LMFDB - Embedded newform 667.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,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, 2, names="a")

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

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
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:	$5.32602181482$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 11 x^{11} + 58 x^{10} + 24 x^{9} - 298 x^{8} + 97 x^{7} + 641 x^{6} - 402 x^{5} + \cdots - 40 $ x^13 - 4x^12 - 11x^11 + 58x^10 + 24x^9 - 298x^8 + 97x^7 + 641x^6 - 402x^5 - 547x^4 + 352x^3 + 219x^2 - 88x - 40
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.24788$ of defining polynomial
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)

$f(q)$	$=$	$q+2.24788 q^{2} +1.20409 q^{3} +3.05297 q^{4} -0.269352 q^{5} +2.70666 q^{6} -0.523800 q^{7} +2.36696 q^{8} -1.55016 q^{9} +O(q^{10})$	\(q+2.24788 q^{2} +1.20409 q^{3} +3.05297 q^{4} -0.269352 q^{5} +2.70666 q^{6} -0.523800 q^{7} +2.36696 q^{8} -1.55016 q^{9} -0.605470 q^{10} +5.54870 q^{11} +3.67606 q^{12} +3.85335 q^{13} -1.17744 q^{14} -0.324325 q^{15} -0.785308 q^{16} -1.23265 q^{17} -3.48457 q^{18} +1.15608 q^{19} -0.822323 q^{20} -0.630704 q^{21} +12.4728 q^{22} -1.00000 q^{23} +2.85004 q^{24} -4.92745 q^{25} +8.66188 q^{26} -5.47882 q^{27} -1.59915 q^{28} +1.00000 q^{29} -0.729043 q^{30} +1.02441 q^{31} -6.49919 q^{32} +6.68116 q^{33} -2.77086 q^{34} +0.141086 q^{35} -4.73259 q^{36} -3.22089 q^{37} +2.59873 q^{38} +4.63980 q^{39} -0.637543 q^{40} -3.67031 q^{41} -1.41775 q^{42} +2.77677 q^{43} +16.9400 q^{44} +0.417538 q^{45} -2.24788 q^{46} -6.71558 q^{47} -0.945584 q^{48} -6.72563 q^{49} -11.0763 q^{50} -1.48423 q^{51} +11.7642 q^{52} -2.58548 q^{53} -12.3157 q^{54} -1.49455 q^{55} -1.23981 q^{56} +1.39203 q^{57} +2.24788 q^{58} -9.36230 q^{59} -0.990153 q^{60} -12.0763 q^{61} +2.30275 q^{62} +0.811973 q^{63} -13.0388 q^{64} -1.03791 q^{65} +15.0185 q^{66} -2.14280 q^{67} -3.76326 q^{68} -1.20409 q^{69} +0.317146 q^{70} +4.70321 q^{71} -3.66916 q^{72} +11.8546 q^{73} -7.24017 q^{74} -5.93311 q^{75} +3.52948 q^{76} -2.90641 q^{77} +10.4297 q^{78} +15.5887 q^{79} +0.211524 q^{80} -1.94653 q^{81} -8.25042 q^{82} +8.53106 q^{83} -1.92552 q^{84} +0.332017 q^{85} +6.24185 q^{86} +1.20409 q^{87} +13.1335 q^{88} +12.2129 q^{89} +0.938575 q^{90} -2.01839 q^{91} -3.05297 q^{92} +1.23348 q^{93} -15.0958 q^{94} -0.311392 q^{95} -7.82563 q^{96} +3.00386 q^{97} -15.1184 q^{98} -8.60137 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * 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 $

$2$	2.24788	1.58949	0.794746	−	0.606942i	$-0.207604\pi$
$2$	2.24788	1.58949	0.794746	+	0.606942i	$0.207604\pi$
$3$	1.20409	0.695184	0.347592	−	0.937646i	$-0.386999\pi$
$3$	1.20409	0.695184	0.347592	+	0.937646i	$0.386999\pi$
$4$	3.05297	1.52649
$5$	−0.269352	−0.120458	−0.0602288	−	0.998185i	$-0.519183\pi$
$5$	−0.269352	−0.120458	−0.0602288	+	0.998185i	$0.519183\pi$
$6$	2.70666	1.10499
$7$	−0.523800	−0.197978	−0.0989889	−	0.995089i	$-0.531561\pi$
$7$	−0.523800	−0.197978	−0.0989889	+	0.995089i	$0.531561\pi$
$8$	2.36696	0.836845
$9$	−1.55016	−0.516720
$10$	−0.605470	−0.191467
$11$	5.54870	1.67300	0.836498	−	0.547969i	$-0.184599\pi$
$11$	5.54870	1.67300	0.836498	+	0.547969i	$0.184599\pi$
$12$	3.67606	1.06119
$13$	3.85335	1.06873	0.534364	−	0.845255i	$-0.320551\pi$
$13$	3.85335	1.06873	0.534364	+	0.845255i	$0.320551\pi$
$14$	−1.17744	−0.314684
$15$	−0.324325	−0.0837402
$16$	−0.785308	−0.196327
$17$	−1.23265	−0.298962	−0.149481	−	0.988765i	$-0.547760\pi$
$17$	−1.23265	−0.298962	−0.149481	+	0.988765i	$0.547760\pi$
$18$	−3.48457	−0.821322
$19$	1.15608	0.265223	0.132611	−	0.991168i	$-0.457664\pi$
$19$	1.15608	0.265223	0.132611	+	0.991168i	$0.457664\pi$
$20$	−0.822323	−0.183877
$21$	−0.630704	−0.137631
$22$	12.4728	2.65922
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.85004	0.581761
$25$	−4.92745	−0.985490
$26$	8.66188	1.69873
$27$	−5.47882	−1.05440
$28$	−1.59915	−0.302210
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−0.729043	−0.133104
$31$	1.02441	0.183989	0.0919945	−	0.995760i	$-0.470676\pi$
$31$	1.02441	0.183989	0.0919945	+	0.995760i	$0.470676\pi$
$32$	−6.49919	−1.14891
$33$	6.68116	1.16304
$34$	−2.77086	−0.475199
$35$	0.141086	0.0238480
$36$	−4.73259	−0.788765
$37$	−3.22089	−0.529511	−0.264755	−	0.964316i	$-0.585291\pi$
$37$	−3.22089	−0.529511	−0.264755	+	0.964316i	$0.585291\pi$
$38$	2.59873	0.421569
$39$	4.63980	0.742962
$40$	−0.637543	−0.100804
$41$	−3.67031	−0.573206	−0.286603	−	0.958049i	$-0.592526\pi$
$41$	−3.67031	−0.573206	−0.286603	+	0.958049i	$0.592526\pi$
$42$	−1.41775	−0.218763
$43$	2.77677	0.423454	0.211727	−	0.977329i	$-0.432091\pi$
$43$	2.77677	0.423454	0.211727	+	0.977329i	$0.432091\pi$
$44$	16.9400	2.55381
$45$	0.417538	0.0622428
$46$	−2.24788	−0.331432
$47$	−6.71558	−0.979567	−0.489784	−	0.871844i	$-0.662924\pi$
$47$	−6.71558	−0.979567	−0.489784	+	0.871844i	$0.662924\pi$
$48$	−0.945584	−0.136483
$49$	−6.72563	−0.960805
$50$	−11.0763	−1.56643
$51$	−1.48423	−0.207834
$52$	11.7642	1.63140
$53$	−2.58548	−0.355143	−0.177572	−	0.984108i	$-0.556824\pi$
$53$	−2.58548	−0.355143	−0.177572	+	0.984108i	$0.556824\pi$
$54$	−12.3157	−1.67596
$55$	−1.49455	−0.201525
$56$	−1.23981	−0.165677
$57$	1.39203	0.184378
$58$	2.24788	0.295161
$59$	−9.36230	−1.21887	−0.609434	−	0.792837i	$-0.708603\pi$
$59$	−9.36230	−1.21887	−0.609434	+	0.792837i	$0.708603\pi$
$60$	−0.990153	−0.127828
$61$	−12.0763	−1.54621	−0.773104	−	0.634279i	$-0.781297\pi$
$61$	−12.0763	−1.54621	−0.773104	+	0.634279i	$0.781297\pi$
$62$	2.30275	0.292449
