LMFDB - Embedded newform 1045.6.a.e.1.5

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			1.5
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)

$f(q)$	$=$	$q-9.74865 q^{2} -7.53353 q^{3} +63.0362 q^{4} +25.0000 q^{5} +73.4417 q^{6} -163.789 q^{7} -302.561 q^{8} -186.246 q^{9} +O(q^{10})$	\(q-9.74865 q^{2} -7.53353 q^{3} +63.0362 q^{4} +25.0000 q^{5} +73.4417 q^{6} -163.789 q^{7} -302.561 q^{8} -186.246 q^{9} -243.716 q^{10} +121.000 q^{11} -474.885 q^{12} -800.976 q^{13} +1596.73 q^{14} -188.338 q^{15} +932.407 q^{16} -2035.89 q^{17} +1815.65 q^{18} -361.000 q^{19} +1575.91 q^{20} +1233.91 q^{21} -1179.59 q^{22} -2068.20 q^{23} +2279.35 q^{24} +625.000 q^{25} +7808.43 q^{26} +3233.74 q^{27} -10324.7 q^{28} +1610.82 q^{29} +1836.04 q^{30} +9955.24 q^{31} +592.255 q^{32} -911.557 q^{33} +19847.1 q^{34} -4094.74 q^{35} -11740.2 q^{36} -3025.32 q^{37} +3519.26 q^{38} +6034.17 q^{39} -7564.04 q^{40} +3446.35 q^{41} -12029.0 q^{42} +265.760 q^{43} +7627.38 q^{44} -4656.15 q^{45} +20162.1 q^{46} +27382.9 q^{47} -7024.31 q^{48} +10020.0 q^{49} -6092.91 q^{50} +15337.4 q^{51} -50490.5 q^{52} +14348.2 q^{53} -31524.6 q^{54} +3025.00 q^{55} +49556.4 q^{56} +2719.60 q^{57} -15703.3 q^{58} +37690.1 q^{59} -11872.1 q^{60} -34893.1 q^{61} -97050.2 q^{62} +30505.1 q^{63} -35610.7 q^{64} -20024.4 q^{65} +8886.45 q^{66} +9096.59 q^{67} -128335. q^{68} +15580.8 q^{69} +39918.2 q^{70} -429.721 q^{71} +56350.8 q^{72} +3621.15 q^{73} +29492.8 q^{74} -4708.45 q^{75} -22756.1 q^{76} -19818.5 q^{77} -58825.0 q^{78} +66678.3 q^{79} +23310.2 q^{80} +20896.3 q^{81} -33597.3 q^{82} -73836.4 q^{83} +77781.2 q^{84} -50897.2 q^{85} -2590.80 q^{86} -12135.1 q^{87} -36609.9 q^{88} -58898.1 q^{89} +45391.2 q^{90} +131191. q^{91} -130371. q^{92} -74998.1 q^{93} -266946. q^{94} -9025.00 q^{95} -4461.77 q^{96} -150166. q^{97} -97681.3 q^{98} -22535.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.74865	−1.72333	−0.861667	−	0.507474i	$-0.830579\pi$
$2$	−9.74865	−1.72333	−0.861667	+	0.507474i	$0.830579\pi$
$3$	−7.53353	−0.483276	−0.241638	−	0.970366i	$-0.577685\pi$
$3$	−7.53353	−0.483276	−0.241638	+	0.970366i	$0.577685\pi$
$4$	63.0362	1.96988
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	73.4417	0.832846
$7$	−163.789	−1.26340	−0.631700	−	0.775213i	$-0.717642\pi$
$7$	−163.789	−1.26340	−0.631700	+	0.775213i	$0.717642\pi$
$8$	−302.561	−1.67143
$9$	−186.246	−0.766444
$10$	−243.716	−0.770699
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−474.885	−0.951997
$13$	−800.976	−1.31450	−0.657251	−	0.753672i	$-0.728281\pi$
$13$	−800.976	−1.31450	−0.657251	+	0.753672i	$0.728281\pi$
$14$	1596.73	2.17726
$15$	−188.338	−0.216128
$16$	932.407	0.910554
$17$	−2035.89	−1.70856	−0.854282	−	0.519810i	$-0.826003\pi$
$17$	−2035.89	−1.70856	−0.854282	+	0.519810i	$0.826003\pi$
$18$	1815.65	1.32084
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	1575.91	0.880958
$21$	1233.91	0.610571
$22$	−1179.59	−0.519605
$23$	−2068.20	−0.815216	−0.407608	−	0.913157i	$-0.633637\pi$
$23$	−2068.20	−0.815216	−0.407608	+	0.913157i	$0.633637\pi$
$24$	2279.35	0.807763
$25$	625.000	0.200000
$26$	7808.43	2.26533
$27$	3233.74	0.853680
$28$	−10324.7	−2.48875
$29$	1610.82	0.355673	0.177837	−	0.984060i	$-0.443090\pi$
$29$	1610.82	0.355673	0.177837	+	0.984060i	$0.443090\pi$
$30$	1836.04	0.372460
$31$	9955.24	1.86058	0.930288	−	0.366830i	$-0.119557\pi$
$31$	9955.24	1.86058	0.930288	+	0.366830i	$0.119557\pi$
$32$	592.255	0.102243
$33$	−911.557	−0.145713
$34$	19847.1	2.94443
$35$	−4094.74	−0.565010
$36$	−11740.2	−1.50981
$37$	−3025.32	−0.363301	−0.181651	−	0.983363i	$-0.558144\pi$
$37$	−3025.32	−0.363301	−0.181651	+	0.983363i	$0.558144\pi$
$38$	3519.26	0.395360
$39$	6034.17	0.635267
$40$	−7564.04	−0.747487
$41$	3446.35	0.320184	0.160092	−	0.987102i	$-0.448821\pi$
$41$	3446.35	0.320184	0.160092	+	0.987102i	$0.448821\pi$
$42$	−12029.0	−1.05222
$43$	265.760	0.0219189	0.0109594	−	0.999940i	$-0.496511\pi$
$43$	265.760	0.0219189	0.0109594	+	0.999940i	$0.496511\pi$
$44$	7627.38	0.593942
$45$	−4656.15	−0.342764
$46$	20162.1	1.40489
$47$	27382.9	1.80815	0.904075	−	0.427373i	$-0.140561\pi$
$47$	27382.9	1.80815	0.904075	+	0.427373i	$0.140561\pi$
$48$	−7024.31	−0.440049
$49$	10020.0	0.596179
$50$	−6092.91	−0.344667
$51$	15337.4	0.825708
$52$	−50490.5	−2.58941
$53$	14348.2	0.701627	0.350814	−	0.936445i	$-0.385905\pi$
$53$	14348.2	0.701627	0.350814	+	0.936445i	$0.385905\pi$
$54$	−31524.6	−1.47118
$55$	3025.00	0.134840
$56$	49556.4	2.11169
$57$	2719.60	0.110871
$58$	−15703.3	−0.612944
$59$	37690.1	1.40960	0.704802	−	0.709404i	$-0.251036\pi$
$59$	37690.1	1.40960	0.704802	+	0.709404i	$0.251036\pi$
$60$	−11872.1	−0.425746
$61$	−34893.1	−1.20065	−0.600323	−	0.799758i	$-0.704961\pi$
$61$	−34893.1	−1.20065	−0.600323	+	0.799758i	$0.704961\pi$
$62$	−97050.2	−3.20640
$63$	30505.1	0.968326
$64$	−35610.7	−1.08675
$65$	−20024.4	−0.587863
$66$	8886.45	0.251113
$67$	9096.59	0.247566	0.123783	−	0.992309i	$-0.460497\pi$
$67$	9096.59	0.247566	0.123783	+	0.992309i	$0.460497\pi$
$68$	−128335.	−3.36567
$69$	15580.8	0.393974
$70$	39918.2	0.973701
$71$	−429.721	−0.0101167	−0.00505837	−	0.999987i	$-0.501610\pi$
$71$	−429.721	−0.0101167	−0.00505837	+	0.999987i	$0.501610\pi$
$72$	56350.8	1.28106
$73$	3621.15	0.0795316	0.0397658	−	0.999209i	$-0.487339\pi$
$73$	3621.15	0.0795316	0.0397658	+	0.999209i	$0.487339\pi$
$74$	29492.8	0.626090
$75$	−4708.45	−0.0966552
$76$	−22756.1	−0.451922
$77$	−19818.5	−0.380929
$78$	−58825.0	−1.09478
$79$	66678.3	1.20203	0.601017	−	0.799236i	$-0.294762\pi$
$79$	66678.3	1.20203	0.601017	+	0.799236i	$0.294762\pi$
$80$	23310.2	0.407212
$81$	20896.3	0.353881
$82$	−33597.3	−0.551785
