LMFDB - Embedded newform 722.2.e.b.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			415.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	722.415
Dual form			722.2.e.b.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-0.326352 + 0.118782i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.347296 - 1.96962i) q^{5} +(-0.326352 - 0.118782i) q^{6} +(0.879385 + 1.52314i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.20574 + 1.85083i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-0.326352 + 0.118782i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.347296 - 1.96962i) q^{5} +(-0.326352 - 0.118782i) q^{6} +(0.879385 + 1.52314i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.20574 + 1.85083i) q^{9} +(1.53209 - 1.28558i) q^{10} +(-2.11334 + 3.66041i) q^{11} +(-0.173648 - 0.300767i) q^{12} +(-1.00000 - 0.363970i) q^{13} +(-0.305407 + 1.73205i) q^{14} +(0.120615 + 0.684040i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(5.46064 + 4.58202i) q^{17} -2.87939 q^{18} +2.00000 q^{20} +(-0.467911 - 0.392624i) q^{21} +(-3.97178 + 1.44561i) q^{22} +(0.652704 + 3.70167i) q^{23} +(0.0603074 - 0.342020i) q^{24} +(0.939693 + 0.342020i) q^{25} +(-0.532089 - 0.921605i) q^{26} +(1.02094 - 1.76833i) q^{27} +(-1.34730 + 1.13052i) q^{28} +(4.87939 - 4.09429i) q^{29} +(-0.347296 + 0.601535i) q^{30} +(4.41147 + 7.64090i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.254900 - 1.44561i) q^{33} +(1.23783 + 7.02006i) q^{34} +(3.30541 - 1.20307i) q^{35} +(-2.20574 - 1.85083i) q^{36} -6.45336 q^{37} +0.369585 q^{39} +(1.53209 + 1.28558i) q^{40} +(-1.76604 + 0.642788i) q^{41} +(-0.106067 - 0.601535i) q^{42} +(0.641559 - 3.63846i) q^{43} +(-3.97178 - 1.44561i) q^{44} +(2.87939 + 4.98724i) q^{45} +(-1.87939 + 3.25519i) q^{46} +(-2.81521 + 2.36224i) q^{47} +(0.266044 - 0.223238i) q^{48} +(1.95336 - 3.38332i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.32635 - 0.846723i) q^{51} +(0.184793 - 1.04801i) q^{52} +(-1.71688 - 9.73692i) q^{53} +(1.91875 - 0.698367i) q^{54} +(6.47565 + 5.43372i) q^{55} -1.75877 q^{56} +6.36959 q^{58} +(-5.58512 - 4.68647i) q^{59} +(-0.652704 + 0.237565i) q^{60} +(0.921274 + 5.22481i) q^{61} +(-1.53209 + 8.68891i) q^{62} +(-4.75877 - 1.73205i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.06418 + 1.84321i) q^{65} +(1.12449 - 0.943555i) q^{66} +(-8.91534 + 7.48086i) q^{67} +(-3.56418 + 6.17334i) q^{68} +(-0.652704 - 1.13052i) q^{69} +(3.30541 + 1.20307i) q^{70} +(0.490200 - 2.78006i) q^{71} +(-0.500000 - 2.83564i) q^{72} +(-0.745100 + 0.271194i) q^{73} +(-4.94356 - 4.14814i) q^{74} -0.347296 q^{75} -7.43376 q^{77} +(0.283119 + 0.237565i) q^{78} +(6.29086 - 2.28969i) q^{79} +(0.347296 + 1.96962i) q^{80} +(1.37686 - 7.80856i) q^{81} +(-1.76604 - 0.642788i) q^{82} +(-0.754900 - 1.30753i) q^{83} +(0.305407 - 0.528981i) q^{84} +(10.9213 - 9.16404i) q^{85} +(2.83022 - 2.37484i) q^{86} +(-1.10607 + 1.91576i) q^{87} +(-2.11334 - 3.66041i) q^{88} +(-11.1887 - 4.07234i) q^{89} +(-1.00000 + 5.67128i) q^{90} +(-0.325008 - 1.84321i) q^{91} +(-3.53209 + 1.28558i) q^{92} +(-2.34730 - 1.96962i) q^{93} -3.67499 q^{94} +0.347296 q^{96} +(1.43969 + 1.20805i) q^{97} +(3.67112 - 1.33618i) q^{98} +(-2.11334 - 11.9854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 3 q^{6} - 6 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 - 3 * q^6 - 6 * q^7 - 3 * q^8 - 3 * q^9	$ 6 q - 3 q^{3} - 3 q^{6} - 6 q^{7} - 3 q^{8} - 3 q^{9} - 6 q^{11} - 6 q^{13} - 6 q^{14} + 12 q^{15} + 24 q^{17} - 6 q^{18} + 12 q^{20} - 12 q^{21} - 9 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{26} + 3 q^{27} - 6 q^{28} + 18 q^{29} + 6 q^{31} + 3 q^{33} - 12 q^{34} + 24 q^{35} - 3 q^{36} - 12 q^{37} - 12 q^{39} - 6 q^{41} + 24 q^{42} + 12 q^{43} - 9 q^{44} + 6 q^{45} - 24 q^{47} - 3 q^{48} - 15 q^{49} + 3 q^{50} - 15 q^{51} - 6 q^{52} + 6 q^{53} + 9 q^{54} + 12 q^{56} + 24 q^{58} - 12 q^{59} - 6 q^{60} - 12 q^{61} - 6 q^{63} - 3 q^{64} + 12 q^{65} - 6 q^{66} - 9 q^{67} - 3 q^{68} - 6 q^{69} + 24 q^{70} - 3 q^{72} - 3 q^{73} - 12 q^{77} + 18 q^{78} + 6 q^{79} + 12 q^{81} - 6 q^{82} - 6 q^{83} + 6 q^{84} + 48 q^{85} - 6 q^{86} + 18 q^{87} - 6 q^{88} - 36 q^{89} - 6 q^{90} - 12 q^{91} - 12 q^{92} - 12 q^{93} - 12 q^{94} + 3 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 - 3 * q^6 - 6 * q^7 - 3 * q^8 - 3 * q^9 - 6 * q^11 - 6 * q^13 - 6 * q^14 + 12 * q^15 + 24 * q^17 - 6 * q^18 + 12 * q^20 - 12 * q^21 - 9 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^26 + 3 * q^27 - 6 * q^28 + 18 * q^29 + 6 * q^31 + 3 * q^33 - 12 * q^34 + 24 * q^35 - 3 * q^36 - 12 * q^37 - 12 * q^39 - 6 * q^41 + 24 * q^42 + 12 * q^43 - 9 * q^44 + 6 * q^45 - 24 * q^47 - 3 * q^48 - 15 * q^49 + 3 * q^50 - 15 * q^51 - 6 * q^52 + 6 * q^53 + 9 * q^54 + 12 * q^56 + 24 * q^58 - 12 * q^59 - 6 * q^60 - 12 * q^61 - 6 * q^63 - 3 * q^64 + 12 * q^65 - 6 * q^66 - 9 * q^67 - 3 * q^68 - 6 * q^69 + 24 * q^70 - 3 * q^72 - 3 * q^73 - 12 * q^77 + 18 * q^78 + 6 * q^79 + 12 * q^81 - 6 * q^82 - 6 * q^83 + 6 * q^84 + 48 * q^85 - 6 * q^86 + 18 * q^87 - 6 * q^88 - 36 * q^89 - 6 * q^90 - 12 * q^91 - 12 * q^92 - 12 * q^93 - 12 * q^94 + 3 * q^97 + 36 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−0.326352	+	0.118782i	−0.188419	+	0.0685790i	−0.434507	−	0.900669i	$-0.643077\pi$
$3$	−0.326352	+	0.118782i	−0.188419	+	0.0685790i	0.246087	+	0.969248i	$0.420855\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.347296	−	1.96962i	0.155316	−	0.880839i	−0.803181	−	0.595735i	$-0.796861\pi$
$5$	0.347296	−	1.96962i	0.155316	−	0.880839i	0.958497	−	0.285104i	$-0.0920281\pi$
$6$	−0.326352	−	0.118782i	−0.133233	−	0.0484927i
$7$	0.879385	+	1.52314i	0.332376	+	0.575693i	0.982977	−	0.183727i	$-0.0588162\pi$
$7$	0.879385	+	1.52314i	0.332376	+	0.575693i	−0.650601	+	0.759420i	$0.725483\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.20574	+	1.85083i	−0.735246	+	0.616944i
$10$	1.53209	−	1.28558i	0.484489	−	0.406535i
$11$	−2.11334	+	3.66041i	−0.637196	+	1.10366i	0.348849	+	0.937179i	$0.386573\pi$
$11$	−2.11334	+	3.66041i	−0.637196	+	1.10366i	−0.986045	+	0.166477i	$0.946761\pi$
$12$	−0.173648	−	0.300767i	−0.0501279	−	0.0868241i
$13$	−1.00000	−	0.363970i	−0.277350	−	0.100947i	0.199600	−	0.979877i	$-0.436036\pi$
$13$	−1.00000	−	0.363970i	−0.277350	−	0.100947i	−0.476950	+	0.878930i	$0.658258\pi$
$14$	−0.305407	+	1.73205i	−0.0816235	+	0.462910i
$15$	0.120615	+	0.684040i	0.0311426	+	0.176618i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	5.46064	+	4.58202i	1.32440	+	1.11130i	0.985352	+	0.170533i	$0.0545491\pi$
$17$	5.46064	+	4.58202i	1.32440	+	1.11130i	0.339047	+	0.940769i	$0.389895\pi$
$18$	−2.87939			−0.678678
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	−0.467911	−	0.392624i	−0.102107	−	0.0856776i
$22$	−3.97178	+	1.44561i	−0.846787	+	0.308205i
$23$	0.652704	+	3.70167i	0.136098	+	0.771851i	0.974089	+	0.226166i	$0.0726192\pi$
$23$	0.652704	+	3.70167i	0.136098	+	0.771851i	−0.837991	+	0.545685i	$0.816270\pi$
$24$	0.0603074	−	0.342020i	0.0123102	−	0.0698146i
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	−0.532089	−	0.921605i	−0.104351	−	0.180742i
$27$	1.02094	−	1.76833i	0.196481	−	0.340315i
$28$	−1.34730	+	1.13052i	−0.254615	+	0.213647i
$29$	4.87939	−	4.09429i	0.906079	−	0.760291i	−0.0652899	−	0.997866i	$-0.520797\pi$
$29$	4.87939	−	4.09429i	0.906079	−	0.760291i	0.971369	+	0.237576i	$0.0763528\pi$
$30$	−0.347296	+	0.601535i	−0.0634073	+	0.109825i
$31$	4.41147	+	7.64090i	0.792324	+	1.37235i	0.924524	+	0.381123i	$0.124462\pi$
$31$	4.41147	+	7.64090i	0.792324	+	1.37235i	−0.132200	+	0.991223i	$0.542204\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	0.254900	−	1.44561i	0.0443724	−	0.251648i
$34$	1.23783	+	7.02006i	0.212285	+	1.20393i
$35$	3.30541	−	1.20307i	0.558716	−	0.203356i
$36$	−2.20574	−	1.85083i	−0.367623	−	0.308472i
$37$	−6.45336			−1.06093			−0.530463	−	0.847708i	$-0.677982\pi$
$37$	−6.45336			−1.06093			−0.530463	+	0.847708i	$0.677982\pi$
$38$		0			0
$39$	0.369585			0.0591810
$40$	1.53209	+	1.28558i	0.242245	+	0.203267i
$41$	−1.76604	+	0.642788i	−0.275810	+	0.100387i	−0.476222	−	0.879325i	$-0.657994\pi$
$41$	−1.76604	+	0.642788i	−0.275810	+	0.100387i	0.200412	+	0.979712i	$0.435772\pi$
$42$	−0.106067	−	0.601535i	−0.0163665	−	0.0928189i
$43$	0.641559	−	3.63846i	0.0978369	−	0.554860i	−0.896004	−	0.444046i	$-0.853543\pi$
$43$	0.641559	−	3.63846i	0.0978369	−	0.554860i	0.993841	−	0.110815i	$-0.0353461\pi$
$44$	−3.97178	−	1.44561i	−0.598769	−	0.217934i
$45$	2.87939	+	4.98724i	0.429233	+	0.743454i
$46$	−1.87939	+	3.25519i	−0.277100	+	0.479952i
$47$	−2.81521	+	2.36224i	−0.410640	+	0.344568i	−0.824589	−	0.565732i	$-0.808594\pi$
$47$	−2.81521	+	2.36224i	−0.410640	+	0.344568i	0.413949	+	0.910300i	$0.364149\pi$
$48$	0.266044	−	0.223238i	0.0384002	−	0.0322216i
$49$	1.95336	−	3.38332i	0.279052	−	0.483332i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−2.32635	−	0.846723i	−0.325754	−	0.118565i
$52$	0.184793	−	1.04801i	0.0256261	−	0.145333i
$53$	−1.71688	−	9.73692i	−0.235832	−	1.33747i	−0.840855	−	0.541261i	$-0.817947\pi$
$53$	−1.71688	−	9.73692i	−0.235832	−	1.33747i	0.605023	−	0.796208i	$-0.293164\pi$
$54$	1.91875	−	0.698367i	0.261109	−	0.0950357i
$55$	6.47565	+	5.43372i	0.873177	+	0.732682i
$56$	−1.75877			−0.235026
$57$		0			0
$58$	6.36959			0.836367
$59$	−5.58512	−	4.68647i	−0.727121	−	0.610127i	0.202224	−	0.979339i	$-0.435183\pi$
$59$	−5.58512	−	4.68647i	−0.727121	−	0.610127i	−0.929345	+	0.369212i	$0.879628\pi$
$60$	−0.652704	+	0.237565i	−0.0842637	+	0.0306695i
