LMFDB - Embedded newform 1053.2.e.p.352.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1053,2,Mod(352,1053)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1053.352"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1053, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1053 = 3^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1053.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-10,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.40824733284$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4678560000.4
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} + 62x^{4} + 171x^{2} + 361 $ x^8 + 9x^6 + 62x^4 + 171*x^2 + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 351)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.1
Root			$1.18512 - 2.05269i$ of defining polynomial
Character	$\chi$	$=$	1053.352
Dual form			1053.2.e.p.703.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18512 - 2.05269i) q^{2} +(-1.80902 + 3.13331i) q^{4} +(-1.91756 + 3.32132i) q^{5} +(2.23607 + 3.87298i) q^{7} +3.83513 q^{8} +9.09017 q^{10} +(1.46489 + 2.53726i) q^{11} +(0.500000 - 0.866025i) q^{13} +(5.30002 - 9.17990i) q^{14} +(-0.927051 - 1.60570i) q^{16} -4.74048 q^{17} +0.763932 q^{19} +(-6.93781 - 12.0166i) q^{20} +(3.47214 - 6.01392i) q^{22} +(-1.46489 + 2.53726i) q^{23} +(-4.85410 - 8.40755i) q^{25} -2.37024 q^{26} -16.1803 q^{28} +(-1.46489 - 2.53726i) q^{29} +(-3.61803 + 6.26662i) q^{31} +(1.63780 - 2.83674i) q^{32} +(5.61803 + 9.73072i) q^{34} -17.1512 q^{35} +3.23607 q^{37} +(-0.905351 - 1.56811i) q^{38} +(-7.35410 + 12.7377i) q^{40} +(2.37024 - 4.10537i) q^{41} +(-0.118034 - 0.204441i) q^{43} -10.6000 q^{44} +6.94427 q^{46} +(1.91756 + 3.32132i) q^{47} +(-6.50000 + 11.2583i) q^{49} +(-11.5054 + 19.9279i) q^{50} +(1.80902 + 3.13331i) q^{52} +5.85955 q^{53} -11.2361 q^{55} +(8.57561 + 14.8534i) q^{56} +(-3.47214 + 6.01392i) q^{58} +(1.01221 - 1.75320i) q^{59} +(-5.11803 - 8.86469i) q^{61} +17.1512 q^{62} -11.4721 q^{64} +(1.91756 + 3.32132i) q^{65} +(1.38197 - 2.39364i) q^{67} +(8.57561 - 14.8534i) q^{68} +(20.3262 + 35.2061i) q^{70} -8.57561 q^{71} -10.4721 q^{73} +(-3.83513 - 6.64264i) q^{74} +(-1.38197 + 2.39364i) q^{76} +(-6.55118 + 11.3470i) q^{77} +(4.47214 + 7.74597i) q^{79} +7.11072 q^{80} -11.2361 q^{82} +(-0.452675 - 0.784057i) q^{83} +(9.09017 - 15.7446i) q^{85} +(-0.279769 + 0.484574i) q^{86} +(5.61803 + 9.73072i) q^{88} +10.3863 q^{89} +4.47214 q^{91} +(-5.30002 - 9.17990i) q^{92} +(4.54508 - 7.87232i) q^{94} +(-1.46489 + 2.53726i) q^{95} +(-9.09017 - 15.7446i) q^{97} +30.8131 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{4} + 28 q^{10} + 4 q^{13} + 6 q^{16} + 24 q^{19} - 8 q^{22} - 12 q^{25} - 40 q^{28} - 20 q^{31} + 36 q^{34} + 8 q^{37} - 32 q^{40} + 8 q^{43} - 16 q^{46} - 52 q^{49} + 10 q^{52} - 72 q^{55}+ \cdots - 28 q^{97}+O(q^{100}) $ 8 * q - 10 * q^4 + 28 * q^10 + 4 * q^13 + 6 * q^16 + 24 * q^19 - 8 * q^22 - 12 * q^25 - 40 * q^28 - 20 * q^31 + 36 * q^34 + 8 * q^37 - 32 * q^40 + 8 * q^43 - 16 * q^46 - 52 * q^49 + 10 * q^52 - 72 * q^55 + 8 * q^58 - 32 * q^61 - 56 * q^64 + 20 * q^67 + 100 * q^70 - 48 * q^73 - 20 * q^76 - 72 * q^82 + 28 * q^85 + 36 * q^88 + 14 * q^94 - 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times$.

$n$	$326$	$730$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.18512	−	2.05269i	−0.838006	−	1.45147i	−0.891559	−	0.452904i	$-0.850388\pi$
$2$	−1.18512	−	2.05269i	−0.838006	−	1.45147i	0.0535531	−	0.998565i	$-0.482945\pi$
$3$		0			0
$3$		0			0
$4$	−1.80902	+	3.13331i	−0.904508	+	1.56665i
$5$	−1.91756	+	3.32132i	−0.857561	+	1.48534i	0.0166884	+	0.999861i	$0.494688\pi$
$5$	−1.91756	+	3.32132i	−0.857561	+	1.48534i	−0.874249	+	0.485478i	$0.838646\pi$
$6$		0			0
$7$	2.23607	+	3.87298i	0.845154	+	1.46385i	0.885487	+	0.464664i	$0.153825\pi$
$7$	2.23607	+	3.87298i	0.845154	+	1.46385i	−0.0403329	+	0.999186i	$0.512842\pi$
$8$	3.83513			1.35592
$9$		0			0
$10$	9.09017			2.87456
$11$	1.46489	+	2.53726i	0.441680	+	0.765013i	0.997814	−	0.0660797i	$-0.0210492\pi$
$11$	1.46489	+	2.53726i	0.441680	+	0.765013i	−0.556134	+	0.831093i	$0.687716\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	5.30002	−	9.17990i	1.41649	−	2.45343i
$15$		0			0
$16$	−0.927051	−	1.60570i	−0.231763	−	0.401425i
$17$	−4.74048			−1.14973			−0.574867	−	0.818247i	$-0.694946\pi$
$17$	−4.74048			−1.14973			−0.574867	+	0.818247i	$0.694946\pi$
$18$		0			0
$19$	0.763932			0.175258			0.0876290	−	0.996153i	$-0.472071\pi$
$19$	0.763932			0.175258			0.0876290	+	0.996153i	$0.472071\pi$
$20$	−6.93781	−	12.0166i	−1.55134	−	2.68700i
$21$		0			0
$22$	3.47214	−	6.01392i	0.740262	−	1.28217i
$23$	−1.46489	+	2.53726i	−0.305450	+	0.529056i	−0.977361	−	0.211576i	$-0.932140\pi$
$23$	−1.46489	+	2.53726i	−0.305450	+	0.529056i	0.671911	+	0.740632i	$0.265474\pi$
$24$		0			0
$25$	−4.85410	−	8.40755i	−0.970820	−	1.68151i
$26$	−2.37024			−0.464842
$27$		0			0
$28$	−16.1803			−3.05780
$29$	−1.46489	−	2.53726i	−0.272023	−	0.471158i	0.697357	−	0.716724i	$-0.254359\pi$
$29$	−1.46489	−	2.53726i	−0.272023	−	0.471158i	−0.969380	+	0.245567i	$0.921026\pi$
$30$		0			0
$31$	−3.61803	+	6.26662i	−0.649818	+	1.12552i	0.333348	+	0.942804i	$0.391822\pi$
$31$	−3.61803	+	6.26662i	−0.649818	+	1.12552i	−0.983166	+	0.182714i	$0.941512\pi$
$32$	1.63780	−	2.83674i	0.289524	−	0.501470i
$33$		0			0
$34$	5.61803	+	9.73072i	0.963485	+	1.66880i
$35$	−17.1512			−2.89908
$36$		0			0
$37$	3.23607			0.532006			0.266003	−	0.963972i	$-0.414297\pi$
$37$	3.23607			0.532006			0.266003	+	0.963972i	$0.414297\pi$
$38$	−0.905351	−	1.56811i	−0.146867	−	0.254382i
$39$		0			0
$40$	−7.35410	+	12.7377i	−1.16279	+	2.01400i
$41$	2.37024	−	4.10537i	0.370169	−	0.641152i	−0.619422	−	0.785058i	$-0.712633\pi$
$41$	2.37024	−	4.10537i	0.370169	−	0.641152i	0.989591	+	0.143906i	$0.0459664\pi$
$42$		0			0
$43$	−0.118034	−	0.204441i	−0.0180000	−	0.0311769i	0.856885	−	0.515507i	$-0.172397\pi$
$43$	−0.118034	−	0.204441i	−0.0180000	−	0.0311769i	−0.874885	+	0.484331i	$0.839063\pi$
$44$	−10.6000			−1.59801
$45$		0			0
$46$	6.94427			1.02388
$47$	1.91756	+	3.32132i	0.279705	+	0.484464i	0.971311	−	0.237811i	$-0.0764299\pi$
$47$	1.91756	+	3.32132i	0.279705	+	0.484464i	−0.691606	+	0.722275i	$0.743097\pi$
$48$		0			0
$49$	−6.50000	+	11.2583i	−0.928571	+	1.60833i
$50$	−11.5054	+	19.9279i	−1.62711	+	2.81823i
$51$		0			0
$52$	1.80902	+	3.13331i	0.250866	+	0.434512i
$53$	5.85955			0.804872			0.402436	−	0.915448i	$-0.368164\pi$
$53$	5.85955			0.804872			0.402436	+	0.915448i	$0.368164\pi$
$54$		0			0
$55$	−11.2361			−1.51507
$56$	8.57561	+	14.8534i	1.14596	+	1.98487i
$57$		0			0
$58$	−3.47214	+	6.01392i	−0.455914	+	0.789666i
$59$	1.01221	−	1.75320i	0.131779	−	0.228248i	−0.792583	−	0.609763i	$-0.791264\pi$
$59$	1.01221	−	1.75320i	0.131779	−	0.228248i	0.924362	+	0.381516i	$0.124598\pi$
$60$		0			0
$61$	−5.11803	−	8.86469i	−0.655297	−	1.13501i	−0.981819	−	0.189818i	$-0.939210\pi$
$61$	−5.11803	−	8.86469i	−0.655297	−	1.13501i	0.326522	−	0.945190i	$-0.394123\pi$
$62$	17.1512			2.17821
$63$		0			0
$64$	−11.4721			−1.43402
