LMFDB - Embedded newform 966.4.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.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:	$56.9958450655$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 264x^{2} - 1037x + 3708 $ x^4 - 2x^3 - 264x^2 - 1037*x + 3708
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-8.32744$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -6.32744 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -6.32744 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +12.6549 q^{10} +39.4055 q^{11} -12.0000 q^{12} -67.4943 q^{13} -14.0000 q^{14} +18.9823 q^{15} +16.0000 q^{16} +40.5591 q^{17} -18.0000 q^{18} +83.3643 q^{19} -25.3098 q^{20} -21.0000 q^{21} -78.8111 q^{22} +23.0000 q^{23} +24.0000 q^{24} -84.9635 q^{25} +134.989 q^{26} -27.0000 q^{27} +28.0000 q^{28} -176.392 q^{29} -37.9646 q^{30} +233.917 q^{31} -32.0000 q^{32} -118.217 q^{33} -81.1182 q^{34} -44.2921 q^{35} +36.0000 q^{36} +128.967 q^{37} -166.729 q^{38} +202.483 q^{39} +50.6195 q^{40} -263.967 q^{41} +42.0000 q^{42} -190.615 q^{43} +157.622 q^{44} -56.9470 q^{45} -46.0000 q^{46} +63.7249 q^{47} -48.0000 q^{48} +49.0000 q^{49} +169.927 q^{50} -121.677 q^{51} -269.977 q^{52} +32.3078 q^{53} +54.0000 q^{54} -249.336 q^{55} -56.0000 q^{56} -250.093 q^{57} +352.783 q^{58} +483.255 q^{59} +75.9293 q^{60} -778.895 q^{61} -467.834 q^{62} +63.0000 q^{63} +64.0000 q^{64} +427.066 q^{65} +236.433 q^{66} -279.612 q^{67} +162.236 q^{68} -69.0000 q^{69} +88.5842 q^{70} +245.286 q^{71} -72.0000 q^{72} -1080.00 q^{73} -257.934 q^{74} +254.890 q^{75} +333.457 q^{76} +275.839 q^{77} -404.966 q^{78} -578.224 q^{79} -101.239 q^{80} +81.0000 q^{81} +527.934 q^{82} +1330.21 q^{83} -84.0000 q^{84} -256.635 q^{85} +381.230 q^{86} +529.175 q^{87} -315.244 q^{88} +251.818 q^{89} +113.894 q^{90} -472.460 q^{91} +92.0000 q^{92} -701.750 q^{93} -127.450 q^{94} -527.483 q^{95} +96.0000 q^{96} +407.405 q^{97} -98.0000 q^{98} +354.650 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} + 10 q^{5} + 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 + 10 * q^5 + 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} + 10 q^{5} + 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9} - 20 q^{10} + 24 q^{11} - 48 q^{12} - 46 q^{13} - 56 q^{14} - 30 q^{15} + 64 q^{16} + 84 q^{17} - 72 q^{18} + 74 q^{19} + 40 q^{20} - 84 q^{21} - 48 q^{22} + 92 q^{23} + 96 q^{24} + 56 q^{25} + 92 q^{26} - 108 q^{27} + 112 q^{28} + 453 q^{29} + 60 q^{30} + 244 q^{31} - 128 q^{32} - 72 q^{33} - 168 q^{34} + 70 q^{35} + 144 q^{36} - 179 q^{37} - 148 q^{38} + 138 q^{39} - 80 q^{40} + 259 q^{41} + 168 q^{42} - 750 q^{43} + 96 q^{44} + 90 q^{45} - 184 q^{46} + 291 q^{47} - 192 q^{48} + 196 q^{49} - 112 q^{50} - 252 q^{51} - 184 q^{52} + 193 q^{53} + 216 q^{54} - 833 q^{55} - 224 q^{56} - 222 q^{57} - 906 q^{58} - 235 q^{59} - 120 q^{60} - 133 q^{61} - 488 q^{62} + 252 q^{63} + 256 q^{64} - 1113 q^{65} + 144 q^{66} + 113 q^{67} + 336 q^{68} - 276 q^{69} - 140 q^{70} - 31 q^{71} - 288 q^{72} - 614 q^{73} + 358 q^{74} - 168 q^{75} + 296 q^{76} + 168 q^{77} - 276 q^{78} - 30 q^{79} + 160 q^{80} + 324 q^{81} - 518 q^{82} + 2468 q^{83} - 336 q^{84} - 2083 q^{85} + 1500 q^{86} - 1359 q^{87} - 192 q^{88} + 565 q^{89} - 180 q^{90} - 322 q^{91} + 368 q^{92} - 732 q^{93} - 582 q^{94} + 141 q^{95} + 384 q^{96} - 459 q^{97} - 392 q^{98} + 216 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 + 10 * q^5 + 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9 - 20 * q^10 + 24 * q^11 - 48 * q^12 - 46 * q^13 - 56 * q^14 - 30 * q^15 + 64 * q^16 + 84 * q^17 - 72 * q^18 + 74 * q^19 + 40 * q^20 - 84 * q^21 - 48 * q^22 + 92 * q^23 + 96 * q^24 + 56 * q^25 + 92 * q^26 - 108 * q^27 + 112 * q^28 + 453 * q^29 + 60 * q^30 + 244 * q^31 - 128 * q^32 - 72 * q^33 - 168 * q^34 + 70 * q^35 + 144 * q^36 - 179 * q^37 - 148 * q^38 + 138 * q^39 - 80 * q^40 + 259 * q^41 + 168 * q^42 - 750 * q^43 + 96 * q^44 + 90 * q^45 - 184 * q^46 + 291 * q^47 - 192 * q^48 + 196 * q^49 - 112 * q^50 - 252 * q^51 - 184 * q^52 + 193 * q^53 + 216 * q^54 - 833 * q^55 - 224 * q^56 - 222 * q^57 - 906 * q^58 - 235 * q^59 - 120 * q^60 - 133 * q^61 - 488 * q^62 + 252 * q^63 + 256 * q^64 - 1113 * q^65 + 144 * q^66 + 113 * q^67 + 336 * q^68 - 276 * q^69 - 140 * q^70 - 31 * q^71 - 288 * q^72 - 614 * q^73 + 358 * q^74 - 168 * q^75 + 296 * q^76 + 168 * q^77 - 276 * q^78 - 30 * q^79 + 160 * q^80 + 324 * q^81 - 518 * q^82 + 2468 * q^83 - 336 * q^84 - 2083 * q^85 + 1500 * q^86 - 1359 * q^87 - 192 * q^88 + 565 * q^89 - 180 * q^90 - 322 * q^91 + 368 * q^92 - 732 * q^93 - 582 * q^94 + 141 * q^95 + 384 * q^96 - 459 * q^97 - 392 * q^98 + 216 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−6.32744	−0.565943	−0.282972	−	0.959128i	$-0.591320\pi$
$5$	−6.32744	−0.565943	−0.282972	+	0.959128i	$0.591320\pi$
$6$	6.00000	0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	12.6549	0.400182
$11$	39.4055	1.08011	0.540055	−	0.841629i	$-0.318403\pi$
$11$	39.4055	1.08011	0.540055	+	0.841629i	$0.318403\pi$
$12$	−12.0000	−0.288675
$13$	−67.4943	−1.43997	−0.719983	−	0.693992i	$-0.755850\pi$
$13$	−67.4943	−1.43997	−0.719983	+	0.693992i	$0.755850\pi$
$14$	−14.0000	−0.267261
$15$	18.9823	0.326748
$16$	16.0000	0.250000
$17$	40.5591	0.578649	0.289324	−	0.957231i	$-0.406569\pi$
$17$	40.5591	0.578649	0.289324	+	0.957231i	$0.406569\pi$
$18$	−18.0000	−0.235702
$19$	83.3643	1.00658	0.503292	−	0.864117i	$-0.332122\pi$
$19$	83.3643	1.00658	0.503292	+	0.864117i	$0.332122\pi$
$20$	−25.3098	−0.282972
$21$	−21.0000	−0.218218
$22$	−78.8111	−0.763754
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	24.0000	0.204124
$25$	−84.9635	−0.679708
$26$	134.989	1.01821
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	−176.392	−1.12949	−0.564743	−	0.825267i	$-0.691025\pi$
$29$	−176.392	−1.12949	−0.564743	+	0.825267i	$0.691025\pi$
$30$	−37.9646	−0.231045
$31$	233.917	1.35525	0.677624	−	0.735408i	$-0.263010\pi$
$31$	233.917	1.35525	0.677624	+	0.735408i	$0.263010\pi$
$32$	−32.0000	−0.176777
$33$	−118.217	−0.623602
$34$	−81.1182	−0.409166
$35$	−44.2921	−0.213907
$36$	36.0000	0.166667
