LMFDB - Embedded newform 43.6.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("43.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.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:	$6.89650425196$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 173x^{6} + 462x^{5} + 9118x^{4} - 14192x^{3} - 167688x^{2} + 106368x + 681984 $ x^8 - 4x^7 - 173x^6 + 462x^5 + 9118x^4 - 14192x^3 - 167688x^2 + 106368*x + 681984
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-6.09504$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.09504 q^{2} +11.1803 q^{3} +33.5297 q^{4} -63.3756 q^{5} -90.5052 q^{6} +223.489 q^{7} -12.3830 q^{8} -118.000 q^{9} +O(q^{10})$	\(q-8.09504 q^{2} +11.1803 q^{3} +33.5297 q^{4} -63.3756 q^{5} -90.5052 q^{6} +223.489 q^{7} -12.3830 q^{8} -118.000 q^{9} +513.028 q^{10} -631.897 q^{11} +374.873 q^{12} +28.5724 q^{13} -1809.15 q^{14} -708.560 q^{15} -972.709 q^{16} -1743.07 q^{17} +955.217 q^{18} -2027.92 q^{19} -2124.97 q^{20} +2498.68 q^{21} +5115.23 q^{22} +2980.86 q^{23} -138.447 q^{24} +891.469 q^{25} -231.295 q^{26} -4036.10 q^{27} +7493.51 q^{28} +766.139 q^{29} +5735.83 q^{30} -8355.33 q^{31} +8270.38 q^{32} -7064.81 q^{33} +14110.3 q^{34} -14163.7 q^{35} -3956.51 q^{36} +14892.6 q^{37} +16416.1 q^{38} +319.449 q^{39} +784.783 q^{40} -5342.20 q^{41} -20226.9 q^{42} -1849.00 q^{43} -21187.3 q^{44} +7478.34 q^{45} -24130.2 q^{46} -6282.09 q^{47} -10875.2 q^{48} +33140.1 q^{49} -7216.48 q^{50} -19488.1 q^{51} +958.024 q^{52} -915.172 q^{53} +32672.4 q^{54} +40046.8 q^{55} -2767.47 q^{56} -22672.8 q^{57} -6201.92 q^{58} -14644.5 q^{59} -23757.8 q^{60} -21324.9 q^{61} +67636.7 q^{62} -26371.7 q^{63} -35822.4 q^{64} -1810.79 q^{65} +57189.9 q^{66} -12868.9 q^{67} -58444.8 q^{68} +33327.0 q^{69} +114656. q^{70} +56454.6 q^{71} +1461.20 q^{72} -25591.3 q^{73} -120556. q^{74} +9966.92 q^{75} -67995.4 q^{76} -141222. q^{77} -2585.95 q^{78} +5795.13 q^{79} +61646.1 q^{80} -16450.9 q^{81} +43245.4 q^{82} -7857.24 q^{83} +83779.9 q^{84} +110468. q^{85} +14967.7 q^{86} +8565.68 q^{87} +7824.80 q^{88} -7560.11 q^{89} -60537.5 q^{90} +6385.60 q^{91} +99947.5 q^{92} -93415.3 q^{93} +50853.8 q^{94} +128520. q^{95} +92465.6 q^{96} +111712. q^{97} -268271. q^{98} +74563.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9}+O(q^{10}) $ 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9	\( 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9} - 617 q^{10} - 532 q^{11} - 4195 q^{12} - 2492 q^{13} - 4240 q^{14} - 1780 q^{15} + 1882 q^{16} - 2534 q^{17} - 3711 q^{18} - 1678 q^{19} - 2607 q^{20} - 2256 q^{21} + 11502 q^{22} - 2488 q^{23} + 19953 q^{24} + 4378 q^{25} + 4586 q^{26} - 8960 q^{27} + 18640 q^{28} - 4360 q^{29} + 25092 q^{30} + 5704 q^{31} - 18294 q^{32} - 12852 q^{33} + 30007 q^{34} + 5640 q^{35} + 67969 q^{36} - 3772 q^{37} - 6559 q^{38} + 11120 q^{39} + 14869 q^{40} - 10698 q^{41} + 78698 q^{42} - 14792 q^{43} - 356 q^{44} - 44912 q^{45} - 19389 q^{46} - 77864 q^{47} - 118727 q^{48} + 7188 q^{49} + 26877 q^{50} - 80246 q^{51} - 60736 q^{52} - 62352 q^{53} + 61026 q^{54} - 49552 q^{55} - 144528 q^{56} - 808 q^{57} + 52951 q^{58} - 26224 q^{59} + 101500 q^{60} - 82540 q^{61} - 9023 q^{62} - 61768 q^{63} + 153858 q^{64} - 5000 q^{65} - 48516 q^{66} + 27784 q^{67} + 40507 q^{68} - 93776 q^{69} + 185910 q^{70} - 9504 q^{71} - 186687 q^{72} + 14260 q^{73} - 15239 q^{74} + 167420 q^{75} + 1279 q^{76} - 218140 q^{77} + 264170 q^{78} + 160248 q^{79} - 1291 q^{80} + 161076 q^{81} - 47781 q^{82} - 77176 q^{83} + 16382 q^{84} + 141096 q^{85} + 22188 q^{86} + 268136 q^{87} + 129544 q^{88} - 265692 q^{89} + 48990 q^{90} + 401148 q^{91} + 190391 q^{92} - 123860 q^{93} + 248737 q^{94} + 135884 q^{95} + 950817 q^{96} + 144742 q^{97} - 292244 q^{98} + 239516 q^{99}+O(q^{100}) \) 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9 - 617 * q^10 - 532 * q^11 - 4195 * q^12 - 2492 * q^13 - 4240 * q^14 - 1780 * q^15 + 1882 * q^16 - 2534 * q^17 - 3711 * q^18 - 1678 * q^19 - 2607 * q^20 - 2256 * q^21 + 11502 * q^22 - 2488 * q^23 + 19953 * q^24 + 4378 * q^25 + 4586 * q^26 - 8960 * q^27 + 18640 * q^28 - 4360 * q^29 + 25092 * q^30 + 5704 * q^31 - 18294 * q^32 - 12852 * q^33 + 30007 * q^34 + 5640 * q^35 + 67969 * q^36 - 3772 * q^37 - 6559 * q^38 + 11120 * q^39 + 14869 * q^40 - 10698 * q^41 + 78698 * q^42 - 14792 * q^43 - 356 * q^44 - 44912 * q^45 - 19389 * q^46 - 77864 * q^47 - 118727 * q^48 + 7188 * q^49 + 26877 * q^50 - 80246 * q^51 - 60736 * q^52 - 62352 * q^53 + 61026 * q^54 - 49552 * q^55 - 144528 * q^56 - 808 * q^57 + 52951 * q^58 - 26224 * q^59 + 101500 * q^60 - 82540 * q^61 - 9023 * q^62 - 61768 * q^63 + 153858 * q^64 - 5000 * q^65 - 48516 * q^66 + 27784 * q^67 + 40507 * q^68 - 93776 * q^69 + 185910 * q^70 - 9504 * q^71 - 186687 * q^72 + 14260 * q^73 - 15239 * q^74 + 167420 * q^75 + 1279 * q^76 - 218140 * q^77 + 264170 * q^78 + 160248 * q^79 - 1291 * q^80 + 161076 * q^81 - 47781 * q^82 - 77176 * q^83 + 16382 * q^84 + 141096 * q^85 + 22188 * q^86 + 268136 * q^87 + 129544 * q^88 - 265692 * q^89 + 48990 * q^90 + 401148 * q^91 + 190391 * q^92 - 123860 * q^93 + 248737 * q^94 + 135884 * q^95 + 950817 * q^96 + 144742 * q^97 - 292244 * q^98 + 239516 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−8.09504	−1.43101	−0.715507	−	0.698605i	$-0.753804\pi$
$2$	−8.09504	−1.43101	−0.715507	+	0.698605i	$0.753804\pi$
$3$	11.1803	0.717218	0.358609	−	0.933488i	$-0.383251\pi$
$3$	11.1803	0.717218	0.358609	+	0.933488i	$0.383251\pi$
$4$	33.5297	1.04780
$5$	−63.3756	−1.13370	−0.566849	−	0.823822i	$-0.691838\pi$
$5$	−63.3756	−1.13370	−0.566849	+	0.823822i	$0.691838\pi$
$6$	−90.5052	−1.02635
$7$	223.489	1.72389	0.861946	−	0.507000i	$-0.169245\pi$
$7$	223.489	1.72389	0.861946	+	0.507000i	$0.169245\pi$
$8$	−12.3830	−0.0684073
$9$	−118.000	−0.485598
$10$	513.028	1.62234
$11$	−631.897	−1.57458	−0.787289	−	0.616584i	$-0.788516\pi$
$11$	−631.897	−1.57458	−0.787289	+	0.616584i	$0.788516\pi$
$12$	374.873	0.751504
$13$	28.5724	0.0468909	0.0234454	−	0.999725i	$-0.492536\pi$
$13$	28.5724	0.0468909	0.0234454	+	0.999725i	$0.492536\pi$
$14$	−1809.15	−2.46692
$15$	−708.560	−0.813109
$16$	−972.709	−0.949911
$17$	−1743.07	−1.46283	−0.731414	−	0.681933i	$-0.761139\pi$
$17$	−1743.07	−1.46283	−0.731414	+	0.681933i	$0.761139\pi$
$18$	955.217	0.694897
$19$	−2027.92	−1.28874	−0.644371	−	0.764713i	$-0.722881\pi$
$19$	−2027.92	−1.28874	−0.644371	+	0.764713i	$0.722881\pi$
$20$	−2124.97	−1.18789
$21$	2498.68	1.23641