$65$	1.91756	+	3.32132i	0.237845	+	0.411959i
$66$		0			0
$67$	1.38197	−	2.39364i	0.168834	−	0.292429i	−0.769176	−	0.639037i	$-0.779333\pi$
$67$	1.38197	−	2.39364i	0.168834	−	0.292429i	0.938010	+	0.346608i	$0.112666\pi$
$68$	8.57561	−	14.8534i	1.03994	−	1.80124i
$69$		0			0
$70$	20.3262	+	35.2061i	2.42945	+	4.20793i
$71$	−8.57561			−1.01774			−0.508869	−	0.860844i	$-0.669936\pi$
$71$	−8.57561			−1.01774			−0.508869	+	0.860844i	$0.669936\pi$
$72$		0			0
$73$	−10.4721			−1.22567			−0.612835	−	0.790211i	$-0.709971\pi$
$73$	−10.4721			−1.22567			−0.612835	+	0.790211i	$0.709971\pi$
$74$	−3.83513	−	6.64264i	−0.445825	−	0.772191i
$75$		0			0
$76$	−1.38197	+	2.39364i	−0.158522	+	0.274569i
$77$	−6.55118	+	11.3470i	−0.746576	+	1.29311i
$78$		0			0
$79$	4.47214	+	7.74597i	0.503155	+	0.871489i	0.999993	+	0.00364646i	$0.00116071\pi$
$79$	4.47214	+	7.74597i	0.503155	+	0.871489i	−0.496839	+	0.867843i	$0.665506\pi$
$80$	7.11072			0.795002
$81$		0			0
$82$	−11.2361			−1.24082
$83$	−0.452675	−	0.784057i	−0.0496876	−	0.0860614i	0.840112	−	0.542413i	$-0.182489\pi$
$83$	−0.452675	−	0.784057i	−0.0496876	−	0.0860614i	−0.889799	+	0.456352i	$0.849156\pi$
$84$		0			0
$85$	9.09017	−	15.7446i	0.985967	−	1.70775i
$86$	−0.279769	+	0.484574i	−0.0301682	+	0.0522529i
$87$		0			0
$88$	5.61803	+	9.73072i	0.598884	+	1.03730i
$89$	10.3863			1.10095			0.550473	−	0.834853i	$-0.314447\pi$
$89$	10.3863			1.10095			0.550473	+	0.834853i	$0.314447\pi$
$90$		0			0
$91$	4.47214			0.468807
$92$	−5.30002	−	9.17990i	−0.552565	−	0.957070i
$93$		0			0
$94$	4.54508	−	7.87232i	0.468790	−	0.811968i
$95$	−1.46489	+	2.53726i	−0.150294	+	0.260318i
$96$		0			0
$97$	−9.09017	−	15.7446i	−0.922967	−	1.59863i	−0.794799	−	0.606873i	$-0.792424\pi$
$97$	−9.09017	−	15.7446i	−0.922967	−	1.59863i	−0.128168	−	0.991752i	$-0.540910\pi$
$98$	30.8131			3.11259
$99$		0			0
$100$	35.1246			3.51246
$101$	2.37024	+	4.10537i	0.235848	+	0.408500i	0.959519	−	0.281645i	$-0.0908800\pi$
$101$	2.37024	+	4.10537i	0.235848	+	0.408500i	−0.723671	+	0.690145i	$0.757547\pi$
$102$		0			0
$103$	0.881966	−	1.52761i	0.0869027	−	0.150520i	−0.819298	−	0.573368i	$-0.805636\pi$
$103$	0.881966	−	1.52761i	0.0869027	−	0.150520i	0.906200	+	0.422848i	$0.138970\pi$
$104$	1.91756	−	3.32132i	0.188033	−	0.325682i
$105$		0			0
$106$	−6.94427	−	12.0278i	−0.674487	−	1.16825i
$107$	−7.67026			−0.741512			−0.370756	−	0.928730i	$-0.620901\pi$
$107$	−7.67026			−0.741512			−0.370756	+	0.928730i	$0.620901\pi$
$108$		0			0
$109$	8.94427			0.856706			0.428353	−	0.903612i	$-0.359094\pi$
$109$	8.94427			0.856706			0.428353	+	0.903612i	$0.359094\pi$
$110$	13.3161	+	23.0641i	1.26964	+	2.19908i
$111$		0			0
$112$	4.14590	−	7.18091i	0.391751	−	0.678532i
$113$	3.83513	−	6.64264i	0.360778	−	0.624887i	−0.627311	−	0.778769i	$-0.715844\pi$
$113$	3.83513	−	6.64264i	0.360778	−	0.624887i	0.988089	+	0.153882i	$0.0491777\pi$
$114$		0			0
$115$	−5.61803	−	9.73072i	−0.523884	−	0.907394i
$116$	10.6000			0.984188
$117$		0			0
$118$	−4.79837			−0.441726
$119$	−10.6000	−	18.3598i	−0.971703	−	1.68304i
$120$		0			0
$121$	1.20820	−	2.09267i	0.109837	−	0.190243i
$122$	−12.1310	+	21.0114i	−1.09829	+	1.90229i
$123$		0			0
$124$	−13.0902	−	22.6728i	−1.17553	−	2.03608i
$125$	18.0566			1.61503
$126$		0			0
$127$	−5.94427			−0.527469			−0.263734	−	0.964595i	$-0.584954\pi$
$127$	−5.94427			−0.527469			−0.263734	+	0.964595i	$0.584954\pi$
$128$	10.3203	+	17.8752i	0.912191	+	1.57996i
$129$		0			0
$130$	4.54508	−	7.87232i	0.398630	−	0.690448i
$131$	−10.0405	+	17.3906i	−0.877242	+	1.51943i	−0.0228870	+	0.999738i	$0.507286\pi$
$131$	−10.0405	+	17.3906i	−0.877242	+	1.51943i	−0.854355	+	0.519690i	$0.826048\pi$
$132$		0			0
$133$	1.70820	+	2.95870i	0.148120	+	0.256551i
$134$	−6.55118			−0.565936
$135$		0			0
$136$	−18.1803			−1.55895
$137$	5.30002	+	9.17990i	0.452811	+	0.784292i	0.998559	−	0.0536575i	$-0.0170879\pi$
$137$	5.30002	+	9.17990i	0.452811	+	0.784292i	−0.545748	+	0.837949i	$0.683755\pi$
$138$		0			0
$139$	−1.59017	+	2.75426i	−0.134876	+	0.233613i	−0.925550	−	0.378625i	$-0.876397\pi$
$139$	−1.59017	+	2.75426i	−0.134876	+	0.233613i	0.790674	+	0.612238i	$0.209730\pi$
$140$	31.0268	−	53.7401i	2.62225	−	4.54186i
$141$		0			0
$142$	10.1631	+	17.6030i	0.852870	+	1.47721i
$143$	2.92978			0.245000
$144$		0			0
$145$	11.2361			0.933105
$146$	12.4107	+	21.4960i	1.02712	+	1.77902i
$147$		0			0
$148$	−5.85410	+	10.1396i	−0.481204	+	0.833470i
$149$	−2.47710	+	4.29047i	−0.202932	+	0.351489i	−0.949472	−	0.313852i	$-0.898380\pi$
$149$	−2.47710	+	4.29047i	−0.202932	+	0.351489i	0.746540	+	0.665341i	$0.231714\pi$
$150$		0			0
$151$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$151$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$152$	2.92978			0.237636
$153$		0			0
$154$	31.0557			2.50254
$155$	−13.8756	−	24.0333i	−1.11452	−	1.93040i
$156$		0			0
$157$	−12.2082	+	21.1452i	−0.974321	+	1.68757i	−0.292162	+	0.956369i	$0.594375\pi$
$157$	−12.2082	+	21.1452i	−0.974321	+	1.68757i	−0.682159	+	0.731204i	$0.738959\pi$
$158$	10.6000	−	18.3598i	0.843293	−	1.46063i
$159$		0			0
$160$	6.28115	+	10.8793i	0.496569	+	0.860082i
$161$	−13.1024			−1.03261
$162$		0			0
$163$	0.944272			0.0739611			0.0369805	−	0.999316i	$-0.488226\pi$
$163$	0.944272			0.0739611			0.0369805	+	0.999316i	$0.488226\pi$
$164$	8.57561	+	14.8534i	0.669642	+	1.15985i
$165$		0			0
$166$	−1.07295	+	1.85840i	−0.0832770	+	0.144240i
$167$	−2.26338	+	3.92028i	−0.175145	+	0.303361i	−0.940212	−	0.340591i	$-0.889373\pi$
$167$	−2.26338	+	3.92028i	−0.175145	+	0.303361i	0.765066	+	0.643952i	$0.222706\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−43.0918			−3.30499
$171$		0			0
$172$	0.854102			0.0651247
$173$	7.67026	+	13.2853i	0.583159	+	1.01006i	0.995102	+	0.0988511i	$0.0315168\pi$
$173$	7.67026	+	13.2853i	0.583159	+	1.01006i	−0.411944	+	0.911209i	$0.635150\pi$
$174$		0			0
$175$	21.7082	−	37.5997i	1.64099	−	2.84227i
$176$	2.71605	−	4.70434i	0.204730	−	0.354603i
$177$		0			0
$178$	−12.3090	−	21.3198i	−0.922600	−	1.59799i
$179$	20.7726			1.55262			0.776309	−	0.630352i	$-0.217090\pi$
$179$	20.7726			1.55262			0.776309	+	0.630352i	$0.217090\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	−5.30002	−	9.17990i	−0.392863	−	0.680459i
$183$		0			0
$184$	−5.61803	+	9.73072i	−0.414167	+	0.717358i
$185$	−6.20537	+	10.7480i	−0.456228	+	0.790209i
$186$		0			0
$187$	−6.94427	−	12.0278i	−0.507815	−	0.879562i
$188$	−13.8756			−1.01198
$189$		0			0
$190$	6.94427			0.503790
$191$	11.8512	+	20.5269i	0.857522	+	1.48527i	0.874285	+	0.485413i	$0.161331\pi$
$191$	11.8512	+	20.5269i	0.857522	+	1.48527i	−0.0167625	+	0.999859i	$0.505336\pi$
$192$		0			0
$193$	7.09017	−	12.2805i	0.510362	−	0.883972i	−0.489566	−	0.871966i	$-0.662845\pi$
$193$	7.09017	−	12.2805i	0.510362	−	0.883972i	0.999928	−	0.0120062i	$-0.00382177\pi$
$194$	−21.5459	+	37.3186i	−1.54690	+	2.67932i
$195$		0			0
$196$	−23.5172	−	40.7330i	−1.67980	−	2.90950i
$197$	−14.4352			−1.02846			−0.514231	−	0.857652i	$-0.671923\pi$
$197$	−14.4352			−1.02846			−0.514231	+	0.857652i	$0.671923\pi$
$198$		0			0
$199$	24.8885			1.76430			0.882151	−	0.470967i	$-0.156095\pi$
