LMFDB - Embedded newform 1045.6.a.e.1.30

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

Embedding invariants

Embedding label			1.30
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.44693 q^{2} +7.63327 q^{3} +9.56289 q^{4} +25.0000 q^{5} +49.2111 q^{6} +186.181 q^{7} -144.650 q^{8} -184.733 q^{9} +O(q^{10})$	\(q+6.44693 q^{2} +7.63327 q^{3} +9.56289 q^{4} +25.0000 q^{5} +49.2111 q^{6} +186.181 q^{7} -144.650 q^{8} -184.733 q^{9} +161.173 q^{10} +121.000 q^{11} +72.9961 q^{12} -69.3239 q^{13} +1200.29 q^{14} +190.832 q^{15} -1238.56 q^{16} -662.079 q^{17} -1190.96 q^{18} -361.000 q^{19} +239.072 q^{20} +1421.17 q^{21} +780.078 q^{22} -1305.46 q^{23} -1104.16 q^{24} +625.000 q^{25} -446.926 q^{26} -3265.00 q^{27} +1780.42 q^{28} -1982.89 q^{29} +1230.28 q^{30} -5605.62 q^{31} -3356.12 q^{32} +923.625 q^{33} -4268.37 q^{34} +4654.51 q^{35} -1766.58 q^{36} -9763.86 q^{37} -2327.34 q^{38} -529.168 q^{39} -3616.26 q^{40} +8167.85 q^{41} +9162.16 q^{42} -4676.49 q^{43} +1157.11 q^{44} -4618.33 q^{45} -8416.22 q^{46} -12446.7 q^{47} -9454.29 q^{48} +17856.2 q^{49} +4029.33 q^{50} -5053.82 q^{51} -662.937 q^{52} +5004.39 q^{53} -21049.2 q^{54} +3025.00 q^{55} -26931.1 q^{56} -2755.61 q^{57} -12783.6 q^{58} +12667.5 q^{59} +1824.90 q^{60} +24501.0 q^{61} -36139.1 q^{62} -34393.7 q^{63} +17997.4 q^{64} -1733.10 q^{65} +5954.55 q^{66} -27831.3 q^{67} -6331.38 q^{68} -9964.94 q^{69} +30007.3 q^{70} -43297.1 q^{71} +26721.7 q^{72} -1194.09 q^{73} -62946.9 q^{74} +4770.79 q^{75} -3452.20 q^{76} +22527.9 q^{77} -3411.51 q^{78} -76836.6 q^{79} -30964.1 q^{80} +19967.6 q^{81} +52657.5 q^{82} +64409.4 q^{83} +13590.5 q^{84} -16552.0 q^{85} -30149.0 q^{86} -15135.9 q^{87} -17502.7 q^{88} +25485.7 q^{89} -29774.1 q^{90} -12906.8 q^{91} -12484.0 q^{92} -42789.2 q^{93} -80243.0 q^{94} -9025.00 q^{95} -25618.1 q^{96} -151037. q^{97} +115118. q^{98} -22352.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) $ 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9} - 600 q^{10} + 4598 q^{11} - 2008 q^{12} - 2663 q^{13} - 1565 q^{14} - 1575 q^{15} + 12390 q^{16} - 3311 q^{17} - 6383 q^{18} - 13718 q^{19} + 14850 q^{20} - 8179 q^{21} - 2904 q^{22} - 3412 q^{23} - 4100 q^{24} + 23750 q^{25} - 1399 q^{26} - 31596 q^{27} - 43653 q^{28} - 13633 q^{29} - 1675 q^{30} - 13789 q^{31} - 58603 q^{32} - 7623 q^{33} - 29149 q^{34} - 18225 q^{35} + 50641 q^{36} - 12103 q^{37} + 8664 q^{38} - 50960 q^{39} - 31800 q^{40} - 37885 q^{41} + 51100 q^{42} - 56119 q^{43} + 71874 q^{44} + 75725 q^{45} - 56291 q^{46} - 37532 q^{47} - 113895 q^{48} + 153501 q^{49} - 15000 q^{50} + 32882 q^{51} - 169554 q^{52} - 51511 q^{53} - 175060 q^{54} + 114950 q^{55} - 84247 q^{56} + 22743 q^{57} - 256962 q^{58} - 154267 q^{59} - 50200 q^{60} - 47165 q^{61} + 143002 q^{62} - 358780 q^{63} + 142292 q^{64} - 66575 q^{65} - 8107 q^{66} - 161712 q^{67} - 210188 q^{68} - 124602 q^{69} - 39125 q^{70} + 6118 q^{71} - 327878 q^{72} - 152182 q^{73} - 167349 q^{74} - 39375 q^{75} - 214434 q^{76} - 88209 q^{77} - 216594 q^{78} - 140433 q^{79} + 309750 q^{80} + 382874 q^{81} - 29842 q^{82} - 515287 q^{83} + 29222 q^{84} - 82775 q^{85} + 204974 q^{86} - 106764 q^{87} - 153912 q^{88} - 271610 q^{89} - 159575 q^{90} - 44332 q^{91} + 236348 q^{92} + 25202 q^{93} - 496224 q^{94} - 342950 q^{95} - 275218 q^{96} - 126390 q^{97} - 285506 q^{98} + 366509 q^{99}+O(q^{100}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9 - 600 * q^10 + 4598 * q^11 - 2008 * q^12 - 2663 * q^13 - 1565 * q^14 - 1575 * q^15 + 12390 * q^16 - 3311 * q^17 - 6383 * q^18 - 13718 * q^19 + 14850 * q^20 - 8179 * q^21 - 2904 * q^22 - 3412 * q^23 - 4100 * q^24 + 23750 * q^25 - 1399 * q^26 - 31596 * q^27 - 43653 * q^28 - 13633 * q^29 - 1675 * q^30 - 13789 * q^31 - 58603 * q^32 - 7623 * q^33 - 29149 * q^34 - 18225 * q^35 + 50641 * q^36 - 12103 * q^37 + 8664 * q^38 - 50960 * q^39 - 31800 * q^40 - 37885 * q^41 + 51100 * q^42 - 56119 * q^43 + 71874 * q^44 + 75725 * q^45 - 56291 * q^46 - 37532 * q^47 - 113895 * q^48 + 153501 * q^49 - 15000 * q^50 + 32882 * q^51 - 169554 * q^52 - 51511 * q^53 - 175060 * q^54 + 114950 * q^55 - 84247 * q^56 + 22743 * q^57 - 256962 * q^58 - 154267 * q^59 - 50200 * q^60 - 47165 * q^61 + 143002 * q^62 - 358780 * q^63 + 142292 * q^64 - 66575 * q^65 - 8107 * q^66 - 161712 * q^67 - 210188 * q^68 - 124602 * q^69 - 39125 * q^70 + 6118 * q^71 - 327878 * q^72 - 152182 * q^73 - 167349 * q^74 - 39375 * q^75 - 214434 * q^76 - 88209 * q^77 - 216594 * q^78 - 140433 * q^79 + 309750 * q^80 + 382874 * q^81 - 29842 * q^82 - 515287 * q^83 + 29222 * q^84 - 82775 * q^85 + 204974 * q^86 - 106764 * q^87 - 153912 * q^88 - 271610 * q^89 - 159575 * q^90 - 44332 * q^91 + 236348 * q^92 + 25202 * q^93 - 496224 * q^94 - 342950 * q^95 - 275218 * q^96 - 126390 * q^97 - 285506 * q^98 + 366509 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	6.44693	1.13967	0.569833	−	0.821760i	$-0.307008\pi$
$2$	6.44693	1.13967	0.569833	+	0.821760i	$0.307008\pi$
$3$	7.63327	0.489674	0.244837	−	0.969564i	$-0.421266\pi$
$3$	7.63327	0.489674	0.244837	+	0.969564i	$0.421266\pi$
$4$	9.56289	0.298840
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	49.2111	0.558065
$7$	186.181	1.43612	0.718058	−	0.695984i	$-0.245031\pi$
$7$	186.181	1.43612	0.718058	+	0.695984i	$0.245031\pi$
$8$	−144.650	−0.799088
$9$	−184.733	−0.760219
$10$	161.173	0.509674
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	72.9961	0.146334
$13$	−69.3239	−0.113769	−0.0568846	−	0.998381i	$-0.518117\pi$
$13$	−69.3239	−0.113769	−0.0568846	+	0.998381i	$0.518117\pi$
$14$	1200.29	1.63669
$15$	190.832	0.218989
$16$	−1238.56	−1.20953
$17$	−662.079	−0.555632	−0.277816	−	0.960634i	$-0.589611\pi$
$17$	−662.079	−0.555632	−0.277816	+	0.960634i	$0.589611\pi$
$18$	−1190.96	−0.866396
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	239.072	0.133645
$21$	1421.17	0.703229
$22$	780.078	0.343622
$23$	−1305.46	−0.514570	−0.257285	−	0.966336i	$-0.582828\pi$
$23$	−1305.46	−0.514570	−0.257285	+	0.966336i	$0.582828\pi$
$24$	−1104.16	−0.391293
$25$	625.000	0.200000
$26$	−446.926	−0.129659
$27$	−3265.00	−0.861934
$28$	1780.42	0.429169
$29$	−1982.89	−0.437828	−0.218914	−	0.975744i	$-0.570251\pi$
$29$	−1982.89	−0.437828	−0.218914	+	0.975744i	$0.570251\pi$
$30$	1230.28	0.249574
$31$	−5605.62	−1.04766	−0.523829	−	0.851823i	$-0.675497\pi$
$31$	−5605.62	−1.04766	−0.523829	+	0.851823i	$0.675497\pi$
