LMFDB - Embedded newform 546.8.a.r.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:	$6$
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} - 264981x^{4} + 17519669x^{3} + 15113237808x^{2} - 1787613752904x - 21984668630064 $ x^6 - x^5 - 264981x^4 + 17519669x^3 + 15113237808x^2 - 1787613752904x - 21984668630064
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			1.4
Root			$-11.2455$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +45.2455 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +45.2455 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +361.964 q^{10} +3722.93 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} -1221.63 q^{15} +4096.00 q^{16} +24360.1 q^{17} +5832.00 q^{18} +16145.2 q^{19} +2895.71 q^{20} +9261.00 q^{21} +29783.4 q^{22} -19748.3 q^{23} -13824.0 q^{24} -76077.8 q^{25} +17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +226116. q^{29} -9773.02 q^{30} -120387. q^{31} +32768.0 q^{32} -100519. q^{33} +194881. q^{34} -15519.2 q^{35} +46656.0 q^{36} -470925. q^{37} +129162. q^{38} -59319.0 q^{39} +23165.7 q^{40} -526838. q^{41} +74088.0 q^{42} +343410. q^{43} +238268. q^{44} +32984.0 q^{45} -157987. q^{46} +861916. q^{47} -110592. q^{48} +117649. q^{49} -608623. q^{50} -657722. q^{51} +140608. q^{52} +181808. q^{53} -157464. q^{54} +168446. q^{55} -175616. q^{56} -435920. q^{57} +1.80893e6 q^{58} -704361. q^{59} -78184.2 q^{60} +852775. q^{61} -963094. q^{62} -250047. q^{63} +262144. q^{64} +99404.3 q^{65} -804153. q^{66} -96440.5 q^{67} +1.55905e6 q^{68} +533205. q^{69} -124154. q^{70} +5.35527e6 q^{71} +373248. q^{72} -3.41008e6 q^{73} -3.76740e6 q^{74} +2.05410e6 q^{75} +1.03329e6 q^{76} -1.27697e6 q^{77} -474552. q^{78} -5.28067e6 q^{79} +185326. q^{80} +531441. q^{81} -4.21470e6 q^{82} -3.16918e6 q^{83} +592704. q^{84} +1.10218e6 q^{85} +2.74728e6 q^{86} -6.10513e6 q^{87} +1.90614e6 q^{88} +1.09078e7 q^{89} +263872. q^{90} -753571. q^{91} -1.26389e6 q^{92} +3.25044e6 q^{93} +6.89533e6 q^{94} +730497. q^{95} -884736. q^{96} +1.10372e7 q^{97} +941192. q^{98} +2.71402e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 203 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 + 203 * q^5 - 1296 * q^6 - 2058 * q^7 + 3072 * q^8 + 4374 * q^9	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 203 q^{5} - 1296 q^{6} - 2058 q^{7} + 3072 q^{8} + 4374 q^{9} + 1624 q^{10} - 2690 q^{11} - 10368 q^{12} + 13182 q^{13} - 16464 q^{14} - 5481 q^{15} + 24576 q^{16} + 2910 q^{17} + 34992 q^{18} - 13055 q^{19} + 12992 q^{20} + 55566 q^{21} - 21520 q^{22} + 11581 q^{23} - 82944 q^{24} + 68081 q^{25} + 105456 q^{26} - 118098 q^{27} - 131712 q^{28} - 92335 q^{29} - 43848 q^{30} - 83081 q^{31} + 196608 q^{32} + 72630 q^{33} + 23280 q^{34} - 69629 q^{35} + 279936 q^{36} - 265114 q^{37} - 104440 q^{38} - 355914 q^{39} + 103936 q^{40} - 367468 q^{41} + 444528 q^{42} + 454955 q^{43} - 172160 q^{44} + 147987 q^{45} + 92648 q^{46} + 733973 q^{47} - 663552 q^{48} + 705894 q^{49} + 544648 q^{50} - 78570 q^{51} + 843648 q^{52} - 1577379 q^{53} - 944784 q^{54} + 2231118 q^{55} - 1053696 q^{56} + 352485 q^{57} - 738680 q^{58} + 2062708 q^{59} - 350784 q^{60} - 271270 q^{61} - 664648 q^{62} - 1500282 q^{63} + 1572864 q^{64} + 445991 q^{65} + 581040 q^{66} - 758674 q^{67} + 186240 q^{68} - 312687 q^{69} - 557032 q^{70} - 6138216 q^{71} + 2239488 q^{72} + 6361979 q^{73} - 2120912 q^{74} - 1838187 q^{75} - 835520 q^{76} + 922670 q^{77} - 2847312 q^{78} - 899781 q^{79} + 831488 q^{80} + 3188646 q^{81} - 2939744 q^{82} + 3313561 q^{83} + 3556224 q^{84} + 5307940 q^{85} + 3639640 q^{86} + 2493045 q^{87} - 1377280 q^{88} + 11210703 q^{89} + 1183896 q^{90} - 4521426 q^{91} + 741184 q^{92} + 2243187 q^{93} + 5871784 q^{94} + 12912395 q^{95} - 5308416 q^{96} + 28682643 q^{97} + 5647152 q^{98} - 1961010 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 203 * q^5 - 1296 * q^6 - 2058 * q^7 + 3072 * q^8 + 4374 * q^9 + 1624 * q^10 - 2690 * q^11 - 10368 * q^12 + 13182 * q^13 - 16464 * q^14 - 5481 * q^15 + 24576 * q^16 + 2910 * q^17 + 34992 * q^18 - 13055 * q^19 + 12992 * q^20 + 55566 * q^21 - 21520 * q^22 + 11581 * q^23 - 82944 * q^24 + 68081 * q^25 + 105456 * q^26 - 118098 * q^27 - 131712 * q^28 - 92335 * q^29 - 43848 * q^30 - 83081 * q^31 + 196608 * q^32 + 72630 * q^33 + 23280 * q^34 - 69629 * q^35 + 279936 * q^36 - 265114 * q^37 - 104440 * q^38 - 355914 * q^39 + 103936 * q^40 - 367468 * q^41 + 444528 * q^42 + 454955 * q^43 - 172160 * q^44 + 147987 * q^45 + 92648 * q^46 + 733973 * q^47 - 663552 * q^48 + 705894 * q^49 + 544648 * q^50 - 78570 * q^51 + 843648 * q^52 - 1577379 * q^53 - 944784 * q^54 + 2231118 * q^55 - 1053696 * q^56 + 352485 * q^57 - 738680 * q^58 + 2062708 * q^59 - 350784 * q^60 - 271270 * q^61 - 664648 * q^62 - 1500282 * q^63 + 1572864 * q^64 + 445991 * q^65 + 581040 * q^66 - 758674 * q^67 + 186240 * q^68 - 312687 * q^69 - 557032 * q^70 - 6138216 * q^71 + 2239488 * q^72 + 6361979 * q^73 - 2120912 * q^74 - 1838187 * q^75 - 835520 * q^76 + 922670 * q^77 - 2847312 * q^78 - 899781 * q^79 + 831488 * q^80 + 3188646 * q^81 - 2939744 * q^82 + 3313561 * q^83 + 3556224 * q^84 + 5307940 * q^85 + 3639640 * q^86 + 2493045 * q^87 - 1377280 * q^88 + 11210703 * q^89 + 1183896 * q^90 - 4521426 * q^91 + 741184 * q^92 + 2243187 * q^93 + 5871784 * q^94 + 12912395 * q^95 - 5308416 * q^96 + 28682643 * q^97 + 5647152 * q^98 - 1961010 * 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
$5$	45.2455	0.161875	0.0809376	−	0.996719i	$-0.474209\pi$
$5$	45.2455	0.161875	0.0809376	+	0.996719i	$0.474209\pi$
$6$	−216.000	−0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	361.964	0.114463
$11$	3722.93	0.843355	0.421678	−	0.906746i	$-0.361441\pi$
$11$	3722.93	0.843355	0.421678	+	0.906746i	$0.361441\pi$
$12$	−1728.00	−0.288675
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−2744.00	−0.267261
$15$	−1221.63	−0.0934587
$16$	4096.00	0.250000
$17$	24360.1	1.20256	0.601281	−	0.799038i	$-0.294657\pi$
$17$	24360.1	1.20256	0.601281	+	0.799038i	$0.294657\pi$
$18$	5832.00	0.235702
$19$	16145.2	0.540015	0.270007	−	0.962858i	$-0.412974\pi$
$19$	16145.2	0.540015	0.270007	+	0.962858i	$0.412974\pi$
$20$	2895.71	0.0809376
$21$	9261.00	0.218218
$22$	29783.4	0.596342
$23$	−19748.3	−0.338441	−0.169221	−	0.985578i	$-0.554125\pi$
$23$	−19748.3	−0.338441	−0.169221	+	0.985578i	$0.554125\pi$
$24$	−13824.0	−0.204124
$25$	−76077.8	−0.973796
$26$	17576.0	0.196116
$27$	−19683.0	−0.192450
$28$	−21952.0	−0.188982
$29$	226116.	1.72162	0.860812	−	0.508923i	$-0.169956\pi$
$29$	226116.	1.72162	0.860812	+	0.508923i	$0.169956\pi$
$30$	−9773.02	−0.0660853
