LMFDB - Embedded newform 756.2.e.b.323.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(323,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("756.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.e (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.8
Character	$\chi$	$=$	756.323
Dual form			756.2.e.b.323.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.932512 + 1.06321i) q^{2} +(-0.260844 - 1.98292i) q^{4} +0.546170i q^{5} -1.00000i q^{7} +(2.35150 + 1.57176i) q^{8} +O(q^{10})$	\(q+(-0.932512 + 1.06321i) q^{2} +(-0.260844 - 1.98292i) q^{4} +0.546170i q^{5} -1.00000i q^{7} +(2.35150 + 1.57176i) q^{8} +(-0.580695 - 0.509310i) q^{10} +4.32940 q^{11} -3.39014 q^{13} +(1.06321 + 0.932512i) q^{14} +(-3.86392 + 1.03446i) q^{16} +0.0960161i q^{17} -7.78185i q^{19} +(1.08301 - 0.142465i) q^{20} +(-4.03722 + 4.60308i) q^{22} -0.716100 q^{23} +4.70170 q^{25} +(3.16135 - 3.60444i) q^{26} +(-1.98292 + 0.260844i) q^{28} +2.80103i q^{29} -1.38048i q^{31} +(2.50330 - 5.07282i) q^{32} +(-0.102086 - 0.0895361i) q^{34} +0.546170 q^{35} +9.87923 q^{37} +(8.27376 + 7.25666i) q^{38} +(-0.858449 + 1.28432i) q^{40} -9.42938i q^{41} -1.12293i q^{43} +(-1.12930 - 8.58485i) q^{44} +(0.667771 - 0.761366i) q^{46} +10.2208 q^{47} -1.00000 q^{49} +(-4.38439 + 4.99891i) q^{50} +(0.884297 + 6.72237i) q^{52} +10.3377i q^{53} +2.36459i q^{55} +(1.57176 - 2.35150i) q^{56} +(-2.97809 - 2.61199i) q^{58} +7.15116 q^{59} +4.47260 q^{61} +(1.46775 + 1.28732i) q^{62} +(3.05913 + 7.39200i) q^{64} -1.85159i q^{65} -10.1781i q^{67} +(0.190392 - 0.0250452i) q^{68} +(-0.509310 + 0.580695i) q^{70} -5.68379 q^{71} +0.760273 q^{73} +(-9.21250 + 10.5037i) q^{74} +(-15.4308 + 2.02985i) q^{76} -4.32940i q^{77} +1.95953i q^{79} +(-0.564993 - 2.11036i) q^{80} +(10.0254 + 8.79301i) q^{82} -3.56402 q^{83} -0.0524411 q^{85} +(1.19391 + 1.04715i) q^{86} +(10.1806 + 6.80479i) q^{88} -5.30500i q^{89} +3.39014i q^{91} +(0.186790 + 1.41997i) q^{92} +(-9.53098 + 10.8669i) q^{94} +4.25021 q^{95} +13.8514 q^{97} +(0.932512 - 1.06321i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4}+O(q^{10}) $ 24 * q + 4 * q^4	$ 24 q + 4 q^{4} + 20 q^{10} + 20 q^{16} - 8 q^{22} - 24 q^{25} - 8 q^{28} - 20 q^{34} + 16 q^{37} - 32 q^{40} + 36 q^{46} - 24 q^{49} + 16 q^{52} - 52 q^{58} + 16 q^{61} + 4 q^{64} + 12 q^{70} + 4 q^{82} - 64 q^{85} - 16 q^{88} + 12 q^{94}+O(q^{100}) $ 24 * q + 4 * q^4 + 20 * q^10 + 20 * q^16 - 8 * q^22 - 24 * q^25 - 8 * q^28 - 20 * q^34 + 16 * q^37 - 32 * q^40 + 36 * q^46 - 24 * q^49 + 16 * q^52 - 52 * q^58 + 16 * q^61 + 4 * q^64 + 12 * q^70 + 4 * q^82 - 64 * q^85 - 16 * q^88 + 12 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.932512	+	1.06321i	−0.659385	+	0.751805i
$2$	−0.932512	+	1.06321i	−0.659385	+	0.751805i
$3$		0			0
$3$		0			0
$4$	−0.260844	−	1.98292i	−0.130422	−	0.991459i
$5$			0.546170i			0.244255i	0.992514	+	0.122127i	$0.0389716\pi$
$5$			0.546170i			0.244255i	−0.992514	+	0.122127i	$0.961028\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.35150	+	1.57176i	0.831382	+	0.555702i
$9$		0			0
$10$	−0.580695	−	0.509310i	−0.183632	−	0.161058i
$11$	4.32940			1.30536			0.652682	−	0.757632i	$-0.273644\pi$
$11$	4.32940			1.30536			0.652682	+	0.757632i	$0.273644\pi$
$12$		0			0
$13$	−3.39014			−0.940256			−0.470128	−	0.882598i	$-0.655792\pi$
$13$	−3.39014			−0.940256			−0.470128	+	0.882598i	$0.655792\pi$
$14$	1.06321	+	0.932512i	0.284156	+	0.249224i
$15$		0			0
$16$	−3.86392	+	1.03446i	−0.965980	+	0.258616i
$17$			0.0960161i			0.0232873i	0.999932	+	0.0116437i	$0.00370638\pi$
$17$			0.0960161i			0.0232873i	−0.999932	+	0.0116437i	$0.996294\pi$
$18$		0			0
$19$		−	7.78185i		−	1.78528i	−0.450772	−	0.892639i	$-0.648851\pi$
$19$		−	7.78185i		−	1.78528i	0.450772	−	0.892639i	$-0.351149\pi$
$20$	1.08301	−	0.142465i	0.242168	−	0.0318561i
$21$		0			0
$22$	−4.03722	+	4.60308i	−0.860738	+	0.981379i
$23$	−0.716100			−0.149317			−0.0746585	−	0.997209i	$-0.523787\pi$
$23$	−0.716100			−0.149317			−0.0746585	+	0.997209i	$0.523787\pi$
$24$		0			0
$25$	4.70170			0.940340
$26$	3.16135	−	3.60444i	0.619991	−	0.706889i
$27$		0			0
$28$	−1.98292	+	0.260844i	−0.374736	+	0.0492948i
$29$			2.80103i			0.520137i	0.965590	+	0.260069i	$0.0837452\pi$
$29$			2.80103i			0.520137i	−0.965590	+	0.260069i	$0.916255\pi$
$30$		0			0
$31$		−	1.38048i		−	0.247942i	−0.992286	−	0.123971i	$-0.960437\pi$
$31$		−	1.38048i		−	0.247942i	0.992286	−	0.123971i	$-0.0395629\pi$
$32$	2.50330	−	5.07282i	0.442525	−	0.896756i
$33$		0			0
$34$	−0.102086	−	0.0895361i	−0.0175075	−	0.0153553i
$35$	0.546170			0.0923196
$36$		0			0
$37$	9.87923			1.62414			0.812068	−	0.583563i	$-0.198342\pi$
$37$	9.87923			1.62414			0.812068	+	0.583563i	$0.198342\pi$
$38$	8.27376	+	7.25666i	1.34218	+	1.17719i
$39$		0			0
$40$	−0.858449	+	1.28432i	−0.135733	+	0.203069i
$41$		−	9.42938i		−	1.47262i	−0.676644	−	0.736311i	$-0.736566\pi$
$41$		−	9.42938i		−	1.47262i	0.676644	−	0.736311i	$-0.263434\pi$
$42$		0			0
$43$		−	1.12293i		−	0.171245i	−0.996328	−	0.0856226i	$-0.972712\pi$
$43$		−	1.12293i		−	0.171245i	0.996328	−	0.0856226i	$-0.0272879\pi$
$44$	−1.12930	−	8.58485i	−0.170248	−	1.29421i
$45$		0			0
$46$	0.667771	−	0.761366i	0.0984575	−	0.112257i
$47$	10.2208			1.49085			0.745426	−	0.666588i	$-0.232246\pi$
$47$	10.2208			1.49085			0.745426	+	0.666588i	$0.232246\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−4.38439	+	4.99891i	−0.620046	+	0.706952i
$51$		0			0
$52$	0.884297	+	6.72237i	0.122630	+	0.932225i
$53$			10.3377i			1.41999i	0.704208	+	0.709994i	$0.251302\pi$
$53$			10.3377i			1.41999i	−0.704208	+	0.709994i	$0.748698\pi$
$54$		0			0
$55$			2.36459i			0.318841i
$56$	1.57176	−	2.35150i	0.210035	−	0.314233i
$57$		0			0
$58$	−2.97809	−	2.61199i	−0.391042	−	0.342971i
$59$	7.15116			0.931001			0.465501	−	0.885048i	$-0.345874\pi$
$59$	7.15116			0.931001			0.465501	+	0.885048i	$0.345874\pi$
$60$		0			0
$61$	4.47260			0.572658			0.286329	−	0.958131i	$-0.407565\pi$
$61$	4.47260			0.572658			0.286329	+	0.958131i	$0.407565\pi$
$62$	1.46775	+	1.28732i	0.186404	+	0.163489i
$63$		0			0
$64$	3.05913	+	7.39200i	0.382392	+	0.924000i
$65$		−	1.85159i		−	0.229662i
$66$		0			0
$67$		−	10.1781i		−	1.24346i	−0.783233	−	0.621728i	$-0.786431\pi$
$67$		−	10.1781i		−	1.24346i	0.783233	−	0.621728i	$-0.213569\pi$
$68$	0.190392	−	0.0250452i	0.0230884	−	0.00303717i
$69$		0			0
$70$	−0.509310	+	0.580695i	−0.0608742	+	0.0694064i
$71$	−5.68379			−0.674542			−0.337271	−	0.941408i	$-0.609504\pi$
$71$	−5.68379			−0.674542			−0.337271	+	0.941408i	$0.609504\pi$
$72$		0			0
