LMFDB - Embedded newform 38.10.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(1,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("38.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.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:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 34433x^{2} - 2723303x - 48270488 $ x^4 - x^3 - 34433x^2 - 2723303x - 48270488
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$219.264$ of defining polynomial
Character	$\chi$	$=$	38.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000 q^{2} -66.6053 q^{3} +256.000 q^{4} -2418.56 q^{5} +1065.68 q^{6} -1533.95 q^{7} -4096.00 q^{8} -15246.7 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} -66.6053 q^{3} +256.000 q^{4} -2418.56 q^{5} +1065.68 q^{6} -1533.95 q^{7} -4096.00 q^{8} -15246.7 q^{9} +38696.9 q^{10} -5815.50 q^{11} -17051.0 q^{12} -135546. q^{13} +24543.2 q^{14} +161089. q^{15} +65536.0 q^{16} -448133. q^{17} +243948. q^{18} +130321. q^{19} -619151. q^{20} +102169. q^{21} +93048.1 q^{22} +2.07551e6 q^{23} +272815. q^{24} +3.89629e6 q^{25} +2.16874e6 q^{26} +2.32650e6 q^{27} -392691. q^{28} -643630. q^{29} -2.57742e6 q^{30} -194155. q^{31} -1.04858e6 q^{32} +387343. q^{33} +7.17012e6 q^{34} +3.70994e6 q^{35} -3.90316e6 q^{36} +9.46515e6 q^{37} -2.08514e6 q^{38} +9.02808e6 q^{39} +9.90641e6 q^{40} -2.34337e7 q^{41} -1.63471e6 q^{42} +3.80295e7 q^{43} -1.48877e6 q^{44} +3.68751e7 q^{45} -3.32081e7 q^{46} -2.28118e7 q^{47} -4.36504e6 q^{48} -3.80006e7 q^{49} -6.23407e7 q^{50} +2.98480e7 q^{51} -3.46998e7 q^{52} -6.65359e7 q^{53} -3.72241e7 q^{54} +1.40651e7 q^{55} +6.28306e6 q^{56} -8.68007e6 q^{57} +1.02981e7 q^{58} -9.14212e7 q^{59} +4.12387e7 q^{60} -4.02765e7 q^{61} +3.10649e6 q^{62} +2.33877e7 q^{63} +1.67772e7 q^{64} +3.27826e8 q^{65} -6.19749e6 q^{66} +2.42739e8 q^{67} -1.14722e8 q^{68} -1.38240e8 q^{69} -5.93591e7 q^{70} -1.83180e8 q^{71} +6.24506e7 q^{72} -1.39336e8 q^{73} -1.51442e8 q^{74} -2.59514e8 q^{75} +3.33622e7 q^{76} +8.92069e6 q^{77} -1.44449e8 q^{78} +2.51527e8 q^{79} -1.58503e8 q^{80} +1.45144e8 q^{81} +3.74939e8 q^{82} -1.30417e8 q^{83} +2.61553e7 q^{84} +1.08383e9 q^{85} -6.08473e8 q^{86} +4.28692e7 q^{87} +2.38203e7 q^{88} +7.10883e8 q^{89} -5.90002e8 q^{90} +2.07921e8 q^{91} +5.31330e8 q^{92} +1.29318e7 q^{93} +3.64988e8 q^{94} -3.15189e8 q^{95} +6.98407e7 q^{96} -1.31644e9 q^{97} +6.08010e8 q^{98} +8.86675e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9}+O(q^{10}) $ 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9	\( 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9} + 22320 q^{10} - 104249 q^{11} + 21504 q^{12} + 120486 q^{13} - 196912 q^{14} - 591090 q^{15} + 262144 q^{16} - 412139 q^{17} - 264608 q^{18} + 521284 q^{19} - 357120 q^{20} + 2437006 q^{21} + 1667984 q^{22} + 3010300 q^{23} - 344064 q^{24} + 9760585 q^{25} - 1927776 q^{26} + 12387978 q^{27} + 3150592 q^{28} + 6153240 q^{29} + 9457440 q^{30} + 12774024 q^{31} - 4194304 q^{32} - 3258022 q^{33} + 6594224 q^{34} + 9823425 q^{35} + 4233728 q^{36} + 20506048 q^{37} - 8340544 q^{38} + 69881444 q^{39} + 5713920 q^{40} + 11620300 q^{41} - 38992096 q^{42} + 7698327 q^{43} - 26687744 q^{44} - 124015815 q^{45} - 48164800 q^{46} - 31581083 q^{47} + 5505024 q^{48} + 18970383 q^{49} - 156169360 q^{50} - 8594812 q^{51} + 30844416 q^{52} + 72549422 q^{53} - 198207648 q^{54} + 21332505 q^{55} - 50409472 q^{56} + 10946964 q^{57} - 98451840 q^{58} - 149234120 q^{59} - 151319040 q^{60} + 129004373 q^{61} - 204384384 q^{62} + 102967551 q^{63} + 67108864 q^{64} + 124691700 q^{65} + 52128352 q^{66} + 132595266 q^{67} - 105507584 q^{68} - 45529972 q^{69} - 157174800 q^{70} - 47138482 q^{71} - 67739648 q^{72} - 39332795 q^{73} - 328096768 q^{74} + 824627010 q^{75} + 133448704 q^{76} - 165933719 q^{77} - 1118103104 q^{78} - 307010840 q^{79} - 91422720 q^{80} + 1305551744 q^{81} - 185924800 q^{82} - 746568232 q^{83} + 623873536 q^{84} - 105005985 q^{85} - 123173232 q^{86} - 82148208 q^{87} + 427003904 q^{88} + 286943482 q^{89} + 1984253040 q^{90} + 3155781114 q^{91} + 770636800 q^{92} + 1151901596 q^{93} + 505297328 q^{94} - 181797795 q^{95} - 88080384 q^{96} + 793519958 q^{97} - 303526128 q^{98} - 1681833809 q^{99}+O(q^{100}) \) 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9 + 22320 * q^10 - 104249 * q^11 + 21504 * q^12 + 120486 * q^13 - 196912 * q^14 - 591090 * q^15 + 262144 * q^16 - 412139 * q^17 - 264608 * q^18 + 521284 * q^19 - 357120 * q^20 + 2437006 * q^21 + 1667984 * q^22 + 3010300 * q^23 - 344064 * q^24 + 9760585 * q^25 - 1927776 * q^26 + 12387978 * q^27 + 3150592 * q^28 + 6153240 * q^29 + 9457440 * q^30 + 12774024 * q^31 - 4194304 * q^32 - 3258022 * q^33 + 6594224 * q^34 + 9823425 * q^35 + 4233728 * q^36 + 20506048 * q^37 - 8340544 * q^38 + 69881444 * q^39 + 5713920 * q^40 + 11620300 * q^41 - 38992096 * q^42 + 7698327 * q^43 - 26687744 * q^44 - 124015815 * q^45 - 48164800 * q^46 - 31581083 * q^47 + 5505024 * q^48 + 18970383 * q^49 - 156169360 * q^50 - 8594812 * q^51 + 30844416 * q^52 + 72549422 * q^53 - 198207648 * q^54 + 21332505 * q^55 - 50409472 * q^56 + 10946964 * q^57 - 98451840 * q^58 - 149234120 * q^59 - 151319040 * q^60 + 129004373 * q^61 - 204384384 * q^62 + 102967551 * q^63 + 67108864 * q^64 + 124691700 * q^65 + 52128352 * q^66 + 132595266 * q^67 - 105507584 * q^68 - 45529972 * q^69 - 157174800 * q^70 - 47138482 * q^71 - 67739648 * q^72 - 39332795 * q^73 - 328096768 * q^74 + 824627010 * q^75 + 133448704 * q^76 - 165933719 * q^77 - 1118103104 * q^78 - 307010840 * q^79 - 91422720 * q^80 + 1305551744 * q^81 - 185924800 * q^82 - 746568232 * q^83 + 623873536 * q^84 - 105005985 * q^85 - 123173232 * q^86 - 82148208 * q^87 + 427003904 * q^88 + 286943482 * q^89 + 1984253040 * q^90 + 3155781114 * q^91 + 770636800 * q^92 + 1151901596 * q^93 + 505297328 * q^94 - 181797795 * q^95 - 88080384 * q^96 + 793519958 * q^97 - 303526128 * q^98 - 1681833809 * 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 $

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	−66.6053	−0.474748	−0.237374	−	0.971418i	$-0.576287\pi$
$3$	−66.6053	−0.474748	−0.237374	+	0.971418i	$0.576287\pi$
$4$	256.000	0.500000
$5$	−2418.56	−1.73058	−0.865289	−	0.501273i	$-0.832865\pi$
$5$	−2418.56	−1.73058	−0.865289	+	0.501273i	$0.832865\pi$
$6$	1065.68	0.335697
$7$	−1533.95	−0.241474	−0.120737	−	0.992685i	$-0.538526\pi$
$7$	−1533.95	−0.241474	−0.120737	+	0.992685i	$0.538526\pi$
$8$	−4096.00	−0.353553
$9$	−15246.7	−0.774615
$10$	38696.9	1.22370
$11$	−5815.50	−0.119762	−0.0598812	−	0.998206i	$-0.519072\pi$
$11$	−5815.50	−0.119762	−0.0598812	+	0.998206i	$0.519072\pi$
$12$	−17051.0	−0.237374
$13$	−135546.	−1.31626	−0.658130	−	0.752904i	$-0.728652\pi$
$13$	−135546.	−1.31626	−0.658130	+	0.752904i	$0.728652\pi$
$14$	24543.2	0.170748
$15$	161089.	0.821588
$16$	65536.0	0.250000
$17$	−448133.	−1.30133	−0.650663	−	0.759366i	$-0.725509\pi$
