LMFDB - Embedded newform 546.8.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("546.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	546.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.1
Root			$-201.135$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -505.603 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -505.603 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -4044.82 q^{10} -974.645 q^{11} -1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +13651.3 q^{15} +4096.00 q^{16} -5660.27 q^{17} +5832.00 q^{18} +15165.4 q^{19} -32358.6 q^{20} +9261.00 q^{21} -7797.16 q^{22} +65731.1 q^{23} -13824.0 q^{24} +177509. q^{25} -17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +44041.7 q^{29} +109210. q^{30} +86262.8 q^{31} +32768.0 q^{32} +26315.4 q^{33} -45282.2 q^{34} +173422. q^{35} +46656.0 q^{36} -428960. q^{37} +121323. q^{38} +59319.0 q^{39} -258869. q^{40} +506507. q^{41} +74088.0 q^{42} +79953.1 q^{43} -62377.3 q^{44} -368584. q^{45} +525849. q^{46} +91123.6 q^{47} -110592. q^{48} +117649. q^{49} +1.42007e6 q^{50} +152827. q^{51} -140608. q^{52} +858983. q^{53} -157464. q^{54} +492783. q^{55} -175616. q^{56} -409467. q^{57} +352334. q^{58} -2.45810e6 q^{59} +873681. q^{60} -46791.0 q^{61} +690102. q^{62} -250047. q^{63} +262144. q^{64} +1.11081e6 q^{65} +210523. q^{66} +771304. q^{67} -362257. q^{68} -1.77474e6 q^{69} +1.38737e6 q^{70} +381154. q^{71} +373248. q^{72} +1.51728e6 q^{73} -3.43168e6 q^{74} -4.79274e6 q^{75} +970588. q^{76} +334303. q^{77} +474552. q^{78} +2.77962e6 q^{79} -2.07095e6 q^{80} +531441. q^{81} +4.05205e6 q^{82} +1.80809e6 q^{83} +592704. q^{84} +2.86185e6 q^{85} +639625. q^{86} -1.18913e6 q^{87} -499018. q^{88} +4.66189e6 q^{89} -2.94867e6 q^{90} +753571. q^{91} +4.20679e6 q^{92} -2.32909e6 q^{93} +728989. q^{94} -7.66768e6 q^{95} -884736. q^{96} -7.20167e6 q^{97} +941192. q^{98} -710516. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) $ 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9} - 2000 q^{10} + 659 q^{11} - 8640 q^{12} - 10985 q^{13} - 13720 q^{14} + 6750 q^{15} + 20480 q^{16} + 24575 q^{17} + 29160 q^{18} - 6446 q^{19} - 16000 q^{20} + 46305 q^{21} + 5272 q^{22} + 30268 q^{23} - 69120 q^{24} + 38965 q^{25} - 87880 q^{26} - 98415 q^{27} - 109760 q^{28} + 130950 q^{29} + 54000 q^{30} + 262979 q^{31} + 163840 q^{32} - 17793 q^{33} + 196600 q^{34} + 85750 q^{35} + 233280 q^{36} - 101549 q^{37} - 51568 q^{38} + 296595 q^{39} - 128000 q^{40} - 247328 q^{41} + 370440 q^{42} - 19092 q^{43} + 42176 q^{44} - 182250 q^{45} + 242144 q^{46} - 126419 q^{47} - 552960 q^{48} + 588245 q^{49} + 311720 q^{50} - 663525 q^{51} - 703040 q^{52} - 302793 q^{53} - 787320 q^{54} + 943985 q^{55} - 878080 q^{56} + 174042 q^{57} + 1047600 q^{58} - 2798636 q^{59} + 432000 q^{60} - 2493751 q^{61} + 2103832 q^{62} - 1250235 q^{63} + 1310720 q^{64} + 549250 q^{65} - 142344 q^{66} + 160188 q^{67} + 1572800 q^{68} - 817236 q^{69} + 686000 q^{70} + 3846088 q^{71} + 1866240 q^{72} + 5655872 q^{73} - 812392 q^{74} - 1052055 q^{75} - 412544 q^{76} - 226037 q^{77} + 2372760 q^{78} + 5647991 q^{79} - 1024000 q^{80} + 2657205 q^{81} - 1978624 q^{82} - 4607669 q^{83} + 2963520 q^{84} + 3873935 q^{85} - 152736 q^{86} - 3535650 q^{87} + 337408 q^{88} - 17424029 q^{89} - 1458000 q^{90} + 3767855 q^{91} + 1937152 q^{92} - 7100433 q^{93} - 1011352 q^{94} - 24593720 q^{95} - 4423680 q^{96} - 18380577 q^{97} + 4705960 q^{98} + 480411 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9 - 2000 * q^10 + 659 * q^11 - 8640 * q^12 - 10985 * q^13 - 13720 * q^14 + 6750 * q^15 + 20480 * q^16 + 24575 * q^17 + 29160 * q^18 - 6446 * q^19 - 16000 * q^20 + 46305 * q^21 + 5272 * q^22 + 30268 * q^23 - 69120 * q^24 + 38965 * q^25 - 87880 * q^26 - 98415 * q^27 - 109760 * q^28 + 130950 * q^29 + 54000 * q^30 + 262979 * q^31 + 163840 * q^32 - 17793 * q^33 + 196600 * q^34 + 85750 * q^35 + 233280 * q^36 - 101549 * q^37 - 51568 * q^38 + 296595 * q^39 - 128000 * q^40 - 247328 * q^41 + 370440 * q^42 - 19092 * q^43 + 42176 * q^44 - 182250 * q^45 + 242144 * q^46 - 126419 * q^47 - 552960 * q^48 + 588245 * q^49 + 311720 * q^50 - 663525 * q^51 - 703040 * q^52 - 302793 * q^53 - 787320 * q^54 + 943985 * q^55 - 878080 * q^56 + 174042 * q^57 + 1047600 * q^58 - 2798636 * q^59 + 432000 * q^60 - 2493751 * q^61 + 2103832 * q^62 - 1250235 * q^63 + 1310720 * q^64 + 549250 * q^65 - 142344 * q^66 + 160188 * q^67 + 1572800 * q^68 - 817236 * q^69 + 686000 * q^70 + 3846088 * q^71 + 1866240 * q^72 + 5655872 * q^73 - 812392 * q^74 - 1052055 * q^75 - 412544 * q^76 - 226037 * q^77 + 2372760 * q^78 + 5647991 * q^79 - 1024000 * q^80 + 2657205 * q^81 - 1978624 * q^82 - 4607669 * q^83 + 2963520 * q^84 + 3873935 * q^85 - 152736 * q^86 - 3535650 * q^87 + 337408 * q^88 - 17424029 * q^89 - 1458000 * q^90 + 3767855 * q^91 + 1937152 * q^92 - 7100433 * q^93 - 1011352 * q^94 - 24593720 * q^95 - 4423680 * q^96 - 18380577 * q^97 + 4705960 * q^98 + 480411 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	64.0000	0.500000
$5$	−505.603	−1.80890	−0.904450	−	0.426581i	$-0.859718\pi$
$5$	−505.603	−1.80890	−0.904450	+	0.426581i	$0.859718\pi$
$6$	−216.000	−0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	−4044.82	−1.27908
$11$	−974.645	−0.220786	−0.110393	−	0.993888i	$-0.535211\pi$
$11$	−974.645	−0.220786	−0.110393	+	0.993888i	$0.535211\pi$
$12$	−1728.00	−0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−2744.00	−0.267261
$15$	13651.3	1.04437
$16$	4096.00	0.250000
$17$	−5660.27	−0.279425	−0.139713	−	0.990192i	$-0.544618\pi$
$17$	−5660.27	−0.279425	−0.139713	+	0.990192i	$0.544618\pi$
$18$	5832.00	0.235702
$19$	15165.4	0.507244	0.253622	−	0.967303i	$-0.418378\pi$
$19$	15165.4	0.507244	0.253622	+	0.967303i	$0.418378\pi$
$20$	−32358.6	−0.904450
$21$	9261.00	0.218218
$22$	−7797.16	−0.156119
$23$	65731.1	1.12648	0.563240	−	0.826293i	$-0.309555\pi$
$23$	65731.1	1.12648	0.563240	+	0.826293i	$0.309555\pi$
$24$	−13824.0	−0.204124
$25$	177509.	2.27212
$26$	−17576.0	−0.196116
$27$	−19683.0	−0.192450
$28$	−21952.0	−0.188982
$29$	44041.7	0.335329	0.167665	−	0.985844i	$-0.446377\pi$
$29$	44041.7	0.335329	0.167665	+	0.985844i	$0.446377\pi$
$30$	109210.	0.738480
$31$	86262.8	0.520065	0.260032	−	0.965600i	$-0.416267\pi$
$31$	86262.8	0.520065	0.260032	+	0.965600i	$0.416267\pi$
$32$	32768.0	0.176777
$33$	26315.4	0.127471
$34$	−45282.2	−0.197584
$35$	173422.	0.683700
$36$	46656.0	0.166667
$37$	−428960.	−1.39223	−0.696115	−	0.717931i	$-0.745089\pi$
$37$	−428960.	−1.39223	−0.696115	+	0.717931i	$0.745089\pi$
