LMFDB - Embedded newform 1045.6.a.f.1.11

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:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-6.07665 q^{2} -12.6619 q^{3} +4.92570 q^{4} +25.0000 q^{5} +76.9417 q^{6} +227.711 q^{7} +164.521 q^{8} -82.6774 q^{9} +O(q^{10})$	\(q-6.07665 q^{2} -12.6619 q^{3} +4.92570 q^{4} +25.0000 q^{5} +76.9417 q^{6} +227.711 q^{7} +164.521 q^{8} -82.6774 q^{9} -151.916 q^{10} -121.000 q^{11} -62.3686 q^{12} -1137.72 q^{13} -1383.72 q^{14} -316.546 q^{15} -1157.36 q^{16} -1535.63 q^{17} +502.402 q^{18} -361.000 q^{19} +123.143 q^{20} -2883.24 q^{21} +735.275 q^{22} -4069.28 q^{23} -2083.14 q^{24} +625.000 q^{25} +6913.56 q^{26} +4123.68 q^{27} +1121.64 q^{28} -7075.24 q^{29} +1923.54 q^{30} -7424.44 q^{31} +1768.20 q^{32} +1532.08 q^{33} +9331.50 q^{34} +5692.78 q^{35} -407.244 q^{36} -5794.70 q^{37} +2193.67 q^{38} +14405.7 q^{39} +4113.03 q^{40} -12211.4 q^{41} +17520.5 q^{42} -8670.54 q^{43} -596.010 q^{44} -2066.93 q^{45} +24727.6 q^{46} -7987.95 q^{47} +14654.3 q^{48} +35045.3 q^{49} -3797.91 q^{50} +19443.9 q^{51} -5604.09 q^{52} +35861.5 q^{53} -25058.2 q^{54} -3025.00 q^{55} +37463.3 q^{56} +4570.93 q^{57} +42993.8 q^{58} +19830.5 q^{59} -1559.21 q^{60} -2344.67 q^{61} +45115.8 q^{62} -18826.5 q^{63} +26290.8 q^{64} -28443.1 q^{65} -9309.95 q^{66} -55478.2 q^{67} -7564.07 q^{68} +51524.6 q^{69} -34593.0 q^{70} +11475.8 q^{71} -13602.2 q^{72} -84336.7 q^{73} +35212.4 q^{74} -7913.66 q^{75} -1778.18 q^{76} -27553.0 q^{77} -87538.5 q^{78} +43603.8 q^{79} -28934.0 q^{80} -32122.9 q^{81} +74204.2 q^{82} -29743.1 q^{83} -14202.0 q^{84} -38390.8 q^{85} +52687.8 q^{86} +89585.7 q^{87} -19907.1 q^{88} +22103.0 q^{89} +12560.0 q^{90} -259072. q^{91} -20044.0 q^{92} +94007.3 q^{93} +48540.0 q^{94} -9025.00 q^{95} -22388.7 q^{96} -95386.9 q^{97} -212958. q^{98} +10004.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) $ 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * 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 $

$2$	−6.07665	−1.07421	−0.537105	−	0.843515i	$-0.680482\pi$
$2$	−6.07665	−1.07421	−0.537105	+	0.843515i	$0.680482\pi$
$3$	−12.6619	−0.812259	−0.406129	−	0.913816i	$-0.633122\pi$
$3$	−12.6619	−0.812259	−0.406129	+	0.913816i	$0.633122\pi$
$4$	4.92570	0.153928
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	76.9417	0.872537
$7$	227.711	1.75646	0.878231	−	0.478236i	$-0.158724\pi$
$7$	227.711	1.75646	0.878231	+	0.478236i	$0.158724\pi$
$8$	164.521	0.908859
$9$	−82.6774	−0.340236
$10$	−151.916	−0.480402
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−62.3686	−0.125030
$13$	−1137.72	−1.86715	−0.933574	−	0.358385i	$-0.883328\pi$
$13$	−1137.72	−1.86715	−0.933574	+	0.358385i	$0.883328\pi$
$14$	−1383.72	−1.88681
$15$	−316.546	−0.363253
$16$	−1157.36	−1.13023
$17$	−1535.63	−1.28874	−0.644369	−	0.764715i	$-0.722880\pi$
$17$	−1535.63	−1.28874	−0.644369	+	0.764715i	$0.722880\pi$
$18$	502.402	0.365485
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	123.143	0.0688388
$21$	−2883.24	−1.42670
$22$	735.275	0.323887
$23$	−4069.28	−1.60397	−0.801987	−	0.597341i	$-0.796224\pi$
$23$	−4069.28	−1.60397	−0.801987	+	0.597341i	$0.796224\pi$
$24$	−2083.14	−0.738229
$25$	625.000	0.200000
$26$	6913.56	2.00571
$27$	4123.68	1.08862
$28$	1121.64	0.270369
$29$	−7075.24	−1.56223	−0.781117	−	0.624384i	$-0.785350\pi$
$29$	−7075.24	−1.56223	−0.781117	+	0.624384i	$0.785350\pi$
$30$	1923.54	0.390210
$31$	−7424.44	−1.38759	−0.693793	−	0.720175i	$-0.744062\pi$
$31$	−7424.44	−1.38759	−0.693793	+	0.720175i	$0.744062\pi$
$32$	1768.20	0.305250
$33$	1532.08	0.244905
$34$	9331.50	1.38438
$35$	5692.78	0.785514
$36$	−407.244	−0.0523719
$37$	−5794.70	−0.695868	−0.347934	−	0.937519i	$-0.613117\pi$
$37$	−5794.70	−0.695868	−0.347934	+	0.937519i	$0.613117\pi$
$38$	2193.67	0.246441
$39$	14405.7	1.51661
$40$	4113.03	0.406454
$41$	−12211.4	−1.13450	−0.567250	−	0.823546i	$-0.691993\pi$
$41$	−12211.4	−1.13450	−0.567250	+	0.823546i	$0.691993\pi$
$42$	17520.5	1.53258
$43$	−8670.54	−0.715113	−0.357557	−	0.933891i	$-0.616390\pi$
$43$	−8670.54	−0.715113	−0.357557	+	0.933891i	$0.616390\pi$
$44$	−596.010	−0.0464111
$45$	−2066.93	−0.152158
$46$	24727.6	1.72301
$47$	−7987.95	−0.527461	−0.263731	−	0.964596i	$-0.584953\pi$
$47$	−7987.95	−0.527461	−0.263731	+	0.964596i	$0.584953\pi$
$48$	14654.3	0.918043
$49$	35045.3	2.08516
$50$	−3797.91	−0.214842
$51$	19443.9	1.04679
$52$	−5604.09	−0.287407
$53$	35861.5	1.75364	0.876818	−	0.480823i	$-0.159662\pi$
$53$	35861.5	1.75364	0.876818	+	0.480823i	$0.159662\pi$
$54$	−25058.2	−1.16941
$55$	−3025.00	−0.134840
$56$	37463.3	1.59638
$57$	4570.93	0.186345
$58$	42993.8	1.67817
$59$	19830.5	0.741658	0.370829	−	0.928701i	$-0.379074\pi$
$59$	19830.5	0.741658	0.370829	+	0.928701i	$0.379074\pi$
$60$	−1559.21	−0.0559149
$61$	−2344.67	−0.0806784	−0.0403392	−	0.999186i	$-0.512844\pi$
$61$	−2344.67	−0.0806784	−0.0403392	+	0.999186i	$0.512844\pi$
$62$	45115.8	1.49056
$63$	−18826.5	−0.597612
$64$	26290.8	0.802331
$65$	−28443.1	−0.835014
$66$	−9309.95	−0.263080
$67$	−55478.2	−1.50986	−0.754928	−	0.655808i	$-0.772328\pi$
$67$	−55478.2	−1.50986	−0.754928	+	0.655808i	$0.772328\pi$
$68$	−7564.07	−0.198373
$69$	51524.6	1.30284
$70$	−34593.0	−0.843807
$71$	11475.8	0.270170	0.135085	−	0.990834i	$-0.456869\pi$
$71$	11475.8	0.270170	0.135085	+	0.990834i	$0.456869\pi$
$72$	−13602.2	−0.309227
$73$	−84336.7	−1.85229	−0.926146	−	0.377165i	$-0.876899\pi$
$73$	−84336.7	−1.85229	−0.926146	+	0.377165i	$0.876899\pi$
$74$	35212.4	0.747509
$75$	−7913.66	−0.162452
$76$	−1778.18	−0.0353136
$77$	−27553.0	−0.529593
$78$	−87538.5	−1.62915
$79$	43603.8	0.786062	0.393031	−	0.919525i	$-0.371426\pi$
