LMFDB - Embedded newform 23.6.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,6,Mod(1,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, 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("23.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	23.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:	$3.68882785570$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.7925.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 13x + 12 $ x^3 - x^2 - 13*x + 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.917748$ of defining polynomial
Character	$\chi$	$=$	23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.164504 q^{2} -1.43100 q^{3} -31.9729 q^{4} -37.9865 q^{5} +0.235406 q^{6} -43.8366 q^{7} +10.5238 q^{8} -240.952 q^{9} +O(q^{10})$	\(q-0.164504 q^{2} -1.43100 q^{3} -31.9729 q^{4} -37.9865 q^{5} +0.235406 q^{6} -43.8366 q^{7} +10.5238 q^{8} -240.952 q^{9} +6.24894 q^{10} -163.213 q^{11} +45.7533 q^{12} +430.356 q^{13} +7.21131 q^{14} +54.3587 q^{15} +1021.40 q^{16} +740.415 q^{17} +39.6377 q^{18} -916.578 q^{19} +1214.54 q^{20} +62.7302 q^{21} +26.8493 q^{22} -529.000 q^{23} -15.0596 q^{24} -1682.03 q^{25} -70.7955 q^{26} +692.536 q^{27} +1401.59 q^{28} -5112.96 q^{29} -8.94223 q^{30} -5702.60 q^{31} -504.787 q^{32} +233.558 q^{33} -121.802 q^{34} +1665.20 q^{35} +7703.95 q^{36} -10913.1 q^{37} +150.781 q^{38} -615.840 q^{39} -399.763 q^{40} +11092.6 q^{41} -10.3194 q^{42} +5528.76 q^{43} +5218.41 q^{44} +9152.92 q^{45} +87.0228 q^{46} +14435.2 q^{47} -1461.63 q^{48} -14885.4 q^{49} +276.701 q^{50} -1059.53 q^{51} -13759.8 q^{52} +6852.79 q^{53} -113.925 q^{54} +6199.90 q^{55} -461.329 q^{56} +1311.62 q^{57} +841.104 q^{58} +4155.17 q^{59} -1738.01 q^{60} -21911.4 q^{61} +938.102 q^{62} +10562.5 q^{63} -32601.9 q^{64} -16347.7 q^{65} -38.4213 q^{66} -15164.2 q^{67} -23673.3 q^{68} +756.999 q^{69} -273.932 q^{70} +14031.4 q^{71} -2535.74 q^{72} -23310.1 q^{73} +1795.25 q^{74} +2406.98 q^{75} +29305.7 q^{76} +7154.72 q^{77} +101.308 q^{78} +64276.8 q^{79} -38799.5 q^{80} +57560.4 q^{81} -1824.78 q^{82} +114349. q^{83} -2005.67 q^{84} -28125.8 q^{85} -909.504 q^{86} +7316.65 q^{87} -1717.63 q^{88} -63420.7 q^{89} -1505.70 q^{90} -18865.4 q^{91} +16913.7 q^{92} +8160.42 q^{93} -2374.66 q^{94} +34817.6 q^{95} +722.351 q^{96} -91987.6 q^{97} +2448.70 q^{98} +39326.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 4 q^{2} - 20 q^{3} + 16 q^{4} - 58 q^{5} - 230 q^{6} - 282 q^{7} - 360 q^{8} + 121 q^{9}+O(q^{10}) $ 3 * q - 4 * q^2 - 20 * q^3 + 16 * q^4 - 58 * q^5 - 230 * q^6 - 282 * q^7 - 360 * q^8 + 121 * q^9	\( 3 q - 4 q^{2} - 20 q^{3} + 16 q^{4} - 58 q^{5} - 230 q^{6} - 282 q^{7} - 360 q^{8} + 121 q^{9} - 156 q^{10} + 136 q^{11} + 620 q^{12} - 1116 q^{13} + 2016 q^{14} + 750 q^{15} + 128 q^{16} - 896 q^{17} + 4282 q^{18} + 1654 q^{19} + 1504 q^{20} - 1670 q^{21} + 1352 q^{22} - 1587 q^{23} + 3600 q^{24} - 7347 q^{25} + 1998 q^{26} - 10700 q^{27} - 10264 q^{28} - 844 q^{29} + 3180 q^{30} - 3020 q^{31} + 6656 q^{32} - 7370 q^{33} - 11212 q^{34} + 1072 q^{35} - 2548 q^{36} + 8938 q^{37} + 10728 q^{38} + 16020 q^{39} + 3440 q^{40} - 12792 q^{41} + 20560 q^{42} - 16730 q^{43} + 5112 q^{44} - 3936 q^{45} + 2116 q^{46} + 22500 q^{47} + 23120 q^{48} + 2887 q^{49} + 15156 q^{50} + 50290 q^{51} - 47412 q^{52} + 17108 q^{53} - 7610 q^{54} - 436 q^{55} + 42640 q^{56} - 61960 q^{57} - 55678 q^{58} + 54176 q^{59} - 2400 q^{60} - 71324 q^{61} - 72710 q^{62} + 40696 q^{63} - 49984 q^{64} + 846 q^{65} - 42860 q^{66} - 62960 q^{67} - 8352 q^{68} + 10580 q^{69} + 9224 q^{70} + 98400 q^{71} - 72840 q^{72} - 81772 q^{73} - 59044 q^{74} + 44800 q^{75} + 31488 q^{76} - 304 q^{77} + 182070 q^{78} + 58224 q^{79} - 17568 q^{80} + 149947 q^{81} + 61926 q^{82} + 9892 q^{83} - 109720 q^{84} + 15536 q^{85} + 191140 q^{86} + 90500 q^{87} - 58400 q^{88} + 27542 q^{89} - 62112 q^{90} + 151974 q^{91} - 8464 q^{92} + 157330 q^{93} - 146990 q^{94} - 20644 q^{95} + 16160 q^{96} - 273672 q^{97} - 401276 q^{98} + 183082 q^{99}+O(q^{100}) \) 3 * q - 4 * q^2 - 20 * q^3 + 16 * q^4 - 58 * q^5 - 230 * q^6 - 282 * q^7 - 360 * q^8 + 121 * q^9 - 156 * q^10 + 136 * q^11 + 620 * q^12 - 1116 * q^13 + 2016 * q^14 + 750 * q^15 + 128 * q^16 - 896 * q^17 + 4282 * q^18 + 1654 * q^19 + 1504 * q^20 - 1670 * q^21 + 1352 * q^22 - 1587 * q^23 + 3600 * q^24 - 7347 * q^25 + 1998 * q^26 - 10700 * q^27 - 10264 * q^28 - 844 * q^29 + 3180 * q^30 - 3020 * q^31 + 6656 * q^32 - 7370 * q^33 - 11212 * q^34 + 1072 * q^35 - 2548 * q^36 + 8938 * q^37 + 10728 * q^38 + 16020 * q^39 + 3440 * q^40 - 12792 * q^41 + 20560 * q^42 - 16730 * q^43 + 5112 * q^44 - 3936 * q^45 + 2116 * q^46 + 22500 * q^47 + 23120 * q^48 + 2887 * q^49 + 15156 * q^50 + 50290 * q^51 - 47412 * q^52 + 17108 * q^53 - 7610 * q^54 - 436 * q^55 + 42640 * q^56 - 61960 * q^57 - 55678 * q^58 + 54176 * q^59 - 2400 * q^60 - 71324 * q^61 - 72710 * q^62 + 40696 * q^63 - 49984 * q^64 + 846 * q^65 - 42860 * q^66 - 62960 * q^67 - 8352 * q^68 + 10580 * q^69 + 9224 * q^70 + 98400 * q^71 - 72840 * q^72 - 81772 * q^73 - 59044 * q^74 + 44800 * q^75 + 31488 * q^76 - 304 * q^77 + 182070 * q^78 + 58224 * q^79 - 17568 * q^80 + 149947 * q^81 + 61926 * q^82 + 9892 * q^83 - 109720 * q^84 + 15536 * q^85 + 191140 * q^86 + 90500 * q^87 - 58400 * q^88 + 27542 * q^89 - 62112 * q^90 + 151974 * q^91 - 8464 * q^92 + 157330 * q^93 - 146990 * q^94 - 20644 * q^95 + 16160 * q^96 - 273672 * q^97 - 401276 * q^98 + 183082 * 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 $

$2$	−0.164504	−0.0290805	−0.0145403	−	0.999894i	$-0.504628\pi$
$2$	−0.164504	−0.0290805	−0.0145403	+	0.999894i	$0.504628\pi$
$3$	−1.43100	−0.0917987	−0.0458994	−	0.998946i	$-0.514615\pi$
$3$	−1.43100	−0.0917987	−0.0458994	+	0.998946i	$0.514615\pi$
$4$	−31.9729	−0.999154
$5$	−37.9865	−0.679523	−0.339761	−	0.940512i	$-0.610346\pi$
$5$	−37.9865	−0.679523	−0.339761	+	0.940512i	$0.610346\pi$
$6$	0.235406	0.00266955
$7$	−43.8366	−0.338136	−0.169068	−	0.985604i	$-0.554076\pi$
$7$	−43.8366	−0.338136	−0.169068	+	0.985604i	$0.554076\pi$
$8$	10.5238	0.0581365
$9$	−240.952	−0.991573
$10$	6.24894	0.0197609
$11$	−163.213	−0.406700	−0.203350	−	0.979106i	$-0.565183\pi$
$11$	−163.213	−0.406700	−0.203350	+	0.979106i	$0.565183\pi$
$12$	45.7533	0.0917211
$13$	430.356	0.706269	0.353134	−	0.935573i	$-0.385116\pi$
$13$	430.356	0.706269	0.353134	+	0.935573i	$0.385116\pi$
$14$	7.21131	0.00983318
$15$	54.3587	0.0623793
$16$	1021.40	0.997464
$17$	740.415	0.621374	0.310687	−	0.950512i	$-0.399441\pi$
$17$	740.415	0.621374	0.310687	+	0.950512i	$0.399441\pi$
