LMFDB - Embedded newform 4641.2.a.ba.1.7

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			1.7
Root			$-0.524651$ 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)

$f(q)$	$=$	$q-0.524651 q^{2} -1.00000 q^{3} -1.72474 q^{4} -2.36230 q^{5} +0.524651 q^{6} -1.00000 q^{7} +1.95419 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.524651 q^{2} -1.00000 q^{3} -1.72474 q^{4} -2.36230 q^{5} +0.524651 q^{6} -1.00000 q^{7} +1.95419 q^{8} +1.00000 q^{9} +1.23938 q^{10} +6.20795 q^{11} +1.72474 q^{12} +1.00000 q^{13} +0.524651 q^{14} +2.36230 q^{15} +2.42422 q^{16} -1.00000 q^{17} -0.524651 q^{18} +5.33456 q^{19} +4.07435 q^{20} +1.00000 q^{21} -3.25700 q^{22} +8.42518 q^{23} -1.95419 q^{24} +0.580444 q^{25} -0.524651 q^{26} -1.00000 q^{27} +1.72474 q^{28} +4.67929 q^{29} -1.23938 q^{30} +3.66357 q^{31} -5.18024 q^{32} -6.20795 q^{33} +0.524651 q^{34} +2.36230 q^{35} -1.72474 q^{36} -7.37305 q^{37} -2.79878 q^{38} -1.00000 q^{39} -4.61637 q^{40} +5.66091 q^{41} -0.524651 q^{42} -10.5034 q^{43} -10.7071 q^{44} -2.36230 q^{45} -4.42027 q^{46} -6.90143 q^{47} -2.42422 q^{48} +1.00000 q^{49} -0.304531 q^{50} +1.00000 q^{51} -1.72474 q^{52} -3.81061 q^{53} +0.524651 q^{54} -14.6650 q^{55} -1.95419 q^{56} -5.33456 q^{57} -2.45499 q^{58} -1.76752 q^{59} -4.07435 q^{60} +3.34391 q^{61} -1.92210 q^{62} -1.00000 q^{63} -2.13062 q^{64} -2.36230 q^{65} +3.25700 q^{66} +5.50521 q^{67} +1.72474 q^{68} -8.42518 q^{69} -1.23938 q^{70} -2.20070 q^{71} +1.95419 q^{72} +14.2628 q^{73} +3.86828 q^{74} -0.580444 q^{75} -9.20073 q^{76} -6.20795 q^{77} +0.524651 q^{78} +6.57083 q^{79} -5.72672 q^{80} +1.00000 q^{81} -2.97000 q^{82} -11.0689 q^{83} -1.72474 q^{84} +2.36230 q^{85} +5.51063 q^{86} -4.67929 q^{87} +12.1315 q^{88} +11.1424 q^{89} +1.23938 q^{90} -1.00000 q^{91} -14.5313 q^{92} -3.66357 q^{93} +3.62084 q^{94} -12.6018 q^{95} +5.18024 q^{96} -4.33876 q^{97} -0.524651 q^{98} +6.20795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.524651	−0.370984	−0.185492	−	0.982646i	$-0.559388\pi$
$2$	−0.524651	−0.370984	−0.185492	+	0.982646i	$0.559388\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.72474	−0.862371
$5$	−2.36230	−1.05645	−0.528226	−	0.849104i	$-0.677142\pi$
$5$	−2.36230	−1.05645	−0.528226	+	0.849104i	$0.677142\pi$
$6$	0.524651	0.214188
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.95419	0.690910
$9$	1.00000	0.333333
$10$	1.23938	0.391926
$11$	6.20795	1.87177	0.935883	−	0.352310i	$-0.114604\pi$
$11$	6.20795	1.87177	0.935883	+	0.352310i	$0.114604\pi$
$12$	1.72474	0.497890
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.524651	0.140219
$15$	2.36230	0.609942
$16$	2.42422	0.606054
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.524651	−0.123661
$19$	5.33456	1.22383	0.611916	−	0.790923i	$-0.290399\pi$
$19$	5.33456	1.22383	0.611916	+	0.790923i	$0.290399\pi$
$20$	4.07435	0.911053
$21$	1.00000	0.218218
$22$	−3.25700	−0.694395
$23$	8.42518	1.75677	0.878385	−	0.477953i	$-0.158621\pi$
$23$	8.42518	1.75677	0.878385	+	0.477953i	$0.158621\pi$
$24$	−1.95419	−0.398897
$25$	0.580444	0.116089
$26$	−0.524651	−0.102892
$27$	−1.00000	−0.192450
$28$	1.72474	0.325946
$29$	4.67929	0.868923	0.434461	−	0.900690i	$-0.356939\pi$
$29$	4.67929	0.868923	0.434461	+	0.900690i	$0.356939\pi$
$30$	−1.23938	−0.226279
$31$	3.66357	0.657997	0.328999	−	0.944330i	$-0.393289\pi$
$31$	3.66357	0.657997	0.328999	+	0.944330i	$0.393289\pi$
$32$	−5.18024	−0.915746
$33$	−6.20795	−1.08066
$34$	0.524651	0.0899768
$35$	2.36230	0.399301
$36$	−1.72474	−0.287457
$37$	−7.37305	−1.21212	−0.606061	−	0.795418i	$-0.707251\pi$
$37$	−7.37305	−1.21212	−0.606061	+	0.795418i	$0.707251\pi$
$38$	−2.79878	−0.454022
$39$	−1.00000	−0.160128
$40$	−4.61637	−0.729912
$41$	5.66091	0.884085	0.442042	−	0.896994i	$-0.354254\pi$
$41$	5.66091	0.884085	0.442042	+	0.896994i	$0.354254\pi$
$42$	−0.524651	−0.0809554
$43$	−10.5034	−1.60176	−0.800879	−	0.598826i	$-0.795634\pi$
$43$	−10.5034	−1.60176	−0.800879	+	0.598826i	$0.795634\pi$
$44$	−10.7071	−1.61416
$45$	−2.36230	−0.352150
$46$	−4.42027	−0.651734
$47$	−6.90143	−1.00668	−0.503339	−	0.864089i	$-0.667895\pi$
$47$	−6.90143	−1.00668	−0.503339	+	0.864089i	$0.667895\pi$
$48$	−2.42422	−0.349906
$49$	1.00000	0.142857
$50$	−0.304531	−0.0430671
$51$	1.00000	0.140028
$52$	−1.72474	−0.239179
$53$	−3.81061	−0.523427	−0.261714	−	0.965146i	$-0.584288\pi$
$53$	−3.81061	−0.523427	−0.261714	+	0.965146i	$0.584288\pi$
$54$	0.524651	0.0713959
$55$	−14.6650	−1.97743
$56$	−1.95419	−0.261139
$57$	−5.33456	−0.706579
$58$	−2.45499	−0.322356
$59$	−1.76752	−0.230112	−0.115056	−	0.993359i	$-0.536705\pi$
$59$	−1.76752	−0.230112	−0.115056	+	0.993359i	$0.536705\pi$
$60$	−4.07435	−0.525996
$61$	3.34391	0.428144	0.214072	−	0.976818i	$-0.431327\pi$
$61$	3.34391	0.428144	0.214072	+	0.976818i	$0.431327\pi$
$62$	−1.92210	−0.244106
$63$	−1.00000	−0.125988
$64$	−2.13062	−0.266327
$65$	−2.36230	−0.293007
$66$	3.25700	0.400909
$67$	5.50521	0.672568	0.336284	−	0.941761i	$-0.390830\pi$
$67$	5.50521	0.672568	0.336284	+	0.941761i	$0.390830\pi$
$68$	1.72474	0.209156
$69$	−8.42518	−1.01427
$70$	−1.23938	−0.148134
$71$	−2.20070	−0.261175	−0.130588	−	0.991437i	$-0.541686\pi$
$71$	−2.20070	−0.261175	−0.130588	+	0.991437i	$0.541686\pi$
$72$	1.95419	0.230303
$73$	14.2628	1.66933	0.834667	−	0.550754i	$-0.185660\pi$
$73$	14.2628	1.66933	0.834667	+	0.550754i	$0.185660\pi$
$74$	3.86828	0.449678
$75$	−0.580444	−0.0670239
$76$	−9.20073	−1.05540
$77$	−6.20795	−0.707461
$78$	0.524651	0.0594050
$79$	6.57083	0.739276	0.369638	−	0.929176i	$-0.379482\pi$
