LMFDB - Embedded newform 1045.4.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,4,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.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:	$61.6569959560$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.68859 q^{2} -3.54772 q^{3} -0.771496 q^{4} -5.00000 q^{5} -9.53836 q^{6} +27.8868 q^{7} -23.5829 q^{8} -14.4137 q^{9} +O(q^{10})$	\(q+2.68859 q^{2} -3.54772 q^{3} -0.771496 q^{4} -5.00000 q^{5} -9.53836 q^{6} +27.8868 q^{7} -23.5829 q^{8} -14.4137 q^{9} -13.4429 q^{10} +11.0000 q^{11} +2.73705 q^{12} -11.6213 q^{13} +74.9762 q^{14} +17.7386 q^{15} -57.2328 q^{16} +123.554 q^{17} -38.7524 q^{18} -19.0000 q^{19} +3.85748 q^{20} -98.9348 q^{21} +29.5745 q^{22} +3.23375 q^{23} +83.6657 q^{24} +25.0000 q^{25} -31.2450 q^{26} +146.924 q^{27} -21.5146 q^{28} -267.510 q^{29} +47.6918 q^{30} +106.646 q^{31} +34.7880 q^{32} -39.0249 q^{33} +332.186 q^{34} -139.434 q^{35} +11.1201 q^{36} -192.637 q^{37} -51.0832 q^{38} +41.2292 q^{39} +117.915 q^{40} +354.453 q^{41} -265.995 q^{42} -232.956 q^{43} -8.48646 q^{44} +72.0683 q^{45} +8.69423 q^{46} -234.327 q^{47} +203.046 q^{48} +434.676 q^{49} +67.2147 q^{50} -438.335 q^{51} +8.96581 q^{52} -728.236 q^{53} +395.019 q^{54} -55.0000 q^{55} -657.654 q^{56} +67.4067 q^{57} -719.225 q^{58} +638.745 q^{59} -13.6853 q^{60} -698.800 q^{61} +286.726 q^{62} -401.952 q^{63} +551.393 q^{64} +58.1066 q^{65} -104.922 q^{66} -340.922 q^{67} -95.3215 q^{68} -11.4725 q^{69} -374.881 q^{70} +317.515 q^{71} +339.917 q^{72} -549.107 q^{73} -517.923 q^{74} -88.6931 q^{75} +14.6584 q^{76} +306.755 q^{77} +110.848 q^{78} -888.087 q^{79} +286.164 q^{80} -132.077 q^{81} +952.977 q^{82} -944.143 q^{83} +76.3278 q^{84} -617.770 q^{85} -626.323 q^{86} +949.052 q^{87} -259.412 q^{88} -758.826 q^{89} +193.762 q^{90} -324.082 q^{91} -2.49483 q^{92} -378.349 q^{93} -630.010 q^{94} +95.0000 q^{95} -123.418 q^{96} +382.749 q^{97} +1168.67 q^{98} -158.550 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 2 q^{2} - 9 q^{3} + 98 q^{4} - 115 q^{5} - 61 q^{6} + 13 q^{7} - 54 q^{8} + 170 q^{9}+O(q^{10}) $ 23 * q - 2 * q^2 - 9 * q^3 + 98 * q^4 - 115 * q^5 - 61 * q^6 + 13 * q^7 - 54 * q^8 + 170 * q^9	\( 23 q - 2 q^{2} - 9 q^{3} + 98 q^{4} - 115 q^{5} - 61 q^{6} + 13 q^{7} - 54 q^{8} + 170 q^{9} + 10 q^{10} + 253 q^{11} - 76 q^{12} - 37 q^{13} - 191 q^{14} + 45 q^{15} + 214 q^{16} - 51 q^{17} - 63 q^{18} - 437 q^{19} - 490 q^{20} - 479 q^{21} - 22 q^{22} + 101 q^{23} - 598 q^{24} + 575 q^{25} - 197 q^{26} - 627 q^{27} + 279 q^{28} - 357 q^{29} + 305 q^{30} - 90 q^{31} - 19 q^{32} - 99 q^{33} + 71 q^{34} - 65 q^{35} + 573 q^{36} - 378 q^{37} + 38 q^{38} + 193 q^{39} + 270 q^{40} - 830 q^{41} + 1480 q^{42} + 260 q^{43} + 1078 q^{44} - 850 q^{45} - 919 q^{46} - 1468 q^{47} + 837 q^{48} + 1200 q^{49} - 50 q^{50} - 1147 q^{51} - 1222 q^{52} + 185 q^{53} - 1406 q^{54} - 1265 q^{55} - 2299 q^{56} + 171 q^{57} - 958 q^{58} - 3665 q^{59} + 380 q^{60} - 2528 q^{61} - 1722 q^{62} + 172 q^{63} - 120 q^{64} + 185 q^{65} - 671 q^{66} + 329 q^{67} - 2240 q^{68} - 1337 q^{69} + 955 q^{70} - 3190 q^{71} - 2488 q^{72} - 2183 q^{73} - 1613 q^{74} - 225 q^{75} - 1862 q^{76} + 143 q^{77} - 2748 q^{78} - 3546 q^{79} - 1070 q^{80} - 2077 q^{81} + 2202 q^{82} - 4324 q^{83} - 8608 q^{84} + 255 q^{85} - 3626 q^{86} + 2921 q^{87} - 594 q^{88} - 4630 q^{89} + 315 q^{90} - 5043 q^{91} + 108 q^{92} - 5644 q^{93} - 8328 q^{94} + 2185 q^{95} - 2016 q^{96} - 774 q^{97} - 6388 q^{98} + 1870 q^{99}+O(q^{100}) \) 23 * q - 2 * q^2 - 9 * q^3 + 98 * q^4 - 115 * q^5 - 61 * q^6 + 13 * q^7 - 54 * q^8 + 170 * q^9 + 10 * q^10 + 253 * q^11 - 76 * q^12 - 37 * q^13 - 191 * q^14 + 45 * q^15 + 214 * q^16 - 51 * q^17 - 63 * q^18 - 437 * q^19 - 490 * q^20 - 479 * q^21 - 22 * q^22 + 101 * q^23 - 598 * q^24 + 575 * q^25 - 197 * q^26 - 627 * q^27 + 279 * q^28 - 357 * q^29 + 305 * q^30 - 90 * q^31 - 19 * q^32 - 99 * q^33 + 71 * q^34 - 65 * q^35 + 573 * q^36 - 378 * q^37 + 38 * q^38 + 193 * q^39 + 270 * q^40 - 830 * q^41 + 1480 * q^42 + 260 * q^43 + 1078 * q^44 - 850 * q^45 - 919 * q^46 - 1468 * q^47 + 837 * q^48 + 1200 * q^49 - 50 * q^50 - 1147 * q^51 - 1222 * q^52 + 185 * q^53 - 1406 * q^54 - 1265 * q^55 - 2299 * q^56 + 171 * q^57 - 958 * q^58 - 3665 * q^59 + 380 * q^60 - 2528 * q^61 - 1722 * q^62 + 172 * q^63 - 120 * q^64 + 185 * q^65 - 671 * q^66 + 329 * q^67 - 2240 * q^68 - 1337 * q^69 + 955 * q^70 - 3190 * q^71 - 2488 * q^72 - 2183 * q^73 - 1613 * q^74 - 225 * q^75 - 1862 * q^76 + 143 * q^77 - 2748 * q^78 - 3546 * q^79 - 1070 * q^80 - 2077 * q^81 + 2202 * q^82 - 4324 * q^83 - 8608 * q^84 + 255 * q^85 - 3626 * q^86 + 2921 * q^87 - 594 * q^88 - 4630 * q^89 + 315 * q^90 - 5043 * q^91 + 108 * q^92 - 5644 * q^93 - 8328 * q^94 + 2185 * q^95 - 2016 * q^96 - 774 * q^97 - 6388 * q^98 + 1870 * 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 $

$2$	2.68859	0.950559	0.475280	−	0.879835i	$-0.342347\pi$
$2$	2.68859	0.950559	0.475280	+	0.879835i	$0.342347\pi$
$3$	−3.54772	−0.682759	−0.341380	−	0.939925i	$-0.610894\pi$
$3$	−3.54772	−0.682759	−0.341380	+	0.939925i	$0.610894\pi$
$4$	−0.771496	−0.0964370
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−9.53836	−0.649003
$7$	27.8868	1.50575	0.752874	−	0.658165i	$-0.228667\pi$
$7$	27.8868	1.50575	0.752874	+	0.658165i	$0.228667\pi$
$8$	−23.5829	−1.04223
$9$	−14.4137	−0.533840
$10$	−13.4429	−0.425103
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	2.73705	0.0658433
$13$	−11.6213	−0.247937	−0.123968	−	0.992286i	$-0.539562\pi$
$13$	−11.6213	−0.247937	−0.123968	+	0.992286i	$0.539562\pi$
$14$	74.9762	1.43130
$15$	17.7386	0.305339
$16$	−57.2328	−0.894263
$17$	123.554	1.76272	0.881360	−	0.472445i	$-0.156628\pi$
$17$	123.554	1.76272	0.881360	+	0.472445i	$0.156628\pi$
$18$	−38.7524	−0.507446
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	3.85748	0.0431280
$21$	−98.9348	−1.02806
$22$	29.5745	0.286604
$23$	3.23375	0.0293167	0.0146584	−	0.999893i	$-0.495334\pi$
$23$	3.23375	0.0293167	0.0146584	+	0.999893i	$0.495334\pi$
$24$	83.6657	0.711591
$25$	25.0000	0.200000
$26$	−31.2450	−0.235678
$27$	146.924	1.04724
$28$	−21.5146	−0.145210
$29$	−267.510	−1.71294	−0.856472	−	0.516193i	$-0.827349\pi$
