LMFDB - Embedded newform 324.3.f.r.55.2

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			55.2
Root			$0.0389494 + 1.41368i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.r.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62609 - 1.16440i) q^{2} +(1.28836 + 3.78684i) q^{4} +(3.61903 + 6.26834i) q^{5} +(-5.95847 - 3.44013i) q^{7} +(2.31438 - 7.65792i) q^{8} +O(q^{10})$	\(q+(-1.62609 - 1.16440i) q^{2} +(1.28836 + 3.78684i) q^{4} +(3.61903 + 6.26834i) q^{5} +(-5.95847 - 3.44013i) q^{7} +(2.31438 - 7.65792i) q^{8} +(1.41395 - 14.4069i) q^{10} +(15.5474 + 8.97632i) q^{11} +(-3.83763 - 6.64697i) q^{13} +(5.68337 + 12.5320i) q^{14} +(-12.6802 + 9.75764i) q^{16} +1.43720 q^{17} +13.8943i q^{19} +(-19.0745 + 21.7806i) q^{20} +(-14.8296 - 32.6997i) q^{22} +(-14.3608 + 8.29122i) q^{23} +(-13.6947 + 23.7199i) q^{25} +(-1.49936 + 15.2771i) q^{26} +(5.35051 - 26.9959i) q^{28} +(-18.7509 + 32.4776i) q^{29} +(-46.7583 + 26.9959i) q^{31} +(31.9810 - 1.10202i) q^{32} +(-2.33703 - 1.67347i) q^{34} -49.7996i q^{35} +44.4415 q^{37} +(16.1785 - 22.5935i) q^{38} +(56.3782 - 13.2069i) q^{40} +(28.4956 + 49.3558i) q^{41} +(58.5593 + 33.8092i) q^{43} +(-13.9611 + 70.4404i) q^{44} +(33.0063 + 3.23938i) q^{46} +(-8.17054 - 4.71726i) q^{47} +(-0.831061 - 1.43944i) q^{49} +(49.8883 - 22.6248i) q^{50} +(20.2267 - 23.0962i) q^{52} +7.82662 q^{53} +129.942i q^{55} +(-40.1343 + 37.6677i) q^{56} +(68.3076 - 30.9781i) q^{58} +(-19.4098 + 11.2062i) q^{59} +(33.5907 - 58.1808i) q^{61} +(107.467 + 10.5473i) q^{62} +(-53.2873 - 35.4466i) q^{64} +(27.7770 - 48.1111i) q^{65} +(-59.9324 + 34.6020i) q^{67} +(1.85164 + 5.44245i) q^{68} +(-57.9865 + 80.9789i) q^{70} -7.14792i q^{71} -80.4410 q^{73} +(-72.2660 - 51.7475i) q^{74} +(-52.6156 + 17.9010i) q^{76} +(-61.7594 - 106.970i) q^{77} +(-40.5680 - 23.4219i) q^{79} +(-107.054 - 44.1709i) q^{80} +(11.1332 - 113.437i) q^{82} +(123.148 + 71.0994i) q^{83} +(5.20128 + 9.00887i) q^{85} +(-55.8556 - 123.163i) q^{86} +(104.723 - 98.2865i) q^{88} -42.1078 q^{89} +52.8077i q^{91} +(-49.8995 - 43.7000i) q^{92} +(7.79330 + 17.1845i) q^{94} +(-87.0944 + 50.2840i) q^{95} +(-31.4478 + 54.4691i) q^{97} +(-0.324695 + 3.30835i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8}+O(q^{10}) $ 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.62609	−	1.16440i	−0.813047	−	0.582198i
$2$	−1.62609	−	1.16440i	−0.813047	−	0.582198i
$3$		0			0
$3$		0			0
$4$	1.28836	+	3.78684i	0.322091	+	0.946709i
$5$	3.61903	+	6.26834i	0.723805	+	1.25367i	0.959464	+	0.281832i	$0.0909420\pi$
$5$	3.61903	+	6.26834i	0.723805	+	1.25367i	−0.235659	+	0.971836i	$0.575725\pi$
$6$		0			0
$7$	−5.95847	−	3.44013i	−0.851211	−	0.491447i	0.00984858	−	0.999952i	$-0.496865\pi$
$7$	−5.95847	−	3.44013i	−0.851211	−	0.491447i	−0.861059	+	0.508505i	$0.830198\pi$
$8$	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	0.995707	−	0.0925568i	$-0.0295040\pi$
$11$	15.5474	+	8.97632i	1.41340	+	0.816029i	0.417697	+	0.908586i	$0.362837\pi$
$12$		0			0
$13$	−3.83763	−	6.64697i	−0.295202	−	0.511305i	0.679830	−	0.733370i	$-0.262054\pi$
$13$	−3.83763	−	6.64697i	−0.295202	−	0.511305i	−0.975032	+	0.222065i	$0.928720\pi$
$14$	5.68337	+	12.5320i	0.405955	+	0.895142i
$15$		0			0
$16$	−12.6802	+	9.75764i	−0.792515	+	0.609852i
$17$	1.43720			0.0845413			0.0422707	−	0.999106i	$-0.486541\pi$
$17$	1.43720			0.0845413			0.0422707	+	0.999106i	$0.486541\pi$
$18$		0			0
$19$			13.8943i			0.731281i	0.930756	+	0.365641i	$0.119150\pi$
$19$			13.8943i			0.731281i	−0.930756	+	0.365641i	$0.880850\pi$
$20$	−19.0745	+	21.7806i	−0.953727	+	1.08903i
$21$		0			0
$22$	−14.8296	−	32.6997i	−0.674074	−	1.48635i
$23$	−14.3608	+	8.29122i	−0.624384	+	0.360488i	−0.778574	−	0.627553i	$-0.784057\pi$
$23$	−14.3608	+	8.29122i	−0.624384	+	0.360488i	0.154190	+	0.988041i	$0.450723\pi$
$24$		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	0.337349	+	0.941380i	$0.390470\pi$
$29$	−18.7509	+	32.4776i	−0.646584	+	1.11992i	−0.983933	+	0.178537i	$0.942864\pi$
$30$		0			0
$31$	−46.7583	+	26.9959i	−1.50833	+	0.870835i	−0.508378	+	0.861134i	$0.669755\pi$
$31$	−46.7583	+	26.9959i	−1.50833	+	0.870835i	−0.999953	+	0.00970102i	$0.996912\pi$
$32$	31.9810	−	1.10202i	0.999407	−	0.0344380i
$33$		0			0
$34$	−2.33703	−	1.67347i	−0.0687361	−	0.0492198i
$35$		−	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	$0.294944\pi$
$38$	16.1785	−	22.5935i	0.425750	−	0.594566i
$39$		0			0
$40$	56.3782	−	13.2069i	1.40945	−	0.330173i
$41$	28.4956	+	49.3558i	0.695014	+	1.20380i	0.970176	+	0.242401i	$0.0779350\pi$
$41$	28.4956	+	49.3558i	0.695014	+	1.20380i	−0.275162	+	0.961398i	$0.588732\pi$
$42$		0			0
$43$	58.5593	+	33.8092i	1.36184	+	0.786261i	0.989869	−	0.141982i	$-0.0453474\pi$
$43$	58.5593	+	33.8092i	1.36184	+	0.786261i	0.371975	+	0.928243i	$0.378681\pi$
$44$	−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	0.410555	−	0.911836i	$-0.365335\pi$
$47$	−8.17054	−	4.71726i	−0.173841	−	0.100367i	−0.584396	+	0.811469i	$0.698668\pi$
$48$		0			0
$49$	−0.831061	−	1.43944i	−0.0169604	−	0.0293763i
$50$	49.8883	−	22.6248i	0.997766	−	0.452495i
$51$		0			0
$52$	20.2267	−	23.0962i	0.388975	−	0.444157i
$53$	7.82662			0.147672			0.0738360	−	0.997270i	$-0.476476\pi$
$53$	7.82662			0.147672			0.0738360	+	0.997270i	$0.476476\pi$
$54$		0			0
$55$			129.942i			2.36259i
$56$	−40.1343	+	37.6677i	−0.716685	+	0.672638i
$57$		0			0
$58$	68.3076	−	30.9781i	1.17772	−	0.534105i
$59$	−19.4098	+	11.2062i	−0.328979	+	0.189936i	−0.655388	−	0.755293i	$-0.727495\pi$
$59$	−19.4098	+	11.2062i	−0.328979	+	0.189936i	0.326409	+	0.945229i	$0.394161\pi$
$60$		0			0
$61$	33.5907	−	58.1808i	0.550667	−	0.953783i	−0.447559	−	0.894254i	$-0.647707\pi$
$61$	33.5907	−	58.1808i	0.550667	−	0.953783i	0.998227	−	0.0595292i	$-0.0189599\pi$
$62$	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	$-0.839413\pi$
$67$	−59.9324	+	34.6020i	−0.894514	+	0.516448i	−0.0190978	+	0.999818i	$0.506079\pi$