$63$	0.811973	0.102299
$64$	−13.0388	−1.62985
$65$	−1.03791	−0.128736
$66$	15.0185	1.84864
$67$	−2.14280	−0.261785	−0.130892	−	0.991397i	$-0.541784\pi$
$67$	−2.14280	−0.261785	−0.130892	+	0.991397i	$0.541784\pi$
$68$	−3.76326	−0.456362
$69$	−1.20409	−0.144956
$70$	0.317146	0.0379061
$71$	4.70321	0.558168	0.279084	−	0.960267i	$-0.409969\pi$
$71$	4.70321	0.558168	0.279084	+	0.960267i	$0.409969\pi$
$72$	−3.66916	−0.432414
$73$	11.8546	1.38748	0.693738	−	0.720227i	$-0.255962\pi$
$73$	11.8546	1.38748	0.693738	+	0.720227i	$0.255962\pi$
$74$	−7.24017	−0.841653
$75$	−5.93311	−0.685097
$76$	3.52948	0.404859
$77$	−2.90641	−0.331216
$78$	10.4297	1.18093
$79$	15.5887	1.75386	0.876931	−	0.480617i	$-0.159587\pi$
$79$	15.5887	1.75386	0.876931	+	0.480617i	$0.159587\pi$
$80$	0.211524	0.0236491
$81$	−1.94653	−0.216281
$82$	−8.25042	−0.911107
$83$	8.53106	0.936406	0.468203	−	0.883621i	$-0.344902\pi$
$83$	8.53106	0.936406	0.468203	+	0.883621i	$0.344902\pi$
$84$	−1.92552	−0.210092
$85$	0.332017	0.0360123
$86$	6.24185	0.673076
$87$	1.20409	0.129092
$88$	13.1335	1.40004
$89$	12.2129	1.29456	0.647280	−	0.762252i	$-0.275906\pi$
$89$	12.2129	1.29456	0.647280	+	0.762252i	$0.275906\pi$
$90$	0.938575	0.0989345
$91$	−2.01839	−0.211584
$92$	−3.05297	−0.318294
$93$	1.23348	0.127906
$94$	−15.0958	−1.55701
$95$	−0.311392	−0.0319481
$96$	−7.82563	−0.798700
$97$	3.00386	0.304996	0.152498	−	0.988304i	$-0.451268\pi$
$97$	3.00386	0.304996	0.152498	+	0.988304i	$0.451268\pi$
$98$	−15.1184	−1.52719
$99$	−8.60137	−0.864470
$100$	−15.0434	−1.50434
$101$	6.57477	0.654214	0.327107	−	0.944987i	$-0.393926\pi$
$101$	6.57477	0.654214	0.327107	+	0.944987i	$0.393926\pi$
$102$	−3.33637	−0.330350
$103$	17.1469	1.68953	0.844766	−	0.535136i	$-0.179740\pi$
$103$	17.1469	1.68953	0.844766	+	0.535136i	$0.179740\pi$
$104$	9.12071	0.894359
$105$	0.169881	0.0165787
$106$	−5.81186	−0.564497
$107$	12.1672	1.17625	0.588123	−	0.808772i	$-0.299867\pi$
$107$	12.1672	1.17625	0.588123	+	0.808772i	$0.299867\pi$
$108$	−16.7267	−1.60952
$109$	3.17086	0.303713	0.151857	−	0.988403i	$-0.451475\pi$
$109$	3.17086	0.303713	0.151857	+	0.988403i	$0.451475\pi$
$110$	−3.35958	−0.320323
$111$	−3.87825	−0.368107
$112$	0.411344	0.0388684
$113$	−12.6858	−1.19338	−0.596688	−	0.802473i	$-0.703517\pi$
$113$	−12.6858	−1.19338	−0.596688	+	0.802473i	$0.703517\pi$
$114$	3.12911	0.293068
$115$	0.269352	0.0251172
$116$	3.05297	0.283461
$117$	−5.97331	−0.552232
$118$	−21.0453	−1.93738
$119$	0.645664	0.0591879
$120$	−0.767662	−0.0700776
$121$	19.7881	1.79892
$122$	−27.1460	−2.45769
$123$	−4.41940	−0.398484
$124$	3.12749	0.280857
$125$	2.67397	0.239168
$126$	1.82522	0.162604
$127$	−11.6051	−1.02978	−0.514892	−	0.857255i	$-0.672168\pi$
$127$	−11.6051	−1.02978	−0.514892	+	0.857255i	$0.672168\pi$
$128$	−16.3113	−1.44173
$129$	3.34349	0.294378
$130$	−2.33309	−0.204626
$131$	9.59459	0.838283	0.419142	−	0.907921i	$-0.362331\pi$
$131$	9.59459	0.838283	0.419142	+	0.907921i	$0.362331\pi$
$132$	20.3974	1.77536
$133$	−0.605554	−0.0525082
$134$	−4.81677	−0.416105
$135$	1.47573	0.127010
$136$	−2.91764	−0.250185
$137$	−0.429683	−0.0367103	−0.0183552	−	0.999832i	$-0.505843\pi$
$137$	−0.429683	−0.0367103	−0.0183552	+	0.999832i	$0.505843\pi$
$138$	−2.70666	−0.230406
$139$	−10.4292	−0.884597	−0.442299	−	0.896868i	$-0.645837\pi$
$139$	−10.4292	−0.884597	−0.442299	+	0.896868i	$0.645837\pi$
$140$	0.430733	0.0364036
$141$	−8.08618	−0.680979
$142$	10.5723	0.887204
$143$	21.3811	1.78798
$144$	1.21735	0.101446
$145$	−0.269352	−0.0223684
$146$	26.6478	2.20538
$147$	−8.09829	−0.667936
$148$	−9.83328	−0.808290
$149$	12.9871	1.06394	0.531970	−	0.846763i	$-0.321452\pi$
$149$	12.9871	1.06394	0.531970	+	0.846763i	$0.321452\pi$
$150$	−13.3369	−1.08896
$151$	−12.8395	−1.04486	−0.522431	−	0.852681i	$-0.674975\pi$
$151$	−12.8395	−1.04486	−0.522431	+	0.852681i	$0.674975\pi$
$152$	2.73639	0.221950
$153$	1.91081	0.154480
$154$	−6.53327	−0.526466
$155$	−0.275926	−0.0221629
$156$	14.1652	1.13412
$157$	−4.11732	−0.328598	−0.164299	−	0.986411i	$-0.552536\pi$
$157$	−4.11732	−0.328598	−0.164299	+	0.986411i	$0.552536\pi$
$158$	35.0415	2.78775
$159$	−3.11316	−0.246890
$160$	1.75057	0.138394
$161$	0.523800	0.0412812
$162$	−4.37557	−0.343778
$163$	−10.6963	−0.837801	−0.418900	−	0.908032i	$-0.637584\pi$
$163$	−10.6963	−0.837801	−0.418900	+	0.908032i	$0.637584\pi$
$164$	−11.2054	−0.874991
$165$	−1.79958	−0.140097
$166$	19.1768	1.48841
$167$	24.3060	1.88085	0.940427	−	0.339997i	$-0.110426\pi$
$167$	24.3060	1.88085	0.940427	+	0.339997i	$0.110426\pi$
$168$	−1.49285	−0.115176
$169$	1.84832	0.142179
$170$	0.746335	0.0572413
$171$	−1.79211	−0.137046
$172$	8.47740	0.646396
$173$	3.04992	0.231881	0.115941	−	0.993256i	$-0.463012\pi$
$173$	3.04992	0.231881	0.115941	+	0.993256i	$0.463012\pi$
$174$	2.70666	0.205191
$175$	2.58100	0.195105
$176$	−4.35744	−0.328454
$177$	−11.2731	−0.847337
$178$	27.4531	2.05769
$179$	−17.7448	−1.32631	−0.663155	−	0.748482i	$-0.730783\pi$
$179$	−17.7448	−1.32631	−0.663155	+	0.748482i	$0.730783\pi$
$180$	1.27473	0.0950128
$181$	−19.4919	−1.44882	−0.724410	−	0.689369i	$-0.757888\pi$
$181$	−19.4919	−1.44882	−0.724410	+	0.689369i	$0.757888\pi$
$182$	−4.53709	−0.336312
$183$	−14.5410	−1.07490
$184$	−2.36696	−0.174494
$185$	0.867551	0.0637836
$186$	2.77272	0.203306
$187$	−6.83963	−0.500163
$188$	−20.5025	−1.49530
$189$	2.86981	0.208748
$190$	−0.699971	−0.0507813
$191$	−14.0435	−1.01615	−0.508075	−	0.861313i	$-0.669643\pi$
$191$	−14.0435	−1.01615	−0.508075	+	0.861313i	$0.669643\pi$
$192$	−15.6999	−1.13304
$193$	20.6882	1.48917	0.744585	−	0.667528i	$-0.232647\pi$
$193$	20.6882	1.48917	0.744585	+	0.667528i	$0.232647\pi$
