LMFDB - Embedded newform 324.3.f.q.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(55,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("324.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.f (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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.119023932416481.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 3 x^{10} + 11 x^{9} - 5 x^{8} - 14 x^{7} + 29 x^{6} - 28 x^{5} - 20 x^{4} + \cdots + 64 $ x^12 - 2x^11 - 3x^10 + 11x^9 - 5x^8 - 14x^7 + 29x^6 - 28x^5 - 20x^4 + 88x^3 - 48x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.1
Root			$-1.40311 - 0.176844i$ of defining polynomial
Character	$\chi$	$=$	324.271
Dual form			324.3.f.q.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.82144 + 0.826041i) q^{2} +(2.63531 - 3.00917i) q^{4} +(-3.61903 + 6.26834i) q^{5} +(5.95847 - 3.44013i) q^{7} +(-2.31438 + 7.65792i) q^{8} +(1.41395 - 14.4069i) q^{10} +(15.5474 - 8.97632i) q^{11} +(-3.83763 + 6.64697i) q^{13} +(-8.01134 + 11.1879i) q^{14} +(-2.11024 - 15.8602i) q^{16} -1.43720 q^{17} +13.8943i q^{19} +(9.32524 + 27.4093i) q^{20} +(-20.9040 + 29.1927i) q^{22} +(-14.3608 - 8.29122i) q^{23} +(-13.6947 - 23.7199i) q^{25} +(1.49936 - 15.2771i) q^{26} +(5.35051 - 26.9959i) q^{28} +(18.7509 + 32.4776i) q^{29} +(46.7583 + 26.9959i) q^{31} +(16.9449 + 27.1454i) q^{32} +(2.61778 - 1.18719i) q^{34} +49.7996i q^{35} +44.4415 q^{37} +(-11.4773 - 25.3078i) q^{38} +(-39.6266 - 42.2215i) q^{40} +(-28.4956 + 49.3558i) q^{41} +(-58.5593 + 33.8092i) q^{43} +(13.9611 - 70.4404i) q^{44} +(33.0063 + 3.23938i) q^{46} +(-8.17054 + 4.71726i) q^{47} +(-0.831061 + 1.43944i) q^{49} +(44.5378 + 31.8921i) q^{50} +(9.88852 + 29.0649i) q^{52} -7.82662 q^{53} +129.942i q^{55} +(12.5540 + 53.5912i) q^{56} +(-60.9816 - 43.6670i) q^{58} +(-19.4098 - 11.2062i) q^{59} +(33.5907 + 58.1808i) q^{61} +(-107.467 - 10.5473i) q^{62} +(-53.2873 - 35.4466i) q^{64} +(-27.7770 - 48.1111i) q^{65} +(59.9324 + 34.6020i) q^{67} +(-3.78748 + 4.32479i) q^{68} +(-41.1365 - 90.7072i) q^{70} +7.14792i q^{71} -80.4410 q^{73} +(-80.9476 + 36.7104i) q^{74} +(41.8105 + 36.6159i) q^{76} +(61.7594 - 106.970i) q^{77} +(40.5680 - 23.4219i) q^{79} +(107.054 + 44.1709i) q^{80} +(11.1332 - 113.437i) q^{82} +(123.148 - 71.0994i) q^{83} +(5.20128 - 9.00887i) q^{85} +(78.7347 - 109.954i) q^{86} +(32.7573 + 139.836i) q^{88} +42.1078 q^{89} +52.8077i q^{91} +(-62.7950 + 21.3642i) q^{92} +(10.9855 - 15.3414i) q^{94} +(-87.0944 - 50.2840i) q^{95} +(-31.4478 - 54.4691i) q^{97} +(0.324695 - 3.30835i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + 3 q^{4} - 2 q^{5} + 14 q^{8} + 18 q^{10} - 6 q^{13} + 15 q^{16} - 20 q^{17} + 67 q^{20} - 48 q^{22} - 146 q^{26} - 96 q^{28} + 22 q^{29} - 31 q^{32} - 81 q^{34} + 108 q^{37} - 168 q^{38}+ \cdots - 814 q^{98}+O(q^{100}) $ 12 * q - q^2 + 3 * q^4 - 2 * q^5 + 14 * q^8 + 18 * q^10 - 6 * q^13 + 15 * q^16 - 20 * q^17 + 67 * q^20 - 48 * q^22 - 146 * q^26 - 96 * q^28 + 22 * q^29 - 31 * q^32 - 81 * q^34 + 108 * q^37 - 168 * q^38 + 81 * q^40 - 92 * q^41 + 336 * q^44 + 240 * q^46 + 66 * q^49 + 48 * q^50 + 117 * q^52 + 232 * q^53 + 312 * q^56 - 201 * q^58 - 54 * q^61 - 624 * q^62 - 510 * q^64 - 82 * q^65 - 53 * q^68 - 264 * q^70 - 156 * q^73 - 383 * q^74 + 192 * q^76 + 168 * q^77 + 754 * q^80 + 300 * q^82 - 66 * q^85 + 144 * q^86 + 336 * q^88 - 500 * q^89 + 504 * q^92 - 216 * q^94 + 204 * q^97 - 814 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.82144	+	0.826041i	−0.910722	+	0.413020i
$2$	−1.82144	+	0.826041i	−0.910722	+	0.413020i
$3$		0			0
$3$		0			0
$4$	2.63531	−	3.00917i	0.658828	−	0.752293i
$5$	−3.61903	+	6.26834i	−0.723805	+	1.25367i	0.235659	+	0.971836i	$0.424275\pi$
$5$	−3.61903	+	6.26834i	−0.723805	+	1.25367i	−0.959464	+	0.281832i	$0.909058\pi$
$6$		0			0
$7$	5.95847	−	3.44013i	0.851211	−	0.491447i	−0.00984858	−	0.999952i	$-0.503135\pi$
$7$	5.95847	−	3.44013i	0.851211	−	0.491447i	0.861059	+	0.508505i	$0.169802\pi$
$8$	−2.31438	+	7.65792i	−0.289297	+	0.957239i
$9$		0			0
$10$	1.41395	−	14.4069i	0.141395	−	1.44069i
$11$	15.5474	−	8.97632i	1.41340	−	0.816029i	0.417697	−	0.908586i	$-0.362837\pi$
$11$	15.5474	−	8.97632i	1.41340	−	0.816029i	0.995707	+	0.0925568i	$0.0295040\pi$
$12$		0			0
$13$	−3.83763	+	6.64697i	−0.295202	+	0.511305i	−0.975032	−	0.222065i	$-0.928720\pi$
$13$	−3.83763	+	6.64697i	−0.295202	+	0.511305i	0.679830	+	0.733370i	$0.262054\pi$
$14$	−8.01134	+	11.1879i	−0.572239	+	0.799138i
$15$		0			0
$16$	−2.11024	−	15.8602i	−0.131890	−	0.991264i
$17$	−1.43720			−0.0845413			−0.0422707	−	0.999106i	$-0.513459\pi$
$17$	−1.43720			−0.0845413			−0.0422707	+	0.999106i	$0.513459\pi$
$18$		0			0
$19$			13.8943i			0.731281i	0.930756	+	0.365641i	$0.119150\pi$
$19$			13.8943i			0.731281i	−0.930756	+	0.365641i	$0.880850\pi$
$20$	9.32524	+	27.4093i	0.466262	+	1.37047i
$21$		0			0
$22$	−20.9040	+	29.1927i	−0.950182	+	1.32694i
$23$	−14.3608	−	8.29122i	−0.624384	−	0.360488i	0.154190	−	0.988041i	$-0.450723\pi$
$23$	−14.3608	−	8.29122i	−0.624384	−	0.360488i	−0.778574	+	0.627553i	$0.784057\pi$
$24$		0			0
$25$	−13.6947	−	23.7199i	−0.547788	−	0.948797i
$26$	1.49936	−	15.2771i	0.0576676	−	0.587581i
$27$		0			0
$28$	5.35051	−	26.9959i	0.191090	−	0.964139i
$29$	18.7509	+	32.4776i	0.646584	+	1.11992i	0.983933	+	0.178537i	$0.0571364\pi$
$29$	18.7509	+	32.4776i	0.646584	+	1.11992i	−0.337349	+	0.941380i	$0.609530\pi$
$30$		0			0
$31$	46.7583	+	26.9959i	1.50833	+	0.870835i	0.999953	+	0.00970102i	$0.00308798\pi$
$31$	46.7583	+	26.9959i	1.50833	+	0.870835i	0.508378	+	0.861134i	$0.330245\pi$
$32$	16.9449	+	27.1454i	0.529528	+	0.848293i
$33$		0			0
$34$	2.61778	−	1.18719i	0.0769936	−	0.0349173i
$35$			49.7996i			1.42285i
$36$		0			0
$37$	44.4415			1.20112			0.600560	−	0.799580i	$-0.294944\pi$
$37$	44.4415			1.20112			0.600560	+	0.799580i	$0.294944\pi$
$38$	−11.4773	−	25.3078i	−0.302034	−	0.665994i
$39$		0			0
$40$	−39.6266	−	42.2215i	−0.990665	−	1.05554i
$41$	−28.4956	+	49.3558i	−0.695014	+	1.20380i	0.275162	+	0.961398i	$0.411268\pi$
$41$	−28.4956	+	49.3558i	−0.695014	+	1.20380i	−0.970176	+	0.242401i	$0.922065\pi$
$42$		0			0
$43$	−58.5593	+	33.8092i	−1.36184	+	0.786261i	−0.989869	−	0.141982i	$-0.954653\pi$
$43$	−58.5593	+	33.8092i	−1.36184	+	0.786261i	−0.371975	+	0.928243i	$0.621319\pi$
$44$	13.9611	−	70.4404i	0.317298	−	1.60092i
$45$		0			0
$46$	33.0063	+	3.23938i	0.717529	+	0.0704212i
$47$	−8.17054	+	4.71726i	−0.173841	+	0.100367i	−0.584396	−	0.811469i	$-0.698668\pi$
$47$	−8.17054	+	4.71726i	−0.173841	+	0.100367i	0.410555	+	0.911836i	$0.365335\pi$
$48$		0			0
$49$	−0.831061	+	1.43944i	−0.0169604	+	0.0293763i
$50$	44.5378	+	31.8921i	0.890755	+	0.637843i
$51$		0			0
$52$	9.88852	+	29.0649i	0.190164	+	0.558941i
$53$	−7.82662			−0.147672			−0.0738360	−	0.997270i	$-0.523524\pi$
$53$	−7.82662			−0.147672			−0.0738360	+	0.997270i	$0.523524\pi$
$54$		0			0
$55$			129.942i			2.36259i
$56$	12.5540	+	53.5912i	0.224179	+	0.956986i
$57$		0			0
$58$	−60.9816	−	43.6670i	−1.05141	−	0.752880i
$59$	−19.4098	−	11.2062i	−0.328979	−	0.189936i	0.326409	−	0.945229i	$-0.394161\pi$
$59$	−19.4098	−	11.2062i	−0.328979	−	0.189936i	−0.655388	+	0.755293i	$0.727495\pi$
$60$		0			0
$61$	33.5907	+	58.1808i	0.550667	+	0.953783i	0.998227	+	0.0595292i	$0.0189599\pi$
$61$	33.5907	+	58.1808i	0.550667	+	0.953783i	−0.447559	+	0.894254i	$0.647707\pi$
$62$	−107.467	−	10.5473i	−1.73334	−	0.170117i
$63$		0			0
$64$	−53.2873	−	35.4466i	−0.832614	−	0.553853i
$65$	−27.7770	−	48.1111i	−0.427338	−	0.740171i