$68$	1.85164	+	5.44245i	0.0272300	+	0.0800360i
$69$		0			0
$70$	−57.9865	+	80.9789i	−0.828379	+	1.15684i
$71$		−	7.14792i		−	0.100675i	−0.998732	−	0.0503375i	$-0.983970\pi$
$71$		−	7.14792i		−	0.100675i	0.998732	−	0.0503375i	$-0.0160297\pi$
$72$		0			0
$73$	−80.4410			−1.10193			−0.550965	−	0.834528i	$-0.685740\pi$
$73$	−80.4410			−1.10193			−0.550965	+	0.834528i	$0.685740\pi$
$74$	−72.2660	−	51.7475i	−0.976567	−	0.699290i
$75$		0			0
$76$	−52.6156	+	17.9010i	−0.692310	+	0.235539i
$77$	−61.7594	−	106.970i	−0.802070	−	1.38923i
$78$		0			0
$79$	−40.5680	−	23.4219i	−0.513519	−	0.296480i	0.220760	−	0.975328i	$-0.429146\pi$
$79$	−40.5680	−	23.4219i	−0.513519	−	0.296480i	−0.734279	+	0.678848i	$0.762480\pi$
$80$	−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	0.999829	−	0.0185165i	$-0.00589432\pi$
$83$	123.148	+	71.0994i	1.48371	+	0.856619i	0.483879	+	0.875135i	$0.339228\pi$
$84$		0			0
$85$	5.20128	+	9.00887i	0.0611915	+	0.105987i
$86$	−55.8556	−	123.163i	−0.649484	−	1.43213i
$87$		0			0
$88$	104.723	−	98.2865i	1.19003	−	1.11689i
$89$	−42.1078			−0.473122			−0.236561	−	0.971617i	$-0.576020\pi$
$89$	−42.1078			−0.473122			−0.236561	+	0.971617i	$0.576020\pi$
$90$		0			0
$91$			52.8077i			0.580304i
$92$	−49.8995	−	43.7000i	−0.542385	−	0.475000i
$93$		0			0
$94$	7.79330	+	17.1845i	0.0829075	+	0.182813i
$95$	−87.0944	+	50.2840i	−0.916783	+	0.529305i
$96$		0			0
$97$	−31.4478	+	54.4691i	−0.324204	+	0.561538i	−0.981351	−	0.192225i	$-0.938430\pi$
$97$	−31.4478	+	54.4691i	−0.324204	+	0.561538i	0.657147	+	0.753762i	$0.271763\pi$
$98$	−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	$-0.757590\pi$
$101$	23.8072	−	41.2352i	0.235715	−	0.408270i	0.959480	+	0.281776i	$0.0909236\pi$
$102$		0			0
$103$	46.5264	−	26.8621i	0.451713	−	0.260797i	−0.256840	−	0.966454i	$-0.582681\pi$
$103$	46.5264	−	26.8621i	0.451713	−	0.260797i	0.708553	+	0.705657i	$0.249348\pi$
$104$	−59.7836	+	14.0046i	−0.574843	+	0.134660i
$105$		0			0
$106$	−12.7268	−	9.11329i	−0.120064	−	0.0859744i
$107$			26.4708i			0.247390i	0.992320	+	0.123695i	$0.0394745\pi$
$107$			26.4708i			0.247390i	−0.992320	+	0.123695i	$0.960525\pi$
$108$		0			0
$109$	83.0647			0.762061			0.381031	−	0.924562i	$-0.375569\pi$
$109$	83.0647			0.762061			0.381031	+	0.924562i	$0.375569\pi$
$110$	151.304	−	211.298i	1.37549	−	1.92089i
$111$		0			0
$112$	109.122	−	14.5190i	0.974307	−	0.129634i
$113$	−7.76382	−	13.4473i	−0.0687064	−	0.119003i	0.829626	−	0.558320i	$-0.188554\pi$
$113$	−7.76382	−	13.4473i	−0.0687064	−	0.119003i	−0.898332	+	0.439317i	$0.855220\pi$
$114$		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
$122$	−122.367	+	55.4946i	−1.00301	+	0.454873i
$123$		0			0
$124$	−162.471	−	142.285i	−1.31025	−	1.14746i
$125$	−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	$-0.212841\pi$
$128$	45.3763	+	119.687i	0.354503	+	0.935055i
$129$		0			0
$130$	−101.188	+	45.8898i	−0.778372	+	0.352998i
$131$	40.7545	−	23.5296i	0.311103	−	0.179615i	−0.336317	−	0.941749i	$-0.609181\pi$
$131$	40.7545	−	23.5296i	0.311103	−	0.179615i	0.647420	+	0.762133i	$0.275848\pi$
$132$		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	$-0.692262\pi$
$137$	58.7486	−	101.756i	0.428822	−	0.742742i	0.996769	+	0.0803237i	$0.0255954\pi$
$138$		0			0
$139$	−34.3777	+	19.8480i	−0.247322	+	0.142791i	−0.618537	−	0.785756i	$-0.712274\pi$
$139$	−34.3777	+	19.8480i	−0.247322	+	0.142791i	0.371216	+	0.928547i	$0.378941\pi$
$140$	188.583	−	64.1600i	1.34702	−	0.458286i
$141$		0			0
$142$	−8.32301	+	11.6232i	−0.0586128	+	0.0818535i
$143$		−	137.791i		−	0.963575i
$144$		0			0
$145$	−271.441			−1.87200
$146$	130.805	+	93.6651i	0.895922	+	0.641542i
$147$		0			0
$148$	57.2567	+	168.292i	0.386870	+	1.13711i
$149$	−57.4136	−	99.4432i	−0.385326	−	0.667404i	0.606488	−	0.795092i	$-0.292578\pi$
$149$	−57.4136	−	99.4432i	−0.385326	−	0.667404i	−0.991814	+	0.127688i	$0.959244\pi$
$150$		0			0
$151$	138.670	+	80.0610i	0.918343	+	0.530206i	0.883106	−	0.469173i	$-0.155448\pi$
$151$	138.670	+	80.0610i	0.918343	+	0.530206i	0.0352370	+	0.999379i	$0.488781\pi$
$152$	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	−0.961935	−	0.273279i	$-0.911892\pi$
$157$	−112.668	−	195.148i	−0.717634	−	1.24298i	0.244301	−	0.969699i	$-0.421441\pi$
$158$	38.6949	+	85.3234i	0.244905	+	0.540022i
$159$		0			0
$160$	122.648	+	196.480i	0.766550	+	1.22800i
$161$	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	$-0.149084\pi$
$164$	−150.189	+	171.496i	−0.915789	+	1.04571i
$165$		0			0
$166$	−117.462	−	259.007i	−0.707602	−	1.56028i
$167$	91.7504	−	52.9721i	0.549403	−	0.317198i	−0.199478	−	0.979902i	$-0.563925\pi$
$167$	91.7504	−	52.9721i	0.549403	−	0.317198i	0.748881	+	0.662704i	$0.230591\pi$
$168$		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	0.460172	+	0.887830i	$0.347788\pi$
$173$	−93.2118	+	161.448i	−0.538797	+	0.933223i	−0.998969	+	0.0453938i	$0.985546\pi$
$174$		0			0
$175$	163.199	−	94.2231i	0.932566	−	0.538417i
$176$	−284.733	+	37.8845i	−1.61780	+	0.215253i
$177$		0			0
$178$	68.4713	+	49.0302i	0.384670	+	0.275451i
$179$			191.597i			1.07037i	0.844734	+	0.535187i	$0.179759\pi$
$179$			191.597i			1.07037i	−0.844734	+	0.535187i	$0.820241\pi$
$180$		0			0
$181$	204.960			1.13237			0.566187	−	0.824277i	$-0.308418\pi$
$181$	204.960			1.13237			0.566187	+	0.824277i	$0.308418\pi$
$182$	61.4891	−	85.8703i	0.337852	−	0.471815i
$183$		0			0
$184$	30.2571	+	129.163i	0.164441	+	0.701973i
$185$	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	0.689602	−	0.724188i	$-0.257785\pi$
$191$	77.7825	+	44.9078i	0.407238	+	0.235119i	−0.282364	+	0.959307i	$0.591119\pi$
$192$		0			0
$193$	−83.7981	−	145.143i	−0.434187	−	0.752034i	0.563042	−	0.826428i	$-0.309631\pi$
$193$	−83.7981	−	145.143i	−0.434187	−	0.752034i	−0.997229	+	0.0743944i	$0.976298\pi$
$194$	114.561	−	51.9543i	0.590519	−	0.267806i
$195$		0			0
$196$	4.38021	−	5.00161i	0.0223480	−	0.0255184i
$197$	−185.277			−0.940492			−0.470246	−	0.882535i	$-0.655835\pi$
