LMFDB - Embedded newform 546.8.a.p.1.6

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:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 302081x^{4} - 2628147x^{3} + 19116974952x^{2} - 78725393748x - 5138711063280 $ x^6 - x^5 - 302081x^4 - 2628147x^3 + 19116974952x^2 - 78725393748x - 5138711063280
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-445.917$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +438.917 q^{5} -216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +438.917 q^{5} -216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -3511.33 q^{10} -613.237 q^{11} +1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +11850.8 q^{15} +4096.00 q^{16} +16657.1 q^{17} -5832.00 q^{18} +1693.74 q^{19} +28090.7 q^{20} +9261.00 q^{21} +4905.90 q^{22} -59980.0 q^{23} -13824.0 q^{24} +114523. q^{25} +17576.0 q^{26} +19683.0 q^{27} +21952.0 q^{28} -134472. q^{29} -94806.0 q^{30} -246211. q^{31} -32768.0 q^{32} -16557.4 q^{33} -133257. q^{34} +150548. q^{35} +46656.0 q^{36} -2910.28 q^{37} -13549.9 q^{38} -59319.0 q^{39} -224725. q^{40} +487387. q^{41} -74088.0 q^{42} +854728. q^{43} -39247.2 q^{44} +319970. q^{45} +479840. q^{46} +1.10441e6 q^{47} +110592. q^{48} +117649. q^{49} -916183. q^{50} +449743. q^{51} -140608. q^{52} +824971. q^{53} -157464. q^{54} -269160. q^{55} -175616. q^{56} +45731.0 q^{57} +1.07577e6 q^{58} -445602. q^{59} +758448. q^{60} +481991. q^{61} +1.96969e6 q^{62} +250047. q^{63} +262144. q^{64} -964300. q^{65} +132459. q^{66} +4.20932e6 q^{67} +1.06606e6 q^{68} -1.61946e6 q^{69} -1.20439e6 q^{70} -2.08192e6 q^{71} -373248. q^{72} +4.93459e6 q^{73} +23282.2 q^{74} +3.09212e6 q^{75} +108400. q^{76} -210340. q^{77} +474552. q^{78} +2.23377e6 q^{79} +1.79780e6 q^{80} +531441. q^{81} -3.89909e6 q^{82} +8.38110e6 q^{83} +592704. q^{84} +7.31110e6 q^{85} -6.83783e6 q^{86} -3.63074e6 q^{87} +313978. q^{88} -8.66671e6 q^{89} -2.55976e6 q^{90} -753571. q^{91} -3.83872e6 q^{92} -6.64770e6 q^{93} -8.83531e6 q^{94} +743412. q^{95} -884736. q^{96} -2.82328e6 q^{97} -941192. q^{98} -447050. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 48 q^{2} + 162 q^{3} + 384 q^{4} - 43 q^{5} - 1296 q^{6} + 2058 q^{7} - 3072 q^{8} + 4374 q^{9}+O(q^{10}) $ 6 * q - 48 * q^2 + 162 * q^3 + 384 * q^4 - 43 * q^5 - 1296 * q^6 + 2058 * q^7 - 3072 * q^8 + 4374 * q^9	\( 6 q - 48 q^{2} + 162 q^{3} + 384 q^{4} - 43 q^{5} - 1296 q^{6} + 2058 q^{7} - 3072 q^{8} + 4374 q^{9} + 344 q^{10} + 7370 q^{11} + 10368 q^{12} - 13182 q^{13} - 16464 q^{14} - 1161 q^{15} + 24576 q^{16} + 7950 q^{17} - 34992 q^{18} - 57145 q^{19} - 2752 q^{20} + 55566 q^{21} - 58960 q^{22} + 31769 q^{23} - 82944 q^{24} + 135721 q^{25} + 105456 q^{26} + 118098 q^{27} + 131712 q^{28} - 36455 q^{29} + 9288 q^{30} + 215069 q^{31} - 196608 q^{32} + 198990 q^{33} - 63600 q^{34} - 14749 q^{35} + 279936 q^{36} + 133074 q^{37} + 457160 q^{38} - 355914 q^{39} + 22016 q^{40} + 516452 q^{41} - 444528 q^{42} - 3085 q^{43} + 471680 q^{44} - 31347 q^{45} - 254152 q^{46} + 1463947 q^{47} + 663552 q^{48} + 705894 q^{49} - 1085768 q^{50} + 214650 q^{51} - 843648 q^{52} - 1344571 q^{53} - 944784 q^{54} - 1568062 q^{55} - 1053696 q^{56} - 1542915 q^{57} + 291640 q^{58} + 1810408 q^{59} - 74304 q^{60} + 4047390 q^{61} - 1720552 q^{62} + 1500282 q^{63} + 1572864 q^{64} + 94471 q^{65} - 1591920 q^{66} + 2393614 q^{67} + 508800 q^{68} + 857763 q^{69} + 117992 q^{70} + 10341084 q^{71} - 2239488 q^{72} + 5180001 q^{73} - 1064592 q^{74} + 3664467 q^{75} - 3657280 q^{76} + 2527910 q^{77} + 2847312 q^{78} + 4624979 q^{79} - 176128 q^{80} + 3188646 q^{81} - 4131616 q^{82} + 11892699 q^{83} + 3556224 q^{84} + 750368 q^{85} + 24680 q^{86} - 984285 q^{87} - 3773440 q^{88} + 9781713 q^{89} + 250776 q^{90} - 4521426 q^{91} + 2033216 q^{92} + 5806863 q^{93} - 11711576 q^{94} + 26244263 q^{95} - 5308416 q^{96} + 5202537 q^{97} - 5647152 q^{98} + 5372730 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 + 162 * q^3 + 384 * q^4 - 43 * q^5 - 1296 * q^6 + 2058 * q^7 - 3072 * q^8 + 4374 * q^9 + 344 * q^10 + 7370 * q^11 + 10368 * q^12 - 13182 * q^13 - 16464 * q^14 - 1161 * q^15 + 24576 * q^16 + 7950 * q^17 - 34992 * q^18 - 57145 * q^19 - 2752 * q^20 + 55566 * q^21 - 58960 * q^22 + 31769 * q^23 - 82944 * q^24 + 135721 * q^25 + 105456 * q^26 + 118098 * q^27 + 131712 * q^28 - 36455 * q^29 + 9288 * q^30 + 215069 * q^31 - 196608 * q^32 + 198990 * q^33 - 63600 * q^34 - 14749 * q^35 + 279936 * q^36 + 133074 * q^37 + 457160 * q^38 - 355914 * q^39 + 22016 * q^40 + 516452 * q^41 - 444528 * q^42 - 3085 * q^43 + 471680 * q^44 - 31347 * q^45 - 254152 * q^46 + 1463947 * q^47 + 663552 * q^48 + 705894 * q^49 - 1085768 * q^50 + 214650 * q^51 - 843648 * q^52 - 1344571 * q^53 - 944784 * q^54 - 1568062 * q^55 - 1053696 * q^56 - 1542915 * q^57 + 291640 * q^58 + 1810408 * q^59 - 74304 * q^60 + 4047390 * q^61 - 1720552 * q^62 + 1500282 * q^63 + 1572864 * q^64 + 94471 * q^65 - 1591920 * q^66 + 2393614 * q^67 + 508800 * q^68 + 857763 * q^69 + 117992 * q^70 + 10341084 * q^71 - 2239488 * q^72 + 5180001 * q^73 - 1064592 * q^74 + 3664467 * q^75 - 3657280 * q^76 + 2527910 * q^77 + 2847312 * q^78 + 4624979 * q^79 - 176128 * q^80 + 3188646 * q^81 - 4131616 * q^82 + 11892699 * q^83 + 3556224 * q^84 + 750368 * q^85 + 24680 * q^86 - 984285 * q^87 - 3773440 * q^88 + 9781713 * q^89 + 250776 * q^90 - 4521426 * q^91 + 2033216 * q^92 + 5806863 * q^93 - 11711576 * q^94 + 26244263 * q^95 - 5308416 * q^96 + 5202537 * q^97 - 5647152 * q^98 + 5372730 * 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
$5$	438.917	1.57032	0.785158	−	0.619295i	$-0.212582\pi$
$5$	438.917	1.57032	0.785158	+	0.619295i	$0.212582\pi$
$6$	−216.000	−0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	−3511.33	−1.11038
$11$	−613.237	−0.138917	−0.0694583	−	0.997585i	$-0.522127\pi$
$11$	−613.237	−0.138917	−0.0694583	+	0.997585i	$0.522127\pi$
$12$	1728.00	0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−2744.00	−0.267261
$15$	11850.8	0.906622
$16$	4096.00	0.250000
$17$	16657.1	0.822298	0.411149	−	0.911568i	$-0.365128\pi$
$17$	16657.1	0.822298	0.411149	+	0.911568i	$0.365128\pi$
$18$	−5832.00	−0.235702
$19$	1693.74	0.0566513	0.0283256	−	0.999599i	$-0.490982\pi$
$19$	1693.74	0.0566513	0.0283256	+	0.999599i	$0.490982\pi$
$20$	28090.7	0.785158
$21$	9261.00	0.218218
$22$	4905.90	0.0982289
$23$	−59980.0	−1.02792	−0.513960	−	0.857814i	$-0.671822\pi$
$23$	−59980.0	−1.02792	−0.513960	+	0.857814i	$0.671822\pi$
$24$	−13824.0	−0.204124
$25$	114523.	1.46589
$26$	17576.0	0.196116
$27$	19683.0	0.192450
$28$	21952.0	0.188982
$29$	−134472.	−1.02385	−0.511927	−	0.859029i	$-0.671068\pi$
