LMFDB - Embedded newform 1045.6.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.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:	$167.601091705$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.31795 q^{2} +4.33678 q^{3} +54.8242 q^{4} -25.0000 q^{5} -40.4099 q^{6} -224.649 q^{7} -212.674 q^{8} -224.192 q^{9} +O(q^{10})$	\(q-9.31795 q^{2} +4.33678 q^{3} +54.8242 q^{4} -25.0000 q^{5} -40.4099 q^{6} -224.649 q^{7} -212.674 q^{8} -224.192 q^{9} +232.949 q^{10} +121.000 q^{11} +237.760 q^{12} +592.087 q^{13} +2093.27 q^{14} -108.420 q^{15} +227.316 q^{16} -205.701 q^{17} +2089.01 q^{18} +361.000 q^{19} -1370.60 q^{20} -974.256 q^{21} -1127.47 q^{22} -3945.06 q^{23} -922.323 q^{24} +625.000 q^{25} -5517.03 q^{26} -2026.11 q^{27} -12316.2 q^{28} +495.555 q^{29} +1010.25 q^{30} -6436.51 q^{31} +4687.46 q^{32} +524.751 q^{33} +1916.71 q^{34} +5616.24 q^{35} -12291.2 q^{36} +12499.5 q^{37} -3363.78 q^{38} +2567.75 q^{39} +5316.86 q^{40} +4582.61 q^{41} +9078.06 q^{42} -2539.10 q^{43} +6633.72 q^{44} +5604.81 q^{45} +36759.8 q^{46} +24512.8 q^{47} +985.821 q^{48} +33660.4 q^{49} -5823.72 q^{50} -892.079 q^{51} +32460.7 q^{52} -15904.7 q^{53} +18879.2 q^{54} -3025.00 q^{55} +47777.2 q^{56} +1565.58 q^{57} -4617.55 q^{58} +7889.80 q^{59} -5944.01 q^{60} -40326.6 q^{61} +59975.1 q^{62} +50364.7 q^{63} -50951.6 q^{64} -14802.2 q^{65} -4889.60 q^{66} +21879.1 q^{67} -11277.4 q^{68} -17108.8 q^{69} -52331.8 q^{70} -36531.0 q^{71} +47680.0 q^{72} +37224.3 q^{73} -116469. q^{74} +2710.49 q^{75} +19791.5 q^{76} -27182.6 q^{77} -23926.2 q^{78} +18644.9 q^{79} -5682.91 q^{80} +45691.9 q^{81} -42700.6 q^{82} +46549.9 q^{83} -53412.8 q^{84} +5142.52 q^{85} +23659.2 q^{86} +2149.11 q^{87} -25733.6 q^{88} +68491.7 q^{89} -52225.3 q^{90} -133012. q^{91} -216284. q^{92} -27913.8 q^{93} -228409. q^{94} -9025.00 q^{95} +20328.5 q^{96} -56288.2 q^{97} -313646. q^{98} -27127.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) $ 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * 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 $

$2$	−9.31795	−1.64720	−0.823598	−	0.567174i	$-0.808037\pi$
$2$	−9.31795	−1.64720	−0.823598	+	0.567174i	$0.808037\pi$
$3$	4.33678	0.278205	0.139102	−	0.990278i	$-0.455578\pi$
$3$	4.33678	0.278205	0.139102	+	0.990278i	$0.455578\pi$
$4$	54.8242	1.71326
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−40.4099	−0.458258
$7$	−224.649	−1.73285	−0.866424	−	0.499310i	$-0.833587\pi$
$7$	−224.649	−1.73285	−0.866424	+	0.499310i	$0.833587\pi$
$8$	−212.674	−1.17487
$9$	−224.192	−0.922602
$10$	232.949	0.736649
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	237.760	0.476636
$13$	592.087	0.971688	0.485844	−	0.874045i	$-0.338512\pi$
$13$	592.087	0.971688	0.485844	+	0.874045i	$0.338512\pi$
$14$	2093.27	2.85434
$15$	−108.420	−0.124417
$16$	227.316	0.221988
$17$	−205.701	−0.172629	−0.0863144	−	0.996268i	$-0.527509\pi$
$17$	−205.701	−0.172629	−0.0863144	+	0.996268i	$0.527509\pi$
$18$	2089.01	1.51971
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−1370.60	−0.766191
$21$	−974.256	−0.482086
$22$	−1127.47	−0.496648
$23$	−3945.06	−1.55501	−0.777506	−	0.628876i	$-0.783515\pi$
$23$	−3945.06	−1.55501	−0.777506	+	0.628876i	$0.783515\pi$
$24$	−922.323	−0.326855
$25$	625.000	0.200000
$26$	−5517.03	−1.60056
$27$	−2026.11	−0.534877
$28$	−12316.2	−2.96881
$29$	495.555	0.109420	0.0547100	−	0.998502i	$-0.482577\pi$
$29$	495.555	0.109420	0.0547100	+	0.998502i	$0.482577\pi$
$30$	1010.25	0.204939
$31$	−6436.51	−1.20295	−0.601473	−	0.798893i	$-0.705419\pi$
$31$	−6436.51	−1.20295	−0.601473	+	0.798893i	$0.705419\pi$
$32$	4687.46	0.809213
$33$	524.751	0.0838819
$34$	1916.71	0.284354
$35$	5616.24	0.774953
$36$	−12291.2	−1.58065
$37$	12499.5	1.50102	0.750511	−	0.660858i	$-0.229807\pi$
$37$	12499.5	1.50102	0.750511	+	0.660858i	$0.229807\pi$
$38$	−3363.78	−0.377893
$39$	2567.75	0.270328
$40$	5316.86	0.525418
$41$	4582.61	0.425749	0.212875	−	0.977080i	$-0.431717\pi$
$41$	4582.61	0.425749	0.212875	+	0.977080i	$0.431717\pi$
$42$	9078.06	0.794091
$43$	−2539.10	−0.209415	−0.104708	−	0.994503i	$-0.533391\pi$
$43$	−2539.10	−0.209415	−0.104708	+	0.994503i	$0.533391\pi$
$44$	6633.72	0.516566
$45$	5604.81	0.412600
$46$	36759.8	2.56141
$47$	24512.8	1.61863	0.809315	−	0.587375i	$-0.199839\pi$
$47$	24512.8	1.61863	0.809315	+	0.587375i	$0.199839\pi$
$48$	985.821	0.0617582
$49$	33660.4	2.00276
$50$	−5823.72	−0.329439
$51$	−892.079	−0.0480262
$52$	32460.7	1.66475
$53$	−15904.7	−0.777744	−0.388872	−	0.921292i	$-0.627135\pi$
$53$	−15904.7	−0.777744	−0.388872	+	0.921292i	$0.627135\pi$
$54$	18879.2	0.881047
$55$	−3025.00	−0.134840
$56$	47777.2	2.03587
$57$	1565.58	0.0638245
$58$	−4617.55	−0.180236
$59$	7889.80	0.295078	0.147539	−	0.989056i	$-0.452865\pi$
$59$	7889.80	0.295078	0.147539	+	0.989056i	$0.452865\pi$
$60$	−5944.01	−0.213158
$61$	−40326.6	−1.38761	−0.693805	−	0.720163i	$-0.744067\pi$
$61$	−40326.6	−1.38761	−0.693805	+	0.720163i	$0.744067\pi$
$62$	59975.1	1.98149
$63$	50364.7	1.59873
$64$	−50951.6	−1.55492
$65$	−14802.2	−0.434552
$66$	−4889.60	−0.138170
$67$	21879.1	0.595446	0.297723	−	0.954652i	$-0.403773\pi$
$67$	21879.1	0.595446	0.297723	+	0.954652i	$0.403773\pi$
$68$	−11277.4	−0.295757
$69$	−17108.8	−0.432611
$70$	−52331.8	−1.27650
$71$	−36531.0	−0.860034	−0.430017	−	0.902821i	$-0.641492\pi$
$71$	−36531.0	−0.860034	−0.430017	+	0.902821i	$0.641492\pi$
$72$	47680.0	1.08394
$73$	37224.3	0.817559	0.408780	−	0.912633i	$-0.365954\pi$
$73$	37224.3	0.817559	0.408780	+	0.912633i	$0.365954\pi$
$74$	−116469.	−2.47248
$75$	2710.49	0.0556409
$76$	19791.5	0.393048
$77$	−27182.6	−0.522473
$78$	−23926.2	−0.445284
$79$	18644.9	0.336119	0.168059	−	0.985777i	$-0.446250\pi$
