LMFDB - Embedded newform 483.6.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,6,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("483.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	483.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:	$77.4653849697$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 268 x^{10} + 83 x^{9} + 25315 x^{8} + 5134 x^{7} - 993368 x^{6} - 511968 x^{5} + \cdots + 102912 $ x^12 - x^11 - 268x^10 + 83x^9 + 25315x^8 + 5134x^7 - 993368x^6 - 511968x^5 + 14212480x^4 + 10085312x^3 - 18833856x^2 + 3290240x + 102912
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-9.71327$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.71327 q^{2} +9.00000 q^{3} +62.3475 q^{4} -24.4259 q^{5} +87.4194 q^{6} -49.0000 q^{7} +294.774 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+9.71327 q^{2} +9.00000 q^{3} +62.3475 q^{4} -24.4259 q^{5} +87.4194 q^{6} -49.0000 q^{7} +294.774 q^{8} +81.0000 q^{9} -237.255 q^{10} -694.439 q^{11} +561.128 q^{12} -607.084 q^{13} -475.950 q^{14} -219.833 q^{15} +868.093 q^{16} +24.5702 q^{17} +786.774 q^{18} -2220.22 q^{19} -1522.89 q^{20} -441.000 q^{21} -6745.27 q^{22} +529.000 q^{23} +2652.96 q^{24} -2528.38 q^{25} -5896.76 q^{26} +729.000 q^{27} -3055.03 q^{28} +4169.08 q^{29} -2135.30 q^{30} +3082.77 q^{31} -1000.74 q^{32} -6249.95 q^{33} +238.657 q^{34} +1196.87 q^{35} +5050.15 q^{36} -7947.41 q^{37} -21565.6 q^{38} -5463.75 q^{39} -7200.11 q^{40} +1851.91 q^{41} -4283.55 q^{42} -4462.71 q^{43} -43296.6 q^{44} -1978.50 q^{45} +5138.32 q^{46} +20689.2 q^{47} +7812.84 q^{48} +2401.00 q^{49} -24558.8 q^{50} +221.132 q^{51} -37850.2 q^{52} +32752.2 q^{53} +7080.97 q^{54} +16962.3 q^{55} -14443.9 q^{56} -19982.0 q^{57} +40495.4 q^{58} -11969.8 q^{59} -13706.0 q^{60} +27223.3 q^{61} +29943.8 q^{62} -3969.00 q^{63} -37499.4 q^{64} +14828.6 q^{65} -60707.4 q^{66} -42452.4 q^{67} +1531.89 q^{68} +4761.00 q^{69} +11625.5 q^{70} -14585.7 q^{71} +23876.7 q^{72} -13235.6 q^{73} -77195.3 q^{74} -22755.4 q^{75} -138425. q^{76} +34027.5 q^{77} -53070.9 q^{78} +33905.5 q^{79} -21203.9 q^{80} +6561.00 q^{81} +17988.1 q^{82} -20420.5 q^{83} -27495.3 q^{84} -600.150 q^{85} -43347.5 q^{86} +37521.7 q^{87} -204702. q^{88} -61538.5 q^{89} -19217.7 q^{90} +29747.1 q^{91} +32981.8 q^{92} +27744.9 q^{93} +200960. q^{94} +54230.9 q^{95} -9006.62 q^{96} -100979. q^{97} +23321.6 q^{98} -56249.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + 108 q^{3} + 153 q^{4} - 162 q^{5} - 9 q^{6} - 588 q^{7} - 492 q^{8} + 972 q^{9}+O(q^{10}) $ 12 * q - q^2 + 108 * q^3 + 153 * q^4 - 162 * q^5 - 9 * q^6 - 588 * q^7 - 492 * q^8 + 972 * q^9	\( 12 q - q^{2} + 108 q^{3} + 153 q^{4} - 162 q^{5} - 9 q^{6} - 588 q^{7} - 492 q^{8} + 972 q^{9} + 528 q^{10} - 1425 q^{11} + 1377 q^{12} - 70 q^{13} + 49 q^{14} - 1458 q^{15} + 3865 q^{16} - 398 q^{17} - 81 q^{18} - 1293 q^{19} - 8593 q^{20} - 5292 q^{21} + 4961 q^{22} + 6348 q^{23} - 4428 q^{24} + 5830 q^{25} - 5187 q^{26} + 8748 q^{27} - 7497 q^{28} - 5127 q^{29} + 4752 q^{30} + 6498 q^{31} - 28485 q^{32} - 12825 q^{33} - 14527 q^{34} + 7938 q^{35} + 12393 q^{36} - 35545 q^{37} - 32617 q^{38} - 630 q^{39} + 35789 q^{40} - 7806 q^{41} + 441 q^{42} - 66142 q^{43} - 83253 q^{44} - 13122 q^{45} - 529 q^{46} - 16432 q^{47} + 34785 q^{48} + 28812 q^{49} - 177328 q^{50} - 3582 q^{51} - 187010 q^{52} - 67456 q^{53} - 729 q^{54} - 10453 q^{55} + 24108 q^{56} - 11637 q^{57} - 92677 q^{58} - 36346 q^{59} - 77337 q^{60} - 8768 q^{61} - 141813 q^{62} - 47628 q^{63} - 24604 q^{64} + 121875 q^{65} + 44649 q^{66} - 123617 q^{67} + 17217 q^{68} + 57132 q^{69} - 25872 q^{70} - 108667 q^{71} - 39852 q^{72} - 107406 q^{73} - 87825 q^{74} + 52470 q^{75} + 120191 q^{76} + 69825 q^{77} - 46683 q^{78} - 39470 q^{79} - 513682 q^{80} + 78732 q^{81} + 150219 q^{82} - 181838 q^{83} - 67473 q^{84} - 52633 q^{85} + 125713 q^{86} - 46143 q^{87} + 120642 q^{88} - 277361 q^{89} + 42768 q^{90} + 3430 q^{91} + 80937 q^{92} + 58482 q^{93} - 40880 q^{94} - 272491 q^{95} - 256365 q^{96} - 169005 q^{97} - 2401 q^{98} - 115425 q^{99}+O(q^{100}) \) 12 * q - q^2 + 108 * q^3 + 153 * q^4 - 162 * q^5 - 9 * q^6 - 588 * q^7 - 492 * q^8 + 972 * q^9 + 528 * q^10 - 1425 * q^11 + 1377 * q^12 - 70 * q^13 + 49 * q^14 - 1458 * q^15 + 3865 * q^16 - 398 * q^17 - 81 * q^18 - 1293 * q^19 - 8593 * q^20 - 5292 * q^21 + 4961 * q^22 + 6348 * q^23 - 4428 * q^24 + 5830 * q^25 - 5187 * q^26 + 8748 * q^27 - 7497 * q^28 - 5127 * q^29 + 4752 * q^30 + 6498 * q^31 - 28485 * q^32 - 12825 * q^33 - 14527 * q^34 + 7938 * q^35 + 12393 * q^36 - 35545 * q^37 - 32617 * q^38 - 630 * q^39 + 35789 * q^40 - 7806 * q^41 + 441 * q^42 - 66142 * q^43 - 83253 * q^44 - 13122 * q^45 - 529 * q^46 - 16432 * q^47 + 34785 * q^48 + 28812 * q^49 - 177328 * q^50 - 3582 * q^51 - 187010 * q^52 - 67456 * q^53 - 729 * q^54 - 10453 * q^55 + 24108 * q^56 - 11637 * q^57 - 92677 * q^58 - 36346 * q^59 - 77337 * q^60 - 8768 * q^61 - 141813 * q^62 - 47628 * q^63 - 24604 * q^64 + 121875 * q^65 + 44649 * q^66 - 123617 * q^67 + 17217 * q^68 + 57132 * q^69 - 25872 * q^70 - 108667 * q^71 - 39852 * q^72 - 107406 * q^73 - 87825 * q^74 + 52470 * q^75 + 120191 * q^76 + 69825 * q^77 - 46683 * q^78 - 39470 * q^79 - 513682 * q^80 + 78732 * q^81 + 150219 * q^82 - 181838 * q^83 - 67473 * q^84 - 52633 * q^85 + 125713 * q^86 - 46143 * q^87 + 120642 * q^88 - 277361 * q^89 + 42768 * q^90 + 3430 * q^91 + 80937 * q^92 + 58482 * q^93 - 40880 * q^94 - 272491 * q^95 - 256365 * q^96 - 169005 * q^97 - 2401 * q^98 - 115425 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	9.71327	1.71708	0.858539	−	0.512747i	$-0.171372\pi$
$2$	9.71327	1.71708	0.858539	+	0.512747i	$0.171372\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	62.3475	1.94836
$5$	−24.4259	−0.436944	−0.218472	−	0.975843i	$-0.570107\pi$
$5$	−24.4259	−0.436944	−0.218472	+	0.975843i	$0.570107\pi$
$6$	87.4194	0.991356
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	294.774	1.62841
$9$	81.0000	0.333333
$10$	−237.255	−0.750267
$11$	−694.439	−1.73042	−0.865212	−	0.501407i	$-0.832816\pi$
$11$	−694.439	−1.73042	−0.865212	+	0.501407i	$0.832816\pi$
$12$	561.128	1.12489
$13$	−607.084	−0.996300	−0.498150	−	0.867091i	$-0.665987\pi$
$13$	−607.084	−0.996300	−0.498150	+	0.867091i	$0.665987\pi$
$14$	−475.950	−0.648995
$15$	−219.833	−0.252269
$16$	868.093	0.847747
$17$	24.5702	0.0206199	0.0103100	−	0.999947i	$-0.496718\pi$
$17$	24.5702	0.0206199	0.0103100	+	0.999947i	$0.496718\pi$
$18$	786.774	0.572360
