LMFDB - Embedded newform 546.8.a.s.1.4

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2 x^{6} - 313738 x^{5} + 10691268 x^{4} + 29687523333 x^{3} - 2032748091218 x^{2} + \cdots + 81\!\cdots\!96 $ x^7 - 2x^6 - 313738x^5 + 10691268x^4 + 29687523333x^3 - 2032748091218x^2 - 846237116901940x + 81946324586652296
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{6}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$111.302$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +200.302 q^{5} +216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +200.302 q^{5} +216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +1602.41 q^{10} +1069.70 q^{11} +1728.00 q^{12} +2197.00 q^{13} +2744.00 q^{14} +5408.15 q^{15} +4096.00 q^{16} +16719.4 q^{17} +5832.00 q^{18} -43894.9 q^{19} +12819.3 q^{20} +9261.00 q^{21} +8557.61 q^{22} -1712.43 q^{23} +13824.0 q^{24} -38004.2 q^{25} +17576.0 q^{26} +19683.0 q^{27} +21952.0 q^{28} +238868. q^{29} +43265.2 q^{30} +307405. q^{31} +32768.0 q^{32} +28881.9 q^{33} +133755. q^{34} +68703.5 q^{35} +46656.0 q^{36} +181002. q^{37} -351159. q^{38} +59319.0 q^{39} +102555. q^{40} -718028. q^{41} +74088.0 q^{42} +649434. q^{43} +68460.9 q^{44} +146020. q^{45} -13699.5 q^{46} -751182. q^{47} +110592. q^{48} +117649. q^{49} -304034. q^{50} +451423. q^{51} +140608. q^{52} +308666. q^{53} +157464. q^{54} +214263. q^{55} +175616. q^{56} -1.18516e6 q^{57} +1.91094e6 q^{58} +1.48361e6 q^{59} +346122. q^{60} -925088. q^{61} +2.45924e6 q^{62} +250047. q^{63} +262144. q^{64} +440063. q^{65} +231056. q^{66} +629175. q^{67} +1.07004e6 q^{68} -46235.7 q^{69} +549628. q^{70} +2.13027e6 q^{71} +373248. q^{72} +4.72296e6 q^{73} +1.44801e6 q^{74} -1.02611e6 q^{75} -2.80927e6 q^{76} +366908. q^{77} +474552. q^{78} -6.86756e6 q^{79} +820436. q^{80} +531441. q^{81} -5.74423e6 q^{82} -1.88267e6 q^{83} +592704. q^{84} +3.34892e6 q^{85} +5.19547e6 q^{86} +6.44943e6 q^{87} +547687. q^{88} -5.37918e6 q^{89} +1.16816e6 q^{90} +753571. q^{91} -109596. q^{92} +8.29994e6 q^{93} -6.00945e6 q^{94} -8.79223e6 q^{95} +884736. q^{96} +8.02699e6 q^{97} +941192. q^{98} +779812. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 56 q^{2} + 189 q^{3} + 448 q^{4} + 625 q^{5} + 1512 q^{6} + 2401 q^{7} + 3584 q^{8} + 5103 q^{9}+O(q^{10}) $ 7 * q + 56 * q^2 + 189 * q^3 + 448 * q^4 + 625 * q^5 + 1512 * q^6 + 2401 * q^7 + 3584 * q^8 + 5103 * q^9	\( 7 q + 56 q^{2} + 189 q^{3} + 448 q^{4} + 625 q^{5} + 1512 q^{6} + 2401 q^{7} + 3584 q^{8} + 5103 q^{9} + 5000 q^{10} + 4678 q^{11} + 12096 q^{12} + 15379 q^{13} + 19208 q^{14} + 16875 q^{15} + 28672 q^{16} + 38552 q^{17} + 40824 q^{18} + 60231 q^{19} + 40000 q^{20} + 64827 q^{21} + 37424 q^{22} + 82047 q^{23} + 96768 q^{24} + 136408 q^{25} + 123032 q^{26} + 137781 q^{27} + 153664 q^{28} + 87523 q^{29} + 135000 q^{30} - 3191 q^{31} + 229376 q^{32} + 126306 q^{33} + 308416 q^{34} + 214375 q^{35} + 326592 q^{36} + 360916 q^{37} + 481848 q^{38} + 415233 q^{39} + 320000 q^{40} + 814350 q^{41} + 518616 q^{42} + 840057 q^{43} + 299392 q^{44} + 455625 q^{45} + 656376 q^{46} + 472723 q^{47} + 774144 q^{48} + 823543 q^{49} + 1091264 q^{50} + 1040904 q^{51} + 984256 q^{52} + 2185687 q^{53} + 1102248 q^{54} + 298354 q^{55} + 1229312 q^{56} + 1626237 q^{57} + 700184 q^{58} + 2046232 q^{59} + 1080000 q^{60} + 2744560 q^{61} - 25528 q^{62} + 1750329 q^{63} + 1835008 q^{64} + 1373125 q^{65} + 1010448 q^{66} + 1960358 q^{67} + 2467328 q^{68} + 2215269 q^{69} + 1715000 q^{70} + 2774656 q^{71} + 2612736 q^{72} + 3696313 q^{73} + 2887328 q^{74} + 3683016 q^{75} + 3854784 q^{76} + 1604554 q^{77} + 3321864 q^{78} + 1532089 q^{79} + 2560000 q^{80} + 3720087 q^{81} + 6514800 q^{82} + 7473863 q^{83} + 4148928 q^{84} - 1656624 q^{85} + 6720456 q^{86} + 2363121 q^{87} + 2395136 q^{88} + 14077309 q^{89} + 3645000 q^{90} + 5274997 q^{91} + 5251008 q^{92} - 86157 q^{93} + 3781784 q^{94} - 1704679 q^{95} + 6193152 q^{96} + 8273673 q^{97} + 6588344 q^{98} + 3410262 q^{99}+O(q^{100}) \) 7 * q + 56 * q^2 + 189 * q^3 + 448 * q^4 + 625 * q^5 + 1512 * q^6 + 2401 * q^7 + 3584 * q^8 + 5103 * q^9 + 5000 * q^10 + 4678 * q^11 + 12096 * q^12 + 15379 * q^13 + 19208 * q^14 + 16875 * q^15 + 28672 * q^16 + 38552 * q^17 + 40824 * q^18 + 60231 * q^19 + 40000 * q^20 + 64827 * q^21 + 37424 * q^22 + 82047 * q^23 + 96768 * q^24 + 136408 * q^25 + 123032 * q^26 + 137781 * q^27 + 153664 * q^28 + 87523 * q^29 + 135000 * q^30 - 3191 * q^31 + 229376 * q^32 + 126306 * q^33 + 308416 * q^34 + 214375 * q^35 + 326592 * q^36 + 360916 * q^37 + 481848 * q^38 + 415233 * q^39 + 320000 * q^40 + 814350 * q^41 + 518616 * q^42 + 840057 * q^43 + 299392 * q^44 + 455625 * q^45 + 656376 * q^46 + 472723 * q^47 + 774144 * q^48 + 823543 * q^49 + 1091264 * q^50 + 1040904 * q^51 + 984256 * q^52 + 2185687 * q^53 + 1102248 * q^54 + 298354 * q^55 + 1229312 * q^56 + 1626237 * q^57 + 700184 * q^58 + 2046232 * q^59 + 1080000 * q^60 + 2744560 * q^61 - 25528 * q^62 + 1750329 * q^63 + 1835008 * q^64 + 1373125 * q^65 + 1010448 * q^66 + 1960358 * q^67 + 2467328 * q^68 + 2215269 * q^69 + 1715000 * q^70 + 2774656 * q^71 + 2612736 * q^72 + 3696313 * q^73 + 2887328 * q^74 + 3683016 * q^75 + 3854784 * q^76 + 1604554 * q^77 + 3321864 * q^78 + 1532089 * q^79 + 2560000 * q^80 + 3720087 * q^81 + 6514800 * q^82 + 7473863 * q^83 + 4148928 * q^84 - 1656624 * q^85 + 6720456 * q^86 + 2363121 * q^87 + 2395136 * q^88 + 14077309 * q^89 + 3645000 * q^90 + 5274997 * q^91 + 5251008 * q^92 - 86157 * q^93 + 3781784 * q^94 - 1704679 * q^95 + 6193152 * q^96 + 8273673 * q^97 + 6588344 * q^98 + 3410262 * 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
$5$	200.302	0.716621	0.358311	−	0.933602i	$-0.383353\pi$
$5$	200.302	0.716621	0.358311	+	0.933602i	$0.383353\pi$
$6$	216.000	0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	1602.41	0.506728
$11$	1069.70	0.242319	0.121160	−	0.992633i	$-0.461339\pi$
$11$	1069.70	0.242319	0.121160	+	0.992633i	$0.461339\pi$
$12$	1728.00	0.288675
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	2744.00	0.267261
$15$	5408.15	0.413742
$16$	4096.00	0.250000
$17$	16719.4	0.825370	0.412685	−	0.910874i	$-0.364591\pi$
$17$	16719.4	0.825370	0.412685	+	0.910874i	$0.364591\pi$
$18$	5832.00	0.235702
$19$	−43894.9	−1.46817	−0.734085	−	0.679057i	$-0.762389\pi$
$19$	−43894.9	−1.46817	−0.734085	+	0.679057i	$0.762389\pi$
$20$	12819.3	0.358311
$21$	9261.00	0.218218
$22$	8557.61	0.171346
$23$	−1712.43	−0.0293472	−0.0146736	−	0.999892i	$-0.504671\pi$
$23$	−1712.43	−0.0293472	−0.0146736	+	0.999892i	$0.504671\pi$
$24$	13824.0	0.204124
$25$	−38004.2	−0.486454
$26$	17576.0	0.196116
$27$	19683.0	0.192450
$28$	21952.0	0.188982
