LMFDB - Embedded newform 285.10.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,10,Mod(1,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("285.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	285.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:	$146.785213307$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 6356 x^{13} + 18436 x^{12} + 15858707 x^{11} - 49616078 x^{10} + \cdots + 15\!\cdots\!00 $ x^15 - 2x^14 - 6356x^13 + 18436x^12 + 15858707x^11 - 49616078x^10 - 19804799606x^9 + 51117957936x^8 + 13077899446663x^7 - 17762605232062x^6 - 4369460380063800x^5 - 1105301955330540x^4 + 617735239298795077x^3 + 844341253042208334x^2 - 21881601450607548510x + 15712212684310961400
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{6}\cdot 5^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$35.4527$ of defining polynomial
Character	$\chi$	$=$	285.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-36.4527 q^{2} -81.0000 q^{3} +816.797 q^{4} +625.000 q^{5} +2952.67 q^{6} -11814.3 q^{7} -11110.7 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-36.4527 q^{2} -81.0000 q^{3} +816.797 q^{4} +625.000 q^{5} +2952.67 q^{6} -11814.3 q^{7} -11110.7 q^{8} +6561.00 q^{9} -22782.9 q^{10} +95589.9 q^{11} -66160.6 q^{12} -16869.7 q^{13} +430665. q^{14} -50625.0 q^{15} -13186.5 q^{16} +183092. q^{17} -239166. q^{18} -130321. q^{19} +510498. q^{20} +956962. q^{21} -3.48451e6 q^{22} +1.48749e6 q^{23} +899964. q^{24} +390625. q^{25} +614947. q^{26} -531441. q^{27} -9.64993e6 q^{28} -333392. q^{29} +1.84542e6 q^{30} +3.14101e6 q^{31} +6.16935e6 q^{32} -7.74278e6 q^{33} -6.67419e6 q^{34} -7.38397e6 q^{35} +5.35901e6 q^{36} -3.83858e6 q^{37} +4.75055e6 q^{38} +1.36645e6 q^{39} -6.94417e6 q^{40} +3.26699e7 q^{41} -3.48838e7 q^{42} -5.89049e6 q^{43} +7.80775e7 q^{44} +4.10062e6 q^{45} -5.42230e7 q^{46} +3.30808e7 q^{47} +1.06811e6 q^{48} +9.92252e7 q^{49} -1.42393e7 q^{50} -1.48305e7 q^{51} -1.37792e7 q^{52} +2.12523e7 q^{53} +1.93724e7 q^{54} +5.97437e7 q^{55} +1.31265e8 q^{56} +1.05560e7 q^{57} +1.21530e7 q^{58} +6.11382e7 q^{59} -4.13504e7 q^{60} +7.35751e7 q^{61} -1.14498e8 q^{62} -7.75139e7 q^{63} -2.18138e8 q^{64} -1.05436e7 q^{65} +2.82245e8 q^{66} -1.46320e8 q^{67} +1.49549e8 q^{68} -1.20487e8 q^{69} +2.69165e8 q^{70} -1.26674e7 q^{71} -7.28971e7 q^{72} -2.02563e8 q^{73} +1.39927e8 q^{74} -3.16406e7 q^{75} -1.06446e8 q^{76} -1.12933e9 q^{77} -4.98107e7 q^{78} -3.71959e7 q^{79} -8.24158e6 q^{80} +4.30467e7 q^{81} -1.19091e9 q^{82} +4.23153e8 q^{83} +7.81644e8 q^{84} +1.14433e8 q^{85} +2.14724e8 q^{86} +2.70047e7 q^{87} -1.06207e9 q^{88} -8.04541e8 q^{89} -1.49479e8 q^{90} +1.99305e8 q^{91} +1.21498e9 q^{92} -2.54422e8 q^{93} -1.20589e9 q^{94} -8.14506e7 q^{95} -4.99717e8 q^{96} -8.98574e8 q^{97} -3.61702e9 q^{98} +6.27165e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) $ 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9} - 10625 q^{10} + 138230 q^{11} - 409455 q^{12} - 176712 q^{13} - 555994 q^{14} - 759375 q^{15} + 1695731 q^{16} - 274992 q^{17} - 111537 q^{18} - 1954815 q^{19} + 3159375 q^{20} - 109512 q^{21} - 1031106 q^{22} + 1714212 q^{23} + 291357 q^{24} + 5859375 q^{25} + 9500004 q^{26} - 7971615 q^{27} + 14545598 q^{28} + 1754340 q^{29} + 860625 q^{30} + 8442914 q^{31} + 35638859 q^{32} - 11196630 q^{33} + 47218266 q^{34} + 845000 q^{35} + 33165855 q^{36} + 2956096 q^{37} + 2215457 q^{38} + 14313672 q^{39} - 2248125 q^{40} - 38550502 q^{41} + 45035514 q^{42} + 50753570 q^{43} + 212125630 q^{44} + 61509375 q^{45} - 117130008 q^{46} - 40252876 q^{47} - 137354211 q^{48} + 110123035 q^{49} - 6640625 q^{50} + 22274352 q^{51} - 87136648 q^{52} + 65532542 q^{53} + 9034497 q^{54} + 86393750 q^{55} - 377288898 q^{56} + 158340015 q^{57} + 211630876 q^{58} + 175407418 q^{59} - 255909375 q^{60} + 151231854 q^{61} - 30983940 q^{62} + 8870472 q^{63} + 836879575 q^{64} - 110445000 q^{65} + 83519586 q^{66} + 40009476 q^{67} - 124850430 q^{68} - 138851172 q^{69} - 347496250 q^{70} + 87578500 q^{71} - 23599917 q^{72} - 360657638 q^{73} + 1373397084 q^{74} - 474609375 q^{75} - 658772655 q^{76} - 304618172 q^{77} - 769500324 q^{78} + 205798286 q^{79} + 1059831875 q^{80} + 645700815 q^{81} - 2327138772 q^{82} - 63321462 q^{83} - 1178193438 q^{84} - 171870000 q^{85} - 848405762 q^{86} - 142101540 q^{87} - 3211126502 q^{88} - 381069174 q^{89} - 69710625 q^{90} + 1476892872 q^{91} - 2382818588 q^{92} - 683876034 q^{93} - 5137318040 q^{94} - 1221759375 q^{95} - 2886747579 q^{96} - 3915268828 q^{97} - 8273557437 q^{98} + 906927030 q^{99}+O(q^{100}) \) 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9 - 10625 * q^10 + 138230 * q^11 - 409455 * q^12 - 176712 * q^13 - 555994 * q^14 - 759375 * q^15 + 1695731 * q^16 - 274992 * q^17 - 111537 * q^18 - 1954815 * q^19 + 3159375 * q^20 - 109512 * q^21 - 1031106 * q^22 + 1714212 * q^23 + 291357 * q^24 + 5859375 * q^25 + 9500004 * q^26 - 7971615 * q^27 + 14545598 * q^28 + 1754340 * q^29 + 860625 * q^30 + 8442914 * q^31 + 35638859 * q^32 - 11196630 * q^33 + 47218266 * q^34 + 845000 * q^35 + 33165855 * q^36 + 2956096 * q^37 + 2215457 * q^38 + 14313672 * q^39 - 2248125 * q^40 - 38550502 * q^41 + 45035514 * q^42 + 50753570 * q^43 + 212125630 * q^44 + 61509375 * q^45 - 117130008 * q^46 - 40252876 * q^47 - 137354211 * q^48 + 110123035 * q^49 - 6640625 * q^50 + 22274352 * q^51 - 87136648 * q^52 + 65532542 * q^53 + 9034497 * q^54 + 86393750 * q^55 - 377288898 * q^56 + 158340015 * q^57 + 211630876 * q^58 + 175407418 * q^59 - 255909375 * q^60 + 151231854 * q^61 - 30983940 * q^62 + 8870472 * q^63 + 836879575 * q^64 - 110445000 * q^65 + 83519586 * q^66 + 40009476 * q^67 - 124850430 * q^68 - 138851172 * q^69 - 347496250 * q^70 + 87578500 * q^71 - 23599917 * q^72 - 360657638 * q^73 + 1373397084 * q^74 - 474609375 * q^75 - 658772655 * q^76 - 304618172 * q^77 - 769500324 * q^78 + 205798286 * q^79 + 1059831875 * q^80 + 645700815 * q^81 - 2327138772 * q^82 - 63321462 * q^83 - 1178193438 * q^84 - 171870000 * q^85 - 848405762 * q^86 - 142101540 * q^87 - 3211126502 * q^88 - 381069174 * q^89 - 69710625 * q^90 + 1476892872 * q^91 - 2382818588 * q^92 - 683876034 * q^93 - 5137318040 * q^94 - 1221759375 * q^95 - 2886747579 * q^96 - 3915268828 * q^97 - 8273557437 * q^98 + 906927030 * 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 $

$2$	−36.4527	−1.61100	−0.805498	−	0.592599i	$-0.798102\pi$
$2$	−36.4527	−1.61100	−0.805498	+	0.592599i	$0.798102\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	816.797	1.59531
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	2952.67	0.930109
$7$	−11814.3	−1.85981	−0.929905	−	0.367800i	$-0.880111\pi$
$7$	−11814.3	−1.85981	−0.929905	+	0.367800i	$0.880111\pi$
$8$	−11110.7	−0.959037
$9$	6561.00	0.333333
$10$	−22782.9	−0.720459
$11$	95589.9	1.96854	0.984271	−	0.176664i	$-0.0565306\pi$
$11$	95589.9	1.96854	0.984271	+	0.176664i	$0.0565306\pi$
