LMFDB - Embedded newform 4730.2.a.w.1.3

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:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 12x^{6} + 7x^{5} + 41x^{4} - 6x^{3} - 28x^{2} + 2x + 4 $ x^8 - x^7 - 12x^6 + 7x^5 + 41x^4 - 6x^3 - 28x^2 + 2x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.843708$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.84371 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.84371 q^{6} +0.526782 q^{7} -1.00000 q^{8} +0.399257 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.84371 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.84371 q^{6} +0.526782 q^{7} -1.00000 q^{8} +0.399257 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.84371 q^{12} +5.89041 q^{13} -0.526782 q^{14} -1.84371 q^{15} +1.00000 q^{16} -7.20596 q^{17} -0.399257 q^{18} -7.63854 q^{19} +1.00000 q^{20} -0.971232 q^{21} -1.00000 q^{22} +3.89041 q^{23} +1.84371 q^{24} +1.00000 q^{25} -5.89041 q^{26} +4.79501 q^{27} +0.526782 q^{28} +8.04808 q^{29} +1.84371 q^{30} +2.80935 q^{31} -1.00000 q^{32} -1.84371 q^{33} +7.20596 q^{34} +0.526782 q^{35} +0.399257 q^{36} -5.62837 q^{37} +7.63854 q^{38} -10.8602 q^{39} -1.00000 q^{40} -1.80726 q^{41} +0.971232 q^{42} -1.00000 q^{43} +1.00000 q^{44} +0.399257 q^{45} -3.89041 q^{46} -8.47301 q^{47} -1.84371 q^{48} -6.72250 q^{49} -1.00000 q^{50} +13.2857 q^{51} +5.89041 q^{52} -6.63743 q^{53} -4.79501 q^{54} +1.00000 q^{55} -0.526782 q^{56} +14.0832 q^{57} -8.04808 q^{58} -2.91366 q^{59} -1.84371 q^{60} -0.160654 q^{61} -2.80935 q^{62} +0.210322 q^{63} +1.00000 q^{64} +5.89041 q^{65} +1.84371 q^{66} -1.49655 q^{67} -7.20596 q^{68} -7.17278 q^{69} -0.526782 q^{70} +9.81253 q^{71} -0.399257 q^{72} -0.652307 q^{73} +5.62837 q^{74} -1.84371 q^{75} -7.63854 q^{76} +0.526782 q^{77} +10.8602 q^{78} -9.25084 q^{79} +1.00000 q^{80} -10.0384 q^{81} +1.80726 q^{82} +0.697543 q^{83} -0.971232 q^{84} -7.20596 q^{85} +1.00000 q^{86} -14.8383 q^{87} -1.00000 q^{88} +10.4841 q^{89} -0.399257 q^{90} +3.10296 q^{91} +3.89041 q^{92} -5.17962 q^{93} +8.47301 q^{94} -7.63854 q^{95} +1.84371 q^{96} -11.7126 q^{97} +6.72250 q^{98} +0.399257 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9	\( 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9} - 8 q^{10} + 8 q^{11} - 7 q^{12} - 2 q^{13} + 6 q^{14} - 7 q^{15} + 8 q^{16} - 8 q^{17} - 7 q^{18} + 8 q^{20} + 14 q^{21} - 8 q^{22} - 18 q^{23} + 7 q^{24} + 8 q^{25} + 2 q^{26} - 22 q^{27} - 6 q^{28} + 8 q^{29} + 7 q^{30} - 11 q^{31} - 8 q^{32} - 7 q^{33} + 8 q^{34} - 6 q^{35} + 7 q^{36} - 17 q^{37} - 6 q^{39} - 8 q^{40} + 12 q^{41} - 14 q^{42} - 8 q^{43} + 8 q^{44} + 7 q^{45} + 18 q^{46} - 19 q^{47} - 7 q^{48} - 2 q^{49} - 8 q^{50} - q^{51} - 2 q^{52} - 7 q^{53} + 22 q^{54} + 8 q^{55} + 6 q^{56} - 3 q^{57} - 8 q^{58} + q^{59} - 7 q^{60} + 6 q^{61} + 11 q^{62} - 15 q^{63} + 8 q^{64} - 2 q^{65} + 7 q^{66} - 22 q^{67} - 8 q^{68} + 8 q^{69} + 6 q^{70} - 14 q^{71} - 7 q^{72} - 13 q^{73} + 17 q^{74} - 7 q^{75} - 6 q^{77} + 6 q^{78} - 8 q^{79} + 8 q^{80} + 28 q^{81} - 12 q^{82} - 4 q^{83} + 14 q^{84} - 8 q^{85} + 8 q^{86} - 30 q^{87} - 8 q^{88} + 5 q^{89} - 7 q^{90} - 8 q^{91} - 18 q^{92} + q^{93} + 19 q^{94} + 7 q^{96} - 23 q^{97} + 2 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9 - 8 * q^10 + 8 * q^11 - 7 * q^12 - 2 * q^13 + 6 * q^14 - 7 * q^15 + 8 * q^16 - 8 * q^17 - 7 * q^18 + 8 * q^20 + 14 * q^21 - 8 * q^22 - 18 * q^23 + 7 * q^24 + 8 * q^25 + 2 * q^26 - 22 * q^27 - 6 * q^28 + 8 * q^29 + 7 * q^30 - 11 * q^31 - 8 * q^32 - 7 * q^33 + 8 * q^34 - 6 * q^35 + 7 * q^36 - 17 * q^37 - 6 * q^39 - 8 * q^40 + 12 * q^41 - 14 * q^42 - 8 * q^43 + 8 * q^44 + 7 * q^45 + 18 * q^46 - 19 * q^47 - 7 * q^48 - 2 * q^49 - 8 * q^50 - q^51 - 2 * q^52 - 7 * q^53 + 22 * q^54 + 8 * q^55 + 6 * q^56 - 3 * q^57 - 8 * q^58 + q^59 - 7 * q^60 + 6 * q^61 + 11 * q^62 - 15 * q^63 + 8 * q^64 - 2 * q^65 + 7 * q^66 - 22 * q^67 - 8 * q^68 + 8 * q^69 + 6 * q^70 - 14 * q^71 - 7 * q^72 - 13 * q^73 + 17 * q^74 - 7 * q^75 - 6 * q^77 + 6 * q^78 - 8 * q^79 + 8 * q^80 + 28 * q^81 - 12 * q^82 - 4 * q^83 + 14 * q^84 - 8 * q^85 + 8 * q^86 - 30 * q^87 - 8 * q^88 + 5 * q^89 - 7 * q^90 - 8 * q^91 - 18 * q^92 + q^93 + 19 * q^94 + 7 * q^96 - 23 * q^97 + 2 * q^98 + 7 * 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
$3$	−1.84371	−1.06447	−0.532233	−	0.846598i	$-0.678647\pi$
$3$	−1.84371	−1.06447	−0.532233	+	0.846598i	$0.678647\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.84371	0.752690
$7$	0.526782	0.199105	0.0995525	−	0.995032i	$-0.468259\pi$
$7$	0.526782	0.199105	0.0995525	+	0.995032i	$0.468259\pi$
$8$	−1.00000	−0.353553
$9$	0.399257	0.133086
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.84371	−0.532233
$13$	5.89041	1.63371	0.816853	−	0.576845i	$-0.195716\pi$
$13$	5.89041	1.63371	0.816853	+	0.576845i	$0.195716\pi$
$14$	−0.526782	−0.140788
$15$	−1.84371	−0.476043
$16$	1.00000	0.250000
$17$	−7.20596	−1.74770	−0.873851	−	0.486194i	$-0.838385\pi$
$17$	−7.20596	−1.74770	−0.873851	+	0.486194i	$0.838385\pi$
$18$	−0.399257	−0.0941059
$19$	−7.63854	−1.75240	−0.876201	−	0.481947i	$-0.839930\pi$
$19$	−7.63854	−1.75240	−0.876201	+	0.481947i	$0.839930\pi$
$20$	1.00000	0.223607
$21$	−0.971232	−0.211940
$22$	−1.00000	−0.213201
$23$	3.89041	0.811207	0.405604	−	0.914049i	$-0.367061\pi$
$23$	3.89041	0.811207	0.405604	+	0.914049i	$0.367061\pi$
$24$	1.84371	0.376345
$25$	1.00000	0.200000
$26$	−5.89041	−1.15521
$27$	4.79501	0.922800
$28$	0.526782	0.0995525
$29$	8.04808	1.49449	0.747245	−	0.664548i	$-0.231376\pi$
$29$	8.04808	1.49449	0.747245	+	0.664548i	$0.231376\pi$
$30$	1.84371	0.336613
$31$	2.80935	0.504574	0.252287	−	0.967652i	$-0.418817\pi$
$31$	2.80935	0.504574	0.252287	+	0.967652i	$0.418817\pi$
$32$	−1.00000	−0.176777
$33$	−1.84371	−0.320948
$34$	7.20596	1.23581
$35$	0.526782	0.0890424
$36$	0.399257	0.0665429
$37$	−5.62837	−0.925299	−0.462649	−	0.886541i	$-0.653101\pi$
$37$	−5.62837	−0.925299	−0.462649	+	0.886541i	$0.653101\pi$
$38$	7.63854	1.23913
$39$	−10.8602	−1.73902
$40$	−1.00000	−0.158114
$41$	−1.80726	−0.282246	−0.141123	−	0.989992i	$-0.545071\pi$