$79$	6.57083	0.739276	0.369638	+	0.929176i	$0.379482\pi$
$80$	−5.72672	−0.640267
$81$	1.00000	0.111111
$82$	−2.97000	−0.327981
$83$	−11.0689	−1.21497	−0.607485	−	0.794331i	$-0.707822\pi$
$83$	−11.0689	−1.21497	−0.607485	+	0.794331i	$0.707822\pi$
$84$	−1.72474	−0.188185
$85$	2.36230	0.256227
$86$	5.51063	0.594227
$87$	−4.67929	−0.501673
$88$	12.1315	1.29322
$89$	11.1424	1.18109	0.590546	−	0.807004i	$-0.298913\pi$
$89$	11.1424	1.18109	0.590546	+	0.807004i	$0.298913\pi$
$90$	1.23938	0.130642
$91$	−1.00000	−0.104828
$92$	−14.5313	−1.51499
$93$	−3.66357	−0.379895
$94$	3.62084	0.373461
$95$	−12.6018	−1.29292
$96$	5.18024	0.528706
$97$	−4.33876	−0.440534	−0.220267	−	0.975440i	$-0.570693\pi$
$97$	−4.33876	−0.440534	−0.220267	+	0.975440i	$0.570693\pi$
$98$	−0.524651	−0.0529977
$99$	6.20795	0.623922
$100$	−1.00112	−0.100112
$101$	5.92009	0.589071	0.294536	−	0.955640i	$-0.404835\pi$
$101$	5.92009	0.589071	0.294536	+	0.955640i	$0.404835\pi$
$102$	−0.524651	−0.0519482
$103$	−5.61607	−0.553368	−0.276684	−	0.960961i	$-0.589236\pi$
$103$	−5.61607	−0.553368	−0.276684	+	0.960961i	$0.589236\pi$
$104$	1.95419	0.191624
$105$	−2.36230	−0.230537
$106$	1.99924	0.194183
$107$	15.5886	1.50701	0.753503	−	0.657444i	$-0.228362\pi$
$107$	15.5886	1.50701	0.753503	+	0.657444i	$0.228362\pi$
$108$	1.72474	0.165963
$109$	15.1231	1.44853	0.724266	−	0.689521i	$-0.242179\pi$
$109$	15.1231	1.44853	0.724266	+	0.689521i	$0.242179\pi$
$110$	7.69401	0.733595
$111$	7.37305	0.699819
$112$	−2.42422	−0.229067
$113$	−0.0945998	−0.00889920	−0.00444960	−	0.999990i	$-0.501416\pi$
$113$	−0.0945998	−0.00889920	−0.00444960	+	0.999990i	$0.501416\pi$
$114$	2.79878	0.262130
$115$	−19.9028	−1.85594
$116$	−8.07057	−0.749334
$117$	1.00000	0.0924500
$118$	0.927333	0.0853679
$119$	1.00000	0.0916698
$120$	4.61637	0.421415
$121$	27.5386	2.50351
$122$	−1.75438	−0.158834
$123$	−5.66091	−0.510427
$124$	−6.31872	−0.567438
$125$	10.4403	0.933809
$126$	0.524651	0.0467396
$127$	4.14752	0.368033	0.184017	−	0.982923i	$-0.441090\pi$
$127$	4.14752	0.368033	0.184017	+	0.982923i	$0.441090\pi$
$128$	11.4783	1.01455
$129$	10.5034	0.924776
$130$	1.23938	0.108701
$131$	−11.0038	−0.961410	−0.480705	−	0.876882i	$-0.659619\pi$
$131$	−11.0038	−0.961410	−0.480705	+	0.876882i	$0.659619\pi$
$132$	10.7071	0.931934
$133$	−5.33456	−0.462565
$134$	−2.88831	−0.249512
$135$	2.36230	0.203314
$136$	−1.95419	−0.167570
$137$	−13.7616	−1.17573	−0.587864	−	0.808959i	$-0.700031\pi$
$137$	−13.7616	−1.17573	−0.587864	+	0.808959i	$0.700031\pi$
$138$	4.42027	0.376279
$139$	−20.5255	−1.74095	−0.870475	−	0.492212i	$-0.836188\pi$
$139$	−20.5255	−1.74095	−0.870475	+	0.492212i	$0.836188\pi$
$140$	−4.07435	−0.344346
$141$	6.90143	0.581205
$142$	1.15460	0.0968918
$143$	6.20795	0.519135
$144$	2.42422	0.202018
$145$	−11.0539	−0.917974
$146$	−7.48299	−0.619296
$147$	−1.00000	−0.0824786
$148$	12.7166	1.04530
$149$	−3.14766	−0.257866	−0.128933	−	0.991653i	$-0.541155\pi$
$149$	−3.14766	−0.257866	−0.128933	+	0.991653i	$0.541155\pi$
$150$	0.304531	0.0248648
$151$	7.67805	0.624831	0.312416	−	0.949946i	$-0.398862\pi$
$151$	7.67805	0.624831	0.312416	+	0.949946i	$0.398862\pi$
$152$	10.4247	0.845557
$153$	−1.00000	−0.0808452
$154$	3.25700	0.262457
$155$	−8.65445	−0.695142
$156$	1.72474	0.138090
$157$	−12.6518	−1.00972	−0.504860	−	0.863201i	$-0.668456\pi$
$157$	−12.6518	−1.00972	−0.504860	+	0.863201i	$0.668456\pi$
$158$	−3.44739	−0.274260
$159$	3.81061	0.302201
$160$	12.2373	0.967441
$161$	−8.42518	−0.663997
$162$	−0.524651	−0.0412204
$163$	−10.5370	−0.825319	−0.412659	−	0.910885i	$-0.635400\pi$
$163$	−10.5370	−0.825319	−0.412659	+	0.910885i	$0.635400\pi$
$164$	−9.76360	−0.762409
$165$	14.6650	1.14167
$166$	5.80731	0.450735
$167$	−18.5731	−1.43723	−0.718614	−	0.695409i	$-0.755223\pi$
$167$	−18.5731	−1.43723	−0.718614	+	0.695409i	$0.755223\pi$
$168$	1.95419	0.150769
$169$	1.00000	0.0769231
$170$	−1.23938	−0.0950561
$171$	5.33456	0.407944
$172$	18.1157	1.38131
$173$	4.10182	0.311856	0.155928	−	0.987768i	$-0.450163\pi$
$173$	4.10182	0.311856	0.155928	+	0.987768i	$0.450163\pi$
$174$	2.45499	0.186113
$175$	−0.580444	−0.0438775
$176$	15.0494	1.13439
$177$	1.76752	0.132855
$178$	−5.84586	−0.438166
$179$	3.02993	0.226468	0.113234	−	0.993568i	$-0.463879\pi$
$179$	3.02993	0.226468	0.113234	+	0.993568i	$0.463879\pi$
$180$	4.07435	0.303684
$181$	2.12308	0.157807	0.0789036	−	0.996882i	$-0.474858\pi$
$181$	2.12308	0.157807	0.0789036	+	0.996882i	$0.474858\pi$
$182$	0.524651	0.0388897
$183$	−3.34391	−0.247189
$184$	16.4644	1.21377
$185$	17.4173	1.28055
$186$	1.92210	0.140935
$187$	−6.20795	−0.453970
$188$	11.9032	0.868129
$189$	1.00000	0.0727393
$190$	6.61154	0.479652
$191$	19.9752	1.44535	0.722677	−	0.691186i	$-0.242912\pi$
$191$	19.9752	1.44535	0.722677	+	0.691186i	$0.242912\pi$
$192$	2.13062	0.153764
$193$	18.3167	1.31846	0.659232	−	0.751940i	$-0.270881\pi$
$193$	18.3167	1.31846	0.659232	+	0.751940i	$0.270881\pi$
$194$	2.27633	0.163431
$195$	2.36230	0.169168
$196$	−1.72474	−0.123196
$197$	7.20467	0.513312	0.256656	−	0.966503i	$-0.417379\pi$
$197$	7.20467	0.513312	0.256656	+	0.966503i	$0.417379\pi$
$198$	−3.25700	−0.231465
$199$	−17.5370	−1.24317	−0.621584	−	0.783347i	$-0.713511\pi$
$199$	−17.5370	−1.24317	−0.621584	+	0.783347i	$0.713511\pi$
$200$	1.13430	0.0802069
$201$	−5.50521	−0.388308
$202$	−3.10598	−0.218536
$203$	−4.67929	−0.328422
$204$	−1.72474	−0.120756
$205$	−13.3727	−0.933992
$206$	2.94648	0.205291
$207$	8.42518	0.585590
$208$	2.42422	0.168089
$209$	33.1166	2.29073
