LMFDB - Embedded newform 37.2.f.a.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,2,Mod(7,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("37.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	37.f (of order $9$, degree $6$, 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:	$0.295446487479$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			33.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	37.33
Dual form			37.2.f.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0603074 + 0.342020i) q^{2} +(-0.439693 - 2.49362i) q^{3} +(1.76604 + 0.642788i) q^{4} +(-2.87939 + 2.41609i) q^{5} +0.879385 q^{6} +(-0.0923963 + 0.0775297i) q^{7} +(-0.673648 + 1.16679i) q^{8} +(-3.20574 + 1.16679i) q^{9} +O(q^{10})$	\(q+(-0.0603074 + 0.342020i) q^{2} +(-0.439693 - 2.49362i) q^{3} +(1.76604 + 0.642788i) q^{4} +(-2.87939 + 2.41609i) q^{5} +0.879385 q^{6} +(-0.0923963 + 0.0775297i) q^{7} +(-0.673648 + 1.16679i) q^{8} +(-3.20574 + 1.16679i) q^{9} +(-0.652704 - 1.13052i) q^{10} +(0.766044 - 1.32683i) q^{11} +(0.826352 - 4.68647i) q^{12} +(-4.14543 - 1.50881i) q^{13} +(-0.0209445 - 0.0362770i) q^{14} +(7.29086 + 6.11776i) q^{15} +(2.52094 + 2.11532i) q^{16} +(4.60607 - 1.67647i) q^{17} +(-0.205737 - 1.16679i) q^{18} +(0.224155 + 1.27125i) q^{19} +(-6.63816 + 2.41609i) q^{20} +(0.233956 + 0.196312i) q^{21} +(0.407604 + 0.342020i) q^{22} +(-1.43969 - 2.49362i) q^{23} +(3.20574 + 1.16679i) q^{24} +(1.58512 - 8.98968i) q^{25} +(0.766044 - 1.32683i) q^{26} +(0.520945 + 0.902302i) q^{27} +(-0.213011 + 0.0775297i) q^{28} +(-0.620615 + 1.07494i) q^{29} +(-2.53209 + 2.12467i) q^{30} +1.69459 q^{31} +(-2.93969 + 2.46669i) q^{32} +(-3.64543 - 1.32683i) q^{33} +(0.295607 + 1.67647i) q^{34} +(0.0787257 - 0.446476i) q^{35} -6.41147 q^{36} +(-3.29813 + 5.11100i) q^{37} -0.448311 q^{38} +(-1.93969 + 11.0005i) q^{39} +(-0.879385 - 4.98724i) q^{40} +(-1.11334 - 0.405223i) q^{41} +(-0.0812519 + 0.0681784i) q^{42} +7.00774 q^{43} +(2.20574 - 1.85083i) q^{44} +(6.41147 - 11.1050i) q^{45} +(0.939693 - 0.342020i) q^{46} +(2.84730 + 4.93166i) q^{47} +(4.16637 - 7.21637i) q^{48} +(-1.21301 + 6.87933i) q^{49} +(2.97906 + 1.08429i) q^{50} +(-6.20574 - 10.7487i) q^{51} +(-6.35117 - 5.32926i) q^{52} +(3.92855 + 3.29644i) q^{53} +(-0.340022 + 0.123758i) q^{54} +(1.00000 + 5.67128i) q^{55} +(-0.0282185 - 0.160035i) q^{56} +(3.07145 - 1.11792i) q^{57} +(-0.330222 - 0.277089i) q^{58} +(-4.53596 - 3.80612i) q^{59} +(8.94356 + 15.4907i) q^{60} +(-7.21688 - 2.62673i) q^{61} +(-0.102196 + 0.579585i) q^{62} +(0.205737 - 0.356347i) q^{63} +(2.62449 + 4.54574i) q^{64} +(15.5817 - 5.67128i) q^{65} +(0.673648 - 1.16679i) q^{66} +(-4.28699 + 3.59721i) q^{67} +9.21213 q^{68} +(-5.58512 + 4.68647i) q^{69} +(0.147956 + 0.0538515i) q^{70} +(-1.42514 - 8.08240i) q^{71} +(0.798133 - 4.52644i) q^{72} -5.86484 q^{73} +(-1.54916 - 1.43626i) q^{74} -23.1138 q^{75} +(-0.421274 + 2.38917i) q^{76} +(0.0320889 + 0.181985i) q^{77} +(-3.64543 - 1.32683i) q^{78} +(9.95336 - 8.35186i) q^{79} -12.3696 q^{80} +(-5.81908 + 4.88279i) q^{81} +(0.205737 - 0.356347i) q^{82} +(12.2023 - 4.44129i) q^{83} +(0.286989 + 0.497079i) q^{84} +(-9.21213 + 15.9559i) q^{85} +(-0.422618 + 2.39679i) q^{86} +(2.95336 + 1.07494i) q^{87} +(1.03209 + 1.78763i) q^{88} +(5.23783 + 4.39506i) q^{89} +(3.41147 + 2.86257i) q^{90} +(0.500000 - 0.181985i) q^{91} +(-0.939693 - 5.32926i) q^{92} +(-0.745100 - 4.22567i) q^{93} +(-1.85844 + 0.676417i) q^{94} +(-3.71688 - 3.11883i) q^{95} +(7.44356 + 6.24589i) q^{96} +(0.875515 + 1.51644i) q^{97} +(-2.27972 - 0.829748i) q^{98} +(-0.907604 + 5.14728i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + 3 q^{7} - 3 q^{8} - 9 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + 3 * q^7 - 3 * q^8 - 9 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + 3 q^{7} - 3 q^{8} - 9 q^{9} - 6 q^{10} + 6 q^{12} - 9 q^{13} + 3 q^{14} + 12 q^{15} + 12 q^{16} + 3 q^{17} + 9 q^{18} + 3 q^{19} - 6 q^{20} + 6 q^{21} + 6 q^{22} - 3 q^{23} + 9 q^{24} - 12 q^{25} - 9 q^{28} - 15 q^{29} - 6 q^{30} + 6 q^{31} - 12 q^{32} - 6 q^{33} + 3 q^{34} + 18 q^{35} - 18 q^{36} - 6 q^{37} - 6 q^{38} - 6 q^{39} + 6 q^{40} - 3 q^{42} - 6 q^{43} + 3 q^{44} + 18 q^{45} + 15 q^{47} + 6 q^{48} - 15 q^{49} + 21 q^{50} - 27 q^{51} - 12 q^{52} + 24 q^{53} + 18 q^{54} + 6 q^{55} - 15 q^{56} + 18 q^{57} + 21 q^{58} + 6 q^{59} + 24 q^{60} - 27 q^{61} - 9 q^{63} + 3 q^{64} + 30 q^{65} + 3 q^{66} - 18 q^{67} + 6 q^{68} - 12 q^{69} - 30 q^{70} + 33 q^{71} - 9 q^{72} + 12 q^{73} - 21 q^{74} - 66 q^{75} + 15 q^{76} - 9 q^{77} - 6 q^{78} + 33 q^{79} - 60 q^{80} - 18 q^{81} - 9 q^{82} + 21 q^{83} - 6 q^{84} - 6 q^{85} + 24 q^{86} - 9 q^{87} - 3 q^{88} + 12 q^{89} + 3 q^{91} - 3 q^{93} - 3 q^{94} - 6 q^{95} + 15 q^{96} + 18 q^{97} + 12 q^{98} - 9 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + 3 * q^7 - 3 * q^8 - 9 * q^9 - 6 * q^10 + 6 * q^12 - 9 * q^13 + 3 * q^14 + 12 * q^15 + 12 * q^16 + 3 * q^17 + 9 * q^18 + 3 * q^19 - 6 * q^20 + 6 * q^21 + 6 * q^22 - 3 * q^23 + 9 * q^24 - 12 * q^25 - 9 * q^28 - 15 * q^29 - 6 * q^30 + 6 * q^31 - 12 * q^32 - 6 * q^33 + 3 * q^34 + 18 * q^35 - 18 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^39 + 6 * q^40 - 3 * q^42 - 6 * q^43 + 3 * q^44 + 18 * q^45 + 15 * q^47 + 6 * q^48 - 15 * q^49 + 21 * q^50 - 27 * q^51 - 12 * q^52 + 24 * q^53 + 18 * q^54 + 6 * q^55 - 15 * q^56 + 18 * q^57 + 21 * q^58 + 6 * q^59 + 24 * q^60 - 27 * q^61 - 9 * q^63 + 3 * q^64 + 30 * q^65 + 3 * q^66 - 18 * q^67 + 6 * q^68 - 12 * q^69 - 30 * q^70 + 33 * q^71 - 9 * q^72 + 12 * q^73 - 21 * q^74 - 66 * q^75 + 15 * q^76 - 9 * q^77 - 6 * q^78 + 33 * q^79 - 60 * q^80 - 18 * q^81 - 9 * q^82 + 21 * q^83 - 6 * q^84 - 6 * q^85 + 24 * q^86 - 9 * q^87 - 3 * q^88 + 12 * q^89 + 3 * q^91 - 3 * q^93 - 3 * q^94 - 6 * q^95 + 15 * q^96 + 18 * q^97 + 12 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.0603074	+	0.342020i	−0.0426438	+	0.241845i	−0.998678	−	0.0514118i	$-0.983628\pi$
$2$	−0.0603074	+	0.342020i	−0.0426438	+	0.241845i	0.956034	+	0.293257i	$0.0947390\pi$
$3$	−0.439693	−	2.49362i	−0.253857	−	1.43969i	−0.798991	−	0.601344i	$-0.794632\pi$
$3$	−0.439693	−	2.49362i	−0.253857	−	1.43969i	0.545134	−	0.838349i	$-0.316479\pi$
$4$	1.76604	+	0.642788i	0.883022	+	0.321394i
$5$	−2.87939	+	2.41609i	−1.28770	+	1.08051i	−0.295567	+	0.955322i	$0.595509\pi$
$5$	−2.87939	+	2.41609i	−1.28770	+	1.08051i	−0.992133	+	0.125187i	$0.960047\pi$
$6$	0.879385			0.359008
$7$	−0.0923963	+	0.0775297i	−0.0349225	+	0.0293035i	−0.660082	−	0.751194i	$-0.729478\pi$
$7$	−0.0923963	+	0.0775297i	−0.0349225	+	0.0293035i	0.625159	+	0.780497i	$0.285034\pi$
$8$	−0.673648	+	1.16679i	−0.238171	+	0.412524i
$9$	−3.20574	+	1.16679i	−1.06858	+	0.388931i
$10$	−0.652704	−	1.13052i	−0.206403	−	0.357501i
$11$	0.766044	−	1.32683i	0.230971	−	0.400054i	−0.727123	−	0.686507i	$-0.759143\pi$
$11$	0.766044	−	1.32683i	0.230971	−	0.400054i	0.958094	+	0.286453i	$0.0924764\pi$
$12$	0.826352	−	4.68647i	0.238547	−	1.35287i
$13$	−4.14543	−	1.50881i	−1.14974	−	0.418469i	−0.304315	−	0.952571i	$-0.598428\pi$
$13$	−4.14543	−	1.50881i	−1.14974	−	0.418469i	−0.845420	+	0.534102i	$0.820650\pi$
$14$	−0.0209445	−	0.0362770i	−0.00559766	−	0.00969543i
$15$	7.29086	+	6.11776i	1.88249	+	1.57960i
$16$	2.52094	+	2.11532i	0.630236	+	0.528831i
$17$	4.60607	−	1.67647i	1.11714	−	0.406604i	0.283529	−	0.958964i	$-0.408495\pi$
$17$	4.60607	−	1.67647i	1.11714	−	0.406604i	0.833606	+	0.552360i	$0.186272\pi$
$18$	−0.205737	−	1.16679i	−0.0484927	−	0.275016i
$19$	0.224155	+	1.27125i	0.0514248	+	0.291644i	0.999664	−	0.0259118i	$-0.00824891\pi$
$19$	0.224155	+	1.27125i	0.0514248	+	0.291644i	−0.948239	+	0.317556i	$0.897138\pi$
$20$	−6.63816	+	2.41609i	−1.48434	+	0.540254i
$21$	0.233956	+	0.196312i	0.0510533	+	0.0428388i
$22$	0.407604	+	0.342020i	0.0869014	+	0.0729189i
$23$	−1.43969	−	2.49362i	−0.300197	−	0.519956i	0.675984	−	0.736917i	$-0.263719\pi$
$23$	−1.43969	−	2.49362i	−0.300197	−	0.519956i	−0.976180	+	0.216961i	$0.930386\pi$
$24$	3.20574	+	1.16679i	0.654368	+	0.238171i
$25$	1.58512	−	8.98968i	0.317024	−	1.79794i
$26$	0.766044	−	1.32683i	0.150234	−	0.260212i
$27$	0.520945	+	0.902302i	0.100256	+	0.173648i
$28$	−0.213011	+	0.0775297i	−0.0402553	+	0.0146517i
$29$	−0.620615	+	1.07494i	−0.115245	+	0.199611i	−0.917878	−	0.396863i	$-0.870099\pi$
$29$	−0.620615	+	1.07494i	−0.115245	+	0.199611i	0.802633	+	0.596474i	$0.203432\pi$
$30$	−2.53209	+	2.12467i	−0.462294	+	0.387911i
$31$	1.69459			0.304358			0.152179	−	0.988353i	$-0.451371\pi$
$31$	1.69459			0.304358			0.152179	+	0.988353i	$0.451371\pi$
$32$	−2.93969	+	2.46669i	−0.519669	+	0.436054i
$33$	−3.64543	−	1.32683i	−0.634588	−	0.230971i
$34$	0.295607	+	1.67647i	0.0506962	+	0.287512i
$35$	0.0787257	−	0.446476i	0.0133071	−	0.0754681i
$36$	−6.41147			−1.06858
$37$	−3.29813	+	5.11100i	−0.542210	+	0.840243i
$37$	−3.29813	+	5.11100i	−0.542210	+	0.840243i
$38$	−0.448311			−0.0727256
$39$	−1.93969	+	11.0005i	−0.310599	+	1.76150i
$40$	−0.879385	−	4.98724i	−0.139043	−	0.788552i
$41$	−1.11334	−	0.405223i	−0.173875	−	0.0632852i	0.253616	−	0.967305i	$-0.418380\pi$
$41$	−1.11334	−	0.405223i	−0.173875	−	0.0632852i	−0.427491	+	0.904020i	$0.640602\pi$
$42$	−0.0812519	+	0.0681784i	−0.0125374	+	0.0105202i
$43$	7.00774			1.06867			0.534335	−	0.845273i	$-0.320562\pi$
$43$	7.00774			1.06867			0.534335	+	0.845273i	$0.320562\pi$
$44$	2.20574	−	1.85083i	0.332527	−	0.279024i
$45$	6.41147	−	11.1050i	0.955766	−	1.65544i
$46$	0.939693	−	0.342020i	0.138550	−	0.0504281i
$47$	2.84730	+	4.93166i	0.415321	+	0.719357i	0.995462	−	0.0951591i	$-0.0303360\pi$
$47$	2.84730	+	4.93166i	0.415321	+	0.719357i	−0.580141	+	0.814516i	$0.697003\pi$
$48$	4.16637	−	7.21637i	0.601364	−	1.04159i
$49$	−1.21301	+	6.87933i	−0.173287	+	0.982761i
$50$	2.97906	+	1.08429i	0.421302	+	0.153341i