$22$	5115.23	2.25324
$23$	2980.86	1.17496	0.587479	−	0.809239i	$-0.300120\pi$
$23$	2980.86	1.17496	0.587479	+	0.809239i	$0.300120\pi$
$24$	−138.447	−0.0490630
$25$	891.469	0.285270
$26$	−231.295	−0.0671015
$27$	−4036.10	−1.06550
$28$	7493.51	1.80630
$29$	766.139	0.169166	0.0845829	−	0.996416i	$-0.473044\pi$
$29$	766.139	0.169166	0.0845829	+	0.996416i	$0.473044\pi$
$30$	5735.83	1.16357
$31$	−8355.33	−1.56156	−0.780781	−	0.624805i	$-0.785178\pi$
$31$	−8355.33	−1.56156	−0.780781	+	0.624805i	$0.785178\pi$
$32$	8270.38	1.42774
$33$	−7064.81	−1.12932
$34$	14110.3	2.09333
$35$	−14163.7	−1.95437
$36$	−3956.51	−0.508811
$37$	14892.6	1.78841	0.894204	−	0.447661i	$-0.147743\pi$
$37$	14892.6	1.78841	0.894204	+	0.447661i	$0.147743\pi$
$38$	16416.1	1.84421
$39$	319.449	0.0336310
$40$	784.783	0.0775532
$41$	−5342.20	−0.496319	−0.248159	−	0.968719i	$-0.579826\pi$
$41$	−5342.20	−0.496319	−0.248159	+	0.968719i	$0.579826\pi$
$42$	−20226.9	−1.76932
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	−21187.3	−1.64985
$45$	7478.34	0.550521
$46$	−24130.2	−1.68138
$47$	−6282.09	−0.414820	−0.207410	−	0.978254i	$-0.566503\pi$
$47$	−6282.09	−0.414820	−0.207410	+	0.978254i	$0.566503\pi$
$48$	−10875.2	−0.681294
$49$	33140.1	1.97181
$50$	−7216.48	−0.408226
$51$	−19488.1	−1.04917
$52$	958.024	0.0491324
$53$	−915.172	−0.0447521	−0.0223760	−	0.999750i	$-0.507123\pi$
$53$	−915.172	−0.0447521	−0.0223760	+	0.999750i	$0.507123\pi$
$54$	32672.4	1.52474
$55$	40046.8	1.78510
$56$	−2767.47	−0.117927
$57$	−22672.8	−0.924310
$58$	−6201.92	−0.242079
$59$	−14644.5	−0.547704	−0.273852	−	0.961772i	$-0.588298\pi$
$59$	−14644.5	−0.547704	−0.273852	+	0.961772i	$0.588298\pi$
$60$	−23757.8	−0.851978
$61$	−21324.9	−0.733775	−0.366887	−	0.930265i	$-0.619577\pi$
$61$	−21324.9	−0.733775	−0.366887	+	0.930265i	$0.619577\pi$
$62$	67636.7	2.23462
$63$	−26371.7	−0.837118
$64$	−35822.4	−1.09321
$65$	−1810.79	−0.0531601
$66$	57189.9	1.61607
$67$	−12868.9	−0.350232	−0.175116	−	0.984548i	$-0.556030\pi$
$67$	−12868.9	−0.350232	−0.175116	+	0.984548i	$0.556030\pi$
$68$	−58444.8	−1.53276
$69$	33327.0	0.842702
$70$	114656.	2.79674
$71$	56454.6	1.32909	0.664544	−	0.747249i	$-0.268626\pi$
$71$	56454.6	1.32909	0.664544	+	0.747249i	$0.268626\pi$
$72$	1461.20	0.0332184
$73$	−25591.3	−0.562064	−0.281032	−	0.959698i	$-0.590677\pi$
$73$	−25591.3	−0.562064	−0.281032	+	0.959698i	$0.590677\pi$
$74$	−120556.	−2.55924
$75$	9966.92	0.204601
$76$	−67995.4	−1.35035
$77$	−141222.	−2.71440
$78$	−2585.95	−0.0481265
$79$	5795.13	0.104471	0.0522355	−	0.998635i	$-0.483365\pi$
$79$	5795.13	0.104471	0.0522355	+	0.998635i	$0.483365\pi$
$80$	61646.1	1.07691
$81$	−16450.9	−0.278597
$82$	43245.4	0.710240
$83$	−7857.24	−0.125192	−0.0625958	−	0.998039i	$-0.519938\pi$
$83$	−7857.24	−0.125192	−0.0625958	+	0.998039i	$0.519938\pi$
$84$	83779.9	1.29551
$85$	110468.	1.65841
$86$	14967.7	0.218228
$87$	8565.68	0.121329
$88$	7824.80	0.107713
$89$	−7560.11	−0.101170	−0.0505852	−	0.998720i	$-0.516109\pi$
$89$	−7560.11	−0.101170	−0.0505852	+	0.998720i	$0.516109\pi$
$90$	−60537.5	−0.787803
$91$	6385.60	0.0808348
$92$	99947.5	1.23113
$93$	−93415.3	−1.11998
$94$	50853.8	0.593613
$95$	128520.	1.46104
$96$	92465.6	1.02400
$97$	111712.	1.20551	0.602754	−	0.797927i	$-0.294070\pi$
$97$	111712.	1.20551	0.602754	+	0.797927i	$0.294070\pi$
$98$	−268271.	−2.82168
$99$	74563.9	0.764611
$100$	29890.7	0.298907
$101$	10492.3	0.102345	0.0511724	−	0.998690i	$-0.483704\pi$
$101$	10492.3	0.102345	0.0511724	+	0.998690i	$0.483704\pi$
$102$	157757.	1.50137
$103$	−11286.6	−0.104826	−0.0524130	−	0.998625i	$-0.516691\pi$
$103$	−11286.6	−0.104826	−0.0524130	+	0.998625i	$0.516691\pi$
$104$	−353.813	−0.00320768
$105$	−158355.	−1.40171
$106$	7408.36	0.0640409
$107$	39045.4	0.329693	0.164847	−	0.986319i	$-0.447287\pi$
$107$	39045.4	0.329693	0.164847	+	0.986319i	$0.447287\pi$
$108$	−135329.	−1.11643
$109$	−14622.8	−0.117887	−0.0589433	−	0.998261i	$-0.518773\pi$
$109$	−14622.8	−0.117887	−0.0589433	+	0.998261i	$0.518773\pi$
$110$	−324181.	−2.55450
$111$	166504.	1.28268
$112$	−217389.	−1.63755
$113$	−859.121	−0.00632934	−0.00316467	−	0.999995i	$-0.501007\pi$
$113$	−859.121	−0.00632934	−0.00316467	+	0.999995i	$0.501007\pi$
$114$	183537.	1.32270
$115$	−188914.	−1.33205
$116$	25688.4	0.177252
$117$	−3371.55	−0.0227701
$118$	118548.	0.783772
$119$	−389557.	−2.52176
$120$	8774.13	0.0556226
$121$	238242.	1.47930
$122$	172626.	1.05004
$123$	−59727.6	−0.355969
$124$	−280152.	−1.63621
$125$	141551.	0.810288
$126$	213480.	1.19793
$127$	193396.	1.06399	0.531997	−	0.846746i	$-0.321442\pi$
$127$	193396.	1.06399	0.531997	+	0.846746i	$0.321442\pi$
$128$	25331.5	0.136658
$129$	−20672.4	−0.109375
$130$	14658.4	0.0760728
$131$	−269599.	−1.37259	−0.686293	−	0.727325i	$-0.740763\pi$
$131$	−269599.	−1.37259	−0.686293	+	0.727325i	$0.740763\pi$
$132$	−236881.	−1.18330
$133$	−453216.	−2.22165
$134$	104175.	0.501187
$135$	255790.	1.20795
$136$	21584.6	0.100068
$137$	148987.	0.678183	0.339091	−	0.940753i	$-0.389880\pi$
$137$	148987.	0.678183	0.339091	+	0.940753i	$0.389880\pi$
$138$	−269784.	−1.20592
$139$	−16355.6	−0.0718008	−0.0359004	−	0.999355i	$-0.511430\pi$
$139$	−16355.6	−0.0718008	−0.0359004	+	0.999355i	$0.511430\pi$
$140$	−474906.	−2.04780
$141$	−70235.8	−0.297516
$142$	−457003.	−1.90194
$143$	−18054.8	−0.0738333
$144$	114780.	0.461275
$145$	−48554.5	−0.191783
$146$	207163.	0.804322
$147$	370518.	1.41422
$148$	499345.	1.87390
$149$	−150536.	−0.555489	−0.277744	−	0.960655i	$-0.589587\pi$
$149$	−150536.	−0.555489	−0.277744	+	0.960655i	$0.589587\pi$
$150$	−80682.6	−0.292787
$151$	428141.	1.52807	0.764037	−	0.645172i	$-0.223214\pi$
$151$	428141.	1.52807	0.764037	+	0.645172i	$0.223214\pi$
$152$	25111.8	0.0881594
$153$	205683.	0.710346
$154$	1.14320e6	3.88435
$155$	529524.	1.77034
$156$	10711.0	0.0352387
$157$	−434190.	−1.40582	−0.702912	−	0.711277i	$-0.748117\pi$
$157$	−434190.	−1.40582	−0.702912	+	0.711277i	$0.748117\pi$
$158$	−46911.8	−0.149499
$159$	−10231.9	−0.0320970
$160$	−524140.	−1.61863
$161$	666189.	2.02550
$162$	133171.	0.398677
$163$	−571830.	−1.68577	−0.842884	−	0.538095i	$-0.819144\pi$
$163$	−571830.	−1.68577	−0.842884	+	0.538095i	$0.819144\pi$
$164$	−179122.	−0.520044
$165$	447737.	1.28030
$166$	63604.7	0.179151
$167$	605744.	1.68073	0.840365	−	0.542020i	$-0.182340\pi$
$167$	605744.	1.68073	0.840365	+	0.542020i	$0.182340\pi$
$168$	−30941.2	−0.0845793
$169$	−370477.	−0.997801
$170$	−894246.	−2.37320
$171$	239295.	0.625810
$172$	−61996.4	−0.159789
