LMFDB - Embedded newform 1148.2.ba.a.113.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.17
Character	$\chi$	$=$	1148.113
Dual form			1148.2.ba.a.701.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.28455i q^{3} +(1.15282 + 3.54801i) q^{5} +(0.587785 + 0.809017i) q^{7} -2.21915 q^{9} +O(q^{10})$	\(q+2.28455i q^{3} +(1.15282 + 3.54801i) q^{5} +(0.587785 + 0.809017i) q^{7} -2.21915 q^{9} +(-0.170591 - 0.0554285i) q^{11} +(-1.72999 + 2.38113i) q^{13} +(-8.10559 + 2.63367i) q^{15} +(2.20009 + 0.714853i) q^{17} +(-0.238808 - 0.328691i) q^{19} +(-1.84824 + 1.34282i) q^{21} +(0.682118 + 0.495588i) q^{23} +(-7.21429 + 5.24149i) q^{25} +1.78389i q^{27} +(4.71296 - 1.53133i) q^{29} +(1.43394 - 4.41323i) q^{31} +(0.126629 - 0.389724i) q^{33} +(-2.19279 + 3.01812i) q^{35} +(1.20270 + 3.70154i) q^{37} +(-5.43980 - 3.95225i) q^{39} +(1.75557 - 6.15776i) q^{41} +(-0.780429 - 0.567015i) q^{43} +(-2.55827 - 7.87356i) q^{45} +(7.77005 - 10.6946i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-1.63312 + 5.02621i) q^{51} +(-10.8610 + 3.52896i) q^{53} -0.669158i q^{55} +(0.750909 - 0.545568i) q^{57} +(-1.25990 - 0.915373i) q^{59} +(1.80030 - 1.30800i) q^{61} +(-1.30438 - 1.79533i) q^{63} +(-10.4426 - 3.39302i) q^{65} +(3.84279 - 1.24860i) q^{67} +(-1.13219 + 1.55833i) q^{69} +(-0.775836 - 0.252084i) q^{71} +13.2778 q^{73} +(-11.9744 - 16.4814i) q^{75} +(-0.0554285 - 0.170591i) q^{77} -8.02141i q^{79} -10.7328 q^{81} -14.2863 q^{83} +8.63004i q^{85} +(3.49840 + 10.7670i) q^{87} +(-5.60107 - 7.70921i) q^{89} -2.94324 q^{91} +(10.0822 + 3.27591i) q^{93} +(0.890896 - 1.22621i) q^{95} +(-1.78899 + 0.581279i) q^{97} +(0.378567 + 0.123004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			2.28455i			1.31898i	0.751712	+	0.659492i	$0.229228\pi$
$3$			2.28455i			1.31898i	−0.751712	+	0.659492i	$0.770772\pi$
$4$		0			0
$5$	1.15282	+	3.54801i	0.515556	+	1.58672i	0.782268	+	0.622942i	$0.214063\pi$
$5$	1.15282	+	3.54801i	0.515556	+	1.58672i	−0.266712	+	0.963776i	$0.585937\pi$
$6$		0			0
$7$	0.587785	+	0.809017i	0.222162	+	0.305780i
$7$	0.587785	+	0.809017i	0.222162	+	0.305780i
$8$		0			0
$9$	−2.21915			−0.739716
$10$		0			0
$11$	−0.170591	−	0.0554285i	−0.0514352	−	0.0167123i	0.283186	−	0.959065i	$-0.408608\pi$
$11$	−0.170591	−	0.0554285i	−0.0514352	−	0.0167123i	−0.334622	+	0.942353i	$0.608608\pi$
$12$		0			0
$13$	−1.72999	+	2.38113i	−0.479814	+	0.660407i	−0.978469	−	0.206393i	$-0.933827\pi$
$13$	−1.72999	+	2.38113i	−0.479814	+	0.660407i	0.498655	+	0.866800i	$0.333827\pi$
$14$		0			0
$15$	−8.10559	+	2.63367i	−2.09285	+	0.680009i
$16$		0			0
$17$	2.20009	+	0.714853i	0.533601	+	0.173377i	0.563409	−	0.826178i	$-0.309490\pi$
$17$	2.20009	+	0.714853i	0.533601	+	0.173377i	−0.0298081	+	0.999556i	$0.509490\pi$
$18$		0			0
$19$	−0.238808	−	0.328691i	−0.0547863	−	0.0754069i	0.780745	−	0.624850i	$-0.214840\pi$
$19$	−0.238808	−	0.328691i	−0.0547863	−	0.0754069i	−0.835531	+	0.549443i	$0.814840\pi$
$20$		0			0
$21$	−1.84824	+	1.34282i	−0.403318	+	0.293028i
$22$		0			0
$23$	0.682118	+	0.495588i	0.142231	+	0.103337i	0.656626	−	0.754217i	$-0.271983\pi$
$23$	0.682118	+	0.495588i	0.142231	+	0.103337i	−0.514394	+	0.857554i	$0.671983\pi$
$24$		0			0
$25$	−7.21429	+	5.24149i	−1.44286	+	1.04830i
$26$		0			0
$27$			1.78389i			0.343310i
$28$		0			0
$29$	4.71296	−	1.53133i	0.875174	−	0.284361i	0.163222	−	0.986589i	$-0.447811\pi$
$29$	4.71296	−	1.53133i	0.875174	−	0.284361i	0.711952	+	0.702228i	$0.247811\pi$
$30$		0			0
$31$	1.43394	−	4.41323i	0.257544	−	0.792639i	−0.735774	−	0.677227i	$-0.763181\pi$
$31$	1.43394	−	4.41323i	0.257544	−	0.792639i	0.993318	−	0.115411i	$-0.0368187\pi$
$32$		0			0
$33$	0.126629	−	0.389724i	0.0220433	−	0.0678422i
$34$		0			0
$35$	−2.19279	+	3.01812i	−0.370649	+	0.510155i
$36$		0			0
$37$	1.20270	+	3.70154i	0.197723	+	0.608529i	0.999934	+	0.0114885i	$0.00365698\pi$
$37$	1.20270	+	3.70154i	0.197723	+	0.608529i	−0.802211	+	0.597041i	$0.796343\pi$
$38$		0			0
$39$	−5.43980	−	3.95225i	−0.871066	−	0.632866i
$40$		0			0
$41$	1.75557	−	6.15776i	0.274174	−	0.961680i
$41$	1.75557	−	6.15776i	0.274174	−	0.961680i
$42$		0			0
$43$	−0.780429	−	0.567015i	−0.119014	−	0.0864690i	0.526686	−	0.850060i	$-0.323434\pi$
$43$	−0.780429	−	0.567015i	−0.119014	−	0.0864690i	−0.645700	+	0.763591i	$0.723434\pi$
$44$		0			0
$45$	−2.55827	−	7.87356i	−0.381365	−	1.17372i
$46$		0			0
$47$	7.77005	−	10.6946i	1.13338	−	1.55996i	0.351888	−	0.936042i	$-0.385540\pi$
$47$	7.77005	−	10.6946i	1.13338	−	1.55996i	0.781489	−	0.623919i	$-0.214460\pi$
$48$		0			0
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$		0			0
$51$	−1.63312	+	5.02621i	−0.228682	+	0.703810i
$52$		0			0
$53$	−10.8610	+	3.52896i	−1.49188	+	0.484740i	−0.937637	−	0.347617i	$-0.886991\pi$
$53$	−10.8610	+	3.52896i	−1.49188	+	0.484740i	−0.554240	+	0.832357i	$0.686991\pi$
$54$		0			0
$55$		−	0.669158i		−	0.0902293i
$56$		0			0
$57$	0.750909	−	0.545568i	0.0994604	−	0.0722622i
$58$		0			0
$59$	−1.25990	−	0.915373i	−0.164025	−	0.119171i	0.502745	−	0.864435i	$-0.332324\pi$
$59$	−1.25990	−	0.915373i	−0.164025	−	0.119171i	−0.666770	+	0.745264i	$0.732324\pi$
$60$		0			0
$61$	1.80030	−	1.30800i	0.230505	−	0.167472i	−0.466538	−	0.884501i	$-0.654499\pi$
$61$	1.80030	−	1.30800i	0.230505	−	0.167472i	0.697043	+	0.717030i	$0.254499\pi$
$62$		0			0
$63$	−1.30438	−	1.79533i	−0.164337	−	0.226190i
$64$		0			0
$65$	−10.4426	−	3.39302i	−1.29525	−	0.420852i
$66$		0			0
$67$	3.84279	−	1.24860i	0.469471	−	0.152540i	−0.0647212	−	0.997903i	$-0.520616\pi$
$67$	3.84279	−	1.24860i	0.469471	−	0.152540i	0.534192	+	0.845363i	$0.320616\pi$
$68$		0			0
$69$	−1.13219	+	1.55833i	−0.136300	+	0.187601i
$70$		0			0
$71$	−0.775836	−	0.252084i	−0.0920748	−	0.0299169i	0.262617	−	0.964900i	$-0.415414\pi$
$71$	−0.775836	−	0.252084i	−0.0920748	−	0.0299169i	−0.354692	+	0.934983i	$0.615414\pi$
$72$		0			0
$73$	13.2778			1.55405			0.777027	−	0.629468i	$-0.216727\pi$
$73$	13.2778			1.55405			0.777027	+	0.629468i	$0.216727\pi$
$74$		0			0
$75$	−11.9744	−	16.4814i	−1.38269	−	1.90311i
$76$		0			0
$77$	−0.0554285	−	0.170591i	−0.00631666	−	0.0194407i
$78$		0			0
$79$		−	8.02141i		−	0.902480i	−0.892403	−	0.451240i	$-0.850982\pi$
$79$		−	8.02141i		−	0.902480i	0.892403	−	0.451240i	$-0.149018\pi$
$80$		0			0
$81$	−10.7328			−1.19254
$82$		0			0
$83$	−14.2863			−1.56812			−0.784062	−	0.620683i	$-0.786856\pi$
$83$	−14.2863			−1.56812			−0.784062	+	0.620683i	$0.786856\pi$
$84$		0			0
