LMFDB - Embedded newform 1875.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, 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("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{15})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + 4x + 1 $ x^4 - x^3 - 4x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.95630$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.209057 q^{2} -1.00000 q^{3} -1.95630 q^{4} +0.209057 q^{6} +0.591023 q^{7} +0.827091 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.209057 q^{2} -1.00000 q^{3} -1.95630 q^{4} +0.209057 q^{6} +0.591023 q^{7} +0.827091 q^{8} +1.00000 q^{9} -0.870796 q^{11} +1.95630 q^{12} +1.15057 q^{13} -0.123557 q^{14} +3.73968 q^{16} -4.93395 q^{17} -0.209057 q^{18} -2.84943 q^{19} -0.591023 q^{21} +0.182046 q^{22} +6.91259 q^{23} -0.827091 q^{24} -0.240534 q^{26} -1.00000 q^{27} -1.15622 q^{28} -7.48883 q^{29} +3.45991 q^{31} -2.43599 q^{32} +0.870796 q^{33} +1.03148 q^{34} -1.95630 q^{36} +10.1681 q^{37} +0.595693 q^{38} -1.15057 q^{39} +9.11409 q^{41} +0.123557 q^{42} -2.81486 q^{43} +1.70353 q^{44} -1.44512 q^{46} +6.68842 q^{47} -3.73968 q^{48} -6.65069 q^{49} +4.93395 q^{51} -2.25085 q^{52} +3.87238 q^{53} +0.209057 q^{54} +0.488830 q^{56} +2.84943 q^{57} +1.56559 q^{58} -11.5277 q^{59} -12.7564 q^{61} -0.723318 q^{62} +0.591023 q^{63} -6.97010 q^{64} -0.182046 q^{66} -7.60292 q^{67} +9.65227 q^{68} -6.91259 q^{69} -15.0566 q^{71} +0.827091 q^{72} -2.98798 q^{73} -2.12571 q^{74} +5.57433 q^{76} -0.514660 q^{77} +0.240534 q^{78} +3.33728 q^{79} +1.00000 q^{81} -1.90536 q^{82} -9.73310 q^{83} +1.15622 q^{84} +0.588467 q^{86} +7.48883 q^{87} -0.720227 q^{88} +0.645045 q^{89} +0.680012 q^{91} -13.5231 q^{92} -3.45991 q^{93} -1.39826 q^{94} +2.43599 q^{96} +11.6970 q^{97} +1.39037 q^{98} -0.870796 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 4 q^{3} + q^{4} - q^{6} + 5 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + q^2 - 4 * q^3 + q^4 - q^6 + 5 * q^7 - 3 * q^8 + 4 * q^9	$ 4 q + q^{2} - 4 q^{3} + q^{4} - q^{6} + 5 q^{7} - 3 q^{8} + 4 q^{9} - 6 q^{11} - q^{12} + 7 q^{13} - 10 q^{14} - 9 q^{16} - 7 q^{17} + q^{18} - 9 q^{19} - 5 q^{21} + 6 q^{22} + 10 q^{23} + 3 q^{24} - 2 q^{26} - 4 q^{27} + 5 q^{28} - 28 q^{29} - 10 q^{31} + 6 q^{33} + 7 q^{34} + q^{36} - 10 q^{37} - 6 q^{38} - 7 q^{39} + 10 q^{42} + q^{43} - 9 q^{44} + 5 q^{46} - 23 q^{47} + 9 q^{48} - 3 q^{49} + 7 q^{51} + 13 q^{52} - q^{54} + 9 q^{57} - 2 q^{58} + 4 q^{59} - 43 q^{61} - 10 q^{62} + 5 q^{63} - 7 q^{64} - 6 q^{66} + 8 q^{67} - 3 q^{68} - 10 q^{69} - 27 q^{71} - 3 q^{72} + 15 q^{73} + 5 q^{74} + 9 q^{76} - 15 q^{77} + 2 q^{78} + 10 q^{79} + 4 q^{81} - 20 q^{82} + 3 q^{83} - 5 q^{84} + 24 q^{86} + 28 q^{87} - 3 q^{88} - 9 q^{89} + 5 q^{91} - 15 q^{92} + 10 q^{93} - 22 q^{94} + 13 q^{97} - 42 q^{98} - 6 q^{99}+O(q^{100}) $ 4 * q + q^2 - 4 * q^3 + q^4 - q^6 + 5 * q^7 - 3 * q^8 + 4 * q^9 - 6 * q^11 - q^12 + 7 * q^13 - 10 * q^14 - 9 * q^16 - 7 * q^17 + q^18 - 9 * q^19 - 5 * q^21 + 6 * q^22 + 10 * q^23 + 3 * q^24 - 2 * q^26 - 4 * q^27 + 5 * q^28 - 28 * q^29 - 10 * q^31 + 6 * q^33 + 7 * q^34 + q^36 - 10 * q^37 - 6 * q^38 - 7 * q^39 + 10 * q^42 + q^43 - 9 * q^44 + 5 * q^46 - 23 * q^47 + 9 * q^48 - 3 * q^49 + 7 * q^51 + 13 * q^52 - q^54 + 9 * q^57 - 2 * q^58 + 4 * q^59 - 43 * q^61 - 10 * q^62 + 5 * q^63 - 7 * q^64 - 6 * q^66 + 8 * q^67 - 3 * q^68 - 10 * q^69 - 27 * q^71 - 3 * q^72 + 15 * q^73 + 5 * q^74 + 9 * q^76 - 15 * q^77 + 2 * q^78 + 10 * q^79 + 4 * q^81 - 20 * q^82 + 3 * q^83 - 5 * q^84 + 24 * q^86 + 28 * q^87 - 3 * q^88 - 9 * q^89 + 5 * q^91 - 15 * q^92 + 10 * q^93 - 22 * q^94 + 13 * q^97 - 42 * q^98 - 6 * 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 $

$2$	−0.209057	−0.147826	−0.0739128	−	0.997265i	$-0.523549\pi$
$2$	−0.209057	−0.147826	−0.0739128	+	0.997265i	$0.523549\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.95630	−0.978148
$5$	0	0
$5$	0	0
$6$	0.209057	0.0853471
$7$	0.591023	0.223386	0.111693	−	0.993743i	$-0.464373\pi$
$7$	0.591023	0.223386	0.111693	+	0.993743i	$0.464373\pi$
$8$	0.827091	0.292421
$9$	1.00000	0.333333
$10$	0	0
$11$	−0.870796	−0.262555	−0.131277	−	0.991346i	$-0.541908\pi$
$11$	−0.870796	−0.262555	−0.131277	+	0.991346i	$0.541908\pi$
$12$	1.95630	0.564734
$13$	1.15057	0.319110	0.159555	−	0.987189i	$-0.448994\pi$
$13$	1.15057	0.319110	0.159555	+	0.987189i	$0.448994\pi$
$14$	−0.123557	−0.0330221
$15$	0	0
$16$	3.73968	0.934920
$17$	−4.93395	−1.19666	−0.598330	−	0.801250i	$-0.704169\pi$
$17$	−4.93395	−1.19666	−0.598330	+	0.801250i	$0.704169\pi$
$18$	−0.209057	−0.0492752
$19$	−2.84943	−0.653704	−0.326852	−	0.945075i	$-0.605988\pi$
$19$	−2.84943	−0.653704	−0.326852	+	0.945075i	$0.605988\pi$
$20$	0	0
$21$	−0.591023	−0.128972
$22$	0.182046	0.0388123
$23$	6.91259	1.44137	0.720687	−	0.693260i	$-0.243826\pi$
$23$	6.91259	1.44137	0.720687	+	0.693260i	$0.243826\pi$
$24$	−0.827091	−0.168829
$25$	0	0
$26$	−0.240534	−0.0471727
$27$	−1.00000	−0.192450
$28$	−1.15622	−0.218504
$29$	−7.48883	−1.39064	−0.695320	−	0.718700i	$-0.744738\pi$
$29$	−7.48883	−1.39064	−0.695320	+	0.718700i	$0.744738\pi$
$30$	0	0
$31$	3.45991	0.621418	0.310709	−	0.950505i	$-0.399434\pi$
$31$	3.45991	0.621418	0.310709	+	0.950505i	$0.399434\pi$
$32$	−2.43599	−0.430626
$33$	0.870796	0.151586
$34$	1.03148	0.176897
$35$	0	0
$36$	−1.95630	−0.326049
$37$	10.1681	1.67163	0.835814	−	0.549013i	$-0.184996\pi$
$37$	10.1681	1.67163	0.835814	+	0.549013i	$0.184996\pi$
$38$	0.595693	0.0966342
$39$	−1.15057	−0.184238
$40$	0	0
$41$	9.11409	1.42338	0.711691	−	0.702493i	$-0.247930\pi$
$41$	9.11409	1.42338	0.711691	+	0.702493i	$0.247930\pi$
$42$	0.123557	0.0190653
