LMFDB - Embedded newform 353.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [353,2,Mod(1,353)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(353, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("353.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	353.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:	$2.81871919135$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} - 14 x^{12} + 71 x^{11} + 47 x^{10} - 452 x^{9} + 101 x^{8} + 1251 x^{7} - 740 x^{6} + \cdots - 1 $ x^14 - 4x^13 - 14x^12 + 71x^11 + 47x^10 - 452x^9 + 101x^8 + 1251x^7 - 740x^6 - 1488x^5 + 1096x^4 + 600x^3 - 410x^2 - 42*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.41172$ of defining polynomial
Character	$\chi$	$=$	353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41172 q^{2} +2.61874 q^{3} -0.00705285 q^{4} +3.04446 q^{5} -3.69692 q^{6} +5.11343 q^{7} +2.83339 q^{8} +3.85779 q^{9} +O(q^{10})$	\(q-1.41172 q^{2} +2.61874 q^{3} -0.00705285 q^{4} +3.04446 q^{5} -3.69692 q^{6} +5.11343 q^{7} +2.83339 q^{8} +3.85779 q^{9} -4.29792 q^{10} -5.60579 q^{11} -0.0184696 q^{12} -4.54347 q^{13} -7.21873 q^{14} +7.97265 q^{15} -3.98584 q^{16} -0.673860 q^{17} -5.44611 q^{18} -1.47041 q^{19} -0.0214721 q^{20} +13.3907 q^{21} +7.91380 q^{22} -3.58108 q^{23} +7.41991 q^{24} +4.26875 q^{25} +6.41410 q^{26} +2.24633 q^{27} -0.0360643 q^{28} -3.94782 q^{29} -11.2551 q^{30} +3.77024 q^{31} -0.0398967 q^{32} -14.6801 q^{33} +0.951300 q^{34} +15.5677 q^{35} -0.0272084 q^{36} -8.44910 q^{37} +2.07580 q^{38} -11.8982 q^{39} +8.62616 q^{40} +7.82680 q^{41} -18.9040 q^{42} +6.68167 q^{43} +0.0395368 q^{44} +11.7449 q^{45} +5.05547 q^{46} -6.32711 q^{47} -10.4379 q^{48} +19.1472 q^{49} -6.02627 q^{50} -1.76466 q^{51} +0.0320444 q^{52} +1.77362 q^{53} -3.17118 q^{54} -17.0666 q^{55} +14.4884 q^{56} -3.85061 q^{57} +5.57320 q^{58} -6.66991 q^{59} -0.0562299 q^{60} -4.03506 q^{61} -5.32251 q^{62} +19.7266 q^{63} +8.02801 q^{64} -13.8324 q^{65} +20.7242 q^{66} -0.538541 q^{67} +0.00475263 q^{68} -9.37790 q^{69} -21.9771 q^{70} -1.60224 q^{71} +10.9306 q^{72} +10.8613 q^{73} +11.9278 q^{74} +11.1787 q^{75} +0.0103705 q^{76} -28.6649 q^{77} +16.7969 q^{78} +16.9961 q^{79} -12.1348 q^{80} -5.69082 q^{81} -11.0492 q^{82} -4.48784 q^{83} -0.0944429 q^{84} -2.05154 q^{85} -9.43263 q^{86} -10.3383 q^{87} -15.8834 q^{88} -8.48296 q^{89} -16.5805 q^{90} -23.2327 q^{91} +0.0252568 q^{92} +9.87327 q^{93} +8.93209 q^{94} -4.47659 q^{95} -0.104479 q^{96} +1.99439 q^{97} -27.0305 q^{98} -21.6260 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4 q^{2} - 2 q^{3} + 16 q^{4} - 4 q^{5} - 8 q^{6} + 29 q^{7} + 3 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q + 4 * q^2 - 2 * q^3 + 16 * q^4 - 4 * q^5 - 8 * q^6 + 29 * q^7 + 3 * q^8 + 14 * q^9	\( 14 q + 4 q^{2} - 2 q^{3} + 16 q^{4} - 4 q^{5} - 8 q^{6} + 29 q^{7} + 3 q^{8} + 14 q^{9} + 15 q^{10} - 7 q^{11} - 4 q^{12} + 2 q^{13} + 8 q^{14} + 16 q^{15} + 12 q^{16} + 8 q^{17} + 5 q^{18} + 14 q^{19} - 5 q^{20} + 6 q^{21} + 25 q^{22} + 16 q^{23} - 23 q^{24} + 24 q^{25} - 2 q^{26} - 8 q^{27} + 39 q^{28} - 9 q^{29} - 15 q^{30} + 28 q^{31} - 10 q^{32} - 10 q^{33} - 26 q^{34} - 16 q^{35} + 36 q^{36} + 8 q^{37} - 24 q^{38} - 23 q^{39} - 4 q^{40} + 14 q^{41} - 44 q^{42} + 11 q^{43} - 41 q^{44} - 37 q^{45} + 27 q^{46} + 14 q^{47} - 71 q^{48} + 39 q^{49} + 4 q^{50} - 6 q^{51} + 3 q^{52} - 27 q^{53} - 50 q^{54} + 3 q^{55} + 19 q^{56} + 7 q^{57} - 11 q^{58} - 25 q^{59} - 2 q^{60} - 3 q^{61} - 3 q^{62} + 56 q^{63} - 15 q^{64} - 41 q^{65} - 38 q^{66} + 37 q^{67} - 17 q^{68} - 32 q^{69} - 32 q^{70} + 3 q^{71} + 29 q^{72} + 14 q^{73} - 29 q^{74} + 15 q^{75} - 18 q^{76} - 43 q^{77} - 67 q^{78} + 39 q^{79} - 44 q^{80} - 26 q^{81} - 42 q^{82} + 9 q^{83} - 78 q^{84} - 12 q^{85} - 24 q^{86} + 26 q^{87} - 21 q^{88} - 95 q^{90} + 12 q^{91} + 61 q^{92} - 7 q^{93} - 52 q^{94} - 81 q^{96} + 24 q^{97} - 24 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q + 4 * q^2 - 2 * q^3 + 16 * q^4 - 4 * q^5 - 8 * q^6 + 29 * q^7 + 3 * q^8 + 14 * q^9 + 15 * q^10 - 7 * q^11 - 4 * q^12 + 2 * q^13 + 8 * q^14 + 16 * q^15 + 12 * q^16 + 8 * q^17 + 5 * q^18 + 14 * q^19 - 5 * q^20 + 6 * q^21 + 25 * q^22 + 16 * q^23 - 23 * q^24 + 24 * q^25 - 2 * q^26 - 8 * q^27 + 39 * q^28 - 9 * q^29 - 15 * q^30 + 28 * q^31 - 10 * q^32 - 10 * q^33 - 26 * q^34 - 16 * q^35 + 36 * q^36 + 8 * q^37 - 24 * q^38 - 23 * q^39 - 4 * q^40 + 14 * q^41 - 44 * q^42 + 11 * q^43 - 41 * q^44 - 37 * q^45 + 27 * q^46 + 14 * q^47 - 71 * q^48 + 39 * q^49 + 4 * q^50 - 6 * q^51 + 3 * q^52 - 27 * q^53 - 50 * q^54 + 3 * q^55 + 19 * q^56 + 7 * q^57 - 11 * q^58 - 25 * q^59 - 2 * q^60 - 3 * q^61 - 3 * q^62 + 56 * q^63 - 15 * q^64 - 41 * q^65 - 38 * q^66 + 37 * q^67 - 17 * q^68 - 32 * q^69 - 32 * q^70 + 3 * q^71 + 29 * q^72 + 14 * q^73 - 29 * q^74 + 15 * q^75 - 18 * q^76 - 43 * q^77 - 67 * q^78 + 39 * q^79 - 44 * q^80 - 26 * q^81 - 42 * q^82 + 9 * q^83 - 78 * q^84 - 12 * q^85 - 24 * q^86 + 26 * q^87 - 21 * q^88 - 95 * q^90 + 12 * q^91 + 61 * q^92 - 7 * q^93 - 52 * q^94 - 81 * q^96 + 24 * q^97 - 24 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.41172	−0.998235	−0.499118	−	0.866534i	$-0.666342\pi$
$2$	−1.41172	−0.998235	−0.499118	+	0.866534i	$0.666342\pi$
$3$	2.61874	1.51193	0.755965	−	0.654612i	$-0.227168\pi$
$3$	2.61874	1.51193	0.755965	+	0.654612i	$0.227168\pi$
$4$	−0.00705285	−0.00352642
$5$	3.04446	1.36152	0.680762	−	0.732504i	$-0.261649\pi$
$5$	3.04446	1.36152	0.680762	+	0.732504i	$0.261649\pi$
$6$	−3.69692	−1.50926
$7$	5.11343	1.93270	0.966348	−	0.257238i	$-0.0828123\pi$
$7$	5.11343	1.93270	0.966348	+	0.257238i	$0.0828123\pi$
$8$	2.83339	1.00176
$9$	3.85779	1.28593
$10$	−4.29792	−1.35912
$11$	−5.60579	−1.69021	−0.845105	−	0.534600i	$-0.820462\pi$
$11$	−5.60579	−1.69021	−0.845105	+	0.534600i	$0.820462\pi$
$12$	−0.0184696	−0.00533170
$13$	−4.54347	−1.26013	−0.630066	−	0.776541i	$-0.716972\pi$
$13$	−4.54347	−1.26013	−0.630066	+	0.776541i	$0.716972\pi$
$14$	−7.21873	−1.92929
$15$	7.97265	2.05853
$16$	−3.98584	−0.996461
$17$	−0.673860	−0.163435	−0.0817175	−	0.996656i	$-0.526041\pi$
$17$	−0.673860	−0.163435	−0.0817175	+	0.996656i	$0.526041\pi$
$18$	−5.44611	−1.28366
$19$	−1.47041	−0.337334	−0.168667	−	0.985673i	$-0.553946\pi$
$19$	−1.47041	−0.337334	−0.168667	+	0.985673i	$0.553946\pi$
$20$	−0.0214721	−0.00480131
