LMFDB - Embedded newform 31.6.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [31,6,Mod(1,31)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(31, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("31.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	31.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:	$4.97189841420$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 199x^{6} + 256x^{5} + 12633x^{4} - 18583x^{3} - 260319x^{2} + 410640x + 275908 $ x^8 - x^7 - 199x^6 + 256x^5 + 12633x^4 - 18583x^3 - 260319x^2 + 410640x + 275908
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 5\cdot 13 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$6.36806$ of defining polynomial
Character	$\chi$	$=$	31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.36806 q^{2} -5.61682 q^{3} -3.18388 q^{4} -13.6922 q^{5} +30.1515 q^{6} +106.967 q^{7} +188.869 q^{8} -211.451 q^{9} +O(q^{10})$	\(q-5.36806 q^{2} -5.61682 q^{3} -3.18388 q^{4} -13.6922 q^{5} +30.1515 q^{6} +106.967 q^{7} +188.869 q^{8} -211.451 q^{9} +73.5006 q^{10} +743.452 q^{11} +17.8833 q^{12} +926.545 q^{13} -574.208 q^{14} +76.9066 q^{15} -911.979 q^{16} -1128.14 q^{17} +1135.08 q^{18} -897.048 q^{19} +43.5943 q^{20} -600.818 q^{21} -3990.90 q^{22} +3315.35 q^{23} -1060.85 q^{24} -2937.52 q^{25} -4973.75 q^{26} +2552.57 q^{27} -340.572 q^{28} +8131.04 q^{29} -412.840 q^{30} +961.000 q^{31} -1148.26 q^{32} -4175.84 q^{33} +6055.93 q^{34} -1464.62 q^{35} +673.236 q^{36} +8527.14 q^{37} +4815.41 q^{38} -5204.24 q^{39} -2586.04 q^{40} +13977.7 q^{41} +3225.23 q^{42} -4877.82 q^{43} -2367.06 q^{44} +2895.23 q^{45} -17797.0 q^{46} -9848.26 q^{47} +5122.42 q^{48} -5364.96 q^{49} +15768.8 q^{50} +6336.56 q^{51} -2950.01 q^{52} +17757.5 q^{53} -13702.4 q^{54} -10179.5 q^{55} +20202.9 q^{56} +5038.56 q^{57} -43647.9 q^{58} +15495.6 q^{59} -244.862 q^{60} -17892.5 q^{61} -5158.71 q^{62} -22618.4 q^{63} +35347.2 q^{64} -12686.4 q^{65} +22416.2 q^{66} -20521.8 q^{67} +3591.86 q^{68} -18621.7 q^{69} +7862.17 q^{70} -2852.46 q^{71} -39936.7 q^{72} -50774.9 q^{73} -45774.2 q^{74} +16499.6 q^{75} +2856.09 q^{76} +79525.2 q^{77} +27936.7 q^{78} +34528.9 q^{79} +12487.0 q^{80} +37045.3 q^{81} -75033.1 q^{82} -40511.1 q^{83} +1912.93 q^{84} +15446.7 q^{85} +26184.5 q^{86} -45670.6 q^{87} +140415. q^{88} +118948. q^{89} -15541.8 q^{90} +99110.2 q^{91} -10555.7 q^{92} -5397.77 q^{93} +52866.1 q^{94} +12282.6 q^{95} +6449.57 q^{96} -102155. q^{97} +28799.4 q^{98} -157204. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 7 q^{2} - 2 q^{3} + 149 q^{4} + 128 q^{5} + 72 q^{6} + 88 q^{7} + 924 q^{8} + 1512 q^{9}+O(q^{10}) $ 8 * q + 7 * q^2 - 2 * q^3 + 149 * q^4 + 128 * q^5 + 72 * q^6 + 88 * q^7 + 924 * q^8 + 1512 * q^9	\( 8 q + 7 q^{2} - 2 q^{3} + 149 q^{4} + 128 q^{5} + 72 q^{6} + 88 q^{7} + 924 q^{8} + 1512 q^{9} + 1581 q^{10} + 574 q^{11} - 46 q^{12} - 122 q^{13} - 309 q^{14} - 524 q^{15} + 833 q^{16} + 1932 q^{17} - 6845 q^{18} - 1796 q^{19} - 37 q^{20} + 996 q^{21} - 9000 q^{22} - 4136 q^{23} - 17468 q^{24} + 3308 q^{25} + 1524 q^{26} - 2624 q^{27} - 21245 q^{28} + 5050 q^{29} - 30450 q^{30} + 7688 q^{31} + 21045 q^{32} + 27920 q^{33} - 24738 q^{34} + 25700 q^{35} + 21637 q^{36} + 23674 q^{37} - 4289 q^{38} + 38652 q^{39} + 36606 q^{40} + 44828 q^{41} - 9994 q^{42} + 21058 q^{43} + 13168 q^{44} - 1344 q^{45} + 6198 q^{46} + 5348 q^{47} - 69588 q^{48} + 19356 q^{49} + 33242 q^{50} + 22300 q^{51} - 60386 q^{52} + 4926 q^{53} - 24476 q^{54} - 56892 q^{55} - 87652 q^{56} + 22072 q^{57} - 25002 q^{58} + 16944 q^{59} - 138556 q^{60} - 73682 q^{61} + 6727 q^{62} - 138784 q^{63} - 1300 q^{64} + 63316 q^{65} - 128796 q^{66} - 134768 q^{67} - 9524 q^{68} + 3992 q^{69} - 142737 q^{70} + 123724 q^{71} + 93232 q^{72} + 70792 q^{73} + 307468 q^{74} - 302902 q^{75} - 65405 q^{76} + 107932 q^{77} + 36820 q^{78} - 26036 q^{79} + 576783 q^{80} + 82528 q^{81} + 142335 q^{82} + 21882 q^{83} + 299144 q^{84} - 130464 q^{85} + 480478 q^{86} - 440244 q^{87} - 71982 q^{88} + 164392 q^{89} + 397969 q^{90} - 60028 q^{91} + 31012 q^{92} - 1922 q^{93} - 170388 q^{94} - 7404 q^{95} - 331010 q^{96} - 131948 q^{97} + 288768 q^{98} - 180150 q^{99}+O(q^{100}) \) 8 * q + 7 * q^2 - 2 * q^3 + 149 * q^4 + 128 * q^5 + 72 * q^6 + 88 * q^7 + 924 * q^8 + 1512 * q^9 + 1581 * q^10 + 574 * q^11 - 46 * q^12 - 122 * q^13 - 309 * q^14 - 524 * q^15 + 833 * q^16 + 1932 * q^17 - 6845 * q^18 - 1796 * q^19 - 37 * q^20 + 996 * q^21 - 9000 * q^22 - 4136 * q^23 - 17468 * q^24 + 3308 * q^25 + 1524 * q^26 - 2624 * q^27 - 21245 * q^28 + 5050 * q^29 - 30450 * q^30 + 7688 * q^31 + 21045 * q^32 + 27920 * q^33 - 24738 * q^34 + 25700 * q^35 + 21637 * q^36 + 23674 * q^37 - 4289 * q^38 + 38652 * q^39 + 36606 * q^40 + 44828 * q^41 - 9994 * q^42 + 21058 * q^43 + 13168 * q^44 - 1344 * q^45 + 6198 * q^46 + 5348 * q^47 - 69588 * q^48 + 19356 * q^49 + 33242 * q^50 + 22300 * q^51 - 60386 * q^52 + 4926 * q^53 - 24476 * q^54 - 56892 * q^55 - 87652 * q^56 + 22072 * q^57 - 25002 * q^58 + 16944 * q^59 - 138556 * q^60 - 73682 * q^61 + 6727 * q^62 - 138784 * q^63 - 1300 * q^64 + 63316 * q^65 - 128796 * q^66 - 134768 * q^67 - 9524 * q^68 + 3992 * q^69 - 142737 * q^70 + 123724 * q^71 + 93232 * q^72 + 70792 * q^73 + 307468 * q^74 - 302902 * q^75 - 65405 * q^76 + 107932 * q^77 + 36820 * q^78 - 26036 * q^79 + 576783 * q^80 + 82528 * q^81 + 142335 * q^82 + 21882 * q^83 + 299144 * q^84 - 130464 * q^85 + 480478 * q^86 - 440244 * q^87 - 71982 * q^88 + 164392 * q^89 + 397969 * q^90 - 60028 * q^91 + 31012 * q^92 - 1922 * q^93 - 170388 * q^94 - 7404 * q^95 - 331010 * q^96 - 131948 * q^97 + 288768 * q^98 - 180150 * 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 $

$2$	−5.36806	−0.948949	−0.474474	−	0.880269i	$-0.657362\pi$
$2$	−5.36806	−0.948949	−0.474474	+	0.880269i	$0.657362\pi$
$3$	−5.61682	−0.360319	−0.180160	−	0.983637i	$-0.557661\pi$
$3$	−5.61682	−0.360319	−0.180160	+	0.983637i	$0.557661\pi$
$4$	−3.18388	−0.0994963
$5$	−13.6922	−0.244933	−0.122467	−	0.992473i	$-0.539080\pi$
$5$	−13.6922	−0.244933	−0.122467	+	0.992473i	$0.539080\pi$
$6$	30.1515	0.341925
$7$	106.967	0.825100	0.412550	−	0.910935i	$-0.364638\pi$
$7$	106.967	0.825100	0.412550	+	0.910935i	$0.364638\pi$
$8$	188.869	1.04337
$9$	−211.451	−0.870170
$10$	73.5006	0.232429
$11$	743.452	1.85255	0.926277	−	0.376842i	$-0.122990\pi$
$11$	743.452	1.85255	0.926277	+	0.376842i	$0.122990\pi$
$12$	17.8833	0.0358505
$13$	926.545	1.52058	0.760288	−	0.649586i	$-0.225058\pi$
$13$	926.545	1.52058	0.760288	+	0.649586i	$0.225058\pi$
$14$	−574.208	−0.782978
$15$	76.9066	0.0882543