$73$	0.760273			0.0889832			0.0444916	−	0.999010i	$-0.485833\pi$
$73$	0.760273			0.0889832			0.0444916	+	0.999010i	$0.485833\pi$
$74$	−9.21250	+	10.5037i	−1.07093	+	1.22103i
$75$		0			0
$76$	−15.4308	+	2.02985i	−1.77003	+	0.232839i
$77$		−	4.32940i		−	0.493381i
$78$		0			0
$79$			1.95953i			0.220464i	0.993906	+	0.110232i	$0.0351594\pi$
$79$			1.95953i			0.220464i	−0.993906	+	0.110232i	$0.964841\pi$
$80$	−0.564993	−	2.11036i	−0.0631681	−	0.235945i
$81$		0			0
$82$	10.0254	+	8.79301i	1.10712	+	0.971025i
$83$	−3.56402			−0.391202			−0.195601	−	0.980684i	$-0.562666\pi$
$83$	−3.56402			−0.391202			−0.195601	+	0.980684i	$0.562666\pi$
$84$		0			0
$85$	−0.0524411			−0.00568804
$86$	1.19391	+	1.04715i	0.128743	+	0.112917i
$87$		0			0
$88$	10.1806	+	6.80479i	1.08526	+	0.725393i
$89$		−	5.30500i		−	0.562329i	−0.959660	−	0.281164i	$-0.909279\pi$
$89$		−	5.30500i		−	0.562329i	0.959660	−	0.281164i	$-0.0907206\pi$
$90$		0			0
$91$			3.39014i			0.355383i
$92$	0.186790	+	1.41997i	0.0194742	+	0.148042i
$93$		0			0
$94$	−9.53098	+	10.8669i	−0.983046	+	1.12083i
$95$	4.25021			0.436063
$96$		0			0
$97$	13.8514			1.40639			0.703197	−	0.710995i	$-0.251755\pi$
$97$	13.8514			1.40639			0.703197	+	0.710995i	$0.251755\pi$
$98$	0.932512	−	1.06321i	0.0941979	−	0.107401i
$99$		0			0
$100$	−1.22641	−	9.32308i	−0.122641	−	0.932308i
$101$			7.60411i			0.756637i	0.925675	+	0.378319i	$0.123498\pi$
$101$			7.60411i			0.756637i	−0.925675	+	0.378319i	$0.876502\pi$
$102$		0			0
$103$		−	1.70783i		−	0.168278i	−0.996454	−	0.0841388i	$-0.973186\pi$
$103$		−	1.70783i		−	0.168278i	0.996454	−	0.0841388i	$-0.0268139\pi$
$104$	−7.97193	−	5.32849i	−0.781712	−	0.522502i
$105$		0			0
$106$	−10.9911	−	9.64000i	−1.06755	−	0.936320i
$107$	−12.0437			−1.16431			−0.582155	−	0.813078i	$-0.697790\pi$
$107$	−12.0437			−1.16431			−0.582155	+	0.813078i	$0.697790\pi$
$108$		0			0
$109$	14.6297			1.40127			0.700634	−	0.713521i	$-0.252900\pi$
$109$	14.6297			1.40127			0.700634	+	0.713521i	$0.252900\pi$
$110$	−2.51406	−	2.20501i	−0.239707	−	0.210239i
$111$		0			0
$112$	1.03446	+	3.86392i	0.0977475	+	0.365106i
$113$			15.7696i			1.48348i	0.670688	+	0.741740i	$0.265999\pi$
$113$			15.7696i			1.48348i	−0.670688	+	0.741740i	$0.734001\pi$
$114$		0			0
$115$		−	0.391112i		−	0.0364714i
$116$	5.55420	−	0.730630i	0.515695	−	0.0678373i
$117$		0			0
$118$	−6.66854	+	7.60320i	−0.613889	+	0.699931i
$119$	0.0960161			0.00880178
$120$		0			0
$121$	7.74373			0.703976
$122$	−4.17075	+	4.75533i	−0.377602	+	0.430527i
$123$		0			0
$124$	−2.73738	+	0.360090i	−0.245824	+	0.0323370i
$125$			5.29878i			0.473937i
$126$		0			0
$127$			6.02905i			0.534992i	0.963559	+	0.267496i	$0.0861961\pi$
$127$			6.02905i			0.534992i	−0.963559	+	0.267496i	$0.913804\pi$
$128$	−10.7120	−	3.64062i	−0.946812	−	0.321788i
$129$		0			0
$130$	1.96864	+	1.72663i	0.172661	+	0.151436i
$131$	−16.0875			−1.40558			−0.702788	−	0.711399i	$-0.748062\pi$
$131$	−16.0875			−1.40558			−0.702788	+	0.711399i	$0.748062\pi$
$132$		0			0
$133$	−7.78185			−0.674772
$134$	10.8215	+	9.49122i	0.934836	+	0.819917i
$135$		0			0
$136$	−0.150914	+	0.225782i	−0.0129408	+	0.0193607i
$137$		−	12.5367i		−	1.07108i	−0.844509	−	0.535541i	$-0.820108\pi$
$137$		−	12.5367i		−	1.07108i	0.844509	−	0.535541i	$-0.179892\pi$
$138$		0			0
$139$			1.60676i			0.136283i	0.997676	+	0.0681417i	$0.0217070\pi$
$139$			1.60676i			0.136283i	−0.997676	+	0.0681417i	$0.978293\pi$
$140$	−0.142465	−	1.08301i	−0.0120405	−	0.0915311i
$141$		0			0
$142$	5.30020	−	6.04308i	0.444783	−	0.507124i
$143$	−14.6773			−1.22738
$144$		0			0
$145$	−1.52984			−0.127046
$146$	−0.708963	+	0.808332i	−0.0586742	+	0.0668980i
$147$		0			0
$148$	−2.57693	−	19.5897i	−0.211823	−	1.61026i
$149$		−	13.8728i		−	1.13651i	−0.822854	−	0.568253i	$-0.807620\pi$
$149$		−	13.8728i		−	1.13651i	0.822854	−	0.568253i	$-0.192380\pi$
$150$		0			0
$151$		−	20.3035i		−	1.65228i	−0.563468	−	0.826138i	$-0.690533\pi$
$151$		−	20.3035i		−	1.65228i	0.563468	−	0.826138i	$-0.309467\pi$
$152$	12.2312	−	18.2990i	0.992082	−	1.48425i
$153$		0			0
$154$	4.60308	+	4.03722i	0.370927	+	0.325328i
$155$	0.753978			0.0605610
$156$		0			0
$157$	−20.8258			−1.66208			−0.831041	−	0.556212i	$-0.812254\pi$
$157$	−20.8258			−1.66208			−0.831041	+	0.556212i	$0.812254\pi$
$158$	−2.08340	−	1.82728i	−0.165746	−	0.145371i
$159$		0			0
$160$	2.77062	+	1.36723i	0.219037	+	0.108089i
$161$			0.716100i			0.0564366i
$162$		0			0
$163$			9.81556i			0.768814i	0.923164	+	0.384407i	$0.125594\pi$
$163$			9.81556i			0.768814i	−0.923164	+	0.384407i	$0.874406\pi$
$164$	−18.6977	+	2.45959i	−1.46004	+	0.192062i
$165$		0			0
$166$	3.32349	−	3.78931i	0.257953	−	0.294108i
$167$	7.70531			0.596255			0.298127	−	0.954526i	$-0.403638\pi$
$167$	7.70531			0.596255			0.298127	+	0.954526i	$0.403638\pi$
$168$		0			0
$169$	−1.50694			−0.115918
$170$	0.0489020	−	0.0557561i	0.00375061	−	0.00427630i
$171$		0			0
$172$	−2.22668	+	0.292909i	−0.169783	+	0.0223341i
$173$		−	15.3623i		−	1.16797i	−0.811763	−	0.583986i	$-0.801492\pi$
$173$		−	15.3623i		−	1.16797i	0.811763	−	0.583986i	$-0.198508\pi$
$174$		0			0
$175$		−	4.70170i		−	0.355415i
$176$	−16.7285	+	4.47861i	−1.26096	+	0.337588i
$177$		0			0
$178$	5.64035	+	4.94698i	0.422762	+	0.370791i
$179$	−18.7031			−1.39794			−0.698968	−	0.715153i	$-0.746357\pi$
$179$	−18.7031			−1.39794			−0.698968	+	0.715153i	$0.746357\pi$
$180$		0			0
$181$	−8.07751			−0.600397			−0.300198	−	0.953877i	$-0.597053\pi$
$181$	−8.07751			−0.600397			−0.300198	+	0.953877i	$0.597053\pi$
$182$	−3.60444	−	3.16135i	−0.267179	−	0.234335i
$183$		0			0
$184$	−1.68391	−	1.12554i	−0.124140	−	0.0829757i
$185$			5.39574i			0.396703i
$186$		0			0
$187$			0.415692i			0.0303984i
$188$	−2.66602	−	20.2669i	−0.194440	−	1.47812i
$189$		0			0
$190$	−3.96337	+	4.51888i	−0.287533	+	0.327834i
$191$	8.39933			0.607754			0.303877	−	0.952711i	$-0.401719\pi$
$191$	8.39933			0.607754			0.303877	+	0.952711i	$0.401719\pi$
$192$		0			0
$193$	−14.8492			−1.06887			−0.534436	−	0.845209i	$-0.679476\pi$
$193$	−14.8492			−1.06887			−0.534436	+	0.845209i	$0.679476\pi$
$194$	−12.9166	+	14.7270i	−0.927355	+	1.05733i
$195$		0			0
$196$	0.260844	+	1.98292i	0.0186317	+	0.141637i
$197$			23.5310i			1.67651i	0.545275	+	0.838257i	$0.316425\pi$
$197$			23.5310i			1.67651i	−0.545275	+	0.838257i	$0.683575\pi$
$198$		0			0
$199$		−	23.6792i		−	1.67857i	−0.543690	−	0.839286i	$-0.682973\pi$
$199$		−	23.6792i		−	1.67857i	0.543690	−	0.839286i	$-0.317027\pi$
$200$	11.0561	+	7.38995i	0.781781	+	0.522548i
$201$		0			0