$83$	−73836.4	−1.17646	−0.588228	−	0.808695i	$-0.700174\pi$
$83$	−73836.4	−1.17646	−0.588228	+	0.808695i	$0.700174\pi$
$84$	77781.2	1.20275
$85$	−50897.2	−0.764093
$86$	−2590.80	−0.0377736
$87$	−12135.1	−0.171888
$88$	−36609.9	−0.503956
$89$	−58898.1	−0.788182	−0.394091	−	0.919071i	$-0.628941\pi$
$89$	−58898.1	−0.788182	−0.394091	+	0.919071i	$0.628941\pi$
$90$	45391.2	0.590698
$91$	131191.	1.66074
$92$	−130371.	−1.60588
$93$	−74998.1	−0.899172
$94$	−266946.	−3.11605
$95$	−9025.00	−0.102598
$96$	−4461.77	−0.0494116
$97$	−150166.	−1.62047	−0.810236	−	0.586104i	$-0.800661\pi$
$97$	−150166.	−1.62047	−0.810236	+	0.586104i	$0.800661\pi$
$98$	−97681.3	−1.02742
$99$	−22535.8	−0.231092
$100$	39397.6	0.393976
$101$	88959.0	0.867734	0.433867	−	0.900977i	$-0.357149\pi$
$101$	88959.0	0.867734	0.433867	+	0.900977i	$0.357149\pi$
$102$	−149519.	−1.42297
$103$	−1217.29	−0.0113058	−0.00565290	−	0.999984i	$-0.501799\pi$
$103$	−1217.29	−0.0113058	−0.00565290	+	0.999984i	$0.501799\pi$
$104$	242344.	2.19710
$105$	30847.8	0.273056
$106$	−139875.	−1.20914
$107$	198823.	1.67883	0.839414	−	0.543493i	$-0.182898\pi$
$107$	198823.	1.67883	0.839414	+	0.543493i	$0.182898\pi$
$108$	203843.	1.68165
$109$	−129300.	−1.04240	−0.521199	−	0.853435i	$-0.674515\pi$
$109$	−129300.	−1.04240	−0.521199	+	0.853435i	$0.674515\pi$
$110$	−29489.7	−0.232374
$111$	22791.3	0.175575
$112$	−152718.	−1.15039
$113$	−59412.2	−0.437703	−0.218851	−	0.975758i	$-0.570231\pi$
$113$	−59412.2	−0.437703	−0.218851	+	0.975758i	$0.570231\pi$
$114$	−26512.5	−0.191068
$115$	−51705.0	−0.364576
$116$	101540.	0.700635
$117$	149178.	1.00749
$118$	−367428.	−2.42922
$119$	333457.	2.15860
$120$	56983.9	0.361242
$121$	14641.0	0.0909091
$122$	340161.	2.06912
$123$	−25963.2	−0.154737
$124$	627541.	3.66512
$125$	15625.0	0.0894427
$126$	−297384.	−1.66875
$127$	−98588.3	−0.542395	−0.271198	−	0.962524i	$-0.587420\pi$
$127$	−98588.3	−0.542395	−0.271198	+	0.962524i	$0.587420\pi$
$128$	328204.	1.77060
$129$	−2002.11	−0.0105929
$130$	195211.	1.01308
$131$	−323254.	−1.64576	−0.822878	−	0.568218i	$-0.807633\pi$
$131$	−323254.	−1.64576	−0.822878	+	0.568218i	$0.807633\pi$
$132$	−57461.1	−0.287038
$133$	59128.0	0.289844
$134$	−88679.5	−0.426639
$135$	80843.4	0.381777
$136$	615981.	2.85575
$137$	370341.	1.68578	0.842889	−	0.538087i	$-0.180853\pi$
$137$	370341.	1.68578	0.842889	+	0.538087i	$0.180853\pi$
$138$	−151892.	−0.678949
$139$	302786.	1.32923	0.664613	−	0.747188i	$-0.268597\pi$
$139$	302786.	1.32923	0.664613	+	0.747188i	$0.268597\pi$
$140$	−258117.	−1.11300
$141$	−206290.	−0.873836
$142$	4189.20	0.0174345
$143$	−96918.1	−0.396337
$144$	−173657.	−0.697889
$145$	40270.5	0.159062
$146$	−35301.3	−0.137059
$147$	−75485.8	−0.288119
$148$	−190705.	−0.715661
$149$	420887.	1.55310	0.776551	−	0.630054i	$-0.216967\pi$
$149$	420887.	1.55310	0.776551	+	0.630054i	$0.216967\pi$
$150$	45901.1	0.166569
$151$	71453.5	0.255024	0.127512	−	0.991837i	$-0.459301\pi$
$151$	71453.5	0.255024	0.127512	+	0.991837i	$0.459301\pi$
$152$	109225.	0.383453
$153$	379176.	1.30952
$154$	193204.	0.656469
$155$	248881.	0.832075
$156$	380371.	1.25140
$157$	379806.	1.22974	0.614869	−	0.788629i	$-0.289209\pi$
$157$	379806.	1.22974	0.614869	+	0.788629i	$0.289209\pi$
$158$	−650024.	−2.07151
$159$	−108092.	−0.339080
$160$	14806.4	0.0457245
$161$	338749.	1.02994
$162$	−203711.	−0.609856
$163$	497077.	1.46540	0.732698	−	0.680554i	$-0.238261\pi$
$163$	497077.	1.46540	0.732698	+	0.680554i	$0.238261\pi$
$164$	217245.	0.630725
$165$	−22788.9	−0.0651649
$166$	719806.	2.02743
$167$	335341.	0.930456	0.465228	−	0.885191i	$-0.345972\pi$
$167$	335341.	0.930456	0.465228	+	0.885191i	$0.345972\pi$
$168$	−373334.	−1.02053
$169$	270269.	0.727913
$170$	496179.	1.31679
$171$	67234.8	0.175834
$172$	16752.5	0.0431776
$173$	−418664.	−1.06353	−0.531765	−	0.846892i	$-0.678471\pi$
$173$	−418664.	−1.06353	−0.531765	+	0.846892i	$0.678471\pi$
$174$	118301.	0.296221
$175$	−102368.	−0.252680
$176$	112821.	0.274542
$177$	−283939.	−0.681228
$178$	574178.	1.35830
$179$	−447312.	−1.04347	−0.521733	−	0.853109i	$-0.674714\pi$
$179$	−447312.	−1.04347	−0.521733	+	0.853109i	$0.674714\pi$
$180$	−293506.	−0.675205
$181$	−759113.	−1.72231	−0.861153	−	0.508346i	$-0.830257\pi$
$181$	−759113.	−1.72231	−0.861153	+	0.508346i	$0.830257\pi$
$182$	−1.27894e6	−2.86201
$183$	262868.	0.580243
$184$	625757.	1.36258
$185$	−75633.0	−0.162473
$186$	731130.	1.54957
$187$	−246342.	−0.515151
$188$	1.72611e6	3.56184
$189$	−529652.	−1.07854
$190$	87981.6	0.176810
$191$	43618.5	0.0865141	0.0432571	−	0.999064i	$-0.486227\pi$
$191$	43618.5	0.0865141	0.0432571	+	0.999064i	$0.486227\pi$
$192$	268274.	0.525201
$193$	1.00576e6	1.94358	0.971790	−	0.235846i	$-0.0757862\pi$
$193$	1.00576e6	1.94358	0.971790	+	0.235846i	$0.0757862\pi$
$194$	1.46391e6	2.79261
$195$	150854.	0.284100
$196$	631622.	1.17440
$197$	−758937.	−1.39329	−0.696643	−	0.717418i	$-0.745324\pi$
$197$	−758937.	−1.39329	−0.696643	+	0.717418i	$0.745324\pi$
$198$	219693.	0.398248
$199$	−214509.	−0.383983	−0.191992	−	0.981397i	$-0.561495\pi$
$199$	−214509.	−0.383983	−0.191992	+	0.981397i	$0.561495\pi$
$200$	−189101.	−0.334286
$201$	−68529.4	−0.119643
$202$	−867231.	−1.49540
$203$	−263835.	−0.449358
$204$	966812.	1.62655
$205$	86158.8	0.143191
$206$	11867.0	0.0194837
$207$	385194.	0.624818
$208$	−746835.	−1.19692
$209$	−43681.0	−0.0691714
$210$	−300725.	−0.470566
$211$	600.907	0.000929183 0	0.000464591	−	1.00000i	$-0.499852\pi$
$211$	600.907	0.000929183 0	0.000464591		1.00000i	$0.499852\pi$
$212$	904454.	1.38212
$213$	3237.32	0.00488918
$214$	−1.93825e6	−2.89318
$215$	6644.00	0.00980242
$216$	−978404.	−1.42687
$217$	−1.63056e6	−2.35065
$218$	1.26050e6	1.79640