$79$	18644.9	0.336119	0.168059	+	0.985777i	$0.446250\pi$
$80$	−5682.91	−0.0992763
$81$	45691.9	0.773797
$82$	−42700.6	−0.701292
$83$	46549.9	0.741693	0.370846	−	0.928694i	$-0.379068\pi$
$83$	46549.9	0.741693	0.370846	+	0.928694i	$0.379068\pi$
$84$	−53412.8	−0.825937
$85$	5142.52	0.0772020
$86$	23659.2	0.344948
$87$	2149.11	0.0304412
$88$	−25733.6	−0.354237
$89$	68491.7	0.916565	0.458282	−	0.888807i	$-0.348465\pi$
$89$	68491.7	0.916565	0.458282	+	0.888807i	$0.348465\pi$
$90$	−52225.3	−0.679634
$91$	−133012.	−1.68379
$92$	−216284.	−2.66413
$93$	−27913.8	−0.334665
$94$	−228409.	−2.66620
$95$	−9025.00	−0.102598
$96$	20328.5	0.225127
$97$	−56288.2	−0.607419	−0.303709	−	0.952765i	$-0.598225\pi$
$97$	−56288.2	−0.607419	−0.303709	+	0.952765i	$0.598225\pi$
$98$	−313646.	−3.29894
$99$	−27127.3	−0.278175
$100$	34265.1	0.342651
$101$	123132.	1.20107	0.600536	−	0.799598i	$-0.294954\pi$
$101$	123132.	1.20107	0.600536	+	0.799598i	$0.294954\pi$
$102$	8312.35	0.0791085
$103$	50905.9	0.472798	0.236399	−	0.971656i	$-0.424033\pi$
$103$	50905.9	0.472798	0.236399	+	0.971656i	$0.424033\pi$
$104$	−125922.	−1.14161
$105$	24356.4	0.215595
$106$	148200.	1.28110
$107$	−41631.5	−0.351530	−0.175765	−	0.984432i	$-0.556240\pi$
$107$	−41631.5	−0.351530	−0.175765	+	0.984432i	$0.556240\pi$
$108$	−111080.	−0.916381
$109$	114266.	0.921194	0.460597	−	0.887609i	$-0.347635\pi$
$109$	114266.	0.921194	0.460597	+	0.887609i	$0.347635\pi$
$110$	28186.8	0.222108
$111$	54207.4	0.417591
$112$	−51066.5	−0.384672
$113$	108966.	0.802779	0.401389	−	0.915908i	$-0.368527\pi$
$113$	108966.	0.802779	0.401389	+	0.915908i	$0.368527\pi$
$114$	−14588.0	−0.105132
$115$	98626.4	0.695422
$116$	27168.4	0.187464
$117$	−132741.	−0.896482
$118$	−73516.8	−0.486051
$119$	46210.5	0.299139
$120$	23058.1	0.146174
$121$	14641.0	0.0909091
$122$	375762.	2.28567
$123$	19873.8	0.118445
$124$	−352877.	−2.06096
$125$	−15625.0	−0.0894427
$126$	−469296.	−2.63342
$127$	−137601.	−0.757030	−0.378515	−	0.925595i	$-0.623565\pi$
$127$	−137601.	−0.757030	−0.378515	+	0.925595i	$0.623565\pi$
$128$	324766.	1.75205
$129$	−11011.5	−0.0582603
$130$	137926.	0.715793
$131$	−145950.	−0.743064	−0.371532	−	0.928420i	$-0.621167\pi$
$131$	−145950.	−0.743064	−0.371532	+	0.928420i	$0.621167\pi$
$132$	28769.0	0.143711
$133$	−81098.5	−0.397542
$134$	−203868.	−0.980816
$135$	50652.8	0.239204
$136$	43747.3	0.202817
$137$	70346.3	0.320214	0.160107	−	0.987100i	$-0.448816\pi$
$137$	70346.3	0.320214	0.160107	+	0.987100i	$0.448816\pi$
$138$	159419.	0.712596
$139$	20259.5	0.0889389	0.0444695	−	0.999011i	$-0.485840\pi$
$139$	20259.5	0.0889389	0.0444695	+	0.999011i	$0.485840\pi$
$140$	307906.	1.32769
$141$	106306.	0.450310
$142$	340394.	1.41664
$143$	71642.5	0.292975
$144$	−50962.5	−0.204807
$145$	−12388.9	−0.0489341
$146$	−346854.	−1.34668
$147$	145978.	0.557177
$148$	685273.	2.57163
$149$	−379001.	−1.39854	−0.699270	−	0.714857i	$-0.746492\pi$
$149$	−379001.	−1.39854	−0.699270	+	0.714857i	$0.746492\pi$
$150$	−25256.2	−0.0916515
$151$	−80266.5	−0.286478	−0.143239	−	0.989688i	$-0.545752\pi$
$151$	−80266.5	−0.286478	−0.143239	+	0.989688i	$0.545752\pi$
$152$	−76775.5	−0.269534
$153$	46116.5	0.159268
$154$	253286.	0.860616
$155$	160913.	0.537974
$156$	140775.	0.463141
$157$	518335.	1.67827	0.839134	−	0.543925i	$-0.183062\pi$
$157$	518335.	1.67827	0.839134	+	0.543925i	$0.183062\pi$
$158$	−173732.	−0.553653
$159$	−68975.4	−0.216372
$160$	−117187.	−0.361891
$161$	886255.	2.69460
$162$	−425755.	−1.27460
$163$	317132.	0.934913	0.467457	−	0.884016i	$-0.345170\pi$
$163$	317132.	0.934913	0.467457	+	0.884016i	$0.345170\pi$
$164$	251238.	0.729417
$165$	−13118.8	−0.0375131
$166$	−433750.	−1.22171
$167$	150634.	0.417958	0.208979	−	0.977920i	$-0.432986\pi$
$167$	150634.	0.417958	0.208979	+	0.977920i	$0.432986\pi$
$168$	207199.	0.566389
$169$	−20726.2	−0.0558217
$170$	−47917.7	−0.127167
$171$	−80933.4	−0.211659
$172$	−139204.	−0.358782
$173$	270554.	0.687287	0.343643	−	0.939100i	$-0.388339\pi$
$173$	270554.	0.687287	0.343643	+	0.939100i	$0.388339\pi$
$174$	−20025.3	−0.0501425
$175$	−140406.	−0.346569
$176$	27505.3	0.0669320
$177$	34216.4	0.0820920
$178$	−638202.	−1.50976
$179$	−795463.	−1.85561	−0.927807	−	0.373061i	$-0.878308\pi$
$179$	−795463.	−1.85561	−0.927807	+	0.373061i	$0.878308\pi$
$180$	307279.	0.706890
$181$	612274.	1.38915	0.694575	−	0.719420i	$-0.255592\pi$
$181$	612274.	1.38915	0.694575	+	0.719420i	$0.255592\pi$
$182$	1.23940e6	2.77353
$183$	−174888.	−0.386040
$184$	839013.	1.82694
$185$	−312487.	−0.671278
$186$	260099.	0.551260
$187$	−24889.8	−0.0520496
$188$	1.34389e6	2.77313
$189$	455165.	0.926860
$190$	84094.5	0.168999
$191$	218992.	0.434355	0.217178	−	0.976132i	$-0.430315\pi$
$191$	218992.	0.434355	0.217178	+	0.976132i	$0.430315\pi$
$192$	−220966.	−0.432586
$193$	−698192.	−1.34922	−0.674608	−	0.738176i	$-0.735687\pi$
$193$	−698192.	−1.34922	−0.674608	+	0.738176i	$0.735687\pi$
$194$	524491.	1.00054
$195$	−64193.8	−0.120894
$196$	1.84540e6	3.43124
$197$	654886.	1.20227	0.601133	−	0.799149i	$-0.294716\pi$
$197$	654886.	1.20227	0.601133	+	0.799149i	$0.294716\pi$
$198$	252771.	0.458209
$199$	472540.	0.845875	0.422937	−	0.906159i	$-0.360999\pi$
$199$	472540.	0.845875	0.422937	+	0.906159i	$0.360999\pi$
$200$	−132922.	−0.234974
$201$	94884.9	0.165656
$202$	−1.14734e6	−1.97840
$203$	−111326.	−0.189608
$204$	−48907.5	−0.0822811
$205$	−114565.	−0.190401
$206$	−474339.	−0.778791
$207$	884451.	1.43466
$208$	134591.	0.215704
$209$	43681.0	0.0691714
$210$	−226952.	−0.355128
$211$	−861092.	−1.33151	−0.665754	−	0.746172i	$-0.731890\pi$
$211$	−861092.	−1.33151	−0.665754	+	0.746172i	$0.731890\pi$
$212$	−871964.	−1.33247
