LMFDB - Embedded newform 1045.6.a.d.1.17

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:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-0.603954 q^{2} -13.9085 q^{3} -31.6352 q^{4} -25.0000 q^{5} +8.40008 q^{6} -27.7104 q^{7} +38.4328 q^{8} -49.5544 q^{9} +O(q^{10})$	\(q-0.603954 q^{2} -13.9085 q^{3} -31.6352 q^{4} -25.0000 q^{5} +8.40008 q^{6} -27.7104 q^{7} +38.4328 q^{8} -49.5544 q^{9} +15.0989 q^{10} +121.000 q^{11} +439.998 q^{12} +632.733 q^{13} +16.7358 q^{14} +347.712 q^{15} +989.116 q^{16} -988.388 q^{17} +29.9286 q^{18} -361.000 q^{19} +790.881 q^{20} +385.409 q^{21} -73.0785 q^{22} -2974.54 q^{23} -534.541 q^{24} +625.000 q^{25} -382.142 q^{26} +4068.98 q^{27} +876.625 q^{28} -3095.62 q^{29} -210.002 q^{30} +6438.75 q^{31} -1827.23 q^{32} -1682.93 q^{33} +596.941 q^{34} +692.760 q^{35} +1567.66 q^{36} +11005.1 q^{37} +218.028 q^{38} -8800.34 q^{39} -960.820 q^{40} +1268.87 q^{41} -232.770 q^{42} -10198.3 q^{43} -3827.86 q^{44} +1238.86 q^{45} +1796.49 q^{46} +8903.49 q^{47} -13757.1 q^{48} -16039.1 q^{49} -377.472 q^{50} +13747.0 q^{51} -20016.6 q^{52} -22942.9 q^{53} -2457.48 q^{54} -3025.00 q^{55} -1064.99 q^{56} +5020.96 q^{57} +1869.61 q^{58} -30054.0 q^{59} -10999.9 q^{60} -11435.5 q^{61} -3888.71 q^{62} +1373.17 q^{63} -30548.1 q^{64} -15818.3 q^{65} +1016.41 q^{66} -64755.8 q^{67} +31267.9 q^{68} +41371.3 q^{69} -418.395 q^{70} -29625.7 q^{71} -1904.51 q^{72} -85242.8 q^{73} -6646.59 q^{74} -8692.80 q^{75} +11420.3 q^{76} -3352.96 q^{77} +5315.01 q^{78} -50905.5 q^{79} -24727.9 q^{80} -44551.7 q^{81} -766.341 q^{82} +88697.1 q^{83} -12192.5 q^{84} +24709.7 q^{85} +6159.29 q^{86} +43055.4 q^{87} +4650.37 q^{88} +47190.4 q^{89} -748.215 q^{90} -17533.3 q^{91} +94100.3 q^{92} -89553.2 q^{93} -5377.30 q^{94} +9025.00 q^{95} +25414.0 q^{96} -16740.6 q^{97} +9686.91 q^{98} -5996.08 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) $ 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9} - 100 q^{10} + 4477 q^{11} + 872 q^{12} + 719 q^{13} - 625 q^{14} - 675 q^{15} + 6940 q^{16} + 119 q^{17} - 4237 q^{18} - 13357 q^{19} - 15400 q^{20} + 2905 q^{21} + 484 q^{22} - 1252 q^{23} + 5884 q^{24} + 23125 q^{25} + 13201 q^{26} + 9918 q^{27} + 15461 q^{28} + 13221 q^{29} - 3525 q^{30} + 6419 q^{31} + 13173 q^{32} + 3267 q^{33} + 35415 q^{34} + 1975 q^{35} + 80543 q^{36} + 9037 q^{37} - 1444 q^{38} - 6184 q^{39} - 1800 q^{40} + 52577 q^{41} - 28578 q^{42} + 963 q^{43} + 74536 q^{44} - 78500 q^{45} - 10531 q^{46} + 49346 q^{47} + 80107 q^{48} + 70288 q^{49} + 2500 q^{50} + 140786 q^{51} + 165062 q^{52} - 34457 q^{53} + 34216 q^{54} - 111925 q^{55} - 64095 q^{56} - 9747 q^{57} - 126140 q^{58} + 56521 q^{59} - 21800 q^{60} + 6613 q^{61} + 494 q^{62} - 125618 q^{63} - 140426 q^{64} - 17975 q^{65} + 17061 q^{66} - 43534 q^{67} - 138520 q^{68} + 34618 q^{69} + 15625 q^{70} + 95986 q^{71} - 42192 q^{72} + 109218 q^{73} - 182005 q^{74} + 16875 q^{75} - 222376 q^{76} - 9559 q^{77} - 369624 q^{78} + 64943 q^{79} - 173500 q^{80} + 388941 q^{81} - 126926 q^{82} + 109741 q^{83} - 112886 q^{84} - 2975 q^{85} + 43866 q^{86} + 142492 q^{87} + 8712 q^{88} - 119092 q^{89} + 105925 q^{90} + 349320 q^{91} + 433396 q^{92} - 108630 q^{93} + 196160 q^{94} + 333925 q^{95} + 376630 q^{96} + 68774 q^{97} + 310926 q^{98} + 379940 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9 - 100 * q^10 + 4477 * q^11 + 872 * q^12 + 719 * q^13 - 625 * q^14 - 675 * q^15 + 6940 * q^16 + 119 * q^17 - 4237 * q^18 - 13357 * q^19 - 15400 * q^20 + 2905 * q^21 + 484 * q^22 - 1252 * q^23 + 5884 * q^24 + 23125 * q^25 + 13201 * q^26 + 9918 * q^27 + 15461 * q^28 + 13221 * q^29 - 3525 * q^30 + 6419 * q^31 + 13173 * q^32 + 3267 * q^33 + 35415 * q^34 + 1975 * q^35 + 80543 * q^36 + 9037 * q^37 - 1444 * q^38 - 6184 * q^39 - 1800 * q^40 + 52577 * q^41 - 28578 * q^42 + 963 * q^43 + 74536 * q^44 - 78500 * q^45 - 10531 * q^46 + 49346 * q^47 + 80107 * q^48 + 70288 * q^49 + 2500 * q^50 + 140786 * q^51 + 165062 * q^52 - 34457 * q^53 + 34216 * q^54 - 111925 * q^55 - 64095 * q^56 - 9747 * q^57 - 126140 * q^58 + 56521 * q^59 - 21800 * q^60 + 6613 * q^61 + 494 * q^62 - 125618 * q^63 - 140426 * q^64 - 17975 * q^65 + 17061 * q^66 - 43534 * q^67 - 138520 * q^68 + 34618 * q^69 + 15625 * q^70 + 95986 * q^71 - 42192 * q^72 + 109218 * q^73 - 182005 * q^74 + 16875 * q^75 - 222376 * q^76 - 9559 * q^77 - 369624 * q^78 + 64943 * q^79 - 173500 * q^80 + 388941 * q^81 - 126926 * q^82 + 109741 * q^83 - 112886 * q^84 - 2975 * q^85 + 43866 * q^86 + 142492 * q^87 + 8712 * q^88 - 119092 * q^89 + 105925 * q^90 + 349320 * q^91 + 433396 * q^92 - 108630 * q^93 + 196160 * q^94 + 333925 * q^95 + 376630 * q^96 + 68774 * q^97 + 310926 * q^98 + 379940 * 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 $

$2$	−0.603954	−0.106765	−0.0533825	−	0.998574i	$-0.517000\pi$
$2$	−0.603954	−0.106765	−0.0533825	+	0.998574i	$0.517000\pi$
$3$	−13.9085	−0.892229	−0.446114	−	0.894976i	$-0.647193\pi$
$3$	−13.9085	−0.892229	−0.446114	+	0.894976i	$0.647193\pi$
$4$	−31.6352	−0.988601
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	8.40008	0.0952589
$7$	−27.7104	−0.213746	−0.106873	−	0.994273i	$-0.534084\pi$
$7$	−27.7104	−0.213746	−0.106873	+	0.994273i	$0.534084\pi$
$8$	38.4328	0.212313
$9$	−49.5544	−0.203927
$10$	15.0989	0.0477468
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	439.998	0.882059
$13$	632.733	1.03839	0.519197	−	0.854655i	$-0.326231\pi$
$13$	632.733	1.03839	0.519197	+	0.854655i	$0.326231\pi$
$14$	16.7358	0.0228206
$15$	347.712	0.399017
$16$	989.116	0.965934
$17$	−988.388	−0.829478	−0.414739	−	0.909940i	$-0.636127\pi$
$17$	−988.388	−0.829478	−0.414739	+	0.909940i	$0.636127\pi$
$18$	29.9286	0.0217723
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	790.881	0.442116
$21$	385.409	0.190710
$22$	−73.0785	−0.0321909
$23$	−2974.54	−1.17247	−0.586233	−	0.810142i	$-0.699390\pi$
$23$	−2974.54	−1.17247	−0.586233	+	0.810142i	$0.699390\pi$
$24$	−534.541	−0.189432
$25$	625.000	0.200000
$26$	−382.142	−0.110864
$27$	4068.98	1.07418
$28$	876.625	0.211309
$29$	−3095.62	−0.683523	−0.341761	−	0.939787i	$-0.611023\pi$
$29$	−3095.62	−0.683523	−0.341761	+	0.939787i	$0.611023\pi$
$30$	−210.002	−0.0426011
$31$	6438.75	1.20337	0.601683	−	0.798735i	$-0.294497\pi$
$31$	6438.75	1.20337	0.601683	+	0.798735i	$0.294497\pi$
$32$	−1827.23	−0.315441
$33$	−1682.93	−0.269017
