LMFDB - Embedded newform 2527.2.a.r.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2527,2,Mod(1,2527)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2527, 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("2527.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2527 = 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2527.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:	$20.1781965908$
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} - 3 x^{14} - 18 x^{13} + 56 x^{12} + 126 x^{11} - 417 x^{10} - 420 x^{9} + 1572 x^{8} + \cdots + 107 $ x^15 - 3x^14 - 18x^13 + 56x^12 + 126x^11 - 417x^10 - 420x^9 + 1572x^8 + 612x^7 - 3113x^6 - 90x^5 + 2976x^4 - 520x^3 - 1035x^2 + 183x + 107
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 133)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-1.62673$ of defining polynomial
Character	$\chi$	$=$	2527.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.62673 q^{2} +1.07589 q^{3} +0.646252 q^{4} +0.0703725 q^{5} +1.75018 q^{6} -1.00000 q^{7} -2.20218 q^{8} -1.84246 q^{9} +O(q^{10})$	\(q+1.62673 q^{2} +1.07589 q^{3} +0.646252 q^{4} +0.0703725 q^{5} +1.75018 q^{6} -1.00000 q^{7} -2.20218 q^{8} -1.84246 q^{9} +0.114477 q^{10} +1.79123 q^{11} +0.695297 q^{12} -2.96780 q^{13} -1.62673 q^{14} +0.0757131 q^{15} -4.87486 q^{16} -0.629612 q^{17} -2.99718 q^{18} +0.0454783 q^{20} -1.07589 q^{21} +2.91385 q^{22} -1.50027 q^{23} -2.36931 q^{24} -4.99505 q^{25} -4.82780 q^{26} -5.20996 q^{27} -0.646252 q^{28} -5.42622 q^{29} +0.123165 q^{30} -6.53051 q^{31} -3.52572 q^{32} +1.92717 q^{33} -1.02421 q^{34} -0.0703725 q^{35} -1.19069 q^{36} +0.691141 q^{37} -3.19303 q^{39} -0.154973 q^{40} +6.72775 q^{41} -1.75018 q^{42} +1.88632 q^{43} +1.15759 q^{44} -0.129658 q^{45} -2.44054 q^{46} -1.39059 q^{47} -5.24482 q^{48} +1.00000 q^{49} -8.12560 q^{50} -0.677394 q^{51} -1.91794 q^{52} +7.37918 q^{53} -8.47520 q^{54} +0.126054 q^{55} +2.20218 q^{56} -8.82700 q^{58} +13.8670 q^{59} +0.0489297 q^{60} -0.168085 q^{61} -10.6234 q^{62} +1.84246 q^{63} +4.01433 q^{64} -0.208851 q^{65} +3.13499 q^{66} -9.23759 q^{67} -0.406888 q^{68} -1.61413 q^{69} -0.114477 q^{70} -11.7888 q^{71} +4.05743 q^{72} -11.2254 q^{73} +1.12430 q^{74} -5.37413 q^{75} -1.79123 q^{77} -5.19419 q^{78} +10.4804 q^{79} -0.343056 q^{80} -0.0779737 q^{81} +10.9442 q^{82} -6.75703 q^{83} -0.695297 q^{84} -0.0443073 q^{85} +3.06853 q^{86} -5.83802 q^{87} -3.94463 q^{88} -4.12780 q^{89} -0.210919 q^{90} +2.96780 q^{91} -0.969554 q^{92} -7.02612 q^{93} -2.26212 q^{94} -3.79329 q^{96} -5.34665 q^{97} +1.62673 q^{98} -3.30027 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 3 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{7} - 9 q^{8} + 21 q^{9}+O(q^{10}) $ 15 * q - 3 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^7 - 9 * q^8 + 21 * q^9	\( 15 q - 3 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{7} - 9 q^{8} + 21 q^{9} - 6 q^{10} - 18 q^{12} - 18 q^{13} + 3 q^{14} + 12 q^{15} - 9 q^{16} - 9 q^{17} - 15 q^{18} - 15 q^{20} + 6 q^{21} - 9 q^{22} - 6 q^{23} + 18 q^{24} + 21 q^{25} + 45 q^{26} - 27 q^{27} - 15 q^{28} - 9 q^{29} - 21 q^{30} - 12 q^{31} - 36 q^{32} - 57 q^{33} - 3 q^{34} + 57 q^{36} - 18 q^{37} - 12 q^{39} - 15 q^{40} - 42 q^{41} - 12 q^{43} + 51 q^{44} - 27 q^{45} - 6 q^{46} - 3 q^{47} - 42 q^{48} + 15 q^{49} + 3 q^{50} + 6 q^{51} - 36 q^{52} - 33 q^{53} - 45 q^{54} + 6 q^{55} + 9 q^{56} - 30 q^{58} - 18 q^{59} + 18 q^{60} - 6 q^{61} + 12 q^{62} - 21 q^{63} - 3 q^{64} - 45 q^{65} + 33 q^{66} - 24 q^{67} - 51 q^{68} - 15 q^{69} + 6 q^{70} + 6 q^{71} + 9 q^{72} - 3 q^{73} - 9 q^{74} - 72 q^{75} - 27 q^{78} + 60 q^{79} + 18 q^{80} + 27 q^{81} + 36 q^{82} - 12 q^{83} + 18 q^{84} - 27 q^{85} - 51 q^{86} - 24 q^{87} - 36 q^{88} - 72 q^{89} + 3 q^{90} + 18 q^{91} - 60 q^{92} + 60 q^{93} - 21 q^{94} + 33 q^{96} - 39 q^{97} - 3 q^{98} + 54 q^{99}+O(q^{100}) \) 15 * q - 3 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^7 - 9 * q^8 + 21 * q^9 - 6 * q^10 - 18 * q^12 - 18 * q^13 + 3 * q^14 + 12 * q^15 - 9 * q^16 - 9 * q^17 - 15 * q^18 - 15 * q^20 + 6 * q^21 - 9 * q^22 - 6 * q^23 + 18 * q^24 + 21 * q^25 + 45 * q^26 - 27 * q^27 - 15 * q^28 - 9 * q^29 - 21 * q^30 - 12 * q^31 - 36 * q^32 - 57 * q^33 - 3 * q^34 + 57 * q^36 - 18 * q^37 - 12 * q^39 - 15 * q^40 - 42 * q^41 - 12 * q^43 + 51 * q^44 - 27 * q^45 - 6 * q^46 - 3 * q^47 - 42 * q^48 + 15 * q^49 + 3 * q^50 + 6 * q^51 - 36 * q^52 - 33 * q^53 - 45 * q^54 + 6 * q^55 + 9 * q^56 - 30 * q^58 - 18 * q^59 + 18 * q^60 - 6 * q^61 + 12 * q^62 - 21 * q^63 - 3 * q^64 - 45 * q^65 + 33 * q^66 - 24 * q^67 - 51 * q^68 - 15 * q^69 + 6 * q^70 + 6 * q^71 + 9 * q^72 - 3 * q^73 - 9 * q^74 - 72 * q^75 - 27 * q^78 + 60 * q^79 + 18 * q^80 + 27 * q^81 + 36 * q^82 - 12 * q^83 + 18 * q^84 - 27 * q^85 - 51 * q^86 - 24 * q^87 - 36 * q^88 - 72 * q^89 + 3 * q^90 + 18 * q^91 - 60 * q^92 + 60 * q^93 - 21 * q^94 + 33 * q^96 - 39 * q^97 - 3 * q^98 + 54 * 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 $

$2$	1.62673	1.15027	0.575136	−	0.818058i	$-0.304949\pi$
$2$	1.62673	1.15027	0.575136	+	0.818058i	$0.304949\pi$
$3$	1.07589	0.621166	0.310583	−	0.950546i	$-0.399476\pi$
$3$	1.07589	0.621166	0.310583	+	0.950546i	$0.399476\pi$
$4$	0.646252	0.323126
$5$	0.0703725	0.0314715	0.0157358	−	0.999876i	$-0.494991\pi$
$5$	0.0703725	0.0314715	0.0157358	+	0.999876i	$0.494991\pi$
$6$	1.75018	0.714510
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.20218	−0.778589
$9$	−1.84246	−0.614153
$10$	0.114477	0.0362008
$11$	1.79123	0.540077	0.270039	−	0.962849i	$-0.412964\pi$
$11$	1.79123	0.540077	0.270039	+	0.962849i	$0.412964\pi$
$12$	0.695297	0.200715
$13$	−2.96780	−0.823119	−0.411559	−	0.911383i	$-0.635016\pi$
$13$	−2.96780	−0.823119	−0.411559	+	0.911383i	$0.635016\pi$
$14$	−1.62673	−0.434762
$15$	0.0757131	0.0195490
$16$	−4.87486	−1.21872
$17$	−0.629612	−0.152703	−0.0763517	−	0.997081i	$-0.524327\pi$
$17$	−0.629612	−0.152703	−0.0763517	+	0.997081i	$0.524327\pi$
$18$	−2.99718	−0.706443
$19$	0	0
$19$	0	0
$20$	0.0454783	0.0101693
$21$	−1.07589	−0.234779
$22$	2.91385	0.621236
$23$	−1.50027	−0.312828	−0.156414	−	0.987692i	$-0.549993\pi$
$23$	−1.50027	−0.312828	−0.156414	+	0.987692i	$0.549993\pi$
$24$	−2.36931	−0.483633
$25$	−4.99505	−0.999010
$26$	−4.82780	−0.946810