$43$	−2.81486	−0.429263	−0.214631	−	0.976695i	$-0.568855\pi$
$43$	−2.81486	−0.429263	−0.214631	+	0.976695i	$0.568855\pi$
$44$	1.70353	0.256817
$45$	0	0
$46$	−1.44512	−0.213072
$47$	6.68842	0.975606	0.487803	−	0.872954i	$-0.337798\pi$
$47$	6.68842	0.975606	0.487803	+	0.872954i	$0.337798\pi$
$48$	−3.73968	−0.539777
$49$	−6.65069	−0.950099
$50$	0	0
$51$	4.93395	0.690892
$52$	−2.25085	−0.312137
$53$	3.87238	0.531912	0.265956	−	0.963985i	$-0.414312\pi$
$53$	3.87238	0.531912	0.265956	+	0.963985i	$0.414312\pi$
$54$	0.209057	0.0284490
$55$	0	0
$56$	0.488830	0.0653226
$57$	2.84943	0.377416
$58$	1.56559	0.205572
$59$	−11.5277	−1.50078	−0.750392	−	0.660993i	$-0.770135\pi$
$59$	−11.5277	−1.50078	−0.750392	+	0.660993i	$0.770135\pi$
$60$	0	0
$61$	−12.7564	−1.63329	−0.816643	−	0.577143i	$-0.804168\pi$
$61$	−12.7564	−1.63329	−0.816643	+	0.577143i	$0.804168\pi$
$62$	−0.723318	−0.0918615
$63$	0.591023	0.0744619
$64$	−6.97010	−0.871263
$65$	0	0
$66$	−0.182046	−0.0224083
$67$	−7.60292	−0.928845	−0.464422	−	0.885614i	$-0.653738\pi$
$67$	−7.60292	−0.928845	−0.464422	+	0.885614i	$0.653738\pi$
$68$	9.65227	1.17051
$69$	−6.91259	−0.832178
$70$	0	0
$71$	−15.0566	−1.78689	−0.893444	−	0.449175i	$-0.851718\pi$
$71$	−15.0566	−1.78689	−0.893444	+	0.449175i	$0.851718\pi$
$72$	0.827091	0.0974736
$73$	−2.98798	−0.349716	−0.174858	−	0.984594i	$-0.555947\pi$
$73$	−2.98798	−0.349716	−0.174858	+	0.984594i	$0.555947\pi$
$74$	−2.12571	−0.247109
$75$	0	0
$76$	5.57433	0.639419
$77$	−0.514660	−0.0586510
$78$	0.240534	0.0272351
$79$	3.33728	0.375474	0.187737	−	0.982219i	$-0.439885\pi$
$79$	3.33728	0.375474	0.187737	+	0.982219i	$0.439885\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−1.90536	−0.210412
$83$	−9.73310	−1.06835	−0.534173	−	0.845375i	$-0.679377\pi$
$83$	−9.73310	−1.06835	−0.534173	+	0.845375i	$0.679377\pi$
$84$	1.15622	0.126153
$85$	0	0
$86$	0.588467	0.0634560
$87$	7.48883	0.802887
$88$	−0.720227	−0.0767765
$89$	0.645045	0.0683746	0.0341873	−	0.999415i	$-0.489116\pi$
$89$	0.645045	0.0683746	0.0341873	+	0.999415i	$0.489116\pi$
$90$	0	0
$91$	0.680012	0.0712847
$92$	−13.5231	−1.40988
$93$	−3.45991	−0.358776
$94$	−1.39826	−0.144220
$95$	0	0
$96$	2.43599	0.248622
$97$	11.6970	1.18765	0.593823	−	0.804596i	$-0.297618\pi$
$97$	11.6970	1.18765	0.593823	+	0.804596i	$0.297618\pi$
$98$	1.39037	0.140449
$99$	−0.870796	−0.0875183
$100$	0	0
$101$	−14.7636	−1.46903	−0.734517	−	0.678591i	$-0.762591\pi$
$101$	−14.7636	−1.46903	−0.734517	+	0.678591i	$0.762591\pi$
$102$	−1.03148	−0.102131
$103$	−1.41969	−0.139887	−0.0699433	−	0.997551i	$-0.522282\pi$
$103$	−1.41969	−0.139887	−0.0699433	+	0.997551i	$0.522282\pi$
$104$	0.951625	0.0933145
$105$	0	0
$106$	−0.809547	−0.0786301
$107$	−14.9579	−1.44603	−0.723016	−	0.690831i	$-0.757245\pi$
$107$	−14.9579	−1.44603	−0.723016	+	0.690831i	$0.757245\pi$
$108$	1.95630	0.188245
$109$	−11.0977	−1.06297	−0.531485	−	0.847068i	$-0.678366\pi$
$109$	−11.0977	−1.06297	−0.531485	+	0.847068i	$0.678366\pi$
$110$	0	0
$111$	−10.1681	−0.965115
$112$	2.21024	0.208848
$113$	−12.1069	−1.13892	−0.569459	−	0.822020i	$-0.692847\pi$
$113$	−12.1069	−1.13892	−0.569459	+	0.822020i	$0.692847\pi$
$114$	−0.595693	−0.0557918
$115$	0	0
$116$	14.6504	1.36025
$117$	1.15057	0.106370
$118$	2.40995	0.221854
$119$	−2.91608	−0.267317
$120$	0	0
$121$	−10.2417	−0.931065
$122$	2.66681	0.241442
$123$	−9.11409	−0.821790
$124$	−6.76860	−0.607838
$125$	0	0
$126$	−0.123557	−0.0110074
$127$	0.541671	0.0480656	0.0240328	−	0.999711i	$-0.492349\pi$
$127$	0.541671	0.0480656	0.0240328	+	0.999711i	$0.492349\pi$
$128$	6.32912	0.559421
$129$	2.81486	0.247835
$130$	0	0
$131$	−2.46747	−0.215583	−0.107792	−	0.994173i	$-0.534378\pi$
$131$	−2.46747	−0.215583	−0.107792	+	0.994173i	$0.534378\pi$
$132$	−1.70353	−0.148274
$133$	−1.68408	−0.146028
$134$	1.58944	0.137307
$135$	0	0
$136$	−4.08083	−0.349928
$137$	−5.64471	−0.482261	−0.241130	−	0.970493i	$-0.577518\pi$
$137$	−5.64471	−0.482261	−0.241130	+	0.970493i	$0.577518\pi$
$138$	1.44512	0.123017
$139$	−0.326034	−0.0276538	−0.0138269	−	0.999904i	$-0.504401\pi$
$139$	−0.326034	−0.0276538	−0.0138269	+	0.999904i	$0.504401\pi$
$140$	0	0
$141$	−6.68842	−0.563267
$142$	3.14768	0.264148
$143$	−1.00191	−0.0837839
$144$	3.73968	0.311640
$145$	0	0
$146$	0.624657	0.0516970
$147$	6.65069	0.548540
$148$	−19.8918	−1.63510
$149$	−0.637614	−0.0522354	−0.0261177	−	0.999659i	$-0.508314\pi$
$149$	−0.637614	−0.0522354	−0.0261177	+	0.999659i	$0.508314\pi$
$150$	0	0
$151$	11.3948	0.927299	0.463649	−	0.886019i	$-0.346540\pi$
$151$	11.3948	0.927299	0.463649	+	0.886019i	$0.346540\pi$
$152$	−2.35674	−0.191157
$153$	−4.93395	−0.398887
$154$	0.107593	0.00867011
$155$	0	0
$156$	2.25085	0.180212
$157$	2.86068	0.228307	0.114154	−	0.993463i	$-0.463584\pi$
$157$	2.86068	0.228307	0.114154	+	0.993463i	$0.463584\pi$
$158$	−0.697683	−0.0555046
$159$	−3.87238	−0.307099
$160$	0	0
$161$	4.08550	0.321982
$162$	−0.209057	−0.0164251
$163$	14.1106	1.10523	0.552614	−	0.833437i	$-0.313630\pi$
$163$	14.1106	1.10523	0.552614	+	0.833437i	$0.313630\pi$
$164$	−17.8299	−1.39228
$165$	0	0
$166$	2.03477	0.157929
$167$	−7.49041	−0.579625	−0.289813	−	0.957083i	$-0.593593\pi$
$167$	−7.49041	−0.579625	−0.289813	+	0.957083i	$0.593593\pi$
$168$	−0.488830	−0.0377140
$169$	−11.6762	−0.898169
$170$	0	0
$171$	−2.84943	−0.217901
$172$	5.50670	0.419882
$173$	20.3231	1.54514	0.772570	−	0.634929i	$-0.218971\pi$
$173$	20.3231	1.54514	0.772570	+	0.634929i	$0.218971\pi$
$174$	−1.56559	−0.118687
$175$	0	0
$176$	−3.25650	−0.245468
$177$	11.5277	0.866478
$178$	−0.134851	−0.0101075
$179$	1.13209	0.0846164	0.0423082	−	0.999105i	$-0.486529\pi$
$179$	1.13209	0.0846164	0.0423082	+	0.999105i	$0.486529\pi$