$31$	−120387.	−0.725793	−0.362896	−	0.931829i	$-0.618212\pi$
$31$	−120387.	−0.725793	−0.362896	+	0.931829i	$0.618212\pi$
$32$	32768.0	0.176777
$33$	−100519.	−0.486911
$34$	194881.	0.850340
$35$	−15519.2	−0.0611831
$36$	46656.0	0.166667
$37$	−470925.	−1.52843	−0.764215	−	0.644962i	$-0.776873\pi$
$37$	−470925.	−1.52843	−0.764215	+	0.644962i	$0.776873\pi$
$38$	129162.	0.381848
$39$	−59319.0	−0.160128
$40$	23165.7	0.0572315
$41$	−526838.	−1.19380	−0.596902	−	0.802314i	$-0.703602\pi$
$41$	−526838.	−1.19380	−0.596902	+	0.802314i	$0.703602\pi$
$42$	74088.0	0.154303
$43$	343410.	0.658678	0.329339	−	0.944212i	$-0.393174\pi$
$43$	343410.	0.658678	0.329339	+	0.944212i	$0.393174\pi$
$44$	238268.	0.421678
$45$	32984.0	0.0539584
$46$	−157987.	−0.239314
$47$	861916.	1.21094	0.605470	−	0.795868i	$-0.292985\pi$
$47$	861916.	1.21094	0.605470	+	0.795868i	$0.292985\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	−608623.	−0.688578
$51$	−657722.	−0.694300
$52$	140608.	0.138675
$53$	181808.	0.167744	0.0838720	−	0.996477i	$-0.473271\pi$
$53$	181808.	0.167744	0.0838720	+	0.996477i	$0.473271\pi$
$54$	−157464.	−0.136083
$55$	168446.	0.136518
$56$	−175616.	−0.133631
$57$	−435920.	−0.311778
$58$	1.80893e6	1.21737
$59$	−704361.	−0.446492	−0.223246	−	0.974762i	$-0.571665\pi$
$59$	−704361.	−0.446492	−0.223246	+	0.974762i	$0.571665\pi$
$60$	−78184.2	−0.0467293
$61$	852775.	0.481039	0.240519	−	0.970644i	$-0.422682\pi$
$61$	852775.	0.481039	0.240519	+	0.970644i	$0.422682\pi$
$62$	−963094.	−0.513213
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	99404.3	0.0448961
$66$	−804153.	−0.344298
$67$	−96440.5	−0.0391740	−0.0195870	−	0.999808i	$-0.506235\pi$
$67$	−96440.5	−0.0391740	−0.0195870	+	0.999808i	$0.506235\pi$
$68$	1.55905e6	0.601281
$69$	533205.	0.195399
$70$	−124154.	−0.0432630
$71$	5.35527e6	1.77573	0.887865	−	0.460103i	$-0.152188\pi$
$71$	5.35527e6	1.77573	0.887865	+	0.460103i	$0.152188\pi$
$72$	373248.	0.117851
$73$	−3.41008e6	−1.02597	−0.512986	−	0.858397i	$-0.671461\pi$
$73$	−3.41008e6	−1.02597	−0.512986	+	0.858397i	$0.671461\pi$
$74$	−3.76740e6	−1.08076
$75$	2.05410e6	0.562222
$76$	1.03329e6	0.270007
$77$	−1.27697e6	−0.318758
$78$	−474552.	−0.113228
$79$	−5.28067e6	−1.20502	−0.602510	−	0.798111i	$-0.705833\pi$
$79$	−5.28067e6	−1.20502	−0.602510	+	0.798111i	$0.705833\pi$
$80$	185326.	0.0404688
$81$	531441.	0.111111
$82$	−4.21470e6	−0.844147
$83$	−3.16918e6	−0.608377	−0.304189	−	0.952612i	$-0.598385\pi$
$83$	−3.16918e6	−0.608377	−0.304189	+	0.952612i	$0.598385\pi$
$84$	592704.	0.109109
$85$	1.10218e6	0.194665
$86$	2.74728e6	0.465756
$87$	−6.10513e6	−0.993980
$88$	1.90614e6	0.298171
$89$	1.09078e7	1.64010	0.820052	−	0.572289i	$-0.193945\pi$
$89$	1.09078e7	1.64010	0.820052	+	0.572289i	$0.193945\pi$
$90$	263872.	0.0381543
$91$	−753571.	−0.104828
$92$	−1.26389e6	−0.169221
$93$	3.25044e6	0.419037
$94$	6.89533e6	0.856263
$95$	730497.	0.0874150
$96$	−884736.	−0.102062
$97$	1.10372e7	1.22788	0.613941	−	0.789352i	$-0.289583\pi$
$97$	1.10372e7	1.22788	0.613941	+	0.789352i	$0.289583\pi$
$98$	941192.	0.101015
$99$	2.71402e6	0.281118
$100$	−4.86898e6	−0.486898
$101$	1.06988e7	1.03327	0.516633	−	0.856207i	$-0.327185\pi$
$101$	1.06988e7	1.03327	0.516633	+	0.856207i	$0.327185\pi$
$102$	−5.26178e6	−0.490944
$103$	2.78324e6	0.250969	0.125484	−	0.992096i	$-0.459951\pi$
$103$	2.78324e6	0.250969	0.125484	+	0.992096i	$0.459951\pi$
$104$	1.12486e6	0.0980581
$105$	419018.	0.0353241
$106$	1.45446e6	0.118613
$107$	1.03594e7	0.817509	0.408754	−	0.912644i	$-0.365963\pi$
$107$	1.03594e7	0.817509	0.408754	+	0.912644i	$0.365963\pi$
$108$	−1.25971e6	−0.0962250
$109$	5.32933e6	0.394166	0.197083	−	0.980387i	$-0.436853\pi$
$109$	5.32933e6	0.394166	0.197083	+	0.980387i	$0.436853\pi$
$110$	1.34757e6	0.0965330
$111$	1.27150e7	0.882440
$112$	−1.40493e6	−0.0944911
$113$	−397565.	−0.0259199	−0.0129599	−	0.999916i	$-0.504125\pi$
$113$	−397565.	−0.0259199	−0.0129599	+	0.999916i	$0.504125\pi$
$114$	−3.48736e6	−0.220460
$115$	−893524.	−0.0547852
$116$	1.44714e7	0.860812
$117$	1.60161e6	0.0924500
$118$	−5.63489e6	−0.315717
$119$	−8.35551e6	−0.454526
$120$	−625474.	−0.0330426
$121$	−5.62696e6	−0.288752
$122$	6.82220e6	0.340146
$123$	1.42246e7	0.689244
$124$	−7.70475e6	−0.362896
$125$	−6.97698e6	−0.319509
$126$	−2.00038e6	−0.0890871
$127$	−1.69684e7	−0.735069	−0.367534	−	0.930010i	$-0.619798\pi$
$127$	−1.69684e7	−0.735069	−0.367534	+	0.930010i	$0.619798\pi$
$128$	2.09715e6	0.0883883
$129$	−9.27207e6	−0.380288
$130$	795235.	0.0317463
$131$	−3.03552e7	−1.17973	−0.589867	−	0.807501i	$-0.700820\pi$
$131$	−3.03552e7	−1.17973	−0.589867	+	0.807501i	$0.700820\pi$
$132$	−6.43322e6	−0.243456
$133$	−5.53780e6	−0.204106
$134$	−771524.	−0.0277002
$135$	−890567.	−0.0311529
$136$	1.24724e7	0.425170
$137$	1.87177e7	0.621915	0.310958	−	0.950424i	$-0.399350\pi$
$137$	1.87177e7	0.621915	0.310958	+	0.950424i	$0.399350\pi$
$138$	4.26564e6	0.138168
$139$	−2.13020e7	−0.672774	−0.336387	−	0.941724i	$-0.609205\pi$
$139$	−2.13020e7	−0.672774	−0.336387	+	0.941724i	$0.609205\pi$
$140$	−993229.	−0.0305915
$141$	−2.32717e7	−0.699136
$142$	4.28422e7	1.25563
$143$	8.17928e6	0.233905
$144$	2.98598e6	0.0833333
$145$	1.02307e7	0.278688
$146$	−2.72807e7	−0.725471
$147$	−3.17652e6	−0.0824786
$148$	−3.01392e7	−0.764215
$149$	1.39114e7	0.344523	0.172261	−	0.985051i	$-0.444893\pi$
$149$	1.39114e7	0.344523	0.172261	+	0.985051i	$0.444893\pi$
$150$	1.64328e7	0.397551
$151$	7.53171e7	1.78022	0.890111	−	0.455744i	$-0.150627\pi$
$151$	7.53171e7	1.78022	0.890111	+	0.455744i	$0.150627\pi$
$152$	8.26634e6	0.190924
$153$	1.77585e7	0.400854
$154$	−1.02157e7	−0.225396
$155$	−5.44696e6	−0.117488
$156$	−3.79642e6	−0.0800641
$157$	5.67481e7	1.17031	0.585157	−	0.810920i	$-0.301033\pi$
$157$	5.67481e7	1.17031	0.585157	+	0.810920i	$0.301033\pi$
$158$	−4.22454e7	−0.852078
$159$	−4.90881e6	−0.0968471
$160$	1.48260e6	0.0286158
$161$	6.77368e6	0.127919
$162$	4.25153e6	0.0785674
$163$	−2.58947e7	−0.468332	−0.234166	−	0.972197i	$-0.575236\pi$
$163$	−2.58947e7	−0.468332	−0.234166	+	0.972197i	$0.575236\pi$
$164$	−3.37176e7	−0.596902
$165$	−4.54804e6	−0.0788189
$166$	−2.53534e7	−0.430188
$167$	1.75791e7	0.292072	0.146036	−	0.989279i	$-0.453349\pi$
$167$	1.75791e7	0.292072	0.146036	+	0.989279i	$0.453349\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	8.81747e6	0.137649
$171$	1.17698e7	0.180005
$172$	2.19782e7	0.329339
$173$	9.70629e7	1.42525	0.712626	−	0.701544i	$-0.247506\pi$
$173$	9.70629e7	1.42525	0.712626	+	0.701544i	$0.247506\pi$
$174$	−4.88411e7	−0.702850
$175$	2.60947e7	0.368060
$176$	1.52491e7	0.210839
$177$	1.90178e7	0.257782
$178$	8.72622e7	1.15973
