LMFDB - Embedded newform 546.8.a.l.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,8,Mod(1,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, 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("546.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	546.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:	$170.562223914$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 122890x^{3} - 6160660x^{2} + 3465881625x + 278845474950 $ x^5 - 2x^4 - 122890x^3 - 6160660x^2 + 3465881625x + 278845474950
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$210.250$ of defining polynomial
Character	$\chi$	$=$	546.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +263.456 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +263.456 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +2107.65 q^{10} +5574.46 q^{11} -1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} -7113.32 q^{15} +4096.00 q^{16} -19070.2 q^{17} +5832.00 q^{18} -19543.7 q^{19} +16861.2 q^{20} +9261.00 q^{21} +44595.7 q^{22} -63087.9 q^{23} -13824.0 q^{24} -8715.87 q^{25} -17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +74872.3 q^{29} -56906.5 q^{30} +45637.1 q^{31} +32768.0 q^{32} -150511. q^{33} -152561. q^{34} -90365.5 q^{35} +46656.0 q^{36} -276845. q^{37} -156349. q^{38} +59319.0 q^{39} +134890. q^{40} -349498. q^{41} +74088.0 q^{42} -668528. q^{43} +356766. q^{44} +192060. q^{45} -504704. q^{46} +287641. q^{47} -110592. q^{48} +117649. q^{49} -69727.0 q^{50} +514895. q^{51} -140608. q^{52} +1.21785e6 q^{53} -157464. q^{54} +1.46863e6 q^{55} -175616. q^{56} +527679. q^{57} +598978. q^{58} -2.13736e6 q^{59} -455252. q^{60} -1.83100e6 q^{61} +365097. q^{62} -250047. q^{63} +262144. q^{64} -578813. q^{65} -1.20408e6 q^{66} +2.86498e6 q^{67} -1.22049e6 q^{68} +1.70337e6 q^{69} -722924. q^{70} +1.35747e6 q^{71} +373248. q^{72} +5.25847e6 q^{73} -2.21476e6 q^{74} +235328. q^{75} -1.25080e6 q^{76} -1.91204e6 q^{77} +474552. q^{78} -1.74898e6 q^{79} +1.07912e6 q^{80} +531441. q^{81} -2.79598e6 q^{82} +1.29216e6 q^{83} +592704. q^{84} -5.02415e6 q^{85} -5.34822e6 q^{86} -2.02155e6 q^{87} +2.85413e6 q^{88} -7.68026e6 q^{89} +1.53648e6 q^{90} +753571. q^{91} -4.03763e6 q^{92} -1.23220e6 q^{93} +2.30113e6 q^{94} -5.14890e6 q^{95} -884736. q^{96} -1.14020e7 q^{97} +941192. q^{98} +4.06378e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) $ 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9} - 2000 q^{10} + 659 q^{11} - 8640 q^{12} - 10985 q^{13} - 13720 q^{14} + 6750 q^{15} + 20480 q^{16} + 24575 q^{17} + 29160 q^{18} - 6446 q^{19} - 16000 q^{20} + 46305 q^{21} + 5272 q^{22} + 30268 q^{23} - 69120 q^{24} + 38965 q^{25} - 87880 q^{26} - 98415 q^{27} - 109760 q^{28} + 130950 q^{29} + 54000 q^{30} + 262979 q^{31} + 163840 q^{32} - 17793 q^{33} + 196600 q^{34} + 85750 q^{35} + 233280 q^{36} - 101549 q^{37} - 51568 q^{38} + 296595 q^{39} - 128000 q^{40} - 247328 q^{41} + 370440 q^{42} - 19092 q^{43} + 42176 q^{44} - 182250 q^{45} + 242144 q^{46} - 126419 q^{47} - 552960 q^{48} + 588245 q^{49} + 311720 q^{50} - 663525 q^{51} - 703040 q^{52} - 302793 q^{53} - 787320 q^{54} + 943985 q^{55} - 878080 q^{56} + 174042 q^{57} + 1047600 q^{58} - 2798636 q^{59} + 432000 q^{60} - 2493751 q^{61} + 2103832 q^{62} - 1250235 q^{63} + 1310720 q^{64} + 549250 q^{65} - 142344 q^{66} + 160188 q^{67} + 1572800 q^{68} - 817236 q^{69} + 686000 q^{70} + 3846088 q^{71} + 1866240 q^{72} + 5655872 q^{73} - 812392 q^{74} - 1052055 q^{75} - 412544 q^{76} - 226037 q^{77} + 2372760 q^{78} + 5647991 q^{79} - 1024000 q^{80} + 2657205 q^{81} - 1978624 q^{82} - 4607669 q^{83} + 2963520 q^{84} + 3873935 q^{85} - 152736 q^{86} - 3535650 q^{87} + 337408 q^{88} - 17424029 q^{89} - 1458000 q^{90} + 3767855 q^{91} + 1937152 q^{92} - 7100433 q^{93} - 1011352 q^{94} - 24593720 q^{95} - 4423680 q^{96} - 18380577 q^{97} + 4705960 q^{98} + 480411 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9 - 2000 * q^10 + 659 * q^11 - 8640 * q^12 - 10985 * q^13 - 13720 * q^14 + 6750 * q^15 + 20480 * q^16 + 24575 * q^17 + 29160 * q^18 - 6446 * q^19 - 16000 * q^20 + 46305 * q^21 + 5272 * q^22 + 30268 * q^23 - 69120 * q^24 + 38965 * q^25 - 87880 * q^26 - 98415 * q^27 - 109760 * q^28 + 130950 * q^29 + 54000 * q^30 + 262979 * q^31 + 163840 * q^32 - 17793 * q^33 + 196600 * q^34 + 85750 * q^35 + 233280 * q^36 - 101549 * q^37 - 51568 * q^38 + 296595 * q^39 - 128000 * q^40 - 247328 * q^41 + 370440 * q^42 - 19092 * q^43 + 42176 * q^44 - 182250 * q^45 + 242144 * q^46 - 126419 * q^47 - 552960 * q^48 + 588245 * q^49 + 311720 * q^50 - 663525 * q^51 - 703040 * q^52 - 302793 * q^53 - 787320 * q^54 + 943985 * q^55 - 878080 * q^56 + 174042 * q^57 + 1047600 * q^58 - 2798636 * q^59 + 432000 * q^60 - 2493751 * q^61 + 2103832 * q^62 - 1250235 * q^63 + 1310720 * q^64 + 549250 * q^65 - 142344 * q^66 + 160188 * q^67 + 1572800 * q^68 - 817236 * q^69 + 686000 * q^70 + 3846088 * q^71 + 1866240 * q^72 + 5655872 * q^73 - 812392 * q^74 - 1052055 * q^75 - 412544 * q^76 - 226037 * q^77 + 2372760 * q^78 + 5647991 * q^79 - 1024000 * q^80 + 2657205 * q^81 - 1978624 * q^82 - 4607669 * q^83 + 2963520 * q^84 + 3873935 * q^85 - 152736 * q^86 - 3535650 * q^87 + 337408 * q^88 - 17424029 * q^89 - 1458000 * q^90 + 3767855 * q^91 + 1937152 * q^92 - 7100433 * q^93 - 1011352 * q^94 - 24593720 * q^95 - 4423680 * q^96 - 18380577 * q^97 + 4705960 * q^98 + 480411 * 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
$5$	263.456	0.942569	0.471285	−	0.881981i	$-0.343790\pi$
$5$	263.456	0.942569	0.471285	+	0.881981i	$0.343790\pi$
$6$	−216.000	−0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	2107.65	0.666497
$11$	5574.46	1.26278	0.631391	−	0.775464i	$-0.282484\pi$
$11$	5574.46	1.26278	0.631391	+	0.775464i	$0.282484\pi$
$12$	−1728.00	−0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−2744.00	−0.267261
$15$	−7113.32	−0.544193
$16$	4096.00	0.250000
$17$	−19070.2	−0.941420	−0.470710	−	0.882288i	$-0.656002\pi$
$17$	−19070.2	−0.941420	−0.470710	+	0.882288i	$0.656002\pi$
$18$	5832.00	0.235702
$19$	−19543.7	−0.653685	−0.326843	−	0.945079i	$-0.605985\pi$
$19$	−19543.7	−0.653685	−0.326843	+	0.945079i	$0.605985\pi$
$20$	16861.2	0.471285
$21$	9261.00	0.218218
$22$	44595.7	0.892922
$23$	−63087.9	−1.08118	−0.540591	−	0.841285i	$-0.681799\pi$
$23$	−63087.9	−1.08118	−0.540591	+	0.841285i	$0.681799\pi$
$24$	−13824.0	−0.204124
$25$	−8715.87	−0.111563
$26$	−17576.0	−0.196116
$27$	−19683.0	−0.192450
$28$	−21952.0	−0.188982
$29$	74872.3	0.570070	0.285035	−	0.958517i	$-0.407995\pi$
$29$	74872.3	0.570070	0.285035	+	0.958517i	$0.407995\pi$