$18$	39.6377	0.0288355
$19$	−916.578	−0.582486	−0.291243	−	0.956649i	$-0.594069\pi$
$19$	−916.578	−0.582486	−0.291243	+	0.956649i	$0.594069\pi$
$20$	1214.54	0.678948
$21$	62.7302	0.0310405
$22$	26.8493	0.0118270
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	−15.0596	−0.00533685
$25$	−1682.03	−0.538249
$26$	−70.7955	−0.0205387
$27$	692.536	0.182824
$28$	1401.59	0.337850
$29$	−5112.96	−1.12896	−0.564478	−	0.825448i	$-0.690923\pi$
$29$	−5112.96	−1.12896	−0.564478	+	0.825448i	$0.690923\pi$
$30$	−8.94223	−0.00181402
$31$	−5702.60	−1.06578	−0.532891	−	0.846184i	$-0.678895\pi$
$31$	−5702.60	−1.06578	−0.532891	+	0.846184i	$0.678895\pi$
$32$	−504.787	−0.0871432
$33$	233.558	0.0373345
$34$	−121.802	−0.0180699
$35$	1665.20	0.229771
$36$	7703.95	0.990734
$37$	−10913.1	−1.31052	−0.655261	−	0.755402i	$-0.727441\pi$
$37$	−10913.1	−1.31052	−0.655261	+	0.755402i	$0.727441\pi$
$38$	150.781	0.0169390
$39$	−615.840	−0.0648346
$40$	−399.763	−0.0395050
$41$	11092.6	1.03056	0.515282	−	0.857021i	$-0.327687\pi$
$41$	11092.6	1.03056	0.515282	+	0.857021i	$0.327687\pi$
$42$	−10.3194	−0.000902673 0
$43$	5528.76	0.455991	0.227996	−	0.973662i	$-0.426783\pi$
$43$	5528.76	0.455991	0.227996	+	0.973662i	$0.426783\pi$
$44$	5218.41	0.406356
$45$	9152.92	0.673796
$46$	87.0228	0.00606371
$47$	14435.2	0.953189	0.476594	−	0.879123i	$-0.341871\pi$
$47$	14435.2	0.953189	0.476594	+	0.879123i	$0.341871\pi$
$48$	−1461.63	−0.0915659
$49$	−14885.4	−0.885664
$50$	276.701	0.0156526
$51$	−1059.53	−0.0570413
$52$	−13759.8	−0.705671
$53$	6852.79	0.335102	0.167551	−	0.985863i	$-0.446414\pi$
$53$	6852.79	0.335102	0.167551	+	0.985863i	$0.446414\pi$
$54$	−113.925	−0.00531661
$55$	6199.90	0.276362
$56$	−461.329	−0.0196580
$57$	1311.62	0.0534715
$58$	841.104	0.0328307
$59$	4155.17	0.155403	0.0777014	−	0.996977i	$-0.475242\pi$
$59$	4155.17	0.155403	0.0777014	+	0.996977i	$0.475242\pi$
$60$	−1738.01	−0.0623266
$61$	−21911.4	−0.753955	−0.376978	−	0.926222i	$-0.623037\pi$
$61$	−21911.4	−0.753955	−0.376978	+	0.926222i	$0.623037\pi$
$62$	938.102	0.0309935
$63$	10562.5	0.335287
$64$	−32601.9	−0.994930
$65$	−16347.7	−0.479925
$66$	−38.4213	−0.00108571
$67$	−15164.2	−0.412699	−0.206349	−	0.978478i	$-0.566158\pi$
$67$	−15164.2	−0.412699	−0.206349	+	0.978478i	$0.566158\pi$
$68$	−23673.3	−0.620849
$69$	756.999	0.0191414
$70$	−273.932	−0.00668187
$71$	14031.4	0.330334	0.165167	−	0.986266i	$-0.447184\pi$
$71$	14031.4	0.330334	0.165167	+	0.986266i	$0.447184\pi$
$72$	−2535.74	−0.0576465
$73$	−23310.1	−0.511962	−0.255981	−	0.966682i	$-0.582398\pi$
$73$	−23310.1	−0.511962	−0.255981	+	0.966682i	$0.582398\pi$
$74$	1795.25	0.0381107
$75$	2406.98	0.0494106
$76$	29305.7	0.581994
$77$	7154.72	0.137520
$78$	101.308	0.00188542
$79$	64276.8	1.15874	0.579371	−	0.815064i	$-0.303298\pi$
$79$	64276.8	1.15874	0.579371	+	0.815064i	$0.303298\pi$
$80$	−38799.5	−0.677799
$81$	57560.4	0.974790
$82$	−1824.78	−0.0299693
$83$	114349.	1.82195	0.910974	−	0.412465i	$-0.135332\pi$
$83$	114349.	1.82195	0.910974	+	0.412465i	$0.135332\pi$
$84$	−2005.67	−0.0310142
$85$	−28125.8	−0.422238
$86$	−909.504	−0.0132605
$87$	7316.65	0.103637
$88$	−1717.63	−0.0236441
$89$	−63420.7	−0.848703	−0.424351	−	0.905498i	$-0.639498\pi$
$89$	−63420.7	−0.848703	−0.424351	+	0.905498i	$0.639498\pi$
$90$	−1505.70	−0.0195943
$91$	−18865.4	−0.238815
$92$	16913.7	0.208338
$93$	8160.42	0.0978375
$94$	−2374.66	−0.0277192
$95$	34817.6	0.395813
$96$	722.351	0.00799964
$97$	−91987.6	−0.992658	−0.496329	−	0.868134i	$-0.665319\pi$
$97$	−91987.6	−0.992658	−0.496329	+	0.868134i	$0.665319\pi$
$98$	2448.70	0.0257556
$99$	39326.6	0.403272
$100$	53779.4	0.537794
$101$	122133.	1.19132	0.595660	−	0.803236i	$-0.296890\pi$
$101$	122133.	1.19132	0.595660	+	0.803236i	$0.296890\pi$
$102$	174.298	0.00165879
$103$	−145517.	−1.35151	−0.675756	−	0.737125i	$-0.736183\pi$
$103$	−145517.	−1.35151	−0.675756	+	0.737125i	$0.736183\pi$
$104$	4528.99	0.0410600
$105$	−2382.90	−0.0210927
$106$	−1127.31	−0.00974495
$107$	−129578.	−1.09414	−0.547068	−	0.837088i	$-0.684256\pi$
$107$	−129578.	−1.09414	−0.547068	+	0.837088i	$0.684256\pi$
$108$	−22142.4	−0.182669
$109$	−10434.1	−0.0841178	−0.0420589	−	0.999115i	$-0.513392\pi$
$109$	−10434.1	−0.0841178	−0.0420589	+	0.999115i	$0.513392\pi$
$110$	−1019.91	−0.00803674
$111$	15616.7	0.120304
$112$	−44774.8	−0.337279
$113$	−253268.	−1.86589	−0.932943	−	0.360025i	$-0.882768\pi$
$113$	−253268.	−1.86589	−0.932943	+	0.360025i	$0.882768\pi$
$114$	−215.768	−0.00155498
$115$	20094.8	0.141690
$116$	163476.	1.12800
$117$	−103695.	−0.700317
$118$	−683.543	−0.00451919
$119$	−32457.3	−0.210109
$120$	572.061	0.00362651
$121$	−134412.	−0.834595
$122$	3604.52	0.0219254
$123$	−15873.6	−0.0946044
$124$	182329.	1.06488
$125$	182602.	1.04527
$126$	−1737.58	−0.00975032
$127$	235260.	1.29431	0.647156	−	0.762358i	$-0.275958\pi$
$127$	235260.	1.29431	0.647156	+	0.762358i	$0.275958\pi$
$128$	21516.3	0.116076
$129$	−7911.65	−0.0418594
$130$	2689.27	0.0139565
$131$	62921.5	0.320347	0.160174	−	0.987089i	$-0.448795\pi$
$131$	62921.5	0.320347	0.160174	+	0.987089i	$0.448795\pi$
$132$	−7467.54	−0.0373029
$133$	40179.7	0.196960
$134$	2494.58	0.0120015
$135$	−26307.0	−0.124233
$136$	7792.00	0.0361245
$137$	−134562.	−0.612521	−0.306260	−	0.951948i	$-0.599078\pi$
$137$	−134562.	−0.612521	−0.306260	+	0.951948i	$0.599078\pi$
$138$	−124.530	−0.000556641 0
$139$	287261.	1.26107	0.630535	−	0.776161i	$-0.282835\pi$
$139$	287261.	1.26107	0.630535	+	0.776161i	$0.282835\pi$
$140$	−53241.3	−0.229577
$141$	−20656.8	−0.0875015
$142$	−2308.22	−0.00960629
$143$	−70239.9	−0.287239
$144$	−246109.	−0.989058
$145$	194223.	0.767152
$146$	3834.61	0.0148881
$147$	21300.9	0.0813028
$148$	348924.	1.30941
$149$	−418105.	−1.54284	−0.771418	−	0.636329i	$-0.780452\pi$
$149$	−418105.	−1.54284	−0.771418	+	0.636329i	$0.780452\pi$
$150$	−395.959	−0.00143689
$151$	486983.	1.73809	0.869043	−	0.494736i	$-0.164735\pi$
$151$	486983.	1.73809	0.869043	+	0.494736i	$0.164735\pi$
$152$	−9645.91	−0.0338637
$153$	−178405.	−0.616138
$154$	−1176.98	−0.00399915
$155$	216622.	0.724223
$156$	19690.2	0.0647797
$157$	−439288.	−1.42233	−0.711165	−	0.703026i	$-0.751832\pi$
$157$	−439288.	−1.42233	−0.711165	+	0.703026i	$0.751832\pi$
$158$	−10573.8	−0.0336968
$159$	−9806.34	−0.0307620
$160$	19175.1	0.0592158
$161$	23189.6	0.0705063
$162$	−9468.93	−0.0283474
$163$	−125475.	−0.369905	−0.184952	−	0.982747i	$-0.559213\pi$
$163$	−125475.	−0.369905	−0.184952	+	0.982747i	$0.559213\pi$
$164$	−354664.	−1.02969
$165$	−8872.05	−0.0253696
$166$	−18810.8	−0.0529832
$167$	−626996.	−1.73970	−0.869848	−	0.493319i	$-0.835783\pi$