$213$	−158427.	−0.239265
$214$	387920.	0.579039
$215$	63477.5	0.0936534
$216$	430902.	0.628412
$217$	1.44596e6	2.08452
$218$	−1.06473e6	−1.51739
$219$	161434.	0.227449
$220$	−165843.	−0.231015
$221$	−121793.	−0.167741
$222$	−505102.	−0.687855
$223$	−146383.	−0.197119	−0.0985596	−	0.995131i	$-0.531424\pi$
$223$	−146383.	−0.197119	−0.0985596	+	0.995131i	$0.531424\pi$
$224$	−1.05304e6	−1.40224
$225$	−140120.	−0.184520
$226$	−1.01534e6	−1.32233
$227$	−43996.2	−0.0566697	−0.0283348	−	0.999598i	$-0.509020\pi$
$227$	−43996.2	−0.0566697	−0.0283348	+	0.999598i	$0.509020\pi$
$228$	85831.5	0.109348
$229$	738965.	0.931183	0.465591	−	0.885000i	$-0.345842\pi$
$229$	738965.	0.931183	0.465591	+	0.885000i	$0.345842\pi$
$230$	−918996.	−1.14550
$231$	−117885.	−0.145354
$232$	−105392.	−0.128554
$233$	731620.	0.882868	0.441434	−	0.897294i	$-0.354470\pi$
$233$	731620.	0.882868	0.441434	+	0.897294i	$0.354470\pi$
$234$	1.23688e6	1.47668
$235$	−612819.	−0.723873
$236$	432552.	0.505543
$237$	80858.9	0.0935097
$238$	−430588.	−0.492741
$239$	−608361.	−0.688916	−0.344458	−	0.938802i	$-0.611937\pi$
$239$	−608361.	−0.688916	−0.344458	+	0.938802i	$0.611937\pi$
$240$	−24645.5	−0.0276191
$241$	458969.	0.509027	0.254513	−	0.967069i	$-0.418085\pi$
$241$	458969.	0.509027	0.254513	+	0.967069i	$0.418085\pi$
$242$	−136424.	−0.149745
$243$	690501.	0.750151
$244$	−2.21087e6	−2.37733
$245$	−841510.	−0.895661
$246$	−185183.	−0.195103
$247$	213743.	0.222921
$248$	1.36888e6	1.41331
$249$	201877.	0.206342
$250$	145593.	0.147330
$251$	−1.51934e6	−1.52220	−0.761099	−	0.648636i	$-0.775340\pi$
$251$	−1.51934e6	−1.52220	−0.761099	+	0.648636i	$0.775340\pi$
$252$	2.76120e6	2.73903
$253$	−477352.	−0.468854
$254$	1.28216e6	1.24698
$255$	22302.0	0.0214780
$256$	−1.39570e6	−1.33104
$257$	−362920.	−0.342750	−0.171375	−	0.985206i	$-0.554821\pi$
$257$	−362920.	−0.342750	−0.171375	+	0.985206i	$0.554821\pi$
$258$	102605.	0.0959662
$259$	−2.80800e6	−2.60104
$260$	−811517.	−0.744499
$261$	−111100.	−0.100951
$262$	1.35996e6	1.22397
$263$	−765528.	−0.682451	−0.341225	−	0.939981i	$-0.610842\pi$
$263$	−765528.	−0.682451	−0.341225	+	0.939981i	$0.610842\pi$
$264$	−111601.	−0.0985504
$265$	397618.	0.347818
$266$	755671.	0.654830
$267$	297034.	0.254993
$268$	1.19950e6	1.02015
$269$	1.20401e6	1.01449	0.507247	−	0.861801i	$-0.330663\pi$
$269$	1.20401e6	1.01449	0.507247	+	0.861801i	$0.330663\pi$
$270$	−471980.	−0.394016
$271$	734109.	0.607208	0.303604	−	0.952798i	$-0.401810\pi$
$271$	734109.	0.607208	0.303604	+	0.952798i	$0.401810\pi$
$272$	−46759.1	−0.0383216
$273$	−576844.	−0.468438
$274$	−655483.	−0.527455
$275$	75625.0	0.0603023
$276$	−937978.	−0.741174
$277$	−389573.	−0.305063	−0.152531	−	0.988299i	$-0.548742\pi$
$277$	−389573.	−0.305063	−0.152531	+	0.988299i	$0.548742\pi$
$278$	−188777.	−0.146500
$279$	1.44302e6	1.10984
$280$	−1.19443e6	−0.910470
$281$	−1.18427e6	−0.894716	−0.447358	−	0.894355i	$-0.647635\pi$
$281$	−1.18427e6	−0.894716	−0.447358	+	0.894355i	$0.647635\pi$
$282$	−990558.	−0.741749
$283$	1.73740e6	1.28954	0.644770	−	0.764377i	$-0.276953\pi$
$283$	1.73740e6	1.28954	0.644770	+	0.764377i	$0.276953\pi$
$284$	−2.00278e6	−1.47346
$285$	−39139.5	−0.0285432
$286$	−667561.	−0.482587
$287$	−1.02948e6	−0.737758
$288$	−1.05089e6	−0.746582
$289$	−1.37754e6	−0.970199
$290$	115439.	0.0806041
$291$	−244110.	−0.168987
$292$	2.04079e6	1.40069
$293$	−2.52946e6	−1.72131	−0.860654	−	0.509191i	$-0.829945\pi$
$293$	−2.52946e6	−1.72131	−0.860654	+	0.509191i	$0.829945\pi$
$294$	−1.36021e6	−0.917780
$295$	−197245.	−0.131963
$296$	−2.65832e6	−1.76351
$297$	−245159.	−0.161271
$298$	3.53152e6	2.30367
$299$	−2.33582e6	−1.51099
$300$	148600.	0.0953271
$301$	570407.	0.362885
$302$	747919.	0.471886
$303$	533998.	0.334144
$304$	82061.2	0.0509277
$305$	1.00817e6	0.620558
$306$	−429711.	−0.262345
$307$	992942.	0.601282	0.300641	−	0.953737i	$-0.402799\pi$
$307$	992942.	0.601282	0.300641	+	0.953737i	$0.402799\pi$
$308$	−1.49026e6	−0.895130
$309$	220768.	0.131535
$310$	−1.49938e6	−0.886149
$311$	1.91616e6	1.12339	0.561695	−	0.827344i	$-0.310149\pi$
$311$	1.91616e6	1.12339	0.561695	+	0.827344i	$0.310149\pi$
$312$	−546095.	−0.317601
$313$	1.28033e6	0.738689	0.369345	−	0.929292i	$-0.379582\pi$
$313$	1.28033e6	0.738689	0.369345	+	0.929292i	$0.379582\pi$
$314$	−4.82982e6	−2.76444
$315$	−1.25912e6	−0.714973
$316$	1.02219e6	0.575857
$317$	807956.	0.451585	0.225793	−	0.974175i	$-0.427503\pi$
$317$	807956.	0.451585	0.225793	+	0.974175i	$0.427503\pi$
$318$	642709.	0.356407
$319$	59962.1	0.0329914
$320$	1.27379e6	0.695382
$321$	−180547.	−0.0977974
$322$	−8.25808e6	−4.43853
$323$	−74257.9	−0.0396038
$324$	2.50502e6	1.32571
$325$	370054.	0.194338
$326$	−2.95502e6	−1.53999
$327$	495547.	0.256280
$328$	−974605.	−0.500200
$329$	−5.50678e6	−2.80484
$330$	122240.	0.0617915
$331$	−583499.	−0.292732	−0.146366	−	0.989231i	$-0.546758\pi$
$331$	−583499.	−0.292732	−0.146366	+	0.989231i	$0.546758\pi$
$332$	2.55206e6	1.27071
$333$	−2.80228e6	−1.38485
$334$	−1.40360e6	−0.688459
$335$	−546977.	−0.266292
$336$	−221464.	−0.107018
$337$	−157357.	−0.0754764	−0.0377382	−	0.999288i	$-0.512015\pi$
$337$	−157357.	−0.0754764	−0.0377382	+	0.999288i	$0.512015\pi$
$338$	193126.	0.0919492
$339$	472563.	0.223337
$340$	281934.	0.132267
$341$	−778818.	−0.362702
$342$	754134.	0.348645
$343$	−3.78610e6	−1.73763
$344$	540002.	0.246036
$345$	427721.	0.193470
$346$	−2.52100e6	−1.13210
$347$	−2.53837e6	−1.13170	−0.565851	−	0.824508i	$-0.691452\pi$
$347$	−2.53837e6	−1.13170	−0.565851	+	0.824508i	$0.691452\pi$
$348$	117823.	0.0521535
$349$	−1.94232e6	−0.853605	−0.426803	−	0.904345i	$-0.640360\pi$
$349$	−1.94232e6	−0.853605	−0.426803	+	0.904345i	$0.640360\pi$
