LMFDB - Embedded newform 43.6.a.b.1.5

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:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + \cdots - 22734604 $ x^10 - 2x^9 - 256x^8 + 266x^7 + 21986x^6 - 10450x^5 - 719484x^4 + 384582x^3 + 8437093x^2 - 5752252*x - 22734604
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.86024$ 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)

$f(q)$	$=$	$q-1.86024 q^{2} -14.8716 q^{3} -28.5395 q^{4} -42.2365 q^{5} +27.6647 q^{6} +202.971 q^{7} +112.618 q^{8} -21.8357 q^{9} +O(q^{10})$	\(q-1.86024 q^{2} -14.8716 q^{3} -28.5395 q^{4} -42.2365 q^{5} +27.6647 q^{6} +202.971 q^{7} +112.618 q^{8} -21.8357 q^{9} +78.5700 q^{10} +436.853 q^{11} +424.428 q^{12} -617.704 q^{13} -377.575 q^{14} +628.124 q^{15} +703.768 q^{16} +833.458 q^{17} +40.6196 q^{18} +1356.52 q^{19} +1205.41 q^{20} -3018.51 q^{21} -812.652 q^{22} -904.822 q^{23} -1674.81 q^{24} -1341.08 q^{25} +1149.08 q^{26} +3938.53 q^{27} -5792.70 q^{28} +5326.52 q^{29} -1168.46 q^{30} +919.124 q^{31} -4912.95 q^{32} -6496.71 q^{33} -1550.43 q^{34} -8572.80 q^{35} +623.180 q^{36} +4962.82 q^{37} -2523.46 q^{38} +9186.24 q^{39} -4756.59 q^{40} -5931.38 q^{41} +5615.15 q^{42} +1849.00 q^{43} -12467.6 q^{44} +922.264 q^{45} +1683.19 q^{46} +17815.9 q^{47} -10466.2 q^{48} +24390.4 q^{49} +2494.73 q^{50} -12394.9 q^{51} +17629.0 q^{52} +24713.3 q^{53} -7326.61 q^{54} -18451.2 q^{55} +22858.2 q^{56} -20173.7 q^{57} -9908.61 q^{58} +33834.6 q^{59} -17926.4 q^{60} +45948.5 q^{61} -1709.79 q^{62} -4432.02 q^{63} -13381.3 q^{64} +26089.6 q^{65} +12085.4 q^{66} -58523.0 q^{67} -23786.5 q^{68} +13456.1 q^{69} +15947.5 q^{70} +1792.64 q^{71} -2459.09 q^{72} -46710.3 q^{73} -9232.03 q^{74} +19944.0 q^{75} -38714.5 q^{76} +88668.8 q^{77} -17088.6 q^{78} -79459.7 q^{79} -29724.7 q^{80} -53266.1 q^{81} +11033.8 q^{82} +91200.9 q^{83} +86146.8 q^{84} -35202.4 q^{85} -3439.58 q^{86} -79213.9 q^{87} +49197.6 q^{88} -16470.2 q^{89} -1715.63 q^{90} -125376. q^{91} +25823.2 q^{92} -13668.8 q^{93} -33141.8 q^{94} -57294.8 q^{95} +73063.4 q^{96} +145639. q^{97} -45372.0 q^{98} -9539.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9}+O(q^{10}) $ 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9} - 17 q^{10} + 745 q^{11} + 4627 q^{12} + 1917 q^{13} + 1936 q^{14} + 1688 q^{15} + 5354 q^{16} + 4017 q^{17} - 2725 q^{18} - 2404 q^{19} + 1311 q^{20} - 228 q^{21} - 5836 q^{22} + 1733 q^{23} - 10711 q^{24} + 7120 q^{25} - 1484 q^{26} - 2324 q^{27} - 15028 q^{28} + 6996 q^{29} - 48420 q^{30} - 4899 q^{31} - 7554 q^{32} - 15734 q^{33} - 27033 q^{34} + 7084 q^{35} + 4433 q^{36} + 1466 q^{37} + 13905 q^{38} - 26542 q^{39} - 93211 q^{40} + 10297 q^{41} - 37642 q^{42} + 18490 q^{43} - 36140 q^{44} + 73822 q^{45} + 17991 q^{46} + 48592 q^{47} + 83607 q^{48} + 29458 q^{49} + 983 q^{50} + 92972 q^{51} + 14232 q^{52} + 127165 q^{53} - 92002 q^{54} + 106672 q^{55} - 7780 q^{56} + 34060 q^{57} - 10305 q^{58} + 99372 q^{59} + 111372 q^{60} + 17408 q^{61} + 28265 q^{62} + 2244 q^{63} + 47202 q^{64} + 54484 q^{65} - 150292 q^{66} - 2021 q^{67} + 192151 q^{68} + 1654 q^{69} - 33194 q^{70} + 11286 q^{71} - 298365 q^{72} + 49892 q^{73} - 125431 q^{74} - 44662 q^{75} - 249803 q^{76} + 98144 q^{77} - 28494 q^{78} - 91524 q^{79} + 12251 q^{80} - 26450 q^{81} - 158909 q^{82} - 105203 q^{83} - 357682 q^{84} - 87212 q^{85} + 14792 q^{86} + 181200 q^{87} - 461824 q^{88} - 62682 q^{89} - 522670 q^{90} - 295304 q^{91} + 183783 q^{92} - 238430 q^{93} + 7259 q^{94} - 305340 q^{95} - 162399 q^{96} + 108383 q^{97} + 354656 q^{98} - 270499 q^{99}+O(q^{100}) \) 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9 - 17 * q^10 + 745 * q^11 + 4627 * q^12 + 1917 * q^13 + 1936 * q^14 + 1688 * q^15 + 5354 * q^16 + 4017 * q^17 - 2725 * q^18 - 2404 * q^19 + 1311 * q^20 - 228 * q^21 - 5836 * q^22 + 1733 * q^23 - 10711 * q^24 + 7120 * q^25 - 1484 * q^26 - 2324 * q^27 - 15028 * q^28 + 6996 * q^29 - 48420 * q^30 - 4899 * q^31 - 7554 * q^32 - 15734 * q^33 - 27033 * q^34 + 7084 * q^35 + 4433 * q^36 + 1466 * q^37 + 13905 * q^38 - 26542 * q^39 - 93211 * q^40 + 10297 * q^41 - 37642 * q^42 + 18490 * q^43 - 36140 * q^44 + 73822 * q^45 + 17991 * q^46 + 48592 * q^47 + 83607 * q^48 + 29458 * q^49 + 983 * q^50 + 92972 * q^51 + 14232 * q^52 + 127165 * q^53 - 92002 * q^54 + 106672 * q^55 - 7780 * q^56 + 34060 * q^57 - 10305 * q^58 + 99372 * q^59 + 111372 * q^60 + 17408 * q^61 + 28265 * q^62 + 2244 * q^63 + 47202 * q^64 + 54484 * q^65 - 150292 * q^66 - 2021 * q^67 + 192151 * q^68 + 1654 * q^69 - 33194 * q^70 + 11286 * q^71 - 298365 * q^72 + 49892 * q^73 - 125431 * q^74 - 44662 * q^75 - 249803 * q^76 + 98144 * q^77 - 28494 * q^78 - 91524 * q^79 + 12251 * q^80 - 26450 * q^81 - 158909 * q^82 - 105203 * q^83 - 357682 * q^84 - 87212 * q^85 + 14792 * q^86 + 181200 * q^87 - 461824 * q^88 - 62682 * q^89 - 522670 * q^90 - 295304 * q^91 + 183783 * q^92 - 238430 * q^93 + 7259 * q^94 - 305340 * q^95 - 162399 * q^96 + 108383 * q^97 + 354656 * q^98 - 270499 * 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 $

$2$	−1.86024	−0.328847	−0.164423	−	0.986390i	$-0.552576\pi$
$2$	−1.86024	−0.328847	−0.164423	+	0.986390i	$0.552576\pi$
$3$	−14.8716	−0.954013	−0.477007	−	0.878900i	$-0.658278\pi$
$3$	−14.8716	−0.954013	−0.477007	+	0.878900i	$0.658278\pi$
$4$	−28.5395	−0.891860
$5$	−42.2365	−0.755550	−0.377775	−	0.925898i	$-0.623311\pi$
$5$	−42.2365	−0.755550	−0.377775	+	0.925898i	$0.623311\pi$
$6$	27.6647	0.313724
$7$	202.971	1.56563	0.782816	−	0.622253i	$-0.213782\pi$
$7$	202.971	1.56563	0.782816	+	0.622253i	$0.213782\pi$
$8$	112.618	0.622132
$9$	−21.8357	−0.0898588
$10$	78.5700	0.248460
$11$	436.853	1.08856	0.544282	−	0.838902i	$-0.316802\pi$
$11$	436.853	1.08856	0.544282	+	0.838902i	$0.316802\pi$
$12$	424.428	0.850846
$13$	−617.704	−1.01373	−0.506864	−	0.862026i	$-0.669196\pi$
$13$	−617.704	−1.01373	−0.506864	+	0.862026i	$0.669196\pi$
$14$	−377.575	−0.514853
$15$	628.124	0.720804
$16$	703.768	0.687273
$17$	833.458	0.699458	0.349729	−	0.936851i	$-0.386274\pi$
$17$	833.458	0.699458	0.349729	+	0.936851i	$0.386274\pi$
$18$	40.6196	0.0295498
$19$	1356.52	0.862071	0.431036	−	0.902335i	$-0.358148\pi$
$19$	1356.52	0.862071	0.431036	+	0.902335i	$0.358148\pi$
$20$	1205.41	0.673844
$21$	−3018.51	−1.49363
$22$	−812.652	−0.357971
$23$	−904.822	−0.356651	−0.178326	−	0.983972i	$-0.557068\pi$
$23$	−904.822	−0.356651	−0.178326	+	0.983972i	$0.557068\pi$
$24$	−1674.81	−0.593522