$29$	−267.510	−1.71294	−0.856472	+	0.516193i	$0.827349\pi$
$30$	47.6918	0.290243
$31$	106.646	0.617875	0.308937	−	0.951082i	$-0.400027\pi$
$31$	106.646	0.617875	0.308937	+	0.951082i	$0.400027\pi$
$32$	34.7880	0.192179
$33$	−39.0249	−0.205860
$34$	332.186	1.67557
$35$	−139.434	−0.673391
$36$	11.1201	0.0514819
$37$	−192.637	−0.855930	−0.427965	−	0.903795i	$-0.640769\pi$
$37$	−192.637	−0.855930	−0.427965	+	0.903795i	$0.640769\pi$
$38$	−51.0832	−0.218073
$39$	41.2292	0.169281
$40$	117.915	0.466099
$41$	354.453	1.35015	0.675076	−	0.737749i	$-0.264111\pi$
$41$	354.453	1.35015	0.675076	+	0.737749i	$0.264111\pi$
$42$	−265.995	−0.977236
$43$	−232.956	−0.826174	−0.413087	−	0.910692i	$-0.635549\pi$
$43$	−232.956	−0.826174	−0.413087	+	0.910692i	$0.635549\pi$
$44$	−8.48646	−0.0290769
$45$	72.0683	0.238740
$46$	8.69423	0.0278673
$47$	−234.327	−0.727238	−0.363619	−	0.931548i	$-0.618459\pi$
$47$	−234.327	−0.727238	−0.363619	+	0.931548i	$0.618459\pi$
$48$	203.046	0.610566
$49$	434.676	1.26728
$50$	67.2147	0.190112
$51$	−438.335	−1.20351
$52$	8.96581	0.0239103
$53$	−728.236	−1.88738	−0.943688	−	0.330836i	$-0.892669\pi$
$53$	−728.236	−1.88738	−0.943688	+	0.330836i	$0.892669\pi$
$54$	395.019	0.995467
$55$	−55.0000	−0.134840
$56$	−657.654	−1.56933
$57$	67.4067	0.156636
$58$	−719.225	−1.62826
$59$	638.745	1.40945	0.704725	−	0.709480i	$-0.251070\pi$
$59$	638.745	1.40945	0.704725	+	0.709480i	$0.251070\pi$
$60$	−13.6853	−0.0294460
$61$	−698.800	−1.46676	−0.733378	−	0.679821i	$-0.762057\pi$
$61$	−698.800	−1.46676	−0.733378	+	0.679821i	$0.762057\pi$
$62$	286.726	0.587327
$63$	−401.952	−0.803828
$64$	551.393	1.07694
$65$	58.1066	0.110881
$66$	−104.922	−0.195682
$67$	−340.922	−0.621645	−0.310823	−	0.950468i	$-0.600605\pi$
$67$	−340.922	−0.621645	−0.310823	+	0.950468i	$0.600605\pi$
$68$	−95.3215	−0.169992
$69$	−11.4725	−0.0200163
$70$	−374.881	−0.640098
$71$	317.515	0.530733	0.265367	−	0.964148i	$-0.414507\pi$
$71$	317.515	0.530733	0.265367	+	0.964148i	$0.414507\pi$
$72$	339.917	0.556383
$73$	−549.107	−0.880384	−0.440192	−	0.897904i	$-0.645090\pi$
$73$	−549.107	−0.880384	−0.440192	+	0.897904i	$0.645090\pi$
$74$	−517.923	−0.813612
$75$	−88.6931	−0.136552
$76$	14.6584	0.0221242
$77$	306.755	0.454000
$78$	110.848	0.160912
$79$	−888.087	−1.26478	−0.632390	−	0.774650i	$-0.717926\pi$
$79$	−888.087	−1.26478	−0.632390	+	0.774650i	$0.717926\pi$
$80$	286.164	0.399927
$81$	−132.077	−0.181176
$82$	952.977	1.28340
$83$	−944.143	−1.24859	−0.624296	−	0.781188i	$-0.714614\pi$
$83$	−944.143	−1.24859	−0.624296	+	0.781188i	$0.714614\pi$
$84$	76.3278	0.0991434
$85$	−617.770	−0.788313
$86$	−626.323	−0.785328
$87$	949.052	1.16953
$88$	−259.412	−0.314244
$89$	−758.826	−0.903768	−0.451884	−	0.892077i	$-0.649248\pi$
$89$	−758.826	−0.903768	−0.451884	+	0.892077i	$0.649248\pi$
$90$	193.762	0.226937
$91$	−324.082	−0.373330
$92$	−2.49483	−0.00282722
$93$	−378.349	−0.421860
$94$	−630.010	−0.691282
$95$	95.0000	0.102598
$96$	−123.418	−0.131212
$97$	382.749	0.400642	0.200321	−	0.979730i	$-0.435801\pi$
$97$	382.749	0.400642	0.200321	+	0.979730i	$0.435801\pi$
$98$	1168.67	1.20462
$99$	−158.550	−0.160959
$100$	−19.2874	−0.0192874
$101$	201.601	0.198614	0.0993072	−	0.995057i	$-0.468337\pi$
$101$	201.601	0.198614	0.0993072	+	0.995057i	$0.468337\pi$
$102$	−1178.50	−1.14401
$103$	1201.93	1.14980	0.574902	−	0.818222i	$-0.305040\pi$
$103$	1201.93	1.14980	0.574902	+	0.818222i	$0.305040\pi$
$104$	274.065	0.258407
$105$	494.674	0.459764
$106$	−1957.93	−1.79406
$107$	618.786	0.559068	0.279534	−	0.960136i	$-0.409820\pi$
$107$	618.786	0.559068	0.279534	+	0.960136i	$0.409820\pi$
$108$	−113.351	−0.100993
$109$	−1498.21	−1.31654	−0.658269	−	0.752783i	$-0.728711\pi$
$109$	−1498.21	−1.31654	−0.658269	+	0.752783i	$0.728711\pi$
$110$	−147.872	−0.128173
$111$	683.424	0.584394
$112$	−1596.04	−1.34653
$113$	−747.633	−0.622401	−0.311201	−	0.950344i	$-0.600731\pi$
$113$	−747.633	−0.622401	−0.311201	+	0.950344i	$0.600731\pi$
$114$	181.229	0.148892
$115$	−16.1688	−0.0131108
$116$	206.383	0.165191
$117$	167.506	0.132358
$118$	1717.32	1.33977
$119$	3445.53	2.65421
$120$	−418.329	−0.318233
$121$	121.000	0.0909091
$122$	−1878.78	−1.39424
$123$	−1257.50	−0.921828
$124$	−82.2767	−0.0595860
$125$	−125.000	−0.0894427
$126$	−1080.68	−0.764086
$127$	−2644.99	−1.84807	−0.924033	−	0.382312i	$-0.875128\pi$
$127$	−2644.99	−1.84807	−0.924033	+	0.382312i	$0.875128\pi$
$128$	1204.16	0.831517
$129$	826.464	0.564078
$130$	156.225	0.105399
$131$	−1636.95	−1.09176	−0.545881	−	0.837862i	$-0.683805\pi$
$131$	−1636.95	−1.09176	−0.545881	+	0.837862i	$0.683805\pi$
$132$	30.1076	0.0198525
$133$	−529.850	−0.345442
$134$	−916.598	−0.590911
$135$	−734.621	−0.468342
$136$	−2913.77	−1.83716
$137$	−1843.69	−1.14976	−0.574881	−	0.818237i	$-0.694952\pi$
$137$	−1843.69	−1.14976	−0.574881	+	0.818237i	$0.694952\pi$
$138$	−30.8447	−0.0190266
$139$	640.534	0.390859	0.195430	−	0.980718i	$-0.437390\pi$
$139$	640.534	0.390859	0.195430	+	0.980718i	$0.437390\pi$
$140$	107.573	0.0649398
$141$	831.328	0.496528
$142$	853.666	0.504494
$143$	−127.835	−0.0747557
$144$	824.935	0.477393
$145$	1337.55	0.766052
$146$	−1476.32	−0.836858
$147$	−1542.11	−0.865246
$148$	148.619	0.0825433
$149$	−2215.27	−1.21800	−0.609000	−	0.793170i	$-0.708429\pi$
$149$	−2215.27	−1.21800	−0.609000	+	0.793170i	$0.708429\pi$
$150$	−238.459	−0.129801
$151$	−329.590	−0.177627	−0.0888135	−	0.996048i	$-0.528308\pi$
$151$	−329.590	−0.177627	−0.0888135	+	0.996048i	$0.528308\pi$
$152$	448.076	0.239104
$153$	−1780.87	−0.941010
$154$	824.739	0.431554
$155$	−533.228	−0.276322
$156$	−31.8082	−0.0163250
$157$	−1132.64	−0.575760	−0.287880	−	0.957666i	$-0.592950\pi$
$157$	−1132.64	−0.575760	−0.287880	+	0.957666i	$0.592950\pi$
$158$	−2387.70	−1.20225
$159$	2583.58	1.28862
$160$	−173.940	−0.0859449
$161$	90.1792	0.0441436
$162$	−355.101	−0.172218
$163$	54.0338	0.0259647	0.0129824	−	0.999916i	$-0.495867\pi$
$163$	54.0338	0.0259647	0.0129824	+	0.999916i	$0.495867\pi$
$164$	−273.459	−0.130205
$165$	195.125	0.0920633
$166$	−2538.41	−1.18686
$167$	3365.02	1.55924	0.779619	−	0.626254i	$-0.215413\pi$
$167$	3365.02	1.55924	0.779619	+	0.626254i	$0.215413\pi$
$168$	2333.17	1.07148
$169$	−2061.94	−0.938527
$170$	−1660.93	−0.749338
$171$	273.860	0.122471
