LMFDB - Embedded newform 1045.6.a.h.1.3

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:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-10.3994 q^{2} +4.60548 q^{3} +76.1474 q^{4} +25.0000 q^{5} -47.8942 q^{6} +17.5294 q^{7} -459.106 q^{8} -221.790 q^{9} +O(q^{10})$	\(q-10.3994 q^{2} +4.60548 q^{3} +76.1474 q^{4} +25.0000 q^{5} -47.8942 q^{6} +17.5294 q^{7} -459.106 q^{8} -221.790 q^{9} -259.985 q^{10} +121.000 q^{11} +350.695 q^{12} -1179.34 q^{13} -182.295 q^{14} +115.137 q^{15} +2337.71 q^{16} +523.779 q^{17} +2306.48 q^{18} +361.000 q^{19} +1903.69 q^{20} +80.7312 q^{21} -1258.33 q^{22} -1602.28 q^{23} -2114.40 q^{24} +625.000 q^{25} +12264.4 q^{26} -2140.58 q^{27} +1334.82 q^{28} -8618.86 q^{29} -1197.35 q^{30} -6219.90 q^{31} -9619.39 q^{32} +557.263 q^{33} -5446.99 q^{34} +438.235 q^{35} -16888.7 q^{36} -11177.2 q^{37} -3754.18 q^{38} -5431.43 q^{39} -11477.7 q^{40} -9086.54 q^{41} -839.556 q^{42} +23495.9 q^{43} +9213.84 q^{44} -5544.74 q^{45} +16662.7 q^{46} -1158.81 q^{47} +10766.3 q^{48} -16499.7 q^{49} -6499.62 q^{50} +2412.25 q^{51} -89803.8 q^{52} -7338.29 q^{53} +22260.7 q^{54} +3025.00 q^{55} -8047.86 q^{56} +1662.58 q^{57} +89630.9 q^{58} -13838.1 q^{59} +8767.38 q^{60} +18999.3 q^{61} +64683.2 q^{62} -3887.84 q^{63} +25229.0 q^{64} -29483.5 q^{65} -5795.20 q^{66} +53885.7 q^{67} +39884.4 q^{68} -7379.27 q^{69} -4557.38 q^{70} -65217.9 q^{71} +101825. q^{72} +25260.8 q^{73} +116236. q^{74} +2878.42 q^{75} +27489.2 q^{76} +2121.06 q^{77} +56483.6 q^{78} -37710.5 q^{79} +58442.8 q^{80} +44036.5 q^{81} +94494.5 q^{82} +13548.1 q^{83} +6147.47 q^{84} +13094.5 q^{85} -244343. q^{86} -39694.0 q^{87} -55551.9 q^{88} +93495.1 q^{89} +57661.9 q^{90} -20673.1 q^{91} -122010. q^{92} -28645.6 q^{93} +12050.9 q^{94} +9025.00 q^{95} -44301.9 q^{96} -41580.1 q^{97} +171587. q^{98} -26836.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) $ 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * 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 $

$2$	−10.3994	−1.83837	−0.919185	−	0.393825i	$-0.871152\pi$
$2$	−10.3994	−1.83837	−0.919185	+	0.393825i	$0.871152\pi$
$3$	4.60548	0.295442	0.147721	−	0.989029i	$-0.452806\pi$
$3$	4.60548	0.295442	0.147721	+	0.989029i	$0.452806\pi$
$4$	76.1474	2.37961
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−47.8942	−0.543131
$7$	17.5294	0.135214	0.0676070	−	0.997712i	$-0.478464\pi$
$7$	17.5294	0.135214	0.0676070	+	0.997712i	$0.478464\pi$
$8$	−459.106	−2.53623
$9$	−221.790	−0.912714
$10$	−259.985	−0.822144
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	350.695	0.703035
$13$	−1179.34	−1.93545	−0.967723	−	0.252016i	$-0.918906\pi$
$13$	−1179.34	−1.93545	−0.967723	+	0.252016i	$0.918906\pi$
$14$	−182.295	−0.248573
$15$	115.137	0.132125
$16$	2337.71	2.28292
$17$	523.779	0.439568	0.219784	−	0.975549i	$-0.429465\pi$
$17$	523.779	0.439568	0.219784	+	0.975549i	$0.429465\pi$
$18$	2306.48	1.67791
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	1903.69	1.06419
$21$	80.7312	0.0399478
$22$	−1258.33	−0.554290
$23$	−1602.28	−0.631566	−0.315783	−	0.948831i	$-0.602267\pi$
$23$	−1602.28	−0.631566	−0.315783	+	0.948831i	$0.602267\pi$
$24$	−2114.40	−0.749307
$25$	625.000	0.200000
$26$	12264.4	3.55807
$27$	−2140.58	−0.565095
$28$	1334.82	0.321756
$29$	−8618.86	−1.90307	−0.951535	−	0.307540i	$-0.900494\pi$
$29$	−8618.86	−1.90307	−0.951535	+	0.307540i	$0.900494\pi$
$30$	−1197.35	−0.242896
$31$	−6219.90	−1.16246	−0.581232	−	0.813738i	$-0.697429\pi$
$31$	−6219.90	−1.16246	−0.581232	+	0.813738i	$0.697429\pi$
$32$	−9619.39	−1.66063
$33$	557.263	0.0890790
$34$	−5446.99	−0.808089
$35$	438.235	0.0604695
$36$	−16888.7	−2.17190
$37$	−11177.2	−1.34223	−0.671117	−	0.741352i	$-0.734185\pi$
$37$	−11177.2	−1.34223	−0.671117	+	0.741352i	$0.734185\pi$
$38$	−3754.18	−0.421751
$39$	−5431.43	−0.571811
$40$	−11477.7	−1.13424
$41$	−9086.54	−0.844187	−0.422094	−	0.906552i	$-0.638705\pi$
$41$	−9086.54	−0.844187	−0.422094	+	0.906552i	$0.638705\pi$
$42$	−839.556	−0.0734389
$43$	23495.9	1.93785	0.968926	−	0.247353i	$-0.0795606\pi$
$43$	23495.9	1.93785	0.968926	+	0.247353i	$0.0795606\pi$
$44$	9213.84	0.717478
$45$	−5544.74	−0.408178
$46$	16662.7	1.16105
$47$	−1158.81	−0.0765185	−0.0382593	−	0.999268i	$-0.512181\pi$
$47$	−1158.81	−0.0765185	−0.0382593	+	0.999268i	$0.512181\pi$
$48$	10766.3	0.674470
$49$	−16499.7	−0.981717
$50$	−6499.62	−0.367674
$51$	2412.25	0.129867
$52$	−89803.8	−4.60560
$53$	−7338.29	−0.358844	−0.179422	−	0.983772i	$-0.557423\pi$
$53$	−7338.29	−0.358844	−0.179422	+	0.983772i	$0.557423\pi$
$54$	22260.7	1.03885
$55$	3025.00	0.134840
$56$	−8047.86	−0.342934
$57$	1662.58	0.0677789
$58$	89630.9	3.49855
$59$	−13838.1	−0.517543	−0.258772	−	0.965939i	$-0.583318\pi$
$59$	−13838.1	−0.517543	−0.258772	+	0.965939i	$0.583318\pi$
$60$	8767.38	0.314407
$61$	18999.3	0.653753	0.326877	−	0.945067i	$-0.394004\pi$
$61$	18999.3	0.653753	0.326877	+	0.945067i	$0.394004\pi$
$62$	64683.2	2.13704
$63$	−3887.84	−0.123412
$64$	25229.0	0.769928
$65$	−29483.5	−0.865558
$66$	−5795.20	−0.163760
$67$	53885.7	1.46651	0.733257	−	0.679952i	$-0.237999\pi$
$67$	53885.7	1.46651	0.733257	+	0.679952i	$0.237999\pi$
$68$	39884.4	1.04600
$69$	−7379.27	−0.186591
$70$	−4557.38	−0.111165
$71$	−65217.9	−1.53540	−0.767699	−	0.640810i	$-0.778598\pi$
$71$	−65217.9	−1.53540	−0.767699	+	0.640810i	$0.778598\pi$
$72$	101825.	2.31485
$73$	25260.8	0.554805	0.277403	−	0.960754i	$-0.410526\pi$
$73$	25260.8	0.554805	0.277403	+	0.960754i	$0.410526\pi$
$74$	116236.	2.46752
$75$	2878.42	0.0590883
$76$	27489.2	0.545919
$77$	2121.06	0.0407686
$78$	56483.6	1.05120
$79$	−37710.5	−0.679821	−0.339910	−	0.940458i	$-0.610397\pi$
