LMFDB - Embedded newform 4334.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} + \cdots + 4 $ x^15 - x^14 - 23x^13 + 19x^12 + 194x^11 - 124x^10 - 761x^9 + 353x^8 + 1417x^7 - 465x^6 - 1128x^5 + 288x^4 + 316x^3 - 79x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.20706$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.20706 q^{3} +1.00000 q^{4} +2.02512 q^{5} +2.20706 q^{6} +2.12256 q^{7} -1.00000 q^{8} +1.87111 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.20706 q^{3} +1.00000 q^{4} +2.02512 q^{5} +2.20706 q^{6} +2.12256 q^{7} -1.00000 q^{8} +1.87111 q^{9} -2.02512 q^{10} +1.00000 q^{11} -2.20706 q^{12} +0.635429 q^{13} -2.12256 q^{14} -4.46956 q^{15} +1.00000 q^{16} +3.24064 q^{17} -1.87111 q^{18} +1.22849 q^{19} +2.02512 q^{20} -4.68462 q^{21} -1.00000 q^{22} -5.39294 q^{23} +2.20706 q^{24} -0.898891 q^{25} -0.635429 q^{26} +2.49153 q^{27} +2.12256 q^{28} -5.91521 q^{29} +4.46956 q^{30} -2.53741 q^{31} -1.00000 q^{32} -2.20706 q^{33} -3.24064 q^{34} +4.29845 q^{35} +1.87111 q^{36} -4.30712 q^{37} -1.22849 q^{38} -1.40243 q^{39} -2.02512 q^{40} -0.808867 q^{41} +4.68462 q^{42} -4.72869 q^{43} +1.00000 q^{44} +3.78921 q^{45} +5.39294 q^{46} +1.75540 q^{47} -2.20706 q^{48} -2.49472 q^{49} +0.898891 q^{50} -7.15228 q^{51} +0.635429 q^{52} -11.0867 q^{53} -2.49153 q^{54} +2.02512 q^{55} -2.12256 q^{56} -2.71135 q^{57} +5.91521 q^{58} +7.21765 q^{59} -4.46956 q^{60} -9.70454 q^{61} +2.53741 q^{62} +3.97154 q^{63} +1.00000 q^{64} +1.28682 q^{65} +2.20706 q^{66} +5.86348 q^{67} +3.24064 q^{68} +11.9025 q^{69} -4.29845 q^{70} -9.29154 q^{71} -1.87111 q^{72} -7.54655 q^{73} +4.30712 q^{74} +1.98390 q^{75} +1.22849 q^{76} +2.12256 q^{77} +1.40243 q^{78} -9.34441 q^{79} +2.02512 q^{80} -11.1123 q^{81} +0.808867 q^{82} -15.1204 q^{83} -4.68462 q^{84} +6.56268 q^{85} +4.72869 q^{86} +13.0552 q^{87} -1.00000 q^{88} +17.1609 q^{89} -3.78921 q^{90} +1.34874 q^{91} -5.39294 q^{92} +5.60022 q^{93} -1.75540 q^{94} +2.48784 q^{95} +2.20706 q^{96} -12.4837 q^{97} +2.49472 q^{98} +1.87111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.20706	−1.27425	−0.637123	−	0.770762i	$-0.719876\pi$
$3$	−2.20706	−1.27425	−0.637123	+	0.770762i	$0.719876\pi$
$4$	1.00000	0.500000
$5$	2.02512	0.905661	0.452831	−	0.891597i	$-0.350414\pi$
$5$	2.02512	0.905661	0.452831	+	0.891597i	$0.350414\pi$
$6$	2.20706	0.901028
$7$	2.12256	0.802254	0.401127	−	0.916022i	$-0.368619\pi$
$7$	2.12256	0.802254	0.401127	+	0.916022i	$0.368619\pi$
$8$	−1.00000	−0.353553
$9$	1.87111	0.623702
$10$	−2.02512	−0.640399
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.20706	−0.637123
$13$	0.635429	0.176236	0.0881181	−	0.996110i	$-0.471915\pi$
$13$	0.635429	0.176236	0.0881181	+	0.996110i	$0.471915\pi$
$14$	−2.12256	−0.567279
$15$	−4.46956	−1.15403
$16$	1.00000	0.250000
$17$	3.24064	0.785970	0.392985	−	0.919545i	$-0.371442\pi$
$17$	3.24064	0.785970	0.392985	+	0.919545i	$0.371442\pi$
$18$	−1.87111	−0.441024
$19$	1.22849	0.281835	0.140918	−	0.990021i	$-0.454995\pi$
$19$	1.22849	0.281835	0.140918	+	0.990021i	$0.454995\pi$
$20$	2.02512	0.452831
$21$	−4.68462	−1.02227
$22$	−1.00000	−0.213201
$23$	−5.39294	−1.12451	−0.562253	−	0.826966i	$-0.690065\pi$
$23$	−5.39294	−1.12451	−0.562253	+	0.826966i	$0.690065\pi$
$24$	2.20706	0.450514
$25$	−0.898891	−0.179778
$26$	−0.635429	−0.124618
$27$	2.49153	0.479496
$28$	2.12256	0.401127
$29$	−5.91521	−1.09843	−0.549214	−	0.835682i	$-0.685073\pi$
$29$	−5.91521	−1.09843	−0.549214	+	0.835682i	$0.685073\pi$
$30$	4.46956	0.816026
$31$	−2.53741	−0.455733	−0.227867	−	0.973692i	$-0.573175\pi$
$31$	−2.53741	−0.455733	−0.227867	+	0.973692i	$0.573175\pi$
$32$	−1.00000	−0.176777
$33$	−2.20706	−0.384200
$34$	−3.24064	−0.555765
$35$	4.29845	0.726570
$36$	1.87111	0.311851
$37$	−4.30712	−0.708086	−0.354043	−	0.935229i	$-0.615193\pi$
$37$	−4.30712	−0.708086	−0.354043	+	0.935229i	$0.615193\pi$
$38$	−1.22849	−0.199287
$39$	−1.40243	−0.224568
$40$	−2.02512	−0.320200
$41$	−0.808867	−0.126324	−0.0631619	−	0.998003i	$-0.520118\pi$
$41$	−0.808867	−0.126324	−0.0631619	+	0.998003i	$0.520118\pi$
$42$	4.68462	0.722853
$43$	−4.72869	−0.721119	−0.360560	−	0.932736i	$-0.617414\pi$
$43$	−4.72869	−0.721119	−0.360560	+	0.932736i	$0.617414\pi$
$44$	1.00000	0.150756
$45$	3.78921	0.564863
$46$	5.39294	0.795145
$47$	1.75540	0.256052	0.128026	−	0.991771i	$-0.459136\pi$
$47$	1.75540	0.256052	0.128026	+	0.991771i	$0.459136\pi$
$48$	−2.20706	−0.318561
$49$	−2.49472	−0.356389
$50$	0.898891	0.127122
$51$	−7.15228	−1.00152
$52$	0.635429	0.0881181
$53$	−11.0867	−1.52288	−0.761438	−	0.648237i	$-0.775506\pi$
$53$	−11.0867	−1.52288	−0.761438	+	0.648237i	$0.775506\pi$
$54$	−2.49153	−0.339055
$55$	2.02512	0.273067
$56$	−2.12256	−0.283640
$57$	−2.71135	−0.359127
$58$	5.91521	0.776705
$59$	7.21765	0.939658	0.469829	−	0.882757i	$-0.344316\pi$
$59$	7.21765	0.939658	0.469829	+	0.882757i	$0.344316\pi$
$60$	−4.46956	−0.577017
$61$	−9.70454	−1.24254	−0.621269	−	0.783597i	$-0.713383\pi$
$61$	−9.70454	−1.24254	−0.621269	+	0.783597i	$0.713383\pi$
$62$	2.53741	0.322252
$63$	3.97154	0.500367
$64$	1.00000	0.125000
$65$	1.28682	0.159610
$66$	2.20706	0.271670
$67$	5.86348	0.716338	0.358169	−	0.933657i	$-0.383401\pi$
$67$	5.86348	0.716338	0.358169	+	0.933657i	$0.383401\pi$
$68$	3.24064	0.392985
$69$	11.9025	1.43290
$70$	−4.29845	−0.513763
$71$	−9.29154	−1.10270	−0.551352	−	0.834273i	$-0.685888\pi$
$71$	−9.29154	−1.10270	−0.551352	+	0.834273i	$0.685888\pi$
$72$	−1.87111	−0.220512
$73$	−7.54655	−0.883257	−0.441629	−	0.897198i	$-0.645599\pi$
