LMFDB - Embedded newform 310.2.h.e.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(101,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("310.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			101.1
Root			$1.14412 + 0.831254i$ of defining polynomial
Character	$\chi$	$=$	310.101
Dual form			310.2.h.e.221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.579108 - 1.78231i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} +1.87403 q^{6} +(2.95314 + 2.14558i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.414214 + 0.300944i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.579108 - 1.78231i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} +1.87403 q^{6} +(2.95314 + 2.14558i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.414214 + 0.300944i) q^{9} +(0.309017 - 0.951057i) q^{10} +(-1.47923 - 1.07472i) q^{11} +(-0.579108 + 1.78231i) q^{12} +(-1.92418 - 5.92201i) q^{13} +(-2.95314 + 2.14558i) q^{14} +(0.579108 + 1.78231i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.86735 - 2.08325i) q^{17} +(-0.158216 - 0.486937i) q^{18} +(2.03225 - 6.25461i) q^{19} +(0.809017 + 0.587785i) q^{20} +(2.11391 - 6.50593i) q^{21} +(1.47923 - 1.07472i) q^{22} +(4.36407 - 3.17068i) q^{23} +(-1.51612 - 1.10153i) q^{24} +1.00000 q^{25} +6.22677 q^{26} +(-3.77212 - 2.74061i) q^{27} +(-1.12800 - 3.47162i) q^{28} +(-2.76419 + 8.50730i) q^{29} -1.87403 q^{30} +(-5.56653 + 0.117415i) q^{31} -1.00000 q^{32} +(-1.05886 + 3.25882i) q^{33} +(1.09523 + 3.37078i) q^{34} +(-2.95314 - 2.14558i) q^{35} +0.511996 q^{36} +10.9907 q^{37} +(5.32049 + 3.86556i) q^{38} +(-9.44056 + 6.85897i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-2.48413 + 7.64537i) q^{41} +(5.53428 + 4.02089i) q^{42} +(0.874032 - 2.68999i) q^{43} +(0.565015 + 1.73894i) q^{44} +(0.414214 - 0.300944i) q^{45} +(1.66693 + 5.13027i) q^{46} +(0.253967 + 0.781630i) q^{47} +(1.51612 - 1.10153i) q^{48} +(1.95440 + 6.01501i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-5.37351 - 3.90409i) q^{51} +(-1.92418 + 5.92201i) q^{52} +(-3.32979 + 2.41923i) q^{53} +(3.77212 - 2.74061i) q^{54} +(1.47923 + 1.07472i) q^{55} +3.65028 q^{56} -12.3246 q^{57} +(-7.23674 - 5.25780i) q^{58} +(-1.05792 - 3.25595i) q^{59} +(0.579108 - 1.78231i) q^{60} +9.38499 q^{61} +(1.60848 - 5.33036i) q^{62} -1.86893 q^{63} +(0.309017 - 0.951057i) q^{64} +(1.92418 + 5.92201i) q^{65} +(-2.77212 - 2.01406i) q^{66} -0.182208 q^{67} -3.54424 q^{68} +(-8.17840 - 5.94196i) q^{69} +(2.95314 - 2.14558i) q^{70} +(-1.52473 + 1.10778i) q^{71} +(-0.158216 + 0.486937i) q^{72} +(12.8448 + 9.33230i) q^{73} +(-3.39631 + 10.4528i) q^{74} +(-0.579108 - 1.78231i) q^{75} +(-5.32049 + 3.86556i) q^{76} +(-2.06246 - 6.34761i) q^{77} +(-3.60597 - 11.0980i) q^{78} +(-4.09398 + 2.97445i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(-3.17479 + 9.77101i) q^{81} +(-6.50354 - 4.72510i) q^{82} +(0.832595 - 2.56246i) q^{83} +(-5.53428 + 4.02089i) q^{84} +(-2.86735 + 2.08325i) q^{85} +(2.28825 + 1.66251i) q^{86} +16.7634 q^{87} -1.82843 q^{88} +(-8.21614 - 5.96937i) q^{89} +(0.158216 + 0.486937i) q^{90} +(7.02379 - 21.6170i) q^{91} -5.39428 q^{92} +(3.43289 + 9.85328i) q^{93} -0.821854 q^{94} +(-2.03225 + 6.25461i) q^{95} +(0.579108 + 1.78231i) q^{96} +(-4.61803 - 3.35520i) q^{97} -6.32456 q^{98} +0.936148 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} + 10 q^{7} + 2 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 + 10 * q^7 + 2 * q^8 + 8 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} + 10 q^{7} + 2 q^{8} + 8 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} - 14 q^{13} - 10 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 12 q^{18} - 4 q^{19} + 2 q^{20} + 22 q^{21} - 2 q^{22} + 18 q^{23} - 2 q^{24} + 8 q^{25} - 16 q^{26} - 22 q^{27} - 10 q^{28} + 2 q^{29} - 8 q^{30} + 2 q^{31} - 8 q^{32} - 26 q^{33} - 8 q^{34} - 10 q^{35} + 8 q^{36} + 40 q^{37} + 4 q^{38} - 22 q^{39} - 2 q^{40} + 12 q^{41} + 18 q^{42} + 2 q^{44} - 8 q^{45} + 12 q^{46} + 10 q^{47} + 2 q^{48} + 2 q^{50} + 2 q^{51} - 14 q^{52} - 36 q^{53} + 22 q^{54} - 2 q^{55} - 48 q^{57} - 2 q^{58} + 16 q^{59} - 2 q^{60} - 4 q^{61} - 2 q^{62} + 56 q^{63} - 2 q^{64} + 14 q^{65} - 14 q^{66} + 4 q^{67} - 12 q^{68} - 30 q^{69} + 10 q^{70} + 20 q^{71} + 12 q^{72} + 28 q^{73} + 10 q^{74} + 2 q^{75} - 4 q^{76} + 18 q^{77} - 18 q^{78} - 18 q^{79} + 2 q^{80} - 42 q^{81} - 2 q^{82} + 6 q^{83} - 18 q^{84} + 2 q^{85} - 8 q^{87} + 8 q^{88} - 28 q^{89} - 12 q^{90} - 18 q^{91} - 12 q^{92} + 38 q^{93} + 4 q^{95} - 2 q^{96} - 28 q^{97} - 40 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 + 10 * q^7 + 2 * q^8 + 8 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 - 14 * q^13 - 10 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 12 * q^18 - 4 * q^19 + 2 * q^20 + 22 * q^21 - 2 * q^22 + 18 * q^23 - 2 * q^24 + 8 * q^25 - 16 * q^26 - 22 * q^27 - 10 * q^28 + 2 * q^29 - 8 * q^30 + 2 * q^31 - 8 * q^32 - 26 * q^33 - 8 * q^34 - 10 * q^35 + 8 * q^36 + 40 * q^37 + 4 * q^38 - 22 * q^39 - 2 * q^40 + 12 * q^41 + 18 * q^42 + 2 * q^44 - 8 * q^45 + 12 * q^46 + 10 * q^47 + 2 * q^48 + 2 * q^50 + 2 * q^51 - 14 * q^52 - 36 * q^53 + 22 * q^54 - 2 * q^55 - 48 * q^57 - 2 * q^58 + 16 * q^59 - 2 * q^60 - 4 * q^61 - 2 * q^62 + 56 * q^63 - 2 * q^64 + 14 * q^65 - 14 * q^66 + 4 * q^67 - 12 * q^68 - 30 * q^69 + 10 * q^70 + 20 * q^71 + 12 * q^72 + 28 * q^73 + 10 * q^74 + 2 * q^75 - 4 * q^76 + 18 * q^77 - 18 * q^78 - 18 * q^79 + 2 * q^80 - 42 * q^81 - 2 * q^82 + 6 * q^83 - 18 * q^84 + 2 * q^85 - 8 * q^87 + 8 * q^88 - 28 * q^89 - 12 * q^90 - 18 * q^91 - 12 * q^92 + 38 * q^93 + 4 * q^95 - 2 * q^96 - 28 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−0.579108	−	1.78231i	−0.334348	−	1.02902i	−0.967042	−	0.254616i	$-0.918051\pi$
$3$	−0.579108	−	1.78231i	−0.334348	−	1.02902i	0.632694	−	0.774402i	$-0.281949\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.87403			0.765070
$7$	2.95314	+	2.14558i	1.11618	+	0.810954i	0.983626	−	0.180222i	$-0.0576816\pi$
$7$	2.95314	+	2.14558i	1.11618	+	0.810954i	0.132556	+	0.991176i	$0.457682\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−0.414214	+	0.300944i	−0.138071	+	0.100315i
$10$	0.309017	−	0.951057i	0.0977198	−	0.300750i
$11$	−1.47923	−	1.07472i	−0.446004	−	0.324041i	0.342012	−	0.939696i	$-0.388892\pi$
$11$	−1.47923	−	1.07472i	−0.446004	−	0.324041i	−0.788016	+	0.615655i	$0.788892\pi$
$12$	−0.579108	+	1.78231i	−0.167174	+	0.514509i
$13$	−1.92418	−	5.92201i	−0.533671	−	1.64247i	−0.746503	−	0.665382i	$-0.768269\pi$
