LMFDB - Embedded newform 4641.2.a.ba.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4641,2,Mod(1,4641)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4641, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4641.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4641 = 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4641.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:	$37.0585715781$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - x^{16} - 29 x^{15} + 26 x^{14} + 339 x^{13} - 266 x^{12} - 2047 x^{11} + 1356 x^{10} + \cdots + 18 $ x^17 - x^16 - 29x^15 + 26x^14 + 339x^13 - 266x^12 - 2047x^11 + 1356x^10 + 6792x^9 - 3573x^8 - 12125x^7 + 4456x^6 + 10521x^5 - 1858x^4 - 3551x^3 + 34x^2 + 323*x + 18
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$2.79555$ of defining polynomial
Character	$\chi$	$=$	4641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.79555 q^{2} -1.00000 q^{3} +5.81513 q^{4} -1.75095 q^{5} -2.79555 q^{6} -1.00000 q^{7} +10.6654 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.79555 q^{2} -1.00000 q^{3} +5.81513 q^{4} -1.75095 q^{5} -2.79555 q^{6} -1.00000 q^{7} +10.6654 q^{8} +1.00000 q^{9} -4.89488 q^{10} +2.58694 q^{11} -5.81513 q^{12} +1.00000 q^{13} -2.79555 q^{14} +1.75095 q^{15} +18.1854 q^{16} -1.00000 q^{17} +2.79555 q^{18} +4.83271 q^{19} -10.1820 q^{20} +1.00000 q^{21} +7.23193 q^{22} -0.476059 q^{23} -10.6654 q^{24} -1.93418 q^{25} +2.79555 q^{26} -1.00000 q^{27} -5.81513 q^{28} +5.85581 q^{29} +4.89488 q^{30} -8.43224 q^{31} +29.5076 q^{32} -2.58694 q^{33} -2.79555 q^{34} +1.75095 q^{35} +5.81513 q^{36} -5.27296 q^{37} +13.5101 q^{38} -1.00000 q^{39} -18.6746 q^{40} +8.39496 q^{41} +2.79555 q^{42} +0.943022 q^{43} +15.0434 q^{44} -1.75095 q^{45} -1.33085 q^{46} +4.26967 q^{47} -18.1854 q^{48} +1.00000 q^{49} -5.40709 q^{50} +1.00000 q^{51} +5.81513 q^{52} +10.4147 q^{53} -2.79555 q^{54} -4.52960 q^{55} -10.6654 q^{56} -4.83271 q^{57} +16.3703 q^{58} +1.00575 q^{59} +10.1820 q^{60} +4.29010 q^{61} -23.5728 q^{62} -1.00000 q^{63} +46.1193 q^{64} -1.75095 q^{65} -7.23193 q^{66} +0.261533 q^{67} -5.81513 q^{68} +0.476059 q^{69} +4.89488 q^{70} +13.2211 q^{71} +10.6654 q^{72} -16.9635 q^{73} -14.7408 q^{74} +1.93418 q^{75} +28.1028 q^{76} -2.58694 q^{77} -2.79555 q^{78} +3.05865 q^{79} -31.8418 q^{80} +1.00000 q^{81} +23.4686 q^{82} -5.80283 q^{83} +5.81513 q^{84} +1.75095 q^{85} +2.63627 q^{86} -5.85581 q^{87} +27.5907 q^{88} -0.445811 q^{89} -4.89488 q^{90} -1.00000 q^{91} -2.76834 q^{92} +8.43224 q^{93} +11.9361 q^{94} -8.46183 q^{95} -29.5076 q^{96} +19.1782 q^{97} +2.79555 q^{98} +2.58694 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9} - q^{10} + 4 q^{11} - 25 q^{12} + 17 q^{13} - q^{14} + 4 q^{15} + 53 q^{16} - 17 q^{17} + q^{18} + 13 q^{19} - 5 q^{20} + 17 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} + 37 q^{25} + q^{26} - 17 q^{27} - 25 q^{28} - 3 q^{29} + q^{30} + 10 q^{31} + 18 q^{32} - 4 q^{33} - q^{34} + 4 q^{35} + 25 q^{36} - 25 q^{38} - 17 q^{39} - 12 q^{41} + q^{42} + 29 q^{43} + 12 q^{44} - 4 q^{45} + 19 q^{46} - 4 q^{47} - 53 q^{48} + 17 q^{49} + 9 q^{50} + 17 q^{51} + 25 q^{52} - 8 q^{53} - q^{54} + 27 q^{55} - 6 q^{56} - 13 q^{57} + 2 q^{58} + 25 q^{59} + 5 q^{60} - 5 q^{61} - 37 q^{62} - 17 q^{63} + 94 q^{64} - 4 q^{65} - 4 q^{66} + 15 q^{67} - 25 q^{68} - 8 q^{69} + q^{70} + 32 q^{71} + 6 q^{72} - 15 q^{73} + 16 q^{74} - 37 q^{75} + 3 q^{76} - 4 q^{77} - q^{78} + 27 q^{79} + 41 q^{80} + 17 q^{81} - 8 q^{82} - 24 q^{83} + 25 q^{84} + 4 q^{85} + 53 q^{86} + 3 q^{87} - 9 q^{88} - 8 q^{89} - q^{90} - 17 q^{91} + 14 q^{92} - 10 q^{93} + 51 q^{94} - 9 q^{95} - 18 q^{96} - 22 q^{97} + q^{98} + 4 q^{99}+O(q^{100}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9 - q^10 + 4 * q^11 - 25 * q^12 + 17 * q^13 - q^14 + 4 * q^15 + 53 * q^16 - 17 * q^17 + q^18 + 13 * q^19 - 5 * q^20 + 17 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 + 37 * q^25 + q^26 - 17 * q^27 - 25 * q^28 - 3 * q^29 + q^30 + 10 * q^31 + 18 * q^32 - 4 * q^33 - q^34 + 4 * q^35 + 25 * q^36 - 25 * q^38 - 17 * q^39 - 12 * q^41 + q^42 + 29 * q^43 + 12 * q^44 - 4 * q^45 + 19 * q^46 - 4 * q^47 - 53 * q^48 + 17 * q^49 + 9 * q^50 + 17 * q^51 + 25 * q^52 - 8 * q^53 - q^54 + 27 * q^55 - 6 * q^56 - 13 * q^57 + 2 * q^58 + 25 * q^59 + 5 * q^60 - 5 * q^61 - 37 * q^62 - 17 * q^63 + 94 * q^64 - 4 * q^65 - 4 * q^66 + 15 * q^67 - 25 * q^68 - 8 * q^69 + q^70 + 32 * q^71 + 6 * q^72 - 15 * q^73 + 16 * q^74 - 37 * q^75 + 3 * q^76 - 4 * q^77 - q^78 + 27 * q^79 + 41 * q^80 + 17 * q^81 - 8 * q^82 - 24 * q^83 + 25 * q^84 + 4 * q^85 + 53 * q^86 + 3 * q^87 - 9 * q^88 - 8 * q^89 - q^90 - 17 * q^91 + 14 * q^92 - 10 * q^93 + 51 * q^94 - 9 * q^95 - 18 * q^96 - 22 * q^97 + q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.79555	1.97676	0.988378	−	0.152017i	$-0.0485768\pi$
$2$	2.79555	1.97676	0.988378	+	0.152017i	$0.0485768\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.81513	2.90756
$5$	−1.75095	−0.783048	−0.391524	−	0.920168i	$-0.628052\pi$
$5$	−1.75095	−0.783048	−0.391524	+	0.920168i	$0.628052\pi$
$6$	−2.79555	−1.14128
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	10.6654	3.77079
$9$	1.00000	0.333333
$10$	−4.89488	−1.54790
$11$	2.58694	0.779991	0.389995	−	0.920817i	$-0.372477\pi$
$11$	2.58694	0.779991	0.389995	+	0.920817i	$0.372477\pi$
$12$	−5.81513	−1.67868
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.79555	−0.747143
$15$	1.75095	0.452093
$16$	18.1854	4.54636
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.79555	0.658919
$19$	4.83271	1.10870	0.554350	−	0.832284i	$-0.312967\pi$
$19$	4.83271	1.10870	0.554350	+	0.832284i	$0.312967\pi$
$20$	−10.1820	−2.27676
$21$	1.00000	0.218218
$22$	7.23193	1.54185
$23$	−0.476059	−0.0992652	−0.0496326	−	0.998768i	$-0.515805\pi$
$23$	−0.476059	−0.0992652	−0.0496326	+	0.998768i	$0.515805\pi$
$24$	−10.6654	−2.17706
$25$	−1.93418	−0.386835
$26$	2.79555	0.548253
$27$	−1.00000	−0.192450
$28$	−5.81513	−1.09896
$29$	5.85581	1.08740	0.543699	−	0.839280i	$-0.317023\pi$
$29$	5.85581	1.08740	0.543699	+	0.839280i	$0.317023\pi$
$30$	4.89488	0.893678
