LMFDB - Embedded newform 4730.2.a.bb.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 22 x^{9} + 21 x^{8} + 165 x^{7} - 130 x^{6} - 535 x^{5} + 323 x^{4} + 710 x^{3} + \cdots + 128 $ x^11 - x^10 - 22x^9 + 21x^8 + 165x^7 - 130x^6 - 535x^5 + 323x^4 + 710x^3 - 343x^2 - 261*x + 128
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.580450$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.580450 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.580450 q^{6} +1.64698 q^{7} -1.00000 q^{8} -2.66308 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.580450 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.580450 q^{6} +1.64698 q^{7} -1.00000 q^{8} -2.66308 q^{9} +1.00000 q^{10} -1.00000 q^{11} -0.580450 q^{12} +2.95295 q^{13} -1.64698 q^{14} +0.580450 q^{15} +1.00000 q^{16} +1.81307 q^{17} +2.66308 q^{18} -3.80194 q^{19} -1.00000 q^{20} -0.955986 q^{21} +1.00000 q^{22} +0.952953 q^{23} +0.580450 q^{24} +1.00000 q^{25} -2.95295 q^{26} +3.28713 q^{27} +1.64698 q^{28} +3.68382 q^{29} -0.580450 q^{30} +3.41206 q^{31} -1.00000 q^{32} +0.580450 q^{33} -1.81307 q^{34} -1.64698 q^{35} -2.66308 q^{36} -2.19499 q^{37} +3.80194 q^{38} -1.71404 q^{39} +1.00000 q^{40} -5.45269 q^{41} +0.955986 q^{42} +1.00000 q^{43} -1.00000 q^{44} +2.66308 q^{45} -0.952953 q^{46} -11.1140 q^{47} -0.580450 q^{48} -4.28747 q^{49} -1.00000 q^{50} -1.05240 q^{51} +2.95295 q^{52} +8.91291 q^{53} -3.28713 q^{54} +1.00000 q^{55} -1.64698 q^{56} +2.20684 q^{57} -3.68382 q^{58} -3.10392 q^{59} +0.580450 q^{60} -9.87214 q^{61} -3.41206 q^{62} -4.38602 q^{63} +1.00000 q^{64} -2.95295 q^{65} -0.580450 q^{66} +6.18592 q^{67} +1.81307 q^{68} -0.553141 q^{69} +1.64698 q^{70} +12.8474 q^{71} +2.66308 q^{72} -0.229098 q^{73} +2.19499 q^{74} -0.580450 q^{75} -3.80194 q^{76} -1.64698 q^{77} +1.71404 q^{78} +15.2682 q^{79} -1.00000 q^{80} +6.08122 q^{81} +5.45269 q^{82} +2.72642 q^{83} -0.955986 q^{84} -1.81307 q^{85} -1.00000 q^{86} -2.13827 q^{87} +1.00000 q^{88} -5.52821 q^{89} -2.66308 q^{90} +4.86344 q^{91} +0.952953 q^{92} -1.98053 q^{93} +11.1140 q^{94} +3.80194 q^{95} +0.580450 q^{96} -3.05239 q^{97} +4.28747 q^{98} +2.66308 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * 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
$3$	−0.580450	−0.335123	−0.167561	−	0.985862i	$-0.553589\pi$
$3$	−0.580450	−0.335123	−0.167561	+	0.985862i	$0.553589\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.580450	0.236968
$7$	1.64698	0.622498	0.311249	−	0.950328i	$-0.399253\pi$
$7$	1.64698	0.622498	0.311249	+	0.950328i	$0.399253\pi$
$8$	−1.00000	−0.353553
$9$	−2.66308	−0.887693
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.580450	−0.167561
$13$	2.95295	0.819002	0.409501	−	0.912310i	$-0.365703\pi$
$13$	2.95295	0.819002	0.409501	+	0.912310i	$0.365703\pi$
$14$	−1.64698	−0.440173
$15$	0.580450	0.149871
$16$	1.00000	0.250000
$17$	1.81307	0.439734	0.219867	−	0.975530i	$-0.429438\pi$
$17$	1.81307	0.439734	0.219867	+	0.975530i	$0.429438\pi$
$18$	2.66308	0.627694
$19$	−3.80194	−0.872226	−0.436113	−	0.899892i	$-0.643645\pi$
$19$	−3.80194	−0.872226	−0.436113	+	0.899892i	$0.643645\pi$
$20$	−1.00000	−0.223607
$21$	−0.955986	−0.208613
$22$	1.00000	0.213201
$23$	0.952953	0.198704	0.0993522	−	0.995052i	$-0.468323\pi$
$23$	0.952953	0.198704	0.0993522	+	0.995052i	$0.468323\pi$
$24$	0.580450	0.118484
$25$	1.00000	0.200000
$26$	−2.95295	−0.579122
$27$	3.28713	0.632609
$28$	1.64698	0.311249
$29$	3.68382	0.684068	0.342034	−	0.939688i	$-0.388884\pi$
$29$	3.68382	0.684068	0.342034	+	0.939688i	$0.388884\pi$
$30$	−0.580450	−0.105975
$31$	3.41206	0.612824	0.306412	−	0.951899i	$-0.400872\pi$
$31$	3.41206	0.612824	0.306412	+	0.951899i	$0.400872\pi$
$32$	−1.00000	−0.176777
$33$	0.580450	0.101043
$34$	−1.81307	−0.310939
$35$	−1.64698	−0.278390
$36$	−2.66308	−0.443846
$37$	−2.19499	−0.360854	−0.180427	−	0.983588i	$-0.557748\pi$
$37$	−2.19499	−0.360854	−0.180427	+	0.983588i	$0.557748\pi$
$38$	3.80194	0.616757
$39$	−1.71404	−0.274466
$40$	1.00000	0.158114
$41$	−5.45269	−0.851568	−0.425784	−	0.904825i	$-0.640002\pi$
$41$	−5.45269	−0.851568	−0.425784	+	0.904825i	$0.640002\pi$
$42$	0.955986	0.147512
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	2.66308	0.396988
$46$	−0.952953	−0.140505
$47$	−11.1140	−1.62115	−0.810574	−	0.585636i	$-0.800845\pi$
$47$	−11.1140	−1.62115	−0.810574	+	0.585636i	$0.800845\pi$
$48$	−0.580450	−0.0837807
$49$	−4.28747	−0.612496
$50$	−1.00000	−0.141421
$51$	−1.05240	−0.147365
$52$	2.95295	0.409501
$53$	8.91291	1.22428	0.612141	−	0.790749i	$-0.290309\pi$
$53$	8.91291	1.22428	0.612141	+	0.790749i	$0.290309\pi$
$54$	−3.28713	−0.447322
$55$	1.00000	0.134840
$56$	−1.64698	−0.220086
$57$	2.20684	0.292303
$58$	−3.68382	−0.483709
$59$	−3.10392	−0.404096	−0.202048	−	0.979376i	$-0.564760\pi$
$59$	−3.10392	−0.404096	−0.202048	+	0.979376i	$0.564760\pi$
$60$	0.580450	0.0749357
$61$	−9.87214	−1.26400	−0.631999	−	0.774969i	$-0.717765\pi$
$61$	−9.87214	−1.26400	−0.631999	+	0.774969i	$0.717765\pi$
$62$	−3.41206	−0.433332
$63$	−4.38602	−0.552587
$64$	1.00000	0.125000
$65$	−2.95295	−0.366269
$66$	−0.580450	−0.0714484
$67$	6.18592	0.755730	0.377865	−	0.925861i	$-0.376658\pi$
$67$	6.18592	0.755730	0.377865	+	0.925861i	$0.376658\pi$
$68$	1.81307	0.219867
$69$	−0.553141	−0.0665904
$70$	1.64698	0.196851
$71$	12.8474	1.52471	0.762356	−	0.647158i	$-0.224043\pi$
$71$	12.8474	1.52471	0.762356	+	0.647158i	$0.224043\pi$
$72$	2.66308	0.313847
$73$	−0.229098	−0.0268138	−0.0134069	−	0.999910i	$-0.504268\pi$
$73$	−0.229098	−0.0268138	−0.0134069	+	0.999910i	$0.504268\pi$