$202$	−8.08479	−	7.09092i	−0.568844	−	0.498916i
$203$	2.80103			0.196593
$204$		0			0
$205$	5.15005			0.359695
$206$	1.81579	+	1.59257i	0.126512	+	0.110960i
$207$		0			0
$208$	13.0992	−	3.50697i	0.908269	−	0.243165i
$209$		−	33.6908i		−	2.33044i
$210$		0			0
$211$			3.20308i			0.220509i	0.993903	+	0.110255i	$0.0351666\pi$
$211$			3.20308i			0.220509i	−0.993903	+	0.110255i	$0.964833\pi$
$212$	20.4987	−	2.69652i	1.40786	−	0.185197i
$213$		0			0
$214$	11.2309	−	12.8050i	0.767729	−	0.875334i
$215$	0.613311			0.0418275
$216$		0			0
$217$	−1.38048			−0.0937132
$218$	−13.6423	+	15.5545i	−0.923976	+	1.05348i
$219$		0			0
$220$	4.68879	−	0.616788i	0.316118	−	0.0415839i
$221$		−	0.325508i		−	0.0218961i
$222$		0			0
$223$			21.1778i			1.41817i	0.705121	+	0.709087i	$0.250892\pi$
$223$			21.1778i			1.41817i	−0.705121	+	0.709087i	$0.749108\pi$
$224$	−5.07282	−	2.50330i	−0.338942	−	0.167259i
$225$		0			0
$226$	−16.7665	−	14.7053i	−1.11529	−	0.978185i
$227$	4.15700			0.275910			0.137955	−	0.990439i	$-0.455947\pi$
$227$	4.15700			0.275910			0.137955	+	0.990439i	$0.455947\pi$
$228$		0			0
$229$	0.319653			0.0211232			0.0105616	−	0.999944i	$-0.496638\pi$
$229$	0.319653			0.0211232			0.0105616	+	0.999944i	$0.496638\pi$
$230$	0.415836	+	0.364717i	0.0274194	+	0.0240487i
$231$		0			0
$232$	−4.40254	+	6.58662i	−0.289041	+	0.432433i
$233$			3.81568i			0.249974i	0.992158	+	0.124987i	$0.0398889\pi$
$233$			3.81568i			0.249974i	−0.992158	+	0.124987i	$0.960111\pi$
$234$		0			0
$235$			5.58228i			0.364148i
$236$	−1.86533	−	14.1802i	−0.121423	−	0.923049i
$237$		0			0
$238$	−0.0895361	+	0.102086i	−0.00580377	+	0.00661722i
$239$	−5.19473			−0.336019			−0.168009	−	0.985785i	$-0.553734\pi$
$239$	−5.19473			−0.336019			−0.168009	+	0.985785i	$0.553734\pi$
$240$		0			0
$241$	−17.4806			−1.12603			−0.563013	−	0.826448i	$-0.690358\pi$
$241$	−17.4806			−1.12603			−0.563013	+	0.826448i	$0.690358\pi$
$242$	−7.22112	+	8.23324i	−0.464191	+	0.529253i
$243$		0			0
$244$	−1.16665	−	8.86880i	−0.0746871	−	0.567767i
$245$		−	0.546170i		−	0.0348935i
$246$		0			0
$247$			26.3816i			1.67862i
$248$	2.16979	−	3.24621i	0.137782	−	0.206134i
$249$		0			0
$250$	−5.63373	−	4.94117i	−0.356308	−	0.312507i
$251$	7.32620			0.462426			0.231213	−	0.972903i	$-0.425731\pi$
$251$	7.32620			0.462426			0.231213	+	0.972903i	$0.425731\pi$
$252$		0			0
$253$	−3.10028			−0.194913
$254$	−6.41016	−	5.62216i	−0.402209	−	0.352766i
$255$		0			0
$256$	13.8598	−	7.99416i	0.866236	−	0.499635i
$257$		−	15.5523i		−	0.970123i	−0.874480	−	0.485062i	$-0.838797\pi$
$257$		−	15.5523i		−	0.970123i	0.874480	−	0.485062i	$-0.161203\pi$
$258$		0			0
$259$		−	9.87923i		−	0.613865i
$260$	−3.67156	+	0.482977i	−0.227700	+	0.0299529i
$261$		0			0
$262$	15.0018	−	17.1045i	0.926816	−	1.05672i
$263$	−21.9908			−1.35601			−0.678005	−	0.735057i	$-0.737155\pi$
$263$	−21.9908			−1.35601			−0.678005	+	0.735057i	$0.737155\pi$
$264$		0			0
$265$	−5.64613			−0.346839
$266$	7.25666	−	8.27376i	0.444935	−	0.507297i
$267$		0			0
$268$	−20.1824	+	2.65490i	−1.23283	+	0.162174i
$269$			26.0711i			1.58958i	0.606883	+	0.794791i	$0.292420\pi$
$269$			26.0711i			1.58958i	−0.606883	+	0.794791i	$0.707580\pi$
$270$		0			0
$271$		−	18.3875i		−	1.11696i	−0.829517	−	0.558481i	$-0.811384\pi$
$271$		−	18.3875i		−	1.11696i	0.829517	−	0.558481i	$-0.188616\pi$
$272$	−0.0993251	−	0.370999i	−0.00602247	−	0.0224951i
$273$		0			0
$274$	13.3292	+	11.6906i	0.805246	+	0.706256i
$275$	20.3555			1.22749
$276$		0			0
$277$	1.01025			0.0607003			0.0303502	−	0.999539i	$-0.490338\pi$
$277$	1.01025			0.0607003			0.0303502	+	0.999539i	$0.490338\pi$
$278$	−1.70833	−	1.49832i	−0.102459	−	0.0898633i
$279$		0			0
$280$	1.28432	+	0.858449i	0.0767529	+	0.0513022i
$281$			15.0496i			0.897784i	0.893586	+	0.448892i	$0.148181\pi$
$281$			15.0496i			0.897784i	−0.893586	+	0.448892i	$0.851819\pi$
$282$		0			0
$283$		−	1.14369i		−	0.0679851i	−0.999422	−	0.0339926i	$-0.989178\pi$
$283$		−	1.14369i		−	0.0679851i	0.999422	−	0.0339926i	$-0.0108223\pi$
$284$	1.48258	+	11.2705i	0.0879749	+	0.668780i
$285$		0			0
$286$	13.6867	−	15.6051i	0.809314	−	0.922748i
$287$	−9.42938			−0.556599
$288$		0			0
$289$	16.9908			0.999458
$290$	1.42659	−	1.62654i	0.0837723	−	0.0955139i
$291$		0			0
$292$	−0.198312	−	1.50756i	−0.0116054	−	0.0882232i
$293$			31.3747i			1.83293i	0.400113	+	0.916466i	$0.368971\pi$
$293$			31.3747i			1.83293i	−0.400113	+	0.916466i	$0.631029\pi$
$294$		0			0
$295$			3.90575i			0.227401i
$296$	23.2310	+	15.5278i	1.35028	+	0.902534i
$297$		0			0
$298$	14.7498	+	12.9366i	0.854430	+	0.749395i
$299$	2.42768			0.140396
$300$		0			0
$301$	−1.12293			−0.0647246
$302$	21.5870	+	18.9333i	1.24219	+	1.08949i
$303$		0			0
$304$	8.05003	+	30.0684i	0.461701	+	1.72454i
$305$			2.44280i			0.139874i
$306$		0			0
$307$			26.0117i			1.48457i	0.670086	+	0.742284i	$0.266257\pi$
$307$			26.0117i			1.48457i	−0.670086	+	0.742284i	$0.733743\pi$
$308$	−8.58485	+	1.12930i	−0.489167	+	0.0643477i
$309$		0			0
$310$	−0.703093	+	0.801639i	−0.0399330	+	0.0455300i
$311$	1.17950			0.0668835			0.0334418	−	0.999441i	$-0.489353\pi$
$311$	1.17950			0.0668835			0.0334418	+	0.999441i	$0.489353\pi$
$312$		0			0
$313$	−25.0849			−1.41788			−0.708942	−	0.705267i	$-0.750827\pi$
$313$	−25.0849			−1.41788			−0.708942	+	0.705267i	$0.750827\pi$
$314$	19.4203	−	22.1423i	1.09595	−	1.24956i
$315$		0			0
$316$	3.88559	−	0.511131i	0.218581	−	0.0287534i
$317$			8.10102i			0.454998i	0.973778	+	0.227499i	$0.0730549\pi$
$317$			8.10102i			0.454998i	−0.973778	+	0.227499i	$0.926945\pi$
$318$		0			0
$319$			12.1268i			0.678969i
$320$	−4.03729	+	1.67081i	−0.225691	+	0.0934010i
$321$		0			0
$322$	−0.761366	−	0.667771i	−0.0424293	−	0.0372134i
$323$	0.747183			0.0415744
$324$		0			0
$325$	−15.9394			−0.884160
$326$	−10.4360	−	9.15313i	−0.577998	−	0.506945i
$327$		0			0
$328$	14.8207	−	22.1732i	0.818338	−	1.22431i
$329$		−	10.2208i		−	0.563489i
$330$		0			0
$331$			29.5057i			1.62178i	0.585199	+	0.810890i	$0.301016\pi$
$331$			29.5057i			1.62178i	−0.585199	+	0.810890i	$0.698984\pi$
$332$	0.929651	+	7.06715i	0.0510212	+	0.387860i
$333$		0			0
$334$	−7.18529	+	8.19239i	−0.393162	+	0.448268i
$335$	5.55899			0.303720
$336$		0			0
$337$	20.7381			1.12968			0.564838	−	0.825202i	$-0.308939\pi$
$337$	20.7381			1.12968			0.564838	+	0.825202i	$0.308939\pi$
$338$	1.40524	−	1.60220i	0.0764349	−	0.0871480i
$339$		0			0
$340$	0.0136789	+	0.103986i	0.000741844	+	0.00563946i
$341$		−	5.97666i		−	0.323654i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	1.76498	−	2.64057i	0.0951613	−	0.142370i