$197$	−185.277			−0.940492			−0.470246	+	0.882535i	$0.655835\pi$
$198$		0			0
$199$		−	137.625i		−	0.691585i	−0.938311	−	0.345793i	$-0.887610\pi$
$199$		−	137.625i		−	0.691585i	0.938311	−	0.345793i	$-0.112390\pi$
$200$	149.951	+	159.770i	0.749753	+	0.798849i
$201$		0			0
$202$	−86.7268	+	39.3314i	−0.429341	+	0.194710i
$203$	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	$-0.409268\pi$
$211$	264.357	−	152.627i	1.25288	−	0.723350i	0.971680	+	0.236300i	$0.0759348\pi$
$212$	10.0835	+	29.6381i	0.0475638	+	0.139802i
$213$		0			0
$214$	30.8225	−	43.0440i	0.144030	−	0.201140i
$215$			489.426i			2.27640i
$216$		0			0
$217$	371.477			1.71188
$218$	−135.071	−	96.7202i	−0.619592	−	0.443671i
$219$		0			0
$220$	−492.070	+	167.413i	−2.23668	+	0.760967i
$221$	−5.51545	−	9.55304i	−0.0249568	−	0.0432264i
$222$		0			0
$223$	−14.9150	−	8.61118i	−0.0668834	−	0.0386152i	0.466185	−	0.884687i	$-0.345628\pi$
$223$	−14.9150	−	8.61118i	−0.0668834	−	0.0386152i	−0.533069	+	0.846072i	$0.678961\pi$
$224$	−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	0.576138	−	0.817352i	$-0.304559\pi$
$227$	35.4937	+	20.4923i	0.156360	+	0.0902744i	−0.419779	+	0.907627i	$0.637892\pi$
$228$		0			0
$229$	66.7264	+	115.573i	0.291381	+	0.504687i	0.974137	−	0.225960i	$-0.0725518\pi$
$229$	66.7264	+	115.573i	0.291381	+	0.504687i	−0.682755	+	0.730647i	$0.739218\pi$
$230$	99.1452	+	218.618i	0.431066	+	0.950514i
$231$		0			0
$232$	205.314	+	218.758i	0.884973	+	0.942924i
$233$	368.345			1.58088			0.790441	−	0.612539i	$-0.209852\pi$
$233$	368.345			1.58088			0.790441	+	0.612539i	$0.209852\pi$
$234$		0			0
$235$		−	68.2876i		−	0.290586i
$236$	−67.4430	−	59.0639i	−0.285775	−	0.250271i
$237$		0			0
$238$	8.16815	+	18.0110i	0.0343200	+	0.0756765i
$239$	249.901	−	144.280i	1.04561	−	0.603683i	0.124192	−	0.992258i	$-0.460366\pi$
$239$	249.901	−	144.280i	1.04561	−	0.603683i	0.921417	+	0.388576i	$0.127033\pi$
$240$		0			0
$241$	51.4937	−	89.1897i	0.213667	−	0.370082i	−0.739193	−	0.673494i	$-0.764793\pi$
$241$	51.4937	−	89.1897i	0.213667	−	0.370082i	0.952859	+	0.303412i	$0.0981260\pi$
$242$	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
$248$	98.5160	+	420.549i	0.397242	+	1.69576i
$249$		0			0
$250$	28.1228	+	20.1379i	0.112491	+	0.0805516i
$251$		−	69.9866i		−	0.278831i	−0.990234	−	0.139416i	$-0.955478\pi$
$251$		−	69.9866i		−	0.278831i	0.990234	−	0.139416i	$-0.0445224\pi$
$252$		0			0
$253$	−297.699			−1.17668
$254$	−183.350	+	256.050i	−0.721849	+	1.00807i
$255$		0			0
$256$	65.5770	−	247.458i	0.256160	−	0.966634i
$257$	48.5410	+	84.0754i	0.188875	+	0.327142i	0.944876	−	0.327430i	$-0.106182\pi$
$257$	48.5410	+	84.0754i	0.188875	+	0.327142i	−0.756000	+	0.654571i	$0.772849\pi$
$258$		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	0.486098	−	0.873904i	$-0.338420\pi$
$263$	−7.27870	−	4.20236i	−0.0276757	−	0.0159785i	−0.513774	+	0.857926i	$0.671753\pi$
$264$		0			0
$265$	28.3247	+	49.0599i	0.106886	+	0.185132i
$266$	−174.124	+	78.9667i	−0.654601	+	0.296867i
$267$		0			0
$268$	−208.247	−	182.374i	−0.777041	−	0.680501i
$269$	−281.198			−1.04535			−0.522673	−	0.852533i	$-0.675065\pi$
$269$	−281.198			−1.04535			−0.522673	+	0.852533i	$0.675065\pi$
$270$		0			0
$271$		−	369.456i		−	1.36331i	−0.731675	−	0.681654i	$-0.761261\pi$
$271$		−	369.456i		−	1.36331i	0.731675	−	0.681654i	$-0.238739\pi$
$272$	−18.2241	+	14.0237i	−0.0670003	+	0.0515577i
$273$		0			0
$274$	−214.015	+	97.0575i	−0.781075	+	0.354224i
$275$	−425.836	+	245.856i	−1.54849	+	0.894023i
$276$		0			0
$277$	−66.4546	+	115.103i	−0.239908	+	0.415533i	−0.960688	−	0.277631i	$-0.910451\pi$
$277$	−66.4546	+	115.103i	−0.239908	+	0.415533i	0.720779	+	0.693164i	$0.243784\pi$
$278$	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	$-0.812183\pi$
$281$	18.6577	−	32.3160i	0.0663974	−	0.115004i	0.897313	+	0.441395i	$0.145516\pi$
$282$		0			0
$283$	135.246	−	78.0842i	0.477900	−	0.275916i	−0.241641	−	0.970366i	$-0.577686\pi$
$283$	135.246	−	78.0842i	0.477900	−	0.275916i	0.719541	+	0.694450i	$0.244352\pi$
$284$	27.0680	−	9.20912i	0.0953098	−	0.0324265i
$285$		0			0
$286$	−160.444	+	224.061i	−0.560991	+	0.783431i
$287$		−	392.113i		−	1.36625i
$288$		0			0
$289$	−286.934			−0.992853
$290$	441.388	+	316.064i	1.52203	+	1.08988i
$291$		0			0
$292$	−103.637	−	304.617i	−0.354922	−	1.04321i
$293$	12.9881	+	22.4961i	0.0443280	+	0.0767784i	0.887338	−	0.461119i	$-0.152552\pi$
$293$	12.9881	+	22.4961i	0.0443280	+	0.0767784i	−0.843010	+	0.537898i	$0.819219\pi$
$294$		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
$302$	−132.267	−	291.653i	−0.437971	−	0.965740i
$303$		0			0
$304$	−135.576	−	176.184i	−0.445974	−	0.579551i
$305$	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	$-0.0582158\pi$
$308$	325.511	−	371.689i	1.05685	−	1.20678i
$309$		0			0
$310$	322.813	+	711.812i	1.04133	+	2.29617i
$311$	280.368	−	161.871i	0.901506	−	0.520485i	0.0238176	−	0.999716i	$-0.492418\pi$
$311$	280.368	−	161.871i	0.901506	−	0.520485i	0.877689	+	0.479232i	$0.159085\pi$
$312$		0			0
$313$	183.090	−	317.122i	0.584953	−	1.01317i	−0.409928	−	0.912118i	$-0.634446\pi$
$313$	183.090	−	317.122i	0.584953	−	1.01317i	0.994881	−	0.101050i	$-0.0322203\pi$
$314$	−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	$-0.800640\pi$
$317$	32.5014	−	56.2941i	0.102528	−	0.177584i	0.912726	+	0.408573i	$0.133973\pi$
$318$		0			0
$319$	−583.059	+	336.629i	−1.82777	+	1.05526i
$320$	29.3430	−	462.305i	0.0916968	−	1.44470i
$321$		0			0
$322$	−185.523	−	132.848i	−0.576160	−	0.412570i
$323$			19.9690i			0.0618235i
$324$		0			0
$325$	210.221			0.646833
$326$	−171.358	+	239.303i	−0.525638	+	0.734060i
$327$		0			0
$328$	443.912	−	103.989i	1.35339	−	0.317039i
$329$	32.4560	+	56.2154i	0.0986504	+	0.170867i
$330$		0			0
$331$	380.566	+	219.720i	1.14975	+	0.663807i	0.948826	−	0.315800i	$-0.102273\pi$
$331$	380.566	+	219.720i	1.14975	+	0.663807i	0.200922	+	0.979607i	$0.435606\pi$
