LMFDB - Embedded newform 1045.6.a.d.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:	$0$
Dimension:	$37$
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)

$f(q)$	$=$	$q-9.18127 q^{2} +5.05214 q^{3} +52.2956 q^{4} -25.0000 q^{5} -46.3850 q^{6} +173.574 q^{7} -186.340 q^{8} -217.476 q^{9} +O(q^{10})$	\(q-9.18127 q^{2} +5.05214 q^{3} +52.2956 q^{4} -25.0000 q^{5} -46.3850 q^{6} +173.574 q^{7} -186.340 q^{8} -217.476 q^{9} +229.532 q^{10} +121.000 q^{11} +264.205 q^{12} +64.2936 q^{13} -1593.63 q^{14} -126.303 q^{15} +37.3736 q^{16} +1393.64 q^{17} +1996.70 q^{18} -361.000 q^{19} -1307.39 q^{20} +876.921 q^{21} -1110.93 q^{22} +2219.03 q^{23} -941.413 q^{24} +625.000 q^{25} -590.297 q^{26} -2326.39 q^{27} +9077.18 q^{28} -3687.02 q^{29} +1159.63 q^{30} -7120.22 q^{31} +5619.73 q^{32} +611.308 q^{33} -12795.4 q^{34} -4339.36 q^{35} -11373.0 q^{36} +14776.6 q^{37} +3314.44 q^{38} +324.820 q^{39} +4658.49 q^{40} -3884.60 q^{41} -8051.25 q^{42} -394.051 q^{43} +6327.77 q^{44} +5436.90 q^{45} -20373.5 q^{46} +11994.6 q^{47} +188.816 q^{48} +13321.0 q^{49} -5738.29 q^{50} +7040.87 q^{51} +3362.28 q^{52} -4764.43 q^{53} +21359.2 q^{54} -3025.00 q^{55} -32343.8 q^{56} -1823.82 q^{57} +33851.5 q^{58} +8444.54 q^{59} -6605.12 q^{60} -7844.07 q^{61} +65372.6 q^{62} -37748.2 q^{63} -52792.2 q^{64} -1607.34 q^{65} -5612.59 q^{66} +43563.6 q^{67} +72881.5 q^{68} +11210.9 q^{69} +39840.8 q^{70} +36915.5 q^{71} +40524.4 q^{72} -28901.8 q^{73} -135668. q^{74} +3157.59 q^{75} -18878.7 q^{76} +21002.5 q^{77} -2982.26 q^{78} +10822.1 q^{79} -934.339 q^{80} +41093.4 q^{81} +35665.6 q^{82} -65868.1 q^{83} +45859.1 q^{84} -34841.1 q^{85} +3617.88 q^{86} -18627.3 q^{87} -22547.1 q^{88} +26622.8 q^{89} -49917.6 q^{90} +11159.7 q^{91} +116046. q^{92} -35972.3 q^{93} -110126. q^{94} +9025.00 q^{95} +28391.7 q^{96} +90663.5 q^{97} -122304. q^{98} -26314.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) $ 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9} - 100 q^{10} + 4477 q^{11} + 872 q^{12} + 719 q^{13} - 625 q^{14} - 675 q^{15} + 6940 q^{16} + 119 q^{17} - 4237 q^{18} - 13357 q^{19} - 15400 q^{20} + 2905 q^{21} + 484 q^{22} - 1252 q^{23} + 5884 q^{24} + 23125 q^{25} + 13201 q^{26} + 9918 q^{27} + 15461 q^{28} + 13221 q^{29} - 3525 q^{30} + 6419 q^{31} + 13173 q^{32} + 3267 q^{33} + 35415 q^{34} + 1975 q^{35} + 80543 q^{36} + 9037 q^{37} - 1444 q^{38} - 6184 q^{39} - 1800 q^{40} + 52577 q^{41} - 28578 q^{42} + 963 q^{43} + 74536 q^{44} - 78500 q^{45} - 10531 q^{46} + 49346 q^{47} + 80107 q^{48} + 70288 q^{49} + 2500 q^{50} + 140786 q^{51} + 165062 q^{52} - 34457 q^{53} + 34216 q^{54} - 111925 q^{55} - 64095 q^{56} - 9747 q^{57} - 126140 q^{58} + 56521 q^{59} - 21800 q^{60} + 6613 q^{61} + 494 q^{62} - 125618 q^{63} - 140426 q^{64} - 17975 q^{65} + 17061 q^{66} - 43534 q^{67} - 138520 q^{68} + 34618 q^{69} + 15625 q^{70} + 95986 q^{71} - 42192 q^{72} + 109218 q^{73} - 182005 q^{74} + 16875 q^{75} - 222376 q^{76} - 9559 q^{77} - 369624 q^{78} + 64943 q^{79} - 173500 q^{80} + 388941 q^{81} - 126926 q^{82} + 109741 q^{83} - 112886 q^{84} - 2975 q^{85} + 43866 q^{86} + 142492 q^{87} + 8712 q^{88} - 119092 q^{89} + 105925 q^{90} + 349320 q^{91} + 433396 q^{92} - 108630 q^{93} + 196160 q^{94} + 333925 q^{95} + 376630 q^{96} + 68774 q^{97} + 310926 q^{98} + 379940 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9 - 100 * q^10 + 4477 * q^11 + 872 * q^12 + 719 * q^13 - 625 * q^14 - 675 * q^15 + 6940 * q^16 + 119 * q^17 - 4237 * q^18 - 13357 * q^19 - 15400 * q^20 + 2905 * q^21 + 484 * q^22 - 1252 * q^23 + 5884 * q^24 + 23125 * q^25 + 13201 * q^26 + 9918 * q^27 + 15461 * q^28 + 13221 * q^29 - 3525 * q^30 + 6419 * q^31 + 13173 * q^32 + 3267 * q^33 + 35415 * q^34 + 1975 * q^35 + 80543 * q^36 + 9037 * q^37 - 1444 * q^38 - 6184 * q^39 - 1800 * q^40 + 52577 * q^41 - 28578 * q^42 + 963 * q^43 + 74536 * q^44 - 78500 * q^45 - 10531 * q^46 + 49346 * q^47 + 80107 * q^48 + 70288 * q^49 + 2500 * q^50 + 140786 * q^51 + 165062 * q^52 - 34457 * q^53 + 34216 * q^54 - 111925 * q^55 - 64095 * q^56 - 9747 * q^57 - 126140 * q^58 + 56521 * q^59 - 21800 * q^60 + 6613 * q^61 + 494 * q^62 - 125618 * q^63 - 140426 * q^64 - 17975 * q^65 + 17061 * q^66 - 43534 * q^67 - 138520 * q^68 + 34618 * q^69 + 15625 * q^70 + 95986 * q^71 - 42192 * q^72 + 109218 * q^73 - 182005 * q^74 + 16875 * q^75 - 222376 * q^76 - 9559 * q^77 - 369624 * q^78 + 64943 * q^79 - 173500 * q^80 + 388941 * q^81 - 126926 * q^82 + 109741 * q^83 - 112886 * q^84 - 2975 * q^85 + 43866 * q^86 + 142492 * q^87 + 8712 * q^88 - 119092 * q^89 + 105925 * q^90 + 349320 * q^91 + 433396 * q^92 - 108630 * q^93 + 196160 * q^94 + 333925 * q^95 + 376630 * q^96 + 68774 * q^97 + 310926 * q^98 + 379940 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−9.18127	−1.62303	−0.811517	−	0.584329i	$-0.801358\pi$
$2$	−9.18127	−1.62303	−0.811517	+	0.584329i	$0.801358\pi$
$3$	5.05214	0.324095	0.162047	−	0.986783i	$-0.448190\pi$
$3$	5.05214	0.324095	0.162047	+	0.986783i	$0.448190\pi$
$4$	52.2956	1.63424
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−46.3850	−0.526017
$7$	173.574	1.33888	0.669438	−	0.742868i	$-0.266535\pi$
$7$	173.574	1.33888	0.669438	+	0.742868i	$0.266535\pi$
$8$	−186.340	−1.02939
$9$	−217.476	−0.894963
$10$	229.532	0.725843
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	264.205	0.529648
$13$	64.2936	0.105514	0.0527569	−	0.998607i	$-0.483199\pi$
$13$	64.2936	0.105514	0.0527569	+	0.998607i	$0.483199\pi$
$14$	−1593.63	−2.17304
$15$	−126.303	−0.144940
$16$	37.3736	0.0364976
$17$	1393.64	1.16958	0.584789	−	0.811185i	$-0.301177\pi$
$17$	1393.64	1.16958	0.584789	+	0.811185i	$0.301177\pi$
$18$	1996.70	1.45255
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−1307.39	−0.730854
$21$	876.921	0.433923
$22$	−1110.93	−0.489363
$23$	2219.03	0.874670	0.437335	−	0.899299i	$-0.355922\pi$
$23$	2219.03	0.874670	0.437335	+	0.899299i	$0.355922\pi$
$24$	−941.413	−0.333620
$25$	625.000	0.200000
$26$	−590.297	−0.171253
$27$	−2326.39	−0.614147
$28$	9077.18	2.18804
$29$	−3687.02	−0.814106	−0.407053	−	0.913405i	$-0.633444\pi$
$29$	−3687.02	−0.814106	−0.407053	+	0.913405i	$0.633444\pi$
$30$	1159.63	0.235242
$31$	−7120.22	−1.33073	−0.665364	−	0.746519i	$-0.731723\pi$
$31$	−7120.22	−1.33073	−0.665364	+	0.746519i	$0.731723\pi$
$32$	5619.73	0.970154
$33$	611.308	0.0977182