$30$	−56906.5	−0.384802
$31$	45637.1	0.275139	0.137569	−	0.990492i	$-0.456071\pi$
$31$	45637.1	0.275139	0.137569	+	0.990492i	$0.456071\pi$
$32$	32768.0	0.176777
$33$	−150511.	−0.729068
$34$	−152561.	−0.665684
$35$	−90365.5	−0.356258
$36$	46656.0	0.166667
$37$	−276845.	−0.898525	−0.449262	−	0.893400i	$-0.648313\pi$
$37$	−276845.	−0.898525	−0.449262	+	0.893400i	$0.648313\pi$
$38$	−156349.	−0.462225
$39$	59319.0	0.160128
$40$	134890.	0.333249
$41$	−349498.	−0.791956	−0.395978	−	0.918260i	$-0.629594\pi$
$41$	−349498.	−0.791956	−0.395978	+	0.918260i	$0.629594\pi$
$42$	74088.0	0.154303
$43$	−668528.	−1.28227	−0.641136	−	0.767427i	$-0.721536\pi$
$43$	−668528.	−1.28227	−0.641136	+	0.767427i	$0.721536\pi$
$44$	356766.	0.631391
$45$	192060.	0.314190
$46$	−504704.	−0.764511
$47$	287641.	0.404118	0.202059	−	0.979373i	$-0.435237\pi$
$47$	287641.	0.404118	0.202059	+	0.979373i	$0.435237\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	−69727.0	−0.0788870
$51$	514895.	0.543529
$52$	−140608.	−0.138675
$53$	1.21785e6	1.12364	0.561820	−	0.827259i	$-0.310101\pi$
$53$	1.21785e6	1.12364	0.561820	+	0.827259i	$0.310101\pi$
$54$	−157464.	−0.136083
$55$	1.46863e6	1.19026
$56$	−175616.	−0.133631
$57$	527679.	0.377405
$58$	598978.	0.403100
$59$	−2.13736e6	−1.35487	−0.677433	−	0.735585i	$-0.736908\pi$
$59$	−2.13736e6	−1.35487	−0.677433	+	0.735585i	$0.736908\pi$
$60$	−455252.	−0.272096
$61$	−1.83100e6	−1.03284	−0.516422	−	0.856334i	$-0.672736\pi$
$61$	−1.83100e6	−1.03284	−0.516422	+	0.856334i	$0.672736\pi$
$62$	365097.	0.194553
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	−578813.	−0.261422
$66$	−1.20408e6	−0.515529
$67$	2.86498e6	1.16375	0.581875	−	0.813279i	$-0.302319\pi$
$67$	2.86498e6	1.16375	0.581875	+	0.813279i	$0.302319\pi$
$68$	−1.22049e6	−0.470710
$69$	1.70337e6	0.624221
$70$	−722924.	−0.251912
$71$	1.35747e6	0.450118	0.225059	−	0.974345i	$-0.427743\pi$
$71$	1.35747e6	0.450118	0.225059	+	0.974345i	$0.427743\pi$
$72$	373248.	0.117851
$73$	5.25847e6	1.58208	0.791042	−	0.611762i	$-0.209539\pi$
$73$	5.25847e6	1.58208	0.791042	+	0.611762i	$0.209539\pi$
$74$	−2.21476e6	−0.635353
$75$	235328.	0.0644110
$76$	−1.25080e6	−0.326843
$77$	−1.91204e6	−0.477287
$78$	474552.	0.113228
$79$	−1.74898e6	−0.399108	−0.199554	−	0.979887i	$-0.563949\pi$
$79$	−1.74898e6	−0.399108	−0.199554	+	0.979887i	$0.563949\pi$
$80$	1.07912e6	0.235642
$81$	531441.	0.111111
$82$	−2.79598e6	−0.559997
$83$	1.29216e6	0.248053	0.124026	−	0.992279i	$-0.460419\pi$
$83$	1.29216e6	0.248053	0.124026	+	0.992279i	$0.460419\pi$
$84$	592704.	0.109109
$85$	−5.02415e6	−0.887353
$86$	−5.34822e6	−0.906703
$87$	−2.02155e6	−0.329130
$88$	2.85413e6	0.446461
$89$	−7.68026e6	−1.15481	−0.577405	−	0.816458i	$-0.695935\pi$
$89$	−7.68026e6	−1.15481	−0.577405	+	0.816458i	$0.695935\pi$
$90$	1.53648e6	0.222166
$91$	753571.	0.104828
$92$	−4.03763e6	−0.540591
$93$	−1.23220e6	−0.158851
$94$	2.30113e6	0.285755
$95$	−5.14890e6	−0.616144
$96$	−884736.	−0.102062
$97$	−1.14020e7	−1.26847	−0.634236	−	0.773140i	$-0.718685\pi$
$97$	−1.14020e7	−1.26847	−0.634236	+	0.773140i	$0.718685\pi$
$98$	941192.	0.101015
$99$	4.06378e6	0.420928
$100$	−557816.	−0.0557816
$101$	−3.20262e6	−0.309301	−0.154650	−	0.987969i	$-0.549425\pi$
$101$	−3.20262e6	−0.309301	−0.154650	+	0.987969i	$0.549425\pi$
$102$	4.11916e6	0.384333
$103$	−1.50537e7	−1.35742	−0.678710	−	0.734407i	$-0.737461\pi$
$103$	−1.50537e7	−1.35742	−0.678710	+	0.734407i	$0.737461\pi$
$104$	−1.12486e6	−0.0980581
$105$	2.43987e6	0.205685
$106$	9.74278e6	0.794534
$107$	−1.47806e7	−1.16641	−0.583203	−	0.812327i	$-0.698201\pi$
$107$	−1.47806e7	−1.16641	−0.583203	+	0.812327i	$0.698201\pi$
$108$	−1.25971e6	−0.0962250
$109$	2.16222e7	1.59922	0.799609	−	0.600521i	$-0.205040\pi$
$109$	2.16222e7	1.59922	0.799609	+	0.600521i	$0.205040\pi$
$110$	1.17490e7	0.841641
$111$	7.47481e6	0.518764
$112$	−1.40493e6	−0.0944911
$113$	−1.77990e7	−1.16044	−0.580219	−	0.814460i	$-0.697033\pi$
$113$	−1.77990e7	−1.16044	−0.580219	+	0.814460i	$0.697033\pi$
$114$	4.22143e6	0.266866
$115$	−1.66209e7	−1.01909
$116$	4.79183e6	0.285035
$117$	−1.60161e6	−0.0924500
$118$	−1.70989e7	−0.958035
$119$	6.54107e6	0.355823
$120$	−3.64202e6	−0.192401
$121$	1.15875e7	0.594620
$122$	−1.46480e7	−0.730331
$123$	9.43644e6	0.457236
$124$	2.92077e6	0.137569
$125$	−2.28788e7	−1.04773
$126$	−2.00038e6	−0.0890871
$127$	4.38389e7	1.89909	0.949547	−	0.313624i	$-0.101543\pi$
$127$	4.38389e7	1.89909	0.949547	+	0.313624i	$0.101543\pi$
$128$	2.09715e6	0.0883883
$129$	1.80503e7	0.740320
$130$	−4.63050e6	−0.184853
$131$	2.84654e7	1.10629	0.553144	−	0.833086i	$-0.313428\pi$
$131$	2.84654e7	1.10629	0.553144	+	0.833086i	$0.313428\pi$
$132$	−9.63267e6	−0.364534
$133$	6.70348e6	0.247070
$134$	2.29198e7	0.822895
$135$	−5.18561e6	−0.181398
$136$	−9.76393e6	−0.332842
$137$	1.31487e7	0.436878	0.218439	−	0.975851i	$-0.429904\pi$
$137$	1.31487e7	0.436878	0.218439	+	0.975851i	$0.429904\pi$
$138$	1.36270e7	0.441391
$139$	1.20103e7	0.379316	0.189658	−	0.981850i	$-0.439262\pi$
$139$	1.20103e7	0.379316	0.189658	+	0.981850i	$0.439262\pi$
$140$	−5.78339e6	−0.178129
$141$	−7.76631e6	−0.233318
$142$	1.08598e7	0.318281
$143$	−1.22471e7	−0.350233
$144$	2.98598e6	0.0833333
$145$	1.97256e7	0.537330
$146$	4.20678e7	1.11870
$147$	−3.17652e6	−0.0824786
$148$	−1.77181e7	−0.449262
$149$	−5.09532e7	−1.26188	−0.630942	−	0.775830i	$-0.717331\pi$
$149$	−5.09532e7	−1.26188	−0.630942	+	0.775830i	$0.717331\pi$
$150$	1.88263e6	0.0455455
$151$	−5.99649e7	−1.41735	−0.708677	−	0.705533i	$-0.750707\pi$
$151$	−5.99649e7	−1.41735	−0.708677	+	0.705533i	$0.750707\pi$
$152$	−1.00064e7	−0.231113
$153$	−1.39022e7	−0.313807
$154$	−1.52963e7	−0.337493
$155$	1.20234e7	0.259337
$156$	3.79642e6	0.0800641
$157$	−4.92495e7	−1.01567	−0.507835	−	0.861454i	$-0.669554\pi$
$157$	−4.92495e7	−1.01567	−0.507835	+	0.861454i	$0.669554\pi$
$158$	−1.39918e7	−0.282212
$159$	−3.28819e7	−0.648734
$160$	8.63293e6	0.166624
$161$	2.16392e7	0.408649
$162$	4.25153e6	0.0785674
$163$	4.61007e7	0.833779	0.416889	−	0.908957i	$-0.363120\pi$
$163$	4.61007e7	0.833779	0.416889	+	0.908957i	$0.363120\pi$
$164$	−2.23679e7	−0.395978
$165$	−3.96529e7	−0.687197
$166$	1.03373e7	0.175400
$167$	−2.59973e7	−0.431937	−0.215968	−	0.976400i	$-0.569291\pi$
$167$	−2.59973e7	−0.431937	−0.215968	+	0.976400i	$0.569291\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	−4.01932e7	−0.627454
$171$	−1.42473e7	−0.217895
$172$	−4.27858e7	−0.641136
$173$	3.75765e7	0.551766	0.275883	−	0.961191i	$-0.411030\pi$
$173$	3.75765e7	0.551766	0.275883	+	0.961191i	$0.411030\pi$
$174$	−1.61724e7	−0.232730
$175$	2.98954e6	0.0421669
