LMFDB - Embedded newform 2645.2.a.v.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2645,2,Mod(1,2645)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2645, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2645.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2645 = 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2645.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:	$21.1204313346$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 18 x^{14} + 88 x^{13} + 93 x^{12} - 728 x^{11} + 58 x^{10} + 2760 x^{9} - 1764 x^{8} + \cdots - 18 $ x^16 - 4x^15 - 18x^14 + 88x^13 + 93x^12 - 728x^11 + 58x^10 + 2760x^9 - 1764x^8 - 4568x^7 + 4414x^6 + 2440x^5 - 2759x^4 - 684x^3 + 558x^2 + 108*x - 18
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.113281$ of defining polynomial
Character	$\chi$	$=$	2645.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.113281 q^{2} +2.52529 q^{3} -1.98717 q^{4} -1.00000 q^{5} +0.286068 q^{6} -0.501381 q^{7} -0.451671 q^{8} +3.37710 q^{9} +O(q^{10})$	\(q+0.113281 q^{2} +2.52529 q^{3} -1.98717 q^{4} -1.00000 q^{5} +0.286068 q^{6} -0.501381 q^{7} -0.451671 q^{8} +3.37710 q^{9} -0.113281 q^{10} -6.19977 q^{11} -5.01818 q^{12} +3.05313 q^{13} -0.0567970 q^{14} -2.52529 q^{15} +3.92317 q^{16} +6.98061 q^{17} +0.382561 q^{18} -3.54142 q^{19} +1.98717 q^{20} -1.26613 q^{21} -0.702317 q^{22} -1.14060 q^{24} +1.00000 q^{25} +0.345862 q^{26} +0.952279 q^{27} +0.996329 q^{28} -8.35422 q^{29} -0.286068 q^{30} +3.59669 q^{31} +1.34776 q^{32} -15.6562 q^{33} +0.790771 q^{34} +0.501381 q^{35} -6.71086 q^{36} -6.85247 q^{37} -0.401176 q^{38} +7.71005 q^{39} +0.451671 q^{40} +3.05506 q^{41} -0.143429 q^{42} -5.28782 q^{43} +12.3200 q^{44} -3.37710 q^{45} -4.71570 q^{47} +9.90715 q^{48} -6.74862 q^{49} +0.113281 q^{50} +17.6281 q^{51} -6.06708 q^{52} -6.35870 q^{53} +0.107875 q^{54} +6.19977 q^{55} +0.226459 q^{56} -8.94312 q^{57} -0.946376 q^{58} -5.33690 q^{59} +5.01818 q^{60} -2.34975 q^{61} +0.407437 q^{62} -1.69321 q^{63} -7.69366 q^{64} -3.05313 q^{65} -1.77355 q^{66} -12.9019 q^{67} -13.8716 q^{68} +0.0567970 q^{70} -6.85230 q^{71} -1.52534 q^{72} -3.29471 q^{73} -0.776255 q^{74} +2.52529 q^{75} +7.03739 q^{76} +3.10845 q^{77} +0.873403 q^{78} -6.07749 q^{79} -3.92317 q^{80} -7.72651 q^{81} +0.346081 q^{82} +3.53631 q^{83} +2.51602 q^{84} -6.98061 q^{85} -0.599010 q^{86} -21.0968 q^{87} +2.80025 q^{88} -1.94781 q^{89} -0.382561 q^{90} -1.53078 q^{91} +9.08268 q^{93} -0.534200 q^{94} +3.54142 q^{95} +3.40349 q^{96} -13.4025 q^{97} -0.764491 q^{98} -20.9372 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 4 q^{3} + 20 q^{4} - 16 q^{5} - 12 q^{6} - 12 q^{7} + 8 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + 4 * q^3 + 20 * q^4 - 16 * q^5 - 12 * q^6 - 12 * q^7 + 8 * q^9	\( 16 q + 4 q^{2} + 4 q^{3} + 20 q^{4} - 16 q^{5} - 12 q^{6} - 12 q^{7} + 8 q^{9} - 4 q^{10} - 16 q^{11} - 4 q^{12} + 8 q^{13} - 8 q^{14} - 4 q^{15} + 28 q^{16} + 8 q^{17} + 4 q^{18} - 32 q^{19} - 20 q^{20} - 16 q^{21} - 44 q^{22} - 28 q^{24} + 16 q^{25} - 20 q^{26} - 8 q^{27} - 52 q^{28} - 12 q^{29} + 12 q^{30} - 12 q^{31} + 4 q^{32} - 20 q^{33} - 24 q^{34} + 12 q^{35} - 4 q^{36} - 28 q^{37} + 20 q^{38} - 8 q^{39} - 4 q^{41} + 8 q^{42} - 48 q^{43} - 32 q^{44} - 8 q^{45} + 48 q^{47} + 24 q^{48} + 12 q^{49} + 4 q^{50} - 24 q^{51} + 12 q^{52} + 4 q^{53} - 44 q^{54} + 16 q^{55} - 64 q^{56} - 52 q^{57} - 28 q^{58} - 40 q^{59} + 4 q^{60} - 16 q^{61} - 4 q^{63} - 16 q^{64} - 8 q^{65} - 8 q^{66} - 68 q^{67} + 4 q^{68} + 8 q^{70} - 24 q^{71} - 12 q^{72} + 52 q^{73} - 40 q^{74} + 4 q^{75} - 24 q^{76} + 44 q^{77} + 12 q^{78} - 72 q^{79} - 28 q^{80} + 20 q^{81} - 20 q^{82} - 12 q^{83} - 32 q^{84} - 8 q^{85} + 56 q^{86} - 104 q^{88} - 48 q^{89} - 4 q^{90} - 48 q^{91} - 48 q^{93} - 60 q^{94} + 32 q^{95} - 108 q^{96} - 4 q^{97} + 8 q^{98} - 24 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 4 * q^3 + 20 * q^4 - 16 * q^5 - 12 * q^6 - 12 * q^7 + 8 * q^9 - 4 * q^10 - 16 * q^11 - 4 * q^12 + 8 * q^13 - 8 * q^14 - 4 * q^15 + 28 * q^16 + 8 * q^17 + 4 * q^18 - 32 * q^19 - 20 * q^20 - 16 * q^21 - 44 * q^22 - 28 * q^24 + 16 * q^25 - 20 * q^26 - 8 * q^27 - 52 * q^28 - 12 * q^29 + 12 * q^30 - 12 * q^31 + 4 * q^32 - 20 * q^33 - 24 * q^34 + 12 * q^35 - 4 * q^36 - 28 * q^37 + 20 * q^38 - 8 * q^39 - 4 * q^41 + 8 * q^42 - 48 * q^43 - 32 * q^44 - 8 * q^45 + 48 * q^47 + 24 * q^48 + 12 * q^49 + 4 * q^50 - 24 * q^51 + 12 * q^52 + 4 * q^53 - 44 * q^54 + 16 * q^55 - 64 * q^56 - 52 * q^57 - 28 * q^58 - 40 * q^59 + 4 * q^60 - 16 * q^61 - 4 * q^63 - 16 * q^64 - 8 * q^65 - 8 * q^66 - 68 * q^67 + 4 * q^68 + 8 * q^70 - 24 * q^71 - 12 * q^72 + 52 * q^73 - 40 * q^74 + 4 * q^75 - 24 * q^76 + 44 * q^77 + 12 * q^78 - 72 * q^79 - 28 * q^80 + 20 * q^81 - 20 * q^82 - 12 * q^83 - 32 * q^84 - 8 * q^85 + 56 * q^86 - 104 * q^88 - 48 * q^89 - 4 * q^90 - 48 * q^91 - 48 * q^93 - 60 * q^94 + 32 * q^95 - 108 * q^96 - 4 * q^97 + 8 * q^98 - 24 * 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 $

$2$	0.113281	0.0801018	0.0400509	−	0.999198i	$-0.487248\pi$
$2$	0.113281	0.0801018	0.0400509	+	0.999198i	$0.487248\pi$
$3$	2.52529	1.45798	0.728989	−	0.684526i	$-0.239991\pi$
$3$	2.52529	1.45798	0.728989	+	0.684526i	$0.239991\pi$
$4$	−1.98717	−0.993584
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.286068	0.116787
$7$	−0.501381	−0.189504	−0.0947522	−	0.995501i	$-0.530206\pi$
$7$	−0.501381	−0.189504	−0.0947522	+	0.995501i	$0.530206\pi$
$8$	−0.451671	−0.159690
$9$	3.37710	1.12570
$10$	−0.113281	−0.0358226
$11$	−6.19977	−1.86930	−0.934650	−	0.355568i	$-0.884287\pi$
$11$	−6.19977	−1.86930	−0.934650	+	0.355568i	$0.884287\pi$
$12$	−5.01818	−1.44862
$13$	3.05313	0.846786	0.423393	−	0.905946i	$-0.360839\pi$
$13$	3.05313	0.846786	0.423393	+	0.905946i	$0.360839\pi$
$14$	−0.0567970	−0.0151796
$15$	−2.52529	−0.652027
$16$	3.92317	0.980792
$17$	6.98061	1.69305	0.846523	−	0.532352i	$-0.178692\pi$
$17$	6.98061	1.69305	0.846523	+	0.532352i	$0.178692\pi$
$18$	0.382561	0.0901705
$19$	−3.54142	−0.812458	−0.406229	−	0.913771i	$-0.633156\pi$
$19$	−3.54142	−0.812458	−0.406229	+	0.913771i	$0.633156\pi$
$20$	1.98717	0.444344
$21$	−1.26613	−0.276293