$19$	−2220.22	−1.41095	−0.705476	−	0.708734i	$-0.749267\pi$
$19$	−2220.22	−1.41095	−0.705476	+	0.708734i	$0.749267\pi$
$20$	−1522.89	−0.851323
$21$	−441.000	−0.218218
$22$	−6745.27	−2.97127
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	2652.96	0.940163
$25$	−2528.38	−0.809080
$26$	−5896.76	−1.71073
$27$	729.000	0.192450
$28$	−3055.03	−0.736411
$29$	4169.08	0.920546	0.460273	−	0.887778i	$-0.347752\pi$
$29$	4169.08	0.920546	0.460273	+	0.887778i	$0.347752\pi$
$30$	−2135.30	−0.433167
$31$	3082.77	0.576152	0.288076	−	0.957608i	$-0.406984\pi$
$31$	3082.77	0.576152	0.288076	+	0.957608i	$0.406984\pi$
$32$	−1000.74	−0.172760
$33$	−6249.95	−0.999060
$34$	238.657	0.0354060
$35$	1196.87	0.165149
$36$	5050.15	0.649453
$37$	−7947.41	−0.954381	−0.477190	−	0.878800i	$-0.658345\pi$
$37$	−7947.41	−0.954381	−0.477190	+	0.878800i	$0.658345\pi$
$38$	−21565.6	−2.42272
$39$	−5463.75	−0.575214
$40$	−7200.11	−0.711523
$41$	1851.91	0.172052	0.0860260	−	0.996293i	$-0.472583\pi$
$41$	1851.91	0.172052	0.0860260	+	0.996293i	$0.472583\pi$
$42$	−4283.55	−0.374697
$43$	−4462.71	−0.368067	−0.184034	−	0.982920i	$-0.558916\pi$
$43$	−4462.71	−0.368067	−0.184034	+	0.982920i	$0.558916\pi$
$44$	−43296.6	−3.37149
$45$	−1978.50	−0.145648
$46$	5138.32	0.358036
$47$	20689.2	1.36615	0.683077	−	0.730347i	$-0.260641\pi$
$47$	20689.2	1.36615	0.683077	+	0.730347i	$0.260641\pi$
$48$	7812.84	0.489447
$49$	2401.00	0.142857
$50$	−24558.8	−1.38925
$51$	221.132	0.0119049
$52$	−37850.2	−1.94115
$53$	32752.2	1.60159	0.800793	−	0.598941i	$-0.204412\pi$
$53$	32752.2	1.60159	0.800793	+	0.598941i	$0.204412\pi$
$54$	7080.97	0.330452
$55$	16962.3	0.756097
$56$	−14443.9	−0.615481
$57$	−19982.0	−0.814613
$58$	40495.4	1.58065
$59$	−11969.8	−0.447668	−0.223834	−	0.974627i	$-0.571857\pi$
$59$	−11969.8	−0.447668	−0.223834	+	0.974627i	$0.571857\pi$
$60$	−13706.0	−0.491512
$61$	27223.3	0.936735	0.468368	−	0.883534i	$-0.344842\pi$
$61$	27223.3	0.936735	0.468368	+	0.883534i	$0.344842\pi$
$62$	29943.8	0.989299
$63$	−3969.00	−0.125988
$64$	−37499.4	−1.14439
$65$	14828.6	0.435327
$66$	−60707.4	−1.71547
$67$	−42452.4	−1.15535	−0.577677	−	0.816266i	$-0.696041\pi$
$67$	−42452.4	−1.15535	−0.577677	+	0.816266i	$0.696041\pi$
$68$	1531.89	0.0401750
$69$	4761.00	0.120386
$70$	11625.5	0.283574
$71$	−14585.7	−0.343384	−0.171692	−	0.985151i	$-0.554923\pi$
$71$	−14585.7	−0.343384	−0.171692	+	0.985151i	$0.554923\pi$
$72$	23876.7	0.542803
$73$	−13235.6	−0.290693	−0.145347	−	0.989381i	$-0.546430\pi$
$73$	−13235.6	−0.290693	−0.145347	+	0.989381i	$0.546430\pi$
$74$	−77195.3	−1.63875
$75$	−22755.4	−0.467123
$76$	−138425.	−2.74904
$77$	34027.5	0.654039
$78$	−53070.9	−0.987688
$79$	33905.5	0.611227	0.305613	−	0.952156i	$-0.401139\pi$
$79$	33905.5	0.611227	0.305613	+	0.952156i	$0.401139\pi$
$80$	−21203.9	−0.370418
$81$	6561.00	0.111111
$82$	17988.1	0.295427
$83$	−20420.5	−0.325366	−0.162683	−	0.986678i	$-0.552015\pi$
$83$	−20420.5	−0.325366	−0.162683	+	0.986678i	$0.552015\pi$
$84$	−27495.3	−0.425167
$85$	−600.150	−0.00900974
$86$	−43347.5	−0.632001
$87$	37521.7	0.531477
$88$	−204702.	−2.81784
$89$	−61538.5	−0.823516	−0.411758	−	0.911293i	$-0.635085\pi$
$89$	−61538.5	−0.823516	−0.411758	+	0.911293i	$0.635085\pi$
$90$	−19217.7	−0.250089
$91$	29747.1	0.376566
$92$	32981.8	0.406261
$93$	27744.9	0.332642
$94$	200960.	2.34579
$95$	54230.9	0.616506
$96$	−9006.62	−0.0997433
$97$	−100979.	−1.08968	−0.544841	−	0.838539i	$-0.683410\pi$
$97$	−100979.	−1.08968	−0.544841	+	0.838539i	$0.683410\pi$
$98$	23321.6	0.245297
$99$	−56249.6	−0.576808
$100$	−157638.	−1.57638
$101$	−10588.4	−0.103283	−0.0516413	−	0.998666i	$-0.516445\pi$
$101$	−10588.4	−0.103283	−0.0516413	+	0.998666i	$0.516445\pi$
$102$	2147.91	0.0204417
$103$	64506.0	0.599110	0.299555	−	0.954079i	$-0.403162\pi$
$103$	64506.0	0.599110	0.299555	+	0.954079i	$0.403162\pi$
$104$	−178952.	−1.62238
$105$	10771.8	0.0953489
$106$	318130.	2.75005
$107$	−76935.6	−0.649633	−0.324816	−	0.945777i	$-0.605303\pi$
$107$	−76935.6	−0.649633	−0.324816	+	0.945777i	$0.605303\pi$
$108$	45451.3	0.374962
$109$	175883.	1.41794	0.708969	−	0.705240i	$-0.249161\pi$
$109$	175883.	1.41794	0.708969	+	0.705240i	$0.249161\pi$
$110$	164759.	1.29828
$111$	−71526.7	−0.551012
$112$	−42536.6	−0.320418
$113$	−262496.	−1.93387	−0.966933	−	0.255030i	$-0.917915\pi$
$113$	−262496.	−1.93387	−0.966933	+	0.255030i	$0.917915\pi$
$114$	−194090.	−1.39876
$115$	−12921.3	−0.0911090
$116$	259932.	1.79355
$117$	−49173.8	−0.332100
$118$	−116266.	−0.768681
$119$	−1203.94	−0.00779360
$120$	−64800.9	−0.410798
$121$	321194.	1.99437
$122$	264427.	1.60845
$123$	16667.2	0.0993343
$124$	192203.	1.12255
$125$	138089.	0.790466
$126$	−38552.0	−0.216332
$127$	−43577.6	−0.239747	−0.119874	−	0.992789i	$-0.538249\pi$
$127$	−43577.6	−0.239747	−0.119874	+	0.992789i	$0.538249\pi$
$128$	−332218.	−1.79225
$129$	−40164.4	−0.212504
$130$	144034.	0.747490
$131$	73389.7	0.373643	0.186822	−	0.982394i	$-0.440181\pi$
$131$	73389.7	0.373643	0.186822	+	0.982394i	$0.440181\pi$
$132$	−389669.	−1.94653
$133$	108791.	0.533290
$134$	−412351.	−1.98383
$135$	−17806.5	−0.0840898
$136$	7242.65	0.0335777
$137$	−417358.	−1.89980	−0.949898	−	0.312560i	$-0.898814\pi$
$137$	−417358.	−1.89980	−0.949898	+	0.312560i	$0.898814\pi$
$138$	46244.9	0.206712
$139$	182292.	0.800257	0.400129	−	0.916459i	$-0.368965\pi$
$139$	182292.	0.800257	0.400129	+	0.916459i	$0.368965\pi$
$140$	74621.8	0.321770
$141$	186203.	0.788749
$142$	−141674.	−0.589618
$143$	421582.	1.72402
$144$	70315.5	0.282582
$145$	−101833.	−0.402226
$146$	−128560.	−0.499143
$147$	21609.0	0.0824786
$148$	−495502.	−1.85948
$149$	−181683.	−0.670423	−0.335211	−	0.942143i	$-0.608808\pi$
$149$	−181683.	−0.670423	−0.335211	+	0.942143i	$0.608808\pi$
$150$	−221029.	−0.802087
$151$	−103680.	−0.370044	−0.185022	−	0.982734i	$-0.559236\pi$
$151$	−103680.	−0.370044	−0.185022	+	0.982734i	$0.559236\pi$
$152$	−654462.	−2.29761
$153$	1990.19	0.00687331
$154$	330518.	1.12304
$155$	−75299.4	−0.251746
$156$	−340651.	−1.12072
$157$	85205.4	0.275879	0.137939	−	0.990441i	$-0.455952\pi$
$157$	85205.4	0.275879	0.137939	+	0.990441i	$0.455952\pi$
$158$	329333.	1.04952
$159$	294769.	0.924676
$160$	24443.9	0.0754866
$161$	−25921.0	−0.0788110
$162$	63728.7	0.190787
$163$	168099.	0.495560	0.247780	−	0.968816i	$-0.420299\pi$
$163$	168099.	0.495560	0.247780	+	0.968816i	$0.420299\pi$
$164$	115462.	0.335219
$165$	152661.	0.436533
$166$	−198350.	−0.558679
$167$	595901.	1.65342	0.826710	−	0.562629i	$-0.190210\pi$
$167$	595901.	1.65342	0.826710	+	0.562629i	$0.190210\pi$