$17$	−448133.	−1.30133	−0.650663	+	0.759366i	$0.725509\pi$
$18$	243948.	0.547735
$19$	130321.	0.229416
$19$	130321.	0.229416
$20$	−619151.	−0.865289
$21$	102169.	0.114639
$22$	93048.1	0.0846848
$23$	2.07551e6	1.54650	0.773249	−	0.634102i	$-0.218630\pi$
$23$	2.07551e6	1.54650	0.773249	+	0.634102i	$0.218630\pi$
$24$	272815.	0.167849
$25$	3.89629e6	1.99490
$26$	2.16874e6	0.930737
$27$	2.32650e6	0.842494
$28$	−392691.	−0.120737
$29$	−643630.	−0.168984	−0.0844920	−	0.996424i	$-0.526927\pi$
$29$	−643630.	−0.168984	−0.0844920	+	0.996424i	$0.526927\pi$
$30$	−2.57742e6	−0.580951
$31$	−194155.	−0.0377591	−0.0188796	−	0.999822i	$-0.506010\pi$
$31$	−194155.	−0.0377591	−0.0188796	+	0.999822i	$0.506010\pi$
$32$	−1.04858e6	−0.176777
$33$	387343.	0.0568569
$34$	7.17012e6	0.920177
$35$	3.70994e6	0.417889
$36$	−3.90316e6	−0.387307
$37$	9.46515e6	0.830271	0.415135	−	0.909760i	$-0.363734\pi$
$37$	9.46515e6	0.830271	0.415135	+	0.909760i	$0.363734\pi$
$38$	−2.08514e6	−0.162221
$39$	9.02808e6	0.624892
$40$	9.90641e6	0.611852
$41$	−2.34337e7	−1.29513	−0.647565	−	0.762010i	$-0.724213\pi$
$41$	−2.34337e7	−1.29513	−0.647565	+	0.762010i	$0.724213\pi$
$42$	−1.63471e6	−0.0810621
$43$	3.80295e7	1.69634	0.848170	−	0.529724i	$-0.177704\pi$
$43$	3.80295e7	1.69634	0.848170	+	0.529724i	$0.177704\pi$
$44$	−1.48877e6	−0.0598812
$45$	3.68751e7	1.34053
$46$	−3.32081e7	−1.09354
$47$	−2.28118e7	−0.681897	−0.340948	−	0.940082i	$-0.610748\pi$
$47$	−2.28118e7	−0.681897	−0.340948	+	0.940082i	$0.610748\pi$
$48$	−4.36504e6	−0.118687
$49$	−3.80006e7	−0.941690
$50$	−6.23407e7	−1.41061
$51$	2.98480e7	0.617802
$52$	−3.46998e7	−0.658130
$53$	−6.65359e7	−1.15828	−0.579141	−	0.815227i	$-0.696612\pi$
$53$	−6.65359e7	−1.15828	−0.579141	+	0.815227i	$0.696612\pi$
$54$	−3.72241e7	−0.595733
$55$	1.40651e7	0.207258
$56$	6.28306e6	0.0853739
$57$	−8.68007e6	−0.108915
$58$	1.02981e7	0.119490
$59$	−9.14212e7	−0.982230	−0.491115	−	0.871095i	$-0.663410\pi$
$59$	−9.14212e7	−0.982230	−0.491115	+	0.871095i	$0.663410\pi$
$60$	4.12387e7	0.410794
$61$	−4.02765e7	−0.372450	−0.186225	−	0.982507i	$-0.559625\pi$
$61$	−4.02765e7	−0.372450	−0.186225	+	0.982507i	$0.559625\pi$
$62$	3.10649e6	0.0266997
$63$	2.33877e7	0.187049
$64$	1.67772e7	0.125000
$65$	3.27826e8	2.27789
$66$	−6.19749e6	−0.0402039
$67$	2.42739e8	1.47164	0.735822	−	0.677175i	$-0.236796\pi$
$67$	2.42739e8	1.47164	0.735822	+	0.677175i	$0.236796\pi$
$68$	−1.14722e8	−0.650663
$69$	−1.38240e8	−0.734197
$70$	−5.93591e7	−0.295492
$71$	−1.83180e8	−0.855491	−0.427745	−	0.903899i	$-0.640692\pi$
$71$	−1.83180e8	−0.855491	−0.427745	+	0.903899i	$0.640692\pi$
$72$	6.24506e7	0.273868
$73$	−1.39336e8	−0.574264	−0.287132	−	0.957891i	$-0.592702\pi$
$73$	−1.39336e8	−0.574264	−0.287132	+	0.957891i	$0.592702\pi$
$74$	−1.51442e8	−0.587090
$75$	−2.59514e8	−0.947075
$76$	3.33622e7	0.114708
$77$	8.92069e6	0.0289195
$78$	−1.44449e8	−0.441865
$79$	2.51527e8	0.726546	0.363273	−	0.931683i	$-0.381659\pi$
$79$	2.51527e8	0.726546	0.363273	+	0.931683i	$0.381659\pi$
$80$	−1.58503e8	−0.432645
$81$	1.45144e8	0.374642
$82$	3.74939e8	0.915795
$83$	−1.30417e8	−0.301636	−0.150818	−	0.988562i	$-0.548191\pi$
$83$	−1.30417e8	−0.301636	−0.150818	+	0.988562i	$0.548191\pi$
$84$	2.61553e7	0.0573196
$85$	1.08383e9	2.25205
$86$	−6.08473e8	−1.19949
$87$	4.28692e7	0.0802247
$88$	2.38203e7	0.0423424
$89$	7.10883e8	1.20100	0.600500	−	0.799625i	$-0.294968\pi$
$89$	7.10883e8	1.20100	0.600500	+	0.799625i	$0.294968\pi$
$90$	−5.90002e8	−0.947899
$91$	2.07921e8	0.317842
$92$	5.31330e8	0.773249
$93$	1.29318e7	0.0179261
$94$	3.64988e8	0.482174
$95$	−3.15189e8	−0.397022
$96$	6.98407e7	0.0839244
$97$	−1.31644e9	−1.50983	−0.754916	−	0.655822i	$-0.772322\pi$
$97$	−1.31644e9	−1.50983	−0.754916	+	0.655822i	$0.772322\pi$
$98$	6.08010e8	0.665876
$99$	8.86675e7	0.0927696
$100$	9.97451e8	0.997451
$101$	1.38054e9	1.32009	0.660044	−	0.751227i	$-0.270538\pi$
$101$	1.38054e9	1.32009	0.660044	+	0.751227i	$0.270538\pi$
$102$	−4.77568e8	−0.436852
$103$	−9.35066e8	−0.818606	−0.409303	−	0.912399i	$-0.634228\pi$
$103$	−9.35066e8	−0.818606	−0.409303	+	0.912399i	$0.634228\pi$
$104$	5.55197e8	0.465368
$105$	−2.47102e8	−0.198392
$106$	1.06457e9	0.819030
$107$	−4.27772e8	−0.315490	−0.157745	−	0.987480i	$-0.550422\pi$
$107$	−4.27772e8	−0.315490	−0.157745	+	0.987480i	$0.550422\pi$
$108$	5.95585e8	0.421247
$109$	−1.13801e8	−0.0772197	−0.0386098	−	0.999254i	$-0.512293\pi$
$109$	−1.13801e8	−0.0772197	−0.0386098	+	0.999254i	$0.512293\pi$
$110$	−2.25042e8	−0.146554
$111$	−6.30429e8	−0.394169
$112$	−1.00529e8	−0.0603684
$113$	1.37096e9	0.790990	0.395495	−	0.918468i	$-0.370573\pi$
$113$	1.37096e9	0.790990	0.395495	+	0.918468i	$0.370573\pi$
$114$	1.38881e8	0.0770143
$115$	−5.01974e9	−2.67634
$116$	−1.64769e8	−0.0844920
$117$	2.06663e9	1.01959
$118$	1.46274e9	0.694541
$119$	6.87413e8	0.314236
$120$	−6.59819e8	−0.290475
$121$	−2.32413e9	−0.985657
$122$	6.44424e8	0.263362
$123$	1.56081e9	0.614860
$124$	−4.97038e7	−0.0188796
$125$	−4.69966e9	−1.72176
$126$	−3.74204e8	−0.132264
$127$	1.64706e9	0.561813	0.280906	−	0.959735i	$-0.409365\pi$
$127$	1.64706e9	0.561813	0.280906	+	0.959735i	$0.409365\pi$
$128$	−2.68435e8	−0.0883883
$129$	−2.53297e9	−0.805334
$130$	−5.24521e9	−1.61071
$131$	−3.65669e9	−1.08485	−0.542423	−	0.840106i	$-0.682493\pi$
$131$	−3.65669e9	−1.08485	−0.542423	+	0.840106i	$0.682493\pi$
$132$	9.91599e7	0.0284285
$133$	−1.99906e8	−0.0553979
$134$	−3.88382e9	−1.04061
$135$	−5.62678e9	−1.45800
$136$	1.83555e9	0.460088
$137$	−3.24163e9	−0.786179	−0.393089	−	0.919500i	$-0.628594\pi$
$137$	−3.24163e9	−0.786179	−0.393089	+	0.919500i	$0.628594\pi$
$138$	2.21184e9	0.519155
$139$	8.69038e9	1.97457	0.987285	−	0.158963i	$-0.0508151\pi$
$139$	8.69038e9	1.97457	0.987285	+	0.158963i	$0.0508151\pi$
$140$	9.49746e8	0.208945
$141$	1.51938e9	0.323729
$142$	2.93088e9	0.604923
$143$	7.88269e8	0.157638
$144$	−9.99210e8	−0.193654
$145$	1.55666e9	0.292440
$146$	2.22938e9	0.406066
$147$	2.53104e9	0.447065
$148$	2.42308e9	0.415135
$149$	−7.11665e9	−1.18287	−0.591435	−	0.806353i	$-0.701438\pi$
$149$	−7.11665e9	−1.18287	−0.591435	+	0.806353i	$0.701438\pi$
$150$	4.15222e9	0.669683
$151$	1.87879e9	0.294091	0.147046	−	0.989130i	$-0.453024\pi$
$151$	1.87879e9	0.294091	0.147046	+	0.989130i	$0.453024\pi$
$152$	−5.33795e8	−0.0811107
$153$	6.83256e9	1.00803
$154$	−1.42731e8	−0.0204491
$155$	4.69576e8	0.0653451
$156$	2.31119e9	0.312446
$157$	4.95963e9	0.651480	0.325740	−	0.945459i	$-0.394387\pi$
$157$	4.95963e9	0.651480	0.325740	+	0.945459i	$0.394387\pi$
$158$	−4.02444e9	−0.513746
$159$	4.43164e9	0.549892
$160$	2.53604e9	0.305926
$161$	−3.18373e9	−0.373439
$162$	−2.32230e9	−0.264912
$163$	2.87539e9	0.319046	0.159523	−	0.987194i	$-0.449004\pi$
$163$	2.87539e9	0.319046	0.159523	+	0.987194i	$0.449004\pi$
$164$	−5.99902e9	−0.647565
$165$	−9.36812e8	−0.0983953
$166$	2.08668e9	0.213289
$167$	1.47841e10	1.47085	0.735427	−	0.677604i	$-0.236982\pi$
