LMFDB - Embedded newform 3750.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3750,2,Mod(1,3750)]

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, 0]))

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

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

chi := DirichletCharacter("3750.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3750 = 2 \cdot 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3750.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:	$29.9439007580$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	3750.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.61803 q^{11} +1.00000 q^{12} +6.47214 q^{13} +2.61803 q^{14} +1.00000 q^{16} -1.23607 q^{17} -1.00000 q^{18} -5.70820 q^{19} -2.61803 q^{21} -3.61803 q^{22} -4.47214 q^{23} -1.00000 q^{24} -6.47214 q^{26} +1.00000 q^{27} -2.61803 q^{28} +8.47214 q^{29} +6.61803 q^{31} -1.00000 q^{32} +3.61803 q^{33} +1.23607 q^{34} +1.00000 q^{36} -8.00000 q^{37} +5.70820 q^{38} +6.47214 q^{39} +5.70820 q^{41} +2.61803 q^{42} +7.70820 q^{43} +3.61803 q^{44} +4.47214 q^{46} -1.70820 q^{47} +1.00000 q^{48} -0.145898 q^{49} -1.23607 q^{51} +6.47214 q^{52} +2.09017 q^{53} -1.00000 q^{54} +2.61803 q^{56} -5.70820 q^{57} -8.47214 q^{58} -3.61803 q^{59} +2.76393 q^{61} -6.61803 q^{62} -2.61803 q^{63} +1.00000 q^{64} -3.61803 q^{66} +1.52786 q^{67} -1.23607 q^{68} -4.47214 q^{69} +5.52786 q^{71} -1.00000 q^{72} -3.52786 q^{73} +8.00000 q^{74} -5.70820 q^{76} -9.47214 q^{77} -6.47214 q^{78} -5.61803 q^{79} +1.00000 q^{81} -5.70820 q^{82} -2.14590 q^{83} -2.61803 q^{84} -7.70820 q^{86} +8.47214 q^{87} -3.61803 q^{88} +3.52786 q^{89} -16.9443 q^{91} -4.47214 q^{92} +6.61803 q^{93} +1.70820 q^{94} -1.00000 q^{96} +3.38197 q^{97} +0.145898 q^{98} +3.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - 3 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9} + 5 q^{11} + 2 q^{12} + 4 q^{13} + 3 q^{14} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} - 3 q^{21} - 5 q^{22} - 2 q^{24} - 4 q^{26} + 2 q^{27} - 3 q^{28} + 8 q^{29} + 11 q^{31} - 2 q^{32} + 5 q^{33} - 2 q^{34} + 2 q^{36} - 16 q^{37} - 2 q^{38} + 4 q^{39} - 2 q^{41} + 3 q^{42} + 2 q^{43} + 5 q^{44} + 10 q^{47} + 2 q^{48} - 7 q^{49} + 2 q^{51} + 4 q^{52} - 7 q^{53} - 2 q^{54} + 3 q^{56} + 2 q^{57} - 8 q^{58} - 5 q^{59} + 10 q^{61} - 11 q^{62} - 3 q^{63} + 2 q^{64} - 5 q^{66} + 12 q^{67} + 2 q^{68} + 20 q^{71} - 2 q^{72} - 16 q^{73} + 16 q^{74} + 2 q^{76} - 10 q^{77} - 4 q^{78} - 9 q^{79} + 2 q^{81} + 2 q^{82} - 11 q^{83} - 3 q^{84} - 2 q^{86} + 8 q^{87} - 5 q^{88} + 16 q^{89} - 16 q^{91} + 11 q^{93} - 10 q^{94} - 2 q^{96} + 9 q^{97} + 7 q^{98} + 5 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - 3 * q^7 - 2 * q^8 + 2 * q^9 + 5 * q^11 + 2 * q^12 + 4 * q^13 + 3 * q^14 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 - 3 * q^21 - 5 * q^22 - 2 * q^24 - 4 * q^26 + 2 * q^27 - 3 * q^28 + 8 * q^29 + 11 * q^31 - 2 * q^32 + 5 * q^33 - 2 * q^34 + 2 * q^36 - 16 * q^37 - 2 * q^38 + 4 * q^39 - 2 * q^41 + 3 * q^42 + 2 * q^43 + 5 * q^44 + 10 * q^47 + 2 * q^48 - 7 * q^49 + 2 * q^51 + 4 * q^52 - 7 * q^53 - 2 * q^54 + 3 * q^56 + 2 * q^57 - 8 * q^58 - 5 * q^59 + 10 * q^61 - 11 * q^62 - 3 * q^63 + 2 * q^64 - 5 * q^66 + 12 * q^67 + 2 * q^68 + 20 * q^71 - 2 * q^72 - 16 * q^73 + 16 * q^74 + 2 * q^76 - 10 * q^77 - 4 * q^78 - 9 * q^79 + 2 * q^81 + 2 * q^82 - 11 * q^83 - 3 * q^84 - 2 * q^86 + 8 * q^87 - 5 * q^88 + 16 * q^89 - 16 * q^91 + 11 * q^93 - 10 * q^94 - 2 * q^96 + 9 * q^97 + 7 * q^98 + 5 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	−2.61803	−0.989524	−0.494762	−	0.869029i	$-0.664745\pi$
$7$	−2.61803	−0.989524	−0.494762	+	0.869029i	$0.664745\pi$
$8$	−1.00000	−0.353553
$9$	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	$0.316363\pi$
$12$	1.00000	0.288675
$13$	6.47214	1.79505	0.897524	−	0.440966i	$-0.145364\pi$
$13$	6.47214	1.79505	0.897524	+	0.440966i	$0.145364\pi$
$14$	2.61803	0.699699
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.23607	−0.299791	−0.149895	−	0.988702i	$-0.547894\pi$
$17$	−1.23607	−0.299791	−0.149895	+	0.988702i	$0.547894\pi$
$18$	−1.00000	−0.235702
$19$	−5.70820	−1.30955	−0.654776	−	0.755823i	$-0.727237\pi$
$19$	−5.70820	−1.30955	−0.654776	+	0.755823i	$0.727237\pi$
$20$	0	0
$21$	−2.61803	−0.571302
$22$	−3.61803	−0.771367
$23$	−4.47214	−0.932505	−0.466252	−	0.884652i	$-0.654396\pi$
$23$	−4.47214	−0.932505	−0.466252	+	0.884652i	$0.654396\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−6.47214	−1.26929
$27$	1.00000	0.192450
$28$	−2.61803	−0.494762
$29$	8.47214	1.57324	0.786618	−	0.617440i	$-0.211830\pi$
$29$	8.47214	1.57324	0.786618	+	0.617440i	$0.211830\pi$
$30$	0	0
$31$	6.61803	1.18863	0.594317	−	0.804231i	$-0.297422\pi$
$31$	6.61803	1.18863	0.594317	+	0.804231i	$0.297422\pi$
$32$	−1.00000	−0.176777
$33$	3.61803	0.629819
$34$	1.23607	0.211984
$35$	0	0
$36$	1.00000	0.166667
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	5.70820	0.925993
$39$	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	$0.352942\pi$
$42$	2.61803	0.403971
$43$	7.70820	1.17549	0.587745	−	0.809046i	$-0.300016\pi$
$43$	7.70820	1.17549	0.587745	+	0.809046i	$0.300016\pi$
$44$	3.61803	0.545439
$45$	0	0
$46$	4.47214	0.659380
