LMFDB - Embedded newform 804.2.ba.b.41.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(41,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 33, 53]))

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

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

chi := DirichletCharacter("804.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.ba (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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			41.12
Character	$\chi$	$=$	804.41
Dual form			804.2.ba.b.353.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0450273 + 1.73147i) q^{3} +(-0.306661 + 2.13288i) q^{5} +(-0.233782 - 2.44828i) q^{7} +(-2.99595 - 0.155926i) q^{9} +O(q^{10})$	\(q+(-0.0450273 + 1.73147i) q^{3} +(-0.306661 + 2.13288i) q^{5} +(-0.233782 - 2.44828i) q^{7} +(-2.99595 - 0.155926i) q^{9} +(-2.54950 + 1.02066i) q^{11} +(-4.81545 - 5.05030i) q^{13} +(-3.67919 - 0.627011i) q^{15} +(0.521893 - 0.180629i) q^{17} +(-2.78507 - 0.265942i) q^{19} +(4.24964 - 0.294547i) q^{21} +(-2.01683 + 0.0960734i) q^{23} +(0.342350 + 0.100523i) q^{25} +(0.404880 - 5.18035i) q^{27} +(-2.51027 + 1.44930i) q^{29} +(-0.313059 + 0.328327i) q^{31} +(-1.65245 - 4.46032i) q^{33} +(5.29357 + 0.252164i) q^{35} +(-1.36757 + 2.36869i) q^{37} +(8.96124 - 8.11038i) q^{39} +(6.42149 + 1.23764i) q^{41} +(0.627825 + 0.544013i) q^{43} +(1.25131 - 6.34216i) q^{45} +(-5.40598 + 10.4861i) q^{47} +(0.934085 - 0.180030i) q^{49} +(0.289253 + 0.911773i) q^{51} +(-8.67995 - 10.0172i) q^{53} +(-1.39512 - 5.75075i) q^{55} +(0.585874 - 4.81028i) q^{57} +(-3.75489 - 12.7880i) q^{59} +(-2.25071 + 5.62201i) q^{61} +(0.318648 + 7.37136i) q^{63} +(12.2484 - 8.72202i) q^{65} +(-8.15679 + 0.683270i) q^{67} +(-0.0755355 - 3.49640i) q^{69} +(-8.87305 - 3.07099i) q^{71} +(9.59379 + 3.84077i) q^{73} +(-0.189467 + 0.588241i) q^{75} +(3.09490 + 6.00326i) q^{77} +(4.42862 - 1.07437i) q^{79} +(8.95137 + 0.934293i) q^{81} +(-6.35474 + 8.08070i) q^{83} +(0.225215 + 1.16852i) q^{85} +(-2.39639 - 4.41170i) q^{87} +(-1.12214 + 1.74608i) q^{89} +(-11.2388 + 12.9702i) q^{91} +(-0.554391 - 0.556835i) q^{93} +(1.42130 - 5.85866i) q^{95} +(7.31896 + 4.22560i) q^{97} +(7.79730 - 2.66032i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) $ 440 * q - 12 * q^7 + 4 * q^9	$ 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) $ 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{53}{66}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.0450273	+	1.73147i	−0.0259965	+	0.999662i
$3$	−0.0450273	+	1.73147i	−0.0259965	+	0.999662i
$4$		0			0
$5$	−0.306661	+	2.13288i	−0.137143	+	0.953851i	0.798774	+	0.601631i	$0.205482\pi$
$5$	−0.306661	+	2.13288i	−0.137143	+	0.953851i	−0.935917	+	0.352220i	$0.885427\pi$
$6$		0			0
$7$	−0.233782	−	2.44828i	−0.0883614	−	0.925362i	−0.925595	−	0.378516i	$-0.876434\pi$
$7$	−0.233782	−	2.44828i	−0.0883614	−	0.925362i	0.837233	−	0.546846i	$-0.184172\pi$
$8$		0			0
$9$	−2.99595	−	0.155926i	−0.998648	−	0.0519754i
$10$		0			0
$11$	−2.54950	+	1.02066i	−0.768702	+	0.307742i	−0.722665	−	0.691198i	$-0.757083\pi$
$11$	−2.54950	+	1.02066i	−0.768702	+	0.307742i	−0.0460363	+	0.998940i	$0.514659\pi$
$12$		0			0
$13$	−4.81545	−	5.05030i	−1.33557	−	1.40070i	−0.850267	−	0.526352i	$-0.823559\pi$
$13$	−4.81545	−	5.05030i	−1.33557	−	1.40070i	−0.485299	−	0.874348i	$-0.661289\pi$
$14$		0			0
$15$	−3.67919	−	0.627011i	−0.949963	−	0.161893i
$16$		0			0
$17$	0.521893	−	0.180629i	0.126578	−	0.0438090i	−0.263045	−	0.964784i	$-0.584727\pi$
$17$	0.521893	−	0.180629i	0.126578	−	0.0438090i	0.389622	+	0.920975i	$0.372605\pi$
$18$		0			0
$19$	−2.78507	−	0.265942i	−0.638940	−	0.0610113i	−0.229442	−	0.973322i	$-0.573690\pi$
$19$	−2.78507	−	0.265942i	−0.638940	−	0.0610113i	−0.409498	+	0.912311i	$0.634296\pi$
$20$		0			0
$21$	4.24964	−	0.294547i	0.927347	−	0.0642754i
$22$		0			0
$23$	−2.01683	+	0.0960734i	−0.420538	+	0.0200327i	−0.256785	−	0.966469i	$-0.582663\pi$
$23$	−2.01683	+	0.0960734i	−0.420538	+	0.0200327i	−0.163753	+	0.986501i	$0.552360\pi$
$24$		0			0
$25$	0.342350	+	0.100523i	0.0684700	+	0.0201046i
$26$		0			0
$27$	0.404880	−	5.18035i	0.0779192	−	0.996960i
$28$		0			0
$29$	−2.51027	+	1.44930i	−0.466145	+	0.269129i	−0.714625	−	0.699508i	$-0.753402\pi$
$29$	−2.51027	+	1.44930i	−0.466145	+	0.269129i	0.248480	+	0.968637i	$0.420069\pi$
$30$		0			0
$31$	−0.313059	+	0.328327i	−0.0562271	+	0.0589693i	−0.751247	−	0.660021i	$-0.770547\pi$
$31$	−0.313059	+	0.328327i	−0.0562271	+	0.0589693i	0.695020	+	0.718991i	$0.255396\pi$
$32$		0			0
$33$	−1.65245	−	4.46032i	−0.287654	−	0.776442i
$34$		0			0
$35$	5.29357	+	0.252164i	0.894776	+	0.0426234i
$36$		0			0
$37$	−1.36757	+	2.36869i	−0.224826	+	0.389411i	−0.956267	−	0.292494i	$-0.905515\pi$
$37$	−1.36757	+	2.36869i	−0.224826	+	0.389411i	0.731441	+	0.681905i	$0.238848\pi$
$38$		0			0
$39$	8.96124	−	8.11038i	1.43495	−	1.29870i
$40$		0			0
$41$	6.42149	+	1.23764i	1.00287	+	0.193287i	0.664149	−	0.747600i	$-0.268794\pi$
$41$	6.42149	+	1.23764i	1.00287	+	0.193287i	0.338720	+	0.940887i	$0.390006\pi$
$42$		0			0
$43$	0.627825	+	0.544013i	0.0957424	+	0.0829613i	0.701417	−	0.712751i	$-0.252551\pi$
$43$	0.627825	+	0.544013i	0.0957424	+	0.0829613i	−0.605674	+	0.795713i	$0.707097\pi$
$44$		0			0
$45$	1.25131	−	6.34216i	0.186534	−	0.945433i
$46$		0			0
$47$	−5.40598	+	10.4861i	−0.788543	+	1.52956i	0.0586520	+	0.998278i	$0.481320\pi$
$47$	−5.40598	+	10.4861i	−0.788543	+	1.52956i	−0.847195	+	0.531282i	$0.821711\pi$
$48$		0			0
$49$	0.934085	−	0.180030i	0.133441	−	0.0257186i
$50$		0			0
$51$	0.289253	+	0.911773i	0.0405036	+	0.127674i
$52$		0			0
$53$	−8.67995	−	10.0172i	−1.19228	−	1.37597i	−0.908929	−	0.416951i	$-0.863099\pi$
$53$	−8.67995	−	10.0172i	−1.19228	−	1.37597i	−0.283353	−	0.959016i	$-0.591447\pi$
$54$		0			0
$55$	−1.39512	−	5.75075i	−0.188118	−	0.775431i
$56$		0			0
$57$	0.585874	−	4.81028i	0.0776009	−	0.637138i
$58$		0			0
$59$	−3.75489	−	12.7880i	−0.488845	−	1.66485i	−0.721595	−	0.692315i	$-0.756591\pi$
$59$	−3.75489	−	12.7880i	−0.488845	−	1.66485i	0.232750	−	0.972536i	$-0.425227\pi$
$60$		0			0
$61$	−2.25071	+	5.62201i	−0.288174	+	0.719824i	0.711676	+	0.702508i	$0.247936\pi$
$61$	−2.25071	+	5.62201i	−0.288174	+	0.719824i	−0.999850	+	0.0173163i	$0.994488\pi$
$62$		0			0
$63$	0.318648	+	7.37136i	0.0401459	+	0.928704i
$64$		0			0
$65$	12.2484	−	8.72202i	1.51922	−	1.08183i
$66$		0			0
$67$	−8.15679	+	0.683270i	−0.996510	+	0.0834747i
$67$	−8.15679	+	0.683270i	−0.996510	+	0.0834747i
$68$		0			0
$69$	−0.0755355	−	3.49640i	−0.00909341	−	0.420917i
$70$		0			0
$71$	−8.87305	−	3.07099i	−1.05304	−	0.364460i	−0.254920	−	0.966962i	$-0.582049\pi$
$71$	−8.87305	−	3.07099i	−1.05304	−	0.364460i	−0.798117	+	0.602502i	$0.794170\pi$
$72$		0			0
$73$	9.59379	+	3.84077i	1.12287	+	0.449528i	0.857431	−	0.514600i	$-0.172059\pi$
$73$	9.59379	+	3.84077i	1.12287	+	0.449528i	0.265437	+	0.964128i	$0.414484\pi$
$74$		0			0