$31$	−8.43224	−1.51447	−0.757237	−	0.653140i	$-0.773451\pi$
$31$	−8.43224	−1.51447	−0.757237	+	0.653140i	$0.773451\pi$
$32$	29.5076	5.21626
$33$	−2.58694	−0.450328
$34$	−2.79555	−0.479434
$35$	1.75095	0.295965
$36$	5.81513	0.969188
$37$	−5.27296	−0.866869	−0.433434	−	0.901185i	$-0.642698\pi$
$37$	−5.27296	−0.866869	−0.433434	+	0.901185i	$0.642698\pi$
$38$	13.5101	2.19163
$39$	−1.00000	−0.160128
$40$	−18.6746	−2.95271
$41$	8.39496	1.31107	0.655536	−	0.755164i	$-0.272443\pi$
$41$	8.39496	1.31107	0.655536	+	0.755164i	$0.272443\pi$
$42$	2.79555	0.431363
$43$	0.943022	0.143809	0.0719047	−	0.997412i	$-0.477092\pi$
$43$	0.943022	0.143809	0.0719047	+	0.997412i	$0.477092\pi$
$44$	15.0434	2.26787
$45$	−1.75095	−0.261016
$46$	−1.33085	−0.196223
$47$	4.26967	0.622796	0.311398	−	0.950280i	$-0.399203\pi$
$47$	4.26967	0.622796	0.311398	+	0.950280i	$0.399203\pi$
$48$	−18.1854	−2.62484
$49$	1.00000	0.142857
$50$	−5.40709	−0.764679
$51$	1.00000	0.140028
$52$	5.81513	0.806413
$53$	10.4147	1.43057	0.715287	−	0.698831i	$-0.246296\pi$
$53$	10.4147	1.43057	0.715287	+	0.698831i	$0.246296\pi$
$54$	−2.79555	−0.380427
$55$	−4.52960	−0.610771
$56$	−10.6654	−1.42522
$57$	−4.83271	−0.640108
$58$	16.3703	2.14952
$59$	1.00575	0.130937	0.0654686	−	0.997855i	$-0.479146\pi$
$59$	1.00575	0.130937	0.0654686	+	0.997855i	$0.479146\pi$
$60$	10.1820	1.31449
$61$	4.29010	0.549291	0.274645	−	0.961546i	$-0.411440\pi$
$61$	4.29010	0.549291	0.274645	+	0.961546i	$0.411440\pi$
$62$	−23.5728	−2.99375
$63$	−1.00000	−0.125988
$64$	46.1193	5.76491
$65$	−1.75095	−0.217179
$66$	−7.23193	−0.890188
$67$	0.261533	0.0319514	0.0159757	−	0.999872i	$-0.494915\pi$
$67$	0.261533	0.0319514	0.0159757	+	0.999872i	$0.494915\pi$
$68$	−5.81513	−0.705188
$69$	0.476059	0.0573108
$70$	4.89488	0.585050
$71$	13.2211	1.56906	0.784530	−	0.620091i	$-0.212904\pi$
$71$	13.2211	1.56906	0.784530	+	0.620091i	$0.212904\pi$
$72$	10.6654	1.25693
$73$	−16.9635	−1.98543	−0.992714	−	0.120493i	$-0.961553\pi$
$73$	−16.9635	−1.98543	−0.992714	+	0.120493i	$0.961553\pi$
$74$	−14.7408	−1.71359
$75$	1.93418	0.223339
$76$	28.1028	3.22362
$77$	−2.58694	−0.294809
$78$	−2.79555	−0.316534
$79$	3.05865	0.344125	0.172063	−	0.985086i	$-0.444957\pi$
$79$	3.05865	0.344125	0.172063	+	0.985086i	$0.444957\pi$
$80$	−31.8418	−3.56002
$81$	1.00000	0.111111
$82$	23.4686	2.59167
$83$	−5.80283	−0.636943	−0.318472	−	0.947932i	$-0.603170\pi$
$83$	−5.80283	−0.636943	−0.318472	+	0.947932i	$0.603170\pi$
$84$	5.81513	0.634482
$85$	1.75095	0.189917
$86$	2.63627	0.284276
$87$	−5.85581	−0.627809
$88$	27.5907	2.94118
$89$	−0.445811	−0.0472559	−0.0236279	−	0.999721i	$-0.507522\pi$
$89$	−0.445811	−0.0472559	−0.0236279	+	0.999721i	$0.507522\pi$
$90$	−4.89488	−0.515965
$91$	−1.00000	−0.104828
$92$	−2.76834	−0.288620
$93$	8.43224	0.874382
$94$	11.9361	1.23112
$95$	−8.46183	−0.868166
$96$	−29.5076	−3.01161
$97$	19.1782	1.94725	0.973625	−	0.228155i	$-0.0732694\pi$
$97$	19.1782	1.94725	0.973625	+	0.228155i	$0.0732694\pi$
$98$	2.79555	0.282394
$99$	2.58694	0.259997
$100$	−11.2475	−1.12475
$101$	−2.53507	−0.252249	−0.126124	−	0.992014i	$-0.540254\pi$
$101$	−2.53507	−0.252249	−0.126124	+	0.992014i	$0.540254\pi$
$102$	2.79555	0.276801
$103$	16.1086	1.58723	0.793616	−	0.608420i	$-0.208196\pi$
$103$	16.1086	1.58723	0.793616	+	0.608420i	$0.208196\pi$
$104$	10.6654	1.04583
$105$	−1.75095	−0.170875
$106$	29.1150	2.82789
$107$	−15.0474	−1.45468	−0.727342	−	0.686275i	$-0.759245\pi$
$107$	−15.0474	−1.45468	−0.727342	+	0.686275i	$0.759245\pi$
$108$	−5.81513	−0.559561
$109$	9.31549	0.892262	0.446131	−	0.894968i	$-0.352802\pi$
$109$	9.31549	0.892262	0.446131	+	0.894968i	$0.352802\pi$
$110$	−12.6627	−1.20734
$111$	5.27296	0.500487
$112$	−18.1854	−1.71836
$113$	−17.4697	−1.64341	−0.821707	−	0.569910i	$-0.806978\pi$
$113$	−17.4697	−1.64341	−0.821707	+	0.569910i	$0.806978\pi$
$114$	−13.5101	−1.26534
$115$	0.833556	0.0777295
$116$	34.0523	3.16168
$117$	1.00000	0.0924500
$118$	2.81162	0.258831
$119$	1.00000	0.0916698
$120$	18.6746	1.70475
$121$	−4.30776	−0.391614
$122$	11.9932	1.08581
$123$	−8.39496	−0.756948
$124$	−49.0345	−4.40343
$125$	12.1414	1.08596
$126$	−2.79555	−0.249048
$127$	−7.65262	−0.679060	−0.339530	−	0.940595i	$-0.610268\pi$
$127$	−7.65262	−0.679060	−0.339530	+	0.940595i	$0.610268\pi$
$128$	69.9137	6.17956
$129$	−0.943022	−0.0830284
$130$	−4.89488	−0.429309
$131$	10.4265	0.910965	0.455482	−	0.890245i	$-0.349467\pi$
$131$	10.4265	0.910965	0.455482	+	0.890245i	$0.349467\pi$
$132$	−15.0434	−1.30936
$133$	−4.83271	−0.419049
$134$	0.731131	0.0631601
$135$	1.75095	0.150698
$136$	−10.6654	−0.914550
$137$	−19.7957	−1.69126	−0.845631	−	0.533767i	$-0.820776\pi$
$137$	−19.7957	−1.69126	−0.845631	+	0.533767i	$0.820776\pi$
$138$	1.33085	0.113289
$139$	12.1209	1.02809	0.514043	−	0.857765i	$-0.328147\pi$
$139$	12.1209	1.02809	0.514043	+	0.857765i	$0.328147\pi$
$140$	10.1820	0.860536
$141$	−4.26967	−0.359571
$142$	36.9604	3.10165
$143$	2.58694	0.216331
$144$	18.1854	1.51545
$145$	−10.2532	−0.851485
$146$	−47.4224	−3.92471
$147$	−1.00000	−0.0824786
$148$	−30.6629	−2.52048
$149$	1.88746	0.154627	0.0773133	−	0.997007i	$-0.475366\pi$
$149$	1.88746	0.154627	0.0773133	+	0.997007i	$0.475366\pi$
$150$	5.40709	0.441487
$151$	−4.40484	−0.358460	−0.179230	−	0.983807i	$-0.557361\pi$
$151$	−4.40484	−0.358460	−0.179230	+	0.983807i	$0.557361\pi$
$152$	51.5428	4.18067
$153$	−1.00000	−0.0808452
$154$	−7.23193	−0.582765
$155$	14.7644	1.18591
$156$	−5.81513	−0.465583
$157$	−1.27669	−0.101891	−0.0509455	−	0.998701i	$-0.516223\pi$
$157$	−1.27669	−0.101891	−0.0509455	+	0.998701i	$0.516223\pi$
$158$	8.55063	0.680252
$159$	−10.4147	−0.825942
$160$	−51.6664	−4.08458
$161$	0.476059	0.0375187
$162$	2.79555	0.219640
$163$	18.8695	1.47797	0.738987	−	0.673719i	$-0.235304\pi$
$163$	18.8695	1.47797	0.738987	+	0.673719i	$0.235304\pi$
$164$	48.8178	3.81203
$165$	4.52960	0.352629
$166$	−16.2221	−1.25908
$167$	−25.4884	−1.97235	−0.986176	−	0.165699i	$-0.947012\pi$
$167$	−25.4884	−1.97235	−0.986176	+	0.165699i	$0.947012\pi$
$168$	10.6654	0.822853
$169$	1.00000	0.0769231
$170$	4.89488	0.375420
$171$	4.83271	0.369567
$172$	5.48379	0.418135