$210$	1.23938	0.0855254
$211$	12.9421	0.890973	0.445486	−	0.895289i	$-0.353031\pi$
$211$	12.9421	0.890973	0.445486	+	0.895289i	$0.353031\pi$
$212$	6.57231	0.451388
$213$	2.20070	0.150790
$214$	−8.17857	−0.559075
$215$	24.8122	1.69218
$216$	−1.95419	−0.132966
$217$	−3.66357	−0.248700
$218$	−7.93435	−0.537382
$219$	−14.2628	−0.963791
$220$	25.2934	1.70528
$221$	−1.00000	−0.0672673
$222$	−3.86828	−0.259622
$223$	−0.176402	−0.0118127	−0.00590636	−	0.999983i	$-0.501880\pi$
$223$	−0.176402	−0.0118127	−0.00590636	+	0.999983i	$0.501880\pi$
$224$	5.18024	0.346120
$225$	0.580444	0.0386963
$226$	0.0496318	0.00330146
$227$	−12.0524	−0.799947	−0.399973	−	0.916527i	$-0.630981\pi$
$227$	−12.0524	−0.799947	−0.399973	+	0.916527i	$0.630981\pi$
$228$	9.20073	0.609333
$229$	24.9793	1.65068	0.825340	−	0.564636i	$-0.190983\pi$
$229$	24.9793	1.65068	0.825340	+	0.564636i	$0.190983\pi$
$230$	10.4420	0.688525
$231$	6.20795	0.408453
$232$	9.14422	0.600347
$233$	−18.2812	−1.19764	−0.598821	−	0.800883i	$-0.704364\pi$
$233$	−18.2812	−1.19764	−0.598821	+	0.800883i	$0.704364\pi$
$234$	−0.524651	−0.0342975
$235$	16.3032	1.06351
$236$	3.04852	0.198442
$237$	−6.57083	−0.426821
$238$	−0.524651	−0.0340081
$239$	−15.3641	−0.993821	−0.496911	−	0.867802i	$-0.665532\pi$
$239$	−15.3641	−0.993821	−0.496911	+	0.867802i	$0.665532\pi$
$240$	5.72672	0.369658
$241$	1.06663	0.0687078	0.0343539	−	0.999410i	$-0.489063\pi$
$241$	1.06663	0.0687078	0.0343539	+	0.999410i	$0.489063\pi$
$242$	−14.4481	−0.928762
$243$	−1.00000	−0.0641500
$244$	−5.76738	−0.369219
$245$	−2.36230	−0.150922
$246$	2.97000	0.189360
$247$	5.33456	0.339430
$248$	7.15931	0.454617
$249$	11.0689	0.701464
$250$	−5.47751	−0.346428
$251$	−21.0887	−1.33111	−0.665554	−	0.746350i	$-0.731805\pi$
$251$	−21.0887	−1.33111	−0.665554	+	0.746350i	$0.731805\pi$
$252$	1.72474	0.108649
$253$	52.3031	3.28826
$254$	−2.17600	−0.136534
$255$	−2.36230	−0.147933
$256$	−1.76087	−0.110055
$257$	−18.0875	−1.12827	−0.564133	−	0.825684i	$-0.690789\pi$
$257$	−18.0875	−1.12827	−0.564133	+	0.825684i	$0.690789\pi$
$258$	−5.51063	−0.343077
$259$	7.37305	0.458139
$260$	4.07435	0.252681
$261$	4.67929	0.289641
$262$	5.77317	0.356668
$263$	26.2033	1.61577	0.807884	−	0.589342i	$-0.200613\pi$
$263$	26.2033	1.61577	0.807884	+	0.589342i	$0.200613\pi$
$264$	−12.1315	−0.746642
$265$	9.00178	0.552975
$266$	2.79878	0.171604
$267$	−11.1424	−0.681903
$268$	−9.49506	−0.580003
$269$	−21.6058	−1.31733	−0.658665	−	0.752437i	$-0.728878\pi$
$269$	−21.6058	−1.31733	−0.658665	+	0.752437i	$0.728878\pi$
$270$	−1.23938	−0.0754263
$271$	22.3402	1.35707	0.678535	−	0.734568i	$-0.262615\pi$
$271$	22.3402	1.35707	0.678535	+	0.734568i	$0.262615\pi$
$272$	−2.42422	−0.146990
$273$	1.00000	0.0605228
$274$	7.22001	0.436177
$275$	3.60337	0.217291
$276$	14.5313	0.874679
$277$	18.2956	1.09928	0.549639	−	0.835402i	$-0.314765\pi$
$277$	18.2956	1.09928	0.549639	+	0.835402i	$0.314765\pi$
$278$	10.7687	0.645865
$279$	3.66357	0.219332
$280$	4.61637	0.275881
$281$	−2.48117	−0.148014	−0.0740071	−	0.997258i	$-0.523579\pi$
$281$	−2.48117	−0.148014	−0.0740071	+	0.997258i	$0.523579\pi$
$282$	−3.62084	−0.215618
$283$	2.98801	0.177619	0.0888094	−	0.996049i	$-0.471694\pi$
$283$	2.98801	0.177619	0.0888094	+	0.996049i	$0.471694\pi$
$284$	3.79564	0.225230
$285$	12.6018	0.746466
$286$	−3.25700	−0.192591
$287$	−5.66091	−0.334153
$288$	−5.18024	−0.305249
$289$	1.00000	0.0588235
$290$	5.79942	0.340554
$291$	4.33876	0.254343
$292$	−24.5996	−1.43959
$293$	1.16364	0.0679807	0.0339903	−	0.999422i	$-0.489178\pi$
$293$	1.16364	0.0679807	0.0339903	+	0.999422i	$0.489178\pi$
$294$	0.524651	0.0305982
$295$	4.17542	0.243102
$296$	−14.4083	−0.837467
$297$	−6.20795	−0.360222
$298$	1.65142	0.0956643
$299$	8.42518	0.487241
$300$	1.00112	0.0577995
$301$	10.5034	0.605408
$302$	−4.02830	−0.231802
$303$	−5.92009	−0.340100
$304$	12.9321	0.741708
$305$	−7.89931	−0.452313
$306$	0.524651	0.0299923
$307$	22.6149	1.29070	0.645349	−	0.763888i	$-0.276712\pi$
$307$	22.6149	1.29070	0.645349	+	0.763888i	$0.276712\pi$
$308$	10.7071	0.610094
$309$	5.61607	0.319487
$310$	4.54056	0.257887
$311$	3.69078	0.209285	0.104642	−	0.994510i	$-0.466630\pi$
$311$	3.69078	0.209285	0.104642	+	0.994510i	$0.466630\pi$
$312$	−1.95419	−0.110634
$313$	−24.1514	−1.36512	−0.682558	−	0.730831i	$-0.739133\pi$
$313$	−24.1514	−1.36512	−0.682558	+	0.730831i	$0.739133\pi$
$314$	6.63776	0.374590
$315$	2.36230	0.133100
$316$	−11.3330	−0.637530
$317$	−3.92574	−0.220492	−0.110246	−	0.993904i	$-0.535164\pi$
$317$	−3.92574	−0.220492	−0.110246	+	0.993904i	$0.535164\pi$
$318$	−1.99924	−0.112112
$319$	29.0488	1.62642
$320$	5.03315	0.281361
$321$	−15.5886	−0.870071
$322$	4.42027	0.246332
$323$	−5.33456	−0.296823
$324$	−1.72474	−0.0958190
$325$	0.580444	0.0321973
$326$	5.52822	0.306180
$327$	−15.1231	−0.836310
$328$	11.0625	0.610823
$329$	6.90143	0.380488
$330$	−7.69401	−0.423541
$331$	12.0676	0.663294	0.331647	−	0.943404i	$-0.392396\pi$
$331$	12.0676	0.663294	0.331647	+	0.943404i	$0.392396\pi$
$332$	19.0910	1.04776
$333$	−7.37305	−0.404041
$334$	9.74438	0.533189
$335$	−13.0049	−0.710536
$336$	2.42422	0.132252
$337$	−34.1869	−1.86228	−0.931139	−	0.364665i	$-0.881183\pi$
$337$	−34.1869	−1.86228	−0.931139	+	0.364665i	$0.881183\pi$
$338$	−0.524651	−0.0285372
$339$	0.0945998	0.00513796
$340$	−4.07435	−0.220963
$341$	22.7433	1.23162
$342$	−2.79878	−0.151341
$343$	−1.00000	−0.0539949
$344$	−20.5257	−1.10667
$345$	19.9028	1.07153
$346$	−2.15202	−0.115694
$347$	18.2120	0.977673	0.488837	−	0.872375i	$-0.337421\pi$