$168$	−129995.	−0.355348
$169$	−2742.61	−0.00738664
$170$	−5829.41	−0.0154704
$171$	−179838.	−0.470317
$172$	−278239.	−0.717128
$173$	−704061.	−1.78853	−0.894263	−	0.447543i	$-0.852299\pi$
$173$	−704061.	−1.78853	−0.894263	+	0.447543i	$0.852299\pi$
$174$	364458.	0.912588
$175$	123890.	0.305804
$176$	−602838.	−1.46696
$177$	−107728.	−0.258461
$178$	−597740.	−1.41404
$179$	235733.	0.549905	0.274953	−	0.961458i	$-0.411338\pi$
$179$	235733.	0.549905	0.274953	+	0.961458i	$0.411338\pi$
$180$	−123354.	−0.283774
$181$	−545218.	−1.23701	−0.618505	−	0.785781i	$-0.712261\pi$
$181$	−545218.	−1.23701	−0.618505	+	0.785781i	$0.712261\pi$
$182$	288941.	0.646593
$183$	245010.	0.540824
$184$	155935.	0.339547
$185$	194123.	0.417010
$186$	269494.	0.571172
$187$	−17062.5	−0.0356812
$188$	1.28992e6	2.66176
$189$	−35721.0	−0.0727393
$190$	526759.	1.05859
$191$	−4001.73	−0.00793714	−0.00396857	−	0.999992i	$-0.501263\pi$
$191$	−4001.73	−0.00793714	−0.00396857	+	0.999992i	$0.501263\pi$
$192$	−337495.	−0.660714
$193$	−790814.	−1.52820	−0.764102	−	0.645096i	$-0.776817\pi$
$193$	−790814.	−1.52820	−0.764102	+	0.645096i	$0.776817\pi$
$194$	−980832.	−1.87107
$195$	133457.	0.251336
$196$	149696.	0.278337
$197$	404405.	0.742423	0.371212	−	0.928548i	$-0.378942\pi$
$197$	404405.	0.742423	0.371212	+	0.928548i	$0.378942\pi$
$198$	−546367.	−0.990425
$199$	136151.	0.243719	0.121860	−	0.992547i	$-0.461114\pi$
$199$	136151.	0.243719	0.121860	+	0.992547i	$0.461114\pi$
$200$	−745298.	−1.31751
$201$	−382071.	−0.667044
$202$	−102848.	−0.177344
$203$	−204285.	−0.347934
$204$	13787.0	0.0231951
$205$	−45234.5	−0.0751770
$206$	626564.	1.02872
$207$	42849.0	0.0695048
$208$	−527005.	−0.844610
$209$	1.54181e6	2.44154
$210$	104630.	0.163722
$211$	−1.03970e6	−1.60768	−0.803841	−	0.594844i	$-0.797214\pi$
$211$	−1.03970e6	−1.60768	−0.803841	+	0.594844i	$0.797214\pi$
$212$	2.04202e6	3.12047
$213$	−131271.	−0.198253
$214$	−747296.	−1.11547
$215$	109006.	0.160825
$216$	214890.	0.313388
$217$	−151056.	−0.217765
$218$	1.70840e6	2.43471
$219$	−119120.	−0.167832
$220$	1.05756e6	1.47315
$221$	−14916.2	−0.0205436
$222$	−694758.	−0.946131
$223$	960229.	1.29304	0.646521	−	0.762896i	$-0.276223\pi$
$223$	960229.	1.29304	0.646521	+	0.762896i	$0.276223\pi$
$224$	49036.0	0.0652973
$225$	−204798.	−0.269693
$226$	−2.54969e6	−3.32060
$227$	−258639.	−0.333141	−0.166571	−	0.986030i	$-0.553269\pi$
$227$	−258639.	−0.333141	−0.166571	+	0.986030i	$0.553269\pi$
$228$	−1.24583e6	−1.58716
$229$	760058.	0.957763	0.478882	−	0.877879i	$-0.341042\pi$
$229$	760058.	0.957763	0.478882	+	0.877879i	$0.341042\pi$
$230$	−125508.	−0.156441
$231$	306248.	0.377609
$232$	1.22893e6	1.49902
$233$	641740.	0.774407	0.387204	−	0.921994i	$-0.373441\pi$
$233$	641740.	0.774407	0.387204	+	0.921994i	$0.373441\pi$
$234$	−477638.	−0.570242
$235$	−505353.	−0.596932
$236$	−746285.	−0.872218
$237$	305149.	0.352892
$238$	−11694.2	−0.0133822
$239$	−889771.	−1.00759	−0.503794	−	0.863824i	$-0.668063\pi$
$239$	−889771.	−1.00759	−0.503794	+	0.863824i	$0.668063\pi$
$240$	−190835.	−0.213861
$241$	1.28515e6	1.42532	0.712660	−	0.701509i	$-0.247490\pi$
$241$	1.28515e6	1.42532	0.712660	+	0.701509i	$0.247490\pi$
$242$	3.11985e6	3.42448
$243$	59049.0	0.0641500
$244$	1.69731e6	1.82510
$245$	−58646.6	−0.0624205
$246$	161893.	0.170565
$247$	1.34786e6	1.40573
$248$	908720.	0.938211
$249$	−183785.	−0.187850
$250$	1.34129e6	1.35729
$251$	1.53967e6	1.54256	0.771282	−	0.636493i	$-0.219616\pi$
$251$	1.53967e6	1.54256	0.771282	+	0.636493i	$0.219616\pi$
$252$	−247457.	−0.245470
$253$	−367358.	−0.360818
$254$	−423281.	−0.411665
$255$	−5401.35	−0.00520177
$256$	−2.02694e6	−1.93304
$257$	−582103.	−0.549752	−0.274876	−	0.961480i	$-0.588637\pi$
$257$	−582103.	−0.549752	−0.274876	+	0.961480i	$0.588637\pi$
$258$	−390127.	−0.364886
$259$	389423.	0.360722
$260$	924524.	0.848173
$261$	337696.	0.306849
$262$	712854.	0.641575
$263$	−1.52609e6	−1.36048	−0.680239	−	0.732990i	$-0.738124\pi$
$263$	−1.52609e6	−1.36048	−0.680239	+	0.732990i	$0.738124\pi$
$264$	−1.84232e6	−1.62688
$265$	−800001.	−0.699803
$266$	1.05671e6	0.915700
$267$	−553846.	−0.475457
$268$	−2.64680e6	−2.25104
$269$	−1.55509e6	−1.31031	−0.655156	−	0.755494i	$-0.727397\pi$
$269$	−1.55509e6	−1.31031	−0.655156	+	0.755494i	$0.727397\pi$
$270$	−172959.	−0.144389
$271$	−1.20709e6	−0.998428	−0.499214	−	0.866479i	$-0.666378\pi$
$271$	−1.20709e6	−0.998428	−0.499214	+	0.866479i	$0.666378\pi$
$272$	21329.2	0.0174805
$273$	267724.	0.217410
$274$	−4.05391e6	−3.26210
$275$	1.75580e6	1.40005
$276$	296837.	0.234555
$277$	26676.4	0.0208895	0.0104447	−	0.999945i	$-0.496675\pi$
$277$	26676.4	0.0208895	0.0104447	+	0.999945i	$0.496675\pi$
$278$	1.77065e6	1.37411
$279$	249705.	0.192051
$280$	352805.	0.268930
$281$	−153418.	−0.115907	−0.0579537	−	0.998319i	$-0.518458\pi$
$281$	−153418.	−0.115907	−0.0579537	+	0.998319i	$0.518458\pi$
$282$	1.80864e6	1.35434
$283$	−1.34775e6	−1.00033	−0.500166	−	0.865930i	$-0.666728\pi$
$283$	−1.34775e6	−1.00033	−0.500166	+	0.865930i	$0.666728\pi$
$284$	−909380.	−0.669036
$285$	488078.	0.355940
$286$	4.09494e6	2.96028
$287$	−90743.5	−0.0650295
$288$	−81059.6	−0.0575868
$289$	−1.41925e6	−0.999575
$290$	−989136.	−0.690655
$291$	−908807.	−0.629128
$292$	−825204.	−0.566375
$293$	1.37722e6	0.937206	0.468603	−	0.883409i	$-0.344758\pi$
$293$	1.37722e6	0.937206	0.468603	+	0.883409i	$0.344758\pi$
$294$	209894.	0.141622
$295$	292372.	0.195605
$296$	−2.34269e6	−1.55412
$297$	−506246.	−0.333020
$298$	−1.76474e6	−1.15117
$299$	−321147.	−0.207743
$300$	−1.41874e6	−0.910123
$301$	218673.	0.139116
$302$	−1.00707e6	−0.635395
$303$	−95295.7	−0.0596303
$304$	−1.92736e6	−1.19613
$305$	−664954.	−0.409300
$306$	19331.2	0.0118020
$307$	−6739.60	−0.00408120	−0.00204060	−	0.999998i	$-0.500650\pi$
$307$	−6739.60	−0.00408120	−0.00204060	+	0.999998i	$0.500650\pi$
$308$	2.12153e6	1.27430
$309$	580554.	0.345897
$310$	−731403.	−0.432268
$311$	1.81172e6	1.06216	0.531080	−	0.847322i	$-0.321786\pi$
$311$	1.81172e6	1.06216	0.531080	+	0.847322i	$0.321786\pi$
$312$	−1.61057e6	−0.936684
$313$	−817437.	−0.471621	−0.235811	−	0.971799i	$-0.575774\pi$
$313$	−817437.	−0.471621	−0.235811	+	0.971799i	$0.575774\pi$
$314$	827623.	0.473706
$315$	96946.3	0.0550497
$316$	2.11392e6	1.19089
$317$	−869294.	−0.485868	−0.242934	−	0.970043i	$-0.578110\pi$
$317$	−869294.	−0.485868	−0.242934	+	0.970043i	$0.578110\pi$
$318$	2.86317e6	1.58774
$319$	−2.89517e6	−1.59293
$320$	915956.	0.500034
$321$	−692421.	−0.375066
$322$	−251778.	−0.135325
$323$	−54551.3	−0.0290937
$324$	409062.	0.216484