$66$		0			0
$67$	59.9324	+	34.6020i	0.894514	+	0.516448i	0.875416	−	0.483370i	$-0.160587\pi$
$67$	59.9324	+	34.6020i	0.894514	+	0.516448i	0.0190978	+	0.999818i	$0.493921\pi$
$68$	−3.78748	+	4.32479i	−0.0556982	+	0.0635999i
$69$		0			0
$70$	−41.1365	−	90.7072i	−0.587665	−	1.29582i
$71$			7.14792i			0.100675i	0.998732	+	0.0503375i	$0.0160297\pi$
$71$			7.14792i			0.100675i	−0.998732	+	0.0503375i	$0.983970\pi$
$72$		0			0
$73$	−80.4410			−1.10193			−0.550965	−	0.834528i	$-0.685740\pi$
$73$	−80.4410			−1.10193			−0.550965	+	0.834528i	$0.685740\pi$
$74$	−80.9476	+	36.7104i	−1.09389	+	0.496087i
$75$		0			0
$76$	41.8105	+	36.6159i	0.550138	+	0.481789i
$77$	61.7594	−	106.970i	0.802070	−	1.38923i
$78$		0			0
$79$	40.5680	−	23.4219i	0.513519	−	0.296480i	−0.220760	−	0.975328i	$-0.570854\pi$
$79$	40.5680	−	23.4219i	0.513519	−	0.296480i	0.734279	+	0.678848i	$0.237520\pi$
$80$	107.054	+	44.1709i	1.33818	+	0.552136i
$81$		0			0
$82$	11.1332	−	113.437i	0.135771	−	1.38338i
$83$	123.148	−	71.0994i	1.48371	−	0.856619i	0.483879	−	0.875135i	$-0.339228\pi$
$83$	123.148	−	71.0994i	1.48371	−	0.856619i	0.999829	+	0.0185165i	$0.00589432\pi$
$84$		0			0
$85$	5.20128	−	9.00887i	0.0611915	−	0.105987i
$86$	78.7347	−	109.954i	0.915519	−	1.27853i
$87$		0			0
$88$	32.7573	+	139.836i	0.372242	+	1.58904i
$89$	42.1078			0.473122			0.236561	−	0.971617i	$-0.423980\pi$
$89$	42.1078			0.473122			0.236561	+	0.971617i	$0.423980\pi$
$90$		0			0
$91$			52.8077i			0.580304i
$92$	−62.7950	+	21.3642i	−0.682554	+	0.232220i
$93$		0			0
$94$	10.9855	−	15.3414i	0.116867	−	0.163207i
$95$	−87.0944	−	50.2840i	−0.916783	−	0.529305i
$96$		0			0
$97$	−31.4478	−	54.4691i	−0.324204	−	0.561538i	0.657147	−	0.753762i	$-0.271763\pi$
$97$	−31.4478	−	54.4691i	−0.324204	−	0.561538i	−0.981351	+	0.192225i	$0.938430\pi$
$98$	0.324695	−	3.30835i	0.00331321	−	0.0337586i
$99$		0			0
$100$	−107.467	−	21.2997i	−1.07467	−	0.212997i
$101$	−23.8072	−	41.2352i	−0.235715	−	0.408270i	0.723766	−	0.690046i	$-0.242410\pi$
$101$	−23.8072	−	41.2352i	−0.235715	−	0.408270i	−0.959480	+	0.281776i	$0.909076\pi$
$102$		0			0
$103$	−46.5264	−	26.8621i	−0.451713	−	0.260797i	0.256840	−	0.966454i	$-0.417319\pi$
$103$	−46.5264	−	26.8621i	−0.451713	−	0.260797i	−0.708553	+	0.705657i	$0.750652\pi$
$104$	−42.0202	−	44.7718i	−0.404040	−	0.430498i
$105$		0			0
$106$	14.2557	−	6.46511i	0.134488	−	0.0609916i
$107$		−	26.4708i		−	0.247390i	−0.992320	−	0.123695i	$-0.960525\pi$
$107$		−	26.4708i		−	0.247390i	0.992320	−	0.123695i	$-0.0394745\pi$
$108$		0			0
$109$	83.0647			0.762061			0.381031	−	0.924562i	$-0.375569\pi$
$109$	83.0647			0.762061			0.381031	+	0.924562i	$0.375569\pi$
$110$	−107.338	−	236.682i	−0.975796	−	2.15166i
$111$		0			0
$112$	−67.1350	−	87.2433i	−0.599420	−	0.778958i
$113$	7.76382	−	13.4473i	0.0687064	−	0.119003i	−0.829626	−	0.558320i	$-0.811446\pi$
$113$	7.76382	−	13.4473i	0.0687064	−	0.119003i	0.898332	+	0.439317i	$0.144780\pi$
$114$		0			0
$115$	103.944	−	60.0123i	0.903864	−	0.521846i
$116$	147.145	+	29.1638i	1.26849	+	0.251412i
$117$		0			0
$118$	44.6106	+	4.37827i	0.378056	+	0.0371039i
$119$	−8.56354	+	4.94416i	−0.0719625	+	0.0415476i
$120$		0			0
$121$	100.649	−	174.329i	0.831808	−	1.44073i
$122$	−109.243	−	78.2257i	−0.895436	−	0.641195i
$123$		0			0
$124$	204.458	−	69.5610i	1.64885	−	0.560976i
$125$	17.2947			0.138358
$126$		0			0
$127$		−	157.463i		−	1.23987i	−0.784654	−	0.619934i	$-0.787159\pi$
$127$		−	157.463i		−	1.23987i	0.784654	−	0.619934i	$-0.212841\pi$
$128$	126.340	+	20.5465i	0.987033	+	0.160519i
$129$		0			0
$130$	90.3359	+	64.6868i	0.694891	+	0.497590i
$131$	40.7545	+	23.5296i	0.311103	+	0.179615i	0.647420	−	0.762133i	$-0.275848\pi$
$131$	40.7545	+	23.5296i	0.311103	+	0.179615i	−0.336317	+	0.941749i	$0.609181\pi$
$132$		0			0
$133$	47.7983	+	82.7891i	0.359386	+	0.622474i
$134$	−137.746	−	13.5190i	−1.02796	−	0.100888i
$135$		0			0
$136$	3.32623	−	11.0060i	0.0244576	−	0.0809263i
$137$	−58.7486	−	101.756i	−0.428822	−	0.742742i	0.567947	−	0.823065i	$-0.307738\pi$
$137$	−58.7486	−	101.756i	−0.428822	−	0.742742i	−0.996769	+	0.0803237i	$0.974405\pi$
$138$		0			0
$139$	34.3777	+	19.8480i	0.247322	+	0.142791i	0.618537	−	0.785756i	$-0.287726\pi$
$139$	34.3777	+	19.8480i	0.247322	+	0.142791i	−0.371216	+	0.928547i	$0.621059\pi$
$140$	149.856	+	131.238i	1.07040	+	0.937412i
$141$		0			0
$142$	−5.90447	−	13.0195i	−0.0415808	−	0.0916869i
$143$			137.791i			0.963575i
$144$		0			0
$145$	−271.441			−1.87200
$146$	146.519	−	66.4475i	1.00355	−	0.455120i
$147$		0			0
$148$	117.117	−	133.732i	0.791332	−	0.903595i
$149$	57.4136	−	99.4432i	0.385326	−	0.667404i	−0.606488	−	0.795092i	$-0.707422\pi$
$149$	57.4136	−	99.4432i	0.385326	−	0.667404i	0.991814	+	0.127688i	$0.0407557\pi$
$150$		0			0
$151$	−138.670	+	80.0610i	−0.918343	+	0.530206i	−0.883106	−	0.469173i	$-0.844552\pi$
$151$	−138.670	+	80.0610i	−0.918343	+	0.530206i	−0.0352370	+	0.999379i	$0.511219\pi$
$152$	−106.402	−	32.1567i	−0.700011	−	0.211557i
$153$		0			0
$154$	−24.1293	+	245.856i	−0.156684	+	1.59647i
$155$	−338.439	+	195.398i	−2.18348	+	1.26063i
$156$		0			0
$157$	−112.668	+	195.148i	−0.717634	+	1.24298i	0.244301	+	0.969699i	$0.421441\pi$
$157$	−112.668	+	195.148i	−0.717634	+	1.24298i	−0.961935	+	0.273279i	$0.911892\pi$
$158$	−54.5448	+	76.1725i	−0.345220	+	0.482105i
$159$		0			0
$160$	−231.480	+	7.97645i	−1.44675	+	0.0498528i
$161$	−114.091			−0.708643
$162$		0			0
$163$		−	147.165i		−	0.902850i	−0.892309	−	0.451425i	$-0.850916\pi$
$163$		−	147.165i		−	0.902850i	0.892309	−	0.451425i	$-0.149084\pi$
$164$	73.4253	+	215.816i	0.447715	+	1.31595i
$165$		0			0
$166$	−165.576	+	231.228i	−0.997443	+	1.39294i
$167$	91.7504	+	52.9721i	0.549403	+	0.317198i	0.748881	−	0.662704i	$-0.230591\pi$
$167$	91.7504	+	52.9721i	0.549403	+	0.317198i	−0.199478	+	0.979902i	$0.563925\pi$
$168$		0			0
$169$	55.0452	+	95.3411i	0.325711	+	0.564149i
$170$	−2.03213	+	20.7056i	−0.0119537	+	0.121798i
$171$		0			0
$172$	−52.5843	+	265.313i	−0.305723	+	1.54252i
$173$	93.2118	+	161.448i	0.538797	+	0.933223i	0.998969	+	0.0453938i	$0.0144543\pi$
$173$	93.2118	+	161.448i	0.538797	+	0.933223i	−0.460172	+	0.887830i	$0.652212\pi$
$174$		0			0
$175$	−163.199	−	94.2231i	−0.932566	−	0.538417i
$176$	−175.175	−	227.644i	−0.995315	−	1.29343i
$177$		0			0
$178$	−76.6970	+	34.7828i	−0.430882	+	0.195409i
$179$		−	191.597i		−	1.07037i	−0.844734	−	0.535187i	$-0.820241\pi$
$179$		−	191.597i		−	1.07037i	0.844734	−	0.535187i	$-0.179759\pi$
$180$		0			0
$181$	204.960			1.13237			0.566187	−	0.824277i	$-0.308418\pi$
$181$	204.960			1.13237			0.566187	+	0.824277i	$0.308418\pi$
$182$	−43.6213	−	96.1863i	−0.239678	−	0.528496i
$183$		0			0
$184$	96.7298	−	90.7849i	0.525706	−	0.493396i
$185$	−160.835	+	278.574i	−0.869377	+	1.50581i
$186$		0			0
$187$	−22.3448	+	12.9008i	−0.119491	+	0.0689882i
$188$	−7.33688	+	37.0180i	−0.0390259	+	0.196904i
$189$		0			0
$190$	200.174	+	19.6459i	1.05355	+	0.103400i
$191$	77.7825	−	44.9078i	0.407238	−	0.235119i	−0.282364	−	0.959307i	$-0.591119\pi$
$191$	77.7825	−	44.9078i	0.407238	−	0.235119i	0.689602	+	0.724188i	$0.257785\pi$
$192$		0			0
$193$	−83.7981	+	145.143i	−0.434187	+	0.752034i	−0.997229	−	0.0743944i	$-0.976298\pi$
$193$	−83.7981	+	145.143i	−0.434187	+	0.752034i	0.563042	+	0.826428i	$0.309631\pi$
$194$	102.274	+	73.2353i	0.527186	+	0.377502i
$195$		0			0
$196$	2.14142	+	6.29418i	0.0109256	+	0.0321132i
$197$	185.277			0.940492			0.470246	−	0.882535i	$-0.344165\pi$
$197$	185.277			0.940492			0.470246	+	0.882535i	$0.344165\pi$