$12$	−66160.6	−0.921051
$13$	−16869.7	−0.163819	−0.0819093	−	0.996640i	$-0.526102\pi$
$13$	−16869.7	−0.163819	−0.0819093	+	0.996640i	$0.526102\pi$
$14$	430665.	2.99615
$15$	−50625.0	−0.258199
$16$	−13186.5	−0.0503026
$17$	183092.	0.531679	0.265839	−	0.964017i	$-0.414351\pi$
$17$	183092.	0.531679	0.265839	+	0.964017i	$0.414351\pi$
$18$	−239166.	−0.536999
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	510498.	0.713443
$21$	956962.	1.07376
$22$	−3.48451e6	−3.17131
$23$	1.48749e6	1.10835	0.554177	−	0.832399i	$-0.313033\pi$
$23$	1.48749e6	1.10835	0.554177	+	0.832399i	$0.313033\pi$
$24$	899964.	0.553700
$25$	390625.	0.200000
$26$	614947.	0.263911
$27$	−531441.	−0.192450
$28$	−9.64993e6	−2.96697
$29$	−333392.	−0.0875314	−0.0437657	−	0.999042i	$-0.513936\pi$
$29$	−333392.	−0.0875314	−0.0437657	+	0.999042i	$0.513936\pi$
$30$	1.84542e6	0.415957
$31$	3.14101e6	0.610860	0.305430	−	0.952215i	$-0.401200\pi$
$31$	3.14101e6	0.610860	0.305430	+	0.952215i	$0.401200\pi$
$32$	6.16935e6	1.04007
$33$	−7.74278e6	−1.13654
$34$	−6.67419e6	−0.856532
$35$	−7.38397e6	−0.831732
$36$	5.35901e6	0.531769
$37$	−3.83858e6	−0.336716	−0.168358	−	0.985726i	$-0.553846\pi$
$37$	−3.83858e6	−0.336716	−0.168358	+	0.985726i	$0.553846\pi$
$38$	4.75055e6	0.369588
$39$	1.36645e6	0.0945808
$40$	−6.94417e6	−0.428894
$41$	3.26699e7	1.80560	0.902798	−	0.430065i	$-0.141509\pi$
$41$	3.26699e7	1.80560	0.902798	+	0.430065i	$0.141509\pi$
$42$	−3.48838e7	−1.72983
$43$	−5.89049e6	−0.262751	−0.131375	−	0.991333i	$-0.541939\pi$
$43$	−5.89049e6	−0.262751	−0.131375	+	0.991333i	$0.541939\pi$
$44$	7.80775e7	3.14043
$45$	4.10062e6	0.149071
$46$	−5.42230e7	−1.78555
$47$	3.30808e7	0.988863	0.494432	−	0.869217i	$-0.335376\pi$
$47$	3.30808e7	0.988863	0.494432	+	0.869217i	$0.335376\pi$
$48$	1.06811e6	0.0290422
$49$	9.92252e7	2.45889
$50$	−1.42393e7	−0.322199
$51$	−1.48305e7	−0.306965
$52$	−1.37792e7	−0.261341
$53$	2.12523e7	0.369969	0.184984	−	0.982741i	$-0.440777\pi$
$53$	2.12523e7	0.369969	0.184984	+	0.982741i	$0.440777\pi$
$54$	1.93724e7	0.310036
$55$	5.97437e7	0.880359
$56$	1.31265e8	1.78363
$57$	1.05560e7	0.132453
$58$	1.21530e7	0.141013
$59$	6.11382e7	0.656869	0.328434	−	0.944527i	$-0.393479\pi$
$59$	6.11382e7	0.656869	0.328434	+	0.944527i	$0.393479\pi$
$60$	−4.13504e7	−0.411906
$61$	7.35751e7	0.680372	0.340186	−	0.940358i	$-0.389510\pi$
$61$	7.35751e7	0.680372	0.340186	+	0.940358i	$0.389510\pi$
$62$	−1.14498e8	−0.984093
$63$	−7.75139e7	−0.619937
$64$	−2.18138e8	−1.62525
$65$	−1.05436e7	−0.0732619
$66$	2.82245e8	1.83096
$67$	−1.46320e8	−0.887088	−0.443544	−	0.896253i	$-0.646279\pi$
$67$	−1.46320e8	−0.887088	−0.443544	+	0.896253i	$0.646279\pi$
$68$	1.49549e8	0.848191
$69$	−1.20487e8	−0.639909
$70$	2.69165e8	1.33992
$71$	−1.26674e7	−0.0591596	−0.0295798	−	0.999562i	$-0.509417\pi$
$71$	−1.26674e7	−0.0591596	−0.0295798	+	0.999562i	$0.509417\pi$
$72$	−7.28971e7	−0.319679
$73$	−2.02563e8	−0.834848	−0.417424	−	0.908712i	$-0.637067\pi$
$73$	−2.02563e8	−0.834848	−0.417424	+	0.908712i	$0.637067\pi$
$74$	1.39927e8	0.542447
$75$	−3.16406e7	−0.115470
$76$	−1.06446e8	−0.365989
$77$	−1.12933e9	−3.66111
$78$	−4.98107e7	−0.152369
$79$	−3.71959e7	−0.107442	−0.0537208	−	0.998556i	$-0.517108\pi$
$79$	−3.71959e7	−0.107442	−0.0537208	+	0.998556i	$0.517108\pi$
$80$	−8.24158e6	−0.0224960
$81$	4.30467e7	0.111111
$82$	−1.19091e9	−2.90881
$83$	4.23153e8	0.978691	0.489345	−	0.872090i	$-0.337236\pi$
$83$	4.23153e8	0.978691	0.489345	+	0.872090i	$0.337236\pi$
$84$	7.81644e8	1.71298
$85$	1.14433e8	0.237774
$86$	2.14724e8	0.423290
$87$	2.70047e7	0.0505363
$88$	−1.06207e9	−1.88790
$89$	−8.04541e8	−1.35923	−0.679615	−	0.733569i	$-0.737853\pi$
$89$	−8.04541e8	−1.35923	−0.679615	+	0.733569i	$0.737853\pi$
$90$	−1.49479e8	−0.240153
$91$	1.99305e8	0.304672
$92$	1.21498e9	1.76817
$93$	−2.54422e8	−0.352680
$94$	−1.20589e9	−1.59305
$95$	−8.14506e7	−0.102598
$96$	−4.99717e8	−0.600487
$97$	−8.98574e8	−1.03058	−0.515289	−	0.857016i	$-0.672315\pi$
$97$	−8.98574e8	−1.03058	−0.515289	+	0.857016i	$0.672315\pi$
$98$	−3.61702e9	−3.96127
$99$	6.27165e8	0.656181
$100$	3.19061e8	0.319061
$101$	−2.00161e9	−1.91397	−0.956983	−	0.290145i	$-0.906296\pi$
$101$	−2.00161e9	−1.91397	−0.956983	+	0.290145i	$0.906296\pi$
$102$	5.40610e8	0.494519
$103$	−9.67875e8	−0.847329	−0.423664	−	0.905819i	$-0.639256\pi$
$103$	−9.67875e8	−0.847329	−0.423664	+	0.905819i	$0.639256\pi$
$104$	1.87434e8	0.157108
$105$	5.98101e8	0.480201
$106$	−7.74703e8	−0.596018
$107$	−2.09963e8	−0.154852	−0.0774259	−	0.996998i	$-0.524670\pi$
$107$	−2.09963e8	−0.154852	−0.0774259	+	0.996998i	$0.524670\pi$
$108$	−4.34080e8	−0.307017
$109$	2.42438e9	1.64506	0.822530	−	0.568722i	$-0.192562\pi$
$109$	2.42438e9	1.64506	0.822530	+	0.568722i	$0.192562\pi$
$110$	−2.17782e9	−1.41825
$111$	3.10925e8	0.194403
$112$	1.55790e8	0.0935533
$113$	−7.93268e8	−0.457685	−0.228843	−	0.973463i	$-0.573494\pi$
$113$	−7.93268e8	−0.457685	−0.228843	+	0.973463i	$0.573494\pi$
$114$	−3.84794e8	−0.213382
$115$	9.29681e8	0.495671
$116$	−2.72314e8	−0.139640
$117$	−1.10682e8	−0.0546062
$118$	−2.22865e9	−1.05821
$119$	−2.16311e9	−0.988821
$120$	5.62478e8	0.247622
$121$	6.77948e9	2.87516
$122$	−2.68201e9	−1.09608
$123$	−2.64626e9	−1.04246
$124$	2.56557e9	0.974509
$125$	2.44141e8	0.0894427
$126$	2.82559e9	0.998715
$127$	−5.57932e9	−1.90311	−0.951557	−	0.307473i	$-0.900516\pi$
$127$	−5.57932e9	−1.90311	−0.951557	+	0.307473i	$0.900516\pi$
$128$	4.79300e9	1.57820
$129$	4.77130e8	0.151699
$130$	3.84342e8	0.118025
$131$	1.83158e9	0.543382	0.271691	−	0.962385i	$-0.412417\pi$
$131$	1.83158e9	0.543382	0.271691	+	0.962385i	$0.412417\pi$
$132$	−6.32428e9	−1.81313
$133$	1.53966e9	0.426670
$134$	5.33375e9	1.42910
$135$	−3.32151e8	−0.0860663
$136$	−2.03428e9	−0.509900
$137$	6.06976e9	1.47207	0.736036	−	0.676942i	$-0.236695\pi$
$137$	6.06976e9	1.47207	0.736036	+	0.676942i	$0.236695\pi$
$138$	4.39206e9	1.03089
$139$	1.77154e9	0.402518	0.201259	−	0.979538i	$-0.435497\pi$
$139$	1.77154e9	0.402518	0.201259	+	0.979538i	$0.435497\pi$
$140$	−6.03120e9	−1.32687
$141$	−2.67955e9	−0.570920
$142$	4.61761e8	0.0953058
$143$	−1.61258e9	−0.322484
$144$	−8.65168e7	−0.0167675
$145$	−2.08370e8	−0.0391452
$146$	7.38396e9	1.34494
$147$	−8.03724e9	−1.41964
$148$	−3.13534e9	−0.537165
$149$	−5.52837e9	−0.918881	−0.459440	−	0.888209i	$-0.651950\pi$
$149$	−5.52837e9	−0.918881	−0.459440	+	0.888209i	$0.651950\pi$
$150$	1.15339e9	0.186022
$151$	−3.54304e9	−0.554600	−0.277300	−	0.960783i	$-0.589440\pi$
$151$	−3.54304e9	−0.554600	−0.277300	+	0.960783i	$0.589440\pi$
$152$	1.44795e9	0.220018
$153$	1.20127e9	0.177226
$154$	4.11672e10	5.89804
$155$	1.96313e9	0.273185
$156$	1.11611e9	0.150885
$157$	−9.11253e9	−1.19699	−0.598495	−	0.801127i	$-0.704234\pi$
$157$	−9.11253e9	−1.19699	−0.598495	+	0.801127i	$0.704234\pi$
$158$	1.35589e9	0.173088
$159$	−1.72144e9	−0.213601
$160$	3.85584e9	0.465135
$161$	−1.75737e10	−2.06133
$162$	−1.56917e9	−0.179000