$22$	−0.702317	−0.149734
$23$	0	0
$23$	0	0
$24$	−1.14060	−0.232824
$25$	1.00000	0.200000
$26$	0.345862	0.0678291
$27$	0.952279	0.183266
$28$	0.996329	0.188288
$29$	−8.35422	−1.55134	−0.775670	−	0.631138i	$-0.782588\pi$
$29$	−8.35422	−1.55134	−0.775670	+	0.631138i	$0.782588\pi$
$30$	−0.286068	−0.0522286
$31$	3.59669	0.645984	0.322992	−	0.946402i	$-0.395311\pi$
$31$	3.59669	0.645984	0.322992	+	0.946402i	$0.395311\pi$
$32$	1.34776	0.238253
$33$	−15.6562	−2.72540
$34$	0.790771	0.135616
$35$	0.501381	0.0847489
$36$	−6.71086	−1.11848
$37$	−6.85247	−1.12654	−0.563269	−	0.826273i	$-0.690457\pi$
$37$	−6.85247	−1.12654	−0.563269	+	0.826273i	$0.690457\pi$
$38$	−0.401176	−0.0650793
$39$	7.71005	1.23460
$40$	0.451671	0.0714154
$41$	3.05506	0.477121	0.238560	−	0.971128i	$-0.423325\pi$
$41$	3.05506	0.477121	0.238560	+	0.971128i	$0.423325\pi$
$42$	−0.143429	−0.0221316
$43$	−5.28782	−0.806384	−0.403192	−	0.915115i	$-0.632099\pi$
$43$	−5.28782	−0.806384	−0.403192	+	0.915115i	$0.632099\pi$
$44$	12.3200	1.85731
$45$	−3.37710	−0.503428
$46$	0	0
$47$	−4.71570	−0.687855	−0.343928	−	0.938996i	$-0.611758\pi$
$47$	−4.71570	−0.687855	−0.343928	+	0.938996i	$0.611758\pi$
$48$	9.90715	1.42997
$49$	−6.74862	−0.964088
$50$	0.113281	0.0160204
$51$	17.6281	2.46842
$52$	−6.06708	−0.841353
$53$	−6.35870	−0.873434	−0.436717	−	0.899599i	$-0.643859\pi$
$53$	−6.35870	−0.873434	−0.436717	+	0.899599i	$0.643859\pi$
$54$	0.107875	0.0146800
$55$	6.19977	0.835977
$56$	0.226459	0.0302619
$57$	−8.94312	−1.18454
$58$	−0.946376	−0.124265
$59$	−5.33690	−0.694805	−0.347403	−	0.937716i	$-0.612936\pi$
$59$	−5.33690	−0.694805	−0.347403	+	0.937716i	$0.612936\pi$
$60$	5.01818	0.647844
$61$	−2.34975	−0.300854	−0.150427	−	0.988621i	$-0.548065\pi$
$61$	−2.34975	−0.300854	−0.150427	+	0.988621i	$0.548065\pi$
$62$	0.407437	0.0517445
$63$	−1.69321	−0.213325
$64$	−7.69366	−0.961708
$65$	−3.05313	−0.378694
$66$	−1.77355	−0.218309
$67$	−12.9019	−1.57622	−0.788110	−	0.615535i	$-0.788940\pi$
$67$	−12.9019	−1.57622	−0.788110	+	0.615535i	$0.788940\pi$
$68$	−13.8716	−1.68218
$69$	0	0
$70$	0.0567970	0.00678854
$71$	−6.85230	−0.813219	−0.406609	−	0.913602i	$-0.633289\pi$
$71$	−6.85230	−0.813219	−0.406609	+	0.913602i	$0.633289\pi$
$72$	−1.52534	−0.179763
$73$	−3.29471	−0.385617	−0.192808	−	0.981236i	$-0.561760\pi$
$73$	−3.29471	−0.385617	−0.192808	+	0.981236i	$0.561760\pi$
$74$	−0.776255	−0.0902378
$75$	2.52529	0.291596
$76$	7.03739	0.807245
$77$	3.10845	0.354241
$78$	0.873403	0.0988934
$79$	−6.07749	−0.683771	−0.341885	−	0.939742i	$-0.611065\pi$
$79$	−6.07749	−0.683771	−0.341885	+	0.939742i	$0.611065\pi$
$80$	−3.92317	−0.438624
$81$	−7.72651	−0.858501
$82$	0.346081	0.0382182
$83$	3.53631	0.388160	0.194080	−	0.980986i	$-0.437828\pi$
$83$	3.53631	0.388160	0.194080	+	0.980986i	$0.437828\pi$
$84$	2.51602	0.274520
$85$	−6.98061	−0.757153
$86$	−0.599010	−0.0645929
$87$	−21.0968	−2.26182
$88$	2.80025	0.298508
$89$	−1.94781	−0.206468	−0.103234	−	0.994657i	$-0.532919\pi$
$89$	−1.94781	−0.206468	−0.103234	+	0.994657i	$0.532919\pi$
$90$	−0.382561	−0.0403255
$91$	−1.53078	−0.160470
$92$	0	0
$93$	9.08268	0.941830
$94$	−0.534200	−0.0550985
$95$	3.54142	0.363342
$96$	3.40349	0.347368
$97$	−13.4025	−1.36082	−0.680410	−	0.732832i	$-0.738198\pi$
$97$	−13.4025	−1.36082	−0.680410	+	0.732832i	$0.738198\pi$
$98$	−0.764491	−0.0772252
$99$	−20.9372	−2.10427
$100$	−1.98717	−0.198717
$101$	16.8703	1.67866	0.839330	−	0.543622i	$-0.182948\pi$
$101$	16.8703	1.67866	0.839330	+	0.543622i	$0.182948\pi$
$102$	1.99693	0.197725
$103$	1.72738	0.170203	0.0851017	−	0.996372i	$-0.472878\pi$
$103$	1.72738	0.170203	0.0851017	+	0.996372i	$0.472878\pi$
$104$	−1.37901	−0.135223
$105$	1.26613	0.123562
$106$	−0.720320	−0.0699637
$107$	12.4577	1.20433	0.602165	−	0.798371i	$-0.294305\pi$
$107$	12.4577	1.20433	0.602165	+	0.798371i	$0.294305\pi$
$108$	−1.89234	−0.182090
$109$	−2.36457	−0.226485	−0.113243	−	0.993567i	$-0.536124\pi$
$109$	−2.36457	−0.226485	−0.113243	+	0.993567i	$0.536124\pi$
$110$	0.702317	0.0669633
$111$	−17.3045	−1.64247
$112$	−1.96700	−0.185864
$113$	9.70650	0.913111	0.456555	−	0.889695i	$-0.349083\pi$
$113$	9.70650	0.913111	0.456555	+	0.889695i	$0.349083\pi$
$114$	−1.01309	−0.0948842
$115$	0	0
$116$	16.6012	1.54139
$117$	10.3107	0.953226
$118$	−0.604570	−0.0556552
$119$	−3.49995	−0.320840
$120$	1.14060	0.104122
$121$	27.4371	2.49429
$122$	−0.266182	−0.0240990
$123$	7.71492	0.695631
$124$	−7.14722	−0.641839
$125$	−1.00000	−0.0894427
$126$	−0.191809	−0.0170877
$127$	3.74546	0.332355	0.166178	−	0.986096i	$-0.446857\pi$
$127$	3.74546	0.332355	0.166178	+	0.986096i	$0.446857\pi$
$128$	−3.56707	−0.315288
$129$	−13.3533	−1.17569
$130$	−0.345862	−0.0303341
$131$	1.51981	0.132786	0.0663930	−	0.997794i	$-0.478851\pi$
$131$	1.51981	0.132786	0.0663930	+	0.997794i	$0.478851\pi$
$132$	31.1115	2.70791
$133$	1.77560	0.153964
$134$	−1.46154	−0.126258
$135$	−0.952279	−0.0819592
$136$	−3.15294	−0.270362
$137$	−9.21062	−0.786917	−0.393458	−	0.919342i	$-0.628721\pi$
$137$	−9.21062	−0.786917	−0.393458	+	0.919342i	$0.628721\pi$
$138$	0	0
$139$	15.2045	1.28963	0.644816	−	0.764338i	$-0.276934\pi$
$139$	15.2045	1.28963	0.644816	+	0.764338i	$0.276934\pi$
$140$	−0.996329	−0.0842051
$141$	−11.9085	−1.00288
$142$	−0.776236	−0.0651403
$143$	−18.9287	−1.58290
$144$	13.2489	1.10408
$145$	8.35422	0.693780
$146$	−0.373228	−0.0308886
$147$	−17.0422	−1.40562
$148$	13.6170	1.11931
$149$	5.57800	0.456968	0.228484	−	0.973548i	$-0.426623\pi$
$149$	5.57800	0.456968	0.228484	+	0.973548i	$0.426623\pi$
$150$	0.286068	0.0233573
$151$	−18.0280	−1.46710	−0.733551	−	0.679635i	$-0.762138\pi$
$151$	−18.0280	−1.46710	−0.733551	+	0.679635i	$0.762138\pi$
$152$	1.59956	0.129741
$153$	23.5742	1.90586
$154$	0.352128	0.0283753
$155$	−3.59669	−0.288893
$156$	−15.3212	−1.22667
$157$	−10.8804	−0.868347	−0.434173	−	0.900829i	$-0.642959\pi$
$157$	−10.8804	−0.868347	−0.434173	+	0.900829i	$0.642959\pi$
$158$	−0.688464	−0.0547713
$159$	−16.0576	−1.27345
$160$	−1.34776	−0.106550
$161$	0	0
$162$	−0.875267	−0.0687675
$163$	−19.2284	−1.50608	−0.753042	−	0.657973i	$-0.771414\pi$
$163$	−19.2284	−1.50608	−0.753042	+	0.657973i	$0.771414\pi$
$164$	−6.07092	−0.474059
$165$	15.6562	1.21884