$41$	−1.80726	−0.282246	−0.141123	+	0.989992i	$0.545071\pi$
$42$	0.971232	0.149864
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	0.399257	0.0595178
$46$	−3.89041	−0.573610
$47$	−8.47301	−1.23592	−0.617958	−	0.786211i	$-0.712040\pi$
$47$	−8.47301	−1.23592	−0.617958	+	0.786211i	$0.712040\pi$
$48$	−1.84371	−0.266116
$49$	−6.72250	−0.960357
$50$	−1.00000	−0.141421
$51$	13.2857	1.86037
$52$	5.89041	0.816853
$53$	−6.63743	−0.911721	−0.455860	−	0.890051i	$-0.650668\pi$
$53$	−6.63743	−0.911721	−0.455860	+	0.890051i	$0.650668\pi$
$54$	−4.79501	−0.652518
$55$	1.00000	0.134840
$56$	−0.526782	−0.0703942
$57$	14.0832	1.86537
$58$	−8.04808	−1.05676
$59$	−2.91366	−0.379326	−0.189663	−	0.981849i	$-0.560740\pi$
$59$	−2.91366	−0.379326	−0.189663	+	0.981849i	$0.560740\pi$
$60$	−1.84371	−0.238022
$61$	−0.160654	−0.0205697	−0.0102848	−	0.999947i	$-0.503274\pi$
$61$	−0.160654	−0.0205697	−0.0102848	+	0.999947i	$0.503274\pi$
$62$	−2.80935	−0.356788
$63$	0.210322	0.0264980
$64$	1.00000	0.125000
$65$	5.89041	0.730616
$66$	1.84371	0.226945
$67$	−1.49655	−0.182833	−0.0914164	−	0.995813i	$-0.529139\pi$
$67$	−1.49655	−0.182833	−0.0914164	+	0.995813i	$0.529139\pi$
$68$	−7.20596	−0.873851
$69$	−7.17278	−0.863502
$70$	−0.526782	−0.0629625
$71$	9.81253	1.16453	0.582267	−	0.812998i	$-0.302166\pi$
$71$	9.81253	1.16453	0.582267	+	0.812998i	$0.302166\pi$
$72$	−0.399257	−0.0470529
$73$	−0.652307	−0.0763468	−0.0381734	−	0.999271i	$-0.512154\pi$
$73$	−0.652307	−0.0763468	−0.0381734	+	0.999271i	$0.512154\pi$
$74$	5.62837	0.654285
$75$	−1.84371	−0.212893
$76$	−7.63854	−0.876201
$77$	0.526782	0.0600324
$78$	10.8602	1.22968
$79$	−9.25084	−1.04080	−0.520400	−	0.853922i	$-0.674217\pi$
$79$	−9.25084	−1.04080	−0.520400	+	0.853922i	$0.674217\pi$
$80$	1.00000	0.111803
$81$	−10.0384	−1.11537
$82$	1.80726	0.199578
$83$	0.697543	0.0765653	0.0382826	−	0.999267i	$-0.487811\pi$
$83$	0.697543	0.0765653	0.0382826	+	0.999267i	$0.487811\pi$
$84$	−0.971232	−0.105970
$85$	−7.20596	−0.781596
$86$	1.00000	0.107833
$87$	−14.8383	−1.59083
$88$	−1.00000	−0.106600
$89$	10.4841	1.11131	0.555654	−	0.831414i	$-0.312468\pi$
$89$	10.4841	1.11131	0.555654	+	0.831414i	$0.312468\pi$
$90$	−0.399257	−0.0420854
$91$	3.10296	0.325279
$92$	3.89041	0.405604
$93$	−5.17962	−0.537102
$94$	8.47301	0.873924
$95$	−7.63854	−0.783698
$96$	1.84371	0.188173
$97$	−11.7126	−1.18924	−0.594619	−	0.804008i	$-0.702697\pi$
$97$	−11.7126	−1.18924	−0.594619	+	0.804008i	$0.702697\pi$
$98$	6.72250	0.679075
$99$	0.399257	0.0401269
$100$	1.00000	0.100000
$101$	19.6520	1.95545	0.977723	−	0.209901i	$-0.0673142\pi$
$101$	19.6520	1.95545	0.977723	+	0.209901i	$0.0673142\pi$
$102$	−13.2857	−1.31548
$103$	−0.603792	−0.0594934	−0.0297467	−	0.999557i	$-0.509470\pi$
$103$	−0.603792	−0.0594934	−0.0297467	+	0.999557i	$0.509470\pi$
$104$	−5.89041	−0.577603
$105$	−0.971232	−0.0947826
$106$	6.63743	0.644684
$107$	−10.0918	−0.975612	−0.487806	−	0.872952i	$-0.662203\pi$
$107$	−10.0918	−0.975612	−0.487806	+	0.872952i	$0.662203\pi$
$108$	4.79501	0.461400
$109$	16.5979	1.58979	0.794894	−	0.606748i	$-0.207526\pi$
$109$	16.5979	1.58979	0.794894	+	0.606748i	$0.207526\pi$
$110$	−1.00000	−0.0953463
$111$	10.3771	0.984948
$112$	0.526782	0.0497762
$113$	1.71905	0.161715	0.0808573	−	0.996726i	$-0.474234\pi$
$113$	1.71905	0.161715	0.0808573	+	0.996726i	$0.474234\pi$
$114$	−14.0832	−1.31902
$115$	3.89041	0.362783
$116$	8.04808	0.747245
$117$	2.35179	0.217423
$118$	2.91366	0.268224
$119$	−3.79597	−0.347976
$120$	1.84371	0.168307
$121$	1.00000	0.0909091
$122$	0.160654	0.0145450
$123$	3.33206	0.300441
$124$	2.80935	0.252287
$125$	1.00000	0.0894427
$126$	−0.210322	−0.0187369
$127$	−10.9238	−0.969329	−0.484665	−	0.874700i	$-0.661058\pi$
$127$	−10.9238	−0.969329	−0.484665	+	0.874700i	$0.661058\pi$
$128$	−1.00000	−0.0883883
$129$	1.84371	0.162329
$130$	−5.89041	−0.516623
$131$	−4.31446	−0.376956	−0.188478	−	0.982077i	$-0.560355\pi$
$131$	−4.31446	−0.376956	−0.188478	+	0.982077i	$0.560355\pi$
$132$	−1.84371	−0.160474
$133$	−4.02385	−0.348912
$134$	1.49655	0.129282
$135$	4.79501	0.412689
$136$	7.20596	0.617906
$137$	−2.68562	−0.229448	−0.114724	−	0.993397i	$-0.536598\pi$
$137$	−2.68562	−0.229448	−0.114724	+	0.993397i	$0.536598\pi$
$138$	7.17278	0.610588
$139$	8.08386	0.685664	0.342832	−	0.939397i	$-0.388614\pi$
$139$	8.08386	0.685664	0.342832	+	0.939397i	$0.388614\pi$
$140$	0.526782	0.0445212
$141$	15.6218	1.31559
$142$	−9.81253	−0.823449
$143$	5.89041	0.492581
$144$	0.399257	0.0332715
$145$	8.04808	0.668357
$146$	0.652307	0.0539854
$147$	12.3943	1.02227
$148$	−5.62837	−0.462649
$149$	20.8051	1.70442	0.852210	−	0.523200i	$-0.175262\pi$
$149$	20.8051	1.70442	0.852210	+	0.523200i	$0.175262\pi$
$150$	1.84371	0.150538
$151$	−13.5775	−1.10492	−0.552462	−	0.833538i	$-0.686312\pi$
$151$	−13.5775	−1.10492	−0.552462	+	0.833538i	$0.686312\pi$
$152$	7.63854	0.619567
$153$	−2.87703	−0.232594
$154$	−0.526782	−0.0424493
$155$	2.80935	0.225652
$156$	−10.8602	−0.869512
$157$	−13.5103	−1.07824	−0.539120	−	0.842229i	$-0.681243\pi$
$157$	−13.5103	−1.07824	−0.539120	+	0.842229i	$0.681243\pi$
$158$	9.25084	0.735957
$159$	12.2375	0.970495
$160$	−1.00000	−0.0790569
$161$	2.04940	0.161515
$162$	10.0384	0.788689
$163$	−7.39647	−0.579336	−0.289668	−	0.957127i	$-0.593545\pi$
$163$	−7.39647	−0.579336	−0.289668	+	0.957127i	$0.593545\pi$
$164$	−1.80726	−0.141123
$165$	−1.84371	−0.143532
$166$	−0.697543	−0.0541398
$167$	11.9003	0.920876	0.460438	−	0.887692i	$-0.347692\pi$
$167$	11.9003	0.920876	0.460438	+	0.887692i	$0.347692\pi$
$168$	0.971232	0.0749322
$169$	21.6970	1.66900
$170$	7.20596	0.552672
$171$	−3.04974	−0.233220
$172$	−1.00000	−0.0762493
$173$	5.09205	0.387142	0.193571	−	0.981086i	$-0.437993\pi$
$173$	5.09205	0.387142	0.193571	+	0.981086i	$0.437993\pi$
$174$	14.8383	1.12489
$175$	0.526782	0.0398210
$176$	1.00000	0.0753778
$177$	5.37193	0.403779
$178$	−10.4841	−0.785813
$179$	−24.0445	−1.79717	−0.898585	−	0.438799i	$-0.855404\pi$
$179$	−24.0445	−1.79717	−0.898585	+	0.438799i	$0.855404\pi$
$180$	0.399257	0.0297589