$61$	0.921274	+	5.22481i	0.117957	+	0.668968i	0.985244	+	0.171158i	$0.0547510\pi$
$61$	0.921274	+	5.22481i	0.117957	+	0.668968i	−0.867286	+	0.497809i	$0.834138\pi$
$62$	−1.53209	+	8.68891i	−0.194575	+	1.10349i
$63$	−4.75877	−	1.73205i	−0.599549	−	0.218218i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.06418	+	1.84321i	−0.131995	+	0.228622i
$66$	1.12449	−	0.943555i	0.138415	−	0.116144i
$67$	−8.91534	+	7.48086i	−1.08918	+	0.913933i	−0.996651	−	0.0817769i	$-0.973940\pi$
$67$	−8.91534	+	7.48086i	−1.08918	+	0.913933i	−0.0925320	+	0.995710i	$0.529496\pi$
$68$	−3.56418	+	6.17334i	−0.432220	+	0.748627i
$69$	−0.652704	−	1.13052i	−0.0785763	−	0.136098i
$70$	3.30541	+	1.20307i	0.395072	+	0.143794i
$71$	0.490200	−	2.78006i	0.0581760	−	0.329933i	−0.941805	−	0.336161i	$-0.890871\pi$
$71$	0.490200	−	2.78006i	0.0581760	−	0.329933i	0.999981	+	0.00622827i	$0.00198253\pi$
$72$	−0.500000	−	2.83564i	−0.0589256	−	0.334183i
$73$	−0.745100	+	0.271194i	−0.0872073	+	0.0317409i	−0.385255	−	0.922810i	$-0.625887\pi$
$73$	−0.745100	+	0.271194i	−0.0872073	+	0.0317409i	0.298048	+	0.954551i	$0.403664\pi$
$74$	−4.94356	−	4.14814i	−0.574678	−	0.482212i
$75$	−0.347296			−0.0401023
$76$		0			0
$77$	−7.43376			−0.847156
$78$	0.283119	+	0.237565i	0.0320569	+	0.0268989i
$79$	6.29086	−	2.28969i	0.707777	−	0.257610i	0.0370493	−	0.999313i	$-0.488204\pi$
$79$	6.29086	−	2.28969i	0.707777	−	0.257610i	0.670728	+	0.741704i	$0.265982\pi$
$80$	0.347296	+	1.96962i	0.0388289	+	0.220210i
$81$	1.37686	−	7.80856i	0.152984	−	0.867617i
$82$	−1.76604	−	0.642788i	−0.195027	−	0.0709840i
$83$	−0.754900	−	1.30753i	−0.0828610	−	0.143520i	0.821617	−	0.570040i	$-0.193072\pi$
$83$	−0.754900	−	1.30753i	−0.0828610	−	0.143520i	−0.904478	+	0.426521i	$0.859739\pi$
$84$	0.305407	−	0.528981i	0.0333227	−	0.0577166i
$85$	10.9213	−	9.16404i	1.18458	−	0.993979i
$86$	2.83022	−	2.37484i	0.305191	−	0.256085i
$87$	−1.10607	+	1.91576i	−0.118583	+	0.205391i
$88$	−2.11334	−	3.66041i	−0.225283	−	0.390201i
$89$	−11.1887	−	4.07234i	−1.18600	−	0.431667i	−0.327680	−	0.944789i	$-0.606267\pi$
$89$	−11.1887	−	4.07234i	−1.18600	−	0.431667i	−0.858316	+	0.513122i	$0.828489\pi$
$90$	−1.00000	+	5.67128i	−0.105409	+	0.597806i
$91$	−0.325008	−	1.84321i	−0.0340701	−	0.193221i
$92$	−3.53209	+	1.28558i	−0.368246	+	0.134030i
$93$	−2.34730	−	1.96962i	−0.243403	−	0.204240i
$94$	−3.67499			−0.379047
$95$		0			0
$96$	0.347296			0.0354458
$97$	1.43969	+	1.20805i	0.146179	+	0.122658i	0.712944	−	0.701220i	$-0.247361\pi$
$97$	1.43969	+	1.20805i	0.146179	+	0.122658i	−0.566766	+	0.823879i	$0.691806\pi$
$98$	3.67112	−	1.33618i	0.370839	−	0.134974i
$99$	−2.11334	−	11.9854i	−0.212399	−	1.20457i
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	2.30541	+	0.839100i	0.229397	+	0.0834935i	0.454161	−	0.890920i	$-0.349939\pi$
$101$	2.30541	+	0.839100i	0.229397	+	0.0834935i	−0.224764	+	0.974413i	$0.572161\pi$
$102$	−1.23783	−	2.14398i	−0.122563	−	0.212285i
$103$	3.71688	−	6.43783i	0.366235	−	0.634338i	−0.622738	−	0.782430i	$-0.713980\pi$
$103$	3.71688	−	6.43783i	0.366235	−	0.634338i	0.988974	+	0.148092i	$0.0473132\pi$
$104$	0.815207	−	0.684040i	0.0799377	−	0.0670757i
$105$	−0.935822	+	0.785248i	−0.0913269	+	0.0766324i
$106$	4.94356	−	8.56250i	0.480161	−	0.831664i
$107$	0.0885259	+	0.153331i	0.00855812	+	0.0148231i	0.870273	−	0.492570i	$-0.163942\pi$
$107$	0.0885259	+	0.153331i	0.00855812	+	0.0148231i	−0.861715	+	0.507393i	$0.830609\pi$
$108$	1.91875	+	0.698367i	0.184632	+	0.0672004i
$109$	0.736482	−	4.17680i	0.0705422	−	0.400064i	−0.929008	−	0.370061i	$-0.879337\pi$
$109$	0.736482	−	4.17680i	0.0705422	−	0.400064i	0.999550	−	0.0300039i	$-0.00955197\pi$
$110$	1.46791	+	8.32494i	0.139960	+	0.793752i
$111$	2.10607	−	0.766546i	0.199899	−	0.0727573i
$112$	−1.34730	−	1.13052i	−0.127308	−	0.106824i
$113$	10.4388			0.982001			0.491001	−	0.871159i	$-0.336631\pi$
$113$	10.4388			0.982001			0.491001	+	0.871159i	$0.336631\pi$
$114$		0			0
$115$	7.51754			0.701014
$116$	4.87939	+	4.09429i	0.453040	+	0.380145i
$117$	2.87939	−	1.04801i	0.266199	−	0.0968886i
$118$	−1.26604	−	7.18009i	−0.116549	−	0.660981i
$119$	−2.17705	+	12.3467i	−0.199570	+	1.13182i
$120$	−0.652704	−	0.237565i	−0.0595834	−	0.0216866i
$121$	−3.43242	−	5.94512i	−0.312038	−	0.540466i
$122$	−2.65270	+	4.59462i	−0.240165	+	0.415977i
$123$	0.500000	−	0.419550i	0.0450835	−	0.0378295i
$124$	−6.75877	+	5.67128i	−0.606956	+	0.509296i
$125$	6.00000	−	10.3923i	0.536656	−	0.929516i
$126$	−2.53209	−	4.38571i	−0.225576	−	0.390710i
$127$	20.6878	+	7.52974i	1.83574	+	0.668156i	0.991150	+	0.132750i	$0.0423807\pi$
$127$	20.6878	+	7.52974i	1.83574	+	0.668156i	0.844595	+	0.535406i	$0.179842\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	0.222811	+	1.26363i	0.0196174	+	0.111256i
$130$	−2.00000	+	0.727940i	−0.175412	+	0.0638446i
$131$	−5.86231	−	4.91906i	−0.512192	−	0.429781i	0.349707	−	0.936859i	$-0.386281\pi$
$131$	−5.86231	−	4.91906i	−0.512192	−	0.429781i	−0.861900	+	0.507078i	$0.830725\pi$
$132$	1.46791			0.127765
$133$		0			0
$134$	−11.6382			−1.00538
$135$	−3.12836	−	2.62500i	−0.269246	−	0.225924i
$136$	−6.69846	+	2.43804i	−0.574388	+	0.209060i
$137$	−0.996130	−	5.64933i	−0.0851051	−	0.482655i	−0.997334	−	0.0729738i	$-0.976751\pi$
$137$	−0.996130	−	5.64933i	−0.0851051	−	0.482655i	0.912229	−	0.409681i	$-0.134360\pi$
$138$	0.226682	−	1.28558i	0.0192964	−	0.109435i
$139$	18.2271	+	6.63414i	1.54601	+	0.562700i	0.967477	−	0.252961i	$-0.0814043\pi$
$139$	18.2271	+	6.63414i	1.54601	+	0.562700i	0.578530	+	0.815661i	$0.303627\pi$
$140$	1.75877	+	3.04628i	0.148643	+	0.257458i
$141$	0.638156	−	1.10532i	0.0537424	−	0.0930846i
$142$	2.16250	−	1.81456i	0.181473	−	0.152274i
$143$	3.44562	−	2.89122i	0.288137	−	0.241776i
$144$	1.43969	−	2.49362i	0.119974	−	0.207802i
$145$	−6.36959	−	11.0324i	−0.528965	−	0.916195i
$146$	−0.745100	−	0.271194i	−0.0616649	−	0.0224442i
$147$	−0.235604	+	1.33618i	−0.0194323	+	0.110206i
$148$	−1.12061	−	6.35532i	−0.0921140	−	0.522404i
$149$	4.86484	−	1.77066i	0.398543	−	0.145058i	−0.134970	−	0.990850i	$-0.543094\pi$
$149$	4.86484	−	1.77066i	0.398543	−	0.145058i	0.533513	+	0.845792i	$0.320872\pi$
$150$	−0.266044	−	0.223238i	−0.0217224	−	0.0182273i
$151$	22.1830			1.80523			0.902615	−	0.430449i	$-0.141645\pi$
$151$	22.1830			1.80523			0.902615	+	0.430449i	$0.141645\pi$
$152$		0			0
$153$	−20.5253			−1.65937
$154$	−5.69459	−	4.77833i	−0.458883	−	0.385049i
$155$	16.5817	−	6.03525i	1.33188	−	0.484763i
$156$	0.0641778	+	0.363970i	0.00513833	+	0.0291409i
$157$	−0.490200	+	2.78006i	−0.0391222	+	0.221873i	−0.998101	−	0.0616064i	$-0.980378\pi$
$157$	−0.490200	+	2.78006i	−0.0391222	+	0.221873i	0.958978	+	0.283479i	$0.0914888\pi$
$158$	6.29086	+	2.28969i	0.500474	+	0.182158i
$159$	1.71688	+	2.97373i	0.136158	+	0.235832i
$160$	−1.00000	+	1.73205i	−0.0790569	+	0.136931i
$161$	−5.06418	+	4.24935i	−0.399113	+	0.334896i
$162$	6.07398	−	5.09667i	0.477217	−	0.400432i
$163$	−1.10947	+	1.92166i	−0.0869004	+	0.150516i	−0.906199	−	0.422851i	$-0.861030\pi$
$163$	−1.10947	+	1.92166i	−0.0869004	+	0.150516i	0.819299	+	0.573366i	$0.194363\pi$
$164$	−0.939693	−	1.62760i	−0.0733777	−	0.127094i
$165$	−2.75877	−	1.00411i	−0.214770	−	0.0781699i
$166$	0.262174	−	1.48686i	0.0203487	−	0.115403i
$167$	0.680045	+	3.85673i	0.0526234	+	0.298442i	0.999749	−	0.0224220i	$-0.00713774\pi$
$167$	0.680045	+	3.85673i	0.0526234	+	0.298442i	−0.947125	+	0.320864i	$0.896027\pi$
$168$	0.573978	−	0.208911i	0.0442834	−	0.0161178i
$169$	−9.09105	−	7.62830i	−0.699312	−	0.586792i
$170$	14.2567			1.09344
$171$		0			0
$172$	3.69459			0.281710
$173$	5.78106	+	4.85088i	0.439526	+	0.368806i	0.835532	−	0.549442i	$-0.185160\pi$
$173$	5.78106	+	4.85088i	0.439526	+	0.368806i	−0.396006	+	0.918248i	$0.629604\pi$
$174$	−2.07873	+	0.756594i	−0.157588	+	0.0573573i
$175$	0.305407	+	1.73205i	0.0230866	+	0.130931i
$176$	0.733956	−	4.16247i	0.0553240	−	0.313758i
$177$	2.37939	+	0.866025i	0.178846	+	0.0650945i
$178$	−5.95336	−	10.3115i	−0.446223	−	0.772882i
$179$	5.49407	−	9.51601i	0.410646	−	0.711260i	−0.584314	−	0.811527i	$-0.698637\pi$
$179$	5.49407	−	9.51601i	0.410646	−	0.711260i	0.994961	+	0.100267i	$0.0319698\pi$
$180$	−4.41147	+	3.70167i	−0.328812	+	0.275906i
$181$	−11.5175	+	9.66436i	−0.856092	+	0.718347i	−0.961122	−	0.276122i	$-0.910950\pi$
$181$	−11.5175	+	9.66436i	−0.856092	+	0.718347i	0.105030	+	0.994469i	$0.466506\pi$
$182$	0.935822	−	1.62089i	0.0693678	−	0.120148i
$183$	−0.921274	−	1.59569i	−0.0681026	−	0.117957i
$184$	−3.53209	−	1.28558i	−0.260389	−	0.0947739i
$185$	−2.24123	+	12.7106i	−0.164778	+	0.934505i
$186$	−0.532089	−	3.01763i	−0.0390147	−	0.221263i
$187$	−28.3123	+	10.3048i	−2.07040	+	0.753563i
$188$	−2.81521	−	2.36224i	−0.205320	−	0.172284i
$189$	3.59121			0.261222
$190$		0			0
$191$	4.53714			0.328296			0.164148	−	0.986436i	$-0.447513\pi$
$191$	4.53714			0.328296			0.164148	+	0.986436i	$0.447513\pi$
$192$	0.266044	+	0.223238i	0.0192001	+	0.0161108i
$193$	−20.6694	+	7.52303i	−1.48781	+	0.541520i	−0.952873	−	0.303370i	$-0.901888\pi$
$193$	−20.6694	+	7.52303i	−1.48781	+	0.541520i	−0.534941	+	0.844890i	$0.679666\pi$
$194$	0.326352	+	1.85083i	0.0234307	+	0.132882i
$195$	0.128356	−	0.727940i	0.00919173	−	0.0521289i
$196$	3.67112	+	1.33618i	0.262223	+	0.0954414i
$197$	−7.96585	−	13.7973i	−0.567543	−	0.983014i	−0.996808	−	0.0798353i	$-0.974561\pi$
$197$	−7.96585	−	13.7973i	−0.567543	−	0.983014i	0.429265	−	0.903179i	$-0.358773\pi$
$198$	6.08512	−	10.5397i	0.432451	−	0.749027i
$199$	−2.50980	+	2.10597i	−0.177915	+	0.149288i	−0.727396	−	0.686218i	$-0.759270\pi$
$199$	−2.50980	+	2.10597i	−0.177915	+	0.149288i	0.549481	+	0.835506i	$0.314825\pi$