$13$	−1.92418	−	5.92201i	−0.533671	−	1.64247i	0.212832	−	0.977089i	$-0.431731\pi$
$14$	−2.95314	+	2.14558i	−0.789260	+	0.573431i
$15$	0.579108	+	1.78231i	0.149525	+	0.460191i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.86735	−	2.08325i	0.695435	−	0.505263i	−0.183007	−	0.983112i	$-0.558583\pi$
$17$	2.86735	−	2.08325i	0.695435	−	0.505263i	0.878442	+	0.477848i	$0.158583\pi$
$18$	−0.158216	−	0.486937i	−0.0372918	−	0.114772i
$19$	2.03225	−	6.25461i	0.466230	−	1.43491i	−0.391200	−	0.920306i	$-0.627940\pi$
$19$	2.03225	−	6.25461i	0.466230	−	1.43491i	0.857430	−	0.514601i	$-0.172060\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$	2.11391	−	6.50593i	0.461292	−	1.41971i
$22$	1.47923	−	1.07472i	0.315373	−	0.229132i
$23$	4.36407	−	3.17068i	0.909971	−	0.661133i	−0.0310366	−	0.999518i	$-0.509881\pi$
$23$	4.36407	−	3.17068i	0.909971	−	0.661133i	0.941007	+	0.338386i	$0.109881\pi$
$24$	−1.51612	−	1.10153i	−0.309477	−	0.224849i
$25$	1.00000			0.200000
$26$	6.22677			1.22117
$27$	−3.77212	−	2.74061i	−0.725945	−	0.527430i
$28$	−1.12800	−	3.47162i	−0.213172	−	0.656075i
$29$	−2.76419	+	8.50730i	−0.513297	+	1.57977i	0.273063	+	0.961996i	$0.411963\pi$
$29$	−2.76419	+	8.50730i	−0.513297	+	1.57977i	−0.786360	+	0.617769i	$0.788037\pi$
$30$	−1.87403			−0.342150
$31$	−5.56653	+	0.117415i	−0.999778	+	0.0210884i
$31$	−5.56653	+	0.117415i	−0.999778	+	0.0210884i
$32$	−1.00000			−0.176777
$33$	−1.05886	+	3.25882i	−0.184323	+	0.567289i
$34$	1.09523	+	3.37078i	0.187831	+	0.578083i
$35$	−2.95314	−	2.14558i	−0.499172	−	0.362669i
$36$	0.511996			0.0853327
$37$	10.9907			1.80686			0.903430	−	0.428735i	$-0.141041\pi$
$37$	10.9907			1.80686			0.903430	+	0.428735i	$0.141041\pi$
$38$	5.32049	+	3.86556i	0.863098	+	0.627077i
$39$	−9.44056	+	6.85897i	−1.51170	+	1.09831i
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	−2.48413	+	7.64537i	−0.387956	+	1.19401i	0.546357	+	0.837553i	$0.316014\pi$
$41$	−2.48413	+	7.64537i	−0.387956	+	1.19401i	−0.934313	+	0.356454i	$0.883986\pi$
$42$	5.53428	+	4.02089i	0.853958	+	0.620437i
$43$	0.874032	−	2.68999i	0.133289	−	0.410220i	−0.862031	−	0.506855i	$-0.830808\pi$
$43$	0.874032	−	2.68999i	0.133289	−	0.410220i	0.995320	+	0.0966349i	$0.0308079\pi$
$44$	0.565015	+	1.73894i	0.0851792	+	0.262155i
$45$	0.414214	−	0.300944i	0.0617473	−	0.0448620i
$46$	1.66693	+	5.13027i	0.245775	+	0.756417i
$47$	0.253967	+	0.781630i	0.0370449	+	0.114012i	0.967869	−	0.251455i	$-0.0809091\pi$
$47$	0.253967	+	0.781630i	0.0370449	+	0.114012i	−0.930824	+	0.365468i	$0.880909\pi$
$48$	1.51612	−	1.10153i	0.218834	−	0.158992i
$49$	1.95440	+	6.01501i	0.279199	+	0.859287i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	−5.37351	−	3.90409i	−0.752442	−	0.546681i
$52$	−1.92418	+	5.92201i	−0.266836	+	0.821235i
$53$	−3.32979	+	2.41923i	−0.457382	+	0.332307i	−0.792503	−	0.609868i	$-0.791223\pi$
$53$	−3.32979	+	2.41923i	−0.457382	+	0.332307i	0.335122	+	0.942175i	$0.391223\pi$
$54$	3.77212	−	2.74061i	0.513321	−	0.372949i
$55$	1.47923	+	1.07472i	0.199459	+	0.144916i
$56$	3.65028			0.487789
$57$	−12.3246			−1.63243
$58$	−7.23674	−	5.25780i	−0.950230	−	0.690383i
$59$	−1.05792	−	3.25595i	−0.137730	−	0.423889i	0.858275	−	0.513190i	$-0.171536\pi$
$59$	−1.05792	−	3.25595i	−0.137730	−	0.423889i	−0.996005	+	0.0893017i	$0.971536\pi$
$60$	0.579108	−	1.78231i	0.0747625	−	0.230095i
$61$	9.38499			1.20162			0.600812	−	0.799390i	$-0.294844\pi$
$61$	9.38499			1.20162			0.600812	+	0.799390i	$0.294844\pi$
$62$	1.60848	−	5.33036i	0.204278	−	0.676957i
$63$	−1.86893			−0.235463
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	1.92418	+	5.92201i	0.238665	+	0.734535i
$66$	−2.77212	−	2.01406i	−0.341225	−	0.247914i
$67$	−0.182208			−0.0222602			−0.0111301	−	0.999938i	$-0.503543\pi$
$67$	−0.182208			−0.0222602			−0.0111301	+	0.999938i	$0.503543\pi$
$68$	−3.54424			−0.429803
$69$	−8.17840	−	5.94196i	−0.984564	−	0.715327i
$70$	2.95314	−	2.14558i	0.352968	−	0.256446i
$71$	−1.52473	+	1.10778i	−0.180952	+	0.131469i	−0.674574	−	0.738207i	$-0.735673\pi$
$71$	−1.52473	+	1.10778i	−0.180952	+	0.131469i	0.493622	+	0.869677i	$0.335673\pi$
$72$	−0.158216	+	0.486937i	−0.0186459	+	0.0573861i
$73$	12.8448	+	9.33230i	1.50337	+	1.09226i	0.969015	+	0.247004i	$0.0794460\pi$
$73$	12.8448	+	9.33230i	1.50337	+	1.09226i	0.534356	+	0.845259i	$0.320554\pi$
$74$	−3.39631	+	10.4528i	−0.394814	+	1.21511i
$75$	−0.579108	−	1.78231i	−0.0668696	−	0.205803i
$76$	−5.32049	+	3.86556i	−0.610302	+	0.443411i
$77$	−2.06246	−	6.34761i	−0.235040	−	0.723377i
$78$	−3.60597	−	11.0980i	−0.408296	−	1.25661i
$79$	−4.09398	+	2.97445i	−0.460608	+	0.334652i	−0.793770	−	0.608218i	$-0.791885\pi$
$79$	−4.09398	+	2.97445i	−0.460608	+	0.334652i	0.333162	+	0.942870i	$0.391885\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	−3.17479	+	9.77101i	−0.352755	+	1.08567i
$82$	−6.50354	−	4.72510i	−0.718196	−	0.521800i
$83$	0.832595	−	2.56246i	0.0913892	−	0.281267i	−0.894907	−	0.446253i	$-0.852758\pi$
$83$	0.832595	−	2.56246i	0.0913892	−	0.281267i	0.986296	+	0.164986i	$0.0527580\pi$
$84$	−5.53428	+	4.02089i	−0.603839	+	0.438715i
$85$	−2.86735	+	2.08325i	−0.311008	+	0.225961i
$86$	2.28825	+	1.66251i	0.246748	+	0.179273i
$87$	16.7634			1.79723
$88$	−1.82843			−0.194911
$89$	−8.21614	−	5.96937i	−0.870909	−	0.632752i	0.0599218	−	0.998203i	$-0.480915\pi$
$89$	−8.21614	−	5.96937i	−0.870909	−	0.632752i	−0.930831	+	0.365451i	$0.880915\pi$
$90$	0.158216	+	0.486937i	0.0166774	+	0.0513277i
$91$	7.02379	−	21.6170i	0.736294	−	2.26608i
$92$	−5.39428			−0.562393
$93$	3.43289	+	9.85328i	0.355974	+	1.02174i
$94$	−0.821854			−0.0847678
$95$	−2.03225	+	6.25461i	−0.208504	+	0.641710i
$96$	0.579108	+	1.78231i	0.0591049	+	0.181906i
$97$	−4.61803	−	3.35520i	−0.468890	−	0.340669i	0.328118	−	0.944637i	$-0.393586\pi$
$97$	−4.61803	−	3.35520i	−0.468890	−	0.340669i	−0.797009	+	0.603968i	$0.793586\pi$
$98$	−6.32456			−0.638877
$99$	0.936148			0.0940864
$100$	−0.809017	−	0.587785i	−0.0809017	−	0.0587785i
$101$	−12.2062	+	8.86830i	−1.21456	+	0.882429i	−0.995637	−	0.0933130i	$-0.970254\pi$
$101$	−12.2062	+	8.86830i	−1.21456	+	0.882429i	−0.218923	+	0.975742i	$0.570254\pi$
$102$	5.37351	−	3.90409i	0.532057	−	0.386562i
$103$	1.59236	−	4.90078i	0.156900	−	0.482888i	−0.841449	−	0.540337i	$-0.818297\pi$
$103$	1.59236	−	4.90078i	0.156900	−	0.482888i	0.998348	+	0.0574492i	$0.0182967\pi$
$104$	−5.03756	−	3.66001i	−0.493974	−	0.358893i
$105$	−2.11391	+	6.50593i	−0.206296	+	0.634914i