$167$	−626996.	−1.73970	−0.869848	+	0.493319i	$0.835783\pi$
$168$	660.162	0.00180458
$169$	−186086.	−0.501185
$170$	4626.81	0.0122789
$171$	220852.	0.577578
$172$	−176771.	−0.455605
$173$	502364.	1.27615	0.638077	−	0.769972i	$-0.279730\pi$
$173$	502364.	1.27615	0.638077	+	0.769972i	$0.279730\pi$
$174$	−1203.62	−0.00301381
$175$	73734.4	0.182002
$176$	−166706.	−0.405668
$177$	−5946.05	−0.0142658
$178$	10433.0	0.0246807
$179$	−131681.	−0.307178	−0.153589	−	0.988135i	$-0.549083\pi$
$179$	−131681.	−0.307178	−0.153589	+	0.988135i	$0.549083\pi$
$180$	−292646.	−0.673226
$181$	343209.	0.778686	0.389343	−	0.921093i	$-0.372702\pi$
$181$	343209.	0.778686	0.389343	+	0.921093i	$0.372702\pi$
$182$	3103.43	0.00694487
$183$	31355.2	0.0692121
$184$	−5567.10	−0.0121223
$185$	414551.	0.890529
$186$	−1342.42	−0.00284516
$187$	−120846.	−0.252713
$188$	−461536.	−0.952383
$189$	−30358.4	−0.0618194
$190$	−5727.64	−0.0115104
$191$	831093.	1.64841	0.824207	−	0.566289i	$-0.191621\pi$
$191$	831093.	1.64841	0.824207	+	0.566289i	$0.191621\pi$
$192$	46653.3	0.0913333
$193$	498764.	0.963832	0.481916	−	0.876217i	$-0.339941\pi$
$193$	498764.	0.963832	0.481916	+	0.876217i	$0.339941\pi$
$194$	15132.3	0.0288670
$195$	23393.6	0.0440565
$196$	475928.	0.884915
$197$	415236.	0.762306	0.381153	−	0.924512i	$-0.375527\pi$
$197$	415236.	0.762306	0.381153	+	0.924512i	$0.375527\pi$
$198$	−6469.39	−0.0117274
$199$	−969194.	−1.73491	−0.867457	−	0.497512i	$-0.834247\pi$
$199$	−969194.	−1.73491	−0.867457	+	0.497512i	$0.834247\pi$
$200$	−17701.4	−0.0312919
$201$	21700.0	0.0378852
$202$	−20091.4	−0.0346442
$203$	224135.	0.381741
$204$	33876.4	0.0569931
$205$	−421370.	−0.700291
$206$	23938.1	0.0393027
$207$	127464.	0.206757
$208$	439567.	0.704477
$209$	149598.	0.236897
$210$	391.997	0.000613387 0
$211$	372669.	0.576259	0.288129	−	0.957592i	$-0.406967\pi$
$211$	372669.	0.576259	0.288129	+	0.957592i	$0.406967\pi$
$212$	−219104.	−0.334819
$213$	−20078.9	−0.0303243
$214$	21316.1	0.0318181
$215$	−210018.	−0.309856
$216$	7288.12	0.0106287
$217$	249983.	0.360380
$218$	1716.45	0.00244619
$219$	33356.8	0.0469974
$220$	−198229.	−0.276128
$221$	318643.	0.438857
$222$	−2569.01	−0.00349851
$223$	−668196.	−0.899791	−0.449895	−	0.893081i	$-0.648539\pi$
$223$	−668196.	−0.899791	−0.449895	+	0.893081i	$0.648539\pi$
$224$	22128.2	0.0294663
$225$	405288.	0.533713
$226$	41663.7	0.0542609
$227$	−1.01295e6	−1.30473	−0.652367	−	0.757903i	$-0.726224\pi$
$227$	−1.01295e6	−1.30473	−0.652367	+	0.757903i	$0.726224\pi$
$228$	−41936.5	−0.0534263
$229$	−342003.	−0.430964	−0.215482	−	0.976508i	$-0.569132\pi$
$229$	−342003.	−0.430964	−0.215482	+	0.976508i	$0.569132\pi$
$230$	−3305.69	−0.00412043
$231$	−10238.4	−0.0126242
$232$	−53807.9	−0.0656335
$233$	−792950.	−0.956877	−0.478438	−	0.878121i	$-0.658797\pi$
$233$	−792950.	−0.956877	−0.478438	+	0.878121i	$0.658797\pi$
$234$	17058.3	0.0203656
$235$	−548343.	−0.647713
$236$	−132853.	−0.155271
$237$	−91980.2	−0.106371
$238$	5339.36	0.00611008
$239$	520763.	0.589719	0.294859	−	0.955541i	$-0.404727\pi$
$239$	520763.	0.589719	0.294859	+	0.955541i	$0.404727\pi$
$240$	55522.1	0.0622211
$241$	−867128.	−0.961702	−0.480851	−	0.876802i	$-0.659672\pi$
$241$	−867128.	−0.961702	−0.480851	+	0.876802i	$0.659672\pi$
$242$	22111.4	0.0242705
$243$	−250655.	−0.272308
$244$	700572.	0.753317
$245$	565442.	0.601829
$246$	2611.27	0.00275115
$247$	−394455.	−0.411392
$248$	−60013.1	−0.0619608
$249$	−163633.	−0.167252
$250$	−30038.8	−0.0303971
$251$	−590873.	−0.591983	−0.295992	−	0.955191i	$-0.595650\pi$
$251$	−590873.	−0.591983	−0.295992	+	0.955191i	$0.595650\pi$
$252$	−337715.	−0.335003
$253$	86339.8	0.0848027
$254$	−38701.3	−0.0376393
$255$	40248.0	0.0387609
$256$	1.03972e6	0.991554
$257$	−448650.	−0.423716	−0.211858	−	0.977300i	$-0.567951\pi$
$257$	−448650.	−0.423716	−0.211858	+	0.977300i	$0.567951\pi$
$258$	1301.50	0.00121729
$259$	478394.	0.443135
$260$	522685.	0.479520
$261$	1.23198e6	1.11944
$262$	−10350.9	−0.00931586
$263$	434704.	0.387529	0.193765	−	0.981048i	$-0.437930\pi$
$263$	434704.	0.387529	0.193765	+	0.981048i	$0.437930\pi$
$264$	2457.93	0.00217050
$265$	−260313.	−0.227710
$266$	−6609.73	−0.00572769
$267$	90755.0	0.0779098
$268$	484845.	0.412350
$269$	873326.	0.735861	0.367930	−	0.929853i	$-0.380067\pi$
$269$	873326.	0.735861	0.367930	+	0.929853i	$0.380067\pi$
$270$	4327.61	0.00361276
$271$	−1.16572e6	−0.964208	−0.482104	−	0.876114i	$-0.660127\pi$
$271$	−1.16572e6	−0.964208	−0.482104	+	0.876114i	$0.660127\pi$
$272$	756262.	0.619798
$273$	26996.3	0.0219229
$274$	22136.0	0.0178124
$275$	274529.	0.218906
$276$	−24203.5	−0.0191252
$277$	−604025.	−0.472994	−0.236497	−	0.971632i	$-0.575999\pi$
$277$	−604025.	−0.472994	−0.236497	+	0.971632i	$0.575999\pi$
$278$	−47255.6	−0.0366726
$279$	1.37405e6	1.05680
$280$	17524.2	0.0133581
$281$	1.72154e6	1.30062	0.650310	−	0.759669i	$-0.274639\pi$
$281$	1.72154e6	1.30062	0.650310	+	0.759669i	$0.274639\pi$
$282$	3398.13	0.00254459
$283$	−2.01557e6	−1.49600	−0.748000	−	0.663699i	$-0.768986\pi$
$283$	−2.01557e6	−1.49600	−0.748000	+	0.663699i	$0.768986\pi$
$284$	−448624.	−0.330055
$285$	−49824.0	−0.0363351
$286$	11554.8	0.00835306
$287$	−486263.	−0.348471
$288$	121630.	0.0864089
$289$	−871642.	−0.613894
$290$	−31950.6	−0.0223092
$291$	131634.	0.0911248
$292$	745293.	0.511529
$293$	1.45451e6	0.989798	0.494899	−	0.868951i	$-0.335205\pi$
$293$	1.45451e6	0.989798	0.494899	+	0.868951i	$0.335205\pi$
$294$	−3504.10	−0.00236433
$295$	−157840.	−0.105600
$296$	−114848.	−0.0761891
$297$	−113031.	−0.0743544
$298$	68780.1	0.0448665
$299$	−227659.	−0.147267
$300$	−76958.3	−0.0493688
$301$	−242362.	−0.154187
$302$	−80110.8	−0.0505445
$303$	−174772.	−0.109362
$304$	−936196.	−0.581009
$305$	832337.	0.512329
$306$	29348.3	0.0179176
$307$	272463.	0.164991	0.0824957	−	0.996591i	$-0.473711\pi$
$307$	272463.	0.164991	0.0824957	+	0.996591i	$0.473711\pi$
$308$	−228757.	−0.137404
$309$	208235.	0.124067
$310$	−35635.2	−0.0210608
$311$	−2.33041e6	−1.36625	−0.683126	−	0.730301i	$-0.739380\pi$
$311$	−2.33041e6	−1.36625	−0.683126	+	0.730301i	$0.739380\pi$
$312$	−6480.99	−0.00376925
$313$	−1.67227e6	−0.964818	−0.482409	−	0.875946i	$-0.660238\pi$
$313$	−1.67227e6	−0.964818	−0.482409	+	0.875946i	$0.660238\pi$
$314$	72264.7	0.0413621
$315$	−401233.	−0.227835
$316$	−2.05512e6	−1.15776
$317$	1.18782e6	0.663901	0.331950	−	0.943297i	$-0.392293\pi$
$317$	1.18782e6	0.663901	0.331950	+	0.943297i	$0.392293\pi$
$318$	1613.19	0.000894574 0
$319$	834503.	0.459146
$320$	1.23843e6	0.676077
$321$	185426.	0.100440
$322$	−3814.78	−0.00205036
