LMFDB - Embedded newform 144.3.m.b.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(19,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("144.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 10x^{12} + 88x^{10} - 752x^{8} + 1408x^{6} + 2560x^{4} - 24576x^{2} + 65536 $ x^16 - 6x^14 + 10x^12 + 88x^10 - 752x^8 + 1408x^6 + 2560x^4 - 24576*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			91.4
Root			$1.99750 + 0.0999235i$ of defining polynomial
Character	$\chi$	$=$	144.91
Dual form			144.3.m.b.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0999235 + 1.99750i) q^{2} +(-3.98003 - 0.399195i) q^{4} +(-6.01265 - 6.01265i) q^{5} +8.23187 q^{7} +(1.19509 - 7.91023i) q^{8} +O(q^{10})$	\(q+(-0.0999235 + 1.99750i) q^{2} +(-3.98003 - 0.399195i) q^{4} +(-6.01265 - 6.01265i) q^{5} +8.23187 q^{7} +(1.19509 - 7.91023i) q^{8} +(12.6111 - 11.4095i) q^{10} +(6.51529 - 6.51529i) q^{11} +(8.82865 - 8.82865i) q^{13} +(-0.822557 + 16.4432i) q^{14} +(15.6813 + 3.17761i) q^{16} -14.1753 q^{17} +(-23.7488 - 23.7488i) q^{19} +(21.5303 + 26.3308i) q^{20} +(12.3633 + 13.6653i) q^{22} -9.42125 q^{23} +47.3040i q^{25} +(16.7531 + 18.5174i) q^{26} +(-32.7631 - 3.28612i) q^{28} +(23.7973 - 23.7973i) q^{29} -24.4148i q^{31} +(-7.91422 + 31.0059i) q^{32} +(1.41645 - 28.3153i) q^{34} +(-49.4954 - 49.4954i) q^{35} +(24.2052 + 24.2052i) q^{37} +(49.8113 - 45.0652i) q^{38} +(-54.7471 + 40.3758i) q^{40} -6.67771i q^{41} +(0.897918 - 0.897918i) q^{43} +(-28.5319 + 23.3302i) q^{44} +(0.941404 - 18.8190i) q^{46} +25.2401i q^{47} +18.7636 q^{49} +(-94.4898 - 4.72678i) q^{50} +(-38.6626 + 31.6139i) q^{52} +(32.6251 + 32.6251i) q^{53} -78.3484 q^{55} +(9.83783 - 65.1160i) q^{56} +(45.1573 + 49.9132i) q^{58} +(-8.31871 + 8.31871i) q^{59} +(-68.4028 + 68.4028i) q^{61} +(48.7687 + 2.43961i) q^{62} +(-61.1435 - 18.9069i) q^{64} -106.167 q^{65} +(-7.71922 - 7.71922i) q^{67} +(56.4183 + 5.65873i) q^{68} +(103.813 - 93.9213i) q^{70} +137.259 q^{71} -52.8655i q^{73} +(-50.7685 + 45.9312i) q^{74} +(85.0404 + 104.001i) q^{76} +(53.6330 - 53.6330i) q^{77} -87.2269i q^{79} +(-75.1802 - 113.392i) q^{80} +(13.3387 + 0.667260i) q^{82} +(9.53893 + 9.53893i) q^{83} +(85.2314 + 85.2314i) q^{85} +(1.70387 + 1.88332i) q^{86} +(-43.7511 - 59.3238i) q^{88} +146.488i q^{89} +(72.6762 - 72.6762i) q^{91} +(37.4969 + 3.76091i) q^{92} +(-50.4172 - 2.52208i) q^{94} +285.586i q^{95} +101.170 q^{97} +(-1.87493 + 37.4804i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4}+O(q^{10}) $ 16 * q - 12 * q^4	$ 16 q - 12 q^{4} + 16 q^{10} + 32 q^{16} - 32 q^{19} + 104 q^{22} - 24 q^{34} + 96 q^{37} - 312 q^{40} - 32 q^{43} - 224 q^{46} + 112 q^{49} - 264 q^{52} - 256 q^{55} + 312 q^{58} - 32 q^{61} + 456 q^{64} - 256 q^{67} + 744 q^{70} + 264 q^{76} - 280 q^{82} + 160 q^{85} - 912 q^{88} + 288 q^{91} - 1104 q^{94}+O(q^{100}) $ 16 * q - 12 * q^4 + 16 * q^10 + 32 * q^16 - 32 * q^19 + 104 * q^22 - 24 * q^34 + 96 * q^37 - 312 * q^40 - 32 * q^43 - 224 * q^46 + 112 * q^49 - 264 * q^52 - 256 * q^55 + 312 * q^58 - 32 * q^61 + 456 * q^64 - 256 * q^67 + 744 * q^70 + 264 * q^76 - 280 * q^82 + 160 * q^85 - 912 * q^88 + 288 * q^91 - 1104 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0999235	+	1.99750i	−0.0499617	+	0.998751i
$2$	−0.0999235	+	1.99750i	−0.0499617	+	0.998751i
$3$		0			0
$3$		0			0
$4$	−3.98003	−	0.399195i	−0.995008	−	0.0997987i
$5$	−6.01265	−	6.01265i	−1.20253	−	1.20253i	−0.973394	−	0.229136i	$-0.926410\pi$
$5$	−6.01265	−	6.01265i	−1.20253	−	1.20253i	−0.229136	−	0.973394i	$-0.573590\pi$
$6$		0			0
$7$	8.23187			1.17598			0.587990	−	0.808868i	$-0.299919\pi$
$7$	8.23187			1.17598			0.587990	+	0.808868i	$0.299919\pi$
$8$	1.19509	−	7.91023i	0.149386	−	0.988779i
$9$		0			0
$10$	12.6111	−	11.4095i	1.26111	−	1.14095i
$11$	6.51529	−	6.51529i	0.592299	−	0.592299i	−0.345953	−	0.938252i	$-0.612444\pi$
$11$	6.51529	−	6.51529i	0.592299	−	0.592299i	0.938252	+	0.345953i	$0.112444\pi$
$12$		0			0
$13$	8.82865	−	8.82865i	0.679127	−	0.679127i	−0.280676	−	0.959803i	$-0.590559\pi$
$13$	8.82865	−	8.82865i	0.679127	−	0.679127i	0.959803	+	0.280676i	$0.0905586\pi$
$14$	−0.822557	+	16.4432i	−0.0587541	+	1.17451i
$15$		0			0
$16$	15.6813	+	3.17761i	0.980080	+	0.198601i
$17$	−14.1753			−0.833844			−0.416922	−	0.908942i	$-0.636891\pi$
$17$	−14.1753			−0.833844			−0.416922	+	0.908942i	$0.636891\pi$
$18$		0			0
$19$	−23.7488	−	23.7488i	−1.24994	−	1.24994i	−0.955748	−	0.294187i	$-0.904951\pi$
$19$	−23.7488	−	23.7488i	−1.24994	−	1.24994i	−0.294187	−	0.955748i	$-0.595049\pi$
$20$	21.5303	+	26.3308i	1.07652	+	1.31654i
$21$		0			0
$22$	12.3633	+	13.6653i	0.561967	+	0.621152i
$23$	−9.42125			−0.409619			−0.204810	−	0.978802i	$-0.565658\pi$
$23$	−9.42125			−0.409619			−0.204810	+	0.978802i	$0.565658\pi$
$24$		0			0
$25$			47.3040i			1.89216i
$26$	16.7531	+	18.5174i	0.644348	+	0.712209i
$27$		0			0
$28$	−32.7631	−	3.28612i	−1.17011	−	0.117361i
$29$	23.7973	−	23.7973i	0.820598	−	0.820598i	−0.165596	−	0.986194i	$-0.552955\pi$
$29$	23.7973	−	23.7973i	0.820598	−	0.820598i	0.986194	+	0.165596i	$0.0529547\pi$
$30$		0			0
$31$		−	24.4148i		−	0.787575i	−0.919202	−	0.393787i	$-0.871165\pi$
$31$		−	24.4148i		−	0.787575i	0.919202	−	0.393787i	$-0.128835\pi$
$32$	−7.91422	+	31.0059i	−0.247319	+	0.968934i
$33$		0			0
$34$	1.41645	−	28.3153i	0.0416603	−	0.832803i
$35$	−49.4954	−	49.4954i	−1.41415	−	1.41415i
$36$		0			0
$37$	24.2052	+	24.2052i	0.654193	+	0.654193i	0.954000	−	0.299807i	$-0.0969221\pi$
$37$	24.2052	+	24.2052i	0.654193	+	0.654193i	−0.299807	+	0.954000i	$0.596922\pi$
$38$	49.8113	−	45.0652i	1.31082	−	1.18593i
$39$		0			0
$40$	−54.7471	+	40.3758i	−1.36868	+	1.00940i
$41$		−	6.67771i		−	0.162871i	−0.996679	−	0.0814355i	$-0.974050\pi$
$41$		−	6.67771i		−	0.162871i	0.996679	−	0.0814355i	$-0.0259505\pi$
$42$		0			0
$43$	0.897918	−	0.897918i	0.0208818	−	0.0208818i	−0.696589	−	0.717471i	$-0.745300\pi$
$43$	0.897918	−	0.897918i	0.0208818	−	0.0208818i	0.717471	+	0.696589i	$0.245300\pi$
$44$	−28.5319	+	23.3302i	−0.648453	+	0.530232i
$45$		0			0
$46$	0.941404	−	18.8190i	0.0204653	−	0.409108i
$47$			25.2401i			0.537023i	0.963276	+	0.268512i	$0.0865318\pi$
$47$			25.2401i			0.537023i	−0.963276	+	0.268512i	$0.913468\pi$
$48$		0			0
$49$	18.7636			0.382931
$50$	−94.4898	−	4.72678i	−1.88980	−	0.0945356i
$51$		0			0
$52$	−38.6626	+	31.6139i	−0.743512	+	0.607960i
$53$	32.6251	+	32.6251i	0.615568	+	0.615568i	0.944391	−	0.328824i	$-0.106652\pi$
$53$	32.6251	+	32.6251i	0.615568	+	0.615568i	−0.328824	+	0.944391i	$0.606652\pi$
$54$		0			0
$55$	−78.3484			−1.42452
$56$	9.83783	−	65.1160i	0.175676	−	1.16279i
$57$		0			0
$58$	45.1573	+	49.9132i	0.778575	+	0.860572i
$59$	−8.31871	+	8.31871i	−0.140995	+	0.140995i	−0.774081	−	0.633086i	$-0.781788\pi$
$59$	−8.31871	+	8.31871i	−0.140995	+	0.140995i	0.633086	+	0.774081i	$0.281788\pi$
$60$		0			0
$61$	−68.4028	+	68.4028i	−1.12136	+	1.12136i	−0.129820	+	0.991538i	$0.541440\pi$
$61$	−68.4028	+	68.4028i	−1.12136	+	1.12136i	−0.991538	+	0.129820i	$0.958560\pi$
$62$	48.7687	+	2.43961i	0.786591	+	0.0393486i
$63$		0			0
$64$	−61.1435	−	18.9069i	−0.955367	−	0.295420i
$65$	−106.167			−1.63334
$66$		0			0
$67$	−7.71922	−	7.71922i	−0.115212	−	0.115212i	0.647150	−	0.762362i	$-0.275961\pi$
$67$	−7.71922	−	7.71922i	−0.115212	−	0.115212i	−0.762362	+	0.647150i	$0.775961\pi$
