LMFDB - Embedded newform 201.2.p.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(2,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 1]))

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

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

chi := DirichletCharacter("201.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.p (of order $66$, degree $20$, minimal)

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:	no
Analytic conductor:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\Q(\zeta_{33})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 $ x^20 - x^19 + x^17 - x^16 + x^14 - x^13 + x^11 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{66}]$

Embedding invariants

Embedding label			11.1
Root			$0.580057 - 0.814576i$ of defining polynomial
Character	$\chi$	$=$	201.11
Dual form			201.2.p.a.128.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.57553 - 0.719520i) q^{3} +(1.57211 - 1.23632i) q^{4} +(-0.656000 + 3.40365i) q^{7} +(1.96458 - 2.26725i) q^{9} +O(q^{10})$	\(q+(1.57553 - 0.719520i) q^{3} +(1.57211 - 1.23632i) q^{4} +(-0.656000 + 3.40365i) q^{7} +(1.96458 - 2.26725i) q^{9} +(1.58734 - 3.07902i) q^{12} +(-6.41722 + 0.305690i) q^{13} +(0.943036 - 3.88725i) q^{16} +(-0.169149 + 0.0326009i) q^{19} +(1.41545 + 5.83456i) q^{21} +(-4.20627 + 2.70320i) q^{25} +(1.46393 - 4.98567i) q^{27} +(3.17669 + 6.16193i) q^{28} +(10.2699 + 0.489217i) q^{31} +(0.285491 - 5.99320i) q^{36} +(-2.33343 + 4.04162i) q^{37} +(-9.89057 + 5.09894i) q^{39} +(-12.7715 - 1.83627i) q^{43} +(-1.31117 - 6.80300i) q^{48} +(-4.65594 - 1.86396i) q^{49} +(-9.71062 + 8.41430i) q^{52} +(-0.243043 + 0.173070i) q^{57} +(10.6430 + 11.1620i) q^{61} +(6.42816 + 8.17407i) q^{63} +(-3.32332 - 7.27706i) q^{64} +(-6.31701 - 5.20532i) q^{67} +(11.4519 - 10.9194i) q^{73} +(-4.68209 + 7.28547i) q^{75} +(-0.225616 + 0.260375i) q^{76} +(-2.20847 + 4.28384i) q^{79} +(-1.28083 - 8.90839i) q^{81} +(9.43860 + 7.42260i) q^{84} +(3.16924 - 22.0425i) q^{91} +(16.5326 - 6.61865i) q^{93} +(13.0982 + 7.56222i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9}+O(q^{10}) $ 20 * q - 2 * q^4 - 6 * q^7 + 6 * q^9	$ 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9} - 6 q^{12} - 3 q^{13} + 4 q^{16} - 8 q^{19} + 6 q^{21} + 10 q^{25} - 12 q^{28} + 15 q^{31} + 6 q^{36} + 10 q^{37} - 3 q^{39} - 12 q^{48} - 5 q^{49} - 154 q^{52} - 75 q^{57} + 15 q^{61} - 15 q^{63} + 16 q^{64} + 5 q^{67} + 60 q^{73} - 32 q^{76} + 134 q^{79} - 18 q^{81} + 186 q^{84} - 12 q^{91} - 15 q^{93} + 9 q^{97}+O(q^{100}) $ 20 * q - 2 * q^4 - 6 * q^7 + 6 * q^9 - 6 * q^12 - 3 * q^13 + 4 * q^16 - 8 * q^19 + 6 * q^21 + 10 * q^25 - 12 * q^28 + 15 * q^31 + 6 * q^36 + 10 * q^37 - 3 * q^39 - 12 * q^48 - 5 * q^49 - 154 * q^52 - 75 * q^57 + 15 * q^61 - 15 * q^63 + 16 * q^64 + 5 * q^67 + 60 * q^73 - 32 * q^76 + 134 * q^79 - 18 * q^81 + 186 * q^84 - 12 * q^91 - 15 * q^93 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$e\left(\frac{59}{66}\right)$

Coefficient data

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

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

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

$2$		0			0		0.945001	−	0.327068i	$-0.106061\pi$
$2$		0			0		−0.945001	+	0.327068i	$0.893939\pi$
$3$	1.57553	−	0.719520i	0.909632	−	0.415415i
$3$	1.57553	−	0.719520i	0.909632	−	0.415415i
$4$	1.57211	−	1.23632i	0.786053	−	0.618159i
$5$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$5$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$6$		0			0
$7$	−0.656000	+	3.40365i	−0.247945	+	1.28646i	0.617944	+	0.786222i	$0.287966\pi$
$7$	−0.656000	+	3.40365i	−0.247945	+	1.28646i	−0.865888	+	0.500237i	$0.833246\pi$
$8$		0			0
$9$	1.96458	−	2.26725i	0.654861	−	0.755750i
$10$		0			0
$11$		0			0		0.690079	−	0.723734i	$-0.257576\pi$
$11$		0			0		−0.690079	+	0.723734i	$0.742424\pi$
$12$	1.58734	−	3.07902i	0.458227	−	0.888835i
$13$	−6.41722	+	0.305690i	−1.77982	+	0.0847831i	−0.911519	−	0.411259i	$-0.865089\pi$
$13$	−6.41722	+	0.305690i	−1.77982	+	0.0847831i	−0.868299	+	0.496042i	$0.834786\pi$
$14$		0			0
$15$		0			0
$16$	0.943036	−	3.88725i	0.235759	−	0.971812i
$17$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$17$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$18$		0			0
$19$	−0.169149	+	0.0326009i	−0.0388055	+	0.00747916i	−0.208617	−	0.977997i	$-0.566896\pi$
$19$	−0.169149	+	0.0326009i	−0.0388055	+	0.00747916i	0.169812	+	0.985477i	$0.445684\pi$
$20$		0			0
$21$	1.41545	+	5.83456i	0.308876	+	1.27320i
$22$		0			0
$23$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$23$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$24$		0			0
$25$	−4.20627	+	2.70320i	−0.841254	+	0.540641i
$26$		0			0
$27$	1.46393	−	4.98567i	0.281733	−	0.959493i
$28$	3.17669	+	6.16193i	0.600339	+	1.16449i
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$		0			0
$31$	10.2699	+	0.489217i	1.84453	+	0.0878660i	0.940541	−	0.339680i	$-0.110319\pi$
$31$	10.2699	+	0.489217i	1.84453	+	0.0878660i	0.903994	+	0.427546i	$0.140622\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.285491	−	5.99320i	0.0475819	−	0.998867i
$37$	−2.33343	+	4.04162i	−0.383614	+	0.664439i	−0.991576	−	0.129527i	$-0.958654\pi$
$37$	−2.33343	+	4.04162i	−0.383614	+	0.664439i	0.607962	+	0.793966i	$0.291987\pi$
$38$		0			0
$39$	−9.89057	+	5.09894i	−1.58376	+	0.816484i
$40$		0			0
