LMFDB - Embedded newform 1045.6.a.d.1.1

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			1.1
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)

$f(q)$	$=$	$q-10.9267 q^{2} +0.166886 q^{3} +87.3933 q^{4} -25.0000 q^{5} -1.82352 q^{6} +16.8566 q^{7} -605.267 q^{8} -242.972 q^{9} +O(q^{10})$	\(q-10.9267 q^{2} +0.166886 q^{3} +87.3933 q^{4} -25.0000 q^{5} -1.82352 q^{6} +16.8566 q^{7} -605.267 q^{8} -242.972 q^{9} +273.168 q^{10} +121.000 q^{11} +14.5847 q^{12} +254.082 q^{13} -184.187 q^{14} -4.17215 q^{15} +3817.00 q^{16} -878.306 q^{17} +2654.89 q^{18} -361.000 q^{19} -2184.83 q^{20} +2.81313 q^{21} -1322.13 q^{22} +3970.99 q^{23} -101.011 q^{24} +625.000 q^{25} -2776.28 q^{26} -81.1020 q^{27} +1473.15 q^{28} +6087.62 q^{29} +45.5880 q^{30} -213.978 q^{31} -22338.8 q^{32} +20.1932 q^{33} +9597.00 q^{34} -421.415 q^{35} -21234.1 q^{36} -13166.9 q^{37} +3944.55 q^{38} +42.4027 q^{39} +15131.7 q^{40} +7723.86 q^{41} -30.7383 q^{42} -14152.8 q^{43} +10574.6 q^{44} +6074.30 q^{45} -43389.9 q^{46} +5781.35 q^{47} +637.004 q^{48} -16522.9 q^{49} -6829.20 q^{50} -146.577 q^{51} +22205.0 q^{52} -24134.9 q^{53} +886.179 q^{54} -3025.00 q^{55} -10202.7 q^{56} -60.2459 q^{57} -66517.7 q^{58} +9837.01 q^{59} -364.618 q^{60} -6613.94 q^{61} +2338.08 q^{62} -4095.69 q^{63} +121945. q^{64} -6352.05 q^{65} -220.646 q^{66} +68453.2 q^{67} -76758.0 q^{68} +662.704 q^{69} +4604.69 q^{70} -27391.6 q^{71} +147063. q^{72} +20640.2 q^{73} +143871. q^{74} +104.304 q^{75} -31549.0 q^{76} +2039.65 q^{77} -463.323 q^{78} -44192.7 q^{79} -95425.0 q^{80} +59028.7 q^{81} -84396.4 q^{82} +44425.7 q^{83} +245.849 q^{84} +21957.6 q^{85} +154644. q^{86} +1015.94 q^{87} -73237.3 q^{88} +59896.5 q^{89} -66372.2 q^{90} +4282.96 q^{91} +347038. q^{92} -35.7100 q^{93} -63171.3 q^{94} +9025.00 q^{95} -3728.03 q^{96} -164928. q^{97} +180541. q^{98} -29399.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.9267	−1.93159	−0.965795	−	0.259307i	$-0.916506\pi$
$2$	−10.9267	−1.93159	−0.965795	+	0.259307i	$0.916506\pi$
$3$	0.166886	0.0107058	0.00535288	−	0.999986i	$-0.498296\pi$
$3$	0.166886	0.0107058	0.00535288	+	0.999986i	$0.498296\pi$
$4$	87.3933	2.73104
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−1.82352	−0.0206791
$7$	16.8566	0.130024	0.0650122	−	0.997884i	$-0.479291\pi$
$7$	16.8566	0.130024	0.0650122	+	0.997884i	$0.479291\pi$
$8$	−605.267	−3.34366
$9$	−242.972	−0.999885
$10$	273.168	0.863833
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	14.5847	0.0292378
$13$	254.082	0.416980	0.208490	−	0.978025i	$-0.433145\pi$
$13$	254.082	0.416980	0.208490	+	0.978025i	$0.433145\pi$
$14$	−184.187	−0.251154
$15$	−4.17215	−0.00478776
$16$	3817.00	3.72754
$17$	−878.306	−0.737095	−0.368547	−	0.929609i	$-0.620145\pi$
$17$	−878.306	−0.737095	−0.368547	+	0.929609i	$0.620145\pi$
$18$	2654.89	1.93137
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−2184.83	−1.22136
$21$	2.81313	0.00139201
$22$	−1322.13	−0.582396
$23$	3970.99	1.56523	0.782617	−	0.622503i	$-0.213884\pi$
$23$	3970.99	1.56523	0.782617	+	0.622503i	$0.213884\pi$
$24$	−101.011	−0.0357964
$25$	625.000	0.200000
$26$	−2776.28	−0.805434
$27$	−81.1020	−0.0214103
$28$	1473.15	0.355102
$29$	6087.62	1.34416	0.672082	−	0.740476i	$-0.265400\pi$
$29$	6087.62	1.34416	0.672082	+	0.740476i	$0.265400\pi$
$30$	45.5880	0.00924799
$31$	−213.978	−0.0399913	−0.0199957	−	0.999800i	$-0.506365\pi$
$31$	−213.978	−0.0399913	−0.0199957	+	0.999800i	$0.506365\pi$
$32$	−22338.8	−3.85642
$33$	20.1932	0.00322791
$34$	9597.00	1.42377
$35$	−421.415	−0.0581487
$36$	−21234.1	−2.73073
$37$	−13166.9	−1.58117	−0.790584	−	0.612354i	$-0.790223\pi$
$37$	−13166.9	−1.58117	−0.790584	+	0.612354i	$0.790223\pi$
$38$	3944.55	0.443137
$39$	42.4027	0.00446408
$40$	15131.7	1.49533
$41$	7723.86	0.717587	0.358794	−	0.933417i	$-0.383188\pi$
$41$	7723.86	0.717587	0.358794	+	0.933417i	$0.383188\pi$
$42$	−30.7383	−0.00268879
$43$	−14152.8	−1.16727	−0.583637	−	0.812015i	$-0.698371\pi$
$43$	−14152.8	−1.16727	−0.583637	+	0.812015i	$0.698371\pi$
$44$	10574.6	0.823439
$45$	6074.30	0.447162
$46$	−43389.9	−3.02339
$47$	5781.35	0.381755	0.190878	−	0.981614i	$-0.438867\pi$
$47$	5781.35	0.381755	0.190878	+	0.981614i	$0.438867\pi$
$48$	637.004	0.0399061
$49$	−16522.9	−0.983094
$50$	−6829.20	−0.386318
$51$	−146.577	−0.00789116
$52$	22205.0	1.13879
$53$	−24134.9	−1.18020	−0.590101	−	0.807330i	$-0.700912\pi$
$53$	−24134.9	−1.18020	−0.590101	+	0.807330i	$0.700912\pi$
$54$	886.179	0.0413559
$55$	−3025.00	−0.134840
$56$	−10202.7	−0.434757
$57$	−60.2459	−0.00245607
$58$	−66517.7	−2.59638
$59$	9837.01	0.367903	0.183951	−	0.982935i	$-0.441111\pi$
$59$	9837.01	0.367903	0.183951	+	0.982935i	$0.441111\pi$
$60$	−364.618	−0.0130756
$61$	−6613.94	−0.227581	−0.113790	−	0.993505i	$-0.536299\pi$
$61$	−6613.94	−0.227581	−0.113790	+	0.993505i	$0.536299\pi$
$62$	2338.08	0.0772468
$63$	−4095.69	−0.130010
$64$	121945.	3.72148
$65$	−6352.05	−0.186479
$66$	−220.646	−0.00623499
$67$	68453.2	1.86297	0.931486	−	0.363776i	$-0.118513\pi$
$67$	68453.2	1.86297	0.931486	+	0.363776i	$0.118513\pi$
$68$	−76758.0	−2.01304
$69$	662.704	0.0167570
$70$	4604.69	0.112319
$71$	−27391.6	−0.644870	−0.322435	−	0.946592i	$-0.604501\pi$
$71$	−27391.6	−0.644870	−0.322435	+	0.946592i	$0.604501\pi$
$72$	147063.	3.34328
$73$	20640.2	0.453322	0.226661	−	0.973974i	$-0.427219\pi$
$73$	20640.2	0.453322	0.226661	+	0.973974i	$0.427219\pi$
$74$	143871.	3.05417
$75$	104.304	0.00214115
$76$	−31549.0	−0.626543
$77$	2039.65	0.0392038
$78$	−463.323	−0.00862278
$79$	−44192.7	−0.796678	−0.398339	−	0.917238i	$-0.630413\pi$
$79$	−44192.7	−0.796678	−0.398339	+	0.917238i	$0.630413\pi$
$80$	−95425.0	−1.66701
$81$	59028.7	0.999656
