LMFDB - Embedded newform 38.10.a.e.1.3

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} - 2x^{3} - 8016x^{2} - 155839x + 2105804 $ x^4 - 2x^3 - 8016x^2 - 155839*x + 2105804
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-31.9926$ 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)

$f(q)$	$=$	$q+16.0000 q^{2} +110.471 q^{3} +256.000 q^{4} -1298.23 q^{5} +1767.54 q^{6} +6626.40 q^{7} +4096.00 q^{8} -7479.16 q^{9} +O(q^{10})$	\(q+16.0000 q^{2} +110.471 q^{3} +256.000 q^{4} -1298.23 q^{5} +1767.54 q^{6} +6626.40 q^{7} +4096.00 q^{8} -7479.16 q^{9} -20771.6 q^{10} +79545.0 q^{11} +28280.6 q^{12} +168923. q^{13} +106022. q^{14} -143417. q^{15} +65536.0 q^{16} -153308. q^{17} -119667. q^{18} -130321. q^{19} -332346. q^{20} +732025. q^{21} +1.27272e6 q^{22} +1.01301e6 q^{23} +452489. q^{24} -267730. q^{25} +2.70276e6 q^{26} -3.00063e6 q^{27} +1.69636e6 q^{28} +5.40193e6 q^{29} -2.29466e6 q^{30} -3.60951e6 q^{31} +1.04858e6 q^{32} +8.78742e6 q^{33} -2.45292e6 q^{34} -8.60258e6 q^{35} -1.91466e6 q^{36} +2.20054e7 q^{37} -2.08514e6 q^{38} +1.86611e7 q^{39} -5.31754e6 q^{40} -2.81420e7 q^{41} +1.17124e7 q^{42} +6.47020e6 q^{43} +2.03635e7 q^{44} +9.70965e6 q^{45} +1.62082e7 q^{46} -4.68666e7 q^{47} +7.23983e6 q^{48} +3.55556e6 q^{49} -4.28368e6 q^{50} -1.69361e7 q^{51} +4.32442e7 q^{52} -8.21904e7 q^{53} -4.80101e7 q^{54} -1.03268e8 q^{55} +2.71417e7 q^{56} -1.43967e7 q^{57} +8.64309e7 q^{58} +1.66093e7 q^{59} -3.67146e7 q^{60} +3.59512e7 q^{61} -5.77522e7 q^{62} -4.95599e7 q^{63} +1.67772e7 q^{64} -2.19300e8 q^{65} +1.40599e8 q^{66} -9.61687e7 q^{67} -3.92468e7 q^{68} +1.11908e8 q^{69} -1.37641e8 q^{70} -3.86399e8 q^{71} -3.06346e7 q^{72} -1.45125e8 q^{73} +3.52087e8 q^{74} -2.95764e7 q^{75} -3.33622e7 q^{76} +5.27097e8 q^{77} +2.98577e8 q^{78} -3.54985e7 q^{79} -8.50806e7 q^{80} -1.84270e8 q^{81} -4.50272e8 q^{82} +3.15916e8 q^{83} +1.87398e8 q^{84} +1.99028e8 q^{85} +1.03523e8 q^{86} +5.96757e8 q^{87} +3.25816e8 q^{88} +8.66694e8 q^{89} +1.55354e8 q^{90} +1.11935e9 q^{91} +2.59331e8 q^{92} -3.98747e8 q^{93} -7.49866e8 q^{94} +1.69186e8 q^{95} +1.15837e8 q^{96} +6.14107e8 q^{97} +5.68890e7 q^{98} -5.94930e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 64 q^{2} + 226 q^{3} + 1024 q^{4} + 866 q^{5} + 3616 q^{6} + 2670 q^{7} + 16384 q^{8} + 50606 q^{9}+O(q^{10}) $ 4 * q + 64 * q^2 + 226 * q^3 + 1024 * q^4 + 866 * q^5 + 3616 * q^6 + 2670 * q^7 + 16384 * q^8 + 50606 * q^9	\( 4 q + 64 q^{2} + 226 q^{3} + 1024 q^{4} + 866 q^{5} + 3616 q^{6} + 2670 q^{7} + 16384 q^{8} + 50606 q^{9} + 13856 q^{10} + 119234 q^{11} + 57856 q^{12} - 6748 q^{13} + 42720 q^{14} + 355904 q^{15} + 262144 q^{16} + 678624 q^{17} + 809696 q^{18} - 521284 q^{19} + 221696 q^{20} + 1586736 q^{21} + 1907744 q^{22} + 2911868 q^{23} + 925696 q^{24} + 268766 q^{25} - 107968 q^{26} + 2802058 q^{27} + 683520 q^{28} + 8291104 q^{29} + 5694464 q^{30} + 3445468 q^{31} + 4194304 q^{32} - 5321788 q^{33} + 10857984 q^{34} + 7715058 q^{35} + 12955136 q^{36} - 1005524 q^{37} - 8340544 q^{38} + 34055900 q^{39} + 3547136 q^{40} + 8514124 q^{41} + 25387776 q^{42} + 13900726 q^{43} + 30523904 q^{44} - 8962202 q^{45} + 46589888 q^{46} - 36334954 q^{47} + 14811136 q^{48} - 30891808 q^{49} + 4300256 q^{50} - 203869074 q^{51} - 1727488 q^{52} - 113969356 q^{53} + 44832928 q^{54} - 178140098 q^{55} + 10936320 q^{56} - 29452546 q^{57} + 132657664 q^{58} - 396773766 q^{59} + 91111424 q^{60} - 298192066 q^{61} + 55127488 q^{62} - 458723694 q^{63} + 67108864 q^{64} - 291187676 q^{65} - 85148608 q^{66} - 113551722 q^{67} + 173727744 q^{68} - 671519716 q^{69} + 123440928 q^{70} + 4659620 q^{71} + 207282176 q^{72} + 136198452 q^{73} - 16088384 q^{74} + 29308274 q^{75} - 133448704 q^{76} + 120551886 q^{77} + 544894400 q^{78} + 67255424 q^{79} + 56754176 q^{80} + 982241180 q^{81} + 136225984 q^{82} + 1376505216 q^{83} + 406204416 q^{84} + 638402178 q^{85} + 222411616 q^{86} + 630635524 q^{87} + 488382464 q^{88} + 1557211260 q^{89} - 143395232 q^{90} + 1422773730 q^{91} + 745438208 q^{92} + 2036686084 q^{93} - 581359264 q^{94} - 112857986 q^{95} + 236978176 q^{96} + 975818188 q^{97} - 494268928 q^{98} + 502820650 q^{99}+O(q^{100}) \) 4 * q + 64 * q^2 + 226 * q^3 + 1024 * q^4 + 866 * q^5 + 3616 * q^6 + 2670 * q^7 + 16384 * q^8 + 50606 * q^9 + 13856 * q^10 + 119234 * q^11 + 57856 * q^12 - 6748 * q^13 + 42720 * q^14 + 355904 * q^15 + 262144 * q^16 + 678624 * q^17 + 809696 * q^18 - 521284 * q^19 + 221696 * q^20 + 1586736 * q^21 + 1907744 * q^22 + 2911868 * q^23 + 925696 * q^24 + 268766 * q^25 - 107968 * q^26 + 2802058 * q^27 + 683520 * q^28 + 8291104 * q^29 + 5694464 * q^30 + 3445468 * q^31 + 4194304 * q^32 - 5321788 * q^33 + 10857984 * q^34 + 7715058 * q^35 + 12955136 * q^36 - 1005524 * q^37 - 8340544 * q^38 + 34055900 * q^39 + 3547136 * q^40 + 8514124 * q^41 + 25387776 * q^42 + 13900726 * q^43 + 30523904 * q^44 - 8962202 * q^45 + 46589888 * q^46 - 36334954 * q^47 + 14811136 * q^48 - 30891808 * q^49 + 4300256 * q^50 - 203869074 * q^51 - 1727488 * q^52 - 113969356 * q^53 + 44832928 * q^54 - 178140098 * q^55 + 10936320 * q^56 - 29452546 * q^57 + 132657664 * q^58 - 396773766 * q^59 + 91111424 * q^60 - 298192066 * q^61 + 55127488 * q^62 - 458723694 * q^63 + 67108864 * q^64 - 291187676 * q^65 - 85148608 * q^66 - 113551722 * q^67 + 173727744 * q^68 - 671519716 * q^69 + 123440928 * q^70 + 4659620 * q^71 + 207282176 * q^72 + 136198452 * q^73 - 16088384 * q^74 + 29308274 * q^75 - 133448704 * q^76 + 120551886 * q^77 + 544894400 * q^78 + 67255424 * q^79 + 56754176 * q^80 + 982241180 * q^81 + 136225984 * q^82 + 1376505216 * q^83 + 406204416 * q^84 + 638402178 * q^85 + 222411616 * q^86 + 630635524 * q^87 + 488382464 * q^88 + 1557211260 * q^89 - 143395232 * q^90 + 1422773730 * q^91 + 745438208 * q^92 + 2036686084 * q^93 - 581359264 * q^94 - 112857986 * q^95 + 236978176 * q^96 + 975818188 * q^97 - 494268928 * q^98 + 502820650 * 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
$3$	110.471	0.787413	0.393707	−	0.919236i	$-0.371193\pi$
$3$	110.471	0.787413	0.393707	+	0.919236i	$0.371193\pi$
$4$	256.000	0.500000
$5$	−1298.23	−0.928936	−0.464468	−	0.885590i	$-0.653754\pi$
$5$	−1298.23	−0.928936	−0.464468	+	0.885590i	$0.653754\pi$
$6$	1767.54	0.556785
$7$	6626.40	1.04313	0.521563	−	0.853213i	$-0.325349\pi$
$7$	6626.40	1.04313	0.521563	+	0.853213i	$0.325349\pi$
$8$	4096.00	0.353553
$9$	−7479.16	−0.379981
$10$	−20771.6	−0.656857
$11$	79545.0	1.63812	0.819060	−	0.573707i	$-0.194495\pi$
$11$	79545.0	1.63812	0.819060	+	0.573707i	$0.194495\pi$
$12$	28280.6	0.393707
$13$	168923.	1.64038	0.820188	−	0.572095i	$-0.193869\pi$
$13$	168923.	1.64038	0.820188	+	0.572095i	$0.193869\pi$
$14$	106022.	0.737601
$15$	−143417.	−0.731457
$16$	65536.0	0.250000
$17$	−153308.	−0.445189	−0.222594	−	0.974911i	$-0.571453\pi$
$17$	−153308.	−0.445189	−0.222594	+	0.974911i	$0.571453\pi$