$16$	−911.979	−0.890604
$17$	−1128.14	−0.946762	−0.473381	−	0.880858i	$-0.656967\pi$
$17$	−1128.14	−0.946762	−0.473381	+	0.880858i	$0.656967\pi$
$18$	1135.08	0.825747
$19$	−897.048	−0.570075	−0.285037	−	0.958516i	$-0.592006\pi$
$19$	−897.048	−0.570075	−0.285037	+	0.958516i	$0.592006\pi$
$20$	43.5943	0.0243700
$21$	−600.818	−0.297300
$22$	−3990.90	−1.75798
$23$	3315.35	1.30680	0.653401	−	0.757012i	$-0.273342\pi$
$23$	3315.35	1.30680	0.653401	+	0.757012i	$0.273342\pi$
$24$	−1060.85	−0.375945
$25$	−2937.52	−0.940008
$26$	−4973.75	−1.44295
$27$	2552.57	0.673859
$28$	−340.572	−0.0820944
$29$	8131.04	1.79536	0.897679	−	0.440650i	$-0.145252\pi$
$29$	8131.04	1.79536	0.897679	+	0.440650i	$0.145252\pi$
$30$	−412.840	−0.0837488
$31$	961.000	0.179605
$31$	961.000	0.179605
$32$	−1148.26	−0.198228
$33$	−4175.84	−0.667512
$34$	6055.93	0.898428
$35$	−1464.62	−0.202095
$36$	673.236	0.0865787
$37$	8527.14	1.02400	0.511999	−	0.858986i	$-0.328905\pi$
$37$	8527.14	1.02400	0.511999	+	0.858986i	$0.328905\pi$
$38$	4815.41	0.540971
$39$	−5204.24	−0.547893
$40$	−2586.04	−0.255555
$41$	13977.7	1.29860	0.649300	−	0.760532i	$-0.275062\pi$
$41$	13977.7	1.29860	0.649300	+	0.760532i	$0.275062\pi$
$42$	3225.23	0.282122
$43$	−4877.82	−0.402305	−0.201152	−	0.979560i	$-0.564469\pi$
$43$	−4877.82	−0.402305	−0.201152	+	0.979560i	$0.564469\pi$
$44$	−2367.06	−0.184322
$45$	2895.23	0.213134
$46$	−17797.0	−1.24009
$47$	−9848.26	−0.650302	−0.325151	−	0.945662i	$-0.605415\pi$
$47$	−9848.26	−0.650302	−0.325151	+	0.945662i	$0.605415\pi$
$48$	5122.42	0.320902
$49$	−5364.96	−0.319210
$50$	15768.8	0.892019
$51$	6336.56	0.341137
$52$	−2950.01	−0.151292
$53$	17757.5	0.868343	0.434171	−	0.900830i	$-0.357041\pi$
$53$	17757.5	0.868343	0.434171	+	0.900830i	$0.357041\pi$
$54$	−13702.4	−0.639457
$55$	−10179.5	−0.453753
$56$	20202.9	0.860881
$57$	5038.56	0.205409
$58$	−43647.9	−1.70370
$59$	15495.6	0.579533	0.289767	−	0.957097i	$-0.406422\pi$
$59$	15495.6	0.579533	0.289767	+	0.957097i	$0.406422\pi$
$60$	−244.862	−0.00878097
$61$	−17892.5	−0.615669	−0.307834	−	0.951440i	$-0.599604\pi$
$61$	−17892.5	−0.615669	−0.307834	+	0.951440i	$0.599604\pi$
$62$	−5158.71	−0.170436
$63$	−22618.4	−0.717977
$64$	35347.2	1.07871
$65$	−12686.4	−0.372440
$66$	22416.2	0.633434
$67$	−20521.8	−0.558508	−0.279254	−	0.960217i	$-0.590087\pi$
$67$	−20521.8	−0.558508	−0.279254	+	0.960217i	$0.590087\pi$
$68$	3591.86	0.0941993
$69$	−18621.7	−0.470866
$70$	7862.17	0.191777
$71$	−2852.46	−0.0671543	−0.0335772	−	0.999436i	$-0.510690\pi$
$71$	−2852.46	−0.0671543	−0.0335772	+	0.999436i	$0.510690\pi$
$72$	−39936.7	−0.907905
$73$	−50774.9	−1.11517	−0.557586	−	0.830119i	$-0.688273\pi$
$73$	−50774.9	−1.11517	−0.557586	+	0.830119i	$0.688273\pi$
$74$	−45774.2	−0.971721
$75$	16499.6	0.338703
$76$	2856.09	0.0567203
$77$	79525.2	1.52854
$78$	27936.7	0.519922
$79$	34528.9	0.622466	0.311233	−	0.950334i	$-0.399258\pi$
$79$	34528.9	0.622466	0.311233	+	0.950334i	$0.399258\pi$
$80$	12487.0	0.218139
$81$	37045.3	0.627365
$82$	−75033.1	−1.23230
$83$	−40511.1	−0.645475	−0.322737	−	0.946489i	$-0.604603\pi$
$83$	−40511.1	−0.645475	−0.322737	+	0.946489i	$0.604603\pi$
$84$	1912.93	0.0295802
$85$	15446.7	0.231893
$86$	26184.5	0.381766
$87$	−45670.6	−0.646902
$88$	140415.	1.93289
$89$	118948.	1.59178	0.795889	−	0.605443i	$-0.207004\pi$
$89$	118948.	1.59178	0.795889	+	0.605443i	$0.207004\pi$
$90$	−15541.8	−0.202253
$91$	99110.2	1.25463
$92$	−10555.7	−0.130022
$93$	−5397.77	−0.0647153
$94$	52866.1	0.617103
$95$	12282.6	0.139630
$96$	6449.57	0.0714254
$97$	−102155.	−1.10238	−0.551188	−	0.834381i	$-0.685825\pi$
$97$	−102155.	−1.10238	−0.551188	+	0.834381i	$0.685825\pi$
$98$	28799.4	0.302914
$99$	−157204.	−1.61204
$100$	9352.73	0.0935273
$101$	43886.2	0.428080	0.214040	−	0.976825i	$-0.431338\pi$
$101$	43886.2	0.428080	0.214040	+	0.976825i	$0.431338\pi$
$102$	−34015.1	−0.323721
$103$	20723.9	0.192477	0.0962385	−	0.995358i	$-0.469319\pi$
$103$	20723.9	0.192477	0.0962385	+	0.995358i	$0.469319\pi$
$104$	174996.	1.58652
$105$	8226.51	0.0728186
$106$	−95323.2	−0.824013
$107$	−214425.	−1.81057	−0.905284	−	0.424806i	$-0.860342\pi$
$107$	−214425.	−1.81057	−0.905284	+	0.424806i	$0.860342\pi$
$108$	−8127.09	−0.0670464
$109$	−112278.	−0.905164	−0.452582	−	0.891723i	$-0.649497\pi$
$109$	−112278.	−0.905164	−0.452582	+	0.891723i	$0.649497\pi$
$110$	54644.1	0.430588
$111$	−47895.4	−0.368966
$112$	−97552.1	−0.734838
$113$	−46368.7	−0.341608	−0.170804	−	0.985305i	$-0.554637\pi$
$113$	−46368.7	−0.341608	−0.170804	+	0.985305i	$0.554637\pi$
$114$	−27047.3	−0.194923
$115$	−45394.4	−0.320079
$116$	−25888.3	−0.178631
$117$	−195919.	−1.32316
$118$	−83181.4	−0.549947
$119$	−120674.	−0.781173
$120$	14525.3	0.0920815
$121$	391670.	2.43196
$122$	96048.2	0.584238
$123$	−78510.2	−0.467911
$124$	−3059.71	−0.0178701
$125$	83009.2	0.475173
$126$	121417.	0.681324
$127$	264196.	1.45350	0.726752	−	0.686899i	$-0.241029\pi$
$127$	264196.	1.45350	0.726752	+	0.686899i	$0.241029\pi$
$128$	−153002.	−0.825415
$129$	27397.9	0.144958
$130$	68101.6	0.353426
$131$	−287688.	−1.46468	−0.732341	−	0.680938i	$-0.761572\pi$
$131$	−287688.	−1.46468	−0.732341	+	0.680938i	$0.761572\pi$
$132$	13295.4	0.0664149
$133$	−95955.0	−0.470369
$134$	110163.	0.529995
$135$	−34950.3	−0.165050
$136$	−213071.	−0.987818
$137$	66239.5	0.301519	0.150760	−	0.988570i	$-0.451828\pi$
$137$	66239.5	0.301519	0.150760	+	0.988570i	$0.451828\pi$
$138$	99962.6	0.446828
$139$	51293.9	0.225180	0.112590	−	0.993642i	$-0.464085\pi$
$139$	51293.9	0.225180	0.112590	+	0.993642i	$0.464085\pi$
$140$	4663.17	0.0201077
$141$	55316.0	0.234316
$142$	15312.2	0.0637260
$143$	688841.	2.81695
$144$	192839.	0.774977
$145$	−111332.	−0.439743
$146$	272563.	1.05824
$147$	30134.0	0.115017
$148$	−27149.4	−0.101884
$149$	−192993.	−0.712159	−0.356079	−	0.934456i	$-0.615887\pi$
$149$	−192993.	−0.712159	−0.356079	+	0.934456i	$0.615887\pi$
$150$	−88570.7	−0.321412
$151$	−63531.5	−0.226750	−0.113375	−	0.993552i	$-0.536166\pi$
$151$	−63531.5	−0.226750	−0.113375	+	0.993552i	$0.536166\pi$
$152$	−169425.	−0.594796
$153$	238547.	0.823843
$154$	−426896.	−1.45051
$155$	−13158.2	−0.0439913
$156$	16569.7	0.0545133
$157$	159785.	0.517353	0.258677	−	0.965964i	$-0.416714\pi$
$157$	159785.	0.517353	0.258677	+	0.965964i	$0.416714\pi$
$158$	−185354.	−0.590688
$159$	−99740.5	−0.312881
$160$	15722.2	0.0485526
$161$	354634.	1.07824
$162$	−198862.	−0.595338
$163$	−30463.2	−0.0898064	−0.0449032	−	0.998991i	$-0.514298\pi$
$163$	−30463.2	−0.0898064	−0.0449032	+	0.998991i	$0.514298\pi$
$164$	−44503.3	−0.129206
$165$	57176.4	0.163496
$166$	217466.	0.612523
