LMFDB - Embedded newform 756.2.e.a.323.4

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			323.4
Character	$\chi$	$=$	756.323
Dual form			756.2.e.a.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25904 + 0.644062i) q^{2} +(1.17037 - 1.62180i) q^{4} +3.70845i q^{5} -1.00000i q^{7} +(-0.429004 + 2.79570i) q^{8} +O(q^{10})$	\(q+(-1.25904 + 0.644062i) q^{2} +(1.17037 - 1.62180i) q^{4} +3.70845i q^{5} -1.00000i q^{7} +(-0.429004 + 2.79570i) q^{8} +(-2.38847 - 4.66909i) q^{10} -3.09952 q^{11} -5.37192 q^{13} +(0.644062 + 1.25904i) q^{14} +(-1.26047 - 3.79621i) q^{16} -6.77136i q^{17} +3.99744i q^{19} +(6.01436 + 4.34025i) q^{20} +(3.90242 - 1.99628i) q^{22} -2.22811 q^{23} -8.75259 q^{25} +(6.76347 - 3.45985i) q^{26} +(-1.62180 - 1.17037i) q^{28} +1.70024i q^{29} -5.12963i q^{31} +(4.03198 + 3.96776i) q^{32} +(4.36117 + 8.52542i) q^{34} +3.70845 q^{35} +10.0134 q^{37} +(-2.57460 - 5.03294i) q^{38} +(-10.3677 - 1.59094i) q^{40} +0.313182i q^{41} -3.71354i q^{43} +(-3.62758 + 5.02680i) q^{44} +(2.80528 - 1.43504i) q^{46} -11.8633 q^{47} -1.00000 q^{49} +(11.0199 - 5.63721i) q^{50} +(-6.28713 + 8.71218i) q^{52} +2.32834i q^{53} -11.4944i q^{55} +(2.79570 + 0.429004i) q^{56} +(-1.09506 - 2.14067i) q^{58} -11.2625 q^{59} -5.02310 q^{61} +(3.30380 + 6.45841i) q^{62} +(-7.63191 - 2.39874i) q^{64} -19.9215i q^{65} -10.0534i q^{67} +(-10.9818 - 7.92499i) q^{68} +(-4.66909 + 2.38847i) q^{70} -1.38706 q^{71} -1.59986 q^{73} +(-12.6073 + 6.44924i) q^{74} +(6.48305 + 4.67848i) q^{76} +3.09952i q^{77} +13.0765i q^{79} +(14.0781 - 4.67439i) q^{80} +(-0.201708 - 0.394309i) q^{82} +5.76905 q^{83} +25.1112 q^{85} +(2.39175 + 4.67550i) q^{86} +(1.32971 - 8.66533i) q^{88} -7.23529i q^{89} +5.37192i q^{91} +(-2.60771 + 3.61355i) q^{92} +(14.9364 - 7.64070i) q^{94} -14.8243 q^{95} -14.1644 q^{97} +(1.25904 - 0.644062i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4}+O(q^{10}) $ 24 * q - 8 * q^4	$ 24 q - 8 q^{4} - 16 q^{10} + 8 q^{16} + 16 q^{22} - 24 q^{25} - 8 q^{28} - 8 q^{34} + 16 q^{37} - 8 q^{40} - 24 q^{49} - 8 q^{52} + 32 q^{58} - 80 q^{61} + 40 q^{64} - 24 q^{70} - 32 q^{82} + 56 q^{85} + 56 q^{88} + 72 q^{94}+O(q^{100}) $ 24 * q - 8 * q^4 - 16 * q^10 + 8 * q^16 + 16 * q^22 - 24 * q^25 - 8 * q^28 - 8 * q^34 + 16 * q^37 - 8 * q^40 - 24 * q^49 - 8 * q^52 + 32 * q^58 - 80 * q^61 + 40 * q^64 - 24 * q^70 - 32 * q^82 + 56 * q^85 + 56 * q^88 + 72 * 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 $

$2$	−1.25904	+	0.644062i	−0.890277	+	0.455420i
$2$	−1.25904	+	0.644062i	−0.890277	+	0.455420i
$3$		0			0
$3$		0			0
$4$	1.17037	−	1.62180i	0.585185	−	0.810900i
$5$			3.70845i			1.65847i	0.558901	+	0.829234i	$0.311223\pi$
$5$			3.70845i			1.65847i	−0.558901	+	0.829234i	$0.688777\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.429004	+	2.79570i	−0.151676	+	0.988430i
$9$		0			0
$10$	−2.38847	−	4.66909i	−0.755300	−	1.47650i
$11$	−3.09952			−0.934540			−0.467270	−	0.884115i	$-0.654762\pi$
$11$	−3.09952			−0.934540			−0.467270	+	0.884115i	$0.654762\pi$
$12$		0			0
$13$	−5.37192			−1.48990			−0.744951	−	0.667119i	$-0.767527\pi$
$13$	−5.37192			−1.48990			−0.744951	+	0.667119i	$0.767527\pi$
$14$	0.644062	+	1.25904i	0.172133	+	0.336493i
$15$		0			0
$16$	−1.26047	−	3.79621i	−0.315118	−	0.949053i
$17$		−	6.77136i		−	1.64230i	−0.570716	−	0.821148i	$-0.693334\pi$
$17$		−	6.77136i		−	1.64230i	0.570716	−	0.821148i	$-0.306666\pi$
$18$		0			0
$19$			3.99744i			0.917075i	0.888675	+	0.458538i	$0.151627\pi$
$19$			3.99744i			0.917075i	−0.888675	+	0.458538i	$0.848373\pi$
$20$	6.01436	+	4.34025i	1.34485	+	0.970510i
$21$		0			0
$22$	3.90242	−	1.99628i	0.831999	−	0.425608i
$23$	−2.22811			−0.464593			−0.232296	−	0.972645i	$-0.574624\pi$
$23$	−2.22811			−0.464593			−0.232296	+	0.972645i	$0.574624\pi$
$24$		0			0
$25$	−8.75259			−1.75052
$26$	6.76347	−	3.45985i	1.32643	−	0.678532i
$27$		0			0
$28$	−1.62180	−	1.17037i	−0.306491	−	0.221179i
$29$			1.70024i			0.315726i	0.987461	+	0.157863i	$0.0504605\pi$
$29$			1.70024i			0.315726i	−0.987461	+	0.157863i	$0.949540\pi$
$30$		0			0
$31$		−	5.12963i		−	0.921309i	−0.887580	−	0.460654i	$-0.847615\pi$
$31$		−	5.12963i		−	0.921309i	0.887580	−	0.460654i	$-0.152385\pi$
$32$	4.03198	+	3.96776i	0.712760	+	0.701408i
$33$		0			0
$34$	4.36117	+	8.52542i	0.747935	+	1.46210i
$35$	3.70845			0.626842
$36$		0			0
$37$	10.0134			1.64619			0.823096	−	0.567903i	$-0.192245\pi$
$37$	10.0134			1.64619			0.823096	+	0.567903i	$0.192245\pi$
$38$	−2.57460	−	5.03294i	−0.417655	−	0.816451i
$39$		0			0
$40$	−10.3677	−	1.59094i	−1.63928	−	0.251550i
$41$			0.313182i			0.0489108i	0.999701	+	0.0244554i	$0.00778517\pi$
$41$			0.313182i			0.0489108i	−0.999701	+	0.0244554i	$0.992215\pi$
$42$		0			0
$43$		−	3.71354i		−	0.566310i	−0.959074	−	0.283155i	$-0.908619\pi$
$43$		−	3.71354i		−	0.566310i	0.959074	−	0.283155i	$-0.0913810\pi$
$44$	−3.62758	+	5.02680i	−0.546878	+	0.757818i
$45$		0			0
$46$	2.80528	−	1.43504i	0.413616	−	0.211585i
$47$	−11.8633			−1.73044			−0.865221	−	0.501392i	$-0.832822\pi$
$47$	−11.8633			−1.73044			−0.865221	+	0.501392i	$0.832822\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	11.0199	−	5.63721i	1.55844	−	0.797221i
$51$		0			0
$52$	−6.28713	+	8.71218i	−0.871868	+	1.20816i
$53$			2.32834i			0.319823i	0.987131	+	0.159911i	$0.0511208\pi$
$53$			2.32834i			0.319823i	−0.987131	+	0.159911i	$0.948879\pi$
$54$		0			0
$55$		−	11.4944i		−	1.54990i
$56$	2.79570	+	0.429004i	0.373592	+	0.0573281i
$57$		0			0
$58$	−1.09506	−	2.14067i	−0.143788	−	0.281084i
$59$	−11.2625			−1.46626			−0.733128	−	0.680090i	$-0.761941\pi$
$59$	−11.2625			−1.46626			−0.733128	+	0.680090i	$0.761941\pi$
$60$		0			0
$61$	−5.02310			−0.643142			−0.321571	−	0.946885i	$-0.604211\pi$
$61$	−5.02310			−0.643142			−0.321571	+	0.946885i	$0.604211\pi$
$62$	3.30380	+	6.45841i	0.419583	+	0.820219i
$63$		0			0
$64$	−7.63191	−	2.39874i	−0.953989	−	0.299842i
$65$		−	19.9215i		−	2.47096i
$66$		0			0
$67$		−	10.0534i		−	1.22822i	−0.789221	−	0.614109i	$-0.789516\pi$
$67$		−	10.0534i		−	1.22822i	0.789221	−	0.614109i	$-0.210484\pi$
$68$	−10.9818	−	7.92499i	−1.33174	−	0.961046i
$69$		0			0
$70$	−4.66909	+	2.38847i	−0.558063	+	0.285477i
$71$	−1.38706			−0.164613			−0.0823066	−	0.996607i	$-0.526229\pi$
$71$	−1.38706			−0.164613			−0.0823066	+	0.996607i	$0.526229\pi$
$72$		0			0
$73$	−1.59986			−0.187250			−0.0936248	−	0.995608i	$-0.529845\pi$
$73$	−1.59986			−0.187250			−0.0936248	+	0.995608i	$0.529845\pi$
$74$	−12.6073	+	6.44924i	−1.46557	+	0.749709i