$85$			8.63004i			0.936060i
$86$		0			0
$87$	3.49840	+	10.7670i	0.375068	+	1.15434i
$88$		0			0
$89$	−5.60107	−	7.70921i	−0.593712	−	0.817175i	0.401402	−	0.915902i	$-0.368523\pi$
$89$	−5.60107	−	7.70921i	−0.593712	−	0.817175i	−0.995115	+	0.0987270i	$0.968523\pi$
$90$		0			0
$91$	−2.94324			−0.308535
$92$		0			0
$93$	10.0822	+	3.27591i	1.04548	+	0.339696i
$94$		0			0
$95$	0.890896	−	1.22621i	0.0914040	−	0.125807i
$96$		0			0
$97$	−1.78899	+	0.581279i	−0.181645	+	0.0590199i	−0.398427	−	0.917200i	$-0.630444\pi$
$97$	−1.78899	+	0.581279i	−0.181645	+	0.0590199i	0.216782	+	0.976220i	$0.430444\pi$
$98$		0			0
$99$	0.378567	+	0.123004i	0.0380475	+	0.0123624i
$100$		0			0
$101$	5.72207	+	7.87576i	0.569368	+	0.783667i	0.992480	−	0.122410i	$-0.0390623\pi$
$101$	5.72207	+	7.87576i	0.569368	+	0.783667i	−0.423112	+	0.906077i	$0.639062\pi$
$102$		0			0
$103$	5.73658	−	4.16787i	0.565242	−	0.410672i	−0.268132	−	0.963382i	$-0.586406\pi$
$103$	5.73658	−	4.16787i	0.565242	−	0.410672i	0.833374	+	0.552710i	$0.186406\pi$
$104$		0			0
$105$	−6.89503	−	5.00953i	−0.672886	−	0.488880i
$106$		0			0
$107$	0.956235	−	0.694746i	0.0924428	−	0.0671636i	−0.540604	−	0.841277i	$-0.681804\pi$
$107$	0.956235	−	0.694746i	0.0924428	−	0.0671636i	0.633047	+	0.774114i	$0.281804\pi$
$108$		0			0
$109$			18.4121i			1.76356i	0.471658	+	0.881782i	$0.343656\pi$
$109$			18.4121i			1.76356i	−0.471658	+	0.881782i	$0.656344\pi$
$110$		0			0
$111$	−8.45634	+	2.74763i	−0.802640	+	0.260794i
$112$		0			0
$113$	−1.89249	+	5.82449i	−0.178031	+	0.547922i	−0.999759	−	0.0219574i	$-0.993010\pi$
$113$	−1.89249	+	5.82449i	−0.178031	+	0.547922i	0.821728	+	0.569880i	$0.193010\pi$
$114$		0			0
$115$	−0.971992	+	2.99148i	−0.0906387	+	0.278957i
$116$		0			0
$117$	3.83911	−	5.28408i	0.354926	−	0.488514i
$118$		0			0
$119$	0.714853	+	2.20009i	0.0655305	+	0.201682i
$120$		0			0
$121$	−8.87316	−	6.44673i	−0.806651	−	0.586066i
$122$		0			0
$123$	14.0677	+	4.01069i	1.26844	+	0.361631i
$124$		0			0
$125$	−11.8230	−	8.58994i	−1.05748	−	0.768307i
$126$		0			0
$127$	1.41857	+	4.36590i	0.125878	+	0.387411i	0.994060	−	0.108834i	$-0.0347117\pi$
$127$	1.41857	+	4.36590i	0.125878	+	0.387411i	−0.868182	+	0.496245i	$0.834712\pi$
$128$		0			0
$129$	1.29537	−	1.78293i	0.114051	−	0.156978i
$130$		0			0
$131$	2.21263	−	6.80979i	0.193319	−	0.594974i	−0.806673	−	0.590998i	$-0.798734\pi$
$131$	2.21263	−	6.80979i	0.193319	−	0.594974i	0.999992	−	0.00397639i	$-0.00126573\pi$
$132$		0			0
$133$	0.125549	−	0.386399i	0.0108865	−	0.0335051i
$134$		0			0
$135$	−6.32926	+	2.05650i	−0.544736	+	0.176995i
$136$		0			0
$137$			19.1845i			1.63905i	0.573046	+	0.819523i	$0.305762\pi$
$137$			19.1845i			1.63905i	−0.573046	+	0.819523i	$0.694238\pi$
$138$		0			0
$139$	14.0484	−	10.2067i	1.19157	−	0.865723i	0.198137	−	0.980174i	$-0.436511\pi$
$139$	14.0484	−	10.2067i	1.19157	−	0.865723i	0.993429	+	0.114451i	$0.0365110\pi$
$140$		0			0
$141$	24.4322	+	17.7510i	2.05756	+	1.49491i
$142$		0			0
$143$	0.427104	−	0.310309i	0.0357162	−	0.0259494i
$144$		0			0
$145$	10.8664	+	14.9563i	0.902402	+	1.24205i
$146$		0			0
$147$	−2.17273	−	0.705963i	−0.179204	−	0.0582269i
$148$		0			0
$149$	0.214659	−	0.0697470i	0.0175856	−	0.00571390i	−0.300211	−	0.953873i	$-0.597057\pi$
$149$	0.214659	−	0.0697470i	0.0175856	−	0.00571390i	0.317797	+	0.948159i	$0.397057\pi$
$150$		0			0
$151$	−2.15187	+	2.96179i	−0.175116	+	0.241027i	−0.887549	−	0.460714i	$-0.847593\pi$
$151$	−2.15187	+	2.96179i	−0.175116	+	0.241027i	0.712432	+	0.701741i	$0.247593\pi$
$152$		0			0
$153$	−4.88233	−	1.58637i	−0.394713	−	0.128250i
$154$		0			0
$155$	17.3112			1.39047
$156$		0			0
$157$	4.49536	+	6.18734i	0.358769	+	0.493803i	0.949805	−	0.312842i	$-0.101281\pi$
$157$	4.49536	+	6.18734i	0.358769	+	0.493803i	−0.591036	+	0.806645i	$0.701281\pi$
$158$		0			0
$159$	−8.06207	−	24.8125i	−0.639364	−	1.96776i
$160$		0			0
$161$			0.843144i			0.0664491i
$162$		0			0
$163$	−14.6940			−1.15092			−0.575461	−	0.817829i	$-0.695177\pi$
$163$	−14.6940			−1.15092			−0.575461	+	0.817829i	$0.695177\pi$
$164$		0			0
$165$	1.52872			0.119011
$166$		0			0
$167$			3.80519i			0.294454i	0.989103	+	0.147227i	$0.0470348\pi$
$167$			3.80519i			0.294454i	−0.989103	+	0.147227i	$0.952965\pi$
$168$		0			0
$169$	1.34031	+	4.12506i	0.103101	+	0.317312i
$170$		0			0
$171$	0.529950	+	0.729414i	0.0405263	+	0.0557797i
$172$		0			0
$173$	−1.68081			−0.127789			−0.0638947	−	0.997957i	$-0.520352\pi$
$173$	−1.68081			−0.127789			−0.0638947	+	0.997957i	$0.520352\pi$
$174$		0			0
$175$	−8.48091	−	2.75561i	−0.641096	−	0.208305i
$176$		0			0
$177$	2.09121	−	2.87830i	0.157185	−	0.216347i
$178$		0			0
$179$	0.732335	−	0.237950i	0.0547373	−	0.0177852i	−0.281520	−	0.959555i	$-0.590839\pi$
$179$	0.732335	−	0.237950i	0.0547373	−	0.0177852i	0.336258	+	0.941770i	$0.390839\pi$
$180$		0			0
$181$	5.80624	+	1.88656i	0.431574	+	0.140227i	0.516745	−	0.856139i	$-0.327144\pi$
$181$	5.80624	+	1.88656i	0.431574	+	0.140227i	−0.0851708	+	0.996366i	$0.527144\pi$
$182$		0			0
$183$	2.98818	+	4.11288i	0.220893	+	0.304032i
$184$		0			0
$185$	−11.7466	+	8.53440i	−0.863627	+	0.627462i
$186$		0			0
$187$	−0.335693	−	0.243896i	−0.0245483	−	0.0178354i
$188$		0			0
$189$	−1.44320	+	1.04854i	−0.104977	+	0.0762704i
$190$		0			0
$191$		−	24.3882i		−	1.76466i	−0.470627	−	0.882332i	$-0.655972\pi$
$191$		−	24.3882i		−	1.76466i	0.470627	−	0.882332i	$-0.344028\pi$
$192$		0			0
$193$	−4.58839	+	1.49086i	−0.330280	+	0.107314i	−0.469463	−	0.882952i	$-0.655552\pi$
$193$	−4.58839	+	1.49086i	−0.330280	+	0.107314i	0.139183	+	0.990267i	$0.455552\pi$
$194$		0			0
$195$	7.75151	−	23.8567i	0.555097	−	1.70841i
$196$		0			0
$197$	4.25268	−	13.0884i	0.302991	−	0.932510i	−0.677428	−	0.735589i	$-0.736906\pi$
$197$	4.25268	−	13.0884i	0.302991	−	0.932510i	0.980419	−	0.196921i	$-0.0630943\pi$
$198$		0			0
$199$	7.32961	−	10.0883i	0.519582	−	0.715143i	−0.465916	−	0.884829i	$-0.654275\pi$
$199$	7.32961	−	10.0883i	0.519582	−	0.715143i	0.985498	+	0.169686i	$0.0542752\pi$
$200$		0			0
$201$	2.85248	+	8.77902i	0.201198	+	0.619225i
$202$		0			0
$203$	4.00908	+	2.91277i	0.281382	+	0.204436i
$204$		0			0
$205$	23.8716	−	0.869983i	1.66727	−	0.0607622i
$206$		0			0
$207$	−1.51372	−	1.09978i	−0.105211	−	0.0764402i
$208$		0			0
$209$	0.0225197	+	0.0693086i	0.00155772	+	0.00479417i
$210$		0			0
$211$	−0.421975	+	0.580799i	−0.0290500	+	0.0399839i	−0.823295	−	0.567614i	$-0.807867\pi$
$211$	−0.421975	+	0.580799i	−0.0290500	+	0.0399839i	0.794245	+	0.607598i	$0.207867\pi$