$167$	−621093.	−1.72332	−0.861659	−	0.507488i	$-0.830574\pi$
$167$	−621093.	−1.72332	−0.861659	+	0.507488i	$0.830574\pi$
$168$	−113476.	−0.310192
$169$	487192.	1.31215
$170$	−82918.9	−0.220055
$171$	189682.	0.496062
$172$	15530.4	0.0400278
$173$	415634.	1.05584	0.527918	−	0.849296i	$-0.322973\pi$
$173$	415634.	1.05584	0.527918	+	0.849296i	$0.322973\pi$
$174$	245163.	0.613877
$175$	−314220.	−0.775600
$176$	−678012.	−1.64989
$177$	−87036.1	−0.208817
$178$	−638521.	−1.51052
$179$	−109841.	−0.256231	−0.128115	−	0.991759i	$-0.540893\pi$
$179$	−109841.	−0.256231	−0.128115	+	0.991759i	$0.540893\pi$
$180$	−9218.07	−0.0212060
$181$	756537.	1.71646	0.858230	−	0.513265i	$-0.171564\pi$
$181$	756537.	1.71646	0.858230	+	0.513265i	$0.171564\pi$
$182$	−532030.	−1.19058
$183$	100499.	0.221837
$184$	626168.	1.36347
$185$	−116755.	−0.250811
$186$	28975.6	0.0614115
$187$	−838718.	−1.75393
$188$	31355.7	0.0647026
$189$	273042.	0.556001
$190$	−65933.5	−0.132502
$191$	−259892.	−0.515477	−0.257739	−	0.966215i	$-0.582977\pi$
$191$	−259892.	−0.515477	−0.257739	+	0.966215i	$0.582977\pi$
$192$	−198539.	−0.388681
$193$	−585324.	−1.13111	−0.565553	−	0.824712i	$-0.691337\pi$
$193$	−585324.	−1.13111	−0.565553	+	0.824712i	$0.691337\pi$
$194$	548374.	1.04610
$195$	71257.5	0.134197
$196$	17081.4	0.0317602
$197$	161196.	0.295930	0.147965	−	0.988993i	$-0.452728\pi$
$197$	161196.	0.295930	0.147965	+	0.988993i	$0.452728\pi$
$198$	843880.	1.52974
$199$	381059.	0.682118	0.341059	−	0.940042i	$-0.389214\pi$
$199$	381059.	0.682118	0.341059	+	0.940042i	$0.389214\pi$
$200$	−554808.	−0.980772
$201$	115268.	0.201241
$202$	−235584.	−0.406226
$203$	869757.	1.48135
$204$	−20174.9	−0.0339418
$205$	−191385.	−0.318070
$206$	−111247.	−0.182651
$207$	−701034.	−1.13714
$208$	−844989.	−1.35423
$209$	−666912.	−1.05609
$210$	−44160.4	−0.0691011
$211$	42857.0	0.0662698	0.0331349	−	0.999451i	$-0.489451\pi$
$211$	42857.0	0.0662698	0.0331349	+	0.999451i	$0.489451\pi$
$212$	−56537.6	−0.0863969
$213$	16021.8	0.0241970
$214$	1.15104e6	1.71814
$215$	66788.1	0.0985378
$216$	482103.	0.703081
$217$	102796.	0.148192
$218$	602714.	0.858954
$219$	285194.	0.401819
$220$	32410.3	0.0451467
$221$	−1.04527e6	−1.43962
$222$	257106.	0.350130
$223$	−619704.	−0.834492	−0.417246	−	0.908794i	$-0.637005\pi$
$223$	−619704.	−0.834492	−0.417246	+	0.908794i	$0.637005\pi$
$224$	−122826.	−0.163558
$225$	621143.	0.817966
$226$	248910.	0.324169
$227$	563235.	0.725479	0.362740	−	0.931891i	$-0.381841\pi$
$227$	563235.	0.725479	0.362740	+	0.931891i	$0.381841\pi$
$228$	−16042.2	−0.0204374
$229$	−1.16795e6	−1.47175	−0.735876	−	0.677116i	$-0.763230\pi$
$229$	−1.16795e6	−1.47175	−0.735876	+	0.677116i	$0.763230\pi$
$230$	243680.	0.303739
$231$	−446679.	−0.550764
$232$	1.53570e6	1.87321
$233$	430753.	0.519803	0.259902	−	0.965635i	$-0.416310\pi$
$233$	430753.	0.519803	0.259902	+	0.965635i	$0.416310\pi$
$234$	1.05171e6	1.25561
$235$	134844.	0.159281
$236$	−49336.2	−0.0576614
$237$	−193943.	−0.224287
$238$	647787.	0.741293
$239$	548878.	0.621557	0.310778	−	0.950482i	$-0.399410\pi$
$239$	548878.	0.621557	0.310778	+	0.950482i	$0.399410\pi$
$240$	−70137.2	−0.0785996
$241$	1.43132e6	1.58743	0.793714	−	0.608291i	$-0.208145\pi$
$241$	1.43132e6	1.58743	0.793714	+	0.608291i	$0.208145\pi$
$242$	−2.10251e6	−2.30781
$243$	−828352.	−0.899911
$244$	56967.7	0.0612568
$245$	73458.0	0.0781851
$246$	421448.	0.444023
$247$	−831155.	−0.866842
$248$	181503.	0.187394
$249$	227544.	0.232577
$250$	−445599.	−0.450914
$251$	−525103.	−0.526091	−0.263045	−	0.964783i	$-0.584727\pi$
$251$	−525103.	−0.526091	−0.263045	+	0.964783i	$0.584727\pi$
$252$	72014.3	0.0714361
$253$	2.46480e6	2.42092
$254$	−1.41822e6	−1.37930
$255$	−86761.4	−0.0835557
$256$	−309787.	−0.295436
$257$	−1.32548e6	−1.25181	−0.625906	−	0.779898i	$-0.715271\pi$
$257$	−1.32548e6	−1.25181	−0.625906	+	0.779898i	$0.715271\pi$
$258$	−147074.	−0.137558
$259$	912126.	0.844900
$260$	40392.1	0.0370564
$261$	−1.71932e6	−1.56227
$262$	1.54433e6	1.38991
$263$	−6433.13	−0.00573500	−0.00286750	−	0.999996i	$-0.500913\pi$
$263$	−6433.13	−0.00573500	−0.00286750	+	0.999996i	$0.500913\pi$
$264$	−788688.	−0.696459
$265$	−243138.	−0.212686
$266$	515092.	0.446356
$267$	−668111.	−0.573549
$268$	65339.1	0.0555695
$269$	−342106.	−0.288257	−0.144128	−	0.989559i	$-0.546038\pi$
$269$	−342106.	−0.288257	−0.144128	+	0.989559i	$0.546038\pi$
$270$	187616.	0.156624
$271$	−611319.	−0.505644	−0.252822	−	0.967513i	$-0.581359\pi$
$271$	−611319.	−0.505644	−0.252822	+	0.967513i	$0.581359\pi$
$272$	1.02884e6	0.843190
$273$	−556685.	−0.452067
$274$	−355578.	−0.286126
$275$	−2.18391e6	−1.74142
$276$	59289.4	0.0468494
$277$	−695380.	−0.544531	−0.272266	−	0.962222i	$-0.587773\pi$
$277$	−695380.	−0.544531	−0.272266	+	0.962222i	$0.587773\pi$
$278$	−275349.	−0.213684
$279$	−203205.	−0.156287
$280$	−276622.	−0.210859
$281$	−349436.	−0.263999	−0.131999	−	0.991250i	$-0.542140\pi$
$281$	−349436.	−0.263999	−0.131999	+	0.991250i	$0.542140\pi$
$282$	−296940.	−0.222354
$283$	−695649.	−0.516326	−0.258163	−	0.966101i	$-0.583117\pi$
$283$	−695649.	−0.516326	−0.258163	+	0.966101i	$0.583117\pi$
$284$	9081.90	0.00668161
$285$	−68988.9	−0.0503115
$286$	−3.69775e6	−2.67314
$287$	1.49516e6	1.07147
$288$	242801.	0.172492
$289$	−147158.	−0.103643
$290$	597636.	0.417294
$291$	573786.	0.397208
$292$	161661.	0.110956
$293$	1.50644e6	1.02514	0.512569	−	0.858646i	$-0.328694\pi$
$293$	1.50644e6	1.02514	0.512569	+	0.858646i	$0.328694\pi$
$294$	−161761.	−0.109146
$295$	−212169.	−0.141947
$296$	1.61051e6	1.06840
$297$	1.89772e6	1.24836
$298$	1.03600e6	0.675802
$299$	3.07182e6	1.98709
$300$	−52532.6	−0.0336997
$301$	−521769.	−0.331942
$302$	341041.	0.215174
$303$	−246501.	−0.154246
$304$	818089.	0.507711
$305$	244988.	0.150798
$306$	−1.28053e6	−0.781785
$307$	1.39509e6	0.844803	0.422401	−	0.906409i	$-0.361187\pi$
$307$	1.39509e6	0.844803	0.422401	+	0.906409i	$0.361187\pi$
$308$	−253199.	−0.152084
$309$	−116403.	−0.0693532
$310$	70634.0	0.0417455
$311$	500225.	0.293268	0.146634	−	0.989191i	$-0.453156\pi$
$311$	500225.	0.293268	0.146634	+	0.989191i	$0.453156\pi$
$312$	−982922.	−0.571653
$313$	−222583.	−0.128419	−0.0642097	−	0.997936i	$-0.520453\pi$
$313$	−222583.	−0.128419	−0.0642097	+	0.997936i	$0.520453\pi$
$314$	−857737.	−0.490942
$315$	309696.	0.175857
$316$	−109936.	−0.0619331
$317$	−521768.	−0.291628	−0.145814	−	0.989312i	$-0.546580\pi$
$317$	−521768.	−0.291628	−0.145814	+	0.989312i	$0.546580\pi$
$318$	535414.	0.296908
$319$	6.04503e6	3.32600
$320$	−483981.	−0.264213
$321$	1.20438e6	0.652383
$322$	−1.90370e6	−1.02320
$323$	1.01200e6	0.539725
$324$	−117948.	−0.0624205