$82$	−84396.4	−1.38608
$83$	44425.7	0.707846	0.353923	−	0.935275i	$-0.384848\pi$
$83$	44425.7	0.707846	0.353923	+	0.935275i	$0.384848\pi$
$84$	245.849	0.00380163
$85$	21957.6	0.329639
$86$	154644.	2.25469
$87$	1015.94	0.0143903
$88$	−73237.3	−1.00815
$89$	59896.5	0.801542	0.400771	−	0.916178i	$-0.368742\pi$
$89$	59896.5	0.801542	0.400771	+	0.916178i	$0.368742\pi$
$90$	−66372.2	−0.863734
$91$	4282.96	0.0542176
$92$	347038.	4.27472
$93$	−35.7100	−0.000428137 0
$94$	−63171.3	−0.737394
$95$	9025.00	0.102598
$96$	−3728.03	−0.0412858
$97$	−164928.	−1.77977	−0.889885	−	0.456185i	$-0.849215\pi$
$97$	−164928.	−1.77977	−0.889885	+	0.456185i	$0.849215\pi$
$98$	180541.	1.89893
$99$	−29399.6	−0.301477
$100$	54620.8	0.546208
$101$	97887.7	0.954827	0.477413	−	0.878679i	$-0.341574\pi$
$101$	97887.7	0.954827	0.477413	+	0.878679i	$0.341574\pi$
$102$	1601.61	0.0152425
$103$	−126313.	−1.17316	−0.586578	−	0.809893i	$-0.699525\pi$
$103$	−126313.	−1.17316	−0.586578	+	0.809893i	$0.699525\pi$
$104$	−153787.	−1.39424
$105$	−70.3284	−0.000622526 0
$106$	263716.	2.27966
$107$	−17298.9	−0.146069	−0.0730346	−	0.997329i	$-0.523268\pi$
$107$	−17298.9	−0.146069	−0.0730346	+	0.997329i	$0.523268\pi$
$108$	−7087.77	−0.0584723
$109$	64800.7	0.522412	0.261206	−	0.965283i	$-0.415880\pi$
$109$	64800.7	0.522412	0.261206	+	0.965283i	$0.415880\pi$
$110$	33053.3	0.260456
$111$	−2197.37	−0.0169276
$112$	64341.6	0.484671
$113$	222419.	1.63861	0.819305	−	0.573358i	$-0.194360\pi$
$113$	222419.	1.63861	0.819305	+	0.573358i	$0.194360\pi$
$114$	658.290	0.00474412
$115$	−99274.8	−0.699994
$116$	532017.	3.67097
$117$	−61734.8	−0.416932
$118$	−107486.	−0.710638
$119$	−14805.3	−0.0958404
$120$	2525.27	0.0160086
$121$	14641.0	0.0909091
$122$	72268.7	0.439593
$123$	1289.00	0.00768231
$124$	−18700.3	−0.109218
$125$	−15625.0	−0.0894427
$126$	44752.4	0.251125
$127$	−104561.	−0.575255	−0.287628	−	0.957742i	$-0.592867\pi$
$127$	−104561.	−0.575255	−0.287628	+	0.957742i	$0.592867\pi$
$128$	−617623.	−3.33195
$129$	−2361.91	−0.0124965
$130$	69407.0	0.360201
$131$	−363447.	−1.85039	−0.925193	−	0.379496i	$-0.876097\pi$
$131$	−363447.	−1.85039	−0.925193	+	0.379496i	$0.876097\pi$
$132$	1764.75	0.00881554
$133$	−6085.23	−0.0298297
$134$	−747969.	−3.59850
$135$	2027.55	0.00957497
$136$	531609.	2.46459
$137$	−300220.	−1.36659	−0.683295	−	0.730142i	$-0.739454\pi$
$137$	−300220.	−1.36659	−0.683295	+	0.730142i	$0.739454\pi$
$138$	−7241.18	−0.0323677
$139$	154043.	0.676246	0.338123	−	0.941102i	$-0.390208\pi$
$139$	154043.	0.676246	0.338123	+	0.941102i	$0.390208\pi$
$140$	−36828.8	−0.158806
$141$	964.828	0.00408698
$142$	299301.	1.24562
$143$	30743.9	0.125724
$144$	−927425.	−3.72711
$145$	−152191.	−0.601129
$146$	−225530.	−0.875632
$147$	−2757.44	−0.0105248
$148$	−1.15069e6	−4.31823
$149$	−15197.0	−0.0560781	−0.0280391	−	0.999607i	$-0.508926\pi$
$149$	−15197.0	−0.0560781	−0.0280391	+	0.999607i	$0.508926\pi$
$150$	−1139.70	−0.00413582
$151$	−180921.	−0.645724	−0.322862	−	0.946446i	$-0.604645\pi$
$151$	−180921.	−0.645724	−0.322862	+	0.946446i	$0.604645\pi$
$152$	218501.	0.767088
$153$	213404.	0.737010
$154$	−22286.7	−0.0757258
$155$	5349.46	0.0178847
$156$	3705.71	0.0121916
$157$	−393049.	−1.27262	−0.636308	−	0.771435i	$-0.719539\pi$
$157$	−393049.	−1.27262	−0.636308	+	0.771435i	$0.719539\pi$
$158$	482882.	1.53886
$159$	−4027.78	−0.0126349
$160$	558469.	1.72464
$161$	66937.4	0.203519
$162$	−644990.	−1.93093
$163$	−380506.	−1.12174	−0.560871	−	0.827903i	$-0.689534\pi$
$163$	−380506.	−1.12174	−0.560871	+	0.827903i	$0.689534\pi$
$164$	675013.	1.95976
$165$	−504.831	−0.00144356
$166$	−485427.	−1.36727
$167$	−4178.37	−0.0115935	−0.00579676	−	0.999983i	$-0.501845\pi$
$167$	−4178.37	−0.0115935	−0.00579676	+	0.999983i	$0.501845\pi$
$168$	−1702.70	−0.00465440
$169$	−306735.	−0.826128
$170$	−239925.	−0.636727
$171$	87712.9	0.229389
$172$	−1.23686e6	−3.18787
$173$	242032.	0.614834	0.307417	−	0.951575i	$-0.400535\pi$
$173$	242032.	0.614834	0.307417	+	0.951575i	$0.400535\pi$
$174$	−11100.9	−0.0277962
$175$	10535.4	0.0260049
$176$	461857.	1.12390
$177$	1641.66	0.00393868
$178$	−654472.	−1.54825
$179$	62625.3	0.146089	0.0730444	−	0.997329i	$-0.476729\pi$
$179$	62625.3	0.146089	0.0730444	+	0.997329i	$0.476729\pi$
$180$	530853.	1.22122
$181$	252694.	0.573322	0.286661	−	0.958032i	$-0.407455\pi$
$181$	252694.	0.573322	0.286661	+	0.958032i	$0.407455\pi$
$182$	−46798.7	−0.104726
$183$	−1103.77	−0.00243642
$184$	−2.40351e6	−5.23361
$185$	329172.	0.707120
$186$	390.193	0.000826985 0
$187$	−106275.	−0.222242
$188$	505251.	1.04259
$189$	−1367.10	−0.00278386
$190$	−98613.7	−0.198177
$191$	426790.	0.846508	0.423254	−	0.906011i	$-0.360888\pi$
$191$	426790.	0.846508	0.423254	+	0.906011i	$0.360888\pi$
$192$	20351.0	0.0398412
$193$	−705711.	−1.36375	−0.681873	−	0.731471i	$-0.738834\pi$
$193$	−705711.	−1.36375	−0.681873	+	0.731471i	$0.738834\pi$
$194$	1.80212e6	3.43779
$195$	−1060.07	−0.00199640
$196$	−1.44399e6	−2.68487
$197$	−374395.	−0.687329	−0.343665	−	0.939092i	$-0.611668\pi$
$197$	−374395.	−0.687329	−0.343665	+	0.939092i	$0.611668\pi$
$198$	321242.	0.582330
$199$	981499.	1.75694	0.878470	−	0.477797i	$-0.158564\pi$
$199$	981499.	1.75694	0.878470	+	0.477797i	$0.158564\pi$
$200$	−378292.	−0.668732
$201$	11423.9	0.0199445
$202$	−1.06959e6	−1.84433
$203$	102617.	0.174774
$204$	−12809.8	−0.0215511
$205$	−193096.	−0.320915
$206$	1.38019e6	2.26606
$207$	−964840.	−1.56506
$208$	969830.	1.55431
$209$	−43681.0	−0.0691714
$210$	768.458	0.00120246
$211$	1.10635e6	1.71076	0.855379	−	0.518003i	$-0.173325\pi$
$211$	1.10635e6	1.71076	0.855379	+	0.518003i	$0.173325\pi$
$212$	−2.10923e6	−3.22318
$213$	−4571.29	−0.00690382