$350$	1.30830e6	0.570868
$351$	−1.19963e6	−0.519734
$352$	567183.	0.243987
$353$	2.09031e6	0.892840	0.446420	−	0.894824i	$-0.352699\pi$
$353$	2.09031e6	0.892840	0.446420	+	0.894824i	$0.352699\pi$
$354$	−318826.	−0.135222
$355$	913274.	0.384619
$356$	3.75500e6	1.57031
$357$	200405.	0.0832220
$358$	7.41209e6	3.05656
$359$	1.19613e6	0.489825	0.244913	−	0.969545i	$-0.421241\pi$
$359$	1.19613e6	0.489825	0.244913	+	0.969545i	$0.421241\pi$
$360$	−1.19200e6	−0.484752
$361$	130321.	0.0526316
$362$	−5.70514e6	−2.28820
$363$	63494.8	0.0252913
$364$	−7.29227e6	−2.88476
$365$	−930607.	−0.365624
$366$	1.62960e6	0.635883
$367$	4.80096e6	1.86064	0.930321	−	0.366745i	$-0.119528\pi$
$367$	4.80096e6	1.86064	0.930321	+	0.366745i	$0.119528\pi$
$368$	−896775.	−0.345195
$369$	−1.02739e6	−0.392797
$370$	2.91173e6	1.10573
$371$	3.57299e6	1.34771
$372$	−1.53035e6	−0.573367
$373$	−5.13953e6	−1.91272	−0.956360	−	0.292192i	$-0.905615\pi$
$373$	−5.13953e6	−1.91272	−0.956360	+	0.292192i	$0.905615\pi$
$374$	231922.	0.0857358
$375$	−67762.2	−0.0248834
$376$	−5.21324e6	−1.90168
$377$	293411.	0.106322
$378$	−4.24120e6	−1.52672
$379$	−1.83431e6	−0.655956	−0.327978	−	0.944685i	$-0.606367\pi$
$379$	−1.83431e6	−0.655956	−0.327978	+	0.944685i	$0.606367\pi$
$380$	−494788.	−0.175776
$381$	−596747.	−0.210609
$382$	−2.04056e6	−0.715468
$383$	3.03341e6	1.05666	0.528328	−	0.849040i	$-0.322819\pi$
$383$	3.03341e6	1.05666	0.528328	+	0.849040i	$0.322819\pi$
$384$	1.40844e6	0.487428
$385$	679565.	0.233657
$386$	6.50572e6	2.22242
$387$	569247.	0.193207
$388$	−3.08596e6	−1.04066
$389$	2.26430e6	0.758682	0.379341	−	0.925257i	$-0.376151\pi$
$389$	2.26430e6	0.758682	0.379341	+	0.925257i	$0.376151\pi$
$390$	598154.	0.199137
$391$	811501.	0.268440
$392$	−7.15870e6	−2.35299
$393$	−632954.	−0.206724
$394$	−6.10220e6	−1.98037
$395$	−466123.	−0.150317
$396$	−1.48723e6	−0.476585
$397$	−5.63011e6	−1.79284	−0.896418	−	0.443209i	$-0.853840\pi$
$397$	−5.63011e6	−1.79284	−0.896418	+	0.443209i	$0.853840\pi$
$398$	−4.40311e6	−1.39332
$399$	−351706.	−0.110598
$400$	142073.	0.0443977
$401$	−821286.	−0.255055	−0.127527	−	0.991835i	$-0.540704\pi$
$401$	−821286.	−0.255055	−0.127527	+	0.991835i	$0.540704\pi$
$402$	−884132.	−0.272868
$403$	−3.81097e6	−1.16889
$404$	6.75063e6	2.05774
$405$	−1.14230e6	−0.346053
$406$	1.03733e6	0.312322
$407$	1.51244e6	0.452575
$408$	189722.	0.0564246
$409$	−2.43177e6	−0.718810	−0.359405	−	0.933182i	$-0.617020\pi$
$409$	−2.43177e6	−0.718810	−0.359405	+	0.933182i	$0.617020\pi$
$410$	1.06751e6	0.313627
$411$	305077.	0.0890849
$412$	2.79088e6	0.810023
$413$	−1.77244e6	−0.511324
$414$	−8.24127e6	−2.36316
$415$	−1.16375e6	−0.331695
$416$	2.77538e6	0.786303
$417$	87861.1	0.0247432
$418$	−407017.	−0.113939
$419$	−6.39433e6	−1.77934	−0.889672	−	0.456600i	$-0.849067\pi$
$419$	−6.39433e6	−1.77934	−0.889672	+	0.456600i	$0.849067\pi$
$420$	1.33532e6	0.369370
$421$	6.05541e6	1.66509	0.832546	−	0.553956i	$-0.186882\pi$
$421$	6.05541e6	1.66509	0.832546	+	0.553956i	$0.186882\pi$
$422$	8.02361e6	2.19325
$423$	−5.49557e6	−1.49335
$424$	3.38253e6	0.913750
$425$	−128563.	−0.0345258
$426$	1.47621e6	0.394117
$427$	9.05936e6	2.40452
$428$	−2.28241e6	−0.602261
$429$	310698.	0.0815070
$430$	−591480.	−0.154266
$431$	−2.32779e6	−0.603602	−0.301801	−	0.953371i	$-0.597588\pi$
$431$	−2.32779e6	−0.603602	−0.301801	+	0.953371i	$0.597588\pi$
$432$	−460568.	−0.118737
$433$	277544.	0.0711397	0.0355699	−	0.999367i	$-0.488675\pi$
$433$	277544.	0.0711397	0.0355699	+	0.999367i	$0.488675\pi$
$434$	−1.34734e7	−3.43362
$435$	−53727.8	−0.0136137
$436$	6.26454e6	1.57824
$437$	−1.42417e6	−0.356744
$438$	−1.50423e6	−0.374653
$439$	−7.37298e6	−1.82592	−0.912960	−	0.408048i	$-0.866210\pi$
$439$	−7.37298e6	−1.82592	−0.912960	+	0.408048i	$0.866210\pi$
$440$	643340.	0.158420
$441$	−7.54640e6	−1.84775
$442$	1.13486e6	0.276303
$443$	−1.29253e6	−0.312920	−0.156460	−	0.987684i	$-0.550008\pi$
$443$	−1.29253e6	−0.312920	−0.156460	+	0.987684i	$0.550008\pi$
$444$	2.97188e6	0.715441
$445$	−1.71229e6	−0.409900
$446$	1.36399e6	0.324694
$447$	−1.64365e6	−0.389081
$448$	1.14463e7	2.69444
$449$	−5.55597e6	−1.30060	−0.650301	−	0.759677i	$-0.725357\pi$
$449$	−5.55597e6	−1.30060	−0.650301	+	0.759677i	$0.725357\pi$
$450$	1.30563e6	0.303941
$451$	554496.	0.128368
$452$	5.97398e6	1.37536
$453$	−348098.	−0.0796996
$454$	409954.	0.0933461
$455$	3.32530e6	0.753013
$456$	−332958.	−0.0749856
$457$	−1.43762e6	−0.321997	−0.160999	−	0.986955i	$-0.551472\pi$
$457$	−1.43762e6	−0.321997	−0.160999	+	0.986955i	$0.551472\pi$
$458$	−6.88564e6	−1.53384
$459$	416772.	0.0923352
$460$	5.40711e6	1.19144
$461$	2.55792e6	0.560577	0.280289	−	0.959916i	$-0.409570\pi$
$461$	2.55792e6	0.560577	0.280289	+	0.959916i	$0.409570\pi$
$462$	1.09845e6	0.239427
$463$	−2.62001e6	−0.568002	−0.284001	−	0.958824i	$-0.591662\pi$
$463$	−2.62001e6	−0.568002	−0.284001	+	0.958824i	$0.591662\pi$
$464$	112648.	0.0242900
$465$	697844.	0.149667
$466$	−6.81720e6	−1.45426
$467$	−6.52402e6	−1.38428	−0.692139	−	0.721764i	$-0.743332\pi$
$467$	−6.52402e6	−1.38428	−0.692139	+	0.721764i	$0.743332\pi$
$468$	−7.27743e6	−1.53590
$469$	−4.91513e6	−1.03182
$470$	5.71022e6	1.19236
$471$	2.24791e6	0.466902
$472$	−1.67796e6	−0.346678
$473$	−307231.	−0.0631411
$474$	−753439.	−0.154029
$475$	225625.	0.0458831
$476$	2.53345e6	0.512502
$477$	3.56572e6	0.717549
$478$	5.66867e6	1.13478
$479$	−4.55714e6	−0.907514	−0.453757	−	0.891126i	$-0.649917\pi$
$479$	−4.55714e6	−0.907514	−0.453757	+	0.891126i	$0.649917\pi$
$480$	−508212.	−0.100680
$481$	7.40077e6	1.45853
$482$	−4.27665e6	−0.838467
$483$	3.84349e6	0.749649
$484$	802681.	0.155750
$485$	1.40721e6	0.271646
$486$	−6.43405e6	−1.23565