$198$		0			0
$199$		−	137.625i		−	0.691585i	−0.938311	−	0.345793i	$-0.887610\pi$
$199$		−	137.625i		−	0.691585i	0.938311	−	0.345793i	$-0.112390\pi$
$200$	213.340	−	49.9761i	1.06670	−	0.249880i
$201$		0			0
$202$	77.4254	+	55.4419i	0.383294	+	0.274465i
$203$	223.454	+	129.011i	1.10076	+	0.635523i
$204$		0			0
$205$	−206.252	−	357.240i	−1.00611	−	1.74263i
$206$	106.934	+	10.4950i	0.519099	+	0.0509465i
$207$		0			0
$208$	113.521	+	46.8389i	0.545773	+	0.225187i
$209$	124.720	+	216.022i	0.596747	+	1.03360i
$210$		0			0
$211$	−264.357	−	152.627i	−1.25288	−	0.723350i	−0.281198	−	0.959650i	$-0.590732\pi$
$211$	−264.357	−	152.627i	−1.25288	−	0.723350i	−0.971680	+	0.236300i	$0.924065\pi$
$212$	−20.6256	+	23.5517i	−0.0972906	+	0.111093i
$213$		0			0
$214$	21.8659	+	48.2150i	0.102177	+	0.225304i
$215$		−	489.426i		−	2.27640i
$216$		0			0
$217$	371.477			1.71188
$218$	−151.298	+	68.6148i	−0.694026	+	0.314747i
$219$		0			0
$220$	391.019	+	342.439i	1.77736	+	1.55654i
$221$	5.51545	−	9.55304i	0.0249568	−	0.0432264i
$222$		0			0
$223$	14.9150	−	8.61118i	0.0668834	−	0.0386152i	−0.466185	−	0.884687i	$-0.654372\pi$
$223$	14.9150	−	8.61118i	0.0668834	−	0.0386152i	0.533069	+	0.846072i	$0.321039\pi$
$224$	194.349	+	103.452i	0.867630	+	0.461841i
$225$		0			0
$226$	−3.03332	+	30.9068i	−0.0134218	+	0.136756i
$227$	35.4937	−	20.4923i	0.156360	−	0.0902744i	−0.419779	−	0.907627i	$-0.637892\pi$
$227$	35.4937	−	20.4923i	0.156360	−	0.0902744i	0.576138	+	0.817352i	$0.304559\pi$
$228$		0			0
$229$	66.7264	−	115.573i	0.291381	−	0.504687i	−0.682755	−	0.730647i	$-0.739218\pi$
$229$	66.7264	−	115.573i	0.291381	−	0.504687i	0.974137	+	0.225960i	$0.0725518\pi$
$230$	−139.756	+	195.171i	−0.607636	+	0.848571i
$231$		0			0
$232$	−292.107	+	68.4278i	−1.25908	+	0.294947i
$233$	−368.345			−1.58088			−0.790441	−	0.612539i	$-0.790148\pi$
$233$	−368.345			−1.58088			−0.790441	+	0.612539i	$0.790148\pi$
$234$		0			0
$235$		−	68.2876i		−	0.290586i
$236$	−84.8723	+	28.8754i	−0.359628	+	0.122353i
$237$		0			0
$238$	11.5139	−	16.0793i	0.0483778	−	0.0675602i
$239$	249.901	+	144.280i	1.04561	+	0.603683i	0.921417	−	0.388576i	$-0.127033\pi$
$239$	249.901	+	144.280i	1.04561	+	0.603683i	0.124192	+	0.992258i	$0.460366\pi$
$240$		0			0
$241$	51.4937	+	89.1897i	0.213667	+	0.370082i	0.952859	−	0.303412i	$-0.0981260\pi$
$241$	51.4937	+	89.1897i	0.213667	+	0.370082i	−0.739193	+	0.673494i	$0.764793\pi$
$242$	−39.3234	+	400.670i	−0.162493	+	1.65566i
$243$		0			0
$244$	263.598	+	52.2444i	1.08032	+	0.214116i
$245$	−6.01526	−	10.4187i	−0.0245521	−	0.0425255i
$246$		0			0
$247$	−92.3552	−	53.3213i	−0.373908	−	0.215876i
$248$	−314.948	+	295.592i	−1.26995	+	1.19190i
$249$		0			0
$250$	−31.5014	+	14.2861i	−0.126005	+	0.0571446i
$251$			69.9866i			0.278831i	0.990234	+	0.139416i	$0.0445224\pi$
$251$			69.9866i			0.278831i	−0.990234	+	0.139416i	$0.955478\pi$
$252$		0			0
$253$	−297.699			−1.17668
$254$	130.071	+	286.810i	0.512091	+	1.12917i
$255$		0			0
$256$	−247.094	+	66.9379i	−0.965210	+	0.261476i
$257$	−48.5410	+	84.0754i	−0.188875	+	0.327142i	−0.944876	−	0.327430i	$-0.893818\pi$
$257$	−48.5410	+	84.0754i	−0.188875	+	0.327142i	0.756000	+	0.654571i	$0.227151\pi$
$258$		0			0
$259$	264.803	−	152.884i	1.02241	−	0.590287i
$260$	−217.976	−	43.2022i	−0.838368	−	0.166162i
$261$		0			0
$262$	−93.6684	−	9.19301i	−0.357513	−	0.0350878i
$263$	−7.27870	+	4.20236i	−0.0276757	+	0.0159785i	−0.513774	−	0.857926i	$-0.671753\pi$
$263$	−7.27870	+	4.20236i	−0.0276757	+	0.0159785i	0.486098	+	0.873904i	$0.338420\pi$
$264$		0			0
$265$	28.3247	−	49.0599i	0.106886	−	0.185132i
$266$	−155.449	−	111.312i	−0.584395	−	0.418467i
$267$		0			0
$268$	262.064	−	89.1599i	0.977852	−	0.332686i
$269$	281.198			1.04535			0.522673	−	0.852533i	$-0.324935\pi$
$269$	281.198			1.04535			0.522673	+	0.852533i	$0.324935\pi$
$270$		0			0
$271$		−	369.456i		−	1.36331i	−0.731675	−	0.681654i	$-0.761261\pi$
$271$		−	369.456i		−	1.36331i	0.731675	−	0.681654i	$-0.238739\pi$
$272$	3.03285	+	22.7944i	0.0111502	+	0.0838028i
$273$		0			0
$274$	191.062	+	136.813i	0.697305	+	0.499319i
$275$	−425.836	−	245.856i	−1.54849	−	0.894023i
$276$		0			0
$277$	−66.4546	−	115.103i	−0.239908	−	0.415533i	0.720779	−	0.693164i	$-0.243784\pi$
$277$	−66.4546	−	115.103i	−0.239908	−	0.415533i	−0.960688	+	0.277631i	$0.910451\pi$
$278$	−79.0123	−	7.75459i	−0.284217	−	0.0278942i
$279$		0			0
$280$	−381.361	−	115.255i	−1.36200	−	0.411625i
$281$	−18.6577	−	32.3160i	−0.0663974	−	0.115004i	0.830916	−	0.556398i	$-0.187817\pi$
$281$	−18.6577	−	32.3160i	−0.0663974	−	0.115004i	−0.897313	+	0.441395i	$0.854484\pi$
$282$		0			0
$283$	−135.246	−	78.0842i	−0.477900	−	0.275916i	0.241641	−	0.970366i	$-0.422314\pi$
$283$	−135.246	−	78.0842i	−0.477900	−	0.275916i	−0.719541	+	0.694450i	$0.755648\pi$
$284$	21.5093	+	18.8370i	0.0757371	+	0.0663275i
$285$		0			0
$286$	−113.821	−	250.979i	−0.397976	−	0.877548i
$287$			392.113i			1.36625i
$288$		0			0
$289$	−286.934			−0.992853
$290$	494.414	−	224.221i	1.70487	−	0.773176i
$291$		0			0
$292$	−211.987	+	242.061i	−0.725983	+	0.828975i
$293$	−12.9881	+	22.4961i	−0.0443280	+	0.0767784i	−0.887338	−	0.461119i	$-0.847448\pi$
$293$	−12.9881	+	22.4961i	−0.0443280	+	0.0767784i	0.843010	+	0.537898i	$0.180781\pi$
$294$		0			0
$295$	140.489	−	81.1113i	0.476233	−	0.274954i
$296$	−102.854	+	340.329i	−0.347481	+	1.14976i
$297$		0			0
$298$	−22.4314	+	228.556i	−0.0752733	+	0.766967i
$299$	110.223	−	63.6373i	0.368639	−	0.212834i
$300$		0			0
$301$	−232.616	+	402.903i	−0.772811	+	1.33855i
$302$	186.446	−	260.374i	0.617369	−	0.862164i
$303$		0			0
$304$	220.367	−	29.3204i	0.724893	−	0.0964488i
$305$	−486.262			−1.59430
$306$		0			0
$307$		−	111.670i		−	0.363745i	−0.983322	−	0.181872i	$-0.941784\pi$
$307$		−	111.670i		−	0.363745i	0.983322	−	0.181872i	$-0.0582158\pi$
$308$	−159.137	−	467.745i	−0.516679	−	1.51865i
$309$		0			0
$310$	455.041	−	635.470i	1.46787	−	2.04990i
$311$	280.368	+	161.871i	0.901506	+	0.520485i	0.877689	−	0.479232i	$-0.159085\pi$
$311$	280.368	+	161.871i	0.901506	+	0.520485i	0.0238176	+	0.999716i	$0.492418\pi$
$312$		0			0
$313$	183.090	+	317.122i	0.584953	+	1.01317i	0.994881	+	0.101050i	$0.0322203\pi$
$313$	183.090	+	317.122i	0.584953	+	1.01317i	−0.409928	+	0.912118i	$0.634446\pi$
$314$	44.0195	−	448.519i	0.140189	−	1.42840i
$315$		0			0
$316$	36.4287	−	183.800i	0.115281	−	0.581646i
$317$	−32.5014	−	56.2941i	−0.102528	−	0.177584i	0.810197	−	0.586157i	$-0.199360\pi$
$317$	−32.5014	−	56.2941i	−0.102528	−	0.177584i	−0.912726	+	0.408573i	$0.866027\pi$
$318$		0			0
$319$	583.059	+	336.629i	1.82777	+	1.05526i
$320$	415.039	−	205.741i	1.29700	−	0.642940i
$321$		0			0
$322$	207.811	−	94.2442i	0.645376	−	0.292684i
$323$		−	19.9690i		−	0.0618235i
$324$		0			0
$325$	210.221			0.646833
$326$	121.564	+	268.052i	0.372895	+	0.822245i
$327$		0			0
$328$	−312.013	−	332.444i	−0.951258	−	1.01355i
$329$	−32.4560	+	56.2154i	−0.0986504	+	0.170867i
$330$		0			0
$331$	−380.566	+	219.720i	−1.14975	+	0.663807i	−0.948826	−	0.315800i	$-0.897727\pi$
$331$	−380.566	+	219.720i	−1.14975	+	0.663807i	−0.200922	+	0.979607i	$0.564394\pi$
$332$	110.583	−	557.942i	0.333080	−	1.68055i
$333$		0			0
$334$	−210.875	−	20.6962i	−0.631363	−	0.0619645i
$335$	−433.794	+	250.451i	−1.29491	+	0.747616i
$336$		0			0
$337$	187.409	−	324.602i	0.556109	−	0.963210i	−0.441707	−	0.897159i	$-0.645627\pi$
$337$	187.409	−	324.602i	0.556109	−	0.963210i	0.997816	−	0.0660503i	$-0.0210398\pi$
$338$	−179.017	−	128.189i	−0.529637	−	0.379257i