$180$	0	0
$181$	4.96450	0.369008	0.184504	−	0.982832i	$-0.440932\pi$
$181$	4.96450	0.369008	0.184504	+	0.982832i	$0.440932\pi$
$182$	−0.142161	−0.0105377
$183$	12.7564	0.942978
$184$	5.71734	0.421488
$185$	0	0
$186$	0.723318	0.0530362
$187$	4.29647	0.314189
$188$	−13.0845	−0.954287
$189$	−0.591023	−0.0429906
$190$	0	0
$191$	6.44610	0.466424	0.233212	−	0.972426i	$-0.425076\pi$
$191$	6.44610	0.466424	0.233212	+	0.972426i	$0.425076\pi$
$192$	6.97010	0.503024
$193$	−18.4312	−1.32671	−0.663353	−	0.748307i	$-0.730867\pi$
$193$	−18.4312	−1.32671	−0.663353	+	0.748307i	$0.730867\pi$
$194$	−2.44533	−0.175564
$195$	0	0
$196$	13.0107	0.929337
$197$	−16.8343	−1.19940	−0.599698	−	0.800227i	$-0.704713\pi$
$197$	−16.8343	−1.19940	−0.599698	+	0.800227i	$0.704713\pi$
$198$	0.182046	0.0129374
$199$	16.9968	1.20487	0.602435	−	0.798168i	$-0.294197\pi$
$199$	16.9968	1.20487	0.602435	+	0.798168i	$0.294197\pi$
$200$	0	0
$201$	7.60292	0.536269
$202$	3.08643	0.217161
$203$	−4.42607	−0.310649
$204$	−9.65227	−0.675794
$205$	0	0
$206$	0.296797	0.0206788
$207$	6.91259	0.480458
$208$	4.30276	0.298343
$209$	2.48127	0.171633
$210$	0	0
$211$	5.00874	0.344816	0.172408	−	0.985026i	$-0.444845\pi$
$211$	5.00874	0.344816	0.172408	+	0.985026i	$0.444845\pi$
$212$	−7.57551	−0.520288
$213$	15.0566	1.03166
$214$	3.12705	0.213761
$215$	0	0
$216$	−0.827091	−0.0562764
$217$	2.04489	0.138816
$218$	2.32006	0.157134
$219$	2.98798	0.201909
$220$	0	0
$221$	−5.67685	−0.381866
$222$	2.12571	0.142669
$223$	15.9452	1.06777	0.533886	−	0.845556i	$-0.320731\pi$
$223$	15.9452	1.06777	0.533886	+	0.845556i	$0.320731\pi$
$224$	−1.43972	−0.0961957
$225$	0	0
$226$	2.53102	0.168361
$227$	−26.8967	−1.78520	−0.892600	−	0.450850i	$-0.851121\pi$
$227$	−26.8967	−1.78520	−0.892600	+	0.450850i	$0.851121\pi$
$228$	−5.57433	−0.369169
$229$	−2.94598	−0.194676	−0.0973378	−	0.995251i	$-0.531033\pi$
$229$	−2.94598	−0.194676	−0.0973378	+	0.995251i	$0.531033\pi$
$230$	0	0
$231$	0.514660	0.0338622
$232$	−6.19394	−0.406652
$233$	−23.4054	−1.53334	−0.766670	−	0.642041i	$-0.778088\pi$
$233$	−23.4054	−1.53334	−0.766670	+	0.642041i	$0.778088\pi$
$234$	−0.240534	−0.0157242
$235$	0	0
$236$	22.5517	1.46799
$237$	−3.33728	−0.216780
$238$	0.609627	0.0395162
$239$	14.7790	0.955973	0.477987	−	0.878367i	$-0.341367\pi$
$239$	14.7790	0.955973	0.477987	+	0.878367i	$0.341367\pi$
$240$	0	0
$241$	−14.3894	−0.926903	−0.463451	−	0.886122i	$-0.653389\pi$
$241$	−14.3894	−0.926903	−0.463451	+	0.886122i	$0.653389\pi$
$242$	2.14110	0.137635
$243$	−1.00000	−0.0641500
$244$	24.9552	1.59760
$245$	0	0
$246$	1.90536	0.121482
$247$	−3.27847	−0.208604
$248$	2.86166	0.181716
$249$	9.73310	0.616810
$250$	0	0
$251$	−18.7342	−1.18249	−0.591247	−	0.806490i	$-0.701364\pi$
$251$	−18.7342	−1.18249	−0.591247	+	0.806490i	$0.701364\pi$
$252$	−1.15622	−0.0728347
$253$	−6.01945	−0.378440
$254$	−0.113240	−0.00710532
$255$	0	0
$256$	12.6171	0.788566
$257$	−6.42218	−0.400605	−0.200302	−	0.979734i	$-0.564192\pi$
$257$	−6.42218	−0.400605	−0.200302	+	0.979734i	$0.564192\pi$
$258$	−0.588467	−0.0366363
$259$	6.00959	0.373418
$260$	0	0
$261$	−7.48883	−0.463547
$262$	0.515841	0.0318687
$263$	−14.2071	−0.876050	−0.438025	−	0.898963i	$-0.644322\pi$
$263$	−14.2071	−0.876050	−0.438025	+	0.898963i	$0.644322\pi$
$264$	0.720227	0.0443269
$265$	0	0
$266$	0.352068	0.0215867
$267$	−0.645045	−0.0394761
$268$	14.8736	0.908547
$269$	−8.67115	−0.528689	−0.264345	−	0.964428i	$-0.585156\pi$
$269$	−8.67115	−0.528689	−0.264345	+	0.964428i	$0.585156\pi$
$270$	0	0
$271$	11.5697	0.702807	0.351403	−	0.936224i	$-0.385705\pi$
$271$	11.5697	0.702807	0.351403	+	0.936224i	$0.385705\pi$
$272$	−18.4514	−1.11878
$273$	−0.680012	−0.0411562
$274$	1.18007	0.0712904
$275$	0	0
$276$	13.5231	0.813993
$277$	19.2540	1.15686	0.578431	−	0.815732i	$-0.303665\pi$
$277$	19.2540	1.15686	0.578431	+	0.815732i	$0.303665\pi$
$278$	0.0681596	0.00408794
$279$	3.45991	0.207139
$280$	0	0
$281$	−3.21917	−0.192040	−0.0960198	−	0.995379i	$-0.530611\pi$
$281$	−3.21917	−0.192040	−0.0960198	+	0.995379i	$0.530611\pi$
$282$	1.39826	0.0832652
$283$	30.6086	1.81949	0.909745	−	0.415167i	$-0.136277\pi$
$283$	30.6086	1.81949	0.909745	+	0.415167i	$0.136277\pi$
$284$	29.4551	1.74784
$285$	0	0
$286$	0.209456	0.0123854
$287$	5.38664	0.317963
$288$	−2.43599	−0.143542
$289$	7.34391	0.431995
$290$	0	0
$291$	−11.6970	−0.685688
$292$	5.84536	0.342074
$293$	−12.6725	−0.740333	−0.370166	−	0.928965i	$-0.620699\pi$
$293$	−12.6725	−0.740333	−0.370166	+	0.928965i	$0.620699\pi$
$294$	−1.39037	−0.0810882
$295$	0	0
$296$	8.40995	0.488819
$297$	0.870796	0.0505287
$298$	0.133298	0.00772173
$299$	7.95341	0.459958
$300$	0	0
$301$	−1.66365	−0.0958911
$302$	−2.38217	−0.137078
$303$	14.7636	0.848147
$304$	−10.6560	−0.611162
$305$	0	0
$306$	1.03148	0.0589656
$307$	28.0055	1.59836	0.799180	−	0.601092i	$-0.205268\pi$
$307$	28.0055	1.59836	0.799180	+	0.601092i	$0.205268\pi$
$308$	1.00683	0.0573693
$309$	1.41969	0.0807636
$310$	0	0
$311$	29.1437	1.65259	0.826293	−	0.563241i	$-0.190446\pi$
$311$	29.1437	1.65259	0.826293	+	0.563241i	$0.190446\pi$
$312$	−0.951625	−0.0538751
$313$	19.1782	1.08402	0.542009	−	0.840373i	$-0.317664\pi$
$313$	19.1782	1.08402	0.542009	+	0.840373i	$0.317664\pi$
$314$	−0.598045	−0.0337497
$315$	0	0
$316$	−6.52871	−0.367269
$317$	19.8985	1.11761	0.558804	−	0.829300i	$-0.311260\pi$
$317$	19.8985	1.11761	0.558804	+	0.829300i	$0.311260\pi$
$318$	0.809547	0.0453971
$319$	6.52124	0.365119
$320$	0	0
$321$	14.9579	0.834867
$322$	−0.854102	−0.0475972
$323$	14.0590	0.782262
$324$	−1.95630	−0.108683
$325$	0	0
$326$	−2.94992	−0.163381
$327$	11.0977	0.613706
$328$	7.53818	0.416226
$329$	3.95301	0.217936