$214$	189020.	0.282146
$215$	353821.	0.522021
$216$	49088.4	0.0715887
$217$	−3606.95	−0.00519985
$218$	−708059.	−1.00909
$219$	3444.56	0.00485315
$220$	−264365.	−0.368253
$221$	−223162.	−0.307354
$222$	24010.0	0.0326972
$223$	−832199.	−1.12064	−0.560318	−	0.828277i	$-0.689321\pi$
$223$	−832199.	−1.12064	−0.560318	+	0.828277i	$0.689321\pi$
$224$	−376556.	−0.501428
$225$	−151858.	−0.199977
$226$	−2.43031e6	−3.16512
$227$	−1.20697e6	−1.55465	−0.777323	−	0.629101i	$-0.783423\pi$
$227$	−1.20697e6	−1.55465	−0.777323	+	0.629101i	$0.783423\pi$
$228$	−5265.09	−0.00670762
$229$	−572656.	−0.721614	−0.360807	−	0.932640i	$-0.617499\pi$
$229$	−572656.	−0.721614	−0.360807	+	0.932640i	$0.617499\pi$
$230$	1.08475e6	1.35210
$231$	340.389	0.000419707 0
$232$	−3.68464e6	−4.49443
$233$	1.33789e6	1.61448	0.807238	−	0.590226i	$-0.200961\pi$
$233$	1.33789e6	1.61448	0.807238	+	0.590226i	$0.200961\pi$
$234$	674559.	0.805342
$235$	−144534.	−0.170726
$236$	859689.	1.00476
$237$	−7375.15	−0.00852904
$238$	161773.	0.185124
$239$	1.49647e6	1.69462	0.847312	−	0.531096i	$-0.178219\pi$
$239$	1.49647e6	1.69462	0.847312	+	0.531096i	$0.178219\pi$
$240$	−15925.1	−0.0178466
$241$	829896.	0.920410	0.460205	−	0.887813i	$-0.347776\pi$
$241$	829896.	0.920410	0.460205	+	0.887813i	$0.347776\pi$
$242$	−159978.	−0.175599
$243$	29558.9	0.0321123
$244$	−578014.	−0.621532
$245$	413071.	0.439653
$246$	−14084.6	−0.0148391
$247$	−91723.5	−0.0956618
$248$	129514.	0.133717
$249$	7414.03	0.00757802
$250$	170730.	0.172767
$251$	124960.	0.125195	0.0625975	−	0.998039i	$-0.480062\pi$
$251$	124960.	0.125195	0.0625975	+	0.998039i	$0.480062\pi$
$252$	−357935.	−0.355061
$253$	480490.	0.471936
$254$	1.14251e6	1.11116
$255$	3664.43	0.00352903
$256$	2.84635e6	2.71449
$257$	1.48546e6	1.40290	0.701452	−	0.712716i	$-0.252535\pi$
$257$	1.48546e6	1.40290	0.701452	+	0.712716i	$0.252535\pi$
$258$	25808.0	0.0241382
$259$	−221949.	−0.205590
$260$	−555126.	−0.509282
$261$	−1.47912e6	−1.34401
$262$	3.97128e6	3.57419
$263$	−1.37698e6	−1.22755	−0.613774	−	0.789482i	$-0.710349\pi$
$263$	−1.37698e6	−1.22755	−0.613774	+	0.789482i	$0.710349\pi$
$264$	−12222.3	−0.0107930
$265$	603373.	0.527802
$266$	66491.7	0.0576187
$267$	9995.90	0.00858111
$268$	5.98235e6	5.08785
$269$	−1.13223e6	−0.954011	−0.477006	−	0.878900i	$-0.658278\pi$
$269$	−1.13223e6	−0.954011	−0.477006	+	0.878900i	$0.658278\pi$
$270$	−22154.5	−0.0184949
$271$	1.19181e6	0.985790	0.492895	−	0.870089i	$-0.335939\pi$
$271$	1.19181e6	0.985790	0.492895	+	0.870089i	$0.335939\pi$
$272$	−3.35249e6	−2.74755
$273$	714.766	0.000580440 0
$274$	3.28042e6	2.63969
$275$	75625.0	0.0603023
$276$	57915.8	0.0457641
$277$	−879759.	−0.688913	−0.344456	−	0.938802i	$-0.611937\pi$
$277$	−879759.	−0.688913	−0.344456	+	0.938802i	$0.611937\pi$
$278$	−1.68318e6	−1.30623
$279$	51990.8	0.0399867
$280$	255069.	0.194429
$281$	1.39913e6	1.05704	0.528520	−	0.848921i	$-0.322747\pi$
$281$	1.39913e6	1.05704	0.528520	+	0.848921i	$0.322747\pi$
$282$	−10542.4	−0.00789436
$283$	−1.39624e6	−1.03632	−0.518159	−	0.855284i	$-0.673383\pi$
$283$	−1.39624e6	−1.03632	−0.518159	+	0.855284i	$0.673383\pi$
$284$	−2.39384e6	−1.76117
$285$	1506.15	0.00109839
$286$	−335930.	−0.242848
$287$	130198.	0.0933039
$288$	5.42769e6	3.85597
$289$	−648436.	−0.456691
$290$	1.66294e6	1.16113
$291$	−27524.1	−0.0190538
$292$	1.80381e6	1.23804
$293$	1.33576e6	0.908992	0.454496	−	0.890749i	$-0.349819\pi$
$293$	1.33576e6	0.908992	0.454496	+	0.890749i	$0.349819\pi$
$294$	30129.7	0.0203295
$295$	−245925.	−0.164531
$296$	7.96947e6	5.28689
$297$	−9813.35	−0.00645544
$298$	166054.	0.108320
$299$	1.00896e6	0.652671
$300$	9115.45	0.00584757
$301$	−238569.	−0.151774
$302$	1.97687e6	1.24727
$303$	16336.1	0.0102221
$304$	−1.37794e6	−0.855156
$305$	165348.	0.101777
$306$	−2.33180e6	−1.42360
$307$	1.08480e6	0.656908	0.328454	−	0.944520i	$-0.393472\pi$
$307$	1.08480e6	0.656908	0.328454	+	0.944520i	$0.393472\pi$
$308$	178252.	0.107067
$309$	−21079.9	−0.0125595
$310$	−58452.0	−0.0345458
$311$	−3.35580e6	−1.96741	−0.983706	−	0.179786i	$-0.942460\pi$
$311$	−3.35580e6	−1.96741	−0.983706	+	0.179786i	$0.942460\pi$
$312$	−25665.0	−0.0149264
$313$	661918.	0.381894	0.190947	−	0.981600i	$-0.438844\pi$
$313$	661918.	0.381894	0.190947	+	0.981600i	$0.438844\pi$
$314$	4.29473e6	2.45817
$315$	102392.	0.0581420
$316$	−3.86215e6	−2.17576
$317$	−669711.	−0.374317	−0.187158	−	0.982330i	$-0.559928\pi$
$317$	−669711.	−0.374317	−0.187158	+	0.982330i	$0.559928\pi$
$318$	44010.5	0.0244055
$319$	736602.	0.405281
$320$	−3.04863e6	−1.66430
$321$	−2886.94	−0.00156378
$322$	−731407.	−0.393115
$323$	317068.	0.169101
$324$	5.15871e6	2.73010
$325$	158801.	0.0833960
$326$	4.15769e6	2.16675
$327$	10814.3	0.00559282
$328$	−4.67500e6	−2.39937
$329$	97454.0	0.0496375
$330$	5516.14	0.00278837
$331$	−167012.	−0.0837871	−0.0418936	−	0.999122i	$-0.513339\pi$
$331$	−167012.	−0.0837871	−0.0418936	+	0.999122i	$0.513339\pi$
$332$	3.88250e6	1.93316
$333$	3.19918e6	1.58099
$334$	45655.9	0.0223939
$335$	−1.71133e6	−0.833147
$336$	10737.7	0.00518877
$337$	−371434.	−0.178159	−0.0890794	−	0.996025i	$-0.528392\pi$
$337$	−371434.	−0.178159	−0.0890794	+	0.996025i	$0.528392\pi$
$338$	3.35161e6	1.59574
$339$	37118.6	0.0175425
$340$	1.91895e6	0.900257
$341$	−25891.4	−0.0120578
$342$	−958415.	−0.443086
$343$	−561828.	−0.257851
$344$	8.56625e6	3.90296
$345$	−16567.6	−0.00749396
$346$	−2.64462e6	−1.18761
$347$	−1.57163e6	−0.700691	−0.350346	−	0.936620i	$-0.613936\pi$
$347$	−1.57163e6	−0.700691	−0.350346	+	0.936620i	$0.613936\pi$
$348$	88786.3	0.0393005
$349$	1.29149e6	0.567582	0.283791	−	0.958886i	$-0.408408\pi$
$349$	1.29149e6	0.567582	0.283791	+	0.958886i	$0.408408\pi$
$350$	−115117.	−0.0502308