$339$		0			0
$340$	−13.4023	−	39.3927i	−0.0394184	−	0.115861i
$341$	969.295			2.84251
$342$		0			0
$343$			348.568i			1.01623i
$344$	−123.380	−	526.689i	−0.358663	−	1.53107i
$345$		0			0
$346$	−303.142	−	217.071i	−0.876134	−	0.627373i
$347$	−284.948	−	164.515i	−0.821177	−	0.474107i	0.0296454	−	0.999560i	$-0.490562\pi$
$347$	−284.948	−	164.515i	−0.821177	−	0.474107i	−0.850822	+	0.525454i	$0.823896\pi$
$348$		0			0
$349$	−186.253	−	322.599i	−0.533676	−	0.924354i	−0.999226	−	0.0393323i	$-0.987477\pi$
$349$	−186.253	−	322.599i	−0.533676	−	0.924354i	0.465550	−	0.885021i	$-0.345856\pi$
$350$	375.090	+	36.8129i	1.07169	+	0.105180i
$351$		0			0
$352$	507.115	+	269.938i	1.44067	+	0.766871i
$353$	−108.879	−	188.584i	−0.308440	−	0.534233i	0.669582	−	0.742738i	$-0.266473\pi$
$353$	−108.879	−	188.584i	−0.308440	−	0.534233i	−0.978021	+	0.208505i	$0.933140\pi$
$354$		0			0
$355$	−44.8056	−	25.8685i	−0.126213	−	0.0728691i
$356$	110.967	−	126.710i	0.311706	−	0.355926i
$357$		0			0
$358$	158.267	+	348.983i	0.442086	+	0.974812i
$359$			145.576i			0.405505i	0.979230	+	0.202753i	$0.0649887\pi$
$359$			145.576i			0.405505i	−0.979230	+	0.202753i	$0.935011\pi$
$360$		0			0
$361$	167.947			0.465228
$362$	−373.323	+	169.305i	−1.03128	+	0.467694i
$363$		0			0
$364$	158.908	+	139.165i	0.436559	+	0.382321i
$365$	291.118	−	504.231i	0.797583	−	1.38146i
$366$		0			0
$367$	46.3123	−	26.7384i	0.126192	−	0.0728568i	−0.435575	−	0.900152i	$-0.643455\pi$
$367$	46.3123	−	26.7384i	0.126192	−	0.0728568i	0.561767	+	0.827295i	$0.310122\pi$
$368$	−101.196	+	245.262i	−0.274989	+	0.666474i
$369$		0			0
$370$	62.8380	−	640.263i	0.169833	−	1.73044i
$371$	−46.6347	+	26.9246i	−0.125700	+	0.0725729i
$372$		0			0
$373$	170.752	−	295.751i	0.457781	−	0.792899i	−0.541063	−	0.840982i	$-0.681978\pi$
$373$	170.752	−	295.751i	0.457781	−	0.792899i	0.998843	+	0.0480829i	$0.0153112\pi$
$374$	30.0433	−	41.9558i	0.0803296	−	0.112181i
$375$		0			0
$376$	−17.2147	−	73.4868i	−0.0457838	−	0.195444i
$377$	−287.837			−0.763492
$378$		0			0
$379$			220.189i			0.580972i	0.956879	+	0.290486i	$0.0938170\pi$
$379$			220.189i			0.580972i	−0.956879	+	0.290486i	$0.906183\pi$
$380$	−380.834	+	129.568i	−1.00220	+	0.340969i
$381$		0			0
$382$	−104.581	+	146.048i	−0.273772	+	0.382326i
$383$	−581.167	−	335.537i	−1.51741	−	0.876075i	−0.999791	−	0.0204616i	$-0.993486\pi$
$383$	−581.167	−	335.537i	−1.51741	−	0.876075i	−0.517616	−	0.855613i	$-0.673180\pi$
$384$		0			0
$385$	447.018	+	774.257i	1.16108	+	2.01106i
$386$	32.7399	−	333.590i	0.0848183	−	0.864222i
$387$		0			0
$388$	−246.782	−	48.9115i	−0.636036	−	0.126061i
$389$	−242.462	−	419.957i	−0.623296	−	1.07958i	−0.988868	−	0.148797i	$-0.952460\pi$
$389$	−242.462	−	419.957i	−0.623296	−	1.07958i	0.365572	−	0.930783i	$-0.380873\pi$
$390$		0			0
$391$	20.6394	+	11.9162i	0.0527862	+	0.0304761i
$392$	−9.09972	−	9.69560i	−0.0232136	−	0.0247337i
$393$		0			0
$394$	−337.472	+	153.046i	−0.856527	+	0.388442i
$395$			339.058i			0.858376i
$396$		0			0
$397$	−279.373			−0.703711			−0.351855	−	0.936054i	$-0.614449\pi$
$397$	−279.373			−0.703711			−0.351855	+	0.936054i	$0.614449\pi$
$398$	113.684	+	250.677i	0.285639	+	0.629842i
$399$		0			0
$400$	−347.304	+	267.256i	−0.868261	+	0.668140i
$401$	291.099	−	504.199i	0.725934	−	1.25735i	−0.232655	−	0.972559i	$-0.574741\pi$
$401$	291.099	−	504.199i	0.725934	−	1.25735i	0.958589	−	0.284795i	$-0.0919255\pi$
$402$		0			0
$403$	−358.882	+	207.200i	−0.890525	+	0.514145i
$404$	−186.823	−	37.0279i	−0.462434	−	0.0916531i
$405$		0			0
$406$	−513.577	−	50.4046i	−1.26497	−	0.124149i
$407$	690.951	−	398.921i	1.69767	−	0.980150i
$408$		0			0
$409$	218.330	−	378.160i	0.533815	−	0.924595i	−0.465404	−	0.885098i	$-0.654091\pi$
$409$	218.330	−	378.160i	0.533815	−	0.924595i	0.999220	−	0.0394972i	$-0.0125756\pi$
$410$	670.771	+	480.319i	1.63603	+	1.17151i
$411$		0			0
$412$	−203.444	+	69.2162i	−0.493797	+	0.168000i
$413$	−154.203			−0.373374
$414$		0			0
$415$			1029.24i			2.48010i
$416$	−245.463	+	8.45825i	−0.590054	+	0.0203323i
$417$		0			0
$418$	−405.613	−	290.447i	−0.970367	−	0.694850i
$419$	656.682	+	379.135i	1.56726	+	0.904858i	0.996487	+	0.0837495i	$0.0266896\pi$
$419$	656.682	+	379.135i	1.56726	+	0.904858i	0.570773	+	0.821108i	$0.306644\pi$
$420$		0			0
$421$	−261.674	−	453.232i	−0.621553	−	1.07656i	−0.989197	−	0.146595i	$-0.953169\pi$
$421$	−261.674	−	453.232i	−0.621553	−	1.07656i	0.367644	−	0.929967i	$-0.380165\pi$
$422$	607.588	+	59.6312i	1.43978	+	0.141306i
$423$		0			0
$424$	18.1137	−	59.9356i	0.0427211	−	0.141358i
$425$	19.6821	+	34.0904i	0.0463108	+	0.0802126i
$426$		0			0
$427$	400.299	+	231.112i	0.937467	+	0.541247i
$428$	−79.6551	−	69.7588i	−0.186110	−	0.162988i
$429$		0			0
$430$	404.286	+	891.462i	0.940199	+	2.07317i
$431$		−	729.146i		−	1.69176i	−0.533377	−	0.845878i	$-0.679077\pi$
$431$		−	729.146i		−	1.69176i	0.533377	−	0.845878i	$-0.320923\pi$
$432$		0			0
$433$	−491.219			−1.13445			−0.567227	−	0.823561i	$-0.691984\pi$
$433$	−491.219			−1.13445			−0.567227	+	0.823561i	$0.691984\pi$
$434$	−676.625	+	306.855i	−1.55904	+	0.707040i
$435$		0			0
$436$	218.901	−	249.956i	0.502068	−	0.573293i
$437$	115.201	−	199.534i	0.263618	−	0.456600i
$438$		0			0
$439$	163.413	−	94.3467i	0.372240	−	0.214913i	−0.302197	−	0.953246i	$-0.597720\pi$
$439$	163.413	−	94.3467i	0.372240	−	0.214913i	0.674436	+	0.738333i	$0.264387\pi$
$440$	−995.087	−	300.735i	−2.26156	−	0.683489i
$441$		0			0
$442$	−2.15488	+	21.9563i	−0.00487530	+	0.0496749i
$443$	357.848	−	206.604i	0.807784	−	0.466375i	−0.0384015	−	0.999262i	$-0.512227\pi$
$443$	357.848	−	206.604i	0.807784	−	0.466375i	0.846186	+	0.532888i	$0.178893\pi$
$444$		0			0
$445$	−152.389	+	263.946i	−0.342448	+	0.593137i
$446$	−20.0537	+	28.0052i	−0.0449633	+	0.0627919i
$447$		0			0
$448$	−439.452	−	27.8925i	−0.980919	−	0.0622600i
$449$	−638.253			−1.42150			−0.710749	−	0.703446i	$-0.751644\pi$
$449$	−638.253			−1.42150			−0.710749	+	0.703446i	$0.751644\pi$
$450$		0			0
$451$			1023.14i			2.26861i
$452$	−20.0052	−	58.8006i	−0.0442594	−	0.130090i
$453$		0			0
$454$	−47.7223	+	66.6448i	−0.105115	+	0.146795i
$455$	−331.017	−	191.112i	−0.727509	−	0.420027i
$456$		0			0
$457$	115.344	+	199.781i	0.252393	+	0.437157i	0.964184	−	0.265234i	$-0.0854492\pi$
$457$	115.344	+	199.781i	0.252393	+	0.437157i	−0.711791	+	0.702391i	$0.752116\pi$
$458$	−26.0699	+	265.629i	−0.0569213	+	0.579976i
$459$		0			0
$460$	93.3386	−	470.938i	0.202910	−	1.02378i
$461$	200.094	+	346.573i	0.434044	+	0.751786i	0.997217	−	0.0745529i	$-0.0237530\pi$
$461$	200.094	+	346.573i	0.434044	+	0.751786i	−0.563173	+	0.826339i	$0.690420\pi$
$462$		0			0
$463$	−256.912	−	148.328i	−0.554886	−	0.320363i	0.196205	−	0.980563i	$-0.437138\pi$
$463$	−256.912	−	148.328i	−0.554886	−	0.320363i	−0.751090	+	0.660200i	$0.770472\pi$
$464$	475.533	−	365.930i	1.02486	−	0.788642i
$465$		0			0
$466$	670.920	−	304.268i	1.43974	−	0.652936i
$467$			127.057i			0.272070i	0.990704	+	0.136035i	$0.0434359\pi$
$467$			127.057i			0.272070i	−0.990704	+	0.136035i	$0.956564\pi$
$468$		0			0
$469$	476.141			1.01523
$470$	56.4084	+	124.382i	0.120018	+	0.264643i
$471$		0			0
$472$	130.738	−	122.703i	0.276987	−	0.259964i
$473$	−606.965	+	1051.29i	−1.28322	+	2.22261i
$474$		0			0
$475$	329.573	−	190.279i	0.693837	−	0.400587i
$476$	−7.68977	+	38.7986i	−0.0161550	+	0.0815096i
$477$		0			0
$478$	−574.361	−	56.3701i	−1.20159	−	0.117929i
$479$	−10.6651	+	6.15749i	−0.0222653	+	0.0128549i	−0.511091	−	0.859526i	$-0.670759\pi$
