LMFDB - Embedded newform 1368.2.e.g.379.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1368,2,Mod(379,1368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1368, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("1368.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1368 = 2^{3} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1368.e (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:	$10.9235349965$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.22
Character	$\chi$	$=$	1368.379
Dual form			1368.2.e.g.379.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.134537 + 1.40780i) q^{2} +(-1.96380 + 0.378802i) q^{4} +2.61555i q^{5} +4.81248i q^{7} +(-0.797481 - 2.71367i) q^{8} +O(q^{10})$	\(q+(0.134537 + 1.40780i) q^{2} +(-1.96380 + 0.378802i) q^{4} +2.61555i q^{5} +4.81248i q^{7} +(-0.797481 - 2.71367i) q^{8} +(-3.68217 + 0.351888i) q^{10} -3.49434 q^{11} -1.50149 q^{13} +(-6.77501 + 0.647456i) q^{14} +(3.71302 - 1.48778i) q^{16} -5.31012 q^{17} +(3.83470 + 2.07245i) q^{19} +(-0.990775 - 5.13641i) q^{20} +(-0.470118 - 4.91934i) q^{22} -2.26423i q^{23} -1.84109 q^{25} +(-0.202006 - 2.11379i) q^{26} +(-1.82298 - 9.45075i) q^{28} +5.12817 q^{29} -1.72573 q^{31} +(2.59404 + 5.02702i) q^{32} +(-0.714407 - 7.47558i) q^{34} -12.5873 q^{35} +10.2996 q^{37} +(-2.40168 + 5.67732i) q^{38} +(7.09774 - 2.08585i) q^{40} -3.90666i q^{41} +0.342152 q^{43} +(6.86219 - 1.32366i) q^{44} +(3.18759 - 0.304623i) q^{46} -0.679062i q^{47} -16.1600 q^{49} +(-0.247695 - 2.59189i) q^{50} +(2.94862 - 0.568767i) q^{52} -10.0708 q^{53} -9.13962i q^{55} +(13.0595 - 3.83786i) q^{56} +(0.689928 + 7.21944i) q^{58} +9.15071i q^{59} +2.65473i q^{61} +(-0.232175 - 2.42948i) q^{62} +(-6.72805 + 4.32821i) q^{64} -3.92721i q^{65} +7.37340i q^{67} +(10.4280 - 2.01148i) q^{68} +(-1.69345 - 17.7204i) q^{70} +9.74773 q^{71} -7.16085 q^{73} +(1.38568 + 14.4998i) q^{74} +(-8.31564 - 2.61728i) q^{76} -16.8165i q^{77} +5.21007 q^{79} +(3.89137 + 9.71158i) q^{80} +(5.49980 - 0.525590i) q^{82} +4.80051 q^{83} -13.8889i q^{85} +(0.0460321 + 0.481681i) q^{86} +(2.78667 + 9.48251i) q^{88} -14.0944i q^{89} -7.22588i q^{91} +(0.857696 + 4.44650i) q^{92} +(0.955984 - 0.0913590i) q^{94} +(-5.42059 + 10.0299i) q^{95} -13.2574i q^{97} +(-2.17411 - 22.7500i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4}+O(q^{10}) $ 40 * q - 4 * q^4	$ 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) $ 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times$.

$n$	$343$	$685$	$1009$	$1217$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	0.134537	+	1.40780i	0.0951320	+	0.995465i
$2$	0.134537	+	1.40780i	0.0951320	+	0.995465i
$3$		0			0
$3$		0			0
$4$	−1.96380	+	0.378802i	−0.981900	+	0.189401i
$5$			2.61555i			1.16971i	0.811138	+	0.584854i	$0.198848\pi$
$5$			2.61555i			1.16971i	−0.811138	+	0.584854i	$0.801152\pi$
$6$		0			0
$7$			4.81248i			1.81895i	0.415763	+	0.909473i	$0.363515\pi$
$7$			4.81248i			1.81895i	−0.415763	+	0.909473i	$0.636485\pi$
$8$	−0.797481	−	2.71367i	−0.281952	−	0.959428i
$9$		0			0
$10$	−3.68217	+	0.351888i	−1.16440	+	0.111277i
$11$	−3.49434			−1.05358			−0.526792	−	0.849994i	$-0.676605\pi$
$11$	−3.49434			−1.05358			−0.526792	+	0.849994i	$0.676605\pi$
$12$		0			0
$13$	−1.50149			−0.416438			−0.208219	−	0.978082i	$-0.566767\pi$
$13$	−1.50149			−0.416438			−0.208219	+	0.978082i	$0.566767\pi$
$14$	−6.77501	+	0.647456i	−1.81070	+	0.173040i
$15$		0			0
$16$	3.71302	−	1.48778i	0.928254	−	0.371946i
$17$	−5.31012			−1.28789			−0.643947	−	0.765071i	$-0.722704\pi$
$17$	−5.31012			−1.28789			−0.643947	+	0.765071i	$0.722704\pi$
$18$		0			0
$19$	3.83470	+	2.07245i	0.879742	+	0.475452i
$19$	3.83470	+	2.07245i	0.879742	+	0.475452i
$20$	−0.990775	−	5.13641i	−0.221544	−	1.14854i
$21$		0			0
$22$	−0.470118	−	4.91934i	−0.100230	−	1.04881i
$23$		−	2.26423i		−	0.472125i	−0.971738	−	0.236063i	$-0.924143\pi$
$23$		−	2.26423i		−	0.472125i	0.971738	−	0.236063i	$-0.0758570\pi$
$24$		0			0
$25$	−1.84109			−0.368219
$26$	−0.202006	−	2.11379i	−0.0396165	−	0.414549i
$27$		0			0
$28$	−1.82298	−	9.45075i	−0.344510	−	1.78602i
$29$	5.12817			0.952277			0.476139	−	0.879370i	$-0.342036\pi$
$29$	5.12817			0.952277			0.476139	+	0.879370i	$0.342036\pi$
$30$		0			0
$31$	−1.72573			−0.309950			−0.154975	−	0.987918i	$-0.549530\pi$
$31$	−1.72573			−0.309950			−0.154975	+	0.987918i	$0.549530\pi$
$32$	2.59404	+	5.02702i	0.458566	+	0.888661i
$33$		0			0
$34$	−0.714407	−	7.47558i	−0.122520	−	1.28205i
$35$	−12.5873			−2.12764
$36$		0			0
$37$	10.2996			1.69324			0.846622	−	0.532195i	$-0.178633\pi$
$37$	10.2996			1.69324			0.846622	+	0.532195i	$0.178633\pi$
$38$	−2.40168	+	5.67732i	−0.389604	+	0.920982i
$39$		0			0
$40$	7.09774	−	2.08585i	1.12225	−	0.329802i
$41$		−	3.90666i		−	0.610118i	−0.952333	−	0.305059i	$-0.901324\pi$
$41$		−	3.90666i		−	0.610118i	0.952333	−	0.305059i	$-0.0986762\pi$
$42$		0			0
$43$	0.342152			0.0521777			0.0260888	−	0.999660i	$-0.491695\pi$
$43$	0.342152			0.0521777			0.0260888	+	0.999660i	$0.491695\pi$
$44$	6.86219	−	1.32366i	1.03451	−	0.199550i
$45$		0			0
$46$	3.18759	−	0.304623i	0.469984	−	0.0449142i
$47$		−	0.679062i		−	0.0990514i	−0.998773	−	0.0495257i	$-0.984229\pi$
$47$		−	0.679062i		−	0.0990514i	0.998773	−	0.0495257i	$-0.0157710\pi$
$48$		0			0
$49$	−16.1600			−2.30857
$50$	−0.247695	−	2.59189i	−0.0350294	−	0.366549i
$51$		0			0
$52$	2.94862	−	0.568767i	0.408900	−	0.0788737i
$53$	−10.0708			−1.38333			−0.691667	−	0.722216i	$-0.743124\pi$
$53$	−10.0708			−1.38333			−0.691667	+	0.722216i	$0.743124\pi$
$54$		0			0
$55$		−	9.13962i		−	1.23239i
$56$	13.0595	−	3.83786i	1.74515	−	0.512856i
$57$		0			0
$58$	0.689928	+	7.21944i	0.0905920	+	0.947958i
$59$			9.15071i			1.19132i	0.803236	+	0.595660i	$0.203110\pi$
$59$			9.15071i			1.19132i	−0.803236	+	0.595660i	$0.796890\pi$
$60$		0			0
$61$			2.65473i			0.339904i	0.985452	+	0.169952i	$0.0543613\pi$
$61$			2.65473i			0.339904i	−0.985452	+	0.169952i	$0.945639\pi$
$62$	−0.232175	−	2.42948i	−0.0294862	−	0.308545i
$63$		0			0
$64$	−6.72805	+	4.32821i	−0.841006	+	0.541026i
$65$		−	3.92721i		−	0.487111i
$66$		0			0
$67$			7.37340i			0.900804i	0.892826	+	0.450402i	$0.148719\pi$
$67$			7.37340i			0.900804i	−0.892826	+	0.450402i	$0.851281\pi$
$68$	10.4280	−	2.01148i	1.26458	−	0.243928i
$69$		0			0
$70$	−1.69345	−	17.7204i	−0.202406	−	2.11799i
$71$	9.74773			1.15684			0.578421	−	0.815738i	$-0.303669\pi$
$71$	9.74773			1.15684			0.578421	+	0.815738i	$0.303669\pi$
$72$		0			0
$73$	−7.16085			−0.838114			−0.419057	−	0.907960i	$-0.637639\pi$
$73$	−7.16085			−0.838114			−0.419057	+	0.907960i	$0.637639\pi$