$27$	−5.20996	−1.00266
$28$	−0.646252	−0.122130
$29$	−5.42622	−1.00762	−0.503812	−	0.863813i	$-0.668070\pi$
$29$	−5.42622	−1.00762	−0.503812	+	0.863813i	$0.668070\pi$
$30$	0.123165	0.0224867
$31$	−6.53051	−1.17291	−0.586457	−	0.809980i	$-0.699478\pi$
$31$	−6.53051	−1.17291	−0.586457	+	0.809980i	$0.699478\pi$
$32$	−3.52572	−0.623265
$33$	1.92717	0.335478
$34$	−1.02421	−0.175650
$35$	−0.0703725	−0.0118951
$36$	−1.19069	−0.198449
$37$	0.691141	0.113623	0.0568115	−	0.998385i	$-0.481907\pi$
$37$	0.691141	0.113623	0.0568115	+	0.998385i	$0.481907\pi$
$38$	0	0
$39$	−3.19303	−0.511293
$40$	−0.154973	−0.0245034
$41$	6.72775	1.05070	0.525349	−	0.850887i	$-0.323935\pi$
$41$	6.72775	1.05070	0.525349	+	0.850887i	$0.323935\pi$
$42$	−1.75018	−0.270059
$43$	1.88632	0.287661	0.143831	−	0.989602i	$-0.454058\pi$
$43$	1.88632	0.287661	0.143831	+	0.989602i	$0.454058\pi$
$44$	1.15759	0.174513
$45$	−0.129658	−0.0193283
$46$	−2.44054	−0.359838
$47$	−1.39059	−0.202838	−0.101419	−	0.994844i	$-0.532338\pi$
$47$	−1.39059	−0.202838	−0.101419	+	0.994844i	$0.532338\pi$
$48$	−5.24482	−0.757025
$49$	1.00000	0.142857
$50$	−8.12560	−1.14913
$51$	−0.677394	−0.0948541
$52$	−1.91794	−0.265971
$53$	7.37918	1.01361	0.506804	−	0.862061i	$-0.330827\pi$
$53$	7.37918	1.01361	0.506804	+	0.862061i	$0.330827\pi$
$54$	−8.47520	−1.15333
$55$	0.126054	0.0169971
$56$	2.20218	0.294279
$57$	0	0
$58$	−8.82700	−1.15904
$59$	13.8670	1.80532	0.902662	−	0.430350i	$-0.141610\pi$
$59$	13.8670	1.80532	0.902662	+	0.430350i	$0.141610\pi$
$60$	0.0489297	0.00631680
$61$	−0.168085	−0.0215211	−0.0107605	−	0.999942i	$-0.503425\pi$
$61$	−0.168085	−0.0215211	−0.0107605	+	0.999942i	$0.503425\pi$
$62$	−10.6234	−1.34917
$63$	1.84246	0.232128
$64$	4.01433	0.501791
$65$	−0.208851	−0.0259048
$66$	3.13499	0.385891
$67$	−9.23759	−1.12855	−0.564276	−	0.825586i	$-0.690844\pi$
$67$	−9.23759	−1.12855	−0.564276	+	0.825586i	$0.690844\pi$
$68$	−0.406888	−0.0493424
$69$	−1.61413	−0.194318
$70$	−0.114477	−0.0136826
$71$	−11.7888	−1.39908	−0.699539	−	0.714594i	$-0.746611\pi$
$71$	−11.7888	−1.39908	−0.699539	+	0.714594i	$0.746611\pi$
$72$	4.05743	0.478173
$73$	−11.2254	−1.31384	−0.656918	−	0.753962i	$-0.728140\pi$
$73$	−11.2254	−1.31384	−0.656918	+	0.753962i	$0.728140\pi$
$74$	1.12430	0.130697
$75$	−5.37413	−0.620551
$76$	0	0
$77$	−1.79123	−0.204130
$78$	−5.19419	−0.588126
$79$	10.4804	1.17913	0.589567	−	0.807720i	$-0.299298\pi$
$79$	10.4804	1.17913	0.589567	+	0.807720i	$0.299298\pi$
$80$	−0.343056	−0.0383548
$81$	−0.0779737	−0.00866374
$82$	10.9442	1.20859
$83$	−6.75703	−0.741681	−0.370840	−	0.928697i	$-0.620930\pi$
$83$	−6.75703	−0.741681	−0.370840	+	0.928697i	$0.620930\pi$
$84$	−0.695297	−0.0758631
$85$	−0.0443073	−0.00480581
$86$	3.06853	0.330888
$87$	−5.83802	−0.625902
$88$	−3.94463	−0.420499
$89$	−4.12780	−0.437546	−0.218773	−	0.975776i	$-0.570205\pi$
$89$	−4.12780	−0.437546	−0.218773	+	0.975776i	$0.570205\pi$
$90$	−0.210919	−0.0222328
$91$	2.96780	0.311110
$92$	−0.969554	−0.101083
$93$	−7.02612	−0.728575
$94$	−2.26212	−0.233319
$95$	0	0
$96$	−3.79329	−0.387151
$97$	−5.34665	−0.542870	−0.271435	−	0.962457i	$-0.587498\pi$
$97$	−5.34665	−0.542870	−0.271435	+	0.962457i	$0.587498\pi$
$98$	1.62673	0.164325
$99$	−3.30027	−0.331690
$100$	−3.22806	−0.322806
$101$	4.98666	0.496191	0.248095	−	0.968736i	$-0.420195\pi$
$101$	4.98666	0.496191	0.248095	+	0.968736i	$0.420195\pi$
$102$	−1.10194	−0.109108
$103$	−3.00139	−0.295736	−0.147868	−	0.989007i	$-0.547241\pi$
$103$	−3.00139	−0.295736	−0.147868	+	0.989007i	$0.547241\pi$
$104$	6.53563	0.640871
$105$	−0.0757131	−0.00738884
$106$	12.0039	1.16593
$107$	−12.5188	−1.21024	−0.605121	−	0.796134i	$-0.706875\pi$
$107$	−12.5188	−1.21024	−0.605121	+	0.796134i	$0.706875\pi$
$108$	−3.36694	−0.323984
$109$	−14.0382	−1.34461	−0.672306	−	0.740274i	$-0.734696\pi$
$109$	−14.0382	−1.34461	−0.672306	+	0.740274i	$0.734696\pi$
$110$	0.205055	0.0195512
$111$	0.743593	0.0705787
$112$	4.87486	0.460631
$113$	−0.420510	−0.0395583	−0.0197791	−	0.999804i	$-0.506296\pi$
$113$	−0.420510	−0.0395583	−0.0197791	+	0.999804i	$0.506296\pi$
$114$	0	0
$115$	−0.105578	−0.00984518
$116$	−3.50670	−0.325589
$117$	5.46804	0.505520
$118$	22.5578	2.07661
$119$	0.629612	0.0577164
$120$	−0.166734	−0.0152207
$121$	−7.79148	−0.708316
$122$	−0.273429	−0.0247551
$123$	7.23833	0.652658
$124$	−4.22035	−0.378999
$125$	−0.703376	−0.0629119
$126$	2.99718	0.267010
$127$	12.3384	1.09485	0.547427	−	0.836854i	$-0.315607\pi$
$127$	12.3384	1.09485	0.547427	+	0.836854i	$0.315607\pi$
$128$	13.5817	1.20046
$129$	2.02947	0.178685
$130$	−0.339744	−0.0297976
$131$	2.98764	0.261031	0.130516	−	0.991446i	$-0.458337\pi$
$131$	2.98764	0.261031	0.130516	+	0.991446i	$0.458337\pi$
$132$	1.24544	0.108402
$133$	0	0
$134$	−15.0271	−1.29814
$135$	−0.366638	−0.0315551
$136$	1.38652	0.118893
$137$	21.3435	1.82350	0.911749	−	0.410748i	$-0.134732\pi$
$137$	21.3435	1.82350	0.911749	+	0.410748i	$0.134732\pi$
$138$	−2.62575	−0.223519
$139$	−7.02613	−0.595949	−0.297974	−	0.954574i	$-0.596311\pi$
$139$	−7.02613	−0.595949	−0.297974	+	0.954574i	$0.596311\pi$
$140$	−0.0454783	−0.00384362
$141$	−1.49612	−0.125996
$142$	−19.1773	−1.60932
$143$	−5.31602	−0.444548
$144$	8.98173	0.748477
$145$	−0.381856	−0.0317114
$146$	−18.2607	−1.51127
$147$	1.07589	0.0887380
$148$	0.446651	0.0367145
$149$	8.06232	0.660491	0.330246	−	0.943895i	$-0.392868\pi$
$149$	8.06232	0.660491	0.330246	+	0.943895i	$0.392868\pi$
$150$	−8.74226	−0.713802
$151$	20.2208	1.64555	0.822773	−	0.568369i	$-0.192426\pi$
$151$	20.2208	1.64555	0.822773	+	0.568369i	$0.192426\pi$
$152$	0	0
$153$	1.16003	0.0937832
$154$	−2.91385	−0.234805
$155$	−0.459568	−0.0369134
$156$	−2.06350	−0.165212
$157$	22.9706	1.83325	0.916626	−	0.399747i	$-0.130902\pi$
$157$	22.9706	1.83325	0.916626	+	0.399747i	$0.130902\pi$
$158$	17.0487	1.35632
$159$	7.93920	0.629619
$160$	−0.248114	−0.0196151
$161$	1.50027	0.118238
$162$	−0.126842	−0.00996566
$163$	−18.0251	−1.41184	−0.705919	−	0.708292i	$-0.749466\pi$
$163$	−18.0251	−1.41184	−0.705919	+	0.708292i	$0.749466\pi$
$164$	4.34782	0.339508
$165$	0.135620	0.0105580
$166$	−10.9919	−0.853135
$167$	−3.67584	−0.284445	−0.142223	−	0.989835i	$-0.545425\pi$
$167$	−3.67584	−0.284445	−0.142223	+	0.989835i	$0.545425\pi$
$168$	2.36931	0.182796
$169$	−4.19219	−0.322476
$170$	−0.0720761	−0.00552798
