LMFDB - Embedded newform 1197.2.db.a.647.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1197,2,Mod(647,1197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1197, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("1197.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1197 = 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1197.db (of order $6$, degree $2$, 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:	$9.55809312195$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.3
Character	$\chi$	$=$	1197.647
Dual form			1197.2.db.a.1160.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18268 + 1.26017i) q^{2} +(2.17605 - 3.76903i) q^{4} +(1.50551 + 2.60762i) q^{5} +(2.61298 - 0.415128i) q^{7} +5.92809i q^{8} +O(q^{10})$	\(q+(-2.18268 + 1.26017i) q^{2} +(2.17605 - 3.76903i) q^{4} +(1.50551 + 2.60762i) q^{5} +(2.61298 - 0.415128i) q^{7} +5.92809i q^{8} +(-6.57208 - 3.79439i) q^{10} +(-4.90986 - 2.83471i) q^{11} -3.34806i q^{13} +(-5.18016 + 4.19889i) q^{14} +(-3.11829 - 5.40103i) q^{16} +(1.01025 - 1.74981i) q^{17} +(0.866025 - 0.500000i) q^{19} +13.1043 q^{20} +14.2888 q^{22} +(6.00268 - 3.46565i) q^{23} +(-2.03312 + 3.52147i) q^{25} +(4.21912 + 7.30772i) q^{26} +(4.12135 - 10.7517i) q^{28} -6.50270i q^{29} +(-4.83312 - 2.79040i) q^{31} +(3.34468 + 1.93105i) q^{32} +5.09234i q^{34} +(5.01637 + 6.18868i) q^{35} +(-3.40706 - 5.90120i) q^{37} +(-1.26017 + 2.18268i) q^{38} +(-15.4582 + 8.92479i) q^{40} +3.22842 q^{41} -10.4191 q^{43} +(-21.3682 + 12.3369i) q^{44} +(-8.73461 + 15.1288i) q^{46} +(-3.56961 - 6.18275i) q^{47} +(6.65534 - 2.16944i) q^{49} -10.2483i q^{50} +(-12.6189 - 7.28554i) q^{52} +(-8.91702 - 5.14824i) q^{53} -17.0707i q^{55} +(2.46092 + 15.4900i) q^{56} +(8.19451 + 14.1933i) q^{58} +(-5.62275 + 9.73889i) q^{59} +(-1.56624 + 0.904269i) q^{61} +14.0655 q^{62} +2.73935 q^{64} +(8.73046 - 5.04053i) q^{65} +(1.12089 - 1.94144i) q^{67} +(-4.39671 - 7.61533i) q^{68} +(-18.7479 - 7.18642i) q^{70} -4.91667i q^{71} +(10.6823 + 6.16741i) q^{73} +(14.8730 + 8.58694i) q^{74} -4.35210i q^{76} +(-14.0061 - 5.36882i) q^{77} +(3.36261 + 5.82421i) q^{79} +(9.38923 - 16.2626i) q^{80} +(-7.04659 + 4.06835i) q^{82} -1.08666 q^{83} +6.08377 q^{85} +(22.7415 - 13.1298i) q^{86} +(16.8044 - 29.1061i) q^{88} +(-4.53732 - 7.85887i) q^{89} +(-1.38987 - 8.74841i) q^{91} -30.1657i q^{92} +(15.5826 + 8.99663i) q^{94} +(2.60762 + 1.50551i) q^{95} +2.54347i q^{97} +(-11.7926 + 13.1220i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 48 q^{4} + 8 q^{7}+O(q^{10}) $ 96 * q + 48 * q^4 + 8 * q^7	$ 96 q + 48 q^{4} + 8 q^{7} + 24 q^{10} - 56 q^{16} + 48 q^{22} - 24 q^{25} + 16 q^{28} - 24 q^{31} - 48 q^{40} - 24 q^{43} - 48 q^{46} + 52 q^{49} - 72 q^{52} + 48 q^{58} - 176 q^{64} + 32 q^{67} - 80 q^{70} - 12 q^{73} + 40 q^{79} + 72 q^{82} + 40 q^{85} - 16 q^{88} - 72 q^{91} + 72 q^{94}+O(q^{100}) $ 96 * q + 48 * q^4 + 8 * q^7 + 24 * q^10 - 56 * q^16 + 48 * q^22 - 24 * q^25 + 16 * q^28 - 24 * q^31 - 48 * q^40 - 24 * q^43 - 48 * q^46 + 52 * q^49 - 72 * q^52 + 48 * q^58 - 176 * q^64 + 32 * q^67 - 80 * q^70 - 12 * q^73 + 40 * q^79 + 72 * q^82 + 40 * q^85 - 16 * q^88 - 72 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	−2.18268	+	1.26017i	−1.54339	+	0.891074i	−0.544763	+	0.838590i	$0.683381\pi$
$2$	−2.18268	+	1.26017i	−1.54339	+	0.891074i	−0.998622	+	0.0524840i	$0.983286\pi$
$3$		0			0
$3$		0			0
$4$	2.17605	−	3.76903i	1.08803	−	1.88451i
$5$	1.50551	+	2.60762i	0.673285	+	1.16616i	0.976967	+	0.213390i	$0.0684504\pi$
$5$	1.50551	+	2.60762i	0.673285	+	1.16616i	−0.303683	+	0.952773i	$0.598216\pi$
$6$		0			0
$7$	2.61298	−	0.415128i	0.987614	−	0.156904i
$7$	2.61298	−	0.415128i	0.987614	−	0.156904i
$8$			5.92809i			2.09590i
$9$		0			0
$10$	−6.57208	−	3.79439i	−2.07827	−	1.19989i
$11$	−4.90986	−	2.83471i	−1.48038	−	0.854697i	−0.480626	−	0.876926i	$-0.659590\pi$
$11$	−4.90986	−	2.83471i	−1.48038	−	0.854697i	−0.999753	+	0.0222287i	$0.992924\pi$
$12$		0			0
$13$		−	3.34806i		−	0.928584i	−0.885682	−	0.464292i	$-0.846309\pi$
$13$		−	3.34806i		−	0.928584i	0.885682	−	0.464292i	$-0.153691\pi$
$14$	−5.18016	+	4.19889i	−1.38446	+	1.12220i
$15$		0			0
$16$	−3.11829	−	5.40103i	−0.779572	−	1.35026i
$17$	1.01025	−	1.74981i	0.245022	−	0.424390i	−0.717116	−	0.696954i	$-0.754538\pi$
$17$	1.01025	−	1.74981i	0.245022	−	0.424390i	0.962138	+	0.272564i	$0.0878716\pi$
$18$		0			0
$19$	0.866025	−	0.500000i	0.198680	−	0.114708i
$19$	0.866025	−	0.500000i	0.198680	−	0.114708i
$20$	13.1043			2.93020
$21$		0			0
$22$	14.2888			3.04639
$23$	6.00268	−	3.46565i	1.25165	−	0.722638i	0.280210	−	0.959939i	$-0.409596\pi$
$23$	6.00268	−	3.46565i	1.25165	−	0.722638i	0.971436	+	0.237301i	$0.0762626\pi$
$24$		0			0
$25$	−2.03312	+	3.52147i	−0.406624	+	0.704294i
$26$	4.21912	+	7.30772i	0.827437	+	1.43316i
$27$		0			0
$28$	4.12135	−	10.7517i	0.778861	−	2.03189i
$29$		−	6.50270i		−	1.20752i	−0.797165	−	0.603761i	$-0.793668\pi$
$29$		−	6.50270i		−	1.20752i	0.797165	−	0.603761i	$-0.206332\pi$
$30$		0			0
$31$	−4.83312	−	2.79040i	−0.868054	−	0.501171i	−0.00135321	−	0.999999i	$-0.500431\pi$
$31$	−4.83312	−	2.79040i	−0.868054	−	0.501171i	−0.866701	+	0.498828i	$0.833764\pi$
$32$	3.34468	+	1.93105i	0.591262	+	0.341365i
$33$		0			0
$34$			5.09234i			0.873330i
$35$	5.01637	+	6.18868i	0.847920	+	1.04608i
$36$		0			0
$37$	−3.40706	−	5.90120i	−0.560117	−	0.970152i	−0.997486	−	0.0708692i	$-0.977423\pi$
$37$	−3.40706	−	5.90120i	−0.560117	−	0.970152i	0.437368	−	0.899282i	$-0.355911\pi$
$38$	−1.26017	+	2.18268i	−0.204426	+	0.354077i
$39$		0			0
$40$	−15.4582	+	8.92479i	−2.44416	+	1.41113i
$41$	3.22842			0.504194			0.252097	−	0.967702i	$-0.418880\pi$
$41$	3.22842			0.504194			0.252097	+	0.967702i	$0.418880\pi$
$42$		0			0
$43$	−10.4191			−1.58889			−0.794447	−	0.607333i	$-0.792239\pi$
$43$	−10.4191			−1.58889			−0.794447	+	0.607333i	$0.792239\pi$
$44$	−21.3682	+	12.3369i	−3.22138	+	1.85986i
$45$		0			0
$46$	−8.73461	+	15.1288i	−1.28785	+	2.23062i
$47$	−3.56961	−	6.18275i	−0.520681	−	0.901847i	−0.999711	−	0.0240478i	$-0.992345\pi$
$47$	−3.56961	−	6.18275i	−0.520681	−	0.901847i	0.479029	−	0.877799i	$-0.340989\pi$
$48$		0			0
$49$	6.65534	−	2.16944i	0.950762	−	0.309921i
$50$		−	10.2483i		−	1.44933i
$51$		0			0
$52$	−12.6189	−	7.28554i	−1.74993	−	1.01032i
$53$	−8.91702	−	5.14824i	−1.22485	−	0.707166i	−0.258899	−	0.965904i	$-0.583360\pi$
$53$	−8.91702	−	5.14824i	−1.22485	−	0.707166i	−0.965947	+	0.258739i	$0.916693\pi$
$54$		0			0
$55$		−	17.0707i		−	2.30182i
$56$	2.46092	+	15.4900i	0.328854	+	2.06994i
$57$		0			0
$58$	8.19451	+	14.1933i	1.07599	+	1.86367i
$59$	−5.62275	+	9.73889i	−0.732020	+	1.26790i	0.223999	+	0.974589i	$0.428089\pi$
$59$	−5.62275	+	9.73889i	−0.732020	+	1.26790i	−0.956019	+	0.293306i	$0.905245\pi$
$60$		0			0
$61$	−1.56624	+	0.904269i	−0.200537	+	0.115780i	−0.596906	−	0.802311i	$-0.703603\pi$
$61$	−1.56624	+	0.904269i	−0.200537	+	0.115780i	0.396369	+	0.918091i	$0.370270\pi$
$62$	14.0655			1.78632
$63$		0			0
$64$	2.73935			0.342418
$65$	8.73046	−	5.04053i	1.08288	−	0.625201i
$66$		0			0
$67$	1.12089	−	1.94144i	0.136938	−	0.237184i	−0.789398	−	0.613882i	$-0.789607\pi$