$212$		0			0
$213$	0.575898	−	1.77243i	0.0394599	−	0.121445i
$214$		0			0
$215$	1.11208	−	3.42263i	0.0758433	−	0.233422i
$216$		0			0
$217$	4.41323	−	1.43394i	0.299589	−	0.0973425i
$218$		0			0
$219$			30.3338i			2.04977i
$220$		0			0
$221$	−5.50830	+	4.00202i	−0.370529	+	0.269205i
$222$		0			0
$223$	1.98086	+	1.43918i	0.132648	+	0.0963747i	0.652131	−	0.758106i	$-0.273875\pi$
$223$	1.98086	+	1.43918i	0.132648	+	0.0963747i	−0.519483	+	0.854481i	$0.673875\pi$
$224$		0			0
$225$	16.0096	−	11.6316i	1.06731	−	0.775443i
$226$		0			0
$227$	12.1759	+	16.7587i	0.808142	+	1.11231i	0.991607	+	0.129286i	$0.0412685\pi$
$227$	12.1759	+	16.7587i	0.808142	+	1.11231i	−0.183465	+	0.983026i	$0.558731\pi$
$228$		0			0
$229$	16.6982	+	5.42559i	1.10345	+	0.358533i	0.803430	−	0.595400i	$-0.203006\pi$
$229$	16.6982	+	5.42559i	1.10345	+	0.358533i	0.300021	+	0.953933i	$0.403006\pi$
$230$		0			0
$231$	0.389724	−	0.126629i	0.0256419	−	0.00833157i
$232$		0			0
$233$	−5.65958	+	7.78974i	−0.370771	+	0.510323i	−0.953110	−	0.302623i	$-0.902138\pi$
$233$	−5.65958	+	7.78974i	−0.370771	+	0.510323i	0.582339	+	0.812946i	$0.302138\pi$
$234$		0			0
$235$	46.9018	+	15.2393i	3.05954	+	0.994104i
$236$		0			0
$237$	18.3253			1.19036
$238$		0			0
$239$	−3.49935	−	4.81644i	−0.226354	−	0.311550i	0.680701	−	0.732561i	$-0.261675\pi$
$239$	−3.49935	−	4.81644i	−0.226354	−	0.311550i	−0.907055	+	0.421011i	$0.861675\pi$
$240$		0			0
$241$	5.75805	+	17.7215i	0.370908	+	1.14154i	0.946198	+	0.323589i	$0.104889\pi$
$241$	5.75805	+	17.7215i	0.370908	+	1.14154i	−0.575289	+	0.817950i	$0.695111\pi$
$242$		0			0
$243$		−	19.1680i		−	1.22963i
$244$		0			0
$245$	−3.73060			−0.238339
$246$		0			0
$247$	1.19579			0.0760864
$248$		0			0
$249$		−	32.6377i		−	2.06833i
$250$		0			0
$251$	5.28543	+	16.2669i	0.333613	+	1.02676i	0.967401	+	0.253249i	$0.0814992\pi$
$251$	5.28543	+	16.2669i	0.333613	+	1.02676i	−0.633788	+	0.773507i	$0.718501\pi$
$252$		0			0
$253$	−0.0888937	−	0.122352i	−0.00558870	−	0.00769219i
$254$		0			0
$255$	−19.7157			−1.23465
$256$		0			0
$257$	19.6529	+	6.38562i	1.22591	+	0.398324i	0.849233	−	0.528019i	$-0.177065\pi$
$257$	19.6529	+	6.38562i	1.22591	+	0.398324i	0.376682	+	0.926343i	$0.377065\pi$
$258$		0			0
$259$	−2.28768	+	3.14872i	−0.142149	+	0.195652i
$260$		0			0
$261$	−10.4588	+	3.39826i	−0.647381	+	0.210347i
$262$		0			0
$263$	4.30906	+	1.40010i	0.265708	+	0.0863337i	0.438841	−	0.898565i	$-0.355389\pi$
$263$	4.30906	+	1.40010i	0.265708	+	0.0863337i	−0.173133	+	0.984898i	$0.555389\pi$
$264$		0			0
$265$	−25.0416	−	34.4668i	−1.53829	−	2.11728i
$266$		0			0
$267$	17.6120	−	12.7959i	1.07784	−	0.783096i
$268$		0			0
$269$	−23.4546	−	17.0408i	−1.43005	−	1.03899i	−0.990007	−	0.141017i	$-0.954963\pi$
$269$	−23.4546	−	17.0408i	−1.43005	−	1.03899i	−0.440044	−	0.897976i	$-0.645037\pi$
$270$		0			0
$271$	−20.8873	+	15.1755i	−1.26882	+	0.921849i	−0.999155	−	0.0411066i	$-0.986912\pi$
$271$	−20.8873	+	15.1755i	−1.26882	+	0.921849i	−0.269661	+	0.962955i	$0.586912\pi$
$272$		0			0
$273$		−	6.72397i		−	0.406953i
$274$		0			0
$275$	1.52122	−	0.494275i	0.0917332	−	0.0298059i
$276$		0			0
$277$	1.98487	−	6.10881i	0.119259	−	0.367043i	−0.873552	−	0.486731i	$-0.838189\pi$
$277$	1.98487	−	6.10881i	0.119259	−	0.367043i	0.992812	+	0.119688i	$0.0381894\pi$
$278$		0			0
$279$	−3.18214	+	9.79361i	−0.190509	+	0.586328i
$280$		0			0
$281$	1.57844	−	2.17253i	0.0941617	−	0.129603i	−0.759337	−	0.650698i	$-0.774476\pi$
$281$	1.57844	−	2.17253i	0.0941617	−	0.129603i	0.853498	+	0.521095i	$0.174476\pi$
$282$		0			0
$283$	1.61238	+	4.96239i	0.0958459	+	0.294983i	0.987473	−	0.157787i	$-0.0504359\pi$
$283$	1.61238	+	4.96239i	0.0958459	+	0.294983i	−0.891627	+	0.452770i	$0.850436\pi$
$284$		0			0
$285$	2.80134	+	2.03529i	0.165937	+	0.120560i
$286$		0			0
$287$	6.01363	−	2.19915i	0.354973	−	0.129812i
$288$		0			0
$289$	−9.42390	−	6.84686i	−0.554347	−	0.402757i
$290$		0			0
$291$	−1.32796	−	4.08703i	−0.0778462	−	0.239586i
$292$		0			0
$293$	−11.6486	+	16.0329i	−0.680518	+	0.936652i	−0.999940	−	0.0109602i	$-0.996511\pi$
$293$	−11.6486	+	16.0329i	−0.680518	+	0.936652i	0.319422	+	0.947612i	$0.396511\pi$
$294$		0			0
$295$	1.79531	−	5.52540i	0.104527	−	0.321701i
$296$		0			0
$297$	0.0988783	−	0.304316i	0.00573750	−	0.0176582i
$298$		0			0
$299$	−2.36012	+	0.766849i	−0.136489	+	0.0443480i
$300$		0			0
$301$		−	0.964663i		−	0.0556023i
$302$		0			0
$303$	−17.9925	+	13.0723i	−1.03364	+	0.750986i
$304$		0			0
$305$	6.71621	+	4.87961i	0.384569	+	0.279406i
$306$		0			0
$307$	4.18354	−	3.03952i	0.238767	−	0.173475i	−0.461967	−	0.886897i	$-0.652856\pi$
$307$	4.18354	−	3.03952i	0.238767	−	0.173475i	0.700734	+	0.713423i	$0.252856\pi$
$308$		0			0
$309$	9.52169	+	13.1055i	0.541670	+	0.745545i
$310$		0			0
$311$	1.88893	+	0.613751i	0.107111	+	0.0348026i	0.362082	−	0.932146i	$-0.382066\pi$
$311$	1.88893	+	0.613751i	0.107111	+	0.0348026i	−0.254971	+	0.966949i	$0.582066\pi$
$312$		0			0
$313$	7.15404	−	2.32449i	0.404370	−	0.131388i	−0.0997681	−	0.995011i	$-0.531810\pi$
$313$	7.15404	−	2.32449i	0.404370	−	0.131388i	0.504139	+	0.863623i	$0.331810\pi$
$314$		0			0
$315$	4.86613	−	6.69765i	0.274175	−	0.377370i
$316$		0			0
$317$	15.5713	+	5.05943i	0.874572	+	0.284166i	0.711702	−	0.702482i	$-0.247925\pi$
$317$	15.5713	+	5.05943i	0.874572	+	0.284166i	0.162870	+	0.986647i	$0.447925\pi$
$318$		0			0
$319$	−0.888869			−0.0497671
$320$		0			0
$321$	1.58718	+	2.18456i	0.0885876	+	0.121930i
$322$		0			0
$323$	−0.290434	−	0.893863i	−0.0161602	−	0.0497359i
$324$		0			0
$325$		−	26.2459i		−	1.45586i
$326$		0			0
$327$	−42.0634			−2.32611
$328$		0			0
$329$	13.2192			0.728798
$330$		0			0
$331$			23.7322i			1.30444i	0.758031	+	0.652219i	$0.226162\pi$
$331$			23.7322i			1.30444i	−0.758031	+	0.652219i	$0.773838\pi$
$332$		0			0
$333$	−2.66898	−	8.21427i	−0.146259	−	0.450139i
$334$		0			0
$335$	8.86007	+	12.1948i	0.484077	+	0.666275i
$336$		0			0
$337$	23.9523			1.30477			0.652383	−	0.757889i	$-0.273769\pi$
$337$	23.9523			1.30477			0.652383	+	0.757889i	$0.273769\pi$
$338$		0			0
$339$	−13.3063	−	4.32349i	−0.722700	−	0.234820i
$340$		0			0
$341$	−0.489237	+	0.673377i	−0.0264937	+	0.0364654i
$342$		0			0
$343$	−0.951057	+	0.309017i	−0.0513522	+	0.0166853i
$344$		0			0
$345$	−6.83418	−	2.22056i	−0.367940	−	0.119551i
$346$		0			0
$347$	−9.10198	−	12.5278i	−0.488620	−	0.672528i	0.491513	−	0.870870i	$-0.336444\pi$