$172$	179.725	0.0796738
$173$	−1392.99	−0.612180	−0.306090	−	0.952003i	$-0.599021\pi$
$173$	−1392.99	−0.612180	−0.306090	+	0.952003i	$0.599021\pi$
$174$	2551.61	1.11171
$175$	697.171	0.301150
$176$	−629.561	−0.269630
$177$	−2266.09	−0.962316
$178$	−2040.17	−0.859085
$179$	−4312.60	−1.80078	−0.900388	−	0.435088i	$-0.856717\pi$
$179$	−4312.60	−1.80078	−0.900388	+	0.435088i	$0.856717\pi$
$180$	−55.6005	−0.0230234
$181$	687.246	0.282224	0.141112	−	0.989994i	$-0.454932\pi$
$181$	687.246	0.282224	0.141112	+	0.989994i	$0.454932\pi$
$182$	−871.323	−0.354872
$183$	2479.15	1.00144
$184$	−76.2614	−0.0305547
$185$	963.187	0.382783
$186$	−1017.22	−0.401003
$187$	1359.09	0.531480
$188$	180.783	0.0701326
$189$	4097.25	1.57688
$190$	255.416	0.0975253
$191$	2651.41	1.00445	0.502224	−	0.864738i	$-0.332515\pi$
$191$	2651.41	1.00445	0.502224	+	0.864738i	$0.332515\pi$
$192$	−1956.19	−0.735291
$193$	−4476.50	−1.66956	−0.834782	−	0.550581i	$-0.814406\pi$
$193$	−4476.50	−1.66956	−0.834782	+	0.550581i	$0.814406\pi$
$194$	1029.05	0.380834
$195$	−206.146	−0.0757048
$196$	−335.351	−0.122213
$197$	4094.66	1.48087	0.740437	−	0.672126i	$-0.234619\pi$
$197$	4094.66	1.48087	0.740437	+	0.672126i	$0.234619\pi$
$198$	−426.276	−0.153001
$199$	3905.74	1.39131	0.695656	−	0.718376i	$-0.255114\pi$
$199$	3905.74	1.39131	0.695656	+	0.718376i	$0.255114\pi$
$200$	−589.573	−0.208446
$201$	1209.50	0.424434
$202$	542.022	0.188795
$203$	−7460.02	−2.57926
$204$	338.174	0.116063
$205$	−1772.26	−0.603806
$206$	3231.50	1.09296
$207$	−46.6102	−0.0156504
$208$	665.121	0.221721
$209$	−209.000	−0.0691714
$210$	1329.97	0.437033
$211$	5001.39	1.63180	0.815901	−	0.578192i	$-0.196241\pi$
$211$	5001.39	1.63180	0.815901	+	0.578192i	$0.196241\pi$
$212$	561.832	0.182013
$213$	−1126.45	−0.362363
$214$	1663.66	0.531427
$215$	1164.78	0.369476
$216$	−3464.90	−1.09147
$217$	2974.01	0.930364
$218$	−4028.08	−1.25145
$219$	1948.08	0.601091
$220$	42.4323	0.0130036
$221$	−1435.86	−0.437043
$222$	1837.45	0.555501
$223$	5802.61	1.74247	0.871236	−	0.490864i	$-0.163319\pi$
$223$	5802.61	1.74247	0.871236	+	0.490864i	$0.163319\pi$
$224$	970.129	0.289373
$225$	−360.342	−0.106768
$226$	−2010.08	−0.591629
$227$	−6640.48	−1.94160	−0.970802	−	0.239882i	$-0.922891\pi$
$227$	−6640.48	−1.94160	−0.970802	+	0.239882i	$0.922891\pi$
$228$	−52.0040	−0.0151055
$229$	2096.73	0.605048	0.302524	−	0.953142i	$-0.402171\pi$
$229$	2096.73	0.605048	0.302524	+	0.953142i	$0.402171\pi$
$230$	−43.4711	−0.0124626
$231$	−1088.28	−0.309973
$232$	6308.68	1.78528
$233$	2177.92	0.612361	0.306181	−	0.951973i	$-0.400949\pi$
$233$	2177.92	0.612361	0.306181	+	0.951973i	$0.400949\pi$
$234$	450.354	0.125814
$235$	1171.64	0.325231
$236$	−492.790	−0.135923
$237$	3150.69	0.863540
$238$	9263.62	2.52299
$239$	1578.83	0.427306	0.213653	−	0.976910i	$-0.431464\pi$
$239$	1578.83	0.427306	0.213653	+	0.976910i	$0.431464\pi$
$240$	−1015.23	−0.273054
$241$	979.887	0.261909	0.130954	−	0.991388i	$-0.458196\pi$
$241$	979.887	0.261909	0.130954	+	0.991388i	$0.458196\pi$
$242$	325.319	0.0864145
$243$	−3498.38	−0.923544
$244$	539.121	0.141450
$245$	−2173.38	−0.566744
$246$	−3380.90	−0.876253
$247$	220.805	0.0568806
$248$	−2515.02	−0.643967
$249$	3349.56	0.852488
$250$	−336.073	−0.0850206
$251$	2215.43	0.557118	0.278559	−	0.960419i	$-0.410143\pi$
$251$	2215.43	0.557118	0.278559	+	0.960419i	$0.410143\pi$
$252$	310.104	0.0775188
$253$	35.5713	0.00883932
$254$	−7111.28	−1.75670
$255$	2191.68	0.538228
$256$	−1173.64	−0.286534
$257$	−6319.57	−1.53387	−0.766933	−	0.641727i	$-0.778218\pi$
$257$	−6319.57	−1.53387	−0.766933	+	0.641727i	$0.778218\pi$
$258$	2222.02	0.536190
$259$	−5372.05	−1.28881
$260$	−44.8291	−0.0106930
$261$	3855.80	0.914438
$262$	−4401.08	−1.03779
$263$	−5604.33	−1.31398	−0.656992	−	0.753897i	$-0.728172\pi$
$263$	−5604.33	−1.31398	−0.656992	+	0.753897i	$0.728172\pi$
$264$	920.323	0.214553
$265$	3641.18	0.844061
$266$	−1424.55	−0.328363
$267$	2692.10	0.617056
$268$	263.020	0.0599496
$269$	317.721	0.0720142	0.0360071	−	0.999352i	$-0.488536\pi$
$269$	317.721	0.0720142	0.0360071	+	0.999352i	$0.488536\pi$
$270$	−1975.09	−0.445186
$271$	2657.50	0.595689	0.297844	−	0.954614i	$-0.403732\pi$
$271$	2657.50	0.595689	0.297844	+	0.954614i	$0.403732\pi$
$272$	−7071.35	−1.57634
$273$	1149.75	0.254895
$274$	−4956.93	−1.09292
$275$	275.000	0.0603023
$276$	8.85096	0.00193031
$277$	−16.3262	−0.00354131	−0.00177066	−	0.999998i	$-0.500564\pi$
$277$	−16.3262	−0.00354131	−0.00177066	+	0.999998i	$0.500564\pi$
$278$	1722.13	0.371535
$279$	−1537.15	−0.329846
$280$	3288.27	0.701827
$281$	−6494.10	−1.37867	−0.689333	−	0.724444i	$-0.742096\pi$
$281$	−6494.10	−1.37867	−0.689333	+	0.724444i	$0.742096\pi$
$282$	2235.10	0.471980
$283$	7706.97	1.61884	0.809421	−	0.587229i	$-0.199781\pi$
$283$	7706.97	1.61884	0.809421	+	0.587229i	$0.199781\pi$
$284$	−244.961	−0.0511824
$285$	−337.034	−0.0700496
$286$	−343.695	−0.0710597
$287$	9884.57	2.03299
$288$	−501.423	−0.102593
$289$	10352.6	2.10718
$290$	3596.12	0.728178
$291$	−1357.89	−0.273542
$292$	423.634	0.0849017
$293$	7398.79	1.47523	0.737614	−	0.675223i	$-0.235953\pi$
$293$	7398.79	1.47523	0.737614	+	0.675223i	$0.235953\pi$
$294$	−4146.10	−0.822468
$295$	−3193.73	−0.630325
$296$	4542.96	0.892074
$297$	1616.17	0.315756
$298$	−5955.95	−1.15778
$299$	−37.5805	−0.00726868
$300$	68.4264	0.0131687
$301$	−6496.41	−1.24401
$302$	−886.132	−0.168845
$303$	−715.225	−0.135606
$304$	1087.42	0.205158
$305$	3494.00	0.655953
$306$	−4788.02	−0.894486
$307$	−1466.94	−0.272712	−0.136356	−	0.990660i	$-0.543539\pi$
$307$	−1466.94	−0.272712	−0.136356	+	0.990660i	$0.543539\pi$
$308$	−236.661	−0.0437824
$309$	−4264.12	−0.785040
$310$	−1433.63	−0.262660
$311$	−2103.23	−0.383483	−0.191741	−	0.981445i	$-0.561413\pi$
$311$	−2103.23	−0.383483	−0.191741	+	0.981445i	$0.561413\pi$
$312$	−972.307	−0.176430
$313$	8484.05	1.53210	0.766049	−	0.642782i	$-0.222220\pi$
$313$	8484.05	1.53210	0.766049	+	0.642782i	$0.222220\pi$
$314$	−3045.20	−0.547294
$315$	2009.76	0.359483
$316$	685.156	0.121972
$317$	705.493	0.124998	0.0624991	−	0.998045i	$-0.480093\pi$
$317$	705.493	0.124998	0.0624991	+	0.998045i	$0.480093\pi$
$318$	6946.18	1.22491
$319$	−2942.61	−0.516472
$320$	−2756.97	−0.481622
$321$	−2195.28	−0.381709