$167$	1.47841e10	1.47085	0.735427	+	0.677604i	$0.236982\pi$
$168$	−4.18485e8	−0.0405310
$169$	7.76823e9	0.732541
$170$	−1.73413e10	−1.59244
$171$	−1.98697e9	−0.177709
$172$	9.73556e9	0.848170
$173$	1.45582e10	1.23566	0.617832	−	0.786310i	$-0.288011\pi$
$173$	1.45582e10	1.23566	0.617832	+	0.786310i	$0.288011\pi$
$174$	−6.85907e8	−0.0567275
$175$	−5.97672e9	−0.481716
$176$	−3.81125e8	−0.0299406
$177$	6.08914e9	0.466311
$178$	−1.13741e10	−0.849235
$179$	−1.82403e10	−1.32799	−0.663994	−	0.747738i	$-0.731140\pi$
$179$	−1.82403e10	−1.32799	−0.663994	+	0.747738i	$0.731140\pi$
$180$	9.44003e9	0.670266
$181$	2.81167e10	1.94720	0.973602	−	0.228252i	$-0.0733011\pi$
$181$	2.81167e10	1.94720	0.973602	+	0.228252i	$0.0733011\pi$
$182$	−3.32673e9	−0.224748
$183$	2.68263e9	0.176820
$184$	−8.50129e9	−0.546770
$185$	−2.28920e10	−1.43685
$186$	−2.06908e8	−0.0126756
$187$	2.60612e9	0.155850
$188$	−5.83981e9	−0.340948
$189$	−3.56874e9	−0.203440
$190$	5.04302e9	0.280737
$191$	2.82317e8	0.0153492	0.00767462	−	0.999971i	$-0.497557\pi$
$191$	2.82317e8	0.0153492	0.00767462	+	0.999971i	$0.497557\pi$
$192$	−1.11745e9	−0.0593435
$193$	1.43117e10	0.742477	0.371239	−	0.928538i	$-0.378933\pi$
$193$	1.43117e10	0.742477	0.371239	+	0.928538i	$0.378933\pi$
$194$	2.10630e10	1.06761
$195$	−2.18349e10	−1.08142
$196$	−9.72816e9	−0.470845
$197$	2.02116e10	0.956100	0.478050	−	0.878333i	$-0.341344\pi$
$197$	2.02116e10	0.956100	0.478050	+	0.878333i	$0.341344\pi$
$198$	−1.41868e9	−0.0655980
$199$	−3.95924e10	−1.78967	−0.894835	−	0.446398i	$-0.852707\pi$
$199$	−3.95924e10	−1.78967	−0.894835	+	0.446398i	$0.852707\pi$
$200$	−1.59592e10	−0.705304
$201$	−1.61677e10	−0.698660
$202$	−2.20886e10	−0.933443
$203$	9.87296e8	0.0408052
$204$	7.64109e9	0.308901
$205$	5.66757e10	2.24132
$206$	1.49611e10	0.578842
$207$	−3.16447e10	−1.19794
$208$	−8.88315e9	−0.329065
$209$	−7.57882e8	−0.0274754
$210$	3.95363e9	0.140284
$211$	−1.31017e10	−0.455047	−0.227523	−	0.973773i	$-0.573063\pi$
$211$	−1.31017e10	−0.455047	−0.227523	+	0.973773i	$0.573063\pi$
$212$	−1.70332e10	−0.579141
$213$	1.22008e10	0.406142
$214$	6.84436e9	0.223085
$215$	−9.19766e10	−2.93565
$216$	−9.52936e9	−0.297867
$217$	2.97825e8	0.00911784
$218$	1.82082e9	0.0546026
$219$	9.28054e9	0.272631
$220$	3.60067e9	0.103629
$221$	6.07426e10	1.71288
$222$	1.00869e10	0.278720
$223$	6.50346e10	1.76105	0.880526	−	0.473997i	$-0.157189\pi$
$223$	6.50346e10	1.76105	0.880526	+	0.473997i	$0.157189\pi$
$224$	1.60846e9	0.0426869
$225$	−5.94058e10	−1.54528
$226$	−2.19353e10	−0.559315
$227$	1.02990e10	0.257442	0.128721	−	0.991681i	$-0.458913\pi$
$227$	1.02990e10	0.257442	0.128721	+	0.991681i	$0.458913\pi$
$228$	−2.22210e9	−0.0544573
$229$	1.71789e10	0.412797	0.206398	−	0.978468i	$-0.433826\pi$
$229$	1.71789e10	0.412797	0.206398	+	0.978468i	$0.433826\pi$
$230$	8.03158e10	1.89246
$231$	−5.94165e8	−0.0137294
$232$	2.63631e9	0.0597448
$233$	−6.52465e10	−1.45029	−0.725146	−	0.688595i	$-0.758228\pi$
$233$	−6.52465e10	−1.45029	−0.725146	+	0.688595i	$0.758228\pi$
$234$	−3.30662e10	−0.720962
$235$	5.51716e10	1.18008
$236$	−2.34038e10	−0.491115
$237$	−1.67530e10	−0.344926
$238$	−1.09986e10	−0.222199
$239$	−1.43024e10	−0.283543	−0.141771	−	0.989899i	$-0.545280\pi$
$239$	−1.43024e10	−0.283543	−0.141771	+	0.989899i	$0.545280\pi$
$240$	1.05571e10	0.205397
$241$	−4.79560e10	−0.915727	−0.457864	−	0.889022i	$-0.651385\pi$
$241$	−4.79560e10	−0.915727	−0.457864	+	0.889022i	$0.651385\pi$
$242$	3.71860e10	0.696965
$243$	−5.54600e10	−1.02035
$244$	−1.03108e10	−0.186225
$245$	9.19066e10	1.62967
$246$	−2.49729e10	−0.434772
$247$	−1.76645e10	−0.301971
$248$	7.95261e8	0.0133499
$249$	8.68647e9	0.143201
$250$	7.51946e10	1.21747
$251$	−1.25023e10	−0.198819	−0.0994096	−	0.995047i	$-0.531695\pi$
$251$	−1.25023e10	−0.198819	−0.0994096	+	0.995047i	$0.531695\pi$
$252$	5.98726e9	0.0935245
$253$	−1.20701e10	−0.185212
$254$	−2.63529e10	−0.397261
$255$	−7.21891e10	−1.06915
$256$	4.29497e9	0.0625000
$257$	1.83653e10	0.262602	0.131301	−	0.991343i	$-0.458085\pi$
$257$	1.83653e10	0.262602	0.131301	+	0.991343i	$0.458085\pi$
$258$	4.05275e10	0.569457
$259$	−1.45191e10	−0.200489
$260$	8.39234e10	1.13895
$261$	9.81326e9	0.130897
$262$	5.85071e10	0.767101
$263$	8.39157e10	1.08154	0.540770	−	0.841171i	$-0.318133\pi$
$263$	8.39157e10	1.08154	0.540770	+	0.841171i	$0.318133\pi$
$264$	−1.58656e9	−0.0201020
$265$	1.60921e11	2.00450
$266$	3.19849e9	0.0391722
$267$	−4.73485e10	−0.570172
$268$	6.21412e10	0.735822
$269$	9.33233e9	0.108669	0.0543344	−	0.998523i	$-0.482696\pi$
$269$	9.33233e9	0.108669	0.0543344	+	0.998523i	$0.482696\pi$
$270$	9.00286e10	1.03096
$271$	−1.57854e11	−1.77785	−0.888924	−	0.458055i	$-0.848546\pi$
$271$	−1.57854e11	−1.77785	−0.888924	+	0.458055i	$0.848546\pi$
$272$	−2.93688e10	−0.325332
$273$	−1.38486e10	−0.150895
$274$	5.18661e10	0.555912
$275$	−2.26589e10	−0.238914
$276$	−3.53894e10	−0.367098
$277$	−1.12981e11	−1.15305	−0.576525	−	0.817080i	$-0.695592\pi$
$277$	−1.12981e11	−1.15305	−0.576525	+	0.817080i	$0.695592\pi$
$278$	−1.39046e11	−1.39623
$279$	2.96024e9	0.0292488
$280$	−1.51959e10	−0.147746
$281$	7.83548e10	0.749699	0.374849	−	0.927086i	$-0.377694\pi$
$281$	7.83548e10	0.749699	0.374849	+	0.927086i	$0.377694\pi$
$282$	−2.43102e10	−0.228911
$283$	8.46004e10	0.784032	0.392016	−	0.919958i	$-0.371778\pi$
$283$	8.46004e10	0.784032	0.392016	+	0.919958i	$0.371778\pi$
$284$	−4.68941e10	−0.427745
$285$	2.09932e10	0.188485
$286$	−1.26123e10	−0.111467
$287$	3.59461e10	0.312740
$288$	1.59874e10	0.136934
$289$	8.22349e10	0.693451
$290$	−2.49065e10	−0.206786
$291$	8.76819e10	0.716789
$292$	−3.56701e10	−0.287132
$293$	−1.06621e11	−0.845157	−0.422579	−	0.906326i	$-0.638875\pi$
$293$	−1.06621e11	−0.845157	−0.422579	+	0.906326i	$0.638875\pi$
$294$	−4.04967e10	−0.316123
$295$	2.21107e11	1.69983
$296$	−3.87693e10	−0.293545
$297$	−1.35298e10	−0.100899
$298$	1.13866e11	0.836416
$299$	−2.81327e11	−2.03559
$300$	−6.64355e10	−0.473538
$301$	−5.83354e10	−0.409622
$302$	−3.00606e10	−0.207954
$303$	−9.19513e10	−0.626709
$304$	8.54072e9	0.0573539
$305$	9.74110e10	0.644553
$306$	−1.09321e11	−0.712782
$307$	1.65292e11	1.06201	0.531006	−	0.847368i	$-0.321814\pi$
$307$	1.65292e11	1.06201	0.531006	+	0.847368i	$0.321814\pi$
$308$	2.28370e9	0.0144597
$309$	6.22803e10	0.388631
$310$	−7.51322e9	−0.0462060
$311$	−1.08969e11	−0.660515	−0.330257	−	0.943891i	$-0.607136\pi$
$311$	−1.08969e11	−0.660515	−0.330257	+	0.943891i	$0.607136\pi$
$312$	−3.69790e10	−0.220933
$313$	9.48622e10	0.558655	0.279328	−	0.960196i	$-0.409888\pi$
$313$	9.48622e10	0.558655	0.279328	+	0.960196i	$0.409888\pi$
$314$	−7.93541e10	−0.460666
$315$	−5.65645e10	−0.323703
$316$	6.43910e10	0.363273
$317$	2.75000e11	1.52956	0.764780	−	0.644291i	$-0.222848\pi$
$317$	2.75000e11	1.52956	0.764780	+	0.644291i	$0.222848\pi$
$318$	−7.09063e10	−0.388833
$319$	3.74303e9	0.0202379
$320$	−4.05767e10	−0.216322