$41$		0			0		−0.371662	−	0.928368i	$-0.621212\pi$
$41$		0			0		0.371662	+	0.928368i	$0.378788\pi$
$42$		0			0
$43$	−12.7715	−	1.83627i	−1.94764	−	0.280028i	−0.948334	−	0.317275i	$-0.897232\pi$
$43$	−12.7715	−	1.83627i	−1.94764	−	0.280028i	−0.999306	+	0.0372462i	$0.988141\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$47$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$48$	−1.31117	−	6.80300i	−0.189251	−	0.981929i
$49$	−4.65594	−	1.86396i	−0.665134	−	0.266279i
$50$		0			0
$51$		0			0
$52$	−9.71062	+	8.41430i	−1.34662	+	1.16685i
$53$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$53$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.243043	+	0.173070i	−0.0321918	+	0.0229237i
$58$		0			0
$59$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$59$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$60$		0			0
$61$	10.6430	+	11.1620i	1.36269	+	1.42915i	0.796122	+	0.605136i	$0.206881\pi$
$61$	10.6430	+	11.1620i	1.36269	+	1.42915i	0.566569	+	0.824014i	$0.308270\pi$
$62$		0			0
$63$	6.42816	+	8.17407i	0.809872	+	1.02984i
$64$	−3.32332	−	7.27706i	−0.415415	−	0.909632i
$65$		0			0
$66$		0			0
$67$	−6.31701	−	5.20532i	−0.771746	−	0.635931i
$67$	−6.31701	−	5.20532i	−0.771746	−	0.635931i
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$71$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$72$		0			0
$73$	11.4519	−	10.9194i	1.34035	−	1.27802i	0.409644	−	0.912245i	$-0.365653\pi$
$73$	11.4519	−	10.9194i	1.34035	−	1.27802i	0.930704	−	0.365774i	$-0.119196\pi$
$74$		0			0
$75$	−4.68209	+	7.28547i	−0.540641	+	0.841254i
$76$	−0.225616	+	0.260375i	−0.0258799	+	0.0298670i
$77$		0			0
$78$		0			0
$79$	−2.20847	+	4.28384i	−0.248473	+	0.481970i	−0.979780	−	0.200078i	$-0.935880\pi$
$79$	−2.20847	+	4.28384i	−0.248473	+	0.481970i	0.731307	+	0.682048i	$0.238911\pi$
$80$		0			0
$81$	−1.28083	−	8.90839i	−0.142315	−	0.989821i
$82$		0			0
$83$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$83$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$84$	9.43860	+	7.42260i	1.02984	+	0.809872i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$89$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$90$		0			0
$91$	3.16924	−	22.0425i	0.332226	−	2.31068i
$92$		0			0
$93$	16.5326	−	6.61865i	1.71435	−	0.686322i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	13.0982	+	7.56222i	1.32992	+	0.767828i	0.985286	−	0.170911i	$-0.0546711\pi$
$97$	13.0982	+	7.56222i	1.32992	+	0.767828i	0.344630	+	0.938739i	$0.388004\pi$
$98$		0			0
$99$		0			0
$100$	−3.27068	+	9.45001i	−0.327068	+	0.945001i
$101$		0			0		−0.945001	−	0.327068i	$-0.893939\pi$
$101$		0			0		0.945001	+	0.327068i	$0.106061\pi$
$102$		0			0
$103$	0.747760	−	15.6974i	0.0736790	−	1.54671i	−0.595345	−	0.803470i	$-0.702984\pi$
$103$	0.747760	−	15.6974i	0.0736790	−	1.54671i	0.669024	−	0.743241i	$-0.266712\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$107$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$108$	−3.86243	−	9.64788i	−0.371662	−	0.928368i
$109$	3.70003	+	5.75735i	0.354398	+	0.551455i	0.971983	−	0.235050i	$-0.0755252\pi$
$109$	3.70003	+	5.75735i	0.354398	+	0.551455i	−0.617585	+	0.786504i	$0.711889\pi$
$110$		0			0
$111$	−0.768362	+	8.04665i	−0.0729297	+	0.763754i
$112$	12.6122	+	5.75980i	1.19174	+	0.544250i
$113$		0			0		0.971812	−	0.235759i	$-0.0757576\pi$
$113$		0			0		−0.971812	+	0.235759i	$0.924242\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−11.9141	+	15.1500i	−1.10146	+	1.40062i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.523401	−	10.9875i	−0.0475819	−	0.998867i
$122$		0			0
$123$		0			0
$124$	16.7503	−	11.9278i	1.50422	−	1.07115i
$125$		0			0
$126$		0			0
$127$	12.7795	+	2.46304i	1.13400	+	0.218560i	0.721510	−	0.692404i	$-0.243448\pi$
$127$	12.7795	+	2.46304i	1.13400	+	0.218560i	0.412486	+	0.910964i	$0.364661\pi$
$128$		0			0
$129$	−21.4431	+	6.29627i	−1.88796	+	0.554356i
$130$		0			0
$131$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$131$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$132$		0			0
$133$		−	0.597112i		−	0.0517762i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$137$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$138$		0			0
$139$	−4.42917	−	15.0844i	−0.375677	−	1.27944i	−0.902951	−	0.429744i	$-0.858604\pi$
$139$	−4.42917	−	15.0844i	−0.375677	−	1.27944i	0.527274	−	0.849695i	$-0.323214\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−6.96068	−	9.77491i	−0.580057	−	0.814576i
$145$		0			0
$146$		0			0
$147$	−8.67672	+	0.413323i	−0.715644	+	0.0340903i
$148$	1.32833	+	9.23873i	0.109188	+	0.759419i
$149$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$149$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$150$		0			0
$151$	−10.8779	−	8.55445i	−0.885228	−	0.696151i	0.0682321	−	0.997669i	$-0.478264\pi$
$151$	−10.8779	−	8.55445i	−0.885228	−	0.696151i	−0.953460	+	0.301518i	$0.902507\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−9.24511	+	20.2440i	−0.740201	+	1.62081i
$157$	−6.51030	−	0.621658i	−0.519578	−	0.0496137i	−0.168027	−	0.985782i	$-0.553740\pi$
$157$	−6.51030	−	0.621658i	−0.519578	−	0.0496137i	−0.351551	+	0.936169i	$0.614346\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	10.6390	+	18.4273i	0.833310	+	1.44334i	0.895399	+	0.445265i	$0.146890\pi$
$163$	10.6390	+	18.4273i	0.833310	+	1.44334i	−0.0620887	+	0.998071i	$0.519776\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$167$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$168$		0			0