$163$	9.95252e9	1.10430	0.552152	−	0.833743i	$-0.313807\pi$
$163$	9.95252e9	1.10430	0.552152	+	0.833743i	$0.313807\pi$
$164$	2.66847e10	2.88048
$165$	−4.83924e9	−0.508275
$166$	−1.54250e10	−1.57667
$167$	3.44151e9	0.342393	0.171196	−	0.985237i	$-0.445237\pi$
$167$	3.44151e9	0.342393	0.171196	+	0.985237i	$0.445237\pi$
$168$	−1.06325e10	−1.02978
$169$	−1.03199e10	−0.973163
$170$	−4.17137e9	−0.383053
$171$	−8.55036e8	−0.0764719
$172$	−4.81134e9	−0.419168
$173$	−1.01528e10	−0.861740	−0.430870	−	0.902414i	$-0.641793\pi$
$173$	−1.01528e10	−0.861740	−0.430870	+	0.902414i	$0.641793\pi$
$174$	−9.84395e8	−0.0814138
$175$	−4.61498e9	−0.371962
$176$	−1.26050e9	−0.0990228
$177$	−4.95219e9	−0.379243
$178$	2.93277e10	2.18971
$179$	−2.04080e9	−0.148580	−0.0742902	−	0.997237i	$-0.523669\pi$
$179$	−2.04080e9	−0.148580	−0.0742902	+	0.997237i	$0.523669\pi$
$180$	3.34938e9	0.237814
$181$	2.27691e10	1.57686	0.788429	−	0.615125i	$-0.210895\pi$
$181$	2.27691e10	1.57686	0.788429	+	0.615125i	$0.210895\pi$
$182$	−7.26520e9	−0.490825
$183$	−5.95958e9	−0.392813
$184$	−1.65270e10	−1.06295
$185$	−2.39911e9	−0.150584
$186$	9.27435e9	0.568166
$187$	1.75017e10	1.04663
$188$	2.70203e10	1.57754
$189$	6.27863e9	0.357921
$190$	2.96909e9	0.165285
$191$	−8.58891e9	−0.466969	−0.233484	−	0.972361i	$-0.575013\pi$
$191$	−8.58891e9	−0.466969	−0.233484	+	0.972361i	$0.575013\pi$
$192$	1.76692e10	0.938340
$193$	8.46339e9	0.439073	0.219536	−	0.975604i	$-0.429546\pi$
$193$	8.46339e9	0.439073	0.219536	+	0.975604i	$0.429546\pi$
$194$	3.27554e10	1.66026
$195$	8.54031e8	0.0422978
$196$	8.10469e10	3.92269
$197$	2.39929e10	1.13497	0.567485	−	0.823384i	$-0.307917\pi$
$197$	2.39929e10	1.13497	0.567485	+	0.823384i	$0.307917\pi$
$198$	−2.28618e10	−1.05710
$199$	−2.64999e10	−1.19786	−0.598930	−	0.800802i	$-0.704407\pi$
$199$	−2.64999e10	−1.19786	−0.598930	+	0.800802i	$0.704407\pi$
$200$	−4.34011e9	−0.191807
$201$	1.18519e10	0.512161
$202$	7.29642e10	3.08339
$203$	3.93881e9	0.162792
$204$	−1.21135e10	−0.489703
$205$	2.04187e10	0.807487
$206$	3.52816e10	1.36504
$207$	9.75942e9	0.369452
$208$	2.22453e8	0.00824051
$209$	−1.24574e10	−0.451615
$210$	−2.18024e10	−0.773602
$211$	1.34998e10	0.468875	0.234438	−	0.972131i	$-0.424675\pi$
$211$	1.34998e10	0.468875	0.234438	+	0.972131i	$0.424675\pi$
$212$	1.73588e10	0.590213
$213$	1.02606e9	0.0341558
$214$	7.65372e9	0.249465
$215$	−3.68156e9	−0.117506
$216$	5.90467e9	0.184567
$217$	−3.71090e10	−1.13608
$218$	−8.83751e10	−2.65018
$219$	1.64076e10	0.482000
$220$	4.87985e10	1.40444
$221$	−3.08872e9	−0.0870989
$222$	−1.13341e10	−0.313182
$223$	4.93406e10	1.33608	0.668040	−	0.744126i	$-0.267134\pi$
$223$	4.93406e10	1.33608	0.668040	+	0.744126i	$0.267134\pi$
$224$	−7.28868e10	−1.93434
$225$	2.56289e9	0.0666667
$226$	2.89168e10	0.737329
$227$	−6.56397e10	−1.64078	−0.820390	−	0.571804i	$-0.806244\pi$
$227$	−6.56397e10	−1.64078	−0.820390	+	0.571804i	$0.806244\pi$
$228$	8.62211e9	0.211304
$229$	−4.43686e10	−1.06614	−0.533072	−	0.846070i	$-0.678963\pi$
$229$	−4.43686e10	−1.06614	−0.533072	+	0.846070i	$0.678963\pi$
$230$	−3.38894e10	−0.798524
$231$	9.14759e10	2.11375
$232$	3.70421e9	0.0839459
$233$	−1.31162e10	−0.291545	−0.145772	−	0.989318i	$-0.546567\pi$
$233$	−1.31162e10	−0.291545	−0.145772	+	0.989318i	$0.546567\pi$
$234$	4.03467e9	0.0879704
$235$	2.06755e10	0.442233
$236$	4.99375e10	1.04791
$237$	3.01287e9	0.0620315
$238$	7.88512e10	1.59299
$239$	6.36237e10	1.26133	0.630665	−	0.776056i	$-0.282782\pi$
$239$	6.36237e10	1.26133	0.630665	+	0.776056i	$0.282782\pi$
$240$	6.67568e8	0.0129881
$241$	2.02480e10	0.386640	0.193320	−	0.981136i	$-0.438075\pi$
$241$	2.02480e10	0.386640	0.193320	+	0.981136i	$0.438075\pi$
$242$	−2.47130e11	−4.63187
$243$	−3.48678e9	−0.0641500
$244$	6.00959e10	1.08540
$245$	6.20158e10	1.09965
$246$	9.64633e10	1.67940
$247$	2.19848e9	0.0375826
$248$	−3.48987e10	−0.585837
$249$	−3.42754e10	−0.565047
$250$	−8.89958e9	−0.144092
$251$	8.40258e10	1.33623	0.668115	−	0.744058i	$-0.267102\pi$
$251$	8.40258e10	1.33623	0.668115	+	0.744058i	$0.267102\pi$
$252$	−6.33132e10	−0.988989
$253$	1.42189e11	2.18184
$254$	2.03381e11	3.06591
$255$	−9.26903e9	−0.137279
$256$	−6.30310e10	−0.917222
$257$	1.09762e11	1.56947	0.784737	−	0.619828i	$-0.212798\pi$
$257$	1.09762e11	1.56947	0.784737	+	0.619828i	$0.212798\pi$
$258$	−1.73927e10	−0.244387
$259$	4.53504e10	0.626227
$260$	−8.61198e9	−0.116875
$261$	−2.18738e9	−0.0291771
$262$	−6.67660e10	−0.875386
$263$	1.62101e10	0.208922	0.104461	−	0.994529i	$-0.466688\pi$
$263$	1.62101e10	0.208922	0.104461	+	0.994529i	$0.466688\pi$
$264$	8.60275e10	1.08998
$265$	1.32827e10	0.165455
$266$	−5.61246e10	−0.687363
$267$	6.51678e10	0.784752
$268$	−1.19514e11	−1.41518
$269$	−1.18031e11	−1.37440	−0.687198	−	0.726470i	$-0.741160\pi$
$269$	−1.18031e11	−1.37440	−0.687198	+	0.726470i	$0.741160\pi$
$270$	1.21078e10	0.138652
$271$	−1.46021e11	−1.64457	−0.822285	−	0.569076i	$-0.807301\pi$
$271$	−1.46021e11	−1.64457	−0.822285	+	0.569076i	$0.807301\pi$
$272$	−2.41435e9	−0.0267448
$273$	−1.61437e10	−0.175902
$274$	−2.21259e11	−2.37150
$275$	3.73398e10	0.393708
$276$	−9.84132e10	−1.02085
$277$	1.26820e10	0.129428	0.0647139	−	0.997904i	$-0.479387\pi$
$277$	1.26820e10	0.129428	0.0647139	+	0.997904i	$0.479387\pi$
$278$	−6.45774e10	−0.648454
$279$	2.06082e10	0.203620
$280$	8.20408e10	0.797662
$281$	8.00945e10	0.766345	0.383173	−	0.923677i	$-0.374831\pi$
$281$	8.00945e10	0.766345	0.383173	+	0.923677i	$0.374831\pi$
$282$	9.76767e10	0.919750
$283$	1.88164e11	1.74380	0.871901	−	0.489683i	$-0.162887\pi$
$283$	1.88164e11	1.74380	0.871901	+	0.489683i	$0.162887\pi$
$284$	−1.03467e10	−0.0943777
$285$	6.59750e9	0.0592349
$286$	5.87827e10	0.519520
$287$	−3.85974e11	−3.35806
$288$	4.04771e10	0.346691
$289$	−8.50652e10	−0.717318
$290$	7.59564e9	0.0630628
$291$	7.27845e10	0.595005
$292$	−1.65453e11	−1.33184
$293$	2.15272e11	1.70641	0.853205	−	0.521575i	$-0.174655\pi$
$293$	2.15272e11	1.70641	0.853205	+	0.521575i	$0.174655\pi$
$294$	2.92979e11	2.28704
$295$	3.82114e10	0.293761
$296$	4.26492e10	0.322923
$297$	−5.08004e10	−0.378846
$298$	2.01524e11	1.48031
$299$	−2.50936e10	−0.181569
$300$	−2.58440e10	−0.184210
$301$	6.95923e10	0.488666
$302$	1.29153e11	0.893458
$303$	1.62131e11	1.10503
$304$	1.71848e9	0.0115402
$305$	4.59844e10	0.304272
$306$	−4.37894e10	−0.285511
$307$	−1.40446e11	−0.902375	−0.451187	−	0.892429i	$-0.648999\pi$
$307$	−1.40446e11	−0.902375	−0.451187	+	0.892429i	$0.648999\pi$
$308$	−9.22435e11	−5.84060
$309$	7.83979e10	0.489205
$310$	−7.15614e10	−0.440100
$311$	3.04278e11	1.84437	0.922187	−	0.386744i	$-0.126400\pi$
$311$	3.04278e11	1.84437	0.922187	+	0.386744i	$0.126400\pi$
$312$	−1.51822e10	−0.0907064
$313$	3.56788e10	0.210117	0.105058	−	0.994466i	$-0.466497\pi$
$313$	3.56788e10	0.210117	0.105058	+	0.994466i	$0.466497\pi$
$314$	3.32176e11	1.92834
$315$	−4.84462e10	−0.277244
$316$	−3.03815e10	−0.171402