$34$	596.941	0.0885593
$35$	692.760	0.0955900
$36$	1567.66	0.201603
$37$	11005.1	1.32157	0.660786	−	0.750575i	$-0.270223\pi$
$37$	11005.1	1.32157	0.660786	+	0.750575i	$0.270223\pi$
$38$	218.028	0.0244936
$39$	−8800.34	−0.926484
$40$	−960.820	−0.0949493
$41$	1268.87	0.117885	0.0589425	−	0.998261i	$-0.481227\pi$
$41$	1268.87	0.117885	0.0589425	+	0.998261i	$0.481227\pi$
$42$	−232.770	−0.0203612
$43$	−10198.3	−0.841115	−0.420558	−	0.907266i	$-0.638166\pi$
$43$	−10198.3	−0.841115	−0.420558	+	0.907266i	$0.638166\pi$
$44$	−3827.86	−0.298074
$45$	1238.86	0.0911991
$46$	1796.49	0.125178
$47$	8903.49	0.587917	0.293958	−	0.955818i	$-0.405027\pi$
$47$	8903.49	0.587917	0.293958	+	0.955818i	$0.405027\pi$
$48$	−13757.1	−0.861834
$49$	−16039.1	−0.954313
$50$	−377.472	−0.0213530
$51$	13747.0	0.740085
$52$	−20016.6	−1.02656
$53$	−22942.9	−1.12191	−0.560957	−	0.827845i	$-0.689567\pi$
$53$	−22942.9	−1.12191	−0.560957	+	0.827845i	$0.689567\pi$
$54$	−2457.48	−0.114685
$55$	−3025.00	−0.134840
$56$	−1064.99	−0.0453810
$57$	5020.96	0.204691
$58$	1869.61	0.0729763
$59$	−30054.0	−1.12402	−0.562008	−	0.827132i	$-0.689971\pi$
$59$	−30054.0	−1.12402	−0.562008	+	0.827132i	$0.689971\pi$
$60$	−10999.9	−0.394469
$61$	−11435.5	−0.393489	−0.196744	−	0.980455i	$-0.563037\pi$
$61$	−11435.5	−0.393489	−0.196744	+	0.980455i	$0.563037\pi$
$62$	−3888.71	−0.128477
$63$	1373.17	0.0435886
$64$	−30548.1	−0.932255
$65$	−15818.3	−0.464384
$66$	1016.41	0.0287216
$67$	−64755.8	−1.76235	−0.881174	−	0.472791i	$-0.843246\pi$
$67$	−64755.8	−1.76235	−0.881174	+	0.472791i	$0.843246\pi$
$68$	31267.9	0.820023
$69$	41371.3	1.04611
$70$	−418.395	−0.0102057
$71$	−29625.7	−0.697466	−0.348733	−	0.937222i	$-0.613388\pi$
$71$	−29625.7	−0.697466	−0.348733	+	0.937222i	$0.613388\pi$
$72$	−1904.51	−0.0432965
$73$	−85242.8	−1.87219	−0.936096	−	0.351745i	$-0.885588\pi$
$73$	−85242.8	−1.87219	−0.936096	+	0.351745i	$0.885588\pi$
$74$	−6646.59	−0.141098
$75$	−8692.80	−0.178446
$76$	11420.3	0.226801
$77$	−3352.96	−0.0644468
$78$	5315.01	0.0989162
$79$	−50905.5	−0.917692	−0.458846	−	0.888516i	$-0.651737\pi$
$79$	−50905.5	−0.917692	−0.458846	+	0.888516i	$0.651737\pi$
$80$	−24727.9	−0.431979
$81$	−44551.7	−0.754486
$82$	−766.341	−0.0125860
$83$	88697.1	1.41324	0.706618	−	0.707596i	$-0.250220\pi$
$83$	88697.1	1.41324	0.706618	+	0.707596i	$0.250220\pi$
$84$	−12192.5	−0.188536
$85$	24709.7	0.370954
$86$	6159.29	0.0898018
$87$	43055.4	0.609859
$88$	4650.37	0.0640148
$89$	47190.4	0.631508	0.315754	−	0.948841i	$-0.397743\pi$
$89$	47190.4	0.631508	0.315754	+	0.948841i	$0.397743\pi$
$90$	−748.215	−0.00973688
$91$	−17533.3	−0.221952
$92$	94100.3	1.15910
$93$	−89553.2	−1.07368
$94$	−5377.30	−0.0627690
$95$	9025.00	0.102598
$96$	25414.0	0.281446
$97$	−16740.6	−0.180652	−0.0903259	−	0.995912i	$-0.528791\pi$
$97$	−16740.6	−0.180652	−0.0903259	+	0.995912i	$0.528791\pi$
$98$	9686.91	0.101887
$99$	−5996.08	−0.0614864
$100$	−19772.0	−0.197720
$101$	−105808.	−1.03208	−0.516041	−	0.856564i	$-0.672595\pi$
$101$	−105808.	−1.03208	−0.516041	+	0.856564i	$0.672595\pi$
$102$	−8302.54	−0.0790152
$103$	−149703.	−1.39039	−0.695195	−	0.718822i	$-0.744682\pi$
$103$	−149703.	−1.39039	−0.695195	+	0.718822i	$0.744682\pi$
$104$	24317.7	0.220465
$105$	−9635.23	−0.0852882
$106$	13856.5	0.119781
$107$	124398.	1.05039	0.525197	−	0.850981i	$-0.323992\pi$
$107$	124398.	1.05039	0.525197	+	0.850981i	$0.323992\pi$
$108$	−128723.	−1.06193
$109$	246419.	1.98659	0.993294	−	0.115617i	$-0.0368844\pi$
$109$	246419.	1.98659	0.993294	+	0.115617i	$0.0368844\pi$
$110$	1826.96	0.0143962
$111$	−153064.	−1.17914
$112$	−27408.8	−0.206464
$113$	45961.1	0.338606	0.169303	−	0.985564i	$-0.445848\pi$
$113$	45961.1	0.338606	0.169303	+	0.985564i	$0.445848\pi$
$114$	−3032.43	−0.0218539
$115$	74363.5	0.524343
$116$	97930.7	0.675731
$117$	−31354.7	−0.211757
$118$	18151.3	0.120006
$119$	27388.6	0.177298
$120$	13363.5	0.0847165
$121$	14641.0	0.0909091
$122$	6906.55	0.0420108
$123$	−17648.1	−0.105180
$124$	−203691.	−1.18965
$125$	−15625.0	−0.0894427
$126$	−829.333	−0.00465374
$127$	−246111.	−1.35401	−0.677004	−	0.735980i	$-0.736722\pi$
$127$	−246111.	−1.35401	−0.677004	+	0.735980i	$0.736722\pi$
$128$	76921.1	0.414973
$129$	141842.	0.750468
$130$	9553.54	0.0495799
$131$	81604.4	0.415466	0.207733	−	0.978186i	$-0.433391\pi$
$131$	81604.4	0.415466	0.207733	+	0.978186i	$0.433391\pi$
$132$	53239.7	0.265951
$133$	10003.5	0.0490367
$134$	39109.6	0.188157
$135$	−101725.	−0.480387
$136$	−37986.5	−0.176109
$137$	196474.	0.894341	0.447171	−	0.894449i	$-0.352432\pi$
$137$	196474.	0.894341	0.447171	+	0.894449i	$0.352432\pi$
$138$	−24986.4	−0.111688
$139$	−179046.	−0.786009	−0.393004	−	0.919537i	$-0.628564\pi$
$139$	−179046.	−0.786009	−0.393004	+	0.919537i	$0.628564\pi$
$140$	−21915.6	−0.0945004
$141$	−123834.	−0.524556
$142$	17892.6	0.0744650
$143$	76560.6	0.313087
$144$	−49015.0	−0.196980
$145$	77390.5	0.305681
$146$	51482.7	0.199885
$147$	223080.	0.851465
$148$	−348150.	−1.30651
$149$	−345559.	−1.27514	−0.637568	−	0.770394i	$-0.720059\pi$
$149$	−345559.	−1.27514	−0.637568	+	0.770394i	$0.720059\pi$
$150$	5250.05	0.0190518
$151$	51224.0	0.182823	0.0914115	−	0.995813i	$-0.470862\pi$
$151$	51224.0	0.182823	0.0914115	+	0.995813i	$0.470862\pi$
$152$	−13874.2	−0.0487080
$153$	48978.9	0.169153
$154$	2025.03	0.00688067
$155$	−160969.	−0.538161
$156$	278401.	0.915924
$157$	−334572.	−1.08328	−0.541640	−	0.840610i	$-0.682196\pi$
$157$	−334572.	−1.08328	−0.541640	+	0.840610i	$0.682196\pi$
$158$	30744.6	0.0979774
$159$	319101.	1.00100
$160$	45680.8	0.141070
$161$	82425.7	0.250610
$162$	26907.2	0.0805528
$163$	336290.	0.991391	0.495695	−	0.868496i	$-0.334913\pi$
$163$	336290.	0.991391	0.495695	+	0.868496i	$0.334913\pi$
$164$	−40141.1	−0.116541
$165$	42073.1	0.120308
$166$	−53569.0	−0.150884
$167$	176391.	0.489423	0.244712	−	0.969596i	$-0.421307\pi$
$167$	176391.	0.489423	0.244712	+	0.969596i	$0.421307\pi$
$168$	14812.4	0.0404903
$169$	29057.5	0.0782604
$170$	−14923.5	−0.0396049
$171$	17889.1	0.0467842
$172$	322625.	0.831528
$173$	236163.	0.599925	0.299963	−	0.953951i	$-0.403026\pi$
$173$	236163.	0.599925	0.299963	+	0.953951i	$0.403026\pi$
$174$	−26003.5	−0.0651116
$175$	−17319.0	−0.0427492
$176$	119683.	0.291240
$177$	418005.	1.00288
$178$	−28500.9	−0.0674230
$179$	−284034.	−0.662579	−0.331290	−	0.943529i	$-0.607484\pi$
$179$	−284034.	−0.662579	−0.331290	+	0.943529i	$0.607484\pi$