$321$	2.84919e10	0.149778
$322$	5.09396e10	0.264061
$323$	−5.84011e10	−0.298545
$324$	3.71569e10	0.187321
$325$	−5.28127e11	−2.62581
$326$	−4.60063e10	−0.225599
$327$	7.57977e9	0.0366599
$328$	9.59844e10	0.457898
$329$	3.49921e10	0.164660
$330$	1.49890e10	0.0695760
$331$	−1.28057e11	−0.586378	−0.293189	−	0.956055i	$-0.594716\pi$
$331$	−1.28057e11	−0.586378	−0.293189	+	0.956055i	$0.594716\pi$
$332$	−3.33868e10	−0.150818
$333$	−1.44313e11	−0.643140
$334$	−2.36545e11	−1.04005
$335$	−5.87078e11	−2.54680
$336$	6.69576e9	0.0286598
$337$	−3.03698e10	−0.128265	−0.0641324	−	0.997941i	$-0.520428\pi$
$337$	−3.03698e10	−0.128265	−0.0641324	+	0.997941i	$0.520428\pi$
$338$	−1.24292e11	−0.517985
$339$	−9.13130e10	−0.375521
$340$	2.77462e11	1.12602
$341$	1.12911e9	0.00452212
$342$	3.17915e10	0.125659
$343$	1.20191e11	0.468867
$344$	−1.55769e11	−0.599747
$345$	3.34341e11	1.27059
$346$	−2.32931e11	−0.873747
$347$	4.03811e11	1.49519	0.747594	−	0.664156i	$-0.231209\pi$
$347$	4.03811e11	1.49519	0.747594	+	0.664156i	$0.231209\pi$
$348$	1.09745e10	0.0401124
$349$	6.29420e10	0.227105	0.113552	−	0.993532i	$-0.463777\pi$
$349$	6.29420e10	0.227105	0.113552	+	0.993532i	$0.463777\pi$
$350$	9.56275e10	0.340625
$351$	−3.15349e11	−1.10894
$352$	6.09800e9	0.0211712
$353$	9.36033e10	0.320852	0.160426	−	0.987048i	$-0.448713\pi$
$353$	9.36033e10	0.320852	0.160426	+	0.987048i	$0.448713\pi$
$354$	−9.74262e10	−0.329732
$355$	4.43031e11	1.48049
$356$	1.81986e11	0.600500
$357$	−4.57853e10	−0.149183
$358$	2.91846e11	0.939030
$359$	3.18605e11	1.01234	0.506171	−	0.862433i	$-0.331060\pi$
$359$	3.18605e11	1.01234	0.506171	+	0.862433i	$0.331060\pi$
$360$	−1.51040e11	−0.473949
$361$	1.69836e10	0.0526316
$362$	−4.49868e11	−1.37688
$363$	1.54799e11	0.467939
$364$	5.32277e10	0.158921
$365$	3.36993e11	0.993810
$366$	−4.29220e10	−0.125030
$367$	9.81213e10	0.282336	0.141168	−	0.989986i	$-0.454914\pi$
$367$	9.81213e10	0.282336	0.141168	+	0.989986i	$0.454914\pi$
$368$	1.36021e11	0.386625
$369$	3.57287e11	1.00323
$370$	3.66272e11	1.01601
$371$	1.02063e11	0.279695
$372$	3.31054e9	0.00896303
$373$	2.24989e11	0.601827	0.300913	−	0.953652i	$-0.402709\pi$
$373$	2.24989e11	0.601827	0.300913	+	0.953652i	$0.402709\pi$
$374$	−4.16979e10	−0.110203
$375$	3.13022e11	0.817400
$376$	9.34370e10	0.241087
$377$	8.72415e10	0.222427
$378$	5.70999e10	0.143854
$379$	6.24000e11	1.55349	0.776744	−	0.629817i	$-0.216870\pi$
$379$	6.24000e11	1.55349	0.776744	+	0.629817i	$0.216870\pi$
$380$	−8.06883e10	−0.198511
$381$	−1.09703e11	−0.266719
$382$	−4.51707e9	−0.0108536
$383$	5.36899e11	1.27497	0.637483	−	0.770465i	$-0.279976\pi$
$383$	5.36899e11	1.27497	0.637483	+	0.770465i	$0.279976\pi$
$384$	1.78792e10	0.0419622
$385$	−2.15752e10	−0.0500474
$386$	−2.28987e11	−0.525011
$387$	−5.79826e11	−1.31401
$388$	−3.37009e11	−0.754916
$389$	−1.30155e11	−0.288195	−0.144097	−	0.989564i	$-0.546028\pi$
$389$	−1.30155e11	−0.288195	−0.144097	+	0.989564i	$0.546028\pi$
$390$	3.49359e11	0.764682
$391$	−9.30103e11	−2.01250
$392$	1.55650e11	0.332938
$393$	2.43555e11	0.515028
$394$	−3.23386e11	−0.676064
$395$	−6.08333e11	−1.25735
$396$	2.26989e10	0.0463848
$397$	−7.36706e11	−1.48846	−0.744230	−	0.667924i	$-0.767183\pi$
$397$	−7.36706e11	−1.48846	−0.744230	+	0.667924i	$0.767183\pi$
$398$	6.33478e11	1.26549
$399$	1.33148e10	0.0263000
$400$	2.55347e11	0.498726
$401$	−5.90469e11	−1.14037	−0.570187	−	0.821515i	$-0.693129\pi$
$401$	−5.90469e11	−1.14037	−0.570187	+	0.821515i	$0.693129\pi$
$402$	2.58683e11	0.494027
$403$	2.63170e10	0.0497008
$404$	3.53418e11	0.660044
$405$	−3.51039e11	−0.648348
$406$	−1.57967e10	−0.0288536
$407$	−5.50446e10	−0.0994352
$408$	−1.22257e11	−0.218426
$409$	−4.27579e11	−0.755547	−0.377773	−	0.925898i	$-0.623310\pi$
$409$	−4.27579e11	−0.755547	−0.377773	+	0.925898i	$0.623310\pi$
$410$	−9.06811e11	−1.58486
$411$	2.15910e11	0.373237
$412$	−2.39377e11	−0.409303
$413$	1.40236e11	0.237183
$414$	5.06316e11	0.847071
$415$	3.15421e11	0.522005
$416$	1.42130e11	0.232684
$417$	−5.78825e11	−0.937422
$418$	1.21261e10	0.0194280
$419$	9.75902e11	1.54683	0.773416	−	0.633899i	$-0.218546\pi$
$419$	9.75902e11	1.54683	0.773416	+	0.633899i	$0.218546\pi$
$420$	−6.32581e10	−0.0991960
$421$	−6.82920e10	−0.105950	−0.0529750	−	0.998596i	$-0.516870\pi$
$421$	−6.82920e10	−0.105950	−0.0529750	+	0.998596i	$0.516870\pi$
$422$	2.09627e11	0.321766
$423$	3.47805e11	0.528207
$424$	2.72531e11	0.409515
$425$	−1.74606e12	−2.59602
$426$	−1.95212e11	−0.287186
$427$	6.17821e10	0.0899368
$428$	−1.09510e11	−0.157745
$429$	−5.25028e10	−0.0748385
$430$	1.47163e12	2.07582
$431$	−2.97113e11	−0.414738	−0.207369	−	0.978263i	$-0.566490\pi$
$431$	−2.97113e11	−0.414738	−0.207369	+	0.978263i	$0.566490\pi$
$432$	1.52470e11	0.210624
$433$	−4.51168e11	−0.616798	−0.308399	−	0.951257i	$-0.599793\pi$
$433$	−4.51168e11	−0.616798	−0.308399	+	0.951257i	$0.599793\pi$
$434$	−4.76520e9	−0.00644729
$435$	−1.03682e11	−0.138835
$436$	−2.91331e10	−0.0386098
$437$	2.70482e11	0.354791
$438$	−1.48489e11	−0.192779
$439$	5.55482e11	0.713805	0.356903	−	0.934142i	$-0.383833\pi$
$439$	5.55482e11	0.713805	0.356903	+	0.934142i	$0.383833\pi$
$440$	−5.76108e10	−0.0732768
$441$	5.79385e11	0.729447
$442$	−9.71881e11	−1.21119
$443$	−1.61691e12	−1.99466	−0.997329	−	0.0730386i	$-0.976730\pi$
$443$	−1.61691e12	−1.99466	−0.997329	+	0.0730386i	$0.976730\pi$
$444$	−1.61390e11	−0.197085
$445$	−1.71931e12	−2.07842
$446$	−1.04055e12	−1.24525
$447$	4.74006e11	0.561565
$448$	−2.57354e10	−0.0301842
$449$	4.52893e11	0.525880	0.262940	−	0.964812i	$-0.415308\pi$
$449$	4.52893e11	0.525880	0.262940	+	0.964812i	$0.415308\pi$
$450$	9.50492e11	1.09268
$451$	1.36279e11	0.155108
$452$	3.50965e11	0.395495
$453$	−1.25137e11	−0.139619
$454$	−1.64784e11	−0.182039
$455$	−5.02868e11	−0.550051
$456$	3.55536e10	0.0385071
$457$	1.10310e12	1.18302	0.591511	−	0.806297i	$-0.298532\pi$
$457$	1.10310e12	1.18302	0.591511	+	0.806297i	$0.298532\pi$
$458$	−2.74863e11	−0.291891
$459$	−1.04258e12	−1.09636
$460$	−1.28505e12	−1.33817
$461$	2.22092e11	0.229023	0.114511	−	0.993422i	$-0.463470\pi$
$461$	2.22092e11	0.229023	0.114511	+	0.993422i	$0.463470\pi$
$462$	9.50664e9	0.00970819
$463$	9.97229e11	1.00851	0.504255	−	0.863555i	$-0.331767\pi$
$463$	9.97229e11	1.00851	0.504255	+	0.863555i	$0.331767\pi$
$464$	−4.21809e10	−0.0422460
$465$	−3.12762e10	−0.0310225
$466$	1.04394e12	1.02551
$467$	8.73582e11	0.849919	0.424959	−	0.905212i	$-0.360288\pi$
$467$	8.73582e11	0.849919	0.424959	+	0.905212i	$0.360288\pi$
$468$	5.29059e11	0.509797
$469$	−3.72349e11	−0.355363
$470$	−8.82745e11	−0.834440
$471$	−3.30338e11	−0.309289
$472$	3.74461e11	0.347271
$473$	−2.21161e11	−0.203158
$474$	2.68049e11	0.243900
$475$	5.07769e11	0.457662
$476$	1.75978e11	0.157118
$477$	1.01446e12	0.897223
$478$	2.28838e11	0.200495
$479$	1.60658e12	1.39442	0.697209	−	0.716868i	$-0.254425\pi$
$479$	1.60658e12	1.39442	0.697209	+	0.716868i	$0.254425\pi$
