LMFDB - Embedded newform 912.3.be.i.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (of order $6$, degree $2$, not 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:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 51 x^{18} + 314 x^{17} + 631 x^{16} - 7264 x^{15} + 8030 x^{14} + 12664 x^{13} + \cdots + 26753228352 $ x^20 - 2x^19 - 51x^18 + 314x^17 + 631x^16 - 7264x^15 + 8030x^14 + 12664x^13 + 393231x^12 - 447686x^11 - 9929427x^10 + 44358366x^9 - 34218119x^8 - 65904712x^7 + 1769085384x^6 - 7530122944x^5 + 6630672896x^4 + 46763900480x^3 - 4377536384x^2 - 53791886208*x + 26753228352
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{22} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.3
Root			$-2.00924 + 3.91523i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.i.673.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(-2.33973 - 4.05253i) q^{5} -3.94782 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(-2.33973 - 4.05253i) q^{5} -3.94782 q^{7} +(1.50000 - 2.59808i) q^{9} +19.3784 q^{11} +(-13.2230 - 7.63431i) q^{13} +(7.01919 + 4.05253i) q^{15} +(0.802147 + 1.38936i) q^{17} +(-10.1147 + 16.0839i) q^{19} +(5.92173 - 3.41891i) q^{21} +(15.9684 - 27.6580i) q^{23} +(1.55133 - 2.68698i) q^{25} +5.19615i q^{27} +(-3.68452 - 2.12726i) q^{29} -7.43590i q^{31} +(-29.0677 + 16.7822i) q^{33} +(9.23684 + 15.9987i) q^{35} -3.72980i q^{37} +26.4460 q^{39} +(-53.4137 + 30.8384i) q^{41} +(28.1611 + 48.7764i) q^{43} -14.0384 q^{45} +(-23.2709 + 40.3064i) q^{47} -33.4147 q^{49} +(-2.40644 - 1.38936i) q^{51} +(-50.8905 - 29.3816i) q^{53} +(-45.3403 - 78.5317i) q^{55} +(1.24302 - 32.8855i) q^{57} +(-55.0501 + 31.7832i) q^{59} +(13.5481 - 23.4660i) q^{61} +(-5.92173 + 10.2567i) q^{63} +71.4489i q^{65} +(-53.4750 - 30.8738i) q^{67} +55.3160i q^{69} +(-62.4861 + 36.0763i) q^{71} +(-18.7010 - 32.3912i) q^{73} +5.37396i q^{75} -76.5026 q^{77} +(-55.7126 + 32.1657i) q^{79} +(-4.50000 - 7.79423i) q^{81} -7.24425 q^{83} +(3.75361 - 6.50145i) q^{85} +7.36904 q^{87} +(-56.2548 - 32.4787i) q^{89} +(52.2021 + 30.1389i) q^{91} +(6.43968 + 11.1538i) q^{93} +(88.8463 + 3.35826i) q^{95} +(127.071 - 73.3643i) q^{97} +(29.0677 - 50.3467i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 30 q^{3} + 4 q^{7} + 30 q^{9}+O(q^{10}) $ 20 * q - 30 * q^3 + 4 * q^7 + 30 * q^9	$ 20 q - 30 q^{3} + 4 q^{7} + 30 q^{9} + 8 q^{11} - 6 q^{13} + 8 q^{17} + 20 q^{19} - 6 q^{21} + 56 q^{23} - 58 q^{25} - 204 q^{29} - 12 q^{33} - 20 q^{35} + 12 q^{39} + 12 q^{41} - 34 q^{43} - 24 q^{47} + 392 q^{49} - 24 q^{51} + 24 q^{55} - 54 q^{57} - 168 q^{59} + 142 q^{61} + 6 q^{63} - 246 q^{67} - 276 q^{71} - 118 q^{73} - 152 q^{77} + 210 q^{79} - 90 q^{81} + 112 q^{83} - 208 q^{85} + 408 q^{87} - 42 q^{91} - 102 q^{93} - 100 q^{95} - 540 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q - 30 * q^3 + 4 * q^7 + 30 * q^9 + 8 * q^11 - 6 * q^13 + 8 * q^17 + 20 * q^19 - 6 * q^21 + 56 * q^23 - 58 * q^25 - 204 * q^29 - 12 * q^33 - 20 * q^35 + 12 * q^39 + 12 * q^41 - 34 * q^43 - 24 * q^47 + 392 * q^49 - 24 * q^51 + 24 * q^55 - 54 * q^57 - 168 * q^59 + 142 * q^61 + 6 * q^63 - 246 * q^67 - 276 * q^71 - 118 * q^73 - 152 * q^77 + 210 * q^79 - 90 * q^81 + 112 * q^83 - 208 * q^85 + 408 * q^87 - 42 * q^91 - 102 * q^93 - 100 * q^95 - 540 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$		0			0
$5$	−2.33973	−	4.05253i	−0.467946	−	0.810506i	0.531383	−	0.847132i	$-0.321672\pi$
$5$	−2.33973	−	4.05253i	−0.467946	−	0.810506i	−0.999329	+	0.0366255i	$0.988339\pi$
$6$		0			0
$7$	−3.94782			−0.563974			−0.281987	−	0.959418i	$-0.590994\pi$
$7$	−3.94782			−0.563974			−0.281987	+	0.959418i	$0.590994\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	19.3784			1.76168			0.880838	−	0.473418i	$-0.156980\pi$
$11$	19.3784			1.76168			0.880838	+	0.473418i	$0.156980\pi$
$12$		0			0
$13$	−13.2230	−	7.63431i	−1.01715	−	0.587254i	−0.103876	−	0.994590i	$-0.533124\pi$
$13$	−13.2230	−	7.63431i	−1.01715	−	0.587254i	−0.913278	+	0.407336i	$0.866458\pi$
$14$		0			0
$15$	7.01919	+	4.05253i	0.467946	+	0.270169i
$16$		0			0
$17$	0.802147	+	1.38936i	0.0471851	+	0.0817270i	0.888653	−	0.458580i	$-0.151642\pi$
$17$	0.802147	+	1.38936i	0.0471851	+	0.0817270i	−0.841468	+	0.540307i	$0.818308\pi$
$18$		0			0
$19$	−10.1147	+	16.0839i	−0.532354	+	0.846522i
$19$	−10.1147	+	16.0839i	−0.532354	+	0.846522i
$20$		0			0
$21$	5.92173	−	3.41891i	0.281987	−	0.162805i
$22$		0			0
$23$	15.9684	−	27.6580i	0.694276	−	1.20252i	−0.276148	−	0.961115i	$-0.589058\pi$
$23$	15.9684	−	27.6580i	0.694276	−	1.20252i	0.970424	−	0.241407i	$-0.0776088\pi$
$24$		0			0
$25$	1.55133	−	2.68698i	0.0620532	−	0.107479i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−3.68452	−	2.12726i	−0.127052	−	0.0733537i	0.435127	−	0.900369i	$-0.356704\pi$
$29$	−3.68452	−	2.12726i	−0.127052	−	0.0733537i	−0.562179	+	0.827015i	$0.690037\pi$
$30$		0			0
$31$		−	7.43590i		−	0.239868i	−0.992782	−	0.119934i	$-0.961732\pi$
$31$		−	7.43590i		−	0.239868i	0.992782	−	0.119934i	$-0.0382682\pi$
$32$		0			0
$33$	−29.0677	+	16.7822i	−0.880838	+	0.508552i
$34$		0			0
$35$	9.23684	+	15.9987i	0.263910	+	0.457105i
$36$		0			0
$37$		−	3.72980i		−	0.100805i	−0.998729	−	0.0504026i	$-0.983950\pi$
$37$		−	3.72980i		−	0.100805i	0.998729	−	0.0504026i	$-0.0160505\pi$
$38$		0			0
$39$	26.4460			0.678103
$40$		0			0
$41$	−53.4137	+	30.8384i	−1.30277	+	0.752157i	−0.980879	−	0.194618i	$-0.937653\pi$
$41$	−53.4137	+	30.8384i	−1.30277	+	0.752157i	−0.321895	+	0.946775i	$0.604320\pi$
$42$		0			0
$43$	28.1611	+	48.7764i	0.654909	+	1.13434i	0.981917	+	0.189314i	$0.0606264\pi$
$43$	28.1611	+	48.7764i	0.654909	+	1.13434i	−0.327008	+	0.945022i	$0.606040\pi$
$44$		0			0
$45$	−14.0384			−0.311964
$46$		0			0
$47$	−23.2709	+	40.3064i	−0.495126	+	0.857584i	−0.999984	−	0.00561857i	$-0.998212\pi$
$47$	−23.2709	+	40.3064i	−0.495126	+	0.857584i	0.504858	+	0.863202i	$0.331545\pi$
$48$		0			0
$49$	−33.4147			−0.681933
$50$		0			0
$51$	−2.40644	−	1.38936i	−0.0471851	−	0.0272423i
$52$		0			0
$53$	−50.8905	−	29.3816i	−0.960198	−	0.554370i	−0.0639637	−	0.997952i	$-0.520374\pi$
$53$	−50.8905	−	29.3816i	−0.960198	−	0.554370i	−0.896234	+	0.443582i	$0.853708\pi$
$54$		0			0
$55$	−45.3403	−	78.5317i	−0.824369	−	1.42785i
$56$		0			0
$57$	1.24302	−	32.8855i	0.0218074	−	0.576938i
$58$		0			0
$59$	−55.0501	+	31.7832i	−0.933052	+	0.538698i	−0.887775	−	0.460277i	$-0.847750\pi$
$59$	−55.0501	+	31.7832i	−0.933052	+	0.538698i	−0.0452763	+	0.998975i	$0.514417\pi$
$60$		0			0
$61$	13.5481	−	23.4660i	0.222100	−	0.384689i	−0.733345	−	0.679856i	$-0.762042\pi$