$200$	−0.766044	+	0.642788i	−0.0541675	+	0.0454519i
$201$	2.02094	−	3.50038i	0.142546	−	0.246898i
$202$	1.22668	+	2.12467i	0.0863090	+	0.149492i
$203$	10.5270	+	3.83153i	0.738853	+	0.268921i
$204$	0.429892	−	2.43804i	0.0300985	−	0.170697i
$205$	0.652704	+	3.70167i	0.0455868	+	0.258536i
$206$	6.98545	−	2.54250i	0.486700	−	0.177144i
$207$	−8.29086	−	6.95686i	−0.576255	−	0.483535i
$208$	1.06418			0.0737875
$209$		0			0
$210$	−1.22163			−0.0843004
$211$	8.78564	+	7.37203i	0.604829	+	0.507512i	0.892994	−	0.450069i	$-0.148601\pi$
$211$	8.78564	+	7.37203i	0.604829	+	0.507512i	−0.288165	+	0.957581i	$0.593045\pi$
$212$	9.29086	−	3.38160i	0.638099	−	0.232249i
$213$	0.170245	+	0.965505i	0.0116650	+	0.0661553i
$214$	−0.0307447	+	0.174362i	−0.00210167	+	0.0119191i
$215$	−6.94356	−	2.52725i	−0.473547	−	0.172357i
$216$	1.02094	+	1.76833i	0.0694665	+	0.120319i
$217$	−7.75877	+	13.4386i	−0.526700	+	0.912271i
$218$	3.24897	−	2.72621i	0.220048	−	0.184642i
$219$	0.210952	−	0.177009i	0.0142548	−	0.0119612i
$220$	−4.22668	+	7.32083i	−0.284963	+	0.493570i
$221$	−3.79292	−	6.56953i	−0.255139	−	0.441914i
$222$	2.10607	+	0.766546i	0.141350	+	0.0514472i
$223$	1.94356	−	11.0225i	0.130151	−	0.738121i	−0.847964	−	0.530054i	$-0.822172\pi$
$223$	1.94356	−	11.0225i	0.130151	−	0.738121i	0.978115	−	0.208067i	$-0.0667172\pi$
$224$	−0.305407	−	1.73205i	−0.0204059	−	0.115728i
$225$	−2.70574	+	0.984808i	−0.180382	+	0.0656539i
$226$	7.99660	+	6.70994i	0.531926	+	0.446339i
$227$	−3.39693			−0.225462			−0.112731	−	0.993626i	$-0.535960\pi$
$227$	−3.39693			−0.225462			−0.112731	+	0.993626i	$0.535960\pi$
$228$		0			0
$229$	4.25671			0.281291			0.140646	−	0.990060i	$-0.455082\pi$
$229$	4.25671			0.281291			0.140646	+	0.990060i	$0.455082\pi$
$230$	5.75877	+	4.83218i	0.379722	+	0.318625i
$231$	2.42602	−	0.883000i	0.159621	−	0.0580971i
$232$	1.10607	+	6.27282i	0.0726168	+	0.411831i
$233$	1.15358	−	6.54228i	0.0755736	−	0.428599i	−0.923422	−	0.383787i	$-0.874620\pi$
$233$	1.15358	−	6.54228i	0.0755736	−	0.428599i	0.998995	−	0.0448126i	$-0.0142691\pi$
$234$	2.87939	+	1.04801i	0.188231	+	0.0685106i
$235$	3.67499	+	6.36527i	0.239730	+	0.415225i
$236$	3.64543	−	6.31407i	0.237297	−	0.411011i
$237$	−1.78106	+	1.49449i	−0.115692	+	0.0970773i
$238$	−9.60401	+	8.05872i	−0.622535	+	0.522369i
$239$	−8.00774	+	13.8698i	−0.517978	+	0.897164i	0.481804	+	0.876279i	$0.339982\pi$
$239$	−8.00774	+	13.8698i	−0.517978	+	0.897164i	−0.999782	+	0.0208848i	$0.993352\pi$
$240$	−0.347296	−	0.601535i	−0.0224179	−	0.0388289i
$241$	8.08512	+	2.94274i	0.520809	+	0.189559i	0.589030	−	0.808111i	$-0.299510\pi$
$241$	8.08512	+	2.94274i	0.520809	+	0.189559i	−0.0682211	+	0.997670i	$0.521732\pi$
$242$	1.19207	−	6.76055i	0.0766289	−	0.434584i
$243$	1.54189	+	8.74449i	0.0989122	+	0.560959i
$244$	−4.98545	+	1.81456i	−0.319161	+	0.116165i
$245$	−5.98545	−	5.02239i	−0.382397	−	0.320869i
$246$	0.652704			0.0416149
$247$		0			0
$248$	−8.82295			−0.560258
$249$	0.401674	+	0.337044i	0.0254551	+	0.0213593i
$250$	11.2763	−	4.10424i	0.713177	−	0.259575i
$251$	−3.45723	−	19.6069i	−0.218219	−	1.23758i	−0.875233	−	0.483701i	$-0.839292\pi$
$251$	−3.45723	−	19.6069i	−0.218219	−	1.23758i	0.657014	−	0.753878i	$-0.271819\pi$
$252$	0.879385	−	4.98724i	0.0553961	−	0.314167i
$253$	−14.9290	−	5.43372i	−0.938579	−	0.341615i
$254$	11.0077	+	19.0660i	0.690687	+	1.19631i
$255$	−2.47565	+	4.28795i	−0.155031	+	0.268522i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	20.2369	−	16.9808i	1.26235	−	1.05923i	0.266918	−	0.963719i	$-0.413995\pi$
$257$	20.2369	−	16.9808i	1.26235	−	1.05923i	0.995428	−	0.0955150i	$-0.0304498\pi$
$258$	−0.641559	+	1.11121i	−0.0399417	+	0.0691811i
$259$	−5.67499	−	9.82938i	−0.352627	−	0.610768i
$260$	−2.00000	−	0.727940i	−0.124035	−	0.0451450i
$261$	−3.18479	+	18.0619i	−0.197134	+	1.11800i
$262$	−1.32888	−	7.53644i	−0.0820984	−	0.465603i
$263$	26.2567	−	9.55666i	1.61906	−	0.589289i	0.635856	−	0.771808i	$-0.280647\pi$
$263$	26.2567	−	9.55666i	1.61906	−	0.589289i	0.983202	+	0.182519i	$0.0584251\pi$
$264$	1.12449	+	0.943555i	0.0692073	+	0.0580718i
$265$	−19.7743			−1.21472
$266$		0			0
$267$	4.13516			0.253068
$268$	−8.91534	−	7.48086i	−0.544591	−	0.456966i
$269$	−13.7023	+	4.98724i	−0.835446	+	0.304077i	−0.724092	−	0.689703i	$-0.757741\pi$
$269$	−13.7023	+	4.98724i	−0.835446	+	0.304077i	−0.111354	+	0.993781i	$0.535519\pi$
$270$	−0.709141	−	4.02174i	−0.0431569	−	0.244755i
$271$	−3.16519	+	17.9507i	−0.192272	+	1.09043i	0.723979	+	0.689822i	$0.242311\pi$
$271$	−3.16519	+	17.9507i	−0.192272	+	1.09043i	−0.916251	+	0.400605i	$0.868800\pi$
$272$	−6.69846	−	2.43804i	−0.406154	−	0.147828i
$273$	0.325008	+	0.562930i	0.0196704	+	0.0340701i
$274$	2.86824	−	4.96794i	0.173277	−	0.300124i
$275$	−3.23783	+	2.71686i	−0.195248	+	0.163833i
$276$	1.00000	−	0.839100i	0.0601929	−	0.0505079i
$277$	8.23442	−	14.2624i	0.494758	−	0.856947i	−0.505223	−	0.862989i	$-0.668590\pi$
$277$	8.23442	−	14.2624i	0.494758	−	0.856947i	0.999982	+	0.00604184i	$0.00192319\pi$
$278$	9.69846	+	16.7982i	0.581675	+	1.00749i
$279$	−23.8726	−	8.68891i	−1.42921	−	0.520191i
$280$	−0.610815	+	3.46410i	−0.0365032	+	0.207020i
$281$	−1.24510	−	7.06131i	−0.0742764	−	0.421243i	−0.999160	−	0.0409910i	$-0.986949\pi$
$281$	−1.24510	−	7.06131i	−0.0742764	−	0.421243i	0.924883	−	0.380252i	$-0.124163\pi$
$282$	1.19934	−	0.436524i	0.0714197	−	0.0259946i
$283$	16.0385	+	13.4579i	0.953389	+	0.799988i	0.979865	−	0.199661i	$-0.0639841\pi$
$283$	16.0385	+	13.4579i	0.953389	+	0.799988i	−0.0264760	+	0.999649i	$0.508429\pi$
$284$	2.82295			0.167511
$285$		0			0
$286$	4.49794			0.265969
$287$	−2.53209	−	2.12467i	−0.149464	−	0.125416i
$288$	2.70574	−	0.984808i	0.159437	−	0.0580304i
$289$	5.87164	+	33.2998i	0.345391	+	1.95881i
$290$	2.21213	−	12.5456i	0.129901	−	0.736705i
$291$	−0.613341	−	0.223238i	−0.0359547	−	0.0130864i
$292$	−0.396459	−	0.686688i	−0.0232010	−	0.0401854i
$293$	−4.73917	+	8.20848i	−0.276865	+	0.479545i	−0.970604	−	0.240682i	$-0.922629\pi$
$293$	−4.73917	+	8.20848i	−0.276865	+	0.479545i	0.693739	+	0.720227i	$0.255962\pi$
$294$	−1.03936	+	0.872129i	−0.0606169	+	0.0508636i
$295$	−11.1702	+	9.37295i	−0.650357	+	0.545714i
$296$	3.22668	−	5.58878i	0.187547	−	0.324841i
$297$	4.31521	+	7.47416i	0.250394	+	0.433695i
$298$	4.86484	+	1.77066i	0.281812	+	0.102571i
$299$	0.694593	−	3.93923i	0.0401693	−	0.227812i
$300$	−0.0603074	−	0.342020i	−0.00348185	−	0.0197465i
$301$	6.10607	−	2.22243i	0.351948	−	0.128099i
$302$	16.9932	+	14.2590i	0.977848	+	0.820512i
$303$	−0.852044			−0.0489487
$304$		0			0
$305$	10.6108			0.607573
$306$	−15.7233	−	13.1934i	−0.898840	−	0.754216i
$307$	−1.24985	+	0.454907i	−0.0713326	+	0.0259629i	−0.377440	−	0.926034i	$-0.623196\pi$
$307$	−1.24985	+	0.454907i	−0.0713326	+	0.0259629i	0.306107	+	0.951997i	$0.400973\pi$
$308$	−1.29086	−	7.32083i	−0.0735535	−	0.417143i
$309$	−0.448311	+	2.54250i	−0.0255035	+	0.144638i
$310$	16.5817	+	6.03525i	0.941778	+	0.342779i
$311$	−3.73917	−	6.47643i	−0.212029	−	0.367245i	0.740320	−	0.672254i	$-0.234674\pi$
$311$	−3.73917	−	6.47643i	−0.212029	−	0.367245i	−0.952349	+	0.305009i	$0.901340\pi$
$312$	−0.184793	+	0.320070i	−0.0104618	+	0.0181204i
$313$	22.4440	−	18.8328i	1.26861	−	1.06449i	0.273903	−	0.961757i	$-0.411685\pi$
$313$	22.4440	−	18.8328i	1.26861	−	1.06449i	0.994709	−	0.102734i	$-0.0327591\pi$
$314$	−2.16250	+	1.81456i	−0.122037	+	0.102401i
$315$	−5.06418	+	8.77141i	−0.285334	+	0.494213i
$316$	3.34730	+	5.79769i	0.188300	+	0.326145i
$317$	−5.26352	−	1.91576i	−0.295629	−	0.107600i	0.189948	−	0.981794i	$-0.439168\pi$
$317$	−5.26352	−	1.91576i	−0.295629	−	0.107600i	−0.485577	+	0.874194i	$0.661390\pi$
$318$	−0.596267	+	3.38160i	−0.0334370	+	0.189631i
$319$	4.67499	+	26.5132i	0.261749	+	1.48445i
$320$	−1.87939	+	0.684040i	−0.105061	+	0.0382390i
$321$	−0.0471036	−	0.0395246i	−0.00262907	−	0.00220605i
$322$	−6.61081			−0.368406
$323$		0			0
$324$	7.92902			0.440501
$325$	−0.815207	−	0.684040i	−0.0452196	−	0.0379437i
$326$	−2.08512	+	0.758922i	−0.115484	+	0.0420328i
$327$	0.255777	+	1.45059i	0.0141445	+	0.0802176i
$328$	0.326352	−	1.85083i	0.0180198	−	0.102195i
$329$	−6.07367	−	2.21064i	−0.334852	−	0.121876i
$330$	−1.46791	−	2.54250i	−0.0808058	−	0.139960i
$331$	−11.4880	+	19.8978i	−0.631436	+	1.09368i	0.355822	+	0.934554i	$0.384201\pi$
$331$	−11.4880	+	19.8978i	−0.631436	+	1.09368i	−0.987258	+	0.159126i	$0.949132\pi$
$332$	1.15657	−	0.970481i	0.0634752	−	0.0532621i
$333$	14.2344	−	11.9441i	0.780042	−	0.654533i
$334$	−1.95811	+	3.39155i	−0.107143	+	0.185577i
$335$	11.6382	+	20.1579i	0.635860	+	1.10134i
$336$	0.573978	+	0.208911i	0.0313131	+	0.0113970i
$337$	0.227864	−	1.29228i	0.0124125	−	0.0703949i	−0.977972	−	0.208735i	$-0.933065\pi$
$337$	0.227864	−	1.29228i	0.0124125	−	0.0703949i	0.990385	+	0.138340i	$0.0441766\pi$
$338$	−2.06077	−	11.6872i	−0.112091	−	0.635702i
$339$	−3.40673	+	1.23995i	−0.185028	+	0.0673447i
$340$	10.9213	+	9.16404i	0.592289	+	0.496990i
$341$	−37.2918			−2.01946
$342$		0			0
$343$	19.1824			1.03575
$344$	2.83022	+	2.37484i	0.152595	+	0.128043i
$345$	−2.45336	+	0.892951i	−0.132085	+	0.0480749i
$346$	1.31046	+	7.43199i	0.0704508	+	0.399546i
$347$	0.419625	−	2.37981i	0.0225267	−	0.127755i	−0.971471	−	0.237160i	$-0.923783\pi$
$347$	0.419625	−	2.37981i	0.0225267	−	0.127755i	0.993997	+	0.109405i	$0.0348945\pi$
$348$	−2.07873	−	0.756594i	−0.111431	−	0.0405577i
$349$	4.24897	+	7.35943i	0.227442	+	0.393941i	0.957049	−	0.289925i	$-0.0936304\pi$
$349$	4.24897	+	7.35943i	0.227442	+	0.393941i	−0.729607	+	0.683866i	$0.760297\pi$
