LMFDB - Embedded newform 1224.2.l.d.1189.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1224,2,Mod(1189,1224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1224, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1224.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1224 = 2^{3} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1224.l (of order $2$, degree $1$, 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:	$9.77368920740$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{16} - 2x^{14} + 2x^{12} - 4x^{11} + 4x^{10} + 8x^{8} - 16x^{7} + 16x^{6} - 64x^{4} - 128x^{2} + 512 $ x^18 - x^16 - 2x^14 + 2x^12 - 4x^11 + 4x^10 + 8x^8 - 16x^7 + 16x^6 - 64x^4 - 128*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 408)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1189.10
Root			$-0.0535843 - 1.41320i$ of defining polynomial
Character	$\chi$	$=$	1224.1189
Dual form			1224.2.l.d.1189.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0535843 + 1.41320i) q^{2} +(-1.99426 - 0.151450i) q^{4} +3.17378 q^{5} +2.51539i q^{7} +(0.320890 - 2.81017i) q^{8} +(-0.170065 + 4.48518i) q^{10} +5.40062 q^{11} +3.61678i q^{13} +(-3.55474 - 0.134785i) q^{14} +(3.95413 + 0.604062i) q^{16} +(4.09928 - 0.442631i) q^{17} -6.87329i q^{19} +(-6.32934 - 0.480670i) q^{20} +(-0.289388 + 7.63215i) q^{22} -7.54740i q^{23} +5.07289 q^{25} +(-5.11123 - 0.193803i) q^{26} +(0.380956 - 5.01633i) q^{28} -3.32236 q^{29} -1.30617i q^{31} +(-1.06554 + 5.55559i) q^{32} +(0.405869 + 5.81681i) q^{34} +7.98329i q^{35} -6.65467 q^{37} +(9.71332 + 0.368300i) q^{38} +(1.01844 - 8.91885i) q^{40} +5.04206i q^{41} +5.85844i q^{43} +(-10.7702 - 0.817926i) q^{44} +(10.6660 + 0.404422i) q^{46} +8.02838 q^{47} +0.672834 q^{49} +(-0.271827 + 7.16900i) q^{50} +(0.547763 - 7.21280i) q^{52} +7.67778i q^{53} +17.1404 q^{55} +(7.06865 + 0.807163i) q^{56} +(0.178026 - 4.69516i) q^{58} -4.23300i q^{59} -3.88181 q^{61} +(1.84588 + 0.0699903i) q^{62} +(-7.79406 - 1.80351i) q^{64} +11.4789i q^{65} +10.8844i q^{67} +(-8.24205 + 0.261884i) q^{68} +(-11.2820 - 0.427779i) q^{70} +4.23091i q^{71} -0.674683i q^{73} +(0.356585 - 9.40436i) q^{74} +(-1.04096 + 13.7071i) q^{76} +13.5846i q^{77} +1.43576i q^{79} +(12.5495 + 1.91716i) q^{80} +(-7.12542 - 0.270175i) q^{82} -16.1494i q^{83} +(13.0102 - 1.40482i) q^{85} +(-8.27913 - 0.313920i) q^{86} +(1.73301 - 15.1766i) q^{88} -9.77068 q^{89} -9.09761 q^{91} +(-1.14306 + 15.0515i) q^{92} +(-0.430195 + 11.3457i) q^{94} -21.8143i q^{95} -0.954796i q^{97} +(-0.0360533 + 0.950847i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{4} + 4 q^{5} - 8 q^{10} + 6 q^{14} + 10 q^{16} + 2 q^{17} + 2 q^{20} + 2 q^{22} + 22 q^{25} - 2 q^{26} - 10 q^{28} - 12 q^{29} + 6 q^{34} - 16 q^{37} + 34 q^{38} - 10 q^{40} - 12 q^{44} + 32 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) $ 18 * q + 2 * q^4 + 4 * q^5 - 8 * q^10 + 6 * q^14 + 10 * q^16 + 2 * q^17 + 2 * q^20 + 2 * q^22 + 22 * q^25 - 2 * q^26 - 10 * q^28 - 12 * q^29 + 6 * q^34 - 16 * q^37 + 34 * q^38 - 10 * q^40 - 12 * q^44 + 32 * q^46 - 18 * q^49 + 14 * q^50 + 8 * q^52 - 16 * q^55 + 14 * q^56 - 6 * q^58 - 16 * q^61 + 6 * q^62 + 2 * q^64 + 36 * q^68 - 32 * q^70 + 6 * q^74 + 62 * q^80 + 34 * q^82 + 16 * q^85 - 14 * q^86 + 16 * q^88 - 20 * q^89 + 2 * q^92 + 12 * q^94 + 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times$.

$n$	$137$	$613$	$649$	$919$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−0.0535843	+	1.41320i	−0.0378898	+	0.999282i
$2$	−0.0535843	+	1.41320i	−0.0378898	+	0.999282i
$3$		0			0
$3$		0			0
$4$	−1.99426	−	0.151450i	−0.997129	−	0.0757252i
$5$	3.17378			1.41936			0.709679	−	0.704525i	$-0.248840\pi$
$5$	3.17378			1.41936			0.709679	+	0.704525i	$0.248840\pi$
$6$		0			0
$7$			2.51539i			0.950727i	0.879790	+	0.475363i	$0.157683\pi$
$7$			2.51539i			0.950727i	−0.879790	+	0.475363i	$0.842317\pi$
$8$	0.320890	−	2.81017i	0.113452	−	0.993544i
$9$		0			0
$10$	−0.170065	+	4.48518i	−0.0537792	+	1.41834i
$11$	5.40062			1.62835			0.814174	−	0.580621i	$-0.197190\pi$
$11$	5.40062			1.62835			0.814174	+	0.580621i	$0.197190\pi$
$12$		0			0
$13$			3.61678i			1.00312i	0.865124	+	0.501558i	$0.167239\pi$
$13$			3.61678i			1.00312i	−0.865124	+	0.501558i	$0.832761\pi$
$14$	−3.55474	−	0.134785i	−0.950044	−	0.0360228i
$15$		0			0
$16$	3.95413	+	0.604062i	0.988531	+	0.151016i
$17$	4.09928	−	0.442631i	0.994221	−	0.107354i
$17$	4.09928	−	0.442631i	0.994221	−	0.107354i
$18$		0			0
$19$		−	6.87329i		−	1.57684i	−0.615137	−	0.788420i	$-0.710899\pi$
$19$		−	6.87329i		−	1.57684i	0.615137	−	0.788420i	$-0.289101\pi$
$20$	−6.32934	−	0.480670i	−1.41528	−	0.107481i
$21$		0			0
$22$	−0.289388	+	7.63215i	−0.0616978	+	1.62718i
$23$		−	7.54740i		−	1.57374i	−0.617118	−	0.786871i	$-0.711700\pi$
$23$		−	7.54740i		−	1.57374i	0.617118	−	0.786871i	$-0.288300\pi$
$24$		0			0
$25$	5.07289			1.01458
$26$	−5.11123	−	0.193803i	−1.00239	−	0.0380078i
$27$		0			0
$28$	0.380956	−	5.01633i	0.0719939	−	0.947997i
$29$	−3.32236			−0.616947			−0.308474	−	0.951233i	$-0.599818\pi$
$29$	−3.32236			−0.616947			−0.308474	+	0.951233i	$0.599818\pi$
$30$		0			0
$31$		−	1.30617i		−	0.234596i	−0.993097	−	0.117298i	$-0.962577\pi$
$31$		−	1.30617i		−	0.234596i	0.993097	−	0.117298i	$-0.0374232\pi$
$32$	−1.06554	+	5.55559i	−0.188362	+	0.982100i
$33$		0			0
$34$	0.405869	+	5.81681i	0.0696059	+	0.997575i
$35$			7.98329i			1.34942i
$36$		0			0
$37$	−6.65467			−1.09402			−0.547010	−	0.837126i	$-0.684234\pi$
$37$	−6.65467			−1.09402			−0.547010	+	0.837126i	$0.684234\pi$
$38$	9.71332	+	0.368300i	1.57571	+	0.0597462i
$39$		0			0
$40$	1.01844	−	8.91885i	0.161029	−	1.41019i
$41$			5.04206i			0.787437i	0.919231	+	0.393718i	$0.128811\pi$
$41$			5.04206i			0.787437i	−0.919231	+	0.393718i	$0.871189\pi$
$42$		0			0
$43$			5.85844i			0.893403i	0.894683	+	0.446702i	$0.147401\pi$
$43$			5.85844i			0.893403i	−0.894683	+	0.446702i	$0.852599\pi$
$44$	−10.7702	−	0.817926i	−1.62367	−	0.123307i
$45$		0			0
$46$	10.6660	+	0.404422i	1.57261	+	0.0596287i
$47$	8.02838			1.17106			0.585530	−	0.810651i	$-0.300886\pi$
$47$	8.02838			1.17106			0.585530	+	0.810651i	$0.300886\pi$
$48$		0			0
$49$	0.672834			0.0961191
$50$	−0.271827	+	7.16900i	−0.0384422	+	1.01385i
$51$		0			0
$52$	0.547763	−	7.21280i	0.0759611	−	1.00024i
$53$			7.67778i			1.05462i	0.849672	+	0.527312i	$0.176800\pi$
$53$			7.67778i			1.05462i	−0.849672	+	0.527312i	$0.823200\pi$
$54$		0			0
$55$	17.1404			2.31121
$56$	7.06865	+	0.807163i	0.944588	+	0.107862i
$57$		0			0
$58$	0.178026	−	4.69516i	0.0233760	−	0.616504i
$59$		−	4.23300i		−	0.551090i	−0.961288	−	0.275545i	$-0.911142\pi$
$59$		−	4.23300i		−	0.551090i	0.961288	−	0.275545i	$-0.0888582\pi$
$60$		0			0
$61$	−3.88181			−0.497015			−0.248507	−	0.968630i	$-0.579940\pi$
$61$	−3.88181			−0.497015			−0.248507	+	0.968630i	$0.579940\pi$