$171$	0	0
$172$	1.21904	0.0929507
$173$	−10.8032	−0.821352	−0.410676	−	0.911781i	$-0.634707\pi$
$173$	−10.8032	−0.821352	−0.410676	+	0.911781i	$0.634707\pi$
$174$	−9.49689	−0.719957
$175$	4.99505	0.377590
$176$	−8.73202	−0.658201
$177$	14.9193	1.12141
$178$	−6.71482	−0.503297
$179$	−2.07152	−0.154833	−0.0774165	−	0.996999i	$-0.524667\pi$
$179$	−2.07152	−0.154833	−0.0774165	+	0.996999i	$0.524667\pi$
$180$	−0.0837919	−0.00624548
$181$	1.12923	0.0839353	0.0419676	−	0.999119i	$-0.486637\pi$
$181$	1.12923	0.0839353	0.0419676	+	0.999119i	$0.486637\pi$
$182$	4.82780	0.357861
$183$	−0.180841	−0.0133682
$184$	3.30387	0.243565
$185$	0.0486373	0.00357589
$186$	−11.4296	−0.838059
$187$	−1.12778	−0.0824716
$188$	−0.898671	−0.0655423
$189$	5.20996	0.378969
$190$	0	0
$191$	−0.301438	−0.0218113	−0.0109056	−	0.999941i	$-0.503471\pi$
$191$	−0.301438	−0.0218113	−0.0109056	+	0.999941i	$0.503471\pi$
$192$	4.31898	0.311696
$193$	3.08381	0.221978	0.110989	−	0.993822i	$-0.464598\pi$
$193$	3.08381	0.221978	0.110989	+	0.993822i	$0.464598\pi$
$194$	−8.69756	−0.624448
$195$	−0.224701	−0.0160912
$196$	0.646252	0.0461608
$197$	27.9203	1.98924	0.994620	−	0.103594i	$-0.0330343\pi$
$197$	27.9203	1.98924	0.994620	+	0.103594i	$0.0330343\pi$
$198$	−5.36866	−0.381534
$199$	−1.47940	−0.104872	−0.0524360	−	0.998624i	$-0.516699\pi$
$199$	−1.47940	−0.104872	−0.0524360	+	0.998624i	$0.516699\pi$
$200$	11.0000	0.777818
$201$	−9.93864	−0.701018
$202$	8.11195	0.570755
$203$	5.42622	0.380846
$204$	−0.437767	−0.0306498
$205$	0.473448	0.0330671
$206$	−4.88245	−0.340177
$207$	2.76419	0.192124
$208$	14.4676	1.00315
$209$	0	0
$210$	−0.123165	−0.00849918
$211$	−27.5844	−1.89899	−0.949495	−	0.313783i	$-0.898404\pi$
$211$	−27.5844	−1.89899	−0.949495	+	0.313783i	$0.898404\pi$
$212$	4.76881	0.327523
$213$	−12.6835	−0.869060
$214$	−20.3648	−1.39211
$215$	0.132745	0.00905313
$216$	11.4733	0.780658
$217$	6.53051	0.443320
$218$	−22.8363	−1.54667
$219$	−12.0773	−0.816110
$220$	0.0814623	0.00549219
$221$	1.86856	0.125693
$222$	1.20962	0.0811847
$223$	−8.92042	−0.597355	−0.298678	−	0.954354i	$-0.596546\pi$
$223$	−8.92042	−0.597355	−0.298678	+	0.954354i	$0.596546\pi$
$224$	3.52572	0.235572
$225$	9.20317	0.613544
$226$	−0.684057	−0.0455028
$227$	−25.3449	−1.68220	−0.841101	−	0.540878i	$-0.818092\pi$
$227$	−25.3449	−1.68220	−0.841101	+	0.540878i	$0.818092\pi$
$228$	0	0
$229$	24.8429	1.64167	0.820834	−	0.571167i	$-0.193509\pi$
$229$	24.8429	1.64167	0.820834	+	0.571167i	$0.193509\pi$
$230$	−0.171747	−0.0113246
$231$	−1.92717	−0.126799
$232$	11.9495	0.784525
$233$	15.8188	1.03632	0.518162	−	0.855283i	$-0.326617\pi$
$233$	15.8188	1.03632	0.518162	+	0.855283i	$0.326617\pi$
$234$	8.89503	0.581486
$235$	−0.0978592	−0.00638363
$236$	8.96155	0.583347
$237$	11.2757	0.732438
$238$	1.02421	0.0663896
$239$	4.00771	0.259237	0.129619	−	0.991564i	$-0.458625\pi$
$239$	4.00771	0.259237	0.129619	+	0.991564i	$0.458625\pi$
$240$	−0.369091	−0.0238247
$241$	−22.6475	−1.45885	−0.729427	−	0.684059i	$-0.760213\pi$
$241$	−22.6475	−1.45885	−0.729427	+	0.684059i	$0.760213\pi$
$242$	−12.6746	−0.814757
$243$	15.5460	0.997275
$244$	−0.108625	−0.00695401
$245$	0.0703725	0.00449593
$246$	11.7748	0.750734
$247$	0	0
$248$	14.3814	0.913219
$249$	−7.26983	−0.460707
$250$	−1.14420	−0.0723658
$251$	27.3031	1.72336	0.861678	−	0.507455i	$-0.169414\pi$
$251$	27.3031	1.72336	0.861678	+	0.507455i	$0.169414\pi$
$252$	1.19069	0.0750065
$253$	−2.68734	−0.168952
$254$	20.0712	1.25938
$255$	−0.0476699	−0.00298520
$256$	14.0651	0.879066
$257$	12.5582	0.783360	0.391680	−	0.920102i	$-0.371894\pi$
$257$	12.5582	0.783360	0.391680	+	0.920102i	$0.371894\pi$
$258$	3.30141	0.205537
$259$	−0.691141	−0.0429454
$260$	−0.134970	−0.00837051
$261$	9.99758	0.618835
$262$	4.86008	0.300257
$263$	16.5291	1.01923	0.509614	−	0.860403i	$-0.329788\pi$
$263$	16.5291	1.01923	0.509614	+	0.860403i	$0.329788\pi$
$264$	−4.24399	−0.261199
$265$	0.519291	0.0318998
$266$	0	0
$267$	−4.44107	−0.271789
$268$	−5.96981	−0.364664
$269$	−29.3061	−1.78682	−0.893411	−	0.449240i	$-0.851695\pi$
$269$	−29.3061	−1.78682	−0.893411	+	0.449240i	$0.851695\pi$
$270$	−0.596420	−0.0362970
$271$	27.8634	1.69258	0.846289	−	0.532724i	$-0.178832\pi$
$271$	27.8634	1.69258	0.846289	+	0.532724i	$0.178832\pi$
$272$	3.06927	0.186102
$273$	3.19303	0.193251
$274$	34.7201	2.09752
$275$	−8.94730	−0.539542
$276$	−1.04313	−0.0627893
$277$	6.40558	0.384874	0.192437	−	0.981309i	$-0.438361\pi$
$277$	6.40558	0.384874	0.192437	+	0.981309i	$0.438361\pi$
$278$	−11.4296	−0.685503
$279$	12.0322	0.720348
$280$	0.154973	0.00926141
$281$	0.486008	0.0289928	0.0144964	−	0.999895i	$-0.495385\pi$
$281$	0.486008	0.0289928	0.0144964	+	0.999895i	$0.495385\pi$
$282$	−2.43379	−0.144930
$283$	−26.3445	−1.56602	−0.783009	−	0.622010i	$-0.786316\pi$
$283$	−26.3445	−1.56602	−0.783009	+	0.622010i	$0.786316\pi$
$284$	−7.61856	−0.452079
$285$	0	0
$286$	−8.64773	−0.511351
$287$	−6.72775	−0.397126
$288$	6.49599	0.382780
$289$	−16.6036	−0.976682
$290$	−0.621177	−0.0364768
$291$	−5.75241	−0.337212
$292$	−7.25445	−0.424534
$293$	−31.4786	−1.83900	−0.919500	−	0.393090i	$-0.871406\pi$
$293$	−31.4786	−1.83900	−0.919500	+	0.393090i	$0.871406\pi$
$294$	1.75018	0.102073
$295$	0.975852	0.0568163
$296$	−1.52202	−0.0884656
$297$	−9.33225	−0.541512
$298$	13.1152	0.759744
$299$	4.45250	0.257495
$300$	−3.47304	−0.200516
$301$	−1.88632	−0.108726
$302$	32.8938	1.89283
$303$	5.36510	0.308217
$304$	0	0
$305$	−0.0118285	−0.000677300 0
$306$	1.88706	0.107876
$307$	−17.2109	−0.982277	−0.491138	−	0.871082i	$-0.663419\pi$
$307$	−17.2109	−0.982277	−0.491138	+	0.871082i	$0.663419\pi$
$308$	−1.15759	−0.0659597
$309$	−3.22917	−0.183701
$310$	−0.747593	−0.0424604
$311$	−28.7474	−1.63012	−0.815058	−	0.579379i	$-0.803295\pi$
$311$	−28.7474	−1.63012	−0.815058	+	0.579379i	$0.803295\pi$
$312$	7.03163	0.398088
$313$	−7.06828	−0.399523	−0.199761	−	0.979845i	$-0.564017\pi$
$313$	−7.06828	−0.399523	−0.199761	+	0.979845i	$0.564017\pi$
$314$	37.3669	2.10874
$315$	0.129658	0.00730542
$316$	6.77296	0.381009
$317$	−6.32125	−0.355037	−0.177518	−	0.984117i	$-0.556807\pi$
$317$	−6.32125	−0.355037	−0.177518	+	0.984117i	$0.556807\pi$
$318$	12.9149	0.724234
$319$	−9.71963	−0.544195
$320$	0.282498	0.0157921
$321$	−13.4689	−0.751761
$322$	2.44054	0.136006
