LMFDB - Embedded newform 722.2.e.l.423.1

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			423.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	722.423
Dual form			722.2.e.l.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-0.266044 + 1.50881i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.53209 + 1.28558i) q^{5} +(0.266044 + 1.50881i) q^{6} +(-1.34730 - 2.33359i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.613341 + 0.223238i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-0.266044 + 1.50881i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.53209 + 1.28558i) q^{5} +(0.266044 + 1.50881i) q^{6} +(-1.34730 - 2.33359i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.613341 + 0.223238i) q^{9} +(1.87939 + 0.684040i) q^{10} +(-1.59240 + 2.75811i) q^{11} +(0.766044 + 1.32683i) q^{12} +(1.00000 + 5.67128i) q^{13} +(-2.06418 - 1.73205i) q^{14} +(-2.34730 + 1.96962i) q^{15} +(0.173648 - 0.984808i) q^{16} +(6.12449 - 2.22913i) q^{17} +0.652704 q^{18} +2.00000 q^{20} +(3.87939 - 1.41198i) q^{21} +(-0.553033 + 3.13641i) q^{22} +(-0.532089 + 0.446476i) q^{23} +(1.17365 + 0.984808i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(2.87939 + 4.98724i) q^{26} +(-2.79813 + 4.84651i) q^{27} +(-2.53209 - 0.921605i) q^{28} +(-2.65270 - 0.965505i) q^{29} +(-1.53209 + 2.65366i) q^{30} +(1.22668 + 2.12467i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-3.73783 - 3.13641i) q^{33} +(4.99273 - 4.18939i) q^{34} +(0.935822 - 5.30731i) q^{35} +(0.613341 - 0.223238i) q^{36} +4.36959 q^{37} -8.82295 q^{39} +(1.87939 - 0.684040i) q^{40} +(0.0603074 - 0.342020i) q^{41} +(3.16250 - 2.65366i) q^{42} +(4.64543 + 3.89798i) q^{43} +(0.553033 + 3.13641i) q^{44} +(0.652704 + 1.13052i) q^{45} +(-0.347296 + 0.601535i) q^{46} +(-7.41147 - 2.69756i) q^{47} +(1.43969 + 0.524005i) q^{48} +(-0.130415 + 0.225885i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.73396 + 9.83375i) q^{51} +(4.41147 + 3.70167i) q^{52} +(-6.29086 + 5.27866i) q^{53} +(-0.971782 + 5.51125i) q^{54} +(-5.98545 + 2.17853i) q^{55} -2.69459 q^{56} -2.82295 q^{58} +(0.539363 - 0.196312i) q^{59} +(-0.532089 + 3.01763i) q^{60} +(2.24897 - 1.88711i) q^{61} +(1.87939 + 1.57699i) q^{62} +(-0.305407 - 1.73205i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-5.75877 + 9.97448i) q^{65} +(-4.58512 - 1.66885i) q^{66} +(-4.65910 - 1.69577i) q^{67} +(3.25877 - 5.64436i) q^{68} +(-0.532089 - 0.921605i) q^{69} +(-0.935822 - 5.30731i) q^{70} +(6.47565 + 5.43372i) q^{71} +(0.500000 - 0.419550i) q^{72} +(2.73783 - 15.5270i) q^{73} +(4.10607 - 1.49449i) q^{74} +1.53209 q^{75} +8.58172 q^{77} +(-8.29086 + 3.01763i) q^{78} +(1.57398 - 8.92647i) q^{79} +(1.53209 - 1.28558i) q^{80} +(-5.06805 - 4.25260i) q^{81} +(-0.0603074 - 0.342020i) q^{82} +(-4.23783 - 7.34013i) q^{83} +(2.06418 - 3.57526i) q^{84} +(12.2490 + 4.45826i) q^{85} +(5.69846 + 2.07407i) q^{86} +(2.16250 - 3.74557i) q^{87} +(1.59240 + 2.75811i) q^{88} +(-1.34389 - 7.62159i) q^{89} +(1.00000 + 0.839100i) q^{90} +(11.8871 - 9.97448i) q^{91} +(-0.120615 + 0.684040i) q^{92} +(-3.53209 + 1.28558i) q^{93} -7.88713 q^{94} +1.53209 q^{96} +(-0.326352 + 0.118782i) q^{97} +(-0.0452926 + 0.256867i) q^{98} +(-1.59240 + 1.33618i) 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 $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−0.266044	+	1.50881i	−0.153601	+	0.871114i	0.806453	+	0.591298i	$0.201384\pi$
$3$	−0.266044	+	1.50881i	−0.153601	+	0.871114i	−0.960054	+	0.279815i	$0.909727\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	1.53209	+	1.28558i	0.685171	+	0.574927i	0.917512	−	0.397708i	$-0.130194\pi$
$5$	1.53209	+	1.28558i	0.685171	+	0.574927i	−0.232341	+	0.972634i	$0.574639\pi$
$6$	0.266044	+	1.50881i	0.108612	+	0.615970i
$7$	−1.34730	−	2.33359i	−0.509230	−	0.882013i	−0.999943	−	0.0106911i	$-0.996597\pi$
$7$	−1.34730	−	2.33359i	−0.509230	−	0.882013i	0.490713	−	0.871321i	$-0.336736\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.613341	+	0.223238i	0.204447	+	0.0744126i
$10$	1.87939	+	0.684040i	0.594314	+	0.216313i
$11$	−1.59240	+	2.75811i	−0.480126	+	0.831602i	−0.999740	−	0.0227990i	$-0.992742\pi$
$11$	−1.59240	+	2.75811i	−0.480126	+	0.831602i	0.519615	+	0.854401i	$0.326076\pi$
$12$	0.766044	+	1.32683i	0.221138	+	0.383022i
$13$	1.00000	+	5.67128i	0.277350	+	1.57293i	0.731396	+	0.681953i	$0.238869\pi$
$13$	1.00000	+	5.67128i	0.277350	+	1.57293i	−0.454046	+	0.890978i	$0.650020\pi$
$14$	−2.06418	−	1.73205i	−0.551675	−	0.462910i
$15$	−2.34730	+	1.96962i	−0.606069	+	0.508553i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	6.12449	−	2.22913i	1.48541	−	0.540644i	0.533170	−	0.846008i	$-0.321001\pi$
$17$	6.12449	−	2.22913i	1.48541	−	0.540644i	0.952236	+	0.305364i	$0.0987783\pi$
$18$	0.652704			0.153844
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	3.87939	−	1.41198i	0.846551	−	0.308119i
$22$	−0.553033	+	3.13641i	−0.117907	+	0.668685i
$23$	−0.532089	+	0.446476i	−0.110948	+	0.0930966i	−0.696574	−	0.717485i	$-0.745293\pi$
$23$	−0.532089	+	0.446476i	−0.110948	+	0.0930966i	0.585626	+	0.810581i	$0.300849\pi$
$24$	1.17365	+	0.984808i	0.239570	+	0.201023i
$25$	−0.173648	−	0.984808i	−0.0347296	−	0.196962i
$26$	2.87939	+	4.98724i	0.564694	+	0.978079i
$27$	−2.79813	+	4.84651i	−0.538501	+	0.932711i
$28$	−2.53209	−	0.921605i	−0.478520	−	0.174167i
$29$	−2.65270	−	0.965505i	−0.492595	−	0.179290i	0.0837656	−	0.996485i	$-0.473305\pi$
$29$	−2.65270	−	0.965505i	−0.492595	−	0.179290i	−0.576360	+	0.817196i	$0.695528\pi$
$30$	−1.53209	+	2.65366i	−0.279720	+	0.484489i
$31$	1.22668	+	2.12467i	0.220319	+	0.381603i	0.954905	−	0.296913i	$-0.0959570\pi$
$31$	1.22668	+	2.12467i	0.220319	+	0.381603i	−0.734586	+	0.678515i	$0.762624\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−3.73783	−	3.13641i	−0.650672	−	0.545979i
$34$	4.99273	−	4.18939i	0.856245	−	0.718475i
$35$	0.935822	−	5.30731i	0.158183	−	0.897099i
$36$	0.613341	−	0.223238i	0.102223	−	0.0372063i
$37$	4.36959			0.718355			0.359178	−	0.933269i	$-0.383057\pi$
$37$	4.36959			0.718355			0.359178	+	0.933269i	$0.383057\pi$
$38$		0			0
$39$	−8.82295			−1.41280
$40$	1.87939	−	0.684040i	0.297157	−	0.108156i
$41$	0.0603074	−	0.342020i	0.00941843	−	0.0534146i	−0.979736	−	0.200292i	$-0.935811\pi$
$41$	0.0603074	−	0.342020i	0.00941843	−	0.0534146i	0.989155	+	0.146877i	$0.0469222\pi$
$42$	3.16250	−	2.65366i	0.487985	−	0.409468i
$43$	4.64543	+	3.89798i	0.708421	+	0.594436i	0.924156	−	0.382016i	$-0.124770\pi$
$43$	4.64543	+	3.89798i	0.708421	+	0.594436i	−0.215734	+	0.976452i	$0.569215\pi$
$44$	0.553033	+	3.13641i	0.0833729	+	0.472831i
$45$	0.652704	+	1.13052i	0.0972993	+	0.168527i
$46$	−0.347296	+	0.601535i	−0.0512061	+	0.0886915i
$47$	−7.41147	−	2.69756i	−1.08107	−	0.393479i	−0.260767	−	0.965402i	$-0.583975\pi$
$47$	−7.41147	−	2.69756i	−1.08107	−	0.393479i	−0.820307	+	0.571923i	$0.806198\pi$
$48$	1.43969	+	0.524005i	0.207802	+	0.0756336i
$49$	−0.130415	+	0.225885i	−0.0186307	+	0.0322693i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	1.73396	+	9.83375i	0.242802	+	1.37700i
$52$	4.41147	+	3.70167i	0.611761	+	0.513329i
$53$	−6.29086	+	5.27866i	−0.864116	+	0.725079i	−0.962851	−	0.270034i	$-0.912965\pi$
$53$	−6.29086	+	5.27866i	−0.864116	+	0.725079i	0.0987347	+	0.995114i	$0.468520\pi$
$54$	−0.971782	+	5.51125i	−0.132243	+	0.749986i
$55$	−5.98545	+	2.17853i	−0.807078	+	0.293752i
$56$	−2.69459			−0.360080
$57$		0			0
$58$	−2.82295			−0.370671
$59$	0.539363	−	0.196312i	0.0702191	−	0.0255576i	−0.306672	−	0.951815i	$-0.599215\pi$
$59$	0.539363	−	0.196312i	0.0702191	−	0.0255576i	0.376891	+	0.926258i	$0.376993\pi$
$60$	−0.532089	+	3.01763i	−0.0686924	+	0.389574i
$61$	2.24897	−	1.88711i	0.287951	−	0.241620i	−0.487357	−	0.873203i	$-0.662039\pi$
$61$	2.24897	−	1.88711i	0.287951	−	0.241620i	0.775308	+	0.631583i	$0.217595\pi$
$62$	1.87939	+	1.57699i	0.238682	+	0.200278i
$63$	−0.305407	−	1.73205i	−0.0384777	−	0.218218i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−5.75877	+	9.97448i	−0.714288	+	1.23718i
$66$	−4.58512	−	1.66885i	−0.564390	−	0.205421i
$67$	−4.65910	−	1.69577i	−0.569200	−	0.207172i	0.0413568	−	0.999144i	$-0.486832\pi$
$67$	−4.65910	−	1.69577i	−0.569200	−	0.207172i	−0.610557	+	0.791973i	$0.709054\pi$
$68$	3.25877	−	5.64436i	0.395184	−	0.684479i
$69$	−0.532089	−	0.921605i	−0.0640560	−	0.110948i
$70$	−0.935822	−	5.30731i	−0.111852	−	0.634345i
$71$	6.47565	+	5.43372i	0.768518	+	0.644864i	0.940329	−	0.340266i	$-0.110517\pi$
$71$	6.47565	+	5.43372i	0.768518	+	0.644864i	−0.171811	+	0.985130i	$0.554962\pi$
$72$	0.500000	−	0.419550i	0.0589256	−	0.0494444i
$73$	2.73783	−	15.5270i	0.320438	−	1.81730i	−0.219525	−	0.975607i	$-0.570451\pi$
$73$	2.73783	−	15.5270i	0.320438	−	1.81730i	0.539963	−	0.841689i	$-0.318438\pi$
$74$	4.10607	−	1.49449i	0.477321	−	0.173730i
$75$	1.53209			0.176910
$76$		0			0
$77$	8.58172			0.977978
$78$	−8.29086	+	3.01763i	−0.938755	+	0.341679i
$79$	1.57398	−	8.92647i	0.177086	−	1.00431i	−0.758622	−	0.651531i	$-0.774127\pi$
$79$	1.57398	−	8.92647i	0.177086	−	1.00431i	0.935708	−	0.352775i	$-0.114762\pi$