$73$	−7.54655	−0.883257	−0.441629	+	0.897198i	$0.645599\pi$
$74$	4.30712	0.500693
$75$	1.98390	0.229082
$76$	1.22849	0.140918
$77$	2.12256	0.241889
$78$	1.40243	0.158794
$79$	−9.34441	−1.05133	−0.525664	−	0.850692i	$-0.676183\pi$
$79$	−9.34441	−1.05133	−0.525664	+	0.850692i	$0.676183\pi$
$80$	2.02512	0.226415
$81$	−11.1123	−1.23470
$82$	0.808867	0.0893244
$83$	−15.1204	−1.65967	−0.829837	−	0.558005i	$-0.811567\pi$
$83$	−15.1204	−1.65967	−0.829837	+	0.558005i	$0.811567\pi$
$84$	−4.68462	−0.511134
$85$	6.56268	0.711823
$86$	4.72869	0.509908
$87$	13.0552	1.39967
$88$	−1.00000	−0.106600
$89$	17.1609	1.81905	0.909525	−	0.415649i	$-0.136446\pi$
$89$	17.1609	1.81905	0.909525	+	0.415649i	$0.136446\pi$
$90$	−3.78921	−0.399418
$91$	1.34874	0.141386
$92$	−5.39294	−0.562253
$93$	5.60022	0.580716
$94$	−1.75540	−0.181056
$95$	2.48784	0.255247
$96$	2.20706	0.225257
$97$	−12.4837	−1.26753	−0.633763	−	0.773527i	$-0.718491\pi$
$97$	−12.4837	−1.26753	−0.633763	+	0.773527i	$0.718491\pi$
$98$	2.49472	0.252005
$99$	1.87111	0.188053
$100$	−0.898891	−0.0898891
$101$	0.783486	0.0779597	0.0389799	−	0.999240i	$-0.487589\pi$
$101$	0.783486	0.0779597	0.0389799	+	0.999240i	$0.487589\pi$
$102$	7.15228	0.708181
$103$	11.7996	1.16265	0.581325	−	0.813671i	$-0.302534\pi$
$103$	11.7996	1.16265	0.581325	+	0.813671i	$0.302534\pi$
$104$	−0.635429	−0.0623089
$105$	−9.48692	−0.925829
$106$	11.0867	1.07684
$107$	3.47156	0.335609	0.167804	−	0.985820i	$-0.446332\pi$
$107$	3.47156	0.335609	0.167804	+	0.985820i	$0.446332\pi$
$108$	2.49153	0.239748
$109$	−9.07313	−0.869048	−0.434524	−	0.900660i	$-0.643083\pi$
$109$	−9.07313	−0.869048	−0.434524	+	0.900660i	$0.643083\pi$
$110$	−2.02512	−0.193088
$111$	9.50607	0.902276
$112$	2.12256	0.200563
$113$	15.1971	1.42962	0.714810	−	0.699319i	$-0.246513\pi$
$113$	15.1971	1.42962	0.714810	+	0.699319i	$0.246513\pi$
$114$	2.71135	0.253941
$115$	−10.9213	−1.01842
$116$	−5.91521	−0.549214
$117$	1.18895	0.109919
$118$	−7.21765	−0.664439
$119$	6.87846	0.630548
$120$	4.46956	0.408013
$121$	1.00000	0.0909091
$122$	9.70454	0.878607
$123$	1.78522	0.160967
$124$	−2.53741	−0.227867
$125$	−11.9460	−1.06848
$126$	−3.97154	−0.353813
$127$	1.95108	0.173130	0.0865652	−	0.996246i	$-0.472411\pi$
$127$	1.95108	0.173130	0.0865652	+	0.996246i	$0.472411\pi$
$128$	−1.00000	−0.0883883
$129$	10.4365	0.918883
$130$	−1.28682	−0.112861
$131$	−5.37918	−0.469982	−0.234991	−	0.971998i	$-0.575506\pi$
$131$	−5.37918	−0.469982	−0.234991	+	0.971998i	$0.575506\pi$
$132$	−2.20706	−0.192100
$133$	2.60755	0.226103
$134$	−5.86348	−0.506527
$135$	5.04565	0.434261
$136$	−3.24064	−0.277883
$137$	−5.06244	−0.432514	−0.216257	−	0.976337i	$-0.569385\pi$
$137$	−5.06244	−0.432514	−0.216257	+	0.976337i	$0.569385\pi$
$138$	−11.9025	−1.01321
$139$	8.78311	0.744974	0.372487	−	0.928037i	$-0.378505\pi$
$139$	8.78311	0.744974	0.372487	+	0.928037i	$0.378505\pi$
$140$	4.29845	0.363285
$141$	−3.87428	−0.326273
$142$	9.29154	0.779729
$143$	0.635429	0.0531372
$144$	1.87111	0.155926
$145$	−11.9790	−0.994803
$146$	7.54655	0.624557
$147$	5.50600	0.454127
$148$	−4.30712	−0.354043
$149$	6.00577	0.492011	0.246006	−	0.969268i	$-0.420882\pi$
$149$	6.00577	0.492011	0.246006	+	0.969268i	$0.420882\pi$
$150$	−1.98390	−0.161985
$151$	−6.13074	−0.498913	−0.249456	−	0.968386i	$-0.580252\pi$
$151$	−6.13074	−0.498913	−0.249456	+	0.968386i	$0.580252\pi$
$152$	−1.22849	−0.0996437
$153$	6.06358	0.490211
$154$	−2.12256	−0.171041
$155$	−5.13857	−0.412740
$156$	−1.40243	−0.112284
$157$	11.7324	0.936348	0.468174	−	0.883636i	$-0.344912\pi$
$157$	11.7324	0.936348	0.468174	+	0.883636i	$0.344912\pi$
$158$	9.34441	0.743401
$159$	24.4690	1.94052
$160$	−2.02512	−0.160100
$161$	−11.4469	−0.902139
$162$	11.1123	0.873063
$163$	16.9577	1.32823	0.664113	−	0.747632i	$-0.268809\pi$
$163$	16.9577	1.32823	0.664113	+	0.747632i	$0.268809\pi$
$164$	−0.808867	−0.0631619
$165$	−4.46956	−0.347955
$166$	15.1204	1.17357
$167$	17.3658	1.34380	0.671902	−	0.740640i	$-0.265478\pi$
$167$	17.3658	1.34380	0.671902	+	0.740640i	$0.265478\pi$
$168$	4.68462	0.361426
$169$	−12.5962	−0.968941
$170$	−6.56268	−0.503335
$171$	2.29864	0.175781
$172$	−4.72869	−0.360560
$173$	17.2937	1.31482	0.657409	−	0.753534i	$-0.271652\pi$
$173$	17.2937	1.31482	0.657409	+	0.753534i	$0.271652\pi$
$174$	−13.0552	−0.989713
$175$	−1.90795	−0.144228
$176$	1.00000	0.0753778
$177$	−15.9298	−1.19736
$178$	−17.1609	−1.28626
$179$	0.268382	0.0200598	0.0100299	−	0.999950i	$-0.496807\pi$
$179$	0.268382	0.0200598	0.0100299	+	0.999950i	$0.496807\pi$
$180$	3.78921	0.282431
$181$	6.74640	0.501456	0.250728	−	0.968058i	$-0.419330\pi$
$181$	6.74640	0.501456	0.250728	+	0.968058i	$0.419330\pi$
$182$	−1.34874	−0.0999751
$183$	21.4185	1.58330
$184$	5.39294	0.397573
$185$	−8.72243	−0.641286
$186$	−5.60022	−0.410628
$187$	3.24064	0.236979
$188$	1.75540	0.128026
$189$	5.28844	0.384677
$190$	−2.48784	−0.180487
$191$	−25.5150	−1.84620	−0.923101	−	0.384558i	$-0.874354\pi$
$191$	−25.5150	−1.84620	−0.923101	+	0.384558i	$0.874354\pi$
$192$	−2.20706	−0.159281
$193$	−23.3802	−1.68294	−0.841471	−	0.540303i	$-0.818310\pi$
$193$	−23.3802	−1.68294	−0.841471	+	0.540303i	$0.818310\pi$
$194$	12.4837	0.896276
$195$	−2.84008	−0.203383
$196$	−2.49472	−0.178194
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−1.87111	−0.132974
$199$	5.05202	0.358128	0.179064	−	0.983837i	$-0.442693\pi$
$199$	5.05202	0.358128	0.179064	+	0.983837i	$0.442693\pi$
$200$	0.898891	0.0635612
$201$	−12.9410	−0.912790
$202$	−0.783486	−0.0551259
$203$	−12.5554	−0.881217