$180$	−39191.6	−0.0901596
$181$	−477289.	−1.08289	−0.541445	−	0.840736i	$-0.682123\pi$
$181$	−477289.	−1.08289	−0.541445	+	0.840736i	$0.682123\pi$
$182$	10589.3	0.0236967
$183$	159051.	0.351082
$184$	−114320.	−0.248930
$185$	−275128.	−0.591025
$186$	54086.1	0.114631
$187$	−119595.	−0.250097
$188$	−281664.	−0.581215
$189$	−112753.	−0.229601
$190$	−5450.69	−0.0109539
$191$	−587151.	−1.16457	−0.582286	−	0.812984i	$-0.697842\pi$
$191$	−587151.	−1.16457	−0.582286	+	0.812984i	$0.697842\pi$
$192$	424878.	0.831785
$193$	98385.1	0.190124	0.0950619	−	0.995471i	$-0.469695\pi$
$193$	98385.1	0.190124	0.0950619	+	0.995471i	$0.469695\pi$
$194$	10110.6	0.0192873
$195$	220009.	0.414336
$196$	507402.	0.943435
$197$	548964.	1.00781	0.503904	−	0.863760i	$-0.331896\pi$
$197$	548964.	1.00781	0.503904	+	0.863760i	$0.331896\pi$
$198$	3621.36	0.00656460
$199$	934448.	1.67272	0.836358	−	0.548183i	$-0.184680\pi$
$199$	934448.	1.67272	0.836358	+	0.548183i	$0.184680\pi$
$200$	24020.5	0.0424626
$201$	900655.	1.57242
$202$	63903.1	0.110190
$203$	85780.9	0.146100
$204$	−434889.	−0.731649
$205$	−31721.8	−0.0527197
$206$	90413.6	0.148445
$207$	147402.	0.239098
$208$	625846.	1.00302
$209$	−43681.0	−0.0691714
$210$	5819.24	0.00910580
$211$	−352342.	−0.544826	−0.272413	−	0.962180i	$-0.587822\pi$
$211$	−352342.	−0.544826	−0.272413	+	0.962180i	$0.587822\pi$
$212$	725805.	1.10913
$213$	412048.	0.622299
$214$	−75130.4	−0.112145
$215$	254957.	0.376158
$216$	156382.	0.228062
$217$	−178420.	−0.257214
$218$	−148826.	−0.212098
$219$	1.18560e6	1.67042
$220$	95696.6	0.133303
$221$	−625385.	−0.861325
$222$	92444.0	0.125891
$223$	28757.8	0.0387252	0.0193626	−	0.999813i	$-0.493836\pi$
$223$	28757.8	0.0387252	0.0193626	+	0.999813i	$0.493836\pi$
$224$	50633.3	0.0674242
$225$	−30971.5	−0.0407855
$226$	−27758.4	−0.0361513
$227$	−827599.	−1.06600	−0.532998	−	0.846117i	$-0.678935\pi$
$227$	−827599.	−1.06600	−0.532998	+	0.846117i	$0.678935\pi$
$228$	−158839.	−0.202358
$229$	321020.	0.404523	0.202261	−	0.979332i	$-0.435171\pi$
$229$	321020.	0.404523	0.202261	+	0.979332i	$0.435171\pi$
$230$	−44912.2	−0.0559815
$231$	46634.5	0.0575013
$232$	−118973.	−0.145121
$233$	717000.	0.865226	0.432613	−	0.901580i	$-0.357592\pi$
$233$	717000.	0.865226	0.432613	+	0.901580i	$0.357592\pi$
$234$	18936.8	0.0226082
$235$	−222587.	−0.262924
$236$	950766.	1.11120
$237$	708017.	0.818791
$238$	−16541.5	−0.0189292
$239$	275625.	0.312122	0.156061	−	0.987747i	$-0.450120\pi$
$239$	275625.	0.312122	0.156061	+	0.987747i	$0.450120\pi$
$240$	343927.	0.385424
$241$	−60894.5	−0.0675360	−0.0337680	−	0.999430i	$-0.510751\pi$
$241$	−60894.5	−0.0675360	−0.0337680	+	0.999430i	$0.510751\pi$
$242$	−8842.50	−0.00970592
$243$	−369118.	−0.401005
$244$	361766.	0.389003
$245$	400978.	0.426782
$246$	10658.6	0.0112296
$247$	−228416.	−0.238224
$248$	247459.	0.255490
$249$	−1.23364e6	−1.26093
$250$	9436.79	0.00954936
$251$	1.30802e6	1.31048	0.655238	−	0.755422i	$-0.272568\pi$
$251$	1.30802e6	1.31048	0.655238	+	0.755422i	$0.272568\pi$
$252$	−43440.6	−0.0430918
$253$	−359920.	−0.353512
$254$	148640.	0.144561
$255$	−343674.	−0.330976
$256$	931084.	0.887951
$257$	1.39798e6	1.32029	0.660143	−	0.751140i	$-0.270496\pi$
$257$	1.39798e6	1.32029	0.660143	+	0.751140i	$0.270496\pi$
$258$	−85666.4	−0.0801237
$259$	−304956.	−0.282480
$260$	500416.	0.459090
$261$	153402.	0.139389
$262$	−49285.4	−0.0443573
$263$	486004.	0.433262	0.216631	−	0.976254i	$-0.430493\pi$
$263$	486004.	0.433262	0.216631	+	0.976254i	$0.430493\pi$
$264$	−64679.5	−0.0571159
$265$	573574.	0.501735
$266$	−6041.63	−0.00523540
$267$	−656347.	−0.563450
$268$	2.04857e6	1.74226
$269$	−1.23084e6	−1.03710	−0.518548	−	0.855048i	$-0.673527\pi$
$269$	−1.23084e6	−1.03710	−0.518548	+	0.855048i	$0.673527\pi$
$270$	61437.0	0.0512886
$271$	1.57977e6	1.30668	0.653342	−	0.757063i	$-0.273366\pi$
$271$	1.57977e6	1.30668	0.653342	+	0.757063i	$0.273366\pi$
$272$	−977630.	−0.801221
$273$	243861.	0.198032
$274$	−118661.	−0.0954844
$275$	75625.0	0.0603023
$276$	−1.30879e6	−1.03418
$277$	1.38300e6	1.08299	0.541493	−	0.840705i	$-0.317859\pi$
$277$	1.38300e6	1.08299	0.541493	+	0.840705i	$0.317859\pi$
$278$	108136.	0.0839183
$279$	−319068.	−0.245399
$280$	26624.7	0.0202950
$281$	324283.	0.244996	0.122498	−	0.992469i	$-0.460910\pi$
$281$	324283.	0.244996	0.122498	+	0.992469i	$0.460910\pi$
$282$	74790.1	0.0560043
$283$	−1.82834e6	−1.35703	−0.678516	−	0.734586i	$-0.737376\pi$
$283$	−1.82834e6	−1.35703	−0.678516	+	0.734586i	$0.737376\pi$
$284$	937216.	0.689515
$285$	−125524.	−0.0915408
$286$	−46239.1	−0.0334268
$287$	−35161.0	−0.0251974
$288$	90547.2	0.0643271
$289$	−442947.	−0.311966
$290$	−46740.4	−0.0326360
$291$	232837.	0.161183
$292$	2.69667e6	1.85085
$293$	−2.84386e6	−1.93526	−0.967629	−	0.252377i	$-0.918788\pi$
$293$	−2.84386e6	−1.93526	−0.967629	+	0.252377i	$0.918788\pi$
$294$	−134730.	−0.0909068
$295$	751350.	0.502675
$296$	422958.	0.280587
$297$	492347.	0.323877
$298$	208702.	0.136140
$299$	−1.88209e6	−1.21748
$300$	274999.	0.176412
$301$	282598.	0.179785
$302$	−30936.9	−0.0195191
$303$	1.47163e6	0.920854
$304$	−357071.	−0.221600
$305$	285889.	0.175973
$306$	−29581.0	−0.0180597
$307$	−2.93972e6	−1.78017	−0.890083	−	0.455799i	$-0.849353\pi$
$307$	−2.93972e6	−1.78017	−0.890083	+	0.455799i	$0.849353\pi$
$308$	106072.	0.0637122
$309$	2.08214e6	1.24055
$310$	97217.8	0.0574568
$311$	373982.	0.219255	0.109627	−	0.993973i	$-0.465034\pi$
$311$	373982.	0.219255	0.109627	+	0.993973i	$0.465034\pi$
$312$	−338222.	−0.196705
$313$	−337696.	−0.194834	−0.0974172	−	0.995244i	$-0.531058\pi$
$313$	−337696.	−0.194834	−0.0974172	+	0.995244i	$0.531058\pi$
$314$	202066.	0.115657
$315$	−34329.3	−0.0194934
$316$	1.61041e6	0.907231
$317$	1.04384e6	0.583428	0.291714	−	0.956506i	$-0.405774\pi$
$317$	1.04384e6	0.583428	0.291714	+	0.956506i	$0.405774\pi$
$318$	−192723.	−0.106872
$319$	−374570.	−0.206090
$320$	763704.	0.416917
$321$	−1.73018e6	−0.937192
$322$	−49781.4	−0.0267564
$323$	356808.	0.190295
$324$	1.40940e6	0.745886
$325$	395458.	0.207679
$326$	−203104.	−0.105846
$327$	−3.42731e6	−1.77249
$328$	48766.3	0.0250285
$329$	−246719.	−0.125665
$330$	−25410.3	−0.0128447
$331$	642595.	0.322380	0.161190	−	0.986923i	$-0.448467\pi$
$331$	642595.	0.322380	0.161190	+	0.986923i	$0.448467\pi$
$332$	−2.80596e6	−1.39713
$333$	−545352.	−0.269505
$334$	−106532.	−0.0522533
$335$	1.61890e6	0.788146