$219$	−27280.0	−0.0384357
$220$	190685.	0.265619
$221$	1.63070e6	2.24591
$222$	−222185.	−0.302574
$223$	108364.	0.145923	0.0729614	−	0.997335i	$-0.476755\pi$
$223$	108364.	0.145923	0.0729614	+	0.997335i	$0.476755\pi$
$224$	−97005.2	−0.129174
$225$	−116404.	−0.153289
$226$	579188.	0.754308
$227$	−1.07507e6	−1.38475	−0.692377	−	0.721536i	$-0.743436\pi$
$227$	−1.07507e6	−1.38475	−0.692377	+	0.721536i	$0.743436\pi$
$228$	171434.	0.218403
$229$	1.02937e6	1.29712	0.648561	−	0.761162i	$-0.275371\pi$
$229$	1.02937e6	1.29712	0.648561	+	0.761162i	$0.275371\pi$
$230$	504054.	0.628286
$231$	149303.	0.184094
$232$	−487371.	−0.594484
$233$	−1.09022e6	−1.31561	−0.657803	−	0.753190i	$-0.728514\pi$
$233$	−1.09022e6	−1.31561	−0.657803	+	0.753190i	$0.728514\pi$
$234$	−1.45429e6	−1.73625
$235$	684572.	0.808630
$236$	2.37584e6	2.77675
$237$	−502323.	−0.580914
$238$	−3.25075e6	−3.71999
$239$	684296.	0.774906	0.387453	−	0.921889i	$-0.373355\pi$
$239$	684296.	0.774906	0.387453	+	0.921889i	$0.373355\pi$
$240$	−175608.	−0.196796
$241$	−320926.	−0.355928	−0.177964	−	0.984037i	$-0.556951\pi$
$241$	−320926.	−0.355928	−0.177964	+	0.984037i	$0.556951\pi$
$242$	−142730.	−0.156667
$243$	−943221.	−1.02470
$244$	−2.19953e6	−2.36513
$245$	250500.	0.266619
$246$	253106.	0.266664
$247$	289152.	0.301567
$248$	−3.01207e6	−3.10983
$249$	556249.	0.568553
$250$	−152323.	−0.154140
$251$	1.03720e6	1.03915	0.519575	−	0.854425i	$-0.326090\pi$
$251$	1.03720e6	1.03915	0.519575	+	0.854425i	$0.326090\pi$
$252$	1.92293e6	1.90749
$253$	−250252.	−0.245797
$254$	961103.	0.934729
$255$	383435.	0.369268
$256$	−2.06001e6	−1.96458
$257$	−1.56935e6	−1.48213	−0.741065	−	0.671434i	$-0.765679\pi$
$257$	−1.56935e6	−1.48213	−0.741065	+	0.671434i	$0.765679\pi$
$258$	19517.9	0.0182551
$259$	495515.	0.458995
$260$	−1.26226e6	−1.15802
$261$	−300008.	−0.272604
$262$	3.15129e6	2.83619
$263$	1.52719e6	1.36146	0.680728	−	0.732536i	$-0.261663\pi$
$263$	1.52719e6	1.36146	0.680728	+	0.732536i	$0.261663\pi$
$264$	275802.	0.243550
$265$	358704.	0.313777
$266$	−576418.	−0.499498
$267$	443711.	0.380909
$268$	573415.	0.487676
$269$	302902.	0.255224	0.127612	−	0.991824i	$-0.459269\pi$
$269$	302902.	0.255224	0.127612	+	0.991824i	$0.459269\pi$
$270$	−788114.	−0.657930
$271$	−2.05001e6	−1.69564	−0.847820	−	0.530284i	$-0.822085\pi$
$271$	−2.05001e6	−1.69564	−0.847820	+	0.530284i	$0.822085\pi$
$272$	−1.89827e6	−1.55574
$273$	−988334.	−0.802596
$274$	−3.61033e6	−2.90516
$275$	75625.0	0.0603023
$276$	982157.	0.776083
$277$	−1.55925e6	−1.22100	−0.610502	−	0.792015i	$-0.709032\pi$
$277$	−1.55925e6	−1.22100	−0.610502	+	0.792015i	$0.709032\pi$
$278$	−2.95175e6	−2.29070
$279$	−1.85412e6	−1.42603
$280$	1.23891e6	0.944375
$281$	1.46440e6	1.10635	0.553175	−	0.833065i	$-0.313416\pi$
$281$	1.46440e6	1.10635	0.553175	+	0.833065i	$0.313416\pi$
$282$	2.01105e6	1.50591
$283$	−905284.	−0.671922	−0.335961	−	0.941876i	$-0.609061\pi$
$283$	−905284.	−0.671922	−0.335961	+	0.941876i	$0.609061\pi$
$284$	−27088.0	−0.0199288
$285$	67990.1	0.0495831
$286$	944820.	0.683021
$287$	−564476.	−0.404521
$288$	−110305.	−0.0783636
$289$	2.72498e6	1.91919
$290$	−392583.	−0.274117
$291$	1.13128e6	0.783135
$292$	228264.	0.156668
$293$	224211.	0.152577	0.0762884	−	0.997086i	$-0.475693\pi$
$293$	224211.	0.152577	0.0762884	+	0.997086i	$0.475693\pi$
$294$	735885.	0.496525
$295$	942252.	0.630394
$296$	915345.	0.607233
$297$	391282.	0.257394
$298$	−4.10308e6	−2.67652
$299$	1.65658e6	1.07160
$300$	−296803.	−0.190399
$301$	−43528.7	−0.0276923
$302$	−696576.	−0.439492
$303$	−670175.	−0.419355
$304$	−336599.	−0.208895
$305$	−872328.	−0.536945
$306$	−3.69645e6	−2.25674
$307$	−2.44680e6	−1.48167	−0.740836	−	0.671685i	$-0.765571\pi$
$307$	−2.44680e6	−1.48167	−0.740836	+	0.671685i	$0.765571\pi$
$308$	−1.24928e6	−0.750386
$309$	9170.50	0.00546383
$310$	−2.42625e6	−1.43394
$311$	−2.28414e6	−1.33913	−0.669565	−	0.742754i	$-0.733519\pi$
$311$	−2.28414e6	−1.33913	−0.669565	+	0.742754i	$0.733519\pi$
$312$	−1.82571e6	−1.06180
$313$	1.25574e6	0.724500	0.362250	−	0.932081i	$-0.382009\pi$
$313$	1.25574e6	0.724500	0.362250	+	0.932081i	$0.382009\pi$
$314$	−3.70260e6	−2.11925
$315$	762628.	0.433048
$316$	4.20315e6	2.36787
$317$	−2.45242e6	−1.37072	−0.685358	−	0.728206i	$-0.740354\pi$
$317$	−2.45242e6	−1.37072	−0.685358	+	0.728206i	$0.740354\pi$
$318$	1.05375e6	0.584348
$319$	194909.	0.107240
$320$	−890268.	−0.486011
$321$	−1.49784e6	−0.811337
$322$	−3.30235e6	−1.77494
$323$	734955.	0.391971
$324$	1.31723e6	0.697104
$325$	−500610.	−0.262900
$326$	−4.84583e6	−2.52537
$327$	974087.	0.503765
$328$	−1.04273e6	−0.535166
$329$	−4.48503e6	−2.28442
$330$	222161.	0.112301
$331$	−1.02798e6	−0.515720	−0.257860	−	0.966182i	$-0.583017\pi$
$331$	−1.02798e6	−0.515720	−0.257860	+	0.966182i	$0.583017\pi$
$332$	−4.65437e6	−2.31748
$333$	563454.	0.278450
$334$	−3.26912e6	−1.60349
$335$	227415.	0.110715
$336$	1.15051e6	0.555957
$337$	4.09023e6	1.96188	0.980942	−	0.194300i	$-0.0622436\pi$
$337$	4.09023e6	1.96188	0.980942	+	0.194300i	$0.0622436\pi$
$338$	−2.63476e6	−1.25444
$339$	447583.	0.211531
$340$	−3.20836e6	−1.50517
$341$	1.20458e6	0.560985
$342$	−655449.	−0.303021
$343$	1.11164e6	0.510187
$344$	−80408.7	−0.0366359
$345$	389521.	0.176191
$346$	4.08141e6	1.83282
$347$	1.22989e6	0.548331	0.274166	−	0.961682i	$-0.411598\pi$
$347$	1.22989e6	0.548331	0.274166	+	0.961682i	$0.411598\pi$
$348$	−764954.	−0.338600
$349$	2.51707e6	1.10619	0.553096	−	0.833117i	$-0.313446\pi$
$349$	2.51707e6	1.10619	0.553096	+	0.833117i	$0.313446\pi$
$350$	997954.	0.435452
$351$	−2.59014e6	−1.12216
$352$	71662.9	0.0308275
$353$	2.47507e6	1.05719	0.528593	−	0.848875i	$-0.322720\pi$