$106$	−1.27187	−	3.91440i	−0.123535	−	0.380200i
$107$	−11.9708	+	8.69728i	−1.15726	+	0.840797i	−0.989429	−	0.145019i	$-0.953676\pi$
$107$	−11.9708	+	8.69728i	−1.15726	+	0.840797i	−0.167830	+	0.985816i	$0.553676\pi$
$108$	1.44082	+	4.43440i	0.138643	+	0.426700i
$109$	4.23397	+	13.0308i	0.405541	+	1.24813i	0.920443	+	0.390877i	$0.127828\pi$
$109$	4.23397	+	13.0308i	0.405541	+	1.24813i	−0.514902	+	0.857249i	$0.672172\pi$
$110$	−1.47923	+	1.07472i	−0.141039	+	0.102471i
$111$	−6.36480	−	19.5888i	−0.604120	−	1.85929i
$112$	−1.12800	+	3.47162i	−0.106586	+	0.328038i
$113$	11.6235	+	8.44497i	1.09345	+	0.794436i	0.979978	−	0.199106i	$-0.0638037\pi$
$113$	11.6235	+	8.44497i	1.09345	+	0.794436i	0.113469	+	0.993542i	$0.463804\pi$
$114$	3.80850	−	11.7213i	0.356698	−	1.09780i
$115$	−4.36407	+	3.17068i	−0.406951	+	0.295667i
$116$	7.23674	−	5.25780i	0.671914	−	0.488174i
$117$	2.57921	+	1.87391i	0.238448	+	0.173243i
$118$	3.42351			0.315160
$119$	12.9375			1.18598
$120$	1.51612	+	1.10153i	0.138403	+	0.100555i
$121$	−2.36610	−	7.28210i	−0.215100	−	0.662009i
$122$	−2.90012	+	8.92565i	−0.262565	+	0.808091i
$123$	15.0650			1.35837
$124$	4.57243	+	3.17693i	0.410616	+	0.285297i
$125$	−1.00000			−0.0894427
$126$	0.577531	−	1.77746i	0.0514506	−	0.158349i
$127$	0.509965	+	1.56951i	0.0452521	+	0.139272i	0.971130	−	0.238552i	$-0.0766727\pi$
$127$	0.509965	+	1.56951i	0.0452521	+	0.139272i	−0.925878	+	0.377823i	$0.876673\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−5.30056			−0.466689
$130$	−6.22677			−0.546124
$131$	−0.636603	−	0.462519i	−0.0556202	−	0.0404105i	0.559628	−	0.828744i	$-0.310944\pi$
$131$	−0.636603	−	0.462519i	−0.0556202	−	0.0404105i	−0.615248	+	0.788334i	$0.710944\pi$
$132$	2.77212	−	2.01406i	0.241282	−	0.175302i
$133$	19.4213	−	14.1104i	1.68404	−	1.22353i
$134$	0.0563053	−	0.173290i	0.00486404	−	0.0149700i
$135$	3.77212	+	2.74061i	0.324653	+	0.235874i
$136$	1.09523	−	3.37078i	0.0939153	−	0.289042i
$137$	−4.76551	−	14.6667i	−0.407145	−	1.25306i	−0.919091	−	0.394045i	$-0.871075\pi$
$137$	−4.76551	−	14.6667i	−0.407145	−	1.25306i	0.511946	−	0.859018i	$-0.328925\pi$
$138$	8.17840	−	5.94196i	0.696192	−	0.505813i
$139$	−1.10029	−	3.38635i	−0.0933256	−	0.287227i	0.893488	−	0.449087i	$-0.148251\pi$
$139$	−1.10029	−	3.38635i	−0.0933256	−	0.287227i	−0.986814	+	0.161860i	$0.948251\pi$
$140$	1.12800	+	3.47162i	0.0953333	+	0.293406i
$141$	1.24603	−	0.905296i	0.104935	−	0.0762397i
$142$	−0.582394	−	1.79242i	−0.0488734	−	0.150417i
$143$	−3.51822	+	10.8280i	−0.294208	+	0.905480i
$144$	−0.414214	−	0.300944i	−0.0345178	−	0.0250786i
$145$	2.76419	−	8.50730i	0.229553	−	0.706492i
$146$	−12.8448	+	9.33230i	−1.06304	+	0.772347i
$147$	9.58881	−	6.96668i	0.790872	−	0.574602i
$148$	−8.89167	−	6.46017i	−0.730891	−	0.531023i
$149$	17.0418			1.39612			0.698061	−	0.716038i	$-0.254046\pi$
$149$	17.0418			1.39612			0.698061	+	0.716038i	$0.254046\pi$
$150$	1.87403			0.153014
$151$	7.02634	+	5.10494i	0.571796	+	0.415434i	0.835757	−	0.549099i	$-0.185029\pi$
$151$	7.02634	+	5.10494i	0.571796	+	0.415434i	−0.263961	+	0.964533i	$0.585029\pi$
$152$	−2.03225	−	6.25461i	−0.164837	−	0.507316i
$153$	−0.560754	+	1.72582i	−0.0453343	+	0.139525i
$154$	6.67427			0.537828
$155$	5.56653	−	0.117415i	0.447114	−	0.00943100i
$156$	11.6692			0.934281
$157$	−3.21117	+	9.88296i	−0.256279	+	0.788746i	0.737296	+	0.675570i	$0.236102\pi$
$157$	−3.21117	+	9.88296i	−0.256279	+	0.788746i	−0.993575	+	0.113176i	$0.963898\pi$
$158$	−1.56376	−	4.81276i	−0.124406	−	0.382882i
$159$	6.24013	+	4.53372i	0.494875	+	0.359547i
$160$	1.00000			0.0790569
$161$	19.6907			1.55184
$162$	−8.31172	−	6.03882i	−0.653030	−	0.474454i
$163$	−5.15983	+	3.74884i	−0.404149	+	0.293632i	−0.771229	−	0.636558i	$-0.780358\pi$
$163$	−5.15983	+	3.74884i	−0.404149	+	0.293632i	0.367080	+	0.930190i	$0.380358\pi$
$164$	6.50354	−	4.72510i	0.507841	−	0.368968i
$165$	1.05886	−	3.25882i	0.0824319	−	0.253699i
$166$	2.17976	+	1.58369i	0.169182	+	0.122918i
$167$	1.90983	−	5.87785i	0.147787	−	0.454842i	−0.849572	−	0.527473i	$-0.823140\pi$
$167$	1.90983	−	5.87785i	0.147787	−	0.454842i	0.997359	+	0.0726311i	$0.0231396\pi$
$168$	−2.11391	−	6.50593i	−0.163091	−	0.501944i
$169$	−20.8506	+	15.1488i	−1.60389	+	1.16529i
$170$	−1.09523	−	3.37078i	−0.0840004	−	0.258527i
$171$	1.04050	+	3.20234i	0.0795692	+	0.244889i
$172$	−2.28825	+	1.66251i	−0.174477	+	0.126765i
$173$	3.96623	+	12.2068i	0.301547	+	0.928067i	0.980943	+	0.194295i	$0.0622418\pi$
$173$	3.96623	+	12.2068i	0.301547	+	0.928067i	−0.679396	+	0.733772i	$0.737758\pi$
$174$	−5.18018	+	15.9429i	−0.392708	+	1.20863i
$175$	2.95314	+	2.14558i	0.223236	+	0.162191i
$176$	0.565015	−	1.73894i	0.0425896	−	0.131077i
$177$	−5.19046	+	3.77109i	−0.390139	+	0.283453i
$178$	8.21614	−	5.96937i	0.615826	−	0.447423i
$179$	11.4200	+	8.29709i	0.853568	+	0.620153i	0.926127	−	0.377211i	$-0.123117\pi$
$179$	11.4200	+	8.29709i	0.853568	+	0.620153i	−0.0725597	+	0.997364i	$0.523117\pi$
$180$	−0.511996			−0.0381619
$181$	2.20654			0.164011			0.0820055	−	0.996632i	$-0.473867\pi$
$181$	2.20654			0.164011			0.0820055	+	0.996632i	$0.473867\pi$
$182$	18.3885	+	13.3600i	1.36305	+	0.990313i
$183$	−5.43492	−	16.7270i	−0.401761	−	1.23649i
$184$	1.66693	−	5.13027i	0.122887	−	0.378208i
$185$	−10.9907			−0.808053
$186$	−10.4318	+	0.220039i	−0.764900	+	0.0161341i
$187$	−6.48039			−0.473893
$188$	0.253967	−	0.781630i	0.0185224	−	0.0570062i
$189$	−5.25941	−	16.1868i	−0.382566	−	1.17742i
$190$	−5.32049	−	3.86556i	−0.385989	−	0.280438i
$191$	18.4221			1.33298			0.666489	−	0.745515i	$-0.267796\pi$
$191$	18.4221			1.33298			0.666489	+	0.745515i	$0.267796\pi$
$192$	−1.87403			−0.135247
$193$	−4.13839	−	3.00672i	−0.297888	−	0.216428i	0.428794	−	0.903402i	$-0.358939\pi$
$193$	−4.13839	−	3.00672i	−0.297888	−	0.216428i	−0.726682	+	0.686974i	$0.758939\pi$
$194$	4.61803	−	3.35520i	0.331556	−	0.240889i
$195$	9.44056	−	6.85897i	0.676052	−	0.491181i
$196$	1.95440	−	6.01501i	0.139600	−	0.429644i
$197$	−3.84438	−	2.79311i	−0.273901	−	0.199001i	0.442352	−	0.896842i	$-0.354144\pi$
$197$	−3.84438	−	2.79311i	−0.273901	−	0.199001i	−0.716253	+	0.697841i	$0.754144\pi$
$198$	−0.289286	+	0.890329i	−0.0205586	+	0.0632729i
$199$	2.59836	+	7.99693i	0.184193	+	0.566887i	0.999934	−	0.0115305i	$-0.00367036\pi$
$199$	2.59836	+	7.99693i	0.184193	+	0.566887i	−0.815741	+	0.578418i	$0.803670\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$	0.105518	+	0.324751i	0.00744266	+	0.0229062i
$202$	−4.66234	−	14.3492i	−0.328041	−	1.00961i