$169$	28.1462	−	2.68763i	2.16509	−	0.206741i
$170$		0			0
$171$	−0.258394	+	0.447551i	−0.0197599	+	0.0342251i
$172$	−22.3484	+	12.9029i	−1.70405	+	0.983834i
$173$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$173$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$174$		0			0
$175$	−6.44145	−	16.0900i	−0.486928	−	1.21629i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$179$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$180$		0			0
$181$	−15.3952	+	21.6195i	−1.14432	+	1.60697i	−0.438186	+	0.898884i	$0.644379\pi$
$181$	−15.3952	+	21.6195i	−1.14432	+	1.60697i	−0.706129	+	0.708083i	$0.749560\pi$
$182$		0			0
$183$	24.7996	+	9.92826i	1.83324	+	0.733918i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	16.0092	+	8.25329i	1.16449	+	0.600339i
$190$		0			0
$191$		0			0		0.814576	−	0.580057i	$-0.196970\pi$
$191$		0			0		−0.814576	+	0.580057i	$0.803030\pi$
$192$	−10.4720	−	9.07402i	−0.755750	−	0.654861i
$193$	−22.5816	−	14.5123i	−1.62546	−	1.04462i	−0.952320	−	0.305100i	$-0.901310\pi$
$193$	−22.5816	−	14.5123i	−1.62546	−	1.04462i	−0.673137	−	0.739518i	$-0.735053\pi$
$194$		0			0
$195$		0			0
$196$	−9.62407	+	2.82588i	−0.687434	+	0.201849i
$197$		0			0		−0.618159	−	0.786053i	$-0.712121\pi$
$197$		0			0		0.618159	+	0.786053i	$0.287879\pi$
$198$		0			0
$199$	−8.92300	−	25.7813i	−0.632534	−	1.82759i	−0.557114	−	0.830436i	$-0.688091\pi$
$199$	−8.92300	−	25.7813i	−0.632534	−	1.82759i	−0.0754209	−	0.997152i	$-0.524030\pi$
$200$		0			0
$201$	−13.6980	−	3.65592i	−0.966180	−	0.257868i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−4.86338	+	25.2336i	−0.337215	+	1.74964i
$209$		0			0
$210$		0			0
$211$	−11.4811	−	16.1229i	−0.790391	−	1.10995i	−0.991465	−	0.130372i	$-0.958383\pi$
$211$	−11.4811	−	16.1229i	−0.790391	−	1.10995i	0.201074	−	0.979576i	$-0.435557\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−8.40221	+	34.6344i	−0.570379	+	2.35113i
$218$		0			0
$219$	10.1861	−	25.4437i	0.688315	−	1.71933i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	11.1686	−	24.4558i	0.747904	−	1.63768i	−0.0221933	−	0.999754i	$-0.507065\pi$
$223$	11.1686	−	24.4558i	0.747904	−	1.63768i	0.770097	−	0.637927i	$-0.220208\pi$
$224$		0			0
$225$	−2.13472	+	14.8473i	−0.142315	+	0.989821i
$226$		0			0
$227$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$227$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$228$	−0.168120	+	0.572563i	−0.0111340	+	0.0379189i
$229$	9.61639	+	18.6532i	0.635469	+	1.23264i	0.958187	+	0.286143i	$0.0923732\pi$
$229$	9.61639	+	18.6532i	0.635469	+	1.23264i	−0.322718	+	0.946495i	$0.604597\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.0950560	−	0.995472i	$-0.530303\pi$
$233$		0			0		0.0950560	+	0.995472i	$0.469697\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.397205	+	8.33836i	−0.0258012	+	0.541635i
$238$		0			0
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$		0			0
$241$	25.9210	+	7.61108i	1.66972	+	0.490273i	0.973715	−	0.227768i	$-0.0731428\pi$
$241$	25.9210	+	7.61108i	1.66972	+	0.490273i	0.696001	+	0.718041i	$0.254961\pi$
$242$		0			0
$243$	−8.42776	−	13.1138i	−0.540641	−	0.841254i
$244$	30.5317	+	4.38979i	1.95459	+	0.281028i
$245$		0			0
$246$		0			0
$247$	1.07550	−	0.260914i	0.0684327	−	0.0166016i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		0.618159	−	0.786053i	$-0.287879\pi$
$251$		0			0		−0.618159	+	0.786053i	$0.712121\pi$
$252$	20.2115	+	4.90326i	1.27320	+	0.308876i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−14.2214	−	7.33162i	−0.888835	−	0.458227i
$257$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$257$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$258$		0			0
$259$	−12.2256	−	10.5935i	−0.759659	−	0.658248i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$263$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−16.3664	−	0.373481i	−0.999740	−	0.0228140i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$	−18.9158	+	8.63857i	−1.14906	+	0.524756i	−0.896595	−	0.442851i	$-0.853967\pi$
$271$	−18.9158	+	8.63857i	−1.14906	+	0.524756i	−0.252460	+	0.967607i	$0.581240\pi$
$272$		0			0
$273$	−10.8668	−	37.0090i	−0.657689	−	2.23988i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−21.7974	+	25.1556i	−1.30968	+	1.51145i	−0.648808	+	0.760952i	$0.724732\pi$
$277$	−21.7974	+	25.1556i	−1.30968	+	1.51145i	−0.660872	+	0.750499i	$0.729813\pi$
$278$		0			0
$279$	21.2853	−	22.3234i	1.27432	−	1.33647i
$280$		0			0
$281$		0			0		0.998867	−	0.0475819i	$-0.0151515\pi$
$281$		0			0		−0.998867	+	0.0475819i	$0.984848\pi$
$282$		0			0
$283$	22.0240	+	25.4171i	1.30919	+	1.51089i	0.676068	+	0.736839i	$0.263682\pi$
$283$	22.0240	+	25.4171i	1.30919	+	1.51089i	0.633125	+	0.774050i	$0.281772\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.00790	+	16.5208i	0.235759	+	0.971812i
$290$		0			0
$291$	26.0777	+	2.49012i	1.52870	+	0.145973i
$292$	4.50381	−	31.3247i	0.263566	−	1.83314i
$293$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$293$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	1.64642	+	17.2421i	0.0950560	+	0.995472i
$301$	14.6281	−	42.2652i	0.843152	−	2.43613i
$302$		0			0
$303$		0			0
$304$	−0.0327863	+	0.688269i	−0.00188042	+	0.0394750i
$305$		0			0
$306$		0			0
$307$	2.90347	−	1.49684i	0.165710	−	0.0854293i	−0.373376	−	0.927680i	$-0.621800\pi$