$351$	−20606.5	−0.00892766
$352$	−2.70299e6	−1.16275
$353$	−1.24422e6	−0.531449	−0.265724	−	0.964049i	$-0.585611\pi$
$353$	−1.24422e6	−0.531449	−0.265724	+	0.964049i	$0.585611\pi$
$354$	−17938.0	−0.00760791
$355$	684791.	0.288395
$356$	5.23455e6	2.18904
$357$	−2470.79	−0.00102604
$358$	−684289.	−0.282184
$359$	−1.50361e6	−0.615741	−0.307870	−	0.951428i	$-0.599616\pi$
$359$	−1.50361e6	−0.615741	−0.307870	+	0.951428i	$0.599616\pi$
$360$	−3.67658e6	−1.49516
$361$	130321.	0.0526316
$362$	−2.76112e6	−1.10742
$363$	2443.38	0.000973250 0
$364$	374302.	0.148070
$365$	−516005.	−0.202732
$366$	12060.6	0.00470617
$367$	−1.07445e6	−0.416409	−0.208205	−	0.978085i	$-0.566762\pi$
$367$	−1.07445e6	−0.416409	−0.208205	+	0.978085i	$0.566762\pi$
$368$	1.51573e7	5.83447
$369$	−1.87668e6	−0.717505
$370$	−3.59677e6	−1.36587
$371$	−406833.	−0.153455
$372$	−3120.82	−0.00116926
$373$	4.17612e6	1.55418	0.777089	−	0.629390i	$-0.216695\pi$
$373$	4.17612e6	1.55418	0.777089	+	0.629390i	$0.216695\pi$
$374$	1.16124e6	0.429281
$375$	−2607.60	−0.000957552 0
$376$	−3.49926e6	−1.27646
$377$	1.54675e6	0.560490
$378$	14938.0	0.00537727
$379$	2.72869e6	0.975791	0.487896	−	0.872902i	$-0.337765\pi$
$379$	2.72869e6	0.975791	0.487896	+	0.872902i	$0.337765\pi$
$380$	788724.	0.280199
$381$	−17449.8	−0.00615854
$382$	−4.66342e6	−1.63511
$383$	−1.53325e6	−0.534092	−0.267046	−	0.963684i	$-0.586048\pi$
$383$	−1.53325e6	−0.534092	−0.267046	+	0.963684i	$0.586048\pi$
$384$	−103073.	−0.0356710
$385$	−50991.2	−0.0175325
$386$	7.71110e6	2.63420
$387$	3.43875e6	1.16714
$388$	−1.44136e7	−4.86062
$389$	−1.83553e6	−0.615018	−0.307509	−	0.951545i	$-0.599495\pi$
$389$	−1.83553e6	−0.615018	−0.307509	+	0.951545i	$0.599495\pi$
$390$	11583.1	0.00385622
$391$	−3.48775e6	−1.15373
$392$	1.00007e7	3.28713
$393$	−60654.2	−0.0198098
$394$	4.09092e6	1.32764
$395$	1.10482e6	0.356285
$396$	−2.56933e6	−0.823345
$397$	5.90657e6	1.88087	0.940435	−	0.339973i	$-0.110418\pi$
$397$	5.90657e6	1.88087	0.940435	+	0.339973i	$0.110418\pi$
$398$	−1.07246e7	−3.39369
$399$	−1015.54	−0.000319349 0
$400$	2.38562e6	0.745508
$401$	−306540.	−0.0951977	−0.0475988	−	0.998867i	$-0.515157\pi$
$401$	−306540.	−0.0951977	−0.0475988	+	0.998867i	$0.515157\pi$
$402$	−124826.	−0.0385246
$403$	−54368.0	−0.0166756
$404$	8.55472e6	2.60767
$405$	−1.47572e6	−0.447060
$406$	−1.12126e6	−0.337592
$407$	−1.59319e6	−0.476740
$408$	88718.3	0.0263853
$409$	1.18654e6	0.350731	0.175366	−	0.984503i	$-0.443889\pi$
$409$	1.18654e6	0.350731	0.175366	+	0.984503i	$0.443889\pi$
$410$	2.10991e6	0.619876
$411$	−50102.6	−0.0146304
$412$	−1.10389e7	−3.20393
$413$	165819.	0.0478364
$414$	1.05425e7	3.02304
$415$	−1.11064e6	−0.316558
$416$	−5.67587e6	−1.60805
$417$	25707.6	0.00723972
$418$	477290.	0.133611
$419$	−1.25932e6	−0.350430	−0.175215	−	0.984530i	$-0.556062\pi$
$419$	−1.25932e6	−0.350430	−0.175215	+	0.984530i	$0.556062\pi$
$420$	−6146.22	−0.00170014
$421$	2.21699e6	0.609619	0.304810	−	0.952413i	$-0.401407\pi$
$421$	2.21699e6	0.609619	0.304810	+	0.952413i	$0.401407\pi$
$422$	−1.20888e7	−3.30448
$423$	−1.40471e6	−0.381711
$424$	1.46081e7	3.94619
$425$	−548941.	−0.147419
$426$	49949.2	0.0133353
$427$	−111489.	−0.0295911
$428$	−1.51181e6	−0.398921
$429$	5130.73	0.00134597
$430$	−3.86611e6	−1.00833
$431$	3.53043e6	0.915449	0.457725	−	0.889094i	$-0.348665\pi$
$431$	3.53043e6	0.915449	0.457725	+	0.889094i	$0.348665\pi$
$432$	−309566.	−0.0798076
$433$	3.46607e6	0.888419	0.444209	−	0.895923i	$-0.353485\pi$
$433$	3.46607e6	0.888419	0.444209	+	0.895923i	$0.353485\pi$
$434$	39412.1	0.0100440
$435$	−25398.5	−0.00643554
$436$	5.66314e6	1.42673
$437$	−1.43353e6	−0.359089
$438$	−37637.8	−0.00937430
$439$	7.63662e6	1.89121	0.945605	−	0.325316i	$-0.105471\pi$
$439$	7.63662e6	1.89121	0.945605	+	0.325316i	$0.105471\pi$
$440$	1.83093e6	0.450859
$441$	4.01459e6	0.982981
$442$	2.43842e6	0.593682
$443$	−2.02910e6	−0.491240	−0.245620	−	0.969366i	$-0.578991\pi$
$443$	−2.02910e6	−0.491240	−0.245620	+	0.969366i	$0.578991\pi$
$444$	−192035.	−0.0462299
$445$	−1.49741e6	−0.358461
$446$	9.09320e6	2.16461
$447$	−2536.18	−0.000600358 0
$448$	2.05558e6	0.483883
$449$	4.70609e6	1.10165	0.550826	−	0.834620i	$-0.314313\pi$
$449$	4.70609e6	1.10165	0.550826	+	0.834620i	$0.314313\pi$
$450$	1.65931e6	0.386274
$451$	934587.	0.216361
$452$	1.94379e7	4.47511
$453$	−30193.2	−0.00691296
$454$	1.31882e7	3.00294
$455$	−107074.	−0.0242468
$456$	36464.9	0.00821225
$457$	6.10289e6	1.36693	0.683463	−	0.729986i	$-0.260473\pi$
$457$	6.10289e6	1.36693	0.683463	+	0.729986i	$0.260473\pi$
$458$	6.25725e6	1.39386
$459$	71232.4	0.0157814
$460$	−8.67595e6	−1.91171
$461$	3.63588e6	0.796815	0.398408	−	0.917208i	$-0.369563\pi$
$461$	3.63588e6	0.796815	0.398408	+	0.917208i	$0.369563\pi$
$462$	−3719.34	−0.000810701 0
$463$	5.82162e6	1.26209	0.631047	−	0.775745i	$-0.282626\pi$
$463$	5.82162e6	1.26209	0.631047	+	0.775745i	$0.282626\pi$
$464$	2.32364e7	5.01043
$465$	892.750	0.000191469 0
$466$	−1.46188e7	−3.11851
$467$	828718.	0.175839	0.0879194	−	0.996128i	$-0.471978\pi$
$467$	828718.	0.175839	0.0879194	+	0.996128i	$0.471978\pi$
$468$	−5.39521e6	−1.13866
$469$	1.15389e6	0.242232
$470$	1.57928e6	0.329773
$471$	−65594.4	−0.0136243
$472$	−5.95402e6	−1.23014
$473$	−1.71249e6	−0.351946
$474$	80586.3	0.0164746
$475$	−225625.	−0.0458831
$476$	−1.29388e6	−0.261744
$477$	5.86411e6	1.18007
$478$	−1.63515e7	−3.27332
$479$	28673.1	0.00571000	0.00285500	−	0.999996i	$-0.499091\pi$
$479$	28673.1	0.00571000	0.00285500	+	0.999996i	$0.499091\pi$
$480$	93200.7	0.0184636
$481$	−3.34546e6	−0.659315
$482$	−9.06805e6	−1.77785
$483$	11170.9	0.00217882
$484$	1.27952e6	0.248276
$485$	4.12319e6	0.795937
$486$	−322982.	−0.0620279
