248$	−1.81439e7	−0.0755353
$249$	−5.08020e7	−0.208537
$250$	1.56250e7	0.0632456
$251$	−1.32101e8	−0.527287	−0.263643	−	0.964620i	$-0.584924\pi$
$251$	−1.32101e8	−0.527287	−0.263643	+	0.964620i	$0.584924\pi$
$252$	1.71094e7	0.0673491
$253$	−2.29989e7	−0.0892865
$254$	−7.87288e7	−0.301450
$255$	−3.91865e7	−0.147995
$256$	1.67772e7	0.0625000
$257$	−1.57465e8	−0.578654	−0.289327	−	0.957230i	$-0.593431\pi$
$257$	−1.57465e8	−0.578654	−0.289327	+	0.957230i	$0.593431\pi$
$258$	−1.20734e8	−0.437684
$259$	−804593.	−0.00287758
$260$	−4.48306e7	−0.158186
$261$	−1.01345e8	−0.352825
$262$	−1.92642e6	−0.00661754
$263$	−3.68824e7	−0.125018	−0.0625091	−	0.998044i	$-0.519910\pi$
$263$	−3.68824e7	−0.125018	−0.0625091	+	0.998044i	$0.519910\pi$
$264$	−3.39004e6	−0.0113394
$265$	4.70753e7	0.155393
$266$	2.01223e7	0.0655528
$267$	−3.47523e7	−0.111736
$268$	−1.33170e8	−0.422605
$269$	−2.60680e8	−0.816535	−0.408267	−	0.912862i	$-0.633867\pi$
$269$	−2.60680e8	−0.816535	−0.408267	+	0.912862i	$0.633867\pi$
$270$	−1.96830e7	−0.0608581
$271$	−1.75797e8	−0.536560	−0.268280	−	0.963341i	$-0.586455\pi$
$271$	−1.75797e8	−0.536560	−0.268280	+	0.963341i	$0.586455\pi$
$272$	4.75579e7	0.143295
$273$	5.54848e7	0.165046
$274$	−4.21982e8	−1.23927
$275$	3.83169e6	0.0111103
$276$	1.62062e8	0.463980
$277$	−3.00486e8	−0.849464	−0.424732	−	0.905319i	$-0.639632\pi$
$277$	−3.00486e8	−0.849464	−0.424732	+	0.905319i	$0.639632\pi$
$278$	3.18919e8	0.890275
$279$	−2.58338e7	−0.0712153
$280$	2.34696e7	0.0638929
$281$	5.77481e8	1.55262	0.776311	−	0.630350i	$-0.217088\pi$
$281$	5.77481e8	1.55262	0.776311	+	0.630350i	$0.217088\pi$
$282$	8.64630e7	0.229593
$283$	2.02175e8	0.530244	0.265122	−	0.964215i	$-0.414588\pi$
$283$	2.02175e8	0.530244	0.265122	+	0.964215i	$0.414588\pi$
$284$	3.55759e8	0.921597
$285$	−2.31491e7	−0.0592349
$286$	−1.09937e7	−0.0277884
$287$	−3.44902e7	−0.0861209
$288$	2.38879e7	0.0589256
$289$	−2.75528e8	−0.671464
$290$	−1.39019e8	−0.334719
$291$	−4.12940e7	−0.0982339
$292$	−2.31996e8	−0.545306
$293$	−5.29199e8	−1.22909	−0.614544	−	0.788883i	$-0.710660\pi$
$293$	−5.29199e8	−1.22909	−0.614544	+	0.788883i	$0.710660\pi$
$294$	1.48838e8	0.341584
$295$	−2.74397e8	−0.622303
$296$	−1.12336e6	−0.00251767
$297$	−4.82683e6	−0.0106909
$298$	3.55978e8	0.779230
$299$	5.25559e8	1.13703
$300$	−2.70000e7	−0.0577350
$301$	2.04975e8	0.433231
$302$	4.22183e8	0.882015
$303$	2.67381e8	0.552181
$304$	2.80945e7	0.0573539
$305$	1.77257e8	0.357729
$306$	6.77143e7	0.135100
$307$	5.33039e8	1.05142	0.525708	−	0.850665i	$-0.323800\pi$
$307$	5.33039e8	1.05142	0.525708	+	0.850665i	$0.323800\pi$
$308$	5.75542e6	0.0112240
$309$	−2.73365e8	−0.527093
$310$	−3.54373e7	−0.0675608
$311$	−4.81441e8	−0.907573	−0.453786	−	0.891111i	$-0.649927\pi$
$311$	−4.81441e8	−0.907573	−0.453786	+	0.891111i	$0.649927\pi$
$312$	7.74673e7	0.144403
$313$	2.90505e8	0.535487	0.267744	−	0.963490i	$-0.413722\pi$
$313$	2.90505e8	0.535487	0.267744	+	0.963490i	$0.413722\pi$
$314$	−6.43379e8	−1.17277
$315$	3.34167e7	0.0602388
$316$	−1.56969e8	−0.279840
$317$	−2.81003e8	−0.495454	−0.247727	−	0.968830i	$-0.579684\pi$
$317$	−2.81003e8	−0.495454	−0.247727	+	0.968830i	$0.579684\pi$
$318$	−8.13460e7	−0.141854
$319$	−3.40914e7	−0.0587999
$320$	3.27680e7	0.0559017
$321$	3.71610e8	0.627076
$322$	−2.75139e8	−0.459259
$323$	7.96386e7	0.131497
$324$	3.40122e7	0.0555556
$325$	−8.75598e7	−0.141486
$326$	−7.29224e8	−1.16573
$327$	−2.17921e8	−0.344653
$328$	−4.81547e7	−0.0753495
$329$	−1.46792e8	−0.227257
$330$	−6.62117e6	−0.0101423
$331$	4.35798e8	0.660522	0.330261	−	0.943890i	$-0.392863\pi$
$331$	4.35798e8	0.660522	0.330261	+	0.943890i	$0.392863\pi$
$332$	1.20420e8	0.180598
$333$	−1.59948e6	−0.00237368
$334$	−1.01361e8	−0.148854
$335$	−2.60098e8	−0.377989
$336$	−4.05555e7	−0.0583260
$337$	−7.32000e8	−1.04185	−0.520926	−	0.853602i	$-0.674413\pi$
$337$	−7.32000e8	−1.04185	−0.520926	+	0.853602i	$0.674413\pi$
$338$	−2.50765e8	−0.353231
$339$	−6.50644e7	−0.0907077
$340$	9.28865e7	0.128167
$341$	−8.69023e6	−0.0118684
$342$	4.00017e7	0.0540738
$343$	−5.54693e8	−0.742203
$344$	2.86184e8	0.379045
$345$	3.16527e8	0.414996
$346$	6.96109e8	0.903464
$347$	1.25729e9	1.61541	0.807703	−	0.589590i	$-0.200711\pi$
$347$	1.25729e9	1.61541	0.807703	+	0.589590i	$0.200711\pi$
$348$	2.40224e8	0.305555
$349$	5.07431e8	0.638981	0.319490	−	0.947589i	$-0.396488\pi$
$349$	5.07431e8	0.638981	0.319490	+	0.947589i	$0.396488\pi$
$350$	4.58391e7	0.0571476
$351$	1.10300e8	0.136145
$352$	8.03564e6	0.00982022
$353$	6.19977e8	0.750177	0.375089	−	0.926989i	$-0.377612\pi$
$353$	6.19977e8	0.750177	0.375089	+	0.926989i	$0.377612\pi$