$38$	121323.	0.358676
$39$	59319.0	0.160128
$40$	−258869.	−0.639542
$41$	506507.	1.14773	0.573867	−	0.818948i	$-0.305442\pi$
$41$	506507.	1.14773	0.573867	+	0.818948i	$0.305442\pi$
$42$	74088.0	0.154303
$43$	79953.1	0.153354	0.0766771	−	0.997056i	$-0.475569\pi$
$43$	79953.1	0.153354	0.0766771	+	0.997056i	$0.475569\pi$
$44$	−62377.3	−0.110393
$45$	−368584.	−0.602966
$46$	525849.	0.796541
$47$	91123.6	0.128023	0.0640116	−	0.997949i	$-0.479611\pi$
$47$	91123.6	0.128023	0.0640116	+	0.997949i	$0.479611\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	1.42007e6	1.60663
$51$	152827.	0.161326
$52$	−140608.	−0.138675
$53$	858983.	0.792536	0.396268	−	0.918135i	$-0.370305\pi$
$53$	858983.	0.792536	0.396268	+	0.918135i	$0.370305\pi$
$54$	−157464.	−0.136083
$55$	492783.	0.399380
$56$	−175616.	−0.133631
$57$	−409467.	−0.292858
$58$	352334.	0.237113
$59$	−2.45810e6	−1.55818	−0.779089	−	0.626914i	$-0.784318\pi$
$59$	−2.45810e6	−1.55818	−0.779089	+	0.626914i	$0.784318\pi$
$60$	873681.	0.522184
$61$	−46791.0	−0.0263942	−0.0131971	−	0.999913i	$-0.504201\pi$
$61$	−46791.0	−0.0263942	−0.0131971	+	0.999913i	$0.504201\pi$
$62$	690102.	0.367741
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	1.11081e6	0.501698
$66$	210523.	0.0901356
$67$	771304.	0.313302	0.156651	−	0.987654i	$-0.449930\pi$
$67$	771304.	0.313302	0.156651	+	0.987654i	$0.449930\pi$
$68$	−362257.	−0.139713
$69$	−1.77474e6	−0.650373
$70$	1.38737e6	0.483449
$71$	381154.	0.126385	0.0631926	−	0.998001i	$-0.479872\pi$
$71$	381154.	0.126385	0.0631926	+	0.998001i	$0.479872\pi$
$72$	373248.	0.117851
$73$	1.51728e6	0.456494	0.228247	−	0.973603i	$-0.426701\pi$
$73$	1.51728e6	0.456494	0.228247	+	0.973603i	$0.426701\pi$
$74$	−3.43168e6	−0.984455
$75$	−4.79274e6	−1.31181
$76$	970588.	0.253622
$77$	334303.	0.0834494
$78$	474552.	0.113228
$79$	2.77962e6	0.634293	0.317147	−	0.948377i	$-0.397275\pi$
$79$	2.77962e6	0.634293	0.317147	+	0.948377i	$0.397275\pi$
$80$	−2.07095e6	−0.452225
$81$	531441.	0.111111
$82$	4.05205e6	0.811571
$83$	1.80809e6	0.347094	0.173547	−	0.984826i	$-0.444477\pi$
$83$	1.80809e6	0.347094	0.173547	+	0.984826i	$0.444477\pi$
$84$	592704.	0.109109
$85$	2.86185e6	0.505452
$86$	639625.	0.108438
$87$	−1.18913e6	−0.193602
$88$	−499018.	−0.0780597
$89$	4.66189e6	0.700965	0.350483	−	0.936569i	$-0.386018\pi$
$89$	4.66189e6	0.700965	0.350483	+	0.936569i	$0.386018\pi$
$90$	−2.94867e6	−0.426362
$91$	753571.	0.104828
$92$	4.20679e6	0.563240
$93$	−2.32909e6	−0.300260
$94$	728989.	0.0905260
$95$	−7.66768e6	−0.917554
$96$	−884736.	−0.102062
$97$	−7.20167e6	−0.801184	−0.400592	−	0.916256i	$-0.631196\pi$
$97$	−7.20167e6	−0.801184	−0.400592	+	0.916256i	$0.631196\pi$
$98$	941192.	0.101015
$99$	−710516.	−0.0735954
$100$	1.13606e7	1.13606
$101$	−1.80857e7	−1.74667	−0.873336	−	0.487118i	$-0.838048\pi$
$101$	−1.80857e7	−1.74667	−0.873336	+	0.487118i	$0.838048\pi$
$102$	1.22262e6	0.114075
$103$	−1.84546e7	−1.66408	−0.832038	−	0.554718i	$-0.812826\pi$
$103$	−1.84546e7	−1.66408	−0.832038	+	0.554718i	$0.812826\pi$
$104$	−1.12486e6	−0.0980581
$105$	−4.68239e6	−0.394734
$106$	6.87186e6	0.560408
$107$	1.63646e7	1.29141	0.645703	−	0.763589i	$-0.276564\pi$
$107$	1.63646e7	1.29141	0.645703	+	0.763589i	$0.276564\pi$
$108$	−1.25971e6	−0.0962250
$109$	1.27087e7	0.939960	0.469980	−	0.882677i	$-0.344261\pi$
$109$	1.27087e7	0.939960	0.469980	+	0.882677i	$0.344261\pi$
$110$	3.94227e6	0.282404
$111$	1.15819e7	0.803804
$112$	−1.40493e6	−0.0944911
$113$	−1.18485e7	−0.772483	−0.386241	−	0.922398i	$-0.626227\pi$
$113$	−1.18485e7	−0.772483	−0.386241	+	0.922398i	$0.626227\pi$
$114$	−3.27573e6	−0.207082
$115$	−3.32338e7	−2.03769
$116$	2.81867e6	0.167665
$117$	−1.60161e6	−0.0924500
$118$	−1.96648e7	−1.10180
$119$	1.94147e6	0.105613
$120$	6.98945e6	0.369240
$121$	−1.85372e7	−0.951253
$122$	−374328.	−0.0186635
$123$	−1.36757e7	−0.662645
$124$	5.52082e6	0.260032
$125$	−5.02489e7	−2.30113
$126$	−2.00038e6	−0.0890871
$127$	−3.61236e7	−1.56487	−0.782435	−	0.622732i	$-0.786023\pi$
$127$	−3.61236e7	−1.56487	−0.782435	+	0.622732i	$0.786023\pi$
$128$	2.09715e6	0.0883883
$129$	−2.15873e6	−0.0885391
$130$	8.88647e6	0.354754
$131$	−1.86594e7	−0.725185	−0.362593	−	0.931948i	$-0.618108\pi$
$131$	−1.86594e7	−0.725185	−0.362593	+	0.931948i	$0.618108\pi$
$132$	1.68419e6	0.0637355
$133$	−5.20174e6	−0.191720
$134$	6.17043e6	0.221538
$135$	9.95178e6	0.348123
$136$	−2.89806e6	−0.0987918
$137$	1.13780e7	0.378047	0.189023	−	0.981973i	$-0.439468\pi$
$137$	1.13780e7	0.378047	0.189023	+	0.981973i	$0.439468\pi$
$138$	−1.41979e7	−0.459883
$139$	−4.35614e7	−1.37578	−0.687892	−	0.725813i	$-0.741464\pi$
$139$	−4.35614e7	−1.37578	−0.687892	+	0.725813i	$0.741464\pi$
$140$	1.10990e7	0.341850
$141$	−2.46034e6	−0.0739142
$142$	3.04923e6	0.0893679
$143$	2.14130e6	0.0612351
$144$	2.98598e6	0.0833333
$145$	−2.22676e7	−0.606576
$146$	1.21382e7	0.322790
$147$	−3.17652e6	−0.0824786
$148$	−2.74534e7	−0.696115
$149$	2.60076e7	0.644093	0.322046	−	0.946724i	$-0.395629\pi$
$149$	2.60076e7	0.644093	0.322046	+	0.946724i	$0.395629\pi$
$150$	−3.83420e7	−0.927588
$151$	5.57190e7	1.31699	0.658497	−	0.752583i	$-0.271192\pi$
$151$	5.57190e7	1.31699	0.658497	+	0.752583i	$0.271192\pi$
$152$	7.76470e6	0.179338
$153$	−4.12634e6	−0.0931418
$154$	2.67443e6	0.0590076
$155$	−4.36147e7	−0.940745
$156$	3.79642e6	0.0800641
$157$	5.82125e7	1.20051	0.600257	−	0.799807i	$-0.295065\pi$
$157$	5.82125e7	1.20051	0.600257	+	0.799807i	$0.295065\pi$
$158$	2.22369e7	0.448513
$159$	−2.31925e7	−0.457571
$160$	−1.65676e7	−0.319771
$161$	−2.25458e7	−0.425769
$162$	4.25153e6	0.0785674
$163$	−5.85066e7	−1.05815	−0.529076	−	0.848574i	$-0.677461\pi$
$163$	−5.85066e7	−1.05815	−0.529076	+	0.848574i	$0.677461\pi$
$164$	3.24164e7	0.573867
$165$	−1.33051e7	−0.230582
$166$	1.44647e7	0.245432
$167$	1.10743e8	1.83996	0.919979	−	0.391969i	$-0.128206\pi$
$167$	1.10743e8	1.83996	0.919979	+	0.391969i	$0.128206\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	2.28948e7	0.357409
$171$	1.10556e7	0.169081
$172$	5.11700e6	0.0766771
$173$	−1.34755e7	−0.197871	−0.0989357	−	0.995094i	$-0.531544\pi$
$173$	−1.34755e7	−0.197871	−0.0989357	+	0.995094i	$0.531544\pi$
$174$	−9.51301e6	−0.136898
$175$	−6.08856e7	−0.858779
$176$	−3.99215e6	−0.0551966
$177$	6.63686e7	0.899614
$178$	3.72951e7	0.495657
$179$	−4.01736e7	−0.523547	−0.261773	−	0.965129i	$-0.584307\pi$
$179$	−4.01736e7	−0.523547	−0.261773	+	0.965129i	$0.584307\pi$
$180$	−2.35894e7	−0.301483
$181$	−9.67467e7	−1.21272	−0.606361	−	0.795189i	$-0.707371\pi$
$181$	−9.67467e7	−1.21272	−0.606361	+	0.795189i	$0.707371\pi$