$323$	−678649.	−0.361942
$324$	−1.84037e6	−0.973966
$325$	−723872.	−0.380148
$326$	20641.3	0.0107570
$327$	14931.2	0.00772191
$328$	116737.	0.0599133
$329$	−632791.	−0.322308
$330$	1459.49	0.000737762 0
$331$	−2.09261e6	−1.04983	−0.524915	−	0.851155i	$-0.675903\pi$
$331$	−2.09261e6	−1.04983	−0.524915	+	0.851155i	$0.675903\pi$
$332$	−3.65606e6	−1.82041
$333$	2.62954e6	1.29948
$334$	103144.	0.0505913
$335$	576035.	0.280438
$336$	64072.8	0.0309618
$337$	2.13994e6	1.02642	0.513211	−	0.858262i	$-0.328456\pi$
$337$	2.13994e6	1.02642	0.513211	+	0.858262i	$0.328456\pi$
$338$	30612.0	0.0145747
$339$	362427.	0.171286
$340$	899263.	0.421881
$341$	930740.	0.433453
$342$	−36331.0	−0.0167963
$343$	1.38929e6	0.637611
$344$	58183.6	0.0265097
$345$	−28755.7	−0.0130070
$346$	−82641.0	−0.0371112
$347$	3.78048e6	1.68548	0.842739	−	0.538322i	$-0.180941\pi$
$347$	3.78048e6	1.68548	0.842739	+	0.538322i	$0.180941\pi$
$348$	−233935.	−0.103549
$349$	3.46473e6	1.52267	0.761334	−	0.648360i	$-0.224545\pi$
$349$	3.46473e6	1.52267	0.761334	+	0.648360i	$0.224545\pi$
$350$	−12129.6	−0.00529270
$351$	298037.	0.129123
$352$	82388.0	0.0354411
$353$	−2.39834e6	−1.02441	−0.512206	−	0.858863i	$-0.671171\pi$
$353$	−2.39834e6	−1.02441	−0.512206	+	0.858863i	$0.671171\pi$
$354$	978.151	0.000414856 0
$355$	−533002.	−0.224470
$356$	2.02774e6	0.847985
$357$	46446.4	0.0192878
$358$	21662.0	0.00893289
$359$	−2.04171e6	−0.836098	−0.418049	−	0.908424i	$-0.637286\pi$
$359$	−2.04171e6	−0.836098	−0.418049	+	0.908424i	$0.637286\pi$
$360$	96323.7	0.0391721
$361$	−1.63598e6	−0.660710
$362$	−56459.3	−0.0226446
$363$	192344.	0.0766148
$364$	603181.	0.238613
$365$	885469.	0.347889
$366$	−5158.07	−0.00201272
$367$	2.41363e6	0.935417	0.467709	−	0.883883i	$-0.345080\pi$
$367$	2.41363e6	0.935417	0.467709	+	0.883883i	$0.345080\pi$
$368$	−540322.	−0.207986
$369$	−2.67279e6	−1.02188
$370$	−68195.4	−0.0258971
$371$	−300403.	−0.113310
$372$	−260913.	−0.0977547
$373$	1.83073e6	0.681321	0.340660	−	0.940186i	$-0.389349\pi$
$373$	1.83073e6	0.681321	0.340660	+	0.940186i	$0.389349\pi$
$374$	19879.6	0.00734901
$375$	−261304.	−0.0959549
$376$	151914.	0.0554150
$377$	−2.20039e6	−0.797347
$378$	4994.09	0.00179774
$379$	5.24532e6	1.87575	0.937874	−	0.346977i	$-0.112792\pi$
$379$	5.24532e6	1.87575	0.937874	+	0.346977i	$0.112792\pi$
$380$	−1.11322e6	−0.395478
$381$	−336657.	−0.118816
$382$	−136718.	−0.0479367
$383$	−754501.	−0.262823	−0.131411	−	0.991328i	$-0.541951\pi$
$383$	−754501.	−0.262823	−0.131411	+	0.991328i	$0.541951\pi$
$384$	−30789.9	−0.0106557
$385$	−271782.	−0.0934479
$386$	−82048.7	−0.0280287
$387$	−1.33217e6	−0.452148
$388$	2.94111e6	0.991819
$389$	2.05221e6	0.687618	0.343809	−	0.939040i	$-0.388283\pi$
$389$	2.05221e6	0.687618	0.343809	+	0.939040i	$0.388283\pi$
$390$	−3848.35	−0.00128119
$391$	−391680.	−0.129565
$392$	−156651.	−0.0514894
$393$	−90040.7	−0.0294074
$394$	−68308.0	−0.0221682
$395$	−2.44165e6	−0.787391
$396$	−1.25739e6	−0.402931
$397$	3.99917e6	1.27348	0.636742	−	0.771077i	$-0.280281\pi$
$397$	3.99917e6	1.27348	0.636742	+	0.771077i	$0.280281\pi$
$398$	159437.	0.0504522
$399$	−57497.2	−0.0180807
$400$	−1.71803e6	−0.536884
$401$	−5.10734e6	−1.58611	−0.793056	−	0.609149i	$-0.791511\pi$
$401$	−5.10734e6	−1.58611	−0.793056	+	0.609149i	$0.791511\pi$
$402$	−3569.74	−0.00110172
$403$	−2.45415e6	−0.752729
$404$	−3.90494e6	−1.19031
$405$	−2.18652e6	−0.662392
$406$	−36871.1	−0.0111012
$407$	1.78116e6	0.532989
$408$	−11150.4	−0.00331618
$409$	−3.06823e6	−0.906942	−0.453471	−	0.891271i	$-0.649814\pi$
$409$	−3.06823e6	−0.906942	−0.453471	+	0.891271i	$0.649814\pi$
$410$	69317.1	0.0203648
$411$	192558.	0.0562286
$412$	4.65260e6	1.35037
$413$	−182149.	−0.0525473
$414$	−20968.3	−0.00601261
$415$	−4.34370e6	−1.23805
$416$	−217239.	−0.0615465
$417$	−411070.	−0.115765
$418$	−24609.5	−0.00688908
$419$	3.33601e6	0.928308	0.464154	−	0.885754i	$-0.346358\pi$
$419$	3.33601e6	0.928308	0.464154	+	0.885754i	$0.346358\pi$
$420$	76188.3	0.0210749
$421$	−2.75080e6	−0.756404	−0.378202	−	0.925723i	$-0.623458\pi$
$421$	−2.75080e6	−0.756404	−0.378202	+	0.925723i	$0.623458\pi$
$422$	−61305.7	−0.0167579
$423$	−3.47820e6	−0.945156
$424$	72117.5	0.0194817
$425$	−1.24540e6	−0.334454
$426$	3303.06	0.000881846 0
$427$	960521.	0.254940
$428$	4.14299e6	1.09321
$429$	100513.	0.0263682
$430$	34548.8	0.00901078
$431$	926380.	0.240213	0.120106	−	0.992761i	$-0.461676\pi$
$431$	926380.	0.240213	0.120106	+	0.992761i	$0.461676\pi$
$432$	707358.	0.182360
$433$	680820.	0.174507	0.0872535	−	0.996186i	$-0.472191\pi$
$433$	680820.	0.174507	0.0872535	+	0.996186i	$0.472191\pi$
$434$	−41123.2	−0.0104800
$435$	−277934.	−0.0704236
$436$	333608.	0.0840467
$437$	484870.	0.121457
$438$	−5487.33	−0.00136671
$439$	2.17406e6	0.538406	0.269203	−	0.963083i	$-0.413240\pi$
$439$	2.17406e6	0.538406	0.269203	+	0.963083i	$0.413240\pi$
$440$	65246.6	0.0160667
$441$	3.58666e6	0.878200
$442$	−52418.1	−0.0127622
$443$	4.17517e6	1.01080	0.505400	−	0.862885i	$-0.331345\pi$
$443$	4.17517e6	1.01080	0.505400	+	0.862885i	$0.331345\pi$
$444$	−499311.	−0.120203
$445$	2.40913e6	0.576713
$446$	109921.	0.0261664
$447$	598308.	0.141630
$448$	1.42915e6	0.336422
$449$	−4.68946e6	−1.09776	−0.548880	−	0.835901i	$-0.684945\pi$
$449$	−4.68946e6	−1.09776	−0.548880	+	0.835901i	$0.684945\pi$
$450$	−66671.7	−0.0155207
$451$	−1.81046e6	−0.419130
$452$	8.09774e6	1.86431
$453$	−696873.	−0.159554
$454$	166634.	0.0379424
$455$	716629.	0.162280
$456$	13803.3	0.00310864
$457$	−1.68983e6	−0.378487	−0.189244	−	0.981930i	$-0.560604\pi$
$457$	−1.68983e6	−0.378487	−0.189244	+	0.981930i	$0.560604\pi$
$458$	56260.9	0.0125326
$459$	512764.	0.113602
$460$	−642491.	−0.141570
$461$	−4.28765e6	−0.939652	−0.469826	−	0.882759i	$-0.655683\pi$
$461$	−4.28765e6	−0.939652	−0.469826	+	0.882759i	$0.655683\pi$
$462$	1684.26	0.000367117 0
$463$	5.26738e6	1.14194	0.570969	−	0.820972i	$-0.306568\pi$
$463$	5.26738e6	1.14194	0.570969	+	0.820972i	$0.306568\pi$
$464$	−5.22239e6	−1.12609
$465$	−309986.	−0.0664828
$466$	130444.	0.0278265
$467$	−3.66305e6	−0.777231	−0.388616	−	0.921400i	$-0.627047\pi$
$467$	−3.66305e6	−0.777231	−0.388616	+	0.921400i	$0.627047\pi$
$468$	3.31544e6	0.699725
$469$	664748.	0.139548
$470$	90204.8	0.0188358
$471$	628621.	0.130568
$472$	43728.3	0.00903457
$473$	−902366.	−0.185451
$474$	15131.1	0.00309332
$475$	1.54171e6	0.313523
$476$	1.03776e6	0.209931
$477$	−1.65119e6	−0.332279
$478$	−85667.7	−0.0171493
$479$	7.03353e6	1.40067	0.700333	−	0.713816i	$-0.253035\pi$
$479$	7.03353e6	1.40067	0.700333	+	0.713816i	$0.253035\pi$
$480$	−27439.6	−0.00543593