$194$	6.75233	0.484789
$195$	−1.24974	−0.0894955
$196$	−20.5332	−1.46665
$197$	1.32494	0.0943983	0.0471991	−	0.998885i	$-0.484970\pi$
$197$	1.32494	0.0943983	0.0471991	+	0.998885i	$0.484970\pi$
$198$	−19.3349	−1.37407
$199$	14.6071	1.03547	0.517736	−	0.855541i	$-0.326775\pi$
$199$	14.6071	1.03547	0.517736	+	0.855541i	$0.326775\pi$
$200$	−11.6631	−0.824702
$201$	−2.58013	−0.181989
$202$	14.7793	1.03987
$203$	−0.523800	−0.0367636
$204$	−4.53131	−0.317255
$205$	0.988604	0.0690471
$206$	38.5441	2.68550
$207$	1.55016	0.107743
$208$	−3.02607	−0.209820
$209$	6.41474	0.443717
$210$	0.381873	0.0263517
$211$	−16.8423	−1.15947	−0.579734	−	0.814806i	$-0.696844\pi$
$211$	−16.8423	−1.15947	−0.579734	+	0.814806i	$0.696844\pi$
$212$	−7.89340	−0.542121
$213$	5.66310	0.388029
$214$	27.3504	1.86963
$215$	−0.747928	−0.0510083
$216$	−12.9681	−0.882368
$217$	−0.536585	−0.0364257
$218$	7.12772	0.482750
$219$	14.2741	0.964551
$220$	−4.56282	−0.307626
$221$	−4.74985	−0.319509
$222$	−8.71785	−0.585104
$223$	5.08575	0.340567	0.170284	−	0.985395i	$-0.445532\pi$
$223$	5.08575	0.340567	0.170284	+	0.985395i	$0.445532\pi$
$224$	3.40428	0.227458
$225$	7.63833	0.509222
$226$	−28.5161	−1.89686
$227$	−2.37457	−0.157606	−0.0788030	−	0.996890i	$-0.525110\pi$
$227$	−2.37457	−0.157606	−0.0788030	+	0.996890i	$0.525110\pi$
$228$	4.24982	0.281451
$229$	11.0268	0.728670	0.364335	−	0.931268i	$-0.381296\pi$
$229$	11.0268	0.728670	0.364335	+	0.931268i	$0.381296\pi$
$230$	0.605470	0.0399235
$231$	−3.49959	−0.230256
$232$	2.36696	0.155398
$233$	−12.7890	−0.837837	−0.418919	−	0.908024i	$-0.637591\pi$
$233$	−12.7890	−0.837837	−0.418919	+	0.908024i	$0.637591\pi$
$234$	−13.4273	−0.877769
$235$	1.80885	0.117996
$236$	−28.5828	−1.86058
$237$	18.7702	1.21926
$238$	1.45138	0.0940788
$239$	7.10384	0.459509	0.229754	−	0.973249i	$-0.426208\pi$
$239$	7.10384	0.459509	0.229754	+	0.973249i	$0.426208\pi$
$240$	0.254695	0.0164405
$241$	2.37432	0.152943	0.0764717	−	0.997072i	$-0.475635\pi$
$241$	2.37432	0.152943	0.0764717	+	0.997072i	$0.475635\pi$
$242$	44.4813	2.85937
$243$	14.0926	0.904044
$244$	−36.8685	−2.36027
$245$	1.81156	0.115736
$246$	−9.93428	−0.633387
$247$	4.45478	0.283451
$248$	2.42473	0.153970
$249$	10.2722	0.650974
$250$	6.01078	0.380155
$251$	−18.8107	−1.18732	−0.593660	−	0.804716i	$-0.702318\pi$
$251$	−18.8107	−1.18732	−0.593660	+	0.804716i	$0.702318\pi$
$252$	2.47893	0.156158
$253$	−5.54870	−0.348844
$254$	−26.0868	−1.63683
$255$	0.399780	0.0250352
$256$	−10.5882	−0.661765
$257$	20.0371	1.24988	0.624939	−	0.780674i	$-0.285124\pi$
$257$	20.0371	1.24988	0.624939	+	0.780674i	$0.285124\pi$
$258$	7.51578	0.467912
$259$	1.68710	0.104831
$260$	−3.16870	−0.196514
$261$	−1.55016	−0.0959524
$262$	21.5675	1.33244
$263$	−19.8158	−1.22189	−0.610947	−	0.791671i	$-0.709211\pi$
$263$	−19.8158	−1.22189	−0.610947	+	0.791671i	$0.709211\pi$
$264$	15.8140	0.973284
$265$	0.696404	0.0427797
$266$	−1.36121	−0.0834614
$267$	14.7054	0.899957
$268$	−6.54192	−0.399611
$269$	21.0353	1.28254	0.641271	−	0.767314i	$-0.278407\pi$
$269$	21.0353	1.28254	0.641271	+	0.767314i	$0.278407\pi$
$270$	3.31726	0.201882
$271$	19.0625	1.15796	0.578982	−	0.815340i	$-0.303450\pi$
$271$	19.0625	1.15796	0.578982	+	0.815340i	$0.303450\pi$
$272$	0.968013	0.0586944
$273$	−2.43033	−0.147090
$274$	−0.965877	−0.0583508
$275$	−27.3410	−1.64872
$276$	−3.67606	−0.221273
$277$	4.40716	0.264801	0.132400	−	0.991196i	$-0.457732\pi$
$277$	4.40716	0.264801	0.132400	+	0.991196i	$0.457732\pi$
$278$	−23.4437	−1.40606
$279$	−1.58799	−0.0950707
$280$	0.333945	0.0199570
$281$	19.7030	1.17538	0.587691	−	0.809086i	$-0.300037\pi$
$281$	19.7030	1.17538	0.587691	+	0.809086i	$0.300037\pi$
$282$	−18.1768	−1.08241
$283$	21.5092	1.27859	0.639294	−	0.768962i	$-0.279227\pi$
$283$	21.5092	1.27859	0.639294	+	0.768962i	$0.279227\pi$
$284$	14.3588	0.852036
$285$	−0.374945	−0.0222098
$286$	48.0622	2.84198
$287$	1.92251	0.113482
$288$	10.0748	0.593662
$289$	−15.4806	−0.910621
$290$	−0.605470	−0.0355544
$291$	3.61693	0.212028
$292$	36.1918	2.11796
$293$	7.30614	0.426829	0.213415	−	0.976962i	$-0.431542\pi$
$293$	7.30614	0.426829	0.213415	+	0.976962i	$0.431542\pi$
$294$	−18.2040	−1.06168
$295$	2.52175	0.146822
$296$	−7.62370	−0.443118
$297$	−30.4003	−1.76401
$298$	29.1934	1.69113
$299$	−3.85335	−0.222845
$300$	−18.1136	−1.04579
$301$	−1.45447	−0.0838345
$302$	−28.8616	−1.66080
$303$	7.91664	0.454799
$304$	−0.907878	−0.0520704
$305$	3.25276	0.186253
$306$	4.29527	0.245544
$307$	−30.0031	−1.71237	−0.856184	−	0.516671i	$-0.827171\pi$
$307$	−30.0031	−1.71237	−0.856184	+	0.516671i	$0.827171\pi$
$308$	−8.87319	−0.505597
$309$	20.6464	1.17453
$310$	−0.620248	−0.0352277
$311$	−15.3682	−0.871453	−0.435727	−	0.900079i	$-0.643509\pi$
$311$	−15.3682	−0.871453	−0.435727	+	0.900079i	$0.643509\pi$
$312$	10.9822	0.621744
$313$	−25.4849	−1.44049	−0.720247	−	0.693718i	$-0.755971\pi$
$313$	−25.4849	−1.44049	−0.720247	+	0.693718i	$0.755971\pi$
$314$	−9.25525	−0.522304
$315$	−0.218706	−0.0123227
$316$	47.5917	2.67724
$317$	5.32609	0.299143	0.149571	−	0.988751i	$-0.452211\pi$
$317$	5.32609	0.299143	0.149571	+	0.988751i	$0.452211\pi$
$318$	−6.99802	−0.392429
$319$	5.54870	0.310668
$320$	3.51202	0.196328
$321$	14.6504	0.817707
$322$	1.17744	0.0656162
$323$	−1.42504	−0.0792916
$324$	−5.94271	−0.330150
$325$	−18.9872	−1.05322
$326$	−24.0441	−1.33168
$327$	3.81801	0.211137
$328$	−8.68746	−0.479685
$329$	3.51762	0.193933
$330$	−4.04524	−0.222683
$331$	−17.6899	−0.972324	−0.486162	−	0.873869i	$-0.661603\pi$
$331$	−17.6899	−0.972324	−0.486162	+	0.873869i	$0.661603\pi$
$332$	26.0451	1.42941