$173$	−85238.8	−0.216532	−0.108266	−	0.994122i	$-0.534530\pi$
$173$	−85238.8	−0.216532	−0.108266	+	0.994122i	$0.534530\pi$
$174$	−69339.6	−0.173623
$175$	199233.	0.491775
$176$	614652.	1.49571
$177$	−163731.	−0.392823
$178$	61199.4	0.144776
$179$	77941.8	0.181818	0.0909092	−	0.995859i	$-0.471023\pi$
$179$	77941.8	0.181818	0.0909092	+	0.995859i	$0.471023\pi$
$180$	250746.	0.576838
$181$	−347661.	−0.788787	−0.394393	−	0.918942i	$-0.629045\pi$
$181$	−347661.	−0.788787	−0.394393	+	0.918942i	$0.629045\pi$
$182$	−51691.7	−0.115676
$183$	−238420.	−0.526277
$184$	−36912.2	−0.0803757
$185$	−943828.	−2.02751
$186$	756201.	1.60271
$187$	1.10144e6	2.30334
$188$	−210637.	−0.434650
$189$	−902023.	−1.83680
$190$	−1.04038e6	−2.09078
$191$	−192163.	−0.381142	−0.190571	−	0.981673i	$-0.561034\pi$
$191$	−192163.	−0.381142	−0.190571	+	0.981673i	$0.561034\pi$
$192$	−400506.	−0.784072
$193$	−271724.	−0.525091	−0.262546	−	0.964920i	$-0.584562\pi$
$193$	−271724.	−0.525091	−0.262546	+	0.964920i	$0.584562\pi$
$194$	−904313.	−1.72510
$195$	−20245.3	−0.0381274
$196$	1.11118e6	2.06606
$197$	76788.1	0.140971	0.0704853	−	0.997513i	$-0.477545\pi$
$197$	76788.1	0.140971	0.0704853	+	0.997513i	$0.477545\pi$
$198$	−603598.	−1.09417
$199$	−694776.	−1.24369	−0.621845	−	0.783140i	$-0.713617\pi$
$199$	−694776.	−1.24369	−0.621845	+	0.783140i	$0.713617\pi$
$200$	−11039.1	−0.0195146
$201$	−143879.	−0.251193
$202$	−84935.3	−0.146457
$203$	171223.	0.291624
$204$	−653432.	−1.09932
$205$	338565.	0.562675
$206$	91365.3	0.150008
$207$	−351743.	−0.570557
$208$	−27792.6	−0.0445422
$209$	1.28143e6	2.02923
$210$	1.28189e6	2.00587
$211$	−433533.	−0.670372	−0.335186	−	0.942152i	$-0.608799\pi$
$211$	−433533.	−0.670372	−0.335186	+	0.942152i	$0.608799\pi$
$212$	−30685.5	−0.0468914
$213$	631181.	0.953246
$214$	−316074.	−0.471796
$215$	117182.	0.172887
$216$	49979.2	0.0728878
$217$	−1.86732e6	−2.69196
$218$	118372.	0.168698
$219$	−286119.	−0.403123
$220$	1.34276e6	1.87043
$221$	−49803.8	−0.0685933
$222$	−1.34786e6	−1.83553
$223$	1.04204e6	1.40320	0.701602	−	0.712569i	$-0.252469\pi$
$223$	1.04204e6	1.40320	0.701602	+	0.712569i	$0.252469\pi$
$224$	1.84834e6	2.46128
$225$	−105194.	−0.138526
$226$	6954.62	0.00905737
$227$	924970.	1.19141	0.595707	−	0.803202i	$-0.296872\pi$
$227$	924970.	1.19141	0.595707	+	0.803202i	$0.296872\pi$
$228$	−760211.	−0.968495
$229$	−137140.	−0.172812	−0.0864062	−	0.996260i	$-0.527538\pi$
$229$	−137140.	−0.172812	−0.0864062	+	0.996260i	$0.527538\pi$
$230$	1.52927e6	1.90618
$231$	−1.57890e6	−1.94682
$232$	−9487.13	−0.0115722
$233$	428602.	0.517208	0.258604	−	0.965983i	$-0.416738\pi$
$233$	428602.	0.517208	0.258604	+	0.965983i	$0.416738\pi$
$234$	27292.8	0.0325843
$235$	398131.	0.470280
$236$	−491027.	−0.573886
$237$	64791.5	0.0749285
$238$	3.15348e6	3.60868
$239$	−1.17134e6	−1.32645	−0.663223	−	0.748422i	$-0.730812\pi$
$239$	−1.17134e6	−1.32645	−0.663223	+	0.748422i	$0.730812\pi$
$240$	689223.	0.772381
$241$	119252.	0.132258	0.0661291	−	0.997811i	$-0.478935\pi$
$241$	119252.	0.132258	0.0661291	+	0.997811i	$0.478935\pi$
$242$	−1.92858e6	−2.11690
$243$	796846.	0.865683
$244$	−715018.	−0.768852
$245$	−2.10028e6	−2.23543
$246$	483497.	0.509397
$247$	−57942.4	−0.0604302
$248$	103464.	0.106822
$249$	−87846.6	−0.0897897
$250$	−1.14586e6	−1.15953
$251$	−141272.	−0.141538	−0.0707690	−	0.997493i	$-0.522545\pi$
$251$	−141272.	−0.141538	−0.0707690	+	0.997493i	$0.522545\pi$
$252$	−884235.	−0.877135
$253$	−1.88360e6	−1.85006
$254$	−1.56555e6	−1.52259
$255$	1.23507e6	1.18944
$256$	941257.	0.897652
$257$	−196749.	−0.185815	−0.0929074	−	0.995675i	$-0.529616\pi$
$257$	−196749.	−0.185815	−0.0929074	+	0.995675i	$0.529616\pi$
$258$	167344.	0.156517
$259$	3.32833e6	3.08302
$260$	−60715.4	−0.0557013
$261$	−90404.5	−0.0821465
$262$	2.18241e6	1.96419
$263$	−1.96879e6	−1.75513	−0.877565	−	0.479457i	$-0.840834\pi$
$263$	−1.96879e6	−1.75513	−0.877565	+	0.479457i	$0.840834\pi$
$264$	87483.9	0.0772535
$265$	57999.6	0.0507353
$266$	3.66880e6	3.17922
$267$	−84524.6	−0.0725612
$268$	−431492.	−0.366974
$269$	−531007.	−0.447424	−0.223712	−	0.974655i	$-0.571818\pi$
$269$	−531007.	−0.447424	−0.223712	+	0.974655i	$0.571818\pi$
$270$	−2.07063e6	−1.72860
$271$	−1.68769e6	−1.39595	−0.697975	−	0.716122i	$-0.745916\pi$
$271$	−1.68769e6	−1.39595	−0.697975	+	0.716122i	$0.745916\pi$
$272$	1.69550e6	1.38956
$273$	71393.2	0.0579762
$274$	−1.20606e6	−0.970489
$275$	−563316.	−0.449180
$276$	1.11745e6	0.882986
$277$	13630.1	0.0106733	0.00533665	−	0.999986i	$-0.498301\pi$
$277$	13630.1	0.0106733	0.00533665	+	0.999986i	$0.498301\pi$
$278$	132399.	0.102748
$279$	985930.	0.758291
$280$	175390.	0.133693
$281$	1.12070e6	0.846692	0.423346	−	0.905968i	$-0.360855\pi$
$281$	1.12070e6	0.846692	0.423346	+	0.905968i	$0.360855\pi$
$282$	568562.	0.425750
$283$	−1.52947e6	−1.13521	−0.567605	−	0.823301i	$-0.692130\pi$
$283$	−1.52947e6	−1.13521	−0.567605	+	0.823301i	$0.692130\pi$
$284$	1.89291e6	1.39262
$285$	1.43690e6	1.04789
$286$	146154.	0.105657
$287$	−1.19392e6	−0.855600
$288$	−975907.	−0.693309
$289$	1.61845e6	1.13987
$290$	393051.	0.274444
$291$	1.24898e6	0.864613
$292$	−858070.	−0.588932
$293$	−1.58484e6	−1.07849	−0.539246	−	0.842148i	$-0.681291\pi$
$293$	−1.58484e6	−1.07849	−0.539246	+	0.842148i	$0.681291\pi$
$294$	−2.99936e6	−2.02376
$295$	928107.	0.620930
$296$	−184416.	−0.122340
$297$	2.55040e6	1.67771
$298$	1.21860e6	0.794912
$299$	85170.4	0.0550948
$300$	334188.	0.214382
$301$	−413230.	−0.262891
$302$	−3.46582e6	−2.18670
$303$	117307.	0.0734035
$304$	1.97257e6	1.22419
$305$	1.35148e6	0.831879
$306$	−1.66501e6	−1.01652
$307$	695751.	0.421316	0.210658	−	0.977560i	$-0.432439\pi$
$307$	695751.	0.421316	0.210658	+	0.977560i	$0.432439\pi$
$308$	−4.73512e6	−2.84416
$309$	−126188.	−0.0751831
$310$	−4.28652e6	−2.53338
$311$	−988763.	−0.579684	−0.289842	−	0.957075i	$-0.593603\pi$
$311$	−988763.	−0.579684	−0.289842	+	0.957075i	$0.593603\pi$
$312$	−3955.75	−0.00230061
$313$	−3.07551e6	−1.77442	−0.887208	−	0.461369i	$-0.847358\pi$
$313$	−3.07551e6	−1.77442	−0.887208	+	0.461369i	$0.847358\pi$
$314$	3.51479e6	2.01176
$315$	1.67132e6	0.949039
$316$	194309.	0.109465
$317$	904527.	0.505561	0.252780	−	0.967524i	$-0.418655\pi$
$317$	904527.	0.505561	0.252780	+	0.967524i	$0.418655\pi$
$318$	82827.9	0.0459313
$319$	−484120.	−0.266365
$320$	2.27027e6	1.23937
$321$	436540.	0.236462
$322$	−5.39283e6	−2.89852
$323$	3.53481e6	1.88521
$324$	−551594.	−0.291915
$325$	25471.4	0.0133766
$326$	4.62899e6	2.41236
$327$	−163488.	−0.0845505
