LMFDB - Embedded newform 667.4.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,4,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("667.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	667.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:	$39.3542739738$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.356870 q^{2} +0.508952 q^{3} -7.87264 q^{4} -0.0507065 q^{5} -0.181630 q^{6} +30.7062 q^{7} +5.66448 q^{8} -26.7410 q^{9} +O(q^{10})$	\(q-0.356870 q^{2} +0.508952 q^{3} -7.87264 q^{4} -0.0507065 q^{5} -0.181630 q^{6} +30.7062 q^{7} +5.66448 q^{8} -26.7410 q^{9} +0.0180956 q^{10} -19.0966 q^{11} -4.00680 q^{12} -20.4705 q^{13} -10.9581 q^{14} -0.0258072 q^{15} +60.9597 q^{16} -16.3956 q^{17} +9.54306 q^{18} +77.8124 q^{19} +0.399194 q^{20} +15.6280 q^{21} +6.81501 q^{22} +23.0000 q^{23} +2.88295 q^{24} -124.997 q^{25} +7.30532 q^{26} -27.3516 q^{27} -241.739 q^{28} -29.0000 q^{29} +0.00920981 q^{30} +161.412 q^{31} -67.0705 q^{32} -9.71925 q^{33} +5.85110 q^{34} -1.55700 q^{35} +210.522 q^{36} +66.7758 q^{37} -27.7689 q^{38} -10.4185 q^{39} -0.287226 q^{40} -209.273 q^{41} -5.57716 q^{42} -25.8386 q^{43} +150.341 q^{44} +1.35594 q^{45} -8.20802 q^{46} -457.947 q^{47} +31.0255 q^{48} +599.868 q^{49} +44.6079 q^{50} -8.34456 q^{51} +161.157 q^{52} +151.264 q^{53} +9.76096 q^{54} +0.968322 q^{55} +173.934 q^{56} +39.6027 q^{57} +10.3492 q^{58} +202.631 q^{59} +0.203171 q^{60} +592.476 q^{61} -57.6032 q^{62} -821.112 q^{63} -463.742 q^{64} +1.03799 q^{65} +3.46851 q^{66} -853.480 q^{67} +129.077 q^{68} +11.7059 q^{69} +0.555648 q^{70} -1187.92 q^{71} -151.474 q^{72} -801.225 q^{73} -23.8303 q^{74} -63.6177 q^{75} -612.589 q^{76} -586.383 q^{77} +3.71805 q^{78} -1090.33 q^{79} -3.09105 q^{80} +708.086 q^{81} +74.6833 q^{82} -205.204 q^{83} -123.033 q^{84} +0.831362 q^{85} +9.22102 q^{86} -14.7596 q^{87} -108.172 q^{88} -513.982 q^{89} -0.483895 q^{90} -628.571 q^{91} -181.071 q^{92} +82.1510 q^{93} +163.428 q^{94} -3.94559 q^{95} -34.1357 q^{96} +644.093 q^{97} -214.075 q^{98} +510.662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9}+O(q^{10}) $ 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9} - 52 q^{10} - 126 q^{11} - 173 q^{12} - 252 q^{13} + 112 q^{14} - 32 q^{15} + 312 q^{16} - 332 q^{17} - 225 q^{18} - 2 q^{19} - 747 q^{20} - 202 q^{21} - 127 q^{22} + 805 q^{23} - 494 q^{24} + 315 q^{25} - 677 q^{26} - 694 q^{27} - 529 q^{28} - 1015 q^{29} + 389 q^{30} - 652 q^{31} + 320 q^{32} - 290 q^{33} - 455 q^{34} - 940 q^{35} + 34 q^{36} - 528 q^{37} - 1218 q^{38} - 268 q^{39} - 806 q^{40} - 68 q^{41} - 1484 q^{42} - 162 q^{43} - 1817 q^{44} - 356 q^{45} - 138 q^{46} - 1200 q^{47} - 2153 q^{48} + 93 q^{49} - 1369 q^{50} - 270 q^{51} - 3134 q^{52} - 1892 q^{53} - 1221 q^{54} - 794 q^{55} + 191 q^{56} - 1764 q^{57} + 174 q^{58} - 1354 q^{59} + 159 q^{60} - 1274 q^{61} - 5413 q^{62} - 2904 q^{63} - 926 q^{64} - 548 q^{65} - 2477 q^{66} - 3212 q^{67} - 3901 q^{68} - 506 q^{69} - 2768 q^{70} - 2342 q^{71} - 2381 q^{72} + 916 q^{73} + 661 q^{74} - 4708 q^{75} - 2810 q^{76} - 5536 q^{77} - 2434 q^{78} + 2622 q^{79} - 5444 q^{80} + 607 q^{81} - 3687 q^{82} - 2702 q^{83} + 346 q^{84} - 3304 q^{85} - 5789 q^{86} + 638 q^{87} - 2252 q^{88} - 1620 q^{89} - 3933 q^{90} - 4016 q^{91} + 2668 q^{92} - 4942 q^{93} - 1413 q^{94} - 4528 q^{95} - 7920 q^{96} + 682 q^{97} + 152 q^{98} - 582 q^{99}+O(q^{100}) \) 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9 - 52 * q^10 - 126 * q^11 - 173 * q^12 - 252 * q^13 + 112 * q^14 - 32 * q^15 + 312 * q^16 - 332 * q^17 - 225 * q^18 - 2 * q^19 - 747 * q^20 - 202 * q^21 - 127 * q^22 + 805 * q^23 - 494 * q^24 + 315 * q^25 - 677 * q^26 - 694 * q^27 - 529 * q^28 - 1015 * q^29 + 389 * q^30 - 652 * q^31 + 320 * q^32 - 290 * q^33 - 455 * q^34 - 940 * q^35 + 34 * q^36 - 528 * q^37 - 1218 * q^38 - 268 * q^39 - 806 * q^40 - 68 * q^41 - 1484 * q^42 - 162 * q^43 - 1817 * q^44 - 356 * q^45 - 138 * q^46 - 1200 * q^47 - 2153 * q^48 + 93 * q^49 - 1369 * q^50 - 270 * q^51 - 3134 * q^52 - 1892 * q^53 - 1221 * q^54 - 794 * q^55 + 191 * q^56 - 1764 * q^57 + 174 * q^58 - 1354 * q^59 + 159 * q^60 - 1274 * q^61 - 5413 * q^62 - 2904 * q^63 - 926 * q^64 - 548 * q^65 - 2477 * q^66 - 3212 * q^67 - 3901 * q^68 - 506 * q^69 - 2768 * q^70 - 2342 * q^71 - 2381 * q^72 + 916 * q^73 + 661 * q^74 - 4708 * q^75 - 2810 * q^76 - 5536 * q^77 - 2434 * q^78 + 2622 * q^79 - 5444 * q^80 + 607 * q^81 - 3687 * q^82 - 2702 * q^83 + 346 * q^84 - 3304 * q^85 - 5789 * q^86 + 638 * q^87 - 2252 * q^88 - 1620 * q^89 - 3933 * q^90 - 4016 * q^91 + 2668 * q^92 - 4942 * q^93 - 1413 * q^94 - 4528 * q^95 - 7920 * q^96 + 682 * q^97 + 152 * q^98 - 582 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.356870	−0.126173	−0.0630864	−	0.998008i	$-0.520094\pi$
$2$	−0.356870	−0.126173	−0.0630864	+	0.998008i	$0.520094\pi$
$3$	0.508952	0.0979478	0.0489739	−	0.998800i	$-0.484405\pi$
$3$	0.508952	0.0979478	0.0489739	+	0.998800i	$0.484405\pi$
$4$	−7.87264	−0.984080
$5$	−0.0507065	−0.00453533	−0.00226766	−	0.999997i	$-0.500722\pi$
$5$	−0.0507065	−0.00453533	−0.00226766	+	0.999997i	$0.500722\pi$
$6$	−0.181630	−0.0123583
$7$	30.7062	1.65798	0.828988	−	0.559266i	$-0.188917\pi$
$7$	30.7062	1.65798	0.828988	+	0.559266i	$0.188917\pi$
$8$	5.66448	0.250337
$9$	−26.7410	−0.990406
$10$	0.0180956	0.000572235 0
$11$	−19.0966	−0.523440	−0.261720	−	0.965144i	$-0.584290\pi$
$11$	−19.0966	−0.523440	−0.261720	+	0.965144i	$0.584290\pi$
$12$	−4.00680	−0.0963885
$13$	−20.4705	−0.436730	−0.218365	−	0.975867i	$-0.570072\pi$
$13$	−20.4705	−0.436730	−0.218365	+	0.975867i	$0.570072\pi$
$14$	−10.9581	−0.209192
$15$	−0.0258072	−0.000444225 0
$16$	60.9597	0.952495
$17$	−16.3956	−0.233912	−0.116956	−	0.993137i	$-0.537314\pi$
$17$	−16.3956	−0.233912	−0.116956	+	0.993137i	$0.537314\pi$
$18$	9.54306	0.124962
$19$	77.8124	0.939546	0.469773	−	0.882787i	$-0.344336\pi$
$19$	77.8124	0.939546	0.469773	+	0.882787i	$0.344336\pi$
$20$	0.399194	0.00446313
$21$	15.6280	0.162395
$22$	6.81501	0.0660439
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	2.88295	0.0245200
$25$	−124.997	−0.999979
$26$	7.30532	0.0551035
$27$	−27.3516	−0.194956
$28$	−241.739	−1.63158
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	0.00920981	5.60491e−5 0
$31$	161.412	0.935176	0.467588	−	0.883946i	$-0.345123\pi$