$79$	43603.8	0.786062	0.393031	+	0.919525i	$0.371426\pi$
$80$	−28934.0	−0.505456
$81$	−32122.9	−0.544003
$82$	74204.2	1.21869
$83$	−29743.1	−0.473904	−0.236952	−	0.971521i	$-0.576148\pi$
$83$	−29743.1	−0.473904	−0.236952	+	0.971521i	$0.576148\pi$
$84$	−14202.0	−0.219610
$85$	−38390.8	−0.576341
$86$	52687.8	0.768182
$87$	89585.7	1.26894
$88$	−19907.1	−0.274031
$89$	22103.0	0.295785	0.147892	−	0.989003i	$-0.452751\pi$
$89$	22103.0	0.295785	0.147892	+	0.989003i	$0.452751\pi$
$90$	12560.0	0.163450
$91$	−259072.	−3.27958
$92$	−20044.0	−0.246897
$93$	94007.3	1.12708
$94$	48540.0	0.566604
$95$	−9025.00	−0.102598
$96$	−22388.7	−0.247942
$97$	−95386.9	−1.02934	−0.514671	−	0.857388i	$-0.672086\pi$
$97$	−95386.9	−1.02934	−0.514671	+	0.857388i	$0.672086\pi$
$98$	−212958.	−2.23990
$99$	10004.0	0.102585
$100$	3078.56	0.0307856
$101$	−34851.2	−0.339950	−0.169975	−	0.985448i	$-0.554369\pi$
$101$	−34851.2	−0.339950	−0.169975	+	0.985448i	$0.554369\pi$
$102$	−118154.	−1.12447
$103$	187766.	1.74391	0.871956	−	0.489585i	$-0.162852\pi$
$103$	187766.	1.74391	0.871956	+	0.489585i	$0.162852\pi$
$104$	−187180.	−1.69697
$105$	−72081.1	−0.638040
$106$	−217918.	−1.88377
$107$	−112354.	−0.948704	−0.474352	−	0.880335i	$-0.657318\pi$
$107$	−112354.	−0.948704	−0.474352	+	0.880335i	$0.657318\pi$
$108$	20312.0	0.167569
$109$	23889.3	0.192591	0.0962957	−	0.995353i	$-0.469301\pi$
$109$	23889.3	0.192591	0.0962957	+	0.995353i	$0.469301\pi$
$110$	18381.9	0.144847
$111$	73371.7	0.565225
$112$	−263544.	−1.98521
$113$	190574.	1.40400	0.701999	−	0.712178i	$-0.252291\pi$
$113$	190574.	1.40400	0.701999	+	0.712178i	$0.252291\pi$
$114$	−27776.0	−0.200174
$115$	−101732.	−0.717319
$116$	−34850.5	−0.240472
$117$	94064.0	0.635271
$118$	−120503.	−0.796697
$119$	−349680.	−2.26362
$120$	−52078.6	−0.330146
$121$	14641.0	0.0909091
$122$	14247.7	0.0866656
$123$	154619.	0.921507
$124$	−36570.6	−0.213589
$125$	15625.0	0.0894427
$126$	114402.	0.641961
$127$	−99831.3	−0.549234	−0.274617	−	0.961554i	$-0.588551\pi$
$127$	−99831.3	−0.549234	−0.274617	+	0.961554i	$0.588551\pi$
$128$	−216342.	−1.16712
$129$	109785.	0.580857
$130$	172839.	0.896981
$131$	52351.2	0.266532	0.133266	−	0.991080i	$-0.457454\pi$
$131$	52351.2	0.266532	0.133266	+	0.991080i	$0.457454\pi$
$132$	7546.60	0.0376978
$133$	−82203.7	−0.402960
$134$	337122.	1.62190
$135$	103092.	0.486845
$136$	−252644.	−1.17128
$137$	−422388.	−1.92269	−0.961347	−	0.275340i	$-0.911210\pi$
$137$	−422388.	−1.92269	−0.961347	+	0.275340i	$0.911210\pi$
$138$	−313097.	−1.39953
$139$	−293883.	−1.29014	−0.645070	−	0.764123i	$-0.723172\pi$
$139$	−293883.	−1.29014	−0.645070	+	0.764123i	$0.723172\pi$
$140$	28040.9	0.120913
$141$	101142.	0.428435
$142$	−69734.4	−0.290219
$143$	137665.	0.562966
$144$	95687.5	0.384546
$145$	−176881.	−0.698653
$146$	512485.	1.98975
$147$	−443739.	−1.69369
$148$	−28543.0	−0.107114
$149$	226601.	0.836173	0.418086	−	0.908407i	$-0.362701\pi$
$149$	226601.	0.836173	0.418086	+	0.908407i	$0.362701\pi$
$150$	48088.6	0.174507
$151$	174997.	0.624581	0.312291	−	0.949987i	$-0.398904\pi$
$151$	174997.	0.624581	0.312291	+	0.949987i	$0.398904\pi$
$152$	−59392.1	−0.208507
$153$	126962.	0.438475
$154$	167430.	0.568895
$155$	−185611.	−0.620547
$156$	70958.2	0.233449
$157$	255352.	0.826781	0.413391	−	0.910554i	$-0.364344\pi$
$157$	255352.	0.826781	0.413391	+	0.910554i	$0.364344\pi$
$158$	−264965.	−0.844396
$159$	−454074.	−1.42441
$160$	44205.0	0.136512
$161$	−926619.	−2.81732
$162$	195199.	0.584374
$163$	369338.	1.08882	0.544409	−	0.838820i	$-0.316754\pi$
$163$	369338.	1.08882	0.544409	+	0.838820i	$0.316754\pi$
$164$	−60149.5	−0.174632
$165$	38302.1	0.109525
$166$	180738.	0.509073
$167$	668078.	1.85369	0.926843	−	0.375449i	$-0.122511\pi$
$167$	668078.	1.85369	0.926843	+	0.375449i	$0.122511\pi$
$168$	−474355.	−1.29667
$169$	923124.	2.48624
$170$	233287.	0.619112
$171$	29846.5	0.0780555
$172$	−42708.5	−0.110076
$173$	104008.	0.264211	0.132105	−	0.991236i	$-0.457826\pi$
$173$	104008.	0.264211	0.132105	+	0.991236i	$0.457826\pi$
$174$	−544381.	−1.36311
$175$	142319.	0.351293
$176$	140041.	0.340778
$177$	−251091.	−0.602418
$178$	−134312.	−0.317735
$179$	−356440.	−0.831484	−0.415742	−	0.909483i	$-0.636478\pi$
$179$	−356440.	−0.831484	−0.415742	+	0.909483i	$0.636478\pi$
$180$	−10181.1	−0.0234214
$181$	211704.	0.480322	0.240161	−	0.970733i	$-0.422800\pi$
$181$	211704.	0.480322	0.240161	+	0.970733i	$0.422800\pi$
$182$	1.57429e6	3.52295
$183$	29687.9	0.0655317
$184$	−669482.	−1.45779
$185$	−144868.	−0.311202
$186$	−571249.	−1.21072
$187$	185811.	0.388569
$188$	−39346.3	−0.0811912
$189$	939007.	1.91212
$190$	54841.8	0.110212
$191$	−876575.	−1.73862	−0.869312	−	0.494263i	$-0.835438\pi$
$191$	−876575.	−1.73862	−0.869312	+	0.494263i	$0.835438\pi$
$192$	−332890.	−0.651700
$193$	377794.	0.730065	0.365033	−	0.930995i	$-0.381058\pi$
$193$	377794.	0.730065	0.365033	+	0.930995i	$0.381058\pi$
$194$	579633.	1.10573
$195$	360143.	0.678247
$196$	172623.	0.320965
$197$	240910.	0.442271	0.221135	−	0.975243i	$-0.429024\pi$
$197$	240910.	0.442271	0.221135	+	0.975243i	$0.429024\pi$
$198$	−60790.6	−0.110198
$199$	287999.	0.515535	0.257768	−	0.966207i	$-0.417013\pi$
$199$	287999.	0.515535	0.257768	+	0.966207i	$0.417013\pi$
$200$	102826.	0.181772
$201$	702457.	1.22639
$202$	211779.	0.365177
$203$	−1.61111e6	−2.74401
$204$	95775.1	0.161130
$205$	−305284.	−0.507364
$206$	−1.14099e6	−1.87333
$207$	336437.	0.545730
$208$	1.31676e6	2.11031
$209$	43681.0	0.0691714
$210$	438012.	0.685390
$211$	−542652.	−0.839103	−0.419551	−	0.907732i	$-0.637813\pi$
$211$	−542652.	−0.839103	−0.419551	+	0.907732i	$0.637813\pi$
$212$	176643.	0.269934
$213$	−145305.	−0.219448
$214$	682739.	1.01911
$215$	−216763.	−0.319808