$25$	−1341.08	−0.429145
$26$	1149.08	0.333362
$27$	3938.53	1.03974
$28$	−5792.70	−1.39632
$29$	5326.52	1.17611	0.588056	−	0.808820i	$-0.299893\pi$
$29$	5326.52	1.17611	0.588056	+	0.808820i	$0.299893\pi$
$30$	−1168.46	−0.237034
$31$	919.124	0.171779	0.0858895	−	0.996305i	$-0.472627\pi$
$31$	919.124	0.171779	0.0858895	+	0.996305i	$0.472627\pi$
$32$	−4912.95	−0.848140
$33$	−6496.71	−1.03850
$34$	−1550.43	−0.230015
$35$	−8572.80	−1.18291
$36$	623.180	0.0801415
$37$	4962.82	0.595969	0.297985	−	0.954571i	$-0.403686\pi$
$37$	4962.82	0.595969	0.297985	+	0.954571i	$0.403686\pi$
$38$	−2523.46	−0.283490
$39$	9186.24	0.967111
$40$	−4756.59	−0.470052
$41$	−5931.38	−0.551057	−0.275528	−	0.961293i	$-0.588853\pi$
$41$	−5931.38	−0.551057	−0.275528	+	0.961293i	$0.588853\pi$
$42$	5615.15	0.491177
$43$	1849.00	0.152499
$43$	1849.00	0.152499
$44$	−12467.6	−0.970847
$45$	922.264	0.0678928
$46$	1683.19	0.117284
$47$	17815.9	1.17642	0.588210	−	0.808708i	$-0.299833\pi$
$47$	17815.9	1.17642	0.588210	+	0.808708i	$0.299833\pi$
$48$	−10466.2	−0.655668
$49$	24390.4	1.45120
$50$	2494.73	0.141123
$51$	−12394.9	−0.667292
$52$	17629.0	0.904104
$53$	24713.3	1.20848	0.604241	−	0.796801i	$-0.293476\pi$
$53$	24713.3	1.20848	0.604241	+	0.796801i	$0.293476\pi$
$54$	−7326.61	−0.341915
$55$	−18451.2	−0.822464
$56$	22858.2	0.974030
$57$	−20173.7	−0.822428
$58$	−9908.61	−0.386761
$59$	33834.6	1.26541	0.632706	−	0.774392i	$-0.281944\pi$
$59$	33834.6	1.26541	0.632706	+	0.774392i	$0.281944\pi$
$60$	−17926.4	−0.642856
$61$	45948.5	1.58105	0.790527	−	0.612427i	$-0.209807\pi$
$61$	45948.5	1.58105	0.790527	+	0.612427i	$0.209807\pi$
$62$	−1709.79	−0.0564890
$63$	−4432.02	−0.140686
$64$	−13381.3	−0.408365
$65$	26089.6	0.765922
$66$	12085.4	0.341509
$67$	−58523.0	−1.59272	−0.796361	−	0.604822i	$-0.793244\pi$
$67$	−58523.0	−1.59272	−0.796361	+	0.604822i	$0.793244\pi$
$68$	−23786.5	−0.623818
$69$	13456.1	0.340250
$70$	15947.5	0.388997
$71$	1792.64	0.0422034	0.0211017	−	0.999777i	$-0.493283\pi$
$71$	1792.64	0.0422034	0.0211017	+	0.999777i	$0.493283\pi$
$72$	−2459.09	−0.0559041
$73$	−46710.3	−1.02590	−0.512951	−	0.858418i	$-0.671448\pi$
$73$	−46710.3	−1.02590	−0.512951	+	0.858418i	$0.671448\pi$
$74$	−9232.03	−0.195983
$75$	19944.0	0.409410
$76$	−38714.5	−0.768847
$77$	88668.8	1.70429
$78$	−17088.6	−0.318031
$79$	−79459.7	−1.43245	−0.716225	−	0.697870i	$-0.754131\pi$
$79$	−79459.7	−1.43245	−0.716225	+	0.697870i	$0.754131\pi$
$80$	−29724.7	−0.519269
$81$	−53266.1	−0.902067
$82$	11033.8	0.181213
$83$	91200.9	1.45313	0.726564	−	0.687099i	$-0.241116\pi$
$83$	91200.9	1.45313	0.726564	+	0.687099i	$0.241116\pi$
$84$	86146.8	1.33211
$85$	−35202.4	−0.528475
$86$	−3439.58	−0.0501487
$87$	−79213.9	−1.12203
$88$	49197.6	0.677231
$89$	−16470.2	−0.220406	−0.110203	−	0.993909i	$-0.535150\pi$
$89$	−16470.2	−0.220406	−0.110203	+	0.993909i	$0.535150\pi$
$90$	−1715.63	−0.0223263
$91$	−125376.	−1.58713
$92$	25823.2	0.318083
$93$	−13668.8	−0.163879
$94$	−33141.8	−0.386862
$95$	−57294.8	−0.651338
$96$	73063.4	0.809137
$97$	145639.	1.57163	0.785813	−	0.618464i	$-0.212245\pi$
$97$	145639.	1.57163	0.785813	+	0.618464i	$0.212245\pi$
$98$	−45372.0	−0.477224
$99$	−9539.00	−0.0978171
$100$	38273.7	0.382737
$101$	−59937.9	−0.584653	−0.292327	−	0.956319i	$-0.594429\pi$
$101$	−59937.9	−0.584653	−0.292327	+	0.956319i	$0.594429\pi$
$102$	23057.4	0.219437
$103$	−176381.	−1.63817	−0.819083	−	0.573675i	$-0.805517\pi$
$103$	−176381.	−1.63817	−0.819083	+	0.573675i	$0.805517\pi$
$104$	−69564.5	−0.630674
$105$	127491.	1.12851
$106$	−45972.6	−0.397406
$107$	145711.	1.23036	0.615180	−	0.788387i	$-0.289083\pi$
$107$	145711.	1.23036	0.615180	+	0.788387i	$0.289083\pi$
$108$	−112404.	−0.927302
$109$	−74113.8	−0.597493	−0.298746	−	0.954333i	$-0.596568\pi$
$109$	−74113.8	−0.597493	−0.298746	+	0.954333i	$0.596568\pi$
$110$	34323.6	0.270465
$111$	−73805.0	−0.568563
$112$	142845.	1.07602
$113$	170870.	1.25884	0.629419	−	0.777066i	$-0.283293\pi$
$113$	170870.	1.25884	0.629419	+	0.777066i	$0.283293\pi$
$114$	37527.8	0.270453
$115$	38216.5	0.269468
$116$	−152016.	−1.04893
$117$	13488.0	0.0910925
$118$	−62940.5	−0.416127
$119$	169168.	1.09509
$120$	70738.1	0.448436
$121$	29789.9	0.184972
$122$	−85475.2	−0.519925
$123$	88209.1	0.525716
$124$	−26231.3	−0.153203
$125$	188632.	1.07979
$126$	8244.62	0.0462641
$127$	117267.	0.645156	0.322578	−	0.946543i	$-0.395451\pi$
$127$	117267.	0.645156	0.322578	+	0.946543i	$0.395451\pi$
$128$	182107.	0.982430
$129$	−27497.6	−0.145486
$130$	−48533.0	−0.251871
$131$	−64361.8	−0.327680	−0.163840	−	0.986487i	$-0.552388\pi$
$131$	−64361.8	−0.327680	−0.163840	+	0.986487i	$0.552388\pi$
$132$	185413.	0.926200
$133$	275335.	1.34969
$134$	108867.	0.523762
$135$	−166350.	−0.785575
$136$	93862.4	0.435155
$137$	−219763.	−1.00035	−0.500176	−	0.865924i	$-0.666731\pi$
$137$	−219763.	−1.00035	−0.500176	+	0.865924i	$0.666731\pi$
$138$	−25031.7	−0.111890
$139$	14710.6	0.0645793	0.0322896	−	0.999479i	$-0.489720\pi$
$139$	14710.6	0.0645793	0.0322896	+	0.999479i	$0.489720\pi$
$140$	244664.	1.05499
$141$	−264950.	−1.12232
$142$	−3334.74	−0.0138785
$143$	−269846.	−1.10351
$144$	−15367.3	−0.0617576
$145$	−224974.	−0.888611
$146$	86892.4	0.337365
$147$	−362724.	−1.38447
$148$	−141636.	−0.531521
$149$	−396393.	−1.46272	−0.731359	−	0.681993i	$-0.761113\pi$
$149$	−396393.	−1.46272	−0.731359	+	0.681993i	$0.761113\pi$
$150$	−37100.5	−0.134633
$151$	70722.8	0.252416	0.126208	−	0.992004i	$-0.459719\pi$
$151$	70722.8	0.252416	0.126208	+	0.992004i	$0.459719\pi$
$152$	152769.	0.536323
$153$	−18199.1	−0.0628525
$154$	−164945.	−0.560451
$155$	−38820.6	−0.129787
$156$	−262171.	−0.862527
$157$	−469441.	−1.51996	−0.759980	−	0.649946i	$-0.774791\pi$
$157$	−469441.	−1.51996	−0.759980	+	0.649946i	$0.774791\pi$
$158$	147814.	0.471057
$159$	−367526.	−1.15291
$160$	207506.	0.640812
$161$	−183653.	−0.558385
$162$	99087.7	0.296642
$163$	660494.	1.94715	0.973576	−	0.228362i	$-0.0733370\pi$
$163$	660494.	1.94715	0.973576	+	0.228362i	$0.0733370\pi$
$164$	169279.	0.491465
$165$	274398.	0.784642
$166$	−169655.	−0.477857
$167$	488059.	1.35419	0.677097	−	0.735894i	$-0.263238\pi$
$167$	488059.	1.35419	0.677097	+	0.735894i	$0.263238\pi$
$168$	−339938.	−0.929238
$169$	10264.9	0.0276464
$170$	65484.8	0.173787
$171$	−29620.6	−0.0774647
$172$	−52769.6	−0.136007
$173$	648829.	1.64822	0.824109	−	0.566431i	$-0.191676\pi$
$173$	648829.	1.64822	0.824109	+	0.566431i	$0.191676\pi$
$174$	147357.	0.368975
$175$	−272200.	−0.671883