$336$	381214.	0.184213
$337$	1.79003e6	0.858588	0.429294	−	0.903165i	$-0.358762\pi$
$337$	1.79003e6	0.858588	0.429294	+	0.903165i	$0.358762\pi$
$338$	−17549.4	−0.00835548
$339$	−639249.	−0.302114
$340$	−781697.	−0.366726
$341$	779089.	0.362828
$342$	−10804.2	−0.00499492
$343$	910179.	0.417726
$344$	−391948.	−0.178580
$345$	−1.03428e6	−0.467834
$346$	−142632.	−0.0640511
$347$	2.15774e6	0.962001	0.481000	−	0.876720i	$-0.340274\pi$
$347$	2.15774e6	0.962001	0.481000	+	0.876720i	$0.340274\pi$
$348$	−1.36207e6	−0.602907
$349$	−511639.	−0.224854	−0.112427	−	0.993660i	$-0.535862\pi$
$349$	−511639.	−0.224854	−0.112427	+	0.993660i	$0.535862\pi$
$350$	10459.9	0.00456412
$351$	2.57458e6	1.11542
$352$	−221095.	−0.0951091
$353$	−1.99302e6	−0.851284	−0.425642	−	0.904892i	$-0.639952\pi$
$353$	−1.99302e6	−0.851284	−0.425642	+	0.904892i	$0.639952\pi$
$354$	−252456.	−0.107072
$355$	740643.	0.311916
$356$	−1.49288e6	−0.624310
$357$	−380934.	−0.158190
$358$	171544.	0.0707403
$359$	3.17267e6	1.29924	0.649619	−	0.760260i	$-0.274928\pi$
$359$	3.17267e6	1.29924	0.649619	+	0.760260i	$0.274928\pi$
$360$	47612.8	0.0193628
$361$	130321.	0.0526316
$362$	288261.	0.115615
$363$	−203634.	−0.0811117
$364$	554669.	0.219422
$365$	2.13107e6	0.837270
$366$	−96059.5	−0.0374833
$367$	−2.31483e6	−0.897127	−0.448564	−	0.893751i	$-0.648064\pi$
$367$	−2.31483e6	−0.897127	−0.448564	+	0.893751i	$0.648064\pi$
$368$	−2.94217e6	−1.13252
$369$	−62878.2	−0.0240400
$370$	166165.	0.0631008
$371$	635758.	0.239804
$372$	2.83304e6	1.06144
$373$	339277.	0.126265	0.0631324	−	0.998005i	$-0.479891\pi$
$373$	339277.	0.126265	0.0631324	+	0.998005i	$0.479891\pi$
$374$	72229.9	0.0267016
$375$	217320.	0.0798034
$376$	342186.	0.124822
$377$	−1.95870e6	−0.709765
$378$	68097.8	0.0245134
$379$	87221.2	0.0311906	0.0155953	−	0.999878i	$-0.495036\pi$
$379$	87221.2	0.0311906	0.0155953	+	0.999878i	$0.495036\pi$
$380$	−285508.	−0.101428
$381$	3.42302e6	1.20808
$382$	354613.	0.124336
$383$	3.85401e6	1.34251	0.671253	−	0.741228i	$-0.265756\pi$
$383$	3.85401e6	1.34251	0.671253	+	0.741228i	$0.265756\pi$
$384$	−1.06985e6	−0.370251
$385$	83823.9	0.0288215
$386$	−59420.1	−0.0202986
$387$	505369.	0.171527
$388$	529594.	0.178593
$389$	−2.59342e6	−0.868957	−0.434478	−	0.900682i	$-0.643067\pi$
$389$	−2.59342e6	−0.868957	−0.434478	+	0.900682i	$0.643067\pi$
$390$	−132875.	−0.0442367
$391$	2.94000e6	0.972536
$392$	−616429.	−0.202613
$393$	−1.13499e6	−0.370691
$394$	−331549.	−0.107599
$395$	1.27264e6	0.410404
$396$	189687.	0.0607856
$397$	770324.	0.245300	0.122650	−	0.992450i	$-0.460861\pi$
$397$	770324.	0.245300	0.122650	+	0.992450i	$0.460861\pi$
$398$	−564364.	−0.178588
$399$	−139133.	−0.0437519
$400$	618197.	0.193187
$401$	752777.	0.233779	0.116889	−	0.993145i	$-0.462708\pi$
$401$	752777.	0.233779	0.116889	+	0.993145i	$0.462708\pi$
$402$	−543954.	−0.167879
$403$	4.07401e6	1.24957
$404$	3.34726e6	1.02032
$405$	1.11379e6	0.337416
$406$	−51807.8	−0.0155984
$407$	1.33162e6	0.398469
$408$	528334.	0.157130
$409$	993061.	0.293540	0.146770	−	0.989171i	$-0.453112\pi$
$409$	993061.	0.293540	0.146770	+	0.989171i	$0.453112\pi$
$410$	19158.5	0.00562863
$411$	−2.73265e6	−0.797957
$412$	4.73588e6	1.37454
$413$	832808.	0.240254
$414$	−89023.8	−0.0255273
$415$	−2.21743e6	−0.632018
$416$	−1.15615e6	−0.327552
$417$	2.49025e6	0.701300
$418$	26381.3	0.00738509
$419$	2.12834e6	0.592252	0.296126	−	0.955149i	$-0.404305\pi$
$419$	2.12834e6	0.592252	0.296126	+	0.955149i	$0.404305\pi$
$420$	304813.	0.0843160
$421$	−847150.	−0.232946	−0.116473	−	0.993194i	$-0.537159\pi$
$421$	−847150.	−0.232946	−0.116473	+	0.993194i	$0.537159\pi$
$422$	212798.	0.0581684
$423$	−441207.	−0.119892
$424$	−881761.	−0.238197
$425$	−617742.	−0.165896
$426$	−248858.	−0.0664398
$427$	316883.	0.0841066
$428$	−3.93535e6	−1.03842
$429$	−1.06484e6	−0.279346
$430$	−153982.	−0.0401606
$431$	1.78519e6	0.462904	0.231452	−	0.972846i	$-0.425652\pi$
$431$	1.78519e6	0.462904	0.231452	+	0.972846i	$0.425652\pi$
$432$	4.02470e6	1.03759
$433$	−7.66374e6	−1.96436	−0.982179	−	0.187946i	$-0.939817\pi$
$433$	−7.66374e6	−1.96436	−0.982179	+	0.187946i	$0.939817\pi$
$434$	107758.	0.0274615
$435$	−1.07638e6	−0.272737
$436$	−7.79552e6	−1.96394
$437$	1.07381e6	0.268982
$438$	−716046.	−0.178343
$439$	−1.91800e6	−0.474992	−0.237496	−	0.971389i	$-0.576327\pi$
$439$	−1.91800e6	−0.474992	−0.237496	+	0.971389i	$0.576327\pi$
$440$	−116259.	−0.0286283
$441$	794809.	0.194611
$442$	377704.	0.0919594
$443$	−5.07852e6	−1.22950	−0.614750	−	0.788722i	$-0.710743\pi$
$443$	−5.07852e6	−1.22950	−0.614750	+	0.788722i	$0.710743\pi$
$444$	4.84223e6	1.16570
$445$	−1.17976e6	−0.282419
$446$	−17368.4	−0.00413450
$447$	4.80619e6	1.13771
$448$	846501.	0.199266
$449$	2.87157e6	0.672207	0.336104	−	0.941825i	$-0.390891\pi$
$449$	2.87157e6	0.672207	0.336104	+	0.941825i	$0.390891\pi$
$450$	18705.4	0.00435447
$451$	153534.	0.0355436
$452$	−1.45399e6	−0.334746
$453$	−712447.	−0.163120
$454$	499832.	0.113811
$455$	438332.	0.0992600
$456$	192969.	0.0434587
$457$	−3.04332e6	−0.681643	−0.340821	−	0.940128i	$-0.610705\pi$
$457$	−3.04332e6	−0.681643	−0.340821	+	0.940128i	$0.610705\pi$
$458$	−193881.	−0.0431889
$459$	−4.02173e6	−0.891008
$460$	−2.35251e6	−0.518366
$461$	3.63015e6	0.795559	0.397779	−	0.917481i	$-0.369781\pi$
$461$	3.63015e6	0.795559	0.397779	+	0.917481i	$0.369781\pi$
$462$	−28165.1	−0.00613913
$463$	−1.87510e6	−0.406510	−0.203255	−	0.979126i	$-0.565152\pi$
$463$	−1.87510e6	−0.406510	−0.203255	+	0.979126i	$0.565152\pi$
$464$	−3.06193e6	−0.660237
$465$	2.23883e6	0.480163
$466$	−433035.	−0.0923759
$467$	−2.80135e6	−0.594394	−0.297197	−	0.954816i	$-0.596052\pi$
$467$	−2.80135e6	−0.594394	−0.297197	+	0.954816i	$0.596052\pi$
$468$	991912.	0.209343
$469$	1.79441e6	0.376695
$470$	134433.	0.0280711
$471$	4.65339e6	0.966534
$472$	−1.15506e6	−0.238643
$473$	−1.23399e6	−0.253606
$474$	−427610.	−0.0874183
$475$	−225625.	−0.0458831
$476$	−866445.	−0.175277
$477$	1.13692e6	0.228789
$478$	−166465.	−0.0333237
$479$	−6.81047e6	−1.35624	−0.678122	−	0.734949i	$-0.737206\pi$
$479$	−6.81047e6	−1.35624	−0.678122	+	0.734949i	$0.737206\pi$
$480$	−635350.	−0.125866
$481$	6.96330e6	1.37231
$482$	36777.5	0.00721049
$483$	−1.14642e6	−0.223601
$484$	−463172.	−0.0898728
$485$	418516.	0.0807900
$486$	222930.	0.0428133
$487$	1.70871e6	0.326472	0.163236	−	0.986587i	$-0.447807\pi$
$487$	1.70871e6	0.326472	0.163236	+	0.986587i	$0.447807\pi$