$32$	−3356.12	−0.579378
$33$	923.625	0.147642
$34$	−4268.37	−0.633235
$35$	4654.51	0.642250
$36$	−1766.58	−0.227184
$37$	−9763.86	−1.17251	−0.586256	−	0.810126i	$-0.699399\pi$
$37$	−9763.86	−1.17251	−0.586256	+	0.810126i	$0.699399\pi$
$38$	−2327.34	−0.261457
$39$	−529.168	−0.0557098
$40$	−3616.26	−0.357363
$41$	8167.85	0.758836	0.379418	−	0.925225i	$-0.376124\pi$
$41$	8167.85	0.758836	0.379418	+	0.925225i	$0.376124\pi$
$42$	9162.16	0.801446
$43$	−4676.49	−0.385699	−0.192850	−	0.981228i	$-0.561773\pi$
$43$	−4676.49	−0.385699	−0.192850	+	0.981228i	$0.561773\pi$
$44$	1157.11	0.0901037
$45$	−4618.33	−0.339980
$46$	−8416.22	−0.586438
$47$	−12446.7	−0.821883	−0.410941	−	0.911662i	$-0.634800\pi$
$47$	−12446.7	−0.821883	−0.410941	+	0.911662i	$0.634800\pi$
$48$	−9454.29	−0.592278
$49$	17856.2	1.06243
$50$	4029.33	0.227933
$51$	−5053.82	−0.272079
$52$	−662.937	−0.0339988
$53$	5004.39	0.244715	0.122358	−	0.992486i	$-0.460955\pi$
$53$	5004.39	0.244715	0.122358	+	0.992486i	$0.460955\pi$
$54$	−21049.2	−0.982317
$55$	3025.00	0.134840
$56$	−26931.1	−1.14758
$57$	−2755.61	−0.112339
$58$	−12783.6	−0.498978
$59$	12667.5	0.473763	0.236881	−	0.971539i	$-0.423875\pi$
$59$	12667.5	0.473763	0.236881	+	0.971539i	$0.423875\pi$
$60$	1824.90	0.0654427
$61$	24501.0	0.843060	0.421530	−	0.906814i	$-0.361493\pi$
$61$	24501.0	0.843060	0.421530	+	0.906814i	$0.361493\pi$
$62$	−36139.1	−1.19398
$63$	−34393.7	−1.09176
$64$	17997.4	0.549237
$65$	−1733.10	−0.0508791
$66$	5954.55	0.168263
$67$	−27831.3	−0.757438	−0.378719	−	0.925512i	$-0.623635\pi$
$67$	−27831.3	−0.757438	−0.378719	+	0.925512i	$0.623635\pi$
$68$	−6331.38	−0.166045
$69$	−9964.94	−0.251972
$70$	30007.3	0.731951
$71$	−43297.1	−1.01933	−0.509663	−	0.860374i	$-0.670230\pi$
$71$	−43297.1	−1.01933	−0.509663	+	0.860374i	$0.670230\pi$
$72$	26721.7	0.607482
$73$	−1194.09	−0.0262258	−0.0131129	−	0.999914i	$-0.504174\pi$
$73$	−1194.09	−0.0262258	−0.0131129	+	0.999914i	$0.504174\pi$
$74$	−62946.9	−1.33627
$75$	4770.79	0.0979349
$76$	−3452.20	−0.0685586
$77$	22527.9	0.433005
$78$	−3411.51	−0.0634906
$79$	−76836.6	−1.38516	−0.692581	−	0.721340i	$-0.743526\pi$
$79$	−76836.6	−1.38516	−0.692581	+	0.721340i	$0.743526\pi$
$80$	−30964.1	−0.540920
$81$	19967.6	0.338152
$82$	52657.5	0.864820
$83$	64409.4	1.02625	0.513126	−	0.858313i	$-0.328487\pi$
$83$	64409.4	1.02625	0.513126	+	0.858313i	$0.328487\pi$
$84$	13590.5	0.210153
$85$	−16552.0	−0.248486
$86$	−30149.0	−0.439569
$87$	−15135.9	−0.214393
$88$	−17502.7	−0.240934
$89$	25485.7	0.341053	0.170527	−	0.985353i	$-0.445453\pi$
$89$	25485.7	0.341053	0.170527	+	0.985353i	$0.445453\pi$
$90$	−29774.1	−0.387464
$91$	−12906.8	−0.163386
$92$	−12484.0	−0.153774
$93$	−42789.2	−0.513011
$94$	−80243.0	−0.936673
$95$	−9025.00	−0.102598
$96$	−25618.1	−0.283706
$97$	−151037.	−1.62988	−0.814939	−	0.579547i	$-0.803229\pi$
$97$	−151037.	−1.62988	−0.814939	+	0.579547i	$0.803229\pi$
$98$	115118.	1.21081
$99$	−22352.7	−0.229215
$100$	5976.80	0.0597680
$101$	175887.	1.71566	0.857830	−	0.513934i	$-0.171812\pi$
$101$	175887.	1.71566	0.857830	+	0.513934i	$0.171812\pi$
$102$	−32581.6	−0.310079
$103$	−84035.2	−0.780492	−0.390246	−	0.920711i	$-0.627610\pi$
$103$	−84035.2	−0.780492	−0.390246	+	0.920711i	$0.627610\pi$
$104$	10027.7	0.0909116
$105$	35529.2	0.314493
$106$	32262.9	0.278894
$107$	−103262.	−0.871925	−0.435962	−	0.899965i	$-0.643592\pi$
$107$	−103262.	−0.871925	−0.435962	+	0.899965i	$0.643592\pi$
$108$	−31222.8	−0.257581
$109$	22270.0	0.179537	0.0897685	−	0.995963i	$-0.471387\pi$
$109$	22270.0	0.179537	0.0897685	+	0.995963i	$0.471387\pi$
$110$	19502.0	0.153673
$111$	−74530.2	−0.574149
$112$	−230597.	−1.73703
$113$	−183396.	−1.35112	−0.675561	−	0.737305i	$-0.736098\pi$
$113$	−183396.	−1.35112	−0.675561	+	0.737305i	$0.736098\pi$
$114$	−17765.2	−0.128029
$115$	−32636.5	−0.230123
$116$	−18962.2	−0.130841
$117$	12806.4	0.0864895
$118$	81666.5	0.539932
$119$	−123266.	−0.797952
$120$	−27603.9	−0.174992
$121$	14641.0	0.0909091
$122$	157956.	0.960808
$123$	62347.4	0.371582
$124$	−53606.0	−0.313083
$125$	15625.0	0.0894427
$126$	−221734.	−1.24425
$127$	−316301.	−1.74017	−0.870084	−	0.492904i	$-0.835935\pi$
$127$	−316301.	−1.74017	−0.870084	+	0.492904i	$0.835935\pi$
$128$	223424.	1.20533
$129$	−35696.9	−0.188867
$130$	−11173.2	−0.0579852
$131$	275948.	1.40491	0.702457	−	0.711727i	$-0.252087\pi$
$131$	275948.	1.40491	0.702457	+	0.711727i	$0.252087\pi$
$132$	8832.52	0.0441215
$133$	−67211.2	−0.329467
$134$	−179427.	−0.863227
$135$	−81625.0	−0.385469
$136$	95770.0	0.443999
$137$	−68660.5	−0.312540	−0.156270	−	0.987714i	$-0.549947\pi$
$137$	−68660.5	−0.312540	−0.156270	+	0.987714i	$0.549947\pi$
$138$	−64243.2	−0.287164
$139$	−22039.2	−0.0967519	−0.0483760	−	0.998829i	$-0.515405\pi$
$139$	−22039.2	−0.0967519	−0.0483760	+	0.998829i	$0.515405\pi$
$140$	44510.6	0.191930
$141$	−95009.0	−0.402455
$142$	−279134.	−1.16169
$143$	−8388.19	−0.0343027
$144$	228804.	0.919511
$145$	−49572.3	−0.195803
$146$	−7698.20	−0.0298887
$147$	136301.	0.520243
$148$	−93370.7	−0.350394
$149$	33449.8	0.123432	0.0617160	−	0.998094i	$-0.480343\pi$
$149$	33449.8	0.123432	0.0617160	+	0.998094i	$0.480343\pi$
$150$	30757.0	0.111613
$151$	460871.	1.64489	0.822445	−	0.568844i	$-0.192609\pi$
$151$	460871.	1.64489	0.822445	+	0.568844i	$0.192609\pi$
$152$	52218.8	0.183323
$153$	122308.	0.422402
$154$	145235.	0.493481
$155$	−140141.	−0.468527
$156$	−5060.37	−0.0166483
$157$	199007.	0.644345	0.322173	−	0.946681i	$-0.395587\pi$
$157$	199007.	0.644345	0.322173	+	0.946681i	$0.395587\pi$
$158$	−495360.	−1.57862
$159$	38199.8	0.119831
$160$	−83902.9	−0.259106
$161$	−243052.	−0.738982
$162$	128729.	0.385381
$163$	501790.	1.47929	0.739644	−	0.672998i	$-0.234994\pi$
$163$	501790.	1.47929	0.739644	+	0.672998i	$0.234994\pi$
$164$	78108.2	0.226771
$165$	23090.6	0.0660277
$166$	415243.	1.16959
$167$	−517076.	−1.43471	−0.717354	−	0.696709i	$-0.754647\pi$
$167$	−517076.	−1.43471	−0.717354	+	0.696709i	$0.754647\pi$
$168$	−205572.	−0.561942
$169$	−366487.	−0.987057
$170$	−106709.	−0.283191
$171$	66688.7	0.174406
$172$	−44720.8	−0.115262
$173$	622908.	1.58237	0.791187	−	0.611575i	$-0.209464\pi$
$173$	622908.	1.58237	0.791187	+	0.611575i	$0.209464\pi$
$174$	−97580.3	−0.244337
$175$	116363.	0.287223
$176$	−149866.	−0.364688
$177$	96694.4	0.231989
$178$	164305.	0.388687
$179$	−385808.	−0.899992	−0.449996	−	0.893031i	$-0.648575\pi$
