LMFDB - Embedded newform 7225.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7225,2,Mod(1,7225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7225, 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("7225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7225 = 5^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7225.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:	$57.6919154604$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1445)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.56155$ of defining polynomial
Character	$\chi$	$=$	7225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.56155 q^{2} +1.56155 q^{3} +0.438447 q^{4} +2.43845 q^{6} +0.438447 q^{7} -2.43845 q^{8} -0.561553 q^{9} +4.56155 q^{11} +0.684658 q^{12} -7.12311 q^{13} +0.684658 q^{14} -4.68466 q^{16} -0.876894 q^{18} -0.561553 q^{19} +0.684658 q^{21} +7.12311 q^{22} +1.56155 q^{23} -3.80776 q^{24} -11.1231 q^{26} -5.56155 q^{27} +0.192236 q^{28} -3.43845 q^{29} -2.43845 q^{32} +7.12311 q^{33} -0.246211 q^{36} +10.0000 q^{37} -0.876894 q^{38} -11.1231 q^{39} +7.00000 q^{41} +1.06913 q^{42} -9.12311 q^{43} +2.00000 q^{44} +2.43845 q^{46} -5.12311 q^{47} -7.31534 q^{48} -6.80776 q^{49} -3.12311 q^{52} +1.12311 q^{53} -8.68466 q^{54} -1.06913 q^{56} -0.876894 q^{57} -5.36932 q^{58} +0.561553 q^{59} -7.43845 q^{61} -0.246211 q^{63} +5.56155 q^{64} +11.1231 q^{66} -3.56155 q^{67} +2.43845 q^{69} -13.6847 q^{71} +1.36932 q^{72} -6.87689 q^{73} +15.6155 q^{74} -0.246211 q^{76} +2.00000 q^{77} -17.3693 q^{78} -9.43845 q^{79} -7.00000 q^{81} +10.9309 q^{82} -7.56155 q^{83} +0.300187 q^{84} -14.2462 q^{86} -5.36932 q^{87} -11.1231 q^{88} +17.4924 q^{89} -3.12311 q^{91} +0.684658 q^{92} -8.00000 q^{94} -3.80776 q^{96} -16.2462 q^{97} -10.6307 q^{98} -2.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} + 5 q^{4} + 9 q^{6} + 5 q^{7} - 9 q^{8} + 3 q^{9} + 5 q^{11} - 11 q^{12} - 6 q^{13} - 11 q^{14} + 3 q^{16} - 10 q^{18} + 3 q^{19} - 11 q^{21} + 6 q^{22} - q^{23} + 13 q^{24} - 14 q^{26}+ \cdots - q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 + 5 * q^4 + 9 * q^6 + 5 * q^7 - 9 * q^8 + 3 * q^9 + 5 * q^11 - 11 * q^12 - 6 * q^13 - 11 * q^14 + 3 * q^16 - 10 * q^18 + 3 * q^19 - 11 * q^21 + 6 * q^22 - q^23 + 13 * q^24 - 14 * q^26 - 7 * q^27 + 21 * q^28 - 11 * q^29 - 9 * q^32 + 6 * q^33 + 16 * q^36 + 20 * q^37 - 10 * q^38 - 14 * q^39 + 14 * q^41 + 31 * q^42 - 10 * q^43 + 4 * q^44 + 9 * q^46 - 2 * q^47 - 27 * q^48 + 7 * q^49 + 2 * q^52 - 6 * q^53 - 5 * q^54 - 31 * q^56 - 10 * q^57 + 14 * q^58 - 3 * q^59 - 19 * q^61 + 16 * q^63 + 7 * q^64 + 14 * q^66 - 3 * q^67 + 9 * q^69 - 15 * q^71 - 22 * q^72 - 22 * q^73 - 10 * q^74 + 16 * q^76 + 4 * q^77 - 10 * q^78 - 23 * q^79 - 14 * q^81 - 7 * q^82 - 11 * q^83 - 53 * q^84 - 12 * q^86 + 14 * q^87 - 14 * q^88 + 2 * q^89 + 2 * q^91 - 11 * q^92 - 16 * q^94 + 13 * q^96 - 16 * q^97 - 46 * q^98 - q^99

Coefficient data

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

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

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

$2$	1.56155	1.10418	0.552092	−	0.833783i	$-0.313830\pi$
$2$	1.56155	1.10418	0.552092	+	0.833783i	$0.313830\pi$
$3$	1.56155	0.901563	0.450781	−	0.892634i	$-0.351145\pi$
$3$	1.56155	0.901563	0.450781	+	0.892634i	$0.351145\pi$
$4$	0.438447	0.219224
$5$	0	0
$5$	0	0
$6$	2.43845	0.995492
$7$	0.438447	0.165717	0.0828587	−	0.996561i	$-0.473595\pi$
$7$	0.438447	0.165717	0.0828587	+	0.996561i	$0.473595\pi$
$8$	−2.43845	−0.862121
$9$	−0.561553	−0.187184
$10$	0	0
$11$	4.56155	1.37536	0.687680	−	0.726014i	$-0.258629\pi$
$11$	4.56155	1.37536	0.687680	+	0.726014i	$0.258629\pi$
$12$	0.684658	0.197644
$13$	−7.12311	−1.97559	−0.987797	−	0.155747i	$-0.950222\pi$
$13$	−7.12311	−1.97559	−0.987797	+	0.155747i	$0.950222\pi$
$14$	0.684658	0.182983
$15$	0	0
$16$	−4.68466	−1.17116
$17$	0	0
$17$	0	0
$18$	−0.876894	−0.206686
$19$	−0.561553	−0.128829	−0.0644145	−	0.997923i	$-0.520518\pi$
$19$	−0.561553	−0.128829	−0.0644145	+	0.997923i	$0.520518\pi$
$20$	0	0
$21$	0.684658	0.149405
$22$	7.12311	1.51865
$23$	1.56155	0.325606	0.162803	−	0.986659i	$-0.447946\pi$
$23$	1.56155	0.325606	0.162803	+	0.986659i	$0.447946\pi$
$24$	−3.80776	−0.777257
$25$	0	0
$26$	−11.1231	−2.18142
$27$	−5.56155	−1.07032
$28$	0.192236	0.0363292
$29$	−3.43845	−0.638504	−0.319252	−	0.947670i	$-0.603432\pi$
$29$	−3.43845	−0.638504	−0.319252	+	0.947670i	$0.603432\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−2.43845	−0.431061
$33$	7.12311	1.23997
$34$	0	0
$35$	0	0
$36$	−0.246211	−0.0410352
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	−0.876894	−0.142251
$39$	−11.1231	−1.78112
$40$	0	0
$41$	7.00000	1.09322	0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000	1.09322	0.546608	+	0.837389i	$0.315919\pi$
$42$	1.06913	0.164970
$43$	−9.12311	−1.39126	−0.695630	−	0.718400i	$-0.744875\pi$
$43$	−9.12311	−1.39126	−0.695630	+	0.718400i	$0.744875\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	2.43845	0.359529
$47$	−5.12311	−0.747282	−0.373641	−	0.927573i	$-0.621891\pi$
$47$	−5.12311	−0.747282	−0.373641	+	0.927573i	$0.621891\pi$
$48$	−7.31534	−1.05588
$49$	−6.80776	−0.972538
$50$	0	0
$51$	0	0
$52$	−3.12311	−0.433097
$53$	1.12311	0.154270	0.0771352	−	0.997021i	$-0.475423\pi$
