LMFDB - Embedded newform 1045.6.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$167.601091705$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-8.03656 q^{2} +17.6855 q^{3} +32.5863 q^{4} +25.0000 q^{5} -142.131 q^{6} +252.455 q^{7} -4.71219 q^{8} +69.7783 q^{9} +O(q^{10})$	\(q-8.03656 q^{2} +17.6855 q^{3} +32.5863 q^{4} +25.0000 q^{5} -142.131 q^{6} +252.455 q^{7} -4.71219 q^{8} +69.7783 q^{9} -200.914 q^{10} -121.000 q^{11} +576.307 q^{12} +694.129 q^{13} -2028.87 q^{14} +442.139 q^{15} -1004.89 q^{16} +1495.72 q^{17} -560.778 q^{18} -361.000 q^{19} +814.659 q^{20} +4464.80 q^{21} +972.424 q^{22} -298.039 q^{23} -83.3377 q^{24} +625.000 q^{25} -5578.41 q^{26} -3063.52 q^{27} +8226.58 q^{28} +1509.86 q^{29} -3553.27 q^{30} -3104.74 q^{31} +8226.68 q^{32} -2139.95 q^{33} -12020.5 q^{34} +6311.37 q^{35} +2273.82 q^{36} -4448.19 q^{37} +2901.20 q^{38} +12276.0 q^{39} -117.805 q^{40} +11345.6 q^{41} -35881.6 q^{42} +3139.10 q^{43} -3942.95 q^{44} +1744.46 q^{45} +2395.21 q^{46} -10746.4 q^{47} -17772.1 q^{48} +46926.4 q^{49} -5022.85 q^{50} +26452.7 q^{51} +22619.1 q^{52} +10578.1 q^{53} +24620.2 q^{54} -3025.00 q^{55} -1189.62 q^{56} -6384.48 q^{57} -12134.1 q^{58} -27355.1 q^{59} +14407.7 q^{60} +29352.8 q^{61} +24951.5 q^{62} +17615.9 q^{63} -33957.6 q^{64} +17353.2 q^{65} +17197.8 q^{66} +20498.5 q^{67} +48740.2 q^{68} -5270.98 q^{69} -50721.7 q^{70} -1037.50 q^{71} -328.809 q^{72} -35462.8 q^{73} +35748.2 q^{74} +11053.5 q^{75} -11763.7 q^{76} -30547.0 q^{77} -98657.2 q^{78} +57640.2 q^{79} -25122.3 q^{80} -71136.1 q^{81} -91179.3 q^{82} +108316. q^{83} +145491. q^{84} +37393.1 q^{85} -25227.6 q^{86} +26702.7 q^{87} +570.175 q^{88} +104741. q^{89} -14019.4 q^{90} +175236. q^{91} -9711.99 q^{92} -54909.1 q^{93} +86363.9 q^{94} -9025.00 q^{95} +145493. q^{96} -36167.1 q^{97} -377127. q^{98} -8443.18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) $ 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−8.03656	−1.42068	−0.710339	−	0.703860i	$-0.751458\pi$
$2$	−8.03656	−1.42068	−0.710339	+	0.703860i	$0.751458\pi$
$3$	17.6855	1.13453	0.567264	−	0.823536i	$-0.308002\pi$
$3$	17.6855	1.13453	0.567264	+	0.823536i	$0.308002\pi$
$4$	32.5863	1.01832
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−142.131	−1.61180
$7$	252.455	1.94732	0.973662	−	0.227995i	$-0.0732169\pi$
$7$	252.455	1.94732	0.973662	+	0.227995i	$0.0732169\pi$
$8$	−4.71219	−0.0260314
$9$	69.7783	0.287154
$10$	−200.914	−0.635346
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	576.307	1.15532
$13$	694.129	1.13915	0.569576	−	0.821938i	$-0.307107\pi$
$13$	694.129	1.13915	0.569576	+	0.821938i	$0.307107\pi$
$14$	−2028.87	−2.76652
$15$	442.139	0.507376
$16$	−1004.89	−0.981341
$17$	1495.72	1.25525	0.627624	−	0.778517i	$-0.284028\pi$
$17$	1495.72	1.25525	0.627624	+	0.778517i	$0.284028\pi$
$18$	−560.778	−0.407953
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	814.659	0.455408
$21$	4464.80	2.20929
$22$	972.424	0.428350
$23$	−298.039	−0.117477	−0.0587385	−	0.998273i	$-0.518708\pi$
$23$	−298.039	−0.117477	−0.0587385	+	0.998273i	$0.518708\pi$
$24$	−83.3377	−0.0295334
$25$	625.000	0.200000
$26$	−5578.41	−1.61837
$27$	−3063.52	−0.808744
$28$	8226.58	1.98301
$29$	1509.86	0.333382	0.166691	−	0.986009i	$-0.446692\pi$
$29$	1509.86	0.333382	0.166691	+	0.986009i	$0.446692\pi$
$30$	−3553.27	−0.720818
$31$	−3104.74	−0.580258	−0.290129	−	0.956987i	$-0.593698\pi$
$31$	−3104.74	−0.580258	−0.290129	+	0.956987i	$0.593698\pi$
$32$	8226.68	1.42020
$33$	−2139.95	−0.342073
$34$	−12020.5	−1.78330
$35$	6311.37	0.870870
$36$	2273.82	0.292415
$37$	−4448.19	−0.534169	−0.267085	−	0.963673i	$-0.586060\pi$
$37$	−4448.19	−0.534169	−0.267085	+	0.963673i	$0.586060\pi$
$38$	2901.20	0.325926
$39$	12276.0	1.29240
$40$	−117.805	−0.0116416
$41$	11345.6	1.05406	0.527031	−	0.849846i	$-0.323305\pi$
$41$	11345.6	1.05406	0.527031	+	0.849846i	$0.323305\pi$
$42$	−35881.6	−3.13869
$43$	3139.10	0.258901	0.129451	−	0.991586i	$-0.458679\pi$
$43$	3139.10	0.258901	0.129451	+	0.991586i	$0.458679\pi$
$44$	−3942.95	−0.307036
$45$	1744.46	0.128419
$46$	2395.21	0.166897
$47$	−10746.4	−0.709606	−0.354803	−	0.934941i	$-0.615452\pi$
$47$	−10746.4	−0.709606	−0.354803	+	0.934941i	$0.615452\pi$
$48$	−17772.1	−1.11336
$49$	46926.4	2.79207
$50$	−5022.85	−0.284135
$51$	26452.7	1.42411
$52$	22619.1	1.16003
$53$	10578.1	0.517269	0.258635	−	0.965975i	$-0.416727\pi$
$53$	10578.1	0.517269	0.258635	+	0.965975i	$0.416727\pi$
$54$	24620.2	1.14896
$55$	−3025.00	−0.134840
$56$	−1189.62	−0.0506917
$57$	−6384.48	−0.260279
$58$	−12134.1	−0.473628
$59$	−27355.1	−1.02308	−0.511538	−	0.859261i	$-0.670924\pi$
$59$	−27355.1	−1.02308	−0.511538	+	0.859261i	$0.670924\pi$
$60$	14407.7	0.516673
$61$	29352.8	1.01001	0.505004	−	0.863117i	$-0.331491\pi$
$61$	29352.8	1.01001	0.505004	+	0.863117i	$0.331491\pi$
$62$	24951.5	0.824360
$63$	17615.9	0.559181
$64$	−33957.6	−1.03630
$65$	17353.2	0.509445
$66$	17197.8	0.485975
$67$	20498.5	0.557873	0.278937	−	0.960309i	$-0.410018\pi$
$67$	20498.5	0.557873	0.278937	+	0.960309i	$0.410018\pi$
$68$	48740.2	1.27825
$69$	−5270.98	−0.133281
$70$	−50721.7	−1.23723
$71$	−1037.50	−0.0244254	−0.0122127	−	0.999925i	$-0.503888\pi$
$71$	−1037.50	−0.0244254	−0.0122127	+	0.999925i	$0.503888\pi$
$72$	−328.809	−0.00747502
$73$	−35462.8	−0.778871	−0.389435	−	0.921054i	$-0.627330\pi$
$73$	−35462.8	−0.778871	−0.389435	+	0.921054i	$0.627330\pi$
$74$	35748.2	0.758882
$75$	11053.5	0.226906
$76$	−11763.7	−0.233619
$77$	−30547.0	−0.587141
$78$	−98657.2	−1.83608
$79$	57640.2	1.03910	0.519550	−	0.854440i	$-0.326099\pi$
$79$	57640.2	1.03910	0.519550	+	0.854440i	$0.326099\pi$
$80$	−25122.3	−0.438869
