LMFDB - Embedded newform 3750.2.c.b.1249.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3750,2,Mod(1249,3750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3750, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("3750.1249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3750 = 2 \cdot 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3750.c (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$29.9439007580$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1249.1
Root			$-1.61803i$ of defining polynomial
Character	$\chi$	$=$	3750.1249
Dual form			3750.2.c.b.1249.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -2.61803i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -2.61803i q^{7} +1.00000i q^{8} -1.00000 q^{9} +3.61803 q^{11} +1.00000i q^{12} -6.47214i q^{13} -2.61803 q^{14} +1.00000 q^{16} -1.23607i q^{17} +1.00000i q^{18} +5.70820 q^{19} -2.61803 q^{21} -3.61803i q^{22} +4.47214i q^{23} +1.00000 q^{24} -6.47214 q^{26} +1.00000i q^{27} +2.61803i q^{28} -8.47214 q^{29} +6.61803 q^{31} -1.00000i q^{32} -3.61803i q^{33} -1.23607 q^{34} +1.00000 q^{36} -8.00000i q^{37} -5.70820i q^{38} -6.47214 q^{39} +5.70820 q^{41} +2.61803i q^{42} -7.70820i q^{43} -3.61803 q^{44} +4.47214 q^{46} -1.70820i q^{47} -1.00000i q^{48} +0.145898 q^{49} -1.23607 q^{51} +6.47214i q^{52} -2.09017i q^{53} +1.00000 q^{54} +2.61803 q^{56} -5.70820i q^{57} +8.47214i q^{58} +3.61803 q^{59} +2.76393 q^{61} -6.61803i q^{62} +2.61803i q^{63} -1.00000 q^{64} -3.61803 q^{66} +1.52786i q^{67} +1.23607i q^{68} +4.47214 q^{69} +5.52786 q^{71} -1.00000i q^{72} +3.52786i q^{73} -8.00000 q^{74} -5.70820 q^{76} -9.47214i q^{77} +6.47214i q^{78} +5.61803 q^{79} +1.00000 q^{81} -5.70820i q^{82} +2.14590i q^{83} +2.61803 q^{84} -7.70820 q^{86} +8.47214i q^{87} +3.61803i q^{88} -3.52786 q^{89} -16.9443 q^{91} -4.47214i q^{92} -6.61803i q^{93} -1.70820 q^{94} -1.00000 q^{96} +3.38197i q^{97} -0.145898i q^{98} -3.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 10 q^{11} - 6 q^{14} + 4 q^{16} - 4 q^{19} - 6 q^{21} + 4 q^{24} - 8 q^{26} - 16 q^{29} + 22 q^{31} + 4 q^{34} + 4 q^{36} - 8 q^{39} - 4 q^{41} - 10 q^{44} + 14 q^{49} + 4 q^{51} + 4 q^{54} + 6 q^{56} + 10 q^{59} + 20 q^{61} - 4 q^{64} - 10 q^{66} + 40 q^{71} - 32 q^{74} + 4 q^{76} + 18 q^{79} + 4 q^{81} + 6 q^{84} - 4 q^{86} - 32 q^{89} - 32 q^{91} + 20 q^{94} - 4 q^{96} - 10 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 10 * q^11 - 6 * q^14 + 4 * q^16 - 4 * q^19 - 6 * q^21 + 4 * q^24 - 8 * q^26 - 16 * q^29 + 22 * q^31 + 4 * q^34 + 4 * q^36 - 8 * q^39 - 4 * q^41 - 10 * q^44 + 14 * q^49 + 4 * q^51 + 4 * q^54 + 6 * q^56 + 10 * q^59 + 20 * q^61 - 4 * q^64 - 10 * q^66 + 40 * q^71 - 32 * q^74 + 4 * q^76 + 18 * q^79 + 4 * q^81 + 6 * q^84 - 4 * q^86 - 32 * q^89 - 32 * q^91 + 20 * q^94 - 4 * q^96 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3750\mathbb{Z}\right)^\times$.

$n$	$2501$	$3127$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	− 2.61803i	− 0.989524i	−0.869029	−	0.494762i	$-0.835255\pi$
$7$	− 2.61803i	− 0.989524i	0.869029	−	0.494762i	$-0.164745\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	3.61803	1.09088	0.545439	−	0.838150i	$-0.316363\pi$
$11$	3.61803	1.09088	0.545439	+	0.838150i	$0.316363\pi$
$12$	1.00000i	0.288675i
$13$	− 6.47214i	− 1.79505i	−0.440966	−	0.897524i	$-0.645364\pi$
$13$	− 6.47214i	− 1.79505i	0.440966	−	0.897524i	$-0.354636\pi$
$14$	−2.61803	−0.699699
$15$	0	0
$16$	1.00000	0.250000
$17$	− 1.23607i	− 0.299791i	−0.988702	−	0.149895i	$-0.952106\pi$
$17$	− 1.23607i	− 0.299791i	0.988702	−	0.149895i	$-0.0478936\pi$
$18$	1.00000i	0.235702i
$19$	5.70820	1.30955	0.654776	−	0.755823i	$-0.272763\pi$
$19$	5.70820	1.30955	0.654776	+	0.755823i	$0.272763\pi$
$20$	0	0
$21$	−2.61803	−0.571302
$22$	− 3.61803i	− 0.771367i
$23$	4.47214i	0.932505i	0.884652	+	0.466252i	$0.154396\pi$
$23$	4.47214i	0.932505i	−0.884652	+	0.466252i	$0.845604\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−6.47214	−1.26929
$27$	1.00000i	0.192450i
$28$	2.61803i	0.494762i
$29$	−8.47214	−1.57324	−0.786618	−	0.617440i	$-0.788170\pi$
$29$	−8.47214	−1.57324	−0.786618	+	0.617440i	$0.788170\pi$
$30$	0	0
$31$	6.61803	1.18863	0.594317	−	0.804231i	$-0.297422\pi$
$31$	6.61803	1.18863	0.594317	+	0.804231i	$0.297422\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 3.61803i	− 0.629819i
$34$	−1.23607	−0.211984
$35$	0	0
$36$	1.00000	0.166667
$37$	− 8.00000i	− 1.31519i	−0.753371	−	0.657596i	$-0.771573\pi$
$37$	− 8.00000i	− 1.31519i	0.753371	−	0.657596i	$-0.228427\pi$
$38$	− 5.70820i	− 0.925993i
$39$	−6.47214	−1.03637
$40$	0	0
$41$	5.70820	0.891472	0.445736	−	0.895165i	$-0.352942\pi$
$41$	5.70820	0.891472	0.445736	+	0.895165i	$0.352942\pi$
$42$	2.61803i	0.403971i
$43$	− 7.70820i	− 1.17549i	−0.809046	−	0.587745i	$-0.800016\pi$
$43$	− 7.70820i	− 1.17549i	0.809046	−	0.587745i	$-0.199984\pi$
$44$	−3.61803	−0.545439
$45$	0	0
$46$	4.47214	0.659380
$47$	− 1.70820i	− 0.249167i	−0.992209	−	0.124584i	$-0.960241\pi$
$47$	− 1.70820i	− 0.249167i	0.992209	−	0.124584i	$-0.0397595\pi$
$48$	− 1.00000i	− 0.144338i
$49$	0.145898	0.0208426
$50$	0	0
$51$	−1.23607	−0.173084
$52$	6.47214i	0.897524i
$53$	− 2.09017i	− 0.287107i	−0.989643	−	0.143553i	$-0.954147\pi$
$53$	− 2.09017i	− 0.287107i	0.989643	−	0.143553i	$-0.0458529\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	2.61803	0.349850
$57$	− 5.70820i	− 0.756070i
$58$	8.47214i	1.11245i
$59$	3.61803	0.471028	0.235514	−	0.971871i	$-0.424323\pi$
$59$	3.61803	0.471028	0.235514	+	0.971871i	$0.424323\pi$
$60$	0	0
$61$	2.76393	0.353885	0.176943	−	0.984221i	$-0.443379\pi$
$61$	2.76393	0.353885	0.176943	+	0.984221i	$0.443379\pi$