$34$	−12795.4	−1.89826
$35$	−4339.36	−0.598764
$36$	−11373.0	−1.46258
$37$	14776.6	1.77448	0.887241	−	0.461306i	$-0.152619\pi$
$37$	14776.6	1.77448	0.887241	+	0.461306i	$0.152619\pi$
$38$	3314.44	0.372349
$39$	324.820	0.0341965
$40$	4658.49	0.460358
$41$	−3884.60	−0.360900	−0.180450	−	0.983584i	$-0.557755\pi$
$41$	−3884.60	−0.360900	−0.180450	+	0.983584i	$0.557755\pi$
$42$	−8051.25	−0.704271
$43$	−394.051	−0.0324998	−0.0162499	−	0.999868i	$-0.505173\pi$
$43$	−394.051	−0.0324998	−0.0162499	+	0.999868i	$0.505173\pi$
$44$	6327.77	0.492742
$45$	5436.90	0.400239
$46$	−20373.5	−1.41962
$47$	11994.6	0.792029	0.396014	−	0.918244i	$-0.370393\pi$
$47$	11994.6	0.792029	0.396014	+	0.918244i	$0.370393\pi$
$48$	188.816	0.0118287
$49$	13321.0	0.792589
$50$	−5738.29	−0.324607
$51$	7040.87	0.379054
$52$	3362.28	0.172435
$53$	−4764.43	−0.232981	−0.116491	−	0.993192i	$-0.537165\pi$
$53$	−4764.43	−0.232981	−0.116491	+	0.993192i	$0.537165\pi$
$54$	21359.2	0.996782
$55$	−3025.00	−0.134840
$56$	−32343.8	−1.37823
$57$	−1823.82	−0.0743524
$58$	33851.5	1.32132
$59$	8444.54	0.315825	0.157912	−	0.987453i	$-0.449524\pi$
$59$	8444.54	0.315825	0.157912	+	0.987453i	$0.449524\pi$
$60$	−6605.12	−0.236866
$61$	−7844.07	−0.269909	−0.134954	−	0.990852i	$-0.543089\pi$
$61$	−7844.07	−0.269909	−0.134954	+	0.990852i	$0.543089\pi$
$62$	65372.6	2.15982
$63$	−37748.2	−1.19824
$64$	−52792.2	−1.61109
$65$	−1607.34	−0.0471872
$66$	−5612.59	−0.158600
$67$	43563.6	1.18560	0.592798	−	0.805351i	$-0.298023\pi$
$67$	43563.6	1.18560	0.592798	+	0.805351i	$0.298023\pi$
$68$	72881.5	1.91137
$69$	11210.9	0.283476
$70$	39840.8	0.971813
$71$	36915.5	0.869086	0.434543	−	0.900651i	$-0.356910\pi$
$71$	36915.5	0.869086	0.434543	+	0.900651i	$0.356910\pi$
$72$	40524.4	0.921266
$73$	−28901.8	−0.634773	−0.317386	−	0.948296i	$-0.602805\pi$
$73$	−28901.8	−0.634773	−0.317386	+	0.948296i	$0.602805\pi$
$74$	−135668.	−2.88004
$75$	3157.59	0.0648189
$76$	−18878.7	−0.374920
$77$	21002.5	0.403686
$78$	−2982.26	−0.0555021
$79$	10822.1	0.195093	0.0975466	−	0.995231i	$-0.468901\pi$
$79$	10822.1	0.195093	0.0975466	+	0.995231i	$0.468901\pi$
$80$	−934.339	−0.0163222
$81$	41093.4	0.695921
$82$	35665.6	0.585753
$83$	−65868.1	−1.04949	−0.524747	−	0.851258i	$-0.675840\pi$
$83$	−65868.1	−1.04949	−0.524747	+	0.851258i	$0.675840\pi$
$84$	45859.1	0.709133
$85$	−34841.1	−0.523051
$86$	3617.88	0.0527483
$87$	−18627.3	−0.263847
$88$	−22547.1	−0.310373
$89$	26622.8	0.356269	0.178135	−	0.984006i	$-0.442994\pi$
$89$	26622.8	0.356269	0.178135	+	0.984006i	$0.442994\pi$
$90$	−49917.6	−0.649602
$91$	11159.7	0.141270
$92$	116046.	1.42942
$93$	−35972.3	−0.431282
$94$	−110126.	−1.28549
$95$	9025.00	0.102598
$96$	28391.7	0.314422
$97$	90663.5	0.978370	0.489185	−	0.872180i	$-0.337294\pi$
$97$	90663.5	0.978370	0.489185	+	0.872180i	$0.337294\pi$
$98$	−122304.	−1.28640
$99$	−26314.6	−0.269841
$100$	32684.8	0.326848
$101$	−78378.5	−0.764529	−0.382264	−	0.924053i	$-0.624856\pi$
$101$	−78378.5	−0.764529	−0.382264	+	0.924053i	$0.624856\pi$
$102$	−64644.1	−0.615218
$103$	183267.	1.70213	0.851063	−	0.525063i	$-0.175958\pi$
$103$	183267.	1.70213	0.851063	+	0.525063i	$0.175958\pi$
$104$	−11980.5	−0.108615
$105$	−21923.0	−0.194056
$106$	43743.5	0.378136
$107$	147455.	1.24508	0.622542	−	0.782586i	$-0.286100\pi$
$107$	147455.	1.24508	0.622542	+	0.782586i	$0.286100\pi$
$108$	−121660.	−1.00366
$109$	−53201.6	−0.428903	−0.214451	−	0.976735i	$-0.568796\pi$
$109$	−53201.6	−0.428903	−0.214451	+	0.976735i	$0.568796\pi$
$110$	27773.3	0.218850
$111$	74653.6	0.575100
$112$	6487.09	0.0488658
$113$	26979.4	0.198763	0.0993817	−	0.995049i	$-0.468314\pi$
$113$	26979.4	0.198763	0.0993817	+	0.995049i	$0.468314\pi$
$114$	16745.0	0.120676
$115$	−55475.9	−0.391164
$116$	−192815.	−1.33044
$117$	−13982.3	−0.0944310
$118$	−77531.6	−0.512594
$119$	241901.	1.56592
$120$	23535.3	0.149199
$121$	14641.0	0.0909091
$122$	72018.5	0.438071
$123$	−19625.5	−0.116966
$124$	−372356.	−2.17473
$125$	−15625.0	−0.0894427
$126$	346577.	1.94479
$127$	−124200.	−0.683301	−0.341651	−	0.939827i	$-0.610986\pi$
$127$	−124200.	−0.683301	−0.341651	+	0.939827i	$0.610986\pi$
$128$	304868.	1.64470
$129$	−1990.80	−0.0105330
$130$	14757.4	0.0765865
$131$	142405.	0.725014	0.362507	−	0.931981i	$-0.381921\pi$
$131$	142405.	0.725014	0.362507	+	0.931981i	$0.381921\pi$
$132$	31968.8	0.159695
$133$	−62660.3	−0.307159
$134$	−399969.	−1.92426
$135$	58159.7	0.274655
$136$	−259691.	−1.20395
$137$	−347530.	−1.58194	−0.790971	−	0.611854i	$-0.790424\pi$
$137$	−347530.	−1.58194	−0.790971	+	0.611854i	$0.790424\pi$
$138$	−102930.	−0.460091
$139$	68877.8	0.302373	0.151186	−	0.988505i	$-0.451691\pi$
$139$	68877.8	0.302373	0.151186	+	0.988505i	$0.451691\pi$
$140$	−226929.	−0.978523
$141$	60598.3	0.256692
$142$	−338931.	−1.41056
$143$	7779.53	0.0318136
$144$	−8127.85	−0.0326640
$145$	92175.6	0.364079
$146$	265356.	1.03026
$147$	67299.7	0.256874
$148$	772754.	2.89993
$149$	273603.	1.00961	0.504807	−	0.863232i	$-0.331564\pi$
$149$	273603.	1.00961	0.504807	+	0.863232i	$0.331564\pi$
$150$	−28990.6	−0.105203
$151$	−222542.	−0.794271	−0.397135	−	0.917760i	$-0.629996\pi$
$151$	−222542.	−0.794271	−0.397135	+	0.917760i	$0.629996\pi$
$152$	67268.6	0.236158
$153$	−303084.	−1.04673
$154$	−192829.	−0.655197
$155$	178005.	0.595119
$156$	16986.7	0.0558852
$157$	−311152.	−1.00745	−0.503724	−	0.863864i	$-0.668037\pi$
$157$	−311152.	−1.00745	−0.503724	+	0.863864i	$0.668037\pi$
$158$	−99360.2	−0.316643
$159$	−24070.5	−0.0755080
$160$	−140493.	−0.433866
$161$	385167.	1.17108
$162$	−377290.	−1.12950
$163$	−264480.	−0.779693	−0.389846	−	0.920880i	$-0.627472\pi$
$163$	−264480.	−0.779693	−0.389846	+	0.920880i	$0.627472\pi$
$164$	−203148.	−0.589797
$165$	−15282.7	−0.0437009
$166$	604753.	1.70336
$167$	−175029.	−0.485644	−0.242822	−	0.970071i	$-0.578073\pi$
$167$	−175029.	−0.485644	−0.242822	+	0.970071i	$0.578073\pi$
$168$	−163405.	−0.446676
$169$	−367159.	−0.988867
$170$	319885.	0.848930
$171$	78508.8	0.205319
$172$	−20607.1	−0.0531125
$173$	156662.	0.397969	0.198985	−	0.980003i	$-0.436236\pi$
$173$	156662.	0.397969	0.198985	+	0.980003i	$0.436236\pi$
$174$	171023.	0.428233
$175$	108484.	0.267775
$176$	4522.20	0.0110044
$177$	42663.0	0.102357
$178$	−244431.	−0.578237
$179$	−197985.	−0.461848	−0.230924	−	0.972972i	$-0.574175\pi$
$179$	−197985.	−0.461848	−0.230924	+	0.972972i	$0.574175\pi$
$180$	284326.	0.654087