$204$	−7.15228	−0.500760
$205$	−1.63805	−0.114406
$206$	−11.7996	−0.822118
$207$	−10.0908	−0.701356
$208$	0.635429	0.0440590
$209$	1.22849	0.0849765
$210$	9.48692	0.654660
$211$	7.13218	0.491000	0.245500	−	0.969397i	$-0.421048\pi$
$211$	7.13218	0.491000	0.245500	+	0.969397i	$0.421048\pi$
$212$	−11.0867	−0.761438
$213$	20.5070	1.40511
$214$	−3.47156	−0.237311
$215$	−9.57617	−0.653089
$216$	−2.49153	−0.169527
$217$	−5.38582	−0.365614
$218$	9.07313	0.614510
$219$	16.6557	1.12549
$220$	2.02512	0.136534
$221$	2.05919	0.138516
$222$	−9.50607	−0.638005
$223$	17.7615	1.18940	0.594698	−	0.803949i	$-0.297272\pi$
$223$	17.7615	1.18940	0.594698	+	0.803949i	$0.297272\pi$
$224$	−2.12256	−0.141820
$225$	−1.68192	−0.112128
$226$	−15.1971	−1.01089
$227$	14.5367	0.964836	0.482418	−	0.875941i	$-0.339759\pi$
$227$	14.5367	0.964836	0.482418	+	0.875941i	$0.339759\pi$
$228$	−2.71135	−0.179564
$229$	−19.4834	−1.28750	−0.643749	−	0.765237i	$-0.722622\pi$
$229$	−19.4834	−1.28750	−0.643749	+	0.765237i	$0.722622\pi$
$230$	10.9213	0.720132
$231$	−4.68462	−0.308226
$232$	5.91521	0.388353
$233$	−14.0135	−0.918056	−0.459028	−	0.888422i	$-0.651802\pi$
$233$	−14.0135	−0.918056	−0.459028	+	0.888422i	$0.651802\pi$
$234$	−1.18895	−0.0777244
$235$	3.55490	0.231896
$236$	7.21765	0.469829
$237$	20.6237	1.33965
$238$	−6.87846	−0.445865
$239$	9.51438	0.615434	0.307717	−	0.951478i	$-0.400435\pi$
$239$	9.51438	0.615434	0.307717	+	0.951478i	$0.400435\pi$
$240$	−4.46956	−0.288509
$241$	−7.90465	−0.509183	−0.254592	−	0.967049i	$-0.581941\pi$
$241$	−7.90465	−0.509183	−0.254592	+	0.967049i	$0.581941\pi$
$242$	−1.00000	−0.0642824
$243$	17.0508	1.09381
$244$	−9.70454	−0.621269
$245$	−5.05211	−0.322767
$246$	−1.78522	−0.113821
$247$	0.780618	0.0496695
$248$	2.53741	0.161126
$249$	33.3715	2.11483
$250$	11.9460	0.755529
$251$	9.69181	0.611742	0.305871	−	0.952073i	$-0.401052\pi$
$251$	9.69181	0.611742	0.305871	+	0.952073i	$0.401052\pi$
$252$	3.97154	0.250184
$253$	−5.39294	−0.339051
$254$	−1.95108	−0.122422
$255$	−14.4842	−0.907037
$256$	1.00000	0.0625000
$257$	−25.0204	−1.56073	−0.780365	−	0.625324i	$-0.784967\pi$
$257$	−25.0204	−1.56073	−0.780365	+	0.625324i	$0.784967\pi$
$258$	−10.4365	−0.649748
$259$	−9.14214	−0.568065
$260$	1.28682	0.0798051
$261$	−11.0680	−0.685091
$262$	5.37918	0.332327
$263$	−4.37082	−0.269516	−0.134758	−	0.990879i	$-0.543026\pi$
$263$	−4.37082	−0.269516	−0.134758	+	0.990879i	$0.543026\pi$
$264$	2.20706	0.135835
$265$	−22.4519	−1.37921
$266$	−2.60755	−0.159879
$267$	−37.8751	−2.31792
$268$	5.86348	0.358169
$269$	−13.9997	−0.853574	−0.426787	−	0.904352i	$-0.640355\pi$
$269$	−13.9997	−0.853574	−0.426787	+	0.904352i	$0.640355\pi$
$270$	−5.04565	−0.307069
$271$	9.96519	0.605342	0.302671	−	0.953095i	$-0.402122\pi$
$271$	9.96519	0.605342	0.302671	+	0.953095i	$0.402122\pi$
$272$	3.24064	0.196493
$273$	−2.97674	−0.180161
$274$	5.06244	0.305833
$275$	−0.898891	−0.0542052
$276$	11.9025	0.716448
$277$	2.41120	0.144875	0.0724374	−	0.997373i	$-0.476922\pi$
$277$	2.41120	0.144875	0.0724374	+	0.997373i	$0.476922\pi$
$278$	−8.78311	−0.526776
$279$	−4.74777	−0.284242
$280$	−4.29845	−0.256881
$281$	−3.62730	−0.216387	−0.108193	−	0.994130i	$-0.534507\pi$
$281$	−3.62730	−0.216387	−0.108193	+	0.994130i	$0.534507\pi$
$282$	3.87428	0.230710
$283$	−29.5762	−1.75812	−0.879060	−	0.476711i	$-0.841829\pi$
$283$	−29.5762	−1.75812	−0.879060	+	0.476711i	$0.841829\pi$
$284$	−9.29154	−0.551352
$285$	−5.49081	−0.325247
$286$	−0.635429	−0.0375737
$287$	−1.71687	−0.101344
$288$	−1.87111	−0.110256
$289$	−6.49826	−0.382250
$290$	11.9790	0.703432
$291$	27.5522	1.61514
$292$	−7.54655	−0.441629
$293$	18.4664	1.07882	0.539409	−	0.842044i	$-0.318648\pi$
$293$	18.4664	1.07882	0.539409	+	0.842044i	$0.318648\pi$
$294$	−5.50600	−0.321116
$295$	14.6166	0.851012
$296$	4.30712	0.250346
$297$	2.49153	0.144573
$298$	−6.00577	−0.347905
$299$	−3.42683	−0.198179
$300$	1.98390	0.114541
$301$	−10.0370	−0.578521
$302$	6.13074	0.352785
$303$	−1.72920	−0.0993399
$304$	1.22849	0.0704588
$305$	−19.6528	−1.12532
$306$	−6.06358	−0.346632
$307$	−17.7304	−1.01193	−0.505963	−	0.862555i	$-0.668863\pi$
$307$	−17.7304	−1.01193	−0.505963	+	0.862555i	$0.668863\pi$
$308$	2.12256	0.120944
$309$	−26.0424	−1.48150
$310$	5.13857	0.291851
$311$	−5.91581	−0.335455	−0.167727	−	0.985833i	$-0.553643\pi$
$311$	−5.91581	−0.335455	−0.167727	+	0.985833i	$0.553643\pi$
$312$	1.40243	0.0793969
$313$	0.826328	0.0467068	0.0233534	−	0.999727i	$-0.492566\pi$
$313$	0.826328	0.0467068	0.0233534	+	0.999727i	$0.492566\pi$
$314$	−11.7324	−0.662098
$315$	8.04285	0.453163
$316$	−9.34441	−0.525664
$317$	−23.2105	−1.30363	−0.651816	−	0.758377i	$-0.725993\pi$
$317$	−23.2105	−1.30363	−0.651816	+	0.758377i	$0.725993\pi$
$318$	−24.4690	−1.37215
$319$	−5.91521	−0.331188
$320$	2.02512	0.113208
$321$	−7.66194	−0.427648
$322$	11.4469	0.637908
$323$	3.98109	0.221514
$324$	−11.1123	−0.617349
$325$	−0.571181	−0.0316834
$326$	−16.9577	−0.939198
$327$	20.0249	1.10738
$328$	0.808867	0.0446622
$329$	3.72596	0.205419
$330$	4.46956	0.246041
$331$	−28.2872	−1.55481	−0.777403	−	0.629003i	$-0.783463\pi$
$331$	−28.2872	−1.55481	−0.777403	+	0.629003i	$0.783463\pi$
$332$	−15.1204	−0.829837
$333$	−8.05908	−0.441635
$334$	−17.3658	−0.950213
$335$	11.8742	0.648759
$336$	−4.68462	−0.255567
$337$	16.8345	0.917034	0.458517	−	0.888686i	$-0.348381\pi$
$337$	16.8345	0.917034	0.458517	+	0.888686i	$0.348381\pi$
$338$	12.5962	0.685145
$339$	−33.5408	−1.82169
$340$	6.56268	0.355911
$341$	−2.53741	−0.137409
$342$	−2.29864	−0.124296
