LMFDB - Embedded newform 1045.6.a.b.1.8

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:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-7.00111 q^{2} -3.95422 q^{3} +17.0156 q^{4} +25.0000 q^{5} +27.6840 q^{6} -243.106 q^{7} +104.908 q^{8} -227.364 q^{9} +O(q^{10})$	\(q-7.00111 q^{2} -3.95422 q^{3} +17.0156 q^{4} +25.0000 q^{5} +27.6840 q^{6} -243.106 q^{7} +104.908 q^{8} -227.364 q^{9} -175.028 q^{10} -121.000 q^{11} -67.2834 q^{12} +1158.90 q^{13} +1702.02 q^{14} -98.8556 q^{15} -1278.97 q^{16} -2263.23 q^{17} +1591.80 q^{18} +361.000 q^{19} +425.389 q^{20} +961.297 q^{21} +847.135 q^{22} -955.519 q^{23} -414.828 q^{24} +625.000 q^{25} -8113.60 q^{26} +1859.92 q^{27} -4136.59 q^{28} -5186.00 q^{29} +692.099 q^{30} +5368.76 q^{31} +5597.16 q^{32} +478.461 q^{33} +15845.1 q^{34} -6077.66 q^{35} -3868.73 q^{36} +4322.08 q^{37} -2527.40 q^{38} -4582.56 q^{39} +2622.69 q^{40} -30.2311 q^{41} -6730.15 q^{42} +6409.05 q^{43} -2058.88 q^{44} -5684.10 q^{45} +6689.70 q^{46} -9534.10 q^{47} +5057.33 q^{48} +42293.7 q^{49} -4375.69 q^{50} +8949.30 q^{51} +19719.4 q^{52} +19713.1 q^{53} -13021.5 q^{54} -3025.00 q^{55} -25503.7 q^{56} -1427.47 q^{57} +36307.8 q^{58} -12007.3 q^{59} -1682.08 q^{60} +30076.7 q^{61} -37587.3 q^{62} +55273.7 q^{63} +1740.67 q^{64} +28972.5 q^{65} -3349.76 q^{66} -49701.5 q^{67} -38510.1 q^{68} +3778.34 q^{69} +42550.4 q^{70} -52641.0 q^{71} -23852.2 q^{72} +5904.26 q^{73} -30259.4 q^{74} -2471.39 q^{75} +6142.62 q^{76} +29415.9 q^{77} +32083.0 q^{78} +73177.0 q^{79} -31974.2 q^{80} +47894.9 q^{81} +211.651 q^{82} -10912.2 q^{83} +16357.0 q^{84} -56580.6 q^{85} -44870.5 q^{86} +20506.6 q^{87} -12693.8 q^{88} -99564.2 q^{89} +39795.0 q^{90} -281736. q^{91} -16258.7 q^{92} -21229.3 q^{93} +66749.3 q^{94} +9025.00 q^{95} -22132.4 q^{96} +61830.9 q^{97} -296103. q^{98} +27511.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) $ 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * 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 $

$2$	−7.00111	−1.23763	−0.618817	−	0.785535i	$-0.712388\pi$
$2$	−7.00111	−1.23763	−0.618817	+	0.785535i	$0.712388\pi$
$3$	−3.95422	−0.253664	−0.126832	−	0.991924i	$-0.540481\pi$
$3$	−3.95422	−0.253664	−0.126832	+	0.991924i	$0.540481\pi$
$4$	17.0156	0.531737
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	27.6840	0.313942
$7$	−243.106	−1.87522	−0.937608	−	0.347694i	$-0.886965\pi$
$7$	−243.106	−1.87522	−0.937608	+	0.347694i	$0.886965\pi$
$8$	104.908	0.579539
$9$	−227.364	−0.935655
$10$	−175.028	−0.553487
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−67.2834	−0.134882
$13$	1158.90	1.90190	0.950951	−	0.309341i	$-0.100108\pi$
$13$	1158.90	1.90190	0.950951	+	0.309341i	$0.100108\pi$
$14$	1702.02	2.32083
$15$	−98.8556	−0.113442
$16$	−1278.97	−1.24899
$17$	−2263.23	−1.89935	−0.949676	−	0.313234i	$-0.898588\pi$
$17$	−2263.23	−1.89935	−0.949676	+	0.313234i	$0.898588\pi$
$18$	1591.80	1.15800
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	425.389	0.237800
$21$	961.297	0.475674
$22$	847.135	0.373161
$23$	−955.519	−0.376634	−0.188317	−	0.982108i	$-0.560303\pi$
$23$	−955.519	−0.376634	−0.188317	+	0.982108i	$0.560303\pi$
$24$	−414.828	−0.147008
$25$	625.000	0.200000
$26$	−8113.60	−2.35386
$27$	1859.92	0.491005
$28$	−4136.59	−0.997121
$29$	−5186.00	−1.14508	−0.572542	−	0.819875i	$-0.694043\pi$
$29$	−5186.00	−1.14508	−0.572542	+	0.819875i	$0.694043\pi$
$30$	692.099	0.140399
$31$	5368.76	1.00339	0.501695	−	0.865045i	$-0.332710\pi$
$31$	5368.76	1.00339	0.501695	+	0.865045i	$0.332710\pi$
$32$	5597.16	0.966257
$33$	478.461	0.0764824
$34$	15845.1	2.35070
$35$	−6077.66	−0.838622
$36$	−3868.73	−0.497522
$37$	4322.08	0.519025	0.259513	−	0.965740i	$-0.416438\pi$
$37$	4322.08	0.519025	0.259513	+	0.965740i	$0.416438\pi$
$38$	−2527.40	−0.283933
$39$	−4582.56	−0.482443
$40$	2622.69	0.259178
$41$	−30.2311	−0.00280862	−0.00140431	−	0.999999i	$-0.500447\pi$
$41$	−30.2311	−0.00280862	−0.00140431	+	0.999999i	$0.500447\pi$
$42$	−6730.15	−0.588710
$43$	6409.05	0.528594	0.264297	−	0.964441i	$-0.414860\pi$
$43$	6409.05	0.528594	0.264297	+	0.964441i	$0.414860\pi$
$44$	−2058.88	−0.160325
$45$	−5684.10	−0.418438
$46$	6689.70	0.466135
$47$	−9534.10	−0.629557	−0.314779	−	0.949165i	$-0.601930\pi$
$47$	−9534.10	−0.629557	−0.314779	+	0.949165i	$0.601930\pi$
$48$	5057.33	0.316824
$49$	42293.7	2.51644
$50$	−4375.69	−0.247527
$51$	8949.30	0.481796
$52$	19719.4	1.01131
$53$	19713.1	0.963975	0.481988	−	0.876178i	$-0.339915\pi$
$53$	19713.1	0.963975	0.481988	+	0.876178i	$0.339915\pi$
$54$	−13021.5	−0.607684
$55$	−3025.00	−0.134840
$56$	−25503.7	−1.08676
$57$	−1427.47	−0.0581944
$58$	36307.8	1.41719
$59$	−12007.3	−0.449070	−0.224535	−	0.974466i	$-0.572086\pi$
$59$	−12007.3	−0.449070	−0.224535	+	0.974466i	$0.572086\pi$
$60$	−1682.08	−0.0603211
$61$	30076.7	1.03492	0.517458	−	0.855709i	$-0.326878\pi$
$61$	30076.7	1.03492	0.517458	+	0.855709i	$0.326878\pi$
$62$	−37587.3	−1.24183
$63$	55273.7	1.75456
$64$	1740.67	0.0531212
$65$	28972.5	0.850557
$66$	−3349.76	−0.0946572
$67$	−49701.5	−1.35264	−0.676321	−	0.736607i	$-0.736427\pi$
$67$	−49701.5	−1.35264	−0.676321	+	0.736607i	$0.736427\pi$
$68$	−38510.1	−1.00995
$69$	3778.34	0.0955384
$70$	42550.4	1.03791
$71$	−52641.0	−1.23930	−0.619652	−	0.784876i	$-0.712726\pi$
$71$	−52641.0	−1.23930	−0.619652	+	0.784876i	$0.712726\pi$
$72$	−23852.2	−0.542248
$73$	5904.26	0.129676	0.0648379	−	0.997896i	$-0.479347\pi$
$73$	5904.26	0.129676	0.0648379	+	0.997896i	$0.479347\pi$
$74$	−30259.4	−0.642363
$75$	−2471.39	−0.0507327
$76$	6142.62	0.121989
$77$	29415.9	0.565399
$78$	32083.0	0.597088
$79$	73177.0	1.31919	0.659595	−	0.751622i	$-0.270728\pi$
$79$	73177.0	1.31919	0.659595	+	0.751622i	$0.270728\pi$