$487$	3.97300e6	0.759095	0.379548	−	0.925172i	$-0.376080\pi$
$487$	3.97300e6	0.759095	0.379548	+	0.925172i	$0.376080\pi$
$488$	4.00320e6	0.760952
$489$	−63501.3	−0.0120091
$490$	−4.51352e6	−0.849229
$491$	5.96643e6	1.11689	0.558446	−	0.829541i	$-0.311398\pi$
$491$	5.96643e6	1.11689	0.558446	+	0.829541i	$0.311398\pi$
$492$	112650.	0.0209807
$493$	−5.34679e6	−0.990777
$494$	1.00224e6	0.184779
$495$	734991.	0.134825
$496$	−816755.	−0.149069
$497$	−461730.	−0.0838489
$498$	−81011.0	−0.0146376
$499$	−3.56989e6	−0.641806	−0.320903	−	0.947112i	$-0.603986\pi$
$499$	−3.56989e6	−0.641806	−0.320903	+	0.947112i	$0.603986\pi$
$500$	−1.36552e6	−0.244272
$501$	−697.312	−0.000124117 0
$502$	−1.36540e6	−0.241825
$503$	6.22051e6	1.09624	0.548121	−	0.836399i	$-0.315343\pi$
$503$	6.22051e6	1.09624	0.548121	+	0.836399i	$0.315343\pi$
$504$	2.47898e6	0.434708
$505$	−2.44719e6	−0.427011
$506$	−5.25018e6	−0.911587
$507$	−51189.9	−0.00884432
$508$	−9.13793e6	−1.57105
$509$	7.18919e6	1.22995	0.614973	−	0.788548i	$-0.289167\pi$
$509$	7.18919e6	1.22995	0.614973	+	0.788548i	$0.289167\pi$
$510$	−40040.2	−0.00681664
$511$	347924.	0.0589429
$512$	−1.13373e7	−1.91132
$513$	29277.8	0.00491185
$514$	−1.62312e7	−2.70984
$515$	3.15783e6	0.524651
$516$	−206415.	−0.0341286
$517$	699544.	0.115104
$518$	2.42517e6	0.397116
$519$	40391.8	0.00658226
$520$	3.84468e6	0.623523
$521$	−1.00431e7	−1.62096	−0.810479	−	0.585768i	$-0.800793\pi$
$521$	−1.00431e7	−1.62096	−0.810479	+	0.585768i	$0.800793\pi$
$522$	1.61620e7	2.59608
$523$	7.14043e6	1.14148	0.570742	−	0.821129i	$-0.306656\pi$
$523$	7.14043e6	1.14148	0.570742	+	0.821129i	$0.306656\pi$
$524$	−3.17628e7	−5.05348
$525$	1758.21	0.000278402 0
$526$	1.50459e7	2.37112
$527$	187938.	0.0294774
$528$	77077.5	0.0120321
$529$	9.33244e6	1.44996
$530$	−6.59289e6	−1.01950
$531$	−2.39012e6	−0.367861
$532$	−531809.	−0.0814660
$533$	1.96249e6	0.299219
$534$	−109222.	−0.0165752
$535$	432472.	0.0653241
$536$	−4.14324e7	−6.22915
$537$	10451.3	0.00156399
$538$	1.23715e7	1.84276
$539$	−1.99927e6	−0.296414
$540$	177194.	0.0261496
$541$	−763341.	−0.112131	−0.0560654	−	0.998427i	$-0.517856\pi$
$541$	−763341.	−0.112131	−0.0560654	+	0.998427i	$0.517856\pi$
$542$	−1.30226e7	−1.90414
$543$	42171.2	0.00613785
$544$	1.96203e7	2.84255
$545$	−1.62002e6	−0.233630
$546$	−7810.05	−0.00112117
$547$	−4.32345e6	−0.617820	−0.308910	−	0.951091i	$-0.599964\pi$
$547$	−4.32345e6	−0.617820	−0.308910	+	0.951091i	$0.599964\pi$
$548$	−2.62372e7	−3.73221
$549$	1.60700e6	0.227555
$550$	−826333.	−0.116479
$551$	−2.19763e6	−0.308373
$552$	−401113.	−0.0560297
$553$	−744939.	−0.103588
$554$	9.61288e6	1.33070
$555$	54934.2	0.00757025
$556$	1.34623e7	1.84685
$557$	−1.19391e6	−0.163054	−0.0815271	−	0.996671i	$-0.525980\pi$
$557$	−1.19391e6	−0.163054	−0.0815271	+	0.996671i	$0.525980\pi$
$558$	−568089.	−0.0772379
$559$	−3.59598e6	−0.486730
$560$	−1.60854e6	−0.216752
$561$	−17735.8	−0.00237927
$562$	−1.52879e7	−2.04177
$563$	−2.70582e6	−0.359773	−0.179886	−	0.983687i	$-0.557573\pi$
$563$	−2.70582e6	−0.359773	−0.179886	+	0.983687i	$0.557573\pi$
$564$	84319.5	0.0111617
$565$	−5.56047e6	−0.732808
$566$	1.52563e7	2.00174
$567$	995023.	0.129980
$568$	1.65793e7	2.15623
$569$	−3.79612e6	−0.491540	−0.245770	−	0.969328i	$-0.579041\pi$
$569$	−3.79612e6	−0.491540	−0.245770	+	0.969328i	$0.579041\pi$
$570$	−16457.3	−0.00212163
$571$	−1.01147e7	−1.29826	−0.649132	−	0.760676i	$-0.724868\pi$
$571$	−1.01147e7	−1.29826	−0.649132	+	0.760676i	$0.724868\pi$
$572$	2.68681e6	0.343358
$573$	71225.4	0.00906250
$574$	−1.42264e6	−0.180225
$575$	2.48187e6	0.313047
$576$	−2.96293e7	−3.72105
$577$	−9.70701e6	−1.21380	−0.606898	−	0.794780i	$-0.707586\pi$
$577$	−9.70701e6	−1.21380	−0.606898	+	0.794780i	$0.707586\pi$
$578$	7.08528e6	0.882140
$579$	−117773.	−0.0145999
$580$	−1.33004e7	−1.64171
$581$	748866.	0.0920373
$582$	300748.	0.0368041
$583$	−2.92032e6	−0.355844
$584$	−1.24928e7	−1.51575
$585$	1.54337e6	0.186458
$586$	−1.45955e7	−1.75580
$587$	−1.18244e7	−1.41639	−0.708196	−	0.706016i	$-0.750491\pi$
$587$	−1.18244e7	−1.41639	−0.708196	+	0.706016i	$0.750491\pi$
$588$	−240981.	−0.0287435
$589$	77246.2	0.00917463
$590$	2.68716e6	0.317807
$591$	−62481.4	−0.00735838
$592$	−5.02579e7	−5.89386
$593$	489207.	0.0571289	0.0285645	−	0.999592i	$-0.490906\pi$
$593$	489207.	0.0571289	0.0285645	+	0.999592i	$0.490906\pi$
$594$	107228.	0.0124693
$595$	370131.	0.0428611
$596$	−1.32812e6	−0.153152
$597$	163799.	0.0188094
$598$	−1.10246e7	−1.26069
$599$	3.04641e6	0.346914	0.173457	−	0.984841i	$-0.444506\pi$
$599$	3.04641e6	0.346914	0.173457	+	0.984841i	$0.444506\pi$
$600$	−63131.7	−0.00715928
$601$	980700.	0.110752	0.0553758	−	0.998466i	$-0.482364\pi$
$601$	980700.	0.110752	0.0553758	+	0.998466i	$0.482364\pi$
$602$	2.60678e6	0.293165
$603$	−1.66322e7	−1.86276
$604$	−1.58113e7	−1.76350
$605$	−366025.	−0.0406558
$606$	−178500.	−0.0197450
$607$	−1.26128e7	−1.38944	−0.694721	−	0.719279i	$-0.744472\pi$
$607$	−1.26128e7	−1.38944	−0.694721	+	0.719279i	$0.744472\pi$
$608$	8.06429e6	0.884723
$609$	17125.3	0.00187109
$610$	−1.80672e6	−0.196592
$611$	1.46894e6	0.159184
$612$	1.86501e7	2.01280
$613$	1.06335e7	1.14294	0.571471	−	0.820622i	$-0.306373\pi$
$613$	1.06335e7	1.14294	0.571471	+	0.820622i	$0.306373\pi$
$614$	−1.18533e7	−1.26888
$615$	−32225.1	−0.00343563
$616$	−1.23453e6	−0.131084
$617$	−1.29441e7	−1.36886	−0.684430	−	0.729078i	$-0.739949\pi$
$617$	−1.29441e7	−1.36886	−0.684430	+	0.729078i	$0.739949\pi$
$618$	230334.	0.0242598
$619$	4.25067e6	0.445893	0.222947	−	0.974831i	$-0.428432\pi$
$619$	4.25067e6	0.445893	0.222947	+	0.974831i	$0.428432\pi$
$620$	467507.	0.0488437
$621$	−322056.	−0.0335121
$622$	3.66679e7	3.80023
