LMFDB - Embedded newform 1205.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(1,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, 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("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} + \cdots - 1 $ x^15 - 2x^14 - 16x^13 + 31x^12 + 99x^11 - 184x^10 - 296x^9 + 519x^8 + 437x^7 - 699x^6 - 297x^5 + 394x^4 + 89x^3 - 57x^2 - 17x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$1.96562$ of defining polynomial
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.96562 q^{2} -0.551502 q^{3} +1.86368 q^{4} -1.00000 q^{5} -1.08405 q^{6} +1.56703 q^{7} -0.267954 q^{8} -2.69585 q^{9} +O(q^{10})$	\(q+1.96562 q^{2} -0.551502 q^{3} +1.86368 q^{4} -1.00000 q^{5} -1.08405 q^{6} +1.56703 q^{7} -0.267954 q^{8} -2.69585 q^{9} -1.96562 q^{10} -3.99112 q^{11} -1.02782 q^{12} -2.71047 q^{13} +3.08019 q^{14} +0.551502 q^{15} -4.25406 q^{16} -7.60012 q^{17} -5.29902 q^{18} +0.708589 q^{19} -1.86368 q^{20} -0.864219 q^{21} -7.84504 q^{22} +8.61987 q^{23} +0.147777 q^{24} +1.00000 q^{25} -5.32776 q^{26} +3.14127 q^{27} +2.92044 q^{28} -5.83317 q^{29} +1.08405 q^{30} +7.20499 q^{31} -7.82597 q^{32} +2.20111 q^{33} -14.9390 q^{34} -1.56703 q^{35} -5.02419 q^{36} -11.5871 q^{37} +1.39282 q^{38} +1.49483 q^{39} +0.267954 q^{40} +9.24605 q^{41} -1.69873 q^{42} +0.217644 q^{43} -7.43816 q^{44} +2.69585 q^{45} +16.9434 q^{46} -2.29372 q^{47} +2.34612 q^{48} -4.54442 q^{49} +1.96562 q^{50} +4.19149 q^{51} -5.05145 q^{52} +13.2571 q^{53} +6.17456 q^{54} +3.99112 q^{55} -0.419892 q^{56} -0.390788 q^{57} -11.4658 q^{58} +1.31384 q^{59} +1.02782 q^{60} -13.1201 q^{61} +14.1623 q^{62} -4.22446 q^{63} -6.87481 q^{64} +2.71047 q^{65} +4.32656 q^{66} -2.79005 q^{67} -14.1642 q^{68} -4.75388 q^{69} -3.08019 q^{70} -3.67764 q^{71} +0.722363 q^{72} -8.82698 q^{73} -22.7759 q^{74} -0.551502 q^{75} +1.32058 q^{76} -6.25419 q^{77} +2.93827 q^{78} +7.53594 q^{79} +4.25406 q^{80} +6.35512 q^{81} +18.1743 q^{82} -5.42978 q^{83} -1.61063 q^{84} +7.60012 q^{85} +0.427806 q^{86} +3.21701 q^{87} +1.06944 q^{88} +13.1423 q^{89} +5.29902 q^{90} -4.24738 q^{91} +16.0647 q^{92} -3.97357 q^{93} -4.50859 q^{94} -0.708589 q^{95} +4.31604 q^{96} -13.0935 q^{97} -8.93263 q^{98} +10.7594 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 2 q^{2} - 7 q^{3} + 6 q^{4} - 15 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 15 * q + 2 * q^2 - 7 * q^3 + 6 * q^4 - 15 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 15 q + 2 q^{2} - 7 q^{3} + 6 q^{4} - 15 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 2 q^{10} - 10 q^{11} - 6 q^{12} - 8 q^{13} - 5 q^{14} + 7 q^{15} - 16 q^{16} - q^{17} - 3 q^{18} - 30 q^{19} - 6 q^{20} - 11 q^{21} - 5 q^{22} + 19 q^{23} - 14 q^{24} + 15 q^{25} - 18 q^{26} - 22 q^{27} - 20 q^{28} - 12 q^{29} + 5 q^{30} - 22 q^{31} - 2 q^{32} + 4 q^{33} - 29 q^{34} + 3 q^{35} - 7 q^{36} - 12 q^{37} - 18 q^{38} - 17 q^{39} - 3 q^{40} - 13 q^{41} - q^{42} - 25 q^{43} - 20 q^{44} - 6 q^{45} - 7 q^{46} + 16 q^{47} - 22 q^{48} - 24 q^{49} + 2 q^{50} - 27 q^{51} - 15 q^{52} - 4 q^{53} - 43 q^{54} + 10 q^{55} - 3 q^{56} + 22 q^{57} - 20 q^{58} - 50 q^{59} + 6 q^{60} - 41 q^{61} + 12 q^{62} + 6 q^{63} - 53 q^{64} + 8 q^{65} + 5 q^{66} - 43 q^{67} + 5 q^{68} - 50 q^{69} + 5 q^{70} - 14 q^{71} + 32 q^{72} - 10 q^{73} - 26 q^{74} - 7 q^{75} - 13 q^{76} - 7 q^{77} + 3 q^{78} - 44 q^{79} + 16 q^{80} + 7 q^{81} - 19 q^{82} + 7 q^{83} - 42 q^{84} + q^{85} + 7 q^{86} + 10 q^{87} - 28 q^{88} + 4 q^{89} + 3 q^{90} - 50 q^{91} + 25 q^{92} + 22 q^{93} - 14 q^{94} + 30 q^{95} + 14 q^{96} + 9 q^{97} + 2 q^{98} - 46 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 - 7 * q^3 + 6 * q^4 - 15 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 2 * q^10 - 10 * q^11 - 6 * q^12 - 8 * q^13 - 5 * q^14 + 7 * q^15 - 16 * q^16 - q^17 - 3 * q^18 - 30 * q^19 - 6 * q^20 - 11 * q^21 - 5 * q^22 + 19 * q^23 - 14 * q^24 + 15 * q^25 - 18 * q^26 - 22 * q^27 - 20 * q^28 - 12 * q^29 + 5 * q^30 - 22 * q^31 - 2 * q^32 + 4 * q^33 - 29 * q^34 + 3 * q^35 - 7 * q^36 - 12 * q^37 - 18 * q^38 - 17 * q^39 - 3 * q^40 - 13 * q^41 - q^42 - 25 * q^43 - 20 * q^44 - 6 * q^45 - 7 * q^46 + 16 * q^47 - 22 * q^48 - 24 * q^49 + 2 * q^50 - 27 * q^51 - 15 * q^52 - 4 * q^53 - 43 * q^54 + 10 * q^55 - 3 * q^56 + 22 * q^57 - 20 * q^58 - 50 * q^59 + 6 * q^60 - 41 * q^61 + 12 * q^62 + 6 * q^63 - 53 * q^64 + 8 * q^65 + 5 * q^66 - 43 * q^67 + 5 * q^68 - 50 * q^69 + 5 * q^70 - 14 * q^71 + 32 * q^72 - 10 * q^73 - 26 * q^74 - 7 * q^75 - 13 * q^76 - 7 * q^77 + 3 * q^78 - 44 * q^79 + 16 * q^80 + 7 * q^81 - 19 * q^82 + 7 * q^83 - 42 * q^84 + q^85 + 7 * q^86 + 10 * q^87 - 28 * q^88 + 4 * q^89 + 3 * q^90 - 50 * q^91 + 25 * q^92 + 22 * q^93 - 14 * q^94 + 30 * q^95 + 14 * q^96 + 9 * q^97 + 2 * q^98 - 46 * 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 $

$2$	1.96562	1.38991	0.694953	−	0.719055i	$-0.255425\pi$
$2$	1.96562	1.38991	0.694953	+	0.719055i	$0.255425\pi$
$3$	−0.551502	−0.318410	−0.159205	−	0.987246i	$-0.550893\pi$
$3$	−0.551502	−0.318410	−0.159205	+	0.987246i	$0.550893\pi$
$4$	1.86368	0.931840
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.08405	−0.442560
$7$	1.56703	0.592281	0.296140	−	0.955144i	$-0.404300\pi$
$7$	1.56703	0.592281	0.296140	+	0.955144i	$0.404300\pi$
$8$	−0.267954	−0.0947362
$9$	−2.69585	−0.898615
$10$	−1.96562	−0.621585
$11$	−3.99112	−1.20337	−0.601684	−	0.798735i	$-0.705503\pi$
$11$	−3.99112	−1.20337	−0.601684	+	0.798735i	$0.705503\pi$
$12$	−1.02782	−0.296707
$13$	−2.71047	−0.751749	−0.375874	−	0.926671i	$-0.622658\pi$
$13$	−2.71047	−0.751749	−0.375874	+	0.926671i	$0.622658\pi$
$14$	3.08019	0.823215
$15$	0.551502	0.142397
$16$	−4.25406	−1.06351
$17$	−7.60012	−1.84330	−0.921650	−	0.388021i	$-0.873159\pi$
$17$	−7.60012	−1.84330	−0.921650	+	0.388021i	$0.873159\pi$
$18$	−5.29902	−1.24899
$19$	0.708589	0.162561	0.0812807	−	0.996691i	$-0.474099\pi$
$19$	0.708589	0.162561	0.0812807	+	0.996691i	$0.474099\pi$
$20$	−1.86368	−0.416731
$21$	−0.864219	−0.188588
$22$	−7.84504	−1.67257
$23$	8.61987	1.79737	0.898684	−	0.438597i	$-0.144524\pi$
$23$	8.61987	1.79737	0.898684	+	0.438597i	$0.144524\pi$
$24$	0.147777	0.0301649
$25$	1.00000	0.200000
$26$	−5.32776	−1.04486