$322$	242.455	0.0419611
$323$	−2347.53	−0.404396
$324$	101.897	0.0174721
$325$	−290.533	−0.0495873
$326$	145.275	0.0246810
$327$	5315.24	0.898879
$328$	−8359.03	−1.40717
$329$	−6534.65	−1.09504
$330$	524.610	0.0875116
$331$	2005.58	0.333042	0.166521	−	0.986038i	$-0.446747\pi$
$331$	2005.58	0.333042	0.166521	+	0.986038i	$0.446747\pi$
$332$	728.403	0.120411
$333$	2776.61	0.456929
$334$	9047.14	1.48215
$335$	1704.61	0.278008
$336$	5662.32	0.919359
$337$	6222.33	1.00579	0.502896	−	0.864347i	$-0.332268\pi$
$337$	6222.33	1.00579	0.502896	+	0.864347i	$0.332268\pi$
$338$	−5543.72	−0.892126
$339$	2652.39	0.424950
$340$	476.607	0.0760225
$341$	1173.10	0.186296
$342$	736.296	0.116416
$343$	2556.56	0.402453
$344$	5493.79	0.861062
$345$	57.3623	0.00895154
$346$	−3745.18	−0.581913
$347$	−3849.83	−0.595589	−0.297795	−	0.954630i	$-0.596251\pi$
$347$	−3849.83	−0.595589	−0.297795	+	0.954630i	$0.596251\pi$
$348$	−732.190	−0.112786
$349$	−3634.74	−0.557488	−0.278744	−	0.960365i	$-0.589918\pi$
$349$	−3634.74	−0.557488	−0.278744	+	0.960365i	$0.589918\pi$
$350$	1874.41	0.286261
$351$	−1707.45	−0.259650
$352$	382.668	0.0579440
$353$	1584.07	0.238842	0.119421	−	0.992844i	$-0.461896\pi$
$353$	1584.07	0.238842	0.119421	+	0.992844i	$0.461896\pi$
$354$	−6092.59	−0.914738
$355$	−1587.57	−0.237351
$356$	585.431	0.0871567
$357$	−12223.8	−1.81219
$358$	−11594.8	−1.71174
$359$	5832.50	0.857458	0.428729	−	0.903433i	$-0.358962\pi$
$359$	5832.50	0.857458	0.428729	+	0.903433i	$0.358962\pi$
$360$	−1699.58	−0.248822
$361$	361.000	0.0526316
$362$	1847.72	0.268271
$363$	−429.274	−0.0620690
$364$	250.028	0.0360029
$365$	2745.53	0.393720
$366$	6665.40	0.951930
$367$	11128.5	1.58285	0.791423	−	0.611269i	$-0.209341\pi$
$367$	11128.5	1.58285	0.791423	+	0.611269i	$0.209341\pi$
$368$	−185.077	−0.0262168
$369$	−5108.96	−0.720764
$370$	2589.61	0.363858
$371$	−20308.2	−2.84191
$372$	291.895	0.0406829
$373$	−11863.3	−1.64680	−0.823401	−	0.567460i	$-0.807926\pi$
$373$	−11863.3	−1.64680	−0.823401	+	0.567460i	$0.807926\pi$
$374$	3654.04	0.505204
$375$	443.465	0.0610679
$376$	5526.13	0.757948
$377$	3108.82	0.424702
$378$	11015.8	1.49892
$379$	5624.24	0.762263	0.381131	−	0.924521i	$-0.375535\pi$
$379$	5624.24	0.762263	0.381131	+	0.924521i	$0.375535\pi$
$380$	−73.2921	−0.00989423
$381$	9383.67	1.26179
$382$	7128.55	0.954787
$383$	3508.63	0.468101	0.234050	−	0.972224i	$-0.424802\pi$
$383$	3508.63	0.468101	0.234050	+	0.972224i	$0.424802\pi$
$384$	−4272.04	−0.567726
$385$	−1533.78	−0.203035
$386$	−12035.5	−1.58702
$387$	3357.75	0.441044
$388$	−295.289	−0.0386367
$389$	−11548.1	−1.50517	−0.752585	−	0.658495i	$-0.771193\pi$
$389$	−11548.1	−1.50517	−0.752585	+	0.658495i	$0.771193\pi$
$390$	−554.242	−0.0719619
$391$	399.543	0.0516772
$392$	−10250.9	−1.32079
$393$	5807.44	0.745411
$394$	11008.8	1.40766
$395$	4440.43	0.565627
$396$	122.321	0.0155224
$397$	−12065.8	−1.52535	−0.762677	−	0.646780i	$-0.776115\pi$
$397$	−12065.8	−1.52535	−0.762677	+	0.646780i	$0.776115\pi$
$398$	10500.9	1.32252
$399$	1879.76	0.235854
$400$	−1430.82	−0.178853
$401$	−11433.9	−1.42389	−0.711946	−	0.702234i	$-0.752186\pi$
$401$	−11433.9	−1.42389	−0.711946	+	0.702234i	$0.752186\pi$
$402$	3251.84	0.403450
$403$	−1239.36	−0.153194
$404$	−155.534	−0.0191538
$405$	660.386	0.0810243
$406$	−20056.9	−2.45174
$407$	−2119.01	−0.258073
$408$	10337.2	1.25434
$409$	10919.5	1.32013	0.660066	−	0.751208i	$-0.270528\pi$
$409$	10919.5	1.32013	0.660066	+	0.751208i	$0.270528\pi$
$410$	−4764.88	−0.573953
$411$	6540.92	0.785011
$412$	−927.286	−0.110884
$413$	17812.6	2.12228
$414$	−125.316	−0.0148766
$415$	4720.71	0.558387
$416$	−404.283	−0.0476481
$417$	−2272.44	−0.266863
$418$	−561.915	−0.0657516
$419$	−4674.10	−0.544975	−0.272488	−	0.962159i	$-0.587846\pi$
$419$	−4674.10	−0.544975	−0.272488	+	0.962159i	$0.587846\pi$
$420$	−381.639	−0.0443383
$421$	5816.73	0.673374	0.336687	−	0.941617i	$-0.390694\pi$
$421$	5816.73	0.673374	0.336687	+	0.941617i	$0.390694\pi$
$422$	13446.7	1.55112
$423$	3377.52	0.388228
$424$	17174.0	1.96708
$425$	3088.85	0.352544
$426$	−3028.57	−0.344448
$427$	−19487.3	−2.20857
$428$	−477.391	−0.0539149
$429$	453.522	0.0510402
$430$	3131.62	0.351209
$431$	5083.37	0.568115	0.284057	−	0.958807i	$-0.408319\pi$
$431$	5083.37	0.568115	0.284057	+	0.958807i	$0.408319\pi$
$432$	−8408.89	−0.936511
$433$	−13010.9	−1.44402	−0.722012	−	0.691880i	$-0.756783\pi$
$433$	−13010.9	−1.44402	−0.722012	+	0.691880i	$0.756783\pi$
$434$	7995.89	0.884366
$435$	−4745.26	−0.523029
$436$	1155.87	0.126963
$437$	−61.4413	−0.00672571
$438$	5237.58	0.571372
$439$	−13556.3	−1.47382	−0.736911	−	0.675990i	$-0.763716\pi$
$439$	−13556.3	−1.47382	−0.736911	+	0.675990i	$0.763716\pi$
$440$	1297.06	0.140534
$441$	−6265.28	−0.676523
$442$	−3860.44	−0.415435
$443$	7029.91	0.753953	0.376977	−	0.926223i	$-0.376964\pi$
$443$	7029.91	0.753953	0.376977	+	0.926223i	$0.376964\pi$
$444$	−527.259	−0.0563572
$445$	3794.13	0.404177
$446$	15600.8	1.65632
$447$	7859.17	0.831601
$448$	15376.6	1.62160
$449$	−8368.48	−0.879583	−0.439792	−	0.898100i	$-0.644948\pi$
$449$	−8368.48	−0.879583	−0.439792	+	0.898100i	$0.644948\pi$
$450$	−968.810	−0.101489
$451$	3898.98	0.407086
$452$	576.796	0.0600226
$453$	1169.29	0.121277
$454$	−17853.5	−1.84561
$455$	1620.41	0.166958
$456$	−1589.65	−0.163250
$457$	3144.10	0.321827	0.160913	−	0.986969i	$-0.448556\pi$
$457$	3144.10	0.321827	0.160913	+	0.986969i	$0.448556\pi$
$458$	5637.25	0.575134
$459$	18153.1	1.84600
$460$	12.4741	0.00126437
$461$	9239.14	0.933426	0.466713	−	0.884409i	$-0.345438\pi$
$461$	9239.14	0.933426	0.466713	+	0.884409i	$0.345438\pi$
$462$	−2925.94	−0.294648
$463$	14913.2	1.49692	0.748460	−	0.663180i	$-0.230794\pi$
$463$	14913.2	1.49692	0.748460	+	0.663180i	$0.230794\pi$
$464$	15310.4	1.53182
$465$	1891.75	0.188661
$466$	5855.53	0.582086
$467$	−18622.7	−1.84530	−0.922650	−	0.385639i	$-0.873981\pi$
$467$	−18622.7	−1.84530	−0.922650	+	0.385639i	$0.873981\pi$
$468$	−129.230	−0.0127643
$469$	−9507.24	−0.936041
$470$	3150.05	0.309151
$471$	4018.29	0.393106
$472$	−15063.5	−1.46897
$473$	−2562.52	−0.249101
$474$	8470.89	0.820846
$475$	−475.000	−0.0458831
$476$	−2658.22	−0.255965
$477$	10496.6	1.00756
$478$	4244.83	0.406180
$479$	−5027.76	−0.479591	−0.239796	−	0.970823i	$-0.577080\pi$