$479$	−10.6651	+	6.15749i	−0.0222653	+	0.0128549i	0.488826	+	0.872381i	$0.337425\pi$
$480$		0			0
$481$	−170.550	+	295.401i	−0.354573	+	0.614139i
$482$	−167.467	−	119.918i	−0.347442	−	0.248793i
$483$		0			0
$484$	−259.344	−	762.281i	−0.535836	−	1.57496i
$485$	455.241			0.938642
$486$		0			0
$487$		−	181.054i		−	0.371773i	−0.982571	−	0.185887i	$-0.940484\pi$
$487$		−	181.054i		−	0.371773i	0.982571	−	0.185887i	$-0.0595157\pi$
$488$	−523.285	+	122.582i	−1.07231	+	0.251194i
$489$		0			0
$490$	19.5628	+	14.0083i	0.0399240	+	0.0285884i
$491$	−430.484	−	248.540i	−0.876749	−	0.506191i	−0.00716404	−	0.999974i	$-0.502280\pi$
$491$	−430.484	−	248.540i	−0.876749	−	0.506191i	−0.869585	+	0.493783i	$0.835614\pi$
$492$		0			0
$493$	−26.9489	−	46.6769i	−0.0546631	−	0.0946792i
$494$	212.265	+	20.8326i	0.429687	+	0.0421712i
$495$		0			0
$496$	329.490	−	798.565i	0.664294	−	1.61001i
$497$	24.5898	+	42.5907i	0.0494764	+	0.0856956i
$498$		0			0
$499$	660.403	+	381.284i	1.32345	+	0.764096i	0.984278	−	0.176628i	$-0.0565189\pi$
$499$	660.403	+	381.284i	1.32345	+	0.764096i	0.339175	+	0.940723i	$0.389852\pi$
$500$	45.5770	−	52.0428i	0.0911540	−	0.104086i
$501$		0			0
$502$	−57.8118	−	127.477i	−0.115163	−	0.253938i
$503$			994.596i			1.97733i	0.150146	+	0.988664i	$0.452026\pi$
$503$			994.596i			1.97733i	−0.150146	+	0.988664i	$0.547974\pi$
$504$		0			0
$505$	344.635			0.682446
$506$	542.242	−	245.911i	1.07162	−	0.485991i
$507$		0			0
$508$	−473.834	−	414.965i	−0.932744	−	0.816860i
$509$	−26.8655	+	46.5325i	−0.0527810	+	0.0914194i	−0.891209	−	0.453593i	$-0.850142\pi$
$509$	−26.8655	+	46.5325i	−0.0527810	+	0.0914194i	0.838428	+	0.545013i	$0.183475\pi$
$510$		0			0
$511$	−479.305	+	276.727i	−0.937975	+	0.541540i
$512$	394.774	−	326.033i	0.771043	−	0.636783i
$513$		0			0
$514$	18.9649	−	193.235i	0.0368967	−	0.375944i
$515$	336.761	−	194.429i	0.653905	−	0.377532i
$516$		0			0
$517$	−84.6874	+	146.683i	−0.163805	+	0.283719i
$518$	−356.036	+	497.208i	−0.687327	+	0.959861i
$519$		0			0
$520$	432.717	−	101.366i	0.832148	−	0.194935i
$521$	616.206			1.18274			0.591369	−	0.806401i	$-0.298588\pi$
$521$	616.206			1.18274			0.591369	+	0.806401i	$0.298588\pi$
$522$		0			0
$523$		−	683.938i		−	1.30772i	−0.756615	−	0.653860i	$-0.773148\pi$
$523$		−	683.938i		−	1.30772i	0.756615	−	0.653860i	$-0.226852\pi$
$524$	178.206	−	60.6294i	0.340087	−	0.115705i
$525$		0			0
$526$	9.78642	−	13.6669i	0.0186054	−	0.0259826i
$527$	−67.2011	−	38.7986i	−0.127516	−	0.0736216i
$528$		0			0
$529$	−127.011	−	219.990i	−0.240097	−	0.415860i
$530$	−11.0665	+	112.757i	−0.0208801	+	0.212749i
$531$		0			0
$532$	375.090	+	74.3418i	0.705057	+	0.139740i
$533$	−218.711	−	378.818i	−0.410339	−	0.710728i
$534$		0			0
$535$	165.928	+	95.7984i	0.310145	+	0.179062i
$536$	−403.686	+	378.876i	−0.753145	+	0.706857i
$537$		0			0
$538$	−512.187	+	232.281i	−0.952020	+	0.431749i
$539$			29.8395i			0.0553608i
$540$		0			0
$541$	518.000			0.957486			0.478743	−	0.877955i	$-0.341093\pi$
$541$	518.000			0.957486			0.478743	+	0.877955i	$0.341093\pi$
$542$	305.186	+	672.944i	0.563073	+	1.24159i
$543$		0			0
$544$	−24.3532	−	39.0134i	−0.0447670	−	0.0717158i
$545$	−300.613	+	520.677i	−0.551584	+	0.955371i
$546$		0			0
$547$	254.839	−	147.131i	0.465885	−	0.268979i	−0.248631	−	0.968598i	$-0.579981\pi$
$547$	254.839	−	147.131i	0.465885	−	0.268979i	0.714515	+	0.699620i	$0.246647\pi$
$548$	−461.021	−	91.3732i	−0.841280	−	0.166739i
$549$		0			0
$550$	978.723	+	96.0559i	1.77950	+	0.174647i
$551$	−451.254	+	260.532i	−0.818974	+	0.472835i
$552$		0			0
$553$	161.149	−	279.118i	0.291408	−	0.504734i
$554$	216.123	+	154.759i	0.390113	+	0.279348i
$555$		0			0
$556$	150.322	−	51.1428i	0.270363	−	0.0919834i
$557$	395.706			0.710424			0.355212	−	0.934786i	$-0.384409\pi$
$557$	395.706			0.710424			0.355212	+	0.934786i	$0.384409\pi$
$558$		0			0
$559$		−	518.989i		−	0.928424i
$560$	789.834	−	105.089i	1.41042	−	0.187660i
$561$		0			0
$562$	60.6783	+	43.4499i	0.107968	+	0.0773129i
$563$	224.519	+	129.626i	0.398791	+	0.230242i	0.685962	−	0.727637i	$-0.259382\pi$
$563$	224.519	+	129.626i	0.398791	+	0.230242i	−0.287171	+	0.957879i	$0.592715\pi$
$564$		0			0
$565$	56.1950	+	97.3325i	0.0994601	+	0.172270i
$566$	310.843	+	30.5074i	0.549193	+	0.0539001i
$567$		0			0
$568$	−54.7382	−	16.5430i	−0.0963700	−	0.0291250i
$569$	123.594	+	214.071i	0.217213	+	0.376224i	0.953955	−	0.299950i	$-0.0969701\pi$
$569$	123.594	+	214.071i	0.217213	+	0.376224i	−0.736742	+	0.676174i	$0.763637\pi$
$570$		0			0
$571$	520.747	+	300.654i	0.911992	+	0.526539i	0.881072	−	0.472983i	$-0.156823\pi$
$571$	520.747	+	300.654i	0.911992	+	0.526539i	0.0309205	+	0.999522i	$0.490156\pi$
$572$	414.637	+	363.123i	0.724891	+	0.634830i
$573$		0			0
$574$	−323.902	−	714.212i	−0.564288	−	1.24427i
$575$			454.184i			0.789885i
$576$		0			0
$577$	−754.648			−1.30788			−0.653941	−	0.756545i	$-0.726886\pi$
$577$	−754.648			−1.30788			−0.653941	+	0.756545i	$0.726886\pi$
$578$	522.635	−	237.020i	0.904213	−	0.410068i
$579$		0			0
$580$	−715.331	+	816.812i	−1.23333	+	1.40830i
$581$	489.182	−	847.287i	0.841965	−	1.45833i
$582$		0			0
$583$	−121.684	+	70.2543i	−0.208720	+	0.120505i
$584$	186.171	−	616.010i	0.318785	−	1.05481i
$585$		0			0
$586$	5.07445	−	51.7040i	0.00865946	−	0.0882321i
$587$	−211.142	+	121.903i	−0.359696	+	0.207671i	−0.668948	−	0.743310i	$-0.733255\pi$
$587$	−211.142	+	121.903i	−0.359696	+	0.207671i	0.309251	+	0.950980i	$0.399922\pi$
$588$		0			0
$589$	−375.090	+	649.675i	−0.636825	+	1.10301i
$590$	−188.891	+	263.789i	−0.320155	+	0.447100i
$591$		0			0
$592$	−93.7823	−	704.852i	−0.158416	−	1.19063i
$593$	−1091.73			−1.84103			−0.920516	−	0.390704i	$-0.872232\pi$
$593$	−1091.73			−1.84103			−0.920516	+	0.390704i	$0.872232\pi$
$594$		0			0
$595$		−	71.5722i		−	0.120289i
$596$	−147.939	−	434.831i	−0.248220	−	0.729583i
$597$		0			0
$598$	−148.198	+	206.960i	−0.247823	+	0.346088i
$599$	−814.688	−	470.361i	−1.36008	−	0.785243i	−0.370447	−	0.928854i	$-0.620795\pi$
$599$	−814.688	−	470.361i	−1.36008	−	0.785243i	−0.989634	+	0.143611i	$0.954129\pi$
$600$		0			0
$601$	−526.113	−	911.255i	−0.875396	−	1.51623i	−0.856340	−	0.516413i	$-0.827267\pi$
$601$	−526.113	−	911.255i	−0.875396	−	1.51623i	−0.0190566	−	0.999818i	$-0.506066\pi$
$602$	90.8829	−	926.015i	0.150968	−	1.53823i
$603$		0			0
$604$	−124.521	+	628.267i	−0.206160	+	1.04018i
$605$	728.501	+	1261.80i	1.20413	+	2.08562i
$606$		0			0
$607$	−380.876	−	219.899i	−0.627474	−	0.362272i	0.152299	−	0.988334i	$-0.451332\pi$
$607$	−380.876	−	219.899i	−0.627474	−	0.362272i	−0.779773	+	0.626062i	$0.784666\pi$
$608$	−377.167	+	235.438i	−0.620340	+	0.387233i
$609$		0			0
$610$	885.700	−	401.673i	1.45197	−	0.658480i
$611$		−	72.4124i		−	0.118515i
$612$		0			0
$613$	449.866			0.733876			0.366938	−	0.930245i	$-0.380406\pi$
$613$	449.866			0.733876			0.366938	+	0.930245i	$0.380406\pi$
$614$	92.2436	+	203.400i	0.150234	+	0.331270i
$615$		0			0
$616$	676.236	+	720.518i	1.09779	+	1.16967i
$617$	−424.268	+	734.854i	−0.687630	+	1.19101i	0.284972	+	0.958536i	$0.408016\pi$
$617$	−424.268	+	734.854i	−0.687630	+	1.19101i	−0.972602	+	0.232475i	$0.925318\pi$
$618$		0			0
$619$	467.583	−	269.959i	0.755384	−	0.436121i	−0.0722522	−	0.997386i	$-0.523019\pi$
$619$	467.583	−	269.959i	0.755384	−	0.436121i	0.827636	+	0.561265i	$0.189685\pi$
$620$	−303.907	+	1533.35i	−0.490172	+	2.47315i
$621$		0			0
$622$	−644.387	−	63.2428i	−1.03599	−	0.101677i
$623$	250.898	−	144.856i	0.402726	−	0.232514i
$624$		0			0
$625$	279.778	−	484.589i	0.447644	−	0.775343i