$350$	−0.879385	+	1.52314i	−0.0470051	+	0.0814153i
$351$	−1.66456	+	1.39673i	−0.0888478	+	0.0745522i
$352$	3.23783	−	2.71686i	0.172577	−	0.144809i
$353$	1.92009	−	3.32570i	0.102196	−	0.177009i	−0.810393	−	0.585887i	$-0.800746\pi$
$353$	1.92009	−	3.32570i	0.102196	−	0.177009i	0.912589	+	0.408878i	$0.134080\pi$
$354$	1.26604	+	2.19285i	0.0672895	+	0.116549i
$355$	−5.30541	−	1.93101i	−0.281582	−	0.102487i
$356$	2.06758	−	11.7258i	0.109582	−	0.621468i
$357$	−0.756082	−	4.28795i	−0.0400161	−	0.226943i
$358$	10.3255	−	3.75817i	0.545718	−	0.198625i
$359$	−18.3286	−	15.3795i	−0.967348	−	0.811701i	0.0147847	−	0.999891i	$-0.495294\pi$
$359$	−18.3286	−	15.3795i	−0.967348	−	0.811701i	−0.982133	+	0.188189i	$0.939738\pi$
$360$	−5.75877			−0.303514
$361$		0			0
$362$	−15.0351			−0.790226
$363$	1.82635	+	1.53249i	0.0958586	+	0.0804349i
$364$	1.75877	−	0.640140i	0.0921846	−	0.0335525i
$365$	0.275378	+	1.56175i	0.0144139	+	0.0817455i
$366$	0.319955	−	1.81456i	0.0167243	−	0.0948484i
$367$	−16.0770	−	5.85154i	−0.839211	−	0.305448i	−0.113577	−	0.993529i	$-0.536231\pi$
$367$	−16.0770	−	5.85154i	−0.839211	−	0.305448i	−0.725634	+	0.688081i	$0.758453\pi$
$368$	−1.87939	−	3.25519i	−0.0979697	−	0.169689i
$369$	2.70574	−	4.68647i	0.140855	−	0.243968i
$370$	−9.88713	+	8.29628i	−0.514007	+	0.431303i
$371$	13.3209	−	11.1776i	0.691586	−	0.580310i
$372$	1.53209	−	2.65366i	0.0794351	−	0.137586i
$373$	1.98040	+	3.43015i	0.102541	+	0.177607i	0.912731	−	0.408561i	$-0.133969\pi$
$373$	1.98040	+	3.43015i	0.102541	+	0.177607i	−0.810190	+	0.586168i	$0.800636\pi$
$374$	−28.3123	−	10.3048i	−1.46399	−	0.532850i
$375$	−0.723689	+	4.10424i	−0.0373711	+	0.211942i
$376$	−0.638156	−	3.61916i	−0.0329104	−	0.186644i
$377$	−6.36959	+	2.31834i	−0.328050	+	0.119401i
$378$	2.75103	+	2.30839i	0.141498	+	0.118731i
$379$	−27.2918			−1.40189			−0.700943	−	0.713218i	$-0.747237\pi$
$379$	−27.2918			−1.40189			−0.700943	+	0.713218i	$0.747237\pi$
$380$		0			0
$381$	−7.64590			−0.391711
$382$	3.47565	+	2.91642i	0.177830	+	0.149217i
$383$	−6.02229	+	2.19193i	−0.307725	+	0.112003i	−0.491267	−	0.871009i	$-0.663466\pi$
$383$	−6.02229	+	2.19193i	−0.307725	+	0.112003i	0.183542	+	0.983012i	$0.441244\pi$
$384$	0.0603074	+	0.342020i	0.00307755	+	0.0174536i
$385$	−2.58172	+	14.6417i	−0.131577	+	0.746208i
$386$	−20.6694	−	7.52303i	−1.05204	−	0.382912i
$387$	5.31908	+	9.21291i	0.270384	+	0.468319i
$388$	−0.939693	+	1.62760i	−0.0477057	+	0.0826286i
$389$	−19.4834	+	16.3485i	−0.987847	+	0.828902i	−0.985255	−	0.171094i	$-0.945270\pi$
$389$	−19.4834	+	16.3485i	−0.987847	+	0.828902i	−0.00259258	+	0.999997i	$0.500825\pi$
$390$	0.566237	−	0.475129i	0.0286725	−	0.0240591i
$391$	−13.3969	+	23.2042i	−0.677512	+	1.17348i
$392$	1.95336	+	3.38332i	0.0986597	+	0.170884i
$393$	2.49747	+	0.909006i	0.125981	+	0.0458533i
$394$	2.76651	−	15.6897i	0.139375	−	0.790434i
$395$	−2.32501	−	13.1858i	−0.116984	−	0.663448i
$396$	11.4363	−	4.16247i	0.574695	−	0.209172i
$397$	17.2986	+	14.5152i	0.868192	+	0.728499i	0.963717	−	0.266928i	$-0.0860085\pi$
$397$	17.2986	+	14.5152i	0.868192	+	0.728499i	−0.0955247	+	0.995427i	$0.530453\pi$
$398$	−3.27631			−0.164227
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	0.585122	+	0.490976i	0.0292196	+	0.0245182i	0.657281	−	0.753646i	$-0.271707\pi$
$401$	0.585122	+	0.490976i	0.0292196	+	0.0245182i	−0.628061	+	0.778164i	$0.716151\pi$
$402$	3.79813	−	1.38241i	0.189434	−	0.0689482i
$403$	−1.63041	−	9.24654i	−0.0812168	−	0.460603i
$404$	−0.426022	+	2.41609i	−0.0211954	+	0.120205i
$405$	−14.9017	−	5.42377i	−0.740470	−	0.269509i
$406$	5.60132	+	9.70177i	0.277989	+	0.481491i
$407$	13.6382	−	23.6220i	0.676018	−	1.17090i
$408$	1.89646	−	1.59132i	0.0938887	−	0.0787820i
$409$	−12.8878	+	10.8142i	−0.637263	+	0.534727i	−0.903176	−	0.429270i	$-0.858771\pi$
$409$	−12.8878	+	10.8142i	−0.637263	+	0.534727i	0.265913	+	0.963997i	$0.414326\pi$
$410$	−1.87939	+	3.25519i	−0.0928162	+	0.160762i
$411$	0.996130	+	1.72535i	0.0491354	+	0.0851051i
$412$	6.98545	+	2.54250i	0.344149	+	0.125260i
$413$	2.22668	−	12.6281i	0.109568	−	0.621390i
$414$	−1.87939	−	10.6585i	−0.0923667	−	0.523838i
$415$	−2.83750	+	1.03276i	−0.139287	+	0.0506964i
$416$	0.815207	+	0.684040i	0.0399688	+	0.0335378i
$417$	−6.73648			−0.329887
$418$		0			0
$419$	35.8931			1.75349			0.876747	−	0.480953i	$-0.159709\pi$
$419$	35.8931			1.75349			0.876747	+	0.480953i	$0.159709\pi$
$420$	−0.935822	−	0.785248i	−0.0456634	−	0.0383162i
$421$	−19.4611	+	7.08326i	−0.948476	+	0.345217i	−0.769508	−	0.638638i	$-0.779498\pi$
$421$	−19.4611	+	7.08326i	−0.948476	+	0.345217i	−0.178969	+	0.983855i	$0.557276\pi$
$422$	1.99154	+	11.2946i	0.0969468	+	0.549813i
$423$	1.83750	−	10.4210i	0.0893421	−	0.506684i
$424$	9.29086	+	3.38160i	0.451204	+	0.164225i
$425$	3.56418	+	6.17334i	0.172888	+	0.299451i
$426$	−0.490200	+	0.849051i	−0.0237503	+	0.0411367i
$427$	−7.14796	+	5.99785i	−0.345914	+	0.290256i
$428$	−0.135630	+	0.113807i	−0.00655590	+	0.00550105i
$429$	−0.781059	+	1.35283i	−0.0377099	+	0.0653155i
$430$	−3.69459	−	6.39922i	−0.178169	−	0.308598i
$431$	17.2199	+	6.26752i	0.829452	+	0.301896i	0.721634	−	0.692275i	$-0.243391\pi$
$431$	17.2199	+	6.26752i	0.829452	+	0.301896i	0.107818	+	0.994171i	$0.465614\pi$
$432$	−0.354570	+	2.01087i	−0.0170593	+	0.0967479i
$433$	0.884438	+	5.01590i	0.0425034	+	0.241049i	0.998657	−	0.0518186i	$-0.0165018\pi$
$433$	0.884438	+	5.01590i	0.0425034	+	0.241049i	−0.956153	+	0.292867i	$0.905391\pi$
$434$	−14.5817	+	5.30731i	−0.699945	+	0.254759i
$435$	3.38919	+	2.84386i	0.162499	+	0.136353i
$436$	4.24123			0.203118
$437$		0			0
$438$	0.275378			0.0131581
$439$	−7.89899	−	6.62804i	−0.376998	−	0.316339i	0.434525	−	0.900660i	$-0.356916\pi$
$439$	−7.89899	−	6.62804i	−0.376998	−	0.316339i	−0.811523	+	0.584321i	$0.801361\pi$
$440$	−7.94356	+	2.89122i	−0.378695	+	0.137834i
$441$	1.95336	+	11.0781i	0.0930173	+	0.527527i
$442$	1.31727	−	7.47059i	0.0626560	−	0.355340i
$443$	8.28446	+	3.01530i	0.393607	+	0.143261i	0.531238	−	0.847222i	$-0.321727\pi$
$443$	8.28446	+	3.01530i	0.393607	+	0.143261i	−0.137632	+	0.990483i	$0.543949\pi$
$444$	1.12061	+	1.94096i	0.0531820	+	0.0921140i
$445$	−11.9067	+	20.6231i	−0.564433	+	0.977627i
$446$	8.57398	−	7.19442i	0.405990	−	0.340666i
$447$	−1.37733	+	1.15571i	−0.0651453	+	0.0546634i
$448$	0.879385	−	1.52314i	0.0415470	−	0.0719616i
$449$	−6.03849	−	10.4590i	−0.284974	−	0.493589i	0.687629	−	0.726062i	$-0.258652\pi$
$449$	−6.03849	−	10.4590i	−0.284974	−	0.493589i	−0.972603	+	0.232473i	$0.925318\pi$
$450$	−2.70574	−	0.984808i	−0.127550	−	0.0464243i
$451$	1.37939	−	7.82288i	0.0649527	−	0.368365i
$452$	1.81268	+	10.2802i	0.0852614	+	0.483541i
$453$	−7.23947	+	2.63495i	−0.340140	+	0.123801i
$454$	−2.60220	−	2.18350i	−0.122127	−	0.102477i
$455$	−3.74329			−0.175488
$456$		0			0
$457$	−0.731429			−0.0342148			−0.0171074	−	0.999854i	$-0.505446\pi$
$457$	−0.731429			−0.0342148			−0.0171074	+	0.999854i	$0.505446\pi$
$458$	3.26083	+	2.73616i	0.152369	+	0.127852i
$459$	13.6775	−	4.97821i	0.638412	−	0.232363i
$460$	1.30541	+	7.40333i	0.0608649	+	0.345182i
$461$	4.00774	−	22.7290i	0.186659	−	1.05860i	−0.737146	−	0.675733i	$-0.763827\pi$
$461$	4.00774	−	22.7290i	0.186659	−	1.05860i	0.923805	−	0.382863i	$-0.125062\pi$
$462$	2.42602	+	0.883000i	0.112869	+	0.0410809i
$463$	−9.02229	−	15.6271i	−0.419301	−	0.726251i	0.576568	−	0.817049i	$-0.304392\pi$
$463$	−9.02229	−	15.6271i	−0.419301	−	0.726251i	−0.995869	+	0.0907980i	$0.971058\pi$
$464$	−3.18479	+	5.51622i	−0.147850	+	0.256084i
$465$	−4.69459	+	3.93923i	−0.217707	+	0.182677i
$466$	5.08899	−	4.27017i	0.235743	−	0.197812i
$467$	−5.48633	+	9.50260i	−0.253877	+	0.439728i	−0.964590	−	0.263754i	$-0.915039\pi$
$467$	−5.48633	+	9.50260i	−0.253877	+	0.439728i	0.710713	+	0.703482i	$0.248373\pi$
$468$	1.53209	+	2.65366i	0.0708208	+	0.122665i
$469$	−19.2344	−	7.00076i	−0.888163	−	0.323265i
$470$	−1.27631	+	7.23832i	−0.0588719	+	0.333879i
$471$	−0.170245	−	0.965505i	−0.00784446	−	0.0444881i
$472$	6.85117	−	2.49362i	0.315351	−	0.114778i
$473$	11.9624	+	10.0377i	0.550034	+	0.461533i
$474$	−2.32501			−0.106791
$475$		0			0
$476$	−12.5371			−0.574639
$477$	21.8084	+	18.2994i	0.998538	+	0.837873i
$478$	−15.0496	+	5.47762i	−0.688354	+	0.250540i
$479$	3.88713	+	22.0450i	0.177607	+	1.00726i	0.935091	+	0.354407i	$0.115317\pi$
$479$	3.88713	+	22.0450i	0.177607	+	1.00726i	−0.757484	+	0.652854i	$0.773572\pi$
$480$	0.120615	−	0.684040i	0.00550529	−	0.0312220i
$481$	6.45336	+	2.34883i	0.294248	+	0.107098i
$482$	4.30200	+	7.45129i	0.195951	+	0.339397i
$483$	1.14796	−	1.98832i	0.0522338	−	0.0904716i
$484$	5.25877	−	4.41263i	0.239035	−	0.200574i
$485$	2.87939	−	2.41609i	0.130746	−	0.109709i
$486$	−4.43969	+	7.68977i	−0.201389	+	0.348815i
$487$	18.8803	+	32.7017i	0.855549	+	1.48185i	0.876135	+	0.482066i	$0.160113\pi$
$487$	18.8803	+	32.7017i	0.855549	+	1.48185i	−0.0205859	+	0.999788i	$0.506553\pi$
$488$	−4.98545	−	1.81456i	−0.225681	−	0.0821411i
$489$	0.133819	−	0.758922i	0.00605148	−	0.0343197i
$490$	−1.35679	−	7.69475i	−0.0612936	−	0.347613i
$491$	1.17587	−	0.427982i	0.0530663	−	0.0193145i	−0.315351	−	0.948975i	$-0.602122\pi$
$491$	1.17587	−	0.427982i	0.0530663	−	0.0193145i	0.368417	+	0.929661i	$0.379900\pi$
$492$	0.500000	+	0.419550i	0.0225417	+	0.0189148i
$493$	45.4047			2.04492
$494$		0			0
$495$	−24.3405			−1.09402
$496$	−6.75877	−	5.67128i	−0.303478	−	0.254648i
$497$	4.66550	−	1.69810i	0.209276	−	0.0761703i
$498$	0.0910521	+	0.516382i	0.00408014	+	0.0231396i
$499$	−1.62015	+	9.18832i	−0.0725278	+	0.411325i	0.926830	+	0.375482i	$0.122523\pi$