$80$	−31974.2	−0.558567
$81$	47894.9	0.811105
$82$	211.651	0.00347605
$83$	−10912.2	−0.173867	−0.0869335	−	0.996214i	$-0.527707\pi$
$83$	−10912.2	−0.173867	−0.0869335	+	0.996214i	$0.527707\pi$
$84$	16357.0	0.252933
$85$	−56580.6	−0.849416
$86$	−44870.5	−0.654206
$87$	20506.6	0.290466
$88$	−12693.8	−0.174737
$89$	−99564.2	−1.33238	−0.666190	−	0.745782i	$-0.732076\pi$
$89$	−99564.2	−1.33238	−0.666190	+	0.745782i	$0.732076\pi$
$90$	39795.0	0.517872
$91$	−281736.	−3.56648
$92$	−16258.7	−0.200270
$93$	−21229.3	−0.254523
$94$	66749.3	0.779161
$95$	9025.00	0.102598
$96$	−22132.4	−0.245104
$97$	61830.9	0.667232	0.333616	−	0.942709i	$-0.391731\pi$
$97$	61830.9	0.667232	0.333616	+	0.942709i	$0.391731\pi$
$98$	−296103.	−3.11443
$99$	27511.1	0.282111
$100$	10634.7	0.106347
$101$	−15939.5	−0.155478	−0.0777392	−	0.996974i	$-0.524770\pi$
$101$	−15939.5	−0.155478	−0.0777392	+	0.996974i	$0.524770\pi$
$102$	−62655.0	−0.596287
$103$	−40454.9	−0.375732	−0.187866	−	0.982195i	$-0.560157\pi$
$103$	−40454.9	−0.375732	−0.187866	+	0.982195i	$0.560157\pi$
$104$	121578.	1.10223
$105$	24032.4	0.212728
$106$	−138014.	−1.19305
$107$	67949.9	0.573759	0.286879	−	0.957967i	$-0.407382\pi$
$107$	67949.9	0.573759	0.286879	+	0.957967i	$0.407382\pi$
$108$	31647.7	0.261085
$109$	110862.	0.893748	0.446874	−	0.894597i	$-0.352537\pi$
$109$	110862.	0.893748	0.446874	+	0.894597i	$0.352537\pi$
$110$	21178.4	0.166882
$111$	−17090.5	−0.131658
$112$	310926.	2.34213
$113$	215941.	1.59089	0.795445	−	0.606026i	$-0.207237\pi$
$113$	215941.	1.59089	0.795445	+	0.606026i	$0.207237\pi$
$114$	9993.91	0.0720233
$115$	−23888.0	−0.168436
$116$	−88242.7	−0.608883
$117$	−263493.	−1.77952
$118$	84064.2	0.555784
$119$	550205.	3.56170
$120$	−10370.7	−0.0657439
$121$	14641.0	0.0909091
$122$	−210570.	−1.28085
$123$	119.540	0.000712446 0
$124$	91352.4	0.533539
$125$	15625.0	0.0894427
$126$	−386977.	−2.17150
$127$	229470.	1.26245	0.631227	−	0.775598i	$-0.282552\pi$
$127$	229470.	1.26245	0.631227	+	0.775598i	$0.282552\pi$
$128$	−191296.	−1.03200
$129$	−25342.8	−0.134085
$130$	−202840.	−1.05268
$131$	−17450.7	−0.0888451	−0.0444226	−	0.999013i	$-0.514145\pi$
$131$	−17450.7	−0.0888451	−0.0444226	+	0.999013i	$0.514145\pi$
$132$	8141.29	0.0406685
$133$	−87761.4	−0.430204
$134$	347966.	1.67407
$135$	46498.1	0.219584
$136$	−237430.	−1.10075
$137$	237762.	1.08228	0.541141	−	0.840932i	$-0.317993\pi$
$137$	237762.	1.08228	0.541141	+	0.840932i	$0.317993\pi$
$138$	−26452.6	−0.118241
$139$	−293602.	−1.28891	−0.644455	−	0.764642i	$-0.722916\pi$
$139$	−293602.	−1.28891	−0.644455	+	0.764642i	$0.722916\pi$
$140$	−103415.	−0.445926
$141$	37700.0	0.159696
$142$	368545.	1.53381
$143$	−140227.	−0.573445
$144$	290792.	1.16863
$145$	−129650.	−0.512097
$146$	−41336.4	−0.160491
$147$	−167239.	−0.638328
$148$	73542.7	0.275985
$149$	486597.	1.79558	0.897789	−	0.440427i	$-0.145173\pi$
$149$	486597.	1.79558	0.897789	+	0.440427i	$0.145173\pi$
$150$	17302.5	0.0627885
$151$	461583.	1.64743	0.823715	−	0.567004i	$-0.191898\pi$
$151$	461583.	1.64743	0.823715	+	0.567004i	$0.191898\pi$
$152$	37871.7	0.132955
$153$	514576.	1.77714
$154$	−205944.	−0.699757
$155$	134219.	0.448729
$156$	−77974.8	−0.256533
$157$	−42504.0	−0.137620	−0.0688099	−	0.997630i	$-0.521920\pi$
$157$	−42504.0	−0.137620	−0.0688099	+	0.997630i	$0.521920\pi$
$158$	−512321.	−1.63267
$159$	−77950.1	−0.244525
$160$	139929.	0.432123
$161$	232293.	0.706271
$162$	−335318.	−1.00385
$163$	42678.8	0.125818	0.0629090	−	0.998019i	$-0.479962\pi$
$163$	42678.8	0.125818	0.0629090	+	0.998019i	$0.479962\pi$
$164$	−514.399	−0.00149345
$165$	11961.5	0.0342040
$166$	76397.5	0.215184
$167$	−456212.	−1.26583	−0.632916	−	0.774221i	$-0.718142\pi$
$167$	−456212.	−1.26583	−0.632916	+	0.774221i	$0.718142\pi$
$168$	100847.	0.275671
$169$	971760.	2.61723
$170$	396127.	1.05127
$171$	−82078.4	−0.214654
$172$	109054.	0.281073
$173$	197780.	0.502420	0.251210	−	0.967933i	$-0.419172\pi$
$173$	197780.	0.502420	0.251210	+	0.967933i	$0.419172\pi$
$174$	−143569.	−0.359491
$175$	−151942.	−0.375043
$176$	154755.	0.376585
$177$	47479.4	0.113913
$178$	697060.	1.64900
$179$	831672.	1.94008	0.970040	−	0.242947i	$-0.0781141\pi$
$179$	831672.	1.94008	0.970040	+	0.242947i	$0.0781141\pi$
$180$	−96718.2	−0.222499
$181$	−226093.	−0.512968	−0.256484	−	0.966548i	$-0.582564\pi$
$181$	−226093.	−0.512968	−0.256484	+	0.966548i	$0.582564\pi$
$182$	1.97247e6	4.41399
$183$	−118930.	−0.262521
$184$	−100241.	−0.218274
$185$	108052.	0.232115
$186$	148628.	0.315007
$187$	273850.	0.572676
$188$	−162228.	−0.334759
$189$	−452160.	−0.920741
$190$	−63185.0	−0.126979
$191$	333452.	0.661379	0.330689	−	0.943740i	$-0.392719\pi$
$191$	333452.	0.661379	0.330689	+	0.943740i	$0.392719\pi$
$192$	−6883.01	−0.0134749
$193$	−831360.	−1.60656	−0.803278	−	0.595605i	$-0.796913\pi$
$193$	−831360.	−1.60656	−0.803278	+	0.595605i	$0.796913\pi$
$194$	−432885.	−0.825788
$195$	−114564.	−0.215755
$196$	719652.	1.33808
$197$	−979775.	−1.79871	−0.899354	−	0.437221i	$-0.855963\pi$
$197$	−979775.	−1.79871	−0.899354	+	0.437221i	$0.855963\pi$
$198$	−192608.	−0.349149
$199$	616022.	1.10272	0.551358	−	0.834269i	$-0.314110\pi$
$199$	616022.	1.10272	0.551358	+	0.834269i	$0.314110\pi$
$200$	65567.3	0.115908
$201$	196531.	0.343116
$202$	111594.	0.192425
$203$	1.26075e6	2.14728
$204$	152277.	0.256189
$205$	−755.776	−0.00125606
$206$	283230.	0.465019
$207$	217251.	0.352400
$208$	−1.48220e6	−2.37546
$209$	−43681.0	−0.0691714
$210$	−168254.	−0.263279
$211$	566973.	0.876710	0.438355	−	0.898802i	$-0.355561\pi$
$211$	566973.	0.876710	0.438355	+	0.898802i	$0.355561\pi$
$212$	335430.	0.512581
$213$	208154.	0.314366
$214$	−475725.	−0.710103
$215$	160226.	0.236394
