LMFDB - Embedded newform 1925.2.a.x.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,2,Mod(1,1925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1925.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:	$15.3712023891$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.11348.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + x + 2 $ x^4 - x^3 - 5*x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.77571$ of defining polynomial
Character	$\chi$	$=$	1925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.649405 q^{2} -2.92887 q^{3} -1.57827 q^{4} -1.90202 q^{6} +1.00000 q^{7} -2.32375 q^{8} +5.57827 q^{9} +O(q^{10})$	\(q+0.649405 q^{2} -2.92887 q^{3} -1.57827 q^{4} -1.90202 q^{6} +1.00000 q^{7} -2.32375 q^{8} +5.57827 q^{9} -1.00000 q^{11} +4.62256 q^{12} -4.48029 q^{13} +0.649405 q^{14} +1.64749 q^{16} -0.928869 q^{17} +3.62256 q^{18} -0.252616 q^{19} -2.92887 q^{21} -0.649405 q^{22} -6.27196 q^{23} +6.80595 q^{24} -2.90952 q^{26} -7.55143 q^{27} -1.57827 q^{28} -9.10285 q^{29} -0.948214 q^{31} +5.71739 q^{32} +2.92887 q^{33} -0.603212 q^{34} -8.80404 q^{36} +0.973152 q^{37} -0.164050 q^{38} +13.1222 q^{39} -6.20833 q^{41} -1.90202 q^{42} +8.83089 q^{43} +1.57827 q^{44} -4.07304 q^{46} -11.8328 q^{47} -4.82530 q^{48} +1.00000 q^{49} +2.72054 q^{51} +7.07113 q^{52} +10.6349 q^{53} -4.90393 q^{54} -2.32375 q^{56} +0.739881 q^{57} -5.91143 q^{58} +10.8945 q^{59} -0.0979789 q^{61} -0.615774 q^{62} +5.57827 q^{63} +0.417907 q^{64} +1.90202 q^{66} +14.7273 q^{67} +1.46601 q^{68} +18.3698 q^{69} +8.00000 q^{71} -12.9625 q^{72} -2.17398 q^{73} +0.631969 q^{74} +0.398698 q^{76} -1.00000 q^{77} +8.52162 q^{78} -4.38232 q^{79} +5.38232 q^{81} -4.03172 q^{82} +5.60512 q^{83} +4.62256 q^{84} +5.73482 q^{86} +26.6611 q^{87} +2.32375 q^{88} +1.55143 q^{89} -4.48029 q^{91} +9.89887 q^{92} +2.77719 q^{93} -7.68427 q^{94} -16.7455 q^{96} +12.6543 q^{97} +0.649405 q^{98} -5.57827 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} + 8 q^{4} + 4 q^{6} + 4 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 + 4 * q^6 + 4 * q^7 - 12 * q^8 + 8 * q^9	$ 4 q - 2 q^{2} - 2 q^{3} + 8 q^{4} + 4 q^{6} + 4 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{11} + 12 q^{12} + 8 q^{13} - 2 q^{14} + 12 q^{16} + 6 q^{17} + 8 q^{18} + 6 q^{19} - 2 q^{21} + 2 q^{22} - 14 q^{23} - 6 q^{24} - 6 q^{26} - 14 q^{27} + 8 q^{28} - 4 q^{29} + 10 q^{31} - 26 q^{32} + 2 q^{33} - 12 q^{36} + 2 q^{37} + 22 q^{38} + 16 q^{39} - 10 q^{41} + 4 q^{42} + 14 q^{43} - 8 q^{44} - 16 q^{46} - 16 q^{47} + 18 q^{48} + 4 q^{49} + 16 q^{51} + 38 q^{52} - 2 q^{53} + 2 q^{54} - 12 q^{56} + 4 q^{57} - 8 q^{58} + 26 q^{59} - 12 q^{61} - 50 q^{62} + 8 q^{63} + 36 q^{64} - 4 q^{66} + 10 q^{67} + 28 q^{68} - 14 q^{69} + 32 q^{71} + 10 q^{72} + 14 q^{73} - 8 q^{74} - 6 q^{76} - 4 q^{77} + 50 q^{78} + 20 q^{79} - 16 q^{81} + 26 q^{82} + 10 q^{83} + 12 q^{84} - 20 q^{86} + 4 q^{87} + 12 q^{88} - 10 q^{89} + 8 q^{91} - 26 q^{92} - 14 q^{93} - 38 q^{94} - 84 q^{96} + 2 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 + 4 * q^6 + 4 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^11 + 12 * q^12 + 8 * q^13 - 2 * q^14 + 12 * q^16 + 6 * q^17 + 8 * q^18 + 6 * q^19 - 2 * q^21 + 2 * q^22 - 14 * q^23 - 6 * q^24 - 6 * q^26 - 14 * q^27 + 8 * q^28 - 4 * q^29 + 10 * q^31 - 26 * q^32 + 2 * q^33 - 12 * q^36 + 2 * q^37 + 22 * q^38 + 16 * q^39 - 10 * q^41 + 4 * q^42 + 14 * q^43 - 8 * q^44 - 16 * q^46 - 16 * q^47 + 18 * q^48 + 4 * q^49 + 16 * q^51 + 38 * q^52 - 2 * q^53 + 2 * q^54 - 12 * q^56 + 4 * q^57 - 8 * q^58 + 26 * q^59 - 12 * q^61 - 50 * q^62 + 8 * q^63 + 36 * q^64 - 4 * q^66 + 10 * q^67 + 28 * q^68 - 14 * q^69 + 32 * q^71 + 10 * q^72 + 14 * q^73 - 8 * q^74 - 6 * q^76 - 4 * q^77 + 50 * q^78 + 20 * q^79 - 16 * q^81 + 26 * q^82 + 10 * q^83 + 12 * q^84 - 20 * q^86 + 4 * q^87 + 12 * q^88 - 10 * q^89 + 8 * q^91 - 26 * q^92 - 14 * q^93 - 38 * q^94 - 84 * q^96 + 2 * q^97 - 2 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.649405	0.459198	0.229599	−	0.973285i	$-0.426258\pi$
$2$	0.649405	0.459198	0.229599	+	0.973285i	$0.426258\pi$
$3$	−2.92887	−1.69098	−0.845492	−	0.533989i	$-0.820693\pi$
$3$	−2.92887	−1.69098	−0.845492	+	0.533989i	$0.820693\pi$
$4$	−1.57827	−0.789137
$5$	0	0
$5$	0	0
$6$	−1.90202	−0.776497
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.32375	−0.821569
$9$	5.57827	1.85942
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.62256	1.33442
$13$	−4.48029	−1.24261	−0.621305	−	0.783569i	$-0.713397\pi$
$13$	−4.48029	−1.24261	−0.621305	+	0.783569i	$0.713397\pi$
$14$	0.649405	0.173561
$15$	0	0
$16$	1.64749	0.411874
$17$	−0.928869	−0.225284	−0.112642	−	0.993636i	$-0.535931\pi$
$17$	−0.928869	−0.225284	−0.112642	+	0.993636i	$0.535931\pi$
$18$	3.62256	0.853845
$19$	−0.252616	−0.0579542	−0.0289771	−	0.999580i	$-0.509225\pi$
$19$	−0.252616	−0.0579542	−0.0289771	+	0.999580i	$0.509225\pi$
$20$	0	0
$21$	−2.92887	−0.639132
$22$	−0.649405	−0.138454
$23$	−6.27196	−1.30779	−0.653897	−	0.756583i	$-0.726867\pi$
$23$	−6.27196	−1.30779	−0.653897	+	0.756583i	$0.726867\pi$
$24$	6.80595	1.38926
$25$	0	0
$26$	−2.90952	−0.570605
$27$	−7.55143	−1.45327
$28$	−1.57827	−0.298266
$29$	−9.10285	−1.69036	−0.845179	−	0.534484i	$-0.820506\pi$
$29$	−9.10285	−1.69036	−0.845179	+	0.534484i	$0.820506\pi$
$30$	0	0
$31$	−0.948214	−0.170304	−0.0851521	−	0.996368i	$-0.527138\pi$
$31$	−0.948214	−0.170304	−0.0851521	+	0.996368i	$0.527138\pi$
$32$	5.71739	1.01070
$33$	2.92887	0.509851
$34$	−0.603212	−0.103450
$35$	0	0
$36$	−8.80404	−1.46734
$37$	0.973152	0.159985	0.0799926	−	0.996795i	$-0.474510\pi$
$37$	0.973152	0.159985	0.0799926	+	0.996795i	$0.474510\pi$
$38$	−0.164050	−0.0266125