$80$	1.53209	−	1.28558i	0.171293	−	0.143732i
$81$	−5.06805	−	4.25260i	−0.563116	−	0.472511i
$82$	−0.0603074	−	0.342020i	−0.00665984	−	0.0377698i
$83$	−4.23783	−	7.34013i	−0.465162	−	0.805684i	0.534047	−	0.845455i	$-0.320671\pi$
$83$	−4.23783	−	7.34013i	−0.465162	−	0.805684i	−0.999209	+	0.0397709i	$0.987337\pi$
$84$	2.06418	−	3.57526i	0.225220	−	0.390093i
$85$	12.2490	+	4.45826i	1.32859	+	0.483566i
$86$	5.69846	+	2.07407i	0.614481	+	0.223653i
$87$	2.16250	−	3.74557i	0.231845	−	0.401567i
$88$	1.59240	+	2.75811i	0.169750	+	0.294016i
$89$	−1.34389	−	7.62159i	−0.142452	−	0.807887i	−0.969377	−	0.245575i	$-0.921023\pi$
$89$	−1.34389	−	7.62159i	−0.142452	−	0.807887i	0.826925	−	0.562312i	$-0.190088\pi$
$90$	1.00000	+	0.839100i	0.105409	+	0.0884489i
$91$	11.8871	−	9.97448i	1.24611	−	1.04561i
$92$	−0.120615	+	0.684040i	−0.0125750	+	0.0713161i
$93$	−3.53209	+	1.28558i	−0.366261	+	0.133308i
$94$	−7.88713			−0.813495
$95$		0			0
$96$	1.53209			0.156368
$97$	−0.326352	+	0.118782i	−0.0331360	+	0.0120605i	−0.358535	−	0.933516i	$-0.616724\pi$
$97$	−0.326352	+	0.118782i	−0.0331360	+	0.0120605i	0.325399	+	0.945577i	$0.394501\pi$
$98$	−0.0452926	+	0.256867i	−0.00457525	+	0.0259475i
$99$	−1.59240	+	1.33618i	−0.160042	+	0.134291i
$100$	−0.766044	−	0.642788i	−0.0766044	−	0.0642788i
$101$	−0.0641778	−	0.363970i	−0.00638593	−	0.0362164i	0.981448	−	0.191727i	$-0.0614088\pi$
$101$	−0.0641778	−	0.363970i	−0.00638593	−	0.0362164i	−0.987834	+	0.155511i	$0.950298\pi$
$102$	4.99273	+	8.64766i	0.494354	+	0.856245i
$103$	4.29086	−	7.43199i	0.422791	−	0.732295i	−0.573420	−	0.819261i	$-0.694384\pi$
$103$	4.29086	−	7.43199i	0.422791	−	0.732295i	0.996211	+	0.0869659i	$0.0277171\pi$
$104$	5.41147	+	1.96962i	0.530639	+	0.193137i
$105$	7.75877	+	2.82396i	0.757178	+	0.275590i
$106$	−4.10607	+	7.11192i	−0.398816	+	0.690770i
$107$	−5.72668	−	9.91890i	−0.553619	−	0.958897i	−0.998010	−	0.0630633i	$-0.979913\pi$
$107$	−5.72668	−	9.91890i	−0.553619	−	0.958897i	0.444390	−	0.895833i	$-0.353420\pi$
$108$	0.971782	+	5.51125i	0.0935097	+	0.530320i
$109$	−6.66044	−	5.58878i	−0.637955	−	0.535308i	0.265435	−	0.964129i	$-0.414485\pi$
$109$	−6.66044	−	5.58878i	−0.637955	−	0.535308i	−0.903389	+	0.428821i	$0.858929\pi$
$110$	−4.87939	+	4.09429i	−0.465231	+	0.390375i
$111$	−1.16250	+	6.59289i	−0.110340	+	0.625769i
$112$	−2.53209	+	0.921605i	−0.239260	+	0.0870835i
$113$	−2.85978			−0.269026			−0.134513	−	0.990912i	$-0.542947\pi$
$113$	−2.85978			−0.269026			−0.134513	+	0.990912i	$0.542947\pi$
$114$		0			0
$115$	−1.38919			−0.129542
$116$	−2.65270	+	0.965505i	−0.246297	+	0.0896449i
$117$	−0.652704	+	3.70167i	−0.0603425	+	0.342219i
$118$	0.439693	−	0.368946i	0.0404770	−	0.0339642i
$119$	−13.4534	−	11.2887i	−1.23327	−	1.03483i
$120$	0.532089	+	3.01763i	0.0485728	+	0.275470i
$121$	0.428548	+	0.742267i	0.0389589	+	0.0674789i
$122$	1.46791	−	2.54250i	0.132898	−	0.230187i
$123$	0.500000	+	0.181985i	0.0450835	+	0.0164090i
$124$	2.30541	+	0.839100i	0.207032	+	0.0753534i
$125$	6.00000	−	10.3923i	0.536656	−	0.929516i
$126$	−0.879385	−	1.52314i	−0.0783419	−	0.135692i
$127$	−1.68954	−	9.58186i	−0.149922	−	0.850252i	−0.963282	−	0.268491i	$-0.913475\pi$
$127$	−1.68954	−	9.58186i	−0.149922	−	0.850252i	0.813360	−	0.581761i	$-0.197636\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	−7.11721	+	5.97205i	−0.626636	+	0.525810i
$130$	−2.00000	+	11.3426i	−0.175412	+	0.994809i
$131$	6.07785	−	2.21216i	0.531024	−	0.193277i	−0.0625715	−	0.998040i	$-0.519930\pi$
$131$	6.07785	−	2.21216i	0.531024	−	0.193277i	0.593596	+	0.804764i	$0.297708\pi$
$132$	−4.87939			−0.424696
$133$		0			0
$134$	−4.95811			−0.428316
$135$	−10.5175	+	3.82807i	−0.905206	+	0.329468i
$136$	1.13176	−	6.41852i	0.0970475	−	0.550384i
$137$	−8.93242	+	7.49519i	−0.763148	+	0.640357i	−0.938944	−	0.344069i	$-0.888194\pi$
$137$	−8.93242	+	7.49519i	−0.763148	+	0.640357i	0.175796	+	0.984427i	$0.443750\pi$
$138$	−0.815207	−	0.684040i	−0.0693951	−	0.0582294i
$139$	−1.43494	−	8.13798i	−0.121710	−	0.690254i	−0.983207	−	0.182492i	$-0.941584\pi$
$139$	−1.43494	−	8.13798i	−0.121710	−	0.690254i	0.861497	−	0.507763i	$-0.169527\pi$
$140$	−2.69459	−	4.66717i	−0.227735	−	0.394448i
$141$	6.04189	−	10.4649i	0.508819	−	0.881300i
$142$	7.94356	+	2.89122i	0.666609	+	0.242626i
$143$	−17.2344	−	6.27282i	−1.44121	−	0.524559i
$144$	0.326352	−	0.565258i	0.0271960	−	0.0471048i
$145$	−2.82295	−	4.88949i	−0.234433	−	0.406050i
$146$	−2.73783	−	15.5270i	−0.226584	−	1.28502i
$147$	−0.306123	−	0.256867i	−0.0252486	−	0.0211861i
$148$	3.34730	−	2.80872i	0.275146	−	0.230875i
$149$	−2.85710	+	16.2034i	−0.234062	+	1.32743i	0.610517	+	0.792003i	$0.290962\pi$
$149$	−2.85710	+	16.2034i	−0.234062	+	1.32743i	−0.844579	+	0.535431i	$0.820149\pi$
$150$	1.43969	−	0.524005i	0.117550	−	0.0427849i
$151$	−4.65539			−0.378850			−0.189425	−	0.981895i	$-0.560662\pi$
$151$	−4.65539			−0.378850			−0.189425	+	0.981895i	$0.560662\pi$
$152$		0			0
$153$	4.25402			0.343917
$154$	8.06418	−	2.93512i	0.649830	−	0.236519i
$155$	−0.852044	+	4.83218i	−0.0684378	+	0.388130i
$156$	−6.75877	+	5.67128i	−0.541135	+	0.454066i
$157$	6.47565	+	5.43372i	0.516813	+	0.433658i	0.863519	−	0.504316i	$-0.168255\pi$
$157$	6.47565	+	5.43372i	0.516813	+	0.433658i	−0.346706	+	0.937974i	$0.612700\pi$
$158$	−1.57398	−	8.92647i	−0.125219	−	0.710152i
$159$	−6.29086	−	10.8961i	−0.498898	−	0.864116i
$160$	1.00000	−	1.73205i	0.0790569	−	0.136931i
$161$	1.75877	+	0.640140i	0.138611	+	0.0504501i
$162$	−6.21688	−	2.26276i	−0.488444	−	0.177779i
$163$	−8.52481	+	14.7654i	−0.667715	+	1.15652i	0.310826	+	0.950467i	$0.399394\pi$
$163$	−8.52481	+	14.7654i	−0.667715	+	1.15652i	−0.978542	+	0.206050i	$0.933939\pi$
$164$	−0.173648	−	0.300767i	−0.0135596	−	0.0234860i
$165$	−1.69459	−	9.61051i	−0.131924	−	0.748177i
$166$	−6.49273	−	5.44804i	−0.503933	−	0.422850i
$167$	2.44562	−	2.05212i	0.189248	−	0.158798i	−0.543241	−	0.839577i	$-0.682803\pi$
$167$	2.44562	−	2.05212i	0.189248	−	0.158798i	0.732489	+	0.680779i	$0.238359\pi$
$168$	0.716881	−	4.06564i	0.0553086	−	0.313671i
$169$	−18.9474	+	6.89630i	−1.45749	+	0.530485i
$170$	13.0351			0.999745
$171$		0			0
$172$	6.06418			0.462389
$173$	9.04963	−	3.29380i	0.688031	−	0.250423i	0.0257389	−	0.999669i	$-0.491806\pi$
$173$	9.04963	−	3.29380i	0.688031	−	0.250423i	0.662292	+	0.749246i	$0.269584\pi$
$174$	0.751030	−	4.25930i	0.0569354	−	0.322897i
$175$	−2.06418	+	1.73205i	−0.156037	+	0.130931i
$176$	2.43969	+	2.04715i	0.183899	+	0.154309i
$177$	0.152704	+	0.866025i	0.0114779	+	0.0650945i
$178$	−3.86959	−	6.70232i	−0.290038	−	0.502360i
$179$	9.40807	−	16.2953i	0.703192	−	1.21796i	−0.264148	−	0.964482i	$-0.585091\pi$
$179$	9.40807	−	16.2953i	0.703192	−	1.21796i	0.967340	−	0.253482i	$-0.0815760\pi$
$180$	1.22668	+	0.446476i	0.0914314	+	0.0332783i
$181$	2.61081	+	0.950259i	0.194060	+	0.0706322i	0.437222	−	0.899354i	$-0.355962\pi$
$181$	2.61081	+	0.950259i	0.194060	+	0.0706322i	−0.243162	+	0.969986i	$0.578185\pi$
$182$	7.75877	−	13.4386i	0.575118	−	0.996134i
$183$	2.24897	+	3.89533i	0.166249	+	0.287951i
$184$	0.120615	+	0.684040i	0.00889184	+	0.0504281i
$185$	6.69459	+	5.61743i	0.492196	+	0.413002i
$186$	−2.87939	+	2.41609i	−0.211127	+	0.177156i
$187$	−3.60442	+	20.4417i	−0.263581	+	1.49484i
$188$	−7.41147	+	2.69756i	−0.540537	+	0.196739i
$189$	15.0797			1.09688
$190$		0			0
$191$	9.56212			0.691891			0.345945	−	0.938255i	$-0.387558\pi$
$191$	9.56212			0.691891			0.345945	+	0.938255i	$0.387558\pi$
$192$	1.43969	−	0.524005i	0.103901	−	0.0378168i
$193$	4.11216	−	23.3212i	0.296000	−	1.67870i	−0.367112	−	0.930177i	$-0.619653\pi$
$193$	4.11216	−	23.3212i	0.296000	−	1.67870i	0.663111	−	0.748521i	$-0.269236\pi$
$194$	−0.266044	+	0.223238i	−0.0191009	+	0.0160275i
$195$	−13.5175	−	11.3426i	−0.968011	−	0.812258i
$196$	0.0452926	+	0.256867i	0.00323519	+	0.0183477i
$197$	11.4611	+	19.8512i	0.816570	+	1.41434i	0.908195	+	0.418547i	$0.137460\pi$
$197$	11.4611	+	19.8512i	0.816570	+	1.41434i	−0.0916253	+	0.995794i	$0.529206\pi$
$198$	−1.03936	+	1.80023i	−0.0738643	+	0.127937i
$199$	−9.47565	−	3.44886i	−0.671711	−	0.244483i	−0.0164267	−	0.999865i	$-0.505229\pi$
$199$	−9.47565	−	3.44886i	−0.671711	−	0.244483i	−0.655284	+	0.755382i	$0.727451\pi$
$200$	−0.939693	−	0.342020i	−0.0664463	−	0.0241845i
$201$	3.79813	−	6.57856i	0.267900	−	0.464016i
$202$	−0.184793	−	0.320070i	−0.0130020	−	0.0225201i
$203$	1.32089	+	7.49113i	0.0927082	+	0.525774i
$204$	7.64930	+	6.41852i	0.535558	+	0.449387i
$205$	0.532089	−	0.446476i	0.0371627	−	0.0311832i
$206$	1.49020	−	8.45134i	0.103827	−	0.588833i
$207$	−0.426022	+	0.155059i	−0.0296106	+	0.0107774i
$208$	5.75877			0.399299
$209$		0			0
$210$	8.25671			0.569767
$211$	−21.0116	+	7.64760i	−1.44650	+	0.526483i	−0.941611	−	0.336702i	$-0.890688\pi$
$211$	−21.0116	+	7.64760i	−1.44650	+	0.526483i	−0.504888	+	0.863185i	$0.668466\pi$
$212$	−1.42602	+	8.08737i	−0.0979396	+	0.555443i
$213$	−9.92127	+	8.32494i	−0.679795	+	0.570415i
$214$	−8.77379	−	7.36208i	−0.599764	−	0.503261i
$215$	2.10607	+	11.9441i	0.143633	+	0.814581i
$216$	2.79813	+	4.84651i	0.190389	+	0.329763i