$68$	56.4183	+	5.65873i	0.829681	+	0.0832165i
$69$		0			0
$70$	103.813	−	93.9213i	1.48304	−	1.34173i
$71$	137.259			1.93322			0.966612	−	0.256245i	$-0.0824853\pi$
$71$	137.259			1.93322			0.966612	+	0.256245i	$0.0824853\pi$
$72$		0			0
$73$		−	52.8655i		−	0.724185i	−0.932142	−	0.362093i	$-0.882062\pi$
$73$		−	52.8655i		−	0.724185i	0.932142	−	0.362093i	$-0.117938\pi$
$74$	−50.7685	+	45.9312i	−0.686061	+	0.620692i
$75$		0			0
$76$	85.0404	+	104.001i	1.11895	+	1.36844i
$77$	53.6330	−	53.6330i	0.696533	−	0.696533i
$78$		0			0
$79$		−	87.2269i		−	1.10414i	−0.833798	−	0.552069i	$-0.813838\pi$
$79$		−	87.2269i		−	1.10414i	0.833798	−	0.552069i	$-0.186162\pi$
$80$	−75.1802	−	113.392i	−0.939753	−	1.41740i
$81$		0			0
$82$	13.3387	+	0.667260i	0.162668	+	0.00813732i
$83$	9.53893	+	9.53893i	0.114927	+	0.114927i	0.762231	−	0.647305i	$-0.224104\pi$
$83$	9.53893	+	9.53893i	0.114927	+	0.114927i	−0.647305	+	0.762231i	$0.724104\pi$
$84$		0			0
$85$	85.2314	+	85.2314i	1.00272	+	1.00272i
$86$	1.70387	+	1.88332i	0.0198124	+	0.0218990i
$87$		0			0
$88$	−43.7511	−	59.3238i	−0.497172	−	0.674135i
$89$			146.488i			1.64593i	0.568089	+	0.822967i	$0.307683\pi$
$89$			146.488i			1.64593i	−0.568089	+	0.822967i	$0.692317\pi$
$90$		0			0
$91$	72.6762	−	72.6762i	0.798640	−	0.798640i
$92$	37.4969	+	3.76091i	0.407574	+	0.0408795i
$93$		0			0
$94$	−50.4172	−	2.52208i	−0.536353	−	0.0268306i
$95$			285.586i			3.00617i
$96$		0			0
$97$	101.170			1.04298			0.521492	−	0.853256i	$-0.325376\pi$
$97$	101.170			1.04298			0.521492	+	0.853256i	$0.325376\pi$
$98$	−1.87493	+	37.4804i	−0.0191319	+	0.382453i
$99$		0			0
$100$	18.8835	−	188.271i	0.188835	−	1.88271i
$101$	47.4912	+	47.4912i	0.470210	+	0.470210i	0.901982	−	0.431773i	$-0.142112\pi$
$101$	47.4912	+	47.4912i	0.470210	+	0.470210i	−0.431773	+	0.901982i	$0.642112\pi$
$102$		0			0
$103$	7.58518			0.0736425			0.0368213	−	0.999322i	$-0.488277\pi$
$103$	7.58518			0.0736425			0.0368213	+	0.999322i	$0.488277\pi$
$104$	−59.2856	−	80.3877i	−0.570054	−	0.772958i
$105$		0			0
$106$	−68.4287	+	61.9087i	−0.645554	+	0.584044i
$107$	119.757	−	119.757i	1.11922	−	1.11922i	0.127367	−	0.991856i	$-0.459347\pi$
$107$	119.757	−	119.757i	1.11922	−	1.11922i	0.991856	−	0.127367i	$-0.0406525\pi$
$108$		0			0
$109$	61.0263	−	61.0263i	0.559874	−	0.559874i	−0.369397	−	0.929272i	$-0.620436\pi$
$109$	61.0263	−	61.0263i	0.559874	−	0.559874i	0.929272	+	0.369397i	$0.120436\pi$
$110$	7.82884	−	156.501i	0.0711713	−	1.42274i
$111$		0			0
$112$	129.086	+	26.1577i	1.15256	+	0.233551i
$113$	−31.6377			−0.279980			−0.139990	−	0.990153i	$-0.544707\pi$
$113$	−31.6377			−0.279980			−0.139990	+	0.990153i	$0.544707\pi$
$114$		0			0
$115$	56.6467	+	56.6467i	0.492580	+	0.492580i
$116$	−104.214	+	85.2144i	−0.898396	+	0.734607i
$117$		0			0
$118$	−15.7854	−	17.4479i	−0.133775	−	0.147863i
$119$	−116.690			−0.980585
$120$		0			0
$121$			36.1019i			0.298363i
$122$	−129.800	−	143.470i	−1.06393	−	1.17598i
$123$		0			0
$124$	−9.74627	+	97.1717i	−0.0785989	+	0.783643i
$125$	134.106	−	134.106i	1.07285	−	1.07285i
$126$		0			0
$127$			87.8736i			0.691918i	0.938250	+	0.345959i	$0.112446\pi$
$127$			87.8736i			0.691918i	−0.938250	+	0.345959i	$0.887554\pi$
$128$	43.8762	−	120.245i	0.342783	−	0.939415i
$129$		0			0
$130$	10.6086	−	212.069i	0.0816046	−	1.63130i
$131$	−176.351	−	176.351i	−1.34619	−	1.34619i	−0.889761	−	0.456428i	$-0.849129\pi$
$131$	−176.351	−	176.351i	−1.34619	−	1.34619i	−0.456428	−	0.889761i	$-0.650871\pi$
$132$		0			0
$133$	−195.497	−	195.497i	−1.46990	−	1.46990i
$134$	16.1905	−	14.6478i	0.120825	−	0.109312i
$135$		0			0
$136$	−16.9408	+	112.130i	−0.124565	+	0.824487i
$137$			97.0224i			0.708192i	0.935209	+	0.354096i	$0.115211\pi$
$137$			97.0224i			0.708192i	−0.935209	+	0.354096i	$0.884789\pi$
$138$		0			0
$139$	−130.221	+	130.221i	−0.936841	+	0.936841i	−0.998121	−	0.0612800i	$-0.980482\pi$
$139$	−130.221	+	130.221i	−0.936841	+	0.936841i	0.0612800	+	0.998121i	$0.480482\pi$
$140$	177.235	+	216.751i	1.26596	+	1.54822i
$141$		0			0
$142$	−13.7154	+	274.175i	−0.0965872	+	1.93081i
$143$		−	115.042i		−	0.804493i
$144$		0			0
$145$	−286.170			−1.97359
$146$	105.599	+	5.28251i	0.723281	+	0.0361816i
$147$		0			0
$148$	−86.6747	−	106.000i	−0.585640	−	0.716215i
$149$	26.3592	+	26.3592i	0.176907	+	0.176907i	0.790006	−	0.613099i	$-0.210077\pi$
$149$	26.3592	+	26.3592i	0.176907	+	0.176907i	−0.613099	+	0.790006i	$0.710077\pi$
$150$		0			0
$151$	196.107			1.29872			0.649360	−	0.760481i	$-0.275037\pi$
$151$	196.107			1.29872			0.649360	+	0.760481i	$0.275037\pi$
$152$	−216.240	+	159.476i	−1.42263	+	1.04919i
$153$		0			0
$154$	101.773	+	112.491i	0.660863	+	0.730463i
$155$	−146.798	+	146.798i	−0.947083	+	0.947083i
$156$		0			0
$157$	98.5323	−	98.5323i	0.627594	−	0.627594i	−0.319868	−	0.947462i	$-0.603638\pi$
$157$	98.5323	−	98.5323i	0.627594	−	0.627594i	0.947462	+	0.319868i	$0.103638\pi$
$158$	174.236	+	8.71602i	1.10276	+	0.0551647i
$159$		0			0
$160$	234.013	−	138.842i	1.46258	−	0.867764i
$161$	−77.5545			−0.481705
$162$		0			0
$163$	−90.6677	−	90.6677i	−0.556244	−	0.556244i	0.371992	−	0.928236i	$-0.378675\pi$
$163$	−90.6677	−	90.6677i	−0.556244	−	0.556244i	−0.928236	+	0.371992i	$0.878675\pi$
$164$	−2.66571	+	26.5775i	−0.0162543	+	0.162058i
$165$		0			0
$166$	−20.0072	+	18.1009i	−0.120525	+	0.109041i
$167$	181.602			1.08744			0.543719	−	0.839267i	$-0.317016\pi$
$167$	181.602			1.08744			0.543719	+	0.839267i	$0.317016\pi$
$168$		0			0
$169$			13.1100i			0.0775741i
$170$	−178.767	+	161.733i	−1.05157	+	0.951373i
$171$		0			0
$172$	−3.93219	+	3.21530i	−0.0228615	+	0.0186936i
$173$	2.66532	−	2.66532i	0.0154065	−	0.0154065i	−0.699362	−	0.714768i	$-0.746532\pi$
$173$	2.66532	−	2.66532i	0.0154065	−	0.0154065i	0.714768	+	0.699362i	$0.246532\pi$
$174$		0			0
$175$			389.400i			2.22514i
$176$	122.871	−	81.4651i	0.698132	−	0.462870i
$177$		0			0
$178$	−292.610	−	14.6376i	−1.64388	−	0.0822337i
$179$	12.7491	+	12.7491i	0.0712241	+	0.0712241i	0.741822	−	0.670597i	$-0.233962\pi$
$179$	12.7491	+	12.7491i	0.0712241	+	0.0712241i	−0.670597	+	0.741822i	$0.733962\pi$
$180$		0			0
$181$	−61.3009	−	61.3009i	−0.338679	−	0.338679i	0.517191	−	0.855870i	$-0.326978\pi$
$181$	−61.3009	−	61.3009i	−0.338679	−	0.338679i	−0.855870	+	0.517191i	$0.826978\pi$
$182$	137.909	+	152.433i	0.757741	+	0.837544i
$183$		0			0
$184$	−11.2592	+	74.5242i	−0.0611916	+	0.405023i
$185$		−	291.074i		−	1.57338i
$186$		0			0
$187$	−92.3566	+	92.3566i	−0.493885	+	0.493885i
$188$	10.0757	−	100.456i	0.0535942	−	0.534342i
$189$		0			0
$190$	−570.459	−	28.5368i	−3.00242	−	0.150194i
$191$			80.1204i			0.419479i	0.977757	+	0.209739i	$0.0672615\pi$
$191$			80.1204i			0.419479i	−0.977757	+	0.209739i	$0.932738\pi$
$192$		0			0
$193$	28.7555			0.148992			0.0744961	−	0.997221i	$-0.476265\pi$
$193$	28.7555			0.148992			0.0744961	+	0.997221i	$0.476265\pi$
$194$	−10.1092	+	202.086i	−0.0521093	+	1.04168i
$195$		0			0
$196$	−74.6798	−	7.49034i	−0.381019	−	0.0382160i
$197$	−92.8030	−	92.8030i	−0.471081	−	0.471081i	0.431183	−	0.902264i	$-0.358096\pi$
$197$	−92.8030	−	92.8030i	−0.471081	−	0.471081i	−0.902264	+	0.431183i	$0.858096\pi$
$198$		0			0
$199$	165.555			0.831934			0.415967	−	0.909380i	$-0.363443\pi$
$199$	165.555			0.831934			0.415967	+	0.909380i	$0.363443\pi$
$200$	374.185	+	56.5326i	1.87093	+	0.282663i