$75$	−0.189467	+	0.588241i	−0.0218778	+	0.0679242i
$76$		0			0
$77$	3.09490	+	6.00326i	0.352696	+	0.684135i
$78$		0			0
$79$	4.42862	−	1.07437i	0.498259	−	0.120876i	0.0212489	−	0.999774i	$-0.493236\pi$
$79$	4.42862	−	1.07437i	0.498259	−	0.120876i	0.477010	+	0.878898i	$0.341721\pi$
$80$		0			0
$81$	8.95137	+	0.934293i	0.994597	+	0.103810i
$82$		0			0
$83$	−6.35474	+	8.08070i	−0.697523	+	0.886972i	−0.997760	−	0.0668921i	$-0.978692\pi$
$83$	−6.35474	+	8.08070i	−0.697523	+	0.886972i	0.300237	+	0.953865i	$0.402934\pi$
$84$		0			0
$85$	0.225215	+	1.16852i	0.0244280	+	0.126744i
$86$		0			0
$87$	−2.39639	−	4.41170i	−0.256920	−	0.472984i
$88$		0			0
$89$	−1.12214	+	1.74608i	−0.118947	+	0.185084i	−0.895621	−	0.444817i	$-0.853269\pi$
$89$	−1.12214	+	1.74608i	−0.118947	+	0.185084i	0.776675	+	0.629902i	$0.216905\pi$
$90$		0			0
$91$	−11.2388	+	12.9702i	−1.17814	+	1.35965i
$92$		0			0
$93$	−0.554391	−	0.556835i	−0.0574876	−	0.0577411i
$94$		0			0
$95$	1.42130	−	5.85866i	0.145822	−	0.601086i
$96$		0			0
$97$	7.31896	+	4.22560i	0.743128	+	0.429045i	0.823205	−	0.567744i	$-0.192183\pi$
$97$	7.31896	+	4.22560i	0.743128	+	0.429045i	−0.0800776	+	0.996789i	$0.525517\pi$
$98$		0			0
$99$	7.79730	−	2.66032i	0.783658	−	0.267372i
$100$		0			0
$101$	0.426724	−	0.599250i	0.0424607	−	0.0596276i	−0.792800	−	0.609482i	$-0.791377\pi$
$101$	0.426724	−	0.599250i	0.0424607	−	0.0596276i	0.835260	+	0.549854i	$0.185317\pi$
$102$		0			0
$103$	−9.36794	−	8.93231i	−0.923050	−	0.880127i	0.0700322	−	0.997545i	$-0.477690\pi$
$103$	−9.36794	−	8.93231i	−0.923050	−	0.880127i	−0.993083	+	0.117418i	$0.962538\pi$
$104$		0			0
$105$	−0.674967	+	9.15427i	−0.0658701	+	0.893365i
$106$		0			0
$107$	−4.80701	+	0.691144i	−0.464711	+	0.0668154i	−0.370694	−	0.928755i	$-0.620880\pi$
$107$	−4.80701	+	0.691144i	−0.464711	+	0.0668154i	−0.0940174	+	0.995571i	$0.529971\pi$
$108$		0			0
$109$	−2.08024	+	7.08464i	−0.199251	+	0.678586i	0.797875	+	0.602823i	$0.205957\pi$
$109$	−2.08024	+	7.08464i	−0.199251	+	0.678586i	−0.997126	+	0.0757630i	$0.975861\pi$
$110$		0			0
$111$	−4.03973	−	2.47455i	−0.383434	−	0.234874i
$112$		0			0
$113$	−1.78929	+	1.40711i	−0.168322	+	0.132370i	−0.698767	−	0.715350i	$-0.746267\pi$
$113$	−1.78929	+	1.40711i	−0.168322	+	0.132370i	0.530445	+	0.847720i	$0.322025\pi$
$114$		0			0
$115$	0.413571	−	4.33111i	0.0385657	−	0.403878i
$116$		0			0
$117$	13.6393	+	15.8813i	1.26096	+	1.46822i
$118$		0			0
$119$	−0.564239	−	1.23551i	−0.0517237	−	0.113259i
$120$		0			0
$121$	−2.50290	+	2.38651i	−0.227537	+	0.216956i
$122$		0			0
$123$	−2.43207	+	11.0629i	−0.219293	+	0.997505i
$124$		0			0
$125$	−4.79509	+	10.4998i	−0.428886	+	0.939128i
$126$		0			0
$127$	−15.4009	+	1.47061i	−1.36661	+	0.130496i	−0.752432	−	0.658670i	$-0.771120\pi$
$127$	−15.4009	+	1.47061i	−1.36661	+	0.130496i	−0.614181	+	0.789165i	$0.710513\pi$
$128$		0			0
$129$	−0.970210	+	1.06256i	−0.0854222	+	0.0935534i
$130$		0			0
$131$	3.50834	+	5.45908i	0.306525	+	0.476962i	0.960005	−	0.279981i	$-0.0903283\pi$
$131$	3.50834	+	5.45908i	0.306525	+	0.476962i	−0.653481	+	0.756943i	$0.726692\pi$
$132$		0			0
$133$			6.88081i			0.596642i
$134$		0			0
$135$	10.9249	+	2.45217i	0.940265	+	0.211049i
$136$		0			0
$137$	10.3235	−	6.63453i	0.881999	−	0.566826i	−0.0194019	−	0.999812i	$-0.506176\pi$
$137$	10.3235	−	6.63453i	0.881999	−	0.566826i	0.901401	+	0.432985i	$0.142540\pi$
$138$		0			0
$139$	−9.86849	−	1.41887i	−0.837034	−	0.120347i	−0.289549	−	0.957163i	$-0.593505\pi$
$139$	−9.86849	−	1.41887i	−0.837034	−	0.120347i	−0.547485	+	0.836816i	$0.684415\pi$
$140$		0			0
$141$	−17.9130	−	9.83243i	−1.50854	−	0.828040i
$142$		0			0
$143$	17.4316	+	7.96076i	1.45771	+	0.665712i
$144$		0			0
$145$	−2.32138	−	5.79853i	−0.192780	−	0.481542i
$146$		0			0
$147$	0.269657	+	1.62544i	0.0222409	+	0.134064i
$148$		0			0
$149$	18.0782	−	8.25602i	1.48102	−	0.676359i	0.499255	−	0.866455i	$-0.333607\pi$
$149$	18.0782	−	8.25602i	1.48102	−	0.676359i	0.981766	+	0.190096i	$0.0608799\pi$
$150$		0			0
$151$	2.76478	+	7.98830i	0.224994	+	0.650079i	0.999839	+	0.0179272i	$0.00570670\pi$
$151$	2.76478	+	7.98830i	0.224994	+	0.650079i	−0.774845	+	0.632151i	$0.782172\pi$
$152$		0			0
$153$	−1.59173	+	0.459778i	−0.128684	+	0.0371708i
$154$		0			0
$155$	−0.604278	−	0.768401i	−0.0485367	−	0.0617195i
$156$		0			0
$157$	0.0842720	+	1.76909i	0.00672563	+	0.141188i	0.999732	+	0.0231313i	$0.00736357\pi$
$157$	0.0842720	+	1.76909i	0.00672563	+	0.141188i	−0.993007	+	0.118057i	$0.962333\pi$
$158$		0			0
$159$	17.7353	−	14.5780i	1.40650	−	1.15611i
$160$		0			0
$161$	0.706714	+	4.91530i	0.0556968	+	0.387380i
$162$		0			0
$163$	−3.78670	−	6.55876i	−0.296598	−	0.513722i	0.678758	−	0.734362i	$-0.262519\pi$
$163$	−3.78670	−	6.55876i	−0.296598	−	0.513722i	−0.975355	+	0.220640i	$0.929185\pi$
$164$		0			0
$165$	10.0200	−	2.15666i	0.780060	−	0.167896i
$166$		0			0
$167$	9.87190	+	7.02975i	0.763910	+	0.543978i	0.894291	−	0.447486i	$-0.147681\pi$
$167$	9.87190	+	7.02975i	0.763910	+	0.543978i	−0.130381	+	0.991464i	$0.541620\pi$
$168$		0			0
$169$	−1.69839	+	35.6536i	−0.130646	+	2.74259i
$170$		0			0
$171$	8.30246	+	1.23101i	0.634905	+	0.0941380i
$172$		0			0
$173$	−20.3597	−	4.93922i	−1.54792	−	0.375522i	−0.631384	−	0.775471i	$-0.717513\pi$
$173$	−20.3597	−	4.93922i	−1.54792	−	0.375522i	−0.916537	+	0.399949i	$0.869028\pi$
$174$		0			0
$175$	0.166073	−	0.861669i	0.0125539	−	0.0651361i
$176$		0			0
$177$	22.3110	−	5.92565i	1.67700	−	0.445399i
$178$		0			0
$179$	−8.09006	−	5.19917i	−0.604679	−	0.388604i	0.202179	−	0.979349i	$-0.435198\pi$
$179$	−8.09006	−	5.19917i	−0.604679	−	0.388604i	−0.806859	+	0.590745i	$0.798834\pi$
$180$		0			0
$181$	5.87750	+	3.03006i	0.436871	+	0.225223i	0.662609	−	0.748965i	$-0.269449\pi$
$181$	5.87750	+	3.03006i	0.436871	+	0.225223i	−0.225738	+	0.974188i	$0.572479\pi$
$182$		0			0
$183$	−9.63297	−	4.15017i	−0.712089	−	0.306790i
$184$		0			0
$185$	−4.63275	−	3.64323i	−0.340606	−	0.267856i
$186$		0			0
$187$	−1.14620	+	0.993190i	−0.0838186	+	0.0726292i
$188$		0			0
$189$	−12.7776	+	0.219815i	−0.929434	+	0.0159892i
$190$		0			0
$191$	−3.46682	+	1.78727i	−0.250850	+	0.129322i	−0.579067	−	0.815280i	$-0.696583\pi$
$191$	−3.46682	+	1.78727i	−0.250850	+	0.129322i	0.328216	+	0.944603i	$0.393553\pi$
$192$		0			0
$193$	26.3811	−	7.74620i	1.89896	−	0.557584i	0.908879	−	0.417060i	$-0.136939\pi$
$193$	26.3811	−	7.74620i	1.89896	−	0.557584i	0.990077	−	0.140524i	$-0.0448787\pi$
$194$		0			0
$195$	14.5504	+	21.6003i	1.04197	+	1.54683i
$196$		0			0
$197$	5.55240	−	16.0426i	0.395592	−	1.14299i	−0.554813	−	0.831975i	$-0.687210\pi$
$197$	5.55240	−	16.0426i	0.395592	−	1.14299i	0.950405	−	0.311014i	$-0.100669\pi$
$198$		0			0
$199$	7.13663	+	10.0220i	0.505902	+	0.710440i	0.985995	−	0.166778i	$-0.0533363\pi$
$199$	7.13663	+	10.0220i	0.505902	+	0.710440i	−0.480092	+	0.877218i	$0.659397\pi$
$200$		0			0
$201$	−0.815780	−	14.1540i	−0.0575407	−	0.998343i