$216$	195120.	0.284556
$217$	−1.30518e6	−1.88157
$218$	−776155.	−1.10613
$219$	−23346.8	−0.0328940
$220$	−51472.1	−0.0716993
$221$	−2.62286e6	−3.61238
$222$	119652.	0.162944
$223$	−151410.	−0.203889	−0.101944	−	0.994790i	$-0.532506\pi$
$223$	−151410.	−0.203889	−0.101944	+	0.994790i	$0.532506\pi$
$224$	−1.36070e6	−1.81194
$225$	−142103.	−0.187131
$226$	−1.51183e6	−1.96894
$227$	−650716.	−0.838160	−0.419080	−	0.907949i	$-0.637647\pi$
$227$	−650716.	−0.838160	−0.419080	+	0.907949i	$0.637647\pi$
$228$	−24289.3	−0.0309441
$229$	−1.16299e6	−1.46550	−0.732752	−	0.680495i	$-0.761765\pi$
$229$	−1.16299e6	−1.46550	−0.732752	+	0.680495i	$0.761765\pi$
$230$	167242.	0.208462
$231$	−116317.	−0.143421
$232$	−544051.	−0.663621
$233$	695392.	0.839150	0.419575	−	0.907721i	$-0.362179\pi$
$233$	695392.	0.839150	0.419575	+	0.907721i	$0.362179\pi$
$234$	1.84474e6	2.20240
$235$	−238353.	−0.281547
$236$	−204310.	−0.238787
$237$	−289358.	−0.334630
$238$	−3.85204e6	−4.40807
$239$	−760286.	−0.860959	−0.430479	−	0.902600i	$-0.641655\pi$
$239$	−760286.	−0.860959	−0.430479	+	0.902600i	$0.641655\pi$
$240$	126433.	0.141688
$241$	276621.	0.306791	0.153396	−	0.988165i	$-0.450979\pi$
$241$	276621.	0.306791	0.153396	+	0.988165i	$0.450979\pi$
$242$	−102503.	−0.112512
$243$	−641349.	−0.696753
$244$	511772.	0.550303
$245$	1.05734e6	1.12538
$246$	−836.915	−0.000881747 0
$247$	418364.	0.436326
$248$	563224.	0.581503
$249$	43149.3	0.0441037
$250$	−109392.	−0.110697
$251$	−603958.	−0.605094	−0.302547	−	0.953135i	$-0.597837\pi$
$251$	−603958.	−0.605094	−0.302547	+	0.953135i	$0.597837\pi$
$252$	940513.	0.932961
$253$	115618.	0.113559
$254$	−1.60654e6	−1.56246
$255$	223732.	0.215466
$256$	1.28358e6	1.22412
$257$	−585078.	−0.552562	−0.276281	−	0.961077i	$-0.589102\pi$
$257$	−585078.	−0.552562	−0.276281	+	0.961077i	$0.589102\pi$
$258$	177428.	0.165948
$259$	−1.05073e6	−0.973285
$260$	492984.	0.452272
$261$	1.17911e6	1.07140
$262$	122174.	0.109958
$263$	−629207.	−0.560924	−0.280462	−	0.959865i	$-0.590488\pi$
$263$	−629207.	−0.560924	−0.280462	+	0.959865i	$0.590488\pi$
$264$	50194.2	0.0443245
$265$	492828.	0.431103
$266$	614428.	0.532435
$267$	393699.	0.337976
$268$	−845700.	−0.719249
$269$	−1.26480e6	−1.06572	−0.532858	−	0.846205i	$-0.678882\pi$
$269$	−1.26480e6	−1.06572	−0.532858	+	0.846205i	$0.678882\pi$
$270$	−325539.	−0.271765
$271$	1.53049e6	1.26592	0.632961	−	0.774184i	$-0.281839\pi$
$271$	1.53049e6	1.26592	0.632961	+	0.774184i	$0.281839\pi$
$272$	2.89459e6	2.37228
$273$	1.11405e6	0.904685
$274$	−1.66460e6	−1.33947
$275$	−75625.0	−0.0603023
$276$	64290.5	0.0508012
$277$	−1.18588e6	−0.928628	−0.464314	−	0.885671i	$-0.653699\pi$
$277$	−1.18588e6	−0.928628	−0.464314	+	0.885671i	$0.653699\pi$
$278$	2.05554e6	1.59520
$279$	−1.22066e6	−0.938826
$280$	−637593.	−0.486014
$281$	237342.	0.179312	0.0896558	−	0.995973i	$-0.471423\pi$
$281$	237342.	0.179312	0.0896558	+	0.995973i	$0.471423\pi$
$282$	−263942.	−0.197645
$283$	−276019.	−0.204867	−0.102434	−	0.994740i	$-0.532663\pi$
$283$	−276019.	−0.204867	−0.102434	+	0.994740i	$0.532663\pi$
$284$	−895716.	−0.658984
$285$	−35686.9	−0.0260253
$286$	981746.	0.709715
$287$	7349.37	0.00526678
$288$	−1.27259e6	−0.904083
$289$	3.70233e6	2.60754
$290$	907694.	0.633789
$291$	−244493.	−0.169252
$292$	100464.	0.0689533
$293$	1.53196e6	1.04251	0.521254	−	0.853402i	$-0.325464\pi$
$293$	1.53196e6	1.04251	0.521254	+	0.853402i	$0.325464\pi$
$294$	1.17086e6	0.790016
$295$	−300181.	−0.200830
$296$	453419.	0.300795
$297$	−225051.	−0.148044
$298$	−3.40672e6	−2.22227
$299$	−1.10735e6	−0.716322
$300$	−42052.1	−0.0269764
$301$	−1.55808e6	−0.991228
$302$	−3.23159e6	−2.03891
$303$	63028.2	0.0394392
$304$	−461708.	−0.286539
$305$	751917.	0.462829
$306$	−3.60261e6	−2.19945
$307$	−874263.	−0.529415	−0.264708	−	0.964329i	$-0.585275\pi$
$307$	−874263.	−0.529415	−0.264708	+	0.964329i	$0.585275\pi$
$308$	500528.	0.300643
$309$	159968.	0.0953096
$310$	−939682.	−0.555362
$311$	−263181.	−0.154296	−0.0771478	−	0.997020i	$-0.524581\pi$
$311$	−263181.	−0.154296	−0.0771478	+	0.997020i	$0.524581\pi$
$312$	−480745.	−0.279594
$313$	1.10532e6	0.637713	0.318857	−	0.947803i	$-0.396701\pi$
$313$	1.10532e6	0.637713	0.318857	+	0.947803i	$0.396701\pi$
$314$	297576.	0.170323
$315$	1.38184e6	0.784661
$316$	1.24515e6	0.701461
$317$	2.94737e6	1.64735	0.823676	−	0.567060i	$-0.191919\pi$
$317$	2.94737e6	1.64735	0.823676	+	0.567060i	$0.191919\pi$
$318$	545737.	0.302633
$319$	627506.	0.345256
$320$	43516.9	0.0237565
$321$	−268689.	−0.145542
$322$	−1.62631e6	−0.874104
$323$	−817024.	−0.435741
$324$	814959.	0.431294
$325$	724314.	0.380380
$326$	−298799.	−0.155717
$327$	−438372.	−0.226711
$328$	−3171.47	−0.00162771
$329$	2.31780e6	1.18056
$330$	−83744.0	−0.0423320
$331$	471055.	0.236321	0.118160	−	0.992995i	$-0.462300\pi$
$331$	471055.	0.236321	0.118160	+	0.992995i	$0.462300\pi$
$332$	−185677.	−0.0924514
$333$	−982686.	−0.485629
$334$	3.19399e6	1.56663
$335$	−1.24254e6	−0.604920
$336$	−1.22947e6	−0.594113
$337$	−2.70564e6	−1.29776	−0.648882	−	0.760889i	$-0.724763\pi$
$337$	−2.70564e6	−1.29776	−0.648882	+	0.760889i	$0.724763\pi$
$338$	−6.80340e6	−3.23917
$339$	−853881.	−0.403551
$340$	−962752.	−0.451666
$341$	−649620.	−0.302533
$342$	574640.	0.265663
$343$	−6.19599e6	−2.84365
$344$	672358.	0.306341
$345$	94458.4	0.0427261
$346$	−1.38468e6	−0.621812
$347$	18751.7	0.00836018	0.00418009	−	0.999991i	$-0.498669\pi$
$347$	18751.7	0.00836018	0.00418009	+	0.999991i	$0.498669\pi$
$348$	348931.	0.154451
$349$	−3.63578e6	−1.59784	−0.798921	−	0.601436i	$-0.794596\pi$
$349$	−3.63578e6	−1.59784	−0.798921	+	0.601436i	$0.794596\pi$
$350$	1.06376e6	0.464166
$351$	2.15547e6	0.933844
$352$	−677256.	−0.291337