$181$	−813887.	−1.84658	−0.923289	−	0.384107i	$-0.874509\pi$
$181$	−813887.	−1.84658	−0.923289	+	0.384107i	$0.874509\pi$
$182$	−102460.	−0.229286
$183$	−39629.3	−0.0874760
$184$	−413494.	−0.900378
$185$	−369416.	−0.793573
$186$	330271.	0.699985
$187$	168631.	0.352641
$188$	627265.	1.29436
$189$	−403801.	−0.822267
$190$	−82860.9	−0.166520
$191$	−502889.	−0.997443	−0.498722	−	0.866762i	$-0.666197\pi$
$191$	−502889.	−0.997443	−0.498722	+	0.866762i	$0.666197\pi$
$192$	−266713.	−0.522146
$193$	88655.6	0.171322	0.0856610	−	0.996324i	$-0.472700\pi$
$193$	88655.6	0.171322	0.0856610	+	0.996324i	$0.472700\pi$
$194$	−832406.	−1.58793
$195$	−8120.51	−0.0152931
$196$	696632.	1.29528
$197$	652284.	1.19749	0.598744	−	0.800941i	$-0.295667\pi$
$197$	652284.	1.19749	0.598744	+	0.800941i	$0.295667\pi$
$198$	241601.	0.437962
$199$	−626168.	−1.12088	−0.560439	−	0.828196i	$-0.689367\pi$
$199$	−626168.	−1.12088	−0.560439	+	0.828196i	$0.689367\pi$
$200$	−116462.	−0.205878
$201$	220089.	0.384245
$202$	719614.	1.24086
$203$	−639972.	−1.08999
$204$	368207.	0.619465
$205$	97115.0	0.161399
$206$	−1.68263e6	−2.76261
$207$	−482586.	−0.782797
$208$	2402.88	0.00385101
$209$	−43681.0	−0.0691714
$210$	201281.	0.314960
$211$	132886.	0.205482	0.102741	−	0.994708i	$-0.467239\pi$
$211$	132886.	0.205482	0.102741	+	0.994708i	$0.467239\pi$
$212$	−249159.	−0.380747
$213$	186502.	0.281666
$214$	−1.35382e6	−2.02081
$215$	9851.27	0.0145344
$216$	433498.	0.632198
$217$	−1.23589e6	−1.78168
$218$	488458.	0.696124
$219$	−146016.	−0.205727
$220$	−158194.	−0.220361
$221$	89602.4	0.123407
$222$	−685415.	−0.933407
$223$	241659.	0.325417	0.162709	−	0.986674i	$-0.447977\pi$
$223$	241659.	0.325417	0.162709	+	0.986674i	$0.447977\pi$
$224$	975441.	1.29892
$225$	−135922.	−0.178993
$226$	−247705.	−0.322600
$227$	516263.	0.664976	0.332488	−	0.943107i	$-0.392112\pi$
$227$	516263.	0.664976	0.332488	+	0.943107i	$0.392112\pi$
$228$	−95377.9	−0.121510
$229$	−660036.	−0.831724	−0.415862	−	0.909428i	$-0.636520\pi$
$229$	−660036.	−0.831724	−0.415862	+	0.909428i	$0.636520\pi$
$230$	509339.	0.634873
$231$	106107.	0.130833
$232$	687039.	0.838033
$233$	−70817.3	−0.0854574	−0.0427287	−	0.999087i	$-0.513605\pi$
$233$	−70817.3	−0.0854574	−0.0427287	+	0.999087i	$0.513605\pi$
$234$	128375.	0.153265
$235$	−299865.	−0.354206
$236$	441613.	0.516133
$237$	54674.5	0.0632286
$238$	−2.22095e6	−2.54154
$239$	−346219.	−0.392063	−0.196031	−	0.980598i	$-0.562805\pi$
$239$	−346219.	−0.392063	−0.196031	+	0.980598i	$0.562805\pi$
$240$	−4720.41	−0.00528995
$241$	−1.07787e6	−1.19543	−0.597717	−	0.801707i	$-0.703925\pi$
$241$	−1.07787e6	−1.19543	−0.597717	+	0.801707i	$0.703925\pi$
$242$	−134423.	−0.147549
$243$	772922.	0.839692
$244$	−410211.	−0.441095
$245$	−333026.	−0.354457
$246$	180187.	0.189839
$247$	−23210.0	−0.0242065
$248$	1.32678e6	1.36984
$249$	−332775.	−0.340135
$250$	143457.	0.145169
$251$	325620.	0.326232	0.163116	−	0.986607i	$-0.447845\pi$
$251$	325620.	0.326232	0.163116	+	0.986607i	$0.447845\pi$
$252$	−1.97407e6	−1.95822
$253$	268503.	0.263723
$254$	1.14031e6	1.10902
$255$	−176022.	−0.169518
$256$	−1.10972e6	−1.05831
$257$	453627.	0.428416	0.214208	−	0.976788i	$-0.431283\pi$
$257$	453627.	0.428416	0.214208	+	0.976788i	$0.431283\pi$
$258$	18278.0	0.0170954
$259$	2.56485e6	2.37581
$260$	−84056.9	−0.0771152
$261$	801839.	0.728594
$262$	−1.30746e6	−1.17672
$263$	2.23377e6	1.99135	0.995676	−	0.0928912i	$-0.0296109\pi$
$263$	2.23377e6	1.99135	0.995676	+	0.0928912i	$0.0296109\pi$
$264$	−113911.	−0.100590
$265$	119111.	0.104192
$266$	575301.	0.498530
$267$	134502.	0.115465
$268$	2.27819e6	1.93755
$269$	2.13806e6	1.80152	0.900761	−	0.434314i	$-0.143009\pi$
$269$	2.13806e6	1.80152	0.900761	+	0.434314i	$0.143009\pi$
$270$	−533979.	−0.445774
$271$	−336278.	−0.278148	−0.139074	−	0.990282i	$-0.544413\pi$
$271$	−336278.	−0.278148	−0.139074	+	0.990282i	$0.544413\pi$
$272$	52085.4	0.0426868
$273$	56380.4	0.0457849
$274$	3.19076e6	2.56754
$275$	75625.0	0.0603023
$276$	586279.	0.463267
$277$	1.66797e6	1.30614	0.653068	−	0.757299i	$-0.273481\pi$
$277$	1.66797e6	1.30614	0.653068	+	0.757299i	$0.273481\pi$
$278$	−632386.	−0.490761
$279$	1.54848e6	1.19095
$280$	808595.	0.616362
$281$	1.77294e6	1.33946	0.669728	−	0.742606i	$-0.266411\pi$
$281$	1.77294e6	1.33946	0.669728	+	0.742606i	$0.266411\pi$
$282$	−556369.	−0.416620
$283$	609280.	0.452221	0.226111	−	0.974102i	$-0.427399\pi$
$283$	609280.	0.452221	0.226111	+	0.974102i	$0.427399\pi$
$284$	1.93052e6	1.42029
$285$	45595.5	0.0332514
$286$	−71425.9	−0.0516346
$287$	−674267.	−0.483200
$288$	−1.22216e6	−0.868252
$289$	522384.	0.367913
$290$	−846288.	−0.590913
$291$	458045.	0.317085
$292$	−1.51144e6	−1.03737
$293$	225293.	0.153313	0.0766564	−	0.997058i	$-0.475576\pi$
$293$	225293.	0.153313	0.0766564	+	0.997058i	$0.475576\pi$
$294$	−617897.	−0.416915
$295$	−211114.	−0.141241
$296$	−2.75348e6	−1.82664
$297$	−281493.	−0.185172
$298$	−2.51202e6	−1.63864
$299$	142670.	0.0922899
$300$	165128.	0.105930
$301$	−68397.1	−0.0435132
$302$	2.04321e6	1.28913
$303$	−395979.	−0.247780
$304$	−13491.9	−0.00837313
$305$	196102.	0.120707
$306$	2.78269e6	1.69888
$307$	−1.45175e6	−0.879115	−0.439557	−	0.898214i	$-0.644865\pi$
$307$	−1.45175e6	−0.879115	−0.439557	+	0.898214i	$0.644865\pi$
$308$	1.09834e6	0.659720
$309$	925891.	0.551650
$310$	−1.63432e6	−0.965899
$311$	1.51665e6	0.889172	0.444586	−	0.895736i	$-0.353351\pi$
$311$	1.51665e6	0.889172	0.444586	+	0.895736i	$0.353351\pi$
$312$	−60526.9	−0.0352016
$313$	1.50638e6	0.869108	0.434554	−	0.900646i	$-0.356906\pi$
$313$	1.50638e6	0.869108	0.434554	+	0.900646i	$0.356906\pi$
$314$	2.85677e6	1.63512
$315$	943706.	0.535871
$316$	565946.	0.318829
$317$	−1.50798e6	−0.842846	−0.421423	−	0.906864i	$-0.638469\pi$
$317$	−1.50798e6	−0.842846	−0.421423	+	0.906864i	$0.638469\pi$
$318$	220998.	0.122552
$319$	−446130.	−0.245462
$320$	1.31981e6	0.720502
$321$	744961.	0.403525
$322$	−3.53632e6	−1.90069
$323$	−503105.	−0.268320
$324$	2.14901e6	1.13730
$325$	40183.5	0.0211028
$326$	2.42826e6	1.26547
$327$	−268782.	−0.139005
$328$	723855.	0.371507
$329$	2.08195e6	1.06043
$330$	140315.	0.0709281
$331$	−2.22801e6	−1.11776	−0.558878	−	0.829250i	$-0.688768\pi$
$331$	−2.22801e6	−1.11776	−0.558878	+	0.829250i	$0.688768\pi$
$332$	−3.44462e6	−1.71512
$333$	−3.21357e6	−1.58810
$334$	1.60698e6	0.788217
$335$	−1.08909e6	−0.530214
