LMFDB - Embedded newform 966.4.a.o.1.5

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:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 560x^{3} + 2247x^{2} + 58113x - 197784 $ x^5 - x^4 - 560x^3 + 2247x^2 + 58113*x - 197784
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$16.2340$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +17.2340 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +17.2340 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -34.4681 q^{10} +63.6092 q^{11} +12.0000 q^{12} +63.3931 q^{13} -14.0000 q^{14} +51.7021 q^{15} +16.0000 q^{16} -41.6910 q^{17} -18.0000 q^{18} +58.1591 q^{19} +68.9361 q^{20} +21.0000 q^{21} -127.218 q^{22} -23.0000 q^{23} -24.0000 q^{24} +172.012 q^{25} -126.786 q^{26} +27.0000 q^{27} +28.0000 q^{28} +212.171 q^{29} -103.404 q^{30} -164.482 q^{31} -32.0000 q^{32} +190.828 q^{33} +83.3820 q^{34} +120.638 q^{35} +36.0000 q^{36} +31.0291 q^{37} -116.318 q^{38} +190.179 q^{39} -137.872 q^{40} +117.291 q^{41} -42.0000 q^{42} -548.291 q^{43} +254.437 q^{44} +155.106 q^{45} +46.0000 q^{46} -246.685 q^{47} +48.0000 q^{48} +49.0000 q^{49} -344.024 q^{50} -125.073 q^{51} +253.572 q^{52} -327.785 q^{53} -54.0000 q^{54} +1096.24 q^{55} -56.0000 q^{56} +174.477 q^{57} -424.342 q^{58} +743.521 q^{59} +206.808 q^{60} +263.290 q^{61} +328.964 q^{62} +63.0000 q^{63} +64.0000 q^{64} +1092.52 q^{65} -381.655 q^{66} +265.960 q^{67} -166.764 q^{68} -69.0000 q^{69} -241.276 q^{70} -490.254 q^{71} -72.0000 q^{72} -1212.15 q^{73} -62.0583 q^{74} +516.035 q^{75} +232.636 q^{76} +445.265 q^{77} -380.359 q^{78} -1211.31 q^{79} +275.744 q^{80} +81.0000 q^{81} -234.583 q^{82} -380.196 q^{83} +84.0000 q^{84} -718.504 q^{85} +1096.58 q^{86} +636.512 q^{87} -508.874 q^{88} -1409.18 q^{89} -310.213 q^{90} +443.752 q^{91} -92.0000 q^{92} -493.446 q^{93} +493.371 q^{94} +1002.31 q^{95} -96.0000 q^{96} -422.937 q^{97} -98.0000 q^{98} +572.483 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} + 6 q^{5} - 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 + 6 * q^5 - 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} + 6 q^{5} - 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9} - 12 q^{10} - 50 q^{11} + 60 q^{12} + 66 q^{13} - 70 q^{14} + 18 q^{15} + 80 q^{16} - 198 q^{17} - 90 q^{18} + 120 q^{19} + 24 q^{20} + 105 q^{21} + 100 q^{22} - 115 q^{23} - 120 q^{24} + 503 q^{25} - 132 q^{26} + 135 q^{27} + 140 q^{28} + 301 q^{29} - 36 q^{30} + 314 q^{31} - 160 q^{32} - 150 q^{33} + 396 q^{34} + 42 q^{35} + 180 q^{36} + 269 q^{37} - 240 q^{38} + 198 q^{39} - 48 q^{40} + 479 q^{41} - 210 q^{42} - 290 q^{43} - 200 q^{44} + 54 q^{45} + 230 q^{46} + 69 q^{47} + 240 q^{48} + 245 q^{49} - 1006 q^{50} - 594 q^{51} + 264 q^{52} + 339 q^{53} - 270 q^{54} + 957 q^{55} - 280 q^{56} + 360 q^{57} - 602 q^{58} + 2065 q^{59} + 72 q^{60} + 531 q^{61} - 628 q^{62} + 315 q^{63} + 320 q^{64} + 1227 q^{65} + 300 q^{66} + 855 q^{67} - 792 q^{68} - 345 q^{69} - 84 q^{70} - 863 q^{71} - 360 q^{72} + 618 q^{73} - 538 q^{74} + 1509 q^{75} + 480 q^{76} - 350 q^{77} - 396 q^{78} + 254 q^{79} + 96 q^{80} + 405 q^{81} - 958 q^{82} - 1700 q^{83} + 420 q^{84} + 1977 q^{85} + 580 q^{86} + 903 q^{87} + 400 q^{88} - 275 q^{89} - 108 q^{90} + 462 q^{91} - 460 q^{92} + 942 q^{93} - 138 q^{94} + 171 q^{95} - 480 q^{96} - 979 q^{97} - 490 q^{98} - 450 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 + 6 * q^5 - 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9 - 12 * q^10 - 50 * q^11 + 60 * q^12 + 66 * q^13 - 70 * q^14 + 18 * q^15 + 80 * q^16 - 198 * q^17 - 90 * q^18 + 120 * q^19 + 24 * q^20 + 105 * q^21 + 100 * q^22 - 115 * q^23 - 120 * q^24 + 503 * q^25 - 132 * q^26 + 135 * q^27 + 140 * q^28 + 301 * q^29 - 36 * q^30 + 314 * q^31 - 160 * q^32 - 150 * q^33 + 396 * q^34 + 42 * q^35 + 180 * q^36 + 269 * q^37 - 240 * q^38 + 198 * q^39 - 48 * q^40 + 479 * q^41 - 210 * q^42 - 290 * q^43 - 200 * q^44 + 54 * q^45 + 230 * q^46 + 69 * q^47 + 240 * q^48 + 245 * q^49 - 1006 * q^50 - 594 * q^51 + 264 * q^52 + 339 * q^53 - 270 * q^54 + 957 * q^55 - 280 * q^56 + 360 * q^57 - 602 * q^58 + 2065 * q^59 + 72 * q^60 + 531 * q^61 - 628 * q^62 + 315 * q^63 + 320 * q^64 + 1227 * q^65 + 300 * q^66 + 855 * q^67 - 792 * q^68 - 345 * q^69 - 84 * q^70 - 863 * q^71 - 360 * q^72 + 618 * q^73 - 538 * q^74 + 1509 * q^75 + 480 * q^76 - 350 * q^77 - 396 * q^78 + 254 * q^79 + 96 * q^80 + 405 * q^81 - 958 * q^82 - 1700 * q^83 + 420 * q^84 + 1977 * q^85 + 580 * q^86 + 903 * q^87 + 400 * q^88 - 275 * q^89 - 108 * q^90 + 462 * q^91 - 460 * q^92 + 942 * q^93 - 138 * q^94 + 171 * q^95 - 480 * q^96 - 979 * q^97 - 490 * q^98 - 450 * 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
$5$	17.2340	1.54146	0.770729	−	0.637163i	$-0.219892\pi$
$5$	17.2340	1.54146	0.770729	+	0.637163i	$0.219892\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−34.4681	−1.08998
$11$	63.6092	1.74354	0.871768	−	0.489918i	$-0.162973\pi$
$11$	63.6092	1.74354	0.871768	+	0.489918i	$0.162973\pi$
$12$	12.0000	0.288675
$13$	63.3931	1.35247	0.676234	−	0.736687i	$-0.263611\pi$
$13$	63.3931	1.35247	0.676234	+	0.736687i	$0.263611\pi$
$14$	−14.0000	−0.267261
$15$	51.7021	0.889961
$16$	16.0000	0.250000
$17$	−41.6910	−0.594797	−0.297399	−	0.954753i	$-0.596119\pi$
$17$	−41.6910	−0.594797	−0.297399	+	0.954753i	$0.596119\pi$
$18$	−18.0000	−0.235702
$19$	58.1591	0.702242	0.351121	−	0.936330i	$-0.385801\pi$
$19$	58.1591	0.702242	0.351121	+	0.936330i	$0.385801\pi$
$20$	68.9361	0.770729
$21$	21.0000	0.218218
$22$	−127.218	−1.23287
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−24.0000	−0.204124
$25$	172.012	1.37609
$26$	−126.786	−0.956339
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	212.171	1.35859	0.679295	−	0.733865i	$-0.262286\pi$
$29$	212.171	1.35859	0.679295	+	0.733865i	$0.262286\pi$
$30$	−103.404	−0.629298
$31$	−164.482	−0.952963	−0.476482	−	0.879184i	$-0.658088\pi$
$31$	−164.482	−0.952963	−0.476482	+	0.879184i	$0.658088\pi$
$32$	−32.0000	−0.176777
$33$	190.828	1.00663
$34$	83.3820	0.420585
$35$	120.638	0.582617
$36$	36.0000	0.166667
$37$	31.0291	0.137869	0.0689346	−	0.997621i	$-0.478040\pi$