$347$	18.2120	0.977673	0.488837	+	0.872375i	$0.337421\pi$
$348$	8.07057	0.432628
$349$	5.24936	0.280992	0.140496	−	0.990081i	$-0.455130\pi$
$349$	5.24936	0.280992	0.140496	+	0.990081i	$0.455130\pi$
$350$	0.304531	0.0162778
$351$	−1.00000	−0.0533761
$352$	−32.1587	−1.71406
$353$	5.28651	0.281373	0.140686	−	0.990054i	$-0.455069\pi$
$353$	5.28651	0.281373	0.140686	+	0.990054i	$0.455069\pi$
$354$	−0.927333	−0.0492872
$355$	5.19871	0.275919
$356$	−19.2177	−1.01854
$357$	−1.00000	−0.0529256
$358$	−1.58966	−0.0840159
$359$	25.4042	1.34078	0.670390	−	0.742009i	$-0.266127\pi$
$359$	25.4042	1.34078	0.670390	+	0.742009i	$0.266127\pi$
$360$	−4.61637	−0.243304
$361$	9.45749	0.497763
$362$	−1.11387	−0.0585440
$363$	−27.5386	−1.44540
$364$	1.72474	0.0904010
$365$	−33.6930	−1.76357
$366$	1.75438	0.0917031
$367$	−8.54147	−0.445861	−0.222931	−	0.974834i	$-0.571562\pi$
$367$	−8.54147	−0.445861	−0.222931	+	0.974834i	$0.571562\pi$
$368$	20.4245	1.06470
$369$	5.66091	0.294695
$370$	−9.13802	−0.475063
$371$	3.81061	0.197837
$372$	6.31872	0.327610
$373$	35.1803	1.82157	0.910783	−	0.412885i	$-0.135479\pi$
$373$	35.1803	1.82157	0.910783	+	0.412885i	$0.135479\pi$
$374$	3.25700	0.168416
$375$	−10.4403	−0.539135
$376$	−13.4867	−0.695523
$377$	4.67929	0.240996
$378$	−0.524651	−0.0269851
$379$	−14.3251	−0.735831	−0.367916	−	0.929859i	$-0.619929\pi$
$379$	−14.3251	−0.735831	−0.367916	+	0.929859i	$0.619929\pi$
$380$	21.7349	1.11497
$381$	−4.14752	−0.212484
$382$	−10.4800	−0.536203
$383$	−10.3858	−0.530689	−0.265344	−	0.964154i	$-0.585486\pi$
$383$	−10.3858	−0.530689	−0.265344	+	0.964154i	$0.585486\pi$
$384$	−11.4783	−0.585750
$385$	14.6650	0.747398
$386$	−9.60986	−0.489129
$387$	−10.5034	−0.533920
$388$	7.48324	0.379904
$389$	11.6760	0.591999	0.295999	−	0.955188i	$-0.404347\pi$
$389$	11.6760	0.591999	0.295999	+	0.955188i	$0.404347\pi$
$390$	−1.23938	−0.0627585
$391$	−8.42518	−0.426080
$392$	1.95419	0.0987014
$393$	11.0038	0.555070
$394$	−3.77994	−0.190430
$395$	−15.5222	−0.781009
$396$	−10.7071	−0.538052
$397$	34.0169	1.70726	0.853630	−	0.520880i	$-0.174396\pi$
$397$	34.0169	1.70726	0.853630	+	0.520880i	$0.174396\pi$
$398$	9.20082	0.461196
$399$	5.33456	0.267062
$400$	1.40712	0.0703562
$401$	−37.2060	−1.85798	−0.928990	−	0.370106i	$-0.879321\pi$
$401$	−37.2060	−1.85798	−0.928990	+	0.370106i	$0.879321\pi$
$402$	2.88831	0.144056
$403$	3.66357	0.182496
$404$	−10.2106	−0.507998
$405$	−2.36230	−0.117383
$406$	2.45499	0.121839
$407$	−45.7715	−2.26881
$408$	1.95419	0.0967467
$409$	−15.4045	−0.761701	−0.380851	−	0.924637i	$-0.624369\pi$
$409$	−15.4045	−0.761701	−0.380851	+	0.924637i	$0.624369\pi$
$410$	7.01602	0.346496
$411$	13.7616	0.678807
$412$	9.68628	0.477209
$413$	1.76752	0.0869742
$414$	−4.42027	−0.217245
$415$	26.1480	1.28356
$416$	−5.18024	−0.253982
$417$	20.5255	1.00514
$418$	−17.3747	−0.849823
$419$	−27.2077	−1.32918	−0.664591	−	0.747207i	$-0.731394\pi$
$419$	−27.2077	−1.32918	−0.664591	+	0.747207i	$0.731394\pi$
$420$	4.07435	0.198808
$421$	−2.98510	−0.145485	−0.0727425	−	0.997351i	$-0.523175\pi$
$421$	−2.98510	−0.145485	−0.0727425	+	0.997351i	$0.523175\pi$
$422$	−6.79009	−0.330537
$423$	−6.90143	−0.335559
$424$	−7.44664	−0.361641
$425$	−0.580444	−0.0281557
$426$	−1.15460	−0.0559405
$427$	−3.34391	−0.161823
$428$	−26.8863	−1.29960
$429$	−6.20795	−0.299723
$430$	−13.0178	−0.627772
$431$	0.0488588	0.00235345	0.00117672	−	0.999999i	$-0.499625\pi$
$431$	0.0488588	0.00235345	0.00117672	+	0.999999i	$0.499625\pi$
$432$	−2.42422	−0.116635
$433$	17.8551	0.858063	0.429032	−	0.903289i	$-0.358855\pi$
$433$	17.8551	0.858063	0.429032	+	0.903289i	$0.358855\pi$
$434$	1.92210	0.0922636
$435$	11.0539	0.529993
$436$	−26.0835	−1.24917
$437$	44.9446	2.14999
$438$	7.48299	0.357551
$439$	−9.99227	−0.476905	−0.238452	−	0.971154i	$-0.576640\pi$
$439$	−9.99227	−0.476905	−0.238452	+	0.971154i	$0.576640\pi$
$440$	−28.6582	−1.36623
$441$	1.00000	0.0476190
$442$	0.524651	0.0249551
$443$	23.5924	1.12091	0.560455	−	0.828185i	$-0.310626\pi$
$443$	23.5924	1.12091	0.560455	+	0.828185i	$0.310626\pi$
$444$	−12.7166	−0.603504
$445$	−26.3216	−1.24777
$446$	0.0925492	0.00438233
$447$	3.14766	0.148879
$448$	2.13062	0.100662
$449$	−7.16044	−0.337922	−0.168961	−	0.985623i	$-0.554041\pi$
$449$	−7.16044	−0.337922	−0.168961	+	0.985623i	$0.554041\pi$
$450$	−0.304531	−0.0143557
$451$	35.1426	1.65480
$452$	0.163160	0.00767441
$453$	−7.67805	−0.360746
$454$	6.32331	0.296767
$455$	2.36230	0.110746
$456$	−10.4247	−0.488183
$457$	20.5470	0.961147	0.480574	−	0.876954i	$-0.340428\pi$
$457$	20.5470	0.961147	0.480574	+	0.876954i	$0.340428\pi$
$458$	−13.1054	−0.612376
$459$	1.00000	0.0466760
$460$	34.3271	1.60051
$461$	−24.7390	−1.15221	−0.576105	−	0.817376i	$-0.695428\pi$
$461$	−24.7390	−1.15221	−0.576105	+	0.817376i	$0.695428\pi$
$462$	−3.25700	−0.151530
$463$	18.9192	0.879249	0.439624	−	0.898182i	$-0.355112\pi$
$463$	18.9192	0.879249	0.439624	+	0.898182i	$0.355112\pi$
$464$	11.3436	0.526614
$465$	8.65445	0.401340
$466$	9.59125	0.444306
$467$	−3.01278	−0.139415	−0.0697074	−	0.997567i	$-0.522207\pi$
$467$	−3.01278	−0.139415	−0.0697074	+	0.997567i	$0.522207\pi$
$468$	−1.72474	−0.0797262
$469$	−5.50521	−0.254207
$470$	−8.55350	−0.394543
$471$	12.6518	0.582963
$472$	−3.45408	−0.158987
$473$	−65.2048	−2.99812
$474$	3.44739	0.158344
$475$	3.09641	0.142073
$476$	−1.72474	−0.0790534
$477$	−3.81061	−0.174476
$478$	8.06079	0.368692
$479$	38.9773	1.78092	0.890459	−	0.455063i	$-0.150383\pi$
$479$	38.9773	1.78092	0.890459	+	0.455063i	$0.150383\pi$
$480$	−12.2373	−0.558552