$336$	32773.7	0.0158371
$337$	577864.	0.277173	0.138586	−	0.990350i	$-0.455744\pi$
$337$	577864.	0.277173	0.138586	+	0.990350i	$0.455744\pi$
$338$	3.37099e6	1.60496
$339$	136304.	0.0644182
$340$	−1.82204e6	−0.854791
$341$	−861546.	−0.401229
$342$	−720810.	−0.333239
$343$	−605073.	−0.277698
$344$	73427.3	0.0334550
$345$	−280272.	−0.126774
$346$	−1.43836e6	−0.645918
$347$	1.53980e6	0.686501	0.343251	−	0.939244i	$-0.388472\pi$
$347$	1.53980e6	0.686501	0.343251	+	0.939244i	$0.388472\pi$
$348$	−974129.	−0.431190
$349$	1.26344e6	0.555251	0.277626	−	0.960689i	$-0.410453\pi$
$349$	1.26344e6	0.555251	0.277626	+	0.960689i	$0.410453\pi$
$350$	−996020.	−0.434608
$351$	−149572.	−0.0648011
$352$	679988.	0.292512
$353$	1.80920e6	0.772767	0.386384	−	0.922338i	$-0.373724\pi$
$353$	1.80920e6	0.772767	0.386384	+	0.922338i	$0.373724\pi$
$354$	−391700.	−0.166129
$355$	−922887.	−0.388667
$356$	1.39226e6	0.582229
$357$	1.22211e6	0.507506
$358$	1.81775e6	0.749594
$359$	2.29905e6	0.941484	0.470742	−	0.882271i	$-0.343986\pi$
$359$	2.29905e6	0.941484	0.470742	+	0.882271i	$0.343986\pi$
$360$	−1.01311e6	−0.412003
$361$	130321.	0.0526316
$362$	7.47251e6	2.99706
$363$	73968.3	0.0294632
$364$	583605.	0.230869
$365$	722546.	0.283879
$366$	363847.	0.141976
$367$	−2.22860e6	−0.863709	−0.431855	−	0.901943i	$-0.642141\pi$
$367$	−2.22860e6	−0.863709	−0.431855	+	0.901943i	$0.642141\pi$
$368$	82933.2	0.0319234
$369$	844807.	0.322992
$370$	3.39171e6	1.28800
$371$	−826982.	−0.311933
$372$	−1.88120e6	−0.704817
$373$	649864.	0.241853	0.120926	−	0.992661i	$-0.461414\pi$
$373$	649864.	0.241853	0.120926	+	0.992661i	$0.461414\pi$
$374$	−1.54824e6	−0.572348
$375$	−78939.6	−0.0289879
$376$	−2.23507e6	−0.815307
$377$	−237052.	−0.0858995
$378$	3.70740e6	1.33457
$379$	−1.83035e6	−0.654541	−0.327271	−	0.944931i	$-0.606129\pi$
$379$	−1.83035e6	−0.654541	−0.327271	+	0.944931i	$0.606129\pi$
$380$	471968.	0.167669
$381$	−627475.	−0.221454
$382$	4.61715e6	1.61888
$383$	−946135.	−0.329576	−0.164788	−	0.986329i	$-0.552694\pi$
$383$	−946135.	−0.329576	−0.164788	+	0.986329i	$0.552694\pi$
$384$	1.54023e6	0.533039
$385$	−525062.	−0.180534
$386$	−813971.	−0.278061
$387$	85696.5	0.0290861
$388$	4.74131e6	1.59889
$389$	5.13328e6	1.71997	0.859985	−	0.510319i	$-0.170473\pi$
$389$	5.13328e6	1.71997	0.859985	+	0.510319i	$0.170473\pi$
$390$	74556.5	0.0248213
$391$	3.09254e6	1.02300
$392$	−2.48224e6	−0.815884
$393$	719449.	0.234973
$394$	−5.98879e6	−1.94356
$395$	−270551.	−0.0872483
$396$	−1.37614e6	−0.440985
$397$	2.25361e6	0.717633	0.358817	−	0.933408i	$-0.383180\pi$
$397$	2.25361e6	0.717633	0.358817	+	0.933408i	$0.383180\pi$
$398$	5.74901e6	1.81922
$399$	−316568.	−0.0995487
$400$	23358.5	0.00729952
$401$	4.14096e6	1.28600	0.642999	−	0.765867i	$-0.277690\pi$
$401$	4.14096e6	1.28600	0.642999	+	0.765867i	$0.277690\pi$
$402$	−2.02070e6	−0.623643
$403$	−457785.	−0.140410
$404$	−4.09886e6	−1.24942
$405$	−1.02734e6	−0.311225
$406$	5.87576e6	1.76909
$407$	1.78797e6	0.535026
$408$	−1.31199e6	−0.390195
$409$	2.17069e6	0.641638	0.320819	−	0.947140i	$-0.396042\pi$
$409$	2.17069e6	0.641638	0.320819	+	0.947140i	$0.396042\pi$
$410$	−891639.	−0.261957
$411$	−1.75577e6	−0.512699
$412$	9.58408e6	2.78168
$413$	1.46576e6	0.422850
$414$	4.43075e6	1.27051
$415$	1.64670e6	0.469348
$416$	361313.	0.102365
$417$	347980.	0.0979973
$418$	401047.	0.112268
$419$	6.14904e6	1.71109	0.855544	−	0.517730i	$-0.173223\pi$
$419$	6.14904e6	1.71109	0.855544	+	0.517730i	$0.173223\pi$
$420$	−1.14648e6	−0.317134
$421$	4.76989e6	1.31160	0.655802	−	0.754933i	$-0.272330\pi$
$421$	4.76989e6	1.31160	0.655802	+	0.754933i	$0.272330\pi$
$422$	−1.22006e6	−0.333504
$423$	−2.60853e6	−0.708836
$424$	887802.	0.239829
$425$	871027.	0.233916
$426$	−1.71232e6	−0.457154
$427$	−1.36153e6	−0.361374
$428$	7.71123e6	2.03477
$429$	39303.2	0.0103106
$430$	−90447.1	−0.0235898
$431$	4.61202e6	1.19591	0.597954	−	0.801530i	$-0.295980\pi$
$431$	4.61202e6	1.19591	0.597954	+	0.801530i	$0.295980\pi$
$432$	−86945.4	−0.0224149
$433$	985398.	0.252576	0.126288	−	0.991994i	$-0.459694\pi$
$433$	985398.	0.252576	0.126288	+	0.991994i	$0.459694\pi$
$434$	1.13470e7	2.89172
$435$	465684.	0.117996
$436$	−2.78221e6	−0.700929
$437$	−801071.	−0.200663
$438$	1.34061e6	0.333901
$439$	−30659.3	−0.00759278	−0.00379639	−	0.999993i	$-0.501208\pi$
$439$	−30659.3	−0.00759278	−0.00379639	+	0.999993i	$0.501208\pi$
$440$	563678.	0.138803
$441$	−2.89701e6	−0.709337
$442$	−822663.	−0.200293
$443$	−1.31507e6	−0.318375	−0.159188	−	0.987248i	$-0.550888\pi$
$443$	−1.31507e6	−0.318375	−0.159188	+	0.987248i	$0.550888\pi$
$444$	3.90406e6	0.939851
$445$	−665570.	−0.159328
$446$	−2.21873e6	−0.528163
$447$	1.38228e6	0.327210
$448$	−9.16337e6	−2.15705
$449$	7.02587e6	1.64469	0.822346	−	0.568988i	$-0.192665\pi$
$449$	7.02587e6	1.64469	0.822346	+	0.568988i	$0.192665\pi$
$450$	1.24794e6	0.290511
$451$	−470037.	−0.108815
$452$	1.41091e6	0.324827
$453$	−1.12431e6	−0.257419
$454$	−4.73995e6	−1.07928
$455$	−278993.	−0.0631779
$456$	339850.	0.0765377
$457$	−1.43258e6	−0.320868	−0.160434	−	0.987047i	$-0.551289\pi$
$457$	−1.43258e6	−0.320868	−0.160434	+	0.987047i	$0.551289\pi$
$458$	6.05997e6	1.34992
$459$	−3.24215e6	−0.718293
$460$	−2.90115e6	−0.639256
$461$	−628310.	−0.137696	−0.0688481	−	0.997627i	$-0.521932\pi$
$461$	−628310.	−0.137696	−0.0688481	+	0.997627i	$0.521932\pi$
$462$	−974201.	−0.212346
$463$	7.84231e6	1.70017	0.850083	−	0.526649i	$-0.176552\pi$
$463$	7.84231e6	1.70017	0.850083	+	0.526649i	$0.176552\pi$
$464$	−137797.	−0.0297129
$465$	899308.	0.192875
$466$	650193.	0.138700
$467$	456108.	0.0967777	0.0483889	−	0.998829i	$-0.484591\pi$
$467$	456108.	0.0967777	0.0483889	+	0.998829i	$0.484591\pi$
$468$	−731214.	−0.154323
$469$	7.56152e6	1.58737
$470$	2.75314e6	0.574888
$471$	−1.57198e6	−0.326509
$472$	−1.57355e6	−0.325107
$473$	−47680.1	−0.00979906
$474$	−501981.	−0.102622
$475$	−225625.	−0.0458831
$476$	1.26503e7	2.55909
$477$	1.03615e6	0.208510
$478$	3.17872e6	0.636331
$479$	7.14589e6	1.42304	0.711521	−	0.702665i	$-0.248007\pi$
$479$	7.14589e6	1.42304	0.711521	+	0.702665i	$0.248007\pi$
$480$	−709791.	−0.140614
$481$	950044.	0.187233
$482$	9.89625e6	1.94023
$483$	1.94592e6	0.379539
$484$	765660.	0.148567
$485$	−2.26659e6	−0.437541
$486$	−7.09640e6	−1.36285
$487$	−6.04922e6	−1.15578	−0.577892	−	0.816113i	$-0.696125\pi$
$487$	−6.04922e6	−1.15578	−0.577892	+	0.816113i	$0.696125\pi$