$217$	3.30541	−	5.72513i	0.224386	−	0.388647i
$218$	−8.17024	−	2.97373i	−0.553359	−	0.201406i
$219$	22.6989	+	8.26173i	1.53385	+	0.558276i
$220$	−3.18479	+	5.51622i	−0.214719	+	0.371904i
$221$	18.7665	+	32.5046i	1.26237	+	2.18649i
$222$	1.16250	+	6.59289i	0.0780221	+	0.442486i
$223$	7.10607	+	5.96270i	0.475857	+	0.399292i	0.848926	−	0.528512i	$-0.177250\pi$
$223$	7.10607	+	5.96270i	0.475857	+	0.399292i	−0.373068	+	0.927804i	$0.621694\pi$
$224$	−2.06418	+	1.73205i	−0.137919	+	0.115728i
$225$	0.113341	−	0.642788i	0.00755605	−	0.0428525i
$226$	−2.68732	+	0.978104i	−0.178758	+	0.0650625i
$227$	−7.73648			−0.513488			−0.256744	−	0.966479i	$-0.582650\pi$
$227$	−7.73648			−0.513488			−0.256744	+	0.966479i	$0.582650\pi$
$228$		0			0
$229$	−23.0351			−1.52220			−0.761101	−	0.648634i	$-0.775341\pi$
$229$	−23.0351			−1.52220			−0.761101	+	0.648634i	$0.775341\pi$
$230$	−1.30541	+	0.475129i	−0.0860760	+	0.0313291i
$231$	−2.28312	+	12.9482i	−0.150218	+	0.851930i
$232$	−2.16250	+	1.81456i	−0.141975	+	0.119131i
$233$	6.43448	+	5.39917i	0.421537	+	0.353711i	0.828747	−	0.559623i	$-0.189054\pi$
$233$	6.43448	+	5.39917i	0.421537	+	0.353711i	−0.407211	+	0.913334i	$0.633499\pi$
$234$	0.652704	+	3.70167i	0.0426686	+	0.241985i
$235$	−7.88713	−	13.6609i	−0.514499	−	0.891139i
$236$	0.286989	−	0.497079i	0.0186814	−	0.0323571i
$237$	13.0496	+	4.74968i	0.847665	+	0.308525i
$238$	−16.5030	−	6.00660i	−1.06973	−	0.389350i
$239$	7.86484	−	13.6223i	0.508734	−	0.881153i	−0.491215	−	0.871038i	$-0.663447\pi$
$239$	7.86484	−	13.6223i	0.508734	−	0.881153i	0.999949	−	0.0101147i	$-0.00321967\pi$
$240$	1.53209	+	2.65366i	0.0988959	+	0.171293i
$241$	−3.03936	−	17.2371i	−0.195783	−	1.11034i	−0.911300	−	0.411743i	$-0.864920\pi$
$241$	−3.03936	−	17.2371i	−0.195783	−	1.11034i	0.715517	−	0.698595i	$-0.246191\pi$
$242$	0.656574	+	0.550931i	0.0422062	+	0.0354152i
$243$	−5.09627	+	4.27628i	−0.326926	+	0.274323i
$244$	0.509800	−	2.89122i	0.0326366	−	0.185091i
$245$	−0.490200	+	0.178418i	−0.0313177	+	0.0113987i
$246$	0.532089			0.0339247
$247$		0			0
$248$	2.45336			0.155789
$249$	12.2023	−	4.44129i	0.773291	−	0.281455i
$250$	2.08378	−	11.8177i	0.131790	−	0.747417i
$251$	6.56283	−	5.50687i	0.414242	−	0.347591i	−0.411725	−	0.911308i	$-0.635074\pi$
$251$	6.56283	−	5.50687i	0.414242	−	0.347591i	0.825968	+	0.563717i	$0.190629\pi$
$252$	−1.34730	−	1.13052i	−0.0848717	−	0.0712158i
$253$	−0.384133	−	2.17853i	−0.0241502	−	0.136963i
$254$	−4.86484	−	8.42615i	−0.305247	−	0.528703i
$255$	−9.98545	+	17.2953i	−0.625313	+	1.08307i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−7.54071	−	2.74459i	−0.470376	−	0.171203i	0.0959465	−	0.995386i	$-0.469412\pi$
$257$	−7.54071	−	2.74459i	−0.470376	−	0.171203i	−0.566323	+	0.824183i	$0.691634\pi$
$258$	−4.64543	+	8.04612i	−0.289212	+	0.500930i
$259$	−5.88713	−	10.1968i	−0.365808	−	0.633598i
$260$	2.00000	+	11.3426i	0.124035	+	0.703436i
$261$	−1.41147	−	1.18437i	−0.0873681	−	0.0733105i
$262$	4.95471	−	4.15749i	0.306103	−	0.256851i
$263$	−1.03508	+	5.87024i	−0.0638259	+	0.361975i	0.936121	+	0.351678i	$0.114389\pi$
$263$	−1.03508	+	5.87024i	−0.0638259	+	0.361975i	−0.999947	+	0.0102968i	$0.996722\pi$
$264$	−4.58512	+	1.66885i	−0.282195	+	0.102710i
$265$	−16.4243			−1.00893
$266$		0			0
$267$	11.8571			0.725643
$268$	−4.65910	+	1.69577i	−0.284600	+	0.103586i
$269$	0.199340	−	1.13052i	0.0121540	−	0.0689288i	−0.978128	−	0.208006i	$-0.933303\pi$
$269$	0.199340	−	1.13052i	0.0121540	−	0.0689288i	0.990282	+	0.139077i	$0.0444137\pi$
$270$	−8.57398	+	7.19442i	−0.521796	+	0.437839i
$271$	15.3628	+	12.8909i	0.933222	+	0.783066i	0.976393	−	0.216001i	$-0.0693015\pi$
$271$	15.3628	+	12.8909i	0.933222	+	0.783066i	−0.0431708	+	0.999068i	$0.513746\pi$
$272$	−1.13176	−	6.41852i	−0.0686230	−	0.389180i
$273$	11.8871	+	20.5891i	0.719442	+	1.24611i
$274$	−5.83022	+	10.0982i	−0.352217	+	0.610057i
$275$	2.99273	+	1.08926i	0.180468	+	0.0656850i
$276$	−1.00000	−	0.363970i	−0.0601929	−	0.0219084i
$277$	−8.68004	+	15.0343i	−0.521533	+	0.903322i	0.478153	+	0.878277i	$0.341306\pi$
$277$	−8.68004	+	15.0343i	−0.521533	+	0.903322i	−0.999686	+	0.0250457i	$0.992027\pi$
$278$	−4.13176	−	7.15642i	−0.247806	−	0.429213i
$279$	0.278066	+	1.57699i	0.0166474	+	0.0944120i
$280$	−4.12836	−	3.46410i	−0.246716	−	0.207020i
$281$	−2.23783	+	1.87776i	−0.133498	+	0.112018i	−0.707092	−	0.707122i	$-0.749993\pi$
$281$	−2.23783	+	1.87776i	−0.133498	+	0.112018i	0.573594	+	0.819140i	$0.305549\pi$
$282$	2.09833	−	11.9002i	0.124953	−	0.708647i
$283$	8.90895	−	3.24259i	0.529582	−	0.192752i	−0.0633697	−	0.997990i	$-0.520185\pi$
$283$	8.90895	−	3.24259i	0.529582	−	0.192752i	0.592952	+	0.805238i	$0.297963\pi$
$284$	8.45336			0.501615
$285$		0			0
$286$	−18.3405			−1.08450
$287$	−0.879385	+	0.320070i	−0.0519085	+	0.0188931i
$288$	0.113341	−	0.642788i	0.00667867	−	0.0378766i
$289$	19.5175	−	16.3772i	1.14809	−	0.963362i
$290$	−4.32501	−	3.62911i	−0.253973	−	0.213109i
$291$	−0.0923963	−	0.524005i	−0.00541637	−	0.0307177i
$292$	−7.88326	−	13.6542i	−0.461333	−	0.799052i
$293$	−13.6459	+	23.6354i	−0.797202	+	1.38079i	0.124230	+	0.992253i	$0.460354\pi$
$293$	−13.6459	+	23.6354i	−0.797202	+	1.38079i	−0.921432	+	0.388541i	$0.872979\pi$
$294$	−0.375515	−	0.136676i	−0.0219005	−	0.00797112i
$295$	1.07873	+	0.392624i	0.0628058	+	0.0228595i
$296$	2.18479	−	3.78417i	0.126988	−	0.219951i
$297$	−8.91147	−	15.4351i	−0.517096	−	0.895637i
$298$	2.85710	+	16.2034i	0.165507	+	0.938638i
$299$	−3.06418	−	2.57115i	−0.177206	−	0.148693i
$300$	1.17365	−	0.984808i	0.0677606	−	0.0568579i
$301$	2.83750	−	16.0922i	0.163551	−	0.927541i
$302$	−4.37464	+	1.59224i	−0.251732	+	0.0916230i
$303$	0.566237			0.0325295
$304$		0			0
$305$	5.87164			0.336209
$306$	3.99747	−	1.45496i	0.228520	−	0.0831746i
$307$	−3.70368	+	21.0046i	−0.211380	+	1.19880i	0.675699	+	0.737178i	$0.263842\pi$
$307$	−3.70368	+	21.0046i	−0.211380	+	1.19880i	−0.887079	+	0.461618i	$0.847269\pi$
$308$	6.57398	−	5.51622i	0.374587	−	0.314316i
$309$	10.0719	+	8.45134i	0.572971	+	0.480780i
$310$	0.852044	+	4.83218i	0.0483929	+	0.274450i
$311$	14.6459	+	25.3674i	0.830493	+	1.43846i	0.897648	+	0.440713i	$0.145274\pi$
$311$	14.6459	+	25.3674i	0.830493	+	1.43846i	−0.0671555	+	0.997743i	$0.521392\pi$
$312$	−4.41147	+	7.64090i	−0.249751	+	0.432581i
$313$	−5.22580	−	1.90204i	−0.295380	−	0.107509i	0.190079	−	0.981769i	$-0.439125\pi$
$313$	−5.22580	−	1.90204i	−0.295380	−	0.107509i	−0.485459	+	0.874259i	$0.661348\pi$
$314$	7.94356	+	2.89122i	0.448281	+	0.163161i
$315$	1.75877	−	3.04628i	0.0990955	−	0.171638i
$316$	−4.53209	−	7.84981i	−0.254950	−	0.441586i
$317$	−0.660444	−	3.74557i	−0.0370943	−	0.210372i	0.960627	−	0.277841i	$-0.0896188\pi$
$317$	−0.660444	−	3.74557i	−0.0370943	−	0.210372i	−0.997721	+	0.0674689i	$0.978508\pi$
$318$	−9.63816	−	8.08737i	−0.540481	−	0.453517i
$319$	6.88713	−	5.77898i	0.385605	−	0.323561i
$320$	0.347296	−	1.96962i	0.0194145	−	0.110105i
$321$	16.4893	−	6.00162i	0.920344	−	0.334978i
$322$	1.87164			0.104303
$323$		0			0
$324$	−6.61587			−0.367548
$325$	5.41147	−	1.96962i	0.300175	−	0.109255i
$326$	−2.96064	+	16.7906i	−0.163975	+	0.929946i
$327$	10.2044	−	8.56250i	0.564304	−	0.473507i
$328$	−0.266044	−	0.223238i	−0.0146898	−	0.0123262i
$329$	3.69047	+	20.9297i	0.203462	+	1.15389i
$330$	−4.87939	−	8.45134i	−0.268601	−	0.465231i
$331$	10.2110	−	17.6859i	0.561245	−	0.972104i	−0.436144	−	0.899877i	$-0.643656\pi$
$331$	10.2110	−	17.6859i	0.561245	−	0.972104i	0.997388	−	0.0722272i	$-0.0230107\pi$
$332$	−7.96451	−	2.89884i	−0.437109	−	0.159095i
$333$	2.68004	+	0.975457i	0.146866	+	0.0534547i
$334$	1.59627	−	2.76481i	0.0873438	−	0.151284i
$335$	−4.95811	−	8.58770i	−0.270891	−	0.469196i
$336$	−0.716881	−	4.06564i	−0.0391091	−	0.221799i
$337$	−15.5587	−	13.0553i	−0.847537	−	0.711168i	0.111709	−	0.993741i	$-0.464368\pi$
$337$	−15.5587	−	13.0553i	−0.847537	−	0.711168i	−0.959246	+	0.282573i	$0.908812\pi$
$338$	−15.4461	+	12.9608i	−0.840156	+	0.704975i
$339$	0.760830	−	4.31488i	0.0413226	−	0.234352i
$340$	12.2490	−	4.45826i	0.664294	−	0.241783i
$341$	−7.81345			−0.423122
$342$		0			0
$343$	−18.1593			−0.980511
$344$	5.69846	−	2.07407i	0.307241	−	0.111826i
$345$	0.369585	−	2.09602i	0.0198978	−	0.112846i
$346$	7.37733	−	6.19031i	0.396607	−	0.332793i
$347$	3.99479	+	3.35202i	0.214451	+	0.179946i	0.743685	−	0.668530i	$-0.233076\pi$
$347$	3.99479	+	3.35202i	0.214451	+	0.179946i	−0.529234	+	0.848476i	$0.677521\pi$
$348$	−0.751030	−	4.25930i	−0.0402594	−	0.228323i
$349$	−7.17024	−	12.4192i	−0.383814	−	0.664786i	0.607790	−	0.794098i	$-0.292056\pi$
$349$	−7.17024	−	12.4192i	−0.383814	−	0.664786i	−0.991604	+	0.129312i	$0.958723\pi$
$350$	−1.34730	+	2.33359i	−0.0720160	+	0.124735i
$351$	−30.2841	−	11.0225i	−1.61644	−	0.588337i
$352$	2.99273	+	1.08926i	0.159513	+	0.0580579i
$353$	−13.1250	+	22.7331i	−0.698571	+	1.20996i	0.270391	+	0.962750i	$0.412847\pi$
$353$	−13.1250	+	22.7331i	−0.698571	+	1.20996i	−0.968962	+	0.247209i	$0.920486\pi$
$354$	0.439693	+	0.761570i	0.0233694	+	0.0404770i
$355$	2.93582	+	16.6499i	0.155817	+	0.883684i
$356$	−5.92855	−	4.97464i	−0.314212	−	0.263656i
