LMFDB - Embedded newform 735.2.g.c.734.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(734,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("735.734");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.g (of order $2$, degree $1$, 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			734.10
Character	$\chi$	$=$	735.734
Dual form			735.2.g.c.734.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.903339 q^{2} +(-1.72180 + 0.188163i) q^{3} -1.18398 q^{4} +(-1.94641 + 1.10068i) q^{5} +(1.55537 - 0.169975i) q^{6} +2.87621 q^{8} +(2.92919 - 0.647957i) q^{9} +(1.75827 - 0.994285i) q^{10} -4.06437i q^{11} +(2.03858 - 0.222781i) q^{12} +2.88298 q^{13} +(3.14422 - 2.26139i) q^{15} -0.230234 q^{16} +6.66864i q^{17} +(-2.64605 + 0.585325i) q^{18} -5.70701i q^{19} +(2.30451 - 1.30318i) q^{20} +3.67151i q^{22} -1.63185 q^{23} +(-4.95226 + 0.541196i) q^{24} +(2.57701 - 4.28474i) q^{25} -2.60431 q^{26} +(-4.92156 + 1.66682i) q^{27} +5.89707i q^{29} +(-2.84029 + 2.04280i) q^{30} +1.87068i q^{31} -5.54444 q^{32} +(0.764764 + 6.99804i) q^{33} -6.02404i q^{34} +(-3.46810 + 0.767168i) q^{36} +1.59973i q^{37} +5.15537i q^{38} +(-4.96392 + 0.542470i) q^{39} +(-5.59828 + 3.16578i) q^{40} -9.12244 q^{41} -7.53359i q^{43} +4.81213i q^{44} +(-4.98821 + 4.48529i) q^{45} +1.47412 q^{46} +6.91446i q^{47} +(0.396417 - 0.0433215i) q^{48} +(-2.32792 + 3.87057i) q^{50} +(-1.25479 - 11.4821i) q^{51} -3.41339 q^{52} -1.51865 q^{53} +(4.44583 - 1.50570i) q^{54} +(4.47357 + 7.91093i) q^{55} +(1.07385 + 9.82633i) q^{57} -5.32705i q^{58} +0.991850 q^{59} +(-3.72269 + 2.67744i) q^{60} +6.16485i q^{61} -1.68986i q^{62} +5.46898 q^{64} +(-5.61146 + 3.17324i) q^{65} +(-0.690841 - 6.32160i) q^{66} +10.0903i q^{67} -7.89553i q^{68} +(2.80973 - 0.307054i) q^{69} +4.81213i q^{71} +(8.42497 - 1.86366i) q^{72} -0.560619 q^{73} -1.44510i q^{74} +(-3.63087 + 7.86236i) q^{75} +6.75699i q^{76} +(4.48410 - 0.490034i) q^{78} +3.79848 q^{79} +(0.448130 - 0.253414i) q^{80} +(8.16030 - 3.79598i) q^{81} +8.24065 q^{82} -4.00431i q^{83} +(-7.34003 - 12.9799i) q^{85} +6.80539i q^{86} +(-1.10961 - 10.1536i) q^{87} -11.6900i q^{88} -10.4109 q^{89} +(4.50604 - 4.05173i) q^{90} +1.93208 q^{92} +(-0.351993 - 3.22094i) q^{93} -6.24610i q^{94} +(6.28159 + 11.1082i) q^{95} +(9.54642 - 1.04326i) q^{96} -14.5370 q^{97} +(-2.63354 - 11.9053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 40 q^{9} + 16 q^{15} - 16 q^{16} + 64 q^{25} + 56 q^{30} - 16 q^{36} - 56 q^{39} - 32 q^{46} - 40 q^{51} + 8 q^{60} - 176 q^{64} + 48 q^{79} - 40 q^{81} - 64 q^{85} + 40 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 + 40 * q^9 + 16 * q^15 - 16 * q^16 + 64 * q^25 + 56 * q^30 - 16 * q^36 - 56 * q^39 - 32 * q^46 - 40 * q^51 + 8 * q^60 - 176 * q^64 + 48 * q^79 - 40 * q^81 - 64 * q^85 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.903339			−0.638757			−0.319378	−	0.947627i	$-0.603474\pi$
$2$	−0.903339			−0.638757			−0.319378	+	0.947627i	$0.603474\pi$
$3$	−1.72180	+	0.188163i	−0.994082	+	0.108636i
$3$	−1.72180	+	0.188163i	−0.994082	+	0.108636i
$4$	−1.18398			−0.591990
$5$	−1.94641	+	1.10068i	−0.870460	+	0.492238i
$5$	−1.94641	+	1.10068i	−0.870460	+	0.492238i
$6$	1.55537	−	0.169975i	0.634976	−	0.0693919i
$7$		0			0
$7$		0			0
$8$	2.87621			1.01689
$9$	2.92919	−	0.647957i	0.976396	−	0.215986i
$10$	1.75827	−	0.994285i	0.556013	−	0.314421i
$11$		−	4.06437i		−	1.22545i	−0.790294	−	0.612727i	$-0.790072\pi$
$11$		−	4.06437i		−	1.22545i	0.790294	−	0.612727i	$-0.209928\pi$
$12$	2.03858	−	0.222781i	0.588486	−	0.0643113i
$13$	2.88298			0.799595			0.399798	−	0.916603i	$-0.369080\pi$
$13$	2.88298			0.799595			0.399798	+	0.916603i	$0.369080\pi$
$14$		0			0
$15$	3.14422	−	2.26139i	0.811834	−	0.583888i
$16$	−0.230234			−0.0575586
$17$			6.66864i			1.61738i	0.588233	+	0.808691i	$0.299824\pi$
$17$			6.66864i			1.61738i	−0.588233	+	0.808691i	$0.700176\pi$
$18$	−2.64605	+	0.585325i	−0.623680	+	0.137962i
$19$		−	5.70701i		−	1.30928i	−0.755941	−	0.654639i	$-0.772821\pi$
$19$		−	5.70701i		−	1.30928i	0.755941	−	0.654639i	$-0.227179\pi$
$20$	2.30451	−	1.30318i	0.515304	−	0.291400i
$21$		0			0
$22$			3.67151i			0.782768i
$23$	−1.63185			−0.340265			−0.170133	−	0.985421i	$-0.554420\pi$
$23$	−1.63185			−0.340265			−0.170133	+	0.985421i	$0.554420\pi$
$24$	−4.95226	+	0.541196i	−1.01088	+	0.110471i
$25$	2.57701	−	4.28474i	0.515403	−	0.856948i
$26$	−2.60431			−0.510747
$27$	−4.92156	+	1.66682i	−0.947154	+	0.320779i
$28$		0			0
$29$			5.89707i			1.09506i	0.836786	+	0.547530i	$0.184432\pi$
$29$			5.89707i			1.09506i	−0.836786	+	0.547530i	$0.815568\pi$
$30$	−2.84029	+	2.04280i	−0.518565	+	0.372963i
$31$			1.87068i			0.335985i	0.985788	+	0.167992i	$0.0537284\pi$
$31$			1.87068i			0.335985i	−0.985788	+	0.167992i	$0.946272\pi$
$32$	−5.54444			−0.980128
$33$	0.764764	+	6.99804i	0.133128	+	1.21820i
$34$		−	6.02404i		−	1.03311i
$35$		0			0
$36$	−3.46810	+	0.767168i	−0.578017	+	0.127861i
$37$			1.59973i			0.262994i	0.991317	+	0.131497i	$0.0419783\pi$
$37$			1.59973i			0.262994i	−0.991317	+	0.131497i	$0.958022\pi$
$38$			5.15537i			0.836311i
$39$	−4.96392	+	0.542470i	−0.794863	+	0.0868647i
$40$	−5.59828	+	3.16578i	−0.885166	+	0.500554i
$41$	−9.12244			−1.42469			−0.712343	−	0.701832i	$-0.752366\pi$
$41$	−9.12244			−1.42469			−0.712343	+	0.701832i	$0.752366\pi$
$42$		0			0
$43$		−	7.53359i		−	1.14886i	−0.818553	−	0.574431i	$-0.805223\pi$
$43$		−	7.53359i		−	1.14886i	0.818553	−	0.574431i	$-0.194777\pi$
$44$			4.81213i			0.725456i
$45$	−4.98821	+	4.48529i	−0.743598	+	0.668627i
$46$	1.47412			0.217347
$47$			6.91446i			1.00858i	0.863535	+	0.504289i	$0.168245\pi$
$47$			6.91446i			1.00858i	−0.863535	+	0.504289i	$0.831755\pi$
$48$	0.396417	−	0.0433215i	0.0572179	−	0.00625292i
$49$		0			0
$50$	−2.32792	+	3.87057i	−0.329217	+	0.547381i
$51$	−1.25479	−	11.4821i	−0.175706	−	1.60781i
$52$	−3.41339			−0.473352
$53$	−1.51865			−0.208603			−0.104301	−	0.994546i	$-0.533261\pi$
$53$	−1.51865			−0.208603			−0.104301	+	0.994546i	$0.533261\pi$
$54$	4.44583	−	1.50570i	0.605001	−	0.204900i
$55$	4.47357	+	7.91093i	0.603216	+	1.06671i
$56$		0			0
$57$	1.07385	+	9.82633i	0.142235	+	1.30153i
$58$		−	5.32705i		−	0.699477i
$59$	0.991850			0.129128			0.0645640	−	0.997914i	$-0.479434\pi$
$59$	0.991850			0.129128			0.0645640	+	0.997914i	$0.479434\pi$
$60$	−3.72269	+	2.67744i	−0.480597	+	0.345656i
$61$			6.16485i			0.789328i	0.918825	+	0.394664i	$0.129139\pi$
$61$			6.16485i			0.789328i	−0.918825	+	0.394664i	$0.870861\pi$
$62$		−	1.68986i		−	0.214612i
$63$		0			0
$64$	5.46898			0.683622
$65$	−5.61146	+	3.17324i	−0.696016	+	0.393591i
$66$	−0.690841	−	6.32160i	−0.0850366	−	0.778135i
$67$			10.0903i			1.23272i	0.787464	+	0.616361i	$0.211394\pi$
$67$			10.0903i			1.23272i	−0.787464	+	0.616361i	$0.788606\pi$
$68$		−	7.89553i		−	0.957474i
$69$	2.80973	−	0.307054i	0.338251	−	0.0369650i
$70$		0			0
$71$			4.81213i			0.571095i	0.958365	+	0.285548i	$0.0921755\pi$
$71$			4.81213i			0.571095i	−0.958365	+	0.285548i	$0.907825\pi$
$72$	8.42497	−	1.86366i	0.992892	−	0.219635i
$73$	−0.560619			−0.0656154			−0.0328077	−	0.999462i	$-0.510445\pi$
$73$	−0.560619			−0.0656154			−0.0328077	+	0.999462i	$0.510445\pi$
$74$		−	1.44510i		−	0.167989i
$75$	−3.63087	+	7.86236i	−0.419257	+	0.907868i
$76$			6.75699i			0.775079i