$29$	−134472.	−1.02385	−0.511927	+	0.859029i	$0.671068\pi$
$30$	−94806.0	−0.641079
$31$	−246211.	−1.48437	−0.742184	−	0.670196i	$-0.766210\pi$
$31$	−246211.	−1.48437	−0.742184	+	0.670196i	$0.766210\pi$
$32$	−32768.0	−0.176777
$33$	−16557.4	−0.0802036
$34$	−133257.	−0.581453
$35$	150548.	0.593524
$36$	46656.0	0.166667
$37$	−2910.28	−0.00944558	−0.00472279	−	0.999989i	$-0.501503\pi$
$37$	−2910.28	−0.00944558	−0.00472279	+	0.999989i	$0.501503\pi$
$38$	−13549.9	−0.0400585
$39$	−59319.0	−0.160128
$40$	−224725.	−0.555191
$41$	487387.	1.10441	0.552205	−	0.833708i	$-0.313787\pi$
$41$	487387.	1.10441	0.552205	+	0.833708i	$0.313787\pi$
$42$	−74088.0	−0.154303
$43$	854728.	1.63941	0.819707	−	0.572784i	$-0.194136\pi$
$43$	854728.	1.63941	0.819707	+	0.572784i	$0.194136\pi$
$44$	−39247.2	−0.0694583
$45$	319970.	0.523439
$46$	479840.	0.726849
$47$	1.10441e6	1.55163	0.775817	−	0.630957i	$-0.217338\pi$
$47$	1.10441e6	1.55163	0.775817	+	0.630957i	$0.217338\pi$
$48$	110592.	0.144338
$49$	117649.	0.142857
$50$	−916183.	−1.03654
$51$	449743.	0.474754
$52$	−140608.	−0.138675
$53$	824971.	0.761155	0.380577	−	0.924749i	$-0.375725\pi$
$53$	824971.	0.761155	0.380577	+	0.924749i	$0.375725\pi$
$54$	−157464.	−0.136083
$55$	−269160.	−0.218143
$56$	−175616.	−0.133631
$57$	45731.0	0.0327076
$58$	1.07577e6	0.723975
$59$	−445602.	−0.282465	−0.141233	−	0.989976i	$-0.545107\pi$
$59$	−445602.	−0.282465	−0.141233	+	0.989976i	$0.545107\pi$
$60$	758448.	0.453311
$61$	481991.	0.271884	0.135942	−	0.990717i	$-0.456594\pi$
$61$	481991.	0.271884	0.135942	+	0.990717i	$0.456594\pi$
$62$	1.96969e6	1.04961
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	−964300.	−0.435527
$66$	132459.	0.0567125
$67$	4.20932e6	1.70982	0.854909	−	0.518777i	$-0.173613\pi$
$67$	4.20932e6	1.70982	0.854909	+	0.518777i	$0.173613\pi$
$68$	1.06606e6	0.411149
$69$	−1.61946e6	−0.593469
$70$	−1.20439e6	−0.419685
$71$	−2.08192e6	−0.690335	−0.345167	−	0.938541i	$-0.612178\pi$
$71$	−2.08192e6	−0.690335	−0.345167	+	0.938541i	$0.612178\pi$
$72$	−373248.	−0.117851
$73$	4.93459e6	1.48464	0.742320	−	0.670046i	$-0.233726\pi$
$73$	4.93459e6	1.48464	0.742320	+	0.670046i	$0.233726\pi$
$74$	23282.2	0.00667903
$75$	3.09212e6	0.846333
$76$	108400.	0.0283256
$77$	−210340.	−0.0525056
$78$	474552.	0.113228
$79$	2.23377e6	0.509735	0.254867	−	0.966976i	$-0.417968\pi$
$79$	2.23377e6	0.509735	0.254867	+	0.966976i	$0.417968\pi$
$80$	1.79780e6	0.392579
$81$	531441.	0.111111
$82$	−3.89909e6	−0.780936
$83$	8.38110e6	1.60889	0.804447	−	0.594024i	$-0.202462\pi$
$83$	8.38110e6	1.60889	0.804447	+	0.594024i	$0.202462\pi$
$84$	592704.	0.109109
$85$	7.31110e6	1.29127
$86$	−6.83783e6	−1.15924
$87$	−3.63074e6	−0.591123
$88$	313978.	0.0491144
$89$	−8.66671e6	−1.30313	−0.651567	−	0.758591i	$-0.725888\pi$
$89$	−8.66671e6	−1.30313	−0.651567	+	0.758591i	$0.725888\pi$
$90$	−2.55976e6	−0.370127
$91$	−753571.	−0.104828
$92$	−3.83872e6	−0.513960
$93$	−6.64770e6	−0.857000
$94$	−8.83531e6	−1.09717
$95$	743412.	0.0889604
$96$	−884736.	−0.102062
$97$	−2.82328e6	−0.314089	−0.157045	−	0.987592i	$-0.550197\pi$
$97$	−2.82328e6	−0.314089	−0.157045	+	0.987592i	$0.550197\pi$
$98$	−941192.	−0.101015
$99$	−447050.	−0.0463055
$100$	7.32946e6	0.732946
$101$	7.84523e6	0.757671	0.378835	−	0.925464i	$-0.376325\pi$
$101$	7.84523e6	0.757671	0.378835	+	0.925464i	$0.376325\pi$
$102$	−3.59794e6	−0.335702
$103$	1.20435e7	1.08599	0.542993	−	0.839737i	$-0.317291\pi$
$103$	1.20435e7	1.08599	0.542993	+	0.839737i	$0.317291\pi$
$104$	1.12486e6	0.0980581
$105$	4.06481e6	0.342671
$106$	−6.59977e6	−0.538218
$107$	6.39831e6	0.504919	0.252460	−	0.967607i	$-0.418761\pi$
$107$	6.39831e6	0.504919	0.252460	+	0.967607i	$0.418761\pi$
$108$	1.25971e6	0.0962250
$109$	−2.95465e6	−0.218531	−0.109266	−	0.994013i	$-0.534850\pi$
$109$	−2.95465e6	−0.218531	−0.109266	+	0.994013i	$0.534850\pi$
$110$	2.15328e6	0.154250
$111$	−78577.5	−0.00545341
$112$	1.40493e6	0.0944911
$113$	−1.06356e7	−0.693406	−0.346703	−	0.937975i	$-0.612699\pi$
$113$	−1.06356e7	−0.693406	−0.346703	+	0.937975i	$0.612699\pi$
$114$	−365848.	−0.0231278
$115$	−2.63262e7	−1.61416
$116$	−8.60620e6	−0.511927
$117$	−1.60161e6	−0.0924500
$118$	3.56482e6	0.199733
$119$	5.71340e6	0.310800
$120$	−6.06758e6	−0.320539
$121$	−1.91111e7	−0.980702
$122$	−3.85593e6	−0.192251
$123$	1.31594e7	0.637631
$124$	−1.57575e7	−0.742184
$125$	1.59756e7	0.731598
$126$	−2.00038e6	−0.0890871
$127$	3.02472e7	1.31030	0.655152	−	0.755497i	$-0.272604\pi$
$127$	3.02472e7	1.31030	0.655152	+	0.755497i	$0.272604\pi$
$128$	−2.09715e6	−0.0883883
$129$	2.30777e7	0.946516
$130$	7.71440e6	0.307964
$131$	2.42926e7	0.944114	0.472057	−	0.881568i	$-0.343512\pi$
$131$	2.42926e7	0.944114	0.472057	+	0.881568i	$0.343512\pi$
$132$	−1.05967e6	−0.0401018
$133$	580954.	0.0214122
$134$	−3.36746e7	−1.20902
$135$	8.63920e6	0.302207
$136$	−8.52846e6	−0.290726
$137$	−3.75416e7	−1.24736	−0.623679	−	0.781681i	$-0.714363\pi$
$137$	−3.75416e7	−1.24736	−0.623679	+	0.781681i	$0.714363\pi$
$138$	1.29557e7	0.419646
$139$	−4.94601e7	−1.56208	−0.781039	−	0.624482i	$-0.785310\pi$
$139$	−4.94601e7	−1.56208	−0.781039	+	0.624482i	$0.785310\pi$
$140$	9.63510e6	0.296762
$141$	2.98192e7	0.895837
$142$	1.66554e7	0.488140
$143$	1.34728e6	0.0385285
$144$	2.98598e6	0.0833333
$145$	−5.90219e7	−1.60778
$146$	−3.94767e7	−1.04980
$147$	3.17652e6	0.0824786
$148$	−186258.	−0.00472279
$149$	4.51637e7	1.11850	0.559251	−	0.828998i	$-0.311089\pi$
$149$	4.51637e7	1.11850	0.559251	+	0.828998i	$0.311089\pi$
$150$	−2.47369e7	−0.598448
$151$	−2.20766e7	−0.521811	−0.260906	−	0.965364i	$-0.584021\pi$
$151$	−2.20766e7	−0.521811	−0.260906	+	0.965364i	$0.584021\pi$
$152$	−867196.	−0.0200293
$153$	1.21431e7	0.274099
$154$	1.68272e6	0.0371270
$155$	−1.08066e8	−2.33093
$156$	−3.79642e6	−0.0800641
$157$	3.45895e7	0.713338	0.356669	−	0.934231i	$-0.383912\pi$
$157$	3.45895e7	0.713338	0.356669	+	0.934231i	$0.383912\pi$
$158$	−1.78702e7	−0.360437
$159$	2.22742e7	0.439453
$160$	−1.43824e7	−0.277595
$161$	−2.05731e7	−0.388517
$162$	−4.25153e6	−0.0785674
$163$	9.40073e7	1.70022	0.850110	−	0.526605i	$-0.176535\pi$
$163$	9.40073e7	1.70022	0.850110	+	0.526605i	$0.176535\pi$
$164$	3.11928e7	0.552205
$165$	−7.26732e6	−0.125945
$166$	−6.70488e7	−1.13766
$167$	−3.56325e7	−0.592023	−0.296012	−	0.955184i	$-0.595657\pi$
$167$	−3.56325e7	−0.592023	−0.296012	+	0.955184i	$0.595657\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	−5.84888e7	−0.913065
$171$	1.23474e6	0.0188838
$172$	5.47026e7	0.819707
$173$	−1.14790e7	−0.168555	−0.0842777	−	0.996442i	$-0.526858\pi$
$173$	−1.14790e7	−0.168555	−0.0842777	+	0.996442i	$0.526858\pi$
$174$	2.90459e7	0.417987
$175$	3.92813e7	0.554055