$480$	−1.68914e11	−0.145238
$481$	−1.28296e12	−1.09285
$482$	7.67296e11	0.647517
$483$	2.12053e11	0.177289
$484$	−5.94977e11	−0.492828
$485$	3.18389e12	2.61288
$486$	8.87359e11	0.721500
$487$	−9.25381e11	−0.745487	−0.372744	−	0.927934i	$-0.621583\pi$
$487$	−9.25381e11	−0.745487	−0.372744	+	0.927934i	$0.621583\pi$
$488$	1.64973e11	0.131681
$489$	−1.91516e11	−0.151466
$490$	−1.47051e12	−1.15235
$491$	−9.28628e11	−0.721066	−0.360533	−	0.932746i	$-0.617405\pi$
$491$	−9.28628e11	−0.721066	−0.360533	+	0.932746i	$0.617405\pi$
$492$	3.99567e11	0.307430
$493$	2.88432e11	0.219903
$494$	2.82632e11	0.213526
$495$	−2.14447e11	−0.160545
$496$	−1.27242e10	−0.00943978
$497$	2.80989e11	0.206579
$498$	−1.38984e11	−0.101259
$499$	1.19609e12	0.863601	0.431800	−	0.901969i	$-0.357878\pi$
$499$	1.19609e12	0.863601	0.431800	+	0.901969i	$0.357878\pi$
$500$	−1.20311e12	−0.860878
$501$	−9.84696e11	−0.698285
$502$	2.00037e11	0.140586
$503$	1.02039e12	0.710741	0.355370	−	0.934726i	$-0.384355\pi$
$503$	1.02039e12	0.710741	0.355370	+	0.934726i	$0.384355\pi$
$504$	−9.57961e10	−0.0661318
$505$	−3.33892e12	−2.28452
$506$	1.93122e11	0.130965
$507$	−5.17405e11	−0.347772
$508$	4.21646e11	0.280906
$509$	−5.49549e11	−0.362891	−0.181446	−	0.983401i	$-0.558078\pi$
$509$	−5.49549e11	−0.362891	−0.181446	+	0.983401i	$0.558078\pi$
$510$	1.15503e12	0.756007
$511$	2.13735e11	0.138670
$512$	−6.87195e10	−0.0441942
$513$	3.03192e11	0.193281
$514$	−2.93844e11	−0.185688
$515$	2.26151e12	1.41666
$516$	−6.48440e11	−0.402667
$517$	1.32662e11	0.0816656
$518$	2.32305e11	0.141767
$519$	−9.69654e11	−0.586629
$520$	−1.34277e12	−0.805356
$521$	1.28517e12	0.764172	0.382086	−	0.924127i	$-0.375206\pi$
$521$	1.28517e12	0.764172	0.382086	+	0.924127i	$0.375206\pi$
$522$	−1.57012e11	−0.0925584
$523$	1.65568e12	0.967654	0.483827	−	0.875164i	$-0.339246\pi$
$523$	1.65568e12	0.967654	0.483827	+	0.875164i	$0.339246\pi$
$524$	−9.36114e11	−0.542423
$525$	3.98081e11	0.228694
$526$	−1.34265e12	−0.764764
$527$	8.70074e10	0.0491370
$528$	2.53849e10	0.0142142
$529$	2.50659e12	1.39166
$530$	−2.57473e12	−1.41740
$531$	1.39388e12	0.760849
$532$	−5.11759e10	−0.0276989
$533$	3.17634e12	1.70473
$534$	7.57577e11	0.403172
$535$	1.03459e12	0.545980
$536$	−9.94259e11	−0.520305
$537$	1.21490e12	0.630460
$538$	−1.49317e11	−0.0768404
$539$	2.20993e11	0.112779
$540$	−1.44046e12	−0.729001
$541$	−1.91314e12	−0.960192	−0.480096	−	0.877216i	$-0.659398\pi$
$541$	−1.91314e12	−0.960192	−0.480096	+	0.877216i	$0.659398\pi$
$542$	2.52567e12	1.25713
$543$	−1.87272e12	−0.924431
$544$	4.69901e11	0.230044
$545$	2.75235e11	0.133635
$546$	2.21578e11	0.106699
$547$	−8.87680e11	−0.423949	−0.211974	−	0.977275i	$-0.567989\pi$
$547$	−8.87680e11	−0.423949	−0.211974	+	0.977275i	$0.567989\pi$
$548$	−8.29858e11	−0.393089
$549$	6.14085e11	0.288505
$550$	3.62543e11	0.168938
$551$	−8.38785e10	−0.0387676
$552$	5.66231e11	0.259578
$553$	−3.85830e11	−0.175442
$554$	1.80770e12	0.815329
$555$	1.52473e12	0.682141
$556$	2.22474e12	0.987285
$557$	−1.28351e12	−0.565001	−0.282501	−	0.959267i	$-0.591164\pi$
$557$	−1.28351e12	−0.565001	−0.282501	+	0.959267i	$0.591164\pi$
$558$	−4.73638e10	−0.0206820
$559$	−5.15475e12	−2.23283
$560$	2.43135e11	0.104472
$561$	−1.73581e11	−0.0739894
$562$	−1.25368e12	−0.530117
$563$	4.00016e12	1.67799	0.838995	−	0.544139i	$-0.183144\pi$
$563$	4.00016e12	1.67799	0.838995	+	0.544139i	$0.183144\pi$
$564$	3.88962e11	0.161865
$565$	−3.31574e12	−1.36887
$566$	−1.35361e12	−0.554394
$567$	−2.22644e11	−0.0904662
$568$	7.50305e11	0.302462
$569$	−1.23909e12	−0.495563	−0.247782	−	0.968816i	$-0.579702\pi$
$569$	−1.23909e12	−0.495563	−0.247782	+	0.968816i	$0.579702\pi$
$570$	−3.35892e11	−0.133279
$571$	−5.04024e12	−1.98421	−0.992107	−	0.125395i	$-0.959980\pi$
$571$	−5.04024e12	−1.98421	−0.992107	+	0.125395i	$0.959980\pi$
$572$	2.01797e11	0.0788192
$573$	−1.88038e10	−0.00728702
$574$	−5.75137e11	−0.221140
$575$	8.08679e12	3.08511
$576$	−2.55798e11	−0.0968268
$577$	−4.83898e12	−1.81745	−0.908725	−	0.417395i	$-0.862943\pi$
$577$	−4.83898e12	−1.81745	−0.908725	+	0.417395i	$0.862943\pi$
$578$	−1.31576e12	−0.490344
$579$	−9.53234e11	−0.352489
$580$	3.98504e11	0.146220
$581$	2.00053e11	0.0728372
$582$	−1.40291e12	−0.506846
$583$	3.86940e11	0.138719
$584$	5.70722e11	0.203033
$585$	−4.99827e12	−1.76449
$586$	1.70593e12	0.597617
$587$	−1.95960e12	−0.681233	−0.340617	−	0.940202i	$-0.610636\pi$
$587$	−1.95960e12	−0.681233	−0.340617	+	0.940202i	$0.610636\pi$
$588$	6.47946e11	0.223533
$589$	−2.53025e10	−0.00866254
$590$	−3.53772e12	−1.20196
$591$	−1.34620e12	−0.453906
$592$	6.20308e11	0.207568
$593$	−4.89414e12	−1.62529	−0.812643	−	0.582762i	$-0.801972\pi$
$593$	−4.89414e12	−1.62529	−0.812643	+	0.582762i	$0.801972\pi$
$594$	2.16477e11	0.0713464
$595$	−1.66255e12	−0.543810
$596$	−1.82186e12	−0.591435
$597$	2.63706e12	0.849642
$598$	4.50123e12	1.43938
$599$	4.50082e12	1.42847	0.714235	−	0.699906i	$-0.246775\pi$
$599$	4.50082e12	1.42847	0.714235	+	0.699906i	$0.246775\pi$
$600$	1.06297e12	0.334842
$601$	−5.43075e12	−1.69795	−0.848974	−	0.528435i	$-0.822779\pi$
$601$	−5.43075e12	−1.69795	−0.848974	+	0.528435i	$0.822779\pi$
$602$	9.33366e11	0.289646
$603$	−3.70098e12	−1.13996
$604$	4.80970e11	0.147046
$605$	5.62104e12	1.70576
$606$	1.47122e12	0.443150
$607$	5.89921e12	1.76378	0.881891	−	0.471454i	$-0.156271\pi$
$607$	5.89921e12	1.76378	0.881891	+	0.471454i	$0.156271\pi$
$608$	−1.36651e11	−0.0405554
$609$	−6.57591e10	−0.0193722
$610$	−1.55858e12	−0.455768
$611$	3.09205e12	0.897554
$612$	1.74914e12	0.504013
$613$	−2.44465e11	−0.0699268	−0.0349634	−	0.999389i	$-0.511131\pi$
$613$	−2.44465e11	−0.0699268	−0.0349634	+	0.999389i	$0.511131\pi$
$614$	−2.64467e12	−0.750955
$615$	−3.77490e12	−1.06406
$616$	−3.65391e10	−0.0102246
$617$	−6.79288e11	−0.188699	−0.0943497	−	0.995539i	$-0.530077\pi$
$617$	−6.79288e11	−0.188699	−0.0943497	+	0.995539i	$0.530077\pi$
$618$	−9.96485e11	−0.274804
$619$	1.31874e12	0.361037	0.180519	−	0.983572i	$-0.442222\pi$
$619$	1.31874e12	0.361037	0.180519	+	0.983572i	$0.442222\pi$
$620$	1.20211e11	0.0326726
$621$	4.82868e12	1.30292
$622$	1.74351e12	0.467054
$623$	−1.09046e12	−0.290010
$624$	5.91664e11	0.156223
$625$	3.75646e12	0.984732
$626$	−1.51780e12	−0.395029
$627$	5.04790e10	0.0130439
$628$	1.26967e12	0.325740
$629$	−4.24164e12	−1.08045
$630$	9.05033e11	0.228893
$631$	−6.44908e12	−1.61944	−0.809721	−	0.586815i	$-0.800382\pi$
$631$	−6.44908e12	−1.61944	−0.809721	+	0.586815i	$0.800382\pi$
$632$	−1.03026e12	−0.256873
$633$	8.72641e11	0.216032
$634$	−4.40001e12	−1.08156
$635$	−3.98350e12	−0.972261
$636$	1.13450e12	0.274946
$637$	5.15083e12	1.23951
$638$	−5.98885e10	−0.0143104
$639$	2.79290e12	0.662676
$640$	6.49226e11	0.152963
$641$	−5.38181e12	−1.25912	−0.629561	−	0.776951i	$-0.716765\pi$
$641$	−5.38181e12	−1.25912	−0.629561	+	0.776951i	$0.716765\pi$
$642$	−4.55870e11	−0.105909