$74$	1.38568	+	14.4998i	0.161082	+	1.68556i
$75$		0			0
$76$	−8.31564	−	2.61728i	−0.953869	−	0.300222i
$77$		−	16.8165i		−	1.91641i
$78$		0			0
$79$	5.21007			0.586178			0.293089	−	0.956085i	$-0.405317\pi$
$79$	5.21007			0.586178			0.293089	+	0.956085i	$0.405317\pi$
$80$	3.89137	+	9.71158i	0.435068	+	1.08579i
$81$		0			0
$82$	5.49980	−	0.525590i	0.607351	−	0.0580417i
$83$	4.80051			0.526925			0.263462	−	0.964670i	$-0.415135\pi$
$83$	4.80051			0.526925			0.263462	+	0.964670i	$0.415135\pi$
$84$		0			0
$85$		−	13.8889i		−	1.50646i
$86$	0.0460321	+	0.481681i	0.00496377	+	0.0519410i
$87$		0			0
$88$	2.78667	+	9.48251i	0.297060	+	1.01084i
$89$		−	14.0944i		−	1.49400i	−0.664823	−	0.747001i	$-0.731493\pi$
$89$		−	14.0944i		−	1.49400i	0.664823	−	0.747001i	$-0.268507\pi$
$90$		0			0
$91$		−	7.22588i		−	0.757478i
$92$	0.857696	+	4.44650i	0.0894210	+	0.463579i
$93$		0			0
$94$	0.955984	−	0.0913590i	0.0986022	−	0.00942296i
$95$	−5.42059	+	10.0299i	−0.556141	+	1.02904i
$96$		0			0
$97$		−	13.2574i		−	1.34608i	−0.739604	−	0.673042i	$-0.764987\pi$
$97$		−	13.2574i		−	1.34608i	0.739604	−	0.673042i	$-0.235013\pi$
$98$	−2.17411	−	22.7500i	−0.219618	−	2.29810i
$99$		0			0
$100$	3.61554	−	0.697410i	0.361554	−	0.0697410i
$101$		−	0.101742i		−	0.0101237i	−0.999987	−	0.00506187i	$-0.998389\pi$
$101$		−	0.101742i		−	0.0101237i	0.999987	−	0.00506187i	$-0.00161125\pi$
$102$		0			0
$103$	−19.3937			−1.91092			−0.955460	−	0.295120i	$-0.904640\pi$
$103$	−19.3937			−1.91092			−0.955460	+	0.295120i	$0.904640\pi$
$104$	1.19741	+	4.07455i	0.117415	+	0.399542i
$105$		0			0
$106$	−1.35490	−	14.1777i	−0.131599	−	1.37706i
$107$		−	2.03827i		−	0.197047i	−0.995135	−	0.0985235i	$-0.968588\pi$
$107$		−	2.03827i		−	0.197047i	0.995135	−	0.0985235i	$-0.0314120\pi$
$108$		0			0
$109$	−18.0323			−1.72718			−0.863589	−	0.504197i	$-0.831788\pi$
$109$	−18.0323			−1.72718			−0.863589	+	0.504197i	$0.831788\pi$
$110$	12.8668	−	1.22962i	1.22680	−	0.117239i
$111$		0			0
$112$	7.15993	+	17.8688i	0.676549	+	1.68845i
$113$			5.54322i			0.521462i	0.965412	+	0.260731i	$0.0839635\pi$
$113$			5.54322i			0.521462i	−0.965412	+	0.260731i	$0.916036\pi$
$114$		0			0
$115$	5.92221			0.552249
$116$	−10.0707	+	1.94256i	−0.935041	+	0.180362i
$117$		0			0
$118$	−12.8824	+	1.23111i	−1.18592	+	0.113333i
$119$		−	25.5548i		−	2.34261i
$120$		0			0
$121$	1.21043			0.110039
$122$	−3.73733	+	0.357160i	−0.338362	+	0.0323357i
$123$		0			0
$124$	3.38899	−	0.653711i	0.304340	−	0.0587050i
$125$			8.26227i			0.739000i
$126$		0			0
$127$	12.4962			1.10886			0.554430	−	0.832231i	$-0.312936\pi$
$127$	12.4962			1.10886			0.554430	+	0.832231i	$0.312936\pi$
$128$	−6.99842	−	8.88944i	−0.618579	−	0.785723i
$129$		0			0
$130$	5.52873	−	0.528355i	0.484901	−	0.0463398i
$131$	−12.5819			−1.09928			−0.549642	−	0.835400i	$-0.685236\pi$
$131$	−12.5819			−1.09928			−0.549642	+	0.835400i	$0.685236\pi$
$132$		0			0
$133$	−9.97362	+	18.4544i	−0.864822	+	1.60020i
$134$	−10.3803	+	0.991994i	−0.896718	+	0.0856952i
$135$		0			0
$136$	4.23472	+	14.4099i	0.363124	+	1.23564i
$137$	1.32093			0.112855			0.0564273	−	0.998407i	$-0.482029\pi$
$137$	1.32093			0.112855			0.0564273	+	0.998407i	$0.482029\pi$
$138$		0			0
$139$	1.41682			0.120173			0.0600864	−	0.998193i	$-0.480862\pi$
$139$	1.41682			0.120173			0.0600864	+	0.998193i	$0.480862\pi$
$140$	24.7189	−	4.76809i	2.08913	−	0.402977i
$141$		0			0
$142$	1.31143	+	13.7229i	0.110053	+	1.15160i
$143$	5.24671			0.438752
$144$		0			0
$145$			13.4130i			1.11389i
$146$	−0.963399	−	10.0810i	−0.0797315	−	0.834313i
$147$		0			0
$148$	−20.2264	+	3.90151i	−1.66260	+	0.320702i
$149$			13.2785i			1.08782i	0.839144	+	0.543909i	$0.183057\pi$
$149$			13.2785i			1.08782i	−0.839144	+	0.543909i	$0.816943\pi$
$150$		0			0
$151$	16.2778			1.32467			0.662334	−	0.749208i	$-0.269566\pi$
$151$	16.2778			1.32467			0.662334	+	0.749208i	$0.269566\pi$
$152$	2.56584	−	12.0589i	0.208117	−	0.978104i
$153$		0			0
$154$	23.6742	−	2.26243i	1.90772	−	0.182312i
$155$		−	4.51373i		−	0.362552i
$156$		0			0
$157$		−	18.3793i		−	1.46683i	−0.679783	−	0.733413i	$-0.737926\pi$
$157$		−	18.3793i		−	1.46683i	0.679783	−	0.733413i	$-0.262074\pi$
$158$	0.700946	+	7.33473i	0.0557643	+	0.583520i
$159$		0			0
$160$	−13.1484	+	6.78483i	−1.03947	+	0.536388i
$161$	10.8966			0.858770
$162$		0			0
$163$	−12.3413			−0.966649			−0.483325	−	0.875441i	$-0.660571\pi$
$163$	−12.3413			−0.966649			−0.483325	+	0.875441i	$0.660571\pi$
$164$	1.47985	+	7.67190i	0.115557	+	0.599075i
$165$		0			0
$166$	0.645847	+	6.75816i	0.0501274	+	0.524535i
$167$	−20.7583			−1.60632			−0.803161	−	0.595762i	$-0.796850\pi$
$167$	−20.7583			−1.60632			−0.803161	+	0.595762i	$0.796850\pi$
$168$		0			0
$169$	−10.7455			−0.826580
$170$	19.5527	−	1.86857i	1.49963	−	0.143313i
$171$		0			0
$172$	−0.671918	+	0.129608i	−0.0512333	+	0.00988251i
$173$	−0.684931			−0.0520743			−0.0260372	−	0.999661i	$-0.508289\pi$
$173$	−0.684931			−0.0520743			−0.0260372	+	0.999661i	$0.508289\pi$
$174$		0			0
$175$		−	8.86022i		−	0.669770i
$176$	−12.9746	+	5.19882i	−0.977994	+	0.391876i
$177$		0			0
$178$	19.8421	−	1.89622i	1.48723	−	0.142127i
$179$			18.7464i			1.40117i	0.713568	+	0.700586i	$0.247078\pi$
$179$			18.7464i			1.40117i	−0.713568	+	0.700586i	$0.752922\pi$
$180$		0			0
$181$	11.8359			0.879758			0.439879	−	0.898057i	$-0.355021\pi$
$181$	11.8359			0.879758			0.439879	+	0.898057i	$0.355021\pi$
$182$	10.1726	−	0.972147i	0.754042	−	0.0720604i
$183$		0			0
$184$	−6.14439	+	1.80568i	−0.452970	+	0.133117i
$185$			26.9391i			1.98060i
$186$		0			0
$187$	18.5554			1.35690
$188$	0.257230	+	1.33354i	0.0187604	+	0.0972586i
$189$		0			0
$190$	−14.8493	−	6.28172i	−1.07728	−	0.455724i
$191$			17.4611i			1.26344i	0.775197	+	0.631720i	$0.217651\pi$
$191$			17.4611i			1.26344i	−0.775197	+	0.631720i	$0.782349\pi$
$192$		0			0
$193$		−	11.0743i		−	0.797149i	−0.917136	−	0.398574i	$-0.869505\pi$
$193$		−	11.0743i		−	0.797149i	0.917136	−	0.398574i	$-0.130495\pi$
$194$	18.6638	−	1.78361i	1.33998	−	0.128056i
$195$		0			0
$196$	31.7349	−	6.12143i	2.26678	−	0.437245i
$197$			20.2434i			1.44228i	0.692788	+	0.721141i	$0.256382\pi$
$197$			20.2434i			1.44228i	−0.692788	+	0.721141i	$0.743618\pi$
$198$		0			0
$199$			12.1969i			0.864613i	0.901727	+	0.432307i	$0.142300\pi$
$199$			12.1969i			0.864613i	−0.901727	+	0.432307i	$0.857700\pi$
$200$	1.46824	+	4.99613i	0.103820	+	0.353279i
$201$		0			0
$202$	0.143233	−	0.0136881i	0.0100778	−	0.000963092i
$203$			24.6792i			1.73214i
$204$		0			0
$205$	10.2181			0.713660
$206$	−2.60917	−	27.3025i	−0.181790	−	1.90225i
$207$		0			0
$208$	−5.57505	+	2.23389i	−0.386560	+	0.154892i