$201$		0			0
$202$	−99.6092	+	90.1183i	−0.493115	+	0.446130i
$203$	195.897	−	195.897i	0.965008	−	0.965008i
$204$		0			0
$205$	−40.1507	+	40.1507i	−0.195857	+	0.195857i
$206$	−0.757938	+	15.1514i	−0.00367931	+	0.0735506i
$207$		0			0
$208$	166.499	−	110.390i	0.800474	−	0.530724i
$209$	−309.460			−1.48067
$210$		0			0
$211$	187.769	+	187.769i	0.889902	+	0.889902i	0.994513	−	0.104611i	$-0.0333598\pi$
$211$	187.769	+	187.769i	0.889902	+	0.889902i	−0.104611	+	0.994513i	$0.533360\pi$
$212$	−116.825	−	142.873i	−0.551062	−	0.673928i
$213$		0			0
$214$	227.248	+	251.181i	1.06191	+	1.17374i
$215$	−10.7977			−0.0502220
$216$		0			0
$217$		−	200.980i		−	0.926173i
$218$	115.802	+	127.998i	0.531203	+	0.587147i
$219$		0			0
$220$	311.829	+	31.2763i	1.41740	+	0.142165i
$221$	−125.149	+	125.149i	−0.566286	+	0.566286i
$222$		0			0
$223$		−	307.192i		−	1.37754i	−0.724979	−	0.688771i	$-0.758151\pi$
$223$		−	307.192i		−	1.37754i	0.724979	−	0.688771i	$-0.241849\pi$
$224$	−65.1488	+	255.236i	−0.290843	+	1.13945i
$225$		0			0
$226$	3.16135	−	63.1964i	0.0139883	−	0.279630i
$227$	−112.960	−	112.960i	−0.497621	−	0.497621i	0.413075	−	0.910697i	$-0.364455\pi$
$227$	−112.960	−	112.960i	−0.497621	−	0.497621i	−0.910697	+	0.413075i	$0.864455\pi$
$228$		0			0
$229$	−7.32210	−	7.32210i	−0.0319742	−	0.0319742i	0.690939	−	0.722913i	$-0.257197\pi$
$229$	−7.32210	−	7.32210i	−0.0319742	−	0.0319742i	−0.722913	+	0.690939i	$0.757197\pi$
$230$	−118.812	+	107.492i	−0.516575	+	0.467355i
$231$		0			0
$232$	−159.802	−	216.682i	−0.688804	−	0.933976i
$233$		−	115.408i		−	0.495315i	−0.968848	−	0.247657i	$-0.920339\pi$
$233$		−	115.408i		−	0.495315i	0.968848	−	0.247657i	$-0.0796607\pi$
$234$		0			0
$235$	151.760	−	151.760i	0.645787	−	0.645787i
$236$	36.4295	−	29.7879i	0.154362	−	0.126220i
$237$		0			0
$238$	11.6600	−	233.088i	0.0489917	−	0.979360i
$239$		−	323.271i		−	1.35260i	−0.736627	−	0.676300i	$-0.763583\pi$
$239$		−	323.271i		−	1.35260i	0.736627	−	0.676300i	$-0.236417\pi$
$240$		0			0
$241$	118.056			0.489860			0.244930	−	0.969541i	$-0.421235\pi$
$241$	118.056			0.489860			0.244930	+	0.969541i	$0.421235\pi$
$242$	−72.1136	−	3.60743i	−0.297990	−	0.0149067i
$243$		0			0
$244$	299.551	−	244.939i	1.22767	−	1.00385i
$245$	−112.819	−	112.819i	−0.460486	−	0.460486i
$246$		0			0
$247$	−419.339			−1.69773
$248$	−193.127	−	29.1779i	−0.778737	−	0.117653i
$249$		0			0
$250$	254.477	+	281.278i	1.01791	+	1.12511i
$251$	−166.229	+	166.229i	−0.662265	+	0.662265i	−0.955913	−	0.293648i	$-0.905130\pi$
$251$	−166.229	+	166.229i	−0.662265	+	0.662265i	0.293648	+	0.955913i	$0.405130\pi$
$252$		0			0
$253$	−61.3822	+	61.3822i	−0.242617	+	0.242617i
$254$	−175.528	−	8.78064i	−0.691054	−	0.0345694i
$255$		0			0
$256$	235.806	+	99.6582i	0.921115	+	0.389290i
$257$	342.745			1.33364			0.666820	−	0.745219i	$-0.267655\pi$
$257$	342.745			1.33364			0.666820	+	0.745219i	$0.267655\pi$
$258$		0			0
$259$	199.254	+	199.254i	0.769319	+	0.769319i
$260$	422.549	+	42.3814i	1.62519	+	0.163005i
$261$		0			0
$262$	369.882	−	334.639i	1.41176	−	1.27725i
$263$	−219.637			−0.835123			−0.417562	−	0.908649i	$-0.637115\pi$
$263$	−219.637			−0.835123			−0.417562	+	0.908649i	$0.637115\pi$
$264$		0			0
$265$		−	392.327i		−	1.48048i
$266$	410.040	−	370.970i	1.54150	−	1.39463i
$267$		0			0
$268$	27.6413	+	33.8042i	0.103139	+	0.126135i
$269$	77.9061	−	77.9061i	0.289614	−	0.289614i	−0.547314	−	0.836928i	$-0.684350\pi$
$269$	77.9061	−	77.9061i	0.289614	−	0.289614i	0.836928	+	0.547314i	$0.184350\pi$
$270$		0			0
$271$			155.092i			0.572294i	0.958186	+	0.286147i	$0.0923746\pi$
$271$			155.092i			0.572294i	−0.958186	+	0.286147i	$0.907625\pi$
$272$	−222.288	−	45.0438i	−0.817234	−	0.165602i
$273$		0			0
$274$	−193.802	−	9.69481i	−0.707308	−	0.0353825i
$275$	308.199	+	308.199i	1.12072	+	1.12072i
$276$		0			0
$277$	−30.0601	−	30.0601i	−0.108520	−	0.108520i	0.650762	−	0.759282i	$-0.274450\pi$
$277$	−30.0601	−	30.0601i	−0.108520	−	0.108520i	−0.759282	+	0.650762i	$0.774450\pi$
$278$	−247.104	−	273.129i	−0.888864	−	0.982477i
$279$		0			0
$280$	−450.671	+	332.368i	−1.60954	+	1.18703i
$281$			265.590i			0.945162i	0.881287	+	0.472581i	$0.156677\pi$
$281$			265.590i			0.945162i	−0.881287	+	0.472581i	$0.843323\pi$
$282$		0			0
$283$	160.221	−	160.221i	0.566153	−	0.566153i	−0.364895	−	0.931049i	$-0.618895\pi$
$283$	160.221	−	160.221i	0.566153	−	0.566153i	0.931049	+	0.364895i	$0.118895\pi$
$284$	−546.295	−	54.7930i	−1.92357	−	0.192933i
$285$		0			0
$286$	229.798	+	11.4954i	0.803488	+	0.0401939i
$287$		−	54.9700i		−	0.191533i
$288$		0			0
$289$	−88.0595			−0.304704
$290$	28.5951	−	571.626i	0.0986039	−	1.97112i
$291$		0			0
$292$	−21.1036	+	210.406i	−0.0722728	+	0.720570i
$293$	173.762	+	173.762i	0.593044	+	0.593044i	0.938453	−	0.345408i	$-0.112260\pi$
$293$	173.762	+	173.762i	0.593044	+	0.593044i	−0.345408	+	0.938453i	$0.612260\pi$
$294$		0			0
$295$	100.035			0.339102
$296$	220.396	−	162.541i	0.744580	−	0.549125i
$297$		0			0
$298$	−55.2864	+	50.0186i	−0.185525	+	0.167848i
$299$	−83.1769	+	83.1769i	−0.278183	+	0.278183i
$300$		0			0
$301$	7.39154	−	7.39154i	0.0245566	−	0.0245566i
$302$	−19.5957	+	391.724i	−0.0648863	+	1.29710i
$303$		0			0
$304$	−296.947	−	447.876i	−0.976799	−	1.47328i
$305$	822.565			2.69693
$306$		0			0
$307$	136.842	+	136.842i	0.445741	+	0.445741i	0.893936	−	0.448195i	$-0.147933\pi$
$307$	136.842	+	136.842i	0.445741	+	0.445741i	−0.448195	+	0.893936i	$0.647933\pi$
$308$	−234.871	+	192.051i	−0.762569	+	0.623542i
$309$		0			0
$310$	−278.560	−	307.898i	−0.898582	−	0.993218i
$311$	−458.117			−1.47305			−0.736523	−	0.676412i	$-0.763534\pi$
$311$	−458.117			−1.47305			−0.736523	+	0.676412i	$0.763534\pi$
$312$		0			0
$313$			170.865i			0.545893i	0.962029	+	0.272947i	$0.0879982\pi$
$313$			170.865i			0.545893i	−0.962029	+	0.272947i	$0.912002\pi$
$314$	186.973	+	206.664i	0.595455	+	0.658166i
$315$		0			0
$316$	−34.8205	+	347.166i	−0.110192	+	1.09863i
$317$	−372.560	+	372.560i	−1.17527	+	1.17527i	−0.194334	+	0.980935i	$0.562254\pi$
$317$	−372.560	+	372.560i	−1.17527	+	1.17527i	−0.980935	+	0.194334i	$0.937746\pi$
$318$		0			0
$319$		−	310.093i		−	0.972079i
$320$	253.954	+	481.315i	0.793607	+	1.50411i
$321$		0			0
$322$	7.74951	−	154.915i	0.0240668	−	0.481103i
$323$	336.647	+	336.647i	1.04225	+	1.04225i
$324$		0			0
$325$	417.630	+	417.630i	1.28502	+	1.28502i
$326$	190.169	−	172.049i	0.583340	−	0.527758i
$327$		0			0
$328$	−52.8222	−	7.98047i	−0.161043	−	0.0243307i
$329$			207.773i			0.631529i
$330$		0			0
$331$	−177.685	+	177.685i	−0.536812	+	0.536812i	−0.922591	−	0.385779i	$-0.873933\pi$
$331$	−177.685	+	177.685i	−0.536812	+	0.536812i	0.385779	+	0.922591i	$0.373933\pi$
$332$	−34.1574	−	41.7731i	−0.102884	−	0.125823i
$333$		0			0
$334$	−18.1463	+	362.751i	−0.0543303	+	1.08608i
$335$			92.8260i			0.277092i
$336$		0			0
$337$	491.680			1.45899			0.729496	−	0.683985i	$-0.239755\pi$
$337$	491.680			1.45899			0.729496	+	0.683985i	$0.239755\pi$
$338$	−26.1873	−	1.31000i	−0.0774772	−	0.00387574i
$339$		0			0
$340$	−305.200	−	373.248i	−0.897646	−	1.09779i
$341$	−159.070	−	159.070i	−0.466480	−	0.466480i
$342$		0			0
$343$	−248.902			−0.725661
$344$	−6.02965	−	8.17583i	−0.0175280	−	0.0237670i
$345$		0			0
$346$	5.05766	+	5.59031i	0.0146175	+	0.0161570i
$347$	176.788	−	176.788i	0.509477	−	0.509477i	−0.404889	−	0.914366i	$-0.632690\pi$