$29$	238868.	1.81872	0.909358	−	0.416015i	$-0.136574\pi$
$29$	238868.	1.81872	0.909358	+	0.416015i	$0.136574\pi$
$30$	43265.2	0.292560
$31$	307405.	1.85330	0.926649	−	0.375927i	$-0.122676\pi$
$31$	307405.	1.85330	0.926649	+	0.375927i	$0.122676\pi$
$32$	32768.0	0.176777
$33$	28881.9	0.139903
$34$	133755.	0.583625
$35$	68703.5	0.270857
$36$	46656.0	0.166667
$37$	181002.	0.587457	0.293729	−	0.955889i	$-0.405104\pi$
$37$	181002.	0.587457	0.293729	+	0.955889i	$0.405104\pi$
$38$	−351159.	−1.03815
$39$	59319.0	0.160128
$40$	102555.	0.253364
$41$	−718028.	−1.62704	−0.813520	−	0.581537i	$-0.802451\pi$
$41$	−718028.	−1.62704	−0.813520	+	0.581537i	$0.802451\pi$
$42$	74088.0	0.154303
$43$	649434.	1.24565	0.622824	−	0.782362i	$-0.285985\pi$
$43$	649434.	1.24565	0.622824	+	0.782362i	$0.285985\pi$
$44$	68460.9	0.121160
$45$	146020.	0.238874
$46$	−13699.5	−0.0207516
$47$	−751182.	−1.05536	−0.527682	−	0.849442i	$-0.676939\pi$
$47$	−751182.	−1.05536	−0.527682	+	0.849442i	$0.676939\pi$
$48$	110592.	0.144338
$49$	117649.	0.142857
$50$	−304034.	−0.343975
$51$	451423.	0.476528
$52$	140608.	0.138675
$53$	308666.	0.284789	0.142394	−	0.989810i	$-0.454520\pi$
$53$	308666.	0.284789	0.142394	+	0.989810i	$0.454520\pi$
$54$	157464.	0.136083
$55$	214263.	0.173651
$56$	175616.	0.133631
$57$	−1.18516e6	−0.847648
$58$	1.91094e6	1.28603
$59$	1.48361e6	0.940456	0.470228	−	0.882545i	$-0.344172\pi$
$59$	1.48361e6	0.940456	0.470228	+	0.882545i	$0.344172\pi$
$60$	346122.	0.206871
$61$	−925088.	−0.521830	−0.260915	−	0.965362i	$-0.584024\pi$
$61$	−925088.	−0.521830	−0.260915	+	0.965362i	$0.584024\pi$
$62$	2.45924e6	1.31048
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	440063.	0.198755
$66$	231056.	0.0989265
$67$	629175.	0.255570	0.127785	−	0.991802i	$-0.459213\pi$
$67$	629175.	0.255570	0.127785	+	0.991802i	$0.459213\pi$
$68$	1.07004e6	0.412685
$69$	−46235.7	−0.0169436
$70$	549628.	0.191525
$71$	2.13027e6	0.706368	0.353184	−	0.935554i	$-0.385099\pi$
$71$	2.13027e6	0.706368	0.353184	+	0.935554i	$0.385099\pi$
$72$	373248.	0.117851
$73$	4.72296e6	1.42097	0.710485	−	0.703713i	$-0.248476\pi$
$73$	4.72296e6	1.42097	0.710485	+	0.703713i	$0.248476\pi$
$74$	1.44801e6	0.415395
$75$	−1.02611e6	−0.280854
$76$	−2.80927e6	−0.734085
$77$	366908.	0.0915881
$78$	474552.	0.113228
$79$	−6.86756e6	−1.56714	−0.783569	−	0.621304i	$-0.786603\pi$
$79$	−6.86756e6	−1.56714	−0.783569	+	0.621304i	$0.786603\pi$
$80$	820436.	0.179155
$81$	531441.	0.111111
$82$	−5.74423e6	−1.15049
$83$	−1.88267e6	−0.361410	−0.180705	−	0.983537i	$-0.557838\pi$
$83$	−1.88267e6	−0.361410	−0.180705	+	0.983537i	$0.557838\pi$
$84$	592704.	0.109109
$85$	3.34892e6	0.591478
$86$	5.19547e6	0.880806
$87$	6.44943e6	1.05004
$88$	547687.	0.0856729
$89$	−5.37918e6	−0.808818	−0.404409	−	0.914578i	$-0.632523\pi$
$89$	−5.37918e6	−0.808818	−0.404409	+	0.914578i	$0.632523\pi$
$90$	1.16816e6	0.168909
$91$	753571.	0.104828
$92$	−109596.	−0.0146736
$93$	8.29994e6	1.07000
$94$	−6.00945e6	−0.746255
$95$	−8.79223e6	−1.05212
$96$	884736.	0.102062
$97$	8.02699e6	0.893000	0.446500	−	0.894784i	$-0.352670\pi$
$97$	8.02699e6	0.893000	0.446500	+	0.894784i	$0.352670\pi$
$98$	941192.	0.101015
$99$	779812.	0.0807731
$100$	−2.43227e6	−0.243227
$101$	1.53211e7	1.47967	0.739835	−	0.672789i	$-0.234904\pi$
$101$	1.53211e7	1.47967	0.739835	+	0.672789i	$0.234904\pi$
$102$	3.61138e6	0.336956
$103$	6.57224e6	0.592629	0.296315	−	0.955090i	$-0.404242\pi$
$103$	6.57224e6	0.592629	0.296315	+	0.955090i	$0.404242\pi$
$104$	1.12486e6	0.0980581
$105$	1.85499e6	0.156380
$106$	2.46933e6	0.201376
$107$	−1.36969e7	−1.08088	−0.540442	−	0.841381i	$-0.681743\pi$
$107$	−1.36969e7	−1.08088	−0.540442	+	0.841381i	$0.681743\pi$
$108$	1.25971e6	0.0962250
$109$	−1.29718e6	−0.0959415	−0.0479707	−	0.998849i	$-0.515275\pi$
$109$	−1.29718e6	−0.0959415	−0.0479707	+	0.998849i	$0.515275\pi$
$110$	1.71411e6	0.122790
$111$	4.88704e6	0.339169
$112$	1.40493e6	0.0944911
$113$	8.94101e6	0.582924	0.291462	−	0.956582i	$-0.405858\pi$
$113$	8.94101e6	0.582924	0.291462	+	0.956582i	$0.405858\pi$
$114$	−9.48130e6	−0.599378
$115$	−343003.	−0.0210308
$116$	1.52875e7	0.909358
$117$	1.60161e6	0.0924500
$118$	1.18689e7	0.665003
$119$	5.73475e6	0.311961
$120$	2.76897e6	0.146280
$121$	−1.83429e7	−0.941281
$122$	−7.40071e6	−0.368989
$123$	−1.93868e7	−0.939372
$124$	1.96739e7	0.926649
$125$	−2.32609e7	−1.06522
$126$	2.00038e6	0.0890871
$127$	2.36870e7	1.02612	0.513058	−	0.858354i	$-0.328513\pi$
$127$	2.36870e7	1.02612	0.513058	+	0.858354i	$0.328513\pi$
$128$	2.09715e6	0.0883883
$129$	1.75347e7	0.719175
$130$	3.52050e6	0.140541
$131$	−8.29885e6	−0.322529	−0.161264	−	0.986911i	$-0.551557\pi$
$131$	−8.29885e6	−0.322529	−0.161264	+	0.986911i	$0.551557\pi$
$132$	1.84844e6	0.0699516
$133$	−1.50559e7	−0.554916
$134$	5.03340e6	0.180715
$135$	3.94254e6	0.137914
$136$	8.56032e6	0.291812
$137$	1.94134e7	0.645029	0.322514	−	0.946565i	$-0.395472\pi$
$137$	1.94134e7	0.645029	0.322514	+	0.946565i	$0.395472\pi$
$138$	−369886.	−0.0119809
$139$	−5.28312e7	−1.66855	−0.834274	−	0.551350i	$-0.814113\pi$
$139$	−5.28312e7	−1.66855	−0.834274	+	0.551350i	$0.814113\pi$
$140$	4.39703e6	0.135429
$141$	−2.02819e7	−0.609315
$142$	1.70422e7	0.499478
$143$	2.35013e6	0.0672073
$144$	2.98598e6	0.0833333
$145$	4.78457e7	1.30333
$146$	3.77837e7	1.00478
$147$	3.17652e6	0.0824786
$148$	1.15841e7	0.293729
$149$	3.30129e7	0.817583	0.408792	−	0.912628i	$-0.365950\pi$
$149$	3.30129e7	0.817583	0.408792	+	0.912628i	$0.365950\pi$
$150$	−8.20890e6	−0.198594
$151$	1.22412e7	0.289337	0.144668	−	0.989480i	$-0.453788\pi$
$151$	1.22412e7	0.289337	0.144668	+	0.989480i	$0.453788\pi$
$152$	−2.24742e7	−0.519077
$153$	1.21884e7	0.275123
$154$	2.93526e6	0.0647626
$155$	6.15738e7	1.32811
$156$	3.79642e6	0.0800641
$157$	1.08586e7	0.223936	0.111968	−	0.993712i	$-0.464285\pi$
$157$	1.08586e7	0.223936	0.111968	+	0.993712i	$0.464285\pi$
$158$	−5.49405e7	−1.10813
$159$	8.33398e6	0.164423
$160$	6.56349e6	0.126682
$161$	−587365.	−0.0110922
$162$	4.25153e6	0.0785674
$163$	−6.77903e6	−0.122606	−0.0613028	−	0.998119i	$-0.519526\pi$
$163$	−6.77903e6	−0.122606	−0.0613028	+	0.998119i	$0.519526\pi$
$164$	−4.59538e7	−0.813520
$165$	5.78510e6	0.100258
$166$	−1.50614e7	−0.255556
$167$	−2.79835e7	−0.464938	−0.232469	−	0.972604i	$-0.574680\pi$
$167$	−2.79835e7	−0.464938	−0.232469	+	0.972604i	$0.574680\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	2.67914e7	0.418238
$171$	−3.19994e7	−0.489390
$172$	4.15638e7	0.622824
$173$	−1.11875e8	−1.64276	−0.821379	−	0.570383i	$-0.806795\pi$
$173$	−1.11875e8	−1.64276	−0.821379	+	0.570383i	$0.806795\pi$
$174$	5.15955e7	0.742488
$175$	−1.30354e7	−0.183862