$353$	2.47507e6	1.05719	0.528593	+	0.848875i	$0.322720\pi$
$354$	2.76803e6	1.17398
$355$	−10743.0	−0.00452435
$356$	−3.71272e6	−1.55263
$357$	−2.51210e6	−1.04320
$358$	4.36069e6	1.79824
$359$	−1.10843e6	−0.453913	−0.226957	−	0.973905i	$-0.572878\pi$
$359$	−1.10843e6	−0.453913	−0.226957	+	0.973905i	$0.572878\pi$
$360$	1.40877e6	0.572907
$361$	130321.	0.0526316
$362$	7.40033e6	2.96811
$363$	−110298.	−0.0439342
$364$	8.26981e6	3.27146
$365$	90528.8	0.0355676
$366$	−2.56261e6	−0.999954
$367$	−2.52623e6	−0.979056	−0.489528	−	0.871988i	$-0.662831\pi$
$367$	−2.52623e6	−0.979056	−0.489528	+	0.871988i	$0.662831\pi$
$368$	−1.92840e6	−0.742298
$369$	−641869.	−0.245403
$370$	737320.	0.279996
$371$	−2.35008e6	−0.886436
$372$	−4.72759e6	−1.77126
$373$	−1.15731e6	−0.430704	−0.215352	−	0.976536i	$-0.569090\pi$
$373$	−1.15731e6	−0.430704	−0.215352	+	0.976536i	$0.569090\pi$
$374$	2.40150e6	0.887778
$375$	−117711.	−0.0432255
$376$	−8.28501e6	−3.02220
$377$	−1.29023e6	−0.467533
$378$	5.16339e6	1.85868
$379$	5.34180e6	1.91025	0.955125	−	0.296205i	$-0.0957210\pi$
$379$	5.34180e6	1.91025	0.955125	+	0.296205i	$0.0957210\pi$
$380$	−568902.	−0.202106
$381$	742718.	0.262127
$382$	−425221.	−0.149093
$383$	1.47606e6	0.514169	0.257085	−	0.966389i	$-0.417238\pi$
$383$	1.47606e6	0.514169	0.257085	+	0.966389i	$0.417238\pi$
$384$	−2.47254e6	−0.855686
$385$	−495463.	−0.170357
$386$	−9.80484e6	−3.34944
$387$	−49496.7	−0.0167996
$388$	−9.46588e6	−3.19214
$389$	−3.61795e6	−1.21224	−0.606119	−	0.795374i	$-0.707275\pi$
$389$	−3.61795e6	−1.21224	−0.606119	+	0.795374i	$0.707275\pi$
$390$	−1.47063e6	−0.489599
$391$	4.21062e6	1.39285
$392$	−3.03166e6	−0.996472
$393$	2.43524e6	0.795355
$394$	7.39862e6	2.40110
$395$	1.66696e6	0.537566
$396$	−1.42057e6	−0.455223
$397$	−2.34531e6	−0.746834	−0.373417	−	0.927664i	$-0.621814\pi$
$397$	−2.34531e6	−0.746834	−0.373417	+	0.927664i	$0.621814\pi$
$398$	2.09117e6	0.661732
$399$	−445442.	−0.140075
$400$	582754.	0.182111
$401$	−2.95329e6	−0.917159	−0.458580	−	0.888653i	$-0.651642\pi$
$401$	−2.95329e6	−0.917159	−0.458580	+	0.888653i	$0.651642\pi$
$402$	668069.	0.206185
$403$	−7.97390e6	−2.44573
$404$	5.60764e6	1.70933
$405$	522408.	0.158261
$406$	2.57204e6	0.774394
$407$	−366064.	−0.109539
$408$	−4.64051e6	−1.38011
$409$	3.95031e6	1.16768	0.583838	−	0.811870i	$-0.301550\pi$
$409$	3.95031e6	1.16768	0.583838	+	0.811870i	$0.301550\pi$
$410$	−839932.	−0.246766
$411$	−2.78997e6	−0.814696
$412$	−76733.5	−0.0222711
$413$	−6.17324e6	−1.78089
$414$	−3.75512e6	−1.07677
$415$	−1.84591e6	−0.526127
$416$	−474382.	−0.134399
$417$	−2.28105e6	−0.642383
$418$	425831.	0.119206
$419$	1.60861e6	0.447625	0.223813	−	0.974632i	$-0.428150\pi$
$419$	1.60861e6	0.447625	0.223813	+	0.974632i	$0.428150\pi$
$420$	1.94453e6	0.537887
$421$	417257.	0.114736	0.0573678	−	0.998353i	$-0.481729\pi$
$421$	417257.	0.114736	0.0573678	+	0.998353i	$0.481729\pi$
$422$	−5858.03	−0.00160129
$423$	−5.09995e6	−1.38585
$424$	−4.34120e6	−1.17272
$425$	−1.27243e6	−0.341713
$426$	−31559.5	−0.00842569
$427$	5.71512e6	1.51690
$428$	1.25330e7	3.30709
$429$	730135.	0.191540
$430$	−64770.0	−0.0168929
$431$	5.31549e6	1.37832	0.689160	−	0.724609i	$-0.257980\pi$
$431$	5.31549e6	1.37832	0.689160	+	0.724609i	$0.257980\pi$
$432$	3.01516e6	0.777321
$433$	229952.	0.0589410	0.0294705	−	0.999566i	$-0.490618\pi$
$433$	229952.	0.0589410	0.0294705	+	0.999566i	$0.490618\pi$
$434$	1.58958e7	4.05096
$435$	−303379.	−0.0768709
$436$	−8.15060e6	−2.05340
$437$	746620.	0.187023
$438$	265944.	0.0662376
$439$	2.81359e6	0.696786	0.348393	−	0.937349i	$-0.386728\pi$
$439$	2.81359e6	0.696786	0.348393	+	0.937349i	$0.386728\pi$
$440$	−915248.	−0.225376
$441$	−1.86618e6	−0.456938
$442$	−1.58971e7	−3.87045
$443$	4.49541e6	1.08833	0.544164	−	0.838979i	$-0.316847\pi$
$443$	4.49541e6	1.08833	0.544164	+	0.838979i	$0.316847\pi$
$444$	1.43668e6	0.345862
$445$	−1.47245e6	−0.352486
$446$	−1.05640e6	−0.251474
$447$	−3.17077e6	−0.750577
$448$	5.83266e6	1.37300
$449$	−4.68907e6	−1.09767	−0.548834	−	0.835931i	$-0.684928\pi$
$449$	−4.68907e6	−1.09767	−0.548834	+	0.835931i	$0.684928\pi$
$450$	1.13478e6	0.264168
$451$	417009.	0.0965392
$452$	−3.74512e6	−0.862223
$453$	−538297.	−0.123247
$454$	1.04805e7	2.38639
$455$	3.27978e6	0.742706
$456$	−822847.	−0.185313
$457$	1.54254e6	0.345498	0.172749	−	0.984966i	$-0.444735\pi$
$457$	1.54254e6	0.345498	0.172749	+	0.984966i	$0.444735\pi$
$458$	−1.00349e7	−2.23538
$459$	−6.58352e6	−1.45857
$460$	−3.25929e6	−0.718171
$461$	−7.37125e6	−1.61543	−0.807717	−	0.589571i	$-0.799297\pi$
$461$	−7.37125e6	−1.61543	−0.807717	+	0.589571i	$0.799297\pi$
$462$	−1.45551e6	−0.317256
$463$	975492.	0.211481	0.105740	−	0.994394i	$-0.466279\pi$
$463$	975492.	0.211481	0.105740	+	0.994394i	$0.466279\pi$
$464$	1.50194e6	0.323860
$465$	−1.87495e6	−0.402122
$466$	1.06282e7	2.26723
$467$	−6.94565e6	−1.47374	−0.736869	−	0.676035i	$-0.763697\pi$
$467$	−6.94565e6	−1.47374	−0.736869	+	0.676035i	$0.763697\pi$
$468$	9.40365e6	1.98464
$469$	−1.48992e6	−0.312775
$470$	−6.67366e6	−1.39354
$471$	−2.86128e6	−0.594303
$472$	−1.14036e7	−2.35606
$473$	32157.0	0.00660879
$474$	4.89697e6	1.00111
$475$	−225625.	−0.0458831
$476$	2.10199e7	4.25219
$477$	−2.67229e6	−0.537758
$478$	−6.67096e6	−1.33542
$479$	8.69595e6	1.73172	0.865861	−	0.500285i	$-0.166771\pi$
$479$	8.69595e6	1.73172	0.865861	+	0.500285i	$0.166771\pi$
$480$	−111544.	−0.0220976
$481$	2.42321e6	0.477560
$482$	3.12859e6	0.613382
$483$	−2.55197e6	−0.497747
$484$	922913.	0.179080
$485$	−3.75414e6	−0.724697
$486$	9.19513e6	1.76591
$487$	4.00124e6	0.764491	0.382245	−	0.924061i	$-0.375151\pi$
$487$	4.00124e6	0.764491	0.382245	+	0.924061i	$0.375151\pi$
$488$	1.05573e7	2.00680