$67$	1.12089	−	1.94144i	0.136938	−	0.237184i	0.926336	+	0.376698i	$0.122940\pi$
$68$	−4.39671	−	7.61533i	−0.533180	−	0.923494i
$69$		0			0
$70$	−18.7479	−	7.18642i	−2.24080	−	0.858941i
$71$		−	4.91667i		−	0.583502i	−0.956494	−	0.291751i	$-0.905762\pi$
$71$		−	4.91667i		−	0.583502i	0.956494	−	0.291751i	$-0.0942378\pi$
$72$		0			0
$73$	10.6823	+	6.16741i	1.25027	+	0.721841i	0.971162	−	0.238420i	$-0.0766295\pi$
$73$	10.6823	+	6.16741i	1.25027	+	0.721841i	0.279103	+	0.960261i	$0.409963\pi$
$74$	14.8730	+	8.58694i	1.72895	+	0.998212i
$75$		0			0
$76$		−	4.35210i		−	0.499220i
$77$	−14.0061	−	5.36882i	−1.59615	−	0.611834i
$78$		0			0
$79$	3.36261	+	5.82421i	0.378323	+	0.655275i	0.990818	−	0.135200i	$-0.0431675\pi$
$79$	3.36261	+	5.82421i	0.378323	+	0.655275i	−0.612495	+	0.790474i	$0.709834\pi$
$80$	9.38923	−	16.2626i	1.04975	−	1.81822i
$81$		0			0
$82$	−7.04659	+	4.06835i	−0.778165	+	0.449274i
$83$	−1.08666			−0.119277			−0.0596385	−	0.998220i	$-0.518995\pi$
$83$	−1.08666			−0.119277			−0.0596385	+	0.998220i	$0.518995\pi$
$84$		0			0
$85$	6.08377			0.659877
$86$	22.7415	−	13.1298i	2.45228	−	1.41582i
$87$		0			0
$88$	16.8044	−	29.1061i	1.79136	−	3.10272i
$89$	−4.53732	−	7.85887i	−0.480955	−	0.833038i	0.518806	−	0.854892i	$-0.326377\pi$
$89$	−4.53732	−	7.85887i	−0.480955	−	0.833038i	−0.999761	+	0.0218536i	$0.993043\pi$
$90$		0			0
$91$	−1.38987	−	8.74841i	−0.145698	−	0.917082i
$92$		−	30.1657i		−	3.14499i
$93$		0			0
$94$	15.5826	+	8.99663i	1.60722	+	0.927931i
$95$	2.60762	+	1.50551i	0.267536	+	0.154462i
$96$		0			0
$97$			2.54347i			0.258250i	0.991628	+	0.129125i	$0.0412168\pi$
$97$			2.54347i			0.258250i	−0.991628	+	0.129125i	$0.958783\pi$
$98$	−11.7926	+	13.1220i	−1.19123	+	1.32553i
$99$		0			0
$100$	8.84834	+	15.3258i	0.884834	+	1.53258i
$101$	8.11423	−	14.0543i	0.807396	−	1.39845i	−0.107266	−	0.994230i	$-0.534210\pi$
$101$	8.11423	−	14.0543i	0.807396	−	1.39845i	0.914662	−	0.404220i	$-0.132457\pi$
$102$		0			0
$103$	1.67510	−	0.967121i	0.165053	−	0.0952932i	−0.415198	−	0.909731i	$-0.636288\pi$
$103$	1.67510	−	0.967121i	0.165053	−	0.0952932i	0.580251	+	0.814438i	$0.302954\pi$
$104$	19.8476			1.94621
$105$		0			0
$106$	25.9506			2.52055
$107$	−10.3106	+	5.95282i	−0.996763	+	0.575481i	−0.907289	−	0.420508i	$-0.861852\pi$
$107$	−10.3106	+	5.95282i	−0.996763	+	0.575481i	−0.0894738	+	0.995989i	$0.528519\pi$
$108$		0			0
$109$	0.349665	−	0.605637i	0.0334918	−	0.0580095i	−0.848794	−	0.528724i	$-0.822671\pi$
$109$	0.349665	−	0.605637i	0.0334918	−	0.0580095i	0.882285	+	0.470715i	$0.156004\pi$
$110$	21.5120	+	37.2599i	2.05109	+	3.55259i
$111$		0			0
$112$	−10.3901	−	12.8183i	−0.981777	−	1.21122i
$113$			8.47563i			0.797320i	0.917099	+	0.398660i	$0.130525\pi$
$113$			8.47563i			0.797320i	−0.917099	+	0.398660i	$0.869475\pi$
$114$		0			0
$115$	18.0742	+	10.4351i	1.68543	+	0.973082i
$116$	−24.5089	−	14.1502i	−2.27559	−	1.31381i
$117$		0			0
$118$		−	28.3425i		−	2.60913i
$119$	1.91337	−	4.99159i	0.175399	−	0.457578i
$120$		0			0
$121$	10.5712	+	18.3098i	0.961014	+	1.66453i
$122$	2.27906	−	3.94745i	0.206337	−	0.357386i
$123$		0			0
$124$	−21.0342	+	12.1441i	−1.88893	+	1.09057i
$125$	2.81157			0.251474
$126$		0			0
$127$	−10.9860			−0.974849			−0.487424	−	0.873165i	$-0.662064\pi$
$127$	−10.9860			−0.974849			−0.487424	+	0.873165i	$0.662064\pi$
$128$	−12.6685	+	7.31414i	−1.11975	+	0.646485i
$129$		0			0
$130$	−12.7038	+	22.0037i	−1.11420	+	1.92985i
$131$	8.30866	+	14.3910i	0.725931	+	1.25735i	0.958590	+	0.284791i	$0.0919243\pi$
$131$	8.30866	+	14.3910i	0.725931	+	1.25735i	−0.232658	+	0.972559i	$0.574742\pi$
$132$		0			0
$133$	2.05534	−	1.66600i	0.178221	−	0.144461i
$134$			5.65004i			0.488089i
$135$		0			0
$136$	10.3730	+	5.98885i	0.889477	+	0.513540i
$137$	1.47587	+	0.852096i	0.126092	+	0.0727995i	0.561719	−	0.827328i	$-0.310140\pi$
$137$	1.47587	+	0.852096i	0.126092	+	0.0727995i	−0.435627	+	0.900127i	$0.643473\pi$
$138$		0			0
$139$		−	4.21153i		−	0.357217i	−0.983920	−	0.178609i	$-0.942840\pi$
$139$		−	4.21153i		−	0.357217i	0.983920	−	0.178609i	$-0.0571596\pi$
$140$	34.2412	−	5.43995i	2.89391	−	0.459760i
$141$		0			0
$142$	6.19584	+	10.7315i	0.519943	+	0.900568i
$143$	−9.49077	+	16.4385i	−0.793658	+	1.37466i
$144$		0			0
$145$	16.9566	−	9.78989i	1.40817	−	0.813006i
$146$	−31.0879			−2.57285
$147$		0			0
$148$	−29.6557			−2.43769
$149$	5.55350	−	3.20631i	0.454960	−	0.262671i	−0.254963	−	0.966951i	$-0.582063\pi$
$149$	5.55350	−	3.20631i	0.454960	−	0.262671i	0.709923	+	0.704280i	$0.248730\pi$
$150$		0			0
$151$	4.51353	−	7.81766i	0.367306	−	0.636192i	−0.621838	−	0.783146i	$-0.713614\pi$
$151$	4.51353	−	7.81766i	0.367306	−	0.636192i	0.989143	+	0.146954i	$0.0469470\pi$
$152$	2.96404	+	5.13387i	0.240416	+	0.416412i
$153$		0			0
$154$	37.3365	−	5.93170i	3.00866	−	0.477990i
$155$		−	16.8039i		−	1.34972i
$156$		0			0
$157$	15.9303	+	9.19735i	1.27137	+	0.734029i	0.975247	−	0.221120i	$-0.0709712\pi$
$157$	15.9303	+	9.19735i	1.27137	+	0.734029i	0.296128	+	0.955148i	$0.404304\pi$
$158$	−14.6790	−	8.47491i	−1.16780	−	0.674227i
$159$		0			0
$160$			11.6289i			0.919343i
$161$	14.2462	−	11.5476i	1.12276	−	0.910075i
$162$		0			0
$163$	−5.20178	−	9.00975i	−0.407435	−	0.705698i	0.587167	−	0.809466i	$-0.300243\pi$
$163$	−5.20178	−	9.00975i	−0.407435	−	0.705698i	−0.994602	+	0.103768i	$0.966910\pi$
$164$	7.02519	−	12.1680i	0.548576	−	0.950161i
$165$		0			0
$166$	2.37184	−	1.36938i	0.184090	−	0.106285i
$167$	21.9162			1.69593			0.847963	−	0.530056i	$-0.177829\pi$
$167$	21.9162			1.69593			0.847963	+	0.530056i	$0.177829\pi$
$168$		0			0
$169$	1.79051			0.137732
$170$	−13.2789	+	7.66658i	−1.01845	+	0.588000i
$171$		0			0
$172$	−22.6724	+	39.2698i	−1.72876	+	2.99430i
$173$	8.26913	+	14.3225i	0.628690	+	1.08892i	0.987815	+	0.155634i	$0.0497419\pi$
$173$	8.26913	+	14.3225i	0.628690	+	1.08892i	−0.359125	+	0.933290i	$0.616925\pi$
$174$		0			0
$175$	−3.85064	+	10.0455i	−0.291081	+	0.759371i
$176$			35.3578i			2.66519i
$177$		0			0
$178$	19.8070	+	11.4356i	1.48460	+	0.857132i
$179$	−13.5070	−	7.79828i	−1.00956	−	0.582870i	−0.0984981	−	0.995137i	$-0.531404\pi$
$179$	−13.5070	−	7.79828i	−1.00956	−	0.582870i	−0.911063	+	0.412267i	$0.864737\pi$
$180$		0			0
$181$			1.47024i			0.109282i	0.998506	+	0.0546409i	$0.0174014\pi$
$181$			1.47024i			0.109282i	−0.998506	+	0.0546409i	$0.982599\pi$
$182$	14.0581	+	17.3435i	1.04206	+	1.28558i
$183$		0			0
$184$	20.5447	+	35.5844i	1.51457	+	2.62332i
$185$	10.2587	−	17.7686i	0.754237	−	1.30638i
$186$		0			0
$187$	−9.92038	+	5.72753i	−0.725450	+	0.418839i
$188$	−31.0706			−2.26606
$189$		0			0
$190$	−7.58879			−0.550548
$191$	11.8568	−	6.84554i	0.857930	−	0.495326i	−0.00538851	−	0.999985i	$-0.501715\pi$
$191$	11.8568	−	6.84554i	0.857930	−	0.495326i	0.863319	+	0.504659i	$0.168382\pi$
$192$		0			0
$193$	9.43503	−	16.3420i	0.679148	−	1.17632i	−0.296089	−	0.955160i	$-0.595683\pi$
$193$	9.43503	−	16.3420i	0.679148	−	1.17632i	0.975238	−	0.221159i	$-0.0709841\pi$
$194$	−3.20520	−	5.55156i	−0.230120	−	0.398579i
$195$		0			0
$196$	6.30565	−	29.8050i	0.450403	−	2.12893i
$197$			8.89509i			0.633749i	0.948467	+	0.316875i	$0.102633\pi$
$197$			8.89509i			0.633749i	−0.948467	+	0.316875i	$0.897367\pi$
$198$		0			0