$325$	−2.72175e6	−1.42935
$326$	163529.	0.0852216
$327$	630644.	0.326148
$328$	2.63995e6	1.35491
$329$	−1.05344e6	−0.536564
$330$	−306927.	−0.155149
$331$	−563156.	−0.282526	−0.141263	−	0.989972i	$-0.545116\pi$
$331$	−563156.	−0.282526	−0.141263	+	0.989972i	$0.545116\pi$
$332$	128983.	0.0642224
$333$	−1.80307e6	−0.891052
$334$	3.33407e6	1.63534
$335$	280989.	0.136797
$336$	547933.	0.264776
$337$	−2.15904e6	−1.03558	−0.517792	−	0.855507i	$-0.673246\pi$
$337$	−2.15904e6	−1.03558	−0.517792	+	0.855507i	$0.673246\pi$
$338$	−2.61528e6	−1.24516
$339$	260445.	0.123088
$340$	−49180.5	−0.0230725
$341$	714457.	0.332729
$342$	−1.01822e6	−0.470737
$343$	−2.37168e6	−1.08848
$344$	−921272.	−0.419751
$345$	254972.	0.115331
$346$	−2.23115e6	−1.00193
$347$	−1.95672e6	−0.872377	−0.436189	−	0.899855i	$-0.643672\pi$
$347$	−1.95672e6	−0.872377	−0.436189	+	0.899855i	$0.643672\pi$
$348$	145410.	0.0643644
$349$	−1.10773e6	−0.486820	−0.243410	−	0.969923i	$-0.578266\pi$
$349$	−1.10773e6	−0.486820	−0.243410	+	0.969923i	$0.578266\pi$
$350$	1.68675e6	0.736005
$351$	2.36507e6	1.02465
$352$	−853675.	−0.367228
$353$	−283459.	−0.121075	−0.0605374	−	0.998166i	$-0.519281\pi$
$353$	−283459.	−0.121075	−0.0605374	+	0.998166i	$0.519281\pi$
$354$	467215.	0.198157
$355$	39056.5	0.0164483
$356$	−378717.	−0.158376
$357$	677806.	0.281472
$358$	589633.	0.243150
$359$	3.91618e6	1.60371	0.801857	−	0.597516i	$-0.203846\pi$
$359$	3.91618e6	1.60371	0.801857	+	0.597516i	$0.203846\pi$
$360$	546820.	0.222376
$361$	−1.67140e6	−0.675015
$362$	−4.06114e6	−1.62883
$363$	−2.19994e6	−0.876283
$364$	−315555.	−0.124831
$365$	695220.	0.273143
$366$	−539486.	−0.210512
$367$	−2.28955e6	−0.887328	−0.443664	−	0.896193i	$-0.646322\pi$
$367$	−2.28955e6	−0.887328	−0.443664	+	0.896193i	$0.646322\pi$
$368$	−3.02353e6	−1.16384
$369$	−2.95560e6	−1.13000
$370$	626749.	0.238007
$371$	1.89947e6	0.716470
$372$	17185.9	0.00643893
$373$	822300.	0.306026	0.153013	−	0.988224i	$-0.451102\pi$
$373$	822300.	0.306026	0.153013	+	0.988224i	$0.451102\pi$
$374$	4.50229e6	1.66439
$375$	−466248.	−0.171214
$376$	−1.86004e6	−0.678503
$377$	7.53377e6	2.72998
$378$	−1.46571e6	−0.527616
$379$	−724944.	−0.259242	−0.129621	−	0.991564i	$-0.541376\pi$
$379$	−724944.	−0.259242	−0.129621	+	0.991564i	$0.541376\pi$
$380$	−39106.2	−0.0138927
$381$	−1.48394e6	−0.523726
$382$	1.39512e6	0.489161
$383$	−47389.6	−0.0165077	−0.00825384	−	0.999966i	$-0.502627\pi$
$383$	−47389.6	−0.0165077	−0.00825384	+	0.999966i	$0.502627\pi$
$384$	859386.	0.297413
$385$	−1.08887e6	−0.374391
$386$	3.14206e6	1.07336
$387$	1.03142e6	0.350073
$388$	325249.	0.109682
$389$	−1.00358e6	−0.336263	−0.168132	−	0.985765i	$-0.553773\pi$
$389$	−1.00358e6	−0.336263	−0.168132	+	0.985765i	$0.553773\pi$
$390$	−382515.	−0.127346
$391$	−3.74018e6	−1.23723
$392$	−1.01328e6	−0.333052
$393$	1.61589e6	0.527753
$394$	−865310.	−0.280822
$395$	−472777.	−0.152463
$396$	500518.	0.160392
$397$	−3.15080e6	−1.00333	−0.501666	−	0.865061i	$-0.667279\pi$
$397$	−3.15080e6	−1.00333	−0.501666	+	0.865061i	$0.667279\pi$
$398$	−2.04555e6	−0.647295
$399$	538962.	0.169483
$400$	2.67896e6	0.837175
$401$	1.91138e6	0.593588	0.296794	−	0.954941i	$-0.404082\pi$
$401$	1.91138e6	0.593588	0.296794	+	0.954941i	$0.404082\pi$
$402$	−618764.	−0.190968
$403$	890410.	0.273103
$404$	−139729.	−0.0425924
$405$	−507231.	−0.153663
$406$	−4.66891e6	−1.40573
$407$	6.33951e6	1.89701
$408$	1.19678e6	0.355930
$409$	−4.37248e6	−1.29247	−0.646233	−	0.763140i	$-0.723657\pi$
$409$	−4.37248e6	−1.29247	−0.646233	+	0.763140i	$0.723657\pi$
$410$	1.02737e6	0.301833
$411$	−372055.	−0.108643
$412$	−65982.5	−0.0191507
$413$	1.65753e6	0.478173
$414$	3.76320e6	1.07909
$415$	554686.	0.158098
$416$	−1.06391e6	−0.301421
$417$	−288109.	−0.0811366
$418$	3.58003e6	1.00218
$419$	−5.15854e6	−1.43546	−0.717731	−	0.696321i	$-0.754819\pi$
$419$	−5.15854e6	−1.43546	−0.717731	+	0.696321i	$0.754819\pi$
$420$	−26192.2	−0.00724518
$421$	−579784.	−0.159427	−0.0797134	−	0.996818i	$-0.525401\pi$
$421$	−579784.	−0.159427	−0.0797134	+	0.996818i	$0.525401\pi$
$422$	−230059.	−0.0628867
$423$	2.08243e6	0.565873
$424$	3.35384e6	0.905999
$425$	3.31394e6	0.889963
$426$	−86005.9	−0.0229617
$427$	−1.91392e6	−0.507988
$428$	682702.	0.180145
$429$	−3.86910e6	−1.01500
$430$	−358523.	−0.0935074
$431$	5.70476e6	1.47926	0.739630	−	0.673014i	$-0.235001\pi$
$431$	5.70476e6	1.47926	0.739630	+	0.673014i	$0.235001\pi$
$432$	−2.32789e6	−0.600141
$433$	1.45702e6	0.373460	0.186730	−	0.982411i	$-0.440211\pi$
$433$	1.45702e6	0.373460	0.186730	+	0.982411i	$0.440211\pi$
$434$	−551814.	−0.140627
$435$	625331.	0.158448
$436$	357479.	0.0900605
$437$	−2.97403e6	−0.744974
$438$	−1.53094e6	−0.381305
$439$	−6.23659e6	−1.54449	−0.772247	−	0.635323i	$-0.780867\pi$
$439$	−6.23659e6	−1.54449	−0.772247	+	0.635323i	$0.780867\pi$
$440$	−1.92259e6	−0.473430
$441$	1.13443e6	0.277767
$442$	5.61109e6	1.36613
$443$	2.27489e6	0.550746	0.275373	−	0.961337i	$-0.411199\pi$
$443$	2.27489e6	0.550746	0.275373	+	0.961337i	$0.411199\pi$
$444$	152493.	0.0367108
$445$	−1.62866e6	−0.389879
$446$	3.32661e6	0.791890
$447$	1.08401e6	0.256605
$448$	3.78101e6	0.890046
$449$	−576339.	−0.134916	−0.0674579	−	0.997722i	$-0.521489\pi$
$449$	−576339.	−0.134916	−0.0674579	+	0.997722i	$0.521489\pi$
$450$	−3.33434e6	−0.776208
$451$	1.03917e7	2.40573
$452$	147632.	0.0339888
$453$	356845.	0.0817023
$454$	−3.02348e6	−0.688443
$455$	−1.35704e6	−0.307300
$456$	951630.	0.214317
$457$	3.96467e6	0.888007	0.444003	−	0.896025i	$-0.353558\pi$
$457$	3.96467e6	0.888007	0.444003	+	0.896025i	$0.353558\pi$
$458$	6.26962e6	1.39662
$459$	−2.87966e6	−0.637983
$460$	144530.	0.0318467
$461$	−2.38383e6	−0.522425	−0.261212	−	0.965281i	$-0.584122\pi$
$461$	−2.38383e6	−0.522425	−0.261212	+	0.965281i	$0.584122\pi$
$462$	2.39780e6	0.522647
$463$	−3.93793e6	−0.853720	−0.426860	−	0.904318i	$-0.640380\pi$
$463$	−3.93793e6	−0.853720	−0.426860	+	0.904318i	$0.640380\pi$
$464$	−7.41533e6	−1.59895
$465$	73907.3	0.0158509
$466$	−2.31231e6	−0.493266
$467$	−4.23265e6	−0.898091	−0.449046	−	0.893509i	$-0.648236\pi$
$467$	−4.23265e6	−0.898091	−0.449046	+	0.893509i	$0.648236\pi$
$468$	623783.	0.131649
$469$	−2.19517e6	−0.460825
$470$	−723853.	−0.151149
$471$	−897485.	−0.186412
$472$	2.92664e6	0.604665
$473$	−3.62643e6	−0.745292
$474$	1.04110e6	0.212836
$475$	2.63510e6	0.535874
$476$	384213.	0.0777238
$477$	−3.75484e6	−0.755606
$478$	−2.94641e6	−0.589825
$479$	−6.78939e6	−1.35205	−0.676023	−	0.736880i	$-0.736298\pi$
$479$	−6.78939e6	−1.35205	−0.676023	+	0.736880i	$0.736298\pi$
$480$	−88308.7	−0.0174945
$481$	7.90077e6	1.55707