$173$	−8.15350	−0.619899	−0.309950	−	0.950753i	$-0.600312\pi$
$173$	−8.15350	−0.619899	−0.309950	+	0.950753i	$0.600312\pi$
$174$	−16.3703	−1.24103
$175$	1.93418	0.146210
$176$	47.0446	3.54612
$177$	−1.00575	−0.0755967
$178$	−1.24629	−0.0934133
$179$	19.9533	1.49138	0.745688	−	0.666295i	$-0.232121\pi$
$179$	19.9533	1.49138	0.745688	+	0.666295i	$0.232121\pi$
$180$	−10.1820	−0.758921
$181$	5.03237	0.374053	0.187027	−	0.982355i	$-0.440115\pi$
$181$	5.03237	0.374053	0.187027	+	0.982355i	$0.440115\pi$
$182$	−2.79555	−0.207220
$183$	−4.29010	−0.317133
$184$	−5.07736	−0.374308
$185$	9.23268	0.678800
$186$	23.5728	1.72844
$187$	−2.58694	−0.189176
$188$	24.8287	1.81082
$189$	1.00000	0.0727393
$190$	−23.6555	−1.71615
$191$	−6.87921	−0.497762	−0.248881	−	0.968534i	$-0.580063\pi$
$191$	−6.87921	−0.497762	−0.248881	+	0.968534i	$0.580063\pi$
$192$	−46.1193	−3.32837
$193$	13.5873	0.978038	0.489019	−	0.872273i	$-0.337355\pi$
$193$	13.5873	0.978038	0.489019	+	0.872273i	$0.337355\pi$
$194$	53.6137	3.84924
$195$	1.75095	0.125388
$196$	5.81513	0.415366
$197$	−13.8425	−0.986234	−0.493117	−	0.869963i	$-0.664143\pi$
$197$	−13.8425	−0.986234	−0.493117	+	0.869963i	$0.664143\pi$
$198$	7.23193	0.513951
$199$	0.882856	0.0625840	0.0312920	−	0.999510i	$-0.490038\pi$
$199$	0.882856	0.0625840	0.0312920	+	0.999510i	$0.490038\pi$
$200$	−20.6287	−1.45867
$201$	−0.261533	−0.0184471
$202$	−7.08692	−0.498634
$203$	−5.85581	−0.410998
$204$	5.81513	0.407140
$205$	−14.6992	−1.02663
$206$	45.0326	3.13757
$207$	−0.476059	−0.0330884
$208$	18.1854	1.26093
$209$	12.5019	0.864776
$210$	−4.89488	−0.337779
$211$	−14.1376	−0.973270	−0.486635	−	0.873605i	$-0.661776\pi$
$211$	−14.1376	−0.973270	−0.486635	+	0.873605i	$0.661776\pi$
$212$	60.5630	4.15948
$213$	−13.2211	−0.905897
$214$	−42.0658	−2.87556
$215$	−1.65118	−0.112610
$216$	−10.6654	−0.725688
$217$	8.43224	0.572418
$218$	26.0420	1.76378
$219$	16.9635	1.14629
$220$	−26.3402	−1.77585
$221$	−1.00000	−0.0672673
$222$	14.7408	0.989340
$223$	−23.2236	−1.55517	−0.777584	−	0.628779i	$-0.783555\pi$
$223$	−23.2236	−1.55517	−0.777584	+	0.628779i	$0.783555\pi$
$224$	−29.5076	−1.97156
$225$	−1.93418	−0.128945
$226$	−48.8376	−3.24863
$227$	−16.4500	−1.09183	−0.545914	−	0.837841i	$-0.683817\pi$
$227$	−16.4500	−1.09183	−0.545914	+	0.837841i	$0.683817\pi$
$228$	−28.1028	−1.86116
$229$	20.3660	1.34583	0.672913	−	0.739722i	$-0.265043\pi$
$229$	20.3660	1.34583	0.672913	+	0.739722i	$0.265043\pi$
$230$	2.33025	0.153652
$231$	2.58694	0.170208
$232$	62.4546	4.10034
$233$	0.725463	0.0475267	0.0237633	−	0.999718i	$-0.492435\pi$
$233$	0.725463	0.0475267	0.0237633	+	0.999718i	$0.492435\pi$
$234$	2.79555	0.182751
$235$	−7.47599	−0.487680
$236$	5.84855	0.380708
$237$	−3.05865	−0.198681
$238$	2.79555	0.181209
$239$	2.77678	0.179615	0.0898076	−	0.995959i	$-0.471375\pi$
$239$	2.77678	0.179615	0.0898076	+	0.995959i	$0.471375\pi$
$240$	31.8418	2.05538
$241$	−12.0915	−0.778880	−0.389440	−	0.921052i	$-0.627331\pi$
$241$	−12.0915	−0.778880	−0.389440	+	0.921052i	$0.627331\pi$
$242$	−12.0426	−0.774125
$243$	−1.00000	−0.0641500
$244$	24.9475	1.59710
$245$	−1.75095	−0.111864
$246$	−23.4686	−1.49630
$247$	4.83271	0.307498
$248$	−89.9332	−5.71076
$249$	5.80283	0.367739
$250$	33.9419	2.14668
$251$	−19.0788	−1.20425	−0.602123	−	0.798403i	$-0.705678\pi$
$251$	−19.0788	−1.20425	−0.602123	+	0.798403i	$0.705678\pi$
$252$	−5.81513	−0.366319
$253$	−1.23154	−0.0774260
$254$	−21.3933	−1.34234
$255$	−1.75095	−0.109649
$256$	103.209	6.45057
$257$	−0.329027	−0.0205241	−0.0102621	−	0.999947i	$-0.503267\pi$
$257$	−0.329027	−0.0205241	−0.0102621	+	0.999947i	$0.503267\pi$
$258$	−2.63627	−0.164127
$259$	5.27296	0.327646
$260$	−10.1820	−0.631460
$261$	5.85581	0.362466
$262$	29.1478	1.80075
$263$	−23.2069	−1.43100	−0.715498	−	0.698614i	$-0.753800\pi$
$263$	−23.2069	−1.43100	−0.715498	+	0.698614i	$0.753800\pi$
$264$	−27.5907	−1.69809
$265$	−18.2357	−1.12021
$266$	−13.5101	−0.828358
$267$	0.445811	0.0272832
$268$	1.52085	0.0929006
$269$	−19.8659	−1.21124	−0.605622	−	0.795752i	$-0.707076\pi$
$269$	−19.8659	−1.21124	−0.605622	+	0.795752i	$0.707076\pi$
$270$	4.89488	0.297893
$271$	−22.2046	−1.34883	−0.674416	−	0.738352i	$-0.735604\pi$
$271$	−22.2046	−1.34883	−0.674416	+	0.738352i	$0.735604\pi$
$272$	−18.1854	−1.10265
$273$	1.00000	0.0605228
$274$	−55.3400	−3.34321
$275$	−5.00359	−0.301728
$276$	2.76834	0.166635
$277$	−13.3777	−0.803787	−0.401893	−	0.915687i	$-0.631648\pi$
$277$	−13.3777	−0.803787	−0.401893	+	0.915687i	$0.631648\pi$
$278$	33.8848	2.03227
$279$	−8.43224	−0.504825
$280$	18.6746	1.11602
$281$	−12.8480	−0.766447	−0.383224	−	0.923656i	$-0.625186\pi$
$281$	−12.8480	−0.766447	−0.383224	+	0.923656i	$0.625186\pi$
$282$	−11.9361	−0.710785
$283$	7.78518	0.462781	0.231390	−	0.972861i	$-0.425673\pi$
$283$	7.78518	0.462781	0.231390	+	0.972861i	$0.425673\pi$
$284$	76.8826	4.56214
$285$	8.46183	0.501236
$286$	7.23193	0.427633
$287$	−8.39496	−0.495539
$288$	29.5076	1.73875
$289$	1.00000	0.0588235
$290$	−28.6635	−1.68318
$291$	−19.1782	−1.12425
$292$	−98.6450	−5.77276
$293$	−2.22408	−0.129932	−0.0649661	−	0.997887i	$-0.520694\pi$
$293$	−2.22408	−0.129932	−0.0649661	+	0.997887i	$0.520694\pi$
$294$	−2.79555	−0.163040
$295$	−1.76101	−0.102530
$296$	−56.2382	−3.26878
$297$	−2.58694	−0.150109
$298$	5.27649	0.305659
$299$	−0.476059	−0.0275312
$300$	11.2475	0.649373
$301$	−0.943022	−0.0543549
$302$	−12.3140	−0.708589
$303$	2.53507	0.145636
$304$	87.8850	5.04055
$305$	−7.51174	−0.430121
$306$	−2.79555	−0.159811
$307$	−7.92373	−0.452231	−0.226116	−	0.974100i	$-0.572603\pi$
$307$	−7.92373	−0.452231	−0.226116	+	0.974100i	$0.572603\pi$
$308$	−15.0434	−0.857176
$309$	−16.1086	−0.916388
$310$	41.2748	2.34425
$311$	−23.4505	−1.32975	−0.664877	−	0.746953i	$-0.731516\pi$
$311$	−23.4505	−1.32975	−0.664877	+	0.746953i	$0.731516\pi$
$312$	−10.6654	−0.603809
$313$	−8.35399	−0.472195	−0.236098	−	0.971729i	$-0.575869\pi$
$313$	−8.35399	−0.472195	−0.236098	+	0.971729i	$0.575869\pi$
$314$	−3.56906	−0.201414
$315$	1.75095	0.0986548
$316$	17.7865	1.00057
$317$	−21.6781	−1.21756	−0.608781	−	0.793339i	$-0.708341\pi$