$307$	2.90347	−	1.49684i	0.165710	−	0.0854293i	0.539086	+	0.842251i	$0.318770\pi$
$308$		0			0
$309$	−10.1165	−	25.2697i	−0.575506	−	1.43755i
$310$		0			0
$311$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$311$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$312$		0			0
$313$	1.38404	+	0.632072i	0.0782308	+	0.0357268i	0.454146	−	0.890927i	$-0.349944\pi$
$313$	1.38404	+	0.632072i	0.0782308	+	0.0357268i	−0.375915	+	0.926654i	$0.622672\pi$
$314$		0			0
$315$		0			0
$316$	1.82424	+	9.46503i	0.102621	+	0.532450i
$317$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$317$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−13.0272	−	12.4214i	−0.723734	−	0.690079i
$325$	26.1662	−	18.6329i	1.45144	−	1.03357i
$326$		0			0
$327$	9.97203	+	6.40863i	0.551455	+	0.354398i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	9.90263	+	12.5922i	0.544298	+	0.692131i	0.977924	−	0.208962i	$-0.0670085\pi$
$331$	9.90263	+	12.5922i	0.544298	+	0.692131i	−0.433626	+	0.901093i	$0.642766\pi$
$332$		0			0
$333$	4.57915	+	13.2306i	0.250936	+	0.725031i
$334$		0			0
$335$		0			0
$336$	24.0152			1.31014
$337$	3.08414	−	1.06743i	0.168004	−	0.0581467i	−0.241771	−	0.970333i	$-0.577728\pi$
$337$	3.08414	−	1.06743i	0.168004	−	0.0581467i	0.409775	+	0.912187i	$0.365607\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−3.71958	+	5.78778i	−0.200839	+	0.312511i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		0.458227	−	0.888835i	$-0.348485\pi$
$347$		0			0		−0.458227	+	0.888835i	$0.651515\pi$
$348$		0			0
$349$	2.88940	+	20.0962i	0.154666	+	1.07573i	0.908266	+	0.418392i	$0.137406\pi$
$349$	2.88940	+	20.0962i	0.154666	+	1.07573i	−0.753600	+	0.657333i	$0.771685\pi$
$350$		0			0
$351$	−7.87026	+	32.4417i	−0.420084	+	1.73161i
$352$		0			0
$353$		0			0		0.371662	−	0.928368i	$-0.378788\pi$
$353$		0			0		−0.371662	+	0.928368i	$0.621212\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$359$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$360$		0			0
$361$	−17.6114	+	7.05056i	−0.926918	+	0.371082i
$362$		0			0
$363$	−8.73039	−	16.9346i	−0.458227	−	0.888835i
$364$	−22.2692	−	38.5714i	−1.16722	−	2.02169i
$365$		0			0
$366$		0			0
$367$	3.58252	+	37.5179i	0.187006	+	1.95842i	0.272711	+	0.962096i	$0.412080\pi$
$367$	3.58252	+	37.5179i	0.187006	+	1.95842i	−0.0857046	+	0.996321i	$0.527314\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	17.8082	−	30.8447i	0.923313	−	1.59923i
$373$	29.1366	−	16.8220i	1.50864	−	0.871011i	0.508686	−	0.860952i	$-0.330131\pi$
$373$	29.1366	−	16.8220i	1.50864	−	0.871011i	0.999949	−	0.0100591i	$-0.00320195\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.466056	+	4.88076i	−0.0239397	+	0.250708i	0.975578	+	0.219653i	$0.0704926\pi$
$379$	−0.466056	+	4.88076i	−0.0239397	+	0.250708i	−0.999518	+	0.0310544i	$0.990113\pi$
$380$		0			0
$381$	21.9067	−	5.31450i	1.12231	−	0.272270i
$382$		0			0
$383$		0			0		−0.189251	−	0.981929i	$-0.560606\pi$
$383$		0			0		0.189251	+	0.981929i	$0.439394\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−29.2540	+	25.3487i	−1.48706	+	1.28855i
$388$	29.9410	−	4.30487i	1.52002	−	0.218546i
$389$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$389$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−37.6979	+	11.0691i	−1.89200	+	0.555542i	−0.898921	+	0.438111i	$0.855648\pi$
$397$	−37.6979	+	11.0691i	−1.89200	+	0.555542i	−0.993081	+	0.117431i	$0.962534\pi$
$398$		0			0
$399$	−0.429634	−	0.940767i	−0.0215086	−	0.0470973i
$400$	6.54136	+	18.9000i	0.327068	+	0.945001i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$	−66.0540			−3.29038
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−4.54221	+	23.5672i	−0.224598	+	1.16532i	0.678073	+	0.734994i	$0.262815\pi$
$409$	−4.54221	+	23.5672i	−0.224598	+	1.16532i	−0.902671	+	0.430331i	$0.858397\pi$
$410$		0			0
$411$		0			0
$412$	−18.2314	−	25.6025i	−0.898198	−	1.26134i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−17.8318	−	20.5790i	−0.873226	−	1.00776i
$418$		0			0
$419$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$419$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$420$		0			0
$421$	−3.61443	+	0.696624i	−0.176156	+	0.0339514i	−0.276567	−	0.960995i	$-0.589197\pi$
$421$	−3.61443	+	0.696624i	−0.176156	+	0.0339514i	0.100410	+	0.994946i	$0.467985\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−44.9734	+	28.9027i	−2.17642	+	1.39870i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$431$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$432$	−18.0000	−	10.3923i	−0.866025	−	0.500000i
$433$	−33.8506	−	1.61250i	−1.62676	−	0.0774919i	−0.785759	−	0.618533i	$-0.787727\pi$
$433$	−33.8506	−	1.61250i	−1.62676	−	0.0774919i	−0.840996	+	0.541041i	$0.818030\pi$
$434$		0			0
$435$		0			0
$436$	12.9348	+	4.47676i	0.619462	+	0.214398i
$437$		0			0
$438$		0			0
$439$	1.36860	−	2.37048i	0.0653196	−	0.113137i	−0.831516	−	0.555501i	$-0.812527\pi$
$439$	1.36860	−	2.37048i	0.0653196	−	0.113137i	0.896836	+	0.442364i	$0.145860\pi$
$440$		0			0
$441$	−13.3730	+	6.89427i	−0.636811	+	0.328299i
$442$		0			0
$443$		0			0		−0.371662	−	0.928368i	$-0.621212\pi$
$443$		0			0		0.371662	+	0.928368i	$0.378788\pi$
$444$	8.74027	+	13.6001i	0.414795	+	0.645433i
$445$		0			0
$446$		0			0
$447$		0			0
$448$	26.9487	−	6.53768i	1.27320	−	0.308876i