$199$	24.8885			1.76430			0.882151	+	0.470967i	$0.156095\pi$
$200$	−18.6161	−	32.2440i	−1.31636	−	2.28000i
$201$		0			0
$202$	5.61803	−	9.73072i	0.395283	−	0.684651i
$203$	6.55118	−	11.3470i	0.459803	−	0.796402i
$204$		0			0
$205$	9.09017	+	15.7446i	0.634885	+	1.09965i
$206$	−4.18094			−0.291300
$207$		0			0
$208$	−1.85410			−0.128559
$209$	1.11908	+	1.93830i	0.0774080	+	0.134075i
$210$		0			0
$211$	−8.20820	+	14.2170i	−0.565076	+	0.978740i	0.431967	+	0.901890i	$0.357820\pi$
$211$	−8.20820	+	14.2170i	−0.565076	+	0.978740i	−0.997043	+	0.0768508i	$0.975513\pi$
$212$	−10.6000	+	18.3598i	−0.728013	+	1.26096i
$213$		0			0
$214$	9.09017	+	15.7446i	0.621391	+	1.07628i
$215$	0.905351			0.0617444
$216$		0			0
$217$	−32.3607			−2.19679
$218$	−10.6000	−	18.3598i	−0.717925	−	1.24348i
$219$		0			0
$220$	20.3262	−	35.2061i	1.37039	−	2.37359i
$221$	−2.37024	+	4.10537i	−0.159440	+	0.276157i
$222$		0			0
$223$	7.56231	+	13.0983i	0.506409	+	0.877127i	0.999972	+	0.00741689i	$0.00236089\pi$
$223$	7.56231	+	13.0983i	0.506409	+	0.877127i	−0.493563	+	0.869710i	$0.664306\pi$
$224$	14.6489			0.978770
$225$		0			0
$226$	−18.1803			−1.20934
$227$	−9.02828	−	15.6374i	−0.599228	−	1.03789i	−0.992935	−	0.118658i	$-0.962141\pi$
$227$	−9.02828	−	15.6374i	−0.599228	−	1.03789i	0.393707	−	0.919236i	$-0.371192\pi$
$228$		0			0
$229$	−2.38197	+	4.12569i	−0.157405	+	0.272633i	−0.933932	−	0.357451i	$-0.883646\pi$
$229$	−2.38197	+	4.12569i	−0.157405	+	0.272633i	0.776527	+	0.630084i	$0.216979\pi$
$230$	−13.3161	+	23.0641i	−0.878037	+	1.52080i
$231$		0			0
$232$	−5.61803	−	9.73072i	−0.368842	−	0.638853i
$233$	−20.0810			−1.31555			−0.657775	−	0.753215i	$-0.728502\pi$
$233$	−20.0810			−1.31555			−0.657775	+	0.753215i	$0.728502\pi$
$234$		0			0
$235$	−14.7082			−0.959457
$236$	3.66222	+	6.34315i	0.238390	+	0.412904i
$237$		0			0
$238$	−25.1246	+	43.5171i	−1.62859	+	2.82079i
$239$	7.32444	−	12.6863i	0.473779	−	0.820609i	−0.525771	−	0.850626i	$-0.676223\pi$
$239$	7.32444	−	12.6863i	0.473779	−	0.820609i	0.999549	+	0.0300175i	$0.00955630\pi$
$240$		0			0
$241$	−6.76393	−	11.7155i	−0.435703	−	0.754660i	0.561650	−	0.827375i	$-0.310167\pi$
$241$	−6.76393	−	11.7155i	−0.435703	−	0.754660i	−0.997353	+	0.0727152i	$0.976834\pi$
$242$	−5.72746			−0.368175
$243$		0			0
$244$	37.0344			2.37089
$245$	−24.9283	−	43.1771i	−1.59261	−	2.75849i
$246$		0			0
$247$	0.381966	−	0.661585i	0.0243039	−	0.0420956i
$248$	−13.8756	+	24.0333i	−0.881103	+	1.52611i
$249$		0			0
$250$	−21.3992	−	37.0645i	−1.35340	−	2.34416i
$251$	−23.0108			−1.45243			−0.726213	−	0.687469i	$-0.758722\pi$
$251$	−23.0108			−1.45243			−0.726213	+	0.687469i	$0.758722\pi$
$252$		0			0
$253$	−8.58359			−0.539646
$254$	7.04467	+	12.2017i	0.442022	+	0.765605i
$255$		0			0
$256$	12.9894	−	22.4982i	0.811835	−	1.40614i
$257$	13.8756	−	24.0333i	0.865538	−	1.49915i	−0.000974931	−	1.00000i	$-0.500310\pi$
$257$	13.8756	−	24.0333i	0.865538	−	1.49915i	0.866512	−	0.499155i	$-0.166356\pi$
$258$		0			0
$259$	7.23607	+	12.5332i	0.449627	+	0.778777i
$260$	−13.8756			−0.860530
$261$		0			0
$262$	47.5967			2.94054
$263$	−14.2214	−	24.6322i	−0.876931	−	1.51889i	−0.854691	−	0.519137i	$-0.826253\pi$
$263$	−14.2214	−	24.6322i	−0.876931	−	1.51889i	−0.0222401	−	0.999753i	$-0.507080\pi$
$264$		0			0
$265$	−11.2361	+	19.4614i	−0.690226	+	1.19551i
$266$	4.04885	−	7.01282i	0.248251	−	0.429983i
$267$		0			0
$268$	5.00000	+	8.66025i	0.305424	+	0.529009i
$269$	−5.43210			−0.331201			−0.165601	−	0.986193i	$-0.552956\pi$
$269$	−5.43210			−0.331201			−0.165601	+	0.986193i	$0.552956\pi$
$270$		0			0
$271$	−1.23607			−0.0750858			−0.0375429	−	0.999295i	$-0.511953\pi$
$271$	−1.23607			−0.0750858			−0.0375429	+	0.999295i	$0.511953\pi$
$272$	4.39467	+	7.61178i	0.266466	+	0.461532i
$273$		0			0
$274$	12.5623	−	21.7586i	0.758917	−	1.31448i
$275$	14.2214	−	24.6322i	0.857585	−	1.48538i
$276$		0			0
$277$	−3.50000	−	6.06218i	−0.210295	−	0.364241i	0.741512	−	0.670940i	$-0.234109\pi$
$277$	−3.50000	−	6.06218i	−0.210295	−	0.364241i	−0.951807	+	0.306699i	$0.900776\pi$
$278$	7.53817			0.452109
$279$		0			0
$280$	−65.7771			−3.93093
$281$	9.58782	+	16.6066i	0.571961	+	0.990666i	0.996364	+	0.0851928i	$0.0271506\pi$
$281$	9.58782	+	16.6066i	0.571961	+	0.990666i	−0.424403	+	0.905473i	$0.639516\pi$
$282$		0			0
$283$	−2.20820	+	3.82472i	−0.131264	+	0.227356i	−0.924164	−	0.381996i	$-0.875237\pi$
$283$	−2.20820	+	3.82472i	−0.131264	+	0.227356i	0.792900	+	0.609352i	$0.208570\pi$
$284$	15.5134	−	26.8700i	0.920552	−	1.59444i
$285$		0			0
$286$	−3.47214	−	6.01392i	−0.205312	−	0.355610i
$287$	21.2001			1.25140
$288$		0			0
$289$	5.47214			0.321890
$290$	−13.3161	−	23.0641i	−0.781947	−	1.35437i
$291$		0			0
$292$	18.9443	−	32.8124i	1.10863	−	1.92020i
$293$	−0.559538	+	0.969148i	−0.0326885	+	0.0566182i	−0.881907	−	0.471424i	$-0.843740\pi$
$293$	−0.559538	+	0.969148i	−0.0326885	+	0.0566182i	0.849218	+	0.528042i	$0.177074\pi$
$294$		0			0
$295$	3.88197	+	6.72376i	0.226017	+	0.391473i
$296$	12.4107			0.721359
$297$		0			0
$298$	11.7426			0.680233
$299$	1.46489	+	2.53726i	0.0847167	+	0.146734i
$300$		0			0
$301$	0.527864	−	0.914287i	0.0304256	−	0.0526986i
$302$		0			0
$303$		0			0
$304$	−0.708204	−	1.22665i	−0.0406183	−	0.0703529i
$305$	39.2566			2.24783
$306$		0			0
$307$	−22.9443			−1.30950			−0.654749	−	0.755846i	$-0.727226\pi$
$307$	−22.9443			−1.30950			−0.654749	+	0.755846i	$0.727226\pi$
$308$	−23.7024	−	41.0537i	−1.35057	−	2.33925i
$309$		0			0
$310$	−32.8885	+	56.9646i	−1.86794	+	3.23537i
$311$	7.67026	−	13.2853i	0.434940	−	0.753339i	−0.562350	−	0.826899i	$-0.690103\pi$
$311$	7.67026	−	13.2853i	0.434940	−	0.753339i	0.997291	+	0.0735603i	$0.0234361\pi$
$312$		0			0
$313$	−15.3541	−	26.5941i	−0.867865	−	1.50319i	−0.864174	−	0.503193i	$-0.832158\pi$
$313$	−15.3541	−	26.5941i	−0.867865	−	1.50319i	−0.00369130	−	0.999993i	$-0.501175\pi$
$314$	57.8727			3.26595
$315$		0			0
$316$	−32.3607			−1.82043
$317$	7.11072	+	12.3161i	0.399378	+	0.691742i	0.993649	−	0.112522i	$-0.0358929\pi$
$317$	7.11072	+	12.3161i	0.399378	+	0.691742i	−0.594272	+	0.804264i	$0.702560\pi$
$318$		0			0
$319$	4.29180	−	7.43361i	0.240294	−	0.416202i
$320$	21.9986	−	38.1026i	1.22976	−	2.13000i
$321$		0			0
$322$	15.5279	+	26.8950i	0.865334	+	1.49880i
$323$	−3.62140			−0.201500
$324$		0			0
$325$	−9.70820			−0.538514
$326$	−1.11908	−	1.93830i	−0.0619798	−	0.107352i
$327$		0			0
$328$	9.09017	−	15.7446i	0.501921	−	0.869352i
$329$	−8.57561	+	14.8534i	−0.472788	+	0.818894i
$330$		0			0
$331$	13.4721	+	23.3344i	0.740496	+	1.28258i	0.952270	+	0.305257i	$0.0987425\pi$
$331$	13.4721	+	23.3344i	0.740496	+	1.28258i	−0.211774	+	0.977319i	$0.567924\pi$
$332$	3.27559			0.179771
$333$		0			0
$334$	10.7295			0.587092
$335$	5.30002	+	9.17990i	0.289571	+	0.501551i
$336$		0			0
$337$	−3.82624	+	6.62724i	−0.208428	+	0.361009i	−0.951220	−	0.308514i	$-0.900168\pi$
$337$	−3.82624	+	6.62724i	−0.208428	+	0.361009i	0.742791	+	0.669523i	$0.233502\pi$
$338$	−1.18512	+	2.05269i	−0.0644620	+	0.111651i
$339$		0			0
$340$	32.8885	+	56.9646i	1.78363	+	3.08934i