$182$	6.02857e6	0.0741249
$183$	1.26336e6	0.0152387
$184$	3.36543e7	0.398271
$185$	2.16883e8	2.51840
$186$	−1.86328e7	−0.212316
$187$	5.51676e6	0.0616933
$188$	5.83191e6	0.0640116
$189$	6.75127e6	0.0727393
$190$	−6.13415e7	−0.648809
$191$	−6.13516e7	−0.637102	−0.318551	−	0.947906i	$-0.603196\pi$
$191$	−6.13516e7	−0.637102	−0.318551	+	0.947906i	$0.603196\pi$
$192$	−7.07789e6	−0.0721688
$193$	−6.42073e7	−0.642886	−0.321443	−	0.946929i	$-0.604168\pi$
$193$	−6.42073e7	−0.642886	−0.321443	+	0.946929i	$0.604168\pi$
$194$	−5.76134e7	−0.566523
$195$	−2.99918e7	−0.289656
$196$	7.52954e6	0.0714286
$197$	6.15065e7	0.573178	0.286589	−	0.958054i	$-0.407479\pi$
$197$	6.15065e7	0.573178	0.286589	+	0.958054i	$0.407479\pi$
$198$	−5.68413e6	−0.0520398
$199$	−7.73282e7	−0.695588	−0.347794	−	0.937571i	$-0.613069\pi$
$199$	−7.73282e7	−0.695588	−0.347794	+	0.937571i	$0.613069\pi$
$200$	9.08846e7	0.803314
$201$	−2.08252e7	−0.180885
$202$	−1.44686e8	−1.23508
$203$	−1.51063e7	−0.126742
$204$	9.78095e6	0.0806632
$205$	−2.56091e8	−2.07614
$206$	−1.47636e8	−1.17668
$207$	4.79180e7	0.375493
$208$	−8.99891e6	−0.0693375
$209$	−1.47809e7	−0.111993
$210$	−3.74591e7	−0.279119
$211$	−1.05409e8	−0.772480	−0.386240	−	0.922398i	$-0.626226\pi$
$211$	−1.05409e8	−0.772480	−0.386240	+	0.922398i	$0.626226\pi$
$212$	5.49749e7	0.396268
$213$	−1.02912e7	−0.0729686
$214$	1.30917e8	0.913162
$215$	−4.04245e7	−0.277402
$216$	−1.00777e7	−0.0680414
$217$	−2.95881e7	−0.196566
$218$	1.01670e8	0.664652
$219$	−4.09665e7	−0.263557
$220$	3.15381e7	0.199690
$221$	1.24356e7	0.0774987
$222$	9.26553e7	0.568375
$223$	−3.47141e7	−0.209623	−0.104811	−	0.994492i	$-0.533424\pi$
$223$	−3.47141e7	−0.209623	−0.104811	+	0.994492i	$0.533424\pi$
$224$	−1.12394e7	−0.0668153
$225$	1.29404e8	0.757372
$226$	−9.47880e7	−0.546228
$227$	−9.94839e7	−0.564498	−0.282249	−	0.959341i	$-0.591080\pi$
$227$	−9.94839e7	−0.564498	−0.282249	+	0.959341i	$0.591080\pi$
$228$	−2.62059e7	−0.146429
$229$	1.36235e7	0.0749660	0.0374830	−	0.999297i	$-0.488066\pi$
$229$	1.36235e7	0.0749660	0.0374830	+	0.999297i	$0.488066\pi$
$230$	−2.65871e8	−1.44086
$231$	−9.02619e6	−0.0481795
$232$	2.25494e7	0.118557
$233$	3.58147e8	1.85488	0.927440	−	0.373971i	$-0.122004\pi$
$233$	3.58147e8	1.85488	0.927440	+	0.373971i	$0.122004\pi$
$234$	−1.28129e7	−0.0653720
$235$	−4.60723e7	−0.231581
$236$	−1.57318e8	−0.779089
$237$	−7.50496e7	−0.366209
$238$	1.55318e7	0.0746796
$239$	1.45807e8	0.690855	0.345428	−	0.938445i	$-0.387734\pi$
$239$	1.45807e8	0.690855	0.345428	+	0.938445i	$0.387734\pi$
$240$	5.59156e7	0.261092
$241$	−1.59927e8	−0.735974	−0.367987	−	0.929831i	$-0.619953\pi$
$241$	−1.59927e8	−0.735974	−0.367987	+	0.929831i	$0.619953\pi$
$242$	−1.48298e8	−0.672638
$243$	−1.43489e7	−0.0641500
$244$	−2.99462e6	−0.0131971
$245$	−5.94836e7	−0.258414
$246$	−1.09405e8	−0.468561
$247$	−3.33185e7	−0.140684
$248$	4.41665e7	0.183871
$249$	−4.88185e7	−0.200395
$250$	−4.01991e8	−1.62714
$251$	−1.33440e7	−0.0532632	−0.0266316	−	0.999645i	$-0.508478\pi$
$251$	−1.33440e7	−0.0532632	−0.0266316	+	0.999645i	$0.508478\pi$
$252$	−1.60030e7	−0.0629941
$253$	−6.40645e7	−0.248711
$254$	−2.88989e8	−1.10653
$255$	−7.72699e7	−0.291823
$256$	1.67772e7	0.0625000
$257$	−7.72175e7	−0.283759	−0.141880	−	0.989884i	$-0.545315\pi$
$257$	−7.72175e7	−0.283759	−0.141880	+	0.989884i	$0.545315\pi$
$258$	−1.72699e7	−0.0626066
$259$	1.47133e8	0.526213
$260$	7.10918e7	0.250849
$261$	3.21064e7	0.111776
$262$	−1.49275e8	−0.512783
$263$	−1.37858e8	−0.467292	−0.233646	−	0.972322i	$-0.575066\pi$
$263$	−1.37858e8	−0.467292	−0.233646	+	0.972322i	$0.575066\pi$
$264$	1.34735e7	0.0450678
$265$	−4.34304e8	−1.43362
$266$	−4.16140e7	−0.135567
$267$	−1.25871e8	−0.404703
$268$	4.93634e7	0.156651
$269$	−4.62689e8	−1.44929	−0.724646	−	0.689121i	$-0.757997\pi$
$269$	−4.62689e8	−1.44929	−0.724646	+	0.689121i	$0.757997\pi$
$270$	7.96142e7	0.246160
$271$	2.27980e8	0.695832	0.347916	−	0.937526i	$-0.386889\pi$
$271$	2.27980e8	0.695832	0.347916	+	0.937526i	$0.386889\pi$
$272$	−2.31845e7	−0.0698564
$273$	−2.03464e7	−0.0605228
$274$	9.10243e7	0.267319
$275$	−1.73008e8	−0.501652
$276$	−1.13583e8	−0.325187
$277$	3.50662e8	0.991309	0.495654	−	0.868520i	$-0.334928\pi$
$277$	3.50662e8	0.991309	0.495654	+	0.868520i	$0.334928\pi$
$278$	−3.48491e8	−0.972826
$279$	6.28856e7	0.173355
$280$	8.87919e7	0.241724
$281$	−2.49198e8	−0.669996	−0.334998	−	0.942219i	$-0.608736\pi$
$281$	−2.49198e8	−0.669996	−0.334998	+	0.942219i	$0.608736\pi$
$282$	−1.96827e7	−0.0522652
$283$	−2.17582e8	−0.570651	−0.285326	−	0.958431i	$-0.592102\pi$
$283$	−2.17582e8	−0.570651	−0.285326	+	0.958431i	$0.592102\pi$
$284$	2.43939e7	0.0631926
$285$	2.07027e8	0.529750
$286$	1.71304e7	0.0432998
$287$	−1.73732e8	−0.433803
$288$	2.38879e7	0.0589256
$289$	−3.78300e8	−0.921921
$290$	−1.78141e8	−0.428914
$291$	1.94445e8	0.462564
$292$	9.71058e7	0.228247
$293$	−8.46928e6	−0.0196703	−0.00983513	−	0.999952i	$-0.503131\pi$
$293$	−8.46928e6	−0.0196703	−0.00983513	+	0.999952i	$0.503131\pi$
$294$	−2.54122e7	−0.0583212
$295$	1.24282e9	2.81859
$296$	−2.19627e8	−0.492227
$297$	1.91839e7	0.0424903
$298$	2.08061e8	0.455442
$299$	−1.44411e8	−0.312429
$300$	−3.06736e8	−0.655903
$301$	−2.74239e7	−0.0579624
$302$	4.45752e8	0.931256
$303$	4.88315e8	1.00844
$304$	6.21176e7	0.126811
$305$	2.36576e7	0.0477444
$306$	−3.30107e7	−0.0658612
$307$	−7.95679e8	−1.56947	−0.784736	−	0.619830i	$-0.787202\pi$
$307$	−7.95679e8	−1.56947	−0.784736	+	0.619830i	$0.787202\pi$
$308$	2.13954e7	0.0417247
$309$	4.98273e8	0.960755
$310$	−3.48917e8	−0.665207
$311$	7.01044e8	1.32155	0.660775	−	0.750584i	$-0.270228\pi$
$311$	7.01044e8	1.32155	0.660775	+	0.750584i	$0.270228\pi$
$312$	3.03713e7	0.0566139
$313$	−5.89581e8	−1.08677	−0.543386	−	0.839483i	$-0.682858\pi$
$313$	−5.89581e8	−1.08677	−0.543386	+	0.839483i	$0.682858\pi$
$314$	4.65700e8	0.848892
$315$	1.26424e8	0.227900
$316$	1.77895e8	0.317147
$317$	1.13340e8	0.199837	0.0999183	−	0.994996i	$-0.468142\pi$
$317$	1.13340e8	0.199837	0.0999183	+	0.994996i	$0.468142\pi$
$318$	−1.85540e8	−0.323552
$319$	−4.29250e7	−0.0740361
$320$	−1.32541e8	−0.226112
$321$	−4.41845e8	−0.745594
$322$	−1.80366e8	−0.301064
$323$	−8.58405e7	−0.141737
$324$	3.40122e7	0.0555556
$325$	−3.89987e8	−0.630172
$326$	−4.68053e8	−0.748226
$327$	−3.43136e8	−0.542686
$328$	2.59331e8	0.405786
$329$	−3.12554e7	−0.0483882
$330$	−1.06441e8	−0.163046
$331$	5.33092e7	0.0807986	0.0403993	−	0.999184i	$-0.487137\pi$
$331$	5.33092e7	0.0807986	0.0403993	+	0.999184i	$0.487137\pi$
$332$	1.15718e8	0.173547