$623$	1.00965e6	0.104220
$624$	161851.	0.0166400
$625$	390625.	0.0400000
$626$	−7.23259e6	−0.737663
$627$	−7289.75	−0.000740532 0
$628$	−3.43498e7	−3.47556
$629$	1.15645e7	1.16547
$630$	−1.11881e6	−0.112307
$631$	1.54494e6	0.154467	0.0772337	−	0.997013i	$-0.475391\pi$
$631$	1.54494e6	0.154467	0.0772337	+	0.997013i	$0.475391\pi$
$632$	2.67484e7	2.66382
$633$	184635.	0.0183149
$634$	7.31775e6	0.723027
$635$	2.61403e6	0.257262
$636$	−352001.	−0.0345065
$637$	−4.19816e6	−0.409930
$638$	−8.04865e6	−0.782837
$639$	6.65541e6	0.644796
$640$	1.54406e7	1.49009
$641$	4.42509e6	0.425380	0.212690	−	0.977120i	$-0.431778\pi$
$641$	4.42509e6	0.425380	0.212690	+	0.977120i	$0.431778\pi$
$642$	31544.8	0.00302058
$643$	1.72824e7	1.64846	0.824228	−	0.566259i	$-0.191610\pi$
$643$	1.72824e7	1.64846	0.824228	+	0.566259i	$0.191610\pi$
$644$	5.84988e6	0.555818
$645$	59047.9	0.00558862
$646$	−3.46452e6	−0.326634
$647$	8.54231e6	0.802259	0.401129	−	0.916021i	$-0.368618\pi$
$647$	8.54231e6	0.802259	0.401129	+	0.916021i	$0.368618\pi$
$648$	−3.57281e7	−3.34251
$649$	1.19028e6	0.110927
$650$	−1.73518e6	−0.161087
$651$	−601.950	−5.56683e−5 0
$652$	−3.32537e7	−3.06352
$653$	1.89325e7	1.73750	0.868751	−	0.495249i	$-0.164923\pi$
$653$	1.89325e7	1.73750	0.868751	+	0.495249i	$0.164923\pi$
$654$	−118165.	−0.0108030
$655$	9.08617e6	0.827518
$656$	2.94820e7	2.67483
$657$	−5.01499e6	−0.453270
$658$	−1.06485e6	−0.0958793
$659$	2.02932e7	1.82027	0.910137	−	0.414308i	$-0.135976\pi$
$659$	2.02932e7	1.82027	0.910137	+	0.414308i	$0.135976\pi$
$660$	−44118.8	−0.00394243
$661$	−5.13373e6	−0.457014	−0.228507	−	0.973542i	$-0.573384\pi$
$661$	−5.13373e6	−0.457014	−0.228507	+	0.973542i	$0.573384\pi$
$662$	1.82489e6	0.161842
$663$	−37242.6	−0.00329045
$664$	−2.68894e7	−2.36680
$665$	152131.	0.0133402
$666$	−3.49566e7	−3.05382
$667$	2.41739e7	2.10393
$668$	−365161.	−0.0316624
$669$	−138882.	−0.0119973
$670$	1.86992e7	1.60930
$671$	−800286.	−0.0686182
$672$	−62841.9	−0.00536817
$673$	1.19203e6	0.101449	0.0507247	−	0.998713i	$-0.483847\pi$
$673$	1.19203e6	0.101449	0.0507247	+	0.998713i	$0.483847\pi$
$674$	4.05856e6	0.344130
$675$	−50688.8	−0.00428206
$676$	−2.68066e7	−2.25619
$677$	1.23603e7	1.03647	0.518235	−	0.855238i	$-0.326589\pi$
$677$	1.23603e7	1.03647	0.518235	+	0.855238i	$0.326589\pi$
$678$	−405585.	−0.0338850
$679$	−2.78012e6	−0.231414
$680$	−1.32902e7	−1.10220
$681$	−201427.	−0.0166437
$682$	282908.	0.0232908
$683$	−2.16761e7	−1.77799	−0.888993	−	0.457920i	$-0.848595\pi$
$683$	−2.16761e7	−1.77799	−0.888993	+	0.457920i	$0.848595\pi$
$684$	7.66552e6	0.626472
$685$	7.50550e6	0.611158
$686$	6.13894e6	0.498062
$687$	−95568.4	−0.00772543
$688$	−5.40214e7	−4.35106
$689$	−6.13224e6	−0.492120
$690$	181029.	0.0144753
$691$	−2.80061e6	−0.223129	−0.111565	−	0.993757i	$-0.535586\pi$
$691$	−2.80061e6	−0.223129	−0.111565	+	0.993757i	$0.535586\pi$
$692$	2.11520e7	1.67914
$693$	−495578.	−0.0391994
$694$	1.71728e7	1.35345
$695$	−3.85107e6	−0.302426
$696$	−614915.	−0.0481162
$697$	−6.78391e6	−0.528930
$698$	−1.41118e7	−1.09634
$699$	223276.	0.0172842
$700$	920721.	0.0710204
$701$	2.05450e6	0.157911	0.0789554	−	0.996878i	$-0.474842\pi$
$701$	2.05450e6	0.157911	0.0789554	+	0.996878i	$0.474842\pi$
$702$	225162.	0.0172446
$703$	4.75324e6	0.362745
$704$	1.47554e7	1.12207
$705$	−24120.7	−0.00182775
$706$	1.35953e7	1.02654
$707$	1.65005e6	0.124151
$708$	143470.	0.0107567
$709$	−46285.5	−0.00345804	−0.00172902	−	0.999999i	$-0.500550\pi$
$709$	−46285.5	−0.00345804	−0.00172902	+	0.999999i	$0.500550\pi$
$710$	−7.48252e6	−0.557060
$711$	1.07376e7	0.796587
$712$	−3.62534e7	−2.68008
$713$	−849706.	−0.0625958
$714$	26997.7	0.00198189
$715$	−768597.	−0.0562256
$716$	5.47303e6	0.398974
$717$	249740.	0.0181422
$718$	1.64295e7	1.18936
$719$	4.88106e6	0.352121	0.176060	−	0.984379i	$-0.443665\pi$
$719$	4.88106e6	0.352121	0.176060	+	0.984379i	$0.443665\pi$
$720$	2.31856e7	1.66681
$721$	−2.12921e6	−0.152539
$722$	−1.42398e6	−0.101663
$723$	138498.	0.00985368
$724$	2.20838e7	1.56577
$725$	3.80476e6	0.268833
$726$	−26698.1	−0.00187992
$727$	−2.55893e7	−1.79565	−0.897826	−	0.440351i	$-0.854854\pi$
$727$	−2.55893e7	−1.79565	−0.897826	+	0.440351i	$0.854854\pi$
$728$	−2.59233e6	−0.181285
$729$	−1.43390e7	−0.999312
$730$	5.63824e6	0.391595
$731$	1.24305e7	0.860391
$732$	−96462.5	−0.00665397
$733$	1.69249e7	1.16350	0.581750	−	0.813368i	$-0.302368\pi$
$733$	1.69249e7	1.16350	0.581750	+	0.813368i	$0.302368\pi$
$734$	1.17402e7	0.804332
$735$	68935.9	0.00470681
$736$	−8.87070e7	−6.03620
$737$	8.28283e6	0.561707
$738$	2.05060e7	1.38593
$739$	1.98474e7	1.33688	0.668440	−	0.743766i	$-0.266962\pi$
$739$	1.98474e7	1.33688	0.668440	+	0.743766i	$0.266962\pi$
$740$	2.87674e7	1.93117
$741$	−15307.4	−0.00102413
$742$	4.44535e6	0.296412
$743$	2.48716e7	1.65284	0.826421	−	0.563053i	$-0.190373\pi$
$743$	2.48716e7	1.65284	0.826421	+	0.563053i	$0.190373\pi$
$744$	21614.1	0.00143154
$745$	379926.	0.0250789
$746$	−4.56313e7	−3.00204
$747$	−1.07942e7	−0.707765
$748$	−9.28772e6	−0.606953
$749$	−291600.	−0.0189926
$750$	28492.5	0.00184960
$751$	−4.62162e6	−0.299016	−0.149508	−	0.988761i	$-0.547769\pi$
$751$	−4.62162e6	−0.299016	−0.149508	+	0.988761i	$0.547769\pi$
$752$	2.20674e7	1.42301
$753$	20854.1	0.00134031
$754$	−1.69009e7	−1.08264
$755$	4.52303e6	0.288776
$756$	−119476.	−0.00760283
$757$	2.76816e7	1.75570	0.877851	−	0.478934i	$-0.158977\pi$
$757$	2.76816e7	1.75570	0.877851	+	0.478934i	$0.158977\pi$
$758$	−2.98157e7	−1.88483
$759$	80187.1	0.00505243
$760$	−5.46253e6	−0.343052
$761$	6.75380e6	0.422753	0.211376	−	0.977405i	$-0.432205\pi$
$761$	6.75380e6	0.422753	0.211376	+	0.977405i	$0.432205\pi$
$762$	190669.	0.0118958
$763$	1.09232e6	0.0679264