$482$	−7.68342e6	−1.50639
$483$	−1.99192e6	−0.388512
$484$	−1.24703e6	−0.241971
$485$	1.39872e6	0.270009
$486$	4.44665e6	0.853969
$487$	2.85540e6	0.545563	0.272781	−	0.962076i	$-0.412056\pi$
$487$	2.85540e6	0.545563	0.272781	+	0.962076i	$0.412056\pi$
$488$	−3.37935e6	−0.642367
$489$	171107.	0.0323590
$490$	−394327.	−0.0741937
$491$	5.82570e6	1.09055	0.545274	−	0.838258i	$-0.316426\pi$
$491$	5.82570e6	1.09055	0.545274	+	0.838258i	$0.316426\pi$
$492$	249967.	0.0465554
$493$	−9.17295e6	−1.69978
$494$	4.46169e6	0.822588
$495$	2.15246e6	0.394842
$496$	−876412.	−0.159957
$497$	−305121.	−0.0554090
$498$	−1.22147e6	−0.220704
$499$	9.76695e6	1.75593	0.877966	−	0.478724i	$-0.158900\pi$
$499$	9.76695e6	1.75593	0.877966	+	0.478724i	$0.158900\pi$
$500$	−264292.	−0.0472779
$501$	3.48857e6	0.620945
$502$	2.81879e6	0.499233
$503$	−8.28348e6	−1.45980	−0.729900	−	0.683554i	$-0.760433\pi$
$503$	−8.28348e6	−1.45980	−0.729900	+	0.683554i	$0.760433\pi$
$504$	−4.27192e6	−0.749113
$505$	−600899.	−0.104851
$506$	−1.32312e7	−2.29733
$507$	−2.73647e6	−0.472794
$508$	−841168.	−0.144618
$509$	−5.12610e6	−0.876986	−0.438493	−	0.898735i	$-0.644488\pi$
$509$	−5.12610e6	−0.876986	−0.438493	+	0.898735i	$0.644488\pi$
$510$	465741.	0.0792901
$511$	−5.43127e6	−0.920129
$512$	6.55902e6	1.10577
$513$	−2.28978e6	−0.384150
$514$	7.11525e6	1.18791
$515$	−283756.	−0.0471440
$516$	−87231.6	−0.0144228
$517$	−7.32171e6	−1.20472
$518$	−4.89635e6	−0.801767
$519$	−2.33455e6	−0.380438
$520$	−2.39608e6	−0.388591
$521$	7.32389e6	1.18208	0.591041	−	0.806642i	$-0.298717\pi$
$521$	7.32389e6	1.18208	0.591041	+	0.806642i	$0.298717\pi$
$522$	9.22941e6	1.48251
$523$	2.43015e6	0.388490	0.194245	−	0.980953i	$-0.437774\pi$
$523$	2.43015e6	0.388490	0.194245	+	0.980953i	$0.437774\pi$
$524$	915964.	0.145730
$525$	1.76492e6	0.279464
$526$	34533.5	0.00544222
$527$	−1.08414e6	−0.170043
$528$	3.80828e6	0.594489
$529$	4.55519e6	0.707729
$530$	1.30518e6	0.201828
$531$	−3.27656e6	−0.504292
$532$	305509.	0.0467999
$533$	1.29509e7	1.97462
$534$	3.58646e6	0.544268
$535$	2.93594e6	0.443469
$536$	−3.87595e6	−0.582728
$537$	616957.	0.0923249
$538$	1.83644e6	0.273541
$539$	−3.98859e6	−0.591354
$540$	111278.	0.0164219
$541$	−7.33508e6	−1.07749	−0.538743	−	0.842470i	$-0.681101\pi$
$541$	−7.33508e6	−1.07749	−0.538743	+	0.842470i	$0.681101\pi$
$542$	3.28160e6	0.479830
$543$	−4.24934e6	−0.618474
$544$	1.29540e6	0.187675
$545$	1.53733e6	0.221705
$546$	2.98832e6	0.428988
$547$	4.84815e6	0.692800	0.346400	−	0.938087i	$-0.387404\pi$
$547$	4.84815e6	0.692800	0.346400	+	0.938087i	$0.387404\pi$
$548$	−210899.	−0.0300001
$549$	3.78340e6	0.535736
$550$	1.17234e7	1.65251
$551$	−7.29393e6	−1.02349
$552$	−3.51707e6	−0.491285
$553$	3.69347e6	0.513597
$554$	3.73284e6	0.516732
$555$	655793.	0.0903721
$556$	−163314.	−0.0224045
$557$	6.78206e6	0.926240	0.463120	−	0.886295i	$-0.346730\pi$
$557$	6.78206e6	0.926240	0.463120	+	0.886295i	$0.346730\pi$
$558$	1.09082e6	0.148308
$559$	−4.51952e6	−0.611735
$560$	1.33570e6	0.179986
$561$	4.71093e6	0.631974
$562$	1.87580e6	0.250521
$563$	−2.35717e6	−0.313415	−0.156707	−	0.987645i	$-0.550088\pi$
$563$	−2.35717e6	−0.313415	−0.156707	+	0.987645i	$0.550088\pi$
$564$	−176120.	−0.0233136
$565$	634888.	0.0836713
$566$	3.73429e6	0.489967
$567$	3.96264e6	0.517639
$568$	−538743.	−0.0700665
$569$	−9.22927e6	−1.19505	−0.597526	−	0.801849i	$-0.703850\pi$
$569$	−9.22927e6	−1.19505	−0.597526	+	0.801849i	$0.703850\pi$
$570$	370337.	0.0477430
$571$	1.53088e7	1.96495	0.982473	−	0.186406i	$-0.0596839\pi$
$571$	1.53088e7	1.96495	0.982473	+	0.186406i	$0.0596839\pi$
$572$	−2.19319e6	−0.280276
$573$	1.45977e6	0.185736
$574$	−8.02610e6	−1.01677
$575$	−9.73891e6	−1.22840
$576$	−7.47422e6	−0.938663
$577$	1.28482e7	1.60658	0.803291	−	0.595586i	$-0.203080\pi$
$577$	1.28482e7	1.60658	0.803291	+	0.595586i	$0.203080\pi$
$578$	789952.	0.0983515
$579$	3.28766e6	0.407559
$580$	354467.	0.0437528
$581$	−4.33338e6	−0.532581
$582$	−3.08012e6	−0.376930
$583$	1.32018e7	1.60865
$584$	−9.58983e6	−1.16353
$585$	2.68256e6	0.324086
$586$	−8.08666e6	−0.972803
$587$	−4.17602e6	−0.500227	−0.250113	−	0.968217i	$-0.580468\pi$
$587$	−4.17602e6	−0.500227	−0.250113	+	0.968217i	$0.580468\pi$
$588$	−95943.2	−0.0114438
$589$	−862063.	−0.102388
$590$	1.13894e6	0.134700
$591$	−905410.	−0.106629
$592$	−7.77657e6	−0.911976
$593$	−4.52475e6	−0.528394	−0.264197	−	0.964469i	$-0.585107\pi$
$593$	−4.52475e6	−0.528394	−0.264197	+	0.964469i	$0.585107\pi$
$594$	−1.01871e7	−1.18463
$595$	1.65230e6	0.191335
$596$	614468.	0.0708572
$597$	−2.14034e6	−0.245780
$598$	−1.64897e7	−1.88565
$599$	8.96821e6	1.02127	0.510633	−	0.859799i	$-0.329411\pi$
$599$	8.96821e6	1.02127	0.510633	+	0.859799i	$0.329411\pi$
$600$	3.11626e6	0.353391
$601$	1.51006e6	0.170533	0.0852667	−	0.996358i	$-0.472826\pi$
$601$	1.51006e6	0.170533	0.0852667	+	0.996358i	$0.472826\pi$
$602$	2.80089e6	0.314996
$603$	4.33937e6	0.485997
$604$	202277.	0.0225607
$605$	−5.36281e6	−0.595668
$606$	1.32324e6	0.146371
$607$	−1.70965e7	−1.88337	−0.941686	−	0.336492i	$-0.890760\pi$
$607$	−1.70965e7	−1.88337	−0.941686	+	0.336492i	$0.890760\pi$
$608$	1.03004e6	0.113005
$609$	−4.88527e6	−0.533759
$610$	−1.31511e6	−0.143099
$611$	−9.12486e6	−0.988833
$612$	−759504.	−0.0819694
$613$	−1.35913e7	−1.46087	−0.730434	−	0.682983i	$-0.760682\pi$
$613$	−1.35913e7	−1.46087	−0.730434	+	0.682983i	$0.760682\pi$
$614$	−7.48892e6	−0.801674
$615$	1.07498e6	0.114607
$616$	1.50199e7	1.59483
$617$	1.19117e7	1.25968	0.629841	−	0.776724i	$-0.283120\pi$
$617$	1.19117e7	1.25968	0.629841	+	0.776724i	$0.283120\pi$
$618$	624857.	0.0658126
$619$	−1.72764e7	−1.81229	−0.906143	−	0.422971i	$-0.860987\pi$
$619$	−1.72764e7	−1.81229	−0.906143	+	0.422971i	$0.860987\pi$
$620$	41894.1	0.00437697
$621$	8.46267e6	0.880599
$622$	−2.68524e6	−0.278296
$623$	1.27236e7	1.31338
$624$	4.74616e6	0.487956
$625$	8.04318e6	0.823622
$626$	1.19484e6	0.121863
$627$	3.74593e6	0.380531
$628$	−508737.	−0.0514747
$629$	−9.61980e6	−0.969481
$630$	−1.66247e6	−0.166879
$631$	3.21887e6	0.321833	0.160916	−	0.986968i	$-0.448555\pi$
$631$	3.21887e6	0.321833	0.160916	+	0.986968i	$0.448555\pi$
$632$	6.52146e6	0.649460
$633$	−240720.	−0.0238783
$634$	2.80088e6	0.276740
$635$	−3.61742e6	−0.356012
$636$	317562.	0.0311305
$637$	−4.97087e6	−0.485383
$638$	−3.24501e7	−3.15620
$639$	603157.	0.0584357
$640$	2.09493e6	0.202172
$641$	8.33063e6	0.800816	0.400408	−	0.916337i	$-0.368868\pi$
$641$	8.33063e6	0.800816	0.400408	+	0.916337i	$0.368868\pi$
$642$	−6.46522e6	−0.619078
$643$	−7.92856e6	−0.756252	−0.378126	−	0.925754i	$-0.623431\pi$
$643$	−7.92856e6	−0.756252	−0.378126	+	0.925754i	$0.623431\pi$