$333$	−3.12712e8	−0.464076
$334$	8.85942e8	1.30105
$335$	−3.89973e8	−0.566732
$336$	3.79331e7	0.0545545
$337$	1.04232e9	1.48353	0.741767	−	0.670658i	$-0.233988\pi$
$337$	1.04232e9	1.48353	0.741767	+	0.670658i	$0.233988\pi$
$338$	3.86145e7	0.0543928
$339$	3.19910e8	0.445993
$340$	1.83158e8	0.252726
$341$	−8.40756e7	−0.114823
$342$	8.84448e7	0.119559
$343$	−4.03536e7	−0.0539949
$344$	4.09360e7	0.0542189
$345$	8.97313e8	1.17646
$346$	−1.07804e8	−0.139916
$347$	−9.08973e7	−0.116788	−0.0583939	−	0.998294i	$-0.518598\pi$
$347$	−9.08973e7	−0.116788	−0.0583939	+	0.998294i	$0.518598\pi$
$348$	−7.61041e7	−0.0968012
$349$	3.96319e8	0.499064	0.249532	−	0.968367i	$-0.419723\pi$
$349$	3.96319e8	0.499064	0.249532	+	0.968367i	$0.419723\pi$
$350$	−4.87085e8	−0.607249
$351$	4.32436e7	0.0533761
$352$	−3.19372e7	−0.0390299
$353$	−2.06329e8	−0.249660	−0.124830	−	0.992178i	$-0.539839\pi$
$353$	−2.06329e8	−0.249660	−0.124830	+	0.992178i	$0.539839\pi$
$354$	5.30949e8	0.636123
$355$	−1.92713e8	−0.228618
$356$	2.98361e8	0.350483
$357$	−5.24198e7	−0.0609756
$358$	−3.21389e8	−0.370204
$359$	−1.59470e9	−1.81907	−0.909534	−	0.415630i	$-0.863561\pi$
$359$	−1.59470e9	−1.81907	−0.909534	+	0.415630i	$0.863561\pi$
$360$	−1.88715e8	−0.213181
$361$	−6.63881e8	−0.742703
$362$	−7.73974e8	−0.857524
$363$	5.00505e8	0.549206
$364$	4.82285e7	0.0524142
$365$	−7.67140e8	−0.825752
$366$	1.01069e7	0.0107754
$367$	8.63511e8	0.911878	0.455939	−	0.890011i	$-0.349303\pi$
$367$	8.63511e8	0.911878	0.455939	+	0.890011i	$0.349303\pi$
$368$	2.69235e8	0.281620
$369$	3.69243e8	0.382578
$370$	1.73507e9	1.78078
$371$	−2.94631e8	−0.299551
$372$	−1.49062e8	−0.150130
$373$	−3.87571e8	−0.386697	−0.193349	−	0.981130i	$-0.561935\pi$
$373$	−3.87571e8	−0.386697	−0.193349	+	0.981130i	$0.561935\pi$
$374$	4.41340e7	0.0436238
$375$	1.35672e9	1.32856
$376$	4.66553e7	0.0452630
$377$	−9.67596e7	−0.0930036
$378$	5.40102e7	0.0514344
$379$	6.80121e8	0.641725	0.320862	−	0.947126i	$-0.396027\pi$
$379$	6.80121e8	0.641725	0.320862	+	0.947126i	$0.396027\pi$
$380$	−4.90732e8	−0.458777
$381$	9.75338e8	0.903478
$382$	−4.90813e8	−0.450499
$383$	1.89713e8	0.172545	0.0862725	−	0.996272i	$-0.472504\pi$
$383$	1.89713e8	0.172545	0.0862725	+	0.996272i	$0.472504\pi$
$384$	−5.66231e7	−0.0510310
$385$	−1.69025e8	−0.150952
$386$	−5.13658e8	−0.454589
$387$	5.82858e7	0.0511181
$388$	−4.60907e8	−0.400592
$389$	5.32318e8	0.458508	0.229254	−	0.973367i	$-0.426371\pi$
$389$	5.32318e8	0.458508	0.229254	+	0.973367i	$0.426371\pi$
$390$	−2.39935e8	−0.204817
$391$	−3.72056e8	−0.314767
$392$	6.02363e7	0.0505076
$393$	5.03805e8	0.418686
$394$	4.92052e8	0.405298
$395$	−1.40538e9	−1.14737
$396$	−4.54730e7	−0.0367977
$397$	3.59479e8	0.288341	0.144171	−	0.989553i	$-0.453949\pi$
$397$	3.59479e8	0.288341	0.144171	+	0.989553i	$0.453949\pi$
$398$	−6.18625e8	−0.491855
$399$	1.40447e8	0.110690
$400$	7.27077e8	0.568029
$401$	1.86285e9	1.44269	0.721344	−	0.692577i	$-0.243525\pi$
$401$	1.86285e9	1.44269	0.721344	+	0.692577i	$0.243525\pi$
$402$	−1.66602e8	−0.127905
$403$	−1.89519e8	−0.144240
$404$	−1.15749e9	−0.873336
$405$	−2.68698e8	−0.200989
$406$	−1.20850e8	−0.0896205
$407$	4.18084e8	0.307385
$408$	7.82476e7	0.0570375
$409$	2.16294e9	1.56319	0.781595	−	0.623786i	$-0.214406\pi$
$409$	2.16294e9	1.56319	0.781595	+	0.623786i	$0.214406\pi$
$410$	−2.04873e9	−1.46805
$411$	−3.07207e8	−0.218265
$412$	−1.18109e9	−0.832038
$413$	8.43127e8	0.588936
$414$	3.83344e8	0.265514
$415$	−9.14176e8	−0.627858
$416$	−7.19913e7	−0.0490290
$417$	1.17616e9	0.794309
$418$	−1.18247e8	−0.0791907
$419$	−1.25174e9	−0.831312	−0.415656	−	0.909522i	$-0.636448\pi$
$419$	−1.25174e9	−0.831312	−0.415656	+	0.909522i	$0.636448\pi$
$420$	−2.99673e8	−0.197367
$421$	−6.62692e7	−0.0432837	−0.0216419	−	0.999766i	$-0.506889\pi$
$421$	−6.62692e7	−0.0432837	−0.0216419	+	0.999766i	$0.506889\pi$
$422$	−8.43268e8	−0.546226
$423$	6.64291e7	0.0426744
$424$	4.39799e8	0.280204
$425$	−1.00475e9	−0.634887
$426$	−8.23293e7	−0.0515966
$427$	1.60493e7	0.00997605
$428$	1.04734e9	0.645703
$429$	−5.78150e7	−0.0353541
$430$	−3.23396e8	−0.196153
$431$	7.93745e8	0.477541	0.238770	−	0.971076i	$-0.423256\pi$
$431$	7.93745e8	0.477541	0.238770	+	0.971076i	$0.423256\pi$
$432$	−8.06216e7	−0.0481125
$433$	−1.05627e8	−0.0625270	−0.0312635	−	0.999511i	$-0.509953\pi$
$433$	−1.05627e8	−0.0625270	−0.0312635	+	0.999511i	$0.509953\pi$
$434$	−2.36705e8	−0.138993
$435$	6.01225e8	0.350207
$436$	8.13358e8	0.469980
$437$	9.96840e8	0.571401
$438$	−3.27732e8	−0.186363
$439$	−3.29223e9	−1.85723	−0.928613	−	0.371051i	$-0.878998\pi$
$439$	−3.29223e9	−1.85723	−0.928613	+	0.371051i	$0.878998\pi$
$440$	2.52305e8	0.141202
$441$	8.57661e7	0.0476190
$442$	9.94849e7	0.0547998
$443$	−1.84176e9	−1.00652	−0.503258	−	0.864136i	$-0.667866\pi$
$443$	−1.84176e9	−1.00652	−0.503258	+	0.864136i	$0.667866\pi$
$444$	7.41243e8	0.401902
$445$	−2.35706e9	−1.26798
$446$	−2.77712e8	−0.148226
$447$	−7.02205e8	−0.371867
$448$	−8.99154e7	−0.0472456
$449$	1.52557e9	0.795369	0.397684	−	0.917522i	$-0.369814\pi$
$449$	1.52557e9	0.795369	0.397684	+	0.917522i	$0.369814\pi$
$450$	1.03523e9	0.535543
$451$	−4.93664e8	−0.253404
$452$	−7.58304e8	−0.386241
$453$	−1.50441e9	−0.760367
$454$	−7.95871e8	−0.399160
$455$	−3.81008e8	−0.189624
$456$	−2.09647e8	−0.103541
$457$	5.43757e8	0.266501	0.133250	−	0.991082i	$-0.457459\pi$
$457$	5.43757e8	0.266501	0.133250	+	0.991082i	$0.457459\pi$
$458$	1.08988e8	0.0530090
$459$	1.11411e8	0.0537755
$460$	−2.12696e9	−1.01884
$461$	−2.01615e9	−0.958449	−0.479224	−	0.877692i	$-0.659082\pi$
$461$	−2.01615e9	−0.958449	−0.479224	+	0.877692i	$0.659082\pi$
$462$	−7.22095e7	−0.0340681
$463$	2.10963e9	0.987811	0.493905	−	0.869516i	$-0.335569\pi$
$463$	2.10963e9	0.987811	0.493905	+	0.869516i	$0.335569\pi$
$464$	1.80395e8	0.0838323
$465$	1.17760e9	0.543139
$466$	2.86518e9	1.31160
$467$	−1.87515e9	−0.851975	−0.425987	−	0.904729i	$-0.640073\pi$
$467$	−1.87515e9	−0.851975	−0.425987	+	0.904729i	$0.640073\pi$
$468$	−1.02503e8	−0.0462250
$469$	−2.64557e8	−0.118417
$470$	−3.68579e8	−0.163752
$471$	−1.57174e9	−0.693117
$472$	−1.25855e9	−0.550899
$473$	−7.79259e7	−0.0338585
$474$	−6.00397e8	−0.258949
$475$	2.69200e9	1.15252
$476$	1.24254e8	0.0528064
$477$	6.26199e8	0.264179
$478$	1.16646e9	0.488508
$479$	3.61742e7	0.0150392	0.00751959	−	0.999972i	$-0.497606\pi$
$479$	3.61742e7	0.0150392	0.00751959	+	0.999972i	$0.497606\pi$
$480$	4.47325e8	0.184620
$481$	9.42425e8	0.386135
$482$	−1.27942e9	−0.520412
$483$	6.08736e8	0.245818
$484$	−1.18638e9	−0.475627
$485$	3.64119e9	1.44926
$486$	−1.14791e8	−0.0453609