$37$	128.967	0.573028	0.286514	−	0.958076i	$-0.407504\pi$
$37$	128.967	0.573028	0.286514	+	0.958076i	$0.407504\pi$
$38$	−166.729	−0.711762
$39$	202.483	0.831364
$40$	50.6195	0.200091
$41$	−263.967	−1.00548	−0.502741	−	0.864437i	$-0.667675\pi$
$41$	−263.967	−1.00548	−0.502741	+	0.864437i	$0.667675\pi$
$42$	42.0000	0.154303
$43$	−190.615	−0.676011	−0.338006	−	0.941144i	$-0.609752\pi$
$43$	−190.615	−0.676011	−0.338006	+	0.941144i	$0.609752\pi$
$44$	157.622	0.540055
$45$	−56.9470	−0.188648
$46$	−46.0000	−0.147442
$47$	63.7249	0.197771	0.0988854	−	0.995099i	$-0.468472\pi$
$47$	63.7249	0.197771	0.0988854	+	0.995099i	$0.468472\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	169.927	0.480626
$51$	−121.677	−0.334083
$52$	−269.977	−0.719983
$53$	32.3078	0.0837324	0.0418662	−	0.999123i	$-0.486670\pi$
$53$	32.3078	0.0837324	0.0418662	+	0.999123i	$0.486670\pi$
$54$	54.0000	0.136083
$55$	−249.336	−0.611282
$56$	−56.0000	−0.133631
$57$	−250.093	−0.581151
$58$	352.783	0.798667
$59$	483.255	1.06635	0.533174	−	0.846006i	$-0.320999\pi$
$59$	483.255	1.06635	0.533174	+	0.846006i	$0.320999\pi$
$60$	75.9293	0.163374
$61$	−778.895	−1.63487	−0.817437	−	0.576018i	$-0.804606\pi$
$61$	−778.895	−1.63487	−0.817437	+	0.576018i	$0.804606\pi$
$62$	−467.834	−0.958305
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	427.066	0.814939
$66$	236.433	0.440953
$67$	−279.612	−0.509852	−0.254926	−	0.966961i	$-0.582051\pi$
$67$	−279.612	−0.509852	−0.254926	+	0.966961i	$0.582051\pi$
$68$	162.236	0.289324
$69$	−69.0000	−0.120386
$70$	88.5842	0.151255
$71$	245.286	0.410001	0.205001	−	0.978762i	$-0.434280\pi$
$71$	245.286	0.410001	0.205001	+	0.978762i	$0.434280\pi$
$72$	−72.0000	−0.117851
$73$	−1080.00	−1.73156	−0.865782	−	0.500421i	$-0.833179\pi$
$73$	−1080.00	−1.73156	−0.865782	+	0.500421i	$0.833179\pi$
$74$	−257.934	−0.405192
$75$	254.890	0.392430
$76$	333.457	0.503292
$77$	275.839	0.408244
$78$	−404.966	−0.587863
$79$	−578.224	−0.823484	−0.411742	−	0.911300i	$-0.635080\pi$
$79$	−578.224	−0.823484	−0.411742	+	0.911300i	$0.635080\pi$
$80$	−101.239	−0.141486
$81$	81.0000	0.111111
$82$	527.934	0.710983
$83$	1330.21	1.75915	0.879575	−	0.475760i	$-0.157827\pi$
$83$	1330.21	1.75915	0.879575	+	0.475760i	$0.157827\pi$
$84$	−84.0000	−0.109109
$85$	−256.635	−0.327482
$86$	381.230	0.478012
$87$	529.175	0.652109
$88$	−315.244	−0.381877
$89$	251.818	0.299917	0.149959	−	0.988692i	$-0.452086\pi$
$89$	251.818	0.299917	0.149959	+	0.988692i	$0.452086\pi$
$90$	113.894	0.133394
$91$	−472.460	−0.544256
$92$	92.0000	0.104257
$93$	−701.750	−0.782453
$94$	−127.450	−0.139845
$95$	−527.483	−0.569669
$96$	96.0000	0.102062
$97$	407.405	0.426450	0.213225	−	0.977003i	$-0.431603\pi$
$97$	407.405	0.426450	0.213225	+	0.977003i	$0.431603\pi$
$98$	−98.0000	−0.101015
$99$	354.650	0.360037
$100$	−339.854	−0.339854
$101$	1167.38	1.15009	0.575044	−	0.818123i	$-0.304985\pi$
$101$	1167.38	1.15009	0.575044	+	0.818123i	$0.304985\pi$
$102$	243.355	0.236232
$103$	1422.95	1.36124	0.680618	−	0.732639i	$-0.261711\pi$
$103$	1422.95	1.36124	0.680618	+	0.732639i	$0.261711\pi$
$104$	539.954	0.509105
$105$	132.876	0.123499
$106$	−64.6156	−0.0592077
$107$	214.445	0.193749	0.0968745	−	0.995297i	$-0.469115\pi$
$107$	214.445	0.193749	0.0968745	+	0.995297i	$0.469115\pi$
$108$	−108.000	−0.0962250
$109$	763.874	0.671247	0.335623	−	0.941996i	$-0.391053\pi$
$109$	763.874	0.671247	0.335623	+	0.941996i	$0.391053\pi$
$110$	498.673	0.432241
$111$	−386.901	−0.330838
$112$	112.000	0.0944911
$113$	−37.3522	−0.0310956	−0.0155478	−	0.999879i	$-0.504949\pi$
$113$	−37.3522	−0.0310956	−0.0155478	+	0.999879i	$0.504949\pi$
$114$	500.186	0.410936
$115$	−145.531	−0.118007
$116$	−705.566	−0.564743
$117$	−607.449	−0.479989
$118$	−966.511	−0.754021
$119$	283.914	0.218709
$120$	−151.859	−0.115523
$121$	221.797	0.166639
$122$	1557.79	1.15603
$123$	791.902	0.580515
$124$	935.667	0.677624
$125$	1328.53	0.950620
$126$	−126.000	−0.0890871
$127$	−1919.66	−1.34128	−0.670640	−	0.741783i	$-0.733980\pi$
$127$	−1919.66	−1.34128	−0.670640	+	0.741783i	$0.733980\pi$
$128$	−128.000	−0.0883883
$129$	571.844	0.390295
$130$	−854.132	−0.576249
$131$	2542.30	1.69558	0.847792	−	0.530328i	$-0.177931\pi$
$131$	2542.30	1.69558	0.847792	+	0.530328i	$0.177931\pi$
$132$	−472.867	−0.311801
$133$	583.550	0.380453
$134$	559.225	0.360520
$135$	170.841	0.108916
$136$	−324.473	−0.204583
$137$	−2921.90	−1.82215	−0.911076	−	0.412238i	$-0.864747\pi$
$137$	−2921.90	−1.82215	−0.911076	+	0.412238i	$0.864747\pi$
$138$	138.000	0.0851257
$139$	2784.78	1.69929	0.849646	−	0.527353i	$-0.176815\pi$
$139$	2784.78	1.69929	0.849646	+	0.527353i	$0.176815\pi$
$140$	−177.168	−0.106953
$141$	−191.175	−0.114183
$142$	−490.572	−0.289915
$143$	−2659.65	−1.55532
$144$	144.000	0.0833333
$145$	1116.11	0.639225
$146$	2160.00	1.22440
$147$	−147.000	−0.0824786
$148$	515.867	0.286514
$149$	2741.26	1.50720	0.753600	−	0.657334i	$-0.228316\pi$
$149$	2741.26	1.50720	0.753600	+	0.657334i	$0.228316\pi$
$150$	−509.781	−0.277490
$151$	−15.0725	−0.00812304	−0.00406152	−	0.999992i	$-0.501293\pi$
$151$	−15.0725	−0.00812304	−0.00406152	+	0.999992i	$0.501293\pi$
$152$	−666.914	−0.355881
$153$	365.032	0.192883
$154$	−551.678	−0.288672
$155$	−1480.09	−0.766994
$156$	809.932	0.415682
$157$	−1359.92	−0.691294	−0.345647	−	0.938365i	$-0.612341\pi$
$157$	−1359.92	−0.691294	−0.345647	+	0.938365i	$0.612341\pi$
$158$	1156.45	0.582291
$159$	−96.9234	−0.0483429
$160$	202.478	0.100046
$161$	161.000	0.0788110
$162$	−162.000	−0.0785674
$163$	−3684.27	−1.77039	−0.885197	−	0.465215i	$-0.845977\pi$
$163$	−3684.27	−1.77039	−0.885197	+	0.465215i	$0.845977\pi$
$164$	−1055.87	−0.502741
$165$	748.009	0.352924
$166$	−2660.42	−1.24391
$167$	3218.96	1.49156	0.745780	−	0.666193i	$-0.232077\pi$
$167$	3218.96	1.49156	0.745780	+	0.666193i	$0.232077\pi$
$168$	168.000	0.0771517
$169$	2358.48	1.07350
$170$	513.271	0.231565
$171$	750.279	0.335528
$172$	−762.459	−0.338006
$173$	1683.93	0.740039	0.370020	−	0.929024i	$-0.379351\pi$
$173$	1683.93	0.740039	0.370020	+	0.929024i	$0.379351\pi$
$174$	−1058.35	−0.461111
$175$	−594.744	−0.256905
$176$	630.489	0.270028
$177$	−1449.77	−0.615656
$178$	−503.636	−0.212073