$51$	−6.20574	−	10.7487i	−0.868977	−	1.50511i
$52$	−6.35117	−	5.32926i	−0.880748	−	0.739036i
$53$	3.92855	+	3.29644i	0.539628	+	0.452801i	0.871411	−	0.490554i	$-0.163206\pi$
$53$	3.92855	+	3.29644i	0.539628	+	0.452801i	−0.331783	+	0.943356i	$0.607650\pi$
$54$	−0.340022	+	0.123758i	−0.0462712	+	0.0168413i
$55$	1.00000	+	5.67128i	0.134840	+	0.764715i
$56$	−0.0282185	−	0.160035i	−0.00377085	−	0.0213856i
$57$	3.07145	−	1.11792i	0.406824	−	0.148072i
$58$	−0.330222	−	0.277089i	−0.0433603	−	0.0363836i
$59$	−4.53596	−	3.80612i	−0.590532	−	0.495515i	0.297855	−	0.954611i	$-0.403729\pi$
$59$	−4.53596	−	3.80612i	−0.590532	−	0.495515i	−0.888387	+	0.459096i	$0.848173\pi$
$60$	8.94356	+	15.4907i	1.15461	+	1.99984i
$61$	−7.21688	−	2.62673i	−0.924027	−	0.336318i	−0.164188	−	0.986429i	$-0.552500\pi$
$61$	−7.21688	−	2.62673i	−0.924027	−	0.336318i	−0.759839	+	0.650111i	$0.774722\pi$
$62$	−0.102196	+	0.579585i	−0.0129790	+	0.0736073i
$63$	0.205737	−	0.356347i	0.0259204	−	0.0448955i
$64$	2.62449	+	4.54574i	0.328061	+	0.568218i
$65$	15.5817	−	5.67128i	1.93267	−	0.703436i
$66$	0.673648	−	1.16679i	0.0829204	−	0.143622i
$67$	−4.28699	+	3.59721i	−0.523739	+	0.439469i	−0.865933	−	0.500160i	$-0.833274\pi$
$67$	−4.28699	+	3.59721i	−0.523739	+	0.439469i	0.342194	+	0.939629i	$0.388830\pi$
$68$	9.21213			1.11714
$69$	−5.58512	+	4.68647i	−0.672370	+	0.564185i
$70$	0.147956	+	0.0538515i	0.0176841	+	0.00643649i
$71$	−1.42514	−	8.08240i	−0.169134	−	0.959204i	−0.944699	−	0.327937i	$-0.893646\pi$
$71$	−1.42514	−	8.08240i	−0.169134	−	0.959204i	0.775566	−	0.631267i	$-0.217465\pi$
$72$	0.798133	−	4.52644i	0.0940609	−	0.533446i
$73$	−5.86484			−0.686427			−0.343214	−	0.939257i	$-0.611515\pi$
$73$	−5.86484			−0.686427			−0.343214	+	0.939257i	$0.611515\pi$
$74$	−1.54916	−	1.43626i	−0.180087	−	0.166962i
$75$	−23.1138			−2.66895
$76$	−0.421274	+	2.38917i	−0.0483235	+	0.274056i
$77$	0.0320889	+	0.181985i	0.00365687	+	0.0207391i
$78$	−3.64543	−	1.32683i	−0.412764	−	0.150234i
$79$	9.95336	−	8.35186i	1.11984	−	0.939658i	0.121244	−	0.992623i	$-0.461312\pi$
$79$	9.95336	−	8.35186i	1.11984	−	0.939658i	0.998596	+	0.0529646i	$0.0168671\pi$
$80$	−12.3696			−1.38296
$81$	−5.81908	+	4.88279i	−0.646564	+	0.542532i
$82$	0.205737	−	0.356347i	0.0227199	−	0.0393519i
$83$	12.2023	−	4.44129i	1.33938	−	0.487494i	0.429763	−	0.902942i	$-0.358597\pi$
$83$	12.2023	−	4.44129i	1.33938	−	0.487494i	0.909617	+	0.415447i	$0.136375\pi$
$84$	0.286989	+	0.497079i	0.0313131	+	0.0542358i
$85$	−9.21213	+	15.9559i	−0.999196	+	1.73066i
$86$	−0.422618	+	2.39679i	−0.0455721	+	0.258452i
$87$	2.95336	+	1.07494i	0.316634	+	0.115245i
$88$	1.03209	+	1.78763i	0.110021	+	0.190562i
$89$	5.23783	+	4.39506i	0.555208	+	0.465875i	0.876700	−	0.481037i	$-0.159740\pi$
$89$	5.23783	+	4.39506i	0.555208	+	0.465875i	−0.321492	+	0.946912i	$0.604184\pi$
$90$	3.41147	+	2.86257i	0.359601	+	0.301741i
$91$	0.500000	−	0.181985i	0.0524142	−	0.0190772i
$92$	−0.939693	−	5.32926i	−0.0979697	−	0.555614i
$93$	−0.745100	−	4.22567i	−0.0772633	−	0.438182i
$94$	−1.85844	+	0.676417i	−0.191684	+	0.0697671i
$95$	−3.71688	−	3.11883i	−0.381344	−	0.319986i
$96$	7.44356	+	6.24589i	0.759705	+	0.637469i
$97$	0.875515	+	1.51644i	0.0888951	+	0.153971i	0.907044	−	0.421035i	$-0.138333\pi$
$97$	0.875515	+	1.51644i	0.0888951	+	0.153971i	−0.818149	+	0.575006i	$0.805000\pi$
$98$	−2.27972	−	0.829748i	−0.230286	−	0.0838172i
$99$	−0.907604	+	5.14728i	−0.0912176	+	0.517321i
$100$	8.57785	−	14.8573i	0.857785	−	1.48573i
$101$	0.358441	+	0.620838i	0.0356662	+	0.0617756i	0.883307	−	0.468794i	$-0.155311\pi$
$101$	0.358441	+	0.620838i	0.0356662	+	0.0617756i	−0.847641	+	0.530570i	$0.821978\pi$
$102$	4.05051	−	1.47426i	0.401060	−	0.145974i
$103$	−0.0432332	+	0.0748822i	−0.00425990	+	0.00737836i	−0.868147	−	0.496306i	$-0.834689\pi$
$103$	−0.0432332	+	0.0748822i	−0.00425990	+	0.00737836i	0.863888	+	0.503685i	$0.168023\pi$
$104$	4.55303	−	3.82045i	0.446462	−	0.374626i
$105$	−1.14796			−0.112029
$106$	−1.36437	+	1.14484i	−0.132519	+	0.111197i
$107$	−15.1027	−	5.49692i	−1.46003	−	0.531407i	−0.514656	−	0.857397i	$-0.672080\pi$
$107$	−15.1027	−	5.49692i	−1.46003	−	0.531407i	−0.945373	+	0.325989i	$0.894303\pi$
$108$	0.340022	+	1.92836i	0.0327187	+	0.185557i
$109$	2.90760	−	16.4898i	0.278498	−	1.57944i	−0.449129	−	0.893467i	$-0.648266\pi$
$109$	2.90760	−	16.4898i	0.278498	−	1.57944i	0.727627	−	0.685973i	$-0.240623\pi$
$110$	−2.00000			−0.190693
$111$	14.1951	+	5.97702i	1.34734	+	0.567314i
$112$	−0.396926			−0.0375060
$113$	−0.0564370	+	0.320070i	−0.00530915	+	0.0301097i	−0.987347	−	0.158573i	$-0.949311\pi$
$113$	−0.0564370	+	0.320070i	−0.00530915	+	0.0301097i	0.982038	+	0.188683i	$0.0604218\pi$
$114$	0.197119	+	1.11792i	0.0184619	+	0.104703i
$115$	10.1702	+	3.70167i	0.948380	+	0.345182i
$116$	−1.78699	+	1.49946i	−0.165918	+	0.139222i
$117$	15.0496			1.39134
$118$	1.57532	−	1.32185i	0.145020	−	0.121686i
$119$	−0.295607	+	0.512007i	−0.0270983	+	0.0469356i
$120$	−12.0496	+	4.38571i	−1.09998	+	0.400358i
$121$	4.32635	+	7.49346i	0.393305	+	0.681224i
$122$	1.33363	−	2.30991i	0.120741	−	0.209129i
$123$	−0.520945	+	2.95442i	−0.0469720	+	0.266391i
$124$	2.99273	+	1.08926i	0.268755	+	0.0978187i
$125$	7.75877	+	13.4386i	0.693966	+	1.20198i
$126$	0.109470	+	0.0918566i	0.00975240	+	0.00818323i
$127$	−11.9855	−	10.0570i	−1.06354	−	0.892413i	−0.0690855	−	0.997611i	$-0.522008\pi$
$127$	−11.9855	−	10.0570i	−1.06354	−	0.892413i	−0.994451	+	0.105197i	$0.966453\pi$
$128$	−8.92514	+	3.24849i	−0.788879	+	0.287128i
$129$	−3.08125	−	17.4746i	−0.271289	−	1.53856i
$130$	1.00000	+	5.67128i	0.0877058	+	0.497404i
$131$	4.81180	−	1.75135i	0.420409	−	0.153016i	−0.123148	−	0.992388i	$-0.539299\pi$
$131$	4.81180	−	1.75135i	0.420409	−	0.153016i	0.543558	+	0.839372i	$0.317077\pi$
$132$	−5.58512	−	4.68647i	−0.486122	−	0.407905i
$133$	−0.119271	−	0.100080i	−0.0103421	−	0.00867803i
$134$	−0.971782	−	1.68317i	−0.0839491	−	0.145404i
$135$	−3.68004	−	1.33943i	−0.316728	−	0.115280i
$136$	−1.14677	+	6.50368i	−0.0983350	+	0.557686i
$137$	−9.69846	+	16.7982i	−0.828596	+	1.43517i	0.0705444	+	0.997509i	$0.477526\pi$
$137$	−9.69846	+	16.7982i	−0.828596	+	1.43517i	−0.899140	+	0.437661i	$0.855807\pi$
$138$	−1.26604	−	2.19285i	−0.107773	−	0.186668i
$139$	−15.4338	+	5.61743i	−1.30907	+	0.476464i	−0.899942	−	0.436010i	$-0.856391\pi$
$139$	−15.4338	+	5.61743i	−1.30907	+	0.476464i	−0.409133	+	0.912475i	$0.634169\pi$
$140$	0.426022	−	0.737892i	0.0360054	−	0.0623632i
$141$	11.0458	−	9.26849i	0.930221	−	0.780548i
$142$	2.85029			0.239191
$143$	−5.17752	+	4.34445i	−0.432966	+	0.363301i
$144$	−10.5496	−	3.83975i	−0.879136	−	0.319979i
$145$	−0.810155	−	4.59462i	−0.0672797	−	0.381562i
$146$	0.353693	−	2.00589i	0.0292718	−	0.166009i
$147$	17.6878			1.45886
$148$	−9.10994	+	6.90625i	−0.748832	+	0.567691i
$149$	10.4415			0.855401			0.427701	−	0.903920i	$-0.359324\pi$
$149$	10.4415			0.855401			0.427701	+	0.903920i	$0.359324\pi$
$150$	1.39393	−	7.90539i	0.113814	−	0.645472i
$151$	−3.33228	−	18.8983i	−0.271177	−	1.53792i	−0.750849	−	0.660474i	$-0.770355\pi$
$151$	−3.33228	−	18.8983i	−0.271177	−	1.53792i	0.479671	−	0.877448i	$-0.340756\pi$
$152$	−1.63429	−	0.594831i	−0.132558	−	0.0482472i
$153$	−12.8097	+	10.7487i	−1.03561	+	0.868977i
$154$	−0.0641778			−0.00517159
$155$	−4.87939	+	4.09429i	−0.391922	+	0.328861i
$156$	−10.4966	+	18.1806i	−0.840400	+	1.45562i
$157$	−2.06670	+	0.752219i	−0.164941	+	0.0600336i	−0.423171	−	0.906050i	$-0.639083\pi$
$157$	−2.06670	+	0.752219i	−0.164941	+	0.0600336i	0.258230	+	0.966083i	$0.416861\pi$
$158$	2.25624	+	3.90793i	0.179497	+	0.310898i
$159$	6.49273	−	11.2457i	0.514907	−	0.891845i
$160$	2.50475	−	14.2051i	0.198018	−	1.12301i
$161$	0.326352	+	0.118782i	0.0257201	+	0.00936136i
$162$	−1.31908	−	2.28471i	−0.103637	−	0.179504i
$163$	2.75284	+	2.30991i	0.215619	+	0.180926i	0.744200	−	0.667957i	$-0.232831\pi$
$163$	2.75284	+	2.30991i	0.215619	+	0.180926i	−0.528581	+	0.848883i	$0.677276\pi$
$164$	−1.70574	−	1.43128i	−0.133196	−	0.111764i
$165$	13.7023	−	4.98724i	1.06673	−	0.388256i
$166$	0.783119	+	4.44129i	0.0607818	+	0.344711i
$167$	3.45589	+	19.5993i	0.267425	+	1.51664i	0.762040	+	0.647529i	$0.224198\pi$
$167$	3.45589	+	19.5993i	0.267425	+	1.51664i	−0.494616	+	0.869112i	$0.664691\pi$
$168$	−0.386659	+	0.140732i	−0.0298314	+	0.0108577i
$169$	4.94949	+	4.15312i	0.380730	+	0.319471i
$170$	−4.90167	−	4.11299i	−0.375941	−	0.315452i
$171$	−2.20187	−	3.81374i	−0.168381	−	0.291644i
$172$	12.3760	+	4.50449i	0.943660	+	0.343464i
$173$	1.17840	−	6.68302i	0.0895918	−	0.508100i	−0.906679	−	0.421821i	$-0.861391\pi$
$173$	1.17840	−	6.68302i	0.0895918	−	0.508100i	0.996271	−	0.0862794i	$-0.0274978\pi$
$174$	−0.545759	+	0.945283i	−0.0413739	+	0.0716617i
$175$	0.550507	+	0.953506i	0.0416144	+	0.0720783i
$176$	4.73783	−	1.72443i	0.357127	−	0.129984i
$177$	−7.49660	+	12.9845i	−0.563479	+	0.975974i
$178$	−1.81908	+	1.52639i	−0.136346	+	0.114408i
$179$	−10.0351			−0.750057			−0.375029	−	0.927013i	$-0.622367\pi$
$179$	−10.0351			−0.750057			−0.375029	+	0.927013i	$0.622367\pi$
$180$	18.4611	−	15.4907i	1.37601	−	1.15461i
$181$	22.8123	+	8.30299i	1.69562	+	0.617156i	0.995315	−	0.0966849i	$-0.0308239\pi$
$181$	22.8123	+	8.30299i	1.69562	+	0.617156i	0.700308	+	0.713841i	$0.253046\pi$
$182$	0.0320889	+	0.181985i	0.00237859	+	0.0134896i
$183$	−3.37686	+	19.1511i	−0.249625	+	1.41569i
$184$	3.87939			0.285992
$185$	−2.85204	−	22.6851i	−0.209686	−	1.66784i
$186$	1.49020			0.109267
$187$	1.30406	−	7.39571i	0.0953625	−	0.540828i
$188$	1.85844	+	10.5397i	0.135541	+	0.768690i
$189$	−0.118089	−	0.0429807i	−0.00858968	−	0.00312639i
$190$	1.29086	−	1.08316i	0.0936488	−	0.0785807i
$191$	−12.3259			−0.891874			−0.445937	−	0.895064i	$-0.647129\pi$
$191$	−12.3259			−0.891874			−0.445937	+	0.895064i	$0.647129\pi$
$192$	10.1814	−	8.54320i	0.734778	−	0.616552i