$353$	−3.82313e6	−1.63298	−0.816492	−	0.577357i	$-0.804084\pi$
$353$	−3.82313e6	−1.63298	−0.816492	+	0.577357i	$0.804084\pi$
$354$	−332408.	−0.140982
$355$	−1.31602e6	−0.554234
$356$	−1.69414e6	−0.708475
$357$	−2.17563e6	−0.903472
$358$	−5.82263e6	−2.40111
$359$	4.07667e6	1.66943	0.834717	−	0.550679i	$-0.185631\pi$
$359$	4.07667e6	1.66943	0.834717	+	0.550679i	$0.185631\pi$
$360$	−596306.	−0.242501
$361$	130321.	0.0526316
$362$	1.58290e6	0.634867
$363$	−57893.8	−0.0230603
$364$	−4.79391e6	−1.89643
$365$	147607.	0.0579927
$366$	832641.	0.324904
$367$	−3.79520e6	−1.47085	−0.735427	−	0.677604i	$-0.763018\pi$
$367$	−3.79520e6	−1.47085	−0.735427	+	0.677604i	$0.763018\pi$
$368$	1.22208e6	0.470413
$369$	6873.46	0.00262790
$370$	−756484.	−0.287273
$371$	−4.79239e6	−1.80766
$372$	−361228.	−0.135339
$373$	1.39348e6	0.518596	0.259298	−	0.965797i	$-0.416509\pi$
$373$	1.39348e6	0.518596	0.259298	+	0.965797i	$0.416509\pi$
$374$	−1.91726e6	−0.708763
$375$	−61784.7	−0.0226884
$376$	−1.00020e6	−0.364853
$377$	−6.01006e6	−2.17784
$378$	3.16562e6	1.13954
$379$	−90134.0	−0.0322322	−0.0161161	−	0.999870i	$-0.505130\pi$
$379$	−90134.0	−0.0322322	−0.0161161	+	0.999870i	$0.505130\pi$
$380$	153566.	0.0545550
$381$	−907374.	−0.320239
$382$	−2.33454e6	−0.818545
$383$	−4.75784e6	−1.65734	−0.828672	−	0.559735i	$-0.810903\pi$
$383$	−4.75784e6	−1.65734	−0.828672	+	0.559735i	$0.810903\pi$
$384$	756426.	0.261781
$385$	735397.	0.252854
$386$	5.82044e6	1.98833
$387$	−1.45719e6	−0.494582
$388$	1.05209e6	0.354791
$389$	−2.60666e6	−0.873393	−0.436697	−	0.899609i	$-0.643852\pi$
$389$	−2.60666e6	−0.873393	−0.436697	+	0.899609i	$0.643852\pi$
$390$	802075.	0.267026
$391$	2.16256e6	0.715361
$392$	4.43694e6	1.45837
$393$	69003.8	0.0225368
$394$	6.85951e6	2.22614
$395$	1.82943e6	0.589959
$396$	468116.	0.150008
$397$	−1.58429e6	−0.504497	−0.252248	−	0.967662i	$-0.581170\pi$
$397$	−1.58429e6	−0.504497	−0.252248	+	0.967662i	$0.581170\pi$
$398$	−4.31284e6	−1.36476
$399$	347028.	0.109127
$400$	−799355.	−0.249799
$401$	−4.85997e6	−1.50929	−0.754644	−	0.656134i	$-0.772191\pi$
$401$	−4.85997e6	−1.50929	−0.754644	+	0.656134i	$0.772191\pi$
$402$	−1.37593e6	−0.424652
$403$	6.22186e6	1.90835
$404$	−271219.	−0.0826736
$405$	1.19737e6	0.362737
$406$	−8.82665e6	−2.65755
$407$	−522972.	−0.156492
$408$	938850.	0.279220
$409$	1.83394e6	0.542098	0.271049	−	0.962566i	$-0.412629\pi$
$409$	1.83394e6	0.542098	0.271049	+	0.962566i	$0.412629\pi$
$410$	5291.28	0.00155454
$411$	−940163.	−0.274535
$412$	−688364.	−0.199791
$413$	2.91904e6	0.842103
$414$	−1.52100e6	−0.436142
$415$	−272805.	−0.0777557
$416$	6.48655e6	1.83773
$417$	1.16097e6	0.326949
$418$	305816.	0.0856089
$419$	490337.	0.136446	0.0682228	−	0.997670i	$-0.478267\pi$
$419$	490337.	0.136446	0.0682228	+	0.997670i	$0.478267\pi$
$420$	408925.	0.113115
$421$	4.07913e6	1.12166	0.560832	−	0.827930i	$-0.310481\pi$
$421$	4.07913e6	1.12166	0.560832	+	0.827930i	$0.310481\pi$
$422$	−3.96944e6	−1.08505
$423$	2.16771e6	0.589048
$424$	2.06806e6	0.558661
$425$	−1.41452e6	−0.379870
$426$	−1.45731e6	−0.389070
$427$	−7.31183e6	−1.94069
$428$	1.15621e6	0.305089
$429$	554489.	0.145462
$430$	−1.12176e6	−0.292570
$431$	−3.84689e6	−0.997509	−0.498754	−	0.866743i	$-0.666209\pi$
$431$	−3.84689e6	−0.997509	−0.498754	+	0.866743i	$0.666209\pi$
$432$	−2.37879e6	−0.613262
$433$	−3.09893e6	−0.794314	−0.397157	−	0.917751i	$-0.630003\pi$
$433$	−3.09893e6	−0.794314	−0.397157	+	0.917751i	$0.630003\pi$
$434$	9.13771e6	2.32870
$435$	512665.	0.129900
$436$	1.88637e6	0.475238
$437$	−344942.	−0.0864058
$438$	163453.	0.0407107
$439$	379849.	0.0940696	0.0470348	−	0.998893i	$-0.485023\pi$
$439$	379849.	0.0940696	0.0470348	+	0.998893i	$0.485023\pi$
$440$	−317346.	−0.0781450
$441$	−9.61608e6	−2.35452
$442$	1.83629e7	4.47081
$443$	−5.00248e6	−1.21109	−0.605545	−	0.795811i	$-0.707045\pi$
$443$	−5.00248e6	−1.21109	−0.605545	+	0.795811i	$0.707045\pi$
$444$	−290804.	−0.0700073
$445$	−2.48910e6	−0.595858
$446$	1.06004e6	0.252340
$447$	−1.92411e6	−0.455472
$448$	−423169.	−0.0996137
$449$	3.11580e6	0.729381	0.364690	−	0.931129i	$-0.381175\pi$
$449$	3.11580e6	0.729381	0.364690	+	0.931129i	$0.381175\pi$
$450$	994876.	0.231600
$451$	3657.96	0.000846832 0
$452$	3.67437e6	0.845934
$453$	−1.82520e6	−0.417893
$454$	4.55574e6	1.03734
$455$	−7.04341e6	−1.59498
$456$	−149753.	−0.0337259
$457$	−3.02931e6	−0.678506	−0.339253	−	0.940695i	$-0.610174\pi$
$457$	−3.02931e6	−0.678506	−0.339253	+	0.940695i	$0.610174\pi$
$458$	8.14222e6	1.81376
$459$	−4.20943e6	−0.932591
$460$	−406468.	−0.0895636
$461$	5.44225e6	1.19269	0.596343	−	0.802730i	$-0.296620\pi$
$461$	5.44225e6	1.19269	0.596343	+	0.802730i	$0.296620\pi$
$462$	814348.	0.177503
$463$	463544.	0.100494	0.0502468	−	0.998737i	$-0.483999\pi$
$463$	463544.	0.100494	0.0502468	+	0.998737i	$0.483999\pi$
$464$	6.63273e6	1.43020
$465$	−530732.	−0.113826
$466$	−4.86851e6	−1.03856
$467$	−5.83069e6	−1.23717	−0.618583	−	0.785720i	$-0.712293\pi$
$467$	−5.83069e6	−1.23717	−0.618583	+	0.785720i	$0.712293\pi$
$468$	−4.48348e6	−0.946238
$469$	1.20828e7	2.53650
$470$	1.66873e6	0.348451
$471$	168070.	0.0349091
$472$	−1.25965e6	−0.260253
$473$	−775495.	−0.159377
$474$	2.02583e6	0.414150
$475$	225625.	0.0458831
$476$	9.36205e6	1.89388
$477$	−4.48206e6	−0.901948
$478$	5.32285e6	1.06555
$479$	−9.59369e6	−1.91050	−0.955250	−	0.295800i	$-0.904414\pi$
$479$	−9.59369e6	−1.91050	−0.955250	+	0.295800i	$0.904414\pi$
$480$	−553310.	−0.109614
$481$	5.00887e6	0.987135
$482$	−1.93666e6	−0.379695
$483$	−918538.	−0.179155
$484$	249125.	0.0483397
$485$	1.54577e6	0.298395
$486$	4.49016e6	0.862324
$487$	−7.21375e6	−1.37828	−0.689142	−	0.724627i	$-0.742012\pi$
$487$	−7.21375e6	−1.37828	−0.689142	+	0.724627i	$0.742012\pi$