$203$	−26.4161	+	19.1924i	−1.85405	+	1.34705i
$204$	2.05250	+	6.31694i	0.143704	+	0.442274i
$205$	2.48413	−	7.64537i	0.173499	−	0.533976i
$206$	4.16885	+	3.02885i	0.290458	+	0.211030i
$207$	−0.853459	+	2.62668i	−0.0593195	+	0.182567i
$208$	5.03756	−	3.66001i	0.349292	−	0.253776i
$209$	−9.72813	+	7.06790i	−0.672909	+	0.488897i
$210$	−5.53428	−	4.02089i	−0.381902	−	0.277468i
$211$	−11.1672			−0.768780			−0.384390	−	0.923171i	$-0.625588\pi$
$211$	−11.1672			−0.768780			−0.384390	+	0.923171i	$0.625588\pi$
$212$	4.11584			0.282677
$213$	2.85739	+	2.07601i	0.195785	+	0.142246i
$214$	−4.57243	−	14.0725i	−0.312565	−	0.961976i
$215$	−0.874032	+	2.68999i	−0.0596085	+	0.183456i
$216$	−4.66260			−0.317250
$217$	−16.6907	−	11.5967i	−1.13304	−	0.787235i
$218$	−13.7014			−0.927977
$219$	9.19453	−	28.2978i	0.621308	−	1.91219i
$220$	−0.565015	−	1.73894i	−0.0380933	−	0.117239i
$221$	−17.8544	−	12.9720i	−1.20101	−	0.872588i
$222$	20.5969			1.38238
$223$	−1.86150			−0.124655			−0.0623277	−	0.998056i	$-0.519852\pi$
$223$	−1.86150			−0.124655			−0.0623277	+	0.998056i	$0.519852\pi$
$224$	−2.95314	−	2.14558i	−0.197315	−	0.143358i
$225$	−0.414214	+	0.300944i	−0.0276142	+	0.0200629i
$226$	−11.6235	+	8.44497i	−0.773184	+	0.561751i
$227$	0.927209	−	2.85366i	0.0615410	−	0.189404i	−0.915559	−	0.402183i	$-0.868252\pi$
$227$	0.927209	−	2.85366i	0.0615410	−	0.189404i	0.977100	+	0.212779i	$0.0682515\pi$
$228$	9.97077	+	7.24419i	0.660331	+	0.479758i
$229$	4.68843	−	14.4295i	0.309820	−	0.953529i	−0.668014	−	0.744149i	$-0.732855\pi$
$229$	4.68843	−	14.4295i	0.309820	−	0.953529i	0.977834	−	0.209380i	$-0.0671446\pi$
$230$	−1.66693	−	5.13027i	−0.109914	−	0.338280i
$231$	−10.1190	+	7.35190i	−0.665783	+	0.483720i
$232$	2.76419	+	8.50730i	0.181478	+	0.558531i
$233$	7.05369	+	21.7090i	0.462103	+	1.42221i	0.862590	+	0.505903i	$0.168841\pi$
$233$	7.05369	+	21.7090i	0.462103	+	1.42221i	−0.400488	+	0.916302i	$0.631159\pi$
$234$	−2.57921	+	1.87391i	−0.168608	+	0.122501i
$235$	−0.253967	−	0.781630i	−0.0165670	−	0.0509879i
$236$	−1.05792	+	3.25595i	−0.0688649	+	0.211944i
$237$	7.67224	+	5.57421i	0.498366	+	0.362084i
$238$	−3.99790	+	12.3043i	−0.259146	+	0.797568i
$239$	16.2270	−	11.7896i	1.04964	−	0.762608i	0.0774954	−	0.996993i	$-0.475308\pi$
$239$	16.2270	−	11.7896i	1.04964	−	0.762608i	0.972144	+	0.234385i	$0.0753077\pi$
$240$	−1.51612	+	1.10153i	−0.0978654	+	0.0711034i
$241$	−0.355771	−	0.258483i	−0.0229172	−	0.0166503i	0.576268	−	0.817261i	$-0.304509\pi$
$241$	−0.355771	−	0.258483i	−0.0229172	−	0.0166503i	−0.599185	+	0.800611i	$0.704509\pi$
$242$	7.65685			0.492201
$243$	5.26572			0.337796
$244$	−7.59261	−	5.51636i	−0.486067	−	0.353149i
$245$	−1.95440	−	6.01501i	−0.124862	−	0.384285i
$246$	−4.65534	+	14.3277i	−0.296814	+	0.913499i
$247$	−40.9503			−2.60561
$248$	−4.43440	+	3.36691i	−0.281585	+	0.213799i
$249$	−5.04927			−0.319984
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−1.04593	−	3.21903i	−0.0660183	−	0.203183i	0.912606	−	0.408841i	$-0.134067\pi$
$251$	−1.04593	−	3.21903i	−0.0660183	−	0.203183i	−0.978624	+	0.205657i	$0.934067\pi$
$252$	1.51200	+	1.09853i	0.0952468	+	0.0692009i
$253$	−9.86305			−0.620085
$254$	−1.65028			−0.103548
$255$	5.37351	+	3.90409i	0.336502	+	0.244483i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	13.9104	−	10.1065i	0.867707	−	0.630426i	−0.0622634	−	0.998060i	$-0.519832\pi$
$257$	13.9104	−	10.1065i	0.867707	−	0.630426i	0.929971	+	0.367633i	$0.119832\pi$
$258$	1.63796	−	5.04114i	0.101975	−	0.313847i
$259$	32.4571	+	23.5815i	2.01679	+	1.46528i
$260$	1.92418	−	5.92201i	0.119332	−	0.367268i
$261$	−1.41525	−	4.35570i	−0.0876020	−	0.269611i
$262$	0.636603	−	0.462519i	0.0393295	−	0.0285745i
$263$	−6.48830	−	19.9689i	−0.400086	−	1.23134i	−0.924929	−	0.380139i	$-0.875876\pi$
$263$	−6.48830	−	19.9689i	−0.400086	−	1.23134i	0.524844	−	0.851199i	$-0.324124\pi$
$264$	1.05886	+	3.25882i	0.0651681	+	0.200567i
$265$	3.32979	−	2.41923i	0.204547	−	0.148612i
$266$	7.41828	+	22.8311i	0.454844	+	1.39986i
$267$	−5.88125	+	18.1006i	−0.359926	+	1.10774i
$268$	0.147409	+	0.107099i	0.00900445	+	0.00654211i
$269$	−2.26951	+	6.98484i	−0.138375	+	0.425873i	−0.996100	−	0.0882353i	$-0.971877\pi$
$269$	−2.26951	+	6.98484i	−0.138375	+	0.425873i	0.857725	+	0.514109i	$0.171877\pi$
$270$	−3.77212	+	2.74061i	−0.229564	+	0.166788i
$271$	1.20972	−	0.878915i	0.0734855	−	0.0533903i	−0.550436	−	0.834877i	$-0.685539\pi$
$271$	1.20972	−	0.878915i	0.0734855	−	0.0533903i	0.623921	+	0.781487i	$0.285539\pi$
$272$	2.86735	+	2.08325i	0.173859	+	0.126316i
$273$	−42.5958			−2.57801
$274$	15.4215			0.931647
$275$	−1.47923	−	1.07472i	−0.0892008	−	0.0648082i
$276$	3.12387	+	9.61429i	0.188035	+	0.578712i
$277$	2.95768	−	9.10281i	0.177710	−	0.546935i	−0.822037	−	0.569434i	$-0.807162\pi$
$277$	2.95768	−	9.10281i	0.177710	−	0.546935i	0.999747	+	0.0224994i	$0.00716238\pi$
$278$	3.56062			0.213552
$279$	2.27040	−	1.72385i	0.135925	−	0.103204i
$280$	−3.65028			−0.218146
$281$	−1.57940	+	4.86091i	−0.0942193	+	0.289977i	−0.987049	−	0.160416i	$-0.948716\pi$
$281$	−1.57940	+	4.86091i	−0.0942193	+	0.289977i	0.892830	+	0.450394i	$0.148716\pi$
$282$	0.475942	+	1.46480i	0.0283419	+	0.0872276i
$283$	−9.24020	−	6.71340i	−0.549273	−	0.399070i	0.278245	−	0.960510i	$-0.410247\pi$
$283$	−9.24020	−	6.71340i	−0.549273	−	0.399070i	−0.827517	+	0.561440i	$0.810247\pi$
$284$	1.88467			0.111834
$285$	12.3246			0.730044
$286$	−9.21082	−	6.69205i	−0.544647	−	0.395709i
$287$	−23.7398	+	17.2479i	−1.40131	+	1.01811i
$288$	0.414214	−	0.300944i	0.0244078	−	0.0177333i
$289$	−1.37152	+	4.22111i	−0.0806777	+	0.248301i
$290$	7.23674	+	5.25780i	0.424956	+	0.308749i
$291$	−3.30567	+	10.1738i	−0.193782	+	0.596398i
$292$	−4.90628	−	15.1000i	−0.287118	−	0.883659i
$293$	−2.41296	+	1.75312i	−0.140967	+	0.102418i	−0.656034	−	0.754732i	$-0.727767\pi$
$293$	−2.41296	+	1.75312i	−0.140967	+	0.102418i	0.515067	+	0.857150i	$0.327767\pi$
$294$	3.66260	+	11.2723i	0.213607	+	0.657415i
$295$	1.05792	+	3.25595i	0.0615946	+	0.189569i
$296$	8.89167	−	6.46017i	0.516818	−	0.375490i
$297$	2.63444	+	8.10797i	0.152866	+	0.470472i
$298$	−5.26622	+	16.2078i	−0.305064	+	0.938890i
$299$	−27.1741	−	19.7431i	−1.57152	−	1.14177i
$300$	−0.579108	+	1.78231i	−0.0334348	+	0.102902i
$301$	8.35274	−	6.06862i	0.481444	−	0.349790i
$302$	−7.02634	+	5.10494i	−0.404321	+	0.293756i
$303$	22.8748	+	16.6195i	1.31412	+	0.954764i
$304$	6.57649			0.377188
$305$	−9.38499			−0.537383
$306$	−1.46807	−	1.06662i	−0.0839242	−	0.0609745i