$481$	−4.69653e6	−0.925581
$482$	142646.	0.0279668
$483$	−33184.3	−0.00647239
$484$	4.29756e6	0.833890
$485$	3.49428e6	0.674534
$486$	41233.8	0.00791887
$487$	5.05170e6	0.965195	0.482598	−	0.875842i	$-0.339693\pi$
$487$	5.05170e6	0.965195	0.482598	+	0.875842i	$0.339693\pi$
$488$	−230592.	−0.0438323
$489$	179555.	0.0339568
$490$	−93017.6	−0.0175015
$491$	−3.90292e6	−0.730610	−0.365305	−	0.930888i	$-0.619035\pi$
$491$	−3.90292e6	−0.730610	−0.365305	+	0.930888i	$0.619035\pi$
$492$	507524.	0.0945244
$493$	−3.78571e6	−0.701505
$494$	64889.6	0.0119635
$495$	−1.49388e6	−0.274033
$496$	−5.82465e6	−1.06308
$497$	−615087.	−0.111698
$498$	26918.3	0.00486379
$499$	1.13818e6	0.204625	0.102312	−	0.994752i	$-0.467376\pi$
$499$	1.13818e6	0.204625	0.102312	+	0.994752i	$0.467376\pi$
$500$	−5.83832e6	−1.04439
$501$	897231.	0.159702
$502$	97201.1	0.0172152
$503$	−7.48030e6	−1.31825	−0.659127	−	0.752032i	$-0.729074\pi$
$503$	−7.48030e6	−1.31825	−0.659127	+	0.752032i	$0.729074\pi$
$504$	111158.	0.0194924
$505$	−4.63939e6	−0.809529
$506$	−14203.3	−0.00246611
$507$	266290.	0.0460081
$508$	−7.52195e6	−1.29322
$509$	3.03026e6	0.518424	0.259212	−	0.965821i	$-0.416537\pi$
$509$	3.03026e6	0.518424	0.259212	+	0.965821i	$0.416537\pi$
$510$	−6620.97	−0.00112719
$511$	1.02184e6	0.173113
$512$	−859561.	−0.144911
$513$	−634763.	−0.106492
$514$	73804.8	0.0123219
$515$	5.52767e6	0.918383
$516$	252959.	0.0418240
$517$	−2.35602e6	−0.387661
$518$	−78697.8	−0.0128866
$519$	−718883.	−0.117149
$520$	−172040.	−0.0279012
$521$	−1.90771e6	−0.307905	−0.153953	−	0.988078i	$-0.549200\pi$
$521$	−1.90771e6	−0.307905	−0.153953	+	0.988078i	$0.549200\pi$
$522$	−202666.	−0.0325540
$523$	2.40656e6	0.384718	0.192359	−	0.981325i	$-0.438386\pi$
$523$	2.40656e6	0.384718	0.192359	+	0.981325i	$0.438386\pi$
$524$	−2.01178e6	−0.320076
$525$	−105514.	−0.0167075
$526$	−71510.7	−0.0112696
$527$	−4.22229e6	−0.662250
$528$	238557.	0.0372398
$529$	279841.	0.0434783
$530$	42822.6	0.00662192
$531$	−1.00120e6	−0.154093
$532$	−1.28466e6	−0.196793
$533$	4.77378e6	0.727855
$534$	−14929.6	−0.00226566
$535$	4.92221e6	0.743490
$536$	−159586.	−0.0239928
$537$	188435.	0.0281985
$538$	−143666.	−0.0213992
$539$	2.42949e6	0.360199
$540$	841112.	0.124128
$541$	−711055.	−0.104450	−0.0522252	−	0.998635i	$-0.516631\pi$
$541$	−711055.	−0.104450	−0.0522252	+	0.998635i	$0.516631\pi$
$542$	191766.	0.0280397
$543$	−491132.	−0.0714823
$544$	−373752.	−0.0541485
$545$	396354.	0.0571600
$546$	−4441.01	−0.000637530 0
$547$	7.21528e6	1.03106	0.515531	−	0.856871i	$-0.327595\pi$
$547$	7.21528e6	1.03106	0.515531	+	0.856871i	$0.327595\pi$
$548$	4.30234e6	0.612003
$549$	5.27960e6	0.747601
$550$	−45161.2	−0.00636589
$551$	4.68643e6	0.657602
$552$	7966.53	0.00111281
$553$	−2.81768e6	−0.391813
$554$	99364.7	0.0137549
$555$	−593222.	−0.0817495
$556$	−9.18457e6	−1.26000
$557$	−920675.	−0.125739	−0.0628693	−	0.998022i	$-0.520025\pi$
$557$	−920675.	−0.125739	−0.0628693	+	0.998022i	$0.520025\pi$
$558$	−226038.	−0.0307323
$559$	2.37934e6	0.322052
$560$	1.70084e6	0.229189
$561$	172930.	0.0231987
$562$	−283200.	−0.0378227
$563$	−7.13949e6	−0.949284	−0.474642	−	0.880179i	$-0.657422\pi$
$563$	−7.13949e6	−0.949284	−0.474642	+	0.880179i	$0.657422\pi$
$564$	660459.	0.0874275
$565$	9.62077e6	1.26791
$566$	331570.	0.0435045
$567$	−2.52325e6	−0.329612
$568$	147663.	0.0192045
$569$	1.32562e7	1.71648	0.858239	−	0.513250i	$-0.171559\pi$
$569$	1.32562e7	1.71648	0.858239	+	0.513250i	$0.171559\pi$
$570$	8196.26	0.00105664
$571$	−8.74927e6	−1.12300	−0.561502	−	0.827475i	$-0.689776\pi$
$571$	−8.74927e6	−1.12300	−0.561502	+	0.827475i	$0.689776\pi$
$572$	2.24578e6	0.286996
$573$	−1.18929e6	−0.151322
$574$	79992.4	0.0101337
$575$	889793.	0.112233
$576$	7.85549e6	0.986545
$577$	2.28815e6	0.286118	0.143059	−	0.989714i	$-0.454306\pi$
$577$	2.28815e6	0.286118	0.143059	+	0.989714i	$0.454306\pi$
$578$	143389.	0.0178524
$579$	−713731.	−0.0884786
$580$	−6.20989e6	−0.766503
$581$	−5.01266e6	−0.616067
$582$	−21654.4	−0.00264996
$583$	−1.11847e6	−0.136286
$584$	−245312.	−0.0297636
$585$	3.93902e6	0.475881
$586$	−239272.	−0.0287838
$587$	1.48384e7	1.77743	0.888714	−	0.458463i	$-0.151600\pi$
$587$	1.48384e7	1.77743	0.888714	+	0.458463i	$0.151600\pi$
$588$	−681054.	−0.0812341
$589$	5.22688e6	0.620804
$590$	25965.4	0.00307090
$591$	−594202.	−0.0699787
$592$	−1.11467e7	−1.30720
$593$	−7.67836e6	−0.896668	−0.448334	−	0.893866i	$-0.647982\pi$
$593$	−7.67836e6	−0.896668	−0.448334	+	0.893866i	$0.647982\pi$
$594$	18594.1	0.00216226
$595$	1.23294e6	0.142774
$596$	1.33680e7	1.54153
$597$	1.38692e6	0.159263
$598$	37450.8	0.00428261
$599$	−599539.	−0.0682733	−0.0341366	−	0.999417i	$-0.510868\pi$
$599$	−599539.	−0.0682733	−0.0341366	+	0.999417i	$0.510868\pi$
$600$	25330.7	0.00287256
$601$	−6.92017e6	−0.781503	−0.390751	−	0.920496i	$-0.627785\pi$
$601$	−6.92017e6	−0.781503	−0.390751	+	0.920496i	$0.627785\pi$
$602$	39869.6	0.00448384
$603$	3.65385e6	0.409221
$604$	−1.55703e7	−1.73662
$605$	5.10585e6	0.567126
$606$	28750.7	0.00318030
$607$	−6.65094e6	−0.732675	−0.366337	−	0.930482i	$-0.619388\pi$
$607$	−6.65094e6	−0.732675	−0.366337	+	0.930482i	$0.619388\pi$
$608$	462677.	0.0507597
$609$	−320737.	−0.0350434
$610$	−136923.	−0.0148988
$611$	6.21229e6	0.673207
$612$	5.70412e6	0.615617
$613$	−1.07456e7	−1.15499	−0.577497	−	0.816393i	$-0.695970\pi$
$613$	−1.07456e7	−1.15499	−0.577497	+	0.816393i	$0.695970\pi$
$614$	−44821.3	−0.00479804
$615$	602980.	0.0642859
$616$	75295.0	0.00799492
$617$	−1.66965e7	−1.76568	−0.882841	−	0.469673i	$-0.844372\pi$
$617$	−1.66965e7	−1.76568	−0.882841	+	0.469673i	$0.844372\pi$
$618$	−34255.5	−0.00360794
$619$	−1.06977e7	−1.12218	−0.561090	−	0.827755i	$-0.689618\pi$
$619$	−1.06977e7	−1.12218	−0.561090	+	0.827755i	$0.689618\pi$
$620$	−6.92603e6	−0.723611
$621$	−366351.	−0.0381214
$622$	383362.	0.0397313
$623$	2.78015e6	0.286977
$624$	−629021.	−0.0646701
$625$	−1.68007e6	−0.172039
$626$	275095.	0.0280574
$627$	−214074.	−0.0217468
$628$	1.40453e7	1.42113
$629$	−8.08024e6	−0.814325
$630$	66004.6	0.00662556
$631$	1.31871e7	1.31849	0.659243	−	0.751930i	$-0.270877\pi$
$631$	1.31871e7	1.31849	0.659243	+	0.751930i	$0.270877\pi$
$632$	676438.	0.0673651
$633$	−533290.	−0.0528998
$634$	−195402.	−0.0193066
$635$	−8.93670e6	−0.879514
$636$	313538.	0.0307360
$637$	−6.40601e6	−0.625517
$638$	−137279.	−0.0133522
$639$	−3.38089e6	−0.327551
$640$	−817330.	−0.0788765
$641$	−849150.	−0.0816280	−0.0408140	−	0.999167i	$-0.512995\pi$
$641$	−849150.	−0.0816280	−0.0408140	+	0.999167i	$0.512995\pi$
$642$	−30503.4	−0.00292086
$643$	−2.31164e6	−0.220491	−0.110246	−	0.993904i	$-0.535164\pi$