$179$	−385808.	−0.899992	−0.449996	+	0.893031i	$0.648575\pi$
$180$	−44164.6	−0.101600
$181$	−226238.	−0.513297	−0.256648	−	0.966505i	$-0.582618\pi$
$181$	−226238.	−0.513297	−0.256648	+	0.966505i	$0.582618\pi$
$182$	−83209.0	−0.186205
$183$	187022.	0.412825
$184$	188836.	0.411187
$185$	−244097.	−0.524363
$186$	−275859.	−0.584662
$187$	−80111.5	−0.167529
$188$	−119026.	−0.245612
$189$	−607880.	−1.23784
$190$	−58183.5	−0.116927
$191$	322356.	0.639370	0.319685	−	0.947524i	$-0.396423\pi$
$191$	322356.	0.639370	0.319685	+	0.947524i	$0.396423\pi$
$192$	137379.	0.268947
$193$	−340674.	−0.658332	−0.329166	−	0.944272i	$-0.606768\pi$
$193$	−340674.	−0.658332	−0.329166	+	0.944272i	$0.606768\pi$
$194$	−973727.	−1.85752
$195$	−13229.2	−0.0249142
$196$	170757.	0.317496
$197$	756732.	1.38924	0.694619	−	0.719378i	$-0.255573\pi$
$197$	756732.	1.38924	0.694619	+	0.719378i	$0.255573\pi$
$198$	−144106.	−0.261228
$199$	−800045.	−1.43213	−0.716064	−	0.698035i	$-0.754058\pi$
$199$	−800045.	−1.43213	−0.716064	+	0.698035i	$0.754058\pi$
$200$	−90406.5	−0.159818
$201$	−212444.	−0.370898
$202$	1.13393e6	1.95528
$203$	−369176.	−0.628772
$204$	−48329.1	−0.0813081
$205$	204196.	0.339362
$206$	−541769.	−0.889500
$207$	241162.	0.391186
$208$	85862.0	0.137608
$209$	−43681.0	−0.0691714
$210$	229054.	0.358418
$211$	−717451.	−1.10939	−0.554697	−	0.832052i	$-0.687166\pi$
$211$	−717451.	−1.10939	−0.554697	+	0.832052i	$0.687166\pi$
$212$	47856.4	0.0731308
$213$	−330499.	−0.499138
$214$	−665720.	−0.993704
$215$	−116912.	−0.172490
$216$	472284.	0.688762
$217$	−1.04366e6	−1.50456
$218$	143573.	0.204612
$219$	−9114.79	−0.0128421
$220$	28927.7	0.0402956
$221$	45897.9	0.0632138
$222$	−480491.	−0.654339
$223$	−1.37835e6	−1.85609	−0.928043	−	0.372473i	$-0.878510\pi$
$223$	−1.37835e6	−1.85609	−0.928043	+	0.372473i	$0.878510\pi$
$224$	−624844.	−0.832054
$225$	−115458.	−0.152044
$226$	−1.18234e6	−1.53983
$227$	−1.27131e6	−1.63752	−0.818759	−	0.574138i	$-0.805337\pi$
$227$	−1.27131e6	−1.63752	−0.818759	+	0.574138i	$0.805337\pi$
$228$	−26351.6	−0.0335714
$229$	812056.	1.02329	0.511643	−	0.859198i	$-0.329037\pi$
$229$	812056.	1.02329	0.511643	+	0.859198i	$0.329037\pi$
$230$	−210405.	−0.262263
$231$	171961.	0.212031
$232$	286826.	0.349864
$233$	−1.36171e6	−1.64321	−0.821606	−	0.570056i	$-0.806922\pi$
$233$	−1.36171e6	−1.64321	−0.821606	+	0.570056i	$0.806922\pi$
$234$	82562.1	0.0985692
$235$	−311168.	−0.367557
$236$	121138.	0.141579
$237$	−586514.	−0.678278
$238$	−794688.	−0.909399
$239$	767642.	0.869289	0.434644	−	0.900602i	$-0.356874\pi$
$239$	767642.	0.869289	0.434644	+	0.900602i	$0.356874\pi$
$240$	−236357.	−0.264875
$241$	−892109.	−0.989408	−0.494704	−	0.869062i	$-0.664723\pi$
$241$	−892109.	−0.989408	−0.494704	+	0.869062i	$0.664723\pi$
$242$	94389.5	0.103606
$243$	945813.	1.02752
$244$	234300.	0.251940
$245$	446405.	0.475132
$246$	401949.	0.423480
$247$	25025.9	0.0261004
$248$	810856.	0.837172
$249$	491654.	0.502529
$250$	100733.	0.101935
$251$	1.00421e6	1.00610	0.503050	−	0.864257i	$-0.332211\pi$
$251$	1.00421e6	1.00610	0.503050	+	0.864257i	$0.332211\pi$
$252$	−328904.	−0.326262
$253$	−157961.	−0.155149
$254$	−2.03917e6	−1.98321
$255$	−126346.	−0.121677
$256$	864480.	0.824432
$257$	−1.10637e6	−1.04489	−0.522443	−	0.852674i	$-0.674979\pi$
$257$	−1.10637e6	−1.04489	−0.522443	+	0.852674i	$0.674979\pi$
$258$	−230135.	−0.215246
$259$	−1.81784e6	−1.68386
$260$	−16573.4	−0.0152047
$261$	366306.	0.332845
$262$	1.77902e6	1.60113
$263$	−619619.	−0.552377	−0.276188	−	0.961103i	$-0.589071\pi$
$263$	−619619.	−0.552377	−0.276188	+	0.961103i	$0.589071\pi$
$264$	−133603.	−0.117979
$265$	125110.	0.109440
$266$	−433306.	−0.375483
$267$	194539.	0.167005
$268$	−266148.	−0.226353
$269$	−1.40045e6	−1.18001	−0.590005	−	0.807400i	$-0.700874\pi$
$269$	−1.40045e6	−1.18001	−0.590005	+	0.807400i	$0.700874\pi$
$270$	−526231.	−0.439306
$271$	−660.553	−0.000546367 0	−0.000273183	−	1.00000i	$-0.500087\pi$
$271$	−660.553	−0.000546367 0	−0.000273183		1.00000i	$0.500087\pi$
$272$	820026.	0.672056
$273$	−98520.8	−0.0800057
$274$	−442649.	−0.356191
$275$	75625.0	0.0603023
$276$	−95293.6	−0.0752993
$277$	1.25805e6	0.985140	0.492570	−	0.870273i	$-0.336057\pi$
$277$	1.25805e6	0.985140	0.492570	+	0.870273i	$0.336057\pi$
$278$	−142085.	−0.110265
$279$	1.03555e6	0.796450
$280$	−673278.	−0.513215
$281$	929113.	0.701944	0.350972	−	0.936386i	$-0.385851\pi$
$281$	929113.	0.701944	0.350972	+	0.936386i	$0.385851\pi$
$282$	−612517.	−0.458664
$283$	−229785.	−0.170552	−0.0852758	−	0.996357i	$-0.527177\pi$
$283$	−229785.	−0.170552	−0.0852758	+	0.996357i	$0.527177\pi$
$284$	−414046.	−0.304616
$285$	−68890.2	−0.0502395
$286$	−54078.1	−0.0390936
$287$	1.52069e6	1.08978
$288$	619986.	0.440454
$289$	−981509.	−0.691273
$290$	−319589.	−0.223150
$291$	−1.15291e6	−0.798109
$292$	−11418.9	−0.00783733
$293$	1.55077e6	1.05531	0.527654	−	0.849459i	$-0.323072\pi$
$293$	1.55077e6	1.05531	0.527654	+	0.849459i	$0.323072\pi$
$294$	878724.	0.592904
$295$	316687.	0.211873
$296$	1.41235e6	0.936941
$297$	−395065.	−0.259883
$298$	215648.	0.140671
$299$	90499.7	0.0585422
$300$	45622.5	0.0292669
$301$	−870672.	−0.553909
$302$	2.97120e6	1.87463
$303$	1.34259e6	0.840114
$304$	447121.	0.277486
$305$	612524.	0.377028
$306$	788510.	0.481398
$307$	1.50085e6	0.908846	0.454423	−	0.890786i	$-0.349845\pi$
$307$	1.50085e6	0.908846	0.454423	+	0.890786i	$0.349845\pi$
$308$	215431.	0.129399
$309$	−641463.	−0.382187
$310$	−903477.	−0.533965
$311$	280677.	0.164553	0.0822764	−	0.996610i	$-0.473781\pi$
$311$	280677.	0.164553	0.0822764	+	0.996610i	$0.473781\pi$
$312$	76544.4	0.0445171
$313$	1.96471e6	1.13354	0.566771	−	0.823875i	$-0.308192\pi$
$313$	1.96471e6	1.13354	0.566771	+	0.823875i	$0.308192\pi$
$314$	1.28298e6	0.734339
$315$	−859844.	−0.488251
$316$	−734780.	−0.413942
$317$	−2.19907e6	−1.22911	−0.614556	−	0.788873i	$-0.710665\pi$
$317$	−2.19907e6	−1.22911	−0.614556	+	0.788873i	$0.710665\pi$
$318$	246271.	0.136567
$319$	−239930.	−0.132010
$320$	449935.	0.245626
$321$	−788223.	−0.426959
$322$	−1.56694e6	−0.842193
$323$	239010.	0.127471
$324$	190947.	0.101053
$325$	−43327.4	−0.0227538
$326$	3.23500e6	1.68590
$327$	169993.	0.0879146
$328$	−1.18148e6	−0.606377
$329$	−2.31734e6	−1.18032
$330$	148864.	0.0752495
$331$	2.21778e6	1.11262	0.556311	−	0.830974i	$-0.312216\pi$
$331$	2.21778e6	1.11262	0.556311	+	0.830974i	$0.312216\pi$
$332$	615940.	0.306686
$333$	1.80371e6	0.891366