$193$	0.731429	−	1.26687i	0.0526494	−	0.0911915i	−0.838500	−	0.544902i	$-0.816567\pi$
$193$	0.731429	−	1.26687i	0.0526494	−	0.0911915i	0.891149	+	0.453711i	$0.149900\pi$
$194$	−0.571452	+	0.207991i	−0.0410278	+	0.0149329i
$195$	−20.9932	−	36.3613i	−1.50335	−	2.60389i
$196$	−6.56418	+	11.3695i	−0.468870	+	0.812106i
$197$	1.27244	−	7.21637i	0.0906577	−	0.514145i	−0.905334	−	0.424700i	$-0.860380\pi$
$197$	1.27244	−	7.21637i	0.0906577	−	0.514145i	0.995992	−	0.0894451i	$-0.0285094\pi$
$198$	−1.70574	−	0.620838i	−0.121221	−	0.0441210i
$199$	2.29679	+	3.97816i	0.162815	+	0.282004i	0.935877	−	0.352326i	$-0.114609\pi$
$199$	2.29679	+	3.97816i	0.162815	+	0.282004i	−0.773062	+	0.634330i	$0.781276\pi$
$200$	9.42127	+	7.90539i	0.666185	+	0.558995i
$201$	10.8550	+	9.10846i	0.765655	+	0.642461i
$202$	−0.233956	+	0.0851529i	−0.0164611	+	0.00599133i
$203$	−0.0259970	−	0.147436i	−0.00182463	−	0.0103480i
$204$	−4.05051	−	22.9716i	−0.283592	−	1.60833i
$205$	4.18479	−	1.52314i	0.292279	−	0.106381i
$206$	−0.0230039	−	0.0193026i	−0.00160276	−	0.00134487i
$207$	7.52481	+	6.31407i	0.523011	+	0.438858i
$208$	−7.25877	−	12.5726i	−0.503305	−	0.871750i
$209$	1.85844	+	0.676417i	0.128551	+	0.0467887i
$210$	0.0692302	−	0.392624i	0.00477734	−	0.0270936i
$211$	−1.97565	+	3.42193i	−0.136009	+	0.235575i	−0.925983	−	0.377566i	$-0.876761\pi$
$211$	−1.97565	+	3.42193i	−0.136009	+	0.235575i	0.789973	+	0.613141i	$0.210094\pi$
$212$	4.81908	+	8.34689i	0.330976	+	0.573267i
$213$	−19.5278	+	7.10754i	−1.33802	+	0.487001i
$214$	2.79086	−	4.83391i	0.190779	−	0.330439i
$215$	−20.1780	+	16.9313i	−1.37613	+	1.15471i
$216$	−1.40373			−0.0955120
$217$	−0.156574	+	0.131381i	−0.0106289	+	0.00891874i
$218$	5.46451	+	1.98892i	0.370103	+	0.134707i
$219$	2.57873	+	14.6247i	0.174254	+	0.988244i
$220$	−1.87939	+	10.6585i	−0.126708	+	0.718597i
$221$	−21.6236			−1.45456
$222$	−2.90033	+	4.49454i	−0.194657	+	0.301654i
$223$	14.5030			0.971192			0.485596	−	0.874183i	$-0.338603\pi$
$223$	14.5030			0.971192			0.485596	+	0.874183i	$0.338603\pi$
$224$	0.0803746	−	0.455827i	0.00537025	−	0.0304562i
$225$	5.40760	+	30.6680i	0.360507	+	2.04454i
$226$	−0.106067	−	0.0386052i	−0.00705546	−	0.00256798i
$227$	−0.407604	+	0.342020i	−0.0270536	+	0.0227007i	−0.656214	−	0.754575i	$-0.727843\pi$
$227$	−0.407604	+	0.342020i	−0.0270536	+	0.0227007i	0.629161	+	0.777275i	$0.283399\pi$
$228$	6.14290			0.406824
$229$	8.20439	−	6.88430i	0.542162	−	0.454928i	−0.330115	−	0.943941i	$-0.607087\pi$
$229$	8.20439	−	6.88430i	0.542162	−	0.454928i	0.872276	+	0.489013i	$0.162643\pi$
$230$	−1.87939	+	3.25519i	−0.123923	+	0.214641i
$231$	0.439693	−	0.160035i	0.0289297	−	0.0105295i
$232$	−0.836152	−	1.44826i	−0.0548961	−	0.0950828i
$233$	5.89693	−	10.2138i	0.386320	−	0.669127i	−0.605631	−	0.795746i	$-0.707079\pi$
$233$	5.89693	−	10.2138i	0.386320	−	0.669127i	0.991951	+	0.126619i	$0.0404125\pi$
$234$	−0.907604	+	5.14728i	−0.0593319	+	0.336488i
$235$	−20.1138	−	7.32083i	−1.31208	−	0.477558i
$236$	−5.56418	−	9.63744i	−0.362197	−	0.627344i
$237$	−25.2028	−	21.1477i	−1.63710	−	1.37369i
$238$	−0.157289	−	0.131981i	−0.0101955	−	0.00855508i
$239$	−3.43969	+	1.25195i	−0.222495	+	0.0809816i	−0.450862	−	0.892593i	$-0.648884\pi$
$239$	−3.43969	+	1.25195i	−0.222495	+	0.0809816i	0.228367	+	0.973575i	$0.426661\pi$
$240$	5.43882	+	30.8451i	0.351074	+	1.99104i
$241$	−2.26904	−	12.8684i	−0.146162	−	0.828923i	−0.966427	−	0.256941i	$-0.917286\pi$
$241$	−2.26904	−	12.8684i	−0.146162	−	0.828923i	0.820266	−	0.571983i	$-0.193826\pi$
$242$	−2.82383	+	1.02779i	−0.181522	+	0.0660687i
$243$	17.1288	+	14.3728i	1.09881	+	0.922015i
$244$	−11.0569	−	9.27784i	−0.707846	−	0.593953i
$245$	−13.1284	−	22.7390i	−0.838740	−	1.45274i
$246$	−0.979055	−	0.356347i	−0.0624223	−	0.0227199i
$247$	0.988856	−	5.60808i	0.0629194	−	0.356834i
$248$	−1.14156	+	1.97724i	−0.0724891	+	0.125555i
$249$	−16.4402	−	28.4752i	−1.04185	−	1.80454i
$250$	−5.06418	+	1.84321i	−0.320287	+	0.116575i
$251$	13.8380	−	23.9681i	0.873444	−	1.51285i	0.0150339	−	0.999887i	$-0.495214\pi$
$251$	13.8380	−	23.9681i	0.873444	−	1.51285i	0.858411	−	0.512963i	$-0.171452\pi$
$252$	0.592396	−	0.497079i	0.0373175	−	0.0313131i
$253$	−4.41147			−0.277347
$254$	4.16250	−	3.49276i	0.261179	−	0.219155i
$255$	43.8384	+	15.9559i	2.74527	+	0.999196i
$256$	1.25015	+	7.08997i	0.0781345	+	0.443123i
$257$	−3.01842	+	17.1183i	−0.188284	+	1.06781i	0.733379	+	0.679819i	$0.237942\pi$
$257$	−3.01842	+	17.1183i	−0.188284	+	1.06781i	−0.921663	+	0.387991i	$0.873169\pi$
$258$	6.16250			0.383661
$259$	−0.0915189	−	0.727940i	−0.00568671	−	0.0452320i
$260$	31.1634			1.93267
$261$	0.735300	−	4.17009i	0.0455139	−	0.258122i
$262$	0.308811	+	1.75135i	0.0190784	+	0.108199i
$263$	13.1027	+	4.76898i	0.807945	+	0.294068i	0.712775	−	0.701393i	$-0.247438\pi$
$263$	13.1027	+	4.76898i	0.807945	+	0.294068i	0.0951702	+	0.995461i	$0.469660\pi$
$264$	4.00387	−	3.35965i	0.246421	−	0.206772i
$265$	−19.2763			−1.18413
$266$	0.0414222	−	0.0347574i	0.00253976	−	0.00213111i
$267$	8.65657	−	14.9936i	0.529774	−	0.917595i
$268$	−9.88326	+	3.59721i	−0.603716	+	0.219735i
$269$	12.7331	+	22.0543i	0.776349	+	1.34468i	0.934033	+	0.357187i	$0.116264\pi$
$269$	12.7331	+	22.0543i	0.776349	+	1.34468i	−0.157683	+	0.987490i	$0.550403\pi$
$270$	0.680045	−	1.17787i	0.0413862	−	0.0716830i
$271$	−3.74123	+	21.2176i	−0.227264	+	1.28888i	0.631047	+	0.775745i	$0.282626\pi$
$271$	−3.74123	+	21.2176i	−0.227264	+	1.28888i	−0.858310	+	0.513131i	$0.828486\pi$
$272$	15.1579	+	5.51703i	0.919084	+	0.334519i
$273$	−0.673648	−	1.16679i	−0.0407710	−	0.0706175i
$274$	−5.16044	−	4.33013i	−0.311754	−	0.261593i
$275$	−10.7135	−	8.98968i	−0.646047	−	0.542098i
$276$	−12.8760	+	4.68647i	−0.775043	+	0.282093i
$277$	1.59745	+	9.05958i	0.0959814	+	0.544338i	0.994442	+	0.105284i	$0.0335751\pi$
$277$	1.59745	+	9.05958i	0.0959814	+	0.544338i	−0.898461	+	0.439054i	$0.855314\pi$
$278$	−0.990505	−	5.61743i	−0.0594065	−	0.336911i
$279$	−5.43242	+	1.97724i	−0.325230	+	0.118374i
$280$	0.467911	+	0.392624i	0.0279630	+	0.0234638i
$281$	−9.10607	−	7.64090i	−0.543222	−	0.455818i	0.329416	−	0.944185i	$-0.393148\pi$
$281$	−9.10607	−	7.64090i	−0.543222	−	0.455818i	−0.872638	+	0.488367i	$0.837593\pi$
$282$	2.50387	+	4.33683i	0.149103	+	0.258255i
$283$	20.4281	+	7.43523i	1.21433	+	0.441979i	0.868203	−	0.496210i	$-0.165275\pi$
$283$	20.4281	+	7.43523i	1.21433	+	0.441979i	0.346124	+	0.938189i	$0.387498\pi$
$284$	2.67840	−	15.1899i	0.158934	−	0.901357i
$285$	−6.14290	+	10.6398i	−0.363874	+	0.630249i
$286$	−1.17365	−	2.03282i	−0.0693993	−	0.120203i
$287$	0.134285	−	0.0488759i	0.00792661	−	0.00288505i
$288$	6.54576	−	11.3376i	0.385713	−	0.668074i
$289$	5.38254	−	4.51649i	0.316620	−	0.265676i
$290$	1.62031			0.0951479
$291$	3.39646	−	2.84997i	0.199104	−	0.167068i
$292$	−10.3576	−	3.76984i	−0.606131	−	0.220613i
$293$	1.80272	+	10.2237i	0.105316	+	0.597277i	0.991094	+	0.133167i	$0.0425146\pi$
$293$	1.80272	+	10.2237i	0.105316	+	0.597277i	−0.885778	+	0.464110i	$0.846374\pi$
$294$	−1.06670	+	6.04958i	−0.0622114	+	0.352819i
$295$	22.2567			1.29584
$296$	−3.74170	−	7.29125i	−0.217482	−	0.423796i
$297$	1.59627			0.0926248
$298$	−0.629700	+	3.57120i	−0.0364775	+	0.206874i
$299$	2.20574	+	12.5094i	0.127561	+	0.723435i
$300$	−40.8200	−	14.8573i	−2.35674	−	0.857785i
$301$	−0.647489	+	0.543308i	−0.0373207	+	0.0313157i
$302$	6.66456			0.383503
$303$	1.39053	−	1.16679i	0.0798838	−	0.0670305i
$304$	−2.12402	+	3.67891i	−0.121821	+	0.211000i
$305$	27.1266	−	9.87328i	1.55326	−	0.565342i
$306$	−2.90373	−	5.02941i	−0.165995	−	0.287512i
$307$	7.79473	−	13.5009i	0.444869	−	0.770535i	−0.553174	−	0.833066i	$-0.686584\pi$
$307$	7.79473	−	13.5009i	0.444869	−	0.770535i	0.998043	+	0.0625303i	$0.0199170\pi$
$308$	−0.0603074	+	0.342020i	−0.00343633	+	0.0194884i
$309$	0.205737	+	0.0748822i	0.0117040	+	0.00425990i
$310$	−1.10607	−	1.91576i	−0.0628204	−	0.108808i
$311$	−16.1047	−	13.5135i	−0.913215	−	0.766278i	0.0595129	−	0.998228i	$-0.481045\pi$
$311$	−16.1047	−	13.5135i	−0.913215	−	0.766278i	−0.972728	+	0.231949i	$0.925490\pi$
$312$	−11.5287	−	9.67372i	−0.652683	−	0.547666i
$313$	−0.178396	+	0.0649308i	−0.0100835	+	0.00367011i	−0.347057	−	0.937844i	$-0.612819\pi$
$313$	−0.178396	+	0.0649308i	−0.0100835	+	0.00367011i	0.336973	+	0.941514i	$0.390597\pi$
$314$	−0.132636	−	0.752219i	−0.00748511	−	0.0424502i
$315$	0.268571	+	1.52314i	0.0151322	+	0.0858192i
$316$	22.9466	−	8.35186i	1.29084	−	0.469829i
$317$	3.15064	+	2.64370i	0.176958	+	0.148485i	0.726965	−	0.686675i	$-0.240930\pi$
$317$	3.15064	+	2.64370i	0.176958	+	0.148485i	−0.550007	+	0.835160i	$0.685375\pi$
$318$	3.45471	+	2.89884i	0.193730	+	0.162559i
$319$	0.950837	+	1.64690i	0.0532367	+	0.0922086i
$320$	−18.5398	−	6.74795i	−1.03641	−	0.377222i
$321$	−7.06670	+	40.0773i	−0.394425	+	2.23690i
$322$	−0.0603074	+	0.104455i	−0.00336080	+	0.00582107i
$323$	3.16369	+	5.47966i	0.176032	+	0.304897i
$324$	−13.4153	+	4.88279i	−0.745297	+	0.271266i
$325$	−20.1348	+	34.8744i	−1.11688	+	1.93448i
$326$	−0.956052	+	0.802222i	−0.0529508	+	0.0444310i
$327$	−42.3979			−2.34461
$328$	1.22281	−	1.02606i	0.0675185	−	0.0566547i
$329$	−0.645430	−	0.234917i	−0.0355837	−	0.0129514i
$330$	0.879385	+	4.98724i	0.0484086	+	0.274539i
$331$	−1.64455	+	9.32672i	−0.0903928	+	0.512643i	0.905669	+	0.423985i	$0.139369\pi$
$331$	−1.64455	+	9.32672i	−0.0903928	+	0.512643i	−0.996062	+	0.0886582i	$0.971742\pi$
$332$	24.4047			1.33938
$333$	4.60947	−	20.2328i	0.252597	−	1.10875i
$334$	−6.91178			−0.378196
$335$	3.65270	−	20.7155i	0.199569	−	1.13181i
$336$	0.174526	+	0.989783i	0.00952115	+	0.0539971i
$337$	−16.1275	−	5.86992i	−0.878520	−	0.319755i	−0.136907	−	0.990584i	$-0.543716\pi$
$337$	−16.1275	−	5.86992i	−0.878520	−	0.319755i	−0.741612	+	0.670829i	$0.765939\pi$
$338$	−1.71894	+	1.44236i	−0.0934981	+	0.0784542i
$339$	0.822948			0.0446964