$62$	1.84588	+	0.0699903i	0.234427	+	0.00888878i
$63$		0			0
$64$	−7.79406	−	1.80351i	−0.974257	−	0.225439i
$65$			11.4789i			1.42378i
$66$		0			0
$67$			10.8844i			1.32974i	0.746960	+	0.664869i	$0.231512\pi$
$67$			10.8844i			1.32974i	−0.746960	+	0.664869i	$0.768488\pi$
$68$	−8.24205	+	0.261884i	−0.999496	+	0.0317580i
$69$		0			0
$70$	−11.2820	−	0.427779i	−1.34845	−	0.0511293i
$71$			4.23091i			0.502116i	0.967972	+	0.251058i	$0.0807785\pi$
$71$			4.23091i			0.502116i	−0.967972	+	0.251058i	$0.919221\pi$
$72$		0			0
$73$		−	0.674683i		−	0.0789656i	−0.999220	−	0.0394828i	$-0.987429\pi$
$73$		−	0.674683i		−	0.0789656i	0.999220	−	0.0394828i	$-0.0125710\pi$
$74$	0.356585	−	9.40436i	0.0414522	−	1.09323i
$75$		0			0
$76$	−1.04096	+	13.7071i	−0.119407	+	1.57231i
$77$			13.5846i			1.54811i
$78$		0			0
$79$			1.43576i			0.161536i	0.996733	+	0.0807680i	$0.0257373\pi$
$79$			1.43576i			0.161536i	−0.996733	+	0.0807680i	$0.974263\pi$
$80$	12.5495	+	1.91716i	1.40308	+	0.214345i
$81$		0			0
$82$	−7.12542	−	0.270175i	−0.786871	−	0.0298358i
$83$		−	16.1494i		−	1.77262i	−0.463088	−	0.886312i	$-0.653259\pi$
$83$		−	16.1494i		−	1.77262i	0.463088	−	0.886312i	$-0.346741\pi$
$84$		0			0
$85$	13.0102	−	1.40482i	1.41116	−	0.152374i
$86$	−8.27913	−	0.313920i	−0.892762	−	0.0338509i
$87$		0			0
$88$	1.73301	−	15.1766i	0.184739	−	1.61783i
$89$	−9.77068			−1.03569			−0.517845	−	0.855475i	$-0.673266\pi$
$89$	−9.77068			−1.03569			−0.517845	+	0.855475i	$0.673266\pi$
$90$		0			0
$91$	−9.09761			−0.953688
$92$	−1.14306	+	15.0515i	−0.119172	+	1.56922i
$93$		0			0
$94$	−0.430195	+	11.3457i	−0.0443712	+	1.17022i
$95$		−	21.8143i		−	2.23810i
$96$		0			0
$97$		−	0.954796i		−	0.0969449i	−0.998825	−	0.0484724i	$-0.984565\pi$
$97$		−	0.954796i		−	0.0969449i	0.998825	−	0.0484724i	$-0.0154353\pi$
$98$	−0.0360533	+	0.950847i	−0.00364193	+	0.0960501i
$99$		0			0
$100$	−10.1167	−	0.768292i	−1.01167	−	0.0768292i
$101$			11.7795i			1.17210i	0.810275	+	0.586050i	$0.199318\pi$
$101$			11.7795i			1.17210i	−0.810275	+	0.586050i	$0.800682\pi$
$102$		0			0
$103$	−3.63788			−0.358451			−0.179225	−	0.983808i	$-0.557359\pi$
$103$	−3.63788			−0.358451			−0.179225	+	0.983808i	$0.557359\pi$
$104$	10.1638	+	1.16059i	0.996639	+	0.113805i
$105$		0			0
$106$	−10.8502	−	0.411408i	−1.05387	−	0.0399595i
$107$	2.78476			0.269213			0.134606	−	0.990899i	$-0.457023\pi$
$107$	2.78476			0.269213			0.134606	+	0.990899i	$0.457023\pi$
$108$		0			0
$109$	−14.7517			−1.41296			−0.706479	−	0.707734i	$-0.749718\pi$
$109$	−14.7517			−1.41296			−0.706479	+	0.707734i	$0.749718\pi$
$110$	−0.918455	+	24.2228i	−0.0875713	+	2.30955i
$111$		0			0
$112$	−1.51945	+	9.94615i	−0.143574	+	0.939823i
$113$			7.57157i			0.712274i	0.934434	+	0.356137i	$0.115906\pi$
$113$			7.57157i			0.712274i	−0.934434	+	0.356137i	$0.884094\pi$
$114$		0			0
$115$		−	23.9538i		−	2.23370i
$116$	6.62565	+	0.503173i	0.615176	+	0.0467185i
$117$		0			0
$118$	5.98207	+	0.226822i	0.550694	+	0.0208807i
$119$	1.11339	+	10.3113i	0.102064	+	0.945232i
$120$		0			0
$121$	18.1667			1.65152
$122$	0.208004	−	5.48577i	0.0188318	−	0.496658i
$123$		0			0
$124$	−0.197820	+	2.60485i	−0.0177648	+	0.233922i
$125$	0.231351			0.0206927
$126$		0			0
$127$	−8.80507			−0.781324			−0.390662	−	0.920534i	$-0.627754\pi$
$127$	−8.80507			−0.781324			−0.390662	+	0.920534i	$0.627754\pi$
$128$	2.96635	−	10.9179i	0.262191	−	0.965016i
$129$		0			0
$130$	−16.2219	−	0.615088i	−1.42276	−	0.0539467i
$131$	−21.0088			−1.83555			−0.917773	−	0.397106i	$-0.870014\pi$
$131$	−21.0088			−1.83555			−0.917773	+	0.397106i	$0.870014\pi$
$132$		0			0
$133$	17.2890			1.49914
$134$	−15.3818	−	0.583231i	−1.32878	−	0.0503835i
$135$		0			0
$136$	0.0715510	−	11.6617i	0.00613545	−	0.999981i
$137$	15.9533			1.36298			0.681490	−	0.731828i	$-0.261332\pi$
$137$	15.9533			1.36298			0.681490	+	0.731828i	$0.261332\pi$
$138$		0			0
$139$	6.61325			0.560929			0.280464	−	0.959864i	$-0.409512\pi$
$139$	6.61325			0.560929			0.280464	+	0.959864i	$0.409512\pi$
$140$	1.20907	−	15.9207i	0.102185	−	1.34555i
$141$		0			0
$142$	−5.97911	−	0.226710i	−0.501756	−	0.0190251i
$143$			19.5329i			1.63342i
$144$		0			0
$145$	−10.5445			−0.875670
$146$	0.953460	+	0.0361524i	0.0789089	+	0.00299199i
$147$		0			0
$148$	13.2711	+	1.00785i	1.09088	+	0.0828449i
$149$		−	15.3325i		−	1.25609i	−0.778178	−	0.628044i	$-0.783856\pi$
$149$		−	15.3325i		−	1.25609i	0.778178	−	0.628044i	$-0.216144\pi$
$150$		0			0
$151$	−1.10540			−0.0899565			−0.0449782	−	0.998988i	$-0.514322\pi$
$151$	−1.10540			−0.0899565			−0.0449782	+	0.998988i	$0.514322\pi$
$152$	−19.3151	−	2.20557i	−1.56666	−	0.178895i
$153$		0			0
$154$	−19.1978	−	0.727923i	−1.54700	−	0.0586577i
$155$		−	4.14551i		−	0.332975i
$156$		0			0
$157$			17.6004i			1.40467i	0.711849	+	0.702333i	$0.247858\pi$
$157$			17.6004i			1.40467i	−0.711849	+	0.702333i	$0.752142\pi$
$158$	−2.02902	−	0.0769343i	−0.161420	−	0.00612056i
$159$		0			0
$160$	−3.38179	+	17.6322i	−0.267354	+	1.39395i
$161$	18.9846			1.49620
$162$		0			0
$163$	−0.345904			−0.0270933			−0.0135467	−	0.999908i	$-0.504312\pi$
$163$	−0.345904			−0.0270933			−0.0135467	+	0.999908i	$0.504312\pi$
$164$	0.763621	−	10.0552i	0.0596288	−	0.785176i
$165$		0			0
$166$	22.8223	+	0.865353i	1.77135	+	0.0671644i
$167$		−	20.7946i		−	1.60913i	−0.593861	−	0.804567i	$-0.702397\pi$
$167$		−	20.7946i		−	1.60913i	0.593861	−	0.804567i	$-0.297603\pi$
$168$		0			0
$169$	−0.0811240			−0.00624031
$170$	1.28814	+	18.4613i	0.0987958	+	1.41592i
$171$		0			0
$172$	0.887262	−	11.6832i	0.0676531	−	0.890838i
$173$	−8.28576			−0.629954			−0.314977	−	0.949099i	$-0.601997\pi$
$173$	−8.28576			−0.629954			−0.314977	+	0.949099i	$0.601997\pi$
$174$		0			0
$175$			12.7603i			0.964587i
$176$	21.3547	+	3.26231i	1.60967	+	0.245906i
$177$		0			0
$178$	0.523555	−	13.8079i	0.0392421	−	1.03495i
$179$		−	17.2101i		−	1.28634i	−0.765722	−	0.643172i	$-0.777618\pi$
$179$		−	17.2101i		−	1.28634i	0.765722	−	0.643172i	$-0.222382\pi$
$180$		0			0
$181$	1.76280			0.131028			0.0655141	−	0.997852i	$-0.479131\pi$
$181$	1.76280			0.131028			0.0655141	+	0.997852i	$0.479131\pi$
$182$	0.487489	−	12.8567i	0.0361351	−	0.953003i
$183$		0			0
$184$	−21.2094	−	2.42189i	−1.56358	−	0.178544i
$185$	−21.1205			−1.55281
$186$		0			0
$187$	22.1386	−	2.39048i	1.61894	−	0.174809i
$188$	−16.0107	−	1.21590i	−1.16770	−	0.0886787i
$189$		0			0
$190$	30.8280	+	1.16890i	2.23650	+	0.0848012i
$191$	−4.73825			−0.342848			−0.171424	−	0.985197i	$-0.554837\pi$
$191$	−4.73825			−0.342848			−0.171424	+	0.985197i	$0.554837\pi$
$192$		0			0
$193$		−	20.9493i		−	1.50796i	−0.656897	−	0.753980i	$-0.728131\pi$
$193$		−	20.9493i		−	1.50796i	0.656897	−	0.753980i	$-0.271869\pi$
$194$	1.34932	+	0.0511621i	0.0968753	+	0.00367322i
$195$		0			0
$196$	−1.34180	−	0.101901i	−0.0958431	−	0.00727864i