$499$	−1.62015	+	9.18832i	−0.0725278	+	0.411325i	−0.999357	+	0.0358434i	$0.988588\pi$
$500$	11.2763	+	4.10424i	0.504292	+	0.183547i
$501$	−0.680045	−	1.17787i	−0.0303822	−	0.0526234i
$502$	9.95471	−	17.2421i	0.444300	−	0.769551i
$503$	−7.42333	+	6.22892i	−0.330990	+	0.277734i	−0.793103	−	0.609087i	$-0.791536\pi$
$503$	−7.42333	+	6.22892i	−0.330990	+	0.277734i	0.462113	+	0.886821i	$0.347091\pi$
$504$	3.87939	−	3.25519i	0.172802	−	0.144998i
$505$	2.45336	−	4.24935i	0.109173	−	0.189094i
$506$	−7.94356	−	13.7587i	−0.353134	−	0.611647i
$507$	3.87299	+	1.40965i	0.172005	+	0.0626049i
$508$	−3.82295	+	21.6810i	−0.169616	+	0.961940i
$509$	5.02734	+	28.5115i	0.222833	+	1.26375i	0.866785	+	0.498683i	$0.166183\pi$
$509$	5.02734	+	28.5115i	0.222833	+	1.26375i	−0.643952	+	0.765066i	$0.722706\pi$
$510$	−4.65270	+	1.69345i	−0.206025	+	0.0749870i
$511$	−1.06830	−	0.896407i	−0.0472587	−	0.0396547i
$512$	1.00000			0.0441942
$513$		0			0
$514$	26.4175			1.16522
$515$	−11.3892	−	9.55666i	−0.501867	−	0.421117i
$516$	−1.20574	+	0.438852i	−0.0530796	+	0.0193194i
$517$	−2.69728	−	15.2970i	−0.118626	−	0.672763i
$518$	1.97090	−	11.1776i	0.0865966	−	0.491113i
$519$	−2.46286	−	0.896407i	−0.108107	−	0.0393479i
$520$	−1.06418	−	1.84321i	−0.0466673	−	0.0808301i
$521$	1.08037	−	1.87126i	0.0473321	−	0.0819815i	−0.841389	−	0.540430i	$-0.818261\pi$
$521$	1.08037	−	1.87126i	0.0473321	−	0.0819815i	0.888721	+	0.458449i	$0.151595\pi$
$522$	−14.0496	+	11.7890i	−0.614936	+	0.515992i
$523$	11.0196	−	9.24654i	0.481853	−	0.404323i	−0.369243	−	0.929333i	$-0.620383\pi$
$523$	11.0196	−	9.24654i	0.481853	−	0.404323i	0.851096	+	0.525010i	$0.175938\pi$
$524$	3.82635	−	6.62744i	0.167155	−	0.289521i
$525$	−0.305407	−	0.528981i	−0.0133291	−	0.0230866i
$526$	26.2567	+	9.55666i	1.14485	+	0.416690i
$527$	−10.9213	+	61.9376i	−0.475738	+	2.69805i
$528$	0.254900	+	1.44561i	0.0110931	+	0.0629121i
$529$	8.33662	−	3.03428i	0.362462	−	0.131925i
$530$	−15.1480	−	12.7106i	−0.657985	−	0.552115i
$531$	20.9932			0.911027
$532$		0			0
$533$	2.00000			0.0866296
$534$	3.16772	+	2.65803i	0.137081	+	0.115024i
$535$	0.332748	−	0.121111i	0.0143860	−	0.00523606i
$536$	−2.02094	−	11.4613i	−0.0872915	−	0.495055i
$537$	−0.662666	+	3.75817i	−0.0285961	+	0.162177i
$538$	−13.7023	−	4.98724i	−0.590750	−	0.215015i
$539$	8.25624	+	14.3002i	0.355622	+	0.615955i
$540$	2.04189	−	3.53666i	0.0878689	−	0.152193i
$541$	9.92127	−	8.32494i	0.426549	−	0.357917i	−0.404099	−	0.914715i	$-0.632415\pi$
$541$	9.92127	−	8.32494i	0.426549	−	0.357917i	0.830648	+	0.556798i	$0.187970\pi$
$542$	−13.9632	+	11.7165i	−0.599769	+	0.503266i
$543$	2.61081	−	4.52206i	0.112041	−	0.194060i
$544$	−3.56418	−	6.17334i	−0.152813	−	0.264680i
$545$	−7.97090	−	2.90117i	−0.341436	−	0.124273i
$546$	−0.112874	+	0.640140i	−0.00483056	+	0.0273955i
$547$	0.242878	+	1.37743i	0.0103847	+	0.0588947i	0.989560	−	0.144123i	$-0.0460361\pi$
$547$	0.242878	+	1.37743i	0.0103847	+	0.0588947i	−0.979175	+	0.203018i	$0.934925\pi$
$548$	5.39053	−	1.96199i	0.230272	−	0.0838122i
$549$	−11.7023	−	9.81942i	−0.499443	−	0.419083i
$550$	−4.22668			−0.180226
$551$		0			0
$552$	1.30541			0.0555618
$553$	9.01960	+	7.56834i	0.383552	+	0.321839i
$554$	15.4757	−	5.63268i	0.657497	−	0.239309i
$555$	−0.778371	−	4.41436i	−0.0330400	−	0.187379i
$556$	−3.36824	+	19.1022i	−0.142845	+	0.810116i
$557$	27.8675	+	10.1429i	1.18078	+	0.429771i	0.856479	−	0.516182i	$-0.172647\pi$
$557$	27.8675	+	10.1429i	1.18078	+	0.429771i	0.324306	+	0.945952i	$0.394869\pi$
$558$	−12.7023	−	22.0011i	−0.537733	−	0.931380i
$559$	−1.96585	+	3.40496i	−0.0831467	+	0.144014i
$560$	−2.69459	+	2.26103i	−0.113867	+	0.0955460i
$561$	8.01573	−	6.72600i	0.338424	−	0.283972i
$562$	3.58512	−	6.20961i	0.151229	−	0.261937i
$563$	−21.0646	−	36.4850i	−0.887769	−	1.53766i	−0.842507	−	0.538686i	$-0.818921\pi$
$563$	−21.0646	−	36.4850i	−0.887769	−	1.53766i	−0.0452621	−	0.998975i	$-0.514412\pi$
$564$	1.19934	+	0.436524i	0.0505013	+	0.0183810i
$565$	3.62536	−	20.5605i	0.152520	−	0.864985i
$566$	3.63563	+	20.6187i	0.152817	+	0.866668i
$567$	13.1043	−	4.76958i	0.550329	−	0.200304i
$568$	2.16250	+	1.81456i	0.0907366	+	0.0761371i
$569$	5.08915			0.213348			0.106674	−	0.994294i	$-0.465980\pi$
$569$	5.08915			0.213348			0.106674	+	0.994294i	$0.465980\pi$
$570$		0			0
$571$	−12.6486			−0.529327			−0.264663	−	0.964341i	$-0.585261\pi$
$571$	−12.6486			−0.529327			−0.264663	+	0.964341i	$0.585261\pi$
$572$	3.44562	+	2.89122i	0.144069	+	0.120888i
$573$	−1.48070	+	0.538932i	−0.0618573	+	0.0225142i
$574$	−0.573978	−	3.25519i	−0.0239574	−	0.135869i
$575$	−0.652704	+	3.70167i	−0.0272196	+	0.154370i
$576$	2.70574	+	0.984808i	0.112739	+	0.0410337i
$577$	−5.00727	−	8.67285i	−0.208456	−	0.361056i	0.742773	−	0.669544i	$-0.233510\pi$
$577$	−5.00727	−	8.67285i	−0.208456	−	0.361056i	−0.951228	+	0.308488i	$0.900177\pi$
$578$	−16.9067	+	29.2833i	−0.703227	+	1.21803i
$579$	5.85188	−	4.91031i	0.243196	−	0.204066i
$580$	9.75877	−	8.18858i	0.405211	−	0.340012i
$581$	1.32770	−	2.29964i	0.0550821	−	0.0954050i
$582$	−0.326352	−	0.565258i	−0.0135277	−	0.0234307i
$583$	39.2695	+	14.2929i	1.62638	+	0.591953i
$584$	0.137689	−	0.780873i	0.00569761	−	0.0323127i
$585$	−1.06418	−	6.03525i	−0.0439983	−	0.249527i
$586$	−8.90673	+	3.24178i	−0.367933	+	0.133917i
$587$	3.39646	+	2.84997i	0.140187	+	0.117631i	0.710185	−	0.704016i	$-0.248611\pi$
$587$	3.39646	+	2.84997i	0.140187	+	0.117631i	−0.569998	+	0.821646i	$0.693056\pi$
$588$	−1.35679			−0.0559532
$589$		0			0
$590$	−14.5817			−0.600320
$591$	4.23854	+	3.55656i	0.174350	+	0.146297i
$592$	6.06418	−	2.20718i	0.249236	−	0.0907145i
$593$	−4.17184	−	23.6597i	−0.171317	−	0.971586i	−0.942310	−	0.334742i	$-0.891351\pi$
$593$	−4.17184	−	23.6597i	−0.171317	−	0.971586i	0.770993	−	0.636844i	$-0.219760\pi$
$594$	−1.49866	+	8.49930i	−0.0614906	+	0.348730i
$595$	23.5621	+	8.57591i	0.965953	+	0.351578i
$596$	2.58853	+	4.48346i	0.106030	+	0.183650i
$597$	0.568926	−	0.985408i	0.0232846	−	0.0403301i
$598$	3.06418	−	2.57115i	0.125304	−	0.105142i
$599$	−26.0273	+	21.8395i	−1.06345	+	0.892339i	−0.994443	−	0.105277i	$-0.966427\pi$
$599$	−26.0273	+	21.8395i	−1.06345	+	0.892339i	−0.0690054	+	0.997616i	$0.521983\pi$
$600$	0.173648	−	0.300767i	0.00708916	−	0.0122788i
$601$	−8.07145	−	13.9802i	−0.329241	−	0.570263i	0.653120	−	0.757254i	$-0.273460\pi$
$601$	−8.07145	−	13.9802i	−0.329241	−	0.570263i	−0.982362	+	0.186991i	$0.940126\pi$
$602$	6.10607	+	2.22243i	0.248865	+	0.0905793i
$603$	5.81908	−	33.0016i	0.236971	−	1.34393i
$604$	3.85204	+	21.8460i	0.156737	+	0.888902i
$605$	−12.9017	+	4.69583i	−0.524528	+	0.190912i
$606$	−0.652704	−	0.547683i	−0.0265143	−	0.0222481i
$607$	8.92221			0.362141			0.181071	−	0.983470i	$-0.442044\pi$
$607$	8.92221			0.362141			0.181071	+	0.983470i	$0.442044\pi$
$608$		0			0
$609$	−3.89064			−0.157657
$610$	8.12836	+	6.82050i	0.329107	+	0.276154i
$611$	3.67499	−	1.33759i	0.148674	−	0.0541130i
$612$	−3.56418	−	20.2135i	−0.144073	−	0.817081i
$613$	4.48515	−	25.4365i	0.181153	−	1.02737i	−0.749645	−	0.661840i	$-0.769776\pi$
$613$	4.48515	−	25.4365i	0.181153	−	1.02737i	0.930799	−	0.365532i	$-0.119113\pi$
$614$	−1.24985	−	0.454907i	−0.0504397	−	0.0183586i
$615$	−0.652704	−	1.13052i	−0.0263196	−	0.0455868i
$616$	3.71688	−	6.43783i	0.149757	−	0.259387i
$617$	14.1932	−	11.9095i	0.571399	−	0.479460i	−0.310711	−	0.950504i	$-0.600567\pi$
$617$	14.1932	−	11.9095i	0.571399	−	0.479460i	0.882110	+	0.471044i	$0.156123\pi$
$618$	−1.97771	+	1.65950i	−0.0795552	+	0.0667548i
$619$	17.6061	−	30.4946i	0.707648	−	1.22568i	−0.258080	−	0.966124i	$-0.583090\pi$
$619$	17.6061	−	30.4946i	0.707648	−	1.22568i	0.965728	−	0.259558i	$-0.0835769\pi$
$620$	8.82295	+	15.2818i	0.354338	+	0.613732i
$621$	7.21213	+	2.62500i	0.289413	+	0.105338i
$622$	1.29860	−	7.36473i	0.0520691	−	0.295299i
$623$	−3.63640	−	20.6231i	−0.145689	−	0.826245i
$624$	−0.347296	+	0.126406i	−0.0139030	+	0.00506027i
$625$	−14.5548	−	12.2130i	−0.582194	−	0.488519i
$626$	29.2986			1.17101
$627$		0			0
$628$	−2.82295			−0.112648
$629$	−35.2395	−	29.5694i	−1.40509	−	1.17901i
$630$	−9.51754	+	3.46410i	−0.379188	+	0.138013i
$631$	−0.319955	−	1.81456i	−0.0127372	−	0.0722363i	0.977777	−	0.209650i	$-0.0672323\pi$
$631$	−0.319955	−	1.81456i	−0.0127372	−	0.0722363i	−0.990514	+	0.137413i	$0.956121\pi$
$632$	−1.16250	+	6.59289i	−0.0462419	+	0.262251i
$633$	−3.74288	−	1.36230i	−0.148766	−	0.0541464i
$634$	−2.80066	−	4.85088i	−0.111228	−	0.192653i
$635$	22.0155	−	38.1319i	0.873658	−	1.51322i
$636$	−2.63041	+	2.20718i	−0.104303	+	0.0875204i
$637$	−3.18479	+	2.67236i	−0.126186	+	0.105883i
$638$	−13.4611	+	23.3153i	−0.532930	+	0.923062i
$639$	4.06418	+	7.03936i	0.160776	+	0.278473i
$640$	−1.87939	−	0.684040i	−0.0742892	−	0.0270391i
$641$	−0.905382	+	5.13468i	−0.0357604	+	0.202808i	−0.997453	−	0.0713214i	$-0.977278\pi$
$641$	−0.905382	+	5.13468i	−0.0357604	+	0.202808i	0.961693	+	0.274129i	$0.0883895\pi$
$642$	−0.0106775	−	0.0605553i	−0.000421408	−	0.00238993i
$643$	−5.54798	+	2.01930i	−0.218791	+	0.0796334i	−0.449090	−	0.893486i	$-0.648252\pi$
$643$	−5.54798	+	2.01930i	−0.218791	+	0.0796334i	0.230299	+	0.973120i	$0.426030\pi$
$644$	−5.06418	−	4.24935i	−0.199557	−	0.167448i
$645$	2.56624			0.101045
$646$		0			0
$647$	−42.6810			−1.67796			−0.838981	−	0.544160i	$-0.816848\pi$
$647$	−42.6810			−1.67796			−0.838981	+	0.544160i	$0.816848\pi$
$648$	6.07398	+	5.09667i	0.238608	+	0.200216i
$649$	28.9577	−	10.5397i	1.13669	−	0.413721i
$650$	−0.184793	−	1.04801i	−0.00724816	−	0.0411064i
$651$	0.935822	−	5.30731i	0.0366778	−	0.208010i