$333$	4.99289	0.273609
$334$	54.6370	2.98960
$335$	0.577167	0.0315340
$336$	0.495297	0.0270207
$337$	−25.5766	−1.39325	−0.696623	−	0.717437i	$-0.745315\pi$
$337$	−25.5766	−1.39325	−0.696623	+	0.717437i	$0.745315\pi$
$338$	4.15481	0.225992
$339$	−15.2749	−0.829616
$340$	1.01364	0.0549723
$341$	5.68413	0.307813
$342$	−4.02844	−0.217833
$343$	7.18949	0.388196
$344$	6.57249	0.354365
$345$	0.324325	0.0174610
$346$	6.85587	0.368574
$347$	15.8634	0.851594	0.425797	−	0.904819i	$-0.359994\pi$
$347$	15.8634	0.851594	0.425797	+	0.904819i	$0.359994\pi$
$348$	3.67606	0.197058
$349$	−5.23461	−0.280202	−0.140101	−	0.990137i	$-0.544743\pi$
$349$	−5.23461	−0.280202	−0.140101	+	0.990137i	$0.544743\pi$
$350$	5.80178	0.310118
$351$	−21.1118	−1.12687
$352$	−36.0621	−1.92211
$353$	10.2100	0.543424	0.271712	−	0.962379i	$-0.412410\pi$
$353$	10.2100	0.543424	0.271712	+	0.962379i	$0.412410\pi$
$354$	−25.3406	−1.34684
$355$	−1.26682	−0.0672357
$356$	37.2855	1.97613
$357$	0.777440	0.0411465
$358$	−39.8883	−2.10816
$359$	−29.7321	−1.56920	−0.784599	−	0.620003i	$-0.787131\pi$
$359$	−29.7321	−1.56920	−0.784599	+	0.620003i	$0.787131\pi$
$360$	0.988293	0.0520876
$361$	−17.6635	−0.929657
$362$	−43.8155	−2.30289
$363$	23.8267	1.25058
$364$	−6.16208	−0.322981
$365$	−3.19306	−0.167132
$366$	−32.6864	−1.70854
$367$	16.1172	0.841310	0.420655	−	0.907221i	$-0.361800\pi$
$367$	16.1172	0.841310	0.420655	+	0.907221i	$0.361800\pi$
$368$	0.785308	0.0409370
$369$	5.68956	0.296187
$370$	1.95015	0.101384
$371$	1.35428	0.0703105
$372$	3.76579	0.195247
$373$	26.1982	1.35649	0.678247	−	0.734834i	$-0.262740\pi$
$373$	26.1982	1.35649	0.678247	+	0.734834i	$0.262740\pi$
$374$	−15.3747	−0.795006
$375$	3.21972	0.166265
$376$	−15.8955	−0.819746
$377$	3.85335	0.198458
$378$	6.45098	0.331803
$379$	25.7346	1.32190	0.660948	−	0.750432i	$-0.270155\pi$
$379$	25.7346	1.32190	0.660948	+	0.750432i	$0.270155\pi$
$380$	−0.950670	−0.0487683
$381$	−13.9736	−0.715888
$382$	−31.5680	−1.61516
$383$	16.3203	0.833926	0.416963	−	0.908923i	$-0.363094\pi$
$383$	16.3203	0.833926	0.416963	+	0.908923i	$0.363094\pi$
$384$	−19.6403	−1.00227
$385$	0.782847	0.0398976
$386$	46.5046	2.36702
$387$	−4.30444	−0.218807
$388$	9.17071	0.465572
$389$	23.8266	1.20806	0.604029	−	0.796962i	$-0.293561\pi$
$389$	23.8266	1.20806	0.604029	+	0.796962i	$0.293561\pi$
$390$	−2.80926	−0.142252
$391$	1.23265	0.0623380
$392$	−15.9193	−0.804045
$393$	11.5528	0.582761
$394$	2.97831	0.150045
$395$	−4.19883	−0.211266
$396$	−26.2597	−1.31960
$397$	9.78710	0.491201	0.245600	−	0.969371i	$-0.421015\pi$
$397$	9.78710	0.491201	0.245600	+	0.969371i	$0.421015\pi$
$398$	32.8351	1.64587
$399$	−0.729144	−0.0365029
$400$	3.86956	0.193478
$401$	8.22037	0.410506	0.205253	−	0.978709i	$-0.434198\pi$
$401$	8.22037	0.410506	0.205253	+	0.978709i	$0.434198\pi$
$402$	−5.79984	−0.289270
$403$	3.94740	0.196634
$404$	20.0726	0.998649
$405$	0.524301	0.0260527
$406$	−1.17744	−0.0584354
$407$	−17.8717	−0.885870
$408$	−3.51311	−0.173925
$409$	12.8235	0.634083	0.317042	−	0.948412i	$-0.397311\pi$
$409$	12.8235	0.634083	0.317042	+	0.948412i	$0.397311\pi$
$410$	2.22226	0.109750
$411$	−0.517379	−0.0255204
$412$	52.3489	2.57905
$413$	4.90398	0.241309
$414$	3.48457	0.171257
$415$	−2.29785	−0.112797
$416$	−25.0437	−1.22787
$417$	−12.5578	−0.614958
$418$	14.4196	0.705284
$419$	−31.8570	−1.55631	−0.778157	−	0.628069i	$-0.783845\pi$
$419$	−31.8570	−1.55631	−0.778157	+	0.628069i	$0.783845\pi$
$420$	0.518643	0.0253072
$421$	−13.4777	−0.656865	−0.328433	−	0.944527i	$-0.606520\pi$
$421$	−13.4777	−0.656865	−0.328433	+	0.944527i	$0.606520\pi$
$422$	−37.8594	−1.84297
$423$	10.4102	0.506162
$424$	−6.11972	−0.297200
$425$	6.07384	0.294624
$426$	12.7300	0.616770
$427$	6.32556	0.306115
$428$	37.1461	1.79552
$429$	25.7449	1.24297
$430$	−1.68125	−0.0810772
$431$	9.35831	0.450774	0.225387	−	0.974269i	$-0.427635\pi$
$431$	9.35831	0.450774	0.225387	+	0.974269i	$0.427635\pi$
$432$	4.30256	0.207007
$433$	−0.463834	−0.0222904	−0.0111452	−	0.999938i	$-0.503548\pi$
$433$	−0.463834	−0.0222904	−0.0111452	+	0.999938i	$0.503548\pi$
$434$	−1.20618	−0.0578984
$435$	−0.324325	−0.0155502
$436$	9.68055	0.463614
$437$	−1.15608	−0.0553027
$438$	32.0864	1.53315
$439$	27.8294	1.32823	0.664113	−	0.747632i	$-0.268809\pi$
$439$	27.8294	1.32823	0.664113	+	0.747632i	$0.268809\pi$
$440$	−3.53754	−0.168645
$441$	10.4258	0.496467
$442$	−10.6771	−0.507858
$443$	23.7520	1.12849	0.564247	−	0.825606i	$-0.309167\pi$
$443$	23.7520	1.12849	0.564247	+	0.825606i	$0.309167\pi$
$444$	−11.8402	−0.561910
$445$	−3.28955	−0.155940
$446$	11.4322	0.541329
$447$	15.6376	0.739634
$448$	6.82972	0.322674
$449$	2.07087	0.0977304	0.0488652	−	0.998805i	$-0.484440\pi$
$449$	2.07087	0.0977304	0.0488652	+	0.998805i	$0.484440\pi$
$450$	17.1701	0.809404
$451$	−20.3655	−0.958972
$452$	−38.7293	−1.82167
$453$	−15.4599	−0.726371
$454$	−5.33776	−0.250514
$455$	0.543656	0.0254870
$456$	3.29487	0.154296
$457$	−18.4284	−0.862044	−0.431022	−	0.902341i	$-0.641847\pi$
$457$	−18.4284	−0.862044	−0.431022	+	0.902341i	$0.641847\pi$
$458$	24.7869	1.15822
$459$	6.75348	0.315226
$460$	0.822323	0.0383410
$461$	21.6633	1.00896	0.504480	−	0.863423i	$-0.331684\pi$
$461$	21.6633	1.00896	0.504480	+	0.863423i	$0.331684\pi$
$462$	−7.86667	−0.365990
$463$	−29.4821	−1.37015	−0.685076	−	0.728472i	$-0.740231\pi$
$463$	−29.4821	−1.37015	−0.685076	+	0.728472i	$0.740231\pi$
$464$	−0.785308	−0.0364570
$465$	−0.332240	−0.0154073
$466$	−28.7482	−1.33174
$467$	−26.6296	−1.23227	−0.616135	−	0.787641i	$-0.711302\pi$
$467$	−26.6296	−1.23227	−0.616135	+	0.787641i	$0.711302\pi$
$468$	−18.2363	−0.842975