$764$	3.72986e7	2.31185
$765$	−5.33510e6	−0.329601
$766$	1.67534e7	1.03165
$767$	2.49941e6	0.153408
$768$	475016.	0.0290606
$769$	−2.10150e7	−1.28148	−0.640742	−	0.767756i	$-0.721373\pi$
$769$	−2.10150e7	−1.28148	−0.640742	+	0.767756i	$0.721373\pi$
$770$	557167.	0.0338656
$771$	247903.	0.0150192
$772$	−6.16744e7	−3.72444
$773$	1.95393e7	1.17614	0.588072	−	0.808809i	$-0.299887\pi$
$773$	1.95393e7	1.17614	0.588072	+	0.808809i	$0.299887\pi$
$774$	−3.75742e7	−2.25444
$775$	−133736.	−0.00799826
$776$	9.98252e7	5.95094
$777$	−37040.1	−0.00220100
$778$	2.00563e7	1.18796
$779$	−2.78831e6	−0.164626
$780$	−92642.9	−0.00545225
$781$	−3.31439e6	−0.194436
$782$	3.81096e7	2.22853
$783$	−493718.	−0.0287789
$784$	−6.30677e7	−3.66452
$785$	9.82621e6	0.569131
$786$	662752.	0.0382644
$787$	−6.22962e6	−0.358529	−0.179265	−	0.983801i	$-0.557372\pi$
$787$	−6.22962e6	−0.358529	−0.179265	+	0.983801i	$0.557372\pi$
$788$	−3.27196e7	−1.87712
$789$	−229799.	−0.0131418
$790$	−1.20720e7	−0.688197
$791$	3.74923e6	0.213059
$792$	1.77946e7	1.00804
$793$	−1.68048e6	−0.0948966
$794$	−6.45394e7	−3.63307
$795$	100695.	0.00565052
$796$	8.57764e7	4.79828
$797$	1.10410e7	0.615692	0.307846	−	0.951436i	$-0.400392\pi$
$797$	1.10410e7	0.615692	0.307846	+	0.951436i	$0.400392\pi$
$798$	11096.5	0.000616851 0
$799$	−5.07780e6	−0.281390
$800$	−1.39617e7	−0.771283
$801$	−1.45532e7	−0.801450
$802$	3.34948e6	0.183883
$803$	2.49746e6	0.136682
$804$	998371.	0.0544693
$805$	−1.67344e6	−0.0910164
$806$	594064.	0.0322104
$807$	−188953.	−0.0102134
$808$	−5.92482e7	−3.19261
$809$	3.12983e7	1.68132	0.840658	−	0.541567i	$-0.182169\pi$
$809$	3.12983e7	1.68132	0.840658	+	0.541567i	$0.182169\pi$
$810$	1.61248e7	0.863536
$811$	9.38358e6	0.500976	0.250488	−	0.968120i	$-0.419409\pi$
$811$	9.38358e6	0.500976	0.250488	+	0.968120i	$0.419409\pi$
$812$	8.96800e6	0.477316
$813$	198897.	0.0105536
$814$	1.74083e7	0.920866
$815$	9.51266e6	0.501658
$816$	−559485.	−0.0294146
$817$	5.10918e6	0.267791
$818$	−1.29650e7	−0.677469
$819$	−1.04064e6	−0.0542114
$820$	−1.68753e7	−0.876431
$821$	1.96997e7	1.02001	0.510003	−	0.860173i	$-0.329644\pi$
$821$	1.96997e7	1.02001	0.510003	+	0.860173i	$0.329644\pi$
$822$	547457.	0.0282599
$823$	−2.98144e7	−1.53436	−0.767179	−	0.641433i	$-0.778340\pi$
$823$	−2.98144e7	−1.53436	−0.767179	+	0.641433i	$0.778340\pi$
$824$	7.64532e7	3.92263
$825$	12620.8	0.000645581 0
$826$	−1.81185e6	−0.0924003
$827$	1.61274e7	0.819977	0.409989	−	0.912091i	$-0.365533\pi$
$827$	1.61274e7	0.819977	0.409989	+	0.912091i	$0.365533\pi$
$828$	−8.43206e7	−4.27423
$829$	3.39896e7	1.71775	0.858875	−	0.512185i	$-0.171164\pi$
$829$	3.39896e7	1.71775	0.858875	+	0.512185i	$0.171164\pi$
$830$	1.21357e7	0.611461
$831$	−146820.	−0.00737533
$832$	3.09841e7	1.55178
$833$	1.45121e7	0.724633
$834$	−280900.	−0.0139842
$835$	104459.	0.00518478
$836$	−3.81743e6	−0.188910
$837$	17354.1	0.000856225 0
$838$	1.37603e7	0.676887
$839$	−3.15728e6	−0.154849	−0.0774244	−	0.996998i	$-0.524670\pi$
$839$	−3.15728e6	−0.154849	−0.0774244	+	0.996998i	$0.524670\pi$
$840$	42567.4	0.00208151
$841$	1.65480e7	0.806779
$842$	−2.42244e7	−1.17753
$843$	233495.	0.0113164
$844$	9.66880e7	4.67215
$845$	7.66839e6	0.369456
$846$	1.53489e7	0.737310
$847$	246798.	0.0118204
$848$	−9.21229e7	−4.39925
$849$	−233013.	−0.0110946
$850$	5.99813e6	0.284753
$851$	−5.22855e7	−2.47490
$852$	−399500.	−0.0188546
$853$	−6.38776e6	−0.300591	−0.150296	−	0.988641i	$-0.548023\pi$
$853$	−6.38776e6	−0.300591	−0.150296	+	0.988641i	$0.548023\pi$
$854$	1.21820e6	0.0571578
$855$	−2.19282e6	−0.102586
$856$	1.04704e7	0.488405
$857$	2.37313e7	1.10375	0.551874	−	0.833928i	$-0.313913\pi$
$857$	2.37313e7	1.10375	0.551874	+	0.833928i	$0.313913\pi$
$858$	−56062.1	−0.00259987
$859$	956169.	0.0442132	0.0221066	−	0.999756i	$-0.492963\pi$
$859$	956169.	0.0442132	0.0221066	+	0.999756i	$0.492963\pi$
$860$	3.09216e7	1.42566
$861$	21728.2	0.000998888 0
$862$	−3.85760e7	−1.76827
$863$	3.45614e7	1.57966	0.789832	−	0.613323i	$-0.210168\pi$
$863$	3.45614e7	1.57966	0.789832	+	0.613323i	$0.210168\pi$
$864$	1.81172e6	0.0825670
$865$	−6.05081e6	−0.274962
$866$	−3.78728e7	−1.71606
$867$	−108215.	−0.00488922
$868$	−315223.	−0.0142010
$869$	−5.34732e6	−0.240208
$870$	277522.	0.0124308
$871$	1.73927e7	0.776822
$872$	−3.92217e7	−1.74677
$873$	4.00728e7	1.77957
$874$	1.56638e7	0.693614
$875$	−263384.	−0.0116297
$876$	301032.	0.0132542
$877$	1.73356e7	0.761095	0.380547	−	0.924761i	$-0.375736\pi$
$877$	1.73356e7	0.761095	0.380547	+	0.924761i	$0.375736\pi$
$878$	−8.34432e7	−3.65304
$879$	222920.	0.00973144
$880$	−1.15464e7	−0.502621
$881$	1.67240e7	0.725941	0.362971	−	0.931801i	$-0.381763\pi$
$881$	1.67240e7	0.725941	0.362971	+	0.931801i	$0.381763\pi$
$882$	−4.38664e7	−1.89872
$883$	−1.45008e7	−0.625881	−0.312940	−	0.949773i	$-0.601314\pi$
$883$	−1.45008e7	−0.625881	−0.312940	+	0.949773i	$0.601314\pi$
$884$	−1.95028e7	−0.839395
$885$	−41041.5	−0.00176143
$886$	2.21714e7	0.948874
$887$	3.10605e7	1.32556	0.662780	−	0.748814i	$-0.269377\pi$
$887$	3.10605e7	1.32556	0.662780	+	0.748814i	$0.269377\pi$
$888$	1.32999e6	0.0566001
$889$	−1.76254e6	−0.0747973
$890$	1.63618e7	0.692399
$891$	7.14247e6	0.301408
$892$	−7.27286e7	−3.06050
$893$	−2.08707e6	−0.0875806
$894$	27712.1	0.00115965
$895$	−1.56563e6	−0.0653329
$896$	−1.04110e7	−0.433235
$897$	168381.	0.00698734
$898$	−5.14221e7	−2.12794
$899$	−1.30262e6	−0.0537549
$900$	−1.32713e7	−0.546145
$901$	2.11978e7	0.869920
$902$	−1.02120e7	−0.417920
$903$	−39813.9	−0.00162486
$904$	−1.34623e8	−5.47895
$905$	−6.31736e6	−0.256398
$906$	329913.	0.0133530
$907$	−5.10155e6	−0.205913	−0.102956	−	0.994686i	$-0.532830\pi$
$907$	−5.10155e6	−0.205913	−0.102956	+	0.994686i	$0.532830\pi$
