LMFDB - Embedded newform 387.3.bn.b.91.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,3,Mod(19,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("387.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	387.bn (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.5449862307$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{42})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			91.6
Character	$\chi$	$=$	387.91
Dual form			387.3.bn.b.370.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.19097 + 0.728319i) q^{2} +(6.04798 + 2.91256i) q^{4} +(-2.28850 + 0.898170i) q^{5} +(10.0706 - 5.81424i) q^{7} +(6.94183 + 5.53593i) q^{8} +O(q^{10})$	\(q+(3.19097 + 0.728319i) q^{2} +(6.04798 + 2.91256i) q^{4} +(-2.28850 + 0.898170i) q^{5} +(10.0706 - 5.81424i) q^{7} +(6.94183 + 5.53593i) q^{8} +(-7.95670 + 1.19928i) q^{10} +(8.52330 - 4.10460i) q^{11} +(3.56642 + 0.537551i) q^{13} +(36.3695 - 11.2185i) q^{14} +(1.37795 + 1.72789i) q^{16} +(-2.56415 + 6.53334i) q^{17} +(10.4891 + 15.3847i) q^{19} +(-16.4568 - 1.23327i) q^{20} +(30.1871 - 6.89000i) q^{22} +(-2.94151 + 39.2518i) q^{23} +(-13.8958 + 12.8934i) q^{25} +(10.9888 + 4.31280i) q^{26} +(77.8409 - 5.83337i) q^{28} +(-4.30310 - 13.9503i) q^{29} +(-32.3496 - 30.0160i) q^{31} +(-12.2712 - 25.4814i) q^{32} +(-12.9405 + 18.9802i) q^{34} +(-17.8243 + 22.3510i) q^{35} +(12.4503 + 7.18816i) q^{37} +(22.2656 + 56.7317i) q^{38} +(-20.8586 - 6.43402i) q^{40} +(16.7860 - 73.5444i) q^{41} +(-42.9996 + 0.190850i) q^{43} +63.5036 q^{44} +(-37.9741 + 123.109i) q^{46} +(52.2411 + 25.1580i) q^{47} +(43.1108 - 74.6700i) q^{49} +(-53.7315 + 31.0219i) q^{50} +(20.0040 + 13.6385i) q^{52} +(-56.3433 + 8.49238i) q^{53} +(-15.8189 + 17.0488i) q^{55} +(102.095 + 15.3884i) q^{56} +(-3.57080 - 47.6490i) q^{58} +(-10.8959 - 13.6630i) q^{59} +(-44.6438 - 48.1146i) q^{61} +(-81.3654 - 119.341i) q^{62} +(-22.5656 - 98.8662i) q^{64} +(-8.64456 + 1.97307i) q^{65} +(-69.2334 + 47.2025i) q^{67} +(-34.5366 + 32.0453i) q^{68} +(-73.1555 + 58.3395i) q^{70} +(-19.1878 + 1.43792i) q^{71} +(0.841669 - 5.58411i) q^{73} +(34.4932 + 32.0050i) q^{74} +(18.6292 + 123.597i) q^{76} +(61.9692 - 90.8921i) q^{77} +(-24.3421 - 42.1618i) q^{79} +(-4.70538 - 2.71665i) q^{80} +(107.127 - 222.453i) q^{82} +(51.4908 + 15.8828i) q^{83} -17.2546i q^{85} +(-137.349 - 30.7084i) q^{86} +(81.8901 + 18.6909i) q^{88} +(-22.0490 + 71.4811i) q^{89} +(39.0413 - 15.3226i) q^{91} +(-132.113 + 228.827i) q^{92} +(148.377 + 118.327i) q^{94} +(-37.8225 - 25.7869i) q^{95} +(13.1648 - 6.33982i) q^{97} +(191.949 - 206.872i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 14 q^{2} + 12 q^{4} + 11 q^{5} - 30 q^{7} + 42 q^{8}+O(q^{10}) $ 72 * q + 14 * q^2 + 12 * q^4 + 11 * q^5 - 30 * q^7 + 42 * q^8	$ 72 q + 14 q^{2} + 12 q^{4} + 11 q^{5} - 30 q^{7} + 42 q^{8} - 13 q^{10} + 42 q^{11} - 24 q^{13} + 108 q^{14} - 40 q^{16} + 7 q^{17} - 38 q^{19} + 55 q^{20} - 98 q^{22} - 30 q^{23} + 49 q^{25} + 79 q^{26} + 66 q^{28} - 27 q^{29} + 330 q^{31} - 56 q^{32} + 109 q^{34} + 31 q^{35} + 69 q^{37} - 262 q^{38} + 239 q^{40} + 94 q^{41} - 19 q^{43} + 64 q^{44} - 9 q^{46} + 66 q^{47} - 6 q^{49} + 495 q^{50} - 452 q^{52} - 16 q^{53} + 328 q^{55} + 1015 q^{56} - 420 q^{58} + 245 q^{59} - 50 q^{61} + 191 q^{62} - 306 q^{64} + 182 q^{65} + 599 q^{67} - 757 q^{68} - 287 q^{70} - 367 q^{71} + 486 q^{73} - 1656 q^{74} + 746 q^{76} - 79 q^{77} + 261 q^{79} - 138 q^{80} + 364 q^{82} + 220 q^{83} + 284 q^{86} - 490 q^{88} + 564 q^{89} - 145 q^{91} + 406 q^{92} - 1666 q^{94} + 353 q^{95} - 99 q^{97} + 500 q^{98}+O(q^{100}) $ 72 * q + 14 * q^2 + 12 * q^4 + 11 * q^5 - 30 * q^7 + 42 * q^8 - 13 * q^10 + 42 * q^11 - 24 * q^13 + 108 * q^14 - 40 * q^16 + 7 * q^17 - 38 * q^19 + 55 * q^20 - 98 * q^22 - 30 * q^23 + 49 * q^25 + 79 * q^26 + 66 * q^28 - 27 * q^29 + 330 * q^31 - 56 * q^32 + 109 * q^34 + 31 * q^35 + 69 * q^37 - 262 * q^38 + 239 * q^40 + 94 * q^41 - 19 * q^43 + 64 * q^44 - 9 * q^46 + 66 * q^47 - 6 * q^49 + 495 * q^50 - 452 * q^52 - 16 * q^53 + 328 * q^55 + 1015 * q^56 - 420 * q^58 + 245 * q^59 - 50 * q^61 + 191 * q^62 - 306 * q^64 + 182 * q^65 + 599 * q^67 - 757 * q^68 - 287 * q^70 - 367 * q^71 + 486 * q^73 - 1656 * q^74 + 746 * q^76 - 79 * q^77 + 261 * q^79 - 138 * q^80 + 364 * q^82 + 220 * q^83 + 284 * q^86 - 490 * q^88 + 564 * q^89 - 145 * q^91 + 406 * q^92 - 1666 * q^94 + 353 * q^95 - 99 * q^97 + 500 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{25}{42}\right)$	$1$

Coefficient data

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

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

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

$2$	3.19097	+	0.728319i	1.59549	+	0.364159i	0.925659	−	0.378358i	$-0.123511\pi$
$2$	3.19097	+	0.728319i	1.59549	+	0.364159i	0.669827	+	0.742517i	$0.266368\pi$
$3$		0			0
$3$		0			0
$4$	6.04798	+	2.91256i	1.51200	+	0.728139i
$5$	−2.28850	+	0.898170i	−0.457700	+	0.179634i	−0.582978	−	0.812488i	$-0.698113\pi$
$5$	−2.28850	+	0.898170i	−0.457700	+	0.179634i	0.125278	+	0.992122i	$0.460018\pi$
$6$		0			0
$7$	10.0706	−	5.81424i	1.43865	−	0.830606i	0.440895	−	0.897559i	$-0.354661\pi$
$7$	10.0706	−	5.81424i	1.43865	−	0.830606i	0.997756	+	0.0669531i	$0.0213278\pi$
$8$	6.94183	+	5.53593i	0.867729	+	0.691991i
$9$		0			0
$10$	−7.95670	+	1.19928i	−0.795670	+	0.119928i
$11$	8.52330	−	4.10460i	0.774845	−	0.373146i	−0.00429875	−	0.999991i	$-0.501368\pi$
$11$	8.52330	−	4.10460i	0.774845	−	0.373146i	0.779144	+	0.626845i	$0.215654\pi$
$12$		0			0
$13$	3.56642	+	0.537551i	0.274340	+	0.0413501i	0.284771	−	0.958595i	$-0.408082\pi$
$13$	3.56642	+	0.537551i	0.274340	+	0.0413501i	−0.0104313	+	0.999946i	$0.503320\pi$
$14$	36.3695	−	11.2185i	2.59782	−	0.801322i
$15$		0			0
$16$	1.37795	+	1.72789i	0.0861218	+	0.107993i
$17$	−2.56415	+	6.53334i	−0.150832	+	0.384314i	−0.986241	−	0.165315i	$-0.947136\pi$
$17$	−2.56415	+	6.53334i	−0.150832	+	0.384314i	0.835409	+	0.549629i	$0.185231\pi$
$18$		0			0
$19$	10.4891	+	15.3847i	0.552060	+	0.809723i	0.996278	−	0.0861954i	$-0.0274709\pi$
$19$	10.4891	+	15.3847i	0.552060	+	0.809723i	−0.444218	+	0.895919i	$0.646519\pi$
$20$	−16.4568	−	1.23327i	−0.822839	−	0.0616633i
$21$		0			0
$22$	30.1871	−	6.89000i	1.37214	−	0.313182i
$23$	−2.94151	+	39.2518i	−0.127892	+	1.70660i	0.452093	+	0.891971i	$0.350677\pi$
$23$	−2.94151	+	39.2518i	−0.127892	+	1.70660i	−0.579985	+	0.814627i	$0.696942\pi$
$24$		0			0
$25$	−13.8958	+	12.8934i	−0.555831	+	0.515736i
$26$	10.9888	+	4.31280i	0.422648	+	0.165877i
$27$		0			0
$28$	77.8409	−	5.83337i	2.78003	−	0.208334i
$29$	−4.30310	−	13.9503i	−0.148383	−	0.481045i	0.850616	−	0.525788i	$-0.176229\pi$
$29$	−4.30310	−	13.9503i	−0.148383	−	0.481045i	−0.998999	+	0.0447429i	$0.985753\pi$
$30$		0			0
$31$	−32.3496	−	30.0160i	−1.04354	−	0.968259i	−0.0440090	−	0.999031i	$-0.514013\pi$
$31$	−32.3496	−	30.0160i	−1.04354	−	0.968259i	−0.999526	+	0.0307717i	$0.990204\pi$
$32$	−12.2712	−	25.4814i	−0.383474	−	0.796292i
$33$		0			0
$34$	−12.9405	+	18.9802i	−0.380602	+	0.558241i
$35$	−17.8243	+	22.3510i	−0.509266	+	0.638599i
$36$		0			0
$37$	12.4503	+	7.18816i	0.336494	+	0.194275i	0.658720	−	0.752388i	$-0.271098\pi$
$37$	12.4503	+	7.18816i	0.336494	+	0.194275i	−0.322227	+	0.946663i	$0.604431\pi$
$38$	22.2656	+	56.7317i	0.585936	+	1.49294i
$39$		0			0
$40$	−20.8586	−	6.43402i	−0.521465	−	0.160851i
$41$	16.7860	−	73.5444i	0.409415	−	1.79377i	−0.177504	−	0.984120i	$-0.556802\pi$
$41$	16.7860	−	73.5444i	0.409415	−	1.79377i	0.586920	−	0.809645i	$-0.300340\pi$
$42$		0			0
$43$	−42.9996	+	0.190850i	−0.999990	+	0.00443838i
$43$	−42.9996	+	0.190850i	−0.999990	+	0.00443838i
$44$	63.5036			1.44326
$45$		0			0
$46$	−37.9741	+	123.109i	−0.825523	+	2.67628i
$47$	52.2411	+	25.1580i	1.11151	+	0.535277i	0.897261	−	0.441501i	$-0.145554\pi$
$47$	52.2411	+	25.1580i	1.11151	+	0.535277i	0.214253	+	0.976778i	$0.431268\pi$
$48$		0			0
$49$	43.1108	−	74.6700i	0.879811	−	1.52388i
$50$	−53.7315	+	31.0219i	−1.07463	+	0.620438i
$51$		0			0
$52$	20.0040	+	13.6385i	0.384692	+	0.262279i