$328$	66152.7	0.0339518
$329$	−1.40398e6	−0.715105
$330$	−3.62445e6	−1.83213
$331$	−2.09309e6	−1.05007	−0.525034	−	0.851081i	$-0.675947\pi$
$331$	−2.09309e6	−1.05007	−0.525034	+	0.851081i	$0.675947\pi$
$332$	−263451.	−0.131176
$333$	−1.75733e6	−0.868446
$334$	−4.90353e6	−2.40515
$335$	815577.	0.397057
$336$	−2.43049e6	−1.17448
$337$	−647484.	−0.310566	−0.155283	−	0.987870i	$-0.549629\pi$
$337$	−647484.	−0.310566	−0.155283	+	0.987870i	$0.549629\pi$
$338$	2.99902e6	1.42787
$339$	−9605.25	−0.00453952
$340$	3.70397e6	1.73768
$341$	5.27970e6	2.45880
$342$	−1.93710e6	−0.895544
$343$	3.65027e6	1.67529
$344$	22896.2	0.0104320
$345$	−2.11212e6	−0.955369
$346$	690012.	0.309860
$347$	−462018.	−0.205985	−0.102992	−	0.994682i	$-0.532842\pi$
$347$	−462018.	−0.205985	−0.102992	+	0.994682i	$0.532842\pi$
$348$	287205.	0.127129
$349$	2.85075e6	1.25284	0.626420	−	0.779486i	$-0.284520\pi$
$349$	2.85075e6	1.25284	0.626420	+	0.779486i	$0.284520\pi$
$350$	−1.61280e6	−0.703737
$351$	−115321.	−0.0499621
$352$	−5.22602e6	−2.24810
$353$	−809444.	−0.345740	−0.172870	−	0.984945i	$-0.555304\pi$
$353$	−809444.	−0.345740	−0.172870	+	0.984945i	$0.555304\pi$
$354$	1.32541e6	0.562136
$355$	−3.57785e6	−1.50678
$356$	−253488.	−0.106007
$357$	−4.35538e6	−1.80865
$358$	−630942.	−0.260185
$359$	3.46118e6	1.41739	0.708694	−	0.705516i	$-0.249285\pi$
$359$	3.46118e6	1.41739	0.708694	+	0.705516i	$0.249285\pi$
$360$	−92604.6	−0.0376596
$361$	1.63635e6	0.660856
$362$	2.81433e6	1.12877
$363$	2.66363e6	1.06098
$364$	214107.	0.0846990
$365$	1.62187e6	0.637210
$366$	1.93002e6	0.753110
$367$	2.13602e6	0.827827	0.413914	−	0.910316i	$-0.364162\pi$
$367$	2.13602e6	0.827827	0.413914	+	0.910316i	$0.364162\pi$
$368$	−2.89951e6	−1.11611
$369$	630381.	0.241011
$370$	7.64033e6	2.90140
$371$	−204531.	−0.0771478
$372$	−3.13219e6	−1.17352
$373$	2.37193e6	0.882734	0.441367	−	0.897327i	$-0.354494\pi$
$373$	2.37193e6	0.882734	0.441367	+	0.897327i	$0.354494\pi$
$374$	−8.91622e6	−3.29611
$375$	1.58259e6	0.581153
$376$	77791.4	0.0283767
$377$	21890.4	0.00793233
$378$	7.30191e6	2.62849
$379$	−5.47562e6	−1.95810	−0.979051	−	0.203616i	$-0.934731\pi$
$379$	−5.47562e6	−1.95810	−0.979051	+	0.203616i	$0.934731\pi$
$380$	4.30925e6	1.53089
$381$	2.16224e6	0.763116
$382$	1.55557e6	0.545419
$383$	3.16966e6	1.10412	0.552059	−	0.833805i	$-0.313842\pi$
$383$	3.16966e6	1.10412	0.552059	+	0.833805i	$0.313842\pi$
$384$	283214.	0.0980138
$385$	8.95001e6	3.07731
$386$	2.19962e6	0.751413
$387$	218182.	0.0740529
$388$	3.74567e6	1.26314
$389$	−311235.	−0.104283	−0.0521416	−	0.998640i	$-0.516605\pi$
$389$	−311235.	−0.104283	−0.0521416	+	0.998640i	$0.516605\pi$
$390$	163886.	0.0545609
$391$	−5.19587e6	−1.71876
$392$	−410376.	−0.134886
$393$	−3.01420e6	−0.984444
$394$	−621603.	−0.201731
$395$	−367270.	−0.118438
$396$	2.50011e6	0.801162
$397$	−496314.	−0.158045	−0.0790224	−	0.996873i	$-0.525180\pi$
$397$	−496314.	−0.158045	−0.0790224	+	0.996873i	$0.525180\pi$
$398$	5.62424e6	1.77974
$399$	−5.06711e6	−1.59341
$400$	−867140.	−0.270981
$401$	−5.63670e6	−1.75051	−0.875253	−	0.483665i	$-0.839305\pi$
$401$	−5.63670e6	−1.75051	−0.875253	+	0.483665i	$0.839305\pi$
$402$	1.16471e6	0.359461
$403$	−238732.	−0.0732230
$404$	351802.	0.107237
$405$	1.04259e6	0.315845
$406$	−1.38606e6	−0.417318
$407$	−9.41059e6	−2.81599
$408$	241323.	0.0717707
$409$	−720515.	−0.212978	−0.106489	−	0.994314i	$-0.533961\pi$
$409$	−720515.	−0.212978	−0.106489	+	0.994314i	$0.533961\pi$
$410$	−2.74070e6	−0.805197
$411$	1.66572e6	0.486405
$412$	−378435.	−0.109837
$413$	−3.27289e6	−0.944182
$414$	2.84737e6	0.816476
$415$	497958.	0.141929
$416$	236305.	0.0669482
$417$	−182861.	−0.0514969
$418$	−1.03733e7	−2.90385
$419$	−3.94151e6	−1.09680	−0.548400	−	0.836216i	$-0.684763\pi$
$419$	−3.94151e6	−1.09680	−0.548400	+	0.836216i	$0.684763\pi$
$420$	−5.30960e6	−1.46872
$421$	4.39506e6	1.20854	0.604268	−	0.796781i	$-0.293466\pi$
$421$	4.39506e6	1.20854	0.604268	+	0.796781i	$0.293466\pi$
$422$	3.50947e6	0.959312
$423$	741288.	0.201436
$424$	11332.6	0.00306137
$425$	−1.55390e6	−0.417301
$426$	−5.10944e6	−1.36411
$427$	−4.76588e6	−1.26495
$428$	1.30918e6	0.345454
$429$	−201859.	−0.0529546
$430$	−948589.	−0.247404
$431$	1.24913e6	0.323903	0.161951	−	0.986799i	$-0.448221\pi$
$431$	1.24913e6	0.323903	0.161951	+	0.986799i	$0.448221\pi$
$432$	3.92595e6	1.01213
$433$	971902.	0.249117	0.124558	−	0.992212i	$-0.460249\pi$
$433$	971902.	0.249117	0.124558	+	0.992212i	$0.460249\pi$
$434$	1.51160e7	3.85224
$435$	−542855.	−0.137550
$436$	−490299.	−0.123522
$437$	−6.04494e6	−1.51422
$438$	2.31615e6	0.576874
$439$	−1.32453e6	−0.328021	−0.164010	−	0.986459i	$-0.552443\pi$
$439$	−1.32453e6	−0.328021	−0.164010	+	0.986459i	$0.552443\pi$
$440$	−495902.	−0.122114
$441$	−3.91054e6	−0.957504
$442$	403164.	0.0981581
$443$	4.76446e6	1.15346	0.576732	−	0.816933i	$-0.304328\pi$
$443$	4.76446e6	1.15346	0.576732	+	0.816933i	$0.304328\pi$
$444$	5.58284e6	1.34399
$445$	479127.	0.114697
$446$	−8.43533e6	−2.00801
$447$	−1.68304e6	−0.398407
$448$	−8.00589e6	−1.88458
$449$	−5.40007e6	−1.26411	−0.632053	−	0.774926i	$-0.717787\pi$
$449$	−5.40007e6	−1.26411	−0.632053	+	0.774926i	$0.717787\pi$
$450$	851546.	0.198233
$451$	3.37572e6	0.781493
$452$	−28806.1	−0.00663190
$453$	4.78676e6	1.09596
$454$	−7.48767e6	−1.70493
$455$	−404692.	−0.0916422
$456$	280758.	0.0632295
$457$	2.12752e6	0.476523	0.238261	−	0.971201i	$-0.423423\pi$
$457$	2.12752e6	0.476523	0.238261	+	0.971201i	$0.423423\pi$
$458$	1.11015e6	0.247297
$459$	7.03522e6	1.55864
$460$	−6.33423e6	−1.39572
$461$	2.80905e6	0.615612	0.307806	−	0.951449i	$-0.400405\pi$
$461$	2.80905e6	0.615612	0.307806	+	0.951449i	$0.400405\pi$
$462$	1.27813e7	2.78593
$463$	−2.85342e6	−0.618605	−0.309302	−	0.950964i	$-0.600096\pi$
$463$	−2.85342e6	−0.618605	−0.309302	+	0.950964i	$0.600096\pi$
$464$	−745230.	−0.160692
$465$	5.92025e6	1.26972
$466$	−3.46955e6	−0.740132
$467$	−559463.	−0.118708	−0.0593539	−	0.998237i	$-0.518904\pi$
$467$	−559463.	−0.118708	−0.0593539	+	0.998237i	$0.518904\pi$
$468$	−113047.	−0.0238586
$469$	−2.87606e6	−0.603762
$470$	−3.22289e6	−0.672978
$471$	−4.85439e6	−1.00828
$472$	181344.	0.0374669
$473$	1.16838e6	0.240121
$474$	−524490.	−0.107224
$475$	−1.80782e6	−0.367640
$476$	−1.30617e7	−2.64231
$477$	107991.	0.0217315
$478$	9.48208e6	1.89816
$479$	5.46747e6	1.08880	0.544399	−	0.838826i	$-0.316758\pi$
$479$	5.46747e6	1.08880	0.544399	+	0.838826i	$0.316758\pi$
$480$	−5.86006e6	−1.16091
$481$	425517.	0.0838600