$18$	−119667.	−0.268687
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	−332346.	−0.464468
$21$	732025.	0.821370
$22$	1.27272e6	1.15833
$23$	1.01301e6	0.754813	0.377406	−	0.926048i	$-0.376816\pi$
$23$	1.01301e6	0.754813	0.377406	+	0.926048i	$0.376816\pi$
$24$	452489.	0.278393
$25$	−267730.	−0.137078
$26$	2.70276e6	1.15992
$27$	−3.00063e6	−1.08661
$28$	1.69636e6	0.521563
$29$	5.40193e6	1.41827	0.709134	−	0.705074i	$-0.249086\pi$
$29$	5.40193e6	1.41827	0.709134	+	0.705074i	$0.249086\pi$
$30$	−2.29466e6	−0.517218
$31$	−3.60951e6	−0.701974	−0.350987	−	0.936380i	$-0.614154\pi$
$31$	−3.60951e6	−0.701974	−0.350987	+	0.936380i	$0.614154\pi$
$32$	1.04858e6	0.176777
$33$	8.78742e6	1.28988
$34$	−2.45292e6	−0.314796
$35$	−8.60258e6	−0.968997
$36$	−1.91466e6	−0.189990
$37$	2.20054e7	1.93029	0.965143	−	0.261722i	$-0.0842905\pi$
$37$	2.20054e7	1.93029	0.965143	+	0.261722i	$0.0842905\pi$
$38$	−2.08514e6	−0.162221
$39$	1.86611e7	1.29165
$40$	−5.31754e6	−0.328429
$41$	−2.81420e7	−1.55535	−0.777674	−	0.628667i	$-0.783601\pi$
$41$	−2.81420e7	−1.55535	−0.777674	+	0.628667i	$0.783601\pi$
$42$	1.17124e7	0.580797
$43$	6.47020e6	0.288609	0.144304	−	0.989533i	$-0.453906\pi$
$43$	6.47020e6	0.288609	0.144304	+	0.989533i	$0.453906\pi$
$44$	2.03635e7	0.819060
$45$	9.70965e6	0.352978
$46$	1.62082e7	0.533733
$47$	−4.68666e7	−1.40095	−0.700476	−	0.713676i	$-0.747029\pi$
$47$	−4.68666e7	−1.40095	−0.700476	+	0.713676i	$0.747029\pi$
$48$	7.23983e6	0.196853
$49$	3.55556e6	0.0881101
$50$	−4.28368e6	−0.0969286
$51$	−1.69361e7	−0.350547
$52$	4.32442e7	0.820188
$53$	−8.21904e7	−1.43080	−0.715401	−	0.698714i	$-0.753756\pi$
$53$	−8.21904e7	−1.43080	−0.715401	+	0.698714i	$0.753756\pi$
$54$	−4.80101e7	−0.768353
$55$	−1.03268e8	−1.52171
$56$	2.71417e7	0.368800
$57$	−1.43967e7	−0.180645
$58$	8.64309e7	1.00287
$59$	1.66093e7	0.178450	0.0892249	−	0.996012i	$-0.471561\pi$
$59$	1.66093e7	0.178450	0.0892249	+	0.996012i	$0.471561\pi$
$60$	−3.67146e7	−0.365728
$61$	3.59512e7	0.332453	0.166226	−	0.986088i	$-0.446842\pi$
$61$	3.59512e7	0.332453	0.166226	+	0.986088i	$0.446842\pi$
$62$	−5.77522e7	−0.496371
$63$	−4.95599e7	−0.396367
$64$	1.67772e7	0.125000
$65$	−2.19300e8	−1.52380
$66$	1.40599e8	0.912081
$67$	−9.61687e7	−0.583038	−0.291519	−	0.956565i	$-0.594161\pi$
$67$	−9.61687e7	−0.583038	−0.291519	+	0.956565i	$0.594161\pi$
$68$	−3.92468e7	−0.222594
$69$	1.11908e8	0.594350
$70$	−1.37641e8	−0.685184
$71$	−3.86399e8	−1.80457	−0.902285	−	0.431141i	$-0.858111\pi$
$71$	−3.86399e8	−1.80457	−0.902285	+	0.431141i	$0.858111\pi$
$72$	−3.06346e7	−0.134343
$73$	−1.45125e8	−0.598121	−0.299060	−	0.954234i	$-0.596673\pi$
$73$	−1.45125e8	−0.598121	−0.299060	+	0.954234i	$0.596673\pi$
$74$	3.52087e8	1.36492
$75$	−2.95764e7	−0.107937
$76$	−3.33622e7	−0.114708
$77$	5.27097e8	1.70876
$78$	2.98577e8	0.913337
$79$	−3.54985e7	−0.102539	−0.0512695	−	0.998685i	$-0.516327\pi$
$79$	−3.54985e7	−0.102539	−0.0512695	+	0.998685i	$0.516327\pi$
$80$	−8.50806e7	−0.232234
$81$	−1.84270e8	−0.475634
$82$	−4.50272e8	−1.09980
$83$	3.15916e8	0.730667	0.365334	−	0.930877i	$-0.380955\pi$
$83$	3.15916e8	0.730667	0.365334	+	0.930877i	$0.380955\pi$
$84$	1.87398e8	0.410685
$85$	1.99028e8	0.413552
$86$	1.03523e8	0.204077
$87$	5.96757e8	1.11676
$88$	3.25816e8	0.579163
$89$	8.66694e8	1.46424	0.732118	−	0.681178i	$-0.238532\pi$
$89$	8.66694e8	1.46424	0.732118	+	0.681178i	$0.238532\pi$
$90$	1.55354e8	0.249593
$91$	1.11935e9	1.71112
$92$	2.59331e8	0.377406
$93$	−3.98747e8	−0.552744
$94$	−7.49866e8	−0.990623
$95$	1.69186e8	0.213113
$96$	1.15837e8	0.139196
$97$	6.14107e8	0.704322	0.352161	−	0.935939i	$-0.385447\pi$
$97$	6.14107e8	0.704322	0.352161	+	0.935939i	$0.385447\pi$
$98$	5.68890e7	0.0623033
$99$	−5.94930e8	−0.622454
$100$	−6.85389e7	−0.0685389
$101$	−1.53743e9	−1.47011	−0.735056	−	0.678006i	$-0.762844\pi$
$101$	−1.53743e9	−1.47011	−0.735056	+	0.678006i	$0.762844\pi$
$102$	−2.70977e8	−0.247874
$103$	−1.65713e9	−1.45074	−0.725368	−	0.688361i	$-0.758330\pi$
$103$	−1.65713e9	−1.45074	−0.725368	+	0.688361i	$0.758330\pi$
$104$	6.91908e8	0.579960
$105$	−9.50335e8	−0.763001
$106$	−1.31505e9	−1.01173
$107$	1.34982e9	0.995520	0.497760	−	0.867315i	$-0.334156\pi$
$107$	1.34982e9	0.995520	0.497760	+	0.867315i	$0.334156\pi$
$108$	−7.68161e8	−0.543307
$109$	1.71831e9	1.16596	0.582979	−	0.812488i	$-0.301887\pi$
$109$	1.71831e9	1.16596	0.582979	+	0.812488i	$0.301887\pi$
$110$	−1.65228e9	−1.07601
$111$	2.43096e9	1.51993
$112$	4.34268e8	0.260781
$113$	−1.80534e9	−1.04161	−0.520805	−	0.853675i	$-0.674368\pi$
$113$	−1.80534e9	−1.04161	−0.520805	+	0.853675i	$0.674368\pi$
$114$	−2.30347e8	−0.127735
$115$	−1.31512e9	−0.701173
$116$	1.38289e9	0.709134
$117$	−1.26340e9	−0.623311
$118$	2.65748e8	0.126183
$119$	−1.01588e9	−0.464387
$120$	−5.87434e8	−0.258609
$121$	3.96946e9	1.68344
$122$	5.75220e8	0.235079
$123$	−3.10888e9	−1.22470
$124$	−9.24036e8	−0.350987
$125$	2.88318e9	1.05627
$126$	−7.92958e8	−0.280274
$127$	−9.77497e8	−0.333425	−0.166713	−	0.986006i	$-0.553315\pi$
$127$	−9.77497e8	−0.333425	−0.166713	+	0.986006i	$0.553315\pi$
$128$	2.68435e8	0.0883883
$129$	7.14769e8	0.227254
$130$	−3.50880e9	−1.07749
$131$	−1.01749e9	−0.301863	−0.150931	−	0.988544i	$-0.548227\pi$
$131$	−1.01749e9	−0.301863	−0.150931	+	0.988544i	$0.548227\pi$
$132$	2.24958e9	0.644939
$133$	−8.63559e8	−0.239309
$134$	−1.53870e9	−0.412270
$135$	3.89550e9	1.00940
$136$	−6.27949e8	−0.157398
$137$	−9.69370e6	−0.00235097	−0.00117548	−	0.999999i	$-0.500374\pi$
$137$	−9.69370e6	−0.00235097	−0.00117548	+	0.999999i	$0.500374\pi$
$138$	1.79053e9	0.420269
$139$	−2.05409e9	−0.466716	−0.233358	−	0.972391i	$-0.574971\pi$
$139$	−2.05409e9	−0.466716	−0.233358	+	0.972391i	$0.574971\pi$
$140$	−2.20226e9	−0.484498
$141$	−5.17740e9	−1.10313
$142$	−6.18239e9	−1.27602
$143$	1.34370e10	2.68713
$144$	−4.90154e8	−0.0949951
$145$	−7.01294e9	−1.31748
$146$	−2.32200e9	−0.422935
$147$	3.92787e8	0.0693791
$148$	5.63339e9	0.965143
$149$	−6.17257e9	−1.02595	−0.512977	−	0.858402i	$-0.671457\pi$
$149$	−6.17257e9	−1.02595	−0.512977	+	0.858402i	$0.671457\pi$
$150$	−4.73222e8	−0.0763228
$151$	4.28860e9	0.671304	0.335652	−	0.941986i	$-0.391043\pi$
$151$	4.28860e9	0.671304	0.335652	+	0.941986i	$0.391043\pi$
$152$	−5.33795e8	−0.0811107
$153$	1.14661e9	0.169163
$154$	8.43355e9	1.20828
$155$	4.68597e9	0.652089
$156$	4.77723e9	0.645826
$157$	−5.63305e9	−0.739938	−0.369969	−	0.929044i	$-0.620632\pi$
$157$	−5.63305e9	−0.739938	−0.369969	+	0.929044i	$0.620632\pi$
$158$	−5.67977e8	−0.0725060
$159$	−9.07965e9	−1.12663
$160$	−1.36129e9	−0.164214
$161$	6.71262e9	0.787364
$162$	−2.94833e9	−0.336324
$163$	2.97548e9	0.330151	0.165075	−	0.986281i	$-0.447213\pi$
$163$	2.97548e9	0.330151	0.165075	+	0.986281i	$0.447213\pi$
$164$	−7.20435e9	−0.777674
$165$	−1.14081e10	−1.19821
$166$	5.05465e9	0.516660
$167$	1.08189e10	1.07637	0.538184	−	0.842827i	$-0.319110\pi$
$167$	1.08189e10	1.07637	0.538184	+	0.842827i	$0.319110\pi$