$47$	−1.70820	−0.249167	−0.124584	−	0.992209i	$-0.539759\pi$
$47$	−1.70820	−0.249167	−0.124584	+	0.992209i	$0.539759\pi$
$48$	1.00000	0.144338
$49$	−0.145898	−0.0208426
$50$	0	0
$51$	−1.23607	−0.173084
$52$	6.47214	0.897524
$53$	2.09017	0.287107	0.143553	−	0.989643i	$-0.454147\pi$
$53$	2.09017	0.287107	0.143553	+	0.989643i	$0.454147\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	2.61803	0.349850
$57$	−5.70820	−0.756070
$58$	−8.47214	−1.11245
$59$	−3.61803	−0.471028	−0.235514	−	0.971871i	$-0.575677\pi$
$59$	−3.61803	−0.471028	−0.235514	+	0.971871i	$0.575677\pi$
$60$	0	0
$61$	2.76393	0.353885	0.176943	−	0.984221i	$-0.443379\pi$
$61$	2.76393	0.353885	0.176943	+	0.984221i	$0.443379\pi$
$62$	−6.61803	−0.840491
$63$	−2.61803	−0.329841
$64$	1.00000	0.125000
$65$	0	0
$66$	−3.61803	−0.445349
$67$	1.52786	0.186658	0.0933292	−	0.995635i	$-0.470249\pi$
$67$	1.52786	0.186658	0.0933292	+	0.995635i	$0.470249\pi$
$68$	−1.23607	−0.149895
$69$	−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	$0.393619\pi$
$72$	−1.00000	−0.117851
$73$	−3.52786	−0.412905	−0.206453	−	0.978457i	$-0.566192\pi$
$73$	−3.52786	−0.412905	−0.206453	+	0.978457i	$0.566192\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	−5.70820	−0.654776
$77$	−9.47214	−1.07945
$78$	−6.47214	−0.732825
$79$	−5.61803	−0.632078	−0.316039	−	0.948746i	$-0.602353\pi$
$79$	−5.61803	−0.632078	−0.316039	+	0.948746i	$0.602353\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−5.70820	−0.630366
$83$	−2.14590	−0.235543	−0.117771	−	0.993041i	$-0.537575\pi$
$83$	−2.14590	−0.235543	−0.117771	+	0.993041i	$0.537575\pi$
$84$	−2.61803	−0.285651
$85$	0	0
$86$	−7.70820	−0.831197
$87$	8.47214	0.908308
$88$	−3.61803	−0.385684
$89$	3.52786	0.373953	0.186976	−	0.982364i	$-0.440131\pi$
$89$	3.52786	0.373953	0.186976	+	0.982364i	$0.440131\pi$
$90$	0	0
$91$	−16.9443	−1.77624
$92$	−4.47214	−0.466252
$93$	6.61803	0.686258
$94$	1.70820	0.176188
$95$	0	0
$96$	−1.00000	−0.102062
$97$	3.38197	0.343387	0.171693	−	0.985150i	$-0.445076\pi$
$97$	3.38197	0.343387	0.171693	+	0.985150i	$0.445076\pi$
$98$	0.145898	0.0147379
$99$	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	$0.430043\pi$
$102$	1.23607	0.122389
$103$	−14.3262	−1.41161	−0.705803	−	0.708408i	$-0.749414\pi$
$103$	−14.3262	−1.41161	−0.705803	+	0.708408i	$0.749414\pi$
$104$	−6.47214	−0.634645
$105$	0	0
$106$	−2.09017	−0.203015
$107$	11.6180	1.12316	0.561579	−	0.827423i	$-0.310194\pi$
$107$	11.6180	1.12316	0.561579	+	0.827423i	$0.310194\pi$
$108$	1.00000	0.0962250
$109$	17.2361	1.65092	0.825458	−	0.564464i	$-0.190917\pi$
$109$	17.2361	1.65092	0.825458	+	0.564464i	$0.190917\pi$
$110$	0	0
$111$	−8.00000	−0.759326
$112$	−2.61803	−0.247381
$113$	19.2361	1.80958	0.904789	−	0.425861i	$-0.140029\pi$
$113$	19.2361	1.80958	0.904789	+	0.425861i	$0.140029\pi$
$114$	5.70820	0.534622
$115$	0	0
$116$	8.47214	0.786618
$117$	6.47214	0.598349
$118$	3.61803	0.333067
$119$	3.23607	0.296650
$120$	0	0
$121$	2.09017	0.190015
$122$	−2.76393	−0.250235
$123$	5.70820	0.514691
$124$	6.61803	0.594317
$125$	0	0
$126$	2.61803	0.233233
$127$	−13.6180	−1.20841	−0.604203	−	0.796831i	$-0.706508\pi$
$127$	−13.6180	−1.20841	−0.604203	+	0.796831i	$0.706508\pi$
$128$	−1.00000	−0.0883883
$129$	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	$0.785527\pi$
$132$	3.61803	0.314909
$133$	14.9443	1.29583
$134$	−1.52786	−0.131987
$135$	0	0
$136$	1.23607	0.105992
$137$	12.1803	1.04064	0.520318	−	0.853972i	$-0.325813\pi$
$137$	12.1803	1.04064	0.520318	+	0.853972i	$0.325813\pi$
$138$	4.47214	0.380693
$139$	10.4721	0.888235	0.444117	−	0.895969i	$-0.353517\pi$
$139$	10.4721	0.888235	0.444117	+	0.895969i	$0.353517\pi$
$140$	0	0
$141$	−1.70820	−0.143857
$142$	−5.52786	−0.463888
$143$	23.4164	1.95818
$144$	1.00000	0.0833333
$145$	0	0
$146$	3.52786	0.291968
$147$	−0.145898	−0.0120335
$148$	−8.00000	−0.657596
$149$	22.0902	1.80970	0.904849	−	0.425733i	$-0.139984\pi$
$149$	22.0902	1.80970	0.904849	+	0.425733i	$0.139984\pi$
$150$	0	0
$151$	18.3262	1.49137	0.745684	−	0.666300i	$-0.232123\pi$
$151$	18.3262	1.49137	0.745684	+	0.666300i	$0.232123\pi$
$152$	5.70820	0.462996
$153$	−1.23607	−0.0999302
$154$	9.47214	0.763286
$155$	0	0
$156$	6.47214	0.518186
$157$	−8.65248	−0.690543	−0.345271	−	0.938503i	$-0.612213\pi$
$157$	−8.65248	−0.690543	−0.345271	+	0.938503i	$0.612213\pi$
$158$	5.61803	0.446947
$159$	2.09017	0.165761
$160$	0	0
$161$	11.7082	0.922736
$162$	−1.00000	−0.0785674
$163$	0.472136	0.0369805	0.0184903	−	0.999829i	$-0.494114\pi$
$163$	0.472136	0.0369805	0.0184903	+	0.999829i	$0.494114\pi$
$164$	5.70820	0.445736
$165$	0	0
$166$	2.14590	0.166554
$167$	−11.7082	−0.906008	−0.453004	−	0.891508i	$-0.649648\pi$
$167$	−11.7082	−0.906008	−0.453004	+	0.891508i	$0.649648\pi$
$168$	2.61803	0.201986
$169$	28.8885	2.22220
$170$	0	0
$171$	−5.70820	−0.436517
$172$	7.70820	0.587745
$173$	−5.09017	−0.386998	−0.193499	−	0.981100i	$-0.561984\pi$
$173$	−5.09017	−0.386998	−0.193499	+	0.981100i	$0.561984\pi$
$174$	−8.47214	−0.642271
$175$	0	0
$176$	3.61803	0.272720
$177$	−3.61803	−0.271948
$178$	−3.52786	−0.264425
$179$	9.85410	0.736530	0.368265	−	0.929721i	$-0.379952\pi$
$179$	9.85410	0.736530	0.368265	+	0.929721i	$0.379952\pi$
$180$	0	0
$181$	−6.65248	−0.494475	−0.247237	−	0.968955i	$-0.579523\pi$