$481$	−7.37305	−0.336182
$482$	−0.559609	−0.0254895
$483$	8.42518	0.383359
$484$	−47.4970	−2.15895
$485$	10.2494	0.465403
$486$	0.524651	0.0237986
$487$	−14.7406	−0.667959	−0.333980	−	0.942580i	$-0.608392\pi$
$487$	−14.7406	−0.667959	−0.333980	+	0.942580i	$0.608392\pi$
$488$	6.53463	0.295809
$489$	10.5370	0.476498
$490$	1.23938	0.0559895
$491$	12.8308	0.579047	0.289524	−	0.957171i	$-0.406503\pi$
$491$	12.8308	0.579047	0.289524	+	0.957171i	$0.406503\pi$
$492$	9.76360	0.440177
$493$	−4.67929	−0.210745
$494$	−2.79878	−0.125923
$495$	−14.6650	−0.659143
$496$	8.88130	0.398782
$497$	2.20070	0.0987149
$498$	−5.80731	−0.260232
$499$	−3.08032	−0.137894	−0.0689470	−	0.997620i	$-0.521964\pi$
$499$	−3.08032	−0.137894	−0.0689470	+	0.997620i	$0.521964\pi$
$500$	−18.0068	−0.805290
$501$	18.5731	0.829784
$502$	11.0642	0.493820
$503$	19.6626	0.876713	0.438357	−	0.898801i	$-0.355561\pi$
$503$	19.6626	0.876713	0.438357	+	0.898801i	$0.355561\pi$
$504$	−1.95419	−0.0870465
$505$	−13.9850	−0.622325
$506$	−27.4408	−1.21989
$507$	−1.00000	−0.0444116
$508$	−7.15341	−0.317381
$509$	−14.7791	−0.655070	−0.327535	−	0.944839i	$-0.606218\pi$
$509$	−14.7791	−0.655070	−0.327535	+	0.944839i	$0.606218\pi$
$510$	1.23938	0.0548807
$511$	−14.2628	−0.630949
$512$	−22.0328	−0.973721
$513$	−5.33456	−0.235526
$514$	9.48960	0.418569
$515$	13.2668	0.584606
$516$	−18.1157	−0.797500
$517$	−42.8437	−1.88426
$518$	−3.86828	−0.169962
$519$	−4.10182	−0.180050
$520$	−4.61637	−0.202441
$521$	15.4681	0.677670	0.338835	−	0.940846i	$-0.389967\pi$
$521$	15.4681	0.677670	0.338835	+	0.940846i	$0.389967\pi$
$522$	−2.45499	−0.107452
$523$	27.7959	1.21543	0.607716	−	0.794155i	$-0.292086\pi$
$523$	27.7959	1.21543	0.607716	+	0.794155i	$0.292086\pi$
$524$	18.9788	0.829092
$525$	0.580444	0.0253327
$526$	−13.7476	−0.599424
$527$	−3.66357	−0.159588
$528$	−15.0494	−0.654942
$529$	47.9836	2.08624
$530$	−4.72279	−0.205145
$531$	−1.76752	−0.0767040
$532$	9.20073	0.398902
$533$	5.66091	0.245201
$534$	5.84586	0.252975
$535$	−36.8249	−1.59208
$536$	10.7582	0.464684
$537$	−3.02993	−0.130751
$538$	11.3355	0.488708
$539$	6.20795	0.267395
$540$	−4.07435	−0.175332
$541$	2.05366	0.0882937	0.0441468	−	0.999025i	$-0.485943\pi$
$541$	2.05366	0.0882937	0.0441468	+	0.999025i	$0.485943\pi$
$542$	−11.7208	−0.503452
$543$	−2.12308	−0.0911101
$544$	5.18024	0.222101
$545$	−35.7253	−1.53030
$546$	−0.524651	−0.0224530
$547$	11.2083	0.479234	0.239617	−	0.970868i	$-0.422978\pi$
$547$	11.2083	0.479234	0.239617	+	0.970868i	$0.422978\pi$
$548$	23.7351	1.01391
$549$	3.34391	0.142715
$550$	−1.89051	−0.0806116
$551$	24.9619	1.06341
$552$	−16.4644	−0.700771
$553$	−6.57083	−0.279420
$554$	−9.59881	−0.407814
$555$	−17.4173	−0.739325
$556$	35.4012	1.50135
$557$	0.203219	0.00861066	0.00430533	−	0.999991i	$-0.498630\pi$
$557$	0.203219	0.00861066	0.00430533	+	0.999991i	$0.498630\pi$
$558$	−1.92210	−0.0813688
$559$	−10.5034	−0.444248
$560$	5.72672	0.241998
$561$	6.20795	0.262100
$562$	1.30175	0.0549109
$563$	−1.11438	−0.0469654	−0.0234827	−	0.999724i	$-0.507475\pi$
$563$	−1.11438	−0.0469654	−0.0234827	+	0.999724i	$0.507475\pi$
$564$	−11.9032	−0.501214
$565$	0.223473	0.00940157
$566$	−1.56766	−0.0658938
$567$	−1.00000	−0.0419961
$568$	−4.30058	−0.180448
$569$	−4.96778	−0.208260	−0.104130	−	0.994564i	$-0.533206\pi$
$569$	−4.96778	−0.208260	−0.104130	+	0.994564i	$0.533206\pi$
$570$	−6.61154	−0.276927
$571$	38.5516	1.61334	0.806668	−	0.591005i	$-0.201269\pi$
$571$	38.5516	1.61334	0.806668	+	0.591005i	$0.201269\pi$
$572$	−10.7071	−0.447687
$573$	−19.9752	−0.834475
$574$	2.97000	0.123965
$575$	4.89035	0.203942
$576$	−2.13062	−0.0887757
$577$	−17.8433	−0.742825	−0.371412	−	0.928468i	$-0.621126\pi$
$577$	−17.8433	−0.742825	−0.371412	+	0.928468i	$0.621126\pi$
$578$	−0.524651	−0.0218226
$579$	−18.3167	−0.761216
$580$	19.0651	0.791634
$581$	11.0689	0.459216
$582$	−2.27633	−0.0943571
$583$	−23.6561	−0.979734
$584$	27.8722	1.15336
$585$	−2.36230	−0.0976689
$586$	−0.610505	−0.0252197
$587$	−6.67652	−0.275569	−0.137785	−	0.990462i	$-0.543998\pi$
$587$	−6.67652	−0.275569	−0.137785	+	0.990462i	$0.543998\pi$
$588$	1.72474	0.0711271
$589$	19.5435	0.805277
$590$	−2.19064	−0.0901870
$591$	−7.20467	−0.296361
$592$	−17.8739	−0.734612
$593$	8.80276	0.361486	0.180743	−	0.983530i	$-0.442150\pi$
$593$	8.80276	0.361486	0.180743	+	0.983530i	$0.442150\pi$
$594$	3.25700	0.133636
$595$	−2.36230	−0.0968447
$596$	5.42890	0.222376
$597$	17.5370	0.717744
$598$	−4.42027	−0.180758
$599$	1.43821	0.0587638	0.0293819	−	0.999568i	$-0.490646\pi$
$599$	1.43821	0.0587638	0.0293819	+	0.999568i	$0.490646\pi$
$600$	−1.13430	−0.0463075
$601$	9.63831	0.393155	0.196577	−	0.980488i	$-0.437017\pi$
$601$	9.63831	0.393155	0.196577	+	0.980488i	$0.437017\pi$
$602$	−5.51063	−0.224597
$603$	5.50521	0.224189
$604$	−13.2427	−0.538836
$605$	−65.0543	−2.64484
$606$	3.10598	0.126172
$607$	20.5981	0.836051	0.418026	−	0.908435i	$-0.362722\pi$
$607$	20.5981	0.836051	0.418026	+	0.908435i	$0.362722\pi$
$608$	−27.6343	−1.12072
$609$	4.67929	0.189615
$610$	4.14438	0.167801
$611$	−6.90143	−0.279202
$612$	1.72474	0.0697186
$613$	44.5730	1.80028	0.900142	−	0.435596i	$-0.143462\pi$
$613$	44.5730	1.80028	0.900142	+	0.435596i	$0.143462\pi$
$614$	−11.8649	−0.478829
$615$	13.3727	0.539241
$616$	−12.1315	−0.488792
$617$	−21.1333	−0.850794	−0.425397	−	0.905007i	$-0.639866\pi$
$617$	−21.1333	−0.850794	−0.425397	+	0.905007i	$0.639866\pi$
$618$	−2.94648	−0.118525
$619$	−9.02254	−0.362647	−0.181323	−	0.983424i	$-0.558038\pi$
$619$	−9.02254	−0.362647	−0.181323	+	0.983424i	$0.558038\pi$