$168$	2.99837e9	0.290398
$169$	1.79304e10	1.69083
$170$	3.18445e9	0.292425
$171$	9.74691e8	0.0871735
$172$	1.65637e9	0.144304
$173$	−1.25112e10	−1.06192	−0.530961	−	0.847396i	$-0.678169\pi$
$173$	−1.25112e10	−1.06192	−0.530961	+	0.847396i	$0.678169\pi$
$174$	9.54811e9	0.789670
$175$	−1.77409e9	−0.142989
$176$	5.21306e9	0.409530
$177$	1.83484e9	0.140514
$178$	1.38671e10	1.03537
$179$	9.45123e9	0.688097	0.344049	−	0.938952i	$-0.388202\pi$
$179$	9.45123e9	0.688097	0.344049	+	0.938952i	$0.388202\pi$
$180$	2.48567e9	0.176489
$181$	1.43226e10	0.991898	0.495949	−	0.868352i	$-0.334820\pi$
$181$	1.43226e10	0.991898	0.495949	+	0.868352i	$0.334820\pi$
$182$	1.79096e10	1.20994
$183$	3.97157e9	0.261778
$184$	4.14930e9	0.266867
$185$	−2.85680e10	−1.79311
$186$	−6.37995e9	−0.390849
$187$	−1.21949e10	−0.729273
$188$	−1.19979e10	−0.700476
$189$	−1.98834e10	−1.13348
$190$	2.70698e9	0.150693
$191$	−1.94359e10	−1.05671	−0.528354	−	0.849024i	$-0.677191\pi$
$191$	−1.94359e10	−1.05671	−0.528354	+	0.849024i	$0.677191\pi$
$192$	1.85340e9	0.0984266
$193$	−1.12972e8	−0.00586088	−0.00293044	−	0.999996i	$-0.500933\pi$
$193$	−1.12972e8	−0.00586088	−0.00293044	+	0.999996i	$0.500933\pi$
$194$	9.82571e9	0.498031
$195$	−2.42263e10	−1.19986
$196$	9.10224e8	0.0440551
$197$	−4.27742e9	−0.202341	−0.101171	−	0.994869i	$-0.532259\pi$
$197$	−4.27742e9	−0.202341	−0.101171	+	0.994869i	$0.532259\pi$
$198$	−9.51887e9	−0.440141
$199$	2.60050e10	1.17549	0.587744	−	0.809047i	$-0.300016\pi$
$199$	2.60050e10	1.17549	0.587744	+	0.809047i	$0.300016\pi$
$200$	−1.09662e9	−0.0484643
$201$	−1.06239e10	−0.459092
$202$	−2.45990e10	−1.03953
$203$	3.57954e10	1.47943
$204$	−4.33563e9	−0.175274
$205$	3.65347e10	1.44482
$206$	−2.65140e10	−1.02583
$207$	−7.57647e9	−0.286814
$208$	1.10705e10	0.410094
$209$	−1.03664e10	−0.375811
$210$	−1.52054e10	−0.539523
$211$	2.44282e10	0.848438	0.424219	−	0.905560i	$-0.360549\pi$
$211$	2.44282e10	0.848438	0.424219	+	0.905560i	$0.360549\pi$
$212$	−2.10407e10	−0.715401
$213$	−4.26859e10	−1.42094
$214$	2.15972e10	0.703939
$215$	−8.39979e9	−0.268099
$216$	−1.22906e10	−0.384176
$217$	−2.39181e10	−0.732247
$218$	2.74930e10	0.824456
$219$	−1.60321e10	−0.470968
$220$	−2.64365e10	−0.760855
$221$	−2.58972e10	−0.730276
$222$	3.88954e10	1.07475
$223$	3.97142e9	0.107541	0.0537705	−	0.998553i	$-0.482876\pi$
$223$	3.97142e9	0.107541	0.0537705	+	0.998553i	$0.482876\pi$
$224$	6.94828e9	0.184400
$225$	2.00239e9	0.0520869
$226$	−2.88854e10	−0.736530
$227$	−6.60469e9	−0.165096	−0.0825479	−	0.996587i	$-0.526306\pi$
$227$	−6.60469e9	−0.165096	−0.0825479	+	0.996587i	$0.526306\pi$
$228$	−3.68555e9	−0.0903225
$229$	−5.39297e10	−1.29589	−0.647945	−	0.761687i	$-0.724372\pi$
$229$	−5.39297e10	−1.29589	−0.647945	+	0.761687i	$0.724372\pi$
$230$	−2.10419e10	−0.495804
$231$	5.82289e10	1.34550
$232$	2.21263e10	0.501433
$233$	3.43822e9	0.0764244	0.0382122	−	0.999270i	$-0.487834\pi$
$233$	3.43822e9	0.0764244	0.0382122	+	0.999270i	$0.487834\pi$
$234$	−2.02144e10	−0.440747
$235$	6.08436e10	1.30140
$236$	4.25197e9	0.0892249
$237$	−3.92156e9	−0.0807405
$238$	−1.62541e10	−0.328371
$239$	−5.49493e10	−1.08936	−0.544680	−	0.838644i	$-0.683349\pi$
$239$	−5.49493e10	−1.08936	−0.544680	+	0.838644i	$0.683349\pi$
$240$	−9.39894e9	−0.182864
$241$	2.55819e10	0.488491	0.244246	−	0.969713i	$-0.421460\pi$
$241$	2.55819e10	0.488491	0.244246	+	0.969713i	$0.421460\pi$
$242$	6.35114e10	1.19037
$243$	3.87049e10	0.712094
$244$	9.20352e9	0.166226
$245$	−4.61593e9	−0.0818487
$246$	−4.97420e10	−0.865995
$247$	−2.20142e10	−0.376328
$248$	−1.47846e10	−0.248185
$249$	3.48995e10	0.575337
$250$	4.61308e10	0.746897
$251$	5.25380e10	0.835491	0.417746	−	0.908564i	$-0.362820\pi$
$251$	5.25380e10	0.835491	0.417746	+	0.908564i	$0.362820\pi$
$252$	−1.26873e10	−0.198184
$253$	8.05800e10	1.23647
$254$	−1.56400e10	−0.235767
$255$	2.19869e10	0.325636
$256$	4.29497e9	0.0625000
$257$	−6.94712e10	−0.993358	−0.496679	−	0.867934i	$-0.665447\pi$
$257$	−6.94712e10	−0.993358	−0.496679	+	0.867934i	$0.665447\pi$
$258$	1.14363e10	0.160693
$259$	1.45817e11	2.01353
$260$	−5.61409e10	−0.761902
$261$	−4.04019e10	−0.538914
$262$	−1.62798e10	−0.213449
$263$	−1.25547e11	−1.61810	−0.809050	−	0.587739i	$-0.800018\pi$
$263$	−1.25547e11	−1.61810	−0.809050	+	0.587739i	$0.800018\pi$
$264$	3.59933e10	0.456041
$265$	1.06702e11	1.32912
$266$	−1.38169e10	−0.169217
$267$	9.57446e10	1.15296
$268$	−2.46192e10	−0.291519
$269$	9.32766e10	1.08614	0.543072	−	0.839686i	$-0.317261\pi$
$269$	9.32766e10	1.08614	0.543072	+	0.839686i	$0.317261\pi$
$270$	6.23280e10	0.713751
$271$	1.92737e10	0.217072	0.108536	−	0.994093i	$-0.465384\pi$
$271$	1.92737e10	0.217072	0.108536	+	0.994093i	$0.465384\pi$
$272$	−1.00472e10	−0.111297
$273$	1.23656e11	1.34736
$274$	−1.55099e8	−0.00166239
$275$	−2.12966e10	−0.224550
$276$	2.86486e10	0.297175
$277$	−2.42551e10	−0.247539	−0.123770	−	0.992311i	$-0.539498\pi$
$277$	−2.42551e10	−0.247539	−0.123770	+	0.992311i	$0.539498\pi$
$278$	−3.28654e10	−0.330018
$279$	2.69961e10	0.266736
$280$	−3.52361e10	−0.342592
$281$	1.50868e10	0.144351	0.0721755	−	0.997392i	$-0.477006\pi$
$281$	1.50868e10	0.144351	0.0721755	+	0.997392i	$0.477006\pi$
$282$	−8.28385e10	−0.780029
$283$	−1.91830e10	−0.177778	−0.0888890	−	0.996042i	$-0.528332\pi$
$283$	−1.91830e10	−0.177778	−0.0888890	+	0.996042i	$0.528332\pi$
$284$	−9.89182e10	−0.902285
$285$	1.86902e10	0.167808
$286$	2.14991e11	1.90009
$287$	−1.86480e11	−1.62242
$288$	−7.84246e9	−0.0671717
$289$	−9.50846e10	−0.801807
$290$	−1.12207e11	−0.931599
$291$	6.78410e10	0.554592
$292$	−3.71519e10	−0.299060
$293$	−1.11692e11	−0.885354	−0.442677	−	0.896681i	$-0.645971\pi$
$293$	−1.11692e11	−0.885354	−0.442677	+	0.896681i	$0.645971\pi$
$294$	6.28458e9	0.0490584
$295$	−2.15626e10	−0.165769
$296$	9.01342e10	0.682459
$297$	−2.38685e11	−1.78001
$298$	−9.87611e10	−0.725459
$299$	1.71121e11	1.23818
$300$	−7.57156e9	−0.0539684
$301$	4.28741e10	0.301055
$302$	6.86176e10	0.474683
$303$	−1.69842e11	−1.15759
$304$	−8.54072e9	−0.0573539
$305$	−4.66729e10	−0.308827
$306$	1.83458e10	0.119616
$307$	−1.86503e11	−1.19829	−0.599146	−	0.800640i	$-0.704493\pi$
$307$	−1.86503e11	−1.19829	−0.599146	+	0.800640i	$0.704493\pi$
$308$	1.34937e11	0.854382
$309$	−1.83064e11	−1.14233
$310$	7.49755e10	0.461097
$311$	−3.82539e10	−0.231875	−0.115937	−	0.993257i	$-0.536987\pi$
$311$	−3.82539e10	−0.231875	−0.115937	+	0.993257i	$0.536987\pi$
$312$	7.64357e10	0.456668
$313$	−1.78799e11	−1.05297	−0.526485	−	0.850185i	$-0.676490\pi$
$313$	−1.78799e11	−1.05297	−0.526485	+	0.850185i	$0.676490\pi$
$314$	−9.01288e10	−0.523215
$315$	6.43400e10	0.368200
$316$	−9.08763e9	−0.0512695
$317$	−8.63549e10	−0.480308	−0.240154	−	0.970735i	$-0.577198\pi$
$317$	−8.63549e10	−0.480308	−0.240154	+	0.970735i	$0.577198\pi$
$318$	−1.45274e11	−0.796649
$319$	4.29697e11	2.32329
$320$	−2.17806e10	−0.116117
$321$	1.49116e11	0.783886