$347$	−9.10198	−	12.5278i	−0.488620	−	0.672528i	−0.980133	+	0.198343i	$0.936444\pi$
$348$		0			0
$349$	24.7336	−	17.9700i	1.32396	−	0.961914i	0.324087	−	0.946027i	$-0.394943\pi$
$349$	24.7336	−	17.9700i	1.32396	−	0.961914i	0.999874	−	0.0158869i	$-0.00505718\pi$
$350$		0			0
$351$	−4.24768	−	3.08612i	−0.226724	−	0.164725i
$352$		0			0
$353$	−21.4939	+	15.6162i	−1.14400	+	0.831168i	−0.987672	−	0.156536i	$-0.949967\pi$
$353$	−21.4939	+	15.6162i	−1.14400	+	0.831168i	−0.156333	+	0.987704i	$0.549967\pi$
$354$		0			0
$355$		−	3.04328i		−	0.161520i
$356$		0			0
$357$	−5.02621	+	1.63312i	−0.266015	+	0.0864336i
$358$		0			0
$359$	2.41790	−	7.44154i	0.127612	−	0.392750i	−0.866756	−	0.498733i	$-0.833799\pi$
$359$	2.41790	−	7.44154i	0.127612	−	0.392750i	0.994368	+	0.105983i	$0.0337989\pi$
$360$		0			0
$361$	5.82031	−	17.9131i	0.306332	−	0.942794i
$362$		0			0
$363$	14.7278	−	20.2711i	0.773011	−	1.06396i
$364$		0			0
$365$	15.3069	+	47.1099i	0.801201	+	2.46584i
$366$		0			0
$367$	20.3452	+	14.7816i	1.06201	+	0.771595i	0.974459	−	0.224565i	$-0.0720963\pi$
$367$	20.3452	+	14.7816i	1.06201	+	0.771595i	0.0875499	+	0.996160i	$0.472096\pi$
$368$		0			0
$369$	−3.89588	+	13.6650i	−0.202811	+	0.711370i
$370$		0			0
$371$	−9.23894	−	6.71248i	−0.479662	−	0.348495i
$372$		0			0
$373$	−4.44324	−	13.6749i	−0.230062	−	0.708059i	−0.997738	−	0.0672208i	$-0.978587\pi$
$373$	−4.44324	−	13.6749i	−0.230062	−	0.708059i	0.767676	−	0.640839i	$-0.221413\pi$
$374$		0			0
$375$	19.6241	−	27.0103i	1.01338	−	1.39480i
$376$		0			0
$377$	−4.50708	+	13.8714i	−0.232126	+	0.714412i
$378$		0			0
$379$	−1.96540	+	6.04889i	−0.100956	+	0.310710i	−0.988760	−	0.149511i	$-0.952230\pi$
$379$	−1.96540	+	6.04889i	−0.100956	+	0.310710i	0.887804	+	0.460222i	$0.152230\pi$
$380$		0			0
$381$	−9.97411	+	3.24078i	−0.510989	+	0.166030i
$382$		0			0
$383$		−	23.7977i		−	1.21601i	−0.793934	−	0.608004i	$-0.791971\pi$
$383$		−	23.7977i		−	1.21601i	0.793934	−	0.608004i	$-0.208029\pi$
$384$		0			0
$385$	0.541360	−	0.393321i	0.0275903	−	0.0200455i
$386$		0			0
$387$	1.73189	+	1.25829i	0.0880368	+	0.0639625i
$388$		0			0
$389$	−3.24816	+	2.35993i	−0.164688	+	0.119653i	−0.667077	−	0.744989i	$-0.732455\pi$
$389$	−3.24816	+	2.35993i	−0.164688	+	0.119653i	0.502389	+	0.864642i	$0.332455\pi$
$390$		0			0
$391$	1.14645	+	1.57795i	0.0579785	+	0.0798005i
$392$		0			0
$393$	15.5573	+	5.05486i	0.784761	+	0.254984i
$394$		0			0
$395$	28.4600	−	9.24723i	1.43198	−	0.465279i
$396$		0			0
$397$	6.92956	−	9.53772i	0.347785	−	0.478684i	−0.598910	−	0.800816i	$-0.704399\pi$
$397$	6.92956	−	9.53772i	0.347785	−	0.478684i	0.946695	+	0.322132i	$0.104399\pi$
$398$		0			0
$399$	0.882747	+	0.286822i	0.0441926	+	0.0143591i
$400$		0			0
$401$	5.25865			0.262604			0.131302	−	0.991342i	$-0.458084\pi$
$401$	5.25865			0.262604			0.131302	+	0.991342i	$0.458084\pi$
$402$		0			0
$403$	8.02776	+	11.0493i	0.399891	+	0.550403i
$404$		0			0
$405$	−12.3730	−	38.0802i	−0.614819	−	1.89222i
$406$		0			0
$407$		−	0.698114i		−	0.0346042i
$408$		0			0
$409$	33.0146			1.63247			0.816234	−	0.577722i	$-0.196058\pi$
$409$	33.0146			1.63247			0.816234	+	0.577722i	$0.196058\pi$
$410$		0			0
$411$	−43.8280			−2.16187
$412$		0			0
$413$		−	1.55733i		−	0.0766310i
$414$		0			0
$415$	−16.4695	−	50.6879i	−0.808455	−	2.48817i
$416$		0			0
$417$	23.3177	+	32.0941i	1.14187	+	1.57165i
$418$		0			0
$419$	−38.1555			−1.86402			−0.932009	−	0.362434i	$-0.881946\pi$
$419$	−38.1555			−1.86402			−0.932009	+	0.362434i	$0.881946\pi$
$420$		0			0
$421$	11.3278	+	3.68061i	0.552081	+	0.179382i	0.571755	−	0.820424i	$-0.306263\pi$
$421$	11.3278	+	3.68061i	0.552081	+	0.179382i	−0.0196738	+	0.999806i	$0.506263\pi$
$422$		0			0
$423$	−17.2429	+	23.7328i	−0.838378	+	1.15393i
$424$		0			0
$425$	−19.6190	+	6.37460i	−0.951662	+	0.309214i
$426$		0			0
$427$	2.11638	+	0.687655i	0.102419	+	0.0332779i
$428$		0			0
$429$	0.708916	+	0.975739i	0.0342268	+	0.0471091i
$430$		0			0
$431$	−18.7745	+	13.6405i	−0.904335	+	0.657038i	−0.939576	−	0.342341i	$-0.888780\pi$
$431$	−18.7745	+	13.6405i	−0.904335	+	0.657038i	0.0352410	+	0.999379i	$0.488780\pi$
$432$		0			0
$433$	−5.81215	−	4.22278i	−0.279314	−	0.202934i	0.439304	−	0.898338i	$-0.355225\pi$
$433$	−5.81215	−	4.22278i	−0.279314	−	0.202934i	−0.718618	+	0.695405i	$0.755225\pi$
$434$		0			0
$435$	−34.1683	+	24.8247i	−1.63824	+	1.19025i
$436$		0			0
$437$		−	0.342556i		−	0.0163867i
$438$		0			0
$439$	−9.36014	+	3.04130i	−0.446735	+	0.145153i	−0.523741	−	0.851878i	$-0.675464\pi$
$439$	−9.36014	+	3.04130i	−0.446735	+	0.145153i	0.0770057	+	0.997031i	$0.475464\pi$
$440$		0			0
$441$	0.685755	−	2.11054i	0.0326550	−	0.100502i
$442$		0			0
$443$	10.9339	−	33.6511i	0.519486	−	1.59881i	−0.255482	−	0.966814i	$-0.582234\pi$
$443$	10.9339	−	33.6511i	0.519486	−	1.59881i	0.774968	−	0.632000i	$-0.217766\pi$
$444$		0			0
$445$	20.8953	−	28.7600i	0.990534	−	1.36335i
$446$		0			0
$447$	0.159340	+	0.490399i	0.00753653	+	0.0231951i
$448$		0			0
$449$	14.0963	+	10.2415i	0.665243	+	0.483328i	0.868430	−	0.495813i	$-0.165130\pi$
$449$	14.0963	+	10.2415i	0.665243	+	0.483328i	−0.203186	+	0.979140i	$0.565130\pi$
$450$		0			0
$451$	−0.640801	+	0.953151i	−0.0301741	+	0.0448821i
$452$		0			0
$453$	−6.76634	−	4.91603i	−0.317910	−	0.230975i
$454$		0			0
$455$	−3.39302	−	10.4426i	−0.159067	−	0.489559i
$456$		0			0
$457$	−13.8422	+	19.0521i	−0.647509	+	0.891220i	−0.998988	−	0.0449757i	$-0.985679\pi$
$457$	−13.8422	+	19.0521i	−0.647509	+	0.891220i	0.351479	+	0.936196i	$0.385679\pi$
$458$		0			0
$459$	−1.27522	+	3.92472i	−0.0595222	+	0.183190i
$460$		0			0
$461$	0.867571	−	2.67011i	0.0404068	−	0.124359i	−0.928818	−	0.370536i	$-0.879174\pi$
$461$	0.867571	−	2.67011i	0.0404068	−	0.124359i	0.969225	+	0.246176i	$0.0791742\pi$
$462$		0			0
$463$	21.9126	−	7.11984i	1.01837	−	0.330887i	0.248185	−	0.968713i	$-0.420166\pi$
$463$	21.9126	−	7.11984i	1.01837	−	0.330887i	0.770181	+	0.637826i	$0.220166\pi$
$464$		0			0
$465$			39.5483i			1.83401i
$466$		0			0
$467$	−18.8079	+	13.6647i	−0.870325	+	0.632328i	−0.930674	−	0.365849i	$-0.880779\pi$
$467$	−18.8079	+	13.6647i	−0.870325	+	0.632328i	0.0603491	+	0.998177i	$0.480779\pi$
$468$		0			0
$469$	3.26887	+	2.37497i	0.150942	+	0.109666i
$470$		0			0
$471$	−14.1353	+	10.2699i	−0.651318	+	0.473210i
$472$		0			0
$473$	0.101706	+	0.139986i	0.00467643	+	0.00643655i
$474$		0			0
$475$	3.44566	+	1.11956i	0.158098	+	0.0513691i
$476$		0			0
$477$	24.1022	−	7.83129i	1.10357	−	0.358570i
$478$		0			0