$27$	3.14127	0.604538
$28$	2.92044	0.551911
$29$	−5.83317	−1.08319	−0.541596	−	0.840639i	$-0.682180\pi$
$29$	−5.83317	−1.08319	−0.541596	+	0.840639i	$0.682180\pi$
$30$	1.08405	0.197919
$31$	7.20499	1.29405	0.647027	−	0.762467i	$-0.276012\pi$
$31$	7.20499	1.29405	0.647027	+	0.762467i	$0.276012\pi$
$32$	−7.82597	−1.38345
$33$	2.20111	0.383164
$34$	−14.9390	−2.56202
$35$	−1.56703	−0.264876
$36$	−5.02419	−0.837365
$37$	−11.5871	−1.90491	−0.952456	−	0.304677i	$-0.901452\pi$
$37$	−11.5871	−1.90491	−0.952456	+	0.304677i	$0.901452\pi$
$38$	1.39282	0.225945
$39$	1.49483	0.239364
$40$	0.267954	0.0423673
$41$	9.24605	1.44399	0.721995	−	0.691898i	$-0.243225\pi$
$41$	9.24605	1.44399	0.721995	+	0.691898i	$0.243225\pi$
$42$	−1.69873	−0.262120
$43$	0.217644	0.0331904	0.0165952	−	0.999862i	$-0.494717\pi$
$43$	0.217644	0.0331904	0.0165952	+	0.999862i	$0.494717\pi$
$44$	−7.43816	−1.12135
$45$	2.69585	0.401873
$46$	16.9434	2.49817
$47$	−2.29372	−0.334573	−0.167287	−	0.985908i	$-0.553501\pi$
$47$	−2.29372	−0.334573	−0.167287	+	0.985908i	$0.553501\pi$
$48$	2.34612	0.338634
$49$	−4.54442	−0.649204
$50$	1.96562	0.277981
$51$	4.19149	0.586925
$52$	−5.05145	−0.700510
$53$	13.2571	1.82101	0.910504	−	0.413500i	$-0.135694\pi$
$53$	13.2571	1.82101	0.910504	+	0.413500i	$0.135694\pi$
$54$	6.17456	0.840251
$55$	3.99112	0.538162
$56$	−0.419892	−0.0561104
$57$	−0.390788	−0.0517612
$58$	−11.4658	−1.50554
$59$	1.31384	0.171048	0.0855239	−	0.996336i	$-0.472744\pi$
$59$	1.31384	0.171048	0.0855239	+	0.996336i	$0.472744\pi$
$60$	1.02782	0.132691
$61$	−13.1201	−1.67985	−0.839927	−	0.542699i	$-0.817402\pi$
$61$	−13.1201	−1.67985	−0.839927	+	0.542699i	$0.817402\pi$
$62$	14.1623	1.79861
$63$	−4.22446	−0.532232
$64$	−6.87481	−0.859351
$65$	2.71047	0.336192
$66$	4.32656	0.532562
$67$	−2.79005	−0.340859	−0.170430	−	0.985370i	$-0.554516\pi$
$67$	−2.79005	−0.340859	−0.170430	+	0.985370i	$0.554516\pi$
$68$	−14.1642	−1.71766
$69$	−4.75388	−0.572300
$70$	−3.08019	−0.368153
$71$	−3.67764	−0.436456	−0.218228	−	0.975898i	$-0.570028\pi$
$71$	−3.67764	−0.436456	−0.218228	+	0.975898i	$0.570028\pi$
$72$	0.722363	0.0851313
$73$	−8.82698	−1.03312	−0.516560	−	0.856251i	$-0.672788\pi$
$73$	−8.82698	−1.03312	−0.516560	+	0.856251i	$0.672788\pi$
$74$	−22.7759	−2.64765
$75$	−0.551502	−0.0636820
$76$	1.32058	0.151481
$77$	−6.25419	−0.712731
$78$	2.93827	0.332694
$79$	7.53594	0.847859	0.423930	−	0.905695i	$-0.360650\pi$
$79$	7.53594	0.847859	0.423930	+	0.905695i	$0.360650\pi$
$80$	4.25406	0.475618
$81$	6.35512	0.706124
$82$	18.1743	2.00701
$83$	−5.42978	−0.595996	−0.297998	−	0.954566i	$-0.596319\pi$
$83$	−5.42978	−0.595996	−0.297998	+	0.954566i	$0.596319\pi$
$84$	−1.61063	−0.175734
$85$	7.60012	0.824349
$86$	0.427806	0.0461315
$87$	3.21701	0.344899
$88$	1.06944	0.114002
$89$	13.1423	1.39308	0.696539	−	0.717519i	$-0.254722\pi$
$89$	13.1423	1.39308	0.696539	+	0.717519i	$0.254722\pi$
$90$	5.29902	0.558566
$91$	−4.24738	−0.445246
$92$	16.0647	1.67486
$93$	−3.97357	−0.412040
$94$	−4.50859	−0.465026
$95$	−0.708589	−0.0726997
$96$	4.31604	0.440504
$97$	−13.0935	−1.32945	−0.664723	−	0.747090i	$-0.731451\pi$
$97$	−13.0935	−1.32945	−0.664723	+	0.747090i	$0.731451\pi$
$98$	−8.93263	−0.902332
$99$	10.7594	1.08136
$100$	1.86368	0.186368
$101$	−4.73983	−0.471631	−0.235815	−	0.971798i	$-0.575776\pi$
$101$	−4.73983	−0.471631	−0.235815	+	0.971798i	$0.575776\pi$
$102$	8.23889	0.815771
$103$	−5.08831	−0.501366	−0.250683	−	0.968069i	$-0.580655\pi$
$103$	−5.08831	−0.501366	−0.250683	+	0.968069i	$0.580655\pi$
$104$	0.726282	0.0712178
$105$	0.864219	0.0843391
$106$	26.0586	2.53103
$107$	−4.89049	−0.472781	−0.236391	−	0.971658i	$-0.575965\pi$
$107$	−4.89049	−0.472781	−0.236391	+	0.971658i	$0.575965\pi$
$108$	5.85432	0.563333
$109$	−14.1111	−1.35160	−0.675801	−	0.737084i	$-0.736202\pi$
$109$	−14.1111	−1.35160	−0.675801	+	0.737084i	$0.736202\pi$
$110$	7.84504	0.747995
$111$	6.39033	0.606543
$112$	−6.66622	−0.629899
$113$	15.0059	1.41164	0.705820	−	0.708391i	$-0.250579\pi$
$113$	15.0059	1.41164	0.705820	+	0.708391i	$0.250579\pi$
$114$	−0.768143	−0.0719432
$115$	−8.61987	−0.803807
$116$	−10.8712	−1.00936
$117$	7.30701	0.675533
$118$	2.58252	0.237741
$119$	−11.9096	−1.09175
$120$	−0.147777	−0.0134902
$121$	4.92902	0.448092
$122$	−25.7892	−2.33484
$123$	−5.09922	−0.459781
$124$	13.4278	1.20585
$125$	−1.00000	−0.0894427
$126$	−8.30371	−0.739753
$127$	6.37046	0.565287	0.282644	−	0.959225i	$-0.408789\pi$
$127$	6.37046	0.565287	0.282644	+	0.959225i	$0.408789\pi$
$128$	2.13866	0.189032
$129$	−0.120031	−0.0105681
$130$	5.32776	0.467276
$131$	15.5677	1.36015	0.680076	−	0.733142i	$-0.261947\pi$
$131$	15.5677	1.36015	0.680076	+	0.733142i	$0.261947\pi$
$132$	4.10216	0.357048
$133$	1.11038	0.0962820
$134$	−5.48420	−0.473763
$135$	−3.14127	−0.270358
$136$	2.03649	0.174627
$137$	2.80386	0.239550	0.119775	−	0.992801i	$-0.461783\pi$
$137$	2.80386	0.239550	0.119775	+	0.992801i	$0.461783\pi$
$138$	−9.34434	−0.795443
$139$	−14.7772	−1.25339	−0.626694	−	0.779266i	$-0.715592\pi$
$139$	−14.7772	−1.25339	−0.626694	+	0.779266i	$0.715592\pi$
$140$	−2.92044	−0.246822
$141$	1.26499	0.106532
$142$	−7.22887	−0.606633
$143$	10.8178	0.904630
$144$	11.4683	0.955690
$145$	5.83317	0.484419
$146$	−17.3505	−1.43594
$147$	2.50626	0.206713
$148$	−21.5947	−1.77507
$149$	8.79693	0.720672	0.360336	−	0.932823i	$-0.382662\pi$
$149$	8.79693	0.720672	0.360336	+	0.932823i	$0.382662\pi$
$150$	−1.08405	−0.0885120
$151$	−16.9267	−1.37748	−0.688739	−	0.725010i	$-0.741835\pi$
$151$	−16.9267	−1.37748	−0.688739	+	0.725010i	$0.741835\pi$
$152$	−0.189869	−0.0154004
$153$	20.4888	1.65642
$154$	−12.2934	−0.990630
$155$	−7.20499	−0.578718
$156$	2.78588	0.223049
$157$	−1.17357	−0.0936615	−0.0468307	−	0.998903i	$-0.514912\pi$
$157$	−1.17357	−0.0936615	−0.0468307	+	0.998903i	$0.514912\pi$
$158$	14.8128	1.17844
$159$	−7.31134	−0.579827
$160$	7.82597	0.618697
$161$	13.5076	1.06455
$162$	12.4918	0.981447
$163$	7.37084	0.577328	0.288664	−	0.957430i	$-0.406789\pi$
$163$	7.37084	0.577328	0.288664	+	0.957430i	$0.406789\pi$
$164$	17.2317	1.34557
$165$	−2.20111	−0.171356
$166$	−10.6729	−0.828379
$167$	15.7056	1.21534	0.607669	−	0.794191i	$-0.292105\pi$
$167$	15.7056	1.21534	0.607669	+	0.794191i	$0.292105\pi$