$488$	1.46166e6	0.277842
$489$	−1.33619e6	−0.252694
$490$	3.05760e6	0.575295
$491$	−6.60520e6	−1.23647	−0.618233	−	0.785995i	$-0.712151\pi$
$491$	−6.60520e6	−1.23647	−0.618233	+	0.785995i	$0.712151\pi$
$492$	−1.02633e6	−0.191150
$493$	−5.13839e6	−0.952160
$494$	213097.	0.0392880
$495$	657865.	0.120677
$496$	−266108.	−0.0485684
$497$	6.40758e6	1.16360
$498$	3.05529e6	0.552051
$499$	−4.06039e6	−0.729988	−0.364994	−	0.931010i	$-0.618929\pi$
$499$	−4.06039e6	−0.729988	−0.364994	+	0.931010i	$0.618929\pi$
$500$	−817119.	−0.146171
$501$	−884269.	−0.157395
$502$	−2.98960e6	−0.529486
$503$	−3.03925e6	−0.535608	−0.267804	−	0.963473i	$-0.586298\pi$
$503$	−3.03925e6	−0.535608	−0.267804	+	0.963473i	$0.586298\pi$
$504$	7.03399e6	1.23346
$505$	1.95946e6	0.341908
$506$	−2.46520e6	−0.428031
$507$	−1.85494e6	−0.320486
$508$	−6.49512e6	−1.11668
$509$	5.12160e6	0.876216	0.438108	−	0.898922i	$-0.355649\pi$
$509$	5.12160e6	0.876216	0.438108	+	0.898922i	$0.355649\pi$
$510$	1.61610e6	0.275134
$511$	−5.01662e6	−0.849882
$512$	432883.	0.0729786
$513$	839826.	0.140895
$514$	−4.16487e6	−0.695334
$515$	−4.58168e6	−0.761214
$516$	−104110.	−0.0172135
$517$	1.45135e6	0.238806
$518$	−2.35485e7	−3.85602
$519$	791480.	0.128980
$520$	299511.	0.0485741
$521$	−1.54576e6	−0.249487	−0.124743	−	0.992189i	$-0.539811\pi$
$521$	−1.54576e6	−0.249487	−0.124743	+	0.992189i	$0.539811\pi$
$522$	−7.36189e6	−1.18253
$523$	−1.32592e6	−0.211965	−0.105982	−	0.994368i	$-0.533799\pi$
$523$	−1.32592e6	−0.211965	−0.105982	+	0.994368i	$0.533799\pi$
$524$	7.44715e6	1.18485
$525$	548076.	0.0867845
$526$	−2.05088e7	−3.23203
$527$	−9.92304e6	−1.55639
$528$	22846.8	0.00356648
$529$	−1.51223e6	−0.234952
$530$	−1.09359e6	−0.169108
$531$	−1.83648e6	−0.282651
$532$	−3.27686e6	−0.501971
$533$	−249755.	−0.0380800
$534$	−1.23490e6	−0.187404
$535$	−3.68636e6	−0.556819
$536$	−8.11762e6	−1.22044
$537$	−1.00024e6	−0.149682
$538$	−1.96301e7	−2.92393
$539$	1.61185e6	0.238975
$540$	3.04150e6	0.448852
$541$	−7.05555e6	−1.03642	−0.518212	−	0.855252i	$-0.673402\pi$
$541$	−7.05555e6	−1.03642	−0.518212	+	0.855252i	$0.673402\pi$
$542$	3.08746e6	0.451443
$543$	−4.11187e6	−0.598466
$544$	7.83190e6	1.13467
$545$	1.33004e6	0.191811
$546$	−517644.	−0.0743104
$547$	1.30039e7	1.85825	0.929124	−	0.369768i	$-0.120563\pi$
$547$	1.30039e7	1.85825	0.929124	+	0.369768i	$0.120563\pi$
$548$	−1.81743e7	−2.58527
$549$	1.70590e6	0.241558
$550$	−694333.	−0.0978726
$551$	1.33102e6	0.186769
$552$	−2.08903e6	−0.291808
$553$	1.87843e6	0.261206
$554$	−1.53141e7	−2.11990
$555$	−1.86634e6	−0.257193
$556$	3.60201e6	0.494149
$557$	−7.09184e6	−0.968548	−0.484274	−	0.874916i	$-0.660916\pi$
$557$	−7.09184e6	−0.968548	−0.484274	+	0.874916i	$0.660916\pi$
$558$	−1.42170e7	−1.93295
$559$	−25335.0	−0.00342918
$560$	−162177.	−0.0218534
$561$	851946.	0.114289
$562$	−1.62778e7	−2.17398
$563$	7.69844e6	1.02360	0.511802	−	0.859103i	$-0.328978\pi$
$563$	7.69844e6	1.02360	0.511802	+	0.859103i	$0.328978\pi$
$564$	3.16903e6	0.419496
$565$	−674485.	−0.0888897
$566$	−5.59396e6	−0.733970
$567$	7.13276e6	0.931752
$568$	−6.87882e6	−0.894629
$569$	−1.14831e7	−1.48689	−0.743444	−	0.668798i	$-0.766809\pi$
$569$	−1.14831e7	−1.48689	−0.743444	+	0.668798i	$0.766809\pi$
$570$	−418625.	−0.0539682
$571$	−4.22724e6	−0.542583	−0.271292	−	0.962497i	$-0.587451\pi$
$571$	−4.22724e6	−0.542583	−0.271292	+	0.962497i	$0.587451\pi$
$572$	406836.	0.0519911
$573$	−2.54066e6	−0.323266
$574$	6.19062e6	0.784250
$575$	1.38690e6	0.174934
$576$	1.14810e7	1.44187
$577$	6.33081e6	0.791625	0.395813	−	0.918331i	$-0.370463\pi$
$577$	6.33081e6	0.791625	0.395813	+	0.918331i	$0.370463\pi$
$578$	−4.79615e6	−0.597135
$579$	447900.	0.0555245
$580$	4.82038e6	0.594992
$581$	−1.14330e7	−1.40514
$582$	−4.20543e6	−0.514639
$583$	−576496.	−0.0702465
$584$	5.38556e6	0.653430
$585$	349558.	0.0422308
$586$	−2.06847e6	−0.248832
$587$	9.05426e6	1.08457	0.542285	−	0.840195i	$-0.317559\pi$
$587$	9.05426e6	1.08457	0.542285	+	0.840195i	$0.317559\pi$
$588$	3.51948e6	0.419793
$589$	2.57040e6	0.305290
$590$	1.93829e6	0.229239
$591$	3.29543e6	0.388099
$592$	552256.	0.0647644
$593$	−4.59638e6	−0.536758	−0.268379	−	0.963313i	$-0.586488\pi$
$593$	−4.59638e6	−0.536758	−0.268379	+	0.963313i	$0.586488\pi$
$594$	2.58446e6	0.300541
$595$	−6.04752e6	−0.700301
$596$	1.43082e7	1.64995
$597$	−3.16348e6	−0.363270
$598$	−1.30989e6	−0.149790
$599$	1.26772e7	1.44364	0.721818	−	0.692083i	$-0.243307\pi$
$599$	1.26772e7	1.44364	0.721818	+	0.692083i	$0.243307\pi$
$600$	−588383.	−0.0667240
$601$	1.05730e7	1.19402	0.597010	−	0.802234i	$-0.296355\pi$
$601$	1.05730e7	1.19402	0.597010	+	0.802234i	$0.296355\pi$
$602$	627972.	0.0706234
$603$	−9.47403e6	−1.06106
$604$	−1.16380e7	−1.29803
$605$	−366025.	−0.0406558
$606$	3.63559e6	0.402155
$607$	−893998.	−0.0984838	−0.0492419	−	0.998787i	$-0.515681\pi$
$607$	−893998.	−0.0984838	−0.0492419	+	0.998787i	$0.515681\pi$
$608$	−2.02872e6	−0.222569
$609$	−3.23323e6	−0.353259
$610$	−1.80046e6	−0.195911
$611$	771176.	0.0835700
$612$	−1.58500e7	−1.71060
$613$	1.41349e7	1.51929	0.759647	−	0.650335i	$-0.225372\pi$
$613$	1.41349e7	1.51929	0.759647	+	0.650335i	$0.225372\pi$
$614$	1.33289e7	1.42683
$615$	490638.	0.0523087
$616$	−3.91360e6	−0.415551
$617$	−5.41392e6	−0.572531	−0.286265	−	0.958150i	$-0.592414\pi$
$617$	−5.41392e6	−0.572531	−0.286265	+	0.958150i	$0.592414\pi$
$618$	−8.50085e6	−0.895347
$619$	8.42521e6	0.883800	0.441900	−	0.897064i	$-0.354305\pi$
$619$	8.42521e6	0.883800	0.441900	+	0.897064i	$0.354305\pi$
$620$	9.30891e6	0.972567
$621$	−5.16233e6	−0.537176
$622$	−1.39248e7	−1.44316
$623$	4.62103e6	0.477000
$624$	12139.7	0.00124809
$625$	390625.	0.0400000
$626$	−1.38305e7	−1.41059
$627$	−220682.	−0.0224181
$628$	−1.62719e7	−1.64641
$629$	2.05934e7	2.07540
$630$	−8.66441e6	−0.869737
$631$	−1.72657e7	−1.72628	−0.863140	−	0.504965i	$-0.831505\pi$
$631$	−1.72657e7	−1.72628	−0.863140	+	0.504965i	$0.831505\pi$
$632$	−2.01658e6	−0.200827
$633$	671358.	0.0665955
$634$	1.38452e7	1.36797
$635$	3.10500e6	0.305582
$636$	−1.25878e6	−0.123398
$637$	856458.	0.0836291
$638$	4.09604e6	0.398393
$639$	−8.02823e6	−0.777799
$640$	−7.62170e6	−0.735532
$641$	−8.69896e6	−0.836223	−0.418112	−	0.908396i	$-0.637308\pi$
$641$	−8.69896e6	−0.836223	−0.418112	+	0.908396i	$0.637308\pi$
$642$	−6.83968e6	−0.654935
$643$	−2.62874e6	−0.250738	−0.125369	−	0.992110i	$-0.540011\pi$