$341$	−21.2001			−1.14805
$342$		0			0
$343$	−26.8328			−1.44884
$344$	−0.452675	−	0.784057i	−0.0244066	−	0.0422735i
$345$		0			0
$346$	18.1803	−	31.4893i	0.977381	−	1.69287i
$347$	−13.8756	+	24.0333i	−0.744882	+	1.29017i	0.205367	+	0.978685i	$0.434161\pi$
$347$	−13.8756	+	24.0333i	−0.744882	+	1.29017i	−0.950250	+	0.311489i	$0.899172\pi$
$348$		0			0
$349$	−0.0901699	−	0.156179i	−0.00482669	−	0.00836007i	0.863602	−	0.504174i	$-0.168203\pi$
$349$	−0.0901699	−	0.156179i	−0.00482669	−	0.00836007i	−0.868429	+	0.495814i	$0.834870\pi$
$350$	−102.907			−5.50063
$351$		0			0
$352$	9.59675			0.511508
$353$	14.3283	+	24.8173i	0.762618	+	1.32089i	0.941497	+	0.337022i	$0.109420\pi$
$353$	14.3283	+	24.8173i	0.762618	+	1.32089i	−0.178878	+	0.983871i	$0.557247\pi$
$354$		0			0
$355$	16.4443	−	28.4823i	0.872771	−	1.51168i
$356$	−18.7890	+	32.5435i	−0.995815	+	1.72480i
$357$		0			0
$358$	−24.6180	−	42.6397i	−1.30110	−	2.25358i
$359$	25.7268			1.35781			0.678905	−	0.734226i	$-0.262455\pi$
$359$	25.7268			1.35781			0.678905	+	0.734226i	$0.262455\pi$
$360$		0			0
$361$	−18.4164			−0.969285
$362$	8.29584	+	14.3688i	0.436020	+	0.755208i
$363$		0			0
$364$	−8.09017	+	14.0126i	−0.424040	+	0.734459i
$365$	20.0810	−	34.7813i	1.05109	−	1.82054i
$366$		0			0
$367$	−3.70820	−	6.42280i	−0.193567	−	0.335267i	0.752863	−	0.658177i	$-0.228672\pi$
$367$	−3.70820	−	6.42280i	−0.193567	−	0.335267i	−0.946430	+	0.322910i	$0.895339\pi$
$368$	5.43210			0.283168
$369$		0			0
$370$	29.4164			1.52929
$371$	13.1024	+	22.6940i	0.680241	+	1.17821i
$372$		0			0
$373$	4.35410	−	7.54153i	0.225447	−	0.390485i	−0.731007	−	0.682370i	$-0.760949\pi$
$373$	4.35410	−	7.54153i	0.225447	−	0.390485i	0.956453	+	0.291885i	$0.0942825\pi$
$374$	−16.4596	+	28.5088i	−0.851105	+	1.47416i
$375$		0			0
$376$	7.35410	+	12.7377i	0.379259	+	0.656896i
$377$	−2.92978			−0.150891
$378$		0			0
$379$	10.0000			0.513665			0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000			0.513665			0.256833	+	0.966456i	$0.417321\pi$
$380$	−5.30002	−	9.17990i	−0.271885	−	0.470919i
$381$		0			0
$382$	28.0902	−	48.6536i	1.43722	−	2.48933i
$383$	12.7565	−	22.0950i	0.651829	−	1.12900i	−0.330850	−	0.943684i	$-0.607335\pi$
$383$	12.7565	−	22.0950i	0.651829	−	1.12900i	0.982679	−	0.185318i	$-0.0593314\pi$
$384$		0			0
$385$	−25.1246	−	43.5171i	−1.28047	−	2.21784i
$386$	−33.6108			−1.71074
$387$		0			0
$388$	65.7771			3.33933
$389$	5.64583	+	9.77886i	0.286255	+	0.495808i	0.972913	−	0.231173i	$-0.0742562\pi$
$389$	5.64583	+	9.77886i	0.286255	+	0.495808i	−0.686658	+	0.726981i	$0.740923\pi$
$390$		0			0
$391$	6.94427	−	12.0278i	0.351187	−	0.608274i
$392$	−24.9283	+	43.1771i	−1.25907	+	2.18077i
$393$		0			0
$394$	17.1074	+	29.6309i	0.861858	+	1.49278i
$395$	−34.3024			−1.72594
$396$		0			0
$397$	−0.291796			−0.0146448			−0.00732241	−	0.999973i	$-0.502331\pi$
$397$	−0.291796			−0.0146448			−0.00732241	+	0.999973i	$0.502331\pi$
$398$	−29.4959	−	51.0884i	−1.47850	−	2.56083i
$399$		0			0
$400$	−9.00000	+	15.5885i	−0.450000	+	0.779423i
$401$	−6.31223	+	10.9331i	−0.315218	+	0.545973i	−0.979484	−	0.201523i	$-0.935411\pi$
$401$	−6.31223	+	10.9331i	−0.315218	+	0.545973i	0.664266	+	0.747496i	$0.268744\pi$
$402$		0			0
$403$	3.61803	+	6.26662i	0.180227	+	0.312163i
$404$	−17.1512			−0.853305
$405$		0			0
$406$	−31.0557			−1.54127
$407$	4.74048	+	8.21075i	0.234977	+	0.406992i
$408$		0			0
$409$	−10.8541	+	18.7999i	−0.536701	+	0.929593i	0.462378	+	0.886683i	$0.346996\pi$
$409$	−10.8541	+	18.7999i	−0.536701	+	0.929593i	−0.999079	+	0.0429102i	$0.986337\pi$
$410$	21.5459	−	37.3186i	1.06408	−	1.84303i
$411$		0			0
$412$	3.19098	+	5.52694i	0.157208	+	0.272293i
$413$	9.05351			0.445494
$414$		0			0
$415$	3.47214			0.170440
$416$	−1.63780	−	2.83674i	−0.0802995	−	0.139083i
$417$		0			0
$418$	2.65248	−	4.59422i	0.129737	−	0.224711i
$419$	−8.92142	+	15.4524i	−0.435840	+	0.754897i	−0.997364	−	0.0725637i	$-0.976882\pi$
$419$	−8.92142	+	15.4524i	−0.435840	+	0.754897i	0.561524	+	0.827461i	$0.310215\pi$
$420$		0			0
$421$	19.5066	+	33.7864i	0.950692	+	1.64665i	0.743931	+	0.668256i	$0.232959\pi$
$421$	19.5066	+	33.7864i	0.950692	+	1.64665i	0.206761	+	0.978391i	$0.433708\pi$
$422$	38.9108			1.89415
$423$		0			0
$424$	22.4721			1.09134
$425$	23.0108	+	39.8558i	1.11619	+	1.93329i
$426$		0			0
$427$	22.8885	−	39.6441i	1.10765	−	1.91851i
$428$	13.8756	−	24.0333i	0.670704	−	1.16169i
$429$		0			0
$430$	−1.07295	−	1.85840i	−0.0517422	−	0.0896201i
$431$	13.3161			0.641413			0.320707	−	0.947179i	$-0.396080\pi$
$431$	13.3161			0.641413			0.320707	+	0.947179i	$0.396080\pi$
$432$		0			0
$433$	24.4721			1.17606			0.588028	−	0.808841i	$-0.299905\pi$
$433$	24.4721			1.17606			0.588028	+	0.808841i	$0.299905\pi$
$434$	38.3513	+	66.4264i	1.84092	+	3.18857i
$435$		0			0
$436$	−16.1803	+	28.0252i	−0.774898	+	1.34216i
$437$	−1.11908	+	1.93830i	−0.0535326	+	0.0927212i
$438$		0			0
$439$	−12.3541	−	21.3979i	−0.589629	−	1.02127i	−0.994281	−	0.106797i	$-0.965941\pi$
$439$	−12.3541	−	21.3979i	−0.589629	−	1.02127i	0.404652	−	0.914471i	$-0.367393\pi$
$440$	−43.0918			−2.05432
$441$		0			0
$442$	11.2361			0.534445
$443$	−1.46489	−	2.53726i	−0.0695989	−	0.120549i	0.829126	−	0.559062i	$-0.188839\pi$
$443$	−1.46489	−	2.53726i	−0.0695989	−	0.120549i	−0.898725	+	0.438513i	$0.855505\pi$
$444$		0			0
$445$	−19.9164	+	34.4962i	−0.944128	+	1.63528i
$446$	17.9245	−	31.0461i	0.848748	−	1.47008i
$447$		0			0
$448$	−25.6525	−	44.4314i	−1.21197	−	2.09919i
$449$	3.83513			0.180991			0.0904954	−	0.995897i	$-0.471155\pi$
$449$	3.83513			0.180991			0.0904954	+	0.995897i	$0.471155\pi$
$450$		0			0
$451$	13.8885			0.653986
$452$	13.8756	+	24.0333i	0.652654	+	1.13043i
$453$		0			0
$454$	−21.3992	+	37.0645i	−1.00431	+	1.73952i
$455$	−8.57561	+	14.8534i	−0.402031	+	0.696337i
$456$		0			0
$457$	3.67376	+	6.36314i	0.171851	+	0.297655i	0.939067	−	0.343734i	$-0.111692\pi$
$457$	3.67376	+	6.36314i	0.171851	+	0.297655i	−0.767216	+	0.641389i	$0.778358\pi$
$458$	11.2917			0.527625
$459$		0			0
$460$	40.6525			1.89543
$461$	−17.6039	−	30.4908i	−0.819895	−	1.42010i	−0.905759	−	0.423793i	$-0.860699\pi$
$461$	−17.6039	−	30.4908i	−0.819895	−	1.42010i	0.0858645	−	0.996307i	$-0.472635\pi$
$462$		0			0
$463$	0.145898	−	0.252703i	0.00678046	−	0.0117441i	−0.862615	−	0.505861i	$-0.831175\pi$
$463$	0.145898	−	0.252703i	0.00678046	−	0.0117441i	0.869396	+	0.494116i	$0.164508\pi$
$464$	−2.71605	+	4.70434i	−0.126090	+	0.218394i
$465$		0			0
$466$	23.7984	+	41.2200i	1.10244	+	1.90948i
$467$	37.6596			1.74268			0.871340	−	0.490679i	$-0.163251\pi$
$467$	37.6596			1.74268			0.871340	+	0.490679i	$0.163251\pi$
$468$		0			0
$469$	12.3607			0.570763
$470$	17.4310	+	30.1913i	0.804031	+	1.39262i
$471$		0			0
$472$	3.88197	−	6.72376i	0.178682	−	0.309486i
$473$	0.345813	−	0.598966i	0.0159005	−	0.0275405i
$474$		0			0
$475$	−3.70820	−	6.42280i	−0.170144	−	0.294698i
$476$	76.7026			3.51566
$477$		0			0
$478$	−34.7214			−1.58812
$479$	16.3527	+	28.3237i	0.747175	+	1.29415i	0.949172	+	0.314759i	$0.101924\pi$
$479$	16.3527	+	28.3237i	0.747175	+	1.29415i	−0.201997	+	0.979386i	$0.564743\pi$