$53$	−56.3433	+	8.49238i	−1.06308	+	0.160234i	−0.657218	−	0.753700i	$-0.728267\pi$
$53$	−56.3433	+	8.49238i	−1.06308	+	0.160234i	−0.405863	+	0.913934i	$0.633029\pi$
$54$		0			0
$55$	−15.8189	+	17.0488i	−0.287617	+	0.309977i
$56$	102.095	+	15.3884i	1.82313	+	0.274793i
$57$		0			0
$58$	−3.57080	−	47.6490i	−0.0615655	−	0.821535i
$59$	−10.8959	−	13.6630i	−0.184677	−	0.231577i	0.680872	−	0.732403i	$-0.261601\pi$
$59$	−10.8959	−	13.6630i	−0.184677	−	0.231577i	−0.865548	+	0.500826i	$0.833030\pi$
$60$		0			0
$61$	−44.6438	−	48.1146i	−0.731866	−	0.788764i	0.251989	−	0.967730i	$-0.418915\pi$
$61$	−44.6438	−	48.1146i	−0.731866	−	0.788764i	−0.983855	+	0.178966i	$0.942725\pi$
$62$	−81.3654	−	119.341i	−1.31235	−	1.92486i
$63$		0			0
$64$	−22.5656	−	98.8662i	−0.352587	−	1.54478i
$65$	−8.64456	+	1.97307i	−0.132993	+	0.0303548i
$66$		0			0
$67$	−69.2334	+	47.2025i	−1.03333	+	0.704515i	−0.956262	−	0.292510i	$-0.905510\pi$
$67$	−69.2334	+	47.2025i	−1.03333	+	0.704515i	−0.0770720	+	0.997026i	$0.524557\pi$
$68$	−34.5366	+	32.0453i	−0.507892	+	0.471255i
$69$		0			0
$70$	−73.1555	+	58.3395i	−1.04508	+	0.833422i
$71$	−19.1878	+	1.43792i	−0.270250	+	0.0202524i	−0.209166	−	0.977880i	$-0.567075\pi$
$71$	−19.1878	+	1.43792i	−0.270250	+	0.0202524i	−0.0610842	+	0.998133i	$0.519456\pi$
$72$		0			0
$73$	0.841669	−	5.58411i	0.0115297	−	0.0764946i	−0.982326	−	0.187178i	$-0.940066\pi$
$73$	0.841669	−	5.58411i	0.0115297	−	0.0764946i	0.993856	+	0.110683i	$0.0353040\pi$
$74$	34.4932	+	32.0050i	0.466124	+	0.432500i
$75$		0			0
$76$	18.6292	+	123.597i	0.245121	+	1.62627i
$77$	61.9692	−	90.8921i	0.804795	−	1.18042i
$78$		0			0
$79$	−24.3421	−	42.1618i	−0.308128	−	0.533694i	0.669825	−	0.742519i	$-0.266369\pi$
$79$	−24.3421	−	42.1618i	−0.308128	−	0.533694i	−0.977953	+	0.208825i	$0.933036\pi$
$80$	−4.70538	−	2.71665i	−0.0588172	−	0.0339581i
$81$		0			0
$82$	107.127	−	222.453i	1.30643	−	2.71284i
$83$	51.4908	+	15.8828i	0.620371	+	0.191359i	0.588979	−	0.808148i	$-0.299530\pi$
$83$	51.4908	+	15.8828i	0.620371	+	0.191359i	0.0313916	+	0.999507i	$0.490006\pi$
$84$		0			0
$85$		−	17.2546i		−	0.202995i
$86$	−137.349	−	30.7084i	−1.59709	−	0.357074i
$87$		0			0
$88$	81.8901	+	18.6909i	0.930570	+	0.212396i
$89$	−22.0490	+	71.4811i	−0.247742	+	0.803159i	0.743224	+	0.669043i	$0.233296\pi$
$89$	−22.0490	+	71.4811i	−0.247742	+	0.803159i	−0.990966	+	0.134116i	$0.957181\pi$
$90$		0			0
$91$	39.0413	−	15.3226i	0.429025	−	0.168380i
$92$	−132.113	+	228.827i	−1.43601	+	2.48725i
$93$		0			0
$94$	148.377	+	118.327i	1.57848	+	1.25879i
$95$	−37.8225	−	25.7869i	−0.398132	−	0.271442i
$96$		0			0
$97$	13.1648	−	6.33982i	0.135719	−	0.0653590i	−0.364792	−	0.931089i	$-0.618860\pi$
$97$	13.1648	−	6.33982i	0.135719	−	0.0653590i	0.500511	+	0.865730i	$0.333145\pi$
$98$	191.949	−	206.872i	1.95866	−	2.11093i
$99$		0			0
$100$	−121.594	+	37.5068i	−1.21594	+	0.375068i
$101$	0.928376	+	12.3883i	0.00919185	+	0.122657i	0.999912	−	0.0132603i	$-0.00422101\pi$
$101$	0.928376	+	12.3883i	0.00919185	+	0.122657i	−0.990720	+	0.135917i	$0.956602\pi$
$102$		0			0
$103$	−27.0445	+	68.9083i	−0.262568	+	0.669013i	−0.999979	−	0.00643147i	$-0.997953\pi$
$103$	−27.0445	+	68.9083i	−0.262568	+	0.669013i	0.737411	+	0.675444i	$0.236048\pi$
$104$	21.7816	+	23.4750i	0.209439	+	0.225721i
$105$		0			0
$106$	−185.975	−	13.9369i	−1.75448	−	0.131480i
$107$	29.6391	+	129.857i	0.277001	+	1.21362i	0.901564	+	0.432646i	$0.142420\pi$
$107$	29.6391	+	129.857i	0.277001	+	1.21362i	−0.624563	+	0.780974i	$0.714723\pi$
$108$		0			0
$109$	−11.3323	+	151.219i	−0.103966	+	1.38733i	0.664426	+	0.747354i	$0.268676\pi$
$109$	−11.3323	+	151.219i	−0.103966	+	1.38733i	−0.768392	+	0.639980i	$0.778943\pi$
$110$	−62.8947	+	42.8809i	−0.571770	+	0.389826i
$111$		0			0
$112$	23.9231	+	9.38912i	0.213599	+	0.0838314i
$113$	−8.79850	+	7.01657i	−0.0778629	+	0.0620936i	−0.661648	−	0.749815i	$-0.730143\pi$
$113$	−8.79850	+	7.01657i	−0.0778629	+	0.0620936i	0.583785	+	0.811908i	$0.301571\pi$
$114$		0			0
$115$	−28.5231	−	92.4696i	−0.248027	−	0.804084i
$116$	14.6060	−	96.9041i	0.125913	−	0.835381i
$117$		0			0
$118$	−24.8175	−	51.5341i	−0.210318	−	0.436730i
$119$	12.1640	+	80.7029i	0.102219	+	0.678176i
$120$		0			0
$121$	−19.6434	+	24.6321i	−0.162342	+	0.203571i
$122$	−107.414	−	186.047i	−0.880446	−	1.52498i
$123$		0			0
$124$	−108.226	−	275.757i	−0.872794	−	2.22384i
$125$	46.8870	−	97.3618i	0.375096	−	0.778895i
$126$		0			0
$127$	−20.4342	+	89.5281i	−0.160899	+	0.704945i	0.828532	+	0.559942i	$0.189177\pi$
$127$	−20.4342	+	89.5281i	−0.160899	+	0.704945i	−0.989431	+	0.145004i	$0.953681\pi$
$128$		−	218.786i		−	1.70926i
$129$		0			0
$130$	−29.0216			−0.223243
$131$	−242.216	−	55.2842i	−1.84898	−	0.422017i	−0.853842	−	0.520533i	$-0.825733\pi$
$131$	−242.216	−	55.2842i	−1.84898	−	0.422017i	−0.995136	+	0.0985156i	$0.968591\pi$
$132$		0			0
$133$	195.082	+	93.9466i	1.46678	+	0.706365i
$134$	−255.300	+	100.198i	−1.90523	+	0.747746i
$135$		0			0
$136$	−53.9680	+	31.1584i	−0.396823	+	0.229106i
$137$	11.0870	+	8.84159i	0.0809270	+	0.0645371i	0.663118	−	0.748515i	$-0.269233\pi$
$137$	11.0870	+	8.84159i	0.0809270	+	0.0645371i	−0.582191	+	0.813052i	$0.697804\pi$
$138$		0			0
$139$	183.187	−	27.6111i	1.31789	−	0.198641i	0.547821	−	0.836596i	$-0.315458\pi$
$139$	183.187	−	27.6111i	1.31789	−	0.198641i	0.770074	+	0.637955i	$0.220219\pi$
$140$	−172.899	+	83.2640i	−1.23500	+	0.594743i
$141$		0			0
$142$	−62.2749	−	9.38643i	−0.438556	−	0.0661016i
$143$	32.6041	−	10.0570i	0.228001	−	0.0703289i
$144$		0			0
$145$	22.3774	+	28.0603i	0.154327	+	0.193520i
$146$	6.75275	−	17.2057i	0.0462517	−	0.117847i
$147$		0			0
$148$	54.3631	+	79.7360i	0.367318	+	0.538757i
$149$	106.910	+	8.01182i	0.717519	+	0.0537706i	0.428486	−	0.903548i	$-0.359047\pi$
$149$	106.910	+	8.01182i	0.717519	+	0.0537706i	0.289033	+	0.957319i	$0.406666\pi$
$150$		0			0
$151$	158.753	−	36.2343i	1.05134	−	0.239962i	0.338268	−	0.941050i	$-0.390159\pi$
$151$	158.753	−	36.2343i	1.05134	−	0.239962i	0.713075	+	0.701088i	$0.247302\pi$
$152$	−12.3550	+	164.865i	−0.0812826	+	1.08464i
$153$		0			0
$154$	263.941	−	244.901i	1.71390	−	1.59027i
$155$	100.992	+	39.6363i	0.651559	+	0.255718i
$156$		0			0
$157$	74.7370	−	5.60076i	0.476032	−	0.0356737i	0.165446	−	0.986219i	$-0.447094\pi$
$157$	74.7370	−	5.60076i	0.476032	−	0.0356737i	0.310586	+	0.950545i	$0.399475\pi$
$158$	−46.9679	−	152.266i	−0.297265	−	0.963709i
$159$		0			0
$160$	50.9692	+	47.2925i	0.318557	+	0.295578i
$161$	198.596	+	412.390i	1.23352	+	2.56143i
$162$		0			0
$163$	46.6676	−	68.4488i	0.286304	−	0.419931i	−0.655963	−	0.754793i	$-0.727737\pi$
$163$	46.6676	−	68.4488i	0.286304	−	0.419931i	0.942267	+	0.334862i	$0.108690\pi$
$164$	315.724	−	395.905i	1.92514	−	2.41405i
$165$		0			0
$166$	152.738	+	88.1833i	0.920108	+	0.531225i
$167$	−38.1388	−	97.1761i	−0.228376	−	0.581893i	0.770050	−	0.637984i	$-0.220231\pi$
$167$	−38.1388	−	97.1761i	−0.228376	−	0.581893i	−0.998426	+	0.0560914i	$0.982136\pi$
$168$		0			0
$169$	−149.061	−	45.9794i	−0.882020	−	0.272067i
$170$	12.5668	−	55.0589i	0.0739226	−	0.323876i
$171$		0			0
$172$	−260.617	−	124.084i	−1.51521	−	0.721421i
$173$	−39.6514			−0.229199			−0.114599	−	0.993412i	$-0.536558\pi$
$173$	−39.6514			−0.229199			−0.114599	+	0.993412i	$0.536558\pi$
$174$		0			0
$175$	−64.9729	+	210.637i	−0.371274	+	1.20364i
$176$	18.8370	+	9.07141i	0.107028	+	0.0515421i
$177$		0			0
$178$	−122.419	+	212.036i	−0.687746	+	1.19121i
$179$	107.352	−	61.9797i	0.599731	−	0.346255i	−0.169205	−	0.985581i	$-0.554120\pi$
$179$	107.352	−	61.9797i	0.599731	−	0.346255i	0.768936	+	0.639326i	$0.220787\pi$
$180$		0			0
$181$	−144.192	−	98.3082i	−0.796639	−	0.543139i	0.0952184	−	0.995456i	$-0.469645\pi$
$181$	−144.192	−	98.3082i	−0.796639	−	0.543139i	−0.891857	+	0.452317i	$0.850597\pi$
$182$	135.739	−	20.4594i	0.745821	−	0.112414i
$183$		0			0
$184$	−237.714	+	256.195i	−1.29193	+	1.39237i
$185$	−34.9486	−	5.26766i	−0.188911	−	0.0284738i
$186$		0			0
$187$	4.96178	+	66.2104i	0.0265336	+	0.354066i
$188$	242.679	+	304.310i	1.29085	+	1.61867i
$189$		0			0
$190$	−101.909	−	109.832i	−0.536366	−	0.578065i