$176$	−2.51182e6	−0.0347292
$177$	−1.20313e7	−0.163081
$178$	6.93337e7	0.921455
$179$	3.18719e7	0.415357	0.207679	−	0.978197i	$-0.433409\pi$
$179$	3.18719e7	0.415357	0.207679	+	0.978197i	$0.433409\pi$
$180$	2.04781e7	0.261719
$181$	1.56681e7	0.196400	0.0981999	−	0.995167i	$-0.468692\pi$
$181$	1.56681e7	0.196400	0.0981999	+	0.995167i	$0.468692\pi$
$182$	6.02857e6	0.0741249
$183$	1.30138e7	0.156973
$184$	3.07098e7	0.363424
$185$	−1.27737e6	−0.0148325
$186$	5.31816e7	0.605991
$187$	−1.02148e7	−0.114231
$188$	7.06825e7	0.775817
$189$	6.75127e6	0.0727393
$190$	−5.94729e6	−0.0629045
$191$	3.16069e6	0.0328220	0.0164110	−	0.999865i	$-0.494776\pi$
$191$	3.16069e6	0.0328220	0.0164110	+	0.999865i	$0.494776\pi$
$192$	7.07789e6	0.0721688
$193$	−1.93300e7	−0.193545	−0.0967724	−	0.995307i	$-0.530852\pi$
$193$	−1.93300e7	−0.193545	−0.0967724	+	0.995307i	$0.530852\pi$
$194$	2.25862e7	0.222095
$195$	−2.60361e7	−0.251452
$196$	7.52954e6	0.0714286
$197$	6.07765e7	0.566375	0.283187	−	0.959065i	$-0.408608\pi$
$197$	6.07765e7	0.566375	0.283187	+	0.959065i	$0.408608\pi$
$198$	3.57640e6	0.0327430
$199$	−1.34769e8	−1.21228	−0.606141	−	0.795357i	$-0.707283\pi$
$199$	−1.34769e8	−1.21228	−0.606141	+	0.795357i	$0.707283\pi$
$200$	−5.86357e7	−0.518271
$201$	1.13652e8	0.987164
$202$	−6.27618e7	−0.535754
$203$	−4.61238e7	−0.386981
$204$	2.87836e7	0.237377
$205$	2.13922e8	1.73427
$206$	−9.63484e7	−0.767908
$207$	−4.37254e7	−0.342640
$208$	−8.99891e6	−0.0693375
$209$	−1.03867e6	−0.00786981
$210$	−3.25185e7	−0.242305
$211$	−2.09419e8	−1.53472	−0.767358	−	0.641219i	$-0.778429\pi$
$211$	−2.09419e8	−1.53472	−0.767358	+	0.641219i	$0.778429\pi$
$212$	5.27981e7	0.380577
$213$	−5.62118e7	−0.398565
$214$	−5.11865e7	−0.357032
$215$	3.75154e8	2.57440
$216$	−1.00777e7	−0.0680414
$217$	−8.44504e7	−0.561038
$218$	2.36372e7	0.154525
$219$	1.33234e8	0.857157
$220$	−1.72262e7	−0.109072
$221$	−3.65958e7	−0.228065
$222$	628620.	0.00385614
$223$	−1.32856e8	−0.802257	−0.401128	−	0.916022i	$-0.631382\pi$
$223$	−1.32856e8	−0.802257	−0.401128	+	0.916022i	$0.631382\pi$
$224$	−1.12394e7	−0.0668153
$225$	8.34872e7	0.488631
$226$	8.50848e7	0.490312
$227$	−2.43707e8	−1.38286	−0.691429	−	0.722445i	$-0.743018\pi$
$227$	−2.43707e8	−1.38286	−0.691429	+	0.722445i	$0.743018\pi$
$228$	2.92679e6	0.0163538
$229$	2.06423e8	1.13589	0.567943	−	0.823068i	$-0.307740\pi$
$229$	2.06423e8	1.13589	0.567943	+	0.823068i	$0.307740\pi$
$230$	2.10610e8	1.14138
$231$	−5.67919e6	−0.0303141
$232$	6.88496e7	0.361987
$233$	3.44118e7	0.178222	0.0891111	−	0.996022i	$-0.471597\pi$
$233$	3.44118e7	0.178222	0.0891111	+	0.996022i	$0.471597\pi$
$234$	1.28129e7	0.0653720
$235$	4.84746e8	2.43656
$236$	−2.85185e7	−0.141233
$237$	6.03119e7	0.294295
$238$	−4.57072e7	−0.219768
$239$	2.90139e8	1.37472	0.687358	−	0.726319i	$-0.258770\pi$
$239$	2.90139e8	1.37472	0.687358	+	0.726319i	$0.258770\pi$
$240$	4.85407e7	0.226656
$241$	−1.56531e8	−0.720343	−0.360172	−	0.932886i	$-0.617282\pi$
$241$	−1.56531e8	−0.720343	−0.360172	+	0.932886i	$0.617282\pi$
$242$	1.52889e8	0.693461
$243$	1.43489e7	0.0641500
$244$	3.08474e7	0.135942
$245$	5.16381e7	0.224331
$246$	−1.05276e8	−0.450873
$247$	−3.72115e6	−0.0157122
$248$	1.26060e8	0.524803
$249$	2.26290e8	0.928896
$250$	−1.27805e8	−0.517318
$251$	3.39741e8	1.35609	0.678046	−	0.735019i	$-0.262827\pi$
$251$	3.39741e8	1.35609	0.678046	+	0.735019i	$0.262827\pi$
$252$	1.60030e7	0.0629941
$253$	3.67820e7	0.142795
$254$	−2.41978e8	−0.926525
$255$	1.97400e8	0.745514
$256$	1.67772e7	0.0625000
$257$	1.78281e8	0.655147	0.327574	−	0.944826i	$-0.393769\pi$
$257$	1.78281e8	0.655147	0.327574	+	0.944826i	$0.393769\pi$
$258$	−1.84621e8	−0.669288
$259$	−998225.	−0.00357009
$260$	−6.17152e7	−0.217764
$261$	−9.80300e7	−0.341285
$262$	−1.94341e8	−0.667590
$263$	1.06970e8	0.362591	0.181296	−	0.983429i	$-0.441971\pi$
$263$	1.06970e8	0.362591	0.181296	+	0.983429i	$0.441971\pi$
$264$	8.47739e6	0.0283562
$265$	3.62093e8	1.19525
$266$	−4.64763e6	−0.0151407
$267$	−2.34001e8	−0.752365
$268$	2.69396e8	0.854909
$269$	−4.33449e8	−1.35770	−0.678852	−	0.734275i	$-0.737522\pi$
$269$	−4.33449e8	−1.35770	−0.678852	+	0.734275i	$0.737522\pi$
$270$	−6.91136e7	−0.213693
$271$	5.07880e8	1.55013	0.775066	−	0.631880i	$-0.217717\pi$
$271$	5.07880e8	1.55013	0.775066	+	0.631880i	$0.217717\pi$
$272$	6.82277e7	0.205575
$273$	−2.03464e7	−0.0605228
$274$	3.00333e8	0.882015
$275$	−7.02297e7	−0.203637
$276$	−1.03645e8	−0.296735
$277$	−1.24580e8	−0.352183	−0.176092	−	0.984374i	$-0.556346\pi$
$277$	−1.24580e8	−0.352183	−0.176092	+	0.984374i	$0.556346\pi$
$278$	3.95680e8	1.10456
$279$	−1.79488e8	−0.494789
$280$	−7.70808e7	−0.209842
$281$	−3.46435e8	−0.931427	−0.465714	−	0.884935i	$-0.654202\pi$
$281$	−3.46435e8	−0.931427	−0.465714	+	0.884935i	$0.654202\pi$
$282$	−2.38553e8	−0.633452
$283$	−4.34781e8	−1.14030	−0.570148	−	0.821542i	$-0.693114\pi$
$283$	−4.34781e8	−1.14030	−0.570148	+	0.821542i	$0.693114\pi$
$284$	−1.33243e8	−0.345167
$285$	2.00721e7	0.0513613
$286$	−1.07783e7	−0.0272438
$287$	1.67174e8	0.417428
$288$	−2.38879e7	−0.0589256
$289$	−1.32878e8	−0.323825
$290$	4.72175e8	1.13687
$291$	−7.62286e7	−0.181339
$292$	3.15814e8	0.742320
$293$	4.82394e8	1.12038	0.560190	−	0.828364i	$-0.310728\pi$
$293$	4.82394e8	1.12038	0.560190	+	0.828364i	$0.310728\pi$
$294$	−2.54122e7	−0.0583212
$295$	−1.95582e8	−0.443560
$296$	1.49006e6	0.00333952
$297$	−1.20704e7	−0.0267345
$298$	−3.61309e8	−0.790901
$299$	1.31776e8	0.285093
$300$	1.97895e8	0.423167
$301$	2.93172e8	0.619640
$302$	1.76613e8	0.368976
$303$	2.11821e8	0.437441
$304$	6.93757e6	0.0141628
$305$	2.11554e8	0.426944
$306$	−9.71445e7	−0.193818
$307$	9.44305e8	1.86264	0.931318	−	0.364206i	$-0.118660\pi$
$307$	9.44305e8	1.86264	0.931318	+	0.364206i	$0.118660\pi$
$308$	−1.34618e7	−0.0262528
$309$	3.25176e8	0.626994
$310$	8.64529e8	1.64821
$311$	2.26285e8	0.426573	0.213287	−	0.976990i	$-0.431583\pi$
$311$	2.26285e8	0.426573	0.213287	+	0.976990i	$0.431583\pi$
$312$	3.03713e7	0.0566139
$313$	−3.80424e8	−0.701233	−0.350616	−	0.936519i	$-0.614028\pi$
$313$	−3.80424e8	−0.701233	−0.350616	+	0.936519i	$0.614028\pi$
$314$	−2.76716e8	−0.504406
$315$	1.09750e8	0.197841
$316$	1.42961e8	0.254867
$317$	−3.24262e8	−0.571726	−0.285863	−	0.958270i	$-0.592280\pi$
$317$	−3.24262e8	−0.571726	−0.285863	+	0.958270i	$0.592280\pi$
$318$	−1.78194e8	−0.310740
$319$	8.24632e7	0.142230
$320$	1.15059e8	0.196290
$321$	1.72754e8	0.291515
$322$	1.64585e8	0.274723
$323$	2.82129e7	0.0465843
$324$	3.40122e7	0.0555556
$325$	−2.51607e8	−0.406565
$326$	−7.52059e8	−1.20224
$327$	−7.97756e7	−0.126169
$328$	−2.49542e8	−0.390468
$329$	3.78814e8	0.586463
$330$	5.81386e7	0.0890565