$449$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$449$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−23.2935	−	5.65094i	−1.09442	−	0.265504i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.73524	+	0.894578i	0.0811710	+	0.0418466i	0.498334	−	0.866985i	$-0.333945\pi$
$457$	1.73524	+	0.894578i	0.0811710	+	0.0418466i	−0.417163	+	0.908832i	$0.636976\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$461$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$462$		0			0
$463$	27.6505	+	28.9990i	1.28503	+	1.34770i	0.906558	+	0.422082i	$0.138700\pi$
$463$	27.6505	+	28.9990i	1.28503	+	1.34770i	0.378468	+	0.925614i	$0.376451\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$467$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$468$			38.5470i			1.78184i
$469$	21.8611	−	18.0862i	1.00945	−	0.835144i
$470$		0			0
$471$	−10.7045	+	3.70485i	−0.493235	+	0.170710i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.623361	−	0.594373i	0.0286018	−	0.0272717i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$479$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$480$		0			0
$481$	13.7387	−	26.6493i	0.626430	−	1.21510i
$482$		0			0
$483$		0			0
$484$	−14.4069	−	16.6265i	−0.654861	−	0.755750i
$485$		0			0
$486$		0			0
$487$	−11.1209	+	27.7786i	−0.503935	+	1.25877i	0.430486	+	0.902597i	$0.358342\pi$
$487$	−11.1209	+	27.7786i	−0.503935	+	1.25877i	−0.934421	+	0.356171i	$0.884082\pi$
$488$		0			0
$489$	30.0208	+	21.3777i	1.35759	+	0.966735i
$490$		0			0
$491$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$491$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	11.5866	−	39.4604i	0.520255	−	1.77183i
$497$		0			0
$498$		0			0
$499$	−37.6965	−	21.7641i	−1.68753	−	0.974295i	−0.956402	−	0.292052i	$-0.905662\pi$
$499$	−37.6965	−	21.7641i	−1.68753	−	0.974295i	−0.731126	−	0.682243i	$-0.761005\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.945001	−	0.327068i	$-0.893939\pi$
$503$		0			0		0.945001	+	0.327068i	$0.106061\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	42.4113	−	24.4862i	1.88355	−	1.08747i
$508$	23.1358	−	11.9273i	1.02649	−	0.529190i
$509$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$509$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$510$		0			0
$511$	29.6534	+	46.1415i	1.31179	+	2.04118i
$512$		0			0
$513$	−0.0850848	+	0.891049i	−0.00375659	+	0.0393408i
$514$		0			0
$515$		0			0
$516$	−25.9267	+	36.4090i	−1.14136	+	1.60281i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$521$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$522$		0			0
$523$	−1.37012	−	28.7624i	−0.0599113	−	1.25769i	−0.806028	−	0.591877i	$-0.798387\pi$
$523$	−1.37012	−	28.7624i	−0.0599113	−	1.25769i	0.746117	−	0.665815i	$-0.231916\pi$
$524$		0			0
$525$	−21.7258	−	20.7155i	−0.948190	−	0.904097i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	22.5844	+	4.35278i	0.981929	+	0.189251i
$530$		0			0
$531$		0			0
$532$	−0.738220	−	0.938724i	−0.0320059	−	0.0406988i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−6.47686	−	22.0581i	−0.278462	−	0.948354i	−0.973367	−	0.229252i	$-0.926372\pi$
$541$	−6.47686	−	22.0581i	−0.278462	−	0.948354i	0.694905	−	0.719101i	$-0.255446\pi$
$542$		0			0
$543$	−8.69989	+	45.1393i	−0.373348	+	1.93711i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	30.2166	−	31.6902i	1.29197	−	1.35498i	0.391425	−	0.920210i	$-0.371982\pi$
$547$	30.2166	−	31.6902i	1.29197	−	1.35498i	0.900543	−	0.434767i	$-0.143169\pi$
$548$		0			0
$549$	46.2160	−	2.20154i	1.97245	−	0.0939595i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−13.1320	−	10.3271i	−0.558427	−	0.439152i
$554$		0			0
$555$		0			0
$556$	−25.6122	−	18.2384i	−1.08620	−	0.773479i
$557$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$557$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$558$		0			0
$559$	82.5191	+	7.87962i	3.49018	+	0.333272i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$563$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	31.1613	+	1.48440i	1.30865	+	0.0623388i
$568$		0			0
$569$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$569$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$570$		0			0
$571$	−27.2781	+	2.60474i	−1.14155	+	0.109005i	−0.648655	−	0.761083i	$-0.724668\pi$
$571$	−27.2781	+	2.60474i	−1.14155	+	0.109005i	−0.492897	+	0.870088i	$0.664062\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−23.0278	−	6.76158i	−0.959493	−	0.281733i
$577$	17.8287	+	44.5339i	0.742218	+	1.85397i	0.421756	+	0.906709i	$0.361414\pi$
$577$	17.8287	+	44.5339i	0.742218	+	1.85397i	0.320462	+	0.947261i	$0.396162\pi$
$578$		0			0
$579$	−46.0198	−	6.61665i	−1.91252	−	0.274979i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.971812	−	0.235759i	$-0.924242\pi$
$587$		0			0		0.971812	+	0.235759i	$0.0757576\pi$
$588$	−13.1297	+	11.3770i	−0.541461	+	0.469178i
$589$	−1.75310	+	0.252058i	−0.0722353	+	0.0103859i
$590$		0			0
$591$		0			0
$592$	13.5103	+	12.8820i	0.555269	+	0.529448i
$593$		0			0		0.814576	−	0.580057i	$-0.196970\pi$
$593$		0			0		−0.814576	+	0.580057i	$0.803030\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−32.6086	−	34.1989i	−1.33458	−	1.39967i
$598$		0			0
$599$		0			0		−0.618159	−	0.786053i	$-0.712121\pi$
$599$		0			0		0.618159	+	0.786053i	$0.287879\pi$
$600$		0			0
$601$	−3.22782	−	9.32618i	−0.131666	−	0.380423i	0.859827	−	0.510585i	$-0.170571\pi$
$601$	−3.22782	−	9.32618i	−0.131666	−	0.380423i	−0.991493	+	0.130163i	$0.958450\pi$