$62$	− 6.61803i	− 0.840491i
$63$	2.61803i	0.329841i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−3.61803	−0.445349
$67$	1.52786i	0.186658i	0.995635	+	0.0933292i	$0.0297509\pi$
$67$	1.52786i	0.186658i	−0.995635	+	0.0933292i	$0.970249\pi$
$68$	1.23607i	0.149895i
$69$	4.47214	0.538382
$70$	0	0
$71$	5.52786	0.656037	0.328018	−	0.944671i	$-0.393619\pi$
$71$	5.52786	0.656037	0.328018	+	0.944671i	$0.393619\pi$
$72$	− 1.00000i	− 0.117851i
$73$	3.52786i	0.412905i	0.978457	+	0.206453i	$0.0661919\pi$
$73$	3.52786i	0.412905i	−0.978457	+	0.206453i	$0.933808\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	−5.70820	−0.654776
$77$	− 9.47214i	− 1.07945i
$78$	6.47214i	0.732825i
$79$	5.61803	0.632078	0.316039	−	0.948746i	$-0.397647\pi$
$79$	5.61803	0.632078	0.316039	+	0.948746i	$0.397647\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 5.70820i	− 0.630366i
$83$	2.14590i	0.235543i	0.993041	+	0.117771i	$0.0375750\pi$
$83$	2.14590i	0.235543i	−0.993041	+	0.117771i	$0.962425\pi$
$84$	2.61803	0.285651
$85$	0	0
$86$	−7.70820	−0.831197
$87$	8.47214i	0.908308i
$88$	3.61803i	0.385684i
$89$	−3.52786	−0.373953	−0.186976	−	0.982364i	$-0.559869\pi$
$89$	−3.52786	−0.373953	−0.186976	+	0.982364i	$0.559869\pi$
$90$	0	0
$91$	−16.9443	−1.77624
$92$	− 4.47214i	− 0.466252i
$93$	− 6.61803i	− 0.686258i
$94$	−1.70820	−0.176188
$95$	0	0
$96$	−1.00000	−0.102062
$97$	3.38197i	0.343387i	0.985150	+	0.171693i	$0.0549238\pi$
$97$	3.38197i	0.343387i	−0.985150	+	0.171693i	$0.945076\pi$
$98$	− 0.145898i	− 0.0147379i
$99$	−3.61803	−0.363626
$100$	0	0
$101$	4.38197	0.436022	0.218011	−	0.975946i	$-0.430043\pi$
$101$	4.38197	0.436022	0.218011	+	0.975946i	$0.430043\pi$
$102$	1.23607i	0.122389i
$103$	14.3262i	1.41161i	0.708408	+	0.705803i	$0.249414\pi$
$103$	14.3262i	1.41161i	−0.708408	+	0.705803i	$0.750586\pi$
$104$	6.47214	0.634645
$105$	0	0
$106$	−2.09017	−0.203015
$107$	11.6180i	1.12316i	0.827423	+	0.561579i	$0.189806\pi$
$107$	11.6180i	1.12316i	−0.827423	+	0.561579i	$0.810194\pi$
$108$	− 1.00000i	− 0.0962250i
$109$	−17.2361	−1.65092	−0.825458	−	0.564464i	$-0.809083\pi$
$109$	−17.2361	−1.65092	−0.825458	+	0.564464i	$0.809083\pi$
$110$	0	0
$111$	−8.00000	−0.759326
$112$	− 2.61803i	− 0.247381i
$113$	− 19.2361i	− 1.80958i	−0.425861	−	0.904789i	$-0.640029\pi$
$113$	− 19.2361i	− 1.80958i	0.425861	−	0.904789i	$-0.359971\pi$
$114$	−5.70820	−0.534622
$115$	0	0
$116$	8.47214	0.786618
$117$	6.47214i	0.598349i
$118$	− 3.61803i	− 0.333067i
$119$	−3.23607	−0.296650
$120$	0	0
$121$	2.09017	0.190015
$122$	− 2.76393i	− 0.250235i
$123$	− 5.70820i	− 0.514691i
$124$	−6.61803	−0.594317
$125$	0	0
$126$	2.61803	0.233233
$127$	− 13.6180i	− 1.20841i	−0.796831	−	0.604203i	$-0.793492\pi$
$127$	− 13.6180i	− 1.20841i	0.796831	−	0.604203i	$-0.206508\pi$
$128$	1.00000i	0.0883883i
$129$	−7.70820	−0.678670
$130$	0	0
$131$	−17.8885	−1.56293	−0.781465	−	0.623949i	$-0.785527\pi$
$131$	−17.8885	−1.56293	−0.781465	+	0.623949i	$0.785527\pi$
$132$	3.61803i	0.314909i
$133$	− 14.9443i	− 1.29583i
$134$	1.52786	0.131987
$135$	0	0
$136$	1.23607	0.105992
$137$	12.1803i	1.04064i	0.853972	+	0.520318i	$0.174187\pi$
$137$	12.1803i	1.04064i	−0.853972	+	0.520318i	$0.825813\pi$
$138$	− 4.47214i	− 0.380693i
$139$	−10.4721	−0.888235	−0.444117	−	0.895969i	$-0.646483\pi$
$139$	−10.4721	−0.888235	−0.444117	+	0.895969i	$0.646483\pi$
$140$	0	0
$141$	−1.70820	−0.143857
$142$	− 5.52786i	− 0.463888i
$143$	− 23.4164i	− 1.95818i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	3.52786	0.291968
$147$	− 0.145898i	− 0.0120335i
$148$	8.00000i	0.657596i
$149$	−22.0902	−1.80970	−0.904849	−	0.425733i	$-0.860016\pi$
$149$	−22.0902	−1.80970	−0.904849	+	0.425733i	$0.860016\pi$
$150$	0	0
$151$	18.3262	1.49137	0.745684	−	0.666300i	$-0.232123\pi$
$151$	18.3262	1.49137	0.745684	+	0.666300i	$0.232123\pi$
$152$	5.70820i	0.462996i
$153$	1.23607i	0.0999302i
$154$	−9.47214	−0.763286
$155$	0	0
$156$	6.47214	0.518186
$157$	− 8.65248i	− 0.690543i	−0.938503	−	0.345271i	$-0.887787\pi$
$157$	− 8.65248i	− 0.690543i	0.938503	−	0.345271i	$-0.112213\pi$
$158$	− 5.61803i	− 0.446947i
$159$	−2.09017	−0.165761
$160$	0	0
$161$	11.7082	0.922736
$162$	− 1.00000i	− 0.0785674i
$163$	− 0.472136i	− 0.0369805i	−0.999829	−	0.0184903i	$-0.994114\pi$
$163$	− 0.472136i	− 0.0369805i	0.999829	−	0.0184903i	$-0.00588597\pi$
$164$	−5.70820	−0.445736
$165$	0	0
$166$	2.14590	0.166554
$167$	− 11.7082i	− 0.906008i	−0.891508	−	0.453004i	$-0.850352\pi$
$167$	− 11.7082i	− 0.906008i	0.891508	−	0.453004i	$-0.149648\pi$
$168$	− 2.61803i	− 0.201986i
$169$	−28.8885	−2.22220
$170$	0	0
$171$	−5.70820	−0.436517
$172$	7.70820i	0.587745i
$173$	5.09017i	0.386998i	0.981100	+	0.193499i	$0.0619837\pi$
$173$	5.09017i	0.386998i	−0.981100	+	0.193499i	$0.938016\pi$
$174$	8.47214	0.642271
$175$	0	0
$176$	3.61803	0.272720
$177$	− 3.61803i	− 0.271948i
$178$	3.52786i	0.264425i
$179$	−9.85410	−0.736530	−0.368265	−	0.929721i	$-0.620048\pi$
$179$	−9.85410	−0.736530	−0.368265	+	0.929721i	$0.620048\pi$
$180$	0	0
$181$	−6.65248	−0.494475	−0.247237	−	0.968955i	$-0.579523\pi$
$181$	−6.65248	−0.494475	−0.247237	+	0.968955i	$0.579523\pi$
$182$	16.9443i	1.25599i
$183$	− 2.76393i	− 0.204316i
$184$	−4.47214	−0.329690
$185$	0	0
$186$	−6.61803	−0.485258
$187$	− 4.47214i	− 0.327035i
$188$	1.70820i	0.124584i
$189$	2.61803	0.190434
$190$	0	0
$191$	4.29180	0.310543	0.155272	−	0.987872i	$-0.450375\pi$
$191$	4.29180	0.310543	0.155272	+	0.987872i	$0.450375\pi$
$192$	1.00000i	0.0721688i
$193$	17.8541i	1.28517i	0.766216	+	0.642583i	$0.222137\pi$
$193$	17.8541i	1.28517i	−0.766216	+	0.642583i	$0.777863\pi$
$194$	3.38197	0.242811
$195$	0	0