$31$	161.412	0.935176	0.467588	+	0.883946i	$0.345123\pi$
$32$	−67.0705	−0.370516
$33$	−9.71925	−0.0512698
$34$	5.85110	0.0295134
$35$	−1.55700	−0.00751947
$36$	210.522	0.974639
$37$	66.7758	0.296699	0.148350	−	0.988935i	$-0.452604\pi$
$37$	66.7758	0.296699	0.148350	+	0.988935i	$0.452604\pi$
$38$	−27.7689	−0.118545
$39$	−10.4185	−0.0427768
$40$	−0.287226	−0.00113536
$41$	−209.273	−0.797145	−0.398572	−	0.917137i	$-0.630494\pi$
$41$	−209.273	−0.797145	−0.398572	+	0.917137i	$0.630494\pi$
$42$	−5.57716	−0.0204899
$43$	−25.8386	−0.0916359	−0.0458179	−	0.998950i	$-0.514589\pi$
$43$	−25.8386	−0.0916359	−0.0458179	+	0.998950i	$0.514589\pi$
$44$	150.341	0.515107
$45$	1.35594	0.00449182
$46$	−8.20802	−0.0263088
$47$	−457.947	−1.42124	−0.710622	−	0.703575i	$-0.751586\pi$
$47$	−457.947	−1.42124	−0.710622	+	0.703575i	$0.751586\pi$
$48$	31.0255	0.0932948
$49$	599.868	1.74889
$50$	44.6079	0.126170
$51$	−8.34456	−0.0229112
$52$	161.157	0.429778
$53$	151.264	0.392032	0.196016	−	0.980601i	$-0.437199\pi$
$53$	151.264	0.392032	0.196016	+	0.980601i	$0.437199\pi$
$54$	9.76096	0.0245981
$55$	0.968322	0.00237397
$56$	173.934	0.415053
$57$	39.6027	0.0920265
$58$	10.3492	0.0234297
$59$	202.631	0.447124	0.223562	−	0.974690i	$-0.428231\pi$
$59$	202.631	0.447124	0.223562	+	0.974690i	$0.428231\pi$
$60$	0.203171	0.000437153 0
$61$	592.476	1.24359	0.621793	−	0.783182i	$-0.286404\pi$
$61$	592.476	1.24359	0.621793	+	0.783182i	$0.286404\pi$
$62$	−57.6032	−0.117994
$63$	−821.112	−1.64207
$64$	−463.742	−0.905746
$65$	1.03799	0.00198072
$66$	3.46851	0.00646885
$67$	−853.480	−1.55626	−0.778129	−	0.628105i	$-0.783831\pi$
$67$	−853.480	−1.55626	−0.778129	+	0.628105i	$0.783831\pi$
$68$	129.077	0.230189
$69$	11.7059	0.0204235
$70$	0.555648	0.000948752 0
$71$	−1187.92	−1.98564	−0.992820	−	0.119616i	$-0.961834\pi$
$71$	−1187.92	−1.98564	−0.992820	+	0.119616i	$0.961834\pi$
$72$	−151.474	−0.247935
$73$	−801.225	−1.28461	−0.642304	−	0.766450i	$-0.722021\pi$
$73$	−801.225	−1.28461	−0.642304	+	0.766450i	$0.722021\pi$
$74$	−23.8303	−0.0374354
$75$	−63.6177	−0.0979458
$76$	−612.589	−0.924589
$77$	−586.383	−0.867852
$78$	3.71805	0.00539727
$79$	−1090.33	−1.55281	−0.776405	−	0.630234i	$-0.782959\pi$
$79$	−1090.33	−1.55281	−0.776405	+	0.630234i	$0.782959\pi$
$80$	−3.09105	−0.00431987
$81$	708.086	0.971311
$82$	74.6833	0.100578
$83$	−205.204	−0.271374	−0.135687	−	0.990752i	$-0.543324\pi$
$83$	−205.204	−0.271374	−0.135687	+	0.990752i	$0.543324\pi$
$84$	−123.033	−0.159810
$85$	0.831362	0.00106087
$86$	9.22102	0.0115620
$87$	−14.7596	−0.0181885
$88$	−108.172	−0.131036
$89$	−513.982	−0.612157	−0.306079	−	0.952006i	$-0.599017\pi$
$89$	−513.982	−0.612157	−0.306079	+	0.952006i	$0.599017\pi$
$90$	−0.483895	−0.000566745 0
$91$	−628.571	−0.724089
$92$	−181.071	−0.205195
$93$	82.1510	0.0915985
$94$	163.428	0.179322
$95$	−3.94559	−0.00426115
$96$	−34.1357	−0.0362912
$97$	644.093	0.674204	0.337102	−	0.941468i	$-0.390553\pi$
$97$	644.093	0.674204	0.337102	+	0.941468i	$0.390553\pi$
$98$	−214.075	−0.220662
$99$	510.662	0.518418
$100$	984.060	0.984060
$101$	−1733.28	−1.70760	−0.853802	−	0.520598i	$-0.825709\pi$
$101$	−1733.28	−1.70760	−0.853802	+	0.520598i	$0.825709\pi$
$102$	2.97793	0.00289077
$103$	−1697.04	−1.62344	−0.811719	−	0.584048i	$-0.801468\pi$
$103$	−1697.04	−1.62344	−0.811719	+	0.584048i	$0.801468\pi$
$104$	−115.955	−0.109330
$105$	−0.792439	−0.000736515 0
$106$	−53.9817	−0.0494638
$107$	−1091.26	−0.985940	−0.492970	−	0.870046i	$-0.664089\pi$
$107$	−1091.26	−0.985940	−0.492970	+	0.870046i	$0.664089\pi$
$108$	215.329	0.191852
$109$	2172.24	1.90884	0.954419	−	0.298471i	$-0.0964765\pi$
$109$	2172.24	1.90884	0.954419	+	0.298471i	$0.0964765\pi$
$110$	−0.345565	−0.000299531 0
$111$	33.9856	0.0290610
$112$	1871.84	1.57921
$113$	−2183.15	−1.81747	−0.908733	−	0.417377i	$-0.862949\pi$
$113$	−2183.15	−1.81747	−0.908733	+	0.417377i	$0.862949\pi$
$114$	−14.1330	−0.0116112
$115$	−1.16625	−0.000945681 0
$116$	228.307	0.182739
$117$	547.401	0.432541
$118$	−72.3131	−0.0564149
$119$	−503.445	−0.387821
$120$	−0.146184	−0.000111206 0
$121$	−966.320	−0.726010
$122$	−211.437	−0.156907
$123$	−106.510	−0.0780786
$124$	−1270.74	−0.920289
$125$	12.6765	0.00907056
$126$	293.031	0.207185
$127$	−560.441	−0.391583	−0.195792	−	0.980646i	$-0.562728\pi$
$127$	−560.441	−0.391583	−0.195792	+	0.980646i	$0.562728\pi$
$128$	702.060	0.484796
$129$	−13.1506	−0.00897553
$130$	−0.370427	−0.000249912 0
$131$	1145.11	0.763734	0.381867	−	0.924217i	$-0.375281\pi$
$131$	1145.11	0.763734	0.381867	+	0.924217i	$0.375281\pi$
$132$	76.5162	0.0504536
$133$	2389.32	1.55775
$134$	304.582	0.196357
$135$	1.38690	0.000884189 0
$136$	−92.8724	−0.0585569
$137$	1608.77	1.00326	0.501629	−	0.865083i	$-0.332734\pi$
$137$	1608.77	1.00326	0.501629	+	0.865083i	$0.332734\pi$
$138$	−4.17749	−0.00257689
$139$	580.103	0.353983	0.176992	−	0.984212i	$-0.443363\pi$
$139$	580.103	0.353983	0.176992	+	0.984212i	$0.443363\pi$
$140$	12.2577	0.00739976
$141$	−233.073	−0.139208
$142$	423.934	0.250534
$143$	390.917	0.228602
$144$	−1630.12	−0.943357
$145$	1.47049	0.000842189 0
$146$	285.934	0.162082
$147$	305.304	0.171300
$148$	−525.702	−0.291976
$149$	−1616.92	−0.889013	−0.444507	−	0.895776i	$-0.646621\pi$
$149$	−1616.92	−0.889013	−0.444507	+	0.895776i	$0.646621\pi$
$150$	22.7033	0.0123581
$151$	1804.50	0.972502	0.486251	−	0.873819i	$-0.338364\pi$
$151$	1804.50	0.972502	0.486251	+	0.873819i	$0.338364\pi$
$152$	440.766	0.235203
$153$	438.434	0.231668
$154$	209.263	0.109499
$155$	−8.18464	−0.00424133
$156$	82.0211	0.0420958
$157$	−337.256	−0.171439	−0.0857197	−	0.996319i	$-0.527319\pi$
$157$	−337.256	−0.171439	−0.0857197	+	0.996319i	$0.527319\pi$
$158$	389.108	0.195922
$159$	76.9861	0.0383987
$160$	3.40091	0.00168041
$161$	706.242	0.345712
$162$	−252.695	−0.122553
$163$	−1401.19	−0.673313	−0.336657	−	0.941628i	$-0.609296\pi$
$163$	−1401.19	−0.673313	−0.336657	+	0.941628i	$0.609296\pi$
$164$	1647.53	0.784454
$165$	0.492829	0.000232525 0
$166$	73.2312	0.0342400
$167$	2790.41	1.29299	0.646493	−	0.762920i	$-0.276235\pi$
$167$	2790.41	1.29299	0.646493	+	0.762920i	$0.276235\pi$
$168$	88.5242	0.0406535
$169$	−1777.96	−0.809267
$170$	−0.296689	−0.000133853 0
$171$	−2080.78	−0.930532
$172$	203.418	0.0901771