$191$	61.2519	+	89.8400i	0.320691	+	0.470367i	0.952405	−	0.304834i	$-0.0986010\pi$
$191$	61.2519	+	89.8400i	0.320691	+	0.470367i	−0.631715	+	0.775201i	$0.717649\pi$
$192$		0			0
$193$	−30.5238	−	133.733i	−0.158154	−	0.692919i	−0.990368	−	0.138464i	$-0.955784\pi$
$193$	−30.5238	−	133.733i	−0.158154	−	0.692919i	0.832213	−	0.554456i	$-0.187074\pi$
$194$	46.6258	−	10.6420i	0.240339	−	0.0548559i
$195$		0			0
$196$	478.214	−	326.041i	2.43987	−	1.66347i
$197$	49.7327	−	46.1452i	0.252450	−	0.234240i	−0.543788	−	0.839223i	$-0.683010\pi$
$197$	49.7327	−	46.1452i	0.252450	−	0.234240i	0.796239	+	0.604983i	$0.206820\pi$
$198$		0			0
$199$	175.258	−	139.763i	0.880693	−	0.702329i	−0.0748458	−	0.997195i	$-0.523846\pi$
$199$	175.258	−	139.763i	0.880693	−	0.702329i	0.955539	+	0.294866i	$0.0952750\pi$
$200$	−167.839	+	12.5778i	−0.839195	+	0.0628890i
$201$		0			0
$202$	−6.06022	+	40.2070i	−0.0300011	+	0.199044i
$203$	−124.445	−	115.468i	−0.613029	−	0.568808i
$204$		0			0
$205$	27.6405	+	183.383i	0.134832	+	0.894551i
$206$	−136.486	+	200.187i	−0.662551	+	0.971784i
$207$		0			0
$208$	3.98551	+	6.90311i	0.0191611	+	0.0331880i
$209$	152.550	+	88.0750i	0.729906	+	0.421411i
$210$		0			0
$211$	−32.9358	+	68.3920i	−0.156094	+	0.324133i	−0.964320	−	0.264740i	$-0.914714\pi$
$211$	−32.9358	+	68.3920i	−0.156094	+	0.324133i	0.808226	+	0.588873i	$0.200428\pi$
$212$	−365.498	−	112.741i	−1.72405	−	0.531798i
$213$		0			0
$214$			435.958i			2.03719i
$215$	98.2331	−	39.0577i	0.456898	−	0.181664i
$216$		0			0
$217$	−500.299	−	114.190i	−2.30553	−	0.526221i
$218$	−146.297	+	474.283i	−0.671088	+	2.17561i
$219$		0			0
$220$	−145.328	+	57.0371i	−0.660582	+	0.259259i
$221$	−12.6568	+	21.9223i	−0.0572707	+	0.0991958i
$222$		0			0
$223$	−166.198	−	132.539i	−0.745283	−	0.594344i	0.175472	−	0.984484i	$-0.443855\pi$
$223$	−166.198	−	132.539i	−0.745283	−	0.594344i	−0.920755	+	0.390141i	$0.872426\pi$
$224$	−271.732	−	185.264i	−1.21309	−	0.827071i
$225$		0			0
$226$	−33.1861	+	15.9816i	−0.146841	+	0.0707149i
$227$	38.5052	−	41.4987i	0.169626	−	0.182814i	−0.642517	−	0.766271i	$-0.722110\pi$
$227$	38.5052	−	41.4987i	0.169626	−	0.182814i	0.812144	+	0.583457i	$0.198300\pi$
$228$		0			0
$229$	95.3329	−	29.4063i	0.416301	−	0.128412i	−0.0795269	−	0.996833i	$-0.525341\pi$
$229$	95.3329	−	29.4063i	0.416301	−	0.128412i	0.495828	+	0.868421i	$0.334865\pi$
$230$	−23.6691	−	315.842i	−0.102909	−	1.37323i
$231$		0			0
$232$	47.3565	−	120.662i	0.204123	−	0.520096i
$233$	−125.769	−	135.547i	−0.539783	−	0.581747i	0.402981	−	0.915208i	$-0.367974\pi$
$233$	−125.769	−	135.547i	−0.539783	−	0.581747i	−0.942764	+	0.333461i	$0.891783\pi$
$234$		0			0
$235$	−142.150	−	10.6527i	−0.604894	−	0.0453305i
$236$	−26.1039	−	114.369i	−0.110610	−	0.484614i
$237$		0			0
$238$	−19.9624	+	266.380i	−0.0838758	+	1.11924i
$239$	139.288	−	94.9650i	0.582795	−	0.397343i	−0.235726	−	0.971820i	$-0.575747\pi$
$239$	139.288	−	94.9650i	0.582795	−	0.397343i	0.818521	+	0.574476i	$0.194794\pi$
$240$		0			0
$241$	20.6296	+	8.09653i	0.0856001	+	0.0335956i	0.407755	−	0.913091i	$-0.366312\pi$
$241$	20.6296	+	8.09653i	0.0856001	+	0.0335956i	−0.322155	+	0.946687i	$0.604407\pi$
$242$	−80.6216	+	64.2936i	−0.333147	+	0.265676i
$243$		0			0
$244$	−129.869	−	421.024i	−0.532249	−	1.72551i
$245$	−31.5926	+	209.603i	−0.128949	+	0.855523i
$246$		0			0
$247$	29.1386	+	60.5069i	0.117970	+	0.244967i
$248$	−58.3989	−	387.451i	−0.235479	−	1.56230i
$249$		0			0
$250$	220.525	−	276.530i	0.882102	−	1.10612i
$251$	−104.670	−	181.293i	−0.417010	−	0.722283i	0.578627	−	0.815592i	$-0.303589\pi$
$251$	−104.670	−	181.293i	−0.417010	−	0.722283i	−0.995637	+	0.0933096i	$0.970255\pi$
$252$		0			0
$253$	136.042	+	346.628i	0.537714	+	1.37007i
$254$	−130.410	+	270.799i	−0.513425	+	1.06614i
$255$		0			0
$256$	69.0834	−	302.674i	0.269857	−	1.18232i
$257$			349.012i			1.35802i	0.734128	+	0.679011i	$0.237591\pi$
$257$			349.012i			1.35802i	−0.734128	+	0.679011i	$0.762409\pi$
$258$		0			0
$259$	167.175			0.645463
$260$	−58.0288	−	13.2447i	−0.223188	−	0.0509412i
$261$		0			0
$262$	−732.640	−	352.821i	−2.79634	−	1.34664i
$263$	117.124	−	45.9679i	0.445339	−	0.174783i	−0.132065	−	0.991241i	$-0.542161\pi$
$263$	117.124	−	45.9679i	0.445339	−	0.174783i	0.577404	+	0.816458i	$0.304066\pi$
$264$		0			0
$265$	121.314	−	70.0407i	0.457789	−	0.264304i
$266$	554.078	+	441.863i	2.08300	+	1.66114i
$267$		0			0
$268$	−556.202	+	83.8340i	−2.07538	+	0.312814i
$269$	−45.6398	+	21.9790i	−0.169665	+	0.0817061i	−0.516788	−	0.856113i	$-0.672873\pi$
$269$	−45.6398	+	21.9790i	−0.169665	+	0.0817061i	0.347124	+	0.937819i	$0.387158\pi$
$270$		0			0
$271$	389.693	+	58.7368i	1.43798	+	0.216741i	0.821312	−	0.570480i	$-0.193243\pi$
$271$	389.693	+	58.7368i	1.43798	+	0.216741i	0.616671	+	0.787221i	$0.288481\pi$
$272$	−14.8222	+	4.57204i	−0.0544933	+	0.0168090i
$273$		0			0
$274$	28.9388	+	36.2881i	0.105616	+	0.132438i
$275$	−65.5155	+	166.931i	−0.238238	+	0.607021i
$276$		0			0
$277$	264.444	+	387.867i	0.954670	+	1.40024i	0.916083	+	0.400988i	$0.131333\pi$
$277$	264.444	+	387.867i	0.954670	+	1.40024i	0.0385867	+	0.999255i	$0.487714\pi$
$278$	604.655	+	45.3127i	2.17502	+	0.162995i
$279$		0			0
$280$	−247.467	+	56.4826i	−0.883809	+	0.201724i
$281$	−12.0972	+	161.425i	−0.0430504	+	0.574468i	0.933416	+	0.358797i	$0.116813\pi$
$281$	−12.0972	+	161.425i	−0.0430504	+	0.574468i	−0.976466	+	0.215671i	$0.930806\pi$
$282$		0			0
$283$	272.275	−	252.634i	0.962103	−	0.892701i	−0.0321795	−	0.999482i	$-0.510245\pi$
$283$	272.275	−	252.634i	0.962103	−	0.892701i	0.994283	+	0.106781i	$0.0340543\pi$
$284$	−120.235	−	47.1889i	−0.423364	−	0.166158i
$285$		0			0
$286$	111.363	−	8.34554i	0.389383	−	0.0291802i
$287$	−258.560	−	838.231i	−0.900906	−	2.92066i
$288$		0			0
$289$	175.742	+	163.065i	0.608105	+	0.564239i
$290$	50.9687	+	105.838i	0.175754	+	0.364957i
$291$		0			0
$292$	21.3544	−	31.3212i	0.0731316	−	0.107264i
$293$	−146.386	+	183.562i	−0.499610	+	0.626491i	−0.966141	−	0.258014i	$-0.916932\pi$
$293$	−146.386	+	183.562i	−0.499610	+	0.626491i	0.466532	+	0.884505i	$0.345503\pi$
$294$		0			0
$295$	37.2070	+	21.4815i	0.126126	+	0.0728186i
$296$	46.6345	+	118.823i	0.157549	+	0.401428i
$297$		0			0
$298$	335.313	+	103.430i	1.12521	+	0.347082i
$299$	−31.5905	+	138.407i	−0.105654	+	0.462900i
$300$		0			0
$301$	−431.920	+	251.932i	−1.43495	+	0.836983i
$302$	532.966			1.76479
$303$		0			0
$304$	−12.1297	+	39.3235i	−0.0399003	+	0.129354i
$305$	145.382	+	70.0125i	0.476664	+	0.229549i
$306$		0			0
$307$	−96.2904	+	166.780i	−0.313650	+	0.543257i	−0.979150	−	0.203141i	$-0.934885\pi$
$307$	−96.2904	+	166.780i	−0.313650	+	0.543257i	0.665500	+	0.746398i	$0.268218\pi$
$308$	639.517	−	369.225i	2.07635	−	1.19878i
$309$		0			0
$310$	293.394	+	200.032i	0.946431	+	0.645266i
$311$	−180.954	+	27.2745i	−0.581847	+	0.0876994i	−0.433369	−	0.901216i	$-0.642675\pi$
$311$	−180.954	+	27.2745i	−0.581847	+	0.0876994i	−0.148478	+	0.988916i	$0.547437\pi$
$312$		0			0
$313$	423.634	−	456.569i	1.35346	−	1.45869i	0.603091	−	0.797672i	$-0.293935\pi$
$313$	423.634	−	456.569i	1.35346	−	1.45869i	0.750373	−	0.661015i	$-0.229874\pi$
$314$	242.563	+	36.5605i	0.772493	+	0.116435i
$315$		0			0
$316$	−24.4222	−	325.892i	−0.0772855	−	1.03130i
$317$	361.671	+	453.521i	1.14092	+	1.43067i	0.885989	+	0.463705i	$0.153480\pi$
$317$	361.671	+	453.521i	1.14092	+	1.43067i	0.254928	+	0.966960i	$0.417948\pi$
$318$		0			0
$319$	−93.9370	−	101.240i	−0.294473	−	0.317367i
$320$	140.440	+	205.988i	0.438875	+	0.643711i
$321$		0			0
$322$	333.365	+	1460.57i	1.03529	+	4.53592i
$323$	−127.409	+	29.0804i	−0.394456	+	0.0900321i
$324$		0			0
$325$	−56.4890	+	38.5136i	−0.173812	+	0.118503i
$326$	198.768	−	184.429i	0.609717	−	0.565734i
$327$		0			0
$328$	523.662	−	417.607i	1.59653	−	1.27319i
$329$	672.372	−	50.3873i	2.04368	−	0.153153i
$330$		0			0
$331$	−67.9011	+	450.494i	−0.205139	+	1.36101i	0.614856	+	0.788640i	$0.289214\pi$
$331$	−67.9011	+	450.494i	−0.205139	+	1.36101i	−0.819995	+	0.572371i	$0.806024\pi$
$332$	265.156	+	246.029i	0.798662	+	0.741050i
$333$		0			0