$75$		0			0
$76$	6.48305	+	4.67848i	0.743657	+	0.536659i
$77$			3.09952i			0.353223i
$78$		0			0
$79$			13.0765i			1.47122i	0.677405	+	0.735610i	$0.263105\pi$
$79$			13.0765i			1.47122i	−0.677405	+	0.735610i	$0.736895\pi$
$80$	14.0781	−	4.67439i	1.57397	−	0.522613i
$81$		0			0
$82$	−0.201708	−	0.394309i	−0.0222750	−	0.0435441i
$83$	5.76905			0.633235			0.316618	−	0.948553i	$-0.397453\pi$
$83$	5.76905			0.633235			0.316618	+	0.948553i	$0.397453\pi$
$84$		0			0
$85$	25.1112			2.72370
$86$	2.39175	+	4.67550i	0.257909	+	0.504172i
$87$		0			0
$88$	1.32971	−	8.66533i	0.141747	−	0.923727i
$89$		−	7.23529i		−	0.766939i	−0.923554	−	0.383470i	$-0.874729\pi$
$89$		−	7.23529i		−	0.766939i	0.923554	−	0.383470i	$-0.125271\pi$
$90$		0			0
$91$			5.37192i			0.563130i
$92$	−2.60771	+	3.61355i	−0.271873	+	0.376738i
$93$		0			0
$94$	14.9364	−	7.64070i	1.54057	−	0.788078i
$95$	−14.8243			−1.52094
$96$		0			0
$97$	−14.1644			−1.43817			−0.719087	−	0.694920i	$-0.755440\pi$
$97$	−14.1644			−1.43817			−0.719087	+	0.694920i	$0.755440\pi$
$98$	1.25904	−	0.644062i	0.127182	−	0.0650600i
$99$		0			0
$100$	−10.2438	+	14.1949i	−1.02438	+	1.41949i
$101$			3.66755i			0.364935i	0.983212	+	0.182468i	$0.0584085\pi$
$101$			3.66755i			0.364935i	−0.983212	+	0.182468i	$0.941592\pi$
$102$		0			0
$103$		−	2.80289i		−	0.276177i	−0.990420	−	0.138088i	$-0.955904\pi$
$103$		−	2.80289i		−	0.276177i	0.990420	−	0.138088i	$-0.0440958\pi$
$104$	2.30458	−	15.0183i	0.225982	−	1.47266i
$105$		0			0
$106$	−1.49960	−	2.93148i	−0.145654	−	0.284731i
$107$	−2.83076			−0.273660			−0.136830	−	0.990595i	$-0.543691\pi$
$107$	−2.83076			−0.273660			−0.136830	+	0.990595i	$0.543691\pi$
$108$		0			0
$109$	4.20330			0.402603			0.201302	−	0.979529i	$-0.435483\pi$
$109$	4.20330			0.402603			0.201302	+	0.979529i	$0.435483\pi$
$110$	7.40310	+	14.4719i	0.705858	+	1.37984i
$111$		0			0
$112$	−3.79621	+	1.26047i	−0.358708	+	0.119103i
$113$		−	5.35036i		−	0.503319i	−0.967816	−	0.251660i	$-0.919024\pi$
$113$		−	5.35036i		−	0.503319i	0.967816	−	0.251660i	$-0.0809764\pi$
$114$		0			0
$115$		−	8.26283i		−	0.770513i
$116$	2.75745	+	1.98991i	0.256022	+	0.184758i
$117$		0			0
$118$	14.1800	−	7.25376i	1.30537	−	0.667763i
$119$	−6.77136			−0.620729
$120$		0			0
$121$	−1.39299			−0.126636
$122$	6.32429	−	3.23518i	0.572574	−	0.292900i
$123$		0			0
$124$	−8.31923	−	6.00356i	−0.747089	−	0.539136i
$125$		−	13.9163i		−	1.24471i
$126$		0			0
$127$		−	3.75974i		−	0.333623i	−0.985989	−	0.166811i	$-0.946653\pi$
$127$		−	3.75974i		−	0.333623i	0.985989	−	0.166811i	$-0.0533471\pi$
$128$	11.1538	−	1.89531i	0.985868	−	0.167523i
$129$		0			0
$130$	12.8307	+	25.0820i	1.12532	+	2.19983i
$131$	−11.3673			−0.993166			−0.496583	−	0.867989i	$-0.665412\pi$
$131$	−11.3673			−0.993166			−0.496583	+	0.867989i	$0.665412\pi$
$132$		0			0
$133$	3.99744			0.346622
$134$	6.47501	+	12.6576i	0.559355	+	1.09345i
$135$		0			0
$136$	18.9307	+	2.90494i	1.62329	+	0.249097i
$137$		−	0.115795i		−	0.00989304i	−0.999988	−	0.00494652i	$-0.998425\pi$
$137$		−	0.115795i		−	0.00989304i	0.999988	−	0.00494652i	$-0.00157453\pi$
$138$		0			0
$139$			19.5727i			1.66013i	0.557666	+	0.830066i	$0.311697\pi$
$139$			19.5727i			1.66013i	−0.557666	+	0.830066i	$0.688303\pi$
$140$	4.34025	−	6.01436i	0.366818	−	0.508306i
$141$		0			0
$142$	1.74636	−	0.893349i	0.146551	−	0.0749682i
$143$	16.6504			1.39237
$144$		0			0
$145$	−6.30524			−0.523622
$146$	2.01429	−	1.03041i	0.166704	−	0.0852772i
$147$		0			0
$148$	11.7194	−	16.2397i	0.963326	−	1.33490i
$149$			1.15392i			0.0945330i	0.998882	+	0.0472665i	$0.0150510\pi$
$149$			1.15392i			0.0945330i	−0.998882	+	0.0472665i	$0.984949\pi$
$150$		0			0
$151$			24.3347i			1.98033i	0.139895	+	0.990166i	$0.455324\pi$
$151$			24.3347i			1.98033i	−0.139895	+	0.990166i	$0.544676\pi$
$152$	−11.1757	−	1.71492i	−0.906465	−	0.139098i
$153$		0			0
$154$	−1.99628	−	3.90242i	−0.160865	−	0.314466i
$155$	19.0230			1.52796
$156$		0			0
$157$	−8.52181			−0.680115			−0.340057	−	0.940405i	$-0.610447\pi$
$157$	−8.52181			−0.680115			−0.340057	+	0.940405i	$0.610447\pi$
$158$	−8.42207	−	16.4638i	−0.670024	−	1.30979i
$159$		0			0
$160$	−14.7143	+	14.9524i	−1.16326	+	1.18209i
$161$			2.22811i			0.175600i
$162$		0			0
$163$			9.39070i			0.735537i	0.929917	+	0.367768i	$0.119878\pi$
$163$			9.39070i			0.735537i	−0.929917	+	0.367768i	$0.880122\pi$
$164$	0.507918	+	0.366538i	0.0396617	+	0.0286218i
$165$		0			0
$166$	−7.26347	+	3.71562i	−0.563754	+	0.288388i
$167$	17.9094			1.38587			0.692936	−	0.720999i	$-0.256317\pi$
$167$	17.9094			1.38587			0.692936	+	0.720999i	$0.256317\pi$
$168$		0			0
$169$	15.8575			1.21981
$170$	−31.6161	+	16.1732i	−2.42484	+	1.24043i
$171$		0			0
$172$	−6.02262	−	4.34621i	−0.459220	−	0.331396i
$173$			18.6764i			1.41994i	0.704234	+	0.709968i	$0.251291\pi$
$173$			18.6764i			1.41994i	−0.704234	+	0.709968i	$0.748709\pi$
$174$		0			0
$175$			8.75259i			0.661634i
$176$	3.90685	+	11.7664i	0.294490	+	0.886927i
$177$		0			0
$178$	4.65997	+	9.10953i	0.349280	+	0.682788i
$179$	−18.7505			−1.40148			−0.700738	−	0.713419i	$-0.747146\pi$
$179$	−18.7505			−1.40148			−0.700738	+	0.713419i	$0.747146\pi$
$180$		0			0
$181$	−17.4065			−1.29382			−0.646909	−	0.762567i	$-0.723939\pi$
$181$	−17.4065			−1.29382			−0.646909	+	0.762567i	$0.723939\pi$
$182$	−3.45985	−	6.76347i	−0.256461	−	0.501342i
$183$		0			0
$184$	0.955869	−	6.22913i	0.0704676	−	0.459218i
$185$			37.1341i			2.73016i
$186$		0			0
$187$			20.9879i			1.53479i
$188$	−13.8845	+	19.2399i	−1.01263	+	1.40321i
$189$		0			0
$190$	18.6644	−	9.54776i	1.35406	−	0.692667i
$191$	7.47731			0.541039			0.270520	−	0.962714i	$-0.412805\pi$
$191$	7.47731			0.541039			0.270520	+	0.962714i	$0.412805\pi$
$192$		0			0
$193$	13.7944			0.992939			0.496470	−	0.868054i	$-0.334629\pi$
$193$	13.7944			0.992939			0.496470	+	0.868054i	$0.334629\pi$
$194$	17.8335	−	9.12272i	1.28037	−	0.654973i
$195$		0			0
$196$	−1.17037	+	1.62180i	−0.0835978	+	0.115843i
$197$		−	16.0235i		−	1.14162i	−0.821081	−	0.570812i	$-0.806628\pi$
$197$		−	16.0235i		−	1.14162i	0.821081	−	0.570812i	$-0.193372\pi$
$198$		0			0
$199$			14.2609i			1.01093i	0.862848	+	0.505463i	$0.168678\pi$
$199$			14.2609i			1.01093i	−0.862848	+	0.505463i	$0.831322\pi$
$200$	3.75490	−	24.4696i	0.265511	−	1.73026i
$201$		0			0
$202$	−2.36213	−	4.61760i	−0.166199	−	0.324893i
$203$	1.70024			0.119333
$204$		0			0
$205$	−1.16142			−0.0811170
$206$	1.80523	+	3.52895i	0.125777	+	0.245874i
$207$		0			0