$644$	−1.12911e6	−0.107281
$645$	−375137.	−0.0355051
$646$	−5.43246e6	−0.512171
$647$	1.34896e7	1.26689	0.633446	−	0.773787i	$-0.281640\pi$
$647$	1.34896e7	1.26689	0.633446	+	0.773787i	$0.281640\pi$
$648$	6.99672e6	0.654572
$649$	1.15202e7	1.07362
$650$	1.46105e7	1.35638
$651$	−577386.	−0.0533966
$652$	96991.4	0.00893540
$653$	1.89398e7	1.73817	0.869086	−	0.494661i	$-0.164708\pi$
$653$	1.89398e7	1.73817	0.869086	+	0.494661i	$0.164708\pi$
$654$	−3.38534e6	−0.309498
$655$	3.93908e6	0.358749
$656$	−1.27473e7	−1.15654
$657$	1.07364e7	0.970390
$658$	5.65496e6	0.509172
$659$	−1.93002e7	−1.73121	−0.865603	−	0.500730i	$-0.833065\pi$
$659$	−1.93002e7	−1.73121	−0.865603	+	0.500730i	$0.833065\pi$
$660$	−182043.	−0.0162672
$661$	3.35975e6	0.299091	0.149545	−	0.988755i	$-0.452219\pi$
$661$	3.35975e6	0.299091	0.149545	+	0.988755i	$0.452219\pi$
$662$	3.02306e6	0.268103
$663$	5.87111e6	0.518724
$664$	−7.65131e6	−0.673466
$665$	1.31383e6	0.115209
$666$	9.67902e6	0.845562
$667$	2.69572e7	2.34618
$668$	1.97749e6	0.171464
$669$	3.48077e6	0.300684
$670$	−1.50837e6	−0.129814
$671$	−1.33022e7	−1.14056
$672$	689894.	0.0589331
$673$	774206.	0.0658899	0.0329450	−	0.999457i	$-0.489511\pi$
$673$	774206.	0.0658899	0.0329450	+	0.999457i	$0.489511\pi$
$674$	1.15898e7	0.982715
$675$	−7.49825e6	−0.633432
$676$	−1.55116e6	−0.130554
$677$	8.24880e6	0.691702	0.345851	−	0.938289i	$-0.387590\pi$
$677$	8.24880e6	0.691702	0.345851	+	0.938289i	$0.387590\pi$
$678$	−1.39808e6	−0.116804
$679$	−1.09273e7	−0.909571
$680$	2.91741e6	0.241950
$681$	−3.16359e6	−0.261404
$682$	−3.83525e6	−0.315742
$683$	−7.63868e6	−0.626565	−0.313283	−	0.949660i	$-0.601429\pi$
$683$	−7.63868e6	−0.626565	−0.313283	+	0.949660i	$0.601429\pi$
$684$	−603925.	−0.0493563
$685$	−906963.	−0.0738522
$686$	1.27313e7	1.03291
$687$	6.56016e6	0.530301
$688$	4.44847e6	0.358294
$689$	1.64531e7	1.32038
$690$	−1.36871e6	−0.109443
$691$	−2.32047e7	−1.84876	−0.924379	−	0.381476i	$-0.875416\pi$
$691$	−2.32047e7	−1.84876	−0.924379	+	0.381476i	$0.875416\pi$
$692$	−1.32333e6	−0.105052
$693$	−1.68157e7	−1.33009
$694$	1.05038e7	0.827841
$695$	−702326.	−0.0551540
$696$	−8.62578e6	−0.674956
$697$	−1.57688e7	−1.22946
$698$	5.94634e6	0.461967
$699$	−2.41947e6	−0.187295
$700$	1.00044e6	0.0771694
$701$	−3.93865e6	−0.302728	−0.151364	−	0.988478i	$-0.548367\pi$
$701$	−3.93865e6	−0.302728	−0.151364	+	0.988478i	$0.548367\pi$
$702$	−1.26959e7	−0.972343
$703$	−7.64925e6	−0.583755
$704$	2.62790e7	1.99837
$705$	−757397.	−0.0573919
$706$	1.52163e6	0.114894
$707$	4.69440e6	0.353209
$708$	277113.	0.0207765
$709$	1.64111e7	1.22609	0.613045	−	0.790048i	$-0.289944\pi$
$709$	1.64111e7	1.22609	0.613045	+	0.790048i	$0.289944\pi$
$710$	−209658.	−0.0156086
$711$	−7.30119e6	−0.541651
$712$	2.24656e7	1.66081
$713$	3.18605e6	0.234708
$714$	−3.63851e6	−0.267102
$715$	−9.43175e6	−0.689965
$716$	349720.	0.0254940
$717$	−3.08295e6	−0.223959
$718$	−2.10223e7	−1.52184
$719$	1.63689e7	1.18086	0.590428	−	0.807091i	$-0.298959\pi$
$719$	1.63689e7	1.18086	0.590428	+	0.807091i	$0.298959\pi$
$720$	−2.64039e6	−0.189818
$721$	2.21678e6	0.158813
$722$	8.97221e6	0.640555
$723$	−8.03947e6	−0.571981
$724$	−2.40873e6	−0.170782
$725$	−2.38851e7	−1.68765
$726$	1.18094e7	0.831547
$727$	−2.42690e7	−1.70300	−0.851501	−	0.524352i	$-0.824307\pi$
$727$	−2.42690e7	−1.70300	−0.851501	+	0.524352i	$0.824307\pi$
$728$	1.87189e7	1.30904
$729$	−4.34930e6	−0.303110
$730$	−3.73199e6	−0.259199
$731$	5.50287e6	0.380887
$732$	−319977.	−0.0220720
$733$	1.40930e7	0.968822	0.484411	−	0.874841i	$-0.339034\pi$
$733$	1.40930e7	0.968822	0.484411	+	0.874841i	$0.339034\pi$
$734$	1.22904e7	0.842029
$735$	−412601.	−0.0281716
$736$	−3.80688e6	−0.259044
$737$	−1.52570e7	−1.03467
$738$	1.58658e7	1.07231
$739$	1.36848e7	0.921778	0.460889	−	0.887458i	$-0.347531\pi$
$739$	1.36848e7	0.921778	0.460889	+	0.887458i	$0.347531\pi$
$740$	371735.	0.0249548
$741$	4.66845e6	0.312340
$742$	−1.01965e7	−0.679893
$743$	−3.07801e6	−0.204549	−0.102275	−	0.994756i	$-0.532612\pi$
$743$	−3.07801e6	−0.204549	−0.102275	+	0.994756i	$0.532612\pi$
$744$	−1.01947e6	−0.0675217
$745$	2.64250e6	0.174431
$746$	−4.41416e6	−0.290403
$747$	8.56613e6	0.561673
$748$	2.67038e6	0.174509
$749$	−2.29364e7	−1.49390
$750$	2.50285e6	0.162473
$751$	5.09009e6	0.329326	0.164663	−	0.986350i	$-0.447346\pi$
$751$	5.09009e6	0.329326	0.164663	+	0.986350i	$0.447346\pi$
$752$	8.98141e6	0.579162
$753$	2.94941e6	0.189561
$754$	−4.04418e7	−2.59061
$755$	869885.	0.0555385
$756$	−869335.	−0.0553200
$757$	2.04350e6	0.129609	0.0648044	−	0.997898i	$-0.479358\pi$
$757$	2.04350e6	0.129609	0.0648044	+	0.997898i	$0.479358\pi$
$758$	3.89154e6	0.246008
$759$	−1.38444e7	−0.872305
$760$	2.31980e6	0.145685
$761$	−1.14458e7	−0.716449	−0.358225	−	0.933635i	$-0.616618\pi$
$761$	−1.14458e7	−0.716449	−0.358225	+	0.933635i	$0.616618\pi$
$762$	7.96589e6	0.496989
$763$	−1.20101e7	−0.746851
$764$	827465.	0.0512881
$765$	−3.26623e6	−0.201787
$766$	254390.	0.0156649
$767$	1.43574e7	0.881224
$768$	1.74002e6	0.106451
$769$	1.94669e7	1.18708	0.593541	−	0.804804i	$-0.297730\pi$
$769$	1.94669e7	1.18708	0.593541	+	0.804804i	$0.297730\pi$
$770$	5.84514e6	0.355278
$771$	7.44497e6	0.451053
$772$	1.86360e6	0.112541
$773$	−2.02032e7	−1.21611	−0.608053	−	0.793896i	$-0.708049\pi$
$773$	−2.02032e7	−1.21611	−0.608053	+	0.793896i	$0.708049\pi$
$774$	−5.53674e6	−0.332202
$775$	−2.82296e6	−0.168830
$776$	−1.92939e7	−1.15018
$777$	−5.12325e6	−0.304434
$778$	5.38730e6	0.319096
$779$	−1.25386e7	−0.740299
$780$	−226875.	−0.0133521
$781$	−2.12067e6	−0.124407
$782$	2.00775e7	1.17407
$783$	2.07551e7	1.20982
$784$	4.89273e6	0.284290
$785$	−2.18781e6	−0.126717
$786$	−8.67422e6	−0.500811
$787$	1.10907e7	0.638295	0.319148	−	0.947705i	$-0.396603\pi$
$787$	1.10907e7	0.638295	0.319148	+	0.947705i	$0.396603\pi$
$788$	−513229.	−0.0294439
$789$	36133.8	0.00206643
$790$	2.53790e6	0.144679
$791$	−4.95994e6	−0.281861
$792$	−2.96910e7	−1.68194
$793$	−1.65782e7	−0.936171
$794$	1.69137e7	0.952110
$795$	1.36567e6	0.0766349
$796$	−1.21325e6	−0.0678682
$797$	−334222.	−0.0186376	−0.00931879	−	0.999957i	$-0.502966\pi$
$797$	−334222.	−0.0186376	−0.00931879	+	0.999957i	$0.502966\pi$
$798$	−2.89318e6	−0.160831
$799$	1.11102e7	0.615681
$800$	3.37304e6	0.186336
$801$	−2.51517e7	−1.38512
$802$	−1.02604e7	−0.563285
$803$	−3.77487e7	−2.06592
$804$	−366998.	−0.0200228
$805$	−4.85572e6	−0.264097
$806$	−4.77978e6	−0.259161
$807$	1.92155e6	0.103864
$808$	8.28877e6	0.446644
$809$	2.45678e7	1.31976	0.659879	−	0.751372i	$-0.270607\pi$
$809$	2.45678e7	1.31976	0.659879	+	0.751372i	$0.270607\pi$