$488$	−439500.	−0.0835428
$489$	−4.67728e6	−0.884548
$490$	−242173.	−0.0455654
$491$	3.20345e6	0.599672	0.299836	−	0.953991i	$-0.403068\pi$
$491$	3.20345e6	0.599672	0.299836	+	0.953991i	$0.403068\pi$
$492$	558301.	0.103981
$493$	3.05967e6	0.566967
$494$	137953.	0.0254340
$495$	149902.	0.0274976
$496$	6.36867e6	1.16237
$497$	820940.	0.149080
$498$	745063.	0.134623
$499$	1.86443e6	0.335193	0.167597	−	0.985856i	$-0.446399\pi$
$499$	1.86443e6	0.335193	0.167597	+	0.985856i	$0.446399\pi$
$500$	494301.	0.0884232
$501$	−2.45332e6	−0.436677
$502$	−789983.	−0.139913
$503$	2.77548e6	0.489123	0.244561	−	0.969634i	$-0.421356\pi$
$503$	2.77548e6	0.489123	0.244561	+	0.969634i	$0.421356\pi$
$504$	52774.8	0.00925444
$505$	2.64520e6	0.461561
$506$	217375.	0.0377427
$507$	−404146.	−0.0698262
$508$	7.78577e6	1.33857
$509$	5.69526e6	0.974359	0.487179	−	0.873302i	$-0.338026\pi$
$509$	5.69526e6	0.974359	0.487179	+	0.873302i	$0.338026\pi$
$510$	207564.	0.0353367
$511$	2.36211e6	0.400173
$512$	−3.02381e6	−0.509776
$513$	−1.46890e6	−0.246434
$514$	−844316.	−0.140960
$515$	3.74257e6	0.621801
$516$	−4.48722e6	−0.741913
$517$	1.07732e6	0.177264
$518$	184180.	0.0301590
$519$	−3.28467e6	−0.535271
$520$	−607942.	−0.0985947
$521$	1.18614e6	0.191444	0.0957221	−	0.995408i	$-0.469484\pi$
$521$	1.18614e6	0.191444	0.0957221	+	0.995408i	$0.469484\pi$
$522$	−92647.6	−0.0148819
$523$	−3.76361e6	−0.601659	−0.300830	−	0.953678i	$-0.597264\pi$
$523$	−3.76361e6	−0.601659	−0.300830	+	0.953678i	$0.597264\pi$
$524$	−2.58158e6	−0.410730
$525$	240881.	0.0381420
$526$	−293525.	−0.0462573
$527$	−6.36398e6	−0.998166
$528$	−1.66461e6	−0.259853
$529$	2.41155e6	0.374678
$530$	−346412.	−0.0535678
$531$	1.48931e6	0.229218
$532$	−316462.	−0.0484777
$533$	802857.	0.122411
$534$	396404.	0.0601568
$535$	−3.10994e6	−0.469751
$536$	−2.48875e6	−0.374170
$537$	3.95048e6	0.591172
$538$	743369.	0.110726
$539$	−1.94074e6	−0.287736
$540$	3.21808e6	0.474912
$541$	3.21274e6	0.471935	0.235967	−	0.971761i	$-0.424174\pi$
$541$	3.21274e6	0.471935	0.235967	+	0.971761i	$0.424174\pi$
$542$	−954109.	−0.139508
$543$	6.63836e6	0.966187
$544$	1.80601e6	0.261652
$545$	−6.16047e6	−0.888429
$546$	−147281.	−0.0211429
$547$	2.73652e6	0.391048	0.195524	−	0.980699i	$-0.437359\pi$
$547$	2.73652e6	0.391048	0.195524	+	0.980699i	$0.437359\pi$
$548$	−6.21549e6	−0.884147
$549$	566681.	0.0802432
$550$	−45674.1	−0.00643818
$551$	1.11752e6	0.156811
$552$	1.59002e6	0.222103
$553$	1.41061e6	0.196153
$554$	−835269.	−0.115625
$555$	3.82661e6	0.527329
$556$	5.66416e6	0.777049
$557$	−5.24145e6	−0.715835	−0.357918	−	0.933753i	$-0.616513\pi$
$557$	−5.24145e6	−0.715835	−0.357918	+	0.933753i	$0.616513\pi$
$558$	192703.	0.0262001
$559$	−6.45278e6	−0.873409
$560$	685220.	0.0923336
$561$	1.66338e6	0.223144
$562$	−195852.	−0.0261570
$563$	−1.99411e6	−0.265142	−0.132571	−	0.991174i	$-0.542323\pi$
$563$	−1.99411e6	−0.265142	−0.132571	+	0.991174i	$0.542323\pi$
$564$	3.91752e6	0.518577
$565$	−1.14903e6	−0.151429
$566$	1.10423e6	0.144884
$567$	1.23454e6	0.161268
$568$	−1.13860e6	−0.148081
$569$	−1.14375e7	−1.48098	−0.740491	−	0.672067i	$-0.765407\pi$
$569$	−1.14375e7	−1.48098	−0.740491	+	0.672067i	$0.765407\pi$
$570$	75810.8	0.00977336
$571$	−3.96844e6	−0.509366	−0.254683	−	0.967025i	$-0.581971\pi$
$571$	−3.96844e6	−0.509366	−0.254683	+	0.967025i	$0.581971\pi$
$572$	−2.42201e6	−0.309519
$573$	8.16638e6	1.03907
$574$	21235.6	0.00269020
$575$	−1.85909e6	−0.234493
$576$	1.51379e6	0.190113
$577$	668367.	0.0835748	0.0417874	−	0.999127i	$-0.486695\pi$
$577$	668367.	0.0835748	0.0417874	+	0.999127i	$0.486695\pi$
$578$	267520.	0.0333070
$579$	−1.36839e6	−0.169634
$580$	−2.44827e6	−0.302196
$581$	−2.45783e6	−0.302073
$582$	−140623.	−0.0172087
$583$	−2.77610e6	−0.338270
$584$	−3.27612e6	−0.397491
$585$	783867.	0.0947006
$586$	1.71756e6	0.206618
$587$	8.32286e6	0.996959	0.498479	−	0.866901i	$-0.333892\pi$
$587$	8.32286e6	0.996959	0.498479	+	0.866901i	$0.333892\pi$
$588$	−7.05718e6	−0.841760
$589$	−2.32439e6	−0.276071
$590$	−453781.	−0.0536681
$591$	−7.63525e6	−0.899196
$592$	1.08853e7	1.27655
$593$	−1.20552e7	−1.40779	−0.703896	−	0.710303i	$-0.748558\pi$
$593$	−1.20552e7	−1.40779	−0.703896	+	0.710303i	$0.748558\pi$
$594$	−297355.	−0.0345788
$595$	−684715.	−0.0792899
$596$	1.09318e7	1.26060
$597$	−1.29967e7	−1.49245
$598$	1.13670e6	0.129984
$599$	7.57855e6	0.863017	0.431508	−	0.902109i	$-0.357982\pi$
$599$	7.57855e6	0.863017	0.431508	+	0.902109i	$0.357982\pi$
$600$	−334088.	−0.0378864
$601$	4.83687e6	0.546233	0.273117	−	0.961981i	$-0.411946\pi$
$601$	4.83687e6	0.546233	0.273117	+	0.961981i	$0.411946\pi$
$602$	−170676.	−0.0191947
$603$	3.20893e6	0.359391
$604$	−1.62048e6	−0.180739
$605$	−366025.	−0.0406558
$606$	−888795.	−0.0983150
$607$	−2.26092e6	−0.249066	−0.124533	−	0.992215i	$-0.539743\pi$
$607$	−2.26092e6	−0.249066	−0.124533	+	0.992215i	$0.539743\pi$
$608$	659630.	0.0723672
$609$	−1.19308e6	−0.130355
$610$	−172664.	−0.0187878
$611$	5.63353e6	0.610489
$612$	−1.54946e6	−0.167225
$613$	1.67365e7	1.79893	0.899465	−	0.436993i	$-0.143956\pi$
$613$	1.67365e7	1.79893	0.899465	+	0.436993i	$0.143956\pi$
$614$	1.77546e6	0.190059
$615$	441202.	0.0470381
$616$	−128864.	−0.0136829
$617$	3.57821e6	0.378402	0.189201	−	0.981938i	$-0.439410\pi$
$617$	3.57821e6	0.378402	0.189201	+	0.981938i	$0.439410\pi$
$618$	−1.25751e6	−0.132447
$619$	−6.60065e6	−0.692405	−0.346202	−	0.938160i	$-0.612529\pi$
$619$	−6.60065e6	−0.692405	−0.346202	+	0.938160i	$0.612529\pi$
$620$	5.09229e6	0.532027
$621$	−1.21034e7	−1.25944
$622$	−225868.	−0.0234088
$623$	−1.30767e6	−0.134982
$624$	−8.70456e6	−0.894922
$625$	390625.	0.0400000
$626$	203953.	0.0208015
$627$	607536.	0.0617168
$628$	1.05843e7	1.07093
$629$	−1.08773e7	−1.09621
$630$	20733.3	0.00208122
$631$	−6.99340e6	−0.699222	−0.349611	−	0.936895i	$-0.613686\pi$
$631$	−6.99340e6	−0.699222	−0.349611	+	0.936895i	$0.613686\pi$
$632$	−1.95644e6	−0.194838
$633$	4.90054e6	0.486110
$634$	−630434.	−0.0622897
$635$	6.15276e6	0.605530
$636$	−1.00948e7	−0.989594
$637$	−1.01485e7	−0.990952
$638$	226223.	0.0220032
$639$	1.46808e6	0.142232
$640$	−1.92303e6	−0.185582
$641$	−5.65050e6	−0.543177	−0.271589	−	0.962413i	$-0.587549\pi$
$641$	−5.65050e6	−0.543177	−0.271589	+	0.962413i	$0.587549\pi$
$642$	1.04495e6	0.100059
$643$	−7.42904e6	−0.708607	−0.354304	−	0.935130i	$-0.615282\pi$