$334$	−50.9247	−	337.863i	−0.152469	−	1.01157i
$335$	116.045	−	170.206i	0.346402	−	0.508079i
$336$		0			0
$337$	105.103	+	182.045i	0.311880	+	0.540192i	0.978769	−	0.204965i	$-0.0657080\pi$
$337$	105.103	+	182.045i	0.311880	+	0.540192i	−0.666890	+	0.745157i	$0.732375\pi$
$338$	−442.163	−	255.283i	−1.30818	−	0.755275i
$339$		0			0
$340$	50.2549	−	104.355i	0.147809	−	0.306928i
$341$	−398.929	−	123.053i	−1.16988	−	0.360860i
$342$		0			0
$343$		−	432.829i		−	1.26189i
$344$	−299.552	−	236.718i	−0.870792	−	0.688133i
$345$		0			0
$346$	−126.527	−	28.8789i	−0.365684	−	0.0834649i
$347$	125.518	−	406.918i	0.361722	−	1.17267i	−0.573677	−	0.819082i	$-0.694484\pi$
$347$	125.518	−	406.918i	0.361722	−	1.17267i	0.935399	−	0.353593i	$-0.115040\pi$
$348$		0			0
$349$	428.427	−	168.145i	1.22758	−	0.481791i	0.339122	−	0.940742i	$-0.389870\pi$
$349$	428.427	−	168.145i	1.22758	−	0.481791i	0.888462	+	0.458951i	$0.151775\pi$
$350$	−360.738	+	624.816i	−1.03068	+	1.78519i
$351$		0			0
$352$	−209.182	−	166.817i	−0.594266	−	0.473911i
$353$	88.7868	+	60.5338i	0.251521	+	0.171484i	0.682517	−	0.730870i	$-0.260885\pi$
$353$	88.7868	+	60.5338i	0.251521	+	0.171484i	−0.430996	+	0.902354i	$0.641838\pi$
$354$		0			0
$355$	42.6197	−	20.5246i	0.120055	−	0.0578157i
$356$	−341.545	+	368.098i	−0.959395	+	1.03398i
$357$		0			0
$358$	387.698	−	119.589i	1.08296	−	0.334047i
$359$	−15.1817	−	202.586i	−0.0422890	−	0.564307i	−0.977599	−	0.210477i	$-0.932498\pi$
$359$	−15.1817	−	202.586i	−0.0422890	−	0.564307i	0.935310	−	0.353830i	$-0.115121\pi$
$360$		0			0
$361$	5.21990	−	13.3001i	0.0144596	−	0.0368423i
$362$	−388.512	−	418.716i	−1.07324	−	1.15667i
$363$		0			0
$364$	280.749	+	21.0392i	0.771288	+	0.0578000i
$365$	3.08932	+	13.5352i	0.00846389	+	0.0370827i
$366$		0			0
$367$	27.8586	−	371.747i	0.0759089	−	1.01293i	−0.821061	−	0.570841i	$-0.806617\pi$
$367$	27.8586	−	371.747i	0.0759089	−	1.01293i	0.896969	−	0.442093i	$-0.145764\pi$
$368$	−71.8761	+	49.0043i	−0.195315	+	0.133164i
$369$		0			0
$370$	−107.684	−	42.2627i	−0.291037	−	0.114223i
$371$	−518.031	+	413.116i	−1.39631	+	1.11352i
$372$		0			0
$373$	−80.8364	−	262.065i	−0.216720	−	0.702587i	−0.997017	−	0.0771792i	$-0.975409\pi$
$373$	−80.8364	−	262.065i	−0.216720	−	0.702587i	0.780298	−	0.625408i	$-0.215068\pi$
$374$	−32.3894	+	214.889i	−0.0866026	+	0.574571i
$375$		0			0
$376$	223.376	+	463.846i	0.594086	+	1.23363i
$377$	−7.84765	−	52.0657i	−0.0208160	−	0.138105i
$378$		0			0
$379$	−100.996	+	126.645i	−0.266481	+	0.334156i	−0.897011	−	0.442008i	$-0.854266\pi$
$379$	−100.996	+	126.645i	−0.266481	+	0.334156i	0.630530	+	0.776165i	$0.282838\pi$
$380$	−153.644	−	266.119i	−0.404326	−	0.700314i
$381$		0			0
$382$	130.021	+	331.288i	0.340369	+	0.867246i
$383$	151.351	−	314.283i	0.395172	−	0.820583i	−0.604540	−	0.796575i	$-0.706643\pi$
$383$	151.351	−	314.283i	0.395172	−	0.820583i	0.999712	−	0.0240083i	$-0.00764282\pi$
$384$		0			0
$385$	−60.1799	+	263.666i	−0.156312	+	0.684846i
$386$		−	448.971i		−	1.16314i
$387$		0			0
$388$	98.0854			0.252797
$389$	−145.759	−	33.2686i	−0.374702	−	0.0855233i	0.0310224	−	0.999519i	$-0.490124\pi$
$389$	−145.759	−	33.2686i	−0.374702	−	0.0855233i	−0.405725	+	0.913995i	$0.632981\pi$
$390$		0			0
$391$	−248.903	−	119.865i	−0.636580	−	0.306561i
$392$	712.636	−	279.689i	1.81795	−	0.713492i
$393$		0			0
$394$	192.304	−	111.027i	0.488082	−	0.281794i
$395$	93.5755	+	74.6240i	0.236900	+	0.188921i
$396$		0			0
$397$	−579.306	+	87.3164i	−1.45921	+	0.219940i	−0.830204	−	0.557460i	$-0.811776\pi$
$397$	−579.306	+	87.3164i	−1.45921	+	0.219940i	−0.629006	+	0.777400i	$0.716538\pi$
$398$	661.035	−	318.338i	1.66089	−	0.799844i
$399$		0			0
$400$	−41.4261	−	6.24397i	−0.103565	−	0.0156099i
$401$	270.048	−	83.2988i	0.673436	−	0.207728i	0.0608688	−	0.998146i	$-0.480613\pi$
$401$	270.048	−	83.2988i	0.673436	−	0.207728i	0.612568	+	0.790418i	$0.290137\pi$
$402$		0			0
$403$	−99.2371	−	124.439i	−0.246246	−	0.308783i
$404$	−30.4669	+	77.6283i	−0.0754130	+	0.192149i
$405$		0			0
$406$	−313.003	−	459.091i	−0.770943	−	1.13077i
$407$	135.622	+	10.1635i	0.333223	+	0.0249716i
$408$		0			0
$409$	548.748	−	125.248i	1.34168	−	0.306230i	0.509375	−	0.860545i	$-0.329877\pi$
$409$	548.748	−	125.248i	1.34168	−	0.306230i	0.832307	+	0.554315i	$0.187020\pi$
$410$	−45.3611	+	605.301i	−0.110637	+	1.47634i
$411$		0			0
$412$	−364.264	+	337.988i	−0.884136	+	0.820358i
$413$	−189.168	−	74.2430i	−0.458034	−	0.179765i
$414$		0			0
$415$	−132.102	+	9.89969i	−0.318318	+	0.0238547i
$416$	−30.0666	−	97.4736i	−0.0722755	−	0.234311i
$417$		0			0
$418$	422.637	+	392.150i	1.01109	+	0.938158i
$419$	185.042	+	384.243i	0.441627	+	0.917049i	0.996378	+	0.0850321i	$0.0270993\pi$
$419$	185.042	+	384.243i	0.441627	+	0.917049i	−0.554751	+	0.832017i	$0.687186\pi$
$420$		0			0
$421$	−391.731	+	574.563i	−0.930476	+	1.36476i	0.000625823		1.00000i	$0.499801\pi$
$421$	−391.731	+	574.563i	−0.930476	+	1.36476i	−0.931102	+	0.364758i	$0.881152\pi$
$422$	−154.909	+	194.249i	−0.367082	+	0.460306i
$423$		0			0
$424$	−438.139	−	252.960i	−1.03335	−	0.596603i
$425$	−48.6061	−	123.846i	−0.114367	−	0.291403i
$426$		0			0
$427$	−729.338	−	224.971i	−1.70805	−	0.526864i
$428$	−198.960	+	871.700i	−0.464860	+	2.03668i
$429$		0			0
$430$	341.906	−	53.0870i	0.795129	−	0.123458i
$431$	−269.250			−0.624710			−0.312355	−	0.949965i	$-0.601118\pi$
$431$	−269.250			−0.624710			−0.312355	+	0.949965i	$0.601118\pi$
$432$		0			0
$433$	129.874	−	421.040i	0.299939	−	0.972378i	−0.672673	−	0.739940i	$-0.734854\pi$
$433$	129.874	−	421.040i	0.299939	−	0.972378i	0.972611	−	0.232437i	$-0.0746701\pi$
$434$	−1513.27	−	728.754i	−3.48681	−	1.67916i
$435$		0			0
$436$	−508.973	+	881.566i	−1.16737	+	2.02194i
$437$	−634.732	+	366.463i	−1.45248	+	0.838587i
$438$		0			0
$439$	−29.7870	−	20.3084i	−0.0678519	−	0.0462607i	0.528919	−	0.848672i	$-0.322598\pi$
$439$	−29.7870	−	20.3084i	−0.0678519	−	0.0462607i	−0.596771	+	0.802412i	$0.703550\pi$
$440$	−204.193	+	30.7772i	−0.464075	+	0.0699481i
$441$		0			0
$442$	−56.3540	+	60.7352i	−0.127498	+	0.137410i
$443$	−300.641	−	45.3143i	−0.678647	−	0.102290i	−0.199331	−	0.979932i	$-0.563877\pi$
$443$	−300.641	−	45.3143i	−0.678647	−	0.102290i	−0.479316	+	0.877643i	$0.659115\pi$
$444$		0			0
$445$	−13.7431	−	183.388i	−0.0308833	−	0.412108i
$446$	−433.804	−	543.972i	−0.972654	−	1.21967i
$447$		0			0
$448$	−802.080	−	864.436i	−1.79036	−	1.92955i
$449$	−268.625	−	394.001i	−0.598275	−	0.877508i	0.400981	−	0.916086i	$-0.368669\pi$
$449$	−268.625	−	394.001i	−0.598275	−	0.877508i	−0.999256	+	0.0385788i	$0.987717\pi$
$450$		0			0
$451$	−158.798	−	695.741i	−0.352103	−	1.54266i
$452$	−73.6494	+	16.8100i	−0.162941	+	0.0371902i
$453$		0			0
$454$	153.093	−	104.377i	0.337210	−	0.229906i
$455$	−75.5837	+	70.1314i	−0.166118	+	0.154135i
$456$		0			0
$457$	−210.233	+	167.655i	−0.460027	+	0.366860i	−0.825911	−	0.563801i	$-0.809338\pi$
$457$	−210.233	+	167.655i	−0.460027	+	0.366860i	0.365883	+	0.930661i	$0.380767\pi$
$458$	325.622	−	24.4020i	0.710964	−	0.0532794i
$459$		0			0
$460$	96.8156	−	642.330i	0.210469	−	1.39637i
$461$	−70.1129	−	65.0552i	−0.152089	−	0.141118i	0.600459	−	0.799656i	$-0.294985\pi$
$461$	−70.1129	−	65.0552i	−0.152089	−	0.141118i	−0.752547	+	0.658538i	$0.771175\pi$
$462$		0			0
$463$	50.2842	+	333.614i	0.108605	+	0.720549i	0.975166	+	0.221477i	$0.0710876\pi$
$463$	50.2842	+	333.614i	0.108605	+	0.720549i	−0.866560	+	0.499072i	$0.833674\pi$
$464$	18.1752	−	26.6581i	0.0391706	−	0.0574527i
$465$		0			0
$466$	−302.605	−	524.127i	−0.649367	−	1.12474i
$467$	470.523	+	271.656i	1.00754	+	0.581705i	0.910471	−	0.413572i	$-0.135719\pi$
$467$	470.523	+	271.656i	1.00754	+	0.581705i	0.0970717	+	0.995277i	$0.469052\pi$
$468$		0			0
$469$	−422.772	+	877.895i	−0.901433	+	1.87185i
$470$	−445.838	−	137.523i	−0.948592	−	0.292602i
$471$		0			0
$472$		−	155.166i		−	0.328741i
$473$	−365.715	+	178.123i	−0.773181	+	0.376581i
$474$		0			0
$475$	−344.116	−	78.5423i	−0.724455	−	0.165352i
$476$	−161.484	+	523.518i	−0.339252	+	1.09983i
$477$		0			0
$478$	513.629	−	201.585i	1.07454	−	0.421725i