$199$	−14.2830	−	8.24631i	−1.01250	−	0.584565i	−0.100575	−	0.994929i	$-0.532068\pi$
$199$	−14.2830	−	8.24631i	−1.01250	−	0.584565i	−0.911922	+	0.410364i	$0.865402\pi$
$200$	−20.8756	−	12.0525i	−1.47613	−	0.852241i
$201$		0			0
$202$			40.9012i			2.87780i
$203$	−2.69946	−	16.9914i	−0.189465	−	1.19257i
$204$		0			0
$205$	4.86041	+	8.41848i	0.339466	+	0.587972i
$206$	−2.43747	+	4.22182i	−0.169827	+	0.294148i
$207$		0			0
$208$	−18.0830	+	10.4402i	−1.25383	+	0.723898i
$209$	−5.66942			−0.392162
$210$		0			0
$211$	6.09182			0.419378			0.209689	−	0.977768i	$-0.432755\pi$
$211$	6.09182			0.419378			0.209689	+	0.977768i	$0.432755\pi$
$212$	−38.8078	+	22.4057i	−2.66533	+	1.53883i
$213$		0			0
$214$	15.0031	−	25.9862i	1.02559	−	1.77638i
$215$	−15.6860	−	27.1690i	−1.06978	−	1.85291i
$216$		0			0
$217$	−13.7872	−	5.28491i	−0.935938	−	0.358763i
$218$			1.76255i			0.119375i
$219$		0			0
$220$	−64.3401	−	37.1468i	−4.33781	−	2.50443i
$221$	−5.85845	−	3.38238i	−0.394082	−	0.227523i
$222$		0			0
$223$			16.4950i			1.10459i	0.833650	+	0.552293i	$0.186247\pi$
$223$			16.4950i			1.10459i	−0.833650	+	0.552293i	$0.813753\pi$
$224$	9.54122	+	3.65733i	0.637500	+	0.244366i
$225$		0			0
$226$	−10.6807	−	18.4995i	−0.710471	−	1.23057i
$227$	−4.02810	+	6.97687i	−0.267354	+	0.463071i	−0.968178	−	0.250264i	$-0.919483\pi$
$227$	−4.02810	+	6.97687i	−0.267354	+	0.463071i	0.700824	+	0.713335i	$0.252816\pi$
$228$		0			0
$229$	−9.96998	+	5.75617i	−0.658835	+	0.380379i	−0.791833	−	0.610738i	$-0.790873\pi$
$229$	−9.96998	+	5.75617i	−0.658835	+	0.380379i	0.132998	+	0.991116i	$0.457540\pi$
$230$	−52.6002			−3.46835
$231$		0			0
$232$	38.5486			2.53084
$233$	8.62355	−	4.97881i	0.564948	−	0.326173i	−0.190181	−	0.981749i	$-0.560908\pi$
$233$	8.62355	−	4.97881i	0.564948	−	0.326173i	0.755129	+	0.655576i	$0.227574\pi$
$234$		0			0
$235$	10.7482	−	18.6164i	0.701134	−	1.21440i
$236$	24.4708	+	42.3846i	1.59291	+	2.75900i
$237$		0			0
$238$	2.11398	+	13.3062i	0.137029	+	0.862513i
$239$			25.2890i			1.63581i	0.575355	+	0.817904i	$0.304864\pi$
$239$			25.2890i			1.63581i	−0.575355	+	0.817904i	$0.695136\pi$
$240$		0			0
$241$	23.3578	+	13.4856i	1.50461	+	0.868686i	0.999986	+	0.00534530i	$0.00170147\pi$
$241$	23.3578	+	13.4856i	1.50461	+	0.868686i	0.504622	+	0.863340i	$0.331632\pi$
$242$	−46.1468	−	26.6429i	−2.96643	−	1.71267i
$243$		0			0
$244$			7.87094i			0.503885i
$245$	15.6768	+	14.0885i	1.00155	+	0.900079i
$246$		0			0
$247$	−1.67403	−	2.89950i	−0.106516	−	0.184491i
$248$	16.5418	−	28.6512i	1.05040	−	1.81935i
$249$		0			0
$250$	−6.13674	+	3.54305i	−0.388121	+	0.224082i
$251$	19.7403			1.24600			0.623000	−	0.782222i	$-0.285914\pi$
$251$	19.7403			1.24600			0.623000	+	0.782222i	$0.285914\pi$
$252$		0			0
$253$	−39.2965			−2.47055
$254$	23.9789	−	13.8442i	1.50457	−	0.868662i
$255$		0			0
$256$	15.6948	−	27.1841i	0.980923	−	1.69901i
$257$	−0.469337	−	0.812916i	−0.0292765	−	0.0507083i	0.851016	−	0.525140i	$-0.175987\pi$
$257$	−0.469337	−	0.812916i	−0.0292765	−	0.0507083i	−0.880292	+	0.474432i	$0.842654\pi$
$258$		0			0
$259$	−11.3523	−	14.0054i	−0.705400	−	0.870251i
$260$		−	43.8738i		−	2.72094i
$261$		0			0
$262$	−36.2702	−	20.9406i	−2.24078	−	1.29372i
$263$	−2.00247	−	1.15613i	−0.123477	−	0.0712897i	0.436989	−	0.899467i	$-0.356045\pi$
$263$	−2.00247	−	1.15613i	−0.123477	−	0.0712897i	−0.560467	+	0.828177i	$0.689378\pi$
$264$		0			0
$265$		−	31.0029i		−	1.90449i
$266$	−2.38671	+	6.22642i	−0.146338	+	0.381766i
$267$		0			0
$268$	−4.87822	−	8.44933i	−0.297985	−	0.516125i
$269$	12.6580	−	21.9243i	0.771773	−	1.33675i	−0.164818	−	0.986324i	$-0.552704\pi$
$269$	12.6580	−	21.9243i	0.771773	−	1.33675i	0.936591	−	0.350425i	$-0.113963\pi$
$270$		0			0
$271$	−25.1179	+	14.5018i	−1.52580	+	0.880924i	−0.526273	+	0.850316i	$0.676411\pi$
$271$	−25.1179	+	14.5018i	−1.52580	+	0.880924i	−0.999531	+	0.0306079i	$0.990256\pi$
$272$	−12.6010			−0.764048
$273$		0			0
$274$	−4.29514			−0.259479
$275$	19.9647	−	11.5266i	1.20392	−	0.695081i
$276$		0			0
$277$	1.94095	−	3.36183i	0.116621	−	0.201993i	−0.801806	−	0.597585i	$-0.796127\pi$
$277$	1.94095	−	3.36183i	0.116621	−	0.201993i	0.918426	+	0.395592i	$0.129461\pi$
$278$	5.30723	+	9.19240i	0.318307	+	0.551324i
$279$		0			0
$280$	−36.6870	+	29.7374i	−2.19247	+	1.77715i
$281$			4.81812i			0.287425i	0.989619	+	0.143713i	$0.0459041\pi$
$281$			4.81812i			0.287425i	−0.989619	+	0.143713i	$0.954096\pi$
$282$		0			0
$283$	3.49692	+	2.01895i	0.207870	+	0.120014i	0.600321	−	0.799759i	$-0.295039\pi$
$283$	3.49692	+	2.01895i	0.207870	+	0.120014i	−0.392451	+	0.919773i	$0.628373\pi$
$284$	−18.5311	−	10.6989i	−1.09962	−	0.634865i
$285$		0			0
$286$		−	47.8399i		−	2.82883i
$287$	8.43579	−	1.34021i	0.497949	−	0.0791099i
$288$		0			0
$289$	6.45879	+	11.1869i	0.379929	+	0.658056i
$290$	−24.6738	+	42.7363i	−1.44890	+	2.50956i
$291$		0			0
$292$	46.4903	−	26.8412i	2.72064	−	1.57076i
$293$	−9.47039			−0.553266			−0.276633	−	0.960976i	$-0.589219\pi$
$293$	−9.47039			−0.553266			−0.276633	+	0.960976i	$0.589219\pi$
$294$		0			0
$295$	−33.8604			−1.97143
$296$	34.9828	−	20.1973i	2.03334	−	1.17395i
$297$		0			0
$298$	−8.08099	+	13.9967i	−0.468119	+	0.810806i
$299$	−11.6032	−	20.0973i	−0.671030	−	1.16226i
$300$		0			0
$301$	−27.2249	+	4.32525i	−1.56921	+	0.249304i
$302$			22.7512i			1.30919i
$303$		0			0
$304$	−5.40103	−	3.11829i	−0.309771	−	0.178846i
$305$	−4.71598	−	2.72277i	−0.270036	−	0.155906i
$306$		0			0
$307$			17.1287i			0.977588i	0.872399	+	0.488794i	$0.162563\pi$
$307$			17.1287i			0.977588i	−0.872399	+	0.488794i	$0.837437\pi$
$308$	−50.7133	+	41.1067i	−2.88966	+	2.34227i
$309$		0			0
$310$	21.1758	+	36.6775i	1.20270	+	2.08314i
$311$	16.7808	−	29.0652i	0.951551	−	1.64813i	0.209479	−	0.977813i	$-0.432823\pi$
$311$	16.7808	−	29.0652i	0.951551	−	1.64813i	0.742072	−	0.670321i	$-0.233843\pi$
$312$		0			0
$313$	2.95647	−	1.70692i	0.167110	−	0.0964808i	−0.414113	−	0.910226i	$-0.635908\pi$
$313$	2.95647	−	1.70692i	0.167110	−	0.0964808i	0.581222	+	0.813745i	$0.302575\pi$
$314$	−46.3609			−2.61629
$315$		0			0
$316$	29.2688			1.64650
$317$	−11.4130	+	6.58931i	−0.641019	+	0.370093i	−0.785007	−	0.619487i	$-0.787341\pi$
$317$	−11.4130	+	6.58931i	−0.641019	+	0.370093i	0.143988	+	0.989579i	$0.454007\pi$
$318$		0			0
$319$	−18.4333	+	31.9274i	−1.03207	+	1.78759i
$320$	4.12411	+	7.14318i	0.230545	+	0.399316i
$321$		0			0
$322$	−16.5430	+	43.1572i	−0.921904	+	2.40506i
$323$		−	2.02050i		−	0.112424i
$324$		0			0
$325$	11.7901	+	6.80700i	0.653996	+	0.377585i
$326$	22.7076	+	13.1102i	1.25766	+	0.726109i
$327$		0			0
$328$			19.1383i			1.05674i
$329$	−11.8940	−	14.6736i	−0.655735	−	0.808979i
$330$		0			0
$331$	9.26214	+	16.0425i	0.509093	+	0.881775i	0.999945	+	0.0105317i	$0.00335241\pi$
$331$	9.26214	+	16.0425i	0.509093	+	0.881775i	−0.490852	+	0.871243i	$0.663314\pi$
$332$	−2.36464	+	4.09567i	−0.129776	+	0.224779i
$333$		0			0
$334$	−47.8359	+	27.6181i	−2.61747	+	1.51120i
$335$	6.75004			0.368794
$336$		0			0
$337$	−16.9291			−0.922190			−0.461095	−	0.887351i	$-0.652543\pi$
$337$	−16.9291			−0.922190			−0.461095	+	0.887351i	$0.652543\pi$
$338$	−3.90811	+	2.25635i	−0.212573	+	0.122729i
$339$		0			0
$340$	13.2386	−	22.9299i	0.717963	−	1.24355i