$79$	−37710.5	−0.679821	−0.339910	+	0.940458i	$0.610397\pi$
$80$	58442.8	1.02095
$81$	44036.5	0.745762
$82$	94494.5	1.55193
$83$	13548.1	0.215866	0.107933	−	0.994158i	$-0.465577\pi$
$83$	13548.1	0.215866	0.107933	+	0.994158i	$0.465577\pi$
$84$	6147.47	0.0950602
$85$	13094.5	0.196581
$86$	−244343.	−3.56249
$87$	−39694.0	−0.562246
$88$	−55551.9	−0.764702
$89$	93495.1	1.25116	0.625582	−	0.780159i	$-0.284862\pi$
$89$	93495.1	1.25116	0.625582	+	0.780159i	$0.284862\pi$
$90$	57661.9	0.750383
$91$	−20673.1	−0.261699
$92$	−122010.	−1.50288
$93$	−28645.6	−0.343440
$94$	12050.9	0.140669
$95$	9025.00	0.102598
$96$	−44301.9	−0.490619
$97$	−41580.1	−0.448701	−0.224350	−	0.974509i	$-0.572026\pi$
$97$	−41580.1	−0.448701	−0.224350	+	0.974509i	$0.572026\pi$
$98$	171587.	1.80476
$99$	−26836.5	−0.275194
$100$	47592.1	0.475921
$101$	112514.	1.09749	0.548746	−	0.835989i	$-0.315105\pi$
$101$	112514.	1.09749	0.548746	+	0.835989i	$0.315105\pi$
$102$	−25086.0	−0.238743
$103$	33029.9	0.306771	0.153386	−	0.988166i	$-0.450982\pi$
$103$	33029.9	0.306771	0.153386	+	0.988166i	$0.450982\pi$
$104$	541443.	4.90873
$105$	2018.28	0.0178652
$106$	76313.8	0.659688
$107$	−38504.1	−0.325123	−0.162561	−	0.986698i	$-0.551976\pi$
$107$	−38504.1	−0.325123	−0.162561	+	0.986698i	$0.551976\pi$
$108$	−163000.	−1.34470
$109$	206122.	1.66172	0.830860	−	0.556482i	$-0.187849\pi$
$109$	206122.	1.66172	0.830860	+	0.556482i	$0.187849\pi$
$110$	−31458.2	−0.247886
$111$	−51476.3	−0.396552
$112$	40978.7	0.308683
$113$	47621.8	0.350840	0.175420	−	0.984494i	$-0.443872\pi$
$113$	47621.8	0.350840	0.175420	+	0.984494i	$0.443872\pi$
$114$	−17289.8	−0.124603
$115$	−40057.0	−0.282445
$116$	−656304.	−4.52856
$117$	261566.	1.76651
$118$	143908.	0.951436
$119$	9181.53	0.0594357
$120$	−52860.1	−0.335100
$121$	14641.0	0.0909091
$122$	−197582.	−1.20184
$123$	−41847.9	−0.249408
$124$	−473629.	−2.76621
$125$	15625.0	0.0894427
$126$	40431.1	0.226877
$127$	70057.0	0.385427	0.192714	−	0.981255i	$-0.438271\pi$
$127$	70057.0	0.385427	0.192714	+	0.981255i	$0.438271\pi$
$128$	45453.9	0.245215
$129$	108210.	0.572522
$130$	306611.	1.59122
$131$	93774.6	0.477427	0.238714	−	0.971090i	$-0.423274\pi$
$131$	93774.6	0.477427	0.238714	+	0.971090i	$0.423274\pi$
$132$	42434.1	0.211973
$133$	6328.11	0.0310202
$134$	−560378.	−2.69600
$135$	−53514.5	−0.252718
$136$	−240470.	−1.11484
$137$	−15270.2	−0.0695093	−0.0347546	−	0.999396i	$-0.511065\pi$
$137$	−15270.2	−0.0695093	−0.0347546	+	0.999396i	$0.511065\pi$
$138$	76739.9	0.343023
$139$	−280829.	−1.23284	−0.616418	−	0.787419i	$-0.711417\pi$
$139$	−280829.	−1.23284	−0.616418	+	0.787419i	$0.711417\pi$
$140$	33370.4	0.143894
$141$	−5336.86	−0.0226067
$142$	678227.	2.82263
$143$	−142700.	−0.583559
$144$	−518480.	−2.08366
$145$	−215471.	−0.851079
$146$	−262697.	−1.01994
$147$	−75989.1	−0.290040
$148$	−851114.	−3.19399
$149$	165365.	0.610208	0.305104	−	0.952319i	$-0.401309\pi$
$149$	165365.	0.610208	0.305104	+	0.952319i	$0.401309\pi$
$150$	−29933.9	−0.108626
$151$	−25515.6	−0.0910674	−0.0455337	−	0.998963i	$-0.514499\pi$
$151$	−25515.6	−0.0910674	−0.0455337	+	0.998963i	$0.514499\pi$
$152$	−165737.	−0.581851
$153$	−116169.	−0.401200
$154$	−22057.7	−0.0749477
$155$	−155497.	−0.519869
$156$	−413589.	−1.36069
$157$	−307962.	−0.997122	−0.498561	−	0.866855i	$-0.666138\pi$
$157$	−307962.	−0.997122	−0.498561	+	0.866855i	$0.666138\pi$
$158$	392166.	1.24976
$159$	−33796.3	−0.106017
$160$	−240485.	−0.742656
$161$	−28087.0	−0.0853966
$162$	−457953.	−1.37099
$163$	−309000.	−0.910939	−0.455469	−	0.890252i	$-0.650529\pi$
$163$	−309000.	−0.910939	−0.455469	+	0.890252i	$0.650529\pi$
$164$	−691916.	−2.00883
$165$	13931.6	0.0398373
$166$	−140892.	−0.396842
$167$	242865.	0.673866	0.336933	−	0.941529i	$-0.390610\pi$
$167$	242865.	0.673866	0.336933	+	0.941529i	$0.390610\pi$
$168$	−37064.2	−0.101317
$169$	1.01955e6	2.74595
$170$	−136175.	−0.361388
$171$	−80066.0	−0.209391
$172$	1.78915e6	4.61132
$173$	571688.	1.45226	0.726129	−	0.687559i	$-0.241318\pi$
$173$	571688.	1.45226	0.726129	+	0.687559i	$0.241318\pi$
$174$	412793.	1.03362
$175$	10955.9	0.0270428
$176$	282863.	0.688327
$177$	−63731.1	−0.152904
$178$	−972293.	−2.30010
$179$	120026.	0.279991	0.139995	−	0.990152i	$-0.455291\pi$
$179$	120026.	0.279991	0.139995	+	0.990152i	$0.455291\pi$
$180$	−422218.	−0.971304
$181$	−660802.	−1.49925	−0.749626	−	0.661861i	$-0.769767\pi$
$181$	−660802.	−1.49925	−0.749626	+	0.661861i	$0.769767\pi$
$182$	214988.	0.481101
$183$	87501.1	0.193146
$184$	735617.	1.60180
$185$	−279430.	−0.600265
$186$	297897.	0.631370
$187$	63377.3	0.132535
$188$	−88240.2	−0.182084
$189$	−37523.0	−0.0764088
$190$	−93854.5	−0.188613
$191$	401961.	0.797262	0.398631	−	0.917111i	$-0.369485\pi$
$191$	401961.	0.797262	0.398631	+	0.917111i	$0.369485\pi$
$192$	116192.	0.227469
$193$	−563987.	−1.08987	−0.544936	−	0.838477i	$-0.683446\pi$
$193$	−563987.	−1.08987	−0.544936	+	0.838477i	$0.683446\pi$
$194$	432408.	0.824878
$195$	−135786.	−0.255722
$196$	−1.25641e6	−2.33610
$197$	−985436.	−1.80910	−0.904550	−	0.426367i	$-0.859793\pi$
$197$	−985436.	−1.80910	−0.904550	+	0.426367i	$0.859793\pi$
$198$	279084.	0.505908
$199$	−1.02682e6	−1.83806	−0.919031	−	0.394186i	$-0.871027\pi$
$199$	−1.02682e6	−1.83806	−0.919031	+	0.394186i	$0.871027\pi$
$200$	−286942.	−0.507246
$201$	248169.	0.433269
$202$	−1.17007e6	−2.01760
$203$	−151083.	−0.257322
$204$	183687.	0.309031
$205$	−227163.	−0.377532
$206$	−343491.	−0.563959
$207$	355369.	0.576439
$208$	−2.75696e6	−4.41847
$209$	43681.0	0.0691714
$210$	−20988.9	−0.0328429
$211$	−973593.	−1.50547	−0.752734	−	0.658325i	$-0.771265\pi$
$211$	−973593.	−1.50547	−0.752734	+	0.658325i	$0.771265\pi$
$212$	−558792.	−0.853907
$213$	−300360.	−0.453621