$620$	14.9267	0.599470
$621$	−8.42518	−0.338091
$622$	−1.93637	−0.0776413
$623$	−11.1424	−0.446411
$624$	−2.42422	−0.0970464
$625$	−27.5653	−1.10261
$626$	12.6710	0.506437
$627$	−33.1166	−1.32255
$628$	21.8210	0.870754
$629$	7.37305	0.293983
$630$	−1.23938	−0.0493781
$631$	46.1126	1.83571	0.917856	−	0.396913i	$-0.129919\pi$
$631$	46.1126	1.83571	0.917856	+	0.396913i	$0.129919\pi$
$632$	12.8406	0.510773
$633$	−12.9421	−0.514403
$634$	2.05964	0.0817989
$635$	−9.79768	−0.388809
$636$	−6.57231	−0.260609
$637$	1.00000	0.0396214
$638$	−15.2405	−0.603376
$639$	−2.20070	−0.0870584
$640$	−27.1152	−1.07182
$641$	−9.38381	−0.370638	−0.185319	−	0.982678i	$-0.559332\pi$
$641$	−9.38381	−0.370638	−0.185319	+	0.982678i	$0.559332\pi$
$642$	8.17857	0.322782
$643$	−1.73335	−0.0683567	−0.0341783	−	0.999416i	$-0.510881\pi$
$643$	−1.73335	−0.0683567	−0.0341783	+	0.999416i	$0.510881\pi$
$644$	14.5313	0.572612
$645$	−24.8122	−0.976981
$646$	2.79878	0.110116
$647$	−21.0303	−0.826786	−0.413393	−	0.910553i	$-0.635656\pi$
$647$	−21.0303	−0.826786	−0.413393	+	0.910553i	$0.635656\pi$
$648$	1.95419	0.0767678
$649$	−10.9727	−0.430716
$650$	−0.304531	−0.0119447
$651$	3.66357	0.143587
$652$	18.1735	0.711731
$653$	−2.45172	−0.0959432	−0.0479716	−	0.998849i	$-0.515276\pi$
$653$	−2.45172	−0.0959432	−0.0479716	+	0.998849i	$0.515276\pi$
$654$	7.93435	0.310258
$655$	25.9943	1.01568
$656$	13.7233	0.535803
$657$	14.2628	0.556445
$658$	−3.62084	−0.141155
$659$	23.7049	0.923411	0.461705	−	0.887033i	$-0.347238\pi$
$659$	23.7049	0.923411	0.461705	+	0.887033i	$0.347238\pi$
$660$	−25.2934	−0.984543
$661$	−44.1129	−1.71579	−0.857896	−	0.513824i	$-0.828228\pi$
$661$	−44.1129	−1.71579	−0.857896	+	0.513824i	$0.828228\pi$
$662$	−6.33126	−0.246071
$663$	1.00000	0.0388368
$664$	−21.6307	−0.839435
$665$	12.6018	0.488677
$666$	3.86828	0.149893
$667$	39.4239	1.52650
$668$	32.0338	1.23942
$669$	0.176402	0.00682008
$670$	6.82305	0.263597
$671$	20.7588	0.801385
$672$	−5.18024	−0.199832
$673$	30.2013	1.16417	0.582087	−	0.813127i	$-0.302236\pi$
$673$	30.2013	1.16417	0.582087	+	0.813127i	$0.302236\pi$
$674$	17.9362	0.690875
$675$	−0.580444	−0.0223413
$676$	−1.72474	−0.0663362
$677$	9.72052	0.373590	0.186795	−	0.982399i	$-0.440190\pi$
$677$	9.72052	0.373590	0.186795	+	0.982399i	$0.440190\pi$
$678$	−0.0496318	−0.00190610
$679$	4.33876	0.166506
$680$	4.61637	0.177030
$681$	12.0524	0.461849
$682$	−11.9323	−0.456910
$683$	22.2499	0.851370	0.425685	−	0.904871i	$-0.360033\pi$
$683$	22.2499	0.851370	0.425685	+	0.904871i	$0.360033\pi$
$684$	−9.20073	−0.351799
$685$	32.5089	1.24210
$686$	0.524651	0.0200313
$687$	−24.9793	−0.953021
$688$	−25.4626	−0.970753
$689$	−3.81061	−0.145173
$690$	−10.4420	−0.397520
$691$	−5.78917	−0.220230	−0.110115	−	0.993919i	$-0.535122\pi$
$691$	−5.78917	−0.220230	−0.110115	+	0.993919i	$0.535122\pi$
$692$	−7.07458	−0.268935
$693$	−6.20795	−0.235820
$694$	−9.55495	−0.362701
$695$	48.4873	1.83923
$696$	−9.14422	−0.346611
$697$	−5.66091	−0.214422
$698$	−2.75408	−0.104244
$699$	18.2812	0.691459
$700$	1.00112	0.0378387
$701$	−14.2508	−0.538247	−0.269123	−	0.963106i	$-0.586734\pi$
$701$	−14.2508	−0.538247	−0.269123	+	0.963106i	$0.586734\pi$
$702$	0.524651	0.0198017
$703$	−39.3320	−1.48343
$704$	−13.2268	−0.498502
$705$	−16.3032	−0.614015
$706$	−2.77357	−0.104385
$707$	−5.92009	−0.222648
$708$	−3.04852	−0.114571
$709$	−26.3322	−0.988925	−0.494462	−	0.869199i	$-0.664635\pi$
$709$	−26.3322	−0.988925	−0.494462	+	0.869199i	$0.664635\pi$
$710$	−2.72750	−0.102361
$711$	6.57083	0.246425
$712$	21.7743	0.816028
$713$	30.8663	1.15595
$714$	0.524651	0.0196346
$715$	−14.6650	−0.548440
$716$	−5.22585	−0.195299
$717$	15.3641	0.573783
$718$	−13.3283	−0.497408
$719$	35.5100	1.32430	0.662150	−	0.749371i	$-0.269644\pi$
$719$	35.5100	1.32430	0.662150	+	0.749371i	$0.269644\pi$
$720$	−5.72672	−0.213422
$721$	5.61607	0.209154
$722$	−4.96188	−0.184662
$723$	−1.06663	−0.0396685
$724$	−3.66176	−0.136088
$725$	2.71607	0.100872
$726$	14.4481	0.536221
$727$	35.8322	1.32894	0.664471	−	0.747314i	$-0.268657\pi$
$727$	35.8322	1.32894	0.664471	+	0.747314i	$0.268657\pi$
$728$	−1.95419	−0.0724270
$729$	1.00000	0.0370370
$730$	17.6770	0.654256
$731$	10.5034	0.388484
$732$	5.76738	0.213169
$733$	19.7698	0.730214	0.365107	−	0.930966i	$-0.381032\pi$
$733$	19.7698	0.730214	0.365107	+	0.930966i	$0.381032\pi$
$734$	4.48129	0.165407
$735$	2.36230	0.0871346
$736$	−43.6445	−1.60876
$737$	34.1760	1.25889
$738$	−2.97000	−0.109327
$739$	−7.64992	−0.281407	−0.140703	−	0.990052i	$-0.544936\pi$
$739$	−7.64992	−0.281407	−0.140703	+	0.990052i	$0.544936\pi$
$740$	−30.0404	−1.10431
$741$	−5.33456	−0.195970
$742$	−1.99924	−0.0733943
$743$	−48.7913	−1.78998	−0.894990	−	0.446085i	$-0.852818\pi$
$743$	−48.7913	−1.78998	−0.894990	+	0.446085i	$0.852818\pi$
$744$	−7.15931	−0.262473
$745$	7.43571	0.272423
$746$	−18.4574	−0.675772
$747$	−11.0689	−0.404990
$748$	10.7071	0.391491
$749$	−15.5886	−0.569595
$750$	5.47751	0.200010
$751$	3.07762	0.112304	0.0561520	−	0.998422i	$-0.482117\pi$
$751$	3.07762	0.112304	0.0561520	+	0.998422i	$0.482117\pi$
$752$	−16.7306	−0.610101
$753$	21.0887	0.768515
$754$	−2.45499	−0.0894056
$755$	−18.1378	−0.660104
$756$	−1.72474	−0.0627282
$757$	24.6910	0.897410	0.448705	−	0.893680i	$-0.351885\pi$
$757$	24.6910	0.897410	0.448705	+	0.893680i	$0.351885\pi$
$758$	7.51568	0.272982
$759$	−52.3031	−1.89848
$760$	−24.6263	−0.893290
$761$	5.18339	0.187898	0.0939489	−	0.995577i	$-0.470051\pi$
$761$	5.18339	0.187898	0.0939489	+	0.995577i	$0.470051\pi$