$166$	0.400597	0.0310924
$167$	−0.792333	−0.0613126	−0.0306563	−	0.999530i	$-0.509760\pi$
$167$	−0.792333	−0.0613126	−0.0306563	+	0.999530i	$0.509760\pi$
$168$	0.571876	0.0441212
$169$	−3.67839	−0.282953
$170$	−0.790771	−0.0606494
$171$	−11.9597	−0.914583
$172$	10.5078	0.801210
$173$	8.64911	0.657580	0.328790	−	0.944403i	$-0.393359\pi$
$173$	8.64911	0.657580	0.328790	+	0.944403i	$0.393359\pi$
$174$	−2.38987	−0.181176
$175$	−0.501381	−0.0379009
$176$	−24.3227	−1.83340
$177$	−13.4772	−1.01301
$178$	−0.220650	−0.0165384
$179$	8.20533	0.613295	0.306648	−	0.951823i	$-0.400793\pi$
$179$	8.20533	0.613295	0.306648	+	0.951823i	$0.400793\pi$
$180$	6.71086	0.500198
$181$	16.8443	1.25203	0.626015	−	0.779811i	$-0.284685\pi$
$181$	16.8443	1.25203	0.626015	+	0.779811i	$0.284685\pi$
$182$	−0.173409	−0.0128539
$183$	−5.93379	−0.438639
$184$	0	0
$185$	6.85247	0.503803
$186$	1.02890	0.0754423
$187$	−43.2782	−3.16481
$188$	9.37088	0.683442
$189$	−0.477455	−0.0347297
$190$	0.401176	0.0291044
$191$	13.9177	1.00705	0.503524	−	0.863981i	$-0.332036\pi$
$191$	13.9177	1.00705	0.503524	+	0.863981i	$0.332036\pi$
$192$	−19.4287	−1.40215
$193$	26.8599	1.93342	0.966708	−	0.255883i	$-0.0823661\pi$
$193$	26.8599	1.93342	0.966708	+	0.255883i	$0.0823661\pi$
$194$	−1.51825	−0.109004
$195$	−7.71005	−0.552128
$196$	13.4106	0.957902
$197$	22.8883	1.63072	0.815361	−	0.578953i	$-0.196539\pi$
$197$	22.8883	1.63072	0.815361	+	0.578953i	$0.196539\pi$
$198$	−2.37179	−0.168556
$199$	26.4627	1.87589	0.937945	−	0.346784i	$-0.112726\pi$
$199$	26.4627	1.87589	0.937945	+	0.346784i	$0.112726\pi$
$200$	−0.451671	−0.0319379
$201$	−32.5811	−2.29809
$202$	1.91109	0.134464
$203$	4.18865	0.293986
$204$	−35.0299	−2.45259
$205$	−3.05506	−0.213375
$206$	0.195679	0.0136336
$207$	0	0
$208$	11.9780	0.830521
$209$	21.9560	1.51873
$210$	0.143429	0.00989754
$211$	−10.9026	−0.750564	−0.375282	−	0.926911i	$-0.622454\pi$
$211$	−10.9026	−0.750564	−0.375282	+	0.926911i	$0.622454\pi$
$212$	12.6358	0.867830
$213$	−17.3041	−1.18565
$214$	1.41122	0.0964691
$215$	5.28782	0.360626
$216$	−0.430117	−0.0292657
$217$	−1.80331	−0.122417
$218$	−0.267862	−0.0181419
$219$	−8.32010	−0.562220
$220$	−12.3200	−0.830613
$221$	21.3127	1.43365
$222$	−1.96027	−0.131565
$223$	−1.06241	−0.0711441	−0.0355720	−	0.999367i	$-0.511325\pi$
$223$	−1.06241	−0.0711441	−0.0355720	+	0.999367i	$0.511325\pi$
$224$	−0.675743	−0.0451500
$225$	3.37710	0.225140
$226$	1.09956	0.0731418
$227$	−3.87761	−0.257366	−0.128683	−	0.991686i	$-0.541075\pi$
$227$	−3.87761	−0.257366	−0.128683	+	0.991686i	$0.541075\pi$
$228$	17.7715	1.17694
$229$	8.37271	0.553284	0.276642	−	0.960973i	$-0.410778\pi$
$229$	8.37271	0.553284	0.276642	+	0.960973i	$0.410778\pi$
$230$	0	0
$231$	7.84974	0.516475
$232$	3.77336	0.247733
$233$	−13.5701	−0.889010	−0.444505	−	0.895776i	$-0.646620\pi$
$233$	−13.5701	−0.889010	−0.444505	+	0.895776i	$0.646620\pi$
$234$	1.16801	0.0763552
$235$	4.71570	0.307618
$236$	10.6053	0.690347
$237$	−15.3474	−0.996922
$238$	−0.396478	−0.0256998
$239$	−2.42699	−0.156989	−0.0784944	−	0.996915i	$-0.525011\pi$
$239$	−2.42699	−0.156989	−0.0784944	+	0.996915i	$0.525011\pi$
$240$	−9.90715	−0.639503
$241$	16.1605	1.04099	0.520494	−	0.853865i	$-0.325748\pi$
$241$	16.1605	1.04099	0.520494	+	0.853865i	$0.325748\pi$
$242$	3.10811	0.199797
$243$	−22.3685	−1.43494
$244$	4.66934	0.298924
$245$	6.74862	0.431153
$246$	0.873955	0.0557213
$247$	−10.8124	−0.687978
$248$	−1.62452	−0.103157
$249$	8.93021	0.565929
$250$	−0.113281	−0.00716453
$251$	−17.9361	−1.13211	−0.566057	−	0.824366i	$-0.691532\pi$
$251$	−17.9361	−1.13211	−0.566057	+	0.824366i	$0.691532\pi$
$252$	3.36470	0.211956
$253$	0	0
$254$	0.424289	0.0266223
$255$	−17.6281	−1.10391
$256$	14.9832	0.936453
$257$	−16.1250	−1.00585	−0.502925	−	0.864330i	$-0.667743\pi$
$257$	−16.1250	−1.00585	−0.502925	+	0.864330i	$0.667743\pi$
$258$	−1.51267	−0.0941750
$259$	3.43570	0.213484
$260$	6.06708	0.376265
$261$	−28.2130	−1.74634
$262$	0.172165	0.0106364
$263$	10.3450	0.637898	0.318949	−	0.947772i	$-0.396670\pi$
$263$	10.3450	0.637898	0.318949	+	0.947772i	$0.396670\pi$
$264$	7.07146	0.435218
$265$	6.35870	0.390612
$266$	0.201142	0.0123328
$267$	−4.91879	−0.301025
$268$	25.6383	1.56611
$269$	14.6854	0.895384	0.447692	−	0.894188i	$-0.352246\pi$
$269$	14.6854	0.895384	0.447692	+	0.894188i	$0.352246\pi$
$270$	−0.107875	−0.00656508
$271$	−10.9413	−0.664635	−0.332318	−	0.943168i	$-0.607831\pi$
$271$	−10.9413	−0.664635	−0.332318	+	0.943168i	$0.607831\pi$
$272$	27.3861	1.66053
$273$	−3.86567	−0.233961
$274$	−1.04339	−0.0630335
$275$	−6.19977	−0.373860
$276$	0	0
$277$	−26.1983	−1.57410	−0.787051	−	0.616887i	$-0.788393\pi$
$277$	−26.1983	−1.57410	−0.787051	+	0.616887i	$0.788393\pi$
$278$	1.72239	0.103302
$279$	12.1464	0.727184
$280$	−0.226459	−0.0135335
$281$	13.6076	0.811761	0.405880	−	0.913926i	$-0.366965\pi$
$281$	13.6076	0.811761	0.405880	+	0.913926i	$0.366965\pi$
$282$	−1.34901	−0.0803323
$283$	−16.3451	−0.971616	−0.485808	−	0.874066i	$-0.661475\pi$
$283$	−16.3451	−0.971616	−0.485808	+	0.874066i	$0.661475\pi$
$284$	13.6167	0.808001
$285$	8.94312	0.529745
$286$	−2.14427	−0.126793
$287$	−1.53175	−0.0904164
$288$	4.55152	0.268201
$289$	31.7289	1.86641
$290$	0.946376	0.0555731
$291$	−33.8453	−1.98404
$292$	6.54714	0.383142
$293$	22.3129	1.30354	0.651768	−	0.758418i	$-0.274028\pi$
$293$	22.3129	1.30354	0.651768	+	0.758418i	$0.274028\pi$
$294$	−1.93056	−0.112593
$295$	5.33690	0.310726
$296$	3.09506	0.179897
$297$	−5.90391	−0.342580
$298$	0.631882	0.0366039
$299$	0	0
$300$	−5.01818	−0.289725
$301$	2.65121	0.152813
$302$	−2.04224	−0.117518
$303$	42.6025	2.44745
$304$	−13.8936	−0.796852
$305$	2.34975	0.134546
$306$	2.67051	0.152663
$307$	−11.8483	−0.676220	−0.338110	−	0.941107i	$-0.609788\pi$
$307$	−11.8483	−0.676220	−0.338110	+	0.941107i	$0.609788\pi$
$308$	−6.17701	−0.351968
$309$	4.36213	0.248153
$310$	−0.407437	−0.0231408
$311$	−30.4520	−1.72678	−0.863389	−	0.504540i	$-0.831662\pi$
$311$	−30.4520	−1.72678	−0.863389	+	0.504540i	$0.831662\pi$
$312$	−3.48240	−0.197152
$313$	13.3111	0.752389	0.376194	−	0.926541i	$-0.377232\pi$
$313$	13.3111	0.752389	0.376194	+	0.926541i	$0.377232\pi$