$181$	−1.85958	−0.138222	−0.0691108	−	0.997609i	$-0.522016\pi$
$181$	−1.85958	−0.138222	−0.0691108	+	0.997609i	$0.522016\pi$
$182$	−3.10296	−0.230007
$183$	0.296200	0.0218957
$184$	−3.89041	−0.286805
$185$	−5.62837	−0.413806
$186$	5.17962	0.379788
$187$	−7.20596	−0.526952
$188$	−8.47301	−0.617958
$189$	2.52593	0.183734
$190$	7.63854	0.554158
$191$	−15.8411	−1.14622	−0.573111	−	0.819478i	$-0.694263\pi$
$191$	−15.8411	−1.14622	−0.573111	+	0.819478i	$0.694263\pi$
$192$	−1.84371	−0.133058
$193$	−2.34648	−0.168904	−0.0844518	−	0.996428i	$-0.526914\pi$
$193$	−2.34648	−0.168904	−0.0844518	+	0.996428i	$0.526914\pi$
$194$	11.7126	0.840918
$195$	−10.8602	−0.777715
$196$	−6.72250	−0.480179
$197$	21.5343	1.53426	0.767128	−	0.641495i	$-0.221685\pi$
$197$	21.5343	1.53426	0.767128	+	0.641495i	$0.221685\pi$
$198$	−0.399257	−0.0283740
$199$	8.62734	0.611576	0.305788	−	0.952100i	$-0.401080\pi$
$199$	8.62734	0.611576	0.305788	+	0.952100i	$0.401080\pi$
$200$	−1.00000	−0.0707107
$201$	2.75920	0.194619
$202$	−19.6520	−1.38271
$203$	4.23958	0.297561
$204$	13.2857	0.930184
$205$	−1.80726	−0.126224
$206$	0.603792	0.0420682
$207$	1.55328	0.107960
$208$	5.89041	0.408427
$209$	−7.63854	−0.528369
$210$	0.971232	0.0670214
$211$	−10.9150	−0.751423	−0.375711	−	0.926737i	$-0.622602\pi$
$211$	−10.9150	−0.751423	−0.375711	+	0.926737i	$0.622602\pi$
$212$	−6.63743	−0.455860
$213$	−18.0914	−1.23961
$214$	10.0918	0.689862
$215$	−1.00000	−0.0681994
$216$	−4.79501	−0.326259
$217$	1.47992	0.100463
$218$	−16.5979	−1.12415
$219$	1.20266	0.0812685
$220$	1.00000	0.0674200
$221$	−42.4461	−2.85523
$222$	−10.3771	−0.696464
$223$	−18.3010	−1.22553	−0.612763	−	0.790267i	$-0.709942\pi$
$223$	−18.3010	−1.22553	−0.612763	+	0.790267i	$0.709942\pi$
$224$	−0.526782	−0.0351971
$225$	0.399257	0.0266172
$226$	−1.71905	−0.114349
$227$	−13.0373	−0.865316	−0.432658	−	0.901558i	$-0.642424\pi$
$227$	−13.0373	−0.865316	−0.432658	+	0.901558i	$0.642424\pi$
$228$	14.0832	0.932685
$229$	26.1503	1.72806	0.864031	−	0.503439i	$-0.167932\pi$
$229$	26.1503	1.72806	0.864031	+	0.503439i	$0.167932\pi$
$230$	−3.89041	−0.256526
$231$	−0.971232	−0.0639024
$232$	−8.04808	−0.528382
$233$	−27.7381	−1.81719	−0.908593	−	0.417683i	$-0.862842\pi$
$233$	−27.7381	−1.81719	−0.908593	+	0.417683i	$0.862842\pi$
$234$	−2.35179	−0.153741
$235$	−8.47301	−0.552718
$236$	−2.91366	−0.189663
$237$	17.0558	1.10790
$238$	3.79597	0.246056
$239$	−11.8971	−0.769562	−0.384781	−	0.923008i	$-0.625723\pi$
$239$	−11.8971	−0.769562	−0.384781	+	0.923008i	$0.625723\pi$
$240$	−1.84371	−0.119011
$241$	−24.6656	−1.58885	−0.794425	−	0.607362i	$-0.792228\pi$
$241$	−24.6656	−1.58885	−0.794425	+	0.607362i	$0.792228\pi$
$242$	−1.00000	−0.0642824
$243$	4.12278	0.264477
$244$	−0.160654	−0.0102848
$245$	−6.72250	−0.429485
$246$	−3.33206	−0.212444
$247$	−44.9942	−2.86291
$248$	−2.80935	−0.178394
$249$	−1.28606	−0.0815011
$250$	−1.00000	−0.0632456
$251$	17.8753	1.12828	0.564141	−	0.825679i	$-0.309207\pi$
$251$	17.8753	1.12828	0.564141	+	0.825679i	$0.309207\pi$
$252$	0.210322	0.0132490
$253$	3.89041	0.244588
$254$	10.9238	0.685419
$255$	13.2857	0.831981
$256$	1.00000	0.0625000
$257$	17.4938	1.09123	0.545617	−	0.838035i	$-0.316295\pi$
$257$	17.4938	1.09123	0.545617	+	0.838035i	$0.316295\pi$
$258$	−1.84371	−0.114784
$259$	−2.96493	−0.184232
$260$	5.89041	0.365308
$261$	3.21326	0.198896
$262$	4.31446	0.266548
$263$	12.1394	0.748546	0.374273	−	0.927319i	$-0.377892\pi$
$263$	12.1394	0.748546	0.374273	+	0.927319i	$0.377892\pi$
$264$	1.84371	0.113472
$265$	−6.63743	−0.407734
$266$	4.02385	0.246718
$267$	−19.3295	−1.18295
$268$	−1.49655	−0.0914164
$269$	−23.0397	−1.40476	−0.702379	−	0.711803i	$-0.747879\pi$
$269$	−23.0397	−1.40476	−0.702379	+	0.711803i	$0.747879\pi$
$270$	−4.79501	−0.291815
$271$	−3.48956	−0.211976	−0.105988	−	0.994367i	$-0.533800\pi$
$271$	−3.48956	−0.211976	−0.105988	+	0.994367i	$0.533800\pi$
$272$	−7.20596	−0.436925
$273$	−5.72096	−0.346248
$274$	2.68562	0.162244
$275$	1.00000	0.0603023
$276$	−7.17278	−0.431751
$277$	−20.5513	−1.23481	−0.617404	−	0.786646i	$-0.711816\pi$
$277$	−20.5513	−1.23481	−0.617404	+	0.786646i	$0.711816\pi$
$278$	−8.08386	−0.484838
$279$	1.12165	0.0671517
$280$	−0.526782	−0.0314813
$281$	1.52433	0.0909339	0.0454670	−	0.998966i	$-0.485522\pi$
$281$	1.52433	0.0909339	0.0454670	+	0.998966i	$0.485522\pi$
$282$	−15.6218	−0.930262
$283$	−14.4127	−0.856745	−0.428372	−	0.903602i	$-0.640913\pi$
$283$	−14.4127	−0.856745	−0.428372	+	0.903602i	$0.640913\pi$
$284$	9.81253	0.582267
$285$	14.0832	0.834219
$286$	−5.89041	−0.348307
$287$	−0.952031	−0.0561966
$288$	−0.399257	−0.0235265
$289$	34.9258	2.05446
$290$	−8.04808	−0.472600
$291$	21.5947	1.26590
$292$	−0.652307	−0.0381734
$293$	15.6013	0.911440	0.455720	−	0.890123i	$-0.349382\pi$
$293$	15.6013	0.911440	0.455720	+	0.890123i	$0.349382\pi$
$294$	−12.3943	−0.722852
$295$	−2.91366	−0.169640
$296$	5.62837	0.327143
$297$	4.79501	0.278235
$298$	−20.8051	−1.20521
$299$	22.9161	1.32527
$300$	−1.84371	−0.106447
$301$	−0.526782	−0.0303632
$302$	13.5775	0.781299
$303$	−36.2325	−2.08150
$304$	−7.63854	−0.438100
$305$	−0.160654	−0.00919904
$306$	2.87703	0.164469
$307$	8.90251	0.508093	0.254047	−	0.967192i	$-0.418238\pi$
$307$	8.90251	0.508093	0.254047	+	0.967192i	$0.418238\pi$
$308$	0.526782	0.0300162
$309$	1.11322	0.0633287
$310$	−2.80935	−0.159560
$311$	−2.14844	−0.121827	−0.0609135	−	0.998143i	$-0.519401\pi$
$311$	−2.14844	−0.121827	−0.0609135	+	0.998143i	$0.519401\pi$
$312$	10.8602	0.614838
$313$	4.21362	0.238168	0.119084	−	0.992884i	$-0.462004\pi$
$313$	4.21362	0.238168	0.119084	+	0.992884i	$0.462004\pi$
$314$	13.5103	0.762431
$315$	0.210322	0.0118503
$316$	−9.25084	−0.520400
$317$	−4.99993	−0.280824	−0.140412	−	0.990093i	$-0.544843\pi$
$317$	−4.99993	−0.280824	−0.140412	+	0.990093i	$0.544843\pi$
$318$	−12.2375	−0.686244
$319$	8.04808	0.450606
$320$	1.00000	0.0559017
$321$	18.6063	1.03850
$322$	−2.04940	−0.114209
$323$	55.0430	3.06267
$324$	−10.0384	−0.557687
$325$	5.89041	0.326741
$326$	7.39647	0.409652
$327$	−30.6016	−1.69227
$328$	1.80726	0.0997891
$329$	−4.46343	−0.246077