$74$	2.19499	0.255162
$75$	−0.580450	−0.0670246
$76$	−3.80194	−0.436113
$77$	−1.64698	−0.187690
$78$	1.71404	0.194077
$79$	15.2682	1.71781	0.858905	−	0.512134i	$-0.171145\pi$
$79$	15.2682	1.71781	0.858905	+	0.512134i	$0.171145\pi$
$80$	−1.00000	−0.111803
$81$	6.08122	0.675691
$82$	5.45269	0.602149
$83$	2.72642	0.299263	0.149632	−	0.988742i	$-0.452191\pi$
$83$	2.72642	0.299263	0.149632	+	0.988742i	$0.452191\pi$
$84$	−0.955986	−0.104307
$85$	−1.81307	−0.196655
$86$	−1.00000	−0.107833
$87$	−2.13827	−0.229247
$88$	1.00000	0.106600
$89$	−5.52821	−0.585989	−0.292995	−	0.956114i	$-0.594652\pi$
$89$	−5.52821	−0.585989	−0.292995	+	0.956114i	$0.594652\pi$
$90$	−2.66308	−0.280713
$91$	4.86344	0.509827
$92$	0.952953	0.0993522
$93$	−1.98053	−0.205371
$94$	11.1140	1.14632
$95$	3.80194	0.390071
$96$	0.580450	0.0592419
$97$	−3.05239	−0.309923	−0.154962	−	0.987920i	$-0.549525\pi$
$97$	−3.05239	−0.309923	−0.154962	+	0.987920i	$0.549525\pi$
$98$	4.28747	0.433100
$99$	2.66308	0.267649
$100$	1.00000	0.100000
$101$	1.68377	0.167542	0.0837709	−	0.996485i	$-0.473304\pi$
$101$	1.68377	0.167542	0.0837709	+	0.996485i	$0.473304\pi$
$102$	1.05240	0.104203
$103$	−1.85743	−0.183018	−0.0915091	−	0.995804i	$-0.529169\pi$
$103$	−1.85743	−0.183018	−0.0915091	+	0.995804i	$0.529169\pi$
$104$	−2.95295	−0.289561
$105$	0.955986	0.0932947
$106$	−8.91291	−0.865698
$107$	−14.8768	−1.43819	−0.719097	−	0.694909i	$-0.755445\pi$
$107$	−14.8768	−1.43819	−0.719097	+	0.694909i	$0.755445\pi$
$108$	3.28713	0.316304
$109$	11.2283	1.07548	0.537738	−	0.843112i	$-0.319279\pi$
$109$	11.2283	1.07548	0.537738	+	0.843112i	$0.319279\pi$
$110$	−1.00000	−0.0953463
$111$	1.27408	0.120930
$112$	1.64698	0.155625
$113$	2.54599	0.239506	0.119753	−	0.992804i	$-0.461790\pi$
$113$	2.54599	0.239506	0.119753	+	0.992804i	$0.461790\pi$
$114$	−2.20684	−0.206689
$115$	−0.952953	−0.0888633
$116$	3.68382	0.342034
$117$	−7.86395	−0.727022
$118$	3.10392	0.285739
$119$	2.98608	0.273734
$120$	−0.580450	−0.0529876
$121$	1.00000	0.0909091
$122$	9.87214	0.893781
$123$	3.16501	0.285380
$124$	3.41206	0.306412
$125$	−1.00000	−0.0894427
$126$	4.38602	0.390738
$127$	−2.73781	−0.242941	−0.121471	−	0.992595i	$-0.538761\pi$
$127$	−2.73781	−0.242941	−0.121471	+	0.992595i	$0.538761\pi$
$128$	−1.00000	−0.0883883
$129$	−0.580450	−0.0511057
$130$	2.95295	0.258991
$131$	−20.4265	−1.78467	−0.892334	−	0.451375i	$-0.850934\pi$
$131$	−20.4265	−1.78467	−0.892334	+	0.451375i	$0.850934\pi$
$132$	0.580450	0.0505217
$133$	−6.26171	−0.542959
$134$	−6.18592	−0.534382
$135$	−3.28713	−0.282911
$136$	−1.81307	−0.155469
$137$	−1.31421	−0.112281	−0.0561405	−	0.998423i	$-0.517879\pi$
$137$	−1.31421	−0.112281	−0.0561405	+	0.998423i	$0.517879\pi$
$138$	0.553141	0.0470865
$139$	19.4516	1.64986	0.824931	−	0.565234i	$-0.191214\pi$
$139$	19.4516	1.64986	0.824931	+	0.565234i	$0.191214\pi$
$140$	−1.64698	−0.139195
$141$	6.45114	0.543284
$142$	−12.8474	−1.07813
$143$	−2.95295	−0.246938
$144$	−2.66308	−0.221923
$145$	−3.68382	−0.305925
$146$	0.229098	0.0189602
$147$	2.48866	0.205261
$148$	−2.19499	−0.180427
$149$	0.630570	0.0516583	0.0258291	−	0.999666i	$-0.491777\pi$
$149$	0.630570	0.0516583	0.0258291	+	0.999666i	$0.491777\pi$
$150$	0.580450	0.0473935
$151$	18.1908	1.48034	0.740172	−	0.672418i	$-0.234744\pi$
$151$	18.1908	1.48034	0.740172	+	0.672418i	$0.234744\pi$
$152$	3.80194	0.308378
$153$	−4.82834	−0.390348
$154$	1.64698	0.132717
$155$	−3.41206	−0.274063
$156$	−1.71404	−0.137233
$157$	18.9796	1.51474	0.757368	−	0.652989i	$-0.226485\pi$
$157$	18.9796	1.51474	0.757368	+	0.652989i	$0.226485\pi$
$158$	−15.2682	−1.21468
$159$	−5.17349	−0.410285
$160$	1.00000	0.0790569
$161$	1.56949	0.123693
$162$	−6.08122	−0.477786
$163$	7.78236	0.609562	0.304781	−	0.952422i	$-0.401417\pi$
$163$	7.78236	0.609562	0.304781	+	0.952422i	$0.401417\pi$
$164$	−5.45269	−0.425784
$165$	−0.580450	−0.0451879
$166$	−2.72642	−0.211611
$167$	−8.48582	−0.656652	−0.328326	−	0.944564i	$-0.606485\pi$
$167$	−8.48582	−0.656652	−0.328326	+	0.944564i	$0.606485\pi$
$168$	0.955986	0.0737560
$169$	−4.28007	−0.329236
$170$	1.81307	0.139056
$171$	10.1249	0.774268
$172$	1.00000	0.0762493
$173$	−4.62742	−0.351816	−0.175908	−	0.984407i	$-0.556286\pi$
$173$	−4.62742	−0.351816	−0.175908	+	0.984407i	$0.556286\pi$
$174$	2.13827	0.162102
$175$	1.64698	0.124500
$176$	−1.00000	−0.0753778
$177$	1.80167	0.135422
$178$	5.52821	0.414357
$179$	11.4038	0.852356	0.426178	−	0.904639i	$-0.359860\pi$
$179$	11.4038	0.852356	0.426178	+	0.904639i	$0.359860\pi$
$180$	2.66308	0.198494
$181$	9.28441	0.690104	0.345052	−	0.938583i	$-0.387861\pi$
$181$	9.28441	0.690104	0.345052	+	0.938583i	$0.387861\pi$
$182$	−4.86344	−0.360502
$183$	5.73028	0.423594
$184$	−0.952953	−0.0702526
$185$	2.19499	0.161379
$186$	1.98053	0.145219
$187$	−1.81307	−0.132585
$188$	−11.1140	−0.810574
$189$	5.41383	0.393798
$190$	−3.80194	−0.275822
$191$	3.13535	0.226866	0.113433	−	0.993546i	$-0.463815\pi$
$191$	3.13535	0.226866	0.113433	+	0.993546i	$0.463815\pi$
$192$	−0.580450	−0.0418903
$193$	16.5144	1.18873	0.594365	−	0.804195i	$-0.297403\pi$
$193$	16.5144	1.18873	0.594365	+	0.804195i	$0.297403\pi$
$194$	3.05239	0.219149
$195$	1.71404	0.122745
$196$	−4.28747	−0.306248
$197$	−2.07563	−0.147882	−0.0739412	−	0.997263i	$-0.523558\pi$
$197$	−2.07563	−0.147882	−0.0739412	+	0.997263i	$0.523558\pi$
$198$	−2.66308	−0.189257
$199$	4.55938	0.323206	0.161603	−	0.986856i	$-0.448334\pi$
$199$	4.55938	0.323206	0.161603	+	0.986856i	$0.448334\pi$
$200$	−1.00000	−0.0707107
$201$	−3.59061	−0.253262
$202$	−1.68377	−0.118470
$203$	6.06716	0.425831