$202$		0			0
$203$	4.13515	+	5.80701i	0.290231	+	0.407572i
$204$		0			0
$205$	−4.60896	+	13.3167i	−0.321903	+	0.930079i
$206$		0			0
$207$	6.05729	+	0.0266461i	0.421011	+	0.00185203i
$208$		0			0
$209$	7.37197	−	2.16461i	0.509930	−	0.149729i
$210$		0			0
$211$	−16.8027	+	8.66237i	−1.15674	+	0.596342i	−0.926316	−	0.376748i	$-0.877042\pi$
$211$	−16.8027	+	8.66237i	−1.15674	+	0.596342i	−0.230426	+	0.973090i	$0.574012\pi$
$212$		0			0
$213$	5.71685	−	15.2251i	0.391712	−	1.04321i
$214$		0			0
$215$	−1.35284	+	1.17224i	−0.0922631	+	0.0799464i
$216$		0			0
$217$	0.877024	+	0.689699i	0.0595363	+	0.0468198i
$218$		0			0
$219$	−7.08215	+	16.4384i	−0.478567	+	1.11080i
$220$		0			0
$221$	−3.42538	−	1.76591i	−0.230416	−	0.118788i
$222$		0			0
$223$	−14.0431	−	9.02498i	−0.940399	−	0.604358i	−0.0218910	−	0.999760i	$-0.506969\pi$
$223$	−14.0431	−	9.02498i	−0.940399	−	0.604358i	−0.918508	+	0.395403i	$0.870605\pi$
$224$		0			0
$225$	−1.00999	−	0.354543i	−0.0673325	−	0.0236362i
$226$		0			0
$227$	1.17258	−	6.08393i	0.0778270	−	0.403805i	−0.922034	−	0.387110i	$-0.873473\pi$
$227$	1.17258	−	6.08393i	0.0778270	−	0.403805i	0.999861	−	0.0166949i	$-0.00531440\pi$
$228$		0			0
$229$	−3.04756	−	0.739331i	−0.201389	−	0.0488563i	0.133796	−	0.991009i	$-0.457283\pi$
$229$	−3.04756	−	0.739331i	−0.201389	−	0.0488563i	−0.335184	+	0.942153i	$0.608799\pi$
$230$		0			0
$231$	−10.5338	+	5.08840i	−0.693073	+	0.334792i
$232$		0			0
$233$	−0.317294	+	6.66082i	−0.0207866	+	0.436365i	0.964354	+	0.264616i	$0.0852450\pi$
$233$	−0.317294	+	6.66082i	−0.0207866	+	0.436365i	−0.985141	+	0.171750i	$0.945058\pi$
$234$		0			0
$235$	−20.7078	−	14.7460i	−1.35083	−	0.961921i
$236$		0			0
$237$	1.66083	+	7.71638i	0.107882	+	0.501233i
$238$		0			0
$239$	12.4911	+	21.6352i	0.807981	+	1.39946i	0.914260	+	0.405127i	$0.132773\pi$
$239$	12.4911	+	21.6352i	0.807981	+	1.39946i	−0.106279	+	0.994336i	$0.533894\pi$
$240$		0			0
$241$	0.00925738	+	0.0643865i	0.000596320	+	0.00414750i	0.990117	−	0.140241i	$-0.0447877\pi$
$241$	0.00925738	+	0.0643865i	0.000596320	+	0.00414750i	−0.989521	+	0.144388i	$0.953879\pi$
$242$		0			0
$243$	−2.02075	+	15.4569i	−0.129631	+	0.991562i
$244$		0			0
$245$	0.0975342	+	2.04749i	0.00623123	+	0.130810i
$246$		0			0
$247$	12.0683	+	15.3461i	0.767887	+	0.976448i
$248$		0			0
$249$	−13.7053	−	11.3669i	−0.868539	−	0.720345i
$250$		0			0
$251$	8.13828	+	23.5140i	0.513684	+	1.48419i	0.841923	+	0.539597i	$0.181423\pi$
$251$	8.13828	+	23.5140i	0.513684	+	1.48419i	−0.328240	+	0.944594i	$0.606455\pi$
$252$		0			0
$253$	5.04384	−	2.30344i	0.317103	−	0.144816i
$254$		0			0
$255$	−2.03340	+	0.337336i	−0.127336	+	0.0211248i
$256$		0			0
$257$	−5.53208	−	13.8185i	−0.345082	−	0.861972i	−0.994805	−	0.101801i	$-0.967539\pi$
$257$	−5.53208	−	13.8185i	−0.345082	−	0.861972i	0.649723	−	0.760171i	$-0.274885\pi$
$258$		0			0
$259$	6.11893	+	2.79442i	0.380212	+	0.173637i
$260$		0			0
$261$	7.74661	−	3.95062i	0.479503	−	0.244537i
$262$		0			0
$263$	13.2735	+	1.90845i	0.818482	+	0.117680i	0.538823	−	0.842419i	$-0.318869\pi$
$263$	13.2735	+	1.90845i	0.818482	+	0.117680i	0.279660	+	0.960099i	$0.409778\pi$
$264$		0			0
$265$	24.0272	−	15.4414i	1.47598	−	0.948555i
$266$		0			0
$267$	−2.97276	−	2.02157i	−0.181930	−	0.123718i
$268$		0			0
$269$		−	9.15469i		−	0.558171i	−0.960266	−	0.279086i	$-0.909969\pi$
$269$		−	9.15469i		−	0.558171i	0.960266	−	0.279086i	$-0.0900313\pi$
$270$		0			0
$271$	−6.35792	−	9.89311i	−0.386216	−	0.600964i	0.592652	−	0.805459i	$-0.298081\pi$
$271$	−6.35792	−	9.89311i	−0.386216	−	0.600964i	−0.978868	+	0.204495i	$0.934445\pi$
$272$		0			0
$273$	−21.9515	−	20.0436i	−1.32856	−	1.21309i
$274$		0			0
$275$	−0.975420	+	0.0931413i	−0.0588200	+	0.00561663i
$276$		0			0
$277$	−4.72997	+	10.3572i	−0.284196	+	0.622303i	−0.996858	−	0.0792046i	$-0.974762\pi$
$277$	−4.72997	+	10.3572i	−0.284196	+	0.622303i	0.712662	+	0.701507i	$0.247489\pi$
$278$		0			0
$279$	0.989103	−	0.934836i	0.0592161	−	0.0559671i
$280$		0			0
$281$	−14.5314	+	13.8556i	−0.866869	+	0.826558i	−0.986073	−	0.166312i	$-0.946814\pi$
$281$	−14.5314	+	13.8556i	−0.866869	+	0.826558i	0.119204	+	0.992870i	$0.461966\pi$
$282$		0			0
$283$	0.292674	+	0.640866i	0.0173976	+	0.0380955i	0.918131	−	0.396276i	$-0.129698\pi$
$283$	0.292674	+	0.640866i	0.0173976	+	0.0380955i	−0.900734	+	0.434372i	$0.856970\pi$
$284$		0			0
$285$	10.0801	+	2.72472i	0.597092	+	0.161399i
$286$		0			0
$287$	1.52886	−	16.0109i	0.0902457	−	0.945096i
$288$		0			0
$289$	−13.1232	+	10.3202i	−0.771950	+	0.607069i
$290$		0			0
$291$	−7.64604	+	12.4823i	−0.448219	+	0.731723i
$292$		0			0
$293$	4.70974	−	16.0399i	0.275146	−	0.937061i	−0.699748	−	0.714390i	$-0.746704\pi$
$293$	4.70974	−	16.0399i	0.275146	−	0.937061i	0.974894	−	0.222671i	$-0.0714775\pi$
$294$		0			0
$295$	28.4266	−	4.08713i	1.65506	−	0.237962i
$296$		0			0
$297$	4.25516	+	13.6205i	0.246909	+	0.790344i
$298$		0			0
$299$	10.1971	+	9.72295i	0.589716	+	0.562293i
$300$		0			0
$301$	1.18512	−	1.66427i	0.0683093	−	0.0959270i
$302$		0			0
$303$	1.01837	+	0.765841i	0.0585037	+	0.0439964i
$304$		0			0
$305$	−11.3008	−	6.52454i	−0.647084	−	0.373594i
$306$		0			0
$307$	2.60375	−	10.7328i	0.148604	−	0.612554i	−0.847984	−	0.530021i	$-0.822184\pi$
$307$	2.60375	−	10.7328i	0.148604	−	0.612554i	0.996588	−	0.0825328i	$-0.0263009\pi$
$308$		0			0
$309$	15.8878	−	15.8181i	0.903825	−	0.899858i
$310$		0			0
$311$	8.51947	−	9.83200i	0.483095	−	0.557521i	−0.460912	−	0.887446i	$-0.652478\pi$
$311$	8.51947	−	9.83200i	0.483095	−	0.557521i	0.944007	+	0.329924i	$0.107023\pi$
$312$		0			0
$313$	7.14245	−	11.1139i	0.403715	−	0.628193i	−0.578560	−	0.815640i	$-0.696385\pi$
$313$	7.14245	−	11.1139i	0.403715	−	0.628193i	0.982275	+	0.187447i	$0.0600213\pi$
$314$		0			0
$315$	−15.8199	−	1.58087i	−0.891351	−	0.0890722i
$316$		0			0
$317$	−1.34794	−	6.99379i	−0.0757080	−	0.392810i	−0.999940	−	0.0109782i	$-0.996505\pi$
$317$	−1.34794	−	6.99379i	−0.0757080	−	0.392810i	0.924232	−	0.381832i	$-0.124707\pi$
$318$		0			0
$319$	4.92066	−	6.25713i	0.275504	−	0.350332i
$320$		0			0
$321$	−0.980245	−	8.35429i	−0.0547119	−	0.466291i
$322$		0			0
$323$	−1.50155	+	0.364271i	−0.0835483	+	0.0202686i
$324$		0			0
$325$	−1.14090	−	2.21303i	−0.0632856	−	0.122757i
$326$		0			0
$327$	−12.1731	−	3.92086i	−0.673177	−	0.216824i
$328$		0			0
$329$	26.9368	+	10.7839i	1.48507	+	0.594534i
$330$		0			0
$331$	15.5053	+	5.36642i	0.852246	+	0.294965i	0.718052	−	0.695990i	$-0.245034\pi$
$331$	15.5053	+	5.36642i	0.852246	+	0.294965i	0.134195	+	0.990955i	$0.457155\pi$
$332$		0			0
$333$	4.46649	−	6.88323i	0.244762	−	0.377199i
$334$		0			0
$335$	1.04404	−	17.6069i	0.0570420	−	0.961970i
$336$		0			0
$337$	−17.8277	+	12.6951i	−0.971138	+	0.691544i	−0.951302	−	0.308259i	$-0.900254\pi$
$337$	−17.8277	+	12.6951i	−0.971138	+	0.691544i	−0.0198353	+	0.999803i	$0.506314\pi$
$338$		0			0
$339$	−2.35580	−	3.16145i	−0.127949	−	0.171706i
$340$		0			0