$488$	3.15527e6	0.599774
$489$	−168761.	−0.0319155
$490$	−7.40258e6	−1.39281
$491$	5.48864e6	1.02745	0.513725	−	0.857955i	$-0.328265\pi$
$491$	5.48864e6	1.02745	0.513725	+	0.857955i	$0.328265\pi$
$492$	2034.05	0.000378833 0
$493$	1.17371e7	2.17492
$494$	−2.92901e6	−0.540012
$495$	687776.	0.126164
$496$	−6.86647e6	−1.25323
$497$	1.27974e7	2.32396
$498$	−302093.	−0.0545842
$499$	−3.69018e6	−0.663431	−0.331716	−	0.943379i	$-0.607627\pi$
$499$	−3.69018e6	−0.663431	−0.331716	+	0.943379i	$0.607627\pi$
$500$	265868.	0.0475600
$501$	1.80396e6	0.321095
$502$	4.22838e6	0.748884
$503$	3.70118e6	0.652260	0.326130	−	0.945325i	$-0.394255\pi$
$503$	3.70118e6	0.652260	0.326130	+	0.945325i	$0.394255\pi$
$504$	5.79863e6	1.01683
$505$	−398487.	−0.0695321
$506$	−809453.	−0.140545
$507$	−3.84256e6	−0.663896
$508$	3.90456e6	0.671293
$509$	−3.44634e6	−0.589609	−0.294804	−	0.955558i	$-0.595255\pi$
$509$	−3.44634e6	−0.589609	−0.294804	+	0.955558i	$0.595255\pi$
$510$	−1.56638e6	−0.266668
$511$	−1.43536e6	−0.243170
$512$	−2.86503e6	−0.483008
$513$	671433.	0.112644
$514$	4.09620e6	0.683869
$515$	−1.01137e6	−0.168033
$516$	−431222.	−0.0712979
$517$	1.15363e6	0.189819
$518$	7.35625e6	1.20457
$519$	−782066.	−0.127446
$520$	3.03944e6	0.492930
$521$	6.02937e6	0.973145	0.486572	−	0.873640i	$-0.338247\pi$
$521$	6.02937e6	0.973145	0.486572	+	0.873640i	$0.338247\pi$
$522$	−8.25508e6	−1.32601
$523$	−9.37886e6	−1.49933	−0.749663	−	0.661820i	$-0.769784\pi$
$523$	−9.37886e6	−1.49933	−0.749663	+	0.661820i	$0.769784\pi$
$524$	−296933.	−0.0472422
$525$	600811.	0.0951348
$526$	4.40515e6	0.694218
$527$	−1.21507e7	−1.90579
$528$	−611937.	−0.0955260
$529$	−5.52333e6	−0.858147
$530$	−3.45035e6	−0.533547
$531$	2.73002e6	0.420174
$532$	−1.49331e6	−0.228755
$533$	−35034.8	−0.00534173
$534$	−2.75633e6	−0.418291
$535$	1.69875e6	0.256593
$536$	−5.21407e6	−0.783908
$537$	−3.28862e6	−0.492127
$538$	8.85501e6	1.31897
$539$	−5.11754e6	−0.758734
$540$	791192.	0.116761
$541$	−4.43894e6	−0.652058	−0.326029	−	0.945360i	$-0.605711\pi$
$541$	−4.43894e6	−0.652058	−0.326029	+	0.945360i	$0.605711\pi$
$542$	−1.07151e7	−1.56675
$543$	894022.	0.130121
$544$	−1.26676e7	−1.83526
$545$	2.77154e6	0.399696
$546$	−7.79958e6	−1.11967
$547$	8.65578e6	1.23691	0.618455	−	0.785820i	$-0.287759\pi$
$547$	8.65578e6	1.23691	0.618455	+	0.785820i	$0.287759\pi$
$548$	4.04565e6	0.575489
$549$	−6.83836e6	−0.968324
$550$	529459.	0.0746321
$551$	−1.87215e6	−0.262700
$552$	396376.	0.0553682
$553$	−1.77898e7	−2.47377
$554$	8.30249e6	1.14930
$555$	−427262.	−0.0588792
$556$	−4.99581e6	−0.685360
$557$	5.92659e6	0.809406	0.404703	−	0.914448i	$-0.367375\pi$
$557$	5.92659e6	0.809406	0.404703	+	0.914448i	$0.367375\pi$
$558$	8.54600e6	1.16192
$559$	7.42746e6	1.00533
$560$	7.77314e6	1.04743
$561$	−1.08287e6	−0.145267
$562$	−1.66166e6	−0.221922
$563$	−1.23886e7	−1.64722	−0.823609	−	0.567158i	$-0.808043\pi$
$563$	−1.23886e7	−1.64722	−0.823609	+	0.567158i	$0.808043\pi$
$564$	641486.	0.0849160
$565$	5.39854e6	0.711467
$566$	1.93244e6	0.253551
$567$	−1.16436e7	−1.52100
$568$	−5.52244e6	−0.718225
$569$	−2.52479e6	−0.326922	−0.163461	−	0.986550i	$-0.552266\pi$
$569$	−2.52479e6	−0.326922	−0.163461	+	0.986550i	$0.552266\pi$
$570$	249848.	0.0322098
$571$	−2.60493e6	−0.334353	−0.167177	−	0.985927i	$-0.553465\pi$
$571$	−2.60493e6	−0.334353	−0.167177	+	0.985927i	$0.553465\pi$
$572$	−2.38604e6	−0.304922
$573$	−1.31854e6	−0.167768
$574$	−51453.7	−0.00651834
$575$	−597199.	−0.0753268
$576$	−395767.	−0.0497031
$577$	−1.44029e7	−1.80098	−0.900491	−	0.434874i	$-0.856793\pi$
$577$	−1.44029e7	−1.80098	−0.900491	+	0.434874i	$0.856793\pi$
$578$	−2.59204e7	−3.22718
$579$	3.28738e6	0.407525
$580$	−2.20607e6	−0.272301
$581$	2.65283e6	0.326038
$582$	1.71173e6	0.209472
$583$	−2.38529e6	−0.290650
$584$	619403.	0.0751521
$585$	−6.58732e6	−0.795827
$586$	−1.07254e7	−1.29024
$587$	−4.73718e6	−0.567446	−0.283723	−	0.958906i	$-0.591570\pi$
$587$	−4.73718e6	−0.567446	−0.283723	+	0.958906i	$0.591570\pi$
$588$	−2.84567e6	−0.339422
$589$	1.93812e6	0.230193
$590$	2.10160e6	0.248554
$591$	3.87425e6	0.456267
$592$	−5.52780e6	−0.648259
$593$	710179.	0.0829337	0.0414668	−	0.999140i	$-0.486797\pi$
$593$	710179.	0.0829337	0.0414668	+	0.999140i	$0.486797\pi$
$594$	1.57561e6	0.183224
$595$	1.37551e7	1.59284
$596$	8.27973e6	0.954774
$597$	−2.43589e6	−0.279719
$598$	7.75270e6	0.886544
$599$	−1.31815e7	−1.50106	−0.750532	−	0.660834i	$-0.770203\pi$
$599$	−1.31815e7	−1.50106	−0.750532	+	0.660834i	$0.770203\pi$
$600$	−259268.	−0.0294016
$601$	1.19379e7	1.34816	0.674079	−	0.738659i	$-0.264541\pi$
$601$	1.19379e7	1.34816	0.674079	+	0.738659i	$0.264541\pi$
$602$	1.09083e7	1.22678
$603$	1.13003e7	1.26561
$604$	7.85409e6	0.875999
$605$	366025.	0.0406558
$606$	−441267.	−0.0488113
$607$	3.84564e6	0.423640	0.211820	−	0.977309i	$-0.432061\pi$
$607$	3.84564e6	0.423640	0.211820	+	0.977309i	$0.432061\pi$
$608$	2.02057e6	0.221674
$609$	−4.98529e6	−0.544687
$610$	−5.26425e6	−0.572812
$611$	−1.10491e7	−1.19736
$612$	8.75581e6	0.944969
$613$	−1.92087e6	−0.206465	−0.103233	−	0.994657i	$-0.532919\pi$
$613$	−1.92087e6	−0.206465	−0.103233	+	0.994657i	$0.532919\pi$
$614$	6.12081e6	0.655222
$615$	2988.51	0.000318615 0
$616$	3.08595e6	0.327671
$617$	1.77226e7	1.87420	0.937099	−	0.349063i	$-0.113500\pi$
$617$	1.77226e7	1.87420	0.937099	+	0.349063i	$0.113500\pi$
$618$	−1.11995e6	−0.117958
$619$	6.88381e6	0.722108	0.361054	−	0.932545i	$-0.382417\pi$
$619$	6.88381e6	0.722108	0.361054	+	0.932545i	$0.382417\pi$
$620$	2.28381e6	0.238606
$621$	−1.77719e6	−0.184929
$622$	1.84256e6	0.190961
$623$	2.42047e7	2.49850
$624$	5.86095e6	0.602568
$625$	390625.	0.0400000
$626$	−7.73844e6	−0.789255