$37$	31.0291	0.137869	0.0689346	+	0.997621i	$0.478040\pi$
$38$	−116.318	−0.496560
$39$	190.179	0.780848
$40$	−137.872	−0.544988
$41$	117.291	0.446776	0.223388	−	0.974730i	$-0.428288\pi$
$41$	117.291	0.446776	0.223388	+	0.974730i	$0.428288\pi$
$42$	−42.0000	−0.154303
$43$	−548.291	−1.94450	−0.972251	−	0.233941i	$-0.924838\pi$
$43$	−548.291	−1.94450	−0.972251	+	0.233941i	$0.924838\pi$
$44$	254.437	0.871768
$45$	155.106	0.513819
$46$	46.0000	0.147442
$47$	−246.685	−0.765590	−0.382795	−	0.923833i	$-0.625039\pi$
$47$	−246.685	−0.765590	−0.382795	+	0.923833i	$0.625039\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	−344.024	−0.973045
$51$	−125.073	−0.343406
$52$	253.572	0.676234
$53$	−327.785	−0.849522	−0.424761	−	0.905305i	$-0.639642\pi$
$53$	−327.785	−0.849522	−0.424761	+	0.905305i	$0.639642\pi$
$54$	−54.0000	−0.136083
$55$	1096.24	2.68759
$56$	−56.0000	−0.133631
$57$	174.477	0.405440
$58$	−424.342	−0.960669
$59$	743.521	1.64065	0.820323	−	0.571900i	$-0.193793\pi$
$59$	743.521	1.64065	0.820323	+	0.571900i	$0.193793\pi$
$60$	206.808	0.444981
$61$	263.290	0.552637	0.276319	−	0.961066i	$-0.410886\pi$
$61$	263.290	0.552637	0.276319	+	0.961066i	$0.410886\pi$
$62$	328.964	0.673847
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	1092.52	2.08477
$66$	−381.655	−0.711796
$67$	265.960	0.484959	0.242479	−	0.970157i	$-0.422039\pi$
$67$	265.960	0.484959	0.242479	+	0.970157i	$0.422039\pi$
$68$	−166.764	−0.297399
$69$	−69.0000	−0.120386
$70$	−241.276	−0.411972
$71$	−490.254	−0.819472	−0.409736	−	0.912204i	$-0.634379\pi$
$71$	−490.254	−0.819472	−0.409736	+	0.912204i	$0.634379\pi$
$72$	−72.0000	−0.117851
$73$	−1212.15	−1.94345	−0.971723	−	0.236123i	$-0.924123\pi$
$73$	−1212.15	−1.94345	−0.971723	+	0.236123i	$0.924123\pi$
$74$	−62.0583	−0.0974882
$75$	516.035	0.794488
$76$	232.636	0.351121
$77$	445.265	0.658995
$78$	−380.359	−0.552143
$79$	−1211.31	−1.72510	−0.862551	−	0.505970i	$-0.831135\pi$
$79$	−1211.31	−1.72510	−0.862551	+	0.505970i	$0.831135\pi$
$80$	275.744	0.385365
$81$	81.0000	0.111111
$82$	−234.583	−0.315919
$83$	−380.196	−0.502795	−0.251397	−	0.967884i	$-0.580890\pi$
$83$	−380.196	−0.502795	−0.251397	+	0.967884i	$0.580890\pi$
$84$	84.0000	0.109109
$85$	−718.504	−0.916855
$86$	1096.58	1.37497
$87$	636.512	0.784383
$88$	−508.874	−0.616433
$89$	−1409.18	−1.67835	−0.839174	−	0.543863i	$-0.816961\pi$
$89$	−1409.18	−1.67835	−0.839174	+	0.543863i	$0.816961\pi$
$90$	−310.213	−0.363325
$91$	443.752	0.511185
$92$	−92.0000	−0.104257
$93$	−493.446	−0.550194
$94$	493.371	0.541354
$95$	1002.31	1.08248
$96$	−96.0000	−0.102062
$97$	−422.937	−0.442708	−0.221354	−	0.975193i	$-0.571048\pi$
$97$	−422.937	−0.442708	−0.221354	+	0.975193i	$0.571048\pi$
$98$	−98.0000	−0.101015
$99$	572.483	0.581179
$100$	688.047	0.688047
$101$	−1425.59	−1.40447	−0.702234	−	0.711946i	$-0.747814\pi$
$101$	−1425.59	−1.40447	−0.702234	+	0.711946i	$0.747814\pi$
$102$	250.146	0.242825
$103$	570.074	0.545350	0.272675	−	0.962106i	$-0.412092\pi$
$103$	570.074	0.545350	0.272675	+	0.962106i	$0.412092\pi$
$104$	−507.145	−0.478169
$105$	361.915	0.336374
$106$	655.569	0.600703
$107$	−1937.89	−1.75087	−0.875433	−	0.483340i	$-0.839424\pi$
$107$	−1937.89	−1.75087	−0.875433	+	0.483340i	$0.839424\pi$
$108$	108.000	0.0962250
$109$	1430.64	1.25716	0.628579	−	0.777746i	$-0.283637\pi$
$109$	1430.64	1.25716	0.628579	+	0.777746i	$0.283637\pi$
$110$	−2192.49	−1.90041
$111$	93.0874	0.0795988
$112$	112.000	0.0944911
$113$	−1345.25	−1.11992	−0.559959	−	0.828521i	$-0.689183\pi$
$113$	−1345.25	−1.11992	−0.559959	+	0.828521i	$0.689183\pi$
$114$	−348.954	−0.286689
$115$	−396.383	−0.321416
$116$	848.683	0.679295
$117$	570.538	0.450823
$118$	−1487.04	−1.16011
$119$	−291.837	−0.224812
$120$	−413.617	−0.314649
$121$	2715.13	2.03992
$122$	−526.580	−0.390773
$123$	351.874	0.257946
$124$	−657.929	−0.476482
$125$	810.202	0.579733
$126$	−126.000	−0.0890871
$127$	553.426	0.386682	0.193341	−	0.981132i	$-0.438068\pi$
$127$	553.426	0.386682	0.193341	+	0.981132i	$0.438068\pi$
$128$	−128.000	−0.0883883
$129$	−1644.87	−1.12266
$130$	−2185.04	−1.47416
$131$	2120.01	1.41394	0.706970	−	0.707244i	$-0.250062\pi$
$131$	2120.01	1.41394	0.706970	+	0.707244i	$0.250062\pi$
$132$	763.311	0.503316
$133$	407.113	0.265423
$134$	−531.921	−0.342918
$135$	465.319	0.296654
$136$	333.528	0.210293
$137$	−1399.30	−0.872630	−0.436315	−	0.899794i	$-0.643717\pi$
$137$	−1399.30	−0.872630	−0.436315	+	0.899794i	$0.643717\pi$
$138$	138.000	0.0851257
$139$	368.618	0.224934	0.112467	−	0.993655i	$-0.464125\pi$
$139$	368.618	0.224934	0.112467	+	0.993655i	$0.464125\pi$
$140$	482.553	0.291308
$141$	−740.056	−0.442014
$142$	980.509	0.579454
$143$	4032.39	2.35808
$144$	144.000	0.0833333
$145$	3656.56	2.09421
$146$	2424.30	1.37422
$147$	147.000	0.0824786
$148$	124.117	0.0689346
$149$	−821.717	−0.451796	−0.225898	−	0.974151i	$-0.572532\pi$
$149$	−821.717	−0.451796	−0.225898	+	0.974151i	$0.572532\pi$
$150$	−1032.07	−0.561788
$151$	−1064.88	−0.573897	−0.286948	−	0.957946i	$-0.592641\pi$
$151$	−1064.88	−0.573897	−0.286948	+	0.957946i	$0.592641\pi$
$152$	−465.272	−0.248280
$153$	−375.219	−0.198266
$154$	−890.529	−0.465980
$155$	−2834.69	−1.46895
$156$	760.717	0.390424
$157$	3228.03	1.64092	0.820461	−	0.571702i	$-0.193717\pi$
$157$	3228.03	1.64092	0.820461	+	0.571702i	$0.193717\pi$
$158$	2422.62	1.21983
$159$	−983.354	−0.490472
$160$	−551.489	−0.272494
$161$	−161.000	−0.0788110
$162$	−162.000	−0.0785674
$163$	3663.11	1.76023	0.880113	−	0.474764i	$-0.157467\pi$
$163$	3663.11	1.76023	0.880113	+	0.474764i	$0.157467\pi$
$164$	469.165	0.223388
$165$	3288.73	1.55168
$166$	760.393	0.355530
$167$	−1857.27	−0.860597	−0.430298	−	0.902687i	$-0.641592\pi$
$167$	−1857.27	−0.860597	−0.430298	+	0.902687i	$0.641592\pi$
$168$	−168.000	−0.0771517
$169$	1821.68	0.829169
$170$	1437.01	0.648314
$171$	523.432	0.234081
$172$	−2193.16	−0.972251
$173$	−1872.41	−0.822872	−0.411436	−	0.911439i	$-0.634973\pi$
$173$	−1872.41	−0.822872	−0.411436	+	0.911439i	$0.634973\pi$
$174$	−1273.02	−0.554642
$175$	1204.08	0.520115
$176$	1017.75	0.435884
$177$	2230.56	0.947228
$178$	2818.36	1.18677