$341$	0.463031	−	1.15660i	0.0250746	−	0.0626332i
$342$		0			0
$343$	−5.50942	−	18.7634i	−0.297481	−	1.01313i
$344$		0			0
$345$	7.48054	+	0.911101i	0.402739	+	0.0490520i
$346$		0			0
$347$	−1.18614	−	4.88934i	−0.0636754	−	0.262473i	0.931072	−	0.364836i	$-0.118875\pi$
$347$	−1.18614	−	4.88934i	−0.0636754	−	0.262473i	−0.994747	+	0.102363i	$0.967360\pi$
$348$		0			0
$349$	−11.0268	−	12.7256i	−0.590252	−	0.681187i	0.379525	−	0.925182i	$-0.376088\pi$
$349$	−11.0268	−	12.7256i	−0.590252	−	0.681187i	−0.969777	+	0.243995i	$0.921542\pi$
$350$		0			0
$351$	−28.1120	+	22.9010i	−1.50051	+	1.22236i
$352$		0			0
$353$	−13.7779	+	2.65548i	−0.733325	+	0.141337i	−0.542224	−	0.840234i	$-0.682418\pi$
$353$	−13.7779	+	2.65548i	−0.733325	+	0.141337i	−0.191100	+	0.981571i	$0.561206\pi$
$354$		0			0
$355$	9.27106	−	17.9834i	0.492057	−	0.954457i
$356$		0			0
$357$	2.16465	−	0.921329i	0.114566	−	0.0487619i
$358$		0			0
$359$	−19.3650	−	16.7799i	−1.02205	−	0.885609i	−0.0285650	−	0.999592i	$-0.509094\pi$
$359$	−19.3650	−	16.7799i	−1.02205	−	0.885609i	−0.993483	+	0.113983i	$0.963639\pi$
$360$		0			0
$361$	−10.9707	−	2.11444i	−0.577407	−	0.111286i
$362$		0			0
$363$	−4.01947	−	4.44115i	−0.210967	−	0.233100i
$364$		0			0
$365$	−11.1339	+	19.2845i	−0.582777	+	1.00940i
$366$		0			0
$367$	16.1306	+	0.768397i	0.842012	+	0.0401100i	0.464155	−	0.885754i	$-0.346358\pi$
$367$	16.1306	+	0.768397i	0.842012	+	0.0401100i	0.377857	+	0.925864i	$0.376661\pi$
$368$		0			0
$369$	−19.0455	−	4.70918i	−0.991467	−	0.245150i
$370$		0			0
$371$	−22.4957	+	23.5928i	−1.16792	+	1.22488i
$372$		0			0
$373$	10.0070	−	5.77757i	0.518145	−	0.299151i	−0.218030	−	0.975942i	$-0.569963\pi$
$373$	10.0070	−	5.77757i	0.518145	−	0.299151i	0.736175	+	0.676791i	$0.236630\pi$
$374$		0			0
$375$	−17.9641	−	8.77530i	−0.927661	−	0.453155i
$376$		0			0
$377$	19.4075	+	5.69855i	0.999536	+	0.293490i
$378$		0			0
$379$	33.6176	−	1.60140i	1.72682	−	0.0822586i	0.839485	−	0.543383i	$-0.182857\pi$
$379$	33.6176	−	1.60140i	1.72682	−	0.0822586i	0.887335	+	0.461124i	$0.152554\pi$
$380$		0			0
$381$	−1.85285	−	26.7324i	−0.0949245	−	1.36954i
$382$		0			0
$383$	−34.1052	−	3.25665i	−1.74269	−	0.166407i	−0.825380	−	0.564577i	$-0.809039\pi$
$383$	−34.1052	−	3.25665i	−1.74269	−	0.166407i	−0.917312	+	0.398170i	$0.869645\pi$
$384$		0			0
$385$	−13.7533	+	4.76006i	−0.700933	+	0.242595i
$386$		0			0
$387$	−1.79610	−	1.72773i	−0.0913011	−	0.0878254i
$388$		0			0
$389$	17.0865	+	17.9198i	0.866318	+	0.908568i	0.996557	−	0.0829147i	$-0.0264229\pi$
$389$	17.0865	+	17.9198i	0.866318	+	0.908568i	−0.130239	+	0.991483i	$0.541574\pi$
$390$		0			0
$391$	−1.03522	+	0.414438i	−0.0523531	+	0.0209590i
$392$		0			0
$393$	−9.61017	+	5.82875i	−0.484769	+	0.294022i
$394$		0			0
$395$	0.933415	+	9.77516i	0.0469652	+	0.491842i
$396$		0			0
$397$	1.99460	−	13.8728i	0.100106	−	0.696254i	−0.876529	−	0.481350i	$-0.840147\pi$
$397$	1.99460	−	13.8728i	0.100106	−	0.696254i	0.976635	−	0.214905i	$-0.0689441\pi$
$398$		0			0
$399$	−11.9139	−	0.309824i	−0.596440	−	0.0155106i
$400$		0			0
$401$	−18.0622			−0.901983			−0.450991	−	0.892528i	$-0.648930\pi$
$401$	−18.0622			−0.901983			−0.450991	+	0.892528i	$0.648930\pi$
$402$		0			0
$403$	3.16567			0.157693
$404$		0			0
$405$	−4.73777	+	18.8057i	−0.235422	+	0.934460i
$406$		0			0
$407$	1.06896	−	7.43480i	0.0529865	−	0.368529i
$408$		0			0
$409$	−1.56485	−	16.3879i	−0.0773770	−	0.810328i	−0.947977	−	0.318338i	$-0.896875\pi$
$409$	−1.56485	−	16.3879i	−0.0773770	−	0.810328i	0.870600	−	0.491991i	$-0.163731\pi$
$410$		0			0
$411$	11.0226	+	18.1736i	0.543706	+	0.896436i
$412$		0			0
$413$	−30.4307	+	12.1826i	−1.49740	+	0.599467i
$414$		0			0
$415$	−15.2864	−	16.0319i	−0.750379	−	0.786975i
$416$		0			0
$417$	2.90108	−	17.0231i	0.142067	−	0.833623i
$418$		0			0
$419$	25.6749	−	8.88615i	1.25430	−	0.434117i	0.382488	−	0.923960i	$-0.375067\pi$
$419$	25.6749	−	8.88615i	1.25430	−	0.434117i	0.871810	+	0.489843i	$0.162946\pi$
$420$		0			0
$421$	−27.0960	−	2.58736i	−1.32058	−	0.126100i	−0.589153	−	0.808021i	$-0.700539\pi$
$421$	−27.0960	−	2.58736i	−1.32058	−	0.126100i	−0.731426	+	0.681921i	$0.761145\pi$
$422$		0			0
$423$	17.8311	−	30.5730i	0.866977	−	1.48651i
$424$		0			0
$425$	0.196827	−	0.00937605i	0.00954754	−	0.000454805i
$426$		0			0
$427$	14.2904	+	4.19605i	0.691562	+	0.203061i
$428$		0			0
$429$	−14.5687	+	29.8238i	−0.703382	+	1.43991i
$430$		0			0
$431$	−29.7965	+	17.2030i	−1.43525	+	0.828640i	−0.997514	−	0.0704650i	$-0.977552\pi$
$431$	−29.7965	+	17.2030i	−1.43525	+	0.828640i	−0.437733	+	0.899105i	$0.644218\pi$
$432$		0			0
$433$	12.8252	−	13.4507i	0.616342	−	0.646400i	−0.339388	−	0.940646i	$-0.610220\pi$
$433$	12.8252	−	13.4507i	0.616342	−	0.646400i	0.955730	+	0.294246i	$0.0950685\pi$
$434$		0			0
$435$	10.1445	−	3.75830i	0.486391	−	0.180197i
$436$		0			0
$437$	5.64257	+	0.268789i	0.269921	+	0.0128579i
$438$		0			0
$439$	−2.80865	+	4.86473i	−0.134050	+	0.232181i	−0.925234	−	0.379397i	$-0.876131\pi$
$439$	−2.80865	+	4.86473i	−0.134050	+	0.232181i	0.791184	+	0.611578i	$0.209465\pi$
$440$		0			0
$441$	−2.82654	+	0.393712i	−0.134597	+	0.0187482i
$442$		0			0
$443$	18.3930	+	3.54496i	0.873878	+	0.168426i	0.606421	−	0.795144i	$-0.292605\pi$
$443$	18.3930	+	3.54496i	0.873878	+	0.168426i	0.267457	+	0.963570i	$0.413817\pi$
$444$		0			0
$445$	−3.38006	−	2.92884i	−0.160230	−	0.138840i
$446$		0			0
$447$	13.4810	+	31.6734i	0.637629	+	1.49810i
$448$		0			0
$449$	−3.99949	+	7.75792i	−0.188747	+	0.366119i	−0.964154	−	0.265343i	$-0.914515\pi$
$449$	−3.99949	+	7.75792i	−0.188747	+	0.366119i	0.775407	+	0.631462i	$0.217545\pi$
$450$		0			0
$451$	−17.6348	+	3.39882i	−0.830389	+	0.160044i
$452$		0			0
$453$	−13.9560	+	4.42742i	−0.655708	+	0.208019i
$454$		0			0
$455$	−24.2174	−	27.9484i	−1.13533	−	1.31024i
$456$		0			0
$457$	8.20283	+	33.8125i	0.383712	+	1.58168i	0.756645	+	0.653826i	$0.226837\pi$
$457$	8.20283	+	33.8125i	0.383712	+	1.58168i	−0.372933	+	0.927858i	$0.621648\pi$
$458$		0			0
$459$	−0.724418	−	2.77672i	−0.0338129	−	0.129606i
$460$		0			0
$461$	−7.58595	−	25.8354i	−0.353313	−	1.20327i	−0.924092	−	0.382170i	$-0.875177\pi$
$461$	−7.58595	−	25.8354i	−0.353313	−	1.20327i	0.570779	−	0.821104i	$-0.306641\pi$
$462$		0			0
$463$	11.8761	−	29.6651i	0.551929	−	1.37865i	−0.345884	−	0.938277i	$-0.612421\pi$
$463$	11.8761	−	29.6651i	0.551929	−	1.37865i	0.897814	−	0.440376i	$-0.145155\pi$
$464$		0			0
$465$	1.35767	−	1.01169i	0.0629604	−	0.0469158i
$466$		0			0
$467$	−7.86651	+	5.60171i	−0.364018	+	0.259216i	−0.747401	−	0.664373i	$-0.768699\pi$
$467$	−7.86651	+	5.60171i	−0.364018	+	0.259216i	0.383382	+	0.923590i	$0.374759\pi$
$468$		0			0
$469$	3.57975	+	19.8103i	0.165297	+	0.914757i
$470$		0			0
$471$	−3.06691	+	0.0662569i	−0.141316	+	0.00305296i
$472$		0			0
$473$	−2.15589	−	0.746161i	−0.0991280	−	0.0343085i
$474$		0			0
$475$	−0.926737	−	0.371009i	−0.0425216	−	0.0170231i
$476$		0			0