$21$	13.3907	2.92210
$22$	7.91380	1.68723
$23$	−3.58108	−0.746706	−0.373353	−	0.927689i	$-0.621792\pi$
$23$	−3.58108	−0.746706	−0.373353	+	0.927689i	$0.621792\pi$
$24$	7.41991	1.51458
$25$	4.26875	0.853750
$26$	6.41410	1.25791
$27$	2.24633	0.432306
$28$	−0.0360643	−0.00681551
$29$	−3.94782	−0.733091	−0.366546	−	0.930400i	$-0.619460\pi$
$29$	−3.94782	−0.733091	−0.366546	+	0.930400i	$0.619460\pi$
$30$	−11.2551	−2.05490
$31$	3.77024	0.677155	0.338577	−	0.940939i	$-0.390054\pi$
$31$	3.77024	0.677155	0.338577	+	0.940939i	$0.390054\pi$
$32$	−0.0398967	−0.00705282
$33$	−14.6801	−2.55548
$34$	0.951300	0.163147
$35$	15.5677	2.63141
$36$	−0.0272084	−0.00453473
$37$	−8.44910	−1.38902	−0.694512	−	0.719481i	$-0.744380\pi$
$37$	−8.44910	−1.38902	−0.694512	+	0.719481i	$0.744380\pi$
$38$	2.07580	0.336739
$39$	−11.8982	−1.90523
$40$	8.62616	1.36391
$41$	7.82680	1.22234	0.611171	−	0.791499i	$-0.290699\pi$
$41$	7.82680	1.22234	0.611171	+	0.791499i	$0.290699\pi$
$42$	−18.9040	−2.91694
$43$	6.68167	1.01894	0.509472	−	0.860487i	$-0.329841\pi$
$43$	6.68167	1.01894	0.509472	+	0.860487i	$0.329841\pi$
$44$	0.0395368	0.00596040
$45$	11.7449	1.75083
$46$	5.05547	0.745388
$47$	−6.32711	−0.922904	−0.461452	−	0.887165i	$-0.652671\pi$
$47$	−6.32711	−0.922904	−0.461452	+	0.887165i	$0.652671\pi$
$48$	−10.4379	−1.50658
$49$	19.1472	2.73532
$50$	−6.02627	−0.852243
$51$	−1.76466	−0.247102
$52$	0.0320444	0.00444376
$53$	1.77362	0.243626	0.121813	−	0.992553i	$-0.461129\pi$
$53$	1.77362	0.243626	0.121813	+	0.992553i	$0.461129\pi$
$54$	−3.17118	−0.431543
$55$	−17.0666	−2.30126
$56$	14.4884	1.93609
$57$	−3.85061	−0.510025
$58$	5.57320	0.731797
$59$	−6.66991	−0.868348	−0.434174	−	0.900829i	$-0.642960\pi$
$59$	−6.66991	−0.868348	−0.434174	+	0.900829i	$0.642960\pi$
$60$	−0.0562299	−0.00725925
$61$	−4.03506	−0.516637	−0.258319	−	0.966060i	$-0.583168\pi$
$61$	−4.03506	−0.516637	−0.258319	+	0.966060i	$0.583168\pi$
$62$	−5.32251	−0.675960
$63$	19.7266	2.48531
$64$	8.02801	1.00350
$65$	−13.8324	−1.71570
$66$	20.7242	2.55097
$67$	−0.538541	−0.0657933	−0.0328966	−	0.999459i	$-0.510473\pi$
$67$	−0.538541	−0.0657933	−0.0328966	+	0.999459i	$0.510473\pi$
$68$	0.00475263	0.000576341 0
$69$	−9.37790	−1.12897
$70$	−21.9771	−2.62677
$71$	−1.60224	−0.190151	−0.0950755	−	0.995470i	$-0.530309\pi$
$71$	−1.60224	−0.190151	−0.0950755	+	0.995470i	$0.530309\pi$
$72$	10.9306	1.28819
$73$	10.8613	1.27122	0.635610	−	0.772011i	$-0.280749\pi$
$73$	10.8613	1.27122	0.635610	+	0.772011i	$0.280749\pi$
$74$	11.9278	1.38657
$75$	11.1787	1.29081
$76$	0.0103705	0.00118958
$77$	−28.6649	−3.26666
$78$	16.7969	1.90187
$79$	16.9961	1.91221	0.956106	−	0.293022i	$-0.0946611\pi$
$79$	16.9961	1.91221	0.956106	+	0.293022i	$0.0946611\pi$
$80$	−12.1348	−1.35671
$81$	−5.69082	−0.632314
$82$	−11.0492	−1.22018
$83$	−4.48784	−0.492605	−0.246302	−	0.969193i	$-0.579216\pi$
$83$	−4.48784	−0.492605	−0.246302	+	0.969193i	$0.579216\pi$
$84$	−0.0944429	−0.0103046
$85$	−2.05154	−0.222521
$86$	−9.43263	−1.01715
$87$	−10.3383	−1.10838
$88$	−15.8834	−1.69318
$89$	−8.48296	−0.899192	−0.449596	−	0.893232i	$-0.648432\pi$
$89$	−8.48296	−0.899192	−0.449596	+	0.893232i	$0.648432\pi$
$90$	−16.5805	−1.74774
$91$	−23.2327	−2.43545
$92$	0.0252568	0.00263320
$93$	9.87327	1.02381
$94$	8.93209	0.921275
$95$	−4.47659	−0.459289
$96$	−0.104479	−0.0106634
$97$	1.99439	0.202500	0.101250	−	0.994861i	$-0.467716\pi$
$97$	1.99439	0.202500	0.101250	+	0.994861i	$0.467716\pi$
$98$	−27.0305	−2.73049
$99$	−21.6260	−2.17349
$100$	−0.0301068	−0.00301068
$101$	−4.10575	−0.408538	−0.204269	−	0.978915i	$-0.565482\pi$
$101$	−4.10575	−0.408538	−0.204269	+	0.978915i	$0.565482\pi$
$102$	2.49121	0.246666
$103$	12.9859	1.27954	0.639771	−	0.768566i	$-0.279029\pi$
$103$	12.9859	1.27954	0.639771	+	0.768566i	$0.279029\pi$
$104$	−12.8734	−1.26234
$105$	40.7676	3.97851
$106$	−2.50386	−0.243196
$107$	−6.07667	−0.587454	−0.293727	−	0.955889i	$-0.594896\pi$
$107$	−6.07667	−0.587454	−0.293727	+	0.955889i	$0.594896\pi$
$108$	−0.0158430	−0.00152449
$109$	10.0360	0.961279	0.480639	−	0.876918i	$-0.340405\pi$
$109$	10.0360	0.961279	0.480639	+	0.876918i	$0.340405\pi$
$110$	24.0933	2.29720
$111$	−22.1260	−2.10011
$112$	−20.3814	−1.92586
$113$	1.11671	0.105052	0.0525258	−	0.998620i	$-0.483273\pi$
$113$	1.11671	0.105052	0.0525258	+	0.998620i	$0.483273\pi$
$114$	5.43597	0.509125
$115$	−10.9024	−1.01666
$116$	0.0278434	0.00258519
$117$	−17.5278	−1.62044
$118$	9.41603	0.866816
$119$	−3.44574	−0.315870
$120$	22.5896	2.06214
$121$	20.4249	1.85681
$122$	5.69637	0.515725
$123$	20.4964	1.84809
$124$	−0.0265909	−0.00238793
$125$	−2.22627	−0.199123
$126$	−27.8483	−2.48093
$127$	3.76595	0.334174	0.167087	−	0.985942i	$-0.446564\pi$
$127$	3.76595	0.334174	0.167087	+	0.985942i	$0.446564\pi$
$128$	−11.2535	−0.994678
$129$	17.4975	1.54057
$130$	19.5275	1.71267
$131$	16.6771	1.45708	0.728542	−	0.685001i	$-0.240198\pi$
$131$	16.6771	1.45708	0.728542	+	0.685001i	$0.240198\pi$
$132$	0.103537	0.00901170
$133$	−7.51882	−0.651964
$134$	0.760268	0.0656771
$135$	6.83886	0.588596
$136$	−1.90931	−0.163722
$137$	8.32520	0.711270	0.355635	−	0.934625i	$-0.384265\pi$
$137$	8.32520	0.711270	0.355635	+	0.934625i	$0.384265\pi$
$138$	13.2389	1.12697
$139$	−18.2291	−1.54617	−0.773085	−	0.634302i	$-0.781288\pi$
$139$	−18.2291	−1.54617	−0.773085	+	0.634302i	$0.781288\pi$
$140$	−0.109796	−0.00927948
$141$	−16.5690	−1.39536
$142$	2.26191	0.189815
$143$	25.4698	2.12989
$144$	−15.3766	−1.28138
$145$	−12.0190	−0.998122
$146$	−15.3331	−1.26898
$147$	50.1415	4.13560
$148$	0.0595902	0.00489829
$149$	1.00216	0.0821003	0.0410502	−	0.999157i	$-0.486930\pi$
$149$	1.00216	0.0821003	0.0410502	+	0.999157i	$0.486930\pi$
$150$	−15.7812	−1.28853
$151$	1.13674	0.0925062	0.0462531	−	0.998930i	$-0.485272\pi$
$151$	1.13674	0.0925062	0.0462531	+	0.998930i	$0.485272\pi$
$152$	−4.16624	−0.337926
$153$	−2.59961	−0.210166
$154$	40.4667	3.26090
$155$	11.4783	0.921963
$156$	0.0839160	0.00671865
$157$	−17.0879	−1.36376	−0.681881	−	0.731463i	$-0.738838\pi$
$157$	−17.0879	−1.36376	−0.681881	+	0.731463i	$0.738838\pi$
$158$	−23.9937	−1.90884
$159$	4.64466	0.368345
$160$	−0.121464	−0.00960258
$161$	−18.3116	−1.44316
$162$	8.03384	0.631198
$163$	−7.00795	−0.548905	−0.274453	−	0.961601i	$-0.588497\pi$
$163$	−7.00795	−0.548905	−0.274453	+	0.961601i	$0.588497\pi$