$179$	3598.81	1.50273	0.751363	−	0.659889i	$-0.229397\pi$
$179$	3598.81	1.50273	0.751363	+	0.659889i	$0.229397\pi$
$180$	−227.788	−0.0943239
$181$	1170.35	0.480614	0.240307	−	0.970697i	$-0.422752\pi$
$181$	1170.35	0.480614	0.240307	+	0.970697i	$0.422752\pi$
$182$	944.920	0.384847
$183$	2336.68	0.943895
$184$	−184.000	−0.0737210
$185$	−816.030	−0.324301
$186$	1403.50	0.553278
$187$	1598.25	0.625005
$188$	254.899	0.0988854
$189$	−189.000	−0.0727393
$190$	1054.97	0.402817
$191$	870.746	0.329869	0.164934	−	0.986305i	$-0.447259\pi$
$191$	870.746	0.329869	0.164934	+	0.986305i	$0.447259\pi$
$192$	−192.000	−0.0721688
$193$	3954.90	1.47503	0.737513	−	0.675333i	$-0.236000\pi$
$193$	3954.90	1.47503	0.737513	+	0.675333i	$0.236000\pi$
$194$	−814.809	−0.301546
$195$	−1281.20	−0.470505
$196$	196.000	0.0714286
$197$	1641.45	0.593646	0.296823	−	0.954932i	$-0.404073\pi$
$197$	1641.45	0.593646	0.296823	+	0.954932i	$0.404073\pi$
$198$	−709.300	−0.254585
$199$	2227.34	0.793427	0.396713	−	0.917943i	$-0.370151\pi$
$199$	2227.34	0.793427	0.396713	+	0.917943i	$0.370151\pi$
$200$	679.708	0.240313
$201$	838.837	0.294363
$202$	−2334.76	−0.813235
$203$	−1234.74	−0.426906
$204$	−486.709	−0.167041
$205$	1670.24	0.569046
$206$	−2845.90	−0.962539
$207$	207.000	0.0695048
$208$	−1079.91	−0.359991
$209$	3285.02	1.08722
$210$	−265.753	−0.0873270
$211$	2537.17	0.827802	0.413901	−	0.910322i	$-0.364166\pi$
$211$	2537.17	0.827802	0.413901	+	0.910322i	$0.364166\pi$
$212$	129.231	0.0418662
$213$	−735.858	−0.236714
$214$	−428.889	−0.137001
$215$	1206.10	0.382584
$216$	216.000	0.0680414
$217$	1637.42	0.512236
$218$	−1527.75	−0.474643
$219$	3239.99	0.999719
$220$	−997.345	−0.305641
$221$	−2737.51	−0.833234
$222$	773.801	0.233938
$223$	6287.25	1.88801	0.944003	−	0.329938i	$-0.107028\pi$
$223$	6287.25	1.88801	0.944003	+	0.329938i	$0.107028\pi$
$224$	−224.000	−0.0668153
$225$	−764.671	−0.226569
$226$	74.7045	0.0219879
$227$	4074.47	1.19133	0.595665	−	0.803233i	$-0.296888\pi$
$227$	4074.47	1.19133	0.595665	+	0.803233i	$0.296888\pi$
$228$	−1000.37	−0.290576
$229$	4520.81	1.30456	0.652278	−	0.757980i	$-0.273813\pi$
$229$	4520.81	1.30456	0.652278	+	0.757980i	$0.273813\pi$
$230$	291.062	0.0834438
$231$	−827.516	−0.235700
$232$	1411.13	0.399334
$233$	3447.27	0.969261	0.484631	−	0.874719i	$-0.338954\pi$
$233$	3447.27	0.969261	0.484631	+	0.874719i	$0.338954\pi$
$234$	1214.90	0.339403
$235$	−403.215	−0.111927
$236$	1933.02	0.533174
$237$	1734.67	0.475439
$238$	−567.827	−0.154650
$239$	2082.19	0.563540	0.281770	−	0.959482i	$-0.409079\pi$
$239$	2082.19	0.563540	0.281770	+	0.959482i	$0.409079\pi$
$240$	303.717	0.0816869
$241$	1047.10	0.279874	0.139937	−	0.990160i	$-0.455310\pi$
$241$	1047.10	0.279874	0.139937	+	0.990160i	$0.455310\pi$
$242$	−443.594	−0.117832
$243$	−243.000	−0.0641500
$244$	−3115.58	−0.817437
$245$	−310.045	−0.0808491
$246$	−1583.80	−0.410486
$247$	−5626.62	−1.44945
$248$	−1871.33	−0.479153
$249$	−3990.63	−1.01565
$250$	−2657.06	−0.672190
$251$	−6923.06	−1.74095	−0.870477	−	0.492209i	$-0.836189\pi$
$251$	−6923.06	−1.74095	−0.870477	+	0.492209i	$0.836189\pi$
$252$	252.000	0.0629941
$253$	906.328	0.225219
$254$	3839.33	0.948428
$255$	769.906	0.189072
$256$	256.000	0.0625000
$257$	−6546.24	−1.58888	−0.794442	−	0.607340i	$-0.792237\pi$
$257$	−6546.24	−1.58888	−0.794442	+	0.607340i	$0.792237\pi$
$258$	−1143.69	−0.275980
$259$	902.768	0.216584
$260$	1708.26	0.407470
$261$	−1587.52	−0.376495
$262$	−5084.60	−1.19896
$263$	5466.43	1.28165	0.640826	−	0.767686i	$-0.278592\pi$
$263$	5466.43	1.28165	0.640826	+	0.767686i	$0.278592\pi$
$264$	945.733	0.220477
$265$	−204.426	−0.0473878
$266$	−1167.10	−0.269021
$267$	−755.453	−0.173157
$268$	−1118.45	−0.254926
$269$	−1699.83	−0.385280	−0.192640	−	0.981269i	$-0.561705\pi$
$269$	−1699.83	−0.385280	−0.192640	+	0.981269i	$0.561705\pi$
$270$	−341.682	−0.0770152
$271$	−5437.70	−1.21888	−0.609441	−	0.792832i	$-0.708606\pi$
$271$	−5437.70	−1.21888	−0.609441	+	0.792832i	$0.708606\pi$
$272$	648.946	0.144662
$273$	1417.38	0.314226
$274$	5843.80	1.28846
$275$	−3348.03	−0.734160
$276$	−276.000	−0.0601929
$277$	5361.60	1.16299	0.581493	−	0.813552i	$-0.302469\pi$
$277$	5361.60	1.16299	0.581493	+	0.813552i	$0.302469\pi$
$278$	−5569.55	−1.20158
$279$	2105.25	0.451749
$280$	354.337	0.0756274
$281$	−1996.15	−0.423774	−0.211887	−	0.977294i	$-0.567961\pi$
$281$	−1996.15	−0.423774	−0.211887	+	0.977294i	$0.567961\pi$
$282$	382.349	0.0807396
$283$	−3990.01	−0.838097	−0.419049	−	0.907964i	$-0.637636\pi$
$283$	−3990.01	−0.838097	−0.419049	+	0.907964i	$0.637636\pi$
$284$	981.144	0.205001
$285$	1582.45	0.328899
$286$	5319.30	1.09978
$287$	−1847.77	−0.380036
$288$	−288.000	−0.0589256
$289$	−3267.96	−0.665166
$290$	−2232.21	−0.452001
$291$	−1222.21	−0.246211
$292$	−4319.99	−0.865782
$293$	8724.19	1.73950	0.869748	−	0.493495i	$-0.164281\pi$
$293$	8724.19	1.73950	0.869748	+	0.493495i	$0.164281\pi$
$294$	294.000	0.0583212
$295$	−3057.77	−0.603492
$296$	−1031.73	−0.202596
$297$	−1063.95	−0.207867
$298$	−5482.52	−1.06575
$299$	−1552.37	−0.300254
$300$	1019.56	0.196215
$301$	−1334.30	−0.255508
$302$	30.1449	0.00574386
$303$	−3502.15	−0.664003
$304$	1333.83	0.251646
$305$	4928.41	0.925246
$306$	−730.064	−0.136389
$307$	−3851.92	−0.716094	−0.358047	−	0.933704i	$-0.616557\pi$
$307$	−3851.92	−0.716094	−0.358047	+	0.933704i	$0.616557\pi$
$308$	1103.36	0.204122
$309$	−4268.85	−0.785910
$310$	2960.19	0.542347
$311$	4147.25	0.756171	0.378085	−	0.925771i	$-0.376583\pi$
$311$	4147.25	0.756171	0.378085	+	0.925771i	$0.376583\pi$
$312$	−1619.86	−0.293932
$313$	−8592.62	−1.55170	−0.775852	−	0.630915i	$-0.782680\pi$
$313$	−8592.62	−1.55170	−0.775852	+	0.630915i	$0.782680\pi$
$314$	2719.83	0.488819
$315$	−398.629	−0.0713022
$316$	−2312.89	−0.411742
$317$	6906.62	1.22370	0.611852	−	0.790972i	$-0.290425\pi$
$317$	6906.62	1.22370	0.611852	+	0.790972i	$0.290425\pi$
$318$	193.847	0.0341836
$319$	−6950.81	−1.21997
$320$	−404.956	−0.0707429
$321$	−643.334	−0.111861
$322$	−322.000	−0.0557278
$323$	3381.18	0.582458
$324$	324.000	0.0555556
$325$	5734.55	0.978756
$326$	7368.54	1.25186
$327$	−2291.62	−0.387544
$328$	2111.74	0.355491