$179$	−418.689	−0.174828	−0.0874142	−	0.996172i	$-0.527860\pi$
$179$	−418.689	−0.174828	−0.0874142	+	0.996172i	$0.527860\pi$
$180$	620.425	0.256910
$181$	1114.06	0.457501	0.228751	−	0.973485i	$-0.426536\pi$
$181$	1114.06	0.457501	0.228751	+	0.973485i	$0.426536\pi$
$182$	−887.503	−0.361462
$183$	789.871	0.319065
$184$	184.000	0.0737210
$185$	534.757	0.212520
$186$	986.893	0.389046
$187$	−2651.93	−1.03705
$188$	−986.741	−0.382795
$189$	189.000	0.0727393
$190$	−2004.63	−0.765427
$191$	3321.89	1.25845	0.629223	−	0.777225i	$-0.283373\pi$
$191$	3321.89	1.25845	0.629223	+	0.777225i	$0.283373\pi$
$192$	192.000	0.0721688
$193$	2432.99	0.907412	0.453706	−	0.891151i	$-0.350102\pi$
$193$	2432.99	0.907412	0.453706	+	0.891151i	$0.350102\pi$
$194$	845.873	0.313042
$195$	3277.55	1.20364
$196$	196.000	0.0714286
$197$	751.393	0.271749	0.135874	−	0.990726i	$-0.456616\pi$
$197$	751.393	0.271749	0.135874	+	0.990726i	$0.456616\pi$
$198$	−1144.97	−0.410956
$199$	1237.19	0.440715	0.220357	−	0.975419i	$-0.429278\pi$
$199$	1237.19	0.440715	0.220357	+	0.975419i	$0.429278\pi$
$200$	−1376.09	−0.486523
$201$	797.881	0.279991
$202$	2851.17	0.993109
$203$	1485.20	0.513499
$204$	−500.292	−0.171703
$205$	2021.40	0.688687
$206$	−1140.15	−0.385621
$207$	−207.000	−0.0695048
$208$	1014.29	0.338117
$209$	3699.45	1.22439
$210$	−723.829	−0.237852
$211$	−1251.19	−0.408225	−0.204112	−	0.978947i	$-0.565431\pi$
$211$	−1251.19	−0.408225	−0.204112	+	0.978947i	$0.565431\pi$
$212$	−1311.14	−0.424761
$213$	−1470.76	−0.473122
$214$	3875.77	1.23805
$215$	−9449.26	−2.99737
$216$	−216.000	−0.0680414
$217$	−1151.37	−0.360186
$218$	−2861.27	−0.888945
$219$	−3636.45	−1.12205
$220$	4384.97	1.34379
$221$	−2642.92	−0.804444
$222$	−186.175	−0.0562848
$223$	−1446.41	−0.434346	−0.217173	−	0.976133i	$-0.569684\pi$
$223$	−1446.41	−0.434346	−0.217173	+	0.976133i	$0.569684\pi$
$224$	−224.000	−0.0668153
$225$	1548.11	0.458698
$226$	2690.50	0.791901
$227$	58.5569	0.0171214	0.00856069	−	0.999963i	$-0.497275\pi$
$227$	58.5569	0.0171214	0.00856069	+	0.999963i	$0.497275\pi$
$228$	697.909	0.202720
$229$	1495.47	0.431543	0.215771	−	0.976444i	$-0.430773\pi$
$229$	1495.47	0.431543	0.215771	+	0.976444i	$0.430773\pi$
$230$	792.765	0.227276
$231$	1335.79	0.380471
$232$	−1697.37	−0.480334
$233$	5098.87	1.43364	0.716820	−	0.697258i	$-0.245597\pi$
$233$	5098.87	1.43364	0.716820	+	0.697258i	$0.245597\pi$
$234$	−1141.08	−0.318780
$235$	−4251.38	−1.18013
$236$	2974.08	0.820323
$237$	−3633.93	−0.995988
$238$	583.674	0.158966
$239$	6118.05	1.65583	0.827915	−	0.560853i	$-0.189527\pi$
$239$	6118.05	1.65583	0.827915	+	0.560853i	$0.189527\pi$
$240$	827.233	0.222490
$241$	5204.58	1.39110	0.695552	−	0.718475i	$-0.255160\pi$
$241$	5204.58	1.39110	0.695552	+	0.718475i	$0.255160\pi$
$242$	−5430.27	−1.44244
$243$	243.000	0.0641500
$244$	1053.16	0.276319
$245$	844.467	0.220208
$246$	−703.748	−0.182396
$247$	3686.88	0.949760
$248$	1315.86	0.336923
$249$	−1140.59	−0.290289
$250$	−1620.40	−0.409933
$251$	−6672.46	−1.67794	−0.838968	−	0.544180i	$-0.816841\pi$
$251$	−6672.46	−1.67794	−0.838968	+	0.544180i	$0.816841\pi$
$252$	252.000	0.0629941
$253$	−1463.01	−0.363553
$254$	−1106.85	−0.273426
$255$	−2155.51	−0.529347
$256$	256.000	0.0625000
$257$	5597.62	1.35864	0.679319	−	0.733843i	$-0.262275\pi$
$257$	5597.62	1.35864	0.679319	+	0.733843i	$0.262275\pi$
$258$	3289.74	0.793839
$259$	217.204	0.0521096
$260$	4370.07	1.04239
$261$	1909.54	0.452864
$262$	−4240.02	−0.999806
$263$	−5113.40	−1.19888	−0.599440	−	0.800420i	$-0.704610\pi$
$263$	−5113.40	−1.19888	−0.599440	+	0.800420i	$0.704610\pi$
$264$	−1526.62	−0.355898
$265$	−5649.05	−1.30950
$266$	−814.227	−0.187682
$267$	−4227.55	−0.968995
$268$	1063.84	0.242479
$269$	−8123.93	−1.84136	−0.920678	−	0.390323i	$-0.872363\pi$
$269$	−8123.93	−1.84136	−0.920678	+	0.390323i	$0.872363\pi$
$270$	−930.638	−0.209766
$271$	−3251.57	−0.728851	−0.364426	−	0.931232i	$-0.618735\pi$
$271$	−3251.57	−0.728851	−0.364426	+	0.931232i	$0.618735\pi$
$272$	−667.056	−0.148699
$273$	1331.25	0.295133
$274$	2798.60	0.617042
$275$	10941.5	2.39927
$276$	−276.000	−0.0601929
$277$	7424.18	1.61038	0.805191	−	0.593016i	$-0.202063\pi$
$277$	7424.18	1.61038	0.805191	+	0.593016i	$0.202063\pi$
$278$	−737.237	−0.159052
$279$	−1480.34	−0.317654
$280$	−965.106	−0.205986
$281$	5273.12	1.11946	0.559730	−	0.828675i	$-0.310905\pi$
$281$	5273.12	1.11946	0.559730	+	0.828675i	$0.310905\pi$
$282$	1480.11	0.312551
$283$	1716.49	0.360547	0.180274	−	0.983617i	$-0.442302\pi$
$283$	1716.49	0.360547	0.180274	+	0.983617i	$0.442302\pi$
$284$	−1961.02	−0.409736
$285$	3006.94	0.624969
$286$	−8064.77	−1.66741
$287$	821.039	0.168866
$288$	−288.000	−0.0589256
$289$	−3174.86	−0.646216
$290$	−7313.12	−1.48083
$291$	−1268.81	−0.255598
$292$	−4848.61	−0.971723
$293$	5186.31	1.03409	0.517043	−	0.855959i	$-0.327033\pi$
$293$	5186.31	1.03409	0.517043	+	0.855959i	$0.327033\pi$
$294$	−294.000	−0.0583212
$295$	12813.9	2.52899
$296$	−248.233	−0.0487441
$297$	1717.45	0.335544
$298$	1643.43	0.319468
$299$	−1458.04	−0.282009
$300$	2064.14	0.397244
$301$	−3838.04	−0.734952
$302$	2129.75	0.405806
$303$	−4276.76	−0.810870
$304$	930.545	0.175561
$305$	4537.55	0.851867
$306$	750.438	0.140195
$307$	−7138.78	−1.32714	−0.663569	−	0.748115i	$-0.730959\pi$
$307$	−7138.78	−1.32714	−0.663569	+	0.748115i	$0.730959\pi$
$308$	1781.06	0.329498
$309$	1710.22	0.314858
$310$	5669.38	1.03871
$311$	−1593.37	−0.290520	−0.145260	−	0.989394i	$-0.546402\pi$
$311$	−1593.37	−0.290520	−0.145260	+	0.989394i	$0.546402\pi$
$312$	−1521.43	−0.276071
$313$	−2619.03	−0.472960	−0.236480	−	0.971636i	$-0.575994\pi$
$313$	−2619.03	−0.472960	−0.236480	+	0.971636i	$0.575994\pi$
$314$	−6456.06	−1.16031
$315$	1085.74	0.194206
$316$	−4845.24	−0.862551
$317$	−5347.01	−0.947375	−0.473688	−	0.880693i	$-0.657077\pi$
$317$	−5347.01	−0.947375	−0.473688	+	0.880693i	$0.657077\pi$
$318$	1966.71	0.346816
$319$	13496.0	2.36875
$320$	1102.98	0.192682
$321$	−5813.66	−1.01086
$322$	322.000	0.0557278
$323$	−2424.71	−0.417692
$324$	324.000	0.0555556
$325$	10904.4	1.86112
$326$	−7326.22	−1.24467
$327$	4291.91	0.725820
$328$	−938.331	−0.157959
$329$	−1726.80	−0.289366