$479$	−6.56209	+	9.03194i	−0.299829	+	0.412680i	−0.932176	−	0.362006i	$-0.882092\pi$
$479$	−6.56209	+	9.03194i	−0.299829	+	0.412680i	0.632346	+	0.774686i	$0.282092\pi$
$480$		0			0
$481$	−10.8945	−	3.53984i	−0.496747	−	0.161403i
$482$		0			0
$483$	−1.92620			−0.0876452
$484$		0			0
$485$	−4.12476	−	5.67725i	−0.187296	−	0.257791i
$486$		0			0
$487$	−8.97216	−	27.6135i	−0.406567	−	1.25129i	−0.919579	−	0.392904i	$-0.871470\pi$
$487$	−8.97216	−	27.6135i	−0.406567	−	1.25129i	0.513012	−	0.858381i	$-0.328530\pi$
$488$		0			0
$489$		−	33.5691i		−	1.51805i
$490$		0			0
$491$	−0.754777			−0.0340626			−0.0170313	−	0.999855i	$-0.505421\pi$
$491$	−0.754777			−0.0340626			−0.0170313	+	0.999855i	$0.505421\pi$
$492$		0			0
$493$	11.4636			0.516295
$494$		0			0
$495$			1.48496i			0.0667441i
$496$		0			0
$497$	−0.252084	−	0.775836i	−0.0113075	−	0.0348010i
$498$		0			0
$499$	−15.7563	−	21.6867i	−0.705349	−	0.970830i	−0.999885	−	0.0151895i	$-0.995165\pi$
$499$	−15.7563	−	21.6867i	−0.705349	−	0.970830i	0.294535	−	0.955641i	$-0.404835\pi$
$500$		0			0
$501$	−8.69312			−0.388380
$502$		0			0
$503$	−18.4766	−	6.00341i	−0.823830	−	0.267679i	−0.133386	−	0.991064i	$-0.542585\pi$
$503$	−18.4766	−	6.00341i	−0.823830	−	0.267679i	−0.690444	+	0.723386i	$0.742585\pi$
$504$		0			0
$505$	−21.3468	+	29.3813i	−0.949918	+	1.30745i
$506$		0			0
$507$	−9.42388	+	3.06200i	−0.418529	+	0.135988i
$508$		0			0
$509$	−31.2628	−	10.1579i	−1.38570	−	0.450241i	−0.481162	−	0.876632i	$-0.659785\pi$
$509$	−31.2628	−	10.1579i	−1.38570	−	0.450241i	−0.904539	+	0.426391i	$0.859785\pi$
$510$		0			0
$511$	7.80452	+	10.7420i	0.345252	+	0.475198i
$512$		0			0
$513$	0.586348	−	0.426007i	0.0258879	−	0.0188087i
$514$		0			0
$515$	21.4009	+	15.5486i	0.943035	+	0.685155i
$516$		0			0
$517$	−1.91828	+	1.39372i	−0.0843661	+	0.0612955i
$518$		0			0
$519$		−	3.83988i		−	0.168552i
$520$		0			0
$521$	−29.8695	+	9.70518i	−1.30860	+	0.425192i	−0.878567	−	0.477619i	$-0.841500\pi$
$521$	−29.8695	+	9.70518i	−1.30860	+	0.425192i	−0.430038	+	0.902811i	$0.641500\pi$
$522$		0			0
$523$	−11.4946	+	35.3767i	−0.502623	+	1.54691i	0.302108	+	0.953274i	$0.402310\pi$
$523$	−11.4946	+	35.3767i	−0.502623	+	1.54691i	−0.804731	+	0.593640i	$0.797690\pi$
$524$		0			0
$525$	6.29533	−	19.3750i	0.274751	−	0.845595i
$526$		0			0
$527$	6.30962	−	8.68445i	0.274851	−	0.378300i
$528$		0			0
$529$	−6.88771	−	21.1982i	−0.299466	−	0.921661i
$530$		0			0
$531$	2.79591	+	2.03135i	0.121332	+	0.0881530i
$532$		0			0
$533$	11.6253	+	14.8331i	0.503547	+	0.642494i
$534$		0			0
$535$	3.56733	+	2.59182i	0.154229	+	0.112054i
$536$		0			0
$537$	0.543608	+	1.67305i	0.0234584	+	0.0721976i
$538$		0			0
$539$	0.105431	−	0.145114i	0.00454124	−	0.00625049i
$540$		0			0
$541$	8.04716	−	24.7666i	0.345974	−	1.06480i	−0.615086	−	0.788460i	$-0.710879\pi$
$541$	8.04716	−	24.7666i	0.345974	−	1.06480i	0.961060	−	0.276339i	$-0.0891214\pi$
$542$		0			0
$543$	−4.30993	+	13.2646i	−0.184957	+	0.569239i
$544$		0			0
$545$	−65.3264	+	21.2258i	−2.79828	+	0.909215i
$546$		0			0
$547$			22.1714i			0.947981i	0.880530	+	0.473990i	$0.157187\pi$
$547$			22.1714i			0.947981i	−0.880530	+	0.473990i	$0.842813\pi$
$548$		0			0
$549$	−3.99514	+	2.90264i	−0.170508	+	0.123882i
$550$		0			0
$551$	−1.62883	−	1.18341i	−0.0693903	−	0.0504150i
$552$		0			0
$553$	6.48946	−	4.71487i	0.275960	−	0.200497i
$554$		0			0
$555$	−19.4972	−	26.8356i	−0.827611	−	1.13911i
$556$		0			0
$557$	0.936148	+	0.304173i	0.0396659	+	0.0128882i	0.328783	−	0.944406i	$-0.393362\pi$
$557$	0.936148	+	0.304173i	0.0396659	+	0.0128882i	−0.289117	+	0.957294i	$0.593362\pi$
$558$		0			0
$559$	2.70027	−	0.877372i	0.114209	−	0.0371089i
$560$		0			0
$561$	0.557190	−	0.766907i	0.0235246	−	0.0323788i
$562$		0			0
$563$	38.0456	+	12.3618i	1.60343	+	0.520986i	0.967953	−	0.251132i	$-0.0808029\pi$
$563$	38.0456	+	12.3618i	1.60343	+	0.520986i	0.635478	+	0.772119i	$0.280803\pi$
$564$		0			0
$565$	−22.8471			−0.961183
$566$		0			0
$567$	−6.30860	−	8.68304i	−0.264936	−	0.364653i
$568$		0			0
$569$	5.02089	+	15.4527i	0.210486	+	0.647811i	0.999443	+	0.0333622i	$0.0106215\pi$
$569$	5.02089	+	15.4527i	0.210486	+	0.647811i	−0.788957	+	0.614449i	$0.789379\pi$
$570$		0			0
$571$			8.72115i			0.364969i	0.983209	+	0.182484i	$0.0584139\pi$
$571$			8.72115i			0.364969i	−0.983209	+	0.182484i	$0.941586\pi$
$572$		0			0
$573$	55.7158			2.32756
$574$		0			0
$575$	−7.51862			−0.313548
$576$		0			0
$577$		−	11.3683i		−	0.473269i	−0.971599	−	0.236634i	$-0.923956\pi$
$577$		−	11.3683i		−	0.473269i	0.971599	−	0.236634i	$-0.0760443\pi$
$578$		0			0
$579$	−3.40594	−	10.4824i	−0.141546	−	0.435633i
$580$		0			0
$581$	−8.39727	−	11.5579i	−0.348377	−	0.479500i
$582$		0			0
$583$	2.04840			0.0848361
$584$		0			0
$585$	23.1738	+	7.52962i	0.958118	+	0.311311i
$586$		0			0
$587$	−11.4326	+	15.7357i	−0.471876	+	0.649481i	−0.976918	−	0.213613i	$-0.931477\pi$
$587$	−11.4326	+	15.7357i	−0.471876	+	0.649481i	0.505043	+	0.863094i	$0.331477\pi$
$588$		0			0
$589$	−1.79302	+	0.582589i	−0.0738803	+	0.0240052i
$590$		0			0
$591$	29.9010	+	9.71544i	1.22996	+	0.399640i
$592$		0			0
$593$	16.3478	+	22.5007i	0.671322	+	0.923995i	0.999789	−	0.0205202i	$-0.00653223\pi$
$593$	16.3478	+	22.5007i	0.671322	+	0.923995i	−0.328468	+	0.944515i	$0.606532\pi$
$594$		0			0
$595$	−6.98185	+	5.07261i	−0.286228	+	0.207957i
$596$		0			0
$597$	23.0473	+	16.7448i	0.943262	+	0.685320i
$598$		0			0
$599$	−23.2031	+	16.8580i	−0.948053	+	0.688801i	−0.950346	−	0.311196i	$-0.899270\pi$
$599$	−23.2031	+	16.8580i	−0.948053	+	0.688801i	0.00229229	+	0.999997i	$0.499270\pi$
$600$		0			0
$601$			34.0639i			1.38950i	0.719253	+	0.694748i	$0.244484\pi$
$601$			34.0639i			1.38950i	−0.719253	+	0.694748i	$0.755516\pi$
$602$		0			0
$603$	−8.52772	+	2.77082i	−0.347276	+	0.112837i
$604$		0			0
$605$	12.6439	−	38.9139i	0.514048	−	1.58208i
$606$		0			0
$607$	9.98901	−	30.7430i	0.405441	−	1.24782i	−0.515085	−	0.857139i	$-0.672240\pi$
$607$	9.98901	−	30.7430i	0.405441	−	1.24782i	0.920526	−	0.390681i	$-0.127760\pi$
$608$		0			0
$609$	−6.65435	+	9.15893i	−0.269648	+	0.371139i
$610$		0			0
$611$	12.0230	+	37.0030i	0.486399	+	1.49698i
$612$		0			0
$613$	−1.32095	−	0.959724i	−0.0533525	−	0.0387629i	0.560789	−	0.827959i	$-0.310498\pi$
$613$	−1.32095	−	0.959724i	−0.0533525	−	0.0387629i	−0.614142	+	0.789196i	$0.710498\pi$
$614$		0			0
$615$	1.98752	+	54.5358i	0.0801444	+	2.19910i
$616$		0			0
$617$	2.95859	+	2.14954i	0.119108	+	0.0865374i	0.645745	−	0.763553i	$-0.276547\pi$