$196$	−0.145898	−0.0104213
$197$	17.0902i	1.21762i	0.793314	+	0.608812i	$0.208354\pi$
$197$	17.0902i	1.21762i	−0.793314	+	0.608812i	$0.791646\pi$
$198$	3.61803i	0.257122i
$199$	−19.5066	−1.38278	−0.691392	−	0.722480i	$-0.743002\pi$
$199$	−19.5066	−1.38278	−0.691392	+	0.722480i	$0.743002\pi$
$200$	0	0
$201$	1.52786	0.107767
$202$	− 4.38197i	− 0.308314i
$203$	22.1803i	1.55675i
$204$	1.23607	0.0865421
$205$	0	0
$206$	14.3262	0.998156
$207$	− 4.47214i	− 0.310835i
$208$	− 6.47214i	− 0.448762i
$209$	20.6525	1.42856
$210$	0	0
$211$	−3.41641	−0.235195	−0.117598	−	0.993061i	$-0.537519\pi$
$211$	−3.41641	−0.235195	−0.117598	+	0.993061i	$0.537519\pi$
$212$	2.09017i	0.143553i
$213$	− 5.52786i	− 0.378763i
$214$	11.6180	0.794192
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	− 17.3262i	− 1.17618i
$218$	17.2361i	1.16737i
$219$	3.52786	0.238391
$220$	0	0
$221$	−8.00000	−0.538138
$222$	8.00000i	0.536925i
$223$	− 8.09017i	− 0.541758i	−0.962613	−	0.270879i	$-0.912686\pi$
$223$	− 8.09017i	− 0.541758i	0.962613	−	0.270879i	$-0.0873143\pi$
$224$	−2.61803	−0.174925
$225$	0	0
$226$	−19.2361	−1.27956
$227$	22.2705i	1.47815i	0.673626	+	0.739073i	$0.264736\pi$
$227$	22.2705i	1.47815i	−0.673626	+	0.739073i	$0.735264\pi$
$228$	5.70820i	0.378035i
$229$	5.52786	0.365292	0.182646	−	0.983179i	$-0.441534\pi$
$229$	5.52786	0.365292	0.182646	+	0.983179i	$0.441534\pi$
$230$	0	0
$231$	−9.47214	−0.623221
$232$	− 8.47214i	− 0.556223i
$233$	18.6525i	1.22196i	0.791644	+	0.610982i	$0.209225\pi$
$233$	18.6525i	1.22196i	−0.791644	+	0.610982i	$0.790775\pi$
$234$	6.47214	0.423097
$235$	0	0
$236$	−3.61803	−0.235514
$237$	− 5.61803i	− 0.364931i
$238$	3.23607i	0.209763i
$239$	−12.2918	−0.795090	−0.397545	−	0.917583i	$-0.630138\pi$
$239$	−12.2918	−0.795090	−0.397545	+	0.917583i	$0.630138\pi$
$240$	0	0
$241$	9.56231	0.615962	0.307981	−	0.951392i	$-0.400347\pi$
$241$	9.56231	0.615962	0.307981	+	0.951392i	$0.400347\pi$
$242$	− 2.09017i	− 0.134361i
$243$	− 1.00000i	− 0.0641500i
$244$	−2.76393	−0.176943
$245$	0	0
$246$	−5.70820	−0.363942
$247$	− 36.9443i	− 2.35071i
$248$	6.61803i	0.420246i
$249$	2.14590	0.135991
$250$	0	0
$251$	13.5623	0.856045	0.428023	−	0.903768i	$-0.359210\pi$
$251$	13.5623	0.856045	0.428023	+	0.903768i	$0.359210\pi$
$252$	− 2.61803i	− 0.164921i
$253$	16.1803i	1.01725i
$254$	−13.6180	−0.854471
$255$	0	0
$256$	1.00000	0.0625000
$257$	22.0000i	1.37232i	0.727450	+	0.686161i	$0.240706\pi$
$257$	22.0000i	1.37232i	−0.727450	+	0.686161i	$0.759294\pi$
$258$	7.70820i	0.479892i
$259$	−20.9443	−1.30141
$260$	0	0
$261$	8.47214	0.524412
$262$	17.8885i	1.10516i
$263$	− 11.7082i	− 0.721959i	−0.932574	−	0.360979i	$-0.882442\pi$
$263$	− 11.7082i	− 0.721959i	0.932574	−	0.360979i	$-0.117558\pi$
$264$	3.61803	0.222675
$265$	0	0
$266$	−14.9443	−0.916292
$267$	3.52786i	0.215902i
$268$	− 1.52786i	− 0.0933292i
$269$	9.09017	0.554237	0.277119	−	0.960836i	$-0.410620\pi$
$269$	9.09017	0.554237	0.277119	+	0.960836i	$0.410620\pi$
$270$	0	0
$271$	−18.0344	−1.09551	−0.547757	−	0.836637i	$-0.684518\pi$
$271$	−18.0344	−1.09551	−0.547757	+	0.836637i	$0.684518\pi$
$272$	− 1.23607i	− 0.0749476i
$273$	16.9443i	1.02551i
$274$	12.1803	0.735841
$275$	0	0
$276$	−4.47214	−0.269191
$277$	− 16.9443i	− 1.01808i	−0.860742	−	0.509041i	$-0.830000\pi$
$277$	− 16.9443i	− 1.01808i	0.860742	−	0.509041i	$-0.170000\pi$
$278$	10.4721i	0.628077i
$279$	−6.61803	−0.396211
$280$	0	0
$281$	5.88854	0.351281	0.175641	−	0.984454i	$-0.443800\pi$
$281$	5.88854	0.351281	0.175641	+	0.984454i	$0.443800\pi$
$282$	1.70820i	0.101722i
$283$	4.58359i	0.272466i	0.990677	+	0.136233i	$0.0434996\pi$
$283$	4.58359i	0.272466i	−0.990677	+	0.136233i	$0.956500\pi$
$284$	−5.52786	−0.328018
$285$	0	0
$286$	−23.4164	−1.38464
$287$	− 14.9443i	− 0.882132i
$288$	1.00000i	0.0589256i
$289$	15.4721	0.910126
$290$	0	0
$291$	3.38197	0.198254
$292$	− 3.52786i	− 0.206453i
$293$	− 22.0902i	− 1.29052i	−0.763962	−	0.645261i	$-0.776749\pi$
$293$	− 22.0902i	− 1.29052i	0.763962	−	0.645261i	$-0.223251\pi$
$294$	−0.145898	−0.00850895
$295$	0	0
$296$	8.00000	0.464991
$297$	3.61803i	0.209940i
$298$	22.0902i	1.27965i
$299$	28.9443	1.67389
$300$	0	0
$301$	−20.1803	−1.16318
$302$	− 18.3262i	− 1.05456i
$303$	− 4.38197i	− 0.251737i
$304$	5.70820	0.327388
$305$	0	0
$306$	1.23607	0.0706613
$307$	− 10.0000i	− 0.570730i	−0.958419	−	0.285365i	$-0.907885\pi$
$307$	− 10.0000i	− 0.570730i	0.958419	−	0.285365i	$-0.0921148\pi$
$308$	9.47214i	0.539725i
$309$	14.3262	0.814991
$310$	0	0
$311$	−1.05573	−0.0598648	−0.0299324	−	0.999552i	$-0.509529\pi$
$311$	−1.05573	−0.0598648	−0.0299324	+	0.999552i	$0.509529\pi$
$312$	− 6.47214i	− 0.366413i
$313$	− 16.2705i	− 0.919664i	−0.888006	−	0.459832i	$-0.847910\pi$
$313$	− 16.2705i	− 0.919664i	0.888006	−	0.459832i	$-0.152090\pi$
$314$	−8.65248	−0.488287
$315$	0	0
$316$	−5.61803	−0.316039
$317$	20.5623i	1.15489i	0.816428	+	0.577447i	$0.195951\pi$
$317$	20.5623i	1.15489i	−0.816428	+	0.577447i	$0.804049\pi$
$318$	2.09017i	0.117211i
$319$	−30.6525	−1.71621
$320$	0	0
$321$	11.6180	0.648455
$322$	− 11.7082i	− 0.652473i
$323$	− 7.05573i	− 0.392591i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−0.472136	−0.0261492
$327$	17.2361i	0.953157i
$328$	5.70820i	0.315183i
$329$	−4.47214	−0.246557
$330$	0	0
$331$	−18.0000	−0.989369	−0.494685	−	0.869072i	$-0.664716\pi$
$331$	−18.0000	−0.989369	−0.494685	+	0.869072i	$0.664716\pi$
$332$	− 2.14590i	− 0.117771i
$333$	8.00000i	0.438397i
$334$	−11.7082	−0.640644
$335$	0	0
$336$	−2.61803	−0.142825
$337$	− 0.909830i	− 0.0495616i	−0.999693	−	0.0247808i	$-0.992111\pi$
$337$	− 0.909830i	− 0.0495616i	0.999693	−	0.0247808i	$-0.00788878\pi$
$338$	28.8885i	1.57133i