$197$	−8.35170			−0.595034			−0.297517	−	0.954716i	$-0.596159\pi$
$197$	−8.35170			−0.595034			−0.297517	+	0.954716i	$0.596159\pi$
$198$		0			0
$199$			12.3310i			0.874121i	0.899432	+	0.437060i	$0.143980\pi$
$199$			12.3310i			0.874121i	−0.899432	+	0.437060i	$0.856020\pi$
$200$	1.62784	−	14.2557i	0.115106	−	1.00803i
$201$		0			0
$202$	−16.6467	−	0.631193i	−1.17126	−	0.0444106i
$203$		−	8.35703i		−	0.586548i
$204$		0			0
$205$			16.0024i			1.11766i
$206$	0.194933	−	5.14104i	0.0135816	−	0.358193i
$207$		0			0
$208$	−2.18476	+	14.3012i	−0.151486	+	0.991611i
$209$		−	37.1200i		−	2.56765i
$210$		0			0
$211$	−16.0368			−1.10402			−0.552010	−	0.833837i	$-0.686139\pi$
$211$	−16.0368			−1.10402			−0.552010	+	0.833837i	$0.686139\pi$
$212$	1.16280	−	15.3115i	0.0798616	−	1.05160i
$213$		0			0
$214$	−0.149219	+	3.93541i	−0.0102004	+	0.269019i
$215$			18.5934i			1.26806i
$216$		0			0
$217$	3.28553			0.223036
$218$	0.790460	−	20.8471i	0.0535367	−	1.41194i
$219$		0			0
$220$	−34.1824	−	2.59592i	−2.30457	−	0.175017i
$221$	1.60090	+	14.8262i	0.107688	+	0.997318i
$222$		0			0
$223$	10.0104			0.670349			0.335174	−	0.942156i	$-0.391205\pi$
$223$	10.0104			0.670349			0.335174	+	0.942156i	$0.391205\pi$
$224$	−13.9745	−	2.68024i	−0.933708	−	0.179081i
$225$		0			0
$226$	−10.7001	−	0.405717i	−0.711762	−	0.0269879i
$227$	−14.0466			−0.932305			−0.466152	−	0.884704i	$-0.654360\pi$
$227$	−14.0466			−0.932305			−0.466152	+	0.884704i	$0.654360\pi$
$228$		0			0
$229$			3.35868i			0.221948i	0.993823	+	0.110974i	$0.0353970\pi$
$229$			3.35868i			0.221948i	−0.993823	+	0.110974i	$0.964603\pi$
$230$	33.8515	+	1.28355i	2.23210	+	0.0846346i
$231$		0			0
$232$	−1.06611	+	9.33639i	−0.0699938	+	0.612964i
$233$		−	15.1152i		−	0.990230i	−0.868827	−	0.495115i	$-0.835126\pi$
$233$		−	15.1152i		−	0.990230i	0.868827	−	0.495115i	$-0.164874\pi$
$234$		0			0
$235$	25.4803			1.66215
$236$	−0.641089	+	8.44169i	−0.0417314	+	0.549507i
$237$		0			0
$238$	−14.6315	+	1.02092i	−0.948421	+	0.0661762i
$239$	−11.3025			−0.731101			−0.365550	−	0.930792i	$-0.619119\pi$
$239$	−11.3025			−0.731101			−0.365550	+	0.930792i	$0.619119\pi$
$240$		0			0
$241$		−	23.8864i		−	1.53866i	−0.638851	−	0.769330i	$-0.720590\pi$
$241$		−	23.8864i		−	1.53866i	0.638851	−	0.769330i	$-0.279410\pi$
$242$	−0.973449	+	25.6731i	−0.0625757	+	1.65033i
$243$		0			0
$244$	7.74133	+	0.587901i	0.495588	+	0.0376365i
$245$	2.13543			0.136427
$246$		0			0
$247$	24.8592			1.58175
$248$	−3.67056	−	0.419138i	−0.233081	−	0.0266153i
$249$		0			0
$250$	−0.0123968	+	0.326945i	−0.000784042	+	0.0206778i
$251$		−	7.16691i		−	0.452371i	−0.974084	−	0.226186i	$-0.927374\pi$
$251$		−	7.16691i		−	0.452371i	0.974084	−	0.226186i	$-0.0726256\pi$
$252$		0			0
$253$		−	40.7606i		−	2.56260i
$254$	0.471813	−	12.4433i	0.0296042	−	0.780763i
$255$		0			0
$256$	15.2702	+	4.77707i	0.954389	+	0.298567i
$257$	5.46601			0.340960			0.170480	−	0.985361i	$-0.445468\pi$
$257$	5.46601			0.340960			0.170480	+	0.985361i	$0.445468\pi$
$258$		0			0
$259$		−	16.7391i		−	1.04011i
$260$	1.73848	−	22.8919i	0.107816	−	1.41969i
$261$		0			0
$262$	1.12574	−	29.6896i	0.0695484	−	1.83423i
$263$	15.2442			0.939997			0.469999	−	0.882667i	$-0.344254\pi$
$263$	15.2442			0.939997			0.469999	+	0.882667i	$0.344254\pi$
$264$		0			0
$265$			24.3676i			1.49689i
$266$	−0.926417	+	24.4327i	−0.0568023	+	1.49807i
$267$		0			0
$268$	1.64844	−	21.7062i	0.100695	−	1.32592i
$269$	6.61819			0.403518			0.201759	−	0.979435i	$-0.435334\pi$
$269$	6.61819			0.403518			0.201759	+	0.979435i	$0.435334\pi$
$270$		0			0
$271$	−11.5920			−0.704166			−0.352083	−	0.935969i	$-0.614527\pi$
$271$	−11.5920			−0.704166			−0.352083	+	0.935969i	$0.614527\pi$
$272$	16.4764	+	0.725999i	0.999031	+	0.0440201i
$273$		0			0
$274$	−0.854844	+	22.5451i	−0.0516430	+	1.36200i
$275$	27.3968			1.65209
$276$		0			0
$277$	16.6679			1.00148			0.500738	−	0.865599i	$-0.333062\pi$
$277$	16.6679			1.00148			0.500738	+	0.865599i	$0.333062\pi$
$278$	−0.354366	+	9.34584i	−0.0212535	+	0.560526i
$279$		0			0
$280$	22.4344	+	2.56176i	1.34071	+	0.153094i
$281$	6.51175			0.388458			0.194229	−	0.980956i	$-0.437779\pi$
$281$	6.51175			0.388458			0.194229	+	0.980956i	$0.437779\pi$
$282$		0			0
$283$	−21.2924			−1.26570			−0.632850	−	0.774275i	$-0.718115\pi$
$283$	−21.2924			−1.26570			−0.632850	+	0.774275i	$0.718115\pi$
$284$	0.640772	−	8.43752i	0.0380228	−	0.500675i
$285$		0			0
$286$	−27.6038	−	1.04665i	−1.63225	−	0.0618900i
$287$	−12.6827			−0.748637
$288$		0			0
$289$	16.6082	−	3.62894i	0.976950	−	0.213467i
$290$	0.565017	−	14.9014i	0.0331789	−	0.875041i
$291$		0			0
$292$	−0.102181	+	1.34549i	−0.00597969	+	0.0787389i
$293$			6.20078i			0.362253i	0.983460	+	0.181127i	$0.0579744\pi$
$293$			6.20078i			0.362253i	−0.983460	+	0.181127i	$0.942026\pi$
$294$		0			0
$295$		−	13.4346i		−	0.782194i
$296$	−2.13542	+	18.7007i	−0.124119	+	1.08696i
$297$		0			0
$298$	21.6679	+	0.821581i	1.25519	+	0.0475929i
$299$	27.2973			1.57864
$300$		0			0
$301$	−14.7362			−0.849382
$302$	0.0592322	−	1.56215i	0.00340843	−	0.0898919i
$303$		0			0
$304$	4.15189	−	27.1778i	0.238127	−	1.55876i
$305$	−12.3200			−0.705442
$306$		0			0
$307$		−	3.96275i		−	0.226166i	−0.993586	−	0.113083i	$-0.963927\pi$
$307$		−	3.96275i		−	0.226166i	0.993586	−	0.113083i	$-0.0360726\pi$
$308$	2.05740	−	27.0913i	0.117231	−	1.54367i
$309$		0			0
$310$	5.85843	+	0.222134i	0.332736	+	0.0126164i
$311$			6.26994i			0.355535i	0.984072	+	0.177768i	$0.0568876\pi$
$311$			6.26994i			0.355535i	−0.984072	+	0.177768i	$0.943112\pi$
$312$		0			0
$313$			10.7509i			0.607675i	0.952724	+	0.303838i	$0.0982681\pi$
$313$			10.7509i			0.607675i	−0.952724	+	0.303838i	$0.901732\pi$
$314$	−24.8729	−	0.943105i	−1.40366	−	0.0532225i
$315$		0			0
$316$	0.217447	−	2.86328i	0.0122323	−	0.161072i
$317$	17.0890			0.959815			0.479908	−	0.877319i	$-0.340670\pi$
$317$	17.0890			0.959815			0.479908	+	0.877319i	$0.340670\pi$
$318$		0			0
$319$	−17.9428			−1.00461
$320$	−24.7366	−	5.72394i	−1.38282	−	0.319978i
$321$		0			0
$322$	−1.01728	+	26.8290i	−0.0566906	+	1.49512i
$323$	−3.04233	−	28.1755i	−0.169280	−	1.56773i
$324$		0			0
$325$			18.3476i			1.01774i
$326$	0.0185350	−	0.488831i	0.00102656	−	0.0270739i
$327$		0			0
$328$	14.1690	+	1.61795i	0.782353	+	0.0893361i
$329$			20.1945i			1.11336i
$330$		0			0
$331$		−	7.05539i		−	0.387799i	−0.981021	−	0.193900i	$-0.937886\pi$
$331$		−	7.05539i		−	0.387799i	0.981021	−	0.193900i	$-0.0621136\pi$
$332$	−2.44583	+	32.2060i	−0.134232	+	1.76753i
$333$		0			0
$334$	29.3869	+	1.11426i	1.60798	+	0.0609698i
$335$			34.5446i			1.88737i
$336$		0			0
$337$			19.8274i			1.08007i	0.841643	+	0.540035i	$0.181589\pi$
$337$			19.8274i			1.08007i	−0.841643	+	0.540035i	$0.818411\pi$
$338$	0.00434697	−	0.114644i	0.000236444	−	0.00623583i
$339$		0			0
$340$	−26.1585	+	0.831161i	−1.41864	+	0.0450760i