$341$	15.8200	+	27.4010i	0.856700	+	1.48385i
$342$		0			0
$343$	16.4897	−	8.43153i	0.890359	−	0.455260i
$344$		−	61.7652i		−	3.33016i
$345$		0			0
$346$	−36.0977	−	20.8410i	−1.94062	−	1.12042i
$347$	3.64035	+	2.10176i	0.195424	+	0.112828i	0.594519	−	0.804081i	$-0.297342\pi$
$347$	3.64035	+	2.10176i	0.195424	+	0.112828i	−0.399095	+	0.916910i	$0.630676\pi$
$348$		0			0
$349$		−	24.2486i		−	1.29800i	−0.760789	−	0.648999i	$-0.775188\pi$
$349$		−	24.2486i		−	1.29800i	0.760789	−	0.648999i	$-0.224812\pi$
$350$	−4.25436	−	26.7786i	−0.227405	−	1.43138i
$351$		0			0
$352$	−10.9479	−	18.9624i	−0.583527	−	1.01070i
$353$	−11.5837	+	20.0635i	−0.616537	+	1.06787i	0.373575	+	0.927600i	$0.378132\pi$
$353$	−11.5837	+	20.0635i	−0.616537	+	1.06787i	−0.990113	+	0.140274i	$0.955202\pi$
$354$		0			0
$355$	12.8208	−	7.40210i	0.680458	−	0.392863i
$356$	−39.4937			−2.09316
$357$		0			0
$358$	39.3086			2.07752
$359$	−23.7559	+	13.7155i	−1.25379	+	0.723874i	−0.971860	−	0.235561i	$-0.924307\pi$
$359$	−23.7559	+	13.7155i	−1.25379	+	0.723874i	−0.281928	+	0.959436i	$0.590974\pi$
$360$		0			0
$361$	0.500000	−	0.866025i	0.0263158	−	0.0455803i
$362$	−1.85275	−	3.20905i	−0.0973781	−	0.168664i
$363$		0			0
$364$	−35.9974	−	13.7985i	−1.88678	−	0.723238i
$365$			37.1404i			1.94402i
$366$		0			0
$367$	−22.3596	−	12.9093i	−1.16716	−	0.673860i	−0.214150	−	0.976801i	$-0.568698\pi$
$367$	−22.3596	−	12.9093i	−1.16716	−	0.673860i	−0.953009	+	0.302941i	$0.902032\pi$
$368$	−37.4362	−	21.6138i	−1.95150	−	1.12670i
$369$		0			0
$370$			51.7109i			2.68832i
$371$	−25.4372	−	9.75056i	−1.32063	−	0.506224i
$372$		0			0
$373$	−7.44131	−	12.8887i	−0.385296	−	0.667353i	0.606514	−	0.795073i	$-0.292567\pi$
$373$	−7.44131	−	12.8887i	−0.385296	−	0.667353i	−0.991810	+	0.127720i	$0.959234\pi$
$374$	14.4353	−	25.0027i	0.746433	−	1.29286i
$375$		0			0
$376$	36.6519	−	21.1610i	1.89018	−	1.09129i
$377$	−21.7714			−1.12129
$378$		0			0
$379$	30.3379			1.55835			0.779177	−	0.626803i	$-0.215637\pi$
$379$	30.3379			1.55835			0.779177	+	0.626803i	$0.215637\pi$
$380$	11.3486	−	6.55213i	0.582172	−	0.336117i
$381$		0			0
$382$	−17.2531	+	29.8832i	−0.882744	+	1.52896i
$383$	−10.2462	−	17.7469i	−0.523554	−	0.906822i	−0.999624	−	0.0274150i	$-0.991272\pi$
$383$	−10.2462	−	17.7469i	−0.523554	−	0.906822i	0.476070	−	0.879407i	$-0.342061\pi$
$384$		0			0
$385$	−7.08654	−	44.6055i	−0.361164	−	2.27331i
$386$			47.5589i			2.42069i
$387$		0			0
$388$	9.58640	+	5.53471i	0.486676	+	0.280982i
$389$	13.3273	+	7.69451i	0.675720	+	0.390127i	0.798241	−	0.602339i	$-0.205764\pi$
$389$	13.3273	+	7.69451i	0.675720	+	0.390127i	−0.122520	+	0.992466i	$0.539098\pi$
$390$		0			0
$391$		−	14.0047i		−	0.708248i
$392$	12.8607	+	39.4534i	0.649561	+	1.99270i
$393$		0			0
$394$	−11.2093	−	19.4151i	−0.564717	−	0.978119i
$395$	−10.1249	+	17.5368i	−0.509438	+	0.882372i
$396$		0			0
$397$	−12.6747	+	7.31773i	−0.636124	+	0.367266i	−0.783120	−	0.621871i	$-0.786373\pi$
$397$	−12.6747	+	7.31773i	−0.636124	+	0.367266i	0.146996	+	0.989137i	$0.453040\pi$
$398$	41.5670			2.08356
$399$		0			0
$400$	25.3594			1.26797
$401$	15.7608	−	9.09950i	0.787057	−	0.454407i	−0.0518688	−	0.998654i	$-0.516518\pi$
$401$	15.7608	−	9.09950i	0.787057	−	0.454407i	0.838925	+	0.544247i	$0.183184\pi$
$402$		0			0
$403$	−9.34243	+	16.1816i	−0.465380	+	0.806061i
$404$	−35.3139	−	61.1655i	−1.75693	−	3.04310i
$405$		0			0
$406$	27.3041	+	33.6850i	1.35508	+	1.67176i
$407$			38.6321i			1.91492i
$408$		0			0
$409$	−4.43719	−	2.56181i	−0.219405	−	0.126674i	0.386270	−	0.922386i	$-0.373763\pi$
$409$	−4.43719	−	2.56181i	−0.219405	−	0.126674i	−0.605675	+	0.795712i	$0.707097\pi$
$410$	−21.2174	−	12.2499i	−1.04785	−	0.604978i
$411$		0			0
$412$		−	8.41801i		−	0.414726i
$413$	−10.6493	+	27.7817i	−0.524015	+	1.36705i
$414$		0			0
$415$	−1.63599	−	2.83361i	−0.0803073	−	0.139096i
$416$	6.46527	−	11.1982i	0.316986	−	0.549036i
$417$		0			0
$418$	12.3745	−	7.14442i	0.605257	−	0.349445i
$419$	0.142789			0.00697569			0.00348784	−	0.999994i	$-0.498890\pi$
$419$	0.142789			0.00697569			0.00348784	+	0.999994i	$0.498890\pi$
$420$		0			0
$421$	10.0412			0.489379			0.244690	−	0.969601i	$-0.421314\pi$
$421$	10.0412			0.489379			0.244690	+	0.969601i	$0.421314\pi$
$422$	−13.2965	+	7.67671i	−0.647262	+	0.373697i
$423$		0			0
$424$	30.5192	−	52.8609i	1.48215	−	2.56715i
$425$	4.10792	+	7.11513i	0.199264	+	0.345135i
$426$		0			0
$427$	−3.71717	+	3.01303i	−0.179886	+	0.145811i
$428$			51.8146i			2.50455i
$429$		0			0
$430$	68.4750	+	39.5341i	3.30216	+	1.90650i
$431$	21.6873	+	12.5211i	1.04464	+	0.603122i	0.921144	−	0.389223i	$-0.127256\pi$
$431$	21.6873	+	12.5211i	1.04464	+	0.603122i	0.123495	+	0.992345i	$0.460590\pi$
$432$		0			0
$433$		−	28.7885i		−	1.38349i	−0.722143	−	0.691743i	$-0.756843\pi$
$433$		−	28.7885i		−	1.38349i	0.722143	−	0.691743i	$-0.243157\pi$
$434$	36.7529	−	5.83900i	1.76420	−	0.280281i
$435$		0			0
$436$	−1.52178	−	2.63580i	−0.0728799	−	0.126232i
$437$	3.46565	−	6.00268i	0.165785	−	0.287147i
$438$		0			0
$439$	4.07680	−	2.35374i	0.194575	−	0.112338i	−0.399547	−	0.916713i	$-0.630833\pi$
$439$	4.07680	−	2.35374i	0.194575	−	0.112338i	0.594123	+	0.804374i	$0.297499\pi$
$440$	101.197			4.82437
$441$		0			0
$442$	17.0495			0.810960
$443$	0.571758	−	0.330105i	0.0271650	−	0.0156837i	−0.486356	−	0.873761i	$-0.661674\pi$
$443$	0.571758	−	0.330105i	0.0271650	−	0.0156837i	0.513521	+	0.858077i	$0.328341\pi$
$444$		0			0
$445$	13.6620	−	23.6632i	0.647639	−	1.12174i
$446$	−20.7864	−	36.0032i	−0.984267	−	1.70480i
$447$		0			0
$448$	7.15786	−	1.13718i	0.338177	−	0.0537267i
$449$		−	5.07897i		−	0.239692i	−0.992793	−	0.119846i	$-0.961760\pi$
$449$		−	5.07897i		−	0.239692i	0.992793	−	0.119846i	$-0.0382400\pi$
$450$		0			0
$451$	−15.8511	−	9.15162i	−0.746398	−	0.430933i
$452$	31.9449	+	18.4434i	1.50256	+	0.867504i
$453$		0			0
$454$		−	20.3043i		−	0.952929i
$455$	20.7201	−	16.7951i	0.971371	−	0.787365i
$456$		0			0
$457$	−2.95773	−	5.12294i	−0.138357	−	0.239641i	0.788518	−	0.615012i	$-0.210849\pi$
$457$	−2.95773	−	5.12294i	−0.138357	−	0.239641i	−0.926875	+	0.375371i	$0.877515\pi$
$458$	14.5075	−	25.1277i	0.677891	−	1.17414i
$459$		0			0
$460$	78.6607	−	45.4148i	3.66758	−	2.11748i
$461$	−15.0809			−0.702388			−0.351194	−	0.936303i	$-0.614224\pi$
$461$	−15.0809			−0.702388			−0.351194	+	0.936303i	$0.614224\pi$
$462$		0			0
$463$	11.1019			0.515947			0.257974	−	0.966152i	$-0.416945\pi$
$463$	11.1019			0.515947			0.257974	+	0.966152i	$0.416945\pi$
$464$	−35.1213	+	20.2773i	−1.63047	+	0.941350i
$465$		0			0
$466$	−12.5483	+	21.7343i	−0.581288	+	1.00682i
$467$	−7.29347	−	12.6327i	−0.337501	−	0.584570i	0.646461	−	0.762947i	$-0.276248\pi$
$467$	−7.29347	−	12.6327i	−0.337501	−	0.584570i	−0.983962	+	0.178378i	$0.942915\pi$
$468$		0			0
$469$	2.12292	−	5.53825i	0.0980272	−	0.255733i
$470$			54.1780i			2.49905i
$471$		0			0
$472$	−57.7330	−	33.3321i	−2.65738	−	1.53424i
$473$	51.1562	+	29.5351i	2.35217	+	1.35802i
$474$		0			0
$475$			4.06624i			0.186572i
$476$	−14.6499	−	18.0735i	−0.671475	−	0.828398i
$477$		0			0
$478$	−31.8684	−	55.1976i	−1.45762	−	2.52468i
$479$	8.20239	−	14.2070i	0.374777	−	0.649132i	−0.615517	−	0.788124i	$-0.711053\pi$