$762$	2.17600	0.0788282
$763$	−15.1231	−0.547493
$764$	−34.4520	−1.24643
$765$	2.36230	0.0854090
$766$	5.44891	0.196877
$767$	−1.76752	−0.0638216
$768$	1.76087	0.0635400
$769$	14.4393	0.520695	0.260348	−	0.965515i	$-0.416163\pi$
$769$	14.4393	0.520695	0.260348	+	0.965515i	$0.416163\pi$
$770$	−7.69401	−0.277273
$771$	18.0875	0.651404
$772$	−31.5916	−1.13700
$773$	32.6694	1.17504	0.587518	−	0.809211i	$-0.300105\pi$
$773$	32.6694	1.17504	0.587518	+	0.809211i	$0.300105\pi$
$774$	5.51063	0.198076
$775$	2.12650	0.0763862
$776$	−8.47876	−0.304370
$777$	−7.37305	−0.264507
$778$	−6.12584	−0.219622
$779$	30.1984	1.08197
$780$	−4.07435	−0.145885
$781$	−13.6618	−0.488859
$782$	4.42027	0.158069
$783$	−4.67929	−0.167224
$784$	2.42422	0.0865792
$785$	29.8872	1.06672
$786$	−5.77317	−0.205922
$787$	−28.2105	−1.00559	−0.502797	−	0.864404i	$-0.667696\pi$
$787$	−28.2105	−1.00559	−0.502797	+	0.864404i	$0.667696\pi$
$788$	−12.4262	−0.442665
$789$	−26.2033	−0.932864
$790$	8.14376	0.289742
$791$	0.0945998	0.00336358
$792$	12.1315	0.431074
$793$	3.34391	0.118746
$794$	−17.8470	−0.633366
$795$	−9.00178	−0.319260
$796$	30.2469	1.07207
$797$	−52.7939	−1.87006	−0.935029	−	0.354572i	$-0.884627\pi$
$797$	−52.7939	−1.87006	−0.935029	+	0.354572i	$0.884627\pi$
$798$	−2.79878	−0.0990757
$799$	6.90143	0.244155
$800$	−3.00684	−0.106308
$801$	11.1424	0.393697
$802$	19.5202	0.689281
$803$	88.5427	3.12460
$804$	9.49506	0.334865
$805$	19.9028	0.701480
$806$	−1.92210	−0.0677029
$807$	21.6058	0.760561
$808$	11.5690	0.406995
$809$	−18.9636	−0.666725	−0.333363	−	0.942799i	$-0.608183\pi$
$809$	−18.9636	−0.666725	−0.333363	+	0.942799i	$0.608183\pi$
$810$	1.23938	0.0435474
$811$	−51.2777	−1.80060	−0.900302	−	0.435266i	$-0.856654\pi$
$811$	−51.2777	−1.80060	−0.900302	+	0.435266i	$0.856654\pi$
$812$	8.07057	0.283222
$813$	−22.3402	−0.783505
$814$	24.0141	0.841692
$815$	24.8914	0.871909
$816$	2.42422	0.0848646
$817$	−56.0312	−1.96028
$818$	8.08196	0.282579
$819$	−1.00000	−0.0349428
$820$	23.0645	0.805448
$821$	−46.4510	−1.62115	−0.810575	−	0.585635i	$-0.800845\pi$
$821$	−46.4510	−1.62115	−0.810575	+	0.585635i	$0.800845\pi$
$822$	−7.22001	−0.251827
$823$	20.8830	0.727936	0.363968	−	0.931411i	$-0.381422\pi$
$823$	20.8830	0.727936	0.363968	+	0.931411i	$0.381422\pi$
$824$	−10.9749	−0.382328
$825$	−3.60337	−0.125453
$826$	−0.927333	−0.0322660
$827$	−9.58021	−0.333137	−0.166568	−	0.986030i	$-0.553269\pi$
$827$	−9.58021	−0.333137	−0.166568	+	0.986030i	$0.553269\pi$
$828$	−14.5313	−0.504996
$829$	13.9883	0.485834	0.242917	−	0.970047i	$-0.421896\pi$
$829$	13.9883	0.485834	0.242917	+	0.970047i	$0.421896\pi$
$830$	−13.7186	−0.476179
$831$	−18.2956	−0.634668
$832$	−2.13062	−0.0738658
$833$	−1.00000	−0.0346479
$834$	−10.7687	−0.372890
$835$	43.8751	1.51836
$836$	−57.1177	−1.97546
$837$	−3.66357	−0.126632
$838$	14.2745	0.493106
$839$	35.7712	1.23496	0.617479	−	0.786587i	$-0.288154\pi$
$839$	35.7712	1.23496	0.617479	+	0.786587i	$0.288154\pi$
$840$	−4.61637	−0.159280
$841$	−7.10422	−0.244973
$842$	1.56614	0.0539726
$843$	2.48117	0.0854561
$844$	−22.3218	−0.768349
$845$	−2.36230	−0.0812655
$846$	3.62084	0.124487
$847$	−27.5386	−0.946238
$848$	−9.23774	−0.317225
$849$	−2.98801	−0.102548
$850$	0.304531	0.0104453
$851$	−62.1193	−2.12942
$852$	−3.79564	−0.130036
$853$	10.6788	0.365636	0.182818	−	0.983147i	$-0.441478\pi$
$853$	10.6788	0.365636	0.182818	+	0.983147i	$0.441478\pi$
$854$	1.75438	0.0600338
$855$	−12.6018	−0.430973
$856$	30.4630	1.04121
$857$	3.35574	0.114630	0.0573150	−	0.998356i	$-0.481746\pi$
$857$	3.35574	0.114630	0.0573150	+	0.998356i	$0.481746\pi$
$858$	3.25700	0.111192
$859$	11.3566	0.387483	0.193742	−	0.981053i	$-0.437938\pi$
$859$	11.3566	0.387483	0.193742	+	0.981053i	$0.437938\pi$
$860$	−42.7947	−1.45929
$861$	5.66091	0.192923
$862$	−0.0256338	−0.000873091 0
$863$	48.0053	1.63412	0.817059	−	0.576554i	$-0.195603\pi$
$863$	48.0053	1.63412	0.817059	+	0.576554i	$0.195603\pi$
$864$	5.18024	0.176235
$865$	−9.68972	−0.329460
$866$	−9.36771	−0.318328
$867$	−1.00000	−0.0339618
$868$	6.31872	0.214471
$869$	40.7914	1.38375
$870$	−5.79942	−0.196619
$871$	5.50521	0.186537
$872$	29.5534	1.00080
$873$	−4.33876	−0.146845
$874$	−23.5802	−0.797612
$875$	−10.4403	−0.352947
$876$	24.5996	0.831145
$877$	−23.0927	−0.779784	−0.389892	−	0.920861i	$-0.627488\pi$
$877$	−23.0927	−0.779784	−0.389892	+	0.920861i	$0.627488\pi$
$878$	5.24245	0.176924
$879$	−1.16364	−0.0392487
$880$	−35.5512	−1.19843
$881$	−18.2674	−0.615443	−0.307721	−	0.951477i	$-0.599566\pi$
$881$	−18.2674	−0.615443	−0.307721	+	0.951477i	$0.599566\pi$
$882$	−0.524651	−0.0176659
$883$	−44.4271	−1.49509	−0.747546	−	0.664210i	$-0.768768\pi$
$883$	−44.4271	−1.49509	−0.747546	+	0.664210i	$0.768768\pi$
$884$	1.72474	0.0580093
$885$	−4.17542	−0.140355
$886$	−12.3778	−0.415840
$887$	−1.98407	−0.0666185	−0.0333092	−	0.999445i	$-0.510605\pi$
$887$	−1.98407	−0.0666185	−0.0333092	+	0.999445i	$0.510605\pi$
$888$	14.4083	0.483512
$889$	−4.14752	−0.139104
$890$	13.8097	0.462901
$891$	6.20795	0.207974
$892$	0.304247	0.0101870
$893$	−36.8161	−1.23200
$894$	−1.65142	−0.0552318
$895$	−7.15759	−0.239252
$896$	−11.4783	−0.383464
$897$	−8.42518	−0.281308
$898$	3.75673	0.125364
$899$	17.1429	0.571749
$900$	−1.00112	−0.0333706
$901$	3.81061	0.126950
$902$	−18.4376	−0.613905
$903$	−10.5034	−0.349532
$904$	−0.184866	−0.00614855
$905$	−5.01534	−0.166716
$906$	4.02830	0.133831
$907$	39.4707	1.31060	0.655301	−	0.755368i	$-0.272542\pi$
$907$	39.4707	1.31060	0.655301	+	0.755368i	$0.272542\pi$
$908$	20.7873	0.689851