$643$	−2.62874e6	−0.250738	−0.125369	+	0.992110i	$0.540011\pi$
$644$	2.01426e7	1.91382
$645$	49769.9	0.00471051
$646$	4.61914e6	0.435492
$647$	−4.46365e6	−0.419208	−0.209604	−	0.977786i	$-0.567217\pi$
$647$	−4.46365e6	−0.419208	−0.209604	+	0.977786i	$0.567217\pi$
$648$	−7.65734e6	−0.716375
$649$	1.02179e6	0.0952247
$650$	−368936.	−0.0342505
$651$	−6.24387e6	−0.577433
$652$	−1.38311e7	−1.27420
$653$	1.25284e6	0.114978	0.0574889	−	0.998346i	$-0.481691\pi$
$653$	1.25284e6	0.114978	0.0574889	+	0.998346i	$0.481691\pi$
$654$	2.46776e6	0.225610
$655$	−3.56012e6	−0.324236
$656$	−145181.	−0.0131720
$657$	6.28546e6	0.568098
$658$	−1.91150e7	−1.72111
$659$	−8.95054e6	−0.802852	−0.401426	−	0.915891i	$-0.631485\pi$
$659$	−8.95054e6	−0.802852	−0.401426	+	0.915891i	$0.631485\pi$
$660$	−799219.	−0.0714177
$661$	1.40704e7	1.25257	0.626285	−	0.779594i	$-0.284575\pi$
$661$	1.40704e7	1.25257	0.626285	+	0.779594i	$0.284575\pi$
$662$	2.04560e7	1.81416
$663$	452683.	0.0399955
$664$	1.22738e7	1.08034
$665$	1.56651e6	0.137366
$666$	2.95046e7	2.57753
$667$	−8.18163e6	−0.712074
$668$	−9.15324e6	−0.793658
$669$	1.22089e6	0.105466
$670$	9.99922e6	0.860556
$671$	−949133.	−0.0813805
$672$	4.92806e6	0.420972
$673$	1.11557e7	0.949423	0.474711	−	0.880141i	$-0.342552\pi$
$673$	1.11557e7	0.949423	0.474711	+	0.880141i	$0.342552\pi$
$674$	−5.30552e6	−0.449861
$675$	−1.45399e6	−0.122829
$676$	−1.92008e7	−1.61604
$677$	6.65369e6	0.557944	0.278972	−	0.960299i	$-0.410006\pi$
$677$	6.65369e6	0.557944	0.278972	+	0.960299i	$0.410006\pi$
$678$	−1.25144e6	−0.104553
$679$	1.57369e7	1.30992
$680$	6.49227e6	0.538424
$681$	2.60823e6	0.215515
$682$	7.91009e6	0.651209
$683$	−8.60760e6	−0.706042	−0.353021	−	0.935615i	$-0.614846\pi$
$683$	−8.60760e6	−0.706042	−0.353021	+	0.935615i	$0.614846\pi$
$684$	4.10567e6	0.335539
$685$	8.68824e6	0.707466
$686$	5.55534e6	0.450713
$687$	−3.33459e6	−0.269557
$688$	−14727.1	−0.00118617
$689$	−306322.	−0.0245828
$690$	2.57325e6	0.205759
$691$	7.71978e6	0.615049	0.307525	−	0.951540i	$-0.400499\pi$
$691$	7.71978e6	0.615049	0.307525	+	0.951540i	$0.400499\pi$
$692$	8.19276e6	0.650377
$693$	−4.56754e6	−0.361284
$694$	−1.41373e7	−1.11421
$695$	−1.72195e6	−0.135225
$696$	3.47101e6	0.271602
$697$	−5.41375e6	−0.422101
$698$	−1.15999e7	−0.901192
$699$	−357779.	−0.0276963
$700$	5.67324e6	0.437609
$701$	−9.57407e6	−0.735871	−0.367935	−	0.929851i	$-0.619935\pi$
$701$	−9.57407e6	−0.735871	−0.367935	+	0.929851i	$0.619935\pi$
$702$	1.37326e6	0.105174
$703$	−5.33437e6	−0.407094
$704$	−6.38786e6	−0.485762
$705$	−1.51496e6	−0.114796
$706$	−1.66107e7	−1.25423
$707$	−1.36045e7	−1.02361
$708$	2.23109e6	0.167276
$709$	2.15746e7	1.61186	0.805928	−	0.592013i	$-0.201667\pi$
$709$	2.15746e7	1.61186	0.805928	+	0.592013i	$0.201667\pi$
$710$	8.47327e6	0.630820
$711$	−2.35354e6	−0.174601
$712$	−4.96088e6	−0.366740
$713$	−1.58000e7	−1.16395
$714$	−1.12206e7	−0.823700
$715$	−194488.	−0.0142275
$716$	−1.03537e7	−0.754769
$717$	−1.74914e6	−0.127065
$718$	−2.11082e7	−1.52806
$719$	−3.56842e6	−0.257427	−0.128713	−	0.991682i	$-0.541085\pi$
$719$	−3.56842e6	−0.257427	−0.128713	+	0.991682i	$0.541085\pi$
$720$	203196.	0.0146078
$721$	3.18105e7	2.27894
$722$	−1.19651e6	−0.0854228
$723$	−5.44557e6	−0.387434
$724$	−4.25627e7	−3.01775
$725$	−2.30439e6	−0.162821
$726$	−679123.	−0.0478197
$727$	2.25733e6	0.158401	0.0792006	−	0.996859i	$-0.474763\pi$
$727$	2.25733e6	0.158401	0.0792006	+	0.996859i	$0.474763\pi$
$728$	−2.07950e6	−0.145422
$729$	−6.08080e6	−0.423781
$730$	−6.63389e6	−0.460745
$731$	−549166.	−0.0380111
$732$	−2.07244e6	−0.142957
$733$	−5.68775e6	−0.391003	−0.195502	−	0.980703i	$-0.562633\pi$
$733$	−5.68775e6	−0.391003	−0.195502	+	0.980703i	$0.562633\pi$
$734$	2.04614e7	1.40183
$735$	−1.68249e6	−0.114877
$736$	1.24704e7	0.848565
$737$	5.27119e6	0.357471
$738$	−7.75640e6	−0.524227
$739$	−2.37164e7	−1.59749	−0.798743	−	0.601672i	$-0.794501\pi$
$739$	−2.37164e7	−1.59749	−0.798743	+	0.601672i	$0.794501\pi$
$740$	−1.93189e7	−1.29689
$741$	−117260.	−0.00784521
$742$	7.59274e6	0.506278
$743$	−1.62029e7	−1.07677	−0.538384	−	0.842700i	$-0.680965\pi$
$743$	−1.62029e7	−1.07677	−0.538384	+	0.842700i	$0.680965\pi$
$744$	6.70307e6	0.443957
$745$	−6.84008e6	−0.451513
$746$	−5.96658e6	−0.392535
$747$	1.43247e7	0.939258
$748$	8.81866e6	0.576300
$749$	2.55943e7	1.66701
$750$	724766.	0.0470484
$751$	1.87416e7	1.21257	0.606285	−	0.795248i	$-0.292659\pi$
$751$	1.87416e7	1.21257	0.606285	+	0.795248i	$0.292659\pi$
$752$	448281.	0.0289072
$753$	1.64508e6	0.105730
$754$	2.17644e6	0.139418
$755$	5.56354e6	0.355209
$756$	−2.11170e7	−1.34378
$757$	6.82643e6	0.432966	0.216483	−	0.976286i	$-0.430541\pi$
$757$	6.82643e6	0.432966	0.216483	+	0.976286i	$0.430541\pi$
$758$	1.68050e7	1.06234
$759$	1.35651e6	0.0854712
$760$	−1.68172e6	−0.105613
$761$	−4.15072e6	−0.259814	−0.129907	−	0.991526i	$-0.541468\pi$
$761$	−4.15072e6	−0.259814	−0.129907	+	0.991526i	$0.541468\pi$
$762$	5.76102e6	0.359428
$763$	−9.23444e6	−0.574247
$764$	−2.62989e7	−1.63006
$765$	7.57710e6	0.468111
$766$	8.68671e6	0.534913
$767$	542930.	0.0333239
$768$	−5.60647e6	−0.342994
$769$	1.06820e7	0.651386	0.325693	−	0.945476i	$-0.394402\pi$
$769$	1.06820e7	0.651386	0.325693	+	0.945476i	$0.394402\pi$
$770$	4.82074e6	0.293013
$771$	2.29178e6	0.138847
$772$	4.63630e6	0.279981
$773$	2.85112e7	1.71620	0.858098	−	0.513485i	$-0.171646\pi$
$773$	2.85112e7	1.71620	0.858098	+	0.513485i	$0.171646\pi$
$774$	−786803.	−0.0472078
$775$	−4.45014e6	−0.266145
$776$	−1.68942e7	−1.00713
$777$	1.29580e7	0.769988
$778$	−4.71300e7	−2.79157
$779$	1.40234e6	0.0827961
$780$	−424667.	−0.0249926
$781$	4.46677e6	0.262039
$782$	−2.83934e7	−1.66036
$783$	8.57744e6	0.499981
$784$	497855.	0.0289276
$785$	7.77879e6	0.450545
$786$	−6.60545e6	−0.381370
$787$	2.20059e7	1.26649	0.633245	−	0.773951i	$-0.281722\pi$
$787$	2.20059e7	1.26649	0.633245	+	0.773951i	$0.281722\pi$
$788$	3.41116e7	1.95698
$789$	1.12853e7	0.645387
$790$	2.48400e6	0.141607
$791$	4.68293e6	0.266120
$792$	4.90345e6	0.277772
$793$	−504324.	−0.0284791
$794$	−2.06910e7	−1.16474
$795$	601763.	0.0337682
$796$	−3.27458e7	−1.83178
$797$	1.18004e7	0.658039	0.329019	−	0.944323i	$-0.393282\pi$
$797$	1.18004e7	0.658039	0.329019	+	0.944323i	$0.393282\pi$
$798$	2.90650e6	0.161571
$799$	1.67162e7	0.926339
$800$	3.51233e6	0.194031
$801$	−5.78981e6	−0.318848
$802$	−3.80193e7	−2.08722