$487$	6.81417e6	1.30194	0.650969	−	0.759104i	$-0.274363\pi$
$487$	6.81417e6	1.30194	0.650969	+	0.759104i	$0.274363\pi$
$488$	8.57645e6	1.63026
$489$	1.37533e6	0.260097
$490$	7.84114e6	1.47533
$491$	−8.89507e6	−1.66512	−0.832560	−	0.553935i	$-0.813126\pi$
$491$	−8.89507e6	−1.66512	−0.832560	+	0.553935i	$0.813126\pi$
$492$	1.08956e6	0.202927
$493$	−101936.	−0.0188890
$494$	−1.99165e6	−0.367194
$495$	678182.	0.124404
$496$	−1.46312e6	−0.267040
$497$	8.20666e6	1.49031
$498$	−1.88108e6	−0.339886
$499$	−6.13597e6	−1.10314	−0.551572	−	0.834128i	$-0.685972\pi$
$499$	−6.13597e6	−1.10314	−0.551572	+	0.834128i	$0.685972\pi$
$500$	−856628.	−0.153238
$501$	653268.	0.116278
$502$	1.41571e7	2.50736
$503$	−3.67944e6	−0.648428	−0.324214	−	0.945984i	$-0.605100\pi$
$503$	−3.67944e6	−0.648428	−0.324214	+	0.945984i	$0.605100\pi$
$504$	−1.07113e7	−1.87830
$505$	−3.07831e6	−0.537136
$506$	4.44794e6	0.772294
$507$	−89885.0	−0.0155298
$508$	−7.54387e6	−1.29699
$509$	4.99063e6	0.853809	0.426904	−	0.904297i	$-0.359604\pi$
$509$	4.99063e6	0.853809	0.426904	+	0.904297i	$0.359604\pi$
$510$	−207809.	−0.0353784
$511$	−8.36242e6	−1.41671
$512$	2.61256e6	0.440444
$513$	−731426.	−0.122709
$514$	3.38167e6	0.564577
$515$	−1.27265e6	−0.211442
$516$	−603697.	−0.0998148
$517$	2.96604e6	0.488035
$518$	2.61648e7	4.28443
$519$	1.17333e6	0.191206
$520$	3.14804e6	0.510543
$521$	−1.05333e7	−1.70008	−0.850038	−	0.526721i	$-0.823421\pi$
$521$	−1.05333e7	−1.70008	−0.850038	+	0.526721i	$0.823421\pi$
$522$	1.03522e6	0.166286
$523$	−5.15783e6	−0.824542	−0.412271	−	0.911061i	$-0.635264\pi$
$523$	−5.15783e6	−0.824542	−0.412271	+	0.911061i	$0.635264\pi$
$524$	−8.00159e6	−1.27306
$525$	−608910.	−0.0964172
$526$	7.13315e6	1.12413
$527$	1.32400e6	0.207663
$528$	119284.	0.0186208
$529$	9.12712e6	1.41806
$530$	−3.70499e6	−0.572924
$531$	−1.76883e6	−0.272239
$532$	−4.44616e6	−0.681092
$533$	2.71331e6	0.413695
$534$	−2.76774e6	−0.420023
$535$	1.04079e6	0.157209
$536$	−4.65313e6	−0.699573
$537$	−3.44975e6	−0.516240
$538$	−1.12189e7	−1.67107
$539$	4.07291e6	0.603855
$540$	2.77700e6	0.409818
$541$	4.11448e6	0.604397	0.302198	−	0.953245i	$-0.402279\pi$
$541$	4.11448e6	0.604397	0.302198	+	0.953245i	$0.402279\pi$
$542$	−6.84039e6	−1.00019
$543$	2.65530e6	0.386468
$544$	−964214.	−0.139694
$545$	−2.85665e6	−0.411970
$546$	5.37500e6	0.771609
$547$	5.75475e6	0.822353	0.411177	−	0.911556i	$-0.365118\pi$
$547$	5.75475e6	0.822353	0.411177	+	0.911556i	$0.365118\pi$
$548$	3.85668e6	0.548608
$549$	9.04092e6	1.28021
$550$	−704670.	−0.0993297
$551$	178895.	0.0251027
$552$	3.63861e6	0.508263
$553$	−4.18857e6	−0.582442
$554$	3.63002e6	0.502498
$555$	−1.35519e6	−0.186753
$556$	1.11071e6	0.152375
$557$	−6.75142e6	−0.922055	−0.461028	−	0.887386i	$-0.652519\pi$
$557$	−6.75142e6	−0.922055	−0.461028	+	0.887386i	$0.652519\pi$
$558$	−1.34460e7	−1.82813
$559$	−1.50337e6	−0.203487
$560$	1.27666e6	0.172031
$561$	−107942.	−0.0144804
$562$	1.10350e7	1.47377
$563$	−295455.	−0.0392844	−0.0196422	−	0.999807i	$-0.506253\pi$
$563$	−295455.	−0.0392844	−0.0196422	+	0.999807i	$0.506253\pi$
$564$	5.82816e6	0.771497
$565$	−2.72416e6	−0.359013
$566$	−1.61890e7	−2.12412
$567$	−1.02647e7	−1.34087
$568$	7.76921e6	1.01043
$569$	−1.24235e7	−1.60866	−0.804329	−	0.594184i	$-0.797475\pi$
$569$	−1.24235e7	−1.60866	−0.804329	+	0.594184i	$0.797475\pi$
$570$	364699.	0.0470162
$571$	2.87412e6	0.368905	0.184453	−	0.982841i	$-0.440949\pi$
$571$	2.87412e6	0.368905	0.184453	+	0.982841i	$0.440949\pi$
$572$	3.92774e6	0.501941
$573$	949721.	0.120840
$574$	9.59266e6	1.21523
$575$	−2.46566e6	−0.311002
$576$	1.14230e7	1.43457
$577$	1.26309e6	0.157942	0.0789708	−	0.996877i	$-0.474837\pi$
$577$	1.26309e6	0.157942	0.0789708	+	0.996877i	$0.474837\pi$
$578$	1.28359e7	1.59811
$579$	−3.02791e6	−0.375358
$580$	−679209.	−0.0838366
$581$	−1.04574e7	−1.28524
$582$	2.27460e6	0.278354
$583$	−1.92447e6	−0.234499
$584$	−7.91666e6	−0.960527
$585$	3.31853e6	0.400919
$586$	2.35694e7	2.83533
$587$	−9.21152e6	−1.10341	−0.551704	−	0.834040i	$-0.686022\pi$
$587$	−9.21152e6	−1.10341	−0.551704	+	0.834040i	$0.686022\pi$
$588$	8.00311e6	0.954587
$589$	−2.32358e6	−0.275975
$590$	1.83792e6	0.217368
$591$	2.84010e6	0.334476
$592$	2.84133e6	0.333210
$593$	−1.57436e7	−1.83852	−0.919259	−	0.393654i	$-0.871211\pi$
$593$	−1.57436e7	−1.83852	−0.919259	+	0.393654i	$0.871211\pi$
$594$	2.28438e6	0.265646
$595$	−1.15526e6	−0.133779
$596$	−2.07784e7	−2.39606
$597$	2.04930e6	0.235326
$598$	2.17650e7	2.48889
$599$	−8.42338e6	−0.959223	−0.479611	−	0.877481i	$-0.659222\pi$
$599$	−8.42338e6	−0.959223	−0.479611	+	0.877481i	$0.659222\pi$
$600$	−576452.	−0.0653709
$601$	9.03668e6	1.02052	0.510261	−	0.860019i	$-0.329549\pi$
$601$	9.03668e6	1.02052	0.510261	+	0.860019i	$0.329549\pi$
$602$	−5.31503e6	−0.597743
$603$	−4.90513e6	−0.549360
$604$	−4.40054e6	−0.490811
$605$	−366025.	−0.0406558
$606$	−4.97577e6	−0.550400
$607$	1.61490e7	1.77899	0.889497	−	0.456941i	$-0.151055\pi$
$607$	1.61490e7	1.77899	0.889497	+	0.456941i	$0.151055\pi$
$608$	1.69217e6	0.185646
$609$	−482797.	−0.0527499
$610$	−9.39404e6	−1.02218
$611$	1.45137e7	1.57280
$612$	2.52830e6	0.272866
$613$	431917.	0.0464247	0.0232123	−	0.999731i	$-0.492611\pi$
$613$	431917.	0.0464247	0.0232123	+	0.999731i	$0.492611\pi$
$614$	−9.25218e6	−0.990429
$615$	−496845.	−0.0529704
$616$	5.78104e6	0.613839
$617$	5.22901e6	0.552976	0.276488	−	0.961017i	$-0.410829\pi$
$617$	5.22901e6	0.552976	0.276488	+	0.961017i	$0.410829\pi$
$618$	−2.05710e6	−0.216663
$619$	8.09877e6	0.849557	0.424779	−	0.905297i	$-0.360352\pi$
$619$	8.09877e6	0.849557	0.424779	+	0.905297i	$0.360352\pi$
$620$	8.82191e6	0.921687
$621$	7.99312e6	0.831740
$622$	−1.78547e7	−1.85044
$623$	−1.53866e7	−1.58827