$53$	1.12311	0.154270	0.0771352	+	0.997021i	$0.475423\pi$
$54$	−8.68466	−1.18183
$55$	0	0
$56$	−1.06913	−0.142869
$57$	−0.876894	−0.116147
$58$	−5.36932	−0.705026
$59$	0.561553	0.0731079	0.0365540	−	0.999332i	$-0.488362\pi$
$59$	0.561553	0.0731079	0.0365540	+	0.999332i	$0.488362\pi$
$60$	0	0
$61$	−7.43845	−0.952396	−0.476198	−	0.879338i	$-0.657985\pi$
$61$	−7.43845	−0.952396	−0.476198	+	0.879338i	$0.657985\pi$
$62$	0	0
$63$	−0.246211	−0.0310197
$64$	5.56155	0.695194
$65$	0	0
$66$	11.1231	1.36916
$67$	−3.56155	−0.435113	−0.217556	−	0.976048i	$-0.569809\pi$
$67$	−3.56155	−0.435113	−0.217556	+	0.976048i	$0.569809\pi$
$68$	0	0
$69$	2.43845	0.293555
$70$	0	0
$71$	−13.6847	−1.62407	−0.812035	−	0.583609i	$-0.801640\pi$
$71$	−13.6847	−1.62407	−0.812035	+	0.583609i	$0.801640\pi$
$72$	1.36932	0.161376
$73$	−6.87689	−0.804880	−0.402440	−	0.915446i	$-0.631838\pi$
$73$	−6.87689	−0.804880	−0.402440	+	0.915446i	$0.631838\pi$
$74$	15.6155	1.81527
$75$	0	0
$76$	−0.246211	−0.0282424
$77$	2.00000	0.227921
$78$	−17.3693	−1.96669
$79$	−9.43845	−1.06191	−0.530954	−	0.847401i	$-0.678166\pi$
$79$	−9.43845	−1.06191	−0.530954	+	0.847401i	$0.678166\pi$
$80$	0	0
$81$	−7.00000	−0.777778
$82$	10.9309	1.20711
$83$	−7.56155	−0.829988	−0.414994	−	0.909824i	$-0.636216\pi$
$83$	−7.56155	−0.829988	−0.414994	+	0.909824i	$0.636216\pi$
$84$	0.300187	0.0327530
$85$	0	0
$86$	−14.2462	−1.53621
$87$	−5.36932	−0.575651
$88$	−11.1231	−1.18573
$89$	17.4924	1.85419	0.927097	−	0.374823i	$-0.122296\pi$
$89$	17.4924	1.85419	0.927097	+	0.374823i	$0.122296\pi$
$90$	0	0
$91$	−3.12311	−0.327390
$92$	0.684658	0.0713806
$93$	0	0
$94$	−8.00000	−0.825137
$95$	0	0
$96$	−3.80776	−0.388628
$97$	−16.2462	−1.64955	−0.824776	−	0.565459i	$-0.808699\pi$
$97$	−16.2462	−1.64955	−0.824776	+	0.565459i	$0.808699\pi$
$98$	−10.6307	−1.07386
$99$	−2.56155	−0.257446
$100$	0	0
$101$	−14.3693	−1.42980	−0.714900	−	0.699226i	$-0.753528\pi$
$101$	−14.3693	−1.42980	−0.714900	+	0.699226i	$0.753528\pi$
$102$	0	0
$103$	−13.8078	−1.36052	−0.680260	−	0.732971i	$-0.738133\pi$
$103$	−13.8078	−1.36052	−0.680260	+	0.732971i	$0.738133\pi$
$104$	17.3693	1.70320
$105$	0	0
$106$	1.75379	0.170343
$107$	−2.87689	−0.278120	−0.139060	−	0.990284i	$-0.544408\pi$
$107$	−2.87689	−0.278120	−0.139060	+	0.990284i	$0.544408\pi$
$108$	−2.43845	−0.234640
$109$	−5.80776	−0.556283	−0.278141	−	0.960540i	$-0.589718\pi$
$109$	−5.80776	−0.556283	−0.278141	+	0.960540i	$0.589718\pi$
$110$	0	0
$111$	15.6155	1.48216
$112$	−2.05398	−0.194082
$113$	8.24621	0.775738	0.387869	−	0.921714i	$-0.373211\pi$
$113$	8.24621	0.775738	0.387869	+	0.921714i	$0.373211\pi$
$114$	−1.36932	−0.128248
$115$	0	0
$116$	−1.50758	−0.139975
$117$	4.00000	0.369800
$118$	0.876894	0.0807247
$119$	0	0
$120$	0	0
$121$	9.80776	0.891615
$122$	−11.6155	−1.05162
$123$	10.9309	0.985603
$124$	0	0
$125$	0	0
$126$	−0.384472	−0.0342515
$127$	−14.4384	−1.28121	−0.640603	−	0.767873i	$-0.721315\pi$
$127$	−14.4384	−1.28121	−0.640603	+	0.767873i	$0.721315\pi$
$128$	13.5616	1.19868
$129$	−14.2462	−1.25431
$130$	0	0
$131$	12.8078	1.11902	0.559510	−	0.828824i	$-0.310989\pi$
$131$	12.8078	1.11902	0.559510	+	0.828824i	$0.310989\pi$
$132$	3.12311	0.271831
$133$	−0.246211	−0.0213492
$134$	−5.56155	−0.480445
$135$	0	0
$136$	0	0
$137$	−11.1231	−0.950311	−0.475156	−	0.879902i	$-0.657608\pi$
$137$	−11.1231	−0.950311	−0.475156	+	0.879902i	$0.657608\pi$
$138$	3.80776	0.324138
$139$	16.5616	1.40473	0.702366	−	0.711816i	$-0.252127\pi$
$139$	16.5616	1.40473	0.702366	+	0.711816i	$0.252127\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	−21.3693	−1.79327
$143$	−32.4924	−2.71715
$144$	2.63068	0.219224
$145$	0	0
$146$	−10.7386	−0.888736
$147$	−10.6307	−0.876804
$148$	4.38447	0.360401
$149$	−14.6847	−1.20301	−0.601507	−	0.798867i	$-0.705433\pi$
$149$	−14.6847	−1.20301	−0.601507	+	0.798867i	$0.705433\pi$
$150$	0	0
$151$	21.0540	1.71335	0.856674	−	0.515858i	$-0.172527\pi$
$151$	21.0540	1.71335	0.856674	+	0.515858i	$0.172527\pi$
$152$	1.36932	0.111066
$153$	0	0
$154$	3.12311	0.251667
$155$	0	0
$156$	−4.87689	−0.390464
$157$	−3.12311	−0.249251	−0.124625	−	0.992204i	$-0.539773\pi$
$157$	−3.12311	−0.249251	−0.124625	+	0.992204i	$0.539773\pi$
$158$	−14.7386	−1.17254
$159$	1.75379	0.139084
$160$	0	0
$161$	0.684658	0.0539586
$162$	−10.9309	−0.858810
$163$	−6.43845	−0.504298	−0.252149	−	0.967688i	$-0.581137\pi$
$163$	−6.43845	−0.504298	−0.252149	+	0.967688i	$0.581137\pi$
$164$	3.06913	0.239659
$165$	0	0
$166$	−11.8078	−0.916460
$167$	7.36932	0.570255	0.285127	−	0.958490i	$-0.407964\pi$
$167$	7.36932	0.570255	0.285127	+	0.958490i	$0.407964\pi$
$168$	−1.66950	−0.128805
$169$	37.7386	2.90297
$170$	0	0
$171$	0.315342	0.0241148
$172$	−4.00000	−0.304997
$173$	0.246211	0.0187191	0.00935955	−	0.999956i	$-0.497021\pi$
$173$	0.246211	0.0187191	0.00935955	+	0.999956i	$0.497021\pi$
$174$	−8.38447	−0.635625
$175$	0	0
$176$	−21.3693	−1.61077
$177$	0.876894	0.0659114
$178$	27.3153	2.04737
$179$	7.43845	0.555976	0.277988	−	0.960585i	$-0.410333\pi$
$179$	7.43845	0.555976	0.277988	+	0.960585i	$0.410333\pi$
$180$	0	0
$181$	−1.31534	−0.0977686	−0.0488843	−	0.998804i	$-0.515567\pi$
$181$	−1.31534	−0.0977686	−0.0488843	+	0.998804i	$0.515567\pi$
$182$	−4.87689	−0.361499
$183$	−11.6155	−0.858645
$184$	−3.80776	−0.280712
$185$	0	0
$186$	0	0
$187$	0	0
$188$	−2.24621	−0.163822