$331$	−1.30516e8	−0.197818	−0.0989092	−	0.995096i	$-0.531535\pi$
$331$	−1.30516e8	−0.197818	−0.0989092	+	0.995096i	$0.531535\pi$
$332$	5.36390e8	0.804447
$333$	−2.12159e6	−0.00314853
$334$	2.85060e8	0.418624
$335$	1.84754e9	2.68496
$336$	3.79331e7	0.0545545
$337$	−1.12353e9	−1.59912	−0.799561	−	0.600584i	$-0.794935\pi$
$337$	−1.12353e9	−1.59912	−0.799561	+	0.600584i	$0.794935\pi$
$338$	−3.86145e7	−0.0543928
$339$	−2.87161e8	−0.400338
$340$	4.67910e8	0.645634
$341$	1.50986e8	0.206203
$342$	−9.87790e6	−0.0133528
$343$	4.03536e7	0.0539949
$344$	−4.37621e8	−0.579620
$345$	−7.10808e8	−0.931935
$346$	9.18320e7	0.119187
$347$	9.67690e8	1.24332	0.621660	−	0.783287i	$-0.286458\pi$
$347$	9.67690e8	1.24332	0.621660	+	0.783287i	$0.286458\pi$
$348$	−2.32367e8	−0.295561
$349$	4.64555e8	0.584990	0.292495	−	0.956267i	$-0.405515\pi$
$349$	4.64555e8	0.584990	0.292495	+	0.956267i	$0.405515\pi$
$350$	−3.14251e8	−0.391776
$351$	−4.32436e7	−0.0533761
$352$	2.00946e7	0.0245572
$353$	4.19259e8	0.507307	0.253653	−	0.967295i	$-0.418368\pi$
$353$	4.19259e8	0.507307	0.253653	+	0.967295i	$0.418368\pi$
$354$	9.62501e7	0.115316
$355$	−9.13789e8	−1.08404
$356$	−5.54669e8	−0.651567
$357$	1.54262e8	0.179440
$358$	−2.54975e8	−0.293702
$359$	1.33446e9	1.52221	0.761105	−	0.648628i	$-0.224657\pi$
$359$	1.33446e9	1.52221	0.761105	+	0.648628i	$0.224657\pi$
$360$	−1.63825e8	−0.185064
$361$	−8.91003e8	−0.996791
$362$	−1.25345e8	−0.138876
$363$	−5.16000e8	−0.566209
$364$	−4.82285e7	−0.0524142
$365$	2.16587e9	2.33135
$366$	−1.04110e8	−0.110996
$367$	1.50489e9	1.58919	0.794593	−	0.607142i	$-0.207684\pi$
$367$	1.50489e9	1.58919	0.794593	+	0.607142i	$0.207684\pi$
$368$	−2.45678e8	−0.256980
$369$	3.55305e8	0.368137
$370$	1.02190e7	0.0104882
$371$	2.82965e8	0.287690
$372$	−4.25453e8	−0.428500
$373$	−8.19165e8	−0.817317	−0.408658	−	0.912687i	$-0.634003\pi$
$373$	−8.19165e8	−0.817317	−0.408658	+	0.912687i	$0.634003\pi$
$374$	8.17183e7	0.0807735
$375$	4.31342e8	0.422388
$376$	−5.65460e8	−0.548586
$377$	2.95435e8	0.283966
$378$	−5.40102e7	−0.0514344
$379$	−8.69668e8	−0.820571	−0.410286	−	0.911957i	$-0.634571\pi$
$379$	−8.69668e8	−0.820571	−0.410286	+	0.911957i	$0.634571\pi$
$380$	4.75783e7	0.0444802
$381$	8.16674e8	0.756505
$382$	−2.52855e7	−0.0232086
$383$	9.21258e8	0.837888	0.418944	−	0.908012i	$-0.362400\pi$
$383$	9.21258e8	0.837888	0.418944	+	0.908012i	$0.362400\pi$
$384$	−5.66231e7	−0.0510310
$385$	−9.23219e7	−0.0824503
$386$	1.54640e8	0.136857
$387$	6.23097e8	0.546471
$388$	−1.80690e8	−0.157045
$389$	1.44157e9	1.24169	0.620843	−	0.783935i	$-0.286791\pi$
$389$	1.44157e9	1.24169	0.620843	+	0.783935i	$0.286791\pi$
$390$	2.08289e8	0.177803
$391$	−9.99096e8	−0.845256
$392$	−6.02363e7	−0.0505076
$393$	6.55900e8	0.545085
$394$	−4.86212e8	−0.400487
$395$	9.80440e8	0.800444
$396$	−2.86112e7	−0.0231528
$397$	1.08851e9	0.873100	0.436550	−	0.899680i	$-0.356200\pi$
$397$	1.08851e9	0.873100	0.436550	+	0.899680i	$0.356200\pi$
$398$	1.07815e9	0.857212
$399$	1.56857e7	0.0123623
$400$	4.69086e8	0.366473
$401$	4.45951e8	0.345368	0.172684	−	0.984977i	$-0.444756\pi$
$401$	4.45951e8	0.345368	0.172684	+	0.984977i	$0.444756\pi$
$402$	−9.09213e8	−0.698031
$403$	5.40926e8	0.411690
$404$	5.02094e8	0.378835
$405$	2.33258e8	0.174480
$406$	3.68991e8	0.273637
$407$	1.78469e6	0.00131215
$408$	−2.30268e8	−0.167851
$409$	3.99616e8	0.288809	0.144405	−	0.989519i	$-0.453873\pi$
$409$	3.99616e8	0.288809	0.144405	+	0.989519i	$0.453873\pi$
$410$	−1.71138e9	−1.22632
$411$	−1.01362e9	−0.720163
$412$	7.70787e8	0.542993
$413$	−1.52842e8	−0.106762
$414$	3.49803e8	0.242283
$415$	3.67860e9	2.52647
$416$	7.19913e7	0.0490290
$417$	−1.33542e9	−0.901866
$418$	8.30933e6	0.00556479
$419$	2.54419e9	1.68966	0.844832	−	0.535032i	$-0.179701\pi$
$419$	2.54419e9	1.68966	0.844832	+	0.535032i	$0.179701\pi$
$420$	2.60148e8	0.171336
$421$	−1.96882e9	−1.28594	−0.642968	−	0.765893i	$-0.722297\pi$
$421$	−1.96882e9	−1.28594	−0.642968	+	0.765893i	$0.722297\pi$
$422$	1.67535e9	1.08521
$423$	8.05118e8	0.517212
$424$	−4.22385e8	−0.269109
$425$	1.90762e9	1.20540
$426$	4.49695e8	0.281828
$427$	1.65323e8	0.102763
$428$	4.09492e8	0.252460
$429$	3.63766e7	0.0222445
$430$	−3.00124e9	−1.82037
$431$	−2.97818e9	−1.79176	−0.895882	−	0.444291i	$-0.853455\pi$
$431$	−2.97818e9	−1.79176	−0.895882	+	0.444291i	$0.853455\pi$
$432$	8.06216e7	0.0481125
$433$	−1.47714e9	−0.874408	−0.437204	−	0.899362i	$-0.644031\pi$
$433$	−1.47714e9	−0.874408	−0.437204	+	0.899362i	$0.644031\pi$
$434$	6.75603e8	0.396714
$435$	−1.59359e9	−0.928249
$436$	−1.89098e8	−0.109266
$437$	−1.01591e8	−0.0582329
$438$	−1.06587e9	−0.606102
$439$	−8.70468e8	−0.491051	−0.245526	−	0.969390i	$-0.578961\pi$
$439$	−8.70468e8	−0.491051	−0.245526	+	0.969390i	$0.578961\pi$
$440$	1.37810e8	0.0771252
$441$	8.57661e7	0.0476190
$442$	2.92766e8	0.161266
$443$	1.46819e9	0.802361	0.401180	−	0.915999i	$-0.368600\pi$
$443$	1.46819e9	0.802361	0.401180	+	0.915999i	$0.368600\pi$
$444$	−5.02896e6	−0.00272670
$445$	−3.80396e9	−2.04633
$446$	1.06285e9	0.567281
$447$	1.21942e9	0.645768
$448$	8.99154e7	0.0472456
$449$	2.67108e8	0.139260	0.0696298	−	0.997573i	$-0.477818\pi$
$449$	2.67108e8	0.139260	0.0696298	+	0.997573i	$0.477818\pi$
$450$	−6.67897e8	−0.345514
$451$	−2.98884e8	−0.153421
$452$	−6.80679e8	−0.346703
$453$	−5.96069e8	−0.301268
$454$	1.94966e9	0.977828
$455$	−3.30755e8	−0.164614
$456$	−2.34143e7	−0.0115639
$457$	−3.53476e9	−1.73242	−0.866210	−	0.499679i	$-0.833451\pi$
$457$	−3.53476e9	−1.73242	−0.866210	+	0.499679i	$0.833451\pi$
$458$	−1.65139e9	−0.803192
$459$	3.27863e8	0.158251
$460$	−1.68488e9	−0.807079
$461$	2.38295e9	1.13282	0.566411	−	0.824123i	$-0.308332\pi$
$461$	2.38295e9	1.13282	0.566411	+	0.824123i	$0.308332\pi$
$462$	4.54335e7	0.0214353
$463$	7.25473e7	0.0339694	0.0169847	−	0.999856i	$-0.494593\pi$
$463$	7.25473e7	0.0339694	0.0169847	+	0.999856i	$0.494593\pi$
$464$	−5.50797e8	−0.255964
$465$	−2.91779e9	−1.34576
$466$	−2.75295e8	−0.126022
$467$	−2.33898e9	−1.06272	−0.531359	−	0.847147i	$-0.678318\pi$
$467$	−2.33898e9	−1.06272	−0.531359	+	0.847147i	$0.678318\pi$
$468$	−1.02503e8	−0.0462250
$469$	1.44380e9	0.646251
$470$	−3.87797e9	−1.72291
$471$	9.33916e8	0.411846
$472$	2.28148e8	0.0998666
$473$	−5.24151e8	−0.227742
$474$	−4.82495e8	−0.208098
$475$	1.93972e8	0.0830447
$476$	3.65658e8	0.155400
$477$	6.01404e8	0.253718
$478$	−2.32111e9	−0.972071
$479$	−3.13204e9	−1.30213	−0.651063	−	0.759024i	$-0.725677\pi$
$479$	−3.13204e9	−1.30213	−0.651063	+	0.759024i	$0.725677\pi$
$480$	−3.88325e8	−0.160270
$481$	6.39388e6	0.00261973
$482$	1.25224e9	0.509360
$483$	−5.55475e8	−0.224310
$484$	−1.22311e9	−0.490351
$485$	−1.23918e9	−0.493219
$486$	−1.14791e8	−0.0453609