$330$	−6577.46	−1.09720
$331$	9888.39	1.64204	0.821020	−	0.570900i	$-0.193405\pi$
$331$	9888.39	1.64204	0.821020	+	0.570900i	$0.193405\pi$
$332$	−1520.79	−0.251397
$333$	279.262	0.0459564
$334$	3714.53	0.608534
$335$	4583.57	0.747544
$336$	336.000	0.0545545
$337$	2140.32	0.345967	0.172983	−	0.984925i	$-0.444659\pi$
$337$	2140.32	0.345967	0.172983	+	0.984925i	$0.444659\pi$
$338$	−3643.37	−0.586311
$339$	−4035.76	−0.646585
$340$	−2874.02	−0.458428
$341$	−10462.6	−1.66153
$342$	−1046.86	−0.165520
$343$	343.000	0.0539949
$344$	4386.33	0.687485
$345$	−1189.15	−0.185570
$346$	3744.83	0.581859
$347$	−4249.91	−0.657485	−0.328742	−	0.944420i	$-0.606625\pi$
$347$	−4249.91	−0.657485	−0.328742	+	0.944420i	$0.606625\pi$
$348$	2546.05	0.392191
$349$	−890.773	−0.136625	−0.0683123	−	0.997664i	$-0.521761\pi$
$349$	−890.773	−0.136625	−0.0683123	+	0.997664i	$0.521761\pi$
$350$	−2408.16	−0.367777
$351$	1711.61	0.260283
$352$	−2035.50	−0.308217
$353$	220.993	0.0333209	0.0166604	−	0.999861i	$-0.494697\pi$
$353$	220.993	0.0333209	0.0166604	+	0.999861i	$0.494697\pi$
$354$	−4461.12	−0.669791
$355$	−8449.06	−1.26318
$356$	−5636.73	−0.839174
$357$	−875.511	−0.129795
$358$	837.378	0.123622
$359$	−5060.63	−0.743982	−0.371991	−	0.928236i	$-0.621325\pi$
$359$	−5060.63	−0.743982	−0.371991	+	0.928236i	$0.621325\pi$
$360$	−1240.85	−0.181663
$361$	−3476.52	−0.506856
$362$	−2228.13	−0.323502
$363$	8145.40	1.17775
$364$	1775.01	0.255592
$365$	−20890.3	−2.99574
$366$	−1579.74	−0.225613
$367$	−6899.36	−0.981318	−0.490659	−	0.871352i	$-0.663244\pi$
$367$	−6899.36	−0.981318	−0.490659	+	0.871352i	$0.663244\pi$
$368$	−368.000	−0.0521286
$369$	1055.62	0.148925
$370$	−1069.51	−0.150274
$371$	−2294.49	−0.321089
$372$	−1973.79	−0.275097
$373$	−931.873	−0.129358	−0.0646791	−	0.997906i	$-0.520602\pi$
$373$	−931.873	−0.129358	−0.0646791	+	0.997906i	$0.520602\pi$
$374$	5303.87	0.733306
$375$	2430.61	0.334709
$376$	1973.48	0.270677
$377$	13450.2	1.83745
$378$	−378.000	−0.0514344
$379$	−2170.10	−0.294118	−0.147059	−	0.989128i	$-0.546981\pi$
$379$	−2170.10	−0.294118	−0.147059	+	0.989128i	$0.546981\pi$
$380$	4009.26	0.541239
$381$	1660.28	0.223251
$382$	−6643.77	−0.889856
$383$	1359.50	0.181376	0.0906882	−	0.995879i	$-0.471093\pi$
$383$	1359.50	0.181376	0.0906882	+	0.995879i	$0.471093\pi$
$384$	−384.000	−0.0510310
$385$	7673.70	1.01581
$386$	−4865.98	−0.641637
$387$	−4934.62	−0.648167
$388$	−1691.75	−0.221354
$389$	−7774.96	−1.01338	−0.506692	−	0.862127i	$-0.669132\pi$
$389$	−7774.96	−1.01338	−0.506692	+	0.862127i	$0.669132\pi$
$390$	−6555.11	−0.851105
$391$	958.893	0.124024
$392$	−392.000	−0.0505076
$393$	6360.03	0.816339
$394$	−1502.79	−0.192156
$395$	−20875.8	−2.65917
$396$	2289.93	0.290589
$397$	−7368.18	−0.931482	−0.465741	−	0.884921i	$-0.654212\pi$
$397$	−7368.18	−0.931482	−0.465741	+	0.884921i	$0.654212\pi$
$398$	−2474.38	−0.311632
$399$	1221.34	0.153242
$400$	2752.19	0.344024
$401$	83.9096	0.0104495	0.00522475	−	0.999986i	$-0.498337\pi$
$401$	83.9096	0.0104495	0.00522475	+	0.999986i	$0.498337\pi$
$402$	−1595.76	−0.197984
$403$	−10427.0	−1.28885
$404$	−5702.35	−0.702234
$405$	1395.96	0.171273
$406$	−2970.39	−0.363099
$407$	1973.74	0.240380
$408$	1000.58	0.121412
$409$	5684.49	0.687237	0.343618	−	0.939109i	$-0.388347\pi$
$409$	5684.49	0.687237	0.343618	+	0.939109i	$0.388347\pi$
$410$	−4042.80	−0.486975
$411$	−4197.90	−0.503813
$412$	2280.30	0.272675
$413$	5204.65	0.620106
$414$	414.000	0.0491473
$415$	−6552.32	−0.775037
$416$	−2028.58	−0.239085
$417$	1105.86	0.129866
$418$	−7398.91	−0.865771
$419$	12696.9	1.48039	0.740195	−	0.672392i	$-0.234733\pi$
$419$	12696.9	1.48039	0.740195	+	0.672392i	$0.234733\pi$
$420$	1447.66	0.168187
$421$	14355.7	1.66189	0.830946	−	0.556353i	$-0.187800\pi$
$421$	14355.7	1.66189	0.830946	+	0.556353i	$0.187800\pi$
$422$	2502.38	0.288658
$423$	−2220.17	−0.255197
$424$	2622.28	0.300351
$425$	−7171.34	−0.818497
$426$	2941.53	0.334548
$427$	1843.03	0.208877
$428$	−7751.55	−0.875433
$429$	12097.2	1.36144
$430$	18898.5	2.11946
$431$	428.667	0.0479076	0.0239538	−	0.999713i	$-0.492375\pi$
$431$	428.667	0.0479076	0.0239538	+	0.999713i	$0.492375\pi$
$432$	432.000	0.0481125
$433$	1957.22	0.217224	0.108612	−	0.994084i	$-0.465359\pi$
$433$	1957.22	0.217224	0.108612	+	0.994084i	$0.465359\pi$
$434$	2302.75	0.254690
$435$	10969.7	1.20909
$436$	5722.55	0.628579
$437$	−1337.66	−0.146428
$438$	7272.91	0.793409
$439$	−14289.1	−1.55349	−0.776746	−	0.629815i	$-0.783131\pi$
$439$	−14289.1	−1.55349	−0.776746	+	0.629815i	$0.783131\pi$
$440$	−8769.95	−0.950206
$441$	441.000	0.0476190
$442$	5285.84	0.568828
$443$	−16390.0	−1.75782	−0.878908	−	0.476991i	$-0.841727\pi$
$443$	−16390.0	−1.75782	−0.878908	+	0.476991i	$0.841727\pi$
$444$	372.350	0.0397994
$445$	−24285.9	−2.58710
$446$	2892.83	0.307129
$447$	−2465.15	−0.260845
$448$	448.000	0.0472456
$449$	14360.4	1.50938	0.754689	−	0.656082i	$-0.227788\pi$
$449$	14360.4	1.50938	0.754689	+	0.656082i	$0.227788\pi$
$450$	−3096.21	−0.324348
$451$	7460.81	0.778971
$452$	−5381.01	−0.559959
$453$	−3194.63	−0.331339
$454$	−117.114	−0.0121067
$455$	7647.63	0.787970
$456$	−1395.82	−0.143345
$457$	−2463.78	−0.252190	−0.126095	−	0.992018i	$-0.540244\pi$
$457$	−2463.78	−0.252190	−0.126095	+	0.992018i	$0.540244\pi$
$458$	−2990.94	−0.305147
$459$	−1125.66	−0.114469
$460$	−1585.53	−0.160708
$461$	8903.87	0.899554	0.449777	−	0.893141i	$-0.351503\pi$
$461$	8903.87	0.899554	0.449777	+	0.893141i	$0.351503\pi$
$462$	−2671.59	−0.269034
$463$	10915.8	1.09568	0.547838	−	0.836584i	$-0.315451\pi$
$463$	10915.8	1.09568	0.547838	+	0.836584i	$0.315451\pi$
$464$	3394.73	0.339648
$465$	−8504.07	−0.848101
$466$	−10197.7	−1.01374
$467$	470.253	0.0465968	0.0232984	−	0.999729i	$-0.492583\pi$
$467$	470.253	0.0465968	0.0232984	+	0.999729i	$0.492583\pi$
$468$	2282.15	0.225411
$469$	1861.72	0.183297
$470$	8502.76	0.834475
$471$	9684.09	0.947387
$472$	−5948.17	−0.580056
$473$	−34876.4	−3.39031
$474$	7267.86	0.704270
$475$	10004.0	0.966351
$476$	−1167.35	−0.112406
$477$	−2950.06	−0.283174
$478$	−12236.1	−1.17085
$479$	−12331.1	−1.17625	−0.588125	−	0.808770i	$-0.700134\pi$