$176$	2.28330e7	0.315696
$177$	5.77088e7	0.782232
$178$	−6.14421e7	−0.816574
$179$	−1.28522e8	−1.67491	−0.837454	−	0.546507i	$-0.815957\pi$
$179$	−1.28522e8	−1.67491	−0.837454	+	0.546507i	$0.815957\pi$
$180$	1.22918e7	0.157095
$181$	6.68089e7	0.837451	0.418726	−	0.908113i	$-0.362477\pi$
$181$	6.68089e7	0.837451	0.418726	+	0.908113i	$0.362477\pi$
$182$	6.02857e6	0.0741249
$183$	4.94371e7	0.596313
$184$	−3.23010e7	−0.382256
$185$	−7.29364e7	−0.846922
$186$	−9.85761e6	−0.112325
$187$	−1.06306e8	−1.18881
$188$	1.84090e7	0.202059
$189$	6.75127e6	0.0727393
$190$	−4.11912e7	−0.435679
$191$	−2.91485e7	−0.302690	−0.151345	−	0.988481i	$-0.548361\pi$
$191$	−2.91485e7	−0.302690	−0.151345	+	0.988481i	$0.548361\pi$
$192$	−7.07789e6	−0.0721688
$193$	7.54119e7	0.755074	0.377537	−	0.925995i	$-0.376771\pi$
$193$	7.54119e7	0.755074	0.377537	+	0.925995i	$0.376771\pi$
$194$	−9.12162e7	−0.896945
$195$	1.56280e7	0.150932
$196$	7.52954e6	0.0714286
$197$	−1.04770e8	−0.976347	−0.488173	−	0.872747i	$-0.662337\pi$
$197$	−1.04770e8	−0.976347	−0.488173	+	0.872747i	$0.662337\pi$
$198$	3.25103e7	0.297641
$199$	−9.99628e7	−0.899192	−0.449596	−	0.893232i	$-0.648432\pi$
$199$	−9.99628e7	−0.899192	−0.449596	+	0.893232i	$0.648432\pi$
$200$	−4.46253e6	−0.0394435
$201$	−7.73544e7	−0.671891
$202$	−2.56210e7	−0.218709
$203$	−2.56812e7	−0.215466
$204$	3.29532e7	0.271764
$205$	−9.20773e7	−0.746473
$206$	−1.20430e8	−0.959841
$207$	−4.59911e7	−0.360394
$208$	−8.99891e6	−0.0693375
$209$	−1.08945e8	−0.825462
$210$	1.95189e7	0.145442
$211$	−1.01353e8	−0.742759	−0.371379	−	0.928481i	$-0.621115\pi$
$211$	−1.01353e8	−0.742759	−0.371379	+	0.928481i	$0.621115\pi$
$212$	7.79423e7	0.561820
$213$	−3.66517e7	−0.259876
$214$	−1.18245e8	−0.824773
$215$	−1.76128e8	−1.20863
$216$	−1.00777e7	−0.0680414
$217$	−1.56535e7	−0.103993
$218$	1.72978e8	1.13082
$219$	−1.41979e8	−0.913416
$220$	9.39921e7	0.595130
$221$	4.18972e7	0.261103
$222$	5.97984e7	0.366821
$223$	6.73090e7	0.406449	0.203224	−	0.979132i	$-0.434858\pi$
$223$	6.73090e7	0.406449	0.203224	+	0.979132i	$0.434858\pi$
$224$	−1.12394e7	−0.0668153
$225$	−6.35387e6	−0.0371877
$226$	−1.42392e8	−0.820554
$227$	−8.87366e7	−0.503515	−0.251757	−	0.967790i	$-0.581009\pi$
$227$	−8.87366e7	−0.503515	−0.251757	+	0.967790i	$0.581009\pi$
$228$	3.37715e7	0.188703
$229$	−1.40808e8	−0.774824	−0.387412	−	0.921907i	$-0.626631\pi$
$229$	−1.40808e8	−0.774824	−0.387412	+	0.921907i	$0.626631\pi$
$230$	−1.32967e8	−0.720605
$231$	5.16251e7	0.275562
$232$	3.83346e7	0.201550
$233$	−2.57726e7	−0.133479	−0.0667395	−	0.997770i	$-0.521260\pi$
$233$	−2.57726e7	−0.133479	−0.0667395	+	0.997770i	$0.521260\pi$
$234$	−1.28129e7	−0.0653720
$235$	7.57808e7	0.380909
$236$	−1.36791e8	−0.677433
$237$	4.72225e7	0.230425
$238$	5.23285e7	0.251605
$239$	−1.78752e8	−0.846953	−0.423476	−	0.905907i	$-0.639190\pi$
$239$	−1.78752e8	−0.846953	−0.423476	+	0.905907i	$0.639190\pi$
$240$	−2.91361e7	−0.136048
$241$	−1.48745e8	−0.684514	−0.342257	−	0.939606i	$-0.611191\pi$
$241$	−1.48745e8	−0.684514	−0.342257	+	0.939606i	$0.611191\pi$
$242$	9.26998e7	0.420460
$243$	−1.43489e7	−0.0641500
$244$	−1.17184e8	−0.516422
$245$	3.09953e7	0.134653
$246$	7.54915e7	0.323315
$247$	4.29375e7	0.181300
$248$	2.33662e7	0.0972763
$249$	−3.48884e7	−0.143213
$250$	−1.83030e8	−0.740854
$251$	1.71509e6	0.00684589	0.00342294	−	0.999994i	$-0.498910\pi$
$251$	1.71509e6	0.00684589	0.00342294	+	0.999994i	$0.498910\pi$
$252$	−1.60030e7	−0.0629941
$253$	−3.51681e8	−1.36530
$254$	3.50711e8	1.34286
$255$	1.35652e8	0.512314
$256$	1.67772e7	0.0625000
$257$	4.50094e8	1.65401	0.827003	−	0.562198i	$-0.190044\pi$
$257$	4.50094e8	1.65401	0.827003	+	0.562198i	$0.190044\pi$
$258$	1.44402e8	0.523485
$259$	9.49577e7	0.339610
$260$	−3.70440e7	−0.130711
$261$	5.45819e7	0.190023
$262$	2.27723e8	0.782264
$263$	−3.42907e8	−1.16233	−0.581167	−	0.813784i	$-0.697404\pi$
$263$	−3.42907e8	−1.16233	−0.581167	+	0.813784i	$0.697404\pi$
$264$	−7.70614e7	−0.257764
$265$	3.20849e8	1.05911
$266$	5.36278e7	0.174705
$267$	2.07367e8	0.666730
$268$	1.83359e8	0.581875
$269$	−4.68870e8	−1.46866	−0.734328	−	0.678795i	$-0.762502\pi$
$269$	−4.68870e8	−1.46866	−0.734328	+	0.678795i	$0.762502\pi$
$270$	−4.14849e7	−0.128267
$271$	−5.41400e8	−1.65244	−0.826221	−	0.563347i	$-0.809514\pi$
$271$	−5.41400e8	−1.65244	−0.826221	+	0.563347i	$0.809514\pi$
$272$	−7.81114e7	−0.235355
$273$	−2.03464e7	−0.0605228
$274$	1.05189e8	0.308919
$275$	−4.85863e7	−0.140880
$276$	1.09016e8	0.312110
$277$	−2.10914e8	−0.596246	−0.298123	−	0.954528i	$-0.596361\pi$
$277$	−2.10914e8	−0.596246	−0.298123	+	0.954528i	$0.596361\pi$
$278$	9.60822e7	0.268217
$279$	3.32694e7	0.0917130
$280$	−4.62671e7	−0.125956
$281$	−2.34658e8	−0.630903	−0.315451	−	0.948942i	$-0.602156\pi$
$281$	−2.34658e8	−0.630903	−0.315451	+	0.948942i	$0.602156\pi$
$282$	−6.21305e7	−0.164981
$283$	2.75003e7	0.0721250	0.0360625	−	0.999350i	$-0.488518\pi$
$283$	2.75003e7	0.0721250	0.0360625	+	0.999350i	$0.488518\pi$
$284$	8.68781e7	0.225059
$285$	1.39020e8	0.355731
$286$	−9.79768e7	−0.247652
$287$	1.19878e8	0.299331
$288$	2.38879e7	0.0589256
$289$	−4.66674e7	−0.113729
$290$	1.57804e8	0.379950
$291$	3.07855e8	0.732352
$292$	3.36542e8	0.791042
$293$	−1.28713e8	−0.298942	−0.149471	−	0.988766i	$-0.547757\pi$
$293$	−1.28713e8	−0.298942	−0.149471	+	0.988766i	$0.547757\pi$
$294$	−2.54122e7	−0.0583212
$295$	−5.63101e8	−1.27705
$296$	−1.41744e8	−0.317677
$297$	−1.09722e8	−0.243023
$298$	−4.07626e8	−0.892287
$299$	1.38604e8	0.299866
$300$	1.50610e7	0.0322055
$301$	2.29305e8	0.484653
$302$	−4.79720e8	−1.00222
$303$	8.64708e7	0.178575
$304$	−8.00509e7	−0.163421
$305$	−4.82389e8	−0.973527
$306$	−1.11217e8	−0.221895
$307$	8.35699e8	1.64841	0.824205	−	0.566291i	$-0.191622\pi$
$307$	8.35699e8	1.64841	0.824205	+	0.566291i	$0.191622\pi$
$308$	−1.22371e8	−0.238644
$309$	4.06451e8	0.783707
$310$	9.61869e7	0.183379
$311$	1.17507e8	0.221514	0.110757	−	0.993848i	$-0.464673\pi$
$311$	1.17507e8	0.221514	0.110757	+	0.993848i	$0.464673\pi$
$312$	3.03713e7	0.0566139
$313$	1.89299e8	0.348934	0.174467	−	0.984663i	$-0.444180\pi$
$313$	1.89299e8	0.348934	0.174467	+	0.984663i	$0.444180\pi$
$314$	−3.93996e8	−0.718187
$315$	−6.58764e7	−0.118753
$316$	−1.11935e8	−0.199554
$317$	−2.62354e8	−0.462573	−0.231286	−	0.972886i	$-0.574293\pi$
$317$	−2.62354e8	−0.462573	−0.231286	+	0.972886i	$0.574293\pi$
$318$	−2.63055e8	−0.458724
$319$	4.17373e8	0.719874
$320$	6.90634e7	0.117821
$321$	3.99077e8	0.673425
$322$	1.73113e8	0.288958
$323$	3.72701e8	0.615392
$324$	3.40122e7	0.0555556
$325$	1.91488e7	0.0309420
$326$	3.68805e8	0.589570
$327$	−5.83800e8	−0.923309