$322$	1.07402e11	0.556751
$323$	1.99792e10	0.102133
$324$	−4.71732e10	−0.237817
$325$	−4.52257e10	−0.224859
$326$	4.76076e10	0.233452
$327$	1.89824e11	0.918090
$328$	−1.15270e11	−0.549899
$329$	−3.10557e11	−1.46137
$330$	−1.82529e11	−0.847265
$331$	1.65094e11	0.755972	0.377986	−	0.925811i	$-0.376617\pi$
$331$	1.65094e11	0.755972	0.377986	+	0.925811i	$0.376617\pi$
$332$	8.08744e10	0.365334
$333$	−1.64582e11	−0.733471
$334$	1.73103e11	0.761107
$335$	1.24849e11	0.541605
$336$	4.79740e10	0.205343
$337$	2.64323e11	1.11635	0.558176	−	0.829723i	$-0.311502\pi$
$337$	2.64323e11	1.11635	0.558176	+	0.829723i	$0.311502\pi$
$338$	2.86887e11	1.19560
$339$	−1.99437e11	−0.820178
$340$	5.09513e10	0.206776
$341$	−2.87119e11	−1.14992
$342$	1.55951e10	0.0616410
$343$	−2.43839e11	−0.951215
$344$	2.65019e10	0.102039
$345$	−1.45283e11	−0.552113
$346$	−2.00180e11	−0.750893
$347$	−2.87067e11	−1.06292	−0.531459	−	0.847084i	$-0.678356\pi$
$347$	−2.87067e11	−1.06292	−0.531459	+	0.847084i	$0.678356\pi$
$348$	1.52770e11	0.558381
$349$	4.15196e11	1.49809	0.749046	−	0.662518i	$-0.230512\pi$
$349$	4.15196e11	1.49809	0.749046	+	0.662518i	$0.230512\pi$
$350$	−2.83854e10	−0.101109
$351$	−5.06875e11	−1.78246
$352$	8.34090e10	0.289582
$353$	−3.17550e11	−1.08849	−0.544247	−	0.838925i	$-0.683184\pi$
$353$	−3.17550e11	−1.08849	−0.544247	+	0.838925i	$0.683184\pi$
$354$	2.93575e10	0.0993582
$355$	5.01634e11	1.67633
$356$	2.21874e11	0.732118
$357$	−1.12225e11	−0.365665
$358$	1.51220e11	0.486558
$359$	2.48204e10	0.0788649	0.0394325	−	0.999222i	$-0.487445\pi$
$359$	2.48204e10	0.0788649	0.0394325	+	0.999222i	$0.487445\pi$
$360$	3.97707e10	0.124796
$361$	1.69836e10	0.0526316
$362$	2.29161e11	0.701378
$363$	4.38510e11	1.32556
$364$	2.86554e11	0.855558
$365$	1.88405e11	0.555616
$366$	6.35451e10	0.185105
$367$	4.55716e11	1.31128	0.655642	−	0.755072i	$-0.272398\pi$
$367$	4.55716e11	1.31128	0.655642	+	0.755072i	$0.272398\pi$
$368$	6.63887e10	0.188703
$369$	2.10478e11	0.591002
$370$	−4.57089e11	−1.26792
$371$	−5.44626e11	−1.49251
$372$	−1.02079e11	−0.276372
$373$	−3.17110e11	−0.848242	−0.424121	−	0.905605i	$-0.639417\pi$
$373$	−3.17110e11	−0.848242	−0.424121	+	0.905605i	$0.639417\pi$
$374$	−1.95118e11	−0.515674
$375$	3.18507e11	0.831723
$376$	−1.91966e11	−0.495311
$377$	9.12509e11	2.32649
$378$	−3.18134e11	−0.801488
$379$	3.62101e11	0.901475	0.450738	−	0.892656i	$-0.351161\pi$
$379$	3.62101e11	0.901475	0.450738	+	0.892656i	$0.351161\pi$
$380$	4.33117e10	0.106556
$381$	−1.07985e11	−0.262544
$382$	−3.10975e11	−0.747205
$383$	−8.03252e11	−1.90747	−0.953734	−	0.300651i	$-0.902796\pi$
$383$	−8.03252e11	−1.90747	−0.953734	+	0.300651i	$0.902796\pi$
$384$	2.96543e10	0.0695981
$385$	−6.84292e11	−1.58733
$386$	−1.80755e9	−0.00414427
$387$	−4.83916e10	−0.109666
$388$	1.57211e11	0.352161
$389$	7.98458e11	1.76799	0.883993	−	0.467500i	$-0.154845\pi$
$389$	7.98458e11	1.76799	0.883993	+	0.467500i	$0.154845\pi$
$390$	−3.87621e11	−0.848431
$391$	−1.55303e11	−0.336034
$392$	1.45636e10	0.0311516
$393$	−1.12403e11	−0.237691
$394$	−6.84388e10	−0.143077
$395$	4.60852e10	0.0952521
$396$	−1.52302e11	−0.311227
$397$	6.82219e11	1.37837	0.689186	−	0.724585i	$-0.257968\pi$
$397$	6.82219e11	1.37837	0.689186	+	0.724585i	$0.257968\pi$
$398$	4.16080e11	0.831196
$399$	−9.53982e10	−0.188435
$400$	−1.75459e10	−0.0342694
$401$	5.92663e11	1.14461	0.572306	−	0.820040i	$-0.306049\pi$
$401$	5.92663e11	1.14461	0.572306	+	0.820040i	$0.306049\pi$
$402$	−1.69982e11	−0.324627
$403$	−6.09729e11	−1.15150
$404$	−3.93583e11	−0.735056
$405$	2.39225e11	0.441834
$406$	5.72726e11	1.04612
$407$	1.75042e12	3.16204
$408$	−6.93701e10	−0.123937
$409$	−7.52816e11	−1.33025	−0.665126	−	0.746731i	$-0.731622\pi$
$409$	−7.52816e11	−1.33025	−0.665126	+	0.746731i	$0.731622\pi$
$410$	5.84556e11	1.02164
$411$	−1.07087e9	−0.00185118
$412$	−4.24225e11	−0.725368
$413$	1.10060e11	0.186146
$414$	−1.21224e11	−0.202808
$415$	−4.10130e11	−0.678743
$416$	1.77128e11	0.289980
$417$	−2.26917e11	−0.367498
$418$	−1.65862e11	−0.265738
$419$	−6.07297e11	−0.962583	−0.481291	−	0.876561i	$-0.659832\pi$
$419$	−6.07297e11	−0.962583	−0.481291	+	0.876561i	$0.659832\pi$
$420$	−2.43286e11	−0.381500
$421$	6.97919e11	1.08277	0.541384	−	0.840775i	$-0.317901\pi$
$421$	6.97919e11	1.08277	0.541384	+	0.840775i	$0.317901\pi$
$422$	3.90851e11	0.599936
$423$	3.50523e11	0.532335
$424$	−3.36652e11	−0.505865
$425$	4.10451e10	0.0610254
$426$	−6.82975e11	−1.00476
$427$	2.38227e11	0.346790
$428$	3.45555e11	0.497760
$429$	1.48440e12	2.11588
$430$	−1.34397e11	−0.189575
$431$	−5.58870e11	−0.780123	−0.390061	−	0.920789i	$-0.627546\pi$
$431$	−5.58870e11	−0.780123	−0.390061	+	0.920789i	$0.627546\pi$
$432$	−1.96649e11	−0.271654
$433$	5.95649e10	0.0814320	0.0407160	−	0.999171i	$-0.487036\pi$
$433$	5.95649e10	0.0814320	0.0407160	+	0.999171i	$0.487036\pi$
$434$	−3.82689e11	−0.517777
$435$	−7.74726e11	−1.03740
$436$	4.39888e11	0.582979
$437$	−1.32017e11	−0.173166
$438$	−2.56513e11	−0.333025
$439$	−1.08818e12	−1.39834	−0.699168	−	0.714958i	$-0.746446\pi$
$439$	−1.08818e12	−1.39834	−0.699168	+	0.714958i	$0.746446\pi$
$440$	−4.22984e11	−0.538006
$441$	−2.65926e10	−0.0334801
$442$	−4.14355e11	−0.516383
$443$	−2.53076e11	−0.312201	−0.156101	−	0.987741i	$-0.549892\pi$
$443$	−2.53076e11	−0.312201	−0.156101	+	0.987741i	$0.549892\pi$
$444$	6.22326e11	0.759966
$445$	−1.12517e12	−1.36018
$446$	6.35428e10	0.0760430
$447$	−6.81890e11	−0.807850
$448$	1.11173e11	0.130391
$449$	−4.65995e11	−0.541094	−0.270547	−	0.962707i	$-0.587204\pi$
$449$	−4.65995e11	−0.541094	−0.270547	+	0.962707i	$0.587204\pi$
$450$	3.20383e10	0.0368310
$451$	−2.23856e12	−2.54785
$452$	−4.62166e11	−0.520805
$453$	4.73766e11	0.528593
$454$	−1.05675e11	−0.116740
$455$	−1.45317e12	−1.58952
$456$	−5.89689e10	−0.0638676
$457$	1.56160e12	1.67474	0.837371	−	0.546634i	$-0.184091\pi$
$457$	1.56160e12	1.67474	0.837371	+	0.546634i	$0.184091\pi$
$458$	−8.62875e11	−0.916333
$459$	4.60020e11	0.483748
$460$	−3.36671e11	−0.350586
$461$	−6.91594e11	−0.713177	−0.356588	−	0.934262i	$-0.616060\pi$
$461$	−6.91594e11	−0.713177	−0.356588	+	0.934262i	$0.616060\pi$
$462$	9.31663e11	0.951415
$463$	5.25589e11	0.531535	0.265768	−	0.964037i	$-0.414375\pi$
$463$	5.25589e11	0.531535	0.265768	+	0.964037i	$0.414375\pi$
$464$	3.54021e11	0.354567
$465$	5.17664e11	0.513464
$466$	5.50115e10	0.0540402
$467$	9.45874e11	0.920254	0.460127	−	0.887853i	$-0.347804\pi$
$467$	9.45874e11	0.920254	0.460127	+	0.887853i	$0.347804\pi$
$468$	−3.23430e11	−0.311655
$469$	−6.37252e11	−0.608182
$470$	9.73497e11	0.920225
$471$	−6.22289e11	−0.582637
$472$	6.80315e10	0.0630916
$473$	5.14672e11	0.472776
$474$	−6.27450e10	−0.0570921
$475$	3.48908e10	0.0314478
$476$	−2.60065e11	−0.232194
$477$	6.14715e11	0.543677
$478$	−8.79189e11	−0.770294
$479$	5.79389e11	0.502875	0.251438	−	0.967873i	$-0.419097\pi$
$479$	5.79389e11	0.502875	0.251438	+	0.967873i	$0.419097\pi$
$480$	−1.50383e11	−0.129304