$208$	6.77115	+	20.3929i	0.469495	+	1.41400i
$209$		−	12.3901i		−	0.857043i
$210$		0			0
$211$			10.5242i			0.724517i	0.932078	+	0.362259i	$0.117994\pi$
$211$			10.5242i			0.724517i	−0.932078	+	0.362259i	$0.882006\pi$
$212$	3.77611	+	2.72502i	0.259344	+	0.187155i
$213$		0			0
$214$	3.56404	−	1.82318i	0.243633	−	0.124630i
$215$	13.7715			0.939206
$216$		0			0
$217$	−5.12963			−0.348222
$218$	−5.29213	+	2.70718i	−0.358428	+	0.183354i
$219$		0			0
$220$	−18.6416	−	13.4527i	−1.25682	−	0.906981i
$221$			36.3752i			2.44686i
$222$		0			0
$223$		−	3.21898i		−	0.215559i	−0.994175	−	0.107779i	$-0.965626\pi$
$223$		−	3.21898i		−	0.215559i	0.994175	−	0.107779i	$-0.0343740\pi$
$224$	3.96776	−	4.03198i	0.265107	−	0.269398i
$225$		0			0
$226$	3.44596	+	6.73632i	0.229222	+	0.448093i
$227$	3.31418			0.219970			0.109985	−	0.993933i	$-0.464920\pi$
$227$	3.31418			0.219970			0.109985	+	0.993933i	$0.464920\pi$
$228$		0			0
$229$	17.1972			1.13642			0.568212	−	0.822882i	$-0.307635\pi$
$229$	17.1972			1.13642			0.568212	+	0.822882i	$0.307635\pi$
$230$	5.32177	+	10.4032i	0.350907	+	0.685969i
$231$		0			0
$232$	−4.75336	−	0.729409i	−0.312073	−	0.0478881i
$233$			1.69519i			0.111056i	0.998457	+	0.0555278i	$0.0176841\pi$
$233$			1.69519i			0.111056i	−0.998457	+	0.0555278i	$0.982316\pi$
$234$		0			0
$235$		−	43.9945i		−	2.86988i
$236$	−13.1813	+	18.2656i	−0.858031	+	1.18899i
$237$		0			0
$238$	8.52542	−	4.36117i	0.552621	−	0.282693i
$239$	−16.7377			−1.08267			−0.541336	−	0.840806i	$-0.682081\pi$
$239$	−16.7377			−1.08267			−0.541336	+	0.840806i	$0.682081\pi$
$240$		0			0
$241$	23.8016			1.53319			0.766596	−	0.642129i	$-0.221949\pi$
$241$	23.8016			1.53319			0.766596	+	0.642129i	$0.221949\pi$
$242$	1.75383	−	0.897172i	0.112741	−	0.0576724i
$243$		0			0
$244$	−5.87888	+	8.14646i	−0.376357	+	0.521524i
$245$		−	3.70845i		−	0.236924i
$246$		0			0
$247$		−	21.4739i		−	1.36635i
$248$	14.3409	+	2.20063i	0.910649	+	0.139740i
$249$		0			0
$250$	8.96294	+	17.5212i	0.566866	+	1.10814i
$251$	−19.6105			−1.23780			−0.618902	−	0.785468i	$-0.712422\pi$
$251$	−19.6105			−1.23780			−0.618902	+	0.785468i	$0.712422\pi$
$252$		0			0
$253$	6.90606			0.434181
$254$	2.42150	+	4.73366i	0.151939	+	0.297016i
$255$		0			0
$256$	−12.8224	+	9.57002i	−0.801402	+	0.598126i
$257$			1.66991i			0.104166i	0.998643	+	0.0520832i	$0.0165861\pi$
$257$			1.66991i			0.104166i	−0.998643	+	0.0520832i	$0.983414\pi$
$258$		0			0
$259$		−	10.0134i		−	0.622202i
$260$	−32.3087	−	23.3155i	−2.00370	−	1.44597i
$261$		0			0
$262$	14.3119	−	7.32125i	0.884193	−	0.452308i
$263$	−2.56491			−0.158159			−0.0790797	−	0.996868i	$-0.525198\pi$
$263$	−2.56491			−0.158159			−0.0790797	+	0.996868i	$0.525198\pi$
$264$		0			0
$265$	−8.63454			−0.530416
$266$	−5.03294	+	2.57460i	−0.308589	+	0.157859i
$267$		0			0
$268$	−16.3046	−	11.7662i	−0.995962	−	0.718734i
$269$			14.5599i			0.887734i	0.896093	+	0.443867i	$0.146394\pi$
$269$			14.5599i			0.887734i	−0.896093	+	0.443867i	$0.853606\pi$
$270$		0			0
$271$			0.896303i			0.0544465i	0.999629	+	0.0272233i	$0.00866650\pi$
$271$			0.896303i			0.0544465i	−0.999629	+	0.0272233i	$0.991333\pi$
$272$	−25.7055	+	8.53510i	−1.55862	+	0.517516i
$273$		0			0
$274$	0.0745791	+	0.145791i	0.00450549	+	0.00880754i
$275$	27.1288			1.63593
$276$		0			0
$277$	−0.801439			−0.0481538			−0.0240769	−	0.999710i	$-0.507665\pi$
$277$	−0.801439			−0.0481538			−0.0240769	+	0.999710i	$0.507665\pi$
$278$	−12.6060	−	24.6428i	−0.756057	−	1.47798i
$279$		0			0
$280$	−1.59094	+	10.3677i	−0.0950769	+	0.619590i
$281$		−	3.08681i		−	0.184144i	−0.995752	−	0.0920720i	$-0.970651\pi$
$281$		−	3.08681i		−	0.184144i	0.995752	−	0.0920720i	$-0.0293490\pi$
$282$		0			0
$283$		−	9.26732i		−	0.550885i	−0.961318	−	0.275443i	$-0.911176\pi$
$283$		−	9.26732i		−	0.550885i	0.961318	−	0.275443i	$-0.0888244\pi$
$284$	−1.62337	+	2.24953i	−0.0963292	+	0.133485i
$285$		0			0
$286$	−20.9635	+	10.7239i	−1.23960	+	0.634115i
$287$	0.313182			0.0184865
$288$		0			0
$289$	−28.8513			−1.69713
$290$	7.93856	−	4.06097i	0.466168	−	0.238468i
$291$		0			0
$292$	−1.87243	+	2.59465i	−0.109576	+	0.151841i
$293$		−	5.10411i		−	0.298185i	−0.988823	−	0.149093i	$-0.952365\pi$
$293$		−	5.10411i		−	0.298185i	0.988823	−	0.149093i	$-0.0476353\pi$
$294$		0			0
$295$		−	41.7665i		−	2.43174i
$296$	−4.29579	+	27.9945i	−0.249688	+	1.62715i
$297$		0			0
$298$	−0.743197	−	1.45284i	−0.0430522	−	0.0841605i
$299$	11.9692			0.692198
$300$		0			0
$301$	−3.71354			−0.214045
$302$	−15.6731	−	30.6384i	−0.901884	−	1.76304i
$303$		0			0
$304$	15.1751	−	5.03865i	0.870353	−	0.288987i
$305$		−	18.6279i		−	1.06663i
$306$		0			0
$307$			15.3553i			0.876372i	0.898884	+	0.438186i	$0.144379\pi$
$307$			15.3553i			0.876372i	−0.898884	+	0.438186i	$0.855621\pi$
$308$	5.02680	+	3.62758i	0.286428	+	0.206701i
$309$		0			0
$310$	−23.9507	+	12.2520i	−1.36031	+	0.695865i
$311$	15.1846			0.861039			0.430520	−	0.902581i	$-0.358330\pi$
$311$	15.1846			0.861039			0.430520	+	0.902581i	$0.358330\pi$
$312$		0			0
$313$	−21.5799			−1.21977			−0.609883	−	0.792492i	$-0.708784\pi$
$313$	−21.5799			−1.21977			−0.609883	+	0.792492i	$0.708784\pi$
$314$	10.7293	−	5.48857i	0.605490	−	0.309738i
$315$		0			0
$316$	21.2075	+	15.3043i	1.19301	+	0.860936i
$317$		−	29.3555i		−	1.64877i	−0.566030	−	0.824385i	$-0.691521\pi$
$317$		−	29.3555i		−	1.64877i	0.566030	−	0.824385i	$-0.308479\pi$
$318$		0			0
$319$		−	5.26992i		−	0.295059i
$320$	8.89559	−	28.3025i	0.497279	−	1.58216i
$321$		0			0
$322$	−1.43504	−	2.80528i	−0.0799716	−	0.156332i
$323$	27.0681			1.50611
$324$		0			0
$325$	47.0182			2.60810
$326$	−6.04819	−	11.8233i	−0.334978	−	0.654831i
$327$		0			0
$328$	−0.875563	−	0.134356i	−0.0483449	−	0.00741859i
$329$			11.8633i			0.654045i
$330$		0			0
$331$		−	12.6478i		−	0.695187i	−0.937645	−	0.347593i	$-0.886999\pi$
$331$		−	12.6478i		−	0.695187i	0.937645	−	0.347593i	$-0.113001\pi$
$332$	6.75192	−	9.35624i	0.370560	−	0.513490i
$333$		0			0
$334$	−22.5487	+	11.5348i	−1.23381	+	0.631154i
$335$	37.2825			2.03696
$336$		0			0
$337$	−29.2314			−1.59233			−0.796167	−	0.605077i	$-0.793142\pi$
$337$	−29.2314			−1.59233			−0.796167	+	0.605077i	$0.793142\pi$
$338$	−19.9653	+	10.2132i	−1.08597	+	0.555526i
$339$		0			0
$340$	29.3894	−	40.7254i	1.59386	−	2.20864i
$341$			15.8994i			0.860999i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	10.3820	+	1.59312i	0.559757	+	0.0858955i
$345$		0			0
$346$	−12.0287	−	23.5143i	−0.646668	−	1.26414i
$347$	22.2016			1.19185			0.595923	−	0.803041i	$-0.296786\pi$