$627$	172724.	0.0175463
$628$	−723231.	−0.0731775
$629$	−9.78184e6	−0.985812
$630$	−9.67443e6	−0.971123
$631$	7.54549e6	0.754421	0.377211	−	0.926128i	$-0.376883\pi$
$631$	7.54549e6	0.754421	0.377211	+	0.926128i	$0.376883\pi$
$632$	7.67683e6	0.764521
$633$	−2.24194e6	−0.222389
$634$	−2.06349e7	−2.03882
$635$	5.73674e6	0.564587
$636$	−1.32637e6	−0.130023
$637$	4.90143e7	4.78602
$638$	−4.39324e6	−0.427300
$639$	1.19687e7	1.15956
$640$	−4.78239e6	−0.461525
$641$	−3.56732e6	−0.342923	−0.171461	−	0.985191i	$-0.554849\pi$
$641$	−3.56732e6	−0.342923	−0.171461	+	0.985191i	$0.554849\pi$
$642$	1.88112e6	0.180127
$643$	1.78390e7	1.70155	0.850773	−	0.525534i	$-0.176134\pi$
$643$	1.78390e7	1.70155	0.850773	+	0.525534i	$0.176134\pi$
$644$	3.95260e6	0.375550
$645$	−633570.	−0.0599647
$646$	5.72008e6	0.539288
$647$	1.72023e7	1.61557	0.807787	−	0.589474i	$-0.200665\pi$
$647$	1.72023e7	1.61557	0.807787	+	0.589474i	$0.200665\pi$
$648$	5.02455e6	0.470066
$649$	1.45288e6	0.135400
$650$	−5.07100e6	−0.470772
$651$	5.16097e6	0.477286
$652$	726204.	0.0669021
$653$	−1.46851e6	−0.134770	−0.0673852	−	0.997727i	$-0.521466\pi$
$653$	−1.46851e6	−0.134770	−0.0673852	+	0.997727i	$0.521466\pi$
$654$	3.06909e6	0.280585
$655$	−436266.	−0.0397327
$656$	38664.6	0.00350795
$657$	−1.34242e6	−0.121332
$658$	−1.62272e7	−1.46110
$659$	−1.53425e7	−1.37621	−0.688103	−	0.725613i	$-0.741556\pi$
$659$	−1.53425e7	−1.37621	−0.688103	+	0.725613i	$0.741556\pi$
$660$	203532.	0.0181875
$661$	−1.26261e7	−1.12400	−0.561998	−	0.827138i	$-0.689967\pi$
$661$	−1.26261e7	−1.12400	−0.561998	+	0.827138i	$0.689967\pi$
$662$	−3.29791e6	−0.292478
$663$	1.03714e7	0.916330
$664$	−1.14477e6	−0.100763
$665$	−2.19404e6	−0.192393
$666$	6.87989e6	0.601030
$667$	4.95532e6	0.431278
$668$	−7.76271e6	−0.673089
$669$	598711.	0.0517192
$670$	8.69915e6	0.748669
$671$	−3.63928e6	−0.312039
$672$	5.38053e6	0.459623
$673$	2.05940e7	1.75268	0.876341	−	0.481691i	$-0.159977\pi$
$673$	2.05940e7	1.75268	0.876341	+	0.481691i	$0.159977\pi$
$674$	1.89425e7	1.60616
$675$	1.16245e6	0.0982010
$676$	1.65351e7	1.39168
$677$	−1.52489e7	−1.27870	−0.639348	−	0.768918i	$-0.720796\pi$
$677$	−1.52489e7	−1.27870	−0.639348	+	0.768918i	$0.720796\pi$
$678$	5.97811e6	0.499448
$679$	−1.50315e7	−1.25120
$680$	−5.93574e6	−0.492269
$681$	2.57308e6	0.212611
$682$	4.54806e6	0.374425
$683$	−3.78825e6	−0.310733	−0.155366	−	0.987857i	$-0.549656\pi$
$683$	−3.78825e6	−0.310733	−0.155366	+	0.987857i	$0.549656\pi$
$684$	−1.39661e6	−0.114139
$685$	5.94404e6	0.484011
$686$	4.33788e7	3.51939
$687$	4.59872e6	0.371745
$688$	−8.19697e6	−0.660210
$689$	2.28456e7	1.83339
$690$	−661314.	−0.0528792
$691$	4.27785e6	0.340824	0.170412	−	0.985373i	$-0.445490\pi$
$691$	4.27785e6	0.340824	0.170412	+	0.985373i	$0.445490\pi$
$692$	3.36534e6	0.267155
$693$	−6.68812e6	−0.529018
$694$	−131282.	−0.0103468
$695$	−7.34006e6	−0.576418
$696$	2.15130e6	0.168336
$697$	68419.7	0.00533457
$698$	2.54545e7	1.97754
$699$	−2.74973e6	−0.212862
$700$	−2.58537e6	−0.199424
$701$	1.71896e7	1.32120	0.660601	−	0.750737i	$-0.270301\pi$
$701$	1.71896e7	1.32120	0.660601	+	0.750737i	$0.270301\pi$
$702$	−1.50907e7	−1.15576
$703$	1.56027e6	0.119073
$704$	−210622.	−0.0160166
$705$	942499.	0.0714181
$706$	2.67661e7	2.02104
$707$	3.87499e6	0.291556
$708$	807889.	0.0605715
$709$	−1.76124e6	−0.131584	−0.0657919	−	0.997833i	$-0.520957\pi$
$709$	−1.76124e6	−0.131584	−0.0657919	+	0.997833i	$0.520957\pi$
$710$	9.21364e6	0.685939
$711$	−1.66378e7	−1.23431
$712$	−1.04450e7	−0.772165
$713$	−5.12995e6	−0.377911
$714$	1.52318e7	1.11817
$715$	−3.50568e6	−0.256452
$716$	1.41514e7	1.03161
$717$	3.00634e6	0.218394
$718$	−2.85412e7	−2.06615
$719$	−2.87984e6	−0.207752	−0.103876	−	0.994590i	$-0.533125\pi$
$719$	−2.87984e6	−0.207752	−0.103876	+	0.994590i	$0.533125\pi$
$720$	7.26979e6	0.522625
$721$	9.83486e6	0.704579
$722$	−912392.	−0.0651386
$723$	−1.09382e6	−0.0778218
$724$	−3.84710e6	−0.272764
$725$	−3.24125e6	−0.229017
$726$	405321.	0.0285402
$727$	−1.10267e7	−0.773764	−0.386882	−	0.922129i	$-0.626448\pi$
$727$	−1.10267e7	−0.773764	−0.386882	+	0.922129i	$0.626448\pi$
$728$	−2.95563e7	−2.06691
$729$	−9.10243e6	−0.634364
$730$	−1.03341e6	−0.0717738
$731$	−1.45051e7	−1.00399
$732$	−2.02366e6	−0.139592
$733$	−1.15398e7	−0.793299	−0.396650	−	0.917970i	$-0.629827\pi$
$733$	−1.15398e7	−0.793299	−0.396650	+	0.917970i	$0.629827\pi$
$734$	2.65706e7	1.82038
$735$	−4.18097e6	−0.285469
$736$	−5.34819e6	−0.363925
$737$	6.01388e6	0.407837
$738$	−48121.8	−0.00325238
$739$	−4.42621e6	−0.298141	−0.149070	−	0.988827i	$-0.547628\pi$
$739$	−4.42621e6	−0.298141	−0.149070	+	0.988827i	$0.547628\pi$
$740$	1.83857e6	0.123424
$741$	−1.65430e6	−0.110680
$742$	3.35521e7	2.23722
$743$	8.10246e6	0.538449	0.269225	−	0.963077i	$-0.413233\pi$
$743$	8.10246e6	0.538449	0.269225	+	0.963077i	$0.413233\pi$
$744$	−2.22711e6	−0.147506
$745$	1.21649e7	0.803007
$746$	−9.75593e6	−0.641832
$747$	2.48104e6	0.162679
$748$	4.65972e6	0.304513
$749$	−1.65191e7	−1.07592
$750$	432562.	0.0280799
$751$	−6.07898e6	−0.393307	−0.196653	−	0.980473i	$-0.563007\pi$
$751$	−6.07898e6	−0.393307	−0.196653	+	0.980473i	$0.563007\pi$
$752$	1.21938e7	0.786312
$753$	2.38819e6	0.153490
$754$	4.20771e7	2.69537
$755$	1.15396e7	0.736753
$756$	−7.69375e6	−0.489591
$757$	9.69900e6	0.615159	0.307580	−	0.951522i	$-0.400481\pi$
$757$	9.69900e6	0.615159	0.307580	+	0.951522i	$0.400481\pi$
$758$	631038.	0.0398917
$759$	−457179.	−0.0288059
$760$	946792.	0.0594594
$761$	4.58726e6	0.287138	0.143569	−	0.989640i	$-0.454142\pi$
$761$	4.58726e6	0.287138	0.143569	+	0.989640i	$0.454142\pi$
$762$	6.35263e6	0.396338
$763$	−2.69512e7	−1.67597
$764$	5.67388e6	0.351679
$765$	1.28644e7	0.794760