$481$	3.71722e12	3.16639
$482$	4.09311e11	0.345415
$483$	7.41550e11	0.619981
$484$	1.01618e12	0.841720
$485$	−7.97250e11	−0.654270
$486$	6.19278e11	0.503527
$487$	−6.91916e11	−0.557408	−0.278704	−	0.960377i	$-0.589905\pi$
$487$	−6.91916e11	−0.557408	−0.278704	+	0.960377i	$0.589905\pi$
$488$	1.47256e11	0.117540
$489$	3.28704e11	0.259965
$490$	−7.38549e10	−0.0578758
$491$	−1.26757e12	−0.984250	−0.492125	−	0.870525i	$-0.663780\pi$
$491$	−1.26757e12	−0.984250	−0.492125	+	0.870525i	$0.663780\pi$
$492$	−7.95872e11	−0.612351
$493$	−8.28158e11	−0.631396
$494$	−3.52227e11	−0.266104
$495$	7.72354e11	0.578220
$496$	−2.36553e11	−0.175494
$497$	−2.56044e12	−1.88239
$498$	5.58392e11	0.406825
$499$	9.48824e11	0.685067	0.342533	−	0.939506i	$-0.388715\pi$
$499$	9.48824e11	0.685067	0.342533	+	0.939506i	$0.388715\pi$
$500$	7.38093e11	0.528136
$501$	1.19518e12	0.847547
$502$	8.40608e11	0.590782
$503$	1.71262e12	1.19291	0.596453	−	0.802648i	$-0.296576\pi$
$503$	1.71262e12	1.19291	0.596453	+	0.802648i	$0.296576\pi$
$504$	−2.02997e11	−0.140137
$505$	1.99594e12	1.36564
$506$	1.28928e12	0.874319
$507$	1.98079e12	1.33138
$508$	−2.50239e11	−0.166713
$509$	7.42133e11	0.490063	0.245031	−	0.969515i	$-0.421202\pi$
$509$	7.42133e11	0.490063	0.245031	+	0.969515i	$0.421202\pi$
$510$	3.51790e11	0.230259
$511$	−9.61655e11	−0.623915
$512$	6.87195e10	0.0441942
$513$	3.91045e11	0.249287
$514$	−1.11154e12	−0.702410
$515$	2.15133e12	1.34764
$516$	1.82981e11	0.113627
$517$	−3.72801e12	−2.29493
$518$	2.33307e12	1.42378
$519$	−1.38213e12	−0.836172
$520$	−8.98254e11	−0.538746
$521$	1.03931e12	0.617982	0.308991	−	0.951065i	$-0.400009\pi$
$521$	1.03931e12	0.617982	0.308991	+	0.951065i	$0.400009\pi$
$522$	−6.46430e11	−0.381070
$523$	−1.96380e12	−1.14773	−0.573866	−	0.818949i	$-0.694557\pi$
$523$	−1.96380e12	−1.14773	−0.573866	+	0.818949i	$0.694557\pi$
$524$	−2.60478e11	−0.150931
$525$	−1.95985e11	−0.112592
$526$	−2.00875e12	−1.14417
$527$	5.53366e11	0.312511
$528$	5.75892e11	0.322469
$529$	−7.74960e11	−0.430258
$530$	1.70723e12	0.939832
$531$	−1.24223e11	−0.0678075
$532$	−2.21071e11	−0.119655
$533$	−4.75383e12	−2.55136
$534$	1.53191e12	0.815265
$535$	−1.75238e12	−0.924775
$536$	−3.93907e11	−0.206135
$537$	1.04409e12	0.541817
$538$	1.49243e12	0.768020
$539$	2.82827e11	0.144335
$540$	9.97248e11	0.504698
$541$	1.82490e11	0.0915905	0.0457952	−	0.998951i	$-0.485418\pi$
$541$	1.82490e11	0.0915905	0.0457952	+	0.998951i	$0.485418\pi$
$542$	3.08379e11	0.153493
$543$	1.58223e12	0.781034
$544$	−1.60755e11	−0.0786990
$545$	−2.23076e12	−1.08310
$546$	1.97849e12	0.952724
$547$	2.66008e12	1.27043	0.635216	−	0.772335i	$-0.280911\pi$
$547$	2.66008e12	1.27043	0.635216	+	0.772335i	$0.280911\pi$
$548$	−2.48159e9	−0.00117548
$549$	−2.68885e11	−0.126326
$550$	−3.40745e11	−0.158781
$551$	−7.03985e11	−0.325373
$552$	4.58377e11	0.210134
$553$	−2.35228e11	−0.106961
$554$	−3.88082e11	−0.175037
$555$	−3.15594e12	−1.41192
$556$	−5.25847e11	−0.233358
$557$	2.58198e12	1.13659	0.568296	−	0.822824i	$-0.307603\pi$
$557$	2.58198e12	1.13659	0.568296	+	0.822824i	$0.307603\pi$
$558$	4.31938e11	0.188611
$559$	1.09296e12	0.473426
$560$	−5.63778e11	−0.242249
$561$	−1.34718e12	−0.574239
$562$	2.41389e11	0.102072
$563$	−2.29062e11	−0.0960871	−0.0480436	−	0.998845i	$-0.515299\pi$
$563$	−2.29062e11	−0.0960871	−0.0480436	+	0.998845i	$0.515299\pi$
$564$	−1.32542e12	−0.551564
$565$	2.34374e12	0.967590
$566$	−3.06928e11	−0.125708
$567$	−1.22105e12	−0.496146
$568$	−1.58269e12	−0.638012
$569$	−2.27916e12	−0.911527	−0.455763	−	0.890101i	$-0.650634\pi$
$569$	−2.27916e12	−0.911527	−0.455763	+	0.890101i	$0.650634\pi$
$570$	2.99043e11	0.118658
$571$	−4.56986e12	−1.79904	−0.899519	−	0.436881i	$-0.856083\pi$
$571$	−4.56986e12	−1.79904	−0.899519	+	0.436881i	$0.856083\pi$
$572$	3.43986e12	1.34357
$573$	−2.14711e12	−0.832066
$574$	−2.98368e12	−1.14723
$575$	−2.71214e11	−0.103468
$576$	−1.25479e11	−0.0474976
$577$	2.31008e12	0.867633	0.433817	−	0.901001i	$-0.357167\pi$
$577$	2.31008e12	0.867633	0.433817	+	0.901001i	$0.357167\pi$
$578$	−1.52135e12	−0.566963
$579$	−1.24801e10	−0.00461493
$580$	−1.79531e12	−0.658740
$581$	2.09338e12	0.762177
$582$	1.08546e12	0.392156
$583$	−6.53783e12	−2.34383
$584$	−5.94431e11	−0.211468
$585$	1.64018e12	0.579016
$586$	−1.78707e12	−0.626040
$587$	−8.67875e11	−0.301707	−0.150854	−	0.988556i	$-0.548202\pi$
$587$	−8.67875e11	−0.301707	−0.150854	+	0.988556i	$0.548202\pi$
$588$	1.00553e11	0.0346895
$589$	4.70395e11	0.161044
$590$	−3.45002e11	−0.117216
$591$	−4.72531e11	−0.159326
$592$	1.44215e12	0.482572
$593$	3.06798e12	1.01884	0.509421	−	0.860518i	$-0.329860\pi$
$593$	3.06798e12	1.01884	0.509421	+	0.860518i	$0.329860\pi$
$594$	−3.81896e12	−1.25865
$595$	1.31884e12	0.431386
$596$	−1.58018e12	−0.512977
$597$	2.87280e12	0.925595
$598$	2.73793e12	0.875523
$599$	3.95998e12	1.25682	0.628409	−	0.777883i	$-0.283706\pi$
$599$	3.95998e12	1.25682	0.628409	+	0.777883i	$0.283706\pi$
$600$	−1.21145e11	−0.0381614
$601$	1.74608e12	0.545920	0.272960	−	0.962025i	$-0.411997\pi$
$601$	1.74608e12	0.545920	0.272960	+	0.962025i	$0.411997\pi$
$602$	6.85986e11	0.212878
$603$	7.19261e11	0.221543
$604$	1.09788e12	0.335652
$605$	−5.15326e12	−1.56381
$606$	−2.71747e12	−0.818537
$607$	9.76046e10	0.0291824	0.0145912	−	0.999894i	$-0.495355\pi$
$607$	9.76046e10	0.0291824	0.0145912	+	0.999894i	$0.495355\pi$
$608$	−1.36651e11	−0.0405554
$609$	3.95435e12	1.16492
$610$	−7.46766e11	−0.218374
$611$	−7.91684e12	−2.29809
$612$	2.93533e11	0.0845815
$613$	2.69418e11	0.0770646	0.0385323	−	0.999257i	$-0.487732\pi$
$613$	2.69418e11	0.0770646	0.0385323	+	0.999257i	$0.487732\pi$
$614$	−2.98404e12	−0.847320
$615$	4.03603e12	1.13767
$616$	2.15899e12	0.604140
$617$	1.59514e12	0.443114	0.221557	−	0.975147i	$-0.428886\pi$
$617$	1.59514e12	0.443114	0.221557	+	0.975147i	$0.428886\pi$
$618$	−2.92903e12	−0.807748
$619$	5.45520e12	1.49349	0.746746	−	0.665109i	$-0.231615\pi$
$619$	5.45520e12	1.49349	0.746746	+	0.665109i	$0.231615\pi$
$620$	1.19961e12	0.326045
$621$	−3.03967e12	−0.820191
$622$	−6.12062e11	−0.163960
$623$	5.74306e12	1.52738
$624$	1.22297e12	0.322913
$625$	−3.22011e12	−0.844132
$626$	−2.86079e12	−0.744562
$627$	−1.14519e12	−0.295918
$628$	−1.44206e12	−0.369969
$629$	−3.37360e12	−0.859341
$630$	1.02944e12	0.260357
$631$	3.67737e12	0.923432	0.461716	−	0.887028i	$-0.347234\pi$
$631$	3.67737e12	0.923432	0.461716	+	0.887028i	$0.347234\pi$
$632$	−1.45402e11	−0.0362530
$633$	2.69861e12	0.668071
$634$	−1.38168e12	−0.339629
$635$	1.26901e12	0.309731
$636$	−2.32439e12	−0.563316
$637$	6.00615e11	0.144534
$638$	6.87515e12	1.64282
$639$	2.88994e12	0.685701
$640$	−3.48490e11	−0.0821071
$641$	−2.04258e12	−0.477880	−0.238940	−	0.971034i	$-0.576800\pi$
$641$	−2.04258e12	−0.477880	−0.238940	+	0.971034i	$0.576800\pi$
$642$	2.38586e12	0.554291
$643$	4.85726e12	1.12058	0.560289	−	0.828297i	$-0.310690\pi$