$357$	20.6117	−	17.2953i	1.09089	−	0.915365i
$358$	3.26739	−	18.5303i	0.172687	−	0.979356i
$359$	31.6587	−	11.5228i	1.67088	−	0.608151i	0.678866	−	0.734263i	$-0.262472\pi$
$359$	31.6587	−	11.5228i	1.67088	−	0.608151i	0.992016	+	0.126111i	$0.0402496\pi$
$360$	1.30541			0.0688010
$361$		0			0
$362$	2.77837			0.146028
$363$	−1.23396	+	0.449123i	−0.0647659	+	0.0235728i
$364$	2.69459	−	15.2818i	0.141235	−	0.800984i
$365$	24.1557	−	20.2690i	1.26437	−	1.06093i
$366$	3.44562	+	2.89122i	0.180106	+	0.151127i
$367$	−1.81790	−	10.3098i	−0.0948934	−	0.538167i	−0.994780	−	0.102043i	$-0.967462\pi$
$367$	−1.81790	−	10.3098i	−0.0948934	−	0.538167i	0.899887	−	0.436124i	$-0.143649\pi$
$368$	0.347296	+	0.601535i	0.0181041	+	0.0313572i
$369$	0.113341	−	0.196312i	0.00590029	−	0.0102196i
$370$	8.21213	+	2.98897i	0.426929	+	0.155389i
$371$	20.7939	+	7.56834i	1.07956	+	0.392929i
$372$	−1.87939	+	3.25519i	−0.0974416	+	0.168774i
$373$	11.9513	+	20.7003i	0.618815	+	1.07182i	0.989702	+	0.143141i	$0.0457203\pi$
$373$	11.9513	+	20.7003i	0.618815	+	1.07182i	−0.370887	+	0.928678i	$0.620946\pi$
$374$	3.60442	+	20.4417i	0.186380	+	1.05701i
$375$	14.0838	+	11.8177i	0.727283	+	0.610263i
$376$	−6.04189	+	5.06975i	−0.311587	+	0.261452i
$377$	2.82295	−	16.0097i	0.145389	−	0.824543i
$378$	14.1702	−	5.15755i	0.728839	−	0.265276i
$379$	−17.8135			−0.915016			−0.457508	−	0.889206i	$-0.651258\pi$
$379$	−17.8135			−0.915016			−0.457508	+	0.889206i	$0.651258\pi$
$380$		0			0
$381$	14.9067			0.763695
$382$	8.98545	−	3.27044i	0.459736	−	0.167330i
$383$	−4.35504	+	24.6986i	−0.222532	+	1.26204i	0.644815	+	0.764338i	$0.276934\pi$
$383$	−4.35504	+	24.6986i	−0.222532	+	1.26204i	−0.867347	+	0.497703i	$0.834177\pi$
$384$	1.17365	−	0.984808i	0.0598925	−	0.0502558i
$385$	13.1480	+	11.0324i	0.670082	+	0.562265i
$386$	−4.11216	−	23.3212i	−0.209303	−	1.18702i
$387$	1.97906	+	3.42782i	0.100601	+	0.174246i
$388$	−0.173648	+	0.300767i	−0.00881565	+	0.0152692i
$389$	8.85029	+	3.22124i	0.448727	+	0.163323i	0.556492	−	0.830853i	$-0.312147\pi$
$389$	8.85029	+	3.22124i	0.448727	+	0.163323i	−0.107764	+	0.994176i	$0.534369\pi$
$390$	−16.5817	−	6.03525i	−0.839648	−	0.305607i
$391$	−2.26352	+	3.92053i	−0.114471	+	0.198270i
$392$	0.130415	+	0.225885i	0.00658695	+	0.0114089i
$393$	1.72075	+	9.75887i	0.0868004	+	0.492270i
$394$	17.5594	+	14.7341i	0.884631	+	0.742294i
$395$	13.8871	−	11.6527i	0.698737	−	0.586310i
$396$	−0.360967	+	2.04715i	−0.0181393	+	0.102873i
$397$	−6.43882	+	2.34354i	−0.323155	+	0.117619i	−0.498504	−	0.866888i	$-0.666117\pi$
$397$	−6.43882	+	2.34354i	−0.323155	+	0.117619i	0.175349	+	0.984506i	$0.443895\pi$
$398$	−10.0838			−0.505454
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	4.46064	−	1.62354i	0.222754	−	0.0810757i	−0.228232	−	0.973607i	$-0.573295\pi$
$401$	4.46064	−	1.62354i	0.222754	−	0.0810757i	0.450986	+	0.892531i	$0.351072\pi$
$402$	1.31908	−	7.48086i	0.0657896	−	0.373111i
$403$	−10.8229	+	9.08153i	−0.539129	+	0.452383i
$404$	−0.283119	−	0.237565i	−0.0140857	−	0.0118193i
$405$	−2.29767	−	13.0307i	−0.114172	−	0.647501i
$406$	3.80335	+	6.58759i	0.188757	+	0.326937i
$407$	−6.95811	+	12.0518i	−0.344901	+	0.597386i
$408$	9.38326	+	3.41523i	0.464540	+	0.169079i
$409$	29.7815	+	10.8396i	1.47260	+	0.535983i	0.948806	−	0.315861i	$-0.102293\pi$
$409$	29.7815	+	10.8396i	1.47260	+	0.535983i	0.523796	+	0.851844i	$0.324515\pi$
$410$	0.347296	−	0.601535i	0.0171517	−	0.0297077i
$411$	−8.93242	−	15.4714i	−0.440604	−	0.763148i
$412$	−1.49020	−	8.45134i	−0.0734169	−	0.416368i
$413$	−1.18479	−	0.994159i	−0.0582998	−	0.0489194i
$414$	−0.347296	+	0.291416i	−0.0170687	+	0.0143223i
$415$	2.94356	−	16.6938i	0.144494	−	0.819465i
$416$	5.41147	−	1.96962i	0.265319	−	0.0965683i
$417$	12.6604			0.619985
$418$		0			0
$419$	−11.0101			−0.537879			−0.268939	−	0.963157i	$-0.586673\pi$
$419$	−11.0101			−0.537879			−0.268939	+	0.963157i	$0.586673\pi$
$420$	7.75877	−	2.82396i	0.378589	−	0.137795i
$421$	1.50475	−	8.53385i	0.0733369	−	0.415914i	−0.925932	−	0.377690i	$-0.876719\pi$
$421$	1.50475	−	8.53385i	0.0733369	−	0.415914i	0.999269	−	0.0382247i	$-0.0121703\pi$
$422$	−17.1288	+	14.3728i	−0.833818	+	0.699656i
$423$	−3.94356	−	3.30904i	−0.191743	−	0.160891i
$424$	1.42602	+	8.08737i	0.0692538	+	0.392758i
$425$	−3.25877	−	5.64436i	−0.158074	−	0.273791i
$426$	−6.47565	+	11.2162i	−0.313746	+	0.543425i
$427$	−7.43376	−	2.70567i	−0.359745	−	0.130936i
$428$	−10.7626	−	3.91728i	−0.520232	−	0.189349i
$429$	14.0496	−	24.3347i	0.678323	−	1.17489i
$430$	6.06418	+	10.5035i	0.292441	+	0.506522i
$431$	5.18984	+	29.4331i	0.249986	+	1.41774i	0.808622	+	0.588328i	$0.200214\pi$
$431$	5.18984	+	29.4331i	0.249986	+	1.41774i	−0.558636	+	0.829413i	$0.688675\pi$
$432$	4.28699	+	3.59721i	0.206258	+	0.173071i
$433$	−7.09421	+	5.95275i	−0.340926	+	0.286071i	−0.797134	−	0.603802i	$-0.793652\pi$
$433$	−7.09421	+	5.95275i	−0.340926	+	0.286071i	0.456208	+	0.889873i	$0.349207\pi$
$434$	1.14796	−	6.51038i	0.0551036	−	0.312508i
$435$	8.12836	−	2.95848i	0.389725	−	0.141848i
$436$	−8.69459			−0.416395
$437$		0			0
$438$	24.1557			1.15420
$439$	19.6040	−	7.13528i	0.935648	−	0.340548i	0.171202	−	0.985236i	$-0.445235\pi$
$439$	19.6040	−	7.13528i	0.935648	−	0.340548i	0.764446	+	0.644688i	$0.223013\pi$
$440$	−1.10607	+	6.27282i	−0.0527297	+	0.299045i
$441$	−0.130415	+	0.109431i	−0.00621024	+	0.00521101i
$442$	28.7520	+	24.1258i	1.36759	+	1.14755i
$443$	4.13769	+	23.4660i	0.196588	+	1.11490i	0.910140	+	0.414301i	$0.135974\pi$
$443$	4.13769	+	23.4660i	0.196588	+	1.11490i	−0.713552	+	0.700602i	$0.752915\pi$
$444$	3.34730	+	5.79769i	0.158856	+	0.275146i
$445$	7.73917	−	13.4046i	0.366872	−	0.635441i
$446$	8.71688	+	3.17269i	0.412756	+	0.150231i
$447$	−23.6878	−	8.62165i	−1.12039	−	0.407790i
$448$	−1.34730	+	2.33359i	−0.0636538	+	0.110252i
$449$	−1.09105	−	1.88976i	−0.0514899	−	0.0891832i	0.839132	−	0.543928i	$-0.183064\pi$
$449$	−1.09105	−	1.88976i	−0.0514899	−	0.0891832i	−0.890622	+	0.454745i	$0.849730\pi$
$450$	−0.113341	−	0.642788i	−0.00534294	−	0.0303013i
$451$	0.847296	+	0.710966i	0.0398976	+	0.0334781i
$452$	−2.19072	+	1.83823i	−0.103043	+	0.0864633i
$453$	1.23854	−	7.02412i	0.0581917	−	0.330022i
$454$	−7.26991	+	2.64603i	−0.341194	+	0.124184i
$455$	31.0351			1.45495
$456$		0			0
$457$	1.78106			0.0833144			0.0416572	−	0.999132i	$-0.486736\pi$
$457$	1.78106			0.0833144			0.0416572	+	0.999132i	$0.486736\pi$
$458$	−21.6459	+	7.87846i	−1.01145	+	0.368136i
$459$	−6.33363	+	35.9198i	−0.295628	+	1.67659i
$460$	−1.06418	+	0.892951i	−0.0496175	+	0.0416341i
$461$	−11.8648	−	9.95578i	−0.552601	−	0.463687i	0.323220	−	0.946324i	$-0.395235\pi$
$461$	−11.8648	−	9.95578i	−0.552601	−	0.463687i	−0.875821	+	0.482637i	$0.839679\pi$
$462$	2.28312	+	12.9482i	0.106220	+	0.602405i
$463$	1.35504	+	2.34699i	0.0629739	+	0.109074i	0.895793	−	0.444471i	$-0.146608\pi$
$463$	1.35504	+	2.34699i	0.0629739	+	0.109074i	−0.832820	+	0.553545i	$0.813275\pi$
$464$	−1.41147	+	2.44474i	−0.0655260	+	0.113494i
$465$	−7.06418	−	2.57115i	−0.327593	−	0.119234i
$466$	7.89306	+	2.87284i	0.365639	+	0.133082i
$467$	−6.45677	+	11.1834i	−0.298784	+	0.517508i	−0.975858	−	0.218406i	$-0.929914\pi$
$467$	−6.45677	+	11.1834i	−0.298784	+	0.517508i	0.677074	+	0.735915i	$0.263248\pi$
$468$	1.87939	+	3.25519i	0.0868746	+	0.150471i
$469$	2.31996	+	13.1571i	0.107126	+	0.607539i
$470$	−12.0838	−	10.1395i	−0.557383	−	0.467700i
$471$	−9.92127	+	8.32494i	−0.457148	+	0.383593i
$472$	0.0996702	−	0.565258i	0.00458769	−	0.0260181i
$473$	−18.1484	+	6.60549i	−0.834465	+	0.303721i
$474$	13.8871			0.637857
$475$		0			0
$476$	−17.5621			−0.804958
$477$	−5.03684	+	1.83326i	−0.230621	+	0.0839391i
$478$	2.73143	−	15.4907i	0.124933	−	0.708528i
$479$	−14.2121	+	11.9254i	−0.649369	+	0.544885i	−0.906879	−	0.421390i	$-0.861542\pi$
$479$	−14.2121	+	11.9254i	−0.649369	+	0.544885i	0.257510	+	0.966276i	$0.417098\pi$
$480$	2.34730	+	1.96962i	0.107139	+	0.0899002i
$481$	4.36959	+	24.7811i	0.199236	+	1.12992i
$482$	−8.75150	−	15.1580i	−0.398620	−	0.690430i
$483$	−1.43376	+	2.48335i	−0.0652385	+	0.112996i
$484$	0.805407	+	0.293144i	0.0366094	+	0.0133247i
$485$	−0.652704	−	0.237565i	−0.0296377	−	0.0107873i
$486$	−3.32635	+	5.76141i	−0.150886	+	0.261343i
$487$	20.5868	+	35.6573i	0.932876	+	1.61579i	0.778379	+	0.627795i	$0.216042\pi$
$487$	20.5868	+	35.6573i	0.932876	+	1.61579i	0.154497	+	0.987993i	$0.450624\pi$
$488$	−0.509800	−	2.89122i	−0.0230776	−	0.130879i
$489$	−20.0103	−	16.7906i	−0.904896	−	0.759298i
$490$	−0.399615	+	0.335316i	−0.0180527	+	0.0151481i
$491$	−3.92056	+	22.2346i	−0.176932	+	1.00343i	0.758957	+	0.651140i	$0.225709\pi$
$491$	−3.92056	+	22.2346i	−0.176932	+	1.00343i	−0.935890	+	0.352293i	$0.885402\pi$
$492$	0.500000	−	0.181985i	0.0225417	−	0.00820452i
$493$	−18.3987			−0.828635
$494$		0			0
$495$	−4.15745			−0.186864
$496$	2.30541	−	0.839100i	0.103516	−	0.0376767i
$497$	3.95542	−	22.4323i	0.177425	−	1.00623i
$498$	9.94743	−	8.34689i	0.445755	−	0.374033i
$499$	−22.4670	−	18.8521i	−1.00576	−	0.843935i	−0.0179902	−	0.999838i	$-0.505727\pi$