$354$	4.74157e8	0.568082
$355$	6.94841e8	0.824302
$356$	8.23758e7	0.0967664
$357$	−1.14962e8	−0.133725
$358$	−7.54948e8	−0.869613
$359$	−4.04534e8	−0.461450	−0.230725	−	0.973019i	$-0.574110\pi$
$359$	−4.04534e8	−0.461450	−0.230725	+	0.973019i	$0.574110\pi$
$360$	4.66560e7	0.0527046
$361$	4.70459e7	0.0526316
$362$	−1.09947e9	−1.21816
$363$	5.24530e8	0.575569
$364$	−1.31520e8	−0.142934
$365$	−4.53117e8	−0.487737
$366$	−3.06301e8	−0.326561
$367$	−4.53322e8	−0.478713	−0.239357	−	0.970932i	$-0.576937\pi$
$367$	−4.53322e8	−0.478713	−0.239357	+	0.970932i	$0.576937\pi$
$368$	−3.84146e8	−0.401818
$369$	−6.85641e7	−0.0710402
$370$	−2.19407e6	−0.00225187
$371$	1.38105e8	0.140411
$372$	6.12357e7	0.0616743
$373$	9.28056e8	0.925962	0.462981	−	0.886368i	$-0.346780\pi$
$373$	9.28056e8	0.925962	0.462981	+	0.886368i	$0.346780\pi$
$374$	2.27784e7	0.0225151
$375$	−5.27344e7	−0.0516398
$376$	−2.04949e8	−0.198833
$377$	7.79037e8	0.748796
$378$	−5.77441e7	−0.0549903
$379$	5.26235e8	0.496527	0.248263	−	0.968693i	$-0.420140\pi$
$379$	5.26235e8	0.496527	0.248263	+	0.968693i	$0.420140\pi$
$380$	5.48720e7	0.0512989
$381$	2.65710e8	0.246133
$382$	−6.25790e8	−0.574390
$383$	1.03523e9	0.941544	0.470772	−	0.882255i	$-0.343975\pi$
$383$	1.03523e9	0.941544	0.470772	+	0.882255i	$0.343975\pi$
$384$	−5.66231e7	−0.0510310
$385$	1.12410e7	0.0100391
$386$	4.90803e8	0.434362
$387$	4.07477e8	0.357367
$388$	9.78821e7	0.0850731
$389$	−1.69743e8	−0.146207	−0.0731037	−	0.997324i	$-0.523290\pi$
$389$	−1.69743e8	−0.146207	−0.0731037	+	0.997324i	$0.523290\pi$
$390$	1.51303e8	0.129158
$391$	−1.08893e9	−0.921257
$392$	−3.52801e8	−0.295821
$393$	6.50167e6	0.00540320
$394$	−5.03190e8	−0.414472
$395$	−3.06581e8	−0.250297
$396$	1.14414e7	0.00925860
$397$	−1.67464e9	−1.34325	−0.671623	−	0.740893i	$-0.734402\pi$
$397$	−1.67464e9	−1.34325	−0.671623	+	0.740893i	$0.734402\pi$
$398$	−1.47192e9	−1.17029
$399$	−6.79126e7	−0.0535236
$400$	6.40000e7	0.0500000
$401$	2.41716e9	1.87198	0.935988	−	0.352031i	$-0.114509\pi$
$401$	2.41716e9	1.87198	0.935988	+	0.352031i	$0.114509\pi$
$402$	4.49449e8	0.345055
$403$	1.98584e8	0.151139
$404$	−6.33792e8	−0.478202
$405$	6.64301e7	0.0496904
$406$	−4.07840e8	−0.302446
$407$	−538048.	−0.000395586 0
$408$	−1.60508e8	−0.117000
$409$	2.65536e8	0.191908	0.0959539	−	0.995386i	$-0.469410\pi$
$409$	2.65536e8	0.191908	0.0959539	+	0.995386i	$0.469410\pi$
$410$	−9.40522e7	−0.0673947
$411$	1.42419e9	1.01186
$412$	6.47975e8	0.456476
$413$	−8.04998e8	−0.562302
$414$	−5.46958e8	−0.378838
$415$	2.35195e8	0.161532
$416$	−1.83626e8	−0.125057
$417$	−1.07635e9	−0.726906
$418$	1.34562e7	0.00901166
$419$	5.77321e8	0.383414	0.191707	−	0.981452i	$-0.438598\pi$
$419$	5.77321e8	0.383414	0.191707	+	0.981452i	$0.438598\pi$
$420$	−7.92100e7	−0.0521684
$421$	2.60084e7	0.0169873	0.00849367	−	0.999964i	$-0.497296\pi$
$421$	2.60084e7	0.0169873	0.00849367	+	0.999964i	$0.497296\pi$
$422$	−1.35678e9	−0.878851
$423$	−2.91813e8	−0.187462
$424$	1.92820e8	0.122849
$425$	1.81419e8	0.114636
$426$	−1.20069e9	−0.752481
$427$	5.20020e8	0.323238
$428$	−8.80855e8	−0.543064
$429$	3.71039e7	0.0226892
$430$	5.58954e8	0.339029
$431$	7.90133e8	0.475368	0.237684	−	0.971343i	$-0.423612\pi$
$431$	7.90133e8	0.475368	0.237684	+	0.971343i	$0.423612\pi$
$432$	−8.06216e7	−0.0481125
$433$	−2.11769e9	−1.25358	−0.626792	−	0.779186i	$-0.715633\pi$
$433$	−2.11769e9	−1.25358	−0.626792	+	0.779186i	$0.715633\pi$
$434$	−1.03962e8	−0.0610468
$435$	4.69188e8	0.273297
$436$	5.16554e8	0.298478
$437$	−6.43276e8	−0.368734
$438$	7.82986e8	0.445241
$439$	−5.65369e8	−0.318938	−0.159469	−	0.987203i	$-0.550978\pi$
$439$	−5.65369e8	−0.318938	−0.159469	+	0.987203i	$0.550978\pi$
$440$	1.56946e7	0.00878348
$441$	−5.02328e8	−0.278903
$442$	−5.20520e8	−0.286721
$443$	−2.34948e9	−1.28398	−0.641991	−	0.766713i	$-0.721891\pi$
$443$	−2.34948e9	−1.28398	−0.641991	+	0.766713i	$0.721891\pi$
$444$	3.79135e6	0.00205567
$445$	1.60890e8	0.0865505
$446$	1.20713e9	0.644290
$447$	−1.20142e9	−0.636239
$448$	9.61316e7	0.0505118
$449$	−1.08989e9	−0.568226	−0.284113	−	0.958791i	$-0.591699\pi$
$449$	−1.08989e9	−0.568226	−0.284113	+	0.958791i	$0.591699\pi$
$450$	9.11250e7	0.0471405
$451$	−2.30643e7	−0.0118392
$452$	1.54227e8	0.0785552
$453$	−1.42487e9	−0.720162
$454$	−2.16919e9	−1.08793
$455$	−2.56874e8	−0.127844
$456$	−9.48188e7	−0.0468293
$457$	−3.68646e9	−1.80677	−0.903385	−	0.428831i	$-0.858926\pi$
$457$	−3.68646e9	−1.80677	−0.903385	+	0.428831i	$0.858926\pi$
$458$	7.68838e8	0.373943
$459$	−2.28536e8	−0.110309
$460$	−7.50286e8	−0.359397
$461$	2.42102e9	1.15092	0.575460	−	0.817830i	$-0.304823\pi$