$334$	−3.33355e6	−1.63509
$335$	−695784.	−0.338737
$336$	−1.76020e6	−0.850580
$337$	1.61761e6	0.775888	0.387944	−	0.921683i	$-0.373185\pi$
$337$	1.61761e6	0.775888	0.387944	+	0.921683i	$0.373185\pi$
$338$	−2.36272e6	−1.12492
$339$	−1.39991e6	−0.661609
$340$	−158285.	−0.0742577
$341$	−678281.	−0.315881
$342$	429937.	0.198765
$343$	195344.	0.0896528
$344$	676457.	0.308208
$345$	−249123.	−0.112685
$346$	4.01585e6	1.80338
$347$	−1.99997e6	−0.891661	−0.445830	−	0.895118i	$-0.647092\pi$
$347$	−1.99997e6	−0.891661	−0.445830	+	0.895118i	$0.647092\pi$
$348$	−144743.	−0.0640693
$349$	−1.30684e6	−0.574328	−0.287164	−	0.957882i	$-0.592712\pi$
$349$	−1.30684e6	−0.574328	−0.287164	+	0.957882i	$0.592712\pi$
$350$	750183.	0.327339
$351$	226343.	0.0980615
$352$	−406090.	−0.174689
$353$	−1.76933e6	−0.755740	−0.377870	−	0.925859i	$-0.623343\pi$
$353$	−1.76933e6	−0.755740	−0.377870	+	0.925859i	$0.623343\pi$
$354$	623382.	0.264391
$355$	−1.08243e6	−0.455857
$356$	243717.	0.101920
$357$	−940924.	−0.390736
$358$	−2.48728e6	−1.02569
$359$	932890.	0.382027	0.191014	−	0.981587i	$-0.438823\pi$
$359$	932890.	0.382027	0.191014	+	0.981587i	$0.438823\pi$
$360$	668044.	0.271674
$361$	130321.	0.0526316
$362$	−1.45854e6	−0.584987
$363$	111759.	0.0445158
$364$	−123426.	−0.0488262
$365$	−29852.2	−0.0117285
$366$	1.20572e6	0.470483
$367$	−1.52685e6	−0.591742	−0.295871	−	0.955228i	$-0.595610\pi$
$367$	−1.52685e6	−0.591742	−0.295871	+	0.955228i	$0.595610\pi$
$368$	1.61690e6	0.622390
$369$	−1.50887e6	−0.576882
$370$	−1.57367e6	−0.597600
$371$	931719.	0.351439
$372$	−409189.	−0.153308
$373$	4.53198e6	1.68662	0.843308	−	0.537430i	$-0.180605\pi$
$373$	4.53198e6	1.68662	0.843308	+	0.537430i	$0.180605\pi$
$374$	−516473.	−0.190928
$375$	119270.	0.0437978
$376$	1.80042e6	0.656757
$377$	137462.	0.0498114
$378$	−3.91896e6	−1.41072
$379$	1.64125e6	0.586918	0.293459	−	0.955972i	$-0.405194\pi$
$379$	1.64125e6	0.586918	0.293459	+	0.955972i	$0.405194\pi$
$380$	−86305.1	−0.0306604
$381$	−2.41441e6	−0.852115
$382$	2.07821e6	0.728669
$383$	−2.02488e6	−0.705345	−0.352673	−	0.935747i	$-0.614727\pi$
$383$	−2.02488e6	−0.705345	−0.352673	+	0.935747i	$0.614727\pi$
$384$	1.70545e6	0.590217
$385$	563196.	0.193646
$386$	−2.19630e6	−0.750279
$387$	863903.	0.293216
$388$	−1.44435e6	−0.487073
$389$	−357117.	−0.119657	−0.0598284	−	0.998209i	$-0.519055\pi$
$389$	−357117.	−0.119657	−0.0598284	+	0.998209i	$0.519055\pi$
$390$	−85287.7	−0.0283939
$391$	864318.	0.285912
$392$	−2.58291e6	−0.848973
$393$	2.10639e6	0.687950
$394$	4.87860e6	1.58327
$395$	−1.92091e6	−0.619463
$396$	−213757.	−0.0684986
$397$	−1.11943e6	−0.356470	−0.178235	−	0.983988i	$-0.557039\pi$
$397$	−1.11943e6	−0.356470	−0.178235	+	0.983988i	$0.557039\pi$
$398$	−5.15783e6	−1.63215
$399$	−513041.	−0.161332
$400$	−774102.	−0.241907
$401$	−3.24465e6	−1.00764	−0.503822	−	0.863808i	$-0.668073\pi$
$401$	−3.24465e6	−1.00764	−0.503822	+	0.863808i	$0.668073\pi$
$402$	−1.36961e6	−0.422700
$403$	388604.	0.119191
$404$	1.68199e6	0.512708
$405$	499189.	0.151226
$406$	−2.38005e6	−0.716590
$407$	−1.18143e6	−0.353526
$408$	731038.	0.217415
$409$	4.50964e6	1.33301	0.666506	−	0.745500i	$-0.267789\pi$
$409$	4.50964e6	1.33301	0.666506	+	0.745500i	$0.267789\pi$
$410$	1.31644e6	0.386759
$411$	−524104.	−0.153043
$412$	−803619.	−0.233242
$413$	2.35844e6	0.680378
$414$	1.55476e6	0.445822
$415$	1.61024e6	0.458954
$416$	232659.	0.0659154
$417$	−168231.	−0.0473769
$418$	−281608.	−0.0788324
$419$	3.05072e6	0.848922	0.424461	−	0.905446i	$-0.360464\pi$
$419$	3.05072e6	0.848922	0.424461	+	0.905446i	$0.360464\pi$
$420$	339761.	0.0939833
$421$	−712245.	−0.195850	−0.0979251	−	0.995194i	$-0.531221\pi$
$421$	−712245.	−0.195850	−0.0979251	+	0.995194i	$0.531221\pi$
$422$	−4.62535e6	−1.26434
$423$	2.29932e6	0.624811
$424$	−723887.	−0.195549
$425$	−413799.	−0.111126
$426$	−2.13070e6	−0.568851
$427$	4.56160e6	1.21073
$428$	−987478.	−0.260566
$429$	−64029.3	−0.0167971
$430$	−753725.	−0.196581
$431$	3.41176e6	0.884678	0.442339	−	0.896848i	$-0.354149\pi$
$431$	3.41176e6	0.884678	0.442339	+	0.896848i	$0.354149\pi$
$432$	4.04391e6	1.04254
$433$	5.49493e6	1.40845	0.704226	−	0.709976i	$-0.251294\pi$
$433$	5.49493e6	1.40845	0.704226	+	0.709976i	$0.251294\pi$
$434$	−6.72839e6	−1.71470
$435$	−378398.	−0.0958796
$436$	212965.	0.0536529
$437$	471272.	0.118050
$438$	−58762.4	−0.0146357
$439$	5.15021e6	1.27545	0.637725	−	0.770264i	$-0.279875\pi$
$439$	5.15021e6	1.27545	0.637725	+	0.770264i	$0.279875\pi$
$440$	−437568.	−0.107749
$441$	−3.29864e6	−0.807678
$442$	295900.	0.0720426
$443$	−3.14531e6	−0.761471	−0.380736	−	0.924684i	$-0.624329\pi$
$443$	−3.14531e6	−0.761471	−0.380736	+	0.924684i	$0.624329\pi$
$444$	−712724.	−0.171579
$445$	637144.	0.152524
$446$	−8.88614e6	−2.11532
$447$	255331.	0.0604414
$448$	3.35077e6	0.788768
$449$	1.65501e6	0.387423	0.193711	−	0.981059i	$-0.437947\pi$
$449$	1.65501e6	0.387423	0.193711	+	0.981059i	$0.437947\pi$
$450$	−744351.	−0.173279
$451$	988310.	0.228798
$452$	−1.75380e6	−0.403769
$453$	3.51795e6	0.805461
$454$	−8.19603e6	−1.86622
$455$	−322669.	−0.0730683
$456$	398600.	0.0897688
$457$	−2.67404e6	−0.598932	−0.299466	−	0.954107i	$-0.596809\pi$
$457$	−2.67404e6	−0.598932	−0.299466	+	0.954107i	$0.596809\pi$
$458$	5.23527e6	1.16621
$459$	2.16169e6	0.478918
$460$	−312100.	−0.0687699
$461$	−970971.	−0.212791	−0.106396	−	0.994324i	$-0.533931\pi$
$461$	−970971.	−0.212791	−0.106396	+	0.994324i	$0.533931\pi$
$462$	1.10862e6	0.241645
$463$	786593.	0.170529	0.0852644	−	0.996358i	$-0.472827\pi$
$463$	786593.	0.170529	0.0852644	+	0.996358i	$0.472827\pi$
$464$	2.45594e6	0.529569
$465$	−1.06973e6	−0.229426
$466$	−8.77882e6	−1.87271
$467$	1.49380e6	0.316956	0.158478	−	0.987363i	$-0.449341\pi$
$467$	1.49380e6	0.316956	0.158478	+	0.987363i	$0.449341\pi$
$468$	122466.	0.0258465
$469$	−5.18166e6	−1.08777
$470$	−2.00608e6	−0.418893
$471$	1.51907e6	0.315519
$472$	−1.83236e6	−0.378578
$473$	−565855.	−0.116293
$474$	−3.78122e6	−0.773011
$475$	−225625.	−0.0458831
$476$	−1.17878e6	−0.238460
$477$	−924476.	−0.186037
$478$	4.94893e6	0.990699
$479$	6.85877e6	1.36586	0.682932	−	0.730482i	$-0.260705\pi$
$479$	6.85877e6	1.36586	0.682932	+	0.730482i	$0.260705\pi$
$480$	−640453.	−0.126877
$481$	676869.	0.133396
$482$	−5.75136e6	−1.12760
$483$	−1.85528e6	−0.361860
$484$	140010.	0.0271673
$485$	−3.77593e6	−0.728903
$486$	6.09759e6	1.17103
$487$	−114316.	−0.0218416	−0.0109208	−	0.999940i	$-0.503476\pi$