$39$	13.1222	2.10123
$40$	0	0
$41$	−6.20833	−0.969579	−0.484789	−	0.874631i	$-0.661104\pi$
$41$	−6.20833	−0.969579	−0.484789	+	0.874631i	$0.661104\pi$
$42$	−1.90202	−0.293488
$43$	8.83089	1.34670	0.673349	−	0.739325i	$-0.264855\pi$
$43$	8.83089	1.34670	0.673349	+	0.739325i	$0.264855\pi$
$44$	1.57827	0.237934
$45$	0	0
$46$	−4.07304	−0.600537
$47$	−11.8328	−1.72599	−0.862996	−	0.505211i	$-0.831415\pi$
$47$	−11.8328	−1.72599	−0.862996	+	0.505211i	$0.831415\pi$
$48$	−4.82530	−0.696472
$49$	1.00000	0.142857
$50$	0	0
$51$	2.72054	0.380951
$52$	7.07113	0.980589
$53$	10.6349	1.46082	0.730410	−	0.683009i	$-0.239329\pi$
$53$	10.6349	1.46082	0.730410	+	0.683009i	$0.239329\pi$
$54$	−4.90393	−0.667340
$55$	0	0
$56$	−2.32375	−0.310524
$57$	0.739881	0.0979996
$58$	−5.91143	−0.776209
$59$	10.8945	1.41835	0.709173	−	0.705035i	$-0.249069\pi$
$59$	10.8945	1.41835	0.709173	+	0.705035i	$0.249069\pi$
$60$	0	0
$61$	−0.0979789	−0.0125449	−0.00627246	−	0.999980i	$-0.501997\pi$
$61$	−0.0979789	−0.0125449	−0.00627246	+	0.999980i	$0.501997\pi$
$62$	−0.615774	−0.0782034
$63$	5.57827	0.702796
$64$	0.417907	0.0522384
$65$	0	0
$66$	1.90202	0.234123
$67$	14.7273	1.79923	0.899614	−	0.436686i	$-0.143848\pi$
$67$	14.7273	1.79923	0.899614	+	0.436686i	$0.143848\pi$
$68$	1.46601	0.177780
$69$	18.3698	2.21146
$70$	0	0
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	−12.9625	−1.52765
$73$	−2.17398	−0.254445	−0.127223	−	0.991874i	$-0.540606\pi$
$73$	−2.17398	−0.254445	−0.127223	+	0.991874i	$0.540606\pi$
$74$	0.631969	0.0734650
$75$	0	0
$76$	0.398698	0.0457338
$77$	−1.00000	−0.113961
$78$	8.52162	0.964883
$79$	−4.38232	−0.493049	−0.246525	−	0.969137i	$-0.579289\pi$
$79$	−4.38232	−0.493049	−0.246525	+	0.969137i	$0.579289\pi$
$80$	0	0
$81$	5.38232	0.598035
$82$	−4.03172	−0.445229
$83$	5.60512	0.615242	0.307621	−	0.951509i	$-0.400467\pi$
$83$	5.60512	0.615242	0.307621	+	0.951509i	$0.400467\pi$
$84$	4.62256	0.504362
$85$	0	0
$86$	5.73482	0.618402
$87$	26.6611	2.85837
$88$	2.32375	0.247712
$89$	1.55143	0.164451	0.0822254	−	0.996614i	$-0.473797\pi$
$89$	1.55143	0.164451	0.0822254	+	0.996614i	$0.473797\pi$
$90$	0	0
$91$	−4.48029	−0.469663
$92$	9.89887	1.03203
$93$	2.77719	0.287982
$94$	−7.68427	−0.792572
$95$	0	0
$96$	−16.7455	−1.70908
$97$	12.6543	1.28485	0.642424	−	0.766350i	$-0.277929\pi$
$97$	12.6543	1.28485	0.642424	+	0.766350i	$0.277929\pi$
$98$	0.649405	0.0655998
$99$	−5.57827	−0.560638
$100$	0	0
$101$	−9.54583	−0.949846	−0.474923	−	0.880027i	$-0.657524\pi$
$101$	−9.54583	−0.949846	−0.474923	+	0.880027i	$0.657524\pi$
$102$	1.76673	0.174932
$103$	6.18899	0.609819	0.304910	−	0.952381i	$-0.401374\pi$
$103$	6.18899	0.609819	0.304910	+	0.952381i	$0.401374\pi$
$104$	10.4111	1.02089
$105$	0	0
$106$	6.90637	0.670806
$107$	6.55893	0.634076	0.317038	−	0.948413i	$-0.397312\pi$
$107$	6.55893	0.634076	0.317038	+	0.948413i	$0.397312\pi$
$108$	11.9182	1.14683
$109$	−7.85774	−0.752635	−0.376317	−	0.926491i	$-0.622810\pi$
$109$	−7.85774	−0.752635	−0.376317	+	0.926491i	$0.622810\pi$
$110$	0	0
$111$	−2.85023	−0.270532
$112$	1.64749	0.155674
$113$	−4.14226	−0.389671	−0.194836	−	0.980836i	$-0.562417\pi$
$113$	−4.14226	−0.389671	−0.194836	+	0.980836i	$0.562417\pi$
$114$	0.480482	0.0450012
$115$	0	0
$116$	14.3668	1.33392
$117$	−24.9923	−2.31054
$118$	7.07495	0.651302
$119$	−0.928869	−0.0851493
$120$	0	0
$121$	1.00000	0.0909091
$122$	−0.0636280	−0.00576060
$123$	18.1834	1.63954
$124$	1.49654	0.134393
$125$	0	0
$126$	3.62256	0.322723
$127$	−3.29881	−0.292722	−0.146361	−	0.989231i	$-0.546756\pi$
$127$	−3.29881	−0.292722	−0.146361	+	0.989231i	$0.546756\pi$
$128$	−11.1634	−0.986713
$129$	−25.8645	−2.27724
$130$	0	0
$131$	11.6081	1.01420	0.507102	−	0.861886i	$-0.330717\pi$
$131$	11.6081	1.01420	0.507102	+	0.861886i	$0.330717\pi$
$132$	−4.62256	−0.402342
$133$	−0.252616	−0.0219046
$134$	9.56399	0.826203
$135$	0	0
$136$	2.15846	0.185086
$137$	8.68863	0.742320	0.371160	−	0.928569i	$-0.378960\pi$
$137$	8.68863	0.742320	0.371160	+	0.928569i	$0.378960\pi$
$138$	11.9294	1.01550
$139$	−15.5582	−1.31963	−0.659815	−	0.751428i	$-0.729365\pi$
$139$	−15.5582	−1.31963	−0.659815	+	0.751428i	$0.729365\pi$
$140$	0	0
$141$	34.6567	2.91862
$142$	5.19524	0.435975
$143$	4.48029	0.374661
$144$	9.19018	0.765848
$145$	0	0
$146$	−1.41179	−0.116841
$147$	−2.92887	−0.241569
$148$	−1.53590	−0.126250
$149$	19.6119	1.60667	0.803335	−	0.595528i	$-0.203057\pi$
$149$	19.6119	1.60667	0.803335	+	0.595528i	$0.203057\pi$
$150$	0	0
$151$	16.8377	1.37023	0.685115	−	0.728435i	$-0.259752\pi$
$151$	16.8377	1.37023	0.685115	+	0.728435i	$0.259752\pi$
$152$	0.587017	0.0476134
$153$	−5.18149	−0.418898
$154$	−0.649405	−0.0523305
$155$	0	0
$156$	−20.7104	−1.65816
$157$	12.0218	0.959443	0.479722	−	0.877421i	$-0.340738\pi$
$157$	12.0218	0.959443	0.479722	+	0.877421i	$0.340738\pi$
$158$	−2.84590	−0.226407
$159$	−31.1483	−2.47022
$160$	0	0
$161$	−6.27196	−0.494300
$162$	3.49530	0.274617
$163$	25.2862	1.98057	0.990286	−	0.139047i	$-0.0444038\pi$
$163$	25.2862	1.98057	0.990286	+	0.139047i	$0.0444038\pi$
$164$	9.79845	0.765130
$165$	0	0
$166$	3.63999	0.282518
$167$	−21.9144	−1.69579	−0.847893	−	0.530167i	$-0.822129\pi$
$167$	−21.9144	−1.69579	−0.847893	+	0.530167i	$0.822129\pi$
$168$	6.80595	0.525091
$169$	7.07304	0.544080
$170$	0	0
$171$	−1.40916	−0.107761
$172$	−13.9376	−1.06273
$173$	−11.9432	−0.908021	−0.454011	−	0.890996i	$-0.650007\pi$
$173$	−11.9432	−0.908021	−0.454011	+	0.890996i	$0.650007\pi$
$174$	17.3138	1.31256
$175$	0	0
$176$	−1.64749	−0.124185
$177$	−31.9086	−2.39840
$178$	1.00750	0.0755155
$179$	16.8720	1.26107	0.630537	−	0.776159i	$-0.282835\pi$
$179$	16.8720	1.26107	0.630537	+	0.776159i	$0.282835\pi$
$180$	0	0