$487$	2.96988e9	1.16516	0.582582	−	0.812772i	$-0.302042\pi$
$487$	2.96988e9	1.16516	0.582582	+	0.812772i	$0.302042\pi$
$488$	−2.46779e8	−0.0961257
$489$	2.53820e9	0.981622
$490$	−4.13105e8	−0.158626
$491$	−4.25451e9	−1.62205	−0.811025	−	0.585012i	$-0.801090\pi$
$491$	−4.25451e9	−1.62205	−0.811025	+	0.585012i	$0.801090\pi$
$492$	8.42204e8	0.318816
$493$	−2.23992e9	−0.841914
$494$	2.97692e7	0.0111102
$495$	−1.96218e8	−0.0727143
$496$	−1.00848e9	−0.371092
$497$	−7.14098e8	−0.260922
$498$	−1.81032e9	−0.656828
$499$	−1.93730e9	−0.697984	−0.348992	−	0.937126i	$-0.613476\pi$
$499$	−1.93730e9	−0.697984	−0.348992	+	0.937126i	$0.613476\pi$
$500$	1.02244e9	0.365799
$501$	−9.62077e8	−0.341805
$502$	−2.71793e9	−0.958903
$503$	−2.02364e9	−0.708998	−0.354499	−	0.935056i	$-0.615349\pi$
$503$	−2.02364e9	−0.708998	−0.354499	+	0.935056i	$0.615349\pi$
$504$	−1.28024e8	−0.0445435
$505$	3.44340e9	1.18978
$506$	−2.94256e8	−0.100971
$507$	1.30324e8	0.0444116
$508$	1.93582e9	0.655152
$509$	−1.24256e9	−0.417641	−0.208821	−	0.977954i	$-0.566962\pi$
$509$	−1.24256e9	−0.417641	−0.208821	+	0.977954i	$0.566962\pi$
$510$	−1.57920e9	−0.527158
$511$	1.69256e9	0.561141
$512$	−1.34218e8	−0.0441942
$513$	3.33379e7	0.0109025
$514$	−1.42625e9	−0.463259
$515$	5.28611e9	1.70534
$516$	1.47697e9	0.473258
$517$	−6.77268e8	−0.215548
$518$	7.98580e6	0.00252444
$519$	−3.09933e8	−0.0973155
$520$	4.93722e8	0.153982
$521$	3.23123e9	1.00100	0.500501	−	0.865736i	$-0.333149\pi$
$521$	3.23123e9	1.00100	0.500501	+	0.865736i	$0.333149\pi$
$522$	7.84240e8	0.241325
$523$	−5.06922e9	−1.54948	−0.774738	−	0.632282i	$-0.782118\pi$
$523$	−5.06922e9	−1.54948	−0.774738	+	0.632282i	$0.782118\pi$
$524$	1.55473e9	0.472057
$525$	1.06060e9	0.319884
$526$	−8.55761e8	−0.256391
$527$	−4.10117e9	−1.22059
$528$	−6.78192e7	−0.0200509
$529$	1.92774e8	0.0566179
$530$	−2.89675e9	−0.845172
$531$	−3.24844e8	−0.0941551
$532$	3.71810e7	0.0107061
$533$	−1.07079e9	−0.306308
$534$	1.87201e9	0.532002
$535$	2.80832e9	0.792883
$536$	−2.15517e9	−0.604512
$537$	8.60540e8	0.239807
$538$	3.46759e9	0.960042
$539$	−7.21468e7	−0.0198452
$540$	5.52909e8	0.151104
$541$	−2.40143e9	−0.652047	−0.326023	−	0.945362i	$-0.605709\pi$
$541$	−2.40143e9	−0.652047	−0.326023	+	0.945362i	$0.605709\pi$
$542$	−4.06304e9	−1.09611
$543$	4.23039e8	0.113392
$544$	−5.45821e8	−0.145363
$545$	−1.29685e9	−0.343163
$546$	1.62771e8	0.0427960
$547$	−3.71482e9	−0.970470	−0.485235	−	0.874384i	$-0.661266\pi$
$547$	−3.71482e9	−0.970470	−0.485235	+	0.874384i	$0.661266\pi$
$548$	−2.40266e9	−0.623679
$549$	3.51371e8	0.0906281
$550$	5.61838e8	0.143993
$551$	−2.27761e8	−0.0580027
$552$	8.29163e8	0.209823
$553$	7.66184e8	0.192662
$554$	9.96640e8	0.249031
$555$	−3.44890e7	−0.00856357
$556$	−3.16544e9	−0.781039
$557$	−3.24801e9	−0.796388	−0.398194	−	0.917301i	$-0.630363\pi$
$557$	−3.24801e9	−0.796388	−0.398194	+	0.917301i	$0.630363\pi$
$558$	1.43590e9	0.349869
$559$	−1.87784e9	−0.454691
$560$	6.16646e8	0.148381
$561$	−2.75799e8	−0.0659513
$562$	2.77148e9	0.658619
$563$	5.28287e9	1.24764	0.623822	−	0.781566i	$-0.285579\pi$
$563$	5.28287e9	1.24764	0.623822	+	0.781566i	$0.285579\pi$
$564$	1.90843e9	0.447918
$565$	−4.66814e9	−1.08887
$566$	3.47825e9	0.806311
$567$	1.82284e8	0.0419961
$568$	1.06594e9	0.244070
$569$	9.03192e8	0.205536	0.102768	−	0.994705i	$-0.467230\pi$
$569$	9.03192e8	0.205536	0.102768	+	0.994705i	$0.467230\pi$
$570$	−1.60577e8	−0.0363179
$571$	−5.41402e9	−1.21701	−0.608504	−	0.793551i	$-0.708230\pi$
$571$	−5.41402e9	−1.21701	−0.608504	+	0.793551i	$0.708230\pi$
$572$	8.62261e7	0.0192643
$573$	8.53385e7	0.0189498
$574$	−1.33739e9	−0.295166
$575$	−6.86908e9	−1.50682
$576$	1.91103e8	0.0416667
$577$	4.61481e8	0.100009	0.0500044	−	0.998749i	$-0.484076\pi$
$577$	4.61481e8	0.100009	0.0500044	+	0.998749i	$0.484076\pi$
$578$	1.06302e9	0.228979
$579$	−5.21910e8	−0.111743
$580$	−3.77740e9	−0.803888
$581$	2.87472e9	0.608105
$582$	6.09829e8	0.128226
$583$	−5.05903e8	−0.105737
$584$	−2.52651e9	−0.524899
$585$	−7.02975e8	−0.145176
$586$	−3.85915e9	−0.792228
$587$	−8.26817e9	−1.68724	−0.843618	−	0.536944i	$-0.819579\pi$
$587$	−8.26817e9	−1.68724	−0.843618	+	0.536944i	$0.819579\pi$
$588$	2.03297e8	0.0412393
$589$	−4.17018e8	−0.0840913
$590$	1.56466e9	0.313644
$591$	1.64096e9	0.326996
$592$	−1.19205e7	−0.00236139
$593$	2.54940e9	0.502049	0.251024	−	0.967981i	$-0.419233\pi$
$593$	2.54940e9	0.502049	0.251024	+	0.967981i	$0.419233\pi$
$594$	9.65628e7	0.0189042
$595$	2.50771e9	0.488054
$596$	2.89047e9	0.559251
$597$	−3.63876e9	−0.699911
$598$	−1.05421e9	−0.201592
$599$	1.70985e9	0.325060	0.162530	−	0.986704i	$-0.448035\pi$
$599$	1.70985e9	0.325060	0.162530	+	0.986704i	$0.448035\pi$
$600$	−1.58316e9	−0.299224
$601$	9.49145e9	1.78350	0.891748	−	0.452533i	$-0.149479\pi$
$601$	9.49145e9	1.78350	0.891748	+	0.452533i	$0.149479\pi$
$602$	−2.34537e9	−0.438152
$603$	3.06859e9	0.569940
$604$	−1.41290e9	−0.260906
$605$	−8.38819e9	−1.54001
$606$	−1.69457e9	−0.309318
$607$	5.68060e9	1.03094	0.515470	−	0.856907i	$-0.327617\pi$
$607$	5.68060e9	1.03094	0.515470	+	0.856907i	$0.327617\pi$
$608$	−5.55005e7	−0.0100146
$609$	−1.24534e9	−0.223423
$610$	−1.69243e9	−0.301895
$611$	−2.42640e9	−0.430346
$612$	7.77156e8	0.137050
$613$	−1.95983e9	−0.343642	−0.171821	−	0.985128i	$-0.554965\pi$
$613$	−1.95983e9	−0.343642	−0.171821	+	0.985128i	$0.554965\pi$
$614$	−7.55444e9	−1.31708
$615$	5.77590e9	1.00128
$616$	1.07694e8	0.0185635
$617$	2.58071e9	0.442325	0.221163	−	0.975237i	$-0.429015\pi$
$617$	2.58071e9	0.442325	0.221163	+	0.975237i	$0.429015\pi$
$618$	−2.60141e9	−0.443352
$619$	1.43435e9	0.243073	0.121537	−	0.992587i	$-0.461218\pi$
$619$	1.43435e9	0.243073	0.121537	+	0.992587i	$0.461218\pi$
$620$	−6.91623e9	−1.16546
$621$	−1.18059e9	−0.197823
$622$	−1.81028e9	−0.301633
$623$	−2.97268e9	−0.492538
$624$	−2.42971e8	−0.0400320
$625$	−1.93513e9	−0.317052
$626$	3.04339e9	0.495846
$627$	−2.80440e7	−0.00454363
$628$	2.21373e9	0.356669
$629$	−4.84769e7	−0.00776708
$630$	−8.77998e8	−0.139895
$631$	−8.72934e9	−1.38318	−0.691590	−	0.722290i	$-0.743089\pi$
$631$	−8.72934e9	−1.38318	−0.691590	+	0.722290i	$0.743089\pi$
$632$	−1.14369e9	−0.180218
$633$	−5.65432e9	−0.886068
$634$	2.59409e9	0.404271
$635$	1.32760e10	2.05759
$636$	1.42555e9	0.219726
$637$	−2.58475e8	−0.0396214
$638$	−6.59705e8	−0.100572
$639$	−1.51772e9	−0.230112
$640$	−9.20475e8	−0.138798
$641$	1.04731e10	1.57062	0.785312	−	0.619100i	$-0.212502\pi$
$641$	1.04731e10	1.57062	0.785312	+	0.619100i	$0.212502\pi$
$642$	−1.38203e9	−0.206132
$643$	9.70622e9	1.43983	0.719916	−	0.694061i	$-0.244180\pi$
$643$	9.70622e9	1.43983	0.719916	+	0.694061i	$0.244180\pi$
$644$	−1.31668e9	−0.194258