$173$	−2006.30	−0.881713	−0.440856	−	0.897578i	$-0.645325\pi$
$173$	−2006.30	−0.881713	−0.440856	+	0.897578i	$0.645325\pi$
$174$	5.26727	0.00229489
$175$	−3838.19	−1.65794
$176$	−1164.12	−0.498574
$177$	103.129	0.0437948
$178$	183.425	0.0772376
$179$	756.975	0.316084	0.158042	−	0.987432i	$-0.449482\pi$
$179$	756.975	0.316084	0.158042	+	0.987432i	$0.449482\pi$
$180$	−10.6748	−0.00442031
$181$	−809.636	−0.332485	−0.166242	−	0.986085i	$-0.553163\pi$
$181$	−809.636	−0.332485	−0.166242	+	0.986085i	$0.553163\pi$
$182$	224.318	0.0913603
$183$	301.542	0.121807
$184$	130.283	0.0521989
$185$	−3.38596	−0.00134563
$186$	−29.3173	−0.0115572
$187$	313.100	0.122439
$188$	3605.25	1.39862
$189$	−839.861	−0.323232
$190$	1.40806	0.000537641 0
$191$	321.138	0.121658	0.0608292	−	0.998148i	$-0.480626\pi$
$191$	321.138	0.121658	0.0608292	+	0.998148i	$0.480626\pi$
$192$	−236.022	−0.0887158
$193$	−1553.36	−0.579342	−0.289671	−	0.957126i	$-0.593546\pi$
$193$	−1553.36	−0.579342	−0.289671	+	0.957126i	$0.593546\pi$
$194$	−229.858	−0.0850661
$195$	0.528285	0.000194007 0
$196$	−4722.55	−1.72105
$197$	2582.66	0.934046	0.467023	−	0.884245i	$-0.345326\pi$
$197$	2582.66	0.934046	0.467023	+	0.884245i	$0.345326\pi$
$198$	−182.240	−0.0654103
$199$	1114.82	0.397121	0.198561	−	0.980089i	$-0.436373\pi$
$199$	1114.82	0.397121	0.198561	+	0.980089i	$0.436373\pi$
$200$	−708.045	−0.250332
$201$	−434.380	−0.152432
$202$	618.557	0.215453
$203$	−890.479	−0.307879
$204$	65.6937	0.0225465
$205$	10.6115	0.00361531
$206$	605.623	0.204834
$207$	−615.042	−0.206514
$208$	−1247.87	−0.415983
$209$	−1485.95	−0.491796
$210$	0.282798	9.29282e−5 0
$211$	−3638.71	−1.18720	−0.593600	−	0.804760i	$-0.702294\pi$
$211$	−3638.71	−1.18720	−0.593600	+	0.804760i	$0.702294\pi$
$212$	−1190.85	−0.385791
$213$	−604.595	−0.194489
$214$	389.437	0.124399
$215$	1.31018	0.000415599 0
$216$	−154.932	−0.0488047
$217$	4956.35	1.55050
$218$	−775.210	−0.240843
$219$	−407.785	−0.125824
$220$	−7.62325	−0.00233618
$221$	335.626	0.102157
$222$	−12.1285	−0.00366671
$223$	3814.16	1.14536	0.572679	−	0.819780i	$-0.305904\pi$
$223$	3814.16	1.14536	0.572679	+	0.819780i	$0.305904\pi$
$224$	−2059.48	−0.614307
$225$	3342.55	0.990386
$226$	779.103	0.229315
$227$	−3381.48	−0.988708	−0.494354	−	0.869261i	$-0.664595\pi$
$227$	−3381.48	−0.988708	−0.494354	+	0.869261i	$0.664595\pi$
$228$	−311.778	−0.0905615
$229$	750.967	0.216704	0.108352	−	0.994113i	$-0.465443\pi$
$229$	750.967	0.216704	0.108352	+	0.994113i	$0.465443\pi$
$230$	0.416200	0.000119319 0
$231$	−298.441	−0.0850042
$232$	−164.270	−0.0464864
$233$	68.5798	0.0192825	0.00964123	−	0.999954i	$-0.496931\pi$
$233$	68.5798	0.0192825	0.00964123	+	0.999954i	$0.496931\pi$
$234$	−195.351	−0.0545748
$235$	23.2209	0.00644580
$236$	−1595.24	−0.440006
$237$	−554.927	−0.152094
$238$	179.665	0.0489325
$239$	4611.54	1.24810	0.624049	−	0.781385i	$-0.285486\pi$
$239$	4611.54	1.24810	0.624049	+	0.781385i	$0.285486\pi$
$240$	−1.57320	−0.000423122 0
$241$	−750.047	−0.200476	−0.100238	−	0.994963i	$-0.531960\pi$
$241$	−750.047	−0.200476	−0.100238	+	0.994963i	$0.531960\pi$
$242$	344.851	0.0916027
$243$	1098.87	0.290094
$244$	−4664.35	−1.22379
$245$	−30.4172	−0.00793177
$246$	38.0102	0.00985139
$247$	−1592.86	−0.410328
$248$	914.315	0.234109
$249$	−104.439	−0.0265805
$250$	−4.52387	−0.00114446
$251$	−5362.38	−1.34849	−0.674244	−	0.738509i	$-0.735530\pi$
$251$	−5362.38	−1.34849	−0.674244	+	0.738509i	$0.735530\pi$
$252$	6464.33	1.61593
$253$	−439.222	−0.109145
$254$	200.005	0.0494071
$255$	0.423123	0.000103910 0
$256$	3459.39	0.844578
$257$	2569.59	0.623684	0.311842	−	0.950134i	$-0.399054\pi$
$257$	2569.59	0.623684	0.311842	+	0.950134i	$0.399054\pi$
$258$	4.69305	0.00113247
$259$	2050.43	0.491920
$260$	−8.17170	−0.00194918
$261$	775.488	0.183914
$262$	−408.658	−0.0963624
$263$	451.913	0.105955	0.0529774	−	0.998596i	$-0.483129\pi$
$263$	451.913	0.105955	0.0529774	+	0.998596i	$0.483129\pi$
$264$	−55.0545	−0.0128347
$265$	−7.67007	−0.00177799
$266$	−852.677	−0.196545
$267$	−261.592	−0.0599595
$268$	6719.15	1.53148
$269$	6683.86	1.51495	0.757476	−	0.652863i	$-0.226432\pi$
$269$	6683.86	1.51495	0.757476	+	0.652863i	$0.226432\pi$
$270$	−0.494944	−0.000111561 0
$271$	1918.99	0.430148	0.215074	−	0.976598i	$-0.431001\pi$
$271$	1918.99	0.430148	0.215074	+	0.976598i	$0.431001\pi$
$272$	−999.469	−0.222800
$273$	−319.912	−0.0709229
$274$	−574.121	−0.126584
$275$	2387.03	0.523429
$276$	−92.1563	−0.0200984
$277$	4472.68	0.970170	0.485085	−	0.874467i	$-0.338789\pi$
$277$	4472.68	0.970170	0.485085	+	0.874467i	$0.338789\pi$
$278$	−207.022	−0.0446631
$279$	−4316.32	−0.926205
$280$	−8.81960	−0.00188240
$281$	−1161.42	−0.246564	−0.123282	−	0.992372i	$-0.539342\pi$
$281$	−1161.42	−0.246564	−0.123282	+	0.992372i	$0.539342\pi$
$282$	83.1768	0.0175642
$283$	−4616.63	−0.969718	−0.484859	−	0.874592i	$-0.661129\pi$
$283$	−4616.63	−0.969718	−0.484859	+	0.874592i	$0.661129\pi$
$284$	9352.09	1.95403
$285$	−2.00812	−0.000417370 0
$286$	−139.507	−0.0288434
$287$	−6425.97	−1.32165
$288$	1793.53	0.366961
$289$	−4644.19	−0.945285
$290$	−0.524774	−0.000106261 0
$291$	327.812	0.0660368
$292$	6307.76	1.26416
$293$	9153.22	1.82504	0.912520	−	0.409031i	$-0.134133\pi$
$293$	9153.22	1.82504	0.912520	+	0.409031i	$0.134133\pi$
$294$	−108.954	−0.0216134
$295$	−10.2747	−0.00202785
$296$	378.250	0.0742748
$297$	522.322	0.102048
$298$	577.030	0.112169
$299$	−470.822	−0.0910646
$300$	500.839	0.0963865
$301$	−793.403	−0.151930
$302$	−643.971	−0.122703
$303$	−882.157	−0.167256
$304$	4743.42	0.894913
$305$	−30.0424	−0.00564007
$306$	−156.464	−0.0292302
$307$	9928.89	1.84584	0.922918	−	0.384997i	$-0.125797\pi$
$307$	9928.89	1.84584	0.922918	+	0.384997i	$0.125797\pi$
$308$	4616.39	0.854036
$309$	−863.711	−0.159012
$310$	2.92086	0.000535140 0
$311$	5136.54	0.936548	0.468274	−	0.883583i	$-0.344876\pi$
$311$	5136.54	0.936548	0.468274	+	0.883583i	$0.344876\pi$
$312$	−59.0153	−0.0107086
$313$	−3197.44	−0.577413	−0.288706	−	0.957418i	$-0.593225\pi$
$313$	−3197.44	−0.577413	−0.288706	+	0.957418i	$0.593225\pi$
$314$	120.357	0.0216310
$315$	41.6357	0.00744733
$316$	8583.80	1.52809
$317$	5300.25	0.939090	0.469545	−	0.882909i	$-0.344418\pi$
$317$	5300.25	0.939090	0.469545	+	0.882909i	$0.344418\pi$
$318$	−27.4741	−0.00484487
$319$	553.801	0.0972004
$320$	23.5147	0.00410785