$479$	8.20239	−	14.2070i	0.374777	−	0.649132i	0.990294	+	0.138991i	$0.0443861\pi$
$480$		0			0
$481$	−19.7576	+	11.4070i	−0.900867	+	0.520116i
$482$	−67.9767			−3.09625
$483$		0			0
$484$	92.0135			4.18243
$485$	−6.63239	+	3.82921i	−0.301161	+	0.173876i
$486$		0			0
$487$	−8.27398	+	14.3309i	−0.374930	+	0.649397i	−0.990316	−	0.138828i	$-0.955666\pi$
$487$	−8.27398	+	14.3309i	−0.374930	+	0.649397i	0.615387	+	0.788225i	$0.289000\pi$
$488$	−5.36059	−	9.28481i	−0.242662	−	0.420304i
$489$		0			0
$490$	−51.9711	−	10.9952i	−2.34782	−	0.496713i
$491$		−	6.62817i		−	0.299125i	−0.988752	−	0.149563i	$-0.952213\pi$
$491$		−	6.62817i		−	0.299125i	0.988752	−	0.149563i	$-0.0477865\pi$
$492$		0			0
$493$	−11.3785	−	6.56936i	−0.512460	−	0.295869i
$494$	7.30772	+	4.21912i	0.328790	+	0.189827i
$495$		0			0
$496$			34.8051i			1.56280i
$497$	−2.04105	−	12.8472i	−0.0915536	−	0.576275i
$498$		0			0
$499$	−2.19023	−	3.79360i	−0.0980484	−	0.169825i	0.812828	−	0.582503i	$-0.197927\pi$
$499$	−2.19023	−	3.79360i	−0.0980484	−	0.169825i	−0.910877	+	0.412678i	$0.864593\pi$
$500$	6.11811	−	10.5969i	0.273610	−	0.473907i
$501$		0			0
$502$	−43.0868	+	24.8762i	−1.92306	+	1.11028i
$503$	−4.28192			−0.190921			−0.0954606	−	0.995433i	$-0.530432\pi$
$503$	−4.28192			−0.190921			−0.0954606	+	0.995433i	$0.530432\pi$
$504$		0			0
$505$	48.8642			2.17443
$506$	85.7714	−	49.5202i	3.81301	−	2.20144i
$507$		0			0
$508$	−23.9061	+	41.4065i	−1.06066	+	1.83712i
$509$	3.04920	+	5.28138i	0.135154	+	0.234093i	0.925656	−	0.378366i	$-0.123514\pi$
$509$	3.04920	+	5.28138i	0.135154	+	0.234093i	−0.790503	+	0.612459i	$0.790181\pi$
$510$		0			0
$511$	30.4728	+	11.6808i	1.34804	+	0.516729i
$512$			49.8556i			2.20333i
$513$		0			0
$514$	2.04882	+	1.18289i	0.0903697	+	0.0521750i
$515$	5.04377	+	2.91202i	0.222255	+	0.128319i
$516$		0			0
$517$			40.4753i			1.78010i
$518$	42.4276	+	16.2633i	1.86416	+	0.714569i
$519$		0			0
$520$	29.8807	+	51.7549i	1.31036	+	2.26960i
$521$	−7.39775	+	12.8133i	−0.324101	+	0.561360i	−0.981330	−	0.192331i	$-0.938395\pi$
$521$	−7.39775	+	12.8133i	−0.324101	+	0.561360i	0.657229	+	0.753691i	$0.271729\pi$
$522$		0			0
$523$	1.84475	−	1.06507i	0.0806653	−	0.0465721i	−0.459125	−	0.888372i	$-0.651837\pi$
$523$	1.84475	−	1.06507i	0.0806653	−	0.0465721i	0.539790	+	0.841800i	$0.318504\pi$
$524$	72.3203			3.15933
$525$		0			0
$526$	5.82765			0.254098
$527$	−9.76533	+	5.63802i	−0.425384	+	0.245596i
$528$		0			0
$529$	12.5215	−	21.6878i	0.544412	−	0.942949i
$530$	39.0689	+	67.6694i	1.69705	+	2.93937i
$531$		0			0
$532$	−1.80668	−	11.3720i	−0.0783295	−	0.493037i
$533$		−	10.8089i		−	0.468186i
$534$		0			0
$535$	−31.0454	−	17.9241i	−1.34221	−	0.774925i
$536$	11.5090	+	6.64473i	0.497113	+	0.287009i
$537$		0			0
$538$			63.8049i			2.75083i
$539$	−38.8265	−	8.21428i	−1.67238	−	0.353814i
$540$		0			0
$541$	13.8990	+	24.0737i	0.597564	+	1.03501i	0.993180	+	0.116595i	$0.0371978\pi$
$541$	13.8990	+	24.0737i	0.597564	+	1.03501i	−0.395616	+	0.918416i	$0.629469\pi$
$542$	36.5495	−	63.3056i	1.56994	−	2.71921i
$543$		0			0
$544$	6.75793	−	3.90169i	0.289744	−	0.167284i
$545$	2.10570			0.0901981
$546$		0			0
$547$	−29.2883			−1.25228			−0.626138	−	0.779712i	$-0.715366\pi$
$547$	−29.2883			−1.25228			−0.626138	+	0.779712i	$0.715366\pi$
$548$	6.42315	−	3.70841i	0.274383	−	0.158415i
$549$		0			0
$550$	−29.0510	+	50.3177i	−1.23874	+	2.14556i
$551$	−3.25135	−	5.63151i	−0.138512	−	0.239910i
$552$		0			0
$553$	11.2042	+	13.8226i	0.476452	+	0.587798i
$554$			9.78371i			0.415670i
$555$		0			0
$556$	−15.8734	−	9.16449i	−0.673181	−	0.388661i
$557$	10.1825	+	5.87884i	0.431444	+	0.249095i	0.699962	−	0.714180i	$-0.253200\pi$
$557$	10.1825	+	5.87884i	0.431444	+	0.249095i	−0.268517	+	0.963275i	$0.586534\pi$
$558$		0			0
$559$			34.8837i			1.47542i
$560$	17.7828	−	46.3916i	0.751460	−	1.96040i
$561$		0			0
$562$	−6.07165	−	10.5164i	−0.256117	−	0.443608i
$563$	14.2401	−	24.6646i	0.600149	−	1.03949i	−0.392649	−	0.919688i	$-0.628441\pi$
$563$	14.2401	−	24.6646i	0.600149	−	1.03949i	0.992798	−	0.119800i	$-0.0382253\pi$
$564$		0			0
$565$	−22.1012	+	12.7601i	−0.929805	+	0.536823i
$566$	−10.1769			−0.427765
$567$		0			0
$568$	29.1465			1.22296
$569$	1.44753	−	0.835731i	0.0606835	−	0.0350357i	−0.469351	−	0.883012i	$-0.655512\pi$
$569$	1.44753	−	0.835731i	0.0606835	−	0.0350357i	0.530035	+	0.847976i	$0.322179\pi$
$570$		0			0
$571$	4.32147	−	7.48500i	0.180848	−	0.313238i	−0.761322	−	0.648374i	$-0.775449\pi$
$571$	4.32147	−	7.48500i	0.180848	−	0.313238i	0.942170	+	0.335137i	$0.108783\pi$
$572$	41.3048	+	71.5420i	1.72704	+	2.99132i
$573$		0			0
$574$	−16.7237	+	13.5558i	−0.698034	+	0.565806i
$575$			28.1843i			1.17537i
$576$		0			0
$577$	−24.6070	−	14.2069i	−1.02440	−	0.591440i	−0.109028	−	0.994039i	$-0.534774\pi$
$577$	−24.6070	−	14.2069i	−1.02440	−	0.591440i	−0.915377	+	0.402599i	$0.868107\pi$
$578$	−28.1949	−	16.2783i	−1.17275	−	0.677089i
$579$		0			0
$580$		−	85.2131i		−	3.53828i
$581$	−2.83943	+	0.451105i	−0.117800	+	0.0187150i
$582$		0			0
$583$	29.1876	+	50.5543i	1.20882	+	2.09375i
$584$	−36.5610	+	63.3254i	−1.51290	+	2.62043i
$585$		0			0
$586$	20.6708	−	11.9343i	0.853903	−	0.493001i
$587$	−17.9101			−0.739227			−0.369614	−	0.929185i	$-0.620510\pi$
$587$	−17.9101			−0.739227			−0.369614	+	0.929185i	$0.620510\pi$
$588$		0			0
$589$	−5.58081			−0.229953
$590$	73.9063	−	42.6698i	3.04268	−	1.75669i
$591$		0			0
$592$	−21.2484	+	36.8033i	−0.873304	+	1.51261i
$593$	5.80499	+	10.0545i	0.238382	+	0.412890i	0.960250	−	0.279141i	$-0.0900496\pi$
$593$	5.80499	+	10.0545i	0.238382	+	0.412890i	−0.721868	+	0.692031i	$0.756716\pi$
$594$		0			0
$595$	15.8968	−	2.52554i	0.651704	−	0.103537i
$596$		−	27.9084i		−	1.14317i
$597$		0			0
$598$	50.6520	+	29.2440i	2.07132	+	1.19588i
$599$	39.4409	+	22.7712i	1.61151	+	0.930406i	0.989021	+	0.147778i	$0.0472122\pi$
$599$	39.4409	+	22.7712i	1.61151	+	0.930406i	0.622490	+	0.782628i	$0.286121\pi$
$600$		0			0
$601$			32.3325i			1.31887i	0.751761	+	0.659436i	$0.229205\pi$
$601$			32.3325i			1.31887i	−0.751761	+	0.659436i	$0.770795\pi$
$602$	53.9725	−	43.7485i	2.19975	−	1.78306i
$603$		0			0
$604$	−19.6433	−	34.0232i	−0.799275	−	1.38439i
$605$	−31.8300	+	55.1311i	−1.29407	+	2.24140i
$606$		0			0
$607$	−13.0192	+	7.51663i	−0.528433	+	0.305091i	−0.740378	−	0.672191i	$-0.765353\pi$
$607$	−13.0192	+	7.51663i	−0.528433	+	0.305091i	0.211945	+	0.977282i	$0.432020\pi$
$608$	3.86210			0.156629
$609$		0			0
$610$	13.7246			0.555693
$611$	−20.7002	+	11.9513i	−0.837440	+	0.483496i
$612$		0			0
$613$	−15.7696	+	27.3138i	−0.636929	+	1.10319i	0.349174	+	0.937058i	$0.386462\pi$
$613$	−15.7696	+	27.3138i	−0.636929	+	1.10319i	−0.986103	+	0.166135i	$0.946871\pi$
$614$	−21.5851	−	37.3865i	−0.871103	−	1.50880i
$615$		0			0
$616$	31.8268	−	83.0296i	1.28234	−	3.34536i
$617$			29.4553i			1.18583i	0.805267	+	0.592913i	$0.202022\pi$
$617$			29.4553i			1.18583i	−0.805267	+	0.592913i	$0.797978\pi$
$618$		0			0
$619$	−21.8229	−	12.5995i	−0.877138	−	0.506416i	−0.00742405	−	0.999972i	$-0.502363\pi$
$619$	−21.8229	−	12.5995i	−0.877138	−	0.506416i	−0.869714	+	0.493557i	$0.835697\pi$
$620$	−63.3345	−	36.5662i	−2.54357	−	1.46853i
$621$		0			0