$643$	−2.31164e6	−0.220491	−0.110246	+	0.993904i	$0.535164\pi$
$644$	−741439.	−0.0704467
$645$	300536.	0.0284444
$646$	111641.	0.0105255
$647$	−1.51827e7	−1.42590	−0.712949	−	0.701216i	$-0.752641\pi$
$647$	−1.51827e7	−1.42590	−0.712949	+	0.701216i	$0.752641\pi$
$648$	605755.	0.0566708
$649$	−678179.	−0.0632023
$650$	119080.	0.0110549
$651$	−357725.	−0.0330824
$652$	4.01182e6	0.369592
$653$	1.57201e7	1.44269	0.721343	−	0.692578i	$-0.243525\pi$
$653$	1.57201e7	1.44269	0.721343	+	0.692578i	$0.243525\pi$
$654$	−2456.24	−0.000224557 0
$655$	−2.39016e6	−0.217683
$656$	1.13300e7	1.02795
$657$	5.61663e6	0.507647
$658$	104097.	0.00937288
$659$	−1.71369e7	−1.53716	−0.768580	−	0.639754i	$-0.779036\pi$
$659$	−1.71369e7	−1.53716	−0.768580	+	0.639754i	$0.779036\pi$
$660$	283666.	0.0253482
$661$	1.52598e7	1.35845	0.679227	−	0.733928i	$-0.262315\pi$
$661$	1.52598e7	1.35845	0.679227	+	0.733928i	$0.262315\pi$
$662$	344244.	0.0305296
$663$	−455978.	−0.0402865
$664$	1.20338e6	0.105922
$665$	−1.52628e6	−0.133839
$666$	−432570.	−0.0377895
$667$	2.70476e6	0.235404
$668$	2.00469e7	1.73823
$669$	956188.	0.0825996
$670$	−94760.3	−0.00815529
$671$	3.57623e6	0.306633
$672$	−31665.4	−0.00270497
$673$	−1.35466e7	−1.15290	−0.576451	−	0.817132i	$-0.695563\pi$
$673$	−1.35466e7	−1.15290	−0.576451	+	0.817132i	$0.695563\pi$
$674$	−352029.	−0.0298489
$675$	−1.16486e6	−0.0984048
$676$	5.94973e6	0.500761
$677$	1.13711e7	0.953520	0.476760	−	0.879034i	$-0.341811\pi$
$677$	1.13711e7	0.953520	0.476760	+	0.879034i	$0.341811\pi$
$678$	−59620.8	−0.00498108
$679$	4.03242e6	0.335654
$680$	−295991.	−0.0245474
$681$	1.44953e6	0.119773
$682$	−153111.	−0.0126050
$683$	−498823.	−0.0409161	−0.0204581	−	0.999791i	$-0.506512\pi$
$683$	−498823.	−0.0409161	−0.0204581	+	0.999791i	$0.506512\pi$
$684$	−7.06127e6	−0.577089
$685$	5.11153e6	0.416222
$686$	−228543.	−0.0185421
$687$	489406.	0.0395619
$688$	5.64709e6	0.454834
$689$	2.94914e6	0.236672
$690$	4730.44	0.000378250 0
$691$	1.03020e7	0.820783	0.410392	−	0.911909i	$-0.365392\pi$
$691$	1.03020e7	0.820783	0.410392	+	0.911909i	$0.365392\pi$
$692$	−1.60621e7	−1.27508
$693$	−1.72394e6	−0.136361
$694$	−621905.	−0.0490146
$695$	−1.09120e7	−0.856926
$696$	76999.1	0.00602508
$697$	8.21315e6	0.640366
$698$	−569962.	−0.0442800
$699$	1.13471e6	0.0878401
$700$	−2.35751e6	−0.181848
$701$	−3.29623e6	−0.253351	−0.126675	−	0.991944i	$-0.540431\pi$
$701$	−3.29623e6	−0.253351	−0.126675	+	0.991944i	$0.540431\pi$
$702$	−49028.4	−0.00375496
$703$	1.00027e7	0.763361
$704$	5.32105e6	0.404637
$705$	784679.	0.0594592
$706$	394537.	0.0297904
$707$	−5.35388e6	−0.402829
$708$	190113.	0.0142537
$709$	1.35819e7	1.01472	0.507359	−	0.861735i	$-0.330622\pi$
$709$	1.35819e7	1.01472	0.507359	+	0.861735i	$0.330622\pi$
$710$	87681.0	0.00652769
$711$	−1.54876e7	−1.14898
$712$	−667428.	−0.0493406
$713$	3.01667e6	0.222231
$714$	−7640.63	−0.000560898 0
$715$	2.66816e6	0.195185
$716$	4.21022e6	0.306918
$717$	−745212.	−0.0541354
$718$	335870.	0.0243142
$719$	−8.30096e6	−0.598834	−0.299417	−	0.954122i	$-0.596792\pi$
$719$	−8.30096e6	−0.598834	−0.299417	+	0.954122i	$0.596792\pi$
$720$	9.34882e6	0.672087
$721$	6.37896e6	0.456995
$722$	269126.	0.0192138
$723$	1.24086e6	0.0882831
$724$	−1.09734e7	−0.778027
$725$	8.60014e6	0.607660
$726$	−31641.5	−0.00222800
$727$	−5.01347e6	−0.351806	−0.175903	−	0.984408i	$-0.556284\pi$
$727$	−5.01347e6	−0.351806	−0.175903	+	0.984408i	$0.556284\pi$
$728$	−198536.	−0.0138839
$729$	−1.36285e7	−0.949792
$730$	−145663.	−0.0101168
$731$	4.09358e6	0.283341
$732$	−1.00252e6	−0.0691536
$733$	−1.48950e7	−1.02395	−0.511977	−	0.858999i	$-0.671087\pi$
$733$	−1.48950e7	−1.02395	−0.511977	+	0.858999i	$0.671087\pi$
$734$	−397052.	−0.0272024
$735$	−809148.	−0.0552471
$736$	267033.	0.0181706
$737$	2.47500e6	0.167844
$738$	439686.	0.0297168
$739$	8.39705e6	0.565608	0.282804	−	0.959178i	$-0.408735\pi$
$739$	8.39705e6	0.565608	0.282804	+	0.959178i	$0.408735\pi$
$740$	−1.32544e7	−0.889776
$741$	564466.	0.0377652
$742$	49417.6	0.00329512
$743$	−1.54362e7	−1.02582	−0.512908	−	0.858444i	$-0.671432\pi$
$743$	−1.54362e7	−1.02582	−0.512908	+	0.858444i	$0.671432\pi$
$744$	85878.8	0.00568792
$745$	1.58823e7	1.04839
$746$	−301163.	−0.0198132
$747$	−2.75526e7	−1.80659
$748$	3.86379e6	0.252499
$749$	5.68025e6	0.369967
$750$	42985.6	0.00279042
$751$	−5.26274e6	−0.340496	−0.170248	−	0.985401i	$-0.554457\pi$
$751$	−5.26274e6	−0.340496	−0.170248	+	0.985401i	$0.554457\pi$
$752$	1.47442e7	0.950771
$753$	845539.	0.0543433
$754$	361974.	0.0231873
$755$	−1.84988e7	−1.18107
$756$	970648.	0.0617671
$757$	−2.58188e7	−1.63756	−0.818779	−	0.574109i	$-0.805348\pi$
$757$	−2.58188e7	−1.63756	−0.818779	+	0.574109i	$0.805348\pi$
$758$	−862878.	−0.0545477
$759$	−123552.	−0.00778478
$760$	366414.	0.0230111
$761$	4.74356e6	0.296922	0.148461	−	0.988918i	$-0.452568\pi$
$761$	4.74356e6	0.296922	0.148461	+	0.988918i	$0.452568\pi$
$762$	55381.5	0.00345524
$763$	457395.	0.0284433
$764$	−2.65725e7	−1.64702
$765$	6.77697e6	0.418680
$766$	124119.	0.00764302
$767$	1.78820e6	0.109756
$768$	−1.48784e6	−0.0910234
$769$	2.16055e7	1.31749	0.658746	−	0.752365i	$-0.271087\pi$
$769$	2.16055e7	1.31749	0.658746	+	0.752365i	$0.271087\pi$
$770$	44709.4	0.00271751
$771$	642018.	0.0388966
$772$	−1.59469e7	−0.963017
$773$	4.60087e6	0.276944	0.138472	−	0.990366i	$-0.455781\pi$
$773$	4.60087e6	0.276944	0.138472	+	0.990366i	$0.455781\pi$
$774$	219147.	0.0131487
$775$	9.59193e6	0.573656
$776$	−968061.	−0.0577096
$777$	−684582.	−0.0406792
$778$	−337597.	−0.0199963
$779$	−1.01673e7	−0.600289
$780$	−747962.	−0.0440193
$781$	−2.29010e6	−0.134347
$782$	64433.0	0.00376783
$783$	−3.54091e6	−0.206400
$784$	−1.52039e7	−0.883417
$785$	1.66870e7	0.966505
$786$	14812.1	0.000855184 0
$787$	3.20780e7	1.84616	0.923082	−	0.384603i	$-0.125662\pi$
$787$	3.20780e7	1.84616	0.923082	+	0.384603i	$0.125662\pi$
$788$	−1.32763e7	−0.761661
$789$	−622062.	−0.0355747
$790$	401662.	0.0228977
$791$	1.11024e7	0.630924
$792$	413866.	0.0234448
$793$	−9.42971e6	−0.532495
$794$	−657881.	−0.0370336
$795$	372508.	0.0209035
$796$	3.09880e7	1.73345
$797$	950693.	0.0530145	0.0265072	−	0.999649i	$-0.491561\pi$
$797$	950693.	0.0530145	0.0265072	+	0.999649i	$0.491561\pi$
$798$	9458.53	0.000525795 0
$799$	1.06881e7	0.592287
$800$	849067.	0.0469047
$801$	1.52813e7	0.841551
$802$	840179.	0.0461250
$803$	3.80452e6	0.208215
$804$	−693813.	−0.0378532
$805$	−880890.	−0.0479106
$806$	403718.	0.0218897
$807$	−1.24973e6	−0.0675511
$808$	1.28530e6	0.0692592
$809$	1.89226e7	1.01650	0.508252	−	0.861208i	$-0.330292\pi$