$345$		0			0
$346$	16.3334	+	14.3255i	0.878088	+	0.770144i
$347$	34.9712			1.87735			0.938676	−	0.344799i	$-0.112053\pi$
$347$	34.9712			1.87735			0.938676	+	0.344799i	$0.112053\pi$
$348$		0			0
$349$	−0.321498			−0.0172094			−0.00860469	−	0.999963i	$-0.502739\pi$
$349$	−0.321498			−0.0172094			−0.00860469	+	0.999963i	$0.502739\pi$
$350$	4.99891	+	4.38439i	0.267203	+	0.234355i
$351$		0			0
$352$	10.8378	−	21.9623i	0.577656	−	1.17059i
$353$		−	25.5472i		−	1.35974i	−0.733331	−	0.679871i	$-0.762036\pi$
$353$		−	25.5472i		−	1.35974i	0.733331	−	0.679871i	$-0.237964\pi$
$354$		0			0
$355$		−	3.10432i		−	0.164760i
$356$	−10.5194	+	1.38378i	−0.557526	+	0.0733399i
$357$		0			0
$358$	17.4409	−	19.8854i	0.921778	−	1.05098i
$359$	3.16705			0.167151			0.0835753	−	0.996501i	$-0.473366\pi$
$359$	3.16705			0.167151			0.0835753	+	0.996501i	$0.473366\pi$
$360$		0			0
$361$	−41.5572			−2.18722
$362$	7.53238	−	8.58812i	0.395893	−	0.451381i
$363$		0			0
$364$	6.72237	−	0.884297i	0.352348	−	0.0463497i
$365$			0.415238i			0.0217346i
$366$		0			0
$367$			30.3530i			1.58442i	0.610251	+	0.792208i	$0.291069\pi$
$367$			30.3530i			1.58442i	−0.610251	+	0.792208i	$0.708931\pi$
$368$	2.76695	−	0.740778i	0.144237	−	0.0386157i
$369$		0			0
$370$	−5.73682	−	5.03159i	−0.298243	−	0.261580i
$371$	10.3377			0.536705
$372$		0			0
$373$	17.0260			0.881572			0.440786	−	0.897612i	$-0.354700\pi$
$373$	17.0260			0.881572			0.440786	+	0.897612i	$0.354700\pi$
$374$	−0.441970	−	0.387638i	−0.0228537	−	0.0200443i
$375$		0			0
$376$	24.0342	+	16.0646i	1.23947	+	0.828469i
$377$		−	9.49587i		−	0.489062i
$378$		0			0
$379$			37.0613i			1.90371i	0.306543	+	0.951857i	$0.400828\pi$
$379$			37.0613i			1.90371i	−0.306543	+	0.951857i	$0.599172\pi$
$380$	−1.10864	−	8.42782i	−0.0568721	−	0.432338i
$381$		0			0
$382$	−7.83248	+	8.93028i	−0.400744	+	0.456913i
$383$	−10.8566			−0.554749			−0.277374	−	0.960762i	$-0.589464\pi$
$383$	−10.8566			−0.554749			−0.277374	+	0.960762i	$0.589464\pi$
$384$		0			0
$385$	2.36459			0.120511
$386$	13.8471	−	15.7879i	0.704798	−	0.803583i
$387$		0			0
$388$	−3.61304	−	27.4661i	−0.183424	−	1.39438i
$389$			27.3658i			1.38750i	0.720215	+	0.693751i	$0.244043\pi$
$389$			27.3658i			1.38750i	−0.720215	+	0.693751i	$0.755957\pi$
$390$		0			0
$391$		−	0.0687571i		−	0.00347720i
$392$	−2.35150	−	1.57176i	−0.118769	−	0.0793859i
$393$		0			0
$394$	−25.0185	−	21.9429i	−1.26041	−	1.10547i
$395$	−1.07024			−0.0538495
$396$		0			0
$397$	−25.2105			−1.26528			−0.632640	−	0.774446i	$-0.718029\pi$
$397$	−25.2105			−1.26528			−0.632640	+	0.774446i	$0.718029\pi$
$398$	25.1760	+	22.0811i	1.26196	+	1.10683i
$399$		0			0
$400$	−18.1670	+	4.86373i	−0.908350	+	0.243187i
$401$		−	30.1462i		−	1.50543i	−0.658347	−	0.752714i	$-0.728744\pi$
$401$		−	30.1462i		−	1.50543i	0.658347	−	0.752714i	$-0.271256\pi$
$402$		0			0
$403$			4.68003i			0.233129i
$404$	15.0783	−	1.98348i	0.750175	−	0.0986820i
$405$		0			0
$406$	−2.61199	+	2.97809i	−0.129631	+	0.147800i
$407$	42.7712			2.12009
$408$		0			0
$409$	21.5021			1.06321			0.531605	−	0.846993i	$-0.321589\pi$
$409$	21.5021			1.06321			0.531605	+	0.846993i	$0.321589\pi$
$410$	−4.80248	+	5.47559i	−0.237177	+	0.270420i
$411$		0			0
$412$	−3.38649	+	0.445477i	−0.166840	+	0.0219471i
$413$		−	7.15116i		−	0.351885i
$414$		0			0
$415$		−	1.94656i		−	0.0955529i
$416$	−8.48654	+	17.1976i	−0.416087	+	0.843181i
$417$		0			0
$418$	35.8205	+	31.4170i	1.75204	+	1.53666i
$419$	0.917403			0.0448181			0.0224090	−	0.999749i	$-0.492866\pi$
$419$	0.917403			0.0448181			0.0224090	+	0.999749i	$0.492866\pi$
$420$		0			0
$421$	−3.17383			−0.154683			−0.0773416	−	0.997005i	$-0.524643\pi$
$421$	−3.17383			−0.154683			−0.0773416	+	0.997005i	$0.524643\pi$
$422$	−3.40556	−	2.98691i	−0.165780	−	0.145401i
$423$		0			0
$424$	−16.2484	+	24.3091i	−0.789090	+	1.18055i
$425$			0.451439i			0.0218980i
$426$		0			0
$427$		−	4.47260i		−	0.216444i
$428$	3.14153	+	23.8817i	0.151851	+	1.15437i
$429$		0			0
$430$	−0.571920	+	0.652080i	−0.0275804	+	0.0314461i
$431$	7.01129			0.337722			0.168861	−	0.985640i	$-0.445991\pi$
$431$	7.01129			0.337722			0.168861	+	0.985640i	$0.445991\pi$
$432$		0			0
$433$	16.6529			0.800288			0.400144	−	0.916452i	$-0.368960\pi$
$433$	16.6529			0.800288			0.400144	+	0.916452i	$0.368960\pi$
$434$	1.28732	−	1.46775i	0.0617931	−	0.0704540i
$435$		0			0
$436$	−3.81606	−	29.0094i	−0.182756	−	1.38930i
$437$			5.57258i			0.266573i
$438$		0			0
$439$		−	15.8377i		−	0.755894i	−0.925827	−	0.377947i	$-0.876630\pi$
$439$		−	15.8377i		−	0.755894i	0.925827	−	0.377947i	$-0.123370\pi$
$440$	−3.71657	+	5.56034i	−0.177181	+	0.265079i
$441$		0			0
$442$	0.346085	+	0.303540i	0.0164616	+	0.0144379i
$443$	11.7934			0.560321			0.280161	−	0.959953i	$-0.409612\pi$
$443$	11.7934			0.560321			0.280161	+	0.959953i	$0.409612\pi$
$444$		0			0
$445$	2.89743			0.137352
$446$	−22.5166	−	19.7486i	−1.06619	−	0.935123i
$447$		0			0
$448$	7.39200	−	3.05913i	0.349239	−	0.144530i
$449$		−	11.4729i		−	0.541441i	−0.962658	−	0.270720i	$-0.912738\pi$
$449$		−	11.4729i		−	0.541441i	0.962658	−	0.270720i	$-0.0872619\pi$
$450$		0			0
$451$		−	40.8236i		−	1.92231i
$452$	31.2698	−	4.11340i	1.47081	−	0.193478i
$453$		0			0
$454$	−3.87645	+	4.41977i	−0.181931	+	0.207430i
$455$	−1.85159			−0.0868041
$456$		0			0
$457$	0.716248			0.0335047			0.0167523	−	0.999860i	$-0.494667\pi$
$457$	0.716248			0.0335047			0.0167523	+	0.999860i	$0.494667\pi$
$458$	−0.298080	+	0.339859i	−0.0139284	+	0.0158806i
$459$		0			0
$460$	−0.775543	+	0.102019i	−0.0361599	+	0.00475667i
$461$		−	25.6559i		−	1.19492i	−0.801900	−	0.597458i	$-0.796177\pi$
$461$		−	25.6559i		−	1.19492i	0.801900	−	0.597458i	$-0.203823\pi$
$462$		0			0
$463$		−	8.41981i		−	0.391302i	−0.980674	−	0.195651i	$-0.937318\pi$
$463$		−	8.41981i		−	0.391302i	0.980674	−	0.195651i	$-0.0626820\pi$
$464$	−2.89756	−	10.8229i	−0.134516	−	0.502443i
$465$		0			0
$466$	−4.05689	−	3.55817i	−0.187932	−	0.164829i
$467$	27.6632			1.28010			0.640050	−	0.768333i	$-0.278914\pi$
$467$	27.6632			1.28010			0.640050	+	0.768333i	$0.278914\pi$
$468$		0			0
$469$	−10.1781			−0.469982
$470$	−5.93515	−	5.20554i	−0.273768	−	0.240114i
$471$		0			0
$472$	16.8160	+	11.2399i	0.774018	+	0.517359i
$473$		−	4.86162i		−	0.223537i
$474$		0			0
$475$		−	36.5879i		−	1.67877i
$476$	−0.0250452	−	0.190392i	−0.00114794	−	0.00872660i
$477$		0			0
$478$	4.84414	−	5.52310i	0.221566	−	0.252621i
$479$	−20.8002			−0.950383			−0.475192	−	0.879882i	$-0.657621\pi$
$479$	−20.8002			−0.950383			−0.475192	+	0.879882i	$0.657621\pi$
$480$		0			0