$81$	−71136.1	−1.20470
$82$	−91179.3	−1.49748
$83$	108316.	1.72583	0.862917	−	0.505346i	$-0.168635\pi$
$83$	108316.	1.72583	0.862917	+	0.505346i	$0.168635\pi$
$84$	145491.	2.24978
$85$	37393.1	0.561364
$86$	−25227.6	−0.367815
$87$	26702.7	0.378231
$88$	570.175	0.00784877
$89$	104741.	1.40165	0.700826	−	0.713333i	$-0.252815\pi$
$89$	104741.	1.40165	0.700826	+	0.713333i	$0.252815\pi$
$90$	−14019.4	−0.182442
$91$	175236.	2.21830
$92$	−9711.99	−0.119630
$93$	−54909.1	−0.658319
$94$	86363.9	1.00812
$95$	−9025.00	−0.102598
$96$	145493.	1.61126
$97$	−36167.1	−0.390287	−0.195144	−	0.980775i	$-0.562517\pi$
$97$	−36167.1	−0.390287	−0.195144	+	0.980775i	$0.562517\pi$
$98$	−377127.	−3.96664
$99$	−8443.18	−0.0865801
$100$	20366.5	0.203665
$101$	−122346.	−1.19340	−0.596699	−	0.802465i	$-0.703521\pi$
$101$	−122346.	−1.19340	−0.596699	+	0.802465i	$0.703521\pi$
$102$	−212589.	−2.02321
$103$	−175705.	−1.63189	−0.815943	−	0.578132i	$-0.803782\pi$
$103$	−175705.	−1.63189	−0.815943	+	0.578132i	$0.803782\pi$
$104$	−3270.87	−0.0296538
$105$	111620.	0.988026
$106$	−85011.3	−0.734872
$107$	34966.7	0.295254	0.147627	−	0.989043i	$-0.452837\pi$
$107$	34966.7	0.295254	0.147627	+	0.989043i	$0.452837\pi$
$108$	−99828.9	−0.823563
$109$	233906.	1.88571	0.942857	−	0.333197i	$-0.108127\pi$
$109$	233906.	1.88571	0.942857	+	0.333197i	$0.108127\pi$
$110$	24310.6	0.191564
$111$	−78668.7	−0.606030
$112$	−253690.	−1.91099
$113$	114489.	0.843468	0.421734	−	0.906720i	$-0.361422\pi$
$113$	114489.	0.843468	0.421734	+	0.906720i	$0.361422\pi$
$114$	51309.3	0.369772
$115$	−7450.97	−0.0525374
$116$	49200.8	0.339490
$117$	48435.2	0.327112
$118$	219841.	1.45346
$119$	377603.	2.44437
$120$	−2083.44	−0.0132077
$121$	14641.0	0.0909091
$122$	−235896.	−1.43490
$123$	200652.	1.19586
$124$	−101172.	−0.590891
$125$	15625.0	0.0894427
$126$	−141571.	−0.794416
$127$	101370.	0.557699	0.278849	−	0.960335i	$-0.410047\pi$
$127$	101370.	0.557699	0.278849	+	0.960335i	$0.410047\pi$
$128$	9648.95	0.0520541
$129$	55516.7	0.293731
$130$	−139460.	−0.723756
$131$	285641.	1.45426	0.727129	−	0.686500i	$-0.240854\pi$
$131$	285641.	1.45426	0.727129	+	0.686500i	$0.240854\pi$
$132$	−69733.2	−0.348341
$133$	−91136.2	−0.446747
$134$	−164738.	−0.792558
$135$	−76588.0	−0.361681
$136$	−7048.15	−0.0326759
$137$	171513.	0.780720	0.390360	−	0.920662i	$-0.372350\pi$
$137$	171513.	0.780720	0.390360	+	0.920662i	$0.372350\pi$
$138$	42360.5	0.189349
$139$	−294579.	−1.29320	−0.646599	−	0.762830i	$-0.723809\pi$
$139$	−294579.	−1.29320	−0.646599	+	0.762830i	$0.723809\pi$
$140$	205664.	0.886827
$141$	−190055.	−0.805067
$142$	8337.94	0.0347007
$143$	−83989.6	−0.343467
$144$	−70119.8	−0.281796
$145$	37746.5	0.149093
$146$	284999.	1.10652
$147$	829918.	3.16769
$148$	−144950.	−0.543957
$149$	24571.6	0.0906708	0.0453354	−	0.998972i	$-0.485564\pi$
$149$	24571.6	0.0906708	0.0453354	+	0.998972i	$0.485564\pi$
$150$	−88831.8	−0.322360
$151$	−304045.	−1.08516	−0.542582	−	0.840003i	$-0.682553\pi$
$151$	−304045.	−1.08516	−0.542582	+	0.840003i	$0.682553\pi$
$152$	1701.10	0.00597202
$153$	104369.	0.360449
$154$	245493.	0.834137
$155$	−77618.6	−0.259499
$156$	400032.	1.31608
$157$	−100919.	−0.326755	−0.163377	−	0.986564i	$-0.552239\pi$
$157$	−100919.	−0.326755	−0.163377	+	0.986564i	$0.552239\pi$
$158$	−463229.	−1.47623
$159$	187079.	0.586856
$160$	205667.	0.635133
$161$	−75241.3	−0.228766
$162$	571690.	1.71148
$163$	71526.0	0.210860	0.105430	−	0.994427i	$-0.466378\pi$
$163$	71526.0	0.210860	0.105430	+	0.994427i	$0.466378\pi$
$164$	369710.	1.07338
$165$	−53498.8	−0.152980
$166$	−870492.	−2.45185
$167$	446807.	1.23974	0.619868	−	0.784706i	$-0.287186\pi$
$167$	446807.	1.23974	0.619868	+	0.784706i	$0.287186\pi$
$168$	−21039.0	−0.0575111
$169$	110522.	0.297669
$170$	−300512.	−0.797517
$171$	−25190.0	−0.0658776
$172$	102292.	0.263645
$173$	−535762.	−1.36100	−0.680498	−	0.732750i	$-0.738237\pi$
$173$	−535762.	−1.36100	−0.680498	+	0.732750i	$0.738237\pi$
$174$	−214598.	−0.537344
$175$	157784.	0.389465
$176$	121592.	0.295885
$177$	−483789.	−1.16071
$178$	−841754.	−1.99129
$179$	−535501.	−1.24919	−0.624593	−	0.780950i	$-0.714735\pi$
$179$	−535501.	−1.24919	−0.624593	+	0.780950i	$0.714735\pi$
$180$	56845.5	0.130772
$181$	−515787.	−1.17024	−0.585119	−	0.810947i	$-0.698952\pi$
$181$	−515787.	−1.17024	−0.585119	+	0.810947i	$0.698952\pi$
$182$	−1.40830e6	−3.15149
$183$	519120.	1.14588
$184$	1404.42	0.00305810
$185$	−111205.	−0.238888
$186$	441280.	0.935259
$187$	−180983.	−0.378471
$188$	−350185.	−0.722608
$189$	−773400.	−1.57489
$190$	72530.0	0.145758
$191$	−89992.9	−0.178495	−0.0892473	−	0.996009i	$-0.528446\pi$
$191$	−89992.9	−0.178495	−0.0892473	+	0.996009i	$0.528446\pi$
$192$	−600559.	−1.17572
$193$	−431028.	−0.832937	−0.416469	−	0.909150i	$-0.636732\pi$
$193$	−431028.	−0.832937	−0.416469	+	0.909150i	$0.636732\pi$
$194$	290659.	0.554472
$195$	306901.	0.577979
$196$	1.52916e6	2.84323
$197$	−1.04532e6	−1.91905	−0.959523	−	0.281632i	$-0.909124\pi$
$197$	−1.04532e6	−1.91905	−0.959523	+	0.281632i	$0.909124\pi$
$198$	67854.1	0.123002
$199$	−805532.	−1.44195	−0.720975	−	0.692961i	$-0.756306\pi$
$199$	−805532.	−1.44195	−0.720975	+	0.692961i	$0.756306\pi$
$200$	−2945.12	−0.00520629
$201$	362528.	0.632923
$202$	983239.	1.69543
$203$	381171.	0.649202
$204$	861997.	1.45021
$205$	283639.	0.471391
$206$	1.41206e6	2.31838
$207$	−20796.6	−0.0337340
$208$	−697526.	−1.11790
$209$	43681.0	0.0691714
$210$	−897041.	−1.40367
$211$	574565.	0.888451	0.444225	−	0.895915i	$-0.353479\pi$
$211$	574565.	0.888451	0.444225	+	0.895915i	$0.353479\pi$
$212$	344700.	0.526747
$213$	−18348.8	−0.0277113
$214$	−281012.	−0.419460
$215$	78477.5	0.115784
$216$	14435.9	0.0210528