$317$	−21.6781	−1.21756	−0.608781	+	0.793339i	$0.708341\pi$
$318$	−29.1150	−1.63269
$319$	15.1486	0.848160
$320$	−80.7525	−4.51420
$321$	15.0474	0.839862
$322$	1.33085	0.0741653
$323$	−4.83271	−0.268899
$324$	5.81513	0.323063
$325$	−1.93418	−0.107289
$326$	52.7508	2.92160
$327$	−9.31549	−0.515148
$328$	89.5356	4.94378
$329$	−4.26967	−0.235395
$330$	12.6627	0.697061
$331$	0.352403	0.0193698	0.00968492	−	0.999953i	$-0.496917\pi$
$331$	0.352403	0.0193698	0.00968492	+	0.999953i	$0.496917\pi$
$332$	−33.7442	−1.85195
$333$	−5.27296	−0.288956
$334$	−71.2543	−3.89886
$335$	−0.457932	−0.0250195
$336$	18.1854	0.992097
$337$	19.8837	1.08313	0.541567	−	0.840658i	$-0.317831\pi$
$337$	19.8837	1.08313	0.541567	+	0.840658i	$0.317831\pi$
$338$	2.79555	0.152058
$339$	17.4697	0.948826
$340$	10.1820	0.552196
$341$	−21.8137	−1.18128
$342$	13.5101	0.730543
$343$	−1.00000	−0.0539949
$344$	10.0577	0.542275
$345$	−0.833556	−0.0448771
$346$	−22.7936	−1.22539
$347$	22.5583	1.21099	0.605496	−	0.795849i	$-0.292975\pi$
$347$	22.5583	1.21099	0.605496	+	0.795849i	$0.292975\pi$
$348$	−34.0523	−1.82540
$349$	−5.19499	−0.278081	−0.139041	−	0.990287i	$-0.544402\pi$
$349$	−5.19499	−0.278081	−0.139041	+	0.990287i	$0.544402\pi$
$350$	5.40709	0.289021
$351$	−1.00000	−0.0533761
$352$	76.3344	4.06864
$353$	−6.74329	−0.358909	−0.179454	−	0.983766i	$-0.557433\pi$
$353$	−6.74329	−0.358909	−0.179454	+	0.983766i	$0.557433\pi$
$354$	−2.81162	−0.149436
$355$	−23.1495	−1.22865
$356$	−2.59245	−0.137399
$357$	−1.00000	−0.0529256
$358$	55.7804	2.94809
$359$	−35.6962	−1.88397	−0.941987	−	0.335648i	$-0.891045\pi$
$359$	−35.6962	−1.88397	−0.941987	+	0.335648i	$0.891045\pi$
$360$	−18.6746	−0.984236
$361$	4.35509	0.229215
$362$	14.0683	0.739412
$363$	4.30776	0.226099
$364$	−5.81513	−0.304795
$365$	29.7022	1.55469
$366$	−11.9932	−0.626895
$367$	29.9132	1.56146	0.780729	−	0.624870i	$-0.214848\pi$
$367$	29.9132	1.56146	0.780729	+	0.624870i	$0.214848\pi$
$368$	−8.65735	−0.451296
$369$	8.39496	0.437024
$370$	25.8105	1.34182
$371$	−10.4147	−0.540706
$372$	49.0345	2.54232
$373$	−1.18550	−0.0613828	−0.0306914	−	0.999529i	$-0.509771\pi$
$373$	−1.18550	−0.0613828	−0.0306914	+	0.999529i	$0.509771\pi$
$374$	−7.23193	−0.373954
$375$	−12.1414	−0.626979
$376$	45.5378	2.34843
$377$	5.85581	0.301590
$378$	2.79555	0.143788
$379$	−17.5616	−0.902080	−0.451040	−	0.892504i	$-0.648947\pi$
$379$	−17.5616	−0.902080	−0.451040	+	0.892504i	$0.648947\pi$
$380$	−49.2066	−2.52425
$381$	7.65262	0.392056
$382$	−19.2312	−0.983954
$383$	31.0401	1.58608	0.793038	−	0.609173i	$-0.208498\pi$
$383$	31.0401	1.58608	0.793038	+	0.609173i	$0.208498\pi$
$384$	−69.9137	−3.56777
$385$	4.52960	0.230850
$386$	37.9841	1.93334
$387$	0.943022	0.0479365
$388$	111.524	5.66175
$389$	−19.0845	−0.967623	−0.483811	−	0.875172i	$-0.660748\pi$
$389$	−19.0845	−0.967623	−0.483811	+	0.875172i	$0.660748\pi$
$390$	4.89488	0.247862
$391$	0.476059	0.0240753
$392$	10.6654	0.538684
$393$	−10.4265	−0.525946
$394$	−38.6974	−1.94954
$395$	−5.35555	−0.269467
$396$	15.0434	0.755958
$397$	−7.35930	−0.369353	−0.184676	−	0.982799i	$-0.559124\pi$
$397$	−7.35930	−0.369353	−0.184676	+	0.982799i	$0.559124\pi$
$398$	2.46807	0.123713
$399$	4.83271	0.241938
$400$	−35.1738	−1.75869
$401$	18.2384	0.910783	0.455391	−	0.890291i	$-0.349499\pi$
$401$	18.2384	0.910783	0.455391	+	0.890291i	$0.349499\pi$
$402$	−0.731131	−0.0364655
$403$	−8.43224	−0.420040
$404$	−14.7417	−0.733429
$405$	−1.75095	−0.0870054
$406$	−16.3703	−0.812442
$407$	−13.6408	−0.676150
$408$	10.6654	0.528016
$409$	−22.5609	−1.11556	−0.557782	−	0.829988i	$-0.688347\pi$
$409$	−22.5609	−1.11556	−0.557782	+	0.829988i	$0.688347\pi$
$410$	−41.0923	−2.02940
$411$	19.7957	0.976451
$412$	93.6738	4.61498
$413$	−1.00575	−0.0494896
$414$	−1.33085	−0.0654077
$415$	10.1605	0.498758
$416$	29.5076	1.44673
$417$	−12.1209	−0.593565
$418$	34.9498	1.70945
$419$	−7.06291	−0.345046	−0.172523	−	0.985006i	$-0.555192\pi$
$419$	−7.06291	−0.345046	−0.172523	+	0.985006i	$0.555192\pi$
$420$	−10.1820	−0.496830
$421$	25.3045	1.23326	0.616632	−	0.787251i	$-0.288496\pi$
$421$	25.3045	1.23326	0.616632	+	0.787251i	$0.288496\pi$
$422$	−39.5223	−1.92392
$423$	4.26967	0.207599
$424$	111.077	5.39439
$425$	1.93418	0.0938213
$426$	−36.9604	−1.79074
$427$	−4.29010	−0.207612
$428$	−87.5024	−4.22959
$429$	−2.58694	−0.124899
$430$	−4.61597	−0.222602
$431$	−0.417049	−0.0200885	−0.0100443	−	0.999950i	$-0.503197\pi$
$431$	−0.417049	−0.0200885	−0.0100443	+	0.999950i	$0.503197\pi$
$432$	−18.1854	−0.874948
$433$	19.9850	0.960418	0.480209	−	0.877154i	$-0.340561\pi$
$433$	19.9850	0.960418	0.480209	+	0.877154i	$0.340561\pi$
$434$	23.5728	1.13153
$435$	10.2532	0.491605
$436$	54.1707	2.59431
$437$	−2.30066	−0.110055
$438$	47.4224	2.26593
$439$	17.1111	0.816671	0.408335	−	0.912832i	$-0.366109\pi$
$439$	17.1111	0.816671	0.408335	+	0.912832i	$0.366109\pi$
$440$	−48.3099	−2.30309
$441$	1.00000	0.0476190
$442$	−2.79555	−0.132971
$443$	−25.0034	−1.18795	−0.593974	−	0.804484i	$-0.702442\pi$
$443$	−25.0034	−1.18795	−0.593974	+	0.804484i	$0.702442\pi$
$444$	30.6629	1.45520
$445$	0.780592	0.0370036
$446$	−64.9229	−3.07419
$447$	−1.88746	−0.0892737
$448$	−46.1193	−2.17893
$449$	−24.5923	−1.16058	−0.580292	−	0.814408i	$-0.697062\pi$
$449$	−24.5923	−1.16058	−0.580292	+	0.814408i	$0.697062\pi$
$450$	−5.40709	−0.254893
$451$	21.7172	1.02262
$452$	−101.589	−4.77833
$453$	4.40484	0.206957
$454$	−45.9870	−2.15828
$455$	1.75095	0.0820858
$456$	−51.5428	−2.41371
$457$	−4.73030	−0.221274	−0.110637	−	0.993861i	$-0.535289\pi$
$457$	−4.73030	−0.221274	−0.110637	+	0.993861i	$0.535289\pi$
$458$	56.9344	2.66037
$459$	1.00000	0.0466760
$460$	4.84723	0.226003
$461$	20.6129	0.960036	0.480018	−	0.877259i	$-0.340630\pi$
$461$	20.6129	0.960036	0.480018	+	0.877259i	$0.340630\pi$
$462$	7.23193	0.336460
$463$	−10.4991	−0.487935	−0.243968	−	0.969783i	$-0.578449\pi$
$463$	−10.4991	−0.487935	−0.243968	+	0.969783i	$0.578449\pi$
$464$	106.491	4.94370
$465$	−14.7644	−0.684684
$466$	2.02807	0.0939486
$467$	−2.14806	−0.0994006	−0.0497003	−	0.998764i	$-0.515827\pi$
$467$	−2.14806	−0.0994006	−0.0497003	+	0.998764i	$0.515827\pi$