$803$	−3.49712e6	−0.191391
$804$	1.15097e7	0.627948
$805$	−9.62918e6	−0.523721
$806$	4.20304e6	0.227891
$807$	1.08018e7	0.583864
$808$	1.46050e7	0.786999
$809$	2.35766e7	1.26651	0.633256	−	0.773943i	$-0.281718\pi$
$809$	2.35766e7	1.26651	0.633256	+	0.773943i	$0.281718\pi$
$810$	9.43224e6	0.505129
$811$	2.33836e7	1.24842	0.624208	−	0.781258i	$-0.285422\pi$
$811$	2.33836e7	1.24842	0.624208	+	0.781258i	$0.285422\pi$
$812$	−3.34678e7	−1.78130
$813$	−1.69892e6	−0.0901462
$814$	−1.64159e7	−0.868366
$815$	6.61200e6	0.348689
$816$	263143.	0.0138346
$817$	142252.	0.00745597
$818$	−1.99297e7	−1.04140
$819$	−2.42697e6	−0.126431
$820$	5.07869e6	0.263765
$821$	−2.64078e6	−0.136733	−0.0683667	−	0.997660i	$-0.521779\pi$
$821$	−2.64078e6	−0.136733	−0.0683667	+	0.997660i	$0.521779\pi$
$822$	1.61202e7	0.832128
$823$	−1.50074e7	−0.772337	−0.386169	−	0.922428i	$-0.626202\pi$
$823$	−1.50074e7	−0.772337	−0.386169	+	0.922428i	$0.626202\pi$
$824$	−3.41500e7	−1.75215
$825$	382068.	0.0195436
$826$	−1.34575e7	−0.686300
$827$	−2.10612e7	−1.07083	−0.535413	−	0.844590i	$-0.679844\pi$
$827$	−2.10612e7	−1.07083	−0.535413	+	0.844590i	$0.679844\pi$
$828$	−2.52372e7	−1.27928
$829$	1.50439e7	0.760281	0.380140	−	0.924929i	$-0.375876\pi$
$829$	1.50439e7	0.760281	0.380140	+	0.924929i	$0.375876\pi$
$830$	−1.51188e7	−0.761768
$831$	8.42681e6	0.423312
$832$	−3.39420e6	−0.169992
$833$	1.85648e7	0.926995
$834$	−3.19490e6	−0.159053
$835$	4.37572e6	0.217187
$836$	−2.28433e6	−0.113043
$837$	1.65644e7	0.817263
$838$	−5.64560e7	−2.77715
$839$	−347050.	−0.0170211	−0.00851053	−	0.999964i	$-0.502709\pi$
$839$	−347050.	−0.0170211	−0.00851053	+	0.999964i	$0.502709\pi$
$840$	4.08513e6	0.199760
$841$	−6.91701e6	−0.337232
$842$	−4.37936e7	−2.12878
$843$	8.95714e6	0.434111
$844$	6.94936e6	0.335806
$845$	9.17898e6	0.442235
$846$	2.39497e7	1.15046
$847$	2.54130e6	0.121716
$848$	−178064.	−0.00850326
$849$	3.07816e6	0.146562
$850$	−7.99713e6	−0.379653
$851$	3.27899e7	1.55209
$852$	9.75324e6	0.460310
$853$	2.77763e7	1.30708	0.653539	−	0.756893i	$-0.273283\pi$
$853$	2.77763e7	1.30708	0.653539	+	0.756893i	$0.273283\pi$
$854$	1.25006e7	0.586523
$855$	−1.96272e6	−0.0918212
$856$	−2.74766e7	−1.28168
$857$	2.39905e7	1.11580	0.557900	−	0.829908i	$-0.311607\pi$
$857$	2.39905e7	1.11580	0.557900	+	0.829908i	$0.311607\pi$
$858$	−360854.	−0.0167345
$859$	−3.88935e7	−1.79843	−0.899216	−	0.437505i	$-0.855862\pi$
$859$	−3.88935e7	−1.79843	−0.899216	+	0.437505i	$0.855862\pi$
$860$	515178.	0.0237526
$861$	−3.40649e6	−0.156603
$862$	−4.23442e7	−1.94100
$863$	2.24893e7	1.02789	0.513947	−	0.857822i	$-0.328183\pi$
$863$	2.24893e7	1.02789	0.513947	+	0.857822i	$0.328183\pi$
$864$	−1.30737e7	−0.595818
$865$	−3.91656e6	−0.177977
$866$	−9.04720e6	−0.409939
$867$	2.63915e6	0.119239
$868$	−6.46315e7	−2.91169
$869$	1.30947e6	0.0588228
$870$	−4.27556e6	−0.191512
$871$	2.80086e6	0.125097
$872$	9.91358e6	0.441509
$873$	−1.97171e7	−0.875605
$874$	7.35485e6	0.325683
$875$	−2.71210e6	−0.119753
$876$	−7.63600e6	−0.336206
$877$	2.54626e7	1.11790	0.558952	−	0.829200i	$-0.311204\pi$
$877$	2.54626e7	1.11790	0.558952	+	0.829200i	$0.311204\pi$
$878$	281491.	0.0123233
$879$	1.13821e6	0.0496878
$880$	−113055.	−0.00492134
$881$	−1.45896e7	−0.633293	−0.316646	−	0.948544i	$-0.602557\pi$
$881$	−1.45896e7	−0.633293	−0.316646	+	0.948544i	$0.602557\pi$
$882$	2.65982e7	1.15128
$883$	1.42918e7	0.616858	0.308429	−	0.951247i	$-0.400197\pi$
$883$	1.42918e7	0.616858	0.308429	+	0.951247i	$0.400197\pi$
$884$	4.68581e6	0.201676
$885$	−1.06657e6	−0.0457755
$886$	1.20740e7	0.516734
$887$	1.45282e7	0.620015	0.310008	−	0.950734i	$-0.399668\pi$
$887$	1.45282e7	0.620015	0.310008	+	0.950734i	$0.399668\pi$
$888$	−1.39109e7	−0.592003
$889$	−2.15579e7	−0.914856
$890$	6.11077e6	0.258596
$891$	4.97230e6	0.209828
$892$	1.26377e7	0.531810
$893$	−4.33005e6	−0.181704
$894$	−1.26911e7	−0.531074
$895$	4.94961e6	0.206545
$896$	5.29172e7	2.20205
$897$	720787.	0.0299107
$898$	−6.45064e7	−2.66939
$899$	2.62524e7	1.08335
$900$	−7.10815e6	−0.292517
$901$	−6.63991e6	−0.272490
$902$	4.31553e6	0.176611
$903$	−345551.	−0.0141024
$904$	−5.02734e6	−0.204605
$905$	2.03472e7	0.825815
$906$	1.03226e7	0.417800
$907$	4.42565e7	1.78632	0.893159	−	0.449742i	$-0.148484\pi$
$907$	4.42565e7	1.78632	0.893159	+	0.449742i	$0.148484\pi$
$908$	2.69983e7	1.08673
$909$	1.70454e7	0.684225
$910$	2.56151e6	0.102540
$911$	−3.91334e7	−1.56225	−0.781126	−	0.624373i	$-0.785354\pi$
$911$	−3.91334e7	−1.56225	−0.781126	+	0.624373i	$0.785354\pi$
$912$	−68162.7	−0.00271369
$913$	−7.97004e6	−0.316434
$914$	1.31529e7	0.520780
$915$	990733.	0.0391204
$916$	−3.45170e7	−1.35924
$917$	2.47178e7	0.970704
$918$	2.97671e7	1.16581
$919$	−3.37680e7	−1.31891	−0.659457	−	0.751742i	$-0.729214\pi$
$919$	−3.37680e7	−1.31891	−0.659457	+	0.751742i	$0.729214\pi$
$920$	1.03374e7	0.402661
$921$	−7.33443e6	−0.284916
$922$	5.76868e6	0.223486
$923$	2.37343e6	0.0917006
$924$	5.54896e6	0.213812
$925$	9.23540e6	0.354896
$926$	−7.20023e7	−2.75943
$927$	−3.98562e7	−1.52334
$928$	−2.07201e7	−0.789808
$929$	3.98508e7	1.51495	0.757474	−	0.652865i	$-0.226433\pi$
$929$	3.98508e7	1.51495	0.757474	+	0.652865i	$0.226433\pi$
$930$	−8.25678e6	−0.313043
$931$	−4.80890e6	−0.181832
$932$	−3.70344e6	−0.139658
$933$	7.66235e6	0.288176
$934$	−4.18765e6	−0.157074
$935$	−4.21577e6	−0.157706
$936$	2.60546e6	0.0972064
$937$	−3.91947e7	−1.45841	−0.729203	−	0.684297i	$-0.760109\pi$
$937$	−3.91947e7	−1.45841	−0.729203	+	0.684297i	$0.760109\pi$
$938$	−6.94243e7	−2.57635
$939$	7.61044e6	0.281673
$940$	−1.56816e7	−0.578857
$941$	−2.23628e7	−0.823290	−0.411645	−	0.911344i	$-0.635046\pi$
$941$	−2.23628e7	−0.823290	−0.411645	+	0.911344i	$0.635046\pi$
$942$	1.44328e7	0.529935
$943$	−8.62006e6	−0.315668
$944$	315603.	0.0115268
$945$	1.00950e7	0.367729
$946$	437764.	0.0159042
$947$	1.44963e7	0.525268	0.262634	−	0.964896i	$-0.415409\pi$
$947$	1.44963e7	0.525268	0.262634	+	0.964896i	$0.415409\pi$
$948$	2.85924e6	0.103331
$949$	−1.85820e6	−0.0669774
$950$	2.07152e6	0.0744699
$951$	−7.61853e6	−0.273162
$952$	−4.50757e7	−1.61194
$953$	3.73854e7	1.33343	0.666713	−	0.745314i	$-0.267701\pi$
$953$	3.73854e7	1.33343	0.666713	+	0.745314i	$0.267701\pi$
$954$	−9.51315e6	−0.338418
$955$	1.25722e7	0.446070
$956$	−1.81057e7	−0.640724
$957$	−2.25391e6	−0.0795530
$958$	−6.56083e7	−2.30965
$959$	−6.03222e7	−2.11802
$960$	6.66784e6	0.233511