$216$	678432.	0.989401
$217$	−1.69063e6	−2.43724
$218$	−145167.	−0.206884
$219$	1.06786e6	1.50454
$220$	−14900.3	−0.0207557
$221$	1.74713e6	2.40627
$222$	−445854.	−0.607170
$223$	140502.	0.189199	0.0945997	−	0.995515i	$-0.469843\pi$
$223$	140502.	0.189199	0.0945997	+	0.995515i	$0.469843\pi$
$224$	402638.	0.536161
$225$	−51673.3	−0.0680472
$226$	−1.15805e6	−1.50819
$227$	227789.	0.293405	0.146703	−	0.989181i	$-0.453134\pi$
$227$	227789.	0.293405	0.146703	+	0.989181i	$0.453134\pi$
$228$	22515.0	0.0286837
$229$	31159.0	0.0392640	0.0196320	−	0.999807i	$-0.493751\pi$
$229$	31159.0	0.0392640	0.0196320	+	0.999807i	$0.493751\pi$
$230$	618189.	0.770552
$231$	348873.	0.430167
$232$	−1.16403e6	−1.41985
$233$	90088.9	0.108713	0.0543565	−	0.998522i	$-0.482689\pi$
$233$	90088.9	0.108713	0.0543565	+	0.998522i	$0.482689\pi$
$234$	−571595.	−0.682415
$235$	−199699.	−0.235888
$236$	97679.2	0.114162
$237$	−552105.	−0.638486
$238$	2.12489e6	2.43161
$239$	−1.00043e6	−1.13290	−0.566450	−	0.824096i	$-0.691684\pi$
$239$	−1.00043e6	−1.13290	−0.566450	+	0.824096i	$0.691684\pi$
$240$	366358.	0.410561
$241$	−233403.	−0.258860	−0.129430	−	0.991589i	$-0.541315\pi$
$241$	−233403.	−0.258860	−0.129430	+	0.991589i	$0.541315\pi$
$242$	−88968.3	−0.0976555
$243$	−595319.	−0.646747
$244$	−11549.2	−0.0124187
$245$	876133.	0.932513
$246$	−939563.	−0.989893
$247$	410719.	0.428353
$248$	−1.22148e6	−1.26112
$249$	376603.	0.384933
$250$	−94947.7	−0.0960803
$251$	1.48735e6	1.49014	0.745072	−	0.666984i	$-0.232415\pi$
$251$	1.48735e6	1.49014	0.745072	+	0.666984i	$0.232415\pi$
$252$	−92734.0	−0.0919893
$253$	492382.	0.483617
$254$	606640.	0.589993
$255$	486099.	0.468138
$256$	473332.	0.451405
$257$	−551814.	−0.521146	−0.260573	−	0.965454i	$-0.583912\pi$
$257$	−551814.	−0.521146	−0.260573	+	0.965454i	$0.583912\pi$
$258$	−667126.	−0.623963
$259$	−1.31952e6	−1.22227
$260$	−140102.	−0.128532
$261$	584962.	0.531528
$262$	−318120.	−0.286311
$263$	923005.	0.822838	0.411419	−	0.911446i	$-0.365033\pi$
$263$	923005.	0.822838	0.411419	+	0.911446i	$0.365033\pi$
$264$	252060.	0.222584
$265$	896538.	0.784249
$266$	499523.	0.432864
$267$	−279865.	−0.240254
$268$	−273269.	−0.232409
$269$	−366571.	−0.308871	−0.154435	−	0.988003i	$-0.549356\pi$
$269$	−366571.	−0.308871	−0.154435	+	0.988003i	$0.549356\pi$
$270$	−626454.	−0.522974
$271$	−2.22527e6	−1.84060	−0.920300	−	0.391213i	$-0.872056\pi$
$271$	−2.22527e6	−1.84060	−0.920300	+	0.391213i	$0.872056\pi$
$272$	1.77728e6	1.45658
$273$	3.28034e6	2.66386
$274$	2.56671e6	2.06538
$275$	−75625.0	−0.0603023
$276$	253795.	0.200544
$277$	1.34756e6	1.05523	0.527615	−	0.849484i	$-0.323086\pi$
$277$	1.34756e6	1.05523	0.527615	+	0.849484i	$0.323086\pi$
$278$	1.78582e6	1.38588
$279$	613833.	0.472107
$280$	936582.	0.713922
$281$	385739.	0.291426	0.145713	−	0.989327i	$-0.453452\pi$
$281$	385739.	0.291426	0.145713	+	0.989327i	$0.453452\pi$
$282$	−614606.	−0.460229
$283$	−2.68888e6	−1.99575	−0.997874	−	0.0651652i	$-0.979243\pi$
$283$	−2.68888e6	−1.99575	−0.997874	+	0.0651652i	$0.979243\pi$
$284$	56526.4	0.0415868
$285$	114273.	0.0833360
$286$	−836540.	−0.604744
$287$	−2.78066e6	−1.99271
$288$	−146190.	−0.103857
$289$	938308.	0.660847
$290$	1.07484e6	0.750500
$291$	1.20778e6	0.836092
$292$	−415418.	−0.285120
$293$	2.03778e6	1.38672	0.693358	−	0.720593i	$-0.256130\pi$
$293$	2.03778e6	1.38672	0.693358	+	0.720593i	$0.256130\pi$
$294$	2.69645e6	1.81938
$295$	495763.	0.331680
$296$	−953351.	−0.632446
$297$	−498965.	−0.328231
$298$	−1.37698e6	−0.898226
$299$	4.62971e6	2.99486
$300$	−38980.3	−0.0250059
$301$	−1.97438e6	−1.25607
$302$	−1.06340e6	−0.670932
$303$	441281.	0.276127
$304$	417807.	0.259294
$305$	−58616.8	−0.0360805
$306$	−771504.	−0.471015
$307$	1.23777e6	0.749537	0.374768	−	0.927118i	$-0.377722\pi$
$307$	1.23777e6	0.749537	0.374768	+	0.927118i	$0.377722\pi$
$308$	−135718.	−0.0815194
$309$	−2.37747e6	−1.41651
$310$	1.12789e6	0.666598
$311$	130129.	0.0762911	0.0381456	−	0.999272i	$-0.487855\pi$
$311$	130129.	0.0762911	0.0381456	+	0.999272i	$0.487855\pi$
$312$	2.37004e6	1.37838
$313$	994057.	0.573522	0.286761	−	0.958002i	$-0.407421\pi$
$313$	994057.	0.573522	0.286761	+	0.958002i	$0.407421\pi$
$314$	−1.55169e6	−0.888137
$315$	−470664.	−0.267260
$316$	214780.	0.120997
$317$	291636.	0.163002	0.0815011	−	0.996673i	$-0.474029\pi$
$317$	291636.	0.163002	0.0815011	+	0.996673i	$0.474029\pi$
$318$	2.75925e6	1.53011
$319$	856104.	0.471031
$320$	657270.	0.358813
$321$	1.42262e6	0.770593
$322$	5.63074e6	3.02640
$323$	554363.	0.295657
$324$	−158228.	−0.0837375
$325$	−711078.	−0.373430
$326$	−2.24434e6	−1.16962
$327$	−302483.	−0.156434
$328$	−2.00903e6	−1.03110
$329$	−1.81894e6	−0.926466
$330$	−232749.	−0.117653
$331$	−3.11968e6	−1.56509	−0.782546	−	0.622593i	$-0.786079\pi$
$331$	−3.11968e6	−1.56509	−0.782546	+	0.622593i	$0.786079\pi$
$332$	−146506.	−0.0729473
$333$	479091.	0.236759
$334$	−4.05968e6	−1.99125
$335$	−1.38696e6	−0.675228
$336$	3.33695e6	1.61251
$337$	−1.24816e6	−0.598680	−0.299340	−	0.954147i	$-0.596766\pi$
$337$	−1.24816e6	−0.598680	−0.299340	+	0.954147i	$0.596766\pi$
$338$	−5.60950e6	−2.67075
$339$	−2.41302e6	−1.14041
$340$	−189102.	−0.0887152
$341$	898358.	0.418373
$342$	−181367.	−0.0838480
$343$	4.15306e6	1.90605
$344$	−1.42649e6	−0.649937
$345$	1.28811e6	0.582649
$346$	−632019.	−0.283818
$347$	−2.51454e6	−1.12107	−0.560537	−	0.828129i	$-0.689405\pi$
$347$	−2.51454e6	−1.12107	−0.560537	+	0.828129i	$0.689405\pi$
$348$	441273.	0.195325
$349$	15124.5	0.00664689	0.00332344	−	0.999994i	$-0.498942\pi$
$349$	15124.5	0.00664689	0.00332344	+	0.999994i	$0.498942\pi$
$350$	−864825.	−0.377362
$351$	−4.69161e6	−2.03261
$352$	−213952.	−0.0920365