$325$	1.53494e6	0.806087
$326$	1.63279e6	0.850916
$327$	1.58294e6	0.818647
$328$	545893.	0.280171
$329$	−1.01377e6	−0.516358
$330$	1.48283e6	0.749562
$331$	1.52087e6	0.762996	0.381498	−	0.924370i	$-0.375408\pi$
$331$	1.52087e6	0.762996	0.381498	+	0.924370i	$0.375408\pi$
$332$	−1.27317e6	−0.633930
$333$	−643741.	−0.318127
$334$	5.78815e6	2.83905
$335$	1.03694e6	0.504824
$336$	−382829.	−0.184994
$337$	1.93539e6	0.928313	0.464157	−	0.885753i	$-0.346357\pi$
$337$	1.93539e6	0.928313	0.464157	+	0.885753i	$0.346357\pi$
$338$	−26639.7	−0.0126834
$339$	−2.36246e6	−1.11652
$340$	−37417.8	−0.0175542
$341$	−2.14080e6	−0.996987
$342$	−1.74681e6	−0.807572
$343$	−117649.	−0.0539949
$344$	−1.31549e6	−0.599364
$345$	−116292.	−0.0526018
$346$	−6.83873e6	−3.07104
$347$	2.21723e6	0.988525	0.494263	−	0.869313i	$-0.335438\pi$
$347$	2.21723e6	0.988525	0.494263	+	0.869313i	$0.335438\pi$
$348$	2.33939e6	1.03551
$349$	555811.	0.244266	0.122133	−	0.992514i	$-0.461026\pi$
$349$	555811.	0.244266	0.122133	+	0.992514i	$0.461026\pi$
$350$	1.20338e6	0.525089
$351$	−442564.	−0.191738
$352$	694950.	0.298949
$353$	−102589.	−0.0438193	−0.0219097	−	0.999760i	$-0.506975\pi$
$353$	−102589.	−0.0438193	−0.0219097	+	0.999760i	$0.506975\pi$
$354$	−1.04639e6	−0.443798
$355$	356268.	0.150039
$356$	−3.83677e6	−1.60450
$357$	−10835.5	−0.00449963
$358$	2.28974e6	0.944231
$359$	−2.12663e6	−0.870873	−0.435437	−	0.900219i	$-0.643406\pi$
$359$	−2.12663e6	−0.870873	−0.435437	+	0.900219i	$0.643406\pi$
$360$	−583209.	−0.237174
$361$	2.45328e6	0.990784
$362$	−5.29584e6	−2.12404
$363$	2.89075e6	1.15145
$364$	1.85466e6	0.733686
$365$	323290.	0.127017
$366$	2.37985e6	0.928638
$367$	768223.	0.297730	0.148865	−	0.988858i	$-0.452438\pi$
$367$	768223.	0.297730	0.148865	+	0.988858i	$0.452438\pi$
$368$	459221.	0.176768
$369$	150005.	0.0573507
$370$	1.88556e6	0.716040
$371$	−1.60486e6	−0.605343
$372$	1.72983e6	0.648106
$373$	−1.45341e6	−0.540897	−0.270449	−	0.962734i	$-0.587172\pi$
$373$	−1.45341e6	−0.540897	−0.270449	+	0.962734i	$0.587172\pi$
$374$	−165733.	−0.0612674
$375$	1.24280e6	0.456376
$376$	6.09864e6	2.22466
$377$	−2.53098e6	−0.917139
$378$	−346968.	−0.124899
$379$	−1.72245e6	−0.615956	−0.307978	−	0.951393i	$-0.599652\pi$
$379$	−1.72245e6	−0.615956	−0.307978	+	0.951393i	$0.599652\pi$
$380$	3.38116e6	1.20118
$381$	−392198.	−0.138418
$382$	−38869.8	−0.0136287
$383$	−4.55729e6	−1.58748	−0.793742	−	0.608254i	$-0.791870\pi$
$383$	−4.55729e6	−1.58748	−0.793742	+	0.608254i	$0.791870\pi$
$384$	−2.98996e6	−1.03476
$385$	−831152.	−0.285778
$386$	−7.68139e6	−2.62405
$387$	−361479.	−0.122689
$388$	−6.29576e6	−2.12309
$389$	1.61710e6	0.541830	0.270915	−	0.962603i	$-0.412674\pi$
$389$	1.61710e6	0.541830	0.270915	+	0.962603i	$0.412674\pi$
$390$	1.29630e6	0.431564
$391$	12997.7	0.00429955
$392$	707751.	0.232630
$393$	660508.	0.215723
$394$	3.92810e6	1.27480
$395$	−828172.	−0.267072
$396$	−3.50702e6	−1.12383
$397$	1.19216e6	0.379627	0.189814	−	0.981820i	$-0.439212\pi$
$397$	1.19216e6	0.379627	0.189814	+	0.981820i	$0.439212\pi$
$398$	1.32248e6	0.418485
$399$	979117.	0.307895
$400$	−2.19487e6	−0.685896
$401$	3.94687e6	1.22572	0.612861	−	0.790190i	$-0.290018\pi$
$401$	3.94687e6	1.22572	0.612861	+	0.790190i	$0.290018\pi$
$402$	−3.71116e6	−1.14537
$403$	−1.87150e6	−0.574020
$404$	−660161.	−0.201232
$405$	−160258.	−0.0485493
$406$	−1.98427e6	−0.597429
$407$	5.51899e6	1.65148
$408$	65183.9	0.0193861
$409$	2.77606e6	0.820581	0.410290	−	0.911955i	$-0.365427\pi$
$409$	2.77606e6	0.820581	0.410290	+	0.911955i	$0.365427\pi$
$410$	−439375.	−0.129085
$411$	−3.75622e6	−1.09685
$412$	4.02179e6	1.16728
$413$	586519.	0.169202
$414$	416204.	0.119345
$415$	498790.	0.142167
$416$	607530.	0.172121
$417$	1.64062e6	0.462029
$418$	1.49760e7	4.19232
$419$	−2.94300e6	−0.818945	−0.409473	−	0.912322i	$-0.634287\pi$
$419$	−2.94300e6	−0.818945	−0.409473	+	0.912322i	$0.634287\pi$
$420$	671596.	0.185774
$421$	−2.10693e6	−0.579356	−0.289678	−	0.957124i	$-0.593548\pi$
$421$	−2.10693e6	−0.579356	−0.289678	+	0.957124i	$0.593548\pi$
$422$	−1.00988e7	−2.76052
$423$	1.67583e6	0.455385
$424$	9.65447e6	2.60804
$425$	−62122.8	−0.0166832
$426$	−1.27507e6	−0.340416
$427$	−1.33394e6	−0.354053
$428$	−4.79675e6	−1.26572
$429$	3.79424e6	0.995364
$430$	1.05880e6	0.276149
$431$	−5.94270e6	−1.54096	−0.770479	−	0.637466i	$-0.779983\pi$
$431$	−5.94270e6	−1.54096	−0.770479	+	0.637466i	$0.779983\pi$
$432$	632840.	0.163149
$433$	5.96398e6	1.52868	0.764340	−	0.644814i	$-0.223065\pi$
$433$	5.96398e6	1.52868	0.764340	+	0.644814i	$0.223065\pi$
$434$	−1.46725e6	−0.373920
$435$	−916501.	−0.232226
$436$	1.09659e7	2.76265
$437$	−1.17450e6	−0.294204
$438$	−1.15704e6	−0.288180
$439$	4.44668e6	1.10122	0.550611	−	0.834762i	$-0.314395\pi$
$439$	4.44668e6	1.10122	0.550611	+	0.834762i	$0.314395\pi$
$440$	5.00003e6	1.23124
$441$	194481.	0.0476190
$442$	−144885.	−0.0352750
$443$	5.22779e6	1.26564	0.632818	−	0.774300i	$-0.281898\pi$
$443$	5.22779e6	1.26564	0.632818	+	0.774300i	$0.281898\pi$
$444$	−4.45951e6	−1.07357
$445$	1.50313e6	0.359830
$446$	9.32696e6	2.22026
$447$	−1.63515e6	−0.387069
$448$	1.83747e6	0.432539
$449$	−4.70020e6	−1.10027	−0.550136	−	0.835075i	$-0.685424\pi$
$449$	−4.70020e6	−1.10027	−0.550136	+	0.835075i	$0.685424\pi$
$450$	−1.98926e6	−0.463085
$451$	−1.28604e6	−0.297723
$452$	−1.63660e7	−3.76787
$453$	−933121.	−0.213645
$454$	−2.51222e6	−0.572030
$455$	−726599.	−0.164538
$456$	−5.89016e6	−1.32652
$457$	−1.54310e6	−0.345625	−0.172812	−	0.984955i	$-0.555285\pi$
$457$	−1.54310e6	−0.345625	−0.172812	+	0.984955i	$0.555285\pi$
$458$	7.38265e6	1.64456
$459$	17911.7	0.00396830
$460$	−805611.	−0.177513
$461$	2.71706e6	0.595452	0.297726	−	0.954651i	$-0.403772\pi$
$461$	2.71706e6	0.595452	0.297726	+	0.954651i	$0.403772\pi$
$462$	2.97466e6	0.648385
$463$	4.86328e6	1.05433	0.527165	−	0.849763i	$-0.323255\pi$
$463$	4.86328e6	1.05433	0.527165	+	0.849763i	$0.323255\pi$
$464$	3.61915e6	0.780390
$465$	−677695.	−0.145346
$466$	6.23339e6	1.32972
$467$	5.65007e6	1.19884	0.599421	−	0.800434i	$-0.295398\pi$
$467$	5.65007e6	1.19884	0.599421	+	0.800434i	$0.295398\pi$
$468$	−3.06586e6	−0.647050
$469$	2.08017e6	0.436683
$470$	−4.90862e6	−1.02498
$471$	766849.	0.159279
$472$	−3.52837e6	−0.728986
$473$	3.09908e6	0.636912
$474$	2.96400e6	0.605943
$475$	5.61355e6	1.14157
$476$	−75062.8	−0.0151847
$477$	2.65293e6	0.533862
$478$	−8.64258e6	−1.73011
$479$	7.92718e6	1.57863	0.789314	−	0.613989i	$-0.210436\pi$
$479$	7.92718e6	1.57863	0.789314	+	0.613989i	$0.210436\pi$
$480$	219995.	0.0435822