$479$	97.5478	−	168.958i	0.203649	−	0.352730i	−0.746053	−	0.665887i	$-0.768053\pi$
$479$	97.5478	−	168.958i	0.203649	−	0.352730i	0.949701	+	0.313157i	$0.101387\pi$
$480$		0			0
$481$	40.5389	+	32.3287i	0.0842804	+	0.0672114i
$482$	59.9317	+	40.8608i	0.124340	+	0.0847734i
$483$		0			0
$484$	−190.545	+	91.7618i	−0.393689	+	0.189591i
$485$	−24.4333	+	26.3329i	−0.0503780	+	0.0542946i
$486$		0			0
$487$	692.009	−	213.457i	1.42096	−	0.438309i	0.513373	−	0.858166i	$-0.328396\pi$
$487$	692.009	−	213.457i	1.42096	−	0.438309i	0.907590	+	0.419857i	$0.137920\pi$
$488$	−43.5511	−	581.149i	−0.0892440	−	1.19088i
$489$		0			0
$490$	−253.469	+	645.828i	−0.517284	+	1.31802i
$491$	−49.5458	−	53.3977i	−0.100908	−	0.108753i	0.680578	−	0.732675i	$-0.261729\pi$
$491$	−49.5458	−	53.3977i	−0.100908	−	0.108753i	−0.781486	+	0.623922i	$0.785538\pi$
$492$		0			0
$493$	102.176	+	7.65702i	0.207253	+	0.0155315i
$494$	48.9121	+	214.298i	0.0990124	+	0.433802i
$495$		0			0
$496$	7.28842	−	97.2572i	0.0146944	−	0.196083i
$497$	−184.871	+	126.043i	−0.371974	+	0.253607i
$498$		0			0
$499$	−177.929	−	69.8318i	−0.356570	−	0.139943i	0.180293	−	0.983613i	$-0.442296\pi$
$499$	−177.929	−	69.8318i	−0.356570	−	0.139943i	−0.536863	+	0.843670i	$0.680391\pi$
$500$	567.143	−	452.282i	1.13429	−	0.904563i
$501$		0			0
$502$	−201.959	−	654.734i	−0.402308	−	1.30425i
$503$	−1.28427	+	8.52056i	−0.00255322	+	0.0169395i	−0.990071	−	0.140567i	$-0.955107\pi$
$503$	−1.28427	+	8.52056i	−0.00255322	+	0.0169395i	0.987518	+	0.157507i	$0.0503455\pi$
$504$		0			0
$505$	−13.2514	−	27.5168i	−0.0262404	−	0.0544888i
$506$	181.649	+	1205.16i	0.358990	+	2.38174i
$507$		0			0
$508$	−384.341	+	481.948i	−0.756577	+	0.948717i
$509$	−145.960	−	252.810i	−0.286758	−	0.496680i	0.686276	−	0.727341i	$-0.259244\pi$
$509$	−145.960	−	252.810i	−0.286758	−	0.496680i	−0.973034	+	0.230662i	$0.925911\pi$
$510$		0			0
$511$	−23.9913	−	61.1287i	−0.0469496	−	0.119626i
$512$	61.1763	−	127.034i	0.119485	−	0.248113i
$513$		0			0
$514$	−254.192	+	1113.69i	−0.494537	+	2.16671i
$515$		−	181.987i		−	0.353373i
$516$		0			0
$517$	548.531			1.06099
$518$	533.450	+	121.757i	1.02983	+	0.235051i
$519$		0			0
$520$	−70.9319	−	34.1590i	−0.136407	−	0.0656904i
$521$	240.317	−	94.3176i	0.461262	−	0.181032i	−0.123320	−	0.992367i	$-0.539354\pi$
$521$	240.317	−	94.3176i	0.461262	−	0.181032i	0.584581	+	0.811335i	$0.301259\pi$
$522$		0			0
$523$	236.462	−	136.521i	0.452125	−	0.261035i	−0.256602	−	0.966517i	$-0.582603\pi$
$523$	236.462	−	136.521i	0.452125	−	0.261035i	0.708727	+	0.705482i	$0.249270\pi$
$524$	−1303.90	−	1039.83i	−2.48836	−	1.98440i
$525$		0			0
$526$	407.219	−	61.3785i	0.774181	−	0.116689i
$527$	279.054	−	134.385i	0.529515	−	0.255001i
$528$		0			0
$529$	−1008.96	−	152.076i	−1.90729	−	0.287478i
$530$	438.122	−	135.143i	0.826644	−	0.254986i
$531$		0			0
$532$	906.228	+	1136.37i	1.70344	+	2.13604i
$533$	99.3999	−	253.267i	0.186491	−	0.475172i
$534$		0			0
$535$	−184.463	−	270.558i	−0.344791	−	0.505715i
$536$	−741.917	−	55.5990i	−1.38417	−	0.103729i
$537$		0			0
$538$	−161.643	+	36.8939i	−0.300452	+	0.0685761i
$539$	60.9550	−	813.387i	0.113089	−	1.50907i
$540$		0			0
$541$	711.610	−	660.278i	1.31536	−	1.22048i	0.357274	−	0.934000i	$-0.383706\pi$
$541$	711.610	−	660.278i	1.31536	−	1.22048i	0.958087	−	0.286477i	$-0.0924843\pi$
$542$	1200.72	+	471.249i	2.21535	+	0.869463i
$543$		0			0
$544$	197.943	−	14.8338i	0.363867	−	0.0272680i
$545$	−109.887	−	356.244i	−0.201627	−	0.653659i
$546$		0			0
$547$	−409.107	−	379.595i	−0.747910	−	0.693959i	0.211058	−	0.977474i	$-0.432309\pi$
$547$	−409.107	−	379.595i	−0.747910	−	0.693959i	−0.958968	+	0.283515i	$0.908500\pi$
$548$	41.3024	+	85.7653i	0.0753693	+	0.156506i
$549$		0			0
$550$	−330.637	+	484.956i	−0.601159	+	0.881738i
$551$	169.486	−	212.529i	0.307597	−	0.385714i
$552$		0			0
$553$	−490.278	−	283.062i	−0.886578	−	0.511866i
$554$	561.341	+	1430.27i	1.01325	+	2.58172i
$555$		0			0
$556$	1188.33	+	366.552i	2.13729	+	0.659266i
$557$	−23.7765	+	104.172i	−0.0426867	+	0.187023i	−0.991776	−	0.127984i	$-0.959150\pi$
$557$	−23.7765	+	104.172i	−0.0426867	+	0.187023i	0.949090	+	0.315006i	$0.102007\pi$
$558$		0			0
$559$	−153.457	−	22.4338i	−0.274521	−	0.0401321i
$560$	−63.1810			−0.112823
$561$		0			0
$562$	−156.171	+	506.293i	−0.277884	+	0.900878i
$563$	−489.111	−	235.543i	−0.868758	−	0.418372i	−0.0542523	−	0.998527i	$-0.517278\pi$
$563$	−489.111	−	235.543i	−0.868758	−	0.418372i	−0.814506	+	0.580155i	$0.802992\pi$
$564$		0			0
$565$	13.8333	−	23.9600i	0.0244837	−	0.0424070i
$566$	1052.82	−	607.847i	1.86011	−	1.07393i
$567$		0			0
$568$	−141.159	−	96.2402i	−0.248519	−	0.169437i
$569$	−1098.33	+	165.546i	−1.93027	+	0.290942i	−0.997568	−	0.0696994i	$-0.977796\pi$
$569$	−1098.33	+	165.546i	−1.93027	+	0.290942i	−0.932705	+	0.360641i	$0.882558\pi$
$570$		0			0
$571$	−100.694	+	108.522i	−0.176346	+	0.190056i	−0.815039	−	0.579406i	$-0.803285\pi$
$571$	−100.694	+	108.522i	−0.176346	+	0.190056i	0.638693	+	0.769461i	$0.279475\pi$
$572$	226.481	+	34.1365i	0.395945	+	0.0596791i
$573$		0			0
$574$	−214.559	−	2863.09i	−0.373795	−	4.98795i
$575$	−465.214	−	583.360i	−0.809067	−	1.01454i
$576$		0			0
$577$	572.494	+	617.002i	0.992191	+	1.06933i	0.997593	+	0.0693418i	$0.0220899\pi$
$577$	572.494	+	617.002i	0.992191	+	1.06933i	−0.00540235	+	0.999985i	$0.501720\pi$
$578$	442.026	+	648.332i	0.764750	+	1.12168i
$579$		0			0
$580$	53.6107	+	234.884i	0.0924322	+	0.404972i
$581$	610.887	−	139.431i	1.05144	−	0.239985i
$582$		0			0
$583$	−445.373	+	303.650i	−0.763933	+	0.520840i
$584$	36.7559	−	34.1045i	0.0629383	−	0.0583982i
$585$		0			0
$586$	−600.804	+	479.125i	−1.02526	+	0.817620i
$587$	−763.130	+	57.1887i	−1.30005	+	0.0974253i	−0.706697	−	0.707516i	$-0.749816\pi$
$587$	−763.130	+	57.1887i	−1.30005	+	0.0974253i	−0.593354	+	0.804942i	$0.702197\pi$
$588$		0			0
$589$	122.470	−	812.533i	0.207928	−	1.37951i
$590$	103.081	+	95.6455i	0.174714	+	0.162111i
$591$		0			0
$592$	4.73545	+	31.4176i	0.00799907	+	0.0530703i
$593$	249.399	−	365.801i	0.420571	−	0.616865i	−0.556226	−	0.831031i	$-0.687751\pi$
$593$	249.399	−	365.801i	0.420571	−	0.616865i	0.976797	+	0.214166i	$0.0687035\pi$
$594$		0			0
$595$	−100.322	−	173.763i	−0.168609	−	0.292039i
$596$	623.257	+	359.838i	1.04573	+	0.603754i
$597$		0			0
$598$	−201.609	+	418.645i	−0.337138	+	0.700075i
$599$	509.104	+	157.038i	0.849924	+	0.262167i	0.688965	−	0.724794i	$-0.258065\pi$
$599$	509.104	+	157.038i	0.849924	+	0.262167i	0.160959	+	0.986961i	$0.448541\pi$
$600$		0			0
$601$		−	377.993i		−	0.628940i	−0.949267	−	0.314470i	$-0.898173\pi$
$601$		−	377.993i		−	0.628940i	0.949267	−	0.314470i	$-0.101827\pi$
$602$	−1561.73	+	489.332i	−2.59424	+	0.812844i
$603$		0			0
$604$	1065.67	+	243.232i	1.76435	+	0.402702i
$605$	22.8302	−	74.0137i	0.0377359	−	0.122337i
$606$		0			0
$607$	−112.105	+	43.9979i	−0.184687	+	0.0724841i	−0.455882	−	0.890040i	$-0.650676\pi$
$607$	−112.105	+	43.9979i	−0.184687	+	0.0724841i	0.271196	+	0.962524i	$0.412581\pi$
$608$	263.310	−	456.066i	0.433076	−	0.750109i
$609$		0			0
$610$	412.920	+	329.293i	0.676918	+	0.539824i
$611$	172.790	+	117.806i	0.282799	+	0.192809i
$612$		0			0
$613$	−707.140	+	340.541i	−1.15357	+	0.555531i	−0.910105	−	0.414378i	$-0.863999\pi$
$613$	−707.140	+	340.541i	−1.15357	+	0.555531i	−0.243468	+	0.969909i	$0.578285\pi$
$614$	−428.729	+	462.060i	−0.698256	+	0.752541i
$615$		0			0
$616$	933.352	−	287.901i	1.51518	−	0.467372i
$617$	6.24089	+	83.2789i	0.0101149	+	0.134974i	0.999975	−	0.00707179i	$-0.00225104\pi$
$617$	6.24089	+	83.2789i	0.0101149	+	0.134974i	−0.989860	+	0.142046i	$0.954632\pi$
$618$		0			0
$619$	−431.897	+	1100.46i	−0.697733	+	1.77780i	−0.0724858	+	0.997369i	$0.523093\pi$
$619$	−431.897	+	1100.46i	−0.697733	+	1.77780i	−0.625248	+	0.780426i	$0.715002\pi$
$620$	495.352	+	533.863i	0.798956	+	0.861069i
$621$		0			0
$622$	−597.285	−	44.7603i	−0.960266	−	0.0719620i
$623$	193.563	+	848.053i	0.310694	+	1.36124i
$624$		0			0
$625$	15.5613	−	207.651i	0.0248981	−	0.332242i
$626$	1684.33	−	1148.36i	2.69063	−	1.83444i