$164$	−0.0552013	−0.00431049
$165$	−44.6930	−3.47935
$166$	6.33557	0.491735
$167$	15.4504	1.19559	0.597795	−	0.801649i	$-0.296044\pi$
$167$	15.4504	1.19559	0.597795	+	0.801649i	$0.296044\pi$
$168$	37.9412	2.92723
$169$	7.64314	0.587934
$170$	2.89620	0.222128
$171$	−5.67252	−0.433788
$172$	−0.0471248	−0.00359323
$173$	0.806790	0.0613391	0.0306696	−	0.999530i	$-0.490236\pi$
$173$	0.806790	0.0613391	0.0306696	+	0.999530i	$0.490236\pi$
$174$	14.5948	1.10643
$175$	21.8280	1.65004
$176$	22.3438	1.68423
$177$	−17.4667	−1.31288
$178$	11.9756	0.897605
$179$	5.40379	0.403898	0.201949	−	0.979396i	$-0.435272\pi$
$179$	5.40379	0.403898	0.201949	+	0.979396i	$0.435272\pi$
$180$	−0.0828350	−0.00617415
$181$	19.3386	1.43743	0.718713	−	0.695307i	$-0.244732\pi$
$181$	19.3386	1.43743	0.718713	+	0.695307i	$0.244732\pi$
$182$	32.7981	2.43116
$183$	−10.5668	−0.781119
$184$	−10.1466	−0.748017
$185$	−25.7230	−1.89119
$186$	−13.9383	−1.02200
$187$	3.77752	0.276240
$188$	0.0446241	0.00325455
$189$	11.4865	0.835516
$190$	6.31969	0.458478
$191$	−10.2501	−0.741670	−0.370835	−	0.928699i	$-0.620928\pi$
$191$	−10.2501	−0.741670	−0.370835	+	0.928699i	$0.620928\pi$
$192$	21.0233	1.51722
$193$	6.11743	0.440342	0.220171	−	0.975461i	$-0.429338\pi$
$193$	6.11743	0.440342	0.220171	+	0.975461i	$0.429338\pi$
$194$	−2.81552	−0.202143
$195$	−36.2235	−2.59402
$196$	−0.135042	−0.00964588
$197$	−9.92518	−0.707140	−0.353570	−	0.935408i	$-0.615032\pi$
$197$	−9.92518	−0.707140	−0.353570	+	0.935408i	$0.615032\pi$
$198$	30.5298	2.16966
$199$	2.18701	0.155033	0.0775165	−	0.996991i	$-0.475301\pi$
$199$	2.18701	0.155033	0.0775165	+	0.996991i	$0.475301\pi$
$200$	12.0950	0.855249
$201$	−1.41030	−0.0994747
$202$	5.79617	0.407817
$203$	−20.1869	−1.41684
$204$	0.0124459	0.000871387 0
$205$	23.8284	1.66425
$206$	−18.3325	−1.27728
$207$	−13.8150	−0.960212
$208$	18.1096	1.25567
$209$	8.24279	0.570166
$210$	−57.5524	−3.97149
$211$	−3.56421	−0.245370	−0.122685	−	0.992446i	$-0.539151\pi$
$211$	−3.56421	−0.245370	−0.122685	+	0.992446i	$0.539151\pi$
$212$	−0.0125091	−0.000859129 0
$213$	−4.19585	−0.287495
$214$	8.57855	0.586417
$215$	20.3421	1.38732
$216$	6.36473	0.433065
$217$	19.2789	1.30873
$218$	−14.1681	−0.959582
$219$	28.4429	1.92199
$220$	0.120368	0.00811523
$221$	3.06166	0.205950
$222$	31.2357	2.09640
$223$	21.3448	1.42935	0.714675	−	0.699456i	$-0.246574\pi$
$223$	21.3448	1.42935	0.714675	+	0.699456i	$0.246574\pi$
$224$	−0.204009	−0.0136310
$225$	16.4679	1.09786
$226$	−1.57648	−0.104866
$227$	10.9439	0.726375	0.363187	−	0.931716i	$-0.381689\pi$
$227$	10.9439	0.726375	0.363187	+	0.931716i	$0.381689\pi$
$228$	0.0271577	0.00179857
$229$	2.66608	0.176179	0.0880897	−	0.996113i	$-0.471924\pi$
$229$	2.66608	0.176179	0.0880897	+	0.996113i	$0.471924\pi$
$230$	15.3912	1.01486
$231$	−75.0658	−4.93896
$232$	−11.1857	−0.734378
$233$	0.210570	0.0137949	0.00689744	−	0.999976i	$-0.497804\pi$
$233$	0.210570	0.0137949	0.00689744	+	0.999976i	$0.497804\pi$
$234$	24.7443	1.61758
$235$	−19.2626	−1.25656
$236$	0.0470418	0.00306216
$237$	44.5083	2.89113
$238$	4.86441	0.315313
$239$	24.4705	1.58286	0.791432	−	0.611257i	$-0.209336\pi$
$239$	24.4705	1.58286	0.791432	+	0.611257i	$0.209336\pi$
$240$	−31.7777	−2.05124
$241$	−24.2611	−1.56280	−0.781399	−	0.624032i	$-0.785493\pi$
$241$	−24.2611	−1.56280	−0.781399	+	0.624032i	$0.785493\pi$
$242$	−28.8342	−1.85353
$243$	−21.6418	−1.38832
$244$	0.0284587	0.00182188
$245$	58.2929	3.72420
$246$	−28.9351	−1.84483
$247$	6.68075	0.425086
$248$	10.6826	0.678343
$249$	−11.7525	−0.744783
$250$	3.14286	0.198772
$251$	13.9457	0.880242	0.440121	−	0.897939i	$-0.354936\pi$
$251$	13.9457	0.880242	0.440121	+	0.897939i	$0.354936\pi$
$252$	−0.139128	−0.00876427
$253$	20.0748	1.26209
$254$	−5.31646	−0.333584
$255$	−5.37245	−0.336436
$256$	−0.169266	−0.0105791
$257$	−18.5108	−1.15468	−0.577338	−	0.816506i	$-0.695908\pi$
$257$	−18.5108	−1.15468	−0.577338	+	0.816506i	$0.695908\pi$
$258$	−24.7016	−1.53785
$259$	−43.2039	−2.68456
$260$	0.0975580	0.00605029
$261$	−15.2299	−0.942704
$262$	−23.5433	−1.45451
$263$	−19.3081	−1.19059	−0.595295	−	0.803507i	$-0.702965\pi$
$263$	−19.3081	−1.19059	−0.595295	+	0.803507i	$0.702965\pi$
$264$	−41.5945	−2.55996
$265$	5.39973	0.331703
$266$	10.6145	0.650814
$267$	−22.2147	−1.35952
$268$	0.00379825	0.000232015 0
$269$	−2.22226	−0.135493	−0.0677467	−	0.997703i	$-0.521581\pi$
$269$	−2.22226	−0.135493	−0.0677467	+	0.997703i	$0.521581\pi$
$270$	−9.65454	−0.587557
$271$	−19.8279	−1.20446	−0.602229	−	0.798323i	$-0.705721\pi$
$271$	−19.8279	−1.20446	−0.602229	+	0.798323i	$0.705721\pi$
$272$	2.68590	0.162857
$273$	−60.8405	−3.68223
$274$	−11.7528	−0.710014
$275$	−23.9297	−1.44302
$276$	0.0661409	0.00398121
$277$	−18.5125	−1.11231	−0.556155	−	0.831078i	$-0.687724\pi$
$277$	−18.5125	−1.11231	−0.556155	+	0.831078i	$0.687724\pi$
$278$	25.7343	1.54344
$279$	14.5448	0.870774
$280$	44.1093	2.63603
$281$	−15.3494	−0.915671	−0.457835	−	0.889037i	$-0.651375\pi$
$281$	−15.3494	−0.915671	−0.457835	+	0.889037i	$0.651375\pi$
$282$	23.3908	1.39290
$283$	24.9708	1.48436	0.742181	−	0.670200i	$-0.233791\pi$
$283$	24.9708	1.48436	0.742181	+	0.670200i	$0.233791\pi$
$284$	0.0113004	0.000670553 0
$285$	−11.7230	−0.694412
$286$	−35.9561	−2.12613
$287$	40.0218	2.36241
$288$	−0.153913	−0.00906943
$289$	−16.5459	−0.973289
$290$	16.9674	0.996360
$291$	5.22280	0.306166
$292$	−0.0766031	−0.00448286
$293$	25.3414	1.48046	0.740230	−	0.672354i	$-0.234717\pi$
$293$	25.3414	1.48046	0.740230	+	0.672354i	$0.234717\pi$
$294$	−70.7857	−4.12830
$295$	−20.3063	−1.18228
$296$	−23.9396	−1.39146
$297$	−12.5925	−0.730688
$298$	−1.41477	−0.0819554
$299$	16.2705	0.940948
$300$	−0.0788419	−0.00455194
$301$	34.1663	1.96931
$302$	−1.60475	−0.0923430
$303$	−10.7519	−0.617680
$304$	5.86081	0.336140
$305$	−12.2846	−0.703414
$306$	3.66992	0.209795
$307$	1.31592	0.0751035	0.0375517	−	0.999295i	$-0.488044\pi$
$307$	1.31592	0.0751035	0.0375517	+	0.999295i	$0.488044\pi$
$308$	0.202169	0.0115196
$309$	34.0068	1.93458
$310$	−16.2042	−0.920336
$311$	14.9157	0.845792	0.422896	−	0.906178i	$-0.361013\pi$
$311$	14.9157	0.845792	0.422896	+	0.906178i	$0.361013\pi$
$312$	−33.7122	−1.90858
$313$	−0.556997	−0.0314833	−0.0157417	−	0.999876i	$-0.505011\pi$
$313$	−0.556997	−0.0314833	−0.0157417	+	0.999876i	$0.505011\pi$