$479$	−12331.1	−1.17625	−0.588125	+	0.808770i	$0.700134\pi$
$480$	−1654.47	−0.157324
$481$	1967.03	0.186464
$482$	−10409.2	−0.983660
$483$	−483.000	−0.0455016
$484$	10860.5	1.01996
$485$	−7288.90	−0.682417
$486$	−486.000	−0.0453609
$487$	5393.86	0.501888	0.250944	−	0.968002i	$-0.419259\pi$
$487$	5393.86	0.501888	0.250944	+	0.968002i	$0.419259\pi$
$488$	−2106.32	−0.195387
$489$	10989.3	1.01627
$490$	−1688.93	−0.155711
$491$	−12185.5	−1.12001	−0.560005	−	0.828489i	$-0.689201\pi$
$491$	−12185.5	−1.12001	−0.560005	+	0.828489i	$0.689201\pi$
$492$	1407.50	0.128973
$493$	−8845.61	−0.808086
$494$	−7373.76	−0.671582
$495$	9866.19	0.895863
$496$	−2631.71	−0.238241
$497$	−3431.78	−0.309731
$498$	2281.18	0.205265
$499$	−3749.72	−0.336394	−0.168197	−	0.985753i	$-0.553794\pi$
$499$	−3749.72	−0.336394	−0.168197	+	0.985753i	$0.553794\pi$
$500$	3240.81	0.289867
$501$	−5571.80	−0.496866
$502$	13344.9	1.18648
$503$	11009.0	0.975875	0.487938	−	0.872879i	$-0.337749\pi$
$503$	11009.0	0.975875	0.487938	+	0.872879i	$0.337749\pi$
$504$	−504.000	−0.0445435
$505$	−24568.6	−2.16493
$506$	2926.02	0.257070
$507$	5465.05	0.478721
$508$	2213.71	0.193341
$509$	−12563.8	−1.09407	−0.547034	−	0.837110i	$-0.684243\pi$
$509$	−12563.8	−1.09407	−0.547034	+	0.837110i	$0.684243\pi$
$510$	4311.02	0.374305
$511$	−8485.06	−0.734554
$512$	−512.000	−0.0441942
$513$	1570.29	0.135147
$514$	−11195.2	−0.960702
$515$	9824.68	0.840635
$516$	−6579.49	−0.561329
$517$	−15691.5	−1.33484
$518$	−434.408	−0.0368471
$519$	−5617.24	−0.475085
$520$	−8740.15	−0.737078
$521$	−16881.5	−1.41956	−0.709779	−	0.704424i	$-0.751205\pi$
$521$	−16881.5	−1.41956	−0.709779	+	0.704424i	$0.751205\pi$
$522$	−3819.07	−0.320223
$523$	7769.27	0.649572	0.324786	−	0.945787i	$-0.394708\pi$
$523$	7769.27	0.649572	0.324786	+	0.945787i	$0.394708\pi$
$524$	8480.04	0.706970
$525$	3612.25	0.300288
$526$	10226.8	0.847737
$527$	6857.42	0.566820
$528$	3053.24	0.251658
$529$	529.000	0.0434783
$530$	11298.1	0.925959
$531$	6691.69	0.546882
$532$	1628.45	0.132711
$533$	7435.46	0.604250
$534$	8455.09	0.685183
$535$	−33397.6	−2.69889
$536$	−2127.68	−0.171459
$537$	−1256.07	−0.100937
$538$	16247.9	1.30204
$539$	3116.85	0.249077
$540$	1861.28	0.148327
$541$	22917.8	1.82128	0.910641	−	0.413199i	$-0.135589\pi$
$541$	22917.8	1.82128	0.910641	+	0.413199i	$0.135589\pi$
$542$	6503.14	0.515376
$543$	3342.19	0.264139
$544$	1334.11	0.105146
$545$	24655.6	1.93786
$546$	−2662.51	−0.208690
$547$	−933.881	−0.0729979	−0.0364989	−	0.999334i	$-0.511621\pi$
$547$	−933.881	−0.0729979	−0.0364989	+	0.999334i	$0.511621\pi$
$548$	−5597.20	−0.436315
$549$	2369.61	0.184212
$550$	−21883.1	−1.69654
$551$	12339.7	0.954060
$552$	552.000	0.0425628
$553$	−8479.17	−0.652027
$554$	−14848.4	−1.13871
$555$	1604.27	0.122698
$556$	1474.47	0.112467
$557$	−5446.05	−0.414285	−0.207143	−	0.978311i	$-0.566416\pi$
$557$	−5446.05	−0.414285	−0.207143	+	0.978311i	$0.566416\pi$
$558$	2960.68	0.224616
$559$	−34757.8	−2.62988
$560$	1930.21	0.145654
$561$	−7955.80	−0.598742
$562$	−10546.2	−0.791577
$563$	−3705.37	−0.277376	−0.138688	−	0.990336i	$-0.544289\pi$
$563$	−3705.37	−0.277376	−0.138688	+	0.990336i	$0.544289\pi$
$564$	−2960.22	−0.221007
$565$	−23184.1	−1.72631
$566$	−3432.98	−0.254945
$567$	567.000	0.0419961
$568$	3922.04	0.289727
$569$	22811.8	1.68070	0.840351	−	0.542043i	$-0.182349\pi$
$569$	22811.8	1.68070	0.840351	+	0.542043i	$0.182349\pi$
$570$	−6013.89	−0.441919
$571$	2410.11	0.176637	0.0883186	−	0.996092i	$-0.471851\pi$
$571$	2410.11	0.176637	0.0883186	+	0.996092i	$0.471851\pi$
$572$	16129.5	1.17904
$573$	9965.66	0.726564
$574$	−1642.08	−0.119406
$575$	−3956.27	−0.286935
$576$	576.000	0.0416667
$577$	−18094.9	−1.30554	−0.652772	−	0.757555i	$-0.726394\pi$
$577$	−18094.9	−1.30554	−0.652772	+	0.757555i	$0.726394\pi$
$578$	6349.72	0.456944
$579$	7298.97	0.523895
$580$	14626.2	1.04711
$581$	−2661.37	−0.190039
$582$	2537.62	0.180735
$583$	−20850.1	−1.48117
$584$	9697.21	0.687112
$585$	9832.66	0.694924
$586$	−10372.6	−0.731210
$587$	11018.4	0.774747	0.387373	−	0.921923i	$-0.373382\pi$
$587$	11018.4	0.774747	0.387373	+	0.921923i	$0.373382\pi$
$588$	588.000	0.0412393
$589$	−9566.13	−0.669211
$590$	−25627.7	−1.78827
$591$	2254.18	0.156894
$592$	496.466	0.0344673
$593$	28075.1	1.94419	0.972095	−	0.234585i	$-0.0753733\pi$
$593$	28075.1	1.94419	0.972095	+	0.234585i	$0.0753733\pi$
$594$	−3434.90	−0.237265
$595$	−5029.53	−0.346539
$596$	−3286.87	−0.225898
$597$	3711.58	0.254447
$598$	2916.08	0.199410
$599$	−23553.7	−1.60664	−0.803319	−	0.595548i	$-0.796935\pi$
$599$	−23553.7	−1.60664	−0.803319	+	0.595548i	$0.796935\pi$
$600$	−4128.28	−0.280894
$601$	4484.76	0.304388	0.152194	−	0.988351i	$-0.451366\pi$
$601$	4484.76	0.304388	0.152194	+	0.988351i	$0.451366\pi$
$602$	7676.07	0.519690
$603$	2393.64	0.161653
$604$	−4259.50	−0.286948
$605$	46792.7	3.14445
$606$	8553.52	0.573372
$607$	−10493.5	−0.701680	−0.350840	−	0.936435i	$-0.614104\pi$
$607$	−10493.5	−0.701680	−0.350840	+	0.936435i	$0.614104\pi$
$608$	−1861.09	−0.124140
$609$	4455.59	0.296469
$610$	−9075.10	−0.602361
$611$	−15638.1	−1.03544
$612$	−1500.88	−0.0991329
$613$	−6030.77	−0.397358	−0.198679	−	0.980065i	$-0.563665\pi$
$613$	−6030.77	−0.397358	−0.198679	+	0.980065i	$0.563665\pi$
$614$	14277.6	0.938429
$615$	6064.21	0.397614
$616$	−3562.12	−0.232990
$617$	9998.95	0.652419	0.326210	−	0.945297i	$-0.394228\pi$
$617$	9998.95	0.652419	0.326210	+	0.945297i	$0.394228\pi$
$618$	−3420.45	−0.222638
$619$	−16146.4	−1.04843	−0.524215	−	0.851586i	$-0.675641\pi$
$619$	−16146.4	−1.04843	−0.524215	+	0.851586i	$0.675641\pi$
$620$	−11338.8	−0.734477
$621$	−621.000	−0.0401286
$622$	3186.74	0.205429
$623$	−9864.27	−0.634356
$624$	3042.87	0.195212
$625$	−7538.42	−0.482459
$626$	5238.07	0.334433
$627$	11098.4	0.706899
$628$	12912.1	0.820461
$629$	−1293.64	−0.0820042
$630$	−2171.49	−0.137324
$631$	7575.48	0.477932	0.238966	−	0.971028i	$-0.423192\pi$
$631$	7575.48	0.477932	0.238966	+	0.971028i	$0.423192\pi$
$632$	9690.49	0.609916
$633$	−3753.57	−0.235689
$634$	10694.0	0.669895
$635$	9537.77	0.596055
$636$	−3933.42	−0.245236
$637$	3106.26	0.193210
$638$	−26992.0	−1.67496
$639$	−4412.29	−0.273157