$61$	13.5481	−	23.4660i	0.222100	−	0.384689i	0.955446	+	0.295167i	$0.0953754\pi$
$62$		0			0
$63$	−5.92173	+	10.2567i	−0.0939957	+	0.162805i
$64$		0			0
$65$			71.4489i			1.09921i
$66$		0			0
$67$	−53.4750	−	30.8738i	−0.798134	−	0.460803i	0.0446842	−	0.999001i	$-0.485772\pi$
$67$	−53.4750	−	30.8738i	−0.798134	−	0.460803i	−0.842818	+	0.538198i	$0.819105\pi$
$68$		0			0
$69$			55.3160i			0.801681i
$70$		0			0
$71$	−62.4861	+	36.0763i	−0.880085	+	0.508118i	−0.870687	−	0.491838i	$-0.836325\pi$
$71$	−62.4861	+	36.0763i	−0.880085	+	0.508118i	−0.00939883	+	0.999956i	$0.502992\pi$
$72$		0			0
$73$	−18.7010	−	32.3912i	−0.256179	−	0.443715i	0.709036	−	0.705172i	$-0.249130\pi$
$73$	−18.7010	−	32.3912i	−0.256179	−	0.443715i	−0.965215	+	0.261457i	$0.915797\pi$
$74$		0			0
$75$			5.37396i			0.0716528i
$76$		0			0
$77$	−76.5026			−0.993540
$78$		0			0
$79$	−55.7126	+	32.1657i	−0.705223	+	0.407160i	−0.809290	−	0.587410i	$-0.800148\pi$
$79$	−55.7126	+	32.1657i	−0.705223	+	0.407160i	0.104067	+	0.994570i	$0.466814\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−7.24425			−0.0872801			−0.0436400	−	0.999047i	$-0.513895\pi$
$83$	−7.24425			−0.0872801			−0.0436400	+	0.999047i	$0.513895\pi$
$84$		0			0
$85$	3.75361	−	6.50145i	0.0441602	−	0.0764877i
$86$		0			0
$87$	7.36904			0.0847016
$88$		0			0
$89$	−56.2548	−	32.4787i	−0.632076	−	0.364929i	0.149480	−	0.988765i	$-0.452240\pi$
$89$	−56.2548	−	32.4787i	−0.632076	−	0.364929i	−0.781556	+	0.623836i	$0.785573\pi$
$90$		0			0
$91$	52.2021	+	30.1389i	0.573649	+	0.331196i
$92$		0			0
$93$	6.43968	+	11.1538i	0.0692438	+	0.119934i
$94$		0			0
$95$	88.8463	+	3.35826i	0.935224	+	0.0353501i
$96$		0			0
$97$	127.071	−	73.3643i	1.31001	−	0.756333i	0.327910	−	0.944709i	$-0.393656\pi$
$97$	127.071	−	73.3643i	1.31001	−	0.756333i	0.982097	+	0.188376i	$0.0603225\pi$
$98$		0			0
$99$	29.0677	−	50.3467i	0.293613	−	0.508552i
$100$		0			0
$101$	−60.9597	+	105.585i	−0.603561	+	1.04540i	0.388716	+	0.921358i	$0.372919\pi$
$101$	−60.9597	+	105.585i	−0.603561	+	1.04540i	−0.992277	+	0.124041i	$0.960415\pi$
$102$		0			0
$103$		−	157.182i		−	1.52604i	−0.646374	−	0.763020i	$-0.723716\pi$
$103$		−	157.182i		−	1.52604i	0.646374	−	0.763020i	$-0.276284\pi$
$104$		0			0
$105$	−27.7105	−	15.9987i	−0.263910	−	0.152368i
$106$		0			0
$107$			173.040i			1.61719i	0.588364	+	0.808597i	$0.299772\pi$
$107$			173.040i			1.61719i	−0.588364	+	0.808597i	$0.700228\pi$
$108$		0			0
$109$	−91.1417	+	52.6207i	−0.836163	+	0.482759i	−0.855958	−	0.517045i	$-0.827032\pi$
$109$	−91.1417	+	52.6207i	−0.836163	+	0.482759i	0.0197954	+	0.999804i	$0.493699\pi$
$110$		0			0
$111$	3.23010	+	5.59469i	0.0291000	+	0.0504026i
$112$		0			0
$113$		−	57.5510i		−	0.509301i	−0.967033	−	0.254650i	$-0.918040\pi$
$113$		−	57.5510i		−	0.509301i	0.967033	−	0.254650i	$-0.0819603\pi$
$114$		0			0
$115$	−149.447			−1.29954
$116$		0			0
$117$	−39.6690	+	22.9029i	−0.339051	+	0.195751i
$118$		0			0
$119$	−3.16673	−	5.48494i	−0.0266112	−	0.0460920i
$120$		0			0
$121$	254.524			2.10350
$122$		0			0
$123$	53.4137	−	92.5153i	0.434258	−	0.752157i
$124$		0			0
$125$	−131.505			−1.05204
$126$		0			0
$127$	−65.9889	−	38.0987i	−0.519597	−	0.299990i	0.217173	−	0.976133i	$-0.430317\pi$
$127$	−65.9889	−	38.0987i	−0.519597	−	0.299990i	−0.736770	+	0.676144i	$0.763650\pi$
$128$		0			0
$129$	−84.4833	−	48.7764i	−0.654909	−	0.378112i
$130$		0			0
$131$	−113.903	−	197.286i	−0.869491	−	1.50600i	−0.862518	−	0.506027i	$-0.831114\pi$
$131$	−113.903	−	197.286i	−0.869491	−	1.50600i	−0.00697352	−	0.999976i	$-0.502220\pi$
$132$		0			0
$133$	39.9312	−	63.4964i	0.300234	−	0.477417i
$134$		0			0
$135$	21.0576	−	12.1576i	0.155982	−	0.0900562i
$136$		0			0
$137$	51.4290	−	89.0777i	0.375394	−	0.650202i	−0.614992	−	0.788534i	$-0.710841\pi$
$137$	51.4290	−	89.0777i	0.375394	−	0.650202i	0.990386	+	0.138331i	$0.0441739\pi$
$138$		0			0
$139$	−119.474	+	206.935i	−0.859523	+	1.48874i	0.0128609	+	0.999917i	$0.495906\pi$
$139$	−119.474	+	206.935i	−0.859523	+	1.48874i	−0.872384	+	0.488821i	$0.837427\pi$
$140$		0			0
$141$		−	80.6129i		−	0.571723i
$142$		0			0
$143$	−256.241	−	147.941i	−1.79190	−	1.03455i
$144$		0			0
$145$			19.9088i			0.137302i
$146$		0			0
$147$	50.1221	−	28.9380i	0.340966	−	0.196857i
$148$		0			0
$149$	61.0326	+	105.712i	0.409615	+	0.709473i	0.994846	−	0.101393i	$-0.0323299\pi$
$149$	61.0326	+	105.712i	0.409615	+	0.709473i	−0.585232	+	0.810866i	$0.698997\pi$
$150$		0			0
$151$			27.9696i			0.185229i	0.995702	+	0.0926146i	$0.0295224\pi$
$151$			27.9696i			0.185229i	−0.995702	+	0.0926146i	$0.970478\pi$
$152$		0			0
$153$	4.81288			0.0314567
$154$		0			0
$155$	−30.1342	+	17.3980i	−0.194414	+	0.112245i
$156$		0			0
$157$	140.481	+	243.321i	0.894785	+	1.54981i	0.834071	+	0.551657i	$0.186004\pi$
$157$	140.481	+	243.321i	0.894785	+	1.54981i	0.0607139	+	0.998155i	$0.480662\pi$
$158$		0			0
$159$	101.781			0.640132
$160$		0			0
$161$	−63.0402	+	109.189i	−0.391554	+	0.678192i
$162$		0			0
$163$	−156.155			−0.958009			−0.479004	−	0.877813i	$-0.659002\pi$
$163$	−156.155			−0.958009			−0.479004	+	0.877813i	$0.659002\pi$
$164$		0			0
$165$	136.021	+	78.5317i	0.824369	+	0.475950i
$166$		0			0
$167$	−165.655	−	95.6412i	−0.991949	−	0.572702i	−0.0860926	−	0.996287i	$-0.527438\pi$
$167$	−165.655	−	95.6412i	−0.991949	−	0.572702i	−0.905856	+	0.423585i	$0.860771\pi$
$168$		0			0
$169$	32.0653	+	55.5386i	0.189735	+	0.328631i
$170$		0			0
$171$	26.6151	+	50.4047i	0.155644	+	0.294764i
$172$		0			0
$173$	79.9046	−	46.1329i	0.461876	−	0.266664i	−0.250957	−	0.967998i	$-0.580745\pi$
$173$	79.9046	−	46.1329i	0.461876	−	0.266664i	0.712833	+	0.701334i	$0.247412\pi$
$174$		0			0
$175$	−6.12437	+	10.6077i	−0.0349964	+	0.0606156i
$176$		0			0
$177$	55.0501	−	95.3495i	0.311017	−	0.538698i
$178$		0			0
$179$			239.687i			1.33904i	0.742796	+	0.669518i	$0.233499\pi$
$179$			239.687i			1.33904i	−0.742796	+	0.669518i	$0.766501\pi$
$180$		0			0
$181$	−164.571	−	95.0153i	−0.909234	−	0.524946i	−0.0290491	−	0.999578i	$-0.509248\pi$
$181$	−164.571	−	95.0153i	−0.909234	−	0.524946i	−0.880184	+	0.474632i	$0.842581\pi$
$182$		0			0
$183$			46.9321i			0.256459i
$184$		0			0
$185$	−15.1151	+	8.72671i	−0.0817033	+	0.0471714i
$186$		0			0
$187$	15.5444	+	26.9236i	0.0831249	+	0.143977i
$188$		0			0
$189$		−	20.5135i		−	0.108537i
$190$		0			0
$191$	276.040			1.44523			0.722617	−	0.691249i	$-0.242939\pi$
$191$	276.040			1.44523			0.722617	+	0.691249i	$0.242939\pi$
$192$		0			0
$193$	144.476	−	83.4131i	0.748579	−	0.432192i	−0.0766010	−	0.997062i	$-0.524407\pi$