$340$	−26.5253	+	22.2574i	−1.43854	+	1.20707i
$341$	1.29813	−	2.24843i	0.0702979	−	0.121759i
$342$	1.43717	−	0.523086i	0.0777131	−	0.0282852i
$343$	−0.843426	−	1.46086i	−0.0455407	−	0.0788788i
$344$	−4.72075	+	8.17658i	−0.254526	+	0.440852i
$345$	4.75877	−	26.9883i	0.256204	−	1.45300i
$346$	2.21466	+	0.806070i	0.119061	+	0.0433346i
$347$	9.56805	+	16.5723i	0.513640	+	0.889650i	0.999875	+	0.0158221i	$0.00503654\pi$
$347$	9.56805	+	16.5723i	0.513640	+	0.889650i	−0.486235	+	0.873828i	$0.661630\pi$
$348$	4.52481	+	3.79677i	0.242556	+	0.203528i
$349$	−1.10354	−	0.925981i	−0.0590712	−	0.0495666i	0.612774	−	0.790258i	$-0.290054\pi$
$349$	−1.10354	−	0.925981i	−0.0590712	−	0.0495666i	−0.671845	+	0.740692i	$0.734498\pi$
$350$	−0.359318	+	0.130781i	−0.0192064	+	0.00699054i
$351$	−0.798133	−	4.52644i	−0.0426012	−	0.241603i
$352$	1.02094	+	5.79006i	0.0544165	+	0.308611i
$353$	−20.4650	+	7.44864i	−1.08924	+	0.396451i	−0.823340	−	0.567549i	$-0.807892\pi$
$353$	−20.4650	+	7.44864i	−1.08924	+	0.396451i	−0.265901	+	0.964000i	$0.585669\pi$
$354$	−3.98886	−	3.34705i	−0.212005	−	0.177894i
$355$	23.6313	+	19.8291i	1.25422	+	1.05242i
$356$	6.42514	+	11.1287i	0.340532	+	0.589819i
$357$	1.40673	+	0.512007i	0.0744519	+	0.0270983i
$358$	0.605189	−	3.43220i	0.0319853	−	0.181397i
$359$	15.2490	−	26.4120i	0.804810	−	1.39397i	−0.111609	−	0.993752i	$-0.535601\pi$
$359$	15.2490	−	26.4120i	0.804810	−	1.39397i	0.916419	−	0.400219i	$-0.131066\pi$
$360$	8.63816	+	14.9617i	0.455271	+	0.788552i
$361$	16.2883	−	5.92847i	0.857281	−	0.312025i
$362$	−4.21554	+	7.30152i	−0.221564	+	0.383760i
$363$	16.7836	−	14.0831i	0.880910	−	0.739171i
$364$	1.00000			0.0524142
$365$	16.8871	−	14.1700i	0.883913	−	0.741691i
$366$	−6.34642	−	2.30991i	−0.331733	−	0.120741i
$367$	−3.86690	−	21.9303i	−0.201850	−	1.14475i	−0.902320	−	0.431068i	$-0.858137\pi$
$367$	−3.86690	−	21.9303i	−0.201850	−	1.14475i	0.700469	−	0.713683i	$-0.252974\pi$
$368$	1.64543	−	9.33170i	0.0857740	−	0.486448i
$369$	4.04189			0.210412
$370$	7.93077	+	0.392624i	0.412301	+	0.0204116i
$371$	−0.618555			−0.0321138
$372$	1.40033	−	7.94166i	0.0726037	−	0.411756i
$373$	−0.862311	−	4.89041i	−0.0446488	−	0.253216i	0.954311	−	0.298815i	$-0.0965914\pi$
$373$	−0.862311	−	4.89041i	−0.0446488	−	0.253216i	−0.998960	+	0.0455993i	$0.985480\pi$
$374$	2.45084	+	0.892032i	0.126730	+	0.0461259i
$375$	30.0993	−	25.2563i	1.55432	−	1.30423i
$376$	−7.67230			−0.395669
$377$	4.19459	−	3.51968i	0.216033	−	0.181273i
$378$	0.0218219	−	0.0377966i	0.00112240	−	0.00194405i
$379$	−3.52956	+	1.28466i	−0.181301	+	0.0659883i	−0.431076	−	0.902316i	$-0.641866\pi$
$379$	−3.52956	+	1.28466i	−0.181301	+	0.0659883i	0.249774	+	0.968304i	$0.419644\pi$
$380$	−4.55943	−	7.89716i	−0.233894	−	0.405116i
$381$	−19.8084	+	34.3092i	−1.01482	+	1.75771i
$382$	0.743345	−	4.21572i	0.0380328	−	0.215695i
$383$	−15.2481	−	5.54985i	−0.779141	−	0.283584i	−0.0783267	−	0.996928i	$-0.524958\pi$
$383$	−15.2481	−	5.54985i	−0.779141	−	0.283584i	−0.700815	+	0.713344i	$0.747180\pi$
$384$	12.0248	+	20.8276i	0.613639	+	1.06285i
$385$	−0.532089	−	0.446476i	−0.0271178	−	0.0227545i
$386$	0.389185	+	0.326565i	0.0198090	+	0.0166217i
$387$	−22.4650	+	8.17658i	−1.14196	+	0.415639i
$388$	0.571452	+	3.24086i	0.0290111	+	0.164530i
$389$	3.60354	+	20.4367i	0.182707	+	1.03618i	0.928867	+	0.370415i	$0.120784\pi$
$389$	3.60354	+	20.4367i	0.182707	+	1.03618i	−0.746160	+	0.665767i	$0.768105\pi$
$390$	13.7023	−	4.98724i	0.693845	−	0.252539i
$391$	−10.8118	−	9.07218i	−0.546776	−	0.458800i
$392$	−7.20961	−	6.04958i	−0.364140	−	0.305550i
$393$	−6.48293	−	11.2288i	−0.327020	−	0.566416i
$394$	2.39141	+	0.870401i	0.120477	+	0.0438502i
$395$	−8.48070	+	48.0965i	−0.426711	+	2.42000i
$396$	−4.91147	+	8.50692i	−0.246811	+	0.427489i
$397$	−12.1163	−	20.9861i	−0.608101	−	1.05326i	−0.991553	−	0.129702i	$-0.958598\pi$
$397$	−12.1163	−	20.9861i	−0.608101	−	1.05326i	0.383452	−	0.923561i	$-0.374735\pi$
$398$	−1.49912	+	0.545636i	−0.0751442	+	0.0273503i
$399$	−0.197119	+	0.341420i	−0.00986829	+	0.0170924i
$400$	23.0121	−	19.3094i	1.15060	−	0.965471i
$401$	29.3259			1.46447			0.732234	−	0.681053i	$-0.238478\pi$
$401$	29.3259			1.46447			0.732234	+	0.681053i	$0.238478\pi$
$402$	−3.76991	+	3.16333i	−0.188026	+	0.157773i
$403$	−7.02481	−	2.55682i	−0.349931	−	0.127364i
$404$	0.233956	+	1.32683i	0.0116397	+	0.0660122i
$405$	4.95811	−	28.1188i	0.246371	−	1.39724i
$406$	0.0519939			0.00258042
$407$	4.25490	+	8.29131i	0.210908	+	0.410985i
$408$	16.7219			0.827859
$409$	4.40538	−	24.9842i	0.217832	−	1.23539i	−0.658092	−	0.752938i	$-0.728636\pi$
$409$	4.40538	−	24.9842i	0.217832	−	1.23539i	0.875924	−	0.482450i	$-0.160253\pi$
$410$	0.268571	+	1.52314i	0.0132638	+	0.0752225i
$411$	46.1528	+	16.7982i	2.27655	+	0.828596i
$412$	−0.124485	+	0.104455i	−0.00613294	+	0.00514615i
$413$	0.714193			0.0351431
$414$	−2.61334	+	2.19285i	−0.128439	+	0.107773i
$415$	−24.4047	+	42.2701i	−1.19798	+	2.07496i
$416$	15.9081	−	5.79006i	0.779957	−	0.283881i
$417$	20.7939	+	36.0160i	1.01828	+	1.76371i
$418$	−0.343426	+	0.594831i	−0.0167975	+	0.0290941i
$419$	−5.76130	+	32.6739i	−0.281458	+	1.59623i	0.436213	+	0.899844i	$0.356319\pi$
$419$	−5.76130	+	32.6739i	−0.281458	+	1.59623i	−0.717671	+	0.696383i	$0.754792\pi$
$420$	−2.02734	−	0.737892i	−0.0989241	−	0.0360054i
$421$	−4.58987	−	7.94989i	−0.223697	−	0.387454i	0.732231	−	0.681056i	$-0.238479\pi$
$421$	−4.58987	−	7.94989i	−0.223697	−	0.387454i	−0.955928	+	0.293602i	$0.905146\pi$
$422$	−1.05122	−	0.882080i	−0.0511727	−	0.0429390i
$423$	−14.8819	−	12.4874i	−0.723583	−	0.607158i
$424$	−6.49273	+	2.36316i	−0.315315	+	0.114765i
$425$	−7.76975	−	44.0645i	−0.376888	−	2.13744i
$426$	−1.25325	−	7.10754i	−0.0607202	−	0.344361i
$427$	0.870462	−	0.316822i	0.0421246	−	0.0153321i
$428$	−23.1386	−	19.4156i	−1.11845	−	0.938489i
$429$	13.1099	+	11.0005i	0.632954	+	0.531111i
$430$	−4.57398	−	7.92236i	−0.220577	−	0.382050i
$431$	−37.2743	−	13.5667i	−1.79544	−	0.653486i	−0.998797	−	0.0490322i	$-0.984386\pi$
$431$	−37.2743	−	13.5667i	−1.79544	−	0.653486i	−0.796640	−	0.604454i	$-0.793391\pi$
$432$	−0.595389	+	3.37662i	−0.0286457	+	0.162458i
$433$	−5.60994	+	9.71670i	−0.269596	+	0.466955i	−0.968758	−	0.248009i	$-0.920224\pi$
$433$	−5.60994	+	9.71670i	−0.269596	+	0.466955i	0.699161	+	0.714964i	$0.253557\pi$
$434$	−0.0354925	−	0.0614747i	−0.00170369	−	0.00295088i
$435$	−11.1010	+	4.04044i	−0.532253	+	0.193724i
$436$	15.7344	−	27.2528i	0.753542	−	1.30517i
$437$	2.84730	−	2.38917i	0.136205	−	0.114289i
$438$	−5.15745			−0.246433
$439$	−10.7096	+	8.98643i	−0.511142	+	0.428899i	−0.861531	−	0.507705i	$-0.830494\pi$
$439$	−10.7096	+	8.98643i	−0.511142	+	0.428899i	0.350389	+	0.936604i	$0.386049\pi$
$440$	−7.29086	−	2.65366i	−0.347578	−	0.126508i
$441$	−4.13816	−	23.4686i	−0.197055	−	1.11755i
$442$	1.30406	−	7.39571i	0.0620280	−	0.351778i
$443$	−11.1797			−0.531165			−0.265583	−	0.964088i	$-0.585564\pi$
$443$	−11.1797			−0.531165			−0.265583	+	0.964088i	$0.585564\pi$
$444$	21.2271	+	19.6801i	1.00740	+	0.933976i
$445$	−25.7006			−1.21832
$446$	−0.874638	+	4.96032i	−0.0414153	+	0.234878i
$447$	−4.59105	−	26.0372i	−0.217149	−	1.23151i
$448$	−0.594922	−	0.216534i	−0.0281074	−	0.0102303i
$449$	−17.1898	+	14.4240i	−0.811239	+	0.680710i	−0.950903	−	0.309489i	$-0.899842\pi$
$449$	−17.1898	+	14.4240i	−0.811239	+	0.680710i	0.139664	+	0.990199i	$0.455398\pi$
$450$	−10.8152			−0.509834
$451$	−1.39053	+	1.16679i	−0.0654775	+	0.0549421i
$452$	−0.305407	+	0.528981i	−0.0143652	+	0.0248812i
$453$	−45.6600	+	16.6189i	−2.14530	+	0.780824i
$454$	−0.0923963	−	0.160035i	−0.00433637	−	0.00751082i
$455$	−1.00000	+	1.73205i	−0.0468807	+	0.0811998i
$456$	−0.764700	+	4.33683i	−0.0358104	+	0.203091i
$457$	36.0959	+	13.1378i	1.68849	+	0.614561i	0.994434	−	0.105357i	$-0.0335987\pi$
$457$	36.0959	+	13.1378i	1.68849	+	0.614561i	0.694059	+	0.719919i	$0.255821\pi$
$458$	1.85978	+	3.22124i	0.0869020	+	0.150519i
$459$	3.91219	+	3.28272i	0.182605	+	0.153224i
$460$	15.5817	+	13.0746i	0.726501	+	0.609607i
$461$	−13.6677	+	4.97464i	−0.636569	+	0.231692i	−0.640088	−	0.768302i	$-0.721102\pi$
$461$	−13.6677	+	4.97464i	−0.636569	+	0.231692i	0.00351889	+	0.999994i	$0.498880\pi$
$462$	0.0282185	+	0.160035i	0.00131284	+	0.00744550i
$463$	−1.92602	−	10.9230i	−0.0895098	−	0.507636i	−0.996292	−	0.0860361i	$-0.972580\pi$
$463$	−1.92602	−	10.9230i	−0.0895098	−	0.507636i	0.906782	−	0.421599i	$-0.138531\pi$
$464$	−3.83837	+	1.39705i	−0.178192	+	0.0648566i
$465$	12.3550	+	10.3671i	0.572951	+	0.480763i
$466$	3.13769	+	2.63283i	0.145351	+	0.121964i
$467$	11.7490	+	20.3498i	0.543678	+	0.941677i	0.998689	+	0.0511914i	$0.0163019\pi$
$467$	11.7490	+	20.3498i	0.543678	+	0.941677i	−0.455011	+	0.890486i	$0.650365\pi$
$468$	26.5783	+	9.67372i	1.22858	+	0.447168i
$469$	0.117211	−	0.664738i	0.00541231	−	0.0306947i
$470$	3.71688	−	6.43783i	0.171447	−	0.296955i
$471$	2.78446	+	4.82283i	0.128301	+	0.222224i
$472$	7.49660	−	2.72854i	0.345059	−	0.125591i
$473$	5.36824	−	9.29807i	0.246832	−	0.427526i
$474$	8.75284	−	7.34451i	0.402031	−	0.337344i
$475$	11.7834			0.540661
$476$	−0.851167	+	0.714214i	−0.0390132	+	0.0327359i
$477$	−16.4402	−	5.98373i	−0.752743	−	0.273976i
$478$	−0.220752	−	1.25195i	−0.0100970	−	0.0572627i
$479$	−5.79157	+	32.8457i	−0.264624	+	1.50076i	0.505480	+	0.862838i	$0.331315\pi$
$479$	−5.79157	+	32.8457i	−0.264624	+	1.50076i	−0.770104	+	0.637918i	$0.779796\pi$
$480$	−36.5235			−1.66706
$481$	21.3837	−	16.2110i	0.975014	−	0.739159i
$482$	4.53807			0.206704
$483$	0.152704	−	0.866025i	0.00694826	−	0.0394055i
$484$	2.82383	+	16.0147i	0.128356	+	0.727941i
$485$	−6.18479	−	2.25108i	−0.280837	−	0.102216i
$486$	−5.94878	+	4.99162i	−0.269842	+	0.226424i
$487$	11.2439			0.509511			0.254755	−	0.967006i	$-0.418005\pi$
$487$	11.2439			0.509511			0.254755	+	0.967006i	$0.418005\pi$