$330$	0	0
$331$	−27.8128	−1.52873	−0.764366	−	0.644783i	$-0.776948\pi$
$331$	−27.8128	−1.52873	−0.764366	+	0.644783i	$0.776948\pi$
$332$	19.0408	1.04500
$333$	10.1681	0.557209
$334$	1.56592	0.0856834
$335$	0	0
$336$	−2.21024	−0.120578
$337$	−31.7776	−1.73104	−0.865518	−	0.500877i	$-0.833011\pi$
$337$	−31.7776	−1.73104	−0.865518	+	0.500877i	$0.833011\pi$
$338$	2.44099	0.132772
$339$	12.1069	0.657555
$340$	0	0
$341$	−3.01287	−0.163156
$342$	0.595693	0.0322114
$343$	−8.06787	−0.435624
$344$	−2.32815	−0.125525
$345$	0	0
$346$	−4.24869	−0.228411
$347$	−27.6962	−1.48681	−0.743404	−	0.668842i	$-0.766790\pi$
$347$	−27.6962	−1.48681	−0.743404	+	0.668842i	$0.766790\pi$
$348$	−14.6504	−0.785342
$349$	−11.3435	−0.607206	−0.303603	−	0.952799i	$-0.598190\pi$
$349$	−11.3435	−0.607206	−0.303603	+	0.952799i	$0.598190\pi$
$350$	0	0
$351$	−1.15057	−0.0614128
$352$	2.12125	0.113063
$353$	−13.2761	−0.706614	−0.353307	−	0.935507i	$-0.614943\pi$
$353$	−13.2761	−0.706614	−0.353307	+	0.935507i	$0.614943\pi$
$354$	−2.40995	−0.128088
$355$	0	0
$356$	−1.26190	−0.0668805
$357$	2.91608	0.154335
$358$	−0.236671	−0.0125085
$359$	0.547922	0.0289182	0.0144591	−	0.999895i	$-0.495397\pi$
$359$	0.547922	0.0289182	0.0144591	+	0.999895i	$0.495397\pi$
$360$	0	0
$361$	−10.8807	−0.572671
$362$	−1.03786	−0.0545489
$363$	10.2417	0.537551
$364$	−1.33030	−0.0697269
$365$	0	0
$366$	−2.66681	−0.139396
$367$	32.3147	1.68681	0.843406	−	0.537277i	$-0.180547\pi$
$367$	32.3147	1.68681	0.843406	+	0.537277i	$0.180547\pi$
$368$	25.8509	1.34757
$369$	9.11409	0.474461
$370$	0	0
$371$	2.28866	0.118821
$372$	6.76860	0.350936
$373$	−15.2740	−0.790860	−0.395430	−	0.918496i	$-0.629404\pi$
$373$	−15.2740	−0.790860	−0.395430	+	0.918496i	$0.629404\pi$
$374$	−0.898206	−0.0464451
$375$	0	0
$376$	5.53193	0.285288
$377$	−8.61641	−0.443768
$378$	0.123557	0.00635511
$379$	11.5928	0.595482	0.297741	−	0.954647i	$-0.403767\pi$
$379$	11.5928	0.595482	0.297741	+	0.954647i	$0.403767\pi$
$380$	0	0
$381$	−0.541671	−0.0277507
$382$	−1.34760	−0.0689493
$383$	−27.1864	−1.38916	−0.694580	−	0.719416i	$-0.744410\pi$
$383$	−27.1864	−1.38916	−0.694580	+	0.719416i	$0.744410\pi$
$384$	−6.32912	−0.322982
$385$	0	0
$386$	3.85317	0.196121
$387$	−2.81486	−0.143088
$388$	−22.8827	−1.16169
$389$	36.2825	1.83959	0.919797	−	0.392394i	$-0.128353\pi$
$389$	36.2825	1.83959	0.919797	+	0.392394i	$0.128353\pi$
$390$	0	0
$391$	−34.1064	−1.72484
$392$	−5.50073	−0.277829
$393$	2.46747	0.124467
$394$	3.51933	0.177301
$395$	0	0
$396$	1.70353	0.0856058
$397$	−24.6879	−1.23905	−0.619525	−	0.784977i	$-0.712675\pi$
$397$	−24.6879	−1.23905	−0.619525	+	0.784977i	$0.712675\pi$
$398$	−3.55330	−0.178111
$399$	1.68408	0.0843094
$400$	0	0
$401$	−34.4435	−1.72003	−0.860014	−	0.510271i	$-0.829545\pi$
$401$	−34.4435	−1.72003	−0.860014	+	0.510271i	$0.829545\pi$
$402$	−1.58944	−0.0792742
$403$	3.98086	0.198301
$404$	28.8820	1.43693
$405$	0	0
$406$	0.925301	0.0459219
$407$	−8.85435	−0.438894
$408$	4.08083	0.202031
$409$	−12.9896	−0.642294	−0.321147	−	0.947029i	$-0.604068\pi$
$409$	−12.9896	−0.642294	−0.321147	+	0.947029i	$0.604068\pi$
$410$	0	0
$411$	5.64471	0.278433
$412$	2.77734	0.136830
$413$	−6.81316	−0.335254
$414$	−1.44512	−0.0710240
$415$	0	0
$416$	−2.80277	−0.137417
$417$	0.326034	0.0159659
$418$	−0.518727	−0.0253718
$419$	18.5116	0.904353	0.452177	−	0.891928i	$-0.350648\pi$
$419$	18.5116	0.904353	0.452177	+	0.891928i	$0.350648\pi$
$420$	0	0
$421$	23.8357	1.16168	0.580841	−	0.814017i	$-0.302724\pi$
$421$	23.8357	1.16168	0.580841	+	0.814017i	$0.302724\pi$
$422$	−1.04711	−0.0509726
$423$	6.68842	0.325202
$424$	3.20281	0.155542
$425$	0	0
$426$	−3.14768	−0.152506
$427$	−7.53931	−0.364853
$428$	29.2620	1.41443
$429$	1.00191	0.0483727
$430$	0	0
$431$	−29.6800	−1.42963	−0.714817	−	0.699312i	$-0.753490\pi$
$431$	−29.6800	−1.42963	−0.714817	+	0.699312i	$0.753490\pi$
$432$	−3.73968	−0.179926
$433$	−18.0164	−0.865811	−0.432906	−	0.901439i	$-0.642512\pi$
$433$	−18.0164	−0.865811	−0.432906	+	0.901439i	$0.642512\pi$
$434$	−0.427497	−0.0205205
$435$	0	0
$436$	21.7104	1.03974
$437$	−19.6970	−0.942233
$438$	−0.624657	−0.0298473
$439$	21.0442	1.00438	0.502191	−	0.864757i	$-0.332527\pi$
$439$	21.0442	1.00438	0.502191	+	0.864757i	$0.332527\pi$
$440$	0	0
$441$	−6.65069	−0.316700
$442$	1.18679	0.0564496
$443$	−4.15877	−0.197589	−0.0987946	−	0.995108i	$-0.531499\pi$
$443$	−4.15877	−0.197589	−0.0987946	+	0.995108i	$0.531499\pi$
$444$	19.8918	0.944024
$445$	0	0
$446$	−3.33346	−0.157844
$447$	0.637614	0.0301581
$448$	−4.11949	−0.194628
$449$	−7.39256	−0.348876	−0.174438	−	0.984668i	$-0.555811\pi$
$449$	−7.39256	−0.348876	−0.174438	+	0.984668i	$0.555811\pi$
$450$	0	0
$451$	−7.93651	−0.373716
$452$	23.6846	1.11403
$453$	−11.3948	−0.535376
$454$	5.62295	0.263898
$455$	0	0
$456$	2.35674	0.110364
$457$	−0.573353	−0.0268203	−0.0134102	−	0.999910i	$-0.504269\pi$
$457$	−0.573353	−0.0268203	−0.0134102	+	0.999910i	$0.504269\pi$
$458$	0.615877	0.0287780
$459$	4.93395	0.230297
$460$	0	0
$461$	3.74666	0.174499	0.0872497	−	0.996186i	$-0.472192\pi$
$461$	3.74666	0.174499	0.0872497	+	0.996186i	$0.472192\pi$
$462$	−0.107593	−0.00500569
$463$	17.3803	0.807732	0.403866	−	0.914818i	$-0.367666\pi$
$463$	17.3803	0.807732	0.403866	+	0.914818i	$0.367666\pi$
$464$	−28.0058	−1.30014
$465$	0	0
$466$	4.89307	0.226667
$467$	10.0211	0.463720	0.231860	−	0.972749i	$-0.425519\pi$
$467$	10.0211	0.463720	0.231860	+	0.972749i	$0.425519\pi$
$468$	−2.25085	−0.104046
$469$	−4.49350	−0.207491
$470$	0	0
$471$	−2.86068	−0.131813
$472$	−9.53449	−0.438860
$473$	2.45117	0.112705
$474$	0.697683	0.0320456
$475$	0	0
$476$	5.70471	0.261475
$477$	3.87238	0.177304
$478$	−3.08965	−0.141317