$353$	−2.55875e6	−1.09293	−0.546464	−	0.837483i	$-0.684026\pi$
$353$	−2.55875e6	−1.09293	−0.546464	+	0.837483i	$0.684026\pi$
$354$	1.52579e6	0.647124
$355$	286895.	0.120824
$356$	108873.	0.0455296
$357$	4.42760e6	1.83865
$358$	2.16596e6	0.893189
$359$	1.57688e6	0.645746	0.322873	−	0.946442i	$-0.395351\pi$
$359$	1.57688e6	0.645746	0.322873	+	0.946442i	$0.395351\pi$
$360$	−340054.	−0.138290
$361$	130321.	0.0526316
$362$	−1.28645e6	−0.515967
$363$	−185382.	−0.0738417
$364$	−1.27611e6	−0.504819
$365$	−2.10842e6	−0.828370
$366$	−180403.	−0.0703949
$367$	676609.	0.262224	0.131112	−	0.991368i	$-0.458145\pi$
$367$	676609.	0.262224	0.131112	+	0.991368i	$0.458145\pi$
$368$	4.70962e6	1.81287
$369$	1.00960e6	0.385998
$370$	880310.	0.334296
$371$	8.16607e6	3.08019
$372$	463052.	0.173489
$373$	1.70559e6	0.634750	0.317375	−	0.948300i	$-0.397199\pi$
$373$	1.70559e6	0.634750	0.317375	+	0.948300i	$0.397199\pi$
$374$	−1.12911e6	−0.417405
$375$	−197842.	−0.0726506
$376$	−1.31419e6	−0.479388
$377$	8.04967e6	2.91692
$378$	−5.70602e6	−2.05402
$379$	−5.11702e6	−1.82986	−0.914932	−	0.403607i	$-0.867756\pi$
$379$	−5.11702e6	−1.82986	−0.914932	+	0.403607i	$0.867756\pi$
$380$	−44454.5	−0.0157927
$381$	1.26405e6	0.446120
$382$	5.32664e6	1.86765
$383$	−1.00430e6	−0.349839	−0.174919	−	0.984583i	$-0.555966\pi$
$383$	−1.00430e6	−0.349839	−0.174919	+	0.984583i	$0.555966\pi$
$384$	2.73930e6	0.948006
$385$	−688826.	−0.236841
$386$	−2.29572e6	−0.784244
$387$	716857.	0.243307
$388$	−469848.	−0.158445
$389$	−2.41598e6	−0.809504	−0.404752	−	0.914427i	$-0.632642\pi$
$389$	−2.41598e6	−0.809504	−0.404752	+	0.914427i	$0.632642\pi$
$390$	−2.18846e6	−0.728580
$391$	6.24891e6	2.06710
$392$	5.76569e6	1.89512
$393$	−662864.	−0.216492
$394$	−1.46392e6	−0.475092
$395$	1.09010e6	0.351538
$396$	49276.5	0.0157907
$397$	3.25396e6	1.03618	0.518092	−	0.855325i	$-0.326643\pi$
$397$	3.25396e6	1.03618	0.518092	+	0.855325i	$0.326643\pi$
$398$	−1.75007e6	−0.553793
$399$	1.04085e6	0.327308
$400$	−723350.	−0.226047
$401$	−388619.	−0.120688	−0.0603438	−	0.998178i	$-0.519220\pi$
$401$	−388619.	−0.120688	−0.0603438	+	0.998178i	$0.519220\pi$
$402$	−4.26859e6	−1.31740
$403$	8.44697e6	2.59083
$404$	−171667.	−0.0523278
$405$	−803071.	−0.243286
$406$	9.79016e6	2.94764
$407$	701159.	0.209812
$408$	3.19894e6	0.951384
$409$	3.63480e6	1.07442	0.537208	−	0.843450i	$-0.319479\pi$
$409$	3.63480e6	1.07442	0.537208	+	0.843450i	$0.319479\pi$
$410$	1.85510e6	0.545015
$411$	5.34822e6	1.56172
$412$	924881.	0.268437
$413$	4.51563e6	1.30270
$414$	−2.04441e6	−0.586229
$415$	−743577.	−0.211936
$416$	−2.01172e6	−0.569948
$417$	3.72110e6	1.04793
$418$	−265434.	−0.0743047
$419$	−3.05554e6	−0.850264	−0.425132	−	0.905131i	$-0.639772\pi$
$419$	−3.05554e6	−0.850264	−0.425132	+	0.905131i	$0.639772\pi$
$420$	−355050.	−0.0982124
$421$	−4.44052e6	−1.22104	−0.610519	−	0.792002i	$-0.709039\pi$
$421$	−4.44052e6	−1.22104	−0.610519	+	0.792002i	$0.709039\pi$
$422$	3.29751e6	0.901373
$423$	660422.	0.179461
$424$	5.89998e6	1.59381
$425$	−959770.	−0.257748
$426$	882967.	0.235733
$427$	−533907.	−0.141709
$428$	−553424.	−0.146032
$429$	−1.74309e6	−0.457274
$430$	1.31720e6	0.343542
$431$	5.07853e6	1.31688	0.658438	−	0.752635i	$-0.271217\pi$
$431$	5.07853e6	1.31688	0.658438	+	0.752635i	$0.271217\pi$
$432$	−4.77258e6	−1.23039
$433$	−5.60744e6	−1.43729	−0.718646	−	0.695376i	$-0.755238\pi$
$433$	−5.60744e6	−1.43729	−0.718646	+	0.695376i	$0.755238\pi$
$434$	1.02734e7	2.61811
$435$	2.23964e6	0.567486
$436$	117672.	0.0296453
$437$	1.46901e6	0.367977
$438$	−6.48901e6	−1.61619
$439$	−709711.	−0.175760	−0.0878801	−	0.996131i	$-0.528009\pi$
$439$	−709711.	−0.175760	−0.0878801	+	0.996131i	$0.528009\pi$
$440$	−497676.	−0.122551
$441$	−2.89745e6	−0.709447
$442$	−1.06167e7	−2.58484
$443$	−1.12792e6	−0.273068	−0.136534	−	0.990635i	$-0.543596\pi$
$443$	−1.12792e6	−0.273068	−0.136534	+	0.990635i	$0.543596\pi$
$444$	361407.	0.0870040
$445$	552574.	0.132279
$446$	−853780.	−0.203240
$447$	−2.86919e6	−0.679189
$448$	5.98670e6	1.40926
$449$	3.60867e6	0.844756	0.422378	−	0.906420i	$-0.361196\pi$
$449$	3.60867e6	0.844756	0.422378	+	0.906420i	$0.361196\pi$
$450$	314001.	0.0730970
$451$	1.47757e6	0.342065
$452$	938709.	0.216115
$453$	−2.21579e6	−0.507321
$454$	−1.38419e6	−0.315179
$455$	−6.47681e6	−1.46667
$456$	752014.	0.169361
$457$	5.11386e6	1.14540	0.572701	−	0.819764i	$-0.305896\pi$
$457$	5.11386e6	1.14540	0.572701	+	0.819764i	$0.305896\pi$
$458$	−189342.	−0.0421778
$459$	−6.33245e6	−1.40294
$460$	−501101.	−0.110416
$461$	−6.38378e6	−1.39903	−0.699513	−	0.714620i	$-0.746600\pi$
$461$	−6.38378e6	−1.39903	−0.699513	+	0.714620i	$0.746600\pi$
$462$	−2.11998e6	−0.462090
$463$	6.71133e6	1.45498	0.727489	−	0.686119i	$-0.240687\pi$
$463$	6.71133e6	1.45498	0.727489	+	0.686119i	$0.240687\pi$
$464$	8.18860e6	1.76569
$465$	2.35018e6	0.504045
$466$	−547439.	−0.116781
$467$	−757387.	−0.160704	−0.0803518	−	0.996767i	$-0.525604\pi$
$467$	−757387.	−0.160704	−0.0803518	+	0.996767i	$0.525604\pi$
$468$	463332.	0.0977861
$469$	−1.26330e7	−2.65201
$470$	1.21350e6	0.253393
$471$	−3.23324e6	−0.671560
$472$	3.26254e6	0.674063
$473$	1.04914e6	0.215615
$474$	3.35495e6	0.685868
$475$	−225625.	−0.0458831
$476$	−1.72242e6	−0.348435
$477$	−2.96494e6	−0.596650
$478$	6.07926e6	1.21697
$479$	−3.51129e6	−0.699242	−0.349621	−	0.936891i	$-0.613690\pi$
$479$	−3.51129e6	−0.699242	−0.349621	+	0.936891i	$0.613690\pi$
$480$	−559717.	−0.110883
$481$	6.59277e6	1.29929
$482$	1.41831e6	0.278070
$483$	1.17327e7	2.28839
$484$	72117.2	0.0139935
$485$	−2.38467e6	−0.460336
$486$	3.61755e6	0.694742
$487$	−4.29284e6	−0.820205	−0.410102	−	0.912039i	$-0.634507\pi$
$487$	−4.29284e6	−0.820205	−0.410102	+	0.912039i	$0.634507\pi$