$321$	−555.396	−0.0965707
$322$	−252.037	−0.0436194
$323$	−1275.78	−0.219772
$324$	−5574.50	−0.955848
$325$	2558.76	0.436721
$326$	500.045	0.0849538
$327$	1105.57	0.186966
$328$	−1185.42	−0.199555
$329$	−14061.8	−2.35639
$330$	−0.175876	−2.93384e−5 0
$331$	−7757.10	−1.28812	−0.644062	−	0.764973i	$-0.722752\pi$
$331$	−7757.10	−1.28812	−0.644062	+	0.764973i	$0.722752\pi$
$332$	1615.50	0.267054
$333$	−1785.65	−0.293853
$334$	−995.817	−0.163140
$335$	43.2770	0.00705813
$336$	952.675	0.154681
$337$	8749.29	1.41426	0.707128	−	0.707085i	$-0.249990\pi$
$337$	8749.29	1.41426	0.707128	+	0.707085i	$0.249990\pi$
$338$	634.501	0.102107
$339$	−1111.12	−0.178017
$340$	−6.54502	−0.00104398
$341$	−3082.42	−0.489509
$342$	742.568	0.117408
$343$	7887.44	1.24164
$344$	−146.362	−0.0229398
$345$	−0.593565	−9.26274e−5 0
$346$	715.990	0.111248
$347$	−5555.63	−0.859486	−0.429743	−	0.902951i	$-0.641396\pi$
$347$	−5555.63	−0.859486	−0.429743	+	0.902951i	$0.641396\pi$
$348$	116.197	0.0178989
$349$	−2617.13	−0.401409	−0.200704	−	0.979652i	$-0.564323\pi$
$349$	−2617.13	−0.401409	−0.200704	+	0.979652i	$0.564323\pi$
$350$	1369.74	0.209187
$351$	559.900	0.0851432
$352$	1280.82	0.193943
$353$	−4070.39	−0.613726	−0.306863	−	0.951754i	$-0.599279\pi$
$353$	−4070.39	−0.613726	−0.306863	+	0.951754i	$0.599279\pi$
$354$	−36.8039	−0.00552571
$355$	60.2354	0.00900553
$356$	4046.40	0.602412
$357$	−256.229	−0.0379863
$358$	−270.142	−0.0398811
$359$	−7581.97	−1.11466	−0.557328	−	0.830293i	$-0.688173\pi$
$359$	−7581.97	−1.11466	−0.557328	+	0.830293i	$0.688173\pi$
$360$	7.68069	0.00112447
$361$	−804.237	−0.117253
$362$	288.935	0.0419505
$363$	−491.810	−0.0711111
$364$	4948.51	0.712562
$365$	40.6273	0.00582611
$366$	−107.611	−0.0153687
$367$	4145.66	0.589651	0.294825	−	0.955551i	$-0.404739\pi$
$367$	4145.66	0.589651	0.294825	+	0.955551i	$0.404739\pi$
$368$	1402.07	0.198609
$369$	5596.16	0.789497
$370$	1.20835	0.000169782 0
$371$	4644.74	0.649981
$372$	−646.745	−0.0901403
$373$	343.034	0.0476183	0.0238092	−	0.999717i	$-0.492421\pi$
$373$	343.034	0.0476183	0.0238092	+	0.999717i	$0.492421\pi$
$374$	−111.736	−0.0154485
$375$	6.45172	0.000888441 0
$376$	−2594.03	−0.355790
$377$	593.645	0.0810988
$378$	299.722	0.0407831
$379$	−9755.12	−1.32213	−0.661064	−	0.750329i	$-0.729895\pi$
$379$	−9755.12	−1.32213	−0.661064	+	0.750329i	$0.729895\pi$
$380$	31.0622	0.00419331
$381$	−285.237	−0.0383547
$382$	−114.605	−0.0153500
$383$	−511.951	−0.0683015	−0.0341508	−	0.999417i	$-0.510873\pi$
$383$	−511.951	−0.0683015	−0.0341508	+	0.999417i	$0.510873\pi$
$384$	357.315	0.0474847
$385$	29.7334	0.00393599
$386$	554.347	0.0730972
$387$	690.948	0.0907568
$388$	−5070.72	−0.663471
$389$	3375.03	0.439899	0.219950	−	0.975511i	$-0.429411\pi$
$389$	3375.03	0.439899	0.219950	+	0.975511i	$0.429411\pi$
$390$	−0.188529	−2.44784e−5 0
$391$	−377.098	−0.0487741
$392$	3397.94	0.437811
$393$	582.808	0.0748061
$394$	−921.676	−0.117851
$395$	55.2869	0.00704250
$396$	−4020.26	−0.510165
$397$	−11907.5	−1.50534	−0.752669	−	0.658399i	$-0.771234\pi$
$397$	−11907.5	−1.50534	−0.752669	+	0.658399i	$0.771234\pi$
$398$	−397.845	−0.0501059
$399$	1216.05	0.152578
$400$	−7619.80	−0.952475
$401$	−3798.70	−0.473062	−0.236531	−	0.971624i	$-0.576011\pi$
$401$	−3798.70	−0.473062	−0.236531	+	0.971624i	$0.576011\pi$
$402$	155.018	0.0192328
$403$	−3304.19	−0.408420
$404$	13645.5	1.68042
$405$	−35.9045	−0.00440521
$406$	317.786	0.0388459
$407$	−1275.19	−0.155304
$408$	−47.2676	−0.00573552
$409$	3692.21	0.446377	0.223188	−	0.974775i	$-0.428354\pi$
$409$	3692.21	0.446377	0.223188	+	0.974775i	$0.428354\pi$
$410$	−3.78693	−0.000456154 0
$411$	818.785	0.0982668
$412$	13360.2	1.59759
$413$	6222.02	0.741322
$414$	219.490	0.0260564
$415$	10.4052	0.00123077
$416$	1372.97	0.161816
$417$	295.244	0.0346719
$418$	530.292	0.0620513
$419$	−10009.1	−1.16700	−0.583502	−	0.812112i	$-0.698318\pi$
$419$	−10009.1	−1.16700	−0.583502	+	0.812112i	$0.698318\pi$
$420$	6.23859	0.000724790 0
$421$	−7349.88	−0.850858	−0.425429	−	0.904992i	$-0.639877\pi$
$421$	−7349.88	−0.850858	−0.425429	+	0.904992i	$0.639877\pi$
$422$	1298.55	0.149792
$423$	12245.9	1.40761
$424$	856.832	0.0981402
$425$	2049.40	0.233908
$426$	215.762	0.0245392
$427$	18192.7	2.06184
$428$	8591.06	0.970245
$429$	198.958	0.0223911
$430$	−0.467565	−5.24372e−5 0
$431$	−16663.7	−1.86232	−0.931161	−	0.364608i	$-0.881203\pi$
$431$	−16663.7	−1.86232	−0.931161	+	0.364608i	$0.881203\pi$
$432$	−1667.34	−0.185694
$433$	−1313.16	−0.145742	−0.0728710	−	0.997341i	$-0.523216\pi$
$433$	−1313.16	−0.145742	−0.0728710	+	0.997341i	$0.523216\pi$
$434$	−1768.77	−0.195631
$435$	0.748407	8.24906e−5 0
$436$	−17101.3	−1.87845
$437$	1789.68	0.195909
$438$	145.526	0.0158756
$439$	16761.6	1.82230	0.911149	−	0.412076i	$-0.135196\pi$
$439$	16761.6	1.82230	0.911149	+	0.412076i	$0.135196\pi$
$440$	5.48504	0.000594293 0
$441$	−16041.1	−1.73211
$442$	−119.775	−0.0128894
$443$	−12937.1	−1.38749	−0.693746	−	0.720219i	$-0.744041\pi$
$443$	−12937.1	−1.38749	−0.693746	+	0.720219i	$0.744041\pi$
$444$	−267.557	−0.0285984
$445$	26.0622	0.00277633
$446$	−1361.16	−0.144513
$447$	−822.933	−0.0870769
$448$	−14239.7	−1.50171
$449$	6917.05	0.727028	0.363514	−	0.931589i	$-0.381577\pi$
$449$	6917.05	0.727028	0.363514	+	0.931589i	$0.381577\pi$
$450$	−1192.86	−0.124960
$451$	3996.40	0.417258
$452$	17187.2	1.78853
$453$	918.402	0.0952545
$454$	1206.75	0.124748
$455$	31.8726	0.00328398
$456$	224.329	0.0230376
$457$	17620.1	1.80357	0.901785	−	0.432184i	$-0.142257\pi$
$457$	17620.1	1.80357	0.901785	+	0.432184i	$0.142257\pi$
$458$	−267.998	−0.0273422
$459$	448.445	0.0456026
$460$	9.18146	0.000930626 0
$461$	412.462	0.0416709	0.0208355	−	0.999783i	$-0.493367\pi$
$461$	412.462	0.0416709	0.0208355	+	0.999783i	$0.493367\pi$
$462$	106.505	0.0107252
$463$	−994.546	−0.0998282	−0.0499141	−	0.998754i	$-0.515895\pi$
$463$	−994.546	−0.0998282	−0.0499141	+	0.998754i	$0.515895\pi$
$464$	−1767.83	−0.176874
$465$	−4.16559	−0.000415429 0
$466$	−24.4741	−0.00243292
$467$	6742.04	0.668061	0.334031	−	0.942562i	$-0.391591\pi$
$467$	6742.04	0.668061	0.334031	+	0.942562i	$0.391591\pi$
$468$	−4309.49	−0.425655
$469$	−26207.1	−2.58024
$470$	−8.28685	−0.000813284 0
$471$	−171.647	−0.0167921
$472$	1147.80	0.111932
$473$	493.429	0.0479659
$474$	198.037	0.0191902