$479$	18.6136	0.850476	0.425238	−	0.905082i	$-0.360190\pi$
$479$	18.6136	0.850476	0.425238	+	0.905082i	$0.360190\pi$
$480$	0	0
$481$	11.6991	0.533433
$482$	3.00820	0.137020
$483$	−4.08550	−0.185897
$484$	20.0358	0.910719
$485$	0	0
$486$	0.209057	0.00948301
$487$	2.07209	0.0938954	0.0469477	−	0.998897i	$-0.485051\pi$
$487$	2.07209	0.0938954	0.0469477	+	0.998897i	$0.485051\pi$
$488$	−10.5507	−0.477607
$489$	−14.1106	−0.638103
$490$	0	0
$491$	−22.2355	−1.00348	−0.501738	−	0.865020i	$-0.667306\pi$
$491$	−22.2355	−1.00348	−0.501738	+	0.865020i	$0.667306\pi$
$492$	17.8299	0.803832
$493$	36.9495	1.66412
$494$	0.685386	0.0308370
$495$	0	0
$496$	12.9390	0.580976
$497$	−8.89878	−0.399165
$498$	−2.03477	−0.0911803
$499$	28.2713	1.26560	0.632798	−	0.774317i	$-0.281906\pi$
$499$	28.2713	1.26560	0.632798	+	0.774317i	$0.281906\pi$
$500$	0	0
$501$	7.49041	0.334647
$502$	3.91652	0.174803
$503$	−3.39793	−0.151506	−0.0757531	−	0.997127i	$-0.524136\pi$
$503$	−3.39793	−0.151506	−0.0757531	+	0.997127i	$0.524136\pi$
$504$	0.488830	0.0217742
$505$	0	0
$506$	1.25841	0.0559431
$507$	11.6762	0.518558
$508$	−1.05967	−0.0470152
$509$	−10.8405	−0.480497	−0.240248	−	0.970711i	$-0.577229\pi$
$509$	−10.8405	−0.480497	−0.240248	+	0.970711i	$0.577229\pi$
$510$	0	0
$511$	−1.76596	−0.0781216
$512$	−15.2959	−0.675991
$513$	2.84943	0.125805
$514$	1.34260	0.0592196
$515$	0	0
$516$	−5.50670	−0.242419
$517$	−5.82425	−0.256150
$518$	−1.25635	−0.0552007
$519$	−20.3231	−0.892087
$520$	0	0
$521$	15.6473	0.685519	0.342760	−	0.939423i	$-0.388638\pi$
$521$	15.6473	0.685519	0.342760	+	0.939423i	$0.388638\pi$
$522$	1.56559	0.0685241
$523$	−18.3578	−0.802729	−0.401364	−	0.915918i	$-0.631464\pi$
$523$	−18.3578	−0.802729	−0.401364	+	0.915918i	$0.631464\pi$
$524$	4.82709	0.210872
$525$	0	0
$526$	2.97010	0.129503
$527$	−17.0710	−0.743626
$528$	3.25650	0.141721
$529$	24.7839	1.07756
$530$	0	0
$531$	−11.5277	−0.500261
$532$	3.29456	0.142837
$533$	10.4864	0.454216
$534$	0.134851	0.00583558
$535$	0	0
$536$	−6.28831	−0.271613
$537$	−1.13209	−0.0488533
$538$	1.81276	0.0781538
$539$	5.79139	0.249453
$540$	0	0
$541$	−13.8856	−0.596988	−0.298494	−	0.954412i	$-0.596484\pi$
$541$	−13.8856	−0.596988	−0.298494	+	0.954412i	$0.596484\pi$
$542$	−2.41872	−0.103893
$543$	−4.96450	−0.213047
$544$	12.0191	0.515313
$545$	0	0
$546$	0.142161	0.00608394
$547$	41.9134	1.79209	0.896043	−	0.443966i	$-0.146429\pi$
$547$	41.9134	1.79209	0.896043	+	0.443966i	$0.146429\pi$
$548$	11.0427	0.471722
$549$	−12.7564	−0.544429
$550$	0	0
$551$	21.3389	0.909068
$552$	−5.71734	−0.243346
$553$	1.97241	0.0838755
$554$	−4.02518	−0.171014
$555$	0	0
$556$	0.637818	0.0270495
$557$	−8.04257	−0.340774	−0.170387	−	0.985377i	$-0.554502\pi$
$557$	−8.04257	−0.340774	−0.170387	+	0.985377i	$0.554502\pi$
$558$	−0.723318	−0.0306205
$559$	−3.23869	−0.136982
$560$	0	0
$561$	−4.29647	−0.181397
$562$	0.672990	0.0283884
$563$	5.67464	0.239158	0.119579	−	0.992825i	$-0.461846\pi$
$563$	5.67464	0.239158	0.119579	+	0.992825i	$0.461846\pi$
$564$	13.0845	0.550958
$565$	0	0
$566$	−6.39893	−0.268967
$567$	0.591023	0.0248206
$568$	−12.4532	−0.522523
$569$	8.25303	0.345985	0.172993	−	0.984923i	$-0.444656\pi$
$569$	8.25303	0.345985	0.172993	+	0.984923i	$0.444656\pi$
$570$	0	0
$571$	−17.5703	−0.735293	−0.367646	−	0.929966i	$-0.619836\pi$
$571$	−17.5703	−0.735293	−0.367646	+	0.929966i	$0.619836\pi$
$572$	1.96003	0.0819531
$573$	−6.44610	−0.269290
$574$	−1.12611	−0.0470031
$575$	0	0
$576$	−6.97010	−0.290421
$577$	29.6207	1.23313	0.616564	−	0.787305i	$-0.288524\pi$
$577$	29.6207	1.23313	0.616564	+	0.787305i	$0.288524\pi$
$578$	−1.53529	−0.0638598
$579$	18.4312	0.765974
$580$	0	0
$581$	−5.75249	−0.238653
$582$	2.44533	0.101362
$583$	−3.37205	−0.139656
$584$	−2.47133	−0.102264
$585$	0	0
$586$	2.64926	0.109440
$587$	−18.1475	−0.749027	−0.374513	−	0.927222i	$-0.622190\pi$
$587$	−18.1475	−0.749027	−0.374513	+	0.927222i	$0.622190\pi$
$588$	−13.0107	−0.536553
$589$	−9.85877	−0.406224
$590$	0	0
$591$	16.8343	0.692471
$592$	38.0255	1.56284
$593$	−26.0022	−1.06778	−0.533891	−	0.845553i	$-0.679271\pi$
$593$	−26.0022	−1.06778	−0.533891	+	0.845553i	$0.679271\pi$
$594$	−0.182046	−0.00746943
$595$	0	0
$596$	1.24736	0.0510939
$597$	−16.9968	−0.695632
$598$	−1.66272	−0.0679935
$599$	20.6259	0.842753	0.421376	−	0.906886i	$-0.361547\pi$
$599$	20.6259	0.842753	0.421376	+	0.906886i	$0.361547\pi$
$600$	0	0
$601$	−17.7602	−0.724452	−0.362226	−	0.932090i	$-0.617983\pi$
$601$	−17.7602	−0.724452	−0.362226	+	0.932090i	$0.617983\pi$
$602$	0.347797	0.0141752
$603$	−7.60292	−0.309615
$604$	−22.2917	−0.907035
$605$	0	0
$606$	−3.08643	−0.125378
$607$	−13.0143	−0.528232	−0.264116	−	0.964491i	$-0.585080\pi$
$607$	−13.0143	−0.528232	−0.264116	+	0.964491i	$0.585080\pi$
$608$	6.94118	0.281502
$609$	4.42607	0.179353
$610$	0	0
$611$	7.69548	0.311326
$612$	9.65227	0.390170
$613$	−21.9959	−0.888407	−0.444204	−	0.895926i	$-0.646513\pi$
$613$	−21.9959	−0.888407	−0.444204	+	0.895926i	$0.646513\pi$
$614$	−5.85475	−0.236278
$615$	0	0
$616$	−0.425671	−0.0171508
$617$	33.3091	1.34097	0.670487	−	0.741922i	$-0.266085\pi$
$617$	33.3091	1.34097	0.670487	+	0.741922i	$0.266085\pi$
$618$	−0.296797	−0.0119389
$619$	−27.9714	−1.12426	−0.562132	−	0.827048i	$-0.690019\pi$
$619$	−27.9714	−1.12426	−0.562132	+	0.827048i	$0.690019\pi$
$620$	0	0
$621$	−6.91259	−0.277393
$622$	−6.09268	−0.244294
$623$	0.381236	0.0152739
$624$	−4.30276	−0.172248
$625$	0	0
$626$	−4.00934	−0.160245
$627$	−2.48127	−0.0990925
$628$	−5.59634	−0.223318
$629$	−50.1690	−2.00037
$630$	0	0
$631$	−23.0172	−0.916301	−0.458150	−	0.888875i	$-0.651488\pi$
$631$	−23.0172	−0.916301	−0.458150	+	0.888875i	$0.651488\pi$