$479$	−5027.76	−0.479591	−0.239796	+	0.970823i	$0.577080\pi$
$480$	617.091	0.0586797
$481$	2238.70	0.212216
$482$	2634.51	0.248960
$483$	−319.931	−0.0301394
$484$	−93.3511	−0.00876700
$485$	−1913.74	−0.179173
$486$	−9405.70	−0.877883
$487$	−15476.6	−1.44006	−0.720032	−	0.693941i	$-0.755873\pi$
$487$	−15476.6	−1.44006	−0.720032	+	0.693941i	$0.755873\pi$
$488$	16479.7	1.52869
$489$	−191.697	−0.0177277
$490$	−5843.33	−0.538724
$491$	−4479.69	−0.411743	−0.205871	−	0.978579i	$-0.566003\pi$
$491$	−4479.69	−0.411743	−0.205871	+	0.978579i	$0.566003\pi$
$492$	970.156	0.0888984
$493$	−33052.0	−3.01944
$494$	593.654	0.0540684
$495$	792.752	0.0719829
$496$	−6103.63	−0.552542
$497$	8854.49	0.799151
$498$	9005.58	0.810340
$499$	−15161.6	−1.36017	−0.680085	−	0.733133i	$-0.738057\pi$
$499$	−15161.6	−1.36017	−0.680085	+	0.733133i	$0.738057\pi$
$500$	96.4370	0.00862559
$501$	−11938.1	−1.06458
$502$	5956.38	0.529574
$503$	15301.7	1.35640	0.678201	−	0.734876i	$-0.262760\pi$
$503$	15301.7	1.35640	0.678201	+	0.734876i	$0.262760\pi$
$504$	9479.20	0.837772
$505$	−1008.01	−0.0888231
$506$	95.6365	0.00840230
$507$	7315.21	0.640788
$508$	2040.60	0.178222
$509$	6250.68	0.544315	0.272158	−	0.962253i	$-0.412263\pi$
$509$	6250.68	0.544315	0.272158	+	0.962253i	$0.412263\pi$
$510$	5892.52	0.511618
$511$	−15312.9	−1.32564
$512$	−12788.8	−1.10388
$513$	−2791.56	−0.240254
$514$	−16990.7	−1.45803
$515$	−6009.66	−0.514208
$516$	−637.614	−0.0543980
$517$	−2577.60	−0.219270
$518$	−14443.2	−1.22509
$519$	4941.94	0.417972
$520$	−1370.33	−0.115563
$521$	−21162.6	−1.77956	−0.889778	−	0.456393i	$-0.849141\pi$
$521$	−21162.6	−1.77956	−0.889778	+	0.456393i	$0.849141\pi$
$522$	10366.7	0.869227
$523$	−4430.72	−0.370443	−0.185222	−	0.982697i	$-0.559300\pi$
$523$	−4430.72	−0.370443	−0.185222	+	0.982697i	$0.559300\pi$
$524$	1262.90	0.105286
$525$	−2473.37	−0.205613
$526$	−15067.7	−1.24902
$527$	13176.5	1.08914
$528$	2233.51	0.184093
$529$	−12156.5	−0.999141
$530$	9789.64	0.802330
$531$	−9206.66	−0.752420
$532$	408.777	0.0333134
$533$	−4119.21	−0.334752
$534$	7237.95	0.586549
$535$	−3093.93	−0.250023
$536$	8039.94	0.647896
$537$	15299.9	1.22950
$538$	854.222	0.0684538
$539$	4781.44	0.382099
$540$	566.757	0.0451655
$541$	−15229.3	−1.21027	−0.605137	−	0.796121i	$-0.706882\pi$
$541$	−15229.3	−1.21027	−0.605137	+	0.796121i	$0.706882\pi$
$542$	7144.92	0.566237
$543$	−2438.16	−0.192691
$544$	4298.20	0.338757
$545$	7491.06	0.588774
$546$	3091.21	0.242293
$547$	1096.83	0.0857347	0.0428674	−	0.999081i	$-0.486351\pi$
$547$	1096.83	0.0857347	0.0428674	+	0.999081i	$0.486351\pi$
$548$	1422.40	0.110880
$549$	10072.3	0.783012
$550$	739.362	0.0573209
$551$	5082.69	0.392976
$552$	270.554	0.0208615
$553$	−24765.9	−1.90444
$554$	−43.8943	−0.00336623
$555$	−3417.12	−0.261349
$556$	−494.170	−0.0376933
$557$	−7420.37	−0.564473	−0.282236	−	0.959345i	$-0.591076\pi$
$557$	−7420.37	−0.564473	−0.282236	+	0.959345i	$0.591076\pi$
$558$	−4132.77	−0.313538
$559$	2707.26	0.204839
$560$	7980.22	0.602189
$561$	−4821.69	−0.362873
$562$	−17460.0	−1.31050
$563$	−3548.33	−0.265620	−0.132810	−	0.991141i	$-0.542400\pi$
$563$	−3548.33	−0.265620	−0.132810	+	0.991141i	$0.542400\pi$
$564$	−641.367	−0.0478837
$565$	3738.16	0.278346
$566$	20720.9	1.53880
$567$	−3683.22	−0.272805
$568$	−7487.93	−0.553145
$569$	−15029.3	−1.10731	−0.553657	−	0.832745i	$-0.686768\pi$
$569$	−15029.3	−1.10731	−0.553657	+	0.832745i	$0.686768\pi$
$570$	−906.144	−0.0665863
$571$	16444.5	1.20522	0.602610	−	0.798036i	$-0.294127\pi$
$571$	16444.5	1.20522	0.602610	+	0.798036i	$0.294127\pi$
$572$	98.6239	0.00720922
$573$	−9406.47	−0.685796
$574$	26575.5	1.93248
$575$	80.8438	0.00586334
$576$	−7947.60	−0.574913
$577$	−6349.84	−0.458141	−0.229070	−	0.973410i	$-0.573569\pi$
$577$	−6349.84	−0.458141	−0.229070	+	0.973410i	$0.573569\pi$
$578$	27833.9	2.00300
$579$	15881.4	1.13991
$580$	−1031.92	−0.0738758
$581$	−26329.2	−1.88007
$582$	−3650.80	−0.260018
$583$	−8010.60	−0.569065
$584$	12949.5	0.917562
$585$	−837.530	−0.0591925
$586$	19892.3	1.40229
$587$	20744.2	1.45861	0.729306	−	0.684188i	$-0.239843\pi$
$587$	20744.2	1.45861	0.729306	+	0.684188i	$0.239843\pi$
$588$	1189.73	0.0834418
$589$	−2026.27	−0.141750
$590$	−8586.62	−0.599162
$591$	−14526.7	−1.01108
$592$	11025.2	0.765426
$593$	2354.80	0.163069	0.0815345	−	0.996671i	$-0.474018\pi$
$593$	2354.80	0.163069	0.0815345	+	0.996671i	$0.474018\pi$
$594$	4345.20	0.300145
$595$	−17227.7	−1.18700
$596$	1709.07	0.117460
$597$	−13856.5	−0.949931
$598$	−101.038	−0.00690932
$599$	18212.7	1.24232	0.621160	−	0.783684i	$-0.286662\pi$
$599$	18212.7	1.24232	0.621160	+	0.783684i	$0.286662\pi$
$600$	2091.64	0.142318
$601$	−9302.54	−0.631379	−0.315689	−	0.948863i	$-0.602236\pi$
$601$	−9302.54	−0.631379	−0.315689	+	0.948863i	$0.602236\pi$
$602$	−17466.2	−1.18251
$603$	4913.94	0.331859
$604$	254.278	0.0171298
$605$	−605.000	−0.0406558
$606$	−1922.94	−0.128901
$607$	−13609.5	−0.910034	−0.455017	−	0.890483i	$-0.650367\pi$
$607$	−13609.5	−0.910034	−0.455017	+	0.890483i	$0.650367\pi$
$608$	−660.973	−0.0440888
$609$	26466.1	1.76102
$610$	9393.92	0.623522
$611$	2723.20	0.180309
$612$	1373.93	0.0907482
$613$	26938.3	1.77493	0.887463	−	0.460880i	$-0.152466\pi$
$613$	26938.3	1.77493	0.887463	+	0.460880i	$0.152466\pi$
$614$	−3943.99	−0.259229
$615$	6287.50	0.412254
$616$	−7234.19	−0.473172
$617$	−4506.61	−0.294050	−0.147025	−	0.989133i	$-0.546970\pi$
$617$	−4506.61	−0.294050	−0.147025	+	0.989133i	$0.546970\pi$
$618$	−11464.5	−0.746227
$619$	−9189.53	−0.596702	−0.298351	−	0.954456i	$-0.596437\pi$
$619$	−9189.53	−0.596702	−0.298351	+	0.954456i	$0.596437\pi$
$620$	411.383	0.0266477
$621$	475.117	0.0307017
$622$	−5654.71	−0.364523
$623$	−21161.3	−1.36085
$624$	−2359.67	−0.151382
$625$	625.000	0.0400000
$626$	22810.1	1.45635
$627$	741.474	0.0472275
$628$	873.826	0.0555246
$629$	−23801.1	−1.50877
$630$	5403.41	0.341710
$631$	10720.8	0.676367	0.338184	−	0.941080i	$-0.390188\pi$
$631$	10720.8	0.676367	0.338184	+	0.941080i	$0.390188\pi$
$632$	20943.7	1.31819
$633$	−17743.6	−1.11413
$634$	1896.78	0.118818
$635$	13224.9	0.826481
$636$	−1993.22	−0.124271
$637$	−5051.52	−0.314205
$638$	−7911.47	−0.490937
$639$	−4576.55	−0.283326
$640$	−6020.82	−0.371866