$339$	−19.2361	−1.04476
$340$	0	0
$341$	23.9443	1.29666
$342$	5.70820i	0.308664i
$343$	− 18.7082i	− 1.01015i
$344$	7.70820	0.415599
$345$	0	0
$346$	5.09017	0.273649
$347$	− 20.5623i	− 1.10384i	−0.833896	−	0.551921i	$-0.813895\pi$
$347$	− 20.5623i	− 1.10384i	0.833896	−	0.551921i	$-0.186105\pi$
$348$	− 8.47214i	− 0.454154i
$349$	27.8885	1.49284	0.746420	−	0.665475i	$-0.231771\pi$
$349$	27.8885	1.49284	0.746420	+	0.665475i	$0.231771\pi$
$350$	0	0
$351$	6.47214	0.345457
$352$	− 3.61803i	− 0.192842i
$353$	− 13.2361i	− 0.704485i	−0.935909	−	0.352242i	$-0.885419\pi$
$353$	− 13.2361i	− 0.704485i	0.935909	−	0.352242i	$-0.114581\pi$
$354$	−3.61803	−0.192296
$355$	0	0
$356$	3.52786	0.186976
$357$	3.23607i	0.171271i
$358$	9.85410i	0.520805i
$359$	−22.1803	−1.17063	−0.585317	−	0.810805i	$-0.699030\pi$
$359$	−22.1803	−1.17063	−0.585317	+	0.810805i	$0.699030\pi$
$360$	0	0
$361$	13.5836	0.714926
$362$	6.65248i	0.349646i
$363$	− 2.09017i	− 0.109705i
$364$	16.9443	0.888121
$365$	0	0
$366$	−2.76393	−0.144473
$367$	30.6180i	1.59825i	0.601166	+	0.799124i	$0.294703\pi$
$367$	30.6180i	1.59825i	−0.601166	+	0.799124i	$0.705297\pi$
$368$	4.47214i	0.233126i
$369$	−5.70820	−0.297157
$370$	0	0
$371$	−5.47214	−0.284099
$372$	6.61803i	0.343129i
$373$	− 11.5279i	− 0.596890i	−0.954427	−	0.298445i	$-0.903532\pi$
$373$	− 11.5279i	− 0.596890i	0.954427	−	0.298445i	$-0.0964680\pi$
$374$	−4.47214	−0.231249
$375$	0	0
$376$	1.70820	0.0880939
$377$	54.8328i	2.82403i
$378$	− 2.61803i	− 0.134657i
$379$	20.1803	1.03659	0.518297	−	0.855201i	$-0.326566\pi$
$379$	20.1803	1.03659	0.518297	+	0.855201i	$0.326566\pi$
$380$	0	0
$381$	−13.6180	−0.697673
$382$	− 4.29180i	− 0.219587i
$383$	− 20.0000i	− 1.02195i	−0.859595	−	0.510976i	$-0.829284\pi$
$383$	− 20.0000i	− 1.02195i	0.859595	−	0.510976i	$-0.170716\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	17.8541	0.908750
$387$	7.70820i	0.391830i
$388$	− 3.38197i	− 0.171693i
$389$	12.3820	0.627791	0.313895	−	0.949458i	$-0.398366\pi$
$389$	12.3820	0.627791	0.313895	+	0.949458i	$0.398366\pi$
$390$	0	0
$391$	5.52786	0.279556
$392$	0.145898i	0.00736896i
$393$	17.8885i	0.902358i
$394$	17.0902	0.860990
$395$	0	0
$396$	3.61803	0.181813
$397$	30.7639i	1.54400i	0.635624	+	0.771999i	$0.280743\pi$
$397$	30.7639i	1.54400i	−0.635624	+	0.771999i	$0.719257\pi$
$398$	19.5066i	0.977776i
$399$	−14.9443	−0.748149
$400$	0	0
$401$	25.7082	1.28381	0.641903	−	0.766786i	$-0.278145\pi$
$401$	25.7082	1.28381	0.641903	+	0.766786i	$0.278145\pi$
$402$	− 1.52786i	− 0.0762029i
$403$	− 42.8328i	− 2.13365i
$404$	−4.38197	−0.218011
$405$	0	0
$406$	22.1803	1.10079
$407$	− 28.9443i	− 1.43471i
$408$	− 1.23607i	− 0.0611945i
$409$	−5.79837	−0.286711	−0.143356	−	0.989671i	$-0.545789\pi$
$409$	−5.79837	−0.286711	−0.143356	+	0.989671i	$0.545789\pi$
$410$	0	0
$411$	12.1803	0.600812
$412$	− 14.3262i	− 0.705803i
$413$	− 9.47214i	− 0.466093i
$414$	−4.47214	−0.219793
$415$	0	0
$416$	−6.47214	−0.317323
$417$	10.4721i	0.512823i
$418$	− 20.6525i	− 1.01015i
$419$	3.09017	0.150965	0.0754823	−	0.997147i	$-0.475950\pi$
$419$	3.09017	0.150965	0.0754823	+	0.997147i	$0.475950\pi$
$420$	0	0
$421$	−22.7639	−1.10945	−0.554723	−	0.832035i	$-0.687176\pi$
$421$	−22.7639	−1.10945	−0.554723	+	0.832035i	$0.687176\pi$
$422$	3.41641i	0.166308i
$423$	1.70820i	0.0830557i
$424$	2.09017	0.101508
$425$	0	0
$426$	−5.52786	−0.267826
$427$	− 7.23607i	− 0.350178i
$428$	− 11.6180i	− 0.561579i
$429$	−23.4164	−1.13055
$430$	0	0
$431$	16.8328	0.810808	0.405404	−	0.914138i	$-0.367131\pi$
$431$	16.8328	0.810808	0.405404	+	0.914138i	$0.367131\pi$
$432$	1.00000i	0.0481125i
$433$	15.5066i	0.745199i	0.927992	+	0.372599i	$0.121533\pi$
$433$	15.5066i	0.745199i	−0.927992	+	0.372599i	$0.878467\pi$
$434$	−17.3262	−0.831686
$435$	0	0
$436$	17.2361	0.825458
$437$	25.5279i	1.22116i
$438$	− 3.52786i	− 0.168568i
$439$	23.5066	1.12191	0.560954	−	0.827847i	$-0.310434\pi$
$439$	23.5066	1.12191	0.560954	+	0.827847i	$0.310434\pi$
$440$	0	0
$441$	−0.145898	−0.00694753
$442$	8.00000i	0.380521i
$443$	16.6180i	0.789547i	0.918779	+	0.394773i	$0.129177\pi$
$443$	16.6180i	0.789547i	−0.918779	+	0.394773i	$0.870823\pi$
$444$	8.00000	0.379663
$445$	0	0
$446$	−8.09017	−0.383081
$447$	22.0902i	1.04483i
$448$	2.61803i	0.123690i
$449$	27.7082	1.30763	0.653815	−	0.756654i	$-0.273167\pi$
$449$	27.7082	1.30763	0.653815	+	0.756654i	$0.273167\pi$
$450$	0	0
$451$	20.6525	0.972487
$452$	19.2361i	0.904789i
$453$	− 18.3262i	− 0.861042i
$454$	22.2705	1.04521
$455$	0	0
$456$	5.70820	0.267311
$457$	4.09017i	0.191330i	0.995414	+	0.0956650i	$0.0304978\pi$
$457$	4.09017i	0.191330i	−0.995414	+	0.0956650i	$0.969502\pi$
$458$	− 5.52786i	− 0.258300i
$459$	1.23607	0.0576947
$460$	0	0
$461$	7.56231	0.352212	0.176106	−	0.984371i	$-0.443650\pi$
$461$	7.56231	0.352212	0.176106	+	0.984371i	$0.443650\pi$
$462$	9.47214i	0.440684i
$463$	− 22.8328i	− 1.06113i	−0.847644	−	0.530565i	$-0.821980\pi$
$463$	− 22.8328i	− 1.06113i	0.847644	−	0.530565i	$-0.178020\pi$
$464$	−8.47214	−0.393309
$465$	0	0
$466$	18.6525	0.864059
$467$	− 10.6738i	− 0.493923i	−0.969025	−	0.246961i	$-0.920568\pi$
$467$	− 10.6738i	− 0.493923i	0.969025	−	0.246961i	$-0.0794321\pi$
$468$	− 6.47214i	− 0.299175i
$469$	4.00000	0.184703
$470$	0	0
$471$	−8.65248	−0.398685
$472$	3.61803i	0.166534i
$473$	− 27.8885i	− 1.28232i
$474$	−5.61803	−0.258045
$475$	0	0
$476$	3.23607	0.148325
$477$	2.09017i	0.0957023i
$478$	12.2918i	0.562214i
$479$	29.1246	1.33074	0.665369	−	0.746515i	$-0.268274\pi$
$479$	29.1246	1.33074	0.665369	+	0.746515i	$0.268274\pi$
$480$	0	0
$481$	−51.7771	−2.36083
$482$	− 9.56231i	− 0.435551i
$483$	− 11.7082i	− 0.532742i
$484$	−2.09017	−0.0950077