$189$	−2.43845	−0.177371
$190$	0	0
$191$	19.6847	1.42433	0.712166	−	0.702011i	$-0.247714\pi$
$191$	19.6847	1.42433	0.712166	+	0.702011i	$0.247714\pi$
$192$	8.68466	0.626761
$193$	1.12311	0.0808429	0.0404215	−	0.999183i	$-0.487130\pi$
$193$	1.12311	0.0808429	0.0404215	+	0.999183i	$0.487130\pi$
$194$	−25.3693	−1.82141
$195$	0	0
$196$	−2.98485	−0.213203
$197$	15.6155	1.11256	0.556280	−	0.830995i	$-0.312228\pi$
$197$	15.6155	1.11256	0.556280	+	0.830995i	$0.312228\pi$
$198$	−4.00000	−0.284268
$199$	−9.68466	−0.686527	−0.343264	−	0.939239i	$-0.611532\pi$
$199$	−9.68466	−0.686527	−0.343264	+	0.939239i	$0.611532\pi$
$200$	0	0
$201$	−5.56155	−0.392282
$202$	−22.4384	−1.57876
$203$	−1.50758	−0.105811
$204$	0	0
$205$	0	0
$206$	−21.5616	−1.50226
$207$	−0.876894	−0.0609484
$208$	33.3693	2.31375
$209$	−2.56155	−0.177186
$210$	0	0
$211$	−7.12311	−0.490375	−0.245187	−	0.969476i	$-0.578849\pi$
$211$	−7.12311	−0.490375	−0.245187	+	0.969476i	$0.578849\pi$
$212$	0.492423	0.0338197
$213$	−21.3693	−1.46420
$214$	−4.49242	−0.307096
$215$	0	0
$216$	13.5616	0.922747
$217$	0	0
$218$	−9.06913	−0.614239
$219$	−10.7386	−0.725650
$220$	0	0
$221$	0	0
$222$	24.3845	1.63658
$223$	−10.6847	−0.715498	−0.357749	−	0.933818i	$-0.616456\pi$
$223$	−10.6847	−0.715498	−0.357749	+	0.933818i	$0.616456\pi$
$224$	−1.06913	−0.0714343
$225$	0	0
$226$	12.8769	0.856558
$227$	22.0540	1.46377	0.731887	−	0.681426i	$-0.238640\pi$
$227$	22.0540	1.46377	0.731887	+	0.681426i	$0.238640\pi$
$228$	−0.384472	−0.0254623
$229$	1.87689	0.124029	0.0620143	−	0.998075i	$-0.480248\pi$
$229$	1.87689	0.124029	0.0620143	+	0.998075i	$0.480248\pi$
$230$	0	0
$231$	3.12311	0.205485
$232$	8.38447	0.550468
$233$	6.24621	0.409203	0.204601	−	0.978845i	$-0.434410\pi$
$233$	6.24621	0.409203	0.204601	+	0.978845i	$0.434410\pi$
$234$	6.24621	0.408328
$235$	0	0
$236$	0.246211	0.0160270
$237$	−14.7386	−0.957377
$238$	0	0
$239$	−15.0540	−0.973761	−0.486880	−	0.873469i	$-0.661865\pi$
$239$	−15.0540	−0.973761	−0.486880	+	0.873469i	$0.661865\pi$
$240$	0	0
$241$	15.4924	0.997955	0.498977	−	0.866615i	$-0.333709\pi$
$241$	15.4924	0.997955	0.498977	+	0.866615i	$0.333709\pi$
$242$	15.3153	0.984507
$243$	5.75379	0.369106
$244$	−3.26137	−0.208788
$245$	0	0
$246$	17.0691	1.08829
$247$	4.00000	0.254514
$248$	0	0
$249$	−11.8078	−0.748287
$250$	0	0
$251$	−13.6847	−0.863768	−0.431884	−	0.901929i	$-0.642151\pi$
$251$	−13.6847	−0.863768	−0.431884	+	0.901929i	$0.642151\pi$
$252$	−0.107951	−0.00680025
$253$	7.12311	0.447826
$254$	−22.5464	−1.41469
$255$	0	0
$256$	10.0540	0.628373
$257$	26.2462	1.63719	0.818597	−	0.574369i	$-0.194752\pi$
$257$	26.2462	1.63719	0.818597	+	0.574369i	$0.194752\pi$
$258$	−22.2462	−1.38499
$259$	4.38447	0.272438
$260$	0	0
$261$	1.93087	0.119518
$262$	20.0000	1.23560
$263$	19.8078	1.22140	0.610700	−	0.791862i	$-0.290888\pi$
$263$	19.8078	1.22140	0.610700	+	0.791862i	$0.290888\pi$
$264$	−17.3693	−1.06901
$265$	0	0
$266$	−0.384472	−0.0235735
$267$	27.3153	1.67167
$268$	−1.56155	−0.0953870
$269$	14.6847	0.895339	0.447670	−	0.894199i	$-0.352254\pi$
$269$	14.6847	0.895339	0.447670	+	0.894199i	$0.352254\pi$
$270$	0	0
$271$	−4.80776	−0.292051	−0.146025	−	0.989281i	$-0.546648\pi$
$271$	−4.80776	−0.292051	−0.146025	+	0.989281i	$0.546648\pi$
$272$	0	0
$273$	−4.87689	−0.295163
$274$	−17.3693	−1.04932
$275$	0	0
$276$	1.06913	0.0643541
$277$	−4.00000	−0.240337	−0.120168	−	0.992754i	$-0.538343\pi$
$277$	−4.00000	−0.240337	−0.120168	+	0.992754i	$0.538343\pi$
$278$	25.8617	1.55108
$279$	0	0
$280$	0	0
$281$	−9.24621	−0.551583	−0.275791	−	0.961218i	$-0.588940\pi$
$281$	−9.24621	−0.551583	−0.275791	+	0.961218i	$0.588940\pi$
$282$	−12.4924	−0.743913
$283$	−22.0540	−1.31097	−0.655486	−	0.755207i	$-0.727536\pi$
$283$	−22.0540	−1.31097	−0.655486	+	0.755207i	$0.727536\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	−50.7386	−3.00024
$287$	3.06913	0.181165
$288$	1.36932	0.0806878
$289$	0	0
$290$	0	0
$291$	−25.3693	−1.48718
$292$	−3.01515	−0.176449
$293$	8.63068	0.504210	0.252105	−	0.967700i	$-0.418877\pi$
$293$	8.63068	0.504210	0.252105	+	0.967700i	$0.418877\pi$
$294$	−16.6004	−0.968153
$295$	0	0
$296$	−24.3845	−1.41732
$297$	−25.3693	−1.47208
$298$	−22.9309	−1.32835
$299$	−11.1231	−0.643266
$300$	0	0
$301$	−4.00000	−0.230556
$302$	32.8769	1.89185
$303$	−22.4384	−1.28906
$304$	2.63068	0.150880
$305$	0	0
$306$	0	0
$307$	−1.75379	−0.100094	−0.0500470	−	0.998747i	$-0.515937\pi$
$307$	−1.75379	−0.100094	−0.0500470	+	0.998747i	$0.515937\pi$
$308$	0.876894	0.0499657
$309$	−21.5616	−1.22659
$310$	0	0
$311$	23.1231	1.31119	0.655596	−	0.755112i	$-0.272418\pi$
$311$	23.1231	1.31119	0.655596	+	0.755112i	$0.272418\pi$
$312$	27.1231	1.53554
$313$	−18.2462	−1.03134	−0.515668	−	0.856788i	$-0.672456\pi$
$313$	−18.2462	−1.03134	−0.515668	+	0.856788i	$0.672456\pi$
$314$	−4.87689	−0.275219
$315$	0	0
$316$	−4.13826	−0.232795
$317$	−6.24621	−0.350822	−0.175411	−	0.984495i	$-0.556125\pi$
$317$	−6.24621	−0.350822	−0.175411	+	0.984495i	$0.556125\pi$
$318$	2.73863	0.153575
$319$	−15.6847	−0.878172
$320$	0	0
$321$	−4.49242	−0.250743
$322$	1.06913	0.0595803
$323$	0	0
$324$	−3.06913	−0.170507
$325$	0	0
$326$	−10.0540	−0.556838
$327$	−9.06913	−0.501524
$328$	−17.0691	−0.942485
$329$	−2.24621	−0.123838
$330$	0	0
$331$	21.9309	1.20543	0.602715	−	0.797957i	$-0.294086\pi$