$307$	8.11093	+	24.9629i	0.462915	+	1.42471i	0.861586	+	0.507612i	$0.169472\pi$
$307$	8.11093	+	24.9629i	0.462915	+	1.42471i	−0.398671	+	0.917094i	$0.630528\pi$
$308$	−2.06246	+	6.34761i	−0.117520	+	0.361689i
$309$	−9.65685			−0.549359
$310$	−1.60848	+	5.33036i	−0.0913557	+	0.302744i
$311$	10.7504			0.609597			0.304799	−	0.952417i	$-0.401411\pi$
$311$	10.7504			0.609597			0.304799	+	0.952417i	$0.401411\pi$
$312$	−3.60597	+	11.0980i	−0.204148	+	0.628303i
$313$	0.460712	+	1.41793i	0.0260410	+	0.0801459i	0.963232	−	0.268670i	$-0.0865840\pi$
$313$	0.460712	+	1.41793i	0.0260410	+	0.0801459i	−0.937191	+	0.348816i	$0.886584\pi$
$314$	−8.40695	−	6.10801i	−0.474432	−	0.344695i
$315$	1.86893			0.105302
$316$	5.06043			0.284672
$317$	11.2847	+	8.19881i	0.633812	+	0.460491i	0.857719	−	0.514119i	$-0.171881\pi$
$317$	11.2847	+	8.19881i	0.633812	+	0.460491i	−0.223907	+	0.974611i	$0.571881\pi$
$318$	−6.24013	+	4.53372i	−0.349929	+	0.254238i
$319$	13.2318	−	9.61350i	0.740841	−	0.538253i
$320$	−0.309017	+	0.951057i	−0.0172746	+	0.0531657i
$321$	22.4336	+	16.2990i	1.25212	+	0.909720i
$322$	−6.08475	+	18.7269i	−0.339090	+	1.04361i
$323$	−7.20278	−	22.1679i	−0.400773	−	1.23345i
$324$	8.31172	−	6.03882i	0.461762	−	0.335490i
$325$	−1.92418	−	5.92201i	−0.106734	−	0.328494i
$326$	−1.97088	−	6.06575i	−0.109157	−	0.335951i
$327$	20.7730	−	15.0925i	1.14875	−	0.834617i
$328$	2.48413	+	7.64537i	0.137163	+	0.422145i
$329$	−0.927051	+	2.85317i	−0.0511100	+	0.157300i
$330$	2.77212	+	2.01406i	0.152600	+	0.110871i
$331$	−5.54708	+	17.0721i	−0.304895	+	0.938370i	0.674822	+	0.737981i	$0.264221\pi$
$331$	−5.54708	+	17.0721i	−0.304895	+	0.938370i	−0.979716	+	0.200389i	$0.935779\pi$
$332$	−2.17976	+	1.58369i	−0.119630	+	0.0869163i
$333$	−4.55250	+	3.30758i	−0.249475	+	0.181254i
$334$	5.00000	+	3.63271i	0.273588	+	0.198773i
$335$	0.182208			0.00995507
$336$	6.84074			0.373193
$337$	17.6227	+	12.8036i	0.959968	+	0.697458i	0.953143	−	0.302519i	$-0.0978276\pi$
$337$	17.6227	+	12.8036i	0.959968	+	0.697458i	0.00682483	+	0.999977i	$0.497828\pi$
$338$	−7.96420	−	24.5113i	−0.433195	−	1.33324i
$339$	8.32029	−	25.6072i	0.451896	−	1.39079i
$340$	3.54424			0.192214
$341$	8.36035	+	5.80879i	0.452739	+	0.314563i
$342$	−3.36714			−0.182074
$343$	0.761901	−	2.34489i	0.0411388	−	0.126612i
$344$	−0.874032	−	2.68999i	−0.0471246	−	0.145035i
$345$	8.17840	+	5.94196i	0.440310	+	0.319904i
$346$	−12.8350			−0.690014
$347$	−14.8499			−0.797185			−0.398592	−	0.917128i	$-0.630501\pi$
$347$	−14.8499			−0.797185			−0.398592	+	0.917128i	$0.630501\pi$
$348$	−13.5619	−	9.85328i	−0.726993	−	0.528191i
$349$	0.622096	−	0.451979i	0.0333000	−	0.0241939i	−0.571011	−	0.820943i	$-0.693449\pi$
$349$	0.622096	−	0.451979i	0.0333000	−	0.0241939i	0.604311	+	0.796749i	$0.293449\pi$
$350$	−2.95314	+	2.14558i	−0.157852	+	0.114686i
$351$	−8.97167	+	27.6120i	−0.478872	+	1.47382i
$352$	1.47923	+	1.07472i	0.0788432	+	0.0572829i
$353$	0.596527	−	1.83592i	0.0317499	−	0.0977163i	−0.933926	−	0.357467i	$-0.883640\pi$
$353$	0.596527	−	1.83592i	0.0317499	−	0.0977163i	0.965676	+	0.259751i	$0.0836404\pi$
$354$	−1.98258	−	6.10176i	−0.105373	−	0.324305i
$355$	1.52473	−	1.10778i	0.0809241	−	0.0587948i
$356$	3.13829	+	9.65865i	0.166329	+	0.511907i
$357$	−7.49220	−	23.0586i	−0.396529	−	1.22039i
$358$	−11.4200	+	8.29709i	−0.603564	+	0.438515i
$359$	−0.376319	−	1.15819i	−0.0198614	−	0.0611270i	0.940635	−	0.339421i	$-0.110231\pi$
$359$	−0.376319	−	1.15819i	−0.0198614	−	0.0611270i	−0.960496	+	0.278294i	$0.910231\pi$
$360$	0.158216	−	0.486937i	0.00833869	−	0.0256638i
$361$	−19.6189	−	14.2539i	−1.03257	−	0.750207i
$362$	−0.681859	+	2.09855i	−0.0358377	+	0.110297i
$363$	−11.6087	+	8.43424i	−0.609301	+	0.442683i
$364$	−18.3885	+	13.3600i	−0.963821	+	0.700257i
$365$	−12.8448	−	9.33230i	−0.672328	−	0.488475i
$366$	17.5878			0.919327
$367$	23.7507			1.23978			0.619889	−	0.784689i	$-0.287177\pi$
$367$	23.7507			1.23978			0.619889	+	0.784689i	$0.287177\pi$
$368$	4.36407	+	3.17068i	0.227493	+	0.165283i
$369$	−1.27187	−	3.91440i	−0.0662107	−	0.203776i
$370$	3.39631	−	10.4528i	0.176566	−	0.543414i
$371$	−15.0240			−0.780007
$372$	3.01435	−	9.98927i	0.156287	−	0.517920i
$373$	22.2480			1.15196			0.575980	−	0.817464i	$-0.304621\pi$
$373$	22.2480			1.15196			0.575980	+	0.817464i	$0.304621\pi$
$374$	2.00255	−	6.16322i	0.103549	−	0.318692i
$375$	0.579108	+	1.78231i	0.0299050	+	0.0920381i
$376$	0.664894	+	0.483074i	0.0342893	+	0.0249126i
$377$	55.6991			2.86865
$378$	17.0198			0.875404
$379$	−27.8708	−	20.2493i	−1.43163	−	1.04014i	−0.989711	−	0.143081i	$-0.954299\pi$
$379$	−27.8708	−	20.2493i	−1.43163	−	1.04014i	−0.441916	−	0.897056i	$-0.645701\pi$
$380$	5.32049	−	3.86556i	0.272936	−	0.198299i
$381$	2.50203	−	1.81783i	0.128183	−	0.0931304i
$382$	−5.69275	+	17.5205i	−0.291266	+	0.896426i
$383$	−17.6436	−	12.8188i	−0.901545	−	0.655011i	0.0373175	−	0.999303i	$-0.488119\pi$
$383$	−17.6436	−	12.8188i	−0.901545	−	0.655011i	−0.938862	+	0.344293i	$0.888119\pi$
$384$	0.579108	−	1.78231i	0.0295525	−	0.0909531i
$385$	2.06246	+	6.34761i	0.105113	+	0.323504i
$386$	4.13839	−	3.00672i	0.210639	−	0.153038i
$387$	0.447501	+	1.37727i	0.0227478	+	0.0700104i
$388$	1.76393	+	5.42882i	0.0895501	+	0.275607i
$389$	12.0537	−	8.75753i	0.611147	−	0.444024i	−0.238671	−	0.971100i	$-0.576712\pi$
$389$	12.0537	−	8.75753i	0.611147	−	0.444024i	0.849818	+	0.527076i	$0.176712\pi$
$390$	3.60597	+	11.0980i	0.182596	+	0.561971i
$391$	5.90799	−	18.1829i	0.298780	−	0.919550i
$392$	5.11667	+	3.71748i	0.258431	+	0.187761i
$393$	−0.455691	+	1.40247i	−0.0229866	+	0.0707454i
$394$	3.84438	−	2.79311i	0.193677	−	0.140715i
$395$	4.09398	−	2.97445i	0.205990	−	0.149661i
$396$	−0.757359	−	0.550254i	−0.0380587	−	0.0276513i
$397$	−15.9773			−0.801880			−0.400940	−	0.916104i	$-0.631316\pi$
$397$	−15.9773			−0.801880			−0.400940	+	0.916104i	$0.631316\pi$
$398$	−8.40847			−0.421478
$399$	−36.3961	−	26.4433i	−1.82209	−	1.32382i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−10.4644	+	32.2061i	−0.522567	+	1.60830i	0.246511	+	0.969140i	$0.420716\pi$
$401$	−10.4644	+	32.2061i	−0.522567	+	1.60830i	−0.769078	+	0.639155i	$0.779284\pi$
$402$	−0.341463			−0.0170306
$403$	11.4063	+	32.7391i	0.568189	+	1.63085i
$404$	15.0877			0.750639
$405$	3.17479	−	9.77101i	0.157757	−	0.485525i
$406$	−10.0901	−	31.0540i	−0.500761	−	1.54119i
$407$	−16.2578	−	11.8120i	−0.805867	−	0.585497i
$408$	−6.64203			−0.328829
$409$	22.3749			1.10637			0.553183	−	0.833060i	$-0.313413\pi$
$409$	22.3749			1.10637			0.553183	+	0.833060i	$0.313413\pi$