$468$	5.81513	0.268804
$469$	−0.261533	−0.0120765
$470$	−20.8995	−0.964023
$471$	1.27669	0.0588268
$472$	10.7267	0.493737
$473$	2.43954	0.112170
$474$	−8.55063	−0.392744
$475$	−9.34731	−0.428884
$476$	5.81513	0.266536
$477$	10.4147	0.476858
$478$	7.76265	0.355055
$479$	5.89088	0.269161	0.134581	−	0.990903i	$-0.457031\pi$
$479$	5.89088	0.269161	0.134581	+	0.990903i	$0.457031\pi$
$480$	51.6664	2.35824
$481$	−5.27296	−0.240426
$482$	−33.8023	−1.53965
$483$	−0.476059	−0.0216614
$484$	−25.0501	−1.13864
$485$	−33.5800	−1.52479
$486$	−2.79555	−0.126809
$487$	11.8226	0.535732	0.267866	−	0.963456i	$-0.413682\pi$
$487$	11.8226	0.535732	0.267866	+	0.963456i	$0.413682\pi$
$488$	45.7556	2.07126
$489$	−18.8695	−0.853309
$490$	−4.89488	−0.221128
$491$	28.4184	1.28250	0.641251	−	0.767331i	$-0.278416\pi$
$491$	28.4184	1.28250	0.641251	+	0.767331i	$0.278416\pi$
$492$	−48.8178	−2.20087
$493$	−5.85581	−0.263733
$494$	13.5101	0.607848
$495$	−4.52960	−0.203590
$496$	−153.344	−6.88535
$497$	−13.2211	−0.593049
$498$	16.2221	0.726931
$499$	−24.1922	−1.08299	−0.541495	−	0.840704i	$-0.682142\pi$
$499$	−24.1922	−1.08299	−0.541495	+	0.840704i	$0.682142\pi$
$500$	70.6037	3.15749
$501$	25.4884	1.13874
$502$	−53.3360	−2.38050
$503$	12.5448	0.559346	0.279673	−	0.960095i	$-0.409774\pi$
$503$	12.5448	0.559346	0.279673	+	0.960095i	$0.409774\pi$
$504$	−10.6654	−0.475075
$505$	4.43877	0.197523
$506$	−3.44282	−0.153052
$507$	−1.00000	−0.0444116
$508$	−44.5010	−1.97441
$509$	1.34900	0.0597933	0.0298966	−	0.999553i	$-0.490482\pi$
$509$	1.34900	0.0597933	0.0298966	+	0.999553i	$0.490482\pi$
$510$	−4.89488	−0.216749
$511$	16.9635	0.750421
$512$	148.699	6.57164
$513$	−4.83271	−0.213369
$514$	−0.919813	−0.0405712
$515$	−28.2054	−1.24288
$516$	−5.48379	−0.241410
$517$	11.0454	0.485775
$518$	14.7408	0.647675
$519$	8.15350	0.357899
$520$	−18.6746	−0.818934
$521$	39.8350	1.74520	0.872601	−	0.488433i	$-0.162431\pi$
$521$	39.8350	1.74520	0.872601	+	0.488433i	$0.162431\pi$
$522$	16.3703	0.716506
$523$	−6.98667	−0.305506	−0.152753	−	0.988264i	$-0.548814\pi$
$523$	−6.98667	−0.305506	−0.152753	+	0.988264i	$0.548814\pi$
$524$	60.6312	2.64869
$525$	−1.93418	−0.0844143
$526$	−64.8761	−2.82873
$527$	8.43224	0.367314
$528$	−47.0446	−2.04735
$529$	−22.7734	−0.990146
$530$	−50.9788	−2.21438
$531$	1.00575	0.0436458
$532$	−28.1028	−1.21841
$533$	8.39496	0.363626
$534$	1.24629	0.0539322
$535$	26.3472	1.13909
$536$	2.78936	0.120482
$537$	−19.9533	−0.861046
$538$	−55.5362	−2.39433
$539$	2.58694	0.111427
$540$	10.1820	0.438163
$541$	5.03954	0.216667	0.108333	−	0.994115i	$-0.465449\pi$
$541$	5.03954	0.216667	0.108333	+	0.994115i	$0.465449\pi$
$542$	−62.0741	−2.66631
$543$	−5.03237	−0.215960
$544$	−29.5076	−1.26513
$545$	−16.3109	−0.698684
$546$	2.79555	0.119639
$547$	−29.4868	−1.26076	−0.630381	−	0.776286i	$-0.717101\pi$
$547$	−29.4868	−1.26076	−0.630381	+	0.776286i	$0.717101\pi$
$548$	−115.115	−4.91745
$549$	4.29010	0.183097
$550$	−13.9878	−0.596442
$551$	28.2995	1.20560
$552$	5.07736	0.216107
$553$	−3.05865	−0.130067
$554$	−37.3980	−1.58889
$555$	−9.23268	−0.391906
$556$	70.4849	2.98922
$557$	−4.70256	−0.199254	−0.0996269	−	0.995025i	$-0.531765\pi$
$557$	−4.70256	−0.199254	−0.0996269	+	0.995025i	$0.531765\pi$
$558$	−23.5728	−0.997916
$559$	0.943022	0.0398856
$560$	31.8418	1.34556
$561$	2.58694	0.109221
$562$	−35.9173	−1.51508
$563$	42.3274	1.78389	0.891945	−	0.452145i	$-0.149341\pi$
$563$	42.3274	1.78389	0.891945	+	0.452145i	$0.149341\pi$
$564$	−24.8287	−1.04548
$565$	30.5886	1.28687
$566$	21.7639	0.914805
$567$	−1.00000	−0.0419961
$568$	141.009	5.91659
$569$	−43.3003	−1.81524	−0.907622	−	0.419788i	$-0.862104\pi$
$569$	−43.3003	−1.81524	−0.907622	+	0.419788i	$0.862104\pi$
$570$	23.6555	0.990821
$571$	−42.8967	−1.79517	−0.897584	−	0.440842i	$-0.854680\pi$
$571$	−42.8967	−1.79517	−0.897584	+	0.440842i	$0.854680\pi$
$572$	15.0434	0.628995
$573$	6.87921	0.287383
$574$	−23.4686	−0.979559
$575$	0.920782	0.0383993
$576$	46.1193	1.92164
$577$	25.6736	1.06881	0.534403	−	0.845230i	$-0.320537\pi$
$577$	25.6736	1.06881	0.534403	+	0.845230i	$0.320537\pi$
$578$	2.79555	0.116280
$579$	−13.5873	−0.564670
$580$	−59.6239	−2.47575
$581$	5.80283	0.240742
$582$	−53.6137	−2.22236
$583$	26.9423	1.11583
$584$	−180.923	−7.48663
$585$	−1.75095	−0.0723929
$586$	−6.21754	−0.256844
$587$	11.0845	0.457508	0.228754	−	0.973484i	$-0.426535\pi$
$587$	11.0845	0.457508	0.228754	+	0.973484i	$0.426535\pi$
$588$	−5.81513	−0.239812
$589$	−40.7506	−1.67910
$590$	−4.92301	−0.202677
$591$	13.8425	0.569403
$592$	−95.8911	−3.94110
$593$	6.38440	0.262176	0.131088	−	0.991371i	$-0.458153\pi$
$593$	6.38440	0.262176	0.131088	+	0.991371i	$0.458153\pi$
$594$	−7.23193	−0.296729
$595$	−1.75095	−0.0717819
$596$	10.9758	0.449586
$597$	−0.882856	−0.0361329
$598$	−1.33085	−0.0544225
$599$	−10.5596	−0.431455	−0.215727	−	0.976454i	$-0.569212\pi$
$599$	−10.5596	−0.431455	−0.215727	+	0.976454i	$0.569212\pi$
$600$	20.6287	0.842165
$601$	−28.0165	−1.14282	−0.571409	−	0.820666i	$-0.693603\pi$
$601$	−28.0165	−1.14282	−0.571409	+	0.820666i	$0.693603\pi$
$602$	−2.63627	−0.107446
$603$	0.261533	0.0106505
$604$	−25.6147	−1.04225
$605$	7.54266	0.306653
$606$	7.08692	0.287886
$607$	−21.8816	−0.888148	−0.444074	−	0.895990i	$-0.646467\pi$
$607$	−21.8816	−0.888148	−0.444074	+	0.895990i	$0.646467\pi$
$608$	142.602	5.78327
$609$	5.85581	0.237290
$610$	−20.9995	−0.850244
$611$	4.26967	0.172733
$612$	−5.81513	−0.235063
$613$	17.4532	0.704929	0.352464	−	0.935825i	$-0.385344\pi$
$613$	17.4532	0.704929	0.352464	+	0.935825i	$0.385344\pi$
$614$	−22.1512	−0.893951
$615$	14.6992	0.592727
$616$	−27.5907	−1.11166
$617$	22.1205	0.890539	0.445269	−	0.895397i	$-0.353108\pi$
$617$	22.1205	0.890539	0.445269	+	0.895397i	$0.353108\pi$
$618$	−45.0326	−1.81148
$619$	38.3616	1.54188	0.770941	−	0.636906i	$-0.219786\pi$
$619$	38.3616	1.54188	0.770941	+	0.636906i	$0.219786\pi$
$620$	85.8570	3.44810
$621$	0.476059	0.0191036
$622$	−65.5571	−2.62860
$623$	0.445811	0.0178610
$624$	−18.1854	−0.728001
$625$	−11.5881	−0.463524
$626$	−23.3540	−0.933415
$627$	−12.5019	−0.499279
$628$	−7.42412	−0.296255
$629$	5.27296	0.210247