$488$	7.92649	−	6.65111i	0.358815	−	0.301082i
$489$	4.54963	−	7.88019i	0.205741	−	0.356355i
$490$	8.56893	−	3.11883i	0.387105	−	0.140895i
$491$	−17.9675	−	31.1206i	−0.810862	−	1.40445i	−0.912261	−	0.409608i	$-0.865665\pi$
$491$	−17.9675	−	31.1206i	−0.810862	−	1.40445i	0.101400	−	0.994846i	$-0.467668\pi$
$492$	−2.81908	+	4.88279i	−0.127094	+	0.220133i
$493$	−1.05649	+	5.99167i	−0.0475821	+	0.269851i
$494$	1.85844	+	0.676417i	0.0836152	+	0.0304334i
$495$	−9.82295	−	17.0138i	−0.441509	−	0.764715i
$496$	4.27197	+	3.58461i	0.191817	+	0.160954i
$497$	0.758304	+	0.636292i	0.0340146	+	0.0285416i
$498$	10.7306	−	3.90560i	0.480848	−	0.175014i
$499$	1.18257	+	6.70669i	0.0529391	+	0.300233i	0.999769	−	0.0215025i	$-0.00684498\pi$
$499$	1.18257	+	6.70669i	0.0529391	+	0.300233i	−0.946830	+	0.321735i	$0.895734\pi$
$500$	5.06418	+	28.7204i	0.226477	+	1.28441i
$501$	47.3537	−	17.2354i	2.11561	−	0.770019i
$502$	7.36303	+	6.17831i	0.328628	+	0.275752i
$503$	−18.7986	−	15.7739i	−0.838188	−	0.703323i	0.118967	−	0.992898i	$-0.462042\pi$
$503$	−18.7986	−	15.7739i	−0.838188	−	0.703323i	−0.957155	+	0.289575i	$0.906486\pi$
$504$	0.277189	+	0.480105i	0.0123470	+	0.0213856i
$505$	−2.53209	−	0.921605i	−0.112676	−	0.0410109i
$506$	0.266044	−	1.50881i	0.0118271	−	0.0670749i
$507$	8.18004	−	14.1683i	0.363289	−	0.629234i
$508$	−14.7023	−	25.4652i	−0.652311	−	1.12984i
$509$	6.36231	−	2.31569i	0.282004	−	0.102641i	−0.197146	−	0.980374i	$-0.563167\pi$
$509$	6.36231	−	2.31569i	0.282004	−	0.102641i	0.479150	+	0.877733i	$0.340945\pi$
$510$	−8.10101	+	14.0314i	−0.358719	+	0.621319i
$511$	0.541889	−	0.454699i	0.0239718	−	0.0201147i
$512$	−21.4962			−0.950006
$513$	−1.03028	+	0.864506i	−0.0454879	+	0.0381689i
$514$	−5.67277	−	2.06472i	−0.250215	−	0.0910709i
$515$	−0.0564370	−	0.320070i	−0.00248691	−	0.0141040i
$516$	5.79086	−	32.8416i	0.254928	−	1.44577i
$517$	8.72462			0.383708
$518$	0.254490	+	0.0125989i	0.0111816	+	0.000553562i
$519$	−17.1830			−0.754252
$520$	−3.87939	+	22.0011i	−0.170122	+	0.964811i
$521$	−0.411474	−	2.33359i	−0.0180270	−	0.102236i	0.974467	−	0.224532i	$-0.0720854\pi$
$521$	−0.411474	−	2.33359i	−0.0180270	−	0.102236i	−0.992494	+	0.122296i	$0.960974\pi$
$522$	1.38191	+	0.502975i	0.0604846	+	0.0220146i
$523$	3.94949	−	3.31402i	0.172699	−	0.144912i	−0.552341	−	0.833618i	$-0.686265\pi$
$523$	3.94949	−	3.31402i	0.172699	−	0.144912i	0.725041	+	0.688706i	$0.241821\pi$
$524$	9.62361			0.420409
$525$	2.13563	−	1.79201i	0.0932065	−	0.0782096i
$526$	−2.42127	+	4.19377i	−0.105573	+	0.182857i
$527$	7.80541	−	2.84094i	0.340009	−	0.123753i
$528$	−6.38326	−	11.0561i	−0.277796	−	0.481156i
$529$	7.35457	−	12.7385i	0.319764	−	0.553847i
$530$	1.16250	−	6.59289i	0.0504959	−	0.286377i
$531$	18.9820	+	6.90890i	0.823751	+	0.299821i
$532$	−0.146307	−	0.253411i	−0.00634321	−	0.0109868i
$533$	4.00387	+	3.35965i	0.173427	+	0.145522i
$534$	4.60607	+	3.86495i	0.199324	+	0.167253i
$535$	56.7674	−	20.6617i	2.45427	−	0.893281i
$536$	−1.30928	−	7.42528i	−0.0565522	−	0.320723i
$537$	4.41235	+	25.0237i	0.190407	+	1.07985i
$538$	−8.31093	+	3.02493i	−0.358309	+	0.130414i
$539$	8.19846	+	6.87933i	0.353133	+	0.296314i
$540$	−5.63816	−	4.73097i	−0.242628	−	0.203589i
$541$	11.5826	+	20.0616i	0.497975	+	0.862517i	0.999997	−	0.00233704i	$-0.000743903\pi$
$541$	11.5826	+	20.0616i	0.497975	+	0.862517i	−0.502023	+	0.864855i	$0.667411\pi$
$542$	−7.03121	−	2.55915i	−0.302016	−	0.109925i
$543$	10.6741	−	60.5359i	0.458070	−	2.59784i
$544$	−9.40508	+	16.2901i	−0.403239	+	0.698431i
$545$	31.4688	+	54.5056i	1.34798	+	2.33477i
$546$	0.439693	−	0.160035i	0.0188171	−	0.00684887i
$547$	−17.9599	+	31.1075i	−0.767911	+	1.33006i	0.170783	+	0.985309i	$0.445370\pi$
$547$	−17.9599	+	31.1075i	−0.767911	+	1.33006i	−0.938694	+	0.344752i	$0.887963\pi$
$548$	−27.9256	+	23.4324i	−1.19292	+	1.00098i
$549$	26.2003			1.11820
$550$	3.72075	−	3.12208i	0.158653	−	0.133126i
$551$	−1.50563	−	0.548003i	−0.0641418	−	0.0233457i
$552$	−1.70574	−	9.67372i	−0.0726010	−	0.411741i
$553$	−0.272136	+	1.54336i	−0.0115724	+	0.0656304i
$554$	−3.19490			−0.135738
$555$	−55.3141	+	17.0864i	−2.34795	+	0.725277i
$556$	−30.8675			−1.30907
$557$	−0.236320	+	1.34024i	−0.0100132	+	0.0567876i	−0.989405	−	0.145182i	$-0.953623\pi$
$557$	−0.236320	+	1.34024i	−0.0100132	+	0.0567876i	0.979392	+	0.201970i	$0.0647343\pi$
$558$	−0.348641	−	1.97724i	−0.0147591	−	0.0837032i
$559$	−29.0501	−	10.5734i	−1.22869	−	0.447206i
$560$	1.14290	−	0.959010i	0.0482965	−	0.0405256i
$561$	−19.0155			−0.802834
$562$	3.16250	−	2.65366i	0.133402	−	0.111938i
$563$	13.3007	−	23.0374i	0.560556	−	0.970911i	−0.436892	−	0.899514i	$-0.643921\pi$
$563$	13.3007	−	23.0374i	0.560556	−	0.970911i	0.997448	−	0.0713974i	$-0.0227459\pi$
$564$	25.4650	−	9.26849i	1.07227	−	0.390274i
$565$	−0.610815	−	1.05796i	−0.0256972	−	0.0445088i
$566$	−3.77497	+	6.53844i	−0.158674	+	0.274831i
$567$	0.159100	−	0.902302i	0.00668158	−	0.0378931i
$568$	10.3905	+	3.78184i	0.435977	+	0.158683i
$569$	3.08466	+	5.34278i	0.129315	+	0.223981i	0.923412	−	0.383811i	$-0.125389\pi$
$569$	3.08466	+	5.34278i	0.129315	+	0.223981i	−0.794096	+	0.607792i	$0.792055\pi$
$570$	−3.26857	−	2.74266i	−0.136905	−	0.114877i
$571$	2.79220	+	2.34294i	0.116850	+	0.0980489i	0.699340	−	0.714789i	$-0.253477\pi$
$571$	2.79220	+	2.34294i	0.116850	+	0.0980489i	−0.582490	+	0.812838i	$0.697922\pi$
$572$	−11.9363	+	4.34445i	−0.499081	+	0.181651i
$573$	5.41963	+	30.7362i	0.226408	+	1.28402i
$574$	0.00861813	+	0.0488759i	0.000359714	+	0.00204004i
$575$	−24.6989	+	8.98968i	−1.03002	+	0.374895i
$576$	−13.7173	−	11.5102i	−0.571556	−	0.479593i
$577$	−22.4447	−	18.8334i	−0.934387	−	0.784044i	0.0422128	−	0.999109i	$-0.486559\pi$
$577$	−22.4447	−	18.8334i	−0.934387	−	0.784044i	−0.976600	+	0.215065i	$0.931004\pi$
$578$	1.22012	+	2.11331i	0.0507504	+	0.0879023i
$579$	−3.48070	−	1.26687i	−0.144653	−	0.0526494i
$580$	1.52259	−	8.63506i	0.0632223	−	0.358551i
$581$	−0.783119	+	1.35640i	−0.0324892	+	0.0562730i
$582$	0.769915	+	1.33353i	0.0319140	+	0.0552767i
$583$	7.38326	−	2.68729i	0.305783	−	0.111296i
$584$	3.95084	−	6.84305i	0.163487	−	0.283167i
$585$	−43.3337	+	36.3613i	−1.79163	+	1.50335i
$586$	−3.60544			−0.148939
$587$	13.7947	−	11.5752i	0.569369	−	0.477758i	−0.312067	−	0.950060i	$-0.601021\pi$
$587$	13.7947	−	11.5752i	0.569369	−	0.477758i	0.881437	+	0.472302i	$0.156577\pi$
$588$	31.2374	+	11.3695i	1.28821	+	0.468870i
$589$	0.379852	+	2.15425i	0.0156515	+	0.0887642i
$590$	−1.34224	+	7.61224i	−0.0552593	+	0.313391i
$591$	−18.5544			−0.763225
$592$	−19.1258	+	5.90793i	−0.786067	+	0.242814i
$593$	10.9118			0.448093			0.224047	−	0.974578i	$-0.428073\pi$
$593$	10.9118			0.448093			0.224047	+	0.974578i	$0.428073\pi$
$594$	−0.0962667	+	0.545955i	−0.00394987	+	0.0224008i
$595$	−0.385888	−	2.18848i	−0.0158199	−	0.0897188i
$596$	18.4402	+	6.71167i	0.755338	+	0.274921i
$597$	8.91013	−	7.47649i	0.364667	−	0.305992i
$598$	−4.41147			−0.180399
$599$	7.91921	−	6.64501i	0.323570	−	0.271508i	−0.466504	−	0.884519i	$-0.654487\pi$
$599$	7.91921	−	6.64501i	0.323570	−	0.271508i	0.790074	+	0.613012i	$0.210042\pi$
$600$	15.5706	−	26.9690i	0.635666	−	1.10101i
$601$	−25.8662	+	9.41452i	−1.05510	+	0.384026i	−0.810587	−	0.585619i	$-0.800852\pi$
$601$	−25.8662	+	9.41452i	−1.05510	+	0.384026i	−0.244517	+	0.969645i	$0.578629\pi$
$602$	−0.146774	−	0.254220i	−0.00598206	−	0.0103612i
$603$	9.54576	−	16.5337i	0.388733	−	0.673306i
$604$	6.26264	−	35.5172i	0.254823	−	1.44517i
$605$	−30.5621	−	11.1237i	−1.24253	−	0.452243i
$606$	0.315207	+	0.545955i	0.0128044	+	0.0221779i
$607$	17.0719	+	14.3250i	0.692928	+	0.581435i	0.919752	−	0.392500i	$-0.128390\pi$
$607$	17.0719	+	14.3250i	0.692928	+	0.581435i	−0.226824	+	0.973936i	$0.572834\pi$
$608$	−3.79473	−	3.18416i	−0.153897	−	0.129135i
$609$	−0.356219	+	0.129653i	−0.0144347	+	0.00525381i
$610$	1.74092	+	9.87328i	0.0704880	+	0.399757i
$611$	−4.36231	−	24.7399i	−0.176480	−	1.00087i
$612$	−29.5317	+	10.7487i	−1.19375	+	0.434489i
$613$	30.3430	+	25.4608i	1.22554	+	1.02835i	0.998516	+	0.0544641i	$0.0173450\pi$
$613$	30.3430	+	25.4608i	1.22554	+	1.02835i	0.227027	+	0.973888i	$0.427099\pi$
$614$	4.14749	+	3.48016i	0.167379	+	0.140448i
$615$	−5.63816	−	9.76557i	−0.227352	−	0.393786i
$616$	−0.233956	−	0.0851529i	−0.00942634	−	0.00343091i
$617$	5.69846	−	32.3176i	0.229411	−	1.30106i	−0.624658	−	0.780898i	$-0.714762\pi$
$617$	5.69846	−	32.3176i	0.229411	−	1.30106i	0.854070	−	0.520159i	$-0.174127\pi$
$618$	−0.0380187	+	0.0658503i	−0.00152934	+	0.00264889i
$619$	−10.5371	−	18.2509i	−0.423523	−	0.733564i	0.572758	−	0.819725i	$-0.305874\pi$
$619$	−10.5371	−	18.2509i	−0.423523	−	0.733564i	−0.996281	+	0.0861605i	$0.972540\pi$
$620$	−11.2490	+	4.09429i	−0.451770	+	0.164431i
$621$	1.50000	−	2.59808i	0.0601929	−	0.104257i
$622$	5.59311	−	4.69318i	0.224263	−	0.188179i
$623$	−0.824703			−0.0330410
$624$	−28.1596	+	23.6287i	−1.12728	+	0.945904i
$625$	−11.9201	−	4.33856i	−0.476804	−	0.173542i
$626$	−0.0114491	−	0.0649308i	−0.000457596	−	0.00259516i
$627$	0.869585	−	4.93166i	0.0347279	−	0.196952i
$628$	−4.13341			−0.164941
$629$	−6.62298	+	29.0708i	−0.264075	+	1.15913i
$630$	−0.537141			−0.0214002
$631$	−5.51320	+	31.2669i	−0.219477	+	1.24472i	0.653489	+	0.756936i	$0.273305\pi$
$631$	−5.51320	+	31.2669i	−0.219477	+	1.24472i	−0.872966	+	0.487781i	$0.837807\pi$
$632$	3.03983	+	17.2397i	0.120918	+	0.685760i
$633$	9.40167	+	3.42193i	0.373683	+	0.136009i
$634$	−1.09421	+	0.918149i	−0.0434565	+	0.0364644i
$635$	58.8093			2.33378
$636$	18.6951	−	15.6870i	0.741307	−	0.622031i
$637$	15.4081	−	26.6876i	0.610490	−	1.05740i
$638$	−0.620615	+	0.225885i	−0.0245704	+	0.00894288i
$639$	13.9991	+	24.2472i	0.553797	+	0.959204i
$640$	17.8503	−	30.9176i	0.705595	−	1.22213i
$641$	−4.18913	+	23.7577i	−0.165461	+	0.938374i	0.783128	+	0.621861i	$0.213623\pi$