$347$	22.2016			1.19185			0.595923	+	0.803041i	$0.296786\pi$
$348$		0			0
$349$	23.4539			1.25546			0.627728	−	0.778433i	$-0.283985\pi$
$349$	23.4539			1.25546			0.627728	+	0.778433i	$0.283985\pi$
$350$	−5.63721	−	11.0199i	−0.301321	−	0.589037i
$351$		0			0
$352$	−12.4972	−	12.2982i	−0.666102	−	0.655494i
$353$			4.21295i			0.224233i	0.993695	+	0.112116i	$0.0357629\pi$
$353$			4.21295i			0.224233i	−0.993695	+	0.112116i	$0.964237\pi$
$354$		0			0
$355$		−	5.14383i		−	0.273006i
$356$	−11.7342	−	8.46796i	−0.621911	−	0.448801i
$357$		0			0
$358$	23.6076	−	12.0764i	1.24770	−	0.638260i
$359$	34.1500			1.80237			0.901183	−	0.433438i	$-0.142700\pi$
$359$	34.1500			1.80237			0.901183	+	0.433438i	$0.142700\pi$
$360$		0			0
$361$	3.02048			0.158973
$362$	21.9155	−	11.2109i	1.15186	−	0.589231i
$363$		0			0
$364$	8.71218	+	6.28713i	0.456642	+	0.329535i
$365$		−	5.93300i		−	0.310547i
$366$		0			0
$367$		−	3.21577i		−	0.167862i	−0.996472	−	0.0839310i	$-0.973252\pi$
$367$		−	3.21577i		−	0.167862i	0.996472	−	0.0839310i	$-0.0267475\pi$
$368$	2.80847	+	8.45837i	0.146401	+	0.440923i
$369$		0			0
$370$	−23.9167	−	46.7534i	−1.24337	−	2.43059i
$371$	2.32834			0.120882
$372$		0			0
$373$	−23.3144			−1.20717			−0.603587	−	0.797297i	$-0.706262\pi$
$373$	−23.3144			−1.20717			−0.603587	+	0.797297i	$0.706262\pi$
$374$	−13.5175	−	26.4247i	−0.698975	−	1.36639i
$375$		0			0
$376$	5.08941	−	33.1663i	0.262466	−	1.71042i
$377$		−	9.13354i		−	0.470401i
$378$		0			0
$379$		−	7.44202i		−	0.382271i	−0.981564	−	0.191135i	$-0.938783\pi$
$379$		−	7.44202i		−	0.382271i	0.981564	−	0.191135i	$-0.0612170\pi$
$380$	−17.3499	+	24.0420i	−0.890031	+	1.23333i
$381$		0			0
$382$	−9.41424	+	4.81585i	−0.481675	+	0.246400i
$383$	−19.7759			−1.01050			−0.505251	−	0.862972i	$-0.668600\pi$
$383$	−19.7759			−1.01050			−0.505251	+	0.862972i	$0.668600\pi$
$384$		0			0
$385$	−11.4944			−0.585809
$386$	−17.3677	+	8.88441i	−0.883990	+	0.452205i
$387$		0			0
$388$	−16.5775	+	22.9718i	−0.841597	+	1.16621i
$389$		−	20.6478i		−	1.04688i	−0.852061	−	0.523442i	$-0.824648\pi$
$389$		−	20.6478i		−	1.04688i	0.852061	−	0.523442i	$-0.175352\pi$
$390$		0			0
$391$			15.0873i			0.762999i
$392$	0.429004	−	2.79570i	0.0216680	−	0.141204i
$393$		0			0
$394$	10.3201	+	20.1742i	0.519919	+	1.01636i
$395$	−48.4935			−2.43997
$396$		0			0
$397$	−8.22224			−0.412662			−0.206331	−	0.978482i	$-0.566152\pi$
$397$	−8.22224			−0.412662			−0.206331	+	0.978482i	$0.566152\pi$
$398$	−9.18487	−	17.9550i	−0.460396	−	0.900003i
$399$		0			0
$400$	11.0324	+	33.2267i	0.551619	+	1.66133i
$401$		−	23.3067i		−	1.16388i	−0.813231	−	0.581941i	$-0.802294\pi$
$401$		−	23.3067i		−	1.16388i	0.813231	−	0.581941i	$-0.197706\pi$
$402$		0			0
$403$			27.5560i			1.37266i
$404$	5.94804	+	4.29239i	0.295926	+	0.213555i
$405$		0			0
$406$	−2.14067	+	1.09506i	−0.106240	+	0.0543468i
$407$	−31.0367			−1.53843
$408$		0			0
$409$	−27.5619			−1.36285			−0.681425	−	0.731888i	$-0.738639\pi$
$409$	−27.5619			−1.36285			−0.681425	+	0.731888i	$0.738639\pi$
$410$	1.46227	−	0.748025i	0.0722165	−	0.0369423i
$411$		0			0
$412$	−4.54572	−	3.28042i	−0.223952	−	0.161614i
$413$			11.2625i			0.554193i
$414$		0			0
$415$			21.3942i			1.05020i
$416$	−21.6595	−	21.3145i	−1.06194	−	1.04503i
$417$		0			0
$418$	7.98001	+	15.5997i	0.390315	+	0.763006i
$419$	−17.3574			−0.847964			−0.423982	−	0.905671i	$-0.639368\pi$
$419$	−17.3574			−0.847964			−0.423982	+	0.905671i	$0.639368\pi$
$420$		0			0
$421$	4.49580			0.219112			0.109556	−	0.993981i	$-0.465057\pi$
$421$	4.49580			0.219112			0.109556	+	0.993981i	$0.465057\pi$
$422$	−6.77825	−	13.2504i	−0.329960	−	0.645021i
$423$		0			0
$424$	−6.50936	−	0.998870i	−0.316122	−	0.0485094i
$425$			59.2669i			2.87487i
$426$		0			0
$427$			5.02310i			0.243085i
$428$	−3.31303	+	4.59092i	−0.160141	+	0.221911i
$429$		0			0
$430$	−17.3388	+	8.86967i	−0.836154	+	0.427734i
$431$	35.8327			1.72600			0.863000	−	0.505204i	$-0.168583\pi$
$431$	35.8327			1.72600			0.863000	+	0.505204i	$0.168583\pi$
$432$		0			0
$433$	12.4386			0.597761			0.298880	−	0.954291i	$-0.403387\pi$
$433$	12.4386			0.597761			0.298880	+	0.954291i	$0.403387\pi$
$434$	6.45841	−	3.30380i	0.310014	−	0.158587i
$435$		0			0
$436$	4.91941	−	6.81691i	0.235597	−	0.326471i
$437$		−	8.90673i		−	0.426067i
$438$		0			0
$439$			6.31421i			0.301361i	0.988583	+	0.150680i	$0.0481464\pi$
$439$			6.31421i			0.301361i	−0.988583	+	0.150680i	$0.951854\pi$
$440$	32.1349	+	4.93115i	1.53197	+	0.235083i
$441$		0			0
$442$	−23.4279	−	45.7979i	−1.11435	−	2.17838i
$443$	16.4021			0.779289			0.389645	−	0.920965i	$-0.372598\pi$
$443$	16.4021			0.779289			0.389645	+	0.920965i	$0.372598\pi$
$444$		0			0
$445$	26.8317			1.27194
$446$	2.07322	+	4.05283i	0.0981698	+	0.191907i
$447$		0			0
$448$	−2.39874	+	7.63191i	−0.113330	+	0.360574i
$449$			24.2262i			1.14330i	0.820496	+	0.571652i	$0.193697\pi$
$449$			24.2262i			1.14330i	−0.820496	+	0.571652i	$0.806303\pi$
$450$		0			0
$451$		−	0.970712i		−	0.0457091i
$452$	−8.67721	−	6.26190i	−0.408142	−	0.294535i
$453$		0			0
$454$	−4.17268	+	2.13453i	−0.195834	+	0.100179i
$455$	−19.9215			−0.933934
$456$		0			0
$457$	−24.7806			−1.15919			−0.579594	−	0.814906i	$-0.696789\pi$
$457$	−24.7806			−1.15919			−0.579594	+	0.814906i	$0.696789\pi$
$458$	−21.6520	+	11.0761i	−1.01173	+	0.517551i
$459$		0			0
$460$	−13.4007	−	9.67056i	−0.624809	−	0.450892i
$461$			23.9689i			1.11634i	0.829725	+	0.558172i	$0.188497\pi$
$461$			23.9689i			1.11634i	−0.829725	+	0.558172i	$0.811503\pi$
$462$		0			0
$463$		−	3.76944i		−	0.175181i	−0.996157	−	0.0875903i	$-0.972083\pi$
$463$		−	3.76944i		−	0.175181i	0.996157	−	0.0875903i	$-0.0279166\pi$
$464$	6.45446	−	2.14310i	0.299641	−	0.0994909i
$465$		0			0
$466$	−1.09181	−	2.13431i	−0.0505769	−	0.0988701i
$467$	1.35188			0.0625576			0.0312788	−	0.999511i	$-0.490042\pi$
$467$	1.35188			0.0625576			0.0312788	+	0.999511i	$0.490042\pi$
$468$		0			0
$469$	−10.0534			−0.464223
$470$	28.3351	+	55.3908i	1.30700	+	2.55499i
$471$		0			0
$472$	4.83168	−	31.4867i	0.222396	−	1.44929i
$473$			11.5102i			0.529239i
$474$		0			0
$475$		−	34.9879i		−	1.60536i
$476$	−7.92499	+	10.9818i	−0.363241	+	0.503349i
$477$		0			0
$478$	21.0735	−	10.7801i	0.963877	−	0.493071i
$479$	−17.8368			−0.814985			−0.407492	−	0.913209i	$-0.633597\pi$
$479$	−17.8368			−0.814985			−0.407492	+	0.913209i	$0.633597\pi$
$480$		0			0
$481$	−53.7911			−2.45266
$482$	−29.9671	+	15.3297i	−1.36497	+	0.698247i
$483$		0			0