$323$	0	0
$324$	−0.0503906	−0.00279948
$325$	14.8243	0.822303
$326$	−29.3221	−1.62400
$327$	−15.1035	−0.835227
$328$	−14.8157	−0.818062
$329$	1.39059	0.0766657
$330$	0.220617	0.0121446
$331$	15.6428	0.859808	0.429904	−	0.902875i	$-0.358547\pi$
$331$	15.6428	0.859808	0.429904	+	0.902875i	$0.358547\pi$
$332$	−4.36675	−0.239656
$333$	−1.27340	−0.0697818
$334$	−5.97961	−0.327190
$335$	−0.650072	−0.0355172
$336$	5.24482	0.286128
$337$	7.49490	0.408273	0.204137	−	0.978942i	$-0.434561\pi$
$337$	7.49490	0.408273	0.204137	+	0.978942i	$0.434561\pi$
$338$	−6.81956	−0.370935
$339$	−0.452423	−0.0245722
$340$	−0.0286337	−0.00155288
$341$	−11.6977	−0.633464
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−4.15402	−0.223970
$345$	−0.113590	−0.00611549
$346$	−17.5739	−0.944778
$347$	8.49577	0.456077	0.228039	−	0.973652i	$-0.426769\pi$
$347$	8.49577	0.456077	0.228039	+	0.973652i	$0.426769\pi$
$348$	−3.77283	−0.202245
$349$	0.621547	0.0332706	0.0166353	−	0.999862i	$-0.494705\pi$
$349$	0.621547	0.0332706	0.0166353	+	0.999862i	$0.494705\pi$
$350$	8.12560	0.434331
$351$	15.4621	0.825305
$352$	−6.31539	−0.336611
$353$	−26.3254	−1.40116	−0.700580	−	0.713574i	$-0.747075\pi$
$353$	−26.3254	−1.40116	−0.700580	+	0.713574i	$0.747075\pi$
$354$	24.2697	1.28992
$355$	−0.829610	−0.0440311
$356$	−2.66760	−0.141382
$357$	0.677394	0.0358515
$358$	−3.36981	−0.178100
$359$	−8.73385	−0.460955	−0.230477	−	0.973078i	$-0.574029\pi$
$359$	−8.73385	−0.460955	−0.230477	+	0.973078i	$0.574029\pi$
$360$	0.285531	0.0150488
$361$	0	0
$362$	1.83696	0.0965484
$363$	−8.38279	−0.439982
$364$	1.91794	0.100528
$365$	−0.789960	−0.0413484
$366$	−0.294180	−0.0153770
$367$	8.46710	0.441979	0.220989	−	0.975276i	$-0.429071\pi$
$367$	8.46710	0.441979	0.220989	+	0.975276i	$0.429071\pi$
$368$	7.31362	0.381249
$369$	−12.3956	−0.645289
$370$	0.0791198	0.00411324
$371$	−7.37918	−0.383108
$372$	−4.54064	−0.235421
$373$	−23.7498	−1.22972	−0.614859	−	0.788637i	$-0.710787\pi$
$373$	−23.7498	−1.22972	−0.614859	+	0.788637i	$0.710787\pi$
$374$	−1.83460	−0.0948648
$375$	−0.756756	−0.0390787
$376$	3.06233	0.157928
$377$	16.1039	0.829394
$378$	8.47520	0.435917
$379$	18.7476	0.962999	0.481500	−	0.876446i	$-0.340092\pi$
$379$	18.7476	0.962999	0.481500	+	0.876446i	$0.340092\pi$
$380$	0	0
$381$	13.2747	0.680086
$382$	−0.490358	−0.0250889
$383$	−13.2080	−0.674895	−0.337447	−	0.941344i	$-0.609564\pi$
$383$	−13.2080	−0.674895	−0.337447	+	0.941344i	$0.609564\pi$
$384$	14.6124	0.745686
$385$	−0.126054	−0.00642428
$386$	5.01653	0.255335
$387$	−3.47546	−0.176668
$388$	−3.45528	−0.175415
$389$	9.58095	0.485773	0.242887	−	0.970055i	$-0.421906\pi$
$389$	9.58095	0.485773	0.242887	+	0.970055i	$0.421906\pi$
$390$	−0.365528	−0.0185092
$391$	0.944589	0.0477699
$392$	−2.20218	−0.111227
$393$	3.21437	0.162144
$394$	45.4188	2.28817
$395$	0.737529	0.0371091
$396$	−2.13281	−0.107178
$397$	16.6627	0.836276	0.418138	−	0.908384i	$-0.362683\pi$
$397$	16.6627	0.836276	0.418138	+	0.908384i	$0.362683\pi$
$398$	−2.40659	−0.120631
$399$	0	0
$400$	24.3502	1.21751
$401$	20.0941	1.00345	0.501726	−	0.865027i	$-0.332699\pi$
$401$	20.0941	1.00345	0.501726	+	0.865027i	$0.332699\pi$
$402$	−16.1675	−0.806361
$403$	19.3812	0.965447
$404$	3.22264	0.160332
$405$	−0.00548720	−0.000272661 0
$406$	8.82700	0.438077
$407$	1.23800	0.0613652
$408$	1.49175	0.0738524
$409$	−10.4852	−0.518461	−0.259231	−	0.965815i	$-0.583469\pi$
$409$	−10.4852	−0.518461	−0.259231	+	0.965815i	$0.583469\pi$
$410$	0.770173	0.0380361
$411$	22.9633	1.13270
$412$	−1.93965	−0.0955599
$413$	−13.8670	−0.682348
$414$	4.49659	0.220995
$415$	−0.475509	−0.0233418
$416$	10.4636	0.513021
$417$	−7.55935	−0.370183
$418$	0	0
$419$	−13.0830	−0.639145	−0.319573	−	0.947562i	$-0.603539\pi$
$419$	−13.0830	−0.639145	−0.319573	+	0.947562i	$0.603539\pi$
$420$	−0.0489297	−0.00238753
$421$	23.6816	1.15417	0.577084	−	0.816685i	$-0.304190\pi$
$421$	23.6816	1.15417	0.577084	+	0.816685i	$0.304190\pi$
$422$	−44.8724	−2.18435
$423$	2.56210	0.124574
$424$	−16.2503	−0.789185
$425$	3.14494	0.152552
$426$	−20.6327	−0.999656
$427$	0.168085	0.00813420
$428$	−8.09032	−0.391060
$429$	−5.71946	−0.276138
$430$	0.215940	0.0104136
$431$	−7.38034	−0.355498	−0.177749	−	0.984076i	$-0.556882\pi$
$431$	−7.38034	−0.355498	−0.177749	+	0.984076i	$0.556882\pi$
$432$	25.3978	1.22195
$433$	−34.6384	−1.66461	−0.832307	−	0.554315i	$-0.812980\pi$
$433$	−34.6384	−1.66461	−0.832307	+	0.554315i	$0.812980\pi$
$434$	10.6234	0.509939
$435$	−0.410836	−0.0196981
$436$	−9.07218	−0.434479
$437$	0	0
$438$	−19.6466	−0.938749
$439$	32.2831	1.54079	0.770394	−	0.637568i	$-0.220059\pi$
$439$	32.2831	1.54079	0.770394	+	0.637568i	$0.220059\pi$
$440$	−0.277593	−0.0132337
$441$	−1.84246	−0.0877361
$442$	3.03964	0.144581
$443$	−16.5437	−0.786013	−0.393006	−	0.919536i	$-0.628565\pi$
$443$	−16.5437	−0.786013	−0.393006	+	0.919536i	$0.628565\pi$
$444$	0.480548	0.0228058
$445$	−0.290484	−0.0137702
$446$	−14.5111	−0.687121
$447$	8.67418	0.410275
$448$	−4.01433	−0.189659
$449$	36.3359	1.71480	0.857399	−	0.514652i	$-0.172079\pi$
$449$	36.3359	1.71480	0.857399	+	0.514652i	$0.172079\pi$
$450$	14.9711	0.705743
$451$	12.0510	0.567458
$452$	−0.271755	−0.0127823
$453$	21.7554	1.02216
$454$	−41.2294	−1.93499
$455$	0.208851	0.00979109
$456$	0	0
$457$	26.6017	1.24438	0.622188	−	0.782868i	$-0.286244\pi$
$457$	26.6017	1.24438	0.622188	+	0.782868i	$0.286244\pi$
$458$	40.4128	1.88836
$459$	3.28025	0.153109
$460$	−0.0682299	−0.00318123
$461$	−0.0614140	−0.00286033	−0.00143017	−	0.999999i	$-0.500455\pi$
$461$	−0.0614140	−0.00286033	−0.00143017	+	0.999999i	$0.500455\pi$
$462$	−3.13499	−0.145853
$463$	−13.0276	−0.605444	−0.302722	−	0.953079i	$-0.597895\pi$
$463$	−13.0276	−0.605444	−0.302722	+	0.953079i	$0.597895\pi$
$464$	26.4521	1.22801
$465$	−0.494445	−0.0229293
$466$	25.7329	1.19205
$467$	15.5514	0.719631	0.359815	−	0.933023i	$-0.382840\pi$
$467$	15.5514	0.719631	0.359815	+	0.933023i	$0.382840\pi$
$468$	3.53373	0.163347
$469$	9.23759	0.426552
$470$	−0.159191	−0.00734291
$471$	24.7138	1.13875
$472$	−30.5376	−1.40561
$473$	3.37884	0.155359
$474$	18.3426	0.842503
$475$	0	0
$476$	0.406888	0.0186497
$477$	−13.5958	−0.622511
$478$	6.51946	0.298193
$479$	−30.0596	−1.37346	−0.686730	−	0.726913i	$-0.740955\pi$
$479$	−30.0596	−1.37346	−0.686730	+	0.726913i	$0.740955\pi$