$645$	1.01292e10	1.48633
$646$	−2.25703e8	−0.0329400
$647$	1.96219e9	0.284823	0.142412	−	0.989808i	$-0.454514\pi$
$647$	1.96219e9	0.284823	0.142412	+	0.989808i	$0.454514\pi$
$648$	−2.72098e8	−0.0392837
$649$	2.73260e8	0.0392391
$650$	2.01285e9	0.287485
$651$	−2.28016e9	−0.323916
$652$	6.01647e9	0.850110
$653$	5.22739e9	0.734664	0.367332	−	0.930090i	$-0.380271\pi$
$653$	5.22739e9	0.734664	0.367332	+	0.930090i	$0.380271\pi$
$654$	6.38205e8	0.0892150
$655$	1.06624e10	1.48256
$656$	1.99634e9	0.276102
$657$	3.59732e9	0.494880
$658$	−3.03051e9	−0.414692
$659$	5.16442e9	0.702947	0.351474	−	0.936198i	$-0.385681\pi$
$659$	5.16442e9	0.702947	0.351474	+	0.936198i	$0.385681\pi$
$660$	−4.65109e8	−0.0629725
$661$	1.33212e9	0.179406	0.0897030	−	0.995969i	$-0.471408\pi$
$661$	1.33212e9	0.179406	0.0897030	+	0.995969i	$0.471408\pi$
$662$	1.04413e9	0.139879
$663$	−9.88085e8	−0.131673
$664$	−4.29112e9	−0.568830
$665$	2.54990e8	0.0336239
$666$	1.69727e7	0.00222634
$667$	8.06562e9	1.05244
$668$	−2.28048e9	−0.296012
$669$	−3.58711e9	−0.463183
$670$	−1.47803e10	−1.89855
$671$	−2.95575e8	−0.0377693
$672$	−3.03464e8	−0.0385758
$673$	−1.19480e10	−1.51093	−0.755463	−	0.655192i	$-0.772588\pi$
$673$	−1.19480e10	−1.51093	−0.755463	+	0.655192i	$0.772588\pi$
$674$	8.98828e9	1.13075
$675$	2.25415e9	0.282111
$676$	3.08916e8	0.0384615
$677$	3.91347e9	0.484732	0.242366	−	0.970185i	$-0.422077\pi$
$677$	3.91347e9	0.484732	0.242366	+	0.970185i	$0.422077\pi$
$678$	2.29729e9	0.283082
$679$	−9.68385e8	−0.118715
$680$	−3.74328e9	−0.456532
$681$	−6.58009e9	−0.798393
$682$	−1.20789e9	−0.145808
$683$	2.60024e9	0.312277	0.156139	−	0.987735i	$-0.450095\pi$
$683$	2.60024e9	0.312277	0.156139	+	0.987735i	$0.450095\pi$
$684$	7.90232e7	0.00944188
$685$	−1.64776e10	−1.95875
$686$	−3.22829e8	−0.0381802
$687$	5.57343e9	0.655804
$688$	3.50097e9	0.409853
$689$	−1.81246e9	−0.211106
$690$	5.68646e9	0.658977
$691$	2.54480e9	0.293414	0.146707	−	0.989180i	$-0.453133\pi$
$691$	2.54480e9	0.293414	0.146707	+	0.989180i	$0.453133\pi$
$692$	−7.34656e8	−0.0842777
$693$	−1.53338e8	−0.0175019
$694$	−7.74152e9	−0.879161
$695$	−2.17088e10	−2.45296
$696$	1.85894e9	0.208993
$697$	8.11847e9	0.908154
$698$	−3.71644e9	−0.413650
$699$	9.29119e8	0.102897
$700$	2.51401e9	0.277028
$701$	−6.53781e9	−0.716835	−0.358418	−	0.933561i	$-0.616684\pi$
$701$	−6.53781e9	−0.716835	−0.358418	+	0.933561i	$0.616684\pi$
$702$	3.45948e8	0.0377426
$703$	−4.92926e6	−0.000535104 0
$704$	−1.60757e8	−0.0173646
$705$	1.30881e10	1.40675
$706$	−3.35407e9	−0.358720
$707$	2.69091e9	0.286373
$708$	−7.70001e8	−0.0815407
$709$	2.52199e9	0.265755	0.132877	−	0.991132i	$-0.457578\pi$
$709$	2.52199e9	0.265755	0.132877	+	0.991132i	$0.457578\pi$
$710$	7.31031e9	0.766535
$711$	1.62842e9	0.169912
$712$	4.43735e9	0.460727
$713$	1.47677e10	1.52581
$714$	−1.23409e9	−0.126883
$715$	5.91345e8	0.0605020
$716$	2.03980e9	0.207679
$717$	7.83375e9	0.793693
$718$	−1.06757e10	−1.07637
$719$	1.27204e10	1.27629	0.638143	−	0.769918i	$-0.279703\pi$
$719$	1.27204e10	1.27629	0.638143	+	0.769918i	$0.279703\pi$
$720$	1.31060e9	0.130860
$721$	4.13094e9	0.410464
$722$	7.12802e9	0.704837
$723$	−4.22633e9	−0.415890
$724$	1.00276e9	0.0981999
$725$	−1.54001e10	−1.50086
$726$	4.12800e9	0.400370
$727$	5.70658e9	0.550815	0.275407	−	0.961328i	$-0.411187\pi$
$727$	5.70658e9	0.550815	0.275407	+	0.961328i	$0.411187\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	−1.73270e10	−1.64852
$731$	1.42373e10	1.34809
$732$	8.32880e8	0.0784863
$733$	−1.61419e10	−1.51387	−0.756937	−	0.653488i	$-0.773305\pi$
$733$	−1.61419e10	−1.51387	−0.756937	+	0.653488i	$0.773305\pi$
$734$	−1.20392e10	−1.12372
$735$	1.39423e9	0.129517
$736$	1.96542e9	0.181712
$737$	−2.58131e9	−0.237522
$738$	−2.84244e9	−0.260312
$739$	−4.00265e9	−0.364831	−0.182416	−	0.983222i	$-0.558392\pi$
$739$	−4.00265e9	−0.364831	−0.182416	+	0.983222i	$0.558392\pi$
$740$	−8.17516e7	−0.00741627
$741$	−1.00471e8	−0.00907146
$742$	−2.26372e9	−0.203427
$743$	−4.09597e9	−0.366350	−0.183175	−	0.983080i	$-0.558637\pi$
$743$	−4.09597e9	−0.366350	−0.183175	+	0.983080i	$0.558637\pi$
$744$	3.40362e9	0.302995
$745$	1.98231e10	1.75640
$746$	6.55332e9	0.577930
$747$	6.10982e9	0.536298
$748$	−6.53746e8	−0.0571155
$749$	2.19462e9	0.190841
$750$	−3.45073e9	−0.298674
$751$	−1.36616e10	−1.17696	−0.588481	−	0.808511i	$-0.700274\pi$
$751$	−1.36616e10	−1.17696	−0.588481	+	0.808511i	$0.700274\pi$
$752$	4.52368e9	0.387909
$753$	9.17300e9	0.782941
$754$	−2.36348e9	−0.200794
$755$	−9.68980e9	−0.819408
$756$	4.32081e8	0.0363696
$757$	5.79115e9	0.485210	0.242605	−	0.970125i	$-0.421998\pi$
$757$	5.79115e9	0.485210	0.242605	+	0.970125i	$0.421998\pi$
$758$	6.95735e9	0.580232
$759$	9.93113e8	0.0824428
$760$	−3.80627e8	−0.0314523
$761$	−1.57699e10	−1.29713	−0.648564	−	0.761160i	$-0.724630\pi$
$761$	−1.57699e10	−1.29713	−0.648564	+	0.761160i	$0.724630\pi$
$762$	−6.53340e9	−0.534930
$763$	−1.01345e9	−0.0825970
$764$	2.02284e8	0.0164110
$765$	5.32979e9	0.430423
$766$	−7.37007e9	−0.592476
$767$	9.78988e8	0.0783418
$768$	4.52985e8	0.0360844
$769$	−1.39801e10	−1.10858	−0.554292	−	0.832322i	$-0.687011\pi$
$769$	−1.39801e10	−1.10858	−0.554292	+	0.832322i	$0.687011\pi$
$770$	7.38575e8	0.0583012
$771$	4.81359e9	0.378250
$772$	−1.23712e9	−0.0967724
$773$	1.10317e10	0.859040	0.429520	−	0.903057i	$-0.358683\pi$
$773$	1.10317e10	0.859040	0.429520	+	0.903057i	$0.358683\pi$
$774$	−4.98478e9	−0.386413
$775$	−2.81968e10	−2.17592
$776$	1.44552e9	0.111047
$777$	−2.69521e7	−0.00206119
$778$	−1.15325e10	−0.878004
$779$	8.25508e8	0.0625662
$780$	−1.66631e9	−0.125726
$781$	1.27671e9	0.0958990
$782$	7.99277e9	0.597686
$783$	−2.64681e9	−0.197041
$784$	4.81890e8	0.0357143
$785$	1.51819e10	1.12017
$786$	−5.24720e9	−0.385433
$787$	−1.59771e10	−1.16838	−0.584192	−	0.811615i	$-0.698589\pi$
$787$	−1.59771e10	−1.16838	−0.584192	+	0.811615i	$0.698589\pi$
$788$	3.88969e9	0.283187
$789$	2.88819e9	0.209342
$790$	−7.84352e9	−0.566000
$791$	−3.64801e9	−0.262083
$792$	2.28890e8	0.0163715
$793$	−1.05893e9	−0.0754072
$794$	−8.70805e9	−0.617375
$795$	9.77652e9	0.690080
$796$	−8.62520e9	−0.606141
$797$	1.94142e9	0.135836	0.0679180	−	0.997691i	$-0.478364\pi$
$797$	1.94142e9	0.135836	0.0679180	+	0.997691i	$0.478364\pi$
$798$	−1.25486e8	−0.00874148
$799$	1.83964e10	1.27591
$800$	−3.75268e9	−0.259136
$801$	−6.31803e9	−0.434378
$802$	−3.56761e9	−0.244212
$803$	−3.02607e9	−0.206241
$804$	7.27370e9	0.493582
$805$	−9.02989e9	−0.610094
$806$	−4.32740e9	−0.291108
$807$	−1.17031e10	−0.783871
$808$	−4.01676e9	−0.267877
$809$	−7.76568e9	−0.515655	−0.257828	−	0.966191i	$-0.583007\pi$
$809$	−7.76568e9	−0.515655	−0.257828	+	0.966191i	$0.583007\pi$