$204$	−1.05240	−0.0736824
$205$	5.45269	0.380833
$206$	1.85743	0.129413
$207$	−2.53779	−0.176389
$208$	2.95295	0.204750
$209$	3.80194	0.262986
$210$	−0.955986	−0.0659693
$211$	−23.5716	−1.62274	−0.811368	−	0.584535i	$-0.801277\pi$
$211$	−23.5716	−1.62274	−0.811368	+	0.584535i	$0.801277\pi$
$212$	8.91291	0.612141
$213$	−7.45729	−0.510965
$214$	14.8768	1.01696
$215$	−1.00000	−0.0681994
$216$	−3.28713	−0.223661
$217$	5.61957	0.381482
$218$	−11.2283	−0.760477
$219$	0.132980	0.00898593
$220$	1.00000	0.0674200
$221$	5.35391	0.360143
$222$	−1.27408	−0.0855107
$223$	7.34985	0.492183	0.246091	−	0.969247i	$-0.420854\pi$
$223$	7.34985	0.492183	0.246091	+	0.969247i	$0.420854\pi$
$224$	−1.64698	−0.110043
$225$	−2.66308	−0.177539
$226$	−2.54599	−0.169356
$227$	−23.1182	−1.53441	−0.767205	−	0.641402i	$-0.778353\pi$
$227$	−23.1182	−1.53441	−0.767205	+	0.641402i	$0.778353\pi$
$228$	2.20684	0.146151
$229$	28.5225	1.88482	0.942409	−	0.334462i	$-0.108555\pi$
$229$	28.5225	1.88482	0.942409	+	0.334462i	$0.108555\pi$
$230$	0.952953	0.0628359
$231$	0.955986	0.0628993
$232$	−3.68382	−0.241855
$233$	15.4512	1.01224	0.506122	−	0.862462i	$-0.331079\pi$
$233$	15.4512	1.01224	0.506122	+	0.862462i	$0.331079\pi$
$234$	7.86395	0.514082
$235$	11.1140	0.725000
$236$	−3.10392	−0.202048
$237$	−8.86244	−0.575677
$238$	−2.98608	−0.193559
$239$	−5.45055	−0.352566	−0.176283	−	0.984339i	$-0.556407\pi$
$239$	−5.45055	−0.352566	−0.176283	+	0.984339i	$0.556407\pi$
$240$	0.580450	0.0374679
$241$	−6.42694	−0.413996	−0.206998	−	0.978341i	$-0.566369\pi$
$241$	−6.42694	−0.413996	−0.206998	+	0.978341i	$0.566369\pi$
$242$	−1.00000	−0.0642824
$243$	−13.3912	−0.859048
$244$	−9.87214	−0.631999
$245$	4.28747	0.273916
$246$	−3.16501	−0.201794
$247$	−11.2270	−0.714355
$248$	−3.41206	−0.216666
$249$	−1.58255	−0.100290
$250$	1.00000	0.0632456
$251$	8.86310	0.559434	0.279717	−	0.960083i	$-0.409759\pi$
$251$	8.86310	0.559434	0.279717	+	0.960083i	$0.409759\pi$
$252$	−4.38602	−0.276294
$253$	−0.952953	−0.0599116
$254$	2.73781	0.171785
$255$	1.05240	0.0659035
$256$	1.00000	0.0625000
$257$	4.29084	0.267655	0.133828	−	0.991005i	$-0.457273\pi$
$257$	4.29084	0.267655	0.133828	+	0.991005i	$0.457273\pi$
$258$	0.580450	0.0361372
$259$	−3.61509	−0.224631
$260$	−2.95295	−0.183134
$261$	−9.81030	−0.607242
$262$	20.4265	1.26195
$263$	23.3413	1.43929	0.719643	−	0.694344i	$-0.244306\pi$
$263$	23.3413	1.43929	0.719643	+	0.694344i	$0.244306\pi$
$264$	−0.580450	−0.0357242
$265$	−8.91291	−0.547515
$266$	6.26171	0.383930
$267$	3.20885	0.196378
$268$	6.18592	0.377865
$269$	9.64797	0.588247	0.294124	−	0.955767i	$-0.404972\pi$
$269$	9.64797	0.588247	0.294124	+	0.955767i	$0.404972\pi$
$270$	3.28713	0.200048
$271$	28.2847	1.71817	0.859086	−	0.511831i	$-0.171032\pi$
$271$	28.2847	1.71817	0.859086	+	0.511831i	$0.171032\pi$
$272$	1.81307	0.109933
$273$	−2.82298	−0.170855
$274$	1.31421	0.0793946
$275$	−1.00000	−0.0603023
$276$	−0.553141	−0.0332952
$277$	−9.51350	−0.571611	−0.285806	−	0.958288i	$-0.592261\pi$
$277$	−9.51350	−0.571611	−0.285806	+	0.958288i	$0.592261\pi$
$278$	−19.4516	−1.16663
$279$	−9.08657	−0.543999
$280$	1.64698	0.0984256
$281$	28.8476	1.72091	0.860453	−	0.509529i	$-0.170181\pi$
$281$	28.8476	1.72091	0.860453	+	0.509529i	$0.170181\pi$
$282$	−6.45114	−0.384160
$283$	−3.77444	−0.224367	−0.112184	−	0.993687i	$-0.535785\pi$
$283$	−3.77444	−0.224367	−0.112184	+	0.993687i	$0.535785\pi$
$284$	12.8474	0.762356
$285$	−2.20684	−0.130722
$286$	2.95295	0.174612
$287$	−8.98045	−0.530099
$288$	2.66308	0.156923
$289$	−13.7128	−0.806634
$290$	3.68382	0.216321
$291$	1.77176	0.103862
$292$	−0.229098	−0.0134069
$293$	−20.0934	−1.17387	−0.586934	−	0.809635i	$-0.699665\pi$
$293$	−20.0934	−1.17387	−0.586934	+	0.809635i	$0.699665\pi$
$294$	−2.48866	−0.145142
$295$	3.10392	0.180717
$296$	2.19499	0.127581
$297$	−3.28713	−0.190739
$298$	−0.630570	−0.0365279
$299$	2.81403	0.162739
$300$	−0.580450	−0.0335123
$301$	1.64698	0.0949301
$302$	−18.1908	−1.04676
$303$	−0.977346	−0.0561471
$304$	−3.80194	−0.218056
$305$	9.87214	0.565277
$306$	4.82834	0.276018
$307$	22.6639	1.29350	0.646749	−	0.762703i	$-0.276128\pi$
$307$	22.6639	1.29350	0.646749	+	0.762703i	$0.276128\pi$
$308$	−1.64698	−0.0938451
$309$	1.07815	0.0613336
$310$	3.41206	0.193792
$311$	4.62256	0.262122	0.131061	−	0.991374i	$-0.458162\pi$
$311$	4.62256	0.262122	0.131061	+	0.991374i	$0.458162\pi$
$312$	1.71404	0.0970384
$313$	0.839632	0.0474588	0.0237294	−	0.999718i	$-0.492446\pi$
$313$	0.839632	0.0474588	0.0237294	+	0.999718i	$0.492446\pi$
$314$	−18.9796	−1.07108
$315$	4.38602	0.247125
$316$	15.2682	0.858905
$317$	27.1016	1.52218	0.761088	−	0.648649i	$-0.224665\pi$
$317$	27.1016	1.52218	0.761088	+	0.648649i	$0.224665\pi$
$318$	5.17349	0.290115
$319$	−3.68382	−0.206254
$320$	−1.00000	−0.0559017
$321$	8.63524	0.481972
$322$	−1.56949	−0.0874643
$323$	−6.89319	−0.383547
$324$	6.08122	0.337846
$325$	2.95295	0.163800
$326$	−7.78236	−0.431025
$327$	−6.51747	−0.360417
$328$	5.45269	0.301075
$329$	−18.3045	−1.00916
$330$	0.580450	0.0319527
$331$	27.7639	1.52604	0.763020	−	0.646375i	$-0.223716\pi$
$331$	27.7639	1.52604	0.763020	+	0.646375i	$0.223716\pi$
$332$	2.72642	0.149632
$333$	5.84542	0.320327
$334$	8.48582	0.464323
$335$	−6.18592	−0.337973
$336$	−0.955986	−0.0521533
$337$	7.90859	0.430808	0.215404	−	0.976525i	$-0.430893\pi$
$337$	7.90859	0.430808	0.215404	+	0.976525i	$0.430893\pi$
$338$	4.28007	0.232805
$339$	−1.47782	−0.0802640
$340$	−1.81307	−0.0983275
$341$	−3.41206	−0.184773
$342$	−10.1249	−0.547490
$343$	−18.5902	−1.00378
$344$	−1.00000	−0.0539164