$168$	0.231571	0.0178661
$169$	−5.65336	−0.434874
$170$	14.9390	1.14577
$171$	−1.91025	−0.146080
$172$	0.405618	0.0309281
$173$	−8.83998	−0.672091	−0.336046	−	0.941846i	$-0.609090\pi$
$173$	−8.83998	−0.672091	−0.336046	+	0.941846i	$0.609090\pi$
$174$	6.32343	0.479378
$175$	1.56703	0.118456
$176$	16.9784	1.27980
$177$	−0.724588	−0.0544633
$178$	25.8328	1.93625
$179$	6.07612	0.454151	0.227075	−	0.973877i	$-0.427084\pi$
$179$	6.07612	0.454151	0.227075	+	0.973877i	$0.427084\pi$
$180$	5.02419	0.374481
$181$	5.98011	0.444498	0.222249	−	0.974990i	$-0.428660\pi$
$181$	5.98011	0.444498	0.222249	+	0.974990i	$0.428660\pi$
$182$	−8.34875	−0.618851
$183$	7.23575	0.534882
$184$	−2.30973	−0.170276
$185$	11.5871	0.851902
$186$	−7.81054	−0.572696
$187$	30.3330	2.21817
$188$	−4.27476	−0.311769
$189$	4.92246	0.358056
$190$	−1.39282	−0.101046
$191$	−8.04857	−0.582374	−0.291187	−	0.956666i	$-0.594050\pi$
$191$	−8.04857	−0.582374	−0.291187	+	0.956666i	$0.594050\pi$
$192$	3.79147	0.273626
$193$	5.00147	0.360014	0.180007	−	0.983665i	$-0.442388\pi$
$193$	5.00147	0.360014	0.180007	+	0.983665i	$0.442388\pi$
$194$	−25.7370	−1.84781
$195$	−1.49483	−0.107047
$196$	−8.46935	−0.604954
$197$	11.3742	0.810376	0.405188	−	0.914233i	$-0.367206\pi$
$197$	11.3742	0.810376	0.405188	+	0.914233i	$0.367206\pi$
$198$	21.1490	1.50299
$199$	−21.8929	−1.55195	−0.775973	−	0.630767i	$-0.782741\pi$
$199$	−21.8929	−1.55195	−0.775973	+	0.630767i	$0.782741\pi$
$200$	−0.267954	−0.0189472
$201$	1.53872	0.108533
$202$	−9.31673	−0.655523
$203$	−9.14074	−0.641554
$204$	7.81159	0.546920
$205$	−9.24605	−0.645772
$206$	−10.0017	−0.696852
$207$	−23.2378	−1.61514
$208$	11.5305	0.799496
$209$	−2.82806	−0.195621
$210$	1.69873	0.117224
$211$	−11.2687	−0.775770	−0.387885	−	0.921708i	$-0.626794\pi$
$211$	−11.2687	−0.775770	−0.387885	+	0.921708i	$0.626794\pi$
$212$	24.7071	1.69689
$213$	2.02823	0.138972
$214$	−9.61286	−0.657122
$215$	−0.217644	−0.0148432
$216$	−0.841717	−0.0572716
$217$	11.2904	0.766443
$218$	−27.7372	−1.87860
$219$	4.86810	0.328956
$220$	7.43816	0.501481
$221$	20.5999	1.38570
$222$	12.5610	0.843038
$223$	1.74920	0.117135	0.0585674	−	0.998283i	$-0.481347\pi$
$223$	1.74920	0.117135	0.0585674	+	0.998283i	$0.481347\pi$
$224$	−12.2635	−0.819390
$225$	−2.69585	−0.179723
$226$	29.4960	1.96205
$227$	4.95808	0.329079	0.164540	−	0.986370i	$-0.447386\pi$
$227$	4.95808	0.329079	0.164540	+	0.986370i	$0.447386\pi$
$228$	−0.728304	−0.0482331
$229$	12.7250	0.840890	0.420445	−	0.907318i	$-0.361874\pi$
$229$	12.7250	0.840890	0.420445	+	0.907318i	$0.361874\pi$
$230$	−16.9434	−1.11722
$231$	3.44920	0.226941
$232$	1.56302	0.102618
$233$	16.6923	1.09355	0.546773	−	0.837281i	$-0.315856\pi$
$233$	16.6923	1.09355	0.546773	+	0.837281i	$0.315856\pi$
$234$	14.3628	0.938928
$235$	2.29372	0.149626
$236$	2.44858	0.159389
$237$	−4.15609	−0.269967
$238$	−23.4098	−1.51743
$239$	−16.8047	−1.08701	−0.543504	−	0.839407i	$-0.682903\pi$
$239$	−16.8047	−1.08701	−0.543504	+	0.839407i	$0.682903\pi$
$240$	−2.34612	−0.151442
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	9.68860	0.622807
$243$	−12.9287	−0.829375
$244$	−24.4516	−1.56536
$245$	4.54442	0.290333
$246$	−10.0231	−0.639053
$247$	−1.92061	−0.122205
$248$	−1.93061	−0.122594
$249$	2.99454	0.189771
$250$	−1.96562	−0.124317
$251$	−17.2016	−1.08576	−0.542879	−	0.839811i	$-0.682666\pi$
$251$	−17.2016	−1.08576	−0.542879	+	0.839811i	$0.682666\pi$
$252$	−7.87305	−0.495955
$253$	−34.4029	−2.16289
$254$	12.5219	0.785696
$255$	−4.19149	−0.262481
$256$	17.9534	1.12209
$257$	−20.4849	−1.27781	−0.638905	−	0.769285i	$-0.720612\pi$
$257$	−20.4849	−1.27781	−0.638905	+	0.769285i	$0.720612\pi$
$258$	−0.235936	−0.0146887
$259$	−18.1573	−1.12824
$260$	5.05145	0.313277
$261$	15.7253	0.973373
$262$	30.6002	1.89048
$263$	27.6830	1.70701	0.853503	−	0.521088i	$-0.174474\pi$
$263$	27.6830	1.70701	0.853503	+	0.521088i	$0.174474\pi$
$264$	−0.589797	−0.0362995
$265$	−13.2571	−0.814379
$266$	2.18259	0.133823
$267$	−7.24799	−0.443570
$268$	−5.19977	−0.317626
$269$	−2.83160	−0.172646	−0.0863228	−	0.996267i	$-0.527512\pi$
$269$	−2.83160	−0.172646	−0.0863228	+	0.996267i	$0.527512\pi$
$270$	−6.17456	−0.375772
$271$	11.6911	0.710181	0.355090	−	0.934832i	$-0.384450\pi$
$271$	11.6911	0.710181	0.355090	+	0.934832i	$0.384450\pi$
$272$	32.3314	1.96038
$273$	2.34244	0.141771
$274$	5.51135	0.332953
$275$	−3.99112	−0.240673
$276$	−8.85971	−0.533292
$277$	−12.8089	−0.769610	−0.384805	−	0.922998i	$-0.625731\pi$
$277$	−12.8089	−0.769610	−0.384805	+	0.922998i	$0.625731\pi$
$278$	−29.0465	−1.74209
$279$	−19.4235	−1.16286
$280$	0.419892	0.0250933
$281$	−12.7989	−0.763518	−0.381759	−	0.924262i	$-0.624681\pi$
$281$	−12.7989	−0.763518	−0.381759	+	0.924262i	$0.624681\pi$
$282$	2.48650	0.148069
$283$	−13.7630	−0.818127	−0.409064	−	0.912506i	$-0.634145\pi$
$283$	−13.7630	−0.818127	−0.409064	+	0.912506i	$0.634145\pi$
$284$	−6.85395	−0.406707
$285$	0.390788	0.0231483
$286$	21.2637	1.25735
$287$	14.4888	0.855248
$288$	21.0976	1.24319
$289$	40.7619	2.39776
$290$	11.4658	0.673296
$291$	7.22111	0.423309
$292$	−16.4507	−0.962702
$293$	−16.5394	−0.966241	−0.483121	−	0.875554i	$-0.660497\pi$
$293$	−16.5394	−0.966241	−0.483121	+	0.875554i	$0.660497\pi$
$294$	4.92637	0.287312
$295$	−1.31384	−0.0764949
$296$	3.10482	0.180464
$297$	−12.5372	−0.727481
$298$	17.2915	1.00167
$299$	−23.3639	−1.35117
$300$	−1.02782	−0.0593414
$301$	0.341054	0.0196580
$302$	−33.2716	−1.91456
$303$	2.61403	0.150172
$304$	−3.01438	−0.172886
$305$	13.1201	0.751254
$306$	40.2732	2.30227
$307$	−11.5276	−0.657914	−0.328957	−	0.944345i	$-0.606697\pi$
$307$	−11.5276	−0.657914	−0.328957	+	0.944345i	$0.606697\pi$
$308$	−11.6558	−0.664151
$309$	2.80621	0.159640
$310$	−14.1623	−0.804364
$311$	−31.2894	−1.77426	−0.887131	−	0.461519i	$-0.847305\pi$
$311$	−31.2894	−1.77426	−0.887131	+	0.461519i	$0.847305\pi$
$312$	−0.400546	−0.0226765
$313$	−12.4308	−0.702629	−0.351314	−	0.936258i	$-0.614265\pi$
$313$	−12.4308	−0.702629	−0.351314	+	0.936258i	$0.614265\pi$
$314$	−2.30681	−0.130181
$315$	4.22446	0.238022
$316$	14.0446	0.790069
$317$	−24.6631	−1.38522	−0.692609	−	0.721313i	$-0.743539\pi$
$317$	−24.6631	−1.38522	−0.692609	+	0.721313i	$0.743539\pi$