$343$	−20.1532	−1.08817
$344$	4.72869	0.254954
$345$	24.1040	1.29772
$346$	−17.2937	−0.929717
$347$	−5.28117	−0.283508	−0.141754	−	0.989902i	$-0.545274\pi$
$347$	−5.28117	−0.283508	−0.141754	+	0.989902i	$0.545274\pi$
$348$	13.0552	0.699833
$349$	−12.4514	−0.666510	−0.333255	−	0.942837i	$-0.608147\pi$
$349$	−12.4514	−0.666510	−0.333255	+	0.942837i	$0.608147\pi$
$350$	1.90795	0.101984
$351$	1.58319	0.0845045
$352$	−1.00000	−0.0533002
$353$	8.77839	0.467227	0.233613	−	0.972330i	$-0.424945\pi$
$353$	8.77839	0.467227	0.233613	+	0.972330i	$0.424945\pi$
$354$	15.9298	0.846658
$355$	−18.8165	−0.998675
$356$	17.1609	0.909525
$357$	−15.1812	−0.803473
$358$	−0.268382	−0.0141844
$359$	−6.04901	−0.319255	−0.159627	−	0.987177i	$-0.551029\pi$
$359$	−6.04901	−0.319255	−0.159627	+	0.987177i	$0.551029\pi$
$360$	−3.78921	−0.199709
$361$	−17.4908	−0.920569
$362$	−6.74640	−0.354583
$363$	−2.20706	−0.115841
$364$	1.34874	0.0706931
$365$	−15.2827	−0.799932
$366$	−21.4185	−1.11956
$367$	9.12380	0.476258	0.238129	−	0.971233i	$-0.423466\pi$
$367$	9.12380	0.476258	0.238129	+	0.971233i	$0.423466\pi$
$368$	−5.39294	−0.281126
$369$	−1.51348	−0.0787884
$370$	8.72243	0.453458
$371$	−23.5322	−1.22173
$372$	5.60022	0.290358
$373$	−14.9250	−0.772789	−0.386395	−	0.922334i	$-0.626280\pi$
$373$	−14.9250	−0.772789	−0.386395	+	0.922334i	$0.626280\pi$
$374$	−3.24064	−0.167569
$375$	26.3654	1.36150
$376$	−1.75540	−0.0905280
$377$	−3.75869	−0.193583
$378$	−5.28844	−0.272008
$379$	−15.5664	−0.799593	−0.399796	−	0.916604i	$-0.630919\pi$
$379$	−15.5664	−0.799593	−0.399796	+	0.916604i	$0.630919\pi$
$380$	2.48784	0.127623
$381$	−4.30615	−0.220611
$382$	25.5150	1.30546
$383$	28.3440	1.44831	0.724155	−	0.689637i	$-0.242230\pi$
$383$	28.3440	1.44831	0.724155	+	0.689637i	$0.242230\pi$
$384$	2.20706	0.112628
$385$	4.29845	0.219069
$386$	23.3802	1.19002
$387$	−8.84789	−0.449764
$388$	−12.4837	−0.633763
$389$	−17.6143	−0.893083	−0.446541	−	0.894763i	$-0.647344\pi$
$389$	−17.6143	−0.893083	−0.446541	+	0.894763i	$0.647344\pi$
$390$	2.84008	0.143813
$391$	−17.4766	−0.883828
$392$	2.49472	0.126002
$393$	11.8722	0.598872
$394$	−1.00000	−0.0503793
$395$	−18.9236	−0.952147
$396$	1.87111	0.0940266
$397$	−4.74127	−0.237958	−0.118979	−	0.992897i	$-0.537962\pi$
$397$	−4.74127	−0.237958	−0.118979	+	0.992897i	$0.537962\pi$
$398$	−5.05202	−0.253235
$399$	−5.75501	−0.288111
$400$	−0.898891	−0.0449445
$401$	−16.8420	−0.841049	−0.420525	−	0.907281i	$-0.638154\pi$
$401$	−16.8420	−0.841049	−0.420525	+	0.907281i	$0.638154\pi$
$402$	12.9410	0.645440
$403$	−1.61235	−0.0803167
$404$	0.783486	0.0389799
$405$	−22.5037	−1.11822
$406$	12.5554	0.623115
$407$	−4.30712	−0.213496
$408$	7.15228	0.354091
$409$	38.2124	1.88948	0.944740	−	0.327821i	$-0.106314\pi$
$409$	38.2124	1.88948	0.944740	+	0.327821i	$0.106314\pi$
$410$	1.63805	0.0808976
$411$	11.1731	0.551129
$412$	11.7996	0.581325
$413$	15.3199	0.753844
$414$	10.0908	0.495934
$415$	−30.6205	−1.50310
$416$	−0.635429	−0.0311545
$417$	−19.3848	−0.949280
$418$	−1.22849	−0.0600874
$419$	−13.0146	−0.635804	−0.317902	−	0.948124i	$-0.602978\pi$
$419$	−13.0146	−0.635804	−0.317902	+	0.948124i	$0.602978\pi$
$420$	−9.48692	−0.462914
$421$	−2.16562	−0.105546	−0.0527730	−	0.998607i	$-0.516806\pi$
$421$	−2.16562	−0.105546	−0.0527730	+	0.998607i	$0.516806\pi$
$422$	−7.13218	−0.347189
$423$	3.28455	0.159700
$424$	11.0867	0.538418
$425$	−2.91298	−0.141300
$426$	−20.5070	−0.993566
$427$	−20.5985	−0.996831
$428$	3.47156	0.167804
$429$	−1.40243	−0.0677099
$430$	9.57617	0.461804
$431$	8.24720	0.397254	0.198627	−	0.980075i	$-0.436352\pi$
$431$	8.24720	0.397254	0.198627	+	0.980075i	$0.436352\pi$
$432$	2.49153	0.119874
$433$	−38.3601	−1.84347	−0.921734	−	0.387823i	$-0.873227\pi$
$433$	−38.3601	−1.84347	−0.921734	+	0.387823i	$0.873227\pi$
$434$	5.38582	0.258528
$435$	26.4384	1.26762
$436$	−9.07313	−0.434524
$437$	−6.62517	−0.316925
$438$	−16.6557	−0.795839
$439$	27.8075	1.32718	0.663589	−	0.748097i	$-0.269032\pi$
$439$	27.8075	1.32718	0.663589	+	0.748097i	$0.269032\pi$
$440$	−2.02512	−0.0965438
$441$	−4.66789	−0.222280
$442$	−2.05919	−0.0979459
$443$	13.7027	0.651036	0.325518	−	0.945536i	$-0.394461\pi$
$443$	13.7027	0.651036	0.325518	+	0.945536i	$0.394461\pi$
$444$	9.50607	0.451138
$445$	34.7528	1.64744
$446$	−17.7615	−0.841029
$447$	−13.2551	−0.626943
$448$	2.12256	0.100282
$449$	1.57760	0.0744514	0.0372257	−	0.999307i	$-0.488148\pi$
$449$	1.57760	0.0744514	0.0372257	+	0.999307i	$0.488148\pi$
$450$	1.68192	0.0792865
$451$	−0.808867	−0.0380880
$452$	15.1971	0.714810
$453$	13.5309	0.635737
$454$	−14.5367	−0.682242
$455$	2.73136	0.128048
$456$	2.71135	0.126971
$457$	−34.3574	−1.60717	−0.803587	−	0.595188i	$-0.797078\pi$
$457$	−34.3574	−1.60717	−0.803587	+	0.595188i	$0.797078\pi$
$458$	19.4834	0.910399
$459$	8.07416	0.376870
$460$	−10.9213	−0.509210
$461$	1.04932	0.0488717	0.0244359	−	0.999701i	$-0.492221\pi$
$461$	1.04932	0.0488717	0.0244359	+	0.999701i	$0.492221\pi$
$462$	4.68462	0.217948
$463$	−23.0262	−1.07012	−0.535058	−	0.844815i	$-0.679710\pi$
$463$	−23.0262	−1.07012	−0.535058	+	0.844815i	$0.679710\pi$
$464$	−5.91521	−0.274607
$465$	11.3411	0.525932
$466$	14.0135	0.649164
$467$	−5.11057	−0.236489	−0.118245	−	0.992984i	$-0.537727\pi$
$467$	−5.11057	−0.236489	−0.118245	+	0.992984i	$0.537727\pi$
$468$	1.18895	0.0549594
$469$	12.4456	0.574685
$470$	−3.55490	−0.163975
$471$	−25.8941	−1.19314
$472$	−7.21765	−0.332219
$473$	−4.72869	−0.217426
$474$	−20.6237	−0.947276
$475$	−1.10428	−0.0506678
$476$	6.87846	0.315274