$331$	21.9309	1.20543	0.602715	+	0.797957i	$0.294086\pi$
$332$	−3.31534	−0.181953
$333$	−5.61553	−0.307729
$334$	11.5076	0.629667
$335$	0	0
$336$	−3.20739	−0.174978
$337$	−1.75379	−0.0955350	−0.0477675	−	0.998858i	$-0.515211\pi$
$337$	−1.75379	−0.0955350	−0.0477675	+	0.998858i	$0.515211\pi$
$338$	58.9309	3.20542
$339$	12.8769	0.699377
$340$	0	0
$341$	0	0
$342$	0.492423	0.0266272
$343$	−6.05398	−0.326884
$344$	22.2462	1.19944
$345$	0	0
$346$	0.384472	0.0206693
$347$	−15.3693	−0.825068	−0.412534	−	0.910942i	$-0.635356\pi$
$347$	−15.3693	−0.825068	−0.412534	+	0.910942i	$0.635356\pi$
$348$	−2.35416	−0.126196
$349$	12.1231	0.648935	0.324467	−	0.945897i	$-0.394815\pi$
$349$	12.1231	0.648935	0.324467	+	0.945897i	$0.394815\pi$
$350$	0	0
$351$	39.6155	2.11452
$352$	−11.1231	−0.592864
$353$	−13.6155	−0.724681	−0.362341	−	0.932046i	$-0.618022\pi$
$353$	−13.6155	−0.724681	−0.362341	+	0.932046i	$0.618022\pi$
$354$	1.36932	0.0727784
$355$	0	0
$356$	7.66950	0.406483
$357$	0	0
$358$	11.6155	0.613900
$359$	2.06913	0.109205	0.0546023	−	0.998508i	$-0.482611\pi$
$359$	2.06913	0.109205	0.0546023	+	0.998508i	$0.482611\pi$
$360$	0	0
$361$	−18.6847	−0.983403
$362$	−2.05398	−0.107955
$363$	15.3153	0.803847
$364$	−1.36932	−0.0717717
$365$	0	0
$366$	−18.1383	−0.948102
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	−7.31534	−0.381339
$369$	−3.93087	−0.204633
$370$	0	0
$371$	0.492423	0.0255653
$372$	0	0
$373$	−18.2462	−0.944753	−0.472377	−	0.881397i	$-0.656604\pi$
$373$	−18.2462	−0.944753	−0.472377	+	0.881397i	$0.656604\pi$
$374$	0	0
$375$	0	0
$376$	12.4924	0.644247
$377$	24.4924	1.26142
$378$	−3.80776	−0.195850
$379$	30.1771	1.55009	0.775046	−	0.631904i	$-0.217727\pi$
$379$	30.1771	1.55009	0.775046	+	0.631904i	$0.217727\pi$
$380$	0	0
$381$	−22.5464	−1.15509
$382$	30.7386	1.57273
$383$	28.3002	1.44607	0.723036	−	0.690810i	$-0.242746\pi$
$383$	28.3002	1.44607	0.723036	+	0.690810i	$0.242746\pi$
$384$	21.1771	1.08069
$385$	0	0
$386$	1.75379	0.0892655
$387$	5.12311	0.260422
$388$	−7.12311	−0.361621
$389$	−5.68466	−0.288224	−0.144112	−	0.989561i	$-0.546032\pi$
$389$	−5.68466	−0.288224	−0.144112	+	0.989561i	$0.546032\pi$
$390$	0	0
$391$	0	0
$392$	16.6004	0.838445
$393$	20.0000	1.00887
$394$	24.3845	1.22847
$395$	0	0
$396$	−1.12311	−0.0564382
$397$	−23.8617	−1.19759	−0.598793	−	0.800904i	$-0.704353\pi$
$397$	−23.8617	−1.19759	−0.598793	+	0.800904i	$0.704353\pi$
$398$	−15.1231	−0.758053
$399$	−0.384472	−0.0192477
$400$	0	0
$401$	15.2462	0.761359	0.380680	−	0.924707i	$-0.375690\pi$
$401$	15.2462	0.761359	0.380680	+	0.924707i	$0.375690\pi$
$402$	−8.68466	−0.433151
$403$	0	0
$404$	−6.30019	−0.313446
$405$	0	0
$406$	−2.35416	−0.116835
$407$	45.6155	2.26108
$408$	0	0
$409$	−9.00000	−0.445021	−0.222511	−	0.974930i	$-0.571425\pi$
$409$	−9.00000	−0.445021	−0.222511	+	0.974930i	$0.571425\pi$
$410$	0	0
$411$	−17.3693	−0.856765
$412$	−6.05398	−0.298258
$413$	0.246211	0.0121153
$414$	−1.36932	−0.0672983
$415$	0	0
$416$	17.3693	0.851601
$417$	25.8617	1.26645
$418$	−4.00000	−0.195646
$419$	13.3693	0.653134	0.326567	−	0.945174i	$-0.394108\pi$
$419$	13.3693	0.653134	0.326567	+	0.945174i	$0.394108\pi$
$420$	0	0
$421$	−36.7386	−1.79053	−0.895266	−	0.445533i	$-0.853014\pi$
$421$	−36.7386	−1.79053	−0.895266	+	0.445533i	$0.853014\pi$
$422$	−11.1231	−0.541464
$423$	2.87689	0.139879
$424$	−2.73863	−0.133000
$425$	0	0
$426$	−33.3693	−1.61675
$427$	−3.26137	−0.157829
$428$	−1.26137	−0.0609704
$429$	−50.7386	−2.44968
$430$	0	0
$431$	32.9848	1.58882	0.794412	−	0.607379i	$-0.207779\pi$
$431$	32.9848	1.58882	0.794412	+	0.607379i	$0.207779\pi$
$432$	26.0540	1.25352
$433$	−2.24621	−0.107946	−0.0539730	−	0.998542i	$-0.517188\pi$
$433$	−2.24621	−0.107946	−0.0539730	+	0.998542i	$0.517188\pi$
$434$	0	0
$435$	0	0
$436$	−2.54640	−0.121950
$437$	−0.876894	−0.0419475
$438$	−16.7689	−0.801251
$439$	−15.4384	−0.736837	−0.368418	−	0.929660i	$-0.620101\pi$
$439$	−15.4384	−0.736837	−0.368418	+	0.929660i	$0.620101\pi$
$440$	0	0
$441$	3.82292	0.182044
$442$	0	0
$443$	13.3153	0.632631	0.316315	−	0.948654i	$-0.397554\pi$
$443$	13.3153	0.632631	0.316315	+	0.948654i	$0.397554\pi$
$444$	6.84658	0.324925
$445$	0	0
$446$	−16.6847	−0.790041
$447$	−22.9309	−1.08459
$448$	2.43845	0.115206
$449$	−10.3153	−0.486811	−0.243406	−	0.969925i	$-0.578265\pi$
$449$	−10.3153	−0.486811	−0.243406	+	0.969925i	$0.578265\pi$
$450$	0	0
$451$	31.9309	1.50357
$452$	3.61553	0.170060
$453$	32.8769	1.54469
$454$	34.4384	1.61628
$455$	0	0
$456$	2.13826	0.100133
$457$	24.2462	1.13419	0.567095	−	0.823652i	$-0.308067\pi$
$457$	24.2462	1.13419	0.567095	+	0.823652i	$0.308067\pi$
$458$	2.93087	0.136951
$459$	0	0
$460$	0	0
$461$	13.8078	0.643092	0.321546	−	0.946894i	$-0.395798\pi$
$461$	13.8078	0.643092	0.321546	+	0.946894i	$0.395798\pi$
$462$	4.87689	0.226894
$463$	−18.9309	−0.879792	−0.439896	−	0.898049i	$-0.644985\pi$
$463$	−18.9309	−0.879792	−0.439896	+	0.898049i	$0.644985\pi$
$464$	16.1080	0.747793
$465$	0	0
$466$	9.75379	0.451836
$467$	−11.8078	−0.546398	−0.273199	−	0.961958i	$-0.588082\pi$
$467$	−11.8078	−0.546398	−0.273199	+	0.961958i	$0.588082\pi$
$468$	1.75379	0.0810689
$469$	−1.56155	−0.0721058
$470$	0	0
$471$	−4.87689	−0.224715
$472$	−1.36932	−0.0630279
$473$	−41.6155	−1.91348
$474$	−23.0152	−1.05712
$475$	0	0
$476$	0	0
$477$	−0.630683	−0.0288770