$330$	1.84371	0.101493
$331$	−25.0935	−1.37926	−0.689632	−	0.724160i	$-0.742228\pi$
$331$	−25.0935	−1.37926	−0.689632	+	0.724160i	$0.742228\pi$
$332$	0.697543	0.0382826
$333$	−2.24717	−0.123144
$334$	−11.9003	−0.651158
$335$	−1.49655	−0.0817653
$336$	−0.971232	−0.0529851
$337$	−20.7616	−1.13095	−0.565477	−	0.824764i	$-0.691308\pi$
$337$	−20.7616	−1.13095	−0.565477	+	0.824764i	$0.691308\pi$
$338$	−21.6970	−1.18016
$339$	−3.16942	−0.172139
$340$	−7.20596	−0.390798
$341$	2.80935	0.152135
$342$	3.04974	0.164911
$343$	−7.22877	−0.390317
$344$	1.00000	0.0539164
$345$	−7.17278	−0.386170
$346$	−5.09205	−0.273751
$347$	−34.1269	−1.83203	−0.916015	−	0.401145i	$-0.868612\pi$
$347$	−34.1269	−1.83203	−0.916015	+	0.401145i	$0.868612\pi$
$348$	−14.8383	−0.795417
$349$	17.4117	0.932025	0.466013	−	0.884778i	$-0.345690\pi$
$349$	17.4117	0.932025	0.466013	+	0.884778i	$0.345690\pi$
$350$	−0.526782	−0.0281577
$351$	28.2446	1.50758
$352$	−1.00000	−0.0533002
$353$	−13.6768	−0.727943	−0.363972	−	0.931410i	$-0.618579\pi$
$353$	−13.6768	−0.727943	−0.363972	+	0.931410i	$0.618579\pi$
$354$	−5.37193	−0.285515
$355$	9.81253	0.520795
$356$	10.4841	0.555654
$357$	6.99866	0.370408
$358$	24.0445	1.27079
$359$	−9.14780	−0.482803	−0.241401	−	0.970425i	$-0.577607\pi$
$359$	−9.14780	−0.482803	−0.241401	+	0.970425i	$0.577607\pi$
$360$	−0.399257	−0.0210427
$361$	39.3473	2.07091
$362$	1.85958	0.0977374
$363$	−1.84371	−0.0967695
$364$	3.10296	0.162640
$365$	−0.652307	−0.0341433
$366$	−0.296200	−0.0154826
$367$	28.3962	1.48227	0.741135	−	0.671356i	$-0.234288\pi$
$367$	28.3962	1.48227	0.741135	+	0.671356i	$0.234288\pi$
$368$	3.89041	0.202802
$369$	−0.721561	−0.0375630
$370$	5.62837	0.292605
$371$	−3.49648	−0.181528
$372$	−5.17962	−0.268551
$373$	−26.1185	−1.35237	−0.676183	−	0.736734i	$-0.736367\pi$
$373$	−26.1185	−1.35237	−0.676183	+	0.736734i	$0.736367\pi$
$374$	7.20596	0.372611
$375$	−1.84371	−0.0952086
$376$	8.47301	0.436962
$377$	47.4065	2.44156
$378$	−2.52593	−0.129920
$379$	23.3670	1.20028	0.600140	−	0.799895i	$-0.295111\pi$
$379$	23.3670	1.20028	0.600140	+	0.799895i	$0.295111\pi$
$380$	−7.63854	−0.391849
$381$	20.1403	1.03182
$382$	15.8411	0.810501
$383$	−29.8275	−1.52412	−0.762058	−	0.647509i	$-0.775811\pi$
$383$	−29.8275	−1.52412	−0.762058	+	0.647509i	$0.775811\pi$
$384$	1.84371	0.0940863
$385$	0.526782	0.0268473
$386$	2.34648	0.119433
$387$	−0.399257	−0.0202954
$388$	−11.7126	−0.594619
$389$	−23.9197	−1.21278	−0.606390	−	0.795168i	$-0.707383\pi$
$389$	−23.9197	−1.21278	−0.606390	+	0.795168i	$0.707383\pi$
$390$	10.8602	0.549928
$391$	−28.0342	−1.41775
$392$	6.72250	0.339538
$393$	7.95460	0.401256
$394$	−21.5343	−1.08488
$395$	−9.25084	−0.465460
$396$	0.399257	0.0200634
$397$	−34.4620	−1.72960	−0.864799	−	0.502118i	$-0.832554\pi$
$397$	−34.4620	−1.72960	−0.864799	+	0.502118i	$0.832554\pi$
$398$	−8.62734	−0.432449
$399$	7.41880	0.371404
$400$	1.00000	0.0500000
$401$	7.52593	0.375827	0.187914	−	0.982186i	$-0.439828\pi$
$401$	7.52593	0.375827	0.187914	+	0.982186i	$0.439828\pi$
$402$	−2.75920	−0.137616
$403$	16.5482	0.824326
$404$	19.6520	0.977723
$405$	−10.0384	−0.498810
$406$	−4.23958	−0.210407
$407$	−5.62837	−0.278988
$408$	−13.2857	−0.657739
$409$	9.24746	0.457257	0.228629	−	0.973514i	$-0.426576\pi$
$409$	9.24746	0.457257	0.228629	+	0.973514i	$0.426576\pi$
$410$	1.80726	0.0892541
$411$	4.95149	0.244239
$412$	−0.603792	−0.0297467
$413$	−1.53486	−0.0755257
$414$	−1.55328	−0.0763394
$415$	0.697543	0.0342410
$416$	−5.89041	−0.288801
$417$	−14.9043	−0.729866
$418$	7.63854	0.373613
$419$	−6.74591	−0.329559	−0.164780	−	0.986330i	$-0.552691\pi$
$419$	−6.74591	−0.329559	−0.164780	+	0.986330i	$0.552691\pi$
$420$	−0.971232	−0.0473913
$421$	−37.6196	−1.83347	−0.916735	−	0.399497i	$-0.869185\pi$
$421$	−37.6196	−1.83347	−0.916735	+	0.399497i	$0.869185\pi$
$422$	10.9150	0.531336
$423$	−3.38291	−0.164483
$424$	6.63743	0.322342
$425$	−7.20596	−0.349540
$426$	18.0914	0.876533
$427$	−0.0846298	−0.00409552
$428$	−10.0918	−0.487806
$429$	−10.8602	−0.524335
$430$	1.00000	0.0482243
$431$	−21.3741	−1.02955	−0.514776	−	0.857325i	$-0.672125\pi$
$431$	−21.3741	−1.02955	−0.514776	+	0.857325i	$0.672125\pi$
$432$	4.79501	0.230700
$433$	−29.9923	−1.44134	−0.720668	−	0.693280i	$-0.756165\pi$
$433$	−29.9923	−1.44134	−0.720668	+	0.693280i	$0.756165\pi$
$434$	−1.47992	−0.0710382
$435$	−14.8383	−0.711442
$436$	16.5979	0.794894
$437$	−29.7171	−1.42156
$438$	−1.20266	−0.0574655
$439$	−26.1904	−1.25000	−0.624999	−	0.780625i	$-0.714901\pi$
$439$	−26.1904	−1.25000	−0.624999	+	0.780625i	$0.714901\pi$
$440$	−1.00000	−0.0476731
$441$	−2.68401	−0.127810
$442$	42.4461	2.01895
$443$	−12.9088	−0.613317	−0.306658	−	0.951820i	$-0.599211\pi$
$443$	−12.9088	−0.613317	−0.306658	+	0.951820i	$0.599211\pi$
$444$	10.3771	0.492474
$445$	10.4841	0.496992
$446$	18.3010	0.866577
$447$	−38.3585	−1.81430
$448$	0.526782	0.0248881
$449$	−14.6849	−0.693021	−0.346511	−	0.938046i	$-0.612634\pi$
$449$	−14.6849	−0.693021	−0.346511	+	0.938046i	$0.612634\pi$
$450$	−0.399257	−0.0188212
$451$	−1.80726	−0.0851005
$452$	1.71905	0.0808573
$453$	25.0330	1.17615
$454$	13.0373	0.611871
$455$	3.10296	0.145469
$456$	−14.0832	−0.659508
$457$	8.15480	0.381465	0.190733	−	0.981642i	$-0.438914\pi$
$457$	8.15480	0.381465	0.190733	+	0.981642i	$0.438914\pi$
$458$	−26.1503	−1.22192
$459$	−34.5526	−1.61278
$460$	3.89041	0.181391
$461$	−7.35296	−0.342462	−0.171231	−	0.985231i	$-0.554774\pi$
$461$	−7.35296	−0.342462	−0.171231	+	0.985231i	$0.554774\pi$
$462$	0.971232	0.0451858
$463$	−25.7336	−1.19594	−0.597971	−	0.801518i	$-0.704026\pi$
$463$	−25.7336	−1.19594	−0.597971	+	0.801518i	$0.704026\pi$
$464$	8.04808	0.373623
$465$	−5.17962	−0.240199
$466$	27.7381	1.28494
$467$	35.0874	1.62365	0.811826	−	0.583899i	$-0.198474\pi$
$467$	35.0874	1.62365	0.811826	+	0.583899i	$0.198474\pi$
$468$	2.35179	0.108712
$469$	−0.788356	−0.0364029
$470$	8.47301	0.390831
$471$	24.9091	1.14775
$472$	2.91366	0.134112
$473$	−1.00000	−0.0459800
$474$	−17.0558	−0.783401
$475$	−7.63854	−0.350480
$476$	−3.79597	−0.173988
$477$	−2.65004	−0.121337