$627$		0			0
$628$	468.321	+	183.802i	0.745734	+	0.292679i
$629$	−78.8870	+	62.9103i	−0.125417	+	0.100016i
$630$		0			0
$631$	−286.027	−	927.278i	−0.453292	−	1.46954i	−0.837575	−	0.546322i	$-0.816027\pi$
$631$	−286.027	−	927.278i	−0.453292	−	1.46954i	0.384283	−	0.923215i	$-0.374449\pi$
$632$	64.4257	−	427.437i	0.101939	−	0.676324i
$633$		0			0
$634$	823.774	+	1710.58i	1.29933	+	2.69808i
$635$	−33.6478	−	223.238i	−0.0529886	−	0.351556i
$636$		0			0
$637$	193.890	−	243.130i	0.304380	−	0.381680i
$638$	−226.015	−	391.470i	−0.354256	−	0.613590i
$639$		0			0
$640$	196.507	+	500.691i	0.307042	+	0.782330i
$641$	16.2904	−	33.8273i	0.0254140	−	0.0527727i	−0.887875	−	0.460084i	$-0.847819\pi$
$641$	16.2904	−	33.8273i	0.0254140	−	0.0527727i	0.913289	+	0.407311i	$0.133534\pi$
$642$		0			0
$643$	8.43714	−	36.9655i	0.0131215	−	0.0574892i	−0.967943	−	0.251169i	$-0.919185\pi$
$643$	8.43714	−	36.9655i	0.0131215	−	0.0574892i	0.981065	+	0.193680i	$0.0620422\pi$
$644$			3072.55i			4.77104i
$645$		0			0
$646$	−427.740			−0.662136
$647$	−755.591	−	172.459i	−1.16784	−	0.266551i	−0.405725	−	0.913995i	$-0.632981\pi$
$647$	−755.591	−	172.459i	−1.16784	−	0.266551i	−0.762113	+	0.647444i	$0.775838\pi$
$648$		0			0
$649$	−148.951	−	71.7308i	−0.229508	−	0.110525i
$650$	−208.305	+	81.7537i	−0.320469	+	0.125775i
$651$		0			0
$652$	481.606	−	278.055i	0.738659	−	0.426465i
$653$	−259.960	−	207.311i	−0.398101	−	0.317475i	0.403894	−	0.914806i	$-0.367656\pi$
$653$	−259.960	−	207.311i	−0.398101	−	0.317475i	−0.801995	+	0.597331i	$0.796228\pi$
$654$		0			0
$655$	603.966	−	91.0332i	0.922086	−	0.138982i
$656$	150.207	−	72.3359i	0.228974	−	0.110268i
$657$		0			0
$658$	2182.22	+	328.917i	3.31644	+	0.499873i
$659$	610.594	−	188.343i	0.926547	−	0.285802i	0.205475	−	0.978662i	$-0.434126\pi$
$659$	610.594	−	188.343i	0.926547	−	0.285802i	0.721072	+	0.692860i	$0.243650\pi$
$660$		0			0
$661$	265.670	+	333.140i	0.401922	+	0.503994i	0.941068	−	0.338218i	$-0.109824\pi$
$661$	265.670	+	333.140i	0.401922	+	0.503994i	−0.539146	+	0.842213i	$0.681253\pi$
$662$	−544.774	+	1388.06i	−0.822922	+	2.09677i
$663$		0			0
$664$	269.515	+	395.305i	0.405895	+	0.595339i
$665$	−530.825	−	39.7798i	−0.798233	−	0.0598193i
$666$		0			0
$667$	560.231	−	127.869i	0.839927	−	0.191708i
$668$	52.3679	−	698.801i	0.0783950	−	1.04611i
$669$		0			0
$670$	494.260	−	458.606i	0.737702	−	0.684487i
$671$	−578.004	−	226.850i	−0.861407	−	0.338077i
$672$		0			0
$673$	592.674	−	44.4147i	0.880644	−	0.0659952i	0.373272	−	0.927722i	$-0.378236\pi$
$673$	592.674	−	44.4147i	0.880644	−	0.0659952i	0.507372	+	0.861727i	$0.330617\pi$
$674$	202.796	+	657.448i	0.300884	+	0.975442i
$675$		0			0
$676$	−767.604	−	712.232i	−1.13551	−	1.05360i
$677$	536.237	+	1113.51i	0.792078	+	1.64477i	0.764047	+	0.645161i	$0.223210\pi$
$677$	536.237	+	1113.51i	0.792078	+	1.64477i	0.0280316	+	0.999607i	$0.491076\pi$
$678$		0			0
$679$	95.7154	−	140.389i	0.140965	−	0.206758i
$680$	95.5202	−	119.779i	0.140471	−	0.176145i
$681$		0			0
$682$	−1183.35	−	683.208i	−1.73512	−	1.00177i
$683$	−231.404	−	589.608i	−0.338805	−	0.863261i	−0.994158	−	0.107938i	$-0.965575\pi$
$683$	−231.404	−	589.608i	−0.338805	−	0.863261i	0.655352	−	0.755323i	$-0.272520\pi$
$684$		0			0
$685$	−33.3139	−	10.2760i	−0.0486334	−	0.0150014i
$686$	315.238	−	1381.15i	0.459530	−	2.01333i
$687$		0			0
$688$	−59.5810	−	74.0357i	−0.0866002	−	0.107610i
$689$	−205.509			−0.298271
$690$		0			0
$691$	−68.7693	+	222.945i	−0.0995215	+	0.322641i	−0.991618	−	0.129204i	$-0.958758\pi$
$691$	−68.7693	+	222.945i	−0.0995215	+	0.322641i	0.892097	+	0.451845i	$0.149234\pi$
$692$	−239.811	−	115.487i	−0.346548	−	0.166889i
$693$		0			0
$694$	696.889	−	1207.05i	1.00416	−	1.73926i
$695$	−394.425	+	227.721i	−0.567518	+	0.327657i
$696$		0			0
$697$	437.449	+	298.247i	0.627616	+	0.427902i
$698$	1489.56	−	224.515i	2.13404	−	0.321655i
$699$		0			0
$700$	−1006.45	+	1084.69i	−1.43778	+	1.54956i
$701$	668.860	+	100.814i	0.954152	+	0.143815i	0.607624	−	0.794225i	$-0.292123\pi$
$701$	668.860	+	100.814i	0.954152	+	0.143815i	0.346527	+	0.938040i	$0.387361\pi$
$702$		0			0
$703$	20.0045	+	266.942i	0.0284559	+	0.379718i
$704$	−598.140	−	750.043i	−0.849630	−	1.06540i
$705$		0			0
$706$	239.228	+	257.827i	0.338850	+	0.365194i
$707$	81.3779	+	119.360i	0.115103	+	0.168825i
$708$		0			0
$709$	61.9956	+	271.620i	0.0874409	+	0.383104i	0.999645	−	0.0266318i	$-0.00847818\pi$
$709$	61.9956	+	271.620i	0.0874409	+	0.383104i	−0.912204	+	0.409735i	$0.865621\pi$
$710$	150.947	−	34.4526i	0.212601	−	0.0485248i
$711$		0			0
$712$	−548.775	+	374.148i	−0.770751	+	0.525489i
$713$	1273.34	−	1181.49i	1.78589	−	1.65706i
$714$		0			0
$715$	−65.5815	+	52.2995i	−0.0917224	+	0.0731462i
$716$	829.782	−	62.1835i	1.15891	−	0.0868485i
$717$		0			0
$718$	99.1028	−	657.504i	0.138026	−	0.915744i
$719$	244.153	+	226.541i	0.339574	+	0.315078i	0.831464	−	0.555579i	$-0.187503\pi$
$719$	244.153	+	226.541i	0.339574	+	0.315078i	−0.491890	+	0.870657i	$0.663694\pi$
$720$		0			0
$721$	128.296	+	851.188i	0.177942	+	1.18057i
$722$	26.3433	−	38.6385i	0.0364865	−	0.0535159i
$723$		0			0
$724$	−585.740	−	1014.53i	−0.809034	−	1.40129i
$725$	239.661	+	138.369i	0.330568	+	0.190853i
$726$		0			0
$727$	109.581	−	227.547i	0.150730	−	0.312994i	−0.811908	−	0.583785i	$-0.801571\pi$
$727$	109.581	−	227.547i	0.150730	−	0.312994i	0.962638	+	0.270791i	$0.0872853\pi$
$728$	355.843	+	109.763i	0.488795	+	0.150773i
$729$		0			0
$730$			45.4404i			0.0622472i
$731$	109.010	−	281.420i	0.149125	−	0.384980i
$732$		0			0
$733$	257.938	+	58.8727i	0.351894	+	0.0803175i	0.394814	−	0.918761i	$-0.370809\pi$
$733$	257.938	+	58.8727i	0.351894	+	0.0803175i	−0.0429202	+	0.999079i	$0.513666\pi$
$734$	359.646	−	1165.94i	0.489981	−	1.58848i
$735$		0			0
$736$	1036.28	−	406.711i	1.40799	−	0.552597i
$737$	−396.349	+	686.497i	−0.537787	+	0.931475i
$738$		0			0
$739$	−197.725	−	157.681i	−0.267558	−	0.213370i	0.480516	−	0.876986i	$-0.340450\pi$
$739$	−197.725	−	157.681i	−0.267558	−	0.213370i	−0.748074	+	0.663616i	$0.769021\pi$
$740$	−196.026	−	133.649i	−0.264900	−	0.180606i
$741$		0			0
$742$	−1953.90	+	940.951i	−2.63329	+	1.26813i
$743$	−371.842	+	400.751i	−0.500461	+	0.539368i	−0.931872	−	0.362787i	$-0.881825\pi$
$743$	−371.842	+	400.751i	−0.500461	+	0.539368i	0.431411	+	0.902155i	$0.358016\pi$
$744$		0			0
$745$	−251.860	+	77.6886i	−0.338067	+	0.104280i
$746$	−67.0798	−	895.117i	−0.0899193	−	1.19989i
$747$		0			0
$748$	−162.833	+	414.891i	−0.217691	+	0.554667i
$749$	1053.50	+	1135.41i	1.40655	+	1.51590i
$750$		0			0
$751$	−560.681	−	42.0172i	−0.746579	−	0.0559483i	−0.303993	−	0.952674i	$-0.598320\pi$
$751$	−560.681	−	42.0172i	−0.746579	−	0.0559483i	−0.442586	+	0.896726i	$0.645939\pi$
$752$	28.5153	+	124.934i	0.0379192	+	0.166135i
$753$		0			0
$754$	12.8788	−	171.856i	0.0170807	−	0.227926i
$755$	−330.761	+	225.509i	−0.438094	+	0.298688i
$756$		0			0
$757$	−215.890	−	84.7305i	−0.285191	−	0.111929i	0.218434	−	0.975852i	$-0.429905\pi$
$757$	−215.890	−	84.7305i	−0.285191	−	0.111929i	−0.503625	+	0.863923i	$0.668001\pi$
$758$	−414.514	+	330.564i	−0.546853	+	0.436100i
$759$		0			0
$760$	−119.803	−	388.391i	−0.157635	−	0.511041i
$761$	84.2525	−	558.979i	0.110713	−	0.734532i	−0.862740	−	0.505647i	$-0.831254\pi$
$761$	84.2525	−	558.979i	0.110713	−	0.734532i	0.973453	−	0.228885i	$-0.0735081\pi$
$762$		0			0
$763$	765.103	+	1588.75i	1.00276	+	2.08224i
$764$	108.786	+	721.750i	0.142391	+	0.944700i
$765$		0			0
$766$	711.855	−	892.638i	0.929315	−	1.16532i
$767$	−31.5148	−	54.5853i	−0.0410884	−	0.0711672i
$768$		0			0
$769$	−27.4741	−	70.0030i	−0.0357271	−	0.0910312i	0.911897	−	0.410420i	$-0.134618\pi$
$769$	−27.4741	−	70.0030i	−0.0357271	−	0.0910312i	−0.947624	+	0.319388i	$0.896523\pi$
$770$	−384.065	+	797.519i	−0.498786	+	1.03574i
$771$		0			0
$772$	204.899	−	897.720i	0.265413	−	1.16285i
$773$			922.060i			1.19283i	0.802675	+	0.596416i	$0.203409\pi$
$773$			922.060i			1.19283i	−0.802675	+	0.596416i	$0.796591\pi$
$774$		0			0
$775$	836.531			1.07940
$776$	126.484	+	28.8693i	0.162995	+	0.0372027i
$777$		0			0