$632$	2.76024	0.109796
$633$	−5.00874	−0.199079
$634$	−4.15991	−0.165211
$635$	0	0
$636$	7.57551	0.300388
$637$	−7.65208	−0.303186
$638$	−1.36331	−0.0539740
$639$	−15.0566	−0.595629
$640$	0	0
$641$	29.1915	1.15300	0.576498	−	0.817099i	$-0.304419\pi$
$641$	29.1915	1.15300	0.576498	+	0.817099i	$0.304419\pi$
$642$	−3.12705	−0.123415
$643$	−29.6236	−1.16824	−0.584119	−	0.811668i	$-0.698560\pi$
$643$	−29.6236	−1.16824	−0.584119	+	0.811668i	$0.698560\pi$
$644$	−7.99244	−0.314946
$645$	0	0
$646$	−2.93912	−0.115638
$647$	49.0862	1.92978	0.964889	−	0.262657i	$-0.0845987\pi$
$647$	49.0862	1.92978	0.964889	+	0.262657i	$0.0845987\pi$
$648$	0.827091	0.0324912
$649$	10.0383	0.394038
$650$	0	0
$651$	−2.04489	−0.0801454
$652$	−27.6045	−1.08108
$653$	−11.6946	−0.457645	−0.228823	−	0.973468i	$-0.573488\pi$
$653$	−11.6946	−0.457645	−0.228823	+	0.973468i	$0.573488\pi$
$654$	−2.32006	−0.0907214
$655$	0	0
$656$	34.0838	1.33075
$657$	−2.98798	−0.116572
$658$	−0.826404	−0.0322166
$659$	1.18709	0.0462424	0.0231212	−	0.999733i	$-0.492640\pi$
$659$	1.18709	0.0462424	0.0231212	+	0.999733i	$0.492640\pi$
$660$	0	0
$661$	3.72234	0.144782	0.0723912	−	0.997376i	$-0.476937\pi$
$661$	3.72234	0.144782	0.0723912	+	0.997376i	$0.476937\pi$
$662$	5.81446	0.225986
$663$	5.67685	0.220471
$664$	−8.05016	−0.312407
$665$	0	0
$666$	−2.12571	−0.0823698
$667$	−51.7672	−2.00443
$668$	14.6535	0.566959
$669$	−15.9452	−0.616479
$670$	0	0
$671$	11.1082	0.428827
$672$	1.43972	0.0555386
$673$	46.9935	1.81147	0.905734	−	0.423847i	$-0.139320\pi$
$673$	46.9935	1.81147	0.905734	+	0.423847i	$0.139320\pi$
$674$	6.64333	0.255892
$675$	0	0
$676$	22.8421	0.878541
$677$	36.4081	1.39928	0.699639	−	0.714497i	$-0.253344\pi$
$677$	36.4081	1.39928	0.699639	+	0.714497i	$0.253344\pi$
$678$	−2.53102	−0.0972034
$679$	6.91317	0.265303
$680$	0	0
$681$	26.8967	1.03069
$682$	0.629862	0.0241187
$683$	4.66507	0.178504	0.0892519	−	0.996009i	$-0.471552\pi$
$683$	4.66507	0.178504	0.0892519	+	0.996009i	$0.471552\pi$
$684$	5.57433	0.213140
$685$	0	0
$686$	1.68664	0.0643964
$687$	2.94598	0.112396
$688$	−10.5267	−0.401326
$689$	4.45543	0.169738
$690$	0	0
$691$	31.9254	1.21450	0.607249	−	0.794511i	$-0.292273\pi$
$691$	31.9254	1.21450	0.607249	+	0.794511i	$0.292273\pi$
$692$	−39.7581	−1.51138
$693$	−0.514660	−0.0195503
$694$	5.79008	0.219788
$695$	0	0
$696$	6.19394	0.234781
$697$	−44.9685	−1.70330
$698$	2.37144	0.0897605
$699$	23.4054	0.885275
$700$	0	0
$701$	−3.09598	−0.116933	−0.0584667	−	0.998289i	$-0.518621\pi$
$701$	−3.09598	−0.116933	−0.0584667	+	0.998289i	$0.518621\pi$
$702$	0.240534	0.00907838
$703$	−28.9733	−1.09275
$704$	6.06954	0.228754
$705$	0	0
$706$	2.77546	0.104456
$707$	−8.72563	−0.328161
$708$	−22.5517	−0.847543
$709$	47.0490	1.76696	0.883481	−	0.468468i	$-0.155194\pi$
$709$	47.0490	1.76696	0.883481	+	0.468468i	$0.155194\pi$
$710$	0	0
$711$	3.33728	0.125158
$712$	0.533511	0.0199942
$713$	23.9169	0.895696
$714$	−0.609627	−0.0228147
$715$	0	0
$716$	−2.21470	−0.0827674
$717$	−14.7790	−0.551931
$718$	−0.114547	−0.00427485
$719$	25.7083	0.958757	0.479378	−	0.877608i	$-0.340862\pi$
$719$	25.7083	0.958757	0.479378	+	0.877608i	$0.340862\pi$
$720$	0	0
$721$	−0.839072	−0.0312487
$722$	2.27469	0.0846553
$723$	14.3894	0.535147
$724$	−9.71202	−0.360945
$725$	0	0
$726$	−2.14110	−0.0794637
$727$	−35.4025	−1.31301	−0.656504	−	0.754323i	$-0.727965\pi$
$727$	−35.4025	−1.31301	−0.656504	+	0.754323i	$0.727965\pi$
$728$	0.562432	0.0208451
$729$	1.00000	0.0370370
$730$	0	0
$731$	13.8884	0.513681
$732$	−24.9552	−0.922372
$733$	25.7565	0.951336	0.475668	−	0.879625i	$-0.342206\pi$
$733$	25.7565	0.951336	0.475668	+	0.879625i	$0.342206\pi$
$734$	−6.75560	−0.249354
$735$	0	0
$736$	−16.8390	−0.620693
$737$	6.62059	0.243873
$738$	−1.90536	−0.0701374
$739$	−22.1071	−0.813222	−0.406611	−	0.913601i	$-0.633289\pi$
$739$	−22.1071	−0.813222	−0.406611	+	0.913601i	$0.633289\pi$
$740$	0	0
$741$	3.27847	0.120437
$742$	−0.478461	−0.0175648
$743$	20.2268	0.742049	0.371025	−	0.928623i	$-0.379007\pi$
$743$	20.2268	0.742049	0.371025	+	0.928623i	$0.379007\pi$
$744$	−2.86166	−0.104914
$745$	0	0
$746$	3.19314	0.116909
$747$	−9.73310	−0.356116
$748$	−8.40516	−0.307323
$749$	−8.84045	−0.323023
$750$	0	0
$751$	−1.23206	−0.0449584	−0.0224792	−	0.999747i	$-0.507156\pi$
$751$	−1.23206	−0.0449584	−0.0224792	+	0.999747i	$0.507156\pi$
$752$	25.0126	0.912114
$753$	18.7342	0.682714
$754$	1.80132	0.0656002
$755$	0	0
$756$	1.15622	0.0420511
$757$	15.2062	0.552678	0.276339	−	0.961060i	$-0.410879\pi$
$757$	15.2062	0.552678	0.276339	+	0.961060i	$0.410879\pi$
$758$	−2.42356	−0.0880275
$759$	6.01945	0.218492
$760$	0	0
$761$	−32.3209	−1.17163	−0.585817	−	0.810444i	$-0.699226\pi$
$761$	−32.3209	−1.17163	−0.585817	+	0.810444i	$0.699226\pi$
$762$	0.113240	0.00410226
$763$	−6.55901	−0.237452
$764$	−12.6105	−0.456231
$765$	0	0
$766$	5.68350	0.205353
$767$	−13.2635	−0.478915
$768$	−12.6171	−0.455279
$769$	−28.8068	−1.03880	−0.519400	−	0.854531i	$-0.673845\pi$
$769$	−28.8068	−1.03880	−0.519400	+	0.854531i	$0.673845\pi$
$770$	0	0
$771$	6.42218	0.231289
$772$	36.0569	1.29771
$773$	−38.2458	−1.37561	−0.687803	−	0.725897i	$-0.741425\pi$
$773$	−38.2458	−1.37561	−0.687803	+	0.725897i	$0.741425\pi$
$774$	0.588467	0.0211520
$775$	0	0
$776$	9.67444	0.347292
$777$	−6.00959	−0.215593
$778$	−7.58510	−0.271939
$779$	−25.9700	−0.930471
$780$	0	0
$781$	13.1112	0.469156
$782$	7.13018	0.254975
$783$	7.48883	0.267629
$784$	−24.8715	−0.888267
$785$	0	0
$786$	−0.515841	−0.0183994
$787$	36.7934	1.31154	0.655771	−	0.754960i	$-0.272344\pi$
$787$	36.7934	1.31154	0.655771	+	0.754960i	$0.272344\pi$
$788$	32.9329	1.17319
$789$	14.2071	0.505788
$790$	0	0