$961$	2.20684e7	0.770835
$962$	−8.72261e6	−0.303885
$963$	−3.20678e7	−1.11430
$964$	−5.63681e7	−1.95362
$965$	−2.21639e6	−0.0766175
$966$	−1.78660e7	−0.616005
$967$	−2.89682e7	−0.996220	−0.498110	−	0.867114i	$-0.665972\pi$
$967$	−2.89682e7	−0.996220	−0.498110	+	0.867114i	$0.665972\pi$
$968$	−2.72820e6	−0.0935810
$969$	−2.54176e6	−0.0869610
$970$	2.08102e7	0.710143
$971$	−1.17610e7	−0.400311	−0.200156	−	0.979764i	$-0.564145\pi$
$971$	−1.17610e7	−0.400311	−0.200156	+	0.979764i	$0.564145\pi$
$972$	4.04204e7	1.37226
$973$	1.19554e7	0.404839
$974$	5.55395e7	1.87588
$975$	203013.	0.00683930
$976$	−293161.	−0.00985103
$977$	−1.40185e7	−0.469856	−0.234928	−	0.972013i	$-0.575485\pi$
$977$	−1.40185e7	−0.469856	−0.234928	+	0.972013i	$0.575485\pi$
$978$	1.22679e7	0.410131
$979$	3.22136e6	0.107419
$980$	−1.74158e7	−0.579267
$981$	1.15701e7	0.383852
$982$	6.06441e7	2.00683
$983$	−2.89578e7	−0.955834	−0.477917	−	0.878405i	$-0.658608\pi$
$983$	−2.89578e7	−0.955834	−0.477917	+	0.878405i	$0.658608\pi$
$984$	3.65702e6	0.120403
$985$	−1.63071e7	−0.535533
$986$	4.71770e7	1.54539
$987$	1.05183e7	0.343679
$988$	−1.21378e6	−0.0395593
$989$	−874412.	−0.0284266
$990$	−6.04003e6	−0.195862
$991$	5.37628e7	1.73899	0.869496	−	0.493940i	$-0.164444\pi$
$991$	5.37628e7	1.73899	0.869496	+	0.493940i	$0.164444\pi$
$992$	−4.00137e7	−1.29101
$993$	−1.12562e7	−0.362259
$994$	−5.88297e7	−1.88856
$995$	1.56542e7	0.501271
$996$	−1.74027e7	−0.555863
$997$	1.75159e7	0.558077	0.279038	−	0.960280i	$-0.409984\pi$
$997$	1.75159e7	0.558077	0.279038	+	0.960280i	$0.409984\pi$
$998$	3.72795e7	1.18480
$999$	−3.43762e7	−1.08979

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.d.1.5	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.d.1.5	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-9.18127 q^{2} +5.05214 q^{3} +52.2956 q^{4} -25.0000 q^{5} -46.3850 q^{6} +173.574 q^{7} -186.340 q^{8} -217.476 q^{9} +O(q^{10})\)	\(q-9.18127 q^{2} +5.05214 q^{3} +52.2956 q^{4} -25.0000 q^{5} -46.3850 q^{6} +173.574 q^{7} -186.340 q^{8} -217.476 q^{9} +229.532 q^{10} +121.000 q^{11} +264.205 q^{12} +64.2936 q^{13} -1593.63 q^{14} -126.303 q^{15} +37.3736 q^{16} +1393.64 q^{17} +1996.70 q^{18} -361.000 q^{19} -1307.39 q^{20} +876.921 q^{21} -1110.93 q^{22} +2219.03 q^{23} -941.413 q^{24} +625.000 q^{25} -590.297 q^{26} -2326.39 q^{27} +9077.18 q^{28} -3687.02 q^{29} +1159.63 q^{30} -7120.22 q^{31} +5619.73 q^{32} +611.308 q^{33} -12795.4 q^{34} -4339.36 q^{35} -11373.0 q^{36} +14776.6 q^{37} +3314.44 q^{38} +324.820 q^{39} +4658.49 q^{40} -3884.60 q^{41} -8051.25 q^{42} -394.051 q^{43} +6327.77 q^{44} +5436.90 q^{45} -20373.5 q^{46} +11994.6 q^{47} +188.816 q^{48} +13321.0 q^{49} -5738.29 q^{50} +7040.87 q^{51} +3362.28 q^{52} -4764.43 q^{53} +21359.2 q^{54} -3025.00 q^{55} -32343.8 q^{56} -1823.82 q^{57} +33851.5 q^{58} +8444.54 q^{59} -6605.12 q^{60} -7844.07 q^{61} +65372.6 q^{62} -37748.2 q^{63} -52792.2 q^{64} -1607.34 q^{65} -5612.59 q^{66} +43563.6 q^{67} +72881.5 q^{68} +11210.9 q^{69} +39840.8 q^{70} +36915.5 q^{71} +40524.4 q^{72} -28901.8 q^{73} -135668. q^{74} +3157.59 q^{75} -18878.7 q^{76} +21002.5 q^{77} -2982.26 q^{78} +10822.1 q^{79} -934.339 q^{80} +41093.4 q^{81} +35665.6 q^{82} -65868.1 q^{83} +45859.1 q^{84} -34841.1 q^{85} +3617.88 q^{86} -18627.3 q^{87} -22547.1 q^{88} +26622.8 q^{89} -49917.6 q^{90} +11159.7 q^{91} +116046. q^{92} -35972.3 q^{93} -110126. q^{94} +9025.00 q^{95} +28391.7 q^{96} +90663.5 q^{97} -122304. q^{98} -26314.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9} - 100 q^{10} + 4477 q^{11} + 872 q^{12} + 719 q^{13} - 625 q^{14} - 675 q^{15} + 6940 q^{16} + 119 q^{17} - 4237 q^{18} - 13357 q^{19} - 15400 q^{20} + 2905 q^{21} + 484 q^{22} - 1252 q^{23} + 5884 q^{24} + 23125 q^{25} + 13201 q^{26} + 9918 q^{27} + 15461 q^{28} + 13221 q^{29} - 3525 q^{30} + 6419 q^{31} + 13173 q^{32} + 3267 q^{33} + 35415 q^{34} + 1975 q^{35} + 80543 q^{36} + 9037 q^{37} - 1444 q^{38} - 6184 q^{39} - 1800 q^{40} + 52577 q^{41} - 28578 q^{42} + 963 q^{43} + 74536 q^{44} - 78500 q^{45} - 10531 q^{46} + 49346 q^{47} + 80107 q^{48} + 70288 q^{49} + 2500 q^{50} + 140786 q^{51} + 165062 q^{52} - 34457 q^{53} + 34216 q^{54} - 111925 q^{55} - 64095 q^{56} - 9747 q^{57} - 126140 q^{58} + 56521 q^{59} - 21800 q^{60} + 6613 q^{61} + 494 q^{62} - 125618 q^{63} - 140426 q^{64} - 17975 q^{65} + 17061 q^{66} - 43534 q^{67} - 138520 q^{68} + 34618 q^{69} + 15625 q^{70} + 95986 q^{71} - 42192 q^{72} + 109218 q^{73} - 182005 q^{74} + 16875 q^{75} - 222376 q^{76} - 9559 q^{77} - 369624 q^{78} + 64943 q^{79} - 173500 q^{80} + 388941 q^{81} - 126926 q^{82} + 109741 q^{83} - 112886 q^{84} - 2975 q^{85} + 43866 q^{86} + 142492 q^{87} + 8712 q^{88} - 119092 q^{89} + 105925 q^{90} + 349320 q^{91} + 433396 q^{92} - 108630 q^{93} + 196160 q^{94} + 333925 q^{95} + 376630 q^{96} + 68774 q^{97} + 310926 q^{98} + 379940 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9 - 100 * q^10 + 4477 * q^11 + 872 * q^12 + 719 * q^13 - 625 * q^14 - 675 * q^15 + 6940 * q^16 + 119 * q^17 - 4237 * q^18 - 13357 * q^19 - 15400 * q^20 + 2905 * q^21 + 484 * q^22 - 1252 * q^23 + 5884 * q^24 + 23125 * q^25 + 13201 * q^26 + 9918 * q^27 + 15461 * q^28 + 13221 * q^29 - 3525 * q^30 + 6419 * q^31 + 13173 * q^32 + 3267 * q^33 + 35415 * q^34 + 1975 * q^35 + 80543 * q^36 + 9037 * q^37 - 1444 * q^38 - 6184 * q^39 - 1800 * q^40 + 52577 * q^41 - 28578 * q^42 + 963 * q^43 + 74536 * q^44 - 78500 * q^45 - 10531 * q^46 + 49346 * q^47 + 80107 * q^48 + 70288 * q^49 + 2500 * q^50 + 140786 * q^51 + 165062 * q^52 - 34457 * q^53 + 34216 * q^54 - 111925 * q^55 - 64095 * q^56 - 9747 * q^57 - 126140 * q^58 + 56521 * q^59 - 21800 * q^60 + 6613 * q^61 + 494 * q^62 - 125618 * q^63 - 140426 * q^64 - 17975 * q^65 + 17061 * q^66 - 43534 * q^67 - 138520 * q^68 + 34618 * q^69 + 15625 * q^70 + 95986 * q^71 - 42192 * q^72 + 109218 * q^73 - 182005 * q^74 + 16875 * q^75 - 222376 * q^76 - 9559 * q^77 - 369624 * q^78 + 64943 * q^79 - 173500 * q^80 + 388941 * q^81 - 126926 * q^82 + 109741 * q^83 - 112886 * q^84 - 2975 * q^85 + 43866 * q^86 + 142492 * q^87 + 8712 * q^88 - 119092 * q^89 + 105925 * q^90 + 349320 * q^91 + 433396 * q^92 - 108630 * q^93 + 196160 * q^94 + 333925 * q^95 + 376630 * q^96 + 68774 * q^97 + 310926 * q^98 + 379940 * q^99

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