$328$	−1.78943e8	−0.279999
$329$	−9.86609e7	−0.152742
$330$	−3.17223e8	−0.485922
$331$	9.94130e8	1.50676	0.753382	−	0.657583i	$-0.228421\pi$
$331$	9.94130e8	1.50676	0.753382	+	0.657583i	$0.228421\pi$
$332$	8.26985e7	0.124026
$333$	−2.01820e8	−0.299508
$334$	−2.07978e8	−0.305425
$335$	7.54796e8	1.09691
$336$	3.79331e7	0.0545545
$337$	−1.00930e9	−1.43653	−0.718263	−	0.695772i	$-0.755063\pi$
$337$	−1.00930e9	−1.43653	−0.718263	+	0.695772i	$0.755063\pi$
$338$	3.86145e7	0.0543928
$339$	4.80574e8	0.669979
$340$	−3.21546e8	−0.443677
$341$	2.54402e8	0.347441
$342$	−1.13979e8	−0.154075
$343$	−4.03536e7	−0.0539949
$344$	−3.42286e8	−0.453351
$345$	4.48764e8	0.588372
$346$	3.00612e8	0.390158
$347$	1.38853e9	1.78403	0.892014	−	0.452008i	$-0.149292\pi$
$347$	1.38853e9	1.78403	0.892014	+	0.452008i	$0.149292\pi$
$348$	−1.29379e8	−0.164565
$349$	−7.71775e8	−0.971855	−0.485928	−	0.873999i	$-0.661518\pi$
$349$	−7.71775e8	−0.971855	−0.485928	+	0.873999i	$0.661518\pi$
$350$	2.39163e7	0.0298165
$351$	4.32436e7	0.0533761
$352$	1.82664e8	0.223231
$353$	−9.89349e8	−1.19712	−0.598561	−	0.801078i	$-0.704260\pi$
$353$	−9.89349e8	−1.19712	−0.598561	+	0.801078i	$0.704260\pi$
$354$	4.61670e8	0.553122
$355$	3.57634e8	0.424267
$356$	−4.91537e8	−0.577405
$357$	−1.76609e8	−0.205435
$358$	−1.02817e9	−1.18434
$359$	3.13046e8	0.357089	0.178545	−	0.983932i	$-0.442861\pi$
$359$	3.13046e8	0.357089	0.178545	+	0.983932i	$0.442861\pi$
$360$	9.83345e7	0.111083
$361$	−5.11917e8	−0.572696
$362$	5.34471e8	0.592167
$363$	−3.12862e8	−0.343304
$364$	4.82285e7	0.0524142
$365$	1.38538e9	1.49122
$366$	3.95497e8	0.421657
$367$	3.48032e8	0.367526	0.183763	−	0.982971i	$-0.441172\pi$
$367$	3.48032e8	0.367526	0.183763	+	0.982971i	$0.441172\pi$
$368$	−2.58408e8	−0.270296
$369$	−2.54784e8	−0.263985
$370$	−5.83491e8	−0.598864
$371$	−4.17722e8	−0.424696
$372$	−7.88609e7	−0.0794257
$373$	2.58649e8	0.258066	0.129033	−	0.991640i	$-0.458813\pi$
$373$	2.58649e8	0.258066	0.129033	+	0.991640i	$0.458813\pi$
$374$	−8.50448e8	−0.840615
$375$	6.17726e8	0.604904
$376$	1.47272e8	0.142877
$377$	−1.64494e8	−0.158109
$378$	5.40102e7	0.0514344
$379$	−1.11110e8	−0.104838	−0.0524188	−	0.998625i	$-0.516693\pi$
$379$	−1.11110e8	−0.104838	−0.0524188	+	0.998625i	$0.516693\pi$
$380$	−3.29530e8	−0.308072
$381$	−1.18365e9	−1.09644
$382$	−2.33188e8	−0.214034
$383$	1.18327e9	1.07619	0.538093	−	0.842885i	$-0.319145\pi$
$383$	1.18327e9	1.07619	0.538093	+	0.842885i	$0.319145\pi$
$384$	−5.66231e7	−0.0510310
$385$	−5.03739e8	−0.449876
$386$	6.03295e8	0.533918
$387$	−4.87357e8	−0.427424
$388$	−7.29729e8	−0.634236
$389$	1.96988e9	1.69674	0.848370	−	0.529403i	$-0.177584\pi$
$389$	1.96988e9	1.69674	0.848370	+	0.529403i	$0.177584\pi$
$390$	1.25024e8	0.106725
$391$	1.20310e9	1.01785
$392$	6.02363e7	0.0505076
$393$	−7.68567e8	−0.638716
$394$	−8.38158e8	−0.690381
$395$	−4.60779e8	−0.376187
$396$	2.60082e8	0.210464
$397$	9.43174e8	0.756528	0.378264	−	0.925698i	$-0.376521\pi$
$397$	9.43174e8	0.756528	0.378264	+	0.925698i	$0.376521\pi$
$398$	−7.99702e8	−0.635825
$399$	−1.80994e8	−0.142646
$400$	−3.57002e7	−0.0278908
$401$	−2.34976e9	−1.81977	−0.909887	−	0.414856i	$-0.863832\pi$
$401$	−2.34976e9	−1.81977	−0.909887	+	0.414856i	$0.863832\pi$
$402$	−6.18835e8	−0.475099
$403$	−1.00265e8	−0.0763098
$404$	−2.04968e8	−0.154650
$405$	1.40011e8	0.104730
$406$	−2.05450e8	−0.152358
$407$	−1.54326e9	−1.13464
$408$	2.63626e8	0.192166
$409$	3.64018e8	0.263082	0.131541	−	0.991311i	$-0.458008\pi$
$409$	3.64018e8	0.263082	0.131541	+	0.991311i	$0.458008\pi$
$410$	−7.36619e8	−0.527836
$411$	−3.55014e8	−0.252232
$412$	−9.63439e8	−0.678710
$413$	7.33115e8	0.512091
$414$	−3.67929e8	−0.254837
$415$	3.40429e8	0.233807
$416$	−7.19913e7	−0.0490290
$417$	−3.24277e8	−0.218998
$418$	−8.71564e8	−0.583690
$419$	−1.96458e9	−1.30473	−0.652365	−	0.757905i	$-0.726223\pi$
$419$	−1.96458e9	−1.30473	−0.652365	+	0.757905i	$0.726223\pi$
$420$	1.56152e8	0.102843
$421$	−2.96665e8	−0.193767	−0.0968834	−	0.995296i	$-0.530887\pi$
$421$	−2.96665e8	−0.193767	−0.0968834	+	0.995296i	$0.530887\pi$
$422$	−8.10823e8	−0.525210
$423$	2.09690e8	0.134706
$424$	6.23538e8	0.397267
$425$	1.66213e8	0.105028
$426$	−2.93214e8	−0.183760
$427$	6.28034e8	0.390379
$428$	−9.45960e8	−0.583203
$429$	3.30672e8	0.202207
$430$	−1.40902e9	−0.854630
$431$	−9.30837e6	−0.00560020	−0.00280010	−	0.999996i	$-0.500891\pi$
$431$	−9.30837e6	−0.00560020	−0.00280010	+	0.999996i	$0.500891\pi$
$432$	−8.06216e7	−0.0481125
$433$	7.68807e7	0.0455103	0.0227551	−	0.999741i	$-0.492756\pi$
$433$	7.68807e7	0.0455103	0.0227551	+	0.999741i	$0.492756\pi$
$434$	−1.25228e8	−0.0735340
$435$	−5.32590e8	−0.310228
$436$	1.38382e9	0.799609
$437$	1.23297e9	0.706753
$438$	−1.13583e9	−0.645883
$439$	−1.38140e9	−0.779280	−0.389640	−	0.920967i	$-0.627401\pi$
$439$	−1.38140e9	−0.779280	−0.389640	+	0.920967i	$0.627401\pi$
$440$	7.51937e8	0.420821
$441$	8.57661e7	0.0476190
$442$	3.35177e8	0.184628
$443$	2.24579e9	1.22732	0.613658	−	0.789572i	$-0.289697\pi$
$443$	2.24579e9	1.22732	0.613658	+	0.789572i	$0.289697\pi$
$444$	4.78388e8	0.259382
$445$	−2.02341e9	−1.08849
$446$	5.38472e8	0.287403
$447$	1.37574e9	0.728549
$448$	−8.99154e7	−0.0472456
$449$	−2.96518e9	−1.54593	−0.772964	−	0.634450i	$-0.781226\pi$
$449$	−2.96518e9	−1.54593	−0.772964	+	0.634450i	$0.781226\pi$
$450$	−5.08309e7	−0.0262957
$451$	−1.94826e9	−1.00007
$452$	−1.13914e9	−0.580219
$453$	1.61905e9	0.818309
$454$	−7.09893e8	−0.356039
$455$	1.98533e8	0.0988081
$456$	2.70172e8	0.133433
$457$	3.26323e9	1.59934	0.799670	−	0.600440i	$-0.205008\pi$
$457$	3.26323e9	1.59934	0.799670	+	0.600440i	$0.205008\pi$
$458$	−1.12646e9	−0.547884
$459$	3.75358e8	0.181176
$460$	−1.06374e9	−0.509545
$461$	5.60770e8	0.266583	0.133291	−	0.991077i	$-0.457445\pi$
$461$	5.60770e8	0.266583	0.133291	+	0.991077i	$0.457445\pi$
$462$	4.13001e8	0.194852
$463$	3.28678e9	1.53900	0.769498	−	0.638650i	$-0.220507\pi$
$463$	3.28678e9	1.53900	0.769498	+	0.638650i	$0.220507\pi$
$464$	3.06677e8	0.142517
$465$	−3.24631e8	−0.149729
$466$	−2.06181e8	−0.0943838
$467$	2.37755e9	1.08024	0.540120	−	0.841588i	$-0.318379\pi$
$467$	2.37755e9	1.08024	0.540120	+	0.841588i	$0.318379\pi$
$468$	−1.02503e8	−0.0462250
$469$	−9.82687e8	−0.439856
$470$	6.06246e8	0.269344
$471$	1.32974e9	0.586397
$472$	−1.09433e9	−0.479017
$473$	−3.72668e9	−1.61923
$474$	3.77780e8	0.162935
$475$	1.70340e8	0.0729272
$476$	4.18628e8	0.177912
$477$	8.87811e8	0.374547
$478$	−1.43002e9	−0.598886
$479$	−7.18023e8	−0.298513	−0.149257	−	0.988798i	$-0.547688\pi$
$479$	−7.18023e8	−0.298513	−0.149257	+	0.988798i	$0.547688\pi$
$480$	−2.33089e8	−0.0962006