$176$	4.38150e6	0.0605799
$177$	4.00575e7	0.542972
$178$	−4.30334e7	−0.571921
$179$	−664107.	−0.00865471	−0.00432736	−	0.999991i	$-0.501377\pi$
$179$	−664107.	−0.00865471	−0.00432736	+	0.999991i	$0.501377\pi$
$180$	9.34528e6	0.119437
$181$	1.17521e8	1.47313	0.736563	−	0.676369i	$-0.236448\pi$
$181$	1.17521e8	1.47313	0.736563	+	0.676369i	$0.236448\pi$
$182$	6.02857e6	0.0741249
$183$	−2.49774e7	−0.301279
$184$	−876766.	−0.0103758
$185$	3.62549e7	0.420984
$186$	6.63996e7	0.756606
$187$	1.78847e7	0.200003
$188$	−4.80756e7	−0.527682
$189$	6.75127e6	0.0727393
$190$	−7.03378e7	−0.743963
$191$	9.62807e7	0.999821	0.499911	−	0.866077i	$-0.333366\pi$
$191$	9.62807e7	0.999821	0.499911	+	0.866077i	$0.333366\pi$
$192$	7.07789e6	0.0721688
$193$	9.82596e7	0.983840	0.491920	−	0.870640i	$-0.336295\pi$
$193$	9.82596e7	0.983840	0.491920	+	0.870640i	$0.336295\pi$
$194$	6.42159e7	0.631446
$195$	1.18817e7	0.114751
$196$	7.52954e6	0.0714286
$197$	−5.63954e7	−0.525547	−0.262773	−	0.964858i	$-0.584637\pi$
$197$	−5.63954e7	−0.525547	−0.262773	+	0.964858i	$0.584637\pi$
$198$	6.23850e6	0.0571152
$199$	3.52238e7	0.316848	0.158424	−	0.987371i	$-0.449359\pi$
$199$	3.52238e7	0.316848	0.158424	+	0.987371i	$0.449359\pi$
$200$	−1.94581e7	−0.171987
$201$	1.69877e7	0.147553
$202$	1.22569e8	1.04628
$203$	8.19317e7	0.687410
$204$	2.88911e7	0.238264
$205$	−1.43822e8	−1.16597
$206$	5.25779e7	0.419052
$207$	−1.24836e6	−0.00978239
$208$	8.99891e6	0.0693375
$209$	−4.69544e7	−0.355766
$210$	1.48400e7	0.110577
$211$	−1.20240e8	−0.881171	−0.440585	−	0.897711i	$-0.645229\pi$
$211$	−1.20240e8	−0.881171	−0.440585	+	0.897711i	$0.645229\pi$
$212$	1.97546e7	0.142394
$213$	5.75174e7	0.407822
$214$	−1.09575e8	−0.764301
$215$	1.30083e8	0.892658
$216$	1.00777e7	0.0680414
$217$	1.05440e8	0.700481
$218$	−1.03774e7	−0.0678409
$219$	1.27520e8	0.820397
$220$	1.37128e7	0.0868257
$221$	3.67325e7	0.228917
$222$	3.90963e7	0.239828
$223$	1.12768e8	0.680958	0.340479	−	0.940252i	$-0.389411\pi$
$223$	1.12768e8	0.680958	0.340479	+	0.940252i	$0.389411\pi$
$224$	1.12394e7	0.0668153
$225$	−2.77051e7	−0.162151
$226$	7.15281e7	0.412190
$227$	−2.11508e7	−0.120015	−0.0600076	−	0.998198i	$-0.519112\pi$
$227$	−2.11508e7	−0.120015	−0.0600076	+	0.998198i	$0.519112\pi$
$228$	−7.58504e7	−0.423824
$229$	2.30286e8	1.26720	0.633598	−	0.773663i	$-0.281577\pi$
$229$	2.30286e8	1.26720	0.633598	+	0.773663i	$0.281577\pi$
$230$	−2.74403e6	−0.0148710
$231$	9.90651e6	0.0528784
$232$	1.22300e8	0.643013
$233$	−2.20048e8	−1.13965	−0.569825	−	0.821766i	$-0.692989\pi$
$233$	−2.20048e8	−1.13965	−0.569825	+	0.821766i	$0.692989\pi$
$234$	1.28129e7	0.0653720
$235$	−1.50463e8	−0.756297
$236$	9.49512e7	0.470228
$237$	−1.85424e8	−0.904788
$238$	4.58780e7	0.220589
$239$	1.46421e8	0.693764	0.346882	−	0.937909i	$-0.387240\pi$
$239$	1.46421e8	0.693764	0.346882	+	0.937909i	$0.387240\pi$
$240$	2.21518e7	0.103435
$241$	−1.99768e8	−0.919317	−0.459658	−	0.888096i	$-0.652028\pi$
$241$	−1.99768e8	−0.919317	−0.459658	+	0.888096i	$0.652028\pi$
$242$	−1.46743e8	−0.665586
$243$	1.43489e7	0.0641500
$244$	−5.92057e7	−0.260915
$245$	2.35653e7	0.102374
$246$	−1.55094e8	−0.664236
$247$	−9.64371e7	−0.407197
$248$	1.57392e8	0.655240
$249$	−5.08321e7	−0.208660
$250$	−1.86087e8	−0.753228
$251$	−1.71849e8	−0.685946	−0.342973	−	0.939345i	$-0.611434\pi$
$251$	−1.71849e8	−0.685946	−0.342973	+	0.939345i	$0.611434\pi$
$252$	1.60030e7	0.0629941
$253$	−1.83179e6	−0.00711139
$254$	1.89496e8	0.725573
$255$	9.04209e7	0.341490
$256$	1.67772e7	0.0625000
$257$	−3.40252e7	−0.125036	−0.0625179	−	0.998044i	$-0.519913\pi$
$257$	−3.40252e7	−0.125036	−0.0625179	+	0.998044i	$0.519913\pi$
$258$	1.40278e8	0.508534
$259$	6.20835e7	0.222038
$260$	2.81640e7	0.0993775
$261$	1.74135e8	0.606239
$262$	−6.63908e7	−0.228062
$263$	3.85776e8	1.30764	0.653822	−	0.756648i	$-0.273164\pi$
$263$	3.85776e8	1.30764	0.653822	+	0.756648i	$0.273164\pi$
$264$	1.47876e7	0.0494632
$265$	6.18263e7	0.204086
$266$	−1.20448e8	−0.392385
$267$	−1.45238e8	−0.466971
$268$	4.02672e7	0.127785
$269$	3.95010e8	1.23730	0.618650	−	0.785666i	$-0.287680\pi$
$269$	3.95010e8	1.23730	0.618650	+	0.785666i	$0.287680\pi$
$270$	3.15403e7	0.0975198
$271$	2.12872e8	0.649721	0.324860	−	0.945762i	$-0.394683\pi$
$271$	2.12872e8	0.649721	0.324860	+	0.945762i	$0.394683\pi$
$272$	6.84826e7	0.206343
$273$	2.03464e7	0.0605228
$274$	1.55307e8	0.456104
$275$	−4.06531e7	−0.117877
$276$	−2.95908e6	−0.00847180
$277$	−9.04934e7	−0.255822	−0.127911	−	0.991786i	$-0.540827\pi$
$277$	−9.04934e7	−0.255822	−0.127911	+	0.991786i	$0.540827\pi$
$278$	−4.22650e8	−1.17984
$279$	2.24098e8	0.617766
$280$	3.51762e7	0.0957626
$281$	−3.63689e8	−0.977818	−0.488909	−	0.872335i	$-0.662605\pi$
$281$	−3.63689e8	−0.977818	−0.488909	+	0.872335i	$0.662605\pi$
$282$	−1.62255e8	−0.430851
$283$	−2.63676e8	−0.691540	−0.345770	−	0.938319i	$-0.612382\pi$
$283$	−2.63676e8	−0.691540	−0.345770	+	0.938319i	$0.612382\pi$
$284$	1.36337e8	0.353184
$285$	−2.37390e8	−0.607443
$286$	1.88011e7	0.0475227
$287$	−2.46284e8	−0.614963
$288$	2.38879e7	0.0589256
$289$	−1.30801e8	−0.318764
$290$	3.82765e8	0.921594
$291$	2.16729e8	0.515574
$292$	3.02270e8	0.710485
$293$	6.71981e8	1.56070	0.780351	−	0.625342i	$-0.215040\pi$
$293$	6.71981e8	1.56070	0.780351	+	0.625342i	$0.215040\pi$
$294$	2.54122e7	0.0583212
$295$	2.97170e8	0.673951
$296$	9.26728e7	0.207697
$297$	2.10549e7	0.0466344
$298$	2.64103e8	0.578119
$299$	−3.76222e6	−0.00813944
$300$	−6.56712e7	−0.140427
$301$	2.22756e8	0.470811
$302$	9.79293e7	0.204592
$303$	4.13669e8	0.854287
$304$	−1.79793e8	−0.367043
$305$	−1.85297e8	−0.373954
$306$	9.75074e7	0.194542
$307$	2.98296e8	0.588388	0.294194	−	0.955746i	$-0.404949\pi$
$307$	2.98296e8	0.588388	0.294194	+	0.955746i	$0.404949\pi$
$308$	2.34821e7	0.0457941
$309$	1.77450e8	0.342155
$310$	4.92591e8	0.939118
$311$	−4.29124e8	−0.808949	−0.404474	−	0.914549i	$-0.632546\pi$
$311$	−4.29124e8	−0.808949	−0.404474	+	0.914549i	$0.632546\pi$
$312$	3.03713e7	0.0566139
$313$	7.74901e7	0.142837	0.0714185	−	0.997446i	$-0.477247\pi$
$313$	7.74901e7	0.142837	0.0714185	+	0.997446i	$0.477247\pi$
$314$	8.68687e7	0.158347
$315$	5.00849e7	0.0902858
$316$	−4.39524e8	−0.783569
$317$	−1.98594e8	−0.350153	−0.175077	−	0.984555i	$-0.556017\pi$
$317$	−1.98594e8	−0.350153	−0.175077	+	0.984555i	$0.556017\pi$
$318$	6.66718e7	0.116265
$319$	2.55517e8	0.440710
$320$	5.25079e7	0.0895777
$321$	−3.69817e8	−0.624049
$322$	−4.69892e6	−0.00784336
$323$	−7.33895e8	−1.21178
$324$	3.40122e7	0.0555556
$325$	−8.34952e7	−0.134918
$326$	−5.42322e7	−0.0866953
$327$	−3.50238e7	−0.0553918
$328$	−3.67630e8	−0.575245
$329$	−2.57655e8	−0.398890
$330$	4.62808e7	0.0708929