$176$	307443.	0.748141
$177$	−503175.	−1.20722
$178$	30638.4	0.0724797
$179$	−203377.	−0.474428	−0.237214	−	0.971457i	$-0.576234\pi$
$179$	−203377.	−0.474428	−0.237214	+	0.971457i	$0.576234\pi$
$180$	−26321.0	−0.0605509
$181$	174043.	0.394875	0.197438	−	0.980315i	$-0.436738\pi$
$181$	174043.	0.394875	0.197438	+	0.980315i	$0.436738\pi$
$182$	233230.	0.521922
$183$	−683327.	−1.50835
$184$	−101899.	−0.221884
$185$	−209612.	−0.450284
$186$	25427.3	0.0538912
$187$	364099.	0.761405
$188$	−508456.	−1.04920
$189$	799409.	1.62785
$190$	106582.	0.214190
$191$	−529048.	−1.04933	−0.524664	−	0.851309i	$-0.675809\pi$
$191$	−529048.	−1.04933	−0.524664	+	0.851309i	$0.675809\pi$
$192$	199001.	0.389586
$193$	−74996.7	−0.144927	−0.0724634	−	0.997371i	$-0.523086\pi$
$193$	−74996.7	−0.144927	−0.0724634	+	0.997371i	$0.523086\pi$
$194$	−270924.	−0.516824
$195$	−387995.	−0.730700
$196$	−696090.	−1.29427
$197$	741584.	1.36143	0.680714	−	0.732549i	$-0.261669\pi$
$197$	741584.	1.36143	0.680714	+	0.732549i	$0.261669\pi$
$198$	17744.8	0.0321669
$199$	−46763.5	−0.0837093	−0.0418547	−	0.999124i	$-0.513327\pi$
$199$	−46763.5	−0.0837093	−0.0418547	+	0.999124i	$0.513327\pi$
$200$	−151029.	−0.266985
$201$	870331.	1.51948
$202$	111499.	0.192261
$203$	1.08113e6	1.84136
$204$	353743.	0.595131
$205$	250521.	0.416351
$206$	328110.	0.538706
$207$	19757.4	0.0320483
$208$	−434720.	−0.696709
$209$	592602.	0.938420
$210$	−237164.	−0.371109
$211$	360269.	0.557084	0.278542	−	0.960424i	$-0.410149\pi$
$211$	360269.	0.557084	0.278542	+	0.960424i	$0.410149\pi$
$212$	−705304.	−1.07780
$213$	−26659.4	−0.0402626
$214$	−271057.	−0.404600
$215$	−78095.3	−0.115220
$216$	443549.	0.646856
$217$	186556.	0.268943
$218$	137869.	0.196484
$219$	694657.	0.978723
$220$	526587.	0.733523
$221$	−514830.	−0.709061
$222$	137295.	0.186970
$223$	−184494.	−0.248440	−0.124220	−	0.992255i	$-0.539643\pi$
$223$	−184494.	−0.248440	−0.124220	+	0.992255i	$0.539643\pi$
$224$	−997189.	−1.32788
$225$	29283.4	0.0385625
$226$	−317859.	−0.413965
$227$	−404674.	−0.521243	−0.260621	−	0.965441i	$-0.583927\pi$
$227$	−404674.	−0.521243	−0.260621	+	0.965441i	$0.583927\pi$
$228$	575746.	0.733490
$229$	605861.	0.763456	0.381728	−	0.924275i	$-0.375329\pi$
$229$	605861.	0.763456	0.381728	+	0.924275i	$0.375329\pi$
$230$	−71091.9	−0.0886136
$231$	−1.31865e6	−1.62592
$232$	599862.	0.731698
$233$	−126192.	−0.152280	−0.0761400	−	0.997097i	$-0.524260\pi$
$233$	−126192.	−0.152280	−0.0761400	+	0.997097i	$0.524260\pi$
$234$	−25090.9	−0.0299555
$235$	−752480.	−0.888844
$236$	−965624.	−1.12857
$237$	1.18169e6	1.36658
$238$	−314693.	−0.360118
$239$	1.31948e6	1.49420	0.747098	−	0.664714i	$-0.231446\pi$
$239$	1.31948e6	1.49420	0.747098	+	0.664714i	$0.231446\pi$
$240$	442054.	0.495390
$241$	1.51669e6	1.68211	0.841055	−	0.540949i	$-0.181935\pi$
$241$	1.51669e6	1.68211	0.841055	+	0.540949i	$0.181935\pi$
$242$	−55416.4	−0.0608275
$243$	−164910.	−0.179156
$244$	−1.31135e6	−1.41008
$245$	−1.03017e6	−1.09646
$246$	−164090.	−0.172880
$247$	−837930.	−0.873907
$248$	103510.	0.106869
$249$	−1.35630e6	−1.38630
$250$	−350900.	−0.355086
$251$	−1.30092e6	−1.30337	−0.651685	−	0.758490i	$-0.725938\pi$
$251$	−1.30092e6	−1.30337	−0.651685	+	0.758490i	$0.725938\pi$
$252$	126488.	0.125472
$253$	−395275.	−0.388238
$254$	−218144.	−0.212158
$255$	523515.	0.504172
$256$	89439.4	0.0852960
$257$	−223343.	−0.210930	−0.105465	−	0.994423i	$-0.533633\pi$
$257$	−223343.	−0.210930	−0.105465	+	0.994423i	$0.533633\pi$
$258$	51152.1	0.0478425
$259$	1.00731e6	0.933069
$260$	−744586.	−0.683095
$261$	−116308.	−0.105684
$262$	119728.	0.107757
$263$	216725.	0.193206	0.0966028	−	0.995323i	$-0.469202\pi$
$263$	216725.	0.193206	0.0966028	+	0.995323i	$0.469202\pi$
$264$	−731646.	−0.646087
$265$	−1.04380e6	−0.913068
$266$	−512190.	−0.443840
$267$	244938.	0.210270
$268$	1.67022e6	1.42048
$269$	1.12157e6	0.945029	0.472515	−	0.881323i	$-0.343346\pi$
$269$	1.12157e6	0.945029	0.472515	+	0.881323i	$0.343346\pi$
$270$	309450.	0.258334
$271$	−318880.	−0.263757	−0.131878	−	0.991266i	$-0.542101\pi$
$271$	−318880.	−0.263757	−0.131878	+	0.991266i	$0.542101\pi$
$272$	586561.	0.480719
$273$	1.86454e6	1.51414
$274$	408812.	0.328963
$275$	−585854.	−0.467152
$276$	−384032.	−0.303455
$277$	−353813.	−0.277061	−0.138530	−	0.990358i	$-0.544238\pi$
$277$	−353813.	−0.277061	−0.138530	+	0.990358i	$0.544238\pi$
$278$	−27365.2	−0.0212367
$279$	−20069.7	−0.0154359
$280$	−965452.	−0.735928
$281$	−248237.	−0.187543	−0.0937717	−	0.995594i	$-0.529892\pi$
$281$	−248237.	−0.187543	−0.0937717	+	0.995594i	$0.529892\pi$
$282$	492871.	0.369072
$283$	−420812.	−0.312336	−0.156168	−	0.987730i	$-0.549914\pi$
$283$	−420812.	−0.312336	−0.156168	+	0.987730i	$0.549914\pi$
$284$	−51161.1	−0.0376395
$285$	852065.	0.621385
$286$	501978.	0.362886
$287$	−1.20390e6	−0.862753
$288$	107278.	0.0762129
$289$	−725205.	−0.510759
$290$	418505.	0.292217
$291$	−2.16589e6	−1.49935
$292$	1.33309e6	0.914960
$293$	−59022.2	−0.0401649	−0.0200824	−	0.999798i	$-0.506393\pi$
$293$	−59022.2	−0.0401649	−0.0200824	+	0.999798i	$0.506393\pi$
$294$	674754.	0.455278
$295$	−1.42906e6	−0.956081
$296$	558903.	0.370772
$297$	1.72056e6	1.13182
$298$	737386.	0.481010
$299$	558912.	0.361548
$300$	−569191.	−0.365136
$301$	375294.	0.238757
$302$	−131561.	−0.0830063
$303$	891373.	0.557767
$304$	954678.	0.592479
$305$	−1.94070e6	−1.19456
$306$	33854.8	0.0206688
$307$	969345.	0.586993	0.293496	−	0.955960i	$-0.405181\pi$
$307$	969345.	0.586993	0.293496	+	0.955960i	$0.405181\pi$
$308$	−2.53056e6	−1.51999
$309$	2.62306e6	1.56283
$310$	72215.6	0.0426802
$311$	−3.12666e6	−1.83307	−0.916537	−	0.399950i	$-0.869028\pi$
$311$	−3.12666e6	−1.83307	−0.916537	+	0.399950i	$0.869028\pi$
$312$	1.03454e6	0.601671
$313$	230443.	0.132955	0.0664773	−	0.997788i	$-0.478824\pi$
$313$	230443.	0.132955	0.0664773	+	0.997788i	$0.478824\pi$
$314$	873274.	0.499834
$315$	187193.	0.106295
$316$	2.26774e6	1.27754
$317$	−580982.	−0.324724	−0.162362	−	0.986731i	$-0.551911\pi$
$317$	−580982.	−0.324724	−0.162362	+	0.986731i	$0.551911\pi$
$318$	683686.	0.379130
$319$	2.32691e6	1.28027
$320$	565180.	0.308540
$321$	−2.16695e6	−1.17378
$322$	341639.	0.183623
$323$	1.13061e6	0.602983
$324$	1.52019e6	0.804517
$325$	828389.	0.435037
$326$	−1.22868e6	−0.640315
$327$	1.10219e6	0.570016
$328$	−667981.	−0.342830
$329$	3.61611e6	1.84184
$330$	−510446.	−0.258027
$331$	−2.54254e6	−1.27555	−0.637776	−	0.770222i	$-0.720145\pi$
$331$	−2.54254e6	−1.27555	−0.637776	+	0.770222i	$0.720145\pi$