$329$	446.074	0.0747503
$330$	−1496.02	−0.249555
$331$	4956.24	0.823020	0.411510	−	0.911405i	$-0.365001\pi$
$331$	4956.24	0.823020	0.411510	+	0.911405i	$0.365001\pi$
$332$	5320.84	0.879575
$333$	1160.70	0.191009
$334$	−6437.92	−1.05469
$335$	1769.23	0.288547
$336$	−336.000	−0.0545545
$337$	−2537.07	−0.410098	−0.205049	−	0.978752i	$-0.565735\pi$
$337$	−2537.07	−0.410098	−0.205049	+	0.978752i	$0.565735\pi$
$338$	−4716.96	−0.759080
$339$	112.057	0.0179531
$340$	−1026.54	−0.163741
$341$	9217.62	1.46382
$342$	−1500.56	−0.237254
$343$	343.000	0.0539949
$344$	1524.92	0.239006
$345$	436.593	0.0681316
$346$	−3367.86	−0.523287
$347$	−12587.1	−1.94730	−0.973649	−	0.228053i	$-0.926764\pi$
$347$	−12587.1	−1.94730	−0.973649	+	0.228053i	$0.926764\pi$
$348$	2116.70	0.326055
$349$	7370.57	1.13048	0.565240	−	0.824926i	$-0.308783\pi$
$349$	7370.57	1.13048	0.565240	+	0.824926i	$0.308783\pi$
$350$	1189.49	0.181660
$351$	1822.35	0.277121
$352$	−1260.98	−0.190938
$353$	−5510.85	−0.830915	−0.415457	−	0.909613i	$-0.636379\pi$
$353$	−5510.85	−0.830915	−0.415457	+	0.909613i	$0.636379\pi$
$354$	2899.53	0.435334
$355$	−1552.03	−0.232038
$356$	1007.27	0.149959
$357$	−851.741	−0.126271
$358$	−7197.62	−1.06259
$359$	8822.45	1.29702	0.648512	−	0.761205i	$-0.275392\pi$
$359$	8822.45	1.29702	0.648512	+	0.761205i	$0.275392\pi$
$360$	455.576	0.0666971
$361$	90.6085	0.0132102
$362$	−2340.69	−0.339845
$363$	−665.391	−0.0962093
$364$	−1889.84	−0.272128
$365$	6833.62	0.979968
$366$	−4673.37	−0.667434
$367$	2240.53	0.318678	0.159339	−	0.987224i	$-0.449064\pi$
$367$	2240.53	0.318678	0.159339	+	0.987224i	$0.449064\pi$
$368$	368.000	0.0521286
$369$	−2375.70	−0.335161
$370$	1632.06	0.229316
$371$	226.154	0.0316479
$372$	−2807.00	−0.391226
$373$	−12369.8	−1.71711	−0.858556	−	0.512720i	$-0.828638\pi$
$373$	−12369.8	−1.71711	−0.858556	+	0.512720i	$0.828638\pi$
$374$	−3196.51	−0.441945
$375$	−3985.59	−0.548841
$376$	−509.799	−0.0699225
$377$	11905.4	1.62642
$378$	378.000	0.0514344
$379$	−2104.14	−0.285178	−0.142589	−	0.989782i	$-0.545543\pi$
$379$	−2104.14	−0.285178	−0.142589	+	0.989782i	$0.545543\pi$
$380$	−2109.93	−0.284835
$381$	5758.99	0.774388
$382$	−1741.49	−0.233252
$383$	−4853.48	−0.647523	−0.323762	−	0.946139i	$-0.604948\pi$
$383$	−4853.48	−0.647523	−0.323762	+	0.946139i	$0.604948\pi$
$384$	384.000	0.0510310
$385$	−1745.35	−0.231043
$386$	−7909.80	−1.04300
$387$	−1715.53	−0.225337
$388$	1629.62	0.213225
$389$	−13543.0	−1.76519	−0.882596	−	0.470132i	$-0.844206\pi$
$389$	−13543.0	−1.76519	−0.882596	+	0.470132i	$0.844206\pi$
$390$	2562.40	0.332698
$391$	932.859	0.120657
$392$	−392.000	−0.0505076
$393$	−7626.89	−0.978946
$394$	−3282.89	−0.419771
$395$	3658.68	0.466046
$396$	1418.60	0.180018
$397$	1688.54	0.213465	0.106732	−	0.994288i	$-0.465961\pi$
$397$	1688.54	0.213465	0.106732	+	0.994288i	$0.465961\pi$
$398$	−4454.68	−0.561038
$399$	−1750.65	−0.219655
$400$	−1359.42	−0.169927
$401$	7912.62	0.985380	0.492690	−	0.870205i	$-0.336014\pi$
$401$	7912.62	0.985380	0.492690	+	0.870205i	$0.336014\pi$
$402$	−1677.67	−0.208146
$403$	−15788.1	−1.95151
$404$	4669.53	0.575044
$405$	−512.523	−0.0628826
$406$	2469.48	0.301868
$407$	5082.01	0.618933
$408$	973.418	0.118116
$409$	4760.70	0.575554	0.287777	−	0.957697i	$-0.407084\pi$
$409$	4760.70	0.575554	0.287777	+	0.957697i	$0.407084\pi$
$410$	−3340.47	−0.402376
$411$	8765.70	1.05202
$412$	5691.79	0.680618
$413$	3382.79	0.403041
$414$	−414.000	−0.0491473
$415$	−8416.82	−0.995580
$416$	2159.82	0.254552
$417$	−8354.33	−0.981087
$418$	−6570.03	−0.768782
$419$	−10024.6	−1.16882	−0.584409	−	0.811459i	$-0.698674\pi$
$419$	−10024.6	−1.16882	−0.584409	+	0.811459i	$0.698674\pi$
$420$	531.505	0.0617495
$421$	−2702.81	−0.312890	−0.156445	−	0.987687i	$-0.550003\pi$
$421$	−2702.81	−0.312890	−0.156445	+	0.987687i	$0.550003\pi$
$422$	−5074.35	−0.585344
$423$	573.524	0.0659236
$424$	−258.462	−0.0296039
$425$	−3446.04	−0.393312
$426$	1471.72	0.167382
$427$	−5452.26	−0.617924
$428$	857.778	0.0968745
$429$	7978.95	0.897966
$430$	−2412.21	−0.270528
$431$	−16717.7	−1.86836	−0.934182	−	0.356797i	$-0.883869\pi$
$431$	−16717.7	−1.86836	−0.934182	+	0.356797i	$0.883869\pi$
$432$	−432.000	−0.0481125
$433$	−10930.0	−1.21308	−0.606539	−	0.795054i	$-0.707443\pi$
$433$	−10930.0	−1.21308	−0.606539	+	0.795054i	$0.707443\pi$
$434$	−3274.84	−0.362205
$435$	−3348.32	−0.369057
$436$	3055.50	0.335623
$437$	1917.38	0.209887
$438$	−6479.99	−0.706908
$439$	7046.99	0.766137	0.383069	−	0.923720i	$-0.374867\pi$
$439$	7046.99	0.766137	0.383069	+	0.923720i	$0.374867\pi$
$440$	1994.69	0.216121
$441$	441.000	0.0476190
$442$	5475.02	0.589185
$443$	3262.32	0.349881	0.174941	−	0.984579i	$-0.444027\pi$
$443$	3262.32	0.349881	0.174941	+	0.984579i	$0.444027\pi$
$444$	−1547.60	−0.165419
$445$	−1593.36	−0.169736
$446$	−12574.5	−1.33502
$447$	−8223.78	−0.870182
$448$	448.000	0.0472456
$449$	−11433.3	−1.20172	−0.600858	−	0.799356i	$-0.705174\pi$
$449$	−11433.3	−1.20172	−0.600858	+	0.799356i	$0.705174\pi$
$450$	1529.34	0.160209
$451$	−10401.8	−1.08603
$452$	−149.409	−0.0155478
$453$	45.2174	0.00468984
$454$	−8148.94	−0.842398
$455$	2989.46	0.308018
$456$	2000.74	0.205468
$457$	6069.74	0.621292	0.310646	−	0.950526i	$-0.399455\pi$
$457$	6069.74	0.621292	0.310646	+	0.950526i	$0.399455\pi$
$458$	−9041.62	−0.922461
$459$	−1095.10	−0.111361
$460$	−582.125	−0.0590037
$461$	14715.9	1.48675	0.743373	−	0.668877i	$-0.233225\pi$
$461$	14715.9	1.48675	0.743373	+	0.668877i	$0.233225\pi$
$462$	1655.03	0.166665
$463$	17625.9	1.76921	0.884605	−	0.466342i	$-0.154428\pi$
$463$	17625.9	1.76921	0.884605	+	0.466342i	$0.154428\pi$
$464$	−2822.27	−0.282372
$465$	4440.28	0.442824
$466$	−6894.53	−0.685371
$467$	−9072.47	−0.898980	−0.449490	−	0.893285i	$-0.648394\pi$
$467$	−9072.47	−0.898980	−0.449490	+	0.893285i	$0.648394\pi$
$468$	−2429.79	−0.239994
$469$	−1957.29	−0.192706
$470$	806.431	0.0791444
$471$	4079.75	0.399119
$472$	−3866.04	−0.377011
$473$	−7511.28	−0.730167
$474$	−3469.34	−0.336186
$475$	−7082.92	−0.684183
$476$	1135.65	0.109354
$477$	290.770	0.0279108
$478$	−4164.39	−0.398483
$479$	−1945.24	−0.185554	−0.0927771	−	0.995687i	$-0.529574\pi$