$482$	−965349.	−0.189263
$483$	7.44821e6	1.45273
$484$	7.98819e6	1.55001
$485$	−7.07981e6	−1.36668
$486$	−6.45050e6	−1.23881
$487$	9.34759e6	1.78598	0.892991	−	0.450074i	$-0.148603\pi$
$487$	9.34759e6	1.78598	0.892991	+	0.450074i	$0.148603\pi$
$488$	264067.	0.0501955
$489$	−6.39325e6	−1.20906
$490$	1.70018e7	3.19893
$491$	−1.04964e7	−1.96488	−0.982438	−	0.186589i	$-0.940257\pi$
$491$	−1.04964e7	−1.96488	−0.982438	+	0.186589i	$0.940257\pi$
$492$	−2.00265e6	−0.372986
$493$	−1.33544e6	−0.247460
$494$	469046.	0.0864766
$495$	−4.72554e6	−0.866838
$496$	8.12730e6	1.48335
$497$	1.26170e7	2.29120
$498$	711122.	0.128490
$499$	5.74842e6	1.03347	0.516734	−	0.856146i	$-0.327148\pi$
$499$	5.74842e6	1.03347	0.516734	+	0.856146i	$0.327148\pi$
$500$	4.74618e6	0.849022
$501$	6.77242e6	1.20545
$502$	1.14361e6	0.202543
$503$	3.10341e6	0.546915	0.273457	−	0.961884i	$-0.411833\pi$
$503$	3.10341e6	0.546915	0.273457	+	0.961884i	$0.411833\pi$
$504$	326562.	0.0572650
$505$	−664953.	−0.116028
$506$	1.52478e7	2.64747
$507$	−4.14205e6	−0.715642
$508$	6.48453e6	1.11486
$509$	−7.92714e6	−1.35620	−0.678098	−	0.734972i	$-0.737195\pi$
$509$	−7.92714e6	−1.35620	−0.678098	+	0.734972i	$0.737195\pi$
$510$	−9.99797e6	−1.70210
$511$	−5.71937e6	−0.968938
$512$	−8.43012e6	−1.42121
$513$	8.18488e6	1.37315
$514$	1.59269e6	0.265904
$515$	715293.	0.118841
$516$	−693141.	−0.114603
$517$	3.96963e6	0.653166
$518$	−2.69429e7	−4.41185
$519$	−952998.	−0.155301
$520$	22423.1	0.00363654
$521$	−4.37136e6	−0.705541	−0.352771	−	0.935710i	$-0.614760\pi$
$521$	−4.37136e6	−0.705541	−0.352771	+	0.935710i	$0.614760\pi$
$522$	731828.	0.117553
$523$	1.11680e6	0.178534	0.0892671	−	0.996008i	$-0.471548\pi$
$523$	1.11680e6	0.178534	0.0892671	+	0.996008i	$0.471548\pi$
$524$	−9.03957e6	−1.43820
$525$	2.22749e6	0.352710
$526$	1.59374e7	2.51162
$527$	1.45640e7	2.28430
$528$	6.87201e6	1.07275
$529$	2.44920e6	0.380527
$530$	−469509.	−0.0726030
$531$	1.72806e6	0.265964
$532$	−1.51962e7	−2.32786
$533$	−152640.	−0.0232728
$534$	684230.	0.103836
$535$	−2.47453e6	−0.373773
$536$	159357.	0.0239584
$537$	871415.	0.130403
$538$	4.29852e6	0.640271
$539$	−2.09411e7	−3.10476
$540$	8.57658e6	1.26570
$541$	−6212.12	−0.000912528 0	−0.000456264	−	1.00000i	$-0.500145\pi$
$541$	−6212.12	−0.000912528 0	−0.000456264		1.00000i	$0.500145\pi$
$542$	1.36619e7	1.99763
$543$	−3.88696e6	−0.565732
$544$	−1.44159e7	−2.08855
$545$	926730.	0.133648
$546$	−577931.	−0.0829648
$547$	−9.82839e6	−1.40448	−0.702238	−	0.711942i	$-0.747816\pi$
$547$	−9.82839e6	−1.40448	−0.702238	+	0.711942i	$0.747816\pi$
$548$	4.99549e6	0.710602
$549$	2.51635e6	0.356319
$550$	4.56007e6	0.642783
$551$	−1.55367e6	−0.218011
$552$	−412690.	−0.0576470
$553$	1.29515e6	0.180097
$554$	−110336.	−0.0152737
$555$	−1.05523e7	−1.45417
$556$	−548398.	−0.0752332
$557$	−6.27045e6	−0.856369	−0.428184	−	0.903691i	$-0.640847\pi$
$557$	−6.27045e6	−0.856369	−0.428184	+	0.903691i	$0.640847\pi$
$558$	−7.98115e6	−1.08513
$559$	−52830.4	−0.00715079
$560$	1.37772e7	1.85648
$561$	1.23145e7	1.65200
$562$	−9.07215e6	−1.21163
$563$	−6.71129e6	−0.892350	−0.446175	−	0.894946i	$-0.647214\pi$
$563$	−6.71129e6	−0.892350	−0.446175	+	0.894946i	$0.647214\pi$
$564$	−2.35499e6	−0.311739
$565$	54447.3	0.00717555
$566$	1.23812e7	1.62450
$567$	−3.67659e6	−0.480272
$568$	−699080.	−0.0909193
$569$	−7.01697e6	−0.908592	−0.454296	−	0.890851i	$-0.650109\pi$
$569$	−7.01697e6	−0.908592	−0.454296	+	0.890851i	$0.650109\pi$
$570$	−1.16318e7	−1.49954
$571$	1.61627e6	0.207455	0.103727	−	0.994606i	$-0.466923\pi$
$571$	1.61627e6	0.207455	0.103727	+	0.994606i	$0.466923\pi$
$572$	−605372.	−0.0773628
$573$	−2.14845e6	−0.273362
$574$	9.66484e6	1.22438
$575$	2.65735e6	0.335181
$576$	4.22705e6	0.530861
$577$	1.08712e7	1.35937	0.679686	−	0.733503i	$-0.262116\pi$
$577$	1.08712e7	1.35937	0.679686	+	0.733503i	$0.262116\pi$
$578$	−1.31014e7	−1.63117
$579$	−3.03796e6	−0.376605
$580$	−1.62802e6	−0.200951
$581$	−1.75600e6	−0.215817
$582$	−1.01105e7	−1.23727
$583$	578294.	0.0704656
$584$	316898.	0.0384493
$585$	213674.	0.0258144
$586$	1.28294e7	1.54334
$587$	8.65320e6	1.03653	0.518264	−	0.855221i	$-0.326578\pi$
$587$	8.65320e6	1.03653	0.518264	+	0.855221i	$0.326578\pi$
$588$	1.24233e7	1.48182
$589$	1.69439e7	2.01245
$590$	−7.51306e6	−0.888560
$591$	858517.	0.101107
$592$	−1.44862e7	−1.69883
$593$	5.13574e6	0.599745	0.299872	−	0.953979i	$-0.403056\pi$
$593$	5.13574e6	0.599745	0.299872	+	0.953979i	$0.403056\pi$
$594$	−2.06456e7	−2.40083
$595$	2.46884e7	2.85891
$596$	−5.04743e6	−0.582043
$597$	−7.76782e6	−0.891997
$598$	−689458.	−0.0788415
$599$	7.56853e6	0.861875	0.430937	−	0.902382i	$-0.358183\pi$
$599$	7.56853e6	0.861875	0.430937	+	0.902382i	$0.358183\pi$
$600$	−123421.	−0.0139962
$601$	2.56891e6	0.290110	0.145055	−	0.989424i	$-0.453664\pi$
$601$	2.56891e6	0.290110	0.145055	+	0.989424i	$0.453664\pi$
$602$	3.34512e6	0.376201
$603$	1.51854e6	0.170072
$604$	1.43554e7	1.60112
$605$	−1.50987e7	−1.67707
$606$	−949604.	−0.105042
$607$	2.62172e6	0.288812	0.144406	−	0.989519i	$-0.453873\pi$
$607$	2.62172e6	0.288812	0.144406	+	0.989519i	$0.453873\pi$
$608$	−1.67716e7	−1.83999
$609$	1.91433e6	0.209158
$610$	−1.09403e7	−1.19043
$611$	−179494.	−0.0194513
$612$	6.89650e6	0.744303
$613$	537167.	0.0577376	0.0288688	−	0.999583i	$-0.490810\pi$
$613$	537167.	0.0577376	0.0288688	+	0.999583i	$0.490810\pi$
$614$	−5.63213e6	−0.602909
$615$	3.78527e6	0.403561
$616$	1.74875e6	0.185685
$617$	1.15522e7	1.22166	0.610830	−	0.791762i	$-0.290836\pi$
$617$	1.15522e7	1.22166	0.610830	+	0.791762i	$0.290836\pi$
$618$	1.02149e6	0.107588
$619$	2.20752e6	0.231568	0.115784	−	0.993274i	$-0.463062\pi$
$619$	2.20752e6	0.231568	0.115784	+	0.993274i	$0.463062\pi$
$620$	1.77548e7	1.85497
$621$	−1.20311e7	−1.25192
$622$	8.00408e6	0.829536
$623$	−1.68960e6	−0.174407
$624$	−310731.	−0.0319465
$625$	−1.17567e7	−1.20389
$626$	2.48963e7	2.53922
$627$	1.43268e7	1.45540
$628$	−1.45583e7	−1.47303
$629$	−2.59589e7	−2.61613
$630$	−1.35294e7	−1.35809
$631$	−1.43943e7	−1.43919	−0.719594	−	0.694395i	$-0.755672\pi$
$631$	−1.43943e7	−1.43919	−0.719594	+	0.694395i	$0.755672\pi$
$632$	−71761.3	−0.00714657
$633$	−4.84704e6	−0.480803
$634$	−7.32219e6	−0.723465
$635$	−1.22566e7	−1.20625
$636$	−343074.	−0.0336314
$637$	946893.	0.0924597
$638$	3.91897e6	0.381172
$639$	−6.66166e6	−0.645402
$640$	−1.60540e6	−0.154929
$641$	4.90224e6	0.471248	0.235624	−	0.971844i	$-0.424287\pi$
$641$	4.90224e6	0.471248	0.235624	+	0.971844i	$0.424287\pi$
$642$	−3.53381e6	−0.338381