$193$	144.476	−	83.4131i	0.748579	−	0.432192i	0.825180	+	0.564869i	$0.191073\pi$
$194$		0			0
$195$	−61.8765	−	107.173i	−0.317315	−	0.549607i
$196$		0			0
$197$	15.7356			0.0798761			0.0399381	−	0.999202i	$-0.487284\pi$
$197$	15.7356			0.0798761			0.0399381	+	0.999202i	$0.487284\pi$
$198$		0			0
$199$	−33.1412	+	57.4022i	−0.166539	+	0.288453i	−0.937201	−	0.348791i	$-0.886592\pi$
$199$	−33.1412	+	57.4022i	−0.166539	+	0.288453i	0.770662	+	0.637244i	$0.219926\pi$
$200$		0			0
$201$	106.950			0.532089
$202$		0			0
$203$	14.5458	+	8.39803i	0.0716543	+	0.0413696i
$204$		0			0
$205$	249.947	+	144.307i	1.21926	+	0.703938i
$206$		0			0
$207$	−47.9051	−	82.9740i	−0.231425	−	0.400841i
$208$		0			0
$209$	−196.008	+	311.681i	−0.937836	+	1.49130i
$210$		0			0
$211$	5.26033	−	3.03705i	0.0249305	−	0.0143936i	−0.487483	−	0.873132i	$-0.662085\pi$
$211$	5.26033	−	3.03705i	0.0249305	−	0.0143936i	0.512413	+	0.858739i	$0.328752\pi$
$212$		0			0
$213$	62.4861	−	108.229i	0.293362	−	0.508118i
$214$		0			0
$215$	131.779	−	228.247i	0.612924	−	1.06162i
$216$		0			0
$217$			29.3556i			0.135279i
$218$		0			0
$219$	56.1031	+	32.3912i	0.256179	+	0.147905i
$220$		0			0
$221$		−	24.4953i		−	0.110839i
$222$		0			0
$223$	200.656	−	115.849i	0.899801	−	0.519500i	0.0226655	−	0.999743i	$-0.492785\pi$
$223$	200.656	−	115.849i	0.899801	−	0.519500i	0.877136	+	0.480243i	$0.159451\pi$
$224$		0			0
$225$	−4.65399	−	8.06094i	−0.0206844	−	0.0358264i
$226$		0			0
$227$			159.880i			0.704316i	0.935941	+	0.352158i	$0.114552\pi$
$227$			159.880i			0.704316i	−0.935941	+	0.352158i	$0.885448\pi$
$228$		0			0
$229$	−50.8060			−0.221860			−0.110930	−	0.993828i	$-0.535383\pi$
$229$	−50.8060			−0.221860			−0.110930	+	0.993828i	$0.535383\pi$
$230$		0			0
$231$	114.754	−	66.2532i	0.496770	−	0.286810i
$232$		0			0
$233$	89.4791	+	154.982i	0.384031	+	0.665160i	0.991634	−	0.129080i	$-0.0412024\pi$
$233$	89.4791	+	154.982i	0.384031	+	0.665160i	−0.607604	+	0.794240i	$0.707869\pi$
$234$		0			0
$235$	217.791			0.926769
$236$		0			0
$237$	55.7126	−	96.4970i	0.235074	−	0.407160i
$238$		0			0
$239$	230.403			0.964029			0.482015	−	0.876163i	$-0.339905\pi$
$239$	230.403			0.964029			0.482015	+	0.876163i	$0.339905\pi$
$240$		0			0
$241$	49.3942	+	28.5178i	0.204955	+	0.118331i	0.598965	−	0.800775i	$-0.295579\pi$
$241$	49.3942	+	28.5178i	0.204955	+	0.118331i	−0.394009	+	0.919106i	$0.628912\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$	78.1814	+	135.414i	0.319108	+	0.552711i
$246$		0			0
$247$	256.537	−	135.459i	1.03861	−	0.548416i
$248$		0			0
$249$	10.8664	−	6.27370i	0.0436400	−	0.0251956i
$250$		0			0
$251$	−132.396	+	229.317i	−0.527475	+	0.913613i	0.472012	+	0.881592i	$0.343528\pi$
$251$	−132.396	+	229.317i	−0.527475	+	0.913613i	−0.999487	+	0.0320214i	$0.989806\pi$
$252$		0			0
$253$	309.442	−	535.969i	1.22309	−	2.11845i
$254$		0			0
$255$			13.0029i			0.0509918i
$256$		0			0
$257$	−336.523	−	194.291i	−1.30943	−	0.755998i	−0.327426	−	0.944877i	$-0.606181\pi$
$257$	−336.523	−	194.291i	−1.30943	−	0.755998i	−0.982000	+	0.188879i	$0.939515\pi$
$258$		0			0
$259$			14.7246i			0.0568516i
$260$		0			0
$261$	−11.0536	+	6.38177i	−0.0423508	+	0.0244512i
$262$		0			0
$263$	178.514	+	309.195i	0.678759	+	1.17565i	0.975355	+	0.220642i	$0.0708152\pi$
$263$	178.514	+	309.195i	0.678759	+	1.17565i	−0.296596	+	0.955003i	$0.595851\pi$
$264$		0			0
$265$			274.980i			1.03766i
$266$		0			0
$267$	112.510			0.421384
$268$		0			0
$269$	57.3739	−	33.1249i	0.213286	−	0.123141i	−0.389552	−	0.921005i	$-0.627370\pi$
$269$	57.3739	−	33.1249i	0.213286	−	0.123141i	0.602838	+	0.797864i	$0.294037\pi$
$270$		0			0
$271$	104.603	+	181.178i	0.385990	+	0.668554i	0.991906	−	0.126975i	$-0.0405267\pi$
$271$	104.603	+	181.178i	0.385990	+	0.668554i	−0.605916	+	0.795528i	$0.707193\pi$
$272$		0			0
$273$	−104.404			−0.382433
$274$		0			0
$275$	30.0623	−	52.0695i	0.109318	−	0.189344i
$276$		0			0
$277$	−378.194			−1.36532			−0.682662	−	0.730735i	$-0.739178\pi$
$277$	−378.194			−1.36532			−0.682662	+	0.730735i	$0.739178\pi$
$278$		0			0
$279$	−19.3190	−	11.1538i	−0.0692438	−	0.0399780i
$280$		0			0
$281$	130.762	+	75.4952i	0.465343	+	0.268666i	0.714288	−	0.699851i	$-0.246750\pi$
$281$	130.762	+	75.4952i	0.465343	+	0.268666i	−0.248945	+	0.968518i	$0.580084\pi$
$282$		0			0
$283$	−5.64143	−	9.77125i	−0.0199344	−	0.0345274i	0.855886	−	0.517164i	$-0.173012\pi$
$283$	−5.64143	−	9.77125i	−0.0199344	−	0.0345274i	−0.875821	+	0.482637i	$0.839679\pi$
$284$		0			0
$285$	−136.178	+	71.9058i	−0.477817	+	0.252301i
$286$		0			0
$287$	210.868	−	121.745i	0.734731	−	0.424197i
$288$		0			0
$289$	143.213	−	248.052i	0.495547	−	0.858313i
$290$		0			0
$291$	−127.071	+	220.093i	−0.436669	+	0.756333i
$292$		0			0
$293$		−	284.454i		−	0.970834i	−0.874283	−	0.485417i	$-0.838668\pi$
$293$		−	284.454i		−	0.970834i	0.874283	−	0.485417i	$-0.161332\pi$
$294$		0			0
$295$	257.604	+	148.728i	0.873236	+	0.504163i
$296$		0			0
$297$			100.693i			0.339035i
$298$		0			0
$299$	−422.299	+	243.815i	−1.41237	+	0.815434i
$300$		0			0
$301$	−111.175	−	192.561i	−0.369352	−	0.639736i
$302$		0			0
$303$		−	211.171i		−	0.696933i
$304$		0			0
$305$	−126.796			−0.415724
$306$		0			0
$307$	470.039	−	271.377i	1.53107	−	0.883964i	0.531757	−	0.846897i	$-0.321532\pi$
$307$	470.039	−	271.377i	1.53107	−	0.883964i	0.999313	−	0.0370670i	$-0.0118015\pi$
$308$		0			0
$309$	136.124	+	235.773i	0.440530	+	0.763020i
$310$		0			0
$311$	−462.767			−1.48800			−0.743998	−	0.668182i	$-0.767073\pi$
$311$	−462.767			−1.48800			−0.743998	+	0.668182i	$0.767073\pi$
$312$		0			0
$313$	77.0082	−	133.382i	0.246033	−	0.426141i	−0.716389	−	0.697701i	$-0.754206\pi$
$313$	77.0082	−	133.382i	0.246033	−	0.426141i	0.962421	+	0.271560i	$0.0875396\pi$
$314$		0			0
$315$	55.4210			0.175940
$316$		0			0
$317$	−62.9859	−	36.3649i	−0.198694	−	0.114716i	0.397352	−	0.917666i	$-0.369929\pi$
$317$	−62.9859	−	36.3649i	−0.198694	−	0.114716i	−0.596046	+	0.802950i	$0.703262\pi$
$318$		0			0
$319$	−71.4002	−	41.2229i	−0.223825	−	0.129225i
$320$		0			0
$321$	−149.857	−	259.559i	−0.466843	−	0.808597i
$322$		0			0
$323$	−30.4598	−	1.15134i	−0.0943029	−	0.00356451i
$324$		0			0
$325$	−41.0265	+	23.6866i	−0.126235	+	0.0728820i
$326$		0			0
$327$	91.1417	−	157.862i	0.278721	−	0.482759i
$328$		0			0
$329$	91.8695	−	159.123i	0.279239	−	0.483655i
$330$		0			0
$331$		−	538.875i		−	1.62802i	−0.580850	−	0.814011i	$-0.697280\pi$
$331$		−	538.875i		−	1.62802i	0.580850	−	0.814011i	$-0.302720\pi$
$332$		0			0
$333$	−9.69029	−	5.59469i	−0.0291000	−	0.0168009i
$334$		0			0
$335$			288.945i			0.862523i
$336$		0			0