$314$	24.1233	1.36136
$315$	60.0568	3.38381
$316$	−0.119871	−0.00674327
$317$	−33.4087	−1.87642	−0.938209	−	0.346070i	$-0.887516\pi$
$317$	−33.4087	−1.87642	−0.938209	+	0.346070i	$0.887516\pi$
$318$	−6.55695	−0.367695
$319$	22.1306	1.23908
$320$	24.4410	1.36629
$321$	−15.9132	−0.888189
$322$	25.8508	1.44061
$323$	0.990848	0.0551322
$324$	0.0401365	0.00222981
$325$	−19.3949	−1.07584
$326$	9.89325	0.547937
$327$	26.2818	1.45339
$328$	22.1764	1.22449
$329$	−32.3532	−1.78369
$330$	63.0939	3.47321
$331$	−6.34767	−0.348900	−0.174450	−	0.984666i	$-0.555815\pi$
$331$	−6.34767	−0.348900	−0.174450	+	0.984666i	$0.555815\pi$
$332$	0.0316521	0.00173713
$333$	−32.5949	−1.78619
$334$	−21.8116	−1.19348
$335$	−1.63957	−0.0895791
$336$	−53.3734	−2.91176
$337$	−10.1315	−0.551899	−0.275950	−	0.961172i	$-0.588992\pi$
$337$	−10.1315	−0.551899	−0.275950	+	0.961172i	$0.588992\pi$
$338$	−10.7900	−0.586896
$339$	2.92438	0.158831
$340$	0.0144692	0.000784703 0
$341$	−21.1352	−1.14453
$342$	8.00799	0.433023
$343$	62.1139	3.35384
$344$	18.9318	1.02073
$345$	−28.5507	−1.53712
$346$	−1.13896	−0.0612309
$347$	−5.85162	−0.314132	−0.157066	−	0.987588i	$-0.550203\pi$
$347$	−5.85162	−0.314132	−0.157066	+	0.987588i	$0.550203\pi$
$348$	0.0729145	0.00390863
$349$	15.0385	0.804994	0.402497	−	0.915421i	$-0.368142\pi$
$349$	15.0385	0.804994	0.402497	+	0.915421i	$0.368142\pi$
$350$	−30.8149	−1.64713
$351$	−10.2061	−0.544763
$352$	0.223653	0.0119207
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	24.6581	1.31056
$355$	−4.87796	−0.258895
$356$	0.0598291	0.00317093
$357$	−9.02349	−0.477574
$358$	−7.62863	−0.403185
$359$	13.9758	0.737614	0.368807	−	0.929506i	$-0.379766\pi$
$359$	13.9758	0.737614	0.368807	+	0.929506i	$0.379766\pi$
$360$	33.2779	1.75390
$361$	−16.8379	−0.886206
$362$	−27.3006	−1.43489
$363$	53.4875	2.80737
$364$	0.163857	0.00858844
$365$	33.0668	1.73080
$366$	14.9173	0.779740
$367$	−33.8149	−1.76512	−0.882562	−	0.470197i	$-0.844183\pi$
$367$	−33.8149	−1.76512	−0.882562	+	0.470197i	$0.844183\pi$
$368$	14.2736	0.744063
$369$	30.1942	1.57185
$370$	36.3136	1.88785
$371$	9.06931	0.470855
$372$	−0.0696346	−0.00361039
$373$	19.5910	1.01438	0.507192	−	0.861833i	$-0.330684\pi$
$373$	19.5910	1.01438	0.507192	+	0.861833i	$0.330684\pi$
$374$	−5.33279	−0.275752
$375$	−5.83001	−0.301060
$376$	−17.9272	−0.924524
$377$	17.9368	0.923792
$378$	−16.2156	−0.834042
$379$	12.4984	0.641998	0.320999	−	0.947079i	$-0.395981\pi$
$379$	12.4984	0.641998	0.320999	+	0.947079i	$0.395981\pi$
$380$	0.0315727	0.00161965
$381$	9.86204	0.505247
$382$	14.4702	0.740361
$383$	−11.7008	−0.597881	−0.298940	−	0.954272i	$-0.596633\pi$
$383$	−11.7008	−0.597881	−0.298940	+	0.954272i	$0.596633\pi$
$384$	−29.4700	−1.50388
$385$	−87.2691	−4.44764
$386$	−8.63608	−0.439565
$387$	25.7765	1.31029
$388$	−0.0140662	−0.000714101 0
$389$	−29.4539	−1.49337	−0.746687	−	0.665175i	$-0.768357\pi$
$389$	−29.4539	−1.49337	−0.746687	+	0.665175i	$0.768357\pi$
$390$	51.1374	2.58944
$391$	2.41314	0.122038
$392$	54.2515	2.74012
$393$	43.6729	2.20301
$394$	14.0116	0.705892
$395$	51.7440	2.60352
$396$	0.152525	0.00766466
$397$	−17.6528	−0.885969	−0.442985	−	0.896529i	$-0.646080\pi$
$397$	−17.6528	−0.885969	−0.442985	+	0.896529i	$0.646080\pi$
$398$	−3.08744	−0.154759
$399$	−19.6898	−0.985724
$400$	−17.0146	−0.850729
$401$	−11.2075	−0.559676	−0.279838	−	0.960047i	$-0.590281\pi$
$401$	−11.2075	−0.559676	−0.279838	+	0.960047i	$0.590281\pi$
$402$	1.99094	0.0992992
$403$	−17.1300	−0.853305
$404$	0.0289573	0.00144068
$405$	−17.3255	−0.860911
$406$	28.4982	1.41434
$407$	47.3639	2.34774
$408$	−4.99998	−0.247536
$409$	−16.2593	−0.803971	−0.401986	−	0.915646i	$-0.631680\pi$
$409$	−16.2593	−0.803971	−0.401986	+	0.915646i	$0.631680\pi$
$410$	−33.6390	−1.66131
$411$	21.8015	1.07539
$412$	−0.0915878	−0.00451221
$413$	−34.1061	−1.67825
$414$	19.5029	0.958517
$415$	−13.6631	−0.670693
$416$	0.181270	0.00888748
$417$	−47.7372	−2.33770
$418$	−11.6365	−0.569160
$419$	12.3354	0.602623	0.301312	−	0.953526i	$-0.402576\pi$
$419$	12.3354	0.602623	0.301312	+	0.953526i	$0.402576\pi$
$420$	−0.287528	−0.0140299
$421$	−4.11586	−0.200595	−0.100297	−	0.994958i	$-0.531979\pi$
$421$	−4.11586	−0.200595	−0.100297	+	0.994958i	$0.531979\pi$
$422$	5.03166	0.244937
$423$	−24.4087	−1.18679
$424$	5.02537	0.244054
$425$	−2.87654	−0.139533
$426$	5.92335	0.286987
$427$	−20.6330	−0.998502
$428$	0.0428578	0.00207161
$429$	66.6987	3.22024
$430$	−28.7173	−1.38487
$431$	24.2345	1.16734	0.583668	−	0.811993i	$-0.301617\pi$
$431$	24.2345	1.16734	0.583668	+	0.811993i	$0.301617\pi$
$432$	−8.95352	−0.430776
$433$	−36.8169	−1.76931	−0.884653	−	0.466249i	$-0.845605\pi$
$433$	−36.8169	−1.76931	−0.884653	+	0.466249i	$0.845605\pi$
$434$	−27.2163	−1.30642
$435$	−31.4746	−1.50909
$436$	−0.0707827	−0.00338988
$437$	5.26563	0.251889
$438$	−40.1534	−1.91860
$439$	13.2117	0.630561	0.315281	−	0.948999i	$-0.397901\pi$
$439$	13.2117	0.630561	0.315281	+	0.948999i	$0.397901\pi$
$440$	−48.3565	−2.30530
$441$	73.8659	3.51742
$442$	−4.32221	−0.205586
$443$	18.2696	0.868016	0.434008	−	0.900909i	$-0.357099\pi$
$443$	18.2696	0.868016	0.434008	+	0.900909i	$0.357099\pi$
$444$	0.156051	0.00740587
$445$	−25.8261	−1.22427
$446$	−30.1328	−1.42683
$447$	2.62440	0.124130
$448$	41.0507	1.93946
$449$	−10.0609	−0.474804	−0.237402	−	0.971411i	$-0.576296\pi$
$449$	−10.0609	−0.474804	−0.237402	+	0.971411i	$0.576296\pi$
$450$	−23.2481	−1.09593
$451$	−43.8755	−2.06601
$452$	−0.00787601	−0.000370456 0
$453$	2.97681	0.139863
$454$	−15.4497	−0.725093
$455$	−70.7312	−3.31593
$456$	−10.9103	−0.510921
$457$	−14.6259	−0.684171	−0.342085	−	0.939669i	$-0.611133\pi$
$457$	−14.6259	−0.684171	−0.342085	+	0.939669i	$0.611133\pi$
$458$	−3.76375	−0.175869
$459$	−1.51371	−0.0706540
$460$	0.0768933	0.00358517
$461$	37.3827	1.74109	0.870543	−	0.492092i	$-0.163768\pi$
$461$	37.3827	1.74109	0.870543	+	0.492092i	$0.163768\pi$
$462$	105.972	4.93025
$463$	22.0440	1.02447	0.512235	−	0.858845i	$-0.328818\pi$
$463$	22.0440	1.02447	0.512235	+	0.858845i	$0.328818\pi$
$464$	15.7354	0.730497
$465$	30.0588	1.39394
$466$	−0.297265	−0.0137705
$467$	8.10108	0.374873	0.187437	−	0.982277i	$-0.439982\pi$
$467$	8.10108	0.374873	0.187437	+	0.982277i	$0.439982\pi$
$468$	0.123621	0.00571437
$469$	−2.75379	−0.127158
$470$	27.1934	1.25434
$471$	−44.7487	−2.06191