$209$	−13.3998	−	7.24185i	−0.926882	−	0.500929i
$210$		0			0
$211$			11.2304i			0.773136i	0.922261	+	0.386568i	$0.126339\pi$
$211$			11.2304i			0.773136i	−0.922261	+	0.386568i	$0.873661\pi$
$212$	19.7771	−	3.81485i	1.35830	−	0.262005i
$213$		0			0
$214$	2.86948	−	0.274223i	0.196153	−	0.0187455i
$215$			0.894915i			0.0610327i
$216$		0			0
$217$		−	8.30505i		−	0.563783i
$218$	−2.42601	−	25.3858i	−0.164310	−	1.71934i
$219$		0			0
$220$	3.46211	+	17.9484i	0.233415	+	1.21008i
$221$	7.97308			0.536327
$222$		0			0
$223$	5.86592			0.392811			0.196406	−	0.980523i	$-0.437073\pi$
$223$	5.86592			0.392811			0.196406	+	0.980523i	$0.437073\pi$
$224$	−24.1924	+	12.4838i	−1.61643	+	0.834106i
$225$		0			0
$226$	−7.80374	+	0.745767i	−0.519097	+	0.0496077i
$227$			13.7884i			0.915168i	0.889166	+	0.457584i	$0.151285\pi$
$227$			13.7884i			0.915168i	−0.889166	+	0.457584i	$0.848715\pi$
$228$		0			0
$229$			7.75918i			0.512741i	0.966579	+	0.256371i	$0.0825268\pi$
$229$			7.75918i			0.512741i	−0.966579	+	0.256371i	$0.917473\pi$
$230$	0.796756	+	8.33728i	0.0525365	+	0.549744i
$231$		0			0
$232$	−4.08962	−	13.9162i	−0.268497	−	0.913642i
$233$	−23.5694			−1.54408			−0.772041	−	0.635573i	$-0.780764\pi$
$233$	−23.5694			−1.54408			−0.772041	+	0.635573i	$0.780764\pi$
$234$		0			0
$235$	1.77612			0.115861
$236$	−3.46631	−	17.9702i	−0.225637	−	1.16976i
$237$		0			0
$238$	35.9761	−	3.43807i	2.33198	−	0.222857i
$239$			13.3670i			0.864640i	0.901720	+	0.432320i	$0.142305\pi$
$239$			13.3670i			0.864640i	−0.901720	+	0.432320i	$0.857695\pi$
$240$		0			0
$241$		−	19.9602i		−	1.28575i	−0.765972	−	0.642873i	$-0.777742\pi$
$241$		−	19.9602i		−	1.28575i	0.765972	−	0.642873i	$-0.222258\pi$
$242$	0.162848	+	1.70405i	0.0104683	+	0.109540i
$243$		0			0
$244$	−1.00562	−	5.21337i	−0.0643782	−	0.333752i
$245$		−	42.2672i		−	2.70035i
$246$		0			0
$247$	−5.75776	−	3.11175i	−0.366357	−	0.197996i
$248$	1.37624	+	4.68307i	0.0873912	+	0.297375i
$249$		0			0
$250$	−11.6316	+	1.11158i	−0.735649	+	0.0703026i
$251$	29.8620			1.88487			0.942435	−	0.334388i	$-0.108530\pi$
$251$	29.8620			1.88487			0.942435	+	0.334388i	$0.108530\pi$
$252$		0			0
$253$			7.91200i			0.497423i
$254$	1.68120	+	17.5922i	0.105488	+	1.10383i
$255$		0			0
$256$	11.5730	−	11.0483i	0.723313	−	0.690521i
$257$		−	0.677951i		−	0.0422894i	−0.999776	−	0.0211447i	$-0.993269\pi$
$257$		−	0.677951i		−	0.0422894i	0.999776	−	0.0211447i	$-0.00673108\pi$
$258$		0			0
$259$			49.5666i			3.07992i
$260$	1.48764	+	7.71226i	0.0922593	+	0.478294i
$261$		0			0
$262$	−1.69273	−	17.7128i	−0.104577	−	1.09430i
$263$		−	3.00903i		−	0.185545i	−0.995687	−	0.0927723i	$-0.970427\pi$
$263$		−	3.00903i		−	0.185545i	0.995687	−	0.0927723i	$-0.0295729\pi$
$264$		0			0
$265$		−	26.3407i		−	1.61810i
$266$	−27.3220	−	11.5580i	−1.67522	−	0.708669i
$267$		0			0
$268$	−2.79306	−	14.4799i	−0.170613	−	0.884499i
$269$	7.04041			0.429261			0.214631	−	0.976695i	$-0.431145\pi$
$269$	7.04041			0.429261			0.214631	+	0.976695i	$0.431145\pi$
$270$		0			0
$271$			22.8229i			1.38639i	0.720750	+	0.693195i	$0.243798\pi$
$271$			22.8229i			1.38639i	−0.720750	+	0.693195i	$0.756202\pi$
$272$	−19.7166	+	7.90031i	−1.19549	+	0.479026i
$273$		0			0
$274$	0.177714	+	1.85960i	0.0107361	+	0.112343i
$275$	6.43341			0.387949
$276$		0			0
$277$			20.9985i			1.26168i	0.775913	+	0.630840i	$0.217290\pi$
$277$			20.9985i			1.26168i	−0.775913	+	0.630840i	$0.782710\pi$
$278$	0.190614	+	1.99459i	0.0114323	+	0.119628i
$279$		0			0
$280$	10.0381	+	34.1577i	0.599892	+	2.04132i
$281$		−	5.03139i		−	0.300148i	−0.988675	−	0.150074i	$-0.952049\pi$
$281$		−	5.03139i		−	0.300148i	0.988675	−	0.150074i	$-0.0479511\pi$
$282$		0			0
$283$	−1.25113			−0.0743719			−0.0371860	−	0.999308i	$-0.511839\pi$
$283$	−1.25113			−0.0743719			−0.0371860	+	0.999308i	$0.511839\pi$
$284$	−19.1426	+	3.69246i	−1.13590	+	0.219107i
$285$		0			0
$286$	0.705877	+	7.38632i	0.0417394	+	0.436762i
$287$	18.8007			1.10977
$288$		0			0
$289$	11.1974			0.658668
$290$	−18.8828	+	1.80454i	−1.10884	+	0.105966i
$291$		0			0
$292$	14.0625	−	2.71255i	0.822944	−	0.158740i
$293$	18.5789			1.08539			0.542695	−	0.839930i	$-0.317404\pi$
$293$	18.5789			1.08539			0.542695	+	0.839930i	$0.317404\pi$
$294$		0			0
$295$	−23.9341			−1.39350
$296$	−8.21374	−	27.9498i	−0.477414	−	1.62455i
$297$		0			0
$298$	−18.6935	+	1.78645i	−1.08289	+	0.103486i
$299$			3.39972i			0.196611i
$300$		0			0
$301$			1.64660i			0.0949084i
$302$	2.18997	+	22.9159i	0.126018	+	1.31866i
$303$		0			0
$304$	17.3217	+	1.98983i	0.993466	+	0.114125i
$305$	−6.94359			−0.397589
$306$		0			0
$307$		−	10.7076i		−	0.611115i	−0.952174	−	0.305557i	$-0.901157\pi$
$307$		−	10.7076i		−	0.611115i	0.952174	−	0.305557i	$-0.0988428\pi$
$308$	6.37011	+	33.0241i	0.362971	+	1.88173i
$309$		0			0
$310$	6.35443	−	0.607264i	0.360907	−	0.0344903i
$311$			13.2171i			0.749472i	0.927132	+	0.374736i	$0.122267\pi$
$311$			13.2171i			0.749472i	−0.927132	+	0.374736i	$0.877733\pi$
$312$		0			0
$313$	−32.4175			−1.83235			−0.916174	−	0.400781i	$-0.868739\pi$
$313$	−32.4175			−1.83235			−0.916174	+	0.400781i	$0.868739\pi$
$314$	25.8743	−	2.47269i	1.46017	−	0.139542i
$315$		0			0
$316$	−10.2315	+	1.97358i	−0.575568	+	0.111023i
$317$	−14.4866			−0.813650			−0.406825	−	0.913506i	$-0.633364\pi$
$317$	−14.4866			−0.813650			−0.406825	+	0.913506i	$0.633364\pi$
$318$		0			0
$319$	−17.9196			−1.00330
$320$	−11.3206	−	17.5975i	−0.632843	−	0.983732i
$321$		0			0
$322$	1.46599	+	15.3402i	0.0816965	+	0.854875i
$323$	−20.3627	−	11.0049i	−1.13301	−	0.612332i
$324$		0			0
$325$	2.76438			0.153340
$326$	−1.66037	−	17.3741i	−0.0919593	−	0.962265i
$327$		0			0
$328$	−10.6014	+	3.11549i	−0.585364	+	0.172024i
$329$	3.26797			0.180169
$330$		0			0
$331$		−	5.22689i		−	0.287296i	−0.989629	−	0.143648i	$-0.954117\pi$
$331$		−	5.22689i		−	0.287296i	0.989629	−	0.143648i	$-0.0458832\pi$
$332$	−9.42725	+	1.81845i	−0.517387	+	0.0998001i
$333$		0			0
$334$	−2.79275	−	29.2235i	−0.152813	−	1.59904i
$335$	−19.2855			−1.05368
$336$		0			0
$337$			18.1981i			0.991312i	0.868519	+	0.495656i	$0.165072\pi$
$337$			18.1981i			0.991312i	−0.868519	+	0.495656i	$0.834928\pi$
$338$	−1.44567	−	15.1276i	−0.0786342	−	0.822831i
$339$		0			0
$340$	5.26114	+	27.2750i	0.285325	+	1.47919i
$341$	6.03030			0.326559
$342$		0			0
$343$		−	44.0821i		−	2.38021i
$344$	−0.272860	−	0.928489i	−0.0147116	−	0.0500608i
$345$		0			0
$346$	−0.0921485	−	0.964245i	−0.00495393	−	0.0518381i
$347$	16.9154			0.908066			0.454033	−	0.890985i	$-0.349985\pi$
$347$	16.9154			0.908066			0.454033	+	0.890985i	$0.349985\pi$
$348$		0			0
$349$		−	28.3766i		−	1.51896i	−0.650528	−	0.759482i	$-0.725453\pi$