$317$	6.23182e10	0.346616	0.173308	−	0.984868i	$-0.444554\pi$
$317$	6.23182e10	0.346616	0.173308	+	0.984868i	$0.444554\pi$
$318$	6.27510e10	0.344111
$319$	−3.18689e10	−0.172309
$320$	−1.36336e11	−0.726835
$321$	1.70070e10	0.0894037
$322$	6.40609e11	3.32079
$323$	−2.38607e10	−0.121975
$324$	3.51604e10	0.177256
$325$	−6.58974e9	−0.0327637
$326$	−3.62796e11	−1.77903
$327$	−1.96375e11	−0.949775
$328$	−3.62985e11	−1.73163
$329$	−3.90829e11	−1.83910
$330$	1.76403e11	0.818830
$331$	1.92962e11	0.883579	0.441789	−	0.897119i	$-0.354344\pi$
$331$	1.92962e11	0.883579	0.441789	+	0.897119i	$0.354344\pi$
$332$	3.45630e11	1.56131
$333$	−2.51849e10	−0.112239
$334$	−1.25452e11	−0.551593
$335$	−9.14499e10	−0.396718
$336$	−1.26190e10	−0.0540130
$337$	−3.61375e11	−1.52624	−0.763121	−	0.646255i	$-0.776334\pi$
$337$	−3.61375e11	−1.52624	−0.763121	+	0.646255i	$0.776334\pi$
$338$	3.76188e11	1.56776
$339$	6.42547e10	0.264245
$340$	9.34682e10	0.379322
$341$	3.00249e11	1.20250
$342$	3.11683e10	0.123196
$343$	−6.95530e11	−2.71326
$344$	6.54473e10	0.251988
$345$	−7.53042e10	−0.286176
$346$	3.70095e11	1.38826
$347$	3.87461e11	1.43465	0.717324	−	0.696740i	$-0.245367\pi$
$347$	3.87461e11	1.43465	0.717324	+	0.696740i	$0.245367\pi$
$348$	2.20574e10	0.0806209
$349$	9.14403e10	0.329931	0.164965	−	0.986299i	$-0.447249\pi$
$349$	9.14403e10	0.329931	0.164965	+	0.986299i	$0.447249\pi$
$350$	1.68228e11	0.599229
$351$	8.96527e9	0.0315269
$352$	5.89727e11	2.04743
$353$	2.83578e11	0.972045	0.486023	−	0.873946i	$-0.338447\pi$
$353$	2.83578e11	0.972045	0.486023	+	0.873946i	$0.338447\pi$
$354$	1.80521e11	0.610959
$355$	−7.91713e9	−0.0264570
$356$	−6.57147e11	−2.16839
$357$	1.75212e11	0.570896
$358$	7.43926e10	0.239362
$359$	−3.09975e11	−0.984923	−0.492461	−	0.870334i	$-0.663903\pi$
$359$	−3.09975e11	−0.984923	−0.492461	+	0.870334i	$0.663903\pi$
$360$	−4.55607e10	−0.142965
$361$	1.69836e10	0.0526316
$362$	−8.29995e11	−2.54031
$363$	−5.49138e11	−1.65997
$364$	1.62792e11	0.486045
$365$	−1.26602e11	−0.373355
$366$	2.17243e11	0.632820
$367$	1.27018e11	0.365484	0.182742	−	0.983161i	$-0.441503\pi$
$367$	1.27018e11	0.365484	0.182742	+	0.983161i	$0.441503\pi$
$368$	−1.96148e10	−0.0557531
$369$	2.14347e11	0.601865
$370$	8.74541e10	0.242590
$371$	−2.51082e11	−0.688071
$372$	−2.07811e11	−0.562633
$373$	−1.66747e11	−0.446035	−0.223017	−	0.974814i	$-0.571591\pi$
$373$	−1.66747e11	−0.446035	−0.223017	+	0.974814i	$0.571591\pi$
$374$	−6.37985e11	−1.68612
$375$	−1.97754e10	−0.0516398
$376$	−3.67550e11	−0.948356
$377$	5.62424e9	0.0143393
$378$	−2.28873e11	−0.576609
$379$	−5.25882e11	−1.30922	−0.654608	−	0.755968i	$-0.727166\pi$
$379$	−5.25882e11	−1.30922	−0.654608	+	0.755968i	$0.727166\pi$
$380$	−6.65286e10	−0.163675
$381$	4.51925e11	1.09876
$382$	3.13089e11	0.752285
$383$	2.06211e11	0.489685	0.244842	−	0.969563i	$-0.421264\pi$
$383$	2.06211e11	0.489685	0.244842	+	0.969563i	$0.421264\pi$
$384$	−3.88233e11	−0.911174
$385$	−7.05832e11	−1.63730
$386$	−3.08513e11	−0.707345
$387$	−3.86475e10	−0.0875835
$388$	−7.33953e11	−1.64409
$389$	2.31217e10	0.0511972	0.0255986	−	0.999672i	$-0.491851\pi$
$389$	2.31217e10	0.0511972	0.0255986	+	0.999672i	$0.491851\pi$
$390$	−3.11317e10	−0.0681416
$391$	2.72348e11	0.589289
$392$	−1.10246e12	−2.35817
$393$	−1.48358e11	−0.313722
$394$	−8.74604e11	−1.82843
$395$	−2.32474e10	−0.0480494
$396$	5.12267e11	1.04681
$397$	−4.48694e11	−0.906553	−0.453277	−	0.891370i	$-0.649745\pi$
$397$	−4.48694e11	−0.906553	−0.453277	+	0.891370i	$0.649745\pi$
$398$	9.65993e11	1.92975
$399$	−1.24712e11	−0.246338
$400$	−5.15099e9	−0.0100605
$401$	−3.22219e11	−0.622302	−0.311151	−	0.950361i	$-0.600714\pi$
$401$	−3.22219e11	−0.622302	−0.311151	+	0.950361i	$0.600714\pi$
$402$	−4.32034e11	−0.825088
$403$	−5.29880e10	−0.100070
$404$	−1.63491e12	−3.05336
$405$	2.69042e10	0.0496904
$406$	−1.43580e11	−0.262257
$407$	−3.66930e11	−0.662839
$408$	1.64776e11	0.294391
$409$	−7.42146e11	−1.31140	−0.655699	−	0.755022i	$-0.727626\pi$
$409$	−7.42146e11	−1.31140	−0.655699	+	0.755022i	$0.727626\pi$
$410$	−7.44316e11	−1.30086
$411$	−4.91651e11	−0.849901
$412$	−7.90558e11	−1.35175
$413$	−7.22308e11	−1.22165
$414$	−3.55757e11	−0.595185
$415$	2.64470e11	0.437684
$416$	−1.04075e11	−0.170384
$417$	−1.43495e11	−0.232394
$418$	4.54104e11	0.727549
$419$	1.13868e12	1.80484	0.902419	−	0.430859i	$-0.141789\pi$
$419$	1.13868e12	1.80484	0.902419	+	0.430859i	$0.141789\pi$
$420$	4.88528e11	0.766068
$421$	8.92523e11	1.38468	0.692341	−	0.721570i	$-0.256579\pi$
$421$	8.92523e11	1.38468	0.692341	+	0.721570i	$0.256579\pi$
$422$	−4.92105e11	−0.755356
$423$	2.17043e11	0.329621
$424$	−2.36127e11	−0.354813
$425$	7.15203e10	0.106336
$426$	−3.74026e10	−0.0550248
$427$	−8.69242e11	−1.26536
$428$	−1.71497e11	−0.247036
$429$	1.30619e11	0.186186
$430$	1.34203e11	0.189301
$431$	4.57772e11	0.639001	0.319501	−	0.947586i	$-0.396485\pi$
$431$	4.57772e11	0.639001	0.319501	+	0.947586i	$0.396485\pi$
$432$	7.00786e9	0.00968074
$433$	1.06478e12	1.45568	0.727838	−	0.685749i	$-0.240525\pi$
$433$	1.06478e12	1.45568	0.727838	+	0.685749i	$0.240525\pi$
$434$	1.35272e12	1.83023
$435$	1.68780e10	0.0226005
$436$	1.98023e12	2.62437
$437$	−1.93851e11	−0.254274
$438$	−5.98101e11	−0.776499
$439$	4.35696e11	0.559877	0.279939	−	0.960018i	$-0.409686\pi$
$439$	4.35696e11	0.559877	0.279939	+	0.960018i	$0.409686\pi$
$440$	−6.63792e11	−0.844297
$441$	6.51017e11	0.819631
$442$	1.12592e11	0.140316
$443$	−9.88791e11	−1.21980	−0.609899	−	0.792479i	$-0.708790\pi$
$443$	−9.88791e11	−1.21980	−0.609899	+	0.792479i	$0.708790\pi$
$444$	2.53963e11	0.310132
$445$	−5.02838e11	−0.607866
$446$	−1.79860e12	−2.15242
$447$	4.47798e11	0.530516
$448$	2.57715e12	3.02266
$449$	1.65503e12	1.92175	0.960877	−	0.276975i	$-0.0893319\pi$
$449$	1.65503e12	1.92175	0.960877	+	0.276975i	$0.0893319\pi$
$450$	−9.34242e10	−0.107400
$451$	3.12291e12	3.55439
$452$	−6.47939e11	−0.730149
$453$	2.86986e11	0.320198
$454$	2.39274e12	2.64329
$455$	1.24566e11	0.136253
$456$	−1.17284e11	−0.127028
$457$	2.23169e11	0.239337	0.119669	−	0.992814i	$-0.461817\pi$
$457$	2.23169e11	0.239337	0.119669	+	0.992814i	$0.461817\pi$
$458$	1.61735e12	1.71755
$459$	−9.73026e10	−0.102322
$460$	7.59361e11	0.790748
$461$	−7.10006e11	−0.732163	−0.366082	−	0.930583i	$-0.619301\pi$
$461$	−7.10006e11	−0.732163	−0.366082	+	0.930583i	$0.619301\pi$
$462$	−3.33454e12	−3.40524
$463$	4.63597e11	0.468842	0.234421	−	0.972135i	$-0.424681\pi$
$463$	4.63597e11	0.468842	0.234421	+	0.972135i	$0.424681\pi$
$464$	4.39628e9	0.00440306
$465$	−1.59014e11	−0.157723
$466$	4.78119e11	0.469677
$467$	5.15792e11	0.501821	0.250910	−	0.968010i	$-0.419270\pi$
$467$	5.15792e11	0.501821	0.250910	+	0.968010i	$0.419270\pi$
$468$	−9.04051e10	−0.0871137
$469$	1.72867e12	1.64982
$470$	−7.53678e11	−0.712436
$471$	7.38115e11	0.691082
$472$	−6.79286e11	−0.629961
$473$	−5.63072e11	−0.517236
$474$	−1.09827e11	−0.0999325
$475$	−5.09066e10	−0.0458831
$476$	−1.76682e12	−1.57747