$314$	−1.23254	−0.0695562
$315$	1.69321	0.0954018
$316$	12.0770	0.679383
$317$	−22.5735	−1.26785	−0.633927	−	0.773393i	$-0.718558\pi$
$317$	−22.5735	−1.26785	−0.633927	+	0.773393i	$0.718558\pi$
$318$	−1.81902	−0.102006
$319$	51.7943	2.89992
$320$	7.69366	0.430089
$321$	31.4593	1.75589
$322$	0	0
$323$	−24.7213	−1.37553
$324$	15.3539	0.852992
$325$	3.05313	0.169357
$326$	−2.17821	−0.120640
$327$	−5.97124	−0.330210
$328$	−1.37988	−0.0761913
$329$	2.36436	0.130352
$330$	1.77355	0.0976310
$331$	17.3256	0.952301	0.476151	−	0.879364i	$-0.342032\pi$
$331$	17.3256	0.952301	0.476151	+	0.879364i	$0.342032\pi$
$332$	−7.02724	−0.385670
$333$	−23.1414	−1.26814
$334$	−0.0897563	−0.00491125
$335$	12.9019	0.704907
$336$	−4.96726	−0.270986
$337$	−3.08625	−0.168119	−0.0840594	−	0.996461i	$-0.526789\pi$
$337$	−3.08625	−0.168119	−0.0840594	+	0.996461i	$0.526789\pi$
$338$	−0.416692	−0.0226650
$339$	24.5117	1.33130
$340$	13.8716	0.752295
$341$	−22.2986	−1.20754
$342$	−1.35481	−0.0732597
$343$	6.89330	0.372203
$344$	2.38835	0.128771
$345$	0	0
$346$	0.979781	0.0526734
$347$	−9.90897	−0.531942	−0.265971	−	0.963981i	$-0.585692\pi$
$347$	−9.90897	−0.531942	−0.265971	+	0.963981i	$0.585692\pi$
$348$	41.9230	2.24731
$349$	−17.3731	−0.929961	−0.464980	−	0.885321i	$-0.653939\pi$
$349$	−17.3731	−0.929961	−0.464980	+	0.885321i	$0.653939\pi$
$350$	−0.0567970	−0.00303593
$351$	2.90743	0.155187
$352$	−8.35582	−0.445366
$353$	24.9109	1.32588	0.662938	−	0.748675i	$-0.269309\pi$
$353$	24.9109	1.32588	0.662938	+	0.748675i	$0.269309\pi$
$354$	−1.52672	−0.0811440
$355$	6.85230	0.363683
$356$	3.87063	0.205143
$357$	−8.83839	−0.467777
$358$	0.929509	0.0491261
$359$	−5.74833	−0.303385	−0.151693	−	0.988428i	$-0.548472\pi$
$359$	−5.74833	−0.303385	−0.151693	+	0.988428i	$0.548472\pi$
$360$	1.52534	0.0803922
$361$	−6.45834	−0.339913
$362$	1.90815	0.100290
$363$	69.2868	3.63661
$364$	3.04192	0.159440
$365$	3.29471	0.172453
$366$	−0.672187	−0.0351358
$367$	7.49151	0.391054	0.195527	−	0.980698i	$-0.437358\pi$
$367$	7.49151	0.391054	0.195527	+	0.980698i	$0.437358\pi$
$368$	0	0
$369$	10.3172	0.537094
$370$	0.776255	0.0403556
$371$	3.18813	0.165520
$372$	−18.0488	−0.935787
$373$	−19.9803	−1.03454	−0.517271	−	0.855821i	$-0.673052\pi$
$373$	−19.9803	−1.03454	−0.517271	+	0.855821i	$0.673052\pi$
$374$	−4.90260	−0.253507
$375$	−2.52529	−0.130405
$376$	2.12994	0.109843
$377$	−25.5065	−1.31365
$378$	−0.0540866	−0.00278192
$379$	−8.88450	−0.456366	−0.228183	−	0.973618i	$-0.573278\pi$
$379$	−8.88450	−0.456366	−0.228183	+	0.973618i	$0.573278\pi$
$380$	−7.03739	−0.361011
$381$	9.45837	0.484567
$382$	1.57661	0.0806664
$383$	−5.38561	−0.275192	−0.137596	−	0.990488i	$-0.543938\pi$
$383$	−5.38561	−0.275192	−0.137596	+	0.990488i	$0.543938\pi$
$384$	−9.00789	−0.459682
$385$	−3.10845	−0.158421
$386$	3.04272	0.154870
$387$	−17.8575	−0.907746
$388$	26.6331	1.35209
$389$	4.79365	0.243048	0.121524	−	0.992589i	$-0.461222\pi$
$389$	4.79365	0.243048	0.121524	+	0.992589i	$0.461222\pi$
$390$	−0.873403	−0.0442265
$391$	0	0
$392$	3.04815	0.153955
$393$	3.83795	0.193599
$394$	2.59281	0.130624
$395$	6.07749	0.305792
$396$	41.6058	2.09077
$397$	−29.1751	−1.46426	−0.732128	−	0.681168i	$-0.761473\pi$
$397$	−29.1751	−1.46426	−0.732128	+	0.681168i	$0.761473\pi$
$398$	2.99772	0.150262
$399$	4.48391	0.224476
$400$	3.92317	0.196158
$401$	13.3918	0.668753	0.334376	−	0.942440i	$-0.391474\pi$
$401$	13.3918	0.668753	0.334376	+	0.942440i	$0.391474\pi$
$402$	−3.69082	−0.184081
$403$	10.9812	0.547010
$404$	−33.5242	−1.66789
$405$	7.72651	0.383933
$406$	0.474495	0.0235488
$407$	42.4837	2.10584
$408$	−7.96208	−0.394182
$409$	1.92003	0.0949392	0.0474696	−	0.998873i	$-0.484884\pi$
$409$	1.92003	0.0949392	0.0474696	+	0.998873i	$0.484884\pi$
$410$	−0.346081	−0.0170917
$411$	−23.2595	−1.14731
$412$	−3.43259	−0.169111
$413$	2.67582	0.131669
$414$	0	0
$415$	−3.53631	−0.173591
$416$	4.11490	0.201749
$417$	38.3959	1.88025
$418$	2.48720	0.121653
$419$	2.14905	0.104988	0.0524941	−	0.998621i	$-0.483283\pi$
$419$	2.14905	0.104988	0.0524941	+	0.998621i	$0.483283\pi$
$420$	−2.51602	−0.122769
$421$	1.96986	0.0960052	0.0480026	−	0.998847i	$-0.484714\pi$
$421$	1.96986	0.0960052	0.0480026	+	0.998847i	$0.484714\pi$
$422$	−1.23506	−0.0601216
$423$	−15.9254	−0.774318
$424$	2.87204	0.139478
$425$	6.98061	0.338609
$426$	−1.96022	−0.0949731
$427$	1.17812	0.0570132
$428$	−24.7555	−1.19660
$429$	−47.8005	−2.30783
$430$	0.599010	0.0288868
$431$	−5.74228	−0.276596	−0.138298	−	0.990391i	$-0.544163\pi$
$431$	−5.74228	−0.276596	−0.138298	+	0.990391i	$0.544163\pi$
$432$	3.73595	0.179746
$433$	14.8410	0.713214	0.356607	−	0.934255i	$-0.383934\pi$
$433$	14.8410	0.713214	0.356607	+	0.934255i	$0.383934\pi$
$434$	−0.204281	−0.00980581
$435$	21.0968	1.01152
$436$	4.69881	0.225032
$437$	0	0
$438$	−0.942510	−0.0450349
$439$	−32.4246	−1.54754	−0.773772	−	0.633465i	$-0.781632\pi$
$439$	−32.4246	−1.54754	−0.773772	+	0.633465i	$0.781632\pi$
$440$	−2.80025	−0.133497
$441$	−22.7907	−1.08527
$442$	2.41433	0.114838
$443$	−23.3020	−1.10711	−0.553555	−	0.832812i	$-0.686729\pi$
$443$	−23.3020	−1.10711	−0.553555	+	0.832812i	$0.686729\pi$
$444$	34.3869	1.63193
$445$	1.94781	0.0923351
$446$	−0.120351	−0.00569877
$447$	14.0861	0.666248
$448$	3.85746	0.182248
$449$	−8.21844	−0.387852	−0.193926	−	0.981016i	$-0.562122\pi$
$449$	−8.21844	−0.387852	−0.193926	+	0.981016i	$0.562122\pi$
$450$	0.382561	0.0180341
$451$	−18.9407	−0.891882
$452$	−19.2884	−0.907252
$453$	−45.5261	−2.13900
$454$	−0.439260	−0.0206155
$455$	1.53078	0.0717642
$456$	4.03934	0.189160
$457$	−27.3857	−1.28105	−0.640524	−	0.767938i	$-0.721283\pi$
$457$	−27.3857	−1.28105	−0.640524	+	0.767938i	$0.721283\pi$
$458$	0.948470	0.0443191
$459$	6.64749	0.310278
$460$	0	0
$461$	−17.3263	−0.806967	−0.403483	−	0.914987i	$-0.632201\pi$
$461$	−17.3263	−0.806967	−0.403483	+	0.914987i	$0.632201\pi$
$462$	0.889227	0.0413706
$463$	27.3662	1.27182	0.635909	−	0.771764i	$-0.280625\pi$
$463$	27.3662	1.27182	0.635909	+	0.771764i	$0.280625\pi$
$464$	−32.7750	−1.52154
$465$	−9.08268	−0.421199
$466$	−1.53724	−0.0712113
$467$	25.8613	1.19672	0.598359	−	0.801228i	$-0.295820\pi$
$467$	25.8613	1.19672	0.598359	+	0.801228i	$0.295820\pi$