$488$	−385748.	−0.0733253
$489$	−4.67651e6	−0.884401
$490$	−5.32395e6	−1.00171
$491$	−3.72159e6	−0.696666	−0.348333	−	0.937371i	$-0.613252\pi$
$491$	−3.72159e6	−0.696666	−0.348333	+	0.937371i	$0.613252\pi$
$492$	761605.	0.141846
$493$	1.08650e7	2.01331
$494$	−2.49579e6	−0.460141
$495$	250099.	0.0458774
$496$	8.59275e6	1.56830
$497$	2.61316e6	0.474543
$498$	−2.28848e6	−0.413499
$499$	−7.81855e6	−1.40564	−0.702821	−	0.711366i	$-0.748077\pi$
$499$	−7.81855e6	−1.40564	−0.702821	+	0.711366i	$0.748077\pi$
$500$	76964.1	0.0137678
$501$	−8.45911e6	−1.50567
$502$	−9.03810e6	−1.60073
$503$	450566.	0.0794033	0.0397016	−	0.999212i	$-0.487359\pi$
$503$	450566.	0.0794033	0.0397016	+	0.999212i	$0.487359\pi$
$504$	−3.09736e6	−0.543145
$505$	−871280.	−0.152030
$506$	−2.99204e6	−0.519506
$507$	−1.16885e7	−2.01947
$508$	−491739.	−0.0845426
$509$	−3.10999e6	−0.532065	−0.266033	−	0.963964i	$-0.585713\pi$
$509$	−3.10999e6	−0.532065	−0.266033	+	0.963964i	$0.585713\pi$
$510$	−2.95385e6	−0.502879
$511$	−1.92044e7	−3.25348
$512$	4.04668e6	0.682219
$513$	−1.48865e6	−0.249746
$514$	3.35318e6	0.559821
$515$	4.69416e6	0.779901
$516$	540769.	0.0894103
$517$	966542.	0.159036
$518$	8.01825e6	1.31297
$519$	−1.31693e6	−0.214607
$520$	−4.67949e6	−0.758910
$521$	8.77961e6	1.41704	0.708518	−	0.705693i	$-0.249364\pi$
$521$	8.77961e6	1.41704	0.708518	+	0.705693i	$0.249364\pi$
$522$	−3.55461e6	−0.570973
$523$	1.64708e6	0.263306	0.131653	−	0.991296i	$-0.457972\pi$
$523$	1.64708e6	0.263306	0.131653	+	0.991296i	$0.457972\pi$
$524$	257867.	0.0410267
$525$	−1.80203e6	−0.285340
$526$	−5.60878e6	−0.883902
$527$	1.14012e7	1.78823
$528$	−1.77317e6	−0.276800
$529$	1.01227e7	1.57274
$530$	−5.44795e6	−0.842449
$531$	−1.63953e6	−0.252339
$532$	−404911.	−0.0620269
$533$	1.38932e7	2.11828
$534$	1.70064e6	0.258083
$535$	−2.80886e6	−0.424273
$536$	−9.12734e6	−1.37225
$537$	4.51319e6	0.675380
$538$	2.22752e6	0.331792
$539$	−4.24048e6	−0.628700
$540$	507801.	0.0749392
$541$	−4.50686e6	−0.662035	−0.331017	−	0.943625i	$-0.607392\pi$
$541$	−4.50686e6	−0.662035	−0.331017	+	0.943625i	$0.607392\pi$
$542$	1.35222e7	1.97719
$543$	−2.68056e6	−0.390145
$544$	−2.71530e6	−0.393388
$545$	597232.	0.0861295
$546$	−1.99335e7	−2.86155
$547$	−1.04941e6	−0.149960	−0.0749801	−	0.997185i	$-0.523889\pi$
$547$	−1.04941e6	−0.149960	−0.0749801	+	0.997185i	$0.523889\pi$
$548$	−2.08056e6	−0.295957
$549$	193851.	0.0274497
$550$	459547.	0.0647773
$551$	2.55416e6	0.358401
$552$	8.47688e6	1.18410
$553$	9.92907e6	1.38069
$554$	−8.18862e6	−1.13354
$555$	1.83429e6	0.252776
$556$	−1.44758e6	−0.198589
$557$	1.13573e7	1.55109	0.775544	−	0.631293i	$-0.217476\pi$
$557$	1.13573e7	1.55109	0.775544	+	0.631293i	$0.217476\pi$
$558$	−3.73005e6	−0.507142
$559$	9.86468e6	1.33522
$560$	−6.58859e6	−0.887815
$561$	−2.35272e6	−0.315619
$562$	−2.34400e6	−0.313053
$563$	−7.76696e6	−1.03271	−0.516357	−	0.856373i	$-0.672712\pi$
$563$	−7.76696e6	−1.03271	−0.516357	+	0.856373i	$0.672712\pi$
$564$	498197.	0.0659482
$565$	4.76434e6	0.627887
$566$	1.63394e7	2.14385
$567$	−7.31473e6	−0.955522
$568$	1.88801e6	0.245546
$569$	−2.05568e6	−0.266180	−0.133090	−	0.991104i	$-0.542490\pi$
$569$	−2.05568e6	−0.266180	−0.133090	+	0.991104i	$0.542490\pi$
$570$	−694399.	−0.0895204
$571$	2.11152e6	0.271023	0.135511	−	0.990776i	$-0.456732\pi$
$571$	2.11152e6	0.271023	0.135511	+	0.990776i	$0.456732\pi$
$572$	678095.	0.0866564
$573$	1.10991e7	1.41221
$574$	1.68971e7	2.14059
$575$	−2.54330e6	−0.320795
$576$	−2.17365e6	−0.272982
$577$	−699388.	−0.0874538	−0.0437269	−	0.999044i	$-0.513923\pi$
$577$	−699388.	−0.0874538	−0.0437269	+	0.999044i	$0.513923\pi$
$578$	−5.70177e6	−0.709888
$579$	−4.78357e6	−0.593002
$580$	−871263.	−0.107542
$581$	−6.77283e6	−0.832395
$582$	−7.33923e6	−0.898138
$583$	−4.33925e6	−0.528741
$584$	−1.38752e7	−1.68347
$585$	2.35160e6	0.284102
$586$	−1.23829e7	−1.48963
$587$	1.50972e7	1.80843	0.904214	−	0.427079i	$-0.140457\pi$
$587$	1.50972e7	1.80843	0.904214	+	0.427079i	$0.140457\pi$
$588$	−2.18573e6	−0.260707
$589$	2.68022e6	0.318334
$590$	−3.01258e6	−0.356294
$591$	−3.05036e6	−0.359238
$592$	6.70656e6	0.786494
$593$	233418.	0.0272582	0.0136291	−	0.999907i	$-0.495662\pi$
$593$	233418.	0.0272582	0.0136291	+	0.999907i	$0.495662\pi$
$594$	3.03204e6	0.352589
$595$	−8.74201e6	−1.01232
$596$	1.11617e6	0.128711
$597$	−3.64660e6	−0.418748
$598$	−2.81332e7	−3.21711
$599$	1.25493e6	0.142906	0.0714531	−	0.997444i	$-0.477236\pi$
$599$	1.25493e6	0.142906	0.0714531	+	0.997444i	$0.477236\pi$
$600$	−1.30196e6	−0.147646
$601$	−9.94932e6	−1.12359	−0.561794	−	0.827277i	$-0.689889\pi$
$601$	−9.94932e6	−1.12359	−0.561794	+	0.827277i	$0.689889\pi$
$602$	1.19976e7	1.34928
$603$	4.58679e6	0.513707
$604$	861985.	0.0961407
$605$	366025.	0.0406558
$606$	−2.68151e6	−0.296618
$607$	−1.64526e7	−1.81244	−0.906218	−	0.422810i	$-0.861044\pi$
$607$	−1.64526e7	−1.81244	−0.906218	+	0.422810i	$0.861044\pi$
$608$	−638320.	−0.0700292
$609$	2.03996e7	2.22884
$610$	356194.	0.0387580
$611$	9.08808e6	0.984848
$612$	625377.	0.0674937
$613$	−5.43143e6	−0.583798	−0.291899	−	0.956449i	$-0.594287\pi$
$613$	−5.43143e6	−0.583798	−0.291899	+	0.956449i	$0.594287\pi$
$614$	−7.52148e6	−0.805160
$615$	3.86546e6	0.412111
$616$	−4.53305e6	−0.481326
$617$	−8.95926e6	−0.947457	−0.473728	−	0.880671i	$-0.657092\pi$
$617$	−8.95926e6	−0.947457	−0.473728	+	0.880671i	$0.657092\pi$
$618$	1.44471e7	1.52163
$619$	−1.06143e7	−1.11344	−0.556718	−	0.830702i	$-0.687940\pi$
$619$	−1.06143e7	−1.11344	−0.556718	+	0.830702i	$0.687940\pi$
$620$	−914265.	−0.0955197
$621$	−1.67804e7	−1.74612
$622$	−790750.	−0.0819527
$623$	5.03309e6	0.519535
$624$	−1.66726e7	−1.71412
$625$	390625.	0.0400000
$626$	−6.04054e6	−0.616084