$481$	4.82474e6	0.950849
$482$	1.24830e7	2.44739
$483$	−233289.	−0.0455016
$484$	2.00257e7	3.88574
$485$	2.46649e6	0.476130
$486$	573559.	0.110151
$487$	3.54512e6	0.677343	0.338672	−	0.940905i	$-0.390022\pi$
$487$	3.54512e6	0.677343	0.338672	+	0.940905i	$0.390022\pi$
$488$	8.02472e6	1.52539
$489$	1.51289e6	0.286112
$490$	−569650.	−0.107181
$491$	−1.02629e7	−1.92117	−0.960585	−	0.277986i	$-0.910333\pi$
$491$	−1.02629e7	−1.92117	−0.960585	+	0.277986i	$0.910333\pi$
$492$	1.03916e6	0.193539
$493$	102435.	0.0189816
$494$	1.30921e7	2.41375
$495$	1.37395e6	0.252032
$496$	2.67613e6	0.488431
$497$	714697.	0.129787
$498$	−1.78515e6	−0.322553
$499$	2.48330e6	0.446455	0.223228	−	0.974766i	$-0.428341\pi$
$499$	2.48330e6	0.446455	0.223228	+	0.974766i	$0.428341\pi$
$500$	8.60949e6	1.54011
$501$	5.36311e6	0.954602
$502$	1.49552e7	2.64871
$503$	6.83608e6	1.20472	0.602361	−	0.798223i	$-0.294227\pi$
$503$	6.83608e6	1.20472	0.602361	+	0.798223i	$0.294227\pi$
$504$	−1.16996e6	−0.205160
$505$	258631.	0.0451287
$506$	−3.56825e6	−0.619553
$507$	−24683.5	−0.00426468
$508$	−2.71696e6	−0.467114
$509$	−7.26476e6	−1.24287	−0.621437	−	0.783464i	$-0.713451\pi$
$509$	−7.26476e6	−1.24287	−0.621437	+	0.783464i	$0.713451\pi$
$510$	−52464.7	−0.00893186
$511$	648542.	0.109872
$512$	−9.05724e6	−1.52694
$513$	−1.61854e6	−0.271538
$514$	−5.65412e6	−0.943967
$515$	−1.57562e6	−0.261777
$516$	−2.50415e6	−0.414034
$517$	−1.43674e7	−2.36402
$518$	3.78257e6	0.619388
$519$	−6.33655e6	−1.03261
$520$	4.37107e6	0.708890
$521$	−2.32584e6	−0.375393	−0.187696	−	0.982227i	$-0.560102\pi$
$521$	−2.32584e6	−0.375393	−0.187696	+	0.982227i	$0.560102\pi$
$522$	3.28013e6	0.526883
$523$	−4.59847e6	−0.735121	−0.367560	−	0.930000i	$-0.619807\pi$
$523$	−4.59847e6	−0.735121	−0.367560	+	0.930000i	$0.619807\pi$
$524$	4.57567e6	0.727992
$525$	1.11501e6	0.176556
$526$	−1.48233e7	−2.33605
$527$	75744.4	0.0118802
$528$	−5.42554e6	−0.846951
$529$	279841.	0.0434783
$530$	−7.77062e6	−1.20162
$531$	−969551.	−0.149223
$532$	6.78284e6	1.03904
$533$	−1.12426e6	−0.171415
$534$	−5.37966e6	−0.816397
$535$	1.87922e6	0.283853
$536$	−1.25138e7	−1.88139
$537$	2.12160e6	0.317488
$538$	−1.51050e7	−2.24991
$539$	−1.66735e6	−0.247203
$540$	−1.11019e6	−0.163837
$541$	−3.27189e6	−0.480624	−0.240312	−	0.970696i	$-0.577250\pi$
$541$	−3.27189e6	−0.480624	−0.240312	+	0.970696i	$0.577250\pi$
$542$	−1.17248e7	−1.71438
$543$	−4.90696e6	−0.714188
$544$	−24588.3	−0.00356231
$545$	−4.29609e6	−0.619559
$546$	2.60047e6	0.373311
$547$	−1.73465e6	−0.247881	−0.123941	−	0.992290i	$-0.539553\pi$
$547$	−1.73465e6	−0.247881	−0.123941	+	0.992290i	$0.539553\pi$
$548$	−2.60212e7	−3.70149
$549$	2.20509e6	0.312245
$550$	1.70546e7	2.40400
$551$	−9.25628e6	−1.29885
$552$	1.40342e6	0.196037
$553$	−1.66137e6	−0.231022
$554$	259115.	0.0358689
$555$	1.74710e6	0.240761
$556$	1.13654e7	1.55919
$557$	2.41024e6	0.329172	0.164586	−	0.986363i	$-0.447371\pi$
$557$	2.41024e6	0.329172	0.164586	+	0.986363i	$0.447371\pi$
$558$	2.42545e6	0.329766
$559$	2.70924e6	0.366705
$560$	1.03899e6	0.140005
$561$	−153563.	−0.0206005
$562$	−1.49019e6	−0.199022
$563$	−9.02516e6	−1.20001	−0.600004	−	0.799997i	$-0.704834\pi$
$563$	−9.02516e6	−1.20001	−0.600004	+	0.799997i	$0.704834\pi$
$564$	1.16093e7	1.53677
$565$	6.41170e6	0.844990
$566$	−1.30911e7	−1.71765
$567$	−321489.	−0.0419961
$568$	−4.29947e6	−0.559170
$569$	−2.97301e6	−0.384961	−0.192480	−	0.981301i	$-0.561653\pi$
$569$	−2.97301e6	−0.384961	−0.192480	+	0.981301i	$0.561653\pi$
$570$	4.74083e6	0.611177
$571$	4.51157e6	0.579079	0.289539	−	0.957166i	$-0.406498\pi$
$571$	4.51157e6	0.579079	0.289539	+	0.957166i	$0.406498\pi$
$572$	2.62846e7	3.35901
$573$	−36015.5	−0.00458251
$574$	−881416.	−0.111661
$575$	−1.33751e6	−0.168705
$576$	−3.03745e6	−0.381464
$577$	1.35945e7	1.69990	0.849952	−	0.526860i	$-0.176631\pi$
$577$	1.35945e7	1.69990	0.849952	+	0.526860i	$0.176631\pi$
$578$	−1.37856e7	−1.71635
$579$	−7.11733e6	−0.882309
$580$	−6.34907e6	−0.783682
$581$	1.00061e6	0.122977
$582$	−8.82748e6	−1.08026
$583$	−2.27444e7	−2.77142
$584$	−3.90149e6	−0.473367
$585$	1.20111e6	0.145109
$586$	1.33773e7	1.60926
$587$	−5.29320e6	−0.634049	−0.317025	−	0.948417i	$-0.602684\pi$
$587$	−5.29320e6	−0.634049	−0.317025	+	0.948417i	$0.602684\pi$
$588$	1.34727e6	0.160698
$589$	−6.84443e6	−0.812923
$590$	2.83989e6	0.335870
$591$	3.63965e6	0.428638
$592$	−6.89910e6	−0.809073
$593$	−1.07744e7	−1.25822	−0.629110	−	0.777316i	$-0.716581\pi$
$593$	−1.07744e7	−1.25822	−0.629110	+	0.777316i	$0.716581\pi$
$594$	−4.91730e6	−0.571822
$595$	29407.3	0.00340536
$596$	−1.13275e7	−1.30622
$597$	1.22536e6	0.140711
$598$	−3.11939e6	−0.356711
$599$	1.05745e7	1.20419	0.602094	−	0.798425i	$-0.294333\pi$
$599$	1.05745e7	1.20419	0.602094	+	0.798425i	$0.294333\pi$
$600$	−6.70769e6	−0.760667
$601$	2.14026e6	0.241702	0.120851	−	0.992671i	$-0.461438\pi$
$601$	2.14026e6	0.241702	0.120851	+	0.992671i	$0.461438\pi$
$602$	2.12403e6	0.238874
$603$	−3.43864e6	−0.385118
$604$	−6.46420e6	−0.720979
$605$	−7.84546e6	−0.871425
$606$	−925632.	−0.102390
$607$	3.08757e6	0.340130	0.170065	−	0.985433i	$-0.445602\pi$
$607$	3.08757e6	0.340130	0.170065	+	0.985433i	$0.445602\pi$
$608$	2.22185e6	0.243757
$609$	−1.83856e6	−0.200880
$610$	−6.45888e6	−0.702801
$611$	−1.25601e7	−1.36110
$612$	124083.	0.0133917
$613$	−1.62648e7	−1.74823	−0.874115	−	0.485718i	$-0.838558\pi$
$613$	−1.62648e7	−1.74823	−0.874115	+	0.485718i	$0.838558\pi$
$614$	−65463.5	−0.00700775
$615$	−407110.	−0.0434035
$616$	1.00304e7	1.06504
$617$	−1.20213e7	−1.27127	−0.635636	−	0.771989i	$-0.719262\pi$
$617$	−1.20213e7	−1.27127	−0.635636	+	0.771989i	$0.719262\pi$
$618$	5.63907e6	0.593932
$619$	−1.29673e7	−1.36026	−0.680131	−	0.733091i	$-0.738077\pi$
$619$	−1.29673e7	−1.36026	−0.680131	+	0.733091i	$0.738077\pi$
$620$	−4.69473e6	−0.490492
$621$	385641.	0.0401286
$622$	1.75977e7	1.82381
$623$	3.01539e6	0.311260
$624$	−4.74304e6	−0.487636
$625$	4.52824e6	0.463691
$626$	−7.93998e6	−0.809811
$627$	1.38763e7	1.40963
$628$	5.31235e6	0.537511
$629$	−195270.	−0.0196792
$630$	941666.	0.0945247
$631$	−1.07707e7	−1.07689	−0.538443	−	0.842662i	$-0.680987\pi$
$631$	−1.07707e7	−1.07689	−0.538443	+	0.842662i	$0.680987\pi$
$632$	9.99444e6	0.995327
$633$	−9.35727e6	−0.928196
$634$	−8.44368e6	−0.834274
$635$	1.06442e6	0.104756
$636$	1.83781e7	1.80160
$637$	−1.45761e6	−0.142329
$638$	−2.81216e7	−2.73519
$639$	−1.18144e6	−0.114461
$640$	8.11472e6	0.783111
$641$	1.33079e7	1.27928	0.639639	−	0.768675i	$-0.279084\pi$