$487$	−1.02235e9	−0.401098	−0.200549	−	0.979684i	$-0.564273\pi$
$487$	−1.02235e9	−0.401098	−0.200549	+	0.979684i	$0.564273\pi$
$488$	−2.39570e7	−0.00933174
$489$	1.57968e9	0.610924
$490$	−4.75869e8	−0.182726
$491$	−3.26756e9	−1.24577	−0.622885	−	0.782313i	$-0.714040\pi$
$491$	−3.26756e9	−1.24577	−0.622885	+	0.782313i	$0.714040\pi$
$492$	−8.75243e8	−0.331323
$493$	−2.49288e8	−0.0936995
$494$	−2.66548e8	−0.0994788
$495$	3.59239e8	0.133127
$496$	3.53332e8	0.130016
$497$	−1.30736e8	−0.0477691
$498$	−3.90548e8	−0.141700
$499$	−5.10252e9	−1.83837	−0.919184	−	0.393828i	$-0.871151\pi$
$499$	−5.10252e9	−1.83837	−0.919184	+	0.393828i	$0.871151\pi$
$500$	−3.21593e9	−1.15056
$501$	−2.99005e9	−1.06230
$502$	−1.06752e8	−0.0376628
$503$	−9.25013e8	−0.324086	−0.162043	−	0.986784i	$-0.551808\pi$
$503$	−9.25013e8	−0.324086	−0.162043	+	0.986784i	$0.551808\pi$
$504$	−1.28024e8	−0.0445435
$505$	9.14420e9	3.15955
$506$	−5.12516e8	−0.175865
$507$	−1.30324e8	−0.0444116
$508$	−2.31191e9	−0.782435
$509$	1.28544e9	0.432056	0.216028	−	0.976387i	$-0.430690\pi$
$509$	1.28544e9	0.432056	0.216028	+	0.976387i	$0.430690\pi$
$510$	−6.18159e8	−0.206350
$511$	−5.20426e8	−0.172539
$512$	1.34218e8	0.0441942
$513$	−2.98501e8	−0.0976192
$514$	−6.17740e8	−0.200648
$515$	9.33067e9	3.01015
$516$	−1.38159e8	−0.0442695
$517$	−8.88132e7	−0.0282657
$518$	1.17707e9	0.372089
$519$	3.63838e8	0.114241
$520$	5.68734e8	0.177377
$521$	1.09976e9	0.340695	0.170348	−	0.985384i	$-0.445511\pi$
$521$	1.09976e9	0.340695	0.170348	+	0.985384i	$0.445511\pi$
$522$	2.56851e8	0.0790378
$523$	−2.00049e8	−0.0611479	−0.0305739	−	0.999533i	$-0.509734\pi$
$523$	−2.00049e8	−0.0611479	−0.0305739	+	0.999533i	$0.509734\pi$
$524$	−1.19420e9	−0.362593
$525$	1.64391e9	0.495816
$526$	−1.10287e9	−0.330425
$527$	−4.88271e8	−0.145319
$528$	1.07788e8	0.0318678
$529$	9.15750e8	0.268957
$530$	−3.47443e9	−1.01372
$531$	−1.79195e9	−0.519392
$532$	−3.32912e8	−0.0958602
$533$	−1.11280e9	−0.318324
$534$	−1.00697e9	−0.286168
$535$	−8.27400e9	−2.33602
$536$	3.94907e8	0.110769
$537$	1.08469e9	0.302270
$538$	−3.70151e9	−1.02480
$539$	−1.14666e8	−0.0315409
$540$	6.36914e8	0.174061
$541$	−6.34229e9	−1.72209	−0.861045	−	0.508529i	$-0.830190\pi$
$541$	−6.34229e9	−1.72209	−0.861045	+	0.508529i	$0.830190\pi$
$542$	1.82384e9	0.492027
$543$	2.61216e9	0.700166
$544$	−1.85476e8	−0.0493959
$545$	−6.42557e9	−1.70029
$546$	−1.62771e8	−0.0427960
$547$	−2.39009e9	−0.624395	−0.312197	−	0.950017i	$-0.601065\pi$
$547$	−2.39009e9	−0.624395	−0.312197	+	0.950017i	$0.601065\pi$
$548$	7.28195e8	0.189023
$549$	−3.41106e7	−0.00879805
$550$	−1.38407e9	−0.354722
$551$	6.67912e8	0.170094
$552$	−9.08667e8	−0.229942
$553$	−9.53408e8	−0.239740
$554$	2.80529e9	0.700961
$555$	−5.85585e9	−1.45400
$556$	−2.78793e9	−0.687892
$557$	4.18084e9	1.02511	0.512554	−	0.858655i	$-0.328699\pi$
$557$	4.18084e9	1.02511	0.512554	+	0.858655i	$0.328699\pi$
$558$	5.03084e8	0.122580
$559$	−1.75657e8	−0.0425328
$560$	7.10335e8	0.170925
$561$	−1.48952e8	−0.0356187
$562$	−1.99358e9	−0.473759
$563$	2.41789e9	0.571027	0.285513	−	0.958375i	$-0.407836\pi$
$563$	2.41789e9	0.571027	0.285513	+	0.958375i	$0.407836\pi$
$564$	−1.57462e8	−0.0369571
$565$	5.99063e9	1.39734
$566$	−1.74066e9	−0.403511
$567$	−1.82284e8	−0.0419961
$568$	1.95151e8	0.0446839
$569$	−3.00544e9	−0.683935	−0.341968	−	0.939712i	$-0.611093\pi$
$569$	−3.00544e9	−0.683935	−0.341968	+	0.939712i	$0.611093\pi$
$570$	1.65622e9	0.374590
$571$	7.47847e9	1.68107	0.840536	−	0.541756i	$-0.182240\pi$
$571$	7.47847e9	1.68107	0.840536	+	0.541756i	$0.182240\pi$
$572$	1.37043e8	0.0306176
$573$	1.65649e9	0.367831
$574$	−1.38985e9	−0.306745
$575$	1.16679e10	2.55949
$576$	1.91103e8	0.0416667
$577$	−2.03084e8	−0.0440110	−0.0220055	−	0.999758i	$-0.507005\pi$
$577$	−2.03084e8	−0.0440110	−0.0220055	+	0.999758i	$0.507005\pi$
$578$	−3.02640e9	−0.651897
$579$	1.73360e9	0.371170
$580$	−1.42513e9	−0.303288
$581$	−6.20175e8	−0.131189
$582$	1.55556e9	0.327082
$583$	−8.37204e8	−0.174981
$584$	7.76846e8	0.161395
$585$	8.09780e8	0.167233
$586$	−6.77543e7	−0.0139090
$587$	5.05213e9	1.03096	0.515480	−	0.856902i	$-0.327614\pi$
$587$	5.05213e9	1.03096	0.515480	+	0.856902i	$0.327614\pi$
$588$	−2.03297e8	−0.0412393
$589$	1.30821e9	0.263800
$590$	9.94256e9	1.99304
$591$	−1.66068e9	−0.330924
$592$	−1.75702e9	−0.348057
$593$	2.67099e9	0.525993	0.262997	−	0.964797i	$-0.415289\pi$
$593$	2.67099e9	0.525993	0.262997	+	0.964797i	$0.415289\pi$
$594$	1.53472e8	0.0300452
$595$	−9.81614e8	−0.191043
$596$	1.66449e9	0.322046
$597$	2.08786e9	0.401598
$598$	−1.15529e9	−0.220921
$599$	3.33264e8	0.0633569	0.0316785	−	0.999498i	$-0.489915\pi$
$599$	3.33264e8	0.0633569	0.0316785	+	0.999498i	$0.489915\pi$
$600$	−2.45389e9	−0.463794
$601$	−2.40003e9	−0.450979	−0.225490	−	0.974246i	$-0.572398\pi$
$601$	−2.40003e9	−0.450979	−0.225490	+	0.974246i	$0.572398\pi$
$602$	−2.19391e8	−0.0409856
$603$	5.62280e8	0.104434
$604$	3.56602e9	0.658497
$605$	9.37248e9	1.72072
$606$	3.90652e9	0.713076
$607$	4.74046e9	0.860321	0.430160	−	0.902752i	$-0.358457\pi$
$607$	4.74046e9	0.860321	0.430160	+	0.902752i	$0.358457\pi$
$608$	4.96941e8	0.0896690
$609$	4.07870e8	0.0731748
$610$	1.89261e8	0.0337604
$611$	−2.00199e8	−0.0355072
$612$	−2.64086e8	−0.0465709
$613$	−1.70938e9	−0.299727	−0.149863	−	0.988707i	$-0.547883\pi$
$613$	−1.70938e9	−0.299727	−0.149863	+	0.988707i	$0.547883\pi$
$614$	−6.36544e9	−1.10978
$615$	6.91446e9	1.19866
$616$	1.71163e8	0.0295038
$617$	2.94186e9	0.504225	0.252113	−	0.967698i	$-0.418875\pi$
$617$	2.94186e9	0.504225	0.252113	+	0.967698i	$0.418875\pi$
$618$	3.98618e9	0.679356
$619$	6.20627e9	1.05175	0.525876	−	0.850561i	$-0.323738\pi$
$619$	6.20627e9	1.05175	0.525876	+	0.850561i	$0.323738\pi$
$620$	−2.79134e9	−0.470372
$621$	−1.29378e9	−0.216791
$622$	5.60835e9	0.934478
$623$	−1.59903e9	−0.264940
$624$	2.42971e8	0.0400320
$625$	1.15381e10	1.89040
$626$	−4.71665e9	−0.768463
$627$	3.99085e8	0.0646590
$628$	3.72560e9	0.600257
$629$	2.42803e9	0.389024
$630$	1.01140e9	0.161150
$631$	−1.37333e7	−0.00217607	−0.00108804	−	0.999999i	$-0.500346\pi$
$631$	−1.37333e7	−0.00217607	−0.00108804	+	0.999999i	$0.500346\pi$
$632$	1.42316e9	0.224257
$633$	2.84603e9	0.445991
$634$	9.06719e8	0.141306
$635$	1.82642e10	2.83069
$636$	−1.48432e9	−0.228785
$637$	−2.58475e8	−0.0396214
$638$	−3.43400e8	−0.0523514
$639$	2.77861e8	0.0421284
$640$	−1.06033e9	−0.159886
$641$	6.38161e9	0.957034	0.478517	−	0.878078i	$-0.341175\pi$
$641$	6.38161e9	0.957034	0.478517	+	0.878078i	$0.341175\pi$
$642$	−3.53476e9	−0.527214
$643$	6.94076e9	1.02960	0.514800	−	0.857310i	$-0.327866\pi$