$481$	6.08228e8	0.249206
$482$	−1.18996e9	−0.484025
$483$	−5.84257e8	−0.235933
$484$	7.41598e8	0.297310
$485$	−3.00393e9	−1.19562
$486$	−1.14791e8	−0.0453609
$487$	4.06005e9	1.59287	0.796434	−	0.604725i	$-0.206717\pi$
$487$	4.06005e9	1.59287	0.796434	+	0.604725i	$0.206717\pi$
$488$	−9.37474e8	−0.365166
$489$	−1.24472e9	−0.481382
$490$	2.47963e8	0.0952139
$491$	1.37747e8	0.0525166	0.0262583	−	0.999655i	$-0.491641\pi$
$491$	1.37747e8	0.0525166	0.0262583	+	0.999655i	$0.491641\pi$
$492$	6.03932e8	0.228618
$493$	−1.42783e9	−0.536675
$494$	3.43500e8	0.128198
$495$	1.07063e9	0.396753
$496$	1.86929e8	0.0687847
$497$	−4.65612e8	−0.170129
$498$	−2.79107e8	−0.101267
$499$	4.44250e9	1.60057	0.800286	−	0.599619i	$-0.204681\pi$
$499$	4.44250e9	1.60057	0.800286	+	0.599619i	$0.204681\pi$
$500$	−1.46424e9	−0.523863
$501$	7.01926e8	0.249379
$502$	1.37207e7	0.00484077
$503$	−2.90716e8	−0.101855	−0.0509274	−	0.998702i	$-0.516218\pi$
$503$	−2.90716e8	−0.101855	−0.0509274	+	0.998702i	$0.516218\pi$
$504$	−1.28024e8	−0.0445435
$505$	−8.43750e8	−0.291537
$506$	−2.81345e9	−0.965412
$507$	−1.30324e8	−0.0444116
$508$	2.80569e9	0.949547
$509$	1.91770e9	0.644569	0.322285	−	0.946643i	$-0.395549\pi$
$509$	1.91770e9	0.644569	0.322285	+	0.946643i	$0.395549\pi$
$510$	1.08522e9	0.362260
$511$	−1.80365e9	−0.597971
$512$	1.34218e8	0.0441942
$513$	3.84678e8	0.125802
$514$	3.60075e9	1.16956
$515$	−3.96600e9	−1.27946
$516$	1.15522e9	0.370160
$517$	1.60344e9	0.510313
$518$	7.59662e8	0.240141
$519$	−1.01457e9	−0.318563
$520$	−2.96352e8	−0.0924265
$521$	−3.56604e8	−0.110472	−0.0552362	−	0.998473i	$-0.517591\pi$
$521$	−3.56604e8	−0.110472	−0.0552362	+	0.998473i	$0.517591\pi$
$522$	4.36655e8	0.134367
$523$	5.29609e9	1.61882	0.809411	−	0.587243i	$-0.199787\pi$
$523$	5.29609e9	1.61882	0.809411	+	0.587243i	$0.199787\pi$
$524$	1.82179e9	0.553144
$525$	−8.07177e7	−0.0243451
$526$	−2.74325e9	−0.821894
$527$	−8.70307e8	−0.259021
$528$	−6.16491e8	−0.182267
$529$	5.75264e8	0.168955
$530$	2.56680e9	0.748903
$531$	−1.55814e9	−0.451622
$532$	4.29023e8	0.123535
$533$	7.67847e8	0.219649
$534$	1.65894e9	0.471449
$535$	−3.89405e9	−1.09942
$536$	1.46687e9	0.411447
$537$	3.47009e9	0.967009
$538$	−3.75096e9	−1.03850
$539$	6.55830e8	0.180398
$540$	−3.31879e8	−0.0906988
$541$	−6.34213e9	−1.72205	−0.861023	−	0.508565i	$-0.830176\pi$
$541$	−6.34213e9	−1.72205	−0.861023	+	0.508565i	$0.830176\pi$
$542$	−4.33120e9	−1.16845
$543$	−1.80384e9	−0.483503
$544$	−6.24891e8	−0.166421
$545$	5.69651e9	1.50737
$546$	−1.62771e8	−0.0427960
$547$	6.14930e8	0.160646	0.0803231	−	0.996769i	$-0.474405\pi$
$547$	6.14930e8	0.160646	0.0803231	+	0.996769i	$0.474405\pi$
$548$	8.41515e8	0.218439
$549$	−1.33480e9	−0.344281
$550$	−3.88690e8	−0.0996172
$551$	−1.46328e9	−0.372646
$552$	8.72128e8	0.220695
$553$	5.99900e8	0.150849
$554$	−1.68731e9	−0.421609
$555$	1.96928e9	0.488971
$556$	7.68657e8	0.189658
$557$	6.66186e9	1.63344	0.816718	−	0.577037i	$-0.195791\pi$
$557$	6.66186e9	1.63344	0.816718	+	0.577037i	$0.195791\pi$
$558$	2.66155e8	0.0648509
$559$	1.46876e9	0.355638
$560$	−3.70137e8	−0.0890644
$561$	2.87026e9	0.686359
$562$	−1.87726e9	−0.446116
$563$	−1.02276e9	−0.241542	−0.120771	−	0.992680i	$-0.538537\pi$
$563$	−1.02276e9	−0.241542	−0.120771	+	0.992680i	$0.538537\pi$
$564$	−4.97044e8	−0.116659
$565$	−4.68927e9	−1.09379
$566$	2.20003e8	0.0510001
$567$	−1.82284e8	−0.0419961
$568$	6.95025e8	0.159141
$569$	4.98399e9	1.13419	0.567093	−	0.823654i	$-0.308068\pi$
$569$	4.98399e9	1.13419	0.567093	+	0.823654i	$0.308068\pi$
$570$	1.11216e9	0.251540
$571$	8.84334e9	1.98788	0.993940	−	0.109925i	$-0.0350610\pi$
$571$	8.84334e9	1.98788	0.993940	+	0.109925i	$0.0350610\pi$
$572$	−7.83814e8	−0.175116
$573$	7.87008e8	0.174758
$574$	9.59022e8	0.211659
$575$	5.49866e8	0.120620
$576$	1.91103e8	0.0416667
$577$	−2.93956e9	−0.637040	−0.318520	−	0.947916i	$-0.603186\pi$
$577$	−2.93956e9	−0.637040	−0.318520	+	0.947916i	$0.603186\pi$
$578$	−3.73339e8	−0.0804185
$579$	−2.03612e9	−0.435942
$580$	1.26244e9	0.268665
$581$	−4.43212e8	−0.0937552
$582$	2.46284e9	0.517851
$583$	6.78885e9	1.41891
$584$	2.69234e9	0.559351
$585$	−4.21955e8	−0.0871406
$586$	−1.02971e9	−0.211384
$587$	7.86563e8	0.160509	0.0802546	−	0.996774i	$-0.474427\pi$
$587$	7.86563e8	0.160509	0.0802546	+	0.996774i	$0.474427\pi$
$588$	−2.03297e8	−0.0412393
$589$	−8.91916e8	−0.179854
$590$	−4.50481e9	−0.903014
$591$	2.82878e9	0.563694
$592$	−1.13396e9	−0.224631
$593$	−9.80323e9	−1.93053	−0.965267	−	0.261265i	$-0.915860\pi$
$593$	−9.80323e9	−1.93053	−0.965267	+	0.261265i	$0.915860\pi$
$594$	−8.77777e8	−0.171843
$595$	1.72328e9	0.335388
$596$	−3.26100e9	−0.630942
$597$	2.69899e9	0.519149
$598$	1.10883e9	0.212037
$599$	1.52096e9	0.289150	0.144575	−	0.989494i	$-0.453818\pi$
$599$	1.52096e9	0.289150	0.144575	+	0.989494i	$0.453818\pi$
$600$	1.20488e8	0.0227727
$601$	−3.82333e9	−0.718424	−0.359212	−	0.933256i	$-0.616955\pi$
$601$	−3.82333e9	−0.718424	−0.359212	+	0.933256i	$0.616955\pi$
$602$	1.83444e9	0.342702
$603$	2.08857e9	0.387916
$604$	−3.83776e9	−0.708677
$605$	3.05279e9	0.560471
$606$	6.91766e8	0.126271
$607$	−4.26815e9	−0.774603	−0.387301	−	0.921953i	$-0.626593\pi$
$607$	−4.26815e9	−0.774603	−0.387301	+	0.921953i	$0.626593\pi$
$608$	−6.40407e8	−0.115556
$609$	6.93392e8	0.124399
$610$	−3.85911e9	−0.688388
$611$	−6.31947e8	−0.112082
$612$	−8.89738e8	−0.156903
$613$	−1.23767e8	−0.0217016	−0.0108508	−	0.999941i	$-0.503454\pi$
$613$	−1.23767e8	−0.0217016	−0.0108508	+	0.999941i	$0.503454\pi$
$614$	6.68559e9	1.16560
$615$	2.48609e9	0.430977
$616$	−9.78965e8	−0.168746
$617$	7.05889e9	1.20987	0.604934	−	0.796275i	$-0.293199\pi$
$617$	7.05889e9	1.20987	0.604934	+	0.796275i	$0.293199\pi$
$618$	3.25161e9	0.554164
$619$	−2.76889e9	−0.469234	−0.234617	−	0.972088i	$-0.575384\pi$
$619$	−2.76889e9	−0.469234	−0.234617	+	0.972088i	$0.575384\pi$
$620$	7.69496e8	0.129669
$621$	1.24176e9	0.208074
$622$	9.40053e8	0.156634
$623$	2.63433e9	0.436477
$624$	2.42971e8	0.0400320
$625$	−5.34662e9	−0.875991
$626$	1.51439e9	0.246734
$627$	2.94153e9	0.476581
$628$	−3.15197e9	−0.507835
$629$	5.27947e9	0.845889
$630$	−5.27011e8	−0.0839707
$631$	−3.59659e9	−0.569886	−0.284943	−	0.958544i	$-0.591975\pi$
$631$	−3.59659e9	−0.569886	−0.284943	+	0.958544i	$0.591975\pi$
$632$	−8.95478e8	−0.141106
$633$	2.73653e9	0.428832
$634$	−2.09883e9	−0.327088
$635$	1.15496e10	1.79003
$636$	−2.10444e9	−0.324367
$637$	−2.58475e8	−0.0396214
$638$	3.33898e9	0.509028
$639$	9.89596e8	0.150039
$640$	5.52508e8	0.0833121
$641$	−4.96273e9	−0.744248	−0.372124	−	0.928183i	$-0.621370\pi$
$641$	−4.96273e9	−0.744248	−0.372124	+	0.928183i	$0.621370\pi$