$477$	1.39436e11	0.123323
$478$	−2.31925e12	−2.03200
$479$	1.93993e12	1.68375	0.841873	−	0.539675i	$-0.181453\pi$
$479$	1.93993e12	1.68375	0.841873	+	0.539675i	$0.181453\pi$
$480$	−3.12323e11	−0.268546
$481$	6.47559e10	0.0551603
$482$	−7.38095e11	−0.622875
$483$	1.42347e12	1.19011
$484$	5.53746e12	4.58676
$485$	−5.61609e11	−0.460889
$486$	1.27103e11	0.103345
$487$	1.27218e12	1.02487	0.512434	−	0.858726i	$-0.328744\pi$
$487$	1.27218e12	1.02487	0.512434	+	0.858726i	$0.328744\pi$
$488$	−8.17469e11	−0.652502
$489$	−8.06154e11	−0.637570
$490$	−2.26064e12	−1.77153
$491$	8.72520e11	0.677499	0.338750	−	0.940877i	$-0.389996\pi$
$491$	8.72520e11	0.677499	0.338750	+	0.940877i	$0.389996\pi$
$492$	−2.16146e12	−1.66305
$493$	−6.10414e10	−0.0465386
$494$	−8.01405e10	−0.0605454
$495$	3.91978e11	0.293453
$496$	−4.14190e10	−0.0307278
$497$	1.49657e11	0.110026
$498$	1.24943e12	0.910289
$499$	−2.96818e11	−0.214308	−0.107154	−	0.994242i	$-0.534174\pi$
$499$	−2.96818e11	−0.214308	−0.107154	+	0.994242i	$0.534174\pi$
$500$	1.99413e11	0.142689
$501$	−2.78762e11	−0.197681
$502$	−3.06297e12	−2.15266
$503$	1.39265e12	0.970031	0.485015	−	0.874506i	$-0.338814\pi$
$503$	1.39265e12	0.970031	0.485015	+	0.874506i	$0.338814\pi$
$504$	8.61232e11	0.594542
$505$	−1.25101e12	−0.855951
$506$	−5.18317e12	−3.51494
$507$	8.35913e11	0.561856
$508$	−4.55717e12	−3.03605
$509$	4.27278e11	0.282150	0.141075	−	0.989999i	$-0.454944\pi$
$509$	4.27278e11	0.282150	0.141075	+	0.989999i	$0.454944\pi$
$510$	3.37881e11	0.221156
$511$	2.39315e12	1.55266
$512$	−1.56366e11	−0.100561
$513$	6.92579e10	0.0441511
$514$	−4.00113e12	−2.52842
$515$	−6.04922e11	−0.378937
$516$	3.89718e11	0.242007
$517$	3.16219e12	1.94662
$518$	−1.65314e12	−1.00885
$519$	8.22373e11	0.497526
$520$	1.17146e11	0.0702609
$521$	−2.66832e12	−1.58660	−0.793302	−	0.608829i	$-0.791640\pi$
$521$	−2.66832e12	−1.58660	−0.793302	+	0.608829i	$0.791640\pi$
$522$	7.97360e10	0.0470043
$523$	−2.25553e11	−0.131823	−0.0659115	−	0.997825i	$-0.520996\pi$
$523$	−2.25553e11	−0.131823	−0.0659115	+	0.997825i	$0.520996\pi$
$524$	1.49603e12	0.866861
$525$	3.73813e11	0.214752
$526$	−5.90901e11	−0.336572
$527$	5.75094e11	0.324781
$528$	1.02100e11	0.0571708
$529$	4.11473e11	0.228450
$530$	−4.84190e11	−0.266547
$531$	4.01128e11	0.218956
$532$	1.25759e12	0.680669
$533$	−5.51133e11	−0.295790
$534$	−2.37554e12	−1.26423
$535$	−1.31227e11	−0.0692518
$536$	1.62571e12	0.850750
$537$	1.65305e11	0.0857829
$538$	4.30256e12	2.21415
$539$	9.48493e12	4.84044
$540$	−2.71300e11	−0.137302
$541$	5.00442e11	0.251169	0.125584	−	0.992083i	$-0.459919\pi$
$541$	5.00442e11	0.251169	0.125584	+	0.992083i	$0.459919\pi$
$542$	5.32284e12	2.64939
$543$	−1.84430e12	−0.910400
$544$	1.12956e12	0.552985
$545$	1.51524e12	0.735693
$546$	5.88481e11	0.283378
$547$	−4.48276e11	−0.214093	−0.107046	−	0.994254i	$-0.534139\pi$
$547$	−4.48276e11	−0.214093	−0.107046	+	0.994254i	$0.534139\pi$
$548$	4.95777e12	2.34841
$549$	4.82726e11	0.226791
$550$	−1.36114e12	−0.634263
$551$	4.34480e10	0.0200811
$552$	1.33869e12	0.613696
$553$	4.39445e11	0.199821
$554$	−4.62291e11	−0.208508
$555$	1.94328e11	0.0869396
$556$	1.44699e12	0.642139
$557$	−2.58324e12	−1.13715	−0.568573	−	0.822633i	$-0.692504\pi$
$557$	−2.58324e12	−1.13715	−0.568573	+	0.822633i	$0.692504\pi$
$558$	−7.51223e11	−0.328031
$559$	9.93711e10	0.0430435
$560$	9.73689e10	0.0418383
$561$	−1.41764e12	−0.604273
$562$	−2.91966e12	−1.23458
$563$	−4.56634e12	−1.91549	−0.957746	−	0.287614i	$-0.907138\pi$
$563$	−4.56634e12	−1.91549	−0.957746	+	0.287614i	$0.907138\pi$
$564$	−2.18865e12	−0.910793
$565$	−4.95793e11	−0.204683
$566$	−6.85907e12	−2.80926
$567$	−5.08569e11	−0.206646
$568$	1.40743e11	0.0567362
$569$	−8.29166e11	−0.331617	−0.165808	−	0.986158i	$-0.553023\pi$
$569$	−8.29166e11	−0.331617	−0.165808	+	0.986158i	$0.553023\pi$
$570$	−2.40497e11	−0.0954271
$571$	−3.46204e12	−1.36292	−0.681460	−	0.731856i	$-0.738655\pi$
$571$	−3.46204e12	−1.36292	−0.681460	+	0.731856i	$0.738655\pi$
$572$	−1.31715e12	−0.514461
$573$	6.95702e11	0.269605
$574$	1.40698e13	5.40983
$575$	5.81051e11	0.221671
$576$	−1.43120e12	−0.541751
$577$	−4.67597e12	−1.75622	−0.878112	−	0.478454i	$-0.841197\pi$
$577$	−4.67597e12	−1.75622	−0.878112	+	0.478454i	$0.841197\pi$
$578$	3.10085e12	1.15560
$579$	−6.85535e11	−0.253499
$580$	−1.70196e11	−0.0624487
$581$	−4.99927e12	−1.82018
$582$	−2.65319e12	−0.958550
$583$	2.03151e12	0.728299
$584$	2.25061e12	0.800650
$585$	−6.91765e10	−0.0244206
$586$	−7.84724e12	−2.74902
$587$	3.44418e12	1.19733	0.598665	−	0.800999i	$-0.295698\pi$
$587$	3.44418e12	1.19733	0.598665	+	0.800999i	$0.295698\pi$
$588$	−6.56480e12	−2.26477
$589$	−4.09339e11	−0.140141
$590$	−1.39291e12	−0.473247
$591$	−1.94342e12	−0.655275
$592$	5.06176e10	0.0169377
$593$	1.29401e12	0.429727	0.214864	−	0.976644i	$-0.431069\pi$
$593$	1.29401e12	0.429727	0.214864	+	0.976644i	$0.431069\pi$
$594$	1.85181e12	0.610320
$595$	−1.35195e12	−0.442214
$596$	−4.51556e12	−1.46590
$597$	2.14649e12	0.691585
$598$	9.14728e11	0.292507
$599$	−1.22394e12	−0.388455	−0.194227	−	0.980957i	$-0.562220\pi$
$599$	−1.22394e12	−0.388455	−0.194227	+	0.980957i	$0.562220\pi$
$600$	3.51549e11	0.110740
$601$	−3.86681e12	−1.20898	−0.604488	−	0.796614i	$-0.706622\pi$
$601$	−3.86681e12	−1.20898	−0.604488	+	0.796614i	$0.706622\pi$
$602$	−2.53683e12	−0.787239
$603$	−9.60005e11	−0.295696
$604$	−2.89394e12	−0.884757
$605$	4.23717e12	1.28581
$606$	−5.91010e12	−1.78020
$607$	−1.23144e12	−0.368184	−0.184092	−	0.982909i	$-0.558935\pi$
$607$	−1.23144e12	−0.368184	−0.184092	+	0.982909i	$0.558935\pi$
$608$	−8.03996e11	−0.238609
$609$	−3.19043e11	−0.0939879
$610$	−1.67626e12	−0.490180
$611$	−5.58065e11	−0.161994
$612$	9.81191e11	0.282730
$613$	−1.02185e12	−0.292292	−0.146146	−	0.989263i	$-0.546687\pi$
$613$	−1.02185e12	−0.292292	−0.146146	+	0.989263i	$0.546687\pi$
$614$	5.11964e12	1.45372
$615$	−1.65391e12	−0.466203
$616$	1.25476e13	3.51114
$617$	−2.72512e11	−0.0757011	−0.0378506	−	0.999283i	$-0.512051\pi$
$617$	−2.72512e11	−0.0757011	−0.0378506	+	0.999283i	$0.512051\pi$
$618$	−2.85781e12	−0.788108
$619$	5.05549e12	1.38406	0.692031	−	0.721868i	$-0.256716\pi$
$619$	5.05549e12	1.38406	0.692031	+	0.721868i	$0.256716\pi$
$620$	1.60348e12	0.435814
$621$	−7.90513e11	−0.213303
$622$	−1.10918e13	−2.97128
$623$	9.50512e12	2.52791
$624$	−1.80187e10	−0.00475766
$625$	1.52588e11	0.0400000
$626$	−1.30059e12	−0.338497
$627$	1.00905e12	0.260740
$628$	−7.44309e12	−1.90957
$629$	−7.02814e11	−0.179025
$630$	1.76599e12	0.446639
$631$	2.46748e12	0.619615	0.309807	−	0.950799i	$-0.399735\pi$
$631$	2.46748e12	0.619615	0.309807	+	0.950799i	$0.399735\pi$
$632$	4.13271e11	0.103041
$633$	−1.09349e12	−0.270705
$634$	−2.27167e12	−0.558397
$635$	−3.48708e12	−0.851098
$636$	−1.40607e12	−0.340760
$637$	−1.67390e12	−0.402813
$638$	1.16171e12	0.277590
$639$	−8.31108e10	−0.0197199
$640$	2.99562e12	0.705793