$487$	−114316.	−0.0218416	−0.0109208	+	0.999940i	$0.503476\pi$
$488$	−3.54408e6	−0.673680
$489$	3.83030e6	0.724370
$490$	2.87794e6	0.541492
$491$	−9.37652e6	−1.75525	−0.877623	−	0.479352i	$-0.840872\pi$
$491$	−9.37652e6	−1.75525	−0.877623	+	0.479352i	$0.840872\pi$
$492$	596221.	0.111044
$493$	1.31283e6	0.243271
$494$	161340.	0.0297458
$495$	−558818.	−0.102508
$496$	6.94292e6	1.26718
$497$	−8.06109e6	−1.46387
$498$	3.16966e6	0.572716
$499$	1.65942e6	0.298336	0.149168	−	0.988812i	$-0.452340\pi$
$499$	1.65942e6	0.298336	0.149168	+	0.988812i	$0.452340\pi$
$500$	149420.	0.0267291
$501$	−3.94698e6	−0.702539
$502$	6.47408e6	1.14662
$503$	7.51971e6	1.32520	0.662600	−	0.748974i	$-0.269453\pi$
$503$	7.51971e6	1.32520	0.662600	+	0.748974i	$0.269453\pi$
$504$	4.97507e6	0.872415
$505$	4.39718e6	0.767266
$506$	−1.01836e6	−0.176818
$507$	−2.79749e6	−0.483336
$508$	−3.02475e6	−0.520032
$509$	2.56661e6	0.439102	0.219551	−	0.975601i	$-0.429541\pi$
$509$	2.56661e6	0.439102	0.219551	+	0.975601i	$0.429541\pi$
$510$	−814541.	−0.138672
$511$	−222316.	−0.0376633
$512$	−1.57632e6	−0.265747
$513$	1.17867e6	0.197741
$514$	−7.13271e6	−1.19082
$515$	−2.10088e6	−0.349046
$516$	−341365.	−0.0564411
$517$	−1.50605e6	−0.247807
$518$	−1.17195e7	−1.91904
$519$	4.75483e6	0.774847
$520$	250693.	0.0406569
$521$	−1.00458e7	−1.62139	−0.810697	−	0.585466i	$-0.800911\pi$
$521$	−1.00458e7	−1.62139	−0.810697	+	0.585466i	$0.800911\pi$
$522$	2.36155e6	0.379333
$523$	7.82091e6	1.25027	0.625134	−	0.780517i	$-0.285044\pi$
$523$	7.82091e6	1.25027	0.625134	+	0.780517i	$0.285044\pi$
$524$	2.63886e6	0.419845
$525$	888229.	0.140646
$526$	−3.99464e6	−0.629526
$527$	3.71136e6	0.582113
$528$	−1.14397e6	−0.178579
$529$	−4.73211e6	−0.735218
$530$	806573.	0.124725
$531$	−2.34011e6	−0.360163
$532$	−642733.	−0.0984581
$533$	−566227.	−0.0863321
$534$	1.25418e6	0.190330
$535$	−2.58154e6	−0.389937
$536$	4.02582e6	0.605260
$537$	−2.94497e6	−0.440703
$538$	−9.02857e6	−1.34482
$539$	2.16060e6	0.320334
$540$	−780571.	−0.115194
$541$	−4.53424e6	−0.666058	−0.333029	−	0.942917i	$-0.608071\pi$
$541$	−4.53424e6	−0.666058	−0.333029	+	0.942917i	$0.608071\pi$
$542$	−4258.54	−0.000622676 0
$543$	−1.72693e6	−0.251348
$544$	2.22201e6	0.321921
$545$	556750.	0.0802914
$546$	−635156.	−0.0911799
$547$	9.13013e6	1.30469	0.652347	−	0.757921i	$-0.273785\pi$
$547$	9.13013e6	1.30469	0.652347	+	0.757921i	$0.273785\pi$
$548$	−656593.	−0.0933995
$549$	−4.52614e6	−0.640910
$550$	487549.	0.0687245
$551$	715824.	0.100445
$552$	1.44143e6	0.201348
$553$	−1.43055e7	−1.98925
$554$	8.11055e6	1.12273
$555$	−1.86325e6	−0.256767
$556$	−210759.	−0.0289134
$557$	−5.56512e6	−0.760040	−0.380020	−	0.924978i	$-0.624083\pi$
$557$	−5.56512e6	−0.760040	−0.380020	+	0.924978i	$0.624083\pi$
$558$	6.67609e6	0.907688
$559$	324193.	0.0438807
$560$	−5.76491e6	−0.776824
$561$	−611512.	−0.0820348
$562$	5.98992e6	0.799982
$563$	9.32046e6	1.23927	0.619636	−	0.784889i	$-0.287280\pi$
$563$	9.32046e6	1.23927	0.619636	+	0.784889i	$0.287280\pi$
$564$	−908561.	−0.120270
$565$	−4.58491e6	−0.604240
$566$	−1.48141e6	−0.194372
$567$	3.71757e6	0.485626
$568$	6.26295e6	0.814532
$569$	−3.23556e6	−0.418956	−0.209478	−	0.977813i	$-0.567176\pi$
$569$	−3.23556e6	−0.418956	−0.209478	+	0.977813i	$0.567176\pi$
$570$	−444130.	−0.0572563
$571$	−2.39843e6	−0.307848	−0.153924	−	0.988083i	$-0.549191\pi$
$571$	−2.39843e6	−0.307848	−0.153924	+	0.988083i	$0.549191\pi$
$572$	−80215.3	−0.0102510
$573$	2.46063e6	0.313083
$574$	9.80381e6	1.24198
$575$	−815913.	−0.102914
$576$	−3.32472e6	−0.417540
$577$	2.86178e6	0.357846	0.178923	−	0.983863i	$-0.442739\pi$
$577$	2.86178e6	0.357846	0.178923	+	0.983863i	$0.442739\pi$
$578$	−6.32772e6	−0.787821
$579$	−2.60045e6	−0.322368
$580$	−474054.	−0.0585137
$581$	1.19918e7	1.47382
$582$	−7.43272e6	−0.909578
$583$	605531.	0.0737844
$584$	172725.	0.0209568
$585$	320161.	0.0386793
$586$	9.99773e6	1.20270
$587$	−6.62670e6	−0.793784	−0.396892	−	0.917865i	$-0.629911\pi$
$587$	−6.62670e6	−0.793784	−0.396892	+	0.917865i	$0.629911\pi$
$588$	1.30343e6	0.155470
$589$	2.02363e6	0.240349
$590$	2.04166e6	0.241465
$591$	5.77634e6	0.680274
$592$	1.20932e7	1.41819
$593$	5.04942e6	0.589664	0.294832	−	0.955549i	$-0.404736\pi$
$593$	5.04942e6	0.589664	0.294832	+	0.955549i	$0.404736\pi$
$594$	−2.54696e6	−0.296180
$595$	−3.08165e6	−0.356855
$596$	319876.	0.0368864
$597$	−6.10696e6	−0.701276
$598$	583445.	0.0667186
$599$	−1.07991e7	−1.22976	−0.614878	−	0.788623i	$-0.710795\pi$
$599$	−1.07991e7	−1.22976	−0.614878	+	0.788623i	$0.710795\pi$
$600$	−690097.	−0.0782586
$601$	6.56818e6	0.741752	0.370876	−	0.928682i	$-0.379058\pi$
$601$	6.56818e6	0.741752	0.370876	+	0.928682i	$0.379058\pi$
$602$	−5.61316e6	−0.631271
$603$	5.14137e6	0.575819
$604$	4.40726e6	0.491560
$605$	366025.	0.0406558
$606$	8.65561e6	0.957450
$607$	1.21781e7	1.34155	0.670776	−	0.741660i	$-0.265961\pi$
$607$	1.21781e7	1.34155	0.670776	+	0.741660i	$0.265961\pi$
$608$	1.21156e6	0.132918
$609$	−2.81802e6	−0.307893
$610$	3.94890e6	0.429686
$611$	862854.	0.0935049
$612$	1.16962e6	0.126231
$613$	9.31770e6	1.00151	0.500757	−	0.865588i	$-0.333055\pi$
$613$	9.31770e6	1.00151	0.500757	+	0.865588i	$0.333055\pi$
$614$	9.67585e6	1.03578
$615$	1.55868e6	0.166177
$616$	−3.25866e6	−0.346009
$617$	3.18257e6	0.336562	0.168281	−	0.985739i	$-0.446178\pi$
$617$	3.18257e6	0.336562	0.168281	+	0.985739i	$0.446178\pi$
$618$	−4.13547e6	−0.435565
$619$	1.04046e7	1.09144	0.545721	−	0.837967i	$-0.316256\pi$
$619$	1.04046e7	1.09144	0.545721	+	0.837967i	$0.316256\pi$
$620$	−1.34015e6	−0.140015
$621$	4.26233e6	0.443525
$622$	1.80950e6	0.187535
$623$	4.74495e6	0.489792
$624$	655408.	0.0673830
$625$	390625.	0.0400000
$626$	1.26663e7	1.29186
$627$	−333429.	−0.0338715
$628$	1.90308e6	0.192556
$629$	6.46445e6	0.651485
$630$	−5.54335e6	−0.556443
$631$	1.29626e7	1.29604	0.648020	−	0.761624i	$-0.275598\pi$
$631$	1.29626e7	1.29604	0.648020	+	0.761624i	$0.275598\pi$
$632$	1.11144e7	1.10687
$633$	−5.47649e6	−0.543242
$634$	−1.41773e7	−1.40078
$635$	−7.90752e6	−0.778227
$636$	365300.	0.0358103
$637$	−1.23786e6	−0.120871
$638$	−1.54681e6	−0.150448
$639$	7.99842e6	0.774912
$640$	5.58559e6	0.539038
$641$	1.19563e7	1.14935	0.574674	−	0.818382i	$-0.305129\pi$
$641$	1.19563e7	1.14935	0.574674	+	0.818382i	$0.305129\pi$
$642$	−5.08161e6	−0.486591
$643$	6.15778e6	0.587349	0.293675	−	0.955905i	$-0.405122\pi$