$479$	−1945.24	−0.185554	−0.0927771	+	0.995687i	$0.529574\pi$
$480$	−607.434	−0.0577614
$481$	−8704.53	−0.825140
$482$	−2094.20	−0.197901
$483$	−483.000	−0.0455016
$484$	887.189	0.0833197
$485$	−2577.83	−0.241347
$486$	486.000	0.0453609
$487$	12612.2	1.17354	0.586771	−	0.809753i	$-0.300399\pi$
$487$	12612.2	1.17354	0.586771	+	0.809753i	$0.300399\pi$
$488$	6231.16	0.578015
$489$	11052.8	1.02214
$490$	620.089	0.0571689
$491$	−9812.04	−0.901856	−0.450928	−	0.892560i	$-0.648907\pi$
$491$	−9812.04	−0.901856	−0.450928	+	0.892560i	$0.648907\pi$
$492$	3167.61	0.290258
$493$	−7154.28	−0.653575
$494$	11253.2	1.02491
$495$	−2244.03	−0.203761
$496$	3742.67	0.338812
$497$	1717.00	0.154966
$498$	7981.26	0.718170
$499$	21498.2	1.92864	0.964322	−	0.264733i	$-0.0852840\pi$
$499$	21498.2	1.92864	0.964322	+	0.264733i	$0.0852840\pi$
$500$	5314.13	0.475310
$501$	−9656.87	−0.861152
$502$	13846.1	1.23104
$503$	7114.90	0.630691	0.315346	−	0.948977i	$-0.397880\pi$
$503$	7114.90	0.630691	0.315346	+	0.948977i	$0.397880\pi$
$504$	−504.000	−0.0445435
$505$	−7386.54	−0.650885
$506$	−1812.66	−0.159254
$507$	−7075.44	−0.619786
$508$	−7678.65	−0.670640
$509$	−1951.30	−0.169921	−0.0849607	−	0.996384i	$-0.527076\pi$
$509$	−1951.30	−0.169921	−0.0849607	+	0.996384i	$0.527076\pi$
$510$	−1539.81	−0.133694
$511$	−7559.99	−0.654470
$512$	−512.000	−0.0441942
$513$	−2250.84	−0.193717
$514$	13092.5	1.12351
$515$	−9003.62	−0.770383
$516$	2287.38	0.195148
$517$	2511.11	0.213614
$518$	−1805.54	−0.153148
$519$	−5051.79	−0.427262
$520$	−3416.53	−0.288124
$521$	3234.88	0.272020	0.136010	−	0.990707i	$-0.456572\pi$
$521$	3234.88	0.272020	0.136010	+	0.990707i	$0.456572\pi$
$522$	3175.05	0.266222
$523$	11316.6	0.946154	0.473077	−	0.881021i	$-0.343143\pi$
$523$	11316.6	0.946154	0.473077	+	0.881021i	$0.343143\pi$
$524$	10169.2	0.847792
$525$	1784.23	0.148324
$526$	−10932.9	−0.906264
$527$	9487.45	0.784212
$528$	−1891.47	−0.155901
$529$	529.000	0.0434783
$530$	408.851	0.0335082
$531$	4349.30	0.355449
$532$	2334.20	0.190226
$533$	17816.3	1.44786
$534$	1510.91	0.122441
$535$	−1356.89	−0.109651
$536$	2236.90	0.180260
$537$	−10796.4	−0.867599
$538$	3399.66	0.272434
$539$	1930.87	0.154302
$540$	683.364	0.0544579
$541$	−1114.88	−0.0885997	−0.0442998	−	0.999018i	$-0.514106\pi$
$541$	−1114.88	−0.0885997	−0.0442998	+	0.999018i	$0.514106\pi$
$542$	10875.4	0.861879
$543$	−3511.04	−0.277483
$544$	−1297.89	−0.102292
$545$	−4833.37	−0.379888
$546$	−2834.76	−0.222192
$547$	−9419.04	−0.736251	−0.368125	−	0.929776i	$-0.620000\pi$
$547$	−9419.04	−0.736251	−0.368125	+	0.929776i	$0.620000\pi$
$548$	−11687.6	−0.911076
$549$	−7010.05	−0.544958
$550$	6696.07	0.519129
$551$	−14704.8	−1.13692
$552$	552.000	0.0425628
$553$	−4047.57	−0.311248
$554$	−10723.2	−0.822355
$555$	2448.09	0.187235
$556$	11139.1	0.849646
$557$	8447.37	0.642597	0.321298	−	0.946978i	$-0.395881\pi$
$557$	8447.37	0.642597	0.321298	+	0.946978i	$0.395881\pi$
$558$	−4210.50	−0.319435
$559$	12865.4	0.973433
$560$	−708.673	−0.0534766
$561$	−4794.76	−0.360847
$562$	3992.30	0.299653
$563$	15674.0	1.17333	0.586663	−	0.809831i	$-0.300441\pi$
$563$	15674.0	1.17333	0.586663	+	0.809831i	$0.300441\pi$
$564$	−764.698	−0.0570915
$565$	236.344	0.0175984
$566$	7980.02	0.592624
$567$	567.000	0.0419961
$568$	−1962.29	−0.144957
$569$	14914.6	1.09886	0.549431	−	0.835539i	$-0.314845\pi$
$569$	14914.6	1.09886	0.549431	+	0.835539i	$0.314845\pi$
$570$	−3164.90	−0.232567
$571$	−902.415	−0.0661382	−0.0330691	−	0.999453i	$-0.510528\pi$
$571$	−902.415	−0.0661382	−0.0330691	+	0.999453i	$0.510528\pi$
$572$	−10638.6	−0.777661
$573$	−2612.24	−0.190450
$574$	3695.54	0.268726
$575$	−1954.16	−0.141729
$576$	576.000	0.0416667
$577$	−4678.82	−0.337577	−0.168788	−	0.985652i	$-0.553985\pi$
$577$	−4678.82	−0.337577	−0.168788	+	0.985652i	$0.553985\pi$
$578$	6535.92	0.470343
$579$	−11864.7	−0.851607
$580$	4464.43	0.319613
$581$	9311.47	0.664896
$582$	2444.43	0.174098
$583$	1273.11	0.0904402
$584$	8639.98	0.612200
$585$	3843.60	0.271646
$586$	−17448.4	−1.23001
$587$	10629.8	0.747428	0.373714	−	0.927544i	$-0.378084\pi$
$587$	10629.8	0.747428	0.373714	+	0.927544i	$0.378084\pi$
$588$	−588.000	−0.0412393
$589$	19500.3	1.36417
$590$	6115.54	0.426733
$591$	−4924.34	−0.342742
$592$	2063.47	0.143257
$593$	1186.68	0.0821776	0.0410888	−	0.999155i	$-0.486917\pi$
$593$	1186.68	0.0821776	0.0410888	+	0.999155i	$0.486917\pi$
$594$	2127.90	0.146984
$595$	−1796.45	−0.123777
$596$	10965.0	0.753600
$597$	−6682.02	−0.458085
$598$	3104.74	0.212311
$599$	3834.21	0.261539	0.130769	−	0.991413i	$-0.458255\pi$
$599$	3834.21	0.261539	0.130769	+	0.991413i	$0.458255\pi$
$600$	−2039.12	−0.138745
$601$	3162.27	0.214629	0.107314	−	0.994225i	$-0.465775\pi$
$601$	3162.27	0.214629	0.107314	+	0.994225i	$0.465775\pi$
$602$	2668.61	0.180672
$603$	−2516.51	−0.169951
$604$	−60.2898	−0.00406152
$605$	−1403.41	−0.0943085
$606$	7004.29	0.469521
$607$	−9276.31	−0.620286	−0.310143	−	0.950690i	$-0.600377\pi$
$607$	−9276.31	−0.620286	−0.310143	+	0.950690i	$0.600377\pi$
$608$	−2667.66	−0.177940
$609$	3704.22	0.246474
$610$	−9856.82	−0.654248
$611$	−4301.07	−0.284783
$612$	1460.13	0.0964414
$613$	3237.74	0.213330	0.106665	−	0.994295i	$-0.465983\pi$
$613$	3237.74	0.213330	0.106665	+	0.994295i	$0.465983\pi$
$614$	7703.84	0.506355
$615$	−5010.71	−0.328539
$616$	−2206.71	−0.144336
$617$	19940.4	1.30109	0.650544	−	0.759469i	$-0.274541\pi$
$617$	19940.4	1.30109	0.650544	+	0.759469i	$0.274541\pi$
$618$	8537.69	0.555722
$619$	10125.1	0.657453	0.328726	−	0.944425i	$-0.393381\pi$
$619$	10125.1	0.657453	0.328726	+	0.944425i	$0.393381\pi$
$620$	−5920.38	−0.383497
$621$	−621.000	−0.0401286
$622$	−8294.51	−0.534694
$623$	1762.72	0.113358
$624$	3239.73	0.207841
$625$	2214.23	0.141711
$626$	17185.2	1.09722
$627$	−9855.05	−0.627708
$628$	−5439.67	−0.345647
$629$	5230.78	0.331582
$630$	797.258	0.0504183
$631$	−13030.3	−0.822072	−0.411036	−	0.911619i	$-0.634833\pi$
$631$	−13030.3	−0.822072	−0.411036	+	0.911619i	$0.634833\pi$
$632$	4625.79	0.291146
$633$	−7611.52	−0.477932
$634$	−13813.2	−0.865290
$635$	12146.6	0.759089
$636$	−387.693	−0.0241715
$637$	−3307.22	−0.205709
$638$	13901.6	0.862649