$331$	−4.61636e8	−0.699683	−0.349841	−	0.936809i	$-0.613765\pi$
$331$	−4.61636e8	−0.699683	−0.349841	+	0.936809i	$0.613765\pi$
$332$	−1.20491e8	−0.180705
$333$	1.31950e8	0.195819
$334$	−2.23868e8	−0.328760
$335$	1.26025e8	0.183147
$336$	3.79331e7	0.0545545
$337$	7.18470e8	1.02260	0.511298	−	0.859404i	$-0.329165\pi$
$337$	7.18470e8	1.02260	0.511298	+	0.859404i	$0.329165\pi$
$338$	3.86145e7	0.0543928
$339$	2.41407e8	0.336551
$340$	2.14331e8	0.295739
$341$	3.28832e8	0.449090
$342$	−2.55995e8	−0.346051
$343$	4.03536e7	0.0539949
$344$	3.32510e8	0.440403
$345$	−9.26109e6	−0.0121421
$346$	−8.95004e8	−1.16160
$347$	−1.03387e9	−1.32835	−0.664176	−	0.747577i	$-0.731217\pi$
$347$	−1.03387e9	−1.32835	−0.664176	+	0.747577i	$0.731217\pi$
$348$	4.12764e8	0.525018
$349$	−5.00334e8	−0.630044	−0.315022	−	0.949084i	$-0.602012\pi$
$349$	−5.00334e8	−0.630044	−0.315022	+	0.949084i	$0.602012\pi$
$350$	−1.04283e8	−0.130010
$351$	4.32436e7	0.0533761
$352$	3.50520e7	0.0428364
$353$	2.97554e8	0.360043	0.180021	−	0.983663i	$-0.442383\pi$
$353$	2.97554e8	0.360043	0.180021	+	0.983663i	$0.442383\pi$
$354$	3.20460e8	0.383939
$355$	4.26697e8	0.506198
$356$	−3.44267e8	−0.404409
$357$	1.54838e8	0.180111
$358$	−5.31286e6	−0.00611981
$359$	4.57465e8	0.521828	0.260914	−	0.965362i	$-0.415976\pi$
$359$	4.57465e8	0.521828	0.260914	+	0.965362i	$0.415976\pi$
$360$	7.47622e7	0.0844547
$361$	1.03289e9	1.15552
$362$	9.40167e8	1.04166
$363$	−4.95259e8	−0.543449
$364$	4.82285e7	0.0524142
$365$	9.46018e8	1.01830
$366$	−1.99819e8	−0.213036
$367$	5.13890e8	0.542674	0.271337	−	0.962484i	$-0.412534\pi$
$367$	5.13890e8	0.542674	0.271337	+	0.962484i	$0.412534\pi$
$368$	−7.01413e6	−0.00733679
$369$	−5.23443e8	−0.542346
$370$	2.90039e8	0.297681
$371$	1.05872e8	0.107640
$372$	5.31196e8	0.535001
$373$	6.90991e8	0.689432	0.344716	−	0.938707i	$-0.387975\pi$
$373$	6.90991e8	0.689432	0.344716	+	0.938707i	$0.387975\pi$
$374$	1.43078e8	0.141424
$375$	−6.28044e8	−0.615008
$376$	−3.84605e8	−0.373128
$377$	5.24793e8	0.504421
$378$	5.40102e7	0.0514344
$379$	−6.42976e8	−0.606677	−0.303339	−	0.952883i	$-0.598101\pi$
$379$	−6.42976e8	−0.606677	−0.303339	+	0.952883i	$0.598101\pi$
$380$	−5.62702e8	−0.526061
$381$	6.39548e8	0.592428
$382$	7.70245e8	0.706980
$383$	1.34279e9	1.22128	0.610638	−	0.791910i	$-0.290913\pi$
$383$	1.34279e9	1.22128	0.610638	+	0.791910i	$0.290913\pi$
$384$	5.66231e7	0.0510310
$385$	7.34923e7	0.0656340
$386$	7.86077e8	0.695680
$387$	4.73437e8	0.415216
$388$	5.13727e8	0.446500
$389$	2.10588e8	0.181388	0.0906941	−	0.995879i	$-0.471091\pi$
$389$	2.10588e8	0.181388	0.0906941	+	0.995879i	$0.471091\pi$
$390$	9.50536e7	0.0811414
$391$	−2.86308e7	−0.0242223
$392$	6.02363e7	0.0505076
$393$	−2.24069e8	−0.186212
$394$	−4.51163e8	−0.371618
$395$	−1.37558e9	−1.12305
$396$	4.99080e7	0.0403866
$397$	−1.22057e9	−0.979030	−0.489515	−	0.871995i	$-0.662826\pi$
$397$	−1.22057e9	−0.979030	−0.489515	+	0.871995i	$0.662826\pi$
$398$	2.81790e8	0.224045
$399$	−4.06511e8	−0.320381
$400$	−1.55665e8	−0.121613
$401$	−2.56294e9	−1.98487	−0.992436	−	0.122761i	$-0.960825\pi$
$401$	−2.56294e9	−1.98487	−0.992436	+	0.122761i	$0.960825\pi$
$402$	1.35902e8	0.104336
$403$	6.75370e8	0.514013
$404$	9.80549e8	0.739835
$405$	1.06449e8	0.0796246
$406$	6.55454e8	0.486072
$407$	1.93618e8	0.142352
$408$	2.31129e8	0.168478
$409$	−9.87235e8	−0.713492	−0.356746	−	0.934201i	$-0.616114\pi$
$409$	−9.87235e8	−0.713492	−0.356746	+	0.934201i	$0.616114\pi$
$410$	−1.15058e9	−0.824466
$411$	5.24161e8	0.372407
$412$	4.20623e8	0.296315
$413$	5.08879e8	0.355459
$414$	−9.98691e6	−0.00691719
$415$	−3.77102e8	−0.258994
$416$	7.19913e7	0.0490290
$417$	−1.42644e9	−0.963337
$418$	−3.75635e8	−0.251565
$419$	2.04575e9	1.35864	0.679320	−	0.733842i	$-0.262275\pi$
$419$	2.04575e9	1.35864	0.679320	+	0.733842i	$0.262275\pi$
$420$	1.18720e8	0.0781898
$421$	1.82942e9	1.19488	0.597442	−	0.801912i	$-0.296184\pi$
$421$	1.82942e9	1.19488	0.597442	+	0.801912i	$0.296184\pi$
$422$	−9.61919e8	−0.623082
$423$	−5.47611e8	−0.351788
$424$	1.58037e8	0.100688
$425$	−6.35406e8	−0.401504
$426$	4.60139e8	0.288373
$427$	−3.17305e8	−0.197233
$428$	−8.76602e8	−0.540442
$429$	6.34536e7	0.0388022
$430$	1.04066e9	0.631204
$431$	−1.42954e9	−0.860053	−0.430027	−	0.902816i	$-0.641496\pi$
$431$	−1.42954e9	−0.860053	−0.430027	+	0.902816i	$0.641496\pi$
$432$	8.06216e7	0.0481125
$433$	−8.53818e8	−0.505426	−0.252713	−	0.967541i	$-0.581323\pi$
$433$	−8.53818e8	−0.505426	−0.252713	+	0.967541i	$0.581323\pi$
$434$	8.43520e8	0.495315
$435$	1.29183e9	0.752478
$436$	−8.30193e7	−0.0479707
$437$	7.51671e7	0.0430866
$438$	1.02016e9	0.580108
$439$	−2.18989e9	−1.23537	−0.617684	−	0.786427i	$-0.711929\pi$
$439$	−2.18989e9	−1.23537	−0.617684	+	0.786427i	$0.711929\pi$
$440$	1.09703e8	0.0613950
$441$	8.57661e7	0.0476190
$442$	2.93860e8	0.161868
$443$	1.32549e9	0.724377	0.362188	−	0.932105i	$-0.382030\pi$
$443$	1.32549e9	0.724377	0.362188	+	0.932105i	$0.382030\pi$
$444$	3.12771e8	0.169584
$445$	−1.07746e9	−0.579617
$446$	9.02146e8	0.481510
$447$	8.91349e8	0.472032
$448$	8.99154e7	0.0472456
$449$	−4.41141e8	−0.229993	−0.114997	−	0.993366i	$-0.536686\pi$
$449$	−4.41141e8	−0.229993	−0.114997	+	0.993366i	$0.536686\pi$
$450$	−2.21640e8	−0.114658
$451$	−7.68076e8	−0.394263
$452$	5.72225e8	0.291462
$453$	3.30511e8	0.167049
$454$	−1.69206e8	−0.0848636
$455$	1.50942e8	0.0751223
$456$	−6.06803e8	−0.299689
$457$	−5.62360e8	−0.275618	−0.137809	−	0.990459i	$-0.544006\pi$
$457$	−5.62360e8	−0.275618	−0.137809	+	0.990459i	$0.544006\pi$
$458$	1.84229e9	0.896043
$459$	3.29087e8	0.158843
$460$	−2.19522e7	−0.0105154
$461$	9.21893e8	0.438255	0.219128	−	0.975696i	$-0.429679\pi$
$461$	9.21893e8	0.438255	0.219128	+	0.975696i	$0.429679\pi$
$462$	7.92520e7	0.0373907
$463$	−2.56393e9	−1.20053	−0.600265	−	0.799801i	$-0.704938\pi$
$463$	−2.56393e9	−1.20053	−0.600265	+	0.799801i	$0.704938\pi$
$464$	9.78403e8	0.454679
$465$	1.66249e9	0.766787
$466$	−1.76038e9	−0.805855
$467$	−2.07570e9	−0.943093	−0.471547	−	0.881841i	$-0.656304\pi$
$467$	−2.07570e9	−0.943093	−0.471547	+	0.881841i	$0.656304\pi$
$468$	1.02503e8	0.0462250
$469$	2.15807e8	0.0965963
$470$	−1.20370e9	−0.534783
$471$	2.93182e8	0.129290
$472$	7.59610e8	0.332501
$473$	6.94700e8	0.301845
$474$	−1.48339e9	−0.639782
$475$	1.66819e9	0.714197
$476$	3.67024e8	0.155980
$477$	2.25017e8	0.0949297
$478$	1.17137e9	0.490566
$479$	−4.08358e9	−1.69772	−0.848862	−	0.528614i	$-0.822712\pi$
$479$	−4.08358e9	−1.69772	−0.848862	+	0.528614i	$0.822712\pi$
$480$	1.77214e8	0.0731399
$481$	3.97660e8	0.162931
$482$	−1.59814e9	−0.650055
$483$	−1.58588e7	−0.00640408
$484$	−1.17395e9	−0.470641
$485$	1.60782e9	0.639943
$486$	1.14791e8	0.0453609