$217$	−783807.	−1.12995
$218$	−1.87980e6	−2.67899
$219$	−627178.	−0.883651
$220$	−98573.7	−0.137311
$221$	1.03823e6	1.42992
$222$	632226.	0.860973
$223$	−88451.2	−0.119108	−0.0595541	−	0.998225i	$-0.518968\pi$
$223$	−88451.2	−0.119108	−0.0595541	+	0.998225i	$0.518968\pi$
$224$	2.07686e6	2.76559
$225$	43611.5	0.0574307
$226$	−920100.	−1.19830
$227$	714801.	0.920705	0.460352	−	0.887736i	$-0.347723\pi$
$227$	714801.	0.920705	0.460352	+	0.887736i	$0.347723\pi$
$228$	−208047.	−0.265048
$229$	−1.32664e6	−1.67172	−0.835859	−	0.548944i	$-0.815030\pi$
$229$	−1.32664e6	−1.67172	−0.835859	+	0.548944i	$0.815030\pi$
$230$	59880.2	0.0746386
$231$	−540241.	−0.666127
$232$	−7114.75	−0.00867840
$233$	156137.	0.188416	0.0942078	−	0.995553i	$-0.469968\pi$
$233$	156137.	0.188416	0.0942078	+	0.995553i	$0.469968\pi$
$234$	−389252.	−0.464720
$235$	−268659.	−0.317345
$236$	−891402.	−1.04182
$237$	1.01940e6	1.17889
$238$	−3.03463e6	−3.47267
$239$	1.54505e6	1.74963	0.874816	−	0.484455i	$-0.160982\pi$
$239$	1.54505e6	1.74963	0.874816	+	0.484455i	$0.160982\pi$
$240$	−444302.	−0.497909
$241$	−596177.	−0.661199	−0.330600	−	0.943771i	$-0.607251\pi$
$241$	−596177.	−0.661199	−0.330600	+	0.943771i	$0.607251\pi$
$242$	−117663.	−0.129152
$243$	−513646.	−0.558018
$244$	956501.	1.02852
$245$	1.17316e6	1.24865
$246$	−1.61256e6	−1.69894
$247$	−250581.	−0.261340
$248$	14630.2	0.0151050
$249$	1.91563e6	1.95801
$250$	−125571.	−0.127069
$251$	1.60655e6	1.60957	0.804786	−	0.593565i	$-0.202280\pi$
$251$	1.60655e6	1.60957	0.804786	+	0.593565i	$0.202280\pi$
$252$	574037.	0.569427
$253$	36062.7	0.0354207
$254$	−814666.	−0.792310
$255$	661318.	0.636883
$256$	1.00910e6	0.962353
$257$	612310.	0.578281	0.289140	−	0.957287i	$-0.406631\pi$
$257$	612310.	0.578281	0.289140	+	0.957287i	$0.406631\pi$
$258$	−446163.	−0.417296
$259$	−1.12297e6	−1.04020
$260$	565478.	0.518779
$261$	105355.	0.0957317
$262$	−2.29557e6	−2.06603
$263$	−1.16877e6	−1.04194	−0.520968	−	0.853576i	$-0.674429\pi$
$263$	−1.16877e6	−1.04194	−0.520968	+	0.853576i	$0.674429\pi$
$264$	10083.9	0.00890465
$265$	264452.	0.231330
$266$	732421.	0.634683
$267$	1.85239e6	1.59021
$268$	667972.	0.568096
$269$	186910.	0.157489	0.0787446	−	0.996895i	$-0.474909\pi$
$269$	186910.	0.157489	0.0787446	+	0.996895i	$0.474909\pi$
$270$	615504.	0.513832
$271$	−973695.	−0.805378	−0.402689	−	0.915337i	$-0.631924\pi$
$271$	−973695.	−0.805378	−0.402689	+	0.915337i	$0.631924\pi$
$272$	−1.50304e6	−1.23183
$273$	3.09915e6	2.51672
$274$	−1.37837e6	−1.10915
$275$	−75625.0	−0.0603023
$276$	−171762.	−0.135723
$277$	1.95663e6	1.53218	0.766090	−	0.642734i	$-0.222200\pi$
$277$	1.95663e6	1.53218	0.766090	+	0.642734i	$0.222200\pi$
$278$	2.36740e6	1.83722
$279$	−216644.	−0.166623
$280$	−29740.4	−0.0226700
$281$	−1.45028e6	−1.09568	−0.547841	−	0.836582i	$-0.684550\pi$
$281$	−1.45028e6	−1.09568	−0.547841	+	0.836582i	$0.684550\pi$
$282$	1.52739e6	1.14374
$283$	−684491.	−0.508044	−0.254022	−	0.967198i	$-0.581754\pi$
$283$	−684491.	−0.508044	−0.254022	+	0.967198i	$0.581754\pi$
$284$	−33808.3	−0.0248730
$285$	−159612.	−0.116400
$286$	674988.	0.487956
$287$	2.86424e6	2.05260
$288$	574044.	0.407816
$289$	817336.	0.575647
$290$	−303352.	−0.211813
$291$	−639634.	−0.442792
$292$	−1.15560e6	−0.793142
$293$	−1.62714e6	−1.10728	−0.553638	−	0.832757i	$-0.686761\pi$
$293$	−1.62714e6	−1.10728	−0.553638	+	0.832757i	$0.686761\pi$
$294$	−6.66969e6	−4.50026
$295$	−683877.	−0.457533
$296$	20960.7	0.0139052
$297$	370686.	0.243846
$298$	−197471.	−0.128814
$299$	−206877.	−0.133824
$300$	360192.	0.231063
$301$	792481.	0.504165
$302$	2.44348e6	1.54167
$303$	−2.16375e6	−1.35394
$304$	362766.	0.225135
$305$	733820.	0.451689
$306$	−838770.	−0.512081
$307$	2.79408e6	1.69197	0.845986	−	0.533205i	$-0.179013\pi$
$307$	2.79408e6	1.69197	0.845986	+	0.533205i	$0.179013\pi$
$308$	−995416.	−0.597899
$309$	−3.10743e6	−1.85142
$310$	623787.	0.368665
$311$	2.76397e6	1.62044	0.810220	−	0.586126i	$-0.199348\pi$
$311$	2.76397e6	1.62044	0.810220	+	0.586126i	$0.199348\pi$
$312$	−57847.1	−0.0336430
$313$	−1.17230e6	−0.676363	−0.338181	−	0.941081i	$-0.609812\pi$
$313$	−1.17230e6	−0.676363	−0.338181	+	0.941081i	$0.609812\pi$
$314$	811038.	0.464213
$315$	440397.	0.250074
$316$	1.87828e6	1.05814
$317$	−1.61697e6	−0.903760	−0.451880	−	0.892079i	$-0.649246\pi$
$317$	−1.61697e6	−0.903760	−0.451880	+	0.892079i	$0.649246\pi$
$318$	−1.50347e6	−0.833733
$319$	−182693.	−0.100518
$320$	−848941.	−0.463450
$321$	618405.	0.334974
$322$	604681.	0.325003
$323$	−539957.	−0.287974
$324$	−2.31807e6	−1.22677
$325$	433831.	0.227831
$326$	−574823.	−0.299565
$327$	4.13676e6	2.13940
$328$	−53462.5	−0.0274388
$329$	−2.71297e6	−1.38183
$330$	429946.	0.217335
$331$	2.87854e6	1.44411	0.722057	−	0.691833i	$-0.243197\pi$
$331$	2.87854e6	1.44411	0.722057	+	0.691833i	$0.243197\pi$
$332$	3.52964e6	1.75746
$333$	−310387.	−0.153389
$334$	−3.59080e6	−1.76126
$335$	512463.	0.249489
$336$	−4.48665e6	−2.16807
$337$	−1.42570e6	−0.683841	−0.341920	−	0.939729i	$-0.611077\pi$
$337$	−1.42570e6	−0.683841	−0.341920	+	0.939729i	$0.611077\pi$
$338$	−888220.	−0.422891
$339$	2.02480e6	0.956938
$340$	1.21851e6	0.571650
$341$	375674.	0.174954
$342$	202441.	0.0935907
$343$	7.60378e6	3.48975
$344$	−14792.1	−0.00673957
$345$	−131774.	−0.0596051
$346$	4.30569e6	1.93354
$347$	−2.34446e6	−1.04525	−0.522623	−	0.852564i	$-0.675046\pi$
$347$	−2.34446e6	−1.04525	−0.522623	+	0.852564i	$0.675046\pi$
$348$	870143.	0.385161
$349$	−815978.	−0.358604	−0.179302	−	0.983794i	$-0.557384\pi$
$349$	−815978.	−0.358604	−0.179302	+	0.983794i	$0.557384\pi$
$350$	−1.26804e6	−0.553304
$351$	−2.12648e6	−0.921283
$352$	−995428.	−0.428206