$643$	−7.42904e6	−0.708607	−0.354304	+	0.935130i	$0.615282\pi$
$644$	−2.60756e6	−0.247753
$645$	−3.54606e6	−0.335619
$646$	−215496.	−0.0203169
$647$	1.40192e7	1.31663	0.658315	−	0.752742i	$-0.271269\pi$
$647$	1.40192e7	1.31663	0.658315	+	0.752742i	$0.271269\pi$
$648$	−1.71224e6	−0.160187
$649$	−3.63653e6	−0.338903
$650$	−238839.	−0.0221728
$651$	2.48155e6	0.229494
$652$	−1.06386e7	−0.980090
$653$	4.54398e6	0.417016	0.208508	−	0.978021i	$-0.433139\pi$
$653$	4.54398e6	0.417016	0.208508	+	0.978021i	$0.433139\pi$
$654$	2.06994e6	0.189240
$655$	−2.04011e6	−0.185802
$656$	1.25506e6	0.113869
$657$	4.22415e6	0.381791
$658$	149007.	0.0134166
$659$	−1.25147e7	−1.12255	−0.561275	−	0.827629i	$-0.689689\pi$
$659$	−1.25147e7	−1.12255	−0.561275	+	0.827629i	$0.689689\pi$
$660$	−1.33099e6	−0.118937
$661$	1.98953e7	1.77112	0.885558	−	0.464529i	$-0.153776\pi$
$661$	1.98953e7	1.77112	0.885558	+	0.464529i	$0.153776\pi$
$662$	−388098.	−0.0344189
$663$	8.69815e6	0.768499
$664$	3.40888e6	0.300048
$665$	−250086.	−0.0219299
$666$	329368.	0.0287737
$667$	9.20806e6	0.801407
$668$	−5.58016e6	−0.483844
$669$	−399977.	−0.0345517
$670$	−977739.	−0.0841465
$671$	−1.38370e6	−0.118641
$672$	−704231.	−0.0601578
$673$	5.77152e6	0.491193	0.245597	−	0.969372i	$-0.421016\pi$
$673$	5.77152e6	0.491193	0.245597	+	0.969372i	$0.421016\pi$
$674$	−1.08109e6	−0.0916672
$675$	2.54312e6	0.214836
$676$	−919242.	−0.0773683
$677$	−1.63196e7	−1.36848	−0.684238	−	0.729259i	$-0.739865\pi$
$677$	−1.63196e7	−1.36848	−0.684238	+	0.729259i	$0.739865\pi$
$678$	386077.	0.0322552
$679$	463889.	0.0386136
$680$	949662.	0.0787584
$681$	1.15106e7	0.951112
$682$	−470534.	−0.0387374
$683$	1.52598e7	1.25169	0.625845	−	0.779947i	$-0.284754\pi$
$683$	1.52598e7	1.25169	0.625845	+	0.779947i	$0.284754\pi$
$684$	−565927.	−0.0462509
$685$	−4.91184e6	−0.399961
$686$	−549707.	−0.0445986
$687$	−4.46490e6	−0.360927
$688$	−1.00873e7	−0.812462
$689$	−1.45167e7	−1.16499
$690$	624660.	0.0499483
$691$	8.92188e6	0.710823	0.355411	−	0.934710i	$-0.384341\pi$
$691$	8.92188e6	0.710823	0.355411	+	0.934710i	$0.384341\pi$
$692$	−7.47108e6	−0.593087
$693$	166154.	0.0131425
$694$	−1.30318e6	−0.102708
$695$	4.47615e6	0.351514
$696$	1.65474e6	0.129481
$697$	−1.25414e6	−0.0977830
$698$	309007.	0.0240065
$699$	−9.97238e6	−0.771980
$700$	547891.	0.0422619
$701$	−4.04005e6	−0.310521	−0.155261	−	0.987874i	$-0.549622\pi$
$701$	−4.04005e6	−0.310521	−0.155261	+	0.987874i	$0.549622\pi$
$702$	−1.55493e6	−0.119088
$703$	−3.97285e6	−0.303189
$704$	−3.69633e6	−0.281086
$705$	3.09585e6	0.234589
$706$	1.20369e6	0.0908874
$707$	2.93198e6	0.220603
$708$	−1.32237e7	−0.991448
$709$	9.83396e6	0.734705	0.367352	−	0.930082i	$-0.380264\pi$
$709$	9.83396e6	0.734705	0.367352	+	0.930082i	$0.380264\pi$
$710$	−447314.	−0.0333017
$711$	2.52259e6	0.187143
$712$	1.81366e6	0.134078
$713$	−1.91523e7	−1.41091
$714$	230067.	0.0168892
$715$	−1.91402e6	−0.140017
$716$	8.98548e6	0.655027
$717$	−3.83352e6	−0.278484
$718$	−1.91615e6	−0.138713
$719$	2.08012e7	1.50061	0.750304	−	0.661093i	$-0.229907\pi$
$719$	2.08012e7	1.50061	0.750304	+	0.661093i	$0.229907\pi$
$720$	1.22538e6	0.0880923
$721$	4.14832e6	0.297190
$722$	−78707.9	−0.00561921
$723$	846950.	0.0602576
$724$	1.50991e7	1.07055
$725$	−1.93476e6	−0.136705
$726$	122986.	0.00865990
$727$	−1.82563e7	−1.28108	−0.640540	−	0.767925i	$-0.721289\pi$
$727$	−1.82563e7	−1.28108	−0.640540	+	0.767925i	$0.721289\pi$
$728$	−673852.	−0.0471234
$729$	1.59599e7	1.11227
$730$	−1.28707e6	−0.0893912
$731$	1.00799e7	0.697687
$732$	−5.03162e6	−0.347080
$733$	−2.27812e7	−1.56609	−0.783043	−	0.621967i	$-0.786334\pi$
$733$	−2.27812e7	−1.56609	−0.783043	+	0.621967i	$0.786334\pi$
$734$	1.39805e6	0.0957818
$735$	−5.57700e6	−0.380787
$736$	5.43517e6	0.369844
$737$	−7.83546e6	−0.531368
$738$	37975.6	0.00256663
$739$	−2.80261e6	−0.188778	−0.0943890	−	0.995535i	$-0.530090\pi$
$739$	−2.80261e6	−0.188778	−0.0943890	+	0.995535i	$0.530090\pi$
$740$	8.70374e6	0.584288
$741$	3.17692e6	0.212550
$742$	−383969.	−0.0256027
$743$	−1.09706e7	−0.729053	−0.364526	−	0.931193i	$-0.618769\pi$
$743$	−1.09706e7	−0.729053	−0.364526	+	0.931193i	$0.618769\pi$
$744$	−3.44178e6	−0.227956
$745$	8.63897e6	0.570258
$746$	−204908.	−0.0134807
$747$	−4.39533e6	−0.288197
$748$	3.78341e6	0.247246
$749$	−3.44710e6	−0.224517
$750$	−131251.	−0.00852021
$751$	−1.60865e7	−1.04079	−0.520395	−	0.853926i	$-0.674215\pi$
$751$	−1.60865e7	−1.04079	−0.520395	+	0.853926i	$0.674215\pi$
$752$	8.80659e6	0.567888
$753$	−1.81925e7	−1.16924
$754$	1.18297e6	0.0757781
$755$	−1.28060e6	−0.0817609
$756$	3.56697e6	0.226984
$757$	−1.62980e7	−1.03370	−0.516851	−	0.856076i	$-0.672896\pi$
$757$	−1.62980e7	−1.03370	−0.516851	+	0.856076i	$0.672896\pi$
$758$	−52677.6	−0.00333007
$759$	5.00593e6	0.315414
$760$	346856.	0.0217829
$761$	1.88314e7	1.17875	0.589373	−	0.807861i	$-0.299375\pi$
$761$	1.88314e7	1.17875	0.589373	+	0.807861i	$0.299375\pi$
$762$	−2.06735e6	−0.128981
$763$	−6.82836e6	−0.424625
$764$	1.85747e7	1.15130
$765$	−1.22447e6	−0.0756477
$766$	−2.32765e6	−0.143333
$767$	−1.90161e7	−1.16717
$768$	−1.29500e7	−0.792255
$769$	8.38136e6	0.511092	0.255546	−	0.966797i	$-0.417745\pi$
$769$	8.38136e6	0.511092	0.255546	+	0.966797i	$0.417745\pi$
$770$	−50625.8	−0.00307713
$771$	−1.94438e7	−1.17800
$772$	−3.11244e6	−0.187957
$773$	3.02567e6	0.182127	0.0910633	−	0.995845i	$-0.470973\pi$
$773$	3.02567e6	0.182127	0.0910633	+	0.995845i	$0.470973\pi$
$774$	−305220.	−0.0183130
$775$	4.02422e6	0.240673
$776$	−643389.	−0.0383548
$777$	4.24148e6	0.252037
$778$	1.56631e6	0.0927742
$779$	−458063.	−0.0270447
$780$	−6.96002e6	−0.409614
$781$	−3.58471e6	−0.210294
$782$	−1.77563e6	−0.103833
$783$	−1.25960e7	−0.734226
$784$	−1.58646e7	−0.921803
$785$	8.36431e6	0.484458
$786$	685484.	0.0395768
$787$	−2.88320e6	−0.165935	−0.0829673	−	0.996552i	$-0.526440\pi$
$787$	−2.88320e6	−0.165935	−0.0829673	+	0.996552i	$0.526440\pi$
$788$	−1.73666e7	−0.996321
$789$	−6.75958e6	−0.386569
$790$	−768615.	−0.0438168
$791$	−1.27360e6	−0.0723756
$792$	−230446.	−0.0130544
$793$	−7.23564e6	−0.408596
$794$	−465240.	−0.0261894
$795$	−7.97753e6	−0.447663
$796$	−2.95615e7	−1.65365
$797$	1.18369e7	0.660076	0.330038	−	0.943968i	$-0.392938\pi$
$797$	1.18369e7	0.660076	0.330038	+	0.943968i	$0.392938\pi$
$798$	84029.8	0.00467118
$799$	−8.80010e6	−0.487664
$800$	−1.14202e6	−0.0630882
$801$	−2.33849e6	−0.128782
$802$	−454643.	−0.0249594
$803$	−1.03144e7	−0.564487