$617$	2.95859	+	2.14954i	0.119108	+	0.0865374i	−0.526636	+	0.850091i	$0.676547\pi$
$618$		0			0
$619$	4.24265	+	13.0575i	0.170526	+	0.524826i	0.999401	−	0.0346084i	$-0.0110184\pi$
$619$	4.24265	+	13.0575i	0.170526	+	0.524826i	−0.828875	+	0.559434i	$0.811018\pi$
$620$		0			0
$621$	−0.884074	+	1.21682i	−0.0354767	+	0.0488294i
$622$		0			0
$623$	2.94466	−	9.06272i	0.117975	−	0.363090i
$624$		0			0
$625$	3.06930	−	9.44632i	0.122772	−	0.377853i
$626$		0			0
$627$	−0.158339	+	0.0514473i	−0.00632343	+	0.00205461i
$628$		0			0
$629$			9.00349i			0.358992i
$630$		0			0
$631$	−11.6797	+	8.48579i	−0.464961	+	0.337814i	−0.795474	−	0.605988i	$-0.792778\pi$
$631$	−11.6797	+	8.48579i	−0.464961	+	0.337814i	0.330513	+	0.943801i	$0.392778\pi$
$632$		0			0
$633$	−1.32686	−	0.964022i	−0.0527380	−	0.0383164i
$634$		0			0
$635$	−13.8549	+	10.0662i	−0.549816	+	0.399464i
$636$		0			0
$637$	−1.72999	−	2.38113i	−0.0685448	−	0.0943438i
$638$		0			0
$639$	1.72170	+	0.559413i	0.0681092	+	0.0221300i
$640$		0			0
$641$	−35.4448	+	11.5167i	−1.39998	+	0.454883i	−0.909186	−	0.416390i	$-0.863295\pi$
$641$	−35.4448	+	11.5167i	−1.39998	+	0.454883i	−0.490799	+	0.871273i	$0.663295\pi$
$642$		0			0
$643$	4.46353	−	6.14353i	0.176025	−	0.242277i	−0.711884	−	0.702297i	$-0.752158\pi$
$643$	4.46353	−	6.14353i	0.176025	−	0.242277i	0.887908	+	0.460020i	$0.152158\pi$
$644$		0			0
$645$	7.81916	+	2.54060i	0.307879	+	0.100036i
$646$		0			0
$647$	−11.9327			−0.469123			−0.234562	−	0.972101i	$-0.575365\pi$
$647$	−11.9327			−0.469123			−0.234562	+	0.972101i	$0.575365\pi$
$648$		0			0
$649$	0.164191	+	0.225989i	0.00644505	+	0.00887085i
$650$		0			0
$651$	3.27591	+	10.0822i	0.128393	+	0.395153i
$652$		0			0
$653$		−	40.5099i		−	1.58527i	−0.609694	−	0.792637i	$-0.708708\pi$
$653$		−	40.5099i		−	1.58527i	0.609694	−	0.792637i	$-0.291292\pi$
$654$		0			0
$655$	26.7120			1.04372
$656$		0			0
$657$	−29.4655			−1.14956
$658$		0			0
$659$			45.8040i			1.78427i	0.451769	+	0.892135i	$0.350793\pi$
$659$			45.8040i			1.78427i	−0.451769	+	0.892135i	$0.649207\pi$
$660$		0			0
$661$	−7.70088	−	23.7009i	−0.299530	−	0.921858i	−0.981662	−	0.190629i	$-0.938947\pi$
$661$	−7.70088	−	23.7009i	−0.299530	−	0.921858i	0.682132	−	0.731229i	$-0.261053\pi$
$662$		0			0
$663$	−9.14279	−	12.5840i	−0.355077	−	0.488721i
$664$		0			0
$665$	1.51568			0.0587757
$666$		0			0
$667$	3.97370	+	1.29113i	0.153862	+	0.0499929i
$668$		0			0
$669$	−3.28787	+	4.52537i	−0.127117	+	0.174961i
$670$		0			0
$671$	−0.379616	+	0.123345i	−0.0146549	+	0.00476167i
$672$		0			0
$673$	−43.7580	−	14.2178i	−1.68675	−	0.548057i	−0.700546	−	0.713608i	$-0.747060\pi$
$673$	−43.7580	−	14.2178i	−1.68675	−	0.548057i	−0.986201	+	0.165550i	$0.947060\pi$
$674$		0			0
$675$	−9.35024	−	12.8695i	−0.359891	−	0.495347i
$676$		0			0
$677$	8.90078	−	6.46679i	0.342085	−	0.248539i	−0.403456	−	0.914999i	$-0.632191\pi$
$677$	8.90078	−	6.46679i	0.342085	−	0.248539i	0.745541	+	0.666460i	$0.232191\pi$
$678$		0			0
$679$	−1.52181	−	1.10566i	−0.0584016	−	0.0424312i
$680$		0			0
$681$	−38.2860	+	27.8164i	−1.46712	+	1.06593i
$682$		0			0
$683$		−	37.0709i		−	1.41848i	−0.704967	−	0.709240i	$-0.749038\pi$
$683$		−	37.0709i		−	1.41848i	0.704967	−	0.709240i	$-0.250962\pi$
$684$		0			0
$685$	−68.0669	+	22.1163i	−2.60070	+	0.845020i
$686$		0			0
$687$	−12.3950	+	38.1479i	−0.472899	+	1.45543i
$688$		0			0
$689$	10.3866	−	31.9666i	0.395697	−	1.21783i
$690$		0			0
$691$	23.0765	−	31.7620i	0.877870	−	1.20828i	−0.0991365	−	0.995074i	$-0.531608\pi$
$691$	23.0765	−	31.7620i	0.877870	−	1.20828i	0.977006	−	0.213210i	$-0.0683920\pi$
$692$		0			0
$693$	0.123004	+	0.378567i	0.00467254	+	0.0143806i
$694$		0			0
$695$	52.4087	+	38.0772i	1.98798	+	1.44435i
$696$		0			0
$697$	8.26432	−	12.2927i	0.313033	−	0.465618i
$698$		0			0
$699$	−17.7960	−	12.9296i	−0.673107	−	0.489041i
$700$		0			0
$701$	−12.1727	−	37.4636i	−0.459755	−	1.41498i	−0.865460	−	0.500977i	$-0.832974\pi$
$701$	−12.1727	−	37.4636i	−0.459755	−	1.41498i	0.405705	−	0.914004i	$-0.367026\pi$
$702$		0			0
$703$	0.929447	−	1.27927i	0.0350548	−	0.0482488i
$704$		0			0
$705$	−34.8149	+	107.149i	−1.31121	+	4.03548i
$706$		0			0
$707$	−3.00827	+	9.25851i	−0.113138	+	0.348202i
$708$		0			0
$709$	−2.96481	+	0.963326i	−0.111346	+	0.0361785i	−0.364160	−	0.931336i	$-0.618644\pi$
$709$	−2.96481	+	0.963326i	−0.111346	+	0.0361785i	0.252814	+	0.967515i	$0.418644\pi$
$710$		0			0
$711$			17.8007i			0.667579i
$712$		0			0
$713$	3.16526	−	2.29970i	0.118540	−	0.0861243i
$714$		0			0
$715$	1.59335	+	1.15764i	0.0595880	+	0.0432932i
$716$		0			0
$717$	11.0034	−	7.99442i	0.410929	−	0.298557i
$718$		0			0
$719$	10.1144	+	13.9213i	0.377205	+	0.519178i	0.954841	−	0.297116i	$-0.0960249\pi$
$719$	10.1144	+	13.9213i	0.377205	+	0.519178i	−0.577637	+	0.816294i	$0.696025\pi$
$720$		0			0
$721$	6.74375	+	2.19118i	0.251151	+	0.0816037i
$722$		0			0
$723$	−40.4855	+	13.1545i	−1.50567	+	0.489222i
$724$		0			0
$725$	−25.9742	+	35.7504i	−0.964657	+	1.32774i
$726$		0			0
$727$	40.2148	+	13.0666i	1.49149	+	0.484613i	0.937522	−	0.347927i	$-0.113114\pi$
$727$	40.2148	+	13.0666i	1.49149	+	0.484613i	0.553964	+	0.832540i	$0.313114\pi$
$728$		0			0
$729$	11.5916			0.429319
$730$		0			0
$731$	−1.31168	−	1.80538i	−0.0485144	−	0.0667743i
$732$		0			0
$733$	−6.79748	−	20.9205i	−0.251070	−	0.772715i	−0.994579	−	0.103988i	$-0.966839\pi$
$733$	−6.79748	−	20.9205i	−0.251070	−	0.772715i	0.743508	−	0.668727i	$-0.233161\pi$
$734$		0			0
$735$		−	8.52272i		−	0.314365i
$736$		0			0
$737$	−0.724754			−0.0266967
$738$		0			0
$739$	−18.0296			−0.663230			−0.331615	−	0.943415i	$-0.607593\pi$
$739$	−18.0296			−0.663230			−0.331615	+	0.943415i	$0.607593\pi$
$740$		0			0
$741$			2.73184i			0.100357i
$742$		0			0
$743$	−15.5792	−	47.9477i	−0.571544	−	1.75903i	−0.647657	−	0.761932i	$-0.724251\pi$
$743$	−15.5792	−	47.9477i	−0.571544	−	1.75903i	0.0761131	−	0.997099i	$-0.475749\pi$
$744$		0			0
$745$	0.494926	+	0.681207i	0.0181327	+	0.0249575i
$746$		0			0
$747$	31.7034			1.15997
$748$		0			0
$749$	1.12412	+	0.365249i	0.0410745	+	0.0133459i
$750$		0			0
$751$	28.3366	−	39.0020i	1.03402	−	1.42320i	0.132131	−	0.991232i	$-0.457818\pi$
$751$	28.3366	−	39.0020i	1.03402	−	1.42320i	0.901887	−	0.431971i	$-0.142182\pi$
$752$		0			0
$753$	−37.1624	+	12.0748i	−1.35427	+	0.440030i
$754$		0			0
$755$	−12.9892	−	4.22043i	−0.472724	−	0.153597i
$756$		0			0
$757$	3.34972	+	4.61050i	0.121748	+	0.167571i	0.865541	−	0.500839i	$-0.166975\pi$