$181$	−8.56571	−0.636684	−0.318342	−	0.947976i	$-0.603126\pi$
$181$	−8.56571	−0.636684	−0.318342	+	0.947976i	$0.603126\pi$
$182$	−2.90952	−0.215668
$183$	0.286967	0.0212132
$184$	14.5745	1.07444
$185$	0	0
$186$	1.80352	0.132241
$187$	0.928869	0.0679256
$188$	18.6754	1.36204
$189$	−7.55143	−0.549285
$190$	0	0
$191$	7.26012	0.525324	0.262662	−	0.964888i	$-0.415400\pi$
$191$	7.26012	0.525324	0.262662	+	0.964888i	$0.415400\pi$
$192$	−1.22399	−0.0883342
$193$	−10.6736	−0.768304	−0.384152	−	0.923270i	$-0.625506\pi$
$193$	−10.6736	−0.768304	−0.384152	+	0.923270i	$0.625506\pi$
$194$	8.21775	0.590000
$195$	0	0
$196$	−1.57827	−0.112734
$197$	−19.2862	−1.37409	−0.687044	−	0.726616i	$-0.741092\pi$
$197$	−19.2862	−1.37409	−0.687044	+	0.726616i	$0.741092\pi$
$198$	−3.62256	−0.257444
$199$	−1.81345	−0.128552	−0.0642762	−	0.997932i	$-0.520474\pi$
$199$	−1.81345	−0.128552	−0.0642762	+	0.997932i	$0.520474\pi$
$200$	0	0
$201$	−43.1344	−3.04246
$202$	−6.19911	−0.436168
$203$	−9.10285	−0.638895
$204$	−4.29375	−0.300623
$205$	0	0
$206$	4.01916	0.280028
$207$	−34.9867	−2.43174
$208$	−7.38126	−0.511798
$209$	0.252616	0.0174738
$210$	0	0
$211$	20.4167	1.40554	0.702771	−	0.711416i	$-0.251946\pi$
$211$	20.4167	1.40554	0.702771	+	0.711416i	$0.251946\pi$
$212$	−16.7848	−1.15279
$213$	−23.4310	−1.60546
$214$	4.25940	0.291166
$215$	0	0
$216$	17.5476	1.19396
$217$	−0.948214	−0.0643690
$218$	−5.10285	−0.345609
$219$	6.36731	0.430263
$220$	0	0
$221$	4.16161	0.279940
$222$	−1.85096	−0.124228
$223$	−28.9574	−1.93913	−0.969567	−	0.244827i	$-0.921269\pi$
$223$	−28.9574	−1.93913	−0.969567	+	0.244827i	$0.921269\pi$
$224$	5.71739	0.382009
$225$	0	0
$226$	−2.69000	−0.178936
$227$	17.7005	1.17482	0.587411	−	0.809289i	$-0.300147\pi$
$227$	17.7005	1.17482	0.587411	+	0.809289i	$0.300147\pi$
$228$	−1.16773	−0.0773351
$229$	18.1321	1.19821	0.599103	−	0.800672i	$-0.295524\pi$
$229$	18.1321	1.19821	0.599103	+	0.800672i	$0.295524\pi$
$230$	0	0
$231$	2.92887	0.192705
$232$	21.1527	1.38874
$233$	3.37481	0.221091	0.110546	−	0.993871i	$-0.464740\pi$
$233$	3.37481	0.221091	0.110546	+	0.993871i	$0.464740\pi$
$234$	−16.2301	−1.06100
$235$	0	0
$236$	−17.1945	−1.11927
$237$	12.8352	0.833738
$238$	−0.603212	−0.0391004
$239$	−24.1021	−1.55904	−0.779519	−	0.626379i	$-0.784536\pi$
$239$	−24.1021	−1.55904	−0.779519	+	0.626379i	$0.784536\pi$
$240$	0	0
$241$	2.05107	0.132121	0.0660604	−	0.997816i	$-0.478957\pi$
$241$	2.05107	0.132121	0.0660604	+	0.997816i	$0.478957\pi$
$242$	0.649405	0.0417453
$243$	6.89018	0.442005
$244$	0.154638	0.00989965
$245$	0	0
$246$	11.8084	0.752875
$247$	1.13180	0.0720145
$248$	2.20341	0.139917
$249$	−16.4167	−1.04036
$250$	0	0
$251$	14.0162	0.884694	0.442347	−	0.896844i	$-0.354146\pi$
$251$	14.0162	0.884694	0.442347	+	0.896844i	$0.354146\pi$
$252$	−8.80404	−0.554603
$253$	6.27196	0.394315
$254$	−2.14226	−0.134417
$255$	0	0
$256$	−8.08536	−0.505335
$257$	16.8502	1.05109	0.525544	−	0.850766i	$-0.323862\pi$
$257$	16.8502	1.05109	0.525544	+	0.850766i	$0.323862\pi$
$258$	−16.7965	−1.04571
$259$	0.973152	0.0604687
$260$	0	0
$261$	−50.7782	−3.14309
$262$	7.53834	0.465720
$263$	7.01429	0.432519	0.216260	−	0.976336i	$-0.430614\pi$
$263$	7.01429	0.432519	0.216260	+	0.976336i	$0.430614\pi$
$264$	−6.80595	−0.418877
$265$	0	0
$266$	−0.164050	−0.0100586
$267$	−4.54392	−0.278084
$268$	−23.2437	−1.41984
$269$	−18.6194	−1.13525	−0.567623	−	0.823289i	$-0.692137\pi$
$269$	−18.6194	−1.13525	−0.567623	+	0.823289i	$0.692137\pi$
$270$	0	0
$271$	19.0530	1.15739	0.578693	−	0.815546i	$-0.303563\pi$
$271$	19.0530	1.15739	0.578693	+	0.815546i	$0.303563\pi$
$272$	−1.53031	−0.0927885
$273$	13.1222	0.794191
$274$	5.64244	0.340872
$275$	0	0
$276$	−28.9925	−1.74514
$277$	23.4435	1.40858	0.704292	−	0.709910i	$-0.251265\pi$
$277$	23.4435	1.40858	0.704292	+	0.709910i	$0.251265\pi$
$278$	−10.1036	−0.605972
$279$	−5.28940	−0.316668
$280$	0	0
$281$	15.9463	0.951277	0.475638	−	0.879641i	$-0.342217\pi$
$281$	15.9463	0.951277	0.475638	+	0.879641i	$0.342217\pi$
$282$	22.5062	1.34023
$283$	−22.9644	−1.36509	−0.682546	−	0.730842i	$-0.739127\pi$
$283$	−22.9644	−1.36509	−0.682546	+	0.730842i	$0.739127\pi$
$284$	−12.6262	−0.749226
$285$	0	0
$286$	2.90952	0.172044
$287$	−6.20833	−0.366466
$288$	31.8931	1.87932
$289$	−16.1372	−0.949247
$290$	0	0
$291$	−37.0627	−2.17266
$292$	3.43114	0.200792
$293$	1.52267	0.0889552	0.0444776	−	0.999010i	$-0.485838\pi$
$293$	1.52267	0.0889552	0.0444776	+	0.999010i	$0.485838\pi$
$294$	−1.90202	−0.110928
$295$	0	0
$296$	−2.26136	−0.131439
$297$	7.55143	0.438178
$298$	12.7361	0.737780
$299$	28.1002	1.62508
$300$	0	0
$301$	8.83089	0.509004
$302$	10.9345	0.629208
$303$	27.9585	1.60617
$304$	−0.416184	−0.0238698
$305$	0	0
$306$	−3.36488	−0.192357
$307$	13.4479	0.767510	0.383755	−	0.923435i	$-0.374631\pi$
$307$	13.4479	0.767510	0.383755	+	0.923435i	$0.374631\pi$
$308$	1.57827	0.0899305
$309$	−18.1267	−1.03119
$310$	0	0
$311$	−2.31869	−0.131481	−0.0657404	−	0.997837i	$-0.520941\pi$
$311$	−2.31869	−0.131481	−0.0657404	+	0.997837i	$0.520941\pi$
$312$	−30.4927	−1.72631
$313$	−18.7646	−1.06064	−0.530320	−	0.847798i	$-0.677928\pi$
$313$	−18.7646	−1.06064	−0.530320	+	0.847798i	$0.677928\pi$
$314$	7.80700	0.440575
$315$	0	0
$316$	6.91649	0.389083
$317$	−33.9062	−1.90436	−0.952180	−	0.305537i	$-0.901164\pi$
$317$	−33.9062	−1.90436	−0.952180	+	0.305537i	$0.901164\pi$
$318$	−20.2279	−1.13432
$319$	9.10285	0.509662
$320$	0	0
$321$	−19.2102	−1.07221
$322$	−4.07304	−0.226982
$323$	0.234648	0.0130561
$324$	−8.49477	−0.471932
$325$	0	0
$326$	16.4210	0.909475
$327$	23.0143	1.27269
$328$	14.4266	0.796576
$329$	−11.8328	−0.652363
$330$	0	0
$331$	−11.6967	−0.642906	−0.321453	−	0.946926i	$-0.604171\pi$