$642$	3.19261e9	0.476183
$643$	−2.65971e9	−0.394545	−0.197273	−	0.980349i	$-0.563208\pi$
$643$	−2.65971e9	−0.394545	−0.197273	+	0.980349i	$0.563208\pi$
$644$	1.38491e9	0.204324
$645$	4.75545e9	0.697803
$646$	2.98161e9	0.435148
$647$	−1.77216e9	−0.257240	−0.128620	−	0.991694i	$-0.541055\pi$
$647$	−1.77216e9	−0.257240	−0.128620	+	0.991694i	$0.541055\pi$
$648$	2.72098e8	0.0392837
$649$	−1.19147e10	−1.71090
$650$	1.53190e8	0.0218793
$651$	4.22645e8	0.0600402
$652$	2.95044e9	0.416889
$653$	5.75860e9	0.809321	0.404660	−	0.914467i	$-0.367390\pi$
$653$	5.75860e9	0.809321	0.404660	+	0.914467i	$0.367390\pi$
$654$	−4.67040e9	−0.652878
$655$	7.49939e9	1.04275
$656$	−1.43154e9	−0.197989
$657$	3.83342e9	0.527361
$658$	−7.89287e8	−0.108005
$659$	5.12540e9	0.697636	0.348818	−	0.937191i	$-0.386583\pi$
$659$	5.12540e9	0.697636	0.348818	+	0.937191i	$0.386583\pi$
$660$	−2.53779e9	−0.343599
$661$	2.11408e9	0.284718	0.142359	−	0.989815i	$-0.454531\pi$
$661$	2.11408e9	0.284718	0.142359	+	0.989815i	$0.454531\pi$
$662$	7.95304e9	1.06544
$663$	−1.13122e9	−0.150748
$664$	6.61588e8	0.0877000
$665$	1.76607e9	0.232880
$666$	−1.61456e9	−0.211784
$667$	−4.72354e9	−0.616350
$668$	−1.66383e9	−0.215968
$669$	−1.81734e9	−0.234663
$670$	6.03837e9	0.775635
$671$	−1.02069e10	−1.30426
$672$	3.03464e8	0.0385758
$673$	7.50694e9	0.949314	0.474657	−	0.880171i	$-0.342572\pi$
$673$	7.50694e9	0.949314	0.474657	+	0.880171i	$0.342572\pi$
$674$	−8.07436e9	−1.01578
$675$	1.71554e8	0.0214703
$676$	3.08916e8	0.0384615
$677$	8.28736e9	1.02649	0.513246	−	0.858241i	$-0.328443\pi$
$677$	8.28736e9	1.02649	0.513246	+	0.858241i	$0.328443\pi$
$678$	3.84459e9	0.473747
$679$	3.91089e9	0.479437
$680$	−2.57237e9	−0.313727
$681$	2.39589e9	0.290704
$682$	2.03522e9	0.245678
$683$	1.29039e10	1.54971	0.774854	−	0.632140i	$-0.217823\pi$
$683$	1.29039e10	1.54971	0.774854	+	0.632140i	$0.217823\pi$
$684$	−9.11830e8	−0.108948
$685$	3.46410e9	0.411788
$686$	−3.22829e8	−0.0381802
$687$	3.80182e9	0.447345
$688$	−2.73829e9	−0.320568
$689$	−2.67561e9	−0.311642
$690$	3.59012e9	0.416041
$691$	6.99048e9	0.805998	0.402999	−	0.915201i	$-0.367968\pi$
$691$	6.99048e9	0.805998	0.402999	+	0.915201i	$0.367968\pi$
$692$	2.40490e9	0.275883
$693$	−1.39388e9	−0.159096
$694$	1.11082e10	1.26150
$695$	3.16418e9	0.357531
$696$	−1.03503e9	−0.116365
$697$	6.66498e9	0.745563
$698$	−6.17420e9	−0.687205
$699$	6.95860e8	0.0770641
$700$	1.91331e8	0.0210834
$701$	1.21500e10	1.33218	0.666090	−	0.745871i	$-0.267967\pi$
$701$	1.21500e10	1.33218	0.666090	+	0.745871i	$0.267967\pi$
$702$	3.45948e8	0.0377426
$703$	5.41056e9	0.587352
$704$	1.46131e9	0.157848
$705$	−2.04608e9	−0.219918
$706$	−7.91479e9	−0.846493
$707$	1.09850e9	0.116905
$708$	3.69336e9	0.391116
$709$	−1.01302e9	−0.106747	−0.0533733	−	0.998575i	$-0.516997\pi$
$709$	−1.01302e9	−0.106747	−0.0533733	+	0.998575i	$0.516997\pi$
$710$	2.86107e9	0.300002
$711$	−1.27501e9	−0.133036
$712$	−3.93229e9	−0.408287
$713$	−2.87915e9	−0.297475
$714$	−1.41287e9	−0.145264
$715$	−3.22657e9	−0.330119
$716$	−8.22539e9	−0.837454
$717$	4.82631e9	0.488988
$718$	2.50436e9	0.252500
$719$	2.95470e9	0.296458	0.148229	−	0.988953i	$-0.452643\pi$
$719$	2.95470e9	0.296458	0.148229	+	0.988953i	$0.452643\pi$
$720$	7.86676e8	0.0785474
$721$	5.16343e9	0.513056
$722$	−4.09533e9	−0.404957
$723$	4.01611e9	0.395204
$724$	4.27577e9	0.418726
$725$	−6.52577e8	−0.0635988
$726$	−2.50289e9	−0.242753
$727$	−1.01207e10	−0.976881	−0.488440	−	0.872597i	$-0.662434\pi$
$727$	−1.01207e10	−0.976881	−0.488440	+	0.872597i	$0.662434\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	1.10830e10	1.05445
$731$	1.27489e10	1.20716
$732$	3.16398e9	0.298157
$733$	5.26083e9	0.493390	0.246695	−	0.969093i	$-0.420655\pi$
$733$	5.26083e9	0.493390	0.246695	+	0.969093i	$0.420655\pi$
$734$	2.78425e9	0.259880
$735$	−8.36874e8	−0.0777418
$736$	−2.06727e9	−0.191128
$737$	1.59707e10	1.46956
$738$	−2.03827e9	−0.186666
$739$	−1.72821e10	−1.57522	−0.787609	−	0.616175i	$-0.788681\pi$
$739$	−1.72821e10	−1.57522	−0.787609	+	0.616175i	$0.788681\pi$
$740$	−4.66793e9	−0.423461
$741$	−1.15931e9	−0.104673
$742$	−3.34177e9	−0.300306
$743$	7.54310e9	0.674666	0.337333	−	0.941385i	$-0.390475\pi$
$743$	7.54310e9	0.674666	0.337333	+	0.941385i	$0.390475\pi$
$744$	−6.30887e8	−0.0561625
$745$	−1.34239e10	−1.18941
$746$	2.06919e9	0.182480
$747$	9.41988e8	0.0826843
$748$	−6.80358e9	−0.594404
$749$	5.06975e9	0.440860
$750$	4.94181e9	0.427732
$751$	1.28944e10	1.11086	0.555432	−	0.831562i	$-0.312553\pi$
$751$	1.28944e10	1.11086	0.555432	+	0.831562i	$0.312553\pi$
$752$	1.17818e9	0.101030
$753$	−4.63075e7	−0.00395247
$754$	−1.31596e9	−0.111800
$755$	−1.57981e10	−1.33595
$756$	4.32081e8	0.0363696
$757$	9.12658e8	0.0764667	0.0382333	−	0.999269i	$-0.487827\pi$
$757$	9.12658e8	0.0764667	0.0382333	+	0.999269i	$0.487827\pi$
$758$	−8.88882e8	−0.0741313
$759$	9.49540e9	0.788255
$760$	−2.63624e9	−0.217840
$761$	−5.38653e9	−0.443060	−0.221530	−	0.975154i	$-0.571105\pi$
$761$	−5.38653e9	−0.443060	−0.221530	+	0.975154i	$0.571105\pi$
$762$	−9.46920e9	−0.775302
$763$	−7.41642e9	−0.604448
$764$	−1.86550e9	−0.151345
$765$	−3.66261e9	−0.295784
$766$	9.46614e9	0.760979
$767$	4.69579e9	0.375772
$768$	−4.52985e8	−0.0360844
$769$	−6.35088e9	−0.503607	−0.251804	−	0.967778i	$-0.581024\pi$
$769$	−6.35088e9	−0.503607	−0.251804	+	0.967778i	$0.581024\pi$
$770$	−4.02991e9	−0.318110
$771$	−1.21525e10	−0.954941
$772$	4.82636e9	0.377537
$773$	−7.73421e9	−0.602265	−0.301132	−	0.953582i	$-0.597365\pi$
$773$	−7.73421e9	−0.602265	−0.301132	+	0.953582i	$0.597365\pi$
$774$	−3.89886e9	−0.302234
$775$	−3.97767e8	−0.0306954
$776$	−5.83783e9	−0.448472
$777$	−2.56386e9	−0.196074
$778$	1.57590e10	1.19978
$779$	6.83047e9	0.517690
$780$	1.00019e9	0.0754659
$781$	7.56717e9	0.568401
$782$	9.62478e9	0.719726
$783$	−1.47371e9	−0.109710
$784$	4.81890e8	0.0357143
$785$	−1.29751e10	−0.957339
$786$	−6.14853e9	−0.451640
$787$	−1.99144e10	−1.45632	−0.728158	−	0.685409i	$-0.759623\pi$
$787$	−1.99144e10	−1.45632	−0.728158	+	0.685409i	$0.759623\pi$
$788$	−6.70526e9	−0.488173
$789$	9.25848e9	0.671074
$790$	−3.68624e9	−0.266004
$791$	6.10507e9	0.438605
$792$	2.08066e9	0.148820
$793$	4.02272e9	0.286460
$794$	7.54539e9	0.534946
$795$	−8.66294e9	−0.611477
$796$	−6.39762e9	−0.449596
$797$	−3.30289e9	−0.231095	−0.115547	−	0.993302i	$-0.536862\pi$
$797$	−3.30289e9	−0.231095	−0.115547	+	0.993302i	$0.536862\pi$
$798$	−1.44795e9	−0.100866
$799$	−5.48536e9	−0.380445
$800$	−2.85602e8	−0.0197218
$801$	−5.59891e9	−0.384937
$802$	−1.87981e10	−1.28677
$803$	2.93131e10	1.99783
$804$	−4.95068e9	−0.335945