$353$	4.01563e6	1.71521	0.857605	−	0.514309i	$-0.171952\pi$
$353$	4.01563e6	1.71521	0.857605	+	0.514309i	$0.171952\pi$
$354$	3.88800e6	1.64899
$355$	−25937.5	−0.0109234
$356$	3.41311e6	1.42733
$357$	6.67811e6	2.77321
$358$	4.30358e6	1.77469
$359$	499384.	0.204502	0.102251	−	0.994759i	$-0.467395\pi$
$359$	499384.	0.204502	0.102251	+	0.994759i	$0.467395\pi$
$360$	−8220.22	−0.00334293
$361$	130321.	0.0526316
$362$	4.14516e6	1.66253
$363$	258934.	0.103139
$364$	5.71031e6	2.25895
$365$	−886569.	−0.348322
$366$	−4.17194e6	−1.62793
$367$	−1.30221e6	−0.504678	−0.252339	−	0.967639i	$-0.581200\pi$
$367$	−1.30221e6	−0.504678	−0.252339	+	0.967639i	$0.581200\pi$
$368$	299497.	0.115285
$369$	791675.	0.302678
$370$	893704.	0.339382
$371$	2.67048e6	1.00729
$372$	−1.78929e6	−0.670382
$373$	2.58425e6	0.961749	0.480875	−	0.876789i	$-0.340319\pi$
$373$	2.58425e6	0.961749	0.480875	+	0.876789i	$0.340319\pi$
$374$	1.45448e6	0.537686
$375$	276337.	0.101475
$376$	50639.0	0.0184721
$377$	1.04804e6	0.379772
$378$	6.21548e6	2.23741
$379$	3.08828e6	1.10438	0.552190	−	0.833718i	$-0.313792\pi$
$379$	3.08828e6	1.10438	0.552190	+	0.833718i	$0.313792\pi$
$380$	−294092.	−0.104478
$381$	1.79278e6	0.632725
$382$	723234.	0.253583
$383$	576184.	0.200708	0.100354	−	0.994952i	$-0.468002\pi$
$383$	576184.	0.200708	0.100354	+	0.994952i	$0.468002\pi$
$384$	170647.	0.0590569
$385$	−763676.	−0.262577
$386$	3.46398e6	1.18334
$387$	219041.	0.0743444
$388$	−1.17855e6	−0.397438
$389$	1.84894e6	0.619512	0.309756	−	0.950816i	$-0.399753\pi$
$389$	1.84894e6	0.619512	0.309756	+	0.950816i	$0.399753\pi$
$390$	−2.46643e6	−0.821122
$391$	−445784.	−0.147463
$392$	−221126.	−0.0726817
$393$	5.05171e6	1.64990
$394$	8.40081e6	2.72634
$395$	1.44100e6	0.464700
$396$	−275132.	−0.0881665
$397$	531071.	0.169113	0.0845563	−	0.996419i	$-0.473053\pi$
$397$	531071.	0.169113	0.0845563	+	0.996419i	$0.473053\pi$
$398$	6.47371e6	2.04854
$399$	−1.61179e6	−0.506847
$400$	−628058.	−0.196268
$401$	−1.77159e6	−0.550178	−0.275089	−	0.961419i	$-0.588707\pi$
$401$	−1.77159e6	−0.550178	−0.275089	+	0.961419i	$0.588707\pi$
$402$	−2.91348e6	−0.899179
$403$	−2.15509e6	−0.661003
$404$	−3.98680e6	−1.21526
$405$	−1.77840e6	−0.538757
$406$	−3.06331e6	−0.922307
$407$	538231.	0.161058
$408$	−124650.	−0.0370717
$409$	4.92861e6	1.45685	0.728427	−	0.685124i	$-0.240252\pi$
$409$	4.92861e6	1.45685	0.728427	+	0.685124i	$0.240252\pi$
$410$	−2.27948e6	−0.669695
$411$	3.03330e6	0.885749
$412$	−5.72557e6	−1.66179
$413$	−6.90592e6	−1.99226
$414$	167134.	0.0479251
$415$	2.70791e6	0.771816
$416$	5.71038e6	1.61782
$417$	−5.20979e6	−1.46717
$418$	−351045.	−0.0982703
$419$	−1.07661e6	−0.299586	−0.149793	−	0.988717i	$-0.547861\pi$
$419$	−1.07661e6	−0.299586	−0.149793	+	0.988717i	$0.547861\pi$
$420$	3.63729e6	1.00613
$421$	946501.	0.260265	0.130133	−	0.991497i	$-0.458460\pi$
$421$	946501.	0.260265	0.130133	+	0.991497i	$0.458460\pi$
$422$	−4.61753e6	−1.26220
$423$	−749864.	−0.203766
$424$	−49845.9	−0.0134653
$425$	934828.	0.251050
$426$	147461.	0.0393689
$427$	7.41025e6	1.96681
$428$	1.13944e6	0.300664
$429$	−1.48540e6	−0.389673
$430$	−630690.	−0.164492
$431$	3.50951e6	0.910025	0.455013	−	0.890485i	$-0.349635\pi$
$431$	3.50951e6	0.910025	0.455013	+	0.890485i	$0.349635\pi$
$432$	3.07851e6	0.793654
$433$	−3.31385e6	−0.849400	−0.424700	−	0.905334i	$-0.639620\pi$
$433$	−3.31385e6	−0.849400	−0.424700	+	0.905334i	$0.639620\pi$
$434$	6.29911e6	1.60530
$435$	667567.	0.169150
$436$	7.62216e6	1.92027
$437$	107592.	0.0269511
$438$	5.04036e6	1.25538
$439$	5.63217e6	1.39481	0.697404	−	0.716678i	$-0.254338\pi$
$439$	5.63217e6	1.39481	0.697404	+	0.716678i	$0.254338\pi$
$440$	14254.4	0.00351008
$441$	3.27444e6	0.801754
$442$	−8.34377e6	−2.03145
$443$	4.14598e6	1.00373	0.501866	−	0.864946i	$-0.332647\pi$
$443$	4.14598e6	1.00373	0.501866	+	0.864946i	$0.332647\pi$
$444$	−2.56352e6	−0.617135
$445$	2.61851e6	0.626838
$446$	710844.	0.169214
$447$	434562.	0.102869
$448$	−8.57276e6	−2.01802
$449$	−5.20503e6	−1.21845	−0.609224	−	0.792998i	$-0.708519\pi$
$449$	−5.20503e6	−1.21845	−0.609224	+	0.792998i	$0.708519\pi$
$450$	−350486.	−0.0815905
$451$	−1.37281e6	−0.317812
$452$	3.73079e6	0.858923
$453$	−5.37720e6	−1.23115
$454$	−5.74454e6	−1.30802
$455$	4.38090e6	0.992054
$456$	30084.9	0.00677543
$457$	−344127.	−0.0770775	−0.0385388	−	0.999257i	$-0.512270\pi$
$457$	−344127.	−0.0770775	−0.0385388	+	0.999257i	$0.512270\pi$
$458$	1.06616e7	2.37497
$459$	−4.58218e6	−1.01517
$460$	−242800.	−0.0535000
$461$	3.35141e6	0.734473	0.367236	−	0.930128i	$-0.380304\pi$
$461$	3.35141e6	0.734473	0.367236	+	0.930128i	$0.380304\pi$
$462$	4.34168e6	0.946352
$463$	3.65646e6	0.792699	0.396349	−	0.918100i	$-0.370277\pi$
$463$	3.65646e6	0.792699	0.396349	+	0.918100i	$0.370277\pi$
$464$	−1.51725e6	−0.327161
$465$	−1.37273e6	−0.294409
$466$	−1.25481e6	−0.267678
$467$	816691.	0.173287	0.0866435	−	0.996239i	$-0.472386\pi$
$467$	816691.	0.173287	0.0866435	+	0.996239i	$0.472386\pi$
$468$	1.57833e6	0.333106
$469$	5.17495e6	1.08636
$470$	2.15910e6	0.450845
$471$	−1.78480e6	−0.370712
$472$	128902.	0.0266321
$473$	−379831.	−0.0780617
$474$	−8.19245e6	−1.67482
$475$	−225625.	−0.0458831
$476$	1.23047e7	2.48916
$477$	738120.	0.148536
$478$	−1.24169e7	−2.48566
$479$	1.81103e6	0.360650	0.180325	−	0.983607i	$-0.442285\pi$
$479$	1.81103e6	0.360650	0.180325	+	0.983607i	$0.442285\pi$
$480$	3.63733e6	0.720576
$481$	−3.08762e6	−0.608501
$482$	4.79121e6	0.939351
$483$	−1.33068e6	−0.259541
$484$	477097.	0.0925748
$485$	−904177.	−0.174542
$486$	4.12795e6	0.792763
$487$	−2.92664e6	−0.559173	−0.279587	−	0.960120i	$-0.590197\pi$
$487$	−2.92664e6	−0.559173	−0.279587	+	0.960120i	$0.590197\pi$
$488$	−138316.	−0.0262920