$757$	3.34972	+	4.61050i	0.121748	+	0.167571i	−0.743793	+	0.668410i	$0.766975\pi$
$758$		0			0
$759$	0.279518	−	0.203082i	0.0101459	−	0.00737140i
$760$		0			0
$761$	−21.8766	−	15.8943i	−0.793027	−	0.576168i	0.115833	−	0.993269i	$-0.463046\pi$
$761$	−21.8766	−	15.8943i	−0.793027	−	0.576168i	−0.908860	+	0.417101i	$0.863046\pi$
$762$		0			0
$763$	−14.8957	+	10.8224i	−0.539262	+	0.391797i
$764$		0			0
$765$		−	19.1513i		−	0.692419i
$766$		0			0
$767$	4.35924	−	1.41640i	0.157403	−	0.0511434i
$768$		0			0
$769$	14.0293	−	43.1776i	0.505908	−	1.55702i	−0.293331	−	0.956011i	$-0.594764\pi$
$769$	14.0293	−	43.1776i	0.505908	−	1.55702i	0.799239	−	0.601014i	$-0.205236\pi$
$770$		0			0
$771$	−14.5882	+	44.8980i	−0.525382	+	1.61696i
$772$		0			0
$773$	19.8092	−	27.2650i	0.712486	−	0.980653i	−0.287254	−	0.957854i	$-0.592742\pi$
$773$	19.8092	−	27.2650i	0.712486	−	0.980653i	0.999740	−	0.0227982i	$-0.00725751\pi$
$774$		0			0
$775$	12.7870	+	39.3543i	0.459322	+	1.41365i
$776$		0			0
$777$	−7.19339	−	5.22630i	−0.258061	−	0.187493i
$778$		0			0
$779$	−2.44324	+	0.893480i	−0.0875383	+	0.0320122i
$780$		0			0
$781$	0.118378	+	0.0860068i	0.00423590	+	0.00307756i
$782$		0			0
$783$	2.73173	+	8.40740i	0.0976240	+	0.300456i
$784$		0			0
$785$	−16.7704	+	23.0825i	−0.598561	+	0.823848i
$786$		0			0
$787$	−0.537568	+	1.65446i	−0.0191622	+	0.0589753i	−0.960180	−	0.279381i	$-0.909871\pi$
$787$	−0.537568	+	1.65446i	−0.0191622	+	0.0589753i	0.941018	+	0.338356i	$0.109871\pi$
$788$		0			0
$789$	−3.19859	+	9.84424i	−0.113873	+	0.350464i
$790$		0			0
$791$	−5.82449	+	1.89249i	−0.207095	+	0.0672893i
$792$		0			0
$793$			6.54958i			0.232583i
$794$		0			0
$795$	78.7409	−	57.2086i	2.79265	−	2.02898i
$796$		0			0
$797$	−27.5997	−	20.0524i	−0.977632	−	0.710292i	−0.0204542	−	0.999791i	$-0.506511\pi$
$797$	−27.5997	−	20.0524i	−0.977632	−	0.710292i	−0.957178	+	0.289499i	$0.906511\pi$
$798$		0			0
$799$	24.7399	−	17.9746i	0.875233	−	0.635894i
$800$		0			0
$801$	12.4296	+	17.1079i	0.439179	+	0.604478i
$802$		0			0
$803$	−2.26508	−	0.735970i	−0.0799331	−	0.0259718i
$804$		0			0
$805$	−2.99148	+	0.971992i	−0.105436	+	0.0342582i
$806$		0			0
$807$	38.9304	−	53.5831i	1.37041	−	1.88621i
$808$		0			0
$809$	−13.0032	−	4.22499i	−0.457168	−	0.148543i	0.0713750	−	0.997450i	$-0.477261\pi$
$809$	−13.0032	−	4.22499i	−0.457168	−	0.148543i	−0.528543	+	0.848907i	$0.677261\pi$
$810$		0			0
$811$	47.0187			1.65105			0.825526	−	0.564365i	$-0.190879\pi$
$811$	47.0187			1.65105			0.825526	+	0.564365i	$0.190879\pi$
$812$		0			0
$813$	−34.6692	−	47.7181i	−1.21590	−	1.67355i
$814$		0			0
$815$	−16.9395	−	52.1344i	−0.593364	−	1.82619i
$816$		0			0
$817$			0.391928i			0.0137118i
$818$		0			0
$819$	6.53149			0.228229
$820$		0			0
$821$	32.0577			1.11882			0.559410	−	0.828891i	$-0.311028\pi$
$821$	32.0577			1.11882			0.559410	+	0.828891i	$0.311028\pi$
$822$		0			0
$823$		−	19.8085i		−	0.690481i	−0.938514	−	0.345240i	$-0.887797\pi$
$823$		−	19.8085i		−	0.690481i	0.938514	−	0.345240i	$-0.112203\pi$
$824$		0			0
$825$	1.12919	+	3.47530i	0.0393135	+	0.120995i
$826$		0			0
$827$	−12.6092	−	17.3551i	−0.438464	−	0.603494i	0.531406	−	0.847117i	$-0.321664\pi$
$827$	−12.6092	−	17.3551i	−0.438464	−	0.603494i	−0.969870	+	0.243623i	$0.921664\pi$
$828$		0			0
$829$	28.8262			1.00117			0.500587	−	0.865686i	$-0.333117\pi$
$829$	28.8262			1.00117			0.500587	+	0.865686i	$0.333117\pi$
$830$		0			0
$831$	13.9559	+	4.53453i	0.484123	+	0.157301i
$832$		0			0
$833$	−1.35973	+	1.87151i	−0.0471119	+	0.0648440i
$834$		0			0
$835$	−13.5008	+	4.38669i	−0.467216	+	0.151808i
$836$		0			0
$837$	7.87271	+	2.55800i	0.272121	+	0.0884174i
$838$		0			0
$839$	−9.88927	−	13.6114i	−0.341416	−	0.469918i	0.603439	−	0.797409i	$-0.293797\pi$
$839$	−9.88927	−	13.6114i	−0.341416	−	0.469918i	−0.944854	+	0.327491i	$0.893797\pi$
$840$		0			0
$841$	−3.59451	+	2.61156i	−0.123949	+	0.0900539i
$842$		0			0
$843$	4.96325	+	3.60601i	0.170944	+	0.124198i
$844$		0			0
$845$	−13.0906	+	9.51088i	−0.450330	+	0.327184i
$846$		0			0
$847$		−	10.9678i		−	0.376859i
$848$		0			0
$849$	−11.3368	+	3.68355i	−0.389078	+	0.126419i
$850$		0			0
$851$	−1.01405	+	3.12093i	−0.0347613	+	0.106984i
$852$		0			0
$853$	−11.7964	+	36.3057i	−0.403902	+	1.24308i	0.517906	+	0.855437i	$0.326712\pi$
$853$	−11.7964	+	36.3057i	−0.403902	+	1.24308i	−0.921808	+	0.387646i	$0.873288\pi$
$854$		0			0
$855$	−1.97703	+	2.72115i	−0.0676130	+	0.0930614i
$856$		0			0
$857$	−11.6467	−	35.8447i	−0.397842	−	1.22443i	−0.926726	−	0.375738i	$-0.877389\pi$
$857$	−11.6467	−	35.8447i	−0.397842	−	1.22443i	0.528884	−	0.848694i	$-0.322611\pi$
$858$		0			0
$859$	1.32039	+	0.959319i	0.0450511	+	0.0327315i	0.610083	−	0.792338i	$-0.291136\pi$
$859$	1.32039	+	0.959319i	0.0450511	+	0.0327315i	−0.565032	+	0.825069i	$0.691136\pi$
$860$		0			0
$861$	5.02406	+	13.7384i	0.171219	+	0.468204i
$862$		0			0
$863$	23.4370	+	17.0280i	0.797804	+	0.579639i	0.910269	−	0.414017i	$-0.135875\pi$
$863$	23.4370	+	17.0280i	0.797804	+	0.579639i	−0.112465	+	0.993656i	$0.535875\pi$
$864$		0			0
$865$	−1.93767	−	5.96352i	−0.0658826	−	0.202766i
$866$		0			0
$867$	15.6420	−	21.5293i	0.531229	−	0.731174i
$868$		0			0
$869$	−0.444615	+	1.36838i	−0.0150825	+	0.0464192i
$870$		0			0
$871$	−3.67492	+	11.3102i	−0.124520	+	0.383233i
$872$		0			0
$873$	3.97004	−	1.28994i	0.134365	−	0.0436580i
$874$		0			0
$875$		−	14.6141i		−	0.494046i
$876$		0			0
$877$	−8.18625	+	5.94766i	−0.276430	+	0.200838i	−0.717359	−	0.696704i	$-0.754649\pi$
$877$	−8.18625	+	5.94766i	−0.276430	+	0.200838i	0.440929	+	0.897542i	$0.354649\pi$
$878$		0			0
$879$	−36.6279	−	26.6117i	−1.23543	−	0.897591i
$880$		0			0
$881$	14.0873	−	10.2350i	0.474612	−	0.344825i	−0.324624	−	0.945843i	$-0.605238\pi$
$881$	14.0873	−	10.2350i	0.474612	−	0.344825i	0.799236	+	0.601018i	$0.205238\pi$
$882$		0			0
$883$	−7.97108	−	10.9712i	−0.268248	−	0.369212i	0.653549	−	0.756884i	$-0.273279\pi$
$883$	−7.97108	−	10.9712i	−0.268248	−	0.369212i	−0.921797	+	0.387672i	$0.873279\pi$
$884$		0			0
$885$	12.6230	+	4.10147i	0.424319	+	0.137870i
$886$		0			0
$887$	48.1951	−	15.6595i	1.61823	−	0.525796i	0.646709	−	0.762737i	$-0.276145\pi$
$887$	48.1951	−	15.6595i	1.61823	−	0.525796i	0.971524	+	0.236941i	$0.0761449\pi$
$888$		0			0
$889$	−2.69828	+	3.71386i	−0.0904973	+	0.124559i
$890$		0			0
$891$	1.83093	+	0.594904i	0.0613383	+	0.0199300i
$892$		0			0
$893$	−5.37075			−0.179725
$894$		0			0