$641$	−4.18913	+	23.7577i	−0.165461	+	0.938374i	−0.948588	+	0.316513i	$0.897488\pi$
$642$	−13.2811	−	4.83391i	−0.524162	−	0.190779i
$643$	−20.5410	−	35.5781i	−0.810058	−	1.40306i	−0.912822	−	0.408357i	$-0.866102\pi$
$643$	−20.5410	−	35.5781i	−0.810058	−	1.40306i	0.102764	−	0.994706i	$-0.467231\pi$
$644$	0.500000	+	0.419550i	0.0197028	+	0.0165326i
$645$	51.0925	+	42.8717i	2.01176	+	1.68807i
$646$	−2.06495	+	0.751580i	−0.0812443	+	0.0295705i
$647$	−3.48902	−	19.7872i	−0.137167	−	0.777915i	−0.973326	−	0.229427i	$-0.926315\pi$
$647$	−3.48902	−	19.7872i	−0.137167	−	0.777915i	0.836158	−	0.548488i	$-0.184796\pi$
$648$	−1.77719	−	10.0789i	−0.0698146	−	0.395938i
$649$	−8.52481	+	3.10278i	−0.334628	+	0.121795i
$650$	−10.7135	−	8.98968i	−0.420217	−	0.352604i
$651$	0.396459	+	0.332669i	0.0155385	+	0.0130383i
$652$	3.37686	+	5.84889i	0.132248	+	0.229060i
$653$	25.7986	+	9.38992i	1.00958	+	0.367456i	0.793270	−	0.608869i	$-0.208377\pi$
$653$	25.7986	+	9.38992i	1.00958	+	0.367456i	0.216307	+	0.976325i	$0.430599\pi$
$654$	2.55690	−	14.5009i	0.0999829	−	0.567031i
$655$	−9.62361	+	16.6686i	−0.376025	+	0.651295i
$656$	−1.94949	−	3.37662i	−0.0761149	−	0.131835i
$657$	18.8011	−	6.84305i	0.733502	−	0.266973i
$658$	0.119271	−	0.206583i	0.00464965	−	0.00805343i
$659$	−15.2854	+	12.8260i	−0.595435	+	0.499629i	−0.889975	−	0.456010i	$-0.849278\pi$
$659$	−15.2854	+	12.8260i	−0.595435	+	0.499629i	0.294540	+	0.955639i	$0.404834\pi$
$660$	27.4047			1.06673
$661$	−17.8648	+	14.9904i	−0.694862	+	0.583058i	−0.920307	−	0.391198i	$-0.872061\pi$
$661$	−17.8648	+	14.9904i	−0.694862	+	0.583058i	0.225445	+	0.974256i	$0.427616\pi$
$662$	−3.09075	−	1.12494i	−0.120125	−	0.0437220i
$663$	9.50774	+	53.9211i	0.369250	+	2.09412i
$664$	−3.03802	+	17.2295i	−0.117898	+	0.668633i
$665$	0.585228			0.0226942
$666$	6.64203	+	2.79672i	0.257373	+	0.108371i
$667$	3.57398			0.138385
$668$	−6.49495	+	36.8347i	−0.251297	+	1.42518i
$669$	−6.37686	−	36.1650i	−0.246544	−	1.39822i
$670$	6.86484	+	2.49860i	0.265212	+	0.0965292i
$671$	−9.01367	+	7.56337i	−0.347969	+	0.291981i
$672$	−1.17200			−0.0452109
$673$	13.7658	−	11.5509i	0.530632	−	0.445253i	−0.337687	−	0.941258i	$-0.609645\pi$
$673$	13.7658	−	11.5509i	0.530632	−	0.445253i	0.868320	+	0.496005i	$0.165200\pi$
$674$	2.98024	−	5.16192i	0.114794	−	0.198830i
$675$	8.93717	−	3.25286i	0.343992	−	0.125203i
$676$	6.07145	+	10.5161i	0.233517	+	0.404464i
$677$	12.4606	−	21.5825i	0.478901	−	0.829481i	−0.520806	−	0.853675i	$-0.674369\pi$
$677$	12.4606	−	21.5825i	0.478901	−	0.829481i	0.999707	+	0.0241938i	$0.00770188\pi$
$678$	−0.0496299	+	0.281465i	−0.00190602	+	0.0108096i
$679$	−0.198463	−	0.0722347i	−0.00761631	−	0.00277211i
$680$	−12.4115	−	21.4973i	−0.475958	−	0.824384i
$681$	1.03209	+	0.866025i	0.0395497	+	0.0331862i
$682$	0.690722	+	0.579585i	0.0264491	+	0.0221935i
$683$	19.9979	−	7.27866i	0.765200	−	0.278510i	0.0702127	−	0.997532i	$-0.477632\pi$
$683$	19.9979	−	7.27866i	0.765200	−	0.278510i	0.694987	+	0.719022i	$0.255410\pi$
$684$	−1.43717	−	8.15058i	−0.0549514	−	0.311645i
$685$	−12.6604	−	71.8009i	−0.483731	−	2.74337i
$686$	0.550507	−	0.200368i	0.0210185	−	0.00765009i
$687$	−20.7743	−	17.4317i	−0.792587	−	0.665060i
$688$	17.6661	+	14.8236i	0.673515	+	0.565146i
$689$	−11.3118	−	19.5926i	−0.430945	−	0.746419i
$690$	8.94356	+	3.25519i	0.340476	+	0.123923i
$691$	−5.19553	+	29.4653i	−0.197647	+	1.12091i	0.710951	+	0.703241i	$0.248265\pi$
$691$	−5.19553	+	29.4653i	−0.197647	+	1.12091i	−0.908598	+	0.417671i	$0.862846\pi$
$692$	6.37686	−	11.0450i	0.242412	−	0.419870i
$693$	−0.315207	−	0.545955i	−0.0119737	−	0.0207391i
$694$	−6.24510	+	2.27303i	−0.237061	+	0.0862831i
$695$	30.8675	−	53.4641i	1.17087	−	2.02801i
$696$	−3.24376	+	2.72183i	−0.122954	+	0.103171i
$697$	−5.80747			−0.219973
$698$	0.383256	−	0.321590i	0.0145064	−	0.0121723i
$699$	−28.0621	−	10.2138i	−1.06141	−	0.386320i
$700$	0.359318	+	2.03779i	0.0135809	+	0.0770214i
$701$	4.38650	−	24.8771i	0.165676	−	0.939594i	−0.782689	−	0.622413i	$-0.786153\pi$
$701$	4.38650	−	24.8771i	0.165676	−	0.939594i	0.948365	−	0.317181i	$-0.102736\pi$
$702$	1.59627			0.0602472
$703$	−7.23664	−	3.04709i	−0.272935	−	0.114923i
$704$	8.04189			0.303090
$705$	−9.41147	+	53.3751i	−0.354457	+	2.01022i
$706$	−1.31340	−	7.44864i	−0.0494303	−	0.280333i
$707$	−0.0812519	−	0.0295733i	−0.00305579	−	0.00111222i
$708$	−21.5856	+	18.1125i	−0.811236	+	0.680708i
$709$	−18.5270			−0.695797			−0.347899	−	0.937532i	$-0.613105\pi$
$709$	−18.5270			−0.695797			−0.347899	+	0.937532i	$0.613105\pi$
$710$	−8.20708	+	6.88656i	−0.308006	+	0.258448i
$711$	−22.1630	+	38.3874i	−0.831176	+	1.43964i
$712$	−8.65657	+	3.15074i	−0.324419	+	0.118079i
$713$	−2.43969	−	4.22567i	−0.0913672	−	0.158253i
$714$	−0.259953	+	0.450251i	−0.00972848	+	0.0168502i
$715$	4.41147	−	25.0187i	0.164980	−	0.935647i
$716$	−17.7224	−	6.45043i	−0.662317	−	0.241064i
$717$	4.63429	+	8.02682i	0.173071	+	0.299767i
$718$	8.11381	+	6.80829i	0.302805	+	0.254083i
$719$	−30.9741	−	25.9903i	−1.15514	−	0.969275i	−0.155310	−	0.987866i	$-0.549638\pi$
$719$	−30.9741	−	25.9903i	−1.15514	−	0.969275i	−0.999827	+	0.0185903i	$0.994082\pi$
$720$	39.6536	−	14.4327i	1.47780	−	0.537877i
$721$	−0.00181100	−	0.0102707i	−6.74452e−5	−	0.000382501i
$722$	1.04535	+	5.92847i	0.0389039	+	0.220635i
$723$	−31.0911	+	11.3162i	−1.15629	+	0.420855i
$724$	34.9504	+	29.3269i	1.29892	+	1.08993i
$725$	8.67958	+	7.28303i	0.322351	+	0.270485i
$726$	3.80453	+	6.58964i	0.141199	+	0.244564i
$727$	20.9449	+	7.62332i	0.776804	+	0.282733i	0.699839	−	0.714300i	$-0.253255\pi$
$727$	20.9449	+	7.62332i	0.776804	+	0.282733i	0.0769644	+	0.997034i	$0.475477\pi$
$728$	−0.124485	+	0.705990i	−0.00461373	+	0.0261657i
$729$	16.9145	−	29.2967i	0.626462	−	1.08506i
$730$	3.82800	+	6.63029i	0.141681	+	0.245398i
$731$	32.2781	−	11.7483i	1.19385	−	0.434526i
$732$	−18.2738	+	31.6511i	−0.675419	+	1.16986i
$733$	−7.81908	+	6.56099i	−0.288804	+	0.242336i	−0.775666	−	0.631143i	$-0.782586\pi$
$733$	−7.81908	+	6.56099i	−0.288804	+	0.242336i	0.486862	+	0.873479i	$0.338141\pi$
$734$	7.73379			0.285460
$735$	−50.9299	+	42.7353i	−1.87858	+	1.57632i
$736$	10.3833	+	3.77920i	0.382732	+	0.139303i
$737$	1.48886	+	8.44372i	0.0548427	+	0.311028i
$738$	−0.243756	+	1.38241i	−0.00897277	+	0.0508871i
$739$	−17.7074			−0.651377			−0.325688	−	0.945477i	$-0.605596\pi$
$739$	−17.7074			−0.651377			−0.325688	+	0.945477i	$0.605596\pi$
$740$	9.54488	−	41.8962i	0.350877	−	1.54014i
$741$	−14.4192			−0.529703
$742$	0.0373035	−	0.211558i	0.00136945	−	0.00776655i
$743$	0.194755	+	1.10451i	0.00714486	+	0.0405205i	0.988172	−	0.153351i	$-0.0490066\pi$
$743$	0.194755	+	1.10451i	0.00714486	+	0.0405205i	−0.981027	+	0.193872i	$0.937895\pi$
$744$	5.43242	+	1.97724i	0.199162	+	0.0724891i
$745$	−30.0651	+	25.2276i	−1.10150	+	0.924269i
$746$	1.72462			0.0631429
$747$	−33.9354	+	28.4752i	−1.24163	+	1.04185i
$748$	7.05690	−	12.2229i	0.258026	−	0.446914i
$749$	1.82160	−	0.663010i	0.0665600	−	0.0242258i
$750$	6.82295	+	11.8177i	0.249139	+	0.431521i
$751$	−11.7417	+	20.3372i	−0.428461	+	0.742116i	−0.996737	−	0.0807225i	$-0.974277\pi$
$751$	−11.7417	+	20.3372i	−0.428461	+	0.742116i	0.568276	+	0.822838i	$0.307611\pi$
$752$	−3.25418	+	18.4554i	−0.118668	+	0.672999i
$753$	−65.8517	−	23.9681i	−2.39977	−	0.873444i
$754$	0.950837	+	1.64690i	0.0346274	+	0.0599765i
$755$	55.2550	+	46.3644i	2.01093	+	1.68737i
$756$	−0.180922	−	0.151812i	−0.00658007	−	0.00552134i
$757$	−28.8371	+	10.4958i	−1.04810	+	0.381478i	−0.807946	−	0.589257i	$-0.799421\pi$
$757$	−28.8371	+	10.4958i	−1.04810	+	0.381478i	−0.240156	+	0.970734i	$0.577199\pi$
$758$	−0.226519	−	1.28466i	−0.00822756	−	0.0466608i
$759$	1.93969	+	11.0005i	0.0704064	+	0.399294i
$760$	6.14290	−	2.23583i	0.222827	−	0.0811022i
$761$	−20.0364	−	16.8126i	−0.726320	−	0.609455i	0.202806	−	0.979219i	$-0.434994\pi$
$761$	−20.0364	−	16.8126i	−0.726320	−	0.609455i	−0.929126	+	0.369764i	$0.879438\pi$
$762$	−10.5398	−	8.84397i	−0.381818	−	0.320383i
$763$	1.00980	+	1.74903i	0.0365572	+	0.0633190i
$764$	−21.7682	−	7.92296i	−0.787544	−	0.286643i
$765$	10.9145	−	61.8990i	0.394613	−	2.23796i
$766$	2.81773	−	4.88046i	0.101809	−	0.176338i
$767$	13.0608	+	22.6219i	0.471597	+	0.816830i
$768$	17.1300	−	6.23481i	0.618126	−	0.224979i
$769$	5.82635	−	10.0915i	0.210104	−	0.363910i	−0.741643	−	0.670795i	$-0.765953\pi$
$769$	5.82635	−	10.0915i	0.210104	−	0.363910i	0.951747	+	0.306884i	$0.0992865\pi$
$770$	0.184793	−	0.155059i	0.00665946	−	0.00558795i
$771$	44.0137			1.58512
$772$	2.10607	−	1.76720i	0.0757990	−	0.0636029i
$773$	1.24985	+	0.454907i	0.0449539	+	0.0163619i	0.364399	−	0.931243i	$-0.381274\pi$
$773$	1.24985	+	0.454907i	0.0449539	+	0.0163619i	−0.319445	+	0.947605i	$0.603497\pi$
$774$	−1.44175	−	8.17658i	−0.0518227	−	0.293901i
$775$	2.68614	−	15.2338i	0.0964889	−	0.547216i
$776$	−2.35916			−0.0846888
$777$	−1.77497	+	0.548284i	−0.0636766	+	0.0196696i
$778$	−7.20708			−0.258386
$779$	0.265578	−	1.50617i	0.00951531	−	0.0539640i
$780$	−13.7023	−	77.7098i	−0.490622	−	2.78246i
$781$	−11.8157	−	4.30055i	−0.422798	−	0.153886i
$782$	3.75490	−	3.15074i	0.134275	−	0.112670i
$783$	−1.29322			−0.0462160
$784$	−17.6099	+	14.7765i	−0.628926	+	0.527732i
$785$	4.13341	−	7.15927i	0.147528	−	0.255525i
$786$	4.23143	−	1.54011i	0.150930	−	0.0549341i
$787$	−6.92767	−	11.9991i	−0.246945	−	0.427721i	0.715732	−	0.698375i	$-0.246093\pi$
$787$	−6.92767	−	11.9991i	−0.246945	−	0.427721i	−0.962677	+	0.270654i	$0.912760\pi$
$788$	6.88578	−	11.9265i	0.245296	−	0.424865i
$789$	6.13088	−	34.7700i	0.218265	−	1.23784i
$790$	−15.9385	−	5.80114i	−0.567067	−	0.206395i
$791$	−0.0196004	−	0.0339488i	−0.000696909	−	0.00120708i
$792$	−5.39440	−	4.52644i	−0.191682	−	0.160840i
$793$	25.9538	+	21.7778i	0.921648	+	0.773354i
$794$	7.90838	−	2.87841i	0.280658	−	0.102151i
$795$	8.47565	+	48.0678i	0.300600	+	1.70479i