$639$	2207.57	0.136667
$640$	809.912	0.0500228
$641$	2642.87	0.162851	0.0814253	−	0.996679i	$-0.474053\pi$
$641$	2642.87	0.162851	0.0814253	+	0.996679i	$0.474053\pi$
$642$	1286.67	0.0790977
$643$	10724.9	0.657774	0.328887	−	0.944369i	$-0.393326\pi$
$643$	10724.9	0.657774	0.328887	+	0.944369i	$0.393326\pi$
$644$	644.000	0.0394055
$645$	−3618.31	−0.220885
$646$	−6762.36	−0.411860
$647$	−27996.6	−1.70118	−0.850588	−	0.525832i	$-0.823754\pi$
$647$	−27996.6	−1.70118	−0.850588	+	0.525832i	$0.823754\pi$
$648$	−648.000	−0.0392837
$649$	19042.9	1.15177
$650$	−11469.1	−0.692085
$651$	−4912.25	−0.295739
$652$	−14737.1	−0.885197
$653$	−8770.67	−0.525609	−0.262805	−	0.964849i	$-0.584647\pi$
$653$	−8770.67	−0.525609	−0.262805	+	0.964849i	$0.584647\pi$
$654$	4583.24	0.274035
$655$	−16086.2	−0.959605
$656$	−4223.48	−0.251370
$657$	−9719.98	−0.577188
$658$	−892.148	−0.0528565
$659$	−2820.51	−0.166725	−0.0833623	−	0.996519i	$-0.526566\pi$
$659$	−2820.51	−0.166725	−0.0833623	+	0.996519i	$0.526566\pi$
$660$	2992.04	0.176462
$661$	8199.16	0.482466	0.241233	−	0.970467i	$-0.422448\pi$
$661$	8199.16	0.482466	0.241233	+	0.970467i	$0.422448\pi$
$662$	−9912.48	−0.581963
$663$	8212.52	0.481068
$664$	−10641.7	−0.621953
$665$	−3692.38	−0.215315
$666$	−2321.40	−0.135064
$667$	−4057.01	−0.235514
$668$	12875.8	0.745780
$669$	−18861.7	−1.09004
$670$	−3538.46	−0.204034
$671$	−30692.8	−1.76584
$672$	672.000	0.0385758
$673$	−2783.16	−0.159410	−0.0797049	−	0.996819i	$-0.525398\pi$
$673$	−2783.16	−0.159410	−0.0797049	+	0.996819i	$0.525398\pi$
$674$	5074.14	0.289983
$675$	2294.01	0.130810
$676$	9433.92	0.536750
$677$	−11336.1	−0.643550	−0.321775	−	0.946816i	$-0.604280\pi$
$677$	−11336.1	−0.643550	−0.321775	+	0.946816i	$0.604280\pi$
$678$	−224.113	−0.0126947
$679$	2851.83	0.161183
$680$	2053.08	0.115783
$681$	−12223.4	−0.687815
$682$	−18435.2	−1.03508
$683$	13972.5	0.782784	0.391392	−	0.920224i	$-0.371994\pi$
$683$	13972.5	0.782784	0.391392	+	0.920224i	$0.371994\pi$
$684$	3001.12	0.167764
$685$	18488.2	1.03124
$686$	−686.000	−0.0381802
$687$	−13562.4	−0.753186
$688$	−3049.84	−0.169003
$689$	−2180.59	−0.120572
$690$	−873.187	−0.0481763
$691$	21495.7	1.18341	0.591703	−	0.806156i	$-0.298456\pi$
$691$	21495.7	1.18341	0.591703	+	0.806156i	$0.298456\pi$
$692$	6735.72	0.370020
$693$	2482.55	0.136081
$694$	25174.2	1.37695
$695$	−17620.5	−0.961704
$696$	−4233.40	−0.230555
$697$	−10706.3	−0.581821
$698$	−14741.1	−0.799370
$699$	−10341.8	−0.559603
$700$	−2378.98	−0.128453
$701$	−13661.0	−0.736044	−0.368022	−	0.929817i	$-0.619965\pi$
$701$	−13661.0	−0.736044	−0.368022	+	0.929817i	$0.619965\pi$
$702$	−3644.69	−0.195954
$703$	10751.2	0.576800
$704$	2521.96	0.135014
$705$	1209.65	0.0646211
$706$	11021.7	0.587546
$707$	8171.67	0.434692
$708$	−5799.06	−0.307828
$709$	25742.5	1.36358	0.681790	−	0.731548i	$-0.261202\pi$
$709$	25742.5	1.36358	0.681790	+	0.731548i	$0.261202\pi$
$710$	3104.07	0.164075
$711$	−5204.01	−0.274495
$712$	−2014.54	−0.106037
$713$	5380.09	0.282589
$714$	1703.48	0.0892874
$715$	16828.8	0.880225
$716$	14395.2	0.751363
$717$	−6246.58	−0.325360
$718$	−17644.9	−0.917134
$719$	−1302.35	−0.0675514	−0.0337757	−	0.999429i	$-0.510753\pi$
$719$	−1302.35	−0.0675514	−0.0337757	+	0.999429i	$0.510753\pi$
$720$	−911.151	−0.0471620
$721$	9960.64	0.514499
$722$	−181.217	−0.00934100
$723$	−3141.30	−0.161585
$724$	4681.38	0.240307
$725$	14986.8	0.767721
$726$	1330.78	0.0680303
$727$	4682.11	0.238858	0.119429	−	0.992843i	$-0.461894\pi$
$727$	4682.11	0.238858	0.119429	+	0.992843i	$0.461894\pi$
$728$	3779.68	0.192423
$729$	729.000	0.0370370
$730$	−13667.2	−0.692942
$731$	−7731.16	−0.391173
$732$	9346.74	0.471947
$733$	−22319.4	−1.12467	−0.562337	−	0.826908i	$-0.690098\pi$
$733$	−22319.4	−1.12467	−0.562337	+	0.826908i	$0.690098\pi$
$734$	−4481.06	−0.225339
$735$	930.134	0.0466782
$736$	−736.000	−0.0368605
$737$	−11018.3	−0.550697
$738$	4751.41	0.236994
$739$	−12232.9	−0.608922	−0.304461	−	0.952525i	$-0.598476\pi$
$739$	−12232.9	−0.608922	−0.304461	+	0.952525i	$0.598476\pi$
$740$	−3264.12	−0.162151
$741$	16879.8	0.836838
$742$	−452.309	−0.0223784
$743$	7607.22	0.375615	0.187807	−	0.982206i	$-0.439862\pi$
$743$	7607.22	0.375615	0.187807	+	0.982206i	$0.439862\pi$
$744$	5614.00	0.276639
$745$	−17345.2	−0.852990
$746$	24739.6	1.21418
$747$	11971.9	0.586383
$748$	6393.01	0.312502
$749$	1501.11	0.0732302
$750$	7971.19	0.388089
$751$	−22305.2	−1.08379	−0.541897	−	0.840445i	$-0.682294\pi$
$751$	−22305.2	−1.08379	−0.541897	+	0.840445i	$0.682294\pi$
$752$	1019.60	0.0494427
$753$	20769.2	1.00514
$754$	−23810.9	−1.15005
$755$	95.3701	0.00459718
$756$	−756.000	−0.0363696
$757$	12317.4	0.591392	0.295696	−	0.955282i	$-0.404448\pi$
$757$	12317.4	0.591392	0.295696	+	0.955282i	$0.404448\pi$
$758$	4208.28	0.201651
$759$	−2718.98	−0.130030
$760$	4219.86	0.201409
$761$	20082.2	0.956608	0.478304	−	0.878194i	$-0.341252\pi$
$761$	20082.2	0.956608	0.478304	+	0.878194i	$0.341252\pi$
$762$	−11518.0	−0.547575
$763$	5347.12	0.253707
$764$	3482.98	0.164934
$765$	−2309.72	−0.109161
$766$	9706.97	0.457868
$767$	−32617.0	−1.53550
$768$	−768.000	−0.0360844
$769$	38054.3	1.78449	0.892246	−	0.451551i	$-0.149129\pi$
$769$	38054.3	1.78449	0.892246	+	0.451551i	$0.149129\pi$
$770$	3490.71	0.163372
$771$	19638.7	0.917343
$772$	15819.6	0.737513
$773$	−4849.56	−0.225649	−0.112824	−	0.993615i	$-0.535990\pi$
$773$	−4849.56	−0.225649	−0.112824	+	0.993615i	$0.535990\pi$
$774$	3431.07	0.159337
$775$	−19874.4	−0.921173
$776$	−3259.24	−0.150773
$777$	−2708.30	−0.125045
$778$	27086.1	1.24818
$779$	−22005.4	−1.01210
$780$	−5124.79	−0.235253
$781$	9665.63	0.442847
$782$	−1865.72	−0.0853171
$783$	4762.57	0.217370
$784$	784.000	0.0357143
$785$	8604.79	0.391233
$786$	15253.8	0.692220
$787$	37264.7	1.68786	0.843929	−	0.536455i	$-0.180237\pi$
$787$	37264.7	1.68786	0.843929	+	0.536455i	$0.180237\pi$
$788$	6565.79	0.296823
$789$	−16399.3	−0.739962
$790$	−7317.35	−0.329544
$791$	−261.466	−0.0117530
$792$	−2837.20	−0.127292
$793$	52571.0	2.35416
$794$	−3377.09	−0.150942
$795$	613.277	0.0273594
$796$	8909.36	0.396713
$797$	33675.1	1.49665	0.748327	−	0.663330i	$-0.230858\pi$