$766$	3.33101e7	2.05118
$767$	−1.39152e7	−0.854087
$768$	−5.07556e6	−0.310514
$769$	11592.6	0.000706911 0	0.000353455	−	1.00000i	$-0.499887\pi$
$769$	11592.6	0.000706911 0	0.000353455		1.00000i	$0.499887\pi$
$770$	−5.14860e6	−0.312941
$771$	2.31353e6	0.140165
$772$	−1.41461e7	−0.854264
$773$	−1.12268e7	−0.675783	−0.337891	−	0.941185i	$-0.609714\pi$
$773$	−1.12268e7	−0.675783	−0.337891	+	0.941185i	$0.609714\pi$
$774$	1.02019e7	0.612111
$775$	3.35547e6	0.200678
$776$	6.48654e6	0.386686
$777$	4.15480e6	0.246887
$778$	1.82495e7	1.08094
$779$	−10913.4	−0.000644343 0
$780$	−1.94937e6	−0.114725
$781$	6.36956e6	0.373665
$782$	−1.51403e7	−0.885355
$783$	−9.64557e6	−0.562242
$784$	−5.40924e7	−3.14301
$785$	−1.06260e6	−0.0615455
$786$	−483103.	−0.0278923
$787$	−2.05734e7	−1.18405	−0.592025	−	0.805920i	$-0.701671\pi$
$787$	−2.05734e7	−1.18405	−0.592025	+	0.805920i	$0.701671\pi$
$788$	−1.66714e7	−0.956439
$789$	2.48802e6	0.142286
$790$	−1.28080e7	−0.730153
$791$	−5.24968e7	−2.98326
$792$	2.88612e6	0.163494
$793$	3.48559e7	1.96831
$794$	1.10918e7	0.624382
$795$	−1.94875e6	−0.109355
$796$	1.04820e7	0.586354
$797$	−2.87404e7	−1.60268	−0.801341	−	0.598208i	$-0.795880\pi$
$797$	−2.87404e7	−1.60268	−0.801341	+	0.598208i	$0.795880\pi$
$798$	−2.42958e6	−0.135059
$799$	2.15778e7	1.19575
$800$	3.49822e6	0.193251
$801$	2.26373e7	1.24665
$802$	3.40252e7	1.86795
$803$	−714416.	−0.0390987
$804$	3.34408e6	0.182447
$805$	5.80732e6	0.315854
$806$	−4.35599e7	−2.36184
$807$	5.00130e6	0.270333
$808$	−1.67217e6	−0.0901058
$809$	2.94368e6	0.158132	0.0790658	−	0.996869i	$-0.474806\pi$
$809$	2.94368e6	0.158132	0.0790658	+	0.996869i	$0.474806\pi$
$810$	−8.38294e6	−0.448936
$811$	2.00474e7	1.07030	0.535151	−	0.844756i	$-0.320255\pi$
$811$	2.00474e7	1.07030	0.535151	+	0.844756i	$0.320255\pi$
$812$	2.14524e7	1.14179
$813$	−6.05190e6	−0.321118
$814$	3.66138e6	0.193680
$815$	1.06697e6	0.0562676
$816$	−1.14459e7	−0.601760
$817$	2.31367e6	0.121268
$818$	−1.28397e7	−0.670919
$819$	6.40568e7	3.33699
$820$	−12860.0	−0.000667890 0
$821$	2.43023e7	1.25832	0.629158	−	0.777278i	$-0.283400\pi$
$821$	2.43023e7	1.25832	0.629158	+	0.777278i	$0.283400\pi$
$822$	6.58218e6	0.339774
$823$	−1.75212e7	−0.901706	−0.450853	−	0.892598i	$-0.648880\pi$
$823$	−1.75212e7	−0.901706	−0.450853	+	0.892598i	$0.648880\pi$
$824$	−4.24403e6	−0.217751
$825$	299038.	0.0152965
$826$	−2.04365e7	−1.04221
$827$	3.37263e7	1.71477	0.857383	−	0.514679i	$-0.172089\pi$
$827$	3.37263e7	1.71477	0.857383	+	0.514679i	$0.172089\pi$
$828$	3.69665e6	0.187384
$829$	6.59371e6	0.333230	0.166615	−	0.986022i	$-0.446716\pi$
$829$	6.59371e6	0.333230	0.166615	+	0.986022i	$0.446716\pi$
$830$	1.90994e6	0.0962330
$831$	4.68924e6	0.235559
$832$	2.01727e6	0.101031
$833$	−9.57203e7	−4.77960
$834$	−8.12808e6	−0.404644
$835$	−1.14053e7	−0.566097
$836$	−743257.	−0.0367810
$837$	9.98548e6	0.492669
$838$	−3.43291e6	−0.168870
$839$	1.60927e7	0.789265	0.394632	−	0.918839i	$-0.370872\pi$
$839$	1.60927e7	0.789265	0.394632	+	0.918839i	$0.370872\pi$
$840$	2.52119e6	0.123284
$841$	6.38344e6	0.311218
$842$	−2.85585e7	−1.38821
$843$	−938502.	−0.0454848
$844$	9.64736e6	0.466179
$845$	2.42940e7	1.17046
$846$	−1.51764e7	−0.729026
$847$	−3.55932e6	−0.170474
$848$	−2.52125e7	−1.20400
$849$	1.09144e6	0.0519674
$850$	9.90318e6	0.470140
$851$	−4.12983e6	−0.195483
$852$	3.54186e6	0.167160
$853$	1.16425e7	0.547867	0.273934	−	0.961749i	$-0.411675\pi$
$853$	1.16425e7	0.547867	0.273934	+	0.961749i	$0.411675\pi$
$854$	5.11910e7	2.40187
$855$	−2.05196e6	−0.0959962
$856$	7.12847e6	0.332515
$857$	2.59558e7	1.20721	0.603604	−	0.797284i	$-0.293731\pi$
$857$	2.59558e7	1.20721	0.603604	+	0.797284i	$0.293731\pi$
$858$	−3.88204e6	−0.180029
$859$	2.19366e7	1.01435	0.507173	−	0.861844i	$-0.330691\pi$
$859$	2.19366e7	1.01435	0.507173	+	0.861844i	$0.330691\pi$
$860$	2.72634e6	0.125700
$861$	−29061.0	−0.00133599
$862$	2.69325e7	1.23455
$863$	−6.01839e6	−0.275077	−0.137538	−	0.990496i	$-0.543919\pi$
$863$	−6.01839e6	−0.275077	−0.137538	+	0.990496i	$0.543919\pi$
$864$	1.04103e7	0.474437
$865$	4.94450e6	0.224689
$866$	2.16960e7	0.983069
$867$	−1.46398e7	−0.661437
$868$	−2.22084e7	−1.00050
$869$	−8.85442e6	−0.397751
$870$	−3.58922e6	−0.160769
$871$	−5.75992e7	−2.57259
$872$	1.16302e7	0.517961
$873$	−1.40581e7	−0.624298
$874$	2.41498e6	0.106939
$875$	−3.79854e6	−0.167724
$876$	−397259.	−0.0174909
$877$	3.01217e6	0.132245	0.0661227	−	0.997811i	$-0.478937\pi$
$877$	3.01217e6	0.132245	0.0661227	+	0.997811i	$0.478937\pi$
$878$	−2.65936e6	−0.116424
$879$	−6.05772e6	−0.264446
$880$	3.86888e6	0.168414
$881$	4.96432e6	0.215486	0.107743	−	0.994179i	$-0.465638\pi$
$881$	4.96432e6	0.215486	0.107743	+	0.994179i	$0.465638\pi$
$882$	6.73233e7	2.91403
$883$	3.73731e7	1.61308	0.806542	−	0.591177i	$-0.201337\pi$
$883$	3.73731e7	1.61308	0.806542	+	0.591177i	$0.201337\pi$
$884$	−4.46294e7	−1.92084
$885$	1.18698e6	0.0509433
$886$	3.50229e7	1.49888
$887$	3.58755e6	0.153105	0.0765524	−	0.997066i	$-0.475609\pi$
$887$	3.58755e6	0.153105	0.0765524	+	0.997066i	$0.475609\pi$
$888$	−1.79292e6	−0.0763008
$889$	−5.57855e7	−2.36738
$890$	1.74265e7	0.737454
$891$	−5.79529e6	−0.244557
$892$	−2.57634e6	−0.108415
$893$	−3.44181e6	−0.144430
$894$	1.34709e7	0.563708
$895$	2.07918e7	0.867630
$896$	4.65052e7	1.93523
$897$	4.37872e6	0.181705
$898$	−2.18141e7	−0.902706
$899$	−2.78424e7	−1.14897
$900$	−2.41796e6	−0.0995044
$901$	−4.46153e7	−1.83093
$902$	−25609.8	−0.00104807
$903$	6.16100e6	0.251438
$904$	2.26539e7	0.921981
$905$	−5.65232e6	−0.229406
$906$	1.27784e7	0.517198
$907$	−2.53531e7	−1.02332	−0.511662	−	0.859187i	$-0.670970\pi$
$907$	−2.53531e7	−1.02332	−0.511662	+	0.859187i	$0.670970\pi$
$908$	−1.10723e7	−0.445680