$341$		−	7.05414i		−	0.382003i
$342$		0			0
$343$			19.3001i			1.04211i
$344$	16.4632	+	1.87991i	0.887635	+	0.101358i
$345$		0			0
$346$	0.443986	−	11.7094i	0.0238688	−	0.629502i
$347$	24.3591			1.30767			0.653833	−	0.756639i	$-0.273160\pi$
$347$	24.3591			1.30767			0.653833	+	0.756639i	$0.273160\pi$
$348$		0			0
$349$		−	1.20575i		−	0.0645421i	−0.999479	−	0.0322710i	$-0.989726\pi$
$349$		−	1.20575i		−	0.0645421i	0.999479	−	0.0322710i	$-0.0102740\pi$
$350$	−18.0328	−	0.683751i	−0.963894	−	0.0365480i
$351$		0			0
$352$	−5.75457	+	30.0037i	−0.306719	+	1.59920i
$353$	−11.4575			−0.609820			−0.304910	−	0.952381i	$-0.598626\pi$
$353$	−11.4575			−0.609820			−0.304910	+	0.952381i	$0.598626\pi$
$354$		0			0
$355$			13.4280i			0.712683i
$356$	19.4852	+	1.47977i	1.03272	+	0.0784278i
$357$		0			0
$358$	24.3213	+	0.922191i	1.28542	+	0.0487393i
$359$	31.0234			1.63735			0.818677	−	0.574254i	$-0.194708\pi$
$359$	31.0234			1.63735			0.818677	+	0.574254i	$0.194708\pi$
$360$		0			0
$361$	−28.2421			−1.48643
$362$	−0.0944585	+	2.49119i	−0.00496463	+	0.130934i
$363$		0			0
$364$	18.1430	+	1.37784i	0.950950	+	0.0722182i
$365$		−	2.14130i		−	0.112081i
$366$		0			0
$367$		−	9.00308i		−	0.469957i	−0.972001	−	0.234978i	$-0.924498\pi$
$367$		−	9.00308i		−	0.469957i	0.972001	−	0.234978i	$-0.0755020\pi$
$368$	4.55910	−	29.8434i	0.237659	−	1.55569i
$369$		0			0
$370$	1.13172	−	29.8474i	0.0588356	−	1.55169i
$371$	−19.3126			−1.00266
$372$		0			0
$373$			23.7413i			1.22928i	0.788809	+	0.614638i	$0.210698\pi$
$373$			23.7413i			1.22928i	−0.788809	+	0.614638i	$0.789302\pi$
$374$	2.19194	+	31.4144i	0.113343	+	1.62440i
$375$		0			0
$376$	2.57623	−	22.5611i	0.132859	−	1.16350i
$377$		−	12.0163i		−	0.618869i
$378$		0			0
$379$	−10.7431			−0.551835			−0.275917	−	0.961181i	$-0.588982\pi$
$379$	−10.7431			−0.551835			−0.275917	+	0.961181i	$0.588982\pi$
$380$	−3.30379	+	43.5034i	−0.169481	+	2.23168i
$381$		0			0
$382$	0.253896	−	6.69609i	0.0129904	−	0.342602i
$383$	13.2678			0.677952			0.338976	−	0.940795i	$-0.389919\pi$
$383$	13.2678			0.677952			0.338976	+	0.940795i	$0.389919\pi$
$384$		0			0
$385$			43.1147i			2.19733i
$386$	29.6054	+	1.12255i	1.50688	+	0.0571363i
$387$		0			0
$388$	−0.144604	+	1.90411i	−0.00734117	+	0.0966665i
$389$			32.5854i			1.65214i	0.563565	+	0.826072i	$0.309429\pi$
$389$			32.5854i			1.65214i	−0.563565	+	0.826072i	$0.690571\pi$
$390$		0			0
$391$	−3.34071	−	30.9389i	−0.168947	−	1.56465i
$392$	0.215906	−	1.89077i	0.0109049	−	0.0954985i
$393$		0			0
$394$	0.447520	−	11.8026i	0.0225457	−	0.594607i
$395$			4.55680i			0.229277i
$396$		0			0
$397$	−13.2519			−0.665092			−0.332546	−	0.943087i	$-0.607908\pi$
$397$	−13.2519			−0.665092			−0.332546	+	0.943087i	$0.607908\pi$
$398$	−17.4261	−	0.660747i	−0.873493	−	0.0331203i
$399$		0			0
$400$	20.0589	+	3.06434i	1.00294	+	0.153217i
$401$			12.2827i			0.613366i	0.951812	+	0.306683i	$0.0992192\pi$
$401$			12.2827i			0.613366i	−0.951812	+	0.306683i	$0.900781\pi$
$402$		0			0
$403$	4.72415			0.235326
$404$	1.78400	−	23.4913i	0.0887574	−	1.16873i
$405$		0			0
$406$	11.8101	+	0.447805i	0.586127	+	0.0222242i
$407$	−35.9393			−1.78145
$408$		0			0
$409$	−16.8564			−0.833493			−0.416747	−	0.909023i	$-0.636830\pi$
$409$	−16.8564			−0.833493			−0.416747	+	0.909023i	$0.636830\pi$
$410$	−22.6145	−	0.857476i	−1.11685	−	0.0423477i
$411$		0			0
$412$	7.25486	+	0.550958i	0.357422	+	0.0271437i
$413$	10.6476			0.523936
$414$		0			0
$415$		−	51.2546i		−	2.51599i
$416$	−20.0934	−	3.85382i	−0.985159	−	0.188949i
$417$		0			0
$418$	52.4579	+	1.98905i	2.56580	+	0.0972876i
$419$	−7.38718			−0.360887			−0.180444	−	0.983585i	$-0.557753\pi$
$419$	−7.38718			−0.360887			−0.180444	+	0.983585i	$0.557753\pi$
$420$		0			0
$421$		−	20.6976i		−	1.00874i	−0.863489	−	0.504369i	$-0.831725\pi$
$421$		−	20.6976i		−	1.00874i	0.863489	−	0.504369i	$-0.168275\pi$
$422$	0.859322	−	22.6632i	0.0418311	−	1.10323i
$423$		0			0
$424$	21.5758	+	2.46372i	1.04782	+	0.119649i
$425$	20.7952	−	2.24542i	1.00872	−	0.108919i
$426$		0			0
$427$		−	9.76425i		−	0.472525i
$428$	−5.55352	−	0.421752i	−0.268440	−	0.0203862i
$429$		0			0
$430$	−26.2762	−	0.996314i	−1.26715	−	0.0480465i
$431$		−	13.1852i		−	0.635107i	−0.948240	−	0.317554i	$-0.897139\pi$
$431$		−	13.1852i		−	0.635107i	0.948240	−	0.317554i	$-0.102861\pi$
$432$		0			0
$433$	14.7426			0.708485			0.354243	−	0.935154i	$-0.384739\pi$
$433$	14.7426			0.708485			0.354243	+	0.935154i	$0.384739\pi$
$434$	−0.176053	+	4.64310i	−0.00845080	+	0.222876i
$435$		0			0
$436$	29.4187	+	2.23415i	1.40890	+	0.106996i
$437$	−51.8755			−2.48154
$438$		0			0
$439$		−	6.15820i		−	0.293915i	−0.989143	−	0.146958i	$-0.953052\pi$
$439$		−	6.15820i		−	0.293915i	0.989143	−	0.146958i	$-0.0469481\pi$
$440$	5.50018	−	48.1673i	0.262211	−	2.29629i
$441$		0			0
$442$	−21.0381	+	1.46794i	−1.00068	+	0.0698228i
$443$		−	2.64879i		−	0.125848i	−0.998018	−	0.0629239i	$-0.979957\pi$
$443$		−	2.64879i		−	0.125848i	0.998018	−	0.0629239i	$-0.0200425\pi$
$444$		0			0
$445$	−31.0100			−1.47002
$446$	−0.536402	+	14.1467i	−0.0253994	+	0.669867i
$447$		0			0
$448$	4.53652	−	19.6051i	0.214330	−	0.926252i
$449$		−	33.2045i		−	1.56702i	−0.621381	−	0.783509i	$-0.713428\pi$
$449$		−	33.2045i		−	1.56702i	0.621381	−	0.783509i	$-0.286572\pi$
$450$		0			0
$451$			27.2302i			1.28222i
$452$	1.14672	−	15.0997i	0.0539370	−	0.710228i
$453$		0			0
$454$	0.752676	−	19.8506i	0.0353248	−	0.931635i
$455$	−28.8738			−1.35363
$456$		0			0
$457$	−21.2316			−0.993171			−0.496585	−	0.867988i	$-0.665413\pi$
$457$	−21.2316			−0.993171			−0.496585	+	0.867988i	$0.665413\pi$
$458$	−4.74648	−	0.179972i	−0.221789	−	0.00840956i
$459$		0			0
$460$	−3.62781	+	47.7701i	−0.169148	+	2.22729i
$461$		−	35.0837i		−	1.63401i	−0.576631	−	0.817004i	$-0.695633\pi$
$461$		−	35.0837i		−	1.63401i	0.576631	−	0.817004i	$-0.304367\pi$
$462$		0			0
$463$	−22.4625			−1.04392			−0.521960	−	0.852970i	$-0.674799\pi$
$463$	−22.4625			−1.04392			−0.521960	+	0.852970i	$0.674799\pi$
$464$	−13.1370	−	2.00691i	−0.609872	−	0.0931686i
$465$		0			0
$466$	21.3608	+	0.809937i	0.989519	+	0.0375196i
$467$			14.3658i			0.664772i	0.943143	+	0.332386i	$0.107854\pi$
$467$			14.3658i			0.664772i	−0.943143	+	0.332386i	$0.892146\pi$
$468$		0			0
$469$	−27.3784			−1.26422
$470$	−1.36535	+	36.0088i	−0.0629787	+	1.66096i
$471$		0			0
$472$	−11.8954	−	1.35833i	−0.547532	−	0.0625221i
$473$			31.6392i			1.45477i
$474$		0			0
$475$		−	34.8675i		−	1.59983i
$476$	−0.658738	−	20.7319i	−0.0301932	−	0.950247i
$477$		0			0
$478$	0.605639	−	15.9727i	0.0277013	−	0.730576i
$479$			7.01618i			0.320577i	0.987070	+	0.160289i	$0.0512425\pi$
$479$			7.01618i			0.320577i	−0.987070	+	0.160289i	$0.948758\pi$
$480$		0			0
$481$		−	24.0685i		−	1.09743i
$482$	33.7563	+	1.27994i	1.53756	+	0.0582995i
$483$		0			0