$480$		0			0
$481$	1.61803	−	2.80252i	0.0737760	−	0.127784i
$482$	−16.0321	+	27.7685i	−0.730244	+	1.26482i
$483$		0			0
$484$	4.37132	+	7.57135i	0.198696	+	0.344152i
$485$	69.7239			3.16600
$486$		0			0
$487$	16.4721			0.746424			0.373212	−	0.927746i	$-0.378256\pi$
$487$	16.4721			0.746424			0.373212	+	0.927746i	$0.378256\pi$
$488$	−19.6283	−	33.9972i	−0.888532	−	1.53898i
$489$		0			0
$490$	−59.0861	+	102.340i	−2.66924	+	4.62326i
$491$	−20.6405	+	35.7504i	−0.931494	+	1.61339i	−0.150724	+	0.988576i	$0.548161\pi$
$491$	−20.6405	+	35.7504i	−0.931494	+	1.61339i	−0.780770	+	0.624819i	$0.785173\pi$
$492$		0			0
$493$	6.94427	+	12.0278i	0.312754	+	0.541706i
$494$	−1.81070			−0.0814673
$495$		0			0
$496$	13.4164			0.602414
$497$	−19.1756	−	33.2132i	−0.860145	−	1.48981i
$498$		0			0
$499$	2.18034	−	3.77646i	0.0976054	−	0.169058i	−0.813088	−	0.582141i	$-0.802215\pi$
$499$	2.18034	−	3.77646i	0.0976054	−	0.169058i	0.910693	+	0.413084i	$0.135548\pi$
$500$	−32.6646	+	56.5768i	−1.46081	+	2.53019i
$501$		0			0
$502$	27.2705	+	47.2339i	1.21714	+	2.10815i
$503$	−10.6000			−0.472632			−0.236316	−	0.971676i	$-0.575940\pi$
$503$	−10.6000			−0.472632			−0.236316	+	0.971676i	$0.575940\pi$
$504$		0			0
$505$	−18.1803			−0.809015
$506$	10.1726	+	17.6194i	0.452226	+	0.783279i
$507$		0			0
$508$	10.7533	−	18.6252i	0.477100	−	0.826362i
$509$	6.09850	−	10.5629i	0.270311	−	0.468193i	−0.698630	−	0.715483i	$-0.746207\pi$
$509$	6.09850	−	10.5629i	0.270311	−	0.468193i	0.968942	+	0.247290i	$0.0795400\pi$
$510$		0			0
$511$	−23.4164	−	40.5584i	−1.03588	−	1.79420i
$512$	−20.2947			−0.896908
$513$		0			0
$514$	−65.7771			−2.90130
$515$	3.38245	+	5.85858i	0.149049	+	0.258160i
$516$		0			0
$517$	−5.61803	+	9.73072i	−0.247081	+	0.427957i
$518$	17.1512	−	29.7068i	0.753581	−	1.30524i
$519$		0			0
$520$	7.35410	+	12.7377i	0.322499	+	0.558584i
$521$	−6.97863			−0.305739			−0.152870	−	0.988246i	$-0.548851\pi$
$521$	−6.97863			−0.305739			−0.152870	+	0.988246i	$0.548851\pi$
$522$		0			0
$523$	−7.65248			−0.334619			−0.167310	−	0.985904i	$-0.553508\pi$
$523$	−7.65248			−0.334619			−0.167310	+	0.985904i	$0.553508\pi$
$524$	−36.3269	−	62.9200i	−1.58695	−	2.74867i
$525$		0			0
$526$	−33.7082	+	58.3843i	−1.46975	+	2.54568i
$527$	17.1512	−	29.7068i	0.747119	−	1.29405i
$528$		0			0
$529$	7.20820	+	12.4850i	0.313400	+	0.542825i
$530$	53.2643			2.31366
$531$		0			0
$532$	−12.3607			−0.535903
$533$	−2.37024	−	4.10537i	−0.102666	−	0.177824i
$534$		0			0
$535$	14.7082	−	25.4754i	0.635891	−	1.10140i
$536$	5.30002	−	9.17990i	0.228926	−	0.396511i
$537$		0			0
$538$	6.43769	+	11.1504i	0.277549	+	0.480728i
$539$	−38.0871			−1.64053
$540$		0			0
$541$	−23.7082			−1.01930			−0.509648	−	0.860383i	$-0.670224\pi$
$541$	−23.7082			−1.01930			−0.509648	+	0.860383i	$0.670224\pi$
$542$	1.46489	+	2.53726i	0.0629223	+	0.108985i
$543$		0			0
$544$	−7.76393	+	13.4475i	−0.332876	+	0.576558i
$545$	−17.1512	+	29.7068i	−0.734677	+	1.27250i
$546$		0			0
$547$	12.6525	+	21.9147i	0.540981	+	0.937006i	0.998848	+	0.0479856i	$0.0152802\pi$
$547$	12.6525	+	21.9147i	0.540981	+	0.937006i	−0.457867	+	0.889021i	$0.651386\pi$
$548$	−38.3513			−1.63829
$549$		0			0
$550$	−67.4164			−2.87465
$551$	−1.11908	−	1.93830i	−0.0476742	−	0.0825741i
$552$		0			0
$553$	−20.0000	+	34.6410i	−0.850487	+	1.47309i
$554$	−8.29584	+	14.3688i	−0.352456	+	0.610472i
$555$		0			0
$556$	−5.75329	−	9.96499i	−0.243994	−	0.422610i
$557$	−16.4596			−0.697415			−0.348708	−	0.937232i	$-0.613379\pi$
$557$	−16.4596			−0.697415			−0.348708	+	0.937232i	$0.613379\pi$
$558$		0			0
$559$	−0.236068			−0.00998461
$560$	15.9000	+	27.5397i	0.671900	+	1.16376i
$561$		0			0
$562$	22.7254	−	39.3616i	0.958614	−	1.66037i
$563$	−1.25116	+	2.16708i	−0.0527303	+	0.0913315i	−0.891186	−	0.453639i	$-0.850126\pi$
$563$	−1.25116	+	2.16708i	−0.0527303	+	0.0913315i	0.838455	+	0.544970i	$0.183459\pi$
$564$		0			0
$565$	14.7082	+	25.4754i	0.618779	+	1.07176i
$566$	10.4679			0.440000
$567$		0			0
$568$	−32.8885			−1.37997
$569$	−2.92978	−	5.07452i	−0.122823	−	0.212735i	0.798057	−	0.602582i	$-0.205861\pi$
$569$	−2.92978	−	5.07452i	−0.122823	−	0.212735i	−0.920880	+	0.389847i	$0.872528\pi$
$570$		0			0
$571$	−3.50000	+	6.06218i	−0.146470	+	0.253694i	−0.929921	−	0.367760i	$-0.880125\pi$
$571$	−3.50000	+	6.06218i	−0.146470	+	0.253694i	0.783450	+	0.621455i	$0.213458\pi$
$572$	−5.30002	+	9.17990i	−0.221605	+	0.383831i
$573$		0			0
$574$	−25.1246	−	43.5171i	−1.04868	−	1.81637i
$575$	28.4429			1.18615
$576$		0			0
$577$	21.4164			0.891577			0.445788	−	0.895138i	$-0.352923\pi$
$577$	21.4164			0.891577			0.445788	+	0.895138i	$0.352923\pi$
$578$	−6.48514	−	11.2326i	−0.269746	−	0.467214i
$579$		0			0
$580$	−20.3262	+	35.2061i	−0.844001	+	1.46185i
$581$	2.02443	−	3.50641i	0.0839873	−	0.145470i
$582$		0			0
$583$	8.58359	+	14.8672i	0.355496	+	0.615737i
$584$	−40.1620			−1.66191
$585$		0			0
$586$	2.65248			0.109573
$587$	4.39467	+	7.61178i	0.181387	+	0.314172i	0.942353	−	0.334620i	$-0.108608\pi$
$587$	4.39467	+	7.61178i	0.181387	+	0.314172i	−0.760966	+	0.648792i	$0.775275\pi$
$588$		0			0
$589$	−2.76393	+	4.78727i	−0.113886	+	0.197256i
$590$	9.20119	−	15.9369i	0.378807	−	0.656113i
$591$		0			0
$592$	−3.00000	−	5.19615i	−0.123299	−	0.213561i
$593$	14.2214			0.584004			0.292002	−	0.956418i	$-0.405679\pi$
$593$	14.2214			0.584004			0.292002	+	0.956418i	$0.405679\pi$
$594$		0			0
$595$	81.3050			3.33318
$596$	−8.96224	−	15.5230i	−0.367108	−	0.635849i
$597$		0			0
$598$	3.47214	−	6.01392i	0.141986	−	0.245927i
$599$	−0.559538	+	0.969148i	−0.0228621	+	0.0395983i	−0.877230	−	0.480070i	$-0.840611\pi$
$599$	−0.559538	+	0.969148i	−0.0228621	+	0.0395983i	0.854368	+	0.519668i	$0.173945\pi$
$600$		0			0
$601$	1.29837	+	2.24885i	0.0529618	+	0.0917325i	0.891291	−	0.453432i	$-0.149801\pi$
$601$	1.29837	+	2.24885i	0.0529618	+	0.0917325i	−0.838329	+	0.545165i	$0.816467\pi$
$602$	−2.50233			−0.101987
$603$		0			0
$604$		0			0
$605$	4.63362	+	8.02566i	0.188383	+	0.326289i
$606$		0			0
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	−0.935713	−	0.352763i	$-0.885242\pi$
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	0.773358	+	0.633970i	$0.218576\pi$
$608$	1.25116	−	2.16708i	0.0507414	−	0.0878867i
$609$		0			0
$610$	−46.5238	−	80.5816i	−1.88369	−	3.26265i
$611$	3.83513			0.155153
$612$		0			0
$613$	−3.05573			−0.123420			−0.0617098	−	0.998094i	$-0.519655\pi$
$613$	−3.05573			−0.123420			−0.0617098	+	0.998094i	$0.519655\pi$
$614$	27.1917	+	47.0974i	1.09737	+	1.90070i
$615$		0			0
$616$	−25.1246	+	43.5171i	−1.01230	+	1.75335i
$617$	15.4474	−	26.7556i	0.621888	−	1.07714i	−0.367246	−	0.930124i	$-0.619699\pi$
$617$	15.4474	−	26.7556i	0.621888	−	1.07714i	0.989134	−	0.147017i	$-0.0469674\pi$
$618$		0			0
$619$	22.6525	+	39.2352i	0.910480	+	1.57700i	0.813388	+	0.581722i	$0.197621\pi$
$619$	22.6525	+	39.2352i	0.910480	+	1.57700i	0.0970922	+	0.995275i	$0.469046\pi$
$620$	100.405			4.03236
$621$		0			0
$622$	−36.3607			−1.45793
$623$	23.2245	+	40.2260i	0.930470	+	1.61162i
$624$		0			0
$625$	−10.3541	+	17.9338i	−0.414164	+	0.717353i