$626$	−595.444	−	426.379i	−0.951188	−	0.681117i
$627$		0			0
$628$	290.316	+	853.314i	0.462286	+	1.35878i
$629$	−63.8714			−0.101544
$630$		0			0
$631$			43.6036i			0.0691024i	0.999403	+	0.0345512i	$0.0110002\pi$
$631$			43.6036i			0.0691024i	−0.999403	+	0.0345512i	$0.989000\pi$
$632$	85.4736	+	364.873i	0.135243	+	0.577331i
$633$		0			0
$634$	105.701	+	75.6891i	0.166720	+	0.119383i
$635$	987.033	+	569.864i	1.55438	+	0.897423i
$636$		0			0
$637$	−6.37860	−	11.0481i	−0.0100135	−	0.0173439i
$638$	−1340.08	−	131.521i	−2.10043	−	0.206145i
$639$		0			0
$640$	−586.021	+	717.585i	−0.915657	+	1.12123i
$641$	−83.6313	−	144.854i	−0.130470	−	0.225981i	0.793388	−	0.608716i	$-0.208315\pi$
$641$	−83.6313	−	144.854i	−0.130470	−	0.225981i	−0.923858	+	0.382736i	$0.874982\pi$
$642$		0			0
$643$	−645.855	−	372.885i	−1.00444	−	0.579914i	−0.0948816	−	0.995489i	$-0.530247\pi$
$643$	−645.855	−	372.885i	−1.00444	−	0.579914i	−0.909559	+	0.415574i	$0.863581\pi$
$644$	−300.667	+	343.321i	−0.466874	+	0.533107i
$645$		0			0
$646$	16.4952	+	36.3724i	0.0255344	+	0.0563040i
$647$		−	596.836i		−	0.922467i	−0.887279	−	0.461233i	$-0.847407\pi$
$647$		−	596.836i		−	0.922467i	0.887279	−	0.461233i	$-0.152593\pi$
$648$		0			0
$649$	−402.363			−0.619974
$650$	−382.905	+	173.651i	−0.589085	+	0.267155i
$651$		0			0
$652$	−442.844	−	387.825i	−0.679208	−	0.594823i
$653$	−395.435	+	684.914i	−0.605567	+	1.04887i	0.386394	+	0.922334i	$0.373720\pi$
$653$	−395.435	+	684.914i	−0.605567	+	1.04887i	−0.991962	+	0.126540i	$0.959613\pi$
$654$		0			0
$655$	−294.983	+	170.309i	−0.450356	+	0.260013i
$656$	842.926	+	347.793i	1.28495	+	0.530173i
$657$		0			0
$658$	12.6805	−	129.203i	0.0192713	−	0.196357i
$659$	−348.635	+	201.284i	−0.529036	+	0.305439i	−0.740624	−	0.671920i	$-0.765470\pi$
$659$	−348.635	+	201.284i	−0.529036	+	0.305439i	0.211588	+	0.977359i	$0.432137\pi$
$660$		0			0
$661$	−243.272	+	421.359i	−0.368036	+	0.637457i	−0.989258	−	0.146177i	$-0.953303\pi$
$661$	−243.272	+	421.359i	−0.368036	+	0.637457i	0.621222	+	0.783634i	$0.286636\pi$
$662$	511.682	−	714.571i	0.772934	−	1.07941i
$663$		0			0
$664$	259.463	+	1107.61i	0.390757	+	1.66808i
$665$	−691.933			−1.04050
$666$		0			0
$667$		−	621.873i		−	0.932343i
$668$	401.193	−	136.495i	0.600589	−	0.204333i
$669$		0			0
$670$	583.249	−	814.514i	0.870521	−	1.21569i
$671$	1044.50	+	603.042i	1.55663	+	0.898721i
$672$		0			0
$673$	85.8636	+	148.720i	0.127583	+	0.220981i	0.922740	−	0.385423i	$-0.125945\pi$
$673$	85.8636	+	148.720i	0.127583	+	0.220981i	−0.795156	+	0.606404i	$0.792611\pi$
$674$	−73.2205	+	746.051i	−0.108636	+	1.10690i
$675$		0			0
$676$	431.959	+	85.6132i	0.638993	+	0.126647i
$677$	106.547	+	184.546i	0.157382	+	0.272593i	0.933924	−	0.357472i	$-0.116361\pi$
$677$	106.547	+	184.546i	0.157382	+	0.272593i	−0.776542	+	0.630065i	$0.783028\pi$
$678$		0			0
$679$	−374.761	−	216.369i	−0.551931	−	0.318658i
$680$	56.9515	+	60.6809i	0.0837522	+	0.0892365i
$681$		0			0
$682$	−1765.52	+	800.677i	−2.58873	+	1.17401i
$683$		−	602.265i		−	0.881794i	−0.897558	−	0.440897i	$-0.854660\pi$
$683$		−	602.265i		−	0.881794i	0.897558	−	0.440897i	$-0.145340\pi$
$684$		0			0
$685$	850.451			1.24153
$686$	−287.931	−	634.897i	−0.419725	−	0.925506i
$687$		0			0
$688$	659.796	+	857.418i	0.959006	+	1.24625i
$689$	30.0357	−	52.0233i	0.0435931	−	0.0755055i
$690$		0			0
$691$	−1062.89	+	613.657i	−1.53818	+	0.888071i	−0.539240	+	0.842152i	$0.681288\pi$
$691$	−1062.89	+	613.657i	−1.53818	+	0.888071i	−0.998945	+	0.0459192i	$0.985378\pi$
$692$	731.466	+	144.975i	1.05703	+	0.209501i
$693$		0			0
$694$	654.913	+	64.2759i	0.943679	+	0.0926166i
$695$	−248.828	+	143.661i	−0.358025	+	0.206706i
$696$		0			0
$697$	40.9539	−	70.9342i	0.0587574	−	0.101771i
$698$	605.729	+	433.744i	0.867807	+	0.621410i
$699$		0			0
$700$	−713.614	+	242.787i	−1.01945	+	0.346839i
$701$	133.314			0.190176			0.0950882	−	0.995469i	$-0.469687\pi$
$701$	133.314			0.190176			0.0950882	+	0.995469i	$0.469687\pi$
$702$		0			0
$703$			617.485i			0.878357i
$704$	−1146.66	−	72.7798i	−1.62878	−	0.103380i
$705$		0			0
$706$	354.095	+	253.557i	0.501552	+	0.359146i
$707$	−283.709	−	163.799i	−0.401285	−	0.231682i
$708$		0			0
$709$	305.128	+	528.497i	0.430364	+	0.745412i	0.996905	−	0.0786216i	$-0.0250519\pi$
$709$	305.128	+	528.497i	0.430364	+	0.745412i	−0.566541	+	0.824034i	$0.691719\pi$
$710$	102.979	+	10.1068i	0.145041	+	0.0142349i
$711$		0			0
$712$	−97.4534	+	322.458i	−0.136873	+	0.452891i
$713$	−447.658	−	775.366i	−0.627851	−	1.08747i
$714$		0			0
$715$	−863.722	−	498.670i	−1.20800	−	0.697440i
$716$	−576.548	−	504.918i	−0.805235	−	0.705192i
$717$		0			0
$718$	−120.252	−	265.159i	−0.167482	−	0.369303i
$719$		−	967.279i		−	1.34531i	−0.739956	−	0.672656i	$-0.765154\pi$
$719$		−	967.279i		−	1.34531i	0.739956	−	0.672656i	$-0.234846\pi$
$720$		0			0
$721$	−369.635			−0.512671
$722$	−305.907	+	138.731i	−0.423693	+	0.192149i
$723$		0			0
$724$	540.133	−	616.759i	0.746040	−	0.851877i
$725$	513.577	−	889.542i	0.708382	−	1.22695i
$726$		0			0
$727$	1209.48	−	698.296i	1.66366	−	0.960517i	0.692722	−	0.721204i	$-0.256411\pi$
$727$	1209.48	−	698.296i	1.66366	−	0.960517i	0.970942	−	0.239313i	$-0.0769223\pi$
$728$	−404.397	−	122.217i	−0.555490	−	0.167880i
$729$		0			0
$730$	−113.740	+	1158.90i	−0.155808	+	1.58754i
$731$	84.1616	−	48.5907i	0.115132	−	0.0664716i
$732$		0			0
$733$	153.115	−	265.202i	0.208888	−	0.361804i	−0.742477	−	0.669872i	$-0.766349\pi$
$733$	153.115	−	265.202i	0.208888	−	0.361804i	0.951364	+	0.308068i	$0.0996823\pi$
$734$	−62.2683	+	86.9584i	−0.0848341	+	0.118472i
$735$		0			0
$736$	−18.2741	−	530.324i	−0.0248290	−	0.720548i
$737$	1242.40			1.68575
$738$		0			0
$739$		−	463.182i		−	0.626769i	−0.949626	−	0.313384i	$-0.898537\pi$
$739$		−	463.182i		−	0.626769i	0.949626	−	0.313384i	$-0.101463\pi$
$740$	414.427	+	1218.11i	0.560037	+	1.64609i
$741$		0			0
$742$	62.7017	−	87.5637i	0.0845036	−	0.118010i
$743$	702.085	+	405.349i	0.944932	+	0.545557i	0.891503	−	0.453015i	$-0.149652\pi$
$743$	702.085	+	405.349i	0.944932	+	0.545557i	0.0534291	+	0.998572i	$0.482985\pi$
$744$		0			0
$745$	415.562	+	719.775i	0.557802	+	0.966141i
$746$	−66.7128	+	679.743i	−0.0894273	+	0.911183i
$747$		0			0
$748$	−20.0649	+	101.237i	−0.0268248	+	0.135344i
$749$	−91.0628	−	157.725i	−0.121579	−	0.210581i
$750$		0			0
$751$	−858.169	−	495.464i	−1.14270	−	0.659739i	−0.195603	−	0.980683i	$-0.562666\pi$
$751$	−858.169	−	495.464i	−1.14270	−	0.659739i	−0.947098	+	0.320944i	$0.896000\pi$
$752$	92.0587	+	119.632i	0.122419	+	0.159085i
$753$		0			0
$754$	524.278	−	237.765i	0.695329	−	0.315338i
$755$		−	1158.97i		−	1.53506i
$756$		0			0
$757$	−320.001			−0.422723			−0.211361	−	0.977408i	$-0.567790\pi$
$757$	−320.001			−0.422723			−0.211361	+	0.977408i	$0.567790\pi$
$758$	−181.885	−	401.061i	−0.239953	−	0.529104i
$759$		0			0
$760$	586.640	−	550.586i	0.771894	−	0.724455i
$761$	317.988	−	550.771i	0.417855	−	0.723746i	−0.577868	−	0.816130i	$-0.696115\pi$
$761$	317.988	−	550.771i	0.417855	−	0.723746i	0.995723	+	0.0923836i	$0.0294486\pi$
$762$		0			0
$763$	494.939	−	285.753i	0.648675	−	0.374512i
$764$	69.8461	−	352.407i	0.0914217	−	0.461266i
$765$		0			0
$766$	1335.73	+	131.094i	1.74377	+	0.171141i
$767$	148.975	−	86.0107i	0.194231	−	0.112139i
$768$		0			0
$769$	−152.926	+	264.876i	−0.198864	+	0.344442i	−0.948160	−	0.317793i	$-0.897058\pi$
$769$	−152.926	+	264.876i	−0.198864	+	0.344442i	0.749297	+	0.662234i	$0.230392\pi$
$770$	−1453.79	−	1041.01i	−1.88803	−	1.35196i
$771$		0			0