$622$			84.5864i			3.39161i
$623$	−15.1184	−	18.6515i	−0.605704	−	0.747256i
$624$		0			0
$625$	14.3984	+	24.9388i	0.575938	+	0.997553i
$626$	−4.30201	+	7.45130i	−0.171943	+	0.297814i
$627$		0			0
$628$	69.3302	−	40.0278i	2.76658	−	1.59728i
$629$	−13.7679			−0.548964
$630$		0			0
$631$	−15.6464			−0.622872			−0.311436	−	0.950267i	$-0.600810\pi$
$631$	−15.6464			−0.622872			−0.311436	+	0.950267i	$0.600810\pi$
$632$	−34.5264	+	19.9338i	−1.37339	+	0.792925i
$633$		0			0
$634$	16.6073	−	28.7647i	0.659560	−	1.14239i
$635$	−16.5395	−	28.6473i	−0.656351	−	1.13683i
$636$		0			0
$637$	−7.26342	−	22.2824i	−0.287787	−	0.882863i
$638$		−	92.9162i		−	3.67859i
$639$		0			0
$640$	−38.1450	−	22.0230i	−1.50781	−	0.870537i
$641$	19.9276	+	11.5052i	0.787094	+	0.454429i	0.838939	−	0.544226i	$-0.183177\pi$
$641$	19.9276	+	11.5052i	0.787094	+	0.454429i	−0.0518444	+	0.998655i	$0.516510\pi$
$642$		0			0
$643$		−	19.1787i		−	0.756333i	−0.925738	−	0.378166i	$-0.876555\pi$
$643$		−	19.1787i		−	0.756333i	0.925738	−	0.378166i	$-0.123445\pi$
$644$	−12.5226	−	78.8225i	−0.493461	−	3.10604i
$645$		0			0
$646$	2.54617	+	4.41010i	0.100178	+	0.173513i
$647$	19.9838	−	34.6129i	0.785643	−	1.36077i	−0.142972	−	0.989727i	$-0.545666\pi$
$647$	19.9838	−	34.6129i	0.785643	−	1.36077i	0.928614	−	0.371046i	$-0.121001\pi$
$648$		0			0
$649$	55.2138	−	31.8777i	2.16733	−	1.25131i
$650$	−34.3119			−1.34582
$651$		0			0
$652$	−45.2773			−1.77320
$653$	−5.15393	+	2.97562i	−0.201689	+	0.116445i	−0.597443	−	0.801911i	$-0.703817\pi$
$653$	−5.15393	+	2.97562i	−0.201689	+	0.116445i	0.395754	+	0.918356i	$0.370483\pi$
$654$		0			0
$655$	−25.0176	+	43.3317i	−0.977517	+	1.69311i
$656$	−10.0671	−	17.4368i	−0.393055	−	0.680792i
$657$		0			0
$658$	44.4518	+	17.0392i	1.73291	+	0.664258i
$659$		−	31.4978i		−	1.22698i	−0.789703	−	0.613489i	$-0.789765\pi$
$659$		−	31.4978i		−	1.22698i	0.789703	−	0.613489i	$-0.210235\pi$
$660$		0			0
$661$	25.7550	+	14.8697i	1.00175	+	0.578363i	0.908767	−	0.417304i	$-0.137025\pi$
$661$	25.7550	+	14.8697i	1.00175	+	0.578363i	0.0929877	+	0.995667i	$0.470358\pi$
$662$	−40.4325	−	23.3437i	−1.57145	−	0.907279i
$663$		0			0
$664$		−	6.44184i		−	0.249992i
$665$	7.43864	+	2.85137i	0.288458	+	0.110571i
$666$		0			0
$667$	−22.5361	−	39.0337i	−0.872602	−	1.51139i
$668$	47.6907	−	82.6028i	1.84521	−	3.19600i
$669$		0			0
$670$	−14.7331	+	8.50619i	−0.569191	+	0.328623i
$671$	10.2534			0.395827
$672$		0			0
$673$	−43.8665			−1.69093			−0.845465	−	0.534031i	$-0.820677\pi$
$673$	−43.8665			−1.69093			−0.845465	+	0.534031i	$0.820677\pi$
$674$	36.9509	−	21.3336i	1.42329	−	0.821739i
$675$		0			0
$676$	3.89625	−	6.74850i	0.149856	−	0.259558i
$677$	−13.1785	−	22.8259i	−0.506492	−	0.877270i	−0.999972	−	0.00751288i	$-0.997609\pi$
$677$	−13.1785	−	22.8259i	−0.506492	−	0.877270i	0.493480	−	0.869757i	$-0.335725\pi$
$678$		0			0
$679$	1.05586	+	6.64603i	0.0405204	+	0.255051i
$680$			36.0651i			1.38303i
$681$		0			0
$682$	−69.0598	−	39.8717i	−2.64443	−	1.52677i
$683$	−16.8993	−	9.75679i	−0.646632	−	0.373333i	0.140532	−	0.990076i	$-0.455119\pi$
$683$	−16.8993	−	9.75679i	−0.646632	−	0.373333i	−0.787165	+	0.616743i	$0.788452\pi$
$684$		0			0
$685$			5.13136i			0.196059i
$686$	−25.3665	+	39.1831i	−0.968496	+	1.49602i
$687$		0			0
$688$	32.4897	+	56.2738i	1.23866	+	2.14542i
$689$	−17.2366	+	29.8547i	−0.656663	+	1.13737i
$690$		0			0
$691$	1.00033	−	0.577540i	0.0380543	−	0.0219707i	−0.480852	−	0.876802i	$-0.659673\pi$
$691$	1.00033	−	0.577540i	0.0380543	−	0.0219707i	0.518906	+	0.854831i	$0.326339\pi$
$692$	71.9761			2.73612
$693$		0			0
$694$	−10.5943			−0.402153
$695$	10.9821	−	6.34050i	0.416573	−	0.240509i
$696$		0			0
$697$	3.26151	−	5.64910i	0.123538	−	0.213975i
$698$	30.5573	+	52.9269i	1.15661	+	2.00331i
$699$		0			0
$700$	29.4827	+	36.3728i	1.11434	+	1.37476i
$701$		−	16.4503i		−	0.621319i	−0.950521	−	0.310659i	$-0.899450\pi$
$701$		−	16.4503i		−	0.621319i	0.950521	−	0.310659i	$-0.100550\pi$
$702$		0			0
$703$	−5.90120	−	3.40706i	−0.222568	−	0.128500i
$704$	−13.4498	−	7.76525i	−0.506909	−	0.292664i
$705$		0			0
$706$		−	58.3896i		−	2.19752i
$707$	15.3680	−	40.0919i	0.577973	−	1.50781i
$708$		0			0
$709$	−1.70687	−	2.95639i	−0.0641029	−	0.111029i	0.832193	−	0.554486i	$-0.187085\pi$
$709$	−1.70687	−	2.95639i	−0.0641029	−	0.111029i	−0.896296	+	0.443457i	$0.853752\pi$
$710$	−18.6558	+	32.3128i	−0.700140	+	1.21268i
$711$		0			0
$712$	46.5880	−	26.8976i	1.74596	−	1.00803i
$713$	−38.6823			−1.44866
$714$		0			0
$715$	−57.1538			−2.13743
$716$	−58.7839	+	33.9389i	−2.19686	+	1.26836i
$717$		0			0
$718$	34.5676	−	59.8728i	1.29005	−	2.23443i
$719$	13.1059	+	22.7000i	0.488766	+	0.846568i	0.999916	−	0.0129235i	$-0.00411379\pi$
$719$	13.1059	+	22.7000i	0.488766	+	0.846568i	−0.511150	+	0.859491i	$0.670780\pi$
$720$		0			0
$721$	3.97553	−	3.22245i	0.148056	−	0.120010i
$722$			2.52034i			0.0937972i
$723$		0			0
$724$	5.54136	+	3.19931i	0.205943	+	0.118901i
$725$	22.8991	+	13.2208i	0.850450	+	0.491008i
$726$		0			0
$727$		−	44.6719i		−	1.65679i	−0.560145	−	0.828395i	$-0.689255\pi$
$727$		−	44.6719i		−	1.65679i	0.560145	−	0.828395i	$-0.310745\pi$
$728$	51.8613	−	8.23929i	1.92211	−	0.305368i
$729$		0			0
$730$	−46.8032	−	81.0655i	−1.73226	−	3.00037i
$731$	−10.5259	+	18.2314i	−0.389314	+	0.674311i
$732$		0			0
$733$	−15.9564	+	9.21243i	−0.589363	+	0.340269i	−0.764846	−	0.644214i	$-0.777185\pi$
$733$	−15.9564	+	9.21243i	−0.589363	+	0.340269i	0.175483	+	0.984483i	$0.443851\pi$
$734$	65.0716			2.40184
$735$		0			0
$736$	26.7694			0.986734
$737$	−11.0068	+	6.35479i	−0.405441	+	0.234082i
$738$		0			0
$739$	−18.9856	+	32.8841i	−0.698397	+	1.20966i	0.270625	+	0.962685i	$0.412770\pi$
$739$	−18.9856	+	32.8841i	−0.698397	+	1.20966i	−0.969022	+	0.246974i	$0.920564\pi$
$740$	−44.6470	−	77.3309i	−1.64126	−	2.84274i
$741$		0			0
$742$	67.8085	−	10.7728i	2.48933	−	0.395483i
$743$		−	36.1620i		−	1.32666i	−0.748328	−	0.663328i	$-0.769143\pi$
$743$		−	36.1620i		−	1.32666i	0.748328	−	0.663328i	$-0.230857\pi$
$744$		0			0
$745$	16.7217	+	9.65427i	0.612635	+	0.353705i
$746$	32.4839	+	18.7546i	1.18932	+	0.686655i
$747$		0			0
$748$			49.8536i			1.82283i
$749$	−24.4702	+	19.8348i	−0.894121	+	0.724749i
$750$		0			0
$751$	−17.4976	−	30.3067i	−0.638495	−	1.10591i	−0.985763	−	0.168140i	$-0.946224\pi$
$751$	−17.4976	−	30.3067i	−0.638495	−	1.10591i	0.347268	−	0.937766i	$-0.387109\pi$
$752$	−22.2622	+	38.5592i	−0.811817	+	1.40611i
$753$		0			0
$754$	47.5200	−	27.4357i	1.73058	−	0.999148i
$755$	27.1806			0.989205
$756$		0			0
$757$	−15.0865			−0.548330			−0.274165	−	0.961683i	$-0.588401\pi$
$757$	−15.0865			−0.548330			−0.274165	+	0.961683i	$0.588401\pi$
$758$	−66.2179	+	38.2309i	−2.40514	+	1.38861i
$759$		0			0
$760$	−8.92479	+	15.4582i	−0.323736	+	0.560728i
$761$	18.0518	+	31.2666i	0.654376	+	1.13341i	0.982050	+	0.188622i	$0.0604021\pi$
$761$	18.0518	+	31.2666i	0.654376	+	1.13341i	−0.327673	+	0.944791i	$0.606265\pi$
$762$		0			0
$763$	0.662251	−	1.72767i	0.0239751	−	0.0625460i
$764$		−	59.5850i		−	2.15571i
$765$		0			0
$766$	44.7281	+	25.8238i	1.61609	+	0.933051i
$767$	32.6064	+	18.8253i	1.17735	+	0.679742i
$768$		0			0
$769$		−	10.8018i		−	0.389523i	−0.980851	−	0.194762i	$-0.937607\pi$