$77$		0			0
$78$	4.48410	−	0.490034i	0.507724	−	0.0554854i
$79$	3.79848			0.427362			0.213681	−	0.976904i	$-0.431455\pi$
$79$	3.79848			0.427362			0.213681	+	0.976904i	$0.431455\pi$
$80$	0.448130	−	0.253414i	0.0501024	−	0.0283325i
$81$	8.16030	−	3.79598i	0.906700	−	0.421776i
$82$	8.24065			0.910028
$83$		−	4.00431i		−	0.439530i	−0.975553	−	0.219765i	$-0.929471\pi$
$83$		−	4.00431i		−	0.439530i	0.975553	−	0.219765i	$-0.0705291\pi$
$84$		0			0
$85$	−7.34003	−	12.9799i	−0.796138	−	1.40787i
$86$			6.80539i			0.733844i
$87$	−1.10961	−	10.1536i	−0.118963	−	1.08858i
$88$		−	11.6900i		−	1.24616i
$89$	−10.4109			−1.10356			−0.551779	−	0.833990i	$-0.686051\pi$
$89$	−10.4109			−1.10356			−0.551779	+	0.833990i	$0.686051\pi$
$90$	4.50604	−	4.05173i	0.474978	−	0.427090i
$91$		0			0
$92$	1.93208			0.201433
$93$	−0.351993	−	3.22094i	−0.0365000	−	0.333996i
$94$		−	6.24610i		−	0.644236i
$95$	6.28159	+	11.1082i	0.644477	+	1.13968i
$96$	9.54642	−	1.04326i	0.974328	−	0.106477i
$97$	−14.5370			−1.47601			−0.738006	−	0.674795i	$-0.764232\pi$
$97$	−14.5370			−1.47601			−0.738006	+	0.674795i	$0.764232\pi$
$98$		0			0
$99$	−2.63354	−	11.9053i	−0.264681	−	1.19653i
$100$	−3.05113	+	5.07304i	−0.305113	+	0.507304i
$101$	13.7973			1.37289			0.686443	−	0.727183i	$-0.259171\pi$
$101$	13.7973			1.37289			0.686443	+	0.727183i	$0.259171\pi$
$102$	1.13350	+	10.3722i	0.112233	+	1.02700i
$103$	−8.31359			−0.819162			−0.409581	−	0.912274i	$-0.634325\pi$
$103$	−8.31359			−0.819162			−0.409581	+	0.912274i	$0.634325\pi$
$104$	8.29206			0.813104
$105$		0			0
$106$	1.37186			0.133246
$107$	−10.7371			−1.03799			−0.518996	−	0.854777i	$-0.673694\pi$
$107$	−10.7371			−1.03799			−0.518996	+	0.854777i	$0.673694\pi$
$108$	5.82702	−	1.97348i	0.560705	−	0.189898i
$109$	0.536675			0.0514042			0.0257021	−	0.999670i	$-0.491818\pi$
$109$	0.536675			0.0514042			0.0257021	+	0.999670i	$0.491818\pi$
$110$	−4.04115	−	7.14625i	−0.385308	−	0.681368i
$111$	−0.301010	−	2.75441i	−0.0285706	−	0.261437i
$112$		0			0
$113$	−12.1028			−1.13854			−0.569270	−	0.822151i	$-0.692774\pi$
$113$	−12.1028			−1.13854			−0.569270	+	0.822151i	$0.692774\pi$
$114$	−0.970048	−	8.87651i	−0.0908533	−	0.831361i
$115$	3.17626	−	1.79615i	0.296187	−	0.167492i
$116$		−	6.98201i		−	0.648264i
$117$	8.44480	−	1.86805i	0.780722	−	0.172701i
$118$	−0.895977			−0.0824813
$119$		0			0
$120$	9.04344	−	6.50424i	0.825549	−	0.593753i
$121$	−5.51913			−0.501739
$122$		−	5.56895i		−	0.504189i
$123$	15.7070	−	1.71650i	1.41625	−	0.154772i
$124$		−	2.21485i		−	0.198899i
$125$	−0.299800	+	11.1763i	−0.0268150	+	0.999640i
$126$		0			0
$127$			22.2883i			1.97777i	0.148697	+	0.988883i	$0.452492\pi$
$127$			22.2883i			1.97777i	−0.148697	+	0.988883i	$0.547508\pi$
$128$	6.14855			0.543460
$129$	1.41754	+	12.9713i	0.124808	+	1.14206i
$130$	5.06905	−	2.86651i	0.444585	−	0.251409i
$131$	−0.114179			−0.00997586			−0.00498793	−	0.999988i	$-0.501588\pi$
$131$	−0.114179			−0.00997586			−0.00498793	+	0.999988i	$0.501588\pi$
$132$	−0.905465	−	8.28553i	−0.0788106	−	0.721163i
$133$		0			0
$134$		−	9.11493i		−	0.787410i
$135$	7.74473	−	8.66136i	0.666560	−	0.745451i
$136$			19.1804i			1.64471i
$137$	12.5438			1.07168			0.535842	−	0.844318i	$-0.319994\pi$
$137$	12.5438			1.07168			0.535842	+	0.844318i	$0.319994\pi$
$138$	−2.53813	+	0.277374i	−0.216060	+	0.0236117i
$139$			2.37640i			0.201564i	0.994909	+	0.100782i	$0.0321344\pi$
$139$			2.37640i			0.201564i	−0.994909	+	0.100782i	$0.967866\pi$
$140$		0			0
$141$	−1.30104	−	11.9053i	−0.109568	−	1.00261i
$142$		−	4.34699i		−	0.364791i
$143$		−	11.7175i		−	0.979868i
$144$	−0.674400	+	0.149182i	−0.0562000	+	0.0124318i
$145$	−6.49078	−	11.4781i	−0.539030	−	0.953206i
$146$	0.506428			0.0419123
$147$		0			0
$148$		−	1.89405i		−	0.155690i
$149$			16.4685i			1.34915i	0.738207	+	0.674575i	$0.235673\pi$
$149$			16.4685i			1.34915i	−0.738207	+	0.674575i	$0.764327\pi$
$150$	3.27991	−	7.10238i	0.267803	−	0.579907i
$151$	−13.1473			−1.06991			−0.534955	−	0.844881i	$-0.679671\pi$
$151$	−13.1473			−1.06991			−0.534955	+	0.844881i	$0.679671\pi$
$152$		−	16.4146i		−	1.33140i
$153$	4.32099	+	19.5337i	0.349332	+	1.57921i
$154$		0			0
$155$	−2.05902	−	3.64111i	−0.165385	−	0.292461i
$156$	5.87717	−	0.642273i	0.470551	−	0.0514230i
$157$	−3.18813			−0.254440			−0.127220	−	0.991874i	$-0.540605\pi$
$157$	−3.18813			−0.254440			−0.127220	+	0.991874i	$0.540605\pi$
$158$	−3.43131			−0.272980
$159$	2.61481	−	0.285753i	0.207368	−	0.0226617i
$160$	10.7918	−	6.10265i	0.853163	−	0.482457i
$161$		0			0
$162$	−7.37152	+	3.42906i	−0.579161	+	0.269412i
$163$			19.2794i			1.51008i	0.655679	+	0.755040i	$0.272383\pi$
$163$			19.2794i			1.51008i	−0.655679	+	0.755040i	$0.727617\pi$
$164$	10.8008			0.843399
$165$	−9.19113	−	12.7793i	−0.715529	−	0.994866i
$166$			3.61725i			0.280753i
$167$			0.883913i			0.0683993i	0.999415	+	0.0341996i	$0.0108882\pi$
$167$			0.883913i			0.0683993i	−0.999415	+	0.0341996i	$0.989112\pi$
$168$		0			0
$169$	−4.68842			−0.360648
$170$	6.63053	+	11.7252i	0.508538	+	0.899285i
$171$	−3.69790	−	16.7169i	−0.282786	−	1.27838i
$172$			8.91962i			0.680114i
$173$		−	12.5161i		−	0.951585i	−0.879558	−	0.475793i	$-0.842161\pi$
$173$		−	12.5161i		−	0.951585i	0.879558	−	0.475793i	$-0.157839\pi$
$174$	1.00235	+	9.17212i	0.0759882	+	0.695337i
$175$		0			0
$176$			0.935758i			0.0705354i
$177$	−1.70777	+	0.186629i	−0.128364	+	0.0140279i
$178$	9.40461			0.704906
$179$			12.1657i			0.909305i	0.890669	+	0.454653i	$0.150237\pi$
$179$			12.1657i			0.909305i	−0.890669	+	0.454653i	$0.849763\pi$
$180$	5.90593	−	5.31049i	0.440202	−	0.395820i
$181$		−	16.1773i		−	1.20245i	−0.799081	−	0.601224i	$-0.794680\pi$
$181$		−	16.1773i		−	1.20245i	0.799081	−	0.601224i	$-0.205320\pi$
$182$		0			0
$183$	−1.16000	−	10.6146i	−0.0857493	−	0.784657i
$184$	−4.69356			−0.346014
$185$	−1.76079	−	3.11373i	−0.129456	−	0.228926i
$186$	0.317969	+	2.90960i	0.0233146	+	0.213342i
$187$	27.1038			1.98203
$188$		−	8.18658i		−	0.597068i
$189$		0			0
$190$	−5.67440	−	10.0344i	−0.411664	−	0.727975i
$191$		−	8.27793i		−	0.598970i	−0.954101	−	0.299485i	$-0.903185\pi$
$191$		−	8.27793i		−	0.598970i	0.954101	−	0.299485i	$-0.0968148\pi$
$192$	−9.41649	+	1.02906i	−0.679576	+	0.0742659i
$193$			15.9253i			1.14633i	0.819440	+	0.573166i	$0.194285\pi$
$193$			15.9253i			1.14633i	−0.819440	+	0.573166i	$0.805715\pi$
$194$	13.1319			0.942812
$195$	9.06473	−	6.51954i	0.649138	−	0.466874i
$196$		0			0
$197$	−23.8738			−1.70094			−0.850468	−	0.526027i	$-0.823681\pi$
$197$	−23.8738			−1.70094			−0.850468	+	0.526027i	$0.823681\pi$
$198$	2.37898	+	10.7545i	0.169067	+	0.764292i
$199$		−	12.2273i		−	0.866768i	−0.901209	−	0.433384i	$-0.857319\pi$
$199$		−	12.2273i		−	0.866768i	0.901209	−	0.433384i	$-0.142681\pi$
$200$	7.41204	−	12.3238i	0.524110	−	0.871426i
$201$	−1.89861	−	17.3734i	−0.133918	−	1.22543i
$202$	−12.4637			−0.876941
$203$		0			0
$204$	1.48565	+	13.5945i	0.104016	+	0.951807i
$205$	17.7560	−	10.0409i	1.24013	−	0.701285i
$206$	7.50998			0.523245
$207$	−4.78001	+	1.05737i	−0.332234	+	0.0734925i
$208$	−0.663761			−0.0460235
$209$	−23.1954			−1.60446
$210$		0			0
$211$	18.8640			1.29865			0.649327	−	0.760510i	$-0.275051\pi$
$211$	18.8640			1.29865			0.649327	+	0.760510i	$0.275051\pi$
$212$	1.79805			0.123491