$469$	1.12240	0.0518276
$470$	4.06608	0.187554
$471$	−4.95764	−0.228436
$472$	−22.1602	−1.02000
$473$	15.4075	0.708437
$474$	42.1932	1.93800
$475$	−5.69652	−0.261374
$476$	1.97119	0.0903496
$477$	4.00791	0.183509
$478$	15.9686	0.730386
$479$	5.87857	0.268599	0.134299	−	0.990941i	$-0.457122\pi$
$479$	5.87857	0.268599	0.134299	+	0.990941i	$0.457122\pi$
$480$	2.10785	0.0962096
$481$	−12.4112	−0.565903
$482$	5.33719	0.243102
$483$	0.630704	0.0286980
$484$	60.4125	2.74602
$485$	−0.809095	−0.0367391
$486$	31.6786	1.43697
$487$	−21.3836	−0.968982	−0.484491	−	0.874796i	$-0.660995\pi$
$487$	−21.3836	−0.968982	−0.484491	+	0.874796i	$0.660995\pi$
$488$	−28.5840	−1.29394
$489$	−12.8794	−0.582425
$490$	4.07217	0.183962
$491$	11.1612	0.503698	0.251849	−	0.967767i	$-0.418961\pi$
$491$	11.1612	0.503698	0.251849	+	0.967767i	$0.418961\pi$
$492$	−13.4923	−0.608280
$493$	−1.23265	−0.0555159
$494$	10.0138	0.450543
$495$	2.31679	0.104132
$496$	−0.804475	−0.0361220
$497$	−2.46354	−0.110505
$498$	23.0907	1.03472
$499$	−14.8871	−0.666437	−0.333218	−	0.942850i	$-0.608135\pi$
$499$	−14.8871	−0.666437	−0.333218	+	0.942850i	$0.608135\pi$
$500$	8.16357	0.365086
$501$	29.2667	1.30754
$502$	−42.2842	−1.88724
$503$	20.3724	0.908362	0.454181	−	0.890909i	$-0.349932\pi$
$503$	20.3724	0.908362	0.454181	+	0.890909i	$0.349932\pi$
$504$	1.92190	0.0856084
$505$	−1.77093	−0.0788051
$506$	−12.4728	−0.554485
$507$	2.22555	0.0988403
$508$	−35.4299	−1.57195
$509$	−5.34563	−0.236941	−0.118470	−	0.992958i	$-0.537799\pi$
$509$	−5.34563	−0.236941	−0.118470	+	0.992958i	$0.537799\pi$
$510$	0.898658	0.0397932
$511$	−6.20945	−0.274690
$512$	8.82144	0.389856
$513$	−6.33394	−0.279650
$514$	45.0410	1.98667
$515$	−4.61854	−0.203517
$516$	10.2076	0.449364
$517$	−37.2627	−1.63881
$518$	3.79240	0.166629
$519$	3.67239	0.161200
$520$	−2.45668	−0.107732
$521$	9.65635	0.423052	0.211526	−	0.977372i	$-0.432157\pi$
$521$	9.65635	0.423052	0.211526	+	0.977372i	$0.432157\pi$
$522$	−3.48457	−0.152516
$523$	1.53071	0.0669333	0.0334667	−	0.999440i	$-0.489345\pi$
$523$	1.53071	0.0669333	0.0334667	+	0.999440i	$0.489345\pi$
$524$	29.2920	1.27963
$525$	3.10776	0.135634
$526$	−44.5436	−1.94219
$527$	−1.26274	−0.0550058
$528$	−5.24677	−0.228336
$529$	1.00000	0.0434783
$530$	1.56543	0.0679981
$531$	14.5131	0.629813
$532$	−1.84874	−0.0801530
$533$	−14.1430	−0.612601
$534$	33.0561	1.43048
$535$	−3.27725	−0.141688
$536$	−5.07192	−0.219073
$537$	−21.3664	−0.922030
$538$	47.2848	2.03859
$539$	−37.3185	−1.60742
$540$	4.50536	0.193880
$541$	30.5325	1.31269	0.656347	−	0.754459i	$-0.272101\pi$
$541$	30.5325	1.31269	0.656347	+	0.754459i	$0.272101\pi$
$542$	42.8503	1.84058
$543$	−23.4701	−1.00720
$544$	8.01125	0.343480
$545$	−0.854076	−0.0365846
$546$	−5.46309	−0.233798
$547$	−38.6838	−1.65400	−0.826999	−	0.562203i	$-0.809954\pi$
$547$	−38.6838	−1.65400	−0.826999	+	0.562203i	$0.809954\pi$
$548$	−1.31181	−0.0560378
$549$	18.7201	0.798956
$550$	−61.4592	−2.62063
$551$	1.15608	0.0492506
$552$	−2.85004	−0.121306
$553$	−8.16534	−0.347226
$554$	9.90678	0.420899
$555$	1.04461	0.0443413
$556$	−31.8402	−1.35033
$557$	33.2707	1.40973	0.704863	−	0.709344i	$-0.251008\pi$
$557$	33.2707	1.40973	0.704863	+	0.709344i	$0.251008\pi$
$558$	−3.56962	−0.151114
$559$	10.6999	0.452557
$560$	−0.110796	−0.00468200
$561$	−8.23555	−0.347705
$562$	44.2900	1.86826
$563$	−28.0392	−1.18171	−0.590855	−	0.806778i	$-0.701210\pi$
$563$	−28.0392	−1.18171	−0.590855	+	0.806778i	$0.701210\pi$
$564$	−24.6869	−1.03951
$565$	3.41693	0.143751
$566$	48.3501	2.03231
$567$	1.01959	0.0428189
$568$	11.1323	0.467100
$569$	12.5671	0.526841	0.263421	−	0.964681i	$-0.415149\pi$
$569$	12.5671	0.526841	0.263421	+	0.964681i	$0.415149\pi$
$570$	−0.842831	−0.0353023
$571$	−29.1558	−1.22013	−0.610065	−	0.792351i	$-0.708857\pi$
$571$	−29.1558	−1.22013	−0.610065	+	0.792351i	$0.708857\pi$
$572$	65.2759	2.72932
$573$	−16.9096	−0.706411
$574$	4.32157	0.180379
$575$	4.92745	0.205489
$576$	20.2122	0.842175
$577$	6.47178	0.269424	0.134712	−	0.990885i	$-0.456989\pi$
$577$	6.47178	0.269424	0.134712	+	0.990885i	$0.456989\pi$
$578$	−34.7985	−1.44743
$579$	24.9105	1.03525
$580$	−0.822323	−0.0341451
$581$	−4.46857	−0.185388
$582$	8.13043	0.337017
$583$	−14.3461	−0.594153
$584$	28.0593	1.16110
$585$	1.60892	0.0665206
$586$	16.4233	0.678441
$587$	3.91626	0.161641	0.0808207	−	0.996729i	$-0.474246\pi$
$587$	3.91626	0.161641	0.0808207	+	0.996729i	$0.474246\pi$
$588$	−24.7239	−1.01959
$589$	1.18430	0.0487980
$590$	5.66860	0.233372
$591$	1.59536	0.0656241
$592$	2.52939	0.103957
$593$	35.0507	1.43936	0.719680	−	0.694306i	$-0.244289\pi$
$593$	35.0507	1.43936	0.719680	+	0.694306i	$0.244289\pi$
$594$	−68.3363	−2.80387
$595$	−0.173911	−0.00712964
$596$	39.6491	1.62409
$597$	17.5883	0.719843
$598$	−8.66188	−0.354211
$599$	−11.1914	−0.457267	−0.228633	−	0.973513i	$-0.573426\pi$
$599$	−11.1914	−0.457267	−0.228633	+	0.973513i	$0.573426\pi$
$600$	−14.0434	−0.573320
$601$	−39.8237	−1.62444	−0.812221	−	0.583350i	$-0.801742\pi$
$601$	−39.8237	−1.62444	−0.812221	+	0.583350i	$0.801742\pi$
$602$	−3.26948	−0.133254
$603$	3.32168	0.135269
$604$	−39.1986	−1.59497
$605$	−5.32996	−0.216694
$606$	17.7957	0.722900
$607$	−1.18071	−0.0479235	−0.0239618	−	0.999713i	$-0.507628\pi$
$607$	−1.18071	−0.0479235	−0.0239618	+	0.999713i	$0.507628\pi$
$608$	−7.51357	−0.304716
$609$	−0.630704	−0.0255574
$610$	7.31183	0.296047
$611$	−25.8775	−1.04689
$612$	5.83365	0.235811
$613$	−21.1441	−0.854001	−0.427000	−	0.904251i	$-0.640430\pi$
$613$	−21.1441	−0.854001	−0.427000	+	0.904251i	$0.640430\pi$
$614$	−67.4435	−2.72180
$615$	1.19037	0.0480004
$616$	−6.87935	−0.277177