$349$		−	28.3766i		−	1.51896i	0.650528	−	0.759482i	$-0.274547\pi$
$350$	12.4734	−	1.19203i	0.666732	−	0.0637165i
$351$		0			0
$352$	−9.06446	−	17.5661i	−0.483137	−	0.936279i
$353$	−2.43957			−0.129845			−0.0649227	−	0.997890i	$-0.520680\pi$
$353$	−2.43957			−0.129845			−0.0649227	+	0.997890i	$0.520680\pi$
$354$		0			0
$355$			25.4957i			1.35317i
$356$	5.33899	+	27.6786i	0.282966	+	1.46696i
$357$		0			0
$358$	−26.3912	+	2.52209i	−1.39482	+	0.133296i
$359$		−	24.6073i		−	1.29872i	−0.760479	−	0.649362i	$-0.775036\pi$
$359$		−	24.6073i		−	1.29872i	0.760479	−	0.649362i	$-0.224964\pi$
$360$		0			0
$361$	10.4099	+	15.8945i	0.547890	+	0.836550i
$362$	1.59237	+	16.6626i	0.0836931	+	0.875768i
$363$		0			0
$364$	2.73718	+	14.1902i	0.143467	+	0.743767i
$365$		−	18.7295i		−	0.980349i
$366$		0			0
$367$			18.9695i			0.990201i	0.868836	+	0.495100i	$0.164869\pi$
$367$			18.9695i			0.990201i	−0.868836	+	0.495100i	$0.835131\pi$
$368$	−3.36869	−	8.40713i	−0.175605	−	0.438252i
$369$		0			0
$370$	−37.9249	+	3.62431i	−1.97162	+	0.188419i
$371$		−	48.4657i		−	2.51621i
$372$		0			0
$373$	20.4231			1.05747			0.528734	−	0.848788i	$-0.322667\pi$
$373$	20.4231			1.05747			0.528734	+	0.848788i	$0.322667\pi$
$374$	2.49638	+	26.1223i	0.129085	+	1.35075i
$375$		0			0
$376$	−1.84275	+	0.541540i	−0.0950328	+	0.0279278i
$377$	−7.69988			−0.396564
$378$		0			0
$379$			26.0452i			1.33785i	0.743330	+	0.668925i	$0.233245\pi$
$379$			26.0452i			1.33785i	−0.743330	+	0.668925i	$0.766755\pi$
$380$	6.84562	−	21.7500i	0.351173	−	1.11575i
$381$		0			0
$382$	−24.5817	+	2.34916i	−1.25771	+	0.120194i
$383$	−23.1300			−1.18189			−0.590944	−	0.806712i	$-0.701245\pi$
$383$	−23.1300			−1.18189			−0.590944	+	0.806712i	$0.701245\pi$
$384$		0			0
$385$	43.9843			2.24165
$386$	15.5905	−	1.48991i	0.793534	−	0.0758344i
$387$		0			0
$388$	5.02193	+	26.0349i	0.254950	+	1.32172i
$389$			17.1821i			0.871166i	0.900148	+	0.435583i	$0.143458\pi$
$389$			17.1821i			0.871166i	−0.900148	+	0.435583i	$0.856542\pi$
$390$		0			0
$391$			12.0233i			0.608047i
$392$	12.8873	+	43.8529i	0.650905	+	2.21490i
$393$		0			0
$394$	−28.4986	+	2.72349i	−1.43574	+	0.137207i
$395$			13.6272i			0.685658i
$396$		0			0
$397$		−	28.3706i		−	1.42388i	−0.702242	−	0.711939i	$-0.747817\pi$
$397$		−	28.3706i		−	1.42388i	0.702242	−	0.711939i	$-0.252183\pi$
$398$	−17.1708	+	1.64093i	−0.860692	+	0.0822524i
$399$		0			0
$400$	−6.83601	+	2.73915i	−0.341801	+	0.136957i
$401$			6.28011i			0.313614i	0.987629	+	0.156807i	$0.0501200\pi$
$401$			6.28011i			0.313614i	−0.987629	+	0.156807i	$0.949880\pi$
$402$		0			0
$403$	2.59116			0.129075
$404$	0.0385402	+	0.199802i	0.00191745	+	0.00994050i
$405$		0			0
$406$	−34.7434	+	3.32027i	−1.72429	+	0.164782i
$407$	−35.9903			−1.78398
$408$		0			0
$409$			2.75238i			0.136097i	0.997682	+	0.0680483i	$0.0216772\pi$
$409$			2.75238i			0.136097i	−0.997682	+	0.0680483i	$0.978323\pi$
$410$	1.37471	+	14.3850i	0.0678919	+	0.710424i
$411$		0			0
$412$	38.0854	−	7.34638i	1.87633	−	0.361930i
$413$	−44.0376			−2.16695
$414$		0			0
$415$			12.5560i			0.616349i
$416$	−3.89492	−	7.54801i	−0.190964	−	0.370072i
$417$		0			0
$418$	8.39230	−	19.8385i	0.410481	−	0.970332i
$419$	33.3577			1.62963			0.814816	−	0.579719i	$-0.196838\pi$
$419$	33.3577			1.62963			0.814816	+	0.579719i	$0.196838\pi$
$420$		0			0
$421$	−0.929028			−0.0452781			−0.0226390	−	0.999744i	$-0.507207\pi$
$421$	−0.929028			−0.0452781			−0.0226390	+	0.999744i	$0.507207\pi$
$422$	−15.8102	+	1.51091i	−0.769629	+	0.0735499i
$423$		0			0
$424$	8.03130	+	27.3289i	0.390034	+	1.32721i
$425$	9.77642			0.474226
$426$		0			0
$427$	−12.7759			−0.618267
$428$	0.772101	+	4.00275i	0.0373209	+	0.193480i
$429$		0			0
$430$	−1.25986	+	0.120399i	−0.0607559	+	0.00580616i
$431$	34.4951			1.66157			0.830786	−	0.556592i	$-0.187891\pi$
$431$	34.4951			1.66157			0.830786	+	0.556592i	$0.187891\pi$
$432$		0			0
$433$		−	24.9055i		−	1.19688i	−0.801166	−	0.598442i	$-0.795787\pi$
$433$		−	24.9055i		−	1.19688i	0.801166	−	0.598442i	$-0.204213\pi$
$434$	11.6918	−	1.11734i	0.561226	−	0.0536338i
$435$		0			0
$436$	35.4117	−	6.83066i	1.69591	−	0.327129i
$437$	4.69250	−	8.68266i	0.224473	−	0.415348i
$438$		0			0
$439$	20.5120			0.978984			0.489492	−	0.872008i	$-0.337182\pi$
$439$	20.5120			0.978984			0.489492	+	0.872008i	$0.337182\pi$
$440$	−24.8020	+	7.28868i	−1.18239	+	0.347474i
$441$		0			0
$442$	1.07267	+	11.2245i	0.0510219	+	0.533895i
$443$	−25.9849			−1.23458			−0.617289	−	0.786736i	$-0.711769\pi$
$443$	−25.9849			−1.23458			−0.617289	+	0.786736i	$0.711769\pi$
$444$		0			0
$445$	36.8646			1.74755
$446$	0.789184	+	8.25805i	0.0373689	+	0.391030i
$447$		0			0
$448$	−20.8294	−	32.3786i	−0.984097	−	1.52974i
$449$		−	36.4806i		−	1.72163i	−0.508920	−	0.860814i	$-0.669955\pi$
$449$		−	36.4806i		−	1.72163i	0.508920	−	0.860814i	$-0.330045\pi$
$450$		0			0
$451$			13.6512i			0.642810i
$452$	−2.09978	−	10.8858i	−0.0987654	−	0.512023i
$453$		0			0
$454$	−19.4113	+	1.85505i	−0.911018	+	0.0870618i
$455$	18.8996			0.886028
$456$		0			0
$457$	23.2770			1.08885			0.544425	−	0.838809i	$-0.316748\pi$
$457$	23.2770			1.08885			0.544425	+	0.838809i	$0.316748\pi$
$458$	−10.9234	+	1.04390i	−0.510416	+	0.0487781i
$459$		0			0
$460$	−11.6300	+	2.24335i	−0.542253	+	0.104597i
$461$			14.2845i			0.665298i	0.943051	+	0.332649i	$0.107942\pi$
$461$			14.2845i			0.665298i	−0.943051	+	0.332649i	$0.892058\pi$
$462$		0			0
$463$			15.6276i			0.726275i	0.931736	+	0.363137i	$0.118294\pi$
$463$			15.6276i			0.726275i	−0.931736	+	0.363137i	$0.881706\pi$
$464$	19.0410	−	7.62961i	0.883956	−	0.354196i
$465$		0			0
$466$	−3.17095	−	33.1810i	−0.146892	−	1.53708i
$467$	8.66870			0.401140			0.200570	−	0.979679i	$-0.435721\pi$
$467$	8.66870			0.401140			0.200570	+	0.979679i	$0.435721\pi$
$468$		0			0
$469$	−35.4843			−1.63851
$470$	0.238954	+	2.50042i	0.0110221	+	0.115336i
$471$		0			0
$472$	24.8320	−	7.29752i	1.14299	−	0.335895i
$473$	−1.19560			−0.0549736
$474$		0			0
$475$	−7.06005	−	3.81557i	−0.323937	−	0.175070i
$476$	9.68023	+	50.1846i	0.443693	+	2.30021i
$477$		0			0
$478$	−18.8181	+	1.79836i	−0.860719	+	0.0822549i
$479$		−	3.41248i		−	0.155920i	−0.996956	−	0.0779602i	$-0.975159\pi$
$479$		−	3.41248i		−	0.155920i	0.996956	−	0.0779602i	$-0.0248407\pi$
$480$		0			0
$481$	−15.4647			−0.705130
$482$	28.0999	−	2.68538i	1.27992	−	0.122316i
$483$		0			0
$484$	−2.37705	+	0.458515i	−0.108048	+	0.0208416i
$485$	34.6754			1.57453
$486$		0			0
$487$	−41.8116			−1.89467			−0.947333	−	0.320250i	$-0.896233\pi$
$487$	−41.8116			−1.89467			−0.947333	+	0.320250i	$0.896233\pi$