$489$	−3.74474e6	−0.708190
$490$	−2.44203e6	−0.459474
$491$	−9.37510e6	−1.75498	−0.877490	−	0.479595i	$-0.840784\pi$
$491$	−9.37510e6	−1.75498	−0.877490	+	0.479595i	$0.840784\pi$
$492$	−1.63662e6	−0.304814
$493$	−3.27944e6	−0.607691
$494$	−2.81884e6	−0.519701
$495$	−563394.	−0.103347
$496$	9.28233e6	1.69415
$497$	70383.8	0.0127815
$498$	−5.42268e6	−0.979807
$499$	8.92270e6	1.60415	0.802075	−	0.597224i	$-0.203730\pi$
$499$	8.92270e6	1.60415	0.802075	+	0.597224i	$0.203730\pi$
$500$	984941.	0.176192
$501$	−2.52630e6	−0.449667
$502$	−1.01113e7	−1.79080
$503$	−6.47340e6	−1.14081	−0.570404	−	0.821364i	$-0.693213\pi$
$503$	−6.47340e6	−1.14081	−0.570404	+	0.821364i	$0.693213\pi$
$504$	−9.22967e6	−1.61849
$505$	2.22398e6	0.388062
$506$	2.43962e6	0.423590
$507$	−2.03608e6	−0.351783
$508$	−6.21463e6	−1.06846
$509$	−3.28818e6	−0.562549	−0.281275	−	0.959627i	$-0.590757\pi$
$509$	−3.28818e6	−0.562549	−0.281275	+	0.959627i	$0.590757\pi$
$510$	−3.73798e6	−0.636372
$511$	−593106.	−0.100480
$512$	9.57975e6	1.61503
$513$	−1.16738e6	−0.195848
$514$	1.52990e7	2.55420
$515$	−30432.3	−0.00505611
$516$	−126205.	−0.0208667
$517$	3.31333e6	0.545178
$518$	−4.83061e6	−0.791002
$519$	3.15401e6	0.513979
$520$	6.05861e6	0.982572
$521$	3.30865e6	0.534019	0.267009	−	0.963694i	$-0.413965\pi$
$521$	3.30865e6	0.534019	0.267009	+	0.963694i	$0.413965\pi$
$522$	2.92468e6	0.469788
$523$	6.88090e6	1.10000	0.549998	−	0.835166i	$-0.314628\pi$
$523$	6.88090e6	1.10000	0.549998	+	0.835166i	$0.314628\pi$
$524$	−2.03767e7	−3.24195
$525$	771195.	0.122114
$526$	−1.48880e7	−2.34625
$527$	−2.02677e7	−3.17891
$528$	−849942.	−0.132680
$529$	−2.15890e6	−0.335423
$530$	−3.49688e6	−0.540743
$531$	−7.01963e6	−1.08038
$532$	3.72721e6	0.570958
$533$	−2.76044e6	−0.420883
$534$	−4.32558e6	−0.656434
$535$	4.97056e6	0.750795
$536$	−2.75228e6	−0.413790
$537$	3.36984e6	0.504282
$538$	−2.95288e6	−0.439836
$539$	1.21242e6	0.179755
$540$	5.09606e6	0.752056
$541$	1.02342e7	1.50335	0.751674	−	0.659535i	$-0.229247\pi$
$541$	1.02342e7	1.50335	0.751674	+	0.659535i	$0.229247\pi$
$542$	1.99849e7	2.92216
$543$	5.71880e6	0.832349
$544$	−1.20576e6	−0.174689
$545$	−3.23251e6	−0.466174
$546$	9.63492e6	1.38314
$547$	−2.52056e6	−0.360187	−0.180094	−	0.983649i	$-0.557640\pi$
$547$	−2.52056e6	−0.360187	−0.180094	+	0.983649i	$0.557640\pi$
$548$	2.33449e7	3.32079
$549$	6.49870e6	0.920229
$550$	−737242.	−0.103921
$551$	−581505.	−0.0815971
$552$	−4.71416e6	−0.658501
$553$	−1.09212e7	−1.51865
$554$	1.52006e7	2.10420
$555$	569783.	0.0785194
$556$	1.90865e7	2.61842
$557$	−1.12386e7	−1.53488	−0.767438	−	0.641123i	$-0.778469\pi$
$557$	−1.12386e7	−1.53488	−0.767438	+	0.641123i	$0.778469\pi$
$558$	1.80752e7	2.45752
$559$	−212867.	−0.0288124
$560$	−3.81796e6	−0.514471
$561$	1.85583e6	0.248960
$562$	−1.42759e7	−1.90661
$563$	−5.75349e6	−0.764998	−0.382499	−	0.923956i	$-0.624937\pi$
$563$	−5.75349e6	−0.764998	−0.382499	+	0.923956i	$0.624937\pi$
$564$	−1.30037e7	−1.72135
$565$	−1.48530e6	−0.195747
$566$	8.82530e6	1.15795
$567$	−3.42260e6	−0.447094
$568$	130017.	0.0169094
$569$	−5.69935e6	−0.737980	−0.368990	−	0.929433i	$-0.620296\pi$
$569$	−5.69935e6	−0.737980	−0.368990	+	0.929433i	$0.620296\pi$
$570$	−662812.	−0.0854482
$571$	−1.33843e7	−1.71793	−0.858966	−	0.512033i	$-0.828893\pi$
$571$	−1.33843e7	−1.71793	−0.858966	+	0.512033i	$0.828893\pi$
$572$	−6.10935e6	−0.780737
$573$	−328601.	−0.0418102
$574$	5.50288e6	0.697125
$575$	−1.29262e6	−0.163043
$576$	6.63235e6	0.832935
$577$	2.30170e6	0.287812	0.143906	−	0.989591i	$-0.454034\pi$
$577$	2.30170e6	0.287812	0.143906	+	0.989591i	$0.454034\pi$
$578$	−2.65648e7	−3.30741
$579$	−7.57695e6	−0.939286
$580$	2.53850e6	0.313333
$581$	1.20936e7	1.48633
$582$	−1.10284e7	−1.34960
$583$	1.73613e6	0.211549
$584$	−1.09562e6	−0.132932
$585$	3.72946e6	0.450564
$586$	−2.18576e6	−0.262941
$587$	−1.40437e6	−0.168223	−0.0841117	−	0.996456i	$-0.526805\pi$
$587$	−1.40437e6	−0.168223	−0.0841117	+	0.996456i	$0.526805\pi$
$588$	−4.75834e6	−0.567560
$589$	−3.59384e6	−0.426845
$590$	−9.18569e6	−1.08638
$591$	5.71748e6	0.673342
$592$	−2.82083e6	−0.330805
$593$	5.18246e6	0.605201	0.302600	−	0.953118i	$-0.402145\pi$
$593$	5.18246e6	0.605201	0.302600	+	0.953118i	$0.402145\pi$
$594$	−3.81447e6	−0.443576
$595$	8.33642e6	0.965355
$596$	2.65312e7	3.05943
$597$	1.61601e6	0.185570
$598$	−1.61494e7	−1.84673
$599$	−207163.	−0.0235909	−0.0117954	−	0.999930i	$-0.503755\pi$
$599$	−207163.	−0.0235909	−0.0117954	+	0.999930i	$0.503755\pi$
$600$	1.42460e6	0.161553
$601$	3.86782e6	0.436797	0.218399	−	0.975860i	$-0.429917\pi$
$601$	3.86782e6	0.436797	0.218399	+	0.975860i	$0.429917\pi$
$602$	424346.	0.0477231
$603$	−1.69420e6	−0.189746
$604$	4.50416e6	0.502367
$605$	366025.	0.0406558
$606$	6.53331e6	0.722689
$607$	−2.22661e6	−0.245286	−0.122643	−	0.992451i	$-0.539137\pi$
$607$	−2.22661e6	−0.245286	−0.122643	+	0.992451i	$0.539137\pi$
$608$	−213804.	−0.0234562
$609$	1.98761e6	0.217164
$610$	8.50402e6	0.925336
$611$	−2.19330e7	−2.37682
$612$	2.39018e7	2.57960
$613$	1.40380e7	1.50888	0.754441	−	0.656368i	$-0.227908\pi$
$613$	1.40380e7	1.50888	0.754441	+	0.656368i	$0.227908\pi$
$614$	2.38530e7	2.55342
$615$	−649080.	−0.0692007
$616$	5.99632e6	0.636697
$617$	8.70313e6	0.920370	0.460185	−	0.887823i	$-0.347783\pi$
$617$	8.70313e6	0.920370	0.460185	+	0.887823i	$0.347783\pi$
$618$	−89400.0	−0.00941600
$619$	1.58767e7	1.66546	0.832729	−	0.553681i	$-0.186777\pi$
$619$	1.58767e7	1.66546	0.832729	+	0.553681i	$0.186777\pi$
$620$	1.56885e7	1.63909
$621$	−6.68801e6	−0.695934
$622$	2.22673e7	2.30777
$623$	9.64689e6	0.995789
$624$	5.62630e6	0.578444
$625$	390625.	0.0400000
$626$	−1.22418e7	−1.24856
$627$	329072.	0.0334289
$628$	2.39415e7	2.42244