$652$	−2.08512	−	0.758922i	−0.0816597	−	0.0297217i
$653$	−3.87939	−	6.71929i	−0.151812	−	0.262946i	0.780082	−	0.625678i	$-0.215178\pi$
$653$	−3.87939	−	6.71929i	−0.151812	−	0.262946i	−0.931894	+	0.362732i	$0.881844\pi$
$654$	−0.736482	+	1.27562i	−0.0287987	+	0.0498808i
$655$	−11.7246	+	9.83813i	−0.458119	+	0.384407i
$656$	1.43969	−	1.20805i	0.0562106	−	0.0471663i
$657$	1.14156	−	1.97724i	0.0445365	−	0.0771394i
$658$	−3.23173	−	5.59753i	−0.125986	−	0.218214i
$659$	−27.2383	−	9.91393i	−1.06105	−	0.386192i	−0.248229	−	0.968701i	$-0.579849\pi$
$659$	−27.2383	−	9.91393i	−1.06105	−	0.386192i	−0.812824	+	0.582509i	$0.802071\pi$
$660$	0.509800	−	2.89122i	0.0198439	−	0.112541i
$661$	−5.68004	−	32.2131i	−0.220928	−	1.25295i	−0.870318	−	0.492490i	$-0.836087\pi$
$661$	−5.68004	−	32.2131i	−0.220928	−	1.25295i	0.649390	−	0.760456i	$-0.275024\pi$
$662$	−21.5903	+	7.85824i	−0.839132	+	0.305419i
$663$	2.01817	+	1.69345i	0.0783792	+	0.0657680i
$664$	1.50980			0.0585916
$665$		0			0
$666$	18.5817			0.720027
$667$	18.3405	+	15.3895i	0.710147	+	0.595884i
$668$	−3.68004	+	1.33943i	−0.142385	+	0.0518240i
$669$	0.674992	+	3.82807i	0.0260967	+	0.148002i
$670$	−4.04189	+	22.9227i	−0.156152	+	0.885581i
$671$	−21.0719	−	7.66955i	−0.813472	−	0.296080i
$672$	0.305407	+	0.528981i	0.0117813	+	0.0204059i
$673$	16.4222	−	28.4441i	0.633030	−	1.09644i	−0.353899	−	0.935284i	$-0.615144\pi$
$673$	16.4222	−	28.4441i	0.633030	−	1.09644i	0.986929	−	0.161156i	$-0.0515222\pi$
$674$	1.00521	−	0.843475i	0.0387194	−	0.0324894i
$675$	1.56418	−	1.31250i	0.0602052	−	0.0505182i
$676$	5.93376	−	10.2776i	0.228222	−	0.395291i
$677$	−12.3209	−	21.3404i	−0.473530	−	0.820178i	0.526011	−	0.850478i	$-0.323687\pi$
$677$	−12.3209	−	21.3404i	−0.473530	−	0.820178i	−0.999541	+	0.0302996i	$0.990354\pi$
$678$	−3.40673	−	1.23995i	−0.130835	−	0.0476199i
$679$	−0.573978	+	3.25519i	−0.0220273	+	0.124923i
$680$	2.47565	+	14.0401i	0.0949369	+	0.538414i
$681$	1.10859	−	0.403495i	0.0424814	−	0.0154620i
$682$	−28.5672	−	23.9707i	−1.09389	−	0.917886i
$683$	29.9905			1.14755			0.573777	−	0.819011i	$-0.305477\pi$
$683$	29.9905			1.14755			0.573777	+	0.819011i	$0.305477\pi$
$684$		0			0
$685$	−11.4730			−0.438359
$686$	14.6946	+	12.3302i	0.561042	+	0.470770i
$687$	−1.38919	+	0.505622i	−0.0530007	+	0.0192907i
$688$	0.641559	+	3.63846i	0.0244592	+	0.138715i
$689$	−1.82707	+	10.3618i	−0.0696057	+	0.394754i
$690$	−2.45336	−	0.892951i	−0.0933979	−	0.0339941i
$691$	−11.2365	−	19.4622i	−0.427456	−	0.740375i	0.569190	−	0.822206i	$-0.307257\pi$
$691$	−11.2365	−	19.4622i	−0.427456	−	0.740375i	−0.996646	+	0.0818304i	$0.973923\pi$
$692$	−3.77332	+	6.53558i	−0.143440	+	0.248445i
$693$	16.3969	−	13.7587i	0.622868	−	0.522648i
$694$	1.85117	−	1.55331i	0.0702693	−	0.0589630i
$695$	19.3969	−	33.5965i	0.735767	−	1.27439i
$696$	−1.10607	−	1.91576i	−0.0419254	−	0.0726168i
$697$	−12.5890	−	4.58202i	−0.476842	−	0.173556i
$698$	−1.47565	+	8.36884i	−0.0558542	+	0.316765i
$699$	0.400634	+	2.27211i	0.0151534	+	0.0859391i
$700$	−1.65270	+	0.601535i	−0.0624663	+	0.0227359i
$701$	−3.69459	−	3.10013i	−0.139543	−	0.117090i	0.570344	−	0.821406i	$-0.306810\pi$
$701$	−3.69459	−	3.10013i	−0.139543	−	0.117090i	−0.709887	+	0.704315i	$0.751254\pi$
$702$	−2.17293			−0.0820121
$703$		0			0
$704$	4.22668			0.159299
$705$	−1.95542	−	1.64079i	−0.0736455	−	0.0617959i
$706$	3.60859	−	1.31342i	0.135811	−	0.0494312i
$707$	0.749275	+	4.24935i	0.0281794	+	0.159813i
$708$	−0.439693	+	2.49362i	−0.0165247	+	0.0937160i
$709$	38.8803	+	14.1513i	1.46018	+	0.531462i	0.945415	−	0.325868i	$-0.105657\pi$
$709$	38.8803	+	14.1513i	1.46018	+	0.531462i	0.514766	+	0.857331i	$0.327879\pi$
$710$	−2.82295	−	4.88949i	−0.105943	−	0.183499i
$711$	−9.63816	+	16.6938i	−0.361459	+	0.626065i
$712$	9.12108	−	7.65350i	0.341827	−	0.286827i
$713$	−25.4047	+	21.3170i	−0.951412	+	0.798330i
$714$	2.17705	−	3.77076i	0.0814741	−	0.141117i
$715$	−4.49794	−	7.79066i	−0.168213	−	0.291354i
$716$	10.3255	+	3.75817i	0.385881	+	0.140449i
$717$	0.965852	−	5.47762i	0.0360704	−	0.204565i
$718$	−4.15476	−	23.5628i	−0.155054	−	0.879357i
$719$	−21.4338	+	7.80125i	−0.799344	+	0.290938i	−0.709215	−	0.704992i	$-0.750950\pi$
$719$	−21.4338	+	7.80125i	−0.799344	+	0.290938i	−0.0901297	+	0.995930i	$0.528728\pi$
$720$	−4.41147	−	3.70167i	−0.164406	−	0.137953i
$721$	13.0743			0.486912
$722$		0			0
$723$	−2.98814			−0.111130
$724$	−11.5175	−	9.66436i	−0.428046	−	0.359173i
$725$	5.98545	−	2.17853i	0.222294	−	0.0809084i
$726$	0.414000	+	2.34791i	0.0153650	+	0.0871392i
$727$	1.56717	−	8.88787i	0.0581231	−	0.329633i	−0.941856	−	0.336015i	$-0.890921\pi$
$727$	1.56717	−	8.88787i	0.0581231	−	0.329633i	0.999980	+	0.00638267i	$0.00203168\pi$
$728$	1.75877	+	0.640140i	0.0651844	+	0.0237252i
$729$	10.3516	+	17.9296i	0.383394	+	0.664058i
$730$	−0.792919	+	1.37338i	−0.0293472	+	0.0508309i
$731$	20.1748	−	16.9287i	0.746193	−	0.626130i
$732$	1.41147	−	1.18437i	0.0521696	−	0.0437755i
$733$	−14.4561	+	25.0386i	−0.533946	+	0.924822i	0.465267	+	0.885170i	$0.345958\pi$
$733$	−14.4561	+	25.0386i	−0.533946	+	0.924822i	−0.999214	+	0.0396520i	$0.987375\pi$
$734$	−8.55438	−	14.8166i	−0.315748	−	0.546891i
$735$	2.54993	+	0.928100i	0.0940558	+	0.0342335i
$736$	0.652704	−	3.70167i	0.0240590	−	0.136445i
$737$	−8.54189	−	48.4435i	−0.314645	−	1.78444i
$738$	5.08512	−	1.85083i	0.187186	−	0.0681301i
$739$	−4.66226	−	3.91210i	−0.171504	−	0.143909i	0.552996	−	0.833184i	$-0.313485\pi$
$739$	−4.66226	−	3.91210i	−0.171504	−	0.143909i	−0.724500	+	0.689275i	$0.757929\pi$
$740$	−12.9067			−0.474461
$741$		0			0
$742$	17.3892			0.638377
$743$	−22.5212	−	18.8975i	−0.826221	−	0.693282i	0.128199	−	0.991748i	$-0.459080\pi$
$743$	−22.5212	−	18.8975i	−0.826221	−	0.693282i	−0.954420	+	0.298466i	$0.903525\pi$
$744$	2.87939	−	1.04801i	0.105563	−	0.0384219i
$745$	−1.79797	−	10.1968i	−0.0658726	−	0.373582i
$746$	−0.687786	+	3.90063i	−0.0251816	+	0.142812i
$747$	4.08512	+	1.48686i	0.149467	+	0.0544015i
$748$	−15.0646	−	26.0927i	−0.550818	−	0.954045i
$749$	−0.155697	+	0.269675i	−0.00568903	+	0.00985369i
$750$	−3.19253	+	2.67885i	−0.116575	+	0.0978179i
$751$	−29.4570	+	24.7173i	−1.07490	+	0.901949i	−0.995487	−	0.0948930i	$-0.969749\pi$
$751$	−29.4570	+	24.7173i	−1.07490	+	0.901949i	−0.0794132	+	0.996842i	$0.525305\pi$
$752$	1.83750	−	3.18264i	0.0670066	−	0.116059i
$753$	3.45723	+	5.98810i	0.125989	+	0.218219i
$754$	−6.36959	−	2.31834i	−0.231967	−	0.0844289i
$755$	7.70409	−	43.6921i	0.280380	−	1.59012i
$756$	0.623608	+	3.53666i	0.0226804	+	0.128627i
$757$	7.14290	−	2.59980i	0.259613	−	0.0944915i	−0.208935	−	0.977930i	$-0.567000\pi$
$757$	7.14290	−	2.59980i	0.259613	−	0.0944915i	0.468548	+	0.883438i	$0.344777\pi$
$758$	−20.9067	−	17.5428i	−0.759366	−	0.637184i
$759$	5.51754			0.200274
$760$		0			0
$761$	−2.89992			−0.105122			−0.0525610	−	0.998618i	$-0.516738\pi$
$761$	−2.89992			−0.105122			−0.0525610	+	0.998618i	$0.516738\pi$
$762$	−5.85710	−	4.91469i	−0.212180	−	0.178040i
$763$	7.00950	−	2.55125i	0.253761	−	0.0923614i
$764$	0.787866	+	4.46821i	0.0285040	+	0.161654i
$765$	−7.12836	+	40.4269i	−0.257726	+	1.46164i
$766$	−6.02229	−	2.19193i	−0.217594	−	0.0791978i
$767$	3.87939	+	6.71929i	0.140076	+	0.242620i
$768$	−0.173648	+	0.300767i	−0.00626599	+	0.0108530i
$769$	−12.9927	+	10.9022i	−0.468530	+	0.393143i	−0.846258	−	0.532773i	$-0.821150\pi$
$769$	−12.9927	+	10.9022i	−0.468530	+	0.393143i	0.377728	+	0.925917i	$0.376705\pi$
$770$	−11.3892	+	9.55666i	−0.410438	+	0.344398i
$771$	−4.58734	+	7.94551i	−0.165209	+	0.286151i
$772$	−10.9979	−	19.0490i	−0.395825	−	0.685588i
$773$	45.0925	+	16.4123i	1.62186	+	0.590310i	0.983736	−	0.179621i	$-0.0574873\pi$
$773$	45.0925	+	16.4123i	1.62186	+	0.590310i	0.638127	+	0.769931i	$0.279709\pi$
$774$	−1.84730	+	10.4765i	−0.0663997	+	0.376571i
$775$	1.53209	+	8.68891i	0.0550343	+	0.312115i
$776$	−1.76604	+	0.642788i	−0.0633973	+	0.0230747i
$777$	3.01960	+	2.53375i	0.108328	+	0.0908976i
$778$	−25.4338			−0.911845
$779$		0			0
$780$	0.739170			0.0264665
$781$	9.14022	+	7.66955i	0.327063	+	0.274438i
$782$	−25.1780	+	9.16404i	−0.900363	+	0.327705i
$783$	−2.25847	−	12.8084i	−0.0807110	−	0.457735i
$784$	−0.678396	+	3.84737i	−0.0242284	+	0.137406i
$785$	5.30541	+	1.93101i	0.189358	+	0.0689207i
$786$	1.32888	+	2.30168i	0.0473995	+	0.0820984i
$787$	−25.2913	+	43.8059i	−0.901538	+	1.56151i	−0.0760408	+	0.997105i	$0.524228\pi$
$787$	−25.2913	+	43.8059i	−0.901538	+	1.56151i	−0.825498	+	0.564406i	$0.809105\pi$
$788$	12.2044	−	10.2407i	0.434763	−	0.364810i
$789$	−7.43376	+	6.23767i	−0.264649	+	0.222067i
$790$	6.69459	−	11.5954i	0.238183	−	0.412545i
$791$	9.17974	+	15.8998i	0.326394	+	0.565331i
$792$	11.4363	+	4.16247i	0.406371	+	0.147907i
$793$	0.980400	−	5.56012i	0.0348150	−	0.197446i
$794$	3.92127	+	22.2387i	0.139161	+	0.789220i
$795$	6.45336	−	2.34883i	0.228877	−	0.0833045i
$796$	−2.50980	−	2.10597i	−0.0889575	−	0.0746442i
$797$	−3.87702			−0.137331			−0.0686656	−	0.997640i	$-0.521874\pi$
$797$	−3.87702			−0.137331			−0.0686656	+	0.997640i	$0.521874\pi$
$798$		0			0
$799$	−26.1967			−0.926771
$800$	−0.766044	−	0.642788i	−0.0270838	−	0.0227260i
$801$	32.2165	−	11.7258i	1.13831	−	0.414312i
$802$	0.132636	+	0.752219i	0.00468356	+	0.0265618i
$803$	0.581967	−	3.30050i	0.0205372	−	0.116472i
$804$	3.79813	+	1.38241i	0.133950	+	0.0487538i
$805$	6.61081	+	11.4503i	0.233001	+	0.403569i
$806$	4.69459	−	8.13127i	0.165360	−	0.286412i
$807$	3.87939	−	3.25519i	0.136561	−	0.114588i
$808$	−1.87939	+	1.57699i	−0.0661165	+	0.0554784i
$809$	8.65317	−	14.9877i	0.304229	−	0.526941i	−0.672860	−	0.739770i	$-0.734934\pi$