$643$	−1.80253e7	−1.71931	−0.859656	−	0.510874i	$-0.829322\pi$
$643$	−1.80253e7	−1.71931	−0.859656	+	0.510874i	$0.829322\pi$
$644$	2.23371e7	2.12233
$645$	1.31013e6	0.123998
$646$	−2.86144e7	−2.69776
$647$	−1.24242e7	−1.16683	−0.583415	−	0.812174i	$-0.698284\pi$
$647$	−1.24242e7	−1.16683	−0.583415	+	0.812174i	$0.698284\pi$
$648$	203712.	0.0190581
$649$	9.25383e6	0.862402
$650$	−206192.	−0.0191421
$651$	−2.08772e7	−1.93073
$652$	−1.91733e7	−1.76635
$653$	−1.28553e7	−1.17977	−0.589887	−	0.807486i	$-0.700828\pi$
$653$	−1.28553e7	−1.17977	−0.589887	+	0.807486i	$0.700828\pi$
$654$	1.32344e6	0.120993
$655$	1.70860e7	1.55610
$656$	5.19641e6	0.471459
$657$	3.01978e6	0.272937
$658$	1.13652e7	1.02333
$659$	−5.18218e6	−0.464835	−0.232417	−	0.972616i	$-0.574664\pi$
$659$	−5.18218e6	−0.464835	−0.232417	+	0.972616i	$0.574664\pi$
$660$	1.50125e7	1.34151
$661$	6.47130e6	0.576087	0.288043	−	0.957617i	$-0.406995\pi$
$661$	6.47130e6	0.576087	0.288043	+	0.957617i	$0.406995\pi$
$662$	1.69436e7	1.50266
$663$	−556823.	−0.0491964
$664$	97296.6	0.00856402
$665$	2.87229e7	2.51868
$666$	1.42257e7	1.24276
$667$	2.28375e6	0.198763
$668$	2.03104e7	1.76108
$669$	1.16503e7	1.00640
$670$	−6.60213e6	−0.568194
$671$	1.34751e7	1.15539
$672$	2.06650e7	1.76527
$673$	6.21171e6	0.528657	0.264328	−	0.964433i	$-0.414850\pi$
$673$	6.21171e6	0.528657	0.264328	+	0.964433i	$0.414850\pi$
$674$	5.24141e6	0.444425
$675$	−3.59806e6	−0.303955
$676$	−1.24220e7	−1.04550
$677$	1.85078e7	1.55197	0.775984	−	0.630752i	$-0.217253\pi$
$677$	1.85078e7	1.55197	0.775984	+	0.630752i	$0.217253\pi$
$678$	77754.9	0.00649611
$679$	2.49663e7	2.07817
$680$	−1.36793e6	−0.113447
$681$	1.03415e7	0.854504
$682$	−4.27394e7	−3.51858
$683$	−4.91590e6	−0.403228	−0.201614	−	0.979465i	$-0.564619\pi$
$683$	−4.91590e6	−0.403228	−0.201614	+	0.979465i	$0.564619\pi$
$684$	8.02348e6	0.655726
$685$	−9.44214e6	−0.768854
$686$	−2.95491e7	−2.39736
$687$	−1.53327e6	−0.123944
$688$	1.79854e6	0.144860
$689$	−26148.7	−0.00209846
$690$	1.70977e7	1.36715
$691$	−1.07645e7	−0.857630	−0.428815	−	0.903392i	$-0.641069\pi$
$691$	−1.07645e7	−0.857630	−0.428815	+	0.903392i	$0.641069\pi$
$692$	−2.85803e6	−0.226883
$693$	1.66642e7	1.31811
$694$	3.74005e6	0.294767
$695$	1.03655e6	0.0814004
$696$	−106069.	−0.00829977
$697$	9.31185e6	0.726029
$698$	−2.30769e7	−1.79283
$699$	4.79192e6	0.370951
$700$	6.68023e6	0.515284
$701$	9.02819e6	0.693914	0.346957	−	0.937881i	$-0.387215\pi$
$701$	9.02819e6	0.693914	0.346957	+	0.937881i	$0.387215\pi$
$702$	933529.	0.0714966
$703$	−3.02010e7	−2.30480
$704$	2.26360e7	1.72135
$705$	4.45124e6	0.337294
$706$	6.55248e6	0.494760
$707$	2.34490e6	0.176431
$708$	−5.48984e6	−0.411601
$709$	4.91059e6	0.366875	0.183438	−	0.983031i	$-0.441277\pi$
$709$	4.91059e6	0.366875	0.183438	+	0.983031i	$0.441277\pi$
$710$	2.89628e7	2.15623
$711$	−683827.	−0.0507308
$712$	93617.2	0.00692079
$713$	−2.49061e7	−1.83477
$714$	3.52570e7	2.58821
$715$	1.14423e6	0.0837047
$716$	2.61336e6	0.190510
$717$	−1.30960e7	−0.951352
$718$	−2.80184e7	−2.02830
$719$	1.44751e7	1.04424	0.522119	−	0.852873i	$-0.325142\pi$
$719$	1.44751e7	1.04424	0.522119	+	0.852873i	$0.325142\pi$
$720$	−7.27425e6	−0.522946
$721$	−2.52242e6	−0.180709
$722$	−1.32463e7	−0.945695
$723$	1.33328e6	0.0948580
$724$	−1.16570e7	−0.826493
$725$	682989.	0.0482579
$726$	−2.15622e7	−1.51828
$727$	1.55189e7	1.08899	0.544495	−	0.838764i	$-0.316721\pi$
$727$	1.55189e7	1.08899	0.544495	+	0.838764i	$0.316721\pi$
$728$	−79073.2	−0.00552969
$729$	1.29066e7	0.899481
$730$	−1.31291e7	−0.911857
$731$	3.22294e6	0.223079
$732$	−7.99414e6	−0.551435
$733$	1.03870e6	0.0714050	0.0357025	−	0.999362i	$-0.488633\pi$
$733$	1.03870e6	0.0714050	0.0357025	+	0.999362i	$0.488633\pi$
$734$	−1.72912e7	−1.18463
$735$	−2.34818e7	−1.60329
$736$	2.46529e7	1.67754
$737$	8.13184e6	0.551467
$738$	−5.10296e6	−0.344891
$739$	1.33918e6	0.0902046	0.0451023	−	0.998982i	$-0.485639\pi$
$739$	1.33918e6	0.0902046	0.0451023	+	0.998982i	$0.485639\pi$
$740$	−3.16463e7	−2.12443
$741$	−647816.	−0.0433417
$742$	1.65568e6	0.110400
$743$	1.56518e7	1.04014	0.520070	−	0.854124i	$-0.325906\pi$
$743$	1.56518e7	1.04014	0.520070	+	0.854124i	$0.325906\pi$
$744$	1.15677e6	0.0766149
$745$	9.54032e6	0.629756
$746$	−1.92009e7	−1.26321
$747$	927157.	0.0607927
$748$	3.69310e7	2.41345
$749$	8.72620e6	0.568356
$750$	−1.28111e7	−0.831639
$751$	1.92274e7	1.24400	0.622002	−	0.783016i	$-0.286320\pi$
$751$	1.92274e7	1.24400	0.622002	+	0.783016i	$0.286320\pi$
$752$	6.11065e6	0.394042
$753$	−1.57947e6	−0.101514
$754$	−177204.	−0.0113513
$755$	−2.71337e7	−1.73237
$756$	−3.02446e7	−1.92461
$757$	−2.73627e7	−1.73548	−0.867739	−	0.497021i	$-0.834427\pi$
$757$	−2.73627e7	−1.73548	−0.867739	+	0.497021i	$0.834427\pi$
$758$	4.43254e7	2.80207
$759$	−2.10592e7	−1.32690
$760$	−1.59147e6	−0.0999461
$761$	5.86301e6	0.366994	0.183497	−	0.983020i	$-0.441258\pi$
$761$	5.86301e6	0.366994	0.183497	+	0.983020i	$0.441258\pi$
$762$	−1.75034e7	−1.09203
$763$	−3.26803e6	−0.203224
$764$	−6.44317e6	−0.399361
$765$	−1.30353e7	−0.805318
$766$	−2.56585e7	−1.58001
$767$	−418430.	−0.0256823
$768$	1.05236e7	0.643813
$769$	−1.36162e7	−0.830308	−0.415154	−	0.909751i	$-0.636272\pi$
$769$	−1.36162e7	−0.830308	−0.415154	+	0.909751i	$0.636272\pi$
$770$	−7.24507e7	−4.40368
$771$	−2.19972e6	−0.133270
$772$	−9.11083e6	−0.550192
$773$	−9.44787e6	−0.568703	−0.284351	−	0.958720i	$-0.591778\pi$
$773$	−9.44787e6	−0.568703	−0.284351	+	0.958720i	$0.591778\pi$
$774$	−1.76620e6	−0.105971
$775$	−7.44851e6	−0.445467
$776$	−1.38333e6	−0.0824655
$777$	3.72118e7	2.21120
$778$	2.51946e6	0.149231
$779$	1.08335e7	0.639627
$780$	−678818.	−0.0399500
$781$	−3.56735e7	−2.09275
$782$	4.20608e7	2.45958
$783$	−3.09221e6	−0.180246
$784$	−3.22357e7	−1.87304
$785$	2.75171e7	1.59378
$786$	2.44001e7	1.40875
$787$	2.97678e7	1.71320	0.856602	−	0.515977i	$-0.172571\pi$
$787$	2.97678e7	1.71320	0.856602	+	0.515977i	$0.172571\pi$
$788$	2.57468e6	0.147709
$789$	−2.20117e7	−1.25881
$790$	2.97307e6	0.169487
$791$	−192004.	−0.0109111
$792$	−923328.	−0.0523050
$793$	−609304.	−0.0344073
$794$	4.01768e6	0.226164
$795$	648455.	0.0363883
$796$	−2.32956e7	−1.30314
$797$	−1.80924e7	−1.00891	−0.504453	−	0.863439i	$-0.668306\pi$
$797$	−1.80924e7	−1.00891	−0.504453	+	0.863439i	$0.668306\pi$
$798$	4.10184e7	2.28019
$799$	1.09501e7	0.606810
$800$	7.37279e6	0.407293
$801$	892095.	0.0491281
$802$	4.56293e7	2.50500
$803$	1.61711e7	0.885013
$804$	−4.82422e6	−0.263201
$805$	−4.22201e7	−2.29631
$806$	1.93254e6	0.104783