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	− 17.7984i	− 0.806521i	−0.915085	−	0.403261i	$-0.867877\pi$
$487$	− 17.7984i	− 0.806521i	0.915085	−	0.403261i	$-0.132123\pi$
$488$	2.76393i	0.125117i
$489$	−0.472136	−0.0213507
$490$	0	0
$491$	−25.2705	−1.14044	−0.570221	−	0.821491i	$-0.693142\pi$
$491$	−25.2705	−1.14044	−0.570221	+	0.821491i	$0.693142\pi$
$492$	5.70820i	0.257346i
$493$	10.4721i	0.471641i
$494$	−36.9443	−1.66220
$495$	0	0
$496$	6.61803	0.297158
$497$	− 14.4721i	− 0.649164i
$498$	− 2.14590i	− 0.0961600i
$499$	−35.5967	−1.59353	−0.796765	−	0.604290i	$-0.793457\pi$
$499$	−35.5967	−1.59353	−0.796765	+	0.604290i	$0.793457\pi$
$500$	0	0
$501$	−11.7082	−0.523084
$502$	− 13.5623i	− 0.605315i
$503$	23.8885i	1.06514i	0.846387	+	0.532569i	$0.178773\pi$
$503$	23.8885i	1.06514i	−0.846387	+	0.532569i	$0.821227\pi$
$504$	−2.61803	−0.116617
$505$	0	0
$506$	16.1803	0.719304
$507$	28.8885i	1.28299i
$508$	13.6180i	0.604203i
$509$	17.5066	0.775965	0.387983	−	0.921667i	$-0.373172\pi$
$509$	17.5066	0.775965	0.387983	+	0.921667i	$0.373172\pi$
$510$	0	0
$511$	9.23607	0.408580
$512$	− 1.00000i	− 0.0441942i
$513$	5.70820i	0.252023i
$514$	22.0000	0.970378
$515$	0	0
$516$	7.70820	0.339335
$517$	− 6.18034i	− 0.271811i
$518$	20.9443i	0.920238i
$519$	5.09017	0.223434
$520$	0	0
$521$	14.1803	0.621252	0.310626	−	0.950532i	$-0.399461\pi$
$521$	14.1803	0.621252	0.310626	+	0.950532i	$0.399461\pi$
$522$	− 8.47214i	− 0.370815i
$523$	11.0557i	0.483433i	0.970347	+	0.241717i	$0.0777104\pi$
$523$	11.0557i	0.483433i	−0.970347	+	0.241717i	$0.922290\pi$
$524$	17.8885	0.781465
$525$	0	0
$526$	−11.7082	−0.510502
$527$	− 8.18034i	− 0.356341i
$528$	− 3.61803i	− 0.157455i
$529$	3.00000	0.130435
$530$	0	0
$531$	−3.61803	−0.157009
$532$	14.9443i	0.647916i
$533$	− 36.9443i	− 1.60023i
$534$	3.52786	0.152666
$535$	0	0
$536$	−1.52786	−0.0659937
$537$	9.85410i	0.425236i
$538$	− 9.09017i	− 0.391905i
$539$	0.527864	0.0227367
$540$	0	0
$541$	−26.1803	−1.12558	−0.562790	−	0.826600i	$-0.690272\pi$
$541$	−26.1803	−1.12558	−0.562790	+	0.826600i	$0.690272\pi$
$542$	18.0344i	0.774646i
$543$	6.65248i	0.285485i
$544$	−1.23607	−0.0529960
$545$	0	0
$546$	16.9443	0.725148
$547$	− 9.70820i	− 0.415093i	−0.978225	−	0.207546i	$-0.933452\pi$
$547$	− 9.70820i	− 0.415093i	0.978225	−	0.207546i	$-0.0665478\pi$
$548$	− 12.1803i	− 0.520318i
$549$	−2.76393	−0.117962
$550$	0	0
$551$	−48.3607	−2.06023
$552$	4.47214i	0.190347i
$553$	− 14.7082i	− 0.625456i
$554$	−16.9443	−0.719893
$555$	0	0
$556$	10.4721	0.444117
$557$	18.3262i	0.776508i	0.921552	+	0.388254i	$0.126922\pi$
$557$	18.3262i	0.776508i	−0.921552	+	0.388254i	$0.873078\pi$
$558$	6.61803i	0.280164i
$559$	−49.8885	−2.11006
$560$	0	0
$561$	−4.47214	−0.188814
$562$	− 5.88854i	− 0.248393i
$563$	21.2705i	0.896445i	0.893922	+	0.448223i	$0.147943\pi$
$563$	21.2705i	0.896445i	−0.893922	+	0.448223i	$0.852057\pi$
$564$	1.70820	0.0719284
$565$	0	0
$566$	4.58359	0.192663
$567$	− 2.61803i	− 0.109947i
$568$	5.52786i	0.231944i
$569$	27.7771	1.16448	0.582238	−	0.813018i	$-0.302177\pi$
$569$	27.7771	1.16448	0.582238	+	0.813018i	$0.302177\pi$
$570$	0	0
$571$	7.88854	0.330125	0.165063	−	0.986283i	$-0.447217\pi$
$571$	7.88854	0.330125	0.165063	+	0.986283i	$0.447217\pi$
$572$	23.4164i	0.979089i
$573$	− 4.29180i	− 0.179292i
$574$	−14.9443	−0.623762
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 8.97871i	− 0.373789i	−0.982380	−	0.186894i	$-0.940158\pi$
$577$	− 8.97871i	− 0.373789i	0.982380	−	0.186894i	$-0.0598422\pi$
$578$	− 15.4721i	− 0.643556i
$579$	17.8541	0.741991
$580$	0	0
$581$	5.61803	0.233075
$582$	− 3.38197i	− 0.140187i
$583$	− 7.56231i	− 0.313199i
$584$	−3.52786	−0.145984
$585$	0	0
$586$	−22.0902	−0.912537
$587$	0.965558i	0.0398528i	0.999801	+	0.0199264i	$0.00634320\pi$
$587$	0.965558i	0.0398528i	−0.999801	+	0.0199264i	$0.993657\pi$
$588$	0.145898i	0.00601673i
$589$	37.7771	1.55658
$590$	0	0
$591$	17.0902	0.702996
$592$	− 8.00000i	− 0.328798i
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	3.61803	0.148450
$595$	0	0
$596$	22.0902	0.904849
$597$	19.5066i	0.798351i
$598$	− 28.9443i	− 1.18362i
$599$	−0.472136	−0.0192910	−0.00964548	−	0.999953i	$-0.503070\pi$
$599$	−0.472136	−0.0192910	−0.00964548	+	0.999953i	$0.503070\pi$
$600$	0	0
$601$	−7.72949	−0.315292	−0.157646	−	0.987496i	$-0.550391\pi$
$601$	−7.72949	−0.315292	−0.157646	+	0.987496i	$0.550391\pi$
$602$	20.1803i	0.822489i
$603$	− 1.52786i	− 0.0622194i
$604$	−18.3262	−0.745684
$605$	0	0
$606$	−4.38197	−0.178005
$607$	− 6.56231i	− 0.266356i	−0.991092	−	0.133178i	$-0.957482\pi$
$607$	− 6.56231i	− 0.266356i	0.991092	−	0.133178i	$-0.0425182\pi$
$608$	− 5.70820i	− 0.231498i
$609$	22.1803	0.898793
$610$	0	0
$611$	−11.0557	−0.447267
$612$	− 1.23607i	− 0.0499651i
$613$	48.2492i	1.94877i	0.224891	+	0.974384i	$0.427797\pi$
$613$	48.2492i	1.94877i	−0.224891	+	0.974384i	$0.572203\pi$
$614$	−10.0000	−0.403567
$615$	0	0
$616$	9.47214	0.381643
$617$	− 2.11146i	− 0.0850040i	−0.999096	−	0.0425020i	$-0.986467\pi$
$617$	− 2.11146i	− 0.0850040i	0.999096	−	0.0425020i	$-0.0135329\pi$
$618$	− 14.3262i	− 0.576286i
$619$	9.41641	0.378477	0.189239	−	0.981931i	$-0.439398\pi$
$619$	9.41641	0.378477	0.189239	+	0.981931i	$0.439398\pi$
$620$	0	0
$621$	−4.47214	−0.179461
$622$	1.05573i	0.0423308i
$623$	9.23607i	0.370035i
$624$	−6.47214	−0.259093
$625$	0	0
$626$	−16.2705	−0.650300
$627$	− 20.6525i	− 0.824780i
$628$	8.65248i	0.345271i
$629$	−9.88854	−0.394282
$630$	0	0
$631$	46.4721	1.85003	0.925013	−	0.379935i	$-0.124054\pi$
$631$	46.4721	1.85003	0.925013	+	0.379935i	$0.124054\pi$
$632$	5.61803i	0.223473i
$633$	3.41641i	0.135790i
$634$	20.5623	0.816633
$635$	0	0