$627$	−553083.	−0.0561851
$628$	1.25779e6	0.127265
$629$	8.89853e6	0.896792
$630$	2.86006e6	0.287094
$631$	−1.21722e7	−1.21701	−0.608506	−	0.793550i	$-0.708231\pi$
$631$	−1.21722e7	−1.21701	−0.608506	+	0.793550i	$0.708231\pi$
$632$	7.17375e6	0.714420
$633$	6.87098e6	0.681568
$634$	−1.77217e6	−0.175099
$635$	−2.49578e6	−0.245625
$636$	−2.23663e6	−0.219256
$637$	−3.98719e7	−3.89330
$638$	−5.20225e6	−0.505987
$639$	−948788.	−0.0919215
$640$	−5.40856e6	−0.521953
$641$	1.00145e7	0.962690	0.481345	−	0.876531i	$-0.340148\pi$
$641$	1.00145e7	0.962690	0.481345	+	0.876531i	$0.340148\pi$
$642$	−8.64474e6	−0.827779
$643$	428660.	0.0408870	0.0204435	−	0.999791i	$-0.493492\pi$
$643$	428660.	0.0408870	0.0204435	+	0.999791i	$0.493492\pi$
$644$	−4.56425e6	−0.433665
$645$	2.74463e6	0.259767
$646$	−3.36867e6	−0.317598
$647$	782225.	0.0734634	0.0367317	−	0.999325i	$-0.488305\pi$
$647$	782225.	0.0734634	0.0367317	+	0.999325i	$0.488305\pi$
$648$	−5.28489e6	−0.494423
$649$	−2.39949e6	−0.223618
$650$	4.32097e6	0.401142
$651$	2.14065e7	1.97967
$652$	1.81925e6	0.167600
$653$	−1.13297e7	−1.03977	−0.519885	−	0.854236i	$-0.674025\pi$
$653$	−1.13297e7	−1.03977	−0.519885	+	0.854236i	$0.674025\pi$
$654$	1.83808e6	0.168043
$655$	1.30878e6	0.119197
$656$	1.41329e7	1.28225
$657$	6.97274e6	0.630217
$658$	1.10531e7	0.995220
$659$	−881108.	−0.0790343	−0.0395171	−	0.999219i	$-0.512582\pi$
$659$	−881108.	−0.0790343	−0.0395171	+	0.999219i	$0.512582\pi$
$660$	188665.	0.0168590
$661$	−3.51732e6	−0.313119	−0.156559	−	0.987669i	$-0.550040\pi$
$661$	−3.51732e6	−0.313119	−0.156559	+	0.987669i	$0.550040\pi$
$662$	1.89572e7	1.68124
$663$	−2.21219e7	−1.95451
$664$	−4.89336e6	−0.430712
$665$	−2.05509e6	−0.180209
$666$	−2.91127e6	−0.254329
$667$	2.87911e7	2.50578
$668$	3.29076e6	0.285335
$669$	−1.77901e6	−0.153679
$670$	8.42804e6	0.725337
$671$	283705.	0.0243255
$672$	−5.09815e6	−0.435501
$673$	1.99955e7	1.70174	0.850872	−	0.525373i	$-0.176074\pi$
$673$	1.99955e7	1.70174	0.850872	+	0.525373i	$0.176074\pi$
$674$	7.58462e6	0.643108
$675$	2.57730e6	0.217724
$676$	4.54703e6	0.382703
$677$	1.47819e7	1.23954	0.619769	−	0.784785i	$-0.287226\pi$
$677$	1.47819e7	1.23954	0.619769	+	0.784785i	$0.287226\pi$
$678$	1.46631e7	1.22504
$679$	−2.17207e7	−1.80800
$680$	−6.31609e6	−0.523813
$681$	−2.88423e6	−0.238321
$682$	−5.45901e6	−0.449420
$683$	1.10884e7	0.909530	0.454765	−	0.890612i	$-0.349723\pi$
$683$	1.10884e7	0.909530	0.454765	+	0.890612i	$0.349723\pi$
$684$	147015.	0.0120149
$685$	−1.05597e7	−0.859855
$686$	−2.52367e7	−2.04749
$687$	−394530.	−0.0318925
$688$	1.00349e7	0.808246
$689$	−4.08005e7	−3.27430
$690$	−7.82743e6	−0.625887
$691$	6.10235e6	0.486186	0.243093	−	0.970003i	$-0.421838\pi$
$691$	6.10235e6	0.486186	0.243093	+	0.970003i	$0.421838\pi$
$692$	512311.	0.0406695
$693$	2.27801e6	0.180187
$694$	1.52800e7	1.20427
$695$	−7.34707e6	−0.576968
$696$	1.47387e7	1.15329
$697$	1.87522e7	1.46207
$698$	−91906.5	−0.00714016
$699$	−1.14069e6	−0.0883031
$700$	701023.	0.0540738
$701$	4.01134e6	0.308315	0.154158	−	0.988046i	$-0.450734\pi$
$701$	4.01134e6	0.308315	0.154158	+	0.988046i	$0.450734\pi$
$702$	2.85093e7	2.18345
$703$	2.09189e6	0.159643
$704$	−3.18119e6	−0.241912
$705$	2.52856e6	0.191602
$706$	1.55486e7	1.17403
$707$	−7.93601e6	−0.597109
$708$	−1.23680e6	−0.0927292
$709$	2.28332e7	1.70589	0.852945	−	0.522001i	$-0.174814\pi$
$709$	2.28332e7	1.70589	0.852945	+	0.522001i	$0.174814\pi$
$710$	−1.74336e6	−0.129790
$711$	−3.60505e6	−0.267447
$712$	3.63641e6	0.268827
$713$	3.02121e7	2.22565
$714$	−2.69050e7	−1.97509
$715$	3.44162e6	0.251766
$716$	−1.75572e6	−0.127989
$717$	1.26673e7	0.920208
$718$	−9.58214e6	−0.693667
$719$	−5.59888e6	−0.403905	−0.201952	−	0.979395i	$-0.564729\pi$
$719$	−5.59888e6	−0.403905	−0.201952	+	0.979395i	$0.564729\pi$
$720$	2.39219e6	0.171974
$721$	4.27564e7	3.06312
$722$	−791915.	−0.0565374
$723$	2.95532e6	0.210261
$724$	1.04279e6	0.0739351
$725$	−4.42203e6	−0.312447
$726$	1.12650e6	0.0793215
$727$	−3.24191e6	−0.227491	−0.113746	−	0.993510i	$-0.536285\pi$
$727$	−3.24191e6	−0.227491	−0.113746	+	0.993510i	$0.536285\pi$
$728$	−4.26229e7	−2.98067
$729$	1.53437e7	1.06933
$730$	1.28121e7	0.889844
$731$	1.33148e7	0.921594
$732$	146234.	0.0100872
$733$	−2.36817e7	−1.62799	−0.813996	−	0.580870i	$-0.802712\pi$
$733$	−2.36817e7	−1.62799	−0.813996	+	0.580870i	$0.802712\pi$
$734$	−4.11152e6	−0.281684
$735$	−1.10935e7	−0.757441
$736$	−7.19529e6	−0.489614
$737$	6.71286e6	0.455239
$738$	−6.13501e6	−0.414643
$739$	−1.70311e7	−1.14718	−0.573589	−	0.819143i	$-0.694449\pi$
$739$	−1.70311e7	−1.14718	−0.573589	+	0.819143i	$0.694449\pi$
$740$	−713575.	−0.0479027
$741$	−5.20046e6	−0.347933
$742$	−4.96224e7	−3.30878
$743$	4.94062e6	0.328329	0.164165	−	0.986433i	$-0.447507\pi$
$743$	4.94062e6	0.328329	0.164165	+	0.986433i	$0.447507\pi$
$744$	1.54662e7	1.02436
$745$	5.66502e6	0.373948
$746$	−1.03643e7	−0.681855
$747$	2.45908e6	0.161239
$748$	915252.	0.0598118
$749$	−2.55843e7	−1.66636
$750$	1.20221e6	0.0780421
$751$	1.14541e7	0.741073	0.370536	−	0.928818i	$-0.379174\pi$
$751$	1.14541e7	0.741073	0.370536	+	0.928818i	$0.379174\pi$
$752$	9.24493e6	0.596155
$753$	−1.88326e7	−1.21038
$754$	−4.89151e7	−3.13339
$755$	4.37493e6	0.279321
$756$	4.62527e6	0.294329
$757$	1.06088e6	0.0672860	0.0336430	−	0.999434i	$-0.489289\pi$
$757$	1.06088e6	0.0672860	0.0336430	+	0.999434i	$0.489289\pi$
$758$	3.10943e7	1.96566
$759$	−6.23448e6	−0.392822
$760$	−1.48480e6	−0.0932470
$761$	−9.58282e6	−0.599835	−0.299917	−	0.953965i	$-0.596959\pi$
$761$	−9.58282e6	−0.599835	−0.299917	+	0.953965i	$0.596959\pi$
$762$	−7.68119e6	−0.479227
$763$	5.43986e6	0.338280
$764$	−4.31775e6	−0.267623
$765$	3.17405e6	0.196092