$478$	11.8971	0.544162
$479$	−15.2906	−0.698647	−0.349323	−	0.937002i	$-0.613589\pi$
$479$	−15.2906	−0.698647	−0.349323	+	0.937002i	$0.613589\pi$
$480$	1.84371	0.0841534
$481$	−33.1534	−1.51167
$482$	24.6656	1.12349
$483$	−3.77849	−0.171927
$484$	1.00000	0.0454545
$485$	−11.7126	−0.531843
$486$	−4.12278	−0.187013
$487$	−23.6677	−1.07248	−0.536242	−	0.844064i	$-0.680157\pi$
$487$	−23.6677	−1.07248	−0.536242	+	0.844064i	$0.680157\pi$
$488$	0.160654	0.00727248
$489$	13.6369	0.616683
$490$	6.72250	0.303692
$491$	−36.7951	−1.66054	−0.830269	−	0.557362i	$-0.811813\pi$
$491$	−36.7951	−1.66054	−0.830269	+	0.557362i	$0.811813\pi$
$492$	3.33206	0.150221
$493$	−57.9941	−2.61192
$494$	44.9942	2.02438
$495$	0.399257	0.0179453
$496$	2.80935	0.126144
$497$	5.16907	0.231864
$498$	1.28606	0.0576299
$499$	−31.2771	−1.40016	−0.700078	−	0.714066i	$-0.746851\pi$
$499$	−31.2771	−1.40016	−0.700078	+	0.714066i	$0.746851\pi$
$500$	1.00000	0.0447214
$501$	−21.9407	−0.980240
$502$	−17.8753	−0.797816
$503$	15.9981	0.713318	0.356659	−	0.934235i	$-0.383916\pi$
$503$	15.9981	0.713318	0.356659	+	0.934235i	$0.383916\pi$
$504$	−0.210322	−0.00936847
$505$	19.6520	0.874502
$506$	−3.89041	−0.172950
$507$	−40.0029	−1.77659
$508$	−10.9238	−0.484665
$509$	7.65897	0.339478	0.169739	−	0.985489i	$-0.445708\pi$
$509$	7.65897	0.339478	0.169739	+	0.985489i	$0.445708\pi$
$510$	−13.2857	−0.588300
$511$	−0.343624	−0.0152010
$512$	−1.00000	−0.0441942
$513$	−36.6269	−1.61712
$514$	−17.4938	−0.771619
$515$	−0.603792	−0.0266063
$516$	1.84371	0.0811647
$517$	−8.47301	−0.372643
$518$	2.96493	0.130271
$519$	−9.38826	−0.412099
$520$	−5.89041	−0.258312
$521$	36.9212	1.61755	0.808773	−	0.588121i	$-0.200132\pi$
$521$	36.9212	1.61755	0.808773	+	0.588121i	$0.200132\pi$
$522$	−3.21326	−0.140640
$523$	41.9065	1.83244	0.916221	−	0.400672i	$-0.131223\pi$
$523$	41.9065	1.83244	0.916221	+	0.400672i	$0.131223\pi$
$524$	−4.31446	−0.188478
$525$	−0.971232	−0.0423881
$526$	−12.1394	−0.529302
$527$	−20.2441	−0.881845
$528$	−1.84371	−0.0802371
$529$	−7.86468	−0.341943
$530$	6.63743	0.288311
$531$	−1.16330	−0.0504829
$532$	−4.02385	−0.174456
$533$	−10.6455	−0.461108
$534$	19.3295	0.836470
$535$	−10.0918	−0.436307
$536$	1.49655	0.0646412
$537$	44.3310	1.91303
$538$	23.0397	0.993314
$539$	−6.72250	−0.289559
$540$	4.79501	0.206344
$541$	−36.0689	−1.55072	−0.775362	−	0.631517i	$-0.782432\pi$
$541$	−36.0689	−1.55072	−0.775362	+	0.631517i	$0.782432\pi$
$542$	3.48956	0.149889
$543$	3.42852	0.147132
$544$	7.20596	0.308953
$545$	16.5979	0.710975
$546$	5.72096	0.244834
$547$	−12.2130	−0.522191	−0.261096	−	0.965313i	$-0.584084\pi$
$547$	−12.2130	−0.522191	−0.261096	+	0.965313i	$0.584084\pi$
$548$	−2.68562	−0.114724
$549$	−0.0641424	−0.00273753
$550$	−1.00000	−0.0426401
$551$	−61.4756	−2.61895
$552$	7.17278	0.305294
$553$	−4.87318	−0.207229
$554$	20.5513	0.873142
$555$	10.3771	0.440482
$556$	8.08386	0.342832
$557$	21.2962	0.902351	0.451175	−	0.892435i	$-0.351005\pi$
$557$	21.2962	0.902351	0.451175	+	0.892435i	$0.351005\pi$
$558$	−1.12165	−0.0474834
$559$	−5.89041	−0.249138
$560$	0.526782	0.0222606
$561$	13.2857	0.560922
$562$	−1.52433	−0.0643000
$563$	31.7347	1.33746	0.668729	−	0.743506i	$-0.266839\pi$
$563$	31.7347	1.33746	0.668729	+	0.743506i	$0.266839\pi$
$564$	15.6218	0.657794
$565$	1.71905	0.0723209
$566$	14.4127	0.605810
$567$	−5.28803	−0.222076
$568$	−9.81253	−0.411725
$569$	19.2618	0.807496	0.403748	−	0.914870i	$-0.367707\pi$
$569$	19.2618	0.807496	0.403748	+	0.914870i	$0.367707\pi$
$570$	−14.0832	−0.589882
$571$	16.8798	0.706397	0.353199	−	0.935548i	$-0.385094\pi$
$571$	16.8798	0.706397	0.353199	+	0.935548i	$0.385094\pi$
$572$	5.89041	0.246291
$573$	29.2063	1.22011
$574$	0.952031	0.0397370
$575$	3.89041	0.162241
$576$	0.399257	0.0166357
$577$	−44.7277	−1.86204	−0.931018	−	0.364973i	$-0.881078\pi$
$577$	−44.7277	−1.86204	−0.931018	+	0.364973i	$0.881078\pi$
$578$	−34.9258	−1.45272
$579$	4.32623	0.179792
$580$	8.04808	0.334178
$581$	0.367453	0.0152445
$582$	−21.5947	−0.895128
$583$	−6.63743	−0.274894
$584$	0.652307	0.0269927
$585$	2.35179	0.0972346
$586$	−15.6013	−0.644485
$587$	−16.5631	−0.683634	−0.341817	−	0.939767i	$-0.611042\pi$
$587$	−16.5631	−0.683634	−0.341817	+	0.939767i	$0.611042\pi$
$588$	12.3943	0.511133
$589$	−21.4593	−0.884217
$590$	2.91366	0.119953
$591$	−39.7029	−1.63316
$592$	−5.62837	−0.231325
$593$	−13.8365	−0.568199	−0.284099	−	0.958795i	$-0.591695\pi$
$593$	−13.8365	−0.568199	−0.284099	+	0.958795i	$0.591695\pi$
$594$	−4.79501	−0.196742
$595$	−3.79597	−0.155620
$596$	20.8051	0.852210
$597$	−15.9063	−0.651001
$598$	−22.9161	−0.937111
$599$	17.2368	0.704278	0.352139	−	0.935948i	$-0.385454\pi$
$599$	17.2368	0.704278	0.352139	+	0.935948i	$0.385454\pi$
$600$	1.84371	0.0752690
$601$	4.81572	0.196437	0.0982186	−	0.995165i	$-0.468686\pi$
$601$	4.81572	0.196437	0.0982186	+	0.995165i	$0.468686\pi$
$602$	0.526782	0.0214700
$603$	−0.597509	−0.0243325
$604$	−13.5775	−0.552462
$605$	1.00000	0.0406558
$606$	36.2325	1.47184
$607$	−20.5621	−0.834591	−0.417295	−	0.908771i	$-0.637022\pi$
$607$	−20.5621	−0.834591	−0.417295	+	0.908771i	$0.637022\pi$
$608$	7.63854	0.309784
$609$	−7.81655	−0.316743
$610$	0.160654	0.00650470
$611$	−49.9095	−2.01912
$612$	−2.87703	−0.116297
$613$	34.0893	1.37685	0.688427	−	0.725306i	$-0.258302\pi$
$613$	34.0893	1.37685	0.688427	+	0.725306i	$0.258302\pi$
$614$	−8.90251	−0.359276
$615$	3.33206	0.134361
$616$	−0.526782	−0.0212247
$617$	10.0658	0.405233	0.202617	−	0.979258i	$-0.435055\pi$
$617$	10.0658	0.405233	0.202617	+	0.979258i	$0.435055\pi$
$618$	−1.11322	−0.0447801
$619$	30.0395	1.20739	0.603694	−	0.797216i	$-0.293695\pi$
$619$	30.0395	1.20739	0.603694	+	0.797216i	$0.293695\pi$
$620$	2.80935	0.112826
$621$	18.6546	0.748582
$622$	2.14844	0.0861447
$623$	5.52281	0.221267
$624$	−10.8602	−0.434756
$625$	1.00000	0.0400000
$626$	−4.21362	−0.168410
$627$	14.0832	0.562430
$628$	−13.5103	−0.539120
$629$	40.5578	1.61715
$630$	−0.210322	−0.00837942
$631$	−2.41275	−0.0960502	−0.0480251	−	0.998846i	$-0.515293\pi$
$631$	−2.41275	−0.0960502	−0.0480251	+	0.998846i	$0.515293\pi$