$214$	400419.	0.597697
$215$	587397.	0.866633
$216$	982753.	1.43321
$217$	−109031.	−0.157181
$218$	−2.14354e6	−3.05486
$219$	116338.	0.163912
$220$	230346.	0.320866
$221$	−617714.	−0.850760
$222$	535322.	0.729009
$223$	204673.	0.275612	0.137806	−	0.990459i	$-0.455995\pi$
$223$	204673.	0.275612	0.137806	+	0.990459i	$0.455995\pi$
$224$	−168622.	−0.224540
$225$	−138618.	−0.182543
$226$	−495238.	−0.644975
$227$	429328.	0.552999	0.276500	−	0.961014i	$-0.410826\pi$
$227$	429328.	0.552999	0.276500	+	0.961014i	$0.410826\pi$
$228$	126601.	0.161287
$229$	86942.5	0.109558	0.0547789	−	0.998499i	$-0.482555\pi$
$229$	86942.5	0.109558	0.0547789	+	0.998499i	$0.482555\pi$
$230$	416569.	0.519239
$231$	9768.48	0.0120447
$232$	3.95697e6	4.82662
$233$	1.06916e6	1.29019	0.645094	−	0.764103i	$-0.276818\pi$
$233$	1.06916e6	1.29019	0.645094	+	0.764103i	$0.276818\pi$
$234$	−2.72012e6	−3.24750
$235$	−28970.2	−0.0342201
$236$	−1.05374e6	−1.23155
$237$	−173675.	−0.200847
$238$	−95482.3	−0.109265
$239$	−49803.3	−0.0563979	−0.0281990	−	0.999602i	$-0.508977\pi$
$239$	−49803.3	−0.0563979	−0.0281990	+	0.999602i	$0.508977\pi$
$240$	269157.	0.301632
$241$	853343.	0.946414	0.473207	−	0.880951i	$-0.343096\pi$
$241$	853343.	0.946414	0.473207	+	0.880951i	$0.343096\pi$
$242$	−152258.	−0.167125
$243$	722970.	0.785424
$244$	1.44675e6	1.55568
$245$	−412493.	−0.439037
$246$	435192.	0.458504
$247$	−425742.	−0.444022
$248$	2.85560e6	2.94827
$249$	62395.7	0.0637758
$250$	−162491.	−0.164429
$251$	−47078.6	−0.0471671	−0.0235835	−	0.999722i	$-0.507508\pi$
$251$	−47078.6	−0.0471671	−0.0235835	+	0.999722i	$0.507508\pi$
$252$	−296049.	−0.293671
$253$	−193876.	−0.190424
$254$	−728551.	−0.708558
$255$	60306.3	0.0580781
$256$	−1.28002e6	−1.22072
$257$	1.67525e6	1.58215	0.791075	−	0.611719i	$-0.209522\pi$
$257$	1.67525e6	1.58215	0.791075	+	0.611719i	$0.209522\pi$
$258$	−1.12532e6	−1.05251
$259$	−195929.	−0.181489
$260$	−2.24509e6	−2.05969
$261$	1.91157e6	1.73696
$262$	−975199.	−0.877688
$263$	1.72292e6	1.53594	0.767972	−	0.640483i	$-0.221266\pi$
$263$	1.72292e6	1.53594	0.767972	+	0.640483i	$0.221266\pi$
$264$	−255843.	−0.225925
$265$	−183457.	−0.160480
$266$	−65808.5	−0.0570267
$267$	430590.	0.369646
$268$	4.10325e6	3.48973
$269$	−140111.	−0.118057	−0.0590285	−	0.998256i	$-0.518800\pi$
$269$	−140111.	−0.118057	−0.0590285	+	0.998256i	$0.518800\pi$
$270$	556518.	0.464590
$271$	−933310.	−0.771974	−0.385987	−	0.922504i	$-0.626139\pi$
$271$	−933310.	−0.771974	−0.385987	+	0.922504i	$0.626139\pi$
$272$	1.22444e6	1.00350
$273$	−95209.6	−0.0773169
$274$	158801.	0.127784
$275$	75625.0	0.0603023
$276$	−561912.	−0.444013
$277$	−402198.	−0.314949	−0.157475	−	0.987523i	$-0.550335\pi$
$277$	−402198.	−0.314949	−0.157475	+	0.987523i	$0.550335\pi$
$278$	2.92045e6	2.26641
$279$	1.37951e6	1.06100
$280$	−201196.	−0.153365
$281$	1.97904e6	1.49516	0.747582	−	0.664170i	$-0.231215\pi$
$281$	1.97904e6	1.49516	0.747582	+	0.664170i	$0.231215\pi$
$282$	55500.1	0.0415596
$283$	−192202.	−0.142657	−0.0713284	−	0.997453i	$-0.522724\pi$
$283$	−192202.	−0.142657	−0.0713284	+	0.997453i	$0.522724\pi$
$284$	−4.96618e6	−3.65364
$285$	41564.4	0.0303117
$286$	1.48400e6	1.07280
$287$	−159281.	−0.114146
$288$	2.13348e6	1.51568
$289$	−1.14551e6	−0.806780
$290$	2.24077e6	1.56460
$291$	−191496.	−0.132565
$292$	1.92355e6	1.32022
$293$	−700378.	−0.476610	−0.238305	−	0.971190i	$-0.576592\pi$
$293$	−700378.	−0.476610	−0.238305	+	0.971190i	$0.576592\pi$
$294$	790241.	0.533201
$295$	−345953.	−0.231452
$296$	5.13152e6	3.40421
$297$	−259010.	−0.170383
$298$	−1.71970e6	−1.12179
$299$	1.88963e6	1.22236
$300$	219185.	0.140607
$301$	411868.	0.262025
$302$	265346.	0.167416
$303$	518178.	0.324245
$304$	843914.	0.523738
$305$	474984.	0.292367
$306$	1.20808e6	0.737554
$307$	2.97389e6	1.80085	0.900427	−	0.435007i	$-0.143254\pi$
$307$	2.97389e6	1.80085	0.900427	+	0.435007i	$0.143254\pi$
$308$	161513.	0.0970131
$309$	152119.	0.0906330
$310$	1.61708e6	0.955712
$311$	306941.	0.179951	0.0899755	−	0.995944i	$-0.471321\pi$
$311$	306941.	0.179951	0.0899755	+	0.995944i	$0.471321\pi$
$312$	2.49360e6	1.45024
$313$	622001.	0.358865	0.179432	−	0.983770i	$-0.442574\pi$
$313$	622001.	0.358865	0.179432	+	0.983770i	$0.442574\pi$
$314$	3.20262e6	1.83308
$315$	−97195.9	−0.0551914
$316$	−2.87156e6	−1.61771
$317$	−1.10326e6	−0.616636	−0.308318	−	0.951283i	$-0.599766\pi$
$317$	−1.10326e6	−0.616636	−0.308318	+	0.951283i	$0.599766\pi$
$318$	351461.	0.194899
$319$	−1.04288e6	−0.573797
$320$	630725.	0.344322
$321$	−177330.	−0.0960548
$322$	292088.	0.156991
$323$	189084.	0.100844
$324$	3.35326e6	1.77462
$325$	−737088.	−0.387089
$326$	3.21341e6	1.67464
$327$	949290.	0.490941
$328$	4.17169e6	2.14105
$329$	−20313.2	−0.0103464
$330$	−144880.	−0.0732358
$331$	673177.	0.337722	0.168861	−	0.985640i	$-0.445991\pi$
$331$	673177.	0.337722	0.168861	+	0.985640i	$0.445991\pi$
$332$	1.03166e6	0.513677
$333$	2.47898e6	1.22508
$334$	−2.52565e6	−1.23881
$335$	1.34714e6	0.655845
$336$	188726.	0.0911978
$337$	2.48675e6	1.19277	0.596387	−	0.802697i	$-0.296602\pi$
$337$	2.48675e6	1.19277	0.596387	+	0.802697i	$0.296602\pi$
$338$	−1.06027e7	−5.04808
$339$	219321.	0.103653
$340$	997111.	0.467785
$341$	−752608.	−0.350496
$342$	832638.	0.384938
$343$	−583846.	−0.267956
$344$	−1.07871e7	−4.91483
$345$	−184482.	−0.0834460
$346$	−5.94521e6	−2.66979
$347$	926625.	0.413124	0.206562	−	0.978434i	$-0.433772\pi$
$347$	926625.	0.413124	0.206562	+	0.978434i	$0.433772\pi$
$348$	−3.02259e6	−1.33792
$349$	−2.86157e6	−1.25759	−0.628797	−	0.777569i	$-0.716452\pi$
$349$	−2.86157e6	−1.25759	−0.628797	+	0.777569i	$0.716452\pi$
$350$	−113934.	−0.0497147
$351$	2.52447e6	1.09371
$352$	−1.16395e6	−0.500698