$337$	−163.217	+	94.2337i	−0.484325	+	0.279625i	−0.722217	−	0.691666i	$-0.756877\pi$
$337$	−163.217	+	94.2337i	−0.484325	+	0.279625i	0.237892	+	0.971292i	$0.423544\pi$
$338$		0			0
$339$	49.8406	+	86.3264i	0.147022	+	0.254650i
$340$		0			0
$341$		−	144.096i		−	0.422569i
$342$		0			0
$343$	325.359			0.948567
$344$		0			0
$345$	224.170	−	129.425i	0.649768	−	0.375144i
$346$		0			0
$347$	50.2667	+	87.0645i	0.144861	+	0.250906i	0.929321	−	0.369273i	$-0.120393\pi$
$347$	50.2667	+	87.0645i	0.144861	+	0.250906i	−0.784460	+	0.620179i	$0.787060\pi$
$348$		0			0
$349$	−94.2449			−0.270043			−0.135021	−	0.990843i	$-0.543110\pi$
$349$	−94.2449			−0.270043			−0.135021	+	0.990843i	$0.543110\pi$
$350$		0			0
$351$	39.6690	−	68.7088i	0.113017	−	0.195751i
$352$		0			0
$353$	218.637			0.619368			0.309684	−	0.950840i	$-0.399777\pi$
$353$	218.637			0.619368			0.309684	+	0.950840i	$0.399777\pi$
$354$		0			0
$355$	292.401	+	168.818i	0.823665	+	0.475543i
$356$		0			0
$357$	9.50020	+	5.48494i	0.0266112	+	0.0153640i
$358$		0			0
$359$	−142.528	−	246.866i	−0.397014	−	0.687648i	0.596342	−	0.802730i	$-0.296620\pi$
$359$	−142.528	−	246.866i	−0.397014	−	0.687648i	−0.993356	+	0.115082i	$0.963287\pi$
$360$		0			0
$361$	−156.384	−	325.369i	−0.433198	−	0.901299i
$362$		0			0
$363$	−381.786	+	220.424i	−1.05175	+	0.607229i
$364$		0			0
$365$	−87.5108	+	151.573i	−0.239756	+	0.415269i
$366$		0			0
$367$	211.429	−	366.206i	0.576101	−	0.997836i	−0.419820	−	0.907607i	$-0.637907\pi$
$367$	211.429	−	366.206i	0.576101	−	0.997836i	0.995921	−	0.0902289i	$-0.0287599\pi$
$368$		0			0
$369$			185.031i			0.501438i
$370$		0			0
$371$	200.906	+	115.993i	0.541527	+	0.312651i
$372$		0			0
$373$		−	112.822i		−	0.302473i	−0.988498	−	0.151237i	$-0.951674\pi$
$373$		−	112.822i		−	0.302473i	0.988498	−	0.151237i	$-0.0483255\pi$
$374$		0			0
$375$	197.258	−	113.887i	0.526021	−	0.303698i
$376$		0			0
$377$	32.4803	+	56.2575i	0.0861546	+	0.149224i
$378$		0			0
$379$		−	149.551i		−	0.394594i	−0.980344	−	0.197297i	$-0.936784\pi$
$379$		−	149.551i		−	0.394594i	0.980344	−	0.197297i	$-0.0632164\pi$
$380$		0			0
$381$	131.978			0.346398
$382$		0			0
$383$	391.265	−	225.897i	1.02158	−	0.589809i	0.107019	−	0.994257i	$-0.465870\pi$
$383$	391.265	−	225.897i	1.02158	−	0.589809i	0.914561	+	0.404448i	$0.132536\pi$
$384$		0			0
$385$	178.995	+	310.029i	0.464923	+	0.805271i
$386$		0			0
$387$	168.967			0.436606
$388$		0			0
$389$	126.626	−	219.322i	0.325516	−	0.563811i	−0.656100	−	0.754674i	$-0.727795\pi$
$389$	126.626	−	219.322i	0.325516	−	0.563811i	0.981617	+	0.190863i	$0.0611285\pi$
$390$		0			0
$391$	51.2359			0.131038
$392$		0			0
$393$	341.710	+	197.286i	0.869491	+	0.502001i
$394$		0			0
$395$	260.705	+	150.518i	0.660012	+	0.381058i
$396$		0			0
$397$	150.685	+	260.994i	0.379559	+	0.657416i	0.990998	−	0.133876i	$-0.0427424\pi$
$397$	150.685	+	260.994i	0.379559	+	0.657416i	−0.611439	+	0.791292i	$0.709409\pi$
$398$		0			0
$399$	−4.90723	+	129.826i	−0.0122988	+	0.325378i
$400$		0			0
$401$	−561.563	+	324.219i	−1.40041	+	0.808526i	−0.994434	−	0.105359i	$-0.966401\pi$
$401$	−561.563	+	324.219i	−1.40041	+	0.808526i	−0.405973	+	0.913885i	$0.633067\pi$
$402$		0			0
$403$	−56.7679	+	98.3249i	−0.140863	+	0.243982i
$404$		0			0
$405$	−21.0576	+	36.4728i	−0.0519940	+	0.0900562i
$406$		0			0
$407$		−	72.2776i		−	0.177586i
$408$		0			0
$409$	−212.163	−	122.493i	−0.518737	−	0.299493i	0.217681	−	0.976020i	$-0.430151\pi$
$409$	−212.163	−	122.493i	−0.518737	−	0.299493i	−0.736418	+	0.676527i	$0.763484\pi$
$410$		0			0
$411$			178.155i			0.433468i
$412$		0			0
$413$	217.328	−	125.474i	0.526217	−	0.303812i
$414$		0			0
$415$	16.9496	+	29.3575i	0.0408424	+	0.0707410i
$416$		0			0
$417$		−	413.869i		−	0.992492i
$418$		0			0
$419$	14.9585			0.0357004			0.0178502	−	0.999841i	$-0.494318\pi$
$419$	14.9585			0.0357004			0.0178502	+	0.999841i	$0.494318\pi$
$420$		0			0
$421$	−139.721	+	80.6681i	−0.331879	+	0.191611i	−0.656675	−	0.754173i	$-0.728038\pi$
$421$	−139.721	+	80.6681i	−0.331879	+	0.191611i	0.324796	+	0.945784i	$0.394704\pi$
$422$		0			0
$423$	69.8128	+	120.919i	0.165042	+	0.285861i
$424$		0			0
$425$	4.97758			0.0117119
$426$		0			0
$427$	−53.4856	+	92.6397i	−0.125259	+	0.216955i
$428$		0			0
$429$	512.482			1.19460
$430$		0			0
$431$	−681.099	−	393.233i	−1.58028	−	0.912373i	−0.994818	−	0.101670i	$-0.967581\pi$
$431$	−681.099	−	393.233i	−1.58028	−	0.912373i	−0.585458	−	0.810703i	$-0.699085\pi$
$432$		0			0
$433$	−566.404	−	327.014i	−1.30809	−	0.755228i	−0.326315	−	0.945261i	$-0.605807\pi$
$433$	−566.404	−	327.014i	−1.30809	−	0.755228i	−0.981778	+	0.190033i	$0.939140\pi$
$434$		0			0
$435$	−17.2416	−	29.8633i	−0.0396358	−	0.0686512i
$436$		0			0
$437$	283.333	+	536.587i	0.648360	+	1.22789i
$438$		0			0
$439$	445.258	−	257.070i	1.01426	−	0.585581i	0.101820	−	0.994803i	$-0.467533\pi$
$439$	445.258	−	257.070i	1.01426	−	0.585581i	0.912435	+	0.409222i	$0.134200\pi$
$440$		0			0
$441$	−50.1221	+	86.8140i	−0.113655	+	0.196857i
$442$		0			0
$443$	−96.8769	+	167.796i	−0.218684	+	0.378771i	−0.954406	−	0.298512i	$-0.903510\pi$
$443$	−96.8769	+	167.796i	−0.218684	+	0.378771i	0.735722	+	0.677284i	$0.236843\pi$
$444$		0			0
$445$			303.966i			0.683069i
$446$		0			0
$447$	−183.098	−	105.712i	−0.409615	−	0.236491i
$448$		0			0
$449$		−	133.827i		−	0.298056i	−0.988833	−	0.149028i	$-0.952386\pi$
$449$		−	133.827i		−	0.298056i	0.988833	−	0.149028i	$-0.0476145\pi$
$450$		0			0
$451$	−1035.07	+	597.601i	−2.29507	+	1.32506i
$452$		0			0
$453$	−24.2224	−	41.9544i	−0.0534710	−	0.0926146i
$454$		0			0
$455$		−	282.067i		−	0.619928i
$456$		0			0
$457$	−523.362			−1.14521			−0.572606	−	0.819831i	$-0.694068\pi$
$457$	−523.362			−1.14521			−0.572606	+	0.819831i	$0.694068\pi$
$458$		0			0
$459$	−7.21932	+	4.16808i	−0.0157284	+	0.00908078i
$460$		0			0
$461$	−50.7350	−	87.8756i	−0.110054	−	0.190620i	0.805738	−	0.592273i	$-0.201769\pi$
$461$	−50.7350	−	87.8756i	−0.110054	−	0.190620i	−0.915792	+	0.401653i	$0.868436\pi$
$462$		0			0
$463$	−847.358			−1.83015			−0.915074	−	0.403286i	$-0.867868\pi$
$463$	−847.358			−1.83015			−0.915074	+	0.403286i	$0.867868\pi$
$464$		0			0
$465$	30.1342	−	52.1940i	0.0648048	−	0.112245i
$466$		0			0
$467$	75.6277			0.161944			0.0809718	−	0.996716i	$-0.474198\pi$
$467$	75.6277			0.161944			0.0809718	+	0.996716i	$0.474198\pi$
$468$		0			0
$469$	211.110	+	121.884i	0.450127	+	0.259881i
$470$		0			0
$471$	−421.444	−	243.321i	−0.894785	−	0.516604i
$472$		0			0
$473$	545.718	+	945.211i	1.15374	+	1.99833i
$474$		0			0
$475$	27.5259	+	52.1295i	0.0579492	+	0.109746i