$766$	6.10280e6	0.375800
$767$	−2.25617e7	−1.38479
$768$	−5.99326e6	−0.366657
$769$	−2.67192e7	−1.62933	−0.814664	−	0.579934i	$-0.803078\pi$
$769$	−2.67192e7	−1.62933	−0.814664	+	0.579934i	$0.803078\pi$
$770$	4.18576e6	0.254418
$771$	6.98699e6	0.423306
$772$	1.86090e6	0.112378
$773$	8.32952e6	0.501385	0.250692	−	0.968067i	$-0.419342\pi$
$773$	8.32952e6	0.501385	0.250692	+	0.968067i	$0.419342\pi$
$774$	−4.35609e6	−0.261363
$775$	−4.64028e6	−0.277517
$776$	−1.56932e7	−0.935527
$777$	1.67075e7	0.992796
$778$	1.46811e7	0.869577
$779$	4.40830e6	0.260272
$780$	1.77396e6	0.104401
$781$	−1.38857e6	−0.0814593
$782$	−3.79724e7	−2.22050
$783$	−2.91760e7	−1.70068
$784$	−4.05600e7	−2.35672
$785$	6.38381e6	0.369748
$786$	4.02799e6	0.232559
$787$	−2.26613e7	−1.30421	−0.652106	−	0.758127i	$-0.726114\pi$
$787$	−2.26613e7	−1.30421	−0.652106	+	0.758127i	$0.726114\pi$
$788$	1.18665e6	0.0680780
$789$	−1.16870e7	−0.668357
$790$	−6.62413e6	−0.377625
$791$	4.33957e7	2.46607
$792$	1.64586e6	0.0932353
$793$	2.66759e6	0.150638
$794$	−1.97732e7	−1.11308
$795$	−1.13518e7	−0.637013
$796$	1.41860e6	0.0793554
$797$	1.76141e7	0.982233	0.491116	−	0.871094i	$-0.336589\pi$
$797$	1.76141e7	0.982233	0.491116	+	0.871094i	$0.336589\pi$
$798$	−6.32489e6	−0.351598
$799$	1.22665e7	0.679760
$800$	1.10512e6	0.0610501
$801$	−1.82742e6	−0.100637
$802$	2.36150e6	0.129644
$803$	1.02047e7	0.558487
$804$	3.46010e6	0.188777
$805$	−2.31655e7	−1.25994
$806$	−5.13293e7	−2.78309
$807$	4.64146e6	0.250883
$808$	−5.73376e6	−0.308966
$809$	−2.40397e7	−1.29139	−0.645694	−	0.763596i	$-0.723432\pi$
$809$	−2.40397e7	−1.29139	−0.645694	+	0.763596i	$0.723432\pi$
$810$	4.87999e6	0.261340
$811$	2.74339e7	1.46465	0.732326	−	0.680954i	$-0.238435\pi$
$811$	2.74339e7	1.46465	0.732326	+	0.680954i	$0.238435\pi$
$812$	−7.93585e6	−0.422380
$813$	2.81761e7	1.49504
$814$	−4.26070e6	−0.225382
$815$	9.23345e6	0.486934
$816$	−2.25036e7	−1.18312
$817$	3.13006e6	0.164058
$818$	−2.20874e7	−1.15415
$819$	2.14194e7	1.11583
$820$	−1.50374e6	−0.0780976
$821$	1.27347e7	0.659374	0.329687	−	0.944090i	$-0.393057\pi$
$821$	1.27347e7	0.659374	0.329687	+	0.944090i	$0.393057\pi$
$822$	−3.24993e7	−1.67762
$823$	2.12504e7	1.09362	0.546812	−	0.837255i	$-0.315841\pi$
$823$	2.12504e7	1.09362	0.546812	+	0.837255i	$0.315841\pi$
$824$	3.08915e7	1.58497
$825$	957553.	0.0489810
$826$	−2.74399e7	−1.39937
$827$	1.63494e7	0.831262	0.415631	−	0.909533i	$-0.363561\pi$
$827$	1.63494e7	0.831262	0.415631	+	0.909533i	$0.363561\pi$
$828$	1.65719e6	0.0840033
$829$	−1.52343e7	−0.769905	−0.384952	−	0.922936i	$-0.625782\pi$
$829$	−1.52343e7	−0.769905	−0.384952	+	0.922936i	$0.625782\pi$
$830$	4.51846e6	0.227664
$831$	−1.70625e7	−0.857120
$832$	−2.99117e7	−1.49807
$833$	−5.38167e7	−2.68723
$834$	−2.26118e7	−1.12569
$835$	1.67020e7	0.828994
$836$	215160.	0.0106474
$837$	−3.06160e7	−1.51055
$838$	1.85675e7	0.913362
$839$	2.80135e7	1.37392	0.686961	−	0.726694i	$-0.258944\pi$
$839$	2.80135e7	1.37392	0.686961	+	0.726694i	$0.258944\pi$
$840$	−1.18589e7	−0.579889
$841$	2.95479e7	1.44058
$842$	2.69835e7	1.31165
$843$	−4.88418e6	−0.236713
$844$	−2.67294e6	−0.129162
$845$	2.30781e7	1.11188
$846$	−4.01316e6	−0.192779
$847$	3.33392e6	0.159678
$848$	−4.15047e7	−1.98202
$849$	3.40463e7	1.62106
$850$	5.83219e6	0.276875
$851$	2.35802e7	1.11615
$852$	−715729.	−0.0337792
$853$	1.02649e7	0.483037	0.241518	−	0.970396i	$-0.422355\pi$
$853$	1.02649e7	0.483037	0.241518	+	0.970396i	$0.422355\pi$
$854$	3.24437e6	0.152225
$855$	746163.	0.0349075
$856$	−1.84847e7	−0.862238
$857$	−1.79343e7	−0.834128	−0.417064	−	0.908877i	$-0.636941\pi$
$857$	−1.79343e7	−0.834128	−0.417064	+	0.908877i	$0.636941\pi$
$858$	1.05922e7	0.491209
$859$	−1.83901e6	−0.0850355	−0.0425178	−	0.999096i	$-0.513538\pi$
$859$	−1.83901e6	−0.0850355	−0.0425178	+	0.999096i	$0.513538\pi$
$860$	−1.06771e6	−0.0492275
$861$	3.52083e7	1.61859
$862$	−3.08605e7	−1.41460
$863$	−1.69451e7	−0.774494	−0.387247	−	0.921976i	$-0.626574\pi$
$863$	−1.69451e7	−0.774494	−0.387247	+	0.921976i	$0.626574\pi$
$864$	7.29149e6	0.332301
$865$	2.60019e6	0.118159
$866$	3.40745e7	1.54395
$867$	−1.18807e7	−0.536778
$868$	−8.32753e6	−0.375160
$869$	−5.27606e6	−0.237007
$870$	−1.36095e7	−0.609600
$871$	6.31189e7	2.81912
$872$	3.93029e6	0.175039
$873$	7.88634e6	0.350219
$874$	−8.92665e6	−0.395285
$875$	3.55798e6	0.157103
$876$	5.25996e6	0.231591
$877$	−1.90281e7	−0.835403	−0.417701	−	0.908584i	$-0.637164\pi$
$877$	−1.90281e7	−0.835403	−0.417701	+	0.908584i	$0.637164\pi$
$878$	4.31267e6	0.188803
$879$	−2.58021e7	−1.12637
$880$	3.50101e6	0.152401
$881$	−2.67742e7	−1.16219	−0.581095	−	0.813836i	$-0.697376\pi$
$881$	−2.67742e7	−1.16219	−0.581095	+	0.813836i	$0.697376\pi$
$882$	1.76068e7	0.762095
$883$	−4.36036e6	−0.188200	−0.0941002	−	0.995563i	$-0.529997\pi$
$883$	−4.36036e6	−0.188200	−0.0941002	+	0.995563i	$0.529997\pi$
$884$	8.60582e6	0.370392
$885$	−6.27728e6	−0.269410
$886$	6.85400e6	0.293332
$887$	2.59343e7	1.10679	0.553395	−	0.832919i	$-0.313332\pi$
$887$	2.59343e7	1.10679	0.553395	+	0.832919i	$0.313332\pi$
$888$	1.20712e7	0.513710
$889$	−2.27327e7	−0.964709
$890$	−3.35780e6	−0.142095
$891$	3.88687e6	0.164023
$892$	692070.	0.0291231
$893$	2.88365e6	0.121008
$894$	1.74351e7	0.729592
$895$	−8.91100e6	−0.371851
$896$	−4.92635e7	−2.05001
$897$	−5.86208e7	−2.43260
$898$	−2.19286e7	−0.907446
$899$	5.25297e7	2.16773
$900$	−254528.	−0.0104744
$901$	−5.50701e7	−2.25998
$902$	−8.97871e6	−0.367449
$903$	2.49993e7	1.02025
$904$	3.13534e7	1.27604
$905$	5.29260e6	0.214806
$906$	1.34646e7	0.544970
$907$	−277001.	−0.0111805	−0.00559027	−	0.999984i	$-0.501779\pi$
$907$	−277001.	−0.0111805	−0.00559027	+	0.999984i	$0.501779\pi$
$908$	1.12202e6	0.0451634