$796$	1.49912	+	8.50195i	0.0531350	+	0.301344i
$797$	−13.5005	+	4.91377i	−0.478211	+	0.174055i	−0.569868	−	0.821736i	$-0.693006\pi$
$797$	−13.5005	+	4.91377i	−0.478211	+	0.174055i	0.0916573	+	0.995791i	$0.470784\pi$
$798$	−0.104885	−	0.0880088i	−0.00371288	−	0.00311548i
$799$	21.3826	+	17.9422i	0.756463	+	0.634748i
$800$	17.5150	+	30.3369i	0.619249	+	1.07257i
$801$	−21.9192	−	7.97794i	−0.774477	−	0.281887i
$802$	−1.76857	+	10.0301i	−0.0624504	+	0.354174i
$803$	−4.49273	+	7.78163i	−0.158545	+	0.274608i
$804$	13.3157	+	23.0634i	0.469608	+	0.813384i
$805$	−1.22668	+	0.446476i	−0.0432348	+	0.0157362i
$806$	1.29813	−	2.24843i	0.0457248	−	0.0791977i
$807$	49.3965	−	41.4486i	1.73884	−	1.45906i
$808$	−0.965852			−0.0339785
$809$	39.4818	−	33.1292i	1.38811	−	1.16476i	0.422006	−	0.906593i	$-0.361326\pi$
$809$	39.4818	−	33.1292i	1.38811	−	1.16476i	0.966101	−	0.258166i	$-0.0831182\pi$
$810$	9.31820	+	3.39155i	0.327408	+	0.119167i
$811$	−0.595333	−	3.37630i	−0.0209050	−	0.118558i	0.972570	−	0.232612i	$-0.0747273\pi$
$811$	−0.595333	−	3.37630i	−0.0209050	−	0.118558i	−0.993475	+	0.114054i	$0.963616\pi$
$812$	0.0488583	−	0.277089i	0.00171459	−	0.00972393i
$813$	54.5536			1.91328
$814$	−3.09240	+	0.955234i	−0.108388	+	0.0334810i
$815$	−13.5074			−0.473145
$816$	7.09256	−	40.2239i	0.248289	−	1.40812i
$817$	1.57082	+	8.90858i	0.0549561	+	0.311672i
$818$	8.27941	+	3.01346i	0.289483	+	0.105363i
$819$	−1.39053	+	1.16679i	−0.0485890	+	0.0407710i
$820$	8.36959			0.292279
$821$	−23.3685	+	19.6085i	−0.815565	+	0.684340i	−0.951929	−	0.306319i	$-0.900903\pi$
$821$	−23.3685	+	19.6085i	−0.815565	+	0.684340i	0.136364	+	0.990659i	$0.456458\pi$
$822$	−8.52869	+	14.7721i	−0.297472	+	0.515237i
$823$	−14.3947	+	5.23924i	−0.501768	+	0.182629i	−0.580489	−	0.814268i	$-0.697139\pi$
$823$	−14.3947	+	5.23924i	−0.501768	+	0.182629i	0.0787211	+	0.996897i	$0.474916\pi$
$824$	−0.0582480	−	0.100888i	−0.00202916	−	0.00351462i
$825$	−17.7062	+	30.6680i	−0.616451	+	1.06772i
$826$	−0.0430711	+	0.244268i	−0.00149864	+	0.00849919i
$827$	32.7012	+	11.9022i	1.13713	+	0.413882i	0.840876	−	0.541227i	$-0.182040\pi$
$827$	32.7012	+	11.9022i	1.13713	+	0.413882i	0.296254	+	0.955109i	$0.404262\pi$
$828$	9.23055	+	15.9878i	0.320784	+	0.555614i
$829$	7.37939	+	6.19204i	0.256297	+	0.215058i	0.761878	−	0.647720i	$-0.224278\pi$
$829$	7.37939	+	6.19204i	0.256297	+	0.215058i	−0.505581	+	0.862779i	$0.668722\pi$
$830$	−12.9855	−	10.8961i	−0.450732	−	0.378209i
$831$	21.8888	−	7.96686i	0.759313	−	0.276367i
$832$	−4.02094	−	22.8039i	−0.139401	−	0.790583i
$833$	5.94578	+	33.7202i	0.206009	+	1.16834i
$834$	−13.5722	+	4.93989i	−0.469968	+	0.171054i
$835$	−57.3046	−	48.0843i	−1.98311	−	1.66402i
$836$	2.84730	+	2.38917i	0.0984758	+	0.0826310i
$837$	0.882789	+	1.52904i	0.0305136	+	0.0528512i
$838$	−10.8277	−	3.94096i	−0.374037	−	0.136138i
$839$	−4.48334	+	25.4263i	−0.154782	+	0.877812i	0.804203	+	0.594355i	$0.202593\pi$
$839$	−4.48334	+	25.4263i	−0.154782	+	0.877812i	−0.958985	+	0.283457i	$0.908519\pi$
$840$	0.773318	−	1.33943i	0.0266820	−	0.0462146i
$841$	13.7297	+	23.7805i	0.473437	+	0.820017i
$842$	2.99582	−	1.09039i	0.103243	−	0.0375774i
$843$	−15.0496	+	26.0667i	−0.518337	+	0.897786i
$844$	−5.68866	+	4.77335i	−0.195812	+	0.164306i
$845$	−24.2858			−0.835457
$846$	5.16843	−	4.33683i	0.177694	−	0.149103i
$847$	−0.980704	−	0.356947i	−0.0336974	−	0.0122649i
$848$	2.93061	+	16.6203i	0.100637	+	0.570744i
$849$	9.55855	−	54.2092i	0.328049	−	1.86046i
$850$	15.5395			0.533001
$851$	17.4932	+	0.866025i	0.599659	+	0.0296870i
$852$	−39.0556			−1.33802
$853$	−4.24035	+	24.0482i	−0.145187	+	0.823396i	0.822030	+	0.569444i	$0.192842\pi$
$853$	−4.24035	+	24.0482i	−0.145187	+	0.823396i	−0.967217	+	0.253952i	$0.918270\pi$
$854$	0.0558643	+	0.316822i	0.00191164	+	0.0108414i
$855$	15.5544	+	5.66133i	0.531948	+	0.193613i
$856$	16.5876	−	13.9187i	0.566954	−	0.475731i
$857$	45.3542			1.54927			0.774635	−	0.632408i	$-0.217933\pi$
$857$	45.3542			1.54927			0.774635	+	0.632408i	$0.217933\pi$
$858$	−4.55303	+	3.82045i	−0.155438	+	0.130428i
$859$	22.0530	−	38.1970i	0.752440	−	1.30326i	−0.194197	−	0.980962i	$-0.562210\pi$
$859$	22.0530	−	38.1970i	0.752440	−	1.30326i	0.946637	−	0.322301i	$-0.104456\pi$
$860$	−46.5185	+	16.9313i	−1.58627	+	0.577354i
$861$	−0.180922	−	0.313366i	−0.00616581	−	0.0106795i
$862$	6.88800	−	11.9304i	0.234606	−	0.406350i
$863$	10.1648	−	57.6473i	0.346013	−	1.96234i	0.0884289	−	0.996082i	$-0.471815\pi$
$863$	10.1648	−	57.6473i	0.346013	−	1.96234i	0.257584	−	0.966256i	$-0.417073\pi$
$864$	−3.75712	−	1.36748i	−0.127820	−	0.0465226i
$865$	12.7537	+	22.0901i	0.433639	+	0.751086i
$866$	−2.98499	−	2.50470i	−0.101434	−	0.0851132i
$867$	−13.6291	−	11.4361i	−0.462868	−	0.388392i
$868$	−0.360967	+	0.131381i	−0.0122520	+	0.00445937i
$869$	−3.45677	−	19.6043i	−0.117263	−	0.665030i
$870$	−0.712438	−	4.04044i	−0.0241539	−	0.136984i
$871$	23.1989	−	8.44372i	0.786066	−	0.286105i
$872$	17.2815	+	14.5009i	0.585226	+	0.491063i
$873$	−4.57604	−	3.83975i	−0.154875	−	0.129956i
$874$	0.645430	+	1.11792i	0.0218320	+	0.0378141i
$875$	−1.75877	−	0.640140i	−0.0594573	−	0.0216407i
$876$	−4.84642	+	27.4854i	−0.163745	+	0.928646i
$877$	3.78998	−	6.56444i	0.127979	−	0.221665i	−0.794915	−	0.606721i	$-0.792484\pi$
$877$	3.78998	−	6.56444i	0.127979	−	0.221665i	0.922893	+	0.385056i	$0.125818\pi$
$878$	−2.42767	−	4.20485i	−0.0819299	−	0.141907i
$879$	24.7015	−	8.99059i	0.833159	−	0.303245i
$880$	−9.47565	+	16.4123i	−0.319424	+	0.553259i
$881$	−9.87346	+	8.28481i	−0.332645	+	0.279122i	−0.793777	−	0.608209i	$-0.791888\pi$
$881$	−9.87346	+	8.28481i	−0.332645	+	0.279122i	0.461131	+	0.887332i	$0.347444\pi$
$882$	8.27631			0.278678
$883$	−20.5155	+	17.2145i	−0.690401	+	0.579315i	−0.919025	−	0.394200i	$-0.871022\pi$
$883$	−20.5155	+	17.2145i	−0.690401	+	0.579315i	0.228624	+	0.973515i	$0.426577\pi$
$884$	−38.1883	−	13.8994i	−1.28441	−	0.467487i
$885$	−9.78611	−	55.4998i	−0.328957	−	1.86561i
$886$	0.674221	−	3.82370i	0.0226509	−	0.128460i
$887$	−42.5307			−1.42804			−0.714020	−	0.700125i	$-0.753127\pi$
$887$	−42.5307			−1.42804			−0.714020	+	0.700125i	$0.753127\pi$
$888$	−16.5364	+	12.5363i	−0.554926	+	0.420690i
$889$	1.88713			0.0632922
$890$	1.54993	−	8.79012i	0.0519539	−	0.294645i
$891$	2.02094	+	11.4613i	0.0677042	+	0.383970i
$892$	25.6129	+	9.32234i	0.857584	+	0.312135i
$893$	−5.63113	+	4.72508i	−0.188439	+	0.158119i
$894$	9.18210			0.307096
$895$	28.8949	−	24.2457i	0.965849	−	0.810443i
$896$	0.572796	−	0.992112i	0.0191358	−	0.0331441i
$897$	30.2237	−	11.0005i	1.00914	−	0.367297i
$898$	−3.89662	−	6.74915i	−0.130032	−	0.225222i
$899$	−1.05169	+	1.82158i	−0.0350758	+	0.0607531i
$900$	−10.1630	+	57.6371i	−0.338766	+	1.92124i
$901$	23.6215	+	8.59754i	0.786948	+	0.286426i
$902$	−0.315207	−	0.545955i	−0.0104953	−	0.0181783i
$903$	1.63950	+	1.37570i	0.0545591	+	0.0457806i
$904$	−0.335437	−	0.281465i	−0.0111565	−	0.00936138i
$905$	−85.7461	+	31.2090i	−2.85030	+	1.03742i
$906$	−2.93036	−	16.6189i	−0.0973547	−	0.552126i
$907$	3.98639	+	22.6079i	0.132366	+	0.750684i	0.976658	+	0.214800i	$0.0689101\pi$
$907$	3.98639	+	22.6079i	0.132366	+	0.750684i	−0.844292	+	0.535883i	$0.819979\pi$
$908$	−0.939693	+	0.342020i	−0.0311848	+	0.0113503i
$909$	−1.87346	−	1.57202i	−0.0621386	−	0.0521405i
$910$	−0.532089	−	0.446476i	−0.0176386	−	0.0148005i
$911$	16.9304	+	29.3242i	0.560928	+	0.971555i	0.997416	+	0.0718454i	$0.0228888\pi$
$911$	16.9304	+	29.3242i	0.560928	+	0.971555i	−0.436488	+	0.899710i	$0.643778\pi$
$912$	10.1077	+	3.67891i	0.334700	+	0.121821i
$913$	3.45471	−	19.5926i	0.114334	−	0.648421i
$914$	−6.67024	+	11.5532i	−0.220632	+	0.382146i
$915$	−36.5476	−	63.3022i	−1.20823	−	2.09271i
$916$	18.9145	−	6.88430i	0.624952	−	0.227464i
$917$	−0.308811	+	0.534876i	−0.0101978	+	0.0176632i
$918$	−1.35869	+	1.14008i	−0.0448434	+	0.0376281i
$919$	−28.6596			−0.945394			−0.472697	−	0.881225i	$-0.656719\pi$
$919$	−28.6596			−0.945394			−0.472697	+	0.881225i	$0.656719\pi$
$920$	−11.1702	+	9.37295i	−0.368272	+	0.309017i
$921$	−37.0933	−	13.5009i	−1.22227	−	0.444869i
$922$	−0.877164	−	4.97464i	−0.0288878	−	0.163831i
$923$	−6.28699	+	35.6553i	−0.206939	+	1.17361i
$924$	0.879385			0.0289297
$925$	40.7183	+	37.7507i	1.33881	+	1.24124i
$926$	3.85204			0.126586
$927$	0.0512224	−	0.290497i	0.00168236	−	0.00954117i
$928$	−0.827123	−	4.69085i	−0.0271517	−	0.153985i
$929$	−29.4873	−	10.7325i	−0.967446	−	0.352121i	−0.190499	−	0.981687i	$-0.561010\pi$
$929$	−29.4873	−	10.7325i	−0.967446	−	0.352121i	−0.776947	+	0.629566i	$0.783233\pi$
$930$	−4.29086	+	3.60046i	−0.140703	+	0.118064i
$931$	−9.01724			−0.295528
$932$	16.9795	−	14.2475i	0.556183	−	0.466693i
$933$	−26.6163	+	46.1008i	−0.871380	+	1.50927i
$934$	−7.66860	+	2.79114i	−0.250924	+	0.0913289i
$935$	14.1138	+	24.4458i	0.461571	+	0.799464i
$936$	−10.1382	+	17.5598i	−0.331376	+	0.573960i
$937$	−6.15095	+	34.8838i	−0.200943	+	1.13960i	0.702755	+	0.711432i	$0.251953\pi$
$937$	−6.15095	+	34.8838i	−0.200943	+	1.13960i	−0.903698	+	0.428171i	$0.859158\pi$
$938$	0.220285	+	0.0801772i	0.00719256	+	0.00261788i
$939$	0.240352	+	0.416302i	0.00784360	+	0.0135855i
$940$	−30.8161	−	25.8578i	−1.00511	−	0.843389i
$941$	9.80999	+	8.23156i	0.319797	+	0.268341i	0.788527	−	0.615000i	$-0.210844\pi$
$941$	9.80999	+	8.23156i	0.319797	+	0.268341i	−0.468730	+	0.883341i	$0.655288\pi$
$942$	−1.81743	+	0.661490i	−0.0592150	+	0.0215525i
$943$	0.592396	+	3.35965i	0.0192911	+	0.109405i
$944$	−3.38372	−	19.1900i	−0.110131	−	0.624583i
$945$	0.443868	−	0.161555i	0.0144390	−	0.00525537i
$946$	2.85638	+	2.39679i	0.0928690	+	0.0779263i
$947$	−9.84595	−	8.26173i	−0.319950	−	0.268470i	0.468640	−	0.883389i	$-0.344744\pi$
$947$	−9.84595	−	8.26173i	−0.319950	−	0.268470i	−0.788590	+	0.614919i	$0.789189\pi$
$948$	−30.9158	−	53.5478i	−1.00410	−	1.73915i