$481$	−33.4920			−1.52710
$482$	16.3009	−	18.5856i	0.742485	−	0.846552i
$483$		0			0
$484$	−2.01990	−	15.3552i	−0.0918138	−	0.697963i
$485$			7.56520i			0.343518i
$486$		0			0
$487$			14.8907i			0.674761i	0.941368	+	0.337380i	$0.109541\pi$
$487$			14.8907i			0.674761i	−0.941368	+	0.337380i	$0.890459\pi$
$488$	10.5173	+	7.02986i	0.476097	+	0.318227i
$489$		0			0
$490$	0.580695	+	0.509310i	0.0262331	+	0.0230083i
$491$	−43.0692			−1.94369			−0.971844	−	0.235626i	$-0.924286\pi$
$491$	−43.0692			−1.94369			−0.971844	+	0.235626i	$0.924286\pi$
$492$		0			0
$493$	−0.268944			−0.0121126
$494$	−28.0492	−	24.6011i	−1.26199	−	1.10686i
$495$		0			0
$496$	1.42806	+	5.33407i	0.0641216	+	0.239507i
$497$			5.68379i			0.254953i
$498$		0			0
$499$			24.6899i			1.10527i	0.833423	+	0.552636i	$0.186378\pi$
$499$			24.6899i			1.10527i	−0.833423	+	0.552636i	$0.813622\pi$
$500$	10.5070	−	1.38215i	0.469889	−	0.0618117i
$501$		0			0
$502$	−6.83177	+	7.78931i	−0.304917	+	0.347654i
$503$	−8.81804			−0.393177			−0.196588	−	0.980486i	$-0.562986\pi$
$503$	−8.81804			−0.393177			−0.196588	+	0.980486i	$0.562986\pi$
$504$		0			0
$505$	−4.15314			−0.184812
$506$	2.89105	−	3.29626i	0.128523	−	0.146537i
$507$		0			0
$508$	11.9551	−	1.57264i	0.530422	−	0.0697746i
$509$			24.9542i			1.10607i	0.833157	+	0.553037i	$0.186531\pi$
$509$			24.9542i			1.10607i	−0.833157	+	0.553037i	$0.813469\pi$
$510$		0			0
$511$		−	0.760273i		−	0.0336325i
$512$	−4.42491	+	22.1905i	−0.195555	+	0.980693i
$513$		0			0
$514$	16.5354	+	14.5027i	0.729344	+	0.639685i
$515$	0.932767			0.0411026
$516$		0			0
$517$	44.2498			1.94610
$518$	10.5037	+	9.21250i	0.461507	+	0.404774i
$519$		0			0
$520$	2.91026	−	4.35403i	0.127624	−	0.190937i
$521$			12.2860i			0.538261i	0.963104	+	0.269131i	$0.0867363\pi$
$521$			12.2860i			0.538261i	−0.963104	+	0.269131i	$0.913264\pi$
$522$		0			0
$523$			7.88092i			0.344609i	0.985044	+	0.172304i	$0.0551212\pi$
$523$			7.88092i			0.344609i	−0.985044	+	0.172304i	$0.944879\pi$
$524$	4.19633	+	31.9003i	0.183318	+	1.39357i
$525$		0			0
$526$	20.5067	−	23.3809i	0.894134	−	1.01946i
$527$	0.132548			0.00577390
$528$		0			0
$529$	−22.4872			−0.977704
$530$	5.26508	−	6.00304i	0.228701	−	0.260755i
$531$		0			0
$532$	2.02985	+	15.4308i	0.0880049	+	0.669008i
$533$			31.9669i			1.38464i
$534$		0			0
$535$		−	6.57792i		−	0.284388i
$536$	15.9976	−	23.9339i	0.690990	−	1.03379i
$537$		0			0
$538$	−27.7191	−	24.3116i	−1.19506	−	1.04815i
$539$	−4.32940			−0.186481
$540$		0			0
$541$	−0.0419231			−0.00180241			−0.000901207	−	1.00000i	$-0.500287\pi$
$541$	−0.0419231			−0.00180241			−0.000901207		1.00000i	$0.500287\pi$
$542$	19.5498	+	17.1466i	0.839737	+	0.736508i
$543$		0			0
$544$	0.487072	+	0.240357i	0.0208831	+	0.0103052i
$545$			7.99029i			0.342266i
$546$		0			0
$547$		−	35.7201i		−	1.52728i	−0.645642	−	0.763640i	$-0.723410\pi$
$547$		−	35.7201i		−	1.52728i	0.645642	−	0.763640i	$-0.276590\pi$
$548$	−24.8592	+	3.27012i	−1.06193	+	0.139693i
$549$		0			0
$550$	−18.9818	+	21.6423i	−0.809386	+	0.922830i
$551$	21.7972			0.928590
$552$		0			0
$553$	1.95953			0.0833277
$554$	−0.942074	+	1.07412i	−0.0400249	+	0.0456348i
$555$		0			0
$556$	3.18607	−	0.419112i	0.135119	−	0.0177743i
$557$			13.6147i			0.576873i	0.957499	+	0.288437i	$0.0931354\pi$
$557$			13.6147i			0.576873i	−0.957499	+	0.288437i	$0.906865\pi$
$558$		0			0
$559$			3.80689i			0.161014i
$560$	−2.11036	+	0.564993i	−0.0891789	+	0.0238753i
$561$		0			0
$562$	−16.0009	−	14.0339i	−0.674959	−	0.591986i
$563$	6.20546			0.261529			0.130765	−	0.991413i	$-0.458257\pi$
$563$	6.20546			0.261529			0.130765	+	0.991413i	$0.458257\pi$
$564$		0			0
$565$	−8.61289			−0.362347
$566$	1.21598	+	1.06650i	0.0511116	+	0.0448284i
$567$		0			0
$568$	−13.3654	−	8.93356i	−0.560802	−	0.374844i
$569$			14.1054i			0.591330i	0.955292	+	0.295665i	$0.0955412\pi$
$569$			14.1054i			0.591330i	−0.955292	+	0.295665i	$0.904459\pi$
$570$		0			0
$571$		−	29.5054i		−	1.23476i	−0.786664	−	0.617381i	$-0.788194\pi$
$571$		−	29.5054i		−	1.23476i	0.786664	−	0.617381i	$-0.211806\pi$
$572$	3.82848	+	29.1039i	0.160077	+	1.21689i
$573$		0			0
$574$	8.79301	−	10.0254i	0.367013	−	0.418454i
$575$	−3.36688			−0.140409
$576$		0			0
$577$	−13.0674			−0.544004			−0.272002	−	0.962297i	$-0.587686\pi$
$577$	−13.0674			−0.544004			−0.272002	+	0.962297i	$0.587686\pi$
$578$	−15.8441	+	18.0648i	−0.659028	+	0.751397i
$579$		0			0
$580$	0.399048	+	3.03354i	0.0165696	+	0.125961i
$581$			3.56402i			0.147860i
$582$		0			0
$583$			44.7559i			1.85360i
$584$	1.78778	+	1.19497i	0.0739790	+	0.0494481i
$585$		0			0
$586$	−33.3580	−	29.2573i	−1.37801	−	1.20861i
$587$	−46.4897			−1.91883			−0.959417	−	0.281992i	$-0.909005\pi$
$587$	−46.4897			−1.91883			−0.959417	+	0.281992i	$0.909005\pi$
$588$		0			0
$589$	−10.7427			−0.442645
$590$	−4.15264	−	3.64216i	−0.170962	−	0.149945i
$591$		0			0
$592$	−38.1726	+	10.2197i	−1.56888	+	0.420027i
$593$		−	31.7588i		−	1.30418i	−0.758143	−	0.652089i	$-0.773893\pi$
$593$		−	31.7588i		−	1.30418i	0.758143	−	0.652089i	$-0.226107\pi$
$594$		0			0
$595$			0.0524411i			0.00214988i
$596$	−27.5086	+	3.61863i	−1.12680	+	0.148225i
$597$		0			0
$598$	−2.26384	+	2.58114i	−0.0925753	+	0.105551i
$599$	−6.57765			−0.268755			−0.134378	−	0.990930i	$-0.542904\pi$
$599$	−6.57765			−0.268755			−0.134378	+	0.990930i	$0.542904\pi$
$600$		0			0
$601$	15.6923			0.640103			0.320052	−	0.947400i	$-0.396300\pi$
$601$	15.6923			0.640103			0.320052	+	0.947400i	$0.396300\pi$
$602$	1.04715	−	1.19391i	0.0426785	−	0.0486603i
$603$		0			0
$604$	−40.2602	+	5.29604i	−1.63816	+	0.215493i
$605$			4.22940i			0.171949i
$606$		0			0
$607$			4.44562i			0.180442i	0.995922	+	0.0902210i	$0.0287573\pi$
$607$			4.44562i			0.180442i	−0.995922	+	0.0902210i	$0.971243\pi$
$608$	−39.4759	−	19.4803i	−1.60096	−	0.790030i
$609$		0			0
$610$	−2.59722	−	2.27794i	−0.105158	−	0.0922312i
$611$	−34.6498			−1.40178
$612$		0			0
$613$	−11.2778			−0.455507			−0.227753	−	0.973719i	$-0.573138\pi$
$613$	−11.2778			−0.455507			−0.227753	+	0.973719i	$0.573138\pi$
$614$	−27.6560	−	24.2562i	−1.11611	−	0.978902i
$615$		0			0
$616$	6.80479	−	10.1806i	0.274173	−	0.410188i
$617$		−	35.3409i		−	1.42277i	−0.702802	−	0.711385i	$-0.748068\pi$
$617$		−	35.3409i		−	1.42277i	0.702802	−	0.711385i	$-0.251932\pi$
$618$		0			0
$619$		−	30.1363i		−	1.21128i	−0.795738	−	0.605641i	$-0.792917\pi$
$619$		−	30.1363i		−	1.21128i	0.795738	−	0.605641i	$-0.207083\pi$
$620$	−0.196670	−	1.49508i	−0.00789847	−	0.0600437i
$621$		0			0
$622$	−1.09990	+	1.25406i	−0.0441020	+	0.0502834i