$410$	6.50354	+	4.72510i	0.321187	+	0.233356i
$411$	−23.3809	+	16.9872i	−1.15330	+	0.837918i
$412$	−4.16885	+	3.02885i	−0.205385	+	0.149221i
$413$	3.86171	−	11.8851i	0.190023	−	0.584829i
$414$	−2.23439	−	1.62338i	−0.109814	−	0.0797846i
$415$	−0.832595	+	2.56246i	−0.0408705	+	0.125786i
$416$	1.92418	+	5.92201i	0.0943406	+	0.290351i
$417$	−5.39835	+	3.92213i	−0.264358	+	0.192067i
$418$	−3.71582	−	11.4361i	−0.181747	−	0.559358i
$419$	6.09998	+	18.7738i	0.298003	+	0.917160i	0.982196	+	0.187859i	$0.0601547\pi$
$419$	6.09998	+	18.7738i	0.298003	+	0.917160i	−0.684193	+	0.729301i	$0.739845\pi$
$420$	5.53428	−	4.02089i	0.270045	−	0.196199i
$421$	−2.49942	−	7.69243i	−0.121814	−	0.374906i	0.871493	−	0.490408i	$-0.163152\pi$
$421$	−2.49942	−	7.69243i	−0.121814	−	0.374906i	−0.993307	+	0.115502i	$0.963152\pi$
$422$	3.45084	−	10.6206i	0.167984	−	0.517003i
$423$	−0.340423	−	0.247332i	−0.0165519	−	0.0120257i
$424$	−1.27187	+	3.91440i	−0.0617673	+	0.190100i
$425$	2.86735	−	2.08325i	0.139087	−	0.101053i
$426$	−2.85739	+	2.07601i	−0.138441	+	0.100583i
$427$	27.7152	+	20.1363i	1.34123	+	0.974462i
$428$	14.7967			0.715225
$429$	21.3362			1.03012
$430$	−2.28825	−	1.66251i	−0.110349	−	0.0801732i
$431$	−10.1624	−	31.2768i	−0.489507	−	1.50655i	−0.825345	−	0.564629i	$-0.809019\pi$
$431$	−10.1624	−	31.2768i	−0.489507	−	1.50655i	0.335838	−	0.941920i	$-0.390981\pi$
$432$	1.44082	−	4.43440i	0.0693216	−	0.213350i
$433$	−7.53399			−0.362060			−0.181030	−	0.983478i	$-0.557943\pi$
$433$	−7.53399			−0.362060			−0.181030	+	0.983478i	$0.557943\pi$
$434$	16.1868	−	12.2902i	0.776992	−	0.589947i
$435$	−16.7634			−0.803744
$436$	4.23397	−	13.0308i	0.202770	−	0.624063i
$437$	−10.9625	−	33.7392i	−0.524408	−	1.61396i
$438$	24.0716	+	17.4890i	1.15018	+	0.835658i
$439$	−10.2727			−0.490289			−0.245144	−	0.969487i	$-0.578835\pi$
$439$	−10.2727			−0.490289			−0.245144	+	0.969487i	$0.578835\pi$
$440$	1.82843			0.0871668
$441$	−2.61972	−	1.90334i	−0.124748	−	0.0906350i
$442$	17.8544	−	12.9720i	0.849245	−	0.617013i
$443$	3.71605	−	2.69987i	0.176555	−	0.128275i	−0.495998	−	0.868324i	$-0.665198\pi$
$443$	3.71605	−	2.69987i	0.176555	−	0.128275i	0.672553	+	0.740049i	$0.265198\pi$
$444$	−6.36480	+	19.5888i	−0.302060	+	0.929646i
$445$	8.21614	+	5.96937i	0.389482	+	0.282975i
$446$	0.575236	−	1.77039i	0.0272382	−	0.0838306i
$447$	−9.86906	−	30.3739i	−0.466791	−	1.43663i
$448$	2.95314	−	2.14558i	0.139523	−	0.101369i
$449$	−4.70143	−	14.4695i	−0.221874	−	0.682858i	−0.998594	−	0.0530119i	$-0.983118\pi$
$449$	−4.70143	−	14.4695i	−0.221874	−	0.682858i	0.776720	−	0.629846i	$-0.216882\pi$
$450$	−0.158216	−	0.486937i	−0.00745835	−	0.0229544i
$451$	11.8913	−	8.63950i	0.559937	−	0.406818i
$452$	−4.43978	−	13.6642i	−0.208830	−	0.642712i
$453$	5.02957	−	15.4794i	0.236310	−	0.727287i
$454$	2.42746	+	1.76366i	0.113927	+	0.0827725i
$455$	−7.02379	+	21.6170i	−0.329281	+	1.01342i
$456$	−9.97077	+	7.24419i	−0.466924	+	0.339240i
$457$	−23.0196	+	16.7247i	−1.07681	+	0.782348i	−0.977124	−	0.212670i	$-0.931784\pi$
$457$	−23.0196	+	16.7247i	−1.07681	+	0.782348i	−0.0996862	+	0.995019i	$0.531784\pi$
$458$	12.2745	+	8.91793i	0.573549	+	0.416707i
$459$	−16.5254			−0.771339
$460$	5.39428			0.251510
$461$	−4.80342	−	3.48989i	−0.223718	−	0.162540i	0.470281	−	0.882517i	$-0.344153\pi$
$461$	−4.80342	−	3.48989i	−0.223718	−	0.162540i	−0.693999	+	0.719976i	$0.744153\pi$
$462$	−3.86512	−	11.8956i	−0.179822	−	0.553435i
$463$	−12.1633	+	37.4347i	−0.565275	+	1.73974i	0.101858	+	0.994799i	$0.467521\pi$
$463$	−12.1633	+	37.4347i	−0.565275	+	1.73974i	−0.667133	+	0.744939i	$0.732479\pi$
$464$	−8.94510			−0.415266
$465$	−3.43289	−	9.85328i	−0.159196	−	0.456935i
$466$	−22.8262			−1.05740
$467$	6.05473	−	18.6345i	0.280179	−	0.862304i	−0.707623	−	0.706590i	$-0.750232\pi$
$467$	6.05473	−	18.6345i	0.280179	−	0.862304i	0.987802	−	0.155713i	$-0.0497676\pi$
$468$	−0.985172	−	3.03205i	−0.0455396	−	0.140156i
$469$	−0.538085	−	0.390942i	−0.0248465	−	0.0180520i
$470$	0.821854			0.0379093
$471$	19.4741			0.897320
$472$	−2.76968	−	2.01229i	−0.127485	−	0.0926231i
$473$	−4.18389	+	3.03977i	−0.192375	+	0.139769i
$474$	−7.67224	+	5.57421i	−0.352398	+	0.256032i
$475$	2.03225	−	6.25461i	0.0932459	−	0.286981i
$476$	−10.4666	−	7.60446i	−0.479738	−	0.348550i
$477$	0.651190	−	2.00416i	0.0298160	−	0.0917641i
$478$	6.19817	+	19.0760i	0.283498	+	0.872517i
$479$	6.10122	−	4.43279i	0.278772	−	0.202540i	−0.439610	−	0.898189i	$-0.644883\pi$
$479$	6.10122	−	4.43279i	0.278772	−	0.202540i	0.718382	+	0.695649i	$0.244883\pi$
$480$	−0.579108	−	1.78231i	−0.0264325	−	0.0813510i
$481$	−21.1481	−	65.0871i	−0.964269	−	2.96772i
$482$	0.355771	−	0.258483i	0.0162049	−	0.0117736i
$483$	−11.4030	−	35.0949i	−0.518855	−	1.59687i
$484$	−2.36610	+	7.28210i	−0.107550	+	0.331005i
$485$	4.61803	+	3.35520i	0.209694	+	0.152352i
$486$	−1.62720	+	5.00800i	−0.0738112	+	0.227168i
$487$	0.684560	−	0.497362i	0.0310204	−	0.0225376i	−0.572167	−	0.820137i	$-0.693897\pi$
$487$	0.684560	−	0.497362i	0.0310204	−	0.0225376i	0.603187	+	0.797599i	$0.293897\pi$
$488$	7.59261	−	5.51636i	0.343702	−	0.249714i
$489$	9.66969	+	7.02544i	0.437279	+	0.317701i
$490$	6.32456			0.285714
$491$	3.11584			0.140616			0.0703081	−	0.997525i	$-0.477602\pi$
$491$	3.11584			0.140616			0.0703081	+	0.997525i	$0.477602\pi$
$492$	−12.1878	−	8.85499i	−0.549471	−	0.399214i
$493$	9.79696	+	30.1519i	0.441233	+	1.35797i
$494$	12.6543	−	38.9461i	0.569346	−	1.75227i
$495$	−0.936148			−0.0420767
$496$	−1.83182	−	5.25780i	−0.0822511	−	0.236082i
$497$	−6.87956			−0.308591
$498$	1.56031	−	4.80214i	0.0699192	−	0.215189i
$499$	4.20601	+	12.9448i	0.188287	+	0.579487i	0.999989	−	0.00458356i	$-0.00145900\pi$
$499$	4.20601	+	12.9448i	0.188287	+	0.579487i	−0.811703	+	0.584071i	$0.801459\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−11.5822			−0.517453
$502$	3.38469			0.151066
$503$	−10.9043	−	7.92246i	−0.486200	−	0.353245i	0.317521	−	0.948251i	$-0.397150\pi$
$503$	−10.9043	−	7.92246i	−0.486200	−	0.353245i	−0.803721	+	0.595006i	$0.797150\pi$
$504$	−1.51200	+	1.09853i	−0.0673497	+	0.0489324i
$505$	12.2062	−	8.86830i	0.543168	−	0.394634i
$506$	3.04785	−	9.38032i	0.135494	−	0.417006i
$507$	39.0746	+	28.3894i	1.73536	+	1.26082i
$508$	0.509965	−	1.56951i	0.0226260	−	0.0696358i
$509$	10.4265	+	32.0896i	0.462148	+	1.42234i	0.862534	+	0.505999i	$0.168876\pi$
$509$	10.4265	+	32.0896i	0.462148	+	1.42234i	−0.400386	+	0.916346i	$0.631124\pi$
$510$	−5.37351	+	3.90409i	−0.237943	+	0.172876i