$641$	1.33079e7	1.27928	0.639639	+	0.768675i	$0.279084\pi$
$642$	−6.72567e6	−0.644018
$643$	−1.68269e7	−1.60501	−0.802504	−	0.596646i	$-0.796500\pi$
$643$	−1.68269e7	−1.60501	−0.802504	+	0.596646i	$0.796500\pi$
$644$	−1.61611e6	−0.153552
$645$	981050.	0.0928521
$646$	−529871.	−0.0499562
$647$	−1.68285e7	−1.58047	−0.790234	−	0.612805i	$-0.790041\pi$
$647$	−1.68285e7	−1.58047	−0.790234	+	0.612805i	$0.790041\pi$
$648$	1.93401e6	0.180934
$649$	8.31227e6	0.774655
$650$	1.49092e7	1.38411
$651$	−1.35950e6	−0.125727
$652$	1.04806e7	0.965530
$653$	−1.51611e7	−1.39139	−0.695694	−	0.718338i	$-0.744903\pi$
$653$	−1.51611e7	−1.39139	−0.695694	+	0.718338i	$0.744903\pi$
$654$	1.53756e7	1.40568
$655$	−1.79261e6	−0.163261
$656$	1.60763e6	0.145857
$657$	−1.07208e6	−0.0968977
$658$	−9.84704e6	−0.886627
$659$	−1.79332e7	−1.60859	−0.804294	−	0.594232i	$-0.797456\pi$
$659$	−1.79332e7	−1.60859	−0.804294	+	0.594232i	$0.797456\pi$
$660$	9.51801e6	0.850523
$661$	−1.47974e7	−1.31729	−0.658645	−	0.752454i	$-0.728870\pi$
$661$	−1.47974e7	−1.31729	−0.658645	+	0.752454i	$0.728870\pi$
$662$	1.47726e7	1.31012
$663$	−134246.	−0.0118609
$664$	−6.01944e6	−0.529829
$665$	−2.65731e6	−0.233017
$666$	−6.25282e6	−0.546249
$667$	2.20544e6	0.191947
$668$	3.71530e7	3.22146
$669$	8.64206e6	0.746538
$670$	1.00720e7	0.866823
$671$	−1.89049e7	−1.62095
$672$	441324.	0.0376994
$673$	−4.92979e6	−0.419557	−0.209778	−	0.977749i	$-0.567274\pi$
$673$	−4.92979e6	−0.419557	−0.209778	+	0.977749i	$0.567274\pi$
$674$	1.87990e7	1.59399
$675$	−1.84319e6	−0.155708
$676$	−170995.	−0.0143918
$677$	1.04172e7	0.873534	0.436767	−	0.899575i	$-0.356123\pi$
$677$	1.04172e7	0.873534	0.436767	+	0.899575i	$0.356123\pi$
$678$	−2.29472e7	−1.91715
$679$	4.94795e6	0.411861
$680$	−176908.	−0.0146715
$681$	−2.32775e6	−0.192339
$682$	−2.07941e7	−1.71191
$683$	−1.53748e7	−1.26112	−0.630560	−	0.776141i	$-0.717175\pi$
$683$	−1.53748e7	−1.26112	−0.630560	+	0.776141i	$0.717175\pi$
$684$	−1.12124e7	−0.916347
$685$	1.01943e7	0.830104
$686$	−1.14276e6	−0.0927135
$687$	6.84053e6	0.552965
$688$	−3.87405e6	−0.312028
$689$	−1.98833e7	−1.59566
$690$	−1.12957e6	−0.0903215
$691$	6.74229e6	0.537171	0.268585	−	0.963256i	$-0.413444\pi$
$691$	6.74229e6	0.537171	0.268585	+	0.963256i	$0.413444\pi$
$692$	−4.38965e7	−3.48469
$693$	2.75623e6	0.218013
$694$	2.15366e7	1.69738
$695$	−4.45263e6	−0.349667
$696$	1.10604e7	0.865462
$697$	45501.8	0.00354770
$698$	5.39874e6	0.419425
$699$	5.77566e6	0.447104
$700$	7.72426e6	0.595816
$701$	−2.34659e7	−1.80361	−0.901806	−	0.432142i	$-0.857758\pi$
$701$	−2.34659e7	−1.80361	−0.901806	+	0.432142i	$0.857758\pi$
$702$	−4.29874e6	−0.329229
$703$	1.76450e7	1.34658
$704$	2.60410e7	1.98028
$705$	−4.54817e6	−0.344639
$706$	−996478.	−0.0752412
$707$	518832.	0.0390372
$708$	−6.71657e6	−0.503575
$709$	1.67113e7	1.24852	0.624260	−	0.781216i	$-0.285400\pi$
$709$	1.67113e7	1.24852	0.624260	+	0.781216i	$0.285400\pi$
$710$	3.46052e6	0.257630
$711$	2.74634e6	0.203742
$712$	−1.81399e7	−1.34102
$713$	1.63079e6	0.120136
$714$	−105248.	−0.00772623
$715$	−1.02975e7	−0.753300
$716$	1.46974e7	1.07141
$717$	−8.00793e6	−0.581732
$718$	−2.06565e7	−1.49536
$719$	−1.30821e7	−0.943743	−0.471872	−	0.881667i	$-0.656421\pi$
$719$	−1.30821e7	−0.943743	−0.471872	+	0.881667i	$0.656421\pi$
$720$	−1.71752e6	−0.123473
$721$	−3.16079e6	−0.226442
$722$	2.38294e7	1.70126
$723$	1.15664e7	0.822909
$724$	−3.39930e7	−2.41014
$725$	−1.05410e7	−0.744795
$726$	2.80786e7	1.97713
$727$	1.11933e7	0.785459	0.392729	−	0.919654i	$-0.371531\pi$
$727$	1.11933e7	0.785459	0.392729	+	0.919654i	$0.371531\pi$
$728$	8.76866e6	0.613203
$729$	531441.	0.0370370
$730$	3.14020e6	0.218097
$731$	−109650.	−0.00758952
$732$	1.52758e7	1.05372
$733$	1.47484e7	1.01387	0.506937	−	0.861983i	$-0.330778\pi$
$733$	1.47484e7	1.01387	0.506937	+	0.861983i	$0.330778\pi$
$734$	7.46195e6	0.511225
$735$	−527819.	−0.0360385
$736$	−529389.	−0.0360230
$737$	2.94806e7	1.99925
$738$	1.45703e6	0.0984756
$739$	−2.34154e7	−1.57721	−0.788607	−	0.614897i	$-0.789198\pi$
$739$	−2.34154e7	−1.57721	−0.788607	+	0.614897i	$0.789198\pi$
$740$	1.21031e7	0.812486
$741$	1.21307e7	0.811599
$742$	−1.55884e7	−1.03942
$743$	8.06764e6	0.536135	0.268068	−	0.963400i	$-0.413615\pi$
$743$	8.06764e6	0.536135	0.268068	+	0.963400i	$0.413615\pi$
$744$	8.17848e6	0.541677
$745$	4.43777e6	0.292937
$746$	−1.41173e7	−0.928764
$747$	−1.65406e6	−0.108455
$748$	−1.06381e6	−0.0695198
$749$	3.76985e6	0.245538
$750$	1.20716e7	0.783633
$751$	1.23190e7	0.797031	0.398515	−	0.917162i	$-0.369526\pi$
$751$	1.23190e7	0.797031	0.398515	+	0.917162i	$0.369526\pi$
$752$	1.79602e7	1.15815
$753$	1.38570e7	0.890600
$754$	−2.45841e7	−1.57480
$755$	2.53248e6	0.161688
$756$	−2.22712e6	−0.141722
$757$	2.61608e7	1.65925	0.829625	−	0.558322i	$-0.188554\pi$
$757$	2.61608e7	1.65925	0.829625	+	0.558322i	$0.188554\pi$
$758$	−1.67307e7	−1.05764
$759$	−3.30622e6	−0.208318
$760$	1.59858e7	1.00392
$761$	2.45934e7	1.53942	0.769708	−	0.638396i	$-0.220402\pi$
$761$	2.45934e7	1.53942	0.769708	+	0.638396i	$0.220402\pi$
$762$	−3.80953e6	−0.237675
$763$	−8.61826e6	−0.535930
$764$	−249498.	−0.0154644
$765$	−48612.1	−0.00300325
$766$	−4.42661e7	−2.72584
$767$	7.26665e6	0.446011
$768$	−1.82425e7	−1.11604
$769$	−3.91002e6	−0.238432	−0.119216	−	0.992868i	$-0.538038\pi$
$769$	−3.91002e6	−0.238432	−0.119216	+	0.992868i	$0.538038\pi$
$770$	−8.07320e6	−0.490703
$771$	−5.23892e6	−0.317399
$772$	−4.93053e7	−2.97749
$773$	−2.34107e7	−1.40918	−0.704590	−	0.709615i	$-0.748869\pi$
$773$	−2.34107e7	−1.40918	−0.704590	+	0.709615i	$0.748869\pi$
$774$	−3.51114e6	−0.210667
$775$	−7.79441e6	−0.466153
$776$	−2.97658e7	−1.77445
$777$	3.50481e6	0.208263
$778$	1.57073e7	0.930365
$779$	−4.11164e6	−0.242757
$780$	8.32071e6	0.489693
$781$	1.01289e7	0.594200
$782$	126250.	0.00738267
$783$	3.03926e6	0.177159
$784$	2.08429e6	0.121107
$785$	−2.08122e6	−0.120543
$786$	6.41569e6	0.370413
$787$	−1.56374e7	−0.899968	−0.449984	−	0.893037i	$-0.648570\pi$
$787$	−1.56374e7	−0.899968	−0.449984	+	0.893037i	$0.648570\pi$
$788$	2.52137e7	1.44651
$789$	−1.37348e7	−0.785473
$790$	−8.04425e6	−0.458583
$791$	1.28623e7	0.730933
$792$	−1.65809e7	−0.939279
$793$	−1.65268e7	−0.933269
$794$	1.15797e7	0.651850
$795$	−7.20001e6	−0.404031
$796$	8.48871e6	0.474853
$797$	−1.70892e7	−0.952964	−0.476482	−	0.879184i	$-0.658088\pi$
$797$	−1.70892e7	−0.952964	−0.476482	+	0.879184i	$0.658088\pi$
$798$	9.51043e6	0.528680
$799$	508339.	0.0281700
$800$	2.53024e6	0.139777
$801$	−4.98462e6	−0.274505
$802$	3.83370e7	2.10466
$803$	9.19128e6	0.503022