$641$	−7949.89	−0.489863	−0.244931	−	0.969540i	$-0.578765\pi$
$641$	−7949.89	−0.489863	−0.244931	+	0.969540i	$0.578765\pi$
$642$	−5902.20	−0.362837
$643$	−20959.5	−1.28548	−0.642739	−	0.766085i	$-0.722202\pi$
$643$	−20959.5	−1.28548	−0.642739	+	0.766085i	$0.722202\pi$
$644$	−69.5729	−0.00425708
$645$	−4132.32	−0.252263
$646$	−6311.53	−0.384402
$647$	−26638.4	−1.61864	−0.809322	−	0.587365i	$-0.800165\pi$
$647$	−26638.4	−1.61864	−0.809322	+	0.587365i	$0.800165\pi$
$648$	3114.77	0.188827
$649$	7026.20	0.424965
$650$	−781.124	−0.0471357
$651$	−10551.0	−0.635215
$652$	−41.6869	−0.00250396
$653$	20287.8	1.21581	0.607905	−	0.794010i	$-0.292010\pi$
$653$	20287.8	1.21581	0.607905	+	0.794010i	$0.292010\pi$
$654$	14290.5	0.854438
$655$	8184.75	0.488251
$656$	−20286.3	−1.20739
$657$	7914.64	0.469984
$658$	−17569.0	−1.04090
$659$	−140.886	−0.00832799	−0.00416399	−	0.999991i	$-0.501325\pi$
$659$	−140.886	−0.00832799	−0.00416399	+	0.999991i	$0.501325\pi$
$660$	−150.538	−0.00887831
$661$	−13235.9	−0.778844	−0.389422	−	0.921060i	$-0.627325\pi$
$661$	−13235.9	−0.778844	−0.389422	+	0.921060i	$0.627325\pi$
$662$	5392.19	0.316576
$663$	5094.04	0.298395
$664$	22265.7	1.30132
$665$	2649.25	0.154487
$666$	7465.17	0.434338
$667$	−865.062	−0.0502179
$668$	−2596.10	−0.150368
$669$	−20586.0	−1.18969
$670$	4582.99	0.264263
$671$	−7686.80	−0.442244
$672$	−3441.75	−0.197572
$673$	21511.0	1.23207	0.616037	−	0.787717i	$-0.288737\pi$
$673$	21511.0	1.23207	0.616037	+	0.787717i	$0.288737\pi$
$674$	16729.3	0.956065
$675$	3673.10	0.209449
$676$	1590.78	0.0905088
$677$	−20937.7	−1.18863	−0.594313	−	0.804234i	$-0.702576\pi$
$677$	−20937.7	−1.18863	−0.594313	+	0.804234i	$0.702576\pi$
$678$	7131.19	0.403941
$679$	10673.7	0.603266
$680$	14568.8	0.821602
$681$	23558.6	1.32565
$682$	3153.99	0.177086
$683$	26290.2	1.47287	0.736434	−	0.676510i	$-0.236508\pi$
$683$	26290.2	1.47287	0.736434	+	0.676510i	$0.236508\pi$
$684$	−211.282	−0.0118108
$685$	9218.47	0.514189
$686$	6873.54	0.382556
$687$	−7438.62	−0.413102
$688$	13332.7	0.738817
$689$	8463.07	0.467950
$690$	154.224	0.00850897
$691$	4284.83	0.235894	0.117947	−	0.993020i	$-0.462369\pi$
$691$	4284.83	0.235894	0.117947	+	0.993020i	$0.462369\pi$
$692$	1074.69	0.0590368
$693$	−4421.47	−0.242363
$694$	−10350.6	−0.566143
$695$	−3202.67	−0.174797
$696$	−22381.4	−1.21892
$697$	43794.0	2.37994
$698$	−9772.33	−0.529926
$699$	−7726.65	−0.418096
$700$	−537.865	−0.0290420
$701$	19947.2	1.07475	0.537373	−	0.843345i	$-0.319417\pi$
$701$	19947.2	1.07475	0.537373	+	0.843345i	$0.319417\pi$
$702$	−4590.64	−0.246813
$703$	3660.11	0.196364
$704$	6065.33	0.324710
$705$	−4156.64	−0.222054
$706$	4258.90	0.227034
$707$	5622.02	0.299063
$708$	1748.28	0.0928029
$709$	28383.8	1.50349	0.751746	−	0.659452i	$-0.229212\pi$
$709$	28383.8	1.50349	0.751746	+	0.659452i	$0.229212\pi$
$710$	−4268.33	−0.225616
$711$	12800.6	0.675189
$712$	17895.3	0.941933
$713$	344.866	0.0181141
$714$	−32864.7	−1.72259
$715$	639.173	0.0334318
$716$	3327.15	0.173661
$717$	−5601.26	−0.291747
$718$	15681.2	0.815064
$719$	429.779	0.0222921	0.0111461	−	0.999938i	$-0.496452\pi$
$719$	429.779	0.0222921	0.0111461	+	0.999938i	$0.496452\pi$
$720$	−4124.67	−0.213497
$721$	33518.1	1.73132
$722$	970.580	0.0500294
$723$	−3476.37	−0.178821
$724$	−530.208	−0.0272169
$725$	−6687.75	−0.342589
$726$	−1154.14	−0.0590003
$727$	−13393.3	−0.683262	−0.341631	−	0.939834i	$-0.610979\pi$
$727$	−13393.3	−0.683262	−0.341631	+	0.939834i	$0.610979\pi$
$728$	7642.81	0.389095
$729$	15977.4	0.811734
$730$	7381.61	0.374254
$731$	−28782.7	−1.45631
$732$	−1912.65	−0.0965761
$733$	36962.3	1.86253	0.931265	−	0.364343i	$-0.118706\pi$
$733$	36962.3	1.86253	0.931265	+	0.364343i	$0.118706\pi$
$734$	29920.0	1.50459
$735$	7710.55	0.386950
$736$	112.496	0.00563404
$737$	−3750.14	−0.187433
$738$	−13735.9	−0.685129
$739$	11037.2	0.549406	0.274703	−	0.961529i	$-0.411421\pi$
$739$	11037.2	0.549406	0.274703	+	0.961529i	$0.411421\pi$
$740$	−743.095	−0.0369145
$741$	−783.356	−0.0388357
$742$	−54600.4	−2.70141
$743$	2165.09	0.106904	0.0534520	−	0.998570i	$-0.482978\pi$
$743$	2165.09	0.106904	0.0534520	+	0.998570i	$0.482978\pi$
$744$	8922.58	0.439674
$745$	11076.4	0.544706
$746$	−31895.5	−1.56538
$747$	13608.6	0.666548
$748$	−1048.54	−0.0512544
$749$	17256.0	0.841816
$750$	1192.30	0.0580486
$751$	−11407.4	−0.554278	−0.277139	−	0.960830i	$-0.589386\pi$
$751$	−11407.4	−0.554278	−0.277139	+	0.960830i	$0.589386\pi$
$752$	13411.2	0.650341
$753$	−7859.73	−0.380378
$754$	8358.34	0.403704
$755$	1647.95	0.0794372
$756$	−3161.02	−0.152070
$757$	21385.8	1.02679	0.513394	−	0.858153i	$-0.328388\pi$
$757$	21385.8	1.02679	0.513394	+	0.858153i	$0.328388\pi$
$758$	15121.3	0.724576
$759$	−126.197	−0.00603513
$760$	−2240.38	−0.106930
$761$	8604.50	0.409872	0.204936	−	0.978775i	$-0.434301\pi$
$761$	8604.50	0.409872	0.204936	+	0.978775i	$0.434301\pi$
$762$	25228.8	1.19940
$763$	−41780.4	−1.98238
$764$	−2045.55	−0.0968659
$765$	8904.33	0.420832
$766$	9433.26	0.444958
$767$	−7423.07	−0.349454
$768$	4163.76	0.195634
$769$	3811.08	0.178714	0.0893571	−	0.996000i	$-0.471519\pi$
$769$	3811.08	0.178714	0.0893571	+	0.996000i	$0.471519\pi$
$770$	−4123.69	−0.192997
$771$	22420.1	1.04726
$772$	3453.60	0.161008
$773$	35807.6	1.66612	0.833059	−	0.553184i	$-0.186587\pi$
$773$	35807.6	1.66612	0.833059	+	0.553184i	$0.186587\pi$
$774$	9027.61	0.419239
$775$	2666.14	0.123575
$776$	−9026.35	−0.417560
$777$	19058.5	0.879951
$778$	−31048.1	−1.43075
$779$	−6734.60	−0.309746
$780$	159.041	0.00730075
$781$	3492.66	0.160022
$782$	1074.21	0.0491222
$783$	−39303.7	−1.79387
$784$	−24877.8	−1.13328
$785$	5663.19	0.257488
$786$	15613.8	0.708558
$787$	−8161.09	−0.369646	−0.184823	−	0.982772i	$-0.559171\pi$
$787$	−8161.09	−0.369646	−0.184823	+	0.982772i	$0.559171\pi$
$788$	−3159.01	−0.142811
$789$	19882.6	0.897136
$790$	11938.5	0.537662
$791$	−20849.1	−0.937180
$792$	3739.08	0.167756
$793$	8120.98	0.363663
$794$	−32440.0	−1.44994
$795$	−12917.9	−0.576290
$796$	−3013.27	−0.134174
$797$	4062.68	0.180561	0.0902807	−	0.995916i	$-0.471224\pi$
$797$	4062.68	0.180561	0.0902807	+	0.995916i	$0.471224\pi$
$798$	5053.90	0.224193
$799$	−28952.1	−1.28192
$800$	869.701	0.0384357
$801$	10937.5	0.482467
$802$	−30741.0	−1.35349