$778$	−440.883	−	212.318i	−0.566688	−	0.272903i
$779$	1307.53	−	513.168i	1.67847	−	0.658753i
$780$		0			0
$781$	−157.641	+	91.0140i	−0.201845	+	0.116535i
$782$	−706.941	−	563.767i	−0.904017	−	0.720930i
$783$		0			0
$784$	188.426	−	28.4007i	0.240339	−	0.0362253i
$785$	−166.005	+	79.9439i	−0.211472	+	0.101839i
$786$		0			0
$787$	−180.076	−	27.1421i	−0.228813	−	0.0344880i	0.0336348	−	0.999434i	$-0.489292\pi$
$787$	−180.076	−	27.1421i	−0.228813	−	0.0344880i	−0.262448	+	0.964946i	$0.584530\pi$
$788$	435.183	−	134.236i	0.552263	−	0.170351i
$789$		0			0
$790$	244.247	+	306.276i	0.309173	+	0.387691i
$791$	−47.8098	+	121.817i	−0.0604422	+	0.154004i
$792$		0			0
$793$	−133.355	−	195.595i	−0.168165	−	0.246652i
$794$	−1912.14	−	143.295i	−2.40824	−	0.180473i
$795$		0			0
$796$	1467.03	−	334.839i	1.84300	−	0.420652i
$797$	−72.2574	+	964.208i	−0.0906617	+	1.20980i	0.747457	+	0.664310i	$0.231274\pi$
$797$	−72.2574	+	964.208i	−0.0906617	+	1.20980i	−0.838119	+	0.545487i	$0.816345\pi$
$798$		0			0
$799$	−298.320	+	276.800i	−0.373366	+	0.346433i
$800$	499.059	+	195.866i	0.623823	+	0.244833i
$801$		0			0
$802$	922.384	−	69.1231i	1.15010	−	0.0861884i
$803$	−15.7468	−	51.0497i	−0.0196099	−	0.0635738i
$804$		0			0
$805$	−824.884	−	765.380i	−1.02470	−	0.950783i
$806$	−226.031	−	469.359i	−0.280436	−	0.582331i
$807$		0			0
$808$	−62.1362	+	91.1371i	−0.0769013	+	0.112793i
$809$	446.873	−	560.361i	0.552377	−	0.692659i	−0.424751	−	0.905310i	$-0.639638\pi$
$809$	446.873	−	560.361i	0.552377	−	0.692659i	0.977128	+	0.212652i	$0.0682099\pi$
$810$		0			0
$811$	1049.80	+	606.103i	1.29445	+	0.747353i	0.979440	−	0.201734i	$-0.0646578\pi$
$811$	1049.80	+	606.103i	1.29445	+	0.747353i	0.315013	+	0.949087i	$0.397991\pi$
$812$	−416.334	−	1060.80i	−0.512726	−	1.30641i
$813$		0			0
$814$	425.364	+	131.207i	0.522560	+	0.161188i
$815$	−45.3201	+	198.561i	−0.0556075	+	0.243633i
$816$		0			0
$817$	−453.965	−	659.535i	−0.555648	−	0.807265i
$818$	1842.26			2.25215
$819$		0			0
$820$	−366.944	+	1189.60i	−0.447492	+	1.45073i
$821$	784.204	+	377.653i	0.955181	+	0.459991i	0.845500	−	0.533976i	$-0.179303\pi$
$821$	784.204	+	377.653i	0.955181	+	0.459991i	0.109681	+	0.993967i	$0.465017\pi$
$822$		0			0
$823$	−216.675	+	375.292i	−0.263275	+	0.456005i	−0.967110	−	0.254358i	$-0.918136\pi$
$823$	−216.675	+	375.292i	−0.263275	+	0.456005i	0.703835	+	0.710363i	$0.251469\pi$
$824$	−569.210	+	328.634i	−0.690789	+	0.398827i
$825$		0			0
$826$	−549.558	−	374.682i	−0.665324	−	0.453610i
$827$	455.928	−	68.7201i	0.551304	−	0.0830957i	0.132518	−	0.991181i	$-0.457694\pi$
$827$	455.928	−	68.7201i	0.551304	−	0.0830957i	0.418786	+	0.908085i	$0.362456\pi$
$828$		0			0
$829$	−494.890	+	533.364i	−0.596972	+	0.643383i	−0.957181	−	0.289489i	$-0.906515\pi$
$829$	−494.890	+	533.364i	−0.596972	+	0.643383i	0.360210	+	0.932871i	$0.382705\pi$
$830$	−428.744	−	64.6228i	−0.516560	−	0.0778588i
$831$		0			0
$832$	−27.3326	−	364.728i	−0.0328517	−	0.438376i
$833$	377.302	+	473.122i	0.452944	+	0.567974i
$834$		0			0
$835$	174.561	+	188.132i	0.209055	+	0.225308i
$836$	666.099	+	976.987i	0.796769	+	1.16864i
$837$		0			0
$838$	310.612	+	1360.88i	0.370659	+	1.62396i
$839$	−1271.59	+	290.232i	−1.51560	+	0.345927i	−0.897799	−	0.440405i	$-0.854835\pi$
$839$	−1271.59	+	290.232i	−1.51560	+	0.345927i	−0.617805	+	0.786332i	$0.711978\pi$
$840$		0			0
$841$	518.773	−	353.693i	0.616852	−	0.420563i
$842$	−1668.47	+	1548.11i	−1.98155	+	1.83861i
$843$		0			0
$844$	−398.391	+	317.706i	−0.472027	+	0.376429i
$845$	382.424	−	28.6587i	0.452573	−	0.0339157i
$846$		0			0
$847$	−54.6035	+	362.270i	−0.0644669	+	0.427710i
$848$	−92.3121	−	85.6531i	−0.108859	−	0.101006i
$849$		0			0
$850$	−64.9012	−	430.591i	−0.0763543	−	0.506578i
$851$	−318.771	+	467.551i	−0.374584	+	0.549413i
$852$		0			0
$853$	−93.8036	−	162.473i	−0.109969	−	0.190472i	0.805788	−	0.592204i	$-0.201742\pi$
$853$	−93.8036	−	162.473i	−0.109969	−	0.190472i	−0.915757	+	0.401732i	$0.868409\pi$
$854$	−2163.45	−	1249.07i	−2.53331	−	1.46261i
$855$		0			0
$856$	−513.131	+	1065.53i	−0.599452	+	1.24478i
$857$	346.797	+	106.973i	0.404663	+	0.124822i	0.490404	−	0.871495i	$-0.336849\pi$
$857$	346.797	+	106.973i	0.404663	+	0.124822i	−0.0857403	+	0.996318i	$0.527326\pi$
$858$		0			0
$859$		−	1532.37i		−	1.78390i	−0.452136	−	0.891949i	$-0.649338\pi$
$859$		−	1532.37i		−	1.78390i	0.452136	−	0.891949i	$-0.350662\pi$
$860$	707.870	+	49.8891i	0.823105	+	0.0580106i
$861$		0			0
$862$	−859.169	−	196.100i	−0.996716	−	0.227494i
$863$	−44.9242	+	145.641i	−0.0520558	+	0.168761i	−0.977868	−	0.209223i	$-0.932906\pi$
$863$	−44.9242	+	145.641i	−0.0520558	+	0.168761i	0.925812	+	0.377984i	$0.123383\pi$
$864$		0			0
$865$	90.7423	−	35.6137i	0.104904	−	0.0411719i
$866$	721.074	−	1248.94i	0.832649	−	1.44219i
$867$		0			0
$868$	−2693.21	−	2147.77i	−3.10278	−	2.47439i
$869$	−380.533	−	259.443i	−0.437898	−	0.298553i
$870$		0			0
$871$	−272.289	+	131.128i	−0.312617	+	0.150548i
$872$	−915.807	+	987.005i	−1.05024	+	1.13189i
$873$		0			0
$874$	−2292.31	+	707.085i	−2.62278	+	0.809022i
$875$	−93.9069	−	1253.10i	−0.107322	−	1.43211i
$876$		0			0
$877$	−298.439	+	760.411i	−0.340296	+	0.867059i	0.653611	+	0.756831i	$0.273253\pi$
$877$	−298.439	+	760.411i	−0.340296	+	0.867059i	−0.993906	+	0.110228i	$0.964842\pi$
$878$	−80.2585	−	86.4981i	−0.0914106	−	0.0985172i
$879$		0			0
$880$	−51.2561	−	3.84111i	−0.0582456	−	0.00436490i
$881$	−141.130	−	618.332i	−0.160193	−	0.701852i	−0.989676	−	0.143320i	$-0.954222\pi$
$881$	−141.130	−	618.332i	−0.160193	−	0.701852i	0.829483	−	0.558532i	$-0.188635\pi$
$882$		0			0
$883$	30.1205	−	401.930i	0.0341115	−	0.455186i	−0.953829	−	0.300351i	$-0.902896\pi$
$883$	30.1205	−	401.930i	0.0341115	−	0.455186i	0.987940	−	0.154835i	$-0.0494847\pi$
$884$	−140.398	+	95.7218i	−0.158821	+	0.108283i
$885$		0			0
$886$	−926.333	−	363.559i	−1.04552	−	0.410337i
$887$	1012.88	−	807.743i	1.14191	−	0.910646i	0.145022	−	0.989428i	$-0.453675\pi$
$887$	1012.88	−	807.743i	1.14191	−	0.910646i	0.996892	+	0.0787829i	$0.0251034\pi$
$888$		0			0
$889$	314.754	+	1020.41i	0.354054	+	1.14781i
$890$	89.7114	−	595.196i	0.100799	−	0.668760i
$891$		0			0
$892$	−619.138	−	1285.65i	−0.694101	−	1.44131i
$893$	160.915	+	1067.60i	0.180196	+	1.19552i
$894$		0			0
$895$	−190.007	+	238.261i	−0.212298	+	0.266213i
$896$	−1272.07	−	2203.29i	−1.41972	−	2.45903i
$897$		0			0
$898$	−570.218	−	1452.89i	−0.634986	−	1.61792i
$899$	−279.529	+	580.448i	−0.310933	+	0.645660i
$900$		0			0
$901$	88.9888	−	389.886i	0.0987667	−	0.432725i
$902$		−	2335.74i		−	2.58952i
$903$		0			0
$904$	−99.9210			−0.110532
$905$	418.280	+	95.4697i	0.462188	+	0.105491i
$906$		0			0
$907$	−725.157	−	349.217i	−0.799511	−	0.385024i	−0.0109188	−	0.999940i	$-0.503476\pi$
$907$	−725.157	−	349.217i	−0.799511	−	0.385024i	−0.788593	+	0.614916i	$0.789190\pi$
$908$	353.746	−	138.835i	0.389588	−	0.152902i
$909$		0			0
$910$	−292.264	+	168.738i	−0.321169	+	0.185427i
$911$	−503.627	−	401.630i	−0.552829	−	0.440867i	0.306808	−	0.951771i	$-0.400739\pi$
$911$	−503.627	−	401.630i	−0.552829	−	0.440867i	−0.859637	+	0.510905i	$0.829310\pi$
$912$		0			0
$913$	504.064	−	75.9754i	0.552096	−	0.0832151i
$914$	−792.952	+	381.866i	−0.867563	+	0.417796i
$915$		0			0
$916$	662.219	+	99.8134i	0.722946	+	0.108967i
$917$	−2760.69	+	851.559i	−3.01056	+	0.928636i
$918$		0			0
$919$	−593.448	−	744.160i	−0.645754	−	0.809750i	0.345955	−	0.938251i	$-0.387555\pi$
$919$	−593.448	−	744.160i	−0.645754	−	0.809750i	−0.991709	+	0.128501i	$0.958984\pi$
$920$	313.903	−	799.811i	0.341198	−	0.869359i
$921$		0			0
$922$	−176.347	−	258.654i	−0.191266	−	0.280536i
$923$	−69.2046	−	5.18616i	−0.0749779	−	0.00561881i
$924$		0			0
$925$	−265.686	+	60.6411i	−0.287228	+	0.0655579i
$926$	−82.5218	+	1101.18i	−0.0891164	+	1.18918i
$927$		0			0
$928$	−302.668	+	280.835i	−0.326151	+	0.302624i
$929$	−894.206	−	350.950i	−0.962546	−	0.377772i	−0.168549	−	0.985693i	$-0.553908\pi$
$929$	−894.206	−	350.950i	−0.962546	−	0.377772i	−0.793997	+	0.607922i	$0.792003\pi$
$930$		0			0
$931$	1600.97	−	119.976i	1.71963	−	0.128868i