$809$	8.65317	−	14.9877i	0.304229	−	0.526941i	0.977089	+	0.212829i	$0.0682678\pi$
$810$	−7.92902	−	13.7335i	−0.278597	−	0.482544i
$811$	−46.0411	−	16.7576i	−1.61672	−	0.588438i	−0.633967	−	0.773360i	$-0.718575\pi$
$811$	−46.0411	−	16.7576i	−1.61672	−	0.588438i	−0.982753	+	0.184922i	$0.940797\pi$
$812$	−1.94532	+	11.0324i	−0.0682673	+	0.387163i
$813$	−1.09926	−	6.23421i	−0.0385527	−	0.218643i
$814$	25.6313	−	9.32905i	0.898378	−	0.326983i
$815$	3.39961	+	2.85262i	0.119083	+	0.0999228i
$816$	2.47565			0.0866652
$817$		0			0
$818$	−16.8239			−0.588233
$819$	4.12836	+	3.46410i	0.144256	+	0.121046i
$820$	−3.53209	+	1.28558i	−0.123346	+	0.0448942i
$821$	−4.95811	−	28.1188i	−0.173039	−	0.981354i	−0.940383	−	0.340118i	$-0.889533\pi$
$821$	−4.95811	−	28.1188i	−0.173039	−	0.981354i	0.767343	−	0.641236i	$-0.221578\pi$
$822$	−0.345952	+	1.96199i	−0.0120665	+	0.0684323i
$823$	−44.2276	−	16.0975i	−1.54168	−	0.561125i	−0.575231	−	0.817991i	$-0.695088\pi$
$823$	−44.2276	−	16.0975i	−1.54168	−	0.561125i	−0.966447	+	0.256866i	$0.917310\pi$
$824$	3.71688	+	6.43783i	0.129484	+	0.224272i
$825$	0.733956	−	1.27125i	0.0255531	−	0.0442592i
$826$	9.82295	−	8.24243i	0.341784	−	0.286791i
$827$	18.9743	−	15.9213i	0.659801	−	0.553639i	−0.250226	−	0.968187i	$-0.580505\pi$
$827$	18.9743	−	15.9213i	0.659801	−	0.553639i	0.910027	+	0.414548i	$0.136060\pi$
$828$	5.41147	−	9.37295i	0.188062	−	0.325732i
$829$	17.2959	+	29.9574i	0.600712	+	1.04046i	0.992713	+	0.120499i	$0.0384494\pi$
$829$	17.2959	+	29.9574i	0.600712	+	1.04046i	−0.392002	+	0.919965i	$0.628217\pi$
$830$	−2.83750	−	1.03276i	−0.0984909	−	0.0358478i
$831$	−0.993193	+	5.63268i	−0.0344535	+	0.195395i
$832$	0.184793	+	1.04801i	0.00640653	+	0.0363332i
$833$	26.1691	−	9.52476i	0.906704	−	0.330013i
$834$	−5.16044	−	4.33013i	−0.178692	−	0.149940i
$835$	7.83244			0.271053
$836$		0			0
$837$	18.0155			0.622706
$838$	27.4957	+	23.0716i	0.949824	+	0.796997i
$839$	−6.31996	+	2.30028i	−0.218189	+	0.0794143i	−0.448802	−	0.893631i	$-0.648149\pi$
$839$	−6.31996	+	2.30028i	−0.218189	+	0.0794143i	0.230613	+	0.973046i	$0.425927\pi$
$840$	−0.212134	−	1.20307i	−0.00731931	−	0.0415099i
$841$	2.00939	−	11.3958i	0.0692893	−	0.392959i
$842$	−19.4611	−	7.08326i	−0.670674	−	0.244105i
$843$	1.24510	+	2.15658i	0.0428835	+	0.0742764i
$844$	−5.73442	+	9.93231i	−0.197387	+	0.341884i
$845$	−18.1821	+	15.2566i	−0.625483	+	0.524843i
$846$	8.10607	−	6.80180i	0.278692	−	0.233851i
$847$	6.03684	−	10.4561i	0.207428	−	0.359276i
$848$	4.94356	+	8.56250i	0.169763	+	0.294038i
$849$	−6.83275	−	2.48692i	−0.234499	−	0.0853508i
$850$	−1.23783	+	7.02006i	−0.0424571	+	0.240786i
$851$	−4.21213	−	23.8882i	−0.144390	−	0.818877i
$852$	−0.921274	+	0.335316i	−0.0315623	+	0.0114878i
$853$	16.5895	+	13.9202i	0.568012	+	0.476619i	0.880986	−	0.473143i	$-0.156881\pi$
$853$	16.5895	+	13.9202i	0.568012	+	0.476619i	−0.312973	+	0.949762i	$0.601325\pi$
$854$	−9.33099			−0.319300
$855$		0			0
$856$	−0.177052			−0.00605150
$857$	−29.4741	−	24.7317i	−1.00681	−	0.844818i	−0.0189008	−	0.999821i	$-0.506017\pi$
$857$	−29.4741	−	24.7317i	−1.00681	−	0.844818i	−0.987914	+	0.155004i	$0.950461\pi$
$858$	−1.46791	+	0.534276i	−0.0501137	+	0.0182399i
$859$	−2.87779	−	16.3208i	−0.0981890	−	0.556858i	−0.993723	−	0.111865i	$-0.964318\pi$
$859$	−2.87779	−	16.3208i	−0.0981890	−	0.556858i	0.895534	−	0.444992i	$-0.146794\pi$
$860$	1.28312	−	7.27693i	0.0437540	−	0.248141i
$861$	1.07873	+	0.392624i	0.0367629	+	0.0133806i
$862$	9.16250	+	15.8699i	0.312076	+	0.540532i
$863$	12.9290	−	22.3937i	0.440109	−	0.762291i	−0.557588	−	0.830118i	$-0.688273\pi$
$863$	12.9290	−	22.3937i	0.440109	−	0.762291i	0.997697	+	0.0678268i	$0.0216065\pi$
$864$	−1.56418	+	1.31250i	−0.0532144	+	0.0446522i
$865$	11.5621	−	9.70177i	0.393124	−	0.329870i
$866$	−2.54664	+	4.41090i	−0.0865382	+	0.149889i
$867$	−5.87164	−	10.1700i	−0.199412	−	0.345391i
$868$	−14.5817	−	5.30731i	−0.494936	−	0.180142i
$869$	−4.91353	+	27.8660i	−0.166680	+	0.945290i
$870$	0.768266	+	4.35705i	0.0260467	+	0.147718i
$871$	11.6382	−	4.23594i	0.394344	−	0.143529i
$872$	3.24897	+	2.72621i	0.110024	+	0.0923211i
$873$	−5.41147			−0.183151
$874$		0			0
$875$	21.1052			0.713488
$876$	0.210952	+	0.177009i	0.00712740	+	0.00598059i
$877$	47.5699	−	17.3140i	1.60632	−	0.584653i	0.625613	−	0.780134i	$-0.284849\pi$
$877$	47.5699	−	17.3140i	1.60632	−	0.584653i	0.980707	+	0.195481i	$0.0626269\pi$
$878$	−1.79055	−	10.1547i	−0.0604283	−	0.342706i
$879$	0.571614	−	3.24178i	0.0192801	−	0.109343i
$880$	−7.94356	−	2.89122i	−0.267777	−	0.0974630i
$881$	−25.4846	−	44.1406i	−0.858597	−	1.48713i	−0.873267	−	0.487241i	$-0.838003\pi$
$881$	−25.4846	−	44.1406i	−0.858597	−	1.48713i	0.0146701	−	0.999892i	$-0.495330\pi$
$882$	−5.62449	+	9.74189i	−0.189386	+	0.328027i
$883$	29.1994	−	24.5012i	0.982638	−	0.824531i	−0.00184735	−	0.999998i	$-0.500588\pi$
$883$	29.1994	−	24.5012i	0.982638	−	0.824531i	0.984485	+	0.175467i	$0.0561436\pi$
$884$	5.81109	−	4.87608i	0.195448	−	0.164000i
$885$	2.53209	−	4.38571i	0.0851152	−	0.147424i
$886$	4.40807	+	7.63500i	0.148092	+	0.256503i
$887$	29.5895	+	10.7697i	0.993517	+	0.361611i	0.787081	−	0.616850i	$-0.211591\pi$
$887$	29.5895	+	10.7697i	0.993517	+	0.361611i	0.206436	+	0.978460i	$0.433814\pi$
$888$	−0.389185	+	2.20718i	−0.0130602	+	0.0740681i
$889$	6.72369	+	38.1319i	0.225505	+	1.27890i
$890$	−22.3773	+	8.14468i	−0.750090	+	0.273010i
$891$	25.6728	+	21.5420i	0.860070	+	0.721685i
$892$	11.1925			0.374754
$893$		0			0
$894$	−1.79797			−0.0601332
$895$	−16.8348	−	14.1261i	−0.562726	−	0.472183i
$896$	1.65270	−	0.601535i	0.0552130	−	0.0200959i
$897$	0.241230	+	1.36808i	0.00805442	+	0.0456789i
$898$	2.09714	−	11.8935i	0.0699826	−	0.396891i
$899$	52.8093	+	19.2210i	1.76129	+	0.641057i
$900$	−1.43969	−	2.49362i	−0.0479898	−	0.0831207i
$901$	35.2395	−	61.0366i	1.17400	−	2.03342i
$902$	6.08512	−	5.10602i	0.202612	−	0.170012i
$903$	−1.72874	+	1.45059i	−0.0575289	+	0.0482725i
$904$	−5.21941	+	9.04028i	−0.173595	+	0.300675i
$905$	15.0351	+	26.0415i	0.499783	+	0.865650i
$906$	−7.23947	−	2.63495i	−0.240515	−	0.0875405i
$907$	1.54647	−	8.77049i	0.0513498	−	0.291219i	−0.948309	−	0.317349i	$-0.897207\pi$
$907$	1.54647	−	8.77049i	0.0513498	−	0.291219i	0.999659	+	0.0261299i	$0.00831834\pi$
$908$	−0.589870	−	3.34532i	−0.0195755	−	0.111018i
$909$	−6.63816	+	2.41609i	−0.220174	+	0.0801367i
$910$	−2.86753	−	2.40614i	−0.0950576	−	0.0797628i
$911$	−44.2959			−1.46759			−0.733795	−	0.679371i	$-0.762253\pi$
$911$	−44.2959			−1.46759			−0.733795	+	0.679371i	$0.762253\pi$
$912$		0			0
$913$	6.38144			0.211195
$914$	−0.560307	−	0.470154i	−0.0185333	−	0.0155513i
$915$	−3.46286	+	1.26038i	−0.114479	+	0.0416668i
$916$	0.739170	+	4.19204i	0.0244229	+	0.138509i
$917$	2.33719	−	13.2549i	0.0771809	−	0.437714i
$918$	13.6775	+	4.97821i	0.451425	+	0.164305i
$919$	27.3969	+	47.4529i	0.903741	+	1.56533i	0.822598	+	0.568623i	$0.192524\pi$
$919$	27.3969	+	47.4529i	0.903741	+	1.56533i	0.0811431	+	0.996702i	$0.474143\pi$
$920$	−3.75877	+	6.51038i	−0.123923	+	0.214641i
$921$	0.353855	−	0.296920i	0.0116599	−	0.00978384i
$922$	17.6800	−	14.8353i	0.582261	−	0.488575i
$923$	−1.50206	+	2.60164i	−0.0494409	+	0.0856341i
$924$	1.29086	+	2.23583i	0.0424662	+	0.0735535i
$925$	−6.06418	−	2.20718i	−0.199389	−	0.0725716i
$926$	3.13341	−	17.7704i	0.102970	−	0.583973i
$927$	3.71688	+	21.0795i	0.122078	+	0.692341i
$928$	−5.98545	+	2.17853i	−0.196482	+	0.0715136i
$929$	23.2952	+	19.5470i	0.764291	+	0.641316i	0.939240	−	0.343261i	$-0.111532\pi$
$929$	23.2952	+	19.5470i	0.764291	+	0.641316i	−0.174949	+	0.984577i	$0.555976\pi$
$930$	−6.12836			−0.200957
$931$		0			0
$932$	6.64321			0.217606
$933$	1.98957	+	1.66945i	0.0651356	+	0.0546553i
$934$	−10.3109	+	3.75287i	−0.337384	+	0.122798i
$935$	10.4638	+	59.3431i	0.342203	+	1.94073i
$936$	−0.532089	+	3.01763i	−0.0173919	+	0.0986342i
$937$	−27.7310	−	10.0933i	−0.905933	−	0.329733i	−0.153305	−	0.988179i	$-0.548992\pi$
$937$	−27.7310	−	10.0933i	−0.905933	−	0.329733i	−0.752628	+	0.658446i	$0.771214\pi$
$938$	−10.2344	−	17.7265i	−0.334166	−	0.578792i
$939$	−5.08765	+	8.81207i	−0.166029	+	0.287571i
$940$	−5.63041	+	4.72448i	−0.183644	+	0.154096i
$941$	−10.3628	+	8.69540i	−0.337817	+	0.283462i	−0.795876	−	0.605460i	$-0.792989\pi$
$941$	−10.3628	+	8.69540i	−0.337817	+	0.283462i	0.458059	+	0.888922i	$0.348545\pi$
$942$	0.490200	−	0.849051i	0.0159716	−	0.0276636i
$943$	−3.53209	−	6.11776i	−0.115021	−	0.199222i
$944$	6.85117	+	2.49362i	0.222986	+	0.0811604i
$945$	1.24722	−	7.07331i	0.0405719	−	0.230095i
$946$	2.71167	+	15.3786i	0.0881639	+	0.500002i
$947$	8.15745	−	2.96907i	0.265082	−	0.0964818i	−0.206060	−	0.978539i	$-0.566064\pi$
$947$	8.15745	−	2.96907i	0.265082	−	0.0964818i	0.471142	+	0.882058i	$0.343842\pi$
$948$	−1.78106	−	1.49449i	−0.0578461	−	0.0485387i
$949$	0.843807			0.0273911
$950$		0			0
$951$	1.94532			0.0630812
$952$	−9.60401	−	8.05872i	−0.311268	−	0.261185i
$953$	−39.3150	+	14.3095i	−1.27354	+	0.463529i	−0.888289	−	0.459284i	$-0.848106\pi$
$953$	−39.3150	+	14.3095i	−1.27354	+	0.463529i	−0.385247	+	0.922813i	$0.625884\pi$
$954$	4.94356	+	28.0363i	0.160054	+	0.907710i
$955$	1.57573	−	8.93642i	0.0509895	−	0.289176i
$956$	−15.0496	−	5.47762i	−0.486740	−	0.177159i
$957$	−4.67499	−	8.09732i	−0.151121	−	0.261749i
$958$	−11.1925	+	19.3860i	−0.361614	+	0.626334i
$959$	7.72874	−	6.48518i	0.249574	−	0.209418i
$960$	0.532089	−	0.446476i	0.0171731	−	0.0144099i
$961$	−23.4222	+	40.5685i	−0.755555	+	1.30866i
$962$	3.43376	+	5.94745i	0.110709	+	0.191754i