$179$	4.75406e6	0.0619554	0.0309777	−	0.999520i	$-0.490138\pi$
$179$	4.75406e6	0.0619554	0.0309777	+	0.999520i	$0.490138\pi$
$180$	2.11097e6	0.0269792
$181$	1.49793e7	0.187766	0.0938830	−	0.995583i	$-0.470072\pi$
$181$	1.49793e7	0.187766	0.0938830	+	0.995583i	$0.470072\pi$
$182$	−6.02857e6	−0.0741249
$183$	−2.30249e7	−0.277728
$184$	−1.01112e7	−0.119657
$185$	−2.13072e7	−0.247415
$186$	2.60035e7	0.296304
$187$	9.06909e7	1.01419
$188$	5.51626e7	0.605470
$189$	6.75127e6	0.0727393
$190$	5.84398e6	0.0618117
$191$	1.53951e8	1.59870	0.799349	−	0.600867i	$-0.205178\pi$
$191$	1.53951e8	1.59870	0.799349	+	0.600867i	$0.205178\pi$
$192$	−7.07789e6	−0.0721688
$193$	−1.74528e8	−1.74749	−0.873747	−	0.486381i	$-0.838317\pi$
$193$	−1.74528e8	−1.74749	−0.873747	+	0.486381i	$0.838317\pi$
$194$	8.82974e7	0.868244
$195$	−2.68392e6	−0.0259208
$196$	7.52954e6	0.0714286
$197$	1.21338e8	1.13075	0.565373	−	0.824835i	$-0.308732\pi$
$197$	1.21338e8	1.13075	0.565373	+	0.824835i	$0.308732\pi$
$198$	2.17121e7	0.198781
$199$	1.00380e8	0.902941	0.451470	−	0.892286i	$-0.350900\pi$
$199$	1.00380e8	0.902941	0.451470	+	0.892286i	$0.350900\pi$
$200$	−3.89519e7	−0.344289
$201$	2.60389e6	0.0226171
$202$	8.55907e7	0.730629
$203$	−7.75578e7	−0.650713
$204$	−4.20942e7	−0.347150
$205$	−2.38370e7	−0.193247
$206$	2.22659e7	0.177462
$207$	−1.43965e7	−0.112814
$208$	8.99891e6	0.0693375
$209$	6.01074e7	0.455424
$210$	3.35215e6	0.0249779
$211$	−6.30327e7	−0.461931	−0.230965	−	0.972962i	$-0.574188\pi$
$211$	−6.30327e7	−0.461931	−0.230965	+	0.972962i	$0.574188\pi$
$212$	1.16357e7	0.0838720
$213$	−1.44592e8	−1.02522
$214$	8.28754e7	0.578066
$215$	1.55378e7	0.106624
$216$	−1.00777e7	−0.0680414
$217$	4.12927e7	0.274324
$218$	4.26346e7	0.278718
$219$	9.20723e7	0.592345
$220$	1.07805e7	0.0682591
$221$	5.35191e7	0.333531
$222$	1.01720e8	0.623979
$223$	2.82615e8	1.70658	0.853292	−	0.521434i	$-0.174603\pi$
$223$	2.82615e8	1.70658	0.853292	+	0.521434i	$0.174603\pi$
$224$	−1.12394e7	−0.0668153
$225$	−5.54607e7	−0.324599
$226$	−3.18052e6	−0.0183281
$227$	2.19590e8	1.24601	0.623005	−	0.782218i	$-0.285912\pi$
$227$	2.19590e8	1.24601	0.623005	+	0.782218i	$0.285912\pi$
$228$	−2.78989e7	−0.155889
$229$	−4.19625e7	−0.230907	−0.115453	−	0.993313i	$-0.536832\pi$
$229$	−4.19625e7	−0.230907	−0.115453	+	0.993313i	$0.536832\pi$
$230$	−7.14819e6	−0.0387390
$231$	3.44781e7	0.184035
$232$	1.15771e8	0.608686
$233$	−9.08700e7	−0.470625	−0.235312	−	0.971920i	$-0.575611\pi$
$233$	−9.08700e7	−0.470625	−0.235312	+	0.971920i	$0.575611\pi$
$234$	1.28129e7	0.0653720
$235$	3.89978e7	0.196021
$236$	−4.50791e7	−0.223246
$237$	1.42578e8	0.695718
$238$	−6.68441e7	−0.321398
$239$	−8.05843e7	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$239$	−8.05843e7	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$240$	−5.00379e6	−0.0233647
$241$	3.77861e8	1.73889	0.869446	−	0.494027i	$-0.164476\pi$
$241$	3.77861e8	1.73889	0.869446	+	0.494027i	$0.164476\pi$
$242$	−4.50157e7	−0.204178
$243$	−1.43489e7	−0.0641500
$244$	5.45776e7	0.240519
$245$	5.32309e6	0.0231250
$246$	1.13797e8	0.487369
$247$	3.54710e7	0.149773
$248$	−6.16380e7	−0.256607
$249$	8.55677e7	0.351247
$250$	−5.58159e7	−0.225927
$251$	5.13358e6	0.0204910	0.0102455	−	0.999948i	$-0.496739\pi$
$251$	5.13358e6	0.0204910	0.0102455	+	0.999948i	$0.496739\pi$
$252$	−1.60030e7	−0.0629941
$253$	−7.35217e7	−0.285426
$254$	−1.35747e8	−0.519772
$255$	−2.97590e7	−0.112390
$256$	1.67772e7	0.0625000
$257$	2.41968e8	0.889183	0.444592	−	0.895733i	$-0.353349\pi$
$257$	2.41968e8	0.889183	0.444592	+	0.895733i	$0.353349\pi$
$258$	−7.41766e7	−0.268904
$259$	1.61527e8	0.577692
$260$	6.36188e6	0.0224480
$261$	1.64839e8	0.573875
$262$	−2.42842e8	−0.834197
$263$	−4.62882e8	−1.56901	−0.784504	−	0.620124i	$-0.787082\pi$
$263$	−4.62882e8	−1.56901	−0.784504	+	0.620124i	$0.787082\pi$
$264$	−5.14658e7	−0.172149
$265$	8.22599e6	0.0271536
$266$	−4.43024e7	−0.144325
$267$	−2.94510e8	−0.946914
$268$	−6.17219e6	−0.0195870
$269$	3.60270e8	1.12848	0.564241	−	0.825610i	$-0.309169\pi$
$269$	3.60270e8	1.12848	0.564241	+	0.825610i	$0.309169\pi$
$270$	−7.12454e6	−0.0220284
$271$	3.52906e8	1.07713	0.538564	−	0.842585i	$-0.318967\pi$
$271$	3.52906e8	1.07713	0.538564	+	0.842585i	$0.318967\pi$
$272$	9.97789e7	0.300641
$273$	2.03464e7	0.0605228
$274$	1.49742e8	0.439761
$275$	−2.83233e8	−0.821256
$276$	3.41251e7	0.0976996
$277$	−6.88485e7	−0.194633	−0.0973163	−	0.995254i	$-0.531026\pi$
$277$	−6.88485e7	−0.194633	−0.0973163	+	0.995254i	$0.531026\pi$
$278$	−1.70416e8	−0.475723
$279$	−8.77619e7	−0.241931
$280$	−7.94583e6	−0.0216315
$281$	7.22937e8	1.94370	0.971848	−	0.235610i	$-0.0757088\pi$
$281$	7.22937e8	1.94370	0.971848	+	0.235610i	$0.0757088\pi$
$282$	−1.86174e8	−0.494364
$283$	1.66278e8	0.436097	0.218048	−	0.975938i	$-0.430031\pi$
$283$	1.66278e8	0.436097	0.218048	+	0.975938i	$0.430031\pi$
$284$	3.42737e8	0.887865
$285$	−1.97234e7	−0.0504691
$286$	6.54342e7	0.165396
$287$	1.80705e8	0.451216
$288$	2.38879e7	0.0589256
$289$	1.83075e8	0.446155
$290$	8.18458e7	0.197062
$291$	−2.98004e8	−0.708918
$292$	−2.18245e8	−0.512986
$293$	9.85330e7	0.228847	0.114423	−	0.993432i	$-0.463498\pi$
$293$	9.85330e7	0.228847	0.114423	+	0.993432i	$0.463498\pi$
$294$	−2.54122e7	−0.0583212
$295$	−3.18692e7	−0.0722759
$296$	−2.41114e8	−0.540382
$297$	−7.32784e7	−0.162304
$298$	1.11291e8	0.243614
$299$	−4.33871e7	−0.0938667
$300$	1.31463e8	0.281111
$301$	−1.17790e8	−0.248957
$302$	6.02537e8	1.25881
$303$	−2.88869e8	−0.596556
$304$	6.61307e7	0.135004
$305$	3.85842e7	0.0778682
$306$	1.42068e8	0.283447
$307$	−6.20104e8	−1.22315	−0.611575	−	0.791186i	$-0.709464\pi$
$307$	−6.20104e8	−1.22315	−0.611575	+	0.791186i	$0.709464\pi$
$308$	−8.17258e7	−0.159379
$309$	−7.51474e7	−0.144897
$310$	−4.35757e7	−0.0830765
$311$	−4.03113e8	−0.759915	−0.379958	−	0.925004i	$-0.624061\pi$
$311$	−4.03113e8	−0.759915	−0.379958	+	0.925004i	$0.624061\pi$
$312$	−3.03713e7	−0.0566139
$313$	4.74610e8	0.874846	0.437423	−	0.899256i	$-0.355891\pi$
$313$	4.74610e8	0.874846	0.437423	+	0.899256i	$0.355891\pi$
$314$	4.53985e8	0.827537
$315$	−1.13135e7	−0.0203944
$316$	−3.37963e8	−0.602510
$317$	−6.83280e8	−1.20473	−0.602367	−	0.798219i	$-0.705776\pi$
$317$	−6.83280e8	−1.20473	−0.602367	+	0.798219i	$0.705776\pi$
$318$	−3.92705e7	−0.0684812
$319$	8.41814e8	1.45194
$320$	1.18608e7	0.0202344
$321$	−2.79705e8	−0.471989
$322$	5.41895e7	0.0904522
$323$	3.93298e8	0.649401
$324$	3.40122e7	0.0555556
$325$	−1.67143e8	−0.270083
$326$	−2.07157e8	−0.331161
$327$	−1.43892e8	−0.227572
$328$	−2.69741e8	−0.422074
$329$	−2.95637e8	−0.457692
$330$	−3.63843e7	−0.0557333