$331$	−11.6967	−0.642906	−0.321453	+	0.946926i	$0.604171\pi$
$332$	−8.84642	−0.485510
$333$	5.42851	0.297480
$334$	−14.2313	−0.778703
$335$	0	0
$336$	−4.82530	−0.263242
$337$	14.0910	0.767586	0.383793	−	0.923419i	$-0.374618\pi$
$337$	14.0910	0.767586	0.383793	+	0.923419i	$0.374618\pi$
$338$	4.59327	0.249841
$339$	12.1321	0.658928
$340$	0	0
$341$	0.948214	0.0513487
$342$	−0.915117	−0.0494839
$343$	1.00000	0.0539949
$344$	−20.5208	−1.10641
$345$	0	0
$346$	−7.75594	−0.416962
$347$	−8.97697	−0.481909	−0.240955	−	0.970536i	$-0.577460\pi$
$347$	−8.97697	−0.481909	−0.240955	+	0.970536i	$0.577460\pi$
$348$	−42.0784	−2.25564
$349$	−17.2545	−0.923614	−0.461807	−	0.886981i	$-0.652799\pi$
$349$	−17.2545	−0.923614	−0.461807	+	0.886981i	$0.652799\pi$
$350$	0	0
$351$	33.8326	1.80585
$352$	−5.71739	−0.304738
$353$	9.14154	0.486555	0.243278	−	0.969957i	$-0.421777\pi$
$353$	9.14154	0.486555	0.243278	+	0.969957i	$0.421777\pi$
$354$	−20.7216	−1.10134
$355$	0	0
$356$	−2.44857	−0.129774
$357$	2.72054	0.143986
$358$	10.9568	0.579083
$359$	−3.55387	−0.187566	−0.0937830	−	0.995593i	$-0.529896\pi$
$359$	−3.55387	−0.187566	−0.0937830	+	0.995593i	$0.529896\pi$
$360$	0	0
$361$	−18.9362	−0.996641
$362$	−5.56261	−0.292364
$363$	−2.92887	−0.153726
$364$	7.07113	0.370628
$365$	0	0
$366$	0.186358	0.00974109
$367$	−28.2055	−1.47232	−0.736158	−	0.676810i	$-0.763362\pi$
$367$	−28.2055	−1.47232	−0.736158	+	0.676810i	$0.763362\pi$
$368$	−10.3330	−0.538646
$369$	−34.6318	−1.80286
$370$	0	0
$371$	10.6349	0.552138
$372$	−4.38317	−0.227257
$373$	−30.3640	−1.57219	−0.786093	−	0.618108i	$-0.787900\pi$
$373$	−30.3640	−1.57219	−0.786093	+	0.618108i	$0.787900\pi$
$374$	0.603212	0.0311913
$375$	0	0
$376$	27.4964	1.41802
$377$	40.7835	2.10045
$378$	−4.90393	−0.252231
$379$	28.1907	1.44806	0.724029	−	0.689769i	$-0.242288\pi$
$379$	28.1907	1.44806	0.724029	+	0.689769i	$0.242288\pi$
$380$	0	0
$381$	9.66178	0.494988
$382$	4.71476	0.241228
$383$	−13.2231	−0.675671	−0.337835	−	0.941205i	$-0.609695\pi$
$383$	−13.2231	−0.675671	−0.337835	+	0.941205i	$0.609695\pi$
$384$	32.6961	1.66851
$385$	0	0
$386$	−6.93150	−0.352804
$387$	49.2611	2.50408
$388$	−19.9719	−1.01392
$389$	1.87274	0.0949519	0.0474759	−	0.998872i	$-0.484882\pi$
$389$	1.87274	0.0949519	0.0474759	+	0.998872i	$0.484882\pi$
$390$	0	0
$391$	5.82583	0.294625
$392$	−2.32375	−0.117367
$393$	−33.9986	−1.71500
$394$	−12.5246	−0.630979
$395$	0	0
$396$	8.80404	0.442420
$397$	28.4583	1.42828	0.714141	−	0.700002i	$-0.246818\pi$
$397$	28.4583	1.42828	0.714141	+	0.700002i	$0.246818\pi$
$398$	−1.17767	−0.0590311
$399$	0.739881	0.0370404
$400$	0	0
$401$	1.27998	0.0639193	0.0319597	−	0.999489i	$-0.489825\pi$
$401$	1.27998	0.0639193	0.0319597	+	0.999489i	$0.489825\pi$
$402$	−28.0117	−1.39710
$403$	4.24828	0.211622
$404$	15.0659	0.749558
$405$	0	0
$406$	−5.91143	−0.293380
$407$	−0.973152	−0.0482374
$408$	−6.32184	−0.312978
$409$	0.680591	0.0336531	0.0168265	−	0.999858i	$-0.494644\pi$
$409$	0.680591	0.0336531	0.0168265	+	0.999858i	$0.494644\pi$
$410$	0	0
$411$	−25.4479	−1.25525
$412$	−9.76792	−0.481231
$413$	10.8945	0.536084
$414$	−22.7205	−1.11665
$415$	0	0
$416$	−25.6156	−1.25591
$417$	45.5680	2.23147
$418$	0.164050	0.00802396
$419$	9.94071	0.485636	0.242818	−	0.970072i	$-0.421928\pi$
$419$	9.94071	0.485636	0.242818	+	0.970072i	$0.421928\pi$
$420$	0	0
$421$	17.6312	0.859294	0.429647	−	0.902997i	$-0.358638\pi$
$421$	17.6312	0.859294	0.429647	+	0.902997i	$0.358638\pi$
$422$	13.2587	0.645422
$423$	−66.0066	−3.20935
$424$	−24.7129	−1.20016
$425$	0	0
$426$	−15.2162	−0.737226
$427$	−0.0979789	−0.00474153
$428$	−10.3518	−0.500372
$429$	−13.1222	−0.633546
$430$	0	0
$431$	29.0336	1.39850	0.699250	−	0.714877i	$-0.253517\pi$
$431$	29.0336	1.39850	0.699250	+	0.714877i	$0.253517\pi$
$432$	−12.4409	−0.598565
$433$	13.5882	0.653008	0.326504	−	0.945196i	$-0.394129\pi$
$433$	13.5882	0.653008	0.326504	+	0.945196i	$0.394129\pi$
$434$	−0.615774	−0.0295581
$435$	0	0
$436$	12.4017	0.593932
$437$	1.58440	0.0757922
$438$	4.13496	0.197576
$439$	−20.3093	−0.969309	−0.484654	−	0.874706i	$-0.661055\pi$
$439$	−20.3093	−0.969309	−0.484654	+	0.874706i	$0.661055\pi$
$440$	0	0
$441$	5.57827	0.265632
$442$	2.70257	0.128548
$443$	−2.19458	−0.104268	−0.0521339	−	0.998640i	$-0.516602\pi$
$443$	−2.19458	−0.104268	−0.0521339	+	0.998640i	$0.516602\pi$
$444$	4.49845	0.213487
$445$	0	0
$446$	−18.8051	−0.890447
$447$	−57.4407	−2.71685
$448$	0.417907	0.0197442
$449$	2.23031	0.105255	0.0526274	−	0.998614i	$-0.483240\pi$
$449$	2.23031	0.105255	0.0526274	+	0.998614i	$0.483240\pi$
$450$	0	0
$451$	6.20833	0.292339
$452$	6.53762	0.307504
$453$	−49.3153	−2.31704
$454$	11.4948	0.539476
$455$	0	0
$456$	−1.71930	−0.0805134
$457$	8.22208	0.384613	0.192306	−	0.981335i	$-0.438403\pi$
$457$	8.22208	0.384613	0.192306	+	0.981335i	$0.438403\pi$
$458$	11.7751	0.550214
$459$	7.01429	0.327399
$460$	0	0
$461$	−23.8314	−1.10994	−0.554970	−	0.831870i	$-0.687270\pi$
$461$	−23.8314	−1.10994	−0.554970	+	0.831870i	$0.687270\pi$
$462$	1.90202	0.0884900
$463$	5.35495	0.248866	0.124433	−	0.992228i	$-0.460289\pi$
$463$	5.35495	0.248866	0.124433	+	0.992228i	$0.460289\pi$
$464$	−14.9969	−0.696214
$465$	0	0
$466$	2.19162	0.101525
$467$	0.729092	0.0337383	0.0168692	−	0.999858i	$-0.494630\pi$
$467$	0.729092	0.0337383	0.0168692	+	0.999858i	$0.494630\pi$
$468$	39.4447	1.82333
$469$	14.7273	0.680044
$470$	0	0
$471$	−35.2102	−1.62240
$472$	−25.3161	−1.16527
$473$	−8.83089	−0.406045
$474$	8.33526	0.382851
$475$	0	0
$476$	1.46601	0.0671944
$477$	59.3246	2.71629
$478$	−15.6520	−0.715907
$479$	25.6937	1.17397	0.586987	−	0.809596i	$-0.300314\pi$
$479$	25.6937	1.17397	0.586987	+	0.809596i	$0.300314\pi$