$626$	−36.3929	+	63.0343i	−1.45455	+	2.51936i
$627$		0			0
$628$	−44.1697	−	76.5042i	−1.76256	−	3.05285i
$629$	−15.3405			−0.611666
$630$		0			0
$631$	19.3050			0.768518			0.384259	−	0.923225i	$-0.374457\pi$
$631$	19.3050			0.768518			0.384259	+	0.923225i	$0.374457\pi$
$632$	17.1512	+	29.7068i	0.682239	+	1.18167i
$633$		0			0
$634$	16.8541	−	29.1922i	0.669362	−	1.15937i
$635$	11.3985	−	19.7428i	0.452336	−	0.783470i
$636$		0			0
$637$	6.50000	+	11.2583i	0.257539	+	0.446071i
$638$	−20.3452			−0.805473
$639$		0			0
$640$	−79.1591			−3.12904
$641$	−16.8054	−	29.1078i	−0.663773	−	1.14969i	−0.979616	−	0.200878i	$-0.935621\pi$
$641$	−16.8054	−	29.1078i	−0.663773	−	1.14969i	0.315843	−	0.948811i	$-0.397713\pi$
$642$		0			0
$643$	−8.90983	+	15.4323i	−0.351369	+	0.608590i	−0.986490	−	0.163824i	$-0.947617\pi$
$643$	−8.90983	+	15.4323i	−0.351369	+	0.608590i	0.635120	+	0.772413i	$0.280951\pi$
$644$	23.7024	−	41.0537i	0.934005	−	1.61774i
$645$		0			0
$646$	4.29180	+	7.43361i	0.168858	+	0.292471i
$647$	25.2489			0.992637			0.496319	−	0.868140i	$-0.334685\pi$
$647$	25.2489			0.992637			0.496319	+	0.868140i	$0.334685\pi$
$648$		0			0
$649$	5.93112			0.232817
$650$	11.5054	+	19.9279i	0.451278	+	0.781637i
$651$		0			0
$652$	−1.70820	+	2.95870i	−0.0668984	+	0.115871i
$653$	12.4107	−	21.4960i	0.485670	−	0.841204i	−0.514195	−	0.857673i	$-0.671909\pi$
$653$	12.4107	−	21.4960i	0.485670	−	0.841204i	0.999864	+	0.0164691i	$0.00524251\pi$
$654$		0			0
$655$	−38.5066	−	66.6953i	−1.50458	−	2.60600i
$656$	−8.78933			−0.343166
$657$		0			0
$658$	40.6525			1.58480
$659$	−4.95420	−	8.58093i	−0.192988	−	0.334266i	0.753251	−	0.657733i	$-0.228485\pi$
$659$	−4.95420	−	8.58093i	−0.192988	−	0.334266i	−0.946239	+	0.323468i	$0.895151\pi$
$660$		0			0
$661$	−1.85410	+	3.21140i	−0.0721162	+	0.124909i	−0.899829	−	0.436244i	$-0.856309\pi$
$661$	−1.85410	+	3.21140i	−0.0721162	+	0.124909i	0.827712	+	0.561153i	$0.189642\pi$
$662$	31.9322	−	55.3082i	1.24108	−	2.14961i
$663$		0			0
$664$	−1.73607	−	3.00696i	−0.0673725	−	0.116693i
$665$	−13.1024			−0.508088
$666$		0			0
$667$	8.58359			0.332358
$668$	−8.18898	−	14.1837i	−0.316841	−	0.548785i
$669$		0			0
$670$	12.5623	−	21.7586i	0.485324	−	0.840606i
$671$	14.9947	−	25.9716i	0.578864	−	1.00262i
$672$		0			0
$673$	2.97214	+	5.14789i	0.114567	+	0.198437i	0.917607	−	0.397489i	$-0.130118\pi$
$673$	2.97214	+	5.14789i	0.114567	+	0.198437i	−0.803039	+	0.595926i	$0.796785\pi$
$674$	18.1382			0.698657
$675$		0			0
$676$	3.61803			0.139155
$677$	−11.8512	−	20.5269i	−0.455478	−	0.788912i	0.543237	−	0.839579i	$-0.317198\pi$
$677$	−11.8512	−	20.5269i	−0.455478	−	0.788912i	−0.998716	+	0.0506675i	$0.983865\pi$
$678$		0			0
$679$	40.6525	−	70.4122i	1.56010	−	2.70217i
$680$	34.8620	−	60.3827i	1.33690	−	2.31557i
$681$		0			0
$682$	25.1246	+	43.5171i	0.962071	+	1.66636i
$683$	19.8673			0.760200			0.380100	−	0.924945i	$-0.375890\pi$
$683$	19.8673			0.760200			0.380100	+	0.924945i	$0.375890\pi$
$684$		0			0
$685$	−40.6525			−1.55325
$686$	31.8001	+	55.0794i	1.21413	+	2.10294i
$687$		0			0
$688$	−0.218847	+	0.379054i	−0.00834347	+	0.0144513i
$689$	2.92978	−	5.07452i	0.111616	−	0.193324i
$690$		0			0
$691$	5.90983	+	10.2361i	0.224821	+	0.389401i	0.956266	−	0.292500i	$-0.0944871\pi$
$691$	5.90983	+	10.2361i	0.224821	+	0.389401i	−0.731445	+	0.681900i	$0.761154\pi$
$692$	−55.5025			−2.10989
$693$		0			0
$694$	65.7771			2.49686
$695$	−6.09850	−	10.5629i	−0.231329	−	0.400674i
$696$		0			0
$697$	−11.2361	+	19.4614i	−0.425596	+	0.737155i
$698$	−0.213724	+	0.370181i	−0.00808959	+	0.0140116i
$699$		0			0
$700$	78.5410	+	136.037i	2.96857	+	5.14172i
$701$	−8.36188			−0.315824			−0.157912	−	0.987453i	$-0.550476\pi$
$701$	−8.36188			−0.315824			−0.157912	+	0.987453i	$0.550476\pi$
$702$		0			0
$703$	2.47214			0.0932384
$704$	−16.8054	−	29.1078i	−0.633377	−	1.09704i
$705$		0			0
$706$	33.9615	−	58.8230i	1.27816	−	2.21383i
$707$	−10.6000	+	18.3598i	−0.398655	+	0.690491i
$708$		0			0
$709$	25.7984	+	44.6841i	0.968878	+	1.67815i	0.698813	+	0.715304i	$0.253712\pi$
$709$	25.7984	+	44.6841i	0.968878	+	1.67815i	0.270065	+	0.962842i	$0.412955\pi$
$710$	−77.9537			−2.92555
$711$		0			0
$712$	39.8328			1.49280
$713$	−10.6000	−	18.3598i	−0.396974	−	0.687580i
$714$		0			0
$715$	−5.61803	+	9.73072i	−0.210103	+	0.363908i
$716$	−37.5780	+	65.0870i	−1.40436	+	2.43242i
$717$		0			0
$718$	−30.4894	−	52.8091i	−1.13785	−	1.97082i
$719$	−8.36188			−0.311846			−0.155923	−	0.987769i	$-0.549835\pi$
$719$	−8.36188			−0.311846			−0.155923	+	0.987769i	$0.549835\pi$
$720$		0			0
$721$	7.88854			0.293785
$722$	21.8256	+	37.8031i	0.812266	+	1.40689i
$723$		0			0
$724$	12.6631	−	21.9332i	0.470621	−	0.815140i
$725$	−14.2214	+	24.6322i	−0.528171	+	0.914819i
$726$		0			0
$727$	0.472136	+	0.817763i	0.0175106	+	0.0303292i	0.874648	−	0.484759i	$-0.161093\pi$
$727$	0.472136	+	0.817763i	0.0175106	+	0.0303292i	−0.857137	+	0.515088i	$0.827759\pi$
$728$	17.1512			0.635666
$729$		0			0
$730$	−95.1935			−3.52327
$731$	0.559538	+	0.969148i	0.0206952	+	0.0358452i
$732$		0			0
$733$	7.38197	−	12.7859i	0.272659	−	0.472259i	−0.696883	−	0.717185i	$-0.745430\pi$
$733$	7.38197	−	12.7859i	0.272659	−	0.472259i	0.969542	+	0.244926i	$0.0787635\pi$
$734$	−8.78933	+	15.2236i	−0.324420	+	0.561912i
$735$		0			0
$736$	4.79837	+	8.31103i	0.176870	+	0.306349i
$737$	8.09770			0.298283
$738$		0			0
$739$	8.11146			0.298385			0.149192	−	0.988808i	$-0.452333\pi$
$739$	8.11146			0.298385			0.149192	+	0.988808i	$0.452333\pi$
$740$	−22.4512	−	38.8867i	−0.825324	−	1.42950i
$741$		0			0
$742$	31.0557	−	53.7901i	1.14009	−	1.97470i
$743$	18.5092	−	32.0589i	0.679038	−	1.17613i	−0.296233	−	0.955116i	$-0.595730\pi$
$743$	18.5092	−	32.0589i	0.679038	−	1.17613i	0.975271	−	0.221013i	$-0.0709362\pi$
$744$		0			0
$745$	−9.50000	−	16.4545i	−0.348053	−	0.602846i
$746$	−20.6405			−0.755703
$747$		0			0
$748$	50.2492			1.83729
$749$	−17.1512	−	29.7068i	−0.626692	−	1.08546i
$750$		0			0
$751$	−21.4164	+	37.0943i	−0.781496	+	1.35359i	0.149574	+	0.988750i	$0.452210\pi$
$751$	−21.4164	+	37.0943i	−0.781496	+	1.35359i	−0.931070	+	0.364840i	$0.881124\pi$
$752$	3.55536	−	6.15806i	0.129651	−	0.224561i
$753$		0			0
$754$	3.47214	+	6.01392i	0.126448	+	0.219014i
$755$		0			0
$756$		0			0
$757$	1.41641			0.0514802			0.0257401	−	0.999669i	$-0.491806\pi$
$757$	1.41641			0.0514802			0.0257401	+	0.999669i	$0.491806\pi$
$758$	−11.8512	−	20.5269i	−0.430455	−	0.745570i
$759$		0			0
$760$	−5.61803	+	9.73072i	−0.203788	+	0.352970i
$761$	−19.9741	+	34.5962i	−0.724062	+	1.25411i	0.235298	+	0.971923i	$0.424394\pi$
$761$	−19.9741	+	34.5962i	−0.724062	+	1.25411i	−0.959359	+	0.282188i	$0.908940\pi$
$762$		0			0
$763$	20.0000	+	34.6410i	0.724049	+	1.25409i
$764$	−85.7561			−3.10255
$765$		0			0
$766$	−60.4721			−2.18495
$767$	−1.01221	−	1.75320i	−0.0365489	−	0.0633045i
$768$		0			0
$769$	−18.7082	+	32.4036i	−0.674635	+	1.16850i	0.301940	+	0.953327i	$0.402366\pi$
$769$	−18.7082	+	32.4036i	−0.674635	+	1.16850i	−0.976575	+	0.215175i	$0.930968\pi$
$770$	−59.5513	+	103.146i	−2.14608	+	3.71712i
$771$		0			0