$461$	2.42102e9	1.15092	0.575460	+	0.817830i	$0.304823\pi$
$462$	−1.94245e7	−0.00916439
$463$	4.16072e9	1.94821	0.974104	−	0.226100i	$-0.0725976\pi$
$463$	4.16072e9	1.94821	0.974104	+	0.226100i	$0.0725976\pi$
$464$	−5.69421e8	−0.264619
$465$	1.19601e8	0.0551632
$466$	3.43066e8	0.157046
$467$	−4.17463e9	−1.89675	−0.948374	−	0.317156i	$-0.897272\pi$
$467$	−4.17463e9	−1.89675	−0.948374	+	0.317156i	$0.897272\pi$
$468$	−2.61452e8	−0.117905
$469$	−7.63049e8	−0.341545
$470$	−4.00292e8	−0.177842
$471$	2.17140e9	0.957563
$472$	−1.12393e9	−0.491973
$473$	1.37071e8	0.0595570
$474$	5.29771e8	0.228488
$475$	1.07172e8	0.0458831
$476$	2.72501e8	0.115810
$477$	2.74543e8	0.115823
$478$	−5.57882e8	−0.233639
$479$	2.64150e9	1.09819	0.549094	−	0.835761i	$-0.314973\pi$
$479$	2.64150e9	1.09819	0.549094	+	0.835761i	$0.314973\pi$
$480$	−1.10592e8	−0.0456435
$481$	1.22952e7	0.00503764
$482$	−6.05125e8	−0.246139
$483$	9.28596e8	0.374983
$484$	−1.24333e9	−0.498457
$485$	1.91176e8	0.0760917
$486$	−1.14791e8	−0.0453609
$487$	1.03507e9	0.406085	0.203043	−	0.979170i	$-0.434917\pi$
$487$	1.03507e9	0.406085	0.203043	+	0.979170i	$0.434917\pi$
$488$	7.26046e8	0.282810
$489$	2.46113e9	0.951817
$490$	−6.89065e8	−0.264590
$491$	−1.05949e8	−0.0403933	−0.0201967	−	0.999796i	$-0.506429\pi$
$491$	−1.05949e8	−0.0403933	−0.0201967	+	0.999796i	$0.506429\pi$
$492$	1.62522e8	0.0615226
$493$	−1.61412e9	−0.606697
$494$	−3.07493e8	−0.114760
$495$	2.23464e7	0.00828114
$496$	−1.45151e8	−0.0534115
$497$	2.03846e9	0.744825
$498$	−4.06416e8	−0.147458
$499$	6.94329e8	0.250157	0.125079	−	0.992147i	$-0.460082\pi$
$499$	6.94329e8	0.250157	0.125079	+	0.992147i	$0.460082\pi$
$500$	1.25000e8	0.0447214
$501$	3.42095e8	0.121539
$502$	−1.05681e9	−0.372848
$503$	−3.94928e9	−1.38366	−0.691830	−	0.722060i	$-0.743195\pi$
$503$	−3.94928e9	−1.38366	−0.691830	+	0.722060i	$0.743195\pi$
$504$	1.36875e8	0.0476230
$505$	−1.23787e9	−0.427717
$506$	−1.83991e8	−0.0631351
$507$	8.46333e8	0.288412
$508$	−6.29831e8	−0.213158
$509$	−1.04448e9	−0.351066	−0.175533	−	0.984474i	$-0.556165\pi$
$509$	−1.04448e9	−0.351066	−0.175533	+	0.984474i	$0.556165\pi$
$510$	−3.13492e8	−0.104648
$511$	−1.32931e9	−0.440710
$512$	1.34218e8	0.0441942
$513$	−1.35006e8	−0.0441511
$514$	−1.25972e9	−0.409170
$515$	1.26558e9	0.408285
$516$	−9.65872e8	−0.309489
$517$	−9.81629e7	−0.0312414
$518$	−6.43674e6	−0.00203475
$519$	−2.34937e9	−0.737675
$520$	−3.58645e8	−0.111854
$521$	2.34185e9	0.725482	0.362741	−	0.931890i	$-0.381841\pi$
$521$	2.34185e9	0.725482	0.362741	+	0.931890i	$0.381841\pi$
$522$	−8.10758e8	−0.249485
$523$	3.20904e9	0.980888	0.490444	−	0.871473i	$-0.336835\pi$
$523$	3.20904e9	0.980888	0.490444	+	0.871473i	$0.336835\pi$
$524$	−1.54114e7	−0.00467931
$525$	−1.54707e8	−0.0466608
$526$	−2.95059e8	−0.0884013
$527$	−4.11456e8	−0.122458
$528$	−2.71203e7	−0.00801818
$529$	5.39094e9	1.58332
$530$	3.76602e8	0.109880
$531$	−1.60028e9	−0.463837
$532$	1.60978e8	0.0463528
$533$	5.27052e8	0.150768
$534$	−2.78018e8	−0.0790095
$535$	−1.72042e9	−0.485731
$536$	−1.06536e9	−0.298827
$537$	2.54795e9	0.710036
$538$	−2.08544e9	−0.577377
$539$	−1.68978e8	−0.0464804
$540$	−1.57464e8	−0.0430331
$541$	−3.37432e9	−0.916211	−0.458106	−	0.888898i	$-0.651472\pi$
$541$	−3.37432e9	−0.916211	−0.458106	+	0.888898i	$0.651472\pi$
$542$	−1.40637e9	−0.379405
$543$	3.71073e9	0.994625
$544$	3.80463e8	0.101325
$545$	1.00889e9	0.266967
$546$	4.43879e8	0.116705
$547$	2.26225e9	0.590997	0.295498	−	0.955343i	$-0.404514\pi$
$547$	2.26225e9	0.590997	0.295498	+	0.955343i	$0.404514\pi$
$548$	−3.37585e9	−0.876297
$549$	1.03376e9	0.266636
$550$	3.06536e7	0.00785618
$551$	−9.53530e8	−0.242831
$552$	1.29649e9	0.328083
$553$	−8.99416e8	−0.226164
$554$	−2.40389e9	−0.600662
$555$	7.40498e6	0.00183865
$556$	2.55136e9	0.629519
$557$	7.09317e9	1.73919	0.869596	−	0.493764i	$-0.164379\pi$
$557$	7.09317e9	1.73919	0.869596	+	0.493764i	$0.164379\pi$
$558$	−2.06670e8	−0.0503568
$559$	−3.13228e9	−0.758436
$560$	1.87757e8	0.0451791
$561$	−7.68772e7	−0.0183835
$562$	4.61985e9	1.09787
$563$	6.49862e9	1.53476	0.767382	−	0.641190i	$-0.221559\pi$
$563$	6.49862e9	1.53476	0.767382	+	0.641190i	$0.221559\pi$
$564$	6.91704e8	0.162347
$565$	3.01224e8	0.0702619
$566$	1.61740e9	0.374939
$567$	1.94886e8	0.0448994
$568$	2.84607e9	0.651668
$569$	−5.96567e9	−1.35758	−0.678791	−	0.734331i	$-0.737496\pi$
$569$	−5.96567e9	−1.35758	−0.678791	+	0.734331i	$0.737496\pi$
$570$	−1.85193e8	−0.0418854
$571$	2.37348e9	0.533531	0.266766	−	0.963761i	$-0.414045\pi$
$571$	2.37348e9	0.533531	0.266766	+	0.963761i	$0.414045\pi$
$572$	−8.79499e7	−0.0196494