$213$	−0.905465	−	8.28553i	−0.0620414	−	0.567715i
$214$	9.69921			0.663025
$215$	8.29206	+	14.6635i	0.565514	+	1.00004i
$216$	−14.1554	+	4.79412i	−0.963156	+	0.326199i
$217$		0			0
$218$	−0.484799			−0.0328348
$219$	0.965273	−	0.105488i	0.0652271	−	0.00712819i
$220$	−5.29661	−	9.36638i	−0.357098	−	0.631481i
$221$			19.2256i			1.29325i
$222$	0.271914	+	2.48817i	0.0182496	+	0.166995i
$223$	19.2779			1.29095			0.645473	−	0.763783i	$-0.276660\pi$
$223$	19.2779			1.29095			0.645473	+	0.763783i	$0.276660\pi$
$224$		0			0
$225$	4.77223	−	14.2206i	0.318149	−	0.948041i
$226$	10.9330			0.727250
$227$		−	11.5017i		−	0.763397i	−0.924287	−	0.381698i	$-0.875339\pi$
$227$		−	11.5017i		−	0.763397i	0.924287	−	0.381698i	$-0.124661\pi$
$228$	−1.27141	−	11.6342i	−0.0842014	−	0.770492i
$229$			17.3732i			1.14806i	0.818836	+	0.574028i	$0.194620\pi$
$229$			17.3732i			1.14806i	−0.818836	+	0.574028i	$0.805380\pi$
$230$	−2.86923	+	1.62253i	−0.189192	+	0.106986i
$231$		0			0
$232$			16.9612i			1.11356i
$233$	0.462850			0.0303223			0.0151611	−	0.999885i	$-0.495174\pi$
$233$	0.462850			0.0303223			0.0151611	+	0.999885i	$0.495174\pi$
$234$	−7.62851	+	1.68748i	−0.498691	+	0.110314i
$235$	−7.61060	−	13.4584i	−0.496461	−	0.877927i
$236$	−1.17433			−0.0764424
$237$	−6.54021	+	0.714732i	−0.424833	+	0.0464268i
$238$		0			0
$239$			17.3055i			1.11940i	0.828696	+	0.559699i	$0.189083\pi$
$239$			17.3055i			1.11940i	−0.828696	+	0.559699i	$0.810917\pi$
$240$	−0.723907	+	0.520649i	−0.0467280	+	0.0336078i
$241$			4.27939i			0.275660i	0.990456	+	0.137830i	$0.0440128\pi$
$241$			4.27939i			0.275660i	−0.990456	+	0.137830i	$0.955987\pi$
$242$	4.98564			0.320489
$243$	−13.3361	+	8.07138i	−0.855514	+	0.517780i
$244$		−	7.29906i		−	0.467274i
$245$		0			0
$246$	−14.1888	+	1.55058i	−0.904642	+	0.0988617i
$247$		−	16.4532i		−	1.04689i
$248$			5.38048i			0.341661i
$249$	0.753463	+	6.89462i	0.0477488	+	0.436929i
$250$	0.270821	−	10.0960i	0.0171282	−	0.638527i
$251$	17.4145			1.09919			0.549597	−	0.835430i	$-0.314781\pi$
$251$	17.4145			1.09919			0.549597	+	0.835430i	$0.314781\pi$
$252$		0			0
$253$			6.63247i			0.416980i
$254$		−	20.1339i		−	1.26331i
$255$	15.0804	+	20.9677i	0.944371	+	1.31305i
$256$	−16.4922			−1.03076
$257$			15.4161i			0.961630i	0.876822	+	0.480815i	$0.159659\pi$
$257$			15.4161i			0.961630i	−0.876822	+	0.480815i	$0.840341\pi$
$258$	−1.28052	−	11.7175i	−0.0797217	−	0.729500i
$259$		0			0
$260$	6.64385	−	3.75704i	0.412034	−	0.233002i
$261$	3.82105	+	17.2736i	0.236517	+	1.06921i
$262$	0.103142			0.00637215
$263$	−6.21170			−0.383030			−0.191515	−	0.981490i	$-0.561340\pi$
$263$	−6.21170			−0.383030			−0.191515	+	0.981490i	$0.561340\pi$
$264$	2.19962	+	20.1278i	0.135377	+	1.23878i
$265$	2.95591	−	1.67155i	0.181580	−	0.102682i
$266$		0			0
$267$	17.9256	−	1.95895i	1.09703	−	0.119886i
$268$		−	11.9467i		−	0.729759i
$269$	−5.99070			−0.365259			−0.182630	−	0.983182i	$-0.558461\pi$
$269$	−5.99070			−0.365259			−0.182630	+	0.983182i	$0.558461\pi$
$270$	−6.99611	+	7.82414i	−0.425770	+	0.476162i
$271$			6.24515i			0.379366i	0.981845	+	0.189683i	$0.0607460\pi$
$271$			6.24515i			0.379366i	−0.981845	+	0.189683i	$0.939254\pi$
$272$		−	1.53535i		−	0.0930942i
$273$		0			0
$274$	−11.3313			−0.684546
$275$	−17.4148	−	10.4739i	−1.05015	−	0.631603i
$276$	−3.32666	+	0.363546i	−0.200241	+	0.0218829i
$277$			8.70424i			0.522987i	0.965205	+	0.261494i	$0.0842150\pi$
$277$			8.70424i			0.522987i	−0.965205	+	0.261494i	$0.915785\pi$
$278$		−	2.14669i		−	0.128750i
$279$	1.21212	+	5.47959i	0.0725679	+	0.328054i
$280$		0			0
$281$			4.36274i			0.260259i	0.991497	+	0.130130i	$0.0415393\pi$
$281$			4.36274i			0.260259i	−0.991497	+	0.130130i	$0.958461\pi$
$282$	1.17528	+	10.7545i	0.0699871	+	0.640423i
$283$	−7.52075			−0.447062			−0.223531	−	0.974697i	$-0.571758\pi$
$283$	−7.52075			−0.447062			−0.223531	+	0.974697i	$0.571758\pi$
$284$		−	5.69747i		−	0.338082i
$285$	−12.9058	−	17.9441i	−0.764473	−	1.06292i
$286$			10.5849i			0.625897i
$287$		0			0
$288$	−16.2407	+	3.59256i	−0.956994	+	0.211694i
$289$	−27.4707			−1.61593
$290$	5.86337	+	10.3686i	0.344309	+	0.608867i
$291$	25.0298	−	2.73533i	1.46728	−	0.160348i
$292$	0.663761			0.0388437
$293$		−	0.105885i		−	0.00618587i	−0.999995	−	0.00309293i	$-0.999015\pi$
$293$		−	0.105885i		−	0.00618587i	0.999995	−	0.00309293i	$-0.000984513\pi$
$294$		0			0
$295$	−1.93055	+	1.09171i	−0.112401	+	0.0635617i
$296$			4.60116i			0.267437i
$297$	6.77457	+	20.0030i	0.393100	+	1.16069i
$298$		−	14.8766i		−	0.861778i
$299$	−4.70461			−0.272074
$300$	4.29888	−	9.30888i	0.248196	−	0.537448i
$301$		0			0
$302$	11.8764			0.683412
$303$	−23.7563	+	2.59615i	−1.36476	+	0.149145i
$304$			1.31395i			0.0753602i
$305$	−6.78552	−	11.9993i	−0.388538	−	0.687079i
$306$	−3.90332	−	17.6455i	−0.223138	−	1.00873i
$307$	−9.31270			−0.531504			−0.265752	−	0.964041i	$-0.585620\pi$
$307$	−9.31270			−0.531504			−0.265752	+	0.964041i	$0.585620\pi$
$308$		0			0
$309$	14.3143	−	1.56431i	0.814314	−	0.0889904i
$310$	1.85999	+	3.28916i	0.105641	+	0.186812i
$311$	−25.3143			−1.43544			−0.717722	−	0.696330i	$-0.754815\pi$
$311$	−25.3143			−1.43544			−0.717722	+	0.696330i	$0.754815\pi$
$312$	−14.2773	+	1.56026i	−0.808291	+	0.0883322i
$313$	−7.64982			−0.432394			−0.216197	−	0.976350i	$-0.569365\pi$
$313$	−7.64982			−0.432394			−0.216197	+	0.976350i	$0.569365\pi$
$314$	2.87996			0.162526
$315$		0			0
$316$	−4.49732			−0.252994
$317$	24.7465			1.38990			0.694950	−	0.719058i	$-0.255426\pi$
$317$	24.7465			1.38990			0.694950	+	0.719058i	$0.255426\pi$
$318$	−2.36206	+	0.258132i	−0.132458	+	0.0144753i
$319$	23.9679			1.34195
$320$	−10.6449	+	6.01959i	−0.595066	+	0.336505i
$321$	18.4871	−	2.02032i	1.03185	−	0.112763i
$322$		0			0
$323$	38.0580			2.11760
$324$	−9.66163	+	4.49436i	−0.536757	+	0.249687i
$325$	7.42948	−	12.3528i	0.412114	−	0.685211i
$326$		−	17.4158i		−	0.964574i
$327$	−0.924047	+	0.100982i	−0.0510999	+	0.00558434i
$328$	−26.2381			−1.44875
$329$		0			0
$330$	8.30270	+	11.5440i	0.457049	+	0.635477i
$331$	−16.3562			−0.899019			−0.449509	−	0.893276i	$-0.648401\pi$
$331$	−16.3562			−0.899019			−0.449509	+	0.893276i	$0.648401\pi$
$332$			4.74102i			0.260197i
$333$	1.03656	+	4.68591i	0.0568029	+	0.256786i
$334$		−	0.798473i		−	0.0436905i
$335$	−11.1061	−	19.6398i	−0.606793	−	1.07304i
$336$		0			0
$337$			3.59256i			0.195699i	0.995201	+	0.0978497i	$0.0311964\pi$
$337$			3.59256i			0.195699i	−0.995201	+	0.0978497i	$0.968804\pi$
$338$	4.23523			0.230366
$339$	20.8387	−	2.27731i	1.13180	−	0.123686i
$340$	8.69044	+	15.3679i	0.471305	+	0.833443i
$341$	7.60315			0.411734
$342$	3.34046	+	15.1010i	0.180631	+	0.816571i
$343$		0			0
$344$		−	21.6682i		−	1.16827i
$345$	−5.13091	+	3.69026i	−0.276239	+	0.198677i
$346$			11.3063i			0.607832i
$347$	−18.9288			−1.01615			−0.508075	−	0.861313i	$-0.669643\pi$
$347$	−18.9288			−1.01615			−0.508075	+	0.861313i	$0.669643\pi$
$348$	1.31376	+	12.0216i	0.0704247	+	0.644427i
$349$			24.1751i			1.29406i	0.762463	+	0.647032i	$0.223990\pi$
$349$			24.1751i			1.29406i	−0.762463	+	0.647032i	$0.776010\pi$
$350$		0			0
$351$	−14.1888	+	4.80540i	−0.757340	+	0.256493i
$352$			22.5347i			1.20110i
$353$			32.1044i			1.70875i	0.519660	+	0.854373i	$0.326058\pi$
$353$			32.1044i			1.70875i	−0.519660	+	0.854373i	$0.673942\pi$