$468$	−20.4891	−0.947110
$469$	6.46878	0.298700
$470$	0.534200	0.0246408
$471$	−27.4761	−1.26603
$472$	2.41052	0.110953
$473$	32.7832	1.50738
$474$	−1.73857	−0.0798553
$475$	−3.54142	−0.162492
$476$	6.95498	0.318781
$477$	−21.4739	−0.983224
$478$	−0.274932	−0.0125751
$479$	−9.64732	−0.440797	−0.220399	−	0.975410i	$-0.570736\pi$
$479$	−9.64732	−0.440797	−0.220399	+	0.975410i	$0.570736\pi$
$480$	−3.40349	−0.155347
$481$	−20.9215	−0.953938
$482$	1.83068	0.0833851
$483$	0	0
$484$	−54.5222	−2.47828
$485$	13.4025	0.608577
$486$	−2.53393	−0.114941
$487$	3.97432	0.180094	0.0900468	−	0.995938i	$-0.471298\pi$
$487$	3.97432	0.180094	0.0900468	+	0.995938i	$0.471298\pi$
$488$	1.06131	0.0480433
$489$	−48.5573	−2.19584
$490$	0.764491	0.0345362
$491$	25.2364	1.13890	0.569451	−	0.822025i	$-0.307156\pi$
$491$	25.2364	1.13890	0.569451	+	0.822025i	$0.307156\pi$
$492$	−15.3308	−0.691168
$493$	−58.3176	−2.62649
$494$	−1.22484	−0.0551083
$495$	20.9372	0.941058
$496$	14.1104	0.633576
$497$	3.43562	0.154108
$498$	1.01162	0.0453320
$499$	−14.0420	−0.628608	−0.314304	−	0.949322i	$-0.601771\pi$
$499$	−14.0420	−0.628608	−0.314304	+	0.949322i	$0.601771\pi$
$500$	1.98717	0.0888688
$501$	−2.00087	−0.0893923
$502$	−2.03182	−0.0906844
$503$	−23.9547	−1.06809	−0.534044	−	0.845456i	$-0.679328\pi$
$503$	−23.9547	−1.06809	−0.534044	+	0.845456i	$0.679328\pi$
$504$	0.764775	0.0340658
$505$	−16.8703	−0.750720
$506$	0	0
$507$	−9.28900	−0.412539
$508$	−7.44285	−0.330223
$509$	−11.5565	−0.512234	−0.256117	−	0.966646i	$-0.582443\pi$
$509$	−11.5565	−0.512234	−0.256117	+	0.966646i	$0.582443\pi$
$510$	−1.99693	−0.0884254
$511$	1.65191	0.0730760
$512$	8.83146	0.390299
$513$	−3.37242	−0.148896
$514$	−1.82666	−0.0805704
$515$	−1.72738	−0.0761173
$516$	26.5352	1.16815
$517$	29.2362	1.28581
$518$	0.389200	0.0171005
$519$	21.8415	0.958737
$520$	1.37901	0.0604736
$521$	−30.9059	−1.35401	−0.677006	−	0.735978i	$-0.736723\pi$
$521$	−30.9059	−1.35401	−0.677006	+	0.735978i	$0.736723\pi$
$522$	−3.19600	−0.139885
$523$	−23.4745	−1.02647	−0.513235	−	0.858248i	$-0.671553\pi$
$523$	−23.4745	−1.02647	−0.513235	+	0.858248i	$0.671553\pi$
$524$	−3.02011	−0.131934
$525$	−1.26613	−0.0552586
$526$	1.17189	0.0510968
$527$	25.1071	1.09368
$528$	−61.4220	−2.67305
$529$	0	0
$530$	0.720320	0.0312887
$531$	−18.0232	−0.782142
$532$	−3.52842	−0.152976
$533$	9.32751	0.404019
$534$	−0.557206	−0.0241127
$535$	−12.4577	−0.538593
$536$	5.82741	0.251706
$537$	20.7208	0.894170
$538$	1.66358	0.0717219
$539$	41.8399	1.80217
$540$	1.89234	0.0814333
$541$	15.4160	0.662787	0.331393	−	0.943493i	$-0.392481\pi$
$541$	15.4160	0.662787	0.331393	+	0.943493i	$0.392481\pi$
$542$	−1.23944	−0.0532385
$543$	42.5369	1.82543
$544$	9.40820	0.403373
$545$	2.36457	0.101287
$546$	−0.437908	−0.0187407
$547$	31.2975	1.33818	0.669091	−	0.743180i	$-0.266684\pi$
$547$	31.2975	1.33818	0.669091	+	0.743180i	$0.266684\pi$
$548$	18.3031	0.781868
$549$	−7.93532	−0.338671
$550$	−0.702317	−0.0299469
$551$	29.5858	1.26040
$552$	0	0
$553$	3.04714	0.129578
$554$	−2.96777	−0.126089
$555$	17.3045	0.734534
$556$	−30.2139	−1.28136
$557$	35.3135	1.49628	0.748141	−	0.663540i	$-0.230947\pi$
$557$	35.3135	1.49628	0.748141	+	0.663540i	$0.230947\pi$
$558$	1.37595	0.0582487
$559$	−16.1444	−0.682835
$560$	1.96700	0.0831211
$561$	−109.290	−4.61423
$562$	1.54148	0.0650235
$563$	12.7665	0.538045	0.269023	−	0.963134i	$-0.413299\pi$
$563$	12.7665	0.538045	0.269023	+	0.963134i	$0.413299\pi$
$564$	23.6642	0.996443
$565$	−9.70650	−0.408356
$566$	−1.85159	−0.0778282
$567$	3.87393	0.162690
$568$	3.09498	0.129863
$569$	−33.5566	−1.40677	−0.703384	−	0.710810i	$-0.748328\pi$
$569$	−33.5566	−1.40677	−0.703384	+	0.710810i	$0.748328\pi$
$570$	1.01309	0.0424335
$571$	3.85906	0.161497	0.0807483	−	0.996735i	$-0.474269\pi$
$571$	3.85906	0.161497	0.0807483	+	0.996735i	$0.474269\pi$
$572$	37.6145	1.57274
$573$	35.1462	1.46825
$574$	−0.173519	−0.00724252
$575$	0	0
$576$	−25.9822	−1.08259
$577$	−0.180157	−0.00750004	−0.00375002	−	0.999993i	$-0.501194\pi$
$577$	−0.180157	−0.00750004	−0.00375002	+	0.999993i	$0.501194\pi$
$578$	3.59428	0.149503
$579$	67.8290	2.81888
$580$	−16.6012	−0.689329
$581$	−1.77304	−0.0735581
$582$	−3.83403	−0.158926
$583$	39.4225	1.63271
$584$	1.48812	0.0615790
$585$	−10.3107	−0.426296
$586$	2.52763	0.104416
$587$	−24.6763	−1.01850	−0.509250	−	0.860619i	$-0.670077\pi$
$587$	−24.6763	−1.01850	−0.509250	+	0.860619i	$0.670077\pi$
$588$	33.8658	1.39660
$589$	−12.7374	−0.524835
$590$	0.604570	0.0248898
$591$	57.7996	2.37756
$592$	−26.8834	−1.10490
$593$	−14.8192	−0.608551	−0.304276	−	0.952584i	$-0.598414\pi$
$593$	−14.8192	−0.608551	−0.304276	+	0.952584i	$0.598414\pi$
$594$	−0.668802	−0.0274413
$595$	3.49995	0.143484
$596$	−11.0844	−0.454035
$597$	66.8260	2.73501
$598$	0	0
$599$	−21.8740	−0.893746	−0.446873	−	0.894598i	$-0.647462\pi$
$599$	−21.8740	−0.893746	−0.446873	+	0.894598i	$0.647462\pi$
$600$	−1.14060	−0.0465648
$601$	−20.4481	−0.834097	−0.417049	−	0.908884i	$-0.636936\pi$
$601$	−20.4481	−0.834097	−0.417049	+	0.908884i	$0.636936\pi$
$602$	0.300332	0.0122406
$603$	−43.5710	−1.77435
$604$	35.8247	1.45769
$605$	−27.4371	−1.11548
$606$	4.82606	0.196045
$607$	32.5583	1.32150	0.660751	−	0.750606i	$-0.270238\pi$
$607$	32.5583	1.32150	0.660751	+	0.750606i	$0.270238\pi$
$608$	−4.77299	−0.193570
$609$	10.5776	0.428625
$610$	0.266182	0.0107774
$611$	−14.3976	−0.582467
$612$	−46.8459	−1.89363
$613$	−9.62065	−0.388574	−0.194287	−	0.980945i	$-0.562239\pi$
$613$	−9.62065	−0.388574	−0.194287	+	0.980945i	$0.562239\pi$
$614$	−1.34219	−0.0541665
$615$	−7.71492	−0.311096
$616$	−1.40400	−0.0565686
$617$	−23.1152	−0.930583	−0.465291	−	0.885158i	$-0.654050\pi$
$617$	−23.1152	−0.930583	−0.465291	+	0.885158i	$0.654050\pi$
$618$	0.494147	0.0198775
$619$	8.36137	0.336072	0.168036	−	0.985781i	$-0.446258\pi$
$619$	8.36137	0.336072	0.168036	+	0.985781i	$0.446258\pi$
$620$	7.14722	0.287039
$621$	0	0
$622$	−3.44964	−0.138318
$623$	0.976596	0.0391265
$624$	30.2478	1.21088
$625$	1.00000	0.0400000
$626$	1.50790	0.0602677
$627$	55.4453	2.21427
$628$	21.6211	0.862775
$629$	−47.8344	−1.90728
$630$	0.191809	0.00764186
$631$	40.9225	1.62910	0.814550	−	0.580093i	$-0.196984\pi$