$573$	2.11204e9	0.468987
$574$	−2.75921e8	−0.0608967
$575$	−1.46540e9	−0.321454
$576$	1.91103e8	0.0416667
$577$	−3.46592e9	−0.751108	−0.375554	−	0.926800i	$-0.622548\pi$
$577$	−3.46592e9	−0.751108	−0.375554	+	0.926800i	$0.622548\pi$
$578$	−2.20422e9	−0.474797
$579$	−1.65646e9	−0.354655
$580$	−1.11215e9	−0.236682
$581$	6.89991e8	0.145958
$582$	−3.30352e8	−0.0694619
$583$	9.23535e7	0.0193025
$584$	−1.85597e9	−0.385590
$585$	−5.10648e8	−0.105457
$586$	−4.23360e9	−0.869096
$587$	1.77355e9	0.361919	0.180959	−	0.983491i	$-0.442080\pi$
$587$	1.77355e9	0.361919	0.180959	+	0.983491i	$0.442080\pi$
$588$	1.19070e9	0.241537
$589$	−2.43064e8	−0.0490137
$590$	−2.19517e9	−0.440034
$591$	1.69827e9	0.338415
$592$	−8.98690e6	−0.00178026
$593$	1.87714e9	0.369662	0.184831	−	0.982770i	$-0.440826\pi$
$593$	1.87714e9	0.369662	0.184831	+	0.982770i	$0.440826\pi$
$594$	−3.86146e7	−0.00755961
$595$	5.32229e8	0.103583
$596$	2.84782e9	0.550999
$597$	4.96774e9	0.955540
$598$	4.20447e9	0.804002
$599$	1.06202e9	0.201901	0.100950	−	0.994891i	$-0.467812\pi$
$599$	1.06202e9	0.201901	0.100950	+	0.994891i	$0.467812\pi$
$600$	−2.16000e8	−0.0408248
$601$	4.08078e9	0.766800	0.383400	−	0.923582i	$-0.374753\pi$
$601$	4.08078e9	0.766800	0.383400	+	0.923582i	$0.374753\pi$
$602$	1.63980e9	0.306340
$603$	−1.51689e9	−0.281737
$604$	3.37746e9	0.623679
$605$	−2.42838e9	−0.445834
$606$	2.13905e9	0.390451
$607$	3.98231e9	0.722728	0.361364	−	0.932425i	$-0.382311\pi$
$607$	3.98231e9	0.722728	0.361364	+	0.932425i	$0.382311\pi$
$608$	2.24756e8	0.0405554
$609$	1.37646e9	0.246946
$610$	1.41806e9	0.252953
$611$	2.24316e9	0.397848
$612$	5.41714e8	0.0955301
$613$	5.08201e8	0.0891094	0.0445547	−	0.999007i	$-0.485813\pi$
$613$	5.08201e8	0.0891094	0.0445547	+	0.999007i	$0.485813\pi$
$614$	4.26431e9	0.743464
$615$	3.17426e8	0.0550275
$616$	4.60433e7	0.00793660
$617$	−4.10933e9	−0.704325	−0.352163	−	0.935939i	$-0.614554\pi$
$617$	−4.10933e9	−0.704325	−0.352163	+	0.935939i	$0.614554\pi$
$618$	−2.18692e9	−0.372711
$619$	2.12359e9	0.359877	0.179938	−	0.983678i	$-0.442410\pi$
$619$	2.12359e9	0.359877	0.179938	+	0.983678i	$0.442410\pi$
$620$	−2.83498e8	−0.0477727
$621$	1.84598e9	0.309320
$622$	−3.85152e9	−0.641751
$623$	4.72004e8	0.0782056
$624$	6.19738e8	0.102109
$625$	2.44141e8	0.0400000
$626$	2.32404e9	0.378647
$627$	−4.54146e7	−0.00735799
$628$	−5.14703e9	−0.829274
$629$	−2.54749e7	−0.00408165
$630$	2.67334e8	0.0425953
$631$	9.84976e9	1.56071	0.780357	−	0.625335i	$-0.215038\pi$
$631$	9.84976e9	1.56071	0.780357	+	0.625335i	$0.215038\pi$
$632$	−1.25575e9	−0.197877
$633$	4.57912e9	0.717579
$634$	−2.24802e9	−0.350339
$635$	−1.23014e9	−0.190654
$636$	−6.50768e8	−0.100306
$637$	3.86140e9	0.591911
$638$	−2.72731e8	−0.0415778
$639$	4.05231e9	0.614398
$640$	2.62144e8	0.0395285
$641$	−8.72917e9	−1.30909	−0.654546	−	0.756022i	$-0.727140\pi$
$641$	−8.72917e9	−1.30909	−0.654546	+	0.756022i	$0.727140\pi$
$642$	2.97288e9	0.443410
$643$	−3.16184e9	−0.469031	−0.234516	−	0.972112i	$-0.575350\pi$
$643$	−3.16184e9	−0.469031	−0.234516	+	0.972112i	$0.575350\pi$
$644$	−2.20112e9	−0.324745
$645$	−1.88647e9	−0.276816
$646$	6.37109e8	0.0929822
$647$	7.06270e8	0.102519	0.0512597	−	0.998685i	$-0.483676\pi$
$647$	7.06270e8	0.102519	0.0512597	+	0.998685i	$0.483676\pi$
$648$	2.72098e8	0.0392837
$649$	−5.38319e8	−0.0773006
$650$	−7.00478e8	−0.100046
$651$	3.50873e8	0.0498445
$652$	−5.83379e9	−0.824298
$653$	−1.79774e9	−0.252656	−0.126328	−	0.991989i	$-0.540319\pi$
$653$	−1.79774e9	−0.252656	−0.126328	+	0.991989i	$0.540319\pi$
$654$	−1.74337e9	−0.243707
$655$	−3.01003e7	−0.00418530
$656$	−3.85238e8	−0.0532802
$657$	−2.64258e9	−0.363537
$658$	−1.17434e9	−0.160695
$659$	2.83836e8	0.0386338	0.0193169	−	0.999813i	$-0.493851\pi$
$659$	2.83836e8	0.0386338	0.0193169	+	0.999813i	$0.493851\pi$
$660$	−5.29693e7	−0.00717168
$661$	7.41312e9	0.998380	0.499190	−	0.866492i	$-0.333631\pi$
$661$	7.41312e9	0.998380	0.499190	+	0.866492i	$0.333631\pi$
$662$	3.48639e9	0.467060
$663$	1.75675e9	0.234107
$664$	9.63357e8	0.127702
$665$	3.14410e8	0.0414592
$666$	−1.27958e7	−0.00167845
$667$	1.30380e10	1.70126
$668$	−8.10892e8	−0.105256
$669$	−4.07406e9	−0.526061
$670$	−2.08078e9	−0.267279
$671$	3.47748e8	0.0444361
$672$	−3.24444e8	−0.0412427
$673$	8.05987e9	1.01924	0.509619	−	0.860400i	$-0.329786\pi$
$673$	8.05987e9	1.01924	0.509619	+	0.860400i	$0.329786\pi$
$674$	−5.85600e9	−0.736701
$675$	−3.07547e8	−0.0384900
$676$	−2.00612e9	−0.249772
$677$	−1.60172e9	−0.198393	−0.0991963	−	0.995068i	$-0.531627\pi$
$677$	−1.60172e9	−0.198393	−0.0991963	+	0.995068i	$0.531627\pi$
$678$	−5.20515e8	−0.0641401