$181$	−6.65248	−0.494475	−0.247237	+	0.968955i	$0.579523\pi$
$182$	16.9443	1.25599
$183$	2.76393	0.204316
$184$	4.47214	0.329690
$185$	0	0
$186$	−6.61803	−0.485258
$187$	−4.47214	−0.327035
$188$	−1.70820	−0.124584
$189$	−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	$0.450375\pi$
$192$	1.00000	0.0721688
$193$	−17.8541	−1.28517	−0.642583	−	0.766216i	$-0.722137\pi$
$193$	−17.8541	−1.28517	−0.642583	+	0.766216i	$0.722137\pi$
$194$	−3.38197	−0.242811
$195$	0	0
$196$	−0.145898	−0.0104213
$197$	17.0902	1.21762	0.608812	−	0.793314i	$-0.291646\pi$
$197$	17.0902	1.21762	0.608812	+	0.793314i	$0.291646\pi$
$198$	−3.61803	−0.257122
$199$	19.5066	1.38278	0.691392	−	0.722480i	$-0.256998\pi$
$199$	19.5066	1.38278	0.691392	+	0.722480i	$0.256998\pi$
$200$	0	0
$201$	1.52786	0.107767
$202$	−4.38197	−0.308314
$203$	−22.1803	−1.55675
$204$	−1.23607	−0.0865421
$205$	0	0
$206$	14.3262	0.998156
$207$	−4.47214	−0.310835
$208$	6.47214	0.448762
$209$	−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	$0.537519\pi$
$212$	2.09017	0.143553
$213$	5.52786	0.378763
$214$	−11.6180	−0.794192
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	−17.3262	−1.17618
$218$	−17.2361	−1.16737
$219$	−3.52786	−0.238391
$220$	0	0
$221$	−8.00000	−0.538138
$222$	8.00000	0.536925
$223$	8.09017	0.541758	0.270879	−	0.962613i	$-0.412686\pi$
$223$	8.09017	0.541758	0.270879	+	0.962613i	$0.412686\pi$
$224$	2.61803	0.174925
$225$	0	0
$226$	−19.2361	−1.27956
$227$	22.2705	1.47815	0.739073	−	0.673626i	$-0.235264\pi$
$227$	22.2705	1.47815	0.739073	+	0.673626i	$0.235264\pi$
$228$	−5.70820	−0.378035
$229$	−5.52786	−0.365292	−0.182646	−	0.983179i	$-0.558466\pi$
$229$	−5.52786	−0.365292	−0.182646	+	0.983179i	$0.558466\pi$
$230$	0	0
$231$	−9.47214	−0.623221
$232$	−8.47214	−0.556223
$233$	−18.6525	−1.22196	−0.610982	−	0.791644i	$-0.709225\pi$
$233$	−18.6525	−1.22196	−0.610982	+	0.791644i	$0.709225\pi$
$234$	−6.47214	−0.423097
$235$	0	0
$236$	−3.61803	−0.235514
$237$	−5.61803	−0.364931
$238$	−3.23607	−0.209763
$239$	12.2918	0.795090	0.397545	−	0.917583i	$-0.369862\pi$
$239$	12.2918	0.795090	0.397545	+	0.917583i	$0.369862\pi$
$240$	0	0
$241$	9.56231	0.615962	0.307981	−	0.951392i	$-0.400347\pi$
$241$	9.56231	0.615962	0.307981	+	0.951392i	$0.400347\pi$
$242$	−2.09017	−0.134361
$243$	1.00000	0.0641500
$244$	2.76393	0.176943
$245$	0	0
$246$	−5.70820	−0.363942
$247$	−36.9443	−2.35071
$248$	−6.61803	−0.420246
$249$	−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	$0.359210\pi$
$252$	−2.61803	−0.164921
$253$	−16.1803	−1.01725
$254$	13.6180	0.854471
$255$	0	0
$256$	1.00000	0.0625000
$257$	22.0000	1.37232	0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000	1.37232	0.686161	+	0.727450i	$0.259294\pi$
$258$	−7.70820	−0.479892
$259$	20.9443	1.30141
$260$	0	0
$261$	8.47214	0.524412
$262$	17.8885	1.10516
$263$	11.7082	0.721959	0.360979	−	0.932574i	$-0.382442\pi$
$263$	11.7082	0.721959	0.360979	+	0.932574i	$0.382442\pi$
$264$	−3.61803	−0.222675
$265$	0	0
$266$	−14.9443	−0.916292
$267$	3.52786	0.215902
$268$	1.52786	0.0933292
$269$	−9.09017	−0.554237	−0.277119	−	0.960836i	$-0.589380\pi$
$269$	−9.09017	−0.554237	−0.277119	+	0.960836i	$0.589380\pi$
$270$	0	0
$271$	−18.0344	−1.09551	−0.547757	−	0.836637i	$-0.684518\pi$
$271$	−18.0344	−1.09551	−0.547757	+	0.836637i	$0.684518\pi$
$272$	−1.23607	−0.0749476
$273$	−16.9443	−1.02551
$274$	−12.1803	−0.735841
$275$	0	0
$276$	−4.47214	−0.269191
$277$	−16.9443	−1.01808	−0.509041	−	0.860742i	$-0.670000\pi$
$277$	−16.9443	−1.01808	−0.509041	+	0.860742i	$0.670000\pi$
$278$	−10.4721	−0.628077
$279$	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	$0.443800\pi$
$282$	1.70820	0.101722
$283$	−4.58359	−0.272466	−0.136233	−	0.990677i	$-0.543500\pi$
$283$	−4.58359	−0.272466	−0.136233	+	0.990677i	$0.543500\pi$
$284$	5.52786	0.328018
$285$	0	0
$286$	−23.4164	−1.38464
$287$	−14.9443	−0.882132
$288$	−1.00000	−0.0589256
$289$	−15.4721	−0.910126
$290$	0	0
$291$	3.38197	0.198254
$292$	−3.52786	−0.206453
$293$	22.0902	1.29052	0.645261	−	0.763962i	$-0.276749\pi$
$293$	22.0902	1.29052	0.645261	+	0.763962i	$0.276749\pi$
$294$	0.145898	0.00850895
$295$	0	0
$296$	8.00000	0.464991
$297$	3.61803	0.209940
$298$	−22.0902	−1.27965
$299$	−28.9443	−1.67389
$300$	0	0
$301$	−20.1803	−1.16318
$302$	−18.3262	−1.05456
$303$	4.38197	0.251737
$304$	−5.70820	−0.327388
$305$	0	0
$306$	1.23607	0.0706613
$307$	−10.0000	−0.570730	−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000	−0.570730	−0.285365	+	0.958419i	$0.592115\pi$
$308$	−9.47214	−0.539725
$309$	−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	$0.509529\pi$
$312$	−6.47214	−0.366413
$313$	16.2705	0.919664	0.459832	−	0.888006i	$-0.347910\pi$
$313$	16.2705	0.919664	0.459832	+	0.888006i	$0.347910\pi$
$314$	8.65248	0.488287
$315$	0	0
$316$	−5.61803	−0.316039
$317$	20.5623	1.15489	0.577447	−	0.816428i	$-0.304049\pi$
$317$	20.5623	1.15489	0.577447	+	0.816428i	$0.304049\pi$
$318$	−2.09017	−0.117211
$319$	30.6525	1.71621
$320$	0	0
$321$	11.6180	0.648455
$322$	−11.7082	−0.652473
$323$	7.05573	0.392591
$324$	1.00000	0.0555556
$325$	0	0
$326$	−0.472136	−0.0261492
$327$	17.2361	0.953157
$328$	−5.70820	−0.315183
$329$	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	$0.664716\pi$