$809$	1.89226e7	1.01650	0.508252	+	0.861208i	$0.330292\pi$
$810$	359691.	0.0192627
$811$	4.78517e6	0.255473	0.127737	−	0.991808i	$-0.459229\pi$
$811$	4.78517e6	0.255473	0.127737	+	0.991808i	$0.459229\pi$
$812$	−7.16625e6	−0.381419
$813$	1.66814e6	0.0885130
$814$	−293009.	−0.0154996
$815$	4.76637e6	0.251359
$816$	−1.08221e6	−0.0568967
$817$	−5.06754e6	−0.265608
$818$	504737.	0.0263744
$819$	4.54565e6	0.236803
$820$	1.34724e7	0.699699
$821$	5.51231e6	0.285414	0.142707	−	0.989765i	$-0.454419\pi$
$821$	5.51231e6	0.285414	0.142707	+	0.989765i	$0.454419\pi$
$822$	−31676.6	−0.00163516
$823$	−1.44617e7	−0.744249	−0.372125	−	0.928183i	$-0.621371\pi$
$823$	−1.44617e7	−0.744249	−0.372125	+	0.928183i	$0.621371\pi$
$824$	−1.53139e6	−0.0785721
$825$	−392852.	−0.0200953
$826$	29964.2	0.00152810
$827$	−2.78469e7	−1.41584	−0.707919	−	0.706294i	$-0.750366\pi$
$827$	−2.78469e7	−1.41584	−0.707919	+	0.706294i	$0.750366\pi$
$828$	−4.07539e6	−0.206582
$829$	1.89279e6	0.0956569	0.0478285	−	0.998856i	$-0.484770\pi$
$829$	1.89279e6	0.0956569	0.0478285	+	0.998856i	$0.484770\pi$
$830$	714557.	0.0360033
$831$	864360.	0.0434202
$832$	−1.40304e7	−0.702687
$833$	−1.10213e7	−0.550329
$834$	67622.8	0.00336650
$835$	2.38174e7	1.18216
$836$	−4.78308e6	−0.236697
$837$	−3.94925e6	−0.194850
$838$	−548788.	−0.0269957
$839$	8.81372e6	0.432269	0.216135	−	0.976364i	$-0.430655\pi$
$839$	8.81372e6	0.432269	0.216135	+	0.976364i	$0.430655\pi$
$840$	−25077.2	−0.00122626
$841$	5.63121e6	0.274544
$842$	452518.	0.0219966
$843$	−2.46352e6	−0.119395
$844$	−1.19153e7	−0.575771
$845$	7.06876e6	0.340566
$846$	572179.	0.0274856
$847$	5.89219e6	0.282207
$848$	6.99946e6	0.334253
$849$	2.88428e6	0.137331
$850$	204874.	0.00972610
$851$	5.77304e6	0.273263
$852$	641981.	0.0302986
$853$	4.21641e6	0.198413	0.0992064	−	0.995067i	$-0.468370\pi$
$853$	4.21641e6	0.198413	0.0992064	+	0.995067i	$0.468370\pi$
$854$	−158010.	−0.00741378
$855$	−8.38937e6	−0.392477
$856$	−1.36365e6	−0.0636092
$857$	1.36923e7	0.636829	0.318415	−	0.947952i	$-0.396850\pi$
$857$	1.36923e7	0.636829	0.318415	+	0.947952i	$0.396850\pi$
$858$	−16534.9	−0.000766801 0
$859$	1.31118e7	0.606291	0.303145	−	0.952944i	$-0.401963\pi$
$859$	1.31118e7	0.606291	0.303145	+	0.952944i	$0.401963\pi$
$860$	6.71489e6	0.309594
$861$	695843.	0.0319892
$862$	−152393.	−0.00698551
$863$	5.67126e6	0.259210	0.129605	−	0.991566i	$-0.458629\pi$
$863$	5.67126e6	0.259210	0.129605	+	0.991566i	$0.458629\pi$
$864$	−349583.	−0.0159319
$865$	−1.90830e7	−0.867176
$866$	−111998.	−0.00507475
$867$	1.24732e6	0.0563547
$868$	−7.99268e6	−0.360075
$869$	−1.04908e7	−0.471260
$870$	45721.3	0.00204795
$871$	−6.52602e6	−0.291476
$872$	−109806.	−0.00489031
$873$	2.21646e7	0.984293
$874$	−79763.2	−0.00353203
$875$	−8.00465e6	−0.353445
$876$	−1.06651e6	−0.0469577
$877$	−2.51970e7	−1.10624	−0.553120	−	0.833101i	$-0.686563\pi$
$877$	−2.51970e7	−1.10624	−0.553120	+	0.833101i	$0.686563\pi$
$878$	−357642.	−0.0156571
$879$	−2.08140e6	−0.0908622
$880$	6.33259e6	0.275661
$881$	−2.99532e7	−1.30018	−0.650090	−	0.759857i	$-0.725269\pi$
$881$	−2.99532e7	−1.30018	−0.650090	+	0.759857i	$0.725269\pi$
$882$	−590021.	−0.0255385
$883$	−2.98802e7	−1.28968	−0.644840	−	0.764318i	$-0.723076\pi$
$883$	−2.98802e7	−1.28968	−0.644840	+	0.764318i	$0.723076\pi$
$884$	−1.01879e7	−0.438486
$885$	225869.	0.00969392
$886$	−686834.	−0.0293946
$887$	−7.65547e6	−0.326710	−0.163355	−	0.986567i	$-0.552232\pi$
$887$	−7.65547e6	−0.326710	−0.163355	+	0.986567i	$0.552232\pi$
$888$	164347.	0.00699406
$889$	−1.03130e7	−0.437654
$890$	−396312.	−0.0167711
$891$	−9.39462e6	−0.396447
$892$	2.13642e7	0.899030
$893$	−1.32310e7	−0.555219
$894$	−98424.3	−0.00411868
$895$	5.00208e6	0.208734
$896$	−943203.	−0.0392496
$897$	325779.	0.0135189
$898$	771436.	0.0319234
$899$	2.91572e7	1.20322
$900$	−1.29583e7	−0.533262
$901$	5.07391e6	0.208224
$902$	297829.	0.0121885
$903$	346820.	0.0141542
$904$	−2.66535e6	−0.108476
$905$	−1.30373e7	−0.529134
$906$	114639.	0.00463992
$907$	−3.50928e7	−1.41644	−0.708222	−	0.705990i	$-0.750502\pi$
$907$	−3.50928e7	−1.41644	−0.708222	+	0.705990i	$0.750502\pi$
$908$	3.23869e7	1.30363
$909$	−2.94282e7	−1.18128
$910$	−117888.	−0.00471919
$911$	−3.03942e7	−1.21337	−0.606687	−	0.794941i	$-0.707502\pi$
$911$	−3.03942e7	−1.21337	−0.606687	+	0.794941i	$0.707502\pi$
$912$	1.33970e6	0.0533359
$913$	−1.86632e7	−0.740985
$914$	277983.	0.0110066
$915$	−1.19107e6	−0.0470312
$916$	1.09348e7	0.430599
$917$	−2.75826e6	−0.108321
$918$	−84351.9	−0.00330361
$919$	3.59276e7	1.40326	0.701632	−	0.712540i	$-0.252455\pi$
$919$	3.59276e7	1.40326	0.701632	+	0.712540i	$0.252455\pi$
$920$	211475.	0.00823737
$921$	−389894.	−0.0151460
$922$	705337.	0.0273256
$923$	6.03848e6	0.233305
$924$	327352.	0.0126135
$925$	1.83562e7	0.705387
$926$	−866507.	−0.0332081
$927$	3.50626e7	1.34012
$928$	2.58096e6	0.0983809
$929$	−9.41890e6	−0.358064	−0.179032	−	0.983843i	$-0.557297\pi$
$929$	−9.41890e6	−0.358064	−0.179032	+	0.983843i	$0.557297\pi$
$930$	50994.0	0.00193335
$931$	1.36436e7	0.515887
$932$	2.53529e7	0.956068
$933$	3.33481e6	0.125420
$934$	602587.	0.0226023
$935$	4.59050e6	0.171724
$936$	−1.09127e6	−0.0407139
$937$	−2.13837e7	−0.795673	−0.397836	−	0.917456i	$-0.630239\pi$
$937$	−2.13837e7	−0.795673	−0.397836	+	0.917456i	$0.630239\pi$
$938$	−109354.	−0.00405814
$939$	2.39302e6	0.0885690
$940$	1.75321e7	0.647165
$941$	4.31706e7	1.58933	0.794666	−	0.607047i	$-0.207646\pi$
$941$	4.31706e7	1.58933	0.794666	+	0.607047i	$0.207646\pi$
$942$	−103411.	−0.00379699
$943$	−5.86800e6	−0.214887
$944$	4.24410e6	0.155009
$945$	1.15321e6	0.0420077
$946$	148443.	0.00539302
$947$	1.75109e7	0.634504	0.317252	−	0.948341i	$-0.397240\pi$
$947$	1.75109e7	0.634504	0.317252	+	0.948341i	$0.397240\pi$
$948$	2.94088e6	0.106281
$949$	−1.00317e7	−0.361582
$950$	−253618.	−0.00911740
$951$	−1.69977e6	−0.0609452
$952$	−341575.	−0.0122150
$953$	−4.05106e6	−0.144489	−0.0722447	−	0.997387i	$-0.523016\pi$
$953$	−4.05106e6	−0.144489	−0.0722447	+	0.997387i	$0.523016\pi$
$954$	271629.	0.00966283
$955$	−3.15703e7	−1.12013
$956$	−1.66503e7	−0.589220
$957$	−1.19417e6	−0.0421490
$958$	−1.15705e6	−0.0407321
$959$	5.89874e6	0.207116
$960$	−1.77219e6	−0.0620630
$961$	3.89048e6	0.135892
$962$	772599.	0.0269164
$963$	3.12221e7	1.08492
$964$	2.77246e7	0.960889
$965$	−1.89463e7	−0.654946
$966$	5458.96	0.000188220 0
$967$	−2.54319e7	−0.874608	−0.437304	−	0.899314i	$-0.644067\pi$
$967$	−2.54319e7	−0.874608	−0.437304	+	0.899314i	$0.644067\pi$
$968$	−1.41453e6	−0.0485204
$969$	971147.	0.0332258
$970$	−574824.	−0.0196158