$475$	−9726.34	−0.939527
$476$	3963.44	0.381647
$477$	−4044.95	−0.388271
$478$	−1645.72	−0.157476
$479$	−295.339	−0.0281719	−0.0140860	−	0.999901i	$-0.504484\pi$
$479$	−295.339	−0.0281719	−0.0140860	+	0.999901i	$0.504484\pi$
$480$	1.73090	0.000164592 0
$481$	−1366.93	−0.129578
$482$	267.669	0.0252946
$483$	359.443	0.0338617
$484$	7607.49	0.714453
$485$	−32.6597	−0.00305773
$486$	−392.155	−0.0366019
$487$	10526.6	0.979477	0.489738	−	0.871869i	$-0.337092\pi$
$487$	10526.6	0.979477	0.489738	+	0.871869i	$0.337092\pi$
$488$	3356.07	0.311316
$489$	−713.140	−0.0659495
$490$	10.8550	0.00100077
$491$	−12741.0	−1.17107	−0.585534	−	0.810648i	$-0.699115\pi$
$491$	−12741.0	−1.17107	−0.585534	+	0.810648i	$0.699115\pi$
$492$	838.514	0.0768356
$493$	475.472	0.0434364
$494$	568.444	0.0517723
$495$	−25.8939	−0.00235120
$496$	9839.63	0.890751
$497$	−36476.5	−3.29215
$498$	37.2712	0.00335374
$499$	18078.0	1.62181	0.810903	−	0.585180i	$-0.198976\pi$
$499$	18078.0	1.62181	0.810903	+	0.585180i	$0.198976\pi$
$500$	−99.7975	−0.00892616
$501$	1420.19	0.126645
$502$	1913.68	0.170142
$503$	5063.56	0.448853	0.224427	−	0.974491i	$-0.427949\pi$
$503$	5063.56	0.448853	0.224427	+	0.974491i	$0.427949\pi$
$504$	−4651.17	−0.411071
$505$	87.8886	0.00774454
$506$	156.745	0.0137711
$507$	−904.895	−0.0792659
$508$	4412.15	0.385349
$509$	8982.89	0.782239	0.391119	−	0.920340i	$-0.372088\pi$
$509$	8982.89	0.782239	0.391119	+	0.920340i	$0.372088\pi$
$510$	−0.151000	−1.31106e−5 0
$511$	−24602.6	−2.12985
$512$	−6851.03	−0.591359
$513$	−2128.29	−0.183170
$514$	−917.011	−0.0786919
$515$	86.0509	0.00736282
$516$	103.530	0.00883265
$517$	8745.23	0.743936
$518$	−731.737	−0.0620669
$519$	−1021.11	−0.0863619
$520$	5.87966	0.000495846 0
$521$	6948.21	0.584274	0.292137	−	0.956377i	$-0.405634\pi$
$521$	6948.21	0.584274	0.292137	+	0.956377i	$0.405634\pi$
$522$	−276.749	−0.0232049
$523$	−10670.8	−0.892163	−0.446081	−	0.894992i	$-0.647181\pi$
$523$	−10670.8	−0.892163	−0.446081	+	0.894992i	$0.647181\pi$
$524$	−9015.08	−0.751576
$525$	−1953.45	−0.162392
$526$	−161.274	−0.0133686
$527$	−2646.44	−0.218749
$528$	−592.482	−0.0488342
$529$	529.000	0.0434783
$530$	2.73722	0.000224334 0
$531$	−5418.55	−0.442835
$532$	−18810.3	−1.53295
$533$	4283.92	0.348137
$534$	93.3545	0.00756525
$535$	55.3337	0.00447156
$536$	−4834.52	−0.389589
$537$	385.264	0.0309597
$538$	−2385.27	−0.191146
$539$	−11455.4	−0.915438
$540$	−10.9186	−0.000870113 0
$541$	−12355.4	−0.981887	−0.490944	−	0.871191i	$-0.663348\pi$
$541$	−12355.4	−0.981887	−0.490944	+	0.871191i	$0.663348\pi$
$542$	−684.830	−0.0542730
$543$	−412.066	−0.0325662
$544$	1099.66	0.0866682
$545$	−110.147	−0.00865720
$546$	114.167	0.00894854
$547$	5023.95	0.392703	0.196351	−	0.980534i	$-0.437091\pi$
$547$	5023.95	0.392703	0.196351	+	0.980534i	$0.437091\pi$
$548$	−12665.2	−0.987286
$549$	−15843.4	−1.23166
$550$	−851.859	−0.0660425
$551$	−2256.56	−0.174469
$552$	66.3077	0.00511276
$553$	−33479.9	−2.57452
$554$	−1596.17	−0.122409
$555$	−1.72329	−0.000131801 0
$556$	−4566.94	−0.348348
$557$	−13047.4	−0.992526	−0.496263	−	0.868172i	$-0.665295\pi$
$557$	−13047.4	−0.992526	−0.496263	+	0.868172i	$0.665295\pi$
$558$	1540.37	0.116862
$559$	528.928	0.0400202
$560$	−94.9143	−0.00716225
$561$	159.353	0.0119926
$562$	414.476	0.0311096
$563$	−10727.5	−0.803041	−0.401520	−	0.915850i	$-0.631518\pi$
$563$	−10727.5	−0.803041	−0.401520	+	0.915850i	$0.631518\pi$
$564$	1834.90	0.136992
$565$	110.700	0.00824280
$566$	1647.54	0.122352
$567$	21742.6	1.61041
$568$	−6728.96	−0.497079
$569$	3049.96	0.224712	0.112356	−	0.993668i	$-0.464160\pi$
$569$	3049.96	0.224712	0.112356	+	0.993668i	$0.464160\pi$
$570$	0.716637	5.26607e−5 0
$571$	12126.2	0.888733	0.444367	−	0.895845i	$-0.353429\pi$
$571$	12126.2	0.888733	0.444367	+	0.895845i	$0.353429\pi$
$572$	−3077.55	−0.224963
$573$	163.444	0.0119162
$574$	2293.24	0.166756
$575$	−2874.94	−0.208510
$576$	12400.9	0.897056
$577$	6199.69	0.447308	0.223654	−	0.974669i	$-0.428202\pi$
$577$	6199.69	0.447308	0.223654	+	0.974669i	$0.428202\pi$
$578$	1657.37	0.119269
$579$	−790.583	−0.0567453
$580$	−11.5766	−0.000828782 0
$581$	−6301.03	−0.449932
$582$	−116.987	−0.00833204
$583$	−2888.63	−0.205205
$584$	−4538.52	−0.321585
$585$	−27.7568	−0.00196171
$586$	−3266.51	−0.230270
$587$	16072.8	1.13014	0.565072	−	0.825042i	$-0.308848\pi$
$587$	16072.8	1.13014	0.565072	+	0.825042i	$0.308848\pi$
$588$	−2403.55	−0.168573
$589$	12559.9	0.878642
$590$	3.66674	0.000255860 0
$591$	1314.45	0.0914878
$592$	4070.63	0.282604
$593$	−11781.5	−0.815867	−0.407933	−	0.913012i	$-0.633750\pi$
$593$	−11781.5	−0.815867	−0.407933	+	0.913012i	$0.633750\pi$
$594$	−186.401	−0.0128756
$595$	25.5279	0.00175890
$596$	12729.4	0.874861
$597$	567.387	0.0388972
$598$	168.022	0.0114899
$599$	−1366.10	−0.0931841	−0.0465920	−	0.998914i	$-0.514836\pi$
$599$	−1366.10	−0.0931841	−0.0465920	+	0.998914i	$0.514836\pi$
$600$	−360.361	−0.0245194
$601$	17875.2	1.21322	0.606609	−	0.795000i	$-0.292529\pi$
$601$	17875.2	1.21322	0.606609	+	0.795000i	$0.292529\pi$
$602$	283.142	0.0191695
$603$	22822.9	1.54133
$604$	−14206.2	−0.957020
$605$	48.9987	0.00329269
$606$	314.816	0.0211032
$607$	5168.05	0.345576	0.172788	−	0.984959i	$-0.444722\pi$
$607$	5168.05	0.345576	0.172788	+	0.984959i	$0.444722\pi$
$608$	−5218.92	−0.348117
$609$	−453.211	−0.0301560
$610$	10.7212	0.000711623 0
$611$	9374.40	0.620700
$612$	−3451.63	−0.227980
$613$	−7011.09	−0.461950	−0.230975	−	0.972960i	$-0.574191\pi$
$613$	−7011.09	−0.461950	−0.230975	+	0.972960i	$0.574191\pi$
$614$	−3543.33	−0.232894
$615$	5.40074	0.000354112 0
$616$	−3321.56	−0.217255
$617$	−18367.7	−1.19847	−0.599235	−	0.800573i	$-0.704529\pi$
$617$	−18367.7	−1.19847	−0.599235	+	0.800573i	$0.704529\pi$
$618$	308.233	0.0200630
$619$	−10658.4	−0.692078	−0.346039	−	0.938220i	$-0.612473\pi$
$619$	−10658.4	−0.692078	−0.346039	+	0.938220i	$0.612473\pi$
$620$	64.4348	0.00417381
$621$	−629.086	−0.0406511
$622$	−1833.08	−0.118167
$623$	−15782.4	−1.01494
$624$	−635.108	−0.0407447
$625$	15624.0	0.999938
$626$	1141.07	0.0728538
$627$	−756.278	−0.0481704
$628$	2655.10	0.168710
$629$	−1094.83	−0.0694016
$630$	−14.8586	−0.000939650 0
$631$	333.929	0.0210674	0.0105337	−	0.999945i	$-0.496647\pi$
$631$	333.929	0.0210674	0.0105337	+	0.999945i	$0.496647\pi$
$632$	−6176.17	−0.388726