$353$	2.64473e6	1.12965	0.564825	−	0.825210i	$-0.308943\pi$
$353$	2.64473e6	1.12965	0.564825	+	0.825210i	$0.308943\pi$
$354$	662765.	0.281094
$355$	−1.63045e6	−0.686651
$356$	7.11941e6	2.97728
$357$	42285.3	0.0175598
$358$	−1.24820e6	−0.514727
$359$	−4.05776e6	−1.66169	−0.830845	−	0.556504i	$-0.812143\pi$
$359$	−4.05776e6	−1.66169	−0.830845	+	0.556504i	$0.812143\pi$
$360$	2.54563e6	1.03523
$361$	130321.	0.0526316
$362$	6.87194e6	2.75618
$363$	67428.8	0.0268583
$364$	−1.57421e6	−0.622742
$365$	631521.	0.248116
$366$	−909958.	−0.355074
$367$	−2.83578e6	−1.09903	−0.549513	−	0.835485i	$-0.685187\pi$
$367$	−2.83578e6	−1.09903	−0.549513	+	0.835485i	$0.685187\pi$
$368$	−3.74567e6	−1.44182
$369$	2.01530e6	0.770502
$370$	2.90590e6	1.10351
$371$	−128636.	−0.0485207
$372$	−2.18129e6	−0.817252
$373$	−3.10551e6	−1.15574	−0.577870	−	0.816128i	$-0.696116\pi$
$373$	−3.10551e6	−1.15574	−0.577870	+	0.816128i	$0.696116\pi$
$374$	−659085.	−0.243648
$375$	71960.6	0.0264251
$376$	532016.	0.194068
$377$	1.01646e7	3.68329
$378$	390217.	0.140468
$379$	−567414.	−0.202909	−0.101455	−	0.994840i	$-0.532350\pi$
$379$	−567414.	−0.202909	−0.101455	+	0.994840i	$0.532350\pi$
$380$	687230.	0.244143
$381$	322646.	0.113871
$382$	−4.18016e6	−1.46566
$383$	−1.68774e6	−0.587907	−0.293954	−	0.955820i	$-0.594971\pi$
$383$	−1.68774e6	−0.587907	−0.293954	+	0.955820i	$0.594971\pi$
$384$	209337.	0.0724466
$385$	53026.4	0.0182323
$386$	5.86512e6	2.00359
$387$	−5.21114e6	−1.76870
$388$	−3.16622e6	−1.06773
$389$	−4.71004e6	−1.57816	−0.789079	−	0.614292i	$-0.789442\pi$
$389$	−4.71004e6	−1.57816	−0.789079	+	0.614292i	$0.789442\pi$
$390$	1.41209e6	0.470111
$391$	−839241.	−0.277616
$392$	7.57513e6	2.48986
$393$	431877.	0.141052
$394$	1.02479e7	3.32580
$395$	−942762.	−0.304025
$396$	−2.04353e6	−0.654853
$397$	2.22697e6	0.709151	0.354576	−	0.935027i	$-0.384625\pi$
$397$	2.22697e6	0.709151	0.354576	+	0.935027i	$0.384625\pi$
$398$	1.06783e7	3.37904
$399$	29144.0	0.00916466
$400$	1.46107e6	0.456584
$401$	3.04723e6	0.946333	0.473167	−	0.880973i	$-0.343111\pi$
$401$	3.04723e6	0.946333	0.473167	+	0.880973i	$0.343111\pi$
$402$	−2.58081e6	−0.796509
$403$	7.33538e6	2.24988
$404$	8.56761e6	2.61160
$405$	1.10091e6	0.333515
$406$	1.57118e6	0.473053
$407$	−1.35244e6	−0.404699
$408$	−1.10748e6	−0.329371
$409$	−1.59613e6	−0.471801	−0.235900	−	0.971777i	$-0.575804\pi$
$409$	−1.59613e6	−0.471801	−0.235900	+	0.971777i	$0.575804\pi$
$410$	2.36236e6	0.694044
$411$	−70326.5	−0.0205359
$412$	2.51515e6	0.729995
$413$	−242574.	−0.0699791
$414$	−3.69562e6	−1.05971
$415$	338704.	0.0965383
$416$	1.13445e7	3.21406
$417$	−1.29335e6	−0.364231
$418$	−454256.	−0.127163
$419$	−4.02099e6	−1.11892	−0.559459	−	0.828858i	$-0.688991\pi$
$419$	−4.02099e6	−1.11892	−0.559459	+	0.828858i	$0.688991\pi$
$420$	153687.	0.0425122
$421$	6.15459e6	1.69236	0.846182	−	0.532895i	$-0.178896\pi$
$421$	6.15459e6	1.69236	0.846182	+	0.532895i	$0.178896\pi$
$422$	1.01248e7	2.76761
$423$	257011.	0.0698395
$424$	3.36906e6	0.910110
$425$	327362.	0.0879136
$426$	3.12356e6	0.833923
$427$	333047.	0.0883966
$428$	−2.93199e6	−0.773665
$429$	−657203.	−0.172408
$430$	−6.10857e6	−1.59319
$431$	−2.56283e6	−0.664550	−0.332275	−	0.943183i	$-0.607816\pi$
$431$	−2.56283e6	−0.664550	−0.332275	+	0.943183i	$0.607816\pi$
$432$	−5.00406e6	−1.29007
$433$	−4.20367e6	−1.07748	−0.538739	−	0.842472i	$-0.681099\pi$
$433$	−4.20367e6	−1.07748	−0.538739	+	0.842472i	$0.681099\pi$
$434$	1.13386e6	0.288957
$435$	−992349.	−0.251444
$436$	1.56956e7	3.95424
$437$	−578423.	−0.144891
$438$	−1.20985e6	−0.301332
$439$	−5.93651e6	−1.47018	−0.735089	−	0.677971i	$-0.762860\pi$
$439$	−5.93651e6	−1.47018	−0.735089	+	0.677971i	$0.762860\pi$
$440$	−1.38880e6	−0.341985
$441$	3.65947e6	0.896027
$442$	6.42385e6	1.56401
$443$	6.86528e6	1.66207	0.831035	−	0.556221i	$-0.187749\pi$
$443$	6.86528e6	1.66207	0.831035	+	0.556221i	$0.187749\pi$
$444$	−3.91979e6	−0.943637
$445$	2.33738e6	0.559537
$446$	−2.12848e6	−0.506677
$447$	761585.	0.180281
$448$	442249.	0.104105
$449$	−2.53789e6	−0.594095	−0.297048	−	0.954863i	$-0.596002\pi$
$449$	−2.53789e6	−0.594095	−0.297048	+	0.954863i	$0.596002\pi$
$450$	1.44155e6	0.335581
$451$	−1.09947e6	−0.254532
$452$	3.62628e6	0.834862
$453$	−117511.	−0.0269051
$454$	−4.46475e6	−1.01662
$455$	−516828.	−0.117036
$456$	−763300.	−0.171903
$457$	−1.35019e6	−0.302416	−0.151208	−	0.988502i	$-0.548316\pi$
$457$	−1.35019e6	−0.302416	−0.151208	+	0.988502i	$0.548316\pi$
$458$	−904150.	−0.201408
$459$	−1.12119e6	−0.248398
$460$	−3.05024e6	−0.672108
$461$	4.14784e6	0.909012	0.454506	−	0.890744i	$-0.349816\pi$
$461$	4.14784e6	0.909012	0.454506	+	0.890744i	$0.349816\pi$
$462$	−101586.	−0.0221427
$463$	2.68067e6	0.581153	0.290576	−	0.956852i	$-0.406153\pi$
$463$	2.68067e6	0.581153	0.290576	+	0.956852i	$0.406153\pi$
$464$	−2.01484e7	−4.34456
$465$	−716140.	−0.153591
$466$	−1.11186e7	−2.37184
$467$	5.67381e6	1.20388	0.601939	−	0.798542i	$-0.294395\pi$
$467$	5.67381e6	1.20388	0.601939	+	0.798542i	$0.294395\pi$
$468$	1.99175e7	4.20360
$469$	944583.	0.198293
$470$	301272.	0.0629093
$471$	−1.41831e6	−0.294591
$472$	6.35316e6	1.31261
$473$	2.84300e6	0.584284
$474$	1.80611e6	0.369232
$475$	225625.	0.0458831
$476$	699150.	0.141434
$477$	1.62756e6	0.327522
$478$	517924.	0.103680
$479$	−4.42734e6	−0.881666	−0.440833	−	0.897589i	$-0.645317\pi$
$479$	−4.42734e6	−0.881666	−0.440833	+	0.897589i	$0.645317\pi$
$480$	−1.10755e6	−0.219411
$481$	1.31817e7	2.59782
$482$	−8.87425e6	−1.73986
$483$	−129354.	−0.0252297
$484$	1.11487e6	0.216328
$485$	−1.03950e6	−0.200665
$486$	−7.51845e6	−1.44390
$487$	−5.43293e6	−1.03803	−0.519017	−	0.854764i	$-0.673702\pi$