$602$		0			0
$603$	−24.2120	+	4.09596i	−0.985991	+	0.166800i
$604$	−27.6772			−1.12617
$605$		0			0
$606$		0			0
$607$	38.5935	−	30.3503i	1.56646	−	1.23188i	0.730905	−	0.682479i	$-0.239098\pi$
$607$	38.5935	−	30.3503i	1.56646	−	1.23188i	0.835558	−	0.549402i	$-0.185144\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	5.07027	+	7.12020i	0.204786	+	0.287582i	0.904178	−	0.427157i	$-0.140485\pi$
$613$	5.07027	+	7.12020i	0.204786	+	0.287582i	−0.699391	+	0.714739i	$0.746545\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$617$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$618$		0			0
$619$	11.6595	−	48.0610i	0.468633	−	1.93173i	0.126990	−	0.991904i	$-0.459469\pi$
$619$	11.6595	−	48.0610i	0.468633	−	1.93173i	0.341644	−	0.939829i	$-0.389016\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	10.4937	+	43.2556i	0.420084	+	1.73161i
$625$	10.3854	−	22.7408i	0.415415	−	0.909632i
$626$		0			0
$627$		0			0
$628$	−11.0034	+	7.07148i	−0.439085	+	0.282183i
$629$		0			0
$630$		0			0
$631$	−13.7241	−	26.6211i	−0.546349	−	1.05977i	−0.986793	−	0.161989i	$-0.948209\pi$
$631$	−13.7241	−	26.6211i	−0.546349	−	1.05977i	0.440444	−	0.897780i	$-0.354821\pi$
$632$		0			0
$633$	−29.6896	−	17.1413i	−1.18005	−	0.681304i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	30.4480	+	10.5381i	1.20639	+	0.417537i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$641$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$642$		0			0
$643$	35.0716	+	10.2979i	1.38309	+	0.406111i	0.886843	−	0.462072i	$-0.152894\pi$
$643$	35.0716	+	10.2979i	1.38309	+	0.406111i	0.496245	+	0.868183i	$0.334712\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.0950560	−	0.995472i	$-0.469697\pi$
$647$		0			0		−0.0950560	+	0.995472i	$0.530303\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	11.6822	+	60.6130i	0.457861	+	2.37561i
$652$	39.5076	+	15.8165i	1.54724	+	0.619420i
$653$		0			0		0.618159	−	0.786053i	$-0.287879\pi$
$653$		0			0		−0.618159	+	0.786053i	$0.712121\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−2.25872	−	47.4164i	−0.0881212	−	1.84989i
$658$		0			0
$659$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$659$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$660$		0			0
$661$	−38.3314	−	33.2144i	−1.49092	−	1.29189i	−0.853156	−	0.521656i	$-0.825315\pi$
$661$	−38.3314	−	33.2144i	−1.49092	−	1.29189i	−0.637763	−	0.770233i	$-0.720140\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		−	46.5668i		−	1.80038i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	40.5080	−	18.4994i	1.56147	−	0.713099i	0.567563	−	0.823330i	$-0.307886\pi$
$673$	40.5080	−	18.4994i	1.56147	−	0.713099i	0.993906	+	0.110231i	$0.0351591\pi$
$674$		0			0
$675$	7.31963	+	24.9284i	0.281733	+	0.959493i
$676$	40.9260	−	39.0228i	1.57408	−	1.50088i
$677$		0			0		0.189251	−	0.981929i	$-0.439394\pi$
$677$		0			0		−0.189251	+	0.981929i	$0.560606\pi$
$678$		0			0
$679$	−34.3316	+	39.6207i	−1.31752	+	1.52050i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.998867	−	0.0475819i	$-0.0151515\pi$
$683$		0			0		−0.998867	+	0.0475819i	$0.984848\pi$
$684$	0.147093	+	1.02305i	0.00562424	+	0.0391175i
$685$		0			0
$686$		0			0
$687$	28.5723	+	22.4695i	1.09010	+	0.857264i
$688$	−19.1820	+	47.9144i	−0.731308	+	1.82672i
$689$		0			0
$690$		0			0
$691$	5.03640	+	20.7603i	0.191594	+	0.789760i	0.983765	+	0.179461i	$0.0574354\pi$
$691$	5.03640	+	20.7603i	0.191594	+	0.789760i	−0.792171	+	0.610299i	$0.791049\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−30.0190	−	17.3315i	−1.13461	−	0.655068i
$701$		0			0		−0.998867	−	0.0475819i	$-0.984848\pi$
$701$		0			0		0.998867	+	0.0475819i	$0.0151515\pi$
$702$		0			0
$703$	0.262938	−	0.759710i	0.00991691	−	0.0286530i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−47.3340	+	24.4024i	−1.77767	+	0.916450i	−0.887674	+	0.460472i	$0.847680\pi$
$709$	−47.3340	+	24.4024i	−1.77767	+	0.916450i	−0.889991	+	0.455978i	$0.849290\pi$
$710$		0			0
$711$	5.37381	+	13.4231i	0.201534	+	0.503406i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$719$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$720$		0			0
$721$	52.9380	+	12.8426i	1.97151	+	0.478284i
$722$		0			0
$723$	46.3156	−	6.65917i	1.72249	−	0.247657i
$724$	2.52573	+	53.0216i	0.0938679	+	1.97053i
$725$		0			0
$726$		0			0
$727$	10.2559	−	7.30321i	0.380371	−	0.270861i	−0.373840	−	0.927493i	$-0.621959\pi$
$727$	10.2559	−	7.30321i	0.380371	−	0.270861i	0.754211	+	0.656632i	$0.228020\pi$
$728$		0			0
$729$	−22.7138	−	14.5973i	−0.841254	−	0.540641i
$730$		0			0
$731$		0			0
$732$	51.2621	−	15.0519i	1.89470	−	0.556334i
$733$	−14.9449	−	19.0040i	−0.552002	−	0.701928i	0.427351	−	0.904086i	$-0.359447\pi$
$733$	−14.9449	−	19.0040i	−0.552002	−	0.701928i	−0.979353	+	0.202158i	$0.935205\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−51.2058	+	17.7225i	−1.88364	+	0.651933i	−0.914999	+	0.403456i	$0.867809\pi$
$739$	−51.2058	+	17.7225i	−1.88364	+	0.651933i	−0.968638	+	0.248477i	$0.920070\pi$
$740$		0			0
$741$	1.50675	−	1.18492i	0.0553520	−	0.0435293i
$742$		0			0
$743$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$743$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−3.49306	−	24.2948i	−0.127464	−	0.886528i	−0.948753	−	0.316017i	$-0.897654\pi$
$751$	−3.49306	−	24.2948i	−0.127464	−	0.886528i	0.821290	−	0.570511i	$-0.193255\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	35.3718	−	6.81735i	1.28646	−	0.247945i