$489$	1.26498e6	0.239227
$490$	−9.42817e6	−1.77393
$491$	5.64423e6	1.05658	0.528289	−	0.849065i	$-0.322834\pi$
$491$	5.64423e6	1.05658	0.528289	+	0.849065i	$0.322834\pi$
$492$	6.53853e6	1.21778
$493$	2.25833e6	0.418476
$494$	2.01381e6	0.371279
$495$	−211079.	−0.0387198
$496$	3.11994e6	0.569431
$497$	−261922.	−0.0475643
$498$	−1.53951e7	−2.78170
$499$	−9.95662e6	−1.79003	−0.895016	−	0.446035i	$-0.852836\pi$
$499$	−9.95662e6	−1.79003	−0.895016	+	0.446035i	$0.852836\pi$
$500$	509162.	0.0910816
$501$	7.90203e6	1.40651
$502$	−1.29112e7	−2.28668
$503$	−4.89131e6	−0.861996	−0.430998	−	0.902353i	$-0.641838\pi$
$503$	−4.89131e6	−0.861996	−0.430998	+	0.902353i	$0.641838\pi$
$504$	−83009.4	−0.0145563
$505$	−3.05864e6	−0.533704
$506$	−289820.	−0.0503213
$507$	1.95465e6	0.337714
$508$	3.30328e6	0.567918
$509$	417662.	0.0714547	0.0357273	−	0.999362i	$-0.488625\pi$
$509$	417662.	0.0714547	0.0357273	+	0.999362i	$0.488625\pi$
$510$	−5.31472e6	−0.904805
$511$	−8.95274e6	−1.51671
$512$	−8.41846e6	−1.41925
$513$	1.10593e6	0.185539
$514$	−4.92087e6	−0.821550
$515$	−4.39261e6	−0.729802
$516$	1.80909e6	0.299113
$517$	1.30031e6	0.213954
$518$	9.02479e6	1.47779
$519$	−9.47524e6	−1.54409
$520$	−81771.8	−0.0132616
$521$	8.07827e6	1.30384	0.651920	−	0.758288i	$-0.273964\pi$
$521$	8.07827e6	1.30384	0.651920	+	0.758288i	$0.273964\pi$
$522$	−846696.	−0.136004
$523$	−476367.	−0.0761531	−0.0380765	−	0.999275i	$-0.512123\pi$
$523$	−476367.	−0.0761531	−0.0380765	+	0.999275i	$0.512123\pi$
$524$	9.30798e6	1.48091
$525$	2.79050e6	0.441859
$526$	9.39292e6	1.48025
$527$	−4.64384e6	−0.728368
$528$	2.15042e6	0.335690
$529$	−6.34752e6	−0.986199
$530$	−2.12528e6	−0.328645
$531$	−1.90879e6	−0.293780
$532$	−2.96979e6	−0.454933
$533$	7.87529e6	1.20074
$534$	−1.48869e7	−2.25918
$535$	874168.	0.132042
$536$	−96593.0	−0.0145222
$537$	−9.47062e6	−1.41724
$538$	−1.50211e6	−0.223741
$539$	−5.67809e6	−0.841842
$540$	−2.49572e6	−0.368309
$541$	−5.87890e6	−0.863580	−0.431790	−	0.901974i	$-0.642118\pi$
$541$	−5.87890e6	−0.863580	−0.431790	+	0.901974i	$0.642118\pi$
$542$	7.82516e6	1.14418
$543$	−9.12198e6	−1.32767
$544$	1.23048e7	1.78270
$545$	5.84766e6	0.843317
$546$	−2.49065e7	−3.57545
$547$	−4.25294e6	−0.607744	−0.303872	−	0.952713i	$-0.598280\pi$
$547$	−4.25294e6	−0.607744	−0.303872	+	0.952713i	$0.598280\pi$
$548$	5.58898e6	0.795026
$549$	2.04819e6	0.290028
$550$	607765.	0.0856700
$551$	−545059.	−0.0764830
$552$	24837.9	0.00346950
$553$	1.45515e7	2.02347
$554$	−1.57246e7	−2.17673
$555$	−1.96672e6	−0.271025
$556$	−9.59926e6	−1.31689
$557$	−6.44470e6	−0.880166	−0.440083	−	0.897957i	$-0.645051\pi$
$557$	−6.44470e6	−0.880166	−0.440083	+	0.897957i	$0.645051\pi$
$558$	1.74107e6	0.236718
$559$	2.17894e6	0.294928
$560$	−6.34225e6	−0.854621
$561$	−3.20078e6	−0.429386
$562$	1.16552e7	1.55661
$563$	4.11109e6	0.546620	0.273310	−	0.961926i	$-0.411881\pi$
$563$	4.11109e6	0.546620	0.273310	+	0.961926i	$0.411881\pi$
$564$	−6.19321e6	−0.819819
$565$	2.86223e6	0.377210
$566$	5.50095e6	0.721767
$567$	−1.79586e7	−2.34594
$568$	4888.90	0.000635829 0
$569$	−9.39478e6	−1.21648	−0.608242	−	0.793752i	$-0.708125\pi$
$569$	−9.39478e6	−1.21648	−0.608242	+	0.793752i	$0.708125\pi$
$570$	1.28273e6	0.165367
$571$	2.35269e6	0.301978	0.150989	−	0.988535i	$-0.451754\pi$
$571$	2.35269e6	0.301978	0.150989	+	0.988535i	$0.451754\pi$
$572$	−2.73692e6	−0.349761
$573$	−1.59157e6	−0.202507
$574$	−2.30187e7	−2.91609
$575$	−186274.	−0.0234954
$576$	−2.36951e6	−0.297579
$577$	−4.33713e6	−0.542329	−0.271165	−	0.962533i	$-0.587409\pi$
$577$	−4.33713e6	−0.542329	−0.271165	+	0.962533i	$0.587409\pi$
$578$	−6.56857e6	−0.817808
$579$	−7.62297e6	−0.944991
$580$	1.23002e6	0.151825
$581$	2.73450e7	3.36076
$582$	5.14046e6	0.629064
$583$	−1.27995e6	−0.155963
$584$	167107.	0.0202751
$585$	1.21088e6	0.146289
$586$	1.30766e7	1.57308
$587$	−9.06038e6	−1.08530	−0.542652	−	0.839958i	$-0.682580\pi$
$587$	−9.06038e6	−1.08530	−0.542652	+	0.839958i	$0.682580\pi$
$588$	2.70440e7	3.22573
$589$	1.12081e6	0.133120
$590$	5.49602e6	0.650007
$591$	−1.84871e7	−2.17721
$592$	4.46996e6	0.524202
$593$	7.07369e6	0.826055	0.413028	−	0.910718i	$-0.364471\pi$
$593$	7.07369e6	0.826055	0.413028	+	0.910718i	$0.364471\pi$
$594$	−2.97904e6	−0.346426
$595$	9.44007e6	1.09316
$596$	800698.	0.0923322
$597$	−1.42463e7	−1.63593
$598$	1.66258e6	0.190121
$599$	−1.41131e7	−1.60714	−0.803572	−	0.595208i	$-0.797070\pi$
$599$	−1.41131e7	−1.60714	−0.803572	+	0.595208i	$0.797070\pi$
$600$	−52086.1	−0.00590668
$601$	1.58253e7	1.78717	0.893583	−	0.448898i	$-0.148183\pi$
$601$	1.58253e7	1.78717	0.893583	+	0.448898i	$0.148183\pi$
$602$	−6.36882e6	−0.716255
$603$	1.43035e6	0.160195
$604$	−9.90771e6	−1.10505
$605$	366025.	0.0406558
$606$	1.73891e7	1.92352
$607$	−4.40311e6	−0.485052	−0.242526	−	0.970145i	$-0.577976\pi$
$607$	−4.40311e6	−0.485052	−0.242526	+	0.970145i	$0.577976\pi$
$608$	−2.96983e6	−0.325816
$609$	6.74122e6	0.736538
$610$	−5.89739e6	−0.641705
$611$	−7.45937e6	−0.808349
$612$	3.40101e6	0.367054
$613$	−1.50174e7	−1.61415	−0.807074	−	0.590451i	$-0.798950\pi$
$613$	−1.50174e7	−1.61415	−0.807074	+	0.590451i	$0.798950\pi$
$614$	−2.24548e7	−2.40375
$615$	5.01631e6	0.534806
$616$	143943.	0.0152841
$617$	−5.18232e6	−0.548039	−0.274019	−	0.961724i	$-0.588353\pi$
$617$	−5.18232e6	−0.548039	−0.274019	+	0.961724i	$0.588353\pi$
$618$	2.49731e7	2.63027
$619$	6.31595e6	0.662540	0.331270	−	0.943536i	$-0.392523\pi$
$619$	6.31595e6	0.662540	0.331270	+	0.943536i	$0.392523\pi$
$620$	−2.52931e6	−0.264254
$621$	913047.	0.0950089
$622$	−2.22128e7	−2.30212
$623$	2.64423e7	2.72947
$624$	−1.23361e7	−1.26829
$625$	390625.	0.0400000
$626$	9.42130e6	0.960893