$484$	−1.63031	+	2.25915i	−0.0741052	+	0.102689i
$485$		−	52.5278i		−	2.38516i
$486$		0			0
$487$			25.2480i			1.14410i	0.820220	+	0.572048i	$0.193851\pi$
$487$			25.2480i			1.14410i	−0.820220	+	0.572048i	$0.806149\pi$
$488$	2.15493	−	14.0431i	0.0975492	−	0.635701i
$489$		0			0
$490$	2.38847	+	4.66909i	0.107900	+	0.210928i
$491$	21.3705			0.964436			0.482218	−	0.876051i	$-0.339831\pi$
$491$	21.3705			0.964436			0.482218	+	0.876051i	$0.339831\pi$
$492$		0			0
$493$	11.5129			0.518516
$494$	13.8305	+	27.0366i	0.622265	+	1.21643i
$495$		0			0
$496$	−19.4732	+	6.46575i	−0.874370	+	0.290321i
$497$			1.38706i			0.0622180i
$498$		0			0
$499$		−	1.62215i		−	0.0726175i	−0.999341	−	0.0363088i	$-0.988440\pi$
$499$		−	1.62215i		−	0.0726175i	0.999341	−	0.0363088i	$-0.0115600\pi$
$500$	−22.5694	−	16.2872i	−1.00934	−	0.728385i
$501$		0			0
$502$	24.6904	−	12.6304i	1.10199	−	0.563721i
$503$	2.28221			0.101759			0.0508793	−	0.998705i	$-0.483798\pi$
$503$	2.28221			0.101759			0.0508793	+	0.998705i	$0.483798\pi$
$504$		0			0
$505$	−13.6009			−0.605233
$506$	−8.69502	+	4.44793i	−0.386541	+	0.197735i
$507$		0			0
$508$	−6.09754	−	4.40028i	−0.270535	−	0.195231i
$509$		−	5.48028i		−	0.242909i	−0.992597	−	0.121455i	$-0.961244\pi$
$509$		−	5.48028i		−	0.242909i	0.992597	−	0.121455i	$-0.0387559\pi$
$510$		0			0
$511$			1.59986i			0.0707737i
$512$	9.98028	−	20.3075i	0.441070	−	0.897473i
$513$		0			0
$514$	−1.07553	−	2.10249i	−0.0474395	−	0.0927369i
$515$	10.3944			0.458031
$516$		0			0
$517$	36.7705			1.61717
$518$	6.44924	+	12.6073i	0.283363	+	0.553932i
$519$		0			0
$520$	55.6946	+	8.54640i	2.44237	+	0.374785i
$521$			23.3627i			1.02354i	0.859123	+	0.511769i	$0.171010\pi$
$521$			23.3627i			1.02354i	−0.859123	+	0.511769i	$0.828990\pi$
$522$		0			0
$523$		−	8.99925i		−	0.393510i	−0.980453	−	0.196755i	$-0.936960\pi$
$523$		−	8.99925i		−	0.393510i	0.980453	−	0.196755i	$-0.0630403\pi$
$524$	−13.3039	+	18.4355i	−0.581186	+	0.805359i
$525$		0			0
$526$	3.22933	−	1.65196i	0.140806	−	0.0720290i
$527$	−34.7346			−1.51306
$528$		0			0
$529$	−18.0355			−0.784153
$530$	10.8712	−	5.56118i	0.472217	−	0.241562i
$531$		0			0
$532$	4.67848	−	6.48305i	0.202838	−	0.281076i
$533$		−	1.68239i		−	0.0728723i
$534$		0			0
$535$		−	10.4977i		−	0.453856i
$536$	28.1063	+	4.31295i	1.21401	+	0.186291i
$537$		0			0
$538$	−9.37748	−	18.3315i	−0.404292	−	0.790328i
$539$	3.09952			0.133506
$540$		0			0
$541$	10.8935			0.468349			0.234175	−	0.972195i	$-0.424761\pi$
$541$	10.8935			0.468349			0.234175	+	0.972195i	$0.424761\pi$
$542$	−0.577274	−	1.12848i	−0.0247960	−	0.0484724i
$543$		0			0
$544$	26.8672	−	27.3020i	1.15192	−	1.17056i
$545$			15.5877i			0.667705i
$546$		0			0
$547$		−	15.4092i		−	0.658848i	−0.944182	−	0.329424i	$-0.893145\pi$
$547$		−	15.4092i		−	0.658848i	0.944182	−	0.329424i	$-0.106855\pi$
$548$	−0.187796	−	0.135523i	−0.00802226	−	0.00578925i
$549$		0			0
$550$	−34.1563	+	17.4726i	−1.45643	+	0.745035i
$551$	−6.79660			−0.289545
$552$		0			0
$553$	13.0765			0.556069
$554$	1.00905	−	0.516176i	0.0428702	−	0.0219302i
$555$		0			0
$556$	31.7429	+	22.9072i	1.34620	+	0.971484i
$557$			43.4137i			1.83950i	0.392508	+	0.919749i	$0.371608\pi$
$557$			43.4137i			1.83950i	−0.392508	+	0.919749i	$0.628392\pi$
$558$		0			0
$559$			19.9488i			0.843746i
$560$	−4.67439	−	14.0781i	−0.197529	−	0.594906i
$561$		0			0
$562$	1.98810	+	3.88643i	0.0838629	+	0.163939i
$563$	−2.33701			−0.0984933			−0.0492466	−	0.998787i	$-0.515682\pi$
$563$	−2.33701			−0.0984933			−0.0492466	+	0.998787i	$0.515682\pi$
$564$		0			0
$565$	19.8415			0.834739
$566$	5.96873	+	11.6679i	0.250884	+	0.490440i
$567$		0			0
$568$	0.595053	−	3.87780i	0.0249679	−	0.162709i
$569$		−	33.5484i		−	1.40642i	−0.710982	−	0.703210i	$-0.751749\pi$
$569$		−	33.5484i		−	1.40642i	0.710982	−	0.703210i	$-0.248251\pi$
$570$		0			0
$571$			40.2393i			1.68396i	0.539508	+	0.841980i	$0.318610\pi$
$571$			40.2393i			1.68396i	−0.539508	+	0.841980i	$0.681390\pi$
$572$	19.4871	−	27.0036i	0.814795	−	1.12908i
$573$		0			0
$574$	−0.394309	+	0.201708i	−0.0164581	+	0.00841914i
$575$	19.5017			0.813278
$576$		0			0
$577$	−30.9268			−1.28750			−0.643750	−	0.765236i	$-0.722623\pi$
$577$	−30.9268			−1.28750			−0.643750	+	0.765236i	$0.722623\pi$
$578$	36.3250	−	18.5820i	1.51092	−	0.772909i
$579$		0			0
$580$	−7.37947	+	10.2258i	−0.306416	+	0.424605i
$581$		−	5.76905i		−	0.239340i
$582$		0			0
$583$		−	7.21674i		−	0.298887i
$584$	0.686347	−	4.47274i	0.0284013	−	0.185083i
$585$		0			0
$586$	3.28736	+	6.42628i	0.135800	+	0.265467i
$587$	1.10515			0.0456146			0.0228073	−	0.999740i	$-0.492740\pi$
$587$	1.10515			0.0456146			0.0228073	+	0.999740i	$0.492740\pi$
$588$		0			0
$589$	20.5054			0.844910
$590$	26.9002	+	52.5858i	1.10746	+	2.16492i
$591$		0			0
$592$	−12.6216	−	38.0129i	−0.518744	−	1.56232i
$593$		−	8.63444i		−	0.354574i	−0.984159	−	0.177287i	$-0.943268\pi$
$593$		−	8.63444i		−	0.354574i	0.984159	−	0.177287i	$-0.0567321\pi$
$594$		0			0
$595$		−	25.1112i		−	1.02946i
$596$	1.87143	+	1.35051i	0.0766568	+	0.0553192i
$597$		0			0
$598$	−15.0697	+	7.70892i	−0.616248	+	0.315241i
$599$	12.0692			0.493133			0.246567	−	0.969126i	$-0.420698\pi$
$599$	12.0692			0.493133			0.246567	+	0.969126i	$0.420698\pi$
$600$		0			0
$601$	22.8797			0.933283			0.466642	−	0.884447i	$-0.345464\pi$
$601$	22.8797			0.933283			0.466642	+	0.884447i	$0.345464\pi$
$602$	4.67550	−	2.39175i	0.190559	−	0.0974804i
$603$		0			0
$604$	39.4661	+	28.4806i	1.60585	+	1.15886i
$605$		−	5.16583i		−	0.210021i
$606$		0			0
$607$		−	34.2205i		−	1.38897i	−0.719509	−	0.694483i	$-0.755633\pi$
$607$		−	34.2205i		−	1.38897i	0.719509	−	0.694483i	$-0.244367\pi$
$608$	−15.8609	+	16.1176i	−0.643244	+	0.653654i
$609$		0			0
$610$	11.9975	+	23.4533i	0.485765	+	0.949596i
$611$	63.7287			2.57819
$612$		0			0
$613$	12.3936			0.500572			0.250286	−	0.968172i	$-0.419475\pi$
$613$	12.3936			0.500572			0.250286	+	0.968172i	$0.419475\pi$
$614$	−9.88974	−	19.3329i	−0.399117	−	0.780213i
$615$		0			0
$616$	−8.66533	−	1.32971i	−0.349136	−	0.0535754i
$617$			11.2291i			0.452068i	0.974119	+	0.226034i	$0.0725760\pi$
$617$			11.2291i			0.452068i	−0.974119	+	0.226034i	$0.927424\pi$
$618$		0			0
$619$		−	5.50469i		−	0.221252i	−0.993862	−	0.110626i	$-0.964714\pi$
$619$		−	5.50469i		−	0.221252i	0.993862	−	0.110626i	$-0.0352856\pi$
$620$	22.2639	−	30.8514i	0.894140	−	1.23902i
$621$		0			0
$622$	−19.1180	+	9.77981i	−0.766563	+	0.392135i
$623$	−7.23529			−0.289876
$624$		0			0
$625$	7.84486			0.313795