$810$	2.72285e6	0.145818
$811$	1.16035e7	0.619492	0.309746	−	0.950819i	$-0.399756\pi$
$811$	1.16035e7	0.619492	0.309746	+	0.950819i	$0.399756\pi$
$812$	−2.76920e6	−0.147389
$813$	3.43367e6	0.182193
$814$	−3.40309e7	−1.80017
$815$	417109.	0.0219966
$816$	−5.77881e6	−0.303818
$817$	4.37564e6	0.229344
$818$	2.34717e7	1.22648
$819$	−2.09570e7	−1.09174
$820$	609347.	0.0316468
$821$	−3.38395e6	−0.175213	−0.0876063	−	0.996155i	$-0.527922\pi$
$821$	−3.38395e6	−0.175213	−0.0876063	+	0.996155i	$0.527922\pi$
$822$	1.99722e6	0.103097
$823$	−4.86583e6	−0.250413	−0.125207	−	0.992131i	$-0.539959\pi$
$823$	−4.86583e6	−0.250413	−0.125207	+	0.992131i	$0.539959\pi$
$824$	3.91411e6	0.200824
$825$	1.22666e7	0.627466
$826$	−8.89770e6	−0.453762
$827$	1.82161e7	0.926174	0.463087	−	0.886313i	$-0.346742\pi$
$827$	1.82161e7	0.926174	0.463087	+	0.886313i	$0.346742\pi$
$828$	2.23201e6	0.113141
$829$	3.39901e7	1.71777	0.858887	−	0.512165i	$-0.171156\pi$
$829$	3.39901e7	1.71777	0.858887	+	0.512165i	$0.171156\pi$
$830$	−2.97759e6	−0.150027
$831$	3.90583e6	0.196205
$832$	3.27508e7	1.64026
$833$	6.05242e6	0.302216
$834$	1.54659e6	0.0769945
$835$	8.50412e6	0.422098
$836$	2.12337e6	0.105077
$837$	2.45302e6	0.121029
$838$	2.76914e7	1.36218
$839$	−5.22758e6	−0.256387	−0.128193	−	0.991749i	$-0.540918\pi$
$839$	−5.22758e6	−0.256387	−0.128193	+	0.991749i	$0.540918\pi$
$840$	1.55374e6	0.0759764
$841$	4.56026e7	2.22331
$842$	3.11232e6	0.151288
$843$	1.96272e6	0.0951239
$844$	−136452.	−0.00659360
$845$	−6.67073e6	−0.321390
$846$	−1.11786e7	−0.536985
$847$	4.18959e7	2.00661
$848$	−1.61944e7	−0.773349
$849$	3.90734e6	0.186042
$850$	−1.77894e7	−0.844529
$851$	2.82704e7	1.33816
$852$	−51011.5	−0.00240751
$853$	−3.49396e7	−1.64417	−0.822083	−	0.569367i	$-0.807188\pi$
$853$	−3.49396e7	−1.64417	−0.822083	+	0.569367i	$0.807188\pi$
$854$	1.02740e7	0.482055
$855$	−2.59716e6	−0.121502
$856$	−4.04982e7	−1.88909
$857$	1.83868e7	0.855174	0.427587	−	0.903974i	$-0.359364\pi$
$857$	1.83868e7	0.855174	0.427587	+	0.903974i	$0.359364\pi$
$858$	2.07696e7	0.963185
$859$	−1.05541e7	−0.488019	−0.244009	−	0.969773i	$-0.578463\pi$
$859$	−1.05541e7	−0.488019	−0.244009	+	0.969773i	$0.578463\pi$
$860$	−212645.	−0.00980415
$861$	−8.39803e6	−0.386073
$862$	−3.06235e7	−1.40374
$863$	−2.57727e7	−1.17797	−0.588984	−	0.808145i	$-0.700472\pi$
$863$	−2.57727e7	−1.17797	−0.588984	+	0.808145i	$0.700472\pi$
$864$	−2.93101e6	−0.133578
$865$	−5.69094e6	−0.258609
$866$	−7.82136e6	−0.354395
$867$	826559.	0.0373444
$868$	−327290.	−0.0147446
$869$	2.56706e7	1.15315
$870$	−3.35682e6	−0.150359
$871$	−1.90144e7	−0.849254
$872$	−2.12058e7	−0.944417
$873$	2.16008e7	0.959255
$874$	1.59648e7	0.706942
$875$	8.87929e6	0.392065
$876$	−908024.	−0.0399795
$877$	2.86971e7	1.25991	0.629953	−	0.776633i	$-0.283074\pi$
$877$	2.86971e7	1.25991	0.629953	+	0.776633i	$0.283074\pi$
$878$	3.34784e7	1.46565
$879$	−8.46140e6	−0.369377
$880$	9.28347e6	0.404114
$881$	2.40953e7	1.04591	0.522954	−	0.852361i	$-0.324830\pi$
$881$	2.40953e7	1.04591	0.522954	+	0.852361i	$0.324830\pi$
$882$	−6.08968e6	−0.263586
$883$	−1.45004e7	−0.625862	−0.312931	−	0.949776i	$-0.601311\pi$
$883$	−1.45004e7	−0.625862	−0.312931	+	0.949776i	$0.601311\pi$
$884$	3.32802e6	0.143237
$885$	1.19171e6	0.0511463
$886$	−1.22118e7	−0.522630
$887$	−9.87494e6	−0.421430	−0.210715	−	0.977548i	$-0.567579\pi$
$887$	−9.87494e6	−0.421430	−0.210715	+	0.977548i	$0.567579\pi$
$888$	−9.04598e6	−0.384967
$889$	2.82604e7	1.19929
$890$	8.74275e6	0.369976
$891$	2.75414e7	1.16223
$892$	1.97307e6	0.0830289
$893$	8.83436e6	0.370721
$894$	−5.81904e6	−0.243505
$895$	1.50396e6	0.0627594
$896$	−1.63662e7	−0.681050
$897$	−1.72539e7	−0.715987
$898$	3.09383e6	0.128028
$899$	7.81393e6	0.322456
$900$	−1.97765e6	−0.0813846
$901$	−2.00329e7	−0.822113
$902$	−5.57835e7	−2.28291
$903$	2.93068e6	0.119605
$904$	−8.75762e6	−0.356422
$905$	−1.03587e7	−0.420419
$906$	−1.91557e6	−0.0775313
$907$	−2.86568e7	−1.15667	−0.578335	−	0.815800i	$-0.696297\pi$
$907$	−2.86568e7	−1.15667	−0.578335	+	0.815800i	$0.696297\pi$
$908$	−1.79327e6	−0.0721825
$909$	−9.27980e6	−0.372502
$910$	7.28465e6	0.291612
$911$	−1.20925e7	−0.482748	−0.241374	−	0.970432i	$-0.577598\pi$
$911$	−1.20925e7	−0.482748	−0.241374	+	0.970432i	$0.577598\pi$
$912$	−4.59506e6	−0.182938
$913$	−3.01181e7	−1.19578
$914$	−2.12826e7	−0.842673
$915$	−1.37605e6	−0.0543354
$916$	3.71861e6	0.146434
$917$	−3.07732e7	−1.20851
$918$	1.54582e7	0.605414
$919$	2.64774e7	1.03416	0.517079	−	0.855937i	$-0.327019\pi$
$919$	2.64774e7	1.03416	0.517079	+	0.855937i	$0.327019\pi$
$920$	−8.57361e6	−0.333960
$921$	−7.83596e6	−0.304399
$922$	1.27966e7	0.495754
$923$	−2.64293e6	−0.102113
$924$	1.42217e6	0.0547990
$925$	−2.50487e7	−0.962565
$926$	2.11391e7	0.810137
$927$	−4.38210e6	−0.167488
$928$	−9.33654e6	−0.355890
$929$	7.65755e6	0.291106	0.145553	−	0.989350i	$-0.453504\pi$
$929$	7.65755e6	0.291106	0.145553	+	0.989350i	$0.453504\pi$
$930$	−396739.	−0.0150417
$931$	4.81262e6	0.181973
$932$	−1.37147e6	−0.0517185
$933$	−2.80967e6	−0.105670
$934$	2.27212e7	0.852243
$935$	1.14839e7	0.429595
$936$	−3.70031e7	−1.38054
$937$	−4.09111e7	−1.52227	−0.761135	−	0.648593i	$-0.775358\pi$
$937$	−4.09111e7	−1.52227	−0.761135	+	0.648593i	$0.775358\pi$
$938$	1.17838e7	0.437299
$939$	1.25021e6	0.0462720
$940$	−429328.	−0.0158478
$941$	2.88659e6	0.106270	0.0531350	−	0.998587i	$-0.483079\pi$
$941$	2.88659e6	0.106270	0.0531350	+	0.998587i	$0.483079\pi$
$942$	4.81776e6	0.176896
$943$	4.63409e7	1.69701
$944$	−1.41317e7	−0.516135
$945$	−3.73855e6	−0.136183
$946$	1.94669e7	0.707243
$947$	−1.12033e6	−0.0405950	−0.0202975	−	0.999794i	$-0.506461\pi$
$947$	−1.12033e6	−0.0405950	−0.0202975	+	0.999794i	$0.506461\pi$
$948$	617492.	0.0223157
$949$	−4.70453e7	−1.69571
$950$	−1.41454e7	−0.508517
$951$	2.93068e6	0.105079
$952$	−2.27917e7	−0.815049
$953$	−3.56043e7	−1.26990	−0.634951	−	0.772552i	$-0.718980\pi$
$953$	−3.56043e7	−1.26990	−0.634951	+	0.772552i	$0.718980\pi$
$954$	2.01562e7	0.717031
$955$	3.55849e6	0.126258
$956$	−1.74756e6	−0.0618426
$957$	−3.39539e7	−1.19842
$958$	3.64459e7	1.28302
$959$	7.08547e6	0.248784
$960$	2.71844e6	0.0952010
$961$	923521.	0.0322581
$962$	−4.24119e7	−1.47758
$963$	4.53403e7	1.57550
$964$	−4.55715e6	−0.157943
$965$	8.01437e6	0.277045
$966$	1.06928e7	0.368678
$967$	1.90104e7	0.653769	0.326884	−	0.945064i	$-0.394001\pi$
$967$	1.90104e7	0.653769	0.326884	+	0.945064i	$0.394001\pi$
$968$	7.39744e7	2.53742
$969$	−5.68420e6	−0.194473
$970$	−7.50845e6	−0.256225
$971$	−1.85527e6	−0.0631478	−0.0315739	−	0.999501i	$-0.510052\pi$
$971$	−1.85527e6	−0.0631478	−0.0315739	+	0.999501i	$0.510052\pi$