$499$	−22.4670	−	18.8521i	−1.00576	−	0.843935i	−0.987772	+	0.155903i	$0.950171\pi$
$500$	−2.08378	−	11.8177i	−0.0931894	−	0.528503i
$501$	2.44562	+	4.23594i	0.109262	+	0.189248i
$502$	4.28359	−	7.41939i	0.191186	−	0.331143i
$503$	−31.5895	−	11.4976i	−1.40850	−	0.512654i	−0.477814	−	0.878461i	$-0.658571\pi$
$503$	−31.5895	−	11.4976i	−1.40850	−	0.512654i	−0.930691	+	0.365807i	$0.880793\pi$
$504$	−1.65270	−	0.601535i	−0.0736173	−	0.0267945i
$505$	0.369585	−	0.640140i	0.0164463	−	0.0284859i
$506$	−1.10607	−	1.91576i	−0.0491707	−	0.0851661i
$507$	−5.36437	−	30.4229i	−0.238240	−	1.35113i
$508$	−7.45336	−	6.25411i	−0.330690	−	0.277481i
$509$	−3.08647	+	2.58985i	−0.136805	+	0.114793i	−0.708623	−	0.705588i	$-0.750683\pi$
$509$	−3.08647	+	2.58985i	−0.136805	+	0.114793i	0.571817	+	0.820381i	$0.306239\pi$
$510$	−3.46791	+	19.6675i	−0.153562	+	0.870892i
$511$	−39.9222	+	14.5305i	−1.76605	+	0.642791i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−8.02465			−0.353952
$515$	16.1284	−	5.87024i	0.710700	−	0.258674i
$516$	−1.61334	+	9.14971i	−0.0710234	+	0.402794i
$517$	19.2422	−	16.1461i	0.846269	−	0.710104i
$518$	−9.01960	−	7.56834i	−0.396298	−	0.332534i
$519$	2.56212	+	14.5305i	0.112465	+	0.637818i
$520$	5.75877	+	9.97448i	0.252539	+	0.437410i
$521$	2.49479	−	4.32110i	0.109299	−	0.189311i	−0.806188	−	0.591660i	$-0.798473\pi$
$521$	2.49479	−	4.32110i	0.109299	−	0.189311i	0.915486	+	0.402349i	$0.131806\pi$
$522$	−1.73143	−	0.630189i	−0.0757826	−	0.0275826i
$523$	−24.9513	−	9.08153i	−1.09104	−	0.397108i	−0.267037	−	0.963686i	$-0.586044\pi$
$523$	−24.9513	−	9.08153i	−1.09104	−	0.397108i	−0.824008	+	0.566579i	$0.808267\pi$
$524$	3.23396	−	5.60138i	0.141276	−	0.244697i
$525$	−2.06418	−	3.57526i	−0.0900881	−	0.156037i
$526$	1.03508	+	5.87024i	0.0451317	+	0.255955i
$527$	12.2490	+	10.2781i	0.533574	+	0.447721i
$528$	−3.73783	+	3.13641i	−0.162668	+	0.136495i
$529$	−3.91013	+	22.1754i	−0.170006	+	0.964150i
$530$	−15.4338	+	5.61743i	−0.670400	+	0.244006i
$531$	0.374638			0.0162579
$532$		0			0
$533$	2.00000			0.0866296
$534$	11.1420	−	4.05537i	0.482163	−	0.175493i
$535$	3.97771	−	22.5587i	0.171971	−	0.975299i
$536$	−3.79813	+	3.18701i	−0.164054	+	0.137658i
$537$	22.0835	+	18.5303i	0.952975	+	0.799641i
$538$	−0.199340	−	1.13052i	−0.00859418	−	0.0487400i
$539$	−0.415345	−	0.719398i	−0.0178902	−	0.0309867i
$540$	−5.59627	+	9.69302i	−0.240825	+	0.417121i
$541$	11.2490	+	4.09429i	0.483631	+	0.176027i	0.572317	−	0.820032i	$-0.306045\pi$
$541$	11.2490	+	4.09429i	0.483631	+	0.176027i	−0.0886862	+	0.996060i	$0.528267\pi$
$542$	18.8452	+	6.85911i	0.809472	+	0.294624i
$543$	−2.12836	+	3.68642i	−0.0913365	+	0.158199i
$544$	−3.25877	−	5.64436i	−0.139719	−	0.242000i
$545$	−3.01960	−	17.1250i	−0.129345	−	0.733555i
$546$	18.2121	+	15.2818i	0.779407	+	0.654000i
$547$	−2.44878	+	2.05477i	−0.104702	+	0.0878556i	−0.693636	−	0.720326i	$-0.743992\pi$
$547$	−2.44878	+	2.05477i	−0.104702	+	0.0878556i	0.588934	+	0.808181i	$0.299548\pi$
$548$	−2.02481	+	11.4833i	−0.0864958	+	0.490542i
$549$	1.80066	−	0.655386i	0.0768503	−	0.0279712i
$550$	3.18479			0.135800
$551$		0			0
$552$	−1.06418			−0.0452944
$553$	−22.9513	+	8.35359i	−0.975989	+	0.355231i
$554$	−3.01455	+	17.0964i	−0.128076	+	0.726354i
$555$	−10.2567	+	8.60640i	−0.435373	+	0.365321i
$556$	−6.33022	−	5.31169i	−0.268461	−	0.225266i
$557$	−4.16344	−	23.6120i	−0.176411	−	1.00047i	−0.936503	−	0.350659i	$-0.885958\pi$
$557$	−4.16344	−	23.6120i	−0.176411	−	1.00047i	0.760093	−	0.649815i	$-0.225154\pi$
$558$	0.800660	+	1.38678i	0.0338946	+	0.0587072i
$559$	−17.4611	+	30.2435i	−0.738526	+	1.27916i
$560$	−5.06418	−	1.84321i	−0.214001	−	0.0778898i
$561$	−29.8837	−	10.8768i	−1.26169	−	0.459218i
$562$	−1.46064	+	2.52990i	−0.0616133	+	0.106717i
$563$	−4.37851	−	7.58380i	−0.184532	−	0.319619i	0.758887	−	0.651223i	$-0.225744\pi$
$563$	−4.37851	−	7.58380i	−0.184532	−	0.319619i	−0.943419	+	0.331604i	$0.892410\pi$
$564$	−2.09833	−	11.9002i	−0.0883555	−	0.501089i
$565$	−4.38144	−	3.67647i	−0.184329	−	0.154670i
$566$	7.26264	−	6.09408i	0.305272	−	0.256153i
$567$	−3.09564	+	17.5562i	−0.130005	+	0.737293i
$568$	7.94356	−	2.89122i	0.333304	−	0.121313i
$569$	36.4201			1.52681			0.763406	−	0.645919i	$-0.223526\pi$
$569$	36.4201			1.52681			0.763406	+	0.645919i	$0.223526\pi$
$570$		0			0
$571$	34.2131			1.43177			0.715886	−	0.698217i	$-0.246023\pi$
$571$	34.2131			1.43177			0.715886	+	0.698217i	$0.246023\pi$
$572$	−17.2344	+	6.27282i	−0.720607	+	0.262280i
$573$	−2.54395	+	14.4274i	−0.106275	+	0.602715i
$574$	−0.716881	+	0.601535i	−0.0299221	+	0.0251076i
$575$	0.532089	+	0.446476i	0.0221896	+	0.0186193i
$576$	−0.113341	−	0.642788i	−0.00472253	−	0.0267828i
$577$	−7.75490	−	13.4319i	−0.322841	−	0.559177i	0.658232	−	0.752815i	$-0.271304\pi$
$577$	−7.75490	−	13.4319i	−0.322841	−	0.559177i	−0.981073	+	0.193638i	$0.937971\pi$
$578$	12.7392	−	22.0649i	0.529880	−	0.917778i
$579$	34.0933	+	12.4090i	1.41687	+	0.515699i
$580$	−5.30541	−	1.93101i	−0.220295	−	0.0801808i
$581$	−11.4192	+	19.7787i	−0.473749	+	0.820557i
$582$	−0.266044	−	0.460802i	−0.0110279	−	0.0191009i
$583$	−4.54158	−	25.7566i	−0.188093	−	1.06673i
$584$	−12.0778	−	10.1345i	−0.499785	−	0.419369i
$585$	−5.75877	+	4.83218i	−0.238096	+	0.199786i
$586$	−4.73917	+	26.8772i	−0.195773	+	1.11029i
$587$	10.8833	−	3.96118i	0.449200	−	0.163495i	−0.107507	−	0.994204i	$-0.534287\pi$
$587$	10.8833	−	3.96118i	0.449200	−	0.163495i	0.556707	+	0.830709i	$0.312065\pi$
$588$	−0.399615			−0.0164798
$589$		0			0
$590$	1.14796			0.0472606
$591$	−33.0009	+	12.0114i	−1.35748	+	0.494081i
$592$	0.758770	−	4.30320i	0.0311853	−	0.176860i
$593$	−35.5390	+	29.8207i	−1.45941	+	1.22459i	−0.534076	+	0.845436i	$0.679340\pi$
$593$	−35.5390	+	29.8207i	−1.45941	+	1.22459i	−0.925334	+	0.379154i	$0.876215\pi$
$594$	−13.6532	−	11.4564i	−0.560196	−	0.470061i
$595$	−6.09926	−	34.5906i	−0.250045	−	1.41808i
$596$	8.22668	+	14.2490i	0.336978	+	0.583663i
$597$	7.72462	−	13.3794i	0.316148	−	0.547584i
$598$	−3.75877	−	1.36808i	−0.153708	−	0.0559450i
$599$	24.0865	+	8.76676i	0.984146	+	0.358200i	0.783451	−	0.621454i	$-0.213458\pi$
$599$	24.0865	+	8.76676i	0.984146	+	0.358200i	0.200695	+	0.979654i	$0.435680\pi$
$600$	0.766044	−	1.32683i	0.0312736	−	0.0541675i
$601$	3.99613	+	6.92150i	0.163006	+	0.282334i	0.935945	−	0.352146i	$-0.114548\pi$
$601$	3.99613	+	6.92150i	0.163006	+	0.282334i	−0.772940	+	0.634480i	$0.781214\pi$
$602$	−2.83750	−	16.0922i	−0.115648	−	0.655871i
$603$	−2.47906	−	2.08017i	−0.100955	−	0.0847113i
$604$	−3.56624	+	2.99243i	−0.145108	+	0.121760i
$605$	−0.297667	+	1.68815i	−0.0121019	+	0.0686331i
$606$	0.532089	−	0.193665i	0.0216146	−	0.00786708i
$607$	26.9905			1.09551			0.547755	−	0.836639i	$-0.315482\pi$
$607$	26.9905			1.09551			0.547755	+	0.836639i	$0.315482\pi$
$608$		0			0
$609$	−11.6541			−0.472249
$610$	5.51754	−	2.00822i	0.223399	−	0.0813105i
$611$	7.88713	−	44.7301i	0.319079	−	1.80959i
$612$	3.25877	−	2.73443i	0.131728	−	0.110533i
$613$	−10.9172	−	9.16058i	−0.440940	−	0.369992i	0.395121	−	0.918629i	$-0.370703\pi$
$613$	−10.9172	−	9.16058i	−0.440940	−	0.369992i	−0.836061	+	0.548637i	$0.815147\pi$
$614$	3.70368	+	21.0046i	0.149468	+	0.847677i
$615$	0.532089	+	0.921605i	0.0214559	+	0.0371627i
$616$	4.29086	−	7.43199i	0.172884	−	0.299443i
$617$	28.7173	+	10.4523i	1.15612	+	0.420792i	0.847709	−	0.530462i	$-0.177982\pi$
$617$	28.7173	+	10.4523i	1.15612	+	0.420792i	0.308408	+	0.951254i	$0.400204\pi$
$618$	12.3550	+	4.49687i	0.496992	+	0.180890i
$619$	14.3375	−	24.8333i	0.576273	−	0.998133i	−0.419629	−	0.907695i	$-0.637840\pi$
$619$	14.3375	−	24.8333i	0.576273	−	0.998133i	0.995902	−	0.0904380i	$-0.0288267\pi$
$620$	2.45336	+	4.24935i	0.0985294	+	0.170658i
$621$	−0.674992	−	3.82807i	−0.0270865	−	0.153615i
$622$	22.4388	+	18.8284i	0.899715	+	0.754950i
$623$	−15.9750	+	13.4046i	−0.640026	+	0.537045i
$624$	−1.53209	+	8.68891i	−0.0613326	+	0.347835i
$625$	17.8542	−	6.49838i	0.714166	−	0.259935i
$626$	−5.56118			−0.222270
$627$		0			0
$628$	8.45336			0.337326
$629$	26.7615	−	9.74037i	1.06705	−	0.388374i
$630$	0.610815	−	3.46410i	0.0243354	−	0.138013i
$631$	−3.44562	+	2.89122i	−0.137168	+	0.115098i	−0.708790	−	0.705419i	$-0.750759\pi$
$631$	−3.44562	+	2.89122i	−0.137168	+	0.115098i	0.571622	+	0.820517i	$0.306314\pi$
$632$	−6.94356	−	5.82634i	−0.276200	−	0.231759i
$633$	−5.94878	−	33.7372i	−0.236443	−	1.34093i
$634$	−1.90167	−	3.29380i	−0.0755251	−	0.130813i
$635$	9.72967	−	16.8523i	0.386110	−	0.668763i
$636$	−11.8229	−	4.30320i	−0.468810	−	0.170633i
$637$	−1.41147	−	0.513735i	−0.0559246	−	0.0203549i
$638$	4.49525	−	7.78601i	0.177969	−	0.308251i
$639$	2.75877	+	4.77833i	0.109135	+	0.189028i
$640$	−0.347296	−	1.96962i	−0.0137281	−	0.0778559i
$641$	8.89234	+	7.46156i	0.351226	+	0.294714i	0.801282	−	0.598286i	$-0.204152\pi$
$641$	8.89234	+	7.46156i	0.351226	+	0.294714i	−0.450056	+	0.893000i	$0.648596\pi$
$642$	13.4422	−	11.2794i	0.530522	−	0.445161i
$643$	4.52276	−	25.6498i	0.178360	−	1.01153i	−0.755834	−	0.654764i	$-0.772768\pi$
$643$	4.52276	−	25.6498i	0.178360	−	1.01153i	0.934194	−	0.356766i	$-0.116121\pi$