$488$	7.20408	−	2.11710i	0.326114	−	0.0958367i
$489$		0			0
$490$	59.5037	−	5.68650i	2.68810	−	0.256890i
$491$	13.0613			0.589448			0.294724	−	0.955582i	$-0.404772\pi$
$491$	13.0613			0.589448			0.294724	+	0.955582i	$0.404772\pi$
$492$		0			0
$493$	−27.2312			−1.22643
$494$	3.60610	−	8.52442i	0.162246	−	0.383532i
$495$		0			0
$496$	−6.40767	+	2.56751i	−0.287713	+	0.115285i
$497$			46.9108i			2.10424i
$498$		0			0
$499$	7.12405			0.318916			0.159458	−	0.987205i	$-0.449025\pi$
$499$	7.12405			0.318916			0.159458	+	0.987205i	$0.449025\pi$
$500$	−3.12977	−	16.2255i	−0.139967	−	0.725624i
$501$		0			0
$502$	4.01754	+	42.0397i	0.179312	+	1.87632i
$503$			6.92730i			0.308873i	0.988003	+	0.154437i	$0.0493562\pi$
$503$			6.92730i			0.308873i	−0.988003	+	0.154437i	$0.950644\pi$
$504$		0			0
$505$	0.266112			0.0118418
$506$	−11.1385	+	1.06446i	−0.495167	+	0.0473209i
$507$		0			0
$508$	−24.5400	+	4.73359i	−1.08879	+	0.210019i
$509$	5.92205			0.262490			0.131245	−	0.991350i	$-0.458103\pi$
$509$	5.92205			0.262490			0.131245	+	0.991350i	$0.458103\pi$
$510$		0			0
$511$		−	34.4614i		−	1.52448i
$512$	17.1108	+	14.8061i	0.756199	+	0.654342i
$513$		0			0
$514$	0.954420	−	0.0912095i	0.0420977	−	0.00402308i
$515$		−	50.7252i		−	2.23522i
$516$		0			0
$517$			2.37288i			0.104359i
$518$	−69.7799	+	6.66854i	−3.06595	+	0.292999i
$519$		0			0
$520$	−10.6572	+	3.13188i	−0.467348	+	0.137342i
$521$			16.9113i			0.740898i	0.928853	+	0.370449i	$0.120796\pi$
$521$			16.9113i			0.740898i	−0.928853	+	0.370449i	$0.879204\pi$
$522$		0			0
$523$		−	20.3406i		−	0.889434i	−0.895671	−	0.444717i	$-0.853304\pi$
$523$		−	20.3406i		−	0.889434i	0.895671	−	0.444717i	$-0.146696\pi$
$524$	24.7083	−	4.76604i	1.07939	−	0.208206i
$525$		0			0
$526$	4.23611	−	0.404826i	0.184703	−	0.0176512i
$527$	9.16384			0.399183
$528$		0			0
$529$	17.8733			0.777098
$530$	37.0825	−	3.54380i	1.61076	−	0.153933i
$531$		0			0
$532$	12.5956	−	40.0188i	0.546089	−	1.73504i
$533$			5.86580i			0.254076i
$534$		0			0
$535$	5.33119			0.230488
$536$	20.0090	−	5.88014i	0.864257	−	0.253984i
$537$		0			0
$538$	0.947196	+	9.91149i	0.0408365	+	0.427315i
$539$	56.4684			2.43227
$540$		0			0
$541$			24.8364i			1.06780i	0.845548	+	0.533900i	$0.179274\pi$
$541$			24.8364i			1.06780i	−0.845548	+	0.533900i	$0.820726\pi$
$542$	−32.1300	+	3.07052i	−1.38010	+	0.131890i
$543$		0			0
$544$	−13.7747	−	26.6941i	−0.590583	−	1.14450i
$545$		−	47.1642i		−	2.02029i
$546$		0			0
$547$		−	22.8518i		−	0.977071i	−0.872544	−	0.488535i	$-0.837531\pi$
$547$		−	22.8518i		−	0.977071i	0.872544	−	0.488535i	$-0.162469\pi$
$548$	−2.59404	+	0.500370i	−0.110812	+	0.0213748i
$549$		0			0
$550$	0.865532	+	9.05695i	0.0369064	+	0.386190i
$551$	19.6650	+	10.6279i	0.837758	+	0.452762i
$552$		0			0
$553$			25.0733i			1.06623i
$554$	−29.5617	+	2.82508i	−1.25596	+	0.120026i
$555$		0			0
$556$	−2.78234	+	0.536693i	−0.117998	+	0.0227609i
$557$		−	5.88751i		−	0.249462i	−0.992191	−	0.124731i	$-0.960193\pi$
$557$		−	5.88751i		−	0.249462i	0.992191	−	0.124731i	$-0.0398067\pi$
$558$		0			0
$559$	−0.513737			−0.0217288
$560$	−46.7368	+	18.7271i	−1.97499	+	0.791366i
$561$		0			0
$562$	7.08319	−	0.676908i	0.298786	−	0.0285536i
$563$		−	6.33319i		−	0.266912i	−0.991055	−	0.133456i	$-0.957393\pi$
$563$		−	6.33319i		−	0.266912i	0.991055	−	0.133456i	$-0.0426075\pi$
$564$		0			0
$565$	−14.4985			−0.609959
$566$	−0.168323	−	1.76134i	−0.00707515	−	0.0740346i
$567$		0			0
$568$	−7.77363	−	26.4522i	−0.326174	−	1.10991i
$569$		−	19.8209i		−	0.830937i	−0.909607	−	0.415469i	$-0.863618\pi$
$569$		−	19.8209i		−	0.830937i	0.909607	−	0.415469i	$-0.136382\pi$
$570$		0			0
$571$	−35.3004			−1.47728			−0.738639	−	0.674101i	$-0.764531\pi$
$571$	−35.3004			−1.47728			−0.738639	+	0.674101i	$0.764531\pi$
$572$	−10.3035	+	1.98747i	−0.430811	+	0.0831001i
$573$		0			0
$574$	2.52939	+	26.4677i	0.105575	+	1.10474i
$575$			4.16866i			0.173845i
$576$		0			0
$577$	28.4776			1.18554			0.592769	−	0.805373i	$-0.298035\pi$
$577$	28.4776			1.18554			0.592769	+	0.805373i	$0.298035\pi$
$578$	1.50646	+	15.7636i	0.0626604	+	0.655681i
$579$		0			0
$580$	−5.08087	−	26.3404i	−0.210971	−	1.09373i
$581$			23.1024i			0.958448i
$582$		0			0
$583$	35.1909			1.45746
$584$	5.71064	+	19.4322i	0.236308	+	0.804111i
$585$		0			0
$586$	2.49955	+	26.1554i	0.103255	+	1.08047i
$587$	−28.0180			−1.15643			−0.578214	−	0.815885i	$-0.696250\pi$
$587$	−28.0180			−1.15643			−0.578214	+	0.815885i	$0.696250\pi$
$588$		0			0
$589$	−6.61767	−	3.57649i	−0.272676	−	0.147367i
$590$	−3.22002	−	33.6944i	−0.132566	−	1.38718i
$591$		0			0
$592$	38.2426	−	15.3236i	1.57176	−	0.629795i
$593$	45.6450			1.87442			0.937208	−	0.348771i	$-0.113401\pi$
$593$	45.6450			1.87442			0.937208	+	0.348771i	$0.113401\pi$
$594$		0			0
$595$	66.8399			2.74017
$596$	−5.02993	−	26.0764i	−0.206034	−	1.06813i
$597$		0			0
$598$	−4.78612	+	0.457387i	−0.195719	+	0.0187040i
$599$	−20.9807			−0.857248			−0.428624	−	0.903483i	$-0.641002\pi$
$599$	−20.9807			−0.857248			−0.428624	+	0.903483i	$0.641002\pi$
$600$		0			0
$601$		−	0.458660i		−	0.0187091i	−0.999956	−	0.00935456i	$-0.997022\pi$
$601$		−	0.458660i		−	0.0187091i	0.999956	−	0.00935456i	$-0.00297769\pi$
$602$	−2.31808	+	0.221528i	−0.0944780	+	0.00902883i
$603$		0			0
$604$	−31.9663	+	6.16607i	−1.30069	+	0.250894i
$605$			3.16595i			0.128714i
$606$		0			0
$607$	−30.1779			−1.22488			−0.612441	−	0.790516i	$-0.709812\pi$
$607$	−30.1779			−1.22488			−0.612441	+	0.790516i	$0.709812\pi$
$608$	−0.470874	+	24.6532i	−0.0190965	+	0.999818i
$609$		0			0
$610$	−0.934169	−	9.77518i	−0.0378234	−	0.395785i
$611$			1.01960i			0.0412487i
$612$		0			0
$613$			15.1288i			0.611045i	0.952185	+	0.305523i	$0.0988311\pi$
$613$			15.1288i			0.611045i	−0.952185	+	0.305523i	$0.901169\pi$
$614$	15.0742	−	1.44057i	0.608343	−	0.0581366i
$615$		0			0
$616$	−45.6344	+	13.4108i	−1.83866	+	0.540337i
$617$	3.05065			0.122815			0.0614073	−	0.998113i	$-0.480441\pi$
$617$	3.05065			0.122815			0.0614073	+	0.998113i	$0.480441\pi$
$618$		0			0
$619$	−14.3298			−0.575962			−0.287981	−	0.957636i	$-0.592984\pi$
$619$	−14.3298			−0.575962			−0.287981	+	0.957636i	$0.592984\pi$
$620$	1.70981	+	8.86407i	0.0686677	+	0.355990i
$621$		0			0
$622$	−18.6070	+	1.77819i	−0.746073	+	0.0712987i
$623$	67.8290			2.71751
$624$		0			0
$625$	−30.8158			−1.23263
$626$	−4.36136	−	45.6374i	−0.174315	−	1.82404i
$627$		0			0
$628$	6.96211	+	36.0932i	0.277818	+	1.44028i
$629$	−54.6921			−2.18072
$630$		0			0
$631$			11.4416i			0.455482i	0.973722	+	0.227741i	$0.0731340\pi$
$631$			11.4416i			0.455482i	−0.973722	+	0.227741i	$0.926866\pi$
$632$	−4.15493	−	14.1384i	−0.165274	−	0.562396i