$331$	−7.91703e8	−1.19995	−0.599977	−	0.800018i	$-0.704823\pi$
$331$	−7.91703e8	−1.19995	−0.599977	+	0.800018i	$0.704823\pi$
$332$	−2.02827e8	−0.304189
$333$	−3.43304e8	−0.509477
$334$	1.40633e8	0.206526
$335$	−4.36350e6	−0.00634129
$336$	3.79331e7	0.0545545
$337$	−5.23438e8	−0.745008	−0.372504	−	0.928031i	$-0.621501\pi$
$337$	−5.23438e8	−0.745008	−0.372504	+	0.928031i	$0.621501\pi$
$338$	3.86145e7	0.0543928
$339$	1.07342e7	0.0149649
$340$	7.05398e7	0.0973325
$341$	−4.48191e8	−0.612101
$342$	9.41588e7	0.127283
$343$	−4.03536e7	−0.0539949
$344$	1.75826e8	0.232878
$345$	2.41251e7	0.0316303
$346$	7.76503e8	1.00781
$347$	2.91343e8	0.374327	0.187164	−	0.982329i	$-0.440071\pi$
$347$	2.91343e8	0.374327	0.187164	+	0.982329i	$0.440071\pi$
$348$	−3.90728e8	−0.496990
$349$	−1.53659e9	−1.93495	−0.967474	−	0.252969i	$-0.918593\pi$
$349$	−1.53659e9	−1.93495	−0.967474	+	0.252969i	$0.918593\pi$
$350$	2.08758e8	0.260258
$351$	−4.32436e7	−0.0533761
$352$	1.21993e8	0.149086
$353$	4.16447e8	0.503904	0.251952	−	0.967740i	$-0.418927\pi$
$353$	4.16447e8	0.503904	0.251952	+	0.967740i	$0.418927\pi$
$354$	1.52142e8	0.182279
$355$	2.42302e8	0.287447
$356$	6.98098e8	0.820052
$357$	2.25599e8	0.262421
$358$	3.80325e7	0.0438091
$359$	8.22125e8	0.937794	0.468897	−	0.883253i	$-0.344652\pi$
$359$	8.22125e8	0.937794	0.468897	+	0.883253i	$0.344652\pi$
$360$	1.68878e7	0.0190772
$361$	−6.33204e8	−0.708384
$362$	1.19835e8	0.132771
$363$	1.51928e8	0.166711
$364$	−4.82285e7	−0.0524142
$365$	−1.54291e8	−0.166079
$366$	−1.84199e8	−0.196383
$367$	−2.14976e8	−0.227018	−0.113509	−	0.993537i	$-0.536209\pi$
$367$	−2.14976e8	−0.227018	−0.113509	+	0.993537i	$0.536209\pi$
$368$	−8.08892e7	−0.0846103
$369$	−3.84065e8	−0.397935
$370$	−1.70458e8	−0.174949
$371$	−6.23601e7	−0.0634013
$372$	2.08028e8	0.209518
$373$	−9.51709e7	−0.0949561	−0.0474781	−	0.998872i	$-0.515118\pi$
$373$	−9.51709e7	−0.0949561	−0.0474781	+	0.998872i	$0.515118\pi$
$374$	7.25527e8	0.717138
$375$	1.88379e8	0.184468
$376$	4.41301e8	0.428132
$377$	4.96777e8	0.477493
$378$	5.40102e7	0.0514344
$379$	3.52162e8	0.332281	0.166140	−	0.986102i	$-0.446870\pi$
$379$	3.52162e8	0.332281	0.166140	+	0.986102i	$0.446870\pi$
$380$	4.67518e7	0.0437075
$381$	4.58147e8	0.424392
$382$	1.23161e9	1.13045
$383$	9.50839e8	0.864791	0.432395	−	0.901684i	$-0.357668\pi$
$383$	9.50839e8	0.864791	0.432395	+	0.901684i	$0.357668\pi$
$384$	−5.66231e7	−0.0510310
$385$	−5.77769e7	−0.0515991
$386$	−1.39623e9	−1.23566
$387$	2.50346e8	0.219559
$388$	7.06379e8	0.613941
$389$	3.05702e7	0.0263314	0.0131657	−	0.999913i	$-0.495809\pi$
$389$	3.05702e7	0.0263314	0.0131657	+	0.999913i	$0.495809\pi$
$390$	−2.14713e7	−0.0183288
$391$	−4.81071e8	−0.406997
$392$	6.02363e7	0.0505076
$393$	8.19591e8	0.681119
$394$	9.70704e8	0.799558
$395$	−2.38926e8	−0.195063
$396$	1.73697e8	0.140559
$397$	−1.02611e9	−0.823052	−0.411526	−	0.911398i	$-0.635004\pi$
$397$	−1.02611e9	−0.823052	−0.411526	+	0.911398i	$0.635004\pi$
$398$	8.03036e8	0.638476
$399$	1.49521e8	0.117841
$400$	−3.11615e8	−0.243449
$401$	1.95089e9	1.51087	0.755434	−	0.655225i	$-0.227426\pi$
$401$	1.95089e9	1.51087	0.755434	+	0.655225i	$0.227426\pi$
$402$	2.08312e7	0.0159927
$403$	−2.64490e8	−0.201299
$404$	6.84726e8	0.516633
$405$	2.40453e7	0.0179861
$406$	−6.20462e8	−0.460123
$407$	−1.75322e9	−1.28901
$408$	−3.36754e8	−0.245472
$409$	1.53654e8	0.111049	0.0555243	−	0.998457i	$-0.482317\pi$
$409$	1.53654e8	0.111049	0.0555243	+	0.998457i	$0.482317\pi$
$410$	−1.90696e8	−0.136647
$411$	−5.05379e8	−0.359063
$412$	1.78127e8	0.125484
$413$	2.41596e8	0.168758
$414$	−1.15172e8	−0.0797714
$415$	−1.43391e8	−0.0984812
$416$	7.19913e7	0.0490290
$417$	5.75154e8	0.388426
$418$	4.80860e8	0.322034
$419$	−8.57510e8	−0.569495	−0.284747	−	0.958603i	$-0.591910\pi$
$419$	−8.57510e8	−0.569495	−0.284747	+	0.958603i	$0.591910\pi$
$420$	2.68172e7	0.0176620
$421$	1.72844e9	1.12893	0.564464	−	0.825458i	$-0.309083\pi$
$421$	1.72844e9	1.12893	0.564464	+	0.825458i	$0.309083\pi$
$422$	−5.04261e8	−0.326634
$423$	6.28337e8	0.403646
$424$	9.30856e7	0.0593065
$425$	−1.85326e9	−1.17105
$426$	−1.15674e9	−0.724939
$427$	−2.92502e8	−0.181816
$428$	6.63003e8	0.408754
$429$	−2.20841e8	−0.135045
$430$	1.24302e8	0.0753943
$431$	−2.49520e9	−1.50119	−0.750594	−	0.660763i	$-0.770233\pi$
$431$	−2.49520e9	−1.50119	−0.750594	+	0.660763i	$0.770233\pi$
$432$	−8.06216e7	−0.0481125
$433$	2.13733e9	1.26521	0.632606	−	0.774474i	$-0.281985\pi$
$433$	2.13733e9	1.26521	0.632606	+	0.774474i	$0.281985\pi$
$434$	3.30341e8	0.193976
$435$	−2.76230e8	−0.160901
$436$	3.41077e8	0.197083
$437$	−3.18841e8	−0.182763
$438$	7.36578e8	0.418851
$439$	1.64700e8	0.0929112	0.0464556	−	0.998920i	$-0.485207\pi$
$439$	1.64700e8	0.0929112	0.0464556	+	0.998920i	$0.485207\pi$
$440$	8.62442e7	0.0482665
$441$	8.57661e7	0.0476190
$442$	4.28153e8	0.235842
$443$	8.32466e8	0.454939	0.227470	−	0.973785i	$-0.426955\pi$
$443$	8.32466e8	0.454939	0.227470	+	0.973785i	$0.426955\pi$
$444$	8.13758e8	0.441220
$445$	4.93528e8	0.265492
$446$	2.26092e9	1.20674
$447$	−3.75607e8	−0.198910
$448$	−8.99154e7	−0.0472456
$449$	−2.55539e8	−0.133228	−0.0666140	−	0.997779i	$-0.521220\pi$
$449$	−2.55539e8	−0.133228	−0.0666140	+	0.997779i	$0.521220\pi$
$450$	−4.43686e8	−0.229526
$451$	−1.96138e9	−1.00680
$452$	−2.54441e7	−0.0129599
$453$	−2.03356e9	−1.02781
$454$	1.75672e9	0.881062
$455$	−3.40957e7	−0.0169691
$456$	−2.23191e8	−0.110230
$457$	7.17790e7	0.0351796	0.0175898	−	0.999845i	$-0.494401\pi$
$457$	7.17790e7	0.0351796	0.0175898	+	0.999845i	$0.494401\pi$
$458$	−3.35700e8	−0.163276
$459$	−4.79479e8	−0.231433
$460$	−5.71855e7	−0.0273926
$461$	6.01481e8	0.285936	0.142968	−	0.989727i	$-0.454335\pi$
$461$	6.01481e8	0.285936	0.142968	+	0.989727i	$0.454335\pi$
$462$	2.75824e8	0.130133
$463$	1.28593e9	0.602120	0.301060	−	0.953605i	$-0.402660\pi$
$463$	1.28593e9	0.602120	0.301060	+	0.953605i	$0.402660\pi$
$464$	9.26171e8	0.430406
$465$	1.47068e8	0.0678316
$466$	−7.26960e8	−0.332782
$467$	2.45950e9	1.11747	0.558736	−	0.829345i	$-0.311286\pi$
$467$	2.45950e9	1.11747	0.558736	+	0.829345i	$0.311286\pi$
$468$	1.02503e8	0.0462250
$469$	3.30791e7	0.0148064
$470$	3.11982e8	0.138608
$471$	−1.53220e9	−0.675681
$472$	−3.60633e8	−0.157859
$473$	1.27849e9	0.555500
$474$	1.14062e9	0.491947
$475$	−1.22829e9	−0.525865
$476$	−5.34752e8	−0.227263
$477$	1.32538e8	0.0559147
$478$	−6.44675e8	−0.269987
$479$	−2.53463e7	−0.0105376	−0.00526878	−	0.999986i	$-0.501677\pi$
$479$	−2.53463e7	−0.0105376	−0.00526878	+	0.999986i	$0.501677\pi$
$480$	−4.00303e7	−0.0165213
$481$	−1.03462e9	−0.423910
$482$	3.02289e9	1.22958
$483$	−1.82889e8	−0.0738539
$484$	−3.60125e8	−0.144376