$643$	6.15778e6	0.587349	0.293675	+	0.955905i	$0.405122\pi$
$644$	−2.32428e6	−0.220838
$645$	−892423.	−0.0844639
$646$	1.54088e6	0.145274
$647$	−1.65501e6	−0.155432	−0.0777158	−	0.996976i	$-0.524763\pi$
$647$	−1.65501e6	−0.155432	−0.0777158	+	0.996976i	$0.524763\pi$
$648$	−2.88832e6	−0.270214
$649$	1.53277e6	0.142845
$650$	−279329.	−0.0259318
$651$	−7.96652e6	−0.736744
$652$	4.79856e6	0.442071
$653$	−1.79462e7	−1.64699	−0.823494	−	0.567326i	$-0.807978\pi$
$653$	−1.79462e7	−1.64699	−0.823494	+	0.567326i	$0.807978\pi$
$654$	1.09593e6	0.100193
$655$	6.89871e6	0.628296
$656$	−1.01164e7	−0.917839
$657$	220588.	0.0199374
$658$	−1.49397e7	−1.34517
$659$	−6.58305e6	−0.590491	−0.295246	−	0.955421i	$-0.595402\pi$
$659$	−6.58305e6	−0.590491	−0.295246	+	0.955421i	$0.595402\pi$
$660$	220813.	0.0197317
$661$	−1.77625e7	−1.58125	−0.790627	−	0.612298i	$-0.790245\pi$
$661$	−1.77625e7	−1.58125	−0.790627	+	0.612298i	$0.790245\pi$
$662$	1.42978e7	1.26802
$663$	350351.	0.0309542
$664$	−9.31685e6	−0.820067
$665$	−1.68028e6	−0.147342
$666$	1.16284e7	1.01586
$667$	2.58859e6	0.225293
$668$	−4.94474e6	−0.428748
$669$	−1.05213e7	−0.908877
$670$	−4.48567e6	−0.386047
$671$	2.96462e6	0.254192
$672$	−4.76960e6	−0.407435
$673$	−1.05590e6	−0.0898637	−0.0449318	−	0.998990i	$-0.514307\pi$
$673$	−1.05590e6	−0.0898637	−0.0449318	+	0.998990i	$0.514307\pi$
$674$	1.04286e7	0.884254
$675$	−2.04063e6	−0.172387
$676$	−3.50468e6	−0.294972
$677$	7.11853e6	0.596923	0.298462	−	0.954422i	$-0.403527\pi$
$677$	7.11853e6	0.596923	0.298462	+	0.954422i	$0.403527\pi$
$678$	−9.02513e6	−0.754014
$679$	−2.81202e7	−2.34069
$680$	2.39425e6	0.198562
$681$	−9.70423e6	−0.801850
$682$	−4.37283e6	−0.359999
$683$	571954.	0.0469148	0.0234574	−	0.999725i	$-0.492533\pi$
$683$	571954.	0.0469148	0.0234574	+	0.999725i	$0.492533\pi$
$684$	637737.	0.0521196
$685$	−1.71651e6	−0.139772
$686$	1.25937e6	0.102174
$687$	6.19864e6	0.501077
$688$	5.79213e6	0.466517
$689$	−346923.	−0.0278411
$690$	−1.60608e6	−0.128424
$691$	−1.40993e7	−1.12332	−0.561659	−	0.827369i	$-0.689837\pi$
$691$	−1.40993e7	−1.12332	−0.561659	+	0.827369i	$0.689837\pi$
$692$	5.95680e6	0.472877
$693$	−4.16164e6	−0.329179
$694$	−1.28937e7	−1.01620
$695$	−550981.	−0.0432688
$696$	2.18942e6	0.171319
$697$	−5.40776e6	−0.421634
$698$	−8.42512e6	−0.654542
$699$	−1.03943e7	−0.804639
$700$	1.11277e6	0.0858338
$701$	2.52129e7	1.93788	0.968941	−	0.247290i	$-0.0795401\pi$
$701$	2.52129e7	1.93788	0.968941	+	0.247290i	$0.0795401\pi$
$702$	1.45921e6	0.111757
$703$	3.52475e6	0.268993
$704$	2.17768e6	0.165601
$705$	−2.37523e6	−0.179983
$706$	−1.14068e7	−0.861292
$707$	3.27468e7	2.46389
$708$	924678.	0.0693278
$709$	−2.40918e7	−1.79992	−0.899961	−	0.435970i	$-0.856405\pi$
$709$	−2.40918e7	−1.79992	−0.899961	+	0.435970i	$0.856405\pi$
$710$	−6.97834e6	−0.519525
$711$	1.41943e7	1.05303
$712$	−3.68652e6	−0.272532
$713$	7.31793e6	0.539094
$714$	−6.06607e6	−0.445309
$715$	−209705.	−0.0153406
$716$	−3.68944e6	−0.268954
$717$	5.85962e6	0.425668
$718$	6.01427e6	0.435384
$719$	5.48099e6	0.395400	0.197700	−	0.980263i	$-0.436653\pi$
$719$	5.48099e6	0.395400	0.197700	+	0.980263i	$0.436653\pi$
$720$	5.72010e6	0.411218
$721$	−1.56457e7	−1.12088
$722$	840170.	0.0599825
$723$	−6.80970e6	−0.484487
$724$	−2.16349e6	−0.153394
$725$	−1.23931e6	−0.0875657
$726$	720500.	0.0507332
$727$	4.32422e6	0.303440	0.151720	−	0.988424i	$-0.451519\pi$
$727$	4.32422e6	0.303440	0.151720	+	0.988424i	$0.451519\pi$
$728$	1.86697e6	0.130560
$729$	2.36753e6	0.164997
$730$	−192455.	−0.0133666
$731$	3.09620e6	0.214307
$732$	1.78847e6	0.123369
$733$	7.03365e6	0.483527	0.241764	−	0.970335i	$-0.422274\pi$
$733$	7.03365e6	0.483527	0.241764	+	0.970335i	$0.422274\pi$
$734$	−9.84352e6	−0.674389
$735$	3.40753e6	0.232660
$736$	4.38128e6	0.298131
$737$	−3.36759e6	−0.228376
$738$	−9.72760e6	−0.657453
$739$	−2.41602e7	−1.62738	−0.813692	−	0.581297i	$-0.802546\pi$
$739$	−2.41602e7	−1.62738	−0.813692	+	0.581297i	$0.802546\pi$
$740$	−2.33427e6	−0.156701
$741$	191030.	0.0127807
$742$	6.00673e6	0.400524
$743$	−1.69603e7	−1.12709	−0.563547	−	0.826084i	$-0.690564\pi$
$743$	−1.69603e7	−1.12709	−0.563547	+	0.826084i	$0.690564\pi$
$744$	6.18948e6	0.409942
$745$	836244.	0.0552004
$746$	2.92174e7	1.92218
$747$	−1.18986e7	−0.780177
$748$	−766097.	−0.0500645
$749$	−1.92253e7	−1.25218
$750$	768924.	0.0499149
$751$	−2.03295e7	−1.31531	−0.657655	−	0.753320i	$-0.728451\pi$
$751$	−2.03295e7	−1.31531	−0.657655	+	0.753320i	$0.728451\pi$
$752$	1.54160e7	0.994096
$753$	7.66542e6	0.492661
$754$	886206.	0.0567683
$755$	1.15218e7	0.735618
$756$	−5.81309e6	−0.369915
$757$	4.78111e6	0.303242	0.151621	−	0.988439i	$-0.451551\pi$
$757$	4.78111e6	0.303242	0.151621	+	0.988439i	$0.451551\pi$
$758$	1.05810e7	0.668891
$759$	−1.20576e6	−0.0759723
$760$	1.30547e6	0.0819847
$761$	1.12282e6	0.0702827	0.0351414	−	0.999382i	$-0.488812\pi$
$761$	1.12282e6	0.0702827	0.0351414	+	0.999382i	$0.488812\pi$
$762$	−1.55655e7	−0.971127
$763$	4.14624e6	0.257836
$764$	3.08265e6	0.191070
$765$	3.05770e6	0.188904
$766$	−1.30542e7	−0.803859
$767$	−878160.	−0.0538996
$768$	6.59880e6	0.403703
$769$	2.11779e7	1.29142	0.645709	−	0.763584i	$-0.276562\pi$
$769$	2.11779e7	1.29142	0.645709	+	0.763584i	$0.276562\pi$
$770$	3.63089e6	0.220692
$771$	−8.44524e6	−0.511654
$772$	−3.25782e6	−0.196736
$773$	8.40419e6	0.505880	0.252940	−	0.967482i	$-0.418603\pi$
$773$	8.40419e6	0.505880	0.252940	+	0.967482i	$0.418603\pi$
$774$	5.56952e6	0.334169
$775$	−3.50352e6	−0.209532
$776$	2.18476e7	1.30242
$777$	−1.38761e7	−0.824544
$778$	−2.30231e6	−0.136369
$779$	−2.94859e6	−0.174089
$780$	−126509.	−0.00744536
$781$	−5.23895e6	−0.307339
$782$	5.57220e6	0.325844
$783$	6.47414e6	0.377379
$784$	−2.21161e7	−1.28504
$785$	4.97517e6	0.288160
$786$	1.35797e7	0.784033
$787$	2.35320e7	1.35432	0.677161	−	0.735835i	$-0.263210\pi$
$787$	2.35320e7	1.35432	0.677161	+	0.735835i	$0.263210\pi$
$788$	7.23654e6	0.415160
$789$	−4.72972e6	−0.270485
$790$	−1.23840e7	−0.705981
$791$	−3.41448e7	−1.94037
$792$	3.23333e6	0.183163
$793$	−1.69850e6	−0.0959143
$794$	−7.21692e6	−0.406257
$795$	954995.	0.0535899
$796$	−7.65074e6	−0.427977
$797$	1.86590e6	0.104050	0.0520250	−	0.998646i	$-0.483432\pi$
$797$	1.86590e6	0.104050	0.0520250	+	0.998646i	$0.483432\pi$
$798$	−3.30754e6	−0.183864
$799$	8.24070e6	0.456664
$800$	−2.09757e6	−0.115876
$801$	−4.70806e6	−0.259275
$802$	−2.09180e7	−1.14838
$803$	−144485.	−0.00790739