$636$	2.09017	0.0828806
$637$	− 0.944272i	− 0.0374134i
$638$	30.6525i	1.21354i
$639$	−5.52786	−0.218679
$640$	0	0
$641$	−13.8197	−0.545844	−0.272922	−	0.962036i	$-0.587990\pi$
$641$	−13.8197	−0.545844	−0.272922	+	0.962036i	$0.587990\pi$
$642$	− 11.6180i	− 0.458527i
$643$	21.8885i	0.863200i	0.902065	+	0.431600i	$0.142051\pi$
$643$	21.8885i	0.863200i	−0.902065	+	0.431600i	$0.857949\pi$
$644$	−11.7082	−0.461368
$645$	0	0
$646$	−7.05573	−0.277604
$647$	22.9443i	0.902032i	0.892516	+	0.451016i	$0.148938\pi$
$647$	22.9443i	0.902032i	−0.892516	+	0.451016i	$0.851062\pi$
$648$	1.00000i	0.0392837i
$649$	13.0902	0.513834
$650$	0	0
$651$	−17.3262	−0.679069
$652$	0.472136i	0.0184903i
$653$	− 3.85410i	− 0.150823i	−0.997153	−	0.0754113i	$-0.975973\pi$
$653$	− 3.85410i	− 0.150823i	0.997153	−	0.0754113i	$-0.0240270\pi$
$654$	17.2361	0.673984
$655$	0	0
$656$	5.70820	0.222868
$657$	− 3.52786i	− 0.137635i
$658$	4.47214i	0.174342i
$659$	20.6180	0.803165	0.401582	−	0.915823i	$-0.368460\pi$
$659$	20.6180	0.803165	0.401582	+	0.915823i	$0.368460\pi$
$660$	0	0
$661$	−30.4721	−1.18523	−0.592614	−	0.805486i	$-0.701904\pi$
$661$	−30.4721	−1.18523	−0.592614	+	0.805486i	$0.701904\pi$
$662$	18.0000i	0.699590i
$663$	8.00000i	0.310694i
$664$	−2.14590	−0.0832770
$665$	0	0
$666$	8.00000	0.309994
$667$	− 37.8885i	− 1.46705i
$668$	11.7082i	0.453004i
$669$	−8.09017	−0.312784
$670$	0	0
$671$	10.0000	0.386046
$672$	2.61803i	0.100993i
$673$	− 31.4508i	− 1.21234i	−0.795335	−	0.606171i	$-0.792705\pi$
$673$	− 31.4508i	− 1.21234i	0.795335	−	0.606171i	$-0.207295\pi$
$674$	−0.909830	−0.0350453
$675$	0	0
$676$	28.8885	1.11110
$677$	− 29.0902i	− 1.11803i	−0.829159	−	0.559013i	$-0.811180\pi$
$677$	− 29.0902i	− 1.11803i	0.829159	−	0.559013i	$-0.188820\pi$
$678$	19.2361i	0.738757i
$679$	8.85410	0.339789
$680$	0	0
$681$	22.2705	0.853408
$682$	− 23.9443i	− 0.916874i
$683$	33.5066i	1.28209i	0.767502	+	0.641047i	$0.221500\pi$
$683$	33.5066i	1.28209i	−0.767502	+	0.641047i	$0.778500\pi$
$684$	5.70820	0.218259
$685$	0	0
$686$	−18.7082	−0.714283
$687$	− 5.52786i	− 0.210901i
$688$	− 7.70820i	− 0.293873i
$689$	−13.5279	−0.515371
$690$	0	0
$691$	11.2361	0.427440	0.213720	−	0.976895i	$-0.431442\pi$
$691$	11.2361	0.427440	0.213720	+	0.976895i	$0.431442\pi$
$692$	− 5.09017i	− 0.193499i
$693$	9.47214i	0.359817i
$694$	−20.5623	−0.780534
$695$	0	0
$696$	−8.47214	−0.321135
$697$	− 7.05573i	− 0.267255i
$698$	− 27.8885i	− 1.05560i
$699$	18.6525	0.705501
$700$	0	0
$701$	40.8328	1.54223	0.771117	−	0.636693i	$-0.219698\pi$
$701$	40.8328	1.54223	0.771117	+	0.636693i	$0.219698\pi$
$702$	− 6.47214i	− 0.244275i
$703$	− 45.6656i	− 1.72231i
$704$	−3.61803	−0.136360
$705$	0	0
$706$	−13.2361	−0.498146
$707$	− 11.4721i	− 0.431454i
$708$	3.61803i	0.135974i
$709$	43.7082	1.64150	0.820748	−	0.571290i	$-0.193557\pi$
$709$	43.7082	1.64150	0.820748	+	0.571290i	$0.193557\pi$
$710$	0	0
$711$	−5.61803	−0.210693
$712$	− 3.52786i	− 0.132212i
$713$	29.5967i	1.10841i
$714$	3.23607	0.121107
$715$	0	0
$716$	9.85410	0.368265
$717$	12.2918i	0.459046i
$718$	22.1803i	0.827763i
$719$	16.5836	0.618464	0.309232	−	0.950987i	$-0.399928\pi$
$719$	16.5836	0.618464	0.309232	+	0.950987i	$0.399928\pi$
$720$	0	0
$721$	37.5066	1.39682
$722$	− 13.5836i	− 0.505529i
$723$	− 9.56231i	− 0.355626i
$724$	6.65248	0.247237
$725$	0	0
$726$	−2.09017	−0.0775735
$727$	8.58359i	0.318348i	0.987251	+	0.159174i	$0.0508831\pi$
$727$	8.58359i	0.318348i	−0.987251	+	0.159174i	$0.949117\pi$
$728$	− 16.9443i	− 0.627996i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−9.52786	−0.352401
$732$	2.76393i	0.102158i
$733$	− 35.8885i	− 1.32557i	−0.748808	−	0.662787i	$-0.769374\pi$
$733$	− 35.8885i	− 1.32557i	0.748808	−	0.662787i	$-0.230626\pi$
$734$	30.6180	1.13013
$735$	0	0
$736$	4.47214	0.164845
$737$	5.52786i	0.203621i
$738$	5.70820i	0.210122i
$739$	48.1803	1.77234	0.886171	−	0.463358i	$-0.153356\pi$
$739$	48.1803	1.77234	0.886171	+	0.463358i	$0.153356\pi$
$740$	0	0
$741$	−36.9443	−1.35718
$742$	5.47214i	0.200888i
$743$	− 39.0132i	− 1.43125i	−0.698483	−	0.715627i	$-0.746141\pi$
$743$	− 39.0132i	− 1.43125i	0.698483	−	0.715627i	$-0.253859\pi$
$744$	6.61803	0.242629
$745$	0	0
$746$	−11.5279	−0.422065
$747$	− 2.14590i	− 0.0785143i
$748$	4.47214i	0.163517i
$749$	30.4164	1.11139
$750$	0	0
$751$	24.7984	0.904906	0.452453	−	0.891788i	$-0.350549\pi$
$751$	24.7984	0.904906	0.452453	+	0.891788i	$0.350549\pi$
$752$	− 1.70820i	− 0.0622918i
$753$	− 13.5623i	− 0.494238i
$754$	54.8328	1.99689
$755$	0	0
$756$	−2.61803	−0.0952170
$757$	17.1246i	0.622405i	0.950344	+	0.311202i	$0.100732\pi$
$757$	17.1246i	0.622405i	−0.950344	+	0.311202i	$0.899268\pi$
$758$	− 20.1803i	− 0.732983i
$759$	16.1803	0.587309
$760$	0	0
$761$	1.41641	0.0513447	0.0256724	−	0.999670i	$-0.491827\pi$
$761$	1.41641	0.0513447	0.0256724	+	0.999670i	$0.491827\pi$
$762$	13.6180i	0.493329i
$763$	45.1246i	1.63362i
$764$	−4.29180	−0.155272
$765$	0	0
$766$	−20.0000	−0.722629
$767$	− 23.4164i	− 0.845517i
$768$	− 1.00000i	− 0.0360844i
$769$	−24.6869	−0.890233	−0.445117	−	0.895473i	$-0.646838\pi$
$769$	−24.6869	−0.890233	−0.445117	+	0.895473i	$0.646838\pi$
$770$	0	0
$771$	22.0000	0.792311
$772$	− 17.8541i	− 0.642583i
$773$	− 1.14590i	− 0.0412151i	−0.999788	−	0.0206075i	$-0.993440\pi$
$773$	− 1.14590i	− 0.0412151i	0.999788	−	0.0206075i	$-0.00656005\pi$
$774$	7.70820	0.277066
$775$	0	0
$776$	−3.38197	−0.121406
$777$	20.9443i	0.751372i
$778$	− 12.3820i	− 0.443915i
$779$	32.5836	1.16743
$780$	0	0
$781$	20.0000	0.715656
$782$	− 5.52786i	− 0.197676i
$783$	− 8.47214i	− 0.302769i
$784$	0.145898	0.00521064
$785$	0	0
$786$	17.8885	0.638063
$787$	− 28.0689i	− 1.00055i	−0.865867	−	0.500274i	$-0.833233\pi$