$631$	40.9225	1.62910	0.814550	+	0.580093i	$0.196984\pi$
$632$	2.74502	0.109191
$633$	−27.5322	−1.09431
$634$	−2.55715	−0.101557
$635$	−3.74546	−0.148634
$636$	31.9091	1.26528
$637$	−20.6044	−0.816377
$638$	5.86731	0.232289
$639$	−23.1409	−0.915440
$640$	3.56707	0.141001
$641$	32.1256	1.26888	0.634442	−	0.772970i	$-0.281230\pi$
$641$	32.1256	1.26888	0.634442	+	0.772970i	$0.281230\pi$
$642$	3.56375	0.140650
$643$	0.111851	0.00441097	0.00220548	−	0.999998i	$-0.499298\pi$
$643$	0.111851	0.00441097	0.00220548	+	0.999998i	$0.499298\pi$
$644$	0	0
$645$	13.3533	0.525785
$646$	−2.80045	−0.110182
$647$	19.8482	0.780313	0.390157	−	0.920748i	$-0.372421\pi$
$647$	19.8482	0.780313	0.390157	+	0.920748i	$0.372421\pi$
$648$	3.48984	0.137094
$649$	33.0876	1.29880
$650$	0.345862	0.0135658
$651$	−4.55389	−0.178481
$652$	38.2100	1.49642
$653$	−1.34328	−0.0525666	−0.0262833	−	0.999655i	$-0.508367\pi$
$653$	−1.34328	−0.0525666	−0.0262833	+	0.999655i	$0.508367\pi$
$654$	−0.676429	−0.0264505
$655$	−1.51981	−0.0593837
$656$	11.9855	0.467956
$657$	−11.1266	−0.434088
$658$	0.267838	0.0104414
$659$	−23.6269	−0.920375	−0.460187	−	0.887822i	$-0.652218\pi$
$659$	−23.6269	−0.920375	−0.460187	+	0.887822i	$0.652218\pi$
$660$	−31.1115	−1.21102
$661$	24.1333	0.938676	0.469338	−	0.883019i	$-0.344493\pi$
$661$	24.1333	0.938676	0.469338	+	0.883019i	$0.344493\pi$
$662$	1.96266	0.0762811
$663$	53.8208	2.09023
$664$	−1.59725	−0.0619852
$665$	−1.77560	−0.0688549
$666$	−2.62149	−0.101581
$667$	0	0
$668$	1.57450	0.0609192
$669$	−2.68289	−0.103726
$670$	1.46154	0.0564643
$671$	14.5679	0.562387
$672$	−1.70645	−0.0658276
$673$	16.5575	0.638247	0.319123	−	0.947713i	$-0.396612\pi$
$673$	16.5575	0.638247	0.319123	+	0.947713i	$0.396612\pi$
$674$	−0.349614	−0.0134666
$675$	0.952279	0.0366532
$676$	7.30957	0.281137
$677$	37.4176	1.43808	0.719038	−	0.694971i	$-0.244583\pi$
$677$	37.4176	1.43808	0.719038	+	0.694971i	$0.244583\pi$
$678$	2.77672	0.106639
$679$	6.71977	0.257881
$680$	3.15294	0.120910
$681$	−9.79209	−0.375234
$682$	−2.52601	−0.0967260
$683$	−42.7978	−1.63761	−0.818806	−	0.574070i	$-0.805364\pi$
$683$	−42.7978	−1.63761	−0.818806	+	0.574070i	$0.805364\pi$
$684$	23.7660	0.908714
$685$	9.21062	0.351920
$686$	0.780881	0.0298142
$687$	21.1435	0.806676
$688$	−20.7450	−0.790896
$689$	−19.4139	−0.739612
$690$	0	0
$691$	−22.3417	−0.849917	−0.424959	−	0.905213i	$-0.639711\pi$
$691$	−22.3417	−0.849917	−0.424959	+	0.905213i	$0.639711\pi$
$692$	−17.1872	−0.653361
$693$	10.4975	0.398768
$694$	−1.12250	−0.0426095
$695$	−15.2045	−0.576741
$696$	9.52883	0.361189
$697$	21.3262	0.807787
$698$	−1.96804	−0.0744915
$699$	−34.2686	−1.29616
$700$	0.996329	0.0376577
$701$	7.26364	0.274344	0.137172	−	0.990547i	$-0.456199\pi$
$701$	7.26364	0.274344	0.137172	+	0.990547i	$0.456199\pi$
$702$	0.329357	0.0124308
$703$	24.2675	0.915265
$704$	47.6989	1.79772
$705$	11.9085	0.448501
$706$	2.82194	0.106205
$707$	−8.45847	−0.318113
$708$	26.7815	1.00651
$709$	0.612928	0.0230190	0.0115095	−	0.999934i	$-0.496336\pi$
$709$	0.612928	0.0230190	0.0115095	+	0.999934i	$0.496336\pi$
$710$	0.776236	0.0291316
$711$	−20.5243	−0.769720
$712$	0.879769	0.0329707
$713$	0	0
$714$	−1.00122	−0.0374698
$715$	18.9287	0.707894
$716$	−16.3054	−0.609360
$717$	−6.12886	−0.228886
$718$	−0.651177	−0.0243017
$719$	31.8816	1.18898	0.594492	−	0.804101i	$-0.297353\pi$
$719$	31.8816	1.18898	0.594492	+	0.804101i	$0.297353\pi$
$720$	−13.2489	−0.493758
$721$	−0.866074	−0.0322543
$722$	−0.731608	−0.0272276
$723$	40.8099	1.51774
$724$	−33.4725	−1.24400
$725$	−8.35422	−0.310268
$726$	7.84888	0.291299
$727$	6.14210	0.227798	0.113899	−	0.993492i	$-0.463666\pi$
$727$	6.14210	0.227798	0.113899	+	0.993492i	$0.463666\pi$
$728$	0.691410	0.0256254
$729$	−33.3075	−1.23361
$730$	0.373228	0.0138138
$731$	−36.9122	−1.36525
$732$	11.7914	0.435824
$733$	13.2938	0.491017	0.245508	−	0.969394i	$-0.421045\pi$
$733$	13.2938	0.491017	0.245508	+	0.969394i	$0.421045\pi$
$734$	0.848646	0.0313241
$735$	17.0422	0.628612
$736$	0	0
$737$	79.9889	2.94643
$738$	1.16875	0.0430222
$739$	−15.7842	−0.580631	−0.290316	−	0.956931i	$-0.593760\pi$
$739$	−15.7842	−0.580631	−0.290316	+	0.956931i	$0.593760\pi$
$740$	−13.6170	−0.500571
$741$	−27.3045	−1.00306
$742$	0.361155	0.0132584
$743$	21.2530	0.779695	0.389848	−	0.920879i	$-0.372528\pi$
$743$	21.2530	0.779695	0.389848	+	0.920879i	$0.372528\pi$
$744$	−4.10238	−0.150401
$745$	−5.57800	−0.204362
$746$	−2.26339	−0.0828688
$747$	11.9425	0.436952
$748$	86.0010	3.14451
$749$	−6.24606	−0.228226
$750$	−0.286068	−0.0104457
$751$	32.2731	1.17766	0.588831	−	0.808256i	$-0.299588\pi$
$751$	32.2731	1.17766	0.588831	+	0.808256i	$0.299588\pi$
$752$	−18.5005	−0.674643
$753$	−45.2938	−1.65060
$754$	−2.88941	−0.105226
$755$	18.0280	0.656108
$756$	0.948783	0.0345069
$757$	−41.1345	−1.49506	−0.747529	−	0.664230i	$-0.768760\pi$
$757$	−41.1345	−1.49506	−0.747529	+	0.664230i	$0.768760\pi$
$758$	−1.00645	−0.0365558
$759$	0	0
$760$	−1.59956	−0.0580220
$761$	28.6007	1.03678	0.518388	−	0.855145i	$-0.326532\pi$
$761$	28.6007	1.03678	0.518388	+	0.855145i	$0.326532\pi$
$762$	1.07145	0.0388147
$763$	1.18555	0.0429199
$764$	−27.6568	−1.00059
$765$	−23.5742	−0.852327
$766$	−0.610088	−0.0220434
$767$	−16.2943	−0.588352
$768$	37.8371	1.36533
$769$	−11.2292	−0.404934	−0.202467	−	0.979289i	$-0.564896\pi$
$769$	−11.2292	−0.404934	−0.202467	+	0.979289i	$0.564896\pi$
$770$	−0.352128	−0.0126898
$771$	−40.7203	−1.46651
$772$	−53.3751	−1.92101
$773$	45.4663	1.63531	0.817654	−	0.575710i	$-0.195274\pi$
$773$	45.4663	1.63531	0.817654	+	0.575710i	$0.195274\pi$
$774$	−2.02291	−0.0727121
$775$	3.59669	0.129197
$776$	6.05353	0.217309
$777$	8.67614	0.311255
$778$	0.543030	0.0194686
$779$	−10.8193	−0.387640
$780$	15.3212	0.548585
$781$	42.4827	1.52015
$782$	0	0
$783$	−7.95555	−0.284308
$784$	−26.4760	−0.945570
$785$	10.8804	0.388336
$786$	0.434767	0.0155076
$787$	−10.3696	−0.369637	−0.184818	−	0.982773i	$-0.559170\pi$
$787$	−10.3696	−0.369637	−0.184818	+	0.982773i	$0.559170\pi$
$788$	−45.4828	−1.62026
$789$	26.1241	0.930041
$790$	0.688464	0.0244945
$791$	−4.86666	−0.173038
$792$	9.45673	0.336030
$793$	−7.17409	−0.254759
$794$	−3.30498	−0.117290