$797$	33675.1	1.49665	0.748327	+	0.663330i	$0.230858\pi$
$798$	3501.30	0.155319
$799$	2584.62	0.114440
$800$	2718.83	0.120157
$801$	2266.36	0.0999724
$802$	−15825.2	−0.696769
$803$	−42557.9	−1.87028
$804$	3355.35	0.147182
$805$	−1018.72	−0.0446026
$806$	31576.1	1.37993
$807$	5099.48	0.222442
$808$	−9339.06	−0.406617
$809$	−9382.60	−0.407756	−0.203878	−	0.978996i	$-0.565355\pi$
$809$	−9382.60	−0.407756	−0.203878	+	0.978996i	$0.565355\pi$
$810$	1025.05	0.0444647
$811$	14059.0	0.608728	0.304364	−	0.952556i	$-0.401556\pi$
$811$	14059.0	0.608728	0.304364	+	0.952556i	$0.401556\pi$
$812$	−4938.96	−0.213453
$813$	16313.1	0.703721
$814$	−10164.0	−0.437652
$815$	23312.0	1.00194
$816$	−1946.84	−0.0835207
$817$	−15890.5	−0.680462
$818$	−9521.40	−0.406978
$819$	−4252.14	−0.181419
$820$	6680.95	0.284523
$821$	13930.4	0.592173	0.296087	−	0.955161i	$-0.404318\pi$
$821$	13930.4	0.592173	0.296087	+	0.955161i	$0.404318\pi$
$822$	−17531.4	−0.743891
$823$	−4200.11	−0.177894	−0.0889470	−	0.996036i	$-0.528350\pi$
$823$	−4200.11	−0.177894	−0.0889470	+	0.996036i	$0.528350\pi$
$824$	−11383.6	−0.481270
$825$	10044.1	0.423867
$826$	−6765.57	−0.284993
$827$	8806.25	0.370282	0.185141	−	0.982712i	$-0.440726\pi$
$827$	8806.25	0.370282	0.185141	+	0.982712i	$0.440726\pi$
$828$	828.000	0.0347524
$829$	504.752	0.0211469	0.0105734	−	0.999944i	$-0.496634\pi$
$829$	504.752	0.0211469	0.0105734	+	0.999944i	$0.496634\pi$
$830$	16833.6	0.703981
$831$	−16084.8	−0.671450
$832$	−4319.64	−0.179996
$833$	1987.40	0.0826641
$834$	16708.7	0.693733
$835$	−20367.8	−0.844138
$836$	13140.1	0.543611
$837$	−6315.75	−0.260818
$838$	20049.2	0.826479
$839$	−23174.7	−0.953610	−0.476805	−	0.879009i	$-0.658205\pi$
$839$	−23174.7	−0.953610	−0.476805	+	0.879009i	$0.658205\pi$
$840$	−1063.01	−0.0436635
$841$	6724.99	0.275739
$842$	5405.62	0.221247
$843$	5988.45	0.244666
$844$	10148.7	0.413901
$845$	−14923.1	−0.607541
$846$	−1147.05	−0.0466150
$847$	1552.58	0.0629838
$848$	516.925	0.0209331
$849$	11970.0	0.483876
$850$	6892.09	0.278114
$851$	2966.24	0.119484
$852$	−2943.43	−0.118357
$853$	−40686.9	−1.63317	−0.816585	−	0.577226i	$-0.804135\pi$
$853$	−40686.9	−1.63317	−0.816585	+	0.577226i	$0.804135\pi$
$854$	10904.5	0.436938
$855$	−4747.34	−0.189890
$856$	−1715.56	−0.0685006
$857$	−30313.4	−1.20827	−0.604134	−	0.796883i	$-0.706481\pi$
$857$	−30313.4	−1.20827	−0.604134	+	0.796883i	$0.706481\pi$
$858$	−15957.9	−0.634958
$859$	−20630.5	−0.819444	−0.409722	−	0.912211i	$-0.634374\pi$
$859$	−20630.5	−0.819444	−0.409722	+	0.912211i	$0.634374\pi$
$860$	4824.42	0.191292
$861$	5543.31	0.219414
$862$	33435.5	1.32113
$863$	23177.8	0.914230	0.457115	−	0.889408i	$-0.348883\pi$
$863$	23177.8	0.914230	0.457115	+	0.889408i	$0.348883\pi$
$864$	864.000	0.0340207
$865$	−10655.0	−0.418821
$866$	21860.0	0.857776
$867$	9803.88	0.384034
$868$	6549.67	0.256118
$869$	−22785.2	−0.889454
$870$	6696.64	0.260963
$871$	18872.2	0.734169
$872$	−6110.99	−0.237321
$873$	3666.64	0.142150
$874$	−3834.76	−0.148413
$875$	9299.72	0.359301
$876$	12960.0	0.499860
$877$	−25441.2	−0.979576	−0.489788	−	0.871842i	$-0.662926\pi$
$877$	−25441.2	−0.979576	−0.489788	+	0.871842i	$0.662926\pi$
$878$	−14094.0	−0.541741
$879$	−26172.6	−1.00430
$880$	−3989.38	−0.152820
$881$	−5089.75	−0.194640	−0.0973202	−	0.995253i	$-0.531027\pi$
$881$	−5089.75	−0.194640	−0.0973202	+	0.995253i	$0.531027\pi$
$882$	−882.000	−0.0336718
$883$	156.860	0.00597822	0.00298911	−	0.999996i	$-0.499049\pi$
$883$	156.860	0.00597822	0.00298911	+	0.999996i	$0.499049\pi$
$884$	−10950.0	−0.416617
$885$	9173.31	0.348426
$886$	−6524.63	−0.247403
$887$	42189.9	1.59707	0.798534	−	0.601950i	$-0.205609\pi$
$887$	42189.9	1.59707	0.798534	+	0.601950i	$0.205609\pi$
$888$	3095.20	0.116969
$889$	−13437.6	−0.506956
$890$	3186.72	0.120022
$891$	3191.85	0.120012
$892$	25149.0	0.944003
$893$	5312.38	0.199073
$894$	16447.6	0.615312
$895$	−22771.3	−0.850458
$896$	−896.000	−0.0334077
$897$	4657.11	0.173351
$898$	22866.6	0.849742
$899$	−41261.0	−1.53073
$900$	−3058.69	−0.113285
$901$	1310.37	0.0484516
$902$	20803.5	0.767940
$903$	4002.91	0.147518
$904$	298.818	0.0109940
$905$	−7405.30	−0.272000
$906$	−90.4348	−0.00331622
$907$	−23874.0	−0.874006	−0.437003	−	0.899460i	$-0.643960\pi$
$907$	−23874.0	−0.874006	−0.437003	+	0.899460i	$0.643960\pi$
$908$	16297.9	0.595665
$909$	10506.4	0.383363
$910$	−5978.93	−0.217802
$911$	40551.9	1.47480	0.737402	−	0.675455i	$-0.236053\pi$
$911$	40551.9	1.47480	0.737402	+	0.675455i	$0.236053\pi$
$912$	−4001.49	−0.145288
$913$	52417.6	1.90008
$914$	−12139.5	−0.439320
$915$	−14785.2	−0.534191
$916$	18083.2	0.652278
$917$	17796.1	0.640871
$918$	2190.19	0.0787441
$919$	−409.889	−0.0147127	−0.00735636	−	0.999973i	$-0.502342\pi$
$919$	−409.889	−0.0147127	−0.00735636	+	0.999973i	$0.502342\pi$
$920$	1164.25	0.0417219
$921$	11555.8	0.413437
$922$	−29431.9	−1.05129
$923$	−16555.4	−0.590388
$924$	−3310.07	−0.117850
$925$	−10957.5	−0.389491
$926$	−35251.8	−1.25102
$927$	12806.5	0.453745
$928$	5644.53	0.199667
$929$	13534.4	0.477986	0.238993	−	0.971021i	$-0.423183\pi$
$929$	13534.4	0.477986	0.238993	+	0.971021i	$0.423183\pi$
$930$	−8880.57	−0.313124
$931$	4084.85	0.143798
$932$	13789.1	0.484631
$933$	−12441.8	−0.436575
$934$	18144.9	0.635675
$935$	−10112.9	−0.353717
$936$	4859.59	0.169702
$937$	19849.4	0.692050	0.346025	−	0.938225i	$-0.387531\pi$
$937$	19849.4	0.692050	0.346025	+	0.938225i	$0.387531\pi$
$938$	3914.57	0.136264
$939$	25777.9	0.895877
$940$	−1612.86	−0.0559635
$941$	45983.8	1.59302	0.796509	−	0.604627i	$-0.206678\pi$
$941$	45983.8	1.59302	0.796509	+	0.604627i	$0.206678\pi$
$942$	−8159.50	−0.282220
$943$	−6071.25	−0.209657
$944$	7732.09	0.266587
$945$	1195.89	0.0411663
$946$	15022.6	0.516306
$947$	−15452.3	−0.530234	−0.265117	−	0.964216i	$-0.585411\pi$
$947$	−15452.3	−0.530234	−0.265117	+	0.964216i	$0.585411\pi$
$948$	6938.68	0.237719
$949$	72893.7	2.49339
$950$	14165.8	0.483790
$951$	−20719.9	−0.706506
$952$	−2271.31	−0.0773252
$953$	10248.5	0.348355	0.174177	−	0.984714i	$-0.444273\pi$
$953$	10248.5	0.348355	0.174177	+	0.984714i	$0.444273\pi$
$954$	−581.540	−0.0197359
$955$	−5509.59	−0.186687
$956$	8328.78	0.281770