$480$	0	0
$481$	−4.36001	−0.198799
$482$	1.33197	0.0606696
$483$	18.3698	0.835853
$484$	−1.57827	−0.0717397
$485$	0	0
$486$	4.47451	0.202968
$487$	31.0366	1.40640	0.703201	−	0.710991i	$-0.251753\pi$
$487$	31.0366	1.40640	0.703201	+	0.710991i	$0.251753\pi$
$488$	0.227678	0.0103065
$489$	−74.0601	−3.34911
$490$	0	0
$491$	−0.136482	−0.00615933	−0.00307966	−	0.999995i	$-0.500980\pi$
$491$	−0.136482	−0.00615933	−0.00307966	+	0.999995i	$0.500980\pi$
$492$	−28.6984	−1.29382
$493$	8.45536	0.380810
$494$	0.734994	0.0330689
$495$	0	0
$496$	−1.56218	−0.0701438
$497$	8.00000	0.358849
$498$	−10.6611	−0.477733
$499$	3.17155	0.141978	0.0709891	−	0.997477i	$-0.477384\pi$
$499$	3.17155	0.141978	0.0709891	+	0.997477i	$0.477384\pi$
$500$	0	0
$501$	64.1844	2.86755
$502$	9.10218	0.406250
$503$	25.7958	1.15018	0.575089	−	0.818091i	$-0.304967\pi$
$503$	25.7958	1.15018	0.575089	+	0.818091i	$0.304967\pi$
$504$	−12.9625	−0.577396
$505$	0	0
$506$	4.07304	0.181069
$507$	−20.7160	−0.920030
$508$	5.20642	0.230998
$509$	9.55821	0.423660	0.211830	−	0.977307i	$-0.432058\pi$
$509$	9.55821	0.423660	0.211830	+	0.977307i	$0.432058\pi$
$510$	0	0
$511$	−2.17398	−0.0961713
$512$	17.0761	0.754664
$513$	1.90761	0.0842232
$514$	10.9426	0.482658
$515$	0	0
$516$	40.8213	1.79706
$517$	11.8328	0.520406
$518$	0.631969	0.0277671
$519$	34.9799	1.53545
$520$	0	0
$521$	−34.6581	−1.51840	−0.759199	−	0.650858i	$-0.774409\pi$
$521$	−34.6581	−1.51840	−0.759199	+	0.650858i	$0.774409\pi$
$522$	−32.9756	−1.44330
$523$	32.5807	1.42466	0.712328	−	0.701847i	$-0.247641\pi$
$523$	32.5807	1.42466	0.712328	+	0.701847i	$0.247641\pi$
$524$	−18.3207	−0.800345
$525$	0	0
$526$	4.55511	0.198612
$527$	0.880766	0.0383668
$528$	4.82530	0.209994
$529$	16.3375	0.710326
$530$	0	0
$531$	60.7726	2.63731
$532$	0.398698	0.0172857
$533$	27.8152	1.20481
$534$	−2.95084	−0.127696
$535$	0	0
$536$	−34.2226	−1.47819
$537$	−49.4159	−2.13246
$538$	−12.0915	−0.521303
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	23.8190	1.02406	0.512030	−	0.858967i	$-0.328893\pi$
$541$	23.8190	1.02406	0.512030	+	0.858967i	$0.328893\pi$
$542$	12.3731	0.531470
$543$	25.0878	1.07662
$544$	−5.31070	−0.227694
$545$	0	0
$546$	8.52162	0.364691
$547$	−18.9456	−0.810055	−0.405027	−	0.914305i	$-0.632738\pi$
$547$	−18.9456	−0.810055	−0.405027	+	0.914305i	$0.632738\pi$
$548$	−13.7130	−0.585792
$549$	−0.546553	−0.0233263
$550$	0	0
$551$	2.29953	0.0979633
$552$	−42.6867	−1.81687
$553$	−4.38232	−0.186355
$554$	15.2243	0.646820
$555$	0	0
$556$	24.5551	1.04137
$557$	−22.4390	−0.950770	−0.475385	−	0.879778i	$-0.657691\pi$
$557$	−22.4390	−0.950770	−0.475385	+	0.879778i	$0.657691\pi$
$558$	−3.43496	−0.145413
$559$	−39.5650	−1.67342
$560$	0	0
$561$	−2.72054	−0.114861
$562$	10.3556	0.436825
$563$	4.59380	0.193606	0.0968028	−	0.995304i	$-0.469138\pi$
$563$	4.59380	0.193606	0.0968028	+	0.995304i	$0.469138\pi$
$564$	−54.6978	−2.30319
$565$	0	0
$566$	−14.9132	−0.626848
$567$	5.38232	0.226036
$568$	−18.5900	−0.780018
$569$	−8.64749	−0.362522	−0.181261	−	0.983435i	$-0.558018\pi$
$569$	−8.64749	−0.362522	−0.181261	+	0.983435i	$0.558018\pi$
$570$	0	0
$571$	31.8176	1.33153	0.665763	−	0.746164i	$-0.268106\pi$
$571$	31.8176	1.33153	0.665763	+	0.746164i	$0.268106\pi$
$572$	−7.07113	−0.295659
$573$	−21.2639	−0.888314
$574$	−4.03172	−0.168281
$575$	0	0
$576$	2.33120	0.0971333
$577$	20.4084	0.849615	0.424807	−	0.905284i	$-0.360342\pi$
$577$	20.4084	0.849615	0.424807	+	0.905284i	$0.360342\pi$
$578$	−10.4796	−0.435893
$579$	31.2616	1.29919
$580$	0	0
$581$	5.60512	0.232540
$582$	−24.0687	−0.997680
$583$	−10.6349	−0.440454
$584$	5.05179	0.209044
$585$	0	0
$586$	0.988828	0.0408481
$587$	21.1733	0.873914	0.436957	−	0.899482i	$-0.356056\pi$
$587$	21.1733	0.873914	0.436957	+	0.899482i	$0.356056\pi$
$588$	4.62256	0.190631
$589$	0.239534	0.00986984
$590$	0	0
$591$	56.4869	2.32356
$592$	1.60326	0.0658937
$593$	25.9461	1.06548	0.532740	−	0.846279i	$-0.321162\pi$
$593$	25.9461	1.06548	0.532740	+	0.846279i	$0.321162\pi$
$594$	4.90393	0.201211
$595$	0	0
$596$	−30.9530	−1.26788
$597$	5.31137	0.217380
$598$	18.2484	0.746234
$599$	25.5844	1.04535	0.522675	−	0.852532i	$-0.324934\pi$
$599$	25.5844	1.04535	0.522675	+	0.852532i	$0.324934\pi$
$600$	0	0
$601$	7.56084	0.308413	0.154207	−	0.988039i	$-0.450718\pi$
$601$	7.56084	0.308413	0.154207	+	0.988039i	$0.450718\pi$
$602$	5.73482	0.233734
$603$	82.1530	3.34553
$604$	−26.5745	−1.08130
$605$	0	0
$606$	18.1564	0.737552
$607$	−10.5908	−0.429869	−0.214934	−	0.976628i	$-0.568954\pi$
$607$	−10.5908	−0.429869	−0.214934	+	0.976628i	$0.568954\pi$
$608$	−1.44431	−0.0585743
$609$	26.6611	1.08036
$610$	0	0
$611$	53.0144	2.14473
$612$	8.17780	0.330568
$613$	21.4672	0.867052	0.433526	−	0.901141i	$-0.357269\pi$
$613$	21.4672	0.867052	0.433526	+	0.901141i	$0.357269\pi$
$614$	8.73310	0.352439
$615$	0	0
$616$	2.32375	0.0936265
$617$	−11.5321	−0.464264	−0.232132	−	0.972684i	$-0.574570\pi$
$617$	−11.5321	−0.464264	−0.232132	+	0.972684i	$0.574570\pi$
$618$	−11.7716	−0.473523
$619$	37.2444	1.49698	0.748490	−	0.663147i	$-0.230779\pi$
$619$	37.2444	1.49698	0.748490	+	0.663147i	$0.230779\pi$
$620$	0	0
$621$	47.3623	1.90058
$622$	−1.50577	−0.0603757
$623$	1.55143	0.0621566
$624$	21.6188	0.865443
$625$	0	0
$626$	−12.1858	−0.487044
$627$	−0.739881	−0.0295480
$628$	−18.9737	−0.757132
$629$	−0.903931	−0.0360421
$630$	0	0
$631$	−44.9166	−1.78810	−0.894052	−	0.447964i	$-0.852149\pi$
$631$	−44.9166	−1.78810	−0.894052	+	0.447964i	$0.852149\pi$
$632$	10.1834	0.405074
$633$	−59.7977	−2.37675
$634$	−22.0188	−0.874479
$635$	0	0
$636$	49.1606	1.94934
$637$	−4.48029	−0.177516
$638$	5.91143	0.234036
$639$	44.6262	1.76538
$640$	0	0