$318$	−14.3713	−0.805905
$319$	23.2809	1.30348
$320$	6.87481	0.384313
$321$	2.69711	0.150538
$322$	26.5508	1.47962
$323$	−5.38536	−0.299650
$324$	11.8439	0.657995
$325$	−2.71047	−0.150350
$326$	14.4883	0.802432
$327$	7.78232	0.430363
$328$	−2.47752	−0.136798
$329$	−3.59432	−0.198161
$330$	−4.32656	−0.238169
$331$	34.0217	1.87000	0.935000	−	0.354648i	$-0.115399\pi$
$331$	34.0217	1.87000	0.935000	+	0.354648i	$0.115399\pi$
$332$	−10.1194	−0.555373
$333$	31.2371	1.71178
$334$	30.8713	1.68920
$335$	2.79005	0.152437
$336$	3.67644	0.200566
$337$	−1.52041	−0.0828222	−0.0414111	−	0.999142i	$-0.513185\pi$
$337$	−1.52041	−0.0828222	−0.0414111	+	0.999142i	$0.513185\pi$
$338$	−11.1124	−0.604434
$339$	−8.27581	−0.449480
$340$	14.1642	0.768162
$341$	−28.7559	−1.55722
$342$	−3.75483	−0.203038
$343$	−18.0904	−0.976791
$344$	−0.0583186	−0.00314433
$345$	4.75388	0.255940
$346$	−17.3761	−0.934144
$347$	27.9625	1.50111	0.750553	−	0.660810i	$-0.229787\pi$
$347$	27.9625	1.50111	0.750553	+	0.660810i	$0.229787\pi$
$348$	5.99547	0.321391
$349$	−5.47515	−0.293078	−0.146539	−	0.989205i	$-0.546813\pi$
$349$	−5.47515	−0.293078	−0.146539	+	0.989205i	$0.546813\pi$
$350$	3.08019	0.164643
$351$	−8.51432	−0.454461
$352$	31.2344	1.66480
$353$	15.0275	0.799834	0.399917	−	0.916551i	$-0.369039\pi$
$353$	15.0275	0.799834	0.399917	+	0.916551i	$0.369039\pi$
$354$	−1.42427	−0.0756990
$355$	3.67764	0.195189
$356$	24.4930	1.29812
$357$	6.56817	0.347625
$358$	11.9434	0.631227
$359$	−3.29197	−0.173743	−0.0868717	−	0.996220i	$-0.527687\pi$
$359$	−3.29197	−0.173743	−0.0868717	+	0.996220i	$0.527687\pi$
$360$	−0.722363	−0.0380719
$361$	−18.4979	−0.973574
$362$	11.7547	0.617811
$363$	−2.71836	−0.142677
$364$	−7.91576	−0.414898
$365$	8.82698	0.462025
$366$	14.2228	0.743436
$367$	1.25892	0.0657149	0.0328574	−	0.999460i	$-0.489539\pi$
$367$	1.25892	0.0657149	0.0328574	+	0.999460i	$0.489539\pi$
$368$	−36.6694	−1.91153
$369$	−24.9259	−1.29759
$370$	22.7759	1.18406
$371$	20.7743	1.07855
$372$	−7.40545	−0.383955
$373$	−11.0430	−0.571785	−0.285893	−	0.958262i	$-0.592290\pi$
$373$	−11.0430	−0.571785	−0.285893	+	0.958262i	$0.592290\pi$
$374$	59.6233	3.08305
$375$	0.551502	0.0284794
$376$	0.614612	0.0316962
$377$	15.8106	0.814289
$378$	9.67570	0.497665
$379$	13.9623	0.717193	0.358597	−	0.933493i	$-0.383255\pi$
$379$	13.9623	0.717193	0.358597	+	0.933493i	$0.383255\pi$
$380$	−1.32058	−0.0677445
$381$	−3.51332	−0.179993
$382$	−15.8205	−0.809445
$383$	−29.4806	−1.50639	−0.753195	−	0.657798i	$-0.771488\pi$
$383$	−29.4806	−1.50639	−0.753195	+	0.657798i	$0.771488\pi$
$384$	−1.17947	−0.0601897
$385$	6.25419	0.318743
$386$	9.83101	0.500385
$387$	−0.586734	−0.0298254
$388$	−24.4021	−1.23883
$389$	−34.1786	−1.73292	−0.866462	−	0.499243i	$-0.833611\pi$
$389$	−34.1786	−1.73292	−0.866462	+	0.499243i	$0.833611\pi$
$390$	−2.93827	−0.148785
$391$	−65.5121	−3.31309
$392$	1.21770	0.0615031
$393$	−8.58559	−0.433086
$394$	22.3573	1.12635
$395$	−7.53594	−0.379174
$396$	20.0521	1.00766
$397$	2.87635	0.144360	0.0721799	−	0.997392i	$-0.477004\pi$
$397$	2.87635	0.144360	0.0721799	+	0.997392i	$0.477004\pi$
$398$	−43.0332	−2.15706
$399$	−0.612376	−0.0306571
$400$	−4.25406	−0.212703
$401$	2.45963	0.122828	0.0614140	−	0.998112i	$-0.480439\pi$
$401$	2.45963	0.122828	0.0614140	+	0.998112i	$0.480439\pi$
$402$	3.02455	0.150851
$403$	−19.5289	−0.972803
$404$	−8.83353	−0.439484
$405$	−6.35512	−0.315788
$406$	−17.9673	−0.891700
$407$	46.2456	2.29231
$408$	−1.12313	−0.0556031
$409$	15.0357	0.743469	0.371734	−	0.928339i	$-0.378763\pi$
$409$	15.0357	0.743469	0.371734	+	0.928339i	$0.378763\pi$
$410$	−18.1743	−0.897563
$411$	−1.54634	−0.0762752
$412$	−9.48298	−0.467193
$413$	2.05883	0.101308
$414$	−45.6769	−2.24490
$415$	5.42978	0.266538
$416$	21.2121	1.04001
$417$	8.14967	0.399091
$418$	−5.55891	−0.271895
$419$	−20.7860	−1.01546	−0.507732	−	0.861515i	$-0.669516\pi$
$419$	−20.7860	−1.01546	−0.507732	+	0.861515i	$0.669516\pi$
$420$	1.61063	0.0785906
$421$	−26.9568	−1.31380	−0.656898	−	0.753980i	$-0.728132\pi$
$421$	−26.9568	−1.31380	−0.656898	+	0.753980i	$0.728132\pi$
$422$	−22.1501	−1.07825
$423$	6.18351	0.300653
$424$	−3.55231	−0.172515
$425$	−7.60012	−0.368660
$426$	3.98673	0.193158
$427$	−20.5595	−0.994945
$428$	−9.11430	−0.440557
$429$	−5.96604	−0.288043
$430$	−0.427806	−0.0206306
$431$	−19.5871	−0.943475	−0.471738	−	0.881739i	$-0.656373\pi$
$431$	−19.5871	−0.943475	−0.471738	+	0.881739i	$0.656373\pi$
$432$	−13.3631	−0.642935
$433$	−15.5844	−0.748940	−0.374470	−	0.927239i	$-0.622175\pi$
$433$	−15.5844	−0.748940	−0.374470	+	0.927239i	$0.622175\pi$
$434$	22.1927	1.06528
$435$	−3.21701	−0.154244
$436$	−26.2986	−1.25948
$437$	6.10795	0.292183
$438$	9.56885	0.457218
$439$	−10.7485	−0.512997	−0.256498	−	0.966545i	$-0.582569\pi$
$439$	−10.7485	−0.512997	−0.256498	+	0.966545i	$0.582569\pi$
$440$	−1.06944	−0.0509834
$441$	12.2511	0.583384
$442$	40.4917	1.92599
$443$	9.12309	0.433451	0.216726	−	0.976233i	$-0.430462\pi$
$443$	9.12309	0.433451	0.216726	+	0.976233i	$0.430462\pi$
$444$	11.9095	0.565201
$445$	−13.1423	−0.623003
$446$	3.43826	0.162806
$447$	−4.85152	−0.229469
$448$	−10.7730	−0.508977
$449$	−27.1275	−1.28023	−0.640113	−	0.768280i	$-0.721113\pi$
$449$	−27.1275	−1.28023	−0.640113	+	0.768280i	$0.721113\pi$
$450$	−5.29902	−0.249798
$451$	−36.9021	−1.73765
$452$	27.9663	1.31542
$453$	9.33513	0.438602
$454$	9.74571	0.457389
$455$	4.24738	0.199120
$456$	0.104713	0.00490366
$457$	22.9878	1.07533	0.537663	−	0.843160i	$-0.319307\pi$
$457$	22.9878	1.07533	0.537663	+	0.843160i	$0.319307\pi$
$458$	25.0125	1.16876
$459$	−23.8741	−1.11435
$460$	−16.0647	−0.749020
$461$	11.7356	0.546582	0.273291	−	0.961931i	$-0.411888\pi$
$461$	11.7356	0.546582	0.273291	+	0.961931i	$0.411888\pi$
$462$	6.77983	0.315426
$463$	32.0892	1.49131	0.745656	−	0.666331i	$-0.232136\pi$
$463$	32.0892	1.49131	0.745656	+	0.666331i	$0.232136\pi$
$464$	24.8146	1.15199
$465$	3.97357	0.184270
$466$	32.8107	1.51993
$467$	−9.59495	−0.444001	−0.222001	−	0.975047i	$-0.571259\pi$
$467$	−9.59495	−0.444001	−0.222001	+	0.975047i	$0.571259\pi$
$468$	13.6179	0.629489
$469$	−4.37209	−0.201884
$470$	4.50859	0.207966
$471$	0.647229	0.0298227
$472$	−0.352050	−0.0162044
$473$	−0.868642	−0.0399402