$633$	−1851.93	−0.116284
$634$	−1891.50	−0.118488
$635$	28.4180	0.00177596
$636$	−606.084	−0.0377874
$637$	−12279.6	−0.763792
$638$	−197.635	−0.0122640
$639$	31766.2	1.96659
$640$	−35.5990	−0.00219871
$641$	−20910.9	−1.28851	−0.644253	−	0.764812i	$-0.722832\pi$
$641$	−20910.9	−1.28851	−0.644253	+	0.764812i	$0.722832\pi$
$642$	198.204	0.0121846
$643$	27592.9	1.69231	0.846156	−	0.532935i	$-0.178911\pi$
$643$	27592.9	1.69231	0.846156	+	0.532935i	$0.178911\pi$
$644$	−5559.99	−0.340208
$645$	0.666820	4.07070e−5 0
$646$	455.288	0.0277292
$647$	−22869.1	−1.38961	−0.694805	−	0.719198i	$-0.744509\pi$
$647$	−22869.1	−1.38961	−0.694805	+	0.719198i	$0.744509\pi$
$648$	4010.93	0.243155
$649$	−3869.57	−0.234043
$650$	−913.146	−0.0551024
$651$	2522.54	0.151868
$652$	11031.1	0.662594
$653$	2971.93	0.178102	0.0890510	−	0.996027i	$-0.471617\pi$
$653$	2971.93	0.178102	0.0890510	+	0.996027i	$0.471617\pi$
$654$	−394.544	−0.0235901
$655$	−58.0647	−0.00346378
$656$	−12757.2	−0.759276
$657$	21425.5	1.27228
$658$	5018.24	0.297312
$659$	2883.78	0.170465	0.0852324	−	0.996361i	$-0.472837\pi$
$659$	2883.78	0.170465	0.0852324	+	0.996361i	$0.472837\pi$
$660$	−3.87987	−0.000228824 0
$661$	6382.86	0.375589	0.187795	−	0.982208i	$-0.439866\pi$
$661$	6382.86	0.375589	0.187795	+	0.982208i	$0.439866\pi$
$662$	2768.28	0.162526
$663$	170.817	0.0100060
$664$	−1162.37	−0.0679350
$665$	−121.154	−0.00706489
$666$	637.245	0.0370762
$667$	−667.000	−0.0387202
$668$	−21967.9	−1.27240
$669$	1941.22	0.112185
$670$	−15.4443	−0.000890544 0
$671$	−11314.3	−0.650943
$672$	−1048.18	−0.0601700
$673$	22170.7	1.26986	0.634931	−	0.772569i	$-0.281028\pi$
$673$	22170.7	1.26986	0.634931	+	0.772569i	$0.281028\pi$
$674$	−3122.36	−0.178441
$675$	3418.87	0.194952
$676$	13997.2	0.796383
$677$	−24443.3	−1.38764	−0.693819	−	0.720149i	$-0.744073\pi$
$677$	−24443.3	−1.38764	−0.693819	+	0.720149i	$0.744073\pi$
$678$	396.526	0.0224609
$679$	19777.6	1.11781
$680$	4.70923	0.000265575 0
$681$	−1721.01	−0.0968418
$682$	1100.03	0.0617627
$683$	−31348.1	−1.75622	−0.878111	−	0.478456i	$-0.841196\pi$
$683$	−31348.1	−1.75622	−0.878111	+	0.478456i	$0.841196\pi$
$684$	16381.2	0.915719
$685$	−81.5749	−0.00455010
$686$	−2814.79	−0.156661
$687$	382.206	0.0212257
$688$	−1575.11	−0.0872827
$689$	−3096.45	−0.171212
$690$	0.211826	1.16871e−5 0
$691$	21016.2	1.15701	0.578504	−	0.815680i	$-0.303637\pi$
$691$	21016.2	1.15701	0.578504	+	0.815680i	$0.303637\pi$
$692$	15794.9	0.867676
$693$	15680.5	0.859526
$694$	1982.64	0.108444
$695$	−29.4150	−0.00160543
$696$	−83.6054	−0.00455324
$697$	3431.15	0.186462
$698$	933.975	0.0506468
$699$	34.9038	0.00188867
$700$	30216.7	1.63155
$701$	360.128	0.0194035	0.00970175	−	0.999953i	$-0.496912\pi$
$701$	360.128	0.0194035	0.00970175	+	0.999953i	$0.496912\pi$
$702$	−199.812	−0.0107428
$703$	5195.98	0.278763
$704$	8855.89	0.474104
$705$	11.8183	0.000631352 0
$706$	1452.60	0.0774355
$707$	−53222.4	−2.83117
$708$	−811.902	−0.0430976
$709$	17207.6	0.911489	0.455744	−	0.890111i	$-0.349373\pi$
$709$	17207.6	0.911489	0.455744	+	0.890111i	$0.349373\pi$
$710$	−21.4962	−0.00113625
$711$	29156.6	1.53791
$712$	−2911.44	−0.153246
$713$	3712.48	0.194998
$714$	91.4407	0.00479283
$715$	−19.8220	−0.00103679
$716$	−5959.39	−0.311052
$717$	2347.05	0.122248
$718$	2705.78	0.140639
$719$	31959.3	1.65769	0.828847	−	0.559475i	$-0.188997\pi$
$719$	31959.3	1.65769	0.828847	+	0.559475i	$0.188997\pi$
$720$	82.6577	0.00427843
$721$	−52109.5	−2.69162
$722$	287.008	0.0147941
$723$	−381.738	−0.0196362
$724$	6373.98	0.327192
$725$	3624.93	0.185692
$726$	175.513	0.00897229
$727$	15067.3	0.768660	0.384330	−	0.923196i	$-0.374433\pi$
$727$	15067.3	0.768660	0.384330	+	0.923196i	$0.374433\pi$
$728$	−3560.52	−0.181266
$729$	−18559.0	−0.942897
$730$	−14.4987	−0.000735097 0
$731$	423.638	0.0214348
$732$	−2373.93	−0.119867
$733$	−14152.7	−0.713155	−0.356577	−	0.934266i	$-0.616056\pi$
$733$	−14152.7	−0.713155	−0.356577	+	0.934266i	$0.616056\pi$
$734$	−1479.46	−0.0743979
$735$	−15.4809	−0.000776900 0
$736$	−1542.62	−0.0772579
$737$	16298.6	0.814608
$738$	−1997.10	−0.0996130
$739$	−33349.5	−1.66005	−0.830027	−	0.557723i	$-0.811675\pi$
$739$	−33349.5	−1.66005	−0.830027	+	0.557723i	$0.811675\pi$
$740$	26.6565	0.00132421
$741$	−810.688	−0.0401908
$742$	−1657.57	−0.0820098
$743$	32232.3	1.59151	0.795753	−	0.605621i	$-0.207075\pi$
$743$	32232.3	1.59151	0.795753	+	0.605621i	$0.207075\pi$
$744$	465.342	0.0229305
$745$	81.9882	0.00403197
$746$	−122.419	−0.00600814
$747$	5487.35	0.268771
$748$	−2464.92	−0.120490
$749$	−33508.3	−1.63467
$750$	−2.30243	−0.000112097 0
$751$	−3434.71	−0.166890	−0.0834450	−	0.996512i	$-0.526592\pi$
$751$	−3434.71	−0.166890	−0.0834450	+	0.996512i	$0.526592\pi$
$752$	−27916.3	−1.35373
$753$	−2729.19	−0.132081
$754$	−211.854	−0.0102325
$755$	−91.4997	−0.00441061
$756$	6611.93	0.318087
$757$	5064.72	0.243171	0.121586	−	0.992581i	$-0.461202\pi$
$757$	5064.72	0.243171	0.121586	+	0.992581i	$0.461202\pi$
$758$	3481.31	0.166817
$759$	−223.543	−0.0106905
$760$	−22.3497	−0.00106672
$761$	−20604.9	−0.981509	−0.490754	−	0.871298i	$-0.663279\pi$
$761$	−20604.9	−0.981509	−0.490754	+	0.871298i	$0.663279\pi$
$762$	101.793	0.00483932
$763$	66701.3	3.16481
$764$	−2528.21	−0.119722
$765$	−22.2314	−0.00105069
$766$	182.700	0.00861779
$767$	−4147.96	−0.195273
$768$	1760.66	0.0827245
$769$	−17104.0	−0.802062	−0.401031	−	0.916064i	$-0.631348\pi$
$769$	−17104.0	−0.802062	−0.401031	+	0.916064i	$0.631348\pi$
$770$	−10.6110	−0.000496615 0
$771$	1307.80	0.0610885
$772$	12229.0	0.570119
$773$	2552.40	0.118762	0.0593812	−	0.998235i	$-0.481087\pi$
$773$	2552.40	0.118762	0.0593812	+	0.998235i	$0.481087\pi$
$774$	−246.579	−0.0114510
$775$	−20176.1	−0.935157
$776$	3648.45	0.168778
$777$	1043.57	0.0481825
$778$	−1204.45	−0.0555033
$779$	−16284.0	−0.748954
$780$	−4.15900	−0.000190918 0
$781$	22685.3	1.03936
$782$	134.575	0.00615396
$783$	793.195	0.0362024
$784$	36567.8	1.66581
$785$	17.1011	0.000777533 0
$786$	−207.987	−0.00943849
$787$	−29589.4	−1.34021	−0.670106	−	0.742265i	$-0.733751\pi$
$787$	−29589.4	−1.34021	−0.670106	+	0.742265i	$0.733751\pi$
$788$	−20332.4	−0.919177
$789$	230.002	0.0103780
$790$	−19.7303	−0.000888572 0
$791$	−67036.2	−3.01332
$792$	2892.63	0.129779
$793$	−12128.3	−0.543112
$794$	4249.43	0.189933
$795$	−3.90369	−0.000174151 0