$332$	−2.60283e6	−1.29599
$333$	−108367.	−0.0535531
$334$	−907906.	−0.445323
$335$	2.47181e6	1.20338
$336$	−2.12433e6	−1.02653
$337$	2.09346e6	1.00413	0.502066	−	0.864829i	$-0.332573\pi$
$337$	2.09346e6	1.00413	0.502066	+	0.864829i	$0.332573\pi$
$338$	−19095.2	−0.00909143
$339$	−2.54111e6	−1.20095
$340$	1.00466e6	0.471326
$341$	401522.	0.186992
$342$	55101.5	0.0254740
$343$	1.53921e6	0.706421
$344$	208231.	0.0948743
$345$	−568341.	−0.257076
$346$	−1.20698e6	−0.542012
$347$	−4.07369e6	−1.81620	−0.908100	−	0.418753i	$-0.862467\pi$
$347$	−4.07369e6	−1.81620	−0.908100	+	0.418753i	$0.862467\pi$
$348$	2.26073e6	1.00069
$349$	−1.01046e6	−0.444073	−0.222037	−	0.975038i	$-0.571270\pi$
$349$	−1.01046e6	−0.444073	−0.222037	+	0.975038i	$0.571270\pi$
$350$	506358.	0.220947
$351$	−2.43284e6	−1.05401
$352$	−2.14624e6	−0.923255
$353$	−655684.	−0.280064	−0.140032	−	0.990147i	$-0.544721\pi$
$353$	−655684.	−0.280064	−0.140032	+	0.990147i	$0.544721\pi$
$354$	936026.	0.396990
$355$	−75714.9	−0.0318868
$356$	470050.	0.196571
$357$	−2.51580e6	−1.04473
$358$	378330.	0.156014
$359$	1.78546e6	0.731162	0.365581	−	0.930780i	$-0.380870\pi$
$359$	1.78546e6	0.731162	0.365581	+	0.930780i	$0.380870\pi$
$360$	103863.	0.0422383
$361$	−635943.	−0.256833
$362$	−323762.	−0.129854
$363$	−443024.	−0.176466
$364$	3.57818e6	1.41549
$365$	1.97288e6	0.775119
$366$	1.27115e6	0.496015
$367$	2.96896e6	1.15064	0.575320	−	0.817928i	$-0.304878\pi$
$367$	2.96896e6	1.15064	0.575320	+	0.817928i	$0.304878\pi$
$368$	−636785.	−0.245117
$369$	129516.	0.0495173
$370$	389929.	0.148075
$371$	5.01609e6	1.89204
$372$	390102.	0.146157
$373$	−3.94005e6	−1.46632	−0.733162	−	0.680055i	$-0.761956\pi$
$373$	−3.94005e6	−1.46632	−0.733162	+	0.680055i	$0.761956\pi$
$374$	−677311.	−0.250386
$375$	−2.80525e6	−1.03013
$376$	2.00639e6	0.731889
$377$	−3.29021e6	−1.19226
$378$	−1.48709e6	−0.535314
$379$	−4.36353e6	−1.56042	−0.780208	−	0.625520i	$-0.784887\pi$
$379$	−4.36353e6	−1.56042	−0.780208	+	0.625520i	$0.784887\pi$
$380$	1.63517e6	0.580902
$381$	−1.74394e6	−0.615487
$382$	984155.	0.345068
$383$	−3.53079e6	−1.22991	−0.614957	−	0.788561i	$-0.710827\pi$
$383$	−3.53079e6	−1.22991	−0.614957	+	0.788561i	$0.710827\pi$
$384$	−2.70822e6	−0.937251
$385$	−3.74506e6	−1.28768
$386$	139512.	0.0476587
$387$	−40374.2	−0.0137033
$388$	−4.15647e6	−1.40167
$389$	−5.57419e6	−1.86770	−0.933851	−	0.357663i	$-0.883574\pi$
$389$	−5.57419e6	−1.86770	−0.933851	+	0.357663i	$0.883574\pi$
$390$	721763.	0.240289
$391$	−754131.	−0.249462
$392$	2.74680e6	0.902841
$393$	957163.	0.312611
$394$	−1.37952e6	−0.447702
$395$	3.35610e6	1.08229
$396$	272238.	0.0872391
$397$	5.87343e6	1.87032	0.935159	−	0.354229i	$-0.115257\pi$
$397$	5.87343e6	1.87032	0.935159	+	0.354229i	$0.115257\pi$
$398$	86991.2	0.0275276
$399$	−4.09468e6	−1.28762
$400$	−943807.	−0.294940
$401$	−46354.8	−0.0143957	−0.00719786	−	0.999974i	$-0.502291\pi$
$401$	−46354.8	−0.0143957	−0.00719786	+	0.999974i	$0.502291\pi$
$402$	−1.61902e6	−0.499676
$403$	−567746.	−0.174137
$404$	1.71060e6	0.521429
$405$	2.24978e6	0.681556
$406$	−2.01116e6	−0.605526
$407$	2.16802e6	0.648751
$408$	−1.39588e6	−0.415144
$409$	2.92397e6	0.864301	0.432150	−	0.901802i	$-0.357755\pi$
$409$	2.92397e6	0.864301	0.432150	+	0.901802i	$0.357755\pi$
$410$	−466029.	−0.136916
$411$	3.26822e6	0.954349
$412$	5.03382e6	1.46101
$413$	6.86747e6	1.98117
$414$	−36753.5	−0.0105390
$415$	−3.85201e6	−1.09791
$416$	3.03475e6	0.859784
$417$	−218770.	−0.0616095
$418$	−1.10238e6	−0.308597
$419$	3.23273e6	0.899569	0.449785	−	0.893137i	$-0.351501\pi$
$419$	3.23273e6	0.899569	0.449785	+	0.893137i	$0.351501\pi$
$420$	−3.63854e6	−1.00648
$421$	−4.62842e6	−1.27271	−0.636353	−	0.771398i	$-0.719558\pi$
$421$	−4.62842e6	−1.27271	−0.636353	+	0.771398i	$0.719558\pi$
$422$	−670186.	−0.183195
$423$	−389022.	−0.105712
$424$	2.78316e6	0.751836
$425$	−1.11773e6	−0.300169
$426$	49592.9	0.0132402
$427$	9.32623e6	2.47535
$428$	−4.15851e6	−1.09731
$429$	4.01304e6	1.05276
$430$	145276.	0.0378898
$431$	1.87590e6	0.486425	0.243213	−	0.969973i	$-0.421799\pi$
$431$	1.87590e6	0.486425	0.243213	+	0.969973i	$0.421799\pi$
$432$	2.77181e6	0.714585
$433$	−3.80994e6	−0.976559	−0.488280	−	0.872687i	$-0.662375\pi$
$433$	−3.80994e6	−0.976559	−0.488280	+	0.872687i	$0.662375\pi$
$434$	−347039.	−0.0884410
$435$	3.34572e6	0.847747
$436$	2.11517e6	0.532880
$437$	−1.22741e6	−0.307459
$438$	−1.29223e6	−0.321850
$439$	2.35939e6	0.584304	0.292152	−	0.956372i	$-0.405629\pi$
$439$	2.35939e6	0.584304	0.292152	+	0.956372i	$0.405629\pi$
$440$	−2.07793e6	−0.511682
$441$	−532581.	−0.130404
$442$	957707.	0.233172
$443$	−2.55633e6	−0.618881	−0.309440	−	0.950919i	$-0.600142\pi$
$443$	−2.55633e6	−0.618881	−0.309440	+	0.950919i	$0.600142\pi$
$444$	2.10636e6	0.507078
$445$	695642.	0.166527
$446$	343204.	0.0816987
$447$	5.89500e6	1.39545
$448$	−2.71602e6	−0.639350
$449$	3.71934e6	0.870662	0.435331	−	0.900270i	$-0.356631\pi$
$449$	3.71934e6	0.870662	0.435331	+	0.900270i	$0.356631\pi$
$450$	−54474.1	−0.0126811
$451$	−2.59115e6	−0.599861
$452$	−4.87655e6	−1.12271
$453$	−1.05176e6	−0.240808
$454$	752790.	0.171409
$455$	5.29545e6	1.19915
$456$	−2.27192e6	−0.511659
$457$	−2.59594e6	−0.581438	−0.290719	−	0.956808i	$-0.593895\pi$
$457$	−2.59594e6	−0.581438	−0.290719	+	0.956808i	$0.593895\pi$
$458$	−1.12705e6	−0.251060
$459$	3.28260e6	0.727254
$460$	−1.09068e6	−0.240327
$461$	−6.62260e6	−1.45136	−0.725682	−	0.688031i	$-0.758475\pi$
$461$	−6.62260e6	−1.45136	−0.725682	+	0.688031i	$0.758475\pi$
$462$	2.45300e6	0.534678
$463$	5.09992e6	1.10563	0.552817	−	0.833303i	$-0.313553\pi$
$463$	5.09992e6	1.10563	0.552817	+	0.833303i	$0.313553\pi$
$464$	3.74864e6	0.808311
$465$	577324.	0.123819
$466$	234748.	0.0500768
$467$	3.91009e6	0.829649	0.414825	−	0.909901i	$-0.363843\pi$
$467$	3.91009e6	0.829649	0.414825	+	0.909901i	$0.363843\pi$
$468$	−384941.	−0.0812417
$469$	−1.18785e7	−2.49362
$470$	1.39979e6	0.292294
$471$	6.98134e6	1.45006
$472$	3.81039e6	0.787253
$473$	807742.	0.166004
$474$	−2.19823e6	−0.449394
$475$	−1.81920e6	−0.369954
$476$	−4.82798e6	−0.976670
$477$	−539631.	−0.108593
$478$	−2.45455e6	−0.491362
$479$	−8.49397e6	−1.69150	−0.845750	−	0.533580i	$-0.820846\pi$
$479$	−8.49397e6	−1.69150	−0.845750	+	0.533580i	$0.820846\pi$
$480$	−3.08594e6	−0.611343
$481$	−3.06555e6	−0.604152
$482$	−2.82141e6	−0.553157
$483$	2.73121e6	0.532706
$484$	−850190.	−0.164969
$485$	−6.15129e6	−1.18744
$486$	306773.	0.0589150