$805$	5.70097e9	0.385180
$806$	−8.02117e8	−0.0539592
$807$	1.26595e10	0.847928
$808$	−1.63974e9	−0.109354
$809$	2.71738e10	1.80439	0.902195	−	0.431328i	$-0.141955\pi$
$809$	2.71738e10	1.80439	0.902195	+	0.431328i	$0.141955\pi$
$810$	1.12009e9	0.0740552
$811$	−2.02266e10	−1.33153	−0.665763	−	0.746163i	$-0.731894\pi$
$811$	−2.02266e10	−1.33153	−0.665763	+	0.746163i	$0.731894\pi$
$812$	−1.64360e9	−0.107733
$813$	1.46178e10	0.954037
$814$	−1.23461e10	−0.802313
$815$	1.21455e10	0.785894
$816$	2.10901e9	0.135882
$817$	1.30655e10	0.838202
$818$	2.91214e9	0.186027
$819$	5.49353e8	0.0349428
$820$	−5.89295e9	−0.373237
$821$	−5.71870e9	−0.360658	−0.180329	−	0.983606i	$-0.557716\pi$
$821$	−5.71870e9	−0.360658	−0.180329	+	0.983606i	$0.557716\pi$
$822$	−2.84011e9	−0.178355
$823$	−1.97812e10	−1.23695	−0.618476	−	0.785804i	$-0.712249\pi$
$823$	−1.97812e10	−1.23695	−0.618476	+	0.785804i	$0.712249\pi$
$824$	−7.70752e9	−0.479920
$825$	1.31183e9	0.0813371
$826$	5.86492e9	0.362103
$827$	1.77245e10	1.08969	0.544846	−	0.838536i	$-0.316588\pi$
$827$	1.77245e10	1.08969	0.544846	+	0.838536i	$0.316588\pi$
$828$	−2.94343e9	−0.180197
$829$	−1.50089e10	−0.914973	−0.457487	−	0.889217i	$-0.651250\pi$
$829$	−1.50089e10	−0.914973	−0.457487	+	0.889217i	$0.651250\pi$
$830$	2.72343e9	0.165327
$831$	5.69466e9	0.344243
$832$	−5.75930e8	−0.0346688
$833$	−2.24359e9	−0.134489
$834$	−2.59422e9	−0.154855
$835$	−6.84914e9	−0.407130
$836$	−6.97251e9	−0.412731
$837$	−8.98275e8	−0.0529505
$838$	−1.57166e10	−0.922583
$839$	5.15686e9	0.301452	0.150726	−	0.988576i	$-0.451839\pi$
$839$	5.15686e9	0.301452	0.150726	+	0.988576i	$0.451839\pi$
$840$	1.24921e9	0.0727208
$841$	−1.16440e10	−0.675020
$842$	−2.37332e9	−0.137014
$843$	6.33575e9	0.364252
$844$	−6.48659e9	−0.371379
$845$	1.27165e9	0.0725053
$846$	1.67752e9	0.0952516
$847$	−3.97450e9	−0.224745
$848$	4.98830e9	0.280910
$849$	−7.42509e8	−0.0416414
$850$	1.32970e9	0.0742658
$851$	1.74656e10	0.971469
$852$	−2.34571e9	−0.129938
$853$	−2.72377e10	−1.50262	−0.751310	−	0.659950i	$-0.770578\pi$
$853$	−2.72377e10	−1.50262	−0.751310	+	0.659950i	$0.770578\pi$
$854$	5.02428e9	0.276039
$855$	−3.75355e9	−0.205381
$856$	−7.56768e9	−0.412387
$857$	−7.52015e9	−0.408125	−0.204063	−	0.978958i	$-0.565415\pi$
$857$	−7.52015e9	−0.408125	−0.204063	+	0.978958i	$0.565415\pi$
$858$	2.64537e9	0.142982
$859$	−1.33202e10	−0.717026	−0.358513	−	0.933525i	$-0.616716\pi$
$859$	−1.33202e10	−0.717026	−0.358513	+	0.933525i	$0.616716\pi$
$860$	−1.12722e10	−0.604315
$861$	−3.23670e9	−0.172819
$862$	−7.44670e7	−0.00395994
$863$	1.18914e10	0.629789	0.314895	−	0.949127i	$-0.398031\pi$
$863$	1.18914e10	0.629789	0.314895	+	0.949127i	$0.398031\pi$
$864$	−6.44973e8	−0.0340207
$865$	9.89977e9	0.520078
$866$	6.15046e8	0.0321806
$867$	1.26002e9	0.0656615
$868$	−1.00183e9	−0.0519964
$869$	−9.74962e9	−0.503986
$870$	−4.26072e9	−0.219364
$871$	−6.29435e9	−0.322766
$872$	1.10706e10	0.565409
$873$	−8.31207e9	−0.422824
$874$	9.86376e9	0.499750
$875$	7.84741e9	0.396003
$876$	−9.08663e9	−0.456708
$877$	−1.84336e9	−0.0922806	−0.0461403	−	0.998935i	$-0.514692\pi$
$877$	−1.84336e9	−0.0922806	−0.0461403	+	0.998935i	$0.514692\pi$
$878$	−1.10512e10	−0.551034
$879$	3.47526e9	0.172594
$880$	6.01549e9	0.297565
$881$	−1.12831e9	−0.0555919	−0.0277959	−	0.999614i	$-0.508849\pi$
$881$	−1.12831e9	−0.0555919	−0.0277959	+	0.999614i	$0.508849\pi$
$882$	6.86129e8	0.0336718
$883$	−1.58656e10	−0.775523	−0.387762	−	0.921760i	$-0.626752\pi$
$883$	−1.58656e10	−0.775523	−0.387762	+	0.921760i	$0.626752\pi$
$884$	2.68142e9	0.130551
$885$	1.52037e10	0.737308
$886$	1.79663e10	0.867844
$887$	−3.31262e10	−1.59382	−0.796910	−	0.604098i	$-0.793534\pi$
$887$	−3.31262e10	−1.59382	−0.796910	+	0.604098i	$0.793534\pi$
$888$	3.82710e9	0.183411
$889$	−1.50367e10	−0.717790
$890$	−1.61873e10	−0.769678
$891$	2.96250e9	0.140309
$892$	4.30777e9	0.203224
$893$	−5.62156e9	−0.264166
$894$	1.10059e10	0.515162
$895$	−3.38599e10	−1.57872
$896$	−7.19323e8	−0.0334077
$897$	−3.74231e9	−0.173128
$898$	−2.37214e10	−1.09314
$899$	3.41695e9	0.156848
$900$	−4.06648e8	−0.0185939
$901$	−2.32246e10	−1.05782
$902$	−1.55861e10	−0.707155
$903$	−6.19124e9	−0.279815
$904$	−9.11311e9	−0.410277
$905$	1.76012e10	0.789356
$906$	1.29524e10	0.578632
$907$	−2.07562e10	−0.923680	−0.461840	−	0.886963i	$-0.652811\pi$
$907$	−2.07562e10	−0.923680	−0.461840	+	0.886963i	$0.652811\pi$
$908$	−5.67914e9	−0.251757
$909$	−2.33471e9	−0.103100
$910$	1.58826e9	0.0698679
$911$	2.18056e10	0.955551	0.477775	−	0.878482i	$-0.341443\pi$
$911$	2.18056e10	0.955551	0.477775	+	0.878482i	$0.341443\pi$
$912$	2.16137e9	0.0943513
$913$	7.20312e9	0.313237
$914$	2.61058e10	1.13090
$915$	1.30245e10	0.562066
$916$	−9.01171e9	−0.387412
$917$	−9.76364e9	−0.418138
$918$	3.00286e9	0.128111
$919$	1.96620e10	0.835647	0.417823	−	0.908528i	$-0.362793\pi$
$919$	1.96620e10	0.835647	0.417823	+	0.908528i	$0.362793\pi$
$920$	−8.50990e9	−0.360302
$921$	−2.25639e10	−0.951710
$922$	4.48616e9	0.188502
$923$	−2.98236e9	−0.124840
$924$	3.30401e9	0.137781
$925$	2.41294e9	0.100242
$926$	2.62942e10	1.08823
$927$	−1.09742e10	−0.452473
$928$	2.45342e9	0.100775
$929$	−1.70180e10	−0.696393	−0.348197	−	0.937421i	$-0.613206\pi$
$929$	−1.70180e10	−0.696393	−0.348197	+	0.937421i	$0.613206\pi$
$930$	−2.59705e9	−0.105874
$931$	−2.29929e9	−0.0933836
$932$	−1.64945e9	−0.0667395
$933$	−3.17268e9	−0.127891
$934$	1.90204e10	0.763845
$935$	−2.80070e10	−1.12053
$936$	−8.20026e8	−0.0326860
$937$	−8.23447e9	−0.326999	−0.163500	−	0.986543i	$-0.552278\pi$
$937$	−8.23447e9	−0.326999	−0.163500	+	0.986543i	$0.552278\pi$
$938$	−7.86150e9	−0.311025
$939$	−5.11107e9	−0.201457
$940$	4.84997e9	0.190455
$941$	−7.54017e9	−0.294997	−0.147498	−	0.989062i	$-0.547122\pi$
$941$	−7.54017e9	−0.294997	−0.147498	+	0.989062i	$0.547122\pi$
$942$	1.06379e10	0.414646
$943$	2.20491e10	0.856249
$944$	−8.75464e9	−0.338716
$945$	1.77866e9	0.0685618
$946$	−2.98135e10	−1.14497
$947$	9.62217e9	0.368170	0.184085	−	0.982910i	$-0.441068\pi$
$947$	9.62217e9	0.368170	0.184085	+	0.982910i	$0.441068\pi$
$948$	3.02224e9	0.115212
$949$	−1.15529e10	−0.438791
$950$	1.36272e9	0.0515673
$951$	7.08355e9	0.267066
$952$	3.34903e9	0.125802
$953$	−1.23489e10	−0.462170	−0.231085	−	0.972934i	$-0.574227\pi$
$953$	−1.23489e10	−0.462170	−0.231085	+	0.972934i	$0.574227\pi$
$954$	7.10249e9	0.264845
$955$	−7.67934e9	−0.285307
$956$	−1.14401e10	−0.423476
$957$	−1.12691e10	−0.415620
$958$	−5.74418e9	−0.211081
$959$	−4.51000e9	−0.165124
$960$	−1.86471e9	−0.0680241
$961$	−2.54299e10	−0.924299
$962$	4.86582e9	0.176215
$963$	−1.07751e10	−0.388802
$964$	−9.51967e9	−0.342257