$643$	4.85726e12	1.12058	0.560289	+	0.828297i	$0.310690\pi$
$644$	1.71843e12	0.393682
$645$	−9.27933e11	−0.211105
$646$	3.19668e11	0.0722191
$647$	6.29988e12	1.41339	0.706696	−	0.707517i	$-0.250185\pi$
$647$	6.29988e12	1.41339	0.706696	+	0.707517i	$0.250185\pi$
$648$	−7.54772e11	−0.168162
$649$	1.32118e12	0.292322
$650$	−7.23611e11	−0.158999
$651$	−2.64225e12	−0.576581
$652$	7.61722e11	0.165075
$653$	9.03282e11	0.194408	0.0972039	−	0.995264i	$-0.469010\pi$
$653$	9.03282e11	0.194408	0.0972039	+	0.995264i	$0.469010\pi$
$654$	3.03718e12	0.649188
$655$	1.32093e12	0.280411
$656$	−1.84431e12	−0.388837
$657$	1.08541e12	0.227274
$658$	−4.96891e12	−1.03334
$659$	−6.61267e12	−1.36582	−0.682908	−	0.730504i	$-0.739285\pi$
$659$	−6.61267e12	−1.36582	−0.682908	+	0.730504i	$0.739285\pi$
$660$	−2.92047e12	−0.599107
$661$	−7.10171e12	−1.44696	−0.723480	−	0.690346i	$-0.757459\pi$
$661$	−7.10171e12	−1.44696	−0.723480	+	0.690346i	$0.757459\pi$
$662$	2.64151e12	0.534553
$663$	−2.86089e12	−0.575029
$664$	1.29399e12	0.258330
$665$	1.12110e12	0.222303
$666$	−2.63331e12	−0.518642
$667$	5.47222e12	1.07053
$668$	2.76965e12	0.538184
$669$	4.38727e11	0.0846792
$670$	1.99758e12	0.382973
$671$	2.85974e12	0.544597
$672$	7.67584e11	0.145199
$673$	3.09509e12	0.581575	0.290787	−	0.956788i	$-0.406083\pi$
$673$	3.09509e12	0.581575	0.290787	+	0.956788i	$0.406083\pi$
$674$	4.22917e12	0.789380
$675$	8.03359e11	0.148951
$676$	4.59019e12	0.845415
$677$	8.23916e11	0.150742	0.0753710	−	0.997156i	$-0.475986\pi$
$677$	8.23916e11	0.150742	0.0753710	+	0.997156i	$0.475986\pi$
$678$	−3.19100e12	−0.579953
$679$	4.06932e12	0.734696
$680$	8.15220e11	0.146213
$681$	−7.29626e11	−0.129999
$682$	−4.59390e12	−0.813115
$683$	7.75339e12	1.36332	0.681661	−	0.731668i	$-0.261258\pi$
$683$	7.75339e12	1.36332	0.681661	+	0.731668i	$0.261258\pi$
$684$	2.49521e11	0.0435868
$685$	1.25846e10	0.00218390
$686$	−3.90142e12	−0.672611
$687$	−5.95767e12	−1.02040
$688$	4.24031e11	0.0721522
$689$	−1.38838e13	−2.34705
$690$	−2.32452e12	−0.390403
$691$	5.91265e12	0.986578	0.493289	−	0.869866i	$-0.335795\pi$
$691$	5.91265e12	0.986578	0.493289	+	0.869866i	$0.335795\pi$
$692$	−3.20288e12	−0.530961
$693$	−3.94224e12	−0.649297
$694$	−4.59307e12	−0.751597
$695$	2.66667e12	0.433549
$696$	2.44432e12	0.394835
$697$	4.31439e12	0.692423
$698$	6.64313e12	1.05931
$699$	3.79824e11	0.0601776
$700$	−4.54166e11	−0.0714946
$701$	−2.98584e12	−0.467019	−0.233510	−	0.972354i	$-0.575021\pi$
$701$	−2.98584e12	−0.467019	−0.233510	+	0.972354i	$0.575021\pi$
$702$	−8.11000e12	−1.26039
$703$	−2.86777e12	−0.442838
$704$	1.33454e12	0.204765
$705$	6.72145e12	1.02474
$706$	−5.08080e12	−0.769681
$707$	−1.01877e13	−1.53351
$708$	4.69720e11	0.0702569
$709$	1.29603e13	1.92623	0.963115	−	0.269091i	$-0.0867232\pi$
$709$	1.29603e13	1.92623	0.963115	+	0.269091i	$0.0867232\pi$
$710$	8.02615e12	1.18534
$711$	2.65499e11	0.0389628
$712$	3.54998e12	0.517685
$713$	−3.65648e12	−0.529859
$714$	−1.79560e12	−0.258564
$715$	−1.74442e13	−2.49617
$716$	2.41951e12	0.344049
$717$	−6.07030e12	−0.857777
$718$	3.97126e11	0.0557659
$719$	−8.09058e12	−1.12902	−0.564508	−	0.825428i	$-0.690934\pi$
$719$	−8.09058e12	−1.12902	−0.564508	+	0.825428i	$0.690934\pi$
$720$	6.36332e11	0.0882444
$721$	−1.09808e13	−1.51330
$722$	2.71737e11	0.0372161
$723$	2.82606e12	0.384644
$724$	3.66658e12	0.495949
$725$	−1.44626e12	−0.194413
$726$	7.01617e12	0.937314
$727$	5.91888e12	0.785841	0.392921	−	0.919572i	$-0.371465\pi$
$727$	5.91888e12	0.785841	0.392921	+	0.919572i	$0.371465\pi$
$728$	4.58486e12	0.604971
$729$	7.90276e12	1.03635
$730$	3.01448e12	0.392880
$731$	−9.91931e11	−0.128485
$732$	1.01672e12	0.130889
$733$	−1.20822e13	−1.54589	−0.772947	−	0.634470i	$-0.781218\pi$
$733$	−1.20822e13	−1.54589	−0.772947	+	0.634470i	$0.781218\pi$
$734$	7.29146e12	0.927218
$735$	−5.09926e11	−0.0644487
$736$	1.06222e12	0.133433
$737$	−7.64974e12	−0.955087
$738$	3.36766e12	0.417902
$739$	8.74611e12	1.07874	0.539368	−	0.842070i	$-0.318663\pi$
$739$	8.74611e12	1.07874	0.539368	+	0.842070i	$0.318663\pi$
$740$	−7.31342e12	−0.896556
$741$	−2.43193e12	−0.296326
$742$	−8.71402e12	−1.05536
$743$	1.16414e13	1.40138	0.700690	−	0.713466i	$-0.252876\pi$
$743$	1.16414e13	1.40138	0.700690	+	0.713466i	$0.252876\pi$
$744$	−1.63327e12	−0.195424
$745$	8.01340e12	0.953046
$746$	−5.07376e12	−0.599798
$747$	−2.36278e12	−0.277639
$748$	−3.12189e12	−0.364636
$749$	8.94447e12	1.03845
$750$	5.09612e12	0.588117
$751$	−1.39046e13	−1.59506	−0.797530	−	0.603279i	$-0.793861\pi$
$751$	−1.39046e13	−1.59506	−0.797530	+	0.603279i	$0.793861\pi$
$752$	−3.07145e12	−0.350238
$753$	5.80393e12	0.657877
$754$	1.46001e13	1.64508
$755$	−5.56758e12	−0.623598
$756$	−5.09014e12	−0.566738
$757$	−1.21283e13	−1.34236	−0.671180	−	0.741295i	$-0.734212\pi$
$757$	−1.21283e13	−1.34236	−0.671180	+	0.741295i	$0.734212\pi$
$758$	5.79362e12	0.637439
$759$	8.90176e12	0.973616
$760$	6.92987e11	0.0753467
$761$	−3.46651e12	−0.374681	−0.187341	−	0.982295i	$-0.559987\pi$
$761$	−3.46651e12	−0.374681	−0.187341	+	0.982295i	$0.559987\pi$
$762$	−1.72776e12	−0.185646
$763$	1.13862e13	1.21624
$764$	−4.97560e12	−0.528354
$765$	−1.48856e12	−0.157142
$766$	−1.28520e13	−1.34878
$767$	2.80568e12	0.292725
$768$	4.74469e11	0.0492133
$769$	−1.40080e13	−1.44447	−0.722235	−	0.691648i	$-0.756885\pi$
$769$	−1.40080e13	−1.44447	−0.722235	+	0.691648i	$0.756885\pi$
$770$	−1.09487e13	−1.12241
$771$	−7.67455e12	−0.782183
$772$	−2.89208e10	−0.00293044
$773$	4.05950e12	0.408945	0.204472	−	0.978872i	$-0.434452\pi$
$773$	4.05950e12	0.408945	0.204472	+	0.978872i	$0.434452\pi$
$774$	−7.74266e11	−0.0775453
$775$	9.66375e11	0.0962250
$776$	2.51538e12	0.249015
$777$	1.61085e13	1.58548
$778$	1.27753e13	1.25015
$779$	3.66749e12	0.356821
$780$	−6.20194e12	−0.599932
$781$	−3.07361e13	−2.95610
$782$	−2.48484e12	−0.237612
$783$	−1.62092e13	−1.54111
$784$	2.33017e11	0.0220275
$785$	7.31298e12	0.687355
$786$	−1.79845e12	−0.168073
$787$	−6.06738e11	−0.0563787	−0.0281893	−	0.999603i	$-0.508974\pi$
$787$	−6.06738e11	−0.0563787	−0.0281893	+	0.999603i	$0.508974\pi$
$788$	−1.09502e12	−0.101171
$789$	−1.38693e13	−1.27411
$790$	7.37363e11	0.0673534
$791$	−1.19629e13	−1.08653
$792$	−2.43683e12	−0.220071
$793$	6.07299e12	0.545347
$794$	1.09155e13	0.974656
$795$	1.17875e13	1.04657
$796$	6.65728e12	0.587744
$797$	1.28883e13	1.13145	0.565723	−	0.824595i	$-0.308597\pi$
$797$	1.28883e13	1.13145	0.565723	+	0.824595i	$0.308597\pi$
$798$	−1.52637e12	−0.133244
$799$	7.18502e12	0.623688
$800$	−2.80735e11	−0.0242321
$801$	−6.48214e12	−0.556381
$802$	9.48261e12	0.809362
$803$	−1.15440e13	−0.979794
$804$	−2.71971e12	−0.229546
$805$	−8.71451e12	−0.731411
$806$	−9.75567e12	−0.814234
$807$	1.03044e13	0.855244
$808$	−6.29733e12	−0.519763
$809$	1.78619e13	1.46609	0.733043	−	0.680182i	$-0.238099\pi$
$809$	1.78619e13	1.46609	0.733043	+	0.680182i	$0.238099\pi$
$810$	3.82760e12	0.312424