$474$	−8.16930	−0.375229
$475$	0.708589	0.0325123
$476$	−22.1957	−1.01734
$477$	−35.7392	−1.63639
$478$	−33.0318	−1.51084
$479$	−15.2874	−0.698500	−0.349250	−	0.937030i	$-0.613564\pi$
$479$	−15.2874	−0.698500	−0.349250	+	0.937030i	$0.613564\pi$
$480$	−4.31604	−0.196999
$481$	31.4065	1.43202
$482$	−1.96562	−0.0895317
$483$	−7.44946	−0.338962
$484$	9.18611	0.417550
$485$	13.0935	0.594547
$486$	−25.4129	−1.15275
$487$	9.59709	0.434886	0.217443	−	0.976073i	$-0.430228\pi$
$487$	9.59709	0.434886	0.217443	+	0.976073i	$0.430228\pi$
$488$	3.51558	0.159143
$489$	−4.06503	−0.183827
$490$	8.93263	0.403535
$491$	31.8169	1.43588	0.717938	−	0.696107i	$-0.245086\pi$
$491$	31.8169	1.43588	0.717938	+	0.696107i	$0.245086\pi$
$492$	−9.50331	−0.428442
$493$	44.3328	1.99665
$494$	−3.77520	−0.169854
$495$	−10.7594	−0.483601
$496$	−30.6504	−1.37624
$497$	−5.76297	−0.258504
$498$	5.88614	0.263764
$499$	8.33168	0.372977	0.186489	−	0.982457i	$-0.440289\pi$
$499$	8.33168	0.372977	0.186489	+	0.982457i	$0.440289\pi$
$500$	−1.86368	−0.0833463
$501$	−8.66168	−0.386975
$502$	−33.8119	−1.50910
$503$	43.1306	1.92310	0.961550	−	0.274630i	$-0.0885555\pi$
$503$	43.1306	1.92310	0.961550	+	0.274630i	$0.0885555\pi$
$504$	1.13196	0.0504217
$505$	4.73983	0.210920
$506$	−67.6232	−3.00622
$507$	3.11784	0.138468
$508$	11.8725	0.526757
$509$	−15.3672	−0.681140	−0.340570	−	0.940219i	$-0.610620\pi$
$509$	−15.3672	−0.681140	−0.340570	+	0.940219i	$0.610620\pi$
$510$	−8.23889	−0.364824
$511$	−13.8321	−0.611897
$512$	31.0123	1.37056
$513$	2.22587	0.0982746
$514$	−40.2656	−1.77604
$515$	5.08831	0.224218
$516$	−0.223699	−0.00984782
$517$	9.15451	0.402615
$518$	−35.6905	−1.56815
$519$	4.87527	0.214001
$520$	−0.726282	−0.0318496
$521$	−25.4224	−1.11378	−0.556888	−	0.830588i	$-0.688005\pi$
$521$	−25.4224	−1.11378	−0.556888	+	0.830588i	$0.688005\pi$
$522$	30.9101	1.35290
$523$	41.1572	1.79968	0.899838	−	0.436223i	$-0.143684\pi$
$523$	41.1572	1.79968	0.899838	+	0.436223i	$0.143684\pi$
$524$	29.0131	1.26744
$525$	−0.864219	−0.0377176
$526$	54.4144	2.37258
$527$	−54.7588	−2.38533
$528$	−9.36365	−0.407500
$529$	51.3022	2.23053
$530$	−26.0586	−1.13191
$531$	−3.54192	−0.153706
$532$	2.06939	0.0897194
$533$	−25.0611	−1.08552
$534$	−14.2468	−0.616520
$535$	4.89049	0.211434
$536$	0.747607	0.0322917
$537$	−3.35100	−0.144606
$538$	−5.56586	−0.239961
$539$	18.1373	0.781230
$540$	−5.85432	−0.251930
$541$	0.834623	0.0358833	0.0179416	−	0.999839i	$-0.494289\pi$
$541$	0.834623	0.0358833	0.0179416	+	0.999839i	$0.494289\pi$
$542$	22.9802	0.987085
$543$	−3.29805	−0.141533
$544$	59.4784	2.55011
$545$	14.1111	0.604455
$546$	4.60436	0.197048
$547$	22.2646	0.951964	0.475982	−	0.879455i	$-0.342093\pi$
$547$	22.2646	0.951964	0.475982	+	0.879455i	$0.342093\pi$
$548$	5.22551	0.223223
$549$	35.3697	1.50954
$550$	−7.84504	−0.334514
$551$	−4.13332	−0.176085
$552$	1.27382	0.0542175
$553$	11.8090	0.502171
$554$	−25.1774	−1.06969
$555$	−6.39033	−0.271254
$556$	−27.5400	−1.16796
$557$	18.7626	0.794996	0.397498	−	0.917603i	$-0.369879\pi$
$557$	18.7626	0.794996	0.397498	+	0.917603i	$0.369879\pi$
$558$	−38.1794	−1.61626
$559$	−0.589917	−0.0249508
$560$	6.66622	0.281699
$561$	−16.7287	−0.706287
$562$	−25.1578	−1.06122
$563$	−2.67002	−0.112528	−0.0562640	−	0.998416i	$-0.517919\pi$
$563$	−2.67002	−0.112528	−0.0562640	+	0.998416i	$0.517919\pi$
$564$	2.35754	0.0992703
$565$	−15.0059	−0.631304
$566$	−27.0529	−1.13712
$567$	9.95864	0.418224
$568$	0.985440	0.0413482
$569$	−25.6604	−1.07574	−0.537869	−	0.843028i	$-0.680771\pi$
$569$	−25.6604	−1.07574	−0.537869	+	0.843028i	$0.680771\pi$
$570$	0.768143	0.0321740
$571$	17.4339	0.729585	0.364792	−	0.931089i	$-0.381140\pi$
$571$	17.4339	0.729585	0.364792	+	0.931089i	$0.381140\pi$
$572$	20.1609	0.842970
$573$	4.43880	0.185434
$574$	28.4796	1.18871
$575$	8.61987	0.359474
$576$	18.5334	0.772225
$577$	−24.5091	−1.02033	−0.510163	−	0.860078i	$-0.670415\pi$
$577$	−24.5091	−1.02033	−0.510163	+	0.860078i	$0.670415\pi$
$578$	80.1226	3.33266
$579$	−2.75832	−0.114632
$580$	10.8712	0.451400
$581$	−8.50862	−0.352997
$582$	14.1940	0.588360
$583$	−52.9108	−2.19134
$584$	2.36523	0.0978738
$585$	−7.30701	−0.302108
$586$	−32.5102	−1.34299
$587$	−2.12931	−0.0878860	−0.0439430	−	0.999034i	$-0.513992\pi$
$587$	−2.12931	−0.0878860	−0.0439430	+	0.999034i	$0.513992\pi$
$588$	4.67087	0.192623
$589$	5.10537	0.210363
$590$	−2.58252	−0.106321
$591$	−6.27288	−0.258032
$592$	49.2923	2.02590
$593$	21.6722	0.889971	0.444986	−	0.895538i	$-0.353209\pi$
$593$	21.6722	0.889971	0.444986	+	0.895538i	$0.353209\pi$
$594$	−24.6434	−1.01113
$595$	11.9096	0.488246
$596$	16.3947	0.671551
$597$	12.0740	0.494155
$598$	−45.9247	−1.87800
$599$	−36.9513	−1.50979	−0.754895	−	0.655846i	$-0.772312\pi$
$599$	−36.9513	−1.50979	−0.754895	+	0.655846i	$0.772312\pi$
$600$	0.147777	0.00603299
$601$	20.9295	0.853731	0.426866	−	0.904315i	$-0.359618\pi$
$601$	20.9295	0.853731	0.426866	+	0.904315i	$0.359618\pi$
$602$	0.670384	0.0273228
$603$	7.52155	0.306301
$604$	−31.5460	−1.28359
$605$	−4.92902	−0.200393
$606$	5.13820	0.208725
$607$	34.6528	1.40652	0.703258	−	0.710935i	$-0.251728\pi$
$607$	34.6528	1.40652	0.703258	+	0.710935i	$0.251728\pi$
$608$	−5.54540	−0.224896
$609$	5.04114	0.204277
$610$	25.7892	1.04417
$611$	6.21706	0.251515
$612$	38.1845	1.54352
$613$	11.7398	0.474166	0.237083	−	0.971489i	$-0.423809\pi$
$613$	11.7398	0.474166	0.237083	+	0.971489i	$0.423809\pi$
$614$	−22.6589	−0.914439
$615$	5.09922	0.205620
$616$	1.67584	0.0675214
$617$	−5.06089	−0.203744	−0.101872	−	0.994798i	$-0.532483\pi$
$617$	−5.06089	−0.203744	−0.101872	+	0.994798i	$0.532483\pi$
$618$	5.51596	0.221884
$619$	−28.6627	−1.15205	−0.576025	−	0.817432i	$-0.695397\pi$
$619$	−28.6627	−1.15205	−0.576025	+	0.817432i	$0.695397\pi$
$620$	−13.4278	−0.539273
$621$	27.0774	1.08658
$622$	−61.5033	−2.46606
$623$	20.5943	0.825093
$624$	−6.35909	−0.254567
$625$	1.00000	0.0400000
$626$	−24.4342	−0.976588
$627$	1.55968	0.0622877
$628$	−2.18717	−0.0872775
$629$	88.0636	3.51133
$630$	8.30371	0.330828
$631$	−22.6225	−0.900586	−0.450293	−	0.892881i	$-0.648681\pi$
$631$	−22.6225	−0.900586	−0.450293	+	0.892881i	$0.648681\pi$
$632$	−2.01929	−0.0803229
$633$	6.21472	0.247013
$634$	−48.4784	−1.92532
$635$	−6.37046	−0.252804