$629$	6.15921e6	0.620723
$630$	−7.43460e6	−0.746287
$631$	−7.60899e6	−0.760770	−0.380385	−	0.924828i	$-0.624209\pi$
$631$	−7.60899e6	−0.760770	−0.380385	+	0.924828i	$0.624209\pi$
$632$	−2.01743e7	−2.00912
$633$	−4526.95	−0.000449052 0
$634$	2.39078e7	2.36220
$635$	−2.46471e6	−0.242567
$636$	−6.81373e6	−0.667947
$637$	−8.02576e6	−0.783678
$638$	−1.90010e6	−0.184810
$639$	80033.8	0.00775392
$640$	8.20511e6	0.791834
$641$	−1.24638e7	−1.19813	−0.599066	−	0.800700i	$-0.704461\pi$
$641$	−1.24638e7	−1.19813	−0.599066	+	0.800700i	$0.704461\pi$
$642$	1.46019e7	1.39821
$643$	−3.19486e6	−0.304737	−0.152368	−	0.988324i	$-0.548690\pi$
$643$	−3.19486e6	−0.304737	−0.152368	+	0.988324i	$0.548690\pi$
$644$	2.13535e7	2.02887
$645$	−50052.7	−0.00473727
$646$	−7.16482e6	−0.675498
$647$	1.39044e7	1.30584	0.652921	−	0.757426i	$-0.273544\pi$
$647$	1.39044e7	1.30584	0.652921	+	0.757426i	$0.273544\pi$
$648$	−6.32242e6	−0.591488
$649$	4.56050e6	0.425012
$650$	4.88027e6	0.453065
$651$	1.22839e7	1.13601
$652$	3.13339e7	2.88666
$653$	1.47953e6	0.135782	0.0678908	−	0.997693i	$-0.478373\pi$
$653$	1.47953e6	0.135782	0.0678908	+	0.997693i	$0.478373\pi$
$654$	−9.49604e6	−0.868156
$655$	−8.08135e6	−0.736005
$656$	3.21340e6	0.291545
$657$	−674425.	−0.0609565
$658$	4.37230e7	3.93682
$659$	−2.13522e6	−0.191526	−0.0957631	−	0.995404i	$-0.530529\pi$
$659$	−2.13522e6	−0.191526	−0.0957631	+	0.995404i	$0.530529\pi$
$660$	−1.43653e6	−0.128367
$661$	−2.61243e6	−0.232563	−0.116281	−	0.993216i	$-0.537097\pi$
$661$	−2.61243e6	−0.232563	−0.116281	+	0.993216i	$0.537097\pi$
$662$	1.00214e7	0.888758
$663$	−1.22849e7	−1.08539
$664$	2.23401e7	1.96637
$665$	1.47820e6	0.129622
$666$	−5.49291e6	−0.479863
$667$	−3.33149e6	−0.289951
$668$	2.11386e7	1.83289
$669$	−816364.	−0.0705210
$670$	−2.21699e6	−0.190799
$671$	−4.22207e6	−0.362008
$672$	730791.	0.0624266
$673$	−2.25221e6	−0.191677	−0.0958386	−	0.995397i	$-0.530553\pi$
$673$	−2.25221e6	−0.191677	−0.0958386	+	0.995397i	$0.530553\pi$
$674$	−3.98743e7	−3.38098
$675$	2.02109e6	0.170736
$676$	1.70367e7	1.43390
$677$	−3.78944e6	−0.317763	−0.158882	−	0.987298i	$-0.550789\pi$
$677$	−3.78944e6	−0.317763	−0.158882	+	0.987298i	$0.550789\pi$
$678$	−4.36333e6	−0.364539
$679$	2.45955e7	2.04730
$680$	1.53995e7	1.27713
$681$	8.09908e6	0.669218
$682$	−1.17431e7	−0.966765
$683$	−2.25566e6	−0.185022	−0.0925108	−	0.995712i	$-0.529489\pi$
$683$	−2.25566e6	−0.185022	−0.0925108	+	0.995712i	$0.529489\pi$
$684$	4.23823e6	0.346373
$685$	9.25853e6	0.753903
$686$	−1.08370e7	−0.879224
$687$	−7.75476e6	−0.626868
$688$	247796.	0.0199583
$689$	−1.14925e7	−0.922290
$690$	−3.79730e6	−0.303635
$691$	2.19368e7	1.74775	0.873873	−	0.486154i	$-0.161600\pi$
$691$	2.19368e7	1.74775	0.873873	+	0.486154i	$0.161600\pi$
$692$	−2.63910e7	−2.09503
$693$	3.69112e6	0.291961
$694$	−1.19898e7	−0.944958
$695$	7.56965e6	0.594448
$696$	3.67163e6	0.287300
$697$	−7.01638e6	−0.547055
$698$	−2.45380e7	−1.90634
$699$	8.21323e6	0.635801
$700$	−6.45292e6	−0.497750
$701$	−2.23707e7	−1.71943	−0.859715	−	0.510774i	$-0.829359\pi$
$701$	−2.23707e7	−1.71943	−0.859715	+	0.510774i	$0.829359\pi$
$702$	2.52504e7	1.93386
$703$	1.09214e6	0.0833470
$704$	−4.30890e6	−0.327668
$705$	−5.15724e6	−0.390791
$706$	−2.41286e7	−1.82188
$707$	−1.45705e7	−1.09629
$708$	−1.78985e7	−1.34194
$709$	2.11557e7	1.58056	0.790281	−	0.612744i	$-0.209934\pi$
$709$	2.11557e7	1.58056	0.790281	+	0.612744i	$0.209934\pi$
$710$	104730.	0.00779696
$711$	−1.24186e7	−0.921292
$712$	1.78203e7	1.31739
$713$	−2.05894e7	−1.51677
$714$	2.44896e7	1.79778
$715$	−2.42295e6	−0.177247
$716$	−2.81969e7	−2.05550
$717$	−5.15516e6	−0.374494
$718$	1.08057e7	0.782244
$719$	−2.26721e7	−1.63557	−0.817785	−	0.575525i	$-0.804798\pi$
$719$	−2.26721e7	−1.63557	−0.817785	+	0.575525i	$0.804798\pi$
$720$	−4.34143e6	−0.312105
$721$	199380.	0.0142838
$722$	−1.27045e6	−0.0907018
$723$	2.41770e6	0.172011
$724$	−4.78516e7	−3.39274
$725$	1.00676e6	0.0711347
$726$	1.07526e6	0.0757133
$727$	−2.25384e7	−1.58156	−0.790781	−	0.612099i	$-0.790325\pi$
$727$	−2.25384e7	−1.58156	−0.790781	+	0.612099i	$0.790325\pi$
$728$	−3.96934e7	−2.77581
$729$	2.02797e6	0.141333
$730$	−882534.	−0.0612949
$731$	−541057.	−0.0374498
$732$	1.65702e7	1.14301
$733$	−5.87971e6	−0.404200	−0.202100	−	0.979365i	$-0.564777\pi$
$733$	−5.87971e6	−0.404200	−0.202100	+	0.979365i	$0.564777\pi$
$734$	2.46273e7	1.68724
$735$	−1.88714e6	−0.128851
$736$	−1.22490e6	−0.0833502
$737$	1.10069e6	0.0746440
$738$	6.25736e6	0.422912
$739$	−2.03136e7	−1.36828	−0.684142	−	0.729349i	$-0.739823\pi$
$739$	−2.03136e7	−1.36828	−0.684142	+	0.729349i	$0.739823\pi$
$740$	−4.76762e6	−0.320053
$741$	−2.17834e6	−0.145740
$742$	2.29101e7	1.52763
$743$	5.44081e6	0.361570	0.180785	−	0.983523i	$-0.442136\pi$
$743$	5.44081e6	0.361570	0.180785	+	0.983523i	$0.442136\pi$
$744$	2.26915e7	1.50290
$745$	1.05222e7	0.694569
$746$	1.12822e7	0.742247
$747$	1.37517e7	0.901688
$748$	−1.55285e7	−1.01479
$749$	−3.25650e7	−2.12103
$750$	1.14753e6	0.0744920
$751$	−1.94407e7	−1.25780	−0.628901	−	0.777485i	$-0.716495\pi$
$751$	−1.94407e7	−1.25780	−0.628901	+	0.777485i	$0.716495\pi$
$752$	2.55320e7	1.64642
$753$	−7.81378e6	−0.502197
$754$	1.25780e7	0.805716
$755$	1.78634e6	0.114050
$756$	−3.33873e7	−2.12460
$757$	−8.35261e6	−0.529764	−0.264882	−	0.964281i	$-0.585333\pi$
$757$	−8.35261e6	−0.529764	−0.264882	+	0.964281i	$0.585333\pi$
$758$	−5.20754e7	−3.29200
$759$	1.88528e6	0.118788
$760$	2.73062e6	0.171485
$761$	3.63665e6	0.227636	0.113818	−	0.993502i	$-0.463692\pi$
$761$	3.63665e6	0.227636	0.113818	+	0.993502i	$0.463692\pi$
$762$	−7.24050e6	−0.451732
$763$	2.11780e7	1.31696
$764$	2.74954e6	0.170423
$765$	9.47939e6	0.585635