$633$		0			0
$634$	−1.94899	−	20.3943i	−0.0774041	−	0.809960i
$635$			32.6844i			1.29704i
$636$		0			0
$637$	24.2640			0.961374
$638$	−2.41085	−	25.2272i	−0.0954463	−	0.998754i
$639$		0			0
$640$	23.2508	−	18.3047i	0.919067	−	0.723557i
$641$		−	13.6910i		−	0.540760i	−0.962754	−	0.270380i	$-0.912851\pi$
$641$		−	13.6910i		−	0.540760i	0.962754	−	0.270380i	$-0.0871494\pi$
$642$		0			0
$643$	7.58609			0.299166			0.149583	−	0.988749i	$-0.452207\pi$
$643$	7.58609			0.299166			0.149583	+	0.988749i	$0.452207\pi$
$644$	−21.3987	+	4.12764i	−0.843226	+	0.162652i
$645$		0			0
$646$	12.7532	−	30.1472i	0.501769	−	1.18613i
$647$		−	27.2526i		−	1.07141i	−0.844405	−	0.535705i	$-0.820046\pi$
$647$		−	27.2526i		−	1.07141i	0.844405	−	0.535705i	$-0.179954\pi$
$648$		0			0
$649$		−	31.9757i		−	1.25516i
$650$	0.371911	+	3.89169i	0.0145875	+	0.152645i
$651$		0			0
$652$	24.2359	−	4.67493i	0.949153	−	0.183084i
$653$		−	3.86565i		−	0.151274i	−0.997135	−	0.0756372i	$-0.975901\pi$
$653$		−	3.86565i		−	0.151274i	0.997135	−	0.0756372i	$-0.0240991\pi$
$654$		0			0
$655$		−	32.9085i		−	1.28584i
$656$	−5.81226	−	14.5055i	−0.226931	−	0.566345i
$657$		0			0
$658$	0.439663	+	4.60065i	0.0171399	+	0.179352i
$659$		−	33.7642i		−	1.31527i	−0.753338	−	0.657633i	$-0.771558\pi$
$659$		−	33.7642i		−	1.31527i	0.753338	−	0.657633i	$-0.228442\pi$
$660$		0			0
$661$	7.29497			0.283741			0.141871	−	0.989885i	$-0.454688\pi$
$661$	7.29497			0.283741			0.141871	+	0.989885i	$0.454688\pi$
$662$	7.35841	−	0.703209i	0.285993	−	0.0273310i
$663$		0			0
$664$	−3.82832	−	13.0270i	−0.148568	−	0.505547i
$665$	−48.2685	−	26.0865i	−1.87177	−	1.01159i
$666$		0			0
$667$		−	11.6114i		−	0.449594i
$668$	40.7651	−	7.86327i	1.57725	−	0.304239i
$669$		0			0
$670$	−2.59461	−	27.1501i	−0.100238	−	1.04890i
$671$		−	9.27655i		−	0.358117i
$672$		0			0
$673$			20.7118i			0.798380i	0.916868	+	0.399190i	$0.130709\pi$
$673$			20.7118i			0.798380i	−0.916868	+	0.399190i	$0.869291\pi$
$674$	−25.6192	+	2.44831i	−0.986816	+	0.0943055i
$675$		0			0
$676$	21.1021	−	4.07043i	0.811618	−	0.156555i
$677$	22.9317			0.881336			0.440668	−	0.897670i	$-0.354742\pi$
$677$	22.9317			0.881336			0.440668	+	0.897670i	$0.354742\pi$
$678$		0			0
$679$	63.8009			2.44846
$680$	−37.6899	+	11.0761i	−1.44534	+	0.424750i
$681$		0			0
$682$	0.811298	+	8.48945i	0.0310662	+	0.325078i
$683$			22.5142i			0.861483i	0.902475	+	0.430741i	$0.141748\pi$
$683$			22.5142i			0.861483i	−0.902475	+	0.430741i	$0.858252\pi$
$684$		0			0
$685$			3.45495i			0.132007i
$686$	62.0588	−	5.93068i	2.36942	−	0.226434i
$687$		0			0
$688$	1.27042	−	0.509048i	0.0484342	−	0.0194073i
$689$	15.1212			0.576073
$690$		0			0
$691$	−13.4002			−0.509766			−0.254883	−	0.966972i	$-0.582037\pi$
$691$	−13.4002			−0.509766			−0.254883	+	0.966972i	$0.582037\pi$
$692$	1.34507	−	0.259453i	0.0511318	−	0.00986293i
$693$		0			0
$694$	2.27575	+	23.8135i	0.0863861	+	0.903948i
$695$			3.70575i			0.140567i
$696$		0			0
$697$			20.7448i			0.785767i
$698$	39.9485	−	3.81770i	1.51207	−	0.144502i
$699$		0			0
$700$	3.35627	+	17.3997i	0.126855	+	0.657647i
$701$			33.0858i			1.24963i	0.780772	+	0.624816i	$0.214826\pi$
$701$			33.0858i			1.24963i	−0.780772	+	0.624816i	$0.785174\pi$
$702$		0			0
$703$	39.4959	+	21.3454i	1.48962	+	0.805057i
$704$	23.5101	−	15.1242i	0.886070	−	0.570016i
$705$		0			0
$706$	−0.328213	−	3.43443i	−0.0123525	−	0.129257i
$707$	0.489633			0.0184145
$708$		0			0
$709$			19.4606i			0.730858i	0.930839	+	0.365429i	$0.119078\pi$
$709$			19.4606i			0.730858i	−0.930839	+	0.365429i	$0.880922\pi$
$710$	−35.8928	+	3.43011i	−1.34703	+	0.128730i
$711$		0			0
$712$	−38.2476	+	11.2400i	−1.43339	+	0.421237i
$713$			3.90746i			0.146335i
$714$		0			0
$715$			13.7230i			0.513212i
$716$	−7.10118	−	36.8142i	−0.265384	−	1.37581i
$717$		0			0
$718$	34.6422	−	3.31059i	1.29283	−	0.123550i
$719$			32.5024i			1.21213i	0.795414	+	0.606067i	$0.207254\pi$
$719$			32.5024i			1.21213i	−0.795414	+	0.606067i	$0.792746\pi$
$720$		0			0
$721$		−	93.3319i		−	3.47586i
$722$	−20.9757	+	16.7935i	−0.780634	+	0.624988i
$723$		0			0
$724$	−23.2434	+	4.48348i	−0.863834	+	0.166627i
$725$	−9.44144			−0.350646
$726$		0			0
$727$		−	11.3190i		−	0.419800i	−0.977723	−	0.209900i	$-0.932686\pi$
$727$		−	11.3190i		−	0.419800i	0.977723	−	0.209900i	$-0.0673139\pi$
$728$	−19.6087	+	5.76250i	−0.726746	+	0.213572i
$729$		0			0
$730$	26.3675	−	2.51982i	0.975903	−	0.0932626i
$731$	−1.81687			−0.0671993
$732$		0			0
$733$		−	14.7845i		−	0.546079i	−0.962003	−	0.273040i	$-0.911971\pi$
$733$		−	14.7845i		−	0.546079i	0.962003	−	0.273040i	$-0.0880290\pi$
$734$	−26.7053	+	2.55210i	−0.985710	+	0.0941998i
$735$		0			0
$736$	11.3823	−	5.87351i	0.419559	−	0.216500i
$737$		−	25.7652i		−	0.949072i
$738$		0			0
$739$	33.9300			1.24813			0.624067	−	0.781371i	$-0.285479\pi$
$739$	33.9300			1.24813			0.624067	+	0.781371i	$0.285479\pi$
$740$	−10.2046	−	52.9030i	−0.375128	−	1.94475i
$741$		0			0
$742$	68.2299	−	6.52042i	2.50480	−	0.239372i
$743$	−14.5846			−0.535056			−0.267528	−	0.963550i	$-0.586207\pi$
$743$	−14.5846			−0.535056			−0.267528	+	0.963550i	$0.586207\pi$
$744$		0			0
$745$	−34.7306			−1.27243
$746$	2.74766	+	28.7516i	0.100599	+	1.05267i
$747$		0			0
$748$	−36.4390	+	7.02882i	−1.33234	+	0.256999i
$749$	9.80913			0.358418
$750$		0			0
$751$	13.8729			0.506229			0.253114	−	0.967436i	$-0.418545\pi$
$751$	13.8729			0.506229			0.253114	+	0.967436i	$0.418545\pi$
$752$	−1.01030	−	2.52137i	−0.0368418	−	0.0919449i
$753$		0			0
$754$	−1.03592	−	10.8399i	−0.0377259	−	0.394766i
$755$			42.5754i			1.54948i
$756$		0			0
$757$			13.4956i			0.490506i	0.969459	+	0.245253i	$0.0788710\pi$
$757$			13.4956i			0.490506i	−0.969459	+	0.245253i	$0.921129\pi$
$758$	−36.6664	+	3.50404i	−1.33178	+	0.127272i
$759$		0			0
$760$	31.5406	+	6.71109i	1.14410	+	0.243437i
$761$	−19.7088			−0.714442			−0.357221	−	0.934020i	$-0.616276\pi$
$761$	−19.7088			−0.714442			−0.357221	+	0.934020i	$0.616276\pi$
$762$		0			0
$763$		−	86.7799i		−	3.14164i
$764$	−6.61430	−	34.2901i	−0.239297	−	1.24057i
$765$		0			0
$766$	−3.11184	−	32.5624i	−0.112435	−	1.17653i
$767$		−	13.7397i		−	0.496111i
$768$		0			0
$769$	18.8060			0.678163			0.339081	−	0.940757i	$-0.389884\pi$
$769$	18.8060			0.678163			0.339081	+	0.940757i	$0.389884\pi$
$770$	5.91751	+	61.9210i	0.213252	+	2.23148i
$771$		0			0
$772$	4.19499	+	21.7478i	0.150981	+	0.782720i
$773$	0.638576			0.0229680			0.0114840	−	0.999934i	$-0.496344\pi$
$773$	0.638576			0.0229680			0.0114840	+	0.999934i	$0.496344\pi$
$774$		0			0
$775$	3.17723			0.114130
$776$	−35.9762	+	10.5725i	−1.29147	+	0.379531i
$777$		0			0