$627$	772522.	0.0784769
$628$	−3.28857e6	−0.332742
$629$	−6.65327e6	−0.670515
$630$	−3.53928e6	−0.355274
$631$	−1.05077e7	−1.05059	−0.525296	−	0.850920i	$-0.676045\pi$
$631$	−1.05077e7	−1.05059	−0.525296	+	0.850920i	$0.676045\pi$
$632$	−271612.	−0.0270493
$633$	1.01615e7	1.00797
$634$	1.29949e7	1.28395
$635$	2.53425e6	0.249411
$636$	6.09621e6	0.597609
$637$	3.25730e7	3.18060
$638$	1.46822e6	0.142804
$639$	−72395.0	−0.00701385
$640$	241224.	0.0232793
$641$	1.39048e7	1.33666	0.668330	−	0.743865i	$-0.267010\pi$
$641$	1.39048e7	1.33666	0.668330	+	0.743865i	$0.267010\pi$
$642$	−4.96985e6	−0.475889
$643$	−3.01219e6	−0.287312	−0.143656	−	0.989628i	$-0.545886\pi$
$643$	−3.01219e6	−0.287312	−0.143656	+	0.989628i	$0.545886\pi$
$644$	−2.45184e6	−0.232958
$645$	1.38792e6	0.131360
$646$	4.33940e6	0.409117
$647$	1.90418e7	1.78833	0.894163	−	0.447742i	$-0.147772\pi$
$647$	1.90418e7	1.78833	0.894163	+	0.447742i	$0.147772\pi$
$648$	335207.	0.0313600
$649$	3.30996e6	0.308469
$650$	−3.48651e6	−0.323674
$651$	−1.38621e7	−1.28196
$652$	2.33077e6	0.214724
$653$	7.99492e6	0.733721	0.366860	−	0.930276i	$-0.380433\pi$
$653$	7.99492e6	0.733721	0.366860	+	0.930276i	$0.380433\pi$
$654$	−3.32453e7	−3.03939
$655$	7.14102e6	0.650364
$656$	−1.14011e7	−1.03440
$657$	−2.47453e6	−0.223656
$658$	2.18030e7	1.96314
$659$	582846.	0.0522806	0.0261403	−	0.999658i	$-0.491678\pi$
$659$	582846.	0.0522806	0.0261403	+	0.999658i	$0.491678\pi$
$660$	−1.74333e6	−0.155783
$661$	6.36666e6	0.566772	0.283386	−	0.959006i	$-0.408542\pi$
$661$	6.36666e6	0.566772	0.283386	+	0.959006i	$0.408542\pi$
$662$	−2.31335e7	−2.05162
$663$	1.83616e7	1.62228
$664$	−510408.	−0.0449259
$665$	−2.27840e6	−0.199791
$666$	2.49445e6	0.217916
$667$	−449997.	−0.0391647
$668$	1.45598e7	1.26245
$669$	−1.56431e6	−0.135132
$670$	−4.11844e6	−0.354443
$671$	−3.55169e6	−0.304529
$672$	3.67305e7	3.13764
$673$	−1.37478e6	−0.117003	−0.0585015	−	0.998287i	$-0.518632\pi$
$673$	−1.37478e6	−0.117003	−0.0585015	+	0.998287i	$0.518632\pi$
$674$	1.14578e7	0.971517
$675$	−1.91470e6	−0.161749
$676$	3.60152e6	0.303123
$677$	4.07760e6	0.341926	0.170963	−	0.985277i	$-0.445312\pi$
$677$	4.07760e6	0.341926	0.170963	+	0.985277i	$0.445312\pi$
$678$	−1.62725e7	−1.35950
$679$	−9.13055e6	−0.760016
$680$	−176204.	−0.0146131
$681$	1.26416e7	1.04457
$682$	−3.01913e6	−0.248554
$683$	1.43600e6	0.117788	0.0588942	−	0.998264i	$-0.481243\pi$
$683$	1.43600e6	0.117788	0.0588942	+	0.998264i	$0.481243\pi$
$684$	−820849.	−0.0670846
$685$	4.28782e6	0.349149
$686$	−6.11083e7	−4.95781
$687$	−2.34623e7	−1.89661
$688$	−3.15446e6	−0.254070
$689$	7.34254e6	0.589248
$690$	1.05901e6	0.0846796
$691$	−1.22234e7	−0.973859	−0.486929	−	0.873441i	$-0.661883\pi$
$691$	−1.22234e7	−0.973859	−0.486929	+	0.873441i	$0.661883\pi$
$692$	−1.74585e7	−1.38593
$693$	−2.13152e6	−0.168600
$694$	1.88414e7	1.48496
$695$	−7.36448e6	−0.578336
$696$	−125828.	−0.00984589
$697$	1.69698e7	1.32311
$698$	6.55766e6	0.509460
$699$	2.76137e6	0.213763
$700$	5.14161e6	0.396601
$701$	1.50318e7	1.15536	0.577679	−	0.816264i	$-0.303959\pi$
$701$	1.50318e7	1.15536	0.577679	+	0.816264i	$0.303959\pi$
$702$	1.70896e7	1.30885
$703$	1.60580e6	0.122547
$704$	4.10887e6	0.312458
$705$	−4.75138e6	−0.360037
$706$	−3.22719e7	−2.43676
$707$	−3.08867e7	−2.32393
$708$	−1.57649e7	−1.18198
$709$	2.64553e6	0.197650	0.0988249	−	0.995105i	$-0.468492\pi$
$709$	2.64553e6	0.197650	0.0988249	+	0.995105i	$0.468492\pi$
$710$	208448.	0.0155186
$711$	4.02204e6	0.298381
$712$	−493558.	−0.0364870
$713$	925334.	0.0681671
$714$	−5.36690e7	−3.93984
$715$	−2.09974e6	−0.153603
$716$	−1.74500e7	−1.27208
$717$	2.73250e7	1.98501
$718$	−4.01333e6	−0.290532
$719$	−2.41777e7	−1.74418	−0.872092	−	0.489343i	$-0.837237\pi$
$719$	−2.41777e7	−1.74418	−0.872092	+	0.489343i	$0.837237\pi$
$720$	−1.75299e6	−0.126023
$721$	−4.43574e7	−3.17781
$722$	−1.04733e6	−0.0747725
$723$	−1.05437e7	−0.750149
$724$	−1.68076e7	−1.19168
$725$	943662.	0.0666763
$726$	−2.08094e6	−0.146527
$727$	9.36391e6	0.657084	0.328542	−	0.944489i	$-0.393443\pi$
$727$	9.36391e6	0.657084	0.328542	+	0.944489i	$0.393443\pi$
$728$	−825747.	−0.0577455
$729$	8.20198e6	0.571610
$730$	7.12497e6	0.494853
$731$	4.69523e6	0.324985
$732$	1.69162e7	1.16688
$733$	5.93516e6	0.408011	0.204006	−	0.978970i	$-0.434604\pi$
$733$	5.93516e6	0.408011	0.204006	+	0.978970i	$0.434604\pi$
$734$	1.04653e7	0.716985
$735$	2.07480e7	1.41663
$736$	−2.45187e6	−0.166841
$737$	−2.48032e6	−0.168205
$738$	−6.36234e6	−0.430008
$739$	1.23234e7	0.830079	0.415039	−	0.909803i	$-0.363768\pi$
$739$	1.23234e7	0.830079	0.415039	+	0.909803i	$0.363768\pi$
$740$	−3.62376e6	−0.243265
$741$	−4.43165e6	−0.296497
$742$	−2.14615e7	−1.43104
$743$	1.08266e7	0.719483	0.359741	−	0.933052i	$-0.382865\pi$
$743$	1.08266e7	0.719483	0.359741	+	0.933052i	$0.382865\pi$
$744$	258742.	0.0171370
$745$	614290.	0.0405492
$746$	−2.07685e7	−1.36633
$747$	7.55814e6	0.495579
$748$	−5.89757e6	−0.385406
$749$	8.82751e6	0.574955
$750$	−2.22080e6	−0.144164
$751$	5.27152e6	0.341064	0.170532	−	0.985352i	$-0.445451\pi$
$751$	5.27152e6	0.341064	0.170532	+	0.985352i	$0.445451\pi$
$752$	1.07990e7	0.696365
$753$	2.84127e7	1.82610
$754$	−8.42262e6	−0.539534
$755$	−7.60112e6	−0.485300
$756$	−2.52023e7	−1.60374
$757$	−2.07680e7	−1.31721	−0.658606	−	0.752488i	$-0.728854\pi$
$757$	−2.07680e7	−1.31721	−0.658606	+	0.752488i	$0.728854\pi$
$758$	−2.48191e7	−1.56897
$759$	637788.	0.0401857
$760$	42527.5	0.00267077
$761$	−2.47178e7	−1.54721	−0.773604	−	0.633670i	$-0.781548\pi$
$761$	−2.47178e7	−1.54721	−0.773604	+	0.633670i	$0.781548\pi$
$762$	−1.44078e7	−0.898898
$763$	5.90508e7	3.67210
$764$	−2.93254e6	−0.181765
$765$	2.60923e6	0.161198
$766$	−4.63054e6	−0.285141