$624$	583691.	0.0600098
$625$	390625.	0.0400000
$626$	−1.19301e7	−1.21677
$627$	189435.	0.0192438
$628$	2.84173e7	2.87530
$629$	−2.57115e6	−0.259120
$630$	1.17324e7	1.17770
$631$	5.82945e6	0.582846	0.291423	−	0.956594i	$-0.405871\pi$
$631$	5.82945e6	0.582846	0.291423	+	0.956594i	$0.405871\pi$
$632$	−3.96529e6	−0.394896
$633$	−3.73437e6	−0.370431
$634$	−7.52849e6	−0.743849
$635$	3.44003e6	0.338554
$636$	−3.78152e6	−0.370701
$637$	1.99299e7	1.94606
$638$	−558724.	−0.0543433
$639$	8.18996e6	0.793469
$640$	−8.11915e6	−0.783539
$641$	−1.98484e6	−0.190801	−0.0954007	−	0.995439i	$-0.530413\pi$
$641$	−1.98484e6	−0.190801	−0.0954007	+	0.995439i	$0.530413\pi$
$642$	1.68233e6	0.161091
$643$	1.49175e7	1.42288	0.711442	−	0.702744i	$-0.248042\pi$
$643$	1.49175e7	1.42288	0.711442	+	0.702744i	$0.248042\pi$
$644$	4.85882e7	4.61653
$645$	275288.	0.0260548
$646$	691932.	0.0652352
$647$	−1.68762e7	−1.58494	−0.792471	−	0.609909i	$-0.791206\pi$
$647$	−1.68762e7	−1.58494	−0.792471	+	0.609909i	$0.791206\pi$
$648$	−9.71751e6	−0.909112
$649$	954666.	0.0889692
$650$	−3.44815e6	−0.320112
$651$	6.27081e6	0.579924
$652$	1.73865e7	1.60175
$653$	1.08107e7	0.992138	0.496069	−	0.868283i	$-0.334776\pi$
$653$	1.08107e7	0.992138	0.496069	+	0.868283i	$0.334776\pi$
$654$	−4.61748e6	−0.422144
$655$	3.64875e6	0.332308
$656$	1.04170e6	0.0945114
$657$	−8.34540e6	−0.754282
$658$	5.13119e7	4.62012
$659$	1.21970e7	1.09405	0.547026	−	0.837116i	$-0.315760\pi$
$659$	1.21970e7	1.09405	0.547026	+	0.837116i	$0.315760\pi$
$660$	−719225.	−0.0642695
$661$	−4.63457e6	−0.412578	−0.206289	−	0.978491i	$-0.566139\pi$
$661$	−4.63457e6	−0.412578	−0.206289	+	0.978491i	$0.566139\pi$
$662$	5.43702e6	0.482187
$663$	−528188.	−0.0466665
$664$	−9.89998e6	−0.871394
$665$	2.02746e6	0.177786
$666$	2.61115e7	2.28111
$667$	−1.95499e6	−0.170149
$668$	8.25840e6	0.716069
$669$	−634832.	−0.0548395
$670$	5.09671e6	0.438634
$671$	−4.87952e6	−0.418380
$672$	−4.56679e6	−0.390110
$673$	3.19108e6	0.271582	0.135791	−	0.990738i	$-0.456642\pi$
$673$	3.19108e6	0.271582	0.135791	+	0.990738i	$0.456642\pi$
$674$	1.46624e6	0.124324
$675$	−1.26632e6	−0.106975
$676$	−1.13630e6	−0.0956368
$677$	−6.00915e6	−0.503897	−0.251948	−	0.967741i	$-0.581071\pi$
$677$	−6.00915e6	−0.503897	−0.251948	+	0.967741i	$0.581071\pi$
$678$	−4.40331e6	−0.367879
$679$	1.26451e7	1.05256
$680$	−1.09368e6	−0.0907024
$681$	−190802.	−0.0157658
$682$	7.25699e6	0.597442
$683$	−1.92899e7	−1.58226	−0.791130	−	0.611649i	$-0.790507\pi$
$683$	−1.92899e7	−1.58226	−0.791130	+	0.611649i	$0.790507\pi$
$684$	−4.43711e6	−0.362627
$685$	−1.75866e6	−0.143204
$686$	3.52787e7	2.86222
$687$	3.20473e6	0.259059
$688$	−577179.	−0.0464878
$689$	−9.41699e6	−0.755725
$690$	−3.98548e6	−0.318683
$691$	6.85699e6	0.546309	0.273155	−	0.961970i	$-0.411933\pi$
$691$	6.85699e6	0.546309	0.273155	+	0.961970i	$0.411933\pi$
$692$	1.48329e7	1.17750
$693$	6.09413e6	0.482035
$694$	2.36524e7	1.86413
$695$	−506488.	−0.0397747
$696$	−457061.	−0.0357644
$697$	−942647.	−0.0734966
$698$	1.80984e7	1.40606
$699$	3.17288e6	0.245618
$700$	−7.69764e6	−0.593762
$701$	1.70356e7	1.30937	0.654685	−	0.755902i	$-0.272801\pi$
$701$	1.70356e7	1.30937	0.654685	+	0.755902i	$0.272801\pi$
$702$	1.11781e7	0.856103
$703$	4.51231e6	0.344358
$704$	−6.16515e6	−0.468826
$705$	−2.65766e6	−0.201385
$706$	−1.94774e7	−1.47068
$707$	−2.76616e7	−2.08127
$708$	1.87588e6	0.140644
$709$	−1.41270e6	−0.105544	−0.0527722	−	0.998607i	$-0.516806\pi$
$709$	−1.41270e6	−0.105544	−0.0527722	+	0.998607i	$0.516806\pi$
$710$	−8.50984e6	−0.633542
$711$	−4.18004e6	−0.310104
$712$	−1.45664e7	−1.07685
$713$	2.53924e7	1.87060
$714$	−1.86736e6	−0.137083
$715$	−1.79106e6	−0.131022
$716$	−4.36106e7	−3.17914
$717$	−2.63833e6	−0.191660
$718$	−1.11454e7	−0.806838
$719$	−2.13739e7	−1.54192	−0.770961	−	0.636882i	$-0.780224\pi$
$719$	−2.13739e7	−1.54192	−0.770961	+	0.636882i	$0.780224\pi$
$720$	1.27406e6	0.0915925
$721$	−1.14360e7	−0.819286
$722$	−1.21432e6	−0.0866945
$723$	1.99045e6	0.141614
$724$	3.35674e7	2.37997
$725$	309722.	0.0218840
$726$	−591641.	−0.0416598
$727$	−4.29645e6	−0.301491	−0.150745	−	0.988573i	$-0.548167\pi$
$727$	−4.29645e6	−0.301491	−0.150745	+	0.988573i	$0.548167\pi$
$728$	2.82883e7	1.97823
$729$	−8.10859e6	−0.565101
$730$	8.67135e6	0.602254
$731$	522295.	0.0361511
$732$	−9.58808e6	−0.661384
$733$	−1.09094e7	−0.749963	−0.374981	−	0.927032i	$-0.622351\pi$
$733$	−1.09094e7	−0.749963	−0.374981	+	0.927032i	$0.622351\pi$
$734$	−4.47351e7	−3.06484
$735$	−3.64944e6	−0.249177
$736$	−1.84923e7	−1.25834
$737$	2.64737e6	0.179534
$738$	9.57314e6	0.647014
$739$	7.39315e6	0.497987	0.248994	−	0.968505i	$-0.419900\pi$
$739$	7.39315e6	0.497987	0.248994	+	0.968505i	$0.419900\pi$
$740$	−1.71318e7	−1.15007
$741$	926958.	0.0620176
$742$	−3.32929e7	−2.21995
$743$	1.80553e7	1.19987	0.599934	−	0.800049i	$-0.295193\pi$
$743$	1.80553e7	1.19987	0.599934	+	0.800049i	$0.295193\pi$
$744$	5.93654e6	0.393189
$745$	9.47503e6	0.625446
$746$	4.78899e7	3.15062
$747$	−1.04361e7	−0.684287
$748$	−1.36456e6	−0.0891742
$749$	9.35250e6	0.609148
$750$	631405.	0.0409878
$751$	−1.48639e7	−0.961687	−0.480844	−	0.876806i	$-0.659670\pi$
$751$	−1.48639e7	−0.961687	−0.480844	+	0.876806i	$0.659670\pi$
$752$	5.57215e6	0.359317
$753$	−6.58905e6	−0.423483
$754$	−2.73399e6	−0.175133
$755$	2.00666e6	0.128117
$756$	2.49540e7	1.58795
$757$	7.68161e6	0.487206	0.243603	−	0.969875i	$-0.421671\pi$
$757$	7.68161e6	0.487206	0.243603	+	0.969875i	$0.421671\pi$
$758$	1.70920e7	1.08049
$759$	−2.07017e6	−0.130437
$760$	1.91939e6	0.120539
$761$	5.53106e6	0.346215	0.173108	−	0.984903i	$-0.444619\pi$
$761$	5.53106e6	0.346215	0.173108	+	0.984903i	$0.444619\pi$
$762$	5.56045e6	0.346915