$477$	−20.7444	−0.949821
$478$	−9.51438	−0.435178
$479$	6.36419	0.290787	0.145394	−	0.989374i	$-0.453555\pi$
$479$	6.36419	0.290787	0.145394	+	0.989374i	$0.453555\pi$
$480$	4.46956	0.204006
$481$	−2.73687	−0.124790
$482$	7.90465	0.360047
$483$	25.2639	1.14955
$484$	1.00000	0.0454545
$485$	−25.2809	−1.14795
$486$	−17.0508	−0.773442
$487$	7.56830	0.342952	0.171476	−	0.985188i	$-0.445146\pi$
$487$	7.56830	0.342952	0.171476	+	0.985188i	$0.445146\pi$
$488$	9.70454	0.439304
$489$	−37.4266	−1.69249
$490$	5.05211	0.228231
$491$	−9.26509	−0.418128	−0.209064	−	0.977902i	$-0.567042\pi$
$491$	−9.26509	−0.418128	−0.209064	+	0.977902i	$0.567042\pi$
$492$	1.78522	0.0804837
$493$	−19.1691	−0.863331
$494$	−0.780618	−0.0351217
$495$	3.78921	0.170313
$496$	−2.53741	−0.113933
$497$	−19.7219	−0.884648
$498$	−33.3715	−1.49541
$499$	−21.2042	−0.949232	−0.474616	−	0.880193i	$-0.657413\pi$
$499$	−21.2042	−0.949232	−0.474616	+	0.880193i	$0.657413\pi$
$500$	−11.9460	−0.534240
$501$	−38.3273	−1.71234
$502$	−9.69181	−0.432567
$503$	8.37020	0.373209	0.186604	−	0.982435i	$-0.440252\pi$
$503$	8.37020	0.373209	0.186604	+	0.982435i	$0.440252\pi$
$504$	−3.97154	−0.176907
$505$	1.58665	0.0706051
$506$	5.39294	0.239745
$507$	27.8006	1.23467
$508$	1.95108	0.0865652
$509$	23.5661	1.04455	0.522275	−	0.852777i	$-0.325083\pi$
$509$	23.5661	1.04455	0.522275	+	0.852777i	$0.325083\pi$
$510$	14.4842	0.641372
$511$	−16.0180	−0.708596
$512$	−1.00000	−0.0441942
$513$	3.06083	0.135139
$514$	25.0204	1.10360
$515$	23.8956	1.05297
$516$	10.4365	0.459441
$517$	1.75540	0.0772025
$518$	9.14214	0.401683
$519$	−38.1683	−1.67540
$520$	−1.28682	−0.0564307
$521$	42.3583	1.85575	0.927876	−	0.372888i	$-0.121632\pi$
$521$	42.3583	1.85575	0.927876	+	0.372888i	$0.121632\pi$
$522$	11.0680	0.484433
$523$	0.240823	0.0105305	0.00526523	−	0.999986i	$-0.498324\pi$
$523$	0.240823	0.0105305	0.00526523	+	0.999986i	$0.498324\pi$
$524$	−5.37918	−0.234991
$525$	4.21096	0.183782
$526$	4.37082	0.190577
$527$	−8.22284	−0.358193
$528$	−2.20706	−0.0960499
$529$	6.08377	0.264512
$530$	22.4519	0.975249
$531$	13.5050	0.586067
$532$	2.60755	0.113052
$533$	−0.513977	−0.0222628
$534$	37.8751	1.63901
$535$	7.03033	0.303948
$536$	−5.86348	−0.253264
$537$	−0.592334	−0.0255611
$538$	13.9997	0.603568
$539$	−2.49472	−0.107455
$540$	5.04565	0.217130
$541$	40.2894	1.73218	0.866089	−	0.499890i	$-0.166626\pi$
$541$	40.2894	1.73218	0.866089	+	0.499890i	$0.166626\pi$
$542$	−9.96519	−0.428042
$543$	−14.8897	−0.638978
$544$	−3.24064	−0.138941
$545$	−18.3742	−0.787063
$546$	2.97674	0.127393
$547$	18.0014	0.769684	0.384842	−	0.922982i	$-0.374256\pi$
$547$	18.0014	0.769684	0.384842	+	0.922982i	$0.374256\pi$
$548$	−5.06244	−0.216257
$549$	−18.1582	−0.774974
$550$	0.898891	0.0383288
$551$	−7.26678	−0.309575
$552$	−11.9025	−0.506605
$553$	−19.8341	−0.843432
$554$	−2.41120	−0.102442
$555$	19.2509	0.817156
$556$	8.78311	0.372487
$557$	21.2309	0.899581	0.449790	−	0.893134i	$-0.351499\pi$
$557$	21.2309	0.899581	0.449790	+	0.893134i	$0.351499\pi$
$558$	4.74777	0.200989
$559$	−3.00475	−0.127087
$560$	4.29845	0.181642
$561$	−7.15228	−0.301969
$562$	3.62730	0.153008
$563$	−8.42253	−0.354967	−0.177484	−	0.984124i	$-0.556796\pi$
$563$	−8.42253	−0.354967	−0.177484	+	0.984124i	$0.556796\pi$
$564$	−3.87428	−0.163136
$565$	30.7759	1.29475
$566$	29.5762	1.24318
$567$	−23.5865	−0.990541
$568$	9.29154	0.389864
$569$	−23.8090	−0.998124	−0.499062	−	0.866566i	$-0.666322\pi$
$569$	−23.8090	−0.998124	−0.499062	+	0.866566i	$0.666322\pi$
$570$	5.49081	0.229985
$571$	2.58667	0.108249	0.0541244	−	0.998534i	$-0.482763\pi$
$571$	2.58667	0.108249	0.0541244	+	0.998534i	$0.482763\pi$
$572$	0.635429	0.0265686
$573$	56.3131	2.35251
$574$	1.71687	0.0716608
$575$	4.84766	0.202161
$576$	1.87111	0.0779628
$577$	−5.31888	−0.221428	−0.110714	−	0.993852i	$-0.535314\pi$
$577$	−5.31888	−0.221428	−0.110714	+	0.993852i	$0.535314\pi$
$578$	6.49826	0.270292
$579$	51.6014	2.14448
$580$	−11.9790	−0.497401
$581$	−32.0939	−1.33148
$582$	−27.5522	−1.14208
$583$	−11.0867	−0.459165
$584$	7.54655	0.312279
$585$	2.40778	0.0995492
$586$	−18.4664	−0.762839
$587$	39.1570	1.61618	0.808090	−	0.589059i	$-0.200501\pi$
$587$	39.1570	1.61618	0.808090	+	0.589059i	$0.200501\pi$
$588$	5.50600	0.227063
$589$	−3.11719	−0.128442
$590$	−14.6166	−0.601756
$591$	−2.20706	−0.0907862
$592$	−4.30712	−0.177022
$593$	43.3093	1.77850	0.889249	−	0.457423i	$-0.151227\pi$
$593$	43.3093	1.77850	0.889249	+	0.457423i	$0.151227\pi$
$594$	−2.49153	−0.102229
$595$	13.9297	0.571063
$596$	6.00577	0.246006
$597$	−11.1501	−0.456343
$598$	3.42683	0.140133
$599$	−17.7106	−0.723635	−0.361818	−	0.932249i	$-0.617844\pi$
$599$	−17.7106	−0.723635	−0.361818	+	0.932249i	$0.617844\pi$
$600$	−1.98390	−0.0809926
$601$	−26.8468	−1.09510	−0.547552	−	0.836772i	$-0.684440\pi$
$601$	−26.8468	−1.09510	−0.547552	+	0.836772i	$0.684440\pi$
$602$	10.0370	0.409076
$603$	10.9712	0.446781
$604$	−6.13074	−0.249456
$605$	2.02512	0.0823328
$606$	1.72920	0.0702439
$607$	43.3191	1.75827	0.879133	−	0.476576i	$-0.158122\pi$
$607$	43.3191	1.75827	0.879133	+	0.476576i	$0.158122\pi$
$608$	−1.22849	−0.0498219
$609$	27.7105	1.12289
$610$	19.6528	0.795720
$611$	1.11543	0.0451256
$612$	6.06358	0.245106
$613$	35.4135	1.43034	0.715170	−	0.698951i	$-0.246349\pi$
$613$	35.4135	1.43034	0.715170	+	0.698951i	$0.246349\pi$
$614$	17.7304	0.715540
$615$	3.61527	0.145782
$616$	−2.12256	−0.0855205
$617$	8.90093	0.358338	0.179169	−	0.983818i	$-0.442659\pi$
$617$	8.90093	0.358338	0.179169	+	0.983818i	$0.442659\pi$