$480$	−0.266943	−0.0121842
$481$	−2.05117	−0.0935251
$482$	−36.8414	−1.67808
$483$	1.61413	0.0734454
$484$	−5.03526	−0.228875
$485$	−0.376257	−0.0170849
$486$	25.2891	1.14714
$487$	12.4091	0.562310	0.281155	−	0.959662i	$-0.409283\pi$
$487$	12.4091	0.562310	0.281155	+	0.959662i	$0.409283\pi$
$488$	0.370154	0.0167561
$489$	−19.3931	−0.876986
$490$	0.114477	0.00517154
$491$	40.9897	1.84984	0.924919	−	0.380164i	$-0.124132\pi$
$491$	40.9897	1.84984	0.924919	+	0.380164i	$0.124132\pi$
$492$	4.67778	0.210891
$493$	3.41641	0.153868
$494$	0	0
$495$	−0.232248	−0.0104388
$496$	31.8353	1.42945
$497$	11.7888	0.528802
$498$	−11.8261	−0.529938
$499$	7.42314	0.332306	0.166153	−	0.986100i	$-0.446866\pi$
$499$	7.42314	0.332306	0.166153	+	0.986100i	$0.446866\pi$
$500$	−0.454558	−0.0203285
$501$	−3.95481	−0.176688
$502$	44.4148	1.98233
$503$	21.9943	0.980677	0.490339	−	0.871532i	$-0.336873\pi$
$503$	21.9943	0.980677	0.490339	+	0.871532i	$0.336873\pi$
$504$	−4.05743	−0.180732
$505$	0.350923	0.0156159
$506$	−4.37158	−0.194340
$507$	−4.51034	−0.200311
$508$	7.97370	0.353776
$509$	−3.42891	−0.151984	−0.0759919	−	0.997108i	$-0.524212\pi$
$509$	−3.42891	−0.151984	−0.0759919	+	0.997108i	$0.524212\pi$
$510$	−0.0775460	−0.00343380
$511$	11.2254	0.496583
$512$	−4.28328	−0.189296
$513$	0	0
$514$	20.4288	0.901077
$515$	−0.211215	−0.00930725
$516$	1.31155	0.0577378
$517$	−2.49087	−0.109548
$518$	−1.12430	−0.0493989
$519$	−11.6231	−0.510196
$520$	0.459928	0.0201692
$521$	−12.7564	−0.558868	−0.279434	−	0.960165i	$-0.590147\pi$
$521$	−12.7564	−0.558868	−0.279434	+	0.960165i	$0.590147\pi$
$522$	16.2634	0.711828
$523$	−18.8295	−0.823358	−0.411679	−	0.911329i	$-0.635057\pi$
$523$	−18.8295	−0.823358	−0.411679	+	0.911329i	$0.635057\pi$
$524$	1.93077	0.0843460
$525$	5.37413	0.234546
$526$	26.8884	1.17239
$527$	4.11169	0.179108
$528$	−9.39470	−0.408852
$529$	−20.7492	−0.902138
$530$	0.844747	0.0366935
$531$	−25.5493	−1.10874
$532$	0	0
$533$	−19.9666	−0.864849
$534$	−7.22442	−0.312631
$535$	−0.880981	−0.0380881
$536$	20.3429	0.878678
$537$	−2.22873	−0.0961770
$538$	−47.6731	−2.05533
$539$	1.79123	0.0771539
$540$	−0.236940	−0.0101963
$541$	−30.8095	−1.32461	−0.662303	−	0.749236i	$-0.730421\pi$
$541$	−30.8095	−1.32461	−0.662303	+	0.749236i	$0.730421\pi$
$542$	45.3262	1.94693
$543$	1.21493	0.0521377
$544$	2.21984	0.0951747
$545$	−0.987899	−0.0423170
$546$	5.19419	0.222291
$547$	10.3292	0.441644	0.220822	−	0.975314i	$-0.429126\pi$
$547$	10.3292	0.441644	0.220822	+	0.975314i	$0.429126\pi$
$548$	13.7933	0.589219
$549$	0.309689	0.0132172
$550$	−14.5548	−0.620621
$551$	0	0
$552$	3.55461	0.151294
$553$	−10.4804	−0.445671
$554$	10.4202	0.442710
$555$	0.0523284	0.00222122
$556$	−4.54065	−0.192566
$557$	−20.8086	−0.881689	−0.440844	−	0.897584i	$-0.645321\pi$
$557$	−20.8086	−0.881689	−0.440844	+	0.897584i	$0.645321\pi$
$558$	19.5731	0.828597
$559$	−5.59821	−0.236779
$560$	0.343056	0.0144968
$561$	−1.21337	−0.0512286
$562$	0.790604	0.0333496
$563$	−17.1580	−0.723122	−0.361561	−	0.932348i	$-0.617756\pi$
$563$	−17.1580	−0.723122	−0.361561	+	0.932348i	$0.617756\pi$
$564$	−0.966873	−0.0407127
$565$	−0.0295923	−0.00124496
$566$	−42.8554	−1.80135
$567$	0.0779737	0.00327459
$568$	25.9612	1.08931
$569$	−23.7998	−0.997738	−0.498869	−	0.866678i	$-0.666251\pi$
$569$	−23.7998	−0.997738	−0.498869	+	0.866678i	$0.666251\pi$
$570$	0	0
$571$	−10.6996	−0.447766	−0.223883	−	0.974616i	$-0.571873\pi$
$571$	−10.6996	−0.447766	−0.223883	+	0.974616i	$0.571873\pi$
$572$	−3.43549	−0.143645
$573$	−0.324314	−0.0135484
$574$	−10.9442	−0.456804
$575$	7.49393	0.312519
$576$	−7.39623	−0.308176
$577$	−21.7342	−0.904807	−0.452404	−	0.891813i	$-0.649433\pi$
$577$	−21.7342	−0.904807	−0.452404	+	0.891813i	$0.649433\pi$
$578$	−27.0096	−1.12345
$579$	3.31785	0.137885
$580$	−0.246775	−0.0102468
$581$	6.75703	0.280329
$582$	−9.35763	−0.387886
$583$	13.2178	0.547427
$584$	24.7204	1.02294
$585$	0.384799	0.0159095
$586$	−51.2072	−2.11535
$587$	26.7636	1.10465	0.552327	−	0.833628i	$-0.313740\pi$
$587$	26.7636	1.10465	0.552327	+	0.833628i	$0.313740\pi$
$588$	0.695297	0.0286735
$589$	0	0
$590$	1.58745	0.0653542
$591$	30.0392	1.23565
$592$	−3.36922	−0.138474
$593$	−33.8053	−1.38822	−0.694108	−	0.719871i	$-0.744201\pi$
$593$	−33.8053	−1.38822	−0.694108	+	0.719871i	$0.744201\pi$
$594$	−15.1811	−0.622886
$595$	0.0443073	0.00181642
$596$	5.21029	0.213422
$597$	−1.59168	−0.0651430
$598$	7.24302	0.296189
$599$	2.77537	0.113399	0.0566993	−	0.998391i	$-0.481942\pi$
$599$	2.77537	0.113399	0.0566993	+	0.998391i	$0.481942\pi$
$600$	11.8348	0.483154
$601$	37.2513	1.51951	0.759755	−	0.650209i	$-0.225319\pi$
$601$	37.2513	1.51951	0.759755	+	0.650209i	$0.225319\pi$
$602$	−3.06853	−0.125064
$603$	17.0199	0.693103
$604$	13.0677	0.531719
$605$	−0.548306	−0.0222918
$606$	8.72757	0.354533
$607$	−38.2873	−1.55403	−0.777016	−	0.629481i	$-0.783268\pi$
$607$	−38.2873	−1.55403	−0.777016	+	0.629481i	$0.783268\pi$
$608$	0	0
$609$	5.83802	0.236569
$610$	−0.0192418	−0.000779080 0
$611$	4.12699	0.166960
$612$	0.749674	0.0303038
$613$	19.1095	0.771825	0.385912	−	0.922535i	$-0.373887\pi$
$613$	19.1095	0.771825	0.385912	+	0.922535i	$0.373887\pi$
$614$	−27.9975	−1.12989
$615$	0.509379	0.0205401
$616$	3.94463	0.158933
$617$	−1.39617	−0.0562077	−0.0281038	−	0.999605i	$-0.508947\pi$
$617$	−1.39617	−0.0562077	−0.0281038	+	0.999605i	$0.508947\pi$
$618$	−5.25299	−0.211306
$619$	−36.2980	−1.45894	−0.729469	−	0.684013i	$-0.760233\pi$
$619$	−36.2980	−1.45894	−0.729469	+	0.684013i	$0.760233\pi$
$620$	−0.296997	−0.0119277
$621$	7.81636	0.313660
$622$	−46.7643	−1.87508
$623$	4.12780	0.165377
$624$	15.5656	0.623121
$625$	24.9257	0.997030
$626$	−11.4982	−0.459560
$627$	0	0
$628$	14.8448	0.592371
$629$	−0.435151	−0.0173506
$630$	0.210919	0.00840322
$631$	−16.0674	−0.639631	−0.319816	−	0.947480i	$-0.603621\pi$
$631$	−16.0674	−0.639631	−0.319816	+	0.947480i	$0.603621\pi$
$632$	−23.0797	−0.918061
$633$	−29.6778	−1.17959
$634$	−10.2830	−0.408389
$635$	0.868282	0.0344567
$636$	5.13072	0.203446
$637$	−2.96780	−0.117588
$638$	−15.8112	−0.625972
$639$	21.7205	0.859248
$640$	0.955775	0.0377803
$641$	−38.9030	−1.53658	−0.768288	−	0.640104i	$-0.778891\pi$
$641$	−38.9030	−1.53658	−0.768288	+	0.640104i	$0.778891\pi$
$642$	−21.9103	−0.864730