$972$	2.63738e6	0.0895378
$973$	5.48678e6	0.185796
$974$	−1.53280e7	−0.517711
$975$	1.52876e7	0.515024
$976$	1.63176e7	0.548317
$977$	−2.56130e7	−0.858468	−0.429234	−	0.903193i	$-0.641216\pi$
$977$	−2.56130e7	−0.858468	−0.429234	+	0.903193i	$0.641216\pi$
$978$	−918512.	−0.0307070
$979$	8.84322e7	2.94886
$980$	−233882.	−0.00777913
$981$	2.37413e7	0.787646
$982$	−3.12727e7	−1.03487
$983$	−1.43949e7	−0.475144	−0.237572	−	0.971370i	$-0.576352\pi$
$983$	−1.43949e7	−0.475144	−0.237572	+	0.971370i	$0.576352\pi$
$984$	−1.48282e7	−0.488202
$985$	−2.20713e6	−0.0724831
$986$	4.92410e7	1.61300
$987$	5.91701e6	0.193335
$988$	2.64630e6	0.0862475
$989$	−1.61717e7	−0.525732
$990$	−1.15546e7	−0.374685
$991$	−1.05431e7	−0.341022	−0.170511	−	0.985356i	$-0.554542\pi$
$991$	−1.05431e7	−0.341022	−0.170511	+	0.985356i	$0.554542\pi$
$992$	−1.10348e6	−0.0356028
$993$	3.16315e6	0.101800
$994$	1.63791e6	0.0525803
$995$	−5.21753e6	−0.167074
$996$	−724473.	−0.0231406
$997$	−2.25125e7	−0.717274	−0.358637	−	0.933477i	$-0.616758\pi$
$997$	−2.25125e7	−0.717274	−0.358637	+	0.933477i	$0.616758\pi$
$998$	−5.24296e7	−1.66629
$999$	2.17661e7	0.690029

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.6.a.b.1.3	✓	8
3.2	odd	2		279.6.a.f.1.6		8
4.3	odd	2		496.6.a.h.1.5		8
5.4	even	2		775.6.a.b.1.6		8
31.30	odd	2		961.6.a.c.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.6.a.b.1.3	✓	8	1.1	even	1	trivial
279.6.a.f.1.6		8	3.2	odd	2
496.6.a.h.1.5		8	4.3	odd	2
775.6.a.b.1.6		8	5.4	even	2
961.6.a.c.1.3		8	31.30	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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	31.a (trivial)

\(f(q)\)	\(=\)	\(q-5.36806 q^{2} -5.61682 q^{3} -3.18388 q^{4} -13.6922 q^{5} +30.1515 q^{6} +106.967 q^{7} +188.869 q^{8} -211.451 q^{9} +O(q^{10})\)	\(q-5.36806 q^{2} -5.61682 q^{3} -3.18388 q^{4} -13.6922 q^{5} +30.1515 q^{6} +106.967 q^{7} +188.869 q^{8} -211.451 q^{9} +73.5006 q^{10} +743.452 q^{11} +17.8833 q^{12} +926.545 q^{13} -574.208 q^{14} +76.9066 q^{15} -911.979 q^{16} -1128.14 q^{17} +1135.08 q^{18} -897.048 q^{19} +43.5943 q^{20} -600.818 q^{21} -3990.90 q^{22} +3315.35 q^{23} -1060.85 q^{24} -2937.52 q^{25} -4973.75 q^{26} +2552.57 q^{27} -340.572 q^{28} +8131.04 q^{29} -412.840 q^{30} +961.000 q^{31} -1148.26 q^{32} -4175.84 q^{33} +6055.93 q^{34} -1464.62 q^{35} +673.236 q^{36} +8527.14 q^{37} +4815.41 q^{38} -5204.24 q^{39} -2586.04 q^{40} +13977.7 q^{41} +3225.23 q^{42} -4877.82 q^{43} -2367.06 q^{44} +2895.23 q^{45} -17797.0 q^{46} -9848.26 q^{47} +5122.42 q^{48} -5364.96 q^{49} +15768.8 q^{50} +6336.56 q^{51} -2950.01 q^{52} +17757.5 q^{53} -13702.4 q^{54} -10179.5 q^{55} +20202.9 q^{56} +5038.56 q^{57} -43647.9 q^{58} +15495.6 q^{59} -244.862 q^{60} -17892.5 q^{61} -5158.71 q^{62} -22618.4 q^{63} +35347.2 q^{64} -12686.4 q^{65} +22416.2 q^{66} -20521.8 q^{67} +3591.86 q^{68} -18621.7 q^{69} +7862.17 q^{70} -2852.46 q^{71} -39936.7 q^{72} -50774.9 q^{73} -45774.2 q^{74} +16499.6 q^{75} +2856.09 q^{76} +79525.2 q^{77} +27936.7 q^{78} +34528.9 q^{79} +12487.0 q^{80} +37045.3 q^{81} -75033.1 q^{82} -40511.1 q^{83} +1912.93 q^{84} +15446.7 q^{85} +26184.5 q^{86} -45670.6 q^{87} +140415. q^{88} +118948. q^{89} -15541.8 q^{90} +99110.2 q^{91} -10555.7 q^{92} -5397.77 q^{93} +52866.1 q^{94} +12282.6 q^{95} +6449.57 q^{96} -102155. q^{97} +28799.4 q^{98} -157204. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 7 q^{2} - 2 q^{3} + 149 q^{4} + 128 q^{5} + 72 q^{6} + 88 q^{7} + 924 q^{8} + 1512 q^{9}+O(q^{10}) \) 8 * q + 7 * q^2 - 2 * q^3 + 149 * q^4 + 128 * q^5 + 72 * q^6 + 88 * q^7 + 924 * q^8 + 1512 * q^9	\( 8 q + 7 q^{2} - 2 q^{3} + 149 q^{4} + 128 q^{5} + 72 q^{6} + 88 q^{7} + 924 q^{8} + 1512 q^{9} + 1581 q^{10} + 574 q^{11} - 46 q^{12} - 122 q^{13} - 309 q^{14} - 524 q^{15} + 833 q^{16} + 1932 q^{17} - 6845 q^{18} - 1796 q^{19} - 37 q^{20} + 996 q^{21} - 9000 q^{22} - 4136 q^{23} - 17468 q^{24} + 3308 q^{25} + 1524 q^{26} - 2624 q^{27} - 21245 q^{28} + 5050 q^{29} - 30450 q^{30} + 7688 q^{31} + 21045 q^{32} + 27920 q^{33} - 24738 q^{34} + 25700 q^{35} + 21637 q^{36} + 23674 q^{37} - 4289 q^{38} + 38652 q^{39} + 36606 q^{40} + 44828 q^{41} - 9994 q^{42} + 21058 q^{43} + 13168 q^{44} - 1344 q^{45} + 6198 q^{46} + 5348 q^{47} - 69588 q^{48} + 19356 q^{49} + 33242 q^{50} + 22300 q^{51} - 60386 q^{52} + 4926 q^{53} - 24476 q^{54} - 56892 q^{55} - 87652 q^{56} + 22072 q^{57} - 25002 q^{58} + 16944 q^{59} - 138556 q^{60} - 73682 q^{61} + 6727 q^{62} - 138784 q^{63} - 1300 q^{64} + 63316 q^{65} - 128796 q^{66} - 134768 q^{67} - 9524 q^{68} + 3992 q^{69} - 142737 q^{70} + 123724 q^{71} + 93232 q^{72} + 70792 q^{73} + 307468 q^{74} - 302902 q^{75} - 65405 q^{76} + 107932 q^{77} + 36820 q^{78} - 26036 q^{79} + 576783 q^{80} + 82528 q^{81} + 142335 q^{82} + 21882 q^{83} + 299144 q^{84} - 130464 q^{85} + 480478 q^{86} - 440244 q^{87} - 71982 q^{88} + 164392 q^{89} + 397969 q^{90} - 60028 q^{91} + 31012 q^{92} - 1922 q^{93} - 170388 q^{94} - 7404 q^{95} - 331010 q^{96} - 131948 q^{97} + 288768 q^{98} - 180150 q^{99}+O(q^{100}) \) 8 * q + 7 * q^2 - 2 * q^3 + 149 * q^4 + 128 * q^5 + 72 * q^6 + 88 * q^7 + 924 * q^8 + 1512 * q^9 + 1581 * q^10 + 574 * q^11 - 46 * q^12 - 122 * q^13 - 309 * q^14 - 524 * q^15 + 833 * q^16 + 1932 * q^17 - 6845 * q^18 - 1796 * q^19 - 37 * q^20 + 996 * q^21 - 9000 * q^22 - 4136 * q^23 - 17468 * q^24 + 3308 * q^25 + 1524 * q^26 - 2624 * q^27 - 21245 * q^28 + 5050 * q^29 - 30450 * q^30 + 7688 * q^31 + 21045 * q^32 + 27920 * q^33 - 24738 * q^34 + 25700 * q^35 + 21637 * q^36 + 23674 * q^37 - 4289 * q^38 + 38652 * q^39 + 36606 * q^40 + 44828 * q^41 - 9994 * q^42 + 21058 * q^43 + 13168 * q^44 - 1344 * q^45 + 6198 * q^46 + 5348 * q^47 - 69588 * q^48 + 19356 * q^49 + 33242 * q^50 + 22300 * q^51 - 60386 * q^52 + 4926 * q^53 - 24476 * q^54 - 56892 * q^55 - 87652 * q^56 + 22072 * q^57 - 25002 * q^58 + 16944 * q^59 - 138556 * q^60 - 73682 * q^61 + 6727 * q^62 - 138784 * q^63 - 1300 * q^64 + 63316 * q^65 - 128796 * q^66 - 134768 * q^67 - 9524 * q^68 + 3992 * q^69 - 142737 * q^70 + 123724 * q^71 + 93232 * q^72 + 70792 * q^73 + 307468 * q^74 - 302902 * q^75 - 65405 * q^76 + 107932 * q^77 + 36820 * q^78 - 26036 * q^79 + 576783 * q^80 + 82528 * q^81 + 142335 * q^82 + 21882 * q^83 + 299144 * q^84 - 130464 * q^85 + 480478 * q^86 - 440244 * q^87 - 71982 * q^88 + 164392 * q^89 + 397969 * q^90 - 60028 * q^91 + 31012 * q^92 - 1922 * q^93 - 170388 * q^94 - 7404 * q^95 - 331010 * q^96 - 131948 * q^97 + 288768 * q^98 - 180150 * q^99

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