$484$	−36.2291	−	2.75135i	−1.64678	−	0.125061i
$485$		−	3.03032i		−	0.137600i
$486$		0			0
$487$		−	24.5769i		−	1.11368i	−0.830619	−	0.556842i	$-0.812013\pi$
$487$		−	24.5769i		−	1.11368i	0.830619	−	0.556842i	$-0.187987\pi$
$488$	−1.24563	+	10.9085i	−0.0563872	+	0.493806i
$489$		0			0
$490$	−0.114425	+	3.01778i	−0.00516921	+	0.136330i
$491$		−	7.60956i		−	0.343415i	−0.985148	−	0.171707i	$-0.945072\pi$
$491$		−	7.60956i		−	0.343415i	0.985148	−	0.171707i	$-0.0549283\pi$
$492$		0			0
$493$	−13.6193	+	1.47058i	−0.613382	+	0.0662317i
$494$	−1.33206	+	35.1310i	−0.0599323	+	1.58062i
$495$		0			0
$496$	0.789010	−	5.16477i	0.0354276	−	0.231905i
$497$	−10.6424			−0.477375
$498$		0			0
$499$	−16.2432			−0.727144			−0.363572	−	0.931566i	$-0.618443\pi$
$499$	−16.2432			−0.727144			−0.363572	+	0.931566i	$0.618443\pi$
$500$	−0.461374	−	0.0350382i	−0.0206333	−	0.00156696i
$501$		0			0
$502$	10.1283	+	0.384033i	0.452046	+	0.0171402i
$503$		−	26.3137i		−	1.17327i	−0.809851	−	0.586636i	$-0.800452\pi$
$503$		−	26.3137i		−	1.17327i	0.809851	−	0.586636i	$-0.199548\pi$
$504$		0			0
$505$			37.3854i			1.66363i
$506$	57.6028	+	2.18413i	2.56076	+	0.0970964i
$507$		0			0
$508$	17.5596	+	1.33353i	0.779081	+	0.0591659i
$509$			7.93657i			0.351782i	0.984410	+	0.175891i	$0.0562806\pi$
$509$			7.93657i			0.351782i	−0.984410	+	0.175891i	$0.943719\pi$
$510$		0			0
$511$	1.69709			0.0750747
$512$	−7.56920	+	21.3239i	−0.334514	+	0.942391i
$513$		0			0
$514$	−0.292892	+	7.72456i	−0.0129189	+	0.340716i
$515$	−11.5458			−0.508770
$516$		0			0
$517$	43.3582			1.90689
$518$	23.6556	+	0.896950i	1.03937	+	0.0394097i
$519$		0			0
$520$	32.2576	+	3.68346i	1.41459	+	0.161530i
$521$			9.50069i			0.416233i	0.978104	+	0.208116i	$0.0667333\pi$
$521$			9.50069i			0.416233i	−0.978104	+	0.208116i	$0.933267\pi$
$522$		0			0
$523$		−	3.17435i		−	0.138805i	−0.997589	−	0.0694024i	$-0.977891\pi$
$523$		−	3.17435i		−	0.138805i	0.997589	−	0.0694024i	$-0.0221092\pi$
$524$	41.8969	+	3.18179i	1.83027	+	0.138997i
$525$		0			0
$526$	−0.816849	+	21.5431i	−0.0356163	+	0.939322i
$527$	−0.578153	−	5.35437i	−0.0251847	−	0.233240i
$528$		0			0
$529$	−33.9632			−1.47666
$530$	−34.4363	−	1.30572i	−1.49582	−	0.0567169i
$531$		0			0
$532$	−34.4787	−	2.61842i	−1.49484	−	0.113523i
$533$	−18.2360			−0.789890
$534$		0			0
$535$	8.83821			0.382109
$536$	30.5869	+	3.49269i	1.32115	+	0.150861i
$537$		0			0
$538$	−0.354631	+	9.35281i	−0.0152892	+	0.403228i
$539$	3.63372			0.156515
$540$		0			0
$541$	19.5892			0.842205			0.421103	−	0.907013i	$-0.361643\pi$
$541$	19.5892			0.842205			0.421103	+	0.907013i	$0.361643\pi$
$542$	0.621151	−	16.3818i	0.0266807	−	0.703660i
$543$		0			0
$544$	−1.90886	+	23.2456i	−0.0818416	+	0.996645i
$545$	−46.8187			−2.00549
$546$		0			0
$547$	−17.5753			−0.751467			−0.375734	−	0.926728i	$-0.622609\pi$
$547$	−17.5753			−0.751467			−0.375734	+	0.926728i	$0.622609\pi$
$548$	−31.8149	−	2.41613i	−1.35907	−	0.103212i
$549$		0			0
$550$	−1.46804	+	38.7171i	−0.0625973	+	1.65090i
$551$			22.8356i			0.972828i
$552$		0			0
$553$	−3.61150			−0.153576
$554$	−0.893136	+	23.5550i	−0.0379457	+	1.00076i
$555$		0			0
$556$	−13.1885	−	1.00158i	−0.559318	−	0.0424764i
$557$			30.3013i			1.28391i	0.766744	+	0.641953i	$0.221875\pi$
$557$			30.3013i			1.28391i	−0.766744	+	0.641953i	$0.778125\pi$
$558$		0			0
$559$	−21.1887			−0.896186
$560$	−4.82240	+	31.5669i	−0.203784	+	1.33395i
$561$		0			0
$562$	−0.348927	+	9.20239i	−0.0147186	+	0.388179i
$563$		−	2.46670i		−	0.103959i	−0.998648	−	0.0519794i	$-0.983447\pi$
$563$		−	2.46670i		−	0.103959i	0.998648	−	0.0519794i	$-0.0165530\pi$
$564$		0			0
$565$			24.0305i			1.01097i
$566$	1.14094	−	30.0903i	0.0479571	−	1.26479i
$567$		0			0
$568$	11.8895	+	1.35766i	0.498874	+	0.0569660i
$569$	−21.6017			−0.905590			−0.452795	−	0.891615i	$-0.649573\pi$
$569$	−21.6017			−0.905590			−0.452795	+	0.891615i	$0.649573\pi$
$570$		0			0
$571$	−10.9931			−0.460046			−0.230023	−	0.973185i	$-0.573880\pi$
$571$	−10.9931			−0.460046			−0.230023	+	0.973185i	$0.573880\pi$
$572$	2.95826	−	38.9536i	0.123691	−	1.62873i
$573$		0			0
$574$	0.679594	−	17.9232i	0.0283657	−	0.748099i
$575$		−	38.2872i		−	1.59668i
$576$		0			0
$577$	10.7397			0.447100			0.223550	−	0.974692i	$-0.428235\pi$
$577$	10.7397			0.447100			0.223550	+	0.974692i	$0.428235\pi$
$578$	4.23847	+	23.6651i	0.176297	+	0.984337i
$579$		0			0
$580$	21.0284	+	1.59696i	0.873155	+	0.0663102i
$581$	40.6219			1.68528
$582$		0			0
$583$			41.4648i			1.71730i
$584$	−1.89597	−	0.216499i	−0.0784558	−	0.00895879i
$585$		0			0
$586$	−8.76292	−	0.332264i	−0.361993	−	0.0137257i
$587$			35.1504i			1.45081i	0.688321	+	0.725406i	$0.258348\pi$
$587$			35.1504i			1.45081i	−0.688321	+	0.725406i	$0.741652\pi$
$588$		0			0
$589$	−8.97771			−0.369920
$590$	18.9858	+	0.719884i	0.781632	+	0.0296372i
$591$		0			0
$592$	−26.3134	−	4.01983i	−1.08147	−	0.165214i
$593$	30.3326			1.24561			0.622805	−	0.782377i	$-0.285993\pi$
$593$	30.3326			1.24561			0.622805	+	0.782377i	$0.285993\pi$
$594$		0			0
$595$	3.53365	+	32.7257i	0.144866	+	1.34162i
$596$	−2.32211	+	30.5770i	−0.0951175	+	1.25248i
$597$		0			0
$598$	−1.46271	+	38.5765i	−0.0598145	+	1.57751i
$599$	−31.3182			−1.27963			−0.639814	−	0.768530i	$-0.720988\pi$
$599$	−31.3182			−1.27963			−0.639814	+	0.768530i	$0.720988\pi$
$600$		0			0
$601$		−	30.7936i		−	1.25610i	−0.778174	−	0.628048i	$-0.783854\pi$
$601$		−	30.7936i		−	1.25610i	0.778174	−	0.628048i	$-0.216146\pi$
$602$	0.789630	−	20.8252i	0.0321829	−	0.848772i
$603$		0			0
$604$	2.20446	+	0.167414i	0.0896982	+	0.00681197i
$605$	57.6571			2.34410
$606$		0			0
$607$		−	2.10908i		−	0.0856050i	−0.999084	−	0.0428025i	$-0.986371\pi$
$607$		−	2.10908i		−	0.0856050i	0.999084	−	0.0428025i	$-0.0136286\pi$
$608$	38.1852	+	7.32375i	1.54861	+	0.297017i
$609$		0			0
$610$	0.660159	−	17.4106i	0.0267291	−	0.704936i
$611$			29.0369i			1.17471i
$612$		0			0
$613$		−	18.9528i		−	0.765497i	−0.923853	−	0.382749i	$-0.874978\pi$
$613$		−	18.9528i		−	0.765497i	0.923853	−	0.382749i	$-0.125022\pi$
$614$	5.60014	+	0.212341i	0.226003	+	0.00856938i
$615$		0			0
$616$	38.1751	+	4.35918i	1.53812	+	0.175636i
$617$		−	7.76650i		−	0.312668i	−0.987704	−	0.156334i	$-0.950032\pi$
$617$		−	7.76650i		−	0.312668i	0.987704	−	0.156334i	$-0.0499676\pi$
$618$		0			0
$619$	17.1983			0.691258			0.345629	−	0.938371i	$-0.387666\pi$
$619$	17.1983			0.691258			0.345629	+	0.938371i	$0.387666\pi$
$620$	−0.627839	+	8.26721i	−0.0252146	+	0.332019i
$621$		0			0
$622$	−8.86066	−	0.335970i	−0.355280	−	0.0134712i
$623$		−	24.5770i		−	0.984658i
$624$		0			0
$625$	−24.6302			−0.985209
$626$	−15.1931	−	0.576078i	−0.607239	−	0.0230247i
$627$		0			0
$628$	2.66559	−	35.0998i	0.106369	−	1.40063i
$629$	−27.2793	+	2.94556i	−1.08770	+	0.117447i
$630$		0			0
$631$	−0.102276			−0.00407152			−0.00203576	−	0.999998i	$-0.500648\pi$