$345$	0.553141	0.0297801
$346$	4.62742	0.248772
$347$	−5.46682	−0.293474	−0.146737	−	0.989176i	$-0.546877\pi$
$347$	−5.46682	−0.293474	−0.146737	+	0.989176i	$0.546877\pi$
$348$	−2.13827	−0.114623
$349$	22.7588	1.21825	0.609126	−	0.793074i	$-0.291521\pi$
$349$	22.7588	1.21825	0.609126	+	0.793074i	$0.291521\pi$
$350$	−1.64698	−0.0880346
$351$	9.70675	0.518108
$352$	1.00000	0.0533002
$353$	−31.4006	−1.67129	−0.835644	−	0.549272i	$-0.814905\pi$
$353$	−31.4006	−1.67129	−0.835644	+	0.549272i	$0.814905\pi$
$354$	−1.80167	−0.0957577
$355$	−12.8474	−0.681872
$356$	−5.52821	−0.292995
$357$	−1.73327	−0.0917343
$358$	−11.4038	−0.602707
$359$	−16.0218	−0.845596	−0.422798	−	0.906224i	$-0.638952\pi$
$359$	−16.0218	−0.845596	−0.422798	+	0.906224i	$0.638952\pi$
$360$	−2.66308	−0.140357
$361$	−4.54522	−0.239222
$362$	−9.28441	−0.487977
$363$	−0.580450	−0.0304657
$364$	4.86344	0.254914
$365$	0.229098	0.0119915
$366$	−5.73028	−0.299526
$367$	−25.5328	−1.33280	−0.666401	−	0.745593i	$-0.732166\pi$
$367$	−25.5328	−1.33280	−0.666401	+	0.745593i	$0.732166\pi$
$368$	0.952953	0.0496761
$369$	14.5209	0.755930
$370$	−2.19499	−0.114112
$371$	14.6793	0.762113
$372$	−1.98053	−0.102686
$373$	12.2063	0.632018	0.316009	−	0.948756i	$-0.397657\pi$
$373$	12.2063	0.632018	0.316009	+	0.948756i	$0.397657\pi$
$374$	1.81307	0.0937515
$375$	0.580450	0.0299743
$376$	11.1140	0.573162
$377$	10.8781	0.560253
$378$	−5.41383	−0.278457
$379$	24.9357	1.28086	0.640431	−	0.768015i	$-0.278756\pi$
$379$	24.9357	1.28086	0.640431	+	0.768015i	$0.278756\pi$
$380$	3.80194	0.195036
$381$	1.58916	0.0814152
$382$	−3.13535	−0.160419
$383$	18.8612	0.963761	0.481881	−	0.876237i	$-0.339954\pi$
$383$	18.8612	0.963761	0.481881	+	0.876237i	$0.339954\pi$
$384$	0.580450	0.0296209
$385$	1.64698	0.0839377
$386$	−16.5144	−0.840559
$387$	−2.66308	−0.135372
$388$	−3.05239	−0.154962
$389$	14.3498	0.727565	0.363782	−	0.931484i	$-0.381485\pi$
$389$	14.3498	0.727565	0.363782	+	0.931484i	$0.381485\pi$
$390$	−1.71404	−0.0867938
$391$	1.72777	0.0873771
$392$	4.28747	0.216550
$393$	11.8565	0.598083
$394$	2.07563	0.104569
$395$	−15.2682	−0.768228
$396$	2.66308	0.133825
$397$	−24.8725	−1.24831	−0.624157	−	0.781299i	$-0.714558\pi$
$397$	−24.8725	−1.24831	−0.624157	+	0.781299i	$0.714558\pi$
$398$	−4.55938	−0.228541
$399$	3.63461	0.181958
$400$	1.00000	0.0500000
$401$	−2.38327	−0.119015	−0.0595075	−	0.998228i	$-0.518953\pi$
$401$	−2.38327	−0.119015	−0.0595075	+	0.998228i	$0.518953\pi$
$402$	3.59061	0.179084
$403$	10.0756	0.501904
$404$	1.68377	0.0837709
$405$	−6.08122	−0.302178
$406$	−6.06716	−0.301108
$407$	2.19499	0.108802
$408$	1.05240	0.0521013
$409$	32.5318	1.60859	0.804296	−	0.594228i	$-0.202542\pi$
$409$	32.5318	1.60859	0.804296	+	0.594228i	$0.202542\pi$
$410$	−5.45269	−0.269289
$411$	0.762835	0.0376279
$412$	−1.85743	−0.0915091
$413$	−5.11209	−0.251549
$414$	2.53779	0.124726
$415$	−2.72642	−0.133835
$416$	−2.95295	−0.144780
$417$	−11.2907	−0.552906
$418$	−3.80194	−0.185959
$419$	−6.83708	−0.334013	−0.167007	−	0.985956i	$-0.553410\pi$
$419$	−6.83708	−0.334013	−0.167007	+	0.985956i	$0.553410\pi$
$420$	0.955986	0.0466474
$421$	19.0503	0.928453	0.464227	−	0.885716i	$-0.346332\pi$
$421$	19.0503	0.928453	0.464227	+	0.885716i	$0.346332\pi$
$422$	23.5716	1.14745
$423$	29.5975	1.43908
$424$	−8.91291	−0.432849
$425$	1.81307	0.0879467
$426$	7.45729	0.361307
$427$	−16.2592	−0.786836
$428$	−14.8768	−0.719097
$429$	1.71404	0.0827547
$430$	1.00000	0.0482243
$431$	16.5797	0.798615	0.399308	−	0.916817i	$-0.369251\pi$
$431$	16.5797	0.798615	0.399308	+	0.916817i	$0.369251\pi$
$432$	3.28713	0.158152
$433$	5.64945	0.271495	0.135748	−	0.990743i	$-0.456656\pi$
$433$	5.64945	0.271495	0.135748	+	0.990743i	$0.456656\pi$
$434$	−5.61957	−0.269748
$435$	2.13827	0.102522
$436$	11.2283	0.537738
$437$	−3.62307	−0.173315
$438$	−0.132980	−0.00635401
$439$	40.1328	1.91543	0.957716	−	0.287716i	$-0.0928958\pi$
$439$	40.1328	1.91543	0.957716	+	0.287716i	$0.0928958\pi$
$440$	−1.00000	−0.0476731
$441$	11.4179	0.543708
$442$	−5.35391	−0.254659
$443$	−11.2633	−0.535137	−0.267569	−	0.963539i	$-0.586220\pi$
$443$	−11.2633	−0.535137	−0.267569	+	0.963539i	$0.586220\pi$
$444$	1.27408	0.0604652
$445$	5.52821	0.262062
$446$	−7.34985	−0.348026
$447$	−0.366014	−0.0173119
$448$	1.64698	0.0778123
$449$	−10.8493	−0.512012	−0.256006	−	0.966675i	$-0.582407\pi$
$449$	−10.8493	−0.512012	−0.256006	+	0.966675i	$0.582407\pi$
$450$	2.66308	0.125539
$451$	5.45269	0.256757
$452$	2.54599	0.119753
$453$	−10.5588	−0.496097
$454$	23.1182	1.08499
$455$	−4.86344	−0.228002
$456$	−2.20684	−0.103345
$457$	−22.2951	−1.04292	−0.521461	−	0.853275i	$-0.674613\pi$
$457$	−22.2951	−1.04292	−0.521461	+	0.853275i	$0.674613\pi$
$458$	−28.5225	−1.33277
$459$	5.95980	0.278179
$460$	−0.952953	−0.0444317
$461$	39.4379	1.83681	0.918404	−	0.395644i	$-0.129479\pi$
$461$	39.4379	1.83681	0.918404	+	0.395644i	$0.129479\pi$
$462$	−0.955986	−0.0444765
$463$	39.4578	1.83376	0.916879	−	0.399166i	$-0.130700\pi$
$463$	39.4578	1.83376	0.916879	+	0.399166i	$0.130700\pi$
$464$	3.68382	0.171017
$465$	1.98053	0.0918448
$466$	−15.4512	−0.715765
$467$	33.2426	1.53829	0.769143	−	0.639077i	$-0.220683\pi$
$467$	33.2426	1.53829	0.769143	+	0.639077i	$0.220683\pi$
$468$	−7.86395	−0.363511
$469$	10.1881	0.470441
$470$	−11.1140	−0.512652
$471$	−11.0167	−0.507622
$472$	3.10392	0.142870
$473$	−1.00000	−0.0459800
$474$	8.86244	0.407065
$475$	−3.80194	−0.174445
$476$	2.98608	0.136867
$477$	−23.7358	−1.08679
$478$	5.45055	0.249302
$479$	36.6264	1.67350	0.836752	−	0.547582i	$-0.184451\pi$