$932$	−365.862	−	1186.10i	−0.392556	−	1.27264i
$933$		0			0
$934$	1303.57	+	1209.54i	1.39569	+	1.29501i
$935$	−70.8233	−	147.066i	−0.0757468	−	0.157290i
$936$		0			0
$937$	−114.430	+	167.838i	−0.122124	+	0.179123i	−0.882432	−	0.470439i	$-0.844095\pi$
$937$	−114.430	+	167.838i	−0.122124	+	0.179123i	0.760308	+	0.649562i	$0.225048\pi$
$938$	−1988.44	+	2493.43i	−2.11987	+	2.65824i
$939$		0			0
$940$	−828.695	−	478.447i	−0.881590	−	0.508986i
$941$	537.978	+	1370.74i	0.571708	+	1.45669i	0.865544	+	0.500833i	$0.166973\pi$
$941$	537.978	+	1370.74i	0.571708	+	1.45669i	−0.293835	+	0.955856i	$0.594932\pi$
$942$		0			0
$943$	2837.37	+	875.213i	3.00888	+	0.928115i
$944$	8.59427	−	37.6539i	0.00910410	−	0.0398877i
$945$		0			0
$946$	−1296.72	+	302.028i	−1.37074	+	0.319269i
$947$	−552.695			−0.583627			−0.291813	−	0.956475i	$-0.594259\pi$
$947$	−552.695			−0.583627			−0.291813	+	0.956475i	$0.594259\pi$
$948$		0			0
$949$	6.00349	−	19.4628i	0.00632612	−	0.0205088i
$950$	−1040.86	−	501.253i	−1.09564	−	0.527634i
$951$		0			0
$952$	−362.325	+	627.566i	−0.380594	+	0.659208i
$953$	731.605	−	422.392i	0.767686	−	0.443224i	−0.0643624	−	0.997927i	$-0.520501\pi$
$953$	731.605	−	422.392i	0.767686	−	0.443224i	0.832049	+	0.554703i	$0.187168\pi$
$954$		0			0
$955$	−220.867	−	150.584i	−0.231274	−	0.157680i
$956$	1119.00	−	168.663i	1.17051	−	0.176425i
$957$		0			0
$958$	434.327	−	468.093i	0.453369	−	0.488615i
$959$	163.059	+	24.5773i	0.170031	+	0.0256280i
$960$		0			0
$961$	73.7182	+	983.701i	0.0767099	+	1.02362i
$962$	105.813	+	132.685i	0.109993	+	0.137926i
$963$		0			0
$964$	101.186	+	109.053i	0.104965	+	0.113125i
$965$	189.969	+	278.633i	0.196859	+	0.288739i
$966$		0			0
$967$	−48.7643	−	213.650i	−0.0504285	−	0.220942i	0.943435	−	0.331559i	$-0.107574\pi$
$967$	−48.7643	−	213.650i	−0.0504285	−	0.220942i	−0.993863	+	0.110617i	$0.964717\pi$
$968$	−272.723	+	62.2472i	−0.281739	+	0.0643050i
$969$		0			0
$970$	−97.1449	+	66.2323i	−0.100149	+	0.0682807i
$971$	907.664	−	842.189i	0.934772	−	0.867342i	−0.0566027	−	0.998397i	$-0.518027\pi$
$971$	907.664	−	842.189i	0.934772	−	0.867342i	0.991375	+	0.131055i	$0.0418364\pi$
$972$		0			0
$973$	1684.26	−	1343.15i	1.73100	−	1.38043i
$974$	2363.65	−	177.131i	2.42674	−	0.181859i
$975$		0			0
$976$	21.6200	−	143.439i	0.0221516	−	0.146966i
$977$	−1187.30	−	1101.65i	−1.21525	−	1.12759i	−0.988113	−	0.153727i	$-0.950872\pi$
$977$	−1187.30	−	1101.65i	−1.21525	−	1.12759i	−0.227139	−	0.973862i	$-0.572937\pi$
$978$		0			0
$979$	105.471	+	699.757i	0.107734	+	0.714767i
$980$	−801.552	+	1175.66i	−0.817910	+	1.19965i
$981$		0			0
$982$	−119.209	−	206.476i	−0.121394	−	0.210260i
$983$	682.278	+	393.914i	0.694078	+	0.400726i	0.805138	−	0.593088i	$-0.202091\pi$
$983$	682.278	+	393.914i	0.694078	+	0.400726i	−0.111060	+	0.993814i	$0.535425\pi$
$984$		0			0
$985$	−72.3671	+	150.272i	−0.0734691	+	0.152560i
$986$	320.463	+	98.8499i	0.325014	+	0.100253i
$987$		0			0
$988$			450.812i			0.456288i
$989$	118.993	−	1688.37i	0.120316	−	1.70715i
$990$		0			0
$991$	−559.554	−	127.715i	−0.564636	−	0.128874i	−0.0693310	−	0.997594i	$-0.522086\pi$
$991$	−559.554	−	127.715i	−0.564636	−	0.128874i	−0.495305	+	0.868719i	$0.664944\pi$
$992$	−367.882	+	1192.64i	−0.370849	+	1.20226i
$993$		0			0
$994$	−681.718	+	267.555i	−0.685833	+	0.269170i
$995$	−275.546	+	477.260i	−0.276931	+	0.479658i
$996$		0			0
$997$	−76.9037	−	61.3287i	−0.0771351	−	0.0615132i	0.584163	−	0.811636i	$-0.301423\pi$
$997$	−76.9037	−	61.3287i	−0.0771351	−	0.0615132i	−0.661298	+	0.750123i	$0.729994\pi$
$998$	−516.905	−	352.420i	−0.517941	−	0.353126i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.3.bn.b.91.6		72
3.2	odd	2		43.3.h.a.5.1	✓	72
43.26	odd	42	inner	387.3.bn.b.370.6		72
129.26	even	42		43.3.h.a.26.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.3.h.a.5.1	✓	72	3.2	odd	2
43.3.h.a.26.1	yes	72	129.26	even	42
387.3.bn.b.91.6		72	1.1	even	1	trivial
387.3.bn.b.370.6		72	43.26	odd	42	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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	387.bn (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(3.19097 + 0.728319i) q^{2} +(6.04798 + 2.91256i) q^{4} +(-2.28850 + 0.898170i) q^{5} +(10.0706 - 5.81424i) q^{7} +(6.94183 + 5.53593i) q^{8} +O(q^{10})\)	\(q+(3.19097 + 0.728319i) q^{2} +(6.04798 + 2.91256i) q^{4} +(-2.28850 + 0.898170i) q^{5} +(10.0706 - 5.81424i) q^{7} +(6.94183 + 5.53593i) q^{8} +(-7.95670 + 1.19928i) q^{10} +(8.52330 - 4.10460i) q^{11} +(3.56642 + 0.537551i) q^{13} +(36.3695 - 11.2185i) q^{14} +(1.37795 + 1.72789i) q^{16} +(-2.56415 + 6.53334i) q^{17} +(10.4891 + 15.3847i) q^{19} +(-16.4568 - 1.23327i) q^{20} +(30.1871 - 6.89000i) q^{22} +(-2.94151 + 39.2518i) q^{23} +(-13.8958 + 12.8934i) q^{25} +(10.9888 + 4.31280i) q^{26} +(77.8409 - 5.83337i) q^{28} +(-4.30310 - 13.9503i) q^{29} +(-32.3496 - 30.0160i) q^{31} +(-12.2712 - 25.4814i) q^{32} +(-12.9405 + 18.9802i) q^{34} +(-17.8243 + 22.3510i) q^{35} +(12.4503 + 7.18816i) q^{37} +(22.2656 + 56.7317i) q^{38} +(-20.8586 - 6.43402i) q^{40} +(16.7860 - 73.5444i) q^{41} +(-42.9996 + 0.190850i) q^{43} +63.5036 q^{44} +(-37.9741 + 123.109i) q^{46} +(52.2411 + 25.1580i) q^{47} +(43.1108 - 74.6700i) q^{49} +(-53.7315 + 31.0219i) q^{50} +(20.0040 + 13.6385i) q^{52} +(-56.3433 + 8.49238i) q^{53} +(-15.8189 + 17.0488i) q^{55} +(102.095 + 15.3884i) q^{56} +(-3.57080 - 47.6490i) q^{58} +(-10.8959 - 13.6630i) q^{59} +(-44.6438 - 48.1146i) q^{61} +(-81.3654 - 119.341i) q^{62} +(-22.5656 - 98.8662i) q^{64} +(-8.64456 + 1.97307i) q^{65} +(-69.2334 + 47.2025i) q^{67} +(-34.5366 + 32.0453i) q^{68} +(-73.1555 + 58.3395i) q^{70} +(-19.1878 + 1.43792i) q^{71} +(0.841669 - 5.58411i) q^{73} +(34.4932 + 32.0050i) q^{74} +(18.6292 + 123.597i) q^{76} +(61.9692 - 90.8921i) q^{77} +(-24.3421 - 42.1618i) q^{79} +(-4.70538 - 2.71665i) q^{80} +(107.127 - 222.453i) q^{82} +(51.4908 + 15.8828i) q^{83} -17.2546i q^{85} +(-137.349 - 30.7084i) q^{86} +(81.8901 + 18.6909i) q^{88} +(-22.0490 + 71.4811i) q^{89} +(39.0413 - 15.3226i) q^{91} +(-132.113 + 228.827i) q^{92} +(148.377 + 118.327i) q^{94} +(-37.8225 - 25.7869i) q^{95} +(13.1648 - 6.33982i) q^{97} +(191.949 - 206.872i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 14 q^{2} + 12 q^{4} + 11 q^{5} - 30 q^{7} + 42 q^{8}+O(q^{10}) \) 72 * q + 14 * q^2 + 12 * q^4 + 11 * q^5 - 30 * q^7 + 42 * q^8	\( 72 q + 14 q^{2} + 12 q^{4} + 11 q^{5} - 30 q^{7} + 42 q^{8} - 13 q^{10} + 42 q^{11} - 24 q^{13} + 108 q^{14} - 40 q^{16} + 7 q^{17} - 38 q^{19} + 55 q^{20} - 98 q^{22} - 30 q^{23} + 49 q^{25} + 79 q^{26} + 66 q^{28} - 27 q^{29} + 330 q^{31} - 56 q^{32} + 109 q^{34} + 31 q^{35} + 69 q^{37} - 262 q^{38} + 239 q^{40} + 94 q^{41} - 19 q^{43} + 64 q^{44} - 9 q^{46} + 66 q^{47} - 6 q^{49} + 495 q^{50} - 452 q^{52} - 16 q^{53} + 328 q^{55} + 1015 q^{56} - 420 q^{58} + 245 q^{59} - 50 q^{61} + 191 q^{62} - 306 q^{64} + 182 q^{65} + 599 q^{67} - 757 q^{68} - 287 q^{70} - 367 q^{71} + 486 q^{73} - 1656 q^{74} + 746 q^{76} - 79 q^{77} + 261 q^{79} - 138 q^{80} + 364 q^{82} + 220 q^{83} + 284 q^{86} - 490 q^{88} + 564 q^{89} - 145 q^{91} + 406 q^{92} - 1666 q^{94} + 353 q^{95} - 99 q^{97} + 500 q^{98}+O(q^{100}) \) 72 * q + 14 * q^2 + 12 * q^4 + 11 * q^5 - 30 * q^7 + 42 * q^8 - 13 * q^10 + 42 * q^11 - 24 * q^13 + 108 * q^14 - 40 * q^16 + 7 * q^17 - 38 * q^19 + 55 * q^20 - 98 * q^22 - 30 * q^23 + 49 * q^25 + 79 * q^26 + 66 * q^28 - 27 * q^29 + 330 * q^31 - 56 * q^32 + 109 * q^34 + 31 * q^35 + 69 * q^37 - 262 * q^38 + 239 * q^40 + 94 * q^41 - 19 * q^43 + 64 * q^44 - 9 * q^46 + 66 * q^47 - 6 * q^49 + 495 * q^50 - 452 * q^52 - 16 * q^53 + 328 * q^55 + 1015 * q^56 - 420 * q^58 + 245 * q^59 - 50 * q^61 + 191 * q^62 - 306 * q^64 + 182 * q^65 + 599 * q^67 - 757 * q^68 - 287 * q^70 - 367 * q^71 + 486 * q^73 - 1656 * q^74 + 746 * q^76 - 79 * q^77 + 261 * q^79 - 138 * q^80 + 364 * q^82 + 220 * q^83 + 284 * q^86 - 490 * q^88 + 564 * q^89 - 145 * q^91 + 406 * q^92 - 1666 * q^94 + 353 * q^95 - 99 * q^97 + 500 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more