$476$		0			0
$477$	−152.671	+	88.1449i	−0.320066	+	0.184790i
$478$		0			0
$479$	−246.600	+	427.125i	−0.514824	+	0.891701i	0.485028	+	0.874498i	$0.338809\pi$
$479$	−246.600	+	427.125i	−0.514824	+	0.891701i	−0.999852	+	0.0172022i	$0.994524\pi$
$480$		0			0
$481$	−28.4744	+	49.3191i	−0.0591983	+	0.102535i
$482$		0			0
$483$		−	218.378i		−	0.452128i
$484$		0			0
$485$	−594.622	−	343.305i	−1.22602	−	0.707846i
$486$		0			0
$487$		−	431.748i		−	0.886546i	−0.896387	−	0.443273i	$-0.853817\pi$
$487$		−	431.748i		−	0.886546i	0.896387	−	0.443273i	$-0.146183\pi$
$488$		0			0
$489$	234.233	−	135.235i	0.479004	−	0.276553i
$490$		0			0
$491$	38.0053	+	65.8272i	0.0774040	+	0.134068i	0.902129	−	0.431466i	$-0.142004\pi$
$491$	38.0053	+	65.8272i	0.0774040	+	0.134068i	−0.824725	+	0.565534i	$0.808670\pi$
$492$		0			0
$493$		−	6.82549i		−	0.0138448i
$494$		0			0
$495$	−272.042			−0.549579
$496$		0			0
$497$	246.684	−	142.423i	0.496346	−	0.286565i
$498$		0			0
$499$	458.229	+	793.676i	0.918295	+	1.59053i	0.802005	+	0.597318i	$0.203767\pi$
$499$	458.229	+	793.676i	0.918295	+	1.59053i	0.116290	+	0.993215i	$0.462900\pi$
$500$		0			0
$501$	331.311			0.661299
$502$		0			0
$503$	−164.601	+	285.098i	−0.327240	+	0.566795i	−0.981963	−	0.189073i	$-0.939452\pi$
$503$	−164.601	+	285.098i	−0.327240	+	0.566795i	0.654724	+	0.755868i	$0.272785\pi$
$504$		0			0
$505$	570.517			1.12974
$506$		0			0
$507$	−96.1958	−	55.5386i	−0.189735	−	0.109544i
$508$		0			0
$509$	−520.177	−	300.324i	−1.02196	−	0.590028i	−0.107287	−	0.994228i	$-0.534216\pi$
$509$	−520.177	−	300.324i	−1.02196	−	0.590028i	−0.914670	+	0.404200i	$0.867550\pi$
$510$		0			0
$511$	73.8284	+	127.875i	0.144478	+	0.250244i
$512$		0			0
$513$	−83.5745	−	52.5577i	−0.162913	−	0.102452i
$514$		0			0
$515$	−636.986	+	367.764i	−1.23687	+	0.714105i
$516$		0			0
$517$	−450.954	+	781.076i	−0.872252	+	1.51078i
$518$		0			0
$519$	−79.9046	+	138.399i	−0.153959	+	0.266664i
$520$		0			0
$521$			960.062i			1.84273i	0.388698	+	0.921365i	$0.372925\pi$
$521$			960.062i			1.84273i	−0.388698	+	0.921365i	$0.627075\pi$
$522$		0			0
$523$	580.646	+	335.236i	1.11022	+	0.640986i	0.938887	−	0.344227i	$-0.111859\pi$
$523$	580.646	+	335.236i	1.11022	+	0.640986i	0.171334	+	0.985213i	$0.445192\pi$
$524$		0			0
$525$		−	21.2154i		−	0.0404104i
$526$		0			0
$527$	10.3311	−	5.96468i	0.0196037	−	0.0113182i
$528$		0			0
$529$	−245.477	−	425.179i	−0.464040	−	0.803740i
$530$		0			0
$531$			190.699i			0.359132i
$532$		0			0
$533$	941.720			1.76683
$534$		0			0
$535$	701.249	−	404.866i	1.31074	−	0.756759i
$536$		0			0
$537$	−207.575	−	359.531i	−0.386546	−	0.669518i
$538$		0			0
$539$	−647.525			−1.20134
$540$		0			0
$541$	381.031	−	659.964i	0.704308	−	1.21990i	−0.262633	−	0.964896i	$-0.584591\pi$
$541$	381.031	−	659.964i	0.704308	−	1.21990i	0.966941	−	0.255001i	$-0.0820759\pi$
$542$		0			0
$543$	329.143			0.606156
$544$		0			0
$545$	426.494	+	246.236i	0.782558	+	0.451810i
$546$		0			0
$547$	246.215	+	142.152i	0.450119	+	0.259876i	0.707880	−	0.706332i	$-0.249652\pi$
$547$	246.215	+	142.152i	0.450119	+	0.259876i	−0.257762	+	0.966209i	$0.582985\pi$
$548$		0			0
$549$	−40.6444	−	70.3981i	−0.0740334	−	0.128230i
$550$		0			0
$551$	71.4825	−	37.7448i	0.129732	−	0.0685024i
$552$		0			0
$553$	219.943	−	126.984i	0.397728	−	0.229628i
$554$		0			0
$555$	15.1151	−	26.1801i	0.0272344	−	0.0471714i
$556$		0			0
$557$	366.164	−	634.214i	0.657386	−	1.13863i	−0.323904	−	0.946090i	$-0.604996\pi$
$557$	366.164	−	634.214i	0.657386	−	1.13863i	0.981290	−	0.192536i	$-0.0616711\pi$
$558$		0			0
$559$		−	859.961i		−	1.53839i
$560$		0			0
$561$	−46.6331	−	26.9236i	−0.0831249	−	0.0479922i
$562$		0			0
$563$		−	420.289i		−	0.746516i	−0.927728	−	0.373258i	$-0.878241\pi$
$563$		−	420.289i		−	0.746516i	0.927728	−	0.373258i	$-0.121759\pi$
$564$		0			0
$565$	−233.227	+	134.654i	−0.412791	+	0.238325i
$566$		0			0
$567$	17.7652	+	30.7702i	0.0313319	+	0.0542685i
$568$		0			0
$569$		−	75.1265i		−	0.132033i	−0.997819	−	0.0660163i	$-0.978971\pi$
$569$		−	75.1265i		−	0.132033i	0.997819	−	0.0660163i	$-0.0210289\pi$
$570$		0			0
$571$	166.499			0.291592			0.145796	−	0.989315i	$-0.453426\pi$
$571$	166.499			0.291592			0.145796	+	0.989315i	$0.453426\pi$
$572$		0			0
$573$	−414.059	+	239.057i	−0.722617	+	0.417203i
$574$		0			0
$575$	−49.5444	−	85.8134i	−0.0861641	−	0.149241i
$576$		0			0
$577$	−663.313			−1.14959			−0.574795	−	0.818298i	$-0.694918\pi$
$577$	−663.313			−1.14959			−0.574795	+	0.818298i	$0.694918\pi$
$578$		0			0
$579$	−144.476	+	250.239i	−0.249526	+	0.432192i
$580$		0			0
$581$	28.5990			0.0492237
$582$		0			0
$583$	−986.178	−	569.370i	−1.69156	−	0.976621i
$584$		0			0
$585$	185.630	+	107.173i	0.317315	+	0.183202i
$586$		0			0
$587$	−418.538	−	724.929i	−0.713012	−	1.23497i	−0.963721	−	0.266910i	$-0.913997\pi$
$587$	−418.538	−	724.929i	−0.713012	−	1.23497i	0.250710	−	0.968062i	$-0.419336\pi$
$588$		0			0
$589$	119.598	+	75.2121i	0.203053	+	0.127695i
$590$		0			0
$591$	−23.6034	+	13.6274i	−0.0399381	+	0.0230583i
$592$		0			0
$593$	−43.7134	+	75.7139i	−0.0737157	+	0.127679i	−0.900527	−	0.434800i	$-0.856819\pi$
$593$	−43.7134	+	75.7139i	−0.0737157	+	0.127679i	0.826811	+	0.562479i	$0.190152\pi$
$594$		0			0
$595$	−14.8186	+	25.6666i	−0.0249052	+	0.0431371i
$596$		0			0
$597$		−	114.804i		−	0.192302i
$598$		0			0
$599$	−252.242	−	145.632i	−0.421105	−	0.243125i	0.274445	−	0.961603i	$-0.411506\pi$
$599$	−252.242	−	145.632i	−0.421105	−	0.243125i	−0.695550	+	0.718478i	$0.744839\pi$
$600$		0			0
$601$			103.857i			0.172808i	0.996260	+	0.0864038i	$0.0275375\pi$
$601$			103.857i			0.172808i	−0.996260	+	0.0864038i	$0.972462\pi$
$602$		0			0
$603$	−160.425	+	92.6214i	−0.266045	+	0.153601i
$604$		0			0
$605$	−595.517	−	1031.47i	−0.984325	−	1.70490i
$606$		0			0
$607$			655.928i			1.08061i	0.841471	+	0.540303i	$0.181690\pi$
$607$			655.928i			1.08061i	−0.841471	+	0.540303i	$0.818310\pi$
$608$		0			0
$609$	−29.0916			−0.0477695
$610$		0			0
$611$	615.423	−	355.315i	1.00724	−	0.581530i
$612$		0			0
$613$	436.652	+	756.304i	0.712320	+	1.23378i	0.963984	+	0.265960i	$0.0856890\pi$
$613$	436.652	+	756.304i	0.712320	+	1.23378i	−0.251664	+	0.967815i	$0.580978\pi$
$614$		0			0
$615$	−499.895			−0.812837
$616$		0			0
$617$	−246.350	+	426.690i	−0.399270	+	0.691556i	−0.993636	−	0.112639i	$-0.964070\pi$
$617$	−246.350	+	426.690i	−0.399270	+	0.691556i	0.594366	+	0.804195i	$0.297403\pi$
$618$		0			0
$619$	−404.540			−0.653537			−0.326769	−	0.945104i	$-0.605960\pi$
$619$	−404.540			−0.653537			−0.326769	+	0.945104i	$0.605960\pi$
$620$		0			0