$479$	36.6264	1.67350	0.836752	+	0.547582i	$0.184451\pi$
$480$	−0.580450	−0.0264938
$481$	−6.48170	−0.295540
$482$	6.42694	0.292739
$483$	−0.911010	−0.0414524
$484$	1.00000	0.0454545
$485$	3.05239	0.138602
$486$	13.3912	0.607439
$487$	31.5638	1.43029	0.715145	−	0.698976i	$-0.246361\pi$
$487$	31.5638	1.43029	0.715145	+	0.698976i	$0.246361\pi$
$488$	9.87214	0.446891
$489$	−4.51727	−0.204278
$490$	−4.28747	−0.193688
$491$	7.65511	0.345470	0.172735	−	0.984968i	$-0.444740\pi$
$491$	7.65511	0.345470	0.172735	+	0.984968i	$0.444740\pi$
$492$	3.16501	0.142690
$493$	6.67902	0.300808
$494$	11.2270	0.505125
$495$	−2.66308	−0.119696
$496$	3.41206	0.153206
$497$	21.1594	0.949130
$498$	1.58255	0.0709157
$499$	11.4695	0.513446	0.256723	−	0.966485i	$-0.417357\pi$
$499$	11.4695	0.513446	0.256723	+	0.966485i	$0.417357\pi$
$500$	−1.00000	−0.0447214
$501$	4.92559	0.220059
$502$	−8.86310	−0.395579
$503$	−18.5495	−0.827080	−0.413540	−	0.910486i	$-0.635708\pi$
$503$	−18.5495	−0.827080	−0.413540	+	0.910486i	$0.635708\pi$
$504$	4.38602	0.195369
$505$	−1.68377	−0.0749269
$506$	0.952953	0.0423639
$507$	2.48436	0.110334
$508$	−2.73781	−0.121471
$509$	−9.83302	−0.435841	−0.217920	−	0.975967i	$-0.569927\pi$
$509$	−9.83302	−0.435841	−0.217920	+	0.975967i	$0.569927\pi$
$510$	−1.05240	−0.0466008
$511$	−0.377318	−0.0166916
$512$	−1.00000	−0.0441942
$513$	−12.4975	−0.551778
$514$	−4.29084	−0.189261
$515$	1.85743	0.0818483
$516$	−0.580450	−0.0255529
$517$	11.1140	0.488795
$518$	3.61509	0.158838
$519$	2.68598	0.117902
$520$	2.95295	0.129496
$521$	−36.0224	−1.57817	−0.789084	−	0.614285i	$-0.789444\pi$
$521$	−36.0224	−1.57817	−0.789084	+	0.614285i	$0.789444\pi$
$522$	9.81030	0.429385
$523$	−15.1116	−0.660783	−0.330392	−	0.943844i	$-0.607181\pi$
$523$	−15.1116	−0.660783	−0.330392	+	0.943844i	$0.607181\pi$
$524$	−20.4265	−0.892334
$525$	−0.955986	−0.0417227
$526$	−23.3413	−1.01773
$527$	6.18629	0.269479
$528$	0.580450	0.0252608
$529$	−22.0919	−0.960517
$530$	8.91291	0.387152
$531$	8.26599	0.358713
$532$	−6.26171	−0.271480
$533$	−16.1015	−0.697436
$534$	−3.20885	−0.138860
$535$	14.8768	0.643180
$536$	−6.18592	−0.267191
$537$	−6.61930	−0.285644
$538$	−9.64797	−0.415954
$539$	4.28747	0.184674
$540$	−3.28713	−0.141456
$541$	38.2711	1.64540	0.822701	−	0.568474i	$-0.192466\pi$
$541$	38.2711	1.64540	0.822701	+	0.568474i	$0.192466\pi$
$542$	−28.2847	−1.21493
$543$	−5.38913	−0.231270
$544$	−1.81307	−0.0777347
$545$	−11.2283	−0.480968
$546$	2.82298	0.120813
$547$	6.64388	0.284072	0.142036	−	0.989862i	$-0.454635\pi$
$547$	6.64388	0.284072	0.142036	+	0.989862i	$0.454635\pi$
$548$	−1.31421	−0.0561405
$549$	26.2903	1.12204
$550$	1.00000	0.0426401
$551$	−14.0057	−0.596662
$552$	0.553141	0.0235433
$553$	25.1464	1.06933
$554$	9.51350	0.404190
$555$	−1.27408	−0.0540817
$556$	19.4516	0.824931
$557$	11.8791	0.503334	0.251667	−	0.967814i	$-0.419021\pi$
$557$	11.8791	0.503334	0.251667	+	0.967814i	$0.419021\pi$
$558$	9.08657	0.384665
$559$	2.95295	0.124897
$560$	−1.64698	−0.0695974
$561$	1.05240	0.0444322
$562$	−28.8476	−1.21686
$563$	46.3455	1.95323	0.976616	−	0.214993i	$-0.0689728\pi$
$563$	46.3455	1.95323	0.976616	+	0.214993i	$0.0689728\pi$
$564$	6.45114	0.271642
$565$	−2.54599	−0.107110
$566$	3.77444	0.158652
$567$	10.0156	0.420617
$568$	−12.8474	−0.539067
$569$	−10.6916	−0.448216	−0.224108	−	0.974564i	$-0.571947\pi$
$569$	−10.6916	−0.448216	−0.224108	+	0.974564i	$0.571947\pi$
$570$	2.20684	0.0924342
$571$	−1.75530	−0.0734572	−0.0367286	−	0.999325i	$-0.511694\pi$
$571$	−1.75530	−0.0734572	−0.0367286	+	0.999325i	$0.511694\pi$
$572$	−2.95295	−0.123469
$573$	−1.81992	−0.0760281
$574$	8.98045	0.374837
$575$	0.952953	0.0397409
$576$	−2.66308	−0.110962
$577$	−14.9153	−0.620932	−0.310466	−	0.950584i	$-0.600485\pi$
$577$	−14.9153	−0.620932	−0.310466	+	0.950584i	$0.600485\pi$
$578$	13.7128	0.570377
$579$	−9.58576	−0.398371
$580$	−3.68382	−0.152962
$581$	4.49035	0.186291
$582$	−1.77176	−0.0734418
$583$	−8.91291	−0.369135
$584$	0.229098	0.00948012
$585$	7.86395	0.325134
$586$	20.0934	0.830050
$587$	2.23127	0.0920945	0.0460472	−	0.998939i	$-0.485338\pi$
$587$	2.23127	0.0920945	0.0460472	+	0.998939i	$0.485338\pi$
$588$	2.48866	0.102631
$589$	−12.9724	−0.534520
$590$	−3.10392	−0.127786
$591$	1.20480	0.0495587
$592$	−2.19499	−0.0902135
$593$	−9.25484	−0.380051	−0.190025	−	0.981779i	$-0.560857\pi$
$593$	−9.25484	−0.380051	−0.190025	+	0.981779i	$0.560857\pi$
$594$	3.28713	0.134873
$595$	−2.98608	−0.122417
$596$	0.630570	0.0258291
$597$	−2.64649	−0.108314
$598$	−2.81403	−0.115074
$599$	−16.4307	−0.671340	−0.335670	−	0.941980i	$-0.608963\pi$
$599$	−16.4307	−0.671340	−0.335670	+	0.941980i	$0.608963\pi$
$600$	0.580450	0.0236968
$601$	−1.35830	−0.0554063	−0.0277032	−	0.999616i	$-0.508819\pi$
$601$	−1.35830	−0.0554063	−0.0277032	+	0.999616i	$0.508819\pi$
$602$	−1.64698	−0.0671257
$603$	−16.4736	−0.670856
$604$	18.1908	0.740172
$605$	−1.00000	−0.0406558
$606$	0.977346	0.0397020
$607$	−2.07452	−0.0842020	−0.0421010	−	0.999113i	$-0.513405\pi$
$607$	−2.07452	−0.0842020	−0.0421010	+	0.999113i	$0.513405\pi$
$608$	3.80194	0.154189
$609$	−3.52168	−0.142706
$610$	−9.87214	−0.399711
$611$	−32.8192	−1.32772
$612$	−4.82834	−0.195174
$613$	−25.5758	−1.03300	−0.516498	−	0.856288i	$-0.672765\pi$
$613$	−25.5758	−1.03300	−0.516498	+	0.856288i	$0.672765\pi$
$614$	−22.6639	−0.914641
$615$	−3.16501	−0.127626
$616$	1.64698	0.0663585
$617$	1.68989	0.0680323	0.0340161	−	0.999421i	$-0.489170\pi$
$617$	1.68989	0.0680323	0.0340161	+	0.999421i	$0.489170\pi$
$618$	−1.07815	−0.0433694
$619$	−12.4520	−0.500490	−0.250245	−	0.968183i	$-0.580511\pi$