$791$	−7.15543	−0.254418
$792$	−0.720227	−0.0255922
$793$	−14.6771	−0.521199
$794$	5.16117	0.183163
$795$	0	0
$796$	−33.2507	−1.17854
$797$	36.6698	1.29891	0.649456	−	0.760399i	$-0.274997\pi$
$797$	36.6698	1.29891	0.649456	+	0.760399i	$0.274997\pi$
$798$	−0.352068	−0.0124631
$799$	−33.0004	−1.16747
$800$	0	0
$801$	0.645045	0.0227915
$802$	7.20066	0.254264
$803$	2.60192	0.0918197
$804$	−14.8736	−0.524550
$805$	0	0
$806$	−0.832227	−0.0293139
$807$	8.67115	0.305239
$808$	−12.2108	−0.429576
$809$	−39.2361	−1.37947	−0.689735	−	0.724062i	$-0.742273\pi$
$809$	−39.2361	−1.37947	−0.689735	+	0.724062i	$0.742273\pi$
$810$	0	0
$811$	6.70444	0.235425	0.117712	−	0.993048i	$-0.462444\pi$
$811$	6.70444	0.235425	0.117712	+	0.993048i	$0.462444\pi$
$812$	8.65870	0.303861
$813$	−11.5697	−0.405766
$814$	1.85106	0.0648797
$815$	0	0
$816$	18.4514	0.645929
$817$	8.02076	0.280611
$818$	2.71557	0.0949475
$819$	0.680012	0.0237616
$820$	0	0
$821$	−30.1557	−1.05244	−0.526220	−	0.850348i	$-0.676391\pi$
$821$	−30.1557	−1.05244	−0.526220	+	0.850348i	$0.676391\pi$
$822$	−1.18007	−0.0411596
$823$	−1.90341	−0.0663487	−0.0331744	−	0.999450i	$-0.510562\pi$
$823$	−1.90341	−0.0663487	−0.0331744	+	0.999450i	$0.510562\pi$
$824$	−1.17422	−0.0409057
$825$	0	0
$826$	1.42434	0.0495590
$827$	−17.5652	−0.610803	−0.305402	−	0.952224i	$-0.598791\pi$
$827$	−17.5652	−0.610803	−0.305402	+	0.952224i	$0.598791\pi$
$828$	−13.5231	−0.469959
$829$	−24.0291	−0.834566	−0.417283	−	0.908777i	$-0.637018\pi$
$829$	−24.0291	−0.834566	−0.417283	+	0.908777i	$0.637018\pi$
$830$	0	0
$831$	−19.2540	−0.667914
$832$	−8.01958	−0.278029
$833$	32.8142	1.13695
$834$	−0.0681596	−0.00236017
$835$	0	0
$836$	−4.85410	−0.167883
$837$	−3.45991	−0.119592
$838$	−3.86999	−0.133687
$839$	1.07320	0.0370511	0.0185255	−	0.999828i	$-0.494103\pi$
$839$	1.07320	0.0370511	0.0185255	+	0.999828i	$0.494103\pi$
$840$	0	0
$841$	27.0826	0.933882
$842$	−4.98302	−0.171726
$843$	3.21917	0.110874
$844$	−9.79857	−0.337281
$845$	0	0
$846$	−1.39826	−0.0480732
$847$	−6.05309	−0.207987
$848$	14.4815	0.497295
$849$	−30.6086	−1.05048
$850$	0	0
$851$	70.2880	2.40944
$852$	−29.4551	−1.00912
$853$	17.2818	0.591716	0.295858	−	0.955232i	$-0.404394\pi$
$853$	17.2818	0.591716	0.295858	+	0.955232i	$0.404394\pi$
$854$	1.57615	0.0539346
$855$	0	0
$856$	−12.3715	−0.422850
$857$	−16.2742	−0.555917	−0.277959	−	0.960593i	$-0.589658\pi$
$857$	−16.2742	−0.555917	−0.277959	+	0.960593i	$0.589658\pi$
$858$	−0.209456	−0.00715072
$859$	−11.2429	−0.383604	−0.191802	−	0.981434i	$-0.561433\pi$
$859$	−11.2429	−0.383604	−0.191802	+	0.981434i	$0.561433\pi$
$860$	0	0
$861$	−5.38664	−0.183576
$862$	6.20480	0.211336
$863$	33.3846	1.13642	0.568212	−	0.822882i	$-0.307635\pi$
$863$	33.3846	1.13642	0.568212	+	0.822882i	$0.307635\pi$
$864$	2.43599	0.0828740
$865$	0	0
$866$	3.76645	0.127989
$867$	−7.34391	−0.249412
$868$	−4.00040	−0.135782
$869$	−2.90609	−0.0985825
$870$	0	0
$871$	−8.74768	−0.296404
$872$	−9.17883	−0.310834
$873$	11.6970	0.395882
$874$	4.11778	0.139286
$875$	0	0
$876$	−5.84536	−0.197497
$877$	−16.1140	−0.544130	−0.272065	−	0.962279i	$-0.587707\pi$
$877$	−16.1140	−0.544130	−0.272065	+	0.962279i	$0.587707\pi$
$878$	−4.39943	−0.148473
$879$	12.6725	0.427431
$880$	0	0
$881$	25.2799	0.851701	0.425851	−	0.904793i	$-0.359975\pi$
$881$	25.2799	0.851701	0.425851	+	0.904793i	$0.359975\pi$
$882$	1.39037	0.0468163
$883$	−31.0260	−1.04411	−0.522053	−	0.852913i	$-0.674834\pi$
$883$	−31.0260	−1.04411	−0.522053	+	0.852913i	$0.674834\pi$
$884$	11.1056	0.373522
$885$	0	0
$886$	0.869420	0.0292087
$887$	38.1973	1.28254	0.641270	−	0.767316i	$-0.278408\pi$
$887$	38.1973	1.28254	0.641270	+	0.767316i	$0.278408\pi$
$888$	−8.40995	−0.282220
$889$	0.320140	0.0107372
$890$	0	0
$891$	−0.870796	−0.0291728
$892$	−31.1936	−1.04444
$893$	−19.0582	−0.637758
$894$	−0.133298	−0.00445814
$895$	0	0
$896$	3.74066	0.124967
$897$	−7.95341	−0.265557
$898$	1.54547	0.0515728
$899$	−25.9107	−0.864169
$900$	0	0
$901$	−19.1061	−0.636517
$902$	1.65918	0.0552447
$903$	1.66365	0.0553628
$904$	−10.0135	−0.333043
$905$	0	0
$906$	2.38217	0.0791423
$907$	−40.9212	−1.35877	−0.679383	−	0.733784i	$-0.737753\pi$
$907$	−40.9212	−1.35877	−0.679383	+	0.733784i	$0.737753\pi$
$908$	52.6180	1.74619
$909$	−14.7636	−0.489678
$910$	0	0
$911$	−45.6189	−1.51142	−0.755710	−	0.654906i	$-0.772708\pi$
$911$	−45.6189	−1.51142	−0.755710	+	0.654906i	$0.772708\pi$
$912$	10.6560	0.352854
$913$	8.47554	0.280500
$914$	0.119863	0.00396473
$915$	0	0
$916$	5.76320	0.190422
$917$	−1.45833	−0.0481583
$918$	−1.03148	−0.0340438
$919$	20.6582	0.681451	0.340725	−	0.940163i	$-0.389327\pi$
$919$	20.6582	0.681451	0.340725	+	0.940163i	$0.389327\pi$
$920$	0	0
$921$	−28.0055	−0.922813
$922$	−0.783265	−0.0257955
$923$	−17.3236	−0.570214
$924$	−1.00683	−0.0331222
$925$	0	0
$926$	−3.63348	−0.119404
$927$	−1.41969	−0.0466289
$928$	18.2427	0.598846
$929$	−23.2327	−0.762239	−0.381119	−	0.924526i	$-0.624461\pi$
$929$	−23.2327	−0.762239	−0.381119	+	0.924526i	$0.624461\pi$
$930$	0	0
$931$	18.9507	0.621084
$932$	45.7879	1.49983
$933$	−29.1437	−0.954121
$934$	−2.09498	−0.0685497
$935$	0	0
$936$	0.951625	0.0311048
$937$	18.3122	0.598232	0.299116	−	0.954217i	$-0.403308\pi$
$937$	18.3122	0.598232	0.299116	+	0.954217i	$0.403308\pi$
$938$	0.939397	0.0306724
$939$	−19.1782	−0.625858
$940$	0	0
$941$	17.3075	0.564209	0.282104	−	0.959384i	$-0.408968\pi$
$941$	17.3075	0.564209	0.282104	+	0.959384i	$0.408968\pi$
$942$	0.598045	0.0194854
$943$	63.0020	2.05163
$944$	−43.1101	−1.40311
$945$	0	0
$946$	−0.512434	−0.0166607
$947$	18.4829	0.600613	0.300307	−	0.953843i	$-0.402911\pi$
$947$	18.4829	0.600613	0.300307	+	0.953843i	$0.402911\pi$