$636$	−13.6260	−0.540306
$637$	12.3175	0.488038
$638$	45.7615	1.81171
$639$	9.91436	0.392206
$640$	−2.13866	−0.0845378
$641$	−24.3789	−0.962909	−0.481454	−	0.876471i	$-0.659891\pi$
$641$	−24.3789	−0.962909	−0.481454	+	0.876471i	$0.659891\pi$
$642$	5.30152	0.209234
$643$	−31.9931	−1.26168	−0.630842	−	0.775911i	$-0.717290\pi$
$643$	−31.9931	−1.26168	−0.630842	+	0.775911i	$0.717290\pi$
$644$	25.1738	0.991987
$645$	0.120031	0.00472622
$646$	−10.5856	−0.416485
$647$	3.55450	0.139742	0.0698710	−	0.997556i	$-0.477741\pi$
$647$	3.55450	0.139742	0.0698710	+	0.997556i	$0.477741\pi$
$648$	−1.70288	−0.0668955
$649$	−5.24370	−0.205833
$650$	−5.32776	−0.208972
$651$	−6.22669	−0.244043
$652$	13.7369	0.537978
$653$	26.0330	1.01875	0.509375	−	0.860545i	$-0.329877\pi$
$653$	26.0330	1.01875	0.509375	+	0.860545i	$0.329877\pi$
$654$	15.2971	0.598165
$655$	−15.5677	−0.608278
$656$	−39.3332	−1.53571
$657$	23.7962	0.928377
$658$	−7.06509	−0.275426
$659$	−13.9243	−0.542412	−0.271206	−	0.962521i	$-0.587423\pi$
$659$	−13.9243	−0.542412	−0.271206	+	0.962521i	$0.587423\pi$
$660$	−4.10216	−0.159677
$661$	18.4645	0.718186	0.359093	−	0.933302i	$-0.383086\pi$
$661$	18.4645	0.718186	0.359093	+	0.933302i	$0.383086\pi$
$662$	66.8738	2.59912
$663$	−11.3609	−0.441220
$664$	1.45493	0.0564624
$665$	−1.11038	−0.0430586
$666$	61.4004	2.37922
$667$	−50.2812	−1.94690
$668$	29.2702	1.13250
$669$	−0.964685	−0.0372969
$670$	5.48420	0.211873
$671$	52.3638	2.02148
$672$	6.76335	0.260902
$673$	21.8721	0.843108	0.421554	−	0.906803i	$-0.361485\pi$
$673$	21.8721	0.843108	0.421554	+	0.906803i	$0.361485\pi$
$674$	−2.98856	−0.115115
$675$	3.14127	0.120908
$676$	−10.5360	−0.405233
$677$	−28.5839	−1.09857	−0.549285	−	0.835635i	$-0.685100\pi$
$677$	−28.5839	−1.09857	−0.549285	+	0.835635i	$0.685100\pi$
$678$	−16.2671	−0.624735
$679$	−20.5179	−0.787406
$680$	−2.03649	−0.0780957
$681$	−2.73439	−0.104782
$682$	−56.5234	−2.16439
$683$	−2.47564	−0.0947278	−0.0473639	−	0.998878i	$-0.515082\pi$
$683$	−2.47564	−0.0947278	−0.0473639	+	0.998878i	$0.515082\pi$
$684$	−3.56009	−0.136123
$685$	−2.80386	−0.107130
$686$	−35.5590	−1.35765
$687$	−7.01785	−0.267748
$688$	−0.925869	−0.0352984
$689$	−35.9331	−1.36894
$690$	9.34434	0.355733
$691$	−39.9523	−1.51986	−0.759929	−	0.650006i	$-0.774767\pi$
$691$	−39.9523	−1.51986	−0.759929	+	0.650006i	$0.774767\pi$
$692$	−16.4749	−0.626282
$693$	16.8603	0.640471
$694$	54.9638	2.08640
$695$	14.7772	0.560532
$696$	−0.862011	−0.0326744
$697$	−70.2712	−2.66171
$698$	−10.7621	−0.407351
$699$	−9.20582	−0.348196
$700$	2.92044	0.110382
$701$	−5.61138	−0.211939	−0.105969	−	0.994369i	$-0.533795\pi$
$701$	−5.61138	−0.211939	−0.105969	+	0.994369i	$0.533795\pi$
$702$	−16.7360	−0.631658
$703$	−8.21051	−0.309665
$704$	27.4382	1.03411
$705$	−1.26499	−0.0476423
$706$	29.5384	1.11169
$707$	−7.42745	−0.279338
$708$	−1.35040	−0.0507511
$709$	28.4660	1.06906	0.534532	−	0.845148i	$-0.320488\pi$
$709$	28.4660	1.06906	0.534532	+	0.845148i	$0.320488\pi$
$710$	7.22887	0.271294
$711$	−20.3157	−0.761899
$712$	−3.52153	−0.131975
$713$	62.1061	2.32589
$714$	12.9106	0.483166
$715$	−10.8178	−0.404563
$716$	11.3239	0.423196
$717$	9.26785	0.346114
$718$	−6.47077	−0.241487
$719$	−5.05643	−0.188573	−0.0942864	−	0.995545i	$-0.530057\pi$
$719$	−5.05643	−0.188573	−0.0942864	+	0.995545i	$0.530057\pi$
$720$	−11.4683	−0.427398
$721$	−7.97352	−0.296949
$722$	−36.3599	−1.35318
$723$	0.551502	0.0205106
$724$	11.1450	0.414201
$725$	−5.83317	−0.216639
$726$	−5.34328	−0.198308
$727$	−47.1191	−1.74755	−0.873776	−	0.486328i	$-0.838336\pi$
$727$	−47.1191	−1.74755	−0.873776	+	0.486328i	$0.838336\pi$
$728$	1.13810	0.0421809
$729$	−11.9352	−0.442043
$730$	17.3505	0.642172
$731$	−1.65412	−0.0611798
$732$	13.4851	0.498425
$733$	37.7391	1.39392	0.696962	−	0.717108i	$-0.254535\pi$
$733$	37.7391	1.39392	0.696962	+	0.717108i	$0.254535\pi$
$734$	2.47456	0.0913375
$735$	−2.50626	−0.0924448
$736$	−67.4589	−2.48657
$737$	11.1354	0.410179
$738$	−48.9950	−1.80353
$739$	−5.83089	−0.214493	−0.107246	−	0.994232i	$-0.534203\pi$
$739$	−5.83089	−0.214493	−0.107246	+	0.994232i	$0.534203\pi$
$740$	21.5947	0.793837
$741$	1.05922	0.0389114
$742$	40.8345	1.49908
$743$	30.8566	1.13202	0.566010	−	0.824398i	$-0.308486\pi$
$743$	30.8566	1.13202	0.566010	+	0.824398i	$0.308486\pi$
$744$	1.06473	0.0390350
$745$	−8.79693	−0.322294
$746$	−21.7064	−0.794728
$747$	14.6379	0.535571
$748$	56.5310	2.06698
$749$	−7.66353	−0.280019
$750$	1.08405	0.0395838
$751$	37.0538	1.35211	0.676057	−	0.736849i	$-0.263687\pi$
$751$	37.0538	1.35211	0.676057	+	0.736849i	$0.263687\pi$
$752$	9.75762	0.355824
$753$	9.48674	0.345716
$754$	31.0778	1.13179
$755$	16.9267	0.616027
$756$	9.17389	0.333651
$757$	39.7535	1.44487	0.722433	−	0.691441i	$-0.243024\pi$
$757$	39.7535	1.44487	0.722433	+	0.691441i	$0.243024\pi$
$758$	27.4446	0.996832
$759$	18.9733	0.688687
$760$	0.189869	0.00688729
$761$	31.2801	1.13390	0.566952	−	0.823751i	$-0.308123\pi$
$761$	31.2801	1.13390	0.566952	+	0.823751i	$0.308123\pi$
$762$	−6.90588	−0.250174
$763$	−22.1125	−0.800527
$764$	−15.0000	−0.542679
$765$	−20.4888	−0.740773
$766$	−57.9478	−2.09374
$767$	−3.56113	−0.128585
$768$	−9.90134	−0.357284
$769$	3.13978	0.113223	0.0566117	−	0.998396i	$-0.481970\pi$
$769$	3.13978	0.113223	0.0566117	+	0.998396i	$0.481970\pi$
$770$	12.2934	0.443023
$771$	11.2974	0.406868
$772$	9.32114	0.335475
$773$	−22.6071	−0.813121	−0.406561	−	0.913624i	$-0.633272\pi$
$773$	−22.6071	−0.813121	−0.406561	+	0.913624i	$0.633272\pi$
$774$	−1.15330	−0.0414545
$775$	7.20499	0.258811
$776$	3.50847	0.125947
$777$	10.0138	0.359244
$778$	−67.1823	−2.40860
$779$	6.55165	0.234737
$780$	−2.78588	−0.0997506
$781$	14.6779	0.525217
$782$	−128.772	−4.60488
$783$	−18.3236	−0.654831
$784$	19.3322	0.690437
$785$	1.17357	0.0418867
$786$	−16.8761	−0.601949
$787$	41.4390	1.47714	0.738571	−	0.674176i	$-0.235501\pi$
$787$	41.4390	1.47714	0.738571	+	0.674176i	$0.235501\pi$
$788$	21.1978	0.755141
$789$	−15.2672	−0.543528
$790$	−14.8128	−0.527017
$791$	23.5147	0.836087
$792$	−2.88304	−0.102444
$793$	35.5616	1.26283
$794$	5.65382	0.200647
$795$	7.31134	0.259307
$796$	−40.8013	−1.44616
$797$	−22.3178	−0.790536	−0.395268	−	0.918566i	$-0.629348\pi$