$619$	−12.4520	−0.500490	−0.250245	+	0.968183i	$0.580511\pi$
$620$	−3.41206	−0.137032
$621$	3.13248	0.125702
$622$	−4.62256	−0.185348
$623$	−9.10483	−0.364777
$624$	−1.71404	−0.0686165
$625$	1.00000	0.0400000
$626$	−0.839632	−0.0335585
$627$	−2.20684	−0.0881326
$628$	18.9796	0.757368
$629$	−3.97966	−0.158680
$630$	−4.38602	−0.174743
$631$	−30.6550	−1.22036	−0.610178	−	0.792265i	$-0.708902\pi$
$631$	−30.6550	−1.22036	−0.610178	+	0.792265i	$0.708902\pi$
$632$	−15.2682	−0.607338
$633$	13.6821	0.543816
$634$	−27.1016	−1.07634
$635$	2.73781	0.108647
$636$	−5.17349	−0.205142
$637$	−12.6607	−0.501635
$638$	3.68382	0.145844
$639$	−34.2137	−1.35347
$640$	1.00000	0.0395285
$641$	2.25111	0.0889136	0.0444568	−	0.999011i	$-0.485844\pi$
$641$	2.25111	0.0889136	0.0444568	+	0.999011i	$0.485844\pi$
$642$	−8.63524	−0.340806
$643$	36.2268	1.42865	0.714323	−	0.699816i	$-0.246735\pi$
$643$	36.2268	1.42865	0.714323	+	0.699816i	$0.246735\pi$
$644$	1.56949	0.0618466
$645$	0.580450	0.0228552
$646$	6.89319	0.271209
$647$	−5.58317	−0.219497	−0.109748	−	0.993959i	$-0.535005\pi$
$647$	−5.58317	−0.219497	−0.109748	+	0.993959i	$0.535005\pi$
$648$	−6.08122	−0.238893
$649$	3.10392	0.121840
$650$	−2.95295	−0.115824
$651$	−3.26188	−0.127843
$652$	7.78236	0.304781
$653$	2.93736	0.114948	0.0574739	−	0.998347i	$-0.481695\pi$
$653$	2.93736	0.114948	0.0574739	+	0.998347i	$0.481695\pi$
$654$	6.51747	0.254853
$655$	20.4265	0.798128
$656$	−5.45269	−0.212892
$657$	0.610105	0.0238024
$658$	18.3045	0.713585
$659$	19.2396	0.749469	0.374735	−	0.927132i	$-0.377734\pi$
$659$	19.2396	0.749469	0.374735	+	0.927132i	$0.377734\pi$
$660$	−0.580450	−0.0225940
$661$	40.4661	1.57395	0.786974	−	0.616986i	$-0.211646\pi$
$661$	40.4661	1.57395	0.786974	+	0.616986i	$0.211646\pi$
$662$	−27.7639	−1.07907
$663$	−3.10767	−0.120692
$664$	−2.72642	−0.105806
$665$	6.26171	0.242819
$666$	−5.84542	−0.226506
$667$	3.51051	0.135927
$668$	−8.48582	−0.328326
$669$	−4.26622	−0.164942
$670$	6.18592	0.238983
$671$	9.87214	0.381110
$672$	0.955986	0.0368780
$673$	41.9506	1.61708	0.808539	−	0.588443i	$-0.200259\pi$
$673$	41.9506	1.61708	0.808539	+	0.588443i	$0.200259\pi$
$674$	−7.90859	−0.304627
$675$	3.28713	0.126522
$676$	−4.28007	−0.164618
$677$	−17.7907	−0.683752	−0.341876	−	0.939745i	$-0.611062\pi$
$677$	−17.7907	−0.683752	−0.341876	+	0.939745i	$0.611062\pi$
$678$	1.47782	0.0567552
$679$	−5.02722	−0.192927
$680$	1.81307	0.0695280
$681$	13.4190	0.514216
$682$	3.41206	0.130654
$683$	−31.1953	−1.19365	−0.596827	−	0.802370i	$-0.703572\pi$
$683$	−31.1953	−1.19365	−0.596827	+	0.802370i	$0.703572\pi$
$684$	10.1249	0.387134
$685$	1.31421	0.0502136
$686$	18.5902	0.709777
$687$	−16.5559	−0.631646
$688$	1.00000	0.0381246
$689$	26.3194	1.00269
$690$	−0.553141	−0.0210577
$691$	−5.32363	−0.202520	−0.101260	−	0.994860i	$-0.532287\pi$
$691$	−5.32363	−0.202520	−0.101260	+	0.994860i	$0.532287\pi$
$692$	−4.62742	−0.175908
$693$	4.38602	0.166611
$694$	5.46682	0.207518
$695$	−19.4516	−0.737841
$696$	2.13827	0.0810510
$697$	−9.88611	−0.374463
$698$	−22.7588	−0.861434
$699$	−8.96866	−0.339226
$700$	1.64698	0.0622498
$701$	−17.5252	−0.661917	−0.330958	−	0.943645i	$-0.607372\pi$
$701$	−17.5252	−0.661917	−0.330958	+	0.943645i	$0.607372\pi$
$702$	−9.70675	−0.366358
$703$	8.34522	0.314746
$704$	−1.00000	−0.0376889
$705$	−6.45114	−0.242964
$706$	31.4006	1.18178
$707$	2.77313	0.104294
$708$	1.80167	0.0677109
$709$	−34.6811	−1.30247	−0.651237	−	0.758874i	$-0.725750\pi$
$709$	−34.6811	−1.30247	−0.651237	+	0.758874i	$0.725750\pi$
$710$	12.8474	0.482156
$711$	−40.6605	−1.52489
$712$	5.52821	0.207178
$713$	3.25153	0.121771
$714$	1.73327	0.0648660
$715$	2.95295	0.110434
$716$	11.4038	0.426178
$717$	3.16377	0.118153
$718$	16.0218	0.597927
$719$	4.09689	0.152788	0.0763942	−	0.997078i	$-0.475659\pi$
$719$	4.09689	0.152788	0.0763942	+	0.997078i	$0.475659\pi$
$720$	2.66308	0.0992471
$721$	−3.05915	−0.113929
$722$	4.54522	0.169156
$723$	3.73052	0.138739
$724$	9.28441	0.345052
$725$	3.68382	0.136814
$726$	0.580450	0.0215425
$727$	−42.1954	−1.56494	−0.782471	−	0.622687i	$-0.786041\pi$
$727$	−42.1954	−1.56494	−0.782471	+	0.622687i	$0.786041\pi$
$728$	−4.86344	−0.180251
$729$	−10.4707	−0.387804
$730$	−0.229098	−0.00847928
$731$	1.81307	0.0670588
$732$	5.73028	0.211797
$733$	21.0209	0.776423	0.388212	−	0.921570i	$-0.373093\pi$
$733$	21.0209	0.776423	0.388212	+	0.921570i	$0.373093\pi$
$734$	25.5328	0.942434
$735$	−2.48866	−0.0917957
$736$	−0.952953	−0.0351263
$737$	−6.18592	−0.227861
$738$	−14.5209	−0.534524
$739$	−14.0102	−0.515373	−0.257686	−	0.966229i	$-0.582960\pi$
$739$	−14.0102	−0.515373	−0.257686	+	0.966229i	$0.582960\pi$
$740$	2.19499	0.0806894
$741$	6.51669	0.239396
$742$	−14.6793	−0.538895
$743$	7.10348	0.260601	0.130301	−	0.991475i	$-0.458406\pi$
$743$	7.10348	0.260601	0.130301	+	0.991475i	$0.458406\pi$
$744$	1.98053	0.0726097
$745$	−0.630570	−0.0231023
$746$	−12.2063	−0.446904
$747$	−7.26067	−0.265654
$748$	−1.81307	−0.0662924
$749$	−24.5017	−0.895274
$750$	−0.580450	−0.0211950
$751$	1.16751	0.0426030	0.0213015	−	0.999773i	$-0.493219\pi$
$751$	1.16751	0.0426030	0.0213015	+	0.999773i	$0.493219\pi$
$752$	−11.1140	−0.405287
$753$	−5.14458	−0.187479
$754$	−10.8781	−0.396159
$755$	−18.1908	−0.662030
$756$	5.41383	0.196899
$757$	−32.6233	−1.18571	−0.592857	−	0.805308i	$-0.702000\pi$
$757$	−32.6233	−1.18571	−0.592857	+	0.805308i	$0.702000\pi$
$758$	−24.9357	−0.905707
$759$	0.553141	0.0200778
$760$	−3.80194	−0.137911
$761$	−22.3050	−0.808556	−0.404278	−	0.914636i	$-0.632477\pi$