$478$	−23.5076	−1.07521
$479$	−20.3153	−0.928232	−0.464116	−	0.885775i	$-0.653628\pi$
$479$	−20.3153	−0.928232	−0.464116	+	0.885775i	$0.653628\pi$
$480$	0	0
$481$	−71.2311	−3.24786
$482$	24.1922	1.10193
$483$	1.06913	0.0486471
$484$	4.30019	0.195463
$485$	0	0
$486$	8.98485	0.407561
$487$	22.3002	1.01052	0.505259	−	0.862968i	$-0.331397\pi$
$487$	22.3002	1.01052	0.505259	+	0.862968i	$0.331397\pi$
$488$	18.1383	0.821080
$489$	−10.0540	−0.454656
$490$	0	0
$491$	22.7386	1.02618	0.513090	−	0.858335i	$-0.328501\pi$
$491$	22.7386	1.02618	0.513090	+	0.858335i	$0.328501\pi$
$492$	4.79261	0.216068
$493$	0	0
$494$	6.24621	0.281030
$495$	0	0
$496$	0	0
$497$	−6.00000	−0.269137
$498$	−18.4384	−0.826247
$499$	−31.0540	−1.39017	−0.695083	−	0.718929i	$-0.744633\pi$
$499$	−31.0540	−1.39017	−0.695083	+	0.718929i	$0.744633\pi$
$500$	0	0
$501$	11.5076	0.514121
$502$	−21.3693	−0.953759
$503$	−20.6847	−0.922283	−0.461142	−	0.887327i	$-0.652560\pi$
$503$	−20.6847	−0.922283	−0.461142	+	0.887327i	$0.652560\pi$
$504$	0.600373	0.0267427
$505$	0	0
$506$	11.1231	0.494482
$507$	58.9309	2.61721
$508$	−6.33050	−0.280870
$509$	−15.8769	−0.703731	−0.351865	−	0.936051i	$-0.614453\pi$
$509$	−15.8769	−0.703731	−0.351865	+	0.936051i	$0.614453\pi$
$510$	0	0
$511$	−3.01515	−0.133383
$512$	−11.4233	−0.504843
$513$	3.12311	0.137888
$514$	40.9848	1.80776
$515$	0	0
$516$	−6.24621	−0.274974
$517$	−23.3693	−1.02778
$518$	6.84658	0.300822
$519$	0.384472	0.0168764
$520$	0	0
$521$	−3.00000	−0.131432	−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000	−0.131432	−0.0657162	+	0.997838i	$0.520933\pi$
$522$	3.01515	0.131970
$523$	−2.19224	−0.0958598	−0.0479299	−	0.998851i	$-0.515262\pi$
$523$	−2.19224	−0.0958598	−0.0479299	+	0.998851i	$0.515262\pi$
$524$	5.61553	0.245315
$525$	0	0
$526$	30.9309	1.34865
$527$	0	0
$528$	−33.3693	−1.45221
$529$	−20.5616	−0.893981
$530$	0	0
$531$	−0.315342	−0.0136847
$532$	−0.107951	−0.00468025
$533$	−49.8617	−2.15975
$534$	42.6543	1.84583
$535$	0	0
$536$	8.68466	0.375120
$537$	11.6155	0.501247
$538$	22.9309	0.988620
$539$	−31.0540	−1.33759
$540$	0	0
$541$	1.87689	0.0806940	0.0403470	−	0.999186i	$-0.487154\pi$
$541$	1.87689	0.0806940	0.0403470	+	0.999186i	$0.487154\pi$
$542$	−7.50758	−0.322478
$543$	−2.05398	−0.0881445
$544$	0	0
$545$	0	0
$546$	−7.61553	−0.325915
$547$	−16.0540	−0.686418	−0.343209	−	0.939259i	$-0.611514\pi$
$547$	−16.0540	−0.686418	−0.343209	+	0.939259i	$0.611514\pi$
$548$	−4.87689	−0.208331
$549$	4.17708	0.178273
$550$	0	0
$551$	1.93087	0.0822578
$552$	−5.94602	−0.253080
$553$	−4.13826	−0.175977
$554$	−6.24621	−0.265376
$555$	0	0
$556$	7.26137	0.307951
$557$	15.7538	0.667509	0.333755	−	0.942660i	$-0.391684\pi$
$557$	15.7538	0.667509	0.333755	+	0.942660i	$0.391684\pi$
$558$	0	0
$559$	64.9848	2.74857
$560$	0	0
$561$	0	0
$562$	−14.4384	−0.609049
$563$	−8.49242	−0.357913	−0.178956	−	0.983857i	$-0.557272\pi$
$563$	−8.49242	−0.357913	−0.178956	+	0.983857i	$0.557272\pi$
$564$	−3.50758	−0.147696
$565$	0	0
$566$	−34.4384	−1.44756
$567$	−3.06913	−0.128891
$568$	33.3693	1.40015
$569$	−3.24621	−0.136088	−0.0680441	−	0.997682i	$-0.521676\pi$
$569$	−3.24621	−0.136088	−0.0680441	+	0.997682i	$0.521676\pi$
$570$	0	0
$571$	−10.5616	−0.441987	−0.220994	−	0.975275i	$-0.570930\pi$
$571$	−10.5616	−0.441987	−0.220994	+	0.975275i	$0.570930\pi$
$572$	−14.2462	−0.595664
$573$	30.7386	1.28412
$574$	4.79261	0.200040
$575$	0	0
$576$	−3.12311	−0.130129
$577$	−28.9848	−1.20665	−0.603327	−	0.797494i	$-0.706159\pi$
$577$	−28.9848	−1.20665	−0.603327	+	0.797494i	$0.706159\pi$
$578$	0	0
$579$	1.75379	0.0728850
$580$	0	0
$581$	−3.31534	−0.137544
$582$	−39.6155	−1.64212
$583$	5.12311	0.212177
$584$	16.7689	0.693904
$585$	0	0
$586$	13.4773	0.556741
$587$	37.6695	1.55479	0.777393	−	0.629015i	$-0.216541\pi$
$587$	37.6695	1.55479	0.777393	+	0.629015i	$0.216541\pi$
$588$	−4.66099	−0.192216
$589$	0	0
$590$	0	0
$591$	24.3845	1.00304
$592$	−46.8466	−1.92538
$593$	−24.0000	−0.985562	−0.492781	−	0.870153i	$-0.664020\pi$
$593$	−24.0000	−0.985562	−0.492781	+	0.870153i	$0.664020\pi$
$594$	−39.6155	−1.62544
$595$	0	0
$596$	−6.43845	−0.263729
$597$	−15.1231	−0.618948
$598$	−17.3693	−0.710284
$599$	−13.6847	−0.559140	−0.279570	−	0.960125i	$-0.590192\pi$
$599$	−13.6847	−0.559140	−0.279570	+	0.960125i	$0.590192\pi$
$600$	0	0
$601$	−5.80776	−0.236904	−0.118452	−	0.992960i	$-0.537793\pi$
$601$	−5.80776	−0.236904	−0.118452	+	0.992960i	$0.537793\pi$
$602$	−6.24621	−0.254577
$603$	2.00000	0.0814463
$604$	9.23106	0.375606
$605$	0	0
$606$	−35.0388	−1.42335
$607$	−38.2462	−1.55237	−0.776183	−	0.630508i	$-0.782847\pi$
$607$	−38.2462	−1.55237	−0.776183	+	0.630508i	$0.782847\pi$
$608$	1.36932	0.0555331
$609$	−2.35416	−0.0953955
$610$	0	0
$611$	36.4924	1.47633
$612$	0	0
$613$	−30.0000	−1.21169	−0.605844	−	0.795583i	$-0.707165\pi$
$613$	−30.0000	−1.21169	−0.605844	+	0.795583i	$0.707165\pi$
$614$	−2.73863	−0.110522
$615$	0	0
$616$	−4.87689	−0.196496
$617$	−8.00000	−0.322068	−0.161034	−	0.986949i	$-0.551483\pi$
$617$	−8.00000	−0.322068	−0.161034	+	0.986949i	$0.551483\pi$
$618$	−33.6695	−1.35439
$619$	17.4384	0.700910	0.350455	−	0.936580i	$-0.386027\pi$
$619$	17.4384	0.700910	0.350455	+	0.936580i	$0.386027\pi$
$620$	0	0
$621$	−8.68466	−0.348503
$622$	36.1080	1.44780
$623$	7.66950	0.307272
$624$	52.1080	2.08599
$625$	0	0