$803$	−6040.17	−0.265446
$804$	−933.122	−0.0409312
$805$	−450.896	−0.0197416
$806$	−3332.14	−0.145620
$807$	−1127.19	−0.0491684
$808$	−4754.34	−0.207002
$809$	−15203.2	−0.660712	−0.330356	−	0.943856i	$-0.607169\pi$
$809$	−15203.2	−0.660712	−0.330356	+	0.943856i	$0.607169\pi$
$810$	1775.51	0.0770184
$811$	−16244.0	−0.703332	−0.351666	−	0.936126i	$-0.614385\pi$
$811$	−16244.0	−0.703332	−0.351666	+	0.936126i	$0.614385\pi$
$812$	5755.37	0.248737
$813$	−9428.07	−0.406712
$814$	−5697.15	−0.245313
$815$	−270.169	−0.0116118
$816$	25087.2	1.07626
$817$	4426.17	0.189537
$818$	29358.0	1.25486
$819$	4671.21	0.199298
$820$	1367.29	0.0582293
$821$	−19598.9	−0.833136	−0.416568	−	0.909105i	$-0.636767\pi$
$821$	−19598.9	−0.833136	−0.416568	+	0.909105i	$0.636767\pi$
$822$	17585.8	0.746200
$823$	−21630.0	−0.916128	−0.458064	−	0.888919i	$-0.651457\pi$
$823$	−21630.0	−0.916128	−0.458064	+	0.888919i	$0.651457\pi$
$824$	−28345.1	−1.19836
$825$	−975.624	−0.0411719
$826$	47890.7	2.01735
$827$	−13441.4	−0.565181	−0.282591	−	0.959241i	$-0.591194\pi$
$827$	−13441.4	−0.565181	−0.282591	+	0.959241i	$0.591194\pi$
$828$	35.9596	0.00150928
$829$	12433.1	0.520890	0.260445	−	0.965489i	$-0.416131\pi$
$829$	12433.1	0.520890	0.260445	+	0.965489i	$0.416131\pi$
$830$	12692.1	0.530780
$831$	57.9207	0.00241786
$832$	−6407.92	−0.267013
$833$	53706.0	2.23386
$834$	−6109.65	−0.253669
$835$	−16825.1	−0.697313
$836$	161.243	0.00667069
$837$	15668.8	0.647065
$838$	−12566.7	−0.518031
$839$	−39848.8	−1.63973	−0.819865	−	0.572558i	$-0.805951\pi$
$839$	−39848.8	−1.63973	−0.819865	+	0.572558i	$0.805951\pi$
$840$	−11665.9	−0.479179
$841$	47172.7	1.93418
$842$	15638.8	0.640082
$843$	23039.3	0.941298
$844$	−3858.56	−0.157366
$845$	10309.7	0.419722
$846$	9080.75	0.369034
$847$	3374.31	0.136886
$848$	41679.0	1.68781
$849$	−27342.2	−1.10528
$850$	8304.65	0.335114
$851$	−622.942	−0.0250930
$852$	869.055	0.0349452
$853$	44085.6	1.76959	0.884795	−	0.465980i	$-0.154298\pi$
$853$	44085.6	1.76959	0.884795	+	0.465980i	$0.154298\pi$
$854$	−52393.4	−2.09937
$855$	−1369.30	−0.0547708
$856$	−14592.8	−0.582677
$857$	10605.0	0.422706	0.211353	−	0.977410i	$-0.432213\pi$
$857$	10605.0	0.422706	0.211353	+	0.977410i	$0.432213\pi$
$858$	1219.33	0.0485167
$859$	−1643.40	−0.0652760	−0.0326380	−	0.999467i	$-0.510391\pi$
$859$	−1643.40	−0.0652760	−0.0326380	+	0.999467i	$0.510391\pi$
$860$	−898.624	−0.0356312
$861$	−35067.7	−1.38804
$862$	13667.1	0.540027
$863$	−22830.8	−0.900546	−0.450273	−	0.892891i	$-0.648673\pi$
$863$	−22830.8	−0.900546	−0.450273	+	0.892891i	$0.648673\pi$
$864$	5111.20	0.201258
$865$	6964.95	0.273775
$866$	−34980.9	−1.37263
$867$	−36728.1	−1.43870
$868$	−2294.44	−0.0897215
$869$	−9768.95	−0.381345
$870$	−12758.0	−0.497170
$871$	3961.97	0.154129
$872$	35332.2	1.37213
$873$	−5516.82	−0.213879
$874$	−165.190	−0.00639319
$875$	−3485.86	−0.134678
$876$	−1502.93	−0.0579674
$877$	−22727.6	−0.875094	−0.437547	−	0.899196i	$-0.644153\pi$
$877$	−22727.6	−0.875094	−0.437547	+	0.899196i	$0.644153\pi$
$878$	−36447.3	−1.40095
$879$	−26248.8	−1.00723
$880$	3147.81	0.120582
$881$	−28863.3	−1.10378	−0.551889	−	0.833918i	$-0.686093\pi$
$881$	−28863.3	−1.10378	−0.551889	+	0.833918i	$0.686093\pi$
$882$	−16844.8	−0.643075
$883$	−7488.87	−0.285414	−0.142707	−	0.989765i	$-0.545581\pi$
$883$	−7488.87	−0.285414	−0.142707	+	0.989765i	$0.545581\pi$
$884$	1107.76	0.0421471
$885$	11330.5	0.430361
$886$	18900.5	0.716677
$887$	−25857.4	−0.978811	−0.489406	−	0.872056i	$-0.662786\pi$
$887$	−25857.4	−0.978811	−0.489406	+	0.872056i	$0.662786\pi$
$888$	−16117.2	−0.609072
$889$	−73760.3	−2.78272
$890$	10200.8	0.384195
$891$	−1452.85	−0.0546266
$892$	−4476.69	−0.168039
$893$	4452.22	0.166840
$894$	21130.1	0.790486
$895$	21563.0	0.805331
$896$	33580.4	1.25205
$897$	133.325	0.00496276
$898$	−22499.4	−0.836096
$899$	−28528.8	−1.05839
$900$	278.002	0.0102964
$901$	−89976.5	−3.32692
$902$	10482.7	0.386959
$903$	23047.5	0.849360
$904$	17631.4	0.648684
$905$	−3436.23	−0.126215
$906$	3143.75	0.115281
$907$	−16164.2	−0.591757	−0.295878	−	0.955226i	$-0.595612\pi$
$907$	−16164.2	−0.591757	−0.295878	+	0.955226i	$0.595612\pi$
$908$	5123.11	0.187243
$909$	−2905.81	−0.106028
$910$	4356.62	0.158704
$911$	−4440.50	−0.161493	−0.0807467	−	0.996735i	$-0.525730\pi$
$911$	−4440.50	−0.161493	−0.0807467	+	0.996735i	$0.525730\pi$
$912$	−3857.88	−0.140074
$913$	−10385.6	−0.376465
$914$	8453.20	0.305916
$915$	−12395.7	−0.447858
$916$	−1617.62	−0.0583490
$917$	−45649.4	−1.64392
$918$	48806.1	1.75473
$919$	−40044.7	−1.43738	−0.718691	−	0.695329i	$-0.755258\pi$
$919$	−40044.7	−1.43738	−0.718691	+	0.695329i	$0.755258\pi$
$920$	381.307	0.0136645
$921$	5204.29	0.186197
$922$	24840.2	0.887277
$923$	−3689.94	−0.131588
$924$	839.606	0.0298929
$925$	−4815.94	−0.171186
$926$	40095.4	1.42291
$927$	−17324.2	−0.613811
$928$	−9306.15	−0.329191
$929$	−21042.1	−0.743131	−0.371566	−	0.928407i	$-0.621179\pi$
$929$	−21042.1	−0.743131	−0.371566	+	0.928407i	$0.621179\pi$
$930$	5086.12	0.179334
$931$	−8258.85	−0.290733
$932$	−1680.26	−0.0590543
$933$	7461.67	0.261826
$934$	−50068.7	−1.75407
$935$	−6795.47	−0.237685
$936$	−3950.28	−0.137948
$937$	−8697.36	−0.303234	−0.151617	−	0.988439i	$-0.548448\pi$
$937$	−8697.36	−0.303234	−0.151617	+	0.988439i	$0.548448\pi$
$938$	−25561.0	−0.889763
$939$	−30099.0	−1.04605
$940$	−903.914	−0.0313643
$941$	40517.6	1.40365	0.701826	−	0.712348i	$-0.252368\pi$
$941$	40517.6	1.40365	0.701826	+	0.712348i	$0.252368\pi$
$942$	10803.5	0.373670
$943$	1146.21	0.0395820
$944$	−36557.2	−1.26042
$945$	−20486.3	−0.705204
$946$	−6889.56	−0.236785
$947$	−13771.2	−0.472550	−0.236275	−	0.971686i	$-0.575927\pi$
$947$	−13771.2	−0.472550	−0.236275	+	0.971686i	$0.575927\pi$
$948$	−2430.74	−0.0832772
$949$	6381.35	0.218280
$950$	−1277.08	−0.0436147
$951$	−2502.89	−0.0853438
$952$	−81255.8	−2.76630
$953$	−18389.1	−0.625060	−0.312530	−	0.949908i	$-0.601176\pi$
$953$	−18389.1	−0.625060	−0.312530	+	0.949908i	$0.601176\pi$
$954$	28220.9	0.957742
$955$	−13257.1	−0.449203
$956$	−1218.06	−0.0412081
$957$	10439.6	0.352626
$958$	−13517.6	−0.455880
$959$	−51414.8	−1.73125
$960$	9780.95	0.328832
$961$	−18417.7	−0.618231
$962$	6018.95	0.201724
$963$	−8918.97	−0.298453
$964$	−755.979	−0.0252577