$810$	−1.86607e9	−0.123376
$811$	−9.86945e9	−0.649711	−0.324855	−	0.945764i	$-0.605316\pi$
$811$	−9.86945e9	−0.649711	−0.324855	+	0.945764i	$0.605316\pi$
$812$	−2.95193e9	−0.193490
$813$	1.37128e10	0.894969
$814$	−1.42775e7	−0.000927829 0
$815$	4.12614e10	2.66988
$816$	1.84215e9	0.118689
$817$	1.44769e9	0.0928749
$818$	−3.19692e9	−0.204219
$819$	−5.49353e8	−0.0349428
$820$	1.36910e10	0.867136
$821$	1.07418e10	0.677445	0.338722	−	0.940886i	$-0.390005\pi$
$821$	1.07418e10	0.677445	0.338722	+	0.940886i	$0.390005\pi$
$822$	8.10899e9	0.509232
$823$	1.14068e10	0.713289	0.356645	−	0.934240i	$-0.383921\pi$
$823$	1.14068e10	0.713289	0.356645	+	0.934240i	$0.383921\pi$
$824$	−6.16630e9	−0.383954
$825$	−1.89620e9	−0.117570
$826$	1.22273e9	0.0754921
$827$	−2.63229e10	−1.61832	−0.809161	−	0.587587i	$-0.800078\pi$
$827$	−2.63229e10	−1.61832	−0.809161	+	0.587587i	$0.800078\pi$
$828$	−2.79843e9	−0.171320
$829$	8.82574e9	0.538035	0.269017	−	0.963135i	$-0.413301\pi$
$829$	8.82574e9	0.538035	0.269017	+	0.963135i	$0.413301\pi$
$830$	−2.94288e10	−1.78649
$831$	−3.36366e9	−0.203333
$832$	−5.75930e8	−0.0346688
$833$	1.95970e9	0.117471
$834$	1.06834e10	0.637716
$835$	−1.56397e10	−0.929663
$836$	−6.64746e7	−0.00393490
$837$	−4.84617e9	−0.285667
$838$	−2.03535e10	−1.19477
$839$	3.61230e9	0.211162	0.105581	−	0.994411i	$-0.466330\pi$
$839$	3.61230e9	0.211162	0.105581	+	0.994411i	$0.466330\pi$
$840$	−2.08118e9	−0.121153
$841$	8.32794e8	0.0482782
$842$	1.57506e10	0.909293
$843$	−9.35373e9	−0.537760
$844$	−1.34028e10	−0.767358
$845$	2.11857e9	0.120794
$846$	−6.44094e9	−0.365724
$847$	−6.55511e9	−0.370671
$848$	3.37908e9	0.190289
$849$	−1.17391e10	−0.658351
$850$	−1.52610e10	−0.852347
$851$	1.74558e8	0.00970929
$852$	−3.59756e9	−0.199282
$853$	3.42387e10	1.88884	0.944421	−	0.328739i	$-0.106624\pi$
$853$	3.42387e10	1.88884	0.944421	+	0.328739i	$0.106624\pi$
$854$	−1.32258e9	−0.0726642
$855$	5.41947e8	0.0296535
$856$	−3.27593e9	−0.178516
$857$	7.73043e9	0.419537	0.209769	−	0.977751i	$-0.432729\pi$
$857$	7.73043e9	0.419537	0.209769	+	0.977751i	$0.432729\pi$
$858$	−2.91013e8	−0.0157292
$859$	−2.16322e10	−1.16446	−0.582231	−	0.813024i	$-0.697820\pi$
$859$	−2.16322e10	−1.16446	−0.582231	+	0.813024i	$0.697820\pi$
$860$	2.40099e10	1.28720
$861$	4.51369e9	0.241002
$862$	2.38255e10	1.26697
$863$	−7.81992e9	−0.414157	−0.207078	−	0.978324i	$-0.566396\pi$
$863$	−7.81992e9	−0.414157	−0.207078	+	0.978324i	$0.566396\pi$
$864$	−6.44973e8	−0.0340207
$865$	−5.03832e9	−0.264685
$866$	1.18171e10	0.618300
$867$	−3.58771e9	−0.186961
$868$	−5.40482e9	−0.280519
$869$	−1.36983e9	−0.0708106
$870$	1.27487e10	0.656372
$871$	−9.24788e9	−0.474218
$872$	1.51278e9	0.0772625
$873$	−2.05817e9	−0.104696
$874$	8.12725e8	0.0411769
$875$	5.47964e9	0.276518
$876$	8.52697e9	0.428578
$877$	−2.90504e10	−1.45430	−0.727150	−	0.686479i	$-0.759156\pi$
$877$	−2.90504e10	−1.45430	−0.727150	+	0.686479i	$0.759156\pi$
$878$	6.96374e9	0.347226
$879$	1.30246e10	0.646852
$880$	−1.10248e9	−0.0545358
$881$	−1.62576e10	−0.801016	−0.400508	−	0.916293i	$-0.631166\pi$
$881$	−1.62576e10	−0.801016	−0.400508	+	0.916293i	$0.631166\pi$
$882$	−6.86129e8	−0.0336718
$883$	1.52535e9	0.0745603	0.0372802	−	0.999305i	$-0.488131\pi$
$883$	1.52535e9	0.0745603	0.0372802	+	0.999305i	$0.488131\pi$
$884$	−2.34213e9	−0.114032
$885$	−5.28072e9	−0.256089
$886$	−1.17455e10	−0.567355
$887$	−1.92252e9	−0.0924991	−0.0462496	−	0.998930i	$-0.514727\pi$
$887$	−1.92252e9	−0.0924991	−0.0462496	+	0.998930i	$0.514727\pi$
$888$	4.02317e7	0.00192807
$889$	1.03748e10	0.495249
$890$	3.04317e10	1.44698
$891$	−3.25900e8	−0.0154352
$892$	−8.50277e9	−0.401128
$893$	1.87059e9	0.0879021
$894$	−9.75535e9	−0.456627
$895$	1.39891e10	0.652242
$896$	−7.19323e8	−0.0334077
$897$	3.55795e9	0.164599
$898$	−2.13687e9	−0.0984715
$899$	3.31084e10	1.51978
$900$	5.34318e9	0.244315
$901$	1.37417e10	0.625896
$902$	2.39107e9	0.108485
$903$	7.91564e9	0.357749
$904$	5.44543e9	0.245156
$905$	6.87699e9	0.308410
$906$	4.76855e9	0.213028
$907$	3.62031e10	1.61109	0.805546	−	0.592534i	$-0.201872\pi$
$907$	3.62031e10	1.61109	0.805546	+	0.592534i	$0.201872\pi$
$908$	−1.55972e10	−0.691429
$909$	5.71917e9	0.252557
$910$	2.64604e9	0.116400
$911$	8.19212e9	0.358990	0.179495	−	0.983759i	$-0.442554\pi$
$911$	8.19212e9	0.358990	0.179495	+	0.983759i	$0.442554\pi$
$912$	1.87314e8	0.00817691
$913$	−5.13960e9	−0.223502
$914$	2.82781e10	1.22501
$915$	5.71195e9	0.246497
$916$	1.32111e10	0.567943
$917$	8.33236e9	0.356842
$918$	−2.62290e9	−0.111901
$919$	−1.64307e10	−0.698317	−0.349159	−	0.937064i	$-0.613533\pi$
$919$	−1.64307e10	−0.698317	−0.349159	+	0.937064i	$0.613533\pi$
$920$	1.34790e10	0.570691
$921$	2.54962e10	1.07539
$922$	−1.90636e10	−0.801026
$923$	4.57398e9	0.191464
$924$	−3.63468e8	−0.0151570
$925$	−3.33293e8	−0.0138462
$926$	−5.80379e8	−0.0240200
$927$	8.77975e9	0.361995
$928$	4.40637e9	0.180994
$929$	−1.47398e10	−0.603167	−0.301583	−	0.953440i	$-0.597515\pi$
$929$	−1.47398e10	−0.603167	−0.301583	+	0.953440i	$0.597515\pi$
$930$	2.33423e10	0.951597
$931$	1.99267e8	0.00809304
$932$	2.20236e9	0.0891111
$933$	6.10968e9	0.246282
$934$	1.87119e10	0.751455
$935$	−4.48344e9	−0.179379
$936$	8.20026e8	0.0326860
$937$	1.81420e10	0.720440	0.360220	−	0.932867i	$-0.382702\pi$
$937$	1.81420e10	0.720440	0.360220	+	0.932867i	$0.382702\pi$
$938$	−1.15504e10	−0.456968
$939$	−1.02714e10	−0.404857
$940$	3.10237e10	1.21828
$941$	3.42264e10	1.33905	0.669526	−	0.742789i	$-0.266497\pi$
$941$	3.42264e10	1.33905	0.669526	+	0.742789i	$0.266497\pi$
$942$	−7.47133e9	−0.291219
$943$	−2.92335e10	−1.13524
$944$	−1.82519e9	−0.0706164
$945$	2.96324e9	0.114224
$946$	4.19321e9	0.161038
$947$	3.63418e10	1.39053	0.695267	−	0.718752i	$-0.255286\pi$
$947$	3.63418e10	1.39053	0.695267	+	0.718752i	$0.255286\pi$
$948$	3.85996e9	0.147148
$949$	−1.08413e10	−0.411765
$950$	−1.55178e9	−0.0587215
$951$	−8.75506e9	−0.330086
$952$	−2.92526e9	−0.109884
$953$	−1.65036e10	−0.617665	−0.308832	−	0.951116i	$-0.599938\pi$
$953$	−1.65036e10	−0.617665	−0.308832	+	0.951116i	$0.599938\pi$
$954$	−4.81123e9	−0.179406
$955$	1.38728e9	0.0515409
$956$	1.85689e10	0.687358
$957$	2.22651e9	0.0821168
$958$	2.50563e10	0.920742
$959$	−1.28768e10	−0.471457
$960$	3.10660e9	0.113328
$961$	3.31073e10	1.20335
$962$	−5.11510e7	−0.00185243
$963$	4.66437e9	0.168306
$964$	−1.00180e10	−0.360172
$965$	−8.48426e9	−0.303926
$966$	4.44380e9	0.158611
$967$	3.80596e10	1.35354	0.676770	−	0.736194i	$-0.263379\pi$
$967$	3.80596e10	1.35354	0.676770	+	0.736194i	$0.263379\pi$
$968$	9.78489e9	0.346731
$969$	7.61749e8	0.0268954
$970$	9.91348e9	0.348759
$971$	−2.09923e10	−0.735855	−0.367928	−	0.929854i	$-0.619933\pi$