$769$		−	10.8018i		−	0.389523i	0.980851	−	0.194762i	$-0.0623933\pi$
$770$	71.6781	+	88.4291i	2.58310	+	3.18676i
$771$		0			0
$772$	−41.0622	−	71.1218i	−1.47786	−	2.55973i
$773$	10.9491	−	18.9644i	0.393813	−	0.682104i	−0.599136	−	0.800647i	$-0.704489\pi$
$773$	10.9491	−	18.9644i	0.393813	−	0.682104i	0.992949	+	0.118543i	$0.0378225\pi$
$774$		0			0
$775$	19.6526	−	11.3465i	0.705944	−	0.407577i
$776$	−15.0779			−0.541265
$777$		0			0
$778$	−38.7855			−1.39053
$779$	2.79589	−	1.61421i	0.100173	−	0.0578350i
$780$		0			0
$781$	−13.9373	+	24.1402i	−0.498717	+	0.863804i
$782$	17.6483	+	30.5677i	0.631102	+	1.09310i
$783$		0			0
$784$	−32.4705	−	29.1807i	−1.15966	−	1.04217i
$785$			55.3868i			1.97684i
$786$		0			0
$787$	3.99112	+	2.30427i	0.142268	+	0.0821384i	0.569444	−	0.822030i	$-0.307158\pi$
$787$	3.99112	+	2.30427i	0.142268	+	0.0821384i	−0.427177	+	0.904168i	$0.640492\pi$
$788$	33.5259	+	19.3562i	1.19431	+	0.689535i
$789$		0			0
$790$		−	51.0362i		−	1.81579i
$791$	3.51847	+	22.1466i	0.125102	+	0.787444i
$792$		0			0
$793$	3.02755	+	5.24386i	0.107511	+	0.186215i
$794$	18.4431	−	31.9445i	0.654523	−	1.13367i
$795$		0			0
$796$	−62.1612	+	35.8888i	−2.20324	+	1.27204i
$797$	−51.7748			−1.83396			−0.916978	−	0.398938i	$-0.869379\pi$
$797$	−51.7748			−1.83396			−0.916978	+	0.398938i	$0.869379\pi$
$798$		0			0
$799$	−14.4248			−0.510313
$800$	−13.6003	+	7.85212i	−0.480842	+	0.277615i
$801$		0			0
$802$	−22.9338	+	39.7225i	−0.809821	+	1.40265i
$803$	−34.9656	−	60.5623i	−1.23391	−	2.13720i
$804$		0			0
$805$	51.5595	+	19.7637i	1.81723	+	0.696580i
$806$		−	47.0922i		−	1.65875i
$807$		0			0
$808$	83.3148	+	48.1018i	2.93101	+	1.69222i
$809$	31.7880	+	18.3528i	1.11761	+	0.645251i	0.940789	−	0.338992i	$-0.110086\pi$
$809$	31.7880	+	18.3528i	1.11761	+	0.645251i	0.176819	+	0.984243i	$0.443419\pi$
$810$		0			0
$811$		−	14.3712i		−	0.504642i	−0.967644	−	0.252321i	$-0.918806\pi$
$811$		−	14.3712i		−	0.504642i	0.967644	−	0.252321i	$-0.0811938\pi$
$812$	−69.9154	−	26.7999i	−2.45355	−	0.940492i
$813$		0			0
$814$	−48.6830	−	84.3214i	−1.70634	−	2.95546i
$815$	15.6627	−	27.1285i	0.548639	−	0.950271i
$816$		0			0
$817$	−9.02319	+	5.20954i	−0.315681	+	0.182259i
$818$	12.9133			0.451502
$819$		0			0
$820$	42.3060			1.47739
$821$	30.0013	−	17.3213i	1.04705	−	0.604517i	0.125231	−	0.992128i	$-0.460033\pi$
$821$	30.0013	−	17.3213i	1.04705	−	0.604517i	0.921823	+	0.387611i	$0.126699\pi$
$822$		0			0
$823$	25.3888	−	43.9748i	0.885000	−	1.53286i	0.0392854	−	0.999228i	$-0.487492\pi$
$823$	25.3888	−	43.9748i	0.885000	−	1.53286i	0.845714	−	0.533636i	$-0.179175\pi$
$824$	5.73317	+	9.93015i	0.199725	+	0.345933i
$825$		0			0
$826$	−11.7658	−	74.0583i	−0.409383	−	2.57682i
$827$			50.8274i			1.76744i	0.468013	+	0.883721i	$0.344970\pi$
$827$			50.8274i			1.76744i	−0.468013	+	0.883721i	$0.655030\pi$
$828$		0			0
$829$	14.2370	+	8.21976i	0.494473	+	0.285484i	0.726428	−	0.687242i	$-0.241179\pi$
$829$	14.2370	+	8.21976i	0.494473	+	0.285484i	−0.231955	+	0.972726i	$0.574512\pi$
$830$	7.14165	+	4.12323i	0.247890	+	0.143120i
$831$		0			0
$832$		−	9.17149i		−	0.317964i
$833$	2.92745	−	13.8372i	0.101430	−	0.479431i
$834$		0			0
$835$	32.9950	+	57.1491i	1.14184	+	1.97773i
$836$	−12.3369	+	21.3682i	−0.426682	+	0.739035i
$837$		0			0
$838$	−0.311662	+	0.179938i	−0.0107662	+	0.00621585i
$839$	−54.7073			−1.88871			−0.944353	−	0.328935i	$-0.893310\pi$
$839$	−54.7073			−1.88871			−0.944353	+	0.328935i	$0.893310\pi$
$840$		0			0
$841$	−13.2852			−0.458109
$842$	−21.9167	+	12.6536i	−0.755301	+	0.436073i
$843$		0			0
$844$	13.2561	−	22.9602i	0.456294	−	0.790324i
$845$	2.69564	+	4.66898i	0.0927327	+	0.160618i
$846$		0			0
$847$	35.2231	+	43.4547i	1.21028	+	1.49312i
$848$			64.2148i			2.20515i
$849$		0			0
$850$	−17.9325	−	10.3534i	−0.615081	−	0.355117i
$851$	−40.9030	−	23.6154i	−1.40214	−	0.809524i
$852$		0			0
$853$		−	24.1115i		−	0.825562i	−0.910830	−	0.412781i	$-0.864557\pi$
$853$		−	24.1115i		−	0.825562i	0.910830	−	0.412781i	$-0.135443\pi$
$854$	4.31645	−	11.2607i	0.147706	−	0.385334i
$855$		0			0
$856$	−35.2888	−	61.1221i	−1.20615	−	2.08911i
$857$	−4.65447	+	8.06178i	−0.158994	+	0.275385i	−0.934506	−	0.355947i	$-0.884158\pi$
$857$	−4.65447	+	8.06178i	−0.158994	+	0.275385i	0.775512	+	0.631332i	$0.217492\pi$
$858$		0			0
$859$	−4.88202	+	2.81864i	−0.166572	+	0.0961706i	−0.580969	−	0.813926i	$-0.697326\pi$
$859$	−4.88202	+	2.81864i	−0.166572	+	0.0961706i	0.414396	+	0.910097i	$0.363993\pi$
$860$	−136.534			−4.65578
$861$		0			0
$862$	−63.1150			−2.14971
$863$	29.7894	−	17.1989i	1.01404	−	0.585457i	0.101669	−	0.994818i	$-0.467582\pi$
$863$	29.7894	−	17.1989i	1.01404	−	0.585457i	0.912373	+	0.409361i	$0.134248\pi$
$864$		0			0
$865$	−24.8985	+	43.1255i	−0.846575	+	1.46631i
$866$	36.2784	+	62.8360i	1.23279	+	2.13525i
$867$		0			0
$868$	−49.9207	+	40.4643i	−1.69442	+	1.37345i
$869$		−	38.1281i		−	1.29341i
$870$		0			0
$871$	−6.50004	−	3.75280i	−0.220246	−	0.127159i
$872$	3.59027	+	2.07284i	0.121582	+	0.0701954i
$873$		0			0
$874$			17.4692i			0.590905i
$875$	7.34657	−	1.16716i	0.248359	−	0.0394572i
$876$		0			0
$877$	25.0717	+	43.4255i	0.846613	+	1.46638i	0.884213	+	0.467083i	$0.154695\pi$
$877$	25.0717	+	43.4255i	0.846613	+	1.46638i	−0.0376006	+	0.999293i	$0.511971\pi$
$878$	−5.93223	+	10.2749i	−0.200203	+	0.346762i
$879$		0			0
$880$	−92.1996	+	53.2315i	−3.10805	+	1.79443i
$881$	−7.60902			−0.256355			−0.128177	−	0.991751i	$-0.540913\pi$
$881$	−7.60902			−0.256355			−0.128177	+	0.991751i	$0.540913\pi$
$882$		0			0
$883$	1.30733			0.0439951			0.0219975	−	0.999758i	$-0.492997\pi$
$883$	1.30733			0.0439951			0.0219975	+	0.999758i	$0.492997\pi$
$884$	−25.4966	+	14.7204i	−0.857542	+	0.495102i
$885$		0			0
$886$	−0.831975	+	1.44102i	−0.0279507	+	0.0484121i
$887$	20.0734	+	34.7682i	0.673999	+	1.16740i	0.976760	+	0.214335i	$0.0687583\pi$
$887$	20.0734	+	34.7682i	0.673999	+	1.16740i	−0.302761	+	0.953067i	$0.597908\pi$
$888$		0			0
$889$	−28.7062	+	4.56059i	−0.962774	+	0.152957i
$890$			68.8655i			2.30838i
$891$		0			0
$892$	62.1700	+	35.8939i	2.08161	+	1.20182i
$893$	−6.18275	−	3.56961i	−0.206898	−	0.119453i
$894$		0			0
$895$		−	46.9615i		−	1.56975i
$896$	−30.0662	+	24.3708i	−1.00444	+	0.814170i
$897$		0			0
$898$	6.40036	+	11.0858i	0.213583	+	0.369936i
$899$	−18.1452	+	31.4284i	−0.605176	+	1.04819i
$900$		0			0
$901$	−18.0168	+	10.4020i	−0.600228	+	0.346542i
$902$	46.1303			1.53597
$903$		0			0
$904$	−50.2442			−1.67110
$905$	−3.83382	+	2.21346i	−0.127440	+	0.0735777i
$906$		0			0
$907$	13.9513	−	24.1643i	0.463244	−	0.802362i	−0.535876	−	0.844297i	$-0.680019\pi$
$907$	13.9513	−	24.1643i	0.463244	−	0.802362i	0.999120	+	0.0419341i	$0.0133520\pi$
$908$	17.5307	+	30.3640i	0.581776	+	1.00767i
$909$		0			0
$910$	−24.0605	+	62.7690i	−0.797599	+	2.08077i
$911$			11.5472i			0.382575i	0.981534	+	0.191288i	$0.0612663\pi$
$911$			11.5472i			0.382575i	−0.981534	+	0.191288i	$0.938734\pi$
$912$		0			0
$913$	5.33537	+	3.08038i	0.176575	+	0.101946i
$914$	12.9115	+	7.45448i	0.427076	+	0.246572i
$915$		0			0
$916$			50.1029i			1.65545i
$917$	27.6845	+	34.1543i	0.914223	+	1.12787i
$918$		0			0