$772$	25.6525	+	44.4314i	0.923253	+	1.59912i
$773$	−44.6887			−1.60734			−0.803671	−	0.595074i	$-0.797123\pi$
$773$	−44.6887			−1.60734			−0.803671	+	0.595074i	$0.797123\pi$
$774$		0			0
$775$	70.2492			2.52343
$776$	−34.8620	−	60.3827i	−1.25147	−	2.16761i
$777$		0			0
$778$	13.3820	−	23.1782i	0.479767	−	0.830980i
$779$	1.81070	−	3.13623i	0.0648751	−	0.112367i
$780$		0			0
$781$	−12.5623	−	21.7586i	−0.449515	−	0.778582i
$782$	−32.9192			−1.17719
$783$		0			0
$784$	24.1033			0.860833
$785$	−46.8200	−	81.0947i	−1.67108	−	2.89439i
$786$		0			0
$787$	−0.944272	+	1.63553i	−0.0336597	+	0.0583002i	−0.882365	−	0.470567i	$-0.844050\pi$
$787$	−0.944272	+	1.63553i	−0.0336597	+	0.0583002i	0.848705	+	0.528867i	$0.177383\pi$
$788$	26.1134	−	45.2298i	0.930253	−	1.61125i
$789$		0			0
$790$	40.6525	+	70.4122i	1.44635	+	2.50515i
$791$	34.3024			1.21965
$792$		0			0
$793$	−10.2361			−0.363493
$794$	0.345813	+	0.598966i	0.0122725	+	0.0212565i
$795$		0			0
$796$	−45.0238	+	77.9835i	−1.59583	+	2.76405i
$797$	−18.0566	+	31.2749i	−0.639596	+	1.10781i	0.345925	+	0.938262i	$0.387565\pi$
$797$	−18.0566	+	31.2749i	−0.639596	+	1.10781i	−0.985521	+	0.169551i	$0.945768\pi$
$798$		0			0
$799$	−9.09017	−	15.7446i	−0.321587	−	0.557005i
$800$	−31.8001			−1.12430
$801$		0			0
$802$	29.9230			1.05662
$803$	−15.3405	−	26.5705i	−0.541355	−	0.937654i
$804$		0			0
$805$	25.1246	−	43.5171i	0.885526	−	1.53378i
$806$	8.57561	−	14.8534i	0.302063	−	0.523188i
$807$		0			0
$808$	9.09017	+	15.7446i	0.319791	+	0.553894i
$809$	43.7834			1.53934			0.769671	−	0.638441i	$-0.220420\pi$
$809$	43.7834			1.53934			0.769671	+	0.638441i	$0.220420\pi$
$810$		0			0
$811$	33.5279			1.17732			0.588661	−	0.808380i	$-0.299655\pi$
$811$	33.5279			1.17732			0.588661	+	0.808380i	$0.299655\pi$
$812$	23.7024	+	41.0537i	0.831791	+	1.44070i
$813$		0			0
$814$	11.2361	−	19.4614i	0.393824	−	0.682123i
$815$	−1.81070	+	3.13623i	−0.0634261	+	0.109857i
$816$		0			0
$817$	−0.0901699	−	0.156179i	−0.00315465	−	0.00546401i
$818$	51.4536			1.79903
$819$		0			0
$820$	−65.7771			−2.29704
$821$	11.1596	+	19.3289i	0.389472	+	0.674585i	0.992379	−	0.123227i	$-0.0393243\pi$
$821$	11.1596	+	19.3289i	0.389472	+	0.674585i	−0.602907	+	0.797812i	$0.705991\pi$
$822$		0			0
$823$	3.93769	−	6.82029i	0.137259	−	0.237740i	−0.789199	−	0.614138i	$-0.789504\pi$
$823$	3.93769	−	6.82029i	0.137259	−	0.237740i	0.926458	+	0.376397i	$0.122837\pi$
$824$	3.38245	−	5.85858i	0.117833	−	0.204093i
$825$		0			0
$826$	−10.7295	−	18.5840i	−0.373327	−	0.646621i
$827$	−31.3726			−1.09093			−0.545467	−	0.838132i	$-0.683648\pi$
$827$	−31.3726			−1.09093			−0.545467	+	0.838132i	$0.683648\pi$
$828$		0			0
$829$	11.1803			0.388309			0.194155	−	0.980971i	$-0.437804\pi$
$829$	11.1803			0.388309			0.194155	+	0.980971i	$0.437804\pi$
$830$	−4.11490	−	7.12721i	−0.142830	−	0.247389i
$831$		0			0
$832$	−5.73607	+	9.93516i	−0.198862	+	0.344440i
$833$	30.8131	−	53.3699i	1.06761	−	1.84916i
$834$		0			0
$835$	−8.68034	−	15.0348i	−0.300396	−	0.520300i
$836$	−8.09770			−0.280065
$837$		0			0
$838$	42.2918			1.46095
$839$	−10.8390	−	18.7737i	−0.374203	−	0.648139i	0.616004	−	0.787743i	$-0.288750\pi$
$839$	−10.8390	−	18.7737i	−0.374203	−	0.648139i	−0.990207	+	0.139604i	$0.955417\pi$
$840$		0			0
$841$	10.2082	−	17.6811i	0.352007	−	0.609694i
$842$	46.2353	−	80.0818i	1.59337	−	2.75980i
$843$		0			0
$844$	−29.6976	−	51.4377i	−1.02223	−	1.77056i
$845$	3.83513			0.131932
$846$		0			0
$847$	10.8065			0.371316
$848$	−5.43210	−	9.40868i	−0.186539	−	0.323095i
$849$		0			0
$850$	54.5410	−	94.4678i	1.87074	−	3.24022i
$851$	−4.74048	+	8.21075i	−0.162502	+	0.281461i
$852$		0			0
$853$	4.05573	+	7.02473i	0.138865	+	0.240522i	0.927067	−	0.374895i	$-0.122321\pi$
$853$	4.05573	+	7.02473i	0.138865	+	0.240522i	−0.788202	+	0.615417i	$0.788988\pi$
$854$	−108.503			−3.71288
$855$		0			0
$856$	−29.4164			−1.00543
$857$	6.20537	+	10.7480i	0.211971	+	0.367145i	0.952331	−	0.305065i	$-0.0986783\pi$
$857$	6.20537	+	10.7480i	0.211971	+	0.367145i	−0.740360	+	0.672210i	$0.765345\pi$
$858$		0			0
$859$	−2.18034	+	3.77646i	−0.0743922	+	0.128851i	−0.900822	−	0.434189i	$-0.857035\pi$
$859$	−2.18034	+	3.77646i	−0.0743922	+	0.128851i	0.826430	+	0.563040i	$0.190368\pi$
$860$	−1.63780	+	2.83674i	−0.0558483	+	0.0967322i
$861$		0			0
$862$	−15.7812	−	27.3338i	−0.537508	−	0.930992i
$863$	−16.2459			−0.553016			−0.276508	−	0.961012i	$-0.589177\pi$
$863$	−16.2459			−0.553016			−0.276508	+	0.961012i	$0.589177\pi$
$864$		0			0
$865$	−58.8328			−2.00038
$866$	−29.0024	−	50.2336i	−0.985542	−	1.70701i
$867$		0			0
$868$	58.5410	−	101.396i	1.98701	−	3.44161i
$869$	−13.1024	+	22.6940i	−0.444467	+	0.769840i
$870$		0			0
$871$	−1.38197	−	2.39364i	−0.0468261	−	0.0811052i
$872$	34.3024			1.16163
$873$		0			0
$874$	5.30495			0.179443
$875$	40.3757	+	69.9328i	1.36495	+	2.36416i
$876$		0			0
$877$	−0.180340	+	0.312358i	−0.00608965	+	0.0105476i	−0.869054	−	0.494717i	$-0.835272\pi$
$877$	−0.180340	+	0.312358i	−0.00608965	+	0.0105476i	0.862965	+	0.505265i	$0.168605\pi$
$878$	−29.2822	+	50.7182i	−0.988226	+	1.71166i
$879$		0			0
$880$	10.4164	+	18.0417i	0.351137	+	0.608187i
$881$	−32.0643			−1.08027			−0.540136	−	0.841577i	$-0.681627\pi$
$881$	−32.0643			−1.08027			−0.540136	+	0.841577i	$0.681627\pi$
$882$		0			0
$883$	41.8885			1.40966			0.704831	−	0.709375i	$-0.251023\pi$
$883$	41.8885			1.40966			0.704831	+	0.709375i	$0.251023\pi$
$884$	−8.57561	−	14.8534i	−0.288429	−	0.499573i
$885$		0			0
$886$	−3.47214	+	6.01392i	−0.116649	+	0.202041i
$887$	−11.7191	+	20.2981i	−0.393489	+	0.681543i	−0.992907	−	0.118893i	$-0.962065\pi$
$887$	−11.7191	+	20.2981i	−0.393489	+	0.681543i	0.599418	+	0.800436i	$0.295399\pi$
$888$		0			0
$889$	−13.2918	−	23.0221i	−0.445793	−	0.772135i
$890$	94.4133			3.16474
$891$		0			0
$892$	−54.7214			−1.83221
$893$	1.46489	+	2.53726i	0.0490206	+	0.0849062i
$894$		0			0
$895$	−39.8328	+	68.9925i	−1.33146	+	2.30616i
$896$	−46.1536	+	79.9404i	−1.54188	+	2.67062i
$897$		0			0
$898$	−4.54508	−	7.87232i	−0.151671	−	0.262703i
$899$	21.2001			0.707062
$900$		0			0
$901$	−27.7771			−0.925389
$902$	−16.4596	−	28.5088i	−0.548044	−	0.949240i
$903$		0			0
$904$	14.7082	−	25.4754i	0.489188	−	0.847298i
$905$	13.4229	−	23.2492i	0.446194	−	0.772830i
$906$		0			0
$907$	−19.9164	−	34.4962i	−0.661313	−	1.14543i	−0.980271	−	0.197659i	$-0.936666\pi$
$907$	−19.9164	−	34.4962i	−0.661313	−	1.14543i	0.318957	−	0.947769i	$-0.396667\pi$
$908$	65.3293			2.16803
$909$		0			0
$910$	40.6525			1.34762
$911$	−4.18094	−	7.24160i	−0.138521	−	0.239925i	0.788416	−	0.615142i	$-0.210901\pi$
$911$	−4.18094	−	7.24160i	−0.138521	−	0.239925i	−0.926937	+	0.375217i	$0.877568\pi$
$912$		0			0
$913$	1.32624	−	2.29711i	0.0438921	−	0.0760233i
$914$	8.70769	−	15.0822i	0.288025	−	0.498874i
$915$		0			0
$916$	−8.61803	−	14.9269i	−0.284748	−	0.493198i
$917$	−89.8049			−2.96562
$918$		0			0
$919$	41.3607			1.36436			0.682181	−	0.731183i	$-0.261031\pi$
$919$	41.3607			1.36436			0.682181	+	0.731183i	$0.261031\pi$
$920$	−21.5459	−	37.3186i	−0.710347	−	1.23036i
$921$		0			0
$922$	−41.7254	+	72.2706i	−1.37415	+	2.38010i