$795$	16.0576	0.569503
$796$	−52.5858	−1.86385
$797$	−23.5681	−0.834826	−0.417413	−	0.908717i	$-0.637063\pi$
$797$	−23.5681	−0.834826	−0.417413	+	0.908717i	$0.637063\pi$
$798$	0.507943	0.0179810
$799$	−32.9184	−1.16457
$800$	1.34776	0.0476506
$801$	−6.57795	−0.232420
$802$	1.51703	0.0535683
$803$	20.4264	0.720833
$804$	64.7441	2.28335
$805$	0	0
$806$	1.24396	0.0438165
$807$	37.0849	1.30545
$808$	−7.61983	−0.268065
$809$	34.1876	1.20197	0.600986	−	0.799260i	$-0.294775\pi$
$809$	34.1876	1.20197	0.600986	+	0.799260i	$0.294775\pi$
$810$	0.875267	0.0307538
$811$	−23.2655	−0.816964	−0.408482	−	0.912766i	$-0.633942\pi$
$811$	−23.2655	−0.816964	−0.408482	+	0.912766i	$0.633942\pi$
$812$	−8.32355	−0.292099
$813$	−27.6299	−0.969023
$814$	4.81260	0.168682
$815$	19.2284	0.673541
$816$	69.1579	2.42101
$817$	18.7264	0.655153
$818$	0.217503	0.00760480
$819$	−5.16960	−0.180641
$820$	6.07092	0.212006
$821$	−6.82939	−0.238347	−0.119174	−	0.992873i	$-0.538025\pi$
$821$	−6.82939	−0.238347	−0.119174	+	0.992873i	$0.538025\pi$
$822$	−2.63486	−0.0919014
$823$	32.4070	1.12964	0.564819	−	0.825215i	$-0.308946\pi$
$823$	32.4070	1.12964	0.564819	+	0.825215i	$0.308946\pi$
$824$	−0.780205	−0.0271797
$825$	−15.6562	−0.545080
$826$	0.303120	0.0105469
$827$	17.1191	0.595290	0.297645	−	0.954677i	$-0.403799\pi$
$827$	17.1191	0.595290	0.297645	+	0.954677i	$0.403799\pi$
$828$	0	0
$829$	27.0835	0.940647	0.470324	−	0.882494i	$-0.344137\pi$
$829$	27.0835	0.940647	0.470324	+	0.882494i	$0.344137\pi$
$830$	−0.400597	−0.0139049
$831$	−66.1583	−2.29501
$832$	−23.4898	−0.814361
$833$	−47.1095	−1.63225
$834$	4.34953	0.150612
$835$	0.792333	0.0274198
$836$	−43.6302	−1.50898
$837$	3.42505	0.118387
$838$	0.243447	0.00840975
$839$	5.81736	0.200838	0.100419	−	0.994945i	$-0.467982\pi$
$839$	5.81736	0.200838	0.100419	+	0.994945i	$0.467982\pi$
$840$	−0.571876	−0.0197316
$841$	40.7930	1.40666
$842$	0.223148	0.00769019
$843$	34.3631	1.18353
$844$	21.6652	0.745748
$845$	3.67839	0.126540
$846$	−1.80404	−0.0620243
$847$	−13.7565	−0.472678
$848$	−24.9463	−0.856658
$849$	−41.2762	−1.41659
$850$	0.790771	0.0271232
$851$	0	0
$852$	34.3861	1.17805
$853$	−24.5624	−0.841000	−0.420500	−	0.907292i	$-0.638145\pi$
$853$	−24.5624	−0.841000	−0.420500	+	0.907292i	$0.638145\pi$
$854$	0.133459	0.00456686
$855$	11.9597	0.409014
$856$	−5.62678	−0.192319
$857$	14.0873	0.481212	0.240606	−	0.970623i	$-0.422654\pi$
$857$	14.0873	0.481212	0.240606	+	0.970623i	$0.422654\pi$
$858$	−5.41489	−0.184861
$859$	−23.7290	−0.809623	−0.404811	−	0.914400i	$-0.632663\pi$
$859$	−23.7290	−0.809623	−0.404811	+	0.914400i	$0.632663\pi$
$860$	−10.5078	−0.358312
$861$	−3.86812	−0.131825
$862$	−0.650491	−0.0221558
$863$	−0.236102	−0.00803701	−0.00401851	−	0.999992i	$-0.501279\pi$
$863$	−0.236102	−0.00803701	−0.00401851	+	0.999992i	$0.501279\pi$
$864$	1.28345	0.0436637
$865$	−8.64911	−0.294079
$866$	1.68121	0.0571297
$867$	80.1247	2.72118
$868$	3.58348	0.121631
$869$	37.6790	1.27817
$870$	2.38987	0.0810243
$871$	−39.3912	−1.33472
$872$	1.06801	0.0361674
$873$	−45.2616	−1.53187
$874$	0	0
$875$	0.501381	0.0169498
$876$	16.5334	0.558613
$877$	17.8626	0.603176	0.301588	−	0.953438i	$-0.402483\pi$
$877$	17.8626	0.603176	0.301588	+	0.953438i	$0.402483\pi$
$878$	−3.67310	−0.123961
$879$	56.3467	1.90053
$880$	24.3227	0.819920
$881$	6.19555	0.208733	0.104367	−	0.994539i	$-0.466718\pi$
$881$	6.19555	0.208733	0.104367	+	0.994539i	$0.466718\pi$
$882$	−2.58176	−0.0869324
$883$	16.9839	0.571554	0.285777	−	0.958296i	$-0.407748\pi$
$883$	16.9839	0.571554	0.285777	+	0.958296i	$0.407748\pi$
$884$	−42.3519	−1.42445
$885$	13.4772	0.453032
$886$	−2.63967	−0.0886816
$887$	−1.86877	−0.0627471	−0.0313735	−	0.999508i	$-0.509988\pi$
$887$	−1.86877	−0.0627471	−0.0313735	+	0.999508i	$0.509988\pi$
$888$	7.81593	0.262285
$889$	−1.87790	−0.0629828
$890$	0.220650	0.00739621
$891$	47.9026	1.60480
$892$	2.11118	0.0706876
$893$	16.7003	0.558853
$894$	1.59569	0.0533677
$895$	−8.20533	−0.274274
$896$	1.78846	0.0597484
$897$	0	0
$898$	−0.930994	−0.0310677
$899$	−30.0475	−1.00214
$900$	−6.71086	−0.223695
$901$	−44.3876	−1.47876
$902$	−2.14562	−0.0714414
$903$	6.69508	0.222798
$904$	−4.38414	−0.145814
$905$	−16.8443	−0.559925
$906$	−5.15724	−0.171338
$907$	−14.9750	−0.497236	−0.248618	−	0.968602i	$-0.579976\pi$
$907$	−14.9750	−0.497236	−0.248618	+	0.968602i	$0.579976\pi$
$908$	7.70545	0.255714
$909$	56.9727	1.88967
$910$	0.173409	0.00574845
$911$	6.38511	0.211548	0.105774	−	0.994390i	$-0.466268\pi$
$911$	6.38511	0.211548	0.105774	+	0.994390i	$0.466268\pi$
$912$	−35.0854	−1.16179
$913$	−21.9243	−0.725588
$914$	−3.10228	−0.102614
$915$	5.93379	0.196165
$916$	−16.6380	−0.549734
$917$	−0.762002	−0.0251635
$918$	0.753035	0.0248539
$919$	−59.7346	−1.97046	−0.985231	−	0.171231i	$-0.945226\pi$
$919$	−59.7346	−1.97046	−0.985231	+	0.171231i	$0.945226\pi$
$920$	0	0
$921$	−29.9205	−0.985914
$922$	−1.96274	−0.0646395
$923$	−20.9210	−0.688623
$924$	−15.5987	−0.513161
$925$	−6.85247	−0.225308
$926$	3.10008	0.101875
$927$	5.83352	0.191598
$928$	−11.2595	−0.369611
$929$	−17.1029	−0.561127	−0.280564	−	0.959835i	$-0.590521\pi$
$929$	−17.1029	−0.561127	−0.280564	+	0.959835i	$0.590521\pi$
$930$	−1.02890	−0.0337388
$931$	23.8997	0.783281
$932$	26.9662	0.883306
$933$	−76.9003	−2.51760
$934$	2.92959	0.0958592
$935$	43.2782	1.41535
$936$	−4.65705	−0.152220
$937$	−24.1459	−0.788813	−0.394407	−	0.918936i	$-0.629050\pi$
$937$	−24.1459	−0.788813	−0.394407	+	0.918936i	$0.629050\pi$
$938$	0.732790	0.0239264
$939$	33.6145	1.09697
$940$	−9.37088	−0.305644
$941$	33.0474	1.07732	0.538658	−	0.842525i	$-0.318932\pi$
$941$	33.0474	1.07732	0.538658	+	0.842525i	$0.318932\pi$
$942$	−3.11252	−0.101411
$943$	0	0
$944$	−20.9376	−0.681460
$945$	0.477455	0.0155316
$946$	3.71372	0.120744
$947$	48.3069	1.56976	0.784882	−	0.619645i	$-0.212724\pi$
$947$	48.3069	1.56976	0.784882	+	0.619645i	$0.212724\pi$
$948$	30.4979	0.990526
$949$	−10.0592	−0.326535
$950$	−0.401176	−0.0130159
$951$	−57.0047	−1.84850
$952$	1.58082	0.0512348
$953$	−16.2320	−0.525805	−0.262902	−	0.964822i	$-0.584680\pi$
$953$	−16.2320	−0.525805	−0.262902	+	0.964822i	$0.584680\pi$
$954$	−2.43259	−0.0787581