$919$	−9.08987	−	15.7441i	−0.299847	−	0.519350i	0.676254	−	0.736669i	$-0.263602\pi$
$919$	−9.08987	−	15.7441i	−0.299847	−	0.519350i	−0.976101	+	0.217318i	$0.930269\pi$
$920$	−61.8604	+	107.145i	−2.03948	+	3.53248i
$921$		0			0
$922$	32.9168	−	19.0045i	1.08406	−	0.625880i
$923$	−16.4613			−0.541831
$924$		0			0
$925$	27.7079			0.911029
$926$	−24.2318	+	13.9902i	−0.796305	+	0.459747i
$927$		0			0
$928$	12.5571	−	21.7495i	0.412206	−	0.713961i
$929$	15.5266	+	26.8928i	0.509411	+	0.882325i	0.999941	+	0.0109009i	$0.00346992\pi$
$929$	15.5266	+	26.8928i	0.509411	+	0.882325i	−0.490530	+	0.871424i	$0.663197\pi$
$930$		0			0
$931$	4.67897	−	5.20646i	0.153347	−	0.170635i
$932$		−	43.3366i		−	1.41954i
$933$		0			0
$934$	31.8386	+	18.3820i	1.04179	+	0.601477i
$935$	−29.8705	−	17.2457i	−0.976869	−	0.563995i
$936$		0			0
$937$		−	17.3894i		−	0.568087i	−0.958811	−	0.284044i	$-0.908324\pi$
$937$		−	17.3894i		−	0.568087i	0.958811	−	0.284044i	$-0.0916760\pi$
$938$	2.34549	+	14.7634i	0.0765830	+	0.482043i
$939$		0			0
$940$	−46.7771	−	81.0204i	−1.52570	−	2.64259i
$941$	19.5785	−	33.9109i	0.638239	−	1.10546i	−0.347580	−	0.937650i	$-0.612996\pi$
$941$	19.5785	−	33.9109i	0.638239	−	1.10546i	0.985819	−	0.167812i	$-0.0536703\pi$
$942$		0			0
$943$	19.3792	−	11.1886i	0.631072	−	0.364350i
$944$	70.1334			2.28265
$945$		0			0
$946$	−148.877			−4.84040
$947$	10.7078	−	6.18217i	0.347958	−	0.200894i	−0.315828	−	0.948817i	$-0.602282\pi$
$947$	10.7078	−	6.18217i	0.347958	−	0.200894i	0.663786	+	0.747923i	$0.268949\pi$
$948$		0			0
$949$	20.6489	−	35.7649i	0.670290	−	1.16098i
$950$	−5.12415	−	8.87529i	−0.166249	−	0.287952i
$951$		0			0
$952$	29.5906	+	11.3426i	0.959036	+	0.367617i
$953$		−	6.83357i		−	0.221361i	−0.993856	−	0.110681i	$-0.964697\pi$
$953$		−	6.83357i		−	0.221361i	0.993856	−	0.110681i	$-0.0353030\pi$
$954$		0			0
$955$	35.7011	+	20.6121i	1.15526	+	0.666991i
$956$	95.3149	+	55.0301i	3.08270	+	1.77980i
$957$		0			0
$958$			41.3456i			1.33581i
$959$	4.21016	+	1.61383i	0.135953	+	0.0521134i
$960$		0			0
$961$	0.0727151	+	0.125946i	0.00234565	+	0.00406278i
$962$	28.7496	−	49.7957i	0.926923	−	1.60548i
$963$		0			0
$964$	101.655	−	58.6908i	3.27410	−	1.89030i
$965$	56.8181			1.82904
$966$		0			0
$967$	−25.6905			−0.826151			−0.413075	−	0.910697i	$-0.635545\pi$
$967$	−25.6905			−0.826151			−0.413075	+	0.910697i	$0.635545\pi$
$968$	−108.542	+	62.6667i	−3.48867	+	2.01418i
$969$		0			0
$970$	9.65091	−	16.7159i	0.309872	−	0.536714i
$971$	−9.94475	−	17.2248i	−0.319142	−	0.552770i	0.661167	−	0.750239i	$-0.270061\pi$
$971$	−9.94475	−	17.2248i	−0.319142	−	0.552770i	−0.980309	+	0.197468i	$0.936728\pi$
$972$		0			0
$973$	−1.74832	−	11.0046i	−0.0560487	−	0.352793i
$974$		−	41.7064i		−	1.33636i
$975$		0			0
$976$	9.76798	+	5.63955i	0.312665	+	0.180517i
$977$	30.7791	+	17.7703i	0.984710	+	0.568523i	0.903689	−	0.428190i	$-0.140849\pi$
$977$	30.7791	+	17.7703i	0.984710	+	0.568523i	0.0810212	+	0.996712i	$0.474182\pi$
$978$		0			0
$979$			51.4479i			1.64428i
$980$	87.2133	−	28.4290i	2.78593	−	0.908130i
$981$		0			0
$982$	8.35261	+	14.4671i	0.266543	+	0.461665i
$983$	−1.05013	+	1.81888i	−0.0334939	+	0.0580132i	−0.882286	−	0.470713i	$-0.843997\pi$
$983$	−1.05013	+	1.81888i	−0.0334939	+	0.0580132i	0.848793	+	0.528726i	$0.177330\pi$
$984$		0			0
$985$	−23.1950	+	13.3917i	−0.739055	+	0.426694i
$986$	33.1140			1.05457
$987$		0			0
$988$	−14.5711			−0.463568
$989$	−62.5424	+	36.1089i	−1.98873	+	1.14820i
$990$		0			0
$991$	1.98852	−	3.44421i	0.0631674	−	0.109409i	−0.832712	−	0.553706i	$-0.813213\pi$
$991$	1.98852	−	3.44421i	0.0631674	−	0.109409i	0.895880	+	0.444297i	$0.146546\pi$
$992$	−10.7768	−	18.6660i	−0.342165	−	0.592647i
$993$		0			0
$994$	20.6446	+	25.4692i	0.654806	+	0.807833i
$995$		−	49.6596i		−	1.57432i
$996$		0			0
$997$	23.6705	+	13.6661i	0.749651	+	0.432811i	0.825568	−	0.564303i	$-0.190855\pi$
$997$	23.6705	+	13.6661i	0.749651	+	0.432811i	−0.0759170	+	0.997114i	$0.524188\pi$
$998$	9.56115	+	5.52013i	0.302653	+	0.174737i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.db.a.647.3	✓	96
3.2	odd	2	inner	1197.2.db.a.647.46	yes	96
7.5	odd	6	inner	1197.2.db.a.1160.46	yes	96
21.5	even	6	inner	1197.2.db.a.1160.3	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1197.2.db.a.647.3	✓	96	1.1	even	1	trivial
1197.2.db.a.647.46	yes	96	3.2	odd	2	inner
1197.2.db.a.1160.3	yes	96	21.5	even	6	inner
1197.2.db.a.1160.46	yes	96	7.5	odd	6	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:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1197.db (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18268 + 1.26017i) q^{2} +(2.17605 - 3.76903i) q^{4} +(1.50551 + 2.60762i) q^{5} +(2.61298 - 0.415128i) q^{7} +5.92809i q^{8} +O(q^{10})\)	\(q+(-2.18268 + 1.26017i) q^{2} +(2.17605 - 3.76903i) q^{4} +(1.50551 + 2.60762i) q^{5} +(2.61298 - 0.415128i) q^{7} +5.92809i q^{8} +(-6.57208 - 3.79439i) q^{10} +(-4.90986 - 2.83471i) q^{11} -3.34806i q^{13} +(-5.18016 + 4.19889i) q^{14} +(-3.11829 - 5.40103i) q^{16} +(1.01025 - 1.74981i) q^{17} +(0.866025 - 0.500000i) q^{19} +13.1043 q^{20} +14.2888 q^{22} +(6.00268 - 3.46565i) q^{23} +(-2.03312 + 3.52147i) q^{25} +(4.21912 + 7.30772i) q^{26} +(4.12135 - 10.7517i) q^{28} -6.50270i q^{29} +(-4.83312 - 2.79040i) q^{31} +(3.34468 + 1.93105i) q^{32} +5.09234i q^{34} +(5.01637 + 6.18868i) q^{35} +(-3.40706 - 5.90120i) q^{37} +(-1.26017 + 2.18268i) q^{38} +(-15.4582 + 8.92479i) q^{40} +3.22842 q^{41} -10.4191 q^{43} +(-21.3682 + 12.3369i) q^{44} +(-8.73461 + 15.1288i) q^{46} +(-3.56961 - 6.18275i) q^{47} +(6.65534 - 2.16944i) q^{49} -10.2483i q^{50} +(-12.6189 - 7.28554i) q^{52} +(-8.91702 - 5.14824i) q^{53} -17.0707i q^{55} +(2.46092 + 15.4900i) q^{56} +(8.19451 + 14.1933i) q^{58} +(-5.62275 + 9.73889i) q^{59} +(-1.56624 + 0.904269i) q^{61} +14.0655 q^{62} +2.73935 q^{64} +(8.73046 - 5.04053i) q^{65} +(1.12089 - 1.94144i) q^{67} +(-4.39671 - 7.61533i) q^{68} +(-18.7479 - 7.18642i) q^{70} -4.91667i q^{71} +(10.6823 + 6.16741i) q^{73} +(14.8730 + 8.58694i) q^{74} -4.35210i q^{76} +(-14.0061 - 5.36882i) q^{77} +(3.36261 + 5.82421i) q^{79} +(9.38923 - 16.2626i) q^{80} +(-7.04659 + 4.06835i) q^{82} -1.08666 q^{83} +6.08377 q^{85} +(22.7415 - 13.1298i) q^{86} +(16.8044 - 29.1061i) q^{88} +(-4.53732 - 7.85887i) q^{89} +(-1.38987 - 8.74841i) q^{91} -30.1657i q^{92} +(15.5826 + 8.99663i) q^{94} +(2.60762 + 1.50551i) q^{95} +2.54347i q^{97} +(-11.7926 + 13.1220i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 48 q^{4} + 8 q^{7}+O(q^{10}) \) 96 * q + 48 * q^4 + 8 * q^7	\( 96 q + 48 q^{4} + 8 q^{7} + 24 q^{10} - 56 q^{16} + 48 q^{22} - 24 q^{25} + 16 q^{28} - 24 q^{31} - 48 q^{40} - 24 q^{43} - 48 q^{46} + 52 q^{49} - 72 q^{52} + 48 q^{58} - 176 q^{64} + 32 q^{67} - 80 q^{70} - 12 q^{73} + 40 q^{79} + 72 q^{82} + 40 q^{85} - 16 q^{88} - 72 q^{91} + 72 q^{94}+O(q^{100}) \) 96 * q + 48 * q^4 + 8 * q^7 + 24 * q^10 - 56 * q^16 + 48 * q^22 - 24 * q^25 + 16 * q^28 - 24 * q^31 - 48 * q^40 - 24 * q^43 - 48 * q^46 + 52 * q^49 - 72 * q^52 + 48 * q^58 - 176 * q^64 + 32 * q^67 - 80 * q^70 - 12 * q^73 + 40 * q^79 + 72 * q^82 + 40 * q^85 - 16 * q^88 - 72 * q^91 + 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more