$472$	−18.8985	−0.869872
$473$	−37.4561	−1.72223
$474$	−62.8332	−2.88603
$475$	−6.27679	−0.287999
$476$	0.0243023	0.00111389
$477$	6.84227	0.313286
$478$	−34.5454	−1.58007
$479$	−24.8904	−1.13727	−0.568635	−	0.822590i	$-0.692528\pi$
$479$	−24.8904	−1.13727	−0.568635	+	0.822590i	$0.692528\pi$
$480$	−0.318083	−0.0145184
$481$	38.3883	1.75035
$482$	34.2499	1.56004
$483$	−47.9533	−2.18195
$484$	−0.144054	−0.00654791
$485$	6.07186	0.275709
$486$	30.5521	1.38587
$487$	19.8035	0.897384	0.448692	−	0.893686i	$-0.351890\pi$
$487$	19.8035	0.897384	0.448692	+	0.893686i	$0.351890\pi$
$488$	−11.4329	−0.517544
$489$	−18.3520	−0.829906
$490$	−82.2932	−3.71763
$491$	11.2839	0.509234	0.254617	−	0.967042i	$-0.418051\pi$
$491$	11.2839	0.509234	0.254617	+	0.967042i	$0.418051\pi$
$492$	−0.144558	−0.00651716
$493$	2.66028	0.119813
$494$	−9.43133	−0.424336
$495$	−65.8395	−2.95926
$496$	−15.0276	−0.674758
$497$	−8.19295	−0.367504
$498$	16.5912	0.743469
$499$	−4.26523	−0.190938	−0.0954689	−	0.995432i	$-0.530435\pi$
$499$	−4.26523	−0.190938	−0.0954689	+	0.995432i	$0.530435\pi$
$500$	0.0157015	0.000702193 0
$501$	40.4606	1.80765
$502$	−19.6873	−0.878688
$503$	37.7929	1.68510	0.842551	−	0.538617i	$-0.181053\pi$
$503$	37.7929	1.68510	0.842551	+	0.538617i	$0.181053\pi$
$504$	55.8931	2.48968
$505$	−12.4998	−0.556234
$506$	−28.3399	−1.25986
$507$	20.0154	0.888915
$508$	−0.0265607	−0.00117844
$509$	28.0857	1.24488	0.622438	−	0.782669i	$-0.286142\pi$
$509$	28.0857	1.24488	0.622438	+	0.782669i	$0.286142\pi$
$510$	7.58438	0.335842
$511$	55.5385	2.45688
$512$	22.7459	1.00524
$513$	−3.30301	−0.145832
$514$	26.1321	1.15264
$515$	39.5352	1.74213
$516$	−0.123407	−0.00543271
$517$	35.4685	1.55990
$518$	60.9918	2.67982
$519$	2.11277	0.0927404
$520$	−39.1927	−1.71871
$521$	10.1363	0.444080	0.222040	−	0.975038i	$-0.428728\pi$
$521$	10.1363	0.444080	0.222040	+	0.975038i	$0.428728\pi$
$522$	21.5003	0.941040
$523$	41.3038	1.80609	0.903045	−	0.429547i	$-0.141327\pi$
$523$	41.3038	1.80609	0.903045	+	0.429547i	$0.141327\pi$
$524$	−0.117621	−0.00513830
$525$	57.1617	2.49474
$526$	27.2576	1.18849
$527$	−2.54061	−0.110671
$528$	58.5126	2.54644
$529$	−10.1759	−0.442430
$530$	−7.62290	−0.331118
$531$	−25.7311	−1.11663
$532$	0.0530291	0.00229910
$533$	−35.5609	−1.54031
$534$	31.3608	1.35712
$535$	−18.5002	−0.799833
$536$	−1.52590	−0.0659087
$537$	14.1511	0.610665
$538$	3.13720	0.135254
$539$	−107.335	−4.62326
$540$	−0.0482335	−0.00207564
$541$	−6.76395	−0.290805	−0.145402	−	0.989373i	$-0.546448\pi$
$541$	−6.76395	−0.290805	−0.145402	+	0.989373i	$0.546448\pi$
$542$	27.9914	1.20233
$543$	50.6427	2.17329
$544$	0.0268848	0.00115268
$545$	30.5544	1.30880
$546$	85.8896	3.67574
$547$	12.9228	0.552541	0.276271	−	0.961080i	$-0.410901\pi$
$547$	12.9228	0.552541	0.276271	+	0.961080i	$0.410901\pi$
$548$	−0.0587164	−0.00250824
$549$	−15.5664	−0.664359
$550$	33.7820	1.44047
$551$	5.80489	0.247297
$552$	−26.5713	−1.13095
$553$	86.9085	3.69572
$554$	26.1345	1.11035
$555$	−67.3617	−2.85935
$556$	0.128567	0.00545245
$557$	−2.96140	−0.125478	−0.0627392	−	0.998030i	$-0.519984\pi$
$557$	−2.96140	−0.125478	−0.0627392	+	0.998030i	$0.519984\pi$
$558$	−20.5331	−0.869237
$559$	−30.3580	−1.28401
$560$	−62.0503	−2.62210
$561$	9.89234	0.417655
$562$	21.6691	0.914055
$563$	31.2075	1.31524	0.657619	−	0.753351i	$-0.271564\pi$
$563$	31.2075	1.31524	0.657619	+	0.753351i	$0.271564\pi$
$564$	0.116859	0.00492065
$565$	3.39979	0.143030
$566$	−35.2518	−1.48174
$567$	−29.0997	−1.22207
$568$	−4.53977	−0.190485
$569$	−40.0483	−1.67891	−0.839456	−	0.543428i	$-0.817126\pi$
$569$	−40.0483	−1.67891	−0.839456	+	0.543428i	$0.817126\pi$
$570$	16.5496	0.693187
$571$	−19.9104	−0.833223	−0.416612	−	0.909085i	$-0.636783\pi$
$571$	−19.9104	−0.833223	−0.416612	+	0.909085i	$0.636783\pi$
$572$	−0.179634	−0.00751089
$573$	−26.8423	−1.12135
$574$	−56.4996	−2.35825
$575$	−15.2867	−0.637500
$576$	30.9704	1.29043
$577$	7.62218	0.317315	0.158658	−	0.987334i	$-0.449283\pi$
$577$	7.62218	0.317315	0.158658	+	0.987334i	$0.449283\pi$
$578$	23.3582	0.971571
$579$	16.0199	0.665766
$580$	0.0847680	0.00351980
$581$	−22.9483	−0.952055
$582$	−7.37312	−0.305625
$583$	−9.94258	−0.411779
$584$	30.7743	1.27345
$585$	−53.3626	−2.20627
$586$	−35.7749	−1.47785
$587$	6.63324	0.273783	0.136891	−	0.990586i	$-0.456289\pi$
$587$	6.63324	0.273783	0.136891	+	0.990586i	$0.456289\pi$
$588$	−0.353641	−0.0145839
$589$	−5.54378	−0.228427
$590$	28.6667	1.18019
$591$	−25.9914	−1.06915
$592$	33.6768	1.38411
$593$	3.29488	0.135304	0.0676522	−	0.997709i	$-0.478449\pi$
$593$	3.29488	0.135304	0.0676522	+	0.997709i	$0.478449\pi$
$594$	17.7770	0.729399
$595$	−10.4904	−0.430065
$596$	−0.00706810	−0.000289521 0
$597$	5.72721	0.234399
$598$	−22.9694	−0.939288
$599$	15.0380	0.614434	0.307217	−	0.951639i	$-0.400602\pi$
$599$	15.0380	0.614434	0.307217	+	0.951639i	$0.400602\pi$
$600$	31.6737	1.29308
$601$	−13.3474	−0.544450	−0.272225	−	0.962234i	$-0.587759\pi$
$601$	−13.3474	−0.544450	−0.272225	+	0.962234i	$0.587759\pi$
$602$	−48.2331	−1.96584
$603$	−2.07758	−0.0846055
$604$	−0.00801722	−0.000326216 0
$605$	62.1829	2.52810
$606$	15.1786	0.616590
$607$	3.16195	0.128340	0.0641698	−	0.997939i	$-0.479560\pi$
$607$	3.16195	0.128340	0.0641698	+	0.997939i	$0.479560\pi$
$608$	0.0586644	0.00237916
$609$	−52.8642	−2.14217
$610$	17.3424	0.702173
$611$	28.7470	1.16298
$612$	0.0183347	0.000741135 0
$613$	−24.1355	−0.974823	−0.487411	−	0.873173i	$-0.662059\pi$
$613$	−24.1355	−0.974823	−0.487411	+	0.873173i	$0.662059\pi$
$614$	−1.85771	−0.0749709
$615$	62.4004	2.51623
$616$	−81.2188	−3.27240
$617$	12.6797	0.510465	0.255233	−	0.966880i	$-0.417848\pi$
$617$	12.6797	0.510465	0.255233	+	0.966880i	$0.417848\pi$
$618$	−48.0079	−1.93116
$619$	−0.839105	−0.0337265	−0.0168632	−	0.999858i	$-0.505368\pi$
$619$	−0.839105	−0.0337265	−0.0168632	+	0.999858i	$0.505368\pi$
$620$	−0.0809550	−0.00325123
$621$	−8.04427	−0.322806
$622$	−21.0568	−0.844300
$623$	−43.3771	−1.73787
$624$	47.4242	1.89849
$625$	−28.1215	−1.12486
$626$	0.786322	0.0314277
$627$	21.5857	0.862050
$628$	0.120518	0.00480920
$629$	5.69351	0.227015
$630$	−84.7832	−3.37784
$631$	−21.6456	−0.861698	−0.430849	−	0.902424i	$-0.641786\pi$
$631$	−21.6456	−0.861698	−0.430849	+	0.902424i	$0.641786\pi$
$632$	48.1566	1.91557
$633$	−9.33373	−0.370983
$634$	47.1636	1.87311