$772$	215.925	+	634.659i	0.279695	+	0.822097i
$773$	187.263			0.242255			0.121128	−	0.992637i	$-0.461349\pi$
$773$	187.263			0.242255			0.121128	+	0.992637i	$0.461349\pi$
$774$		0			0
$775$		−	1478.80i		−	1.90813i
$776$	489.902	−	114.762i	0.631317	−	0.147890i
$777$		0			0
$778$	788.532	+	564.644i	1.01354	+	0.725763i
$779$	−685.766	−	395.927i	−0.880315	−	0.508250i
$780$		0			0
$781$	64.1621	+	111.132i	0.0821537	+	0.142294i
$782$	−47.4368	−	4.65564i	−0.0606608	−	0.00595350i
$783$		0			0
$784$	24.5836	+	10.1432i	0.0313566	+	0.0129378i
$785$	−815.501	−	1412.49i	−1.03885	−	1.79935i
$786$		0			0
$787$	−160.626	−	92.7376i	−0.204099	−	0.117837i	0.394467	−	0.918910i	$-0.370929\pi$
$787$	−160.626	−	92.7376i	−0.204099	−	0.117837i	−0.598566	+	0.801073i	$0.704263\pi$
$788$	488.263	−	557.530i	0.619623	−	0.707526i
$789$		0			0
$790$	−280.076	−	617.576i	−0.354527	−	0.781741i
$791$		−	106.834i		−	0.135062i
$792$		0			0
$793$	−515.634			−0.650232
$794$	508.862	−	230.774i	0.640885	−	0.290647i
$795$		0			0
$796$	−414.139	−	362.686i	−0.520275	−	0.455636i
$797$	546.202	−	946.049i	0.685322	−	1.18701i	−0.288014	−	0.957626i	$-0.592995\pi$
$797$	546.202	−	946.049i	0.685322	−	1.18701i	0.973336	−	0.229386i	$-0.0736718\pi$
$798$		0			0
$799$	11.7427	−	6.77967i	0.0146968	−	0.00848519i
$800$	411.831	−	773.679i	0.514789	−	0.967099i
$801$		0			0
$802$	−113.732	+	1158.83i	−0.141811	+	1.44493i
$803$	−1250.65	+	722.064i	−1.55747	+	0.899208i
$804$		0			0
$805$	412.900	−	715.164i	0.512919	−	0.888402i
$806$	482.527	−	673.855i	0.598668	−	0.836048i
$807$		0			0
$808$	370.875	−	86.8794i	0.459003	−	0.107524i
$809$	−51.1143			−0.0631821			−0.0315911	−	0.999501i	$-0.510057\pi$
$809$	−51.1143			−0.0631821			−0.0315911	+	0.999501i	$0.510057\pi$
$810$		0			0
$811$			680.159i			0.838667i	0.907832	+	0.419333i	$0.137736\pi$
$811$			680.159i			0.838667i	−0.907832	+	0.419333i	$0.862264\pi$
$812$	977.088	−	332.427i	1.20331	−	0.409392i
$813$		0			0
$814$	−929.004	+	1297.37i	−1.14128	+	1.59382i
$815$	922.477	+	532.593i	1.13187	+	0.653488i
$816$		0			0
$817$	−469.757	−	813.643i	−0.574978	−	0.995891i
$818$	−85.3016	+	869.146i	−0.104281	+	1.06253i
$819$		0			0
$820$	−1618.54	−	320.789i	−1.97382	−	0.391207i
$821$	62.1337	+	107.619i	0.0756805	+	0.131082i	0.901382	−	0.433025i	$-0.142554\pi$
$821$	62.1337	+	107.619i	0.0756805	+	0.131082i	−0.825702	+	0.564107i	$0.809220\pi$
$822$		0			0
$823$	959.409	+	553.915i	1.16575	+	0.673044i	0.952674	−	0.303992i	$-0.0983197\pi$
$823$	959.409	+	553.915i	1.16575	+	0.673044i	0.213072	+	0.977036i	$0.431653\pi$
$824$	313.387	−	294.127i	0.380324	−	0.356950i
$825$		0			0
$826$	280.873	−	127.378i	0.340040	−	0.154211i
$827$			856.831i			1.03607i	0.855359	+	0.518036i	$0.173337\pi$
$827$			856.831i			1.03607i	−0.855359	+	0.518036i	$0.826663\pi$
$828$		0			0
$829$	−59.5071			−0.0717818			−0.0358909	−	0.999356i	$-0.511427\pi$
$829$	−59.5071			−0.0717818			−0.0358909	+	0.999356i	$0.511427\pi$
$830$	−850.196	−	1874.71i	−1.02433	−	2.25868i
$831$		0			0
$832$	440.109	−	218.168i	0.528977	−	0.262221i
$833$	1.19440	−	2.06877i	0.00143386	−	0.00248351i
$834$		0			0
$835$	−664.094	+	383.415i	−0.795322	+	0.459179i
$836$	978.723	+	193.980i	1.17072	+	0.232034i
$837$		0			0
$838$	−1509.29	−	148.128i	−1.80106	−	0.176764i
$839$	−402.435	+	232.346i	−0.479660	+	0.276932i	−0.720275	−	0.693689i	$-0.755984\pi$
$839$	−402.435	+	232.346i	−0.479660	+	0.276932i	0.240615	+	0.970621i	$0.422651\pi$
$840$		0			0
$841$	−282.695	+	489.643i	−0.336142	+	0.582215i
$842$	851.012	+	609.384i	1.01070	+	0.723734i
$843$		0			0
$844$	−1155.94	+	393.277i	−1.36960	+	0.465969i
$845$	−796.840			−0.943006
$846$		0			0
$847$		−	1384.98i		−	1.63516i
$848$	16.5161	+	124.132i	0.0194765	+	0.146382i
$849$		0			0
$850$	−64.0098	−	45.8355i	−0.0753057	−	0.0539241i
$851$	−638.216	−	368.474i	−0.749960	−	0.432990i
$852$		0			0
$853$	683.164	+	1183.28i	0.800896	+	1.38719i	0.919027	+	0.394195i	$0.128977\pi$
$853$	683.164	+	1183.28i	0.800896	+	1.38719i	−0.118131	+	0.992998i	$0.537690\pi$
$854$	−920.029	−	90.2955i	−1.07732	−	0.105732i
$855$		0			0
$856$	202.711	+	61.2633i	0.236812	+	0.0715693i
$857$	838.799	+	1452.84i	0.978762	+	1.69527i	0.666916	+	0.745133i	$0.267614\pi$
$857$	838.799	+	1452.84i	0.978762	+	1.69527i	0.311846	+	0.950133i	$0.399053\pi$
$858$		0			0
$859$	−1424.63	−	822.513i	−1.65848	−	0.957524i	−0.973417	−	0.229039i	$-0.926442\pi$
$859$	−1424.63	−	822.513i	−1.65848	−	0.957524i	−0.685063	−	0.728484i	$-0.740225\pi$
$860$	−1472.77	−	1289.79i	−1.71252	−	1.49976i
$861$		0			0
$862$	602.305	+	1328.10i	0.698729	+	1.54072i
$863$			294.311i			0.341033i	0.985355	+	0.170516i	$0.0545436\pi$
$863$			294.311i			0.341033i	−0.985355	+	0.170516i	$0.945456\pi$
$864$		0			0
$865$	−1349.34			−1.55994
$866$	894.727	−	405.767i	1.03317	−	0.468553i
$867$		0			0
$868$	978.959	−	1117.84i	1.12783	−	1.28783i
$869$	420.486	−	728.303i	0.483873	−	0.838093i
$870$		0			0
$871$	−459.997	+	265.579i	−0.528125	+	0.304913i
$872$	−192.243	+	636.102i	−0.220462	+	0.729475i
$873$		0			0
$874$	−45.0090	+	458.601i	−0.0514977	+	0.524715i
$875$	103.050	−	59.4960i	0.117772	−	0.0679955i
$876$		0			0
$877$	−359.584	+	622.818i	−0.410016	+	0.710169i	−0.994891	−	0.100954i	$-0.967810\pi$
$877$	−359.584	+	622.818i	−0.410016	+	0.710169i	0.584875	+	0.811124i	$0.301144\pi$
$878$	−219.714	+	306.833i	−0.250244	+	0.349468i
$879$		0			0
$880$	2060.91	−	274.210i	2.34195	−	0.311602i
$881$	−16.3083			−0.0185112			−0.00925559	−	0.999957i	$-0.502946\pi$
$881$	−16.3083			−0.0185112			−0.00925559	+	0.999957i	$0.502946\pi$
$882$		0			0
$883$		−	1190.35i		−	1.34807i	−0.738698	−	0.674036i	$-0.764559\pi$
$883$		−	1190.35i		−	1.34807i	0.738698	−	0.674036i	$-0.235441\pi$
$884$	−14.2118	−	41.7722i	−0.0160767	−	0.0472536i
$885$		0			0
$886$	−481.138	+	671.915i	−0.543045	+	0.758369i
$887$	−346.987	−	200.333i	−0.391192	−	0.225855i	0.291485	−	0.956575i	$-0.405851\pi$
$887$	−346.987	−	200.333i	−0.391192	−	0.225855i	−0.682676	+	0.730721i	$0.739184\pi$
$888$		0			0
$889$	−541.693	−	938.241i	−0.609329	−	1.05539i
$890$	59.5384	−	606.643i	0.0668971	−	0.681621i
$891$		0			0
$892$	13.3932	−	67.5750i	0.0150148	−	0.0757567i
$893$	−65.5433	−	113.524i	−0.0733967	−	0.127127i
$894$		0			0
$895$	1200.99	+	693.394i	1.34189	+	0.774742i
$896$	823.477	−	312.201i	0.919059	−	0.348438i
$897$		0			0
$898$	1162.54	−	527.223i	1.29459	−	0.587108i
$899$			2024.79i			2.25227i
$900$		0			0
$901$	11.2484			0.0124844
$902$	−845.156	−	1863.59i	−0.936981	−	2.06607i
$903$		0			0
$904$	85.0101	+	90.5769i	0.0940378	+	0.100196i
$905$	−741.755	+	1284.76i	−0.819618	+	1.41962i
$906$		0			0
$907$	1091.40	−	630.121i	1.20331	−	0.694731i	0.242019	−	0.970271i	$-0.422190\pi$
$907$	1091.40	−	630.121i	1.20331	−	0.694731i	0.961289	+	0.275541i	$0.0888569\pi$
$908$	31.8722	−	160.810i	0.0351015	−	0.177104i
$909$		0			0
$910$	760.795	+	74.6675i	0.836038	+	0.0820522i
$911$	−835.193	+	482.199i	−0.916788	+	0.529308i	−0.882609	−	0.470108i	$-0.844215\pi$
$911$	−835.193	+	482.199i	−0.916788	+	0.529308i	−0.0341788	+	0.999416i	$0.510882\pi$
$912$		0			0
$913$	1276.42	−	2210.83i	1.39805	−	2.42150i
$914$	−375.119	−	268.611i	−0.410414	−	0.293885i
$915$		0			0
$916$	−171.936	−	505.363i	−0.187703	−	0.551707i
$917$	323.779			0.353086
$918$		0			0
$919$		−	424.406i		−	0.461813i	−0.972976	−	0.230906i	$-0.925831\pi$
$919$		−	424.406i		−	0.461813i	0.972976	−	0.230906i	$-0.0741691\pi$
$920$	219.003	+	934.888i	0.238047	+	1.01618i
$921$		0			0
$922$	−650.744	−	465.978i	−0.705796	−	0.505399i