$804$	−2.38212e7	−1.29964
$805$	633143.	0.0344360
$806$	−1.81784e7	−0.985638
$807$	−1.39958e7	−0.756509
$808$	−3.12118e6	−0.168186
$809$	−1.75370e7	−0.942071	−0.471035	−	0.882114i	$-0.656120\pi$
$809$	−1.75370e7	−0.942071	−0.471035	+	0.882114i	$0.656120\pi$
$810$	−1.55663e6	−0.0833629
$811$	1.79913e7	0.960526	0.480263	−	0.877124i	$-0.340541\pi$
$811$	1.79913e7	0.960526	0.480263	+	0.877124i	$0.340541\pi$
$812$	−1.27367e7	−0.677900
$813$	−1.08638e7	−0.576443
$814$	5.36075e7	2.83573
$815$	−4.10597e6	−0.216532
$816$	191963.	0.0100924
$817$	9.90819e6	0.519325
$818$	2.69646e7	1.40900
$819$	2.40951e6	0.125522
$820$	−2.82026e6	−0.146472
$821$	−2.64450e6	−0.136926	−0.0684628	−	0.997654i	$-0.521809\pi$
$821$	−2.64450e6	−0.136926	−0.0684628	+	0.997654i	$0.521809\pi$
$822$	−3.64852e7	−1.88337
$823$	−1.96733e7	−1.01246	−0.506230	−	0.862399i	$-0.668961\pi$
$823$	−1.96733e7	−1.01246	−0.506230	+	0.862399i	$0.668961\pi$
$824$	1.90147e7	0.975597
$825$	1.58022e7	0.808320
$826$	5.69701e6	0.290534
$827$	9.19687e6	0.467602	0.233801	−	0.972284i	$-0.424884\pi$
$827$	9.19687e6	0.467602	0.233801	+	0.972284i	$0.424884\pi$
$828$	2.67153e6	0.135420
$829$	1.33246e7	0.673394	0.336697	−	0.941613i	$-0.390690\pi$
$829$	1.33246e7	0.673394	0.336697	+	0.941613i	$0.390690\pi$
$830$	4.84488e6	0.244111
$831$	240088.	0.0120606
$832$	2.27653e7	1.14016
$833$	58993.1	0.00294570
$834$	1.59358e7	0.793340
$835$	−1.45554e7	−0.722451
$836$	9.61279e7	4.75701
$837$	2.24734e6	0.110881
$838$	−2.85861e7	−1.40619
$839$	−2.23909e7	−1.09816	−0.549082	−	0.835769i	$-0.685022\pi$
$839$	−2.23909e7	−1.09816	−0.549082	+	0.835769i	$0.685022\pi$
$840$	3.17525e6	0.155267
$841$	−3.12992e6	−0.152596
$842$	−2.04652e7	−0.994800
$843$	−1.38076e6	−0.0669192
$844$	−6.48225e7	−3.13235
$845$	66990.6	0.00322754
$846$	1.62778e7	0.781931
$847$	−1.57385e7	−0.753799
$848$	2.84319e7	1.35774
$849$	−1.21298e7	−0.577542
$850$	−603415.	−0.0286463
$851$	−4.20418e6	−0.199002
$852$	−8.18442e6	−0.386268
$853$	−3.90398e7	−1.83711	−0.918555	−	0.395293i	$-0.870643\pi$
$853$	−3.90398e7	−1.83711	−0.918555	+	0.395293i	$0.870643\pi$
$854$	−1.29569e7	−0.607936
$855$	4.39270e6	0.205502
$856$	−2.26786e7	−1.05787
$857$	1.91804e7	0.892085	0.446042	−	0.895012i	$-0.352833\pi$
$857$	1.91804e7	0.892085	0.446042	+	0.895012i	$0.352833\pi$
$858$	3.68545e7	1.70912
$859$	1.98780e7	0.919157	0.459578	−	0.888137i	$-0.348001\pi$
$859$	1.98780e7	0.919157	0.459578	+	0.888137i	$0.348001\pi$
$860$	6.79623e6	0.313344
$861$	−816691.	−0.0375448
$862$	−5.77230e7	−2.64595
$863$	3.22593e7	1.47444	0.737222	−	0.675650i	$-0.236137\pi$
$863$	3.22593e7	1.47444	0.737222	+	0.675650i	$0.236137\pi$
$864$	−729536.	−0.0332478
$865$	1.71973e7	0.781485
$866$	5.79297e7	2.62486
$867$	−1.27733e7	−0.577105
$868$	−9.41796e6	−0.424285
$869$	−2.35453e7	−1.05768
$870$	−8.90222e6	−0.398750
$871$	2.57721e7	1.15108
$872$	5.18456e7	2.30898
$873$	−8.17926e6	−0.363227
$874$	−1.14082e7	−0.505171
$875$	−6.76635e6	−0.298768
$876$	−7.42683e6	−0.326997
$877$	−3.11294e7	−1.36669	−0.683347	−	0.730093i	$-0.739476\pi$
$877$	−3.11294e7	−1.36669	−0.683347	+	0.730093i	$0.739476\pi$
$878$	4.31918e7	1.89089
$879$	1.23950e7	0.541096
$880$	1.47248e7	0.640979
$881$	−2.05415e7	−0.891647	−0.445824	−	0.895121i	$-0.647089\pi$
$881$	−2.05415e7	−0.891647	−0.445824	+	0.895121i	$0.647089\pi$
$882$	1.88905e6	0.0817657
$883$	−3.26452e7	−1.40902	−0.704510	−	0.709694i	$-0.748833\pi$
$883$	−3.26452e7	−1.40902	−0.704510	+	0.709694i	$0.748833\pi$
$884$	−929987.	−0.0400264
$885$	2.63135e6	0.112933
$886$	5.07789e7	2.17320
$887$	−3.54676e7	−1.51364	−0.756820	−	0.653623i	$-0.773248\pi$
$887$	−3.54676e7	−1.51364	−0.756820	+	0.653623i	$0.773248\pi$
$888$	−2.10842e7	−0.897273
$889$	2.13530e6	0.0906160
$890$	1.46003e7	0.617856
$891$	−4.55621e6	−0.192269
$892$	5.98679e7	2.51931
$893$	−4.59346e7	−1.92758
$894$	−1.58826e7	−0.664627
$895$	−5.75799e6	−0.240278
$896$	1.62787e7	0.677406
$897$	−2.89032e6	−0.119940
$898$	−4.56543e7	−1.88926
$899$	1.28523e7	0.530374
$900$	−1.27687e7	−0.525460
$901$	804728.	0.0330246
$902$	−1.24916e7	−0.511214
$903$	1.96805e6	0.0803189
$904$	−7.73769e7	−3.14913
$905$	1.33174e7	0.540504
$906$	−9.06366e6	−0.366845
$907$	8.01603e6	0.323550	0.161775	−	0.986828i	$-0.448278\pi$
$907$	8.01603e6	0.323550	0.161775	+	0.986828i	$0.448278\pi$
$908$	−1.61255e7	−0.649079
$909$	−857661.	−0.0344275
$910$	−7.05765e6	−0.282525
$911$	−1.41427e7	−0.564595	−0.282297	−	0.959327i	$-0.591097\pi$
$911$	−1.41427e7	−0.564595	−0.282297	+	0.959327i	$0.591097\pi$
$912$	−1.73462e7	−0.690586
$913$	1.41808e7	0.563021
$914$	−1.49886e7	−0.593465
$915$	−5.98459e6	−0.236310
$916$	4.73878e7	1.86607
$917$	−3.59610e6	−0.141224
$918$	173981.	0.00681389
$919$	3.40286e7	1.32909	0.664547	−	0.747246i	$-0.268624\pi$
$919$	3.40286e7	1.32909	0.664547	+	0.747246i	$0.268624\pi$
$920$	−3.80886e6	−0.148363
$921$	−60656.4	−0.00235628
$922$	2.63915e7	1.02244
$923$	8.85471e6	0.342114
$924$	1.90938e7	0.735719
$925$	2.00941e7	0.772171
$926$	4.72383e7	1.81037
$927$	5.22498e6	0.199703
$928$	−4.17215e6	−0.159034
$929$	2.13760e7	0.812621	0.406310	−	0.913735i	$-0.366815\pi$
$929$	2.13760e7	0.812621	0.406310	+	0.913735i	$0.366815\pi$
$930$	−6.58263e6	−0.249570
$931$	−5.33075e6	−0.201565
$932$	4.00109e7	1.50882
$933$	1.63055e7	0.613238
$934$	5.48807e7	2.05851
$935$	416767.	0.0155907
$936$	−1.44951e7	−0.540795
$937$	2.63944e7	0.982117	0.491058	−	0.871127i	$-0.336610\pi$
$937$	2.63944e7	0.982117	0.491058	+	0.871127i	$0.336610\pi$
$938$	2.02052e7	0.749818
$939$	−7.35693e6	−0.272291
$940$	−3.15075e7	−1.16304
$941$	−5.00614e6	−0.184301	−0.0921507	−	0.995745i	$-0.529374\pi$
$941$	−5.00614e6	−0.184301	−0.0921507	+	0.995745i	$0.529374\pi$
$942$	7.44861e6	0.273494
$943$	979659.	0.0358753
$944$	−1.03909e7	−0.379509
$945$	872517.	0.0317830
$946$	3.01022e7	1.09363
$947$	7.85603e6	0.284661	0.142331	−	0.989819i	$-0.454540\pi$
$947$	7.85603e6	0.284661	0.142331	+	0.989819i	$0.454540\pi$
$948$	1.90253e7	0.687560
$949$	8.03508e6	0.289618
$950$	5.45259e7	1.96017
$951$	−7.82364e6	−0.280516
$952$	−354890.	−0.0126912
$953$	−2.43168e7	−0.867309	−0.433654	−	0.901079i	$-0.642776\pi$
$953$	−2.43168e7	−0.867309	−0.433654	+	0.901079i	$0.642776\pi$
$954$	2.57686e7	0.916683
$955$	97745.7	0.00346808
$956$	−5.54750e7	−1.96315
$957$	−2.60565e7	−0.919681
$958$	7.69988e7	2.71063
$959$	2.04505e7	0.718055
$960$	8.24360e6	0.288695
$961$	−1.91257e7	−0.668049
$962$	4.68640e7	1.63268
$963$	−6.23179e6	−0.216544
$964$	8.01262e7	2.77704
$965$	1.93163e7	0.667738
$966$	−2.26600e6	−0.0781298