$617$	5.73209	0.230765	0.115383	−	0.993321i	$-0.463191\pi$
$617$	5.73209	0.230765	0.115383	+	0.993321i	$0.463191\pi$
$618$	46.4108	1.86691
$619$	−22.8935	−0.920169	−0.460084	−	0.887875i	$-0.652181\pi$
$619$	−22.8935	−0.920169	−0.460084	+	0.887875i	$0.652181\pi$
$620$	−0.842393	−0.0338313
$621$	5.47882	0.219857
$622$	−34.5460	−1.38517
$623$	−6.39710	−0.256294
$624$	−3.64367	−0.145863
$625$	23.9170	0.956680
$626$	−57.2871	−2.28965
$627$	7.72394	0.308465
$628$	−12.5701	−0.501600
$629$	3.97024	0.158304
$630$	−0.491626	−0.0195868
$631$	−10.5614	−0.420444	−0.210222	−	0.977654i	$-0.567419\pi$
$631$	−10.5614	−0.420444	−0.210222	+	0.977654i	$0.567419\pi$
$632$	36.8977	1.46771
$633$	−20.2797	−0.806044
$634$	11.9724	0.475485
$635$	3.12584	0.124045
$636$	−9.50439	−0.376874
$637$	−25.9162	−1.02684
$638$	12.4728	0.493804
$639$	−7.29072	−0.288416
$640$	4.39347	0.173667
$641$	6.79362	0.268332	0.134166	−	0.990959i	$-0.457164\pi$
$641$	6.79362	0.268332	0.134166	+	0.990959i	$0.457164\pi$
$642$	32.9324	1.29974
$643$	−18.1869	−0.717221	−0.358610	−	0.933487i	$-0.616749\pi$
$643$	−18.1869	−0.717221	−0.358610	+	0.933487i	$0.616749\pi$
$644$	1.59915	0.0630152
$645$	−0.900575	−0.0354601
$646$	−3.20333	−0.126033
$647$	5.56073	0.218615	0.109307	−	0.994008i	$-0.465137\pi$
$647$	5.56073	0.218615	0.109307	+	0.994008i	$0.465137\pi$
$648$	−4.60735	−0.180994
$649$	−51.9486	−2.03916
$650$	−42.6810	−1.67409
$651$	−0.646098	−0.0253226
$652$	−32.6556	−1.27889
$653$	−8.03210	−0.314320	−0.157160	−	0.987573i	$-0.550234\pi$
$653$	−8.03210	−0.314320	−0.157160	+	0.987573i	$0.550234\pi$
$654$	8.58244	0.335600
$655$	−2.58432	−0.100978
$656$	2.88232	0.112536
$657$	−18.3765	−0.716937
$658$	7.90719	0.308254
$659$	22.4860	0.875929	0.437965	−	0.898992i	$-0.355700\pi$
$659$	22.4860	0.875929	0.437965	+	0.898992i	$0.355700\pi$
$660$	−5.49407	−0.213856
$661$	36.6866	1.42694	0.713471	−	0.700685i	$-0.247122\pi$
$661$	36.6866	1.42694	0.713471	+	0.700685i	$0.247122\pi$
$662$	−39.7648	−1.54550
$663$	−5.71926	−0.222118
$664$	20.1926	0.783626
$665$	0.163107	0.00632502
$666$	11.2234	0.434899
$667$	−1.00000	−0.0387202
$668$	74.2055	2.87110
$669$	6.12372	0.236757
$670$	1.29740	0.0501231
$671$	−67.0077	−2.58680
$672$	4.09907	0.158125
$673$	−38.4756	−1.48313	−0.741563	−	0.670884i	$-0.765915\pi$
$673$	−38.4756	−1.48313	−0.741563	+	0.670884i	$0.765915\pi$
$674$	−57.4932	−2.21456
$675$	26.9966	1.03910
$676$	5.64287	0.217034
$677$	−33.2780	−1.27898	−0.639488	−	0.768801i	$-0.720854\pi$
$677$	−33.2780	−1.27898	−0.639488	+	0.768801i	$0.720854\pi$
$678$	−34.3361	−1.31867
$679$	−1.57342	−0.0603825
$680$	0.785870	0.0301367
$681$	−2.85921	−0.109565
$682$	12.7773	0.489266
$683$	31.0886	1.18957	0.594786	−	0.803884i	$-0.297237\pi$
$683$	31.0886	1.18957	0.594786	+	0.803884i	$0.297237\pi$
$684$	−5.47125	−0.209198
$685$	0.115736	0.00442204
$686$	16.1611	0.617034
$687$	13.2773	0.506560
$688$	−2.18062	−0.0831354
$689$	−9.96277	−0.379551
$690$	0.729043	0.0277542
$691$	24.8234	0.944327	0.472163	−	0.881511i	$-0.343473\pi$
$691$	24.8234	0.944327	0.472163	+	0.881511i	$0.343473\pi$
$692$	9.31133	0.353964
$693$	4.50540	0.171146
$694$	35.6591	1.35360
$695$	2.80913	0.106557
$696$	2.85004	0.108030
$697$	4.52422	0.171367
$698$	−11.7668	−0.445380
$699$	−15.3992	−0.582451
$700$	7.87972	0.297825
$701$	3.01635	0.113926	0.0569630	−	0.998376i	$-0.481858\pi$
$701$	3.01635	0.113926	0.0569630	+	0.998376i	$0.481858\pi$
$702$	−47.4568	−1.79114
$703$	−3.72360	−0.140438
$704$	−72.3484	−2.72673
$705$	2.17803	0.0820292
$706$	22.9509	0.863768
$707$	−3.44387	−0.129520
$708$	−34.4164	−1.29345
$709$	−12.6925	−0.476678	−0.238339	−	0.971182i	$-0.576603\pi$
$709$	−12.6925	−0.476678	−0.238339	+	0.971182i	$0.576603\pi$
$710$	−2.84765	−0.106871
$711$	−24.1649	−0.906255
$712$	28.9073	1.08335
$713$	−1.02441	−0.0383644
$714$	1.74759	0.0654020
$715$	−5.75903	−0.215376
$716$	−54.1744	−2.02459
$717$	8.55368	0.319443
$718$	−66.8342	−2.49423
$719$	−2.39678	−0.0893850	−0.0446925	−	0.999001i	$-0.514231\pi$
$719$	−2.39678	−0.0893850	−0.0446925	+	0.999001i	$0.514231\pi$
$720$	−0.327896	−0.0122199
$721$	−8.98154	−0.334490
$722$	−39.7054	−1.47768
$723$	2.85891	0.106324
$724$	−59.5082	−2.21160
$725$	−4.92745	−0.183001
$726$	53.5597	1.98779
$727$	−8.07624	−0.299531	−0.149766	−	0.988722i	$-0.547852\pi$
$727$	−8.07624	−0.299531	−0.149766	+	0.988722i	$0.547852\pi$
$728$	−4.77743	−0.177063
$729$	22.8085	0.844758
$730$	−7.17762	−0.265655
$731$	−3.42280	−0.126597
$732$	−44.3932	−1.64082
$733$	−0.860098	−0.0317684	−0.0158842	−	0.999874i	$-0.505056\pi$
$733$	−0.860098	−0.0317684	−0.0158842	+	0.999874i	$0.505056\pi$
$734$	36.2295	1.33726
$735$	2.18129	0.0804580
$736$	6.49919	0.239563
$737$	−11.8898	−0.437965
$738$	12.7895	0.470787
$739$	−42.8187	−1.57511	−0.787556	−	0.616243i	$-0.788654\pi$
$739$	−42.8187	−1.57511	−0.787556	+	0.616243i	$0.788654\pi$
$740$	2.64861	0.0973648
$741$	5.36397	0.197050
$742$	3.04425	0.111758
$743$	5.30074	0.194465	0.0972327	−	0.995262i	$-0.469001\pi$
$743$	5.30074	0.194465	0.0972327	+	0.995262i	$0.469001\pi$
$744$	2.91960	0.107038
$745$	−3.49808	−0.128160
$746$	58.8905	2.15614
$747$	−13.2245	−0.483859
$748$	−20.8812	−0.763492
$749$	−6.37317	−0.232871
$750$	7.23754	0.264278
$751$	−44.6836	−1.63053	−0.815264	−	0.579090i	$-0.803408\pi$
$751$	−44.6836	−1.63053	−0.815264	+	0.579090i	$0.803408\pi$
$752$	5.27379	0.192315
$753$	−22.6498	−0.825406
$754$	8.66188	0.315447
$755$	3.45833	0.125862
$756$	8.76143	0.318650
$757$	0.442932	0.0160986	0.00804931	−	0.999968i	$-0.497438\pi$
$757$	0.442932	0.0160986	0.00804931	+	0.999968i	$0.497438\pi$
$758$	57.8482	2.10114