$923$	−4.28780	+	7.42669i	−0.141135	+	0.244453i
$924$		0			0
$925$	−15.7082	−	27.2074i	−0.516483	−	0.894574i
$926$	−0.691626			−0.0227283
$927$		0			0
$928$	−9.59675			−0.315029
$929$	−11.1596	−	19.3289i	−0.366134	−	0.634162i	0.622824	−	0.782362i	$-0.285985\pi$
$929$	−11.1596	−	19.3289i	−0.366134	−	0.634162i	−0.988957	+	0.148200i	$0.952652\pi$
$930$		0			0
$931$	−4.96556	+	8.60060i	−0.162740	+	0.281873i
$932$	36.3269	−	62.9200i	1.18993	−	2.06101i
$933$		0			0
$934$	−44.6312	−	77.3035i	−1.46038	−	2.52945i
$935$	53.2643			1.74193
$936$		0			0
$937$	−46.4853			−1.51861			−0.759304	−	0.650736i	$-0.774461\pi$
$937$	−46.4853			−1.51861			−0.759304	+	0.650736i	$0.774461\pi$
$938$	−14.6489	−	25.3726i	−0.478303	−	0.828445i
$939$		0			0
$940$	26.6074	−	46.0854i	0.867837	−	1.50314i
$941$	11.1596	−	19.3289i	0.363792	−	0.630105i	−0.624790	−	0.780793i	$-0.714815\pi$
$941$	11.1596	−	19.3289i	0.363792	−	0.630105i	0.988581	+	0.150687i	$0.0481487\pi$
$942$		0			0
$943$	6.94427	+	12.0278i	0.226137	+	0.391680i
$944$	−3.75349			−0.122166
$945$		0			0
$946$	−1.63932			−0.0532989
$947$	−2.60919	−	4.51925i	−0.0847873	−	0.146856i	0.820513	−	0.571627i	$-0.193688\pi$
$947$	−2.60919	−	4.51925i	−0.0847873	−	0.146856i	−0.905301	+	0.424772i	$0.860354\pi$
$948$		0			0
$949$	−5.23607	+	9.06914i	−0.169970	+	0.294397i
$950$	−8.78933	+	15.2236i	−0.285164	+	0.493918i
$951$		0			0
$952$	−40.6525	−	70.4122i	−1.31755	−	2.28207i
$953$	−0.691626			−0.0224040			−0.0112020	−	0.999937i	$-0.503566\pi$
$953$	−0.691626			−0.0224040			−0.0112020	+	0.999937i	$0.503566\pi$
$954$		0			0
$955$	−90.9017			−2.94151
$956$	26.5001	+	45.8995i	0.857074	+	1.48450i
$957$		0			0
$958$	38.7599	−	67.1341i	1.25227	−	2.16900i
$959$	−23.7024	+	41.0537i	−0.765390	+	1.32569i
$960$		0			0
$961$	−10.6803	−	18.4989i	−0.344527	−	0.596738i
$962$	−7.67026			−0.247299
$963$		0			0
$964$	48.9443			1.57639
$965$	27.1917	+	47.0974i	0.875332	+	1.51612i
$966$		0			0
$967$	−5.38197	+	9.32184i	−0.173072	+	0.299770i	−0.939492	−	0.342569i	$-0.888703\pi$
$967$	−5.38197	+	9.32184i	−0.173072	+	0.299770i	0.766420	+	0.642340i	$0.222036\pi$
$968$	4.63362	−	8.02566i	0.148930	−	0.257954i
$969$		0			0
$970$	−82.6312	−	143.121i	−2.65313	−	4.59535i
$971$	−45.3299			−1.45471			−0.727353	−	0.686264i	$-0.759250\pi$
$971$	−45.3299			−1.45471			−0.727353	+	0.686264i	$0.759250\pi$
$972$		0			0
$973$	−14.2229			−0.455966
$974$	−19.5215	−	33.8121i	−0.625508	−	1.08341i
$975$		0			0
$976$	−9.48936	+	16.4360i	−0.303747	+	0.526105i
$977$	18.1634	−	31.4600i	0.581099	−	1.00649i	−0.414250	−	0.910163i	$-0.635956\pi$
$977$	18.1634	−	31.4600i	0.581099	−	1.00649i	0.995349	−	0.0963306i	$-0.0307106\pi$
$978$		0			0
$979$	15.2148	+	26.3528i	0.486267	+	0.842238i
$980$	180.383			5.76213
$981$		0			0
$982$	97.8460			3.12239
$983$	20.4268	+	35.3803i	0.651514	+	1.12846i	0.982756	+	0.184909i	$0.0591991\pi$
$983$	20.4268	+	35.3803i	0.651514	+	1.12846i	−0.331242	+	0.943546i	$0.607468\pi$
$984$		0			0
$985$	27.6803	−	47.9438i	0.881969	−	1.52762i
$986$	16.4596	−	28.5088i	0.524180	−	0.907906i
$987$		0			0
$988$	1.38197	+	2.39364i	0.0439662	+	0.0761517i
$989$	0.691626			0.0219924
$990$		0			0
$991$	12.3475			0.392232			0.196116	−	0.980581i	$-0.437167\pi$
$991$	12.3475			0.392232			0.196116	+	0.980581i	$0.437167\pi$
$992$	11.8512	+	20.5269i	0.376276	+	0.651729i
$993$		0			0
$994$	−45.4508	+	78.7232i	−1.44161	+	2.49695i
$995$	−47.7254	+	82.6628i	−1.51300	+	2.62059i
$996$		0			0
$997$	7.55573	+	13.0869i	0.239292	+	0.414466i	0.960511	−	0.278241i	$-0.0897512\pi$
$997$	7.55573	+	13.0869i	0.239292	+	0.414466i	−0.721219	+	0.692707i	$0.756418\pi$
$998$	−10.3359			−0.327176
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1053.2.e.p.352.1		8
3.2	odd	2	inner	1053.2.e.p.352.4		8
9.2	odd	6	inner	1053.2.e.p.703.4		8
9.4	even	3		351.2.a.f.1.4	yes	4
9.5	odd	6		351.2.a.f.1.1	✓	4
9.7	even	3	inner	1053.2.e.p.703.1		8
36.23	even	6		5616.2.a.ch.1.1		4
36.31	odd	6		5616.2.a.ch.1.4		4
45.4	even	6		8775.2.a.bo.1.1		4
45.14	odd	6		8775.2.a.bo.1.4		4
117.77	odd	6		4563.2.a.ba.1.4		4
117.103	even	6		4563.2.a.ba.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.a.f.1.1	✓	4	9.5	odd	6
351.2.a.f.1.4	yes	4	9.4	even	3
1053.2.e.p.352.1		8	1.1	even	1	trivial
1053.2.e.p.352.4		8	3.2	odd	2	inner
1053.2.e.p.703.1		8	9.7	even	3	inner
1053.2.e.p.703.4		8	9.2	odd	6	inner
4563.2.a.ba.1.1		4	117.103	even	6
4563.2.a.ba.1.4		4	117.77	odd	6
5616.2.a.ch.1.1		4	36.23	even	6
5616.2.a.ch.1.4		4	36.31	odd	6
8775.2.a.bo.1.1		4	45.4	even	6
8775.2.a.bo.1.4		4	45.14	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1053 = 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1053.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.18512 - 2.05269i) q^{2} +(-1.80902 + 3.13331i) q^{4} +(-1.91756 + 3.32132i) q^{5} +(2.23607 + 3.87298i) q^{7} +3.83513 q^{8} +9.09017 q^{10} +(1.46489 + 2.53726i) q^{11} +(0.500000 - 0.866025i) q^{13} +(5.30002 - 9.17990i) q^{14} +(-0.927051 - 1.60570i) q^{16} -4.74048 q^{17} +0.763932 q^{19} +(-6.93781 - 12.0166i) q^{20} +(3.47214 - 6.01392i) q^{22} +(-1.46489 + 2.53726i) q^{23} +(-4.85410 - 8.40755i) q^{25} -2.37024 q^{26} -16.1803 q^{28} +(-1.46489 - 2.53726i) q^{29} +(-3.61803 + 6.26662i) q^{31} +(1.63780 - 2.83674i) q^{32} +(5.61803 + 9.73072i) q^{34} -17.1512 q^{35} +3.23607 q^{37} +(-0.905351 - 1.56811i) q^{38} +(-7.35410 + 12.7377i) q^{40} +(2.37024 - 4.10537i) q^{41} +(-0.118034 - 0.204441i) q^{43} -10.6000 q^{44} +6.94427 q^{46} +(1.91756 + 3.32132i) q^{47} +(-6.50000 + 11.2583i) q^{49} +(-11.5054 + 19.9279i) q^{50} +(1.80902 + 3.13331i) q^{52} +5.85955 q^{53} -11.2361 q^{55} +(8.57561 + 14.8534i) q^{56} +(-3.47214 + 6.01392i) q^{58} +(1.01221 - 1.75320i) q^{59} +(-5.11803 - 8.86469i) q^{61} +17.1512 q^{62} -11.4721 q^{64} +(1.91756 + 3.32132i) q^{65} +(1.38197 - 2.39364i) q^{67} +(8.57561 - 14.8534i) q^{68} +(20.3262 + 35.2061i) q^{70} -8.57561 q^{71} -10.4721 q^{73} +(-3.83513 - 6.64264i) q^{74} +(-1.38197 + 2.39364i) q^{76} +(-6.55118 + 11.3470i) q^{77} +(4.47214 + 7.74597i) q^{79} +7.11072 q^{80} -11.2361 q^{82} +(-0.452675 - 0.784057i) q^{83} +(9.09017 - 15.7446i) q^{85} +(-0.279769 + 0.484574i) q^{86} +(5.61803 + 9.73072i) q^{88} +10.3863 q^{89} +4.47214 q^{91} +(-5.30002 - 9.17990i) q^{92} +(4.54508 - 7.87232i) q^{94} +(-1.46489 + 2.53726i) q^{95} +(-9.09017 - 15.7446i) q^{97} +30.8131 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{4} + 28 q^{10} + 4 q^{13} + 6 q^{16} + 24 q^{19} - 8 q^{22} - 12 q^{25} - 40 q^{28} - 20 q^{31} + 36 q^{34} + 8 q^{37} - 32 q^{40} + 8 q^{43} - 16 q^{46} - 52 q^{49} + 10 q^{52} - 72 q^{55}+ \cdots - 28 q^{97}+O(q^{100}) \) 8 * q - 10 * q^4 + 28 * q^10 + 4 * q^13 + 6 * q^16 + 24 * q^19 - 8 * q^22 - 12 * q^25 - 40 * q^28 - 20 * q^31 + 36 * q^34 + 8 * q^37 - 32 * q^40 + 8 * q^43 - 16 * q^46 - 52 * q^49 + 10 * q^52 - 72 * q^55 + 8 * q^58 - 32 * q^61 - 56 * q^64 + 20 * q^67 + 100 * q^70 - 48 * q^73 - 20 * q^76 - 72 * q^82 + 28 * q^85 + 36 * q^88 + 14 * q^94 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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