$949$	24.3123	+	8.84894i	0.789210	+	0.287249i
$950$	−0.710627	+	4.03017i	−0.0230558	+	0.130756i
$951$	5.20708	−	9.01893i	0.168851	−	0.292459i
$952$	−0.398270	−	0.689825i	−0.0129080	−	0.0223573i
$953$	−35.4261	+	12.8940i	−1.14756	+	0.417679i	−0.844639	−	0.535336i	$-0.820185\pi$
$953$	−35.4261	+	12.8940i	−1.14756	+	0.417679i	−0.302924	+	0.953015i	$0.597963\pi$
$954$	3.03802	−	5.26200i	0.0983595	−	0.170364i
$955$	35.4911	−	29.7806i	1.14847	−	0.963677i
$956$	−6.87939			−0.222495
$957$	3.68866	−	3.09516i	0.119238	−	0.100052i
$958$	−10.8846	−	3.96167i	−0.351665	−	0.127996i
$959$	−0.406260	−	2.30401i	−0.0131188	−	0.0744004i
$960$	−8.67499	+	49.1983i	−0.279984	+	1.58787i
$961$	−28.1284			−0.907366
$962$	4.25490	+	8.29131i	0.137183	+	0.267323i
$963$	54.8289			1.76684
$964$	4.26440	−	24.1846i	0.137347	−	0.778933i
$965$	0.954813	+	5.41501i	0.0307365	+	0.174315i
$966$	0.286989	+	0.104455i	0.00923372	+	0.00336080i
$967$	22.4813	−	18.8641i	0.722951	−	0.606628i	−0.205249	−	0.978710i	$-0.565800\pi$
$967$	22.4813	−	18.8641i	0.722951	−	0.606628i	0.928200	+	0.372082i	$0.121356\pi$
$968$	−11.6578			−0.374694
$969$	12.2732	−	10.2984i	0.394271	−	0.330832i
$970$	1.14290	−	1.97957i	0.0366964	−	0.0635601i
$971$	53.8512	−	19.6002i	1.72817	−	0.629002i	0.729670	−	0.683799i	$-0.239673\pi$
$971$	53.8512	−	19.6002i	1.72817	−	0.629002i	0.998498	+	0.0547972i	$0.0174512\pi$
$972$	21.0116	+	36.3932i	0.673948	+	1.16731i
$973$	0.990505	−	1.71560i	0.0317541	−	0.0549997i
$974$	−0.678091	+	3.84565i	−0.0217274	+	0.123222i
$975$	95.8167	+	34.8744i	3.06859	+	1.11688i
$976$	−12.6370	−	21.8879i	−0.404500	−	0.700614i
$977$	−11.6374	−	9.76497i	−0.372315	−	0.312409i	0.437362	−	0.899286i	$-0.355913\pi$
$977$	−11.6374	−	9.76497i	−0.372315	−	0.312409i	−0.809676	+	0.586877i	$0.800357\pi$
$978$	2.42081	+	2.03130i	0.0774089	+	0.0649538i
$979$	9.84389	−	3.58288i	0.314612	−	0.114509i
$980$	−8.56893	−	48.5968i	−0.273724	−	1.55237i
$981$	9.91921	+	56.2547i	0.316696	+	1.79607i
$982$	11.7275	−	4.26844i	0.374238	−	0.136212i
$983$	−12.0947	−	10.1486i	−0.385760	−	0.323691i	0.429199	−	0.903210i	$-0.358796\pi$
$983$	−12.0947	−	10.1486i	−0.385760	−	0.323691i	−0.814959	+	0.579519i	$0.803240\pi$
$984$	−3.09627	−	2.59808i	−0.0987054	−	0.0828236i
$985$	13.7716	+	23.8530i	0.438799	+	0.760021i
$986$	−1.98556	−	0.722684i	−0.0632330	−	0.0230149i
$987$	−0.302004	+	1.71275i	−0.00961288	+	0.0545174i
$988$	5.35117	−	9.26849i	0.170243	−	0.294870i
$989$	−10.0890	−	17.4746i	−0.320811	−	0.555661i
$990$	6.41147	−	2.33359i	0.203770	−	0.0741662i
$991$	−0.393466	+	0.681504i	−0.0124989	+	0.0216487i	−0.872207	−	0.489137i	$-0.837312\pi$
$991$	−0.393466	+	0.681504i	−0.0124989	+	0.0216487i	0.859708	+	0.510785i	$0.170645\pi$
$992$	−4.98158	+	4.18004i	−0.158165	+	0.132717i
$993$	23.9804			0.760995
$994$	−0.263356	+	0.220982i	−0.00835315	+	0.00700912i
$995$	−16.2249	−	5.90539i	−0.514365	−	0.187213i
$996$	−10.7306	−	60.8560i	−0.340011	−	1.92830i
$997$	8.86753	−	50.2902i	0.280837	−	1.59271i	−0.438949	−	0.898512i	$-0.644649\pi$
$997$	8.86753	−	50.2902i	0.280837	−	1.59271i	0.719786	−	0.694196i	$-0.244240\pi$
$998$	−2.36514			−0.0748673
$999$	−6.32981	−	0.313366i	−0.200266	−	0.00991447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.2.f.a.33.1	yes	6
3.2	odd	2		333.2.x.c.181.1		6
4.3	odd	2		592.2.bc.a.33.1		6
5.2	odd	4		925.2.bc.a.699.1		12
5.3	odd	4		925.2.bc.a.699.2		12
5.4	even	2		925.2.p.b.551.1		6
37.3	even	18		1369.2.a.k.1.2		3
37.9	even	9	inner	37.2.f.a.9.1	✓	6
37.18	odd	36		1369.2.b.f.1368.3		6
37.19	odd	36		1369.2.b.f.1368.4		6
37.34	even	9		1369.2.a.j.1.2		3
111.83	odd	18		333.2.x.c.46.1		6
148.83	odd	18		592.2.bc.a.305.1		6
185.9	even	18		925.2.p.b.601.1		6
185.83	odd	36		925.2.bc.a.749.1		12
185.157	odd	36		925.2.bc.a.749.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.f.a.9.1	✓	6	37.9	even	9	inner
37.2.f.a.33.1	yes	6	1.1	even	1	trivial
333.2.x.c.46.1		6	111.83	odd	18
333.2.x.c.181.1		6	3.2	odd	2
592.2.bc.a.33.1		6	4.3	odd	2
592.2.bc.a.305.1		6	148.83	odd	18
925.2.p.b.551.1		6	5.4	even	2
925.2.p.b.601.1		6	185.9	even	18
925.2.bc.a.699.1		12	5.2	odd	4
925.2.bc.a.699.2		12	5.3	odd	4
925.2.bc.a.749.1		12	185.83	odd	36
925.2.bc.a.749.2		12	185.157	odd	36
1369.2.a.j.1.2		3	37.34	even	9
1369.2.a.k.1.2		3	37.3	even	18
1369.2.b.f.1368.3		6	37.18	odd	36
1369.2.b.f.1368.4		6	37.19	odd	36

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	37.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0603074 + 0.342020i) q^{2} +(-0.439693 - 2.49362i) q^{3} +(1.76604 + 0.642788i) q^{4} +(-2.87939 + 2.41609i) q^{5} +0.879385 q^{6} +(-0.0923963 + 0.0775297i) q^{7} +(-0.673648 + 1.16679i) q^{8} +(-3.20574 + 1.16679i) q^{9} +O(q^{10})\)	\(q+(-0.0603074 + 0.342020i) q^{2} +(-0.439693 - 2.49362i) q^{3} +(1.76604 + 0.642788i) q^{4} +(-2.87939 + 2.41609i) q^{5} +0.879385 q^{6} +(-0.0923963 + 0.0775297i) q^{7} +(-0.673648 + 1.16679i) q^{8} +(-3.20574 + 1.16679i) q^{9} +(-0.652704 - 1.13052i) q^{10} +(0.766044 - 1.32683i) q^{11} +(0.826352 - 4.68647i) q^{12} +(-4.14543 - 1.50881i) q^{13} +(-0.0209445 - 0.0362770i) q^{14} +(7.29086 + 6.11776i) q^{15} +(2.52094 + 2.11532i) q^{16} +(4.60607 - 1.67647i) q^{17} +(-0.205737 - 1.16679i) q^{18} +(0.224155 + 1.27125i) q^{19} +(-6.63816 + 2.41609i) q^{20} +(0.233956 + 0.196312i) q^{21} +(0.407604 + 0.342020i) q^{22} +(-1.43969 - 2.49362i) q^{23} +(3.20574 + 1.16679i) q^{24} +(1.58512 - 8.98968i) q^{25} +(0.766044 - 1.32683i) q^{26} +(0.520945 + 0.902302i) q^{27} +(-0.213011 + 0.0775297i) q^{28} +(-0.620615 + 1.07494i) q^{29} +(-2.53209 + 2.12467i) q^{30} +1.69459 q^{31} +(-2.93969 + 2.46669i) q^{32} +(-3.64543 - 1.32683i) q^{33} +(0.295607 + 1.67647i) q^{34} +(0.0787257 - 0.446476i) q^{35} -6.41147 q^{36} +(-3.29813 + 5.11100i) q^{37} -0.448311 q^{38} +(-1.93969 + 11.0005i) q^{39} +(-0.879385 - 4.98724i) q^{40} +(-1.11334 - 0.405223i) q^{41} +(-0.0812519 + 0.0681784i) q^{42} +7.00774 q^{43} +(2.20574 - 1.85083i) q^{44} +(6.41147 - 11.1050i) q^{45} +(0.939693 - 0.342020i) q^{46} +(2.84730 + 4.93166i) q^{47} +(4.16637 - 7.21637i) q^{48} +(-1.21301 + 6.87933i) q^{49} +(2.97906 + 1.08429i) q^{50} +(-6.20574 - 10.7487i) q^{51} +(-6.35117 - 5.32926i) q^{52} +(3.92855 + 3.29644i) q^{53} +(-0.340022 + 0.123758i) q^{54} +(1.00000 + 5.67128i) q^{55} +(-0.0282185 - 0.160035i) q^{56} +(3.07145 - 1.11792i) q^{57} +(-0.330222 - 0.277089i) q^{58} +(-4.53596 - 3.80612i) q^{59} +(8.94356 + 15.4907i) q^{60} +(-7.21688 - 2.62673i) q^{61} +(-0.102196 + 0.579585i) q^{62} +(0.205737 - 0.356347i) q^{63} +(2.62449 + 4.54574i) q^{64} +(15.5817 - 5.67128i) q^{65} +(0.673648 - 1.16679i) q^{66} +(-4.28699 + 3.59721i) q^{67} +9.21213 q^{68} +(-5.58512 + 4.68647i) q^{69} +(0.147956 + 0.0538515i) q^{70} +(-1.42514 - 8.08240i) q^{71} +(0.798133 - 4.52644i) q^{72} -5.86484 q^{73} +(-1.54916 - 1.43626i) q^{74} -23.1138 q^{75} +(-0.421274 + 2.38917i) q^{76} +(0.0320889 + 0.181985i) q^{77} +(-3.64543 - 1.32683i) q^{78} +(9.95336 - 8.35186i) q^{79} -12.3696 q^{80} +(-5.81908 + 4.88279i) q^{81} +(0.205737 - 0.356347i) q^{82} +(12.2023 - 4.44129i) q^{83} +(0.286989 + 0.497079i) q^{84} +(-9.21213 + 15.9559i) q^{85} +(-0.422618 + 2.39679i) q^{86} +(2.95336 + 1.07494i) q^{87} +(1.03209 + 1.78763i) q^{88} +(5.23783 + 4.39506i) q^{89} +(3.41147 + 2.86257i) q^{90} +(0.500000 - 0.181985i) q^{91} +(-0.939693 - 5.32926i) q^{92} +(-0.745100 - 4.22567i) q^{93} +(-1.85844 + 0.676417i) q^{94} +(-3.71688 - 3.11883i) q^{95} +(7.44356 + 6.24589i) q^{96} +(0.875515 + 1.51644i) q^{97} +(-2.27972 - 0.829748i) q^{98} +(-0.907604 + 5.14728i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + 3 q^{7} - 3 q^{8} - 9 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + 3 * q^7 - 3 * q^8 - 9 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + 3 q^{7} - 3 q^{8} - 9 q^{9} - 6 q^{10} + 6 q^{12} - 9 q^{13} + 3 q^{14} + 12 q^{15} + 12 q^{16} + 3 q^{17} + 9 q^{18} + 3 q^{19} - 6 q^{20} + 6 q^{21} + 6 q^{22} - 3 q^{23} + 9 q^{24} - 12 q^{25} - 9 q^{28} - 15 q^{29} - 6 q^{30} + 6 q^{31} - 12 q^{32} - 6 q^{33} + 3 q^{34} + 18 q^{35} - 18 q^{36} - 6 q^{37} - 6 q^{38} - 6 q^{39} + 6 q^{40} - 3 q^{42} - 6 q^{43} + 3 q^{44} + 18 q^{45} + 15 q^{47} + 6 q^{48} - 15 q^{49} + 21 q^{50} - 27 q^{51} - 12 q^{52} + 24 q^{53} + 18 q^{54} + 6 q^{55} - 15 q^{56} + 18 q^{57} + 21 q^{58} + 6 q^{59} + 24 q^{60} - 27 q^{61} - 9 q^{63} + 3 q^{64} + 30 q^{65} + 3 q^{66} - 18 q^{67} + 6 q^{68} - 12 q^{69} - 30 q^{70} + 33 q^{71} - 9 q^{72} + 12 q^{73} - 21 q^{74} - 66 q^{75} + 15 q^{76} - 9 q^{77} - 6 q^{78} + 33 q^{79} - 60 q^{80} - 18 q^{81} - 9 q^{82} + 21 q^{83} - 6 q^{84} - 6 q^{85} + 24 q^{86} - 9 q^{87} - 3 q^{88} + 12 q^{89} + 3 q^{91} - 3 q^{93} - 3 q^{94} - 6 q^{95} + 15 q^{96} + 18 q^{97} + 12 q^{98} - 9 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + 3 * q^7 - 3 * q^8 - 9 * q^9 - 6 * q^10 + 6 * q^12 - 9 * q^13 + 3 * q^14 + 12 * q^15 + 12 * q^16 + 3 * q^17 + 9 * q^18 + 3 * q^19 - 6 * q^20 + 6 * q^21 + 6 * q^22 - 3 * q^23 + 9 * q^24 - 12 * q^25 - 9 * q^28 - 15 * q^29 - 6 * q^30 + 6 * q^31 - 12 * q^32 - 6 * q^33 + 3 * q^34 + 18 * q^35 - 18 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^39 + 6 * q^40 - 3 * q^42 - 6 * q^43 + 3 * q^44 + 18 * q^45 + 15 * q^47 + 6 * q^48 - 15 * q^49 + 21 * q^50 - 27 * q^51 - 12 * q^52 + 24 * q^53 + 18 * q^54 + 6 * q^55 - 15 * q^56 + 18 * q^57 + 21 * q^58 + 6 * q^59 + 24 * q^60 - 27 * q^61 - 9 * q^63 + 3 * q^64 + 30 * q^65 + 3 * q^66 - 18 * q^67 + 6 * q^68 - 12 * q^69 - 30 * q^70 + 33 * q^71 - 9 * q^72 + 12 * q^73 - 21 * q^74 - 66 * q^75 + 15 * q^76 - 9 * q^77 - 6 * q^78 + 33 * q^79 - 60 * q^80 - 18 * q^81 - 9 * q^82 + 21 * q^83 - 6 * q^84 - 6 * q^85 + 24 * q^86 - 9 * q^87 - 3 * q^88 + 12 * q^89 + 3 * q^91 - 3 * q^93 - 3 * q^94 - 6 * q^95 + 15 * q^96 + 18 * q^97 + 12 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more