$347$	176.788	−	176.788i	0.509477	−	0.509477i	0.914366	+	0.404889i	$0.132690\pi$
$348$		0			0
$349$	−272.298	+	272.298i	−0.780223	+	0.780223i	−0.979868	−	0.199645i	$-0.936021\pi$
$349$	−272.298	+	272.298i	−0.780223	+	0.780223i	0.199645	+	0.979868i	$0.436021\pi$
$350$	−777.827	−	38.9102i	−2.22236	−	0.111172i
$351$		0			0
$352$	150.449	+	253.576i	0.427412	+	0.720386i
$353$	168.099			0.476200			0.238100	−	0.971241i	$-0.423475\pi$
$353$	168.099			0.476200			0.238100	+	0.971241i	$0.423475\pi$
$354$		0			0
$355$	−825.290	−	825.290i	−2.32476	−	2.32476i
$356$	58.4773	−	583.027i	0.164262	−	1.63772i
$357$		0			0
$358$	−26.7403	+	24.1925i	−0.0746937	+	0.0675767i
$359$	476.009			1.32593			0.662965	−	0.748651i	$-0.269298\pi$
$359$	476.009			1.32593			0.662965	+	0.748651i	$0.269298\pi$
$360$		0			0
$361$			767.008i			2.12468i
$362$	128.574	−	116.323i	0.355177	−	0.321335i
$363$		0			0
$364$	−318.266	+	260.242i	−0.874356	+	0.714950i
$365$	−317.862	+	317.862i	−0.870855	+	0.870855i
$366$		0			0
$367$		−	104.894i		−	0.285814i	−0.989736	−	0.142907i	$-0.954355\pi$
$367$		−	104.894i		−	0.285814i	0.989736	−	0.142907i	$-0.0456450\pi$
$368$	−147.737	−	29.9371i	−0.401460	−	0.0813508i
$369$		0			0
$370$	581.422	+	29.0852i	1.57141	+	0.0786086i
$371$	268.565	+	268.565i	0.723896	+	0.723896i
$372$		0			0
$373$	−122.301	−	122.301i	−0.327884	−	0.327884i	0.523898	−	0.851781i	$-0.324477\pi$
$373$	−122.301	−	122.301i	−0.327884	−	0.327884i	−0.851781	+	0.523898i	$0.824477\pi$
$374$	−175.254	−	193.711i	−0.468593	−	0.517944i
$375$		0			0
$376$	199.655	+	30.1642i	0.530997	+	0.0802240i
$377$		−	420.197i		−	1.11458i
$378$		0			0
$379$	75.5625	−	75.5625i	0.199373	−	0.199373i	−0.600358	−	0.799731i	$-0.704975\pi$
$379$	75.5625	−	75.5625i	0.199373	−	0.199373i	0.799731	+	0.600358i	$0.204975\pi$
$380$	114.005	−	1136.64i	0.300012	−	2.99116i
$381$		0			0
$382$	−160.041	−	8.00591i	−0.418955	−	0.0209579i
$383$		−	501.509i		−	1.30942i	−0.755878	−	0.654712i	$-0.772790\pi$
$383$		−	501.509i		−	1.30942i	0.755878	−	0.654712i	$-0.227210\pi$
$384$		0			0
$385$	−644.953			−1.67520
$386$	−2.87335	+	57.4392i	−0.00744391	+	0.148806i
$387$		0			0
$388$	−402.658	−	40.3863i	−1.03778	−	0.104089i
$389$	22.6053	+	22.6053i	0.0581114	+	0.0581114i	0.735565	−	0.677454i	$-0.236917\pi$
$389$	22.6053	+	22.6053i	0.0581114	+	0.0581114i	−0.677454	+	0.735565i	$0.736917\pi$
$390$		0			0
$391$	133.549			0.341559
$392$	22.4242	−	148.425i	0.0572047	−	0.378634i
$393$		0			0
$394$	194.647	−	176.101i	0.494029	−	0.446957i
$395$	−524.465	+	524.465i	−1.32776	+	1.32776i
$396$		0			0
$397$	−6.09563	+	6.09563i	−0.0153542	+	0.0153542i	−0.714742	−	0.699388i	$-0.753456\pi$
$397$	−6.09563	+	6.09563i	−0.0153542	+	0.0153542i	0.699388	+	0.714742i	$0.253456\pi$
$398$	−16.5428	+	330.696i	−0.0415649	+	0.830895i
$399$		0			0
$400$	−150.314	+	741.787i	−0.375785	+	1.85447i
$401$	−598.130			−1.49160			−0.745798	−	0.666172i	$-0.767932\pi$
$401$	−598.130			−1.49160			−0.745798	+	0.666172i	$0.767932\pi$
$402$		0			0
$403$	−215.550	−	215.550i	−0.534863	−	0.534863i
$404$	−170.058	−	207.975i	−0.420936	−	0.514789i
$405$		0			0
$406$	371.729	+	410.878i	0.915589	+	1.01202i
$407$	315.407			0.774957
$408$		0			0
$409$			271.241i			0.663181i	0.943423	+	0.331591i	$0.107585\pi$
$409$			271.241i			0.663181i	−0.943423	+	0.331591i	$0.892415\pi$
$410$	−76.1892	−	84.2132i	−0.185827	−	0.205398i
$411$		0			0
$412$	−30.1892	−	3.02796i	−0.0732749	−	0.00734943i
$413$	−68.4785	+	68.4785i	−0.165808	+	0.165808i
$414$		0			0
$415$		−	114.709i		−	0.276406i
$416$	203.868	+	343.612i	0.490068	+	0.825990i
$417$		0			0
$418$	30.9224	−	618.148i	0.0739769	−	1.47882i
$419$	412.163	+	412.163i	0.983681	+	0.983681i	0.999869	−	0.0161876i	$-0.00515289\pi$
$419$	412.163	+	412.163i	0.983681	+	0.983681i	−0.0161876	+	0.999869i	$0.505153\pi$
$420$		0			0
$421$	135.609	+	135.609i	0.322111	+	0.322111i	0.849576	−	0.527466i	$-0.176858\pi$
$421$	135.609	+	135.609i	0.322111	+	0.322111i	−0.527466	+	0.849576i	$0.676858\pi$
$422$	−393.832	+	356.307i	−0.933252	+	0.844330i
$423$		0			0
$424$	297.062	−	219.082i	0.700618	−	0.516703i
$425$		−	670.550i		−	1.57777i
$426$		0			0
$427$	−563.083	+	563.083i	−1.31869	+	1.31869i
$428$	−524.442	+	428.829i	−1.22533	+	1.00194i
$429$		0			0
$430$	1.07895	−	21.5685i	0.00250918	−	0.0501593i
$431$		−	204.169i		−	0.473710i	−0.971545	−	0.236855i	$-0.923883\pi$
$431$		−	204.169i		−	0.473710i	0.971545	−	0.236855i	$-0.0761166\pi$
$432$		0			0
$433$	317.530			0.733325			0.366663	−	0.930354i	$-0.380500\pi$
$433$	317.530			0.733325			0.366663	+	0.930354i	$0.380500\pi$
$434$	401.457	+	20.0826i	0.925016	+	0.0462732i
$435$		0			0
$436$	−267.248	+	218.525i	−0.612954	+	0.501204i
$437$	223.743	+	223.743i	0.511998	+	0.511998i
$438$		0			0
$439$	226.050			0.514921			0.257461	−	0.966289i	$-0.417114\pi$
$439$	226.050			0.514921			0.257461	+	0.966289i	$0.417114\pi$
$440$	−93.6335	+	619.754i	−0.212803	+	1.40853i
$441$		0			0
$442$	−237.480	−	262.491i	−0.537286	−	0.593871i
$443$	157.388	−	157.388i	0.355278	−	0.355278i	−0.506791	−	0.862069i	$-0.669169\pi$
$443$	157.388	−	157.388i	0.355278	−	0.355278i	0.862069	+	0.506791i	$0.169169\pi$
$444$		0			0
$445$	880.782	−	880.782i	1.97929	−	1.97929i
$446$	613.617	+	30.6957i	1.37582	+	0.0688244i
$447$		0			0
$448$	−503.325	−	155.639i	−1.12349	−	0.347409i
$449$	458.567			1.02131			0.510653	−	0.859787i	$-0.329404\pi$
$449$	458.567			1.02131			0.510653	+	0.859787i	$0.329404\pi$
$450$		0			0
$451$	−43.5072	−	43.5072i	−0.0964684	−	0.0964684i
$452$	125.919	+	12.6296i	0.278582	+	0.0279416i
$453$		0			0
$454$	236.925	−	214.351i	0.521862	−	0.472138i
$455$	−873.954			−1.92078
$456$		0			0
$457$			548.682i			1.20062i	0.799768	+	0.600309i	$0.204956\pi$
$457$			548.682i			1.20062i	−0.799768	+	0.600309i	$0.795044\pi$
$458$	15.3576	−	13.8943i	0.0335318	−	0.0303368i
$459$		0			0
$460$	−202.842	−	248.069i	−0.440962	−	0.539280i
$461$	−359.058	+	359.058i	−0.778868	+	0.778868i	−0.979638	−	0.200770i	$-0.935656\pi$
$461$	−359.058	+	359.058i	−0.778868	+	0.778868i	0.200770	+	0.979638i	$0.435656\pi$
$462$		0			0
$463$			126.697i			0.273643i	0.990596	+	0.136822i	$0.0436887\pi$
$463$			126.697i			0.273643i	−0.990596	+	0.136822i	$0.956311\pi$
$464$	448.792	−	297.554i	0.967223	−	0.641280i
$465$		0			0
$466$	230.528	+	11.5320i	0.494696	+	0.0247468i
$467$	−526.834	−	526.834i	−1.12812	−	1.12812i	−0.990482	−	0.137643i	$-0.956047\pi$
$467$	−526.834	−	526.834i	−1.12812	−	1.12812i	−0.137643	−	0.990482i	$-0.543953\pi$
$468$		0			0
$469$	−63.5436	−	63.5436i	−0.135487	−	0.135487i
$470$	287.976	+	318.305i	0.612716	+	0.677245i
$471$		0			0
$472$	55.8613	+	75.7445i	0.118350	+	0.160476i
$473$		−	11.7004i		−	0.0247366i
$474$		0			0
$475$	1123.41	−	1123.41i	2.36508	−	2.36508i
$476$	464.428	+	46.5819i	0.975689	+	0.0978611i
$477$		0			0
$478$	645.735	+	32.3024i	1.35091	+	0.0675782i
$479$		−	712.831i		−	1.48817i	−0.668087	−	0.744083i	$-0.732887\pi$
$479$		−	712.831i		−	1.48817i	0.668087	−	0.744083i	$-0.267113\pi$
$480$		0			0
$481$	427.398			0.888560
$482$	−11.7966	+	235.818i	−0.0244743	+	0.489248i
$483$		0			0
$484$	14.4117	−	143.687i	0.0297762	−	0.296873i
$485$	−608.297	−	608.297i	−1.25422	−	1.25422i
$486$		0			0
$487$	579.851			1.19066			0.595330	−	0.803481i	$-0.297021\pi$
$487$	579.851			1.19066			0.595330	+	0.803481i	$0.297021\pi$