$332$	−2.14590	−0.117771
$333$	−8.00000	−0.438397
$334$	11.7082	0.640644
$335$	0	0
$336$	−2.61803	−0.142825
$337$	−0.909830	−0.0495616	−0.0247808	−	0.999693i	$-0.507889\pi$
$337$	−0.909830	−0.0495616	−0.0247808	+	0.999693i	$0.507889\pi$
$338$	−28.8885	−1.57133
$339$	19.2361	1.04476
$340$	0	0
$341$	23.9443	1.29666
$342$	5.70820	0.308664
$343$	18.7082	1.01015
$344$	−7.70820	−0.415599
$345$	0	0
$346$	5.09017	0.273649
$347$	−20.5623	−1.10384	−0.551921	−	0.833896i	$-0.686105\pi$
$347$	−20.5623	−1.10384	−0.551921	+	0.833896i	$0.686105\pi$
$348$	8.47214	0.454154
$349$	−27.8885	−1.49284	−0.746420	−	0.665475i	$-0.768229\pi$
$349$	−27.8885	−1.49284	−0.746420	+	0.665475i	$0.768229\pi$
$350$	0	0
$351$	6.47214	0.345457
$352$	−3.61803	−0.192842
$353$	13.2361	0.704485	0.352242	−	0.935909i	$-0.385419\pi$
$353$	13.2361	0.704485	0.352242	+	0.935909i	$0.385419\pi$
$354$	3.61803	0.192296
$355$	0	0
$356$	3.52786	0.186976
$357$	3.23607	0.171271
$358$	−9.85410	−0.520805
$359$	22.1803	1.17063	0.585317	−	0.810805i	$-0.300970\pi$
$359$	22.1803	1.17063	0.585317	+	0.810805i	$0.300970\pi$
$360$	0	0
$361$	13.5836	0.714926
$362$	6.65248	0.349646
$363$	2.09017	0.109705
$364$	−16.9443	−0.888121
$365$	0	0
$366$	−2.76393	−0.144473
$367$	30.6180	1.59825	0.799124	−	0.601166i	$-0.205297\pi$
$367$	30.6180	1.59825	0.799124	+	0.601166i	$0.205297\pi$
$368$	−4.47214	−0.233126
$369$	5.70820	0.297157
$370$	0	0
$371$	−5.47214	−0.284099
$372$	6.61803	0.343129
$373$	11.5279	0.596890	0.298445	−	0.954427i	$-0.403532\pi$
$373$	11.5279	0.596890	0.298445	+	0.954427i	$0.403532\pi$
$374$	4.47214	0.231249
$375$	0	0
$376$	1.70820	0.0880939
$377$	54.8328	2.82403
$378$	2.61803	0.134657
$379$	−20.1803	−1.03659	−0.518297	−	0.855201i	$-0.673434\pi$
$379$	−20.1803	−1.03659	−0.518297	+	0.855201i	$0.673434\pi$
$380$	0	0
$381$	−13.6180	−0.697673
$382$	−4.29180	−0.219587
$383$	20.0000	1.02195	0.510976	−	0.859595i	$-0.329284\pi$
$383$	20.0000	1.02195	0.510976	+	0.859595i	$0.329284\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	17.8541	0.908750
$387$	7.70820	0.391830
$388$	3.38197	0.171693
$389$	−12.3820	−0.627791	−0.313895	−	0.949458i	$-0.601634\pi$
$389$	−12.3820	−0.627791	−0.313895	+	0.949458i	$0.601634\pi$
$390$	0	0
$391$	5.52786	0.279556
$392$	0.145898	0.00736896
$393$	−17.8885	−0.902358
$394$	−17.0902	−0.860990
$395$	0	0
$396$	3.61803	0.181813
$397$	30.7639	1.54400	0.771999	−	0.635624i	$-0.219257\pi$
$397$	30.7639	1.54400	0.771999	+	0.635624i	$0.219257\pi$
$398$	−19.5066	−0.977776
$399$	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	$0.278145\pi$
$402$	−1.52786	−0.0762029
$403$	42.8328	2.13365
$404$	4.38197	0.218011
$405$	0	0
$406$	22.1803	1.10079
$407$	−28.9443	−1.43471
$408$	1.23607	0.0611945
$409$	5.79837	0.286711	0.143356	−	0.989671i	$-0.454211\pi$
$409$	5.79837	0.286711	0.143356	+	0.989671i	$0.454211\pi$
$410$	0	0
$411$	12.1803	0.600812
$412$	−14.3262	−0.705803
$413$	9.47214	0.466093
$414$	4.47214	0.219793
$415$	0	0
$416$	−6.47214	−0.317323
$417$	10.4721	0.512823
$418$	20.6525	1.01015
$419$	−3.09017	−0.150965	−0.0754823	−	0.997147i	$-0.524050\pi$
$419$	−3.09017	−0.150965	−0.0754823	+	0.997147i	$0.524050\pi$
$420$	0	0
$421$	−22.7639	−1.10945	−0.554723	−	0.832035i	$-0.687176\pi$
$421$	−22.7639	−1.10945	−0.554723	+	0.832035i	$0.687176\pi$
$422$	3.41641	0.166308
$423$	−1.70820	−0.0830557
$424$	−2.09017	−0.101508
$425$	0	0
$426$	−5.52786	−0.267826
$427$	−7.23607	−0.350178
$428$	11.6180	0.561579
$429$	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	$0.367131\pi$
$432$	1.00000	0.0481125
$433$	−15.5066	−0.745199	−0.372599	−	0.927992i	$-0.621533\pi$
$433$	−15.5066	−0.745199	−0.372599	+	0.927992i	$0.621533\pi$
$434$	17.3262	0.831686
$435$	0	0
$436$	17.2361	0.825458
$437$	25.5279	1.22116
$438$	3.52786	0.168568
$439$	−23.5066	−1.12191	−0.560954	−	0.827847i	$-0.689566\pi$
$439$	−23.5066	−1.12191	−0.560954	+	0.827847i	$0.689566\pi$
$440$	0	0
$441$	−0.145898	−0.00694753
$442$	8.00000	0.380521
$443$	−16.6180	−0.789547	−0.394773	−	0.918779i	$-0.629177\pi$
$443$	−16.6180	−0.789547	−0.394773	+	0.918779i	$0.629177\pi$
$444$	−8.00000	−0.379663
$445$	0	0
$446$	−8.09017	−0.383081
$447$	22.0902	1.04483
$448$	−2.61803	−0.123690
$449$	−27.7082	−1.30763	−0.653815	−	0.756654i	$-0.726833\pi$
$449$	−27.7082	−1.30763	−0.653815	+	0.756654i	$0.726833\pi$
$450$	0	0
$451$	20.6525	0.972487
$452$	19.2361	0.904789
$453$	18.3262	0.861042
$454$	−22.2705	−1.04521
$455$	0	0
$456$	5.70820	0.267311
$457$	4.09017	0.191330	0.0956650	−	0.995414i	$-0.469502\pi$
$457$	4.09017	0.191330	0.0956650	+	0.995414i	$0.469502\pi$
$458$	5.52786	0.258300
$459$	−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	$0.443650\pi$
$462$	9.47214	0.440684
$463$	22.8328	1.06113	0.530565	−	0.847644i	$-0.321980\pi$
$463$	22.8328	1.06113	0.530565	+	0.847644i	$0.321980\pi$
$464$	8.47214	0.393309
$465$	0	0
$466$	18.6525	0.864059
$467$	−10.6738	−0.493923	−0.246961	−	0.969025i	$-0.579432\pi$
$467$	−10.6738	−0.493923	−0.246961	+	0.969025i	$0.579432\pi$
$468$	6.47214	0.299175
$469$	−4.00000	−0.184703
$470$	0	0
$471$	−8.65248	−0.398685
$472$	3.61803	0.166534
$473$	27.8885	1.28232
$474$	5.61803	0.258045
$475$	0	0
$476$	3.23607	0.148325
$477$	2.09017	0.0957023
$478$	−12.2918	−0.562214