$955$	−13.9177	−0.450366
$956$	4.82283	0.155982
$957$	130.796	4.22802
$958$	−1.09286	−0.0353087
$959$	4.61803	0.149124
$960$	19.4287	0.627060
$961$	−18.0638	−0.582705
$962$	−2.37001	−0.0764122
$963$	42.0708	1.35571
$964$	−32.1136	−1.03431
$965$	−26.8599	−0.864650
$966$	0	0
$967$	−25.7729	−0.828799	−0.414400	−	0.910095i	$-0.636008\pi$
$967$	−25.7729	−0.828799	−0.414400	+	0.910095i	$0.636008\pi$
$968$	−12.3926	−0.398312
$969$	−62.4284	−2.00549
$970$	1.51825	0.0487481
$971$	−24.4811	−0.785636	−0.392818	−	0.919616i	$-0.628500\pi$
$971$	−24.4811	−0.785636	−0.392818	+	0.919616i	$0.628500\pi$
$972$	44.4500	1.42573
$973$	−7.62327	−0.244391
$974$	0.450215	0.0144258
$975$	7.71005	0.246919
$976$	−9.21845	−0.295075
$977$	−4.35357	−0.139283	−0.0696416	−	0.997572i	$-0.522186\pi$
$977$	−4.35357	−0.139283	−0.0696416	+	0.997572i	$0.522186\pi$
$978$	−5.50062	−0.175891
$979$	12.0760	0.385950
$980$	−13.4106	−0.428387
$981$	−7.98540	−0.254954
$982$	2.85881	0.0912281
$983$	57.7581	1.84220	0.921099	−	0.389328i	$-0.127293\pi$
$983$	57.7581	1.84220	0.921099	+	0.389328i	$0.127293\pi$
$984$	−3.48461	−0.111085
$985$	−22.8883	−0.729281
$986$	−6.60628	−0.210387
$987$	5.97071	0.190050
$988$	21.4861	0.683564
$989$	0	0
$990$	2.37179	0.0753805
$991$	−4.42302	−0.140502	−0.0702509	−	0.997529i	$-0.522380\pi$
$991$	−4.42302	−0.140502	−0.0702509	+	0.997529i	$0.522380\pi$
$992$	4.84748	0.153908
$993$	43.7522	1.38843
$994$	0.389190	0.0123444
$995$	−26.4627	−0.838923
$996$	−17.7458	−0.562298
$997$	−11.6089	−0.367657	−0.183829	−	0.982958i	$-0.558849\pi$
$997$	−11.6089	−0.367657	−0.183829	+	0.982958i	$0.558849\pi$
$998$	−1.59070	−0.0503526
$999$	−6.52546	−0.206457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2645.2.a.v.1.8	✓	16
23.22	odd	2		2645.2.a.w.1.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2645.2.a.v.1.8	✓	16	1.1	even	1	trivial
2645.2.a.w.1.8	yes	16	23.22	odd	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:	\( N \)	\(=\)	\( 2645 = 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2645.a (trivial)

\(f(q)\)	\(=\)	\(q+0.113281 q^{2} +2.52529 q^{3} -1.98717 q^{4} -1.00000 q^{5} +0.286068 q^{6} -0.501381 q^{7} -0.451671 q^{8} +3.37710 q^{9} +O(q^{10})\)	\(q+0.113281 q^{2} +2.52529 q^{3} -1.98717 q^{4} -1.00000 q^{5} +0.286068 q^{6} -0.501381 q^{7} -0.451671 q^{8} +3.37710 q^{9} -0.113281 q^{10} -6.19977 q^{11} -5.01818 q^{12} +3.05313 q^{13} -0.0567970 q^{14} -2.52529 q^{15} +3.92317 q^{16} +6.98061 q^{17} +0.382561 q^{18} -3.54142 q^{19} +1.98717 q^{20} -1.26613 q^{21} -0.702317 q^{22} -1.14060 q^{24} +1.00000 q^{25} +0.345862 q^{26} +0.952279 q^{27} +0.996329 q^{28} -8.35422 q^{29} -0.286068 q^{30} +3.59669 q^{31} +1.34776 q^{32} -15.6562 q^{33} +0.790771 q^{34} +0.501381 q^{35} -6.71086 q^{36} -6.85247 q^{37} -0.401176 q^{38} +7.71005 q^{39} +0.451671 q^{40} +3.05506 q^{41} -0.143429 q^{42} -5.28782 q^{43} +12.3200 q^{44} -3.37710 q^{45} -4.71570 q^{47} +9.90715 q^{48} -6.74862 q^{49} +0.113281 q^{50} +17.6281 q^{51} -6.06708 q^{52} -6.35870 q^{53} +0.107875 q^{54} +6.19977 q^{55} +0.226459 q^{56} -8.94312 q^{57} -0.946376 q^{58} -5.33690 q^{59} +5.01818 q^{60} -2.34975 q^{61} +0.407437 q^{62} -1.69321 q^{63} -7.69366 q^{64} -3.05313 q^{65} -1.77355 q^{66} -12.9019 q^{67} -13.8716 q^{68} +0.0567970 q^{70} -6.85230 q^{71} -1.52534 q^{72} -3.29471 q^{73} -0.776255 q^{74} +2.52529 q^{75} +7.03739 q^{76} +3.10845 q^{77} +0.873403 q^{78} -6.07749 q^{79} -3.92317 q^{80} -7.72651 q^{81} +0.346081 q^{82} +3.53631 q^{83} +2.51602 q^{84} -6.98061 q^{85} -0.599010 q^{86} -21.0968 q^{87} +2.80025 q^{88} -1.94781 q^{89} -0.382561 q^{90} -1.53078 q^{91} +9.08268 q^{93} -0.534200 q^{94} +3.54142 q^{95} +3.40349 q^{96} -13.4025 q^{97} -0.764491 q^{98} -20.9372 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 4 q^{3} + 20 q^{4} - 16 q^{5} - 12 q^{6} - 12 q^{7} + 8 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + 4 * q^3 + 20 * q^4 - 16 * q^5 - 12 * q^6 - 12 * q^7 + 8 * q^9	\( 16 q + 4 q^{2} + 4 q^{3} + 20 q^{4} - 16 q^{5} - 12 q^{6} - 12 q^{7} + 8 q^{9} - 4 q^{10} - 16 q^{11} - 4 q^{12} + 8 q^{13} - 8 q^{14} - 4 q^{15} + 28 q^{16} + 8 q^{17} + 4 q^{18} - 32 q^{19} - 20 q^{20} - 16 q^{21} - 44 q^{22} - 28 q^{24} + 16 q^{25} - 20 q^{26} - 8 q^{27} - 52 q^{28} - 12 q^{29} + 12 q^{30} - 12 q^{31} + 4 q^{32} - 20 q^{33} - 24 q^{34} + 12 q^{35} - 4 q^{36} - 28 q^{37} + 20 q^{38} - 8 q^{39} - 4 q^{41} + 8 q^{42} - 48 q^{43} - 32 q^{44} - 8 q^{45} + 48 q^{47} + 24 q^{48} + 12 q^{49} + 4 q^{50} - 24 q^{51} + 12 q^{52} + 4 q^{53} - 44 q^{54} + 16 q^{55} - 64 q^{56} - 52 q^{57} - 28 q^{58} - 40 q^{59} + 4 q^{60} - 16 q^{61} - 4 q^{63} - 16 q^{64} - 8 q^{65} - 8 q^{66} - 68 q^{67} + 4 q^{68} + 8 q^{70} - 24 q^{71} - 12 q^{72} + 52 q^{73} - 40 q^{74} + 4 q^{75} - 24 q^{76} + 44 q^{77} + 12 q^{78} - 72 q^{79} - 28 q^{80} + 20 q^{81} - 20 q^{82} - 12 q^{83} - 32 q^{84} - 8 q^{85} + 56 q^{86} - 104 q^{88} - 48 q^{89} - 4 q^{90} - 48 q^{91} - 48 q^{93} - 60 q^{94} + 32 q^{95} - 108 q^{96} - 4 q^{97} + 8 q^{98} - 24 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 4 * q^3 + 20 * q^4 - 16 * q^5 - 12 * q^6 - 12 * q^7 + 8 * q^9 - 4 * q^10 - 16 * q^11 - 4 * q^12 + 8 * q^13 - 8 * q^14 - 4 * q^15 + 28 * q^16 + 8 * q^17 + 4 * q^18 - 32 * q^19 - 20 * q^20 - 16 * q^21 - 44 * q^22 - 28 * q^24 + 16 * q^25 - 20 * q^26 - 8 * q^27 - 52 * q^28 - 12 * q^29 + 12 * q^30 - 12 * q^31 + 4 * q^32 - 20 * q^33 - 24 * q^34 + 12 * q^35 - 4 * q^36 - 28 * q^37 + 20 * q^38 - 8 * q^39 - 4 * q^41 + 8 * q^42 - 48 * q^43 - 32 * q^44 - 8 * q^45 + 48 * q^47 + 24 * q^48 + 12 * q^49 + 4 * q^50 - 24 * q^51 + 12 * q^52 + 4 * q^53 - 44 * q^54 + 16 * q^55 - 64 * q^56 - 52 * q^57 - 28 * q^58 - 40 * q^59 + 4 * q^60 - 16 * q^61 - 4 * q^63 - 16 * q^64 - 8 * q^65 - 8 * q^66 - 68 * q^67 + 4 * q^68 + 8 * q^70 - 24 * q^71 - 12 * q^72 + 52 * q^73 - 40 * q^74 + 4 * q^75 - 24 * q^76 + 44 * q^77 + 12 * q^78 - 72 * q^79 - 28 * q^80 + 20 * q^81 - 20 * q^82 - 12 * q^83 - 32 * q^84 - 8 * q^85 + 56 * q^86 - 104 * q^88 - 48 * q^89 - 4 * q^90 - 48 * q^91 - 48 * q^93 - 60 * q^94 + 32 * q^95 - 108 * q^96 - 4 * q^97 + 8 * q^98 - 24 * q^99

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