$354$	1.54269	−	0.168590i	0.0819932	−	0.00896043i
$355$	−5.29661	−	9.36638i	−0.281115	−	0.497116i
$356$	12.3263			0.653295
$357$		0			0
$358$		−	10.9897i		−	0.580825i
$359$		−	17.0670i		−	0.900764i	−0.892836	−	0.450382i	$-0.851288\pi$
$359$		−	17.0670i		−	0.900764i	0.892836	−	0.450382i	$-0.148712\pi$
$360$	−14.3471	+	12.9006i	−0.756161	+	0.679923i
$361$	−13.5700			−0.714210
$362$			14.6136i			0.768071i
$363$	9.50284	−	1.03850i	0.498770	−	0.0545069i
$364$		0			0
$365$	1.09119	−	0.617061i	0.0571157	−	0.0322984i
$366$	1.04787	+	9.58861i	0.0547730	+	0.501205i
$367$	−15.6751			−0.818231			−0.409116	−	0.912483i	$-0.634163\pi$
$367$	−15.6751			−0.818231			−0.409116	+	0.912483i	$0.634163\pi$
$368$	0.375709			0.0195852
$369$	−26.7214	+	5.91095i	−1.39106	+	0.307712i
$370$	1.59059	+	2.81275i	0.0826907	+	0.146228i
$371$		0			0
$372$	0.416753	+	3.81353i	0.0216076	+	0.197722i
$373$		−	1.04874i		−	0.0543017i	−0.999631	−	0.0271508i	$-0.991357\pi$
$373$		−	1.04874i		−	0.0543017i	0.999631	−	0.0271508i	$-0.00864345\pi$
$374$	−24.4839			−1.26603
$375$	−1.58677	−	19.2998i	−0.0819405	−	0.996637i
$376$			19.8875i			1.02562i
$377$			17.0012i			0.875604i
$378$		0			0
$379$	−19.7185			−1.01287			−0.506436	−	0.862278i	$-0.669037\pi$
$379$	−19.7185			−1.01287			−0.506436	+	0.862278i	$0.669037\pi$
$380$	−7.43727	−	13.1519i	−0.381524	−	0.674676i
$381$	−4.19383	−	38.3760i	−0.214856	−	1.96606i
$382$			7.47777i			0.382596i
$383$			2.75894i			0.140975i	0.997513	+	0.0704876i	$0.0224555\pi$
$383$			2.75894i			0.140975i	−0.997513	+	0.0704876i	$0.977544\pi$
$384$	−10.5866	+	1.15693i	−0.540244	+	0.0590392i
$385$		0			0
$386$		−	14.3860i		−	0.732227i
$387$	−4.88145	−	22.0673i	−0.248138	−	1.12174i
$388$	17.2115			0.873783
$389$		−	31.9024i		−	1.61752i	−0.588141	−	0.808758i	$-0.700140\pi$
$389$		−	31.9024i		−	1.61752i	0.588141	−	0.808758i	$-0.299860\pi$
$390$	−8.18852	+	5.88936i	−0.414642	+	0.298219i
$391$		−	10.8822i		−	0.550339i
$392$		0			0
$393$	0.196593	−	0.0214842i	0.00991682	−	0.00108374i
$394$	21.5661			1.08648
$395$	−7.39339	+	4.18090i	−0.372002	+	0.210364i
$396$	3.11806	+	14.0957i	0.156688	+	0.708333i
$397$	−18.8205			−0.944572			−0.472286	−	0.881445i	$-0.656571\pi$
$397$	−18.8205			−0.944572			−0.472286	+	0.881445i	$0.656571\pi$
$398$			11.0454i			0.553654i
$399$		0			0
$400$	−0.593317	+	0.986494i	−0.0296658	+	0.0493247i
$401$		−	3.28917i		−	0.164253i	−0.996622	−	0.0821266i	$-0.973829\pi$
$401$		−	3.28917i		−	0.164253i	0.996622	−	0.0821266i	$-0.0261712\pi$
$402$	1.71509	+	15.6941i	0.0855410	+	0.782750i
$403$			5.39314i			0.268652i
$404$	−16.3358			−0.812735
$405$	−11.7051	+	16.3704i	−0.581633	+	0.813452i
$406$		0			0
$407$	6.50190			0.322287
$408$	−3.60904	−	33.0248i	−0.178674	−	1.63497i
$409$			4.14914i			0.205162i	0.994725	+	0.102581i	$0.0327100\pi$
$409$			4.14914i			0.205162i	−0.994725	+	0.102581i	$0.967290\pi$
$410$	−16.0397	+	9.07031i	−0.792143	+	0.447951i
$411$	−21.5978	+	2.36027i	−1.06534	+	0.116423i
$412$	9.84311			0.484935
$413$		0			0
$414$	4.31797	−	0.955165i	0.212217	−	0.0469438i
$415$	4.40746	+	7.79403i	0.216354	+	0.382594i
$416$	−15.9845			−0.783706
$417$	−0.447150	−	4.09169i	−0.0218970	−	0.200371i
$418$	20.9533			1.02486
$419$	22.6231			1.10521			0.552606	−	0.833443i	$-0.313633\pi$
$419$	22.6231			1.10521			0.552606	+	0.833443i	$0.313633\pi$
$420$		0			0
$421$	31.9233			1.55584			0.777922	−	0.628360i	$-0.216274\pi$
$421$	31.9233			1.55584			0.777922	+	0.628360i	$0.216274\pi$
$422$	−17.0406			−0.829524
$423$	4.48028	+	20.2538i	0.217839	+	0.984772i
$424$	−4.36796			−0.212127
$425$	28.5734	+	17.1852i	1.38601	+	0.833603i
$426$	0.817941	+	7.48464i	0.0396294	+	0.362632i
$427$		0			0
$428$	12.7125			0.614481
$429$	2.20480	+	20.1752i	0.106449	+	0.974068i
$430$	−7.49054	−	13.2461i	−0.361226	−	0.638782i
$431$			25.0448i			1.20636i	0.797604	+	0.603182i	$0.206101\pi$
$431$			25.0448i			1.20636i	−0.797604	+	0.603182i	$0.793899\pi$
$432$	1.13311	−	0.383758i	0.0545168	−	0.0184636i
$433$	5.10220			0.245196			0.122598	−	0.992456i	$-0.460877\pi$
$433$	5.10220			0.245196			0.122598	+	0.992456i	$0.460877\pi$
$434$		0			0
$435$	13.3356	+	18.5417i	0.639392	+	0.889006i
$436$	−0.635412			−0.0304307
$437$			9.31302i			0.445502i
$438$	−0.871968	+	0.0952910i	−0.0416643	+	0.00455318i
$439$		−	11.2880i		−	0.538746i	−0.963036	−	0.269373i	$-0.913184\pi$
$439$		−	11.2880i		−	0.538746i	0.963036	−	0.269373i	$-0.0868165\pi$
$440$	12.8669	+	22.7535i	0.613407	+	1.08473i
$441$		0			0
$442$		−	17.3672i		−	0.826073i
$443$	21.9182			1.04136			0.520681	−	0.853751i	$-0.325678\pi$
$443$	21.9182			1.04136			0.520681	+	0.853751i	$0.325678\pi$
$444$	0.356389	+	3.26117i	0.0169135	+	0.154768i
$445$	20.2640	−	11.4591i	0.960604	−	0.543214i
$446$	−17.4145			−0.824601
$447$	−3.09875	−	28.3554i	−0.146566	−	1.34116i
$448$		0			0
$449$			0.449397i			0.0212083i	0.999944	+	0.0106042i	$0.00337548\pi$
$449$			0.449397i			0.0212083i	−0.999944	+	0.0106042i	$0.996625\pi$
$450$	−4.31094	+	12.8460i	−0.203220	+	0.605568i
$451$			37.0770i			1.74589i
$452$	14.3295			0.674004
$453$	22.6370	−	2.47383i	1.06358	−	0.116231i
$454$			10.3900i			0.487625i
$455$		0			0
$456$	3.08861	+	28.2626i	0.144638	+	1.32352i
$457$			9.29288i			0.434702i	0.976093	+	0.217351i	$0.0697417\pi$
$457$			9.29288i			0.434702i	−0.976093	+	0.217351i	$0.930258\pi$
$458$		−	15.6939i		−	0.733328i
$459$	−11.1154	−	32.8201i	−0.518823	−	1.53191i
$460$	−3.76062	+	2.12660i	−0.175340	+	0.0991533i
$461$	−20.8668			−0.971863			−0.485931	−	0.873997i	$-0.661519\pi$
$461$	−20.8668			−0.971863			−0.485931	+	0.873997i	$0.661519\pi$
$462$		0			0
$463$		−	2.45294i		−	0.113998i	−0.998374	−	0.0569989i	$-0.981847\pi$
$463$		−	2.45294i		−	0.113998i	0.998374	−	0.0569989i	$-0.0181532\pi$
$464$		−	1.35771i		−	0.0630300i
$465$	4.23034	+	5.88184i	0.196178	+	0.272764i
$466$	−0.418110			−0.0193686
$467$		−	7.97995i		−	0.369268i	−0.982807	−	0.184634i	$-0.940890\pi$
$467$		−	7.97995i		−	0.369268i	0.982807	−	0.184634i	$-0.0591100\pi$
$468$	−9.99847	+	2.21173i	−0.462179	+	0.102237i
$469$		0			0
$470$	6.87495	+	12.1575i	0.317118	+	0.560782i
$471$	5.48932	−	0.599887i	0.252935	−	0.0276414i
$472$	2.85277			0.131309
$473$	−30.6193			−1.40788
$474$	5.90803	−	0.645645i	0.271365	−	0.0296555i
$475$	−24.4531	−	14.7071i	−1.12198	−	0.674806i
$476$		0			0
$477$	−4.44841	+	0.984021i	−0.203679	+	0.0450552i
$478$		−	15.6327i		−	0.715023i
$479$	13.8929			0.634784			0.317392	−	0.948294i	$-0.397193\pi$
$479$	13.8929			0.634784			0.317392	+	0.948294i	$0.397193\pi$
$480$	−17.4329	+	12.5381i	−0.795702	+	0.572286i
$481$			4.61199i			0.210289i
$482$		−	3.86574i		−	0.176080i
$483$		0			0
$484$	6.53454			0.297024
$485$	28.2950	−	16.0006i	1.28481	−	0.726549i
$486$	12.0471	−	7.29119i	0.546465	−	0.330735i
$487$		−	26.5108i		−	1.20132i	−0.799505	−	0.600659i	$-0.794905\pi$
$487$		−	26.5108i		−	1.20132i	0.799505	−	0.600659i	$-0.205095\pi$
$488$			17.7314i			0.802663i
$489$	−3.62767	−	33.1953i	−0.164049	−	1.50114i
$490$		0			0
$491$		−	2.54611i		−	0.114905i	−0.998348	−	0.0574523i	$-0.981702\pi$
$491$		−	2.54611i		−	0.114905i	0.998348	−	0.0574523i	$-0.0182977\pi$
$492$	−18.5968	+	2.03231i	−0.838408	+	0.0916234i
$493$	−39.3255			−1.77113
$494$			14.8628i			0.668710i
$495$	18.2299	+	20.2739i	0.819372	+	0.911246i