$643$	6.94076e9	1.02960	0.514800	+	0.857310i	$0.327866\pi$
$644$	−1.44293e9	−0.212885
$645$	1.09146e9	0.160158
$646$	−6.86724e8	−0.100223
$647$	−3.89714e9	−0.565694	−0.282847	−	0.959165i	$-0.591279\pi$
$647$	−3.89714e9	−0.565694	−0.282847	+	0.959165i	$0.591279\pi$
$648$	2.72098e8	0.0392837
$649$	2.39577e9	0.344024
$650$	−3.11990e9	−0.445599
$651$	7.98879e8	0.113487
$652$	−3.74442e9	−0.529076
$653$	3.80268e9	0.534433	0.267216	−	0.963637i	$-0.413896\pi$
$653$	3.80268e9	0.534433	0.267216	+	0.963637i	$0.413896\pi$
$654$	−2.74508e9	−0.383737
$655$	9.43426e9	1.31179
$656$	2.07465e9	0.286934
$657$	1.10610e9	0.152165
$658$	−2.50043e8	−0.0342156
$659$	1.47769e9	0.201134	0.100567	−	0.994930i	$-0.467934\pi$
$659$	1.47769e9	0.201134	0.100567	+	0.994930i	$0.467934\pi$
$660$	−8.51529e8	−0.115291
$661$	3.33396e9	0.449009	0.224505	−	0.974473i	$-0.427924\pi$
$661$	3.33396e9	0.449009	0.224505	+	0.974473i	$0.427924\pi$
$662$	4.26473e8	0.0571332
$663$	−3.35762e8	−0.0447439
$664$	9.25743e8	0.122716
$665$	2.63002e9	0.346803
$666$	−2.50169e9	−0.328152
$667$	2.89491e9	0.377741
$668$	7.08754e9	0.919979
$669$	9.37280e8	0.121026
$670$	−3.11979e9	−0.400740
$671$	4.56046e7	0.00582747
$672$	3.03464e8	0.0385758
$673$	−5.49101e9	−0.694383	−0.347192	−	0.937794i	$-0.612865\pi$
$673$	−5.49101e9	−0.694383	−0.347192	+	0.937794i	$0.612865\pi$
$674$	8.33858e9	1.04902
$675$	−3.49391e9	−0.437269
$676$	3.08916e8	0.0384615
$677$	1.53710e10	1.90389	0.951946	−	0.306265i	$-0.0990794\pi$
$677$	1.53710e10	1.90389	0.951946	+	0.306265i	$0.0990794\pi$
$678$	2.55928e9	0.315365
$679$	2.47017e9	0.302819
$680$	1.46527e9	0.178704
$681$	2.68607e9	0.325913
$682$	−6.72605e8	−0.0811922
$683$	1.15224e9	0.138379	0.0691897	−	0.997604i	$-0.477959\pi$
$683$	1.15224e9	0.138379	0.0691897	+	0.997604i	$0.477959\pi$
$684$	7.07559e8	0.0845407
$685$	−5.75277e9	−0.683849
$686$	−3.22829e8	−0.0381802
$687$	−3.67835e8	−0.0432817
$688$	3.27488e8	0.0383385
$689$	−1.88719e9	−0.219810
$690$	7.17850e9	0.831883
$691$	3.87769e9	0.447095	0.223548	−	0.974693i	$-0.428236\pi$
$691$	3.87769e9	0.447095	0.223548	+	0.974693i	$0.428236\pi$
$692$	−8.62431e8	−0.0989357
$693$	2.43707e8	0.0278165
$694$	−7.27178e8	−0.0825815
$695$	2.20248e10	2.48865
$696$	−6.08833e8	−0.0684488
$697$	−2.86696e9	−0.320706
$698$	3.17055e9	0.352891
$699$	−9.66998e9	−1.07092
$700$	−3.89668e9	−0.429390
$701$	−1.12046e10	−1.22852	−0.614260	−	0.789104i	$-0.710545\pi$
$701$	−1.12046e10	−1.22852	−0.614260	+	0.789104i	$0.710545\pi$
$702$	3.45948e8	0.0377426
$703$	−6.50536e9	−0.706200
$704$	−2.55497e8	−0.0275983
$705$	1.24395e9	0.133703
$706$	−1.65063e9	−0.176536
$707$	6.20341e9	0.660180
$708$	4.24759e9	0.449807
$709$	−5.78180e9	−0.609258	−0.304629	−	0.952471i	$-0.598532\pi$
$709$	−5.78180e9	−0.609258	−0.304629	+	0.952471i	$0.598532\pi$
$710$	−1.54170e9	−0.161657
$711$	2.02634e9	0.211431
$712$	2.38689e9	0.247829
$713$	5.67014e9	0.585842
$714$	−4.19358e8	−0.0431163
$715$	−1.08264e9	−0.110768
$716$	−2.57111e9	−0.261773
$717$	−3.93680e9	−0.398865
$718$	−1.27576e10	−1.28627
$719$	4.57616e8	0.0459145	0.0229573	−	0.999736i	$-0.492692\pi$
$719$	4.57616e8	0.0459145	0.0229573	+	0.999736i	$0.492692\pi$
$720$	−1.50972e9	−0.150742
$721$	6.32991e9	0.628962
$722$	−5.31105e9	−0.525170
$723$	4.31803e9	0.424915
$724$	−6.19179e9	−0.606361
$725$	7.81780e9	0.761907
$726$	4.00404e9	0.388348
$727$	−1.72274e10	−1.66284	−0.831419	−	0.555646i	$-0.812471\pi$
$727$	−1.72274e10	−1.66284	−0.831419	+	0.555646i	$0.812471\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	−6.13712e9	−0.583895
$731$	−4.52556e8	−0.0428511
$732$	8.08548e7	0.00761934
$733$	−5.67159e8	−0.0531913	−0.0265957	−	0.999646i	$-0.508467\pi$
$733$	−5.67159e8	−0.0531913	−0.0265957	+	0.999646i	$0.508467\pi$
$734$	6.90809e9	0.644795
$735$	1.60606e9	0.149195
$736$	2.15388e9	0.199135
$737$	−7.51747e8	−0.0691728
$738$	2.95395e9	0.270524
$739$	−6.70030e9	−0.610715	−0.305358	−	0.952238i	$-0.598776\pi$
$739$	−6.70030e9	−0.610715	−0.305358	+	0.952238i	$0.598776\pi$
$740$	1.38805e10	1.25920
$741$	8.99598e8	0.0812241
$742$	−2.35705e9	−0.211814
$743$	−1.91086e10	−1.70910	−0.854552	−	0.519366i	$-0.826168\pi$
$743$	−1.91086e10	−1.70910	−0.854552	+	0.519366i	$0.826168\pi$
$744$	−1.19250e9	−0.106158
$745$	−1.31495e10	−1.16510
$746$	−3.10057e9	−0.273436
$747$	1.31810e9	0.115698
$748$	3.53072e8	0.0308467
$749$	−5.61307e9	−0.488106
$750$	1.08538e10	0.939432
$751$	−7.77506e9	−0.669829	−0.334914	−	0.942249i	$-0.608707\pi$
$751$	−7.77506e9	−0.669829	−0.334914	+	0.942249i	$0.608707\pi$
$752$	3.73242e8	0.0320058
$753$	3.60287e8	0.0307515
$754$	−7.74077e8	−0.0657634
$755$	−2.81717e10	−2.38231
$756$	4.32081e8	0.0363696
$757$	−5.51645e9	−0.462194	−0.231097	−	0.972931i	$-0.574231\pi$
$757$	−5.51645e9	−0.462194	−0.231097	+	0.972931i	$0.574231\pi$
$758$	5.44097e9	0.453768
$759$	1.72974e9	0.143594
$760$	−3.92585e9	−0.324404
$761$	6.54076e9	0.537999	0.269000	−	0.963140i	$-0.413307\pi$
$761$	6.54076e9	0.537999	0.269000	+	0.963140i	$0.413307\pi$
$762$	7.80270e9	0.638856
$763$	−4.35909e9	−0.355271
$764$	−3.92650e9	−0.318551
$765$	2.08629e9	0.168484
$766$	1.51771e9	0.122008
$767$	5.40044e9	0.432161
$768$	−4.52985e8	−0.0360844
$769$	−2.15875e10	−1.71183	−0.855915	−	0.517116i	$-0.827006\pi$
$769$	−2.15875e10	−1.71183	−0.855915	+	0.517116i	$0.827006\pi$
$770$	−1.35220e9	−0.106739
$771$	2.08487e9	0.163828
$772$	−4.10927e9	−0.321443
$773$	−6.96542e8	−0.0542399	−0.0271199	−	0.999632i	$-0.508634\pi$
$773$	−6.96542e8	−0.0542399	−0.0271199	+	0.999632i	$0.508634\pi$
$774$	4.66286e8	0.0361459
$775$	1.53124e10	1.18165
$776$	−3.68726e9	−0.283261
$777$	−3.97260e9	−0.303809
$778$	4.25854e9	0.324214
$779$	7.68139e9	0.582182
$780$	−1.91948e9	−0.144828
$781$	−3.71490e8	−0.0279041
$782$	−2.97645e9	−0.222574
$783$	−8.66873e8	−0.0645341
$784$	4.81890e8	0.0357143
$785$	−2.94324e10	−2.17161
$786$	4.03044e9	0.296056
$787$	−2.34452e10	−1.71452	−0.857260	−	0.514884i	$-0.827835\pi$
$787$	−2.34452e10	−1.71452	−0.857260	+	0.514884i	$0.827835\pi$
$788$	3.93642e9	0.286589
$789$	3.72218e9	0.269791
$790$	−1.12431e10	−0.811315
$791$	4.06404e9	0.291971
$792$	−3.63784e8	−0.0260199
$793$	1.02800e8	0.00732042
$794$	2.87583e9	0.203888
$795$	1.17262e10	0.827700
$796$	−4.94900e9	−0.347794
$797$	−3.48843e9	−0.244077	−0.122038	−	0.992525i	$-0.538943\pi$
$797$	−3.48843e9	−0.244077	−0.122038	+	0.992525i	$0.538943\pi$
$798$	1.12358e9	0.0782695
$799$	−5.15784e8	−0.0357729
$800$	5.81662e9	0.401657
$801$	3.39851e9	0.233655
$802$	1.49028e10	1.02013
$803$	−1.47881e9	−0.100788
$804$	−1.33281e9	−0.0904426