$811$	1.19538e13	0.970316	0.485158	−	0.874426i	$-0.338762\pi$
$811$	1.19538e13	0.970316	0.485158	+	0.874426i	$0.338762\pi$
$812$	9.16361e12	0.739715
$813$	2.12918e12	0.170925
$814$	2.80067e13	2.23590
$815$	−3.86285e12	−0.306689
$816$	−1.10992e12	−0.0876368
$817$	−8.43202e11	−0.0662114
$818$	−1.20451e13	−0.940630
$819$	−8.37179e12	−0.650191
$820$	9.35289e12	0.722410
$821$	1.77563e12	0.136398	0.0681990	−	0.997672i	$-0.478275\pi$
$821$	1.77563e12	0.136398	0.0681990	+	0.997672i	$0.478275\pi$
$822$	−1.71340e10	−0.00130899
$823$	2.41865e13	1.83770	0.918848	−	0.394611i	$-0.129121\pi$
$823$	2.41865e13	1.83770	0.918848	+	0.394611i	$0.129121\pi$
$824$	−6.78759e12	−0.512913
$825$	−2.35265e12	−0.176813
$826$	1.76095e12	0.131625
$827$	1.65137e13	1.22764	0.613818	−	0.789447i	$-0.289633\pi$
$827$	1.65137e13	1.22764	0.613818	+	0.789447i	$0.289633\pi$
$828$	−1.93958e12	−0.143407
$829$	−4.23002e12	−0.311062	−0.155531	−	0.987831i	$-0.549709\pi$
$829$	−4.23002e12	−0.311062	−0.155531	+	0.987831i	$0.549709\pi$
$830$	−6.56208e12	−0.479944
$831$	−2.67949e12	−0.194916
$832$	2.83405e12	0.205047
$833$	−5.45095e11	−0.0392256
$834$	−3.63068e12	−0.259860
$835$	−1.40455e13	−0.999878
$836$	−2.65379e12	−0.187905
$837$	1.08308e13	0.762775
$838$	−9.71675e12	−0.680649
$839$	−5.54430e12	−0.386294	−0.193147	−	0.981170i	$-0.561869\pi$
$839$	−5.54430e12	−0.386294	−0.193147	+	0.981170i	$0.561869\pi$
$840$	−3.89257e12	−0.269761
$841$	1.46737e13	1.01148
$842$	1.11667e13	0.765633
$843$	1.66666e12	0.113664
$844$	6.25362e12	0.424219
$845$	−2.32778e13	−1.57067
$846$	5.60837e12	0.376417
$847$	2.63032e13	1.75604
$848$	−5.38643e12	−0.357700
$849$	−2.11917e12	−0.139985
$850$	6.56721e11	0.0431515
$851$	2.22917e13	1.45700
$852$	−1.09276e13	−0.710471
$853$	3.02800e13	1.95833	0.979164	−	0.203070i	$-0.0650918\pi$
$853$	3.02800e13	1.95833	0.979164	+	0.203070i	$0.0650918\pi$
$854$	3.81164e12	0.245217
$855$	−1.26537e12	−0.0809786
$856$	5.52888e12	0.351970
$857$	−2.95108e12	−0.186882	−0.0934408	−	0.995625i	$-0.529787\pi$
$857$	−2.95108e12	−0.186882	−0.0934408	+	0.995625i	$0.529787\pi$
$858$	2.37503e13	1.49616
$859$	2.96662e13	1.85906	0.929529	−	0.368748i	$-0.120214\pi$
$859$	2.96662e13	1.85906	0.929529	+	0.368748i	$0.120214\pi$
$860$	−2.15035e12	−0.134050
$861$	−2.06007e13	−1.27752
$862$	−8.94192e12	−0.551630
$863$	−1.79928e13	−1.10421	−0.552103	−	0.833776i	$-0.686175\pi$
$863$	−1.79928e13	−1.10421	−0.552103	+	0.833776i	$0.686175\pi$
$864$	−3.14639e12	−0.192088
$865$	1.62424e13	0.986459
$866$	9.53039e11	0.0575811
$867$	−1.05041e13	−0.631353
$868$	−6.12303e12	−0.366123
$869$	−2.82373e12	−0.167971
$870$	−1.23956e13	−0.733553
$871$	−1.62451e13	−0.956402
$872$	7.03820e12	0.412228
$873$	−4.59300e12	−0.267629
$874$	−2.11227e12	−0.122447
$875$	1.91051e13	1.10182
$876$	−4.10421e12	−0.235484
$877$	2.28542e12	0.130457	0.0652286	−	0.997870i	$-0.479222\pi$
$877$	2.28542e12	0.130457	0.0652286	+	0.997870i	$0.479222\pi$
$878$	−1.74109e13	−0.988773
$879$	−1.23387e13	−0.697140
$880$	−6.76774e12	−0.380427
$881$	−6.70706e12	−0.375094	−0.187547	−	0.982256i	$-0.560054\pi$
$881$	−6.70706e12	−0.375094	−0.187547	+	0.982256i	$0.560054\pi$
$882$	−4.25482e11	−0.0236740
$883$	2.88774e13	1.59858	0.799292	−	0.600942i	$-0.205208\pi$
$883$	2.88774e13	1.59858	0.799292	+	0.600942i	$0.205208\pi$
$884$	−6.62968e12	−0.365138
$885$	−2.38204e12	−0.130528
$886$	−4.04922e12	−0.220760
$887$	1.52010e13	0.824547	0.412273	−	0.911060i	$-0.364735\pi$
$887$	1.52010e13	0.824547	0.412273	+	0.911060i	$0.364735\pi$
$888$	9.95721e12	0.537377
$889$	−6.47729e12	−0.347805
$890$	−1.80027e13	−0.961793
$891$	−1.46578e13	−0.779146
$892$	1.01668e12	0.0537705
$893$	6.10771e12	0.321400
$894$	−1.09102e13	−0.571236
$895$	−1.22698e13	−0.639198
$896$	1.77876e12	0.0922001
$897$	1.89039e13	0.974956
$898$	−7.45591e12	−0.382611
$899$	−1.94983e13	−0.995587
$900$	5.12613e11	0.0260434
$901$	1.26004e13	0.636977
$902$	−3.58169e13	−1.80160
$903$	4.73635e12	0.237055
$904$	−7.39466e12	−0.368265
$905$	−1.85939e13	−0.921410
$906$	7.58025e12	0.373772
$907$	−1.79548e13	−0.880943	−0.440472	−	0.897766i	$-0.645189\pi$
$907$	−1.79548e13	−0.880943	−0.440472	+	0.897766i	$0.645189\pi$
$908$	−1.69080e12	−0.0825479
$909$	1.14987e13	0.558614
$910$	−2.32507e13	−1.12396
$911$	1.67238e13	0.804455	0.402228	−	0.915540i	$-0.368236\pi$
$911$	1.67238e13	0.804455	0.402228	+	0.915540i	$0.368236\pi$
$912$	−9.43502e11	−0.0451612
$913$	2.51295e13	1.19692
$914$	2.49857e13	1.18422
$915$	−5.15600e12	−0.243175
$916$	−1.38060e13	−0.647945
$917$	−6.74230e12	−0.314881
$918$	7.36032e12	0.342062
$919$	−1.78585e13	−0.825896	−0.412948	−	0.910755i	$-0.635501\pi$
$919$	−1.78585e13	−0.825896	−0.412948	+	0.910755i	$0.635501\pi$
$920$	−5.38673e12	−0.247902
$921$	−2.06031e13	−0.943551
$922$	−1.10655e13	−0.504292
$923$	−6.52716e13	−2.96017
$924$	1.49066e13	0.672752
$925$	−5.89151e12	−0.264599
$926$	8.40943e12	0.375852
$927$	1.23939e13	0.551251
$928$	5.66434e12	0.250717
$929$	−1.20609e13	−0.531260	−0.265630	−	0.964075i	$-0.585580\pi$
$929$	−1.20609e13	−0.531260	−0.265630	+	0.964075i	$0.585580\pi$
$930$	8.28262e12	0.363074
$931$	−4.63364e11	−0.0202139
$932$	8.80185e11	0.0382122
$933$	−4.22594e12	−0.182581
$934$	1.51340e13	0.650718
$935$	1.58317e13	0.677448
$936$	−5.17489e12	−0.220374
$937$	−1.10432e13	−0.468021	−0.234011	−	0.972234i	$-0.575185\pi$
$937$	−1.10432e13	−0.468021	−0.234011	+	0.972234i	$0.575185\pi$
$938$	−1.01960e13	−0.430050
$939$	−1.97521e13	−0.829122
$940$	1.55759e13	0.650698
$941$	−6.63330e12	−0.275789	−0.137894	−	0.990447i	$-0.544033\pi$
$941$	−6.63330e12	−0.275789	−0.137894	+	0.990447i	$0.544033\pi$
$942$	−9.95662e12	−0.411986
$943$	−2.85082e13	−1.17400
$944$	1.08850e12	0.0446125
$945$	2.58132e13	1.05293
$946$	8.23475e12	0.334303
$947$	−1.84983e13	−0.747408	−0.373704	−	0.927548i	$-0.621912\pi$
$947$	−1.84983e13	−0.747408	−0.373704	+	0.927548i	$0.621912\pi$
$948$	−1.00392e12	−0.0403702
$949$	−2.45149e13	−0.981142
$950$	5.58253e11	0.0222369
$951$	−9.53971e12	−0.378201
$952$	−4.16104e12	−0.164186
$953$	1.01857e13	0.400012	0.200006	−	0.979795i	$-0.435904\pi$
$953$	1.01857e13	0.400012	0.200006	+	0.979795i	$0.435904\pi$
$954$	9.83543e12	0.384438
$955$	2.52323e13	0.981614
$956$	−1.40670e13	−0.544680
$957$	4.74690e13	1.82939
$958$	9.27022e12	0.355587
$959$	−6.42343e10	−0.00245236
$960$	−2.40613e12	−0.0914321
$961$	−1.34110e13	−0.507232
$962$	5.94755e13	2.23898
$963$	−1.00955e13	−0.378278
$964$	6.54898e12	0.244246
$965$	1.46663e11	0.00544438
$966$	1.18648e13	0.438393
$967$	1.52208e13	0.559782	0.279891	−	0.960032i	$-0.409702\pi$
$967$	1.52208e13	0.559782	0.279891	+	0.960032i	$0.409702\pi$
$968$	1.62589e13	0.595186
$969$	2.20712e12	0.0804211
$970$	−1.27560e13	−0.462639
$971$	2.88262e13	1.04064	0.520320	−	0.853972i	$-0.325813\pi$
$971$	2.88262e13	1.04064	0.520320	+	0.853972i	$0.325813\pi$
$972$	9.90845e12	0.356047
$973$	−1.36112e13	−0.486843
$974$	−1.10707e13	−0.394147
$975$	−4.99613e12	−0.177057