$631$	−0.102276			−0.00407152			−0.00203576	+	0.999998i	$0.500648\pi$
$632$	4.03473	+	0.460722i	0.160493	+	0.0183265i
$633$		0			0
$634$	−0.915703	+	24.1502i	−0.0363672	+	0.959126i
$635$	−27.9454			−1.10898
$636$		0			0
$637$			2.43349i			0.0964185i
$638$	0.961453	−	25.3568i	0.0380643	−	1.00388i
$639$		0			0
$640$	9.41456	−	34.6511i	0.372143	−	1.36970i
$641$		−	47.2480i		−	1.86618i	−0.359639	−	0.933091i	$-0.617100\pi$
$641$		−	47.2480i		−	1.86618i	0.359639	−	0.933091i	$-0.382900\pi$
$642$		0			0
$643$	22.6820			0.894491			0.447245	−	0.894411i	$-0.352405\pi$
$643$	22.6820			0.894491			0.447245	+	0.894411i	$0.352405\pi$
$644$	−37.8602	−	2.87523i	−1.49190	−	0.113300i
$645$		0			0
$646$	39.9806	−	2.78965i	1.57302	−	0.109757i
$647$	42.0519			1.65323			0.826615	−	0.562768i	$-0.190264\pi$
$647$	42.0519			1.65323			0.826615	+	0.562768i	$0.190264\pi$
$648$		0			0
$649$		−	22.8608i		−	0.897366i
$650$	−25.9287	−	0.983141i	−1.01701	−	0.0385619i
$651$		0			0
$652$	0.689822	+	0.0523873i	0.0270155	+	0.00205165i
$653$	42.6516			1.66909			0.834544	−	0.550942i	$-0.185731\pi$
$653$	42.6516			1.66909			0.834544	+	0.550942i	$0.185731\pi$
$654$		0			0
$655$	−66.6773			−2.60530
$656$	−3.04571	+	19.9369i	−0.118915	+	0.778406i
$657$		0			0
$658$	−28.5388	−	1.08211i	−1.11256	−	0.0421849i
$659$		−	1.41696i		−	0.0551970i	−0.999619	−	0.0275985i	$-0.991214\pi$
$659$		−	1.41696i		−	0.0551970i	0.999619	−	0.0275985i	$-0.00878600\pi$
$660$		0			0
$661$			11.2234i			0.436541i	0.975888	+	0.218270i	$0.0700415\pi$
$661$			11.2234i			0.436541i	−0.975888	+	0.218270i	$0.929959\pi$
$662$	9.97066	+	0.378058i	0.387521	+	0.0146936i
$663$		0			0
$664$	−45.3824	−	5.18218i	−1.76118	−	0.201107i
$665$	54.8714			2.12782
$666$		0			0
$667$			25.0752i			0.970916i
$668$	−3.14935	+	41.4698i	−0.121852	+	1.60451i
$669$		0			0
$670$	−48.8184	−	1.85105i	−1.88602	−	0.0715122i
$671$	−20.9642			−0.809313
$672$		0			0
$673$			22.9936i			0.886337i	0.896438	+	0.443169i	$0.146146\pi$
$673$			22.9936i			0.886337i	−0.896438	+	0.443169i	$0.853854\pi$
$674$	−28.0201	−	1.06244i	−1.07929	−	0.0409236i
$675$		0			0
$676$	0.161782	+	0.0122863i	0.00622239	+	0.000472548i
$677$	−39.4852			−1.51754			−0.758771	−	0.651358i	$-0.774200\pi$
$677$	−39.4852			−1.51754			−0.758771	+	0.651358i	$0.774200\pi$
$678$		0			0
$679$	2.40168			0.0921681
$680$	0.227087	−	37.0116i	0.00870840	−	1.41933i
$681$		0			0
$682$	9.96890	+	0.377991i	0.381729	+	0.0144740i
$683$	20.6340			0.789537			0.394768	−	0.918781i	$-0.370825\pi$
$683$	20.6340			0.789537			0.394768	+	0.918781i	$0.370825\pi$
$684$		0			0
$685$	50.6322			1.93456
$686$	−27.2749	−	1.03418i	−1.04136	−	0.0394853i
$687$		0			0
$688$	−3.53886	+	23.1650i	−0.134918	+	0.883157i
$689$	−27.7689			−1.05791
$690$		0			0
$691$	−19.5064			−0.742057			−0.371028	−	0.928622i	$-0.620995\pi$
$691$	−19.5064			−0.742057			−0.371028	+	0.928622i	$0.620995\pi$
$692$	16.5239	+	1.25488i	0.628146	+	0.0477034i
$693$		0			0
$694$	−1.30527	+	34.4243i	−0.0495472	+	1.30673i
$695$	20.9890			0.796159
$696$		0			0
$697$	2.23177	+	20.6688i	0.0845344	+	0.782886i
$698$	1.70396	+	0.0646090i	0.0644957	+	0.00244549i
$699$		0			0
$700$	1.93255	−	25.4473i	0.0730435	−	0.961817i
$701$			22.6742i			0.856392i	0.903686	+	0.428196i	$0.140851\pi$
$701$			22.6742i			0.856392i	−0.903686	+	0.428196i	$0.859149\pi$
$702$		0			0
$703$			45.7394i			1.72510i
$704$	−42.0927	−	9.74007i	−1.58643	−	0.367093i
$705$		0			0
$706$	0.613941	−	16.1917i	0.0231060	−	0.609383i
$707$	−29.6299			−1.11435
$708$		0			0
$709$	2.38593			0.0896056			0.0448028	−	0.998996i	$-0.485734\pi$
$709$	2.38593			0.0896056			0.0448028	+	0.998996i	$0.485734\pi$
$710$	−18.9764	−	0.719528i	−0.712171	−	0.0270034i
$711$		0			0
$712$	−3.13531	+	27.4572i	−0.117501	+	1.02900i
$713$	−9.85821			−0.369193
$714$		0			0
$715$			61.9931i			2.31841i
$716$	−2.60648	+	34.3214i	−0.0974086	+	1.28265i
$717$		0			0
$718$	−1.66237	+	43.8423i	−0.0620390	+	1.63618i
$719$			29.3055i			1.09291i	0.837489	+	0.546455i	$0.184023\pi$
$719$			29.3055i			1.09291i	−0.837489	+	0.546455i	$0.815977\pi$
$720$		0			0
$721$		−	9.15067i		−	0.340789i
$722$	1.51333	−	39.9117i	0.0563204	−	1.48536i
$723$		0			0
$724$	−3.51548	−	0.266977i	−0.130652	−	0.00992213i
$725$	−16.8540			−0.625942
$726$		0			0
$727$	21.2949			0.789785			0.394892	−	0.918727i	$-0.370782\pi$
$727$	21.2949			0.789785			0.394892	+	0.918727i	$0.370782\pi$
$728$	−2.91933	+	25.5658i	−0.108198	+	0.947531i
$729$		0			0
$730$	3.02608	+	0.114740i	0.112000	+	0.00424671i
$731$	2.59313	+	24.0154i	0.0959103	+	0.888240i
$732$		0			0
$733$		−	34.3060i		−	1.26712i	−0.773693	−	0.633561i	$-0.781593\pi$
$733$		−	34.3060i		−	1.26712i	0.773693	−	0.633561i	$-0.218407\pi$
$734$	12.7231	+	0.482423i	0.469619	+	0.0178066i
$735$		0			0
$736$	41.9303	+	8.04204i	1.54557	+	0.296434i
$737$			58.7823i			2.16527i
$738$		0			0
$739$			35.2799i			1.29779i	0.760877	+	0.648896i	$0.224769\pi$
$739$			35.2799i			1.29779i	−0.760877	+	0.648896i	$0.775231\pi$
$740$	42.1196	+	3.19870i	1.54835	+	0.117587i
$741$		0			0
$742$	1.03485	−	27.2925i	0.0379906	−	1.00194i
$743$			19.0184i			0.697719i	0.937175	+	0.348859i	$0.113431\pi$
$743$			19.0184i			0.697719i	−0.937175	+	0.348859i	$0.886569\pi$
$744$		0			0
$745$		−	48.6620i		−	1.78284i
$746$	−33.5511	−	1.27216i	−1.22839	−	0.0465770i
$747$		0			0
$748$	−44.5122	+	1.41433i	−1.62753	+	0.0517131i
$749$			7.00474i			0.255948i
$750$		0			0
$751$			38.5164i			1.40548i	0.711446	+	0.702741i	$0.248041\pi$
$751$			38.5164i			1.40548i	−0.711446	+	0.702741i	$0.751959\pi$
$752$	31.7452	+	4.84964i	1.15763	+	0.176848i
$753$		0			0
$754$	16.9814	+	0.643883i	0.618425	+	0.0234488i
$755$	−3.50831			−0.127681
$756$		0			0
$757$		−	13.2396i		−	0.481200i	−0.970624	−	0.240600i	$-0.922656\pi$
$757$		−	13.2396i		−	0.481200i	0.970624	−	0.240600i	$-0.0773442\pi$
$758$	0.575660	−	15.1821i	0.0209089	−	0.551438i
$759$		0			0
$760$	−61.3019	−	7.00000i	−2.22365	−	0.253917i
$761$	−23.2876			−0.844173			−0.422087	−	0.906556i	$-0.638702\pi$
$761$	−23.2876			−0.844173			−0.422087	+	0.906556i	$0.638702\pi$
$762$		0			0
$763$		−	37.1063i		−	1.34334i
$764$	9.44929	+	0.717610i	0.341863	+	0.0259622i
$765$		0			0
$766$	−0.710944	+	18.7500i	−0.0256875	+	0.677465i
$767$	15.3098			0.552806
$768$		0			0
$769$	18.6064			0.670964			0.335482	−	0.942047i	$-0.391101\pi$
$769$	18.6064			0.670964			0.335482	+	0.942047i	$0.391101\pi$
$770$	−60.9296	−	2.31027i	−2.19575	−	0.0832563i
$771$		0			0
$772$	−3.17277	+	41.7782i	−0.114191	+	1.50363i
$773$		−	14.1210i		−	0.507898i	−0.967218	−	0.253949i	$-0.918270\pi$
$773$		−	14.1210i		−	0.507898i	0.967218	−	0.253949i	$-0.0817295\pi$
$774$		0			0
$775$		−	6.62608i		−	0.238016i
$776$	−2.68314	−	0.306385i	−0.0963190	−	0.0109986i
$777$		0			0
$778$	−46.0496	−	1.74606i	−1.65096	−	0.0625994i