$957$	20852.4	0.704350
$958$	3890.49	0.131207
$959$	−20453.3	−0.688709
$960$	1214.87	0.0408435
$961$	24926.1	0.836698
$962$	17409.1	0.583462
$963$	1930.00	0.0645830
$964$	4188.40	0.139937
$965$	−25024.4	−0.834781
$966$	966.000	0.0321745
$967$	29348.2	0.975982	0.487991	−	0.872849i	$-0.337730\pi$
$967$	29348.2	0.975982	0.487991	+	0.872849i	$0.337730\pi$
$968$	−1774.38	−0.0589160
$969$	−10143.5	−0.336282
$970$	5155.66	0.170658
$971$	−5043.22	−0.166678	−0.0833391	−	0.996521i	$-0.526558\pi$
$971$	−5043.22	−0.166678	−0.0833391	+	0.996521i	$0.526558\pi$
$972$	−972.000	−0.0320750
$973$	19493.4	0.642272
$974$	−25224.5	−0.829819
$975$	−17203.7	−0.565085
$976$	−12462.3	−0.408718
$977$	−32799.7	−1.07406	−0.537029	−	0.843564i	$-0.680453\pi$
$977$	−32799.7	−1.07406	−0.537029	+	0.843564i	$0.680453\pi$
$978$	−22105.6	−0.722761
$979$	9923.02	0.323944
$980$	−1240.18	−0.0404245
$981$	6874.87	0.223749
$982$	19624.1	0.637709
$983$	−46129.6	−1.49675	−0.748375	−	0.663276i	$-0.769166\pi$
$983$	−46129.6	−1.49675	−0.748375	+	0.663276i	$0.769166\pi$
$984$	−6335.21	−0.205243
$985$	−10386.2	−0.335970
$986$	14308.6	0.462148
$987$	−1338.22	−0.0431571
$988$	−22506.5	−0.724723
$989$	−4384.14	−0.140958
$990$	4488.05	0.144080
$991$	−42755.7	−1.37051	−0.685257	−	0.728301i	$-0.740310\pi$
$991$	−42755.7	−1.37051	−0.685257	+	0.728301i	$0.740310\pi$
$992$	−7485.34	−0.239576
$993$	−14868.7	−0.475171
$994$	−3434.01	−0.109578
$995$	−14093.4	−0.449035
$996$	−15962.5	−0.507823
$997$	20530.3	0.652158	0.326079	−	0.945343i	$-0.394273\pi$
$997$	20530.3	0.652158	0.326079	+	0.945343i	$0.394273\pi$
$998$	−42996.5	−1.36376
$999$	−3482.10	−0.110279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.i.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.i.1.2	✓	4	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -6.32744 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -6.32744 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +12.6549 q^{10} +39.4055 q^{11} -12.0000 q^{12} -67.4943 q^{13} -14.0000 q^{14} +18.9823 q^{15} +16.0000 q^{16} +40.5591 q^{17} -18.0000 q^{18} +83.3643 q^{19} -25.3098 q^{20} -21.0000 q^{21} -78.8111 q^{22} +23.0000 q^{23} +24.0000 q^{24} -84.9635 q^{25} +134.989 q^{26} -27.0000 q^{27} +28.0000 q^{28} -176.392 q^{29} -37.9646 q^{30} +233.917 q^{31} -32.0000 q^{32} -118.217 q^{33} -81.1182 q^{34} -44.2921 q^{35} +36.0000 q^{36} +128.967 q^{37} -166.729 q^{38} +202.483 q^{39} +50.6195 q^{40} -263.967 q^{41} +42.0000 q^{42} -190.615 q^{43} +157.622 q^{44} -56.9470 q^{45} -46.0000 q^{46} +63.7249 q^{47} -48.0000 q^{48} +49.0000 q^{49} +169.927 q^{50} -121.677 q^{51} -269.977 q^{52} +32.3078 q^{53} +54.0000 q^{54} -249.336 q^{55} -56.0000 q^{56} -250.093 q^{57} +352.783 q^{58} +483.255 q^{59} +75.9293 q^{60} -778.895 q^{61} -467.834 q^{62} +63.0000 q^{63} +64.0000 q^{64} +427.066 q^{65} +236.433 q^{66} -279.612 q^{67} +162.236 q^{68} -69.0000 q^{69} +88.5842 q^{70} +245.286 q^{71} -72.0000 q^{72} -1080.00 q^{73} -257.934 q^{74} +254.890 q^{75} +333.457 q^{76} +275.839 q^{77} -404.966 q^{78} -578.224 q^{79} -101.239 q^{80} +81.0000 q^{81} +527.934 q^{82} +1330.21 q^{83} -84.0000 q^{84} -256.635 q^{85} +381.230 q^{86} +529.175 q^{87} -315.244 q^{88} +251.818 q^{89} +113.894 q^{90} -472.460 q^{91} +92.0000 q^{92} -701.750 q^{93} -127.450 q^{94} -527.483 q^{95} +96.0000 q^{96} +407.405 q^{97} -98.0000 q^{98} +354.650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} + 10 q^{5} + 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 + 10 * q^5 + 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} + 10 q^{5} + 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9} - 20 q^{10} + 24 q^{11} - 48 q^{12} - 46 q^{13} - 56 q^{14} - 30 q^{15} + 64 q^{16} + 84 q^{17} - 72 q^{18} + 74 q^{19} + 40 q^{20} - 84 q^{21} - 48 q^{22} + 92 q^{23} + 96 q^{24} + 56 q^{25} + 92 q^{26} - 108 q^{27} + 112 q^{28} + 453 q^{29} + 60 q^{30} + 244 q^{31} - 128 q^{32} - 72 q^{33} - 168 q^{34} + 70 q^{35} + 144 q^{36} - 179 q^{37} - 148 q^{38} + 138 q^{39} - 80 q^{40} + 259 q^{41} + 168 q^{42} - 750 q^{43} + 96 q^{44} + 90 q^{45} - 184 q^{46} + 291 q^{47} - 192 q^{48} + 196 q^{49} - 112 q^{50} - 252 q^{51} - 184 q^{52} + 193 q^{53} + 216 q^{54} - 833 q^{55} - 224 q^{56} - 222 q^{57} - 906 q^{58} - 235 q^{59} - 120 q^{60} - 133 q^{61} - 488 q^{62} + 252 q^{63} + 256 q^{64} - 1113 q^{65} + 144 q^{66} + 113 q^{67} + 336 q^{68} - 276 q^{69} - 140 q^{70} - 31 q^{71} - 288 q^{72} - 614 q^{73} + 358 q^{74} - 168 q^{75} + 296 q^{76} + 168 q^{77} - 276 q^{78} - 30 q^{79} + 160 q^{80} + 324 q^{81} - 518 q^{82} + 2468 q^{83} - 336 q^{84} - 2083 q^{85} + 1500 q^{86} - 1359 q^{87} - 192 q^{88} + 565 q^{89} - 180 q^{90} - 322 q^{91} + 368 q^{92} - 732 q^{93} - 582 q^{94} + 141 q^{95} + 384 q^{96} - 459 q^{97} - 392 q^{98} + 216 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 + 10 * q^5 + 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9 - 20 * q^10 + 24 * q^11 - 48 * q^12 - 46 * q^13 - 56 * q^14 - 30 * q^15 + 64 * q^16 + 84 * q^17 - 72 * q^18 + 74 * q^19 + 40 * q^20 - 84 * q^21 - 48 * q^22 + 92 * q^23 + 96 * q^24 + 56 * q^25 + 92 * q^26 - 108 * q^27 + 112 * q^28 + 453 * q^29 + 60 * q^30 + 244 * q^31 - 128 * q^32 - 72 * q^33 - 168 * q^34 + 70 * q^35 + 144 * q^36 - 179 * q^37 - 148 * q^38 + 138 * q^39 - 80 * q^40 + 259 * q^41 + 168 * q^42 - 750 * q^43 + 96 * q^44 + 90 * q^45 - 184 * q^46 + 291 * q^47 - 192 * q^48 + 196 * q^49 - 112 * q^50 - 252 * q^51 - 184 * q^52 + 193 * q^53 + 216 * q^54 - 833 * q^55 - 224 * q^56 - 222 * q^57 - 906 * q^58 - 235 * q^59 - 120 * q^60 - 133 * q^61 - 488 * q^62 + 252 * q^63 + 256 * q^64 - 1113 * q^65 + 144 * q^66 + 113 * q^67 + 336 * q^68 - 276 * q^69 - 140 * q^70 - 31 * q^71 - 288 * q^72 - 614 * q^73 + 358 * q^74 - 168 * q^75 + 296 * q^76 + 168 * q^77 - 276 * q^78 - 30 * q^79 + 160 * q^80 + 324 * q^81 - 518 * q^82 + 2468 * q^83 - 336 * q^84 - 2083 * q^85 + 1500 * q^86 - 1359 * q^87 - 192 * q^88 + 565 * q^89 - 180 * q^90 - 322 * q^91 + 368 * q^92 - 732 * q^93 - 582 * q^94 + 141 * q^95 + 384 * q^96 - 459 * q^97 - 392 * q^98 + 216 * q^99

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