$644$	1.75877	−	0.640140i	0.0693053	−	0.0252251i
$645$	−18.5817			−0.731654
$646$		0			0
$647$	−2.31490			−0.0910082			−0.0455041	−	0.998964i	$-0.514489\pi$
$647$	−2.31490			−0.0910082			−0.0455041	+	0.998964i	$0.514489\pi$
$648$	−6.21688	+	2.26276i	−0.244222	+	0.0888896i
$649$	−0.317429	+	1.80023i	−0.0124602	+	0.0706652i
$650$	4.41147	−	3.70167i	0.173032	−	0.145191i
$651$	7.75877	+	6.51038i	0.304090	+	0.255162i
$652$	2.96064	+	16.7906i	0.115947	+	0.657571i
$653$	−1.65270	−	2.86257i	−0.0646753	−	0.112021i	0.831875	−	0.554964i	$-0.187268\pi$
$653$	−1.65270	−	2.86257i	−0.0646753	−	0.112021i	−0.896550	+	0.442943i	$0.853934\pi$
$654$	6.66044	−	11.5362i	0.260444	−	0.451102i
$655$	12.1557	+	4.42431i	0.474962	+	0.172872i
$656$	−0.326352	−	0.118782i	−0.0127419	−	0.00463767i
$657$	5.14543	−	8.91215i	0.200742	−	0.347696i
$658$	10.6263	+	18.4053i	0.414256	+	0.717513i
$659$	2.38754	+	13.5404i	0.0930052	+	0.527459i	0.995340	+	0.0964237i	$0.0307404\pi$
$659$	2.38754	+	13.5404i	0.0930052	+	0.527459i	−0.902335	+	0.431035i	$0.858149\pi$
$660$	−7.47565	−	6.27282i	−0.290989	−	0.244169i
$661$	2.55438	−	2.14338i	0.0993538	−	0.0833677i	−0.591758	−	0.806116i	$-0.701566\pi$
$661$	2.55438	−	2.14338i	0.0993538	−	0.0833677i	0.691112	+	0.722748i	$0.257121\pi$
$662$	3.54623	−	20.1116i	0.137828	−	0.781661i
$663$	−54.0360	+	19.6675i	−2.09858	+	0.763822i
$664$	−8.47565			−0.328919
$665$		0			0
$666$	2.85204			0.110514
$667$	1.84255	−	0.670633i	0.0713438	−	0.0259670i
$668$	0.554378	−	3.14403i	0.0214495	−	0.121646i
$669$	−10.8871	+	9.13538i	−0.420921	+	0.353194i
$670$	−7.59627	−	6.37402i	−0.293469	−	0.246250i
$671$	1.62361	+	9.20794i	0.0626787	+	0.355468i
$672$	−2.06418	−	3.57526i	−0.0796274	−	0.137919i
$673$	19.4905	−	33.7585i	0.751304	−	1.30130i	−0.195887	−	0.980626i	$-0.562759\pi$
$673$	19.4905	−	33.7585i	0.751304	−	1.30130i	0.947191	−	0.320670i	$-0.103908\pi$
$674$	−19.0856	−	6.94659i	−0.735149	−	0.267573i
$675$	5.25877	+	1.91404i	0.202410	+	0.0736713i
$676$	−10.0817	+	17.4620i	−0.387758	+	0.671617i
$677$	−21.7939	−	37.7481i	−0.837606	−	1.45078i	−0.891891	−	0.452250i	$-0.850621\pi$
$677$	−21.7939	−	37.7481i	−0.837606	−	1.45078i	0.0542853	−	0.998525i	$-0.482712\pi$
$678$	−0.760830	−	4.31488i	−0.0292195	−	0.165712i
$679$	0.716881	+	0.601535i	0.0275114	+	0.0230848i
$680$	9.98545	−	8.37879i	0.382925	−	0.321312i
$681$	2.05825	−	11.6729i	0.0788722	−	0.447307i
$682$	−7.34224	+	2.67236i	−0.281149	+	0.102330i
$683$	−32.9317			−1.26010			−0.630048	−	0.776556i	$-0.716965\pi$
$683$	−32.9317			−1.26010			−0.630048	+	0.776556i	$0.716965\pi$
$684$		0			0
$685$	−23.3209			−0.891045
$686$	−17.0642	+	6.21085i	−0.651513	+	0.237131i
$687$	6.12836	−	34.7556i	0.233811	−	1.32601i
$688$	4.64543	−	3.89798i	0.177105	−	0.148609i
$689$	−36.2276	−	30.3986i	−1.38016	−	1.15809i
$690$	−0.369585	−	2.09602i	−0.0140699	−	0.0797942i
$691$	−17.1604	−	29.7228i	−0.652814	−	1.13071i	−0.982437	−	0.186594i	$-0.940255\pi$
$691$	−17.1604	−	29.7228i	−0.652814	−	1.13071i	0.329623	−	0.944113i	$-0.393078\pi$
$692$	4.81521	−	8.34018i	0.183047	−	0.317046i
$693$	5.26352	+	1.91576i	0.199945	+	0.0727739i
$694$	4.90033	+	1.78357i	0.186014	+	0.0677035i
$695$	8.26352	−	14.3128i	0.313453	−	0.542917i
$696$	−2.16250	−	3.74557i	−0.0819695	−	0.141975i
$697$	−0.393056	−	2.22913i	−0.0148881	−	0.0844343i
$698$	−10.9855	−	9.21789i	−0.415805	−	0.348902i
$699$	−9.85819	+	8.27201i	−0.372871	+	0.312876i
$700$	−0.467911	+	2.65366i	−0.0176854	+	0.100299i
$701$	−6.06418	+	2.20718i	−0.229041	+	0.0833640i	−0.453991	−	0.891006i	$-0.650000\pi$
$701$	−6.06418	+	2.20718i	−0.229041	+	0.0833640i	0.224950	+	0.974370i	$0.427778\pi$
$702$	−32.2276			−1.21635
$703$		0			0
$704$	3.18479			0.120031
$705$	22.7101	−	8.26579i	0.855311	−	0.311308i
$706$	−4.55825	+	25.8511i	−0.171552	+	0.972919i
$707$	−0.762889	+	0.640140i	−0.0286914	+	0.0240749i
$708$	0.673648	+	0.565258i	0.0253172	+	0.0212437i
$709$	−0.586771	−	3.32774i	−0.0220367	−	0.124976i	0.971805	−	0.235786i	$-0.0757665\pi$
$709$	−0.586771	−	3.32774i	−0.0220367	−	0.124976i	−0.993842	+	0.110810i	$0.964655\pi$
$710$	8.45336	+	14.6417i	0.317249	+	0.549492i
$711$	2.95811	−	5.12360i	0.110938	−	0.192150i
$712$	−7.27244	−	2.64695i	−0.272546	−	0.0991987i
$713$	−1.60132	−	0.582832i	−0.0599699	−	0.0218272i
$714$	13.4534	−	23.3019i	0.503479	−	0.872052i
$715$	−18.3405	−	31.7667i	−0.685895	−	1.18801i
$716$	−3.26739	−	18.5303i	−0.122108	−	0.692509i
$717$	18.4611	+	15.4907i	0.689443	+	0.578511i
$718$	25.8084	−	21.6558i	0.963161	−	0.808188i
$719$	−5.41828	+	30.7286i	−0.202068	+	1.14598i	0.699920	+	0.714221i	$0.253219\pi$
$719$	−5.41828	+	30.7286i	−0.202068	+	1.14598i	−0.901988	+	0.431762i	$0.857892\pi$
$720$	1.22668	−	0.446476i	0.0457157	−	0.0166392i
$721$	−23.1242			−0.861192
$722$		0			0
$723$	26.8161			0.997303
$724$	2.61081	−	0.950259i	0.0970302	−	0.0353161i
$725$	−0.490200	+	2.78006i	−0.0182056	+	0.103249i
$726$	−1.00593	+	0.844075i	−0.0373336	+	0.0313266i
$727$	−19.6578	−	16.4948i	−0.729066	−	0.611759i	0.200811	−	0.979630i	$-0.435642\pi$
$727$	−19.6578	−	16.4948i	−0.729066	−	0.611759i	−0.929877	+	0.367871i	$0.880087\pi$
$728$	−2.69459	−	15.2818i	−0.0998683	−	0.566381i
$729$	−15.0201	−	26.0155i	−0.556299	−	0.963538i
$730$	15.7665	−	27.3084i	0.583545	−	1.01073i
$731$	37.1400	+	13.5178i	1.37367	+	0.499975i
$732$	4.22668	+	1.53839i	0.156223	+	0.0568604i
$733$	11.9368	−	20.6751i	0.440894	−	0.763651i	−0.556862	−	0.830605i	$-0.687995\pi$
$733$	11.9368	−	20.6751i	0.440894	−	0.763651i	0.997756	+	0.0669540i	$0.0213281\pi$
$734$	−5.23442	−	9.06629i	−0.193206	−	0.334643i
$735$	−0.138785	−	0.787087i	−0.00511915	−	0.0290321i
$736$	0.532089	+	0.446476i	0.0196131	+	0.0164573i
$737$	12.0963	−	10.1500i	0.445572	−	0.373879i
$738$	0.0393628	−	0.223238i	0.00144897	−	0.00821750i
$739$	43.1698	−	15.7125i	1.58803	−	0.577995i	0.611098	−	0.791555i	$-0.290728\pi$
$739$	43.1698	−	15.7125i	1.58803	−	0.577995i	0.976930	+	0.213560i	$0.0685059\pi$
$740$	8.73917			0.321258
$741$		0			0
$742$	22.1284			0.812357
$743$	−47.9350	+	17.4469i	−1.75856	+	0.640065i	−0.999934	−	0.0114562i	$-0.996353\pi$
$743$	−47.9350	+	17.4469i	−1.75856	+	0.640065i	−0.758630	+	0.651521i	$0.774131\pi$
$744$	−0.652704	+	3.70167i	−0.0239293	+	0.135710i
$745$	−25.2080	+	21.1520i	−0.923550	+	0.774951i
$746$	18.3105	+	15.3643i	0.670394	+	0.562527i
$747$	−0.960637	−	5.44804i	−0.0351479	−	0.199334i
$748$	10.3785	+	17.9761i	0.379476	+	0.657271i
$749$	−15.4311	+	26.7274i	−0.563839	+	0.976598i
$750$	17.2763	+	6.28806i	0.630842	+	0.229608i
$751$	−34.1762	−	12.4391i	−1.24711	−	0.453910i	−0.367685	−	0.929950i	$-0.619849\pi$
$751$	−34.1762	−	12.4391i	−1.24711	−	0.453910i	−0.879424	+	0.476040i	$0.842072\pi$
$752$	−3.94356	+	6.83045i	−0.143807	+	0.249081i
$753$	6.56283	+	11.3672i	0.239163	+	0.414242i
$754$	−2.82295	−	16.0097i	−0.102806	−	0.583040i
$755$	−7.13247	−	5.98486i	−0.259577	−	0.217811i
$756$	11.5517	−	9.69302i	0.420131	−	0.352532i
$757$	−1.00774	+	5.71518i	−0.0366270	+	0.207722i	−0.997629	−	0.0688189i	$-0.978077\pi$
$757$	−1.00774	+	5.71518i	−0.0366270	+	0.207722i	0.961002	+	0.276541i	$0.0891881\pi$
$758$	−16.7392	+	6.09256i	−0.607994	+	0.221292i
$759$	3.38919			0.123020
$760$		0			0
$761$	22.6355			0.820535			0.410268	−	0.911965i	$-0.365435\pi$
$761$	22.6355			0.820535			0.410268	+	0.911965i	$0.365435\pi$
$762$	14.0077	−	5.09840i	0.507447	−	0.184696i
$763$	−4.06830	+	23.0725i	−0.147282	+	0.835279i
$764$	7.32501	−	6.14641i	0.265009	−	0.222369i
$765$	6.51754	+	5.46887i	0.235642	+	0.197727i
$766$	4.35504	+	24.6986i	0.157354	+	0.892398i
$767$	1.65270	+	2.86257i	0.0596757	+	0.103361i
$768$	0.766044	−	1.32683i	0.0276422	−	0.0478778i
$769$	−10.2451	−	3.72891i	−0.369448	−	0.134468i	0.150623	−	0.988591i	$-0.451872\pi$
$769$	−10.2451	−	3.72891i	−0.369448	−	0.134468i	−0.520071	+	0.854123i	$0.674094\pi$
$770$	16.1284	+	5.87024i	0.581226	+	0.211549i
$771$	6.14724	−	10.6473i	0.221387	−	0.383454i
$772$	−11.8405	−	20.5083i	−0.426149	−	0.738111i
$773$	0.911779	+	5.17095i	0.0327944	+	0.185986i	0.996805	−	0.0798791i	$-0.0254534\pi$
$773$	0.911779	+	5.17095i	0.0327944	+	0.185986i	−0.964010	+	0.265865i	$0.914342\pi$
$774$	3.03209	+	2.54422i	0.108986	+	0.0914503i
$775$	1.87939	−	1.57699i	0.0675095	−	0.0566472i
$776$	−0.0603074	+	0.342020i	−0.00216491	+	0.0122778i
$777$	16.9513	−	6.16977i	0.608125	−	0.221339i
$778$	9.41828			0.337662
$779$		0			0
$780$	−17.6459			−0.631824
$781$	−25.2986	+	9.20794i	−0.905255	+	0.329486i
$782$	−0.786112	+	4.45826i	−0.0281113	+	0.159427i
$783$	12.1019	−	10.1547i	0.432488	−	0.362901i
$784$	0.199807	+	0.167658i	0.00713597	+	0.00598779i
$785$	2.93582	+	16.6499i	0.104784	+	0.594260i
$786$	4.95471	+	8.58180i	0.176729	+	0.306103i
$787$	−1.19372	+	2.06758i	−0.0425514	+	0.0737011i	−0.886517	−	0.462697i	$-0.846882\pi$
$787$	−1.19372	+	2.06758i	−0.0425514	+	0.0737011i	0.843965	+	0.536398i	$0.180215\pi$
$788$	21.5398	+	7.83986i	0.767325	+	0.279283i
$789$	−8.58172	−	3.12349i	−0.305517	−	0.111199i
$790$	9.06418	−	15.6996i	0.322489	−	0.558567i
$791$	3.85298	+	6.67355i	0.136996	+	0.237284i
$792$	0.360967	+	2.04715i	0.0128264	+	0.0727421i