$640$	−2205.96	−0.136247
$641$	−7295.29	−0.449527	−0.224763	−	0.974413i	$-0.572161\pi$
$641$	−7295.29	−0.449527	−0.224763	+	0.974413i	$0.572161\pi$
$642$	11627.3	0.714788
$643$	10316.2	0.632710	0.316355	−	0.948641i	$-0.397541\pi$
$643$	10316.2	0.632710	0.316355	+	0.948641i	$0.397541\pi$
$644$	−644.000	−0.0394055
$645$	−28347.8	−1.73053
$646$	4849.42	0.295353
$647$	−277.886	−0.0168853	−0.00844266	−	0.999964i	$-0.502687\pi$
$647$	−277.886	−0.0168853	−0.00844266	+	0.999964i	$0.502687\pi$
$648$	−648.000	−0.0392837
$649$	47294.8	2.86053
$650$	−21808.7	−1.31601
$651$	−3454.12	−0.207954
$652$	14652.4	0.880113
$653$	−6256.21	−0.374922	−0.187461	−	0.982272i	$-0.560026\pi$
$653$	−6256.21	−0.374922	−0.187461	+	0.982272i	$0.560026\pi$
$654$	−8583.82	−0.513232
$655$	36536.3	2.17953
$656$	1876.66	0.111694
$657$	−10909.4	−0.647815
$658$	3453.59	0.204613
$659$	−24778.9	−1.46472	−0.732358	−	0.680920i	$-0.761580\pi$
$659$	−24778.9	−1.46472	−0.732358	+	0.680920i	$0.761580\pi$
$660$	13154.9	0.775840
$661$	−5004.37	−0.294474	−0.147237	−	0.989101i	$-0.547038\pi$
$661$	−5004.37	−0.294474	−0.147237	+	0.989101i	$0.547038\pi$
$662$	−19776.8	−1.16110
$663$	−7928.76	−0.464446
$664$	3041.57	0.177765
$665$	7016.20	0.409138
$666$	−558.524	−0.0324961
$667$	−4879.93	−0.283286
$668$	−7429.07	−0.430298
$669$	−4339.24	−0.250770
$670$	−9167.14	−0.528593
$671$	16747.7	0.963543
$672$	−672.000	−0.0385758
$673$	27180.6	1.55681	0.778406	−	0.627761i	$-0.216028\pi$
$673$	27180.6	1.55681	0.778406	+	0.627761i	$0.216028\pi$
$674$	−4280.64	−0.244635
$675$	4644.32	0.264829
$676$	7286.73	0.414584
$677$	2042.92	0.115976	0.0579880	−	0.998317i	$-0.481532\pi$
$677$	2042.92	0.115976	0.0579880	+	0.998317i	$0.481532\pi$
$678$	8071.51	0.457204
$679$	−2960.56	−0.167328
$680$	5748.03	0.324157
$681$	175.671	0.00988504
$682$	20925.2	1.17488
$683$	−24821.4	−1.39058	−0.695288	−	0.718731i	$-0.744723\pi$
$683$	−24821.4	−1.39058	−0.695288	+	0.718731i	$0.744723\pi$
$684$	2093.73	0.117040
$685$	−24115.6	−1.34512
$686$	−686.000	−0.0381802
$687$	4486.40	0.249151
$688$	−8772.65	−0.486125
$689$	−20779.3	−1.14895
$690$	2378.30	0.131218
$691$	−14499.4	−0.798238	−0.399119	−	0.916899i	$-0.630684\pi$
$691$	−14499.4	−0.798238	−0.399119	+	0.916899i	$0.630684\pi$
$692$	−7489.65	−0.411436
$693$	4007.38	0.219665
$694$	8499.83	0.464912
$695$	6352.78	0.346726
$696$	−5092.10	−0.277321
$697$	−4889.99	−0.265741
$698$	1781.55	0.0966082
$699$	15296.6	0.827713
$700$	4816.33	0.260057
$701$	12914.2	0.695811	0.347906	−	0.937530i	$-0.386893\pi$
$701$	12914.2	0.695811	0.347906	+	0.937530i	$0.386893\pi$
$702$	−3423.23	−0.184048
$703$	1804.63	0.0968175
$704$	4070.99	0.217942
$705$	−12754.1	−0.681346
$706$	−441.986	−0.0235614
$707$	−9979.11	−0.530839
$708$	8922.25	0.473614
$709$	2247.37	0.119044	0.0595218	−	0.998227i	$-0.481042\pi$
$709$	2247.37	0.119044	0.0595218	+	0.998227i	$0.481042\pi$
$710$	16898.1	0.893204
$711$	−10901.8	−0.575034
$712$	11273.5	0.593386
$713$	3783.09	0.198707
$714$	1751.02	0.0917792
$715$	69494.3	3.63488
$716$	−1674.76	−0.0874142
$717$	18354.1	0.955994
$718$	10121.3	0.526075
$719$	−7120.49	−0.369331	−0.184666	−	0.982801i	$-0.559120\pi$
$719$	−7120.49	−0.369331	−0.184666	+	0.982801i	$0.559120\pi$
$720$	2481.70	0.128455
$721$	3990.52	0.206123
$722$	6953.05	0.358401
$723$	15613.7	0.803155
$724$	4456.26	0.228751
$725$	36495.9	1.86955
$726$	−16290.8	−0.832794
$727$	13831.0	0.705589	0.352794	−	0.935701i	$-0.385232\pi$
$727$	13831.0	0.705589	0.352794	+	0.935701i	$0.385232\pi$
$728$	−3550.01	−0.180731
$729$	729.000	0.0370370
$730$	41780.5	2.11831
$731$	22858.8	1.15658
$732$	3159.48	0.159533
$733$	19525.5	0.983891	0.491945	−	0.870626i	$-0.336286\pi$
$733$	19525.5	0.983891	0.491945	+	0.870626i	$0.336286\pi$
$734$	13798.7	0.693897
$735$	2533.40	0.127137
$736$	736.000	0.0368605
$737$	16917.5	0.845543
$738$	−2111.24	−0.105306
$739$	−471.369	−0.0234636	−0.0117318	−	0.999931i	$-0.503734\pi$
$739$	−471.369	−0.0234636	−0.0117318	+	0.999931i	$0.503734\pi$
$740$	2139.03	0.106260
$741$	11060.6	0.548344
$742$	4588.98	0.227044
$743$	−17814.6	−0.879617	−0.439808	−	0.898092i	$-0.644954\pi$
$743$	−17814.6	−0.879617	−0.439808	+	0.898092i	$0.644954\pi$
$744$	3947.57	0.194523
$745$	−14161.5	−0.696425
$746$	1863.75	0.0914700
$747$	−3421.77	−0.167598
$748$	−10607.7	−0.518525
$749$	−13565.2	−0.661765
$750$	−4861.21	−0.236675
$751$	17527.3	0.851638	0.425819	−	0.904808i	$-0.359986\pi$
$751$	17527.3	0.851638	0.425819	+	0.904808i	$0.359986\pi$
$752$	−3946.97	−0.191398
$753$	−20017.4	−0.968757
$754$	−26900.3	−1.29927
$755$	−18352.1	−0.884638
$756$	756.000	0.0363696
$757$	5478.66	0.263045	0.131523	−	0.991313i	$-0.458013\pi$
$757$	5478.66	0.263045	0.131523	+	0.991313i	$0.458013\pi$
$758$	4340.21	0.207973
$759$	−4389.04	−0.209897
$760$	−8018.52	−0.382713
$761$	−8729.34	−0.415819	−0.207910	−	0.978148i	$-0.566666\pi$
$761$	−8729.34	−0.415819	−0.207910	+	0.978148i	$0.566666\pi$
$762$	−3320.56	−0.157862
$763$	10014.5	0.475161
$764$	13287.5	0.629223
$765$	−6466.53	−0.305618
$766$	−2719.00	−0.128253
$767$	47134.1	2.21892
$768$	768.000	0.0360844
$769$	16310.5	0.764851	0.382426	−	0.923986i	$-0.375089\pi$
$769$	16310.5	0.764851	0.382426	+	0.923986i	$0.375089\pi$
$770$	−15347.4	−0.718289
$771$	16792.9	0.784410
$772$	9731.96	0.453706
$773$	10028.5	0.466624	0.233312	−	0.972402i	$-0.425044\pi$
$773$	10028.5	0.466624	0.233312	+	0.972402i	$0.425044\pi$
$774$	9869.23	0.458323
$775$	−28292.9	−1.31137
$776$	3383.49	0.156521
$777$	651.612	0.0300855
$778$	15549.9	0.716570
$779$	6821.55	0.313745
$780$	13110.2	0.601822
$781$	−31184.7	−1.42878
$782$	−1917.79	−0.0876981
$783$	5728.61	0.261461
$784$	784.000	0.0357143
$785$	55632.0	2.52941
$786$	−12720.1	−0.577239
$787$	32677.2	1.48007	0.740037	−	0.672567i	$-0.234808\pi$
$787$	32677.2	1.48007	0.740037	+	0.672567i	$0.234808\pi$
$788$	3005.57	0.135874
$789$	−15340.2	−0.692174
$790$	41751.5	1.88032
$791$	−9416.76	−0.423289
$792$	−4579.86	−0.205478
$793$	16690.8	0.747424
$794$	14736.4	0.658657
$795$	−16947.1	−0.756042
$796$	4948.77	0.220357
$797$	22815.7	1.01402	0.507009	−	0.861941i	$-0.330751\pi$
$797$	22815.7	1.01402	0.507009	+	0.861941i	$0.330751\pi$