$796$	−8776.54	−0.390799
$797$	−23553.1	−1.04679	−0.523397	−	0.852089i	$-0.675336\pi$
$797$	−23553.1	−1.04679	−0.523397	+	0.852089i	$0.675336\pi$
$798$	−433.972	−0.0192512
$799$	7508.30	0.332446
$800$	8383.64	0.370508
$801$	13744.4	0.606284
$802$	1355.64	0.0596876
$803$	15300.7	0.672415
$804$	3419.72	0.150005
$805$	−35.8110	−0.00156792
$806$	1179.17	0.0515315
$807$	3401.76	0.148386
$808$	−9818.14	−0.427476
$809$	5750.95	0.249929	0.124964	−	0.992161i	$-0.460118\pi$
$809$	5750.95	0.249929	0.124964	+	0.992161i	$0.460118\pi$
$810$	12.8133	0.000555818 0
$811$	779.583	0.0337545	0.0168772	−	0.999858i	$-0.494628\pi$
$811$	779.583	0.0337545	0.0168772	+	0.999858i	$0.494628\pi$
$812$	7010.42	0.302977
$813$	976.672	0.0421321
$814$	455.078	0.0195952
$815$	71.0496	0.00305369
$816$	−508.681	−0.0218228
$817$	−2010.56	−0.0860962
$818$	−1317.64	−0.0563206
$819$	16808.6	0.717142
$820$	−83.5405	−0.00355776
$821$	−16252.5	−0.690883	−0.345441	−	0.938440i	$-0.612271\pi$
$821$	−16252.5	−0.690883	−0.345441	+	0.938440i	$0.612271\pi$
$822$	−292.200	−0.0123986
$823$	39943.4	1.69179	0.845893	−	0.533353i	$-0.179068\pi$
$823$	39943.4	1.69179	0.845893	+	0.533353i	$0.179068\pi$
$824$	−9612.84	−0.406407
$825$	1214.88	0.0512688
$826$	−2220.46	−0.0935346
$827$	−36663.9	−1.54163	−0.770815	−	0.637059i	$-0.780151\pi$
$827$	−36663.9	−1.54163	−0.770815	+	0.637059i	$0.780151\pi$
$828$	4842.01	0.203226
$829$	−35797.7	−1.49976	−0.749882	−	0.661572i	$-0.769890\pi$
$829$	−35797.7	−1.49976	−0.749882	+	0.661572i	$0.769890\pi$
$830$	−3.71330	−0.000155290 0
$831$	2276.38	0.0950260
$832$	9493.03	0.395567
$833$	−9835.19	−0.409086
$834$	−105.364	−0.00437465
$835$	−141.492	−0.00586412
$836$	11698.4	0.483967
$837$	−4414.87	−0.182318
$838$	3571.94	0.147244
$839$	29102.2	1.19752	0.598760	−	0.800929i	$-0.295660\pi$
$839$	29102.2	1.19752	0.598760	+	0.800929i	$0.295660\pi$
$840$	−4.48875	−0.000184377 0
$841$	841.000	0.0344828
$842$	2622.96	0.107355
$843$	−591.106	−0.0241504
$844$	28646.3	1.16830
$845$	90.1540	0.00367029
$846$	−4370.22	−0.177602
$847$	−29672.0	−1.20371
$848$	9221.01	0.373409
$849$	−2349.64	−0.0949818
$850$	−731.372	−0.0295128
$851$	1535.84	0.0618661
$852$	4759.76	0.191393
$853$	35538.7	1.42652	0.713261	−	0.700899i	$-0.247218\pi$
$853$	35538.7	1.42652	0.713261	+	0.700899i	$0.247218\pi$
$854$	−6492.42	−0.260148
$855$	105.509	0.00422027
$856$	−6181.39	−0.246817
$857$	−37616.9	−1.49938	−0.749690	−	0.661789i	$-0.769797\pi$
$857$	−37616.9	−1.49938	−0.749690	+	0.661789i	$0.769797\pi$
$858$	−71.0022	−0.00282515
$859$	25324.6	1.00590	0.502949	−	0.864316i	$-0.332248\pi$
$859$	25324.6	1.00590	0.502949	+	0.864316i	$0.332248\pi$
$860$	−10.3146	−0.000408983 0
$861$	−3270.51	−0.129452
$862$	5946.77	0.234974
$863$	−48875.5	−1.92786	−0.963929	−	0.266160i	$-0.914245\pi$
$863$	−48875.5	−1.92786	−0.963929	+	0.266160i	$0.914245\pi$
$864$	1834.48	0.0722342
$865$	101.733	0.00399886
$866$	468.627	0.0183887
$867$	−2363.67	−0.0925886
$868$	−39019.5	−1.52582
$869$	20821.7	0.812803
$870$	−0.267085	−1.04081e−5 0
$871$	17471.2	0.679665
$872$	12304.6	0.477852
$873$	−17223.7	−0.667736
$874$	−638.685	−0.0247184
$875$	389.246	0.0150388
$876$	3210.35	0.123821
$877$	−27894.4	−1.07403	−0.537016	−	0.843572i	$-0.680449\pi$
$877$	−27894.4	−1.07403	−0.537016	+	0.843572i	$0.680449\pi$
$878$	−5981.73	−0.229924
$879$	4658.55	0.178759
$880$	59.0286	0.00226120
$881$	34425.3	1.31648	0.658240	−	0.752808i	$-0.271301\pi$
$881$	34425.3	1.31648	0.658240	+	0.752808i	$0.271301\pi$
$882$	5724.58	0.218545
$883$	−17096.4	−0.651575	−0.325788	−	0.945443i	$-0.605629\pi$
$883$	−17096.4	−0.651575	−0.325788	+	0.945443i	$0.605629\pi$
$884$	−2642.26	−0.100530
$885$	−5.22933	−0.000198624 0
$886$	4616.86	0.175064
$887$	43117.3	1.63217	0.816086	−	0.577931i	$-0.196140\pi$
$887$	43117.3	1.63217	0.816086	+	0.577931i	$0.196140\pi$
$888$	192.511	0.00727505
$889$	−17209.0	−0.649236
$890$	−9.30084	−0.000350298 0
$891$	−13522.0	−0.508423
$892$	−30027.5	−1.12712
$893$	−35633.9	−1.33532
$894$	293.680	0.0109867
$895$	−38.3835	−0.00143354
$896$	21557.6	0.803781
$897$	−239.625	−0.00891958
$898$	−2468.49	−0.0917311
$899$	−4680.95	−0.173658
$900$	−26314.7	−0.974619
$901$	−2480.06	−0.0917012
$902$	−1426.20	−0.0526465
$903$	−403.804	−0.0148812
$904$	−12366.4	−0.454979
$905$	41.0538	0.00150793
$906$	−327.750	−0.0120185
$907$	18397.2	0.673503	0.336752	−	0.941594i	$-0.390672\pi$
$907$	18397.2	0.673503	0.336752	+	0.941594i	$0.390672\pi$
$908$	26621.2	0.972969
$909$	46349.6	1.69122
$910$	−11.3744	−0.000414349 0
$911$	19131.5	0.695779	0.347890	−	0.937536i	$-0.386898\pi$
$911$	19131.5	0.695779	0.347890	+	0.937536i	$0.386898\pi$
$912$	2414.17	0.0876548
$913$	3918.70	0.142048
$914$	−6288.08	−0.227561
$915$	−15.2901	−0.000552432 0
$916$	−5912.09	−0.213254
$917$	35162.1	1.26625
$918$	−160.037	−0.00575381
$919$	14293.9	0.513071	0.256535	−	0.966535i	$-0.417419\pi$
$919$	14293.9	0.513071	0.256535	+	0.966535i	$0.417419\pi$
$920$	−6.60619	−0.000236739 0
$921$	5053.32	0.180796
$922$	−147.196	−0.00525773
$923$	24317.4	0.867190
$924$	2349.52	0.0836509
$925$	−8346.80	−0.296693
$926$	354.924	0.0125956
$927$	45380.4	1.60786
$928$	1945.05	0.0688031
$929$	28956.0	1.02262	0.511311	−	0.859396i	$-0.329160\pi$
$929$	28956.0	1.02262	0.511311	+	0.859396i	$0.329160\pi$
$930$	1.48657	5.24158e−5 0
$931$	46677.2	1.64316
$932$	−539.904	−0.0189755
$933$	2614.25	0.0917329
$934$	−2406.04	−0.0842911
$935$	−15.8762	−0.000555302 0
$936$	3100.74	0.108281
$937$	17875.9	0.623246	0.311623	−	0.950206i	$-0.399127\pi$
$937$	17875.9	0.623246	0.311623	+	0.950206i	$0.399127\pi$
$938$	9352.54	0.325556
$939$	−1627.34	−0.0565563
$940$	−182.810	−0.00634319
$941$	37424.0	1.29648	0.648240	−	0.761436i	$-0.275505\pi$
$941$	37424.0	1.29648	0.648240	+	0.761436i	$0.275505\pi$
$942$	61.2558	0.00211871
$943$	−4813.28	−0.166216
$944$	12352.3	0.425883
$945$	42.5864	0.00146596
$946$	−176.090	−0.00605199
$947$	−56242.3	−1.92992	−0.964958	−	0.262404i	$-0.915485\pi$
$947$	−56242.3	−1.92992	−0.964958	+	0.262404i	$0.915485\pi$
$948$	4368.74	0.149673
$949$	16401.5	0.561027
$950$	3471.05	0.118543
$951$	2697.57	0.0919818
$952$	−2851.75	−0.0970860
$953$	−1943.37	−0.0660565	−0.0330282	−	0.999454i	$-0.510515\pi$
$953$	−1943.37	−0.0660565	−0.0330282	+	0.999454i	$0.510515\pi$
$954$	1443.52	0.0489893