$948$	6.52871	0.212043
$949$	−3.43787	−0.111598
$950$	0	0
$951$	−19.8985	−0.645252
$952$	−2.41186	−0.0781689
$953$	20.8872	0.676604	0.338302	−	0.941038i	$-0.390148\pi$
$953$	20.8872	0.676604	0.338302	+	0.941038i	$0.390148\pi$
$954$	−0.809547	−0.0262100
$955$	0	0
$956$	−28.9121	−0.935083
$957$	−6.52124	−0.210802
$958$	−3.89130	−0.125722
$959$	−3.33616	−0.107730
$960$	0	0
$961$	−19.0290	−0.613840
$962$	−2.44578	−0.0788551
$963$	−14.9579	−0.482011
$964$	28.1499	0.906647
$965$	0	0
$966$	0.854102	0.0274803
$967$	−51.2510	−1.64812	−0.824061	−	0.566501i	$-0.808297\pi$
$967$	−51.2510	−1.64812	−0.824061	+	0.566501i	$0.808297\pi$
$968$	−8.47083	−0.272263
$969$	−14.0590	−0.451639
$970$	0	0
$971$	−38.6012	−1.23877	−0.619385	−	0.785087i	$-0.712618\pi$
$971$	−38.6012	−1.23877	−0.619385	+	0.785087i	$0.712618\pi$
$972$	1.95630	0.0627482
$973$	−0.192693	−0.00617747
$974$	−0.433185	−0.0138801
$975$	0	0
$976$	−47.7048	−1.52699
$977$	2.91913	0.0933912	0.0466956	−	0.998909i	$-0.485131\pi$
$977$	2.91913	0.0933912	0.0466956	+	0.998909i	$0.485131\pi$
$978$	2.94992	0.0943280
$979$	−0.561702	−0.0179521
$980$	0	0
$981$	−11.0977	−0.354323
$982$	4.64849	0.148339
$983$	0.980138	0.0312615	0.0156308	−	0.999878i	$-0.495024\pi$
$983$	0.980138	0.0312615	0.0156308	+	0.999878i	$0.495024\pi$
$984$	−7.53818	−0.240308
$985$	0	0
$986$	−7.72456	−0.246000
$987$	−3.95301	−0.125826
$988$	6.41365	0.204045
$989$	−19.4580	−0.618728
$990$	0	0
$991$	37.0913	1.17824	0.589122	−	0.808044i	$-0.299474\pi$
$991$	37.0913	1.17824	0.589122	+	0.808044i	$0.299474\pi$
$992$	−8.42830	−0.267599
$993$	27.8128	0.882613
$994$	1.86035	0.0590068
$995$	0	0
$996$	−19.0408	−0.603331
$997$	16.7675	0.531031	0.265515	−	0.964107i	$-0.414458\pi$
$997$	16.7675	0.531031	0.265515	+	0.964107i	$0.414458\pi$
$998$	−5.91031	−0.187088
$999$	−10.1681	−0.321705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.g.1.2	yes	4
3.2	odd	2		5625.2.a.j.1.3		4
5.2	odd	4		1875.2.b.d.1249.4		8
5.3	odd	4		1875.2.b.d.1249.5		8
5.4	even	2		1875.2.a.f.1.3	✓	4
15.14	odd	2		5625.2.a.m.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.f.1.3	✓	4	5.4	even	2
1875.2.a.g.1.2	yes	4	1.1	even	1	trivial
1875.2.b.d.1249.4		8	5.2	odd	4
1875.2.b.d.1249.5		8	5.3	odd	4
5625.2.a.j.1.3		4	3.2	odd	2
5625.2.a.m.1.2		4	15.14	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q-0.209057 q^{2} -1.00000 q^{3} -1.95630 q^{4} +0.209057 q^{6} +0.591023 q^{7} +0.827091 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.209057 q^{2} -1.00000 q^{3} -1.95630 q^{4} +0.209057 q^{6} +0.591023 q^{7} +0.827091 q^{8} +1.00000 q^{9} -0.870796 q^{11} +1.95630 q^{12} +1.15057 q^{13} -0.123557 q^{14} +3.73968 q^{16} -4.93395 q^{17} -0.209057 q^{18} -2.84943 q^{19} -0.591023 q^{21} +0.182046 q^{22} +6.91259 q^{23} -0.827091 q^{24} -0.240534 q^{26} -1.00000 q^{27} -1.15622 q^{28} -7.48883 q^{29} +3.45991 q^{31} -2.43599 q^{32} +0.870796 q^{33} +1.03148 q^{34} -1.95630 q^{36} +10.1681 q^{37} +0.595693 q^{38} -1.15057 q^{39} +9.11409 q^{41} +0.123557 q^{42} -2.81486 q^{43} +1.70353 q^{44} -1.44512 q^{46} +6.68842 q^{47} -3.73968 q^{48} -6.65069 q^{49} +4.93395 q^{51} -2.25085 q^{52} +3.87238 q^{53} +0.209057 q^{54} +0.488830 q^{56} +2.84943 q^{57} +1.56559 q^{58} -11.5277 q^{59} -12.7564 q^{61} -0.723318 q^{62} +0.591023 q^{63} -6.97010 q^{64} -0.182046 q^{66} -7.60292 q^{67} +9.65227 q^{68} -6.91259 q^{69} -15.0566 q^{71} +0.827091 q^{72} -2.98798 q^{73} -2.12571 q^{74} +5.57433 q^{76} -0.514660 q^{77} +0.240534 q^{78} +3.33728 q^{79} +1.00000 q^{81} -1.90536 q^{82} -9.73310 q^{83} +1.15622 q^{84} +0.588467 q^{86} +7.48883 q^{87} -0.720227 q^{88} +0.645045 q^{89} +0.680012 q^{91} -13.5231 q^{92} -3.45991 q^{93} -1.39826 q^{94} +2.43599 q^{96} +11.6970 q^{97} +1.39037 q^{98} -0.870796 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 4 q^{3} + q^{4} - q^{6} + 5 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + q^2 - 4 * q^3 + q^4 - q^6 + 5 * q^7 - 3 * q^8 + 4 * q^9	\( 4 q + q^{2} - 4 q^{3} + q^{4} - q^{6} + 5 q^{7} - 3 q^{8} + 4 q^{9} - 6 q^{11} - q^{12} + 7 q^{13} - 10 q^{14} - 9 q^{16} - 7 q^{17} + q^{18} - 9 q^{19} - 5 q^{21} + 6 q^{22} + 10 q^{23} + 3 q^{24} - 2 q^{26} - 4 q^{27} + 5 q^{28} - 28 q^{29} - 10 q^{31} + 6 q^{33} + 7 q^{34} + q^{36} - 10 q^{37} - 6 q^{38} - 7 q^{39} + 10 q^{42} + q^{43} - 9 q^{44} + 5 q^{46} - 23 q^{47} + 9 q^{48} - 3 q^{49} + 7 q^{51} + 13 q^{52} - q^{54} + 9 q^{57} - 2 q^{58} + 4 q^{59} - 43 q^{61} - 10 q^{62} + 5 q^{63} - 7 q^{64} - 6 q^{66} + 8 q^{67} - 3 q^{68} - 10 q^{69} - 27 q^{71} - 3 q^{72} + 15 q^{73} + 5 q^{74} + 9 q^{76} - 15 q^{77} + 2 q^{78} + 10 q^{79} + 4 q^{81} - 20 q^{82} + 3 q^{83} - 5 q^{84} + 24 q^{86} + 28 q^{87} - 3 q^{88} - 9 q^{89} + 5 q^{91} - 15 q^{92} + 10 q^{93} - 22 q^{94} + 13 q^{97} - 42 q^{98} - 6 q^{99}+O(q^{100}) \) 4 * q + q^2 - 4 * q^3 + q^4 - q^6 + 5 * q^7 - 3 * q^8 + 4 * q^9 - 6 * q^11 - q^12 + 7 * q^13 - 10 * q^14 - 9 * q^16 - 7 * q^17 + q^18 - 9 * q^19 - 5 * q^21 + 6 * q^22 + 10 * q^23 + 3 * q^24 - 2 * q^26 - 4 * q^27 + 5 * q^28 - 28 * q^29 - 10 * q^31 + 6 * q^33 + 7 * q^34 + q^36 - 10 * q^37 - 6 * q^38 - 7 * q^39 + 10 * q^42 + q^43 - 9 * q^44 + 5 * q^46 - 23 * q^47 + 9 * q^48 - 3 * q^49 + 7 * q^51 + 13 * q^52 - q^54 + 9 * q^57 - 2 * q^58 + 4 * q^59 - 43 * q^61 - 10 * q^62 + 5 * q^63 - 7 * q^64 - 6 * q^66 + 8 * q^67 - 3 * q^68 - 10 * q^69 - 27 * q^71 - 3 * q^72 + 15 * q^73 + 5 * q^74 + 9 * q^76 - 15 * q^77 + 2 * q^78 + 10 * q^79 + 4 * q^81 - 20 * q^82 + 3 * q^83 - 5 * q^84 + 24 * q^86 + 28 * q^87 - 3 * q^88 - 9 * q^89 + 5 * q^91 - 15 * q^92 + 10 * q^93 - 22 * q^94 + 13 * q^97 - 42 * q^98 - 6 * q^99

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