$635$	11.4653	0.454986
$636$	−0.0327581	−0.00129894
$637$	−86.9948	−3.44686
$638$	−31.2422	−1.23689
$639$	−6.18111	−0.244521
$640$	−34.2608	−1.35428
$641$	17.8646	0.705608	0.352804	−	0.935697i	$-0.385228\pi$
$641$	17.8646	0.705608	0.352804	+	0.935697i	$0.385228\pi$
$642$	22.4650	0.886622
$643$	−26.4832	−1.04440	−0.522198	−	0.852824i	$-0.674888\pi$
$643$	−26.4832	−1.04440	−0.522198	+	0.852824i	$0.674888\pi$
$644$	0.129149	0.00508918
$645$	53.2706	2.09753
$646$	−1.39880	−0.0550349
$647$	−14.5194	−0.570816	−0.285408	−	0.958406i	$-0.592129\pi$
$647$	−14.5194	−0.570816	−0.285408	+	0.958406i	$0.592129\pi$
$648$	−16.1243	−0.633424
$649$	37.3901	1.46769
$650$	27.3802	1.07394
$651$	50.4863	1.97871
$652$	0.0494260	0.00193567
$653$	−13.3955	−0.524206	−0.262103	−	0.965040i	$-0.584416\pi$
$653$	−13.3955	−0.524206	−0.262103	+	0.965040i	$0.584416\pi$
$654$	−37.1024	−1.45082
$655$	50.7728	1.98386
$656$	−31.1964	−1.21802
$657$	41.9006	1.63470
$658$	45.6737	1.78054
$659$	4.84784	0.188845	0.0944225	−	0.995532i	$-0.469900\pi$
$659$	4.84784	0.188845	0.0944225	+	0.995532i	$0.469900\pi$
$660$	0.315213	0.0122697
$661$	27.5713	1.07240	0.536199	−	0.844092i	$-0.319860\pi$
$661$	27.5713	1.07240	0.536199	+	0.844092i	$0.319860\pi$
$662$	8.96112	0.348284
$663$	8.01770	0.311382
$664$	−12.7158	−0.493469
$665$	−22.8908	−0.887666
$666$	46.0148	1.78304
$667$	14.1374	0.547404
$668$	−0.108970	−0.00421616
$669$	55.8963	2.16108
$670$	2.31461	0.0894211
$671$	22.6197	0.873225
$672$	−0.534247	−0.0206090
$673$	43.9898	1.69568	0.847840	−	0.530252i	$-0.177903\pi$
$673$	43.9898	1.69568	0.847840	+	0.530252i	$0.177903\pi$
$674$	14.3028	0.550925
$675$	9.58901	0.369081
$676$	−0.0539059	−0.00207330
$677$	−42.1977	−1.62179	−0.810895	−	0.585191i	$-0.801019\pi$
$677$	−42.1977	−1.62179	−0.810895	+	0.585191i	$0.801019\pi$
$678$	−4.12840	−0.158550
$679$	10.1982	0.391371
$680$	−5.81282	−0.222912
$681$	28.6593	1.09823
$682$	29.8369	1.14251
$683$	−0.993542	−0.0380168	−0.0190084	−	0.999819i	$-0.506051\pi$
$683$	−0.993542	−0.0380168	−0.0190084	+	0.999819i	$0.506051\pi$
$684$	0.0400074	0.00152972
$685$	25.3458	0.968411
$686$	−87.6873	−3.34792
$687$	6.98176	0.266371
$688$	−26.6321	−1.01534
$689$	−8.05842	−0.307001
$690$	40.3055	1.53440
$691$	16.5834	0.630861	0.315431	−	0.948949i	$-0.397851\pi$
$691$	16.5834	0.630861	0.315431	+	0.948949i	$0.397851\pi$
$692$	−0.00569017	−0.000216308 0
$693$	−110.583	−4.20070
$694$	8.26084	0.313577
$695$	−55.4978	−2.10515
$696$	−29.2925	−1.11033
$697$	−5.27417	−0.199773
$698$	−21.2302	−0.803573
$699$	0.551427	0.0208569
$700$	−0.153949	−0.00581874
$701$	−32.7630	−1.23744	−0.618721	−	0.785611i	$-0.712349\pi$
$701$	−32.7630	−1.23744	−0.618721	+	0.785611i	$0.712349\pi$
$702$	14.4082	0.543802
$703$	12.4236	0.468565
$704$	−45.0034	−1.69613
$705$	−50.4438	−1.89982
$706$	−1.41172	−0.0531307
$707$	−20.9945	−0.789580
$708$	0.123190	0.00462977
$709$	37.9061	1.42359	0.711797	−	0.702385i	$-0.247882\pi$
$709$	37.9061	1.42359	0.711797	+	0.702385i	$0.247882\pi$
$710$	6.88630	0.258438
$711$	65.5674	2.45897
$712$	−24.0356	−0.900771
$713$	−13.5015	−0.505635
$714$	12.7386	0.476731
$715$	77.5418	2.89990
$716$	−0.0381121	−0.00142432
$717$	64.0818	2.39318
$718$	−19.7299	−0.736312
$719$	−28.7241	−1.07123	−0.535614	−	0.844463i	$-0.679920\pi$
$719$	−28.7241	−1.07123	−0.535614	+	0.844463i	$0.679920\pi$
$720$	−46.8133	−1.74463
$721$	66.4027	2.47297
$722$	23.7704	0.884642
$723$	−63.5336	−2.36284
$724$	−0.136392	−0.00506897
$725$	−16.8522	−0.625876
$726$	−75.5093	−2.80241
$727$	15.4970	0.574752	0.287376	−	0.957818i	$-0.407217\pi$
$727$	15.4970	0.574752	0.287376	+	0.957818i	$0.407217\pi$
$728$	−65.8275	−2.43973
$729$	−39.6016	−1.46673
$730$	−46.6810	−1.72774
$731$	−4.50251	−0.166531
$732$	0.0745259	0.00275456
$733$	19.2671	0.711646	0.355823	−	0.934553i	$-0.384201\pi$
$733$	19.2671	0.711646	0.355823	+	0.934553i	$0.384201\pi$
$734$	47.7371	1.76201
$735$	152.654	5.63073
$736$	0.142873	0.00526638
$737$	3.01895	0.111204
$738$	−42.6256	−1.56907
$739$	−4.55240	−0.167463	−0.0837313	−	0.996488i	$-0.526684\pi$
$739$	−4.55240	−0.167463	−0.0837313	+	0.996488i	$0.526684\pi$
$740$	0.181420	0.00666914
$741$	17.4951	0.642700
$742$	−12.8033	−0.470024
$743$	0.520108	0.0190809	0.00954045	−	0.999954i	$-0.496963\pi$
$743$	0.520108	0.0190809	0.00954045	+	0.999954i	$0.496963\pi$
$744$	27.9748	1.02561
$745$	3.05104	0.111782
$746$	−27.6570	−1.01259
$747$	−17.3132	−0.633455
$748$	−0.0266423	−0.000974138 0
$749$	−31.0727	−1.13537
$750$	8.23032	0.300529
$751$	−44.3885	−1.61976	−0.809879	−	0.586597i	$-0.800467\pi$
$751$	−44.3885	−1.61976	−0.809879	+	0.586597i	$0.800467\pi$
$752$	25.2189	0.919638
$753$	36.5200	1.33086
$754$	−25.3217	−0.922162
$755$	3.46075	0.125950
$756$	−0.0810122	−0.00294639
$757$	25.5363	0.928133	0.464066	−	0.885800i	$-0.346390\pi$
$757$	25.5363	0.928133	0.464066	+	0.885800i	$0.346390\pi$
$758$	−17.6442	−0.640865
$759$	52.5706	1.90819
$760$	−12.6839	−0.460095
$761$	50.7385	1.83927	0.919634	−	0.392776i	$-0.128485\pi$
$761$	50.7385	1.83927	0.919634	+	0.392776i	$0.128485\pi$
$762$	−13.9224	−0.504356
$763$	51.3186	1.85786
$764$	0.0722923	0.00261544
$765$	−7.91442	−0.286146
$766$	16.5182	0.596825
$767$	30.3045	1.09423
$768$	−0.443264	−0.0159949
$769$	3.90315	0.140751	0.0703756	−	0.997521i	$-0.477580\pi$
$769$	3.90315	0.140751	0.0703756	+	0.997521i	$0.477580\pi$
$770$	123.199	4.43979
$771$	−48.4751	−1.74579
$772$	−0.0431453	−0.00155283
$773$	45.3052	1.62951	0.814757	−	0.579803i	$-0.196870\pi$
$773$	45.3052	1.62951	0.814757	+	0.579803i	$0.196870\pi$
$774$	−36.3891	−1.30798
$775$	16.0942	0.578121
$776$	5.65090	0.202856
$777$	−113.140	−4.05887
$778$	41.5807	1.49074
$779$	−11.5086	−0.412338
$780$	0.255479	0.00914761
$781$	8.98183	0.321395
$782$	−3.40668	−0.121823
$783$	−8.86809	−0.316920
$784$	−76.3178	−2.72564
$785$	−52.0234	−1.85680
$786$	−61.6539	−2.19912
$787$	21.2385	0.757069	0.378534	−	0.925587i	$-0.376428\pi$
$787$	21.2385	0.757069	0.378534	+	0.925587i	$0.376428\pi$
$788$	0.0700008	0.00249367
$789$	−50.5629	−1.80009
$790$	−73.0479	−2.59893
$791$	5.71024	0.203033
$792$	−61.2749	−2.17731
$793$	18.3332	0.651031
$794$	24.9208	0.884405
$795$	14.1405	0.501511
$796$	−0.0154246	−0.000546712 0
$797$	37.9180	1.34312	0.671562	−	0.740949i	$-0.265624\pi$
$797$	37.9180	1.34312	0.671562	+	0.740949i	$0.265624\pi$