$623$	−5.30500			−0.212540
$624$		0			0
$625$	20.6145			0.824578
$626$	23.3920	−	26.6706i	0.934932	−	1.06597i
$627$		0			0
$628$	5.43228	+	41.2959i	0.216772	+	1.64788i
$629$			0.948565i			0.0378218i
$630$		0			0
$631$		−	1.06139i		−	0.0422535i	−0.999777	−	0.0211267i	$-0.993275\pi$
$631$		−	1.06139i		−	0.0422535i	0.999777	−	0.0211267i	$-0.00672535\pi$
$632$	−3.07991	+	4.60784i	−0.122512	+	0.183290i
$633$		0			0
$634$	−8.61311	−	7.55429i	−0.342070	−	0.300019i
$635$	−3.29289			−0.130674
$636$		0			0
$637$	3.39014			0.134322
$638$	−12.8933	−	11.3084i	−0.510452	−	0.447702i
$639$		0			0
$640$	1.98840	−	5.85055i	0.0785984	−	0.231263i
$641$		−	17.6125i		−	0.695651i	−0.937559	−	0.347825i	$-0.886920\pi$
$641$		−	17.6125i		−	0.695651i	0.937559	−	0.347825i	$-0.113080\pi$
$642$		0			0
$643$			7.86528i			0.310176i	0.987901	+	0.155088i	$0.0495662\pi$
$643$			7.86528i			0.310176i	−0.987901	+	0.155088i	$0.950434\pi$
$644$	1.41997	−	0.186790i	0.0559545	−	0.00736056i
$645$		0			0
$646$	−0.696757	+	0.794414i	−0.0274135	+	0.0312558i
$647$	27.9700			1.09962			0.549808	−	0.835291i	$-0.314701\pi$
$647$	27.9700			1.09962			0.549808	+	0.835291i	$0.314701\pi$
$648$		0			0
$649$	30.9602			1.21530
$650$	14.8637	−	16.9470i	0.583002	−	0.664716i
$651$		0			0
$652$	19.4634	−	2.56033i	0.762247	−	0.100270i
$653$			14.0209i			0.548679i	0.961633	+	0.274340i	$0.0884592\pi$
$653$			14.0209i			0.548679i	−0.961633	+	0.274340i	$0.911541\pi$
$654$		0			0
$655$		−	8.78654i		−	0.343319i
$656$	9.75434	+	36.4344i	0.380843	+	1.42252i
$657$		0			0
$658$	10.8669	+	9.53098i	0.423634	+	0.371556i
$659$	−10.0407			−0.391130			−0.195565	−	0.980691i	$-0.562654\pi$
$659$	−10.0407			−0.391130			−0.195565	+	0.980691i	$0.562654\pi$
$660$		0			0
$661$	−4.09723			−0.159364			−0.0796818	−	0.996820i	$-0.525390\pi$
$661$	−4.09723			−0.159364			−0.0796818	+	0.996820i	$0.525390\pi$
$662$	−31.3708	−	27.5144i	−1.21926	−	1.06938i
$663$		0			0
$664$	−8.38080	−	5.60179i	−0.325238	−	0.217391i
$665$		−	4.25021i		−	0.164816i
$666$		0			0
$667$		−	2.00581i		−	0.0776654i
$668$	−2.00988	−	15.2790i	−0.0777646	−	0.591162i
$669$		0			0
$670$	−5.18382	+	5.91039i	−0.200269	+	0.228338i
$671$	19.3637			0.747527
$672$		0			0
$673$	18.2300			0.702716			0.351358	−	0.936241i	$-0.385720\pi$
$673$	18.2300			0.702716			0.351358	+	0.936241i	$0.385720\pi$
$674$	−19.3385	+	22.0490i	−0.744892	+	0.849296i
$675$		0			0
$676$	0.393075	+	2.98813i	0.0151183	+	0.114928i
$677$			41.9357i			1.61172i	0.592106	+	0.805860i	$0.298297\pi$
$677$			41.9357i			1.61172i	−0.592106	+	0.805860i	$0.701703\pi$
$678$		0			0
$679$		−	13.8514i		−	0.531567i
$680$	−0.123315	−	0.0824250i	−0.00472893	−	0.00316085i
$681$		0			0
$682$	6.35446	+	5.57331i	0.243325	+	0.213413i
$683$	15.5075			0.593379			0.296689	−	0.954974i	$-0.404117\pi$
$683$	15.5075			0.593379			0.296689	+	0.954974i	$0.404117\pi$
$684$		0			0
$685$	6.84717			0.261617
$686$	−1.06321	−	0.932512i	−0.0405937	−	0.0356035i
$687$		0			0
$688$	1.16163	+	4.33891i	0.0442867	+	0.165420i
$689$		−	35.0462i		−	1.33515i
$690$		0			0
$691$			0.133779i			0.00508917i	0.999997	+	0.00254459i	$0.000809968\pi$
$691$			0.133779i			0.00508917i	−0.999997	+	0.00254459i	$0.999190\pi$
$692$	−30.4621	+	4.00715i	−1.15800	+	0.152329i
$693$		0			0
$694$	−32.6111	+	37.1818i	−1.23790	+	1.41140i
$695$	−0.877563			−0.0332879
$696$		0			0
$697$	0.905372			0.0342934
$698$	0.299800	−	0.341820i	0.0113476	−	0.0129381i
$699$		0			0
$700$	−9.32308	+	1.22641i	−0.352379	+	0.0463539i
$701$		−	34.1981i		−	1.29164i	−0.763488	−	0.645822i	$-0.776515\pi$
$701$		−	34.1981i		−	1.29164i	0.763488	−	0.645822i	$-0.223485\pi$
$702$		0			0
$703$		−	76.8786i		−	2.89953i
$704$	13.2442	+	32.0030i	0.499160	+	1.20616i
$705$		0			0
$706$	27.1622	+	23.8231i	1.02226	+	0.896595i
$707$	7.60411			0.285982
$708$		0			0
$709$	50.7558			1.90617			0.953087	−	0.302697i	$-0.0978869\pi$
$709$	50.7558			1.90617			0.953087	+	0.302697i	$0.0978869\pi$
$710$	3.30055	+	2.89481i	0.123867	+	0.108640i
$711$		0			0
$712$	8.33819	−	12.4747i	0.312487	−	0.467510i
$713$			0.988562i			0.0370219i
$714$		0			0
$715$		−	8.01630i		−	0.299793i
$716$	4.87858	+	37.0867i	0.182321	+	1.38600i
$717$		0			0
$718$	−2.95331	+	3.36725i	−0.110217	+	0.125665i
$719$	−38.0420			−1.41873			−0.709364	−	0.704843i	$-0.751018\pi$
$719$	−38.0420			−1.41873			−0.709364	+	0.704843i	$0.751018\pi$
$720$		0			0
$721$	−1.70783			−0.0636030
$722$	38.7525	−	44.1841i	1.44222	−	1.64436i
$723$		0			0
$724$	2.10697	+	16.0170i	0.0783048	+	0.595269i
$725$			13.1696i			0.489106i
$726$		0			0
$727$			9.97341i			0.369893i	0.982749	+	0.184947i	$0.0592112\pi$
$727$			9.97341i			0.369893i	−0.982749	+	0.184947i	$0.940789\pi$
$728$	−5.32849	+	7.97193i	−0.197487	+	0.295459i
$729$		0			0
$730$	−0.441487	−	0.387215i	−0.0163402	−	0.0143315i
$731$	0.107819			0.00398784
$732$		0			0
$733$	21.6381			0.799221			0.399610	−	0.916685i	$-0.369145\pi$
$733$	21.6381			0.799221			0.399610	+	0.916685i	$0.369145\pi$
$734$	−32.2718	−	28.3046i	−1.19117	−	1.04474i
$735$		0			0
$736$	−1.79261	+	3.63264i	−0.0660765	+	0.133901i
$737$		−	44.0652i		−	1.62316i
$738$		0			0
$739$		−	1.62532i		−	0.0597882i	−0.999553	−	0.0298941i	$-0.990483\pi$
$739$		−	1.62532i		−	0.0597882i	0.999553	−	0.0298941i	$-0.00951700\pi$
$740$	10.6993	−	1.40744i	0.393314	−	0.0517387i
$741$		0			0
$742$	−9.64000	+	10.9911i	−0.353896	+	0.403498i
$743$	0.901684			0.0330796			0.0165398	−	0.999863i	$-0.494735\pi$
$743$	0.901684			0.0330796			0.0165398	+	0.999863i	$0.494735\pi$
$744$		0			0
$745$	7.57692			0.277597
$746$	−15.8769	+	18.1023i	−0.581296	+	0.662771i
$747$		0			0
$748$	0.824284	−	0.108431i	0.0301388	−	0.00396462i
$749$			12.0437i			0.440068i
$750$		0			0
$751$			5.79695i			0.211534i	0.994391	+	0.105767i	$0.0337297\pi$
$751$			5.79695i			0.211534i	−0.994391	+	0.105767i	$0.966270\pi$
$752$	−39.4922	+	10.5730i	−1.44013	+	0.385558i
$753$		0			0
$754$	10.0961	+	8.85501i	0.367680	+	0.322481i
$755$	11.0892			0.403576
$756$		0			0
$757$	33.8699			1.23102			0.615511	−	0.788128i	$-0.288950\pi$
$757$	33.8699			1.23102			0.615511	+	0.788128i	$0.288950\pi$
$758$	−39.4041	−	34.5601i	−1.43122	−	1.25528i
$759$		0			0
$760$	9.99439	+	6.68032i	0.362535	+	0.242321i
$761$			13.2036i			0.478630i	0.970942	+	0.239315i	$0.0769229\pi$
$761$			13.2036i			0.478630i	−0.970942	+	0.239315i	$0.923077\pi$
$762$		0			0
$763$		−	14.6297i		−	0.529630i
$764$	−2.19091	−	16.6552i	−0.0792644	−	0.602563i
$765$		0			0
$766$	10.1240	−	11.5429i	0.365793	−	0.417063i
$767$	−24.2434			−0.875380
$768$		0			0