$761$	−22.3050	−0.808556	−0.404278	+	0.914636i	$0.632477\pi$
$762$	−1.58916	−0.0575692
$763$	18.4928	0.669483
$764$	3.13535	0.113433
$765$	4.82834	0.174569
$766$	−18.8612	−0.681482
$767$	−9.16574	−0.330956
$768$	−0.580450	−0.0209452
$769$	−42.7788	−1.54264	−0.771322	−	0.636445i	$-0.780404\pi$
$769$	−42.7788	−1.54264	−0.771322	+	0.636445i	$0.780404\pi$
$770$	−1.64698	−0.0593529
$771$	−2.49062	−0.0896973
$772$	16.5144	0.594365
$773$	41.5959	1.49610	0.748051	−	0.663642i	$-0.230990\pi$
$773$	41.5959	1.49610	0.748051	+	0.663642i	$0.230990\pi$
$774$	2.66308	0.0957224
$775$	3.41206	0.122565
$776$	3.05239	0.109574
$777$	2.09838	0.0752789
$778$	−14.3498	−0.514466
$779$	20.7308	0.742759
$780$	1.71404	0.0613725
$781$	−12.8474	−0.459718
$782$	−1.72777	−0.0617849
$783$	12.1092	0.432748
$784$	−4.28747	−0.153124
$785$	−18.9796	−0.677410
$786$	−11.8565	−0.422909
$787$	−48.7051	−1.73615	−0.868074	−	0.496434i	$-0.834642\pi$
$787$	−48.7051	−1.73615	−0.868074	+	0.496434i	$0.834642\pi$
$788$	−2.07563	−0.0739412
$789$	−13.5484	−0.482337
$790$	15.2682	0.543219
$791$	4.19318	0.149092
$792$	−2.66308	−0.0946284
$793$	−29.1520	−1.03522
$794$	24.8725	0.882692
$795$	5.17349	0.183485
$796$	4.55938	0.161603
$797$	−49.6197	−1.75762	−0.878811	−	0.477170i	$-0.841662\pi$
$797$	−49.6197	−1.75762	−0.878811	+	0.477170i	$0.841662\pi$
$798$	−3.63461	−0.128664
$799$	−20.1505	−0.712874
$800$	−1.00000	−0.0353553
$801$	14.7221	0.520178
$802$	2.38327	0.0841564
$803$	0.229098	0.00808468
$804$	−3.59061	−0.126631
$805$	−1.56949	−0.0553173
$806$	−10.0756	−0.354899
$807$	−5.60016	−0.197135
$808$	−1.68377	−0.0592350
$809$	−25.6526	−0.901897	−0.450949	−	0.892550i	$-0.648914\pi$
$809$	−25.6526	−0.901897	−0.450949	+	0.892550i	$0.648914\pi$
$810$	6.08122	0.213672
$811$	12.0142	0.421876	0.210938	−	0.977499i	$-0.432348\pi$
$811$	12.0142	0.421876	0.210938	+	0.977499i	$0.432348\pi$
$812$	6.06716	0.212916
$813$	−16.4178	−0.575799
$814$	−2.19499	−0.0769343
$815$	−7.78236	−0.272604
$816$	−1.05240	−0.0368412
$817$	−3.80194	−0.133013
$818$	−32.5318	−1.13745
$819$	−12.9517	−0.452570
$820$	5.45269	0.190416
$821$	36.3661	1.26918	0.634592	−	0.772847i	$-0.281168\pi$
$821$	36.3661	1.26918	0.634592	+	0.772847i	$0.281168\pi$
$822$	−0.762835	−0.0266069
$823$	46.3560	1.61587	0.807934	−	0.589273i	$-0.200586\pi$
$823$	46.3560	1.61587	0.807934	+	0.589273i	$0.200586\pi$
$824$	1.85743	0.0647067
$825$	0.580450	0.0202087
$826$	5.11209	0.177872
$827$	51.0586	1.77548	0.887741	−	0.460344i	$-0.152274\pi$
$827$	51.0586	1.77548	0.887741	+	0.460344i	$0.152274\pi$
$828$	−2.53779	−0.0881943
$829$	30.4558	1.05777	0.528886	−	0.848693i	$-0.322610\pi$
$829$	30.4558	1.05777	0.528886	+	0.848693i	$0.322610\pi$
$830$	2.72642	0.0946354
$831$	5.52211	0.191560
$832$	2.95295	0.102375
$833$	−7.77348	−0.269335
$834$	11.2907	0.390964
$835$	8.48582	0.293664
$836$	3.80194	0.131493
$837$	11.2159	0.387678
$838$	6.83708	0.236183
$839$	8.16121	0.281756	0.140878	−	0.990027i	$-0.455007\pi$
$839$	8.16121	0.281756	0.140878	+	0.990027i	$0.455007\pi$
$840$	−0.955986	−0.0329847
$841$	−15.4295	−0.532051
$842$	−19.0503	−0.656515
$843$	−16.7446	−0.576715
$844$	−23.5716	−0.811368
$845$	4.28007	0.147239
$846$	−29.5975	−1.01758
$847$	1.64698	0.0565908
$848$	8.91291	0.306070
$849$	2.19087	0.0751906
$850$	−1.81307	−0.0621877
$851$	−2.09172	−0.0717033
$852$	−7.45729	−0.255483
$853$	30.0565	1.02911	0.514557	−	0.857456i	$-0.327956\pi$
$853$	30.0565	1.02911	0.514557	+	0.857456i	$0.327956\pi$
$854$	16.2592	0.556377
$855$	−10.1249	−0.346263
$856$	14.8768	0.508479
$857$	−12.2194	−0.417407	−0.208703	−	0.977979i	$-0.566924\pi$
$857$	−12.2194	−0.417407	−0.208703	+	0.977979i	$0.566924\pi$
$858$	−1.71404	−0.0585164
$859$	−20.1048	−0.685966	−0.342983	−	0.939342i	$-0.611437\pi$
$859$	−20.1048	−0.685966	−0.342983	+	0.939342i	$0.611437\pi$
$860$	−1.00000	−0.0340997
$861$	5.21270	0.177648
$862$	−16.5797	−0.564706
$863$	17.6080	0.599384	0.299692	−	0.954036i	$-0.403116\pi$
$863$	17.6080	0.599384	0.299692	+	0.954036i	$0.403116\pi$
$864$	−3.28713	−0.111830
$865$	4.62742	0.157337
$866$	−5.64945	−0.191976
$867$	7.95958	0.270322
$868$	5.61957	0.190741
$869$	−15.2682	−0.517939
$870$	−2.13827	−0.0724942
$871$	18.2667	0.618944
$872$	−11.2283	−0.380238
$873$	8.12876	0.275117
$874$	3.62307	0.122552
$875$	−1.64698	−0.0556779
$876$	0.132980	0.00449296
$877$	21.5061	0.726211	0.363105	−	0.931748i	$-0.381717\pi$
$877$	21.5061	0.726211	0.363105	+	0.931748i	$0.381717\pi$
$878$	−40.1328	−1.35441
$879$	11.6632	0.393390
$880$	1.00000	0.0337100
$881$	−10.0368	−0.338150	−0.169075	−	0.985603i	$-0.554078\pi$
$881$	−10.0368	−0.338150	−0.169075	+	0.985603i	$0.554078\pi$
$882$	−11.4179	−0.384460
$883$	−5.17892	−0.174284	−0.0871422	−	0.996196i	$-0.527773\pi$
$883$	−5.17892	−0.174284	−0.0871422	+	0.996196i	$0.527773\pi$
$884$	5.35391	0.180071
$885$	−1.80167	−0.0605625
$886$	11.2633	0.378399
$887$	22.7889	0.765175	0.382588	−	0.923919i	$-0.375033\pi$
$887$	22.7889	0.765175	0.382588	+	0.923919i	$0.375033\pi$
$888$	−1.27408	−0.0427553
$889$	−4.50911	−0.151231
$890$	−5.52821	−0.185306
$891$	−6.08122	−0.203729
$892$	7.34985	0.246091
$893$	42.2549	1.41401
$894$	0.366014	0.0122413
$895$	−11.4038	−0.381185
$896$	−1.64698	−0.0550216
$897$	−1.63340	−0.0545377
$898$	10.8493	0.362047
$899$	12.5694	0.419213
$900$	−2.66308	−0.0887693
$901$	16.1597	0.538358
$902$	−5.45269	−0.181555
$903$	−0.955986	−0.0318132
$904$	−2.54599	−0.0846782
$905$	−9.28441	−0.308624
$906$	10.5588	0.350793
$907$	42.9039	1.42460	0.712300	−	0.701875i	$-0.247654\pi$
$907$	42.9039	1.42460	0.712300	+	0.701875i	$0.247654\pi$