$626$	27.1699	−	13.8988i	1.08593	−	0.555506i
$627$		0			0
$628$	−9.97367	+	13.8207i	−0.397993	+	0.551505i
$629$		−	67.8042i		−	2.70353i
$630$		0			0
$631$		−	20.3606i		−	0.810541i	−0.914197	−	0.405271i	$-0.867177\pi$
$631$		−	20.3606i		−	0.810541i	0.914197	−	0.405271i	$-0.132823\pi$
$632$	−36.5580	−	5.60987i	−1.45420	−	0.223149i
$633$		0			0
$634$	18.9068	+	36.9598i	0.750883	+	1.46786i
$635$	13.9428			0.553303
$636$		0			0
$637$	5.37192			0.212843
$638$	3.39415	+	6.63504i	0.134376	+	0.262684i
$639$		0			0
$640$	7.02866	+	41.3634i	0.277832	+	1.63503i
$641$			45.4430i			1.79489i	0.441128	+	0.897444i	$0.354579\pi$
$641$			45.4430i			1.79489i	−0.441128	+	0.897444i	$0.645421\pi$
$642$		0			0
$643$			41.2006i			1.62479i	0.583104	+	0.812397i	$0.301838\pi$
$643$			41.2006i			1.62479i	−0.583104	+	0.812397i	$0.698162\pi$
$644$	3.61355	+	2.60771i	0.142394	+	0.102758i
$645$		0			0
$646$	−34.0798	+	17.4335i	−1.34085	+	0.685913i
$647$	−24.1616			−0.949891			−0.474946	−	0.880015i	$-0.657532\pi$
$647$	−24.1616			−0.949891			−0.474946	+	0.880015i	$0.657532\pi$
$648$		0			0
$649$	34.9084			1.37028
$650$	−59.1979	+	30.2826i	−2.32193	+	1.18778i
$651$		0			0
$652$	15.2298	+	10.9906i	0.596447	+	0.430425i
$653$		−	7.43712i		−	0.291037i	−0.989356	−	0.145518i	$-0.953515\pi$
$653$		−	7.43712i		−	0.291037i	0.989356	−	0.145518i	$-0.0464850\pi$
$654$		0			0
$655$		−	42.1551i		−	1.64713i
$656$	1.18890	−	0.394756i	0.0464189	−	0.0154126i
$657$		0			0
$658$	−7.64070	−	14.9364i	−0.297865	−	0.582281i
$659$	−42.6889			−1.66292			−0.831461	−	0.555583i	$-0.812495\pi$
$659$	−42.6889			−1.66292			−0.831461	+	0.555583i	$0.812495\pi$
$660$		0			0
$661$	−5.23583			−0.203650			−0.101825	−	0.994802i	$-0.532468\pi$
$661$	−5.23583			−0.203650			−0.101825	+	0.994802i	$0.532468\pi$
$662$	8.14597	+	15.9241i	0.316602	+	0.618908i
$663$		0			0
$664$	−2.47495	+	16.1285i	−0.0960465	+	0.625909i
$665$			14.8243i			0.574862i
$666$		0			0
$667$		−	3.78832i		−	0.146684i
$668$	20.9606	−	29.0455i	0.810991	−	1.12380i
$669$		0			0
$670$	−46.9402	+	24.0122i	−1.81346	+	0.927673i
$671$	15.5692			0.601042
$672$		0			0
$673$	5.26751			0.203048			0.101524	−	0.994833i	$-0.467628\pi$
$673$	5.26751			0.203048			0.101524	+	0.994833i	$0.467628\pi$
$674$	36.8035	−	18.8268i	1.41762	−	0.725181i
$675$		0			0
$676$	18.5592	−	25.7177i	0.713814	−	0.989143i
$677$		−	42.2272i		−	1.62292i	−0.584406	−	0.811462i	$-0.698672\pi$
$677$		−	42.2272i		−	1.62292i	0.584406	−	0.811462i	$-0.301328\pi$
$678$		0			0
$679$			14.1644i			0.543578i
$680$	−10.7728	+	70.2035i	−0.413119	+	2.69218i
$681$		0			0
$682$	−10.2402	−	20.0180i	−0.392117	−	0.766528i
$683$	−50.0549			−1.91530			−0.957649	−	0.287939i	$-0.907030\pi$
$683$	−50.0549			−1.91530			−0.957649	+	0.287939i	$0.907030\pi$
$684$		0			0
$685$	0.429420			0.0164073
$686$	−0.644062	−	1.25904i	−0.0245904	−	0.0480704i
$687$		0			0
$688$	−14.0974	+	4.68081i	−0.537458	+	0.178454i
$689$		−	12.5077i		−	0.476504i
$690$		0			0
$691$		−	7.39662i		−	0.281381i	−0.990054	−	0.140690i	$-0.955068\pi$
$691$		−	7.39662i		−	0.281381i	0.990054	−	0.140690i	$-0.0449322\pi$
$692$	30.2893	+	21.8582i	1.15143	+	0.830925i
$693$		0			0
$694$	−27.9528	+	14.2992i	−1.06107	+	0.542791i
$695$	−72.5842			−2.75328
$696$		0			0
$697$	2.12067			0.0803259
$698$	−29.5294	+	15.1057i	−1.11770	+	0.571760i
$699$		0			0
$700$	14.1949	+	10.2438i	0.536519	+	0.387178i
$701$		−	7.51421i		−	0.283808i	−0.989880	−	0.141904i	$-0.954678\pi$
$701$		−	7.51421i		−	0.283808i	0.989880	−	0.141904i	$-0.0453224\pi$
$702$		0			0
$703$			40.0279i			1.50968i
$704$	23.6552	+	7.43493i	0.891540	+	0.280214i
$705$		0			0
$706$	−2.71340	−	5.30427i	−0.102120	−	0.199629i
$707$	3.66755			0.137933
$708$		0			0
$709$	49.4124			1.85572			0.927861	−	0.372926i	$-0.121645\pi$
$709$	49.4124			1.85572			0.927861	+	0.372926i	$0.121645\pi$
$710$	3.31294	+	6.47629i	0.124332	+	0.243051i
$711$		0			0
$712$	20.2277	+	3.10397i	0.758066	+	0.116326i
$713$			11.4294i			0.428033i
$714$		0			0
$715$			61.7470i			2.30921i
$716$	−21.9450	+	30.4095i	−0.820122	+	1.13646i
$717$		0			0
$718$	−42.9962	+	21.9947i	−1.60460	+	0.820834i
$719$	−48.7375			−1.81760			−0.908800	−	0.417231i	$-0.863000\pi$
$719$	−48.7375			−1.81760			−0.908800	+	0.417231i	$0.863000\pi$
$720$		0			0
$721$	−2.80289			−0.104385
$722$	−3.80291	+	1.94537i	−0.141530	+	0.0723993i
$723$		0			0
$724$	−20.3721	+	28.2299i	−0.757122	+	1.04916i
$725$		−	14.8815i		−	0.552684i
$726$		0			0
$727$			10.1542i			0.376599i	0.982112	+	0.188299i	$0.0602975\pi$
$727$			10.1542i			0.376599i	−0.982112	+	0.188299i	$0.939702\pi$
$728$	−15.0183	−	2.30458i	−0.556615	−	0.0854133i
$729$		0			0
$730$	3.82122	+	7.46989i	0.141430	+	0.276473i
$731$	−25.1457			−0.930048
$732$		0			0
$733$	−24.7642			−0.914685			−0.457342	−	0.889291i	$-0.651199\pi$
$733$	−24.7642			−0.914685			−0.457342	+	0.889291i	$0.651199\pi$
$734$	2.07116	+	4.04879i	0.0764478	+	0.149444i
$735$		0			0
$736$	−8.98369	−	8.84061i	−0.331143	−	0.325869i
$737$			31.1607i			1.14782i
$738$		0			0
$739$		−	4.42148i		−	0.162647i	−0.996688	−	0.0813234i	$-0.974085\pi$
$739$		−	4.42148i		−	0.162647i	0.996688	−	0.0813234i	$-0.0259147\pi$
$740$	60.2241	+	43.4607i	2.21388	+	1.59765i
$741$		0			0
$742$	−2.93148	+	1.49960i	−0.107618	+	0.0550519i
$743$	6.43718			0.236157			0.118079	−	0.993004i	$-0.462327\pi$
$743$	6.43718			0.236157			0.118079	+	0.993004i	$0.462327\pi$
$744$		0			0
$745$	−4.27926			−0.156780
$746$	29.3538	−	15.0159i	1.07472	−	0.549772i
$747$		0			0
$748$	34.0382	+	24.5636i	1.24456	+	0.898136i
$749$			2.83076i			0.103434i
$750$		0			0
$751$		−	29.8965i		−	1.09094i	−0.838130	−	0.545470i	$-0.816351\pi$
$751$		−	29.8965i		−	1.09094i	0.838130	−	0.545470i	$-0.183649\pi$
$752$	14.9533	+	45.0356i	0.545292	+	1.64228i
$753$		0			0
$754$	5.88256	+	11.4995i	0.214230	+	0.418787i
$755$	−90.2441			−3.28432
$756$		0			0
$757$	−20.8644			−0.758329			−0.379164	−	0.925329i	$-0.623789\pi$
$757$	−20.8644			−0.758329			−0.379164	+	0.925329i	$0.623789\pi$
$758$	4.79312	+	9.36981i	0.174094	+	0.340327i
$759$		0			0
$760$	6.35969	−	41.4443i	0.230690	−	1.50334i
$761$		−	37.3281i		−	1.35314i	−0.736377	−	0.676572i	$-0.763465\pi$
$761$		−	37.3281i		−	1.35314i	0.736377	−	0.676572i	$-0.236535\pi$
$762$		0			0
$763$		−	4.20330i		−	0.152170i
$764$	8.75122	−	12.1267i	0.316608	−	0.438729i
$765$		0			0
$766$	24.8987	−	12.7369i	0.899626	−	0.460203i
$767$	60.5014			2.18458
$768$		0			0
$769$	−7.98299			−0.287874			−0.143937	−	0.989587i	$-0.545976\pi$