$477$	24.4427	+	31.3644i	1.11915	+	1.43608i
$478$		0			0
$479$	−12.3046	−	23.8677i	−0.562214	−	1.09054i	−0.983038	−	0.183400i	$-0.941289\pi$
$479$	−12.3046	−	23.8677i	−0.562214	−	1.09054i	0.420825	−	0.907142i	$-0.361741\pi$
$480$		0			0
$481$	18.5480	−	4.49971i	0.845718	−	0.205169i
$482$		0			0
$483$	−8.54250	+	1.00233i	−0.388697	+	0.0456075i
$484$		0			0
$485$	−11.2571	+	14.3146i	−0.511160	+	0.649993i
$486$		0			0
$487$	−6.53877	−	33.9264i	−0.296300	−	1.53735i	−0.759151	−	0.650915i	$-0.774385\pi$
$487$	−6.53877	−	33.9264i	−0.296300	−	1.53735i	0.462851	−	0.886436i	$-0.346827\pi$
$488$		0			0
$489$	11.5268	−	6.26122i	0.521259	−	0.283142i
$490$		0			0
$491$	−4.02285	+	6.25968i	−0.181549	+	0.282495i	−0.920085	−	0.391718i	$-0.871881\pi$
$491$	−4.02285	+	6.25968i	−0.181549	+	0.282495i	0.738537	+	0.674213i	$0.235517\pi$
$492$		0			0
$493$	−1.04830	+	1.20981i	−0.0472133	+	0.0544870i
$494$		0			0
$495$	3.28300	+	17.4465i	0.147560	+	0.784161i
$496$		0			0
$497$	−5.44428	+	22.4416i	−0.244209	+	1.00665i
$498$		0			0
$499$	−4.30141	−	2.48342i	−0.192557	−	0.111173i	0.400622	−	0.916243i	$-0.368794\pi$
$499$	−4.30141	−	2.48342i	−0.192557	−	0.111173i	−0.593179	+	0.805070i	$0.702127\pi$
$500$		0			0
$501$	−12.6163	+	16.7763i	−0.563653	+	0.749511i
$502$		0			0
$503$	0.0854197	−	0.119955i	0.00380867	−	0.00534853i	−0.812667	−	0.582728i	$-0.801985\pi$
$503$	0.0854197	−	0.119955i	0.00380867	−	0.00534853i	0.816476	+	0.577380i	$0.195925\pi$
$504$		0			0
$505$	1.14727	+	1.09392i	0.0510527	+	0.0486786i
$506$		0			0
$507$	−61.6566	−	4.54609i	−2.73826	−	0.201899i
$508$		0			0
$509$	−6.04361	+	0.868940i	−0.267878	+	0.0385151i	−0.274945	−	0.961460i	$-0.588660\pi$
$509$	−6.04361	+	0.868940i	−0.267878	+	0.0385151i	0.00706679	+	0.999975i	$0.497751\pi$
$510$		0			0
$511$	7.16043	−	24.3862i	0.316759	−	1.07878i
$512$		0			0
$513$	−2.50530	+	14.3200i	−0.110612	+	0.632243i
$514$		0			0
$515$	21.9243	−	17.2414i	0.966099	−	0.759749i
$516$		0			0
$517$	3.07970	−	32.2520i	0.135445	−	1.41844i
$518$		0			0
$519$	9.46882	−	35.0298i	0.415635	−	1.53764i
$520$		0			0
$521$	10.9594	+	23.9977i	0.480140	+	1.05136i	0.982425	+	0.186658i	$0.0597656\pi$
$521$	10.9594	+	23.9977i	0.480140	+	1.05136i	−0.502285	+	0.864702i	$0.667507\pi$
$522$		0			0
$523$	15.1168	−	14.4138i	0.661011	−	0.630273i	−0.283414	−	0.958998i	$-0.591467\pi$
$523$	15.1168	−	14.4138i	0.661011	−	0.630273i	0.944426	+	0.328724i	$0.106619\pi$
$524$		0			0
$525$	1.48447	+	0.326348i	0.0647877	+	0.0142430i
$526$		0			0
$527$	−0.104078	+	0.227899i	−0.00453371	+	0.00992744i
$528$		0			0
$529$	−18.8375	+	1.79876i	−0.819021	+	0.0782070i
$530$		0			0
$531$	9.25545	+	38.8975i	0.401652	+	1.68801i
$532$		0			0
$533$	−24.6719	−	38.3902i	−1.06866	−	1.66287i
$534$		0			0
$535$		−	10.4647i		−	0.452428i
$536$		0			0
$537$	9.36645	−	13.7736i	0.404192	−	0.594373i
$538$		0			0
$539$	−2.19770	+	1.41237i	−0.0946614	+	0.0608352i
$540$		0			0
$541$	32.9306	+	4.73471i	1.41580	+	0.203561i	0.807369	−	0.590047i	$-0.200891\pi$
$541$	32.9306	+	4.73471i	1.41580	+	0.203561i	0.608430	+	0.793608i	$0.291800\pi$
$542$		0			0
$543$	−5.51110	+	10.0403i	−0.236504	+	0.430869i
$544$		0			0
$545$	−14.4727	−	6.60948i	−0.619944	−	0.283119i
$546$		0			0
$547$	6.50868	+	16.2579i	0.278291	+	0.695137i	0.999996	+	0.00293625i	$0.000934640\pi$
$547$	6.50868	+	16.2579i	0.278291	+	0.695137i	−0.721705	+	0.692201i	$0.756641\pi$
$548$		0			0
$549$	7.61963	−	16.4923i	0.325198	−	0.703873i
$550$		0			0
$551$	7.37671	−	3.36883i	0.314258	−	0.143517i
$552$		0			0
$553$	−3.66569	−	10.5913i	−0.155881	−	0.450389i
$554$		0			0
$555$	6.51673	−	7.85740i	0.276620	−	0.333528i
$556$		0			0
$557$	16.6237	+	21.1388i	0.704369	+	0.895679i	0.998187	−	0.0601829i	$-0.0191684\pi$
$557$	16.6237	+	21.1388i	0.704369	+	0.895679i	−0.293818	+	0.955861i	$0.594926\pi$
$558$		0			0
$559$	−0.275829	−	5.79037i	−0.0116663	−	0.244907i
$560$		0			0
$561$	−1.66806	−	2.02933i	−0.0704257	−	0.0856784i
$562$		0			0
$563$	−6.20782	−	43.1764i	−0.261629	−	1.81967i	−0.520622	−	0.853788i	$-0.674300\pi$
$563$	−6.20782	−	43.1764i	−0.261629	−	1.81967i	0.258993	−	0.965879i	$-0.416609\pi$
$564$		0			0
$565$	−2.45249	−	4.24784i	−0.103177	−	0.178708i
$566$		0			0
$567$	0.194738	−	22.1339i	0.00817822	−	0.929536i
$568$		0			0
$569$	−24.2621	−	17.2770i	−1.01712	−	0.724289i	−0.0554414	−	0.998462i	$-0.517657\pi$
$569$	−24.2621	−	17.2770i	−1.01712	−	0.724289i	−0.961680	+	0.274173i	$0.911596\pi$
$570$		0			0
$571$	−0.750998	+	15.7654i	−0.0314283	+	0.659761i	0.927109	+	0.374793i	$0.122286\pi$
$571$	−0.750998	+	15.7654i	−0.0314283	+	0.659761i	−0.958537	+	0.284968i	$0.908017\pi$
$572$		0			0
$573$	−2.93849	−	6.08316i	−0.122757	−	0.254127i
$574$		0			0
$575$	−0.700119	−	0.169847i	−0.0291970	−	0.00708312i
$576$		0			0
$577$	7.92014	−	41.0936i	0.329720	−	1.71075i	−0.317343	−	0.948311i	$-0.602791\pi$
$577$	7.92014	−	41.0936i	0.329720	−	1.71075i	0.647063	−	0.762437i	$-0.275997\pi$
$578$		0			0
$579$	12.2244	+	46.0268i	0.508029	+	1.91281i
$580$		0			0
$581$	21.2694	+	13.6690i	0.882405	+	0.567087i
$582$		0			0
$583$	32.3537	+	16.6795i	1.33995	+	0.690793i
$584$		0			0
$585$	−38.0554	+	24.2209i	−1.57340	+	1.00141i
$586$		0			0
$587$	26.8181	+	21.0900i	1.10690	+	0.870477i	0.992413	−	0.122947i	$-0.0392346\pi$
$587$	26.8181	+	21.0900i	1.10690	+	0.870477i	0.114489	+	0.993425i	$0.463477\pi$
$588$		0			0
$589$	0.959209	−	0.831159i	0.0395235	−	0.0342473i
$590$		0			0
$591$	27.5272	+	10.3361i	1.13232	+	0.425172i
$592$		0			0
$593$	26.4914	−	13.6573i	1.08787	−	0.560837i	0.181532	−	0.983385i	$-0.441895\pi$
$593$	26.4914	−	13.6573i	1.08787	−	0.560837i	0.906341	+	0.422548i	$0.138864\pi$
$594$		0			0
$595$	2.80822	−	0.824569i	0.115126	−	0.0338040i
$596$		0			0
$597$	−17.6741	+	11.9056i	−0.723352	+	0.487262i
$598$		0			0
$599$	−4.85131	+	14.0169i	−0.198219	+	0.572717i	−0.999679	−	0.0253316i	$-0.991936\pi$
$599$	−4.85131	+	14.0169i	−0.198219	+	0.572717i	0.801460	+	0.598049i	$0.204057\pi$
$600$		0			0
$601$	22.9200	+	32.1867i	0.934927	+	1.31292i	0.949743	+	0.313031i	$0.101344\pi$
$601$	22.9200	+	32.1867i	0.934927	+	1.31292i	−0.0148163	+	0.999890i	$0.504716\pi$
$602$		0			0
$603$	24.5438	−	0.775182i	0.999502	−	0.0315678i
$604$		0			0
$605$	−4.32259	−	6.07023i	−0.175738	−	0.246790i
$606$		0			0
$607$	−4.68718	+	13.5427i	−0.190247	+	0.549682i	−0.999274	−	0.0380889i	$-0.987873\pi$
$607$	−4.68718	+	13.5427i	−0.190247	+	0.549682i	0.809028	+	0.587771i	$0.199994\pi$
$608$		0			0
$609$	−10.2408	+	6.89840i	−0.414980	+	0.279537i
$610$		0			0
$611$	78.9903	−	23.1937i	3.19561	−	0.938315i
$612$		0			0
$613$	14.1715	−	7.30591i	0.572381	−	0.295083i	−0.147633	−	0.989042i	$-0.547165\pi$
$613$	14.1715	−	7.30591i	0.572381	−	0.295083i	0.720014	+	0.693959i	$0.244135\pi$
$614$		0			0
$615$	−22.8499	−	8.57986i	−0.921396	−	0.345973i
$616$		0			0
$617$	10.1060	−	8.75690i	0.406852	−	0.352539i	−0.427265	−	0.904126i	$-0.640523\pi$