$496$		−	0.430695i		−	0.0193388i
$497$		0			0
$498$	−0.680632	−	6.22818i	−0.0304999	−	0.279091i
$499$	29.6496			1.32730			0.663649	−	0.748044i	$-0.269007\pi$
$499$	29.6496			1.32730			0.663649	+	0.748044i	$0.269007\pi$
$500$	0.354958	−	13.2325i	0.0158742	−	0.591777i
$501$	−0.166320	−	1.52192i	−0.00743061	−	0.0679945i
$502$	−15.7312			−0.702118
$503$		−	31.2378i		−	1.39283i	−0.717642	−	0.696413i	$-0.754778\pi$
$503$		−	31.2378i		−	1.39283i	0.717642	−	0.696413i	$-0.245222\pi$
$504$		0			0
$505$	−26.8553	+	15.1864i	−1.19504	+	0.675787i
$506$		−	5.99136i		−	0.266349i
$507$	8.07252	−	0.882186i	0.358513	−	0.0391793i
$508$		−	26.3889i		−	1.17082i
$509$	38.0143			1.68496			0.842478	−	0.538731i	$-0.181096\pi$
$509$	38.0143			1.68496			0.842478	+	0.538731i	$0.181096\pi$
$510$	−13.6227	−	18.9409i	−0.603223	−	0.838717i
$511$		0			0
$512$	2.60093			0.114946
$513$	9.51255	+	28.0874i	0.419989	+	1.24009i
$514$		−	13.9260i		−	0.614248i
$515$	16.1816	−	9.15058i	0.713048	−	0.403223i
$516$	−1.67834	−	15.3578i	−0.0738848	−	0.676089i
$517$	28.1030			1.23597
$518$		0			0
$519$	2.35507	+	21.5503i	0.103376	+	0.945953i
$520$	−16.1397	+	9.12690i	−0.707775	+	0.400241i
$521$	−39.1414			−1.71481			−0.857407	−	0.514639i	$-0.827926\pi$
$521$	−39.1414			−1.71481			−0.857407	+	0.514639i	$0.827926\pi$
$522$	−3.45170	−	15.6040i	−0.151077	−	0.682966i
$523$	−7.97176			−0.348581			−0.174290	−	0.984694i	$-0.555763\pi$
$523$	−7.97176			−0.348581			−0.174290	+	0.984694i	$0.555763\pi$
$524$	0.135186			0.00590561
$525$		0			0
$526$	5.61127			0.244663
$527$	−12.4749			−0.543416
$528$	−0.176075	−	1.61119i	−0.00766267	−	0.0701179i
$529$	−20.3371			−0.884220
$530$	−2.67019	+	1.50997i	−0.115986	+	0.0655890i
$531$	2.90532	−	0.642677i	0.126080	−	0.0278898i
$532$		0			0
$533$	−26.2998			−1.13917
$534$	−16.1929	+	1.76960i	−0.700734	+	0.0765780i
$535$	20.8987	−	11.8181i	0.903531	−	0.510940i
$536$			29.0217i			1.25355i
$537$	−2.28913	−	20.9469i	−0.0987831	−	0.903923i
$538$	5.41163			0.233312
$539$		0			0
$540$	−9.16960	+	10.2549i	−0.394597	+	0.441299i
$541$	−8.08347			−0.347536			−0.173768	−	0.984787i	$-0.555594\pi$
$541$	−8.08347			−0.347536			−0.173768	+	0.984787i	$0.555594\pi$
$542$		−	5.64148i		−	0.242323i
$543$	3.04396	+	27.8540i	0.130629	+	1.19533i
$544$		−	36.9739i		−	1.58524i
$545$	−1.04459	+	0.590707i	−0.0447453	+	0.0253031i
$546$		0			0
$547$		−	37.0430i		−	1.58384i	−0.610623	−	0.791922i	$-0.709081\pi$
$547$		−	37.0430i		−	1.58384i	0.610623	−	0.791922i	$-0.290919\pi$
$548$	−14.8515			−0.634426
$549$	3.99456	+	18.0580i	0.170484	+	0.770697i
$550$	15.7314	+	9.46152i	0.670791	+	0.403441i
$551$	33.6547			1.43374
$552$	8.08137	−	0.883153i	0.343966	−	0.0375895i
$553$		0			0
$554$		−	7.86288i		−	0.334062i
$555$	3.61761	+	5.02990i	0.153559	+	0.213507i
$556$		−	2.81361i		−	0.119324i
$557$	−8.88856			−0.376620			−0.188310	−	0.982110i	$-0.560301\pi$
$557$	−8.88856			−0.376620			−0.188310	+	0.982110i	$0.560301\pi$
$558$	−1.09496	−	4.94992i	−0.0463533	−	0.209547i
$559$		−	21.7192i		−	0.918624i
$560$		0			0
$561$	−46.6674	+	5.09993i	−1.97030	+	0.215319i
$562$		−	3.94103i		−	0.166242i
$563$		−	39.4078i		−	1.66084i	−0.557136	−	0.830421i	$-0.688100\pi$
$563$		−	39.4078i		−	1.66084i	0.557136	−	0.830421i	$-0.311900\pi$
$564$	1.54041	+	14.0957i	0.0648630	+	0.593534i
$565$	23.5571	−	13.3213i	0.991054	−	0.560433i
$566$	6.79378			0.285564
$567$		0			0
$568$			13.8407i			0.580744i
$569$		−	17.4528i		−	0.731659i	−0.930682	−	0.365830i	$-0.880785\pi$
$569$		−	17.4528i		−	0.731659i	0.930682	−	0.365830i	$-0.119215\pi$
$570$	11.6583	+	16.2096i	0.488312	+	0.678945i
$571$	−19.3889			−0.811399			−0.405700	−	0.914006i	$-0.632972\pi$
$571$	−19.3889			−0.811399			−0.405700	+	0.914006i	$0.632972\pi$
$572$			13.8733i			0.580071i
$573$	1.55760	+	14.2529i	0.0650696	+	0.595425i
$574$		0			0
$575$	−4.20531	+	6.99207i	−0.175374	+	0.291590i
$576$	16.0197	−	3.54367i	0.667486	−	0.147653i
$577$	41.7306			1.73727			0.868633	−	0.495455i	$-0.164999\pi$
$577$	41.7306			1.73727			0.868633	+	0.495455i	$0.164999\pi$
$578$	24.8154			1.03218
$579$	−2.99656	−	27.4203i	−0.124533	−	1.13955i
$580$	7.68495	+	13.5899i	0.319100	+	0.564288i
$581$		0			0
$582$	−22.6104	+	2.47093i	−0.937232	+	0.102423i
$583$			6.17236i			0.255633i
$584$	−1.61246			−0.0667240
$585$	−14.3809	+	12.9310i	−0.594577	+	0.534631i
$586$			0.0956500i			0.00395126i
$587$		−	19.5477i		−	0.806820i	−0.915019	−	0.403410i	$-0.867825\pi$
$587$		−	19.5477i		−	0.806820i	0.915019	−	0.403410i	$-0.132175\pi$
$588$		0			0
$589$	10.6760			0.439897
$590$	1.74394	−	0.986182i	0.0717967	−	0.0406005i
$591$	41.1059	−	4.49216i	1.69087	−	0.184783i
$592$		−	0.368312i		−	0.0151375i
$593$			2.63145i			0.108061i	0.998539	+	0.0540303i	$0.0172067\pi$
$593$			2.63145i			0.108061i	−0.998539	+	0.0540303i	$0.982793\pi$
$594$	−6.11973	−	18.0695i	−0.251096	−	0.741401i
$595$		0			0
$596$		−	19.4983i		−	0.798683i
$597$	2.30072	+	21.0529i	0.0941621	+	0.861639i
$598$	4.24985			0.173789
$599$			31.2146i			1.27539i	0.770287	+	0.637697i	$0.220113\pi$
$599$			31.2146i			1.27539i	−0.770287	+	0.637697i	$0.779887\pi$
$600$	−10.4432	+	22.6138i	−0.426340	+	0.923205i
$601$			15.6798i			0.639593i	0.947486	+	0.319797i	$0.103615\pi$
$601$			15.6798i			0.639593i	−0.947486	+	0.319797i	$0.896385\pi$
$602$		0			0
$603$	6.53806	+	29.5563i	0.266251	+	1.20363i
$604$	15.5661			0.633376
$605$	10.7425	−	6.07479i	0.436744	−	0.246975i
$606$	21.4599	−	2.34520i	0.871751	−	0.0952672i
$607$	−4.81384			−0.195388			−0.0976940	−	0.995217i	$-0.531147\pi$
$607$	−4.81384			−0.195388			−0.0976940	+	0.995217i	$0.531147\pi$
$608$			31.6422i			1.28326i
$609$		0			0
$610$	6.12962	+	10.8394i	0.248181	+	0.438876i
$611$			19.9343i			0.806454i
$612$	−5.11597	−	23.1275i	−0.206801	−	0.934874i
$613$			40.0717i			1.61848i	0.587478	+	0.809240i	$0.300121\pi$
$613$			40.0717i			1.61848i	−0.587478	+	0.809240i	$0.699879\pi$
$614$	8.41253			0.339502
$615$	−28.6830	+	20.6294i	−1.15661	+	0.831857i
$616$		0			0
$617$	18.4205			0.741583			0.370791	−	0.928716i	$-0.379087\pi$
$617$	18.4205			0.741583			0.370791	+	0.928716i	$0.379087\pi$
$618$	−12.9307	+	1.41310i	−0.520149	+	0.0568432i
$619$		−	11.0209i		−	0.442968i	−0.975164	−	0.221484i	$-0.928910\pi$
$619$		−	11.0209i		−	0.442968i	0.975164	−	0.221484i	$-0.0710901\pi$
$620$	2.43784	+	4.31100i	0.0979059	+	0.173134i
$621$	8.03126	−	2.72000i	0.322284	−	0.109150i
$622$	22.8674			0.916899
$623$		0			0
$624$	1.14286	−	0.124895i	0.0457512	−	0.00499981i
$625$	−11.7180	−	22.0837i	−0.468720	−	0.883347i
$626$	6.91038			0.276194
$627$	39.9379	−	4.36452i	1.59497	−	0.174302i
$628$	3.77468			0.150626
$629$	−10.6680			−0.425362
$630$		0			0
$631$	16.0604			0.639355			0.319678	−	0.947526i	$-0.396425\pi$
$631$	16.0604			0.639355			0.319678	+	0.947526i	$0.396425\pi$
$632$	10.9252			0.434582
$633$	−32.4801	+	3.54951i	−1.29097	+	0.141080i
$634$	−22.3545			−0.887809
$635$	−24.5322	−	43.3821i	−0.973532	−	1.72157i
$636$	−3.09588	+	0.338326i	−0.122760	+	0.0134155i
$637$		0			0
$638$	−21.6511			−0.857177
$639$	3.11806	+	14.0957i	0.123348	+	0.557615i
$640$	−11.9676	+	6.76757i	−0.473060	+	0.267512i
$641$		−	39.7927i		−	1.57172i	−0.618405	−	0.785859i	$-0.712221\pi$
$641$		−	39.7927i		−	1.57172i	0.618405	−	0.785859i	$-0.287779\pi$
$642$	−16.7001	+	1.82503i	−0.659100	+	0.0720282i