$488$	459.334	+	622.830i	0.941259	+	1.27629i
$489$		0			0
$490$	236.630	−	214.083i	0.482918	−	0.436905i
$491$	−131.309	+	131.309i	−0.267432	+	0.267432i	−0.828065	−	0.560632i	$-0.810558\pi$
$491$	−131.309	+	131.309i	−0.267432	+	0.267432i	0.560632	+	0.828065i	$0.310558\pi$
$492$		0			0
$493$	−337.336	+	337.336i	−0.684251	+	0.684251i
$494$	41.9018	−	837.630i	0.0848215	−	1.69561i
$495$		0			0
$496$	77.5809	−	382.856i	0.156413	−	0.771887i
$497$	1129.90			2.27343
$498$		0			0
$499$	329.208	+	329.208i	0.659736	+	0.659736i	0.955318	−	0.295582i	$-0.0955134\pi$
$499$	329.208	+	329.208i	0.659736	+	0.659736i	−0.295582	+	0.955318i	$0.595513\pi$
$500$	−587.281	+	480.212i	−1.17456	+	0.960424i
$501$		0			0
$502$	−315.432	−	348.652i	−0.628350	−	0.694526i
$503$	254.299			0.505564			0.252782	−	0.967523i	$-0.418654\pi$
$503$	254.299			0.505564			0.252782	+	0.967523i	$0.418654\pi$
$504$		0			0
$505$		−	571.096i		−	1.13088i
$506$	−116.478	−	128.745i	−0.230193	−	0.254436i
$507$		0			0
$508$	35.0787	−	349.740i	0.0690525	−	0.688464i
$509$	326.512	−	326.512i	0.641477	−	0.641477i	−0.309442	−	0.950918i	$-0.600142\pi$
$509$	326.512	−	326.512i	0.641477	−	0.641477i	0.950918	+	0.309442i	$0.100142\pi$
$510$		0			0
$511$		−	435.182i		−	0.851628i
$512$	−222.630	+	461.064i	−0.434824	+	0.900515i
$513$		0			0
$514$	−34.2483	+	684.634i	−0.0666309	+	1.33197i
$515$	−45.6071	−	45.6071i	−0.0885574	−	0.0885574i
$516$		0			0
$517$	164.447	+	164.447i	0.318079	+	0.318079i
$518$	−417.920	+	378.099i	−0.806795	+	0.729922i
$519$		0			0
$520$	−126.879	+	839.807i	−0.243999	+	1.61501i
$521$			775.042i			1.48760i	0.668400	+	0.743802i	$0.266980\pi$
$521$			775.042i			1.48760i	−0.668400	+	0.743802i	$0.733020\pi$
$522$		0			0
$523$	−461.875	+	461.875i	−0.883126	+	0.883126i	−0.993851	−	0.110725i	$-0.964683\pi$
$523$	−461.875	+	461.875i	−0.883126	+	0.883126i	0.110725	+	0.993851i	$0.464683\pi$
$524$	631.483	+	772.279i	1.20512	+	1.47382i
$525$		0			0
$526$	21.9469	−	438.726i	0.0417242	−	0.834080i
$527$			346.089i			0.656715i
$528$		0			0
$529$	−440.240			−0.832212
$530$	783.673	+	39.2027i	1.47863	+	0.0739673i
$531$		0			0
$532$	700.042	+	856.124i	1.31587	+	1.60926i
$533$	−58.9551	−	58.9551i	−0.110610	−	0.110610i
$534$		0			0
$535$	−1440.11			−2.69180
$536$	−70.2860	+	51.8356i	−0.131131	+	0.0967083i
$537$		0			0
$538$	147.833	+	163.402i	0.274783	+	0.303722i
$539$	122.251	−	122.251i	0.226810	−	0.226810i
$540$		0			0
$541$	−426.071	+	426.071i	−0.787563	+	0.787563i	−0.981094	−	0.193531i	$-0.938006\pi$
$541$	−426.071	+	426.071i	−0.787563	+	0.787563i	0.193531	+	0.981094i	$0.438006\pi$
$542$	−309.796	−	15.4973i	−0.571579	−	0.0285928i
$543$		0			0
$544$	112.187	−	439.519i	0.206226	−	0.807940i
$545$	−733.860			−1.34653
$546$		0			0
$547$	−111.138	−	111.138i	−0.203178	−	0.203178i	0.598182	−	0.801360i	$-0.295890\pi$
$547$	−111.138	−	111.138i	−0.203178	−	0.203178i	−0.801360	+	0.598182i	$0.795890\pi$
$548$	38.7308	−	386.152i	0.0706767	−	0.704657i
$549$		0			0
$550$	−646.425	+	584.832i	−1.17532	+	1.06333i
$551$	−1130.32			−2.05139
$552$		0			0
$553$		−	718.041i		−	1.29845i
$554$	63.0488	−	57.0414i	0.113807	−	0.102963i
$555$		0			0
$556$	570.266	−	466.299i	1.02566	−	0.838668i
$557$	233.731	−	233.731i	0.419625	−	0.419625i	−0.465449	−	0.885075i	$-0.654107\pi$
$557$	233.731	−	233.731i	0.419625	−	0.419625i	0.885075	+	0.465449i	$0.154107\pi$
$558$		0			0
$559$		−	15.8548i		−	0.0283628i
$560$	−618.874	−	933.428i	−1.10513	−	1.66684i
$561$		0			0
$562$	−530.517	−	26.5387i	−0.943981	−	0.0472219i
$563$	−261.362	−	261.362i	−0.464231	−	0.464231i	0.435809	−	0.900039i	$-0.356462\pi$
$563$	−261.362	−	261.362i	−0.464231	−	0.464231i	−0.900039	+	0.435809i	$0.856462\pi$
$564$		0			0
$565$	190.227	+	190.227i	0.336684	+	0.336684i
$566$	304.033	+	336.052i	0.537160	+	0.593732i
$567$		0			0
$568$	164.037	−	1085.75i	0.288797	−	1.91153i
$569$		−	453.881i		−	0.797682i	−0.917020	−	0.398841i	$-0.869413\pi$
$569$		−	453.881i		−	0.797682i	0.917020	−	0.398841i	$-0.130587\pi$
$570$		0			0
$571$	−289.009	+	289.009i	−0.506146	+	0.506146i	−0.913341	−	0.407195i	$-0.866507\pi$
$571$	−289.009	+	289.009i	−0.506146	+	0.506146i	0.407195	+	0.913341i	$0.366507\pi$
$572$	−45.9243	+	457.872i	−0.0802873	+	0.800476i
$573$		0			0
$574$	109.803	+	5.49280i	0.191294	+	0.00956933i
$575$		−	445.662i		−	0.775065i
$576$		0			0
$577$	588.041			1.01913			0.509567	−	0.860431i	$-0.329806\pi$
$577$	588.041			1.01913			0.509567	+	0.860431i	$0.329806\pi$
$578$	8.79921	−	175.899i	0.0152235	−	0.304324i
$579$		0			0
$580$	1138.97	+	114.238i	1.96374	+	0.196962i
$581$	78.5232	+	78.5232i	0.135152	+	0.135152i
$582$		0			0
$583$	425.124			0.729201
$584$	−418.179	−	63.1791i	−0.716059	−	0.108183i
$585$		0			0
$586$	−364.453	+	329.727i	−0.621933	+	0.562674i
$587$	392.596	−	392.596i	0.668818	−	0.668818i	−0.288624	−	0.957442i	$-0.593198\pi$
$587$	392.596	−	392.596i	0.668818	−	0.668818i	0.957442	+	0.288624i	$0.0931978\pi$
$588$		0			0
$589$	−579.822	+	579.822i	−0.984417	+	0.984417i
$590$	−9.99585	+	199.820i	−0.0169421	+	0.338678i
$591$		0			0
$592$	302.653	+	456.483i	0.511239	+	0.771086i
$593$	−1008.70			−1.70101			−0.850505	−	0.525967i	$-0.823703\pi$
$593$	−1008.70			−1.70101			−0.850505	+	0.525967i	$0.823703\pi$
$594$		0			0
$595$	701.614	+	701.614i	1.17918	+	1.17918i
$596$	−94.3879	−	115.433i	−0.158369	−	0.193679i
$597$		0			0
$598$	−157.835	−	174.457i	−0.263938	−	0.291735i
$599$	526.819			0.879498			0.439749	−	0.898121i	$-0.355067\pi$
$599$	526.819			0.879498			0.439749	+	0.898121i	$0.355067\pi$
$600$		0			0
$601$		−	867.891i		−	1.44408i	−0.691853	−	0.722039i	$-0.743205\pi$
$601$		−	867.891i		−	1.44408i	0.691853	−	0.722039i	$-0.256795\pi$
$602$	14.0260	+	15.5032i	0.0232991	+	0.0257528i
$603$		0			0
$604$	−780.511	−	78.2848i	−1.29224	−	0.129611i
$605$	217.068	−	217.068i	0.358790	−	0.358790i
$606$		0			0
$607$			98.8497i			0.162850i	0.996679	+	0.0814248i	$0.0259470\pi$
$607$			98.8497i			0.162850i	−0.996679	+	0.0814248i	$0.974053\pi$
$608$	924.305	−	548.399i	1.52024	−	0.901971i
$609$		0			0
$610$	−82.1935	+	1643.07i	−0.134743	+	2.69356i
$611$	222.836	+	222.836i	0.364707	+	0.364707i
$612$		0			0
$613$	−616.976	−	616.976i	−1.00649	−	1.00649i	−0.999979	−	0.00650651i	$-0.997929\pi$
$613$	−616.976	−	616.976i	−1.00649	−	1.00649i	−0.00650651	−	0.999979i	$-0.502071\pi$
$614$	−287.017	+	259.669i	−0.467454	+	0.422914i
$615$		0			0
$616$	−360.153	−	488.346i	−0.584664	−	0.792769i
$617$		−	1073.62i		−	1.74007i	−0.492993	−	0.870033i	$-0.664097\pi$
$617$		−	1073.62i		−	1.74007i	0.492993	−	0.870033i	$-0.335903\pi$
$618$		0			0
$619$	397.119	−	397.119i	0.641549	−	0.641549i	−0.309387	−	0.950936i	$-0.600124\pi$
$619$	397.119	−	397.119i	0.641549	−	0.641549i	0.950936	+	0.309387i	$0.100124\pi$
$620$	642.861	−	525.659i	1.03687	−	0.847837i
$621$		0			0
$622$	45.7767	−	915.091i	0.0735960	−	1.47121i
$623$			1205.87i			1.93559i
$624$		0			0
$625$	−430.067			−0.688107
$626$	−341.302	−	17.0734i	−0.545211	−	0.0272738i
$627$		0			0
$628$	−431.495	+	352.828i	−0.687094	+	0.561828i
$629$	−343.117	−	343.117i	−0.545495	−	0.545495i
$630$		0			0
$631$	−381.081			−0.603931			−0.301966	−	0.953319i	$-0.597643\pi$
$631$	−381.081			−0.603931			−0.301966	+	0.953319i	$0.597643\pi$
$632$	−689.985	−	104.244i	−1.09175	−	0.164943i
$633$		0			0