$769$	23.8172			0.858872			0.429436	−	0.903097i	$-0.358712\pi$
$769$	23.8172			0.858872			0.429436	+	0.903097i	$0.358712\pi$
$770$	−2.20501	+	2.51406i	−0.0794630	+	0.0906006i
$771$		0			0
$772$	3.87333	+	29.4448i	0.139404	+	1.05974i
$773$		−	26.4363i		−	0.950847i	−0.879757	−	0.475423i	$-0.842295\pi$
$773$		−	26.4363i		−	0.950847i	0.879757	−	0.475423i	$-0.157705\pi$
$774$		0			0
$775$		−	6.49061i		−	0.233149i
$776$	32.5715	+	21.7710i	1.16925	+	0.781535i
$777$		0			0
$778$	−29.0957	−	25.5189i	−1.04313	−	0.914898i
$779$	−73.3780			−2.62904
$780$		0			0
$781$	−24.6074			−0.880522
$782$	0.0731034	+	0.0641168i	0.00261417	+	0.00229281i
$783$		0			0
$784$	3.86392	−	1.03446i	0.137997	−	0.0369451i
$785$		−	11.3744i		−	0.405971i
$786$		0			0
$787$			23.3744i			0.833207i	0.909088	+	0.416604i	$0.136780\pi$
$787$			23.3744i			0.833207i	−0.909088	+	0.416604i	$0.863220\pi$
$788$	46.6600	−	6.13791i	1.66219	−	0.218654i
$789$		0			0
$790$	0.998008	−	1.13789i	0.0355075	−	0.0404843i
$791$	15.7696			0.560703
$792$		0			0
$793$	−15.1628			−0.538445
$794$	23.5091	−	26.8041i	0.834307	−	0.951244i
$795$		0			0
$796$	−46.9539	+	6.17656i	−1.66424	+	0.218922i
$797$			10.6022i			0.375549i	0.982212	+	0.187775i	$0.0601274\pi$
$797$			10.6022i			0.375549i	−0.982212	+	0.187775i	$0.939873\pi$
$798$		0			0
$799$			0.981358i			0.0347180i
$800$	11.7698	−	23.8509i	0.416124	−	0.843255i
$801$		0			0
$802$	32.0518	+	28.1117i	1.13179	+	0.992658i
$803$	3.29153			0.116155
$804$		0			0
$805$	−0.391112			−0.0137849
$806$	−4.97587	−	4.36418i	−0.175267	−	0.153722i
$807$		0			0
$808$	−11.9518	+	17.8811i	−0.420465	+	0.629055i
$809$		−	0.238439i		−	0.00838306i	−0.999991	−	0.00419153i	$-0.998666\pi$
$809$		−	0.238439i		−	0.00838306i	0.999991	−	0.00419153i	$-0.00133421\pi$
$810$		0			0
$811$			38.2987i			1.34485i	0.740166	+	0.672425i	$0.234747\pi$
$811$			38.2987i			1.34485i	−0.740166	+	0.672425i	$0.765253\pi$
$812$	−0.730630	−	5.55420i	−0.0256401	−	0.194914i
$813$		0			0
$814$	−39.8846	+	45.4749i	−1.39795	+	1.59389i
$815$	−5.36097			−0.187787
$816$		0			0
$817$	−8.73847			−0.305720
$818$	−20.0509	+	22.8613i	−0.701065	+	0.799326i
$819$		0			0
$820$	−1.34336	−	10.2121i	−0.0469120	−	0.356622i
$821$			38.3125i			1.33712i	0.743660	+	0.668558i	$0.233088\pi$
$821$			38.3125i			1.33712i	−0.743660	+	0.668558i	$0.766912\pi$
$822$		0			0
$823$			11.0368i			0.384718i	0.981325	+	0.192359i	$0.0616138\pi$
$823$			11.0368i			0.384718i	−0.981325	+	0.192359i	$0.938386\pi$
$824$	2.68430	−	4.01597i	0.0935122	−	0.139903i
$825$		0			0
$826$	7.60320	+	6.66854i	0.264549	+	0.232028i
$827$	21.5781			0.750342			0.375171	−	0.926956i	$-0.377584\pi$
$827$	21.5781			0.750342			0.375171	+	0.926956i	$0.377584\pi$
$828$		0			0
$829$	39.2618			1.36362			0.681809	−	0.731531i	$-0.261194\pi$
$829$	39.2618			1.36362			0.681809	+	0.731531i	$0.261194\pi$
$830$	2.06961	+	1.81519i	0.0718372	+	0.0630062i
$831$		0			0
$832$	−10.3709	−	25.0599i	−0.359546	−	0.868797i
$833$		−	0.0960161i		−	0.00332676i
$834$		0			0
$835$			4.20841i			0.145638i
$836$	−66.8060	+	8.78802i	−2.31053	+	0.303940i
$837$		0			0
$838$	−0.855489	+	0.975395i	−0.0295524	+	0.0336944i
$839$	−45.4839			−1.57028			−0.785140	−	0.619319i	$-0.787409\pi$
$839$	−45.4839			−1.57028			−0.785140	+	0.619319i	$0.787409\pi$
$840$		0			0
$841$	21.1543			0.729457
$842$	2.95964	−	3.37446i	0.101996	−	0.116292i
$843$		0			0
$844$	6.35144	−	0.835503i	0.218626	−	0.0287592i
$845$		−	0.823045i		−	0.0283136i
$846$		0			0
$847$		−	7.74373i		−	0.266078i
$848$	−10.6939	−	39.9439i	−0.367231	−	1.37168i
$849$		0			0
$850$	−0.479975	−	0.420972i	−0.0164630	−	0.0144392i
$851$	−7.07451			−0.242511
$852$		0			0
$853$	−40.2554			−1.37832			−0.689159	−	0.724610i	$-0.742020\pi$
$853$	−40.2554			−1.37832			−0.689159	+	0.724610i	$0.742020\pi$
$854$	4.75533	+	4.17075i	0.162724	+	0.142720i
$855$		0			0
$856$	−28.3208	−	18.9299i	−0.967986	−	0.647009i
$857$			38.9387i			1.33012i	0.746789	+	0.665061i	$0.231594\pi$
$857$			38.9387i			1.33012i	−0.746789	+	0.665061i	$0.768406\pi$
$858$		0			0
$859$		−	49.6846i		−	1.69522i	−0.530622	−	0.847608i	$-0.678042\pi$
$859$		−	49.6846i		−	1.69522i	0.530622	−	0.847608i	$-0.321958\pi$
$860$	−0.159978	−	1.21615i	−0.00545521	−	0.0414702i
$861$		0			0
$862$	−6.53811	+	7.45450i	−0.222689	+	0.253901i
$863$	31.3183			1.06609			0.533044	−	0.846088i	$-0.321048\pi$
$863$	31.3183			1.06609			0.533044	+	0.846088i	$0.321048\pi$
$864$		0			0
$865$	8.39042			0.285283
$866$	−15.5290	+	17.7056i	−0.527698	+	0.601661i
$867$		0			0
$868$	0.360090	+	2.73738i	0.0122222	+	0.0929127i
$869$			8.48359i			0.287786i
$870$		0			0
$871$			34.5053i			1.16917i
$872$	34.4017	+	22.9944i	1.16499	+	0.778687i
$873$		0			0
$874$	−5.92484	−	5.19649i	−0.200411	−	0.175774i
$875$	5.29878			0.179131
$876$		0			0
$877$	−3.69361			−0.124724			−0.0623621	−	0.998054i	$-0.519863\pi$
$877$	−3.69361			−0.124724			−0.0623621	+	0.998054i	$0.519863\pi$
$878$	16.8389	+	14.7689i	0.568285	+	0.498425i
$879$		0			0
$880$	−2.44608	−	9.13659i	−0.0824574	−	0.307995i
$881$			53.3419i			1.79713i	0.438836	+	0.898567i	$0.355391\pi$
$881$			53.3419i			1.79713i	−0.438836	+	0.898567i	$0.644609\pi$
$882$		0			0
$883$			46.3560i			1.56001i	0.625776	+	0.780003i	$0.284782\pi$
$883$			46.3560i			1.56001i	−0.625776	+	0.780003i	$0.715218\pi$
$884$	−0.645456	+	0.0849067i	−0.0217090	+	0.00285572i
$885$		0			0
$886$	−10.9975	+	12.5389i	−0.369468	+	0.421252i
$887$	−30.4446			−1.02223			−0.511115	−	0.859512i	$-0.670767\pi$
$887$	−30.4446			−1.02223			−0.511115	+	0.859512i	$0.670767\pi$
$888$		0			0
$889$	6.02905			0.202208
$890$	−2.70189	+	3.08059i	−0.0905676	+	0.103262i
$891$		0			0
$892$	41.9939	−	5.52410i	1.40606	−	0.184961i
$893$		−	79.5364i		−	2.66159i
$894$		0			0
$895$		−	10.2151i		−	0.341452i
$896$	−3.64062	+	10.7120i	−0.121625	+	0.357861i
$897$		0			0
$898$	12.1982	+	10.6986i	0.407058	+	0.357018i
$899$	3.86676			0.128964
$900$		0			0
$901$	−0.992583			−0.0330677
$902$	43.4042	+	38.0685i	1.44520	+	1.26754i
$903$		0			0
$904$	−24.7861	+	37.0823i	−0.824372	+	1.23334i
$905$		−	4.41170i		−	0.146650i
$906$		0			0
$907$		−	18.3798i		−	0.610291i	−0.952306	−	0.305145i	$-0.901295\pi$
$907$		−	18.3798i		−	0.610291i	0.952306	−	0.305145i	$-0.0987051\pi$
$908$	−1.08433	−	8.24298i	−0.0359846	−	0.273553i
$909$		0			0
$910$	1.72663	−	1.96864i	0.0572374	−	0.0652598i
$911$	−13.4574			−0.445863			−0.222932	−	0.974834i	$-0.571563\pi$
$911$	−13.4574			−0.445863			−0.222932	+	0.974834i	$0.571563\pi$
$912$		0			0
$913$	−15.4301			−0.510661
$914$	−0.667910	+	0.761524i	−0.0220925	+	0.0251890i
$915$		0			0