$763$	−2.56698e7	−1.59629
$764$	1.20061e7	0.744161
$765$	−1.15291e6	−0.0712267
$766$	−2.82651e7	−1.74052
$767$	4.67145e6	0.286723
$768$	−6.05285e6	−0.370303
$769$	−1.41379e7	−0.862124	−0.431062	−	0.902322i	$-0.641861\pi$
$769$	−1.41379e7	−0.862124	−0.431062	+	0.902322i	$0.641861\pi$
$770$	−6.33215e6	−0.384879
$771$	−1.57390e6	−0.0953547
$772$	−3.82778e7	−2.31155
$773$	7.85248e6	0.472670	0.236335	−	0.971672i	$-0.424054\pi$
$773$	7.85248e6	0.472670	0.236335	+	0.971672i	$0.424054\pi$
$774$	−5.30421e6	−0.318250
$775$	−4.02282e6	−0.240589
$776$	1.19711e7	0.713639
$777$	−1.21777e7	−0.723622
$778$	−2.10986e7	−1.24970
$779$	1.65432e6	0.0976735
$780$	−3.51937e6	−0.207123
$781$	−4.42025e6	−0.259310
$782$	−7.56152e6	−0.442173
$783$	−1.00405e6	−0.0585262
$784$	7.65155e6	0.444590
$785$	−1.29584e7	−0.750544
$786$	5.89783e6	0.340515
$787$	1.32855e7	0.764612	0.382306	−	0.924036i	$-0.375130\pi$
$787$	1.32855e7	0.764612	0.382306	+	0.924036i	$0.375130\pi$
$788$	3.59036e7	2.05979
$789$	−3.31993e6	−0.189861
$790$	4.34331e6	0.247601
$791$	−2.44792e7	−1.39109
$792$	5.76928e6	0.326820
$793$	−2.38769e7	−1.34832
$794$	5.24611e7	2.95315
$795$	1.72438e6	0.0967645
$796$	2.59066e7	1.44920
$797$	−1.07339e7	−0.598568	−0.299284	−	0.954164i	$-0.596748\pi$
$797$	−1.07339e7	−0.598568	−0.299284	+	0.954164i	$0.596748\pi$
$798$	3.27718e6	0.182177
$799$	−5.04229e6	−0.279422
$800$	2.92966e6	0.161843
$801$	−1.53553e7	−0.845625
$802$	7.65270e6	0.420125
$803$	4.50414e6	0.246503
$804$	5.20198e6	0.283811
$805$	−2.21564e7	−1.20506
$806$	3.55105e7	1.92539
$807$	5.22153e6	0.282237
$808$	−2.61871e7	−1.41110
$809$	−1.79240e7	−0.962858	−0.481429	−	0.876485i	$-0.659882\pi$
$809$	−1.79240e7	−0.962858	−0.481429	+	0.876485i	$0.659882\pi$
$810$	1.06439e7	0.570016
$811$	2.23418e7	1.19280	0.596398	−	0.802689i	$-0.296598\pi$
$811$	2.23418e7	1.19280	0.596398	+	0.802689i	$0.296598\pi$
$812$	−6.10336e6	−0.324847
$813$	3.18367e6	0.168928
$814$	−1.40928e7	−0.745480
$815$	−7.92830e6	−0.418106
$816$	−202784.	−0.0106613
$817$	−916615.	−0.0480432
$818$	2.26591e7	1.18402
$819$	2.98203e7	1.55347
$820$	−6.28095e6	−0.326205
$821$	−2.08946e7	−1.08187	−0.540936	−	0.841064i	$-0.681930\pi$
$821$	−2.08946e7	−1.08187	−0.540936	+	0.841064i	$0.681930\pi$
$822$	−2.84269e6	−0.146740
$823$	1.15102e7	0.592358	0.296179	−	0.955132i	$-0.404288\pi$
$823$	1.15102e7	0.592358	0.296179	+	0.955132i	$0.404288\pi$
$824$	−1.08264e7	−0.555477
$825$	327969.	0.0167764
$826$	1.65155e7	0.842252
$827$	2.21024e7	1.12376	0.561882	−	0.827217i	$-0.310078\pi$
$827$	2.21024e7	1.12376	0.561882	+	0.827217i	$0.310078\pi$
$828$	4.84893e7	2.45793
$829$	1.47998e7	0.747944	0.373972	−	0.927440i	$-0.377996\pi$
$829$	1.47998e7	0.747944	0.373972	+	0.927440i	$0.377996\pi$
$830$	1.08438e7	0.546367
$831$	−1.68949e6	−0.0848699
$832$	−3.01678e7	−1.51090
$833$	−6.92396e6	−0.345734
$834$	−818685.	−0.0407569
$835$	−3.76586e6	−0.186917
$836$	2.39477e6	0.118508
$837$	1.30411e7	0.643428
$838$	5.95820e7	2.93093
$839$	−2.08995e7	−1.02502	−0.512508	−	0.858682i	$-0.671284\pi$
$839$	−2.08995e7	−1.02502	−0.512508	+	0.858682i	$0.671284\pi$
$840$	−5.17998e6	−0.253297
$841$	−2.02656e7	−0.988027
$842$	−5.64240e7	−2.74273
$843$	−5.13592e6	−0.248914
$844$	−4.72087e7	−2.28121
$845$	518155.	0.0249642
$846$	5.12075e7	2.45984
$847$	−3.28909e6	−0.157532
$848$	−3.61540e6	−0.172650
$849$	7.53474e6	0.358756
$850$	1.19794e6	0.0568707
$851$	−4.93111e7	−2.33411
$852$	−8.68562e6	−0.409923
$853$	1.24912e7	0.587802	0.293901	−	0.955836i	$-0.405046\pi$
$853$	1.24912e7	0.587802	0.293901	+	0.955836i	$0.405046\pi$
$854$	−8.44146e7	−3.96071
$855$	2.02334e6	0.0946570
$856$	8.85396e6	0.413003
$857$	3.99377e7	1.85751	0.928754	−	0.370696i	$-0.120881\pi$
$857$	3.99377e7	1.85751	0.928754	+	0.370696i	$0.120881\pi$
$858$	−2.89507e6	−0.134258
$859$	−658506.	−0.0304493	−0.0152246	−	0.999884i	$-0.504846\pi$
$859$	−658506.	−0.0304493	−0.0152246	+	0.999884i	$0.504846\pi$
$860$	3.48010e6	0.160452
$861$	−4.46464e6	−0.205248
$862$	2.16902e7	0.994250
$863$	1.16036e7	0.530355	0.265178	−	0.964200i	$-0.414569\pi$
$863$	1.16036e7	0.530355	0.265178	+	0.964200i	$0.414569\pi$
$864$	−9.49732e6	−0.432829
$865$	−6.76384e6	−0.307364
$866$	−2.58614e6	−0.117181
$867$	−5.97411e6	−0.269914
$868$	7.92735e7	3.57132
$869$	2.25603e6	0.101344
$870$	500633.	0.0224244
$871$	1.29543e7	0.578588
$872$	−2.43015e7	−1.08228
$873$	1.26194e7	0.560406
$874$	1.32703e7	0.587627
$875$	3.51015e6	0.154991
$876$	8.85046e6	0.389678
$877$	9.17274e6	0.402717	0.201359	−	0.979518i	$-0.435464\pi$
$877$	9.17274e6	0.402717	0.201359	+	0.979518i	$0.435464\pi$
$878$	6.87011e7	3.00765
$879$	−1.09697e7	−0.478876
$880$	−687632.	−0.0299329
$881$	−1.08491e7	−0.470928	−0.235464	−	0.971883i	$-0.575661\pi$
$881$	−1.08491e7	−0.470928	−0.235464	+	0.971883i	$0.575661\pi$
$882$	7.03170e7	3.04361
$883$	−1.80078e7	−0.777248	−0.388624	−	0.921396i	$-0.627049\pi$
$883$	−1.80078e7	−0.777248	−0.388624	+	0.921396i	$0.627049\pi$
$884$	−6.67718e6	−0.287384
$885$	−855409.	−0.0367126
$886$	1.20438e7	0.515440
$887$	−4.21708e7	−1.79971	−0.899856	−	0.436188i	$-0.856328\pi$
$887$	−4.21708e7	−1.79971	−0.899856	+	0.436188i	$0.856328\pi$
$888$	−1.15285e7	−0.490616
$889$	3.09120e7	1.31182
$890$	1.59551e7	0.675186
$891$	5.52872e6	0.233309
$892$	−8.02534e6	−0.337716
$893$	8.84910e6	0.371339
$894$	1.53154e7	0.640892
$895$	1.98866e7	0.829856
$896$	−7.29585e7	−3.03603
$897$	−1.01299e7	−0.420363
$898$	5.17703e7	2.14235
$899$	−3.18964e6	−0.131626
$900$	−7.68197e6	−0.316131
$901$	3.27162e6	0.134261
$902$	−5.16677e6	−0.211448
$903$	2.47373e6	0.100956
$904$	−2.31743e7	−0.943162
$905$	−1.53069e7	−0.621247
$906$	3.24356e6	0.131281
$907$	6.84019e6	0.276089	0.138045	−	0.990426i	$-0.455918\pi$