$485$	4.99382e8	0.198764
$486$	−1.14791e8	−0.0453609
$487$	3.70470e8	0.145345	0.0726727	−	0.997356i	$-0.476847\pi$
$487$	3.70470e8	0.145345	0.0726727	+	0.997356i	$0.476847\pi$
$488$	4.36621e8	0.170073
$489$	6.99156e8	0.270392
$490$	4.25847e7	0.0163519
$491$	2.53115e9	0.965011	0.482506	−	0.875893i	$-0.339727\pi$
$491$	2.53115e9	0.965011	0.482506	+	0.875893i	$0.339727\pi$
$492$	9.10375e8	0.344622
$493$	5.50820e9	2.07036
$494$	2.83768e8	0.105906
$495$	1.22797e8	0.0455061
$496$	−4.93104e8	−0.181448
$497$	−1.83686e9	−0.671163
$498$	6.84542e8	0.248369
$499$	−4.12645e9	−1.48670	−0.743352	−	0.668901i	$-0.766765\pi$
$499$	−4.12645e9	−1.48670	−0.743352	+	0.668901i	$0.766765\pi$
$500$	−4.46527e8	−0.159754
$501$	−4.74636e8	−0.168628
$502$	4.10686e7	0.0144893
$503$	−1.78396e9	−0.625025	−0.312512	−	0.949914i	$-0.601171\pi$
$503$	−1.78396e9	−0.625025	−0.312512	+	0.949914i	$0.601171\pi$
$504$	−1.28024e8	−0.0445435
$505$	4.84074e8	0.167260
$506$	−5.88174e8	−0.201827
$507$	−1.30324e8	−0.0444116
$508$	−1.08598e9	−0.367534
$509$	−1.87446e9	−0.630034	−0.315017	−	0.949086i	$-0.602010\pi$
$509$	−1.87446e9	−0.630034	−0.315017	+	0.949086i	$0.602010\pi$
$510$	−2.38072e8	−0.0794716
$511$	1.16966e9	0.387781
$512$	1.34218e8	0.0441942
$513$	−3.17786e8	−0.103926
$514$	1.93574e9	0.628747
$515$	1.25929e8	0.0406256
$516$	−5.93413e8	−0.190144
$517$	3.20885e9	1.02125
$518$	1.29222e9	0.408490
$519$	−2.62070e9	−0.822870
$520$	5.08950e7	0.0158732
$521$	5.40774e9	1.67527	0.837633	−	0.546234i	$-0.183939\pi$
$521$	5.40774e9	1.67527	0.837633	+	0.546234i	$0.183939\pi$
$522$	1.31871e9	0.405791
$523$	−4.58115e9	−1.40029	−0.700147	−	0.713999i	$-0.746882\pi$
$523$	−4.58115e9	−1.40029	−0.700147	+	0.713999i	$0.746882\pi$
$524$	−1.94273e9	−0.589867
$525$	−7.04557e8	−0.212500
$526$	−3.70306e9	−1.10946
$527$	−2.93263e9	−0.872811
$528$	−4.11726e8	−0.121728
$529$	−3.01483e9	−0.885458
$530$	6.58079e7	0.0192005
$531$	−5.13479e8	−0.148831
$532$	−3.54419e8	−0.102053
$533$	−1.15746e9	−0.331102
$534$	−2.35608e9	−0.669570
$535$	4.68717e8	0.132334
$536$	−4.93775e7	−0.0138501
$537$	−1.28360e8	−0.0357700
$538$	2.88216e9	0.797957
$539$	4.37999e8	0.120479
$540$	−5.69963e7	−0.0155764
$541$	−4.46285e9	−1.21177	−0.605887	−	0.795550i	$-0.707182\pi$
$541$	−4.46285e9	−1.21177	−0.605887	+	0.795550i	$0.707182\pi$
$542$	2.82325e9	0.761644
$543$	−4.04442e8	−0.108407
$544$	7.98231e8	0.212585
$545$	2.41128e8	0.0638057
$546$	1.62771e8	0.0427960
$547$	−1.06071e9	−0.277102	−0.138551	−	0.990355i	$-0.544245\pi$
$547$	−1.06071e9	−0.277102	−0.138551	+	0.990355i	$0.544245\pi$
$548$	1.19793e9	0.310958
$549$	6.21673e8	0.160346
$550$	−2.26586e9	−0.580716
$551$	3.65069e9	0.929703
$552$	2.73001e8	0.0690840
$553$	1.81127e9	0.455455
$554$	−5.50788e8	−0.137626
$555$	5.75295e8	0.142845
$556$	−1.36333e9	−0.336387
$557$	7.57958e8	0.185846	0.0929228	−	0.995673i	$-0.470379\pi$
$557$	7.57958e8	0.185846	0.0929228	+	0.995673i	$0.470379\pi$
$558$	−7.02095e8	−0.171071
$559$	7.54472e8	0.182685
$560$	−6.35666e7	−0.0152958
$561$	−2.44865e9	−0.585541
$562$	5.78349e9	1.37440
$563$	−7.07097e9	−1.66993	−0.834967	−	0.550300i	$-0.814513\pi$
$563$	−7.07097e9	−1.66993	−0.834967	+	0.550300i	$0.814513\pi$
$564$	−1.48939e9	−0.349568
$565$	−1.79880e7	−0.00419579
$566$	1.33023e9	0.308367
$567$	−1.82284e8	−0.0419961
$568$	2.74190e9	0.627816
$569$	2.97246e9	0.676431	0.338216	−	0.941069i	$-0.390177\pi$
$569$	2.97246e9	0.676431	0.338216	+	0.941069i	$0.390177\pi$
$570$	−1.57787e8	−0.0356870
$571$	−1.74612e9	−0.392508	−0.196254	−	0.980553i	$-0.562878\pi$
$571$	−1.74612e9	−0.392508	−0.196254	+	0.980553i	$0.562878\pi$
$572$	5.23474e8	0.116952
$573$	−4.15668e9	−0.923009
$574$	1.44564e9	0.319058
$575$	1.50241e9	0.329573
$576$	1.91103e8	0.0416667
$577$	−2.37230e9	−0.514107	−0.257053	−	0.966397i	$-0.582752\pi$
$577$	−2.37230e9	−0.514107	−0.257053	+	0.966397i	$0.582752\pi$
$578$	1.46460e9	0.315480
$579$	4.71227e9	1.00892
$580$	6.54767e8	0.139344
$581$	1.08703e9	0.229945
$582$	−2.38403e9	−0.501281
$583$	6.76858e8	0.141468
$584$	−1.74596e9	−0.362736
$585$	7.24658e7	0.0149654
$586$	7.88264e8	0.161819
$587$	−2.43530e9	−0.496958	−0.248479	−	0.968637i	$-0.579931\pi$
$587$	−2.43530e9	−0.496958	−0.248479	+	0.968637i	$0.579931\pi$
$588$	−2.03297e8	−0.0412393
$589$	−1.94367e9	−0.391939
$590$	−2.54953e8	−0.0511068
$591$	−3.27613e9	−0.652837
$592$	−1.92891e9	−0.382108
$593$	−9.78771e9	−1.92748	−0.963740	−	0.266844i	$-0.914019\pi$
$593$	−9.78771e9	−1.92748	−0.963740	+	0.266844i	$0.914019\pi$
$594$	−5.86228e8	−0.114766
$595$	−3.78049e8	−0.0735764
$596$	8.90328e8	0.172261
$597$	−2.71025e9	−0.521313
$598$	−3.47097e8	−0.0663738
$599$	−6.71217e9	−1.27605	−0.638027	−	0.770014i	$-0.720249\pi$
$599$	−6.71217e9	−1.27605	−0.638027	+	0.770014i	$0.720249\pi$
$600$	1.05170e9	0.198775
$601$	6.12890e9	1.15165	0.575827	−	0.817571i	$-0.304680\pi$
$601$	6.12890e9	1.15165	0.575827	+	0.817571i	$0.304680\pi$
$602$	−9.42317e8	−0.176039
$603$	−7.03051e7	−0.0130580
$604$	4.82029e9	0.890111
$605$	−2.54595e8	−0.0467418
$606$	−2.31095e9	−0.421829
$607$	−7.16389e9	−1.30013	−0.650067	−	0.759877i	$-0.725259\pi$
$607$	−7.16389e9	−1.30013	−0.650067	+	0.759877i	$0.725259\pi$
$608$	5.29046e8	0.0954620
$609$	2.09406e9	0.375689
$610$	3.08674e8	0.0550612
$611$	1.89363e9	0.335854
$612$	1.13654e9	0.200427
$613$	2.29204e9	0.401893	0.200946	−	0.979602i	$-0.435598\pi$
$613$	2.29204e9	0.401893	0.200946	+	0.979602i	$0.435598\pi$
$614$	−4.96083e9	−0.864898
$615$	6.43600e8	0.111571
$616$	−6.53806e8	−0.112698
$617$	−3.39556e9	−0.581988	−0.290994	−	0.956725i	$-0.593986\pi$
$617$	−3.39556e9	−0.581988	−0.290994	+	0.956725i	$0.593986\pi$
$618$	−6.01179e8	−0.102458
$619$	1.75199e9	0.296904	0.148452	−	0.988920i	$-0.452571\pi$
$619$	1.75199e9	0.296904	0.148452	+	0.988920i	$0.452571\pi$
$620$	−3.48605e8	−0.0587439
$621$	3.88707e8	0.0651331
$622$	−3.22490e9	−0.537341
$623$	−3.74137e9	−0.619901
$624$	−2.42971e8	−0.0400320
$625$	5.62790e9	0.922076
$626$	3.79688e9	0.618609
$627$	−1.62290e9	−0.262939
$628$	3.63188e9	0.585157
$629$	−1.14718e10	−1.83803
$630$	−9.05080e7	−0.0144210
$631$	−8.12154e9	−1.28687	−0.643436	−	0.765500i	$-0.722492\pi$
$631$	−8.12154e9	−1.28687	−0.643436	+	0.765500i	$0.722492\pi$
$632$	−2.70370e9	−0.426039
$633$	1.70188e9	0.266696
$634$	−5.46624e9	−0.851876
$635$	−7.67744e8	−0.118989
$636$	−3.14164e8	−0.0484235
$637$	2.58475e8	0.0396214
$638$	6.73451e9	1.02668
$639$	3.90399e9	0.591910
$640$	9.48867e7	0.0143079
$641$	−1.03353e10	−1.54996	−0.774981	−	0.631985i	$-0.782241\pi$
$641$	−1.03353e10	−1.54996	−0.774981	+	0.631985i	$0.782241\pi$
$642$	−2.23764e9	−0.333747
$643$	8.14924e9	1.20887	0.604434	−	0.796655i	$-0.293399\pi$