$804$	−2.03158e6	−0.110839
$805$	−6.07629e6	−0.330483
$806$	2.50530e6	0.135838
$807$	−1.06900e7	−0.577820
$808$	−2.54422e7	−1.37096
$809$	−5.89490e6	−0.316669	−0.158334	−	0.987386i	$-0.550612\pi$
$809$	−5.89490e6	−0.316669	−0.158334	+	0.987386i	$0.550612\pi$
$810$	3.21823e6	0.172348
$811$	2.82541e7	1.50844	0.754222	−	0.656619i	$-0.228014\pi$
$811$	2.82541e7	1.50844	0.754222	+	0.656619i	$0.228014\pi$
$812$	−3.53039e6	−0.187902
$813$	−5042.18	−0.000267542 0
$814$	−7.61658e6	−0.402902
$815$	1.25448e7	0.661558
$816$	6.25948e6	0.329089
$817$	1.68821e6	0.0884855
$818$	2.90733e7	1.51919
$819$	2.38431e6	0.124209
$820$	1.95271e6	0.101415
$821$	−260893.	−0.0135084	−0.00675421	−	0.999977i	$-0.502150\pi$
$821$	−260893.	−0.0135084	−0.00675421	+	0.999977i	$0.502150\pi$
$822$	−3.37886e6	−0.174418
$823$	1.70835e7	0.879177	0.439588	−	0.898199i	$-0.355124\pi$
$823$	1.70835e7	0.879177	0.439588	+	0.898199i	$0.355124\pi$
$824$	1.21557e7	0.623682
$825$	577266.	0.0295285
$826$	1.52047e7	0.775404
$827$	−5.44694e6	−0.276942	−0.138471	−	0.990367i	$-0.544219\pi$
$827$	−5.44694e6	−0.276942	−0.138471	+	0.990367i	$0.544219\pi$
$828$	2.30621e6	0.116902
$829$	1.77923e7	0.899180	0.449590	−	0.893235i	$-0.351570\pi$
$829$	1.77923e7	0.899180	0.449590	+	0.893235i	$0.351570\pi$
$830$	1.03811e7	0.523055
$831$	9.60302e6	0.482398
$832$	−1.24765e6	−0.0624862
$833$	−1.18222e7	−0.590319
$834$	−1.08458e6	−0.0539939
$835$	−1.29269e7	−0.641621
$836$	−417716.	−0.0206712
$837$	1.83024e7	0.903013
$838$	1.96678e7	0.967488
$839$	−3.66468e7	−1.79734	−0.898671	−	0.438624i	$-0.855466\pi$
$839$	−3.66468e7	−1.79734	−0.898671	+	0.438624i	$0.855466\pi$
$840$	−5.13931e6	−0.251308
$841$	−1.65793e7	−0.808306
$842$	−4.59179e6	−0.223204
$843$	7.09216e6	0.343724
$844$	−6.86090e6	−0.331532
$845$	−9.16218e6	−0.441425
$846$	1.48236e7	0.712076
$847$	2.72587e6	0.130556
$848$	−6.19825e6	−0.295992
$849$	−1.75401e6	−0.0835147
$850$	−2.66773e6	−0.126647
$851$	1.27463e7	0.603340
$852$	−3.16052e6	−0.149163
$853$	1.26348e7	0.594562	0.297281	−	0.954790i	$-0.403920\pi$
$853$	1.26348e7	0.594562	0.297281	+	0.954790i	$0.403920\pi$
$854$	2.94083e7	1.37983
$855$	1.66722e6	0.0779968
$856$	1.49368e7	0.696745
$857$	−1.37113e6	−0.0637715	−0.0318858	−	0.999492i	$-0.510151\pi$
$857$	−1.37113e6	−0.0637715	−0.0318858	+	0.999492i	$0.510151\pi$
$858$	−412792.	−0.0191431
$859$	3.93670e7	1.82033	0.910164	−	0.414249i	$-0.135956\pi$
$859$	3.93670e7	1.82033	0.910164	+	0.414249i	$0.135956\pi$
$860$	−1.11802e6	−0.0515470
$861$	1.16079e7	0.533635
$862$	2.19954e7	1.00824
$863$	−1.19874e7	−0.547898	−0.273949	−	0.961744i	$-0.588330\pi$
$863$	−1.19874e7	−0.547898	−0.273949	+	0.961744i	$0.588330\pi$
$864$	1.09577e7	0.499386
$865$	1.55727e7	0.707659
$866$	3.54254e7	1.60517
$867$	−7.49212e6	−0.338499
$868$	−9.98039e6	−0.449623
$869$	−9.29723e6	−0.417642
$870$	−2.43951e6	−0.109271
$871$	1.92938e6	0.0861731
$872$	−3.22136e6	−0.143466
$873$	2.79016e7	1.23906
$874$	3.03825e6	0.134538
$875$	2.90907e6	0.128450
$876$	−87163.7	−0.00383774
$877$	1.62604e7	0.713891	0.356946	−	0.934125i	$-0.383818\pi$
$877$	1.62604e7	0.713891	0.356946	+	0.934125i	$0.383818\pi$
$878$	3.32030e7	1.45359
$879$	1.18375e7	0.516757
$880$	−3.74665e6	−0.163094
$881$	3.61065e7	1.56728	0.783638	−	0.621218i	$-0.213362\pi$
$881$	3.61065e7	1.56728	0.783638	+	0.621218i	$0.213362\pi$
$882$	−2.12661e7	−0.920483
$883$	−9.01855e6	−0.389256	−0.194628	−	0.980877i	$-0.562350\pi$
$883$	−9.01855e6	−0.389256	−0.194628	+	0.980877i	$0.562350\pi$
$884$	438916.	0.0188908
$885$	2.41736e6	0.103749
$886$	−2.02776e7	−0.867824
$887$	3.51979e7	1.50213	0.751065	−	0.660228i	$-0.229540\pi$
$887$	3.51979e7	1.50213	0.751065	+	0.660228i	$0.229540\pi$
$888$	1.07808e7	0.458796
$889$	−5.88891e7	−2.49908
$890$	4.10762e6	0.173826
$891$	2.41607e6	0.101957
$892$	−1.31810e7	−0.554673
$893$	4.49326e6	0.188553
$894$	1.64610e6	0.0688831
$895$	−9.64520e6	−0.402489
$896$	4.15971e7	1.73099
$897$	690808.	0.0286666
$898$	1.06697e7	0.441533
$899$	1.11153e7	0.458695
$900$	−1.10411e6	−0.0454368
$901$	−3.31330e6	−0.135972
$902$	6.37156e6	0.260753
$903$	−6.64607e6	−0.271235
$904$	2.65283e7	1.07967
$905$	−5.65594e6	−0.229553
$906$	2.26800e7	0.917957
$907$	1.57928e7	0.637441	0.318720	−	0.947849i	$-0.396747\pi$
$907$	1.57928e7	0.637441	0.318720	+	0.947849i	$0.396747\pi$
$908$	−1.21574e7	−0.489356
$909$	−3.24922e7	−1.30428
$910$	−2.08022e6	−0.0832735
$911$	1.17344e7	0.468453	0.234226	−	0.972182i	$-0.424744\pi$
$911$	1.17344e7	0.468453	0.234226	+	0.972182i	$0.424744\pi$
$912$	3.41300e6	0.135878
$913$	7.79354e6	0.309427
$914$	−1.72394e7	−0.682583
$915$	4.67556e6	0.184621
$916$	7.76560e6	0.305799
$917$	5.13762e7	2.01762
$918$	1.39362e7	0.545807
$919$	−4.30394e7	−1.68104	−0.840519	−	0.541783i	$-0.817750\pi$
$919$	−4.30394e7	−1.68104	−0.840519	+	0.541783i	$0.817750\pi$
$920$	4.72089e6	0.183888
$921$	1.14564e7	0.445038
$922$	−6.25978e6	−0.242511
$923$	3.00153e6	0.115968
$924$	1.64444e6	0.0633635
$925$	−6.10242e6	−0.234502
$926$	5.07111e6	0.194346
$927$	1.55241e7	0.593345
$928$	6.65481e6	0.253668
$929$	1.08934e7	0.414117	0.207059	−	0.978329i	$-0.433611\pi$
$929$	1.08934e7	0.414117	0.207059	+	0.978329i	$0.433611\pi$
$930$	−6.89648e6	−0.261469
$931$	−6.44609e6	−0.243738
$932$	−1.30218e7	−0.491058
$933$	2.14248e6	0.0805773
$934$	9.63039e6	0.361224
$935$	−2.00279e6	−0.0749214
$936$	−1.85246e6	−0.0691128
$937$	1.42661e7	0.530832	0.265416	−	0.964134i	$-0.414491\pi$
$937$	1.42661e7	0.530832	0.265416	+	0.964134i	$0.414491\pi$
$938$	−3.34058e7	−1.23969
$939$	1.49972e7	0.555066
$940$	−2.97566e6	−0.109841
$941$	−2.31007e7	−0.850454	−0.425227	−	0.905087i	$-0.639806\pi$
$941$	−2.31007e7	−0.850454	−0.425227	+	0.905087i	$0.639806\pi$
$942$	9.79335e6	0.359587
$943$	−1.06628e7	−0.390474
$944$	−1.56895e7	−0.573032
$945$	−1.51970e7	−0.553577
$946$	−3.64803e6	−0.132535
$947$	2.43388e7	0.881909	0.440955	−	0.897529i	$-0.354640\pi$
$947$	2.43388e7	0.881909	0.440955	+	0.897529i	$0.354640\pi$
$948$	−5.60877e6	−0.202697
$949$	82778.8	0.00298369
$950$	−1.45459e6	−0.0522915
$951$	−1.67861e7	−0.601864
$952$	1.78305e7	0.637634
$953$	2.19976e7	0.784591	0.392296	−	0.919839i	$-0.371681\pi$
$953$	2.19976e7	0.784591	0.392296	+	0.919839i	$0.371681\pi$
$954$	−5.96003e6	−0.212020
$955$	8.05890e6	0.285935
$956$	7.34087e6	0.259778
$957$	−1.83145e6	−0.0646420
$958$	4.42180e7	1.55663
$959$	−1.27833e7	−0.448843
$960$	3.43447e6	0.120277
$961$	2.79388e6	0.0975886
$962$	4.36373e6	0.152027