$487$	7.46234e6	1.42578	0.712890	−	0.701276i	$-0.247386\pi$
$487$	7.46234e6	1.42578	0.712890	+	0.701276i	$0.247386\pi$
$488$	5.17463e6	0.983625
$489$	−9.82260e6	−1.85761
$490$	1.91635e6	0.360567
$491$	2.46640e6	0.461700	0.230850	−	0.972989i	$-0.425849\pi$
$491$	2.46640e6	0.461700	0.230850	+	0.972989i	$0.425849\pi$
$492$	−2.51745e6	−0.468864
$493$	4.43943e6	0.822641
$494$	1.55875e6	0.287382
$495$	402894.	0.0739057
$496$	646850.	0.118059
$497$	363855.	0.0660750
$498$	2.52305e6	0.455882
$499$	−2.03466e6	−0.365798	−0.182899	−	0.983132i	$-0.558548\pi$
$499$	−2.03466e6	−0.365798	−0.182899	+	0.983132i	$0.558548\pi$
$500$	−5.38345e6	−0.963021
$501$	−7.25821e6	−1.29192
$502$	2.42003e6	0.428609
$503$	−5.11148e6	−0.900797	−0.450398	−	0.892828i	$-0.648718\pi$
$503$	−5.11148e6	−0.900797	−0.450398	+	0.892828i	$0.648718\pi$
$504$	−499125.	−0.0875253
$505$	2.53157e6	0.441734
$506$	735305.	0.127671
$507$	−152656.	−0.0263750
$508$	−3.34673e6	−0.575389
$509$	5.43324e6	0.929532	0.464766	−	0.885433i	$-0.346138\pi$
$509$	5.43324e6	0.929532	0.464766	+	0.885433i	$0.346138\pi$
$510$	−973864.	−0.165795
$511$	−9.48086e6	−1.60618
$512$	−5.99380e6	−1.01048
$513$	5.34271e6	0.896330
$514$	415471.	0.0693638
$515$	7.44970e6	1.23772
$516$	784767.	0.129753
$517$	7.78292e6	1.28061
$518$	−1.87384e6	−0.306837
$519$	−9.64911e6	−1.57242
$520$	2.93816e6	0.476505
$521$	8.89569e6	1.43577	0.717886	−	0.696161i	$-0.245110\pi$
$521$	8.89569e6	1.43577	0.717886	+	0.696161i	$0.245110\pi$
$522$	216361.	0.0347539
$523$	5.98910e6	0.957430	0.478715	−	0.877970i	$-0.341103\pi$
$523$	5.98910e6	0.957430	0.478715	+	0.877970i	$0.341103\pi$
$524$	1.83686e6	0.292245
$525$	4.04805e6	0.640985
$526$	−403160.	−0.0635351
$527$	766051.	0.120152
$528$	−4.57217e6	−0.713737
$529$	−5.61764e6	−0.872800
$530$	1.94172e6	0.300260
$531$	−738803.	−0.113708
$532$	−7.85794e6	−1.20373
$533$	3.66384e6	0.558622
$534$	−455642.	−0.0691466
$535$	−6.15431e6	−0.929598
$536$	−6.59075e6	−0.990884
$537$	3.02454e6	0.452610
$538$	−2.08639e6	−0.310770
$539$	1.06550e7	1.57973
$540$	4.74754e6	0.700623
$541$	3.07873e6	0.452249	0.226125	−	0.974098i	$-0.427394\pi$
$541$	3.07873e6	0.452249	0.226125	+	0.974098i	$0.427394\pi$
$542$	593193.	0.0867356
$543$	−2.58830e6	−0.376716
$544$	−4.09474e6	−0.593238
$545$	3.13031e6	0.451435
$546$	−3.46850e6	−0.497920
$547$	−1.37829e7	−1.96958	−0.984789	−	0.173755i	$-0.944410\pi$
$547$	−1.37829e7	−1.96958	−0.984789	+	0.173755i	$0.944410\pi$
$548$	6.27192e6	0.892174
$549$	−1.00332e6	−0.142072
$550$	1.08983e6	0.153621
$551$	7.22555e6	1.01389
$552$	1.51540e6	0.211680
$553$	−1.61280e7	−2.24269
$554$	658177.	0.0911105
$555$	3.11727e6	0.429577
$556$	−419833.	−0.0575956
$557$	3.17087e6	0.433053	0.216526	−	0.976277i	$-0.430527\pi$
$557$	3.17087e6	0.433053	0.216526	+	0.976277i	$0.430527\pi$
$558$	37334.5	0.00507603
$559$	−1.14213e6	−0.154592
$560$	−6.03326e6	−0.812984
$561$	−5.41473e6	−0.726390
$562$	461781.	0.0616730
$563$	1.15175e7	1.53139	0.765697	−	0.643201i	$-0.222394\pi$
$563$	1.15175e7	1.53139	0.765697	+	0.643201i	$0.222394\pi$
$564$	7.56155e6	1.00095
$565$	−7.21696e6	−0.951115
$566$	782812.	0.102711
$567$	−1.08115e7	−1.41230
$568$	201884.	0.0262561
$569$	−1.09971e7	−1.42397	−0.711983	−	0.702197i	$-0.752203\pi$
$569$	−1.09971e7	−1.42397	−0.711983	+	0.702197i	$0.752203\pi$
$570$	−1.58505e6	−0.204341
$571$	−2.17295e6	−0.278907	−0.139454	−	0.990229i	$-0.544535\pi$
$571$	−2.17295e6	−0.278907	−0.139454	+	0.990229i	$0.544535\pi$
$572$	7.70127e6	0.984175
$573$	7.86778e6	1.00107
$574$	2.23955e6	0.283714
$575$	1.21344e6	0.153055
$576$	292190.	0.0366952
$577$	−1.05167e7	−1.31505	−0.657524	−	0.753434i	$-0.728396\pi$
$577$	−1.05167e7	−1.31505	−0.657524	+	0.753434i	$0.728396\pi$
$578$	1.34905e6	0.167962
$579$	1.11532e6	0.138262
$580$	6.42064e6	0.792517
$581$	1.85112e7	2.27506
$582$	4.02907e6	0.493057
$583$	1.07961e7	1.31551
$584$	−5.26042e6	−0.638246
$585$	−569686.	−0.0688249
$586$	109795.	0.0132081
$587$	2.96292e6	0.354915	0.177457	−	0.984128i	$-0.443213\pi$
$587$	2.96292e6	0.354915	0.177457	+	0.984128i	$0.443213\pi$
$588$	1.03520e7	1.23475
$589$	1.24681e6	0.148086
$590$	2.65839e6	0.314404
$591$	−1.10285e7	−1.29882
$592$	3.49267e6	0.409594
$593$	7.54824e6	0.881473	0.440737	−	0.897636i	$-0.354717\pi$
$593$	7.54824e6	0.881473	0.440737	+	0.897636i	$0.354717\pi$
$594$	−3.20065e6	−0.372197
$595$	−7.14507e6	−0.827398
$596$	1.13129e7	1.30454
$597$	695447.	0.0798598
$598$	−1.03971e6	−0.118894
$599$	7.70971e6	0.877953	0.438976	−	0.898499i	$-0.355341\pi$
$599$	7.70971e6	0.877953	0.438976	+	0.898499i	$0.355341\pi$
$600$	2.24605e6	0.254707
$601$	3.40171e6	0.384159	0.192079	−	0.981379i	$-0.438477\pi$
$601$	3.40171e6	0.384159	0.192079	+	0.981379i	$0.438477\pi$
$602$	−698137.	−0.0785144
$603$	1.27789e6	0.143120
$604$	−2.01839e6	−0.225120
$605$	−1.25822e6	−0.139756
$606$	−1.65817e6	−0.183420
$607$	5.29342e6	0.583129	0.291564	−	0.956551i	$-0.405824\pi$
$607$	5.29342e6	0.583129	0.291564	+	0.956551i	$0.405824\pi$
$608$	−6.66453e6	−0.731157
$609$	−1.60782e7	−1.75668
$610$	3.61017e6	0.392829
$611$	−1.10049e7	−1.19257
$612$	519395.	0.0560556
$613$	1.51319e7	1.62646	0.813229	−	0.581944i	$-0.197708\pi$
$613$	1.51319e7	1.62646	0.813229	+	0.581944i	$0.197708\pi$
$614$	−1.80321e6	−0.193031
$615$	−3.72565e6	−0.397204
$616$	9.98570e6	1.06029
$617$	2.54291e6	0.268917	0.134458	−	0.990919i	$-0.457071\pi$
$617$	2.54291e6	0.268917	0.134458	+	0.990919i	$0.457071\pi$
$618$	−4.87952e6	−0.513932
$619$	8.70953e6	0.913626	0.456813	−	0.889563i	$-0.348991\pi$
$619$	8.70953e6	0.913626	0.456813	+	0.889563i	$0.348991\pi$
$620$	1.10792e6	0.115752
$621$	−3.56367e6	−0.370824
$622$	5.81634e6	0.602801
$623$	−3.34297e6	−0.345074
$624$	6.46498e6	0.664669
$625$	−3.77627e6	−0.386690
$626$	−428680.	−0.0437217
$627$	−8.81293e6	−0.895265
$628$	1.33976e7	1.35559
$629$	4.13630e6	0.416855
$630$	−348224.	−0.0349548
$631$	1.28039e7	1.28018	0.640089	−	0.768301i	$-0.278898\pi$
$631$	1.28039e7	1.28018	0.640089	+	0.768301i	$0.278898\pi$
$632$	−8.94859e6	−0.891173
$633$	−5.35777e6	−0.531465
$634$	1.08077e6	0.106785
$635$	−4.95293e6	−0.487447
$636$	1.04890e7	1.02823
$637$	−1.50660e7	−1.47113
$638$	−4.32861e6	−0.421014
$639$	−39143.6	−0.00379235
$640$	−7.69156e6	−0.742274
$641$	−1.14881e7	−1.10434	−0.552170	−	0.833732i	$-0.686200\pi$
$641$	−1.14881e7	−1.10434	−0.552170	+	0.833732i	$0.686200\pi$
$642$	4.03105e6	0.385994
$643$	−1.13485e7	−1.08246	−0.541230	−	0.840875i	$-0.682041\pi$
$643$	−1.13485e7	−1.08246	−0.541230	+	0.840875i	$0.682041\pi$