$634$	−706.963	−	781.418i	−1.11508	−	1.23252i
$635$	528.354	−	528.354i	0.832053	−	0.832053i
$636$		0			0
$637$	165.657	−	165.657i	0.260059	−	0.260059i
$638$	619.412	+	30.9856i	0.970865	+	0.0485668i
$639$		0			0
$640$	−986.804	+	459.179i	−1.54188	+	0.717468i
$641$	−485.443			−0.757321			−0.378661	−	0.925536i	$-0.623615\pi$
$641$	−485.443			−0.757321			−0.378661	+	0.925536i	$0.623615\pi$
$642$		0			0
$643$	457.641	+	457.641i	0.711728	+	0.711728i	0.966897	−	0.255168i	$-0.0821308\pi$
$643$	457.641	+	457.641i	0.711728	+	0.711728i	−0.255168	+	0.966897i	$0.582131\pi$
$644$	308.669	+	30.9593i	0.479300	+	0.0480735i
$645$		0			0
$646$	−706.092	+	638.814i	−1.09302	+	0.988877i
$647$	845.780			1.30723			0.653617	−	0.756826i	$-0.273251\pi$
$647$	845.780			1.30723			0.653617	+	0.756826i	$0.273251\pi$
$648$		0			0
$649$			108.398i			0.167023i
$650$	−875.948	+	792.486i	−1.34761	+	1.21921i
$651$		0			0
$652$	324.666	+	397.054i	0.497954	+	0.608979i
$653$	−11.1039	+	11.1039i	−0.0170044	+	0.0170044i	−0.715558	−	0.698553i	$-0.753827\pi$
$653$	−11.1039	+	11.1039i	−0.0170044	+	0.0170044i	0.698553	+	0.715558i	$0.253827\pi$
$654$		0			0
$655$			2120.67i			3.23766i
$656$	21.2192	−	104.715i	0.0323463	−	0.159627i
$657$		0			0
$658$	−415.027	−	20.7614i	−0.630741	−	0.0315523i
$659$	−296.711	−	296.711i	−0.450245	−	0.450245i	0.445191	−	0.895436i	$-0.353136\pi$
$659$	−296.711	−	296.711i	−0.450245	−	0.450245i	−0.895436	+	0.445191i	$0.853136\pi$
$660$		0			0
$661$	−0.564899	−	0.564899i	−0.000854613	−	0.000854613i	0.706679	−	0.707534i	$-0.250192\pi$
$661$	−0.564899	−	0.564899i	−0.000854613	−	0.000854613i	−0.707534	+	0.706679i	$0.750192\pi$
$662$	−337.171	−	372.680i	−0.509321	−	0.562961i
$663$		0			0
$664$	86.8551	−	64.0553i	0.130806	−	0.0964688i
$665$			2350.91i			3.53520i
$666$		0			0
$667$	−224.201	+	224.201i	−0.336133	+	0.336133i
$668$	−722.782	−	72.4946i	−1.08201	−	0.108525i
$669$		0			0
$670$	−185.420	−	9.27550i	−0.276746	−	0.0138440i
$671$			891.329i			1.32836i
$672$		0			0
$673$	−1091.24			−1.62146			−0.810731	−	0.585419i	$-0.800930\pi$
$673$	−1091.24			−1.62146			−0.810731	+	0.585419i	$0.800930\pi$
$674$	−49.1304	+	982.132i	−0.0728938	+	1.45717i
$675$		0			0
$676$	5.23345	−	52.1783i	0.00774180	−	0.0771868i
$677$	494.409	+	494.409i	0.730294	+	0.730294i	0.970678	−	0.240384i	$-0.0772733\pi$
$677$	494.409	+	494.409i	0.730294	+	0.730294i	−0.240384	+	0.970678i	$0.577273\pi$
$678$		0			0
$679$	832.814			1.22653
$680$	776.060	−	572.341i	1.14126	−	0.841678i
$681$		0			0
$682$	333.637	−	301.847i	0.489204	−	0.442591i
$683$	−845.268	+	845.268i	−1.23758	+	1.23758i	−0.276594	+	0.960987i	$0.589206\pi$
$683$	−845.268	+	845.268i	−1.23758	+	1.23758i	−0.960987	+	0.276594i	$0.910794\pi$
$684$		0			0
$685$	583.362	−	583.362i	0.851623	−	0.851623i
$686$	24.8711	−	497.182i	0.0362553	−	0.724755i
$687$		0			0
$688$	16.9338	−	11.2273i	0.0246130	−	0.0163187i
$689$	576.071			0.836097
$690$		0			0
$691$	457.715	+	457.715i	0.662395	+	0.662395i	0.955944	−	0.293549i	$-0.0948364\pi$
$691$	457.715	+	457.715i	0.662395	+	0.662395i	−0.293549	+	0.955944i	$0.594836\pi$
$692$	−11.6720	+	9.54407i	−0.0168671	+	0.0137920i
$693$		0			0
$694$	335.470	+	370.801i	0.483386	+	0.534295i
$695$	1565.95			2.25316
$696$		0			0
$697$			94.6589i			0.135809i
$698$	−516.707	−	571.125i	−0.740268	−	0.818230i
$699$		0			0
$700$	155.446	−	1549.82i	0.222066	−	2.21403i
$701$	−199.252	+	199.252i	−0.284239	+	0.284239i	−0.834797	−	0.550558i	$-0.814415\pi$
$701$	−199.252	+	199.252i	−0.284239	+	0.284239i	0.550558	+	0.834797i	$0.314415\pi$
$702$		0			0
$703$		−	1149.69i		−	1.63540i
$704$	−521.552	+	275.184i	−0.740841	+	0.390886i
$705$		0			0
$706$	−16.7970	+	335.777i	−0.0237918	+	0.475605i
$707$	390.941	+	390.941i	0.552958	+	0.552958i
$708$		0			0
$709$	−547.374	−	547.374i	−0.772036	−	0.772036i	0.206426	−	0.978462i	$-0.433817\pi$
$709$	−547.374	−	547.374i	−0.772036	−	0.772036i	−0.978462	+	0.206426i	$0.933817\pi$
$710$	1730.98	−	1566.05i	2.43801	−	2.20571i
$711$		0			0
$712$	1158.75	+	175.067i	1.62746	+	0.245880i
$713$			230.018i			0.322606i
$714$		0			0
$715$	−691.710	+	691.710i	−0.967427	+	0.967427i
$716$	−45.6525	−	55.8313i	−0.0637605	−	0.0779766i
$717$		0			0
$718$	−47.5644	+	950.828i	−0.0662457	+	1.32427i
$719$			90.5082i			0.125881i	0.998017	+	0.0629403i	$0.0200478\pi$
$719$			90.5082i			0.125881i	−0.998017	+	0.0629403i	$0.979952\pi$
$720$		0			0
$721$	62.4402			0.0866022
$722$	−1532.10	−	76.6421i	−2.12202	−	0.106153i
$723$		0			0
$724$	219.508	+	268.450i	0.303188	+	0.370788i
$725$	1125.71	+	1125.71i	1.55270	+	1.55270i
$726$		0			0
$727$	−222.068			−0.305459			−0.152729	−	0.988268i	$-0.548806\pi$
$727$	−222.068			−0.305459			−0.152729	+	0.988268i	$0.548806\pi$
$728$	−488.031	−	661.741i	−0.670372	−	0.908984i
$729$		0			0
$730$	−603.168	−	666.692i	−0.826258	−	0.913277i
$731$	−12.7283	+	12.7283i	−0.0174122	+	0.0174122i
$732$		0			0
$733$	201.142	−	201.142i	0.274410	−	0.274410i	−0.556463	−	0.830873i	$-0.687842\pi$
$733$	201.142	−	201.142i	0.274410	−	0.274410i	0.830873	+	0.556463i	$0.187842\pi$
$734$	209.526	+	10.4814i	0.285457	+	0.0142798i
$735$		0			0
$736$	74.5618	−	292.114i	0.101307	−	0.396894i
$737$	−100.586			−0.136480
$738$		0			0
$739$	−771.595	−	771.595i	−1.04411	−	1.04411i	−0.998981	−	0.0451261i	$-0.985631\pi$
$739$	−771.595	−	771.595i	−1.04411	−	1.04411i	−0.0451261	−	0.998981i	$-0.514369\pi$
$740$	−116.195	+	1158.48i	−0.157021	+	1.56552i
$741$		0			0
$742$	−563.296	+	509.624i	−0.759159	+	0.686825i
$743$	−754.171			−1.01503			−0.507517	−	0.861641i	$-0.669437\pi$
$743$	−754.171			−1.01503			−0.507517	+	0.861641i	$0.669437\pi$
$744$		0			0
$745$		−	316.977i		−	0.425473i
$746$	256.517	−	232.075i	0.343856	−	0.311093i
$747$		0			0
$748$	404.450	−	330.714i	0.540709	−	0.442131i
$749$	985.822	−	985.822i	1.31618	−	1.31618i
$750$		0			0
$751$			606.477i			0.807559i	0.914856	+	0.403780i	$0.132304\pi$
$751$			606.477i			0.807559i	−0.914856	+	0.403780i	$0.867696\pi$
$752$	−80.2033	+	395.797i	−0.106653	+	0.526326i
$753$		0			0
$754$	839.344	+	41.9875i	1.11319	+	0.0556863i
$755$	−1179.12	−	1179.12i	−1.56175	−	1.56175i
$756$		0			0
$757$	−852.254	−	852.254i	−1.12583	−	1.12583i	−0.990848	−	0.134983i	$-0.956902\pi$
$757$	−852.254	−	852.254i	−1.12583	−	1.12583i	−0.134983	−	0.990848i	$-0.543098\pi$
$758$	143.386	+	158.487i	0.189163	+	0.209085i
$759$		0			0
$760$	2259.05	+	341.301i	2.97244	+	0.449081i
$761$		−	1373.25i		−	1.80453i	−0.431180	−	0.902266i	$-0.641903\pi$
$761$		−	1373.25i		−	1.80453i	0.431180	−	0.902266i	$-0.358097\pi$
$762$		0			0
$763$	502.360	−	502.360i	0.658401	−	0.658401i
$764$	31.9837	−	318.882i	0.0418634	−	0.417385i
$765$		0			0
$766$	1001.77	+	50.1126i	1.30779	+	0.0654211i
$767$			146.886i			0.191507i
$768$		0			0
$769$	515.727			0.670647			0.335323	−	0.942103i	$-0.391154\pi$
$769$	515.727			0.670647			0.335323	+	0.942103i	$0.391154\pi$
$770$	64.4460	−	1288.30i	0.0836961	−	1.67311i
$771$		0			0
$772$	−114.448	−	11.4791i	−0.148248	−	0.0148692i
$773$	448.985	+	448.985i	0.580834	+	0.580834i	0.935132	−	0.354299i	$-0.115280\pi$
$773$	448.985	+	448.985i	0.580834	+	0.580834i	−0.354299	+	0.935132i	$0.615280\pi$
$774$		0			0
$775$	1154.92			1.49022
$776$	120.907	−	800.274i	0.155808	−	1.03128i
$777$		0			0
$778$	−47.4130	+	42.8954i	−0.0609422	+	0.0551355i
$779$	−158.587	+	158.587i	−0.203578	+	0.203578i