$679$	5.60853e8	0.0687551
$680$	7.43092e8	0.0906278
$681$	7.32101e9	0.888293
$682$	−6.95219e7	−0.00839221
$683$	1.36700e10	1.64170	0.820852	−	0.571141i	$-0.193499\pi$
$683$	1.36700e10	1.64170	0.820852	+	0.571141i	$0.193499\pi$
$684$	3.20014e8	0.0382360
$685$	−6.59346e9	−0.783784
$686$	−4.43754e9	−0.524817
$687$	−2.59483e9	−0.305323
$688$	2.28947e9	0.268026
$689$	−2.11041e9	−0.245810
$690$	2.53222e9	0.293446
$691$	1.41874e10	1.63580	0.817901	−	0.575359i	$-0.195138\pi$
$691$	1.41874e10	1.63580	0.817901	+	0.575359i	$0.195138\pi$
$692$	5.56887e9	0.638846
$693$	6.55578e7	0.00748269
$694$	1.00583e10	1.14226
$695$	4.98312e9	0.563059
$696$	1.92180e9	0.216060
$697$	−1.09202e9	−0.122157
$698$	4.05945e9	0.451828
$699$	−1.15785e9	−0.128227
$700$	3.66713e8	0.0404094
$701$	6.23622e9	0.683767	0.341884	−	0.939742i	$-0.388935\pi$
$701$	6.23622e9	0.683767	0.341884	+	0.939742i	$0.388935\pi$
$702$	8.82401e8	0.0962689
$703$	−1.50491e7	−0.00163368
$704$	6.42852e7	0.00694395
$705$	1.35098e9	0.145207
$706$	4.95981e9	0.530455
$707$	−3.63155e9	−0.386478
$708$	3.79326e9	0.401695
$709$	2.47675e9	0.260988	0.130494	−	0.991449i	$-0.458344\pi$
$709$	2.47675e9	0.260988	0.130494	+	0.991449i	$0.458344\pi$
$710$	5.55873e9	0.582869
$711$	−1.78798e9	−0.186560
$712$	6.59006e8	0.0684242
$713$	3.32351e9	0.343387
$714$	−9.19692e8	−0.0945581
$715$	−1.71777e8	−0.0175750
$716$	−6.03958e9	−0.614909
$717$	1.88285e9	0.190765
$718$	−3.23628e9	−0.326295
$719$	−8.43359e9	−0.846177	−0.423089	−	0.906088i	$-0.639054\pi$
$719$	−8.43359e9	−0.846177	−0.423089	+	0.906088i	$0.639054\pi$
$720$	3.73248e8	0.0372678
$721$	3.71283e9	0.368919
$722$	3.76367e8	0.0372161
$723$	2.04230e9	0.200972
$724$	−8.79579e9	−0.861371
$725$	−2.17217e9	−0.211695
$726$	4.19624e9	0.406988
$727$	−5.72907e9	−0.552985	−0.276493	−	0.961016i	$-0.589172\pi$
$727$	−5.72907e9	−0.552985	−0.276493	+	0.961016i	$0.589172\pi$
$728$	−1.05216e9	−0.101070
$729$	3.87420e8	0.0370370
$730$	−3.62494e9	−0.344882
$731$	6.48991e9	0.614508
$732$	−2.45041e9	−0.230913
$733$	−4.73042e8	−0.0443645	−0.0221823	−	0.999754i	$-0.507061\pi$
$733$	−4.73042e8	−0.0443645	−0.0221823	+	0.999754i	$0.507061\pi$
$734$	−3.62658e9	−0.338502
$735$	2.32559e9	0.216037
$736$	−3.07317e9	−0.284128
$737$	−5.10266e8	−0.0469527
$738$	−5.48513e8	−0.0502330
$739$	−1.09231e10	−0.995613	−0.497806	−	0.867288i	$-0.665861\pi$
$739$	−1.09231e10	−0.995613	−0.497806	+	0.867288i	$0.665861\pi$
$740$	−1.75525e7	−0.00159232
$741$	1.03779e9	0.0937012
$742$	1.10484e9	0.0992853
$743$	3.48107e9	0.311352	0.155676	−	0.987808i	$-0.450244\pi$
$743$	3.48107e9	0.311352	0.155676	+	0.987808i	$0.450244\pi$
$744$	4.89885e8	0.0436103
$745$	5.56215e9	0.492829
$746$	7.42445e9	0.654754
$747$	1.37165e9	0.120399
$748$	1.82227e8	0.0159205
$749$	−5.04720e9	−0.438898
$750$	−4.21875e8	−0.0365148
$751$	1.09971e10	0.947414	0.473707	−	0.880683i	$-0.342916\pi$
$751$	1.09971e10	0.947414	0.473707	+	0.880683i	$0.342916\pi$
$752$	−1.63959e9	−0.140596
$753$	3.56672e9	0.304429
$754$	6.23229e9	0.529478
$755$	6.59660e9	0.557835
$756$	−4.61952e8	−0.0388840
$757$	1.04677e10	0.877034	0.438517	−	0.898723i	$-0.355504\pi$
$757$	1.04677e10	0.877034	0.438517	+	0.898723i	$0.355504\pi$
$758$	4.20988e9	0.351098
$759$	6.20971e8	0.0515496
$760$	4.38976e8	0.0362738
$761$	1.22987e10	1.01161	0.505804	−	0.862648i	$-0.331196\pi$
$761$	1.22987e10	1.01161	0.505804	+	0.862648i	$0.331196\pi$
$762$	2.12568e9	0.174042
$763$	2.95980e9	0.241227
$764$	−5.00632e9	−0.406155
$765$	1.05804e9	0.0854447
$766$	8.28183e9	0.665772
$767$	1.23014e10	0.984395
$768$	−4.52985e8	−0.0360844
$769$	1.66676e10	1.32170	0.660848	−	0.750520i	$-0.270197\pi$
$769$	1.66676e10	1.32170	0.660848	+	0.750520i	$0.270197\pi$
$770$	8.99284e7	0.00709871
$771$	4.25156e9	0.334086
$772$	3.92643e9	0.307140
$773$	−1.61558e10	−1.25806	−0.629028	−	0.777383i	$-0.716547\pi$
$773$	−1.61558e10	−1.25806	−0.629028	+	0.777383i	$0.716547\pi$
$774$	3.25982e9	0.252697
$775$	−5.53708e8	−0.0427292
$776$	7.83057e8	0.0601557
$777$	2.17240e7	0.00166137
$778$	−1.35795e9	−0.103384
$779$	−6.45104e8	−0.0488932
$780$	1.21043e9	0.0913287
$781$	1.36316e9	0.102392
$782$	−8.71143e9	−0.651427
$783$	2.73631e9	0.203704
$784$	−2.82241e9	−0.209177
$785$	−1.00528e10	−0.741725
$786$	5.20133e7	0.00382064
$787$	8.30265e9	0.607163	0.303581	−	0.952805i	$-0.401818\pi$
$787$	8.30265e9	0.607163	0.303581	+	0.952805i	$0.401818\pi$
$788$	−4.02552e9	−0.293076
$789$	9.95824e8	0.0721793
$790$	−2.45264e9	−0.176986
$791$	8.83701e8	0.0634874
$792$	9.15310e7	0.00654682
$793$	−7.94655e9	−0.565878
$794$	−1.33971e10	−0.949818
$795$	−1.27103e9	−0.0897163