$787$	− 28.0689i	− 1.00055i	0.865867	−	0.500274i	$-0.166767\pi$
$788$	− 17.0902i	− 0.608812i
$789$	−11.7082	−0.416823
$790$	0	0
$791$	−50.3607	−1.79062
$792$	− 3.61803i	− 0.128561i
$793$	− 17.8885i	− 0.635241i
$794$	30.7639	1.09177
$795$	0	0
$796$	19.5066	0.691392
$797$	− 1.50658i	− 0.0533657i	−0.999644	−	0.0266829i	$-0.991506\pi$
$797$	− 1.50658i	− 0.0533657i	0.999644	−	0.0266829i	$-0.00849443\pi$
$798$	14.9443i	0.529021i
$799$	−2.11146	−0.0746979
$800$	0	0
$801$	3.52786	0.124651
$802$	− 25.7082i	− 0.907788i
$803$	12.7639i	0.450429i
$804$	−1.52786	−0.0538836
$805$	0	0
$806$	−42.8328	−1.50872
$807$	− 9.09017i	− 0.319989i
$808$	4.38197i	0.154157i
$809$	30.8328	1.08402	0.542012	−	0.840371i	$-0.317663\pi$
$809$	30.8328	1.08402	0.542012	+	0.840371i	$0.317663\pi$
$810$	0	0
$811$	−5.70820	−0.200442	−0.100221	−	0.994965i	$-0.531955\pi$
$811$	−5.70820	−0.200442	−0.100221	+	0.994965i	$0.531955\pi$
$812$	− 22.1803i	− 0.778377i
$813$	18.0344i	0.632495i
$814$	−28.9443	−1.01450
$815$	0	0
$816$	−1.23607	−0.0432710
$817$	− 44.0000i	− 1.53937i
$818$	5.79837i	0.202735i
$819$	16.9443	0.592081
$820$	0	0
$821$	−45.0902	−1.57366	−0.786829	−	0.617171i	$-0.788279\pi$
$821$	−45.0902	−1.57366	−0.786829	+	0.617171i	$0.788279\pi$
$822$	− 12.1803i	− 0.424838i
$823$	2.96556i	0.103373i	0.998663	+	0.0516864i	$0.0164596\pi$
$823$	2.96556i	0.103373i	−0.998663	+	0.0516864i	$0.983540\pi$
$824$	−14.3262	−0.499078
$825$	0	0
$826$	−9.47214	−0.329578
$827$	− 44.1033i	− 1.53362i	−0.641872	−	0.766811i	$-0.721842\pi$
$827$	− 44.1033i	− 1.53362i	0.641872	−	0.766811i	$-0.278158\pi$
$828$	4.47214i	0.155417i
$829$	−25.8885	−0.899146	−0.449573	−	0.893244i	$-0.648424\pi$
$829$	−25.8885	−0.899146	−0.449573	+	0.893244i	$0.648424\pi$
$830$	0	0
$831$	−16.9443	−0.587790
$832$	6.47214i	0.224381i
$833$	− 0.180340i	− 0.00624841i
$834$	10.4721	0.362620
$835$	0	0
$836$	−20.6525	−0.714281
$837$	6.61803i	0.228753i
$838$	− 3.09017i	− 0.106748i
$839$	−6.36068	−0.219595	−0.109798	−	0.993954i	$-0.535020\pi$
$839$	−6.36068	−0.219595	−0.109798	+	0.993954i	$0.535020\pi$
$840$	0	0
$841$	42.7771	1.47507
$842$	22.7639i	0.784497i
$843$	− 5.88854i	− 0.202812i
$844$	3.41641	0.117598
$845$	0	0
$846$	1.70820	0.0587293
$847$	− 5.47214i	− 0.188025i
$848$	− 2.09017i	− 0.0717767i
$849$	4.58359	0.157308
$850$	0	0
$851$	35.7771	1.22642
$852$	5.52786i	0.189382i
$853$	− 43.5967i	− 1.49272i	−0.665540	−	0.746362i	$-0.731799\pi$
$853$	− 43.5967i	− 1.49272i	0.665540	−	0.746362i	$-0.268201\pi$
$854$	−7.23607	−0.247613
$855$	0	0
$856$	−11.6180	−0.397096
$857$	16.0689i	0.548903i	0.961601	+	0.274451i	$0.0884962\pi$
$857$	16.0689i	0.548903i	−0.961601	+	0.274451i	$0.911504\pi$
$858$	23.4164i	0.799423i
$859$	2.29180	0.0781951	0.0390975	−	0.999235i	$-0.487552\pi$
$859$	2.29180	0.0781951	0.0390975	+	0.999235i	$0.487552\pi$
$860$	0	0
$861$	−14.9443	−0.509299
$862$	− 16.8328i	− 0.573328i
$863$	− 10.1803i	− 0.346543i	−0.984874	−	0.173271i	$-0.944566\pi$
$863$	− 10.1803i	− 0.346543i	0.984874	−	0.173271i	$-0.0554338\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	15.5066	0.526935
$867$	− 15.4721i	− 0.525461i
$868$	17.3262i	0.588091i
$869$	20.3262	0.689520
$870$	0	0
$871$	9.88854	0.335061
$872$	− 17.2361i	− 0.583687i
$873$	− 3.38197i	− 0.114462i
$874$	25.5279	0.863493
$875$	0	0
$876$	−3.52786	−0.119195
$877$	37.1246i	1.25361i	0.779177	+	0.626805i	$0.215638\pi$
$877$	37.1246i	1.25361i	−0.779177	+	0.626805i	$0.784362\pi$
$878$	− 23.5066i	− 0.793309i
$879$	−22.0902	−0.745083
$880$	0	0
$881$	−23.5967	−0.794995	−0.397497	−	0.917603i	$-0.630121\pi$
$881$	−23.5967	−0.794995	−0.397497	+	0.917603i	$0.630121\pi$
$882$	0.145898i	0.00491264i
$883$	− 30.0689i	− 1.01190i	−0.862563	−	0.505949i	$-0.831142\pi$
$883$	− 30.0689i	− 1.01190i	0.862563	−	0.505949i	$-0.168858\pi$
$884$	8.00000	0.269069
$885$	0	0
$886$	16.6180	0.558294
$887$	− 23.4164i	− 0.786246i	−0.919486	−	0.393123i	$-0.871395\pi$
$887$	− 23.4164i	− 0.786246i	0.919486	−	0.393123i	$-0.128605\pi$
$888$	− 8.00000i	− 0.268462i
$889$	−35.6525	−1.19575
$890$	0	0
$891$	3.61803	0.121209
$892$	8.09017i	0.270879i
$893$	− 9.75078i	− 0.326297i
$894$	22.0902	0.738806
$895$	0	0
$896$	2.61803	0.0874624
$897$	− 28.9443i	− 0.966421i
$898$	− 27.7082i	− 0.924635i
$899$	−56.0689	−1.87000
$900$	0	0
$901$	−2.58359	−0.0860719
$902$	− 20.6525i	− 0.687652i
$903$	20.1803i	0.671560i
$904$	19.2361	0.639782
$905$	0	0
$906$	−18.3262	−0.608848
$907$	− 30.4721i	− 1.01181i	−0.862589	−	0.505905i	$-0.831159\pi$
$907$	− 30.4721i	− 1.01181i	0.862589	−	0.505905i	$-0.168841\pi$
$908$	− 22.2705i	− 0.739073i
$909$	−4.38197	−0.145341
$910$	0	0
$911$	18.1803	0.602342	0.301171	−	0.953570i	$-0.402623\pi$
$911$	18.1803	0.602342	0.301171	+	0.953570i	$0.402623\pi$
$912$	− 5.70820i	− 0.189018i
$913$	7.76393i	0.256949i
$914$	4.09017	0.135291
$915$	0	0
$916$	−5.52786	−0.182646
$917$	46.8328i	1.54656i
$918$	− 1.23607i	− 0.0407963i
$919$	40.7214	1.34327	0.671637	−	0.740881i	$-0.265592\pi$
$919$	40.7214	1.34327	0.671637	+	0.740881i	$0.265592\pi$
$920$	0	0
$921$	−10.0000	−0.329511
$922$	− 7.56231i	− 0.249051i
$923$	− 35.7771i	− 1.17762i
$924$	9.47214	0.311610
$925$	0	0
$926$	−22.8328	−0.750333
$927$	− 14.3262i	− 0.470535i
$928$	8.47214i	0.278111i
$929$	19.0132	0.623801	0.311901	−	0.950115i	$-0.399034\pi$
$929$	19.0132	0.623801	0.311901	+	0.950115i	$0.399034\pi$
$930$	0	0
$931$	0.832816	0.0272944
$932$	− 18.6525i	− 0.610982i
$933$	1.05573i	0.0345630i
$934$	−10.6738	−0.349256
$935$	0	0
$936$	−6.47214	−0.211548
$937$	8.68692i	0.283789i	0.989882	+	0.141895i	$0.0453194\pi$
$937$	8.68692i	0.283789i	−0.989882	+	0.141895i	$0.954681\pi$
$938$	− 4.00000i	− 0.130605i