$759$	−6.68116	−0.242511
$760$	−0.737050	−0.0267356
$761$	−3.31916	−0.120320	−0.0601598	−	0.998189i	$-0.519161\pi$
$761$	−3.31916	−0.120320	−0.0601598	+	0.998189i	$0.519161\pi$
$762$	−31.4110	−1.13790
$763$	−1.66090	−0.0601285
$764$	−42.8743	−1.55114
$765$	−0.514679	−0.0186083
$766$	36.6860	1.32552
$767$	−36.0762	−1.30264
$768$	−12.7492	−0.460049
$769$	−29.7530	−1.07292	−0.536460	−	0.843926i	$-0.680239\pi$
$769$	−29.7530	−1.07292	−0.536460	+	0.843926i	$0.680239\pi$
$770$	1.75975	0.0634169
$771$	24.1265	0.868895
$772$	63.1605	2.27320
$773$	2.24387	0.0807065	0.0403532	−	0.999185i	$-0.487152\pi$
$773$	2.24387	0.0807065	0.0403532	+	0.999185i	$0.487152\pi$
$774$	−9.67586	−0.347792
$775$	−5.04771	−0.181319
$776$	7.11001	0.255234
$777$	2.03143	0.0728771
$778$	53.5595	1.92020
$779$	−4.24317	−0.152027
$780$	−3.81541	−0.136614
$781$	26.0967	0.933814
$782$	2.77086	0.0990857
$783$	−5.47882	−0.195797
$784$	5.28169	0.188632
$785$	1.10901	0.0395822
$786$	25.9693	0.926294
$787$	−7.21639	−0.257236	−0.128618	−	0.991694i	$-0.541054\pi$
$787$	−7.21639	−0.257236	−0.128618	+	0.991694i	$0.541054\pi$
$788$	4.04501	0.144098
$789$	−23.8601	−0.849441
$790$	−9.43847	−0.335806
$791$	6.64481	0.236262
$792$	−20.3591	−0.723428
$793$	−46.5341	−1.65248
$794$	22.0002	0.780759
$795$	0.838535	0.0297398
$796$	44.5951	1.58063
$797$	35.4558	1.25591	0.627954	−	0.778251i	$-0.283893\pi$
$797$	35.4558	1.25591	0.627954	+	0.778251i	$0.283893\pi$
$798$	−1.63903	−0.0580210
$799$	8.27798	0.292854
$800$	32.0244	1.13223
$801$	−18.9319	−0.668925
$802$	18.4784	0.652495
$803$	65.7777	2.32124
$804$	−7.87708	−0.277803
$805$	−0.141086	−0.00497264
$806$	8.87329	0.312548
$807$	25.3284	0.891602
$808$	15.5622	0.547476
$809$	24.9091	0.875757	0.437879	−	0.899034i	$-0.355730\pi$
$809$	24.9091	0.875757	0.437879	+	0.899034i	$0.355730\pi$
$810$	1.17857	0.0414106
$811$	42.7906	1.50258	0.751290	−	0.659972i	$-0.229432\pi$
$811$	42.7906	1.50258	0.751290	+	0.659972i	$0.229432\pi$
$812$	−1.59915	−0.0561191
$813$	22.9530	0.804998
$814$	−40.1736	−1.40808
$815$	2.88107	0.100920
$816$	1.16558	0.0408034
$817$	3.21017	0.112310
$818$	28.8258	1.00787
$819$	3.12882	0.109330
$820$	3.01818	0.105399
$821$	24.8159	0.866081	0.433041	−	0.901374i	$-0.357441\pi$
$821$	24.8159	0.866081	0.433041	+	0.901374i	$0.357441\pi$
$822$	−1.16301	−0.0405645
$823$	−44.6078	−1.55493	−0.777466	−	0.628925i	$-0.783495\pi$
$823$	−44.6078	−1.55493	−0.777466	+	0.628925i	$0.783495\pi$
$824$	40.5859	1.41388
$825$	−32.9211	−1.14616
$826$	11.0236	0.383559
$827$	−7.93280	−0.275850	−0.137925	−	0.990443i	$-0.544043\pi$
$827$	−7.93280	−0.275850	−0.137925	+	0.990443i	$0.544043\pi$
$828$	4.73259	0.164469
$829$	−29.9622	−1.04063	−0.520315	−	0.853974i	$-0.674185\pi$
$829$	−29.9622	−1.04063	−0.520315	+	0.853974i	$0.674185\pi$
$830$	−5.16530	−0.179290
$831$	5.30664	0.184085
$832$	−50.2431	−1.74186
$833$	8.29038	0.287245
$834$	−28.2284	−0.977471
$835$	−6.54685	−0.226563
$836$	19.5840	0.677327
$837$	−5.61254	−0.193998
$838$	−71.6107	−2.47375
$839$	−40.7880	−1.40816	−0.704079	−	0.710122i	$-0.748640\pi$
$839$	−40.7880	−1.40816	−0.704079	+	0.710122i	$0.748640\pi$
$840$	0.402101	0.0138738
$841$	1.00000	0.0344828
$842$	−30.2964	−1.04408
$843$	23.7242	0.817106
$844$	−51.4189	−1.76991
$845$	−0.497848	−0.0171265
$846$	23.4009	0.804540
$847$	−10.3650	−0.356146
$848$	2.03040	0.0697242
$849$	25.8991	0.888854
$850$	13.6533	0.468303
$851$	3.22089	0.110411
$852$	17.2893	0.592321
$853$	38.3184	1.31200	0.655999	−	0.754762i	$-0.272248\pi$
$853$	38.3184	1.31200	0.655999	+	0.754762i	$0.272248\pi$
$854$	14.2191	0.486568
$855$	0.482706	0.0165082
$856$	28.7992	0.984335
$857$	3.97430	0.135760	0.0678798	−	0.997694i	$-0.478377\pi$
$857$	3.97430	0.135760	0.0678798	+	0.997694i	$0.478377\pi$
$858$	57.8714	1.97570
$859$	−3.76808	−0.128565	−0.0642826	−	0.997932i	$-0.520476\pi$
$859$	−3.76808	−0.128565	−0.0642826	+	0.997932i	$0.520476\pi$
$860$	−2.28340	−0.0778634
$861$	2.31488	0.0788909
$862$	21.0364	0.716502
$863$	17.9279	0.610274	0.305137	−	0.952309i	$-0.401298\pi$
$863$	17.9279	0.610274	0.305137	+	0.952309i	$0.401298\pi$
$864$	35.6079	1.21140
$865$	−0.821502	−0.0279319
$866$	−1.04264	−0.0354304
$867$	−18.6400	−0.633049
$868$	−1.63818	−0.0556034
$869$	86.4968	2.93420
$870$	−0.729043	−0.0247169
$871$	−8.25697	−0.279777
$872$	7.50529	0.254161
$873$	−4.65646	−0.157597
$874$	−2.59873	−0.0879033
$875$	−1.40063	−0.0473499
$876$	43.5783	1.47237
$877$	−20.5426	−0.693675	−0.346838	−	0.937925i	$-0.612745\pi$
$877$	−20.5426	−0.693675	−0.346838	+	0.937925i	$0.612745\pi$
$878$	62.5572	2.11120
$879$	8.79727	0.296725
$880$	1.17368	0.0395649
$881$	20.4710	0.689685	0.344843	−	0.938661i	$-0.387932\pi$
$881$	20.4710	0.689685	0.344843	+	0.938661i	$0.387932\pi$
$882$	23.4360	0.789130
$883$	−39.4560	−1.32780	−0.663901	−	0.747821i	$-0.731100\pi$
$883$	−39.4560	−1.32780	−0.663901	+	0.747821i	$0.731100\pi$
$884$	−14.5012	−0.487727
$885$	3.03642	0.102068
$886$	53.3918	1.79373
$887$	−1.87545	−0.0629713	−0.0314857	−	0.999504i	$-0.510024\pi$
$887$	−1.87545	−0.0629713	−0.0314857	+	0.999504i	$0.510024\pi$
$888$	−9.17964	−0.308049
$889$	6.07874	0.203874
$890$	−7.39453	−0.247865
$891$	−10.8007	−0.361838
$892$	15.5267	0.519871
$893$	−7.76373	−0.259803
$894$	35.1515	1.17564
$895$	4.77960	0.159764
$896$	8.54385	0.285430
$897$	−4.63980	−0.154918
$898$	4.65507	0.155342
$899$	1.02441	0.0341659
$900$	23.3196	0.777320
$901$	3.18700	0.106174
$902$	−45.7791	−1.52428
$903$	−1.75132	−0.0582804
$904$	−30.0266	−0.998671
$905$	5.25017	0.174522
$906$	−34.7521	−1.15456
$907$	−29.4070	−0.976443	−0.488222	−	0.872720i	$-0.662354\pi$
$907$	−29.4070	−0.976443	−0.488222	+	0.872720i	$0.662354\pi$