$632$	9.25084	0.367979
$633$	20.1242	0.799863
$634$	4.99993	0.198573
$635$	−10.9238	−0.433497
$636$	12.2375	0.485248
$637$	−39.5983	−1.56894
$638$	−8.04808	−0.318627
$639$	3.91773	0.154983
$640$	−1.00000	−0.0395285
$641$	32.7454	1.29337	0.646683	−	0.762759i	$-0.276156\pi$
$641$	32.7454	1.29337	0.646683	+	0.762759i	$0.276156\pi$
$642$	−18.6063	−0.734334
$643$	35.2464	1.38998	0.694991	−	0.719018i	$-0.255408\pi$
$643$	35.2464	1.38998	0.694991	+	0.719018i	$0.255408\pi$
$644$	2.04940	0.0807577
$645$	1.84371	0.0725959
$646$	−55.0430	−2.16564
$647$	−34.0720	−1.33951	−0.669754	−	0.742583i	$-0.733600\pi$
$647$	−34.0720	−1.33951	−0.669754	+	0.742583i	$0.733600\pi$
$648$	10.0384	0.394344
$649$	−2.91366	−0.114371
$650$	−5.89041	−0.231041
$651$	−2.72853	−0.106940
$652$	−7.39647	−0.289668
$653$	−18.7291	−0.732928	−0.366464	−	0.930432i	$-0.619432\pi$
$653$	−18.7291	−0.732928	−0.366464	+	0.930432i	$0.619432\pi$
$654$	30.6016	1.19662
$655$	−4.31446	−0.168580
$656$	−1.80726	−0.0705616
$657$	−0.260439	−0.0101607
$658$	4.46343	0.174003
$659$	−26.9154	−1.04848	−0.524238	−	0.851572i	$-0.675650\pi$
$659$	−26.9154	−1.04848	−0.524238	+	0.851572i	$0.675650\pi$
$660$	−1.84371	−0.0717662
$661$	−27.3557	−1.06401	−0.532007	−	0.846740i	$-0.678562\pi$
$661$	−27.3557	−1.06401	−0.532007	+	0.846740i	$0.678562\pi$
$662$	25.0935	0.975287
$663$	78.2581	3.03929
$664$	−0.697543	−0.0270699
$665$	−4.02385	−0.156038
$666$	2.24717	0.0870761
$667$	31.3104	1.21234
$668$	11.9003	0.460438
$669$	33.7417	1.30453
$670$	1.49655	0.0578168
$671$	−0.160654	−0.00620199
$672$	0.971232	0.0374661
$673$	5.68801	0.219257	0.109628	−	0.993973i	$-0.465034\pi$
$673$	5.68801	0.219257	0.109628	+	0.993973i	$0.465034\pi$
$674$	20.7616	0.799706
$675$	4.79501	0.184560
$676$	21.6970	0.834499
$677$	−46.1017	−1.77183	−0.885915	−	0.463847i	$-0.846469\pi$
$677$	−46.1017	−1.77183	−0.885915	+	0.463847i	$0.846469\pi$
$678$	3.16942	0.121721
$679$	−6.17001	−0.236783
$680$	7.20596	0.276336
$681$	24.0370	0.921099
$682$	−2.80935	−0.107576
$683$	−6.90132	−0.264072	−0.132036	−	0.991245i	$-0.542151\pi$
$683$	−6.90132	−0.264072	−0.132036	+	0.991245i	$0.542151\pi$
$684$	−3.04974	−0.116610
$685$	−2.68562	−0.102612
$686$	7.22877	0.275996
$687$	−48.2135	−1.83946
$688$	−1.00000	−0.0381246
$689$	−39.0972	−1.48948
$690$	7.17278	0.273063
$691$	−22.7919	−0.867045	−0.433522	−	0.901143i	$-0.642729\pi$
$691$	−22.7919	−0.867045	−0.433522	+	0.901143i	$0.642729\pi$
$692$	5.09205	0.193571
$693$	0.210322	0.00798946
$694$	34.1269	1.29544
$695$	8.08386	0.306638
$696$	14.8383	0.562445
$697$	13.0230	0.493282
$698$	−17.4117	−0.659041
$699$	51.1410	1.93433
$700$	0.526782	0.0199105
$701$	21.5915	0.815498	0.407749	−	0.913094i	$-0.366314\pi$
$701$	21.5915	0.815498	0.407749	+	0.913094i	$0.366314\pi$
$702$	−28.2446	−1.06602
$703$	42.9925	1.62149
$704$	1.00000	0.0376889
$705$	15.6218	0.588349
$706$	13.6768	0.514734
$707$	10.3523	0.389339
$708$	5.37193	0.201890
$709$	−3.13688	−0.117808	−0.0589040	−	0.998264i	$-0.518761\pi$
$709$	−3.13688	−0.117808	−0.0589040	+	0.998264i	$0.518761\pi$
$710$	−9.81253	−0.368258
$711$	−3.69347	−0.138516
$712$	−10.4841	−0.392906
$713$	10.9295	0.409314
$714$	−6.99866	−0.261918
$715$	5.89041	0.220289
$716$	−24.0445	−0.898585
$717$	21.9348	0.819171
$718$	9.14780	0.341393
$719$	−11.6082	−0.432913	−0.216456	−	0.976292i	$-0.569450\pi$
$719$	−11.6082	−0.432913	−0.216456	+	0.976292i	$0.569450\pi$
$720$	0.399257	0.0148794
$721$	−0.318067	−0.0118454
$722$	−39.3473	−1.46435
$723$	45.4762	1.69128
$724$	−1.85958	−0.0691108
$725$	8.04808	0.298898
$726$	1.84371	0.0684264
$727$	−15.5092	−0.575203	−0.287601	−	0.957750i	$-0.592858\pi$
$727$	−15.5092	−0.575203	−0.287601	+	0.957750i	$0.592858\pi$
$728$	−3.10296	−0.115004
$729$	22.5139	0.833848
$730$	0.652307	0.0241430
$731$	7.20596	0.266522
$732$	0.296200	0.0109478
$733$	31.2579	1.15454	0.577268	−	0.816555i	$-0.304119\pi$
$733$	31.2579	1.15454	0.577268	+	0.816555i	$0.304119\pi$
$734$	−28.3962	−1.04812
$735$	12.3943	0.457172
$736$	−3.89041	−0.143403
$737$	−1.49655	−0.0551262
$738$	0.721561	0.0265610
$739$	18.9309	0.696386	0.348193	−	0.937423i	$-0.386795\pi$
$739$	18.9309	0.696386	0.348193	+	0.937423i	$0.386795\pi$
$740$	−5.62837	−0.206903
$741$	82.9561	3.04747
$742$	3.49648	0.128360
$743$	−4.58551	−0.168226	−0.0841130	−	0.996456i	$-0.526806\pi$
$743$	−4.58551	−0.168226	−0.0841130	+	0.996456i	$0.526806\pi$
$744$	5.17962	0.189894
$745$	20.8051	0.762240
$746$	26.1185	0.956267
$747$	0.278499	0.0101898
$748$	−7.20596	−0.263476
$749$	−5.31618	−0.194249
$750$	1.84371	0.0673227
$751$	−20.7377	−0.756731	−0.378365	−	0.925656i	$-0.623514\pi$
$751$	−20.7377	−0.756731	−0.378365	+	0.925656i	$0.623514\pi$
$752$	−8.47301	−0.308979
$753$	−32.9569	−1.20102
$754$	−47.4065	−1.72644
$755$	−13.5775	−0.494137
$756$	2.52593	0.0918670
$757$	45.9361	1.66958	0.834789	−	0.550570i	$-0.185590\pi$
$757$	45.9361	1.66958	0.834789	+	0.550570i	$0.185590\pi$
$758$	−23.3670	−0.848727
$759$	−7.17278	−0.260356
$760$	7.63854	0.277079
$761$	52.4758	1.90224	0.951122	−	0.308814i	$-0.0999322\pi$
$761$	52.4758	1.90224	0.951122	+	0.308814i	$0.0999322\pi$
$762$	−20.1403	−0.729605
$763$	8.74347	0.316535
$764$	−15.8411	−0.573111
$765$	−2.87703	−0.104019
$766$	29.8275	1.07771
$767$	−17.1626	−0.619707
$768$	−1.84371	−0.0665291
$769$	−30.8563	−1.11271	−0.556353	−	0.830946i	$-0.687800\pi$
$769$	−30.8563	−1.11271	−0.556353	+	0.830946i	$0.687800\pi$
$770$	−0.526782	−0.0189839
$771$	−32.2535	−1.16158
$772$	−2.34648	−0.0844518
$773$	15.1562	0.545131	0.272565	−	0.962137i	$-0.412128\pi$
$773$	15.1562	0.545131	0.272565	+	0.962137i	$0.412128\pi$
$774$	0.399257	0.0143510
$775$	2.80935	0.100915
$776$	11.7126	0.420459
$777$	5.46646	0.196108
$778$	23.9197	0.857564
$779$	13.8048	0.494609
$780$	−10.8602	−0.388858
$781$	9.81253	0.351120
$782$	28.0342	1.00250
$783$	38.5906	1.37912
$784$	−6.72250	−0.240089
$785$	−13.5103	−0.482204
$786$	−7.95460	−0.283731
$787$	42.9607	1.53139	0.765693	−	0.643207i	$-0.222396\pi$
$787$	42.9607	1.53139	0.765693	+	0.643207i	$0.222396\pi$
$788$	21.5343	0.767128
$789$	−22.3815	−0.796801