$479$	−29.1246	−1.33074	−0.665369	−	0.746515i	$-0.731726\pi$
$479$	−29.1246	−1.33074	−0.665369	+	0.746515i	$0.731726\pi$
$480$	0	0
$481$	−51.7771	−2.36083
$482$	−9.56231	−0.435551
$483$	11.7082	0.532742
$484$	2.09017	0.0950077
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−17.7984	−0.806521	−0.403261	−	0.915085i	$-0.632123\pi$
$487$	−17.7984	−0.806521	−0.403261	+	0.915085i	$0.632123\pi$
$488$	−2.76393	−0.125117
$489$	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	$0.693142\pi$
$492$	5.70820	0.257346
$493$	−10.4721	−0.471641
$494$	36.9443	1.66220
$495$	0	0
$496$	6.61803	0.297158
$497$	−14.4721	−0.649164
$498$	2.14590	0.0961600
$499$	35.5967	1.59353	0.796765	−	0.604290i	$-0.206543\pi$
$499$	35.5967	1.59353	0.796765	+	0.604290i	$0.206543\pi$
$500$	0	0
$501$	−11.7082	−0.523084
$502$	−13.5623	−0.605315
$503$	−23.8885	−1.06514	−0.532569	−	0.846387i	$-0.678773\pi$
$503$	−23.8885	−1.06514	−0.532569	+	0.846387i	$0.678773\pi$
$504$	2.61803	0.116617
$505$	0	0
$506$	16.1803	0.719304
$507$	28.8885	1.28299
$508$	−13.6180	−0.604203
$509$	−17.5066	−0.775965	−0.387983	−	0.921667i	$-0.626828\pi$
$509$	−17.5066	−0.775965	−0.387983	+	0.921667i	$0.626828\pi$
$510$	0	0
$511$	9.23607	0.408580
$512$	−1.00000	−0.0441942
$513$	−5.70820	−0.252023
$514$	−22.0000	−0.970378
$515$	0	0
$516$	7.70820	0.339335
$517$	−6.18034	−0.271811
$518$	−20.9443	−0.920238
$519$	−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	$0.399461\pi$
$522$	−8.47214	−0.370815
$523$	−11.0557	−0.483433	−0.241717	−	0.970347i	$-0.577710\pi$
$523$	−11.0557	−0.483433	−0.241717	+	0.970347i	$0.577710\pi$
$524$	−17.8885	−0.781465
$525$	0	0
$526$	−11.7082	−0.510502
$527$	−8.18034	−0.356341
$528$	3.61803	0.157455
$529$	−3.00000	−0.130435
$530$	0	0
$531$	−3.61803	−0.157009
$532$	14.9443	0.647916
$533$	36.9443	1.60023
$534$	−3.52786	−0.152666
$535$	0	0
$536$	−1.52786	−0.0659937
$537$	9.85410	0.425236
$538$	9.09017	0.391905
$539$	−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	$0.690272\pi$
$542$	18.0344	0.774646
$543$	−6.65248	−0.285485
$544$	1.23607	0.0529960
$545$	0	0
$546$	16.9443	0.725148
$547$	−9.70820	−0.415093	−0.207546	−	0.978225i	$-0.566548\pi$
$547$	−9.70820	−0.415093	−0.207546	+	0.978225i	$0.566548\pi$
$548$	12.1803	0.520318
$549$	2.76393	0.117962
$550$	0	0
$551$	−48.3607	−2.06023
$552$	4.47214	0.190347
$553$	14.7082	0.625456
$554$	16.9443	0.719893
$555$	0	0
$556$	10.4721	0.444117
$557$	18.3262	0.776508	0.388254	−	0.921552i	$-0.373078\pi$
$557$	18.3262	0.776508	0.388254	+	0.921552i	$0.373078\pi$
$558$	−6.61803	−0.280164
$559$	49.8885	2.11006
$560$	0	0
$561$	−4.47214	−0.188814
$562$	−5.88854	−0.248393
$563$	−21.2705	−0.896445	−0.448223	−	0.893922i	$-0.647943\pi$
$563$	−21.2705	−0.896445	−0.448223	+	0.893922i	$0.647943\pi$
$564$	−1.70820	−0.0719284
$565$	0	0
$566$	4.58359	0.192663
$567$	−2.61803	−0.109947
$568$	−5.52786	−0.231944
$569$	−27.7771	−1.16448	−0.582238	−	0.813018i	$-0.697823\pi$
$569$	−27.7771	−1.16448	−0.582238	+	0.813018i	$0.697823\pi$
$570$	0	0
$571$	7.88854	0.330125	0.165063	−	0.986283i	$-0.447217\pi$
$571$	7.88854	0.330125	0.165063	+	0.986283i	$0.447217\pi$
$572$	23.4164	0.979089
$573$	4.29180	0.179292
$574$	14.9443	0.623762
$575$	0	0
$576$	1.00000	0.0416667
$577$	−8.97871	−0.373789	−0.186894	−	0.982380i	$-0.559842\pi$
$577$	−8.97871	−0.373789	−0.186894	+	0.982380i	$0.559842\pi$
$578$	15.4721	0.643556
$579$	−17.8541	−0.741991
$580$	0	0
$581$	5.61803	0.233075
$582$	−3.38197	−0.140187
$583$	7.56231	0.313199
$584$	3.52786	0.145984
$585$	0	0
$586$	−22.0902	−0.912537
$587$	0.965558	0.0398528	0.0199264	−	0.999801i	$-0.493657\pi$
$587$	0.965558	0.0398528	0.0199264	+	0.999801i	$0.493657\pi$
$588$	−0.145898	−0.00601673
$589$	−37.7771	−1.55658
$590$	0	0
$591$	17.0902	0.702996
$592$	−8.00000	−0.328798
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	−3.61803	−0.148450
$595$	0	0
$596$	22.0902	0.904849
$597$	19.5066	0.798351
$598$	28.9443	1.18362
$599$	0.472136	0.0192910	0.00964548	−	0.999953i	$-0.496930\pi$
$599$	0.472136	0.0192910	0.00964548	+	0.999953i	$0.496930\pi$
$600$	0	0
$601$	−7.72949	−0.315292	−0.157646	−	0.987496i	$-0.550391\pi$
$601$	−7.72949	−0.315292	−0.157646	+	0.987496i	$0.550391\pi$
$602$	20.1803	0.822489
$603$	1.52786	0.0622194
$604$	18.3262	0.745684
$605$	0	0
$606$	−4.38197	−0.178005
$607$	−6.56231	−0.266356	−0.133178	−	0.991092i	$-0.542518\pi$
$607$	−6.56231	−0.266356	−0.133178	+	0.991092i	$0.542518\pi$
$608$	5.70820	0.231498
$609$	−22.1803	−0.898793
$610$	0	0
$611$	−11.0557	−0.447267
$612$	−1.23607	−0.0499651
$613$	−48.2492	−1.94877	−0.974384	−	0.224891i	$-0.927797\pi$
$613$	−48.2492	−1.94877	−0.974384	+	0.224891i	$0.927797\pi$
$614$	10.0000	0.403567
$615$	0	0
$616$	9.47214	0.381643
$617$	−2.11146	−0.0850040	−0.0425020	−	0.999096i	$-0.513533\pi$
$617$	−2.11146	−0.0850040	−0.0425020	+	0.999096i	$0.513533\pi$
$618$	14.3262	0.576286
$619$	−9.41641	−0.378477	−0.189239	−	0.981931i	$-0.560602\pi$
$619$	−9.41641	−0.378477	−0.189239	+	0.981931i	$0.560602\pi$
$620$	0	0
$621$	−4.47214	−0.179461
$622$	1.05573	0.0423308
$623$	−9.23607	−0.370035
$624$	6.47214	0.259093
$625$	0	0
$626$	−16.2705	−0.650300
$627$	−20.6525	−0.824780
$628$	−8.65248	−0.345271
$629$	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	$0.124054\pi$
$632$	5.61803	0.223473