$767$	−1.89880e7	−1.16544
$768$	1.78465e7	1.09182
$769$	−3.60513e6	−0.219839	−0.109920	−	0.993940i	$-0.535059\pi$
$769$	−3.60513e6	−0.219839	−0.109920	+	0.993940i	$0.535059\pi$
$770$	6.13733e6	0.373037
$771$	1.08290e7	0.656076
$772$	−1.40456e7	−0.848200
$773$	−2.49356e7	−1.50097	−0.750483	−	0.660889i	$-0.770179\pi$
$773$	−2.49356e7	−1.50097	−0.750483	+	0.660889i	$0.770179\pi$
$774$	−1.76034e6	−0.105619
$775$	−1.94046e6	−0.116052
$776$	170426.	0.0101597
$777$	−1.98603e7	−1.18014
$778$	−1.48592e7	−0.880127
$779$	−4.09575e6	−0.241819
$780$	1.00008e7	0.588570
$781$	125538.	0.00736455
$782$	3.58257e6	0.209497
$783$	−4.62548e6	−0.269620
$784$	−4.71560e7	−2.73998
$785$	−2.52296e6	−0.146129
$786$	−4.05984e7	−2.34397
$787$	−7.22316e6	−0.415710	−0.207855	−	0.978160i	$-0.566648\pi$
$787$	−7.22316e6	−0.415710	−0.207855	+	0.978160i	$0.566648\pi$
$788$	−3.40633e7	−1.95421
$789$	−2.06704e7	−1.18210
$790$	−1.15807e7	−0.660188
$791$	2.89033e7	1.64251
$792$	39785.9	0.00225380
$793$	2.03746e7	1.15055
$794$	−4.26798e6	−0.240255
$795$	4.67697e6	0.262450
$796$	−2.62493e7	−1.46837
$797$	−1.82177e7	−1.01589	−0.507947	−	0.861388i	$-0.669596\pi$
$797$	−1.82177e7	−1.01589	−0.507947	+	0.861388i	$0.669596\pi$
$798$	1.29533e7	0.720066
$799$	−1.60736e7	−0.890731
$800$	5.14167e6	0.284040
$801$	7.30862e6	0.402489
$802$	1.42375e7	0.781625
$803$	4.29099e6	0.234838
$804$	1.18134e7	0.644520
$805$	−1.88103e6	−0.102307
$806$	1.73195e7	0.939072
$807$	3.30560e6	0.178676
$808$	576516.	0.0310659
$809$	−9.68104e6	−0.520057	−0.260028	−	0.965601i	$-0.583732\pi$
$809$	−9.68104e6	−0.520057	−0.260028	+	0.965601i	$0.583732\pi$
$810$	1.42922e7	0.765399
$811$	−2.56707e7	−1.37052	−0.685261	−	0.728297i	$-0.740312\pi$
$811$	−2.56707e7	−1.37052	−0.685261	+	0.728297i	$0.740312\pi$
$812$	1.24210e7	0.661098
$813$	−1.72203e7	−0.913724
$814$	−4.32553e6	−0.228812
$815$	1.78815e6	0.0942996
$816$	−2.65821e7	−1.39754
$817$	−1.13322e6	−0.0593960
$818$	−3.96090e7	−2.06972
$819$	1.22277e7	0.636993
$820$	9.24276e6	0.480029
$821$	−4.35954e6	−0.225726	−0.112863	−	0.993611i	$-0.536002\pi$
$821$	−4.35954e6	−0.225726	−0.112863	+	0.993611i	$0.536002\pi$
$822$	−2.43773e7	−1.25836
$823$	−2.52820e7	−1.30110	−0.650552	−	0.759462i	$-0.725463\pi$
$823$	−2.52820e7	−1.30110	−0.650552	+	0.759462i	$0.725463\pi$
$824$	827954.	0.0424803
$825$	−1.33747e6	−0.0684146
$826$	5.54998e7	2.83036
$827$	1.43905e7	0.731666	0.365833	−	0.930681i	$-0.380784\pi$
$827$	1.43905e7	0.731666	0.365833	+	0.930681i	$0.380784\pi$
$828$	−677687.	−0.0343521
$829$	1.65390e7	0.835837	0.417919	−	0.908484i	$-0.362760\pi$
$829$	1.65390e7	0.835837	0.417919	+	0.908484i	$0.362760\pi$
$830$	−2.17623e7	−1.09650
$831$	3.46041e7	1.73830
$832$	−2.35710e7	−1.18051
$833$	7.01890e7	3.50474
$834$	4.18688e7	2.08437
$835$	1.11702e7	0.554427
$836$	1.42340e6	0.0704389
$837$	9.51144e6	0.469281
$838$	8.65221e6	0.425615
$839$	3.62990e7	1.78029	0.890144	−	0.455680i	$-0.150604\pi$
$839$	3.62990e7	1.78029	0.890144	+	0.455680i	$0.150604\pi$
$840$	−525975.	−0.0257198
$841$	−1.82315e7	−0.888857
$842$	−7.60662e6	−0.369753
$843$	−2.56489e7	−1.24308
$844$	1.87230e7	0.904730
$845$	2.76306e6	0.133122
$846$	6.02633e6	0.289485
$847$	3.69619e6	0.177030
$848$	−1.06298e7	−0.507617
$849$	−1.21056e7	−0.576390
$850$	−7.51280e6	−0.356660
$851$	1.32573e6	0.0627527
$852$	−597919.	−0.0282191
$853$	−2.60449e7	−1.22560	−0.612802	−	0.790237i	$-0.709958\pi$
$853$	−2.60449e7	−1.22560	−0.612802	+	0.790237i	$0.709958\pi$
$854$	−5.95530e7	−2.79421
$855$	−629749.	−0.0294613
$856$	−164770.	−0.00768588
$857$	1.99699e7	0.928805	0.464403	−	0.885624i	$-0.346269\pi$
$857$	1.99699e7	0.928805	0.464403	+	0.885624i	$0.346269\pi$
$858$	1.19375e7	0.553600
$859$	−2.70368e7	−1.25018	−0.625091	−	0.780552i	$-0.714938\pi$
$859$	−2.70368e7	−1.25018	−0.625091	+	0.780552i	$0.714938\pi$
$860$	2.55730e6	0.117906
$861$	5.06557e7	2.32873
$862$	−2.82044e7	−1.29285
$863$	4.13875e7	1.89165	0.945827	−	0.324671i	$-0.105253\pi$
$863$	4.13875e7	1.89165	0.945827	+	0.324671i	$0.105253\pi$
$864$	−2.52026e7	−1.14858
$865$	−1.33941e7	−0.608656
$866$	2.66319e7	1.20672
$867$	1.44550e7	0.653087
$868$	−2.55414e7	−1.15066
$869$	−6.97446e6	−0.313301
$870$	−5.36494e6	−0.240307
$871$	1.42286e7	0.635503
$872$	−1.10221e6	−0.0490879
$873$	−2.52368e6	−0.112072
$874$	−864670.	−0.0382888
$875$	3.94460e6	0.174174
$876$	−2.04374e7	−0.899842
$877$	2.44126e7	1.07180	0.535902	−	0.844280i	$-0.319972\pi$
$877$	2.44126e7	1.07180	0.535902	+	0.844280i	$0.319972\pi$
$878$	−4.52633e7	−1.98157
$879$	−2.87769e7	−1.25624
$880$	3.03980e6	0.132324
$881$	4.04052e7	1.75387	0.876936	−	0.480608i	$-0.159584\pi$
$881$	4.04052e7	1.75387	0.876936	+	0.480608i	$0.159584\pi$
$882$	−2.63153e7	−1.13903
$883$	2.59011e7	1.11794	0.558968	−	0.829189i	$-0.311197\pi$
$883$	2.59011e7	1.11794	0.558968	+	0.829189i	$0.311197\pi$
$884$	3.38320e7	1.45612
$885$	−1.20947e7	−0.519085
$886$	−3.33194e7	−1.42598
$887$	1.98283e7	0.846206	0.423103	−	0.906082i	$-0.360941\pi$
$887$	1.98283e7	0.846206	0.423103	+	0.906082i	$0.360941\pi$
$888$	370702.	0.0157758
$889$	2.55913e7	1.08602
$890$	−2.10439e7	−0.890534
$891$	8.60747e6	0.363230
$892$	−2.88230e6	−0.121291
$893$	3.87944e6	0.162795
$894$	−3.49238e6	−0.146143
$895$	−1.33875e7	−0.558653
$896$	2.43592e6	0.101366
$897$	−3.65874e6	−0.151827
$898$	4.18305e7	1.73102
$899$	−4.68773e6	−0.193447
$900$	1.42114e6	0.0584830
$901$	1.58219e7	0.649301
$902$	1.10327e7	0.451508
$903$	1.40155e7	0.571989
$904$	−539495.	−0.0219567
$905$	−1.28947e7	−0.523346
$906$	4.32142e7	1.74906
$907$	−4.70559e7	−1.89931	−0.949655	−	0.313297i	$-0.898566\pi$
$907$	−4.70559e7	−1.89931	−0.949655	+	0.313297i	$0.898566\pi$
$908$	2.32927e7	0.937575