$805$	1.13992e10	0.770174
$806$	−1.51615e9	−0.101993
$807$	1.24926e10	0.836749
$808$	−9.25990e9	−0.617542
$809$	−9.81709e9	−0.651873	−0.325936	−	0.945392i	$-0.605680\pi$
$809$	−9.81709e9	−0.651873	−0.325936	+	0.945392i	$0.605680\pi$
$810$	−2.14958e9	−0.142121
$811$	9.75834e9	0.642396	0.321198	−	0.947012i	$-0.395914\pi$
$811$	9.75834e9	0.642396	0.321198	+	0.947012i	$0.395914\pi$
$812$	−9.66804e8	−0.0633712
$813$	−6.15546e9	−0.401739
$814$	3.34467e9	0.217354
$815$	2.95811e10	1.91409
$816$	6.25981e8	0.0403316
$817$	1.21252e9	0.0777881
$818$	1.73035e10	1.10534
$819$	5.49353e8	0.0349428
$820$	−1.63898e10	−1.03807
$821$	−1.62521e9	−0.102496	−0.0512482	−	0.998686i	$-0.516320\pi$
$821$	−1.62521e9	−0.102496	−0.0512482	+	0.998686i	$0.516320\pi$
$822$	−2.45766e9	−0.154337
$823$	2.42225e10	1.51467	0.757337	−	0.653024i	$-0.226500\pi$
$823$	2.42225e10	1.51467	0.757337	+	0.653024i	$0.226500\pi$
$824$	−9.44873e9	−0.588340
$825$	4.67123e9	0.289629
$826$	6.74502e9	0.416440
$827$	−1.15579e10	−0.710576	−0.355288	−	0.934757i	$-0.615617\pi$
$827$	−1.15579e10	−0.710576	−0.355288	+	0.934757i	$0.615617\pi$
$828$	3.06675e9	0.187747
$829$	1.35985e10	0.828991	0.414496	−	0.910051i	$-0.363958\pi$
$829$	1.35985e10	0.828991	0.414496	+	0.910051i	$0.363958\pi$
$830$	−7.31341e9	−0.443963
$831$	−9.46786e9	−0.572332
$832$	−5.75930e8	−0.0346688
$833$	−6.65925e8	−0.0399179
$834$	9.40926e9	0.561661
$835$	−5.59918e10	−3.32830
$836$	−9.45979e8	−0.0559963
$837$	−1.69791e9	−0.100087
$838$	−1.00139e10	−0.587826
$839$	2.11117e10	1.23412	0.617058	−	0.786918i	$-0.288325\pi$
$839$	2.11117e10	1.23412	0.617058	+	0.786918i	$0.288325\pi$
$840$	−2.39738e9	−0.139560
$841$	−1.53102e10	−0.887554
$842$	−5.30154e8	−0.0306062
$843$	6.72834e9	0.386823
$844$	−6.74614e9	−0.386240
$845$	−2.44045e9	−0.139146
$846$	5.31433e8	0.0301753
$847$	6.35827e9	0.359540
$848$	3.51839e9	0.198134
$849$	5.87472e9	0.329466
$850$	−8.03800e9	−0.448933
$851$	−2.81960e10	−1.56832
$852$	−6.58634e8	−0.0364843
$853$	−3.53583e10	−1.95061	−0.975304	−	0.220865i	$-0.929112\pi$
$853$	−3.53583e10	−1.95061	−0.975304	+	0.220865i	$0.929112\pi$
$854$	1.28394e8	0.00705413
$855$	−5.58974e9	−0.305851
$856$	8.37869e9	0.456581
$857$	−7.75588e9	−0.420919	−0.210459	−	0.977603i	$-0.567496\pi$
$857$	−7.75588e9	−0.420919	−0.210459	+	0.977603i	$0.567496\pi$
$858$	−4.62520e8	−0.0249991
$859$	2.62466e10	1.41285	0.706427	−	0.707786i	$-0.250306\pi$
$859$	2.62466e10	1.41285	0.706427	+	0.707786i	$0.250306\pi$
$860$	−2.58717e9	−0.138701
$861$	4.69076e9	0.250456
$862$	6.34996e9	0.337672
$863$	8.24013e8	0.0436412	0.0218206	−	0.999762i	$-0.493054\pi$
$863$	8.24013e8	0.0436412	0.0218206	+	0.999762i	$0.493054\pi$
$864$	−6.44973e8	−0.0340207
$865$	6.81324e9	0.357929
$866$	−8.45016e8	−0.0442132
$867$	1.02141e10	0.532272
$868$	−1.89364e9	−0.0982830
$869$	−2.70914e9	−0.140043
$870$	4.80980e9	0.247634
$871$	−1.69455e9	−0.0868944
$872$	6.50687e9	0.332326
$873$	−5.25002e9	−0.267061
$874$	7.97472e9	0.404041
$875$	1.72354e10	0.869745
$876$	−2.62186e9	−0.131778
$877$	−2.28657e10	−1.14468	−0.572342	−	0.820015i	$-0.693965\pi$
$877$	−2.28657e10	−1.14468	−0.572342	+	0.820015i	$0.693965\pi$
$878$	−2.63379e10	−1.31326
$879$	2.28671e8	0.0113566
$880$	2.01844e9	0.0998450
$881$	−3.19129e10	−1.57236	−0.786178	−	0.618000i	$-0.787943\pi$
$881$	−3.19129e10	−1.57236	−0.786178	+	0.618000i	$0.787943\pi$
$882$	6.86129e8	0.0336718
$883$	3.33372e10	1.62955	0.814774	−	0.579779i	$-0.196861\pi$
$883$	3.33372e10	1.62955	0.814774	+	0.579779i	$0.196861\pi$
$884$	7.95879e8	0.0387493
$885$	−3.35561e10	−1.62731
$886$	−1.47341e10	−0.711715
$887$	−3.95761e10	−1.90415	−0.952073	−	0.305872i	$-0.901052\pi$
$887$	−3.95761e10	−1.90415	−0.952073	+	0.305872i	$0.901052\pi$
$888$	5.92994e9	0.284188
$889$	1.23904e10	0.591465
$890$	−1.88565e10	−0.896594
$891$	−5.17966e8	−0.0245318
$892$	−2.22170e9	−0.104811
$893$	1.38193e9	0.0649390
$894$	−5.61764e9	−0.262950
$895$	2.03119e10	0.947044
$896$	−7.19323e8	−0.0334077
$897$	3.89910e9	0.180381
$898$	1.22045e10	0.562411
$899$	3.79916e9	0.174393
$900$	8.28186e9	0.378686
$901$	−4.86208e9	−0.221455
$902$	−3.94931e9	−0.179184
$903$	7.40446e8	0.0334646
$904$	−6.06643e9	−0.273114
$905$	4.89154e10	2.19369
$906$	−1.20353e10	−0.537661
$907$	−1.06912e10	−0.475773	−0.237886	−	0.971293i	$-0.576455\pi$
$907$	−1.06912e10	−0.475773	−0.237886	+	0.971293i	$0.576455\pi$
$908$	−6.36697e9	−0.282249
$909$	−1.31845e10	−0.582224
$910$	−3.04806e9	−0.134085
$911$	−9.80586e9	−0.429706	−0.214853	−	0.976646i	$-0.568927\pi$
$911$	−9.80586e9	−0.429706	−0.214853	+	0.976646i	$0.568927\pi$
$912$	−1.67718e9	−0.0732144
$913$	−1.76225e9	−0.0766336
$914$	4.35006e9	0.188444
$915$	−6.38756e8	−0.0275652
$916$	8.71904e8	0.0374830
$917$	6.40019e9	0.274094
$918$	8.91289e8	0.0380250
$919$	4.41172e10	1.87501	0.937506	−	0.347970i	$-0.113129\pi$
$919$	4.41172e10	1.87501	0.937506	+	0.347970i	$0.113129\pi$
$920$	−1.70157e10	−0.720432
$921$	2.14833e10	0.906136
$922$	−1.61292e10	−0.677725
$923$	−8.37396e8	−0.0350530
$924$	−5.77676e8	−0.0240898
$925$	−7.61443e10	−3.16331
$926$	1.68771e10	0.698488
$927$	−1.34534e10	−0.554692
$928$	1.44316e9	0.0592784
$929$	2.93273e9	0.120010	0.0600050	−	0.998198i	$-0.480888\pi$
$929$	2.93273e9	0.120010	0.0600050	+	0.998198i	$0.480888\pi$
$930$	9.42077e9	0.384057
$931$	1.78420e9	0.0724635
$932$	2.29214e10	0.927440
$933$	−1.89282e10	−0.762998
$934$	−1.50012e10	−0.602437
$935$	−2.78929e9	−0.111597
$936$	−8.20026e8	−0.0326860
$937$	−3.65235e10	−1.45039	−0.725193	−	0.688546i	$-0.758250\pi$
$937$	−3.65235e10	−1.45039	−0.725193	+	0.688546i	$0.758250\pi$
$938$	−2.11646e9	−0.0837335
$939$	1.59187e10	0.627448
$940$	−2.94863e9	−0.115790
$941$	4.53786e10	1.77537	0.887683	−	0.460455i	$-0.152314\pi$
$941$	4.53786e10	1.77537	0.887683	+	0.460455i	$0.152314\pi$
$942$	−1.25739e10	−0.490108
$943$	3.32932e10	1.29290
$944$	−1.00684e10	−0.389544
$945$	−3.41346e9	−0.131578
$946$	−6.23407e8	−0.0239416
$947$	2.59610e10	0.993338	0.496669	−	0.867940i	$-0.334556\pi$
$947$	2.59610e10	0.993338	0.496669	+	0.867940i	$0.334556\pi$
$948$	−4.80318e9	−0.183105
$949$	−3.33346e9	−0.126609
$950$	2.15360e10	0.814953
$951$	−3.06018e9	−0.115376
$952$	9.94034e8	0.0373398
$953$	−3.90857e10	−1.46283	−0.731414	−	0.681934i	$-0.761139\pi$
$953$	−3.90857e10	−1.46283	−0.731414	+	0.681934i	$0.761139\pi$
$954$	5.00959e9	0.186803
$955$	3.10195e10	1.15245
$956$	9.33167e9	0.345428
$957$	1.15898e9	0.0427447
$958$	2.89393e8	0.0106343
$959$	−3.90267e9	−0.142888
$960$	3.57860e9	0.130546
$961$	−2.00713e10	−0.729533
$962$	7.53940e9	0.273039
$963$	1.19298e10	0.430469