$796$	−1.17754e10	−0.827522
$797$	−1.75424e10	−1.22740	−0.613698	−	0.789541i	$-0.710319\pi$
$797$	−1.75424e10	−1.22740	−0.613698	+	0.789541i	$0.710319\pi$
$798$	−5.43301e8	−0.0378469
$799$	−4.64771e9	−0.322348
$800$	5.12000e8	0.0353553
$801$	9.38312e8	0.0645110
$802$	1.93373e10	1.32369
$803$	−8.88937e8	−0.0605852
$804$	3.59559e9	0.243991
$805$	−4.29905e9	−0.290461
$806$	1.58868e9	0.106872
$807$	7.03836e9	0.471426
$808$	−5.07033e9	−0.338140
$809$	4.64294e9	0.308300	0.154150	−	0.988047i	$-0.450736\pi$
$809$	4.64294e9	0.308300	0.154150	+	0.988047i	$0.450736\pi$
$810$	5.31441e8	0.0351364
$811$	1.76425e9	0.116142	0.0580708	−	0.998312i	$-0.481505\pi$
$811$	1.76425e9	0.116142	0.0580708	+	0.998312i	$0.481505\pi$
$812$	−3.26272e9	−0.213862
$813$	4.74651e9	0.309783
$814$	−4.30438e6	−0.000279721 0
$815$	−1.13941e10	−0.737274
$816$	−1.28406e9	−0.0827315
$817$	3.83386e9	0.245957
$818$	2.12429e9	0.135699
$819$	−1.49809e9	−0.0952894
$820$	−7.52418e8	−0.0476552
$821$	−2.60493e10	−1.64284	−0.821420	−	0.570324i	$-0.806818\pi$
$821$	−2.60493e10	−1.64284	−0.821420	+	0.570324i	$0.806818\pi$
$822$	1.13935e10	0.715494
$823$	2.78945e10	1.74429	0.872146	−	0.489246i	$-0.162728\pi$
$823$	2.78945e10	1.74429	0.872146	+	0.489246i	$0.162728\pi$
$824$	5.18380e9	0.322778
$825$	−1.03456e8	−0.00641454
$826$	−6.43998e9	−0.397608
$827$	−1.12799e10	−0.693485	−0.346742	−	0.937960i	$-0.612712\pi$
$827$	−1.12799e10	−0.693485	−0.346742	+	0.937960i	$0.612712\pi$
$828$	−4.37567e9	−0.267879
$829$	−1.95734e10	−1.19323	−0.596616	−	0.802527i	$-0.703489\pi$
$829$	−1.95734e10	−1.19323	−0.596616	+	0.802527i	$0.703489\pi$
$830$	1.88156e9	0.114220
$831$	8.11312e9	0.490438
$832$	−1.46901e9	−0.0884286
$833$	−8.00060e9	−0.479585
$834$	−8.61082e9	−0.514000
$835$	−1.58377e9	−0.0941435
$836$	1.07649e8	0.00637220
$837$	6.97512e8	0.0411162
$838$	4.61857e9	0.271115
$839$	−2.86271e9	−0.167344	−0.0836720	−	0.996493i	$-0.526665\pi$
$839$	−2.86271e9	−0.167344	−0.0836720	+	0.996493i	$0.526665\pi$
$840$	−6.33680e8	−0.0368886
$841$	2.07635e9	0.120369
$842$	2.08067e8	0.0120119
$843$	−1.55920e10	−0.896407
$844$	−1.08542e10	−0.621441
$845$	−3.91821e9	−0.223403
$846$	−2.33450e9	−0.132555
$847$	−7.12414e9	−0.402847
$848$	1.54256e9	0.0868675
$849$	−5.45874e9	−0.306137
$850$	1.45135e9	0.0810600
$851$	2.05772e8	0.0114455
$852$	−9.60548e9	−0.532084
$853$	3.16082e10	1.74373	0.871863	−	0.489750i	$-0.162912\pi$
$853$	3.16082e10	1.74373	0.871863	+	0.489750i	$0.162912\pi$
$854$	4.16016e9	0.228564
$855$	6.25026e8	0.0341993
$856$	−7.04684e9	−0.384004
$857$	5.94532e9	0.322658	0.161329	−	0.986901i	$-0.448422\pi$
$857$	5.94532e9	0.322658	0.161329	+	0.986901i	$0.448422\pi$
$858$	2.96831e8	0.0160437
$859$	1.64941e10	0.887875	0.443937	−	0.896058i	$-0.353581\pi$
$859$	1.64941e10	0.887875	0.443937	+	0.896058i	$0.353581\pi$
$860$	4.47163e9	0.239729
$861$	9.31234e8	0.0497219
$862$	6.32107e9	0.336136
$863$	−2.11340e10	−1.11930	−0.559648	−	0.828730i	$-0.689064\pi$
$863$	−2.11340e10	−1.11930	−0.559648	+	0.828730i	$0.689064\pi$
$864$	−6.44973e8	−0.0340207
$865$	1.08767e10	0.571401
$866$	−1.69415e10	−0.886418
$867$	7.43925e9	0.387670
$868$	−8.31700e8	−0.0431666
$869$	−6.01458e8	−0.0310911
$870$	3.75351e9	0.193250
$871$	1.16603e10	0.597926
$872$	4.13243e9	0.211056
$873$	1.11494e9	0.0567154
$874$	−5.14621e9	−0.260734
$875$	7.16236e8	0.0361433
$876$	6.26389e9	0.314833
$877$	2.68223e10	1.34276	0.671379	−	0.741114i	$-0.265702\pi$
$877$	2.68223e10	1.34276	0.671379	+	0.741114i	$0.265702\pi$
$878$	−4.52295e9	−0.225523
$879$	1.42884e10	0.709614
$880$	1.25557e8	0.00621086
$881$	−2.63018e9	−0.129590	−0.0647948	−	0.997899i	$-0.520639\pi$
$881$	−2.63018e9	−0.129590	−0.0647948	+	0.997899i	$0.520639\pi$
$882$	−4.01863e9	−0.197214
$883$	−1.01194e10	−0.494642	−0.247321	−	0.968934i	$-0.579550\pi$
$883$	−1.01194e10	−0.494642	−0.247321	+	0.968934i	$0.579550\pi$
$884$	−4.16416e9	−0.202742
$885$	7.40871e9	0.359287
$886$	−1.87958e10	−0.907912
$887$	−1.08537e10	−0.522212	−0.261106	−	0.965310i	$-0.584087\pi$
$887$	−1.08537e10	−0.522212	−0.261106	+	0.965310i	$0.584087\pi$
$888$	3.03308e7	0.00145358
$889$	−3.60886e9	−0.172272
$890$	1.28712e9	0.0612005
$891$	1.30324e8	0.00617240
$892$	9.65703e9	0.455582
$893$	−2.74560e9	−0.129020
$894$	−9.61140e9	−0.449889
$895$	−1.17961e10	−0.549992
$896$	7.69052e8	0.0357172
$897$	−1.41901e10	−0.656465
$898$	−8.71913e9	−0.401796
$899$	4.92645e9	0.226139
$900$	7.29000e8	0.0333333
$901$	4.37266e9	0.199163
$902$	−1.84514e8	−0.00837157
$903$	−5.53434e9	−0.250126
$904$	1.23381e9	0.0555469
$905$	−1.71793e10	−0.770433
$906$	−1.13989e10	−0.509232
$907$	4.10349e10	1.82611	0.913056	−	0.407834i	$-0.133716\pi$