$641$	3.56399	0.140769	0.0703845	−	0.997520i	$-0.477577\pi$
$641$	3.56399	0.140769	0.0703845	+	0.997520i	$0.477577\pi$
$642$	−12.4752	−0.492358
$643$	28.3129	1.11655	0.558276	−	0.829655i	$-0.311463\pi$
$643$	28.3129	1.11655	0.558276	+	0.829655i	$0.311463\pi$
$644$	9.89887	0.390070
$645$	0	0
$646$	0.152381	0.00599536
$647$	14.3917	0.565797	0.282899	−	0.959150i	$-0.408704\pi$
$647$	14.3917	0.565797	0.282899	+	0.959150i	$0.408704\pi$
$648$	−12.5071	−0.491327
$649$	−10.8945	−0.427647
$650$	0	0
$651$	2.77719	0.108847
$652$	−39.9086	−1.56294
$653$	−16.2556	−0.636130	−0.318065	−	0.948069i	$-0.603033\pi$
$653$	−16.2556	−0.636130	−0.318065	+	0.948069i	$0.603033\pi$
$654$	14.9456	0.584419
$655$	0	0
$656$	−10.2282	−0.399344
$657$	−12.1271	−0.473122
$658$	−7.68427	−0.299564
$659$	−46.1762	−1.79877	−0.899385	−	0.437157i	$-0.855986\pi$
$659$	−46.1762	−1.79877	−0.899385	+	0.437157i	$0.855986\pi$
$660$	0	0
$661$	−18.8213	−0.732063	−0.366032	−	0.930602i	$-0.619284\pi$
$661$	−18.8213	−0.732063	−0.366032	+	0.930602i	$0.619284\pi$
$662$	−7.59586	−0.295221
$663$	−12.1888	−0.473374
$664$	−13.0249	−0.505464
$665$	0	0
$666$	3.52530	0.136603
$667$	57.0927	2.21064
$668$	34.5869	1.33821
$669$	84.8125	3.27904
$670$	0	0
$671$	0.0979789	0.00378243
$672$	−16.7455	−0.645971
$673$	−5.54709	−0.213824	−0.106912	−	0.994268i	$-0.534096\pi$
$673$	−5.54709	−0.213824	−0.106912	+	0.994268i	$0.534096\pi$
$674$	9.15077	0.352474
$675$	0	0
$676$	−11.1632	−0.429354
$677$	14.0148	0.538633	0.269317	−	0.963052i	$-0.413202\pi$
$677$	14.0148	0.538633	0.269317	+	0.963052i	$0.413202\pi$
$678$	7.87867	0.302578
$679$	12.6543	0.485627
$680$	0	0
$681$	−51.8424	−1.98660
$682$	0.615774	0.0235792
$683$	8.01638	0.306738	0.153369	−	0.988169i	$-0.450988\pi$
$683$	8.01638	0.306738	0.153369	+	0.988169i	$0.450988\pi$
$684$	2.22405	0.0850385
$685$	0	0
$686$	0.649405	0.0247944
$687$	−53.1067	−2.02615
$688$	14.5488	0.554670
$689$	−47.6476	−1.81523
$690$	0	0
$691$	−6.20537	−0.236063	−0.118032	−	0.993010i	$-0.537658\pi$
$691$	−6.20537	−0.236063	−0.118032	+	0.993010i	$0.537658\pi$
$692$	18.8496	0.716553
$693$	−5.57827	−0.211901
$694$	−5.82969	−0.221292
$695$	0	0
$696$	−61.9536	−2.34834
$697$	5.76673	0.218430
$698$	−11.2052	−0.424122
$699$	−9.88438	−0.373862
$700$	0	0
$701$	20.7995	0.785586	0.392793	−	0.919627i	$-0.371509\pi$
$701$	20.7995	0.785586	0.392793	+	0.919627i	$0.371509\pi$
$702$	21.9711	0.829244
$703$	−0.245834	−0.00927181
$704$	−0.417907	−0.0157505
$705$	0	0
$706$	5.93656	0.223425
$707$	−9.54583	−0.359008
$708$	50.3605	1.89266
$709$	−22.4752	−0.844075	−0.422037	−	0.906578i	$-0.638685\pi$
$709$	−22.4752	−0.844075	−0.422037	+	0.906578i	$0.638685\pi$
$710$	0	0
$711$	−24.4458	−0.916788
$712$	−3.60512	−0.135108
$713$	5.94716	0.222723
$714$	1.76673	0.0661181
$715$	0	0
$716$	−26.6287	−0.995160
$717$	70.5920	2.63631
$718$	−2.30790	−0.0861300
$719$	−6.25525	−0.233281	−0.116641	−	0.993174i	$-0.537213\pi$
$719$	−6.25525	−0.233281	−0.116641	+	0.993174i	$0.537213\pi$
$720$	0	0
$721$	6.18899	0.230490
$722$	−12.2972	−0.457656
$723$	−6.00730	−0.223414
$724$	13.5190	0.502431
$725$	0	0
$726$	−1.90202	−0.0705906
$727$	−53.2735	−1.97580	−0.987902	−	0.155077i	$-0.950437\pi$
$727$	−53.2735	−1.97580	−0.987902	+	0.155077i	$0.950437\pi$
$728$	10.4111	0.385860
$729$	−36.3274	−1.34546
$730$	0	0
$731$	−8.20274	−0.303389
$732$	−0.452913	−0.0167401
$733$	3.68968	0.136281	0.0681407	−	0.997676i	$-0.478293\pi$
$733$	3.68968	0.136281	0.0681407	+	0.997676i	$0.478293\pi$
$734$	−18.3168	−0.676085
$735$	0	0
$736$	−35.8592	−1.32179
$737$	−14.7273	−0.542488
$738$	−22.4900	−0.827870
$739$	22.3131	0.820800	0.410400	−	0.911906i	$-0.365389\pi$
$739$	22.3131	0.820800	0.410400	+	0.911906i	$0.365389\pi$
$740$	0	0
$741$	−3.31488	−0.121775
$742$	6.90637	0.253541
$743$	−21.4411	−0.786597	−0.393298	−	0.919411i	$-0.628666\pi$
$743$	−21.4411	−0.786597	−0.393298	+	0.919411i	$0.628666\pi$
$744$	−6.45350	−0.236597
$745$	0	0
$746$	−19.7185	−0.721946
$747$	31.2669	1.14400
$748$	−1.46601	−0.0536026
$749$	6.55893	0.239658
$750$	0	0
$751$	27.0889	0.988488	0.494244	−	0.869323i	$-0.335445\pi$
$751$	27.0889	0.988488	0.494244	+	0.869323i	$0.335445\pi$
$752$	−19.4945	−0.710890
$753$	−41.0516	−1.49600
$754$	26.4850	0.964526
$755$	0	0
$756$	11.9182	0.433461
$757$	−12.1171	−0.440405	−0.220202	−	0.975454i	$-0.570672\pi$
$757$	−12.1171	−0.440405	−0.220202	+	0.975454i	$0.570672\pi$
$758$	18.3072	0.664946
$759$	−18.3698	−0.666780
$760$	0	0
$761$	21.3619	0.774369	0.387184	−	0.922002i	$-0.373448\pi$
$761$	21.3619	0.774369	0.387184	+	0.922002i	$0.373448\pi$
$762$	6.27440	0.227298
$763$	−7.85774	−0.284469
$764$	−11.4585	−0.414552
$765$	0	0
$766$	−8.58717	−0.310267
$767$	−48.8107	−1.76245
$768$	23.6810	0.854514
$769$	−3.48346	−0.125617	−0.0628084	−	0.998026i	$-0.520006\pi$
$769$	−3.48346	−0.125617	−0.0628084	+	0.998026i	$0.520006\pi$
$770$	0	0
$771$	−49.3521	−1.77737
$772$	16.8459	0.606297
$773$	−35.0371	−1.26020	−0.630099	−	0.776515i	$-0.716986\pi$
$773$	−35.0371	−1.26020	−0.630099	+	0.776515i	$0.716986\pi$
$774$	31.9904	1.14987
$775$	0	0
$776$	−29.4053	−1.05559
$777$	−2.85023	−0.102252
$778$	1.21617	0.0436018
$779$	1.56833	0.0561912
$780$	0	0
$781$	−8.00000	−0.286263
$782$	3.78332	0.135291
$783$	68.7395	2.45655
$784$	1.64749	0.0588391
$785$	0	0
$786$	−22.0788	−0.787525
$787$	−3.01429	−0.107448	−0.0537238	−	0.998556i	$-0.517109\pi$
$787$	−3.01429	−0.107448	−0.0537238	+	0.998556i	$0.517109\pi$
$788$	30.4390	1.08434
$789$	−20.5439	−0.731383
$790$	0	0
$791$	−4.14226	−0.147282
$792$	12.9625	0.460602
$793$	0.438974	0.0155884
$794$	18.4810	0.655865
$795$	0	0
$796$	2.86213	0.101445
$797$	13.8161	0.489391	0.244695	−	0.969600i	$-0.421312\pi$
$797$	13.8161	0.489391	0.244695	+	0.969600i	$0.421312\pi$