$643$	−15.9792	−0.630158	−0.315079	−	0.949066i	$-0.602031\pi$
$643$	−15.9792	−0.630158	−0.315079	+	0.949066i	$0.602031\pi$
$644$	0.969554	0.0382058
$645$	0.142819	0.00562350
$646$	0	0
$647$	1.82497	0.0717468	0.0358734	−	0.999356i	$-0.488579\pi$
$647$	1.82497	0.0717468	0.0358734	+	0.999356i	$0.488579\pi$
$648$	0.171712	0.00674550
$649$	24.8390	0.975015
$650$	24.1151	0.945872
$651$	7.02612	0.275375
$652$	−11.6488	−0.456202
$653$	21.7882	0.852639	0.426320	−	0.904573i	$-0.359810\pi$
$653$	21.7882	0.852639	0.426320	+	0.904573i	$0.359810\pi$
$654$	−24.5694	−0.960738
$655$	0.210247	0.00821505
$656$	−32.7969	−1.28050
$657$	20.6824	0.806896
$658$	2.26212	0.0881864
$659$	17.3650	0.676444	0.338222	−	0.941066i	$-0.390175\pi$
$659$	17.3650	0.676444	0.338222	+	0.941066i	$0.390175\pi$
$660$	0.0876446	0.00341156
$661$	−29.8564	−1.16128	−0.580639	−	0.814161i	$-0.697197\pi$
$661$	−29.8564	−1.16128	−0.580639	+	0.814161i	$0.697197\pi$
$662$	25.4467	0.989013
$663$	2.01037	0.0780762
$664$	14.8802	0.577465
$665$	0	0
$666$	−2.07148	−0.0802681
$667$	8.14081	0.315213
$668$	−2.37552	−0.0919117
$669$	−9.59740	−0.371057
$670$	−1.05749	−0.0408545
$671$	−0.301079	−0.0116230
$672$	3.79329	0.146329
$673$	−10.2499	−0.395105	−0.197553	−	0.980292i	$-0.563299\pi$
$673$	−10.2499	−0.395105	−0.197553	+	0.980292i	$0.563299\pi$
$674$	12.1922	0.469625
$675$	26.0240	1.00166
$676$	−2.70921	−0.104200
$677$	−27.8896	−1.07189	−0.535943	−	0.844254i	$-0.680044\pi$
$677$	−27.8896	−1.07189	−0.535943	+	0.844254i	$0.680044\pi$
$678$	−0.735970	−0.0282648
$679$	5.34665	0.205186
$680$	0.0975729	0.00374175
$681$	−27.2684	−1.04493
$682$	−19.0290	−0.728656
$683$	12.8899	0.493220	0.246610	−	0.969115i	$-0.420683\pi$
$683$	12.8899	0.493220	0.246610	+	0.969115i	$0.420683\pi$
$684$	0	0
$685$	1.50199	0.0573883
$686$	−1.62673	−0.0621089
$687$	26.7283	1.01975
$688$	−9.19555	−0.350577
$689$	−21.8999	−0.834320
$690$	−0.184781	−0.00703448
$691$	−7.93990	−0.302048	−0.151024	−	0.988530i	$-0.548257\pi$
$691$	−7.93990	−0.302048	−0.151024	+	0.988530i	$0.548257\pi$
$692$	−6.98159	−0.265400
$693$	3.30027	0.125367
$694$	13.8203	0.524613
$695$	−0.494446	−0.0187554
$696$	12.8564	0.487320
$697$	−4.23587	−0.160445
$698$	1.01109	0.0382703
$699$	17.0193	0.643729
$700$	3.22806	0.122009
$701$	27.2807	1.03038	0.515190	−	0.857076i	$-0.327721\pi$
$701$	27.2807	1.03038	0.515190	+	0.857076i	$0.327721\pi$
$702$	25.1527	0.949326
$703$	0	0
$704$	7.19060	0.271006
$705$	−0.105286	−0.00396530
$706$	−42.8243	−1.61171
$707$	−4.98666	−0.187543
$708$	9.64165	0.362355
$709$	−23.1636	−0.869926	−0.434963	−	0.900448i	$-0.643239\pi$
$709$	−23.1636	−0.869926	−0.434963	+	0.900448i	$0.643239\pi$
$710$	−1.34955	−0.0506478
$711$	−19.3096	−0.724168
$712$	9.09018	0.340669
$713$	9.79754	0.366921
$714$	1.10194	0.0412390
$715$	−0.374101	−0.0139906
$716$	−1.33873	−0.0500305
$717$	4.31186	0.161029
$718$	−14.2076	−0.530224
$719$	47.8513	1.78455	0.892276	−	0.451490i	$-0.149107\pi$
$719$	47.8513	1.78455	0.892276	+	0.451490i	$0.149107\pi$
$720$	0.632066	0.0235557
$721$	3.00139	0.111778
$722$	0	0
$723$	−24.3662	−0.906190
$724$	0.729769	0.0271217
$725$	27.1042	1.00663
$726$	−13.6365	−0.506099
$727$	−25.8343	−0.958142	−0.479071	−	0.877776i	$-0.659026\pi$
$727$	−25.8343	−0.958142	−0.479071	+	0.877776i	$0.659026\pi$
$728$	−6.53563	−0.242227
$729$	16.9597	0.628137
$730$	−1.28505	−0.0475619
$731$	−1.18765	−0.0439268
$732$	−0.116869	−0.00431960
$733$	25.3697	0.937053	0.468526	−	0.883450i	$-0.344785\pi$
$733$	25.3697	0.937053	0.468526	+	0.883450i	$0.344785\pi$
$734$	13.7737	0.508396
$735$	0.0757131	0.00279272
$736$	5.28954	0.194975
$737$	−16.5467	−0.609505
$738$	−20.1643	−0.742258
$739$	−34.0306	−1.25184	−0.625919	−	0.779888i	$-0.715276\pi$
$739$	−34.0306	−1.25184	−0.625919	+	0.779888i	$0.715276\pi$
$740$	0.0314319	0.00115546
$741$	0	0
$742$	−12.0039	−0.440679
$743$	−4.56048	−0.167308	−0.0836540	−	0.996495i	$-0.526659\pi$
$743$	−4.56048	−0.167308	−0.0836540	+	0.996495i	$0.526659\pi$
$744$	15.4728	0.567260
$745$	0.567365	0.0207867
$746$	−38.6345	−1.41451
$747$	12.4496	0.455505
$748$	−0.728831	−0.0266487
$749$	12.5188	0.457428
$750$	−1.23104	−0.0449512
$751$	−14.6017	−0.532822	−0.266411	−	0.963860i	$-0.585838\pi$
$751$	−14.6017	−0.532822	−0.266411	+	0.963860i	$0.585838\pi$
$752$	6.77894	0.247202
$753$	29.3752	1.07049
$754$	26.1967	0.954029
$755$	1.42299	0.0517879
$756$	3.36694	0.122455
$757$	−24.9389	−0.906420	−0.453210	−	0.891404i	$-0.649721\pi$
$757$	−24.9389	−0.906420	−0.453210	+	0.891404i	$0.649721\pi$
$758$	30.4973	1.10771
$759$	−2.89128	−0.104947
$760$	0	0
$761$	−45.2806	−1.64142	−0.820711	−	0.571344i	$-0.806422\pi$
$761$	−45.2806	−1.64142	−0.820711	+	0.571344i	$0.806422\pi$
$762$	21.5944	0.782284
$763$	14.0382	0.508215
$764$	−0.194805	−0.00704779
$765$	0.0816344	0.00295150
$766$	−21.4858	−0.776313
$767$	−41.1543	−1.48600
$768$	15.1325	0.546046
$769$	48.1115	1.73495	0.867473	−	0.497484i	$-0.165743\pi$
$769$	48.1115	1.73495	0.867473	+	0.497484i	$0.165743\pi$
$770$	−0.205055	−0.00738967
$771$	13.5113	0.486597
$772$	1.99292	0.0717267
$773$	−24.5434	−0.882765	−0.441382	−	0.897319i	$-0.645512\pi$
$773$	−24.5434	−0.882765	−0.441382	+	0.897319i	$0.645512\pi$
$774$	−5.65364	−0.203216
$775$	32.6202	1.17175
$776$	11.7743	0.422673
$777$	−0.743593	−0.0266762
$778$	15.5856	0.558772
$779$	0	0
$780$	−0.145213	−0.00519948
$781$	−21.1166	−0.755611
$782$	1.53659	0.0549484
$783$	28.2704	1.01030
$784$	−4.87486	−0.174102
$785$	1.61650	0.0576952
$786$	5.22892	0.186509
$787$	9.19502	0.327767	0.163884	−	0.986480i	$-0.447598\pi$
$787$	9.19502	0.327767	0.163884	+	0.986480i	$0.447598\pi$
$788$	18.0435	0.642775
$789$	17.7835	0.633110
$790$	1.19976	0.0426856
$791$	0.420510	0.0149516
$792$	7.26781	0.258250
$793$	0.498842	0.0177144
$794$	27.1057	0.961944
$795$	0.558701	0.0198151
$796$	−0.956066	−0.0338869
$797$	−50.7437	−1.79743	−0.898716	−	0.438530i	$-0.855499\pi$
$797$	−50.7437	−1.79743	−0.898716	+	0.438530i	$0.855499\pi$
$798$	0	0
$799$	0.875532	0.0309741
$800$	17.6111	0.622648
$801$	7.60530	0.268720
$802$	32.6877	1.15424
$803$	−20.1074	−0.709573
$804$	−6.42287	−0.226517
$805$	0.105578	0.00372113
$806$	31.5280	1.11053
$807$	−31.5301	−1.10991
$808$	−10.9815	−0.386329
$809$	−2.23136	−0.0784504	−0.0392252	−	0.999230i	$-0.512489\pi$
$809$	−2.23136	−0.0784504	−0.0392252	+	0.999230i	$0.512489\pi$