$643$	22.4164			0.884016			0.442008	−	0.897011i	$-0.354266\pi$
$643$	22.4164			0.884016			0.442008	+	0.897011i	$0.354266\pi$
$644$		0			0
$645$	−17.0364	−	23.6873i	−0.670807	−	0.932685i
$646$	−34.3793			−1.35263
$647$		−	25.5715i		−	1.00532i	−0.864484	−	0.502660i	$-0.832355\pi$
$647$		−	25.5715i		−	1.00532i	0.864484	−	0.502660i	$-0.167645\pi$
$648$	23.4708	−	10.9180i	0.922018	−	0.428901i
$649$		−	4.03125i		−	0.158240i
$650$	−6.71134	+	11.1588i	−0.263240	+	0.437684i
$651$		0			0
$652$		−	22.8264i		−	0.893952i
$653$	16.9984			0.665199			0.332600	−	0.943068i	$-0.392074\pi$
$653$	16.9984			0.665199			0.332600	+	0.943068i	$0.392074\pi$
$654$	0.834728	−	0.0912212i	0.0326404	−	0.00356703i
$655$	0.222239	−	0.125674i	0.00868359	−	0.00491050i
$656$	2.10030			0.0820029
$657$	−1.64216	+	0.363257i	−0.0640667	+	0.0141720i
$658$		0			0
$659$			2.82840i			0.110179i	0.998481	+	0.0550894i	$0.0175444\pi$
$659$			2.82840i			0.110179i	−0.998481	+	0.0550894i	$0.982456\pi$
$660$	10.8821	+	15.1304i	0.423586	+	0.588950i
$661$			14.5840i			0.567252i	0.958935	+	0.283626i	$0.0915374\pi$
$661$			14.5840i			0.567252i	−0.958935	+	0.283626i	$0.908463\pi$
$662$	14.7752			0.574254
$663$	−3.61754	−	33.1026i	−0.140493	−	1.28560i
$664$		−	11.5172i		−	0.446956i
$665$		0			0
$666$	−0.936361	−	4.23296i	−0.0362833	−	0.164024i
$667$		−	9.62317i		−	0.372611i
$668$		−	1.04654i		−	0.0404917i
$669$	−33.1927	+	3.62739i	−1.28331	+	0.140243i
$670$	10.0326	+	17.7414i	0.387593	+	0.685409i
$671$	25.0563			0.967286
$672$		0			0
$673$		−	13.2666i		−	0.511390i	−0.966757	−	0.255695i	$-0.917696\pi$
$673$		−	13.2666i		−	0.511390i	0.966757	−	0.255695i	$-0.0823043\pi$
$674$		−	3.24530i		−	0.125004i
$675$	−5.54104	+	25.3830i	−0.213275	+	0.976992i
$676$	5.55099			0.213500
$677$		−	27.3389i		−	1.05072i	−0.850880	−	0.525360i	$-0.823931\pi$
$677$		−	27.3389i		−	1.05072i	0.850880	−	0.525360i	$-0.176069\pi$
$678$	−18.8244	+	2.05718i	−0.722946	+	0.0790055i
$679$		0			0
$680$	−21.1115	−	37.3329i	−0.809588	−	1.43165i
$681$	2.16420	+	19.8037i	0.0829323	+	0.758879i
$682$	−6.86822			−0.262998
$683$	−5.07338			−0.194127			−0.0970637	−	0.995278i	$-0.530945\pi$
$683$	−5.07338			−0.194127			−0.0970637	+	0.995278i	$0.530945\pi$
$684$	4.37824	+	19.7925i	0.167406	+	0.756785i
$685$	−24.4153	+	13.8066i	−0.932859	+	0.527524i
$686$		0			0
$687$	−3.26900	−	29.9132i	−0.124720	−	1.14126i
$688$			1.73449i			0.0661268i
$689$	−4.37824			−0.166798
$690$	4.63495	−	3.33355i	0.176449	−	0.126906i
$691$			34.2569i			1.30319i	0.758566	+	0.651596i	$0.225900\pi$
$691$			34.2569i			1.30319i	−0.758566	+	0.651596i	$0.774100\pi$
$692$			14.8189i			0.563329i
$693$		0			0
$694$	17.0991			0.649073
$695$	−2.61565	−	4.62545i	−0.0992173	−	0.175453i
$696$	−3.19147	−	29.2038i	−0.120972	−	1.10697i
$697$		−	60.8343i		−	2.30426i
$698$		−	21.8383i		−	0.826592i
$699$	−0.796935	+	0.0870911i	−0.0301428	+	0.00329409i
$700$		0			0
$701$		−	17.6912i		−	0.668188i	−0.942540	−	0.334094i	$-0.891570\pi$
$701$		−	17.6912i		−	0.668188i	0.942540	−	0.334094i	$-0.108430\pi$
$702$	12.8172	−	4.34091i	0.483756	−	0.163837i
$703$	9.12967			0.344332
$704$		−	22.2280i		−	0.837748i
$705$	15.6363	+	21.7406i	0.588897	+	0.818798i
$706$		−	29.0012i		−	1.09147i
$707$		0			0
$708$	2.02196	−	0.220965i	0.0759900	−	0.00830439i
$709$	15.6175			0.586527			0.293264	−	0.956032i	$-0.405259\pi$
$709$	15.6175			0.586527			0.293264	+	0.956032i	$0.405259\pi$
$710$	4.78463	+	8.46101i	0.179564	+	0.317536i
$711$	11.1265	−	2.46125i	0.417275	−	0.0923041i
$712$	−29.9441			−1.12220
$713$		−	3.05268i		−	0.114324i
$714$		0			0
$715$	12.8972	+	22.8071i	0.482328	+	0.852936i
$716$		−	14.4039i		−	0.538299i
$717$	−3.25625	−	29.7966i	−0.121607	−	1.11277i
$718$			15.4173i			0.575369i
$719$	16.1436			0.602054			0.301027	−	0.953616i	$-0.402671\pi$
$719$	16.1436			0.602054			0.301027	+	0.953616i	$0.402671\pi$
$720$	1.14846	−	1.03267i	0.0428004	−	0.0384852i
$721$		0			0
$722$	12.2583			0.456207
$723$	−0.805223	−	7.36826i	−0.0299466	−	0.274029i
$724$			19.1536i			0.711836i
$725$	25.2674	+	15.1968i	0.938409	+	0.564396i
$726$	−8.58428	+	0.938113i	−0.318592	+	0.0348166i
$727$	16.8426			0.624657			0.312329	−	0.949974i	$-0.398891\pi$
$727$	16.8426			0.624657			0.312329	+	0.949974i	$0.398891\pi$
$728$		0			0
$729$	21.4434	−	16.4067i	0.794201	−	0.607655i
$730$	−0.985717	+	0.557415i	−0.0364830	+	0.0206309i
$731$	50.2388			1.85815
$732$	1.37341	+	12.5675i	0.0507627	+	0.464509i
$733$	22.1743			0.819028			0.409514	−	0.912304i	$-0.365698\pi$
$733$	22.1743			0.819028			0.409514	+	0.912304i	$0.365698\pi$
$734$	14.1599			0.522651
$735$		0			0
$736$	9.04773			0.333504
$737$	41.0106			1.51065
$738$	24.1384	−	5.33959i	0.888548	−	0.196553i
$739$	42.4525			1.56164			0.780820	−	0.624757i	$-0.214802\pi$
$739$	42.4525			1.56164			0.780820	+	0.624757i	$0.214802\pi$
$740$	2.08474	+	3.68659i	0.0766364	+	0.135522i
$741$	3.09588	+	28.3291i	0.113730	+	1.04070i
$742$		0			0
$743$	−24.5486			−0.900600			−0.450300	−	0.892877i	$-0.648683\pi$
$743$	−24.5486			−0.900600			−0.450300	+	0.892877i	$0.648683\pi$
$744$	−1.01241	−	9.26411i	−0.0371166	−	0.339639i
$745$	−18.1265	−	32.0544i	−0.664103	−	1.17438i
$746$			0.947367i			0.0346856i
$747$	−2.59462	−	11.7294i	−0.0949323	−	0.429156i
$748$	−32.0904			−1.17334
$749$		0			0
$750$	1.43339	+	17.4343i	0.0523401	+	0.636609i
$751$	25.3766			0.926006			0.463003	−	0.886357i	$-0.346772\pi$
$751$	25.3766			0.926006			0.463003	+	0.886357i	$0.346772\pi$
$752$		−	1.59195i		−	0.0580523i
$753$	−29.9843	+	3.27676i	−1.09269	+	0.119412i
$754$		−	15.3578i		−	0.559298i
$755$	25.5900	−	14.4709i	0.931314	−	0.526651i
$756$		0			0
$757$		−	18.9214i		−	0.687709i	−0.939023	−	0.343854i	$-0.888267\pi$
$757$		−	18.9214i		−	0.687709i	0.939023	−	0.343854i	$-0.111733\pi$
$758$	17.8125			0.646979
$759$	−1.24798	−	11.4198i	−0.0452989	−	0.414512i
$760$	18.0672	+	31.9495i	0.655365	+	1.15893i
$761$	−10.2582			−0.371859			−0.185929	−	0.982563i	$-0.559530\pi$
$761$	−10.2582			−0.371859			−0.185929	+	0.982563i	$0.559530\pi$
$762$	3.78845	+	34.6665i	0.137241	+	1.25583i
$763$		0			0
$764$			9.80090i			0.354584i
$765$	−29.9107	−	33.2645i	−1.08143	−	1.20268i
$766$		−	2.49226i		−	0.0900489i
$767$	2.85949			0.103250
$768$	28.3962	−	3.10321i	1.02466	−	0.111978i
$769$			17.8947i			0.645298i	0.946519	+	0.322649i	$0.104573\pi$
$769$			17.8947i			0.645298i	−0.946519	+	0.322649i	$0.895427\pi$
$770$		0			0
$771$	−2.90074	−	26.5434i	−0.104468	−	0.955939i
$772$		−	18.8553i		−	0.678616i
$773$		−	10.3218i		−	0.371251i	−0.982621	−	0.185626i	$-0.940569\pi$
$773$		−	10.3218i		−	0.371251i	0.982621	−	0.185626i	$-0.0594311\pi$
$774$	4.40960	+	19.9343i	0.158500	+	0.716522i
$775$	8.01539	+	4.82078i	0.287921	+	0.173167i
$776$	−41.8116			−1.50095
$777$		0			0
$778$			28.8187i			1.03320i
$779$			52.0619i			1.86531i
$780$	−10.7324	+	7.71901i	−0.384283	+	0.276385i
$781$	19.5583			0.699851
$782$			9.83035i			0.351533i
$783$	−9.82935	−	29.0228i	−0.351272	−	1.03719i
$784$		0			0
$785$	6.20540	−	3.50911i	0.221480	−	0.125245i
$786$	−0.177590	+	0.0194075i	−0.00633444	+	0.000692244i
$787$	12.5268			0.446531			0.223265	−	0.974758i	$-0.428328\pi$
$787$	12.5268			0.446531			0.223265	+	0.974758i	$0.428328\pi$
$788$	28.2661			1.00694
$789$	10.6953	−	1.16881i	0.380763	−	0.0416108i