$487$	−5.43293e6	−1.03803	−0.519017	+	0.854764i	$0.673702\pi$
$488$	−8.72272e6	−1.65807
$489$	−1.42309e6	−0.269129
$490$	4.28968e6	0.807113
$491$	−3.83113e6	−0.717172	−0.358586	−	0.933497i	$-0.616741\pi$
$491$	−3.83113e6	−0.717172	−0.358586	+	0.933497i	$0.616741\pi$
$492$	−3.18661e6	−0.593493
$493$	−4.51438e6	−0.836528
$494$	4.42746e6	0.816277
$495$	−670913.	−0.123070
$496$	−1.45403e7	−2.65381
$497$	−1.14323e6	−0.207607
$498$	−648877.	−0.117244
$499$	−1.99786e6	−0.359181	−0.179591	−	0.983741i	$-0.557477\pi$
$499$	−1.99786e6	−0.359181	−0.179591	+	0.983741i	$0.557477\pi$
$500$	1.18980e6	0.212839
$501$	1.11851e6	0.199088
$502$	489589.	0.0867106
$503$	4.51472e6	0.795630	0.397815	−	0.917466i	$-0.369769\pi$
$503$	4.51472e6	0.795630	0.397815	+	0.917466i	$0.369769\pi$
$504$	1.78493e6	0.313000
$505$	2.81284e6	0.490813
$506$	2.01619e6	0.350071
$507$	4.69553e6	0.811268
$508$	5.33466e6	0.917165
$509$	403453.	0.0690238	0.0345119	−	0.999404i	$-0.489012\pi$
$509$	403453.	0.0690238	0.0345119	+	0.999404i	$0.489012\pi$
$510$	−627149.	−0.106769
$511$	442807.	0.0750174
$512$	1.18569e7	1.99893
$513$	−772749.	−0.129642
$514$	−1.74216e7	−2.90858
$515$	825749.	0.137192
$516$	8.23989e6	1.36238
$517$	−140216.	−0.0230712
$518$	2.03755e6	0.333644
$519$	2.63290e6	0.429057
$520$	1.35361e7	2.19525
$521$	4.77703e6	0.771016	0.385508	−	0.922704i	$-0.374026\pi$
$521$	4.77703e6	0.771016	0.385508	+	0.922704i	$0.374026\pi$
$522$	−1.98792e7	−3.19318
$523$	5.59206e6	0.893959	0.446980	−	0.894544i	$-0.352500\pi$
$523$	5.59206e6	0.893959	0.446980	+	0.894544i	$0.352500\pi$
$524$	7.14070e6	1.13609
$525$	50457.0	0.00798957
$526$	−1.79173e7	−2.82364
$527$	−3.25785e6	−0.510981
$528$	1.30272e6	0.203360
$529$	−3.86904e6	−0.601124
$530$	1.90784e6	0.295021
$531$	3.06915e6	0.472369
$532$	481869.	0.0738159
$533$	1.07161e7	1.63388
$534$	−4.47787e6	−0.679546
$535$	−962603.	−0.145399
$536$	−2.47393e7	−3.71941
$537$	552778.	0.0827209
$538$	1.45707e6	0.217033
$539$	−1.99647e6	−0.295999
$540$	−4.07499e6	−0.601370
$541$	187719.	0.0275750	0.0137875	−	0.999905i	$-0.495611\pi$
$541$	187719.	0.0275750	0.0137875	+	0.999905i	$0.495611\pi$
$542$	9.70586e6	1.41917
$543$	−3.04331e6	−0.442942
$544$	−5.03843e6	−0.729959
$545$	5.15305e6	0.743144
$546$	990123.	0.142137
$547$	3.96469e6	0.566553	0.283277	−	0.959038i	$-0.408579\pi$
$547$	3.96469e6	0.566553	0.283277	+	0.959038i	$0.408579\pi$
$548$	−1.16279e6	−0.165405
$549$	−4.21386e6	−0.596690
$550$	−786454.	−0.110858
$551$	−3.11141e6	−0.436594
$552$	3.38787e6	0.473237
$553$	−661042.	−0.0919213
$554$	4.18261e6	0.578993
$555$	−1.28691e6	−0.177343
$556$	−2.13844e7	−2.93366
$557$	3.90678e6	0.533558	0.266779	−	0.963758i	$-0.414041\pi$
$557$	3.90678e6	0.533558	0.266779	+	0.963758i	$0.414041\pi$
$558$	−1.43461e7	−1.95051
$559$	−2.77096e7	−3.75061
$560$	1.02447e6	0.138047
$561$	291883.	0.0391563
$562$	−2.05808e7	−2.74866
$563$	−3.58052e6	−0.476075	−0.238038	−	0.971256i	$-0.576504\pi$
$563$	−3.58052e6	−0.476075	−0.238038	+	0.971256i	$0.576504\pi$
$564$	−406388.	−0.0537952
$565$	1.19054e6	0.156901
$566$	1.99879e6	0.262256
$567$	771933.	0.100837
$568$	2.99420e7	3.89412
$569$	1.49494e7	1.93572	0.967860	−	0.251488i	$-0.0809199\pi$
$569$	1.49494e7	1.93572	0.967860	+	0.251488i	$0.0809199\pi$
$570$	−432245.	−0.0557241
$571$	1.05216e7	1.35049	0.675245	−	0.737594i	$-0.264038\pi$
$571$	1.05216e7	1.35049	0.675245	+	0.737594i	$0.264038\pi$
$572$	−1.08663e7	−1.38864
$573$	1.85122e6	0.235544
$574$	1.65643e6	0.209843
$575$	−1.00143e6	−0.126313
$576$	−5.59553e6	−0.702725
$577$	3.26405e6	0.408147	0.204074	−	0.978956i	$-0.434582\pi$
$577$	3.26405e6	0.408147	0.204074	+	0.978956i	$0.434582\pi$
$578$	1.19126e7	1.48316
$579$	−2.59743e6	−0.321994
$580$	−1.64076e7	−2.02523
$581$	237491.	0.0291881
$582$	1.99145e6	0.243703
$583$	−887933.	−0.108195
$584$	−1.15974e7	−1.40711
$585$	6.53914e6	0.790007
$586$	7.28351e6	0.876186
$587$	−1.36291e7	−1.63257	−0.816285	−	0.577649i	$-0.803970\pi$
$587$	−1.36291e7	−1.63257	−0.816285	+	0.577649i	$0.803970\pi$
$588$	−5.78637e6	−0.690181
$589$	−2.24538e6	−0.266687
$590$	3.59770e6	0.425495
$591$	−4.53840e6	−0.534484
$592$	−2.61290e7	−3.06421
$593$	3.75960e6	0.439041	0.219520	−	0.975608i	$-0.429551\pi$
$593$	3.75960e6	0.439041	0.219520	+	0.975608i	$0.429551\pi$
$594$	2.69355e6	0.313226
$595$	229538.	0.0265805
$596$	1.25921e7	1.45206
$597$	−4.72898e6	−0.543040
$598$	−1.96511e7	−2.24716
$599$	1.11999e7	1.27540	0.637700	−	0.770285i	$-0.279886\pi$
$599$	1.11999e7	1.27540	0.637700	+	0.770285i	$0.279886\pi$
$600$	−1.32150e6	−0.149861
$601$	−8.04308e6	−0.908314	−0.454157	−	0.890922i	$-0.650060\pi$
$601$	−8.04308e6	−0.908314	−0.454157	+	0.890922i	$0.650060\pi$
$602$	−4.28318e6	−0.481698
$603$	−1.19513e7	−1.33851
$604$	−1.94294e6	−0.216705
$605$	366025.	0.0406558
$606$	−5.38874e6	−0.596082
$607$	1.06759e7	1.17607	0.588035	−	0.808835i	$-0.299902\pi$
$607$	1.06759e7	1.17607	0.588035	+	0.808835i	$0.299902\pi$
$608$	−3.47260e6	−0.380974
$609$	−695811.	−0.0760235
$610$	−4.93954e6	−0.537480
$611$	1.36663e6	0.148097
$612$	−8.84595e6	−0.954698
$613$	−1.94356e6	−0.208904	−0.104452	−	0.994530i	$-0.533309\pi$
$613$	−1.94356e6	−0.208904	−0.104452	+	0.994530i	$0.533309\pi$
$614$	−3.09266e7	−3.31064
$615$	−1.04620e6	−0.111539
$616$	−973791.	−0.103398
$617$	1.43916e7	1.52193	0.760967	−	0.648791i	$-0.224725\pi$
$617$	1.43916e7	1.52193	0.760967	+	0.648791i	$0.224725\pi$
$618$	−1.58194e6	−0.166617
$619$	1.66008e7	1.74141	0.870707	−	0.491801i	$-0.163661\pi$
$619$	1.66008e7	1.74141	0.870707	+	0.491801i	$0.163661\pi$
$620$	−1.18407e7	−1.23708
$621$	3.42981e6	0.356895
$622$	−3.19200e6	−0.330817
$623$	1.63891e6	0.169175
$624$	−1.26971e7	−1.30540
$625$	390625.	0.0400000
$626$	−6.46844e6	−0.659726