$798$	0.480482	0.0170089
$799$	10.9911	0.388838
$800$	0	0
$801$	8.65428	0.305784
$802$	0.831227	0.0293517
$803$	2.17398	0.0767182
$804$	68.0779	2.40092
$805$	0	0
$806$	2.75885	0.0971764
$807$	54.5338	1.91968
$808$	22.1821	0.780364
$809$	47.3908	1.66617	0.833086	−	0.553143i	$-0.186572\pi$
$809$	47.3908	1.66617	0.833086	+	0.553143i	$0.186572\pi$
$810$	0	0
$811$	51.8157	1.81950	0.909748	−	0.415161i	$-0.136275\pi$
$811$	51.8157	1.81950	0.909748	+	0.415161i	$0.136275\pi$
$812$	14.3668	0.504176
$813$	−55.8037	−1.95712
$814$	−0.631969	−0.0221505
$815$	0	0
$816$	4.48207	0.156904
$817$	−2.23083	−0.0780468
$818$	0.441979	0.0154534
$819$	−24.9923	−0.873302
$820$	0	0
$821$	−20.3330	−0.709625	−0.354813	−	0.934937i	$-0.615455\pi$
$821$	−20.3330	−0.709625	−0.354813	+	0.934937i	$0.615455\pi$
$822$	−16.5260	−0.576409
$823$	31.5993	1.10148	0.550742	−	0.834676i	$-0.314345\pi$
$823$	31.5993	1.10148	0.550742	+	0.834676i	$0.314345\pi$
$824$	−14.3816	−0.501008
$825$	0	0
$826$	7.07495	0.246169
$827$	−38.9728	−1.35522	−0.677608	−	0.735423i	$-0.736983\pi$
$827$	−38.9728	−1.35522	−0.677608	+	0.735423i	$0.736983\pi$
$828$	55.2186	1.91898
$829$	−16.0286	−0.556695	−0.278348	−	0.960480i	$-0.589787\pi$
$829$	−16.0286	−0.556695	−0.278348	+	0.960480i	$0.589787\pi$
$830$	0	0
$831$	−68.6630	−2.38189
$832$	−1.87235	−0.0649119
$833$	−0.928869	−0.0321834
$834$	29.5920	1.02469
$835$	0	0
$836$	−0.398698	−0.0137893
$837$	7.16037	0.247498
$838$	6.45554	0.223003
$839$	36.9414	1.27536	0.637680	−	0.770301i	$-0.279894\pi$
$839$	36.9414	1.27536	0.637680	+	0.770301i	$0.279894\pi$
$840$	0	0
$841$	53.8619	1.85731
$842$	11.4498	0.394587
$843$	−46.7046	−1.60859
$844$	−32.2231	−1.10916
$845$	0	0
$846$	−42.8650	−1.47373
$847$	1.00000	0.0343604
$848$	17.5210	0.601673
$849$	67.2597	2.30835
$850$	0	0
$851$	−6.10357	−0.209228
$852$	36.9805	1.26693
$853$	−21.4908	−0.735830	−0.367915	−	0.929860i	$-0.619928\pi$
$853$	−21.4908	−0.735830	−0.367915	+	0.929860i	$0.619928\pi$
$854$	−0.0636280	−0.00217730
$855$	0	0
$856$	−15.2413	−0.520937
$857$	−46.5543	−1.59027	−0.795133	−	0.606435i	$-0.792599\pi$
$857$	−46.5543	−1.59027	−0.795133	+	0.606435i	$0.792599\pi$
$858$	−8.52162	−0.290923
$859$	−15.2613	−0.520709	−0.260355	−	0.965513i	$-0.583839\pi$
$859$	−15.2613	−0.520709	−0.260355	+	0.965513i	$0.583839\pi$
$860$	0	0
$861$	18.1834	0.619688
$862$	18.8546	0.642189
$863$	−42.7848	−1.45641	−0.728206	−	0.685358i	$-0.759646\pi$
$863$	−42.7848	−1.45641	−0.728206	+	0.685358i	$0.759646\pi$
$864$	−43.1744	−1.46882
$865$	0	0
$866$	8.82425	0.299860
$867$	47.2638	1.60516
$868$	1.49654	0.0507959
$869$	4.38232	0.148660
$870$	0	0
$871$	−65.9827	−2.23574
$872$	18.2594	0.618341
$873$	70.5890	2.38908
$874$	1.02892	0.0348036
$875$	0	0
$876$	−10.0494	−0.339536
$877$	38.8058	1.31038	0.655189	−	0.755465i	$-0.272589\pi$
$877$	38.8058	1.31038	0.655189	+	0.755465i	$0.272589\pi$
$878$	−13.1889	−0.445105
$879$	−4.45970	−0.150422
$880$	0	0
$881$	27.9667	0.942220	0.471110	−	0.882074i	$-0.343853\pi$
$881$	27.9667	0.942220	0.471110	+	0.882074i	$0.343853\pi$
$882$	3.62256	0.121978
$883$	26.7660	0.900748	0.450374	−	0.892840i	$-0.351291\pi$
$883$	26.7660	0.900748	0.450374	+	0.892840i	$0.351291\pi$
$884$	−6.56815	−0.220911
$885$	0	0
$886$	−1.42517	−0.0478796
$887$	10.4839	0.352016	0.176008	−	0.984389i	$-0.443682\pi$
$887$	10.4839	0.352016	0.176008	+	0.984389i	$0.443682\pi$
$888$	6.62323	0.222261
$889$	−3.29881	−0.110639
$890$	0	0
$891$	−5.38232	−0.180314
$892$	45.7028	1.53024
$893$	2.98916	0.100028
$894$	−37.3023	−1.24757
$895$	0	0
$896$	−11.1634	−0.372942
$897$	−82.3019	−2.74798
$898$	1.44837	0.0483328
$899$	8.63145	0.287875
$900$	0	0
$901$	−9.87846	−0.329099
$902$	4.03172	0.134242
$903$	−25.8645	−0.860717
$904$	9.62557	0.320142
$905$	0	0
$906$	−32.0256	−1.06398
$907$	−59.6241	−1.97979	−0.989893	−	0.141818i	$-0.954705\pi$
$907$	−59.6241	−1.97979	−0.989893	+	0.141818i	$0.954705\pi$
$908$	−27.9362	−0.927095
$909$	−53.2493	−1.76617
$910$	0	0
$911$	−26.3131	−0.871792	−0.435896	−	0.899997i	$-0.643568\pi$
$911$	−26.3131	−0.871792	−0.435896	+	0.899997i	$0.643568\pi$
$912$	1.21895	0.0403634
$913$	−5.60512	−0.185502
$914$	5.33946	0.176614
$915$	0	0
$916$	−28.6175	−0.945548
$917$	11.6081	0.383333
$918$	4.55511	0.150341
$919$	−34.1607	−1.12686	−0.563429	−	0.826165i	$-0.690518\pi$
$919$	−34.1607	−1.12686	−0.563429	+	0.826165i	$0.690518\pi$
$920$	0	0
$921$	−39.3870	−1.29785
$922$	−15.4762	−0.509683
$923$	−35.8424	−1.17977
$924$	−4.62256	−0.152071
$925$	0	0
$926$	3.47753	0.114279
$927$	34.5239	1.13391
$928$	−52.0445	−1.70844
$929$	−27.6686	−0.907776	−0.453888	−	0.891059i	$-0.649963\pi$
$929$	−27.6686	−0.907776	−0.453888	+	0.891059i	$0.649963\pi$
$930$	0	0
$931$	−0.252616	−0.00827917
$932$	−5.32638	−0.174471
$933$	6.79113	0.222332
$934$	0.473476	0.0154926
$935$	0	0
$936$	58.0758	1.89827
$937$	−11.2851	−0.368667	−0.184333	−	0.982864i	$-0.559013\pi$
$937$	−11.2851	−0.368667	−0.184333	+	0.982864i	$0.559013\pi$
$938$	9.56399	0.312275
$939$	54.9591	1.79352
$940$	0	0
$941$	−44.1813	−1.44027	−0.720134	−	0.693835i	$-0.755920\pi$
$941$	−44.1813	−1.44027	−0.720134	+	0.693835i	$0.755920\pi$
$942$	−22.8657	−0.745005
$943$	38.9384	1.26801
$944$	17.9487	0.584179
$945$	0	0
$946$	−5.73482	−0.186455
$947$	−23.2214	−0.754593	−0.377296	−	0.926093i	$-0.623146\pi$
$947$	−23.2214	−0.754593	−0.377296	+	0.926093i	$0.623146\pi$
$948$	−20.2575	−0.657933
$949$	9.74008	0.316176
$950$	0	0
$951$	99.3067	3.22024
$952$	2.15846	0.0699560
$953$	−3.91006	−0.126659	−0.0633296	−	0.997993i	$-0.520172\pi$
$953$	−3.91006	−0.126659	−0.0633296	+	0.997993i	$0.520172\pi$
$954$	38.5256	1.24731
$955$	0	0
$956$	38.0398	1.23029
$957$	−26.6611	−0.861830