$617$	10.1060	−	8.75690i	0.406852	−	0.352539i	0.834117	+	0.551587i	$0.185978\pi$
$618$		0			0
$619$	−35.1858	−	27.6704i	−1.41424	−	1.11217i	−0.977102	−	0.212770i	$-0.931751\pi$
$619$	−35.1858	−	27.6704i	−1.41424	−	1.11217i	−0.437133	−	0.899397i	$-0.644006\pi$
$620$		0			0
$621$	−0.318880	+	10.4868i	−0.0127962	+	0.420820i
$622$		0			0
$623$	4.53723	+	2.33911i	0.181780	+	0.0937143i
$624$		0			0
$625$	−19.4234	−	12.4827i	−0.776937	−	0.499307i
$626$		0			0
$627$	3.41600	+	12.8618i	0.136422	+	0.513650i
$628$		0			0
$629$	−0.285868	+	1.48323i	−0.0113983	+	0.0591401i
$630$		0			0
$631$	32.3998	+	7.86012i	1.28982	+	0.312906i	0.821274	−	0.570534i	$-0.193264\pi$
$631$	32.3998	+	7.86012i	1.28982	+	0.312906i	0.468544	+	0.883440i	$0.344779\pi$
$632$		0			0
$633$	−14.2420	−	29.4833i	−0.566069	−	1.17185i
$634$		0			0
$635$	1.58624	−	33.2993i	0.0629480	−	1.32144i
$636$		0			0
$637$	−5.40724	−	3.85048i	−0.214243	−	0.152562i
$638$		0			0
$639$	26.1043	+	10.5841i	1.03267	+	0.418699i
$640$		0			0
$641$	5.04283	+	8.73443i	0.199180	+	0.344989i	0.948263	−	0.317487i	$-0.102839\pi$
$641$	5.04283	+	8.73443i	0.199180	+	0.344989i	−0.749083	+	0.662476i	$0.769506\pi$
$642$		0			0
$643$	1.46628	+	10.1982i	0.0578245	+	0.402178i	0.998092	+	0.0617419i	$0.0196656\pi$
$643$	1.46628	+	10.1982i	0.0578245	+	0.402178i	−0.940268	+	0.340436i	$0.889425\pi$
$644$		0			0
$645$	−1.96879	−	2.39518i	−0.0775209	−	0.0943102i
$646$		0			0
$647$	−2.21980	−	46.5994i	−0.0872694	−	1.83201i	−0.441969	−	0.897030i	$-0.645720\pi$
$647$	−2.21980	−	46.5994i	−0.0872694	−	1.83201i	0.354700	−	0.934980i	$-0.384583\pi$
$648$		0			0
$649$	22.6253	+	28.7704i	0.888120	+	1.12934i
$650$		0			0
$651$	−1.23368	+	1.48748i	−0.0483517	+	0.0582990i
$652$		0			0
$653$	14.8700	+	42.9640i	0.581907	+	1.68131i	0.722607	+	0.691259i	$0.242944\pi$
$653$	14.8700	+	42.9640i	0.581907	+	1.68131i	−0.140700	+	0.990052i	$0.544935\pi$
$654$		0			0
$655$	−12.7194	+	5.80875i	−0.496988	+	0.226967i
$656$		0			0
$657$	−28.1436	−	13.0027i	−1.09799	−	0.507282i
$658$		0			0
$659$	9.29668	+	23.2220i	0.362147	+	0.904600i	0.991809	+	0.127731i	$0.0407693\pi$
$659$	9.29668	+	23.2220i	0.362147	+	0.904600i	−0.629662	+	0.776870i	$0.716806\pi$
$660$		0			0
$661$	−1.56815	−	0.716148i	−0.0609938	−	0.0278549i	0.384685	−	0.923048i	$-0.374310\pi$
$661$	−1.56815	−	0.716148i	−0.0609938	−	0.0278549i	−0.445678	+	0.895193i	$0.647037\pi$
$662$		0			0
$663$	3.21184	−	5.85141i	0.124738	−	0.227250i
$664$		0			0
$665$	−14.6759	−	2.11008i	−0.569107	−	0.0818253i
$666$		0			0
$667$	4.92354	−	3.16417i	0.190640	−	0.122517i
$668$		0			0
$669$	16.2588	−	23.9089i	0.628600	−	0.924370i
$670$		0			0
$671$		−	16.6305i		−	0.642013i
$672$		0			0
$673$	−1.62999	−	2.53631i	−0.0628314	−	0.0977675i	0.808416	−	0.588611i	$-0.200325\pi$
$673$	−1.62999	−	2.53631i	−0.0628314	−	0.0977675i	−0.871248	+	0.490844i	$0.836689\pi$
$674$		0			0
$675$	0.659356	−	1.73279i	0.0253786	−	0.0666953i
$676$		0			0
$677$	29.1487	−	2.78336i	1.12028	−	0.106973i	0.481558	−	0.876414i	$-0.340071\pi$
$677$	29.1487	−	2.78336i	1.12028	−	0.106973i	0.638718	+	0.769441i	$0.279465\pi$
$678$		0			0
$679$	8.63441	−	18.9067i	0.331358	−	0.725574i
$680$		0			0
$681$	10.4813	+	2.30423i	0.401645	+	0.0882982i
$682$		0			0
$683$	−5.63357	+	5.37160i	−0.215563	+	0.205539i	−0.790165	−	0.612894i	$-0.790005\pi$
$683$	−5.63357	+	5.37160i	−0.215563	+	0.205539i	0.574602	+	0.818433i	$0.305157\pi$
$684$		0			0
$685$	10.9848	+	24.0534i	0.419708	+	0.919032i
$686$		0			0
$687$	1.41735	−	5.24346i	0.0540752	−	0.200050i
$688$		0			0
$689$	−8.79196	+	92.0736i	−0.334947	+	3.50772i
$690$		0			0
$691$	−11.2652	+	8.85907i	−0.428549	+	0.337015i	−0.809023	−	0.587777i	$-0.800003\pi$
$691$	−11.2652	+	8.85907i	−0.428549	+	0.337015i	0.380474	+	0.924792i	$0.375761\pi$
$692$		0			0
$693$	−8.33607	−	18.4680i	−0.316661	−	0.701542i
$694$		0			0
$695$	6.05256	−	20.6131i	0.229587	−	0.781901i
$696$		0			0
$697$	3.57489	−	0.513991i	0.135408	−	0.0194688i
$698$		0			0
$699$	−11.5187	−	0.849303i	−0.435677	−	0.0321236i
$700$		0			0
$701$	18.2157	+	17.3687i	0.687999	+	0.656006i	0.951143	−	0.308751i	$-0.0999109\pi$
$701$	18.2157	+	17.3687i	0.687999	+	0.656006i	−0.263144	+	0.964757i	$0.584759\pi$
$702$		0			0
$703$	4.43870	−	6.23329i	0.167409	−	0.235093i
$704$		0			0
$705$	26.4646	−	35.1909i	0.996713	−	1.32537i
$706$		0			0
$707$	−1.56689	−	0.904646i	−0.0589291	−	0.0340227i
$708$		0			0
$709$	−6.67711	+	27.5234i	−0.250764	+	1.03366i	0.697602	+	0.716486i	$0.254250\pi$
$709$	−6.67711	+	27.5234i	−0.250764	+	1.03366i	−0.948366	+	0.317178i	$0.897265\pi$
$710$		0			0
$711$	−13.4354	+	2.52822i	−0.503868	+	0.0948157i
$712$		0			0
$713$	0.599844	−	0.692257i	0.0224643	−	0.0259252i
$714$		0			0
$715$	−22.3249	+	34.7382i	−0.834904	+	1.29914i
$716$		0			0
$717$	−38.0230	+	20.6537i	−1.42000	+	0.771327i
$718$		0			0
$719$	−0.513994	−	2.66685i	−0.0191687	−	0.0994569i	0.971084	−	0.238737i	$-0.0767333\pi$
$719$	−0.513994	−	2.66685i	−0.0191687	−	0.0994569i	−0.990253	+	0.139280i	$0.955521\pi$
$720$		0			0
$721$	−19.6787	+	25.0235i	−0.732874	+	0.931925i
$722$		0			0
$723$	−0.111900	+	0.0131297i	−0.00416160	+	0.000488298i
$724$		0			0
$725$	−1.00508	+	0.243829i	−0.0373277	+	0.00905560i
$726$		0			0
$727$	16.5228	+	32.0498i	0.612798	+	1.18866i	0.967307	+	0.253610i	$0.0816179\pi$
$727$	16.5228	+	32.0498i	0.612798	+	1.18866i	−0.354508	+	0.935053i	$0.615352\pi$
$728$		0			0
$729$	−26.6721	−	4.19485i	−0.987857	−	0.155365i
$730$		0			0
$731$	0.425922	+	0.170513i	0.0157533	+	0.00630667i
$732$		0			0
$733$	6.38116	+	2.20854i	0.235694	+	0.0815743i	0.442362	−	0.896837i	$-0.354141\pi$
$733$	6.38116	+	2.20854i	0.235694	+	0.0815743i	−0.206668	+	0.978411i	$0.566262\pi$
$734$		0			0
$735$	−3.54956	+	0.0766840i	−0.130927	+	0.00282853i
$736$		0			0
$737$	20.0983	−	10.0673i	0.740330	−	0.370835i
$738$		0			0
$739$	−9.54596	+	6.79764i	−0.351154	+	0.250055i	−0.741999	−	0.670401i	$-0.766122\pi$
$739$	−9.54596	+	6.79764i	−0.351154	+	0.250055i	0.390845	+	0.920456i	$0.372183\pi$
$740$		0			0
$741$	−27.1146	+	20.2048i	−0.996080	+	0.742243i
$742$		0			0
$743$	−13.4166	+	33.5130i	−0.492207	+	1.22947i	0.449573	+	0.893244i	$0.351576\pi$
$743$	−13.4166	+	33.5130i	−0.492207	+	1.22947i	−0.941780	+	0.336230i	$0.890848\pi$
$744$		0			0
$745$	12.0652	+	41.0902i	0.442034	+	1.50543i
$746$		0			0
$747$	20.2984	−	23.2185i	0.742681	−	0.849519i
$748$		0			0
$749$	2.81591	+	11.6073i	0.102891	+	0.424122i
$750$		0			0
$751$	−24.0876	−	27.7986i	−0.878971	−	1.01439i	−0.999764	−	0.0217085i	$-0.993089\pi$
$751$	−24.0876	−	27.7986i	−0.878971	−	1.01439i	0.120794	−	0.992678i	$-0.461456\pi$
$752$		0			0
$753$	−41.0801	+	13.0324i	−1.49704	+	0.474926i
$754$		0			0
$755$	−17.8859	+	3.44722i	−0.650934	+	0.125457i
$756$		0			0
$757$	−16.4736	+	31.9542i	−0.598742	+	1.16140i	0.373547	+	0.927611i	$0.378142\pi$
$757$	−16.4736	+	31.9542i	−0.598742	+	1.16140i	−0.972288	+	0.233785i	$0.924889\pi$
$758$		0			0