$798$	27.7965	0.983985
$799$	4.26359	0.150835
$800$	−0.170309	−0.00602134
$801$	−32.7255	−1.15630
$802$	15.8218	0.558688
$803$	−60.8862	−2.14863
$804$	0.00994662	0.000350790 0
$805$	−55.7490	−1.96489
$806$	24.1827	0.851799
$807$	−5.81951	−0.204856
$808$	−11.6332	−0.409255
$809$	−31.3642	−1.10271	−0.551353	−	0.834272i	$-0.685888\pi$
$809$	−31.3642	−1.10271	−0.551353	+	0.834272i	$0.685888\pi$
$810$	24.4587	0.859392
$811$	8.51099	0.298861	0.149431	−	0.988772i	$-0.452256\pi$
$811$	8.51099	0.298861	0.149431	+	0.988772i	$0.452256\pi$
$812$	0.142375	0.00499639
$813$	−51.9240	−1.82106
$814$	−66.8645	−2.34360
$815$	−21.3355	−0.747348
$816$	7.03367	0.246228
$817$	−9.82476	−0.343725
$818$	22.9536	0.802553
$819$	−89.6271	−3.13182
$820$	−0.168058	−0.00586885
$821$	25.3744	0.885571	0.442786	−	0.896627i	$-0.353990\pi$
$821$	25.3744	0.885571	0.442786	+	0.896627i	$0.353990\pi$
$822$	−30.7776	−1.07349
$823$	−40.2080	−1.40156	−0.700782	−	0.713376i	$-0.747165\pi$
$823$	−40.2080	−1.40156	−0.700782	+	0.713376i	$0.747165\pi$
$824$	36.7942	1.28179
$825$	−62.6657	−2.18174
$826$	48.1482	1.67529
$827$	−35.4154	−1.23151	−0.615757	−	0.787936i	$-0.711150\pi$
$827$	−35.4154	−1.23151	−0.615757	+	0.787936i	$0.711150\pi$
$828$	0.0974354	0.00338611
$829$	−31.3464	−1.08870	−0.544352	−	0.838857i	$-0.683225\pi$
$829$	−31.3464	−1.08870	−0.544352	+	0.838857i	$0.683225\pi$
$830$	19.2884	0.669510
$831$	−48.4795	−1.68174
$832$	−36.4751	−1.26454
$833$	−12.9025	−0.447046
$834$	67.3915	2.33358
$835$	47.0382	1.62783
$836$	−0.0581351	−0.00201065
$837$	8.46919	0.292738
$838$	−17.4141	−0.601560
$839$	−5.45174	−0.188215	−0.0941076	−	0.995562i	$-0.530000\pi$
$839$	−5.45174	−0.188215	−0.0941076	+	0.995562i	$0.530000\pi$
$840$	115.511	3.98550
$841$	−13.4147	−0.462577
$842$	5.81043	0.200241
$843$	−40.1962	−1.38443
$844$	0.0251378	0.000865280 0
$845$	23.2693	0.800487
$846$	34.4581	1.18470
$847$	104.442	3.58865
$848$	−7.06939	−0.242764
$849$	65.3921	2.24425
$850$	4.06086	0.139286
$851$	30.2569	1.03719
$852$	0.0295927	0.00101383
$853$	−13.5404	−0.463614	−0.231807	−	0.972762i	$-0.574464\pi$
$853$	−13.5404	−0.463614	−0.231807	+	0.972762i	$0.574464\pi$
$854$	29.1280	0.996740
$855$	−17.2698	−0.590613
$856$	−17.2176	−0.588485
$857$	−47.6033	−1.62610	−0.813049	−	0.582196i	$-0.802194\pi$
$857$	−47.6033	−1.62610	−0.813049	+	0.582196i	$0.802194\pi$
$858$	−94.1597	−3.21456
$859$	−20.5547	−0.701318	−0.350659	−	0.936503i	$-0.614042\pi$
$859$	−20.5547	−0.701318	−0.350659	+	0.936503i	$0.614042\pi$
$860$	−0.143470	−0.00489227
$861$	104.807	3.57180
$862$	−34.2123	−1.16528
$863$	−30.6136	−1.04210	−0.521049	−	0.853527i	$-0.674459\pi$
$863$	−30.6136	−1.04210	−0.521049	+	0.853527i	$0.674459\pi$
$864$	−0.0896212	−0.00304898
$865$	2.45624	0.0835147
$866$	51.9751	1.76618
$867$	−43.3294	−1.47154
$868$	−0.135971	−0.00461515
$869$	−95.2767	−3.23204
$870$	44.4332	1.50643
$871$	2.44685	0.0829082
$872$	28.4360	0.962966
$873$	7.69396	0.260401
$874$	−7.43359	−0.251445
$875$	−11.3839	−0.384845
$876$	−0.200603	−0.00677776
$877$	42.5599	1.43715	0.718574	−	0.695451i	$-0.244795\pi$
$877$	42.5599	1.43715	0.718574	+	0.695451i	$0.244795\pi$
$878$	−18.6512	−0.629448
$879$	66.3625	2.23835
$880$	68.0249	2.29312
$881$	12.9370	0.435860	0.217930	−	0.975964i	$-0.430070\pi$
$881$	12.9370	0.435860	0.217930	+	0.975964i	$0.430070\pi$
$882$	−104.278	−3.51122
$883$	−55.0299	−1.85190	−0.925951	−	0.377643i	$-0.876735\pi$
$883$	−55.0299	−1.85190	−0.925951	+	0.377643i	$0.876735\pi$
$884$	−0.0215935	−0.000726267 0
$885$	−53.1768	−1.78752
$886$	−25.7916	−0.866484
$887$	−12.3418	−0.414395	−0.207198	−	0.978299i	$-0.566434\pi$
$887$	−12.3418	−0.414395	−0.207198	+	0.978299i	$0.566434\pi$
$888$	−62.6916	−2.10379
$889$	19.2569	0.645857
$890$	36.4591	1.22211
$891$	31.9016	1.06874
$892$	−0.150541	−0.00504050
$893$	9.30341	0.311327
$894$	−3.70491	−0.123911
$895$	16.4516	0.549917
$896$	−57.5440	−1.92241
$897$	42.6082	1.42265
$898$	14.2032	0.473966
$899$	−14.8842	−0.496416
$900$	−0.116146	−0.00387153
$901$	−1.19517	−0.0398170
$902$	61.9398	2.06237
$903$	89.4725	2.97746
$904$	3.16409	0.105236
$905$	58.8756	1.95709
$906$	−4.20242	−0.139616
$907$	7.11084	0.236111	0.118056	−	0.993007i	$-0.462334\pi$
$907$	7.11084	0.236111	0.118056	+	0.993007i	$0.462334\pi$
$908$	−0.0771859	−0.00256150
$909$	−15.8391	−0.525351
$910$	99.8525	3.31008
$911$	18.8259	0.623731	0.311865	−	0.950126i	$-0.399046\pi$
$911$	18.8259	0.623731	0.311865	+	0.950126i	$0.399046\pi$
$912$	15.3479	0.508220
$913$	25.1579	0.832605
$914$	20.6476	0.682963
$915$	−32.1702	−1.06351
$916$	−0.0188035	−0.000621284 0
$917$	85.2772	2.81610
$918$	2.13693	0.0705293
$919$	−6.66602	−0.219892	−0.109946	−	0.993938i	$-0.535068\pi$
$919$	−6.66602	−0.219892	−0.109946	+	0.993938i	$0.535068\pi$
$920$	−30.8909	−1.01844
$921$	3.44605	0.113551
$922$	−52.7738	−1.73801
$923$	7.27973	0.239615
$924$	0.529427	0.0174169
$925$	−36.0671	−1.18588
$926$	−31.1199	−1.02266
$927$	50.0970	1.64540
$928$	0.157505	0.00517036
$929$	27.0434	0.887265	0.443633	−	0.896209i	$-0.353690\pi$
$929$	27.0434	0.887265	0.443633	+	0.896209i	$0.353690\pi$
$930$	−42.4345	−1.39148
$931$	−28.1542	−0.922715
$932$	−0.00148512	−4.86466e−5 0
$933$	39.0603	1.27878
$934$	−11.4364	−0.374212
$935$	11.5005	0.376107
$936$	−49.6630	−1.62329
$937$	−10.2554	−0.335029	−0.167515	−	0.985870i	$-0.553574\pi$
$937$	−10.2554	−0.335029	−0.167515	+	0.985870i	$0.553574\pi$
$938$	3.88758	0.126934
$939$	−1.45863	−0.0476005
$940$	0.135856	0.00443115
$941$	−25.7686	−0.840031	−0.420015	−	0.907517i	$-0.637975\pi$
$941$	−25.7686	−0.840031	−0.420015	+	0.907517i	$0.637975\pi$
$942$	63.1726	2.05827
$943$	−28.0284	−0.912730
$944$	26.5852	0.865275
$945$	34.9701	1.13758
$946$	52.8774	1.71919
$947$	−12.4435	−0.404360	−0.202180	−	0.979348i	$-0.564803\pi$
$947$	−12.4435	−0.404360	−0.202180	+	0.979348i	$0.564803\pi$
$948$	−0.313911	−0.0101953
$949$	−49.3480	−1.60190
$950$	8.86106	0.287491
$951$	−87.4885	−2.83701
$952$	−9.76313	−0.316425
$953$	19.3343	0.626301	0.313150	−	0.949704i	$-0.398616\pi$
$953$	19.3343	0.626301	0.313150	+	0.949704i	$0.398616\pi$
$954$	−9.65936	−0.312733
$955$	−31.2060	−1.00980
$956$	−0.172587	−0.00558185
$957$	57.9544	1.87340
$958$	35.1382	1.13526
$959$	42.5704	1.37467
$960$	64.0045	2.06574
$961$	−16.7853	−0.541462
$962$	−54.1934	−1.74727
$963$	−23.4425	−0.755425