$908$	−23.1182	−0.767205
$909$	−4.48402	−0.148726
$910$	4.86344	0.161222
$911$	24.6793	0.817661	0.408830	−	0.912610i	$-0.365937\pi$
$911$	24.6793	0.817661	0.408830	+	0.912610i	$0.365937\pi$
$912$	2.20684	0.0730757
$913$	−2.72642	−0.0902313
$914$	22.2951	0.737457
$915$	−5.73028	−0.189437
$916$	28.5225	0.942409
$917$	−33.6419	−1.11095
$918$	−5.95980	−0.196703
$919$	50.1392	1.65394	0.826969	−	0.562247i	$-0.190063\pi$
$919$	50.1392	1.65394	0.826969	+	0.562247i	$0.190063\pi$
$920$	0.952953	0.0314179
$921$	−13.1553	−0.433480
$922$	−39.4379	−1.29882
$923$	37.9379	1.24874
$924$	0.955986	0.0314496
$925$	−2.19499	−0.0721708
$926$	−39.4578	−1.29666
$927$	4.94649	0.162464
$928$	−3.68382	−0.120927
$929$	−18.0484	−0.592149	−0.296075	−	0.955165i	$-0.595678\pi$
$929$	−18.0484	−0.592149	−0.296075	+	0.955165i	$0.595678\pi$
$930$	−1.98053	−0.0649440
$931$	16.3007	0.534235
$932$	15.4512	0.506122
$933$	−2.68317	−0.0878429
$934$	−33.2426	−1.08773
$935$	1.81307	0.0592937
$936$	7.86395	0.257041
$937$	−37.8450	−1.23634	−0.618172	−	0.786043i	$-0.712126\pi$
$937$	−37.8450	−1.23634	−0.618172	+	0.786043i	$0.712126\pi$
$938$	−10.1881	−0.332652
$939$	−0.487364	−0.0159045
$940$	11.1140	0.362500
$941$	51.9990	1.69512	0.847559	−	0.530700i	$-0.178071\pi$
$941$	51.9990	1.69512	0.847559	+	0.530700i	$0.178071\pi$
$942$	11.0167	0.358943
$943$	−5.19616	−0.169210
$944$	−3.10392	−0.101024
$945$	−5.41383	−0.176112
$946$	1.00000	0.0325128
$947$	−37.0303	−1.20332	−0.601662	−	0.798751i	$-0.705495\pi$
$947$	−37.0303	−1.20332	−0.601662	+	0.798751i	$0.705495\pi$
$948$	−8.86244	−0.287839
$949$	−0.676514	−0.0219606
$950$	3.80194	0.123351
$951$	−15.7311	−0.510116
$952$	−2.98608	−0.0967794
$953$	−21.6469	−0.701213	−0.350607	−	0.936523i	$-0.614025\pi$
$953$	−21.6469	−0.701213	−0.350607	+	0.936523i	$0.614025\pi$
$954$	23.7358	0.768474
$955$	−3.13535	−0.101458
$956$	−5.45055	−0.176283
$957$	2.13827	0.0691205
$958$	−36.6264	−1.18335
$959$	−2.16448	−0.0698947
$960$	0.580450	0.0187339
$961$	−19.3579	−0.624447
$962$	6.48170	0.208978
$963$	39.6181	1.27668
$964$	−6.42694	−0.206998
$965$	−16.5144	−0.531616
$966$	0.911010	0.0293113
$967$	−39.3479	−1.26534	−0.632671	−	0.774421i	$-0.718041\pi$
$967$	−39.3479	−1.26534	−0.632671	+	0.774421i	$0.718041\pi$
$968$	−1.00000	−0.0321412
$969$	4.00115	0.128535
$970$	−3.05239	−0.0980064
$971$	33.1960	1.06531	0.532655	−	0.846332i	$-0.321194\pi$
$971$	33.1960	1.06531	0.532655	+	0.846332i	$0.321194\pi$
$972$	−13.3912	−0.429524
$973$	32.0363	1.02704
$974$	−31.5638	−1.01137
$975$	−1.71404	−0.0548932
$976$	−9.87214	−0.315999
$977$	−49.9804	−1.59901	−0.799507	−	0.600657i	$-0.794906\pi$
$977$	−49.9804	−1.59901	−0.799507	+	0.600657i	$0.794906\pi$
$978$	4.51727	0.144446
$979$	5.52821	0.176682
$980$	4.28747	0.136958
$981$	−29.9019	−0.954693
$982$	−7.65511	−0.244284
$983$	55.7541	1.77828	0.889139	−	0.457636i	$-0.151304\pi$
$983$	55.7541	1.77828	0.889139	+	0.457636i	$0.151304\pi$
$984$	−3.16501	−0.100897
$985$	2.07563	0.0661350
$986$	−6.67902	−0.212703
$987$	10.6249	0.338193
$988$	−11.2270	−0.357177
$989$	0.952953	0.0303021
$990$	2.66308	0.0846382
$991$	−36.7684	−1.16799	−0.583994	−	0.811758i	$-0.698511\pi$
$991$	−36.7684	−1.16799	−0.583994	+	0.811758i	$0.698511\pi$
$992$	−3.41206	−0.108333
$993$	−16.1155	−0.511411
$994$	−21.1594	−0.671136
$995$	−4.55938	−0.144542
$996$	−1.58255	−0.0501450
$997$	−20.1652	−0.638637	−0.319319	−	0.947647i	$-0.603454\pi$
$997$	−20.1652	−0.638637	−0.319319	+	0.947647i	$0.603454\pi$
$998$	−11.4695	−0.363061
$999$	−7.21522	−0.228279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bb.1.5	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bb.1.5	✓	11	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.580450 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.580450 q^{6} +1.64698 q^{7} -1.00000 q^{8} -2.66308 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.580450 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.580450 q^{6} +1.64698 q^{7} -1.00000 q^{8} -2.66308 q^{9} +1.00000 q^{10} -1.00000 q^{11} -0.580450 q^{12} +2.95295 q^{13} -1.64698 q^{14} +0.580450 q^{15} +1.00000 q^{16} +1.81307 q^{17} +2.66308 q^{18} -3.80194 q^{19} -1.00000 q^{20} -0.955986 q^{21} +1.00000 q^{22} +0.952953 q^{23} +0.580450 q^{24} +1.00000 q^{25} -2.95295 q^{26} +3.28713 q^{27} +1.64698 q^{28} +3.68382 q^{29} -0.580450 q^{30} +3.41206 q^{31} -1.00000 q^{32} +0.580450 q^{33} -1.81307 q^{34} -1.64698 q^{35} -2.66308 q^{36} -2.19499 q^{37} +3.80194 q^{38} -1.71404 q^{39} +1.00000 q^{40} -5.45269 q^{41} +0.955986 q^{42} +1.00000 q^{43} -1.00000 q^{44} +2.66308 q^{45} -0.952953 q^{46} -11.1140 q^{47} -0.580450 q^{48} -4.28747 q^{49} -1.00000 q^{50} -1.05240 q^{51} +2.95295 q^{52} +8.91291 q^{53} -3.28713 q^{54} +1.00000 q^{55} -1.64698 q^{56} +2.20684 q^{57} -3.68382 q^{58} -3.10392 q^{59} +0.580450 q^{60} -9.87214 q^{61} -3.41206 q^{62} -4.38602 q^{63} +1.00000 q^{64} -2.95295 q^{65} -0.580450 q^{66} +6.18592 q^{67} +1.81307 q^{68} -0.553141 q^{69} +1.64698 q^{70} +12.8474 q^{71} +2.66308 q^{72} -0.229098 q^{73} +2.19499 q^{74} -0.580450 q^{75} -3.80194 q^{76} -1.64698 q^{77} +1.71404 q^{78} +15.2682 q^{79} -1.00000 q^{80} +6.08122 q^{81} +5.45269 q^{82} +2.72642 q^{83} -0.955986 q^{84} -1.81307 q^{85} -1.00000 q^{86} -2.13827 q^{87} +1.00000 q^{88} -5.52821 q^{89} -2.66308 q^{90} +4.86344 q^{91} +0.952953 q^{92} -1.98053 q^{93} +11.1140 q^{94} +3.80194 q^{95} +0.580450 q^{96} -3.05239 q^{97} +4.28747 q^{98} +2.66308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * q^99

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