$618$	26.0424	1.04758
$619$	24.2485	0.974628	0.487314	−	0.873227i	$-0.337977\pi$
$619$	24.2485	0.974628	0.487314	+	0.873227i	$0.337977\pi$
$620$	−5.13857	−0.206370
$621$	−13.4367	−0.539196
$622$	5.91581	0.237202
$623$	36.4251	1.45934
$624$	−1.40243	−0.0561421
$625$	−19.6975	−0.787902
$626$	−0.826328	−0.0330267
$627$	−2.71135	−0.108281
$628$	11.7324	0.468174
$629$	−13.9578	−0.556535
$630$	−8.04285	−0.320435
$631$	−35.4896	−1.41282	−0.706409	−	0.707804i	$-0.749686\pi$
$631$	−35.4896	−1.41282	−0.706409	+	0.707804i	$0.749686\pi$
$632$	9.34441	0.371701
$633$	−15.7411	−0.625654
$634$	23.2105	0.921808
$635$	3.95117	0.156798
$636$	24.4690	0.970259
$637$	−1.58522	−0.0628086
$638$	5.91521	0.234185
$639$	−17.3855	−0.687758
$640$	−2.02512	−0.0800499
$641$	−35.5430	−1.40386	−0.701931	−	0.712244i	$-0.747679\pi$
$641$	−35.5430	−1.40386	−0.701931	+	0.712244i	$0.747679\pi$
$642$	7.66194	0.302393
$643$	−2.04564	−0.0806720	−0.0403360	−	0.999186i	$-0.512843\pi$
$643$	−2.04564	−0.0806720	−0.0403360	+	0.999186i	$0.512843\pi$
$644$	−11.4469	−0.451069
$645$	21.1352	0.832196
$646$	−3.98109	−0.156634
$647$	−19.2056	−0.755051	−0.377525	−	0.925999i	$-0.623225\pi$
$647$	−19.2056	−0.755051	−0.377525	+	0.925999i	$0.623225\pi$
$648$	11.1123	0.436532
$649$	7.21765	0.283318
$650$	0.571181	0.0224036
$651$	11.8868	0.465882
$652$	16.9577	0.664113
$653$	25.5354	0.999278	0.499639	−	0.866234i	$-0.333466\pi$
$653$	25.5354	0.999278	0.499639	+	0.866234i	$0.333466\pi$
$654$	−20.0249	−0.783036
$655$	−10.8935	−0.425644
$656$	−0.808867	−0.0315809
$657$	−14.1204	−0.550889
$658$	−3.72596	−0.145253
$659$	−17.9985	−0.701122	−0.350561	−	0.936540i	$-0.614009\pi$
$659$	−17.9985	−0.701122	−0.350561	+	0.936540i	$0.614009\pi$
$660$	−4.46956	−0.173977
$661$	−14.2298	−0.553473	−0.276737	−	0.960946i	$-0.589253\pi$
$661$	−14.2298	−0.553473	−0.276737	+	0.960946i	$0.589253\pi$
$662$	28.2872	1.09941
$663$	−4.54476	−0.176504
$664$	15.1204	0.586784
$665$	5.28060	0.204773
$666$	8.05908	0.312283
$667$	31.9004	1.23519
$668$	17.3658	0.671902
$669$	−39.2006	−1.51558
$670$	−11.8742	−0.458742
$671$	−9.70454	−0.374639
$672$	4.68462	0.180713
$673$	−24.2346	−0.934175	−0.467087	−	0.884211i	$-0.654697\pi$
$673$	−24.2346	−0.934175	−0.467087	+	0.884211i	$0.654697\pi$
$674$	−16.8345	−0.648441
$675$	−2.23962	−0.0862029
$676$	−12.5962	−0.484470
$677$	24.7916	0.952817	0.476408	−	0.879224i	$-0.341938\pi$
$677$	24.7916	0.952817	0.476408	+	0.879224i	$0.341938\pi$
$678$	33.5408	1.28813
$679$	−26.4974	−1.01688
$680$	−6.56268	−0.251667
$681$	−32.0834	−1.22944
$682$	2.53741	0.0971626
$683$	2.41055	0.0922372	0.0461186	−	0.998936i	$-0.485315\pi$
$683$	2.41055	0.0922372	0.0461186	+	0.998936i	$0.485315\pi$
$684$	2.29864	0.0878905
$685$	−10.2520	−0.391711
$686$	20.1532	0.769451
$687$	43.0010	1.64059
$688$	−4.72869	−0.180280
$689$	−7.04481	−0.268386
$690$	−24.1040	−0.917625
$691$	−43.8893	−1.66963	−0.834813	−	0.550534i	$-0.814424\pi$
$691$	−43.8893	−1.66963	−0.834813	+	0.550534i	$0.814424\pi$
$692$	17.2937	0.657409
$693$	3.97154	0.150866
$694$	5.28117	0.200471
$695$	17.7868	0.674694
$696$	−13.0552	−0.494857
$697$	−2.62124	−0.0992867
$698$	12.4514	0.471293
$699$	30.9287	1.16983
$700$	−1.90795	−0.0721139
$701$	4.17268	0.157600	0.0787999	−	0.996890i	$-0.474891\pi$
$701$	4.17268	0.157600	0.0787999	+	0.996890i	$0.474891\pi$
$702$	−1.58319	−0.0597537
$703$	−5.29126	−0.199563
$704$	1.00000	0.0376889
$705$	−7.84587	−0.295493
$706$	−8.77839	−0.330379
$707$	1.66300	0.0625435
$708$	−15.9298	−0.598678
$709$	−21.2880	−0.799486	−0.399743	−	0.916627i	$-0.630901\pi$
$709$	−21.2880	−0.799486	−0.399743	+	0.916627i	$0.630901\pi$
$710$	18.8165	0.706170
$711$	−17.4844	−0.655716
$712$	−17.1609	−0.643131
$713$	13.6841	0.512474
$714$	15.1812	0.568141
$715$	1.28682	0.0481243
$716$	0.268382	0.0100299
$717$	−20.9988	−0.784214
$718$	6.04901	0.225747
$719$	−21.6864	−0.808765	−0.404383	−	0.914590i	$-0.632514\pi$
$719$	−21.6864	−0.808765	−0.404383	+	0.914590i	$0.632514\pi$
$720$	3.78921	0.141216
$721$	25.0454	0.932740
$722$	17.4908	0.650941
$723$	17.4460	0.648824
$724$	6.74640	0.250728
$725$	5.31713	0.197473
$726$	2.20706	0.0819116
$727$	29.7912	1.10489	0.552447	−	0.833548i	$-0.313694\pi$
$727$	29.7912	1.10489	0.552447	+	0.833548i	$0.313694\pi$
$728$	−1.34874	−0.0499876
$729$	−4.29538	−0.159088
$730$	15.2827	0.565637
$731$	−15.3240	−0.566778
$732$	21.4185	0.791650
$733$	−14.1287	−0.521857	−0.260928	−	0.965358i	$-0.584029\pi$
$733$	−14.1287	−0.521857	−0.260928	+	0.965358i	$0.584029\pi$
$734$	−9.12380	−0.336766
$735$	11.1503	0.411285
$736$	5.39294	0.198786
$737$	5.86348	0.215984
$738$	1.51348	0.0557118
$739$	−0.789748	−0.0290514	−0.0145257	−	0.999894i	$-0.504624\pi$
$739$	−0.789748	−0.0290514	−0.0145257	+	0.999894i	$0.504624\pi$
$740$	−8.72243	−0.320643
$741$	−1.72287	−0.0632912
$742$	23.5322	0.863896
$743$	−23.5061	−0.862355	−0.431178	−	0.902267i	$-0.641902\pi$
$743$	−23.5061	−0.862355	−0.431178	+	0.902267i	$0.641902\pi$
$744$	−5.60022	−0.205314
$745$	12.1624	0.445596
$746$	14.9250	0.546445
$747$	−28.2918	−1.03514
$748$	3.24064	0.118490
$749$	7.36861	0.269243
$750$	−26.3654	−0.962729
$751$	53.7065	1.95978	0.979890	−	0.199539i	$-0.0639445\pi$
$751$	53.7065	1.95978	0.979890	+	0.199539i	$0.0639445\pi$
$752$	1.75540	0.0640130
$753$	−21.3904	−0.779509
$754$	3.75869	0.136884
$755$	−12.4155	−0.451846
$756$	5.28844	0.192339
$757$	32.6669	1.18730	0.593649	−	0.804724i	$-0.297687\pi$
$757$	32.6669	1.18730	0.593649	+	0.804724i	$0.297687\pi$
$758$	15.5664	0.565397
$759$	11.9025	0.432034
$760$	−2.48784	−0.0902434