$971$	−4.42829e6	−0.150726	−0.0753630	−	0.997156i	$-0.524012\pi$
$971$	−4.42829e6	−0.150726	−0.0753630	+	0.997156i	$0.524012\pi$
$972$	8.01418e6	0.272078
$973$	−1.25925e7	−0.426414
$974$	−831026.	−0.0280684
$975$	1.03586e6	0.0348971
$976$	−2.23804e7	−0.752043
$977$	5.60569e7	1.87885	0.939427	−	0.342750i	$-0.111358\pi$
$977$	5.60569e7	1.87885	0.939427	+	0.342750i	$0.111358\pi$
$978$	−29537.6	−0.000987481 0
$979$	1.03511e7	0.345167
$980$	−1.80788e7	−0.601320
$981$	2.51412e6	0.0834090
$982$	642046.	0.0212465
$983$	3.41997e7	1.12886	0.564428	−	0.825482i	$-0.309097\pi$
$983$	3.41997e7	1.12886	0.564428	+	0.825482i	$0.309097\pi$
$984$	−167050.	−0.00549997
$985$	−1.57733e7	−0.518004
$986$	622766.	0.0204001
$987$	905525.	0.0295874
$988$	1.26119e7	0.411044
$989$	−2.92471e6	−0.0950807
$990$	245749.	0.00796901
$991$	−904509.	−0.0292569	−0.0146285	−	0.999893i	$-0.504657\pi$
$991$	−904509.	−0.0292569	−0.0146285	+	0.999893i	$0.504657\pi$
$992$	2.87860e6	0.0928757
$993$	2.99453e6	0.0963730
$994$	101184.	0.00324824
$995$	3.68163e7	1.17891
$996$	5.23183e6	0.167111
$997$	−4.00447e7	−1.27587	−0.637936	−	0.770089i	$-0.720212\pi$
$997$	−4.00447e7	−1.27587	−0.637936	+	0.770089i	$0.720212\pi$
$998$	−187235.	−0.00595060
$999$	−7.55772e6	−0.239595

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.6.a.a.1.2	✓	3
3.2	odd	2		207.6.a.b.1.2		3
4.3	odd	2		368.6.a.e.1.2		3
5.4	even	2		575.6.a.b.1.2		3
23.22	odd	2		529.6.a.a.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.6.a.a.1.2	✓	3	1.1	even	1	trivial
207.6.a.b.1.2		3	3.2	odd	2
368.6.a.e.1.2		3	4.3	odd	2
529.6.a.a.1.2		3	23.22	odd	2
575.6.a.b.1.2		3	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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q-0.164504 q^{2} -1.43100 q^{3} -31.9729 q^{4} -37.9865 q^{5} +0.235406 q^{6} -43.8366 q^{7} +10.5238 q^{8} -240.952 q^{9} +O(q^{10})\)	\(q-0.164504 q^{2} -1.43100 q^{3} -31.9729 q^{4} -37.9865 q^{5} +0.235406 q^{6} -43.8366 q^{7} +10.5238 q^{8} -240.952 q^{9} +6.24894 q^{10} -163.213 q^{11} +45.7533 q^{12} +430.356 q^{13} +7.21131 q^{14} +54.3587 q^{15} +1021.40 q^{16} +740.415 q^{17} +39.6377 q^{18} -916.578 q^{19} +1214.54 q^{20} +62.7302 q^{21} +26.8493 q^{22} -529.000 q^{23} -15.0596 q^{24} -1682.03 q^{25} -70.7955 q^{26} +692.536 q^{27} +1401.59 q^{28} -5112.96 q^{29} -8.94223 q^{30} -5702.60 q^{31} -504.787 q^{32} +233.558 q^{33} -121.802 q^{34} +1665.20 q^{35} +7703.95 q^{36} -10913.1 q^{37} +150.781 q^{38} -615.840 q^{39} -399.763 q^{40} +11092.6 q^{41} -10.3194 q^{42} +5528.76 q^{43} +5218.41 q^{44} +9152.92 q^{45} +87.0228 q^{46} +14435.2 q^{47} -1461.63 q^{48} -14885.4 q^{49} +276.701 q^{50} -1059.53 q^{51} -13759.8 q^{52} +6852.79 q^{53} -113.925 q^{54} +6199.90 q^{55} -461.329 q^{56} +1311.62 q^{57} +841.104 q^{58} +4155.17 q^{59} -1738.01 q^{60} -21911.4 q^{61} +938.102 q^{62} +10562.5 q^{63} -32601.9 q^{64} -16347.7 q^{65} -38.4213 q^{66} -15164.2 q^{67} -23673.3 q^{68} +756.999 q^{69} -273.932 q^{70} +14031.4 q^{71} -2535.74 q^{72} -23310.1 q^{73} +1795.25 q^{74} +2406.98 q^{75} +29305.7 q^{76} +7154.72 q^{77} +101.308 q^{78} +64276.8 q^{79} -38799.5 q^{80} +57560.4 q^{81} -1824.78 q^{82} +114349. q^{83} -2005.67 q^{84} -28125.8 q^{85} -909.504 q^{86} +7316.65 q^{87} -1717.63 q^{88} -63420.7 q^{89} -1505.70 q^{90} -18865.4 q^{91} +16913.7 q^{92} +8160.42 q^{93} -2374.66 q^{94} +34817.6 q^{95} +722.351 q^{96} -91987.6 q^{97} +2448.70 q^{98} +39326.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 4 q^{2} - 20 q^{3} + 16 q^{4} - 58 q^{5} - 230 q^{6} - 282 q^{7} - 360 q^{8} + 121 q^{9}+O(q^{10}) \) 3 * q - 4 * q^2 - 20 * q^3 + 16 * q^4 - 58 * q^5 - 230 * q^6 - 282 * q^7 - 360 * q^8 + 121 * q^9	\( 3 q - 4 q^{2} - 20 q^{3} + 16 q^{4} - 58 q^{5} - 230 q^{6} - 282 q^{7} - 360 q^{8} + 121 q^{9} - 156 q^{10} + 136 q^{11} + 620 q^{12} - 1116 q^{13} + 2016 q^{14} + 750 q^{15} + 128 q^{16} - 896 q^{17} + 4282 q^{18} + 1654 q^{19} + 1504 q^{20} - 1670 q^{21} + 1352 q^{22} - 1587 q^{23} + 3600 q^{24} - 7347 q^{25} + 1998 q^{26} - 10700 q^{27} - 10264 q^{28} - 844 q^{29} + 3180 q^{30} - 3020 q^{31} + 6656 q^{32} - 7370 q^{33} - 11212 q^{34} + 1072 q^{35} - 2548 q^{36} + 8938 q^{37} + 10728 q^{38} + 16020 q^{39} + 3440 q^{40} - 12792 q^{41} + 20560 q^{42} - 16730 q^{43} + 5112 q^{44} - 3936 q^{45} + 2116 q^{46} + 22500 q^{47} + 23120 q^{48} + 2887 q^{49} + 15156 q^{50} + 50290 q^{51} - 47412 q^{52} + 17108 q^{53} - 7610 q^{54} - 436 q^{55} + 42640 q^{56} - 61960 q^{57} - 55678 q^{58} + 54176 q^{59} - 2400 q^{60} - 71324 q^{61} - 72710 q^{62} + 40696 q^{63} - 49984 q^{64} + 846 q^{65} - 42860 q^{66} - 62960 q^{67} - 8352 q^{68} + 10580 q^{69} + 9224 q^{70} + 98400 q^{71} - 72840 q^{72} - 81772 q^{73} - 59044 q^{74} + 44800 q^{75} + 31488 q^{76} - 304 q^{77} + 182070 q^{78} + 58224 q^{79} - 17568 q^{80} + 149947 q^{81} + 61926 q^{82} + 9892 q^{83} - 109720 q^{84} + 15536 q^{85} + 191140 q^{86} + 90500 q^{87} - 58400 q^{88} + 27542 q^{89} - 62112 q^{90} + 151974 q^{91} - 8464 q^{92} + 157330 q^{93} - 146990 q^{94} - 20644 q^{95} + 16160 q^{96} - 273672 q^{97} - 401276 q^{98} + 183082 q^{99}+O(q^{100}) \) 3 * q - 4 * q^2 - 20 * q^3 + 16 * q^4 - 58 * q^5 - 230 * q^6 - 282 * q^7 - 360 * q^8 + 121 * q^9 - 156 * q^10 + 136 * q^11 + 620 * q^12 - 1116 * q^13 + 2016 * q^14 + 750 * q^15 + 128 * q^16 - 896 * q^17 + 4282 * q^18 + 1654 * q^19 + 1504 * q^20 - 1670 * q^21 + 1352 * q^22 - 1587 * q^23 + 3600 * q^24 - 7347 * q^25 + 1998 * q^26 - 10700 * q^27 - 10264 * q^28 - 844 * q^29 + 3180 * q^30 - 3020 * q^31 + 6656 * q^32 - 7370 * q^33 - 11212 * q^34 + 1072 * q^35 - 2548 * q^36 + 8938 * q^37 + 10728 * q^38 + 16020 * q^39 + 3440 * q^40 - 12792 * q^41 + 20560 * q^42 - 16730 * q^43 + 5112 * q^44 - 3936 * q^45 + 2116 * q^46 + 22500 * q^47 + 23120 * q^48 + 2887 * q^49 + 15156 * q^50 + 50290 * q^51 - 47412 * q^52 + 17108 * q^53 - 7610 * q^54 - 436 * q^55 + 42640 * q^56 - 61960 * q^57 - 55678 * q^58 + 54176 * q^59 - 2400 * q^60 - 71324 * q^61 - 72710 * q^62 + 40696 * q^63 - 49984 * q^64 + 846 * q^65 - 42860 * q^66 - 62960 * q^67 - 8352 * q^68 + 10580 * q^69 + 9224 * q^70 + 98400 * q^71 - 72840 * q^72 - 81772 * q^73 - 59044 * q^74 + 44800 * q^75 + 31488 * q^76 - 304 * q^77 + 182070 * q^78 + 58224 * q^79 - 17568 * q^80 + 149947 * q^81 + 61926 * q^82 + 9892 * q^83 - 109720 * q^84 + 15536 * q^85 + 191140 * q^86 + 90500 * q^87 - 58400 * q^88 + 27542 * q^89 - 62112 * q^90 + 151974 * q^91 - 8464 * q^92 + 157330 * q^93 - 146990 * q^94 - 20644 * q^95 + 16160 * q^96 - 273672 * q^97 - 401276 * q^98 + 183082 * q^99

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