$633$	−3.41641	−0.135790
$634$	−20.5623	−0.816633
$635$	0	0
$636$	2.09017	0.0828806
$637$	−0.944272	−0.0374134
$638$	−30.6525	−1.21354
$639$	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	$0.587990\pi$
$642$	−11.6180	−0.458527
$643$	−21.8885	−0.863200	−0.431600	−	0.902065i	$-0.642051\pi$
$643$	−21.8885	−0.863200	−0.431600	+	0.902065i	$0.642051\pi$
$644$	11.7082	0.461368
$645$	0	0
$646$	−7.05573	−0.277604
$647$	22.9443	0.902032	0.451016	−	0.892516i	$-0.351062\pi$
$647$	22.9443	0.902032	0.451016	+	0.892516i	$0.351062\pi$
$648$	−1.00000	−0.0392837
$649$	−13.0902	−0.513834
$650$	0	0
$651$	−17.3262	−0.679069
$652$	0.472136	0.0184903
$653$	3.85410	0.150823	0.0754113	−	0.997153i	$-0.475973\pi$
$653$	3.85410	0.150823	0.0754113	+	0.997153i	$0.475973\pi$
$654$	−17.2361	−0.673984
$655$	0	0
$656$	5.70820	0.222868
$657$	−3.52786	−0.137635
$658$	−4.47214	−0.174342
$659$	−20.6180	−0.803165	−0.401582	−	0.915823i	$-0.631540\pi$
$659$	−20.6180	−0.803165	−0.401582	+	0.915823i	$0.631540\pi$
$660$	0	0
$661$	−30.4721	−1.18523	−0.592614	−	0.805486i	$-0.701904\pi$
$661$	−30.4721	−1.18523	−0.592614	+	0.805486i	$0.701904\pi$
$662$	18.0000	0.699590
$663$	−8.00000	−0.310694
$664$	2.14590	0.0832770
$665$	0	0
$666$	8.00000	0.309994
$667$	−37.8885	−1.46705
$668$	−11.7082	−0.453004
$669$	8.09017	0.312784
$670$	0	0
$671$	10.0000	0.386046
$672$	2.61803	0.100993
$673$	31.4508	1.21234	0.606171	−	0.795335i	$-0.292705\pi$
$673$	31.4508	1.21234	0.606171	+	0.795335i	$0.292705\pi$
$674$	0.909830	0.0350453
$675$	0	0
$676$	28.8885	1.11110
$677$	−29.0902	−1.11803	−0.559013	−	0.829159i	$-0.688820\pi$
$677$	−29.0902	−1.11803	−0.559013	+	0.829159i	$0.688820\pi$
$678$	−19.2361	−0.738757
$679$	−8.85410	−0.339789
$680$	0	0
$681$	22.2705	0.853408
$682$	−23.9443	−0.916874
$683$	−33.5066	−1.28209	−0.641047	−	0.767502i	$-0.721500\pi$
$683$	−33.5066	−1.28209	−0.641047	+	0.767502i	$0.721500\pi$
$684$	−5.70820	−0.218259
$685$	0	0
$686$	−18.7082	−0.714283
$687$	−5.52786	−0.210901
$688$	7.70820	0.293873
$689$	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	$0.431442\pi$
$692$	−5.09017	−0.193499
$693$	−9.47214	−0.359817
$694$	20.5623	0.780534
$695$	0	0
$696$	−8.47214	−0.321135
$697$	−7.05573	−0.267255
$698$	27.8885	1.05560
$699$	−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	$0.219698\pi$
$702$	−6.47214	−0.244275
$703$	45.6656	1.72231
$704$	3.61803	0.136360
$705$	0	0
$706$	−13.2361	−0.498146
$707$	−11.4721	−0.431454
$708$	−3.61803	−0.135974
$709$	−43.7082	−1.64150	−0.820748	−	0.571290i	$-0.806443\pi$
$709$	−43.7082	−1.64150	−0.820748	+	0.571290i	$0.806443\pi$
$710$	0	0
$711$	−5.61803	−0.210693
$712$	−3.52786	−0.132212
$713$	−29.5967	−1.10841
$714$	−3.23607	−0.121107
$715$	0	0
$716$	9.85410	0.368265
$717$	12.2918	0.459046
$718$	−22.1803	−0.827763
$719$	−16.5836	−0.618464	−0.309232	−	0.950987i	$-0.600072\pi$
$719$	−16.5836	−0.618464	−0.309232	+	0.950987i	$0.600072\pi$
$720$	0	0
$721$	37.5066	1.39682
$722$	−13.5836	−0.505529
$723$	9.56231	0.355626
$724$	−6.65248	−0.247237
$725$	0	0
$726$	−2.09017	−0.0775735
$727$	8.58359	0.318348	0.159174	−	0.987251i	$-0.449117\pi$
$727$	8.58359	0.318348	0.159174	+	0.987251i	$0.449117\pi$
$728$	16.9443	0.627996
$729$	1.00000	0.0370370
$730$	0	0
$731$	−9.52786	−0.352401
$732$	2.76393	0.102158
$733$	35.8885	1.32557	0.662787	−	0.748808i	$-0.269374\pi$
$733$	35.8885	1.32557	0.662787	+	0.748808i	$0.269374\pi$
$734$	−30.6180	−1.13013
$735$	0	0
$736$	4.47214	0.164845
$737$	5.52786	0.203621
$738$	−5.70820	−0.210122
$739$	−48.1803	−1.77234	−0.886171	−	0.463358i	$-0.846644\pi$
$739$	−48.1803	−1.77234	−0.886171	+	0.463358i	$0.846644\pi$
$740$	0	0
$741$	−36.9443	−1.35718
$742$	5.47214	0.200888
$743$	39.0132	1.43125	0.715627	−	0.698483i	$-0.246141\pi$
$743$	39.0132	1.43125	0.715627	+	0.698483i	$0.246141\pi$
$744$	−6.61803	−0.242629
$745$	0	0
$746$	−11.5279	−0.422065
$747$	−2.14590	−0.0785143
$748$	−4.47214	−0.163517
$749$	−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	$0.350549\pi$
$752$	−1.70820	−0.0622918
$753$	13.5623	0.494238
$754$	−54.8328	−1.99689
$755$	0	0
$756$	−2.61803	−0.0952170
$757$	17.1246	0.622405	0.311202	−	0.950344i	$-0.399268\pi$
$757$	17.1246	0.622405	0.311202	+	0.950344i	$0.399268\pi$
$758$	20.1803	0.732983
$759$	−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	$0.491827\pi$
$762$	13.6180	0.493329
$763$	−45.1246	−1.63362
$764$	4.29180	0.155272
$765$	0	0
$766$	−20.0000	−0.722629
$767$	−23.4164	−0.845517
$768$	1.00000	0.0360844
$769$	24.6869	0.890233	0.445117	−	0.895473i	$-0.353162\pi$
$769$	24.6869	0.890233	0.445117	+	0.895473i	$0.353162\pi$
$770$	0	0
$771$	22.0000	0.792311
$772$	−17.8541	−0.642583
$773$	1.14590	0.0412151	0.0206075	−	0.999788i	$-0.493440\pi$
$773$	1.14590	0.0412151	0.0206075	+	0.999788i	$0.493440\pi$
$774$	−7.70820	−0.277066
$775$	0	0
$776$	−3.38197	−0.121406
$777$	20.9443	0.751372
$778$	12.3820	0.443915
$779$	−32.5836	−1.16743
$780$	0	0
$781$	20.0000	0.715656
$782$	−5.52786	−0.197676
$783$	8.47214	0.302769
$784$	−0.145898	−0.00521064
$785$	0	0
$786$	17.8885	0.638063
$787$	−28.0689	−1.00055	−0.500274	−	0.865867i	$-0.666767\pi$
$787$	−28.0689	−1.00055	−0.500274	+	0.865867i	$0.666767\pi$
$788$	17.0902	0.608812
$789$	11.7082	0.416823
$790$	0	0
$791$	−50.3607	−1.79062