$641$	1.57170e12	0.367713	0.183857	−	0.982953i	$-0.441142\pi$
$641$	1.57170e12	0.367713	0.183857	+	0.982953i	$0.441142\pi$
$642$	−6.19951e11	−0.144029
$643$	2.74560e12	0.633414	0.316707	−	0.948523i	$-0.397423\pi$
$643$	2.74560e12	0.633414	0.316707	+	0.948523i	$0.397423\pi$
$644$	−1.43542e13	−3.28845
$645$	2.98206e11	0.0678419
$646$	8.69788e11	0.196502
$647$	1.57859e12	0.354161	0.177080	−	0.984196i	$-0.443335\pi$
$647$	1.57859e12	0.354161	0.177080	+	0.984196i	$0.443335\pi$
$648$	−4.78278e11	−0.106560
$649$	5.84419e12	1.29307
$650$	2.40214e11	0.0527822
$651$	3.00583e12	0.655918
$652$	8.12919e12	1.76170
$653$	−1.46072e12	−0.314381	−0.157191	−	0.987568i	$-0.550244\pi$
$653$	−1.46072e12	−0.314381	−0.157191	+	0.987568i	$0.550244\pi$
$654$	7.15839e12	1.53008
$655$	1.14474e12	0.243008
$656$	−4.30803e11	−0.0908262
$657$	−1.32902e12	−0.278283
$658$	1.42467e13	2.96278
$659$	1.48318e12	0.306344	0.153172	−	0.988200i	$-0.451051\pi$
$659$	1.48318e12	0.306344	0.153172	+	0.988200i	$0.451051\pi$
$660$	−3.95268e12	−0.810855
$661$	−6.87930e12	−1.40164	−0.700822	−	0.713336i	$-0.747183\pi$
$661$	−6.87930e12	−1.40164	−0.700822	+	0.713336i	$0.747183\pi$
$662$	−7.03397e12	−1.42344
$663$	2.50186e11	0.0502866
$664$	−4.70151e12	−0.938601
$665$	9.62286e11	0.190812
$666$	9.18059e11	0.180816
$667$	−4.95917e11	−0.0970159
$668$	2.81101e12	0.546222
$669$	−3.99659e12	−0.771386
$670$	3.33359e12	0.639111
$671$	7.03303e12	1.33934
$672$	5.90383e12	1.11679
$673$	−1.28416e12	−0.241296	−0.120648	−	0.992695i	$-0.538497\pi$
$673$	−1.28416e12	−0.241296	−0.120648	+	0.992695i	$0.538497\pi$
$674$	1.31731e13	2.45877
$675$	−2.07594e11	−0.0384900
$676$	−8.42927e12	−1.55249
$677$	−9.23697e12	−1.68998	−0.844988	−	0.534785i	$-0.820393\pi$
$677$	−9.23697e12	−1.68998	−0.844988	+	0.534785i	$0.820393\pi$
$678$	−2.34226e12	−0.425697
$679$	1.06161e13	1.91668
$680$	−1.27142e12	−0.228034
$681$	5.31682e12	0.947305
$682$	−1.09449e13	−1.93723
$683$	1.49089e12	0.262152	0.131076	−	0.991372i	$-0.458157\pi$
$683$	1.49089e12	0.262152	0.131076	+	0.991372i	$0.458157\pi$
$684$	−6.98391e11	−0.121996
$685$	3.79360e12	0.658331
$686$	2.53539e13	4.37106
$687$	3.59386e12	0.615539
$688$	7.76752e10	0.0132170
$689$	−3.58521e11	−0.0606078
$690$	2.74504e12	0.461028
$691$	−1.20099e12	−0.200396	−0.100198	−	0.994968i	$-0.531948\pi$
$691$	−1.20099e12	−0.200396	−0.100198	+	0.994968i	$0.531948\pi$
$692$	−8.29274e12	−1.37474
$693$	−7.40955e12	−1.22037
$694$	−1.41240e13	−2.31121
$695$	1.10721e12	0.180011
$696$	−3.00041e11	−0.0484662
$697$	5.98160e12	0.959997
$698$	−3.33324e12	−0.531517
$699$	1.06241e12	0.168323
$700$	−3.76950e12	−0.593394
$701$	−8.76705e11	−0.137127	−0.0685634	−	0.997647i	$-0.521842\pi$
$701$	−8.76705e11	−0.137127	−0.0685634	+	0.997647i	$0.521842\pi$
$702$	−3.26808e11	−0.0507897
$703$	5.00248e11	0.0772479
$704$	−2.08518e13	−3.19938
$705$	−1.67472e12	−0.255323
$706$	−1.03372e13	−1.56596
$707$	2.36478e13	3.55961
$708$	−4.04494e12	−0.605009
$709$	1.03651e13	1.54052	0.770260	−	0.637730i	$-0.220126\pi$
$709$	1.03651e13	1.54052	0.770260	+	0.637730i	$0.220126\pi$
$710$	2.88600e11	0.0426221
$711$	−2.44042e11	−0.0358139
$712$	8.93899e12	1.30355
$713$	4.67222e12	0.677049
$714$	−6.38695e12	−0.919712
$715$	−1.00786e12	−0.144219
$716$	−1.66692e12	−0.237031
$717$	−5.15352e12	−0.728229
$718$	1.12994e13	1.58671
$719$	8.99817e12	1.25567	0.627833	−	0.778348i	$-0.283942\pi$
$719$	8.99817e12	1.25567	0.627833	+	0.778348i	$0.283942\pi$
$720$	−5.40730e10	−0.00749867
$721$	1.14348e13	1.57587
$722$	−6.19096e11	−0.0847892
$723$	−1.64009e12	−0.223227
$724$	1.85978e13	2.51557
$725$	−1.30231e11	−0.0175063
$726$	2.00175e13	2.67421
$727$	1.28053e12	0.170014	0.0850072	−	0.996380i	$-0.472909\pi$
$727$	1.28053e12	0.170014	0.0850072	+	0.996380i	$0.472909\pi$
$728$	−2.21441e12	−0.292191
$729$	2.82430e11	0.0370370
$730$	4.61498e12	0.601474
$731$	−1.07850e12	−0.139699
$732$	−4.86777e12	−0.626658
$733$	1.05419e12	0.134881	0.0674406	−	0.997723i	$-0.478517\pi$
$733$	1.05419e12	0.134881	0.0674406	+	0.997723i	$0.478517\pi$
$734$	−4.63016e12	−0.588794
$735$	−5.02328e12	−0.634884
$736$	9.17684e12	1.15277
$737$	−1.39867e13	−1.74627
$738$	−7.81353e12	−0.969602
$739$	−5.82336e12	−0.718247	−0.359123	−	0.933290i	$-0.616924\pi$
$739$	−5.82336e12	−0.718247	−0.359123	+	0.933290i	$0.616924\pi$
$740$	−1.95959e12	−0.240227
$741$	−1.78077e11	−0.0216983
$742$	9.15262e12	1.10848
$743$	−6.48172e12	−0.780262	−0.390131	−	0.920759i	$-0.627570\pi$
$743$	−6.48172e12	−0.780262	−0.390131	+	0.920759i	$0.627570\pi$
$744$	2.82680e12	0.338233
$745$	−3.45523e12	−0.410936
$746$	6.07838e12	0.718560
$747$	2.77630e12	0.326230
$748$	1.42954e13	1.66970
$749$	2.48058e12	0.287995
$750$	7.20866e11	0.0831915
$751$	9.69899e12	1.11262	0.556310	−	0.830975i	$-0.312217\pi$
$751$	9.69899e12	1.11262	0.556310	+	0.830975i	$0.312217\pi$
$752$	−4.36221e11	−0.0497424
$753$	−6.80609e12	−0.771472
$754$	−2.05018e11	−0.0231005
$755$	−2.21440e12	−0.248025
$756$	5.12837e12	0.570993
$757$	8.49820e11	0.0940580	0.0470290	−	0.998894i	$-0.485025\pi$
$757$	8.49820e11	0.0940580	0.0470290	+	0.998894i	$0.485025\pi$
$758$	1.91698e13	2.10914
$759$	−1.15173e13	−1.25969
$760$	9.04971e11	0.0983951
$761$	−7.06141e12	−0.763238	−0.381619	−	0.924320i	$-0.624633\pi$
$761$	−7.06141e12	−0.763238	−0.381619	+	0.924320i	$0.624633\pi$
$762$	−1.64739e13	−1.77010
$763$	−2.86425e13	−3.05950
$764$	−7.01540e12	−0.744959
$765$	7.50792e11	0.0792580
$766$	−7.51693e12	−0.788880
$767$	−1.03139e12	−0.107607
$768$	5.10551e12	0.529558
$769$	−9.71694e12	−1.00198	−0.500992	−	0.865452i	$-0.667031\pi$
$769$	−9.71694e12	−1.00198	−0.500992	+	0.865452i	$0.667031\pi$
$770$	2.57295e13	2.63768
$771$	−8.89075e12	−0.906137
$772$	6.91288e12	0.700456
$773$	9.65653e12	0.972778	0.486389	−	0.873743i	$-0.338314\pi$
$773$	9.65653e12	0.972778	0.486389	+	0.873743i	$0.338314\pi$
$774$	1.40881e12	0.141097
$775$	1.22696e12	0.122172
$776$	9.98376e12	0.988363
$777$	−3.67338e12	−0.361552
$778$	−8.42846e11	−0.0824784
$779$	−4.25757e12	−0.414232
$780$	6.97570e11	0.0674780
$781$	−1.21088e12	−0.116458
$782$	−9.92779e12	−0.949341
$783$	1.77178e11	0.0168454
$784$	−1.30844e12	−0.123689
$785$	−5.69533e12	−0.535310
$786$	5.40805e12	0.505405
$787$	2.91353e12	0.270728	0.135364	−	0.990796i	$-0.456780\pi$
$787$	2.91353e12	0.270728	0.135364	+	0.990796i	$0.456780\pi$
$788$	1.95973e13	1.81062
$789$	−1.31302e12	−0.120621
$790$	8.47431e11	0.0774074
$791$	9.37195e12	0.851208
$792$	−6.96823e12	−0.629302
$793$	−1.24119e12	−0.111458
$794$	1.63561e13	1.46045
$795$	−1.07590e12	−0.0955255
$796$	−2.16451e13	−1.91095
$797$	1.12774e13	0.990027	0.495013	−	0.868885i	$-0.335163\pi$
$797$	1.12774e13	0.990027	0.495013	+	0.868885i	$0.335163\pi$
$798$	4.54610e12	0.396849
$799$	6.05684e12	0.525758
$800$	2.40990e12	0.208015
$801$	−5.27859e12	−0.453077
$802$	1.17457e13	1.00253
$803$	−1.93630e13	−1.64343
$804$	9.68061e12	0.817053
$805$	−1.09836e13	−0.921854
$806$	1.93156e12	0.161213
$807$	9.56054e12	0.793508