$332$	−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	0.997816	+	0.0660503i	$0.0210398\pi$
$337$	187.409	+	324.602i	0.556109	+	0.963210i	−0.441707	+	0.897159i	$0.645627\pi$
$338$	−200.524	+	90.9392i	−0.593265	+	0.269051i
$339$		0			0
$340$	−27.4140	+	31.3031i	−0.0806294	+	0.0920679i
$341$	−969.295			−2.84251
$342$		0			0
$343$			348.568i			1.01623i
$344$	394.436	−	370.195i	1.14662	−	1.07615i
$345$		0			0
$346$	339.560	−	153.994i	0.981388	−	0.445068i
$347$	−284.948	+	164.515i	−0.821177	+	0.474107i	−0.850822	−	0.525454i	$-0.823896\pi$
$347$	−284.948	+	164.515i	−0.821177	+	0.474107i	0.0296454	+	0.999560i	$0.490562\pi$
$348$		0			0
$349$	−186.253	+	322.599i	−0.533676	+	0.924354i	0.465550	+	0.885021i	$0.345856\pi$
$349$	−186.253	+	322.599i	−0.533676	+	0.924354i	−0.999226	+	0.0393323i	$0.987477\pi$
$350$	−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	$-0.733527\pi$
$353$	108.879	−	188.584i	0.308440	−	0.534233i	0.978021	+	0.208505i	$0.0668599\pi$
$354$		0			0
$355$	44.8056	−	25.8685i	0.126213	−	0.0728691i
$356$	−54.2502	−	159.455i	−0.152388	−	0.447908i
$357$		0			0
$358$	223.095	−	311.554i	0.623169	−	0.870264i
$359$		−	145.576i		−	0.405505i	−0.979230	−	0.202753i	$-0.935011\pi$
$359$		−	145.576i		−	0.405505i	0.979230	−	0.202753i	$-0.0649887\pi$
$360$		0			0
$361$	167.947			0.465228
$362$	−333.284	−	238.654i	−0.920673	−	0.659266i
$363$		0			0
$364$	−199.974	+	68.0355i	−0.549379	+	0.186911i
$365$	−291.118	−	504.231i	−0.797583	−	1.38146i
$366$		0			0
$367$	−46.3123	−	26.7384i	−0.126192	−	0.0728568i	0.435575	−	0.900152i	$-0.356545\pi$
$367$	−46.3123	−	26.7384i	−0.126192	−	0.0728568i	−0.561767	+	0.827295i	$0.689878\pi$
$368$	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	0.998843	−	0.0480829i	$-0.0153112\pi$
$373$	170.752	+	295.751i	0.457781	+	0.792899i	−0.541063	+	0.840982i	$0.681978\pi$
$374$	−21.3132	−	46.9962i	−0.0569871	−	0.125658i
$375$		0			0
$376$	−55.0341	+	51.6518i	−0.146367	+	0.137372i
$377$	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	$0.906183\pi$
$380$	−302.626	−	265.028i	−0.796385	−	0.697443i
$381$		0			0
$382$	−74.1913	−	163.594i	−0.194218	−	0.428256i
$383$	−581.167	+	335.537i	−1.51741	+	0.876075i	−0.517616	+	0.855613i	$0.673180\pi$
$383$	−581.167	+	335.537i	−1.51741	+	0.876075i	−0.999791	+	0.0204616i	$0.993486\pi$
$384$		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	−0.365572	−	0.930783i	$-0.619127\pi$
$389$	242.462	−	419.957i	0.623296	−	1.07958i	0.988868	−	0.148797i	$-0.0475401\pi$
$390$		0			0
$391$	−20.6394	+	11.9162i	−0.0527862	+	0.0304761i
$392$	−12.9465	+	3.03279i	−0.0330268	+	0.00773670i
$393$		0			0
$394$	301.278	+	215.736i	0.764664	+	0.547553i
$395$		−	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	$0.614449\pi$
$398$	−160.251	+	223.792i	−0.402640	+	0.562291i
$399$		0			0
$400$	−57.7983	−	434.402i	−0.144496	−	1.08601i
$401$	−291.099	−	504.199i	−0.725934	−	1.25735i	−0.958589	−	0.284795i	$-0.908075\pi$
$401$	−291.099	−	504.199i	−0.725934	−	1.25735i	0.232655	−	0.972559i	$-0.425259\pi$
$402$		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	0.999220	+	0.0394972i	$0.0125756\pi$
$409$	218.330	+	378.160i	0.533815	+	0.924595i	−0.465404	+	0.885098i	$0.654091\pi$
$410$	751.354	−	340.746i	1.83257	−	0.831087i
$411$		0			0
$412$	161.665	+	141.580i	0.392391	+	0.343641i
$413$	154.203			0.373374
$414$		0			0
$415$			1029.24i			2.48010i
$416$	−130.056	−	208.348i	−0.312635	−	0.500836i
$417$		0			0
$418$	454.341	−	206.048i	1.08694	−	0.492937i
$419$	656.682	−	379.135i	1.56726	−	0.904858i	0.570773	−	0.821108i	$-0.306644\pi$
$419$	656.682	−	379.135i	1.56726	−	0.904858i	0.996487	−	0.0837495i	$-0.0266896\pi$
$420$		0			0
$421$	−261.674	+	453.232i	−0.621553	+	1.07656i	0.367644	+	0.929967i	$0.380165\pi$
$421$	−261.674	+	453.232i	−0.621553	+	1.07656i	−0.989197	+	0.146595i	$0.953169\pi$
$422$	−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
$428$	−100.240	+	34.1040i	−0.234207	+	0.0796822i
$429$		0			0
$430$	569.886	−	795.853i	1.32532	−	1.85082i
$431$			729.146i			1.69176i	0.533377	+	0.845878i	$0.320923\pi$
$431$			729.146i			1.69176i	−0.533377	+	0.845878i	$0.679077\pi$
$432$		0			0
$433$	−491.219			−1.13445			−0.567227	−	0.823561i	$-0.691984\pi$
$433$	−491.219			−1.13445			−0.567227	+	0.823561i	$0.691984\pi$
$434$	−604.057	−	432.546i	−1.39184	−	0.996651i
$435$		0			0
$436$	107.017	+	314.552i	0.245453	+	0.721450i
$437$	−115.201	−	199.534i	−0.263618	−	0.456600i
$438$		0			0
$439$	−163.413	−	94.3467i	−0.372240	−	0.214913i	0.302197	−	0.953246i	$-0.402280\pi$
$439$	−163.413	−	94.3467i	−0.372240	−	0.214913i	−0.674436	+	0.738333i	$0.735613\pi$
$440$	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	0.846186	−	0.532888i	$-0.178893\pi$
$443$	357.848	+	206.604i	0.807784	+	0.466375i	−0.0384015	+	0.999262i	$0.512227\pi$
$444$		0			0
$445$	−152.389	−	263.946i	−0.342448	−	0.593137i
$446$	14.2264	+	31.3696i	0.0318977	+	0.0703353i
$447$		0			0
$448$	195.570	+	394.523i	0.436541	+	0.880631i
$449$	638.253			1.42150			0.710749	−	0.703446i	$-0.248356\pi$
$449$	638.253			1.42150			0.710749	+	0.703446i	$0.248356\pi$
$450$		0			0
$451$			1023.14i			2.26861i
$452$	40.9202	−	46.7254i	0.0905314	−	0.103375i
$453$		0			0
$454$	−33.8549	−	74.6511i	−0.0745704	−	0.164430i
$455$	−331.017	+	191.112i	−0.727509	+	0.420027i
$456$		0			0
$457$	115.344	−	199.781i	0.252393	−	0.437157i	−0.711791	−	0.702391i	$-0.752116\pi$
$457$	115.344	−	199.781i	0.252393	−	0.437157i	0.964184	+	0.265234i	$0.0854492\pi$
$458$	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	$-0.976247\pi$
$461$	−200.094	+	346.573i	−0.434044	+	0.751786i	0.563173	+	0.826339i	$0.309580\pi$
$462$		0			0
$463$	256.912	−	148.328i	0.554886	−	0.320363i	−0.196205	−	0.980563i	$-0.562862\pi$
$463$	256.912	−	148.328i	0.554886	−	0.320363i	0.751090	+	0.660200i	$0.229528\pi$
$464$	−79.1381	−	594.788i	−0.170556	−	1.28187i
$465$		0			0
$466$	−598.964	−	428.900i	−1.28533	−	0.920386i