$643$	−7.16838e12	−1.65376	−0.826878	−	0.562381i	$-0.809885\pi$
$643$	−7.16838e12	−1.65376	−0.826878	+	0.562381i	$0.809885\pi$
$644$	−8.15034e11	−0.186719
$645$	6.12613e12	1.39369
$646$	9.34417e11	0.211103
$647$	−1.24135e12	−0.278501	−0.139250	−	0.990257i	$-0.544469\pi$
$647$	−1.24135e12	−0.278501	−0.139250	+	0.990257i	$0.544469\pi$
$648$	−5.94510e11	−0.132456
$649$	5.31661e11	0.117634
$650$	8.45003e12	1.85673
$651$	−1.98367e10	−0.00432867
$652$	7.36100e11	0.159523
$653$	6.46167e12	1.39071	0.695353	−	0.718669i	$-0.255248\pi$
$653$	6.46167e12	1.39071	0.695353	+	0.718669i	$0.255248\pi$
$654$	−1.21276e11	−0.0259224
$655$	8.84392e12	1.87741
$656$	−1.53575e12	−0.323782
$657$	2.12443e12	0.444834
$658$	−5.59874e11	−0.116432
$659$	3.48331e12	0.719462	0.359731	−	0.933056i	$-0.382869\pi$
$659$	3.48331e12	0.719462	0.359731	+	0.933056i	$0.382869\pi$
$660$	−2.39824e11	−0.0491977
$661$	−2.69783e12	−0.549678	−0.274839	−	0.961490i	$-0.588625\pi$
$661$	−2.69783e12	−0.549678	−0.274839	+	0.961490i	$0.588625\pi$
$662$	2.04891e12	0.414632
$663$	−4.04578e12	−0.813188
$664$	5.34189e11	0.106645
$665$	4.83484e11	0.0958704
$666$	2.30900e12	0.454769
$667$	−1.33586e12	−0.261333
$668$	3.78472e12	0.735427
$669$	−4.33165e12	−0.836056
$670$	9.39325e12	1.80086
$671$	2.34228e11	0.0446054
$672$	−1.07132e11	−0.0202655
$673$	−7.15485e12	−1.34441	−0.672207	−	0.740364i	$-0.734653\pi$
$673$	−7.15485e12	−1.34441	−0.672207	+	0.740364i	$0.734653\pi$
$674$	4.85917e11	0.0906970
$675$	9.06474e12	1.68069
$676$	1.98867e12	0.366271
$677$	3.99069e12	0.730127	0.365064	−	0.930983i	$-0.381047\pi$
$677$	3.99069e12	0.730127	0.365064	+	0.930983i	$0.381047\pi$
$678$	1.46101e12	0.265533
$679$	2.01935e12	0.364585
$680$	−4.43938e12	−0.796219
$681$	−6.85969e11	−0.122220
$682$	−1.80658e10	−0.00319762
$683$	−7.70306e12	−1.35447	−0.677236	−	0.735766i	$-0.736823\pi$
$683$	−7.70306e12	−1.35447	−0.677236	+	0.735766i	$0.736823\pi$
$684$	−5.08664e11	−0.0888544
$685$	7.84008e12	1.36054
$686$	−1.92306e12	−0.331539
$687$	−1.14421e12	−0.195974
$688$	2.49230e12	0.424085
$689$	9.01868e12	1.52460
$690$	−5.34946e12	−0.898439
$691$	−6.94842e12	−1.15940	−0.579702	−	0.814828i	$-0.696831\pi$
$691$	−6.94842e12	−1.15940	−0.579702	+	0.814828i	$0.696831\pi$
$692$	3.72690e12	0.617832
$693$	−1.36011e11	−0.0224014
$694$	−6.46098e12	−1.05726
$695$	−2.10182e13	−3.41715
$696$	−1.75592e11	−0.0283637
$697$	1.05014e13	1.68539
$698$	−1.00707e12	−0.160587
$699$	4.34576e12	0.688523
$700$	−1.53004e12	−0.240858
$701$	8.89057e12	1.39059	0.695294	−	0.718725i	$-0.255274\pi$
$701$	8.89057e12	1.39059	0.695294	+	0.718725i	$0.255274\pi$
$702$	5.04558e12	0.784140
$703$	1.23351e12	0.190477
$704$	−9.75680e10	−0.0149703
$705$	−3.67472e12	−0.560239
$706$	−1.49765e12	−0.226877
$707$	−2.11768e12	−0.318767
$708$	1.55882e12	0.233156
$709$	5.07939e12	0.754924	0.377462	−	0.926025i	$-0.376797\pi$
$709$	5.07939e12	0.754924	0.377462	+	0.926025i	$0.376797\pi$
$710$	−7.08850e12	−1.04687
$711$	−3.83497e12	−0.562793
$712$	−2.91178e12	−0.424617
$713$	−4.02972e11	−0.0583944
$714$	7.32565e11	0.105488
$715$	−1.90647e12	−0.272806
$716$	−4.66953e12	−0.663994
$717$	9.52615e11	0.134611
$718$	−5.09768e12	−0.715834
$719$	−2.62697e11	−0.0366585	−0.0183293	−	0.999832i	$-0.505835\pi$
$719$	−2.62697e11	−0.0366585	−0.0183293	+	0.999832i	$0.505835\pi$
$720$	2.41665e12	0.335133
$721$	1.43434e12	0.197672
$722$	−2.71737e11	−0.0372161
$723$	3.19412e12	0.434739
$724$	7.19789e12	0.973602
$725$	−2.50777e12	−0.337106
$726$	−2.47679e12	−0.330882
$727$	−5.69375e12	−0.755951	−0.377976	−	0.925816i	$-0.623380\pi$
$727$	−5.69375e12	−0.755951	−0.377976	+	0.925816i	$0.623380\pi$
$728$	−8.51644e11	−0.112374
$729$	8.37055e11	0.109769
$730$	−5.39189e12	−0.702730
$731$	−1.70423e13	−2.20749
$732$	6.86753e11	0.0884098
$733$	−1.28415e13	−1.64304	−0.821521	−	0.570178i	$-0.806874\pi$
$733$	−1.28415e13	−1.64304	−0.821521	+	0.570178i	$0.806874\pi$
$734$	−1.56994e12	−0.199642
$735$	−6.12147e12	−0.773682
$736$	−2.17633e12	−0.273385
$737$	−1.41165e12	−0.176248
$738$	−5.71660e12	−0.709388
$739$	2.66001e12	0.328083	0.164042	−	0.986453i	$-0.447547\pi$
$739$	2.66001e12	0.328083	0.164042	+	0.986453i	$0.447547\pi$
$740$	−5.86035e12	−0.718425
$741$	1.17655e12	0.143360
$742$	−1.63300e12	−0.197774
$743$	1.02254e13	1.23092	0.615462	−	0.788166i	$-0.288969\pi$
$743$	1.02254e13	1.23092	0.615462	+	0.788166i	$0.288969\pi$
$744$	−5.29686e10	−0.00633782
$745$	1.72120e13	2.04705
$746$	−3.59982e12	−0.425556
$747$	1.98844e12	0.233652
$748$	6.67166e11	0.0779250
$749$	6.56181e11	0.0761826
$750$	−5.00836e12	−0.577989
$751$	7.08317e12	0.812546	0.406273	−	0.913752i	$-0.366828\pi$
$751$	7.08317e12	0.812546	0.406273	+	0.913752i	$0.366828\pi$
$752$	−1.49499e12	−0.170474
$753$	8.32720e11	0.0943890
$754$	−1.39586e12	−0.157280
$755$	−4.54396e12	−0.508948
$756$	−9.13598e11	−0.101720
$757$	1.55185e13	1.71758	0.858792	−	0.512325i	$-0.171216\pi$
$757$	1.55185e13	1.71758	0.858792	+	0.512325i	$0.171216\pi$
$758$	−9.98399e12	−1.09848
$759$	8.03934e11	0.0879291
$760$	1.29101e12	0.140368
$761$	3.36663e12	0.363885	0.181943	−	0.983309i	$-0.441761\pi$
$761$	3.36663e12	0.363885	0.181943	+	0.983309i	$0.441761\pi$
$762$	1.75524e12	0.188599
$763$	1.74565e11	0.0186465
$764$	7.22732e10	0.00767462
$765$	−1.65249e13	−1.74447
$766$	−8.59039e12	−0.901537
$767$	1.23918e13	1.29287
$768$	−2.86067e11	−0.0296717
$769$	−9.31790e12	−0.960836	−0.480418	−	0.877040i	$-0.659515\pi$
$769$	−9.31790e12	−0.960836	−0.480418	+	0.877040i	$0.659515\pi$
$770$	3.45203e11	0.0353888
$771$	−1.22322e12	−0.124670
$772$	3.66379e12	0.371239
$773$	−7.33840e12	−0.739254	−0.369627	−	0.929180i	$-0.620514\pi$
$773$	−7.33840e12	−0.739254	−0.369627	+	0.929180i	$0.620514\pi$
$774$	9.27722e12	0.929145
$775$	−7.56487e11	−0.0753258
$776$	5.39214e12	0.533806
$777$	9.67046e11	0.0951815
$778$	2.08247e12	0.203784
$779$	−3.05390e12	−0.297123
$780$	−5.58974e12	−0.540712
$781$	1.06528e12	0.102456
$782$	1.48817e13	1.42305
$783$	−1.49741e12	−0.142368
$784$	−2.49041e12	−0.235423
$785$	−1.19951e13	−1.12744
$786$	−3.89688e12	−0.364180
$787$	1.81540e13	1.68689	0.843443	−	0.537219i	$-0.180525\pi$
$787$	1.81540e13	1.68689	0.843443	+	0.537219i	$0.180525\pi$
$788$	5.17417e12	0.478050
$789$	−5.58923e12	−0.513459
$790$	9.73333e12	0.889077
$791$	−2.10298e12	−0.191003
$792$	−3.63182e11	−0.0327990
$793$	5.45932e12	0.490241
$794$	1.17873e13	1.05250
$795$	−1.07182e13	−0.951632
$796$	−1.01356e13	−0.894835
$797$	5.44638e12	0.478129	0.239065	−	0.971004i	$-0.423159\pi$
$797$	5.44638e12	0.478129	0.239065	+	0.971004i	$0.423159\pi$
$798$	−2.13037e11	−0.0185969
$799$	1.02227e13	0.887371
$800$	−4.08556e12	−0.352652
$801$	−1.08386e13	−0.930312
$802$	9.44751e12	0.806367
$803$	8.10312e11	0.0687753
$804$	−4.13893e12	−0.349330
$805$	7.70002e12	0.646265
$806$	−4.21072e11	−0.0351438
$807$	−6.21582e11	−0.0515903
$808$	−5.65469e12	−0.466722
$809$	2.44611e11	0.0200774	0.0100387	−	0.999950i	$-0.496805\pi$