$766$	−1.43896e7	−0.886086
$767$	−3.01888e7	−1.85293
$768$	1.55191e7	0.949432
$769$	2.65094e7	1.61653	0.808266	−	0.588817i	$-0.200406\pi$
$769$	2.65094e7	1.61653	0.808266	+	0.588817i	$0.200406\pi$
$770$	4.83010e6	0.293582
$771$	1.18227e7	0.716278
$772$	6.33995e7	3.82862
$773$	5.36449e6	0.322909	0.161454	−	0.986880i	$-0.448382\pi$
$773$	5.36449e6	0.322909	0.161454	+	0.986880i	$0.448382\pi$
$774$	482526.	0.0289513
$775$	6.22202e6	0.372115
$776$	4.54343e7	2.70851
$777$	−3.73298e6	−0.221821
$778$	3.52701e7	2.08909
$779$	−1.24413e6	−0.0734553
$780$	9.50929e6	0.559643
$781$	−51996.3	−0.00305031
$782$	−4.10478e7	−2.40034
$783$	5.20896e6	0.303631
$784$	9.34270e6	0.542853
$785$	9.49515e6	0.549956
$786$	−2.37403e7	−1.37066
$787$	3.45530e7	1.98861	0.994305	−	0.106574i	$-0.0339881\pi$
$787$	3.45530e7	1.98861	0.994305	+	0.106574i	$0.0339881\pi$
$788$	−4.78405e7	−2.74461
$789$	−1.15051e7	−0.657959
$790$	−1.62506e7	−0.926406
$791$	9.73108e6	0.552993
$792$	6.81845e6	0.386254
$793$	2.79485e7	1.57825
$794$	2.28636e7	1.28704
$795$	−2.70231e6	−0.151641
$796$	−1.35218e7	−0.756402
$797$	7.79905e6	0.434906	0.217453	−	0.976071i	$-0.430225\pi$
$797$	7.79905e6	0.434906	0.217453	+	0.976071i	$0.430225\pi$
$798$	4.34246e6	0.241395
$799$	−5.57485e7	−3.08934
$800$	370160.	0.0204486
$801$	1.09695e7	0.604098
$802$	2.87906e7	1.58057
$803$	438159.	0.0239797
$804$	−4.31983e6	−0.235682
$805$	8.46873e6	0.460605
$806$	7.77348e7	4.21481
$807$	−2.28192e6	−0.123343
$808$	−2.69156e7	−1.45036
$809$	1.43708e7	0.771985	0.385993	−	0.922502i	$-0.373859\pi$
$809$	1.43708e7	0.771985	0.385993	+	0.922502i	$0.373859\pi$
$810$	−5.09278e6	−0.272736
$811$	−1.83075e7	−0.977412	−0.488706	−	0.872449i	$-0.662531\pi$
$811$	−1.83075e7	−0.977412	−0.488706	+	0.872449i	$0.662531\pi$
$812$	−1.66312e7	−0.885182
$813$	1.54438e7	0.819462
$814$	3.56863e6	0.188773
$815$	1.24269e7	0.655345
$816$	1.43007e7	0.751851
$817$	−95939.3	−0.00502854
$818$	−3.85102e7	−2.01230
$819$	−2.44339e7	−1.27287
$820$	5.43113e6	0.282069
$821$	1.34761e6	0.0697758	0.0348879	−	0.999391i	$-0.488893\pi$
$821$	1.34761e6	0.0697758	0.0348879	+	0.999391i	$0.488893\pi$
$822$	2.71985e7	1.40399
$823$	−3.15042e7	−1.62132	−0.810661	−	0.585516i	$-0.800892\pi$
$823$	−3.15042e7	−1.62132	−0.810661	+	0.585516i	$0.800892\pi$
$824$	368306.	0.0188969
$825$	−569723.	−0.0291426
$826$	6.01807e7	3.06907
$827$	1.12035e7	0.569629	0.284814	−	0.958583i	$-0.408068\pi$
$827$	1.12035e7	0.569629	0.284814	+	0.958583i	$0.408068\pi$
$828$	2.42812e7	1.23082
$829$	−2.86838e7	−1.44961	−0.724804	−	0.688956i	$-0.758069\pi$
$829$	−2.86838e7	−1.44961	−0.724804	+	0.688956i	$0.758069\pi$
$830$	1.79951e7	0.906693
$831$	1.17467e7	0.590082
$832$	2.85233e7	1.42854
$833$	−2.03995e7	−1.01861
$834$	2.22371e7	1.10704
$835$	8.38353e6	0.416112
$836$	−2.75349e6	−0.136260
$837$	3.21926e7	1.58834
$838$	−1.56817e7	−0.771408
$839$	2.55832e7	1.25473	0.627364	−	0.778726i	$-0.284134\pi$
$839$	2.55832e7	1.25473	0.627364	+	0.778726i	$0.284134\pi$
$840$	−9.33335e6	−0.456394
$841$	−1.79164e7	−0.873496
$842$	−4.06769e6	−0.197728
$843$	−1.10321e7	−0.534672
$844$	37878.9	0.00183038
$845$	6.75672e6	0.325533
$846$	4.97177e7	2.38828
$847$	−2.39804e6	−0.114855
$848$	1.33783e7	0.638869
$849$	6.81998e6	0.324724
$850$	1.24045e7	0.588885
$851$	6.25696e6	0.296169
$852$	204068.	0.00963111
$853$	1.21802e7	0.573167	0.286584	−	0.958055i	$-0.407480\pi$
$853$	1.21802e7	0.573167	0.286584	+	0.958055i	$0.407480\pi$
$854$	−5.57147e7	−2.61412
$855$	1.68087e6	0.0786355
$856$	−6.01560e7	−2.80605
$857$	1.02188e7	0.475276	0.237638	−	0.971354i	$-0.423627\pi$
$857$	1.02188e7	0.475276	0.237638	+	0.971354i	$0.423627\pi$
$858$	−7.11783e6	−0.330088
$859$	2.89637e7	1.33928	0.669640	−	0.742685i	$-0.266448\pi$
$859$	2.89637e7	1.33928	0.669640	+	0.742685i	$0.266448\pi$
$860$	418813.	0.0193096
$861$	4.25250e6	0.195495
$862$	−5.18189e7	−2.37531
$863$	−7.47159e6	−0.341496	−0.170748	−	0.985315i	$-0.554618\pi$
$863$	−7.47159e6	−0.341496	−0.170748	+	0.985315i	$0.554618\pi$
$864$	1.91520e6	0.0872829
$865$	−1.04666e7	−0.475625
$866$	−2.24172e6	−0.101575
$867$	−2.05287e7	−0.927499
$868$	−1.02785e8	−4.63051
$869$	8.06807e6	0.362427
$870$	2.95753e6	0.132474
$871$	−7.28614e6	−0.325426
$872$	3.91213e7	1.74230
$873$	2.79677e7	1.24200
$874$	−7.27854e6	−0.322304
$875$	−2.55921e6	−0.113002
$876$	−1.71963e6	−0.0757138
$877$	2.19350e7	0.963028	0.481514	−	0.876438i	$-0.340087\pi$
$877$	2.19350e7	0.963028	0.481514	+	0.876438i	$0.340087\pi$
$878$	−2.74287e7	−1.20079
$879$	−1.68910e6	−0.0737367
$880$	2.82053e6	0.122779
$881$	2.95032e7	1.28065	0.640324	−	0.768105i	$-0.278800\pi$
$881$	2.95032e7	1.28065	0.640324	+	0.768105i	$0.278800\pi$
$882$	1.81928e7	0.787457
$883$	−5.24647e6	−0.226446	−0.113223	−	0.993570i	$-0.536118\pi$
$883$	−5.24647e6	−0.226446	−0.113223	+	0.993570i	$0.536118\pi$
$884$	1.02793e8	4.42418
$885$	−7.09848e6	−0.304654
$886$	−4.38242e7	−1.87555
$887$	−3.40838e7	−1.45458	−0.727292	−	0.686328i	$-0.759222\pi$
$887$	−3.40838e7	−1.45458	−0.727292	+	0.686328i	$0.759222\pi$
$888$	−6.89578e6	−0.293461
$889$	1.61477e7	0.685262
$890$	1.43544e7	0.607451
$891$	2.52846e6	0.106699
$892$	6.83087e6	0.287451
$893$	−9.88522e6	−0.414818
$894$	3.09107e7	1.29350
$895$	−1.11828e7	−0.466652
$896$	−5.37564e7	−2.23697
$897$	−1.24799e7	−0.517880
$898$	4.57121e7	1.89165
$899$	1.60361e7	0.661758
$900$	−7.33765e6	−0.301961
$901$	−2.92112e7	−1.19878
$902$	−4.06527e6	−0.166369
$903$	327924.	0.0133830
$904$	1.79758e7	0.731590
$905$	−1.89778e7	−0.770238
$906$	5.24767e6	0.212396
$907$	2.66042e7	1.07382	0.536911	−	0.843639i	$-0.319591\pi$
$907$	2.66042e7	1.07382	0.536911	+	0.843639i	$0.319591\pi$
$908$	−6.77684e7	−2.72780
$909$	−1.65683e7	−0.665070