$971$	−2.09923e10	−0.735855	−0.367928	+	0.929854i	$0.619933\pi$
$972$	9.18330e8	0.0320750
$973$	−1.69648e10	−0.590410
$974$	−2.37590e10	−0.823896
$975$	−6.79338e9	−0.234731
$976$	1.97423e9	0.0679711
$977$	−1.01782e10	−0.349172	−0.174586	−	0.984642i	$-0.555859\pi$
$977$	−1.01782e10	−0.349172	−0.174586	+	0.984642i	$0.555859\pi$
$978$	−2.03056e10	−0.694112
$979$	5.31475e9	0.181027
$980$	3.30484e9	0.112165
$981$	−2.15394e9	−0.0728437
$982$	3.40361e10	1.14696
$983$	−8.08833e9	−0.271595	−0.135797	−	0.990737i	$-0.543360\pi$
$983$	−8.08833e9	−0.271595	−0.135797	+	0.990737i	$0.543360\pi$
$984$	−6.73763e9	−0.225437
$985$	2.66758e10	0.889387
$986$	1.79193e10	0.595323
$987$	1.02280e10	0.338594
$988$	−2.38154e8	−0.00785612
$989$	−5.12666e10	−1.68518
$990$	1.56974e9	0.0514168
$991$	−4.00185e10	−1.30618	−0.653090	−	0.757281i	$-0.726527\pi$
$991$	−4.00185e10	−1.30618	−0.653090	+	0.757281i	$0.726527\pi$
$992$	8.06784e9	0.262402
$993$	−3.52394e9	−0.114210
$994$	5.71279e9	0.184500
$995$	−5.91522e10	−1.90366
$996$	1.44825e10	0.464448
$997$	−4.41698e10	−1.41154	−0.705769	−	0.708442i	$-0.749398\pi$
$997$	−4.41698e10	−1.41154	−0.705769	+	0.708442i	$0.749398\pi$
$998$	1.54984e10	0.493549
$999$	−5.72830e7	−0.00181780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.p.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.p.1.6	✓	6	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)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +438.917 q^{5} -216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +438.917 q^{5} -216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -3511.33 q^{10} -613.237 q^{11} +1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +11850.8 q^{15} +4096.00 q^{16} +16657.1 q^{17} -5832.00 q^{18} +1693.74 q^{19} +28090.7 q^{20} +9261.00 q^{21} +4905.90 q^{22} -59980.0 q^{23} -13824.0 q^{24} +114523. q^{25} +17576.0 q^{26} +19683.0 q^{27} +21952.0 q^{28} -134472. q^{29} -94806.0 q^{30} -246211. q^{31} -32768.0 q^{32} -16557.4 q^{33} -133257. q^{34} +150548. q^{35} +46656.0 q^{36} -2910.28 q^{37} -13549.9 q^{38} -59319.0 q^{39} -224725. q^{40} +487387. q^{41} -74088.0 q^{42} +854728. q^{43} -39247.2 q^{44} +319970. q^{45} +479840. q^{46} +1.10441e6 q^{47} +110592. q^{48} +117649. q^{49} -916183. q^{50} +449743. q^{51} -140608. q^{52} +824971. q^{53} -157464. q^{54} -269160. q^{55} -175616. q^{56} +45731.0 q^{57} +1.07577e6 q^{58} -445602. q^{59} +758448. q^{60} +481991. q^{61} +1.96969e6 q^{62} +250047. q^{63} +262144. q^{64} -964300. q^{65} +132459. q^{66} +4.20932e6 q^{67} +1.06606e6 q^{68} -1.61946e6 q^{69} -1.20439e6 q^{70} -2.08192e6 q^{71} -373248. q^{72} +4.93459e6 q^{73} +23282.2 q^{74} +3.09212e6 q^{75} +108400. q^{76} -210340. q^{77} +474552. q^{78} +2.23377e6 q^{79} +1.79780e6 q^{80} +531441. q^{81} -3.89909e6 q^{82} +8.38110e6 q^{83} +592704. q^{84} +7.31110e6 q^{85} -6.83783e6 q^{86} -3.63074e6 q^{87} +313978. q^{88} -8.66671e6 q^{89} -2.55976e6 q^{90} -753571. q^{91} -3.83872e6 q^{92} -6.64770e6 q^{93} -8.83531e6 q^{94} +743412. q^{95} -884736. q^{96} -2.82328e6 q^{97} -941192. q^{98} -447050. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} + 162 q^{3} + 384 q^{4} - 43 q^{5} - 1296 q^{6} + 2058 q^{7} - 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 6 * q - 48 * q^2 + 162 * q^3 + 384 * q^4 - 43 * q^5 - 1296 * q^6 + 2058 * q^7 - 3072 * q^8 + 4374 * q^9	\( 6 q - 48 q^{2} + 162 q^{3} + 384 q^{4} - 43 q^{5} - 1296 q^{6} + 2058 q^{7} - 3072 q^{8} + 4374 q^{9} + 344 q^{10} + 7370 q^{11} + 10368 q^{12} - 13182 q^{13} - 16464 q^{14} - 1161 q^{15} + 24576 q^{16} + 7950 q^{17} - 34992 q^{18} - 57145 q^{19} - 2752 q^{20} + 55566 q^{21} - 58960 q^{22} + 31769 q^{23} - 82944 q^{24} + 135721 q^{25} + 105456 q^{26} + 118098 q^{27} + 131712 q^{28} - 36455 q^{29} + 9288 q^{30} + 215069 q^{31} - 196608 q^{32} + 198990 q^{33} - 63600 q^{34} - 14749 q^{35} + 279936 q^{36} + 133074 q^{37} + 457160 q^{38} - 355914 q^{39} + 22016 q^{40} + 516452 q^{41} - 444528 q^{42} - 3085 q^{43} + 471680 q^{44} - 31347 q^{45} - 254152 q^{46} + 1463947 q^{47} + 663552 q^{48} + 705894 q^{49} - 1085768 q^{50} + 214650 q^{51} - 843648 q^{52} - 1344571 q^{53} - 944784 q^{54} - 1568062 q^{55} - 1053696 q^{56} - 1542915 q^{57} + 291640 q^{58} + 1810408 q^{59} - 74304 q^{60} + 4047390 q^{61} - 1720552 q^{62} + 1500282 q^{63} + 1572864 q^{64} + 94471 q^{65} - 1591920 q^{66} + 2393614 q^{67} + 508800 q^{68} + 857763 q^{69} + 117992 q^{70} + 10341084 q^{71} - 2239488 q^{72} + 5180001 q^{73} - 1064592 q^{74} + 3664467 q^{75} - 3657280 q^{76} + 2527910 q^{77} + 2847312 q^{78} + 4624979 q^{79} - 176128 q^{80} + 3188646 q^{81} - 4131616 q^{82} + 11892699 q^{83} + 3556224 q^{84} + 750368 q^{85} + 24680 q^{86} - 984285 q^{87} - 3773440 q^{88} + 9781713 q^{89} + 250776 q^{90} - 4521426 q^{91} + 2033216 q^{92} + 5806863 q^{93} - 11711576 q^{94} + 26244263 q^{95} - 5308416 q^{96} + 5202537 q^{97} - 5647152 q^{98} + 5372730 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 + 162 * q^3 + 384 * q^4 - 43 * q^5 - 1296 * q^6 + 2058 * q^7 - 3072 * q^8 + 4374 * q^9 + 344 * q^10 + 7370 * q^11 + 10368 * q^12 - 13182 * q^13 - 16464 * q^14 - 1161 * q^15 + 24576 * q^16 + 7950 * q^17 - 34992 * q^18 - 57145 * q^19 - 2752 * q^20 + 55566 * q^21 - 58960 * q^22 + 31769 * q^23 - 82944 * q^24 + 135721 * q^25 + 105456 * q^26 + 118098 * q^27 + 131712 * q^28 - 36455 * q^29 + 9288 * q^30 + 215069 * q^31 - 196608 * q^32 + 198990 * q^33 - 63600 * q^34 - 14749 * q^35 + 279936 * q^36 + 133074 * q^37 + 457160 * q^38 - 355914 * q^39 + 22016 * q^40 + 516452 * q^41 - 444528 * q^42 - 3085 * q^43 + 471680 * q^44 - 31347 * q^45 - 254152 * q^46 + 1463947 * q^47 + 663552 * q^48 + 705894 * q^49 - 1085768 * q^50 + 214650 * q^51 - 843648 * q^52 - 1344571 * q^53 - 944784 * q^54 - 1568062 * q^55 - 1053696 * q^56 - 1542915 * q^57 + 291640 * q^58 + 1810408 * q^59 - 74304 * q^60 + 4047390 * q^61 - 1720552 * q^62 + 1500282 * q^63 + 1572864 * q^64 + 94471 * q^65 - 1591920 * q^66 + 2393614 * q^67 + 508800 * q^68 + 857763 * q^69 + 117992 * q^70 + 10341084 * q^71 - 2239488 * q^72 + 5180001 * q^73 - 1064592 * q^74 + 3664467 * q^75 - 3657280 * q^76 + 2527910 * q^77 + 2847312 * q^78 + 4624979 * q^79 - 176128 * q^80 + 3188646 * q^81 - 4131616 * q^82 + 11892699 * q^83 + 3556224 * q^84 + 750368 * q^85 + 24680 * q^86 - 984285 * q^87 - 3773440 * q^88 + 9781713 * q^89 + 250776 * q^90 - 4521426 * q^91 + 2033216 * q^92 + 5806863 * q^93 - 11711576 * q^94 + 26244263 * q^95 - 5308416 * q^96 + 5202537 * q^97 - 5647152 * q^98 + 5372730 * q^99

Introduction

L-functions

Modular forms

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