$908$	−7.24951	−0.240583
$909$	−10.1919	−0.338045
$910$	1.22207	0.0405113
$911$	35.4638	1.17497	0.587483	−	0.809236i	$-0.300119\pi$
$911$	35.4638	1.17497	0.587483	+	0.809236i	$0.300119\pi$
$912$	−1.09317	−0.0361985
$913$	47.3363	1.56660
$914$	−41.4248	−1.37021
$915$	3.91663	0.129480
$916$	33.6645	1.11231
$917$	−5.02565	−0.165962
$918$	15.1810	0.501049
$919$	28.5662	0.942312	0.471156	−	0.882050i	$-0.343837\pi$
$919$	28.5662	0.942312	0.471156	+	0.882050i	$0.343837\pi$
$920$	0.637543	0.0210192
$921$	−36.1266	−1.19041
$922$	48.6965	1.60374
$923$	18.1231	0.596530
$924$	−10.6842	−0.351483
$925$	15.8708	0.521827
$926$	−66.2724	−2.17785
$927$	−26.5804	−0.873014
$928$	−6.49919	−0.213346
$929$	−5.87915	−0.192889	−0.0964444	−	0.995338i	$-0.530747\pi$
$929$	−5.87915	−0.192889	−0.0964444	+	0.995338i	$0.530747\pi$
$930$	−0.746837	−0.0244897
$931$	−7.77536	−0.254827
$932$	−39.0445	−1.27895
$933$	−18.5048	−0.605820
$934$	−59.8601	−1.95868
$935$	1.84226	0.0602485
$936$	−14.1386	−0.462133
$937$	−21.0807	−0.688676	−0.344338	−	0.938846i	$-0.611897\pi$
$937$	−21.0807	−0.688676	−0.344338	+	0.938846i	$0.611897\pi$
$938$	2.52302	0.0823796
$939$	−30.6862	−1.00141
$940$	5.52237	0.180120
$941$	31.1274	1.01473	0.507363	−	0.861733i	$-0.330620\pi$
$941$	31.1274	1.01473	0.507363	+	0.861733i	$0.330620\pi$
$942$	−11.1442	−0.363097
$943$	3.67031	0.119522
$944$	7.35229	0.239297
$945$	−0.772987	−0.0251453
$946$	34.6342	1.12605
$947$	−24.5911	−0.799103	−0.399551	−	0.916711i	$-0.630834\pi$
$947$	−24.5911	−0.799103	−0.399551	+	0.916711i	$0.630834\pi$
$948$	57.3049	1.86118
$949$	45.6800	1.48283
$950$	−12.8051	−0.415452
$951$	6.41311	0.207959
$952$	1.52826	0.0495311
$953$	−10.9892	−0.355975	−0.177987	−	0.984033i	$-0.556959\pi$
$953$	−10.9892	−0.355975	−0.177987	+	0.984033i	$0.556959\pi$
$954$	9.00930	0.291687
$955$	3.78263	0.122403
$956$	21.6878	0.701434
$957$	6.68116	0.215971
$958$	13.2143	0.426936
$959$	0.225068	0.00726783
$960$	4.22880	0.136484
$961$	−29.9506	−0.966148
$962$	−27.8989	−0.899498
$963$	−18.8611	−0.607789
$964$	7.24874	0.233466
$965$	−5.57240	−0.179382
$966$	1.41775	0.0456153
$967$	−35.4663	−1.14052	−0.570260	−	0.821464i	$-0.693158\pi$
$967$	−35.4663	−1.14052	−0.570260	+	0.821464i	$0.693158\pi$
$968$	46.8376	1.50542
$969$	−1.71589	−0.0551222
$970$	−1.81875	−0.0583965
$971$	41.1371	1.32015	0.660076	−	0.751199i	$-0.270524\pi$
$971$	41.1371	1.32015	0.660076	+	0.751199i	$0.270524\pi$
$972$	43.0244	1.38001
$973$	5.46284	0.175131
$974$	−48.0677	−1.54019
$975$	−22.8624	−0.732182
$976$	9.48360	0.303562
$977$	33.2895	1.06503	0.532513	−	0.846422i	$-0.321248\pi$
$977$	33.2895	1.06503	0.532513	+	0.846422i	$0.321248\pi$
$978$	−28.9513	−0.925761
$979$	67.7655	2.16580
$980$	5.53064	0.176670
$981$	−4.91534	−0.156935
$982$	25.0890	0.800624
$983$	−47.5664	−1.51713	−0.758567	−	0.651595i	$-0.774100\pi$
$983$	−47.5664	−1.51713	−0.758567	+	0.651595i	$0.774100\pi$
$984$	−10.4605	−0.333469
$985$	−0.356875	−0.0113710
$986$	−2.77086	−0.0882421
$987$	4.23554	0.134819
$988$	13.6003	0.432683
$989$	−2.77677	−0.0882962
$990$	5.20788	0.165517
$991$	−17.3992	−0.552705	−0.276352	−	0.961056i	$-0.589126\pi$
$991$	−17.3992	−0.552705	−0.276352	+	0.961056i	$0.589126\pi$
$992$	−6.65782	−0.211386
$993$	−21.3003	−0.675944
$994$	−5.53775	−0.175647
$995$	−3.93445	−0.124731
$996$	31.3607	0.993702
$997$	32.5771	1.03173	0.515863	−	0.856671i	$-0.327471\pi$
$997$	32.5771	1.03173	0.515863	+	0.856671i	$0.327471\pi$
$998$	−33.4644	−1.05930
$999$	17.6467	0.558315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.c.1.11	✓	13
3.2	odd	2		6003.2.a.o.1.3		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.c.1.11	✓	13	1.1	even	1	trivial
6003.2.a.o.1.3		13	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+2.24788 q^{2} +1.20409 q^{3} +3.05297 q^{4} -0.269352 q^{5} +2.70666 q^{6} -0.523800 q^{7} +2.36696 q^{8} -1.55016 q^{9} +O(q^{10})\)	\(q+2.24788 q^{2} +1.20409 q^{3} +3.05297 q^{4} -0.269352 q^{5} +2.70666 q^{6} -0.523800 q^{7} +2.36696 q^{8} -1.55016 q^{9} -0.605470 q^{10} +5.54870 q^{11} +3.67606 q^{12} +3.85335 q^{13} -1.17744 q^{14} -0.324325 q^{15} -0.785308 q^{16} -1.23265 q^{17} -3.48457 q^{18} +1.15608 q^{19} -0.822323 q^{20} -0.630704 q^{21} +12.4728 q^{22} -1.00000 q^{23} +2.85004 q^{24} -4.92745 q^{25} +8.66188 q^{26} -5.47882 q^{27} -1.59915 q^{28} +1.00000 q^{29} -0.729043 q^{30} +1.02441 q^{31} -6.49919 q^{32} +6.68116 q^{33} -2.77086 q^{34} +0.141086 q^{35} -4.73259 q^{36} -3.22089 q^{37} +2.59873 q^{38} +4.63980 q^{39} -0.637543 q^{40} -3.67031 q^{41} -1.41775 q^{42} +2.77677 q^{43} +16.9400 q^{44} +0.417538 q^{45} -2.24788 q^{46} -6.71558 q^{47} -0.945584 q^{48} -6.72563 q^{49} -11.0763 q^{50} -1.48423 q^{51} +11.7642 q^{52} -2.58548 q^{53} -12.3157 q^{54} -1.49455 q^{55} -1.23981 q^{56} +1.39203 q^{57} +2.24788 q^{58} -9.36230 q^{59} -0.990153 q^{60} -12.0763 q^{61} +2.30275 q^{62} +0.811973 q^{63} -13.0388 q^{64} -1.03791 q^{65} +15.0185 q^{66} -2.14280 q^{67} -3.76326 q^{68} -1.20409 q^{69} +0.317146 q^{70} +4.70321 q^{71} -3.66916 q^{72} +11.8546 q^{73} -7.24017 q^{74} -5.93311 q^{75} +3.52948 q^{76} -2.90641 q^{77} +10.4297 q^{78} +15.5887 q^{79} +0.211524 q^{80} -1.94653 q^{81} -8.25042 q^{82} +8.53106 q^{83} -1.92552 q^{84} +0.332017 q^{85} +6.24185 q^{86} +1.20409 q^{87} +13.1335 q^{88} +12.2129 q^{89} +0.938575 q^{90} -2.01839 q^{91} -3.05297 q^{92} +1.23348 q^{93} -15.0958 q^{94} -0.311392 q^{95} -7.82563 q^{96} +3.00386 q^{97} -15.1184 q^{98} -8.60137 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * q^99

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