$963$	−0.479055	−	0.174362i	−0.0154373	−	0.00561873i
$964$	−1.49407	+	8.47329i	−0.0481208	+	0.272906i
$965$	7.63909	+	43.3234i	0.245911	+	1.39463i
$966$	2.15745	−	0.785248i	0.0694149	−	0.0252649i
$967$	−10.7784	−	9.04413i	−0.346609	−	0.290840i	0.452818	−	0.891603i	$-0.350419\pi$
$967$	−10.7784	−	9.04413i	−0.346609	−	0.290840i	−0.799427	+	0.600764i	$0.794863\pi$
$968$	6.86484			0.220644
$969$		0			0
$970$	3.75877			0.120687
$971$	28.6666	+	24.0541i	0.919955	+	0.771934i	0.973987	−	0.226606i	$-0.0727628\pi$
$971$	28.6666	+	24.0541i	0.919955	+	0.771934i	−0.0540319	+	0.998539i	$0.517207\pi$
$972$	−8.34389	+	3.03693i	−0.267630	+	0.0974095i
$973$	5.92396	+	33.5965i	0.189914	+	1.07705i
$974$	−6.55707	+	37.1870i	−0.210102	+	1.19155i
$975$	0.347296	+	0.126406i	0.0111224	+	0.00404822i
$976$	−2.65270	−	4.59462i	−0.0849110	−	0.147070i
$977$	−24.8769	+	43.0881i	−0.795883	+	1.37851i	0.126394	+	0.991980i	$0.459660\pi$
$977$	−24.8769	+	43.0881i	−0.795883	+	1.37851i	−0.922277	+	0.386530i	$0.873674\pi$
$978$	0.590337	−	0.495351i	0.0188769	−	0.0158396i
$979$	38.5519	−	32.3489i	1.23212	−	1.03388i
$980$	3.90673	−	6.76665i	0.124796	−	0.216153i
$981$	6.10607	+	10.5760i	0.194952	+	0.337666i
$982$	1.17587	+	0.427982i	0.0375235	+	0.0136574i
$983$	−3.88619	+	22.0397i	−0.123950	+	0.702957i	0.857975	+	0.513691i	$0.171722\pi$
$983$	−3.88619	+	22.0397i	−0.123950	+	0.702957i	−0.981926	+	0.189266i	$0.939389\pi$
$984$	0.113341	+	0.642788i	0.00361317	+	0.0204913i
$985$	−29.9418	+	10.8979i	−0.954025	+	0.347237i
$986$	34.7820	+	29.1856i	1.10768	+	0.929457i
$987$	2.24474			0.0714508
$988$		0			0
$989$	13.8871			0.441585
$990$	−18.6459	−	15.6458i	−0.592605	−	0.497255i
$991$	−45.2404	+	16.4662i	−1.43711	+	0.523065i	−0.938960	−	0.344027i	$-0.888209\pi$
$991$	−45.2404	+	16.4662i	−1.43711	+	0.523065i	−0.498149	+	0.867091i	$0.665987\pi$
$992$	−1.53209	−	8.68891i	−0.0486439	−	0.275873i
$993$	1.38562	−	7.85824i	0.0439713	−	0.249374i
$994$	4.66550	+	1.69810i	0.147981	+	0.0538605i
$995$	3.27631	+	5.67474i	0.103866	+	0.179901i
$996$	−0.262174	+	0.454099i	−0.00830730	+	0.0143887i
$997$	−32.6732	+	27.4161i	−1.03477	+	0.868277i	−0.991411	−	0.130783i	$-0.958251\pi$
$997$	−32.6732	+	27.4161i	−1.03477	+	0.868277i	−0.0433608	+	0.999059i	$0.513806\pi$
$998$	−7.14724	+	5.99725i	−0.226242	+	0.189840i
$999$	−6.58853	+	11.4117i	−0.208452	+	0.361049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.b.415.1		6
19.2	odd	18		722.2.c.l.653.2		6
19.3	odd	18		722.2.c.l.429.2		6
19.4	even	9		38.2.e.a.9.1	✓	6
19.5	even	9		722.2.a.l.1.2		3
19.6	even	9	inner	722.2.e.b.595.1		6
19.7	even	3		722.2.e.m.423.1		6
19.8	odd	6		722.2.e.k.245.1		6
19.9	even	9		722.2.e.m.99.1		6
19.10	odd	18		722.2.e.a.99.1		6
19.11	even	3		38.2.e.a.17.1	yes	6
19.12	odd	6		722.2.e.a.423.1		6
19.13	odd	18		722.2.e.l.595.1		6
19.14	odd	18		722.2.a.k.1.2		3
19.15	odd	18		722.2.e.k.389.1		6
19.16	even	9		722.2.c.k.429.2		6
19.17	even	9		722.2.c.k.653.2		6
19.18	odd	2		722.2.e.l.415.1		6
57.5	odd	18		6498.2.a.bl.1.1		3
57.11	odd	6		342.2.u.c.55.1		6
57.14	even	18		6498.2.a.bq.1.1		3
57.23	odd	18		342.2.u.c.199.1		6
76.11	odd	6		304.2.u.c.17.1		6
76.23	odd	18		304.2.u.c.161.1		6
76.43	odd	18		5776.2.a.bn.1.2		3
76.71	even	18		5776.2.a.bo.1.2		3
95.4	even	18		950.2.l.d.351.1		6
95.23	odd	36		950.2.u.b.199.2		12
95.42	odd	36		950.2.u.b.199.1		12
95.49	even	6		950.2.l.d.701.1		6
95.68	odd	12		950.2.u.b.549.1		12
95.87	odd	12		950.2.u.b.549.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.9.1	✓	6	19.4	even	9
38.2.e.a.17.1	yes	6	19.11	even	3
304.2.u.c.17.1		6	76.11	odd	6
304.2.u.c.161.1		6	76.23	odd	18
342.2.u.c.55.1		6	57.11	odd	6
342.2.u.c.199.1		6	57.23	odd	18
722.2.a.k.1.2		3	19.14	odd	18
722.2.a.l.1.2		3	19.5	even	9
722.2.c.k.429.2		6	19.16	even	9
722.2.c.k.653.2		6	19.17	even	9
722.2.c.l.429.2		6	19.3	odd	18
722.2.c.l.653.2		6	19.2	odd	18
722.2.e.a.99.1		6	19.10	odd	18
722.2.e.a.423.1		6	19.12	odd	6
722.2.e.b.415.1		6	1.1	even	1	trivial
722.2.e.b.595.1		6	19.6	even	9	inner
722.2.e.k.245.1		6	19.8	odd	6
722.2.e.k.389.1		6	19.15	odd	18
722.2.e.l.415.1		6	19.18	odd	2
722.2.e.l.595.1		6	19.13	odd	18
722.2.e.m.99.1		6	19.9	even	9
722.2.e.m.423.1		6	19.7	even	3
950.2.l.d.351.1		6	95.4	even	18
950.2.l.d.701.1		6	95.49	even	6
950.2.u.b.199.1		12	95.42	odd	36
950.2.u.b.199.2		12	95.23	odd	36
950.2.u.b.549.1		12	95.68	odd	12
950.2.u.b.549.2		12	95.87	odd	12
5776.2.a.bn.1.2		3	76.43	odd	18
5776.2.a.bo.1.2		3	76.71	even	18
6498.2.a.bl.1.1		3	57.5	odd	18
6498.2.a.bq.1.1		3	57.14	even	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-0.326352 + 0.118782i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.347296 - 1.96962i) q^{5} +(-0.326352 - 0.118782i) q^{6} +(0.879385 + 1.52314i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.20574 + 1.85083i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-0.326352 + 0.118782i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.347296 - 1.96962i) q^{5} +(-0.326352 - 0.118782i) q^{6} +(0.879385 + 1.52314i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.20574 + 1.85083i) q^{9} +(1.53209 - 1.28558i) q^{10} +(-2.11334 + 3.66041i) q^{11} +(-0.173648 - 0.300767i) q^{12} +(-1.00000 - 0.363970i) q^{13} +(-0.305407 + 1.73205i) q^{14} +(0.120615 + 0.684040i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(5.46064 + 4.58202i) q^{17} -2.87939 q^{18} +2.00000 q^{20} +(-0.467911 - 0.392624i) q^{21} +(-3.97178 + 1.44561i) q^{22} +(0.652704 + 3.70167i) q^{23} +(0.0603074 - 0.342020i) q^{24} +(0.939693 + 0.342020i) q^{25} +(-0.532089 - 0.921605i) q^{26} +(1.02094 - 1.76833i) q^{27} +(-1.34730 + 1.13052i) q^{28} +(4.87939 - 4.09429i) q^{29} +(-0.347296 + 0.601535i) q^{30} +(4.41147 + 7.64090i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.254900 - 1.44561i) q^{33} +(1.23783 + 7.02006i) q^{34} +(3.30541 - 1.20307i) q^{35} +(-2.20574 - 1.85083i) q^{36} -6.45336 q^{37} +0.369585 q^{39} +(1.53209 + 1.28558i) q^{40} +(-1.76604 + 0.642788i) q^{41} +(-0.106067 - 0.601535i) q^{42} +(0.641559 - 3.63846i) q^{43} +(-3.97178 - 1.44561i) q^{44} +(2.87939 + 4.98724i) q^{45} +(-1.87939 + 3.25519i) q^{46} +(-2.81521 + 2.36224i) q^{47} +(0.266044 - 0.223238i) q^{48} +(1.95336 - 3.38332i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.32635 - 0.846723i) q^{51} +(0.184793 - 1.04801i) q^{52} +(-1.71688 - 9.73692i) q^{53} +(1.91875 - 0.698367i) q^{54} +(6.47565 + 5.43372i) q^{55} -1.75877 q^{56} +6.36959 q^{58} +(-5.58512 - 4.68647i) q^{59} +(-0.652704 + 0.237565i) q^{60} +(0.921274 + 5.22481i) q^{61} +(-1.53209 + 8.68891i) q^{62} +(-4.75877 - 1.73205i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.06418 + 1.84321i) q^{65} +(1.12449 - 0.943555i) q^{66} +(-8.91534 + 7.48086i) q^{67} +(-3.56418 + 6.17334i) q^{68} +(-0.652704 - 1.13052i) q^{69} +(3.30541 + 1.20307i) q^{70} +(0.490200 - 2.78006i) q^{71} +(-0.500000 - 2.83564i) q^{72} +(-0.745100 + 0.271194i) q^{73} +(-4.94356 - 4.14814i) q^{74} -0.347296 q^{75} -7.43376 q^{77} +(0.283119 + 0.237565i) q^{78} +(6.29086 - 2.28969i) q^{79} +(0.347296 + 1.96962i) q^{80} +(1.37686 - 7.80856i) q^{81} +(-1.76604 - 0.642788i) q^{82} +(-0.754900 - 1.30753i) q^{83} +(0.305407 - 0.528981i) q^{84} +(10.9213 - 9.16404i) q^{85} +(2.83022 - 2.37484i) q^{86} +(-1.10607 + 1.91576i) q^{87} +(-2.11334 - 3.66041i) q^{88} +(-11.1887 - 4.07234i) q^{89} +(-1.00000 + 5.67128i) q^{90} +(-0.325008 - 1.84321i) q^{91} +(-3.53209 + 1.28558i) q^{92} +(-2.34730 - 1.96962i) q^{93} -3.67499 q^{94} +0.347296 q^{96} +(1.43969 + 1.20805i) q^{97} +(3.67112 - 1.33618i) q^{98} +(-2.11334 - 11.9854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 3 q^{6} - 6 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 - 3 * q^6 - 6 * q^7 - 3 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} - 3 q^{6} - 6 q^{7} - 3 q^{8} - 3 q^{9} - 6 q^{11} - 6 q^{13} - 6 q^{14} + 12 q^{15} + 24 q^{17} - 6 q^{18} + 12 q^{20} - 12 q^{21} - 9 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{26} + 3 q^{27} - 6 q^{28} + 18 q^{29} + 6 q^{31} + 3 q^{33} - 12 q^{34} + 24 q^{35} - 3 q^{36} - 12 q^{37} - 12 q^{39} - 6 q^{41} + 24 q^{42} + 12 q^{43} - 9 q^{44} + 6 q^{45} - 24 q^{47} - 3 q^{48} - 15 q^{49} + 3 q^{50} - 15 q^{51} - 6 q^{52} + 6 q^{53} + 9 q^{54} + 12 q^{56} + 24 q^{58} - 12 q^{59} - 6 q^{60} - 12 q^{61} - 6 q^{63} - 3 q^{64} + 12 q^{65} - 6 q^{66} - 9 q^{67} - 3 q^{68} - 6 q^{69} + 24 q^{70} - 3 q^{72} - 3 q^{73} - 12 q^{77} + 18 q^{78} + 6 q^{79} + 12 q^{81} - 6 q^{82} - 6 q^{83} + 6 q^{84} + 48 q^{85} - 6 q^{86} + 18 q^{87} - 6 q^{88} - 36 q^{89} - 6 q^{90} - 12 q^{91} - 12 q^{92} - 12 q^{93} - 12 q^{94} + 3 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 - 3 * q^6 - 6 * q^7 - 3 * q^8 - 3 * q^9 - 6 * q^11 - 6 * q^13 - 6 * q^14 + 12 * q^15 + 24 * q^17 - 6 * q^18 + 12 * q^20 - 12 * q^21 - 9 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^26 + 3 * q^27 - 6 * q^28 + 18 * q^29 + 6 * q^31 + 3 * q^33 - 12 * q^34 + 24 * q^35 - 3 * q^36 - 12 * q^37 - 12 * q^39 - 6 * q^41 + 24 * q^42 + 12 * q^43 - 9 * q^44 + 6 * q^45 - 24 * q^47 - 3 * q^48 - 15 * q^49 + 3 * q^50 - 15 * q^51 - 6 * q^52 + 6 * q^53 + 9 * q^54 + 12 * q^56 + 24 * q^58 - 12 * q^59 - 6 * q^60 - 12 * q^61 - 6 * q^63 - 3 * q^64 + 12 * q^65 - 6 * q^66 - 9 * q^67 - 3 * q^68 - 6 * q^69 + 24 * q^70 - 3 * q^72 - 3 * q^73 - 12 * q^77 + 18 * q^78 + 6 * q^79 + 12 * q^81 - 6 * q^82 - 6 * q^83 + 6 * q^84 + 48 * q^85 - 6 * q^86 + 18 * q^87 - 6 * q^88 - 36 * q^89 - 6 * q^90 - 12 * q^91 - 12 * q^92 - 12 * q^93 - 12 * q^94 + 3 * q^97 + 36 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more