$467$		−	127.057i		−	0.272070i	−0.990704	−	0.136035i	$-0.956564\pi$
$467$		−	127.057i		−	0.272070i	0.990704	−	0.136035i	$-0.0434359\pi$
$468$		0			0
$469$	476.141			1.01523
$470$	−79.5138	+	111.042i	−0.169178	+	0.236260i
$471$		0			0
$472$	40.8949	+	174.574i	0.0866417	+	0.369860i
$473$	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	0.488826	−	0.872381i	$-0.337425\pi$
$479$	−10.6651	−	6.15749i	−0.0222653	−	0.0128549i	−0.511091	+	0.859526i	$0.670759\pi$
$480$		0			0
$481$	−170.550	−	295.401i	−0.354573	−	0.614139i
$482$	−187.586	+	85.0717i	−0.389182	+	0.176497i
$483$		0			0
$484$	−530.482	+	605.739i	−1.09604	+	1.25153i
$485$	−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	$-0.0595157\pi$
$488$	−367.802	−	391.887i	−0.753693	−	0.803047i
$489$		0			0
$490$	−21.9129	+	9.93770i	−0.0447202	+	0.0202810i
$491$	−430.484	+	248.540i	−0.876749	+	0.506191i	−0.869585	−	0.493783i	$-0.835614\pi$
$491$	−430.484	+	248.540i	−0.876749	+	0.506191i	−0.00716404	+	0.999974i	$0.502280\pi$
$492$		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	$-0.943481\pi$
$499$	−660.403	+	381.284i	−1.32345	+	0.764096i	−0.339175	+	0.940723i	$0.610148\pi$
$500$	−22.2819	−	65.4923i	−0.0445638	−	0.130985i
$501$		0			0
$502$	−81.4921	+	113.805i	−0.162335	+	0.226703i
$503$		−	994.596i		−	1.97733i	−0.150146	−	0.988664i	$-0.547974\pi$
$503$		−	994.596i		−	1.97733i	0.150146	−	0.988664i	$-0.452026\pi$
$504$		0			0
$505$	344.635			0.682446
$506$	484.086	+	346.639i	0.956692	+	0.685058i
$507$		0			0
$508$	596.287	−	202.870i	1.17379	−	0.399350i
$509$	26.8655	+	46.5325i	0.0527810	+	0.0914194i	0.891209	−	0.453593i	$-0.149858\pi$
$509$	26.8655	+	46.5325i	0.0527810	+	0.0914194i	−0.838428	+	0.545013i	$0.816525\pi$
$510$		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
$518$	252.577	+	556.940i	0.487601	+	1.07517i
$519$		0			0
$520$	−304.144	−	324.061i	−0.584893	−	0.623194i
$521$	−616.206			−1.18274			−0.591369	−	0.806401i	$-0.701412\pi$
$521$	−616.206			−1.18274			−0.591369	+	0.806401i	$0.701412\pi$
$522$		0			0
$523$		−	683.938i		−	1.30772i	−0.756615	−	0.653860i	$-0.773148\pi$
$523$		−	683.938i		−	1.30772i	0.756615	−	0.653860i	$-0.226852\pi$
$524$	141.609	+	124.016i	0.270247	+	0.236671i
$525$		0			0
$526$	6.94264	+	15.3087i	0.0131989	+	0.0291040i
$527$	−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
$536$	126.273	+	539.040i	0.235584	+	1.00567i
$537$		0			0
$538$	457.255	+	327.426i	0.849916	+	0.608599i
$539$		−	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	$0.341093\pi$
$542$	−430.193	+	600.771i	−0.793715	+	1.10843i
$543$		0			0
$544$	45.9632	−	1.58382i	0.0844912	−	0.00291143i
$545$	300.613	+	520.677i	0.551584	+	0.955371i
$546$		0			0
$547$	−254.839	−	147.131i	−0.465885	−	0.268979i	0.248631	−	0.968598i	$-0.420019\pi$
$547$	−254.839	−	147.131i	−0.465885	−	0.268979i	−0.714515	+	0.699620i	$0.753353\pi$
$548$	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
$554$	242.087	−	109.788i	0.436979	−	0.198174i
$555$		0			0
$556$	−119.452	−	104.611i	−0.214842	−	0.188150i
$557$	−395.706			−0.710424			−0.355212	−	0.934786i	$-0.615591\pi$
$557$	−395.706			−0.710424			−0.355212	+	0.934786i	$0.615591\pi$
$558$		0			0
$559$		−	518.989i		−	0.928424i
$560$	485.927	+	631.471i	0.867727	+	1.12763i
$561$		0			0
$562$	−67.9678	+	30.8240i	−0.120939	+	0.0548470i
$563$	224.519	−	129.626i	0.398791	−	0.230242i	−0.287171	−	0.957879i	$-0.592715\pi$
$563$	224.519	−	129.626i	0.398791	−	0.230242i	0.685962	+	0.727637i	$0.259382\pi$
$564$		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	$-0.903030\pi$
$569$	−123.594	+	214.071i	−0.217213	+	0.376224i	0.736742	+	0.676174i	$0.236363\pi$
$570$		0			0
$571$	−520.747	+	300.654i	−0.911992	+	0.526539i	−0.881072	−	0.472983i	$-0.843177\pi$
$571$	−520.747	+	300.654i	−0.911992	+	0.526539i	−0.0309205	+	0.999522i	$0.509844\pi$
$572$	521.792	−	177.525i	0.912225	−	0.310359i
$573$		0			0
$574$	−456.575	+	637.613i	−0.795427	+	1.11082i
$575$		−	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	$0.726886\pi$
$578$	466.582	+	334.105i	0.807236	+	0.578037i
$579$		0			0
$580$	−349.714	−	1027.90i	−0.602955	−	1.77224i
$581$	−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	0.309251	−	0.950980i	$-0.399922\pi$
$587$	−211.142	−	121.903i	−0.359696	−	0.207671i	−0.668948	+	0.743310i	$0.733255\pi$
$588$		0			0
$589$	−375.090	−	649.675i	−0.636825	−	1.10301i
$590$	134.002	+	295.479i	0.227123	+	0.500812i
$591$		0			0
$592$	−563.528	+	433.644i	−0.951906	+	0.732506i
$593$	1091.73			1.84103			0.920516	−	0.390704i	$-0.127768\pi$
$593$	1091.73			1.84103			0.920516	+	0.390704i	$0.127768\pi$
$594$		0			0
$595$		−	71.5722i		−	0.120289i
$596$	302.605	−	345.535i	0.507727	−	0.579756i
$597$		0			0
$598$	−105.134	−	231.823i	−0.175809	−	0.387665i
$599$	−814.688	+	470.361i	−1.36008	+	0.785243i	−0.989634	−	0.143611i	$-0.954129\pi$
$599$	−814.688	+	470.361i	−1.36008	+	0.785243i	−0.370447	+	0.928854i	$0.620795\pi$
$600$		0			0
$601$	−526.113	+	911.255i	−0.875396	+	1.51623i	−0.0190566	+	0.999818i	$0.506066\pi$
$601$	−526.113	+	911.255i	−0.875396	+	1.51623i	−0.856340	+	0.516413i	$0.827267\pi$
$602$	−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	$-0.548668\pi$
$607$	380.876	−	219.899i	0.627474	−	0.362272i	0.779773	+	0.626062i	$0.215334\pi$
$608$	15.3118	+	444.355i	0.0251838	+	0.730847i
$609$		0			0
$610$	−790.708	−	566.202i	−1.29624	−	0.928200i
$611$			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	$0.380406\pi$
$614$	−130.028	+	181.585i	−0.211771	+	0.295742i
$615$		0			0
$616$	−962.105	+	225.378i	−1.56186	+	0.365874i
$617$	424.268	+	734.854i	0.687630	+	1.19101i	0.972602	+	0.232475i	$0.0746823\pi$
$617$	424.268	+	734.854i	0.687630	+	1.19101i	−0.284972	+	0.958536i	$0.591984\pi$
$618$		0			0
$619$	−467.583	−	269.959i	−0.755384	−	0.436121i	0.0722522	−	0.997386i	$-0.476981\pi$
$619$	−467.583	−	269.959i	−0.755384	−	0.436121i	−0.827636	+	0.561265i	$0.810315\pi$