$967$	−3.33260e7	−1.14608	−0.573042	−	0.819526i	$-0.694237\pi$
$967$	−3.33260e7	−1.14608	−0.573042	+	0.819526i	$0.694237\pi$
$968$	9.46796e7	3.24764
$969$	−490962.	−0.0167973
$970$	2.39577e7	0.817552
$971$	−3.47245e7	−1.18192	−0.590959	−	0.806701i	$-0.701251\pi$
$971$	−3.47245e7	−1.18192	−0.590959	+	0.806701i	$0.701251\pi$
$972$	3.68156e6	0.124987
$973$	−8.93229e6	−0.302469
$974$	3.44347e7	1.16305
$975$	1.38144e7	0.465394
$976$	2.36324e7	0.794114
$977$	2.91866e7	0.978244	0.489122	−	0.872215i	$-0.337317\pi$
$977$	2.91866e7	0.978244	0.489122	+	0.872215i	$0.337317\pi$
$978$	1.46951e7	0.491277
$979$	4.27347e7	1.42503
$980$	−3.65647e6	−0.121618
$981$	1.42465e7	0.472646
$982$	−9.96862e7	−3.29880
$983$	1.26152e7	0.416400	0.208200	−	0.978086i	$-0.433239\pi$
$983$	1.26152e7	0.416400	0.208200	+	0.978086i	$0.433239\pi$
$984$	4.91304e6	0.161757
$985$	−9.87796e6	−0.324397
$986$	994981.	0.0325929
$987$	−9.12395e6	−0.298119
$988$	8.40357e7	2.73887
$989$	−2.36077e6	−0.0767473
$990$	1.33455e7	0.432760
$991$	4.86623e7	1.57401	0.787007	−	0.616944i	$-0.211629\pi$
$991$	4.86623e7	1.57401	0.787007	+	0.616944i	$0.211629\pi$
$992$	−3.08504e6	−0.0995363
$993$	1.36878e7	0.440516
$994$	6.94204e6	0.222855
$995$	−3.32562e6	−0.106492
$996$	−1.14585e7	−0.366000
$997$	−4.67380e7	−1.48913	−0.744565	−	0.667550i	$-0.767343\pi$
$997$	−4.67380e7	−1.48913	−0.744565	+	0.667550i	$0.767343\pi$
$998$	2.41210e7	0.766599
$999$	−5.79367e6	−0.183671

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.6.a.b.1.12	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.6.a.b.1.12	✓	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q+9.71327 q^{2} +9.00000 q^{3} +62.3475 q^{4} -24.4259 q^{5} +87.4194 q^{6} -49.0000 q^{7} +294.774 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+9.71327 q^{2} +9.00000 q^{3} +62.3475 q^{4} -24.4259 q^{5} +87.4194 q^{6} -49.0000 q^{7} +294.774 q^{8} +81.0000 q^{9} -237.255 q^{10} -694.439 q^{11} +561.128 q^{12} -607.084 q^{13} -475.950 q^{14} -219.833 q^{15} +868.093 q^{16} +24.5702 q^{17} +786.774 q^{18} -2220.22 q^{19} -1522.89 q^{20} -441.000 q^{21} -6745.27 q^{22} +529.000 q^{23} +2652.96 q^{24} -2528.38 q^{25} -5896.76 q^{26} +729.000 q^{27} -3055.03 q^{28} +4169.08 q^{29} -2135.30 q^{30} +3082.77 q^{31} -1000.74 q^{32} -6249.95 q^{33} +238.657 q^{34} +1196.87 q^{35} +5050.15 q^{36} -7947.41 q^{37} -21565.6 q^{38} -5463.75 q^{39} -7200.11 q^{40} +1851.91 q^{41} -4283.55 q^{42} -4462.71 q^{43} -43296.6 q^{44} -1978.50 q^{45} +5138.32 q^{46} +20689.2 q^{47} +7812.84 q^{48} +2401.00 q^{49} -24558.8 q^{50} +221.132 q^{51} -37850.2 q^{52} +32752.2 q^{53} +7080.97 q^{54} +16962.3 q^{55} -14443.9 q^{56} -19982.0 q^{57} +40495.4 q^{58} -11969.8 q^{59} -13706.0 q^{60} +27223.3 q^{61} +29943.8 q^{62} -3969.00 q^{63} -37499.4 q^{64} +14828.6 q^{65} -60707.4 q^{66} -42452.4 q^{67} +1531.89 q^{68} +4761.00 q^{69} +11625.5 q^{70} -14585.7 q^{71} +23876.7 q^{72} -13235.6 q^{73} -77195.3 q^{74} -22755.4 q^{75} -138425. q^{76} +34027.5 q^{77} -53070.9 q^{78} +33905.5 q^{79} -21203.9 q^{80} +6561.00 q^{81} +17988.1 q^{82} -20420.5 q^{83} -27495.3 q^{84} -600.150 q^{85} -43347.5 q^{86} +37521.7 q^{87} -204702. q^{88} -61538.5 q^{89} -19217.7 q^{90} +29747.1 q^{91} +32981.8 q^{92} +27744.9 q^{93} +200960. q^{94} +54230.9 q^{95} -9006.62 q^{96} -100979. q^{97} +23321.6 q^{98} -56249.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + 108 q^{3} + 153 q^{4} - 162 q^{5} - 9 q^{6} - 588 q^{7} - 492 q^{8} + 972 q^{9}+O(q^{10}) \) 12 * q - q^2 + 108 * q^3 + 153 * q^4 - 162 * q^5 - 9 * q^6 - 588 * q^7 - 492 * q^8 + 972 * q^9	\( 12 q - q^{2} + 108 q^{3} + 153 q^{4} - 162 q^{5} - 9 q^{6} - 588 q^{7} - 492 q^{8} + 972 q^{9} + 528 q^{10} - 1425 q^{11} + 1377 q^{12} - 70 q^{13} + 49 q^{14} - 1458 q^{15} + 3865 q^{16} - 398 q^{17} - 81 q^{18} - 1293 q^{19} - 8593 q^{20} - 5292 q^{21} + 4961 q^{22} + 6348 q^{23} - 4428 q^{24} + 5830 q^{25} - 5187 q^{26} + 8748 q^{27} - 7497 q^{28} - 5127 q^{29} + 4752 q^{30} + 6498 q^{31} - 28485 q^{32} - 12825 q^{33} - 14527 q^{34} + 7938 q^{35} + 12393 q^{36} - 35545 q^{37} - 32617 q^{38} - 630 q^{39} + 35789 q^{40} - 7806 q^{41} + 441 q^{42} - 66142 q^{43} - 83253 q^{44} - 13122 q^{45} - 529 q^{46} - 16432 q^{47} + 34785 q^{48} + 28812 q^{49} - 177328 q^{50} - 3582 q^{51} - 187010 q^{52} - 67456 q^{53} - 729 q^{54} - 10453 q^{55} + 24108 q^{56} - 11637 q^{57} - 92677 q^{58} - 36346 q^{59} - 77337 q^{60} - 8768 q^{61} - 141813 q^{62} - 47628 q^{63} - 24604 q^{64} + 121875 q^{65} + 44649 q^{66} - 123617 q^{67} + 17217 q^{68} + 57132 q^{69} - 25872 q^{70} - 108667 q^{71} - 39852 q^{72} - 107406 q^{73} - 87825 q^{74} + 52470 q^{75} + 120191 q^{76} + 69825 q^{77} - 46683 q^{78} - 39470 q^{79} - 513682 q^{80} + 78732 q^{81} + 150219 q^{82} - 181838 q^{83} - 67473 q^{84} - 52633 q^{85} + 125713 q^{86} - 46143 q^{87} + 120642 q^{88} - 277361 q^{89} + 42768 q^{90} + 3430 q^{91} + 80937 q^{92} + 58482 q^{93} - 40880 q^{94} - 272491 q^{95} - 256365 q^{96} - 169005 q^{97} - 2401 q^{98} - 115425 q^{99}+O(q^{100}) \) 12 * q - q^2 + 108 * q^3 + 153 * q^4 - 162 * q^5 - 9 * q^6 - 588 * q^7 - 492 * q^8 + 972 * q^9 + 528 * q^10 - 1425 * q^11 + 1377 * q^12 - 70 * q^13 + 49 * q^14 - 1458 * q^15 + 3865 * q^16 - 398 * q^17 - 81 * q^18 - 1293 * q^19 - 8593 * q^20 - 5292 * q^21 + 4961 * q^22 + 6348 * q^23 - 4428 * q^24 + 5830 * q^25 - 5187 * q^26 + 8748 * q^27 - 7497 * q^28 - 5127 * q^29 + 4752 * q^30 + 6498 * q^31 - 28485 * q^32 - 12825 * q^33 - 14527 * q^34 + 7938 * q^35 + 12393 * q^36 - 35545 * q^37 - 32617 * q^38 - 630 * q^39 + 35789 * q^40 - 7806 * q^41 + 441 * q^42 - 66142 * q^43 - 83253 * q^44 - 13122 * q^45 - 529 * q^46 - 16432 * q^47 + 34785 * q^48 + 28812 * q^49 - 177328 * q^50 - 3582 * q^51 - 187010 * q^52 - 67456 * q^53 - 729 * q^54 - 10453 * q^55 + 24108 * q^56 - 11637 * q^57 - 92677 * q^58 - 36346 * q^59 - 77337 * q^60 - 8768 * q^61 - 141813 * q^62 - 47628 * q^63 - 24604 * q^64 + 121875 * q^65 + 44649 * q^66 - 123617 * q^67 + 17217 * q^68 + 57132 * q^69 - 25872 * q^70 - 108667 * q^71 - 39852 * q^72 - 107406 * q^73 - 87825 * q^74 + 52470 * q^75 + 120191 * q^76 + 69825 * q^77 - 46683 * q^78 - 39470 * q^79 - 513682 * q^80 + 78732 * q^81 + 150219 * q^82 - 181838 * q^83 - 67473 * q^84 - 52633 * q^85 + 125713 * q^86 - 46143 * q^87 + 120642 * q^88 - 277361 * q^89 + 42768 * q^90 + 3430 * q^91 + 80937 * q^92 + 58482 * q^93 - 40880 * q^94 - 272491 * q^95 - 256365 * q^96 - 169005 * q^97 - 2401 * q^98 - 115425 * q^99

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