$963$	1.90758e7	0.662854
$964$	−8.53114e6	−0.295675
$965$	−8.51684e6	−0.294415
$966$	−1.19608e7	−0.412400
$967$	1.46779e6	0.0504774	0.0252387	−	0.999681i	$-0.491965\pi$
$967$	1.46779e6	0.0504774	0.0252387	+	0.999681i	$0.491965\pi$
$968$	−2.11783e6	−0.0726444
$969$	1.82443e6	0.0624191
$970$	−2.43432e7	−0.830707
$971$	−1.99093e7	−0.677656	−0.338828	−	0.940848i	$-0.610030\pi$
$971$	−1.99093e7	−0.677656	−0.338828	+	0.940848i	$0.610030\pi$
$972$	9.04470e6	0.307064
$973$	−4.10328e6	−0.138947
$974$	−736988.	−0.0248922
$975$	−330730.	−0.0111420
$976$	−3.03460e7	−1.01971
$977$	−1.37243e7	−0.459995	−0.229997	−	0.973191i	$-0.573872\pi$
$977$	−1.37243e7	−0.459995	−0.229997	+	0.973191i	$0.573872\pi$
$978$	2.46937e7	0.825540
$979$	3.08378e6	0.102831
$980$	4.26892e6	0.141989
$981$	−4.11401e6	−0.136487
$982$	−6.04497e7	−2.00039
$983$	−1.45989e7	−0.481878	−0.240939	−	0.970540i	$-0.577455\pi$
$983$	−1.45989e7	−0.481878	−0.240939	+	0.970540i	$0.577455\pi$
$984$	−9.01857e6	−0.296927
$985$	1.89183e7	0.621286
$986$	8.46372e6	0.277248
$987$	−1.76888e7	−0.577972
$988$	239320.	0.00779986
$989$	6.10498e6	0.198469
$990$	−3.60266e6	−0.116825
$991$	1.80787e7	0.584766	0.292383	−	0.956301i	$-0.405552\pi$
$991$	1.80787e7	0.584766	0.292383	+	0.956301i	$0.405552\pi$
$992$	1.88131e7	0.606990
$993$	1.69289e7	0.544822
$994$	−5.19693e7	−1.66832
$995$	−2.00011e7	−0.640467
$996$	4.70164e6	0.150176
$997$	−2.97430e7	−0.947647	−0.473824	−	0.880620i	$-0.657127\pi$
$997$	−2.97430e7	−0.947647	−0.473824	+	0.880620i	$0.657127\pi$
$998$	1.06982e7	0.340004
$999$	3.18790e7	1.01063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.e.1.30	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.e.1.30	✓	38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+6.44693 q^{2} +7.63327 q^{3} +9.56289 q^{4} +25.0000 q^{5} +49.2111 q^{6} +186.181 q^{7} -144.650 q^{8} -184.733 q^{9} +O(q^{10})\)	\(q+6.44693 q^{2} +7.63327 q^{3} +9.56289 q^{4} +25.0000 q^{5} +49.2111 q^{6} +186.181 q^{7} -144.650 q^{8} -184.733 q^{9} +161.173 q^{10} +121.000 q^{11} +72.9961 q^{12} -69.3239 q^{13} +1200.29 q^{14} +190.832 q^{15} -1238.56 q^{16} -662.079 q^{17} -1190.96 q^{18} -361.000 q^{19} +239.072 q^{20} +1421.17 q^{21} +780.078 q^{22} -1305.46 q^{23} -1104.16 q^{24} +625.000 q^{25} -446.926 q^{26} -3265.00 q^{27} +1780.42 q^{28} -1982.89 q^{29} +1230.28 q^{30} -5605.62 q^{31} -3356.12 q^{32} +923.625 q^{33} -4268.37 q^{34} +4654.51 q^{35} -1766.58 q^{36} -9763.86 q^{37} -2327.34 q^{38} -529.168 q^{39} -3616.26 q^{40} +8167.85 q^{41} +9162.16 q^{42} -4676.49 q^{43} +1157.11 q^{44} -4618.33 q^{45} -8416.22 q^{46} -12446.7 q^{47} -9454.29 q^{48} +17856.2 q^{49} +4029.33 q^{50} -5053.82 q^{51} -662.937 q^{52} +5004.39 q^{53} -21049.2 q^{54} +3025.00 q^{55} -26931.1 q^{56} -2755.61 q^{57} -12783.6 q^{58} +12667.5 q^{59} +1824.90 q^{60} +24501.0 q^{61} -36139.1 q^{62} -34393.7 q^{63} +17997.4 q^{64} -1733.10 q^{65} +5954.55 q^{66} -27831.3 q^{67} -6331.38 q^{68} -9964.94 q^{69} +30007.3 q^{70} -43297.1 q^{71} +26721.7 q^{72} -1194.09 q^{73} -62946.9 q^{74} +4770.79 q^{75} -3452.20 q^{76} +22527.9 q^{77} -3411.51 q^{78} -76836.6 q^{79} -30964.1 q^{80} +19967.6 q^{81} +52657.5 q^{82} +64409.4 q^{83} +13590.5 q^{84} -16552.0 q^{85} -30149.0 q^{86} -15135.9 q^{87} -17502.7 q^{88} +25485.7 q^{89} -29774.1 q^{90} -12906.8 q^{91} -12484.0 q^{92} -42789.2 q^{93} -80243.0 q^{94} -9025.00 q^{95} -25618.1 q^{96} -151037. q^{97} +115118. q^{98} -22352.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9} - 600 q^{10} + 4598 q^{11} - 2008 q^{12} - 2663 q^{13} - 1565 q^{14} - 1575 q^{15} + 12390 q^{16} - 3311 q^{17} - 6383 q^{18} - 13718 q^{19} + 14850 q^{20} - 8179 q^{21} - 2904 q^{22} - 3412 q^{23} - 4100 q^{24} + 23750 q^{25} - 1399 q^{26} - 31596 q^{27} - 43653 q^{28} - 13633 q^{29} - 1675 q^{30} - 13789 q^{31} - 58603 q^{32} - 7623 q^{33} - 29149 q^{34} - 18225 q^{35} + 50641 q^{36} - 12103 q^{37} + 8664 q^{38} - 50960 q^{39} - 31800 q^{40} - 37885 q^{41} + 51100 q^{42} - 56119 q^{43} + 71874 q^{44} + 75725 q^{45} - 56291 q^{46} - 37532 q^{47} - 113895 q^{48} + 153501 q^{49} - 15000 q^{50} + 32882 q^{51} - 169554 q^{52} - 51511 q^{53} - 175060 q^{54} + 114950 q^{55} - 84247 q^{56} + 22743 q^{57} - 256962 q^{58} - 154267 q^{59} - 50200 q^{60} - 47165 q^{61} + 143002 q^{62} - 358780 q^{63} + 142292 q^{64} - 66575 q^{65} - 8107 q^{66} - 161712 q^{67} - 210188 q^{68} - 124602 q^{69} - 39125 q^{70} + 6118 q^{71} - 327878 q^{72} - 152182 q^{73} - 167349 q^{74} - 39375 q^{75} - 214434 q^{76} - 88209 q^{77} - 216594 q^{78} - 140433 q^{79} + 309750 q^{80} + 382874 q^{81} - 29842 q^{82} - 515287 q^{83} + 29222 q^{84} - 82775 q^{85} + 204974 q^{86} - 106764 q^{87} - 153912 q^{88} - 271610 q^{89} - 159575 q^{90} - 44332 q^{91} + 236348 q^{92} + 25202 q^{93} - 496224 q^{94} - 342950 q^{95} - 275218 q^{96} - 126390 q^{97} - 285506 q^{98} + 366509 q^{99}+O(q^{100}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9 - 600 * q^10 + 4598 * q^11 - 2008 * q^12 - 2663 * q^13 - 1565 * q^14 - 1575 * q^15 + 12390 * q^16 - 3311 * q^17 - 6383 * q^18 - 13718 * q^19 + 14850 * q^20 - 8179 * q^21 - 2904 * q^22 - 3412 * q^23 - 4100 * q^24 + 23750 * q^25 - 1399 * q^26 - 31596 * q^27 - 43653 * q^28 - 13633 * q^29 - 1675 * q^30 - 13789 * q^31 - 58603 * q^32 - 7623 * q^33 - 29149 * q^34 - 18225 * q^35 + 50641 * q^36 - 12103 * q^37 + 8664 * q^38 - 50960 * q^39 - 31800 * q^40 - 37885 * q^41 + 51100 * q^42 - 56119 * q^43 + 71874 * q^44 + 75725 * q^45 - 56291 * q^46 - 37532 * q^47 - 113895 * q^48 + 153501 * q^49 - 15000 * q^50 + 32882 * q^51 - 169554 * q^52 - 51511 * q^53 - 175060 * q^54 + 114950 * q^55 - 84247 * q^56 + 22743 * q^57 - 256962 * q^58 - 154267 * q^59 - 50200 * q^60 - 47165 * q^61 + 143002 * q^62 - 358780 * q^63 + 142292 * q^64 - 66575 * q^65 - 8107 * q^66 - 161712 * q^67 - 210188 * q^68 - 124602 * q^69 - 39125 * q^70 + 6118 * q^71 - 327878 * q^72 - 152182 * q^73 - 167349 * q^74 - 39375 * q^75 - 214434 * q^76 - 88209 * q^77 - 216594 * q^78 - 140433 * q^79 + 309750 * q^80 + 382874 * q^81 - 29842 * q^82 - 515287 * q^83 + 29222 * q^84 - 82775 * q^85 + 204974 * q^86 - 106764 * q^87 - 153912 * q^88 - 271610 * q^89 - 159575 * q^90 - 44332 * q^91 + 236348 * q^92 + 25202 * q^93 - 496224 * q^94 - 342950 * q^95 - 275218 * q^96 - 126390 * q^97 - 285506 * q^98 + 366509 * q^99

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