$939$	−16.2705	−0.530968
$940$	0	0
$941$	−4.43769	−0.144665	−0.0723323	−	0.997381i	$-0.523044\pi$
$941$	−4.43769	−0.144665	−0.0723323	+	0.997381i	$0.523044\pi$
$942$	8.65248i	0.281913i
$943$	25.5279i	0.831302i
$944$	3.61803	0.117757
$945$	0	0
$946$	−27.8885	−0.906735
$947$	33.5623i	1.09063i	0.838232	+	0.545314i	$0.183590\pi$
$947$	33.5623i	1.09063i	−0.838232	+	0.545314i	$0.816410\pi$
$948$	5.61803i	0.182465i
$949$	22.8328	0.741185
$950$	0	0
$951$	20.5623	0.666778
$952$	− 3.23607i	− 0.104882i
$953$	5.30495i	0.171844i	0.996302	+	0.0859221i	$0.0273836\pi$
$953$	5.30495i	0.171844i	−0.996302	+	0.0859221i	$0.972616\pi$
$954$	2.09017	0.0676718
$955$	0	0
$956$	12.2918	0.397545
$957$	30.6525i	0.990854i
$958$	− 29.1246i	− 0.940973i
$959$	31.8885	1.02973
$960$	0	0
$961$	12.7984	0.412851
$962$	51.7771i	1.66936i
$963$	− 11.6180i	− 0.374386i
$964$	−9.56231	−0.307981
$965$	0	0
$966$	−11.7082	−0.376705
$967$	− 10.9098i	− 0.350836i	−0.984494	−	0.175418i	$-0.943872\pi$
$967$	− 10.9098i	− 0.350836i	0.984494	−	0.175418i	$-0.0561278\pi$
$968$	2.09017i	0.0671806i
$969$	−7.05573	−0.226663
$970$	0	0
$971$	−14.2148	−0.456174	−0.228087	−	0.973641i	$-0.573247\pi$
$971$	−14.2148	−0.456174	−0.228087	+	0.973641i	$0.573247\pi$
$972$	1.00000i	0.0320750i
$973$	27.4164i	0.878930i
$974$	−17.7984	−0.570297
$975$	0	0
$976$	2.76393	0.0884713
$977$	0.763932i	0.0244404i	0.999925	+	0.0122202i	$0.00388990\pi$
$977$	0.763932i	0.0244404i	−0.999925	+	0.0122202i	$0.996110\pi$
$978$	0.472136i	0.0150972i
$979$	−12.7639	−0.407937
$980$	0	0
$981$	17.2361	0.550305
$982$	25.2705i	0.806414i
$983$	40.1803i	1.28155i	0.767727	+	0.640777i	$0.221388\pi$
$983$	40.1803i	1.28155i	−0.767727	+	0.640777i	$0.778612\pi$
$984$	5.70820	0.181971
$985$	0	0
$986$	10.4721	0.333501
$987$	4.47214i	0.142350i
$988$	36.9443i	1.17535i
$989$	34.4721	1.09615
$990$	0	0
$991$	29.4508	0.935537	0.467769	−	0.883851i	$-0.345058\pi$
$991$	29.4508	0.935537	0.467769	+	0.883851i	$0.345058\pi$
$992$	− 6.61803i	− 0.210123i
$993$	18.0000i	0.571213i
$994$	−14.4721	−0.459028
$995$	0	0
$996$	−2.14590	−0.0679954
$997$	5.59675i	0.177251i	0.996065	+	0.0886254i	$0.0282474\pi$
$997$	5.59675i	0.177251i	−0.996065	+	0.0886254i	$0.971753\pi$
$998$	35.5967i	1.12680i
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3750.2.c.b.1249.1		4
5.2	odd	4		3750.2.a.f.1.2		2
5.3	odd	4		3750.2.a.d.1.1		2
5.4	even	2	inner	3750.2.c.b.1249.4		4
25.3	odd	20		750.2.g.b.451.1		4
25.4	even	10		750.2.h.b.49.2		8
25.6	even	5		750.2.h.b.199.2		8
25.8	odd	20		750.2.g.b.301.1		4
25.17	odd	20		150.2.g.a.61.1	✓	4
25.19	even	10		750.2.h.b.199.1		8
25.21	even	5		750.2.h.b.49.1		8
25.22	odd	20		150.2.g.a.91.1	yes	4
75.17	even	20		450.2.h.c.361.1		4
75.47	even	20		450.2.h.c.91.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.a.61.1	✓	4	25.17	odd	20
150.2.g.a.91.1	yes	4	25.22	odd	20
450.2.h.c.91.1		4	75.47	even	20
450.2.h.c.361.1		4	75.17	even	20
750.2.g.b.301.1		4	25.8	odd	20
750.2.g.b.451.1		4	25.3	odd	20
750.2.h.b.49.1		8	25.21	even	5
750.2.h.b.49.2		8	25.4	even	10
750.2.h.b.199.1		8	25.19	even	10
750.2.h.b.199.2		8	25.6	even	5
3750.2.a.d.1.1		2	5.3	odd	4
3750.2.a.f.1.2		2	5.2	odd	4
3750.2.c.b.1249.1		4	1.1	even	1	trivial
3750.2.c.b.1249.4		4	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 3750 = 2 \cdot 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3750.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -2.61803i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -2.61803i q^{7} +1.00000i q^{8} -1.00000 q^{9} +3.61803 q^{11} +1.00000i q^{12} -6.47214i q^{13} -2.61803 q^{14} +1.00000 q^{16} -1.23607i q^{17} +1.00000i q^{18} +5.70820 q^{19} -2.61803 q^{21} -3.61803i q^{22} +4.47214i q^{23} +1.00000 q^{24} -6.47214 q^{26} +1.00000i q^{27} +2.61803i q^{28} -8.47214 q^{29} +6.61803 q^{31} -1.00000i q^{32} -3.61803i q^{33} -1.23607 q^{34} +1.00000 q^{36} -8.00000i q^{37} -5.70820i q^{38} -6.47214 q^{39} +5.70820 q^{41} +2.61803i q^{42} -7.70820i q^{43} -3.61803 q^{44} +4.47214 q^{46} -1.70820i q^{47} -1.00000i q^{48} +0.145898 q^{49} -1.23607 q^{51} +6.47214i q^{52} -2.09017i q^{53} +1.00000 q^{54} +2.61803 q^{56} -5.70820i q^{57} +8.47214i q^{58} +3.61803 q^{59} +2.76393 q^{61} -6.61803i q^{62} +2.61803i q^{63} -1.00000 q^{64} -3.61803 q^{66} +1.52786i q^{67} +1.23607i q^{68} +4.47214 q^{69} +5.52786 q^{71} -1.00000i q^{72} +3.52786i q^{73} -8.00000 q^{74} -5.70820 q^{76} -9.47214i q^{77} +6.47214i q^{78} +5.61803 q^{79} +1.00000 q^{81} -5.70820i q^{82} +2.14590i q^{83} +2.61803 q^{84} -7.70820 q^{86} +8.47214i q^{87} +3.61803i q^{88} -3.52786 q^{89} -16.9443 q^{91} -4.47214i q^{92} -6.61803i q^{93} -1.70820 q^{94} -1.00000 q^{96} +3.38197i q^{97} -0.145898i q^{98} -3.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 10 q^{11} - 6 q^{14} + 4 q^{16} - 4 q^{19} - 6 q^{21} + 4 q^{24} - 8 q^{26} - 16 q^{29} + 22 q^{31} + 4 q^{34} + 4 q^{36} - 8 q^{39} - 4 q^{41} - 10 q^{44} + 14 q^{49} + 4 q^{51} + 4 q^{54} + 6 q^{56} + 10 q^{59} + 20 q^{61} - 4 q^{64} - 10 q^{66} + 40 q^{71} - 32 q^{74} + 4 q^{76} + 18 q^{79} + 4 q^{81} + 6 q^{84} - 4 q^{86} - 32 q^{89} - 32 q^{91} + 20 q^{94} - 4 q^{96} - 10 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 10 * q^11 - 6 * q^14 + 4 * q^16 - 4 * q^19 - 6 * q^21 + 4 * q^24 - 8 * q^26 - 16 * q^29 + 22 * q^31 + 4 * q^34 + 4 * q^36 - 8 * q^39 - 4 * q^41 - 10 * q^44 + 14 * q^49 + 4 * q^51 + 4 * q^54 + 6 * q^56 + 10 * q^59 + 20 * q^61 - 4 * q^64 - 10 * q^66 + 40 * q^71 - 32 * q^74 + 4 * q^76 + 18 * q^79 + 4 * q^81 + 6 * q^84 - 4 * q^86 - 32 * q^89 - 32 * q^91 + 20 * q^94 - 4 * q^96 - 10 * q^99

Introduction

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