$778$	−24.1889	+	2.31163i	−0.867215	+	0.0828758i
$779$	8.09635	−	14.9809i	0.290082	−	0.536746i
$780$		0			0
$781$	−34.0619			−1.21883
$782$	−16.9265	+	1.61758i	−0.605289	+	0.0578447i
$783$		0			0
$784$	−60.0022	+	24.0425i	−2.14294	+	0.858661i
$785$	48.0719			1.71576
$786$		0			0
$787$		−	5.69613i		−	0.203045i	−0.994833	−	0.101522i	$-0.967629\pi$
$787$		−	5.69613i		−	0.203045i	0.994833	−	0.101522i	$-0.0323714\pi$
$788$	−7.66824	−	39.7540i	−0.273170	−	1.41618i
$789$		0			0
$790$	−19.1843	+	1.83336i	−0.682548	+	0.0652280i
$791$	−26.6766			−0.948511
$792$		0			0
$793$		−	3.98605i		−	0.141549i
$794$	39.9401	−	3.81689i	1.41742	−	0.135456i
$795$		0			0
$796$	−4.62020	−	23.9522i	−0.163759	−	0.848964i
$797$	−0.349816			−0.0123911			−0.00619557	−	0.999981i	$-0.501972\pi$
$797$	−0.349816			−0.0123911			−0.00619557	+	0.999981i	$0.501972\pi$
$798$		0			0
$799$			3.60590i			0.127568i
$800$	−4.77587	−	9.25522i	−0.168852	−	0.327221i
$801$		0			0
$802$	−8.84114	+	0.844907i	−0.312191	+	0.0298347i
$803$	25.0225			0.883024
$804$		0			0
$805$			28.5005i			1.00451i
$806$	0.348607	+	3.64784i	0.0122792	+	0.128490i
$807$		0			0
$808$	−0.276096	+	0.0811376i	−0.00971301	+	0.00285441i
$809$	−11.1848			−0.393236			−0.196618	−	0.980480i	$-0.562996\pi$
$809$	−11.1848			−0.393236			−0.196618	+	0.980480i	$0.562996\pi$
$810$		0			0
$811$		−	11.3206i		−	0.397520i	−0.980048	−	0.198760i	$-0.936309\pi$
$811$		−	11.3206i		−	0.397520i	0.980048	−	0.198760i	$-0.0636914\pi$
$812$	−9.34854	−	48.4650i	−0.328069	−	1.70079i
$813$		0			0
$814$	−4.84203	−	50.6672i	−0.169713	−	1.77588i
$815$		−	32.2794i		−	1.13070i
$816$		0			0
$817$	1.31205	+	0.709092i	0.0459029	+	0.0248080i
$818$	−3.87480	+	0.370297i	−0.135479	+	0.0129471i
$819$		0			0
$820$	−20.0662	+	3.87062i	−0.700743	+	0.135168i
$821$			16.9782i			0.592542i	0.955104	+	0.296271i	$0.0957432\pi$
$821$			16.9782i			0.592542i	−0.955104	+	0.296271i	$0.904257\pi$
$822$		0			0
$823$			5.17146i			0.180266i	0.995930	+	0.0901329i	$0.0287292\pi$
$823$			5.17146i			0.180266i	−0.995930	+	0.0901329i	$0.971271\pi$
$824$	15.4661	+	52.6282i	0.538788	+	1.83339i
$825$		0			0
$826$	−5.92468	−	61.9961i	−0.206146	−	2.15712i
$827$		−	0.733529i		−	0.0255073i	−0.999919	−	0.0127536i	$-0.995940\pi$
$827$		−	0.733529i		−	0.0255073i	0.999919	−	0.0127536i	$-0.00405972\pi$
$828$		0			0
$829$	−18.3783			−0.638304			−0.319152	−	0.947703i	$-0.603398\pi$
$829$	−18.3783			−0.638304			−0.319152	+	0.947703i	$0.603398\pi$
$830$	−17.6763	+	1.68924i	−0.613553	+	0.0586345i
$831$		0			0
$832$	10.1021	−	6.49875i	0.350226	−	0.225304i
$833$	85.8113			2.97319
$834$		0			0
$835$		−	54.2942i		−	1.87893i
$836$	29.0577	+	9.14567i	1.00498	+	0.316310i
$837$		0			0
$838$	4.48785	+	46.9610i	0.155030	+	1.62224i
$839$	37.9165			1.30902			0.654511	−	0.756052i	$-0.272875\pi$
$839$	37.9165			1.30902			0.654511	+	0.756052i	$0.272875\pi$
$840$		0			0
$841$	−2.70187			−0.0931678
$842$	−0.124989	−	1.30789i	−0.00430739	−	0.0450727i
$843$		0			0
$844$	−4.25412	−	22.0543i	−0.146433	−	0.759142i
$845$		−	28.1055i		−	0.966858i
$846$		0			0
$847$			5.82519i			0.200156i
$848$	−37.3932	+	14.9832i	−1.28409	+	0.514525i
$849$		0			0
$850$	1.31529	+	13.7632i	0.0451141	+	0.472075i
$851$		−	23.3207i		−	0.799423i
$852$		0			0
$853$		−	46.5801i		−	1.59487i	−0.603404	−	0.797436i	$-0.706189\pi$
$853$		−	46.5801i		−	1.59487i	0.603404	−	0.797436i	$-0.293811\pi$
$854$	−1.71883	−	17.9858i	−0.0588170	−	0.615463i
$855$		0			0
$856$	−5.53120	+	1.62548i	−0.189053	+	0.0555578i
$857$			25.6585i			0.876477i	0.898859	+	0.438238i	$0.144397\pi$
$857$			25.6585i			0.876477i	−0.898859	+	0.438238i	$0.855603\pi$
$858$		0			0
$859$	−15.5918			−0.531986			−0.265993	−	0.963975i	$-0.585700\pi$
$859$	−15.5918			−0.531986			−0.265993	+	0.963975i	$0.585700\pi$
$860$	−0.338996	−	1.75743i	−0.0115597	−	0.0599280i
$861$		0			0
$862$	4.64087	+	48.5622i	0.158069	+	1.65404i
$863$	−31.1083			−1.05894			−0.529470	−	0.848329i	$-0.677609\pi$
$863$	−31.1083			−1.05894			−0.529470	+	0.848329i	$0.677609\pi$
$864$		0			0
$865$		−	1.79147i		−	0.0609118i
$866$	35.0620	−	3.35072i	1.19146	−	0.113862i
$867$		0			0
$868$	3.14597	+	16.3094i	0.106781	+	0.553579i
$869$	−18.2058			−0.617588
$870$		0			0
$871$		−	11.0711i		−	0.375128i
$872$	14.3804	+	48.9337i	0.486981	+	1.65710i
$873$		0			0
$874$	12.8548	+	5.43797i	0.434819	+	0.183942i
$875$	−39.7620			−1.34420
$876$		0			0
$877$	0.487909			0.0164755			0.00823776	−	0.999966i	$-0.497378\pi$
$877$	0.487909			0.0164755			0.00823776	+	0.999966i	$0.497378\pi$
$878$	2.75962	+	28.8768i	0.0931327	+	0.974544i
$879$		0			0
$880$	−13.5978	−	33.9356i	−0.458381	−	1.14397i
$881$	13.5269			0.455732			0.227866	−	0.973693i	$-0.426825\pi$
$881$	13.5269			0.455732			0.227866	+	0.973693i	$0.426825\pi$
$882$		0			0
$883$	34.7988			1.17107			0.585537	−	0.810646i	$-0.300884\pi$
$883$	34.7988			1.17107			0.585537	+	0.810646i	$0.300884\pi$
$884$	−15.6575	+	3.02022i	−0.526619	+	0.101581i
$885$		0			0
$886$	−3.49592	−	36.5815i	−0.117448	−	1.22898i
$887$	18.9849			0.637449			0.318725	−	0.947847i	$-0.396745\pi$
$887$	18.9849			0.637449			0.318725	+	0.947847i	$0.396745\pi$
$888$		0			0
$889$			60.1377i			2.01696i
$890$	4.95965	+	51.8979i	0.166248	+	1.73962i
$891$		0			0
$892$	−11.5195	+	2.22202i	−0.385701	+	0.0743989i
$893$	1.40732	−	2.60400i	0.0470942	−	0.0871397i
$894$		0			0
$895$	−49.0321			−1.63896
$896$	42.7802	−	33.6798i	1.42919	−	1.12516i
$897$		0			0
$898$	51.3574	−	4.90799i	1.71382	−	0.163782i
$899$	−8.84984			−0.295159
$900$		0			0
$901$	53.4773			1.78159
$902$	−19.2182	+	1.83659i	−0.639895	+	0.0611518i
$903$		0			0
$904$	15.0425	−	4.42061i	0.500305	−	0.147027i
$905$			30.9574i			1.02906i
$906$		0			0
$907$			20.6905i			0.687016i	0.939150	+	0.343508i	$0.111615\pi$
$907$			20.6905i			0.687016i	−0.939150	+	0.343508i	$0.888385\pi$
$908$	−5.22308	−	27.0777i	−0.173334	−	0.898603i
$909$		0			0
$910$	2.54270	+	26.6069i	0.0842896	+	0.882010i
$911$	−29.8333			−0.988420			−0.494210	−	0.869342i	$-0.664543\pi$
$911$	−29.8333			−0.988420			−0.494210	+	0.869342i	$0.664543\pi$
$912$		0			0
$913$	−16.7746			−0.555160
$914$	3.13161	+	32.7693i	0.103584	+	1.08391i
$915$		0			0
$916$	−2.93920	−	15.2375i	−0.0971138	−	0.503461i
$917$		−	60.5500i		−	1.99954i
$918$		0			0
$919$		−	35.6710i		−	1.17668i	−0.808615	−	0.588338i	$-0.799782\pi$
$919$		−	35.6710i		−	1.17668i	0.808615	−	0.588338i	$-0.200218\pi$
$920$	−4.72285	−	16.0709i	−0.155708	−	0.529843i
$921$		0			0
$922$	−20.1098	+	1.92180i	−0.662280	+	0.0632911i
$923$	−14.6361			−0.481753
$924$		0			0
$925$	−18.9625			−0.623484
$926$	−22.0005	+	2.10249i	−0.722981	+	0.0690920i
$927$		0			0