$620$	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
$626$	−666.977	+	302.480i	−1.06546	+	0.483195i
$627$		0			0
$628$	593.834	−	678.078i	0.945595	−	1.07974i
$629$	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	$0.989000\pi$
$632$	−273.253	+	256.459i	−0.432362	+	0.405789i
$633$		0			0
$634$	−118.399	+	53.6950i	−0.186749	+	0.0846924i
$635$	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	$-0.791685\pi$
$641$	83.6313	−	144.854i	0.130470	−	0.225981i	0.923858	+	0.382736i	$0.125018\pi$
$642$		0			0
$643$	645.855	−	372.885i	1.00444	−	0.579914i	0.0948816	−	0.995489i	$-0.469753\pi$
$643$	645.855	−	372.885i	1.00444	−	0.579914i	0.909559	+	0.415574i	$0.136419\pi$
$644$	146.991	+	432.045i	0.228247	+	0.670878i
$645$		0			0
$646$	23.2518	−	32.4714i	0.0359935	−	0.0502654i
$647$			596.836i			0.922467i	0.887279	+	0.461233i	$0.152593\pi$
$647$			596.836i			0.922467i	−0.887279	+	0.461233i	$0.847407\pi$
$648$		0			0
$649$	−402.363			−0.619974
$650$	−341.839	−	244.780i	−0.525906	−	0.376585i
$651$		0			0
$652$	557.288	−	189.601i	0.854736	−	0.290800i
$653$	395.435	+	684.914i	0.605567	+	1.04887i	0.991962	+	0.126540i	$0.0403871\pi$
$653$	395.435	+	684.914i	0.605567	+	1.04887i	−0.386394	+	0.922334i	$0.626280\pi$
$654$		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	0.211588	−	0.977359i	$-0.432137\pi$
$659$	−348.635	−	201.284i	−0.529036	−	0.305439i	−0.740624	+	0.671920i	$0.765470\pi$
$660$		0			0
$661$	−243.272	−	421.359i	−0.368036	−	0.637457i	0.621222	−	0.783634i	$-0.286636\pi$
$661$	−243.272	−	421.359i	−0.368036	−	0.637457i	−0.989258	+	0.146177i	$0.953303\pi$
$662$	−362.995	−	800.416i	−0.548332	−	1.20909i
$663$		0			0
$664$	829.483	−	778.504i	1.24922	−	1.17245i
$665$	691.933			1.04050
$666$		0			0
$667$		−	621.873i		−	0.932343i
$668$	318.804	+	279.196i	0.477252	+	0.417958i
$669$		0			0
$670$	413.766	+	912.366i	0.617561	+	1.36174i
$671$	1044.50	−	603.042i	1.55663	−	0.898721i
$672$		0			0
$673$	85.8636	−	148.720i	0.127583	−	0.220981i	−0.795156	−	0.606404i	$-0.792611\pi$
$673$	85.8636	−	148.720i	0.127583	−	0.220981i	0.922740	+	0.385423i	$0.125945\pi$
$674$	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	$-0.883639\pi$
$677$	−106.547	+	184.546i	−0.157382	+	0.272593i	0.776542	+	0.630065i	$0.216972\pi$
$678$		0			0
$679$	374.761	−	216.369i	0.551931	−	0.318658i
$680$	81.0269	−	18.9810i	0.119157	−	0.0279132i
$681$		0			0
$682$	1576.17	+	1128.64i	2.31109	+	1.65490i
$683$			602.265i			0.881794i	0.897558	+	0.440897i	$0.145340\pi$
$683$			602.265i			0.881794i	−0.897558	+	0.440897i	$0.854660\pi$
$684$		0			0
$685$	850.451			1.24153
$686$	405.871	−	566.805i	0.591649	−	0.826246i
$687$		0			0
$688$	−1072.44	+	142.691i	−1.55879	+	0.207400i
$689$	−30.0357	−	52.0233i	−0.0435931	−	0.0755055i
$690$		0			0
$691$	1062.89	+	613.657i	1.53818	+	0.888071i	0.998945	+	0.0459192i	$0.0146217\pi$
$691$	1062.89	+	613.657i	1.53818	+	0.888071i	0.539240	+	0.842152i	$0.318712\pi$
$692$	−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
$698$	678.498	−	307.705i	0.972060	−	0.440838i
$699$		0			0
$700$	567.067	+	496.615i	0.810096	+	0.709449i
$701$	−133.314			−0.190176			−0.0950882	−	0.995469i	$-0.530313\pi$
$701$	−133.314			−0.190176			−0.0950882	+	0.995469i	$0.530313\pi$
$702$		0			0
$703$			617.485i			0.878357i
$704$	−510.302	−	1029.43i	−0.724861	−	1.46226i
$705$		0			0
$706$	−396.635	+	179.877i	−0.561805	+	0.254784i
$707$	−283.709	+	163.799i	−0.401285	+	0.231682i
$708$		0			0
$709$	305.128	−	528.497i	0.430364	−	0.745412i	−0.566541	−	0.824034i	$-0.691719\pi$
$709$	305.128	−	528.497i	0.430364	−	0.745412i	0.996905	+	0.0786216i	$0.0250519\pi$
$710$	−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
$716$	−725.546	+	246.846i	−1.01333	+	0.344757i
$717$		0			0
$718$	−169.509	+	236.721i	−0.236084	+	0.329695i
$719$			967.279i			1.34531i	0.739956	+	0.672656i	$0.234846\pi$
$719$			967.279i			1.34531i	−0.739956	+	0.672656i	$0.765154\pi$
$720$		0			0
$721$	−369.635			−0.512671
$722$	−273.098	−	195.557i	−0.378252	−	0.270855i
$723$		0			0
$724$	264.063	+	776.149i	0.364727	+	1.07203i
$725$	−513.577	−	889.542i	−0.708382	−	1.22695i
$726$		0			0
$727$	−1209.48	−	698.296i	−1.66366	−	0.960517i	−0.970942	−	0.239313i	$-0.923078\pi$
$727$	−1209.48	−	698.296i	−1.66366	−	0.960517i	−0.692722	−	0.721204i	$-0.743589\pi$
$728$	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	0.951364	−	0.308068i	$-0.0996823\pi$
$733$	153.115	+	265.202i	0.208888	+	0.361804i	−0.742477	+	0.669872i	$0.766349\pi$
$734$	44.1741	+	97.4051i	0.0601827	+	0.132705i
$735$		0			0
$736$	−450.137	+	280.988i	−0.611599	+	0.381777i
$737$	−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	$-0.101463\pi$
$740$	−847.700	+	967.960i	−1.14554	+	1.30805i
$741$		0			0
$742$	44.4816	+	98.0831i	0.0599482	+	0.132188i
$743$	702.085	−	405.349i	0.944932	−	0.545557i	0.0534291	−	0.998572i	$-0.482985\pi$
$743$	702.085	−	405.349i	0.944932	−	0.545557i	0.891503	+	0.453015i	$0.149652\pi$
$744$		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	$-0.437334\pi$
$751$	858.169	−	495.464i	1.14270	−	0.659739i	0.947098	+	0.320944i	$0.104000\pi$
$752$	149.634	−	19.9091i	0.198981	−	0.0264749i
$753$		0			0
$754$	−468.049	−	335.156i	−0.620755	−	0.444504i
$755$			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	$0.567790\pi$
$758$	256.387	−	358.047i	0.338241	−	0.472358i
$759$		0			0
$760$	183.501	+	783.338i	0.241449	+	1.03071i
$761$	−317.988	−	550.771i	−0.417855	−	0.723746i	0.577868	−	0.816130i	$-0.303885\pi$
$761$	−317.988	−	550.771i	−0.417855	−	0.723746i	−0.995723	+	0.0923836i	$0.970551\pi$
$762$		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	0.749297	−	0.662234i	$-0.230392\pi$
$769$	−152.926	−	264.876i	−0.198864	−	0.344442i	−0.948160	+	0.317793i	$0.897058\pi$
$770$	−1628.44	+	738.510i	−2.11485	+	0.959103i
$771$		0			0
$772$	441.669	−	504.326i	0.572110	−	0.653272i
$773$	−187.263			−0.242255			−0.121128	−	0.992637i	$-0.538651\pi$