$798$	−2442.68	−0.108358
$799$	10284.6	0.455371
$800$	−5504.38	−0.243261
$801$	−12682.6	−0.559449
$802$	−167.819	−0.00738891
$803$	−77104.0	−3.38847
$804$	3191.52	0.139996
$805$	−2774.68	−0.121484
$806$	20854.1	0.911356
$807$	−24371.8	−1.06311
$808$	11404.7	0.496554
$809$	−29830.5	−1.29640	−0.648199	−	0.761471i	$-0.724478\pi$
$809$	−29830.5	−1.29640	−0.648199	+	0.761471i	$0.724478\pi$
$810$	−2791.91	−0.121108
$811$	36185.9	1.56678	0.783390	−	0.621531i	$-0.213489\pi$
$811$	36185.9	1.56678	0.783390	+	0.621531i	$0.213489\pi$
$812$	5940.78	0.256749
$813$	−9754.71	−0.420803
$814$	−3947.48	−0.169974
$815$	63130.1	2.71332
$816$	−2001.17	−0.0858516
$817$	−31888.1	−1.36551
$818$	−11369.0	−0.485950
$819$	3993.76	0.170395
$820$	8085.61	0.344344
$821$	−5640.11	−0.239758	−0.119879	−	0.992789i	$-0.538251\pi$
$821$	−5640.11	−0.239758	−0.119879	+	0.992789i	$0.538251\pi$
$822$	8395.80	0.356250
$823$	27186.3	1.15147	0.575733	−	0.817638i	$-0.304717\pi$
$823$	27186.3	1.15147	0.575733	+	0.817638i	$0.304717\pi$
$824$	−4560.59	−0.192810
$825$	32824.6	1.38522
$826$	−10409.3	−0.438481
$827$	−10622.5	−0.446651	−0.223325	−	0.974744i	$-0.571691\pi$
$827$	−10622.5	−0.446651	−0.223325	+	0.974744i	$0.571691\pi$
$828$	−828.000	−0.0347524
$829$	3855.95	0.161547	0.0807736	−	0.996732i	$-0.474261\pi$
$829$	3855.95	0.161547	0.0807736	+	0.996732i	$0.474261\pi$
$830$	13104.6	0.548034
$831$	22272.5	0.929754
$832$	4057.16	0.169058
$833$	−2042.86	−0.0849710
$834$	−2211.71	−0.0918288
$835$	−32008.2	−1.32657
$836$	14797.8	0.612193
$837$	−4441.02	−0.183398
$838$	−25393.8	−1.04679
$839$	−8096.11	−0.333145	−0.166573	−	0.986029i	$-0.553270\pi$
$839$	−8096.11	−0.333145	−0.166573	+	0.986029i	$0.553270\pi$
$840$	−2895.32	−0.118926
$841$	20627.4	0.845768
$842$	−28711.5	−1.17513
$843$	15819.4	0.646320
$844$	−5004.75	−0.204112
$845$	31394.9	1.27813
$846$	4440.34	0.180451
$847$	19005.9	0.771018
$848$	−5244.55	−0.212381
$849$	5149.48	0.208162
$850$	14342.7	0.578765
$851$	−713.670	−0.0287477
$852$	−5883.05	−0.236561
$853$	−30491.4	−1.22392	−0.611960	−	0.790889i	$-0.709619\pi$
$853$	−30491.4	−1.22392	−0.611960	+	0.790889i	$0.709619\pi$
$854$	−3686.06	−0.147698
$855$	9020.83	0.360826
$856$	15503.1	0.619025
$857$	10814.6	0.431063	0.215532	−	0.976497i	$-0.430852\pi$
$857$	10814.6	0.431063	0.215532	+	0.976497i	$0.430852\pi$
$858$	−24194.3	−0.962681
$859$	−24548.2	−0.975058	−0.487529	−	0.873107i	$-0.662102\pi$
$859$	−24548.2	−0.975058	−0.487529	+	0.873107i	$0.662102\pi$
$860$	−37797.0	−1.49868
$861$	2463.12	0.0974946
$862$	−857.334	−0.0338758
$863$	−12770.8	−0.503734	−0.251867	−	0.967762i	$-0.581044\pi$
$863$	−12770.8	−0.503734	−0.251867	+	0.967762i	$0.581044\pi$
$864$	−864.000	−0.0340207
$865$	−32269.2	−1.26842
$866$	−3914.44	−0.153601
$867$	−9524.58	−0.373093
$868$	−4605.50	−0.180093
$869$	−77050.5	−3.00778
$870$	−21939.3	−0.854958
$871$	16860.0	0.655891
$872$	−11445.1	−0.444472
$873$	−3806.43	−0.147569
$874$	2675.32	0.103540
$875$	5671.41	0.219119
$876$	−14545.8	−0.561025
$877$	−23217.0	−0.893937	−0.446969	−	0.894550i	$-0.647496\pi$
$877$	−23217.0	−0.893937	−0.446969	+	0.894550i	$0.647496\pi$
$878$	28578.2	1.09848
$879$	15558.9	0.597030
$880$	17539.9	0.671897
$881$	−2996.92	−0.114607	−0.0573034	−	0.998357i	$-0.518250\pi$
$881$	−2996.92	−0.114607	−0.0573034	+	0.998357i	$0.518250\pi$
$882$	−882.000	−0.0336718
$883$	−6261.90	−0.238652	−0.119326	−	0.992855i	$-0.538073\pi$
$883$	−6261.90	−0.238652	−0.119326	+	0.992855i	$0.538073\pi$
$884$	−10571.7	−0.402222
$885$	38441.6	1.46011
$886$	32780.0	1.24296
$887$	38133.1	1.44350	0.721751	−	0.692153i	$-0.243338\pi$
$887$	38133.1	1.44350	0.721751	+	0.692153i	$0.243338\pi$
$888$	−744.699	−0.0281424
$889$	3873.98	0.146152
$890$	48571.8	1.82936
$891$	5152.35	0.193726
$892$	−5785.66	−0.217173
$893$	−14347.0	−0.537630
$894$	4930.30	0.184445
$895$	−7215.70	−0.269491
$896$	−896.000	−0.0334077
$897$	−4374.12	−0.162818
$898$	−28720.9	−1.06729
$899$	−34898.3	−1.29469
$900$	6192.42	0.229349
$901$	13665.7	0.505293
$902$	−14921.6	−0.550816
$903$	−11514.1	−0.424325
$904$	10762.0	0.395951
$905$	19199.8	0.705219
$906$	6389.26	0.234292
$907$	−47321.1	−1.73238	−0.866191	−	0.499714i	$-0.833439\pi$
$907$	−47321.1	−1.73238	−0.866191	+	0.499714i	$0.833439\pi$
$908$	234.227	0.00856069
$909$	−12830.3	−0.468156
$910$	−15295.3	−0.557179
$911$	−32616.9	−1.18622	−0.593111	−	0.805121i	$-0.702100\pi$
$911$	−32616.9	−1.18622	−0.593111	+	0.805121i	$0.702100\pi$
$912$	2791.63	0.101360
$913$	−24184.0	−0.876642
$914$	4927.57	0.178325
$915$	13612.7	0.491826
$916$	5981.87	0.215771
$917$	14840.1	0.534419
$918$	2251.31	0.0809416
$919$	−18468.9	−0.662930	−0.331465	−	0.943467i	$-0.607543\pi$
$919$	−18468.9	−0.662930	−0.331465	+	0.943467i	$0.607543\pi$
$920$	3171.06	0.113638
$921$	−21416.3	−0.766224
$922$	−17807.7	−0.636081
$923$	−31078.7	−1.10831
$924$	5343.18	0.190235
$925$	5337.38	0.189721
$926$	−21831.5	−0.774760
$927$	5130.67	0.181783
$928$	−6789.47	−0.240167
$929$	8101.53	0.286117	0.143058	−	0.989714i	$-0.454306\pi$
$929$	8101.53	0.286117	0.143058	+	0.989714i	$0.454306\pi$
$930$	17008.1	0.599698
$931$	2849.79	0.100320
$932$	20395.5	0.716820
$933$	−4780.11	−0.167732
$934$	−940.505	−0.0329489
$935$	−45703.5	−1.59857
$936$	−4564.30	−0.159390
$937$	7885.18	0.274917	0.137459	−	0.990508i	$-0.456107\pi$
$937$	7885.18	0.274917	0.137459	+	0.990508i	$0.456107\pi$
$938$	−3723.45	−0.129611
$939$	−7857.10	−0.273064
$940$	−17005.5	−0.590063
$941$	−12258.0	−0.424655	−0.212327	−	0.977199i	$-0.568104\pi$
$941$	−12258.0	−0.424655	−0.212327	+	0.977199i	$0.568104\pi$
$942$	−19368.2	−0.669904
$943$	−2697.70	−0.0931593
$944$	11896.3	0.410162
$945$	3257.23	0.112125
$946$	69752.7	2.39731
$947$	42665.8	1.46405	0.732024	−	0.681279i	$-0.238576\pi$
$947$	42665.8	1.46405	0.732024	+	0.681279i	$0.238576\pi$
$948$	−14535.7	−0.497994
$949$	−76842.0	−2.62845
$950$	−20008.1	−0.683314
$951$	−16041.0	−0.546967
$952$	2334.70	0.0794831
$953$	−30230.8	−1.02757	−0.513784	−	0.857920i	$-0.671757\pi$
$953$	−30230.8	−1.02757	−0.513784	+	0.857920i	$0.671757\pi$
$954$	5900.12	0.200234
$955$	57249.5	1.93984
$956$	24472.2	0.827915