$630$	4.89488	0.195017
$631$	22.1342	0.881149	0.440574	−	0.897716i	$-0.354775\pi$
$631$	22.1342	0.881149	0.440574	+	0.897716i	$0.354775\pi$
$632$	32.6218	1.29762
$633$	14.1376	0.561918
$634$	−60.6022	−2.40682
$635$	13.3994	0.531737
$636$	−60.5630	−2.40148
$637$	1.00000	0.0396214
$638$	42.3488	1.67661
$639$	13.2211	0.523020
$640$	−122.415	−4.83889
$641$	−24.1124	−0.952383	−0.476192	−	0.879342i	$-0.657983\pi$
$641$	−24.1124	−0.952383	−0.476192	+	0.879342i	$0.657983\pi$
$642$	42.0658	1.66020
$643$	−45.8085	−1.80651	−0.903255	−	0.429105i	$-0.858829\pi$
$643$	−45.8085	−1.80651	−0.903255	+	0.429105i	$0.858829\pi$
$644$	2.76834	0.109088
$645$	1.65118	0.0650153
$646$	−13.5101	−0.531548
$647$	−33.1952	−1.30504	−0.652519	−	0.757772i	$-0.726288\pi$
$647$	−33.1952	−1.30504	−0.652519	+	0.757772i	$0.726288\pi$
$648$	10.6654	0.418976
$649$	2.60181	0.102130
$650$	−5.40709	−0.212084
$651$	−8.43224	−0.330486
$652$	109.729	4.29731
$653$	−11.5482	−0.451917	−0.225959	−	0.974137i	$-0.572551\pi$
$653$	−11.5482	−0.451917	−0.225959	+	0.974137i	$0.572551\pi$
$654$	−26.0420	−1.01832
$655$	−18.2562	−0.713330
$656$	152.666	5.96061
$657$	−16.9635	−0.661809
$658$	−11.9361	−0.465318
$659$	−10.3428	−0.402899	−0.201450	−	0.979499i	$-0.564565\pi$
$659$	−10.3428	−0.402899	−0.201450	+	0.979499i	$0.564565\pi$
$660$	26.3402	1.02529
$661$	3.72335	0.144822	0.0724108	−	0.997375i	$-0.476931\pi$
$661$	3.72335	0.144822	0.0724108	+	0.997375i	$0.476931\pi$
$662$	0.985163	0.0382894
$663$	1.00000	0.0388368
$664$	−61.8895	−2.40178
$665$	8.46183	0.328136
$666$	−14.7408	−0.571196
$667$	−2.78771	−0.107941
$668$	−148.218	−5.73474
$669$	23.2236	0.897877
$670$	−1.28017	−0.0494574
$671$	11.0982	0.428442
$672$	29.5076	1.13828
$673$	−16.1378	−0.622065	−0.311033	−	0.950399i	$-0.600675\pi$
$673$	−16.1378	−0.622065	−0.311033	+	0.950399i	$0.600675\pi$
$674$	55.5859	2.14109
$675$	1.93418	0.0744464
$676$	5.81513	0.223659
$677$	−11.2792	−0.433495	−0.216748	−	0.976228i	$-0.569545\pi$
$677$	−11.2792	−0.433495	−0.216748	+	0.976228i	$0.569545\pi$
$678$	48.8376	1.87560
$679$	−19.1782	−0.735991
$680$	18.6746	0.716137
$681$	16.4500	0.630367
$682$	−60.9813	−2.33510
$683$	−20.3970	−0.780468	−0.390234	−	0.920716i	$-0.627606\pi$
$683$	−20.3970	−0.780468	−0.390234	+	0.920716i	$0.627606\pi$
$684$	28.1028	1.07454
$685$	34.6613	1.32434
$686$	−2.79555	−0.106735
$687$	−20.3660	−0.777013
$688$	17.1493	0.653810
$689$	10.4147	0.396770
$690$	−2.33025	−0.0887111
$691$	17.4533	0.663954	0.331977	−	0.943287i	$-0.392284\pi$
$691$	17.4533	0.663954	0.331977	+	0.943287i	$0.392284\pi$
$692$	−47.4137	−1.80240
$693$	−2.58694	−0.0982696
$694$	63.0629	2.39383
$695$	−21.2232	−0.805041
$696$	−62.4546	−2.36734
$697$	−8.39496	−0.317982
$698$	−14.5229	−0.549699
$699$	−0.725463	−0.0274395
$700$	11.2475	0.425115
$701$	20.8074	0.785883	0.392941	−	0.919564i	$-0.371458\pi$
$701$	20.8074	0.785883	0.392941	+	0.919564i	$0.371458\pi$
$702$	−2.79555	−0.105511
$703$	−25.4827	−0.961097
$704$	119.308	4.49658
$705$	7.47599	0.281562
$706$	−18.8512	−0.709475
$707$	2.53507	0.0953410
$708$	−5.84855	−0.219802
$709$	38.9191	1.46164	0.730818	−	0.682572i	$-0.239139\pi$
$709$	38.9191	1.46164	0.730818	+	0.682572i	$0.239139\pi$
$710$	−64.7158	−2.42874
$711$	3.05865	0.114708
$712$	−4.75475	−0.178192
$713$	4.01424	0.150335
$714$	−2.79555	−0.104621
$715$	−4.52960	−0.169397
$716$	116.031	4.33627
$717$	−2.77678	−0.103701
$718$	−99.7908	−3.72416
$719$	4.78927	0.178610	0.0893048	−	0.996004i	$-0.471535\pi$
$719$	4.78927	0.178610	0.0893048	+	0.996004i	$0.471535\pi$
$720$	−31.8418	−1.18667
$721$	−16.1086	−0.599917
$722$	12.1749	0.453103
$723$	12.0915	0.449686
$724$	29.2639	1.08758
$725$	−11.3262	−0.420644
$726$	12.0426	0.446942
$727$	42.4230	1.57338	0.786691	−	0.617347i	$-0.211793\pi$
$727$	42.4230	1.57338	0.786691	+	0.617347i	$0.211793\pi$
$728$	−10.6654	−0.395286
$729$	1.00000	0.0370370
$730$	83.0343	3.07324
$731$	−0.943022	−0.0348789
$732$	−24.9475	−0.922084
$733$	−8.26981	−0.305453	−0.152726	−	0.988269i	$-0.548805\pi$
$733$	−8.26981	−0.305453	−0.152726	+	0.988269i	$0.548805\pi$
$734$	83.6241	3.08662
$735$	1.75095	0.0645847
$736$	−14.0474	−0.517793
$737$	0.676570	0.0249218
$738$	23.4686	0.863890
$739$	−14.6572	−0.539173	−0.269586	−	0.962976i	$-0.586887\pi$
$739$	−14.6572	−0.539173	−0.269586	+	0.962976i	$0.586887\pi$
$740$	53.6892	1.97365
$741$	−4.83271	−0.177534
$742$	−29.1150	−1.06884
$743$	30.2896	1.11122	0.555609	−	0.831444i	$-0.312485\pi$
$743$	30.2896	1.11122	0.555609	+	0.831444i	$0.312485\pi$
$744$	89.9332	3.29711
$745$	−3.30484	−0.121080
$746$	−3.31413	−0.121339
$747$	−5.80283	−0.212314
$748$	−15.0434	−0.550040
$749$	15.0474	0.549819
$750$	−33.9419	−1.23938
$751$	31.1400	1.13631	0.568157	−	0.822920i	$-0.307656\pi$
$751$	31.1400	1.13631	0.568157	+	0.822920i	$0.307656\pi$
$752$	77.6459	2.83146
$753$	19.0788	0.695272
$754$	16.3703	0.596169
$755$	7.71265	0.280692
$756$	5.81513	0.211494
$757$	47.1930	1.71526	0.857629	−	0.514269i	$-0.171937\pi$
$757$	47.1930	1.71526	0.857629	+	0.514269i	$0.171937\pi$
$758$	−49.0945	−1.78319
$759$	1.23154	0.0447019
$760$	−90.2488	−3.27367
$761$	−50.2780	−1.82258	−0.911289	−	0.411768i	$-0.864912\pi$
$761$	−50.2780	−1.82258	−0.911289	+	0.411768i	$0.864912\pi$
$762$	21.3933	0.774998
$763$	−9.31549	−0.337243
$764$	−40.0035	−1.44727
$765$	1.75095	0.0633057
$766$	86.7743	3.13528
$767$	1.00575	0.0363155
$768$	−103.209	−3.72424
$769$	37.9801	1.36960	0.684798	−	0.728733i	$-0.259890\pi$
$769$	37.9801	1.36960	0.684798	+	0.728733i	$0.259890\pi$
$770$	12.6627	0.456333
$771$	0.329027	0.0118496
$772$	79.0121	2.84371
$773$	−10.0837	−0.362686	−0.181343	−	0.983420i	$-0.558044\pi$
$773$	−10.0837	−0.362686	−0.181343	+	0.983420i	$0.558044\pi$
$774$	2.63627	0.0947587
$775$	16.3094	0.585852
$776$	204.543	7.34266
$777$	−5.27296	−0.189166
$778$	−53.3518	−1.91275
$779$	40.5704	1.45359
$780$	10.1820	0.364574
$781$	34.2022	1.22385
$782$	1.33085	0.0475911
$783$	−5.85581	−0.209270
$784$	18.1854	0.649480
$785$	2.23542	0.0797857
$786$	−29.1478	−1.03967
$787$	−12.6556	−0.451124	−0.225562	−	0.974229i	$-0.572422\pi$
$787$	−12.6556	−0.451124	−0.225562	+	0.974229i	$0.572422\pi$