$626$	−28.4924	−1.13879
$627$	−4.00000	−0.159745
$628$	−1.36932	−0.0546417
$629$	0	0
$630$	0	0
$631$	33.4384	1.33116	0.665582	−	0.746325i	$-0.268183\pi$
$631$	33.4384	1.33116	0.665582	+	0.746325i	$0.268183\pi$
$632$	23.0152	0.915494
$633$	−11.1231	−0.442104
$634$	−9.75379	−0.387372
$635$	0	0
$636$	0.768944	0.0304906
$637$	48.4924	1.92134
$638$	−24.4924	−0.969664
$639$	7.68466	0.304000
$640$	0	0
$641$	28.9309	1.14270	0.571350	−	0.820706i	$-0.306420\pi$
$641$	28.9309	1.14270	0.571350	+	0.820706i	$0.306420\pi$
$642$	−7.01515	−0.276866
$643$	16.6847	0.657979	0.328989	−	0.944334i	$-0.393292\pi$
$643$	16.6847	0.657979	0.328989	+	0.944334i	$0.393292\pi$
$644$	0.300187	0.0118290
$645$	0	0
$646$	0	0
$647$	−5.80776	−0.228327	−0.114163	−	0.993462i	$-0.536419\pi$
$647$	−5.80776	−0.228327	−0.114163	+	0.993462i	$0.536419\pi$
$648$	17.0691	0.670539
$649$	2.56155	0.100550
$650$	0	0
$651$	0	0
$652$	−2.82292	−0.110554
$653$	46.7386	1.82902	0.914512	−	0.404559i	$-0.132575\pi$
$653$	46.7386	1.82902	0.914512	+	0.404559i	$0.132575\pi$
$654$	−14.1619	−0.553775
$655$	0	0
$656$	−32.7926	−1.28034
$657$	3.86174	0.150661
$658$	−3.50758	−0.136740
$659$	45.3002	1.76464	0.882322	−	0.470646i	$-0.155979\pi$
$659$	45.3002	1.76464	0.882322	+	0.470646i	$0.155979\pi$
$660$	0	0
$661$	−3.06913	−0.119375	−0.0596877	−	0.998217i	$-0.519010\pi$
$661$	−3.06913	−0.119375	−0.0596877	+	0.998217i	$0.519010\pi$
$662$	34.2462	1.33102
$663$	0	0
$664$	18.4384	0.715551
$665$	0	0
$666$	−8.76894	−0.339790
$667$	−5.36932	−0.207901
$668$	3.23106	0.125013
$669$	−16.6847	−0.645066
$670$	0	0
$671$	−33.9309	−1.30989
$672$	−1.66950	−0.0644025
$673$	30.2462	1.16591	0.582953	−	0.812506i	$-0.301897\pi$
$673$	30.2462	1.16591	0.582953	+	0.812506i	$0.301897\pi$
$674$	−2.73863	−0.105488
$675$	0	0
$676$	16.5464	0.636400
$677$	0.384472	0.0147765	0.00738823	−	0.999973i	$-0.497648\pi$
$677$	0.384472	0.0147765	0.00738823	+	0.999973i	$0.497648\pi$
$678$	20.1080	0.772241
$679$	−7.12311	−0.273360
$680$	0	0
$681$	34.4384	1.31968
$682$	0	0
$683$	−9.31534	−0.356442	−0.178221	−	0.983991i	$-0.557034\pi$
$683$	−9.31534	−0.356442	−0.178221	+	0.983991i	$0.557034\pi$
$684$	0.138261	0.00528653
$685$	0	0
$686$	−9.45360	−0.360940
$687$	2.93087	0.111820
$688$	42.7386	1.62940
$689$	−8.00000	−0.304776
$690$	0	0
$691$	5.36932	0.204258	0.102129	−	0.994771i	$-0.467434\pi$
$691$	5.36932	0.204258	0.102129	+	0.994771i	$0.467434\pi$
$692$	0.107951	0.00410367
$693$	−1.12311	−0.0426633
$694$	−24.0000	−0.911028
$695$	0	0
$696$	13.0928	0.496281
$697$	0	0
$698$	18.9309	0.716544
$699$	9.75379	0.368922
$700$	0	0
$701$	25.8769	0.977357	0.488678	−	0.872464i	$-0.337479\pi$
$701$	25.8769	0.977357	0.488678	+	0.872464i	$0.337479\pi$
$702$	61.8617	2.33482
$703$	−5.61553	−0.211794
$704$	25.3693	0.956142
$705$	0	0
$706$	−21.2614	−0.800182
$707$	−6.30019	−0.236943
$708$	0.384472	0.0144493
$709$	28.8617	1.08393	0.541963	−	0.840403i	$-0.317681\pi$
$709$	28.8617	1.08393	0.541963	+	0.840403i	$0.317681\pi$
$710$	0	0
$711$	5.30019	0.198773
$712$	−42.6543	−1.59854
$713$	0	0
$714$	0	0
$715$	0	0
$716$	3.26137	0.121883
$717$	−23.5076	−0.877907
$718$	3.23106	0.120582
$719$	−10.8078	−0.403062	−0.201531	−	0.979482i	$-0.564592\pi$
$719$	−10.8078	−0.403062	−0.201531	+	0.979482i	$0.564592\pi$
$720$	0	0
$721$	−6.05398	−0.225462
$722$	−29.1771	−1.08586
$723$	24.1922	0.899719
$724$	−0.576708	−0.0214332
$725$	0	0
$726$	23.9157	0.887595
$727$	−22.7386	−0.843329	−0.421665	−	0.906752i	$-0.638554\pi$
$727$	−22.7386	−0.843329	−0.421665	+	0.906752i	$0.638554\pi$
$728$	7.61553	0.282250
$729$	29.9848	1.11055
$730$	0	0
$731$	0	0
$732$	−5.09280	−0.188235
$733$	−14.2462	−0.526196	−0.263098	−	0.964769i	$-0.584744\pi$
$733$	−14.2462	−0.526196	−0.263098	+	0.964769i	$0.584744\pi$
$734$	12.4924	0.461104
$735$	0	0
$736$	−3.80776	−0.140356
$737$	−16.2462	−0.598437
$738$	−6.13826	−0.225952
$739$	−11.1231	−0.409170	−0.204585	−	0.978849i	$-0.565584\pi$
$739$	−11.1231	−0.409170	−0.204585	+	0.978849i	$0.565584\pi$
$740$	0	0
$741$	6.24621	0.229460
$742$	0.768944	0.0282288
$743$	44.9309	1.64835	0.824177	−	0.566332i	$-0.191638\pi$
$743$	44.9309	1.64835	0.824177	+	0.566332i	$0.191638\pi$
$744$	0	0
$745$	0	0
$746$	−28.4924	−1.04318
$747$	4.24621	0.155361
$748$	0	0
$749$	−1.26137	−0.0460893
$750$	0	0
$751$	26.7386	0.975707	0.487853	−	0.872926i	$-0.337780\pi$
$751$	26.7386	0.975707	0.487853	+	0.872926i	$0.337780\pi$
$752$	24.0000	0.875190
$753$	−21.3693	−0.778741
$754$	38.2462	1.39284
$755$	0	0
$756$	−1.06913	−0.0388839
$757$	11.5076	0.418250	0.209125	−	0.977889i	$-0.432938\pi$
$757$	11.5076	0.418250	0.209125	+	0.977889i	$0.432938\pi$
$758$	47.1231	1.71159
$759$	11.1231	0.403743
$760$	0	0
$761$	−21.1922	−0.768218	−0.384109	−	0.923288i	$-0.625491\pi$
$761$	−21.1922	−0.768218	−0.384109	+	0.923288i	$0.625491\pi$
$762$	−35.2074	−1.27543
$763$	−2.54640	−0.0921858
$764$	8.63068	0.312247
$765$	0	0
$766$	44.1922	1.59673
$767$	−4.00000	−0.144432
$768$	15.6998	0.566518
$769$	−28.9309	−1.04327	−0.521637	−	0.853168i	$-0.674678\pi$
$769$	−28.9309	−1.04327	−0.521637	+	0.853168i	$0.674678\pi$
$770$	0	0
$771$	40.9848	1.47603
$772$	0.492423	0.0177227
$773$	−8.38447	−0.301568	−0.150784	−	0.988567i	$-0.548180\pi$
$773$	−8.38447	−0.301568	−0.150784	+	0.988567i	$0.548180\pi$
$774$	8.00000	0.287554
$775$	0	0
$776$	39.6155	1.42211