$761$	3.39284	0.122990	0.0614952	−	0.998107i	$-0.480413\pi$
$761$	3.39284	0.122990	0.0614952	+	0.998107i	$0.480413\pi$
$762$	4.30615	0.155995
$763$	−19.2583	−0.697197
$764$	−25.5150	−0.923101
$765$	12.2795	0.443965
$766$	−28.3440	−1.02411
$767$	4.58630	0.165602
$768$	−2.20706	−0.0796404
$769$	−49.7255	−1.79315	−0.896573	−	0.442896i	$-0.853951\pi$
$769$	−49.7255	−1.79315	−0.896573	+	0.442896i	$0.853951\pi$
$770$	−4.29845	−0.154905
$771$	55.2215	1.98875
$772$	−23.3802	−0.841471
$773$	23.1661	0.833228	0.416614	−	0.909083i	$-0.363217\pi$
$773$	23.1661	0.833228	0.416614	+	0.909083i	$0.363217\pi$
$774$	8.84789	0.318031
$775$	2.28086	0.0819309
$776$	12.4837	0.448138
$777$	20.1772	0.723854
$778$	17.6143	0.631505
$779$	−0.993685	−0.0356024
$780$	−2.84008	−0.101691
$781$	−9.29154	−0.332477
$782$	17.4766	0.624961
$783$	−14.7379	−0.526691
$784$	−2.49472	−0.0890972
$785$	23.7595	0.848014
$786$	−11.8722	−0.423466
$787$	−49.0093	−1.74699	−0.873496	−	0.486832i	$-0.838153\pi$
$787$	−49.0093	−1.74699	−0.873496	+	0.486832i	$0.838153\pi$
$788$	1.00000	0.0356235
$789$	9.64665	0.343430
$790$	18.9236	0.673270
$791$	32.2567	1.14692
$792$	−1.87111	−0.0664869
$793$	−6.16654	−0.218980
$794$	4.74127	0.168261
$795$	49.5527	1.75745
$796$	5.05202	0.179064
$797$	−45.7470	−1.62044	−0.810221	−	0.586124i	$-0.800653\pi$
$797$	−45.7470	−1.62044	−0.810221	+	0.586124i	$0.800653\pi$
$798$	5.75501	0.203725
$799$	5.68863	0.201249
$800$	0.898891	0.0317806
$801$	32.1098	1.13455
$802$	16.8420	0.594712
$803$	−7.54655	−0.266312
$804$	−12.9410	−0.456395
$805$	−23.1813	−0.817032
$806$	1.61235	0.0567925
$807$	30.8981	1.08766
$808$	−0.783486	−0.0275629
$809$	46.0583	1.61932	0.809661	−	0.586897i	$-0.199651\pi$
$809$	46.0583	1.61932	0.809661	+	0.586897i	$0.199651\pi$
$810$	22.5037	0.790699
$811$	22.4036	0.786696	0.393348	−	0.919390i	$-0.371317\pi$
$811$	22.4036	0.786696	0.393348	+	0.919390i	$0.371317\pi$
$812$	−12.5554	−0.440609
$813$	−21.9938	−0.771355
$814$	4.30712	0.150964
$815$	34.3413	1.20292
$816$	−7.15228	−0.250380
$817$	−5.80916	−0.203237
$818$	−38.2124	−1.33606
$819$	2.52363	0.0881828
$820$	−1.63805	−0.0572032
$821$	56.1442	1.95945	0.979723	−	0.200359i	$-0.0642107\pi$
$821$	56.1442	1.95945	0.979723	+	0.200359i	$0.0642107\pi$
$822$	−11.1731	−0.389707
$823$	−9.81225	−0.342033	−0.171017	−	0.985268i	$-0.554705\pi$
$823$	−9.81225	−0.342033	−0.171017	+	0.985268i	$0.554705\pi$
$824$	−11.7996	−0.411059
$825$	1.98390	0.0690707
$826$	−15.3199	−0.533049
$827$	25.8959	0.900487	0.450244	−	0.892906i	$-0.351337\pi$
$827$	25.8959	0.900487	0.450244	+	0.892906i	$0.351337\pi$
$828$	−10.0908	−0.350678
$829$	5.32411	0.184914	0.0924570	−	0.995717i	$-0.470528\pi$
$829$	5.32411	0.184914	0.0924570	+	0.995717i	$0.470528\pi$
$830$	30.6205	1.06285
$831$	−5.32165	−0.184606
$832$	0.635429	0.0220295
$833$	−8.08449	−0.280111
$834$	19.3848	0.671242
$835$	35.1678	1.21703
$836$	1.22849	0.0424882
$837$	−6.32205	−0.218522
$838$	13.0146	0.449581
$839$	11.8219	0.408138	0.204069	−	0.978957i	$-0.434583\pi$
$839$	11.8219	0.408138	0.204069	+	0.978957i	$0.434583\pi$
$840$	9.48692	0.327330
$841$	5.98972	0.206542
$842$	2.16562	0.0746323
$843$	8.00566	0.275730
$844$	7.13218	0.245500
$845$	−25.5089	−0.877532
$846$	−3.28455	−0.112925
$847$	2.12256	0.0729322
$848$	−11.0867	−0.380719
$849$	65.2763	2.24028
$850$	2.91298	0.0999144
$851$	23.2280	0.796247
$852$	20.5070	0.702557
$853$	35.4312	1.21314	0.606570	−	0.795030i	$-0.292545\pi$
$853$	35.4312	1.21314	0.606570	+	0.795030i	$0.292545\pi$
$854$	20.5985	0.704866
$855$	4.65501	0.159198
$856$	−3.47156	−0.118656
$857$	9.77042	0.333751	0.166876	−	0.985978i	$-0.446632\pi$
$857$	9.77042	0.333751	0.166876	+	0.985978i	$0.446632\pi$
$858$	1.40243	0.0478781
$859$	−51.1547	−1.74537	−0.872687	−	0.488279i	$-0.837625\pi$
$859$	−51.1547	−1.74537	−0.872687	+	0.488279i	$0.837625\pi$
$860$	−9.57617	−0.326545
$861$	3.78923	0.129137
$862$	−8.24720	−0.280901
$863$	−24.6616	−0.839489	−0.419745	−	0.907642i	$-0.637880\pi$
$863$	−24.6616	−0.839489	−0.419745	+	0.907642i	$0.637880\pi$
$864$	−2.49153	−0.0847637
$865$	35.0219	1.19078
$866$	38.3601	1.30353
$867$	14.3420	0.487081
$868$	−5.38582	−0.182807
$869$	−9.34441	−0.316987
$870$	−26.4384	−0.896345
$871$	3.72582	0.126245
$872$	9.07313	0.307255
$873$	−23.3583	−0.790559
$874$	6.62517	0.224100
$875$	−25.3561	−0.857191
$876$	16.6557	0.562743
$877$	−5.78164	−0.195232	−0.0976160	−	0.995224i	$-0.531122\pi$
$877$	−5.78164	−0.195232	−0.0976160	+	0.995224i	$0.531122\pi$
$878$	−27.8075	−0.938457
$879$	−40.7564	−1.37468
$880$	2.02512	0.0682668
$881$	−26.6157	−0.896706	−0.448353	−	0.893856i	$-0.647989\pi$
$881$	−26.6157	−0.896706	−0.448353	+	0.893856i	$0.647989\pi$
$882$	4.66789	0.157176
$883$	29.2760	0.985215	0.492607	−	0.870252i	$-0.336044\pi$
$883$	29.2760	0.985215	0.492607	+	0.870252i	$0.336044\pi$
$884$	2.05919	0.0692582
$885$	−32.2597	−1.08440
$886$	−13.7027	−0.460352
$887$	42.6217	1.43110	0.715549	−	0.698563i	$-0.246177\pi$
$887$	42.6217	1.43110	0.715549	+	0.698563i	$0.246177\pi$
$888$	−9.50607	−0.319003
$889$	4.14130	0.138895
$890$	−34.7528	−1.16492
$891$	−11.1123	−0.372275
$892$	17.7615	0.594698
$893$	2.15650	0.0721644
$894$	13.2551	0.443316
$895$	0.543505	0.0181674
$896$	−2.12256	−0.0709099
$897$	7.56321	0.252528
$898$	−1.57760	−0.0526451
$899$	15.0093	0.500590
$900$	−1.68192	−0.0560640
$901$	−35.9280	−1.19694
$902$	0.808867	0.0269323
$903$	22.1521	0.737177
$904$	−15.1971	−0.505447
$905$	13.6623	0.454149
$906$	−13.5309	−0.449534
$907$	55.0138	1.82670	0.913352	−	0.407171i	$-0.133485\pi$