$790$	9.25084	0.329130
$791$	0.905564	0.0321982
$792$	−0.399257	−0.0141870
$793$	−0.946320	−0.0336048
$794$	34.4620	1.22301
$795$	12.2375	0.434019
$796$	8.62734	0.305788
$797$	−32.0526	−1.13536	−0.567680	−	0.823249i	$-0.692159\pi$
$797$	−32.0526	−1.13536	−0.567680	+	0.823249i	$0.692159\pi$
$798$	−7.41880	−0.262623
$799$	61.0561	2.16001
$800$	−1.00000	−0.0353553
$801$	4.18584	0.147899
$802$	−7.52593	−0.265750
$803$	−0.652307	−0.0230194
$804$	2.75920	0.0973096
$805$	2.04940	0.0722319
$806$	−16.5482	−0.582887
$807$	42.4785	1.49532
$808$	−19.6520	−0.691354
$809$	−17.7819	−0.625177	−0.312589	−	0.949889i	$-0.601196\pi$
$809$	−17.7819	−0.625177	−0.312589	+	0.949889i	$0.601196\pi$
$810$	10.0384	0.352712
$811$	47.1429	1.65541	0.827705	−	0.561163i	$-0.189646\pi$
$811$	47.1429	1.65541	0.827705	+	0.561163i	$0.189646\pi$
$812$	4.23958	0.148780
$813$	6.43372	0.225641
$814$	5.62837	0.197274
$815$	−7.39647	−0.259087
$816$	13.2857	0.465092
$817$	7.63854	0.267239
$818$	−9.24746	−0.323330
$819$	1.23888	0.0432900
$820$	−1.80726	−0.0631122
$821$	40.2195	1.40367	0.701835	−	0.712339i	$-0.252364\pi$
$821$	40.2195	1.40367	0.701835	+	0.712339i	$0.252364\pi$
$822$	−4.95149	−0.172703
$823$	53.6556	1.87032	0.935158	−	0.354230i	$-0.115257\pi$
$823$	53.6556	1.87032	0.935158	+	0.354230i	$0.115257\pi$
$824$	0.603792	0.0210341
$825$	−1.84371	−0.0641897
$826$	1.53486	0.0534047
$827$	30.9452	1.07607	0.538035	−	0.842923i	$-0.319167\pi$
$827$	30.9452	1.07607	0.538035	+	0.842923i	$0.319167\pi$
$828$	1.55328	0.0539801
$829$	−28.1206	−0.976670	−0.488335	−	0.872656i	$-0.662396\pi$
$829$	−28.1206	−0.976670	−0.488335	+	0.872656i	$0.662396\pi$
$830$	−0.697543	−0.0242121
$831$	37.8906	1.31441
$832$	5.89041	0.204213
$833$	48.4421	1.67842
$834$	14.9043	0.516093
$835$	11.9003	0.411828
$836$	−7.63854	−0.264184
$837$	13.4709	0.465621
$838$	6.74591	0.233034
$839$	−18.9715	−0.654968	−0.327484	−	0.944857i	$-0.606201\pi$
$839$	−18.9715	−0.654968	−0.327484	+	0.944857i	$0.606201\pi$
$840$	0.971232	0.0335107
$841$	35.7716	1.23350
$842$	37.6196	1.29646
$843$	−2.81042	−0.0967960
$844$	−10.9150	−0.375711
$845$	21.6970	0.746398
$846$	3.38291	0.116307
$847$	0.526782	0.0181004
$848$	−6.63743	−0.227930
$849$	26.5728	0.911975
$850$	7.20596	0.247162
$851$	−21.8967	−0.750609
$852$	−18.0914	−0.619803
$853$	−55.9063	−1.91419	−0.957097	−	0.289768i	$-0.906422\pi$
$853$	−55.9063	−1.91419	−0.957097	+	0.289768i	$0.906422\pi$
$854$	0.0846298	0.00289597
$855$	−3.04974	−0.104299
$856$	10.0918	0.344931
$857$	29.6040	1.01125	0.505626	−	0.862753i	$-0.331262\pi$
$857$	29.6040	1.01125	0.505626	+	0.862753i	$0.331262\pi$
$858$	10.8602	0.370761
$859$	4.31461	0.147213	0.0736063	−	0.997287i	$-0.476549\pi$
$859$	4.31461	0.147213	0.0736063	+	0.997287i	$0.476549\pi$
$860$	−1.00000	−0.0340997
$861$	1.75527	0.0598194
$862$	21.3741	0.728003
$863$	23.9154	0.814088	0.407044	−	0.913409i	$-0.366560\pi$
$863$	23.9154	0.814088	0.407044	+	0.913409i	$0.366560\pi$
$864$	−4.79501	−0.163130
$865$	5.09205	0.173135
$866$	29.9923	1.01918
$867$	−64.3930	−2.18690
$868$	1.47992	0.0502316
$869$	−9.25084	−0.313813
$870$	14.8383	0.503066
$871$	−8.81530	−0.298695
$872$	−16.5979	−0.562075
$873$	−4.67636	−0.158271
$874$	29.7171	1.00520
$875$	0.526782	0.0178085
$876$	1.20266	0.0406343
$877$	−31.1655	−1.05238	−0.526192	−	0.850366i	$-0.676381\pi$
$877$	−31.1655	−1.05238	−0.526192	+	0.850366i	$0.676381\pi$
$878$	26.1904	0.883883
$879$	−28.7643	−0.970196
$880$	1.00000	0.0337100
$881$	−23.7527	−0.800247	−0.400124	−	0.916461i	$-0.631033\pi$
$881$	−23.7527	−0.800247	−0.400124	+	0.916461i	$0.631033\pi$
$882$	2.68401	0.0903753
$883$	−33.6169	−1.13130	−0.565650	−	0.824646i	$-0.691375\pi$
$883$	−33.6169	−1.13130	−0.565650	+	0.824646i	$0.691375\pi$
$884$	−42.4461	−1.42762
$885$	5.37193	0.180576
$886$	12.9088	0.433680
$887$	−7.64450	−0.256677	−0.128339	−	0.991730i	$-0.540964\pi$
$887$	−7.64450	−0.256677	−0.128339	+	0.991730i	$0.540964\pi$
$888$	−10.3771	−0.348232
$889$	−5.75446	−0.192998
$890$	−10.4841	−0.351426
$891$	−10.0384	−0.336298
$892$	−18.3010	−0.612763
$893$	64.7214	2.16582
$894$	38.3585	1.28290
$895$	−24.0445	−0.803719
$896$	−0.526782	−0.0175986
$897$	−42.2507	−1.41071
$898$	14.6849	0.490040
$899$	22.6099	0.754082
$900$	0.399257	0.0133086
$901$	47.8290	1.59342
$902$	1.80726	0.0601751
$903$	0.971232	0.0323206
$904$	−1.71905	−0.0571747
$905$	−1.85958	−0.0618146
$906$	−25.0330	−0.831666
$907$	−30.1758	−1.00197	−0.500986	−	0.865455i	$-0.667029\pi$
$907$	−30.1758	−1.00197	−0.500986	+	0.865455i	$0.667029\pi$
$908$	−13.0373	−0.432658
$909$	7.84620	0.260242
$910$	−3.10296	−0.102862
$911$	−50.5305	−1.67415	−0.837075	−	0.547089i	$-0.815736\pi$
$911$	−50.5305	−1.67415	−0.837075	+	0.547089i	$0.815736\pi$
$912$	14.0832	0.466342
$913$	0.697543	0.0230853
$914$	−8.15480	−0.269737
$915$	0.296200	0.00979205
$916$	26.1503	0.864031
$917$	−2.27278	−0.0750538
$918$	34.5526	1.14041
$919$	18.5373	0.611490	0.305745	−	0.952113i	$-0.401094\pi$
$919$	18.5373	0.611490	0.305745	+	0.952113i	$0.401094\pi$
$920$	−3.89041	−0.128263
$921$	−16.4136	−0.540847
$922$	7.35296	0.242157
$923$	57.7999	1.90251
$924$	−0.971232	−0.0319512
$925$	−5.62837	−0.185060
$926$	25.7336	0.845658
$927$	−0.241069	−0.00791773
$928$	−8.04808	−0.264191
$929$	17.3909	0.570578	0.285289	−	0.958442i	$-0.407910\pi$
$929$	17.3909	0.570578	0.285289	+	0.958442i	$0.407910\pi$
$930$	5.17962	0.169846
$931$	51.3501	1.68293
$932$	−27.7381	−0.908593
$933$	3.96110	0.129681
$934$	−35.0874	−1.14810
$935$	−7.20596	−0.235660
$936$	−2.35179	−0.0768707
$937$	29.9119	0.977180	0.488590	−	0.872513i	$-0.337511\pi$
$937$	29.9119	0.977180	0.488590	+	0.872513i	$0.337511\pi$
$938$	0.788356	0.0257407
$939$	−7.76868	−0.253521
$940$	−8.47301	−0.276359
$941$	−24.3246	−0.792960	−0.396480	−	0.918043i	$-0.629768\pi$
$941$	−24.3246	−0.792960	−0.396480	+	0.918043i	$0.629768\pi$
$942$	−24.9091	−0.811582
$943$	−7.03098	−0.228960
$944$	−2.91366	−0.0948315
$945$	2.52593	0.0821683
$946$	1.00000	0.0325128
$947$	−52.5982	−1.70921	−0.854606	−	0.519277i	$-0.826201\pi$
$947$	−52.5982	−1.70921	−0.854606	+	0.519277i	$0.826201\pi$