$643$	8.14924e9	1.20887	0.604434	+	0.796655i	$0.293399\pi$
$644$	4.33516e8	0.0639594
$645$	−4.19519e8	−0.0615592
$646$	3.14639e9	0.459196
$647$	−3.31452e9	−0.481122	−0.240561	−	0.970634i	$-0.577331\pi$
$647$	−3.31452e9	−0.481122	−0.240561	+	0.970634i	$0.577331\pi$
$648$	2.72098e8	0.0392837
$649$	−2.62229e9	−0.376551
$650$	−1.33714e9	−0.190977
$651$	−1.11490e9	−0.158381
$652$	−1.65726e9	−0.234166
$653$	−2.59491e9	−0.364692	−0.182346	−	0.983234i	$-0.558369\pi$
$653$	−2.59491e9	−0.364692	−0.182346	+	0.983234i	$0.558369\pi$
$654$	−1.15113e9	−0.160918
$655$	−1.37344e9	−0.190970
$656$	−2.15793e9	−0.298451
$657$	−2.48595e9	−0.341990
$658$	−2.36510e9	−0.323637
$659$	4.26176e9	0.580083	0.290042	−	0.957014i	$-0.406331\pi$
$659$	4.26176e9	0.580083	0.290042	+	0.957014i	$0.406331\pi$
$660$	−2.91074e8	−0.0394094
$661$	1.39258e10	1.87549	0.937743	−	0.347329i	$-0.112911\pi$
$661$	1.39258e10	1.87549	0.937743	+	0.347329i	$0.112911\pi$
$662$	−6.33362e9	−0.848495
$663$	−1.44502e9	−0.192564
$664$	−1.62262e9	−0.215094
$665$	−2.50561e8	−0.0330398
$666$	−2.74643e9	−0.360254
$667$	−4.46542e9	−0.582669
$668$	1.12506e9	0.146036
$669$	−7.63059e9	−0.985296
$670$	−3.49080e7	−0.00448397
$671$	3.17482e9	0.405687
$672$	3.03464e8	0.0385758
$673$	−6.26914e9	−0.792785	−0.396392	−	0.918081i	$-0.629738\pi$
$673$	−6.26914e9	−0.792785	−0.396392	+	0.918081i	$0.629738\pi$
$674$	−4.18750e9	−0.526800
$675$	1.49744e9	0.187407
$676$	3.08916e8	0.0384615
$677$	−9.16513e9	−1.13521	−0.567607	−	0.823299i	$-0.692131\pi$
$677$	−9.16513e9	−1.13521	−0.567607	+	0.823299i	$0.692131\pi$
$678$	8.58739e7	0.0105817
$679$	−3.78575e9	−0.464096
$680$	5.64318e8	0.0688244
$681$	−5.92892e9	−0.719384
$682$	−3.58553e9	−0.432821
$683$	9.24488e9	1.11027	0.555135	−	0.831760i	$-0.312667\pi$
$683$	9.24488e9	1.11027	0.555135	+	0.831760i	$0.312667\pi$
$684$	7.53270e8	0.0900025
$685$	8.46893e8	0.100673
$686$	−3.22829e8	−0.0381802
$687$	1.13299e9	0.133314
$688$	1.40661e9	0.164670
$689$	3.99432e8	0.0465238
$690$	1.93001e8	0.0223660
$691$	8.26194e9	0.952597	0.476298	−	0.879284i	$-0.341978\pi$
$691$	8.26194e9	0.952597	0.476298	+	0.879284i	$0.341978\pi$
$692$	6.21202e9	0.712626
$693$	−9.30908e8	−0.106253
$694$	2.33074e9	0.264689
$695$	−9.63820e8	−0.108905
$696$	−3.12583e9	−0.351425
$697$	−1.28338e10	−1.43562
$698$	−1.22927e10	−1.36822
$699$	2.45349e9	0.271715
$700$	1.67006e9	0.184030
$701$	−1.01497e10	−1.11286	−0.556430	−	0.830894i	$-0.687829\pi$
$701$	−1.01497e10	−1.11286	−0.556430	+	0.830894i	$0.687829\pi$
$702$	−3.45948e8	−0.0377426
$703$	−7.60317e9	−0.825375
$704$	9.75944e8	0.105419
$705$	−1.05294e9	−0.113173
$706$	3.33157e9	0.356314
$707$	−3.66970e9	−0.390538
$708$	1.21714e9	0.128891
$709$	−1.11510e10	−1.17504	−0.587518	−	0.809211i	$-0.699895\pi$
$709$	−1.11510e10	−1.17504	−0.587518	+	0.809211i	$0.699895\pi$
$710$	1.93841e9	0.203256
$711$	−3.84961e9	−0.401673
$712$	5.58478e9	0.579864
$713$	2.37744e9	0.245638
$714$	1.80479e9	0.185559
$715$	3.70075e8	0.0378634
$716$	3.04260e8	0.0309777
$717$	2.17578e9	0.220443
$718$	6.57700e9	0.663120
$719$	−1.37090e10	−1.37549	−0.687743	−	0.725954i	$-0.741398\pi$
$719$	−1.37090e10	−1.37549	−0.687743	+	0.725954i	$0.741398\pi$
$720$	1.35102e8	0.0134896
$721$	−9.54650e8	−0.0948573
$722$	−5.06563e9	−0.500903
$723$	−1.02023e10	−1.00395
$724$	9.58677e8	0.0938830
$725$	−1.72024e10	−1.67651
$726$	1.21542e9	0.117883
$727$	1.87696e9	0.181170	0.0905848	−	0.995889i	$-0.471126\pi$
$727$	1.87696e9	0.181170	0.0905848	+	0.995889i	$0.471126\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	−1.23433e9	−0.117436
$731$	8.36550e9	0.792102
$732$	−1.47360e9	−0.138864
$733$	1.20773e10	1.13267	0.566336	−	0.824174i	$-0.308360\pi$
$733$	1.20773e10	1.13267	0.566336	+	0.824174i	$0.308360\pi$
$734$	−1.71981e9	−0.160526
$735$	−1.43723e8	−0.0133512
$736$	−6.47114e8	−0.0598285
$737$	−3.59041e8	−0.0330376
$738$	−3.07252e9	−0.281382
$739$	1.37380e10	1.25218	0.626091	−	0.779750i	$-0.284654\pi$
$739$	1.37380e10	1.25218	0.626091	+	0.779750i	$0.284654\pi$
$740$	−1.36366e9	−0.123707
$741$	−9.57717e8	−0.0864716
$742$	−4.98881e8	−0.0448315
$743$	−2.15574e10	−1.92813	−0.964065	−	0.265667i	$-0.914408\pi$
$743$	−2.15574e10	−1.92813	−0.964065	+	0.265667i	$0.914408\pi$
$744$	1.66423e9	0.148152
$745$	6.29427e8	0.0557697
$746$	−7.61367e8	−0.0671441
$747$	−2.31033e9	−0.202792
$748$	5.80422e9	0.507093
$749$	−3.55328e9	−0.308989
$750$	1.50703e9	0.130439
$751$	−1.91870e9	−0.165298	−0.0826488	−	0.996579i	$-0.526338\pi$
$751$	−1.91870e9	−0.165298	−0.0826488	+	0.996579i	$0.526338\pi$
$752$	3.53041e9	0.302735
$753$	−1.38607e8	−0.0118305
$754$	3.97421e9	0.337638
$755$	3.40776e9	0.288174
$756$	4.32081e8	0.0363696
$757$	1.18531e9	0.0993110	0.0496555	−	0.998766i	$-0.484188\pi$
$757$	1.18531e9	0.0993110	0.0496555	+	0.998766i	$0.484188\pi$
$758$	2.81730e9	0.234958
$759$	1.98509e9	0.164791
$760$	3.74015e8	0.0309059
$761$	9.79789e9	0.805910	0.402955	−	0.915220i	$-0.367983\pi$
$761$	9.79789e9	0.805910	0.402955	+	0.915220i	$0.367983\pi$
$762$	3.66518e9	0.300091
$763$	−1.82796e9	−0.148981
$764$	9.85288e9	0.799349
$765$	8.03492e8	0.0648883
$766$	7.60671e9	0.611500
$767$	−1.54748e9	−0.123835
$768$	−4.52985e8	−0.0360844
$769$	4.65848e9	0.369404	0.184702	−	0.982795i	$-0.440868\pi$
$769$	4.65848e9	0.369404	0.184702	+	0.982795i	$0.440868\pi$
$770$	−4.62215e8	−0.0364860
$771$	−6.53312e9	−0.513370
$772$	−1.11698e10	−0.873747
$773$	−2.61317e9	−0.203488	−0.101744	−	0.994811i	$-0.532442\pi$
$773$	−2.61317e9	−0.203488	−0.101744	+	0.994811i	$0.532442\pi$
$774$	2.00277e9	0.155252
$775$	9.15876e9	0.706775
$776$	5.65103e9	0.434122
$777$	−4.36124e9	−0.333531
$778$	2.44561e8	0.0186191
$779$	−8.50590e9	−0.644672
$780$	−1.71771e8	−0.0129604
$781$	1.99373e10	1.49757
$782$	−3.84857e9	−0.287790
$783$	−4.45064e9	−0.331327
$784$	4.81890e8	0.0357143
$785$	2.56760e9	0.189445
$786$	6.55673e9	0.481624
$787$	−2.85339e9	−0.208665	−0.104332	−	0.994542i	$-0.533271\pi$
$787$	−2.85339e9	−0.208665	−0.104332	+	0.994542i	$0.533271\pi$
$788$	7.76563e9	0.565373
$789$	1.24978e10	0.905867
$790$	−1.91141e9	−0.137930
$791$	1.36365e8	0.00979680
$792$	1.38958e9	0.0993904
$793$	1.87355e9	0.133416
$794$	−8.20888e9	−0.581986
$795$	−2.22102e8	−0.0156771
$796$	6.42429e9	0.451470
$797$	2.55168e9	0.178534	0.0892671	−	0.996008i	$-0.471548\pi$
$797$	2.55168e9	0.178534	0.0892671	+	0.996008i	$0.471548\pi$
$798$	1.19617e9	0.0833261
$799$	2.09963e10	1.45623
$800$	−2.49292e9	−0.172145
$801$	7.95177e9	0.546701
$802$	1.56071e10	1.06834
$803$	−1.26955e10	−0.865258
$804$	1.66649e8	0.0113086
$805$	3.06479e8	0.0207069
$806$	−2.11592e9	−0.142340
$807$	−9.72728e9	−0.651529