$909$	−8.53708e6	−0.342688
$910$	−3.52074e7	−1.40939
$911$	1.35740e7	0.541893	0.270946	−	0.962594i	$-0.412663\pi$
$911$	1.35740e7	0.541893	0.270946	+	0.962594i	$0.412663\pi$
$912$	6.41572e6	0.255422
$913$	−1.31063e7	−0.520358
$914$	2.76559e6	0.109502
$915$	1.29780e7	0.512454
$916$	−4.32302e7	−1.70235
$917$	7.21113e7	2.83191
$918$	3.68250e7	1.44223
$919$	1.98297e7	0.774511	0.387255	−	0.921972i	$-0.373423\pi$
$919$	1.98297e7	0.774511	0.387255	+	0.921972i	$0.373423\pi$
$920$	35110.4	0.00136762
$921$	4.94148e7	1.91959
$922$	−2.69338e7	−1.04345
$923$	−720159.	−0.0278243
$924$	−1.76045e7	−0.678333
$925$	−2.78012e6	−0.106834
$926$	−2.93854e7	−1.12617
$927$	−1.22604e7	−0.468602
$928$	1.24211e7	0.473469
$929$	−1.12004e7	−0.425790	−0.212895	−	0.977075i	$-0.568289\pi$
$929$	−1.12004e7	−0.425790	−0.212895	+	0.977075i	$0.568289\pi$
$930$	1.10320e7	0.418261
$931$	−1.69404e7	−0.640546
$932$	5.08794e6	0.191868
$933$	4.88824e7	1.83843
$934$	−6.56339e6	−0.246185
$935$	−4.52457e6	−0.169258
$936$	−228236.	−0.00851519
$937$	−5.82466e6	−0.216731	−0.108366	−	0.994111i	$-0.534562\pi$
$937$	−5.82466e6	−0.216731	−0.108366	+	0.994111i	$0.534562\pi$
$938$	−4.15888e7	−1.54337
$939$	−2.07328e7	−0.767352
$940$	−8.75462e6	−0.323160
$941$	−2.76929e7	−1.01952	−0.509758	−	0.860318i	$-0.670265\pi$
$941$	−2.76929e7	−1.01952	−0.509758	+	0.860318i	$0.670265\pi$
$942$	1.43437e7	0.526663
$943$	−3.38142e6	−0.123828
$944$	2.74889e7	1.00399
$945$	−1.93350e7	−0.704311
$946$	3.05254e6	0.110900
$947$	−3.42402e7	−1.24068	−0.620342	−	0.784331i	$-0.713006\pi$
$947$	−3.42402e7	−1.24068	−0.620342	+	0.784331i	$0.713006\pi$
$948$	3.32184e7	1.20049
$949$	−2.46157e7	−0.887253
$950$	1.81325e6	0.0651851
$951$	−2.85969e7	−1.02534
$952$	−1.77934e6	−0.0636306
$953$	3.02068e6	0.107739	0.0538694	−	0.998548i	$-0.482845\pi$
$953$	3.02068e6	0.107739	0.0538694	+	0.998548i	$0.482845\pi$
$954$	−5.93195e6	−0.211021
$955$	−2.24982e6	−0.0798252
$956$	5.03474e7	1.78169
$957$	−3.23102e6	−0.114041
$958$	−1.45544e7	−0.512367
$959$	4.32993e7	1.52032
$960$	−1.50140e7	−0.525796
$961$	−1.89897e7	−0.663300
$962$	2.48138e7	0.864483
$963$	2.43992e6	0.0847832
$964$	−1.94272e7	−0.673315
$965$	−1.07757e7	−0.372501
$966$	1.06941e7	0.368725
$967$	4.69871e7	1.61589	0.807947	−	0.589256i	$-0.200579\pi$
$967$	4.69871e7	1.61589	0.807947	+	0.589256i	$0.200579\pi$
$968$	−68991.2	−0.00236649
$969$	−9.54943e6	−0.326714
$970$	7.26648e6	0.247967
$971$	1.33355e7	0.453901	0.226950	−	0.973906i	$-0.427124\pi$
$971$	1.33355e7	0.453901	0.226950	+	0.973906i	$0.427124\pi$
$972$	−1.67378e7	−0.568242
$973$	−7.43679e7	−2.51828
$974$	2.35201e7	0.794405
$975$	7.67253e6	0.258480
$976$	−2.94964e7	−0.991163
$977$	2.84687e7	0.954182	0.477091	−	0.878854i	$-0.341691\pi$
$977$	2.84687e7	0.954182	0.477091	+	0.878854i	$0.341691\pi$
$978$	−1.01661e7	−0.339864
$979$	−1.26736e7	−0.422614
$980$	3.82290e7	1.27153
$981$	1.63216e7	0.541490
$982$	−4.53602e7	−1.50106
$983$	−5.90506e7	−1.94913	−0.974564	−	0.224108i	$-0.928053\pi$
$983$	−5.90506e7	−1.94913	−0.974564	+	0.224108i	$0.928053\pi$
$984$	−945513.	−0.0311301
$985$	−2.61331e7	−0.858223
$986$	−1.81492e7	−0.594520
$987$	−4.79804e7	−1.56773
$988$	−8.16551e6	−0.266128
$989$	−935574.	−0.0304150
$990$	1.69635e6	0.0550083
$991$	−4.00897e7	−1.29673	−0.648364	−	0.761331i	$-0.724546\pi$
$991$	−4.00897e7	−1.29673	−0.648364	+	0.761331i	$0.724546\pi$
$992$	−2.55417e7	−0.824083
$993$	5.09085e7	1.63839
$994$	2.10495e6	0.0675735
$995$	−2.01383e7	−0.644859
$996$	6.24235e7	1.99388
$997$	6.41292e6	0.204323	0.102162	−	0.994768i	$-0.467424\pi$
$997$	6.41292e6	0.204323	0.102162	+	0.994768i	$0.467424\pi$
$998$	8.00170e7	2.54306
$999$	1.36271e7	0.432006

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.f.1.6	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.f.1.6	✓	38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-8.03656 q^{2} +17.6855 q^{3} +32.5863 q^{4} +25.0000 q^{5} -142.131 q^{6} +252.455 q^{7} -4.71219 q^{8} +69.7783 q^{9} +O(q^{10})\)	\(q-8.03656 q^{2} +17.6855 q^{3} +32.5863 q^{4} +25.0000 q^{5} -142.131 q^{6} +252.455 q^{7} -4.71219 q^{8} +69.7783 q^{9} -200.914 q^{10} -121.000 q^{11} +576.307 q^{12} +694.129 q^{13} -2028.87 q^{14} +442.139 q^{15} -1004.89 q^{16} +1495.72 q^{17} -560.778 q^{18} -361.000 q^{19} +814.659 q^{20} +4464.80 q^{21} +972.424 q^{22} -298.039 q^{23} -83.3377 q^{24} +625.000 q^{25} -5578.41 q^{26} -3063.52 q^{27} +8226.58 q^{28} +1509.86 q^{29} -3553.27 q^{30} -3104.74 q^{31} +8226.68 q^{32} -2139.95 q^{33} -12020.5 q^{34} +6311.37 q^{35} +2273.82 q^{36} -4448.19 q^{37} +2901.20 q^{38} +12276.0 q^{39} -117.805 q^{40} +11345.6 q^{41} -35881.6 q^{42} +3139.10 q^{43} -3942.95 q^{44} +1744.46 q^{45} +2395.21 q^{46} -10746.4 q^{47} -17772.1 q^{48} +46926.4 q^{49} -5022.85 q^{50} +26452.7 q^{51} +22619.1 q^{52} +10578.1 q^{53} +24620.2 q^{54} -3025.00 q^{55} -1189.62 q^{56} -6384.48 q^{57} -12134.1 q^{58} -27355.1 q^{59} +14407.7 q^{60} +29352.8 q^{61} +24951.5 q^{62} +17615.9 q^{63} -33957.6 q^{64} +17353.2 q^{65} +17197.8 q^{66} +20498.5 q^{67} +48740.2 q^{68} -5270.98 q^{69} -50721.7 q^{70} -1037.50 q^{71} -328.809 q^{72} -35462.8 q^{73} +35748.2 q^{74} +11053.5 q^{75} -11763.7 q^{76} -30547.0 q^{77} -98657.2 q^{78} +57640.2 q^{79} -25122.3 q^{80} -71136.1 q^{81} -91179.3 q^{82} +108316. q^{83} +145491. q^{84} +37393.1 q^{85} -25227.6 q^{86} +26702.7 q^{87} +570.175 q^{88} +104741. q^{89} -14019.4 q^{90} +175236. q^{91} -9711.99 q^{92} -54909.1 q^{93} +86363.9 q^{94} -9025.00 q^{95} +145493. q^{96} -36167.1 q^{97} -377127. q^{98} -8443.18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * q^99

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