$916$	−0.0833793	−	0.633845i	−0.00275493	−	0.0209428i
$917$			16.0875i			0.531258i
$918$		0			0
$919$		−	56.3374i		−	1.85840i	−0.369579	−	0.929199i	$-0.620498\pi$
$919$		−	56.3374i		−	1.85840i	0.369579	−	0.929199i	$-0.379502\pi$
$920$	0.614735	−	0.919702i	0.0202672	−	0.0303217i
$921$		0			0
$922$	27.2777	+	23.9245i	0.898344	+	0.787910i
$923$	19.2688			0.634242
$924$		0			0
$925$	46.4491			1.52724
$926$	8.95205	+	7.85157i	0.294183	+	0.258019i
$927$		0			0
$928$	14.2091	+	7.01180i	0.466437	+	0.230174i
$929$		−	10.6011i		−	0.347812i	−0.984762	−	0.173906i	$-0.944361\pi$
$929$		−	10.6011i		−	0.347812i	0.984762	−	0.173906i	$-0.0556389\pi$
$930$		0			0
$931$			7.78185i			0.255040i
$932$	7.56619	−	0.995297i	0.247839	−	0.0326020i
$933$		0			0
$934$	−25.7962	+	29.4119i	−0.844079	+	0.962385i
$935$	−0.227039			−0.00742496
$936$		0			0
$937$	20.1206			0.657312			0.328656	−	0.944450i	$-0.393404\pi$
$937$	20.1206			0.657312			0.328656	+	0.944450i	$0.393404\pi$
$938$	9.49122	−	10.8215i	0.309899	−	0.353335i
$939$		0			0
$940$	11.0692	−	1.45610i	0.361037	−	0.0474928i
$941$			31.6197i			1.03077i	0.856958	+	0.515386i	$0.172351\pi$
$941$			31.6197i			1.03077i	−0.856958	+	0.515386i	$0.827649\pi$
$942$		0			0
$943$			6.75237i			0.219888i
$944$	−27.6315	+	7.39760i	−0.899329	+	0.240771i
$945$		0			0
$946$	5.16894	+	4.53352i	0.168057	+	0.147397i
$947$	17.3640			0.564255			0.282127	−	0.959377i	$-0.408960\pi$
$947$	17.3640			0.564255			0.282127	+	0.959377i	$0.408960\pi$
$948$		0			0
$949$	−2.57743			−0.0836670
$950$	38.9007	+	34.1186i	1.26211	+	1.10696i
$951$		0			0
$952$	0.225782	+	0.150914i	0.00731764	+	0.00489116i
$953$		−	33.7037i		−	1.09177i	−0.837860	−	0.545886i	$-0.816193\pi$
$953$		−	33.7037i		−	1.09177i	0.837860	−	0.545886i	$-0.183807\pi$
$954$		0			0
$955$			4.58747i			0.148447i
$956$	1.35501	+	10.3007i	0.0438242	+	0.333149i
$957$		0			0
$958$	19.3964	−	22.1150i	0.626669	−	0.714503i
$959$	−12.5367			−0.404831
$960$		0			0
$961$	29.0943			0.938525
$962$	31.2317	−	35.6091i	1.00695	−	1.14808i
$963$		0			0
$964$	4.55971	+	34.6626i	0.146858	+	1.11641i
$965$		−	8.11021i		−	0.261077i
$966$		0			0
$967$		−	13.7843i		−	0.443272i	−0.975129	−	0.221636i	$-0.928860\pi$
$967$		−	13.7843i		−	0.443272i	0.975129	−	0.221636i	$-0.0711397\pi$
$968$	18.2094	+	12.1713i	0.585273	+	0.391200i
$969$		0			0
$970$	−8.04342	−	7.05464i	−0.258259	−	0.226511i
$971$	48.4808			1.55582			0.777911	−	0.628374i	$-0.216279\pi$
$971$	48.4808			1.55582			0.777911	+	0.628374i	$0.216279\pi$
$972$		0			0
$973$	1.60676			0.0515103
$974$	−15.8320	−	13.8857i	−0.507288	−	0.444927i
$975$		0			0
$976$	−17.2818	+	4.62674i	−0.553176	+	0.148098i
$977$			13.2147i			0.422775i	0.977402	+	0.211388i	$0.0677983\pi$
$977$			13.2147i			0.422775i	−0.977402	+	0.211388i	$0.932202\pi$
$978$		0			0
$979$		−	22.9675i		−	0.734044i
$980$	−1.08301	+	0.142465i	−0.0345955	+	0.00455088i
$981$		0			0
$982$	40.1626	−	45.7918i	1.28164	−	1.46127i
$983$	−23.1147			−0.737243			−0.368621	−	0.929580i	$-0.620170\pi$
$983$	−23.1147			−0.737243			−0.368621	+	0.929580i	$0.620170\pi$
$984$		0			0
$985$	−12.8519			−0.409497
$986$	0.250793	−	0.285944i	0.00798688	−	0.00910632i
$987$		0			0
$988$	52.3125	−	6.88146i	1.66428	−	0.218929i
$989$			0.804130i			0.0255698i
$990$		0			0
$991$		−	4.38292i		−	0.139228i	−0.997574	−	0.0696140i	$-0.977823\pi$
$991$		−	4.38292i		−	0.139228i	0.997574	−	0.0696140i	$-0.0221768\pi$
$992$	−7.00293	−	3.45576i	−0.222343	−	0.109720i
$993$		0			0
$994$	−6.04308	−	5.30020i	−0.191675	−	0.168112i
$995$	12.9329			0.409999
$996$		0			0
$997$	−44.6903			−1.41536			−0.707679	−	0.706534i	$-0.750258\pi$
$997$	−44.6903			−1.41536			−0.707679	+	0.706534i	$0.750258\pi$
$998$	−26.2506	−	23.0236i	−0.830949	−	0.728800i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.e.b.323.8	yes	24
3.2	odd	2	inner	756.2.e.b.323.17	yes	24
4.3	odd	2	inner	756.2.e.b.323.18	yes	24
12.11	even	2	inner	756.2.e.b.323.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.e.b.323.7	✓	24	12.11	even	2	inner
756.2.e.b.323.8	yes	24	1.1	even	1	trivial
756.2.e.b.323.17	yes	24	3.2	odd	2	inner
756.2.e.b.323.18	yes	24	4.3	odd	2	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.932512 + 1.06321i) q^{2} +(-0.260844 - 1.98292i) q^{4} +0.546170i q^{5} -1.00000i q^{7} +(2.35150 + 1.57176i) q^{8} +O(q^{10})\)	\(q+(-0.932512 + 1.06321i) q^{2} +(-0.260844 - 1.98292i) q^{4} +0.546170i q^{5} -1.00000i q^{7} +(2.35150 + 1.57176i) q^{8} +(-0.580695 - 0.509310i) q^{10} +4.32940 q^{11} -3.39014 q^{13} +(1.06321 + 0.932512i) q^{14} +(-3.86392 + 1.03446i) q^{16} +0.0960161i q^{17} -7.78185i q^{19} +(1.08301 - 0.142465i) q^{20} +(-4.03722 + 4.60308i) q^{22} -0.716100 q^{23} +4.70170 q^{25} +(3.16135 - 3.60444i) q^{26} +(-1.98292 + 0.260844i) q^{28} +2.80103i q^{29} -1.38048i q^{31} +(2.50330 - 5.07282i) q^{32} +(-0.102086 - 0.0895361i) q^{34} +0.546170 q^{35} +9.87923 q^{37} +(8.27376 + 7.25666i) q^{38} +(-0.858449 + 1.28432i) q^{40} -9.42938i q^{41} -1.12293i q^{43} +(-1.12930 - 8.58485i) q^{44} +(0.667771 - 0.761366i) q^{46} +10.2208 q^{47} -1.00000 q^{49} +(-4.38439 + 4.99891i) q^{50} +(0.884297 + 6.72237i) q^{52} +10.3377i q^{53} +2.36459i q^{55} +(1.57176 - 2.35150i) q^{56} +(-2.97809 - 2.61199i) q^{58} +7.15116 q^{59} +4.47260 q^{61} +(1.46775 + 1.28732i) q^{62} +(3.05913 + 7.39200i) q^{64} -1.85159i q^{65} -10.1781i q^{67} +(0.190392 - 0.0250452i) q^{68} +(-0.509310 + 0.580695i) q^{70} -5.68379 q^{71} +0.760273 q^{73} +(-9.21250 + 10.5037i) q^{74} +(-15.4308 + 2.02985i) q^{76} -4.32940i q^{77} +1.95953i q^{79} +(-0.564993 - 2.11036i) q^{80} +(10.0254 + 8.79301i) q^{82} -3.56402 q^{83} -0.0524411 q^{85} +(1.19391 + 1.04715i) q^{86} +(10.1806 + 6.80479i) q^{88} -5.30500i q^{89} +3.39014i q^{91} +(0.186790 + 1.41997i) q^{92} +(-9.53098 + 10.8669i) q^{94} +4.25021 q^{95} +13.8514 q^{97} +(0.932512 - 1.06321i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4}+O(q^{10}) \) 24 * q + 4 * q^4	\( 24 q + 4 q^{4} + 20 q^{10} + 20 q^{16} - 8 q^{22} - 24 q^{25} - 8 q^{28} - 20 q^{34} + 16 q^{37} - 32 q^{40} + 36 q^{46} - 24 q^{49} + 16 q^{52} - 52 q^{58} + 16 q^{61} + 4 q^{64} + 12 q^{70} + 4 q^{82} - 64 q^{85} - 16 q^{88} + 12 q^{94}+O(q^{100}) \) 24 * q + 4 * q^4 + 20 * q^10 + 20 * q^16 - 8 * q^22 - 24 * q^25 - 8 * q^28 - 20 * q^34 + 16 * q^37 - 32 * q^40 + 36 * q^46 - 24 * q^49 + 16 * q^52 - 52 * q^58 + 16 * q^61 + 4 * q^64 + 12 * q^70 + 4 * q^82 - 64 * q^85 - 16 * q^88 + 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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