$908$	−1.05481e8	−4.24580
$909$	−2.37840e7	−0.954717
$910$	1.16997e6	0.0468350
$911$	2.10896e7	0.841923	0.420961	−	0.907079i	$-0.361693\pi$
$911$	2.10896e7	0.841923	0.420961	+	0.907079i	$0.361693\pi$
$912$	−229959.	−0.00915509
$913$	5.37551e6	0.213424
$914$	−6.66845e7	−2.64034
$915$	27594.4	0.00108960
$916$	−5.00463e7	−1.97076
$917$	−6.12648e6	−0.240595
$918$	−778336.	−0.0304832
$919$	−1.80763e7	−0.706028	−0.353014	−	0.935618i	$-0.614843\pi$
$919$	−1.80763e7	−0.706028	−0.353014	+	0.935618i	$0.614843\pi$
$920$	6.00878e7	2.34054
$921$	181038.	0.00703269
$922$	−3.97283e7	−1.53912
$923$	−6.95972e6	−0.268898
$924$	29747.7	0.00114624
$925$	−8.22929e6	−0.316234
$926$	−6.36113e7	−2.43785
$927$	3.06906e7	1.17302
$928$	−1.35990e8	−5.18366
$929$	−1.55747e7	−0.592079	−0.296039	−	0.955176i	$-0.595666\pi$
$929$	−1.55747e7	−0.592079	−0.296039	+	0.955176i	$0.595666\pi$
$930$	−9754.84	−0.000369839 0
$931$	5.96475e6	0.225537
$932$	1.16923e8	4.40920
$933$	−560037.	−0.0210626
$934$	−9.05517e6	−0.339648
$935$	2.65687e6	0.0993899
$936$	3.73660e7	1.39408
$937$	−8.73547e6	−0.325040	−0.162520	−	0.986705i	$-0.551962\pi$
$937$	−8.73547e6	−0.325040	−0.162520	+	0.986705i	$0.551962\pi$
$938$	−1.26082e7	−0.467893
$939$	110465.	0.00408847
$940$	−1.26313e7	−0.466260
$941$	3.28391e7	1.20897	0.604487	−	0.796615i	$-0.293378\pi$
$941$	3.28391e7	1.20897	0.604487	+	0.796615i	$0.293378\pi$
$942$	716731.	0.0263166
$943$	3.06714e7	1.12319
$944$	3.75479e7	1.37137
$945$	34177.6	0.00124498
$946$	1.87120e7	0.679816
$947$	−2.24165e7	−0.812256	−0.406128	−	0.913816i	$-0.633121\pi$
$947$	−2.24165e7	−0.812256	−0.406128	+	0.913816i	$0.633121\pi$
$948$	−644539.	−0.0232931
$949$	5.24430e6	0.189026
$950$	2.46534e6	0.0886274
$951$	−111766.	−0.00400734
$952$	8.96113e6	0.320457
$953$	1.81143e7	0.646085	0.323042	−	0.946385i	$-0.395294\pi$
$953$	1.81143e7	0.646085	0.323042	+	0.946385i	$0.395294\pi$
$954$	−6.40755e7	−2.27940
$955$	−1.06698e7	−0.378570
$956$	1.30781e8	4.62809
$957$	122929.	0.00433884
$958$	−313303.	−0.0110294
$959$	−5.06069e6	−0.177690
$960$	−508775.	−0.0178175
$961$	−2.85834e7	−0.998401
$962$	3.65549e7	1.27353
$963$	4.20315e6	0.146052
$964$	7.25273e7	2.51368
$965$	1.76428e7	0.609886
$966$	−122062.	−0.00420859
$967$	5.52945e7	1.90158	0.950792	−	0.309829i	$-0.100272\pi$
$967$	5.52945e7	1.90158	0.950792	+	0.309829i	$0.100272\pi$
$968$	−8.86171e6	−0.303969
$969$	52914.3	0.00181036
$970$	−4.50529e7	−1.53742
$971$	−4.99370e7	−1.69971	−0.849854	−	0.527019i	$-0.823310\pi$
$971$	−4.99370e7	−1.69971	−0.849854	+	0.527019i	$0.823310\pi$
$972$	2.58325e6	0.0877001
$973$	2.59664e6	0.0879285
$974$	−4.34119e7	−1.46626
$975$	26501.7	0.000892817 0
$976$	−2.52454e7	−0.848316
$977$	3.06906e7	1.02865	0.514326	−	0.857594i	$-0.328042\pi$
$977$	3.06906e7	1.02865	0.514326	+	0.857594i	$0.328042\pi$
$978$	693861.	0.0231966
$979$	7.24748e6	0.241674
$980$	3.60997e7	1.20071
$981$	−1.57448e7	−0.522352
$982$	−6.51935e7	−2.15738
$983$	5.68629e6	0.187692	0.0938459	−	0.995587i	$-0.470084\pi$
$983$	5.68629e6	0.187692	0.0938459	+	0.995587i	$0.470084\pi$
$984$	−780192.	−0.0256870
$985$	9.35989e6	0.307383
$986$	5.84229e7	1.91378
$987$	16263.7	0.000531407 0
$988$	−8.01602e6	−0.261256
$989$	−5.62008e7	−1.82706
$990$	−8.03104e6	−0.260426
$991$	3.30412e7	1.06874	0.534369	−	0.845251i	$-0.320549\pi$
$991$	3.30412e7	1.06874	0.534369	+	0.845251i	$0.320549\pi$
$992$	4.78001e6	0.154223
$993$	−27872.0	−0.000897004 0
$994$	5.04520e6	0.161962
$995$	−2.45375e7	−0.785728
$996$	647936.	0.0206959
$997$	2.89818e7	0.923395	0.461698	−	0.887037i	$-0.347241\pi$
$997$	2.89818e7	0.923395	0.461698	+	0.887037i	$0.347241\pi$
$998$	3.90073e7	1.23971
$999$	1.06786e6	0.0338532

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.d.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-10.9267 q^{2} +0.166886 q^{3} +87.3933 q^{4} -25.0000 q^{5} -1.82352 q^{6} +16.8566 q^{7} -605.267 q^{8} -242.972 q^{9} +O(q^{10})\)	\(q-10.9267 q^{2} +0.166886 q^{3} +87.3933 q^{4} -25.0000 q^{5} -1.82352 q^{6} +16.8566 q^{7} -605.267 q^{8} -242.972 q^{9} +273.168 q^{10} +121.000 q^{11} +14.5847 q^{12} +254.082 q^{13} -184.187 q^{14} -4.17215 q^{15} +3817.00 q^{16} -878.306 q^{17} +2654.89 q^{18} -361.000 q^{19} -2184.83 q^{20} +2.81313 q^{21} -1322.13 q^{22} +3970.99 q^{23} -101.011 q^{24} +625.000 q^{25} -2776.28 q^{26} -81.1020 q^{27} +1473.15 q^{28} +6087.62 q^{29} +45.5880 q^{30} -213.978 q^{31} -22338.8 q^{32} +20.1932 q^{33} +9597.00 q^{34} -421.415 q^{35} -21234.1 q^{36} -13166.9 q^{37} +3944.55 q^{38} +42.4027 q^{39} +15131.7 q^{40} +7723.86 q^{41} -30.7383 q^{42} -14152.8 q^{43} +10574.6 q^{44} +6074.30 q^{45} -43389.9 q^{46} +5781.35 q^{47} +637.004 q^{48} -16522.9 q^{49} -6829.20 q^{50} -146.577 q^{51} +22205.0 q^{52} -24134.9 q^{53} +886.179 q^{54} -3025.00 q^{55} -10202.7 q^{56} -60.2459 q^{57} -66517.7 q^{58} +9837.01 q^{59} -364.618 q^{60} -6613.94 q^{61} +2338.08 q^{62} -4095.69 q^{63} +121945. q^{64} -6352.05 q^{65} -220.646 q^{66} +68453.2 q^{67} -76758.0 q^{68} +662.704 q^{69} +4604.69 q^{70} -27391.6 q^{71} +147063. q^{72} +20640.2 q^{73} +143871. q^{74} +104.304 q^{75} -31549.0 q^{76} +2039.65 q^{77} -463.323 q^{78} -44192.7 q^{79} -95425.0 q^{80} +59028.7 q^{81} -84396.4 q^{82} +44425.7 q^{83} +245.849 q^{84} +21957.6 q^{85} +154644. q^{86} +1015.94 q^{87} -73237.3 q^{88} +59896.5 q^{89} -66372.2 q^{90} +4282.96 q^{91} +347038. q^{92} -35.7100 q^{93} -63171.3 q^{94} +9025.00 q^{95} -3728.03 q^{96} -164928. q^{97} +180541. q^{98} -29399.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) \) 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

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