$779$	34.6555			1.24166
$780$		0			0
$781$			22.8495i			0.817620i
$782$	43.9018	−	3.06325i	1.56992	−	0.109542i
$783$		0			0
$784$	2.66047	+	0.406433i	0.0950168	+	0.0145155i
$785$			55.8599i			1.99372i
$786$		0			0
$787$	36.6396			1.30606			0.653030	−	0.757332i	$-0.273497\pi$
$787$	36.6396			1.30606			0.653030	+	0.757332i	$0.273497\pi$
$788$	16.6554	+	1.26487i	0.593326	+	0.0450591i
$789$		0			0
$790$	−6.43966	−	0.244173i	−0.229113	−	0.00868727i
$791$	−19.0454			−0.677177
$792$		0			0
$793$		−	14.0397i		−	0.498563i
$794$	0.710091	−	18.7275i	0.0252002	−	0.664614i
$795$		0			0
$796$	1.86753	−	24.5912i	0.0661930	−	0.871611i
$797$		−	38.0109i		−	1.34642i	−0.739453	−	0.673208i	$-0.764916\pi$
$797$		−	38.0109i		−	1.34642i	0.739453	−	0.673208i	$-0.235084\pi$
$798$		0			0
$799$	32.9106	−	3.55361i	1.16429	−	0.125718i
$800$	−5.40536	+	28.1829i	−0.191108	+	0.996418i
$801$		0			0
$802$	−17.3578	−	0.658157i	−0.612926	−	0.0232403i
$803$		−	3.64370i		−	0.128584i
$804$		0			0
$805$	60.2531			2.12364
$806$	−0.253140	+	6.67615i	−0.00891647	+	0.235157i
$807$		0			0
$808$	33.1022	+	3.77991i	1.16453	+	0.132977i
$809$		−	1.43730i		−	0.0505328i	−0.999681	−	0.0252664i	$-0.991957\pi$
$809$		−	1.43730i		−	0.0505328i	0.999681	−	0.0252664i	$-0.00804340\pi$
$810$		0			0
$811$	32.8607			1.15390			0.576948	−	0.816781i	$-0.304244\pi$
$811$	32.8607			1.15390			0.576948	+	0.816781i	$0.304244\pi$
$812$	−1.26567	+	16.6661i	−0.0444165	+	0.584864i
$813$		0			0
$814$	1.92578	−	50.7894i	0.0674986	−	1.78017i
$815$	−1.09783			−0.0384551
$816$		0			0
$817$	40.2667			1.40875
$818$	0.903235	−	23.8214i	0.0315809	−	0.832895i
$819$		0			0
$820$	2.42357	−	31.9129i	0.0846346	−	1.11445i
$821$	−20.4356			−0.713207			−0.356604	−	0.934256i	$-0.616065\pi$
$821$	−20.4356			−0.713207			−0.356604	+	0.934256i	$0.616065\pi$
$822$		0			0
$823$			35.9374i			1.25270i	0.779543	+	0.626349i	$0.215451\pi$
$823$			35.9374i			1.25270i	−0.779543	+	0.626349i	$0.784549\pi$
$824$	−1.16736	+	10.2230i	−0.0406669	+	0.356136i
$825$		0			0
$826$	−0.570545	+	15.0472i	−0.0198518	+	0.523559i
$827$	−54.9541			−1.91094			−0.955470	−	0.295089i	$-0.904651\pi$
$827$	−54.9541			−1.91094			−0.955470	+	0.295089i	$0.904651\pi$
$828$		0			0
$829$		−	15.4841i		−	0.537785i	−0.963170	−	0.268893i	$-0.913342\pi$
$829$		−	15.4841i		−	0.537785i	0.963170	−	0.268893i	$-0.0866577\pi$
$830$	72.4329	+	2.74644i	2.51418	+	0.0953303i
$831$		0			0
$832$	6.52290	−	28.1894i	0.226141	−	0.977292i
$833$	2.75813	−	0.297817i	0.0955636	−	0.0103188i
$834$		0			0
$835$		−	65.9976i		−	2.28394i
$836$	−5.62184	+	74.0269i	−0.194435	+	2.56027i
$837$		0			0
$838$	0.395837	−	10.4395i	0.0136739	−	0.360628i
$839$		−	23.2368i		−	0.802224i	−0.916029	−	0.401112i	$-0.868624\pi$
$839$		−	23.2368i		−	0.802224i	0.916029	−	0.401112i	$-0.131376\pi$
$840$		0			0
$841$	−17.9619			−0.619376
$842$	29.2497	+	1.10906i	1.00801	+	0.0382208i
$843$		0			0
$844$	31.9816	+	2.42878i	1.10085	+	0.0836022i
$845$	−0.257470			−0.00885723
$846$		0			0
$847$			45.6962i			1.57014i
$848$	−4.63786	+	30.3589i	−0.159265	+	1.04253i
$849$		0			0
$850$	2.05893	+	29.5081i	0.0706207	+	1.01212i
$851$			50.2254i			1.72171i
$852$		0			0
$853$	−34.7441			−1.18962			−0.594808	−	0.803868i	$-0.702772\pi$
$853$	−34.7441			−1.18962			−0.594808	+	0.803868i	$0.702772\pi$
$854$	13.7988	+	0.523210i	0.472186	+	0.0179039i
$855$		0			0
$856$	0.893601	−	7.82563i	0.0305427	−	0.267474i
$857$		−	40.0894i		−	1.36943i	−0.728811	−	0.684715i	$-0.759927\pi$
$857$		−	40.0894i		−	1.36943i	0.728811	−	0.684715i	$-0.240073\pi$
$858$		0			0
$859$			18.2273i			0.621906i	0.950425	+	0.310953i	$0.100648\pi$
$859$			18.2273i			0.621906i	−0.950425	+	0.310953i	$0.899352\pi$
$860$	2.81598	−	37.0800i	0.0960240	−	1.26442i
$861$		0			0
$862$	18.6333	+	0.706517i	0.634651	+	0.0240641i
$863$	−36.4069			−1.23930			−0.619652	−	0.784877i	$-0.712726\pi$
$863$	−36.4069			−1.23930			−0.619652	+	0.784877i	$0.712726\pi$
$864$		0			0
$865$	−26.2972			−0.894131
$866$	−0.789973	+	20.8342i	−0.0268444	+	0.707977i
$867$		0			0
$868$	−6.55219	−	0.497595i	−0.222396	−	0.0168895i
$869$			7.75401i			0.263037i
$870$		0			0
$871$	−39.3664			−1.33388
$872$	−4.73368	+	41.4548i	−0.160303	+	1.40384i
$873$		0			0
$874$	2.77971	−	73.3103i	0.0940250	−	2.47976i
$875$			0.581938i			0.0196731i
$876$		0			0
$877$	−34.0214			−1.14882			−0.574410	−	0.818568i	$-0.694768\pi$
$877$	−34.0214			−1.14882			−0.574410	+	0.818568i	$0.694768\pi$
$878$	8.70276	+	0.329983i	0.293704	+	0.0111364i
$879$		0			0
$880$	67.7753	+	10.3539i	2.28470	+	0.349029i
$881$			56.8188i			1.91427i	0.289637	+	0.957137i	$0.406466\pi$
$881$			56.8188i			1.91427i	−0.289637	+	0.957137i	$0.593534\pi$
$882$		0			0
$883$		−	25.0090i		−	0.841619i	−0.907149	−	0.420810i	$-0.861746\pi$
$883$		−	25.0090i		−	0.841619i	0.907149	−	0.420810i	$-0.138254\pi$
$884$	−0.947176	−	29.8097i	−0.0318570	−	1.00261i
$885$		0			0
$886$	3.74326	+	0.141933i	0.125757	+	0.00476835i
$887$		−	20.9573i		−	0.703679i	−0.936060	−	0.351839i	$-0.885556\pi$
$887$		−	20.9573i		−	0.703679i	0.936060	−	0.351839i	$-0.114444\pi$
$888$		0			0
$889$		−	22.1482i		−	0.742825i
$890$	1.66165	−	43.8233i	0.0556986	−	1.46896i
$891$		0			0
$892$	−19.9634	−	1.51609i	−0.668424	−	0.0507623i
$893$		−	55.1814i		−	1.84657i
$894$		0			0
$895$		−	54.6211i		−	1.82578i
$896$	27.4628	+	7.46153i	0.917466	+	0.249272i
$897$		0			0
$898$	46.9245	+	1.77924i	1.56589	+	0.0593740i
$899$			4.33958i			0.144733i
$900$		0			0
$901$	3.39843	+	31.4734i	0.113218	+	1.04853i
$902$	−38.4817	−	1.45911i	−1.28130	−	0.0485831i
$903$		0			0
$904$	21.2774	+	2.42964i	0.707675	+	0.0808087i
$905$	5.59475			0.185976
$906$		0			0
$907$	27.8495			0.924727			0.462363	−	0.886691i	$-0.347002\pi$
$907$	27.8495			0.924727			0.462363	+	0.886691i	$0.347002\pi$
$908$	28.0125	+	2.12736i	0.929628	+	0.0705989i
$909$		0			0
$910$	1.54718	−	40.8044i	0.0512886	−	1.35265i
$911$		−	21.9920i		−	0.728626i	−0.931276	−	0.364313i	$-0.881304\pi$
$911$		−	21.9920i		−	0.728626i	0.931276	−	0.364313i	$-0.118696\pi$
$912$		0			0
$913$		−	87.2166i		−	2.88645i
$914$	1.13768	−	30.0044i	0.0376310	−	0.992458i
$915$		0			0
$916$	0.508674	−	6.69808i	0.0168070	−	0.221311i
$917$		−	52.8452i		−	1.74510i
$918$		0			0
$919$	11.9263			0.393412			0.196706	−	0.980462i	$-0.436975\pi$
$919$	11.9263			0.393412			0.196706	+	0.980462i	$0.436975\pi$
$920$	−67.3141	−	7.68654i	−2.21928	−	0.253418i
$921$		0			0
$922$	49.5802	+	1.87993i	1.63284	+	0.0619123i
$923$	−15.3023			−0.503680
$924$		0			0
$925$	−33.7584			−1.10997
$926$	1.20363	−	31.7439i	0.0395539	−	1.04317i
$927$		0			0
$928$	3.54011	−	18.4577i	0.116210	−	0.605904i
$929$		−	33.2071i		−	1.08949i	−0.838602	−	0.544744i	$-0.816627\pi$
$929$		−	33.2071i		−	1.08949i	0.838602	−	0.544744i	$-0.183373\pi$
$930$		0			0
$931$		−	4.62458i		−	0.151565i
$932$	−2.28920	+	30.1436i	−0.0749854	+	0.987387i