$790$	6.67873	−	3.77677i	0.237619	−	0.134371i
$791$		0			0
$792$	−7.57462	−	34.2422i	−0.269152	−	1.21674i
$793$			17.7731i			0.631143i
$794$	17.0012			0.603352
$795$	−4.77497	+	3.43426i	−0.169351	+	0.121801i
$796$			14.4768i			0.513118i
$797$			23.4184i			0.829521i	0.909931	+	0.414761i	$0.136135\pi$
$797$			23.4184i			0.829521i	−0.909931	+	0.414761i	$0.863865\pi$
$798$		0			0
$799$	−46.1100			−1.63126
$800$	−14.2881	+	23.7565i	−0.505161	+	0.839919i
$801$	−30.4956	+	6.74585i	−1.07751	+	0.238353i
$802$			2.97123i			0.104918i
$803$			2.27856i			0.0804088i
$804$	2.24792	+	20.5698i	0.0792780	+	0.725440i
$805$		0			0
$806$		−	4.87184i		−	0.171603i
$807$	10.3148	−	1.12723i	0.363098	−	0.0396803i
$808$	39.6841			1.39608
$809$			10.9751i			0.385863i	0.981212	+	0.192932i	$0.0617995\pi$
$809$			10.9751i			0.385863i	−0.981212	+	0.192932i	$0.938200\pi$
$810$	10.5737	−	14.7880i	0.371522	−	0.519598i
$811$			35.5390i			1.24794i	0.781448	+	0.623971i	$0.214482\pi$
$811$			35.5390i			1.24794i	−0.781448	+	0.623971i	$0.785518\pi$
$812$		0			0
$813$	−1.17511	−	10.7529i	−0.0412127	−	0.377121i
$814$	−5.87341			−0.205863
$815$	−21.2204	−	37.5256i	−0.743319	−	1.31446i
$816$	0.288896	+	2.64356i	0.0101134	+	0.0925432i
$817$	−42.9943			−1.50418
$818$		−	3.74808i		−	0.131048i
$819$		0			0
$820$	−21.0227	+	11.8882i	−0.734146	+	0.415154i
$821$		−	45.6211i		−	1.59219i	−0.605173	−	0.796094i	$-0.706896\pi$
$821$		−	45.6211i		−	1.59219i	0.605173	−	0.796094i	$-0.293104\pi$
$822$	19.5102	−	2.13212i	0.680495	−	0.0743663i
$823$			13.8784i			0.483769i	0.970305	+	0.241885i	$0.0777655\pi$
$823$			13.8784i			0.483769i	−0.970305	+	0.241885i	$0.922234\pi$
$824$	−23.9116			−0.833001
$825$	31.9556	+	14.7572i	1.11255	+	0.513781i
$826$		0			0
$827$	−12.3739			−0.430283			−0.215141	−	0.976583i	$-0.569021\pi$
$827$	−12.3739			−0.430283			−0.215141	+	0.976583i	$0.569021\pi$
$828$	5.65943	−	1.25191i	0.196679	−	0.0435068i
$829$			10.6696i			0.370569i	0.982685	+	0.185284i	$0.0593206\pi$
$829$			10.6696i			0.370569i	−0.982685	+	0.185284i	$0.940679\pi$
$830$	−3.98143	−	7.04065i	−0.138197	−	0.244384i
$831$	−1.63781	−	14.9870i	−0.0568152	−	0.519892i
$832$	15.7670			0.546621
$833$		0			0
$834$	0.403928	+	3.69618i	0.0139869	+	0.127988i
$835$	−0.972905	−	1.72046i	−0.0336687	−	0.0595389i
$836$	27.4629			0.949825
$837$	−3.11809	−	9.20667i	−0.107777	−	0.318229i
$838$	−20.4363			−0.705962
$839$	−17.5497			−0.605883			−0.302941	−	0.953009i	$-0.597969\pi$
$839$	−17.5497			−0.605883			−0.302941	+	0.953009i	$0.597969\pi$
$840$		0			0
$841$	−5.77548			−0.199154
$842$	−28.8375			−0.993807
$843$	−0.820905	−	7.51176i	−0.0282735	−	0.258719i
$844$	−22.3346			−0.768789
$845$	9.12558	−	5.16044i	0.313930	−	0.177525i
$846$	−4.04721	−	18.2960i	−0.139146	−	0.629030i
$847$		0			0
$848$	0.349645			0.0120069
$849$	12.9492	−	1.41513i	0.444416	−	0.0485670i
$850$	−25.8114	−	15.5240i	−0.885325	−	0.532470i
$851$		−	2.61053i		−	0.0894876i
$852$	1.07205	+	9.80990i	0.0367279	+	0.336082i
$853$	−29.6157			−1.01402			−0.507011	−	0.861940i	$-0.669250\pi$
$853$	−29.6157			−1.01402			−0.507011	+	0.861940i	$0.669250\pi$
$854$		0			0
$855$	25.5976	+	28.4678i	0.875419	+	0.973577i
$856$	−30.8821			−1.05553
$857$			44.6019i			1.52357i	0.647828	+	0.761787i	$0.275677\pi$
$857$			44.6019i			1.52357i	−0.647828	+	0.761787i	$0.724323\pi$
$858$	−1.99168	−	18.2250i	−0.0679949	−	0.622193i
$859$			6.43276i			0.219483i	0.993960	+	0.109741i	$0.0350023\pi$
$859$			6.43276i			0.219483i	−0.993960	+	0.109741i	$0.964998\pi$
$860$	−9.81763	−	17.3612i	−0.334778	−	0.592013i
$861$		0			0
$862$		−	22.6239i		−	0.770573i
$863$	−53.3510			−1.81609			−0.908045	−	0.418872i	$-0.862425\pi$
$863$	−53.3510			−1.81609			−0.908045	+	0.418872i	$0.862425\pi$
$864$	27.2873	−	9.24158i	0.928333	−	0.314405i
$865$	13.7763	+	24.3615i	0.468407	+	0.828317i
$866$	−4.60902			−0.156621
$867$	47.2991	−	5.16897i	1.60636	−	0.175547i
$868$		0			0
$869$		−	15.4384i		−	0.523713i
$870$	−12.0465	−	16.7494i	−0.408416	−	0.567859i
$871$			29.0901i			0.985679i
$872$	1.54359			0.0522726
$873$	−42.5817	+	9.41937i	−1.44117	+	0.318797i
$874$		−	8.41281i		−	0.284567i
$875$		0			0
$876$	−1.14286	+	0.124895i	−0.0386138	+	0.00421982i
$877$			35.4862i			1.19828i	0.800643	+	0.599142i	$0.204492\pi$
$877$			35.4862i			1.19828i	−0.800643	+	0.599142i	$0.795508\pi$
$878$			10.1969i			0.344128i
$879$	0.0199236	+	0.182313i	0.000672007	+	0.00614926i
$880$	−1.02997	−	1.82137i	−0.0347202	−	0.0613983i
$881$	−25.0114			−0.842655			−0.421327	−	0.906909i	$-0.638436\pi$
$881$	−25.0114			−0.842655			−0.421327	+	0.906909i	$0.638436\pi$
$882$		0			0
$883$			30.1344i			1.01410i	0.861916	+	0.507051i	$0.169264\pi$
$883$			30.1344i			1.01410i	−0.861916	+	0.507051i	$0.830736\pi$
$884$		−	22.7627i		−	0.765591i
$885$	3.11860	−	2.24296i	0.104830	−	0.0753963i
$886$	−19.7995			−0.665178
$887$		−	9.05903i		−	0.304172i	−0.988367	−	0.152086i	$-0.951401\pi$
$887$		−	9.05903i		−	0.304172i	0.988367	−	0.152086i	$-0.0485991\pi$
$888$	−0.865767	−	7.92227i	−0.0290532	−	0.265854i
$889$		0			0
$890$	−18.3052	+	10.3515i	−0.613592	+	0.346982i
$891$	−15.4283	−	33.1665i	−0.516867	−	1.11112i
$892$	−22.8247			−0.764227
$893$	39.4609			1.32051
$894$	2.79922	+	25.6145i	0.0936200	+	0.856678i
$895$	−13.3905	−	23.6794i	−0.447595	−	0.791514i
$896$		0			0
$897$	8.10039	−	0.885232i	0.270464	−	0.0295570i
$898$		−	0.405957i		−	0.0135470i
$899$	−11.0316			−0.367923
$900$	−5.65022	+	16.8369i	−0.188341	+	0.561230i
$901$		−	10.1273i		−	0.337390i
$902$		−	33.4931i		−	1.11520i
$903$		0			0
$904$	−34.8104			−1.15778
$905$	17.8060	+	31.4876i	0.591891	+	1.04668i
$906$	−20.4489	+	2.23470i	−0.679368	+	0.0742431i
$907$		−	9.48346i		−	0.314893i	−0.987528	−	0.157447i	$-0.949674\pi$
$907$		−	9.48346i		−	0.314893i	0.987528	−	0.157447i	$-0.0503262\pi$
$908$			13.6178i			0.451923i
$909$	40.4150	−	8.94009i	1.34048	−	0.296524i
$910$		0			0
$911$			56.8415i			1.88324i	0.336672	+	0.941622i	$0.390699\pi$
$911$			56.8415i			1.88324i	−0.336672	+	0.941622i	$0.609301\pi$
$912$	−0.247236	−	2.26236i	−0.00818682	−	0.0749142i
$913$	−16.2750			−0.538625
$914$		−	8.39461i		−	0.277669i
$915$	13.9411	+	19.3836i	0.460880	+	0.640803i
$916$		−	20.5695i		−	0.679637i
$917$		0			0
$918$	10.0410	+	29.6476i	0.331402	+	0.978518i
$919$	−57.3678			−1.89239			−0.946195	−	0.323598i	$-0.895107\pi$
$919$	−57.3678			−1.89239			−0.946195	+	0.323598i	$0.895107\pi$
$920$	9.13558	−	5.16610i	0.301191	−	0.170321i
$921$	16.0346	−	1.75230i	0.528358	−	0.0577404i
$922$	18.8498			0.620784
$923$			13.8733i			0.456645i
$924$		0			0
$925$	6.85442	+	4.12252i	0.225372	+	0.135548i
$926$			2.21584i			0.0728169i
$927$	−24.3521	+	5.38685i	−0.799827	+	0.176927i
$928$		−	32.6960i		−	1.07330i
$929$	−10.2934			−0.337714			−0.168857	−	0.985641i	$-0.554008\pi$
$929$	−10.2934			−0.337714			−0.168857	+	0.985641i	$0.554008\pi$
$930$	−3.82143	−	5.31329i	−0.125310	−	0.174230i
$931$		0			0
$932$	−0.548005			−0.0179505
$933$	43.5862	−	4.76321i	1.42695	−	0.155941i
$934$			7.20859i			0.235872i
$935$	−52.7551	+	29.8326i	−1.72528	+	0.975631i
$936$	24.2890	−	5.37290i	0.793912	−	0.175619i
$937$	−29.0347			−0.948522			−0.474261	−	0.880384i	$-0.657285\pi$
$937$	−29.0347			−0.948522			−0.474261	+	0.880384i	$0.657285\pi$
$938$		0			0
$939$	13.1715	−	1.43941i	0.429835	−	0.0469735i