$792$	−3.61803	−0.128561
$793$	17.8885	0.635241
$794$	−30.7639	−1.09177
$795$	0	0
$796$	19.5066	0.691392
$797$	−1.50658	−0.0533657	−0.0266829	−	0.999644i	$-0.508494\pi$
$797$	−1.50658	−0.0533657	−0.0266829	+	0.999644i	$0.508494\pi$
$798$	−14.9443	−0.529021
$799$	2.11146	0.0746979
$800$	0	0
$801$	3.52786	0.124651
$802$	−25.7082	−0.907788
$803$	−12.7639	−0.450429
$804$	1.52786	0.0538836
$805$	0	0
$806$	−42.8328	−1.50872
$807$	−9.09017	−0.319989
$808$	−4.38197	−0.154157
$809$	−30.8328	−1.08402	−0.542012	−	0.840371i	$-0.682337\pi$
$809$	−30.8328	−1.08402	−0.542012	+	0.840371i	$0.682337\pi$
$810$	0	0
$811$	−5.70820	−0.200442	−0.100221	−	0.994965i	$-0.531955\pi$
$811$	−5.70820	−0.200442	−0.100221	+	0.994965i	$0.531955\pi$
$812$	−22.1803	−0.778377
$813$	−18.0344	−0.632495
$814$	28.9443	1.01450
$815$	0	0
$816$	−1.23607	−0.0432710
$817$	−44.0000	−1.53937
$818$	−5.79837	−0.202735
$819$	−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	$0.788279\pi$
$822$	−12.1803	−0.424838
$823$	−2.96556	−0.103373	−0.0516864	−	0.998663i	$-0.516460\pi$
$823$	−2.96556	−0.103373	−0.0516864	+	0.998663i	$0.516460\pi$
$824$	14.3262	0.499078
$825$	0	0
$826$	−9.47214	−0.329578
$827$	−44.1033	−1.53362	−0.766811	−	0.641872i	$-0.778158\pi$
$827$	−44.1033	−1.53362	−0.766811	+	0.641872i	$0.778158\pi$
$828$	−4.47214	−0.155417
$829$	25.8885	0.899146	0.449573	−	0.893244i	$-0.351576\pi$
$829$	25.8885	0.899146	0.449573	+	0.893244i	$0.351576\pi$
$830$	0	0
$831$	−16.9443	−0.587790
$832$	6.47214	0.224381
$833$	0.180340	0.00624841
$834$	−10.4721	−0.362620
$835$	0	0
$836$	−20.6525	−0.714281
$837$	6.61803	0.228753
$838$	3.09017	0.106748
$839$	6.36068	0.219595	0.109798	−	0.993954i	$-0.464980\pi$
$839$	6.36068	0.219595	0.109798	+	0.993954i	$0.464980\pi$
$840$	0	0
$841$	42.7771	1.47507
$842$	22.7639	0.784497
$843$	5.88854	0.202812
$844$	−3.41641	−0.117598
$845$	0	0
$846$	1.70820	0.0587293
$847$	−5.47214	−0.188025
$848$	2.09017	0.0717767
$849$	−4.58359	−0.157308
$850$	0	0
$851$	35.7771	1.22642
$852$	5.52786	0.189382
$853$	43.5967	1.49272	0.746362	−	0.665540i	$-0.231799\pi$
$853$	43.5967	1.49272	0.746362	+	0.665540i	$0.231799\pi$
$854$	7.23607	0.247613
$855$	0	0
$856$	−11.6180	−0.397096
$857$	16.0689	0.548903	0.274451	−	0.961601i	$-0.411504\pi$
$857$	16.0689	0.548903	0.274451	+	0.961601i	$0.411504\pi$
$858$	−23.4164	−0.799423
$859$	−2.29180	−0.0781951	−0.0390975	−	0.999235i	$-0.512448\pi$
$859$	−2.29180	−0.0781951	−0.0390975	+	0.999235i	$0.512448\pi$
$860$	0	0
$861$	−14.9443	−0.509299
$862$	−16.8328	−0.573328
$863$	10.1803	0.346543	0.173271	−	0.984874i	$-0.444566\pi$
$863$	10.1803	0.346543	0.173271	+	0.984874i	$0.444566\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	15.5066	0.526935
$867$	−15.4721	−0.525461
$868$	−17.3262	−0.588091
$869$	−20.3262	−0.689520
$870$	0	0
$871$	9.88854	0.335061
$872$	−17.2361	−0.583687
$873$	3.38197	0.114462
$874$	−25.5279	−0.863493
$875$	0	0
$876$	−3.52786	−0.119195
$877$	37.1246	1.25361	0.626805	−	0.779177i	$-0.284362\pi$
$877$	37.1246	1.25361	0.626805	+	0.779177i	$0.284362\pi$
$878$	23.5066	0.793309
$879$	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	$0.630121\pi$
$882$	0.145898	0.00491264
$883$	30.0689	1.01190	0.505949	−	0.862563i	$-0.331142\pi$
$883$	30.0689	1.01190	0.505949	+	0.862563i	$0.331142\pi$
$884$	−8.00000	−0.269069
$885$	0	0
$886$	16.6180	0.558294
$887$	−23.4164	−0.786246	−0.393123	−	0.919486i	$-0.628605\pi$
$887$	−23.4164	−0.786246	−0.393123	+	0.919486i	$0.628605\pi$
$888$	8.00000	0.268462
$889$	35.6525	1.19575
$890$	0	0
$891$	3.61803	0.121209
$892$	8.09017	0.270879
$893$	9.75078	0.326297
$894$	−22.0902	−0.738806
$895$	0	0
$896$	2.61803	0.0874624
$897$	−28.9443	−0.966421
$898$	27.7082	0.924635
$899$	56.0689	1.87000
$900$	0	0
$901$	−2.58359	−0.0860719
$902$	−20.6525	−0.687652
$903$	−20.1803	−0.671560
$904$	−19.2361	−0.639782
$905$	0	0
$906$	−18.3262	−0.608848
$907$	−30.4721	−1.01181	−0.505905	−	0.862589i	$-0.668841\pi$
$907$	−30.4721	−1.01181	−0.505905	+	0.862589i	$0.668841\pi$
$908$	22.2705	0.739073
$909$	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	$0.402623\pi$
$912$	−5.70820	−0.189018
$913$	−7.76393	−0.256949
$914$	−4.09017	−0.135291
$915$	0	0
$916$	−5.52786	−0.182646
$917$	46.8328	1.54656
$918$	1.23607	0.0407963
$919$	−40.7214	−1.34327	−0.671637	−	0.740881i	$-0.734408\pi$
$919$	−40.7214	−1.34327	−0.671637	+	0.740881i	$0.734408\pi$
$920$	0	0
$921$	−10.0000	−0.329511
$922$	−7.56231	−0.249051
$923$	35.7771	1.17762
$924$	−9.47214	−0.311610
$925$	0	0
$926$	−22.8328	−0.750333
$927$	−14.3262	−0.470535
$928$	−8.47214	−0.278111
$929$	−19.0132	−0.623801	−0.311901	−	0.950115i	$-0.600966\pi$
$929$	−19.0132	−0.623801	−0.311901	+	0.950115i	$0.600966\pi$
$930$	0	0
$931$	0.832816	0.0272944
$932$	−18.6525	−0.610982
$933$	−1.05573	−0.0345630
$934$	10.6738	0.349256
$935$	0	0
$936$	−6.47214	−0.211548
$937$	8.68692	0.283789	0.141895	−	0.989882i	$-0.454681\pi$
$937$	8.68692	0.283789	0.141895	+	0.989882i	$0.454681\pi$
$938$	4.00000	0.130605
$939$	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	$0.523044\pi$
$942$	8.65248	0.281913
$943$	−25.5279	−0.831302
$944$	−3.61803	−0.117757
$945$	0	0
$946$	−27.8885	−0.906735
$947$	33.5623	1.09063	0.545314	−	0.838232i	$-0.316410\pi$