$965$	22382.5	0.746651
$966$	−860.162	−0.0286493
$967$	17866.2	0.594146	0.297073	−	0.954855i	$-0.403989\pi$
$967$	17866.2	0.594146	0.297073	+	0.954855i	$0.403989\pi$
$968$	−2853.54	−0.0947480
$969$	8328.37	0.276105
$970$	−5145.27	−0.170314
$971$	3585.52	0.118502	0.0592508	−	0.998243i	$-0.481129\pi$
$971$	3585.52	0.118502	0.0592508	+	0.998243i	$0.481129\pi$
$972$	2698.99	0.0890638
$973$	17862.5	0.588535
$974$	−41610.2	−1.36887
$975$	1030.73	0.0338562
$976$	39994.3	1.31167
$977$	−21383.3	−0.700216	−0.350108	−	0.936709i	$-0.613855\pi$
$977$	−21383.3	−0.700216	−0.350108	+	0.936709i	$0.613855\pi$
$978$	−515.394	−0.0168512
$979$	−8347.08	−0.272496
$980$	1676.76	0.0546551
$981$	21594.7	0.702820
$982$	−12044.0	−0.391386
$983$	34404.6	1.11631	0.558156	−	0.829736i	$-0.311509\pi$
$983$	34404.6	1.11631	0.558156	+	0.829736i	$0.311509\pi$
$984$	29655.5	0.960756
$985$	−20473.3	−0.662267
$986$	−88863.1	−2.87016
$987$	23183.1	0.747647
$988$	−170.350	−0.00548539
$989$	−753.323	−0.0242207
$990$	2131.38	0.0684240
$991$	−32178.7	−1.03147	−0.515737	−	0.856747i	$-0.672482\pi$
$991$	−32178.7	−1.03147	−0.515737	+	0.856747i	$0.672482\pi$
$992$	3709.99	0.118742
$993$	−7115.25	−0.227387
$994$	23806.1	0.759640
$995$	−19528.7	−0.622213
$996$	−2584.17	−0.0822114
$997$	41215.6	1.30924	0.654619	−	0.755959i	$-0.272829\pi$
$997$	41215.6	1.30924	0.654619	+	0.755959i	$0.272829\pi$
$998$	−40763.2	−1.29292
$999$	−28303.1	−0.896367

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.f.1.17	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.f.1.17	✓	23	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q+2.68859 q^{2} -3.54772 q^{3} -0.771496 q^{4} -5.00000 q^{5} -9.53836 q^{6} +27.8868 q^{7} -23.5829 q^{8} -14.4137 q^{9} +O(q^{10})\)	\(q+2.68859 q^{2} -3.54772 q^{3} -0.771496 q^{4} -5.00000 q^{5} -9.53836 q^{6} +27.8868 q^{7} -23.5829 q^{8} -14.4137 q^{9} -13.4429 q^{10} +11.0000 q^{11} +2.73705 q^{12} -11.6213 q^{13} +74.9762 q^{14} +17.7386 q^{15} -57.2328 q^{16} +123.554 q^{17} -38.7524 q^{18} -19.0000 q^{19} +3.85748 q^{20} -98.9348 q^{21} +29.5745 q^{22} +3.23375 q^{23} +83.6657 q^{24} +25.0000 q^{25} -31.2450 q^{26} +146.924 q^{27} -21.5146 q^{28} -267.510 q^{29} +47.6918 q^{30} +106.646 q^{31} +34.7880 q^{32} -39.0249 q^{33} +332.186 q^{34} -139.434 q^{35} +11.1201 q^{36} -192.637 q^{37} -51.0832 q^{38} +41.2292 q^{39} +117.915 q^{40} +354.453 q^{41} -265.995 q^{42} -232.956 q^{43} -8.48646 q^{44} +72.0683 q^{45} +8.69423 q^{46} -234.327 q^{47} +203.046 q^{48} +434.676 q^{49} +67.2147 q^{50} -438.335 q^{51} +8.96581 q^{52} -728.236 q^{53} +395.019 q^{54} -55.0000 q^{55} -657.654 q^{56} +67.4067 q^{57} -719.225 q^{58} +638.745 q^{59} -13.6853 q^{60} -698.800 q^{61} +286.726 q^{62} -401.952 q^{63} +551.393 q^{64} +58.1066 q^{65} -104.922 q^{66} -340.922 q^{67} -95.3215 q^{68} -11.4725 q^{69} -374.881 q^{70} +317.515 q^{71} +339.917 q^{72} -549.107 q^{73} -517.923 q^{74} -88.6931 q^{75} +14.6584 q^{76} +306.755 q^{77} +110.848 q^{78} -888.087 q^{79} +286.164 q^{80} -132.077 q^{81} +952.977 q^{82} -944.143 q^{83} +76.3278 q^{84} -617.770 q^{85} -626.323 q^{86} +949.052 q^{87} -259.412 q^{88} -758.826 q^{89} +193.762 q^{90} -324.082 q^{91} -2.49483 q^{92} -378.349 q^{93} -630.010 q^{94} +95.0000 q^{95} -123.418 q^{96} +382.749 q^{97} +1168.67 q^{98} -158.550 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 2 q^{2} - 9 q^{3} + 98 q^{4} - 115 q^{5} - 61 q^{6} + 13 q^{7} - 54 q^{8} + 170 q^{9}+O(q^{10}) \) 23 * q - 2 * q^2 - 9 * q^3 + 98 * q^4 - 115 * q^5 - 61 * q^6 + 13 * q^7 - 54 * q^8 + 170 * q^9	\( 23 q - 2 q^{2} - 9 q^{3} + 98 q^{4} - 115 q^{5} - 61 q^{6} + 13 q^{7} - 54 q^{8} + 170 q^{9} + 10 q^{10} + 253 q^{11} - 76 q^{12} - 37 q^{13} - 191 q^{14} + 45 q^{15} + 214 q^{16} - 51 q^{17} - 63 q^{18} - 437 q^{19} - 490 q^{20} - 479 q^{21} - 22 q^{22} + 101 q^{23} - 598 q^{24} + 575 q^{25} - 197 q^{26} - 627 q^{27} + 279 q^{28} - 357 q^{29} + 305 q^{30} - 90 q^{31} - 19 q^{32} - 99 q^{33} + 71 q^{34} - 65 q^{35} + 573 q^{36} - 378 q^{37} + 38 q^{38} + 193 q^{39} + 270 q^{40} - 830 q^{41} + 1480 q^{42} + 260 q^{43} + 1078 q^{44} - 850 q^{45} - 919 q^{46} - 1468 q^{47} + 837 q^{48} + 1200 q^{49} - 50 q^{50} - 1147 q^{51} - 1222 q^{52} + 185 q^{53} - 1406 q^{54} - 1265 q^{55} - 2299 q^{56} + 171 q^{57} - 958 q^{58} - 3665 q^{59} + 380 q^{60} - 2528 q^{61} - 1722 q^{62} + 172 q^{63} - 120 q^{64} + 185 q^{65} - 671 q^{66} + 329 q^{67} - 2240 q^{68} - 1337 q^{69} + 955 q^{70} - 3190 q^{71} - 2488 q^{72} - 2183 q^{73} - 1613 q^{74} - 225 q^{75} - 1862 q^{76} + 143 q^{77} - 2748 q^{78} - 3546 q^{79} - 1070 q^{80} - 2077 q^{81} + 2202 q^{82} - 4324 q^{83} - 8608 q^{84} + 255 q^{85} - 3626 q^{86} + 2921 q^{87} - 594 q^{88} - 4630 q^{89} + 315 q^{90} - 5043 q^{91} + 108 q^{92} - 5644 q^{93} - 8328 q^{94} + 2185 q^{95} - 2016 q^{96} - 774 q^{97} - 6388 q^{98} + 1870 q^{99}+O(q^{100}) \) 23 * q - 2 * q^2 - 9 * q^3 + 98 * q^4 - 115 * q^5 - 61 * q^6 + 13 * q^7 - 54 * q^8 + 170 * q^9 + 10 * q^10 + 253 * q^11 - 76 * q^12 - 37 * q^13 - 191 * q^14 + 45 * q^15 + 214 * q^16 - 51 * q^17 - 63 * q^18 - 437 * q^19 - 490 * q^20 - 479 * q^21 - 22 * q^22 + 101 * q^23 - 598 * q^24 + 575 * q^25 - 197 * q^26 - 627 * q^27 + 279 * q^28 - 357 * q^29 + 305 * q^30 - 90 * q^31 - 19 * q^32 - 99 * q^33 + 71 * q^34 - 65 * q^35 + 573 * q^36 - 378 * q^37 + 38 * q^38 + 193 * q^39 + 270 * q^40 - 830 * q^41 + 1480 * q^42 + 260 * q^43 + 1078 * q^44 - 850 * q^45 - 919 * q^46 - 1468 * q^47 + 837 * q^48 + 1200 * q^49 - 50 * q^50 - 1147 * q^51 - 1222 * q^52 + 185 * q^53 - 1406 * q^54 - 1265 * q^55 - 2299 * q^56 + 171 * q^57 - 958 * q^58 - 3665 * q^59 + 380 * q^60 - 2528 * q^61 - 1722 * q^62 + 172 * q^63 - 120 * q^64 + 185 * q^65 - 671 * q^66 + 329 * q^67 - 2240 * q^68 - 1337 * q^69 + 955 * q^70 - 3190 * q^71 - 2488 * q^72 - 2183 * q^73 - 1613 * q^74 - 225 * q^75 - 1862 * q^76 + 143 * q^77 - 2748 * q^78 - 3546 * q^79 - 1070 * q^80 - 2077 * q^81 + 2202 * q^82 - 4324 * q^83 - 8608 * q^84 + 255 * q^85 - 3626 * q^86 + 2921 * q^87 - 594 * q^88 - 4630 * q^89 + 315 * q^90 - 5043 * q^91 + 108 * q^92 - 5644 * q^93 - 8328 * q^94 + 2185 * q^95 - 2016 * q^96 - 774 * q^97 - 6388 * q^98 + 1870 * q^99

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