$644$	5.24137e6	0.498001
$645$	1.16140e6	0.109922
$646$	−2.10320e6	−0.198289
$647$	−6.22456e6	−0.584585	−0.292293	−	0.956329i	$-0.594418\pi$
$647$	−6.22456e6	−0.584585	−0.292293	+	0.956329i	$0.594418\pi$
$648$	−5.99872e6	−0.561205
$649$	1.47808e7	1.37748
$650$	−1.54100e6	−0.143060
$651$	−2.77438e6	−0.256575
$652$	−1.88502e7	−1.73659
$653$	−382501.	−0.0351034	−0.0175517	−	0.999846i	$-0.505587\pi$
$653$	−382501.	−0.0351034	−0.0175517	+	0.999846i	$0.505587\pi$
$654$	−2.05034e6	−0.187448
$655$	2.71842e6	0.247579
$656$	−4.17432e6	−0.378727
$657$	1.01995e6	0.0921863
$658$	−6.72683e6	−0.605684
$659$	−2.06346e7	−1.85090	−0.925449	−	0.378872i	$-0.876312\pi$
$659$	−2.06346e7	−1.85090	−0.925449	+	0.378872i	$0.876312\pi$
$660$	−7.83119e6	−0.699790
$661$	−3.78028e6	−0.336527	−0.168264	−	0.985742i	$-0.553816\pi$
$661$	−3.78028e6	−0.336527	−0.168264	+	0.985742i	$0.553816\pi$
$662$	4.72973e6	0.419461
$663$	7.65635e6	0.676453
$664$	1.02709e7	0.904038
$665$	−1.16292e7	−1.01976
$666$	201588.	0.0176108
$667$	−4.81956e6	−0.419462
$668$	−1.39290e7	−1.20775
$669$	2.74373e6	0.237015
$670$	−4.59816e6	−0.395728
$671$	2.00728e7	1.72108
$672$	1.48298e7	1.26681
$673$	−7.82427e6	−0.665895	−0.332948	−	0.942945i	$-0.608043\pi$
$673$	−7.82427e6	−0.665895	−0.332948	+	0.942945i	$0.608043\pi$
$674$	−3.89435e6	−0.330206
$675$	−5.28187e6	−0.446199
$676$	−292955.	−0.0246567
$677$	5.22258e6	0.437939	0.218969	−	0.975732i	$-0.429730\pi$
$677$	5.22258e6	0.437939	0.218969	+	0.975732i	$0.429730\pi$
$678$	4.72707e6	0.394928
$679$	2.95606e7	2.46059
$680$	−3.96442e6	−0.328781
$681$	6.01814e6	0.497273
$682$	−746928.	−0.0614919
$683$	−1.18085e7	−0.968598	−0.484299	−	0.874902i	$-0.660925\pi$
$683$	−1.18085e7	−0.968598	−0.484299	+	0.874902i	$0.660925\pi$
$684$	845358.	0.0690877
$685$	9.28202e6	0.755816
$686$	−2.86330e6	−0.232304
$687$	−9.01012e6	−0.728348
$688$	1.30127e6	0.104808
$689$	−1.52655e7	−1.22507
$690$	1.05725e6	0.0845386
$691$	1.90341e7	1.51648	0.758241	−	0.651974i	$-0.226059\pi$
$691$	1.90341e7	1.51648	0.758241	+	0.651974i	$0.226059\pi$
$692$	−1.85172e7	−1.46998
$693$	−1.93614e6	−0.153146
$694$	7.57803e6	0.597252
$695$	−621324.	−0.0487928
$696$	−8.92091e6	−0.698049
$697$	−4.94356e6	−0.385441
$698$	1.87969e6	0.146032
$699$	1.87668e6	0.145277
$700$	7.76847e6	0.599225
$701$	2.48342e7	1.90878	0.954390	−	0.298564i	$-0.0965075\pi$
$701$	2.48342e7	1.90878	0.954390	+	0.298564i	$0.0965075\pi$
$702$	4.52567e6	0.346609
$703$	6.73218e6	0.513768
$704$	−5.84567e6	−0.444532
$705$	1.11906e7	0.847969
$706$	1.21973e6	0.0920983
$707$	−1.21657e7	−0.915352
$708$	1.43604e7	1.07667
$709$	−1.83486e7	−1.37084	−0.685422	−	0.728146i	$-0.740382\pi$
$709$	−1.83486e7	−1.37084	−0.685422	+	0.728146i	$0.740382\pi$
$710$	140848.	0.0104859
$711$	1.73506e6	0.128718
$712$	−1.85484e6	−0.137122
$713$	−831644.	−0.0612651
$714$	4.67999e6	0.343558
$715$	1.13974e7	0.833756
$716$	5.80429e6	0.423123
$717$	−1.96228e7	−1.42548
$718$	−3.32138e6	−0.240440
$719$	−387175.	−0.0279309	−0.0139655	−	0.999902i	$-0.504445\pi$
$719$	−387175.	−0.0279309	−0.0139655	+	0.999902i	$0.504445\pi$
$720$	649060.	0.0466609
$721$	−3.58002e7	−2.56476
$722$	1.18301e6	0.0844587
$723$	−2.25556e7	−1.60476
$724$	−4.96710e6	−0.352173
$725$	−7.14328e6	−0.504723
$726$	824130.	0.0580302
$727$	5.28478e6	0.370843	0.185422	−	0.982659i	$-0.440635\pi$
$727$	5.28478e6	0.370843	0.185422	+	0.982659i	$0.440635\pi$
$728$	−1.41196e7	−0.987403
$729$	1.53961e7	1.07298
$730$	−3.67003e6	−0.254896
$731$	1.54106e6	0.106666
$732$	1.95018e7	1.34523
$733$	2.20879e7	1.51843	0.759215	−	0.650840i	$-0.225583\pi$
$733$	2.20879e7	1.51843	0.759215	+	0.650840i	$0.225583\pi$
$734$	−5.52298e6	−0.378385
$735$	1.53202e7	1.04603
$736$	4.44535e6	0.302490
$737$	−2.55660e7	−1.73378
$738$	−240931.	−0.0162836
$739$	−1.90903e7	−1.28588	−0.642941	−	0.765916i	$-0.722286\pi$
$739$	−1.90903e7	−1.28588	−0.642941	+	0.765916i	$0.722286\pi$
$740$	5.98223e6	0.401591
$741$	1.24613e7	0.833719
$742$	−9.33112e6	−0.622191
$743$	−8.08984e6	−0.537610	−0.268805	−	0.963195i	$-0.586629\pi$
$743$	−8.08984e6	−0.537610	−0.268805	+	0.963195i	$0.586629\pi$
$744$	−1.53936e6	−0.101955
$745$	1.67423e7	1.10516
$746$	7.32944e6	0.482196
$747$	−1.99144e6	−0.130576
$748$	−1.03912e7	−0.679066
$749$	2.95751e7	1.92629
$750$	5.21844e6	0.338756
$751$	3.66332e6	0.237015	0.118507	−	0.992953i	$-0.462189\pi$
$751$	3.66332e6	0.237015	0.118507	+	0.992953i	$0.462189\pi$
$752$	1.25382e7	0.808522
$753$	1.93468e7	1.24343
$754$	6.12059e6	0.392071
$755$	−2.98708e6	−0.190713
$756$	−2.28147e7	−1.45181
$757$	3.20177e6	0.203072	0.101536	−	0.994832i	$-0.467624\pi$
$757$	3.20177e6	0.203072	0.101536	+	0.994832i	$0.467624\pi$
$758$	8.11722e6	0.513138
$759$	5.87836e6	0.370384
$760$	−6.45243e6	−0.405218
$761$	−1.65236e7	−1.03429	−0.517147	−	0.855897i	$-0.673006\pi$
$761$	−1.65236e7	−1.03429	−0.517147	+	0.855897i	$0.673006\pi$
$762$	3.24415e6	0.202401
$763$	−1.50430e7	−0.935454
$764$	1.50988e7	0.935854
$765$	768668.	0.0474882
$766$	6.56811e6	0.404453
$767$	−2.08998e7	−1.28278
$768$	−1.33011e6	−0.0813735
$769$	1.98289e7	1.20916	0.604579	−	0.796545i	$-0.293342\pi$
$769$	1.98289e7	1.20916	0.604579	+	0.796545i	$0.293342\pi$
$770$	6.96671e6	0.423449
$771$	3.32146e6	0.201230
$772$	2.14037e6	0.129254
$773$	2.13192e7	1.28329	0.641643	−	0.767004i	$-0.278253\pi$
$773$	2.13192e7	1.28329	0.641643	+	0.767004i	$0.278253\pi$
$774$	75105.7	0.00450630
$775$	−1.23262e6	−0.0737180
$776$	1.64016e7	0.977759
$777$	−1.49803e7	−0.890160
$778$	1.03693e7	0.614188
$779$	−8.04606e6	−0.475050
$780$	1.10732e7	0.651682
$781$	783122.	0.0459411
$782$	1.40286e6	0.0820350
$783$	2.09787e7	1.22285
$784$	1.71652e7	0.997374
$785$	1.98276e7	1.14841
$786$	−1.78055e6	−0.102801
$787$	2.08248e7	1.19852	0.599258	−	0.800556i	$-0.295462\pi$
$787$	2.08248e7	1.19852	0.599258	+	0.800556i	$0.295462\pi$
$788$	−2.11645e7	−1.21420
$789$	−3.22305e6	−0.184321
$790$	−6.24315e6	−0.355907
$791$	3.46817e7	1.97088
$792$	−1.07426e6	−0.0608552
$793$	−2.83826e7	−1.60276
$794$	−1.09260e7	−0.615048
$795$	1.55230e7	0.871079
$796$	1.33461e6	0.0746570
$797$	−1.52522e7	−0.850527	−0.425263	−	0.905070i	$-0.639819\pi$
$797$	−1.52522e7	−0.850527	−0.425263	+	0.905070i	$0.639819\pi$
$798$	7.61708e6	0.423430
$799$	1.48488e7	0.822856
$800$	6.58865e6	0.363975
$801$	359637.	0.0198054
$802$	86231.0	0.00473399
$803$	−2.04056e7	−1.11676
$804$	−2.48388e7	−1.35516
$805$	7.75686e6	0.421887
$806$	1.05614e6	0.0572645
$807$	−1.66795e7	−0.901571
$808$	−6.75009e6	−0.363732