$958$	16.6856	0.539087
$959$	8.68863	0.280570
$960$	0	0
$961$	−30.1009	−0.970996
$962$	−2.83141	−0.0912883
$963$	36.5875	1.17902
$964$	−3.23714	−0.104261
$965$	0	0
$966$	11.9294	0.383822
$967$	−36.7360	−1.18135	−0.590675	−	0.806909i	$-0.701139\pi$
$967$	−36.7360	−1.18135	−0.590675	+	0.806909i	$0.701139\pi$
$968$	−2.32375	−0.0746881
$969$	−0.687252	−0.0220777
$970$	0	0
$971$	−10.7605	−0.345320	−0.172660	−	0.984981i	$-0.555236\pi$
$971$	−10.7605	−0.345320	−0.172660	+	0.984981i	$0.555236\pi$
$972$	−10.8746	−0.348803
$973$	−15.5582	−0.498773
$974$	20.1553	0.645818
$975$	0	0
$976$	−0.161420	−0.00516692
$977$	−40.2992	−1.28928	−0.644642	−	0.764484i	$-0.722994\pi$
$977$	−40.2992	−1.28928	−0.644642	+	0.764484i	$0.722994\pi$
$978$	−48.0950	−1.53791
$979$	−1.55143	−0.0495838
$980$	0	0
$981$	−43.8326	−1.39947
$982$	−0.0886318	−0.00282835
$983$	48.7296	1.55423	0.777116	−	0.629357i	$-0.216682\pi$
$983$	48.7296	1.55423	0.777116	+	0.629357i	$0.216682\pi$
$984$	−42.2536	−1.34700
$985$	0	0
$986$	5.49095	0.174867
$987$	34.6567	1.10314
$988$	−1.78628	−0.0568293
$989$	−55.3870	−1.76120
$990$	0	0
$991$	19.2350	0.611020	0.305510	−	0.952189i	$-0.401173\pi$
$991$	19.2350	0.611020	0.305510	+	0.952189i	$0.401173\pi$
$992$	−5.42130	−0.172127
$993$	34.2580	1.08714
$994$	5.19524	0.164783
$995$	0	0
$996$	25.9100	0.820990
$997$	−22.1740	−0.702257	−0.351129	−	0.936327i	$-0.614202\pi$
$997$	−22.1740	−0.702257	−0.351129	+	0.936327i	$0.614202\pi$
$998$	2.05962	0.0651962
$999$	−7.34869	−0.232502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.a.x.1.3		4
5.2	odd	4		1925.2.b.p.1849.5		8
5.3	odd	4		1925.2.b.p.1849.4		8
5.4	even	2		385.2.a.h.1.2	✓	4
15.14	odd	2		3465.2.a.bk.1.3		4
20.19	odd	2		6160.2.a.br.1.1		4
35.34	odd	2		2695.2.a.l.1.2		4
55.54	odd	2		4235.2.a.r.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.a.h.1.2	✓	4	5.4	even	2
1925.2.a.x.1.3		4	1.1	even	1	trivial
1925.2.b.p.1849.4		8	5.3	odd	4
1925.2.b.p.1849.5		8	5.2	odd	4
2695.2.a.l.1.2		4	35.34	odd	2
3465.2.a.bk.1.3		4	15.14	odd	2
4235.2.a.r.1.3		4	55.54	odd	2
6160.2.a.br.1.1		4	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1925.a (trivial)

\(f(q)\)	\(=\)	\(q+0.649405 q^{2} -2.92887 q^{3} -1.57827 q^{4} -1.90202 q^{6} +1.00000 q^{7} -2.32375 q^{8} +5.57827 q^{9} +O(q^{10})\)	\(q+0.649405 q^{2} -2.92887 q^{3} -1.57827 q^{4} -1.90202 q^{6} +1.00000 q^{7} -2.32375 q^{8} +5.57827 q^{9} -1.00000 q^{11} +4.62256 q^{12} -4.48029 q^{13} +0.649405 q^{14} +1.64749 q^{16} -0.928869 q^{17} +3.62256 q^{18} -0.252616 q^{19} -2.92887 q^{21} -0.649405 q^{22} -6.27196 q^{23} +6.80595 q^{24} -2.90952 q^{26} -7.55143 q^{27} -1.57827 q^{28} -9.10285 q^{29} -0.948214 q^{31} +5.71739 q^{32} +2.92887 q^{33} -0.603212 q^{34} -8.80404 q^{36} +0.973152 q^{37} -0.164050 q^{38} +13.1222 q^{39} -6.20833 q^{41} -1.90202 q^{42} +8.83089 q^{43} +1.57827 q^{44} -4.07304 q^{46} -11.8328 q^{47} -4.82530 q^{48} +1.00000 q^{49} +2.72054 q^{51} +7.07113 q^{52} +10.6349 q^{53} -4.90393 q^{54} -2.32375 q^{56} +0.739881 q^{57} -5.91143 q^{58} +10.8945 q^{59} -0.0979789 q^{61} -0.615774 q^{62} +5.57827 q^{63} +0.417907 q^{64} +1.90202 q^{66} +14.7273 q^{67} +1.46601 q^{68} +18.3698 q^{69} +8.00000 q^{71} -12.9625 q^{72} -2.17398 q^{73} +0.631969 q^{74} +0.398698 q^{76} -1.00000 q^{77} +8.52162 q^{78} -4.38232 q^{79} +5.38232 q^{81} -4.03172 q^{82} +5.60512 q^{83} +4.62256 q^{84} +5.73482 q^{86} +26.6611 q^{87} +2.32375 q^{88} +1.55143 q^{89} -4.48029 q^{91} +9.89887 q^{92} +2.77719 q^{93} -7.68427 q^{94} -16.7455 q^{96} +12.6543 q^{97} +0.649405 q^{98} -5.57827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} + 8 q^{4} + 4 q^{6} + 4 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 + 4 * q^6 + 4 * q^7 - 12 * q^8 + 8 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} + 8 q^{4} + 4 q^{6} + 4 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{11} + 12 q^{12} + 8 q^{13} - 2 q^{14} + 12 q^{16} + 6 q^{17} + 8 q^{18} + 6 q^{19} - 2 q^{21} + 2 q^{22} - 14 q^{23} - 6 q^{24} - 6 q^{26} - 14 q^{27} + 8 q^{28} - 4 q^{29} + 10 q^{31} - 26 q^{32} + 2 q^{33} - 12 q^{36} + 2 q^{37} + 22 q^{38} + 16 q^{39} - 10 q^{41} + 4 q^{42} + 14 q^{43} - 8 q^{44} - 16 q^{46} - 16 q^{47} + 18 q^{48} + 4 q^{49} + 16 q^{51} + 38 q^{52} - 2 q^{53} + 2 q^{54} - 12 q^{56} + 4 q^{57} - 8 q^{58} + 26 q^{59} - 12 q^{61} - 50 q^{62} + 8 q^{63} + 36 q^{64} - 4 q^{66} + 10 q^{67} + 28 q^{68} - 14 q^{69} + 32 q^{71} + 10 q^{72} + 14 q^{73} - 8 q^{74} - 6 q^{76} - 4 q^{77} + 50 q^{78} + 20 q^{79} - 16 q^{81} + 26 q^{82} + 10 q^{83} + 12 q^{84} - 20 q^{86} + 4 q^{87} + 12 q^{88} - 10 q^{89} + 8 q^{91} - 26 q^{92} - 14 q^{93} - 38 q^{94} - 84 q^{96} + 2 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 + 4 * q^6 + 4 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^11 + 12 * q^12 + 8 * q^13 - 2 * q^14 + 12 * q^16 + 6 * q^17 + 8 * q^18 + 6 * q^19 - 2 * q^21 + 2 * q^22 - 14 * q^23 - 6 * q^24 - 6 * q^26 - 14 * q^27 + 8 * q^28 - 4 * q^29 + 10 * q^31 - 26 * q^32 + 2 * q^33 - 12 * q^36 + 2 * q^37 + 22 * q^38 + 16 * q^39 - 10 * q^41 + 4 * q^42 + 14 * q^43 - 8 * q^44 - 16 * q^46 - 16 * q^47 + 18 * q^48 + 4 * q^49 + 16 * q^51 + 38 * q^52 - 2 * q^53 + 2 * q^54 - 12 * q^56 + 4 * q^57 - 8 * q^58 + 26 * q^59 - 12 * q^61 - 50 * q^62 + 8 * q^63 + 36 * q^64 - 4 * q^66 + 10 * q^67 + 28 * q^68 - 14 * q^69 + 32 * q^71 + 10 * q^72 + 14 * q^73 - 8 * q^74 - 6 * q^76 - 4 * q^77 + 50 * q^78 + 20 * q^79 - 16 * q^81 + 26 * q^82 + 10 * q^83 + 12 * q^84 - 20 * q^86 + 4 * q^87 + 12 * q^88 - 10 * q^89 + 8 * q^91 - 26 * q^92 - 14 * q^93 - 38 * q^94 - 84 * q^96 + 2 * q^97 - 2 * q^98 - 8 * q^99

Introduction

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