$928$	13.3027	+	25.7794i	0.436682	+	0.846251i
$929$	5.05272			0.165774			0.0828872	−	0.996559i	$-0.473586\pi$
$929$	5.05272			0.165774			0.0828872	+	0.996559i	$0.473586\pi$
$930$		0			0
$931$	−61.9687	−	33.4907i	−2.03094	−	1.09761i
$932$	46.2856	−	8.92814i	1.51613	−	0.292451i
$933$		0			0
$934$	1.16626	+	12.2038i	0.0381612	+	0.399320i
$935$			48.5325i			1.58718i
$936$		0			0
$937$	5.91078			0.193097			0.0965484	−	0.995328i	$-0.469220\pi$
$937$	5.91078			0.193097			0.0965484	+	0.995328i	$0.469220\pi$
$938$	−4.77395	−	49.9548i	−0.155875	−	1.63108i
$939$		0			0
$940$	−3.48794	+	0.672798i	−0.113764	+	0.0219443i
$941$	−19.2287			−0.626837			−0.313418	−	0.949615i	$-0.601474\pi$
$941$	−19.2287			−0.626837			−0.313418	+	0.949615i	$0.601474\pi$
$942$		0			0
$943$	−8.84559			−0.288052
$944$	13.6143	+	33.9767i	0.443107	+	1.10585i
$945$		0			0
$946$	−0.160852	−	1.68316i	−0.00522975	−	0.0547243i
$947$	−26.5034			−0.861245			−0.430623	−	0.902532i	$-0.641706\pi$
$947$	−26.5034			−0.861245			−0.430623	+	0.902532i	$0.641706\pi$
$948$		0			0
$949$	10.7519			0.349022
$950$	4.42172	−	10.4525i	0.143460	−	0.339123i
$951$		0			0
$952$	−69.3475	+	20.3795i	−2.24757	+	0.660504i
$953$			37.0464i			1.20005i	0.799981	+	0.600025i	$0.204843\pi$
$953$			37.0464i			1.20005i	−0.799981	+	0.600025i	$0.795157\pi$
$954$		0			0
$955$	−45.6703			−1.47786
$956$	−5.06345	−	26.2501i	−0.163764	−	0.848990i
$957$		0			0
$958$	4.80409	−	0.459105i	0.155213	−	0.0148330i
$959$			6.35694i			0.205276i
$960$		0			0
$961$	−28.0219			−0.903931
$962$	−2.08058	−	21.7712i	−0.0670805	−	0.701932i
$963$		0			0
$964$	7.56095	+	39.1978i	0.243522	+	1.26247i
$965$	28.9655			0.932432
$966$		0			0
$967$			49.4739i			1.59097i	0.605970	+	0.795487i	$0.292785\pi$
$967$			49.4739i			1.59097i	−0.605970	+	0.795487i	$0.707215\pi$
$968$	−0.965299	−	3.28472i	−0.0310259	−	0.105575i
$969$		0			0
$970$	4.66512	+	48.8159i	0.149788	+	1.56739i
$971$		−	13.1840i		−	0.423095i	−0.977368	−	0.211548i	$-0.932150\pi$
$971$		−	13.1840i		−	0.423095i	0.977368	−	0.211548i	$-0.0678503\pi$
$972$		0			0
$973$			6.81840i			0.218588i
$974$	−5.62521	−	58.8624i	−0.180243	−	1.88607i
$975$		0			0
$976$	3.94967	+	9.85708i	0.126426	+	0.315517i
$977$			28.8518i			0.923049i	0.887127	+	0.461525i	$0.152697\pi$
$977$			28.8518i			0.923049i	−0.887127	+	0.461525i	$0.847303\pi$
$978$		0			0
$979$			49.2506i			1.57406i
$980$	16.0109	+	83.0042i	0.511449	+	2.65147i
$981$		0			0
$982$	1.75723	+	18.3877i	0.0560754	+	0.586775i
$983$	9.02606			0.287887			0.143943	−	0.989586i	$-0.454022\pi$
$983$	9.02606			0.287887			0.143943	+	0.989586i	$0.454022\pi$
$984$		0			0
$985$	−52.9476			−1.68705
$986$	−3.66360	−	38.3361i	−0.116673	−	1.22087i
$987$		0			0
$988$	12.4858	+	3.92981i	0.397227	+	0.125024i
$989$		−	0.774712i		−	0.0246344i
$990$		0			0
$991$	12.9609			0.411717			0.205858	−	0.978582i	$-0.434001\pi$
$991$	12.9609			0.411717			0.205858	+	0.978582i	$0.434001\pi$
$992$	−4.47661	−	8.67529i	−0.142133	−	0.275441i
$993$		0			0
$994$	−66.0410	+	6.31123i	−2.09469	+	0.200180i
$995$	−31.9015			−1.01135
$996$		0			0
$997$		−	5.01059i		−	0.158687i	−0.996847	−	0.0793435i	$-0.974718\pi$
$997$		−	5.01059i		−	0.158687i	0.996847	−	0.0793435i	$-0.0252824\pi$
$998$	0.958448	+	10.0292i	0.0303391	+	0.317470i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.e.g.379.22		40
3.2	odd	2		456.2.e.a.379.19	✓	40
4.3	odd	2		5472.2.e.g.5167.4		40
8.3	odd	2	inner	1368.2.e.g.379.20		40
8.5	even	2		5472.2.e.g.5167.33		40
12.11	even	2		1824.2.e.a.1519.7		40
19.18	odd	2	inner	1368.2.e.g.379.19		40
24.5	odd	2		1824.2.e.a.1519.37		40
24.11	even	2		456.2.e.a.379.21	yes	40
57.56	even	2		456.2.e.a.379.22	yes	40
76.75	even	2		5472.2.e.g.5167.34		40
152.37	odd	2		5472.2.e.g.5167.3		40
152.75	even	2	inner	1368.2.e.g.379.21		40
228.227	odd	2		1824.2.e.a.1519.38		40
456.227	odd	2		456.2.e.a.379.20	yes	40
456.341	even	2		1824.2.e.a.1519.8		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.e.a.379.19	✓	40	3.2	odd	2
456.2.e.a.379.20	yes	40	456.227	odd	2
456.2.e.a.379.21	yes	40	24.11	even	2
456.2.e.a.379.22	yes	40	57.56	even	2
1368.2.e.g.379.19		40	19.18	odd	2	inner
1368.2.e.g.379.20		40	8.3	odd	2	inner
1368.2.e.g.379.21		40	152.75	even	2	inner
1368.2.e.g.379.22		40	1.1	even	1	trivial
1824.2.e.a.1519.7		40	12.11	even	2
1824.2.e.a.1519.8		40	456.341	even	2
1824.2.e.a.1519.37		40	24.5	odd	2
1824.2.e.a.1519.38		40	228.227	odd	2
5472.2.e.g.5167.3		40	152.37	odd	2
5472.2.e.g.5167.4		40	4.3	odd	2
5472.2.e.g.5167.33		40	8.5	even	2
5472.2.e.g.5167.34		40	76.75	even	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:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.134537 + 1.40780i) q^{2} +(-1.96380 + 0.378802i) q^{4} +2.61555i q^{5} +4.81248i q^{7} +(-0.797481 - 2.71367i) q^{8} +O(q^{10})\)	\(q+(0.134537 + 1.40780i) q^{2} +(-1.96380 + 0.378802i) q^{4} +2.61555i q^{5} +4.81248i q^{7} +(-0.797481 - 2.71367i) q^{8} +(-3.68217 + 0.351888i) q^{10} -3.49434 q^{11} -1.50149 q^{13} +(-6.77501 + 0.647456i) q^{14} +(3.71302 - 1.48778i) q^{16} -5.31012 q^{17} +(3.83470 + 2.07245i) q^{19} +(-0.990775 - 5.13641i) q^{20} +(-0.470118 - 4.91934i) q^{22} -2.26423i q^{23} -1.84109 q^{25} +(-0.202006 - 2.11379i) q^{26} +(-1.82298 - 9.45075i) q^{28} +5.12817 q^{29} -1.72573 q^{31} +(2.59404 + 5.02702i) q^{32} +(-0.714407 - 7.47558i) q^{34} -12.5873 q^{35} +10.2996 q^{37} +(-2.40168 + 5.67732i) q^{38} +(7.09774 - 2.08585i) q^{40} -3.90666i q^{41} +0.342152 q^{43} +(6.86219 - 1.32366i) q^{44} +(3.18759 - 0.304623i) q^{46} -0.679062i q^{47} -16.1600 q^{49} +(-0.247695 - 2.59189i) q^{50} +(2.94862 - 0.568767i) q^{52} -10.0708 q^{53} -9.13962i q^{55} +(13.0595 - 3.83786i) q^{56} +(0.689928 + 7.21944i) q^{58} +9.15071i q^{59} +2.65473i q^{61} +(-0.232175 - 2.42948i) q^{62} +(-6.72805 + 4.32821i) q^{64} -3.92721i q^{65} +7.37340i q^{67} +(10.4280 - 2.01148i) q^{68} +(-1.69345 - 17.7204i) q^{70} +9.74773 q^{71} -7.16085 q^{73} +(1.38568 + 14.4998i) q^{74} +(-8.31564 - 2.61728i) q^{76} -16.8165i q^{77} +5.21007 q^{79} +(3.89137 + 9.71158i) q^{80} +(5.49980 - 0.525590i) q^{82} +4.80051 q^{83} -13.8889i q^{85} +(0.0460321 + 0.481681i) q^{86} +(2.78667 + 9.48251i) q^{88} -14.0944i q^{89} -7.22588i q^{91} +(0.857696 + 4.44650i) q^{92} +(0.955984 - 0.0913590i) q^{94} +(-5.42059 + 10.0299i) q^{95} -13.2574i q^{97} +(-2.17411 - 22.7500i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4}+O(q^{10}) \) 40 * q - 4 * q^4	\( 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) \) 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Introduction

L-functions

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