$627$	201172.	0.0204361
$628$	−2.34505e7	−2.37276
$629$	−5.85437e6	−0.590003
$630$	1.01078e6	0.101462
$631$	5.10606e6	0.510519	0.255260	−	0.966873i	$-0.417839\pi$
$631$	5.10606e6	0.510519	0.255260	+	0.966873i	$0.417839\pi$
$632$	1.73131e7	1.72418
$633$	−4.48386e6	−0.444778
$634$	1.14732e7	1.13360
$635$	1.75143e6	0.172368
$636$	−2.57350e6	−0.252280
$637$	1.94588e7	1.90006
$638$	1.08453e7	1.05485
$639$	1.44647e7	1.40138
$640$	1.13635e6	0.109663
$641$	−8.86087e6	−0.851788	−0.425894	−	0.904773i	$-0.640040\pi$
$641$	−8.86087e6	−0.851788	−0.425894	+	0.904773i	$0.640040\pi$
$642$	1.84412e6	0.176584
$643$	−9.61670e6	−0.917273	−0.458637	−	0.888624i	$-0.651662\pi$
$643$	−9.61670e6	−0.917273	−0.458637	+	0.888624i	$0.651662\pi$
$644$	−2.13875e6	−0.203210
$645$	2.70524e6	0.256040
$646$	−1.96636e6	−0.185388
$647$	1.02489e7	0.962537	0.481269	−	0.876573i	$-0.340176\pi$
$647$	1.02489e7	0.962537	0.481269	+	0.876573i	$0.340176\pi$
$648$	−2.02174e7	−1.89142
$649$	−1.67441e6	−0.156045
$650$	7.66527e6	0.711613
$651$	−502140.	−0.0464379
$652$	−2.35295e7	−2.16768
$653$	6.88595e6	0.631947	0.315974	−	0.948768i	$-0.397669\pi$
$653$	6.88595e6	0.631947	0.315974	+	0.948768i	$0.397669\pi$
$654$	−9.87204e6	−0.902532
$655$	2.34437e6	0.213512
$656$	−2.12417e7	−1.92721
$657$	−5.60259e6	−0.506379
$658$	211245.	0.0190205
$659$	4.29760e6	0.385490	0.192745	−	0.981249i	$-0.438261\pi$
$659$	4.29760e6	0.385490	0.192745	+	0.981249i	$0.438261\pi$
$660$	1.06085e6	0.0947972
$661$	−1.56580e7	−1.39390	−0.696951	−	0.717119i	$-0.745460\pi$
$661$	−1.56580e7	−1.39390	−0.696951	+	0.717119i	$0.745460\pi$
$662$	−7.00064e6	−0.620859
$663$	−2.84487e6	−0.251350
$664$	−6.22004e6	−0.547486
$665$	158203.	0.0138727
$666$	−2.57799e7	−2.25214
$667$	1.38098e7	1.20191
$668$	1.84935e7	1.60354
$669$	942617.	0.0814273
$670$	−1.40095e7	−1.20569
$671$	2.29892e6	0.197114
$672$	−776585.	−0.0663385
$673$	2.42138e6	0.206075	0.103037	−	0.994677i	$-0.467144\pi$
$673$	2.42138e6	0.206075	0.103037	+	0.994677i	$0.467144\pi$
$674$	−2.58607e7	−2.19276
$675$	−1.33786e6	−0.113019
$676$	7.76363e7	6.53428
$677$	1.79025e7	1.50121	0.750606	−	0.660751i	$-0.229762\pi$
$677$	1.79025e7	1.50121	0.750606	+	0.660751i	$0.229762\pi$
$678$	−2.28081e6	−0.190552
$679$	−728875.	−0.0606706
$680$	−6.01176e6	−0.498574
$681$	1.97726e6	0.163379
$682$	7.82667e6	0.644341
$683$	−7.19215e6	−0.589938	−0.294969	−	0.955507i	$-0.595309\pi$
$683$	−7.19215e6	−0.589938	−0.294969	+	0.955507i	$0.595309\pi$
$684$	−6.09682e6	−0.498268
$685$	−381755.	−0.0310855
$686$	6.07165e6	0.492602
$687$	400412.	0.0323679
$688$	5.49266e7	4.42396
$689$	8.65435e6	0.694522
$690$	1.91850e6	0.153405
$691$	8.04002e6	0.640563	0.320282	−	0.947322i	$-0.396222\pi$
$691$	8.04002e6	0.640563	0.320282	+	0.947322i	$0.396222\pi$
$692$	4.35326e7	3.45580
$693$	−470428.	−0.0372100
$694$	−9.63634e6	−0.759475
$695$	−7.02073e6	−0.551341
$696$	1.82238e7	1.42598
$697$	−4.75934e6	−0.371078
$698$	2.97586e7	2.31192
$699$	4.92399e6	0.381175
$700$	834261.	0.0643512
$701$	5.41836e6	0.416459	0.208230	−	0.978080i	$-0.433230\pi$
$701$	5.41836e6	0.416459	0.208230	+	0.978080i	$0.433230\pi$
$702$	−2.62530e7	−2.01065
$703$	−4.03496e6	−0.307929
$704$	3.05271e6	0.232142
$705$	−133422.	−0.0101100
$706$	−2.75036e7	−2.07672
$707$	1.97229e6	0.148396
$708$	−4.85296e6	−0.363851
$709$	−1.07777e7	−0.805211	−0.402605	−	0.915374i	$-0.631895\pi$
$709$	−1.07777e7	−0.805211	−0.402605	+	0.915374i	$0.631895\pi$
$710$	1.69557e7	1.26232
$711$	8.36380e6	0.620482
$712$	−4.29242e7	−3.17324
$713$	9.96602e6	0.734172
$714$	−439742.	−0.0322814
$715$	−3.56751e6	−0.260975
$716$	9.13969e6	0.666268
$717$	−229368.	−0.0166623
$718$	4.21982e7	3.05480
$719$	−7.22577e6	−0.521269	−0.260635	−	0.965438i	$-0.583932\pi$
$719$	−7.22577e6	−0.521269	−0.260635	+	0.965438i	$0.583932\pi$
$720$	−1.29620e7	−0.931839
$721$	578995.	0.0414798
$722$	−1.35526e6	−0.0967564
$723$	3.93005e6	0.279610
$724$	−5.03184e7	−3.56763
$725$	−5.38679e6	−0.380614
$726$	−701219.	−0.0493756
$727$	−5.88011e6	−0.412619	−0.206310	−	0.978487i	$-0.566145\pi$
$727$	−5.88011e6	−0.412619	−0.206310	+	0.978487i	$0.566145\pi$
$728$	9.49117e6	0.663730
$729$	−7.37124e6	−0.513715
$730$	−6.56743e6	−0.456130
$731$	1.23066e7	0.851817
$732$	6.66298e6	0.459611
$733$	−1.18117e7	−0.811991	−0.405995	−	0.913875i	$-0.633075\pi$
$733$	−1.18117e7	−0.811991	−0.405995	+	0.913875i	$0.633075\pi$
$734$	2.94904e7	2.02042
$735$	−1.89973e6	−0.129710
$736$	1.54130e7	1.04880
$737$	6.52016e6	0.442171
$738$	−2.09579e7	−1.41647
$739$	−8.61950e6	−0.580592	−0.290296	−	0.956937i	$-0.593754\pi$
$739$	−8.61950e6	−0.580592	−0.290296	+	0.956937i	$0.593754\pi$
$740$	−2.12778e7	−1.42839
$741$	−1.96075e6	−0.131182
$742$	1.33773e6	0.0891990
$743$	−3.93239e6	−0.261327	−0.130663	−	0.991427i	$-0.541711\pi$
$743$	−3.93239e6	−0.261327	−0.130663	+	0.991427i	$0.541711\pi$
$744$	1.31514e7	0.871042
$745$	4.13413e6	0.272893
$746$	3.22954e7	2.12468
$747$	−3.00484e6	−0.197024
$748$	4.82602e6	0.315380
$749$	−674954.	−0.0439612
$750$	−748347.	−0.0485791
$751$	2.75397e6	0.178180	0.0890901	−	0.996024i	$-0.471604\pi$
$751$	2.75397e6	0.178180	0.0890901	+	0.996024i	$0.471604\pi$
$752$	−2.70896e6	−0.174686
$753$	−216819.	−0.0139351
$754$	−1.05705e8	−6.77125
$755$	−637889.	−0.0407266
$756$	−2.85728e6	−0.181823
$757$	−8.33183e6	−0.528446	−0.264223	−	0.964462i	$-0.585116\pi$
$757$	−8.33183e6	−0.528446	−0.264223	+	0.964462i	$0.585116\pi$
$758$	5.90076e6	0.373023
$759$	−892891.	−0.0562593
$760$	−4.14344e6	−0.260212
$761$	−7.95440e6	−0.497904	−0.248952	−	0.968516i	$-0.580086\pi$
$761$	−7.95440e6	−0.497904	−0.248952	+	0.968516i	$0.580086\pi$
$762$	−3.35532e6	−0.209337
$763$	3.61319e6	0.224688
$764$	3.06083e7	1.89717
$765$	−2.90422e6	−0.179422