$907$	4.10349e10	1.82611	0.913056	+	0.407834i	$0.133716\pi$
$908$	−1.73535e10	−0.769284
$909$	−7.21928e9	−0.318802
$910$	−2.05499e9	−0.0903994
$911$	−2.98641e10	−1.30868	−0.654342	−	0.756199i	$-0.727054\pi$
$911$	−2.98641e10	−1.30868	−0.654342	+	0.756199i	$0.727054\pi$
$912$	−7.58551e8	−0.0331133
$913$	4.61411e8	0.0200651
$914$	−2.94917e10	−1.27758
$915$	−4.78595e9	−0.206535
$916$	6.15070e9	0.264418
$917$	−8.83053e7	−0.00378176
$918$	−1.82829e9	−0.0780000
$919$	2.59453e10	1.10269	0.551346	−	0.834277i	$-0.314114\pi$
$919$	2.59453e10	1.10269	0.551346	+	0.834277i	$0.314114\pi$
$920$	−6.00229e9	−0.254132
$921$	−1.43921e10	−0.607035
$922$	1.93681e10	0.813823
$923$	−3.11501e10	−1.30393
$924$	−1.55396e8	−0.00648020
$925$	−3.42823e7	−0.00142421
$926$	3.32858e10	1.37759
$927$	7.38085e9	0.304318
$928$	−4.55537e9	−0.187114
$929$	−3.56736e10	−1.45979	−0.729897	−	0.683557i	$-0.760432\pi$
$929$	−3.56736e10	−1.45979	−0.729897	+	0.683557i	$0.760432\pi$
$930$	9.56807e8	0.0390062
$931$	−4.72630e9	−0.191954
$932$	2.74453e9	0.111048
$933$	1.29989e10	0.523987
$934$	−3.33971e10	−1.34120
$935$	3.55913e8	0.0142398
$936$	−2.09162e9	−0.0833713
$937$	−4.07302e10	−1.61744	−0.808720	−	0.588194i	$-0.799839\pi$
$937$	−4.07302e10	−1.61744	−0.808720	+	0.588194i	$0.799839\pi$
$938$	−6.10439e9	−0.241508
$939$	−7.84365e9	−0.309164
$940$	−3.20233e9	−0.125753
$941$	8.40974e9	0.329018	0.164509	−	0.986376i	$-0.447396\pi$
$941$	8.40974e9	0.329018	0.164509	+	0.986376i	$0.447396\pi$
$942$	1.73712e10	0.677099
$943$	8.82076e9	0.342543
$944$	−8.99143e9	−0.347878
$945$	−9.02251e8	−0.0347789
$946$	1.09657e9	0.0421131
$947$	−3.10726e10	−1.18892	−0.594460	−	0.804125i	$-0.702634\pi$
$947$	−3.10726e10	−1.18892	−0.594460	+	0.804125i	$0.702634\pi$
$948$	4.23817e9	0.161566
$949$	2.03135e10	0.771531
$950$	8.57375e8	0.0324443
$951$	7.58707e9	0.286050
$952$	2.18001e9	0.0818897
$953$	−2.66578e10	−0.997699	−0.498849	−	0.866689i	$-0.666244\pi$
$953$	−2.66578e10	−0.997699	−0.498849	+	0.866689i	$0.666244\pi$
$954$	2.19634e9	0.0818994
$955$	−9.77797e9	−0.363276
$956$	−4.46306e9	−0.165207
$957$	9.20467e8	0.0339482
$958$	2.11320e10	0.776536
$959$	−1.93433e10	−0.708214
$960$	−8.84736e8	−0.0322749
$961$	−2.62568e10	−0.954355
$962$	9.83614e7	0.00356215
$963$	−1.00335e10	−0.362043
$964$	−4.84100e9	−0.174046
$965$	7.66880e9	0.274715
$966$	7.42877e9	0.265153
$967$	−3.55676e10	−1.26492	−0.632458	−	0.774595i	$-0.717954\pi$
$967$	−3.55676e10	−1.26492	−0.632458	+	0.774595i	$0.717954\pi$
$968$	−9.94664e9	−0.352462
$969$	−2.15024e9	−0.0759196
$970$	1.52941e9	0.0538049
$971$	1.00433e10	0.352055	0.176028	−	0.984385i	$-0.443675\pi$
$971$	1.00433e10	0.352055	0.176028	+	0.984385i	$0.443675\pi$
$972$	−9.18330e8	−0.0320750
$973$	1.46190e10	0.508771
$974$	8.28054e9	0.287146
$975$	2.36411e9	0.0816868
$976$	5.80837e9	0.199977
$977$	−3.37487e10	−1.15778	−0.578890	−	0.815406i	$-0.696514\pi$
$977$	−3.37487e10	−1.15778	−0.578890	+	0.815406i	$0.696514\pi$
$978$	1.96890e10	0.673036
$979$	3.15639e8	0.0107511
$980$	−5.51252e9	−0.187094
$981$	5.88387e9	0.198986
$982$	−8.47588e8	−0.0285624
$983$	−5.03360e10	−1.69021	−0.845107	−	0.534598i	$-0.820463\pi$
$983$	−5.03360e10	−1.69021	−0.845107	+	0.534598i	$0.820463\pi$
$984$	1.30018e9	0.0435031
$985$	−7.86234e9	−0.262135
$986$	−1.29130e10	−0.429000
$987$	3.96338e9	0.131207
$988$	−2.45994e9	−0.0811477
$989$	−5.24219e10	−1.72316
$990$	1.78772e8	0.00585565
$991$	3.13247e10	1.02242	0.511209	−	0.859456i	$-0.329198\pi$
$991$	3.13247e10	1.02242	0.511209	+	0.859456i	$0.329198\pi$
$992$	−1.16121e9	−0.0377676
$993$	−1.17666e10	−0.381353
$994$	1.63077e10	0.526671
$995$	−2.29988e10	−0.740158
$996$	−3.25133e9	−0.104269
$997$	1.78772e10	0.571303	0.285651	−	0.958334i	$-0.407790\pi$
$997$	1.78772e10	0.571303	0.285651	+	0.958334i	$0.407790\pi$
$998$	5.55463e9	0.176888
$999$	4.31858e7	0.00137045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.8.a.a.