$964$	0.171110	0.00551109
$965$	18.6243	0.599537
$966$	67.6965	2.17810
$967$	54.8580	1.76411	0.882057	−	0.471142i	$-0.156158\pi$
$967$	54.8580	1.76411	0.882057	+	0.471142i	$0.156158\pi$
$968$	57.8718	1.86007
$969$	2.59477	0.0833560
$970$	−8.57175	−0.275222
$971$	−21.2781	−0.682846	−0.341423	−	0.939910i	$-0.610909\pi$
$971$	−21.2781	−0.682846	−0.341423	+	0.939910i	$0.610909\pi$
$972$	0.152636	0.00489580
$973$	−93.2132	−2.98828
$974$	−27.9570	−0.895801
$975$	−50.7903	−1.62659
$976$	16.0831	0.514809
$977$	16.2306	0.519261	0.259631	−	0.965708i	$-0.416399\pi$
$977$	16.2306	0.519261	0.259631	+	0.965708i	$0.416399\pi$
$978$	25.9078	0.828441
$979$	47.5537	1.51982
$980$	−0.411131	−0.0131331
$981$	38.7170	1.23614
$982$	−15.9296	−0.508335
$983$	−7.43350	−0.237092	−0.118546	−	0.992949i	$-0.537823\pi$
$983$	−7.43350	−0.237092	−0.118546	+	0.992949i	$0.537823\pi$
$984$	58.0742	1.85134
$985$	−30.2168	−0.962788
$986$	−3.75556	−0.119601
$987$	−84.7247	−2.69682
$988$	−0.0471183	−0.00149903
$989$	−23.9276	−0.760852
$990$	92.9468	2.95404
$991$	17.4924	0.555665	0.277832	−	0.960630i	$-0.410384\pi$
$991$	17.4924	0.555665	0.277832	+	0.960630i	$0.410384\pi$
$992$	−0.150420	−0.00477585
$993$	−16.6229	−0.527512
$994$	11.5661	0.366855
$995$	6.65827	0.211081
$996$	0.0828885	0.00262642
$997$	−24.6866	−0.781833	−0.390916	−	0.920426i	$-0.627842\pi$
$997$	−24.6866	−0.781833	−0.390916	+	0.920426i	$0.627842\pi$
$998$	6.02130	0.190601
$999$	−18.9795	−0.600484

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	353.2.a.d.1.4	✓	14
3.2	odd	2		3177.2.a.h.1.11		14
4.3	odd	2		5648.2.a.p.1.1		14
5.4	even	2		8825.2.a.i.1.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
353.2.a.d.1.4	✓	14	1.1	even	1	trivial
3177.2.a.h.1.11		14	3.2	odd	2
5648.2.a.p.1.1		14	4.3	odd	2
8825.2.a.i.1.11		14	5.4	even	2

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:	\( N \)	\(=\)	\( 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	353.a (trivial)

\(f(q)\)	\(=\)	\(q-1.41172 q^{2} +2.61874 q^{3} -0.00705285 q^{4} +3.04446 q^{5} -3.69692 q^{6} +5.11343 q^{7} +2.83339 q^{8} +3.85779 q^{9} +O(q^{10})\)	\(q-1.41172 q^{2} +2.61874 q^{3} -0.00705285 q^{4} +3.04446 q^{5} -3.69692 q^{6} +5.11343 q^{7} +2.83339 q^{8} +3.85779 q^{9} -4.29792 q^{10} -5.60579 q^{11} -0.0184696 q^{12} -4.54347 q^{13} -7.21873 q^{14} +7.97265 q^{15} -3.98584 q^{16} -0.673860 q^{17} -5.44611 q^{18} -1.47041 q^{19} -0.0214721 q^{20} +13.3907 q^{21} +7.91380 q^{22} -3.58108 q^{23} +7.41991 q^{24} +4.26875 q^{25} +6.41410 q^{26} +2.24633 q^{27} -0.0360643 q^{28} -3.94782 q^{29} -11.2551 q^{30} +3.77024 q^{31} -0.0398967 q^{32} -14.6801 q^{33} +0.951300 q^{34} +15.5677 q^{35} -0.0272084 q^{36} -8.44910 q^{37} +2.07580 q^{38} -11.8982 q^{39} +8.62616 q^{40} +7.82680 q^{41} -18.9040 q^{42} +6.68167 q^{43} +0.0395368 q^{44} +11.7449 q^{45} +5.05547 q^{46} -6.32711 q^{47} -10.4379 q^{48} +19.1472 q^{49} -6.02627 q^{50} -1.76466 q^{51} +0.0320444 q^{52} +1.77362 q^{53} -3.17118 q^{54} -17.0666 q^{55} +14.4884 q^{56} -3.85061 q^{57} +5.57320 q^{58} -6.66991 q^{59} -0.0562299 q^{60} -4.03506 q^{61} -5.32251 q^{62} +19.7266 q^{63} +8.02801 q^{64} -13.8324 q^{65} +20.7242 q^{66} -0.538541 q^{67} +0.00475263 q^{68} -9.37790 q^{69} -21.9771 q^{70} -1.60224 q^{71} +10.9306 q^{72} +10.8613 q^{73} +11.9278 q^{74} +11.1787 q^{75} +0.0103705 q^{76} -28.6649 q^{77} +16.7969 q^{78} +16.9961 q^{79} -12.1348 q^{80} -5.69082 q^{81} -11.0492 q^{82} -4.48784 q^{83} -0.0944429 q^{84} -2.05154 q^{85} -9.43263 q^{86} -10.3383 q^{87} -15.8834 q^{88} -8.48296 q^{89} -16.5805 q^{90} -23.2327 q^{91} +0.0252568 q^{92} +9.87327 q^{93} +8.93209 q^{94} -4.47659 q^{95} -0.104479 q^{96} +1.99439 q^{97} -27.0305 q^{98} -21.6260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4 q^{2} - 2 q^{3} + 16 q^{4} - 4 q^{5} - 8 q^{6} + 29 q^{7} + 3 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q + 4 * q^2 - 2 * q^3 + 16 * q^4 - 4 * q^5 - 8 * q^6 + 29 * q^7 + 3 * q^8 + 14 * q^9	\( 14 q + 4 q^{2} - 2 q^{3} + 16 q^{4} - 4 q^{5} - 8 q^{6} + 29 q^{7} + 3 q^{8} + 14 q^{9} + 15 q^{10} - 7 q^{11} - 4 q^{12} + 2 q^{13} + 8 q^{14} + 16 q^{15} + 12 q^{16} + 8 q^{17} + 5 q^{18} + 14 q^{19} - 5 q^{20} + 6 q^{21} + 25 q^{22} + 16 q^{23} - 23 q^{24} + 24 q^{25} - 2 q^{26} - 8 q^{27} + 39 q^{28} - 9 q^{29} - 15 q^{30} + 28 q^{31} - 10 q^{32} - 10 q^{33} - 26 q^{34} - 16 q^{35} + 36 q^{36} + 8 q^{37} - 24 q^{38} - 23 q^{39} - 4 q^{40} + 14 q^{41} - 44 q^{42} + 11 q^{43} - 41 q^{44} - 37 q^{45} + 27 q^{46} + 14 q^{47} - 71 q^{48} + 39 q^{49} + 4 q^{50} - 6 q^{51} + 3 q^{52} - 27 q^{53} - 50 q^{54} + 3 q^{55} + 19 q^{56} + 7 q^{57} - 11 q^{58} - 25 q^{59} - 2 q^{60} - 3 q^{61} - 3 q^{62} + 56 q^{63} - 15 q^{64} - 41 q^{65} - 38 q^{66} + 37 q^{67} - 17 q^{68} - 32 q^{69} - 32 q^{70} + 3 q^{71} + 29 q^{72} + 14 q^{73} - 29 q^{74} + 15 q^{75} - 18 q^{76} - 43 q^{77} - 67 q^{78} + 39 q^{79} - 44 q^{80} - 26 q^{81} - 42 q^{82} + 9 q^{83} - 78 q^{84} - 12 q^{85} - 24 q^{86} + 26 q^{87} - 21 q^{88} - 95 q^{90} + 12 q^{91} + 61 q^{92} - 7 q^{93} - 52 q^{94} - 81 q^{96} + 24 q^{97} - 24 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q + 4 * q^2 - 2 * q^3 + 16 * q^4 - 4 * q^5 - 8 * q^6 + 29 * q^7 + 3 * q^8 + 14 * q^9 + 15 * q^10 - 7 * q^11 - 4 * q^12 + 2 * q^13 + 8 * q^14 + 16 * q^15 + 12 * q^16 + 8 * q^17 + 5 * q^18 + 14 * q^19 - 5 * q^20 + 6 * q^21 + 25 * q^22 + 16 * q^23 - 23 * q^24 + 24 * q^25 - 2 * q^26 - 8 * q^27 + 39 * q^28 - 9 * q^29 - 15 * q^30 + 28 * q^31 - 10 * q^32 - 10 * q^33 - 26 * q^34 - 16 * q^35 + 36 * q^36 + 8 * q^37 - 24 * q^38 - 23 * q^39 - 4 * q^40 + 14 * q^41 - 44 * q^42 + 11 * q^43 - 41 * q^44 - 37 * q^45 + 27 * q^46 + 14 * q^47 - 71 * q^48 + 39 * q^49 + 4 * q^50 - 6 * q^51 + 3 * q^52 - 27 * q^53 - 50 * q^54 + 3 * q^55 + 19 * q^56 + 7 * q^57 - 11 * q^58 - 25 * q^59 - 2 * q^60 - 3 * q^61 - 3 * q^62 + 56 * q^63 - 15 * q^64 - 41 * q^65 - 38 * q^66 + 37 * q^67 - 17 * q^68 - 32 * q^69 - 32 * q^70 + 3 * q^71 + 29 * q^72 + 14 * q^73 - 29 * q^74 + 15 * q^75 - 18 * q^76 - 43 * q^77 - 67 * q^78 + 39 * q^79 - 44 * q^80 - 26 * q^81 - 42 * q^82 + 9 * q^83 - 78 * q^84 - 12 * q^85 - 24 * q^86 + 26 * q^87 - 21 * q^88 - 95 * q^90 + 12 * q^91 + 61 * q^92 - 7 * q^93 - 52 * q^94 - 81 * q^96 + 24 * q^97 - 24 * q^98 - 14 * q^99

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