$907$	6.84019e6	0.276089	0.138045	+	0.990426i	$0.455918\pi$
$908$	−2.41206e6	−0.0970896
$909$	−2.76053e7	−1.10811
$910$	−3.09850e7	−1.24036
$911$	−3.66998e7	−1.46510	−0.732550	−	0.680713i	$-0.761670\pi$
$911$	−3.66998e7	−1.46510	−0.732550	+	0.680713i	$0.761670\pi$
$912$	355881.	0.0141683
$913$	5.63254e6	0.223629
$914$	1.33956e7	0.530393
$915$	4.37220e6	0.172642
$916$	4.05131e7	1.59535
$917$	3.27876e7	1.28762
$918$	−3.88346e6	−0.152094
$919$	3.05216e7	1.19212	0.596058	−	0.802941i	$-0.296733\pi$
$919$	3.05216e7	1.19212	0.596058	+	0.802941i	$0.296733\pi$
$920$	−2.09753e7	−0.817032
$921$	4.30617e6	0.167279
$922$	−2.38346e7	−0.923381
$923$	−2.16295e7	−0.835685
$924$	−6.46294e6	−0.249029
$925$	7.81217e6	0.300204
$926$	2.44131e7	0.935611
$927$	−1.14127e7	−0.436204
$928$	2.32289e6	0.0885441
$929$	2.72547e7	1.03610	0.518051	−	0.855350i	$-0.326658\pi$
$929$	2.72547e7	1.03610	0.518051	+	0.855350i	$0.326658\pi$
$930$	−6.50247e6	−0.246531
$931$	1.21514e7	0.459465
$932$	4.01105e7	1.51258
$933$	8.30996e6	0.312532
$934$	6.07905e7	2.28018
$935$	622245.	0.0232773
$936$	2.82307e7	1.05325
$937$	3.44249e7	1.28092	0.640462	−	0.767990i	$-0.278743\pi$
$937$	3.44249e7	1.28092	0.640462	+	0.767990i	$0.278743\pi$
$938$	4.57989e7	1.69961
$939$	5.55252e6	0.205507
$940$	−3.35973e7	−1.24018
$941$	−4.94711e7	−1.82128	−0.910642	−	0.413196i	$-0.864413\pi$
$941$	−4.94711e7	−1.82128	−0.910642	+	0.413196i	$0.864413\pi$
$942$	−2.09459e7	−0.769079
$943$	−1.80787e7	−0.662045
$944$	1.79348e6	0.0655038
$945$	−1.13791e7	−0.414504
$946$	2.86276e6	0.104006
$947$	4.38567e7	1.58914	0.794568	−	0.607175i	$-0.207697\pi$
$947$	4.38567e7	1.58914	0.794568	+	0.607175i	$0.207697\pi$
$948$	4.43302e6	0.160206
$949$	2.20400e7	0.794413
$950$	−2.10236e6	−0.0755785
$951$	3.50393e6	0.125633
$952$	−9.82780e6	−0.351450
$953$	1.58004e7	0.563556	0.281778	−	0.959480i	$-0.409076\pi$
$953$	1.58004e7	0.563556	0.281778	+	0.959480i	$0.409076\pi$
$954$	−3.32252e7	−1.18194
$955$	−5.47480e6	−0.194250
$956$	−3.33529e7	−1.18029
$957$	260043.	0.00917835
$958$	4.24632e7	1.49485
$959$	−1.58033e7	−0.554881
$960$	5.52415e6	0.193458
$961$	1.27996e7	0.447081
$962$	−6.89600e7	−2.40248
$963$	9.33347e6	0.324323
$964$	2.51626e7	0.872093
$965$	1.74548e7	0.603388
$966$	−3.58135e7	−1.23482
$967$	−1.54446e7	−0.531141	−0.265570	−	0.964091i	$-0.585560\pi$
$967$	−1.54446e7	−0.531141	−0.265570	+	0.964091i	$0.585560\pi$
$968$	−3.11377e6	−0.106806
$969$	−322040.	−0.0110180
$970$	−1.31123e7	−0.447454
$971$	4.86941e7	1.65740	0.828702	−	0.559691i	$-0.189080\pi$
$971$	4.86941e7	1.65740	0.828702	+	0.559691i	$0.189080\pi$
$972$	3.78561e7	1.28520
$973$	−4.55129e6	−0.154118
$974$	−6.34941e7	−2.14455
$975$	1.60484e6	0.0540656
$976$	−9.16690e6	−0.308033
$977$	−8.45452e6	−0.283369	−0.141685	−	0.989912i	$-0.545252\pi$
$977$	−8.45452e6	−0.283369	−0.141685	+	0.989912i	$0.545252\pi$
$978$	−1.28153e7	−0.428431
$979$	8.28750e6	0.276355
$980$	−4.61351e7	−1.53450
$981$	−2.56176e7	−0.849895
$982$	8.28838e7	2.74278
$983$	−3.55658e7	−1.17395	−0.586974	−	0.809605i	$-0.699681\pi$
$983$	−3.55658e7	−1.17395	−0.586974	+	0.809605i	$0.699681\pi$
$984$	−4.22665e6	−0.139158
$985$	−1.63722e7	−0.537669
$986$	949834.	0.0311140
$987$	−2.38817e7	−0.780319
$988$	1.17183e7	0.381920
$989$	1.00169e7	0.325643
$990$	−6.31926e6	−0.204917
$991$	404638.	0.0130883	0.00654414	−	0.999979i	$-0.497917\pi$
$991$	404638.	0.0130883	0.00654414	+	0.999979i	$0.497917\pi$
$992$	−3.01709e7	−0.973440
$993$	−2.53051e6	−0.0814394
$994$	−7.64693e7	−2.45483
$995$	−1.18135e7	−0.378287
$996$	1.10677e7	0.353517
$997$	−1.67674e7	−0.534229	−0.267114	−	0.963665i	$-0.586070\pi$
$997$	−1.67674e7	−0.534229	−0.267114	+	0.963665i	$0.586070\pi$
$998$	5.71747e7	1.81709
$999$	−2.53253e7	−0.802862

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.a.1.4	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.a.1.4	✓	35	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-9.31795 q^{2} +4.33678 q^{3} +54.8242 q^{4} -25.0000 q^{5} -40.4099 q^{6} -224.649 q^{7} -212.674 q^{8} -224.192 q^{9} +O(q^{10})\)	\(q-9.31795 q^{2} +4.33678 q^{3} +54.8242 q^{4} -25.0000 q^{5} -40.4099 q^{6} -224.649 q^{7} -212.674 q^{8} -224.192 q^{9} +232.949 q^{10} +121.000 q^{11} +237.760 q^{12} +592.087 q^{13} +2093.27 q^{14} -108.420 q^{15} +227.316 q^{16} -205.701 q^{17} +2089.01 q^{18} +361.000 q^{19} -1370.60 q^{20} -974.256 q^{21} -1127.47 q^{22} -3945.06 q^{23} -922.323 q^{24} +625.000 q^{25} -5517.03 q^{26} -2026.11 q^{27} -12316.2 q^{28} +495.555 q^{29} +1010.25 q^{30} -6436.51 q^{31} +4687.46 q^{32} +524.751 q^{33} +1916.71 q^{34} +5616.24 q^{35} -12291.2 q^{36} +12499.5 q^{37} -3363.78 q^{38} +2567.75 q^{39} +5316.86 q^{40} +4582.61 q^{41} +9078.06 q^{42} -2539.10 q^{43} +6633.72 q^{44} +5604.81 q^{45} +36759.8 q^{46} +24512.8 q^{47} +985.821 q^{48} +33660.4 q^{49} -5823.72 q^{50} -892.079 q^{51} +32460.7 q^{52} -15904.7 q^{53} +18879.2 q^{54} -3025.00 q^{55} +47777.2 q^{56} +1565.58 q^{57} -4617.55 q^{58} +7889.80 q^{59} -5944.01 q^{60} -40326.6 q^{61} +59975.1 q^{62} +50364.7 q^{63} -50951.6 q^{64} -14802.2 q^{65} -4889.60 q^{66} +21879.1 q^{67} -11277.4 q^{68} -17108.8 q^{69} -52331.8 q^{70} -36531.0 q^{71} +47680.0 q^{72} +37224.3 q^{73} -116469. q^{74} +2710.49 q^{75} +19791.5 q^{76} -27182.6 q^{77} -23926.2 q^{78} +18644.9 q^{79} -5682.91 q^{80} +45691.9 q^{81} -42700.6 q^{82} +46549.9 q^{83} -53412.8 q^{84} +5142.52 q^{85} +23659.2 q^{86} +2149.11 q^{87} -25733.6 q^{88} +68491.7 q^{89} -52225.3 q^{90} -133012. q^{91} -216284. q^{92} -27913.8 q^{93} -228409. q^{94} -9025.00 q^{95} +20328.5 q^{96} -56288.2 q^{97} -313646. q^{98} -27127.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more