$773$	−187.263			−0.242255			−0.121128	+	0.992637i	$0.538651\pi$
$774$		0			0
$775$		−	1478.80i		−	1.90813i
$776$	344.338	+	366.886i	0.443735	+	0.472792i
$777$		0			0
$778$	−883.262	+	400.567i	−1.13530	+	0.514868i
$779$	−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	$-0.629071\pi$
$787$	160.626	−	92.7376i	0.204099	−	0.117837i	0.598566	+	0.801073i	$0.295737\pi$
$788$	−238.704	−	701.613i	−0.302924	−	0.890372i
$789$		0			0
$790$	−394.798	+	551.341i	−0.499745	+	0.697900i
$791$			106.834i			0.135062i
$792$		0			0
$793$	−515.634			−0.650232
$794$	454.287	+	325.301i	0.572150	+	0.409699i
$795$		0			0
$796$	521.165	−	177.312i	0.654730	−	0.222753i
$797$	−546.202	−	946.049i	−0.685322	−	1.18701i	−0.973336	−	0.229386i	$-0.926328\pi$
$797$	−546.202	−	946.049i	−0.685322	−	1.18701i	0.288014	−	0.957626i	$-0.407005\pi$
$798$		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
$806$	−342.312	−	754.808i	−0.424705	−	0.936486i
$807$		0			0
$808$	−260.677	−	277.747i	−0.322620	−	0.343746i
$809$	51.1143			0.0631821			0.0315911	−	0.999501i	$-0.489943\pi$
$809$	51.1143			0.0631821			0.0315911	+	0.999501i	$0.489943\pi$
$810$		0			0
$811$			680.159i			0.838667i	0.907832	+	0.419333i	$0.137736\pi$
$811$			680.159i			0.838667i	−0.907832	+	0.419333i	$0.862264\pi$
$812$	776.434	+	679.970i	0.956199	+	0.837401i
$813$		0			0
$814$	−659.050	−	1453.22i	−0.809643	−	1.78529i
$815$	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	$-0.857446\pi$
$821$	−62.1337	+	107.619i	−0.0756805	+	0.131082i	0.825702	+	0.564107i	$0.190780\pi$
$822$		0			0
$823$	−959.409	+	553.915i	−1.16575	+	0.673044i	−0.952674	−	0.303992i	$-0.901680\pi$
$823$	−959.409	+	553.915i	−1.16575	+	0.673044i	−0.213072	+	0.977036i	$0.568347\pi$
$824$	−98.0276	−	418.464i	−0.118966	−	0.507845i
$825$		0			0
$826$	−250.749	−	179.554i	−0.303570	−	0.217378i
$827$		−	856.831i		−	1.03607i	−0.855359	−	0.518036i	$-0.826663\pi$
$827$		−	856.831i		−	1.03607i	0.855359	−	0.518036i	$-0.173337\pi$
$828$		0			0
$829$	−59.5071			−0.0717818			−0.0358909	−	0.999356i	$-0.511427\pi$
$829$	−59.5071			−0.0717818			−0.0358909	+	0.999356i	$0.511427\pi$
$830$	1198.45	−	1673.64i	1.44391	−	2.01644i
$831$		0			0
$832$	−31.1154	+	490.230i	−0.0373983	+	0.589219i
$833$	−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	0.240615	−	0.970621i	$-0.422651\pi$
$839$	−402.435	−	232.346i	−0.479660	−	0.276932i	−0.720275	+	0.693689i	$0.755984\pi$
$840$		0			0
$841$	−282.695	−	489.643i	−0.336142	−	0.582215i
$842$	953.248	−	432.306i	1.13212	−	0.513428i
$843$		0			0
$844$	918.561	+	804.439i	1.08834	+	0.953127i
$845$	796.840			0.943006
$846$		0			0
$847$		−	1384.98i		−	1.63516i
$848$	−99.2434	+	76.3693i	−0.117032	+	0.0900582i
$849$		0			0
$850$	71.6996	−	32.5164i	0.0843524	−	0.0382546i
$851$	−638.216	+	368.474i	−0.749960	+	0.432990i
$852$		0			0
$853$	683.164	−	1183.28i	0.800896	−	1.38719i	−0.118131	−	0.992998i	$-0.537690\pi$
$853$	683.164	−	1183.28i	0.800896	−	1.38719i	0.919027	−	0.394195i	$-0.128977\pi$
$854$	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	−0.311846	+	0.950133i	$0.600947\pi$
$857$	−838.799	+	1452.84i	−0.978762	+	1.69527i	−0.666916	+	0.745133i	$0.732386\pi$
$858$		0			0
$859$	1424.63	−	822.513i	1.65848	−	0.957524i	0.685063	−	0.728484i	$-0.259775\pi$
$859$	1424.63	−	822.513i	1.65848	−	0.957524i	0.973417	−	0.229039i	$-0.0735585\pi$
$860$	−1853.38	+	630.558i	−2.15509	+	0.733207i
$861$		0			0
$862$	849.015	−	1185.66i	0.984937	−	1.37548i
$863$		−	294.311i		−	0.341033i	−0.985355	−	0.170516i	$-0.945456\pi$
$863$		−	294.311i		−	0.341033i	0.985355	−	0.170516i	$-0.0545436\pi$
$864$		0			0
$865$	−1349.34			−1.55994
$866$	798.768	+	571.973i	0.922365	+	0.660477i
$867$		0			0
$868$	478.597	+	1406.72i	0.551380	+	1.62065i
$869$	−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	0.584875	−	0.811124i	$-0.301144\pi$
$877$	−359.584	−	622.818i	−0.410016	−	0.710169i	−0.994891	+	0.100954i	$0.967810\pi$
$878$	155.868	+	343.694i	0.177527	+	0.391451i
$879$		0			0
$880$	−1267.93	−	1647.70i	−1.44083	−	1.87238i
$881$	16.3083			0.0185112			0.00925559	−	0.999957i	$-0.497054\pi$
$881$	16.3083			0.0185112			0.00925559	+	0.999957i	$0.497054\pi$
$882$		0			0
$883$		−	1190.35i		−	1.34807i	−0.738698	−	0.674036i	$-0.764559\pi$
$883$		−	1190.35i		−	1.34807i	0.738698	−	0.674036i	$-0.235441\pi$
$884$	29.0699	−	33.1939i	0.0328845	−	0.0375496i
$885$		0			0
$886$	−341.326	−	752.635i	−0.385244	−	0.849475i
$887$	−346.987	+	200.333i	−0.391192	+	0.225855i	−0.682676	−	0.730721i	$-0.739184\pi$
$887$	−346.987	+	200.333i	−0.391192	+	0.225855i	0.291485	+	0.956575i	$0.405851\pi$
$888$		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
$896$	141.365	−	869.252i	0.157773	−	0.970148i
$897$		0			0
$898$	−1037.86	−	743.179i	−1.15574	−	0.827593i
$899$		−	2024.79i		−	2.25227i
$900$		0			0
$901$	11.2484			0.0124844
$902$	1191.34	−	1663.72i	1.32078	−	1.84448i
$903$		0			0
$904$	−120.947	+	28.3325i	−0.133791	+	0.0313413i
$905$	741.755	+	1284.76i	0.819618	+	1.41962i
$906$		0			0
$907$	−1091.40	−	630.121i	−1.20331	−	0.694731i	−0.242019	−	0.970271i	$-0.577810\pi$
$907$	−1091.40	−	630.121i	−1.20331	−	0.694731i	−0.961289	+	0.275541i	$0.911143\pi$
$908$	−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	−0.0341788	−	0.999416i	$-0.510882\pi$
$911$	−835.193	−	482.199i	−0.916788	−	0.529308i	−0.882609	+	0.470108i	$0.844215\pi$
$912$		0			0
$913$	1276.42	+	2210.83i	1.39805	+	2.42150i
$914$	−420.183	+	190.557i	−0.459719	+	0.208487i
$915$		0			0
$916$	−351.690	+	401.582i	−0.383941	+	0.438409i
$917$	−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	$-0.0741691\pi$
$920$	−700.136	+	657.106i	−0.761017	+	0.714246i
$921$		0			0
$922$	728.921	−	330.572i	0.790586	−	0.358538i
$923$	−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	$-0.680453\pi$
$929$	429.229	−	743.447i	0.462033	−	0.800265i	0.999062	+	0.0432985i	$0.0137867\pi$
$930$		0			0
$931$	20.0001	−	11.5470i	0.0214823	−	0.0124028i
$932$	474.563	+	1394.86i	0.509187	+	1.49663i