$809$	1.69851e6	0.0912426	0.0456213	−	0.998959i	$-0.485473\pi$
$809$	1.69851e6	0.0912426	0.0456213	+	0.998959i	$0.485473\pi$
$810$	−4.18512e6	−0.224128
$811$	−8.51667e6	−0.454693	−0.227346	−	0.973814i	$-0.573005\pi$
$811$	−8.51667e6	−0.454693	−0.227346	+	0.973814i	$0.573005\pi$
$812$	−3.08550e7	−1.64223
$813$	4.74225e6	0.251627
$814$	−4.03304e6	−0.213340
$815$	−2.78970e7	−1.47117
$816$	−8.72310e6	−0.458612
$817$	2.50821e6	0.131465
$818$	−5.43929e6	−0.284223
$819$	2.73768e6	0.142617
$820$	−7.14975e6	−0.371326
$821$	1.11108e7	0.575293	0.287647	−	0.957737i	$-0.407127\pi$
$821$	1.11108e7	0.575293	0.287647	+	0.957737i	$0.407127\pi$
$822$	−6.07968e6	−0.313835
$823$	−1.20698e7	−0.621157	−0.310578	−	0.950548i	$-0.600523\pi$
$823$	−1.20698e7	−0.621157	−0.310578	+	0.950548i	$0.600523\pi$
$824$	−1.98636e7	−1.01916
$825$	8.71259e6	0.445669
$826$	−1.27751e7	−0.651501
$827$	1.25034e7	0.635719	0.317859	−	0.948138i	$-0.397036\pi$
$827$	1.25034e7	0.635719	0.317859	+	0.948138i	$0.397036\pi$
$828$	−563867.	−0.0285825
$829$	−4.43044e6	−0.223903	−0.111952	−	0.993714i	$-0.535710\pi$
$829$	−4.43044e6	−0.223903	−0.111952	+	0.993714i	$0.535710\pi$
$830$	7.16565e6	0.361044
$831$	5.26177e6	0.264319
$832$	8.26568e6	0.413971
$833$	2.03284e7	1.01506
$834$	406964.	0.0202601
$835$	−2.06139e7	−1.02316
$836$	−1.69126e7	−0.836939
$837$	3.62000e6	0.178605
$838$	−6.01365e6	−0.295821
$839$	−2.49502e7	−1.22369	−0.611843	−	0.790979i	$-0.709572\pi$
$839$	−2.49502e7	−1.22369	−0.611843	+	0.790979i	$0.709572\pi$
$840$	1.43578e7	0.702085
$841$	7.86071e6	0.383241
$842$	8.60998e6	0.418525
$843$	3.69169e6	0.178919
$844$	−1.02819e7	−0.496840
$845$	−433554.	−0.0208882
$846$	723674.	0.0347630
$847$	6.04651e6	0.289598
$848$	1.73924e7	0.830558
$849$	6.25815e6	0.297973
$850$	2.07925e6	0.0987096
$851$	−4.49047e6	−0.212553
$852$	760847.	0.0359086
$853$	1.87125e7	0.880561	0.440280	−	0.897860i	$-0.354879\pi$
$853$	1.87125e7	0.880561	0.440280	+	0.897860i	$0.354879\pi$
$854$	−1.73490e7	−0.814011
$855$	1.25107e6	0.0585285
$856$	1.64096e7	0.765446
$857$	−9.57836e6	−0.445491	−0.222746	−	0.974877i	$-0.571502\pi$
$857$	−9.57836e6	−0.445491	−0.222746	+	0.974877i	$0.571502\pi$
$858$	−7.46522e6	−0.346198
$859$	−2.56964e7	−1.18820	−0.594100	−	0.804391i	$-0.702492\pi$
$859$	−2.56964e7	−1.18820	−0.594100	+	0.804391i	$0.702492\pi$
$860$	2.22880e6	0.102760
$861$	1.79039e7	0.823077
$862$	−3.48962e6	−0.159959
$863$	−3.20924e7	−1.46681	−0.733406	−	0.679791i	$-0.762071\pi$
$863$	−3.20924e7	−1.46681	−0.733406	+	0.679791i	$0.762071\pi$
$864$	−1.93498e7	−0.881845
$865$	−2.74043e7	−1.24531
$866$	7.08740e6	0.321139
$867$	1.07849e7	0.487271
$868$	−5.32421e6	−0.239859
$869$	−3.47122e7	−1.55931
$870$	−6.22384e6	−0.278779
$871$	3.61499e7	1.61459
$872$	−8.34654e6	−0.371720
$873$	−3.18014e6	−0.141225
$874$	2.28328e6	0.101107
$875$	3.82868e7	1.69055
$876$	−1.98252e7	−0.872884
$877$	5.49507e6	0.241254	0.120627	−	0.992698i	$-0.461510\pi$
$877$	5.49507e6	0.241254	0.120627	+	0.992698i	$0.461510\pi$
$878$	−4.38903e6	−0.192147
$879$	877754.	0.0383178
$880$	−1.29853e7	−0.565258
$881$	−2.28313e7	−0.991038	−0.495519	−	0.868597i	$-0.665022\pi$
$881$	−2.28313e7	−0.991038	−0.495519	+	0.868597i	$0.665022\pi$
$882$	990729.	0.0428828
$883$	−2.80025e7	−1.20864	−0.604318	−	0.796743i	$-0.706554\pi$
$883$	−2.80025e7	−1.20864	−0.604318	+	0.796743i	$0.706554\pi$
$884$	1.46930e7	0.632383
$885$	2.12524e7	0.912114
$886$	4.75538e6	0.203517
$887$	−4.93689e6	−0.210690	−0.105345	−	0.994436i	$-0.533595\pi$
$887$	−4.93689e6	−0.210690	−0.105345	+	0.994436i	$0.533595\pi$
$888$	−8.31177e6	−0.353721
$889$	2.38018e7	1.01008
$890$	−1.29406e6	−0.0547620
$891$	−2.32695e7	−0.981957
$892$	5.26538e6	0.221573
$893$	2.41676e7	1.01416
$894$	−1.09661e7	−0.458890
$895$	8.58995e6	0.358454
$896$	3.69625e7	1.53812
$897$	−8.31191e6	−0.344921
$898$	−6.91886e6	−0.286315
$899$	4.89574e6	0.202031
$900$	−835733.	−0.0343923
$901$	2.05975e7	0.845282
$902$	4.82015e6	0.197262
$903$	−5.58122e6	−0.227777
$904$	1.92430e7	0.783164
$905$	−7.35097e6	−0.298348
$906$	1.95653e6	0.0791891
$907$	−1.84794e7	−0.745880	−0.372940	−	0.927856i	$-0.621650\pi$
$907$	−1.84794e7	−0.745880	−0.372940	+	0.927856i	$0.621650\pi$
$908$	1.15492e7	0.464876
$909$	1.30879e6	0.0525363
$910$	−9.85081e6	−0.394338
$911$	1.37578e6	0.0549229	0.0274615	−	0.999623i	$-0.491258\pi$
$911$	1.37578e6	0.0549229	0.0274615	+	0.999623i	$0.491258\pi$
$912$	−1.41976e7	−0.565233
$913$	3.98414e7	1.58182
$914$	4.82906e6	0.191204
$915$	2.88614e7	1.13963
$916$	−1.72910e7	−0.680896
$917$	−1.30636e7	−0.513027
$918$	−6.10642e6	−0.239155
$919$	−2.38412e7	−0.931192	−0.465596	−	0.884997i	$-0.654160\pi$
$919$	−2.38412e7	−0.931192	−0.465596	+	0.884997i	$0.654160\pi$
$920$	4.30387e6	0.167645
$921$	−1.44157e7	−0.559999
$922$	1.23196e7	0.477276
$923$	−1.10732e6	−0.0427828
$924$	3.76335e7	1.45009
$925$	−6.65552e6	−0.255757
$926$	−9.48708e6	−0.363584
$927$	3.85139e6	0.147204
$928$	−2.61690e7	−0.997508
$929$	4.74191e6	0.180266	0.0901331	−	0.995930i	$-0.471271\pi$
$929$	4.74191e6	0.180266	0.0901331	+	0.995930i	$0.471271\pi$
$930$	−1.07396e6	−0.0407175
$931$	3.30861e7	1.25104
$932$	3.60147e6	0.135812
$933$	4.64985e7	1.74878
$934$	−7.27370e6	−0.272828
$935$	−1.53783e7	−0.575279
$936$	1.51899e6	0.0566716
$937$	−1.07340e7	−0.399404	−0.199702	−	0.979857i	$-0.563997\pi$
$937$	−1.07340e7	−0.399404	−0.199702	+	0.979857i	$0.563997\pi$
$938$	2.20969e7	0.820018
$939$	−3.42706e6	−0.126840
$940$	2.14754e7	0.792724
$941$	2.93932e7	1.08211	0.541057	−	0.840986i	$-0.318024\pi$
$941$	2.93932e7	1.08211	0.541057	+	0.840986i	$0.318024\pi$
$942$	−1.29870e7	−0.476849
$943$	5.36685e6	0.196535
$944$	2.38117e7	0.869683
$945$	−3.37642e7	−1.22992
$946$	−1.50259e6	−0.0545901
$947$	4.42575e7	1.60366	0.801830	−	0.597552i	$-0.203860\pi$
$947$	4.42575e7	1.60366	0.801830	+	0.597552i	$0.203860\pi$
$948$	−3.37249e7	−1.21879
$949$	2.88531e7	1.03999
$950$	3.38415e6	0.121658
$951$	8.64013e6	0.309791
$952$	1.90514e7	0.681293
$953$	2.46336e7	0.878609	0.439304	−	0.898338i	$-0.355225\pi$
$953$	2.46336e7	0.878609	0.439304	+	0.898338i	$0.355225\pi$
$954$	1.00384e6	0.0357104
$955$	2.23451e7	0.792820
$956$	−3.76573e7	−1.33261
$957$	−3.46049e7	−1.22140
$958$	1.58008e7	0.556244
$959$	−4.46056e7	−1.56618
$960$	−8.40512e6	−0.294351
$961$	−2.77844e7	−0.970492
$962$	5.70266e6	0.198673
$963$	−3.18170e6	−0.110559
$964$	−4.32856e7	−1.50021
$965$	3.16760e6	0.109499
$966$	−5.08071e6	−0.175179
$967$	−1.51031e7	−0.519397	−0.259698	−	0.965690i	$-0.583623\pi$