$947$	33.5623	1.09063	0.545314	+	0.838232i	$0.316410\pi$
$948$	−5.61803	−0.182465
$949$	−22.8328	−0.741185
$950$	0	0
$951$	20.5623	0.666778
$952$	−3.23607	−0.104882
$953$	−5.30495	−0.171844	−0.0859221	−	0.996302i	$-0.527384\pi$
$953$	−5.30495	−0.171844	−0.0859221	+	0.996302i	$0.527384\pi$
$954$	−2.09017	−0.0676718
$955$	0	0
$956$	12.2918	0.397545
$957$	30.6525	0.990854
$958$	29.1246	0.940973
$959$	−31.8885	−1.02973
$960$	0	0
$961$	12.7984	0.412851
$962$	51.7771	1.66936
$963$	11.6180	0.374386
$964$	9.56231	0.307981
$965$	0	0
$966$	−11.7082	−0.376705
$967$	−10.9098	−0.350836	−0.175418	−	0.984494i	$-0.556128\pi$
$967$	−10.9098	−0.350836	−0.175418	+	0.984494i	$0.556128\pi$
$968$	−2.09017	−0.0671806
$969$	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	$0.573247\pi$
$972$	1.00000	0.0320750
$973$	−27.4164	−0.878930
$974$	17.7984	0.570297
$975$	0	0
$976$	2.76393	0.0884713
$977$	0.763932	0.0244404	0.0122202	−	0.999925i	$-0.496110\pi$
$977$	0.763932	0.0244404	0.0122202	+	0.999925i	$0.496110\pi$
$978$	−0.472136	−0.0150972
$979$	12.7639	0.407937
$980$	0	0
$981$	17.2361	0.550305
$982$	25.2705	0.806414
$983$	−40.1803	−1.28155	−0.640777	−	0.767727i	$-0.721388\pi$
$983$	−40.1803	−1.28155	−0.640777	+	0.767727i	$0.721388\pi$
$984$	−5.70820	−0.181971
$985$	0	0
$986$	10.4721	0.333501
$987$	4.47214	0.142350
$988$	−36.9443	−1.17535
$989$	−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	$0.345058\pi$
$992$	−6.61803	−0.210123
$993$	−18.0000	−0.571213
$994$	14.4721	0.459028
$995$	0	0
$996$	−2.14590	−0.0679954
$997$	5.59675	0.177251	0.0886254	−	0.996065i	$-0.471753\pi$
$997$	5.59675	0.177251	0.0886254	+	0.996065i	$0.471753\pi$
$998$	−35.5967	−1.12680
$999$	−8.00000	−0.253109

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.a.61.1	✓	4	25.19	even	10
150.2.g.a.91.1	yes	4	25.4	even	10
450.2.h.c.91.1		4	75.29	odd	10
450.2.h.c.361.1		4	75.44	odd	10
750.2.g.b.301.1		4	25.6	even	5
750.2.g.b.451.1		4	25.21	even	5
750.2.h.b.49.1		8	25.22	odd	20
750.2.h.b.49.2		8	25.3	odd	20
750.2.h.b.199.1		8	25.8	odd	20
750.2.h.b.199.2		8	25.17	odd	20
3750.2.a.d.1.1		2	1.1	even	1	trivial
3750.2.a.f.1.2		2	5.4	even	2
3750.2.c.b.1249.1		4	5.2	odd	4
3750.2.c.b.1249.4		4	5.3	odd	4

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.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.61803 q^{11} +1.00000 q^{12} +6.47214 q^{13} +2.61803 q^{14} +1.00000 q^{16} -1.23607 q^{17} -1.00000 q^{18} -5.70820 q^{19} -2.61803 q^{21} -3.61803 q^{22} -4.47214 q^{23} -1.00000 q^{24} -6.47214 q^{26} +1.00000 q^{27} -2.61803 q^{28} +8.47214 q^{29} +6.61803 q^{31} -1.00000 q^{32} +3.61803 q^{33} +1.23607 q^{34} +1.00000 q^{36} -8.00000 q^{37} +5.70820 q^{38} +6.47214 q^{39} +5.70820 q^{41} +2.61803 q^{42} +7.70820 q^{43} +3.61803 q^{44} +4.47214 q^{46} -1.70820 q^{47} +1.00000 q^{48} -0.145898 q^{49} -1.23607 q^{51} +6.47214 q^{52} +2.09017 q^{53} -1.00000 q^{54} +2.61803 q^{56} -5.70820 q^{57} -8.47214 q^{58} -3.61803 q^{59} +2.76393 q^{61} -6.61803 q^{62} -2.61803 q^{63} +1.00000 q^{64} -3.61803 q^{66} +1.52786 q^{67} -1.23607 q^{68} -4.47214 q^{69} +5.52786 q^{71} -1.00000 q^{72} -3.52786 q^{73} +8.00000 q^{74} -5.70820 q^{76} -9.47214 q^{77} -6.47214 q^{78} -5.61803 q^{79} +1.00000 q^{81} -5.70820 q^{82} -2.14590 q^{83} -2.61803 q^{84} -7.70820 q^{86} +8.47214 q^{87} -3.61803 q^{88} +3.52786 q^{89} -16.9443 q^{91} -4.47214 q^{92} +6.61803 q^{93} +1.70820 q^{94} -1.00000 q^{96} +3.38197 q^{97} +0.145898 q^{98} +3.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - 3 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9} + 5 q^{11} + 2 q^{12} + 4 q^{13} + 3 q^{14} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} - 3 q^{21} - 5 q^{22} - 2 q^{24} - 4 q^{26} + 2 q^{27} - 3 q^{28} + 8 q^{29} + 11 q^{31} - 2 q^{32} + 5 q^{33} - 2 q^{34} + 2 q^{36} - 16 q^{37} - 2 q^{38} + 4 q^{39} - 2 q^{41} + 3 q^{42} + 2 q^{43} + 5 q^{44} + 10 q^{47} + 2 q^{48} - 7 q^{49} + 2 q^{51} + 4 q^{52} - 7 q^{53} - 2 q^{54} + 3 q^{56} + 2 q^{57} - 8 q^{58} - 5 q^{59} + 10 q^{61} - 11 q^{62} - 3 q^{63} + 2 q^{64} - 5 q^{66} + 12 q^{67} + 2 q^{68} + 20 q^{71} - 2 q^{72} - 16 q^{73} + 16 q^{74} + 2 q^{76} - 10 q^{77} - 4 q^{78} - 9 q^{79} + 2 q^{81} + 2 q^{82} - 11 q^{83} - 3 q^{84} - 2 q^{86} + 8 q^{87} - 5 q^{88} + 16 q^{89} - 16 q^{91} + 11 q^{93} - 10 q^{94} - 2 q^{96} + 9 q^{97} + 7 q^{98} + 5 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - 3 * q^7 - 2 * q^8 + 2 * q^9 + 5 * q^11 + 2 * q^12 + 4 * q^13 + 3 * q^14 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 - 3 * q^21 - 5 * q^22 - 2 * q^24 - 4 * q^26 + 2 * q^27 - 3 * q^28 + 8 * q^29 + 11 * q^31 - 2 * q^32 + 5 * q^33 - 2 * q^34 + 2 * q^36 - 16 * q^37 - 2 * q^38 + 4 * q^39 - 2 * q^41 + 3 * q^42 + 2 * q^43 + 5 * q^44 + 10 * q^47 + 2 * q^48 - 7 * q^49 + 2 * q^51 + 4 * q^52 - 7 * q^53 - 2 * q^54 + 3 * q^56 + 2 * q^57 - 8 * q^58 - 5 * q^59 + 10 * q^61 - 11 * q^62 - 3 * q^63 + 2 * q^64 - 5 * q^66 + 12 * q^67 + 2 * q^68 + 20 * q^71 - 2 * q^72 - 16 * q^73 + 16 * q^74 + 2 * q^76 - 10 * q^77 - 4 * q^78 - 9 * q^79 + 2 * q^81 + 2 * q^82 - 11 * q^83 - 3 * q^84 - 2 * q^86 + 8 * q^87 - 5 * q^88 + 16 * q^89 - 16 * q^91 + 11 * q^93 - 10 * q^94 - 2 * q^96 + 9 * q^97 + 7 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more