$807$	−5.93683e6	−0.320901
$808$	−129926.	−0.00700113
$809$	−1.57182e7	−0.844366	−0.422183	−	0.906511i	$-0.638736\pi$
$809$	−1.57182e7	−0.844366	−0.422183	+	0.906511i	$0.638736\pi$
$810$	−8.43977e6	−0.451979
$811$	−1.57562e6	−0.0841202	−0.0420601	−	0.999115i	$-0.513392\pi$
$811$	−1.57562e6	−0.0841202	−0.0420601	+	0.999115i	$0.513392\pi$
$812$	5.74106e6	0.305564
$813$	−1.88690e7	−1.00120
$814$	7.61791e7	4.02972
$815$	3.62401e7	1.91115
$816$	1.89563e7	0.996617
$817$	3.74962e6	0.196531
$818$	5.83260e6	0.304775
$819$	−753503.	−0.0392532
$820$	1.13520e7	0.589573
$821$	2.61911e7	1.35611	0.678056	−	0.735010i	$-0.262823\pi$
$821$	2.61911e7	1.35611	0.678056	+	0.735010i	$0.262823\pi$
$822$	−1.34841e7	−0.696053
$823$	−3.66910e7	−1.88825	−0.944126	−	0.329585i	$-0.893091\pi$
$823$	−3.66910e7	−1.88825	−0.944126	+	0.329585i	$0.893091\pi$
$824$	139762.	0.00717086
$825$	−6.29806e6	−0.322160
$826$	2.64942e7	1.35114
$827$	1.38402e7	0.703685	0.351843	−	0.936059i	$-0.385555\pi$
$827$	1.38402e7	0.703685	0.351843	+	0.936059i	$0.385555\pi$
$828$	−1.17938e7	−0.597832
$829$	−2.83219e7	−1.43132	−0.715660	−	0.698449i	$-0.753874\pi$
$829$	−2.83219e7	−1.43132	−0.715660	+	0.698449i	$0.753874\pi$
$830$	−4.03099e6	−0.203103
$831$	152389.	0.00765509
$832$	−1.02353e6	−0.0512617
$833$	−5.77657e7	−2.88441
$834$	1.48027e6	0.0736928
$835$	−3.83894e7	−1.90544
$836$	4.29661e7	2.12623
$837$	3.37229e7	1.66384
$838$	3.19067e7	1.56954
$839$	2.80231e7	1.37439	0.687197	−	0.726471i	$-0.258841\pi$
$839$	2.80231e7	1.37439	0.687197	+	0.726471i	$0.258841\pi$
$840$	1.96092e6	0.0958873
$841$	−1.99242e7	−0.971383
$842$	−3.55782e7	−1.72943
$843$	1.25298e7	0.607263
$844$	−1.45362e7	−0.702418
$845$	2.34792e7	1.13120
$846$	−6.00076e6	−0.288257
$847$	5.32444e7	2.55015
$848$	890197.	0.0425105
$849$	−1.71000e7	−0.814193
$850$	1.25789e7	0.597164
$851$	4.43928e7	2.10130
$852$	2.11633e7	0.998815
$853$	−2.38300e7	−1.12138	−0.560689	−	0.828027i	$-0.689463\pi$
$853$	−2.38300e7	−1.12138	−0.560689	+	0.828027i	$0.689463\pi$
$854$	3.85800e7	1.81016
$855$	−1.51654e7	−0.709479
$856$	−483501.	−0.0225534
$857$	−3.83129e7	−1.78194	−0.890971	−	0.454061i	$-0.849975\pi$
$857$	−3.83129e7	−1.78194	−0.890971	+	0.454061i	$0.849975\pi$
$858$	1.63405e6	0.0757789
$859$	2.68650e7	1.24224	0.621118	−	0.783717i	$-0.286679\pi$
$859$	2.68650e7	1.24224	0.621118	+	0.783717i	$0.286679\pi$
$860$	3.92906e6	0.181152
$861$	−1.33484e7	−0.613652
$862$	−1.01118e7	−0.463510
$863$	−1.63558e7	−0.747558	−0.373779	−	0.927518i	$-0.621938\pi$
$863$	−1.63558e7	−0.747558	−0.373779	+	0.927518i	$0.621938\pi$
$864$	−3.33801e7	−1.52126
$865$	5.40206e6	0.245482
$866$	−7.86758e6	−0.356489
$867$	1.80948e7	0.817535
$868$	−6.26107e7	−2.82065
$869$	−3.66192e6	−0.164498
$870$	4.39444e6	0.196836
$871$	−367696.	−0.0164227
$872$	181075.	0.00806431
$873$	−1.31820e7	−0.585392
$874$	4.89341e7	2.16687
$875$	3.16351e7	1.39685
$876$	−9.59350e6	−0.422393
$877$	−2.30604e7	−1.01243	−0.506217	−	0.862406i	$-0.668957\pi$
$877$	−2.30604e7	−1.01243	−0.506217	+	0.862406i	$0.668957\pi$
$878$	1.07221e7	0.469402
$879$	−1.77191e7	−0.773515
$880$	−3.89539e7	−1.69568
$881$	−3.15095e7	−1.36774	−0.683868	−	0.729606i	$-0.739704\pi$
$881$	−3.15095e7	−1.36774	−0.683868	+	0.729606i	$0.739704\pi$
$882$	3.16560e7	1.37020
$883$	2.86348e7	1.23593	0.617963	−	0.786208i	$-0.287958\pi$
$883$	2.86348e7	1.23593	0.617963	+	0.786208i	$0.287958\pi$
$884$	−1.66991e6	−0.0718723
$885$	1.03765e7	0.445343
$886$	−3.85685e7	−1.65063
$887$	−2.45670e7	−1.04844	−0.524220	−	0.851583i	$-0.675643\pi$
$887$	−2.45670e7	−1.04844	−0.524220	+	0.851583i	$0.675643\pi$
$888$	−2.06183e6	−0.0877446
$889$	4.32219e7	1.83421
$890$	−3.87855e6	−0.164132
$891$	1.03953e7	0.438673
$892$	3.49392e7	1.47028
$893$	1.27396e7	0.534596
$894$	1.36243e7	0.570126
$895$	−4.93961e6	−0.206127
$896$	5.66130e6	0.235584
$897$	952233.	0.0395150
$898$	4.37138e7	1.80895
$899$	−6.40134e6	−0.264163
$900$	−3.52711e6	−0.145149
$901$	1.59521e6	0.0654646
$902$	−2.73266e7	−1.11833
$903$	−4.62005e6	−0.188550
$904$	10638.5	0.000432973 0
$905$	2.20332e7	0.894245
$906$	−3.87490e7	−1.56834
$907$	1.90832e7	0.770254	0.385127	−	0.922864i	$-0.374158\pi$
$907$	1.90832e7	0.770254	0.385127	+	0.922864i	$0.374158\pi$
$908$	3.10140e7	1.24837
$909$	−1.23809e6	−0.0496984
$910$	3.27600e6	0.131141
$911$	−3.04616e7	−1.21606	−0.608032	−	0.793912i	$-0.708041\pi$
$911$	−3.04616e7	−1.21606	−0.608032	+	0.793912i	$0.708041\pi$
$912$	2.20540e7	0.878012
$913$	4.96497e6	0.197124
$914$	−1.72224e7	−0.681911
$915$	1.51100e7	0.596639
$916$	−4.59826e6	−0.181073
$917$	−6.02522e7	−2.36619
$918$	−5.69504e7	−2.23044
$919$	2.73866e7	1.06967	0.534834	−	0.844957i	$-0.320374\pi$
$919$	2.73866e7	1.06967	0.534834	+	0.844957i	$0.320374\pi$
$920$	2.33933e6	0.0911218
$921$	7.77872e6	0.302175
$922$	−2.27394e7	−0.880950
$923$	1.61304e6	0.0623221
$924$	−5.29402e7	−2.03989
$925$	1.32763e7	0.510179
$926$	2.30986e7	0.885232
$927$	1.33182e6	0.0509033
$928$	6.33626e6	0.241525
$929$	−2.65451e7	−1.00913	−0.504563	−	0.863375i	$-0.668346\pi$
$929$	−2.65451e7	−1.00913	−0.504563	+	0.863375i	$0.668346\pi$
$930$	−4.79247e7	−1.81699
$931$	−6.72054e7	−2.54115
$932$	1.43709e7	0.541932
$933$	−1.10547e7	−0.415760
$934$	4.52888e6	0.169873
$935$	−6.98046e7	−2.61129
$936$	41750.0	0.00155764
$937$	−2.34660e7	−0.873151	−0.436576	−	0.899668i	$-0.643809\pi$
$937$	−2.34660e7	−0.873151	−0.436576	+	0.899668i	$0.643809\pi$
$938$	2.32818e7	0.863993
$939$	−3.43852e7	−1.27264
$940$	1.33492e7	0.492761
$941$	−2.18303e7	−0.803686	−0.401843	−	0.915709i	$-0.631630\pi$
$941$	−2.18303e7	−0.803686	−0.401843	+	0.915709i	$0.631630\pi$
$942$	3.92965e7	1.44287
$943$	−1.59244e7	−0.583154
$944$	1.42449e7	0.520270
$945$	5.71662e7	2.08238
$946$	−9.45806e6	−0.343617
$947$	1.87197e7	0.678305	0.339152	−	0.940731i	$-0.389860\pi$
$947$	1.87197e7	0.678305	0.339152	+	0.940731i	$0.389860\pi$
$948$	2.17244e6	0.0785103
$949$	−731206.	−0.0263557
$950$	1.46344e7	0.526098
$951$	1.01129e7	0.362598
$952$	4.82390e6	0.172507
$953$	5.37413e7	1.91680	0.958399	−	0.285432i	$-0.0921372\pi$
$953$	5.37413e7	1.91680	0.958399	+	0.285432i	$0.0921372\pi$
$954$	−874188.	−0.0310981
$955$	1.21785e7	0.432099
$956$	−3.92748e7	−1.38986
$957$	−5.41262e6	−0.191042
$958$	−4.42594e7	−1.55809
$959$	3.32969e7	1.16911
$960$	2.53823e7	0.888901
$961$	4.11823e7	1.43847
$962$	−3.44458e6	−0.120005
$963$	−4.60736e6	−0.160098
$964$	3.99848e6	0.138581
$965$	1.72207e7	0.595295
$966$	−6.02936e7	−2.07887
$967$	1.78136e7	0.612611	0.306306	−	0.951933i	$-0.400907\pi$