$808$	2.22393e13	1.83556
$809$	1.46910e13	1.20582	0.602912	−	0.797808i	$-0.294007\pi$
$809$	1.46910e13	1.20582	0.602912	+	0.797808i	$0.294007\pi$
$810$	−9.80730e11	−0.0800510
$811$	−1.74204e12	−0.141405	−0.0707024	−	0.997497i	$-0.522524\pi$
$811$	−1.74204e12	−0.141405	−0.0707024	+	0.997497i	$0.522524\pi$
$812$	3.21721e12	0.259703
$813$	1.18277e13	0.949493
$814$	1.33756e13	1.06783
$815$	6.22032e12	0.493860
$816$	1.95562e11	0.0154411
$817$	7.67655e11	0.0602791
$818$	2.70532e13	2.11266
$819$	1.30764e12	0.101557
$820$	1.66779e13	1.28819
$821$	−2.32540e12	−0.178630	−0.0893149	−	0.996003i	$-0.528468\pi$
$821$	−2.32540e12	−0.178630	−0.0893149	+	0.996003i	$0.528468\pi$
$822$	1.79220e13	1.36919
$823$	−3.14851e11	−0.0239225	−0.0119612	−	0.999928i	$-0.503807\pi$
$823$	−3.14851e11	−0.0239225	−0.0119612	+	0.999928i	$0.503807\pi$
$824$	1.07537e13	0.812619
$825$	−3.02452e12	−0.227308
$826$	2.63300e13	1.96807
$827$	1.57386e13	1.17001	0.585006	−	0.811029i	$-0.301092\pi$
$827$	1.57386e13	1.17001	0.585006	+	0.811029i	$0.301092\pi$
$828$	7.97147e12	0.589389
$829$	−7.30710e12	−0.537341	−0.268670	−	0.963232i	$-0.586584\pi$
$829$	−7.30710e12	−0.537341	−0.268670	+	0.963232i	$0.586584\pi$
$830$	−9.64065e12	−0.705107
$831$	−1.02724e12	−0.0747252
$832$	3.67993e12	0.266247
$833$	1.81673e13	1.30734
$834$	5.23077e12	0.374385
$835$	2.15094e12	0.153123
$836$	−1.01751e13	−0.720464
$837$	−1.66926e12	−0.117560
$838$	−4.15079e13	−2.90759
$839$	2.38448e12	0.166136	0.0830681	−	0.996544i	$-0.473528\pi$
$839$	2.38448e12	0.166136	0.0830681	+	0.996544i	$0.473528\pi$
$840$	−6.64531e12	−0.460530
$841$	−1.43960e13	−0.992338
$842$	−3.25349e13	−2.23072
$843$	−6.48766e12	−0.442450
$844$	1.10266e13	0.748000
$845$	−6.44994e12	−0.435212
$846$	−7.91181e12	−0.531018
$847$	−8.00951e13	−5.34725
$848$	−2.80244e11	−0.0186104
$849$	−1.52413e13	−1.00678
$850$	−2.60711e12	−0.171306
$851$	−5.70985e12	−0.373200
$852$	8.38083e11	0.0544890
$853$	−2.30156e13	−1.48851	−0.744256	−	0.667894i	$-0.767196\pi$
$853$	−2.30156e13	−1.48851	−0.744256	+	0.667894i	$0.767196\pi$
$854$	3.16862e13	2.03849
$855$	−5.34398e11	−0.0341993
$856$	2.33283e12	0.148509
$857$	1.24046e13	0.785541	0.392771	−	0.919636i	$-0.371517\pi$
$857$	1.24046e13	0.785541	0.392771	+	0.919636i	$0.371517\pi$
$858$	−4.76140e12	−0.299945
$859$	1.06162e13	0.665276	0.332638	−	0.943055i	$-0.392061\pi$
$859$	1.06162e13	0.665276	0.332638	+	0.943055i	$0.392061\pi$
$860$	−3.00709e12	−0.187458
$861$	3.12639e13	1.93878
$862$	−1.66870e13	−1.02943
$863$	8.84193e12	0.542623	0.271312	−	0.962492i	$-0.412543\pi$
$863$	8.84193e12	0.542623	0.271312	+	0.962492i	$0.412543\pi$
$864$	−3.27864e12	−0.200162
$865$	−6.34547e12	−0.385382
$866$	−3.88141e13	−2.34509
$867$	6.89028e12	0.414144
$868$	−3.03105e13	−1.81240
$869$	−3.55555e12	−0.211504
$870$	−6.15247e11	−0.0364093
$871$	2.46838e12	0.145322
$872$	−2.69365e13	−1.57767
$873$	−5.89554e12	−0.343526
$874$	7.06639e12	0.409634
$875$	−2.88436e12	−0.166346
$876$	1.34017e13	0.768937
$877$	−4.28830e12	−0.244786	−0.122393	−	0.992482i	$-0.539057\pi$
$877$	−4.28830e12	−0.244786	−0.122393	+	0.992482i	$0.539057\pi$
$878$	−1.58823e13	−0.901960
$879$	−1.74370e13	−0.985197
$880$	−7.87811e11	−0.0442843
$881$	1.35648e13	0.758616	0.379308	−	0.925271i	$-0.376162\pi$
$881$	1.35648e13	0.758616	0.379308	+	0.925271i	$0.376162\pi$
$882$	−2.37313e13	−1.32042
$883$	3.08940e13	1.71022	0.855108	−	0.518451i	$-0.173491\pi$
$883$	3.08940e13	1.71022	0.855108	+	0.518451i	$0.173491\pi$
$884$	−2.52285e12	−0.138950
$885$	−3.09512e12	−0.169603
$886$	3.60441e13	1.96509
$887$	4.62365e12	0.250800	0.125400	−	0.992106i	$-0.459979\pi$
$887$	4.62365e12	0.250800	0.125400	+	0.992106i	$0.459979\pi$
$888$	−3.45459e12	−0.186440
$889$	6.59160e13	3.53943
$890$	1.83298e13	0.979270
$891$	4.11483e12	0.218727
$892$	4.03012e13	2.13146
$893$	−4.31113e12	−0.226861
$894$	−1.63234e13	−0.854659
$895$	−1.27550e12	−0.0664472
$896$	−5.66261e13	−2.93515
$897$	2.03258e12	0.104829
$898$	−6.03303e13	−3.09594
$899$	−1.04719e12	−0.0534694
$900$	2.09336e12	0.106354
$901$	3.89113e12	0.196704
$902$	−1.13838e14	−5.72611
$903$	−5.63698e12	−0.282132
$904$	8.81374e12	0.438937
$905$	1.42307e13	0.705193
$906$	−1.04614e13	−0.515838
$907$	2.75167e13	1.35009	0.675045	−	0.737776i	$-0.264124\pi$
$907$	2.75167e13	1.35009	0.675045	+	0.737776i	$0.264124\pi$
$908$	−5.36144e13	−2.61755
$909$	−1.31326e13	−0.637988
$910$	−4.54075e12	−0.219503
$911$	−3.06176e13	−1.47278	−0.736390	−	0.676557i	$-0.763471\pi$
$911$	−3.06176e13	−1.47278	−0.736390	+	0.676557i	$0.763471\pi$
$912$	−1.39197e11	−0.00666274
$913$	4.04491e13	1.92659
$914$	−8.13510e12	−0.385571
$915$	−3.72474e12	−0.175671
$916$	−3.62401e13	−1.70083
$917$	−2.16389e13	−1.01059
$918$	3.54694e12	0.164840
$919$	1.52873e13	0.706988	0.353494	−	0.935437i	$-0.384994\pi$
$919$	1.52873e13	0.706988	0.353494	+	0.935437i	$0.384994\pi$
$920$	−1.03294e13	−0.475367
$921$	1.13761e13	0.520986
$922$	2.58816e13	1.17951
$923$	2.13696e11	0.00969144
$924$	7.47172e13	3.37207
$925$	−1.49945e12	−0.0673431
$926$	−1.68994e13	−0.755302
$927$	−6.35023e12	−0.282443
$928$	−2.05681e12	−0.0910392
$929$	−3.69049e12	−0.162560	−0.0812800	−	0.996691i	$-0.525901\pi$
$929$	−3.69049e12	−0.162560	−0.0812800	+	0.996691i	$0.525901\pi$
$930$	5.79647e12	0.254092
$931$	−1.29311e13	−0.564109
$932$	−1.07132e13	−0.465103
$933$	−2.46465e13	−1.06485
$934$	−1.88020e13	−0.808431
$935$	1.09386e13	0.468068
$936$	1.22976e12	0.0523694
$937$	3.09955e13	1.31362	0.656811	−	0.754055i	$-0.271905\pi$
$937$	3.09955e13	1.31362	0.656811	+	0.754055i	$0.271905\pi$
$938$	−6.30148e13	−2.65785
$939$	−2.88998e12	−0.121311
$940$	1.68877e13	0.705497
$941$	−3.33184e13	−1.38526	−0.692629	−	0.721294i	$-0.743548\pi$
$941$	−3.33184e13	−1.38526	−0.692629	+	0.721294i	$0.743548\pi$
$942$	−2.69062e13	−1.11333
$943$	4.85961e13	2.00124
$944$	−8.06200e11	−0.0330422
$945$	3.92414e12	0.160067
$946$	2.05255e13	0.833264
$947$	1.17967e13	0.476633	0.238316	−	0.971188i	$-0.423404\pi$
$947$	1.17967e13	0.476633	0.238316	+	0.971188i	$0.423404\pi$
$948$	2.46090e12	0.0989593
$949$	3.41719e12	0.136764
$950$	1.85568e12	0.0739175
$951$	−5.04778e12	−0.200119
$952$	2.40336e13	0.948316
$953$	2.07064e13	0.813180	0.406590	−	0.913611i	$-0.366718\pi$
$953$	2.07064e13	0.813180	0.406590	+	0.913611i	$0.366718\pi$
$954$	−5.08283e12	−0.198673
$955$	−5.36807e12	−0.208835
$956$	5.19677e13	2.01221
$957$	2.58138e12	0.0994828
$958$	−7.07157e13	−2.71251
$959$	−7.17103e13	−2.73778
$960$	1.10432e13	0.419638
$961$	−1.65737e13	−0.626850
$962$	−2.36053e12	−0.0888630
$963$	−1.37757e12	−0.0516172
$964$	1.65385e13	0.616809
$965$	5.28962e12	0.196359
$966$	−5.18893e13	−1.91726
$967$	2.68913e13	0.988992	0.494496	−	0.869180i	$-0.335353\pi$
$967$	2.68913e13	0.988992	0.494496	+	0.869180i	$0.335353\pi$
$968$	−7.53245e13	−2.75738
$969$	1.93272e12	0.0704226
$970$	2.04721e13	0.742490
$971$	3.11390e13	1.12413	0.562067	−	0.827092i	$-0.310006\pi$