$909$	3.62406e6	0.145474
$910$	4.93117e7	1.97400
$911$	−2.68142e7	−1.07046	−0.535228	−	0.844708i	$-0.679774\pi$
$911$	−2.68142e7	−1.07046	−0.535228	+	0.844708i	$0.679774\pi$
$912$	1.82570e6	0.0726844
$913$	1.32038e6	0.0524229
$914$	2.12085e7	0.839741
$915$	−2.97325e6	−0.117403
$916$	−1.97889e7	−0.779263
$917$	4.24237e6	0.166604
$918$	2.94707e7	1.15421
$919$	2.87718e7	1.12377	0.561886	−	0.827215i	$-0.310076\pi$
$919$	2.87718e7	1.12377	0.561886	+	0.827215i	$0.310076\pi$
$920$	−2.50603e6	−0.0976151
$921$	3.45703e6	0.134293
$922$	−3.81018e7	−1.47611
$923$	−6.10057e7	−2.35704
$924$	−1.97920e6	−0.0762622
$925$	2.70130e6	0.103805
$926$	−3.24532e6	−0.124374
$927$	9.19800e6	0.351556
$928$	−2.90269e7	−1.10645
$929$	1.04124e7	0.395834	0.197917	−	0.980219i	$-0.436582\pi$
$929$	1.04124e7	0.395834	0.197917	+	0.980219i	$0.436582\pi$
$930$	3.71571e6	0.140875
$931$	1.52680e7	0.577310
$932$	1.18325e7	0.446207
$933$	1.04068e6	0.0391392
$934$	4.08213e7	1.53116
$935$	6.84626e6	0.256109
$936$	−2.76424e7	−1.03130
$937$	−7.21927e6	−0.268624	−0.134312	−	0.990939i	$-0.542882\pi$
$937$	−7.21927e6	−0.268624	−0.134312	+	0.990939i	$0.542882\pi$
$938$	−8.45928e7	−3.13925
$939$	−4.37066e6	−0.161765
$940$	−4.05570e6	−0.149709
$941$	1.91021e7	0.703245	0.351623	−	0.936142i	$-0.385630\pi$
$941$	1.91021e7	0.703245	0.351623	+	0.936142i	$0.385630\pi$
$942$	−1.17668e6	−0.0432047
$943$	28886.4	0.00105782
$944$	1.53569e7	0.560885
$945$	−1.13040e7	−0.411768
$946$	5.42933e6	0.197250
$947$	−1.21745e7	−0.441139	−0.220570	−	0.975371i	$-0.570792\pi$
$947$	−1.21745e7	−0.441139	−0.220570	+	0.975371i	$0.570792\pi$
$948$	−4.92360e6	−0.177935
$949$	6.84246e6	0.246631
$950$	−1.57963e6	−0.0567865
$951$	−1.16546e7	−0.417873
$952$	5.77207e7	2.06414
$953$	3.64590e7	1.30039	0.650193	−	0.759769i	$-0.274688\pi$
$953$	3.64590e7	1.30039	0.650193	+	0.759769i	$0.274688\pi$
$954$	3.13794e7	1.11628
$955$	8.33631e6	0.295778
$956$	−1.29367e7	−0.457803
$957$	−2.48130e6	−0.0875788
$958$	6.71665e7	2.36450
$959$	−5.78014e7	−2.02951
$960$	−172075.	−0.00602616
$961$	194397.	0.00679018
$962$	−3.50676e7	−1.22171
$963$	−1.54494e7	−0.536840
$964$	4.70687e6	0.163132
$965$	−2.07840e7	−0.718473
$966$	6.43079e6	0.221728
$967$	−109938.	−0.00378077	−0.00189038	−	0.999998i	$-0.500602\pi$
$967$	−109938.	−0.00378077	−0.00189038	+	0.999998i	$0.500602\pi$
$968$	1.53595e6	0.0526853
$969$	3.23070e6	0.110532
$970$	−1.08221e7	−0.369304
$971$	1.91183e6	0.0650732	0.0325366	−	0.999471i	$-0.489641\pi$
$971$	1.91183e6	0.0650732	0.0325366	+	0.999471i	$0.489641\pi$
$972$	−1.09129e7	−0.370489
$973$	7.13766e7	2.41698
$974$	5.05042e7	1.70581
$975$	−2.86410e6	−0.0964887
$976$	−3.84671e7	−1.29260
$977$	−4.27374e7	−1.43242	−0.716212	−	0.697883i	$-0.754126\pi$
$977$	−4.27374e7	−1.43242	−0.716212	+	0.697883i	$0.754126\pi$
$978$	1.18152e6	0.0394996
$979$	1.20473e7	0.401728
$980$	1.79913e7	0.598408
$981$	−2.52060e7	−0.836239
$982$	−3.84266e7	−1.27161
$983$	−1.93576e7	−0.638952	−0.319476	−	0.947594i	$-0.603507\pi$
$983$	−1.93576e7	−0.638952	−0.319476	+	0.947594i	$0.603507\pi$
$984$	12540.7	0.000412890 0
$985$	−2.44944e7	−0.804407
$986$	−8.21727e7	−2.69175
$987$	−9.16511e6	−0.299464
$988$	7.11869e6	0.232011
$989$	−6.12397e6	−0.199087
$990$	−4.81520e6	−0.156144
$991$	−1.02739e7	−0.332315	−0.166158	−	0.986099i	$-0.553136\pi$
$991$	−1.02739e7	−0.332315	−0.166158	+	0.986099i	$0.553136\pi$
$992$	3.00498e7	0.969532
$993$	−1.86266e6	−0.0599459
$994$	−8.95958e7	−2.87622
$995$	1.54005e7	0.493149
$996$	734209.	0.0234516
$997$	−2.39789e7	−0.763996	−0.381998	−	0.924163i	$-0.624764\pi$
$997$	−2.39789e7	−0.763996	−0.381998	+	0.924163i	$0.624764\pi$
$998$	2.58353e7	0.821085
$999$	8.03874e6	0.254844

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.b.1.8	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.b.1.8	✓	36	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)

\(f(q)\)	\(=\)	\(q-7.00111 q^{2} -3.95422 q^{3} +17.0156 q^{4} +25.0000 q^{5} +27.6840 q^{6} -243.106 q^{7} +104.908 q^{8} -227.364 q^{9} +O(q^{10})\)	\(q-7.00111 q^{2} -3.95422 q^{3} +17.0156 q^{4} +25.0000 q^{5} +27.6840 q^{6} -243.106 q^{7} +104.908 q^{8} -227.364 q^{9} -175.028 q^{10} -121.000 q^{11} -67.2834 q^{12} +1158.90 q^{13} +1702.02 q^{14} -98.8556 q^{15} -1278.97 q^{16} -2263.23 q^{17} +1591.80 q^{18} +361.000 q^{19} +425.389 q^{20} +961.297 q^{21} +847.135 q^{22} -955.519 q^{23} -414.828 q^{24} +625.000 q^{25} -8113.60 q^{26} +1859.92 q^{27} -4136.59 q^{28} -5186.00 q^{29} +692.099 q^{30} +5368.76 q^{31} +5597.16 q^{32} +478.461 q^{33} +15845.1 q^{34} -6077.66 q^{35} -3868.73 q^{36} +4322.08 q^{37} -2527.40 q^{38} -4582.56 q^{39} +2622.69 q^{40} -30.2311 q^{41} -6730.15 q^{42} +6409.05 q^{43} -2058.88 q^{44} -5684.10 q^{45} +6689.70 q^{46} -9534.10 q^{47} +5057.33 q^{48} +42293.7 q^{49} -4375.69 q^{50} +8949.30 q^{51} +19719.4 q^{52} +19713.1 q^{53} -13021.5 q^{54} -3025.00 q^{55} -25503.7 q^{56} -1427.47 q^{57} +36307.8 q^{58} -12007.3 q^{59} -1682.08 q^{60} +30076.7 q^{61} -37587.3 q^{62} +55273.7 q^{63} +1740.67 q^{64} +28972.5 q^{65} -3349.76 q^{66} -49701.5 q^{67} -38510.1 q^{68} +3778.34 q^{69} +42550.4 q^{70} -52641.0 q^{71} -23852.2 q^{72} +5904.26 q^{73} -30259.4 q^{74} -2471.39 q^{75} +6142.62 q^{76} +29415.9 q^{77} +32083.0 q^{78} +73177.0 q^{79} -31974.2 q^{80} +47894.9 q^{81} +211.651 q^{82} -10912.2 q^{83} +16357.0 q^{84} -56580.6 q^{85} -44870.5 q^{86} +20506.6 q^{87} -12693.8 q^{88} -99564.2 q^{89} +39795.0 q^{90} -281736. q^{91} -16258.7 q^{92} -21229.3 q^{93} +66749.3 q^{94} +9025.00 q^{95} -22132.4 q^{96} +61830.9 q^{97} -296103. q^{98} +27511.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * q^99

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