$780$		0			0
$781$	894.282	−	894.282i	1.14505	−	1.14505i
$782$	−13.3447	+	266.765i	−0.0170649	+	0.341132i
$783$		0			0
$784$	294.238	+	59.6236i	0.375303	+	0.0760505i
$785$	−1184.88			−1.50940
$786$		0			0
$787$	70.0485	+	70.0485i	0.0890070	+	0.0890070i	0.750208	−	0.661201i	$-0.229953\pi$
$787$	70.0485	+	70.0485i	0.0890070	+	0.0890070i	−0.661201	+	0.750208i	$0.729953\pi$
$788$	332.312	+	406.405i	0.421716	+	0.515743i
$789$		0			0
$790$	−995.214	−	1100.03i	−1.25976	−	1.39244i
$791$	−260.437			−0.329251
$792$		0			0
$793$			1207.81i			1.52309i
$794$	−11.5669	−	12.7851i	−0.0145679	−	0.0161022i
$795$		0			0
$796$	−658.914	−	66.0887i	−0.827781	−	0.0830260i
$797$	584.026	−	584.026i	0.732780	−	0.732780i	−0.238390	−	0.971170i	$-0.576620\pi$
$797$	584.026	−	584.026i	0.732780	−	0.732780i	0.971170	+	0.238390i	$0.0766195\pi$
$798$		0			0
$799$		−	357.787i		−	0.447794i
$800$	−1466.70	−	374.374i	−1.83338	−	0.467968i
$801$		0			0
$802$	59.7673	−	1194.77i	0.0745228	−	1.48973i
$803$	−344.434	−	344.434i	−0.428935	−	0.428935i
$804$		0			0
$805$	466.308	+	466.308i	0.579265	+	0.579265i
$806$	452.100	−	409.023i	0.560918	−	0.507472i
$807$		0			0
$808$	432.423	−	318.910i	0.535176	−	0.394691i
$809$			1252.15i			1.54778i	0.633321	+	0.773889i	$0.281691\pi$
$809$			1252.15i			1.54778i	−0.633321	+	0.773889i	$0.718309\pi$
$810$		0			0
$811$	−255.775	+	255.775i	−0.315382	+	0.315382i	−0.846990	−	0.531608i	$-0.821588\pi$
$811$	−255.775	+	255.775i	−0.315382	+	0.315382i	0.531608	+	0.846990i	$0.321588\pi$
$812$	−857.875	+	701.473i	−1.05650	+	0.863883i
$813$		0			0
$814$	−31.5166	+	630.027i	−0.0387182	+	0.773989i
$815$			1090.31i			1.33780i
$816$		0			0
$817$	−42.6489			−0.0522018
$818$	−541.805	−	27.1034i	−0.662353	−	0.0331337i
$819$		0			0
$820$	175.829	−	143.773i	0.214426	−	0.175333i
$821$	228.380	+	228.380i	0.278173	+	0.278173i	0.832379	−	0.554206i	$-0.186978\pi$
$821$	228.380	+	228.380i	0.278173	+	0.278173i	−0.554206	+	0.832379i	$0.686978\pi$
$822$		0			0
$823$	1050.55			1.27649			0.638246	−	0.769832i	$-0.279660\pi$
$823$	1050.55			1.27649			0.638246	+	0.769832i	$0.279660\pi$
$824$	9.06498	−	60.0005i	0.0110012	−	0.0728162i
$825$		0			0
$826$	−129.943	−	143.629i	−0.157316	−	0.173885i
$827$	78.0300	−	78.0300i	0.0943531	−	0.0943531i	−0.658355	−	0.752708i	$-0.728747\pi$
$827$	78.0300	−	78.0300i	0.0943531	−	0.0943531i	0.752708	+	0.658355i	$0.228747\pi$
$828$		0			0
$829$	−517.848	+	517.848i	−0.624665	+	0.624665i	−0.946721	−	0.322056i	$-0.895626\pi$
$829$	−517.848	+	517.848i	−0.624665	+	0.624665i	0.322056	+	0.946721i	$0.395626\pi$
$830$	229.131	+	11.4621i	0.276061	+	0.0138097i
$831$		0			0
$832$	−706.737	+	372.892i	−0.849443	+	0.448188i
$833$	−265.981			−0.319305
$834$		0			0
$835$	−1091.91	−	1091.91i	−1.30768	−	1.30768i
$836$	1231.66	+	123.535i	1.47328	+	0.147769i
$837$		0			0
$838$	−864.480	+	782.111i	−1.03160	+	0.933306i
$839$	649.581			0.774232			0.387116	−	0.922031i	$-0.373471\pi$
$839$	649.581			0.774232			0.387116	+	0.922031i	$0.373471\pi$
$840$		0			0
$841$		−	291.627i		−	0.346762i
$842$	−284.429	+	257.328i	−0.337802	+	0.305615i
$843$		0			0
$844$	−672.371	−	822.284i	−0.796648	−	0.974270i
$845$	78.8260	−	78.8260i	0.0932852	−	0.0932852i
$846$		0			0
$847$			297.186i			0.350869i
$848$	407.933	+	615.273i	0.481054	+	0.725558i
$849$		0			0
$850$	1339.43	+	67.0037i	1.57580	+	0.0788279i
$851$	−228.043	−	228.043i	−0.267970	−	0.267970i
$852$		0			0
$853$	1124.04	+	1124.04i	1.31775	+	1.31775i	0.915551	+	0.402202i	$0.131755\pi$
$853$	1124.04	+	1124.04i	1.31775	+	1.31775i	0.402202	+	0.915551i	$0.368245\pi$
$854$	−1068.49	−	1181.02i	−1.25116	−	1.38293i
$855$		0			0
$856$	−804.184	−	1090.42i	−0.939467	−	1.27386i
$857$			596.973i			0.696585i	0.937386	+	0.348292i	$0.113238\pi$
$857$			596.973i			0.696585i	−0.937386	+	0.348292i	$0.886762\pi$
$858$		0			0
$859$	701.595	−	701.595i	0.816758	−	0.816758i	−0.168879	−	0.985637i	$-0.554015\pi$
$859$	701.595	−	701.595i	0.816758	−	0.816758i	0.985637	+	0.168879i	$0.0540147\pi$
$860$	42.9753	+	4.31040i	0.0499713	+	0.00501210i
$861$		0			0
$862$	407.828	+	20.4013i	0.473118	+	0.0236674i
$863$			437.703i			0.507187i	0.967311	+	0.253594i	$0.0816126\pi$
$863$			437.703i			0.507187i	−0.967311	+	0.253594i	$0.918387\pi$
$864$		0			0
$865$	−32.0513			−0.0370535
$866$	−31.7287	+	634.266i	−0.0366382	+	0.732409i
$867$		0			0
$868$	−80.2300	+	799.905i	−0.0924309	+	0.921549i
$869$	−568.309	−	568.309i	−0.653981	−	0.653981i
$870$		0			0
$871$	−136.301			−0.156487
$872$	−409.800	−	555.664i	−0.469954	−	0.637229i
$873$		0			0
$874$	−469.284	+	424.570i	−0.536939	+	0.485778i
$875$	1103.94	−	1103.94i	1.26165	−	1.26165i
$876$		0			0
$877$	769.110	−	769.110i	0.876978	−	0.876978i	−0.116243	−	0.993221i	$-0.537085\pi$
$877$	769.110	−	769.110i	0.876978	−	0.876978i	0.993221	+	0.116243i	$0.0370850\pi$
$878$	−22.5877	+	451.536i	−0.0257264	+	0.514278i
$879$		0			0
$880$	−1228.60	−	248.961i	−1.39614	−	0.282910i
$881$	−351.923			−0.399459			−0.199729	−	0.979851i	$-0.564006\pi$
$881$	−351.923			−0.399459			−0.199729	+	0.979851i	$0.564006\pi$
$882$		0			0
$883$	661.014	+	661.014i	0.748601	+	0.748601i	0.974216	−	0.225616i	$-0.0724394\pi$
$883$	661.014	+	661.014i	0.748601	+	0.748601i	−0.225616	+	0.974216i	$0.572439\pi$
$884$	548.056	−	448.138i	0.619973	−	0.506944i
$885$		0			0
$886$	298.656	+	330.110i	0.337084	+	0.372584i
$887$	−794.853			−0.896114			−0.448057	−	0.894005i	$-0.647884\pi$
$887$	−794.853			−0.896114			−0.448057	+	0.894005i	$0.647884\pi$
$888$		0			0
$889$			723.364i			0.813683i
$890$	1671.35	+	1847.38i	1.87793	+	2.07570i
$891$		0			0
$892$	−122.629	+	1222.63i	−0.137477	+	1.37066i
$893$	599.421	−	599.421i	0.671244	−	0.671244i
$894$		0			0
$895$		−	153.312i		−	0.171298i
$896$	361.183	−	989.841i	0.403106	−	1.10473i
$897$		0			0
$898$	−45.8216	+	915.988i	−0.0510263	+	1.02003i
$899$	−581.008	−	581.008i	−0.646282	−	0.646282i
$900$		0			0
$901$	−462.472	−	462.472i	−0.513288	−	0.513288i
$902$	91.2532	−	82.5584i	0.101168	−	0.0915282i
$903$		0			0
$904$	−37.8099	+	250.262i	−0.0418252	+	0.276838i
$905$			737.162i			0.814544i
$906$		0			0
$907$	−943.805	+	943.805i	−1.04058	+	1.04058i	−0.0414379	+	0.999141i	$0.513194\pi$
$907$	−943.805	+	943.805i	−1.04058	+	1.04058i	−0.999141	+	0.0414379i	$0.986806\pi$
$908$	404.491	+	494.678i	0.445475	+	0.544799i
$909$		0			0
$910$	87.3285	−	1745.72i	0.0959654	−	1.91838i
$911$			190.842i			0.209487i	0.994499	+	0.104743i	$0.0334021\pi$
$911$			190.842i			0.209487i	−0.994499	+	0.104743i	$0.966598\pi$
$912$		0			0
$913$	124.298			0.136142
$914$	−1095.99	−	54.8262i	−1.19912	−	0.0599849i
$915$		0			0
$916$	26.2192	+	32.0651i	0.0286236	+	0.0350056i
$917$	−1451.70	−	1451.70i	−1.58309	−	1.58309i
$918$		0			0
$919$	−925.230			−1.00678			−0.503389	−	0.864060i	$-0.667914\pi$
$919$	−925.230			−1.00678			−0.503389	+	0.864060i	$0.667914\pi$
$920$	515.786	−	380.390i	0.560637	−	0.413468i
$921$		0			0
$922$	−681.341	−	753.098i	−0.738982	−	0.816809i
$923$	1211.81	−	1211.81i	1.31290	−	1.31290i
$924$		0			0
$925$	−1145.00	+	1145.00i	−1.23784	+	1.23784i
$926$	−253.077	−	12.6600i	−0.273301	−	0.0136717i
$927$		0			0
$928$	549.520	+	926.195i	0.592155	+	0.998055i
$929$	−91.8388			−0.0988577			−0.0494289	−	0.998778i	$-0.515740\pi$
$929$	−91.8388			−0.0988577			−0.0494289	+	0.998778i	$0.515740\pi$
$930$		0			0