$955$	−16.2838	−0.000551760 0
$956$	−36305.0	−1.22823
$957$	281.858	0.00952057
$958$	105.398	0.00355453
$959$	49399.1	1.66338
$960$	11.9679	0.000402355 0
$961$	−3737.13	−0.125445
$962$	487.818	0.0163492
$963$	29181.2	0.976481
$964$	5904.85	0.197285
$965$	78.7652	0.00262751
$966$	−128.275	−0.00427243
$967$	13184.7	0.438462	0.219231	−	0.975673i	$-0.429645\pi$
$967$	13184.7	0.438462	0.219231	+	0.975673i	$0.429645\pi$
$968$	−5473.70	−0.181747
$969$	−649.310	−0.0215261
$970$	11.6553	0.000385803 0
$971$	33985.0	1.12320	0.561601	−	0.827408i	$-0.310186\pi$
$971$	33985.0	1.12320	0.561601	+	0.827408i	$0.310186\pi$
$972$	−8651.04	−0.285476
$973$	17812.7	0.586896
$974$	−3756.63	−0.123583
$975$	1302.29	0.0427759
$976$	36117.1	1.18451
$977$	−14902.9	−0.488010	−0.244005	−	0.969774i	$-0.578461\pi$
$977$	−14902.9	−0.488010	−0.244005	+	0.969774i	$0.578461\pi$
$978$	254.499	0.00832103
$979$	9815.31	0.320428
$980$	239.464	0.00780550
$981$	−58087.9	−1.89052
$982$	4546.89	0.147757
$983$	50377.4	1.63458	0.817289	−	0.576228i	$-0.195476\pi$
$983$	50377.4	1.63458	0.817289	+	0.576228i	$0.195476\pi$
$984$	−603.322	−0.0195459
$985$	−130.958	−0.00423620
$986$	−169.682	−0.00548050
$987$	−7156.77	−0.230803
$988$	12540.0	0.403796
$989$	−594.287	−0.0191074
$990$	9.24075	0.000296657 0
$991$	37498.0	1.20198	0.600990	−	0.799256i	$-0.294773\pi$
$991$	37498.0	1.20198	0.600990	+	0.799256i	$0.294773\pi$
$992$	−10826.0	−0.346498
$993$	−3947.99	−0.126169
$994$	13017.4	0.415379
$995$	−56.5284	−0.00180107
$996$	822.210	0.0261574
$997$	−29907.2	−0.950022	−0.475011	−	0.879980i	$-0.657556\pi$
$997$	−29907.2	−0.950022	−0.475011	+	0.879980i	$0.657556\pi$
$998$	−6451.50	−0.204628
$999$	−1826.42	−0.0578433

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.a.1.18	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.a.1.18	✓	35	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q-0.356870 q^{2} +0.508952 q^{3} -7.87264 q^{4} -0.0507065 q^{5} -0.181630 q^{6} +30.7062 q^{7} +5.66448 q^{8} -26.7410 q^{9} +O(q^{10})\)	\(q-0.356870 q^{2} +0.508952 q^{3} -7.87264 q^{4} -0.0507065 q^{5} -0.181630 q^{6} +30.7062 q^{7} +5.66448 q^{8} -26.7410 q^{9} +0.0180956 q^{10} -19.0966 q^{11} -4.00680 q^{12} -20.4705 q^{13} -10.9581 q^{14} -0.0258072 q^{15} +60.9597 q^{16} -16.3956 q^{17} +9.54306 q^{18} +77.8124 q^{19} +0.399194 q^{20} +15.6280 q^{21} +6.81501 q^{22} +23.0000 q^{23} +2.88295 q^{24} -124.997 q^{25} +7.30532 q^{26} -27.3516 q^{27} -241.739 q^{28} -29.0000 q^{29} +0.00920981 q^{30} +161.412 q^{31} -67.0705 q^{32} -9.71925 q^{33} +5.85110 q^{34} -1.55700 q^{35} +210.522 q^{36} +66.7758 q^{37} -27.7689 q^{38} -10.4185 q^{39} -0.287226 q^{40} -209.273 q^{41} -5.57716 q^{42} -25.8386 q^{43} +150.341 q^{44} +1.35594 q^{45} -8.20802 q^{46} -457.947 q^{47} +31.0255 q^{48} +599.868 q^{49} +44.6079 q^{50} -8.34456 q^{51} +161.157 q^{52} +151.264 q^{53} +9.76096 q^{54} +0.968322 q^{55} +173.934 q^{56} +39.6027 q^{57} +10.3492 q^{58} +202.631 q^{59} +0.203171 q^{60} +592.476 q^{61} -57.6032 q^{62} -821.112 q^{63} -463.742 q^{64} +1.03799 q^{65} +3.46851 q^{66} -853.480 q^{67} +129.077 q^{68} +11.7059 q^{69} +0.555648 q^{70} -1187.92 q^{71} -151.474 q^{72} -801.225 q^{73} -23.8303 q^{74} -63.6177 q^{75} -612.589 q^{76} -586.383 q^{77} +3.71805 q^{78} -1090.33 q^{79} -3.09105 q^{80} +708.086 q^{81} +74.6833 q^{82} -205.204 q^{83} -123.033 q^{84} +0.831362 q^{85} +9.22102 q^{86} -14.7596 q^{87} -108.172 q^{88} -513.982 q^{89} -0.483895 q^{90} -628.571 q^{91} -181.071 q^{92} +82.1510 q^{93} +163.428 q^{94} -3.94559 q^{95} -34.1357 q^{96} +644.093 q^{97} -214.075 q^{98} +510.662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9}+O(q^{10}) \) 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9} - 52 q^{10} - 126 q^{11} - 173 q^{12} - 252 q^{13} + 112 q^{14} - 32 q^{15} + 312 q^{16} - 332 q^{17} - 225 q^{18} - 2 q^{19} - 747 q^{20} - 202 q^{21} - 127 q^{22} + 805 q^{23} - 494 q^{24} + 315 q^{25} - 677 q^{26} - 694 q^{27} - 529 q^{28} - 1015 q^{29} + 389 q^{30} - 652 q^{31} + 320 q^{32} - 290 q^{33} - 455 q^{34} - 940 q^{35} + 34 q^{36} - 528 q^{37} - 1218 q^{38} - 268 q^{39} - 806 q^{40} - 68 q^{41} - 1484 q^{42} - 162 q^{43} - 1817 q^{44} - 356 q^{45} - 138 q^{46} - 1200 q^{47} - 2153 q^{48} + 93 q^{49} - 1369 q^{50} - 270 q^{51} - 3134 q^{52} - 1892 q^{53} - 1221 q^{54} - 794 q^{55} + 191 q^{56} - 1764 q^{57} + 174 q^{58} - 1354 q^{59} + 159 q^{60} - 1274 q^{61} - 5413 q^{62} - 2904 q^{63} - 926 q^{64} - 548 q^{65} - 2477 q^{66} - 3212 q^{67} - 3901 q^{68} - 506 q^{69} - 2768 q^{70} - 2342 q^{71} - 2381 q^{72} + 916 q^{73} + 661 q^{74} - 4708 q^{75} - 2810 q^{76} - 5536 q^{77} - 2434 q^{78} + 2622 q^{79} - 5444 q^{80} + 607 q^{81} - 3687 q^{82} - 2702 q^{83} + 346 q^{84} - 3304 q^{85} - 5789 q^{86} + 638 q^{87} - 2252 q^{88} - 1620 q^{89} - 3933 q^{90} - 4016 q^{91} + 2668 q^{92} - 4942 q^{93} - 1413 q^{94} - 4528 q^{95} - 7920 q^{96} + 682 q^{97} + 152 q^{98} - 582 q^{99}+O(q^{100}) \) 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9 - 52 * q^10 - 126 * q^11 - 173 * q^12 - 252 * q^13 + 112 * q^14 - 32 * q^15 + 312 * q^16 - 332 * q^17 - 225 * q^18 - 2 * q^19 - 747 * q^20 - 202 * q^21 - 127 * q^22 + 805 * q^23 - 494 * q^24 + 315 * q^25 - 677 * q^26 - 694 * q^27 - 529 * q^28 - 1015 * q^29 + 389 * q^30 - 652 * q^31 + 320 * q^32 - 290 * q^33 - 455 * q^34 - 940 * q^35 + 34 * q^36 - 528 * q^37 - 1218 * q^38 - 268 * q^39 - 806 * q^40 - 68 * q^41 - 1484 * q^42 - 162 * q^43 - 1817 * q^44 - 356 * q^45 - 138 * q^46 - 1200 * q^47 - 2153 * q^48 + 93 * q^49 - 1369 * q^50 - 270 * q^51 - 3134 * q^52 - 1892 * q^53 - 1221 * q^54 - 794 * q^55 + 191 * q^56 - 1764 * q^57 + 174 * q^58 - 1354 * q^59 + 159 * q^60 - 1274 * q^61 - 5413 * q^62 - 2904 * q^63 - 926 * q^64 - 548 * q^65 - 2477 * q^66 - 3212 * q^67 - 3901 * q^68 - 506 * q^69 - 2768 * q^70 - 2342 * q^71 - 2381 * q^72 + 916 * q^73 + 661 * q^74 - 4708 * q^75 - 2810 * q^76 - 5536 * q^77 - 2434 * q^78 + 2622 * q^79 - 5444 * q^80 + 607 * q^81 - 3687 * q^82 - 2702 * q^83 + 346 * q^84 - 3304 * q^85 - 5789 * q^86 + 638 * q^87 - 2252 * q^88 - 1620 * q^89 - 3933 * q^90 - 4016 * q^91 + 2668 * q^92 - 4942 * q^93 - 1413 * q^94 - 4528 * q^95 - 7920 * q^96 + 682 * q^97 + 152 * q^98 - 582 * q^99

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