$965$	1.98677e10	0.711709
$966$	−4.67406e9	−0.166830
$967$	−1.03312e10	−0.367415	−0.183707	−	0.982981i	$-0.558810\pi$
$967$	−1.03312e10	−0.367415	−0.183707	+	0.982981i	$0.558810\pi$
$968$	5.93278e9	0.210230
$969$	−1.00629e10	−0.355297
$970$	−2.40315e10	−0.845433
$971$	−1.13378e10	−0.397432	−0.198716	−	0.980057i	$-0.563677\pi$
$971$	−1.13378e10	−0.397432	−0.198716	+	0.980057i	$0.563677\pi$
$972$	−9.18330e8	−0.0320750
$973$	−4.11952e9	−0.143368
$974$	3.24804e10	1.12633
$975$	−5.17017e8	−0.0178644
$976$	−7.49979e9	−0.258211
$977$	−2.44113e10	−0.837453	−0.418727	−	0.908112i	$-0.637523\pi$
$977$	−2.44113e10	−0.837453	−0.418727	+	0.908112i	$0.637523\pi$
$978$	−9.95775e9	−0.340389
$979$	−4.28133e10	−1.45828
$980$	1.98370e9	0.0673264
$981$	1.57626e10	0.533073
$982$	1.10197e9	0.0371348
$983$	−1.46088e10	−0.490544	−0.245272	−	0.969454i	$-0.578877\pi$
$983$	−1.46088e10	−0.490544	−0.245272	+	0.969454i	$0.578877\pi$
$984$	4.83146e9	0.161657
$985$	−2.76022e10	−0.920274
$986$	−1.14226e10	−0.379487
$987$	2.66384e9	0.0881858
$988$	2.74800e9	0.0906498
$989$	4.21761e10	1.38637
$990$	8.56503e9	0.280547
$991$	9.90885e9	0.323419	0.161709	−	0.986838i	$-0.448299\pi$
$991$	9.90885e9	0.323419	0.161709	+	0.986838i	$0.448299\pi$
$992$	1.49544e9	0.0486381
$993$	−2.68415e10	−0.869931
$994$	−3.72490e9	−0.120299
$995$	−2.63358e10	−0.847551
$996$	−2.23286e9	−0.0716067
$997$	5.71418e10	1.82608	0.913042	−	0.407866i	$-0.133727\pi$
$997$	5.71418e10	1.82608	0.913042	+	0.407866i	$0.133727\pi$
$998$	3.55400e10	1.13178
$999$	5.44913e9	0.172921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.l.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.l.1.5	✓	5	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	546.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +263.456 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +263.456 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +2107.65 q^{10} +5574.46 q^{11} -1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} -7113.32 q^{15} +4096.00 q^{16} -19070.2 q^{17} +5832.00 q^{18} -19543.7 q^{19} +16861.2 q^{20} +9261.00 q^{21} +44595.7 q^{22} -63087.9 q^{23} -13824.0 q^{24} -8715.87 q^{25} -17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +74872.3 q^{29} -56906.5 q^{30} +45637.1 q^{31} +32768.0 q^{32} -150511. q^{33} -152561. q^{34} -90365.5 q^{35} +46656.0 q^{36} -276845. q^{37} -156349. q^{38} +59319.0 q^{39} +134890. q^{40} -349498. q^{41} +74088.0 q^{42} -668528. q^{43} +356766. q^{44} +192060. q^{45} -504704. q^{46} +287641. q^{47} -110592. q^{48} +117649. q^{49} -69727.0 q^{50} +514895. q^{51} -140608. q^{52} +1.21785e6 q^{53} -157464. q^{54} +1.46863e6 q^{55} -175616. q^{56} +527679. q^{57} +598978. q^{58} -2.13736e6 q^{59} -455252. q^{60} -1.83100e6 q^{61} +365097. q^{62} -250047. q^{63} +262144. q^{64} -578813. q^{65} -1.20408e6 q^{66} +2.86498e6 q^{67} -1.22049e6 q^{68} +1.70337e6 q^{69} -722924. q^{70} +1.35747e6 q^{71} +373248. q^{72} +5.25847e6 q^{73} -2.21476e6 q^{74} +235328. q^{75} -1.25080e6 q^{76} -1.91204e6 q^{77} +474552. q^{78} -1.74898e6 q^{79} +1.07912e6 q^{80} +531441. q^{81} -2.79598e6 q^{82} +1.29216e6 q^{83} +592704. q^{84} -5.02415e6 q^{85} -5.34822e6 q^{86} -2.02155e6 q^{87} +2.85413e6 q^{88} -7.68026e6 q^{89} +1.53648e6 q^{90} +753571. q^{91} -4.03763e6 q^{92} -1.23220e6 q^{93} +2.30113e6 q^{94} -5.14890e6 q^{95} -884736. q^{96} -1.14020e7 q^{97} +941192. q^{98} +4.06378e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) \) 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9} - 2000 q^{10} + 659 q^{11} - 8640 q^{12} - 10985 q^{13} - 13720 q^{14} + 6750 q^{15} + 20480 q^{16} + 24575 q^{17} + 29160 q^{18} - 6446 q^{19} - 16000 q^{20} + 46305 q^{21} + 5272 q^{22} + 30268 q^{23} - 69120 q^{24} + 38965 q^{25} - 87880 q^{26} - 98415 q^{27} - 109760 q^{28} + 130950 q^{29} + 54000 q^{30} + 262979 q^{31} + 163840 q^{32} - 17793 q^{33} + 196600 q^{34} + 85750 q^{35} + 233280 q^{36} - 101549 q^{37} - 51568 q^{38} + 296595 q^{39} - 128000 q^{40} - 247328 q^{41} + 370440 q^{42} - 19092 q^{43} + 42176 q^{44} - 182250 q^{45} + 242144 q^{46} - 126419 q^{47} - 552960 q^{48} + 588245 q^{49} + 311720 q^{50} - 663525 q^{51} - 703040 q^{52} - 302793 q^{53} - 787320 q^{54} + 943985 q^{55} - 878080 q^{56} + 174042 q^{57} + 1047600 q^{58} - 2798636 q^{59} + 432000 q^{60} - 2493751 q^{61} + 2103832 q^{62} - 1250235 q^{63} + 1310720 q^{64} + 549250 q^{65} - 142344 q^{66} + 160188 q^{67} + 1572800 q^{68} - 817236 q^{69} + 686000 q^{70} + 3846088 q^{71} + 1866240 q^{72} + 5655872 q^{73} - 812392 q^{74} - 1052055 q^{75} - 412544 q^{76} - 226037 q^{77} + 2372760 q^{78} + 5647991 q^{79} - 1024000 q^{80} + 2657205 q^{81} - 1978624 q^{82} - 4607669 q^{83} + 2963520 q^{84} + 3873935 q^{85} - 152736 q^{86} - 3535650 q^{87} + 337408 q^{88} - 17424029 q^{89} - 1458000 q^{90} + 3767855 q^{91} + 1937152 q^{92} - 7100433 q^{93} - 1011352 q^{94} - 24593720 q^{95} - 4423680 q^{96} - 18380577 q^{97} + 4705960 q^{98} + 480411 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9 - 2000 * q^10 + 659 * q^11 - 8640 * q^12 - 10985 * q^13 - 13720 * q^14 + 6750 * q^15 + 20480 * q^16 + 24575 * q^17 + 29160 * q^18 - 6446 * q^19 - 16000 * q^20 + 46305 * q^21 + 5272 * q^22 + 30268 * q^23 - 69120 * q^24 + 38965 * q^25 - 87880 * q^26 - 98415 * q^27 - 109760 * q^28 + 130950 * q^29 + 54000 * q^30 + 262979 * q^31 + 163840 * q^32 - 17793 * q^33 + 196600 * q^34 + 85750 * q^35 + 233280 * q^36 - 101549 * q^37 - 51568 * q^38 + 296595 * q^39 - 128000 * q^40 - 247328 * q^41 + 370440 * q^42 - 19092 * q^43 + 42176 * q^44 - 182250 * q^45 + 242144 * q^46 - 126419 * q^47 - 552960 * q^48 + 588245 * q^49 + 311720 * q^50 - 663525 * q^51 - 703040 * q^52 - 302793 * q^53 - 787320 * q^54 + 943985 * q^55 - 878080 * q^56 + 174042 * q^57 + 1047600 * q^58 - 2798636 * q^59 + 432000 * q^60 - 2493751 * q^61 + 2103832 * q^62 - 1250235 * q^63 + 1310720 * q^64 + 549250 * q^65 - 142344 * q^66 + 160188 * q^67 + 1572800 * q^68 - 817236 * q^69 + 686000 * q^70 + 3846088 * q^71 + 1866240 * q^72 + 5655872 * q^73 - 812392 * q^74 - 1052055 * q^75 - 412544 * q^76 - 226037 * q^77 + 2372760 * q^78 + 5647991 * q^79 - 1024000 * q^80 + 2657205 * q^81 - 1978624 * q^82 - 4607669 * q^83 + 2963520 * q^84 + 3873935 * q^85 - 152736 * q^86 - 3535650 * q^87 + 337408 * q^88 - 17424029 * q^89 - 1458000 * q^90 + 3767855 * q^91 + 1937152 * q^92 - 7100433 * q^93 - 1011352 * q^94 - 24593720 * q^95 - 4423680 * q^96 - 18380577 * q^97 + 4705960 * q^98 + 480411 * q^99

Introduction

L-functions

Modular forms

Varieties

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