$777$	6.84658	0.245620
$778$	−8.87689	−0.318252
$779$	−3.93087	−0.140838
$780$	0	0
$781$	−62.4233	−2.23368
$782$	0	0
$783$	19.1231	0.683404
$784$	31.8920	1.13900
$785$	0	0
$786$	31.2311	1.11397
$787$	−5.31534	−0.189471	−0.0947357	−	0.995502i	$-0.530201\pi$
$787$	−5.31534	−0.189471	−0.0947357	+	0.995502i	$0.530201\pi$
$788$	6.84658	0.243899
$789$	30.9309	1.10117
$790$	0	0
$791$	3.61553	0.128553
$792$	6.24621	0.221949
$793$	52.9848	1.88155
$794$	−37.2614	−1.32236
$795$	0	0
$796$	−4.24621	−0.150503
$797$	−12.2462	−0.433783	−0.216892	−	0.976196i	$-0.569592\pi$
$797$	−12.2462	−0.433783	−0.216892	+	0.976196i	$0.569592\pi$
$798$	−0.600373	−0.0212530
$799$	0	0
$800$	0	0
$801$	−9.82292	−0.347076
$802$	23.8078	0.840681
$803$	−31.3693	−1.10700
$804$	−2.43845	−0.0859974
$805$	0	0
$806$	0	0
$807$	22.9309	0.807205
$808$	35.0388	1.23266
$809$	20.7538	0.729664	0.364832	−	0.931073i	$-0.381126\pi$
$809$	20.7538	0.729664	0.364832	+	0.931073i	$0.381126\pi$
$810$	0	0
$811$	−42.6695	−1.49833	−0.749164	−	0.662384i	$-0.769545\pi$
$811$	−42.6695	−1.49833	−0.749164	+	0.662384i	$0.769545\pi$
$812$	−0.660993	−0.0231963
$813$	−7.50758	−0.263302
$814$	71.2311	2.49665
$815$	0	0
$816$	0	0
$817$	5.12311	0.179235
$818$	−14.0540	−0.491386
$819$	1.75379	0.0612823
$820$	0	0
$821$	−11.1771	−0.390083	−0.195041	−	0.980795i	$-0.562484\pi$
$821$	−11.1771	−0.390083	−0.195041	+	0.980795i	$0.562484\pi$
$822$	−27.1231	−0.946027
$823$	−12.1922	−0.424995	−0.212497	−	0.977162i	$-0.568160\pi$
$823$	−12.1922	−0.424995	−0.212497	+	0.977162i	$0.568160\pi$
$824$	33.6695	1.17293
$825$	0	0
$826$	0.384472	0.0133775
$827$	13.1771	0.458212	0.229106	−	0.973401i	$-0.426420\pi$
$827$	13.1771	0.458212	0.229106	+	0.973401i	$0.426420\pi$
$828$	−0.384472	−0.0133613
$829$	5.63068	0.195562	0.0977809	−	0.995208i	$-0.468826\pi$
$829$	5.63068	0.195562	0.0977809	+	0.995208i	$0.468826\pi$
$830$	0	0
$831$	−6.24621	−0.216679
$832$	−39.6155	−1.37342
$833$	0	0
$834$	40.3845	1.39840
$835$	0	0
$836$	−1.12311	−0.0388434
$837$	0	0
$838$	20.8769	0.721180
$839$	−47.6847	−1.64626	−0.823129	−	0.567855i	$-0.807773\pi$
$839$	−47.6847	−1.64626	−0.823129	+	0.567855i	$0.807773\pi$
$840$	0	0
$841$	−17.1771	−0.592313
$842$	−57.3693	−1.97708
$843$	−14.4384	−0.497287
$844$	−3.12311	−0.107502
$845$	0	0
$846$	4.49242	0.154453
$847$	4.30019	0.147756
$848$	−5.26137	−0.180676
$849$	−34.4384	−1.18192
$850$	0	0
$851$	15.6155	0.535293
$852$	−9.36932	−0.320988
$853$	34.9848	1.19786	0.598929	−	0.800802i	$-0.295593\pi$
$853$	34.9848	1.19786	0.598929	+	0.800802i	$0.295593\pi$
$854$	−5.09280	−0.174272
$855$	0	0
$856$	7.01515	0.239773
$857$	−20.7386	−0.708418	−0.354209	−	0.935166i	$-0.615250\pi$
$857$	−20.7386	−0.708418	−0.354209	+	0.935166i	$0.615250\pi$
$858$	−79.2311	−2.70490
$859$	16.8769	0.575832	0.287916	−	0.957656i	$-0.407038\pi$
$859$	16.8769	0.575832	0.287916	+	0.957656i	$0.407038\pi$
$860$	0	0
$861$	4.79261	0.163332
$862$	51.5076	1.75436
$863$	−16.0000	−0.544646	−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000	−0.544646	−0.272323	+	0.962206i	$0.587792\pi$
$864$	13.5616	0.461373
$865$	0	0
$866$	−3.50758	−0.119192
$867$	0	0
$868$	0	0
$869$	−43.0540	−1.46051
$870$	0	0
$871$	25.3693	0.859607
$872$	14.1619	0.479583
$873$	9.12311	0.308770
$874$	−1.36932	−0.0463178
$875$	0	0
$876$	−4.70832	−0.159080
$877$	29.7538	1.00471	0.502357	−	0.864660i	$-0.332466\pi$
$877$	29.7538	1.00471	0.502357	+	0.864660i	$0.332466\pi$
$878$	−24.1080	−0.813604
$879$	13.4773	0.454577
$880$	0	0
$881$	20.5616	0.692736	0.346368	−	0.938099i	$-0.387415\pi$
$881$	20.5616	0.692736	0.346368	+	0.938099i	$0.387415\pi$
$882$	5.96969	0.201010
$883$	−28.4924	−0.958846	−0.479423	−	0.877584i	$-0.659154\pi$
$883$	−28.4924	−0.958846	−0.479423	+	0.877584i	$0.659154\pi$
$884$	0	0
$885$	0	0
$886$	20.7926	0.698541
$887$	−3.06913	−0.103051	−0.0515257	−	0.998672i	$-0.516408\pi$
$887$	−3.06913	−0.103051	−0.0515257	+	0.998672i	$0.516408\pi$
$888$	−38.0776	−1.27780
$889$	−6.33050	−0.212318
$890$	0	0
$891$	−31.9309	−1.06972
$892$	−4.68466	−0.156854
$893$	2.87689	0.0962716
$894$	−35.8078	−1.19759
$895$	0	0
$896$	5.94602	0.198643
$897$	−17.3693	−0.579945
$898$	−16.1080	−0.537529
$899$	0	0
$900$	0	0
$901$	0	0
$902$	49.8617	1.66021
$903$	−6.24621	−0.207861
$904$	−20.1080	−0.668780
$905$	0	0
$906$	51.3390	1.70562
$907$	−20.6307	−0.685031	−0.342515	−	0.939512i	$-0.611279\pi$
$907$	−20.6307	−0.685031	−0.342515	+	0.939512i	$0.611279\pi$
$908$	9.66950	0.320894
$909$	8.06913	0.267636
$910$	0	0
$911$	37.3693	1.23810	0.619050	−	0.785351i	$-0.287518\pi$
$911$	37.3693	1.23810	0.619050	+	0.785351i	$0.287518\pi$
$912$	4.10795	0.136028
$913$	−34.4924	−1.14153
$914$	37.8617	1.25236
$915$	0	0
$916$	0.822919	0.0271900
$917$	5.61553	0.185441
$918$	0	0
$919$	−48.0000	−1.58337	−0.791687	−	0.610927i	$-0.790797\pi$
$919$	−48.0000	−1.58337	−0.791687	+	0.610927i	$0.790797\pi$
$920$	0	0
$921$	−2.73863	−0.0902411
$922$	21.5616	0.710092
$923$	97.4773	3.20850
$924$	1.36932	0.0450472
$925$	0	0
$926$	−29.5616	−0.971453
$927$	7.75379	0.254668
$928$	8.38447	0.275234
$929$	−49.7386	−1.63187	−0.815936	−	0.578142i	$-0.803778\pi$
$929$	−49.7386	−1.63187	−0.815936	+	0.578142i	$0.803778\pi$
$930$	0	0
$931$	3.82292	0.125291
$932$	2.73863	0.0897069
$933$	36.1080	1.18212
$934$	−18.4384	−0.603324
$935$	0	0
$936$	−9.75379	−0.318813