$757$	−13.9758	−	9.95214i	−0.507960	−	0.361717i	0.297161	−	0.954827i	$-0.403960\pi$
$757$	−13.9758	−	9.95214i	−0.507960	−	0.361717i	−0.805121	+	0.593111i	$0.797900\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$761$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$762$		0			0
$763$	−22.0233	+	8.81678i	−0.797295	+	0.319189i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−27.6814	−	1.31863i	−0.998867	−	0.0475819i
$769$	4.59575	+	48.1289i	0.165727	+	1.73557i	0.570626	+	0.821210i	$0.306701\pi$
$769$	4.59575	+	48.1289i	0.165727	+	1.73557i	−0.404899	+	0.914362i	$0.632693\pi$
$770$		0			0
$771$		0			0
$772$	−53.4424	+	5.10313i	−1.92344	+	0.183666i
$773$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$773$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$774$		0			0
$775$	−44.5206	+	25.7040i	−1.59923	+	0.923313i
$776$		0			0
$777$	−26.8839	−	7.89384i	−0.964456	−	0.283190i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−11.6364	+	16.3410i	−0.415585	+	0.583607i
$785$		0			0
$786$		0			0
$787$	−16.9139	+	21.5077i	−0.602915	+	0.766668i	−0.987704	−	0.156336i	$-0.950032\pi$
$787$	−16.9139	+	21.5077i	−0.602915	+	0.766668i	0.384789	+	0.923004i	$0.374274\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−71.7104	−	68.3757i	−2.54651	−	2.42809i
$794$		0			0
$795$		0			0
$796$	−45.9018	−	29.4993i	−1.62695	−	1.04557i
$797$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$797$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−26.0545	+	11.1876i	−0.918873	+	0.394555i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$809$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$810$		0			0
$811$	10.6796	−	55.4113i	0.375013	−	1.94575i	0.0544830	−	0.998515i	$-0.482649\pi$
$811$	10.6796	−	55.4113i	0.375013	−	1.94575i	0.320530	−	0.947238i	$-0.396139\pi$
$812$		0			0
$813$	−23.5868	+	27.2206i	−0.827226	+	0.954669i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	2.22016	−	0.105759i	0.0776736	−	0.00370005i
$818$		0			0
$819$	−43.7497	−	50.4898i	−1.52874	−	1.76426i
$820$		0			0
$821$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$821$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$822$		0			0
$823$	−39.2011	+	7.55540i	−1.36647	+	0.263365i	−0.819159	−	0.573567i	$-0.805559\pi$
$823$	−39.2011	+	7.55540i	−1.36647	+	0.263365i	−0.547307	+	0.836932i	$0.684347\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$827$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$828$		0			0
$829$	−12.4041	+	7.97163i	−0.430812	+	0.276866i	−0.738023	−	0.674775i	$-0.764241\pi$
$829$	−12.4041	+	7.97163i	−0.430812	+	0.276866i	0.307211	+	0.951641i	$0.400604\pi$
$830$		0			0
$831$	−16.2425	+	55.3170i	−0.563447	+	1.91892i
$832$	23.5510	+	45.6826i	0.816484	+	1.58376i
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	17.4735	−	50.4863i	0.603972	−	1.74506i
$838$		0			0
$839$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$839$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$840$		0			0
$841$	−14.5000	+	25.1147i	−0.500000	+	0.866025i
$842$		0			0
$843$		0			0
$844$	−37.9826	−	11.1527i	−1.30741	−	0.383891i
$845$		0			0
$846$		0			0
$847$	37.7411	+	5.42635i	1.29680	+	0.186452i
$848$		0			0
$849$	52.9876	+	24.1986i	1.81853	+	0.830495i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	44.9124	+	17.9802i	1.53777	+	0.615630i	0.977171	−	0.212457i	$-0.0681464\pi$
$853$	44.9124	+	17.9802i	1.53777	+	0.615630i	0.560600	+	0.828087i	$0.310571\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$857$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$858$		0			0
$859$	51.2960	+	26.4449i	1.75020	+	0.902290i	0.955348	+	0.295484i	$0.0954809\pi$
$859$	51.2960	+	26.4449i	1.75020	+	0.902290i	0.794850	+	0.606806i	$0.207549\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$863$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	18.2016	+	23.1452i	0.618159	+	0.786053i
$868$	29.6099	+	64.8367i	1.00503	+	2.20070i
$869$		0			0
$870$		0			0
$871$	42.1289	+	31.4727i	1.42748	+	1.06641i
$872$		0			0
$873$	42.8778	−	14.8402i	1.45120	−	0.502264i
$874$		0			0
$875$		0			0
$876$	−15.4429	−	52.5935i	−0.521766	−	1.77697i
$877$	17.5197	−	16.7050i	0.591598	−	0.564088i	−0.334011	−	0.942569i	$-0.608402\pi$
$877$	17.5197	−	16.7050i	0.591598	−	0.564088i	0.925609	+	0.378481i	$0.123554\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$881$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$882$		0			0
$883$	14.5444	−	28.2123i	0.489460	−	0.949419i	−0.506722	−	0.862110i	$-0.669143\pi$
$883$	14.5444	−	28.2123i	0.489460	−	0.949419i	0.996181	−	0.0873094i	$-0.0278269\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$887$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$888$		0			0
$889$	−16.7667	+	41.8812i	−0.562337	+	1.40465i
$890$		0			0
$891$		0			0
$892$	−12.6769	−	52.2550i	−0.424455	−	1.74963i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	15.0000	+	25.9808i	0.500000	+	0.866025i
$901$		0			0
$902$		0			0
$903$	−7.36362	−	77.1154i	−0.245046	−	2.56624i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.22249	−	25.6633i	0.0405922	−	0.852135i	−0.883143	−	0.469103i	$-0.844577\pi$