$511$	17.9093	+	55.1192i	0.792261	+	2.43833i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−24.8073	+	18.0236i	−1.09527	+	0.795760i
$514$	5.31330	+	16.3527i	0.234360	+	0.721285i
$515$	−1.59236	+	4.90078i	−0.0701677	+	0.215954i
$516$	4.28825	+	3.11559i	0.188779	+	0.137156i
$517$	0.464360	−	1.42915i	0.0204225	−	0.0628541i
$518$	−32.4571	+	23.5815i	−1.42608	+	1.03611i
$519$	19.4594	−	14.1381i	0.854175	−	0.620594i
$520$	5.03756	+	3.66001i	0.220912	+	0.160502i
$521$	14.5687			0.638268			0.319134	−	0.947710i	$-0.396608\pi$
$521$	14.5687			0.638268			0.319134	+	0.947710i	$0.396608\pi$
$522$	4.57986			0.200455
$523$	36.9164	+	26.8213i	1.61424	+	1.17281i	0.847344	+	0.531044i	$0.178200\pi$
$523$	36.9164	+	26.8213i	1.61424	+	1.17281i	0.766897	+	0.641771i	$0.221800\pi$
$524$	0.243161	+	0.748371i	0.0106225	+	0.0326928i
$525$	2.11391	−	6.50593i	0.0922584	−	0.283942i
$526$	20.9966			0.915494
$527$	−15.7166	+	11.9332i	−0.684626	+	0.519817i
$528$	−3.42653			−0.149121
$529$	1.88448	−	5.79982i	0.0819338	−	0.252166i
$530$	1.27187	+	3.91440i	0.0552463	+	0.170031i
$531$	1.41806	+	1.03028i	0.0615387	+	0.0447105i
$532$	−24.0060			−1.04079
$533$	50.0559			2.16816
$534$	−15.3973	−	11.1868i	−0.666307	−	0.484100i
$535$	11.9708	−	8.69728i	0.517542	−	0.376016i
$536$	−0.147409	+	0.107099i	−0.00636711	+	0.00462597i
$537$	8.17460	−	25.1588i	0.352760	−	1.08568i
$538$	−5.94166	−	4.31687i	−0.256163	−	0.186114i
$539$	3.57347	−	10.9980i	0.153920	−	0.473718i
$540$	−1.44082	−	4.43440i	−0.0620031	−	0.190826i
$541$	1.38515	−	1.00637i	0.0595521	−	0.0432671i	−0.557611	−	0.830102i	$-0.688282\pi$
$541$	1.38515	−	1.00637i	0.0595521	−	0.0432671i	0.617163	+	0.786835i	$0.288282\pi$
$542$	0.462073	+	1.42212i	0.0198477	+	0.0610851i
$543$	−1.27783	−	3.93274i	−0.0548368	−	0.168770i
$544$	−2.86735	+	2.08325i	−0.122937	+	0.0893188i
$545$	−4.23397	−	13.0308i	−0.181363	−	0.558179i
$546$	13.1628	−	40.5110i	0.563316	−	1.73371i
$547$	21.8354	+	15.8644i	0.933615	+	0.678311i	0.946875	−	0.321601i	$-0.104221\pi$
$547$	21.8354	+	15.8644i	0.933615	+	0.678311i	−0.0132606	+	0.999912i	$0.504221\pi$
$548$	−4.76551	+	14.6667i	−0.203572	+	0.626532i
$549$	−3.88739	+	2.82435i	−0.165910	+	0.120540i
$550$	1.47923	−	1.07472i	0.0630745	−	0.0458263i
$551$	47.5923	+	34.5779i	2.02750	+	1.47307i
$552$	−10.1091			−0.430270
$553$	−18.4720			−0.785510
$554$	7.74331	+	5.62584i	0.328982	+	0.239019i
$555$	6.36480	+	19.5888i	0.270171	+	0.831500i
$556$	−1.10029	+	3.38635i	−0.0466628	+	0.143613i
$557$	−4.48260			−0.189934			−0.0949670	−	0.995480i	$-0.530275\pi$
$557$	−4.48260			−0.189934			−0.0949670	+	0.995480i	$0.530275\pi$
$558$	0.937884	+	2.69197i	0.0397038	+	0.113960i
$559$	−17.6120			−0.744907
$560$	1.12800	−	3.47162i	0.0476667	−	0.146703i
$561$	3.75284	+	11.5501i	0.158445	+	0.487644i
$562$	−4.13493	−	3.00421i	−0.174422	−	0.126725i
$563$	29.0236			1.22320			0.611599	−	0.791168i	$-0.290527\pi$
$563$	29.0236			1.22320			0.611599	+	0.791168i	$0.290527\pi$
$564$	−1.54018			−0.0648533
$565$	−11.6235	−	8.44497i	−0.489004	−	0.355282i
$566$	9.24020	−	6.71340i	0.388394	−	0.282185i
$567$	−30.3401	+	22.0434i	−1.27416	+	0.925735i
$568$	−0.582394	+	1.79242i	−0.0244367	+	0.0752085i
$569$	−14.1596	−	10.2875i	−0.593599	−	0.431275i	0.250002	−	0.968245i	$-0.419569\pi$
$569$	−14.1596	−	10.2875i	−0.593599	−	0.431275i	−0.843601	+	0.536970i	$0.819569\pi$
$570$	−3.80850	+	11.7213i	−0.159520	+	0.490953i
$571$	−6.46129	−	19.8858i	−0.270397	−	0.832195i	−0.990401	−	0.138225i	$-0.955860\pi$
$571$	−6.46129	−	19.8858i	−0.270397	−	0.832195i	0.720004	−	0.693970i	$-0.244140\pi$
$572$	9.21082	−	6.69205i	0.385124	−	0.279809i
$573$	−10.6684	−	32.8339i	−0.445679	−	1.37166i
$574$	−9.06778	−	27.9078i	−0.378482	−	1.16485i
$575$	4.36407	−	3.17068i	0.181994	−	0.132227i
$576$	0.158216	+	0.486937i	0.00659231	+	0.0202891i
$577$	−1.74749	+	5.37821i	−0.0727488	+	0.223898i	−0.980819	−	0.194920i	$-0.937555\pi$
$577$	−1.74749	+	5.37821i	−0.0727488	+	0.223898i	0.908070	+	0.418818i	$0.137555\pi$
$578$	−3.59069	−	2.60879i	−0.149353	−	0.108511i
$579$	−2.96233	+	9.11711i	−0.123110	+	0.378894i
$580$	−7.23674	+	5.25780i	−0.300489	+	0.218318i
$581$	7.95675	−	5.78092i	0.330102	−	0.239833i
$582$	−8.65434	−	6.28775i	−0.358734	−	0.260636i
$583$	7.52552			0.311675
$584$	15.8771			0.656997
$585$	−2.57921	−	1.87391i	−0.106637	−	0.0774766i
$586$	−0.921668	−	2.83660i	−0.0380738	−	0.117179i
$587$	−1.55667	+	4.79093i	−0.0642505	+	0.197743i	−0.978029	−	0.208471i	$-0.933151\pi$
$587$	−1.55667	+	4.79093i	−0.0642505	+	0.197743i	0.913778	+	0.406214i	$0.133151\pi$
$588$	−11.8524			−0.488786
$589$	−10.5782	+	35.0551i	−0.435866	+	1.44442i
$590$	−3.42351			−0.140944
$591$	−2.75187	+	8.46939i	−0.113197	+	0.348384i
$592$	3.39631	+	10.4528i	0.139588	+	0.429607i
$593$	−11.6704	−	8.47903i	−0.479245	−	0.348192i	0.321788	−	0.946812i	$-0.395716\pi$
$593$	−11.6704	−	8.47903i	−0.479245	−	0.348192i	−0.801033	+	0.598620i	$0.795716\pi$
$594$	−8.52522			−0.349794
$595$	−12.9375			−0.530385
$596$	−13.7871	−	10.0169i	−0.564743	−	0.410310i
$597$	12.7483	−	9.26217i	0.521752	−	0.379075i
$598$	27.1741	−	19.7431i	1.11123	−	0.807356i
$599$	−14.0869	+	43.3551i	−0.575577	+	1.77144i	0.0586309	+	0.998280i	$0.481326\pi$
$599$	−14.0869	+	43.3551i	−0.575577	+	1.77144i	−0.634208	+	0.773163i	$0.718674\pi$
$600$	−1.51612	−	1.10153i	−0.0618955	−	0.0449697i
$601$	−1.82772	+	5.62513i	−0.0745541	+	0.229454i	−0.981388	−	0.192033i	$-0.938492\pi$
$601$	−1.82772	+	5.62513i	−0.0745541	+	0.229454i	0.906834	+	0.421487i	$0.138492\pi$
$602$	3.19046	+	9.81924i	0.130034	+	0.400202i
$603$	0.0754729	−	0.0548343i	0.00307349	−	0.00223302i
$604$	−2.68382	−	8.25996i	−0.109203	−	0.336093i
$605$	2.36610	+	7.28210i	0.0961956	+	0.296060i
$606$	−22.8748	+	16.6195i	−0.929224	+	0.675120i
$607$	8.83223	+	27.1828i	0.358489	+	1.10332i	0.953959	+	0.299938i	$0.0969660\pi$
$607$	8.83223	+	27.1828i	0.358489	+	1.10332i	−0.595470	+	0.803378i	$0.703034\pi$
$608$	−2.03225	+	6.25461i	−0.0824185	+	0.253658i
$609$	49.5047	+	35.9673i	2.00603	+	1.45747i
$610$	2.90012	−	8.92565i	0.117422	−	0.361389i
$611$	4.14015	−	3.00799i	0.167492	−	0.121690i
$612$	1.46807	−	1.06662i	0.0593434	−	0.0431155i
$613$	−37.7359	−	27.4167i	−1.52414	−	1.10735i	−0.959389	−	0.282088i	$-0.908973\pi$
$613$	−37.7359	−	27.4167i	−1.52414	−	1.10735i	−0.564749	−	0.825263i	$-0.691027\pi$
$614$	−26.2475			−1.05926
$615$	−15.0650			−0.607480
$616$	−5.39960	−	3.92304i	−0.217556	−	0.158064i
$617$	−7.33953	−	22.5888i	−0.295478	−	0.909389i	−0.983060	−	0.183282i	$-0.941328\pi$