$804$	−2.84924e7	−1.55449
$805$	−2.06064e6	−0.112076
$806$	−2.46052e6	−0.133410
$807$	1.71190e7	0.925328
$808$	−4.06649e6	−0.219125
$809$	2.82031e7	1.51504	0.757522	−	0.652809i	$-0.226410\pi$
$809$	2.82031e7	1.51504	0.757522	+	0.652809i	$0.226410\pi$
$810$	−672679.	−0.0360243
$811$	2.68230e7	1.43204	0.716021	−	0.698079i	$-0.245962\pi$
$811$	2.68230e7	1.43204	0.716021	+	0.698079i	$0.245962\pi$
$812$	−2.71370e6	−0.144435
$813$	−2.19722e7	−1.16586
$814$	−804238.	−0.0425425
$815$	−8.40725e6	−0.443363
$816$	1.35973e7	0.714873
$817$	3.68158e6	0.192965
$818$	−599763.	−0.0313398
$819$	868850.	0.0452621
$820$	1.00353e6	0.0521188
$821$	2.95861e7	1.53190	0.765948	−	0.642902i	$-0.222270\pi$
$821$	2.95861e7	1.53190	0.765948	+	0.642902i	$0.222270\pi$
$822$	1.65040e6	0.0851939
$823$	3.05869e7	1.57411	0.787055	−	0.616882i	$-0.211605\pi$
$823$	3.05869e7	1.57411	0.787055	+	0.616882i	$0.211605\pi$
$824$	−5.75349e6	−0.295198
$825$	−1.05183e6	−0.0538034
$826$	−502978.	−0.0256507
$827$	−3.04455e7	−1.54796	−0.773979	−	0.633212i	$-0.781736\pi$
$827$	−3.04455e7	−1.54796	−0.773979	+	0.633212i	$0.781736\pi$
$828$	−4.66308e6	−0.236373
$829$	−1.96040e7	−0.990737	−0.495369	−	0.868683i	$-0.664967\pi$
$829$	−1.96040e7	−0.990737	−0.495369	+	0.868683i	$0.664967\pi$
$830$	1.33923e6	0.0674774
$831$	−1.92354e7	−0.966271
$832$	−1.93288e7	−0.968048
$833$	1.58529e7	0.791582
$834$	−1.50400e6	−0.0748743
$835$	−4.40977e6	−0.218877
$836$	1.38186e6	0.0683830
$837$	2.61992e7	1.29263
$838$	−1.28542e6	−0.0632318
$839$	1.96280e7	0.962656	0.481328	−	0.876541i	$-0.340155\pi$
$839$	1.96280e7	0.962656	0.481328	+	0.876541i	$0.340155\pi$
$840$	−370309.	−0.0181078
$841$	−1.09283e7	−0.532797
$842$	511640.	0.0248705
$843$	−4.51028e6	−0.218592
$844$	1.11464e7	0.538616
$845$	−726438.	−0.0349991
$846$	266469.	0.0128003
$847$	−405708.	−0.0194314
$848$	−2.26932e7	−1.08369
$849$	2.54294e7	1.21078
$850$	373088.	0.0177119
$851$	−3.27352e7	−1.54950
$852$	−1.30352e7	−0.615206
$853$	−9.16224e6	−0.431151	−0.215575	−	0.976487i	$-0.569163\pi$
$853$	−9.16224e6	−0.431151	−0.215575	+	0.976487i	$0.569163\pi$
$854$	−191383.	−0.00897964
$855$	−447228.	−0.0209225
$856$	4.78094e6	0.223012
$857$	9.42829e6	0.438511	0.219256	−	0.975667i	$-0.429637\pi$
$857$	9.42829e6	0.438511	0.219256	+	0.975667i	$0.429637\pi$
$858$	643116.	0.0298244
$859$	1.59538e7	0.737703	0.368851	−	0.929488i	$-0.379751\pi$
$859$	1.59538e7	0.737703	0.368851	+	0.929488i	$0.379751\pi$
$860$	−8.06562e6	−0.371871
$861$	489035.	0.0224819
$862$	−1.07817e6	−0.0494219
$863$	1.37880e7	0.630195	0.315097	−	0.949059i	$-0.397963\pi$
$863$	1.37880e7	0.630195	0.315097	+	0.949059i	$0.397963\pi$
$864$	−7.43497e6	−0.338840
$865$	−5.90408e6	−0.268295
$866$	4.62855e6	0.209725
$867$	6.16071e6	0.278345
$868$	5.64437e6	0.254282
$869$	−6.15956e6	−0.276694
$870$	650087.	0.0291188
$871$	−4.09731e7	−1.83001
$872$	9.47056e6	0.421779
$873$	829571.	0.0368399
$874$	−648532.	−0.0287179
$875$	432975.	0.0191180
$876$	−3.75066e7	−1.65138
$877$	−2.79140e7	−1.22553	−0.612763	−	0.790267i	$-0.709942\pi$
$877$	−2.79140e7	−1.22553	−0.612763	+	0.790267i	$0.709942\pi$
$878$	1.15838e6	0.0507126
$879$	3.95537e7	1.72669
$880$	−2.99208e6	−0.130246
$881$	3.36835e7	1.46210	0.731050	−	0.682324i	$-0.239031\pi$
$881$	3.36835e7	1.46210	0.731050	+	0.682324i	$0.239031\pi$
$882$	−480029.	−0.0207776
$883$	−3.82003e7	−1.64879	−0.824395	−	0.566014i	$-0.808485\pi$
$883$	−3.82003e7	−1.64879	−0.824395	+	0.566014i	$0.808485\pi$
$884$	1.97842e7	0.851507
$885$	−1.04501e7	−0.448501
$886$	3.06720e6	0.131268
$887$	1.88221e7	0.803264	0.401632	−	0.915801i	$-0.368443\pi$
$887$	1.88221e7	0.803264	0.401632	+	0.915801i	$0.368443\pi$
$888$	−5.88269e6	−0.250348
$889$	6.81982e6	0.289413
$890$	712522.	0.0301525
$891$	−5.39075e6	−0.227486
$892$	−909760.	−0.0382838
$893$	−3.21416e6	−0.134877
$894$	−2.90272e6	−0.121468
$895$	7.10085e6	0.296314
$896$	−2.13151e6	−0.0886988
$897$	2.61770e7	1.08627
$898$	−1.73430e6	−0.0717683
$899$	−1.99319e7	−0.822527
$900$	979790.	0.0403206
$901$	2.26765e7	0.930603
$902$	−92727.3	−0.00379482
$903$	−3.93051e6	−0.160409
$904$	1.76641e6	0.0718905
$905$	1.19322e7	0.484283
$906$	430286.	0.0174155
$907$	3.84052e7	1.55014	0.775072	−	0.631873i	$-0.217714\pi$
$907$	3.84052e7	1.55014	0.775072	+	0.631873i	$0.217714\pi$
$908$	2.61813e7	1.05384
$909$	5.24324e6	0.210470
$910$	−264732.	−0.0105975
$911$	3.03802e7	1.21281	0.606407	−	0.795154i	$-0.292610\pi$
$911$	3.03802e7	1.21281	0.606407	+	0.795154i	$0.292610\pi$
$912$	4.96631e6	0.197718
$913$	1.07324e7	0.426106
$914$	1.83803e6	0.0727757
$915$	−3.97627e6	−0.157009
$916$	−1.01555e7	−0.399912
$917$	−2.26129e6	−0.0888041
$918$	2.42894e6	0.0951286
$919$	1.72654e7	0.674355	0.337177	−	0.941441i	$-0.390528\pi$
$919$	1.72654e7	0.674355	0.337177	+	0.941441i	$0.390528\pi$
$920$	2.85800e6	0.111325
$921$	4.08870e7	1.58831
$922$	−2.19244e6	−0.0849379
$923$	−1.87452e7	−0.724244
$924$	−1.47529e6	−0.0568458
$925$	6.87820e6	0.264314
$926$	1.13247e6	0.0434011
$927$	7.41842e6	0.283539
$928$	5.65641e6	0.215611
$929$	186898.	0.00710502	0.00355251	−	0.999994i	$-0.498869\pi$
$929$	186898.	0.00710502	0.00355251	+	0.999994i	$0.498869\pi$
$930$	−1.35215e6	−0.0512647
$931$	5.79013e6	0.218934
$932$	−2.26825e7	−0.855363
$933$	−5.20152e6	−0.195626
$934$	1.69189e6	0.0634606
$935$	2.98987e6	0.111847
$936$	−1.20505e6	−0.0449588
$937$	−2.94660e7	−1.09641	−0.548204	−	0.836344i	$-0.684688\pi$
$937$	−2.94660e7	−1.09641	−0.548204	+	0.836344i	$0.684688\pi$
$938$	−1.08374e6	−0.0402178
$939$	4.69684e6	0.173837
$940$	7.04160e6	0.259927
$941$	1.65598e6	0.0609651	0.0304826	−	0.999535i	$-0.490296\pi$
$941$	1.65598e6	0.0609651	0.0304826	+	0.999535i	$0.490296\pi$
$942$	−2.81044e6	−0.103192
$943$	−3.77431e6	−0.138216
$944$	−2.97269e7	−1.08572
$945$	2.81883e6	0.102681
$946$	745275.	0.0270762
$947$	3.16248e7	1.14591	0.572957	−	0.819585i	$-0.305796\pi$
$947$	3.16248e7	1.14591	0.572957	+	0.819585i	$0.305796\pi$
$948$	−2.23983e7	−0.809458
$949$	−5.39359e7	−1.94407
$950$	136267.	0.00489872
$951$	−1.45183e7	−0.520551
$952$	1.05262e6	0.0376426
$953$	4.88386e6	0.174193	0.0870966	−	0.996200i	$-0.472241\pi$
$953$	4.88386e6	0.174193	0.0870966	+	0.996200i	$0.472241\pi$
$954$	−686650.	−0.0244267
$955$	1.46788e7	0.520813
$956$	−8.71946e6	−0.308564
$957$	5.20970e6	0.183879
$958$	4.11321e6	0.144800
$959$	−5.44437e6	−0.191162
$960$	−1.06220e7	−0.371986
$961$	1.28284e7	0.448088