$940$	9.01079	+	15.9344i	0.293900	+	0.519724i
$941$	14.9717			0.488062			0.244031	−	0.969767i	$-0.421530\pi$
$941$	14.9717			0.488062			0.244031	+	0.969767i	$0.421530\pi$
$942$	−4.95872	+	0.541902i	−0.161564	+	0.0176561i
$943$	14.8865			0.484771
$944$	−0.228358			−0.00743242
$945$		0			0
$946$	27.6596			0.899292
$947$	−14.5086			−0.471465			−0.235733	−	0.971818i	$-0.575749\pi$
$947$	−14.5086			−0.471465			−0.235733	+	0.971818i	$0.575749\pi$
$948$	7.74348	−	0.846228i	0.251496	−	0.0274842i
$949$	−1.61625			−0.0524658
$950$	22.0894	+	13.2854i	0.716675	+	0.431037i
$951$	−42.6085	+	4.65637i	−1.38167	+	0.150993i
$952$		0			0
$953$	34.9591			1.13244			0.566218	−	0.824256i	$-0.308406\pi$
$953$	34.9591			1.13244			0.566218	+	0.824256i	$0.308406\pi$
$954$	4.01842	−	0.888904i	0.130101	−	0.0287793i
$955$	9.11134	+	16.1122i	0.294836	+	0.521380i
$956$		−	20.4893i		−	0.662672i
$957$	−41.2679	+	4.50987i	−1.33400	+	0.145783i
$958$	−12.5500			−0.405473
$959$		0			0
$960$	17.1957	−	12.3675i	0.554988	−	0.399159i
$961$	27.5005			0.887114
$962$		−	4.16619i		−	0.134323i
$963$	−31.4509	+	6.95717i	−1.01349	+	0.224192i
$964$		−	5.06671i		−	0.163188i
$965$	−17.5287	−	30.9972i	−0.564268	−	0.997836i
$966$		0			0
$967$		−	46.6810i		−	1.50116i	−0.660779	−	0.750581i	$-0.729774\pi$
$967$		−	46.6810i		−	1.50116i	0.660779	−	0.750581i	$-0.270226\pi$
$968$	−15.8742			−0.510216
$969$	−65.5283	+	7.16110i	−2.10507	+	0.230048i
$970$	−25.5600	+	14.4540i	−0.820681	+	0.464088i
$971$	−1.31338			−0.0421484			−0.0210742	−	0.999778i	$-0.506709\pi$
$971$	−1.31338			−0.0421484			−0.0210742	+	0.999778i	$0.506709\pi$
$972$	15.7897	−	9.55635i	0.506456	−	0.306520i
$973$		0			0
$974$			23.9482i			0.767350i
$975$	−10.4677	+	22.6670i	−0.335236	+	0.725926i
$976$		−	1.41936i		−	0.0454326i
$977$	−53.0752			−1.69803			−0.849013	−	0.528372i	$-0.822803\pi$
$977$	−53.0752			−1.69803			−0.849013	+	0.528372i	$0.822803\pi$
$978$	3.27701	+	29.9866i	0.104787	+	0.958865i
$979$			42.3140i			1.35236i
$980$		0			0
$981$	1.57202	−	0.347743i	0.0501908	−	0.0111026i
$982$			2.30000i			0.0733961i
$983$			21.1136i			0.673418i	0.941609	+	0.336709i	$0.109314\pi$
$983$			21.1136i			0.673418i	−0.941609	+	0.336709i	$0.890686\pi$
$984$	45.1767	−	4.93703i	1.44018	−	0.157387i
$985$	46.4681	−	26.2773i	1.48060	−	0.837266i
$986$	35.5242			1.13132
$987$		0			0
$988$			19.4803i			0.619750i
$989$			12.2937i			0.390918i
$990$	−16.4678	−	18.3142i	−0.523379	−	0.582064i
$991$	−53.6348			−1.70377			−0.851883	−	0.523732i	$-0.824539\pi$
$991$	−53.6348			−1.70377			−0.851883	+	0.523732i	$0.824539\pi$
$992$		−	10.3719i		−	0.329308i
$993$	28.1621	−	3.07763i	0.893698	−	0.0976657i
$994$		0			0
$995$	13.4583	+	23.7993i	0.426657	+	0.754488i
$996$	−0.892084	−	8.16309i	−0.0282668	−	0.258658i
$997$	38.8870			1.23156			0.615781	−	0.787917i	$-0.288841\pi$
$997$	38.8870			1.23156			0.615781	+	0.787917i	$0.288841\pi$
$998$	−26.7836			−0.847820
$999$	−2.66646	−	7.87316i	−0.0843629	−	0.249096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.g.c.734.10	yes	32
3.2	odd	2	inner	735.2.g.c.734.21	yes	32
5.4	even	2	inner	735.2.g.c.734.23	yes	32
7.2	even	3		735.2.p.g.374.23		64
7.3	odd	6		735.2.p.g.509.21		64
7.4	even	3		735.2.p.g.509.24		64
7.5	odd	6		735.2.p.g.374.22		64
7.6	odd	2	inner	735.2.g.c.734.11	yes	32
15.14	odd	2	inner	735.2.g.c.734.12	yes	32
21.2	odd	6		735.2.p.g.374.12		64
21.5	even	6		735.2.p.g.374.9		64
21.11	odd	6		735.2.p.g.509.11		64
21.17	even	6		735.2.p.g.509.10		64
21.20	even	2	inner	735.2.g.c.734.24	yes	32
35.4	even	6		735.2.p.g.509.9		64
35.9	even	6		735.2.p.g.374.10		64
35.19	odd	6		735.2.p.g.374.11		64
35.24	odd	6		735.2.p.g.509.12		64
35.34	odd	2	inner	735.2.g.c.734.22	yes	32
105.44	odd	6		735.2.p.g.374.21		64
105.59	even	6		735.2.p.g.509.23		64
105.74	odd	6		735.2.p.g.509.22		64
105.89	even	6		735.2.p.g.374.24		64
105.104	even	2	inner	735.2.g.c.734.9	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.g.c.734.9	✓	32	105.104	even	2	inner
735.2.g.c.734.10	yes	32	1.1	even	1	trivial
735.2.g.c.734.11	yes	32	7.6	odd	2	inner
735.2.g.c.734.12	yes	32	15.14	odd	2	inner
735.2.g.c.734.21	yes	32	3.2	odd	2	inner
735.2.g.c.734.22	yes	32	35.34	odd	2	inner
735.2.g.c.734.23	yes	32	5.4	even	2	inner
735.2.g.c.734.24	yes	32	21.20	even	2	inner
735.2.p.g.374.9		64	21.5	even	6
735.2.p.g.374.10		64	35.9	even	6
735.2.p.g.374.11		64	35.19	odd	6
735.2.p.g.374.12		64	21.2	odd	6
735.2.p.g.374.21		64	105.44	odd	6
735.2.p.g.374.22		64	7.5	odd	6
735.2.p.g.374.23		64	7.2	even	3
735.2.p.g.374.24		64	105.89	even	6
735.2.p.g.509.9		64	35.4	even	6
735.2.p.g.509.10		64	21.17	even	6
735.2.p.g.509.11		64	21.11	odd	6
735.2.p.g.509.12		64	35.24	odd	6
735.2.p.g.509.21		64	7.3	odd	6
735.2.p.g.509.22		64	105.74	odd	6
735.2.p.g.509.23		64	105.59	even	6
735.2.p.g.509.24		64	7.4	even	3

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.903339 q^{2} +(-1.72180 + 0.188163i) q^{3} -1.18398 q^{4} +(-1.94641 + 1.10068i) q^{5} +(1.55537 - 0.169975i) q^{6} +2.87621 q^{8} +(2.92919 - 0.647957i) q^{9} +(1.75827 - 0.994285i) q^{10} -4.06437i q^{11} +(2.03858 - 0.222781i) q^{12} +2.88298 q^{13} +(3.14422 - 2.26139i) q^{15} -0.230234 q^{16} +6.66864i q^{17} +(-2.64605 + 0.585325i) q^{18} -5.70701i q^{19} +(2.30451 - 1.30318i) q^{20} +3.67151i q^{22} -1.63185 q^{23} +(-4.95226 + 0.541196i) q^{24} +(2.57701 - 4.28474i) q^{25} -2.60431 q^{26} +(-4.92156 + 1.66682i) q^{27} +5.89707i q^{29} +(-2.84029 + 2.04280i) q^{30} +1.87068i q^{31} -5.54444 q^{32} +(0.764764 + 6.99804i) q^{33} -6.02404i q^{34} +(-3.46810 + 0.767168i) q^{36} +1.59973i q^{37} +5.15537i q^{38} +(-4.96392 + 0.542470i) q^{39} +(-5.59828 + 3.16578i) q^{40} -9.12244 q^{41} -7.53359i q^{43} +4.81213i q^{44} +(-4.98821 + 4.48529i) q^{45} +1.47412 q^{46} +6.91446i q^{47} +(0.396417 - 0.0433215i) q^{48} +(-2.32792 + 3.87057i) q^{50} +(-1.25479 - 11.4821i) q^{51} -3.41339 q^{52} -1.51865 q^{53} +(4.44583 - 1.50570i) q^{54} +(4.47357 + 7.91093i) q^{55} +(1.07385 + 9.82633i) q^{57} -5.32705i q^{58} +0.991850 q^{59} +(-3.72269 + 2.67744i) q^{60} +6.16485i q^{61} -1.68986i q^{62} +5.46898 q^{64} +(-5.61146 + 3.17324i) q^{65} +(-0.690841 - 6.32160i) q^{66} +10.0903i q^{67} -7.89553i q^{68} +(2.80973 - 0.307054i) q^{69} +4.81213i q^{71} +(8.42497 - 1.86366i) q^{72} -0.560619 q^{73} -1.44510i q^{74} +(-3.63087 + 7.86236i) q^{75} +6.75699i q^{76} +(4.48410 - 0.490034i) q^{78} +3.79848 q^{79} +(0.448130 - 0.253414i) q^{80} +(8.16030 - 3.79598i) q^{81} +8.24065 q^{82} -4.00431i q^{83} +(-7.34003 - 12.9799i) q^{85} +6.80539i q^{86} +(-1.10961 - 10.1536i) q^{87} -11.6900i q^{88} -10.4109 q^{89} +(4.50604 - 4.05173i) q^{90} +1.93208 q^{92} +(-0.351993 - 3.22094i) q^{93} -6.24610i q^{94} +(6.28159 + 11.1082i) q^{95} +(9.54642 - 1.04326i) q^{96} -14.5370 q^{97} +(-2.63354 - 11.9053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 40 q^{9} + 16 q^{15} - 16 q^{16} + 64 q^{25} + 56 q^{30} - 16 q^{36} - 56 q^{39} - 32 q^{46} - 40 q^{51} + 8 q^{60} - 176 q^{64} + 48 q^{79} - 40 q^{81} - 64 q^{85} + 40 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 + 40 * q^9 + 16 * q^15 - 16 * q^16 + 64 * q^25 + 56 * q^30 - 16 * q^36 - 56 * q^39 - 32 * q^46 - 40 * q^51 + 8 * q^60 - 176 * q^64 + 48 * q^79 - 40 * q^81 - 64 * q^85 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more