$621$	143.715	+	82.9740i	0.231425	+	0.133614i
$622$		0			0
$623$	222.084	+	128.220i	0.356475	+	0.205811i
$624$		0			0
$625$	268.904	+	465.755i	0.430246	+	0.745207i
$626$		0			0
$627$	24.0878	−	637.269i	0.0384176	−	1.01638i
$628$		0			0
$629$	5.18203	−	2.99184i	0.00823852	−	0.00475651i
$630$		0			0
$631$	270.126	−	467.872i	0.428092	−	0.741477i	−0.568611	−	0.822606i	$-0.692519\pi$
$631$	270.126	−	467.872i	0.428092	−	0.741477i	0.996704	+	0.0811289i	$0.0258525\pi$
$632$		0			0
$633$	−5.26033	+	9.11116i	−0.00831016	+	0.0143936i
$634$		0			0
$635$			356.563i			0.561516i
$636$		0			0
$637$	441.843	+	255.098i	0.693631	+	0.400468i
$638$		0			0
$639$			216.458i			0.338745i
$640$		0			0
$641$	872.388	−	503.673i	1.36098	−	0.785762i	0.371225	−	0.928543i	$-0.378938\pi$
$641$	872.388	−	503.673i	1.36098	−	0.785762i	0.989754	+	0.142781i	$0.0456046\pi$
$642$		0			0
$643$	−383.801	−	664.763i	−0.596891	−	1.03385i	−0.993277	−	0.115762i	$-0.963069\pi$
$643$	−383.801	−	664.763i	−0.596891	−	1.03385i	0.396386	−	0.918084i	$-0.370264\pi$
$644$		0			0
$645$			456.495i			0.707744i
$646$		0			0
$647$	−962.536			−1.48769			−0.743846	−	0.668352i	$-0.767000\pi$
$647$	−962.536			−1.48769			−0.743846	+	0.668352i	$0.767000\pi$
$648$		0			0
$649$	−1066.78	+	615.908i	−1.64373	+	0.949011i
$650$		0			0
$651$	−25.4227	−	44.0334i	−0.0390518	−	0.0676396i
$652$		0			0
$653$	−1020.58			−1.56291			−0.781455	−	0.623961i	$-0.785522\pi$
$653$	−1020.58			−1.56291			−0.781455	+	0.623961i	$0.785522\pi$
$654$		0			0
$655$	−533.006	+	923.194i	−0.813750	+	1.40946i
$656$		0			0
$657$	−112.206			−0.170786
$658$		0			0
$659$	−25.6046	−	14.7828i	−0.0388538	−	0.0224322i	0.480447	−	0.877024i	$-0.340474\pi$
$659$	−25.6046	−	14.7828i	−0.0388538	−	0.0224322i	−0.519301	+	0.854591i	$0.673808\pi$
$660$		0			0
$661$	8.61074	+	4.97141i	0.0130268	+	0.00752104i	0.506499	−	0.862240i	$-0.330939\pi$
$661$	8.61074	+	4.97141i	0.0130268	+	0.00752104i	−0.493472	+	0.869761i	$0.664273\pi$
$662$		0			0
$663$	21.2136	+	36.7430i	0.0319964	+	0.0554193i
$664$		0			0
$665$	−350.749	−	13.2578i	−0.527443	−	0.0199365i
$666$		0			0
$667$	−117.671	+	67.9376i	−0.176419	+	0.101856i
$668$		0			0
$669$	−200.656	+	347.546i	−0.299934	+	0.519500i
$670$		0			0
$671$	262.541	−	454.735i	0.391269	−	0.677697i
$672$		0			0
$673$		−	914.332i		−	1.35859i	−0.733864	−	0.679296i	$-0.762285\pi$
$673$		−	914.332i		−	1.35859i	0.733864	−	0.679296i	$-0.237715\pi$
$674$		0			0
$675$	13.9620	+	8.06094i	0.0206844	+	0.0119421i
$676$		0			0
$677$		−	5.92519i		−	0.00875213i	−0.999990	−	0.00437606i	$-0.998607\pi$
$677$		−	5.92519i		−	0.00875213i	0.999990	−	0.00437606i	$-0.00139295\pi$
$678$		0			0
$679$	−501.652	+	289.629i	−0.738810	+	0.426552i
$680$		0			0
$681$	−138.460	−	239.820i	−0.203319	−	0.352158i
$682$		0			0
$683$			264.458i			0.387201i	0.981080	+	0.193601i	$0.0620166\pi$
$683$			264.458i			0.387201i	−0.981080	+	0.193601i	$0.937983\pi$
$684$		0			0
$685$	−481.320			−0.702657
$686$		0			0
$687$	76.2089	−	43.9993i	0.110930	−	0.0640455i
$688$		0			0
$689$	448.617	+	777.027i	0.651113	+	1.12776i
$690$		0			0
$691$	−788.543			−1.14116			−0.570581	−	0.821241i	$-0.693282\pi$
$691$	−788.543			−1.14116			−0.570581	+	0.821241i	$0.693282\pi$
$692$		0			0
$693$	−114.754	+	198.760i	−0.165590	+	0.286810i
$694$		0			0
$695$	1118.15			1.60884
$696$		0			0
$697$	−85.6913	−	49.4739i	−0.122943	−	0.0709812i
$698$		0			0
$699$	−268.437	−	154.982i	−0.384031	−	0.221720i
$700$		0			0
$701$	−515.363	−	892.635i	−0.735183	−	1.27337i	−0.954643	−	0.297752i	$-0.903763\pi$
$701$	−515.363	−	892.635i	−0.735183	−	1.27337i	0.219460	−	0.975621i	$-0.429570\pi$
$702$		0			0
$703$	59.9897	+	37.7259i	0.0853339	+	0.0536641i
$704$		0			0
$705$	−326.686	+	188.612i	−0.463385	+	0.267535i
$706$		0			0
$707$	240.658	−	416.832i	0.340393	−	0.589578i
$708$		0			0
$709$	369.792	−	640.498i	0.521568	−	0.903383i	−0.478117	−	0.878296i	$-0.658681\pi$
$709$	369.792	−	640.498i	0.521568	−	0.903383i	0.999685	−	0.0250866i	$-0.00798616\pi$
$710$		0			0
$711$			192.994i			0.271440i
$712$		0			0
$713$	−205.662	−	118.739i	−0.288446	−	0.166534i
$714$		0			0
$715$			1384.57i			1.93646i
$716$		0			0
$717$	−345.604	+	199.535i	−0.482015	+	0.278291i
$718$		0			0
$719$	286.874	+	496.881i	0.398991	+	0.691072i	0.993602	−	0.112942i	$-0.0360273\pi$
$719$	286.874	+	496.881i	0.398991	+	0.691072i	−0.594611	+	0.804013i	$0.702694\pi$
$720$		0			0
$721$			620.527i			0.860648i
$722$		0			0
$723$	−98.7884			−0.136637
$724$		0			0
$725$	−11.4318	+	6.60015i	−0.0157680	+	0.00910366i
$726$		0			0
$727$	132.019	+	228.664i	0.181595	+	0.314531i	0.942424	−	0.334421i	$-0.108541\pi$
$727$	132.019	+	228.664i	0.181595	+	0.314531i	−0.760829	+	0.648952i	$0.775207\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−45.1787	+	78.2517i	−0.0618039	+	0.107048i
$732$		0			0
$733$	−626.432			−0.854614			−0.427307	−	0.904107i	$-0.640538\pi$
$733$	−626.432			−0.854614			−0.427307	+	0.904107i	$0.640538\pi$
$734$		0			0
$735$	−234.544	−	135.414i	−0.319108	−	0.184237i
$736$		0			0
$737$	−1036.26	−	598.286i	−1.40605	−	0.811785i
$738$		0			0
$739$	−304.320	−	527.098i	−0.411800	−	0.713259i	0.583286	−	0.812267i	$-0.301767\pi$
$739$	−304.320	−	527.098i	−0.411800	−	0.713259i	−0.995087	+	0.0990076i	$0.968433\pi$
$740$		0			0
$741$	−267.494	+	425.355i	−0.360991	+	0.574029i
$742$		0			0
$743$	−10.7871	+	6.22796i	−0.0145184	+	0.00838218i	−0.507242	−	0.861804i	$-0.669335\pi$
$743$	−10.7871	+	6.22796i	−0.0145184	+	0.00838218i	0.492723	+	0.870186i	$0.336001\pi$
$744$		0			0
$745$	285.599	−	494.673i	0.383355	−	0.663990i
$746$		0			0
$747$	−10.8664	+	18.8211i	−0.0145467	+	0.0251956i
$748$		0			0
$749$		−	683.130i		−	0.912056i
$750$		0			0
$751$	158.562	+	91.5457i	0.211134	+	0.121898i	0.601838	−	0.798618i	$-0.294435\pi$
$751$	158.562	+	91.5457i	0.211134	+	0.121898i	−0.390704	+	0.920516i	$0.627768\pi$
$752$		0			0
$753$		−	458.634i		−	0.609076i
$754$		0			0
$755$	113.348	−	65.4413i	0.150129	−	0.0866772i
$756$		0			0
$757$	574.146	+	994.450i	0.758449	+	1.31367i	0.943641	+	0.330970i	$0.107376\pi$
$757$	574.146	+	994.450i	0.758449	+	1.31367i	−0.185193	+	0.982702i	$0.559291\pi$
$758$		0			0
$759$			1071.94i			1.41230i
$760$		0			0
$761$	872.192			1.14611			0.573056	−	0.819516i	$-0.305758\pi$
$761$	872.192			1.14611			0.573056	+	0.819516i	$0.305758\pi$
$762$		0			0
$763$	359.811	−	207.737i	0.471574	−	0.272264i
$764$		0			0
$765$	−11.2608	−	19.5044i	−0.0147201	−	0.0254959i
$766$		0			0
$767$	970.570			1.26541
$768$		0			0
$769$	516.956	−	895.394i	0.672244	−	1.16436i	−0.305022	−	0.952345i	$-0.598664\pi$