$759$	3.76122	+	8.83695i	0.136524	+	0.320761i
$760$		0			0
$761$	0.118608	+	0.102774i	0.00429952	+	0.00372556i	0.657008	−	0.753884i	$-0.271822\pi$
$761$	0.118608	+	0.102774i	0.00429952	+	0.00372556i	−0.652708	+	0.757609i	$0.726367\pi$
$762$		0			0
$763$	17.8315	+	3.43674i	0.645544	+	0.124418i
$764$		0			0
$765$	−0.492527	−	3.53595i	−0.0178074	−	0.127843i
$766$		0			0
$767$	−46.5016	+	80.5431i	−1.67908	+	2.90824i
$768$		0			0
$769$	−46.3240	−	2.20669i	−1.67049	−	0.0795751i	−0.809148	−	0.587605i	$-0.800071\pi$
$769$	−46.3240	−	2.20669i	−1.67049	−	0.0795751i	−0.861340	+	0.508030i	$0.830374\pi$
$770$		0			0
$771$	24.1753	−	8.95639i	0.870652	−	0.322557i
$772$		0			0
$773$	28.4381	−	29.8250i	1.02285	−	1.07273i	0.0255199	−	0.999674i	$-0.491876\pi$
$773$	28.4381	−	29.8250i	1.02285	−	1.07273i	0.997328	−	0.0730574i	$-0.0232756\pi$
$774$		0			0
$775$	−0.140180	+	0.0809331i	−0.00503542	+	0.00290720i
$776$		0			0
$777$	−5.11397	+	10.4689i	−0.183462	+	0.375570i
$778$		0			0
$779$	−17.5552	−	5.15467i	−0.628980	−	0.184685i
$780$		0			0
$781$	25.7562	−	1.22692i	0.921631	−	0.0439027i
$782$		0			0
$783$	6.49155	+	13.5909i	0.231989	+	0.485698i
$784$		0			0
$785$	−3.79908	−	0.362768i	−0.135595	−	0.0129478i
$786$		0			0
$787$	23.0071	−	7.96283i	0.820114	−	0.283844i	0.115385	−	0.993321i	$-0.463190\pi$
$787$	23.0071	−	7.96283i	0.820114	−	0.283844i	0.704729	+	0.709477i	$0.251069\pi$
$788$		0			0
$789$	−3.90208	+	22.8968i	−0.138918	+	0.815146i
$790$		0			0
$791$	3.86331	+	4.05172i	0.137363	+	0.144063i
$792$		0			0
$793$	39.2310	−	15.7057i	1.39313	−	0.557727i
$794$		0			0
$795$	25.6543	+	42.2976i	0.909864	+	1.50014i
$796$		0			0
$797$	−2.68671	−	28.1365i	−0.0951681	−	0.996645i	−0.909349	−	0.416034i	$-0.863420\pi$
$797$	−2.68671	−	28.1365i	−0.0951681	−	0.996645i	0.814181	−	0.580611i	$-0.197186\pi$
$798$		0			0
$799$	−0.927243	+	6.44912i	−0.0328035	+	0.228153i
$800$		0			0
$801$	3.63413	−	5.05620i	0.128406	−	0.178652i
$802$		0			0
$803$	−28.3795			−1.00149
$804$		0			0
$805$	−10.7004			−0.377141
$806$		0			0
$807$	15.8510	+	0.412211i	0.557983	+	0.0145105i
$808$		0			0
$809$	1.33803	−	9.30620i	0.0470426	−	0.327188i	−0.952687	−	0.303952i	$-0.901694\pi$
$809$	1.33803	−	9.30620i	0.0470426	−	0.327188i	0.999730	−	0.0232366i	$-0.00739711\pi$
$810$		0			0
$811$	2.07284	+	21.7078i	0.0727873	+	0.762263i	0.956015	+	0.293318i	$0.0947596\pi$
$811$	2.07284	+	21.7078i	0.0727873	+	0.762263i	−0.883227	+	0.468945i	$0.844634\pi$
$812$		0			0
$813$	17.4159	−	10.5631i	0.610801	−	0.370462i
$814$		0			0
$815$	15.1503	−	6.06525i	0.530690	−	0.212456i
$816$		0			0
$817$	−1.60386	−	1.68208i	−0.0561120	−	0.0588486i
$818$		0			0
$819$	35.6931	−	37.1057i	1.24722	−	1.29658i
$820$		0			0
$821$	30.1184	−	10.4241i	1.05114	−	0.363803i	0.253751	−	0.967269i	$-0.418335\pi$
$821$	30.1184	−	10.4241i	1.05114	−	0.363803i	0.797388	+	0.603466i	$0.206214\pi$
$822$		0			0
$823$	−11.0091	−	1.05125i	−0.383755	−	0.0366441i	−0.0986037	−	0.995127i	$-0.531438\pi$
$823$	−11.0091	−	1.05125i	−0.383755	−	0.0366441i	−0.285151	+	0.958483i	$0.592044\pi$
$824$		0			0
$825$	−0.117350	−	1.69310i	−0.00408562	−	0.0589462i
$826$		0			0
$827$	28.6623	−	1.36535i	0.996685	−	0.0474780i	0.457106	−	0.889412i	$-0.348886\pi$
$827$	28.6623	−	1.36535i	0.996685	−	0.0474780i	0.539580	+	0.841934i	$0.318583\pi$
$828$		0			0
$829$	−11.4805	−	3.37097i	−0.398733	−	0.117079i	0.0762173	−	0.997091i	$-0.475716\pi$
$829$	−11.4805	−	3.37097i	−0.398733	−	0.117079i	−0.474950	+	0.880013i	$0.657534\pi$
$830$		0			0
$831$	−17.7201	−	8.65613i	−0.614704	−	0.300278i
$832$		0			0
$833$	0.454974	−	0.262679i	0.0157639	−	0.00910130i
$834$		0			0
$835$	−18.0209	+	18.8998i	−0.623639	+	0.654054i
$836$		0			0
$837$	1.57410	+	1.75469i	0.0544088	+	0.0606510i
$838$		0			0
$839$	−7.50028	−	0.357283i	−0.258939	−	0.0123348i	−0.0822887	−	0.996609i	$-0.526223\pi$
$839$	−7.50028	−	0.357283i	−0.258939	−	0.0123348i	−0.176650	+	0.984274i	$0.556526\pi$
$840$		0			0
$841$	−10.2990	+	17.8385i	−0.355139	+	0.615119i
$842$		0			0
$843$	−23.3362	−	25.7844i	−0.803743	−	0.888064i
$844$		0			0
$845$	−75.5239	−	14.5560i	−2.59810	−	0.500743i
$846$		0			0
$847$	6.42798	+	5.56988i	0.220868	+	0.191383i
$848$		0			0
$849$	−1.12282	+	0.477898i	−0.0385349	+	0.0164014i
$850$		0			0
$851$	2.53058	−	4.90864i	0.0867471	−	0.168266i
$852$		0			0
$853$	7.14229	−	1.37656i	0.244547	−	0.0471327i	−0.0655045	−	0.997852i	$-0.520866\pi$
$853$	7.14229	−	1.37656i	0.244547	−	0.0471327i	0.310052	+	0.950720i	$0.399654\pi$
$854$		0			0
$855$	−5.17164	+	17.3306i	−0.176866	+	0.592694i
$856$		0			0
$857$	−2.53153	−	2.92154i	−0.0864755	−	0.0997980i	0.710863	−	0.703331i	$-0.248305\pi$
$857$	−2.53153	−	2.92154i	−0.0864755	−	0.0997980i	−0.797338	+	0.603533i	$0.793759\pi$
$858$		0			0
$859$	−1.00173	−	4.12919i	−0.0341786	−	0.140886i	0.952166	−	0.305582i	$-0.0988510\pi$
$859$	−1.00173	−	4.12919i	−0.0341786	−	0.140886i	−0.986344	+	0.164696i	$0.947336\pi$
$860$		0			0
$861$	27.6535	+	3.36810i	0.942430	+	0.114784i
$862$		0			0
$863$	1.22638	+	4.17668i	0.0417466	+	0.142176i	0.977729	−	0.209870i	$-0.0673042\pi$
$863$	1.22638	+	4.17668i	0.0417466	+	0.142176i	−0.935983	+	0.352046i	$0.885486\pi$
$864$		0			0
$865$	16.7783	−	41.9101i	0.570478	−	1.42499i
$866$		0			0
$867$	−17.2781	−	23.1870i	−0.586795	−	0.787471i
$868$		0			0
$869$	−10.1942	+	7.25924i	−0.345814	+	0.246253i
$870$		0			0
$871$	42.7293	+	37.9039i	1.44783	+	1.28433i
$872$		0			0
$873$	−21.2683	−	13.8009i	−0.719824	−	0.467090i
$874$		0			0
$875$	26.8274	+	9.28505i	0.906931	+	0.313892i
$876$		0			0
$877$	−33.1871	−	13.2861i	−1.12065	−	0.448641i	−0.263992	−	0.964525i	$-0.585039\pi$
$877$	−33.1871	−	13.2861i	−1.12065	−	0.448641i	−0.856658	+	0.515884i	$0.827463\pi$
$878$		0			0
$879$	27.5605	+	8.87698i	0.929591	+	0.299413i
$880$		0			0
$881$	−3.25892	−	6.32142i	−0.109796	−	0.212974i	0.827536	−	0.561413i	$-0.189742\pi$
$881$	−3.25892	−	6.32142i	−0.109796	−	0.212974i	−0.937331	+	0.348439i	$0.886712\pi$
$882$		0			0
$883$	−3.38521	+	0.821244i	−0.113922	+	0.0276371i	−0.292314	−	0.956322i	$-0.594425\pi$
$883$	−3.38521	+	0.821244i	−0.113922	+	0.0276371i	0.178393	+	0.983959i	$0.442910\pi$
$884$		0			0
$885$	5.79675	+	49.4037i	0.194856	+	1.66069i
$886$		0			0
$887$	−6.30023	+	8.01140i	−0.211541	+	0.268996i	−0.880231	−	0.474545i	$-0.842613\pi$
$887$	−6.30023	+	8.01140i	−0.211541	+	0.268996i	0.668690	+	0.743541i	$0.266855\pi$
$888$		0			0
$889$	7.20094	+	37.3620i	0.241512	+	1.25308i
$890$		0			0
$891$	−23.7751	+	6.75437i	−0.796495	+	0.226280i
$892$		0			0
$893$	17.8448	−	27.7670i	0.597152	−	0.929187i
$894$		0			0
$895$	13.5701	−	15.6607i	0.453598	−	0.523480i
$896$		0			0
$897$	−17.2941	+	17.2182i	−0.577433	+	0.574899i
$898$		0			0
$899$	0.310017	−	1.27791i	0.0103396	−	0.0426206i
$900$		0			0
$901$	−6.33940	−	3.66005i	−0.211196	−	0.121934i
$902$		0			0
$903$	2.82827	+	2.12694i	0.0941188	+	0.0707800i
$904$		0			0
$905$	−8.26515	+	11.6068i	−0.274743	+	0.385822i