$766$	1.75515e7	1.08079
$767$	1.63198e7	1.00168
$768$	−5.89511e6	−0.360653
$769$	1.06106e7	0.647027	0.323513	−	0.946224i	$-0.395136\pi$
$769$	1.06106e7	0.647027	0.323513	+	0.946224i	$0.395136\pi$
$770$	−551443.	−0.0335176
$771$	7.71534e6	0.467433
$772$	−4.29461e7	−2.59347
$773$	−5.28477e6	−0.318110	−0.159055	−	0.987270i	$-0.550845\pi$
$773$	−5.28477e6	−0.318110	−0.159055	+	0.987270i	$0.550845\pi$
$774$	5.41927e7	3.25153
$775$	−3.88744e6	−0.232493
$776$	1.90897e7	1.13801
$777$	−902348.	−0.0536193
$778$	4.89815e7	2.90124
$779$	−3.28024e6	−0.193670
$780$	−1.03397e7	−0.608517
$781$	−7.89137e6	−0.462940
$782$	8.72760e6	0.510361
$783$	1.84493e7	1.07542
$784$	−3.85716e7	−2.24118
$785$	−7.69906e6	−0.445927
$786$	−4.49126e6	−0.259306
$787$	−155005.	−0.00892088	−0.00446044	−	0.999990i	$-0.501420\pi$
$787$	−155005.	−0.00892088	−0.00446044	+	0.999990i	$0.501420\pi$
$788$	−7.50384e7	−4.30495
$789$	7.93487e6	0.453782
$790$	9.80416e6	0.558911
$791$	834781.	0.0474385
$792$	1.23208e7	0.697954
$793$	−2.24067e7	−1.26530
$794$	−2.31592e7	−1.30368
$795$	−844908.	−0.0474124
$796$	−7.81894e7	−4.37386
$797$	−2.17112e6	−0.121071	−0.0605353	−	0.998166i	$-0.519281\pi$
$797$	−2.17112e6	−0.121071	−0.0605353	+	0.998166i	$0.519281\pi$
$798$	−303080.	−0.0168480
$799$	−606959.	−0.0336351
$800$	−6.01212e6	−0.332126
$801$	−2.07362e7	−1.14195
$802$	−3.16893e7	−1.73971
$803$	3.05656e6	0.167280
$804$	1.88974e7	1.03101
$805$	−702175.	−0.0381905
$806$	−7.62836e7	−4.13612
$807$	−645279.	−0.0348789
$808$	−5.16557e7	−2.78349
$809$	−1.02870e7	−0.552609	−0.276304	−	0.961070i	$-0.589110\pi$
$809$	−1.02870e7	−0.552609	−0.276304	+	0.961070i	$0.589110\pi$
$810$	−1.14488e7	−0.613124
$811$	3.91210e6	0.208861	0.104431	−	0.994532i	$-0.466698\pi$
$811$	3.91210e6	0.208861	0.104431	+	0.994532i	$0.466698\pi$
$812$	−1.15046e7	−0.612325
$813$	−4.29834e6	−0.228073
$814$	1.40645e7	0.743986
$815$	−7.72499e6	−0.407384
$816$	5.63915e6	0.296475
$817$	8.48201e6	0.444574
$818$	1.65987e7	0.867345
$819$	4.58508e6	0.238857
$820$	−1.72979e7	−0.898378
$821$	1.29705e7	0.671581	0.335790	−	0.941937i	$-0.390997\pi$
$821$	1.29705e7	0.671581	0.335790	+	0.941937i	$0.390997\pi$
$822$	731353.	0.0377527
$823$	1.66854e7	0.858691	0.429346	−	0.903140i	$-0.358744\pi$
$823$	1.66854e7	0.858691	0.429346	+	0.903140i	$0.358744\pi$
$824$	−1.51643e7	−0.778042
$825$	348289.	0.0178158
$826$	2.52262e6	0.128648
$827$	2.16447e7	1.10049	0.550247	−	0.835002i	$-0.314534\pi$
$827$	2.16447e7	1.10049	0.550247	+	0.835002i	$0.314534\pi$
$828$	2.70604e7	1.37170
$829$	3.42379e7	1.73030	0.865150	−	0.501513i	$-0.167223\pi$
$829$	3.42379e7	1.73030	0.865150	+	0.501513i	$0.167223\pi$
$830$	−3.52231e6	−0.177473
$831$	−1.85231e6	−0.0930490
$832$	−2.97536e7	−1.49015
$833$	−8.64221e6	−0.431531
$834$	1.34501e7	0.669591
$835$	6.07162e6	0.301362
$836$	3.32620e6	0.164601
$837$	1.33142e7	0.656902
$838$	4.18159e7	2.05699
$839$	3.85428e7	1.89033	0.945166	−	0.326591i	$-0.105900\pi$
$839$	3.85428e7	1.89033	0.945166	+	0.326591i	$0.105900\pi$
$840$	−926606.	−0.0453103
$841$	5.37736e7	2.62168
$842$	−6.40040e7	−3.11119
$843$	9.11442e6	0.441733
$844$	−7.41366e7	−3.58242
$845$	2.54888e7	1.22803
$846$	−2.67276e6	−0.128391
$847$	256648.	0.0122922
$848$	−1.71548e7	−0.819212
$849$	−885184.	−0.0421468
$850$	−3.40437e6	−0.161618
$851$	1.79090e7	0.847709
$852$	−2.28716e7	−1.07944
$853$	1.60947e7	0.757374	0.378687	−	0.925525i	$-0.376376\pi$
$853$	1.60947e7	0.757374	0.378687	+	0.925525i	$0.376376\pi$
$854$	−3.46349e6	−0.162506
$855$	−2.00165e6	−0.0936425
$856$	1.76775e7	0.824586
$857$	−1.08311e7	−0.503755	−0.251878	−	0.967759i	$-0.581048\pi$
$857$	−1.08311e7	−0.503755	−0.251878	+	0.967759i	$0.581048\pi$
$858$	6.83451e6	0.316949
$859$	3.89167e7	1.79950	0.899752	−	0.436401i	$-0.143747\pi$
$859$	3.89167e7	1.79950	0.899752	+	0.436401i	$0.143747\pi$
$860$	4.47287e7	2.06225
$861$	−733567.	−0.0337235
$862$	2.66519e7	1.22169
$863$	−9.37096e6	−0.428309	−0.214154	−	0.976800i	$-0.568700\pi$
$863$	−9.37096e6	−0.428309	−0.214154	+	0.976800i	$0.568700\pi$
$864$	2.05911e7	0.938413
$865$	1.42922e7	0.649469
$866$	4.37156e7	1.98081
$867$	−5.27563e6	−0.238356
$868$	−8.30243e6	−0.374030
$869$	−4.56297e6	−0.204974
$870$	1.03198e7	0.462247
$871$	−6.35496e7	−2.83836
$872$	−9.46319e7	−4.21450
$873$	9.22204e6	0.409535
$874$	6.01525e6	0.266364
$875$	273897.	0.0120939
$876$	8.85885e6	0.390047
$877$	−7.92492e6	−0.347933	−0.173967	−	0.984752i	$-0.555658\pi$
$877$	−7.92492e6	−0.347933	−0.173967	+	0.984752i	$0.555658\pi$
$878$	6.17361e7	2.70273
$879$	−3.22558e6	−0.140810
$880$	7.07158e6	0.307829
$881$	193413.	0.00839548	0.00419774	−	0.999991i	$-0.498664\pi$
$881$	193413.	0.00839548	0.00419774	+	0.999991i	$0.498664\pi$
$882$	−3.80562e7	−1.64723
$883$	−5.14962e6	−0.222266	−0.111133	−	0.993806i	$-0.535448\pi$
$883$	−5.14962e6	−0.222266	−0.111133	+	0.993806i	$0.535448\pi$
$884$	−4.70373e7	−2.02447
$885$	−1.59328e6	−0.0683807
$886$	−7.13948e7	−3.05550
$887$	−3.15561e7	−1.34671	−0.673356	−	0.739318i	$-0.735148\pi$
$887$	−3.15561e7	−1.34671	−0.673356	+	0.739318i	$0.735148\pi$
$888$	2.36331e7	1.00575
$889$	1.22806e6	0.0521152
$890$	−2.43073e7	−1.02864
$891$	5.32841e6	0.224856
$892$	1.55853e7	0.655849
$893$	−418329.	−0.0175546
$894$	−7.92003e6	−0.331423
$895$	3.00066e6	0.125216
$896$	796779.	0.0331564
$897$	8.70267e6	0.361137
$898$	2.63925e7	1.09217
$899$	5.36084e7	2.21225
$900$	−1.05554e7	−0.434380
$901$	−3.84364e6	−0.157736
$902$	1.14338e7	0.467924
$903$	1.89685e6	0.0774130
$904$	−2.18635e7	−0.889812
$905$	−1.65201e7	−0.670486
$906$	1.22205e6	0.0494615
$907$	5.96299e6	0.240683	0.120342	−	0.992733i	$-0.461601\pi$
$907$	5.96299e6	0.240683	0.120342	+	0.992733i	$0.461601\pi$