$487$	2.58099e8	0.101259	0.0506296	−	0.998718i	$-0.483877\pi$
$487$	2.58099e8	0.101259	0.0506296	+	0.998718i	$0.483877\pi$
$488$	−4.73645e8	−0.184495
$489$	−1.83034e8	−0.0707864
$490$	1.88522e8	0.0723897
$491$	−2.91012e9	−1.10949	−0.554747	−	0.832019i	$-0.687185\pi$
$491$	−2.91012e9	−1.10949	−0.554747	+	0.832019i	$0.687185\pi$
$492$	−1.24075e9	−0.469686
$493$	3.99372e9	1.50111
$494$	−7.71497e8	−0.287932
$495$	1.56198e8	0.0578838
$496$	1.25913e9	0.463325
$497$	7.30683e8	0.266982
$498$	−4.06656e8	−0.147545
$499$	1.01404e9	0.365345	0.182673	−	0.983174i	$-0.441525\pi$
$499$	1.01404e9	0.365345	0.182673	+	0.983174i	$0.441525\pi$
$500$	−1.48870e9	−0.532612
$501$	−7.55555e8	−0.268432
$502$	−1.37479e9	−0.485037
$503$	−4.73277e9	−1.65816	−0.829082	−	0.559127i	$-0.811136\pi$
$503$	−4.73277e9	−1.65816	−0.829082	+	0.559127i	$0.811136\pi$
$504$	1.28024e8	0.0445435
$505$	3.06884e9	1.06036
$506$	−1.46543e7	−0.00502851
$507$	1.30324e8	0.0444116
$508$	1.51597e9	0.513058
$509$	4.64045e9	1.55972	0.779862	−	0.625952i	$-0.215289\pi$
$509$	4.64045e9	1.55972	0.779862	+	0.625952i	$0.215289\pi$
$510$	7.23367e8	0.241470
$511$	1.61998e9	0.537076
$512$	1.34218e8	0.0441942
$513$	−8.63983e8	−0.282549
$514$	−2.72201e8	−0.0884137
$515$	1.31643e9	0.424691
$516$	1.12222e9	0.359588
$517$	−8.03540e8	−0.255735
$518$	4.96668e8	0.157005
$519$	−3.02064e9	−0.948446
$520$	2.25312e8	0.0702705
$521$	−5.43731e9	−1.68443	−0.842213	−	0.539145i	$-0.818748\pi$
$521$	−5.43731e9	−1.68443	−0.842213	+	0.539145i	$0.818748\pi$
$522$	1.39308e9	0.428675
$523$	8.96634e8	0.274069	0.137034	−	0.990566i	$-0.456243\pi$
$523$	8.96634e8	0.274069	0.137034	+	0.990566i	$0.456243\pi$
$524$	−5.31127e8	−0.161264
$525$	−3.51957e8	−0.106153
$526$	3.08620e9	0.924644
$527$	5.13962e9	1.52966
$528$	1.18300e8	0.0349758
$529$	−3.40189e9	−0.999139
$530$	4.94611e8	0.144311
$531$	1.08155e9	0.313485
$532$	−9.63581e8	−0.277458
$533$	−1.57751e9	−0.451260
$534$	−1.16190e9	−0.330199
$535$	−2.74352e9	−0.774585
$536$	3.22138e8	0.0903576
$537$	−1.79309e7	−0.00499680
$538$	3.16008e9	0.874904
$539$	1.25849e8	0.0346171
$540$	2.52323e8	0.0689569
$541$	−3.66597e9	−0.995402	−0.497701	−	0.867349i	$-0.665822\pi$
$541$	−3.66597e9	−0.995402	−0.497701	+	0.867349i	$0.665822\pi$
$542$	1.70298e9	0.459422
$543$	3.17306e9	0.850509
$544$	5.47860e8	0.145906
$545$	−2.59827e8	−0.0687537
$546$	1.62771e8	0.0427960
$547$	−1.96391e9	−0.513057	−0.256528	−	0.966537i	$-0.582579\pi$
$547$	−1.96391e9	−0.513057	−0.256528	+	0.966537i	$0.582579\pi$
$548$	1.24246e9	0.322514
$549$	−6.74389e8	−0.173943
$550$	−3.25225e8	−0.0833517
$551$	−1.04851e10	−2.67018
$552$	−2.36727e7	−0.00599047
$553$	−2.35557e9	−0.592323
$554$	−7.23948e8	−0.180893
$555$	9.78883e8	0.243055
$556$	−3.38120e9	−0.834274
$557$	−2.83473e9	−0.695053	−0.347526	−	0.937670i	$-0.612978\pi$
$557$	−2.83473e9	−0.695053	−0.347526	+	0.937670i	$0.612978\pi$
$558$	1.79279e9	0.436827
$559$	1.42681e9	0.345481
$560$	2.81410e8	0.0677144
$561$	4.82888e8	0.115472
$562$	−2.90951e9	−0.691422
$563$	1.13518e9	0.268093	0.134047	−	0.990975i	$-0.457203\pi$
$563$	1.13518e9	0.268093	0.134047	+	0.990975i	$0.457203\pi$
$564$	−1.29804e9	−0.304657
$565$	1.79090e9	0.417736
$566$	−2.10941e9	−0.488993
$567$	1.82284e8	0.0419961
$568$	1.09070e9	0.249739
$569$	−2.82692e8	−0.0643309	−0.0321655	−	0.999483i	$-0.510240\pi$
$569$	−2.82692e8	−0.0643309	−0.0321655	+	0.999483i	$0.510240\pi$
$570$	−1.89912e9	−0.429527
$571$	−4.14101e9	−0.930850	−0.465425	−	0.885087i	$-0.654098\pi$
$571$	−4.14101e9	−0.930850	−0.465425	+	0.885087i	$0.654098\pi$
$572$	1.50409e8	0.0336037
$573$	2.59958e9	0.577247
$574$	−1.97027e9	−0.434845
$575$	6.50796e7	0.0142760
$576$	1.91103e8	0.0416667
$577$	−8.03637e9	−1.74158	−0.870792	−	0.491651i	$-0.836394\pi$
$577$	−8.03637e9	−1.74158	−0.870792	+	0.491651i	$0.836394\pi$
$578$	−1.04641e9	−0.225400
$579$	2.65301e9	0.568020
$580$	3.06212e9	0.651665
$581$	−6.45755e8	−0.136600
$582$	1.73383e9	0.364566
$583$	3.30180e8	0.0690099
$584$	2.41816e9	0.502388
$585$	3.20806e8	0.0662517
$586$	5.37584e9	1.10358
$587$	6.34917e7	0.0129564	0.00647819	−	0.999979i	$-0.497938\pi$
$587$	6.34917e7	0.0129564	0.00647819	+	0.999979i	$0.497938\pi$
$588$	2.03297e8	0.0412393
$589$	−1.34935e10	−2.72096
$590$	2.37736e9	0.476555
$591$	−1.52267e9	−0.303425
$592$	7.41382e8	0.146864
$593$	−2.63392e9	−0.518695	−0.259347	−	0.965784i	$-0.583507\pi$
$593$	−2.63392e9	−0.518695	−0.259347	+	0.965784i	$0.583507\pi$
$594$	1.68439e8	0.0329755
$595$	1.14868e9	0.223558
$596$	2.11283e9	0.408792
$597$	9.51043e8	0.182932
$598$	−3.00977e7	−0.00575545
$599$	−3.36709e9	−0.640120	−0.320060	−	0.947397i	$-0.603703\pi$
$599$	−3.36709e9	−0.640120	−0.320060	+	0.947397i	$0.603703\pi$
$600$	−5.25370e8	−0.0992969
$601$	1.62448e8	0.0305249	0.0152625	−	0.999884i	$-0.495142\pi$
$601$	1.62448e8	0.0305249	0.0152625	+	0.999884i	$0.495142\pi$
$602$	1.78205e9	0.332913
$603$	4.58668e8	0.0851899
$604$	7.83435e8	0.144668
$605$	−3.67412e9	−0.674542
$606$	3.30935e9	0.604072
$607$	7.09490e9	1.28761	0.643807	−	0.765188i	$-0.277354\pi$
$607$	7.09490e9	1.28761	0.643807	+	0.765188i	$0.277354\pi$
$608$	−1.43835e9	−0.259538
$609$	2.21216e9	0.396876
$610$	−1.48237e9	−0.264426
$611$	−1.65035e9	−0.292705
$612$	7.80059e8	0.137562
$613$	−8.60985e9	−1.50968	−0.754839	−	0.655911i	$-0.772285\pi$
$613$	−8.60985e9	−1.50968	−0.754839	+	0.655911i	$0.772285\pi$
$614$	2.38637e9	0.416053
$615$	−3.88320e9	−0.673174
$616$	1.87857e8	0.0323813
$617$	5.66822e9	0.971513	0.485756	−	0.874094i	$-0.338544\pi$
$617$	5.66822e9	0.971513	0.485756	+	0.874094i	$0.338544\pi$
$618$	1.41960e9	0.241940
$619$	−1.91700e9	−0.324867	−0.162434	−	0.986719i	$-0.551934\pi$
$619$	−1.91700e9	−0.324867	−0.162434	+	0.986719i	$0.551934\pi$
$620$	3.94073e9	0.664057
$621$	−3.37058e7	−0.00564786
$622$	−3.43299e9	−0.572013
$623$	−1.84506e9	−0.305705
$624$	2.42971e8	0.0400320
$625$	−1.69012e9	−0.276909
$626$	6.19921e8	0.101001
$627$	−1.26777e9	−0.205402
$628$	6.94949e8	0.111968
$629$	3.02623e9	0.484870
$630$	4.00679e8	0.0638417
$631$	4.23525e9	0.671083	0.335542	−	0.942025i	$-0.391081\pi$
$631$	4.23525e9	0.671083	0.335542	+	0.942025i	$0.391081\pi$
$632$	−3.51619e9	−0.554067
$633$	−3.24648e9	−0.508744
$634$	−1.58875e9	−0.247596
$635$	4.74454e9	0.735336
$636$	5.33375e8	0.0822115
$637$	2.58475e8	0.0396214
$638$	2.04414e9	0.311629
$639$	1.55297e9	0.235456
$640$	4.20063e8	0.0633410
$641$	9.70971e8	0.145614	0.0728070	−	0.997346i	$-0.476804\pi$
$641$	9.70971e8	0.145614	0.0728070	+	0.997346i	$0.476804\pi$
$642$	−2.95853e9	−0.441269
$643$	−1.09653e10	−1.62661	−0.813303	−	0.581840i	$-0.802333\pi$
$643$	−1.09653e10	−1.62661	−0.813303	+	0.581840i	$0.802333\pi$
$644$	−3.75913e7	−0.00554609