$931$	−445.613	−	445.613i	−0.478639	−	0.478639i
$932$	−46.0704	+	459.329i	−0.0494318	+	0.492842i
$933$		0			0
$934$	1105.00	−	999.710i	1.18308	−	1.07035i
$935$	1110.62			1.18782
$936$		0			0
$937$		−	1615.44i		−	1.72406i	−0.506857	−	0.862030i	$-0.669193\pi$
$937$		−	1615.44i		−	1.72406i	0.506857	−	0.862030i	$-0.330807\pi$
$938$	133.278	−	120.579i	0.142087	−	0.128549i
$939$		0			0
$940$	−664.591	+	543.427i	−0.707012	+	0.578114i
$941$	−484.931	+	484.931i	−0.515336	+	0.515336i	−0.916157	−	0.400820i	$-0.868725\pi$
$941$	−484.931	+	484.931i	−0.515336	+	0.515336i	0.400820	+	0.916157i	$0.368725\pi$
$942$		0			0
$943$			62.9124i			0.0667151i
$944$	−156.882	+	104.014i	−0.166188	+	0.110185i
$945$		0			0
$946$	23.3716	+	1.16914i	0.0247057	+	0.00123588i
$947$	1053.02	+	1053.02i	1.11195	+	1.11195i	0.992887	+	0.119064i	$0.0379895\pi$
$947$	1053.02	+	1053.02i	1.11195	+	1.11195i	0.119064	+	0.992887i	$0.462010\pi$
$948$		0			0
$949$	−466.731	−	466.731i	−0.491814	−	0.491814i
$950$	2131.76	+	2356.27i	2.24396	+	2.48029i
$951$		0			0
$952$	−139.455	+	923.042i	−0.146486	+	0.969581i
$953$		−	1256.72i		−	1.31870i	−0.751838	−	0.659348i	$-0.770832\pi$
$953$		−	1256.72i		−	1.31870i	0.751838	−	0.659348i	$-0.229168\pi$
$954$		0			0
$955$	481.736	−	481.736i	0.504436	−	0.504436i
$956$	−129.048	+	1286.63i	−0.134988	+	1.34585i
$957$		0			0
$958$	1423.88	+	71.2286i	1.48631	+	0.0743514i
$959$			798.675i			0.832821i
$960$		0			0
$961$	364.917			0.379726
$962$	−42.7071	+	853.728i	−0.0443940	+	0.887451i
$963$		0			0
$964$	−469.868	−	47.1274i	−0.487414	−	0.0488874i
$965$	−172.897	−	172.897i	−0.179168	−	0.179168i
$966$		0			0
$967$	−1842.43			−1.90530			−0.952651	−	0.304066i	$-0.901656\pi$
$967$	−1842.43			−1.90530			−0.952651	+	0.304066i	$0.901656\pi$
$968$	285.574	+	43.1451i	0.295015	+	0.0445714i
$969$		0			0
$970$	1275.86	−	1154.29i	1.31532	−	1.18999i
$971$	−802.530	+	802.530i	−0.826498	+	0.826498i	−0.987031	−	0.160532i	$-0.948679\pi$
$971$	−802.530	+	802.530i	−0.826498	+	0.826498i	0.160532	+	0.987031i	$0.448679\pi$
$972$		0			0
$973$	−1071.96	+	1071.96i	−1.10171	+	1.10171i
$974$	−57.9408	+	1158.25i	−0.0594874	+	1.18917i
$975$		0			0
$976$	−1290.00	+	855.286i	−1.32172	+	0.876318i
$977$	−1505.64			−1.54109			−0.770544	−	0.637387i	$-0.780015\pi$
$977$	−1505.64			−1.54109			−0.770544	+	0.637387i	$0.780015\pi$
$978$		0			0
$979$	954.413	+	954.413i	0.974886	+	0.974886i
$980$	403.987	+	494.061i	0.412232	+	0.504143i
$981$		0			0
$982$	−249.170	−	275.411i	−0.253737	−	0.280460i
$983$	−764.708			−0.777933			−0.388966	−	0.921252i	$-0.627168\pi$
$983$	−764.708			−0.777933			−0.388966	+	0.921252i	$0.627168\pi$
$984$		0			0
$985$			1115.98i			1.13298i
$986$	−640.121	−	707.536i	−0.649210	−	0.717583i
$987$		0			0
$988$	1668.98	+	167.398i	1.68925	+	0.169431i
$989$	−8.45951	+	8.45951i	−0.00855360	+	0.00855360i
$990$		0			0
$991$		−	1683.22i		−	1.69851i	−0.527984	−	0.849254i	$-0.677052\pi$
$991$		−	1683.22i		−	1.69851i	0.527984	−	0.849254i	$-0.322948\pi$
$992$	757.003	+	193.224i	0.763108	+	0.194783i
$993$		0			0
$994$	−112.903	+	2256.97i	−0.113585	+	2.27060i
$995$	−995.424	−	995.424i	−1.00043	−	1.00043i
$996$		0			0
$997$	942.082	+	942.082i	0.944917	+	0.944917i	0.998560	−	0.0536431i	$-0.0170833\pi$
$997$	942.082	+	942.082i	0.944917	+	0.944917i	−0.0536431	+	0.998560i	$0.517083\pi$
$998$	−690.490	+	624.699i	−0.691874	+	0.625950i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.m.b.91.4	yes	16
3.2	odd	2	inner	144.3.m.b.91.5	yes	16
4.3	odd	2		576.3.m.b.271.1		16
8.3	odd	2		1152.3.m.d.415.8		16
8.5	even	2		1152.3.m.e.415.8		16
12.11	even	2		576.3.m.b.271.8		16
16.3	odd	4	inner	144.3.m.b.19.4	✓	16
16.5	even	4		1152.3.m.d.991.8		16
16.11	odd	4		1152.3.m.e.991.8		16
16.13	even	4		576.3.m.b.559.1		16
24.5	odd	2		1152.3.m.e.415.1		16
24.11	even	2		1152.3.m.d.415.1		16
48.5	odd	4		1152.3.m.d.991.1		16
48.11	even	4		1152.3.m.e.991.1		16
48.29	odd	4		576.3.m.b.559.8		16
48.35	even	4	inner	144.3.m.b.19.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.m.b.19.4	✓	16	16.3	odd	4	inner
144.3.m.b.19.5	yes	16	48.35	even	4	inner
144.3.m.b.91.4	yes	16	1.1	even	1	trivial
144.3.m.b.91.5	yes	16	3.2	odd	2	inner
576.3.m.b.271.1		16	4.3	odd	2
576.3.m.b.271.8		16	12.11	even	2
576.3.m.b.559.1		16	16.13	even	4
576.3.m.b.559.8		16	48.29	odd	4
1152.3.m.d.415.1		16	24.11	even	2
1152.3.m.d.415.8		16	8.3	odd	2
1152.3.m.d.991.1		16	48.5	odd	4
1152.3.m.d.991.8		16	16.5	even	4
1152.3.m.e.415.1		16	24.5	odd	2
1152.3.m.e.415.8		16	8.5	even	2
1152.3.m.e.991.1		16	48.11	even	4
1152.3.m.e.991.8		16	16.11	odd	4

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0999235 + 1.99750i) q^{2} +(-3.98003 - 0.399195i) q^{4} +(-6.01265 - 6.01265i) q^{5} +8.23187 q^{7} +(1.19509 - 7.91023i) q^{8} +O(q^{10})\)	\(q+(-0.0999235 + 1.99750i) q^{2} +(-3.98003 - 0.399195i) q^{4} +(-6.01265 - 6.01265i) q^{5} +8.23187 q^{7} +(1.19509 - 7.91023i) q^{8} +(12.6111 - 11.4095i) q^{10} +(6.51529 - 6.51529i) q^{11} +(8.82865 - 8.82865i) q^{13} +(-0.822557 + 16.4432i) q^{14} +(15.6813 + 3.17761i) q^{16} -14.1753 q^{17} +(-23.7488 - 23.7488i) q^{19} +(21.5303 + 26.3308i) q^{20} +(12.3633 + 13.6653i) q^{22} -9.42125 q^{23} +47.3040i q^{25} +(16.7531 + 18.5174i) q^{26} +(-32.7631 - 3.28612i) q^{28} +(23.7973 - 23.7973i) q^{29} -24.4148i q^{31} +(-7.91422 + 31.0059i) q^{32} +(1.41645 - 28.3153i) q^{34} +(-49.4954 - 49.4954i) q^{35} +(24.2052 + 24.2052i) q^{37} +(49.8113 - 45.0652i) q^{38} +(-54.7471 + 40.3758i) q^{40} -6.67771i q^{41} +(0.897918 - 0.897918i) q^{43} +(-28.5319 + 23.3302i) q^{44} +(0.941404 - 18.8190i) q^{46} +25.2401i q^{47} +18.7636 q^{49} +(-94.4898 - 4.72678i) q^{50} +(-38.6626 + 31.6139i) q^{52} +(32.6251 + 32.6251i) q^{53} -78.3484 q^{55} +(9.83783 - 65.1160i) q^{56} +(45.1573 + 49.9132i) q^{58} +(-8.31871 + 8.31871i) q^{59} +(-68.4028 + 68.4028i) q^{61} +(48.7687 + 2.43961i) q^{62} +(-61.1435 - 18.9069i) q^{64} -106.167 q^{65} +(-7.71922 - 7.71922i) q^{67} +(56.4183 + 5.65873i) q^{68} +(103.813 - 93.9213i) q^{70} +137.259 q^{71} -52.8655i q^{73} +(-50.7685 + 45.9312i) q^{74} +(85.0404 + 104.001i) q^{76} +(53.6330 - 53.6330i) q^{77} -87.2269i q^{79} +(-75.1802 - 113.392i) q^{80} +(13.3387 + 0.667260i) q^{82} +(9.53893 + 9.53893i) q^{83} +(85.2314 + 85.2314i) q^{85} +(1.70387 + 1.88332i) q^{86} +(-43.7511 - 59.3238i) q^{88} +146.488i q^{89} +(72.6762 - 72.6762i) q^{91} +(37.4969 + 3.76091i) q^{92} +(-50.4172 - 2.52208i) q^{94} +285.586i q^{95} +101.170 q^{97} +(-1.87493 + 37.4804i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4}+O(q^{10}) \) 16 * q - 12 * q^4	\( 16 q - 12 q^{4} + 16 q^{10} + 32 q^{16} - 32 q^{19} + 104 q^{22} - 24 q^{34} + 96 q^{37} - 312 q^{40} - 32 q^{43} - 224 q^{46} + 112 q^{49} - 264 q^{52} - 256 q^{55} + 312 q^{58} - 32 q^{61} + 456 q^{64} - 256 q^{67} + 744 q^{70} + 264 q^{76} - 280 q^{82} + 160 q^{85} - 912 q^{88} + 288 q^{91} - 1104 q^{94}+O(q^{100}) \) 16 * q - 12 * q^4 + 16 * q^10 + 32 * q^16 - 32 * q^19 + 104 * q^22 - 24 * q^34 + 96 * q^37 - 312 * q^40 - 32 * q^43 - 224 * q^46 + 112 * q^49 - 264 * q^52 - 256 * q^55 + 312 * q^58 - 32 * q^61 + 456 * q^64 - 256 * q^67 + 744 * q^70 + 264 * q^76 - 280 * q^82 + 160 * q^85 - 912 * q^88 + 288 * q^91 - 1104 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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