$907$	1.22249	−	25.6633i	0.0405922	−	0.852135i	0.923735	−	0.383031i	$-0.125120\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$911$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$912$	0.443568	+	1.10798i	0.0146880	+	0.0366888i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	38.1793	+	17.4359i	1.26148	+	0.576098i
$917$		0			0
$918$		0			0
$919$	8.43382	+	43.7588i	0.278206	+	1.44347i	0.804898	+	0.593413i	$0.202220\pi$
$919$	8.43382	+	43.7588i	0.278206	+	1.44347i	−0.526692	+	0.850056i	$0.676568\pi$
$920$		0			0
$921$	3.49749	−	4.44742i	0.115246	−	0.146548i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.11029	−	23.3079i	−0.0365062	−	0.766359i
$926$		0			0
$927$	−34.1209	−	32.5342i	−1.12068	−	1.06856i
$928$		0			0
$929$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$929$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$930$		0			0
$931$	0.848316	+	0.163499i	0.0278024	+	0.00535848i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	61.1186i		−	1.99666i	−0.0577898	−	0.998329i	$-0.518405\pi$
$937$		−	61.1186i		−	1.99666i	0.0577898	−	0.998329i	$-0.481595\pi$
$938$		0			0
$939$	2.63539			0.0860027
$940$		0			0
$941$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$941$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$947$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$948$	9.68441	+	13.5999i	0.314535	+	0.441703i
$949$	−70.1517	+	73.5730i	−2.27722	+	2.38828i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$953$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	74.3726	+	7.10172i	2.39912	+	0.229088i
$962$		0			0
$963$		0			0
$964$	50.1602	−	20.0811i	1.61555	−	0.646770i
$965$		0			0
$966$		0			0
$967$	−12.7536	−	22.0899i	−0.410129	−	0.710365i	0.584774	−	0.811196i	$-0.301183\pi$
$967$	−12.7536	−	22.0899i	−0.410129	−	0.710365i	−0.994904	+	0.100831i	$0.967850\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$971$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$972$	−29.4622	−	10.1970i	−0.945001	−	0.327068i
$973$	54.2475	−	5.18001i	1.73909	−	0.166063i
$974$		0			0
$975$	27.8189	−	48.1837i	0.890918	−	1.54311i
$976$	53.4262	−	30.8456i	1.71013	−	0.987345i
$977$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$977$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	20.3224	+	2.92191i	0.648843	+	0.0932896i
$982$		0			0
$983$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$983$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	1.36823	−	1.73985i	0.0435293	−	0.0553520i
$989$		0			0
$990$		0			0
$991$	−30.4993	+	4.38514i	−0.968842	+	0.139298i	−0.608528	−	0.793533i	$-0.708240\pi$
$991$	−30.4993	+	4.38514i	−0.968842	+	0.139298i	−0.360314	+	0.932831i	$0.617331\pi$
$992$		0			0
$993$	24.6622	+	12.7143i	0.782632	+	0.403475i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−44.2204	−	28.4187i	−1.40047	−	0.900030i	−0.400606	−	0.916251i	$-0.631200\pi$
$997$	−44.2204	−	28.4187i	−1.40047	−	0.900030i	−0.999868	+	0.0162206i	$0.994837\pi$
$998$		0			0
$999$	16.7342	+	17.5504i	0.529448	+	0.555269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.p.a.11.1	✓	20
3.2	odd	2	CM	201.2.p.a.11.1	✓	20
67.61	odd	66	inner	201.2.p.a.128.1	yes	20
201.128	even	66	inner	201.2.p.a.128.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.p.a.11.1	✓	20	1.1	even	1	trivial
201.2.p.a.11.1	✓	20	3.2	odd	2	CM
201.2.p.a.128.1	yes	20	67.61	odd	66	inner
201.2.p.a.128.1	yes	20	201.128	even	66	inner

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.57553 - 0.719520i) q^{3} +(1.57211 - 1.23632i) q^{4} +(-0.656000 + 3.40365i) q^{7} +(1.96458 - 2.26725i) q^{9} +O(q^{10})\)	\(q+(1.57553 - 0.719520i) q^{3} +(1.57211 - 1.23632i) q^{4} +(-0.656000 + 3.40365i) q^{7} +(1.96458 - 2.26725i) q^{9} +(1.58734 - 3.07902i) q^{12} +(-6.41722 + 0.305690i) q^{13} +(0.943036 - 3.88725i) q^{16} +(-0.169149 + 0.0326009i) q^{19} +(1.41545 + 5.83456i) q^{21} +(-4.20627 + 2.70320i) q^{25} +(1.46393 - 4.98567i) q^{27} +(3.17669 + 6.16193i) q^{28} +(10.2699 + 0.489217i) q^{31} +(0.285491 - 5.99320i) q^{36} +(-2.33343 + 4.04162i) q^{37} +(-9.89057 + 5.09894i) q^{39} +(-12.7715 - 1.83627i) q^{43} +(-1.31117 - 6.80300i) q^{48} +(-4.65594 - 1.86396i) q^{49} +(-9.71062 + 8.41430i) q^{52} +(-0.243043 + 0.173070i) q^{57} +(10.6430 + 11.1620i) q^{61} +(6.42816 + 8.17407i) q^{63} +(-3.32332 - 7.27706i) q^{64} +(-6.31701 - 5.20532i) q^{67} +(11.4519 - 10.9194i) q^{73} +(-4.68209 + 7.28547i) q^{75} +(-0.225616 + 0.260375i) q^{76} +(-2.20847 + 4.28384i) q^{79} +(-1.28083 - 8.90839i) q^{81} +(9.43860 + 7.42260i) q^{84} +(3.16924 - 22.0425i) q^{91} +(16.5326 - 6.61865i) q^{93} +(13.0982 + 7.56222i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9}+O(q^{10}) \) 20 * q - 2 * q^4 - 6 * q^7 + 6 * q^9	\( 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9} - 6 q^{12} - 3 q^{13} + 4 q^{16} - 8 q^{19} + 6 q^{21} + 10 q^{25} - 12 q^{28} + 15 q^{31} + 6 q^{36} + 10 q^{37} - 3 q^{39} - 12 q^{48} - 5 q^{49} - 154 q^{52} - 75 q^{57} + 15 q^{61} - 15 q^{63} + 16 q^{64} + 5 q^{67} + 60 q^{73} - 32 q^{76} + 134 q^{79} - 18 q^{81} + 186 q^{84} - 12 q^{91} - 15 q^{93} + 9 q^{97}+O(q^{100}) \) 20 * q - 2 * q^4 - 6 * q^7 + 6 * q^9 - 6 * q^12 - 3 * q^13 + 4 * q^16 - 8 * q^19 + 6 * q^21 + 10 * q^25 - 12 * q^28 + 15 * q^31 + 6 * q^36 + 10 * q^37 - 3 * q^39 - 12 * q^48 - 5 * q^49 - 154 * q^52 - 75 * q^57 + 15 * q^61 - 15 * q^63 + 16 * q^64 + 5 * q^67 + 60 * q^73 - 32 * q^76 + 134 * q^79 - 18 * q^81 + 186 * q^84 - 12 * q^91 - 15 * q^93 + 9 * q^97

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