$933$		0			0
$934$	−147.944	+	206.606i	−0.158398	+	0.221205i
$935$			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	$0.348572\pi$
$938$	−774.250	−	554.417i	−0.825427	−	0.591063i
$939$		0			0
$940$	258.594	−	87.9793i	0.275100	−	0.0935950i
$941$	468.553	+	811.558i	0.497931	+	0.862442i	0.999997	−	0.00238755i	$-0.000759981\pi$
$941$	468.553	+	811.558i	0.497931	+	0.862442i	−0.502066	+	0.864829i	$0.667427\pi$
$942$		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	0.847408	−	0.530943i	$-0.178162\pi$
$947$	768.302	+	443.580i	0.811301	+	0.468405i	−0.0361062	+	0.999348i	$0.511495\pi$
$948$		0			0
$949$	308.702	+	534.688i	0.325292	+	0.563423i
$950$	314.356	+	693.165i	0.330901	+	0.729647i
$951$		0			0
$952$	−57.6812	+	54.1362i	−0.0605895	+	0.0568657i
$953$	1078.46			1.13164			0.565821	−	0.824528i	$-0.308559\pi$
$953$	1078.46			1.13164			0.565821	+	0.824528i	$0.308559\pi$
$954$		0			0
$955$			650.090i			0.680722i
$956$	868.328	+	760.447i	0.908293	+	0.795447i
$957$		0			0
$958$	10.1727	+	22.4311i	0.0106187	+	0.0234145i
$959$	−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	$-0.686275\pi$
$967$	−103.113	+	59.5324i	−0.106632	+	0.0615640i	0.445736	+	0.895165i	$0.352942\pi$
$968$	1567.93	−	367.297i	1.61977	−	0.379439i
$969$		0			0
$970$	740.265	+	530.081i	0.763160	+	0.546475i
$971$			1516.56i			1.56185i	0.624624	+	0.780926i	$0.285252\pi$
$971$			1516.56i			1.56185i	−0.624624	+	0.780926i	$0.714748\pi$
$972$		0			0
$973$	273.118			0.280697
$974$	−210.818	+	294.410i	−0.216446	+	0.302269i
$975$		0			0
$976$	141.769	+	1065.51i	0.145255	+	1.09171i
$977$	−789.151	−	1366.85i	−0.807729	−	1.39903i	−0.914434	−	0.404736i	$-0.867363\pi$
$977$	−789.151	−	1366.85i	−0.807729	−	1.39903i	0.106705	−	0.994291i	$-0.465970\pi$
$978$		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	0.737837	−	0.674979i	$-0.235847\pi$
$983$	513.330	+	296.371i	0.522207	+	0.301497i	−0.215630	+	0.976475i	$0.569180\pi$
$984$		0			0
$985$	−670.522	−	1161.38i	−0.680733	−	1.17906i
$986$	98.1718	−	44.5218i	0.0995657	−	0.0451539i
$987$		0			0
$988$	320.906	+	281.037i	0.324804	+	0.284450i
$989$	−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	$0.594020\pi$
$992$	−1465.63	+	914.884i	−1.47745	+	0.922262i
$993$		0			0
$994$	89.5777	−	40.6243i	0.0901184	−	0.0408695i
$995$	862.683	−	498.070i	0.867018	−	0.500573i
$996$		0			0
$997$	−34.8563	+	60.3729i	−0.0349612	+	0.0605546i	−0.882977	−	0.469417i	$-0.844464\pi$
$997$	−34.8563	+	60.3729i	−0.0349612	+	0.0605546i	0.848015	+	0.529972i	$0.177797\pi$
$998$	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.r.55.2		12
3.2	odd	2		324.3.f.q.55.5		12
4.3	odd	2	inner	324.3.f.r.55.6		12
9.2	odd	6		324.3.d.f.163.3	yes	6
9.4	even	3	inner	324.3.f.r.271.6		12
9.5	odd	6		324.3.f.q.271.1		12
9.7	even	3		324.3.d.e.163.4	yes	6
12.11	even	2		324.3.f.q.55.1		12
36.7	odd	6		324.3.d.e.163.3	✓	6
36.11	even	6		324.3.d.f.163.4	yes	6
36.23	even	6		324.3.f.q.271.5		12
36.31	odd	6	inner	324.3.f.r.271.2		12

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

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)

\(f(q)\)	\(=\)	\(q+(-1.62609 - 1.16440i) q^{2} +(1.28836 + 3.78684i) q^{4} +(3.61903 + 6.26834i) q^{5} +(-5.95847 - 3.44013i) q^{7} +(2.31438 - 7.65792i) q^{8} +O(q^{10})\)	\(q+(-1.62609 - 1.16440i) q^{2} +(1.28836 + 3.78684i) q^{4} +(3.61903 + 6.26834i) q^{5} +(-5.95847 - 3.44013i) q^{7} +(2.31438 - 7.65792i) q^{8} +(1.41395 - 14.4069i) q^{10} +(15.5474 + 8.97632i) q^{11} +(-3.83763 - 6.64697i) q^{13} +(5.68337 + 12.5320i) q^{14} +(-12.6802 + 9.75764i) q^{16} +1.43720 q^{17} +13.8943i q^{19} +(-19.0745 + 21.7806i) q^{20} +(-14.8296 - 32.6997i) q^{22} +(-14.3608 + 8.29122i) q^{23} +(-13.6947 + 23.7199i) q^{25} +(-1.49936 + 15.2771i) q^{26} +(5.35051 - 26.9959i) q^{28} +(-18.7509 + 32.4776i) q^{29} +(-46.7583 + 26.9959i) q^{31} +(31.9810 - 1.10202i) q^{32} +(-2.33703 - 1.67347i) q^{34} -49.7996i q^{35} +44.4415 q^{37} +(16.1785 - 22.5935i) q^{38} +(56.3782 - 13.2069i) q^{40} +(28.4956 + 49.3558i) q^{41} +(58.5593 + 33.8092i) q^{43} +(-13.9611 + 70.4404i) q^{44} +(33.0063 + 3.23938i) q^{46} +(-8.17054 - 4.71726i) q^{47} +(-0.831061 - 1.43944i) q^{49} +(49.8883 - 22.6248i) q^{50} +(20.2267 - 23.0962i) q^{52} +7.82662 q^{53} +129.942i q^{55} +(-40.1343 + 37.6677i) q^{56} +(68.3076 - 30.9781i) q^{58} +(-19.4098 + 11.2062i) q^{59} +(33.5907 - 58.1808i) q^{61} +(107.467 + 10.5473i) q^{62} +(-53.2873 - 35.4466i) q^{64} +(27.7770 - 48.1111i) q^{65} +(-59.9324 + 34.6020i) q^{67} +(1.85164 + 5.44245i) q^{68} +(-57.9865 + 80.9789i) q^{70} -7.14792i q^{71} -80.4410 q^{73} +(-72.2660 - 51.7475i) q^{74} +(-52.6156 + 17.9010i) q^{76} +(-61.7594 - 106.970i) q^{77} +(-40.5680 - 23.4219i) q^{79} +(-107.054 - 44.1709i) q^{80} +(11.1332 - 113.437i) q^{82} +(123.148 + 71.0994i) q^{83} +(5.20128 + 9.00887i) q^{85} +(-55.8556 - 123.163i) q^{86} +(104.723 - 98.2865i) q^{88} -42.1078 q^{89} +52.8077i q^{91} +(-49.8995 - 43.7000i) q^{92} +(7.79330 + 17.1845i) q^{94} +(-87.0944 + 50.2840i) q^{95} +(-31.4478 + 54.4691i) q^{97} +(-0.324695 + 3.30835i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8}+O(q^{10}) \) 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8	\( 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8} + 18 q^{10} - 6 q^{13} + 15 q^{16} + 20 q^{17} - 67 q^{20} - 48 q^{22} + 146 q^{26} - 96 q^{28} - 22 q^{29} + 31 q^{32} - 81 q^{34} + 108 q^{37} + 168 q^{38} + 81 q^{40} + 92 q^{41} - 336 q^{44} + 240 q^{46} + 66 q^{49} - 48 q^{50} + 117 q^{52} - 232 q^{53} - 312 q^{56} - 201 q^{58} - 54 q^{61} + 624 q^{62} - 510 q^{64} + 82 q^{65} + 53 q^{68} - 264 q^{70} - 156 q^{73} + 383 q^{74} + 192 q^{76} - 168 q^{77} - 754 q^{80} + 300 q^{82} - 66 q^{85} - 144 q^{86} + 336 q^{88} + 500 q^{89} - 504 q^{92} - 216 q^{94} + 204 q^{97} + 814 q^{98}+O(q^{100}) \) 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

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