$908$	3.26922e7	1.31592
$909$	−2.49543e7	−1.00170
$910$	5.37470e6	0.215155
$911$	−2.58958e7	−1.03379	−0.516896	−	0.856048i	$-0.672913\pi$
$911$	−2.58958e7	−1.03379	−0.516896	+	0.856048i	$0.672913\pi$
$912$	3.88663e6	0.154734
$913$	1.63933e6	0.0650861
$914$	1.40412e7	0.555953
$915$	2.18753e6	0.0863775
$916$	6.62045e6	0.260705
$917$	1.64381e6	0.0645548
$918$	1.16597e7	0.456647
$919$	3.01315e7	1.17688	0.588440	−	0.808541i	$-0.299742\pi$
$919$	3.01315e7	1.17688	0.588440	+	0.808541i	$0.299742\pi$
$920$	1.83904e7	0.716345
$921$	1.36962e7	0.532047
$922$	−4.31350e7	−1.67110
$923$	7.69142e7	2.97168
$924$	743844.	0.0286617
$925$	−6.98574e6	−0.268447
$926$	−2.78773e7	−1.06837
$927$	−7.32570e6	−0.279995
$928$	8.29081e7	3.16029
$929$	−2.11549e7	−0.804213	−0.402106	−	0.915593i	$-0.631722\pi$
$929$	−2.11549e7	−0.804213	−0.402106	+	0.915593i	$0.631722\pi$
$930$	7.44743e6	0.282357
$931$	−5.95640e6	−0.225221
$932$	8.14138e7	3.07014
$933$	1.41361e6	0.0531650
$934$	−5.90042e7	−2.21317
$935$	1.58443e6	0.0592713
$936$	−1.20086e8	−4.48027
$937$	−3.78996e6	−0.141021	−0.0705107	−	0.997511i	$-0.522463\pi$
$937$	−3.78996e6	−0.141021	−0.0705107	+	0.997511i	$0.522463\pi$
$938$	−9.82309e6	−0.364536
$939$	2.86461e6	0.106023
$940$	−2.20600e6	−0.0814304
$941$	4.60591e7	1.69567	0.847835	−	0.530260i	$-0.177906\pi$
$941$	4.60591e7	1.69567	0.847835	+	0.530260i	$0.177906\pi$
$942$	1.47496e7	0.541568
$943$	1.45592e7	0.533160
$944$	−3.23495e7	−1.18151
$945$	−938076.	−0.0341711
$946$	−2.95655e7	−1.07413
$947$	−3.23248e7	−1.17128	−0.585640	−	0.810571i	$-0.699157\pi$
$947$	−3.23248e7	−1.17128	−0.585640	+	0.810571i	$0.699157\pi$
$948$	−1.32249e7	−0.477938
$949$	−2.97911e7	−1.07380
$950$	−2.34636e6	−0.0843502
$951$	−5.08103e6	−0.182180
$952$	−4.21530e6	−0.150743
$953$	3.32408e7	1.18560	0.592801	−	0.805349i	$-0.298022\pi$
$953$	3.32408e7	1.18560	0.592801	+	0.805349i	$0.298022\pi$
$954$	−1.69256e7	−0.602106
$955$	1.00490e7	0.356546
$956$	−3.79239e6	−0.134205
$957$	−4.80297e6	−0.169524
$958$	4.60417e7	1.62083
$959$	−267677.	−0.00939863
$960$	2.90479e6	0.101727
$961$	1.00580e7	0.351320
$962$	−1.37082e8	−4.77576
$963$	8.53981e6	0.296744
$964$	6.49799e7	2.25209
$965$	−1.40997e7	−0.487406
$966$	1.34520e6	0.0463815
$967$	−1.33927e7	−0.460575	−0.230288	−	0.973123i	$-0.573967\pi$
$967$	−1.33927e7	−0.460575	−0.230288	+	0.973123i	$0.573967\pi$
$968$	−6.72178e6	−0.230566
$969$	870823.	0.0297934
$970$	1.08102e7	0.368897
$971$	1.85569e7	0.631623	0.315811	−	0.948822i	$-0.397723\pi$
$971$	1.85569e7	0.631623	0.315811	+	0.948822i	$0.397723\pi$
$972$	5.50523e7	1.86900
$973$	−4.92276e6	−0.166697
$974$	5.64992e7	1.90829
$975$	−3.39464e6	−0.114362
$976$	4.44150e7	1.49247
$977$	−3.22101e7	−1.07958	−0.539792	−	0.841799i	$-0.681497\pi$
$977$	−3.22101e7	−1.07958	−0.539792	+	0.841799i	$0.681497\pi$
$978$	1.47993e7	0.494759
$979$	1.13129e7	0.377240
$980$	−3.14103e7	−1.04474
$981$	−4.57157e7	−1.51668
$982$	3.98415e7	1.31843
$983$	−5.20533e7	−1.71816	−0.859082	−	0.511838i	$-0.828965\pi$
$983$	−5.20533e7	−1.71816	−0.859082	+	0.511838i	$0.828965\pi$
$984$	1.92126e7	0.632556
$985$	−2.46359e7	−0.809054
$986$	4.69468e7	1.53785
$987$	−93551.9	−0.00305675
$988$	−3.24192e7	−1.05660
$989$	−3.76470e7	−1.22388
$990$	6.97709e6	0.226249
$991$	−3.24316e6	−0.104902	−0.0524511	−	0.998623i	$-0.516703\pi$
$991$	−3.24316e6	−0.104902	−0.0524511	+	0.998623i	$0.516703\pi$
$992$	5.98316e7	1.93042
$993$	3.10030e6	0.0997772
$994$	1.18889e7	0.381659
$995$	−2.56704e7	−0.822006
$996$	4.75127e6	0.151761
$997$	4.38785e7	1.39802	0.699011	−	0.715111i	$-0.253624\pi$
$997$	4.38785e7	1.39802	0.699011	+	0.715111i	$0.253624\pi$
$998$	2.07765e7	0.660308
$999$	2.39256e7	0.758490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.h.1.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.h.1.3	✓	40	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)

\(f(q)\)	\(=\)	\(q-10.3994 q^{2} +4.60548 q^{3} +76.1474 q^{4} +25.0000 q^{5} -47.8942 q^{6} +17.5294 q^{7} -459.106 q^{8} -221.790 q^{9} +O(q^{10})\)	\(q-10.3994 q^{2} +4.60548 q^{3} +76.1474 q^{4} +25.0000 q^{5} -47.8942 q^{6} +17.5294 q^{7} -459.106 q^{8} -221.790 q^{9} -259.985 q^{10} +121.000 q^{11} +350.695 q^{12} -1179.34 q^{13} -182.295 q^{14} +115.137 q^{15} +2337.71 q^{16} +523.779 q^{17} +2306.48 q^{18} +361.000 q^{19} +1903.69 q^{20} +80.7312 q^{21} -1258.33 q^{22} -1602.28 q^{23} -2114.40 q^{24} +625.000 q^{25} +12264.4 q^{26} -2140.58 q^{27} +1334.82 q^{28} -8618.86 q^{29} -1197.35 q^{30} -6219.90 q^{31} -9619.39 q^{32} +557.263 q^{33} -5446.99 q^{34} +438.235 q^{35} -16888.7 q^{36} -11177.2 q^{37} -3754.18 q^{38} -5431.43 q^{39} -11477.7 q^{40} -9086.54 q^{41} -839.556 q^{42} +23495.9 q^{43} +9213.84 q^{44} -5544.74 q^{45} +16662.7 q^{46} -1158.81 q^{47} +10766.3 q^{48} -16499.7 q^{49} -6499.62 q^{50} +2412.25 q^{51} -89803.8 q^{52} -7338.29 q^{53} +22260.7 q^{54} +3025.00 q^{55} -8047.86 q^{56} +1662.58 q^{57} +89630.9 q^{58} -13838.1 q^{59} +8767.38 q^{60} +18999.3 q^{61} +64683.2 q^{62} -3887.84 q^{63} +25229.0 q^{64} -29483.5 q^{65} -5795.20 q^{66} +53885.7 q^{67} +39884.4 q^{68} -7379.27 q^{69} -4557.38 q^{70} -65217.9 q^{71} +101825. q^{72} +25260.8 q^{73} +116236. q^{74} +2878.42 q^{75} +27489.2 q^{76} +2121.06 q^{77} +56483.6 q^{78} -37710.5 q^{79} +58442.8 q^{80} +44036.5 q^{81} +94494.5 q^{82} +13548.1 q^{83} +6147.47 q^{84} +13094.5 q^{85} -244343. q^{86} -39694.0 q^{87} -55551.9 q^{88} +93495.1 q^{89} +57661.9 q^{90} -20673.1 q^{91} -122010. q^{92} -28645.6 q^{93} +12050.9 q^{94} +9025.00 q^{95} -44301.9 q^{96} -41580.1 q^{97} +171587. q^{98} -26836.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * q^99

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