$937$	41.2311	1.34696	0.673480	−	0.739205i	$-0.264799\pi$
$937$	41.2311	1.34696	0.673480	+	0.739205i	$0.264799\pi$
$938$	−2.43845	−0.0796181
$939$	−28.4924	−0.929815
$940$	0	0
$941$	21.1080	0.688100	0.344050	−	0.938951i	$-0.388201\pi$
$941$	21.1080	0.688100	0.344050	+	0.938951i	$0.388201\pi$
$942$	−7.61553	−0.248127
$943$	10.9309	0.355958
$944$	−2.63068	−0.0856214
$945$	0	0
$946$	−64.9848	−2.11284
$947$	−13.8078	−0.448692	−0.224346	−	0.974510i	$-0.572025\pi$
$947$	−13.8078	−0.448692	−0.224346	+	0.974510i	$0.572025\pi$
$948$	−6.46211	−0.209880
$949$	48.9848	1.59012
$950$	0	0
$951$	−9.75379	−0.316288
$952$	0	0
$953$	7.50758	0.243194	0.121597	−	0.992580i	$-0.461198\pi$
$953$	7.50758	0.243194	0.121597	+	0.992580i	$0.461198\pi$
$954$	−0.984845	−0.0318855
$955$	0	0
$956$	−6.60037	−0.213471
$957$	−24.4924	−0.791728
$958$	−31.7235	−1.02494
$959$	−4.87689	−0.157483
$960$	0	0
$961$	−31.0000	−1.00000
$962$	−111.231	−3.58623
$963$	1.61553	0.0520597
$964$	6.79261	0.218775
$965$	0	0
$966$	1.66950	0.0537154
$967$	11.4233	0.367348	0.183674	−	0.982987i	$-0.441201\pi$
$967$	11.4233	0.367348	0.183674	+	0.982987i	$0.441201\pi$
$968$	−23.9157	−0.768680
$969$	0	0
$970$	0	0
$971$	−0.0691303	−0.00221850	−0.00110925	−	0.999999i	$-0.500353\pi$
$971$	−0.0691303	−0.00221850	−0.00110925	+	0.999999i	$0.500353\pi$
$972$	2.52273	0.0809167
$973$	7.26137	0.232789
$974$	34.8229	1.11580
$975$	0	0
$976$	34.8466	1.11541
$977$	−32.3542	−1.03510	−0.517551	−	0.855653i	$-0.673156\pi$
$977$	−32.3542	−1.03510	−0.517551	+	0.855653i	$0.673156\pi$
$978$	−15.6998	−0.502025
$979$	79.7926	2.55018
$980$	0	0
$981$	3.26137	0.104127
$982$	35.5076	1.13309
$983$	8.82292	0.281407	0.140704	−	0.990052i	$-0.455064\pi$
$983$	8.82292	0.281407	0.140704	+	0.990052i	$0.455064\pi$
$984$	−26.6543	−0.849710
$985$	0	0
$986$	0	0
$987$	−3.50758	−0.111647
$988$	1.75379	0.0557955
$989$	−14.2462	−0.453003
$990$	0	0
$991$	20.8769	0.663176	0.331588	−	0.943424i	$-0.392416\pi$
$991$	20.8769	0.663176	0.331588	+	0.943424i	$0.392416\pi$
$992$	0	0
$993$	34.2462	1.08677
$994$	−9.36932	−0.297177
$995$	0	0
$996$	−5.17708	−0.164042
$997$	−12.9848	−0.411234	−0.205617	−	0.978633i	$-0.565920\pi$
$997$	−12.9848	−0.411234	−0.205617	+	0.978633i	$0.565920\pi$
$998$	−48.4924	−1.53500
$999$	−55.6155	−1.75960

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7225.2.a.j.1.2		2
5.4	even	2		1445.2.a.i.1.1	yes	2
17.16	even	2		7225.2.a.k.1.2		2
85.4	even	4		1445.2.d.d.866.4		4
85.64	even	4		1445.2.d.d.866.3		4
85.84	even	2		1445.2.a.h.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1445.2.a.h.1.1	✓	2	85.84	even	2
1445.2.a.i.1.1	yes	2	5.4	even	2
1445.2.d.d.866.3		4	85.64	even	4
1445.2.d.d.866.4		4	85.4	even	4
7225.2.a.j.1.2		2	1.1	even	1	trivial
7225.2.a.k.1.2		2	17.16	even	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:	\( N \)	\(=\)	\( 7225 = 5^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7225.a (trivial)

\(f(q)\)	\(=\)	\(q+1.56155 q^{2} +1.56155 q^{3} +0.438447 q^{4} +2.43845 q^{6} +0.438447 q^{7} -2.43845 q^{8} -0.561553 q^{9} +4.56155 q^{11} +0.684658 q^{12} -7.12311 q^{13} +0.684658 q^{14} -4.68466 q^{16} -0.876894 q^{18} -0.561553 q^{19} +0.684658 q^{21} +7.12311 q^{22} +1.56155 q^{23} -3.80776 q^{24} -11.1231 q^{26} -5.56155 q^{27} +0.192236 q^{28} -3.43845 q^{29} -2.43845 q^{32} +7.12311 q^{33} -0.246211 q^{36} +10.0000 q^{37} -0.876894 q^{38} -11.1231 q^{39} +7.00000 q^{41} +1.06913 q^{42} -9.12311 q^{43} +2.00000 q^{44} +2.43845 q^{46} -5.12311 q^{47} -7.31534 q^{48} -6.80776 q^{49} -3.12311 q^{52} +1.12311 q^{53} -8.68466 q^{54} -1.06913 q^{56} -0.876894 q^{57} -5.36932 q^{58} +0.561553 q^{59} -7.43845 q^{61} -0.246211 q^{63} +5.56155 q^{64} +11.1231 q^{66} -3.56155 q^{67} +2.43845 q^{69} -13.6847 q^{71} +1.36932 q^{72} -6.87689 q^{73} +15.6155 q^{74} -0.246211 q^{76} +2.00000 q^{77} -17.3693 q^{78} -9.43845 q^{79} -7.00000 q^{81} +10.9309 q^{82} -7.56155 q^{83} +0.300187 q^{84} -14.2462 q^{86} -5.36932 q^{87} -11.1231 q^{88} +17.4924 q^{89} -3.12311 q^{91} +0.684658 q^{92} -8.00000 q^{94} -3.80776 q^{96} -16.2462 q^{97} -10.6307 q^{98} -2.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} + 5 q^{4} + 9 q^{6} + 5 q^{7} - 9 q^{8} + 3 q^{9} + 5 q^{11} - 11 q^{12} - 6 q^{13} - 11 q^{14} + 3 q^{16} - 10 q^{18} + 3 q^{19} - 11 q^{21} + 6 q^{22} - q^{23} + 13 q^{24} - 14 q^{26}+ \cdots - q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 + 5 * q^4 + 9 * q^6 + 5 * q^7 - 9 * q^8 + 3 * q^9 + 5 * q^11 - 11 * q^12 - 6 * q^13 - 11 * q^14 + 3 * q^16 - 10 * q^18 + 3 * q^19 - 11 * q^21 + 6 * q^22 - q^23 + 13 * q^24 - 14 * q^26 - 7 * q^27 + 21 * q^28 - 11 * q^29 - 9 * q^32 + 6 * q^33 + 16 * q^36 + 20 * q^37 - 10 * q^38 - 14 * q^39 + 14 * q^41 + 31 * q^42 - 10 * q^43 + 4 * q^44 + 9 * q^46 - 2 * q^47 - 27 * q^48 + 7 * q^49 + 2 * q^52 - 6 * q^53 - 5 * q^54 - 31 * q^56 - 10 * q^57 + 14 * q^58 - 3 * q^59 - 19 * q^61 + 16 * q^63 + 7 * q^64 + 14 * q^66 - 3 * q^67 + 9 * q^69 - 15 * q^71 - 22 * q^72 - 22 * q^73 - 10 * q^74 + 16 * q^76 + 4 * q^77 - 10 * q^78 - 23 * q^79 - 14 * q^81 - 7 * q^82 - 11 * q^83 - 53 * q^84 - 12 * q^86 + 14 * q^87 - 14 * q^88 + 2 * q^89 + 2 * q^91 - 11 * q^92 - 16 * q^94 + 13 * q^96 - 16 * q^97 - 46 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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