$769$	516.956	−	895.394i	0.672244	−	1.16436i	0.977266	−	0.212016i	$-0.0680029\pi$
$770$		0			0
$771$	673.045			0.872951
$772$		0			0
$773$	388.981	+	224.578i	0.503210	+	0.290528i	0.730038	−	0.683407i	$-0.239502\pi$
$773$	388.981	+	224.578i	0.503210	+	0.290528i	−0.226828	+	0.973935i	$0.572836\pi$
$774$		0			0
$775$	−19.9801	−	11.5355i	−0.0257808	−	0.0148846i
$776$		0			0
$777$	−12.7518	−	22.0869i	−0.0164116	−	0.0284258i
$778$		0			0
$779$	44.2630	−	1171.02i	0.0568203	−	1.50324i
$780$		0			0
$781$	−1210.88	+	699.103i	−1.55043	+	0.895138i
$782$		0			0
$783$	11.0536	−	19.1453i	0.0141169	−	0.0244512i
$784$		0			0
$785$	657.376	−	1138.61i	0.837422	−	1.45046i
$786$		0			0
$787$			141.308i			0.179552i	0.995962	+	0.0897762i	$0.0286152\pi$
$787$			141.308i			0.179552i	−0.995962	+	0.0897762i	$0.971385\pi$
$788$		0			0
$789$	−535.541	−	309.195i	−0.678759	−	0.391882i
$790$		0			0
$791$			227.201i			0.287232i
$792$		0			0
$793$	−358.294	+	206.861i	−0.451821	+	0.260859i
$794$		0			0
$795$	−238.140	−	412.470i	−0.299547	−	0.518831i
$796$		0			0
$797$			1074.10i			1.34768i	0.738878	+	0.673839i	$0.235356\pi$
$797$			1074.10i			1.34768i	−0.738878	+	0.673839i	$0.764644\pi$
$798$		0			0
$799$	−74.6668			−0.0934504
$800$		0			0
$801$	−168.764	+	97.4361i	−0.210692	+	0.121643i
$802$		0			0
$803$	−362.397	−	627.690i	−0.451304	−	0.781681i
$804$		0			0
$805$	589.988			0.732905
$806$		0			0
$807$	−57.3739	+	99.3746i	−0.0710954	+	0.123141i
$808$		0			0
$809$	242.419			0.299653			0.149827	−	0.988712i	$-0.452128\pi$
$809$	242.419			0.299653			0.149827	+	0.988712i	$0.452128\pi$
$810$		0			0
$811$	−179.138	−	103.426i	−0.220886	−	0.127528i	0.385475	−	0.922718i	$-0.374038\pi$
$811$	−179.138	−	103.426i	−0.220886	−	0.127528i	−0.606360	+	0.795190i	$0.707371\pi$
$812$		0			0
$813$	−313.810	−	181.178i	−0.385990	−	0.222851i
$814$		0			0
$815$	365.361	+	632.825i	0.448296	+	0.776472i
$816$		0			0
$817$	−1069.36	−	40.4201i	−1.30888	−	0.0494739i
$818$		0			0
$819$	156.606	−	90.4166i	0.191216	−	0.110399i
$820$		0			0
$821$	703.143	−	1217.88i	0.856447	−	1.48341i	−0.0188483	−	0.999822i	$-0.506000\pi$
$821$	703.143	−	1217.88i	0.856447	−	1.48341i	0.875296	−	0.483588i	$-0.160667\pi$
$822$		0			0
$823$	−273.933	+	474.465i	−0.332846	+	0.576507i	−0.983069	−	0.183237i	$-0.941342\pi$
$823$	−273.933	+	474.465i	−0.332846	+	0.576507i	0.650222	+	0.759744i	$0.274676\pi$
$824$		0			0
$825$			104.139i			0.126229i
$826$		0			0
$827$	1057.69	+	610.656i	1.27894	+	0.738399i	0.976654	−	0.214817i	$-0.0689155\pi$
$827$	1057.69	+	610.656i	1.27894	+	0.738399i	0.302290	+	0.953216i	$0.402249\pi$
$828$		0			0
$829$			173.838i			0.209696i	0.994488	+	0.104848i	$0.0334356\pi$
$829$			173.838i			0.209696i	−0.994488	+	0.104848i	$0.966564\pi$
$830$		0			0
$831$	567.292	−	327.526i	0.682662	−	0.394135i
$832$		0			0
$833$	−26.8035	−	46.4250i	−0.0321771	−	0.0557323i
$834$		0			0
$835$			895.098i			1.07197i
$836$		0			0
$837$	38.6381			0.0461626
$838$		0			0
$839$	38.4785	−	22.2156i	0.0458624	−	0.0264787i	−0.476894	−	0.878961i	$-0.658237\pi$
$839$	38.4785	−	22.2156i	0.0458624	−	0.0264787i	0.522756	+	0.852482i	$0.324904\pi$
$840$		0			0
$841$	−411.450	−	712.652i	−0.489238	−	0.847386i
$842$		0			0
$843$	−261.523			−0.310229
$844$		0			0
$845$	150.048	−	259.891i	0.177572	−	0.307563i
$846$		0			0
$847$	−1004.81			−1.18632
$848$		0			0
$849$	16.9243	+	9.77125i	0.0199344	+	0.0115091i
$850$		0			0
$851$	−103.159	−	59.5587i	−0.121221	−	0.0699867i
$852$		0			0
$853$	251.377	+	435.398i	0.294698	+	0.510432i	0.974915	−	0.222579i	$-0.0714477\pi$
$853$	251.377	+	435.398i	0.294698	+	0.510432i	−0.680217	+	0.733011i	$0.738114\pi$
$854$		0			0
$855$	141.994	−	225.792i	0.166075	−	0.264084i
$856$		0			0
$857$	−912.584	+	526.881i	−1.06486	+	0.614796i	−0.926772	−	0.375624i	$-0.877428\pi$
$857$	−912.584	+	526.881i	−1.06486	+	0.614796i	−0.138086	+	0.990420i	$0.544095\pi$
$858$		0			0
$859$	73.4561	−	127.230i	0.0855136	−	0.148114i	−0.820096	−	0.572225i	$-0.806080\pi$
$859$	73.4561	−	127.230i	0.0855136	−	0.148114i	0.905610	+	0.424112i	$0.139414\pi$
$860$		0			0
$861$	−210.868	+	365.234i	−0.244910	+	0.424197i
$862$		0			0
$863$		−	290.509i		−	0.336627i	−0.985734	−	0.168314i	$-0.946168\pi$
$863$		−	290.509i		−	0.336627i	0.985734	−	0.168314i	$-0.0538321\pi$
$864$		0			0
$865$	−373.910	−	215.877i	−0.432266	−	0.249569i
$866$		0			0
$867$			496.105i			0.572209i
$868$		0			0
$869$	−1079.62	+	623.320i	−1.24237	+	0.717285i
$870$		0			0
$871$	471.400	+	816.489i	0.541217	+	0.937415i
$872$		0			0
$873$		−	440.186i		−	0.504222i
$874$		0			0
$875$	519.159			0.593325
$876$		0			0
$877$	−1225.93	+	707.789i	−1.39786	+	0.807056i	−0.994169	−	0.107837i	$-0.965607\pi$
$877$	−1225.93	+	707.789i	−1.39786	+	0.807056i	−0.403694	+	0.914894i	$0.632274\pi$
$878$		0			0
$879$	246.345	+	426.682i	0.280256	+	0.485417i
$880$		0			0
$881$	107.877			0.122449			0.0612243	−	0.998124i	$-0.480500\pi$
$881$	107.877			0.122449			0.0612243	+	0.998124i	$0.480500\pi$
$882$		0			0
$883$	390.301	−	676.021i	0.442017	−	0.765596i	−0.555822	−	0.831301i	$-0.687596\pi$
$883$	390.301	−	676.021i	0.442017	−	0.765596i	0.997839	+	0.0657056i	$0.0209298\pi$
$884$		0			0
$885$	−515.209			−0.582157
$886$		0			0
$887$	320.543	+	185.066i	0.361379	+	0.208642i	0.669686	−	0.742645i	$-0.266429\pi$
$887$	320.543	+	185.066i	0.361379	+	0.208642i	−0.308306	+	0.951287i	$0.599762\pi$
$888$		0			0
$889$	260.512	+	150.407i	0.293040	+	0.169187i
$890$		0			0
$891$	−87.2030	−	151.040i	−0.0978709	−	0.169517i
$892$		0			0
$893$	−412.906	−	781.977i	−0.462381	−	0.875674i
$894$		0			0
$895$	971.341	−	560.804i	1.08530	−	0.626596i
$896$		0			0
$897$	422.299	−	731.444i	0.470791	−	0.815434i
$898$		0			0
$899$	−15.8181	+	27.3977i	−0.0175952	+	0.0304758i
$900$		0			0
$901$		−	94.2735i		−	0.104632i
$902$		0			0
$903$	333.525	+	192.561i	0.369352	+	0.213245i
$904$		0			0
$905$			889.240i			0.982586i
$906$		0			0
$907$	−288.815	+	166.747i	−0.318429	+	0.183845i	−0.650692	−	0.759342i	$-0.725521\pi$
$907$	−288.815	+	166.747i	−0.318429	+	0.183845i	0.332263	+	0.943187i	$0.392188\pi$
$908$		0			0
$909$	182.879	+	316.756i	0.201187	+	0.348466i
$910$		0			0
$911$			326.591i			0.358498i	0.983804	+	0.179249i	$0.0573667\pi$
$911$			326.591i			0.358498i	−0.983804	+	0.179249i	$0.942633\pi$
$912$		0			0
$913$	−140.382			−0.153759
$914$		0			0
$915$	190.194	−	109.808i	0.207862	−	0.120009i
$916$		0			0
$917$	449.670	+	778.851i	0.490371	+	0.849347i
$918$		0			0
$919$	−874.662			−0.951755			−0.475877	−	0.879512i	$-0.657869\pi$
$919$	−874.662			−0.951755			−0.475877	+	0.879512i	$0.657869\pi$