$769$	−7.98299			−0.287874			−0.143937	+	0.989587i	$0.545976\pi$
$770$	14.4719	−	7.40310i	0.521532	−	0.266789i
$771$		0			0
$772$	16.1445	−	22.3717i	0.581053	−	0.805174i
$773$			12.9265i			0.464935i	0.972604	+	0.232467i	$0.0746799\pi$
$773$			12.9265i			0.464935i	−0.972604	+	0.232467i	$0.925320\pi$
$774$		0			0
$775$			44.8975i			1.61277i
$776$	6.07657	−	39.5994i	0.218136	−	1.42153i
$777$		0			0
$778$	13.2984	+	25.9964i	0.476772	+	0.932016i
$779$	−1.25193			−0.0448549
$780$		0			0
$781$	4.29920			0.153838
$782$	−9.71717	−	18.9956i	−0.347485	−	0.679280i
$783$		0			0
$784$	1.26047	+	3.79621i	0.0450168	+	0.135579i
$785$		−	31.6027i		−	1.12795i
$786$		0			0
$787$		−	47.1345i		−	1.68016i	−0.542460	−	0.840082i	$-0.682507\pi$
$787$		−	47.1345i		−	1.68016i	0.542460	−	0.840082i	$-0.317493\pi$
$788$	−25.9869	−	18.7534i	−0.925743	−	0.668061i
$789$		0			0
$790$	61.0553	−	31.2328i	2.17225	−	1.11121i
$791$	−5.35036			−0.190237
$792$		0			0
$793$	26.9837			0.958219
$794$	10.3521	−	5.29563i	0.367384	−	0.187935i
$795$		0			0
$796$	23.1283	+	16.6905i	0.819760	+	0.591578i
$797$		−	52.8546i		−	1.87221i	−0.351727	−	0.936103i	$-0.614405\pi$
$797$		−	52.8546i		−	1.87221i	0.351727	−	0.936103i	$-0.385595\pi$
$798$		0			0
$799$			80.3307i			2.84190i
$800$	−35.2902	−	34.7282i	−1.24770	−	1.22783i
$801$		0			0
$802$	15.0110	+	29.3441i	0.530055	+	1.03618i
$803$	4.95880			0.174992
$804$		0			0
$805$	−8.26283			−0.291226
$806$	−17.7477	−	34.6941i	−0.625137	−	1.22205i
$807$		0			0
$808$	−10.2534	−	1.57340i	−0.360713	−	0.0553519i
$809$		−	19.1288i		−	0.672533i	−0.941767	−	0.336267i	$-0.890836\pi$
$809$		−	19.1288i		−	0.672533i	0.941767	−	0.336267i	$-0.109164\pi$
$810$		0			0
$811$		−	26.6426i		−	0.935549i	−0.883848	−	0.467775i	$-0.845056\pi$
$811$		−	26.6426i		−	0.935549i	0.883848	−	0.467775i	$-0.154944\pi$
$812$	1.98991	−	2.75745i	0.0698320	−	0.0967674i
$813$		0			0
$814$	39.0765	−	19.9895i	1.36963	−	0.700633i
$815$	−34.8249			−1.21986
$816$		0			0
$817$	14.8447			0.519349
$818$	34.7016	−	17.7516i	1.21331	−	0.620669i
$819$		0			0
$820$	−1.35929	+	1.88359i	−0.0474684	+	0.0657778i
$821$			13.8206i			0.482343i	0.970482	+	0.241172i	$0.0775317\pi$
$821$			13.8206i			0.482343i	−0.970482	+	0.241172i	$0.922468\pi$
$822$		0			0
$823$		−	8.34236i		−	0.290796i	−0.989373	−	0.145398i	$-0.953554\pi$
$823$		−	8.34236i		−	0.290796i	0.989373	−	0.145398i	$-0.0464463\pi$
$824$	7.83604	+	1.20245i	0.272982	+	0.0418894i
$825$		0			0
$826$	−7.25376	−	14.1800i	−0.252391	−	0.493385i
$827$	26.1509			0.909356			0.454678	−	0.890656i	$-0.349754\pi$
$827$	26.1509			0.909356			0.454678	+	0.890656i	$0.349754\pi$
$828$		0			0
$829$	−10.9742			−0.381149			−0.190575	−	0.981673i	$-0.561035\pi$
$829$	−10.9742			−0.381149			−0.190575	+	0.981673i	$0.561035\pi$
$830$	−13.7792	−	26.9362i	−0.478283	−	0.934969i
$831$		0			0
$832$	40.9980	+	12.8858i	1.42135	+	0.446736i
$833$			6.77136i			0.234614i
$834$		0			0
$835$			66.4161i			2.29842i
$836$	−20.0943	−	14.5010i	−0.694977	−	0.501529i
$837$		0			0
$838$	21.8537	−	11.1792i	0.754923	−	0.386180i
$839$	23.8650			0.823912			0.411956	−	0.911204i	$-0.364846\pi$
$839$	23.8650			0.823912			0.411956	+	0.911204i	$0.364846\pi$
$840$		0			0
$841$	26.1092			0.900317
$842$	−5.66039	+	2.89557i	−0.195070	+	0.0997879i
$843$		0			0
$844$	17.0682	+	12.3172i	0.587511	+	0.423976i
$845$			58.8068i			2.02301i
$846$		0			0
$847$			1.39299i			0.0478637i
$848$	8.83888	−	2.93481i	0.303528	−	0.100782i
$849$		0			0
$850$	−38.1715	−	74.6195i	−1.30927	−	2.55943i
$851$	−22.3109			−0.764809
$852$		0			0
$853$	16.2531			0.556497			0.278248	−	0.960509i	$-0.410246\pi$
$853$	16.2531			0.556497			0.278248	+	0.960509i	$0.410246\pi$
$854$	−3.23518	−	6.32429i	−0.110706	−	0.216413i
$855$		0			0
$856$	1.21441	−	7.91395i	0.0415076	−	0.270493i
$857$			16.3980i			0.560144i	0.959979	+	0.280072i	$0.0903584\pi$
$857$			16.3980i			0.560144i	−0.959979	+	0.280072i	$0.909642\pi$
$858$		0			0
$859$			24.9751i			0.852139i	0.904691	+	0.426069i	$0.140102\pi$
$859$			24.9751i			0.852139i	−0.904691	+	0.426069i	$0.859898\pi$
$860$	16.1177	−	22.3346i	0.549609	−	0.761603i
$861$		0			0
$862$	−45.1148	+	23.0784i	−1.53662	+	0.786055i
$863$	28.6505			0.975275			0.487637	−	0.873046i	$-0.337859\pi$
$863$	28.6505			0.975275			0.487637	+	0.873046i	$0.337859\pi$
$864$		0			0
$865$	−69.2603			−2.35492
$866$	−15.6607	+	8.01122i	−0.532172	+	0.272232i
$867$		0			0
$868$	−6.00356	+	8.31923i	−0.203774	+	0.282373i
$869$		−	40.5308i		−	1.37491i
$870$		0			0
$871$			54.0060i			1.82992i
$872$	−1.80323	+	11.7512i	−0.0610652	+	0.397945i
$873$		0			0
$874$	5.73648	+	11.2139i	0.194039	+	0.379317i
$875$	−13.9163			−0.470456
$876$		0			0
$877$	−0.450917			−0.0152264			−0.00761319	−	0.999971i	$-0.502423\pi$
$877$	−0.450917			−0.0152264			−0.00761319	+	0.999971i	$0.502423\pi$
$878$	−4.06674	−	7.94985i	−0.137246	−	0.268294i
$879$		0			0
$880$	−43.6352	+	14.4884i	−1.47094	+	0.488402i
$881$		−	0.688635i		−	0.0232007i	−0.999933	−	0.0116003i	$-0.996307\pi$
$881$		−	0.688635i		−	0.0232007i	0.999933	−	0.0116003i	$-0.00369259\pi$
$882$		0			0
$883$		−	10.1904i		−	0.342933i	−0.985190	−	0.171467i	$-0.945149\pi$
$883$		−	10.1904i		−	0.342933i	0.985190	−	0.171467i	$-0.0548506\pi$
$884$	58.9933	+	42.5724i	1.98416	+	1.43187i
$885$		0			0
$886$	−20.6510	+	10.5640i	−0.693783	+	0.354904i
$887$	34.4422			1.15646			0.578228	−	0.815875i	$-0.303744\pi$
$887$	34.4422			1.15646			0.578228	+	0.815875i	$0.303744\pi$
$888$		0			0
$889$	−3.75974			−0.126098
$890$	−33.7822	+	17.2813i	−1.13238	+	0.579269i
$891$		0			0
$892$	−5.22054	−	3.76739i	−0.174797	−	0.126142i
$893$		−	47.4228i		−	1.58695i
$894$		0			0
$895$		−	69.5351i		−	2.32430i
$896$	−1.89531	−	11.1538i	−0.0633179	−	0.372623i
$897$		0			0
$898$	−15.6031	−	30.5017i	−0.520683	−	1.01786i
$899$	8.72159			0.290881
$900$		0			0
$901$	15.7660			0.525243
$902$	0.625198	+	1.22217i	0.0208168	+	0.0406937i
$903$		0			0
$904$	14.9580	+	2.29533i	0.497496	+	0.0763414i
$905$		−	64.5512i		−	2.14576i
$906$		0			0
$907$		−	45.8513i		−	1.52247i	−0.648478	−	0.761233i	$-0.724594\pi$
$907$		−	45.8513i		−	1.52247i	0.648478	−	0.761233i	$-0.275406\pi$
$908$	3.87881	−	5.37493i	0.128723	−	0.178373i
$909$		0			0
$910$	25.0820	−	12.8307i	0.831459	−	0.425332i
$911$	−22.6899			−0.751748			−0.375874	−	0.926671i	$-0.622658\pi$
$911$	−22.6899			−0.751748			−0.375874	+	0.926671i	$0.622658\pi$
$912$		0			0
$913$	−17.8813			−0.591783
$914$	31.1998	−	15.9602i	1.03200	−	0.527918i
$915$		0			0