$910$	−3.19735e7	−1.27993
$911$	−2.41867e7	−0.965564	−0.482782	−	0.875740i	$-0.660374\pi$
$911$	−2.41867e7	−0.965564	−0.482782	+	0.875740i	$0.660374\pi$
$912$	2.53578e6	0.100954
$913$	−8.93421e6	−0.354715
$914$	−1.50377e7	−0.595408
$915$	6.57170e6	0.259493
$916$	6.48873e7	2.55518
$917$	5.29456e7	2.07925
$918$	6.41804e7	2.51360
$919$	−1.48431e7	−0.579742	−0.289871	−	0.957066i	$-0.593612\pi$
$919$	−1.48431e7	−0.579742	−0.289871	+	0.957066i	$0.593612\pi$
$920$	1.56439e7	0.609363
$921$	1.84330e7	0.716057
$922$	7.18598e7	2.78393
$923$	344196.	0.0132985
$924$	9.41152e6	0.362644
$925$	−1.89082e6	−0.0726603
$926$	−9.50973e6	−0.364452
$927$	226716.	0.00866527
$928$	954015.	0.0363652
$929$	−3.25317e7	−1.23671	−0.618355	−	0.785899i	$-0.712200\pi$
$929$	−3.25317e7	−1.23671	−0.618355	+	0.785899i	$0.712200\pi$
$930$	1.82783e7	0.692990
$931$	−3.61721e6	−0.136773
$932$	−6.87236e7	−2.59159
$933$	1.72077e7	0.647169
$934$	6.77107e7	2.53974
$935$	−6.15856e6	−0.230383
$936$	−4.51357e7	−1.68395
$937$	−2.45720e7	−0.914307	−0.457153	−	0.889388i	$-0.651131\pi$
$937$	−2.45720e7	−0.914307	−0.457153	+	0.889388i	$0.651131\pi$
$938$	1.45248e7	0.539016
$939$	−9.46014e6	−0.350134
$940$	4.31529e7	1.59291
$941$	3.03778e6	0.111836	0.0559181	−	0.998435i	$-0.482191\pi$
$941$	3.03778e6	0.111836	0.0559181	+	0.998435i	$0.482191\pi$
$942$	2.78936e7	1.02418
$943$	−7.12774e6	−0.261019
$944$	3.51425e7	1.28352
$945$	−1.32413e7	−0.482337
$946$	−313487.	−0.0113892
$947$	1.18046e7	0.427736	0.213868	−	0.976863i	$-0.431394\pi$
$947$	1.18046e7	0.427736	0.213868	+	0.976863i	$0.431394\pi$
$948$	−3.16645e7	−1.14433
$949$	−2.90045e6	−0.104544
$950$	2.19954e6	0.0790720
$951$	1.84754e7	0.662434
$952$	−1.00891e8	−3.60795
$953$	−2.87324e7	−1.02480	−0.512401	−	0.858746i	$-0.671244\pi$
$953$	−2.87324e7	−1.02480	−0.512401	+	0.858746i	$0.671244\pi$
$954$	2.60512e7	0.926737
$955$	1.09046e6	0.0386903
$956$	4.31354e7	1.52647
$957$	−1.46835e6	−0.0518263
$958$	−8.47738e7	−2.98434
$959$	−6.06580e7	−2.12981
$960$	6.70686e6	0.234877
$961$	7.04776e7	2.46174
$962$	−2.36230e7	−0.822996
$963$	−3.70299e7	−1.28673
$964$	−2.02299e7	−0.701136
$965$	2.51441e7	0.869196
$966$	2.48783e7	0.857785
$967$	2.01267e6	0.0692159	0.0346080	−	0.999401i	$-0.488982\pi$
$967$	2.01267e6	0.0692159	0.0346080	+	0.999401i	$0.488982\pi$
$968$	−4.42980e6	−0.151948
$969$	−5.53680e6	−0.189430
$970$	3.65978e7	1.24889
$971$	−4.53789e7	−1.54456	−0.772282	−	0.635280i	$-0.780885\pi$
$971$	−4.53789e7	−1.54456	−0.772282	+	0.635280i	$0.780885\pi$
$972$	−5.94571e7	−2.01854
$973$	−4.95931e7	−1.67934
$974$	−3.90067e7	−1.31747
$975$	3.77136e6	0.127053
$976$	−3.25346e7	−1.09325
$977$	−3.98431e6	−0.133542	−0.0667708	−	0.997768i	$-0.521270\pi$
$977$	−3.98431e6	−0.133542	−0.0667708	+	0.997768i	$0.521270\pi$
$978$	3.65062e7	1.22045
$979$	−7.12668e6	−0.237646
$980$	1.57905e7	0.525209
$981$	2.40817e7	0.798939
$982$	9.13946e7	3.02442
$983$	7.94372e6	0.262205	0.131102	−	0.991369i	$-0.458148\pi$
$983$	7.94372e6	0.262205	0.131102	+	0.991369i	$0.458148\pi$
$984$	7.85546e6	0.258633
$985$	−1.89734e7	−0.623097
$986$	3.19701e7	1.04725
$987$	3.37881e7	1.10400
$988$	1.82271e7	0.594052
$989$	−549644.	−0.0178686
$990$	5.49233e6	0.178102
$991$	1.10387e7	0.357055	0.178527	−	0.983935i	$-0.442867\pi$
$991$	1.10387e7	0.357055	0.178527	+	0.983935i	$0.442867\pi$
$992$	5.89604e6	0.190231
$993$	7.74430e6	0.249235
$994$	−686147.	−0.0220268
$995$	−5.36272e6	−0.171723
$996$	3.50638e7	1.11998
$997$	−2.77294e7	−0.883494	−0.441747	−	0.897140i	$-0.645641\pi$
$997$	−2.77294e7	−0.883494	−0.441747	+	0.897140i	$0.645641\pi$
$998$	−8.69843e7	−2.76449
$999$	−9.78309e6	−0.310143

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.e.1.5	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.e.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-9.74865 q^{2} -7.53353 q^{3} +63.0362 q^{4} +25.0000 q^{5} +73.4417 q^{6} -163.789 q^{7} -302.561 q^{8} -186.246 q^{9} +O(q^{10})\)	\(q-9.74865 q^{2} -7.53353 q^{3} +63.0362 q^{4} +25.0000 q^{5} +73.4417 q^{6} -163.789 q^{7} -302.561 q^{8} -186.246 q^{9} -243.716 q^{10} +121.000 q^{11} -474.885 q^{12} -800.976 q^{13} +1596.73 q^{14} -188.338 q^{15} +932.407 q^{16} -2035.89 q^{17} +1815.65 q^{18} -361.000 q^{19} +1575.91 q^{20} +1233.91 q^{21} -1179.59 q^{22} -2068.20 q^{23} +2279.35 q^{24} +625.000 q^{25} +7808.43 q^{26} +3233.74 q^{27} -10324.7 q^{28} +1610.82 q^{29} +1836.04 q^{30} +9955.24 q^{31} +592.255 q^{32} -911.557 q^{33} +19847.1 q^{34} -4094.74 q^{35} -11740.2 q^{36} -3025.32 q^{37} +3519.26 q^{38} +6034.17 q^{39} -7564.04 q^{40} +3446.35 q^{41} -12029.0 q^{42} +265.760 q^{43} +7627.38 q^{44} -4656.15 q^{45} +20162.1 q^{46} +27382.9 q^{47} -7024.31 q^{48} +10020.0 q^{49} -6092.91 q^{50} +15337.4 q^{51} -50490.5 q^{52} +14348.2 q^{53} -31524.6 q^{54} +3025.00 q^{55} +49556.4 q^{56} +2719.60 q^{57} -15703.3 q^{58} +37690.1 q^{59} -11872.1 q^{60} -34893.1 q^{61} -97050.2 q^{62} +30505.1 q^{63} -35610.7 q^{64} -20024.4 q^{65} +8886.45 q^{66} +9096.59 q^{67} -128335. q^{68} +15580.8 q^{69} +39918.2 q^{70} -429.721 q^{71} +56350.8 q^{72} +3621.15 q^{73} +29492.8 q^{74} -4708.45 q^{75} -22756.1 q^{76} -19818.5 q^{77} -58825.0 q^{78} +66678.3 q^{79} +23310.2 q^{80} +20896.3 q^{81} -33597.3 q^{82} -73836.4 q^{83} +77781.2 q^{84} -50897.2 q^{85} -2590.80 q^{86} -12135.1 q^{87} -36609.9 q^{88} -58898.1 q^{89} +45391.2 q^{90} +131191. q^{91} -130371. q^{92} -74998.1 q^{93} -266946. q^{94} -9025.00 q^{95} -4461.77 q^{96} -150166. q^{97} -97681.3 q^{98} -22535.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) \) 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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