$808$	5.47780e9	0.365314
$809$	9.89115e9	0.656791	0.328395	−	0.944540i	$-0.393492\pi$
$809$	9.89115e9	0.656791	0.328395	+	0.944540i	$0.393492\pi$
$810$	1.92362e8	0.0127181
$811$	2.28009e10	1.50099	0.750497	−	0.660874i	$-0.229814\pi$
$811$	2.28009e10	1.50099	0.750497	+	0.660874i	$0.229814\pi$
$812$	−4.96370e9	−0.325356
$813$	−9.52847e9	−0.621880
$814$	−1.40258e10	−0.911467
$815$	−1.17162e9	−0.0758114
$816$	−2.69403e9	−0.173575
$817$	5.54442e9	0.355696
$818$	1.22924e9	0.0785233
$819$	−5.49353e8	−0.0349428
$820$	−1.52557e9	−0.0966237
$821$	−1.42769e10	−0.900396	−0.450198	−	0.892929i	$-0.648647\pi$
$821$	−1.42769e10	−0.900396	−0.450198	+	0.892929i	$0.648647\pi$
$822$	−4.04303e9	−0.253896
$823$	−2.44680e10	−1.53003	−0.765014	−	0.644013i	$-0.777268\pi$
$823$	−2.44680e10	−1.53003	−0.765014	+	0.644013i	$0.777268\pi$
$824$	1.42502e9	0.0887309
$825$	7.64728e9	0.474153
$826$	1.93277e9	0.119330
$827$	5.12659e9	0.315181	0.157590	−	0.987505i	$-0.449627\pi$
$827$	5.12659e9	0.315181	0.157590	+	0.987505i	$0.449627\pi$
$828$	−9.21379e8	−0.0564069
$829$	−1.62718e10	−0.991962	−0.495981	−	0.868333i	$-0.665191\pi$
$829$	−1.62718e10	−0.991962	−0.495981	+	0.868333i	$0.665191\pi$
$830$	−1.14713e9	−0.0696367
$831$	1.85891e9	0.112371
$832$	5.75930e8	0.0346688
$833$	2.86594e9	0.171795
$834$	4.60124e9	0.274659
$835$	7.95376e8	0.0472792
$836$	3.84688e9	0.227712
$837$	2.36957e9	0.139679
$838$	−6.86008e9	−0.402694
$839$	1.65243e10	0.965953	0.482976	−	0.875633i	$-0.339556\pi$
$839$	1.65243e10	0.965953	0.482976	+	0.875633i	$0.339556\pi$
$840$	2.14537e8	0.0124889
$841$	3.38786e10	1.96399
$842$	1.38275e10	0.798273
$843$	−1.95193e10	−1.12219
$844$	−4.03409e9	−0.230965
$845$	2.18391e8	0.0124519
$846$	5.02669e9	0.285421
$847$	1.93005e9	0.109138
$848$	7.44685e8	0.0419360
$849$	−4.48951e9	−0.251781
$850$	−1.48261e10	−0.828058
$851$	9.29999e9	0.517284
$852$	−9.25391e9	−0.512609
$853$	5.24311e9	0.289246	0.144623	−	0.989487i	$-0.453803\pi$
$853$	5.24311e9	0.289246	0.144623	+	0.989487i	$0.453803\pi$
$854$	−2.34002e9	−0.128563
$855$	5.32533e8	0.0291383
$856$	5.30403e9	0.289033
$857$	3.67505e10	1.99448	0.997241	−	0.0742354i	$-0.0236516\pi$
$857$	3.67505e10	1.99448	0.997241	+	0.0742354i	$0.0236516\pi$
$858$	−1.76672e9	−0.0954912
$859$	−1.21564e10	−0.654380	−0.327190	−	0.944959i	$-0.606102\pi$
$859$	−1.21564e10	−0.654380	−0.327190	+	0.944959i	$0.606102\pi$
$860$	9.94416e8	0.0533118
$861$	−4.87904e9	−0.260510
$862$	−1.99616e10	−1.06150
$863$	−1.50179e10	−0.795372	−0.397686	−	0.917522i	$-0.630187\pi$
$863$	−1.50179e10	−0.795372	−0.397686	+	0.917522i	$0.630187\pi$
$864$	−6.44973e8	−0.0340207
$865$	4.39166e9	0.230713
$866$	1.70986e10	0.894639
$867$	−4.94302e9	−0.257588
$868$	2.64273e9	0.137162
$869$	−1.96596e10	−1.01626
$870$	−2.20984e9	−0.113774
$871$	−2.11880e8	−0.0108649
$872$	2.72862e9	0.139359
$873$	8.04610e9	0.409294
$874$	−2.55073e9	−0.129233
$875$	2.39311e9	0.120763
$876$	5.89263e9	0.296172
$877$	2.52800e10	1.26555	0.632773	−	0.774338i	$-0.281917\pi$
$877$	2.52800e10	1.26555	0.632773	+	0.774338i	$0.281917\pi$
$878$	1.31760e9	0.0656981
$879$	−2.66039e9	−0.132125
$880$	6.89954e8	0.0341296
$881$	−1.19057e10	−0.586595	−0.293298	−	0.956021i	$-0.594753\pi$
$881$	−1.19057e10	−0.586595	−0.293298	+	0.956021i	$0.594753\pi$
$882$	6.86129e8	0.0336718
$883$	1.07352e10	0.524744	0.262372	−	0.964967i	$-0.415495\pi$
$883$	1.07352e10	0.524744	0.262372	+	0.964967i	$0.415495\pi$
$884$	3.42522e9	0.166765
$885$	8.60468e8	0.0417285
$886$	6.65973e9	0.321691
$887$	8.48147e9	0.408073	0.204037	−	0.978963i	$-0.434594\pi$
$887$	8.48147e9	0.408073	0.204037	+	0.978963i	$0.434594\pi$
$888$	6.51007e9	0.311989
$889$	5.82016e9	0.277830
$890$	3.94822e9	0.187731
$891$	1.97852e9	0.0937061
$892$	1.80873e10	0.853292
$893$	1.39158e10	0.653925
$894$	−3.00486e9	−0.140651
$895$	2.15100e8	0.0100290
$896$	−7.19323e8	−0.0334077
$897$	1.17145e9	0.0541940
$898$	−2.04431e9	−0.0942064
$899$	−2.72214e10	−1.24954
$900$	−3.54949e9	−0.162299
$901$	4.42885e9	0.201723
$902$	−1.56910e10	−0.711916
$903$	3.18032e9	0.143735
$904$	−2.03553e8	−0.00916406
$905$	6.77747e8	0.0303947
$906$	−1.62685e10	−0.726772
$907$	2.28935e10	1.01879	0.509397	−	0.860532i	$-0.329868\pi$
$907$	2.28935e10	1.01879	0.509397	+	0.860532i	$0.329868\pi$
$908$	1.40537e10	0.623005
$909$	7.79945e9	0.344422
$910$	−2.72765e8	−0.0119990
$911$	6.83396e9	0.299473	0.149737	−	0.988726i	$-0.452157\pi$
$911$	6.83396e9	0.299473	0.149737	+	0.988726i	$0.452157\pi$
$912$	−1.78553e9	−0.0779444
$913$	−1.17986e10	−0.513078
$914$	5.74232e8	0.0248757
$915$	−1.04177e9	−0.0449573
$916$	−2.68560e9	−0.115453
$917$	1.04118e10	0.445897
$918$	−3.83584e9	−0.163648
$919$	2.41526e10	1.02650	0.513251	−	0.858239i	$-0.328441\pi$
$919$	2.41526e10	1.02650	0.513251	+	0.858239i	$0.328441\pi$
$920$	−4.57484e8	−0.0193695
$921$	1.67428e10	0.706186
$922$	4.81185e9	0.202187
$923$	1.17655e10	0.492499
$924$	2.20660e9	0.0920176
$925$	3.58269e10	1.48838
$926$	1.02874e10	0.425763
$927$	2.02898e9	0.0836563
$928$	7.40937e9	0.304343
$929$	−3.37778e10	−1.38222	−0.691110	−	0.722750i	$-0.742878\pi$
$929$	−3.37778e10	−1.38222	−0.691110	+	0.722750i	$0.742878\pi$
$930$	1.17654e9	0.0479642
$931$	1.89947e9	0.0771450
$932$	−5.81568e9	−0.235312
$933$	1.08840e10	0.438737
$934$	1.96760e10	0.790173
$935$	4.10335e9	0.164172
$936$	8.20026e8	0.0326860
$937$	3.03888e10	1.20677	0.603385	−	0.797450i	$-0.293818\pi$
$937$	3.03888e10	1.20677	0.603385	+	0.797450i	$0.293818\pi$
$938$	2.64633e8	0.0104697
$939$	−1.28145e10	−0.505092
$940$	2.49586e9	0.0980105
$941$	−2.49435e10	−0.975873	−0.487937	−	0.872879i	$-0.662250\pi$
$941$	−2.49435e10	−0.975873	−0.487937	+	0.872879i	$0.662250\pi$
$942$	−1.22576e10	−0.477779
$943$	1.04042e10	0.404033
$944$	−2.88506e9	−0.111623
$945$	3.05464e8	0.0117747
$946$	1.02279e10	0.392798
$947$	−4.07511e10	−1.55925	−0.779623	−	0.626249i	$-0.784589\pi$
$947$	−4.07511e10	−1.55925	−0.779623	+	0.626249i	$0.784589\pi$
$948$	9.12500e9	0.347859
$949$	−7.49196e9	−0.284553
$950$	−9.82633e9	−0.371842
$951$	1.84486e10	0.695553
$952$	−4.27802e9	−0.160699
$953$	−4.32313e8	−0.0161798	−0.00808989	−	0.999967i	$-0.502575\pi$
$953$	−4.32313e8	−0.0161798	−0.00808989	+	0.999967i	$0.502575\pi$
$954$	1.06030e9	0.0395377
$955$	6.96560e9	0.258789
$956$	−5.15740e9	−0.190910
$957$	−2.27290e10	−0.838278
$958$	−2.02770e8	−0.00745118
$959$	−6.42018e9	−0.235062
$960$	−3.20242e8	−0.0116823
$961$	−1.30196e10	−0.473225
$962$	−8.27698e9	−0.299750
$963$	7.55202e9	0.272503
$964$	2.41831e10	0.869446
$965$	−7.89663e9	−0.282876
$966$	−1.46312e9	−0.0522226
$967$	2.43671e9	0.0866583	0.0433292	−	0.999061i	$-0.486204\pi$