$962$	−4.20552e6	−0.146515
$963$	−6.16444e6	−0.214204
$964$	1.92641e6	0.0667662
$965$	−2.45963e6	−0.0850259
$966$	692383.	0.0238728
$967$	1.91439e6	0.0658363	0.0329181	−	0.999458i	$-0.489520\pi$
$967$	1.91439e6	0.0658363	0.0329181	+	0.999458i	$0.489520\pi$
$968$	562694.	0.0193012
$969$	−4.96265e6	−0.169787
$970$	−252764.	−0.00862555
$971$	−4.82037e7	−1.64071	−0.820355	−	0.571854i	$-0.806224\pi$
$971$	−4.82037e7	−1.64071	−0.820355	+	0.571854i	$0.806224\pi$
$972$	1.16771e7	0.396434
$973$	4.96143e6	0.168006
$974$	−1.03198e6	−0.0348558
$975$	−5.50022e6	−0.185297
$976$	−1.13111e7	−0.380084
$977$	−5.55944e7	−1.86335	−0.931675	−	0.363292i	$-0.881653\pi$
$977$	−5.55944e7	−1.86335	−0.931675	+	0.363292i	$0.881653\pi$
$978$	2.82486e6	0.0944388
$979$	5.71004e6	0.190407
$980$	−1.26850e7	−0.421917
$981$	−1.22111e7	−0.405120
$982$	−1.93473e6	−0.0640240
$983$	−5.42420e7	−1.79041	−0.895204	−	0.445657i	$-0.852970\pi$
$983$	−5.42420e7	−1.79041	−0.895204	+	0.445657i	$0.852970\pi$
$984$	−678265.	−0.0223312
$985$	−1.37241e7	−0.450706
$986$	−1.84790e6	−0.0605323
$987$	3.43149e6	0.112122
$988$	7.22601e6	0.235508
$989$	3.03352e7	0.986180
$990$	−90534.0	−0.00293578
$991$	3.99547e7	1.29236	0.646181	−	0.763184i	$-0.276365\pi$
$991$	3.99547e7	1.29236	0.646181	+	0.763184i	$0.276365\pi$
$992$	−1.17651e7	−0.379591
$993$	−8.93752e6	−0.287636
$994$	−495810.	−0.0159166
$995$	−2.33612e7	−0.748062
$996$	3.90266e7	1.24656
$997$	−4.59352e7	−1.46355	−0.731776	−	0.681545i	$-0.761308\pi$
$997$	−4.59352e7	−1.46355	−0.731776	+	0.681545i	$0.761308\pi$
$998$	−1.12603e6	−0.0357869
$999$	4.47797e7	1.41960

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.d.1.17	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.d.1.17	✓	37	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)

\(f(q)\)	\(=\)	\(q-0.603954 q^{2} -13.9085 q^{3} -31.6352 q^{4} -25.0000 q^{5} +8.40008 q^{6} -27.7104 q^{7} +38.4328 q^{8} -49.5544 q^{9} +O(q^{10})\)	\(q-0.603954 q^{2} -13.9085 q^{3} -31.6352 q^{4} -25.0000 q^{5} +8.40008 q^{6} -27.7104 q^{7} +38.4328 q^{8} -49.5544 q^{9} +15.0989 q^{10} +121.000 q^{11} +439.998 q^{12} +632.733 q^{13} +16.7358 q^{14} +347.712 q^{15} +989.116 q^{16} -988.388 q^{17} +29.9286 q^{18} -361.000 q^{19} +790.881 q^{20} +385.409 q^{21} -73.0785 q^{22} -2974.54 q^{23} -534.541 q^{24} +625.000 q^{25} -382.142 q^{26} +4068.98 q^{27} +876.625 q^{28} -3095.62 q^{29} -210.002 q^{30} +6438.75 q^{31} -1827.23 q^{32} -1682.93 q^{33} +596.941 q^{34} +692.760 q^{35} +1567.66 q^{36} +11005.1 q^{37} +218.028 q^{38} -8800.34 q^{39} -960.820 q^{40} +1268.87 q^{41} -232.770 q^{42} -10198.3 q^{43} -3827.86 q^{44} +1238.86 q^{45} +1796.49 q^{46} +8903.49 q^{47} -13757.1 q^{48} -16039.1 q^{49} -377.472 q^{50} +13747.0 q^{51} -20016.6 q^{52} -22942.9 q^{53} -2457.48 q^{54} -3025.00 q^{55} -1064.99 q^{56} +5020.96 q^{57} +1869.61 q^{58} -30054.0 q^{59} -10999.9 q^{60} -11435.5 q^{61} -3888.71 q^{62} +1373.17 q^{63} -30548.1 q^{64} -15818.3 q^{65} +1016.41 q^{66} -64755.8 q^{67} +31267.9 q^{68} +41371.3 q^{69} -418.395 q^{70} -29625.7 q^{71} -1904.51 q^{72} -85242.8 q^{73} -6646.59 q^{74} -8692.80 q^{75} +11420.3 q^{76} -3352.96 q^{77} +5315.01 q^{78} -50905.5 q^{79} -24727.9 q^{80} -44551.7 q^{81} -766.341 q^{82} +88697.1 q^{83} -12192.5 q^{84} +24709.7 q^{85} +6159.29 q^{86} +43055.4 q^{87} +4650.37 q^{88} +47190.4 q^{89} -748.215 q^{90} -17533.3 q^{91} +94100.3 q^{92} -89553.2 q^{93} -5377.30 q^{94} +9025.00 q^{95} +25414.0 q^{96} -16740.6 q^{97} +9686.91 q^{98} -5996.08 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9} - 100 q^{10} + 4477 q^{11} + 872 q^{12} + 719 q^{13} - 625 q^{14} - 675 q^{15} + 6940 q^{16} + 119 q^{17} - 4237 q^{18} - 13357 q^{19} - 15400 q^{20} + 2905 q^{21} + 484 q^{22} - 1252 q^{23} + 5884 q^{24} + 23125 q^{25} + 13201 q^{26} + 9918 q^{27} + 15461 q^{28} + 13221 q^{29} - 3525 q^{30} + 6419 q^{31} + 13173 q^{32} + 3267 q^{33} + 35415 q^{34} + 1975 q^{35} + 80543 q^{36} + 9037 q^{37} - 1444 q^{38} - 6184 q^{39} - 1800 q^{40} + 52577 q^{41} - 28578 q^{42} + 963 q^{43} + 74536 q^{44} - 78500 q^{45} - 10531 q^{46} + 49346 q^{47} + 80107 q^{48} + 70288 q^{49} + 2500 q^{50} + 140786 q^{51} + 165062 q^{52} - 34457 q^{53} + 34216 q^{54} - 111925 q^{55} - 64095 q^{56} - 9747 q^{57} - 126140 q^{58} + 56521 q^{59} - 21800 q^{60} + 6613 q^{61} + 494 q^{62} - 125618 q^{63} - 140426 q^{64} - 17975 q^{65} + 17061 q^{66} - 43534 q^{67} - 138520 q^{68} + 34618 q^{69} + 15625 q^{70} + 95986 q^{71} - 42192 q^{72} + 109218 q^{73} - 182005 q^{74} + 16875 q^{75} - 222376 q^{76} - 9559 q^{77} - 369624 q^{78} + 64943 q^{79} - 173500 q^{80} + 388941 q^{81} - 126926 q^{82} + 109741 q^{83} - 112886 q^{84} - 2975 q^{85} + 43866 q^{86} + 142492 q^{87} + 8712 q^{88} - 119092 q^{89} + 105925 q^{90} + 349320 q^{91} + 433396 q^{92} - 108630 q^{93} + 196160 q^{94} + 333925 q^{95} + 376630 q^{96} + 68774 q^{97} + 310926 q^{98} + 379940 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9 - 100 * q^10 + 4477 * q^11 + 872 * q^12 + 719 * q^13 - 625 * q^14 - 675 * q^15 + 6940 * q^16 + 119 * q^17 - 4237 * q^18 - 13357 * q^19 - 15400 * q^20 + 2905 * q^21 + 484 * q^22 - 1252 * q^23 + 5884 * q^24 + 23125 * q^25 + 13201 * q^26 + 9918 * q^27 + 15461 * q^28 + 13221 * q^29 - 3525 * q^30 + 6419 * q^31 + 13173 * q^32 + 3267 * q^33 + 35415 * q^34 + 1975 * q^35 + 80543 * q^36 + 9037 * q^37 - 1444 * q^38 - 6184 * q^39 - 1800 * q^40 + 52577 * q^41 - 28578 * q^42 + 963 * q^43 + 74536 * q^44 - 78500 * q^45 - 10531 * q^46 + 49346 * q^47 + 80107 * q^48 + 70288 * q^49 + 2500 * q^50 + 140786 * q^51 + 165062 * q^52 - 34457 * q^53 + 34216 * q^54 - 111925 * q^55 - 64095 * q^56 - 9747 * q^57 - 126140 * q^58 + 56521 * q^59 - 21800 * q^60 + 6613 * q^61 + 494 * q^62 - 125618 * q^63 - 140426 * q^64 - 17975 * q^65 + 17061 * q^66 - 43534 * q^67 - 138520 * q^68 + 34618 * q^69 + 15625 * q^70 + 95986 * q^71 - 42192 * q^72 + 109218 * q^73 - 182005 * q^74 + 16875 * q^75 - 222376 * q^76 - 9559 * q^77 - 369624 * q^78 + 64943 * q^79 - 173500 * q^80 + 388941 * q^81 - 126926 * q^82 + 109741 * q^83 - 112886 * q^84 - 2975 * q^85 + 43866 * q^86 + 142492 * q^87 + 8712 * q^88 - 119092 * q^89 + 105925 * q^90 + 349320 * q^91 + 433396 * q^92 - 108630 * q^93 + 196160 * q^94 + 333925 * q^95 + 376630 * q^96 + 68774 * q^97 + 310926 * q^98 + 379940 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more