$645$	3.51223e9	0.515376
$646$	−5.87116e9	−0.856861
$647$	1.25322e10	1.81913	0.909565	−	0.415562i	$-0.136415\pi$
$647$	1.25322e10	1.81913	0.909565	+	0.415562i	$0.136415\pi$
$648$	2.72098e8	0.0392837
$649$	1.58702e9	0.227891
$650$	−6.67962e8	−0.0954014
$651$	2.84688e9	0.404423
$652$	−4.33858e8	−0.0613028
$653$	−1.21952e10	−1.71394	−0.856968	−	0.515370i	$-0.827654\pi$
$653$	−1.21952e10	−1.71394	−0.856968	+	0.515370i	$0.827654\pi$
$654$	−2.80190e8	−0.0391679
$655$	−1.66228e9	−0.231131
$656$	−2.94104e9	−0.406760
$657$	3.44304e9	0.473656
$658$	−2.06124e9	−0.282058
$659$	1.18979e9	0.161946	0.0809732	−	0.996716i	$-0.474197\pi$
$659$	1.18979e9	0.161946	0.0809732	+	0.996716i	$0.474197\pi$
$660$	3.70247e8	0.0501288
$661$	−8.67599e9	−1.16846	−0.584230	−	0.811588i	$-0.698603\pi$
$661$	−8.67599e9	−1.16846	−0.584230	+	0.811588i	$0.698603\pi$
$662$	−3.69308e9	−0.494750
$663$	9.91777e8	0.132165
$664$	−9.63926e8	−0.127778
$665$	−3.01573e9	−0.397665
$666$	1.05560e9	0.138465
$667$	−4.09045e8	−0.0533742
$668$	−1.79094e9	−0.232469
$669$	3.04474e9	0.393151
$670$	1.00820e9	0.129504
$671$	−9.89568e8	−0.126449
$672$	3.03464e8	0.0385758
$673$	8.21154e9	1.03842	0.519209	−	0.854647i	$-0.326227\pi$
$673$	8.21154e9	1.03842	0.519209	+	0.854647i	$0.326227\pi$
$674$	5.74776e9	0.723085
$675$	−7.48036e8	−0.0936180
$676$	3.08916e8	0.0384615
$677$	−1.18079e10	−1.46256	−0.731280	−	0.682077i	$-0.761077\pi$
$677$	−1.18079e10	−1.46256	−0.731280	+	0.682077i	$0.761077\pi$
$678$	1.93126e9	0.237978
$679$	2.75326e9	0.337522
$680$	1.71465e9	0.209119
$681$	−5.71072e8	−0.0692908
$682$	2.63066e9	0.317555
$683$	−2.96868e9	−0.356526	−0.178263	−	0.983983i	$-0.557048\pi$
$683$	−2.96868e9	−0.356526	−0.178263	+	0.983983i	$0.557048\pi$
$684$	−2.04796e9	−0.244695
$685$	3.88853e9	0.462241
$686$	3.22829e8	0.0381802
$687$	6.21773e9	0.731616
$688$	2.66008e9	0.311412
$689$	6.78139e8	0.0789862
$690$	−7.40887e7	−0.00858579
$691$	−1.05676e10	−1.21843	−0.609217	−	0.793004i	$-0.708516\pi$
$691$	−1.05676e10	−1.21843	−0.609217	+	0.793004i	$0.708516\pi$
$692$	−7.16003e9	−0.821379
$693$	2.67476e8	0.0305294
$694$	−8.27096e9	−0.939286
$695$	−1.05822e10	−1.19572
$696$	3.30211e9	0.371244
$697$	−1.20050e10	−1.34291
$698$	−4.00267e9	−0.445508
$699$	−5.94130e9	−0.657978
$700$	−8.34268e8	−0.0919311
$701$	1.11871e10	1.22660	0.613300	−	0.789850i	$-0.289842\pi$
$701$	1.11871e10	1.22660	0.613300	+	0.789850i	$0.289842\pi$
$702$	3.45948e8	0.0377426
$703$	−7.94504e9	−0.862487
$704$	2.80416e8	0.0302899
$705$	−4.06250e9	−0.436648
$706$	2.38043e9	0.254589
$707$	5.25513e9	0.559262
$708$	2.56368e9	0.271486
$709$	−4.68103e9	−0.493264	−0.246632	−	0.969109i	$-0.579324\pi$
$709$	−4.68103e9	−0.493264	−0.246632	+	0.969109i	$0.579324\pi$
$710$	3.41358e9	0.357936
$711$	−5.00645e9	−0.522380
$712$	−2.75414e9	−0.285960
$713$	−5.26411e8	−0.0543891
$714$	1.23871e9	0.127357
$715$	4.70736e8	0.0481622
$716$	−4.25029e7	−0.00432736
$717$	3.95338e9	0.400545
$718$	3.65972e9	0.368988
$719$	−1.59720e10	−1.60254	−0.801268	−	0.598305i	$-0.795841\pi$
$719$	−1.59720e10	−1.60254	−0.801268	+	0.598305i	$0.795841\pi$
$720$	5.98098e8	0.0597185
$721$	2.25428e9	0.223993
$722$	8.26312e9	0.817079
$723$	−5.39372e9	−0.530768
$724$	7.52133e9	0.736563
$725$	−9.07798e9	−0.884721
$726$	−3.96207e9	−0.384276
$727$	−8.17319e9	−0.788899	−0.394449	−	0.918918i	$-0.629065\pi$
$727$	−8.17319e9	−0.788899	−0.394449	+	0.918918i	$0.629065\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	7.56815e9	0.720045
$731$	1.08581e10	1.02812
$732$	−1.59855e9	−0.150639
$733$	−1.78126e10	−1.67057	−0.835284	−	0.549819i	$-0.814697\pi$
$733$	−1.78126e10	−1.67057	−0.835284	+	0.549819i	$0.814697\pi$
$734$	4.11112e9	0.383729
$735$	6.36263e8	0.0591059
$736$	−5.61130e7	−0.00518790
$737$	6.73029e8	0.0619295
$738$	−4.18754e9	−0.383497
$739$	−1.36619e10	−1.24525	−0.622626	−	0.782520i	$-0.713934\pi$
$739$	−1.36619e10	−1.24525	−0.622626	+	0.782520i	$0.713934\pi$
$740$	2.32032e9	0.210492
$741$	−2.60380e9	−0.235095
$742$	8.46979e8	0.0761131
$743$	−3.85782e8	−0.0345049	−0.0172525	−	0.999851i	$-0.505492\pi$
$743$	−3.85782e8	−0.0345049	−0.0172525	+	0.999851i	$0.505492\pi$
$744$	4.24957e9	0.378303
$745$	6.61255e9	0.585898
$746$	5.52793e9	0.487502
$747$	−1.37247e9	−0.120470
$748$	1.14462e9	0.100002
$749$	−4.69804e9	−0.408536
$750$	−5.02435e9	−0.434876
$751$	−8.59646e9	−0.740594	−0.370297	−	0.928913i	$-0.620744\pi$
$751$	−8.59646e9	−0.740594	−0.370297	+	0.928913i	$0.620744\pi$
$752$	−3.07684e9	−0.263841
$753$	−4.63993e9	−0.396031
$754$	4.19834e9	0.356679
$755$	2.45193e9	0.207345
$756$	4.32081e8	0.0363696
$757$	1.16756e10	0.978236	0.489118	−	0.872218i	$-0.337319\pi$
$757$	1.16756e10	0.978236	0.489118	+	0.872218i	$0.337319\pi$
$758$	−5.14381e9	−0.428986
$759$	−4.94584e7	−0.00410576
$760$	−4.50162e9	−0.371981
$761$	−1.49745e10	−1.23171	−0.615853	−	0.787861i	$-0.711189\pi$
$761$	−1.49745e10	−1.23171	−0.615853	+	0.787861i	$0.711189\pi$
$762$	5.11638e9	0.418910
$763$	−4.44932e8	−0.0362625
$764$	6.16196e9	0.499911
$765$	2.44136e9	0.197159
$766$	1.07423e10	0.863572
$767$	3.25950e9	0.260836
$768$	4.52985e8	0.0360844
$769$	−1.50818e9	−0.119594	−0.0597972	−	0.998211i	$-0.519045\pi$
$769$	−1.50818e9	−0.119594	−0.0597972	+	0.998211i	$0.519045\pi$
$770$	5.87938e8	0.0464103
$771$	−9.18680e8	−0.0721895
$772$	6.28861e9	0.491920
$773$	8.96413e9	0.698040	0.349020	−	0.937115i	$-0.386515\pi$
$773$	8.96413e9	0.698040	0.349020	+	0.937115i	$0.386515\pi$
$774$	3.78750e9	0.293602
$775$	−1.16827e10	−0.901544
$776$	4.10982e9	0.315723
$777$	1.67625e9	0.128194
$778$	1.68470e9	0.128261
$779$	3.15178e10	2.38877
$780$	7.60429e8	0.0573756
$781$	2.27876e9	0.171167
$782$	−2.29046e8	−0.0171277
$783$	4.70164e9	0.350012
$784$	4.81890e8	0.0357143
$785$	2.17499e9	0.160478
$786$	−1.79255e9	−0.131672
$787$	−1.89044e10	−1.38245	−0.691227	−	0.722638i	$-0.742929\pi$
$787$	−1.89044e10	−1.38245	−0.691227	+	0.722638i	$0.742929\pi$
$788$	−3.60930e9	−0.262773
$789$	1.04159e10	0.754969
$790$	−1.10047e10	−0.794113
$791$	3.06677e9	0.220325
$792$	3.99264e8	0.0285576
$793$	−2.03242e9	−0.144730
$794$	−9.76456e9	−0.692279
$795$	1.66931e9	0.117829
$796$	2.25432e9	0.158424
$797$	−2.18649e10	−1.52983	−0.764917	−	0.644129i	$-0.777220\pi$
$797$	−2.18649e10	−1.52983	−0.764917	+	0.644129i	$0.777220\pi$
$798$	−3.25208e9	−0.226544
$799$	−1.25593e10	−0.871066
$800$	−1.24532e9	−0.0859937
$801$	−3.92142e9	−0.269606
$802$	−2.05035e10	−1.40352
$803$	5.05216e9	0.344328
$804$	1.08721e9	0.0737766
$805$	−1.17650e8	−0.00794890
$806$	5.40296e9	0.363462
$807$	1.06653e10	0.714356
$808$	7.84439e9	0.523142
$809$	1.90691e10	1.26622	0.633111	−	0.774061i	$-0.281778\pi$