$933$		0			0
$934$	−20.3018	−	0.769783i	−0.664295	−	0.0251881i
$935$	70.2632	−	7.58687i	2.29785	−	0.248117i
$936$		0			0
$937$	30.7131			1.00335			0.501677	−	0.865055i	$-0.332717\pi$
$937$	30.7131			1.00335			0.501677	+	0.865055i	$0.332717\pi$
$938$	1.46705	−	38.6911i	0.0479009	−	1.26331i
$939$		0			0
$940$	−50.8144	−	3.85901i	−1.65738	−	0.125867i
$941$	−11.5870			−0.377724			−0.188862	−	0.982004i	$-0.560480\pi$
$941$	−11.5870			−0.377724			−0.188862	+	0.982004i	$0.560480\pi$
$942$		0			0
$943$	38.0544			1.23922
$944$	2.55699	−	16.7378i	0.0832231	−	0.544769i
$945$		0			0
$946$	−44.7124	−	1.69536i	−1.45373	−	0.0551210i
$947$	27.4089			0.890669			0.445334	−	0.895364i	$-0.353085\pi$
$947$	27.4089			0.890669			0.445334	+	0.895364i	$0.353085\pi$
$948$		0			0
$949$	2.44018			0.0792116
$950$	49.2746	+	1.86835i	1.59868	+	0.0606172i
$951$		0			0
$952$	29.3336	+	0.179978i	0.950709	+	0.00583313i
$953$	33.5870			1.08799			0.543994	−	0.839089i	$-0.316911\pi$
$953$	33.5870			1.08799			0.543994	+	0.839089i	$0.316911\pi$
$954$		0			0
$955$	−15.0382			−0.486624
$956$	22.5402	+	1.71177i	0.729002	+	0.0553627i
$957$		0			0
$958$	−9.91525	−	0.375957i	−0.320347	−	0.0121466i
$959$			40.1286i			1.29582i
$960$		0			0
$961$	29.2939			0.944965
$962$	34.0135	+	1.28969i	1.09664	+	0.0415813i
$963$		0			0
$964$	−3.61761	+	47.6357i	−0.116515	+	1.53424i
$965$		−	66.4884i		−	2.14034i
$966$		0			0
$967$	37.3601			1.20142			0.600710	−	0.799467i	$-0.294885\pi$
$967$	37.3601			1.20142			0.600710	+	0.799467i	$0.294885\pi$
$968$	5.82951	−	51.0514i	0.187368	−	1.64085i
$969$		0			0
$970$	4.28244	+	0.162377i	0.137501	+	0.00521362i
$971$		−	7.46186i		−	0.239463i	−0.992806	−	0.119731i	$-0.961797\pi$
$971$		−	7.46186i		−	0.239463i	0.992806	−	0.119731i	$-0.0382033\pi$
$972$		0			0
$973$			16.6349i			0.533290i
$974$	34.7320	+	1.31693i	1.11288	+	0.0421972i
$975$		0			0
$976$	−15.3492	−	2.34485i	−0.491315	−	0.0750569i
$977$	31.4037			1.00469			0.502346	−	0.864666i	$-0.332470\pi$
$977$	31.4037			1.00469			0.502346	+	0.864666i	$0.332470\pi$
$978$		0			0
$979$	−52.7677			−1.68646
$980$	−4.25859	−	0.323411i	−0.136036	−	0.0103310i
$981$		0			0
$982$	10.7538	+	0.407753i	0.343168	+	0.0130119i
$983$		−	2.30014i		−	0.0733630i	−0.999327	−	0.0366815i	$-0.988321\pi$
$983$		−	2.30014i		−	0.0733630i	0.999327	−	0.0366815i	$-0.0116787\pi$
$984$		0			0
$985$	−26.5065			−0.844567
$986$	−1.34844	−	19.3256i	−0.0429432	−	0.615451i
$987$		0			0
$988$	−49.5756	−	3.76493i	−1.57721	−	0.119779i
$989$	44.2160			1.40599
$990$		0			0
$991$		−	18.2755i		−	0.580539i	−0.956945	−	0.290269i	$-0.906255\pi$
$991$		−	18.2755i		−	0.580539i	0.956945	−	0.290269i	$-0.0937450\pi$
$992$	7.25657	+	1.39178i	0.230396	+	0.0441890i
$993$		0			0
$994$	0.570263	−	15.0398i	0.0180877	−	0.477032i
$995$			39.1359i			1.24069i
$996$		0			0
$997$	6.78517			0.214888			0.107444	−	0.994211i	$-0.465733\pi$
$997$	6.78517			0.214888			0.107444	+	0.994211i	$0.465733\pi$
$998$	0.870378	−	22.9548i	0.0275513	−	0.726622i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1224.2.l.d.1189.10		18
3.2	odd	2		408.2.l.b.373.9	yes	18
4.3	odd	2		4896.2.l.d.3025.15		18
8.3	odd	2		4896.2.l.c.3025.3		18
8.5	even	2		1224.2.l.c.1189.9		18
12.11	even	2		1632.2.l.a.1393.3		18
17.16	even	2		1224.2.l.c.1189.10		18
24.5	odd	2		408.2.l.a.373.10	yes	18
24.11	even	2		1632.2.l.b.1393.15		18
51.50	odd	2		408.2.l.a.373.9	✓	18
68.67	odd	2		4896.2.l.c.3025.4		18
136.67	odd	2		4896.2.l.d.3025.16		18
136.101	even	2	inner	1224.2.l.d.1189.9		18
204.203	even	2		1632.2.l.b.1393.16		18
408.101	odd	2		408.2.l.b.373.10	yes	18
408.203	even	2		1632.2.l.a.1393.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
408.2.l.a.373.9	✓	18	51.50	odd	2
408.2.l.a.373.10	yes	18	24.5	odd	2
408.2.l.b.373.9	yes	18	3.2	odd	2
408.2.l.b.373.10	yes	18	408.101	odd	2
1224.2.l.c.1189.9		18	8.5	even	2
1224.2.l.c.1189.10		18	17.16	even	2
1224.2.l.d.1189.9		18	136.101	even	2	inner
1224.2.l.d.1189.10		18	1.1	even	1	trivial
1632.2.l.a.1393.3		18	12.11	even	2
1632.2.l.a.1393.4		18	408.203	even	2
1632.2.l.b.1393.15		18	24.11	even	2
1632.2.l.b.1393.16		18	204.203	even	2
4896.2.l.c.3025.3		18	8.3	odd	2
4896.2.l.c.3025.4		18	68.67	odd	2
4896.2.l.d.3025.15		18	4.3	odd	2
4896.2.l.d.3025.16		18	136.67	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1224.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0535843 + 1.41320i) q^{2} +(-1.99426 - 0.151450i) q^{4} +3.17378 q^{5} +2.51539i q^{7} +(0.320890 - 2.81017i) q^{8} +(-0.170065 + 4.48518i) q^{10} +5.40062 q^{11} +3.61678i q^{13} +(-3.55474 - 0.134785i) q^{14} +(3.95413 + 0.604062i) q^{16} +(4.09928 - 0.442631i) q^{17} -6.87329i q^{19} +(-6.32934 - 0.480670i) q^{20} +(-0.289388 + 7.63215i) q^{22} -7.54740i q^{23} +5.07289 q^{25} +(-5.11123 - 0.193803i) q^{26} +(0.380956 - 5.01633i) q^{28} -3.32236 q^{29} -1.30617i q^{31} +(-1.06554 + 5.55559i) q^{32} +(0.405869 + 5.81681i) q^{34} +7.98329i q^{35} -6.65467 q^{37} +(9.71332 + 0.368300i) q^{38} +(1.01844 - 8.91885i) q^{40} +5.04206i q^{41} +5.85844i q^{43} +(-10.7702 - 0.817926i) q^{44} +(10.6660 + 0.404422i) q^{46} +8.02838 q^{47} +0.672834 q^{49} +(-0.271827 + 7.16900i) q^{50} +(0.547763 - 7.21280i) q^{52} +7.67778i q^{53} +17.1404 q^{55} +(7.06865 + 0.807163i) q^{56} +(0.178026 - 4.69516i) q^{58} -4.23300i q^{59} -3.88181 q^{61} +(1.84588 + 0.0699903i) q^{62} +(-7.79406 - 1.80351i) q^{64} +11.4789i q^{65} +10.8844i q^{67} +(-8.24205 + 0.261884i) q^{68} +(-11.2820 - 0.427779i) q^{70} +4.23091i q^{71} -0.674683i q^{73} +(0.356585 - 9.40436i) q^{74} +(-1.04096 + 13.7071i) q^{76} +13.5846i q^{77} +1.43576i q^{79} +(12.5495 + 1.91716i) q^{80} +(-7.12542 - 0.270175i) q^{82} -16.1494i q^{83} +(13.0102 - 1.40482i) q^{85} +(-8.27913 - 0.313920i) q^{86} +(1.73301 - 15.1766i) q^{88} -9.77068 q^{89} -9.09761 q^{91} +(-1.14306 + 15.0515i) q^{92} +(-0.430195 + 11.3457i) q^{94} -21.8143i q^{95} -0.954796i q^{97} +(-0.0360533 + 0.950847i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{4} + 4 q^{5} - 8 q^{10} + 6 q^{14} + 10 q^{16} + 2 q^{17} + 2 q^{20} + 2 q^{22} + 22 q^{25} - 2 q^{26} - 10 q^{28} - 12 q^{29} + 6 q^{34} - 16 q^{37} + 34 q^{38} - 10 q^{40} - 12 q^{44} + 32 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) \) 18 * q + 2 * q^4 + 4 * q^5 - 8 * q^10 + 6 * q^14 + 10 * q^16 + 2 * q^17 + 2 * q^20 + 2 * q^22 + 22 * q^25 - 2 * q^26 - 10 * q^28 - 12 * q^29 + 6 * q^34 - 16 * q^37 + 34 * q^38 - 10 * q^40 - 12 * q^44 + 32 * q^46 - 18 * q^49 + 14 * q^50 + 8 * q^52 - 16 * q^55 + 14 * q^56 - 6 * q^58 - 16 * q^61 + 6 * q^62 + 2 * q^64 + 36 * q^68 - 32 * q^70 + 6 * q^74 + 62 * q^80 + 34 * q^82 + 16 * q^85 - 14 * q^86 + 16 * q^88 - 20 * q^89 + 2 * q^92 + 12 * q^94 + 60 * q^98

Introduction

L-functions

Modular forms

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