$788$	−80.4957	−2.86754
$789$	23.2069	0.826186
$790$	−14.9717	−0.532670
$791$	17.4697	0.621152
$792$	27.5907	0.980393
$793$	4.29010	0.152346
$794$	−20.5733	−0.730120
$795$	18.2357	0.646753
$796$	5.13392	0.181967
$797$	−20.4248	−0.723482	−0.361741	−	0.932279i	$-0.617818\pi$
$797$	−20.4248	−0.723482	−0.361741	+	0.932279i	$0.617818\pi$
$798$	13.5101	0.478253
$799$	−4.26967	−0.151050
$800$	−57.0729	−2.01783
$801$	−0.445811	−0.0157520
$802$	50.9865	1.80040
$803$	−43.8835	−1.54862
$804$	−1.52085	−0.0536362
$805$	−0.833556	−0.0293790
$806$	−23.5728	−0.830316
$807$	19.8659	0.699312
$808$	−27.0375	−0.951176
$809$	−29.8395	−1.04910	−0.524551	−	0.851379i	$-0.675767\pi$
$809$	−29.8395	−1.04910	−0.524551	+	0.851379i	$0.675767\pi$
$810$	−4.89488	−0.171988
$811$	20.8849	0.733367	0.366683	−	0.930346i	$-0.380493\pi$
$811$	20.8849	0.733367	0.366683	+	0.930346i	$0.380493\pi$
$812$	−34.0523	−1.19500
$813$	22.2046	0.778748
$814$	−38.1336	−1.33658
$815$	−33.0396	−1.15733
$816$	18.1854	0.636618
$817$	4.55735	0.159442
$818$	−63.0702	−2.20520
$819$	−1.00000	−0.0349428
$820$	−85.4774	−2.98500
$821$	−11.3782	−0.397102	−0.198551	−	0.980091i	$-0.563624\pi$
$821$	−11.3782	−0.397102	−0.198551	+	0.980091i	$0.563624\pi$
$822$	55.3400	1.93021
$823$	52.3915	1.82625	0.913127	−	0.407675i	$-0.133660\pi$
$823$	52.3915	1.82625	0.913127	+	0.407675i	$0.133660\pi$
$824$	171.805	5.98511
$825$	5.00359	0.174203
$826$	−2.81162	−0.0978289
$827$	18.7895	0.653375	0.326687	−	0.945132i	$-0.394068\pi$
$827$	18.7895	0.653375	0.326687	+	0.945132i	$0.394068\pi$
$828$	−2.76834	−0.0962066
$829$	−8.08412	−0.280773	−0.140387	−	0.990097i	$-0.544835\pi$
$829$	−8.08412	−0.280773	−0.140387	+	0.990097i	$0.544835\pi$
$830$	28.4041	0.985922
$831$	13.3777	0.464066
$832$	46.1193	1.59890
$833$	−1.00000	−0.0346479
$834$	−33.8848	−1.17333
$835$	44.6289	1.54445
$836$	72.7003	2.51439
$837$	8.43224	0.291461
$838$	−19.7447	−0.682071
$839$	25.2693	0.872394	0.436197	−	0.899851i	$-0.356325\pi$
$839$	25.2693	0.872394	0.436197	+	0.899851i	$0.356325\pi$
$840$	−18.6746	−0.644334
$841$	5.29057	0.182433
$842$	70.7401	2.43786
$843$	12.8480	0.442509
$844$	−82.2117	−2.82984
$845$	−1.75095	−0.0602345
$846$	11.9361	0.410372
$847$	4.30776	0.148016
$848$	189.397	6.50391
$849$	−7.78518	−0.267187
$850$	5.40709	0.185462
$851$	2.51024	0.0860499
$852$	−76.8826	−2.63395
$853$	−41.6819	−1.42716	−0.713580	−	0.700574i	$-0.752927\pi$
$853$	−41.6819	−1.42716	−0.713580	+	0.700574i	$0.752927\pi$
$854$	−11.9932	−0.410399
$855$	−8.46183	−0.289389
$856$	−160.486	−5.48530
$857$	−23.1368	−0.790338	−0.395169	−	0.918608i	$-0.629314\pi$
$857$	−23.1368	−0.790338	−0.395169	+	0.918608i	$0.629314\pi$
$858$	−7.23193	−0.246894
$859$	12.7623	0.435445	0.217722	−	0.976011i	$-0.430137\pi$
$859$	12.7623	0.435445	0.217722	+	0.976011i	$0.430137\pi$
$860$	−9.60184	−0.327420
$861$	8.39496	0.286100
$862$	−1.16588	−0.0397101
$863$	15.7463	0.536010	0.268005	−	0.963418i	$-0.413636\pi$
$863$	15.7463	0.536010	0.268005	+	0.963418i	$0.413636\pi$
$864$	−29.5076	−1.00387
$865$	14.2764	0.485411
$866$	55.8692	1.89851
$867$	−1.00000	−0.0339618
$868$	49.0345	1.66434
$869$	7.91254	0.268415
$870$	28.6635	0.971783
$871$	0.261533	0.00886172
$872$	99.3533	3.36453
$873$	19.1782	0.649083
$874$	−6.43161	−0.217552
$875$	−12.1414	−0.410454
$876$	98.6450	3.33290
$877$	−8.24156	−0.278298	−0.139149	−	0.990271i	$-0.544437\pi$
$877$	−8.24156	−0.278298	−0.139149	+	0.990271i	$0.544437\pi$
$878$	47.8352	1.61436
$879$	2.22408	0.0750164
$880$	−82.3727	−2.77678
$881$	−11.9653	−0.403121	−0.201561	−	0.979476i	$-0.564601\pi$
$881$	−11.9653	−0.403121	−0.201561	+	0.979476i	$0.564601\pi$
$882$	2.79555	0.0941312
$883$	53.2977	1.79361	0.896806	−	0.442425i	$-0.145882\pi$
$883$	53.2977	1.79361	0.896806	+	0.442425i	$0.145882\pi$
$884$	−5.81513	−0.195584
$885$	1.76101	0.0591958
$886$	−69.8984	−2.34828
$887$	8.20307	0.275432	0.137716	−	0.990472i	$-0.456024\pi$
$887$	8.20307	0.275432	0.137716	+	0.990472i	$0.456024\pi$
$888$	56.2382	1.88723
$889$	7.65262	0.256661
$890$	2.18219	0.0731471
$891$	2.58694	0.0866657
$892$	−135.048	−4.52175
$893$	20.6341	0.690494
$894$	−5.27649	−0.176472
$895$	−34.9371	−1.16782
$896$	−69.9137	−2.33565
$897$	0.476059	0.0158952
$898$	−68.7493	−2.29419
$899$	−49.3776	−1.64684
$900$	−11.2475	−0.374916
$901$	−10.4147	−0.346965
$902$	60.7117	2.02148
$903$	0.943022	0.0313818
$904$	−186.322	−6.19697
$905$	−8.81143	−0.292902
$906$	12.3140	0.409104
$907$	16.4740	0.547009	0.273505	−	0.961871i	$-0.411817\pi$
$907$	16.4740	0.547009	0.273505	+	0.961871i	$0.411817\pi$
$908$	−95.6591	−3.17456
$909$	−2.53507	−0.0840829
$910$	4.89488	0.162264
$911$	−42.3402	−1.40279	−0.701397	−	0.712771i	$-0.747440\pi$
$911$	−42.3402	−1.40279	−0.701397	+	0.712771i	$0.747440\pi$
$912$	−87.8850	−2.91016
$913$	−15.0116	−0.496810
$914$	−13.2238	−0.437405
$915$	7.51174	0.248331
$916$	118.431	3.91307
$917$	−10.4265	−0.344312
$918$	2.79555	0.0922671
$919$	20.2720	0.668710	0.334355	−	0.942447i	$-0.391482\pi$
$919$	20.2720	0.668710	0.334355	+	0.942447i	$0.391482\pi$
$920$	8.89020	0.293101
$921$	7.92373	0.261096
$922$	57.6244	1.89776
$923$	13.2211	0.435179
$924$	15.0434	0.494891
$925$	10.1988	0.335335
$926$	−29.3509	−0.964529
$927$	16.1086	0.529077
$928$	172.791	5.67215
$929$	44.0783	1.44616	0.723081	−	0.690763i	$-0.242725\pi$
$929$	44.0783	1.44616	0.723081	+	0.690763i	$0.242725\pi$
$930$	−41.2748	−1.35345
$931$	4.83271	0.158386
$932$	4.21866	0.138187
$933$	23.4505	0.767734
$934$	−6.00503	−0.196491
$935$	4.52960	0.148134
$936$	10.6654	0.348609
$937$	−15.7633	−0.514963	−0.257482	−	0.966283i	$-0.582893\pi$
$937$	−15.7633	−0.514963	−0.257482	+	0.966283i	$0.582893\pi$
$938$	−0.731131	−0.0238723
$939$	8.35399	0.272622
$940$	−43.4738	−1.41796
$941$	3.00286	0.0978904	0.0489452	−	0.998801i	$-0.484414\pi$
$941$	3.00286	0.0978904	0.0489452	+	0.998801i	$0.484414\pi$
$942$	3.56906	0.116286
$943$	−3.99650	−0.130144
$944$	18.2900	0.595288
$945$	−1.75095	−0.0569584
$946$	6.81986	0.221733
$947$	−1.59706	−0.0518975	−0.0259488	−	0.999663i	$-0.508261\pi$
$947$	−1.59706	−0.0518975	−0.0259488	+	0.999663i	$0.508261\pi$
$948$	−17.7865	−0.577677