$906$		0			0
$907$	−1.53755	−	1.46605i	−0.0510534	−	0.0486793i	0.664123	−	0.747623i	$-0.268805\pi$
$907$	−1.53755	−	1.46605i	−0.0510534	−	0.0486793i	−0.715176	+	0.698944i	$0.753654\pi$
$908$		0			0
$909$	−1.37188	+	1.72878i	−0.0455024	+	0.0573401i
$910$		0			0
$911$	29.7778	−	4.28140i	0.986583	−	0.141849i	0.369909	−	0.929068i	$-0.379389\pi$
$911$	29.7778	−	4.28140i	0.986583	−	0.141849i	0.616674	+	0.787219i	$0.288480\pi$
$912$		0			0
$913$	7.95369	−	27.0878i	0.263229	−	0.896474i
$914$		0			0
$915$	11.8059	−	19.2732i	0.390290	−	0.637153i
$916$		0			0
$917$	12.5452	−	9.86562i	0.414278	−	0.325791i
$918$		0			0
$919$	−1.50036	+	15.7125i	−0.0494923	+	0.518306i	0.936401	+	0.350932i	$0.114135\pi$
$919$	−1.50036	+	15.7125i	−0.0494923	+	0.518306i	−0.985893	+	0.167375i	$0.946471\pi$
$920$		0			0
$921$	18.4663	+	4.99158i	0.608484	+	0.164478i
$922$		0			0
$923$	27.2183	+	59.5997i	0.895901	+	1.96175i
$924$		0			0
$925$	−0.706294	+	0.673450i	−0.0232228	+	0.0221429i
$926$		0			0
$927$	26.6730	+	28.2214i	0.876058	+	0.926913i
$928$		0			0
$929$	17.5384	−	38.4038i	0.575418	−	1.25999i	−0.368445	−	0.929650i	$-0.620110\pi$
$929$	17.5384	−	38.4038i	0.575418	−	1.25999i	0.943862	−	0.330339i	$-0.107163\pi$
$930$		0			0
$931$	−2.64937	+	0.252984i	−0.0868297	+	0.00829123i
$932$		0			0
$933$	16.6402	+	15.1939i	0.544774	+	0.497425i
$934$		0			0
$935$	−1.76685	−	2.74928i	−0.0577823	−	0.0899110i
$936$		0			0
$937$		−	41.0031i		−	1.33951i	−0.742581	−	0.669756i	$-0.766399\pi$
$937$		−	41.0031i		−	1.33951i	0.742581	−	0.669756i	$-0.233601\pi$
$938$		0			0
$939$	18.9217	+	12.8673i	0.617486	+	0.419910i
$940$		0			0
$941$	37.4772	−	24.0851i	1.22172	−	0.785152i	0.239139	−	0.970985i	$-0.423135\pi$
$941$	37.4772	−	24.0851i	1.22172	−	0.785152i	0.982581	+	0.185833i	$0.0594984\pi$
$942$		0			0
$943$	−13.0700	−	1.87918i	−0.425616	−	0.0611944i
$944$		0			0
$945$	3.44956	−	27.3204i	0.112214	−	0.888734i
$946$		0			0
$947$	−15.7829	−	7.20782i	−0.512876	−	0.234223i	0.142128	−	0.989848i	$-0.454606\pi$
$947$	−15.7829	−	7.20782i	−0.512876	−	0.234223i	−0.655004	+	0.755626i	$0.727333\pi$
$948$		0			0
$949$	−26.8013	−	66.9465i	−0.870009	−	2.17318i
$950$		0			0
$951$	12.1702	−	2.01900i	0.394646	−	0.0654707i
$952$		0			0
$953$	−35.4125	+	16.1724i	−1.14712	+	0.523874i	−0.895988	−	0.444078i	$-0.853531\pi$
$953$	−35.4125	+	16.1724i	−1.14712	+	0.523874i	−0.251136	+	0.967952i	$0.580804\pi$
$954$		0			0
$955$	−2.74888	−	7.94238i	−0.0889518	−	0.257009i
$956$		0			0
$957$	10.6124	+	8.80170i	0.343052	+	0.284518i
$958$		0			0
$959$	−18.6566	−	23.7239i	−0.602455	−	0.766083i
$960$		0			0
$961$	1.46525	+	30.7593i	0.0472660	+	0.992236i
$962$		0			0
$963$	14.5093	−	1.32109i	0.467556	−	0.0425715i
$964$		0			0
$965$	8.43161	+	58.6431i	0.271423	+	1.88779i
$966$		0			0
$967$	−26.8720	−	46.5436i	−0.864145	−	1.49674i	−0.867894	−	0.496750i	$-0.834527\pi$
$967$	−26.8720	−	46.5436i	−0.864145	−	1.49674i	0.00374909	−	0.999993i	$-0.498807\pi$
$968$		0			0
$969$	−0.563113	−	2.61628i	−0.0180898	−	0.0840470i
$970$		0			0
$971$	9.99233	+	7.11551i	0.320669	+	0.228348i	0.729044	−	0.684467i	$-0.239965\pi$
$971$	9.99233	+	7.11551i	0.320669	+	0.228348i	−0.408375	+	0.912814i	$0.633904\pi$
$972$		0			0
$973$	−1.16672	+	24.4925i	−0.0374034	+	0.785194i
$974$		0			0
$975$	3.88316	−	1.87578i	0.124361	−	0.0600730i
$976$		0			0
$977$	−25.7156	−	6.23853i	−0.822714	−	0.199588i	−0.197761	−	0.980250i	$-0.563367\pi$
$977$	−25.7156	−	6.23853i	−0.822714	−	0.199588i	−0.624954	+	0.780662i	$0.714882\pi$
$978$		0			0
$979$	1.07873	−	5.59696i	0.0344762	−	0.178880i
$980$		0			0
$981$	7.33696	−	20.9008i	0.234251	−	0.667312i
$982$		0			0
$983$	20.3730	+	13.0929i	0.649799	+	0.417600i	0.823593	−	0.567182i	$-0.191966\pi$
$983$	20.3730	+	13.0929i	0.649799	+	0.417600i	−0.173794	+	0.984782i	$0.555603\pi$
$984$		0			0
$985$	32.5142	+	16.7622i	1.03599	+	0.534089i
$986$		0			0
$987$	−19.8848	+	46.1546i	−0.632940	+	1.46912i
$988$		0			0
$989$	−1.31848	−	1.03687i	−0.0419253	−	0.0329704i
$990$		0			0
$991$	21.8626	−	18.9441i	0.694490	−	0.601779i	−0.234398	−	0.972141i	$-0.575312\pi$
$991$	21.8626	−	18.9441i	0.694490	−	0.601779i	0.928887	+	0.370362i	$0.120766\pi$
$992$		0			0
$993$	−9.98994	+	26.6052i	−0.317021	+	0.844290i
$994$		0			0
$995$	−23.5642	+	12.1482i	−0.747035	+	0.385123i
$996$		0			0
$997$	−19.8213	+	5.82007i	−0.627748	+	0.184324i	−0.580106	−	0.814541i	$-0.696989\pi$
$997$	−19.8213	+	5.82007i	−0.627748	+	0.184324i	−0.0476422	+	0.998864i	$0.515171\pi$
$998$		0			0
$999$	11.7170	+	8.04351i	0.370708	+	0.254485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.ba.b.41.12	✓	440
3.2	odd	2	inner	804.2.ba.b.41.19	yes	440
67.18	odd	66	inner	804.2.ba.b.353.19	yes	440
201.152	even	66	inner	804.2.ba.b.353.12	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.ba.b.41.12	✓	440	1.1	even	1	trivial
804.2.ba.b.41.19	yes	440	3.2	odd	2	inner
804.2.ba.b.353.12	yes	440	201.152	even	66	inner
804.2.ba.b.353.19	yes	440	67.18	odd	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.ba (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0450273 + 1.73147i) q^{3} +(-0.306661 + 2.13288i) q^{5} +(-0.233782 - 2.44828i) q^{7} +(-2.99595 - 0.155926i) q^{9} +O(q^{10})\)	\(q+(-0.0450273 + 1.73147i) q^{3} +(-0.306661 + 2.13288i) q^{5} +(-0.233782 - 2.44828i) q^{7} +(-2.99595 - 0.155926i) q^{9} +(-2.54950 + 1.02066i) q^{11} +(-4.81545 - 5.05030i) q^{13} +(-3.67919 - 0.627011i) q^{15} +(0.521893 - 0.180629i) q^{17} +(-2.78507 - 0.265942i) q^{19} +(4.24964 - 0.294547i) q^{21} +(-2.01683 + 0.0960734i) q^{23} +(0.342350 + 0.100523i) q^{25} +(0.404880 - 5.18035i) q^{27} +(-2.51027 + 1.44930i) q^{29} +(-0.313059 + 0.328327i) q^{31} +(-1.65245 - 4.46032i) q^{33} +(5.29357 + 0.252164i) q^{35} +(-1.36757 + 2.36869i) q^{37} +(8.96124 - 8.11038i) q^{39} +(6.42149 + 1.23764i) q^{41} +(0.627825 + 0.544013i) q^{43} +(1.25131 - 6.34216i) q^{45} +(-5.40598 + 10.4861i) q^{47} +(0.934085 - 0.180030i) q^{49} +(0.289253 + 0.911773i) q^{51} +(-8.67995 - 10.0172i) q^{53} +(-1.39512 - 5.75075i) q^{55} +(0.585874 - 4.81028i) q^{57} +(-3.75489 - 12.7880i) q^{59} +(-2.25071 + 5.62201i) q^{61} +(0.318648 + 7.37136i) q^{63} +(12.2484 - 8.72202i) q^{65} +(-8.15679 + 0.683270i) q^{67} +(-0.0755355 - 3.49640i) q^{69} +(-8.87305 - 3.07099i) q^{71} +(9.59379 + 3.84077i) q^{73} +(-0.189467 + 0.588241i) q^{75} +(3.09490 + 6.00326i) q^{77} +(4.42862 - 1.07437i) q^{79} +(8.95137 + 0.934293i) q^{81} +(-6.35474 + 8.08070i) q^{83} +(0.225215 + 1.16852i) q^{85} +(-2.39639 - 4.41170i) q^{87} +(-1.12214 + 1.74608i) q^{89} +(-11.2388 + 12.9702i) q^{91} +(-0.554391 - 0.556835i) q^{93} +(1.42130 - 5.85866i) q^{95} +(7.31896 + 4.22560i) q^{97} +(7.79730 - 2.66032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 440 * q - 12 * q^7 + 4 * q^9	\( 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) \) 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more