$809$	2.44611e11	0.0200774	0.0100387	+	0.999950i	$0.496805\pi$
$810$	5.61663e12	0.458451
$811$	1.86901e13	1.51711	0.758555	−	0.651609i	$-0.225906\pi$
$811$	1.86901e13	1.51711	0.758555	+	0.651609i	$0.225906\pi$
$812$	2.52748e11	0.0204026
$813$	1.05139e13	0.844030
$814$	8.80714e11	0.0703113
$815$	−6.95430e12	−0.552134
$816$	1.95612e12	0.154450
$817$	4.95605e12	0.389167
$818$	6.84126e12	0.534252
$819$	−3.17011e12	−0.246205
$820$	1.45090e13	1.12066
$821$	2.98096e12	0.228987	0.114494	−	0.993424i	$-0.463475\pi$
$821$	2.98096e12	0.228987	0.114494	+	0.993424i	$0.463475\pi$
$822$	−3.45456e12	−0.263918
$823$	−1.01707e13	−0.772774	−0.386387	−	0.922337i	$-0.626277\pi$
$823$	−1.01707e13	−0.772774	−0.386387	+	0.922337i	$0.626277\pi$
$824$	3.83003e12	0.289421
$825$	1.50920e12	0.113424
$826$	−2.24377e12	−0.167713
$827$	1.99682e13	1.48445	0.742223	−	0.670153i	$-0.233771\pi$
$827$	1.99682e13	1.48445	0.742223	+	0.670153i	$0.233771\pi$
$828$	−8.10105e12	−0.598970
$829$	2.35288e13	1.73023	0.865115	−	0.501574i	$-0.167245\pi$
$829$	2.35288e13	1.73023	0.865115	+	0.501574i	$0.167245\pi$
$830$	−5.04674e12	−0.369113
$831$	7.52516e12	0.547408
$832$	−2.27409e12	−0.164533
$833$	1.70293e13	1.22545
$834$	9.26121e12	0.662858
$835$	−3.57561e13	−2.54543
$836$	−1.94018e11	−0.0137377
$837$	−4.51704e11	−0.0318119
$838$	−1.56144e13	−1.09378
$839$	9.16607e12	0.638637	0.319319	−	0.947647i	$-0.396546\pi$
$839$	9.16607e12	0.638637	0.319319	+	0.947647i	$0.396546\pi$
$840$	1.01213e12	0.0701422
$841$	−1.40929e13	−0.971444
$842$	1.09267e12	0.0749179
$843$	−5.21884e12	−0.355918
$844$	−3.35403e12	−0.227523
$845$	−1.87879e13	−1.26772
$846$	−5.56488e12	−0.373499
$847$	3.56509e12	0.238010
$848$	−4.36050e12	−0.289571
$849$	−5.63484e12	−0.372217
$850$	2.79369e13	1.83566
$851$	1.96450e13	1.28401
$852$	3.12339e12	0.203071
$853$	9.94411e12	0.643125	0.321562	−	0.946888i	$-0.395792\pi$
$853$	9.94411e12	0.643125	0.321562	+	0.946888i	$0.395792\pi$
$854$	−9.88514e11	−0.0635949
$855$	4.80560e12	0.307539
$856$	1.75216e12	0.111543
$857$	−1.90800e13	−1.20827	−0.604137	−	0.796880i	$-0.706482\pi$
$857$	−1.90800e13	−1.20827	−0.604137	+	0.796880i	$0.706482\pi$
$858$	8.40045e11	0.0529188
$859$	3.10124e12	0.194342	0.0971710	−	0.995268i	$-0.469021\pi$
$859$	3.10124e12	0.194342	0.0971710	+	0.995268i	$0.469021\pi$
$860$	−2.35460e13	−1.46782
$861$	−2.39420e12	−0.148473
$862$	4.75381e12	0.293264
$863$	−2.40338e13	−1.47494	−0.737470	−	0.675380i	$-0.763980\pi$
$863$	−2.40338e13	−1.47494	−0.737470	+	0.675380i	$0.763980\pi$
$864$	−2.43952e12	−0.148933
$865$	−3.52099e13	−2.13842
$866$	7.21869e12	0.436142
$867$	−5.47728e12	−0.329214
$868$	7.62431e10	0.00455892
$869$	−1.46276e12	−0.0870129
$870$	1.65890e12	0.0981713
$871$	−3.29023e13	−1.93707
$872$	4.66130e11	0.0273013
$873$	2.00714e13	1.16954
$874$	−4.32772e12	−0.250875
$875$	7.20905e12	0.415759
$876$	2.37582e12	0.136315
$877$	−5.20893e12	−0.297338	−0.148669	−	0.988887i	$-0.547499\pi$
$877$	−5.20893e12	−0.297338	−0.148669	+	0.988887i	$0.547499\pi$
$878$	−8.88771e12	−0.504736
$879$	7.10151e12	0.401237
$880$	9.21772e11	0.0518145
$881$	−7.36387e12	−0.411826	−0.205913	−	0.978570i	$-0.566016\pi$
$881$	−7.36387e12	−0.411826	−0.205913	+	0.978570i	$0.566016\pi$
$882$	−9.27016e12	−0.515797
$883$	2.98715e13	1.65362	0.826808	−	0.562485i	$-0.190155\pi$
$883$	2.98715e13	1.65362	0.826808	+	0.562485i	$0.190155\pi$
$884$	1.55501e13	0.856442
$885$	−1.47269e13	−0.806988
$886$	2.58705e13	1.41044
$887$	−1.43208e13	−0.776802	−0.388401	−	0.921490i	$-0.626973\pi$
$887$	−1.43208e13	−0.776802	−0.388401	+	0.921490i	$0.626973\pi$
$888$	2.58224e12	0.139360
$889$	−2.52650e12	−0.135663
$890$	2.75090e13	1.46967
$891$	−8.44086e11	−0.0448680
$892$	1.66489e13	0.880526
$893$	−2.97285e12	−0.156438
$894$	−7.58410e12	−0.397086
$895$	4.41153e13	2.29819
$896$	4.11766e11	0.0213435
$897$	1.87379e13	0.966394
$898$	−7.24628e12	−0.371853
$899$	1.24964e11	0.00638069
$900$	−1.52079e13	−0.772640
$901$	2.98169e13	1.50730
$902$	−2.18046e12	−0.109678
$903$	3.88544e12	0.194467
$904$	−5.61544e12	−0.279657
$905$	−6.80020e13	−3.36979
$906$	2.00220e12	0.0987257
$907$	−3.98348e13	−1.95448	−0.977238	−	0.212146i	$-0.931955\pi$
$907$	−3.98348e13	−1.95448	−0.977238	+	0.212146i	$0.931955\pi$
$908$	2.63655e12	0.128721
$909$	−2.10487e13	−1.02256
$910$	8.04589e12	0.388945
$911$	−8.77892e12	−0.422288	−0.211144	−	0.977455i	$-0.567719\pi$
$911$	−8.77892e12	−0.422288	−0.211144	+	0.977455i	$0.567719\pi$
$912$	−5.68857e11	−0.0272287
$913$	7.58442e11	0.0361247
$914$	−1.76496e13	−0.836522
$915$	−6.48809e12	−0.306000
$916$	4.39780e12	0.206398
$917$	5.60918e12	0.261962
$918$	1.66813e13	0.775244
$919$	2.89837e12	0.134040	0.0670200	−	0.997752i	$-0.478651\pi$
$919$	2.89837e12	0.134040	0.0670200	+	0.997752i	$0.478651\pi$
$920$	2.05608e13	0.946228
$921$	−1.10093e13	−0.504188
$922$	−3.55347e12	−0.161943
$923$	2.48293e13	1.12605
$924$	−1.52106e11	−0.00686472
$925$	3.68790e13	1.65631
$926$	−1.59557e13	−0.713125
$927$	1.42567e13	0.634104
$928$	6.74895e11	0.0298724
$929$	1.09141e13	0.480749	0.240375	−	0.970680i	$-0.422730\pi$
$929$	1.09141e13	0.480749	0.240375	+	0.970680i	$0.422730\pi$
$930$	5.00420e11	0.0219362
$931$	−4.95228e12	−0.216039
$932$	−1.67031e13	−0.725146
$933$	7.25793e12	0.313578
$934$	−1.39773e13	−0.600983
$935$	−6.30304e12	−0.269711
$936$	−8.46494e12	−0.360481
$937$	3.31892e13	1.40659	0.703296	−	0.710897i	$-0.251711\pi$
$937$	3.31892e13	1.40659	0.703296	+	0.710897i	$0.251711\pi$
$938$	5.95759e12	0.251280
$939$	−6.31832e12	−0.265220
$940$	1.41239e13	0.590038
$941$	−4.06875e13	−1.69164	−0.845819	−	0.533471i	$-0.820888\pi$
$941$	−4.06875e13	−1.69164	−0.845819	+	0.533471i	$0.820888\pi$
$942$	5.28540e12	0.218700
$943$	−4.86368e13	−2.00292
$944$	−5.99138e12	−0.245557
$945$	8.63120e12	0.352069
$946$	3.53857e12	0.143654
$947$	−1.90875e13	−0.771211	−0.385606	−	0.922664i	$-0.626007\pi$
$947$	−1.90875e13	−0.771211	−0.385606	+	0.922664i	$0.626007\pi$
$948$	−4.28878e12	−0.172463
$949$	1.88865e13	0.755882
$950$	−8.12430e12	−0.323616
$951$	−1.83165e13	−0.726155
$952$	−2.81564e12	−0.111099
$953$	−2.79671e12	−0.109832	−0.0549161	−	0.998491i	$-0.517489\pi$
$953$	−2.79671e12	−0.109832	−0.0549161	+	0.998491i	$0.517489\pi$
$954$	−1.62313e13	−0.634432
$955$	−6.82800e11	−0.0265631
$956$	−3.66141e12	−0.141771
$957$	−2.49306e11	−0.00960790
$958$	−2.57053e13	−0.986002
$959$	4.97250e12	0.189842
$960$	2.70262e12	0.102699
$961$	−2.64019e13	−0.998574
$962$	2.05274e13	0.772764
$963$	6.52213e12	0.244383
$964$	−1.22767e13	−0.457864
$965$	−3.46136e13	−1.28492
$966$	−3.39285e12	−0.125362
$967$	−1.90809e10	−0.000701745 0	−0.000350873	−	1.00000i	$-0.500112\pi$
$967$	−1.90809e10	−0.000701745 0	−0.000350873		1.00000i	$0.500112\pi$
$968$	9.51963e12	0.348482
$969$	3.88982e12	0.141733
$970$	−5.09422e13	−1.84759
$971$	−4.13526e12	−0.149285	−0.0746426	−	0.997210i	$-0.523782\pi$
$971$	−4.13526e12	−0.149285	−0.0746426	+	0.997210i	$0.523782\pi$