$976$	2.35610e12	0.0831131
$977$	3.08944e13	1.08481	0.542405	−	0.840117i	$-0.317514\pi$
$977$	3.08944e13	1.08481	0.542405	+	0.840117i	$0.317514\pi$
$978$	5.25926e12	0.183823
$979$	6.89412e13	2.39859
$980$	−1.18168e12	−0.0409243
$981$	−1.28515e13	−0.443041
$982$	−2.02811e13	−0.695969
$983$	−2.62760e13	−0.897571	−0.448786	−	0.893639i	$-0.648143\pi$
$983$	−2.62760e13	−0.897571	−0.448786	+	0.893639i	$0.648143\pi$
$984$	−1.27340e13	−0.432997
$985$	5.55307e12	0.187962
$986$	−1.32505e13	−0.446465
$987$	−3.43075e13	−1.15070
$988$	−5.63563e12	−0.188164
$989$	6.55438e12	0.217846
$990$	1.23577e13	0.408863
$991$	−2.46450e13	−0.811703	−0.405852	−	0.913939i	$-0.633025\pi$
$991$	−2.46450e13	−0.811703	−0.405852	+	0.913939i	$0.633025\pi$
$992$	−3.78485e12	−0.124093
$993$	1.82381e13	0.595262
$994$	−4.09670e13	−1.33105
$995$	−3.37604e13	−1.09195
$996$	8.93427e12	0.287668
$997$	−1.55367e13	−0.498000	−0.249000	−	0.968503i	$-0.580102\pi$
$997$	−1.55367e13	−0.498000	−0.249000	+	0.968503i	$0.580102\pi$
$998$	1.51812e13	0.484415
$999$	−6.60301e13	−2.09748

Twists

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

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

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +110.471 q^{3} +256.000 q^{4} -1298.23 q^{5} +1767.54 q^{6} +6626.40 q^{7} +4096.00 q^{8} -7479.16 q^{9} +O(q^{10})\)	\(q+16.0000 q^{2} +110.471 q^{3} +256.000 q^{4} -1298.23 q^{5} +1767.54 q^{6} +6626.40 q^{7} +4096.00 q^{8} -7479.16 q^{9} -20771.6 q^{10} +79545.0 q^{11} +28280.6 q^{12} +168923. q^{13} +106022. q^{14} -143417. q^{15} +65536.0 q^{16} -153308. q^{17} -119667. q^{18} -130321. q^{19} -332346. q^{20} +732025. q^{21} +1.27272e6 q^{22} +1.01301e6 q^{23} +452489. q^{24} -267730. q^{25} +2.70276e6 q^{26} -3.00063e6 q^{27} +1.69636e6 q^{28} +5.40193e6 q^{29} -2.29466e6 q^{30} -3.60951e6 q^{31} +1.04858e6 q^{32} +8.78742e6 q^{33} -2.45292e6 q^{34} -8.60258e6 q^{35} -1.91466e6 q^{36} +2.20054e7 q^{37} -2.08514e6 q^{38} +1.86611e7 q^{39} -5.31754e6 q^{40} -2.81420e7 q^{41} +1.17124e7 q^{42} +6.47020e6 q^{43} +2.03635e7 q^{44} +9.70965e6 q^{45} +1.62082e7 q^{46} -4.68666e7 q^{47} +7.23983e6 q^{48} +3.55556e6 q^{49} -4.28368e6 q^{50} -1.69361e7 q^{51} +4.32442e7 q^{52} -8.21904e7 q^{53} -4.80101e7 q^{54} -1.03268e8 q^{55} +2.71417e7 q^{56} -1.43967e7 q^{57} +8.64309e7 q^{58} +1.66093e7 q^{59} -3.67146e7 q^{60} +3.59512e7 q^{61} -5.77522e7 q^{62} -4.95599e7 q^{63} +1.67772e7 q^{64} -2.19300e8 q^{65} +1.40599e8 q^{66} -9.61687e7 q^{67} -3.92468e7 q^{68} +1.11908e8 q^{69} -1.37641e8 q^{70} -3.86399e8 q^{71} -3.06346e7 q^{72} -1.45125e8 q^{73} +3.52087e8 q^{74} -2.95764e7 q^{75} -3.33622e7 q^{76} +5.27097e8 q^{77} +2.98577e8 q^{78} -3.54985e7 q^{79} -8.50806e7 q^{80} -1.84270e8 q^{81} -4.50272e8 q^{82} +3.15916e8 q^{83} +1.87398e8 q^{84} +1.99028e8 q^{85} +1.03523e8 q^{86} +5.96757e8 q^{87} +3.25816e8 q^{88} +8.66694e8 q^{89} +1.55354e8 q^{90} +1.11935e9 q^{91} +2.59331e8 q^{92} -3.98747e8 q^{93} -7.49866e8 q^{94} +1.69186e8 q^{95} +1.15837e8 q^{96} +6.14107e8 q^{97} +5.68890e7 q^{98} -5.94930e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 64 q^{2} + 226 q^{3} + 1024 q^{4} + 866 q^{5} + 3616 q^{6} + 2670 q^{7} + 16384 q^{8} + 50606 q^{9}+O(q^{10}) \) 4 * q + 64 * q^2 + 226 * q^3 + 1024 * q^4 + 866 * q^5 + 3616 * q^6 + 2670 * q^7 + 16384 * q^8 + 50606 * q^9	\( 4 q + 64 q^{2} + 226 q^{3} + 1024 q^{4} + 866 q^{5} + 3616 q^{6} + 2670 q^{7} + 16384 q^{8} + 50606 q^{9} + 13856 q^{10} + 119234 q^{11} + 57856 q^{12} - 6748 q^{13} + 42720 q^{14} + 355904 q^{15} + 262144 q^{16} + 678624 q^{17} + 809696 q^{18} - 521284 q^{19} + 221696 q^{20} + 1586736 q^{21} + 1907744 q^{22} + 2911868 q^{23} + 925696 q^{24} + 268766 q^{25} - 107968 q^{26} + 2802058 q^{27} + 683520 q^{28} + 8291104 q^{29} + 5694464 q^{30} + 3445468 q^{31} + 4194304 q^{32} - 5321788 q^{33} + 10857984 q^{34} + 7715058 q^{35} + 12955136 q^{36} - 1005524 q^{37} - 8340544 q^{38} + 34055900 q^{39} + 3547136 q^{40} + 8514124 q^{41} + 25387776 q^{42} + 13900726 q^{43} + 30523904 q^{44} - 8962202 q^{45} + 46589888 q^{46} - 36334954 q^{47} + 14811136 q^{48} - 30891808 q^{49} + 4300256 q^{50} - 203869074 q^{51} - 1727488 q^{52} - 113969356 q^{53} + 44832928 q^{54} - 178140098 q^{55} + 10936320 q^{56} - 29452546 q^{57} + 132657664 q^{58} - 396773766 q^{59} + 91111424 q^{60} - 298192066 q^{61} + 55127488 q^{62} - 458723694 q^{63} + 67108864 q^{64} - 291187676 q^{65} - 85148608 q^{66} - 113551722 q^{67} + 173727744 q^{68} - 671519716 q^{69} + 123440928 q^{70} + 4659620 q^{71} + 207282176 q^{72} + 136198452 q^{73} - 16088384 q^{74} + 29308274 q^{75} - 133448704 q^{76} + 120551886 q^{77} + 544894400 q^{78} + 67255424 q^{79} + 56754176 q^{80} + 982241180 q^{81} + 136225984 q^{82} + 1376505216 q^{83} + 406204416 q^{84} + 638402178 q^{85} + 222411616 q^{86} + 630635524 q^{87} + 488382464 q^{88} + 1557211260 q^{89} - 143395232 q^{90} + 1422773730 q^{91} + 745438208 q^{92} + 2036686084 q^{93} - 581359264 q^{94} - 112857986 q^{95} + 236978176 q^{96} + 975818188 q^{97} - 494268928 q^{98} + 502820650 q^{99}+O(q^{100}) \) 4 * q + 64 * q^2 + 226 * q^3 + 1024 * q^4 + 866 * q^5 + 3616 * q^6 + 2670 * q^7 + 16384 * q^8 + 50606 * q^9 + 13856 * q^10 + 119234 * q^11 + 57856 * q^12 - 6748 * q^13 + 42720 * q^14 + 355904 * q^15 + 262144 * q^16 + 678624 * q^17 + 809696 * q^18 - 521284 * q^19 + 221696 * q^20 + 1586736 * q^21 + 1907744 * q^22 + 2911868 * q^23 + 925696 * q^24 + 268766 * q^25 - 107968 * q^26 + 2802058 * q^27 + 683520 * q^28 + 8291104 * q^29 + 5694464 * q^30 + 3445468 * q^31 + 4194304 * q^32 - 5321788 * q^33 + 10857984 * q^34 + 7715058 * q^35 + 12955136 * q^36 - 1005524 * q^37 - 8340544 * q^38 + 34055900 * q^39 + 3547136 * q^40 + 8514124 * q^41 + 25387776 * q^42 + 13900726 * q^43 + 30523904 * q^44 - 8962202 * q^45 + 46589888 * q^46 - 36334954 * q^47 + 14811136 * q^48 - 30891808 * q^49 + 4300256 * q^50 - 203869074 * q^51 - 1727488 * q^52 - 113969356 * q^53 + 44832928 * q^54 - 178140098 * q^55 + 10936320 * q^56 - 29452546 * q^57 + 132657664 * q^58 - 396773766 * q^59 + 91111424 * q^60 - 298192066 * q^61 + 55127488 * q^62 - 458723694 * q^63 + 67108864 * q^64 - 291187676 * q^65 - 85148608 * q^66 - 113551722 * q^67 + 173727744 * q^68 - 671519716 * q^69 + 123440928 * q^70 + 4659620 * q^71 + 207282176 * q^72 + 136198452 * q^73 - 16088384 * q^74 + 29308274 * q^75 - 133448704 * q^76 + 120551886 * q^77 + 544894400 * q^78 + 67255424 * q^79 + 56754176 * q^80 + 982241180 * q^81 + 136225984 * q^82 + 1376505216 * q^83 + 406204416 * q^84 + 638402178 * q^85 + 222411616 * q^86 + 630635524 * q^87 + 488382464 * q^88 + 1557211260 * q^89 - 143395232 * q^90 + 1422773730 * q^91 + 745438208 * q^92 + 2036686084 * q^93 - 581359264 * q^94 - 112857986 * q^95 + 236978176 * q^96 + 975818188 * q^97 - 494268928 * q^98 + 502820650 * q^99

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