$797$	−22.3178	−0.790536	−0.395268	+	0.918566i	$0.629348\pi$
$798$	−1.20370	−0.0426106
$799$	17.4326	0.616720
$800$	−7.82597	−0.276690
$801$	−35.4295	−1.25184
$802$	4.83471	0.170719
$803$	35.2295	1.24322
$804$	2.86768	0.101135
$805$	−13.5076	−0.476080
$806$	−38.3865	−1.35211
$807$	1.56163	0.0549721
$808$	1.27006	0.0446805
$809$	−5.65747	−0.198906	−0.0994531	−	0.995042i	$-0.531709\pi$
$809$	−5.65747	−0.198906	−0.0994531	+	0.995042i	$0.531709\pi$
$810$	−12.4918	−0.438916
$811$	−47.8682	−1.68088	−0.840441	−	0.541904i	$-0.817704\pi$
$811$	−47.8682	−1.68088	−0.840441	+	0.541904i	$0.817704\pi$
$812$	−17.0354	−0.597826
$813$	−6.44764	−0.226129
$814$	90.9014	3.18609
$815$	−7.37084	−0.258189
$816$	−17.8308	−0.624203
$817$	0.154220	0.00539547
$818$	29.5546	1.03335
$819$	11.4503	0.400105
$820$	−17.2317	−0.601756
$821$	−3.39747	−0.118572	−0.0592862	−	0.998241i	$-0.518882\pi$
$821$	−3.39747	−0.118572	−0.0592862	+	0.998241i	$0.518882\pi$
$822$	−3.03952	−0.106015
$823$	−1.21618	−0.0423933	−0.0211967	−	0.999775i	$-0.506748\pi$
$823$	−1.21618	−0.0423933	−0.0211967	+	0.999775i	$0.506748\pi$
$824$	1.36343	0.0474975
$825$	2.20111	0.0766328
$826$	4.04689	0.140809
$827$	55.7826	1.93975	0.969875	−	0.243603i	$-0.0783295\pi$
$827$	55.7826	1.93975	0.969875	+	0.243603i	$0.0783295\pi$
$828$	−43.3079	−1.50505
$829$	−47.8332	−1.66132	−0.830659	−	0.556782i	$-0.812036\pi$
$829$	−47.8332	−1.66132	−0.830659	+	0.556782i	$0.812036\pi$
$830$	10.6729	0.370462
$831$	7.06412	0.245051
$832$	18.6339	0.646016
$833$	34.5382	1.19668
$834$	16.0192	0.554699
$835$	−15.7056	−0.543515
$836$	−5.27060	−0.182288
$837$	22.6328	0.782304
$838$	−40.8576	−1.41140
$839$	−35.3573	−1.22067	−0.610334	−	0.792144i	$-0.708965\pi$
$839$	−35.3573	−1.22067	−0.610334	+	0.792144i	$0.708965\pi$
$840$	−0.231571	−0.00798997
$841$	5.02589	0.173306
$842$	−52.9870	−1.82605
$843$	7.05861	0.243112
$844$	−21.0013	−0.722894
$845$	5.65336	0.194481
$846$	12.1545	0.417879
$847$	7.72391	0.265397
$848$	−56.3966	−1.93667
$849$	7.59034	0.260500
$850$	−14.9390	−0.512403
$851$	−99.8795	−3.42383
$852$	3.77997	0.129500
$853$	−38.5021	−1.31829	−0.659143	−	0.752018i	$-0.729081\pi$
$853$	−38.5021	−1.31829	−0.659143	+	0.752018i	$0.729081\pi$
$854$	−40.4123	−1.38288
$855$	1.91025	0.0653290
$856$	1.31043	0.0447895
$857$	3.21574	0.109848	0.0549238	−	0.998491i	$-0.482508\pi$
$857$	3.21574	0.109848	0.0549238	+	0.998491i	$0.482508\pi$
$858$	−11.7270	−0.400353
$859$	8.56250	0.292149	0.146074	−	0.989274i	$-0.453336\pi$
$859$	8.56250	0.292149	0.146074	+	0.989274i	$0.453336\pi$
$860$	−0.405618	−0.0138315
$861$	−7.99062	−0.272319
$862$	−38.5008	−1.31134
$863$	−21.7491	−0.740350	−0.370175	−	0.928962i	$-0.620702\pi$
$863$	−21.7491	−0.740350	−0.370175	+	0.928962i	$0.620702\pi$
$864$	−24.5835	−0.836347
$865$	8.83998	0.300568
$866$	−30.6331	−1.04096
$867$	−22.4803	−0.763470
$868$	21.0417	0.714202
$869$	−30.0768	−1.02029
$870$	−6.32343	−0.214384
$871$	7.56236	0.256241
$872$	3.78114	0.128046
$873$	35.2981	1.19466
$874$	12.0059	0.406107
$875$	−1.56703	−0.0529752
$876$	9.07258	0.306534
$877$	21.9167	0.740074	0.370037	−	0.929017i	$-0.379345\pi$
$877$	21.9167	0.740074	0.370037	+	0.929017i	$0.379345\pi$
$878$	−21.1275	−0.713017
$879$	9.12151	0.307661
$880$	−16.9784	−0.572343
$881$	0.352879	0.0118888	0.00594441	−	0.999982i	$-0.498108\pi$
$881$	0.352879	0.0118888	0.00594441	+	0.999982i	$0.498108\pi$
$882$	24.0810	0.810849
$883$	−55.2411	−1.85901	−0.929505	−	0.368810i	$-0.879765\pi$
$883$	−55.2411	−1.85901	−0.929505	+	0.368810i	$0.879765\pi$
$884$	38.3916	1.29125
$885$	0.724588	0.0243567
$886$	17.9326	0.602457
$887$	−6.24830	−0.209797	−0.104899	−	0.994483i	$-0.533452\pi$
$887$	−6.24830	−0.209797	−0.104899	+	0.994483i	$0.533452\pi$
$888$	−1.71232	−0.0574615
$889$	9.98269	0.334809
$890$	−25.8328	−0.865916
$891$	−25.3640	−0.849727
$892$	3.25994	0.109151
$893$	−1.62530	−0.0543887
$894$	−9.53628	−0.318941
$895$	−6.07612	−0.203102
$896$	3.35133	0.111960
$897$	12.8852	0.430226
$898$	−53.3225	−1.77940
$899$	−42.0279	−1.40171
$900$	−5.02419	−0.167473
$901$	−100.756	−3.35667
$902$	−72.5356	−2.41517
$903$	−0.188092	−0.00625931
$904$	−4.02091	−0.133733
$905$	−5.98011	−0.198786
$906$	18.3494	0.609616
$907$	−16.6946	−0.554335	−0.277168	−	0.960822i	$-0.589396\pi$
$907$	−16.6946	−0.554335	−0.277168	+	0.960822i	$0.589396\pi$
$908$	9.24026	0.306649
$909$	12.7779	0.423815
$910$	8.34875	0.276758
$911$	17.3319	0.574232	0.287116	−	0.957896i	$-0.407303\pi$
$911$	17.3319	0.574232	0.287116	+	0.957896i	$0.407303\pi$
$912$	1.66244	0.0550488
$913$	21.6709	0.717202
$914$	45.1854	1.49460
$915$	−7.23575	−0.239207
$916$	23.7153	0.783574
$917$	24.3949	0.805592
$918$	−46.9274	−1.54884
$919$	42.2047	1.39220	0.696102	−	0.717943i	$-0.254916\pi$
$919$	42.2047	1.39220	0.696102	+	0.717943i	$0.254916\pi$
$920$	2.30973	0.0761496
$921$	6.35749	0.209486
$922$	23.0678	0.759698
$923$	9.96814	0.328105
$924$	6.42820	0.211472
$925$	−11.5871	−0.380982
$926$	63.0753	2.07278
$927$	13.7173	0.450535
$928$	45.6502	1.49854
$929$	−27.1814	−0.891794	−0.445897	−	0.895084i	$-0.647115\pi$
$929$	−27.1814	−0.891794	−0.445897	+	0.895084i	$0.647115\pi$
$930$	7.81054	0.256118
$931$	−3.22013	−0.105535
$932$	31.1090	1.01901
$933$	17.2562	0.564942
$934$	−18.8601	−0.617120
$935$	−30.3330	−0.991995
$936$	−1.95794	−0.0639974
$937$	−15.4398	−0.504397	−0.252199	−	0.967676i	$-0.581154\pi$
$937$	−15.4398	−0.504397	−0.252199	+	0.967676i	$0.581154\pi$
$938$	−8.59389	−0.280600
$939$	6.85560	0.223724
$940$	4.27476	0.139427
$941$	3.16013	0.103017	0.0515086	−	0.998673i	$-0.483597\pi$
$941$	3.16013	0.103017	0.0515086	+	0.998673i	$0.483597\pi$
$942$	1.27221	0.0414508
$943$	79.6998	2.59538
$944$	−5.58917	−0.181912
$945$	−4.92246	−0.160128
$946$	−1.70742	−0.0555131
$947$	35.0516	1.13902	0.569512	−	0.821983i	$-0.307132\pi$
$947$	35.0516	1.13902	0.569512	+	0.821983i	$0.307132\pi$
$948$	−7.74561	−0.251566
$949$	23.9253	0.776647
$950$	1.39282	0.0451890
$951$	13.6018	0.441067
$952$	3.19123	0.103428
$953$	15.8937	0.514848	0.257424	−	0.966298i	$-0.417126\pi$
$953$	15.8937	0.514848	0.257424	+	0.966298i	$0.417126\pi$
$954$	−70.2498	−2.27442
$955$	8.04857	0.260446
$956$	−31.3186	−1.01292
$957$	−12.8395	−0.415041
$958$	−30.0493	−0.970850
$959$	4.39373	0.141881