$920$		0			0
$921$	−470.039	+	814.131i	−0.510357	+	0.883964i
$922$		0			0
$923$	1101.67			1.19358
$924$		0			0
$925$	−10.0219	−	5.78614i	−0.0108345	−	0.00625529i
$926$		0			0
$927$	−408.371	−	235.773i	−0.440530	−	0.254340i
$928$		0			0
$929$	124.288	+	215.274i	0.133787	+	0.231727i	0.925134	−	0.379642i	$-0.123953\pi$
$929$	124.288	+	215.274i	0.133787	+	0.231727i	−0.791346	+	0.611368i	$0.790619\pi$
$930$		0			0
$931$	337.981	−	537.439i	0.363030	−	0.577271i
$932$		0			0
$933$	694.150	−	400.768i	0.743998	−	0.429547i
$934$		0			0
$935$	72.7392	−	125.988i	0.0777959	−	0.134746i
$936$		0			0
$937$	913.478	−	1582.19i	0.974897	−	1.68857i	0.294620	−	0.955614i	$-0.404807\pi$
$937$	913.478	−	1582.19i	0.974897	−	1.68857i	0.680276	−	0.732956i	$-0.261860\pi$
$938$		0			0
$939$			266.764i			0.284094i
$940$		0			0
$941$	−1174.62	−	678.166i	−1.24827	−	0.720687i	−0.277502	−	0.960725i	$-0.589507\pi$
$941$	−1174.62	−	678.166i	−1.24827	−	0.720687i	−0.970763	+	0.240038i	$0.922840\pi$
$942$		0			0
$943$			1969.76i			2.08882i
$944$		0			0
$945$	−83.1315	+	47.9960i	−0.0879699	+	0.0507894i
$946$		0			0
$947$	−478.965	−	829.592i	−0.505771	−	0.876021i	−0.999978	−	0.00667692i	$-0.997875\pi$
$947$	−478.965	−	829.592i	−0.505771	−	0.876021i	0.494206	−	0.869345i	$-0.335459\pi$
$948$		0			0
$949$			571.078i			0.601768i
$950$		0			0
$951$	125.972			0.132463
$952$		0			0
$953$	136.474	−	78.7933i	0.143205	−	0.0826793i	−0.426686	−	0.904400i	$-0.640319\pi$
$953$	136.474	−	78.7933i	0.143205	−	0.0826793i	0.569890	+	0.821721i	$0.306986\pi$
$954$		0			0
$955$	−645.858	−	1118.66i	−0.676291	−	1.17137i
$956$		0			0
$957$	142.800			0.149217
$958$		0			0
$959$	−203.033	+	351.663i	−0.211713	+	0.366698i
$960$		0			0
$961$	905.707			0.942463
$962$		0			0
$963$	449.570	+	259.559i	0.466843	+	0.269532i
$964$		0			0
$965$	−676.069	−	390.328i	−0.700589	−	0.404485i
$966$		0			0
$967$	−359.447	−	622.581i	−0.371714	−	0.643827i	0.618115	−	0.786087i	$-0.287896\pi$
$967$	−359.447	−	622.581i	−0.371714	−	0.643827i	−0.989829	+	0.142260i	$0.954563\pi$
$968$		0			0
$969$	46.6868	−	24.6520i	0.0481804	−	0.0254406i
$970$		0			0
$971$	1159.84	−	669.635i	1.19448	−	0.689635i	0.235163	−	0.971956i	$-0.424438\pi$
$971$	1159.84	−	669.635i	1.19448	−	0.689635i	0.959320	+	0.282321i	$0.0911044\pi$
$972$		0			0
$973$	471.661	−	816.941i	0.484749	−	0.839610i
$974$		0			0
$975$	41.0265	−	71.0599i	0.0420784	−	0.0728820i
$976$		0			0
$977$			1527.02i			1.56297i	0.623926	+	0.781483i	$0.285537\pi$
$977$			1527.02i			1.56297i	−0.623926	+	0.781483i	$0.714463\pi$
$978$		0			0
$979$	−1090.13	−	629.386i	−1.11351	−	0.642887i
$980$		0			0
$981$			315.724i			0.321839i
$982$		0			0
$983$	524.286	−	302.697i	0.533353	−	0.307932i	−0.209028	−	0.977910i	$-0.567030\pi$
$983$	524.286	−	302.697i	0.533353	−	0.307932i	0.742381	+	0.669978i	$0.233697\pi$
$984$		0			0
$985$	−36.8170	−	63.7690i	−0.0373777	−	0.0647401i
$986$		0			0
$987$			318.245i			0.322437i
$988$		0			0
$989$	1798.75			1.81875
$990$		0			0
$991$	−1423.50	+	821.857i	−1.43643	+	0.829321i	−0.997599	−	0.0692508i	$-0.977939\pi$
$991$	−1423.50	+	821.857i	−1.43643	+	0.829321i	−0.438827	+	0.898572i	$0.644606\pi$
$992$		0			0
$993$	466.680	+	808.313i	0.469969	+	0.814011i
$994$		0			0
$995$	310.166			0.311724
$996$		0			0
$997$	671.544	−	1163.15i	0.673565	−	1.16665i	−0.303322	−	0.952888i	$-0.598096\pi$
$997$	671.544	−	1163.15i	0.673565	−	1.16665i	0.976886	−	0.213760i	$-0.0685710\pi$
$998$		0			0
$999$	19.3806			0.0194000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.i.145.3		20
4.3	odd	2		456.3.w.b.145.3	✓	20
12.11	even	2		1368.3.bv.b.145.8		20
19.8	odd	6	inner	912.3.be.i.673.3		20
76.27	even	6		456.3.w.b.217.3	yes	20
228.179	odd	6		1368.3.bv.b.217.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.3.w.b.145.3	✓	20	4.3	odd	2
456.3.w.b.217.3	yes	20	76.27	even	6
912.3.be.i.145.3		20	1.1	even	1	trivial
912.3.be.i.673.3		20	19.8	odd	6	inner
1368.3.bv.b.145.8		20	12.11	even	2
1368.3.bv.b.217.8		20	228.179	odd	6

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-2.33973 - 4.05253i) q^{5} -3.94782 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-2.33973 - 4.05253i) q^{5} -3.94782 q^{7} +(1.50000 - 2.59808i) q^{9} +19.3784 q^{11} +(-13.2230 - 7.63431i) q^{13} +(7.01919 + 4.05253i) q^{15} +(0.802147 + 1.38936i) q^{17} +(-10.1147 + 16.0839i) q^{19} +(5.92173 - 3.41891i) q^{21} +(15.9684 - 27.6580i) q^{23} +(1.55133 - 2.68698i) q^{25} +5.19615i q^{27} +(-3.68452 - 2.12726i) q^{29} -7.43590i q^{31} +(-29.0677 + 16.7822i) q^{33} +(9.23684 + 15.9987i) q^{35} -3.72980i q^{37} +26.4460 q^{39} +(-53.4137 + 30.8384i) q^{41} +(28.1611 + 48.7764i) q^{43} -14.0384 q^{45} +(-23.2709 + 40.3064i) q^{47} -33.4147 q^{49} +(-2.40644 - 1.38936i) q^{51} +(-50.8905 - 29.3816i) q^{53} +(-45.3403 - 78.5317i) q^{55} +(1.24302 - 32.8855i) q^{57} +(-55.0501 + 31.7832i) q^{59} +(13.5481 - 23.4660i) q^{61} +(-5.92173 + 10.2567i) q^{63} +71.4489i q^{65} +(-53.4750 - 30.8738i) q^{67} +55.3160i q^{69} +(-62.4861 + 36.0763i) q^{71} +(-18.7010 - 32.3912i) q^{73} +5.37396i q^{75} -76.5026 q^{77} +(-55.7126 + 32.1657i) q^{79} +(-4.50000 - 7.79423i) q^{81} -7.24425 q^{83} +(3.75361 - 6.50145i) q^{85} +7.36904 q^{87} +(-56.2548 - 32.4787i) q^{89} +(52.2021 + 30.1389i) q^{91} +(6.43968 + 11.1538i) q^{93} +(88.8463 + 3.35826i) q^{95} +(127.071 - 73.3643i) q^{97} +(29.0677 - 50.3467i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} + 4 q^{7} + 30 q^{9}+O(q^{10}) \) 20 * q - 30 * q^3 + 4 * q^7 + 30 * q^9	\( 20 q - 30 q^{3} + 4 q^{7} + 30 q^{9} + 8 q^{11} - 6 q^{13} + 8 q^{17} + 20 q^{19} - 6 q^{21} + 56 q^{23} - 58 q^{25} - 204 q^{29} - 12 q^{33} - 20 q^{35} + 12 q^{39} + 12 q^{41} - 34 q^{43} - 24 q^{47} + 392 q^{49} - 24 q^{51} + 24 q^{55} - 54 q^{57} - 168 q^{59} + 142 q^{61} + 6 q^{63} - 246 q^{67} - 276 q^{71} - 118 q^{73} - 152 q^{77} + 210 q^{79} - 90 q^{81} + 112 q^{83} - 208 q^{85} + 408 q^{87} - 42 q^{91} - 102 q^{93} - 100 q^{95} - 540 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 4 * q^7 + 30 * q^9 + 8 * q^11 - 6 * q^13 + 8 * q^17 + 20 * q^19 - 6 * q^21 + 56 * q^23 - 58 * q^25 - 204 * q^29 - 12 * q^33 - 20 * q^35 + 12 * q^39 + 12 * q^41 - 34 * q^43 - 24 * q^47 + 392 * q^49 - 24 * q^51 + 24 * q^55 - 54 * q^57 - 168 * q^59 + 142 * q^61 + 6 * q^63 - 246 * q^67 - 276 * q^71 - 118 * q^73 - 152 * q^77 + 210 * q^79 - 90 * q^81 + 112 * q^83 - 208 * q^85 + 408 * q^87 - 42 * q^91 - 102 * q^93 - 100 * q^95 - 540 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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