$895$	1.68850	+	2.32402i	0.0564403	+	0.0776834i
$896$		0			0
$897$	−1.75190	−	5.39180i	−0.0584943	−	0.180027i
$898$		0			0
$899$		−	22.9952i		−	0.766933i
$900$		0			0
$901$	−26.4179			−0.880109
$902$		0			0
$903$	2.20382			0.0733385
$904$		0			0
$905$			22.7754i			0.757081i
$906$		0			0
$907$	−2.86913	−	8.83028i	−0.0952680	−	0.293205i	0.892055	−	0.451926i	$-0.149263\pi$
$907$	−2.86913	−	8.83028i	−0.0952680	−	0.293205i	−0.987323	+	0.158721i	$0.949263\pi$
$908$		0			0
$909$	−12.6981	−	17.4775i	−0.421171	−	0.579692i
$910$		0			0
$911$	−26.9394			−0.892541			−0.446270	−	0.894898i	$-0.647248\pi$
$911$	−26.9394			−0.892541			−0.446270	+	0.894898i	$0.647248\pi$
$912$		0			0
$913$	2.43712	+	0.791867i	0.0806568	+	0.0262070i
$914$		0			0
$915$	−11.1477	+	15.3435i	−0.368531	+	0.507240i
$916$		0			0
$917$	6.80979	−	2.21263i	0.224879	−	0.0730676i
$918$		0			0
$919$	20.6956	+	6.72441i	0.682685	+	0.221818i	0.629770	−	0.776781i	$-0.283149\pi$
$919$	20.6956	+	6.72441i	0.682685	+	0.221818i	0.0529142	+	0.998599i	$0.483149\pi$
$920$		0			0
$921$	6.94392	+	9.55749i	0.228810	+	0.314930i
$922$		0			0
$923$	1.94244	−	1.41126i	0.0639361	−	0.0464523i
$924$		0			0
$925$	−28.0782	−	20.4000i	−0.923207	−	0.670749i
$926$		0			0
$927$	−12.7303	+	9.24912i	−0.418119	+	0.303781i
$928$		0			0
$929$		−	59.9519i		−	1.96696i	−0.181020	−	0.983479i	$-0.557940\pi$
$929$		−	59.9519i		−	1.96696i	0.181020	−	0.983479i	$-0.442060\pi$
$930$		0			0
$931$	0.386399	−	0.125549i	0.0126637	−	0.00411469i
$932$		0			0
$933$	−1.40214	+	4.31535i	−0.0459041	+	0.141278i
$934$		0			0
$935$	0.478350	−	1.47221i	0.0156437	−	0.0481464i
$936$		0			0
$937$	31.2518	−	43.0145i	1.02095	−	1.40522i	0.109419	−	0.993996i	$-0.465101\pi$
$937$	31.2518	−	43.0145i	1.02095	−	1.40522i	0.911534	−	0.411225i	$-0.134899\pi$
$938$		0			0
$939$	5.31040	+	16.3437i	0.173298	+	0.533358i
$940$		0			0
$941$	−36.6395	−	26.6201i	−1.19441	−	0.867791i	−0.200689	−	0.979655i	$-0.564318\pi$
$941$	−36.6395	−	26.6201i	−1.19441	−	0.867791i	−0.993724	+	0.111864i	$0.964318\pi$
$942$		0			0
$943$	4.24922	−	3.33028i	0.138374	−	0.108449i
$944$		0			0
$945$	−5.38399	−	3.91170i	−0.175141	−	0.127247i
$946$		0			0
$947$	−15.0742	−	46.3937i	−0.489847	−	1.50759i	−0.824836	−	0.565372i	$-0.808733\pi$
$947$	−15.0742	−	46.3937i	−0.489847	−	1.50759i	0.334989	−	0.942222i	$-0.391267\pi$
$948$		0			0
$949$	−22.9706	+	31.6163i	−0.745656	+	1.02631i
$950$		0			0
$951$	−11.5585	+	35.5734i	−0.374810	+	1.15355i
$952$		0			0
$953$	4.89053	−	15.0515i	0.158420	−	0.487566i	−0.840072	−	0.542476i	$-0.817487\pi$
$953$	4.89053	−	15.0515i	0.158420	−	0.487566i	0.998491	+	0.0549098i	$0.0174871\pi$
$954$		0			0
$955$	86.5294	−	28.1151i	2.80002	−	0.909783i
$956$		0			0
$957$		−	2.03066i		−	0.0656420i
$958$		0			0
$959$	−15.5206	+	11.2764i	−0.501187	+	0.364134i
$960$		0			0
$961$	7.65915	+	5.56470i	0.247070	+	0.179507i
$962$		0			0
$963$	−2.12203	+	1.54174i	−0.0683814	+	0.0496820i
$964$		0			0
$965$	−10.5792	−	14.5610i	−0.340555	−	0.468734i
$966$		0			0
$967$	10.7557	+	3.49472i	0.345878	+	0.112383i	0.476804	−	0.879009i	$-0.341795\pi$
$967$	10.7557	+	3.49472i	0.345878	+	0.112383i	−0.130926	+	0.991392i	$0.541795\pi$
$968$		0			0
$969$	2.04207	−	0.663509i	0.0656008	−	0.0213150i
$970$		0			0
$971$	2.56242	−	3.52687i	0.0822321	−	0.113183i	−0.765919	−	0.642937i	$-0.777716\pi$
$971$	2.56242	−	3.52687i	0.0822321	−	0.113183i	0.848151	+	0.529754i	$0.177716\pi$
$972$		0			0
$973$	16.5148	+	5.36599i	0.529441	+	0.172026i
$974$		0			0
$975$	59.9600			1.92026
$976$		0			0
$977$	7.57102	+	10.4206i	0.242218	+	0.333385i	0.912767	−	0.408481i	$-0.133941\pi$
$977$	7.57102	+	10.4206i	0.242218	+	0.333385i	−0.670549	+	0.741866i	$0.733941\pi$
$978$		0			0
$979$	0.528184	+	1.62558i	0.0168808	+	0.0519539i
$980$		0			0
$981$		−	40.8593i		−	1.30454i
$982$		0			0
$983$	43.5071			1.38766			0.693830	−	0.720139i	$-0.255922\pi$
$983$	43.5071			1.38766			0.693830	+	0.720139i	$0.255922\pi$
$984$		0			0
$985$	51.3403			1.63584
$986$		0			0
$987$			30.1998i			0.961272i
$988$		0			0
$989$	−0.251339	−	0.773542i	−0.00799212	−	0.0245972i
$990$		0			0
$991$	35.1227	+	48.3422i	1.11571	+	1.53564i	0.812727	+	0.582645i	$0.197982\pi$
$991$	35.1227	+	48.3422i	1.11571	+	1.53564i	0.302982	+	0.952996i	$0.402018\pi$
$992$		0			0
$993$	−54.2172			−1.72053
$994$		0			0
$995$	44.2432	+	14.3755i	1.40260	+	0.455734i
$996$		0			0
$997$	26.1483	−	35.9900i	0.828125	−	1.13982i	−0.160144	−	0.987094i	$-0.551196\pi$
$997$	26.1483	−	35.9900i	0.828125	−	1.13982i	0.988269	−	0.152723i	$-0.0488041\pi$
$998$		0			0
$999$	−6.60314	+	2.14549i	−0.208914	+	0.0678803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.113.17	✓	80
41.4	even	10	inner	1148.2.ba.a.701.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.17	✓	80	1.1	even	1	trivial
1148.2.ba.a.701.4	yes	80	41.4	even	10	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+2.28455i q^{3} +(1.15282 + 3.54801i) q^{5} +(0.587785 + 0.809017i) q^{7} -2.21915 q^{9} +O(q^{10})\)	\(q+2.28455i q^{3} +(1.15282 + 3.54801i) q^{5} +(0.587785 + 0.809017i) q^{7} -2.21915 q^{9} +(-0.170591 - 0.0554285i) q^{11} +(-1.72999 + 2.38113i) q^{13} +(-8.10559 + 2.63367i) q^{15} +(2.20009 + 0.714853i) q^{17} +(-0.238808 - 0.328691i) q^{19} +(-1.84824 + 1.34282i) q^{21} +(0.682118 + 0.495588i) q^{23} +(-7.21429 + 5.24149i) q^{25} +1.78389i q^{27} +(4.71296 - 1.53133i) q^{29} +(1.43394 - 4.41323i) q^{31} +(0.126629 - 0.389724i) q^{33} +(-2.19279 + 3.01812i) q^{35} +(1.20270 + 3.70154i) q^{37} +(-5.43980 - 3.95225i) q^{39} +(1.75557 - 6.15776i) q^{41} +(-0.780429 - 0.567015i) q^{43} +(-2.55827 - 7.87356i) q^{45} +(7.77005 - 10.6946i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-1.63312 + 5.02621i) q^{51} +(-10.8610 + 3.52896i) q^{53} -0.669158i q^{55} +(0.750909 - 0.545568i) q^{57} +(-1.25990 - 0.915373i) q^{59} +(1.80030 - 1.30800i) q^{61} +(-1.30438 - 1.79533i) q^{63} +(-10.4426 - 3.39302i) q^{65} +(3.84279 - 1.24860i) q^{67} +(-1.13219 + 1.55833i) q^{69} +(-0.775836 - 0.252084i) q^{71} +13.2778 q^{73} +(-11.9744 - 16.4814i) q^{75} +(-0.0554285 - 0.170591i) q^{77} -8.02141i q^{79} -10.7328 q^{81} -14.2863 q^{83} +8.63004i q^{85} +(3.49840 + 10.7670i) q^{87} +(-5.60107 - 7.70921i) q^{89} -2.94324 q^{91} +(10.0822 + 3.27591i) q^{93} +(0.890896 - 1.22621i) q^{95} +(-1.78899 + 0.581279i) q^{97} +(0.378567 + 0.123004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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