$907$	55.0138	1.82670	0.913352	+	0.407171i	$0.133485\pi$
$908$	14.5367	0.482418
$909$	1.46599	0.0486237
$910$	−2.73136	−0.0905436
$911$	−40.3607	−1.33721	−0.668605	−	0.743617i	$-0.733108\pi$
$911$	−40.3607	−1.33721	−0.668605	+	0.743617i	$0.733108\pi$
$912$	−2.71135	−0.0897818
$913$	−15.1204	−0.500411
$914$	34.3574	1.13644
$915$	43.3750	1.43393
$916$	−19.4834	−0.643749
$917$	−11.4177	−0.377045
$918$	−8.07416	−0.266487
$919$	−6.50386	−0.214543	−0.107271	−	0.994230i	$-0.534211\pi$
$919$	−6.50386	−0.214543	−0.107271	+	0.994230i	$0.534211\pi$
$920$	10.9213	0.360066
$921$	39.1320	1.28944
$922$	−1.04932	−0.0345575
$923$	−5.90411	−0.194336
$924$	−4.68462	−0.154113
$925$	3.87163	0.127298
$926$	23.0262	0.756687
$927$	22.0783	0.725147
$928$	5.91521	0.194176
$929$	36.2007	1.18771	0.593854	−	0.804573i	$-0.297606\pi$
$929$	36.2007	1.18771	0.593854	+	0.804573i	$0.297606\pi$
$930$	−11.3411	−0.371890
$931$	−3.06474	−0.100443
$932$	−14.0135	−0.459028
$933$	13.0565	0.427452
$934$	5.11057	0.167223
$935$	6.56268	0.214623
$936$	−1.18895	−0.0388622
$937$	−21.9721	−0.717796	−0.358898	−	0.933377i	$-0.616847\pi$
$937$	−21.9721	−0.717796	−0.358898	+	0.933377i	$0.616847\pi$
$938$	−12.4456	−0.406363
$939$	−1.82375	−0.0595160
$940$	3.55490	0.115948
$941$	14.3714	0.468496	0.234248	−	0.972177i	$-0.424737\pi$
$941$	14.3714	0.468496	0.234248	+	0.972177i	$0.424737\pi$
$942$	25.8941	0.843675
$943$	4.36217	0.142052
$944$	7.21765	0.234915
$945$	10.7097	0.348387
$946$	4.72869	0.153743
$947$	24.9583	0.811037	0.405519	−	0.914087i	$-0.367091\pi$
$947$	24.9583	0.811037	0.405519	+	0.914087i	$0.367091\pi$
$948$	20.6237	0.669825
$949$	−4.79530	−0.155662
$950$	1.10428	0.0358275
$951$	51.2270	1.66115
$952$	−6.87846	−0.222932
$953$	8.55197	0.277026	0.138513	−	0.990361i	$-0.455768\pi$
$953$	8.55197	0.277026	0.138513	+	0.990361i	$0.455768\pi$
$954$	20.7444	0.671625
$955$	−51.6709	−1.67203
$956$	9.51438	0.307717
$957$	13.0552	0.422015
$958$	−6.36419	−0.205618
$959$	−10.7454	−0.346986
$960$	−4.46956	−0.144254
$961$	−24.5615	−0.792307
$962$	2.73687	0.0882401
$963$	6.49566	0.209320
$964$	−7.90465	−0.254592
$965$	−47.3476	−1.52417
$966$	−25.2639	−0.812852
$967$	−41.1685	−1.32389	−0.661944	−	0.749553i	$-0.730269\pi$
$967$	−41.1685	−1.32389	−0.661944	+	0.749553i	$0.730269\pi$
$968$	−1.00000	−0.0321412
$969$	−8.78651	−0.282263
$970$	25.2809	0.811722
$971$	27.5906	0.885425	0.442713	−	0.896664i	$-0.354016\pi$
$971$	27.5906	0.885425	0.442713	+	0.896664i	$0.354016\pi$
$972$	17.0508	0.546906
$973$	18.6427	0.597658
$974$	−7.56830	−0.242504
$975$	1.26063	0.0403725
$976$	−9.70454	−0.310635
$977$	35.5169	1.13629	0.568143	−	0.822930i	$-0.307662\pi$
$977$	35.5169	1.13629	0.568143	+	0.822930i	$0.307662\pi$
$978$	37.4266	1.19677
$979$	17.1609	0.548464
$980$	−5.05211	−0.161384
$981$	−16.9768	−0.542027
$982$	9.26509	0.295661
$983$	46.0458	1.46863	0.734316	−	0.678808i	$-0.237503\pi$
$983$	46.0458	1.46863	0.734316	+	0.678808i	$0.237503\pi$
$984$	−1.78522	−0.0569106
$985$	2.02512	0.0645257
$986$	19.1691	0.610467
$987$	−8.22340	−0.261754
$988$	0.780618	0.0248348
$989$	25.5016	0.810902
$990$	−3.78921	−0.120429
$991$	−53.1613	−1.68872	−0.844362	−	0.535773i	$-0.820020\pi$
$991$	−53.1613	−1.68872	−0.844362	+	0.535773i	$0.820020\pi$
$992$	2.53741	0.0805630
$993$	62.4315	1.98120
$994$	19.7219	0.625540
$995$	10.2309	0.324343
$996$	33.3715	1.05742
$997$	25.0921	0.794675	0.397338	−	0.917673i	$-0.369934\pi$
$997$	25.0921	0.794675	0.397338	+	0.917673i	$0.369934\pi$
$998$	21.2042	0.671208
$999$	−10.7313	−0.339524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.a.1.3	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.a.1.3	✓	15	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.20706 q^{3} +1.00000 q^{4} +2.02512 q^{5} +2.20706 q^{6} +2.12256 q^{7} -1.00000 q^{8} +1.87111 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.20706 q^{3} +1.00000 q^{4} +2.02512 q^{5} +2.20706 q^{6} +2.12256 q^{7} -1.00000 q^{8} +1.87111 q^{9} -2.02512 q^{10} +1.00000 q^{11} -2.20706 q^{12} +0.635429 q^{13} -2.12256 q^{14} -4.46956 q^{15} +1.00000 q^{16} +3.24064 q^{17} -1.87111 q^{18} +1.22849 q^{19} +2.02512 q^{20} -4.68462 q^{21} -1.00000 q^{22} -5.39294 q^{23} +2.20706 q^{24} -0.898891 q^{25} -0.635429 q^{26} +2.49153 q^{27} +2.12256 q^{28} -5.91521 q^{29} +4.46956 q^{30} -2.53741 q^{31} -1.00000 q^{32} -2.20706 q^{33} -3.24064 q^{34} +4.29845 q^{35} +1.87111 q^{36} -4.30712 q^{37} -1.22849 q^{38} -1.40243 q^{39} -2.02512 q^{40} -0.808867 q^{41} +4.68462 q^{42} -4.72869 q^{43} +1.00000 q^{44} +3.78921 q^{45} +5.39294 q^{46} +1.75540 q^{47} -2.20706 q^{48} -2.49472 q^{49} +0.898891 q^{50} -7.15228 q^{51} +0.635429 q^{52} -11.0867 q^{53} -2.49153 q^{54} +2.02512 q^{55} -2.12256 q^{56} -2.71135 q^{57} +5.91521 q^{58} +7.21765 q^{59} -4.46956 q^{60} -9.70454 q^{61} +2.53741 q^{62} +3.97154 q^{63} +1.00000 q^{64} +1.28682 q^{65} +2.20706 q^{66} +5.86348 q^{67} +3.24064 q^{68} +11.9025 q^{69} -4.29845 q^{70} -9.29154 q^{71} -1.87111 q^{72} -7.54655 q^{73} +4.30712 q^{74} +1.98390 q^{75} +1.22849 q^{76} +2.12256 q^{77} +1.40243 q^{78} -9.34441 q^{79} +2.02512 q^{80} -11.1123 q^{81} +0.808867 q^{82} -15.1204 q^{83} -4.68462 q^{84} +6.56268 q^{85} +4.72869 q^{86} +13.0552 q^{87} -1.00000 q^{88} +17.1609 q^{89} -3.78921 q^{90} +1.34874 q^{91} -5.39294 q^{92} +5.60022 q^{93} -1.75540 q^{94} +2.48784 q^{95} +2.20706 q^{96} -12.4837 q^{97} +2.49472 q^{98} +1.87111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

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