$967$	1.78136e7	0.612611	0.306306	+	0.951933i	$0.400907\pi$
$968$	−2.95016e6	−0.101195
$969$	3.95203e7	1.35211
$970$	5.73114e7	1.95574
$971$	3.06231e7	1.04232	0.521160	−	0.853459i	$-0.325500\pi$
$971$	3.06231e7	1.04232	0.521160	+	0.853459i	$0.325500\pi$
$972$	2.67180e7	0.907065
$973$	−3.65529e6	−0.123777
$974$	−7.56691e7	−2.55577
$975$	284779.	0.00959392
$976$	2.07429e7	0.697021
$977$	−1.93935e7	−0.650011	−0.325005	−	0.945712i	$-0.605366\pi$
$977$	−1.93935e7	−0.650011	−0.325005	+	0.945712i	$0.605366\pi$
$978$	5.17536e7	1.73019
$979$	4.77721e6	0.159301
$980$	−7.04217e7	−2.34229
$981$	1.72550e6	0.0572455
$982$	8.49685e7	2.81177
$983$	3.41089e7	1.12586	0.562929	−	0.826505i	$-0.309675\pi$
$983$	3.41089e7	1.12586	0.562929	+	0.826505i	$0.309675\pi$
$984$	739609.	0.0243509
$985$	−4.86650e6	−0.159818
$986$	1.08104e7	0.354120
$987$	−1.56969e7	−0.512886
$988$	−1.94279e6	−0.0633190
$989$	−5.51162e6	−0.179179
$990$	3.82534e7	1.24046
$991$	−1.15321e7	−0.373013	−0.186507	−	0.982454i	$-0.559717\pi$
$991$	−1.15321e7	−0.373013	−0.186507	+	0.982454i	$0.559717\pi$
$992$	−6.91017e7	−2.22951
$993$	−2.34014e7	−0.753128
$994$	−1.02135e8	−3.27875
$995$	4.40319e7	1.40997
$996$	−2.94547e6	−0.0940819
$997$	3.45745e7	1.10159	0.550793	−	0.834642i	$-0.314325\pi$
$997$	3.45745e7	1.10159	0.550793	+	0.834642i	$0.314325\pi$
$998$	−4.65337e7	−1.47891
$999$	−6.01081e7	−1.90554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.a.a.1.2	✓	8
3.2	odd	2		387.6.a.c.1.7		8
4.3	odd	2		688.6.a.e.1.2		8
5.4	even	2		1075.6.a.a.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.a.a.1.2	✓	8	1.1	even	1	trivial
387.6.a.c.1.7		8	3.2	odd	2
688.6.a.e.1.2		8	4.3	odd	2
1075.6.a.a.1.7		8	5.4	even	2

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q-8.09504 q^{2} +11.1803 q^{3} +33.5297 q^{4} -63.3756 q^{5} -90.5052 q^{6} +223.489 q^{7} -12.3830 q^{8} -118.000 q^{9} +O(q^{10})\)	\(q-8.09504 q^{2} +11.1803 q^{3} +33.5297 q^{4} -63.3756 q^{5} -90.5052 q^{6} +223.489 q^{7} -12.3830 q^{8} -118.000 q^{9} +513.028 q^{10} -631.897 q^{11} +374.873 q^{12} +28.5724 q^{13} -1809.15 q^{14} -708.560 q^{15} -972.709 q^{16} -1743.07 q^{17} +955.217 q^{18} -2027.92 q^{19} -2124.97 q^{20} +2498.68 q^{21} +5115.23 q^{22} +2980.86 q^{23} -138.447 q^{24} +891.469 q^{25} -231.295 q^{26} -4036.10 q^{27} +7493.51 q^{28} +766.139 q^{29} +5735.83 q^{30} -8355.33 q^{31} +8270.38 q^{32} -7064.81 q^{33} +14110.3 q^{34} -14163.7 q^{35} -3956.51 q^{36} +14892.6 q^{37} +16416.1 q^{38} +319.449 q^{39} +784.783 q^{40} -5342.20 q^{41} -20226.9 q^{42} -1849.00 q^{43} -21187.3 q^{44} +7478.34 q^{45} -24130.2 q^{46} -6282.09 q^{47} -10875.2 q^{48} +33140.1 q^{49} -7216.48 q^{50} -19488.1 q^{51} +958.024 q^{52} -915.172 q^{53} +32672.4 q^{54} +40046.8 q^{55} -2767.47 q^{56} -22672.8 q^{57} -6201.92 q^{58} -14644.5 q^{59} -23757.8 q^{60} -21324.9 q^{61} +67636.7 q^{62} -26371.7 q^{63} -35822.4 q^{64} -1810.79 q^{65} +57189.9 q^{66} -12868.9 q^{67} -58444.8 q^{68} +33327.0 q^{69} +114656. q^{70} +56454.6 q^{71} +1461.20 q^{72} -25591.3 q^{73} -120556. q^{74} +9966.92 q^{75} -67995.4 q^{76} -141222. q^{77} -2585.95 q^{78} +5795.13 q^{79} +61646.1 q^{80} -16450.9 q^{81} +43245.4 q^{82} -7857.24 q^{83} +83779.9 q^{84} +110468. q^{85} +14967.7 q^{86} +8565.68 q^{87} +7824.80 q^{88} -7560.11 q^{89} -60537.5 q^{90} +6385.60 q^{91} +99947.5 q^{92} -93415.3 q^{93} +50853.8 q^{94} +128520. q^{95} +92465.6 q^{96} +111712. q^{97} -268271. q^{98} +74563.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9}+O(q^{10}) \) 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9	\( 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9} - 617 q^{10} - 532 q^{11} - 4195 q^{12} - 2492 q^{13} - 4240 q^{14} - 1780 q^{15} + 1882 q^{16} - 2534 q^{17} - 3711 q^{18} - 1678 q^{19} - 2607 q^{20} - 2256 q^{21} + 11502 q^{22} - 2488 q^{23} + 19953 q^{24} + 4378 q^{25} + 4586 q^{26} - 8960 q^{27} + 18640 q^{28} - 4360 q^{29} + 25092 q^{30} + 5704 q^{31} - 18294 q^{32} - 12852 q^{33} + 30007 q^{34} + 5640 q^{35} + 67969 q^{36} - 3772 q^{37} - 6559 q^{38} + 11120 q^{39} + 14869 q^{40} - 10698 q^{41} + 78698 q^{42} - 14792 q^{43} - 356 q^{44} - 44912 q^{45} - 19389 q^{46} - 77864 q^{47} - 118727 q^{48} + 7188 q^{49} + 26877 q^{50} - 80246 q^{51} - 60736 q^{52} - 62352 q^{53} + 61026 q^{54} - 49552 q^{55} - 144528 q^{56} - 808 q^{57} + 52951 q^{58} - 26224 q^{59} + 101500 q^{60} - 82540 q^{61} - 9023 q^{62} - 61768 q^{63} + 153858 q^{64} - 5000 q^{65} - 48516 q^{66} + 27784 q^{67} + 40507 q^{68} - 93776 q^{69} + 185910 q^{70} - 9504 q^{71} - 186687 q^{72} + 14260 q^{73} - 15239 q^{74} + 167420 q^{75} + 1279 q^{76} - 218140 q^{77} + 264170 q^{78} + 160248 q^{79} - 1291 q^{80} + 161076 q^{81} - 47781 q^{82} - 77176 q^{83} + 16382 q^{84} + 141096 q^{85} + 22188 q^{86} + 268136 q^{87} + 129544 q^{88} - 265692 q^{89} + 48990 q^{90} + 401148 q^{91} + 190391 q^{92} - 123860 q^{93} + 248737 q^{94} + 135884 q^{95} + 950817 q^{96} + 144742 q^{97} - 292244 q^{98} + 239516 q^{99}+O(q^{100}) \) 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9 - 617 * q^10 - 532 * q^11 - 4195 * q^12 - 2492 * q^13 - 4240 * q^14 - 1780 * q^15 + 1882 * q^16 - 2534 * q^17 - 3711 * q^18 - 1678 * q^19 - 2607 * q^20 - 2256 * q^21 + 11502 * q^22 - 2488 * q^23 + 19953 * q^24 + 4378 * q^25 + 4586 * q^26 - 8960 * q^27 + 18640 * q^28 - 4360 * q^29 + 25092 * q^30 + 5704 * q^31 - 18294 * q^32 - 12852 * q^33 + 30007 * q^34 + 5640 * q^35 + 67969 * q^36 - 3772 * q^37 - 6559 * q^38 + 11120 * q^39 + 14869 * q^40 - 10698 * q^41 + 78698 * q^42 - 14792 * q^43 - 356 * q^44 - 44912 * q^45 - 19389 * q^46 - 77864 * q^47 - 118727 * q^48 + 7188 * q^49 + 26877 * q^50 - 80246 * q^51 - 60736 * q^52 - 62352 * q^53 + 61026 * q^54 - 49552 * q^55 - 144528 * q^56 - 808 * q^57 + 52951 * q^58 - 26224 * q^59 + 101500 * q^60 - 82540 * q^61 - 9023 * q^62 - 61768 * q^63 + 153858 * q^64 - 5000 * q^65 - 48516 * q^66 + 27784 * q^67 + 40507 * q^68 - 93776 * q^69 + 185910 * q^70 - 9504 * q^71 - 186687 * q^72 + 14260 * q^73 - 15239 * q^74 + 167420 * q^75 + 1279 * q^76 - 218140 * q^77 + 264170 * q^78 + 160248 * q^79 - 1291 * q^80 + 161076 * q^81 - 47781 * q^82 - 77176 * q^83 + 16382 * q^84 + 141096 * q^85 + 22188 * q^86 + 268136 * q^87 + 129544 * q^88 - 265692 * q^89 + 48990 * q^90 + 401148 * q^91 + 190391 * q^92 - 123860 * q^93 + 248737 * q^94 + 135884 * q^95 + 950817 * q^96 + 144742 * q^97 - 292244 * q^98 + 239516 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more