$793$	12.9513	+	10.8674i	0.459914	+	0.385914i
$794$	−5.24897	+	4.40441i	−0.186279	+	0.156307i
$795$	4.36959	−	24.7811i	0.154973	−	0.878897i
$796$	−9.47565	+	3.44886i	−0.335856	+	0.122241i
$797$	−31.0951			−1.10145			−0.550723	−	0.834688i	$-0.685648\pi$
$797$	−31.0951			−1.10145			−0.550723	+	0.834688i	$0.685648\pi$
$798$		0			0
$799$	−51.4047			−1.81857
$800$	−0.939693	+	0.342020i	−0.0332232	+	0.0120922i
$801$	0.877164	−	4.97464i	0.0309931	−	0.175770i
$802$	3.63634	−	3.05126i	0.128404	−	0.107744i
$803$	38.4654	+	32.2763i	1.35742	+	1.13901i
$804$	−1.31908	−	7.48086i	−0.0465203	−	0.263830i
$805$	1.87164	+	3.24178i	0.0659668	+	0.114258i
$806$	−7.06418	+	12.2355i	−0.248825	+	0.430978i
$807$	1.65270	+	0.601535i	0.0581779	+	0.0211750i
$808$	−0.347296	−	0.126406i	−0.0122178	−	0.00444693i
$809$	−11.1518	+	19.3155i	−0.392077	+	0.679098i	−0.992723	−	0.120417i	$-0.961577\pi$
$809$	−11.1518	+	19.3155i	−0.392077	+	0.679098i	0.600646	+	0.799515i	$0.294910\pi$
$810$	−6.61587	−	11.4590i	−0.232458	−	0.402629i
$811$	−0.576342	−	3.26860i	−0.0202381	−	0.114776i	0.973015	−	0.230741i	$-0.0741150\pi$
$811$	−0.576342	−	3.26860i	−0.0202381	−	0.114776i	−0.993253	+	0.115965i	$0.963004\pi$
$812$	5.82707	+	4.88949i	0.204490	+	0.171587i
$813$	−23.5371	+	19.7500i	−0.825484	+	0.692663i
$814$	−2.41653	+	13.7048i	−0.0846992	+	0.480353i
$815$	−32.0428	+	11.6626i	−1.12241	+	0.408524i
$816$	9.98545			0.349561
$817$		0			0
$818$	31.6928			1.10811
$819$	9.51754	−	3.46410i	0.332570	−	0.121046i
$820$	0.120615	−	0.684040i	0.00421205	−	0.0238877i
$821$	−1.40373	+	1.17787i	−0.0489906	+	0.0411080i	−0.666954	−	0.745099i	$-0.732402\pi$
$821$	−1.40373	+	1.17787i	−0.0489906	+	0.0411080i	0.617964	+	0.786207i	$0.287958\pi$
$822$	−13.6853	−	11.4833i	−0.477328	−	0.400526i
$823$	−5.94532	−	33.7176i	−0.207241	−	1.17532i	−0.893875	−	0.448317i	$-0.852024\pi$
$823$	−5.94532	−	33.7176i	−0.207241	−	1.17532i	0.686634	−	0.727003i	$-0.259088\pi$
$824$	−4.29086	−	7.43199i	−0.149479	−	0.258906i
$825$	−2.43969	+	4.22567i	−0.0849392	+	0.147119i
$826$	−1.45336	−	0.528981i	−0.0505690	−	0.0184056i
$827$	−18.6677	−	6.79449i	−0.649140	−	0.236268i	−0.00359941	−	0.999994i	$-0.501146\pi$
$827$	−18.6677	−	6.79449i	−0.649140	−	0.236268i	−0.645541	+	0.763726i	$0.723368\pi$
$828$	−0.226682	+	0.392624i	−0.00787773	+	0.0136446i
$829$	−17.8675	−	30.9475i	−0.620565	−	1.07485i	−0.989381	−	0.145347i	$-0.953570\pi$
$829$	−17.8675	−	30.9475i	−0.620565	−	1.07485i	0.368816	−	0.929502i	$-0.379763\pi$
$830$	−2.94356	−	16.6938i	−0.102173	−	0.579449i
$831$	−20.3746	−	17.0964i	−0.706788	−	0.593066i
$832$	4.41147	−	3.70167i	0.152940	−	0.128332i
$833$	−0.295197	+	1.67414i	−0.0102280	+	0.0580056i
$834$	11.8969	−	4.33013i	0.411957	−	0.149940i
$835$	6.38507			0.220964
$836$		0			0
$837$	−13.7297			−0.474567
$838$	−10.3461	+	3.76568i	−0.357401	+	0.130083i
$839$	9.44562	−	53.5688i	0.326099	−	1.84940i	−0.175737	−	0.984437i	$-0.556231\pi$
$839$	9.44562	−	53.5688i	0.326099	−	1.84940i	0.501836	−	0.864963i	$-0.332658\pi$
$840$	6.32501	−	5.30731i	0.218233	−	0.183120i
$841$	−16.1107	−	13.5184i	−0.555540	−	0.466153i
$842$	−1.50475	−	8.53385i	−0.0518570	−	0.294096i
$843$	−2.23783	−	3.87603i	−0.0770748	−	0.133498i
$844$	−11.1800	+	19.3644i	−0.384833	+	0.666550i
$845$	−37.8949	−	13.7926i	−1.30362	−	0.474480i
$846$	−4.83750	−	1.76070i	−0.166317	−	0.0605343i
$847$	1.15476	−	2.00011i	0.0396781	−	0.0687245i
$848$	4.10607	+	7.11192i	0.141003	+	0.244224i
$849$	2.52229	+	14.3046i	0.0865647	+	0.490933i
$850$	−4.99273	−	4.18939i	−0.171249	−	0.143695i
$851$	−2.32501	+	1.95091i	−0.0797002	+	0.0668764i
$852$	−2.24897	+	12.7545i	−0.0770485	+	0.436963i
$853$	−15.0128	+	5.46421i	−0.514028	+	0.187091i	−0.585993	−	0.810316i	$-0.699295\pi$
$853$	−15.0128	+	5.46421i	−0.514028	+	0.187091i	0.0719646	+	0.997407i	$0.477073\pi$
$854$	−7.91085			−0.270704
$855$		0			0
$856$	−11.4534			−0.391468
$857$	−24.4457	+	8.89750i	−0.835048	+	0.303933i	−0.723929	−	0.689874i	$-0.757666\pi$
$857$	−24.4457	+	8.89750i	−0.835048	+	0.303933i	−0.111119	+	0.993807i	$0.535444\pi$
$858$	4.87939	−	27.6724i	0.166579	−	0.944719i
$859$	40.8075	−	34.2416i	1.39233	−	1.16831i	0.427951	−	0.903802i	$-0.359236\pi$
$859$	40.8075	−	34.2416i	1.39233	−	1.16831i	0.964384	−	0.264505i	$-0.0852087\pi$
$860$	9.29086	+	7.79596i	0.316816	+	0.265840i
$861$	−0.248970	−	1.41198i	−0.00848489	−	0.0481202i
$862$	14.9436	+	25.8830i	0.508980	+	0.881579i
$863$	1.61587	−	2.79876i	0.0550048	−	0.0952710i	−0.837212	−	0.546879i	$-0.815816\pi$
$863$	1.61587	−	2.79876i	0.0550048	−	0.0952710i	0.892217	+	0.451608i	$0.149149\pi$
$864$	5.25877	+	1.91404i	0.178907	+	0.0651168i
$865$	18.0993	+	6.58759i	0.615393	+	0.223985i
$866$	−4.63041	+	8.02011i	−0.157348	+	0.272535i
$867$	19.5175	+	33.8054i	0.662850	+	1.14809i
$868$	−1.14796	−	6.51038i	−0.0389642	−	0.220977i
$869$	22.1138	+	18.5557i	0.750160	+	0.629459i
$870$	6.62630	−	5.56012i	0.224652	−	0.188506i
$871$	4.95811	−	28.1188i	0.167999	−	0.952771i
$872$	−8.17024	+	2.97373i	−0.276679	+	0.100703i
$873$	−0.226682			−0.00767201
$874$		0			0
$875$	−32.3351			−1.09313
$876$	22.6989	−	8.26173i	0.766926	−	0.279138i
$877$	−2.03590	+	11.5462i	−0.0687476	+	0.389887i	0.930947	+	0.365155i	$0.118984\pi$
$877$	−2.03590	+	11.5462i	−0.0687476	+	0.389887i	−0.999694	+	0.0247314i	$0.992127\pi$
$878$	15.9813	−	13.4099i	0.539344	−	0.452563i
$879$	−32.0310	−	26.8772i	−1.08038	−	0.906544i
$880$	1.10607	+	6.27282i	0.0372855	+	0.211457i
$881$	−13.5236	−	23.4236i	−0.455623	−	0.789162i	0.543101	−	0.839667i	$-0.317250\pi$
$881$	−13.5236	−	23.4236i	−0.455623	−	0.789162i	−0.998724	+	0.0505056i	$0.983917\pi$
$882$	−0.0851223	+	0.147436i	−0.00286622	+	0.00496443i
$883$	−13.6077	−	4.95280i	−0.457936	−	0.166675i	0.102744	−	0.994708i	$-0.467238\pi$
$883$	−13.6077	−	4.95280i	−0.457936	−	0.166675i	−0.560680	+	0.828033i	$0.689460\pi$
$884$	35.2695	+	12.8370i	1.18624	+	0.431757i
$885$	−0.879385	+	1.52314i	−0.0295602	+	0.0511998i
$886$	11.9140	+	20.6357i	0.400259	+	0.693268i
$887$	2.01279	+	11.4151i	0.0675830	+	0.383282i	0.999773	+	0.0213125i	$0.00678449\pi$
$887$	2.01279	+	11.4151i	0.0675830	+	0.383282i	−0.932190	+	0.361970i	$0.882104\pi$
$888$	5.12836	+	4.30320i	0.172096	+	0.144406i
$889$	−20.0838	+	16.8523i	−0.673588	+	0.565208i
$890$	2.68779	−	15.2432i	0.0900948	−	0.510953i
$891$	19.7995	−	7.20642i	0.663307	−	0.241424i
$892$	9.27631			0.310594
$893$		0			0
$894$	−25.2080			−0.843082
$895$	35.3628	−	12.8710i	1.18205	−	0.430230i
$896$	−0.467911	+	2.65366i	−0.0156318	+	0.0886524i
$897$	4.69459	−	3.93923i	0.156748	−	0.131527i
$898$	−1.67159	−	1.40263i	−0.0557816	−	0.0468064i
$899$	−1.20264	−	6.82050i	−0.0401102	−	0.227476i
$900$	−0.326352	−	0.565258i	−0.0108784	−	0.0188419i
$901$	−26.7615	+	46.3522i	−0.891553	+	1.54422i
$902$	1.03936	+	0.378297i	0.0346070	+	0.0125959i
$903$	23.5253	+	8.56250i	0.782872	+	0.284942i
$904$	−1.42989	+	2.47665i	−0.0475575	+	0.0823720i
$905$	2.77837	+	4.81228i	0.0923562	+	0.159966i
$906$	−1.23854	−	7.02412i	−0.0411478	−	0.233361i
$907$	−32.1575	−	26.9834i	−1.06777	−	0.895968i	−0.0729237	−	0.997338i	$-0.523233\pi$
$907$	−32.1575	−	26.9834i	−1.06777	−	0.895968i	−0.994849	+	0.101370i	$0.967677\pi$
$908$	−5.92649	+	4.97291i	−0.196677	+	0.165032i
$909$	0.0418891	−	0.237565i	0.00138937	−	0.00787952i
$910$	29.1634	−	10.6146i	0.966759	−	0.351871i
$911$	44.8675			1.48653			0.743264	−	0.668999i	$-0.233277\pi$
$911$	44.8675			1.48653			0.743264	+	0.668999i	$0.233277\pi$
$912$		0			0
$913$	26.9932			0.893344
$914$	1.67365	−	0.609158i	0.0553594	−	0.0201492i
$915$	−1.56212	+	8.85921i	−0.0516420	+	0.292877i
$916$	−17.6459	+	14.8067i	−0.583037	+	0.489226i
$917$	−13.3509	−	11.2028i	−0.440886	−	0.369947i
$918$	6.33363	+	35.9198i	0.209041	+	1.18553i
$919$	16.2635	+	28.1692i	0.536484	+	0.929217i	0.999090	+	0.0426535i	$0.0135811\pi$
$919$	16.2635	+	28.1692i	0.536484	+	0.929217i	−0.462606	+	0.886564i	$0.653086\pi$
$920$	−0.694593	+	1.20307i	−0.0229000	+	0.0396640i
$921$	−30.7067	−	11.1763i	−1.01182	−	0.368272i
$922$	−14.5544	−	5.29736i	−0.479323	−	0.174459i
$923$	−24.3405	+	42.1590i	−0.801177	+	1.38768i
$924$	6.57398	+	11.3865i	0.216268	+	0.374587i
$925$	−0.758770	−	4.30320i	−0.0249482	−	0.141488i
$926$	2.07604	+	1.74200i	0.0682228	+	0.0572457i
$927$	4.29086	−	3.60046i	0.140930	−	0.118255i
$928$	−0.490200	+	2.78006i	−0.0160916	+	0.0912600i
$929$	−11.1261	+	4.04958i	−0.365037	+	0.132862i	−0.518025	−	0.855366i	$-0.673333\pi$
$929$	−11.1261	+	4.04958i	−0.365037	+	0.132862i	0.152988	+	0.988228i	$0.451110\pi$
$930$	−7.51754			−0.246510
$931$		0			0
$932$	8.39961			0.275139
$933$	−42.1712	+	15.3491i	−1.38062	+	0.502505i
$934$	−2.24241	+	12.7173i	−0.0733739	+	0.416124i
$935$	−31.8016	+	26.6847i	−1.04002	+	0.872683i
$936$	2.87939	+	2.41609i	0.0941157	+	0.0789724i
$937$	−0.132636	−	0.752219i	−0.00433304	−	0.0245739i	0.982565	−	0.185922i	$-0.0595271\pi$
$937$	−0.132636	−	0.752219i	−0.00433304	−	0.0245739i	−0.986898	+	0.161348i	$0.948416\pi$
$938$	6.68004	+	11.5702i	0.218111	+	0.377780i
$939$	4.26011	−	7.37874i	0.139024	−	0.240796i