$809$	1.90691e10	1.26622	0.633111	+	0.774061i	$0.281778\pi$
$810$	8.51589e8	0.0563031
$811$	−3.08069e8	−0.0202803	−0.0101402	−	0.999949i	$-0.503228\pi$
$811$	−3.08069e8	−0.0202803	−0.0101402	+	0.999949i	$0.503228\pi$
$812$	5.24363e9	0.343705
$813$	5.74755e9	0.375116
$814$	1.54894e9	0.100658
$815$	−1.35785e9	−0.0878619
$816$	1.84903e9	0.119132
$817$	−2.85068e10	−1.82882
$818$	−7.89788e9	−0.504515
$819$	5.49353e8	0.0349428
$820$	−9.20463e9	−0.582986
$821$	3.11295e10	1.96323	0.981615	−	0.190870i	$-0.0611308\pi$
$821$	3.11295e10	1.96323	0.981615	+	0.190870i	$0.0611308\pi$
$822$	4.19329e9	0.263332
$823$	−1.60349e10	−1.00269	−0.501346	−	0.865247i	$-0.667162\pi$
$823$	−1.60349e10	−1.00269	−0.501346	+	0.865247i	$0.667162\pi$
$824$	3.36499e9	0.209526
$825$	−1.09763e9	−0.0680564
$826$	4.07103e9	0.251347
$827$	1.43238e10	0.880618	0.440309	−	0.897846i	$-0.354869\pi$
$827$	1.43238e10	0.880618	0.440309	+	0.897846i	$0.354869\pi$
$828$	−7.98953e7	−0.00489119
$829$	−1.85305e10	−1.12965	−0.564827	−	0.825210i	$-0.691057\pi$
$829$	−1.85305e10	−1.12965	−0.564827	+	0.825210i	$0.691057\pi$
$830$	−3.01682e9	−0.183137
$831$	−2.44332e9	−0.147699
$832$	5.75930e8	0.0346688
$833$	1.96702e9	0.117910
$834$	−1.14115e10	−0.681182
$835$	−5.60515e9	−0.333184
$836$	−3.00508e9	−0.177883
$837$	6.05066e9	0.356668
$838$	1.63660e10	0.960703
$839$	1.39496e10	0.815447	0.407724	−	0.913105i	$-0.366323\pi$
$839$	1.39496e10	0.815447	0.407724	+	0.913105i	$0.366323\pi$
$840$	9.49757e8	0.0552885
$841$	3.98080e10	2.30773
$842$	1.46354e10	0.844911
$843$	−9.81960e9	−0.564543
$844$	−7.69536e9	−0.440585
$845$	9.66819e8	0.0551247
$846$	−4.38089e9	−0.248752
$847$	−6.29162e9	−0.355771
$848$	1.26430e9	0.0711972
$849$	−7.11924e9	−0.399261
$850$	−5.08325e9	−0.283906
$851$	−3.09953e8	−0.0172402
$852$	3.68111e9	0.203911
$853$	−2.63628e10	−1.45435	−0.727177	−	0.686450i	$-0.759168\pi$
$853$	−2.63628e10	−1.45435	−0.727177	+	0.686450i	$0.759168\pi$
$854$	−2.53844e9	−0.139465
$855$	−6.40953e9	−0.350707
$856$	−7.01282e9	−0.382151
$857$	1.46096e10	0.792878	0.396439	−	0.918061i	$-0.370246\pi$
$857$	1.46096e10	0.792878	0.396439	+	0.918061i	$0.370246\pi$
$858$	5.07629e8	0.0274373
$859$	−6.60305e9	−0.355442	−0.177721	−	0.984081i	$-0.556872\pi$
$859$	−6.60305e9	−0.355442	−0.177721	+	0.984081i	$0.556872\pi$
$860$	8.32530e9	0.446329
$861$	−6.64966e9	−0.355049
$862$	−1.14363e10	−0.608149
$863$	1.40909e10	0.746279	0.373139	−	0.927775i	$-0.378281\pi$
$863$	1.40909e10	0.746279	0.373139	+	0.927775i	$0.378281\pi$
$864$	6.44973e8	0.0340207
$865$	−2.24089e10	−1.17724
$866$	−6.83055e9	−0.357390
$867$	−3.53163e9	−0.184038
$868$	6.74816e9	0.350241
$869$	−7.34624e9	−0.379748
$870$	1.03347e10	0.532083
$871$	1.38230e9	0.0708823
$872$	−6.64154e8	−0.0339204
$873$	5.85167e9	0.297667
$874$	6.01337e8	0.0304669
$875$	−7.97848e9	−0.402617
$876$	8.16128e9	0.410198
$877$	1.69803e10	0.850053	0.425027	−	0.905181i	$-0.360265\pi$
$877$	1.69803e10	0.850053	0.425027	+	0.905181i	$0.360265\pi$
$878$	−1.75191e10	−0.873537
$879$	1.81435e10	0.901072
$880$	8.77622e8	0.0434128
$881$	−3.49607e10	−1.72252	−0.861261	−	0.508164i	$-0.830325\pi$
$881$	−3.49607e10	−1.72252	−0.861261	+	0.508164i	$0.830325\pi$
$882$	6.86129e8	0.0336718
$883$	−2.16243e10	−1.05701	−0.528506	−	0.848929i	$-0.677248\pi$
$883$	−2.16243e10	−1.05701	−0.528506	+	0.848929i	$0.677248\pi$
$884$	2.35088e9	0.114458
$885$	8.02360e9	0.389106
$886$	1.06039e10	0.512212
$887$	1.29056e10	0.620934	0.310467	−	0.950584i	$-0.399515\pi$
$887$	1.29056e10	0.620934	0.310467	+	0.950584i	$0.399515\pi$
$888$	2.50216e9	0.119914
$889$	8.12463e9	0.387835
$890$	−8.61967e9	−0.409851
$891$	5.68483e8	0.0269244
$892$	7.21717e9	0.340479
$893$	3.29730e10	1.54945
$894$	7.13079e9	0.333777
$895$	−1.33022e8	−0.00620215
$896$	7.19323e8	0.0334077
$897$	−1.01580e8	−0.00469931
$898$	−3.52913e9	−0.162630
$899$	7.34293e10	3.37062
$900$	−1.77312e9	−0.0810756
$901$	5.16070e9	0.235056
$902$	−6.14461e9	−0.278786
$903$	6.01441e9	0.271823
$904$	4.57780e9	0.206095
$905$	2.35396e10	1.05567
$906$	2.64409e9	0.118121
$907$	−1.51022e9	−0.0672069	−0.0336035	−	0.999435i	$-0.510698\pi$
$907$	−1.51022e9	−0.0672069	−0.0336035	+	0.999435i	$0.510698\pi$
$908$	−1.35365e9	−0.0600076
$909$	1.11691e10	0.493223
$910$	1.20753e9	0.0531195
$911$	1.44911e10	0.635021	0.317511	−	0.948255i	$-0.397153\pi$
$911$	1.44911e10	0.635021	0.317511	+	0.948255i	$0.397153\pi$
$912$	−4.85442e9	−0.211912
$913$	−2.01389e9	−0.0875768
$914$	−4.49888e9	−0.194892
$915$	−5.00302e9	−0.215903
$916$	1.47383e10	0.633598
$917$	−2.84651e9	−0.121904
$918$	2.63270e9	0.112319
$919$	−1.01023e10	−0.429355	−0.214678	−	0.976685i	$-0.568870\pi$
$919$	−1.01023e10	−0.429355	−0.214678	+	0.976685i	$0.568870\pi$
$920$	−1.75618e8	−0.00743551
$921$	8.05400e9	0.339706
$922$	7.37514e9	0.309893
$923$	4.68021e9	0.195911
$924$	6.34016e8	0.0264392
$925$	−6.87882e9	−0.285771
$926$	−2.05114e10	−0.848903
$927$	4.79116e9	0.197543
$928$	7.82722e9	0.321507
$929$	3.63265e10	1.48651	0.743256	−	0.669007i	$-0.233281\pi$
$929$	3.63265e10	1.48651	0.743256	+	0.669007i	$0.233281\pi$
$930$	1.32999e10	0.542200
$931$	−5.16419e9	−0.209739
$932$	−1.40831e10	−0.569825
$933$	−1.15863e10	−0.467047
$934$	−1.66056e10	−0.666868
$935$	3.58235e9	0.143327
$936$	8.20026e8	0.0326860
$937$	−3.46698e10	−1.37677	−0.688387	−	0.725344i	$-0.741681\pi$
$937$	−3.46698e10	−1.37677	−0.688387	+	0.725344i	$0.741681\pi$
$938$	1.72646e9	0.0683039
$939$	2.09223e9	0.0824670
$940$	−9.62963e9	−0.378148
$941$	7.50031e9	0.293437	0.146719	−	0.989178i	$-0.453129\pi$
$941$	7.50031e9	0.293437	0.146719	+	0.989178i	$0.453129\pi$
$942$	2.34545e9	0.0914216
$943$	1.22958e9	0.0477490
$944$	6.07688e9	0.235114
$945$	1.35229e9	0.0521265
$946$	5.55760e9	0.213436
$947$	−9.42257e9	−0.360533	−0.180266	−	0.983618i	$-0.557696\pi$
$947$	−9.42257e9	−0.360533	−0.180266	+	0.983618i	$0.557696\pi$
$948$	−1.18671e10	−0.452394
$949$	1.03764e10	0.394106
$950$	1.33455e10	0.505013
$951$	−5.36203e9	−0.202161
$952$	2.93619e9	0.110295
$953$	4.57017e9	0.171044	0.0855219	−	0.996336i	$-0.472744\pi$
$953$	4.57017e9	0.171044	0.0855219	+	0.996336i	$0.472744\pi$
$954$	1.80014e9	0.0671254
$955$	1.92852e10	0.716493
$956$	9.37097e9	0.346882
$957$	6.89897e9	0.254444
$958$	−3.26687e10	−1.20047
$959$	6.65879e9	0.243798
$960$	1.41771e9	0.0517177
$961$	6.69854e10	2.43472
$962$	3.18128e9	0.115210
$963$	−9.98505e9	−0.360295
$964$	−1.27851e10	−0.459658
$965$	1.96816e10	0.705041
$966$	−1.26871e8	−0.00452837
$967$	5.07341e10	1.80429	0.902147	−	0.431430i	$-0.141991\pi$
$967$	5.07341e10	1.80429	0.902147	+	0.431430i	$0.141991\pi$
$968$	−9.39157e9	−0.332793
$969$	−1.98152e10	−0.699624
$970$	1.28626e10	0.452508
$971$	5.19862e10	1.82230	0.911152	−	0.412071i	$-0.135194\pi$