$909$	2.88141e6	0.115663
$910$	3.93573e7	1.57551
$911$	−2.83116e7	−1.13023	−0.565116	−	0.825011i	$-0.691169\pi$
$911$	−2.83116e7	−1.13023	−0.565116	+	0.825011i	$0.691169\pi$
$912$	−5.29021e6	−0.210613
$913$	3.59891e6	0.142888
$914$	−3.10751e7	−1.23040
$915$	742197.	0.0293067
$916$	153480.	0.00604383
$917$	1.19209e7	0.468153
$918$	3.84801e7	1.50706
$919$	−3.23493e6	−0.126350	−0.0631752	−	0.998002i	$-0.520123\pi$
$919$	−3.23493e6	−0.126350	−0.0631752	+	0.998002i	$0.520123\pi$
$920$	−1.67370e7	−0.651942
$921$	−1.56724e7	−0.608818
$922$	3.87920e7	1.50285
$923$	−1.30563e7	−0.504447
$924$	1.71844e6	0.0662148
$925$	−3.62169e6	−0.139174
$926$	−4.07824e7	−1.56295
$927$	−1.55240e7	−0.593342
$928$	−1.25104e7	−0.476873
$929$	2.66257e7	1.01219	0.506094	−	0.862478i	$-0.331089\pi$
$929$	2.66257e7	1.01219	0.506094	+	0.862478i	$0.331089\pi$
$930$	−1.42812e7	−0.541450
$931$	−1.26514e7	−0.478369
$932$	443751.	0.0167340
$933$	−1.64768e6	−0.0619681
$934$	4.60238e6	0.172629
$935$	4.64529e6	0.173773
$936$	1.54755e7	0.577372
$937$	−2.75141e7	−1.02378	−0.511890	−	0.859051i	$-0.671054\pi$
$937$	−2.75141e7	−1.02378	−0.511890	+	0.859051i	$0.671054\pi$
$938$	7.67663e7	2.84881
$939$	−1.25866e7	−0.465848
$940$	−983656.	−0.0363098
$941$	5.38259e6	0.198160	0.0990802	−	0.995079i	$-0.468410\pi$
$941$	5.38259e6	0.198160	0.0990802	+	0.995079i	$0.468410\pi$
$942$	1.96472e7	0.721397
$943$	4.96914e7	1.81971
$944$	−2.29510e7	−0.838248
$945$	2.34752e7	0.855125
$946$	−6.37523e6	−0.231616
$947$	−2.35164e7	−0.852112	−0.426056	−	0.904697i	$-0.640097\pi$
$947$	−2.35164e7	−0.852112	−0.426056	+	0.904697i	$0.640097\pi$
$948$	−2.71951e6	−0.0982810
$949$	9.59519e7	3.45850
$950$	1.37104e6	0.0492882
$951$	−3.69266e6	−0.132400
$952$	−5.75298e7	−2.05731
$953$	−1.18453e7	−0.422487	−0.211244	−	0.977433i	$-0.567751\pi$
$953$	−1.18453e7	−0.422487	−0.211244	+	0.977433i	$0.567751\pi$
$954$	1.80169e7	0.640928
$955$	−2.19144e7	−0.777537
$956$	−4.92782e6	−0.174385
$957$	−1.08399e7	−0.382599
$958$	2.13369e7	0.751133
$959$	−9.61824e7	−3.37714
$960$	−8.32226e6	−0.291449
$961$	2.64932e7	0.925393
$962$	−4.00620e7	−1.39571
$963$	9.28916e6	0.322783
$964$	−1.14968e6	−0.0398458
$965$	9.44485e6	0.326495
$966$	−7.12956e7	−2.45822
$967$	−4.34322e7	−1.49364	−0.746819	−	0.665028i	$-0.768420\pi$
$967$	−4.34322e7	−1.49364	−0.746819	+	0.665028i	$0.768420\pi$
$968$	2.40875e6	0.0826236
$969$	−7.01927e6	−0.240150
$970$	1.44908e7	0.494497
$971$	5.24871e7	1.78651	0.893253	−	0.449554i	$-0.148417\pi$
$971$	5.24871e7	1.78651	0.893253	+	0.449554i	$0.148417\pi$
$972$	−2.93237e6	−0.0995526
$973$	−6.69203e7	−2.26608
$974$	2.60861e7	0.881073
$975$	9.00357e6	0.303321
$976$	2.71363e6	0.0911855
$977$	−2.67697e7	−0.897236	−0.448618	−	0.893724i	$-0.648084\pi$
$977$	−2.67697e7	−0.897236	−0.448618	+	0.893724i	$0.648084\pi$
$978$	2.84175e7	0.950033
$979$	−2.67446e6	−0.0891824
$980$	4.31557e6	0.143540
$981$	−1.97510e6	−0.0655266
$982$	2.26148e7	0.748366
$983$	5.19118e7	1.71349	0.856747	−	0.515737i	$-0.172482\pi$
$983$	5.19118e7	1.71349	0.856747	+	0.515737i	$0.172482\pi$
$984$	2.54380e7	0.837520
$985$	6.02274e6	0.197790
$986$	−6.60226e7	−2.16272
$987$	2.30312e7	0.752530
$988$	2.02308e6	0.0659356
$989$	3.52828e7	1.14702
$990$	−1.51976e6	−0.0492820
$991$	1.97861e7	0.639995	0.319998	−	0.947418i	$-0.396318\pi$
$991$	1.97861e7	0.639995	0.319998	+	0.947418i	$0.396318\pi$
$992$	−1.31279e7	−0.423561
$993$	3.95009e7	1.27126
$994$	−1.58793e7	−0.509759
$995$	7.19998e6	0.230554
$996$	1.85503e6	0.0592520
$997$	−5.84514e6	−0.186233	−0.0931167	−	0.995655i	$-0.529683\pi$
$997$	−5.84514e6	−0.186233	−0.0931167	+	0.995655i	$0.529683\pi$
$998$	4.75106e7	1.50996
$999$	−2.38955e7	−0.757534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.f.1.11	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.f.1.11	✓	38	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)

\(f(q)\)	\(=\)	\(q-6.07665 q^{2} -12.6619 q^{3} +4.92570 q^{4} +25.0000 q^{5} +76.9417 q^{6} +227.711 q^{7} +164.521 q^{8} -82.6774 q^{9} +O(q^{10})\)	\(q-6.07665 q^{2} -12.6619 q^{3} +4.92570 q^{4} +25.0000 q^{5} +76.9417 q^{6} +227.711 q^{7} +164.521 q^{8} -82.6774 q^{9} -151.916 q^{10} -121.000 q^{11} -62.3686 q^{12} -1137.72 q^{13} -1383.72 q^{14} -316.546 q^{15} -1157.36 q^{16} -1535.63 q^{17} +502.402 q^{18} -361.000 q^{19} +123.143 q^{20} -2883.24 q^{21} +735.275 q^{22} -4069.28 q^{23} -2083.14 q^{24} +625.000 q^{25} +6913.56 q^{26} +4123.68 q^{27} +1121.64 q^{28} -7075.24 q^{29} +1923.54 q^{30} -7424.44 q^{31} +1768.20 q^{32} +1532.08 q^{33} +9331.50 q^{34} +5692.78 q^{35} -407.244 q^{36} -5794.70 q^{37} +2193.67 q^{38} +14405.7 q^{39} +4113.03 q^{40} -12211.4 q^{41} +17520.5 q^{42} -8670.54 q^{43} -596.010 q^{44} -2066.93 q^{45} +24727.6 q^{46} -7987.95 q^{47} +14654.3 q^{48} +35045.3 q^{49} -3797.91 q^{50} +19443.9 q^{51} -5604.09 q^{52} +35861.5 q^{53} -25058.2 q^{54} -3025.00 q^{55} +37463.3 q^{56} +4570.93 q^{57} +42993.8 q^{58} +19830.5 q^{59} -1559.21 q^{60} -2344.67 q^{61} +45115.8 q^{62} -18826.5 q^{63} +26290.8 q^{64} -28443.1 q^{65} -9309.95 q^{66} -55478.2 q^{67} -7564.07 q^{68} +51524.6 q^{69} -34593.0 q^{70} +11475.8 q^{71} -13602.2 q^{72} -84336.7 q^{73} +35212.4 q^{74} -7913.66 q^{75} -1778.18 q^{76} -27553.0 q^{77} -87538.5 q^{78} +43603.8 q^{79} -28934.0 q^{80} -32122.9 q^{81} +74204.2 q^{82} -29743.1 q^{83} -14202.0 q^{84} -38390.8 q^{85} +52687.8 q^{86} +89585.7 q^{87} -19907.1 q^{88} +22103.0 q^{89} +12560.0 q^{90} -259072. q^{91} -20044.0 q^{92} +94007.3 q^{93} +48540.0 q^{94} -9025.00 q^{95} -22388.7 q^{96} -95386.9 q^{97} -212958. q^{98} +10004.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * q^99

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