$964$	−1.02353e10	−0.367987
$965$	3.24634e10	1.16292
$966$	4.86988e9	0.173820
$967$	2.11853e10	0.753429	0.376715	−	0.926329i	$-0.377054\pi$
$967$	2.11853e10	0.753429	0.376715	+	0.926329i	$0.377054\pi$
$968$	−9.49107e9	−0.336319
$969$	2.31769e9	0.0818319
$970$	2.91295e10	1.02478
$971$	−2.09826e10	−0.735517	−0.367758	−	0.929921i	$-0.619875\pi$
$971$	−2.09826e10	−0.735517	−0.367758	+	0.929921i	$0.619875\pi$
$972$	−9.18330e8	−0.0320750
$973$	1.49416e10	0.519997
$974$	−8.17884e9	−0.283619
$975$	1.05297e10	0.363830
$976$	−1.91656e8	−0.00659854
$977$	−3.18014e10	−1.09098	−0.545488	−	0.838118i	$-0.683656\pi$
$977$	−3.18014e10	−1.09098	−0.545488	+	0.838118i	$0.683656\pi$
$978$	1.26374e10	0.431989
$979$	−4.54368e9	−0.154764
$980$	−3.80695e9	−0.129207
$981$	9.26466e9	0.313320
$982$	−2.61405e10	−0.880893
$983$	4.32852e9	0.145346	0.0726728	−	0.997356i	$-0.476847\pi$
$983$	4.32852e9	0.145346	0.0726728	+	0.997356i	$0.476847\pi$
$984$	−7.00195e9	−0.234280
$985$	−3.10979e10	−1.03682
$986$	−1.99430e9	−0.0662555
$987$	8.43896e8	0.0279369
$988$	−2.13238e9	−0.0703421
$989$	5.25540e9	0.172750
$990$	2.87391e9	0.0941348
$991$	−3.54394e10	−1.15672	−0.578360	−	0.815782i	$-0.696307\pi$
$991$	−3.54394e10	−1.15672	−0.578360	+	0.815782i	$0.696307\pi$
$992$	2.82666e9	0.0919353
$993$	−1.43935e9	−0.0466491
$994$	−1.04589e9	−0.0337779
$995$	3.90973e10	1.25825
$996$	−3.12438e9	−0.100197
$997$	−3.65554e10	−1.16820	−0.584102	−	0.811680i	$-0.698553\pi$
$997$	−3.65554e10	−1.16820	−0.584102	+	0.811680i	$0.698553\pi$
$998$	−4.08201e10	−1.29992
$999$	8.44322e9	0.267935

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.l.1.1	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	546.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -505.603 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -505.603 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -4044.82 q^{10} -974.645 q^{11} -1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +13651.3 q^{15} +4096.00 q^{16} -5660.27 q^{17} +5832.00 q^{18} +15165.4 q^{19} -32358.6 q^{20} +9261.00 q^{21} -7797.16 q^{22} +65731.1 q^{23} -13824.0 q^{24} +177509. q^{25} -17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +44041.7 q^{29} +109210. q^{30} +86262.8 q^{31} +32768.0 q^{32} +26315.4 q^{33} -45282.2 q^{34} +173422. q^{35} +46656.0 q^{36} -428960. q^{37} +121323. q^{38} +59319.0 q^{39} -258869. q^{40} +506507. q^{41} +74088.0 q^{42} +79953.1 q^{43} -62377.3 q^{44} -368584. q^{45} +525849. q^{46} +91123.6 q^{47} -110592. q^{48} +117649. q^{49} +1.42007e6 q^{50} +152827. q^{51} -140608. q^{52} +858983. q^{53} -157464. q^{54} +492783. q^{55} -175616. q^{56} -409467. q^{57} +352334. q^{58} -2.45810e6 q^{59} +873681. q^{60} -46791.0 q^{61} +690102. q^{62} -250047. q^{63} +262144. q^{64} +1.11081e6 q^{65} +210523. q^{66} +771304. q^{67} -362257. q^{68} -1.77474e6 q^{69} +1.38737e6 q^{70} +381154. q^{71} +373248. q^{72} +1.51728e6 q^{73} -3.43168e6 q^{74} -4.79274e6 q^{75} +970588. q^{76} +334303. q^{77} +474552. q^{78} +2.77962e6 q^{79} -2.07095e6 q^{80} +531441. q^{81} +4.05205e6 q^{82} +1.80809e6 q^{83} +592704. q^{84} +2.86185e6 q^{85} +639625. q^{86} -1.18913e6 q^{87} -499018. q^{88} +4.66189e6 q^{89} -2.94867e6 q^{90} +753571. q^{91} +4.20679e6 q^{92} -2.32909e6 q^{93} +728989. q^{94} -7.66768e6 q^{95} -884736. q^{96} -7.20167e6 q^{97} +941192. q^{98} -710516. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) \) 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9} - 2000 q^{10} + 659 q^{11} - 8640 q^{12} - 10985 q^{13} - 13720 q^{14} + 6750 q^{15} + 20480 q^{16} + 24575 q^{17} + 29160 q^{18} - 6446 q^{19} - 16000 q^{20} + 46305 q^{21} + 5272 q^{22} + 30268 q^{23} - 69120 q^{24} + 38965 q^{25} - 87880 q^{26} - 98415 q^{27} - 109760 q^{28} + 130950 q^{29} + 54000 q^{30} + 262979 q^{31} + 163840 q^{32} - 17793 q^{33} + 196600 q^{34} + 85750 q^{35} + 233280 q^{36} - 101549 q^{37} - 51568 q^{38} + 296595 q^{39} - 128000 q^{40} - 247328 q^{41} + 370440 q^{42} - 19092 q^{43} + 42176 q^{44} - 182250 q^{45} + 242144 q^{46} - 126419 q^{47} - 552960 q^{48} + 588245 q^{49} + 311720 q^{50} - 663525 q^{51} - 703040 q^{52} - 302793 q^{53} - 787320 q^{54} + 943985 q^{55} - 878080 q^{56} + 174042 q^{57} + 1047600 q^{58} - 2798636 q^{59} + 432000 q^{60} - 2493751 q^{61} + 2103832 q^{62} - 1250235 q^{63} + 1310720 q^{64} + 549250 q^{65} - 142344 q^{66} + 160188 q^{67} + 1572800 q^{68} - 817236 q^{69} + 686000 q^{70} + 3846088 q^{71} + 1866240 q^{72} + 5655872 q^{73} - 812392 q^{74} - 1052055 q^{75} - 412544 q^{76} - 226037 q^{77} + 2372760 q^{78} + 5647991 q^{79} - 1024000 q^{80} + 2657205 q^{81} - 1978624 q^{82} - 4607669 q^{83} + 2963520 q^{84} + 3873935 q^{85} - 152736 q^{86} - 3535650 q^{87} + 337408 q^{88} - 17424029 q^{89} - 1458000 q^{90} + 3767855 q^{91} + 1937152 q^{92} - 7100433 q^{93} - 1011352 q^{94} - 24593720 q^{95} - 4423680 q^{96} - 18380577 q^{97} + 4705960 q^{98} + 480411 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9 - 2000 * q^10 + 659 * q^11 - 8640 * q^12 - 10985 * q^13 - 13720 * q^14 + 6750 * q^15 + 20480 * q^16 + 24575 * q^17 + 29160 * q^18 - 6446 * q^19 - 16000 * q^20 + 46305 * q^21 + 5272 * q^22 + 30268 * q^23 - 69120 * q^24 + 38965 * q^25 - 87880 * q^26 - 98415 * q^27 - 109760 * q^28 + 130950 * q^29 + 54000 * q^30 + 262979 * q^31 + 163840 * q^32 - 17793 * q^33 + 196600 * q^34 + 85750 * q^35 + 233280 * q^36 - 101549 * q^37 - 51568 * q^38 + 296595 * q^39 - 128000 * q^40 - 247328 * q^41 + 370440 * q^42 - 19092 * q^43 + 42176 * q^44 - 182250 * q^45 + 242144 * q^46 - 126419 * q^47 - 552960 * q^48 + 588245 * q^49 + 311720 * q^50 - 663525 * q^51 - 703040 * q^52 - 302793 * q^53 - 787320 * q^54 + 943985 * q^55 - 878080 * q^56 + 174042 * q^57 + 1047600 * q^58 - 2798636 * q^59 + 432000 * q^60 - 2493751 * q^61 + 2103832 * q^62 - 1250235 * q^63 + 1310720 * q^64 + 549250 * q^65 - 142344 * q^66 + 160188 * q^67 + 1572800 * q^68 - 817236 * q^69 + 686000 * q^70 + 3846088 * q^71 + 1866240 * q^72 + 5655872 * q^73 - 812392 * q^74 - 1052055 * q^75 - 412544 * q^76 - 226037 * q^77 + 2372760 * q^78 + 5647991 * q^79 - 1024000 * q^80 + 2657205 * q^81 - 1978624 * q^82 - 4607669 * q^83 + 2963520 * q^84 + 3873935 * q^85 - 152736 * q^86 - 3535650 * q^87 + 337408 * q^88 - 17424029 * q^89 - 1458000 * q^90 + 3767855 * q^91 + 1937152 * q^92 - 7100433 * q^93 - 1011352 * q^94 - 24593720 * q^95 - 4423680 * q^96 - 18380577 * q^97 + 4705960 * q^98 + 480411 * q^99

Introduction

L-functions

Modular forms

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