$949$	−16.9635	−0.550659
$950$	−26.1309	−0.847799
$951$	21.6781	0.702959
$952$	10.6654	0.345667
$953$	−18.7157	−0.606260	−0.303130	−	0.952949i	$-0.598032\pi$
$953$	−18.7157	−0.606260	−0.303130	+	0.952949i	$0.598032\pi$
$954$	29.1150	0.942632
$955$	12.0451	0.389772
$956$	16.1474	0.522243
$957$	−15.1486	−0.489686
$958$	16.4683	0.532066
$959$	19.7957	0.639237
$960$	80.7525	2.60628
$961$	40.1027	1.29363
$962$	−14.7408	−0.475264
$963$	−15.0474	−0.484895
$964$	−70.3134	−2.26464
$965$	−23.7907	−0.765851
$966$	−1.33085	−0.0428194
$967$	−37.0107	−1.19018	−0.595092	−	0.803657i	$-0.702885\pi$
$967$	−37.0107	−1.19018	−0.595092	+	0.803657i	$0.702885\pi$
$968$	−45.9439	−1.47669
$969$	4.83271	0.155249
$970$	−93.8748	−3.01414
$971$	23.6643	0.759425	0.379712	−	0.925105i	$-0.376023\pi$
$971$	23.6643	0.759425	0.379712	+	0.925105i	$0.376023\pi$
$972$	−5.81513	−0.186520
$973$	−12.1209	−0.388580
$974$	33.0506	1.05901
$975$	1.93418	0.0619432
$976$	78.0173	2.49727
$977$	−48.2605	−1.54399	−0.771995	−	0.635628i	$-0.780741\pi$
$977$	−48.2605	−1.54399	−0.771995	+	0.635628i	$0.780741\pi$
$978$	−52.7508	−1.68678
$979$	−1.15328	−0.0368591
$980$	−10.1820	−0.325252
$981$	9.31549	0.297421
$982$	79.4451	2.53520
$983$	26.9408	0.859278	0.429639	−	0.903001i	$-0.358641\pi$
$983$	26.9408	0.859278	0.429639	+	0.903001i	$0.358641\pi$
$984$	−89.5356	−2.85429
$985$	24.2374	0.772269
$986$	−16.3703	−0.521335
$987$	4.26967	0.135905
$988$	28.1028	0.894070
$989$	−0.448934	−0.0142753
$990$	−12.6627	−0.402448
$991$	20.4839	0.650694	0.325347	−	0.945595i	$-0.394519\pi$
$991$	20.4839	0.650694	0.325347	+	0.945595i	$0.394519\pi$
$992$	−248.815	−7.89989
$993$	−0.352403	−0.0111832
$994$	−36.9604	−1.17231
$995$	−1.54584	−0.0490063
$996$	33.7442	1.06923
$997$	37.2934	1.18109	0.590547	−	0.807003i	$-0.298912\pi$
$997$	37.2934	1.18109	0.590547	+	0.807003i	$0.298912\pi$
$998$	−67.6305	−2.14081
$999$	5.27296	0.166829

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.ba.1.17	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.ba.1.17	✓	17	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:	\( N \)	\(=\)	\( 4641 = 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4641.a (trivial)

\(f(q)\)	\(=\)	\(q+2.79555 q^{2} -1.00000 q^{3} +5.81513 q^{4} -1.75095 q^{5} -2.79555 q^{6} -1.00000 q^{7} +10.6654 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.79555 q^{2} -1.00000 q^{3} +5.81513 q^{4} -1.75095 q^{5} -2.79555 q^{6} -1.00000 q^{7} +10.6654 q^{8} +1.00000 q^{9} -4.89488 q^{10} +2.58694 q^{11} -5.81513 q^{12} +1.00000 q^{13} -2.79555 q^{14} +1.75095 q^{15} +18.1854 q^{16} -1.00000 q^{17} +2.79555 q^{18} +4.83271 q^{19} -10.1820 q^{20} +1.00000 q^{21} +7.23193 q^{22} -0.476059 q^{23} -10.6654 q^{24} -1.93418 q^{25} +2.79555 q^{26} -1.00000 q^{27} -5.81513 q^{28} +5.85581 q^{29} +4.89488 q^{30} -8.43224 q^{31} +29.5076 q^{32} -2.58694 q^{33} -2.79555 q^{34} +1.75095 q^{35} +5.81513 q^{36} -5.27296 q^{37} +13.5101 q^{38} -1.00000 q^{39} -18.6746 q^{40} +8.39496 q^{41} +2.79555 q^{42} +0.943022 q^{43} +15.0434 q^{44} -1.75095 q^{45} -1.33085 q^{46} +4.26967 q^{47} -18.1854 q^{48} +1.00000 q^{49} -5.40709 q^{50} +1.00000 q^{51} +5.81513 q^{52} +10.4147 q^{53} -2.79555 q^{54} -4.52960 q^{55} -10.6654 q^{56} -4.83271 q^{57} +16.3703 q^{58} +1.00575 q^{59} +10.1820 q^{60} +4.29010 q^{61} -23.5728 q^{62} -1.00000 q^{63} +46.1193 q^{64} -1.75095 q^{65} -7.23193 q^{66} +0.261533 q^{67} -5.81513 q^{68} +0.476059 q^{69} +4.89488 q^{70} +13.2211 q^{71} +10.6654 q^{72} -16.9635 q^{73} -14.7408 q^{74} +1.93418 q^{75} +28.1028 q^{76} -2.58694 q^{77} -2.79555 q^{78} +3.05865 q^{79} -31.8418 q^{80} +1.00000 q^{81} +23.4686 q^{82} -5.80283 q^{83} +5.81513 q^{84} +1.75095 q^{85} +2.63627 q^{86} -5.85581 q^{87} +27.5907 q^{88} -0.445811 q^{89} -4.89488 q^{90} -1.00000 q^{91} -2.76834 q^{92} +8.43224 q^{93} +11.9361 q^{94} -8.46183 q^{95} -29.5076 q^{96} +19.1782 q^{97} +2.79555 q^{98} +2.58694 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9} - q^{10} + 4 q^{11} - 25 q^{12} + 17 q^{13} - q^{14} + 4 q^{15} + 53 q^{16} - 17 q^{17} + q^{18} + 13 q^{19} - 5 q^{20} + 17 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} + 37 q^{25} + q^{26} - 17 q^{27} - 25 q^{28} - 3 q^{29} + q^{30} + 10 q^{31} + 18 q^{32} - 4 q^{33} - q^{34} + 4 q^{35} + 25 q^{36} - 25 q^{38} - 17 q^{39} - 12 q^{41} + q^{42} + 29 q^{43} + 12 q^{44} - 4 q^{45} + 19 q^{46} - 4 q^{47} - 53 q^{48} + 17 q^{49} + 9 q^{50} + 17 q^{51} + 25 q^{52} - 8 q^{53} - q^{54} + 27 q^{55} - 6 q^{56} - 13 q^{57} + 2 q^{58} + 25 q^{59} + 5 q^{60} - 5 q^{61} - 37 q^{62} - 17 q^{63} + 94 q^{64} - 4 q^{65} - 4 q^{66} + 15 q^{67} - 25 q^{68} - 8 q^{69} + q^{70} + 32 q^{71} + 6 q^{72} - 15 q^{73} + 16 q^{74} - 37 q^{75} + 3 q^{76} - 4 q^{77} - q^{78} + 27 q^{79} + 41 q^{80} + 17 q^{81} - 8 q^{82} - 24 q^{83} + 25 q^{84} + 4 q^{85} + 53 q^{86} + 3 q^{87} - 9 q^{88} - 8 q^{89} - q^{90} - 17 q^{91} + 14 q^{92} - 10 q^{93} + 51 q^{94} - 9 q^{95} - 18 q^{96} - 22 q^{97} + q^{98} + 4 q^{99}+O(q^{100}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9 - q^10 + 4 * q^11 - 25 * q^12 + 17 * q^13 - q^14 + 4 * q^15 + 53 * q^16 - 17 * q^17 + q^18 + 13 * q^19 - 5 * q^20 + 17 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 + 37 * q^25 + q^26 - 17 * q^27 - 25 * q^28 - 3 * q^29 + q^30 + 10 * q^31 + 18 * q^32 - 4 * q^33 - q^34 + 4 * q^35 + 25 * q^36 - 25 * q^38 - 17 * q^39 - 12 * q^41 + q^42 + 29 * q^43 + 12 * q^44 - 4 * q^45 + 19 * q^46 - 4 * q^47 - 53 * q^48 + 17 * q^49 + 9 * q^50 + 17 * q^51 + 25 * q^52 - 8 * q^53 - q^54 + 27 * q^55 - 6 * q^56 - 13 * q^57 + 2 * q^58 + 25 * q^59 + 5 * q^60 - 5 * q^61 - 37 * q^62 - 17 * q^63 + 94 * q^64 - 4 * q^65 - 4 * q^66 + 15 * q^67 - 25 * q^68 - 8 * q^69 + q^70 + 32 * q^71 + 6 * q^72 - 15 * q^73 + 16 * q^74 - 37 * q^75 + 3 * q^76 - 4 * q^77 - q^78 + 27 * q^79 + 41 * q^80 + 17 * q^81 - 8 * q^82 - 24 * q^83 + 25 * q^84 + 4 * q^85 + 53 * q^86 + 3 * q^87 - 9 * q^88 - 8 * q^89 - q^90 - 17 * q^91 + 14 * q^92 - 10 * q^93 + 51 * q^94 - 9 * q^95 - 18 * q^96 - 22 * q^97 + q^98 + 4 * q^99

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