$967$	2.43671e9	0.0866583	0.0433292	+	0.999061i	$0.486204\pi$
$968$	−2.88100e9	−0.102089
$969$	−1.06191e10	−0.374932
$970$	3.99506e9	0.140547
$971$	−1.69523e10	−0.594240	−0.297120	−	0.954840i	$-0.596026\pi$
$971$	−1.69523e10	−0.594240	−0.297120	+	0.954840i	$0.596026\pi$
$972$	−9.18330e8	−0.0320750
$973$	7.30659e9	0.254284
$974$	2.96376e9	0.102775
$975$	4.51286e9	0.155932
$976$	3.49297e9	0.120260
$977$	−1.45782e10	−0.500119	−0.250059	−	0.968231i	$-0.580450\pi$
$977$	−1.45782e10	−0.500119	−0.250059	+	0.968231i	$0.580450\pi$
$978$	5.59325e9	0.191196
$979$	4.06089e10	1.38319
$980$	3.40678e8	0.0115625
$981$	3.88508e9	0.131389
$982$	2.02492e10	0.682366
$983$	−3.82318e10	−1.28377	−0.641886	−	0.766800i	$-0.721848\pi$
$983$	−3.82318e10	−1.28377	−0.641886	+	0.766800i	$0.721848\pi$
$984$	7.28300e9	0.243684
$985$	5.49000e9	0.183040
$986$	4.40656e10	1.46397
$987$	7.98220e9	0.264249
$988$	2.27014e9	0.0748866
$989$	−6.78178e9	−0.222924
$990$	9.82376e8	0.0321777
$991$	1.67284e9	0.0546005	0.0273002	−	0.999627i	$-0.491309\pi$
$991$	1.67284e9	0.0546005	0.0273002	+	0.999627i	$0.491309\pi$
$992$	−3.94483e9	−0.128303
$993$	2.13760e10	0.692793
$994$	−1.46949e10	−0.474584
$995$	4.54172e9	0.146164
$996$	5.47634e9	0.175623
$997$	4.99020e10	1.59472	0.797360	−	0.603504i	$-0.206229\pi$
$997$	4.99020e10	1.59472	0.797360	+	0.603504i	$0.206229\pi$
$998$	−3.30116e10	−1.05126
$999$	9.26921e9	0.294147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.r.1.4	✓	6

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

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +45.2455 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +45.2455 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +361.964 q^{10} +3722.93 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} -1221.63 q^{15} +4096.00 q^{16} +24360.1 q^{17} +5832.00 q^{18} +16145.2 q^{19} +2895.71 q^{20} +9261.00 q^{21} +29783.4 q^{22} -19748.3 q^{23} -13824.0 q^{24} -76077.8 q^{25} +17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +226116. q^{29} -9773.02 q^{30} -120387. q^{31} +32768.0 q^{32} -100519. q^{33} +194881. q^{34} -15519.2 q^{35} +46656.0 q^{36} -470925. q^{37} +129162. q^{38} -59319.0 q^{39} +23165.7 q^{40} -526838. q^{41} +74088.0 q^{42} +343410. q^{43} +238268. q^{44} +32984.0 q^{45} -157987. q^{46} +861916. q^{47} -110592. q^{48} +117649. q^{49} -608623. q^{50} -657722. q^{51} +140608. q^{52} +181808. q^{53} -157464. q^{54} +168446. q^{55} -175616. q^{56} -435920. q^{57} +1.80893e6 q^{58} -704361. q^{59} -78184.2 q^{60} +852775. q^{61} -963094. q^{62} -250047. q^{63} +262144. q^{64} +99404.3 q^{65} -804153. q^{66} -96440.5 q^{67} +1.55905e6 q^{68} +533205. q^{69} -124154. q^{70} +5.35527e6 q^{71} +373248. q^{72} -3.41008e6 q^{73} -3.76740e6 q^{74} +2.05410e6 q^{75} +1.03329e6 q^{76} -1.27697e6 q^{77} -474552. q^{78} -5.28067e6 q^{79} +185326. q^{80} +531441. q^{81} -4.21470e6 q^{82} -3.16918e6 q^{83} +592704. q^{84} +1.10218e6 q^{85} +2.74728e6 q^{86} -6.10513e6 q^{87} +1.90614e6 q^{88} +1.09078e7 q^{89} +263872. q^{90} -753571. q^{91} -1.26389e6 q^{92} +3.25044e6 q^{93} +6.89533e6 q^{94} +730497. q^{95} -884736. q^{96} +1.10372e7 q^{97} +941192. q^{98} +2.71402e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 203 q^{5} - 1296 q^{6} - 2058 q^{7} + 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 203 * q^5 - 1296 * q^6 - 2058 * q^7 + 3072 * q^8 + 4374 * q^9	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 203 q^{5} - 1296 q^{6} - 2058 q^{7} + 3072 q^{8} + 4374 q^{9} + 1624 q^{10} - 2690 q^{11} - 10368 q^{12} + 13182 q^{13} - 16464 q^{14} - 5481 q^{15} + 24576 q^{16} + 2910 q^{17} + 34992 q^{18} - 13055 q^{19} + 12992 q^{20} + 55566 q^{21} - 21520 q^{22} + 11581 q^{23} - 82944 q^{24} + 68081 q^{25} + 105456 q^{26} - 118098 q^{27} - 131712 q^{28} - 92335 q^{29} - 43848 q^{30} - 83081 q^{31} + 196608 q^{32} + 72630 q^{33} + 23280 q^{34} - 69629 q^{35} + 279936 q^{36} - 265114 q^{37} - 104440 q^{38} - 355914 q^{39} + 103936 q^{40} - 367468 q^{41} + 444528 q^{42} + 454955 q^{43} - 172160 q^{44} + 147987 q^{45} + 92648 q^{46} + 733973 q^{47} - 663552 q^{48} + 705894 q^{49} + 544648 q^{50} - 78570 q^{51} + 843648 q^{52} - 1577379 q^{53} - 944784 q^{54} + 2231118 q^{55} - 1053696 q^{56} + 352485 q^{57} - 738680 q^{58} + 2062708 q^{59} - 350784 q^{60} - 271270 q^{61} - 664648 q^{62} - 1500282 q^{63} + 1572864 q^{64} + 445991 q^{65} + 581040 q^{66} - 758674 q^{67} + 186240 q^{68} - 312687 q^{69} - 557032 q^{70} - 6138216 q^{71} + 2239488 q^{72} + 6361979 q^{73} - 2120912 q^{74} - 1838187 q^{75} - 835520 q^{76} + 922670 q^{77} - 2847312 q^{78} - 899781 q^{79} + 831488 q^{80} + 3188646 q^{81} - 2939744 q^{82} + 3313561 q^{83} + 3556224 q^{84} + 5307940 q^{85} + 3639640 q^{86} + 2493045 q^{87} - 1377280 q^{88} + 11210703 q^{89} + 1183896 q^{90} - 4521426 q^{91} + 741184 q^{92} + 2243187 q^{93} + 5871784 q^{94} + 12912395 q^{95} - 5308416 q^{96} + 28682643 q^{97} + 5647152 q^{98} - 1961010 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 203 * q^5 - 1296 * q^6 - 2058 * q^7 + 3072 * q^8 + 4374 * q^9 + 1624 * q^10 - 2690 * q^11 - 10368 * q^12 + 13182 * q^13 - 16464 * q^14 - 5481 * q^15 + 24576 * q^16 + 2910 * q^17 + 34992 * q^18 - 13055 * q^19 + 12992 * q^20 + 55566 * q^21 - 21520 * q^22 + 11581 * q^23 - 82944 * q^24 + 68081 * q^25 + 105456 * q^26 - 118098 * q^27 - 131712 * q^28 - 92335 * q^29 - 43848 * q^30 - 83081 * q^31 + 196608 * q^32 + 72630 * q^33 + 23280 * q^34 - 69629 * q^35 + 279936 * q^36 - 265114 * q^37 - 104440 * q^38 - 355914 * q^39 + 103936 * q^40 - 367468 * q^41 + 444528 * q^42 + 454955 * q^43 - 172160 * q^44 + 147987 * q^45 + 92648 * q^46 + 733973 * q^47 - 663552 * q^48 + 705894 * q^49 + 544648 * q^50 - 78570 * q^51 + 843648 * q^52 - 1577379 * q^53 - 944784 * q^54 + 2231118 * q^55 - 1053696 * q^56 + 352485 * q^57 - 738680 * q^58 + 2062708 * q^59 - 350784 * q^60 - 271270 * q^61 - 664648 * q^62 - 1500282 * q^63 + 1572864 * q^64 + 445991 * q^65 + 581040 * q^66 - 758674 * q^67 + 186240 * q^68 - 312687 * q^69 - 557032 * q^70 - 6138216 * q^71 + 2239488 * q^72 + 6361979 * q^73 - 2120912 * q^74 - 1838187 * q^75 - 835520 * q^76 + 922670 * q^77 - 2847312 * q^78 - 899781 * q^79 + 831488 * q^80 + 3188646 * q^81 - 2939744 * q^82 + 3313561 * q^83 + 3556224 * q^84 + 5307940 * q^85 + 3639640 * q^86 + 2493045 * q^87 - 1377280 * q^88 + 11210703 * q^89 + 1183896 * q^90 - 4521426 * q^91 + 741184 * q^92 + 2243187 * q^93 + 5871784 * q^94 + 12912395 * q^95 - 5308416 * q^96 + 28682643 * q^97 + 5647152 * q^98 - 1961010 * q^99

Introduction

L-functions

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