$971$	5.19862e10	1.82230	0.911152	+	0.412071i	$0.135194\pi$
$972$	9.18330e8	0.0320750
$973$	−1.81211e10	−0.630652
$974$	2.06479e9	0.0716010
$975$	−2.25437e9	−0.0778949
$976$	−3.78916e9	−0.130457
$977$	−1.87185e10	−0.642156	−0.321078	−	0.947053i	$-0.604045\pi$
$977$	−1.87185e10	−0.642156	−0.321078	+	0.947053i	$0.604045\pi$
$978$	−1.46427e9	−0.0500536
$979$	−5.75412e9	−0.195992
$980$	1.50818e9	0.0511872
$981$	−9.45642e8	−0.0319805
$982$	−2.32809e10	−0.784531
$983$	4.41632e10	1.48294	0.741470	−	0.670986i	$-0.234129\pi$
$983$	4.41632e10	1.48294	0.741470	+	0.670986i	$0.234129\pi$
$984$	−9.92602e9	−0.332118
$985$	−1.12961e10	−0.376618
$986$	3.19498e10	1.06145
$987$	−6.95669e9	−0.230299
$988$	−6.17197e9	−0.203599
$989$	−1.11211e9	−0.0365562
$990$	1.24958e9	0.0409300
$991$	4.18362e9	0.136551	0.0682754	−	0.997667i	$-0.478250\pi$
$991$	4.18362e9	0.136551	0.0682754	+	0.997667i	$0.478250\pi$
$992$	1.00731e10	0.327620
$993$	−1.24642e10	−0.403962
$994$	5.84547e9	0.188785
$995$	7.05539e9	0.227060
$996$	−3.25325e9	−0.104330
$997$	4.54561e10	1.45264	0.726322	−	0.687355i	$-0.241228\pi$
$997$	4.54561e10	1.45264	0.726322	+	0.687355i	$0.241228\pi$
$998$	8.11232e9	0.258338
$999$	3.56265e9	0.113056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.s.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.s.1.4	✓	7	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)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +200.302 q^{5} +216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +200.302 q^{5} +216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +1602.41 q^{10} +1069.70 q^{11} +1728.00 q^{12} +2197.00 q^{13} +2744.00 q^{14} +5408.15 q^{15} +4096.00 q^{16} +16719.4 q^{17} +5832.00 q^{18} -43894.9 q^{19} +12819.3 q^{20} +9261.00 q^{21} +8557.61 q^{22} -1712.43 q^{23} +13824.0 q^{24} -38004.2 q^{25} +17576.0 q^{26} +19683.0 q^{27} +21952.0 q^{28} +238868. q^{29} +43265.2 q^{30} +307405. q^{31} +32768.0 q^{32} +28881.9 q^{33} +133755. q^{34} +68703.5 q^{35} +46656.0 q^{36} +181002. q^{37} -351159. q^{38} +59319.0 q^{39} +102555. q^{40} -718028. q^{41} +74088.0 q^{42} +649434. q^{43} +68460.9 q^{44} +146020. q^{45} -13699.5 q^{46} -751182. q^{47} +110592. q^{48} +117649. q^{49} -304034. q^{50} +451423. q^{51} +140608. q^{52} +308666. q^{53} +157464. q^{54} +214263. q^{55} +175616. q^{56} -1.18516e6 q^{57} +1.91094e6 q^{58} +1.48361e6 q^{59} +346122. q^{60} -925088. q^{61} +2.45924e6 q^{62} +250047. q^{63} +262144. q^{64} +440063. q^{65} +231056. q^{66} +629175. q^{67} +1.07004e6 q^{68} -46235.7 q^{69} +549628. q^{70} +2.13027e6 q^{71} +373248. q^{72} +4.72296e6 q^{73} +1.44801e6 q^{74} -1.02611e6 q^{75} -2.80927e6 q^{76} +366908. q^{77} +474552. q^{78} -6.86756e6 q^{79} +820436. q^{80} +531441. q^{81} -5.74423e6 q^{82} -1.88267e6 q^{83} +592704. q^{84} +3.34892e6 q^{85} +5.19547e6 q^{86} +6.44943e6 q^{87} +547687. q^{88} -5.37918e6 q^{89} +1.16816e6 q^{90} +753571. q^{91} -109596. q^{92} +8.29994e6 q^{93} -6.00945e6 q^{94} -8.79223e6 q^{95} +884736. q^{96} +8.02699e6 q^{97} +941192. q^{98} +779812. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 56 q^{2} + 189 q^{3} + 448 q^{4} + 625 q^{5} + 1512 q^{6} + 2401 q^{7} + 3584 q^{8} + 5103 q^{9}+O(q^{10}) \) 7 * q + 56 * q^2 + 189 * q^3 + 448 * q^4 + 625 * q^5 + 1512 * q^6 + 2401 * q^7 + 3584 * q^8 + 5103 * q^9	\( 7 q + 56 q^{2} + 189 q^{3} + 448 q^{4} + 625 q^{5} + 1512 q^{6} + 2401 q^{7} + 3584 q^{8} + 5103 q^{9} + 5000 q^{10} + 4678 q^{11} + 12096 q^{12} + 15379 q^{13} + 19208 q^{14} + 16875 q^{15} + 28672 q^{16} + 38552 q^{17} + 40824 q^{18} + 60231 q^{19} + 40000 q^{20} + 64827 q^{21} + 37424 q^{22} + 82047 q^{23} + 96768 q^{24} + 136408 q^{25} + 123032 q^{26} + 137781 q^{27} + 153664 q^{28} + 87523 q^{29} + 135000 q^{30} - 3191 q^{31} + 229376 q^{32} + 126306 q^{33} + 308416 q^{34} + 214375 q^{35} + 326592 q^{36} + 360916 q^{37} + 481848 q^{38} + 415233 q^{39} + 320000 q^{40} + 814350 q^{41} + 518616 q^{42} + 840057 q^{43} + 299392 q^{44} + 455625 q^{45} + 656376 q^{46} + 472723 q^{47} + 774144 q^{48} + 823543 q^{49} + 1091264 q^{50} + 1040904 q^{51} + 984256 q^{52} + 2185687 q^{53} + 1102248 q^{54} + 298354 q^{55} + 1229312 q^{56} + 1626237 q^{57} + 700184 q^{58} + 2046232 q^{59} + 1080000 q^{60} + 2744560 q^{61} - 25528 q^{62} + 1750329 q^{63} + 1835008 q^{64} + 1373125 q^{65} + 1010448 q^{66} + 1960358 q^{67} + 2467328 q^{68} + 2215269 q^{69} + 1715000 q^{70} + 2774656 q^{71} + 2612736 q^{72} + 3696313 q^{73} + 2887328 q^{74} + 3683016 q^{75} + 3854784 q^{76} + 1604554 q^{77} + 3321864 q^{78} + 1532089 q^{79} + 2560000 q^{80} + 3720087 q^{81} + 6514800 q^{82} + 7473863 q^{83} + 4148928 q^{84} - 1656624 q^{85} + 6720456 q^{86} + 2363121 q^{87} + 2395136 q^{88} + 14077309 q^{89} + 3645000 q^{90} + 5274997 q^{91} + 5251008 q^{92} - 86157 q^{93} + 3781784 q^{94} - 1704679 q^{95} + 6193152 q^{96} + 8273673 q^{97} + 6588344 q^{98} + 3410262 q^{99}+O(q^{100}) \) 7 * q + 56 * q^2 + 189 * q^3 + 448 * q^4 + 625 * q^5 + 1512 * q^6 + 2401 * q^7 + 3584 * q^8 + 5103 * q^9 + 5000 * q^10 + 4678 * q^11 + 12096 * q^12 + 15379 * q^13 + 19208 * q^14 + 16875 * q^15 + 28672 * q^16 + 38552 * q^17 + 40824 * q^18 + 60231 * q^19 + 40000 * q^20 + 64827 * q^21 + 37424 * q^22 + 82047 * q^23 + 96768 * q^24 + 136408 * q^25 + 123032 * q^26 + 137781 * q^27 + 153664 * q^28 + 87523 * q^29 + 135000 * q^30 - 3191 * q^31 + 229376 * q^32 + 126306 * q^33 + 308416 * q^34 + 214375 * q^35 + 326592 * q^36 + 360916 * q^37 + 481848 * q^38 + 415233 * q^39 + 320000 * q^40 + 814350 * q^41 + 518616 * q^42 + 840057 * q^43 + 299392 * q^44 + 455625 * q^45 + 656376 * q^46 + 472723 * q^47 + 774144 * q^48 + 823543 * q^49 + 1091264 * q^50 + 1040904 * q^51 + 984256 * q^52 + 2185687 * q^53 + 1102248 * q^54 + 298354 * q^55 + 1229312 * q^56 + 1626237 * q^57 + 700184 * q^58 + 2046232 * q^59 + 1080000 * q^60 + 2744560 * q^61 - 25528 * q^62 + 1750329 * q^63 + 1835008 * q^64 + 1373125 * q^65 + 1010448 * q^66 + 1960358 * q^67 + 2467328 * q^68 + 2215269 * q^69 + 1715000 * q^70 + 2774656 * q^71 + 2612736 * q^72 + 3696313 * q^73 + 2887328 * q^74 + 3683016 * q^75 + 3854784 * q^76 + 1604554 * q^77 + 3321864 * q^78 + 1532089 * q^79 + 2560000 * q^80 + 3720087 * q^81 + 6514800 * q^82 + 7473863 * q^83 + 4148928 * q^84 - 1656624 * q^85 + 6720456 * q^86 + 2363121 * q^87 + 2395136 * q^88 + 14077309 * q^89 + 3645000 * q^90 + 5274997 * q^91 + 5251008 * q^92 - 86157 * q^93 + 3781784 * q^94 - 1704679 * q^95 + 6193152 * q^96 + 8273673 * q^97 + 6588344 * q^98 + 3410262 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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