$810$	−0.00892620	−0.000313635 0
$811$	−12.3783	−0.434660	−0.217330	−	0.976098i	$-0.569735\pi$
$811$	−12.3783	−0.434660	−0.217330	+	0.976098i	$0.569735\pi$
$812$	3.50670	0.123061
$813$	29.9779	1.05137
$814$	2.01389	0.0705866
$815$	−1.26847	−0.0444327
$816$	3.30220	0.115600
$817$	0	0
$818$	−17.0566	−0.596371
$819$	−5.46804	−0.191069
$820$	0.305967	0.0106848
$821$	−45.1557	−1.57594	−0.787972	−	0.615712i	$-0.788869\pi$
$821$	−45.1557	−1.57594	−0.787972	+	0.615712i	$0.788869\pi$
$822$	37.3551	1.30291
$823$	−9.04098	−0.315149	−0.157574	−	0.987507i	$-0.550367\pi$
$823$	−9.04098	−0.315149	−0.157574	+	0.987507i	$0.550367\pi$
$824$	6.60961	0.230257
$825$	−9.62632	−0.335145
$826$	−22.5578	−0.784886
$827$	−27.1582	−0.944385	−0.472192	−	0.881496i	$-0.656537\pi$
$827$	−27.1582	−0.944385	−0.472192	+	0.881496i	$0.656537\pi$
$828$	1.78636	0.0620804
$829$	24.7728	0.860394	0.430197	−	0.902735i	$-0.358444\pi$
$829$	24.7728	0.860394	0.430197	+	0.902735i	$0.358444\pi$
$830$	−0.773525	−0.0268494
$831$	6.89171	0.239071
$832$	−11.9137	−0.413034
$833$	−0.629612	−0.0218148
$834$	−12.2970	−0.425811
$835$	−0.258678	−0.00895193
$836$	0	0
$837$	34.0237	1.17603
$838$	−21.2825	−0.735191
$839$	−31.2342	−1.07832	−0.539161	−	0.842202i	$-0.681259\pi$
$839$	−31.2342	−1.07832	−0.539161	+	0.842202i	$0.681259\pi$
$840$	0.166734	0.00575287
$841$	0.443863	0.0153056
$842$	38.5235	1.32761
$843$	0.522891	0.0180093
$844$	−17.8265	−0.613613
$845$	−0.295014	−0.0101488
$846$	4.16785	0.143294
$847$	7.79148	0.267718
$848$	−35.9725	−1.23530
$849$	−28.3438	−0.972758
$850$	5.11597	0.175476
$851$	−1.03690	−0.0355445
$852$	−8.19675	−0.280816
$853$	−30.1395	−1.03196	−0.515979	−	0.856601i	$-0.672572\pi$
$853$	−30.1395	−1.03196	−0.515979	+	0.856601i	$0.672572\pi$
$854$	0.273429	0.00935654
$855$	0	0
$856$	27.5688	0.942281
$857$	−26.1825	−0.894377	−0.447189	−	0.894440i	$-0.647575\pi$
$857$	−26.1825	−0.894377	−0.447189	+	0.894440i	$0.647575\pi$
$858$	−9.30401	−0.317634
$859$	−21.6548	−0.738854	−0.369427	−	0.929260i	$-0.620446\pi$
$859$	−21.6548	−0.738854	−0.369427	+	0.929260i	$0.620446\pi$
$860$	0.0857867	0.00292530
$861$	−7.23833	−0.246681
$862$	−12.0058	−0.408920
$863$	43.2467	1.47214	0.736068	−	0.676908i	$-0.236680\pi$
$863$	43.2467	1.47214	0.736068	+	0.676908i	$0.236680\pi$
$864$	18.3689	0.624921
$865$	−0.760247	−0.0258492
$866$	−56.3473	−1.91476
$867$	−17.8637	−0.606682
$868$	4.22035	0.143248
$869$	18.7728	0.636823
$870$	−0.668319	−0.0226581
$871$	27.4153	0.928931
$872$	30.9146	1.04690
$873$	9.85098	0.333405
$874$	0	0
$875$	0.703376	0.0237784
$876$	−7.80500	−0.263706
$877$	18.7951	0.634666	0.317333	−	0.948314i	$-0.397213\pi$
$877$	18.7951	0.634666	0.317333	+	0.948314i	$0.397213\pi$
$878$	52.5159	1.77233
$879$	−33.8676	−1.14232
$880$	−0.614494	−0.0207146
$881$	−9.14385	−0.308064	−0.154032	−	0.988066i	$-0.549226\pi$
$881$	−9.14385	−0.308064	−0.154032	+	0.988066i	$0.549226\pi$
$882$	−2.99718	−0.100920
$883$	20.6049	0.693409	0.346704	−	0.937974i	$-0.387301\pi$
$883$	20.6049	0.693409	0.346704	+	0.937974i	$0.387301\pi$
$884$	1.20756	0.0406146
$885$	1.04991	0.0352924
$886$	−26.9121	−0.904129
$887$	29.0240	0.974531	0.487265	−	0.873254i	$-0.337994\pi$
$887$	29.0240	0.974531	0.487265	+	0.873254i	$0.337994\pi$
$888$	−1.63753	−0.0549518
$889$	−12.3384	−0.413816
$890$	−0.472538	−0.0158395
$891$	−0.139669	−0.00467909
$892$	−5.76484	−0.193021
$893$	0	0
$894$	14.1106	0.471927
$895$	−0.145778	−0.00487283
$896$	−13.5817	−0.453732
$897$	4.79041	0.159947
$898$	59.1088	1.97248
$899$	35.4360	1.18186
$900$	5.94756	0.198252
$901$	−4.64602	−0.154781
$902$	19.6037	0.652731
$903$	−2.02947	−0.0675367
$904$	0.926040	0.0307996
$905$	0.0794669	0.00264157
$906$	35.3902	1.17576
$907$	16.4653	0.546722	0.273361	−	0.961912i	$-0.411865\pi$
$907$	16.4653	0.546722	0.273361	+	0.961912i	$0.411865\pi$
$908$	−16.3792	−0.543563
$909$	−9.18771	−0.304737
$910$	0.339744	0.0112624
$911$	28.9644	0.959634	0.479817	−	0.877368i	$-0.340703\pi$
$911$	28.9644	0.959634	0.479817	+	0.877368i	$0.340703\pi$
$912$	0	0
$913$	−12.1034	−0.400565
$914$	43.2738	1.43137
$915$	−0.0127262	−0.000420716 0
$916$	16.0548	0.530465
$917$	−2.98764	−0.0986605
$918$	5.33609	0.176117
$919$	−21.6498	−0.714162	−0.357081	−	0.934073i	$-0.616228\pi$
$919$	−21.6498	−0.714162	−0.357081	+	0.934073i	$0.616228\pi$
$920$	0.232502	0.00766536
$921$	−18.5170	−0.610157
$922$	−0.0999040	−0.00329016
$923$	34.9869	1.15161
$924$	−1.24544	−0.0409719
$925$	−3.45228	−0.113510
$926$	−21.1924	−0.696425
$927$	5.52993	0.181627
$928$	19.1313	0.628017
$929$	17.2379	0.565558	0.282779	−	0.959185i	$-0.408744\pi$
$929$	17.2379	0.565558	0.282779	+	0.959185i	$0.408744\pi$
$930$	−0.804329	−0.0263750
$931$	0	0
$932$	10.2229	0.334863
$933$	−30.9291	−1.01257
$934$	25.2979	0.827771
$935$	−0.0793648	−0.00259551
$936$	−12.0416	−0.393593
$937$	13.8094	0.451133	0.225566	−	0.974228i	$-0.427577\pi$
$937$	13.8094	0.451133	0.225566	+	0.974228i	$0.427577\pi$
$938$	15.0271	0.490651
$939$	−7.60470	−0.248170
$940$	−0.0632417	−0.00206272
$941$	−43.5822	−1.42074	−0.710369	−	0.703829i	$-0.751472\pi$
$941$	−43.5822	−1.42074	−0.710369	+	0.703829i	$0.751472\pi$
$942$	40.2028	1.30988
$943$	−10.0935	−0.328688
$944$	−67.5995	−2.20018
$945$	0.366638	0.0119267
$946$	5.49646	0.178705
$947$	15.0471	0.488965	0.244482	−	0.969654i	$-0.421382\pi$
$947$	15.0471	0.488965	0.244482	+	0.969654i	$0.421382\pi$
$948$	7.28697	0.236670
$949$	33.3148	1.08144
$950$	0	0
$951$	−6.80098	−0.220537
$952$	−1.38652	−0.0449374
$953$	−36.5243	−1.18314	−0.591569	−	0.806255i	$-0.701491\pi$
$953$	−36.5243	−1.18314	−0.591569	+	0.806255i	$0.701491\pi$
$954$	−22.1168	−0.716057
$955$	−0.0212129	−0.000686434 0
$956$	2.58999	0.0837662
$957$	−10.4573	−0.338035
$958$	−48.8989	−1.57985
$959$	−21.3435	−0.689218
$960$	0.303937	0.00980953
$961$	11.6476	0.375728
$962$	−3.33669	−0.107579
$963$	23.0654	0.743273
$964$	−14.6360	−0.471393
$965$	0.217015	0.00698597
$966$	2.62575	0.0844822
$967$	15.9234	0.512061	0.256030	−	0.966669i	$-0.417585\pi$
$967$	15.9234	0.512061	0.256030	+	0.966669i	$0.417585\pi$
$968$	17.1583	0.551488
$969$	0	0
$970$	−0.612069	−0.0196523
$971$	−0.945739	−0.0303502	−0.0151751	−	0.999885i	$-0.504831\pi$
$971$	−0.945739	−0.0303502	−0.0151751	+	0.999885i	$0.504831\pi$
$972$	10.0466	0.322245
$973$	7.02613	0.225247
$974$	20.1863	0.646809