$960$	−3.79147	−0.122369
$961$	20.9118	0.674575
$962$	61.7335	1.99037
$963$	13.1840	0.424848
$964$	−1.86368	−0.0600251
$965$	−5.00147	−0.161003
$966$	−14.6428	−0.471126
$967$	−15.7577	−0.506733	−0.253366	−	0.967370i	$-0.581538\pi$
$967$	−15.7577	−0.506733	−0.253366	+	0.967370i	$0.581538\pi$
$968$	−1.32075	−0.0424506
$969$	2.97004	0.0954114
$970$	25.7370	0.826364
$971$	−5.24444	−0.168302	−0.0841511	−	0.996453i	$-0.526818\pi$
$971$	−5.24444	−0.168302	−0.0841511	+	0.996453i	$0.526818\pi$
$972$	−24.0949	−0.772845
$973$	−23.1563	−0.742357
$974$	18.8643	0.604450
$975$	1.49483	0.0478729
$976$	55.8136	1.78655
$977$	21.5907	0.690747	0.345374	−	0.938465i	$-0.387752\pi$
$977$	21.5907	0.690747	0.345374	+	0.938465i	$0.387752\pi$
$978$	−7.99033	−0.255502
$979$	−52.4523	−1.67638
$980$	8.46935	0.270544
$981$	38.0414	1.21457
$982$	62.5401	1.99573
$983$	−39.1399	−1.24837	−0.624184	−	0.781277i	$-0.714568\pi$
$983$	−39.1399	−1.24837	−0.624184	+	0.781277i	$0.714568\pi$
$984$	1.36636	0.0435579
$985$	−11.3742	−0.362411
$986$	87.1417	2.77516
$987$	1.98228	0.0630966
$988$	−3.57940	−0.113876
$989$	1.87606	0.0596553
$990$	−21.1490	−0.672160
$991$	−59.9001	−1.90279	−0.951394	−	0.307976i	$-0.900348\pi$
$991$	−59.9001	−1.90279	−0.951394	+	0.307976i	$0.900348\pi$
$992$	−56.3860	−1.79026
$993$	−18.7630	−0.595426
$994$	−11.3278	−0.359297
$995$	21.8929	0.694051
$996$	5.58086	0.176836
$997$	51.5191	1.63163	0.815813	−	0.578316i	$-0.196290\pi$
$997$	51.5191	1.63163	0.815813	+	0.578316i	$0.196290\pi$
$998$	16.3770	0.518403
$999$	−36.3983	−1.15159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.c.1.13	✓	15
5.4	even	2		6025.2.a.i.1.3		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.c.1.13	✓	15	1.1	even	1	trivial
6025.2.a.i.1.3		15	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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.a (trivial)

\(f(q)\)	\(=\)	\(q+1.96562 q^{2} -0.551502 q^{3} +1.86368 q^{4} -1.00000 q^{5} -1.08405 q^{6} +1.56703 q^{7} -0.267954 q^{8} -2.69585 q^{9} +O(q^{10})\)	\(q+1.96562 q^{2} -0.551502 q^{3} +1.86368 q^{4} -1.00000 q^{5} -1.08405 q^{6} +1.56703 q^{7} -0.267954 q^{8} -2.69585 q^{9} -1.96562 q^{10} -3.99112 q^{11} -1.02782 q^{12} -2.71047 q^{13} +3.08019 q^{14} +0.551502 q^{15} -4.25406 q^{16} -7.60012 q^{17} -5.29902 q^{18} +0.708589 q^{19} -1.86368 q^{20} -0.864219 q^{21} -7.84504 q^{22} +8.61987 q^{23} +0.147777 q^{24} +1.00000 q^{25} -5.32776 q^{26} +3.14127 q^{27} +2.92044 q^{28} -5.83317 q^{29} +1.08405 q^{30} +7.20499 q^{31} -7.82597 q^{32} +2.20111 q^{33} -14.9390 q^{34} -1.56703 q^{35} -5.02419 q^{36} -11.5871 q^{37} +1.39282 q^{38} +1.49483 q^{39} +0.267954 q^{40} +9.24605 q^{41} -1.69873 q^{42} +0.217644 q^{43} -7.43816 q^{44} +2.69585 q^{45} +16.9434 q^{46} -2.29372 q^{47} +2.34612 q^{48} -4.54442 q^{49} +1.96562 q^{50} +4.19149 q^{51} -5.05145 q^{52} +13.2571 q^{53} +6.17456 q^{54} +3.99112 q^{55} -0.419892 q^{56} -0.390788 q^{57} -11.4658 q^{58} +1.31384 q^{59} +1.02782 q^{60} -13.1201 q^{61} +14.1623 q^{62} -4.22446 q^{63} -6.87481 q^{64} +2.71047 q^{65} +4.32656 q^{66} -2.79005 q^{67} -14.1642 q^{68} -4.75388 q^{69} -3.08019 q^{70} -3.67764 q^{71} +0.722363 q^{72} -8.82698 q^{73} -22.7759 q^{74} -0.551502 q^{75} +1.32058 q^{76} -6.25419 q^{77} +2.93827 q^{78} +7.53594 q^{79} +4.25406 q^{80} +6.35512 q^{81} +18.1743 q^{82} -5.42978 q^{83} -1.61063 q^{84} +7.60012 q^{85} +0.427806 q^{86} +3.21701 q^{87} +1.06944 q^{88} +13.1423 q^{89} +5.29902 q^{90} -4.24738 q^{91} +16.0647 q^{92} -3.97357 q^{93} -4.50859 q^{94} -0.708589 q^{95} +4.31604 q^{96} -13.0935 q^{97} -8.93263 q^{98} +10.7594 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 2 q^{2} - 7 q^{3} + 6 q^{4} - 15 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 15 * q + 2 * q^2 - 7 * q^3 + 6 * q^4 - 15 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 15 q + 2 q^{2} - 7 q^{3} + 6 q^{4} - 15 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 2 q^{10} - 10 q^{11} - 6 q^{12} - 8 q^{13} - 5 q^{14} + 7 q^{15} - 16 q^{16} - q^{17} - 3 q^{18} - 30 q^{19} - 6 q^{20} - 11 q^{21} - 5 q^{22} + 19 q^{23} - 14 q^{24} + 15 q^{25} - 18 q^{26} - 22 q^{27} - 20 q^{28} - 12 q^{29} + 5 q^{30} - 22 q^{31} - 2 q^{32} + 4 q^{33} - 29 q^{34} + 3 q^{35} - 7 q^{36} - 12 q^{37} - 18 q^{38} - 17 q^{39} - 3 q^{40} - 13 q^{41} - q^{42} - 25 q^{43} - 20 q^{44} - 6 q^{45} - 7 q^{46} + 16 q^{47} - 22 q^{48} - 24 q^{49} + 2 q^{50} - 27 q^{51} - 15 q^{52} - 4 q^{53} - 43 q^{54} + 10 q^{55} - 3 q^{56} + 22 q^{57} - 20 q^{58} - 50 q^{59} + 6 q^{60} - 41 q^{61} + 12 q^{62} + 6 q^{63} - 53 q^{64} + 8 q^{65} + 5 q^{66} - 43 q^{67} + 5 q^{68} - 50 q^{69} + 5 q^{70} - 14 q^{71} + 32 q^{72} - 10 q^{73} - 26 q^{74} - 7 q^{75} - 13 q^{76} - 7 q^{77} + 3 q^{78} - 44 q^{79} + 16 q^{80} + 7 q^{81} - 19 q^{82} + 7 q^{83} - 42 q^{84} + q^{85} + 7 q^{86} + 10 q^{87} - 28 q^{88} + 4 q^{89} + 3 q^{90} - 50 q^{91} + 25 q^{92} + 22 q^{93} - 14 q^{94} + 30 q^{95} + 14 q^{96} + 9 q^{97} + 2 q^{98} - 46 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 - 7 * q^3 + 6 * q^4 - 15 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 2 * q^10 - 10 * q^11 - 6 * q^12 - 8 * q^13 - 5 * q^14 + 7 * q^15 - 16 * q^16 - q^17 - 3 * q^18 - 30 * q^19 - 6 * q^20 - 11 * q^21 - 5 * q^22 + 19 * q^23 - 14 * q^24 + 15 * q^25 - 18 * q^26 - 22 * q^27 - 20 * q^28 - 12 * q^29 + 5 * q^30 - 22 * q^31 - 2 * q^32 + 4 * q^33 - 29 * q^34 + 3 * q^35 - 7 * q^36 - 12 * q^37 - 18 * q^38 - 17 * q^39 - 3 * q^40 - 13 * q^41 - q^42 - 25 * q^43 - 20 * q^44 - 6 * q^45 - 7 * q^46 + 16 * q^47 - 22 * q^48 - 24 * q^49 + 2 * q^50 - 27 * q^51 - 15 * q^52 - 4 * q^53 - 43 * q^54 + 10 * q^55 - 3 * q^56 + 22 * q^57 - 20 * q^58 - 50 * q^59 + 6 * q^60 - 41 * q^61 + 12 * q^62 + 6 * q^63 - 53 * q^64 + 8 * q^65 + 5 * q^66 - 43 * q^67 + 5 * q^68 - 50 * q^69 + 5 * q^70 - 14 * q^71 + 32 * q^72 - 10 * q^73 - 26 * q^74 - 7 * q^75 - 13 * q^76 - 7 * q^77 + 3 * q^78 - 44 * q^79 + 16 * q^80 + 7 * q^81 - 19 * q^82 + 7 * q^83 - 42 * q^84 + q^85 + 7 * q^86 + 10 * q^87 - 28 * q^88 + 4 * q^89 + 3 * q^90 - 50 * q^91 + 25 * q^92 + 22 * q^93 - 14 * q^94 + 30 * q^95 + 14 * q^96 + 9 * q^97 + 2 * q^98 - 46 * q^99

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