$972$	−1.41977e13	−0.510177
$973$	−1.33306e13	−0.476807
$974$	1.48061e13	0.527139
$975$	3.51761e13	1.24660
$976$	−2.63956e12	−0.0931124
$977$	3.74336e13	1.31443	0.657213	−	0.753705i	$-0.271735\pi$
$977$	3.74336e13	1.31443	0.657213	+	0.753705i	$0.271735\pi$
$978$	3.06426e12	0.107103
$979$	−4.13414e12	−0.143835
$980$	2.35281e13	0.814835
$981$	1.73510e12	0.0598155
$982$	1.48581e13	0.509871
$983$	1.37412e13	0.469390	0.234695	−	0.972069i	$-0.424591\pi$
$983$	1.37412e13	0.469390	0.234695	+	0.972069i	$0.424591\pi$
$984$	−6.39307e12	−0.217386
$985$	−4.88830e13	−1.65461
$986$	−4.61491e12	−0.155495
$987$	−2.33066e12	−0.0781721
$988$	−4.52211e12	−0.150985
$989$	7.89307e13	2.62339
$990$	3.43116e12	0.113523
$991$	−2.92261e13	−0.962584	−0.481292	−	0.876560i	$-0.659832\pi$
$991$	−2.92261e13	−0.962584	−0.481292	+	0.876560i	$0.659832\pi$
$992$	2.03587e11	0.00667494
$993$	8.52927e12	0.278381
$994$	−4.49582e12	−0.146073
$995$	9.57564e13	3.09716
$996$	2.22374e12	0.0716006
$997$	1.27081e13	0.407335	0.203668	−	0.979040i	$-0.434714\pi$
$997$	1.27081e13	0.407335	0.203668	+	0.979040i	$0.434714\pi$
$998$	−1.91375e13	−0.610658
$999$	2.20207e13	0.699499

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.a.d.1.2	✓	4
3.2	odd	2		342.10.a.l.1.4		4
4.3	odd	2		304.10.a.e.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.a.d.1.2	✓	4	1.1	even	1	trivial
304.10.a.e.1.3		4	4.3	odd	2
342.10.a.l.1.4		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} -66.6053 q^{3} +256.000 q^{4} -2418.56 q^{5} +1065.68 q^{6} -1533.95 q^{7} -4096.00 q^{8} -15246.7 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} -66.6053 q^{3} +256.000 q^{4} -2418.56 q^{5} +1065.68 q^{6} -1533.95 q^{7} -4096.00 q^{8} -15246.7 q^{9} +38696.9 q^{10} -5815.50 q^{11} -17051.0 q^{12} -135546. q^{13} +24543.2 q^{14} +161089. q^{15} +65536.0 q^{16} -448133. q^{17} +243948. q^{18} +130321. q^{19} -619151. q^{20} +102169. q^{21} +93048.1 q^{22} +2.07551e6 q^{23} +272815. q^{24} +3.89629e6 q^{25} +2.16874e6 q^{26} +2.32650e6 q^{27} -392691. q^{28} -643630. q^{29} -2.57742e6 q^{30} -194155. q^{31} -1.04858e6 q^{32} +387343. q^{33} +7.17012e6 q^{34} +3.70994e6 q^{35} -3.90316e6 q^{36} +9.46515e6 q^{37} -2.08514e6 q^{38} +9.02808e6 q^{39} +9.90641e6 q^{40} -2.34337e7 q^{41} -1.63471e6 q^{42} +3.80295e7 q^{43} -1.48877e6 q^{44} +3.68751e7 q^{45} -3.32081e7 q^{46} -2.28118e7 q^{47} -4.36504e6 q^{48} -3.80006e7 q^{49} -6.23407e7 q^{50} +2.98480e7 q^{51} -3.46998e7 q^{52} -6.65359e7 q^{53} -3.72241e7 q^{54} +1.40651e7 q^{55} +6.28306e6 q^{56} -8.68007e6 q^{57} +1.02981e7 q^{58} -9.14212e7 q^{59} +4.12387e7 q^{60} -4.02765e7 q^{61} +3.10649e6 q^{62} +2.33877e7 q^{63} +1.67772e7 q^{64} +3.27826e8 q^{65} -6.19749e6 q^{66} +2.42739e8 q^{67} -1.14722e8 q^{68} -1.38240e8 q^{69} -5.93591e7 q^{70} -1.83180e8 q^{71} +6.24506e7 q^{72} -1.39336e8 q^{73} -1.51442e8 q^{74} -2.59514e8 q^{75} +3.33622e7 q^{76} +8.92069e6 q^{77} -1.44449e8 q^{78} +2.51527e8 q^{79} -1.58503e8 q^{80} +1.45144e8 q^{81} +3.74939e8 q^{82} -1.30417e8 q^{83} +2.61553e7 q^{84} +1.08383e9 q^{85} -6.08473e8 q^{86} +4.28692e7 q^{87} +2.38203e7 q^{88} +7.10883e8 q^{89} -5.90002e8 q^{90} +2.07921e8 q^{91} +5.31330e8 q^{92} +1.29318e7 q^{93} +3.64988e8 q^{94} -3.15189e8 q^{95} +6.98407e7 q^{96} -1.31644e9 q^{97} +6.08010e8 q^{98} +8.86675e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9}+O(q^{10}) \) 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9	\( 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9} + 22320 q^{10} - 104249 q^{11} + 21504 q^{12} + 120486 q^{13} - 196912 q^{14} - 591090 q^{15} + 262144 q^{16} - 412139 q^{17} - 264608 q^{18} + 521284 q^{19} - 357120 q^{20} + 2437006 q^{21} + 1667984 q^{22} + 3010300 q^{23} - 344064 q^{24} + 9760585 q^{25} - 1927776 q^{26} + 12387978 q^{27} + 3150592 q^{28} + 6153240 q^{29} + 9457440 q^{30} + 12774024 q^{31} - 4194304 q^{32} - 3258022 q^{33} + 6594224 q^{34} + 9823425 q^{35} + 4233728 q^{36} + 20506048 q^{37} - 8340544 q^{38} + 69881444 q^{39} + 5713920 q^{40} + 11620300 q^{41} - 38992096 q^{42} + 7698327 q^{43} - 26687744 q^{44} - 124015815 q^{45} - 48164800 q^{46} - 31581083 q^{47} + 5505024 q^{48} + 18970383 q^{49} - 156169360 q^{50} - 8594812 q^{51} + 30844416 q^{52} + 72549422 q^{53} - 198207648 q^{54} + 21332505 q^{55} - 50409472 q^{56} + 10946964 q^{57} - 98451840 q^{58} - 149234120 q^{59} - 151319040 q^{60} + 129004373 q^{61} - 204384384 q^{62} + 102967551 q^{63} + 67108864 q^{64} + 124691700 q^{65} + 52128352 q^{66} + 132595266 q^{67} - 105507584 q^{68} - 45529972 q^{69} - 157174800 q^{70} - 47138482 q^{71} - 67739648 q^{72} - 39332795 q^{73} - 328096768 q^{74} + 824627010 q^{75} + 133448704 q^{76} - 165933719 q^{77} - 1118103104 q^{78} - 307010840 q^{79} - 91422720 q^{80} + 1305551744 q^{81} - 185924800 q^{82} - 746568232 q^{83} + 623873536 q^{84} - 105005985 q^{85} - 123173232 q^{86} - 82148208 q^{87} + 427003904 q^{88} + 286943482 q^{89} + 1984253040 q^{90} + 3155781114 q^{91} + 770636800 q^{92} + 1151901596 q^{93} + 505297328 q^{94} - 181797795 q^{95} - 88080384 q^{96} + 793519958 q^{97} - 303526128 q^{98} - 1681833809 q^{99}+O(q^{100}) \) 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9 + 22320 * q^10 - 104249 * q^11 + 21504 * q^12 + 120486 * q^13 - 196912 * q^14 - 591090 * q^15 + 262144 * q^16 - 412139 * q^17 - 264608 * q^18 + 521284 * q^19 - 357120 * q^20 + 2437006 * q^21 + 1667984 * q^22 + 3010300 * q^23 - 344064 * q^24 + 9760585 * q^25 - 1927776 * q^26 + 12387978 * q^27 + 3150592 * q^28 + 6153240 * q^29 + 9457440 * q^30 + 12774024 * q^31 - 4194304 * q^32 - 3258022 * q^33 + 6594224 * q^34 + 9823425 * q^35 + 4233728 * q^36 + 20506048 * q^37 - 8340544 * q^38 + 69881444 * q^39 + 5713920 * q^40 + 11620300 * q^41 - 38992096 * q^42 + 7698327 * q^43 - 26687744 * q^44 - 124015815 * q^45 - 48164800 * q^46 - 31581083 * q^47 + 5505024 * q^48 + 18970383 * q^49 - 156169360 * q^50 - 8594812 * q^51 + 30844416 * q^52 + 72549422 * q^53 - 198207648 * q^54 + 21332505 * q^55 - 50409472 * q^56 + 10946964 * q^57 - 98451840 * q^58 - 149234120 * q^59 - 151319040 * q^60 + 129004373 * q^61 - 204384384 * q^62 + 102967551 * q^63 + 67108864 * q^64 + 124691700 * q^65 + 52128352 * q^66 + 132595266 * q^67 - 105507584 * q^68 - 45529972 * q^69 - 157174800 * q^70 - 47138482 * q^71 - 67739648 * q^72 - 39332795 * q^73 - 328096768 * q^74 + 824627010 * q^75 + 133448704 * q^76 - 165933719 * q^77 - 1118103104 * q^78 - 307010840 * q^79 - 91422720 * q^80 + 1305551744 * q^81 - 185924800 * q^82 - 746568232 * q^83 + 623873536 * q^84 - 105005985 * q^85 - 123173232 * q^86 - 82148208 * q^87 + 427003904 * q^88 + 286943482 * q^89 + 1984253040 * q^90 + 3155781114 * q^91 + 770636800 * q^92 + 1151901596 * q^93 + 505297328 * q^94 - 181797795 * q^95 - 88080384 * q^96 + 793519958 * q^97 - 303526128 * q^98 - 1681833809 * q^99

Introduction

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