$975$	15.9493	0.510787
$976$	0.819390	0.0262280
$977$	−2.65305	−0.0848785	−0.0424392	−	0.999099i	$-0.513513\pi$
$977$	−2.65305	−0.0848785	−0.0424392	+	0.999099i	$0.513513\pi$
$978$	−31.5473	−1.00877
$979$	−7.39386	−0.236309
$980$	0.0454783	0.00145275
$981$	25.8647	0.825797
$982$	66.6792	2.12782
$983$	−33.5822	−1.07111	−0.535553	−	0.844501i	$-0.679897\pi$
$983$	−33.5822	−1.07111	−0.535553	+	0.844501i	$0.679897\pi$
$984$	−15.9401	−0.508153
$985$	1.96482	0.0626044
$986$	5.55758	0.176990
$987$	1.49612	0.0476221
$988$	0	0
$989$	−2.82999	−0.0899885
$990$	−0.377805	−0.0120074
$991$	−31.5984	−1.00376	−0.501878	−	0.864939i	$-0.667357\pi$
$991$	−31.5984	−1.00376	−0.501878	+	0.864939i	$0.667357\pi$
$992$	23.0247	0.731037
$993$	16.8300	0.534083
$994$	19.1773	0.608266
$995$	−0.104109	−0.00330048
$996$	−4.69814	−0.148866
$997$	−34.0716	−1.07906	−0.539529	−	0.841967i	$-0.681398\pi$
$997$	−34.0716	−1.07906	−0.539529	+	0.841967i	$0.681398\pi$
$998$	12.0755	0.382242
$999$	−3.60082	−0.113925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2527.2.a.r.1.11		15
19.6	even	9		133.2.v.b.36.4	✓	30
19.16	even	9		133.2.v.b.85.4	yes	30
19.18	odd	2		2527.2.a.s.1.5		15
133.6	odd	18		931.2.w.b.834.4		30
133.16	even	9		931.2.x.e.655.4		30
133.25	even	9		931.2.x.e.226.4		30
133.44	even	9		931.2.v.d.606.2		30
133.54	odd	18		931.2.x.d.655.4		30
133.73	odd	18		931.2.v.e.275.2		30
133.82	odd	18		931.2.v.e.606.2		30
133.101	odd	18		931.2.x.d.226.4		30
133.111	odd	18		931.2.w.b.883.4		30
133.130	even	9		931.2.v.d.275.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.v.b.36.4	✓	30	19.6	even	9
133.2.v.b.85.4	yes	30	19.16	even	9
931.2.v.d.275.2		30	133.130	even	9
931.2.v.d.606.2		30	133.44	even	9
931.2.v.e.275.2		30	133.73	odd	18
931.2.v.e.606.2		30	133.82	odd	18
931.2.w.b.834.4		30	133.6	odd	18
931.2.w.b.883.4		30	133.111	odd	18
931.2.x.d.226.4		30	133.101	odd	18
931.2.x.d.655.4		30	133.54	odd	18
931.2.x.e.226.4		30	133.25	even	9
931.2.x.e.655.4		30	133.16	even	9
2527.2.a.r.1.11		15	1.1	even	1	trivial
2527.2.a.s.1.5		15	19.18	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:	\( N \)	\(=\)	\( 2527 = 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2527.a (trivial)

\(f(q)\)	\(=\)	\(q+1.62673 q^{2} +1.07589 q^{3} +0.646252 q^{4} +0.0703725 q^{5} +1.75018 q^{6} -1.00000 q^{7} -2.20218 q^{8} -1.84246 q^{9} +O(q^{10})\)	\(q+1.62673 q^{2} +1.07589 q^{3} +0.646252 q^{4} +0.0703725 q^{5} +1.75018 q^{6} -1.00000 q^{7} -2.20218 q^{8} -1.84246 q^{9} +0.114477 q^{10} +1.79123 q^{11} +0.695297 q^{12} -2.96780 q^{13} -1.62673 q^{14} +0.0757131 q^{15} -4.87486 q^{16} -0.629612 q^{17} -2.99718 q^{18} +0.0454783 q^{20} -1.07589 q^{21} +2.91385 q^{22} -1.50027 q^{23} -2.36931 q^{24} -4.99505 q^{25} -4.82780 q^{26} -5.20996 q^{27} -0.646252 q^{28} -5.42622 q^{29} +0.123165 q^{30} -6.53051 q^{31} -3.52572 q^{32} +1.92717 q^{33} -1.02421 q^{34} -0.0703725 q^{35} -1.19069 q^{36} +0.691141 q^{37} -3.19303 q^{39} -0.154973 q^{40} +6.72775 q^{41} -1.75018 q^{42} +1.88632 q^{43} +1.15759 q^{44} -0.129658 q^{45} -2.44054 q^{46} -1.39059 q^{47} -5.24482 q^{48} +1.00000 q^{49} -8.12560 q^{50} -0.677394 q^{51} -1.91794 q^{52} +7.37918 q^{53} -8.47520 q^{54} +0.126054 q^{55} +2.20218 q^{56} -8.82700 q^{58} +13.8670 q^{59} +0.0489297 q^{60} -0.168085 q^{61} -10.6234 q^{62} +1.84246 q^{63} +4.01433 q^{64} -0.208851 q^{65} +3.13499 q^{66} -9.23759 q^{67} -0.406888 q^{68} -1.61413 q^{69} -0.114477 q^{70} -11.7888 q^{71} +4.05743 q^{72} -11.2254 q^{73} +1.12430 q^{74} -5.37413 q^{75} -1.79123 q^{77} -5.19419 q^{78} +10.4804 q^{79} -0.343056 q^{80} -0.0779737 q^{81} +10.9442 q^{82} -6.75703 q^{83} -0.695297 q^{84} -0.0443073 q^{85} +3.06853 q^{86} -5.83802 q^{87} -3.94463 q^{88} -4.12780 q^{89} -0.210919 q^{90} +2.96780 q^{91} -0.969554 q^{92} -7.02612 q^{93} -2.26212 q^{94} -3.79329 q^{96} -5.34665 q^{97} +1.62673 q^{98} -3.30027 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 3 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{7} - 9 q^{8} + 21 q^{9}+O(q^{10}) \) 15 * q - 3 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^7 - 9 * q^8 + 21 * q^9	\( 15 q - 3 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{7} - 9 q^{8} + 21 q^{9} - 6 q^{10} - 18 q^{12} - 18 q^{13} + 3 q^{14} + 12 q^{15} - 9 q^{16} - 9 q^{17} - 15 q^{18} - 15 q^{20} + 6 q^{21} - 9 q^{22} - 6 q^{23} + 18 q^{24} + 21 q^{25} + 45 q^{26} - 27 q^{27} - 15 q^{28} - 9 q^{29} - 21 q^{30} - 12 q^{31} - 36 q^{32} - 57 q^{33} - 3 q^{34} + 57 q^{36} - 18 q^{37} - 12 q^{39} - 15 q^{40} - 42 q^{41} - 12 q^{43} + 51 q^{44} - 27 q^{45} - 6 q^{46} - 3 q^{47} - 42 q^{48} + 15 q^{49} + 3 q^{50} + 6 q^{51} - 36 q^{52} - 33 q^{53} - 45 q^{54} + 6 q^{55} + 9 q^{56} - 30 q^{58} - 18 q^{59} + 18 q^{60} - 6 q^{61} + 12 q^{62} - 21 q^{63} - 3 q^{64} - 45 q^{65} + 33 q^{66} - 24 q^{67} - 51 q^{68} - 15 q^{69} + 6 q^{70} + 6 q^{71} + 9 q^{72} - 3 q^{73} - 9 q^{74} - 72 q^{75} - 27 q^{78} + 60 q^{79} + 18 q^{80} + 27 q^{81} + 36 q^{82} - 12 q^{83} + 18 q^{84} - 27 q^{85} - 51 q^{86} - 24 q^{87} - 36 q^{88} - 72 q^{89} + 3 q^{90} + 18 q^{91} - 60 q^{92} + 60 q^{93} - 21 q^{94} + 33 q^{96} - 39 q^{97} - 3 q^{98} + 54 q^{99}+O(q^{100}) \) 15 * q - 3 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^7 - 9 * q^8 + 21 * q^9 - 6 * q^10 - 18 * q^12 - 18 * q^13 + 3 * q^14 + 12 * q^15 - 9 * q^16 - 9 * q^17 - 15 * q^18 - 15 * q^20 + 6 * q^21 - 9 * q^22 - 6 * q^23 + 18 * q^24 + 21 * q^25 + 45 * q^26 - 27 * q^27 - 15 * q^28 - 9 * q^29 - 21 * q^30 - 12 * q^31 - 36 * q^32 - 57 * q^33 - 3 * q^34 + 57 * q^36 - 18 * q^37 - 12 * q^39 - 15 * q^40 - 42 * q^41 - 12 * q^43 + 51 * q^44 - 27 * q^45 - 6 * q^46 - 3 * q^47 - 42 * q^48 + 15 * q^49 + 3 * q^50 + 6 * q^51 - 36 * q^52 - 33 * q^53 - 45 * q^54 + 6 * q^55 + 9 * q^56 - 30 * q^58 - 18 * q^59 + 18 * q^60 - 6 * q^61 + 12 * q^62 - 21 * q^63 - 3 * q^64 - 45 * q^65 + 33 * q^66 - 24 * q^67 - 51 * q^68 - 15 * q^69 + 6 * q^70 + 6 * q^71 + 9 * q^72 - 3 * q^73 - 9 * q^74 - 72 * q^75 - 27 * q^78 + 60 * q^79 + 18 * q^80 + 27 * q^81 + 36 * q^82 - 12 * q^83 + 18 * q^84 - 27 * q^85 - 51 * q^86 - 24 * q^87 - 36 * q^88 - 72 * q^89 + 3 * q^90 + 18 * q^91 - 60 * q^92 + 60 * q^93 - 21 * q^94 + 33 * q^96 - 39 * q^97 - 3 * q^98 + 54 * q^99

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