$940$	−14.8229	−	5.39511i	−0.483471	−	0.175969i
$941$	−20.1976	−	7.35132i	−0.658422	−	0.239646i	−0.00886735	−	0.999961i	$-0.502823\pi$
$941$	−20.1976	−	7.35132i	−0.658422	−	0.239646i	−0.649555	+	0.760315i	$0.725045\pi$
$942$	−6.47565	+	11.2162i	−0.210988	+	0.365442i
$943$	0.120615	+	0.208911i	0.00392776	+	0.00680307i
$944$	−0.0996702	−	0.565258i	−0.00324399	−	0.0183976i
$945$	23.1034	+	19.3860i	0.751553	+	0.630628i
$946$	−14.7947	+	12.4143i	−0.481018	+	0.403622i
$947$	5.50206	−	31.2037i	0.178793	−	1.01398i	−0.754881	−	0.655861i	$-0.772306\pi$
$947$	5.50206	−	31.2037i	0.178793	−	1.01398i	0.933674	−	0.358124i	$-0.116583\pi$
$948$	13.0496	−	4.74968i	0.423832	−	0.154262i
$949$	90.7957			2.94735
$950$		0			0
$951$	5.82707			0.188956
$952$	−16.5030	+	6.00660i	−0.534865	+	0.194675i
$953$	−9.70192	+	55.0223i	−0.314276	+	1.78235i	0.261974	+	0.965075i	$0.415627\pi$
$953$	−9.70192	+	55.0223i	−0.314276	+	1.78235i	−0.576250	+	0.817273i	$0.695485\pi$
$954$	−4.10607	+	3.44540i	−0.132939	+	0.111549i
$955$	14.6500	+	12.2928i	0.474063	+	0.397786i
$956$	−2.73143	−	15.4907i	−0.0883407	−	0.501005i
$957$	6.88713	+	11.9289i	0.222629	+	0.385605i
$958$	−9.27631	+	16.0670i	−0.299704	+	0.519103i
$959$	29.5253	+	10.7463i	0.953421	+	0.347017i
$960$	2.87939	+	1.04801i	0.0929318	+	0.0338244i
$961$	12.4905	−	21.6342i	0.402920	−	0.697877i
$962$	12.5817	+	21.7922i	0.405651	+	0.702608i
$963$	−1.29813	−	7.36208i	−0.0418318	−	0.237240i
$964$	−13.4081	−	11.2507i	−0.431845	−	0.362361i
$965$	36.2814	−	30.4437i	1.16794	−	0.980017i
$966$	−0.497941	+	2.82396i	−0.0160210	+	0.0908595i
$967$	−20.2567	+	7.37284i	−0.651412	+	0.237095i	−0.646524	−	0.762894i	$-0.723778\pi$
$967$	−20.2567	+	7.37284i	−0.651412	+	0.237095i	−0.00488775	+	0.999988i	$0.501556\pi$
$968$	0.857097			0.0275481
$969$		0			0
$970$	−0.694593			−0.0223020
$971$	45.7220	−	16.6414i	1.46729	−	0.534049i	0.519926	−	0.854211i	$-0.325960\pi$
$971$	45.7220	−	16.6414i	1.46729	−	0.534049i	0.947363	+	0.320162i	$0.103737\pi$
$972$	−1.15523	+	6.55163i	−0.0370540	+	0.210144i
$973$	−17.0574	+	14.3128i	−0.546834	+	0.458848i
$974$	31.5408	+	26.4658i	1.01063	+	0.848020i
$975$	1.53209	+	8.68891i	0.0490661	+	0.278268i
$976$	−1.46791	−	2.54250i	−0.0469867	−	0.0813833i
$977$	−25.2741	+	43.7760i	−0.808590	+	1.40052i	0.105251	+	0.994446i	$0.466435\pi$
$977$	−25.2741	+	43.7760i	−0.808590	+	1.40052i	−0.913841	+	0.406073i	$0.866898\pi$
$978$	−24.5462	−	8.93410i	−0.784902	−	0.285681i
$979$	23.1612	+	8.42999i	0.740236	+	0.269424i
$980$	−0.260830	+	0.451771i	−0.00833190	+	0.0144313i
$981$	−2.83750	−	4.91469i	−0.0905943	−	0.156914i
$982$	3.92056	+	22.2346i	0.125110	+	0.709534i
$983$	23.0273	+	19.3222i	0.734458	+	0.616284i	0.931343	−	0.364143i	$-0.118638\pi$
$983$	23.0273	+	19.3222i	0.734458	+	0.616284i	−0.196885	+	0.980427i	$0.563083\pi$
$984$	0.407604	−	0.342020i	0.0129939	−	0.0109032i
$985$	−7.96080	+	45.1479i	−0.253652	+	1.43853i
$986$	−17.2891	+	6.29272i	−0.550597	+	0.200401i
$987$	−32.5609			−1.03642
$988$		0			0
$989$	−4.21213			−0.133938
$990$	−3.90673	+	1.42193i	−0.124164	+	0.0451920i
$991$	−0.478016	+	2.71096i	−0.0151847	+	0.0861166i	−0.991458	−	0.130424i	$-0.958366\pi$
$991$	−0.478016	+	2.71096i	−0.0151847	+	0.0861166i	0.976274	+	0.216540i	$0.0694773\pi$
$992$	1.87939	−	1.57699i	0.0596705	−	0.0500695i
$993$	23.9681	+	20.1116i	0.760606	+	0.638224i
$994$	−3.95542	−	22.4323i	−0.125458	−	0.711510i
$995$	−10.0838	−	17.4656i	−0.319677	−	0.553697i
$996$	6.49273	−	11.2457i	0.205730	−	0.356335i
$997$	−8.17974	−	2.97718i	−0.259055	−	0.0942883i	0.209228	−	0.977867i	$-0.432905\pi$
$997$	−8.17974	−	2.97718i	−0.259055	−	0.0942883i	−0.468283	+	0.883579i	$0.655127\pi$
$998$	−27.5599	−	10.0310i	−0.872393	−	0.317525i
$999$	−12.2267	+	21.1772i	−0.386835	+	0.670018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.l.423.1		6
19.2	odd	18		722.2.a.l.1.3		3
19.3	odd	18		722.2.c.k.653.1		6
19.4	even	9	inner	722.2.e.l.99.1		6
19.5	even	9		722.2.c.l.429.3		6
19.6	even	9		722.2.e.a.389.1		6
19.7	even	3		722.2.e.a.245.1		6
19.8	odd	6		38.2.e.a.35.1	yes	6
19.9	even	9		722.2.e.k.595.1		6
19.10	odd	18		38.2.e.a.25.1	✓	6
19.11	even	3		722.2.e.k.415.1		6
19.12	odd	6		722.2.e.m.245.1		6
19.13	odd	18		722.2.e.m.389.1		6
19.14	odd	18		722.2.c.k.429.1		6
19.15	odd	18		722.2.e.b.99.1		6
19.16	even	9		722.2.c.l.653.3		6
19.17	even	9		722.2.a.k.1.1		3
19.18	odd	2		722.2.e.b.423.1		6
57.2	even	18		6498.2.a.bl.1.2		3
57.8	even	6		342.2.u.c.73.1		6
57.17	odd	18		6498.2.a.bq.1.2		3
57.29	even	18		342.2.u.c.253.1		6
76.27	even	6		304.2.u.c.225.1		6
76.55	odd	18		5776.2.a.bo.1.3		3
76.59	even	18		5776.2.a.bn.1.1		3
76.67	even	18		304.2.u.c.177.1		6
95.8	even	12		950.2.u.b.149.2		12
95.27	even	12		950.2.u.b.149.1		12
95.29	odd	18		950.2.l.d.101.1		6
95.48	even	36		950.2.u.b.899.1		12
95.67	even	36		950.2.u.b.899.2		12
95.84	odd	6		950.2.l.d.301.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.25.1	✓	6	19.10	odd	18
38.2.e.a.35.1	yes	6	19.8	odd	6
304.2.u.c.177.1		6	76.67	even	18
304.2.u.c.225.1		6	76.27	even	6
342.2.u.c.73.1		6	57.8	even	6
342.2.u.c.253.1		6	57.29	even	18
722.2.a.k.1.1		3	19.17	even	9
722.2.a.l.1.3		3	19.2	odd	18
722.2.c.k.429.1		6	19.14	odd	18
722.2.c.k.653.1		6	19.3	odd	18
722.2.c.l.429.3		6	19.5	even	9
722.2.c.l.653.3		6	19.16	even	9
722.2.e.a.245.1		6	19.7	even	3
722.2.e.a.389.1		6	19.6	even	9
722.2.e.b.99.1		6	19.15	odd	18
722.2.e.b.423.1		6	19.18	odd	2
722.2.e.k.415.1		6	19.11	even	3
722.2.e.k.595.1		6	19.9	even	9
722.2.e.l.99.1		6	19.4	even	9	inner
722.2.e.l.423.1		6	1.1	even	1	trivial
722.2.e.m.245.1		6	19.12	odd	6
722.2.e.m.389.1		6	19.13	odd	18
950.2.l.d.101.1		6	95.29	odd	18
950.2.l.d.301.1		6	95.84	odd	6
950.2.u.b.149.1		12	95.27	even	12
950.2.u.b.149.2		12	95.8	even	12
950.2.u.b.899.1		12	95.48	even	36
950.2.u.b.899.2		12	95.67	even	36
5776.2.a.bn.1.1		3	76.59	even	18
5776.2.a.bo.1.3		3	76.55	odd	18
6498.2.a.bl.1.2		3	57.2	even	18
6498.2.a.bq.1.2		3	57.17	odd	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)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.266044 + 1.50881i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.53209 + 1.28558i) q^{5} +(0.266044 + 1.50881i) q^{6} +(-1.34730 - 2.33359i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.613341 + 0.223238i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.266044 + 1.50881i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.53209 + 1.28558i) q^{5} +(0.266044 + 1.50881i) q^{6} +(-1.34730 - 2.33359i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.613341 + 0.223238i) q^{9} +(1.87939 + 0.684040i) q^{10} +(-1.59240 + 2.75811i) q^{11} +(0.766044 + 1.32683i) q^{12} +(1.00000 + 5.67128i) q^{13} +(-2.06418 - 1.73205i) q^{14} +(-2.34730 + 1.96962i) q^{15} +(0.173648 - 0.984808i) q^{16} +(6.12449 - 2.22913i) q^{17} +0.652704 q^{18} +2.00000 q^{20} +(3.87939 - 1.41198i) q^{21} +(-0.553033 + 3.13641i) q^{22} +(-0.532089 + 0.446476i) q^{23} +(1.17365 + 0.984808i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(2.87939 + 4.98724i) q^{26} +(-2.79813 + 4.84651i) q^{27} +(-2.53209 - 0.921605i) q^{28} +(-2.65270 - 0.965505i) q^{29} +(-1.53209 + 2.65366i) q^{30} +(1.22668 + 2.12467i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-3.73783 - 3.13641i) q^{33} +(4.99273 - 4.18939i) q^{34} +(0.935822 - 5.30731i) q^{35} +(0.613341 - 0.223238i) q^{36} +4.36959 q^{37} -8.82295 q^{39} +(1.87939 - 0.684040i) q^{40} +(0.0603074 - 0.342020i) q^{41} +(3.16250 - 2.65366i) q^{42} +(4.64543 + 3.89798i) q^{43} +(0.553033 + 3.13641i) q^{44} +(0.652704 + 1.13052i) q^{45} +(-0.347296 + 0.601535i) q^{46} +(-7.41147 - 2.69756i) q^{47} +(1.43969 + 0.524005i) q^{48} +(-0.130415 + 0.225885i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.73396 + 9.83375i) q^{51} +(4.41147 + 3.70167i) q^{52} +(-6.29086 + 5.27866i) q^{53} +(-0.971782 + 5.51125i) q^{54} +(-5.98545 + 2.17853i) q^{55} -2.69459 q^{56} -2.82295 q^{58} +(0.539363 - 0.196312i) q^{59} +(-0.532089 + 3.01763i) q^{60} +(2.24897 - 1.88711i) q^{61} +(1.87939 + 1.57699i) q^{62} +(-0.305407 - 1.73205i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-5.75877 + 9.97448i) q^{65} +(-4.58512 - 1.66885i) q^{66} +(-4.65910 - 1.69577i) q^{67} +(3.25877 - 5.64436i) q^{68} +(-0.532089 - 0.921605i) q^{69} +(-0.935822 - 5.30731i) q^{70} +(6.47565 + 5.43372i) q^{71} +(0.500000 - 0.419550i) q^{72} +(2.73783 - 15.5270i) q^{73} +(4.10607 - 1.49449i) q^{74} +1.53209 q^{75} +8.58172 q^{77} +(-8.29086 + 3.01763i) q^{78} +(1.57398 - 8.92647i) q^{79} +(1.53209 - 1.28558i) q^{80} +(-5.06805 - 4.25260i) q^{81} +(-0.0603074 - 0.342020i) q^{82} +(-4.23783 - 7.34013i) q^{83} +(2.06418 - 3.57526i) q^{84} +(12.2490 + 4.45826i) q^{85} +(5.69846 + 2.07407i) q^{86} +(2.16250 - 3.74557i) q^{87} +(1.59240 + 2.75811i) q^{88} +(-1.34389 - 7.62159i) q^{89} +(1.00000 + 0.839100i) q^{90} +(11.8871 - 9.97448i) q^{91} +(-0.120615 + 0.684040i) q^{92} +(-3.53209 + 1.28558i) q^{93} -7.88713 q^{94} +1.53209 q^{96} +(-0.326352 + 0.118782i) q^{97} +(-0.0452926 + 0.256867i) q^{98} +(-1.59240 + 1.33618i) 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