$957$	40488.1	1.36760
$958$	24662.3	0.831734
$959$	−9795.10	−0.329823
$960$	3308.93	0.111245
$961$	−2736.63	−0.0918608
$962$	−3934.07	−0.131850
$963$	−17441.0	−0.583622
$964$	20818.3	0.695552
$965$	41930.2	1.39874
$966$	966.000	0.0321745
$967$	26406.9	0.878168	0.439084	−	0.898446i	$-0.355303\pi$
$967$	26406.9	0.878168	0.439084	+	0.898446i	$0.355303\pi$
$968$	−21721.1	−0.721221
$969$	−7274.13	−0.241154
$970$	14577.8	0.482541
$971$	−51849.2	−1.71361	−0.856807	−	0.515638i	$-0.827555\pi$
$971$	−51849.2	−1.71361	−0.856807	+	0.515638i	$0.827555\pi$
$972$	972.000	0.0320750
$973$	2580.33	0.0850170
$974$	−10787.7	−0.354888
$975$	32713.1	1.07452
$976$	4212.64	0.138159
$977$	−36365.2	−1.19081	−0.595407	−	0.803424i	$-0.703009\pi$
$977$	−36365.2	−1.19081	−0.595407	+	0.803424i	$0.703009\pi$
$978$	−21978.7	−0.718609
$979$	−89637.0	−2.92626
$980$	3377.87	0.110104
$981$	12875.7	0.419052
$982$	24371.0	0.791967
$983$	42492.4	1.37874	0.689369	−	0.724411i	$-0.257888\pi$
$983$	42492.4	1.37874	0.689369	+	0.724411i	$0.257888\pi$
$984$	−2814.99	−0.0911978
$985$	12949.5	0.418890
$986$	17691.2	0.571403
$987$	−5180.39	−0.167066
$988$	14747.5	0.474880
$989$	12610.7	0.405457
$990$	−19732.4	−0.633471
$991$	1136.53	0.0364308	0.0182154	−	0.999834i	$-0.494202\pi$
$991$	1136.53	0.0364308	0.0182154	+	0.999834i	$0.494202\pi$
$992$	5263.43	0.168462
$993$	29665.2	0.948032
$994$	6863.56	0.219013
$995$	21321.8	0.679343
$996$	−4562.36	−0.145144
$997$	−39157.8	−1.24387	−0.621936	−	0.783068i	$-0.713654\pi$
$997$	−39157.8	−1.24387	−0.621936	+	0.783068i	$0.713654\pi$
$998$	7499.44	0.237866
$999$	837.787	0.0265329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.o.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.o.1.5	✓	5	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +17.2340 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +17.2340 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -34.4681 q^{10} +63.6092 q^{11} +12.0000 q^{12} +63.3931 q^{13} -14.0000 q^{14} +51.7021 q^{15} +16.0000 q^{16} -41.6910 q^{17} -18.0000 q^{18} +58.1591 q^{19} +68.9361 q^{20} +21.0000 q^{21} -127.218 q^{22} -23.0000 q^{23} -24.0000 q^{24} +172.012 q^{25} -126.786 q^{26} +27.0000 q^{27} +28.0000 q^{28} +212.171 q^{29} -103.404 q^{30} -164.482 q^{31} -32.0000 q^{32} +190.828 q^{33} +83.3820 q^{34} +120.638 q^{35} +36.0000 q^{36} +31.0291 q^{37} -116.318 q^{38} +190.179 q^{39} -137.872 q^{40} +117.291 q^{41} -42.0000 q^{42} -548.291 q^{43} +254.437 q^{44} +155.106 q^{45} +46.0000 q^{46} -246.685 q^{47} +48.0000 q^{48} +49.0000 q^{49} -344.024 q^{50} -125.073 q^{51} +253.572 q^{52} -327.785 q^{53} -54.0000 q^{54} +1096.24 q^{55} -56.0000 q^{56} +174.477 q^{57} -424.342 q^{58} +743.521 q^{59} +206.808 q^{60} +263.290 q^{61} +328.964 q^{62} +63.0000 q^{63} +64.0000 q^{64} +1092.52 q^{65} -381.655 q^{66} +265.960 q^{67} -166.764 q^{68} -69.0000 q^{69} -241.276 q^{70} -490.254 q^{71} -72.0000 q^{72} -1212.15 q^{73} -62.0583 q^{74} +516.035 q^{75} +232.636 q^{76} +445.265 q^{77} -380.359 q^{78} -1211.31 q^{79} +275.744 q^{80} +81.0000 q^{81} -234.583 q^{82} -380.196 q^{83} +84.0000 q^{84} -718.504 q^{85} +1096.58 q^{86} +636.512 q^{87} -508.874 q^{88} -1409.18 q^{89} -310.213 q^{90} +443.752 q^{91} -92.0000 q^{92} -493.446 q^{93} +493.371 q^{94} +1002.31 q^{95} -96.0000 q^{96} -422.937 q^{97} -98.0000 q^{98} +572.483 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} + 6 q^{5} - 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 + 6 * q^5 - 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} + 6 q^{5} - 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9} - 12 q^{10} - 50 q^{11} + 60 q^{12} + 66 q^{13} - 70 q^{14} + 18 q^{15} + 80 q^{16} - 198 q^{17} - 90 q^{18} + 120 q^{19} + 24 q^{20} + 105 q^{21} + 100 q^{22} - 115 q^{23} - 120 q^{24} + 503 q^{25} - 132 q^{26} + 135 q^{27} + 140 q^{28} + 301 q^{29} - 36 q^{30} + 314 q^{31} - 160 q^{32} - 150 q^{33} + 396 q^{34} + 42 q^{35} + 180 q^{36} + 269 q^{37} - 240 q^{38} + 198 q^{39} - 48 q^{40} + 479 q^{41} - 210 q^{42} - 290 q^{43} - 200 q^{44} + 54 q^{45} + 230 q^{46} + 69 q^{47} + 240 q^{48} + 245 q^{49} - 1006 q^{50} - 594 q^{51} + 264 q^{52} + 339 q^{53} - 270 q^{54} + 957 q^{55} - 280 q^{56} + 360 q^{57} - 602 q^{58} + 2065 q^{59} + 72 q^{60} + 531 q^{61} - 628 q^{62} + 315 q^{63} + 320 q^{64} + 1227 q^{65} + 300 q^{66} + 855 q^{67} - 792 q^{68} - 345 q^{69} - 84 q^{70} - 863 q^{71} - 360 q^{72} + 618 q^{73} - 538 q^{74} + 1509 q^{75} + 480 q^{76} - 350 q^{77} - 396 q^{78} + 254 q^{79} + 96 q^{80} + 405 q^{81} - 958 q^{82} - 1700 q^{83} + 420 q^{84} + 1977 q^{85} + 580 q^{86} + 903 q^{87} + 400 q^{88} - 275 q^{89} - 108 q^{90} + 462 q^{91} - 460 q^{92} + 942 q^{93} - 138 q^{94} + 171 q^{95} - 480 q^{96} - 979 q^{97} - 490 q^{98} - 450 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 + 6 * q^5 - 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9 - 12 * q^10 - 50 * q^11 + 60 * q^12 + 66 * q^13 - 70 * q^14 + 18 * q^15 + 80 * q^16 - 198 * q^17 - 90 * q^18 + 120 * q^19 + 24 * q^20 + 105 * q^21 + 100 * q^22 - 115 * q^23 - 120 * q^24 + 503 * q^25 - 132 * q^26 + 135 * q^27 + 140 * q^28 + 301 * q^29 - 36 * q^30 + 314 * q^31 - 160 * q^32 - 150 * q^33 + 396 * q^34 + 42 * q^35 + 180 * q^36 + 269 * q^37 - 240 * q^38 + 198 * q^39 - 48 * q^40 + 479 * q^41 - 210 * q^42 - 290 * q^43 - 200 * q^44 + 54 * q^45 + 230 * q^46 + 69 * q^47 + 240 * q^48 + 245 * q^49 - 1006 * q^50 - 594 * q^51 + 264 * q^52 + 339 * q^53 - 270 * q^54 + 957 * q^55 - 280 * q^56 + 360 * q^57 - 602 * q^58 + 2065 * q^59 + 72 * q^60 + 531 * q^61 - 628 * q^62 + 315 * q^63 + 320 * q^64 + 1227 * q^65 + 300 * q^66 + 855 * q^67 - 792 * q^68 - 345 * q^69 - 84 * q^70 - 863 * q^71 - 360 * q^72 + 618 * q^73 - 538 * q^74 + 1509 * q^75 + 480 * q^76 - 350 * q^77 - 396 * q^78 + 254 * q^79 + 96 * q^80 + 405 * q^81 - 958 * q^82 - 1700 * q^83 + 420 * q^84 + 1977 * q^85 + 580 * q^86 + 903 * q^87 + 400 * q^88 - 275 * q^89 - 108 * q^90 + 462 * q^91 - 460 * q^92 + 942 * q^93 - 138 * q^94 + 171 * q^95 - 480 * q^96 - 979 * q^97 - 490 * q^98 - 450 * q^99

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