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.8.a.a.1.4	✓	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} -216.000 q^{6} +366.713 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} -216.000 q^{6} +366.713 q^{7} +512.000 q^{8} +729.000 q^{9} +1000.00 q^{10} +245.228 q^{11} -1728.00 q^{12} -5603.82 q^{13} +2933.70 q^{14} -3375.00 q^{15} +4096.00 q^{16} +11610.8 q^{17} +5832.00 q^{18} +6859.00 q^{19} +8000.00 q^{20} -9901.24 q^{21} +1961.83 q^{22} -93785.8 q^{23} -13824.0 q^{24} +15625.0 q^{25} -44830.6 q^{26} -19683.0 q^{27} +23469.6 q^{28} -139019. q^{29} -27000.0 q^{30} -35437.3 q^{31} +32768.0 q^{32} -6621.17 q^{33} +92886.5 q^{34} +45839.1 q^{35} +46656.0 q^{36} -2194.07 q^{37} +54872.0 q^{38} +151303. q^{39} +64000.0 q^{40} -94052.2 q^{41} -79210.0 q^{42} +558954. q^{43} +15694.6 q^{44} +91125.0 q^{45} -750286. q^{46} -400292. q^{47} -110592. q^{48} -689065. q^{49} +125000. q^{50} -313492. q^{51} -358645. q^{52} +376602. q^{53} -157464. q^{54} +30653.6 q^{55} +187757. q^{56} -185193. q^{57} -1.11215e6 q^{58} -2.19517e6 q^{59} -216000. q^{60} +1.41806e6 q^{61} -283498. q^{62} +267334. q^{63} +262144. q^{64} -700478. q^{65} -52969.3 q^{66} -2.08078e6 q^{67} +743092. q^{68} +2.53222e6 q^{69} +366713. q^{70} +5.55873e6 q^{71} +373248. q^{72} -3.62494e6 q^{73} -17552.5 q^{74} -421875. q^{75} +438976. q^{76} +89928.4 q^{77} +1.21043e6 q^{78} -2.45264e6 q^{79} +512000. q^{80} +531441. q^{81} -752418. q^{82} +1.88156e6 q^{83} -633680. q^{84} +1.45135e6 q^{85} +4.47163e6 q^{86} +3.75351e6 q^{87} +125557. q^{88} +1.28712e6 q^{89} +729000. q^{90} -2.05499e6 q^{91} -6.00229e6 q^{92} +956807. q^{93} -3.20233e6 q^{94} +857375. q^{95} -884736. q^{96} +1.52941e6 q^{97} -5.51252e6 q^{98} +178772. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} - 108 q^{3} + 256 q^{4} + 500 q^{5} - 864 q^{6} - 1496 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) \) 4 * q + 32 * q^2 - 108 * q^3 + 256 * q^4 + 500 * q^5 - 864 * q^6 - 1496 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} - 108 q^{3} + 256 q^{4} + 500 q^{5} - 864 q^{6} - 1496 q^{7} + 2048 q^{8} + 2916 q^{9} + 4000 q^{10} - 2912 q^{11} - 6912 q^{12} - 3696 q^{13} - 11968 q^{14} - 13500 q^{15} + 16384 q^{16} + 16 q^{17} + 23328 q^{18} + 27436 q^{19} + 32000 q^{20} + 40392 q^{21} - 23296 q^{22} - 73016 q^{23} - 55296 q^{24} + 62500 q^{25} - 29568 q^{26} - 78732 q^{27} - 95744 q^{28} - 137784 q^{29} - 108000 q^{30} + 198072 q^{31} + 131072 q^{32} + 78624 q^{33} + 128 q^{34} - 187000 q^{35} + 186624 q^{36} + 207256 q^{37} + 219488 q^{38} + 99792 q^{39} + 256000 q^{40} - 504056 q^{41} + 323136 q^{42} - 250368 q^{43} - 186368 q^{44} + 364500 q^{45} - 584128 q^{46} - 1000376 q^{47} - 442368 q^{48} - 940908 q^{49} + 500000 q^{50} - 432 q^{51} - 236544 q^{52} - 2178688 q^{53} - 629856 q^{54} - 364000 q^{55} - 765952 q^{56} - 740772 q^{57} - 1102272 q^{58} + 327976 q^{59} - 864000 q^{60} + 572936 q^{61} + 1584576 q^{62} - 1090584 q^{63} + 1048576 q^{64} - 462000 q^{65} + 628992 q^{66} + 2017152 q^{67} + 1024 q^{68} + 1971432 q^{69} - 1496000 q^{70} + 2828960 q^{71} + 1492992 q^{72} - 132392 q^{73} + 1658048 q^{74} - 1687500 q^{75} + 1755904 q^{76} - 2304704 q^{77} + 798336 q^{78} + 3418408 q^{79} + 2048000 q^{80} + 2125764 q^{81} - 4032448 q^{82} - 3201760 q^{83} + 2585088 q^{84} + 2000 q^{85} - 2002944 q^{86} + 3720168 q^{87} - 1490944 q^{88} - 1389392 q^{89} + 2916000 q^{90} - 7865280 q^{91} - 4673024 q^{92} - 5347944 q^{93} - 8003008 q^{94} + 3429500 q^{95} - 3538944 q^{96} - 21061144 q^{97} - 7527264 q^{98} - 2122848 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 - 108 * q^3 + 256 * q^4 + 500 * q^5 - 864 * q^6 - 1496 * q^7 + 2048 * q^8 + 2916 * q^9 + 4000 * q^10 - 2912 * q^11 - 6912 * q^12 - 3696 * q^13 - 11968 * q^14 - 13500 * q^15 + 16384 * q^16 + 16 * q^17 + 23328 * q^18 + 27436 * q^19 + 32000 * q^20 + 40392 * q^21 - 23296 * q^22 - 73016 * q^23 - 55296 * q^24 + 62500 * q^25 - 29568 * q^26 - 78732 * q^27 - 95744 * q^28 - 137784 * q^29 - 108000 * q^30 + 198072 * q^31 + 131072 * q^32 + 78624 * q^33 + 128 * q^34 - 187000 * q^35 + 186624 * q^36 + 207256 * q^37 + 219488 * q^38 + 99792 * q^39 + 256000 * q^40 - 504056 * q^41 + 323136 * q^42 - 250368 * q^43 - 186368 * q^44 + 364500 * q^45 - 584128 * q^46 - 1000376 * q^47 - 442368 * q^48 - 940908 * q^49 + 500000 * q^50 - 432 * q^51 - 236544 * q^52 - 2178688 * q^53 - 629856 * q^54 - 364000 * q^55 - 765952 * q^56 - 740772 * q^57 - 1102272 * q^58 + 327976 * q^59 - 864000 * q^60 + 572936 * q^61 + 1584576 * q^62 - 1090584 * q^63 + 1048576 * q^64 - 462000 * q^65 + 628992 * q^66 + 2017152 * q^67 + 1024 * q^68 + 1971432 * q^69 - 1496000 * q^70 + 2828960 * q^71 + 1492992 * q^72 - 132392 * q^73 + 1658048 * q^74 - 1687500 * q^75 + 1755904 * q^76 - 2304704 * q^77 + 798336 * q^78 + 3418408 * q^79 + 2048000 * q^80 + 2125764 * q^81 - 4032448 * q^82 - 3201760 * q^83 + 2585088 * q^84 + 2000 * q^85 - 2002944 * q^86 + 3720168 * q^87 - 1490944 * q^88 - 1389392 * q^89 + 2916000 * q^90 - 7865280 * q^91 - 4673024 * q^92 - 5347944 * q^93 - 8003008 * q^94 + 3429500 * q^95 - 3538944 * q^96 - 21061144 * q^97 - 7527264 * q^98 - 2122848 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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