$971$	3.11390e13	1.12413	0.562067	+	0.827092i	$0.310006\pi$
$972$	−2.84800e12	−0.102339
$973$	−2.09296e13	−0.748606
$974$	−4.63744e13	−1.65106
$975$	5.33769e11	0.0189162
$976$	−9.70200e11	−0.0342245
$977$	−4.21292e13	−1.47930	−0.739652	−	0.672990i	$-0.765010\pi$
$977$	−4.21292e13	−1.47930	−0.739652	+	0.672990i	$0.765010\pi$
$978$	2.93865e13	1.02712
$979$	−7.69059e13	−2.67570
$980$	5.06543e13	1.75428
$981$	1.59064e13	0.548353
$982$	−3.18057e13	−1.09145
$983$	−5.68734e13	−1.94276	−0.971379	−	0.237536i	$-0.923660\pi$
$983$	−5.68734e13	−1.94276	−0.971379	+	0.237536i	$0.923660\pi$
$984$	2.94017e13	0.999759
$985$	1.49955e13	0.507574
$986$	2.22512e12	0.0749735
$987$	3.16571e13	1.06180
$988$	1.79571e12	0.0599558
$989$	−8.76205e12	−0.291221
$990$	−1.42887e13	−0.472751
$991$	6.65317e12	0.219128	0.109564	−	0.993980i	$-0.465055\pi$
$991$	6.65317e12	0.219128	0.109564	+	0.993980i	$0.465055\pi$
$992$	1.93780e13	0.635340
$993$	−1.56299e13	−0.510134
$994$	−5.45540e12	−0.177251
$995$	−1.65625e13	−0.535699
$996$	−2.79960e13	−0.901424
$997$	3.13287e13	1.00419	0.502093	−	0.864814i	$-0.332564\pi$
$997$	3.13287e13	1.00419	0.502093	+	0.864814i	$0.332564\pi$
$998$	1.08198e13	0.345249
$999$	2.03998e12	0.0648009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.h.1.2	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.h.1.2	✓	15	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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	285.a (trivial)

\(f(q)\)	\(=\)	\(q-36.4527 q^{2} -81.0000 q^{3} +816.797 q^{4} +625.000 q^{5} +2952.67 q^{6} -11814.3 q^{7} -11110.7 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-36.4527 q^{2} -81.0000 q^{3} +816.797 q^{4} +625.000 q^{5} +2952.67 q^{6} -11814.3 q^{7} -11110.7 q^{8} +6561.00 q^{9} -22782.9 q^{10} +95589.9 q^{11} -66160.6 q^{12} -16869.7 q^{13} +430665. q^{14} -50625.0 q^{15} -13186.5 q^{16} +183092. q^{17} -239166. q^{18} -130321. q^{19} +510498. q^{20} +956962. q^{21} -3.48451e6 q^{22} +1.48749e6 q^{23} +899964. q^{24} +390625. q^{25} +614947. q^{26} -531441. q^{27} -9.64993e6 q^{28} -333392. q^{29} +1.84542e6 q^{30} +3.14101e6 q^{31} +6.16935e6 q^{32} -7.74278e6 q^{33} -6.67419e6 q^{34} -7.38397e6 q^{35} +5.35901e6 q^{36} -3.83858e6 q^{37} +4.75055e6 q^{38} +1.36645e6 q^{39} -6.94417e6 q^{40} +3.26699e7 q^{41} -3.48838e7 q^{42} -5.89049e6 q^{43} +7.80775e7 q^{44} +4.10062e6 q^{45} -5.42230e7 q^{46} +3.30808e7 q^{47} +1.06811e6 q^{48} +9.92252e7 q^{49} -1.42393e7 q^{50} -1.48305e7 q^{51} -1.37792e7 q^{52} +2.12523e7 q^{53} +1.93724e7 q^{54} +5.97437e7 q^{55} +1.31265e8 q^{56} +1.05560e7 q^{57} +1.21530e7 q^{58} +6.11382e7 q^{59} -4.13504e7 q^{60} +7.35751e7 q^{61} -1.14498e8 q^{62} -7.75139e7 q^{63} -2.18138e8 q^{64} -1.05436e7 q^{65} +2.82245e8 q^{66} -1.46320e8 q^{67} +1.49549e8 q^{68} -1.20487e8 q^{69} +2.69165e8 q^{70} -1.26674e7 q^{71} -7.28971e7 q^{72} -2.02563e8 q^{73} +1.39927e8 q^{74} -3.16406e7 q^{75} -1.06446e8 q^{76} -1.12933e9 q^{77} -4.98107e7 q^{78} -3.71959e7 q^{79} -8.24158e6 q^{80} +4.30467e7 q^{81} -1.19091e9 q^{82} +4.23153e8 q^{83} +7.81644e8 q^{84} +1.14433e8 q^{85} +2.14724e8 q^{86} +2.70047e7 q^{87} -1.06207e9 q^{88} -8.04541e8 q^{89} -1.49479e8 q^{90} +1.99305e8 q^{91} +1.21498e9 q^{92} -2.54422e8 q^{93} -1.20589e9 q^{94} -8.14506e7 q^{95} -4.99717e8 q^{96} -8.98574e8 q^{97} -3.61702e9 q^{98} +6.27165e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) \) 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9} - 10625 q^{10} + 138230 q^{11} - 409455 q^{12} - 176712 q^{13} - 555994 q^{14} - 759375 q^{15} + 1695731 q^{16} - 274992 q^{17} - 111537 q^{18} - 1954815 q^{19} + 3159375 q^{20} - 109512 q^{21} - 1031106 q^{22} + 1714212 q^{23} + 291357 q^{24} + 5859375 q^{25} + 9500004 q^{26} - 7971615 q^{27} + 14545598 q^{28} + 1754340 q^{29} + 860625 q^{30} + 8442914 q^{31} + 35638859 q^{32} - 11196630 q^{33} + 47218266 q^{34} + 845000 q^{35} + 33165855 q^{36} + 2956096 q^{37} + 2215457 q^{38} + 14313672 q^{39} - 2248125 q^{40} - 38550502 q^{41} + 45035514 q^{42} + 50753570 q^{43} + 212125630 q^{44} + 61509375 q^{45} - 117130008 q^{46} - 40252876 q^{47} - 137354211 q^{48} + 110123035 q^{49} - 6640625 q^{50} + 22274352 q^{51} - 87136648 q^{52} + 65532542 q^{53} + 9034497 q^{54} + 86393750 q^{55} - 377288898 q^{56} + 158340015 q^{57} + 211630876 q^{58} + 175407418 q^{59} - 255909375 q^{60} + 151231854 q^{61} - 30983940 q^{62} + 8870472 q^{63} + 836879575 q^{64} - 110445000 q^{65} + 83519586 q^{66} + 40009476 q^{67} - 124850430 q^{68} - 138851172 q^{69} - 347496250 q^{70} + 87578500 q^{71} - 23599917 q^{72} - 360657638 q^{73} + 1373397084 q^{74} - 474609375 q^{75} - 658772655 q^{76} - 304618172 q^{77} - 769500324 q^{78} + 205798286 q^{79} + 1059831875 q^{80} + 645700815 q^{81} - 2327138772 q^{82} - 63321462 q^{83} - 1178193438 q^{84} - 171870000 q^{85} - 848405762 q^{86} - 142101540 q^{87} - 3211126502 q^{88} - 381069174 q^{89} - 69710625 q^{90} + 1476892872 q^{91} - 2382818588 q^{92} - 683876034 q^{93} - 5137318040 q^{94} - 1221759375 q^{95} - 2886747579 q^{96} - 3915268828 q^{97} - 8273557437 q^{98} + 906927030 q^{99}+O(q^{100}) \) 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9 - 10625 * q^10 + 138230 * q^11 - 409455 * q^12 - 176712 * q^13 - 555994 * q^14 - 759375 * q^15 + 1695731 * q^16 - 274992 * q^17 - 111537 * q^18 - 1954815 * q^19 + 3159375 * q^20 - 109512 * q^21 - 1031106 * q^22 + 1714212 * q^23 + 291357 * q^24 + 5859375 * q^25 + 9500004 * q^26 - 7971615 * q^27 + 14545598 * q^28 + 1754340 * q^29 + 860625 * q^30 + 8442914 * q^31 + 35638859 * q^32 - 11196630 * q^33 + 47218266 * q^34 + 845000 * q^35 + 33165855 * q^36 + 2956096 * q^37 + 2215457 * q^38 + 14313672 * q^39 - 2248125 * q^40 - 38550502 * q^41 + 45035514 * q^42 + 50753570 * q^43 + 212125630 * q^44 + 61509375 * q^45 - 117130008 * q^46 - 40252876 * q^47 - 137354211 * q^48 + 110123035 * q^49 - 6640625 * q^50 + 22274352 * q^51 - 87136648 * q^52 + 65532542 * q^53 + 9034497 * q^54 + 86393750 * q^55 - 377288898 * q^56 + 158340015 * q^57 + 211630876 * q^58 + 175407418 * q^59 - 255909375 * q^60 + 151231854 * q^61 - 30983940 * q^62 + 8870472 * q^63 + 836879575 * q^64 - 110445000 * q^65 + 83519586 * q^66 + 40009476 * q^67 - 124850430 * q^68 - 138851172 * q^69 - 347496250 * q^70 + 87578500 * q^71 - 23599917 * q^72 - 360657638 * q^73 + 1373397084 * q^74 - 474609375 * q^75 - 658772655 * q^76 - 304618172 * q^77 - 769500324 * q^78 + 205798286 * q^79 + 1059831875 * q^80 + 645700815 * q^81 - 2327138772 * q^82 - 63321462 * q^83 - 1178193438 * q^84 - 171870000 * q^85 - 848405762 * q^86 - 142101540 * q^87 - 3211126502 * q^88 - 381069174 * q^89 - 69710625 * q^90 + 1476892872 * q^91 - 2382818588 * q^92 - 683876034 * q^93 - 5137318040 * q^94 - 1221759375 * q^95 - 2886747579 * q^96 - 3915268828 * q^97 - 8273557437 * q^98 + 906927030 * q^99

Introduction

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