$948$	17.0558	0.553948
$949$	−3.84236	−0.124728
$950$	7.63854	0.247827
$951$	9.21842	0.298928
$952$	3.79597	0.123028
$953$	59.6850	1.93339	0.966694	−	0.255935i	$-0.0823834\pi$
$953$	59.6850	1.93339	0.966694	+	0.255935i	$0.0823834\pi$
$954$	2.65004	0.0857983
$955$	−15.8411	−0.512606
$956$	−11.8971	−0.384781
$957$	−14.8383	−0.479654
$958$	15.2906	0.494018
$959$	−1.41474	−0.0456842
$960$	−1.84371	−0.0595054
$961$	−23.1075	−0.745405
$962$	33.1534	1.06891
$963$	−4.02923	−0.129840
$964$	−24.6656	−0.794425
$965$	−2.34648	−0.0755360
$966$	3.77849	0.121571
$967$	−14.9537	−0.480879	−0.240439	−	0.970664i	$-0.577292\pi$
$967$	−14.9537	−0.480879	−0.240439	+	0.970664i	$0.577292\pi$
$968$	−1.00000	−0.0321412
$969$	−101.483	−3.26011
$970$	11.7126	0.376070
$971$	−9.04987	−0.290424	−0.145212	−	0.989401i	$-0.546386\pi$
$971$	−9.04987	−0.290424	−0.145212	+	0.989401i	$0.546386\pi$
$972$	4.12278	0.132238
$973$	4.25843	0.136519
$974$	23.6677	0.758361
$975$	−10.8602	−0.347805
$976$	−0.160654	−0.00514242
$977$	42.7717	1.36839	0.684193	−	0.729301i	$-0.260154\pi$
$977$	42.7717	1.36839	0.684193	+	0.729301i	$0.260154\pi$
$978$	−13.6369	−0.436061
$979$	10.4841	0.335072
$980$	−6.72250	−0.214742
$981$	6.62683	0.211578
$982$	36.7951	1.17418
$983$	1.78248	0.0568523	0.0284261	−	0.999596i	$-0.490950\pi$
$983$	1.78248	0.0568523	0.0284261	+	0.999596i	$0.490950\pi$
$984$	−3.33206	−0.106222
$985$	21.5343	0.686140
$986$	57.9941	1.84691
$987$	8.22926	0.261940
$988$	−44.9942	−1.43145
$989$	−3.89041	−0.123708
$990$	−0.399257	−0.0126892
$991$	−0.178225	−0.00566150	−0.00283075	−	0.999996i	$-0.500901\pi$
$991$	−0.178225	−0.00566150	−0.00283075	+	0.999996i	$0.500901\pi$
$992$	−2.80935	−0.0891970
$993$	46.2651	1.46818
$994$	−5.16907	−0.163953
$995$	8.62734	0.273505
$996$	−1.28606	−0.0407505
$997$	−42.2595	−1.33837	−0.669186	−	0.743095i	$-0.733357\pi$
$997$	−42.2595	−1.33837	−0.669186	+	0.743095i	$0.733357\pi$
$998$	31.2771	0.990060
$999$	−26.9881	−0.853866

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.w.1.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.w.1.3	✓	8	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.84371 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.84371 q^{6} +0.526782 q^{7} -1.00000 q^{8} +0.399257 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.84371 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.84371 q^{6} +0.526782 q^{7} -1.00000 q^{8} +0.399257 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.84371 q^{12} +5.89041 q^{13} -0.526782 q^{14} -1.84371 q^{15} +1.00000 q^{16} -7.20596 q^{17} -0.399257 q^{18} -7.63854 q^{19} +1.00000 q^{20} -0.971232 q^{21} -1.00000 q^{22} +3.89041 q^{23} +1.84371 q^{24} +1.00000 q^{25} -5.89041 q^{26} +4.79501 q^{27} +0.526782 q^{28} +8.04808 q^{29} +1.84371 q^{30} +2.80935 q^{31} -1.00000 q^{32} -1.84371 q^{33} +7.20596 q^{34} +0.526782 q^{35} +0.399257 q^{36} -5.62837 q^{37} +7.63854 q^{38} -10.8602 q^{39} -1.00000 q^{40} -1.80726 q^{41} +0.971232 q^{42} -1.00000 q^{43} +1.00000 q^{44} +0.399257 q^{45} -3.89041 q^{46} -8.47301 q^{47} -1.84371 q^{48} -6.72250 q^{49} -1.00000 q^{50} +13.2857 q^{51} +5.89041 q^{52} -6.63743 q^{53} -4.79501 q^{54} +1.00000 q^{55} -0.526782 q^{56} +14.0832 q^{57} -8.04808 q^{58} -2.91366 q^{59} -1.84371 q^{60} -0.160654 q^{61} -2.80935 q^{62} +0.210322 q^{63} +1.00000 q^{64} +5.89041 q^{65} +1.84371 q^{66} -1.49655 q^{67} -7.20596 q^{68} -7.17278 q^{69} -0.526782 q^{70} +9.81253 q^{71} -0.399257 q^{72} -0.652307 q^{73} +5.62837 q^{74} -1.84371 q^{75} -7.63854 q^{76} +0.526782 q^{77} +10.8602 q^{78} -9.25084 q^{79} +1.00000 q^{80} -10.0384 q^{81} +1.80726 q^{82} +0.697543 q^{83} -0.971232 q^{84} -7.20596 q^{85} +1.00000 q^{86} -14.8383 q^{87} -1.00000 q^{88} +10.4841 q^{89} -0.399257 q^{90} +3.10296 q^{91} +3.89041 q^{92} -5.17962 q^{93} +8.47301 q^{94} -7.63854 q^{95} +1.84371 q^{96} -11.7126 q^{97} +6.72250 q^{98} +0.399257 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9	\( 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9} - 8 q^{10} + 8 q^{11} - 7 q^{12} - 2 q^{13} + 6 q^{14} - 7 q^{15} + 8 q^{16} - 8 q^{17} - 7 q^{18} + 8 q^{20} + 14 q^{21} - 8 q^{22} - 18 q^{23} + 7 q^{24} + 8 q^{25} + 2 q^{26} - 22 q^{27} - 6 q^{28} + 8 q^{29} + 7 q^{30} - 11 q^{31} - 8 q^{32} - 7 q^{33} + 8 q^{34} - 6 q^{35} + 7 q^{36} - 17 q^{37} - 6 q^{39} - 8 q^{40} + 12 q^{41} - 14 q^{42} - 8 q^{43} + 8 q^{44} + 7 q^{45} + 18 q^{46} - 19 q^{47} - 7 q^{48} - 2 q^{49} - 8 q^{50} - q^{51} - 2 q^{52} - 7 q^{53} + 22 q^{54} + 8 q^{55} + 6 q^{56} - 3 q^{57} - 8 q^{58} + q^{59} - 7 q^{60} + 6 q^{61} + 11 q^{62} - 15 q^{63} + 8 q^{64} - 2 q^{65} + 7 q^{66} - 22 q^{67} - 8 q^{68} + 8 q^{69} + 6 q^{70} - 14 q^{71} - 7 q^{72} - 13 q^{73} + 17 q^{74} - 7 q^{75} - 6 q^{77} + 6 q^{78} - 8 q^{79} + 8 q^{80} + 28 q^{81} - 12 q^{82} - 4 q^{83} + 14 q^{84} - 8 q^{85} + 8 q^{86} - 30 q^{87} - 8 q^{88} + 5 q^{89} - 7 q^{90} - 8 q^{91} - 18 q^{92} + q^{93} + 19 q^{94} + 7 q^{96} - 23 q^{97} + 2 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9 - 8 * q^10 + 8 * q^11 - 7 * q^12 - 2 * q^13 + 6 * q^14 - 7 * q^15 + 8 * q^16 - 8 * q^17 - 7 * q^18 + 8 * q^20 + 14 * q^21 - 8 * q^22 - 18 * q^23 + 7 * q^24 + 8 * q^25 + 2 * q^26 - 22 * q^27 - 6 * q^28 + 8 * q^29 + 7 * q^30 - 11 * q^31 - 8 * q^32 - 7 * q^33 + 8 * q^34 - 6 * q^35 + 7 * q^36 - 17 * q^37 - 6 * q^39 - 8 * q^40 + 12 * q^41 - 14 * q^42 - 8 * q^43 + 8 * q^44 + 7 * q^45 + 18 * q^46 - 19 * q^47 - 7 * q^48 - 2 * q^49 - 8 * q^50 - q^51 - 2 * q^52 - 7 * q^53 + 22 * q^54 + 8 * q^55 + 6 * q^56 - 3 * q^57 - 8 * q^58 + q^59 - 7 * q^60 + 6 * q^61 + 11 * q^62 - 15 * q^63 + 8 * q^64 - 2 * q^65 + 7 * q^66 - 22 * q^67 - 8 * q^68 + 8 * q^69 + 6 * q^70 - 14 * q^71 - 7 * q^72 - 13 * q^73 + 17 * q^74 - 7 * q^75 - 6 * q^77 + 6 * q^78 - 8 * q^79 + 8 * q^80 + 28 * q^81 - 12 * q^82 - 4 * q^83 + 14 * q^84 - 8 * q^85 + 8 * q^86 - 30 * q^87 - 8 * q^88 + 5 * q^89 - 7 * q^90 - 8 * q^91 - 18 * q^92 + q^93 + 19 * q^94 + 7 * q^96 - 23 * q^97 + 2 * q^98 + 7 * q^99

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