$916$	20.1271	−	27.8905i	0.665018	−	0.921526i
$917$			11.3673i			0.375382i
$918$		0			0
$919$		−	56.4402i		−	1.86179i	−0.365288	−	0.930895i	$-0.619030\pi$
$919$		−	56.4402i		−	1.86179i	0.365288	−	0.930895i	$-0.380970\pi$
$920$	23.1004	+	3.54479i	0.761598	+	0.116868i
$921$		0			0
$922$	−15.4375	−	30.1779i	−0.508406	−	0.993855i
$923$	7.45115			0.245258
$924$		0			0
$925$	−87.6431			−2.88169
$926$	2.42775	+	4.74588i	0.0797808	+	0.155959i
$927$		0			0
$928$	−6.74614	+	6.85532i	−0.221453	+	0.225037i
$929$		−	8.38659i		−	0.275155i	−0.990491	−	0.137578i	$-0.956068\pi$
$929$		−	8.38659i		−	0.275155i	0.990491	−	0.137578i	$-0.0439316\pi$
$930$		0			0
$931$		−	3.99744i		−	0.131011i
$932$	2.74926	+	1.98400i	0.0900549	+	0.0649880i
$933$		0			0
$934$	−1.70207	+	0.870695i	−0.0556936	+	0.0284900i
$935$	−77.8327			−2.54540
$936$		0			0
$937$	−20.8481			−0.681079			−0.340539	−	0.940230i	$-0.610610\pi$
$937$	−20.8481			−0.681079			−0.340539	+	0.940230i	$0.610610\pi$
$938$	12.6576	−	6.47501i	0.413287	−	0.211416i
$939$		0			0
$940$	−71.3502	−	51.4898i	−2.32719	−	1.67941i
$941$			41.8110i			1.36300i	0.731819	+	0.681499i	$0.238672\pi$
$941$			41.8110i			1.36300i	−0.731819	+	0.681499i	$0.761328\pi$
$942$		0			0
$943$		−	0.697803i		−	0.0227236i
$944$	14.1961	+	42.7549i	0.462043	+	1.39155i
$945$		0			0
$946$	−7.41327	−	14.4918i	−0.241026	−	0.471169i
$947$	11.8126			0.383859			0.191929	−	0.981409i	$-0.438526\pi$
$947$	11.8126			0.383859			0.191929	+	0.981409i	$0.438526\pi$
$948$		0			0
$949$	8.59432			0.278984
$950$	22.5344	+	44.0513i	0.731112	+	1.42921i
$951$		0			0
$952$	2.90494	−	18.9307i	0.0941497	−	0.613548i
$953$		−	23.1277i		−	0.749178i	−0.927191	−	0.374589i	$-0.877784\pi$
$953$		−	23.1277i		−	0.749178i	0.927191	−	0.374589i	$-0.122216\pi$
$954$		0			0
$955$			27.7292i			0.897296i
$956$	−19.5893	+	27.1452i	−0.633563	+	0.877939i
$957$		0			0
$958$	22.4573	−	11.4880i	0.725562	−	0.371161i
$959$	−0.115795			−0.00373922
$960$		0			0
$961$	4.68690			0.151190
$962$	67.7252	−	34.6448i	2.18355	−	1.11699i
$963$		0			0
$964$	27.8566	−	38.6014i	0.897201	−	1.24327i
$965$			51.1556i			1.64676i
$966$		0			0
$967$		−	7.29830i		−	0.234698i	−0.993091	−	0.117349i	$-0.962560\pi$
$967$		−	7.29830i		−	0.234698i	0.993091	−	0.117349i	$-0.0374396\pi$
$968$	0.597599	−	3.89439i	0.0192076	−	0.125170i
$969$		0			0
$970$	33.8311	+	66.1347i	1.08625	+	2.12346i
$971$	53.0104			1.70119			0.850593	−	0.525825i	$-0.176243\pi$
$971$	53.0104			1.70119			0.850593	+	0.525825i	$0.176243\pi$
$972$		0			0
$973$	19.5727			0.627471
$974$	−16.2613	−	31.7883i	−0.521045	−	1.01856i
$975$		0			0
$976$	6.33147	+	19.0687i	0.202665	+	0.610375i
$977$		−	50.3128i		−	1.60965i	−0.593514	−	0.804824i	$-0.702260\pi$
$977$		−	50.3128i		−	1.60965i	0.593514	−	0.804824i	$-0.297740\pi$
$978$		0			0
$979$			22.4259i			0.716735i
$980$	−6.01436	−	4.34025i	−0.192122	−	0.138644i
$981$		0			0
$982$	−26.9063	+	13.7639i	−0.858615	+	0.439224i
$983$	47.2977			1.50856			0.754281	−	0.656552i	$-0.227986\pi$
$983$	47.2977			1.50856			0.754281	+	0.656552i	$0.227986\pi$
$984$		0			0
$985$	59.4222			1.89335
$986$	−14.4952	+	7.41503i	−0.461622	+	0.236143i
$987$		0			0
$988$	−34.8264	−	25.1324i	−1.10798	−	0.799569i
$989$			8.27417i			0.263103i
$990$		0			0
$991$		−	2.13662i		−	0.0678718i	−0.999424	−	0.0339359i	$-0.989196\pi$
$991$		−	2.13662i		−	0.0678718i	0.999424	−	0.0339359i	$-0.0108042\pi$
$992$	20.3532	−	20.6825i	0.646214	−	0.656672i
$993$		0			0
$994$	−0.893349	−	1.74636i	−0.0283353	−	0.0553912i
$995$	−52.8857			−1.67659
$996$		0			0
$997$	−2.23653			−0.0708317			−0.0354159	−	0.999373i	$-0.511276\pi$
$997$	−2.23653			−0.0708317			−0.0354159	+	0.999373i	$0.511276\pi$
$998$	1.04477	+	2.04236i	0.0330715	+	0.0646497i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.e.a.323.4	yes	24
3.2	odd	2	inner	756.2.e.a.323.21	yes	24
4.3	odd	2	inner	756.2.e.a.323.22	yes	24
12.11	even	2	inner	756.2.e.a.323.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.e.a.323.3	✓	24	12.11	even	2	inner
756.2.e.a.323.4	yes	24	1.1	even	1	trivial
756.2.e.a.323.21	yes	24	3.2	odd	2	inner
756.2.e.a.323.22	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)

\(f(q)\)	\(=\)	\(q+(-1.25904 + 0.644062i) q^{2} +(1.17037 - 1.62180i) q^{4} +3.70845i q^{5} -1.00000i q^{7} +(-0.429004 + 2.79570i) q^{8} +O(q^{10})\)	\(q+(-1.25904 + 0.644062i) q^{2} +(1.17037 - 1.62180i) q^{4} +3.70845i q^{5} -1.00000i q^{7} +(-0.429004 + 2.79570i) q^{8} +(-2.38847 - 4.66909i) q^{10} -3.09952 q^{11} -5.37192 q^{13} +(0.644062 + 1.25904i) q^{14} +(-1.26047 - 3.79621i) q^{16} -6.77136i q^{17} +3.99744i q^{19} +(6.01436 + 4.34025i) q^{20} +(3.90242 - 1.99628i) q^{22} -2.22811 q^{23} -8.75259 q^{25} +(6.76347 - 3.45985i) q^{26} +(-1.62180 - 1.17037i) q^{28} +1.70024i q^{29} -5.12963i q^{31} +(4.03198 + 3.96776i) q^{32} +(4.36117 + 8.52542i) q^{34} +3.70845 q^{35} +10.0134 q^{37} +(-2.57460 - 5.03294i) q^{38} +(-10.3677 - 1.59094i) q^{40} +0.313182i q^{41} -3.71354i q^{43} +(-3.62758 + 5.02680i) q^{44} +(2.80528 - 1.43504i) q^{46} -11.8633 q^{47} -1.00000 q^{49} +(11.0199 - 5.63721i) q^{50} +(-6.28713 + 8.71218i) q^{52} +2.32834i q^{53} -11.4944i q^{55} +(2.79570 + 0.429004i) q^{56} +(-1.09506 - 2.14067i) q^{58} -11.2625 q^{59} -5.02310 q^{61} +(3.30380 + 6.45841i) q^{62} +(-7.63191 - 2.39874i) q^{64} -19.9215i q^{65} -10.0534i q^{67} +(-10.9818 - 7.92499i) q^{68} +(-4.66909 + 2.38847i) q^{70} -1.38706 q^{71} -1.59986 q^{73} +(-12.6073 + 6.44924i) q^{74} +(6.48305 + 4.67848i) q^{76} +3.09952i q^{77} +13.0765i q^{79} +(14.0781 - 4.67439i) q^{80} +(-0.201708 - 0.394309i) q^{82} +5.76905 q^{83} +25.1112 q^{85} +(2.39175 + 4.67550i) q^{86} +(1.32971 - 8.66533i) q^{88} -7.23529i q^{89} +5.37192i q^{91} +(-2.60771 + 3.61355i) q^{92} +(14.9364 - 7.64070i) q^{94} -14.8243 q^{95} -14.1644 q^{97} +(1.25904 - 0.644062i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4}+O(q^{10}) \) 24 * q - 8 * q^4	\( 24 q - 8 q^{4} - 16 q^{10} + 8 q^{16} + 16 q^{22} - 24 q^{25} - 8 q^{28} - 8 q^{34} + 16 q^{37} - 8 q^{40} - 24 q^{49} - 8 q^{52} + 32 q^{58} - 80 q^{61} + 40 q^{64} - 24 q^{70} - 32 q^{82} + 56 q^{85} + 56 q^{88} + 72 q^{94}+O(q^{100}) \) 24 * q - 8 * q^4 - 16 * q^10 + 8 * q^16 + 16 * q^22 - 24 * q^25 - 8 * q^28 - 8 * q^34 + 16 * q^37 - 8 * q^40 - 24 * q^49 - 8 * q^52 + 32 * q^58 - 80 * q^61 + 40 * q^64 - 24 * q^70 - 32 * q^82 + 56 * q^85 + 56 * q^88 + 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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