$923$	−47.5120	−	27.4311i	−0.0514756	−	0.0297195i
$924$		0			0
$925$	−608.613	−	1054.15i	−0.657960	−	1.13962i
$926$	590.476	+	57.9517i	0.637663	+	0.0625829i
$927$		0			0
$928$	−563.883	+	1059.33i	−0.607633	+	1.14152i
$929$	−429.229	−	743.447i	−0.462033	−	0.800265i	0.537029	−	0.843564i	$-0.319547\pi$
$929$	−429.229	−	743.447i	−0.462033	−	0.800265i	−0.999062	+	0.0432985i	$0.986213\pi$
$930$		0			0
$931$	−20.0001	−	11.5470i	−0.0214823	−	0.0124028i
$932$	−970.706	+	1108.41i	−1.04153	+	1.18929i
$933$		0			0
$934$	−104.954	−	231.426i	−0.112370	−	0.247780i
$935$		−	186.753i		−	0.199736i
$936$		0			0
$937$	858.258			0.915964			0.457982	−	0.888962i	$-0.348572\pi$
$937$	858.258			0.915964			0.457982	+	0.888962i	$0.348572\pi$
$938$	−867.264	+	393.312i	−0.924589	+	0.419309i
$939$		0			0
$940$	−205.489	−	179.959i	−0.218606	−	0.191446i
$941$	−468.553	+	811.558i	−0.497931	+	0.862442i	−0.999997	−	0.00238755i	$-0.999240\pi$
$941$	−468.553	+	811.558i	−0.497931	+	0.862442i	0.502066	+	0.864829i	$0.332573\pi$
$942$		0			0
$943$	818.439	−	472.526i	0.867910	−	0.501088i
$944$	−136.774	+	331.491i	−0.144888	+	0.351156i
$945$		0			0
$946$	237.141	−	2416.25i	0.250677	−	2.55418i
$947$	768.302	−	443.580i	0.811301	−	0.468405i	−0.0361062	−	0.999348i	$-0.511495\pi$
$947$	768.302	−	443.580i	0.811301	−	0.468405i	0.847408	+	0.530943i	$0.178162\pi$
$948$		0			0
$949$	308.702	−	534.688i	0.325292	−	0.563423i
$950$	−443.120	+	618.823i	−0.466442	+	0.651392i
$951$		0			0
$952$	−18.0427	−	77.0215i	−0.0189524	−	0.0809049i
$953$	−1078.46			−1.13164			−0.565821	−	0.824528i	$-0.691441\pi$
$953$	−1078.46			−1.13164			−0.565821	+	0.824528i	$0.691441\pi$
$954$		0			0
$955$			650.090i			0.680722i
$956$	1092.73	−	371.770i	1.14302	−	0.388881i
$957$		0			0
$958$	14.3395	−	20.0253i	0.0149682	−	0.0209033i
$959$	−700.104	−	404.205i	−0.730036	−	0.421486i
$960$		0			0
$961$	977.056	+	1692.31i	1.01671	+	1.76099i
$962$	66.6337	−	678.937i	0.0692658	−	0.705756i
$963$		0			0
$964$	404.089	+	80.0894i	0.419180	+	0.0830803i
$965$	−606.535	−	1050.55i	−0.628534	−	1.08865i
$966$		0			0
$967$	103.113	+	59.5324i	0.106632	+	0.0615640i	0.552368	−	0.833601i	$-0.313725\pi$
$967$	103.113	+	59.5324i	0.106632	+	0.0615640i	−0.445736	+	0.895165i	$0.647058\pi$
$968$	1102.06	+	1174.22i	1.13849	+	1.21304i
$969$		0			0
$970$	−829.196	+	376.048i	−0.854842	+	0.387678i
$971$		−	1516.56i		−	1.56185i	−0.624624	−	0.780926i	$-0.714748\pi$
$971$		−	1516.56i		−	1.56185i	0.624624	−	0.780926i	$-0.285252\pi$
$972$		0			0
$973$	273.118			0.280697
$974$	149.558	+	329.779i	0.153550	+	0.338582i
$975$		0			0
$976$	851.876	−	655.532i	0.872824	−	0.671651i
$977$	789.151	−	1366.85i	0.807729	−	1.39903i	−0.106705	−	0.994291i	$-0.534030\pi$
$977$	789.151	−	1366.85i	0.807729	−	1.39903i	0.914434	−	0.404736i	$-0.132637\pi$
$978$		0			0
$979$	654.669	−	377.974i	0.668712	−	0.386081i
$980$	−47.2039	−	9.35568i	−0.0481672	−	0.00954661i
$981$		0			0
$982$	989.406	+	97.1044i	1.00754	+	0.0988843i
$983$	513.330	−	296.371i	0.522207	−	0.301497i	−0.215630	−	0.976475i	$-0.569180\pi$
$983$	513.330	−	296.371i	0.522207	−	0.301497i	0.737837	+	0.674979i	$0.235847\pi$
$984$		0			0
$985$	−670.522	+	1161.38i	−0.680733	+	1.17906i
$986$	87.6429	+	62.7584i	0.0888873	+	0.0636495i
$987$		0			0
$988$	−403.838	+	137.394i	−0.408743	+	0.139063i
$989$	1121.28			1.13375
$990$		0			0
$991$			1896.17i			1.91339i	0.291098	+	0.956693i	$0.405980\pi$
$991$			1896.17i			1.91339i	−0.291098	+	0.956693i	$0.594020\pi$
$992$	59.4998	+	1726.71i	0.0599796	+	1.74064i
$993$		0			0
$994$	−79.9705	−	57.2644i	−0.0804532	−	0.0576101i
$995$	862.683	+	498.070i	0.867018	+	0.500573i
$996$		0			0
$997$	−34.8563	−	60.3729i	−0.0349612	−	0.0605546i	0.848015	−	0.529972i	$-0.177797\pi$
$997$	−34.8563	−	60.3729i	−0.0349612	−	0.0605546i	−0.882977	+	0.469417i	$0.844464\pi$
$998$	−1517.84	−	148.967i	−1.52088	−	0.149266i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.f.q.271.1		12
3.2	odd	2		324.3.f.r.271.6		12
4.3	odd	2	inner	324.3.f.q.271.5		12
9.2	odd	6		324.3.f.r.55.2		12
9.4	even	3		324.3.d.f.163.3	yes	6
9.5	odd	6		324.3.d.e.163.4	yes	6
9.7	even	3	inner	324.3.f.q.55.5		12
12.11	even	2		324.3.f.r.271.2		12
36.7	odd	6	inner	324.3.f.q.55.1		12
36.11	even	6		324.3.f.r.55.6		12
36.23	even	6		324.3.d.e.163.3	✓	6
36.31	odd	6		324.3.d.f.163.4	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.d.e.163.3	✓	6	36.23	even	6
324.3.d.e.163.4	yes	6	9.5	odd	6
324.3.d.f.163.3	yes	6	9.4	even	3
324.3.d.f.163.4	yes	6	36.31	odd	6
324.3.f.q.55.1		12	36.7	odd	6	inner
324.3.f.q.55.5		12	9.7	even	3	inner
324.3.f.q.271.1		12	1.1	even	1	trivial
324.3.f.q.271.5		12	4.3	odd	2	inner
324.3.f.r.55.2		12	9.2	odd	6
324.3.f.r.55.6		12	36.11	even	6
324.3.f.r.271.2		12	12.11	even	2
324.3.f.r.271.6		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.82144 + 0.826041i) q^{2} +(2.63531 - 3.00917i) q^{4} +(-3.61903 + 6.26834i) q^{5} +(5.95847 - 3.44013i) q^{7} +(-2.31438 + 7.65792i) q^{8} +(1.41395 - 14.4069i) q^{10} +(15.5474 - 8.97632i) q^{11} +(-3.83763 + 6.64697i) q^{13} +(-8.01134 + 11.1879i) q^{14} +(-2.11024 - 15.8602i) q^{16} -1.43720 q^{17} +13.8943i q^{19} +(9.32524 + 27.4093i) q^{20} +(-20.9040 + 29.1927i) q^{22} +(-14.3608 - 8.29122i) q^{23} +(-13.6947 - 23.7199i) q^{25} +(1.49936 - 15.2771i) q^{26} +(5.35051 - 26.9959i) q^{28} +(18.7509 + 32.4776i) q^{29} +(46.7583 + 26.9959i) q^{31} +(16.9449 + 27.1454i) q^{32} +(2.61778 - 1.18719i) q^{34} +49.7996i q^{35} +44.4415 q^{37} +(-11.4773 - 25.3078i) q^{38} +(-39.6266 - 42.2215i) q^{40} +(-28.4956 + 49.3558i) q^{41} +(-58.5593 + 33.8092i) q^{43} +(13.9611 - 70.4404i) q^{44} +(33.0063 + 3.23938i) q^{46} +(-8.17054 + 4.71726i) q^{47} +(-0.831061 + 1.43944i) q^{49} +(44.5378 + 31.8921i) q^{50} +(9.88852 + 29.0649i) q^{52} -7.82662 q^{53} +129.942i q^{55} +(12.5540 + 53.5912i) q^{56} +(-60.9816 - 43.6670i) q^{58} +(-19.4098 - 11.2062i) q^{59} +(33.5907 + 58.1808i) q^{61} +(-107.467 - 10.5473i) q^{62} +(-53.2873 - 35.4466i) q^{64} +(-27.7770 - 48.1111i) q^{65} +(59.9324 + 34.6020i) q^{67} +(-3.78748 + 4.32479i) q^{68} +(-41.1365 - 90.7072i) q^{70} +7.14792i q^{71} -80.4410 q^{73} +(-80.9476 + 36.7104i) q^{74} +(41.8105 + 36.6159i) q^{76} +(61.7594 - 106.970i) q^{77} +(40.5680 - 23.4219i) q^{79} +(107.054 + 44.1709i) q^{80} +(11.1332 - 113.437i) q^{82} +(123.148 - 71.0994i) q^{83} +(5.20128 - 9.00887i) q^{85} +(78.7347 - 109.954i) q^{86} +(32.7573 + 139.836i) q^{88} +42.1078 q^{89} +52.8077i q^{91} +(-62.7950 + 21.3642i) q^{92} +(10.9855 - 15.3414i) q^{94} +(-87.0944 - 50.2840i) q^{95} +(-31.4478 - 54.4691i) q^{97} +(0.324695 - 3.30835i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + 3 q^{4} - 2 q^{5} + 14 q^{8} + 18 q^{10} - 6 q^{13} + 15 q^{16} - 20 q^{17} + 67 q^{20} - 48 q^{22} - 146 q^{26} - 96 q^{28} + 22 q^{29} - 31 q^{32} - 81 q^{34} + 108 q^{37} - 168 q^{38}+ \cdots - 814 q^{98}+O(q^{100}) \) 12 * q - q^2 + 3 * q^4 - 2 * q^5 + 14 * q^8 + 18 * q^10 - 6 * q^13 + 15 * q^16 - 20 * q^17 + 67 * q^20 - 48 * q^22 - 146 * q^26 - 96 * q^28 + 22 * q^29 - 31 * q^32 - 81 * q^34 + 108 * q^37 - 168 * q^38 + 81 * q^40 - 92 * q^41 + 336 * q^44 + 240 * q^46 + 66 * q^49 + 48 * q^50 + 117 * q^52 + 232 * q^53 + 312 * q^56 - 201 * q^58 - 54 * q^61 - 624 * q^62 - 510 * q^64 - 82 * q^65 - 53 * q^68 - 264 * q^70 - 156 * q^73 - 383 * q^74 + 192 * q^76 + 168 * q^77 + 754 * q^80 + 300 * q^82 - 66 * q^85 + 144 * q^86 + 336 * q^88 - 500 * q^89 + 504 * q^92 - 216 * q^94 + 204 * q^97 - 814 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more