$909$	5.92009	0.196357
$910$	−1.23938	−0.0410851
$911$	30.1046	0.997411	0.498706	−	0.866771i	$-0.333809\pi$
$911$	30.1046	0.997411	0.498706	+	0.866771i	$0.333809\pi$
$912$	−12.9321	−0.428225
$913$	−68.7152	−2.27414
$914$	−10.7800	−0.356570
$915$	7.89931	0.261143
$916$	−43.0829	−1.42350
$917$	11.0038	0.363379
$918$	−0.524651	−0.0173161
$919$	−26.0147	−0.858144	−0.429072	−	0.903270i	$-0.641159\pi$
$919$	−26.0147	−0.858144	−0.429072	+	0.903270i	$0.641159\pi$
$920$	−38.8937	−1.28229
$921$	−22.6149	−0.745185
$922$	12.9793	0.427451
$923$	−2.20070	−0.0724369
$924$	−10.7071	−0.352238
$925$	−4.27965	−0.140714
$926$	−9.92596	−0.326187
$927$	−5.61607	−0.184456
$928$	−24.2399	−0.795713
$929$	51.4715	1.68872	0.844362	−	0.535773i	$-0.179980\pi$
$929$	51.4715	1.68872	0.844362	+	0.535773i	$0.179980\pi$
$930$	−4.54056	−0.148891
$931$	5.33456	0.174833
$932$	31.5304	1.03281
$933$	−3.69078	−0.120831
$934$	1.58066	0.0517207
$935$	14.6650	0.479597
$936$	1.95419	0.0638746
$937$	29.2525	0.955637	0.477818	−	0.878459i	$-0.341428\pi$
$937$	29.2525	0.955637	0.477818	+	0.878459i	$0.341428\pi$
$938$	2.88831	0.0943067
$939$	24.1514	0.788151
$940$	−28.1189	−0.917136
$941$	−36.1910	−1.17979	−0.589896	−	0.807479i	$-0.700831\pi$
$941$	−36.1910	−1.17979	−0.589896	+	0.807479i	$0.700831\pi$
$942$	−6.63776	−0.216270
$943$	47.6941	1.55313
$944$	−4.28486	−0.139460
$945$	−2.36230	−0.0768455
$946$	34.2097	1.11225
$947$	26.2440	0.852815	0.426408	−	0.904531i	$-0.359779\pi$
$947$	26.2440	0.852815	0.426408	+	0.904531i	$0.359779\pi$
$948$	11.3330	0.368078
$949$	14.2628	0.462990
$950$	−1.62454	−0.0527069
$951$	3.92574	0.127301
$952$	1.95419	0.0633356
$953$	−56.5943	−1.83327	−0.916634	−	0.399727i	$-0.869105\pi$
$953$	−56.5943	−1.83327	−0.916634	+	0.399727i	$0.869105\pi$
$954$	1.99924	0.0647277
$955$	−47.1873	−1.52695
$956$	26.4991	0.857042
$957$	−29.0488	−0.939014
$958$	−20.4495	−0.660692
$959$	13.7616	0.444384
$960$	−5.03315	−0.162444
$961$	−17.5782	−0.567040
$962$	3.86828	0.124718
$963$	15.5886	0.502335
$964$	−1.83967	−0.0592516
$965$	−43.2694	−1.39289
$966$	−4.42027	−0.142220
$967$	35.3481	1.13672	0.568360	−	0.822780i	$-0.307578\pi$
$967$	35.3481	1.13672	0.568360	+	0.822780i	$0.307578\pi$
$968$	53.8156	1.72970
$969$	5.33456	0.171371
$970$	−5.37738	−0.172657
$971$	55.5101	1.78140	0.890702	−	0.454588i	$-0.150214\pi$
$971$	55.5101	1.78140	0.890702	+	0.454588i	$0.150214\pi$
$972$	1.72474	0.0553211
$973$	20.5255	0.658018
$974$	7.73365	0.247802
$975$	−0.580444	−0.0185891
$976$	8.10636	0.259478
$977$	13.6359	0.436252	0.218126	−	0.975921i	$-0.430006\pi$
$977$	13.6359	0.436252	0.218126	+	0.975921i	$0.430006\pi$
$978$	−5.52822	−0.176773
$979$	69.1714	2.21073
$980$	4.07435	0.130150
$981$	15.1231	0.482844
$982$	−6.73170	−0.214817
$983$	−26.6078	−0.848658	−0.424329	−	0.905508i	$-0.639490\pi$
$983$	−26.6078	−0.848658	−0.424329	+	0.905508i	$0.639490\pi$
$984$	−11.0625	−0.352659
$985$	−17.0196	−0.542289
$986$	2.45499	0.0781829
$987$	−6.90143	−0.219675
$988$	−9.20073	−0.292714
$989$	−88.4933	−2.81392
$990$	7.69401	0.244532
$991$	3.67845	0.116850	0.0584248	−	0.998292i	$-0.481392\pi$
$991$	3.67845	0.116850	0.0584248	+	0.998292i	$0.481392\pi$
$992$	−18.9782	−0.602558
$993$	−12.0676	−0.382953
$994$	−1.15460	−0.0366217
$995$	41.4277	1.31335
$996$	−19.0910	−0.604922
$997$	21.0371	0.666251	0.333125	−	0.942883i	$-0.391897\pi$
$997$	21.0371	0.666251	0.333125	+	0.942883i	$0.391897\pi$
$998$	1.61609	0.0511564
$999$	7.37305	0.233273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.ba.1.7	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.ba.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-0.524651 q^{2} -1.00000 q^{3} -1.72474 q^{4} -2.36230 q^{5} +0.524651 q^{6} -1.00000 q^{7} +1.95419 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.524651 q^{2} -1.00000 q^{3} -1.72474 q^{4} -2.36230 q^{5} +0.524651 q^{6} -1.00000 q^{7} +1.95419 q^{8} +1.00000 q^{9} +1.23938 q^{10} +6.20795 q^{11} +1.72474 q^{12} +1.00000 q^{13} +0.524651 q^{14} +2.36230 q^{15} +2.42422 q^{16} -1.00000 q^{17} -0.524651 q^{18} +5.33456 q^{19} +4.07435 q^{20} +1.00000 q^{21} -3.25700 q^{22} +8.42518 q^{23} -1.95419 q^{24} +0.580444 q^{25} -0.524651 q^{26} -1.00000 q^{27} +1.72474 q^{28} +4.67929 q^{29} -1.23938 q^{30} +3.66357 q^{31} -5.18024 q^{32} -6.20795 q^{33} +0.524651 q^{34} +2.36230 q^{35} -1.72474 q^{36} -7.37305 q^{37} -2.79878 q^{38} -1.00000 q^{39} -4.61637 q^{40} +5.66091 q^{41} -0.524651 q^{42} -10.5034 q^{43} -10.7071 q^{44} -2.36230 q^{45} -4.42027 q^{46} -6.90143 q^{47} -2.42422 q^{48} +1.00000 q^{49} -0.304531 q^{50} +1.00000 q^{51} -1.72474 q^{52} -3.81061 q^{53} +0.524651 q^{54} -14.6650 q^{55} -1.95419 q^{56} -5.33456 q^{57} -2.45499 q^{58} -1.76752 q^{59} -4.07435 q^{60} +3.34391 q^{61} -1.92210 q^{62} -1.00000 q^{63} -2.13062 q^{64} -2.36230 q^{65} +3.25700 q^{66} +5.50521 q^{67} +1.72474 q^{68} -8.42518 q^{69} -1.23938 q^{70} -2.20070 q^{71} +1.95419 q^{72} +14.2628 q^{73} +3.86828 q^{74} -0.580444 q^{75} -9.20073 q^{76} -6.20795 q^{77} +0.524651 q^{78} +6.57083 q^{79} -5.72672 q^{80} +1.00000 q^{81} -2.97000 q^{82} -11.0689 q^{83} -1.72474 q^{84} +2.36230 q^{85} +5.51063 q^{86} -4.67929 q^{87} +12.1315 q^{88} +11.1424 q^{89} +1.23938 q^{90} -1.00000 q^{91} -14.5313 q^{92} -3.66357 q^{93} +3.62084 q^{94} -12.6018 q^{95} +5.18024 q^{96} -4.33876 q^{97} -0.524651 q^{98} +6.20795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) \) 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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