$967$	−1.51031e7	−0.519397	−0.259698	+	0.965690i	$0.583623\pi$
$968$	3.35488e6	0.115077
$969$	−1.68139e7	−0.575253
$970$	1.14429e7	0.390487
$971$	2.95351e7	1.00529	0.502643	−	0.864494i	$-0.332361\pi$
$971$	2.95351e7	1.00529	0.502643	+	0.864494i	$0.332361\pi$
$972$	4.70646e6	0.159782
$973$	2.98583e6	0.101107
$974$	−1.38817e7	−0.468863
$975$	−1.23195e7	−0.415031
$976$	3.23371e7	1.08662
$977$	2.11745e7	0.709705	0.354852	−	0.934922i	$-0.384531\pi$
$977$	2.11745e7	0.709705	0.354852	+	0.934922i	$0.384531\pi$
$978$	1.82724e7	0.610869
$979$	−7.19505e6	−0.239926
$980$	2.94004e7	0.977886
$981$	1.61833e6	0.0536900
$982$	−4.58810e6	−0.151829
$983$	−1.08531e7	−0.358236	−0.179118	−	0.983828i	$-0.557324\pi$
$983$	−1.08531e7	−0.358236	−0.179118	+	0.983828i	$0.557324\pi$
$984$	9.93394e6	0.327065
$985$	−3.13219e7	−1.02863
$986$	−8.25841e6	−0.270523
$987$	−5.37774e7	−1.75714
$988$	2.39141e7	0.779402
$989$	−1.67302e6	−0.0543888
$990$	−749479.	−0.0243037
$991$	−1.68782e7	−0.545936	−0.272968	−	0.962023i	$-0.588005\pi$
$991$	−1.68782e7	−0.545936	−0.272968	+	0.962023i	$0.588005\pi$
$992$	−4.51561e6	−0.145693
$993$	3.78116e7	1.21689
$994$	−676857.	−0.0217286
$995$	1.97513e6	0.0632466
$996$	3.87082e7	1.23639
$997$	−1.21396e7	−0.386783	−0.193392	−	0.981122i	$-0.561949\pi$
$997$	−1.21396e7	−0.386783	−0.193392	+	0.981122i	$0.561949\pi$
$998$	3.78496e6	0.120291
$999$	1.95462e7	0.619653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.a.b.1.5	✓	10
3.2	odd	2		387.6.a.e.1.6		10
4.3	odd	2		688.6.a.h.1.8		10
5.4	even	2		1075.6.a.b.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.a.b.1.5	✓	10	1.1	even	1	trivial
387.6.a.e.1.6		10	3.2	odd	2
688.6.a.h.1.8		10	4.3	odd	2
1075.6.a.b.1.6		10	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)

\(f(q)\)	\(=\)	\(q-1.86024 q^{2} -14.8716 q^{3} -28.5395 q^{4} -42.2365 q^{5} +27.6647 q^{6} +202.971 q^{7} +112.618 q^{8} -21.8357 q^{9} +O(q^{10})\)	\(q-1.86024 q^{2} -14.8716 q^{3} -28.5395 q^{4} -42.2365 q^{5} +27.6647 q^{6} +202.971 q^{7} +112.618 q^{8} -21.8357 q^{9} +78.5700 q^{10} +436.853 q^{11} +424.428 q^{12} -617.704 q^{13} -377.575 q^{14} +628.124 q^{15} +703.768 q^{16} +833.458 q^{17} +40.6196 q^{18} +1356.52 q^{19} +1205.41 q^{20} -3018.51 q^{21} -812.652 q^{22} -904.822 q^{23} -1674.81 q^{24} -1341.08 q^{25} +1149.08 q^{26} +3938.53 q^{27} -5792.70 q^{28} +5326.52 q^{29} -1168.46 q^{30} +919.124 q^{31} -4912.95 q^{32} -6496.71 q^{33} -1550.43 q^{34} -8572.80 q^{35} +623.180 q^{36} +4962.82 q^{37} -2523.46 q^{38} +9186.24 q^{39} -4756.59 q^{40} -5931.38 q^{41} +5615.15 q^{42} +1849.00 q^{43} -12467.6 q^{44} +922.264 q^{45} +1683.19 q^{46} +17815.9 q^{47} -10466.2 q^{48} +24390.4 q^{49} +2494.73 q^{50} -12394.9 q^{51} +17629.0 q^{52} +24713.3 q^{53} -7326.61 q^{54} -18451.2 q^{55} +22858.2 q^{56} -20173.7 q^{57} -9908.61 q^{58} +33834.6 q^{59} -17926.4 q^{60} +45948.5 q^{61} -1709.79 q^{62} -4432.02 q^{63} -13381.3 q^{64} +26089.6 q^{65} +12085.4 q^{66} -58523.0 q^{67} -23786.5 q^{68} +13456.1 q^{69} +15947.5 q^{70} +1792.64 q^{71} -2459.09 q^{72} -46710.3 q^{73} -9232.03 q^{74} +19944.0 q^{75} -38714.5 q^{76} +88668.8 q^{77} -17088.6 q^{78} -79459.7 q^{79} -29724.7 q^{80} -53266.1 q^{81} +11033.8 q^{82} +91200.9 q^{83} +86146.8 q^{84} -35202.4 q^{85} -3439.58 q^{86} -79213.9 q^{87} +49197.6 q^{88} -16470.2 q^{89} -1715.63 q^{90} -125376. q^{91} +25823.2 q^{92} -13668.8 q^{93} -33141.8 q^{94} -57294.8 q^{95} +73063.4 q^{96} +145639. q^{97} -45372.0 q^{98} -9539.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9}+O(q^{10}) \) 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9} - 17 q^{10} + 745 q^{11} + 4627 q^{12} + 1917 q^{13} + 1936 q^{14} + 1688 q^{15} + 5354 q^{16} + 4017 q^{17} - 2725 q^{18} - 2404 q^{19} + 1311 q^{20} - 228 q^{21} - 5836 q^{22} + 1733 q^{23} - 10711 q^{24} + 7120 q^{25} - 1484 q^{26} - 2324 q^{27} - 15028 q^{28} + 6996 q^{29} - 48420 q^{30} - 4899 q^{31} - 7554 q^{32} - 15734 q^{33} - 27033 q^{34} + 7084 q^{35} + 4433 q^{36} + 1466 q^{37} + 13905 q^{38} - 26542 q^{39} - 93211 q^{40} + 10297 q^{41} - 37642 q^{42} + 18490 q^{43} - 36140 q^{44} + 73822 q^{45} + 17991 q^{46} + 48592 q^{47} + 83607 q^{48} + 29458 q^{49} + 983 q^{50} + 92972 q^{51} + 14232 q^{52} + 127165 q^{53} - 92002 q^{54} + 106672 q^{55} - 7780 q^{56} + 34060 q^{57} - 10305 q^{58} + 99372 q^{59} + 111372 q^{60} + 17408 q^{61} + 28265 q^{62} + 2244 q^{63} + 47202 q^{64} + 54484 q^{65} - 150292 q^{66} - 2021 q^{67} + 192151 q^{68} + 1654 q^{69} - 33194 q^{70} + 11286 q^{71} - 298365 q^{72} + 49892 q^{73} - 125431 q^{74} - 44662 q^{75} - 249803 q^{76} + 98144 q^{77} - 28494 q^{78} - 91524 q^{79} + 12251 q^{80} - 26450 q^{81} - 158909 q^{82} - 105203 q^{83} - 357682 q^{84} - 87212 q^{85} + 14792 q^{86} + 181200 q^{87} - 461824 q^{88} - 62682 q^{89} - 522670 q^{90} - 295304 q^{91} + 183783 q^{92} - 238430 q^{93} + 7259 q^{94} - 305340 q^{95} - 162399 q^{96} + 108383 q^{97} + 354656 q^{98} - 270499 q^{99}+O(q^{100}) \) 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9 - 17 * q^10 + 745 * q^11 + 4627 * q^12 + 1917 * q^13 + 1936 * q^14 + 1688 * q^15 + 5354 * q^16 + 4017 * q^17 - 2725 * q^18 - 2404 * q^19 + 1311 * q^20 - 228 * q^21 - 5836 * q^22 + 1733 * q^23 - 10711 * q^24 + 7120 * q^25 - 1484 * q^26 - 2324 * q^27 - 15028 * q^28 + 6996 * q^29 - 48420 * q^30 - 4899 * q^31 - 7554 * q^32 - 15734 * q^33 - 27033 * q^34 + 7084 * q^35 + 4433 * q^36 + 1466 * q^37 + 13905 * q^38 - 26542 * q^39 - 93211 * q^40 + 10297 * q^41 - 37642 * q^42 + 18490 * q^43 - 36140 * q^44 + 73822 * q^45 + 17991 * q^46 + 48592 * q^47 + 83607 * q^48 + 29458 * q^49 + 983 * q^50 + 92972 * q^51 + 14232 * q^52 + 127165 * q^53 - 92002 * q^54 + 106672 * q^55 - 7780 * q^56 + 34060 * q^57 - 10305 * q^58 + 99372 * q^59 + 111372 * q^60 + 17408 * q^61 + 28265 * q^62 + 2244 * q^63 + 47202 * q^64 + 54484 * q^65 - 150292 * q^66 - 2021 * q^67 + 192151 * q^68 + 1654 * q^69 - 33194 * q^70 + 11286 * q^71 - 298365 * q^72 + 49892 * q^73 - 125431 * q^74 - 44662 * q^75 - 249803 * q^76 + 98144 * q^77 - 28494 * q^78 - 91524 * q^79 + 12251 * q^80 - 26450 * q^81 - 158909 * q^82 - 105203 * q^83 - 357682 * q^84 - 87212 * q^85 + 14792 * q^86 + 181200 * q^87 - 461824 * q^88 - 62682 * q^89 - 522670 * q^90 - 295304 * q^91 + 183783 * q^92 - 238430 * q^93 + 7259 * q^94 - 305340 * q^95 - 162399 * q^96 + 108383 * q^97 + 354656 * q^98 - 270499 * q^99

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