$617$	−7.33953	−	22.5888i	−0.295478	−	0.909389i	0.687582	−	0.726107i	$-0.258672\pi$
$618$	2.98413	−	9.18421i	0.120039	−	0.369443i
$619$	−2.98958			−0.120161			−0.0600806	−	0.998194i	$-0.519136\pi$
$619$	−2.98958			−0.120161			−0.0600806	+	0.998194i	$0.519136\pi$
$620$	−4.57243	−	3.17693i	−0.183633	−	0.127589i
$621$	−25.1514			−1.00929
$622$	−3.32204	+	10.2242i	−0.133202	+	0.409953i
$623$	−11.4556	−	35.2568i	−0.458960	−	1.41253i
$624$	−9.44056	−	6.85897i	−0.377925	−	0.274578i
$625$	1.00000			0.0400000
$626$	−1.49090			−0.0595882
$627$	18.2308	+	13.2455i	0.728069	+	0.528973i
$628$	8.40695	−	6.10801i	0.335474	−	0.243736i
$629$	31.5142	−	22.8964i	1.25655	−	0.912941i
$630$	−0.577531	+	1.77746i	−0.0230094	+	0.0708156i
$631$	−39.0903	−	28.4008i	−1.55616	−	1.13062i	−0.939071	−	0.343725i	$-0.888311\pi$
$631$	−39.0903	−	28.4008i	−1.55616	−	1.13062i	−0.617090	−	0.786892i	$-0.711689\pi$
$632$	−1.56376	+	4.81276i	−0.0622030	+	0.191441i
$633$	6.46699	+	19.9034i	0.257040	+	0.791088i
$634$	−11.2847	+	8.19881i	−0.448172	+	0.325616i
$635$	−0.509965	−	1.56951i	−0.0202373	−	0.0622841i
$636$	−2.38352	−	7.33571i	−0.0945126	−	0.290880i
$637$	31.8604	−	23.1479i	1.26235	−	0.917153i
$638$	5.05412	+	15.5550i	0.200094	+	0.615827i
$639$	0.298184	−	0.917715i	0.0117960	−	0.0363042i
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	−6.53277	+	20.1058i	−0.258029	+	0.794131i	0.735189	+	0.677862i	$0.237093\pi$
$641$	−6.53277	+	20.1058i	−0.258029	+	0.794131i	−0.993218	+	0.116269i	$0.962907\pi$
$642$	−22.4336	+	16.2990i	−0.885384	+	0.643269i
$643$	17.8984	−	13.0040i	0.705845	−	0.512827i	−0.175985	−	0.984393i	$-0.556311\pi$
$643$	17.8984	−	13.0040i	0.705845	−	0.512827i	0.881831	+	0.471566i	$0.156311\pi$
$644$	−15.9301	−	11.5739i	−0.627733	−	0.456075i
$645$	5.30056			0.208709
$646$	23.3087			0.917068
$647$	21.4238	+	15.5653i	0.842255	+	0.611934i	0.923000	−	0.384801i	$-0.125730\pi$
$647$	21.4238	+	15.5653i	0.842255	+	0.611934i	−0.0807448	+	0.996735i	$0.525730\pi$
$648$	3.17479	+	9.77101i	0.124718	+	0.383842i
$649$	−1.93433	+	5.95327i	−0.0759293	+	0.233686i
$650$	6.22677			0.244234
$651$	−11.0032	+	36.4637i	−0.431250	+	1.42912i
$652$	6.37790			0.249778
$653$	13.9300	−	42.8722i	0.545123	−	1.67772i	−0.175573	−	0.984466i	$-0.556178\pi$
$653$	13.9300	−	42.8722i	0.545123	−	1.67772i	0.720697	−	0.693251i	$-0.243822\pi$
$654$	7.93460	+	24.4202i	0.310267	+	0.954905i
$655$	0.636603	+	0.462519i	0.0248741	+	0.0180721i
$656$	−8.03882			−0.313863
$657$	−8.12899			−0.317142
$658$	−2.42705	−	1.76336i	−0.0946163	−	0.0687428i
$659$	8.55519	−	6.21571i	0.333263	−	0.242130i	−0.408551	−	0.912735i	$-0.633966\pi$
$659$	8.55519	−	6.21571i	0.333263	−	0.242130i	0.741814	+	0.670606i	$0.233966\pi$
$660$	−2.77212	+	2.01406i	−0.107905	+	0.0783974i
$661$	−8.27708	+	25.4742i	−0.321941	+	0.990833i	0.650861	+	0.759197i	$0.274408\pi$
$661$	−8.27708	+	25.4742i	−0.321941	+	0.990833i	−0.972802	+	0.231636i	$0.925592\pi$
$662$	−14.5224	−	10.5512i	−0.564430	−	0.410083i
$663$	−12.7804	+	39.3342i	−0.496351	+	1.52761i
$664$	−0.832595	−	2.56246i	−0.0323110	−	0.0994429i
$665$	−19.4213	+	14.1104i	−0.753126	+	0.547178i
$666$	−1.73890	−	5.35178i	−0.0673810	−	0.207377i
$667$	14.9108	+	45.8908i	0.577349	+	1.77690i
$668$	−5.00000	+	3.63271i	−0.193456	+	0.140554i
$669$	1.07801	+	3.31778i	0.0416783	+	0.128273i
$670$	−0.0563053	+	0.173290i	−0.00217526	+	0.00669477i
$671$	−13.8825	−	10.0863i	−0.535930	−	0.389376i
$672$	−2.11391	+	6.50593i	−0.0815457	+	0.250972i
$673$	−14.1733	+	10.2975i	−0.546341	+	0.396940i	−0.826435	−	0.563033i	$-0.809635\pi$
$673$	−14.1733	+	10.2975i	−0.546341	+	0.396940i	0.280093	+	0.959973i	$0.409635\pi$
$674$	−17.6227	+	12.8036i	−0.678800	+	0.493177i
$675$	−3.77212	−	2.74061i	−0.145189	−	0.105486i
$676$	25.7727			0.991258
$677$	−8.94187			−0.343664			−0.171832	−	0.985126i	$-0.554969\pi$
$677$	−8.94187			−0.343664			−0.171832	+	0.985126i	$0.554969\pi$
$678$	21.7828	+	15.8261i	0.836564	+	0.607799i
$679$	−6.43885	−	19.8167i	−0.247100	−	0.760497i
$680$	−1.09523	+	3.37078i	−0.0420002	+	0.129263i
$681$	−5.62306			−0.215476
$682$	−8.10798	+	6.15615i	−0.310470	+	0.235731i
$683$	−36.6619			−1.40283			−0.701415	−	0.712754i	$-0.747448\pi$
$683$	−36.6619			−1.40283			−0.701415	+	0.712754i	$0.747448\pi$
$684$	1.04050	−	3.20234i	0.0397846	−	0.122444i
$685$	4.76551	+	14.6667i	0.182081	+	0.560387i
$686$	1.99468	+	1.44922i	0.0761573	+	0.0553315i
$687$	−28.4330			−1.08479
$688$	2.82843			0.107833
$689$	20.7338	+	15.0640i	0.789896	+	0.573893i
$690$	−8.17840	+	5.94196i	−0.311346	+	0.226206i
$691$	33.7120	−	24.4932i	1.28247	−	0.931766i	0.282842	−	0.959167i	$-0.408723\pi$
$691$	33.7120	−	24.4932i	1.28247	−	0.931766i	0.999625	+	0.0274004i	$0.00872292\pi$
$692$	3.96623	−	12.2068i	0.150774	−	0.464033i
$693$	2.76457	+	2.00858i	0.105018	+	0.0762997i
$694$	4.58887	−	14.1231i	0.174191	−	0.536106i
$695$	1.10029	+	3.38635i	0.0417365	+	0.128452i
$696$	13.5619	−	9.85328i	0.514062	−	0.373488i
$697$	8.80437	+	27.0971i	0.333489	+	1.02637i
$698$	0.237620	+	0.731318i	0.00899403	+	0.0276808i
$699$	34.6074	−	25.1437i	1.30897	−	0.951023i
$700$	−1.12800	−	3.47162i	−0.0426344	−	0.131215i
$701$	2.27567	−	7.00380i	0.0859510	−	0.264530i	−0.898839	−	0.438279i	$-0.855588\pi$
$701$	2.27567	−	7.00380i	0.0859510	−	0.264530i	0.984790	+	0.173749i	$0.0555882\pi$
$702$	−23.4881	−	17.0651i	−0.886503	−	0.644082i
$703$	22.3358	−	68.7426i	0.842412	−	2.59268i
$704$	−1.47923	+	1.07472i	−0.0557505	+	0.0405051i
$705$	−1.24603	+	0.905296i	−0.0469283	+	0.0340954i
$706$	1.56173	+	1.13466i	0.0587764	+	0.0427036i
$707$	−55.0742			−2.07128
$708$	6.41577			0.241119
$709$	−5.41887	−	3.93704i	−0.203510	−	0.147859i	0.481362	−	0.876522i	$-0.340142\pi$
$709$	−5.41887	−	3.93704i	−0.203510	−	0.147859i	−0.684872	+	0.728663i	$0.740142\pi$
$710$	0.582394	+	1.79242i	0.0218569	+	0.0672685i
$711$	0.800639	−	2.46411i	0.0300263	−	0.0924115i
$712$	−10.1557			−0.380601
$713$	−23.9204	+	18.1621i	−0.895826	+	0.680175i
$714$	24.2453			0.907356
$715$	3.51822	−	10.8280i	0.131574	−	0.404943i
$716$	−4.36204	−	13.4250i	−0.163017	−	0.501715i
$717$	−30.4100	−	22.0941i	−1.13568	−	0.825121i
$718$	1.21779			0.0454477
$719$	−30.5639			−1.13984			−0.569920	−	0.821700i	$-0.693026\pi$
$719$	−30.5639			−1.13984			−0.569920	+	0.821700i	$0.693026\pi$
$720$	0.414214	+	0.300944i	0.0154368	+	0.0112155i
$721$	15.2175	−	11.0561i	0.566728	−	0.411752i
$722$	19.6189	−	14.2539i	0.730138	−	0.530476i
$723$	−0.254667	+	0.783784i	−0.00947116	+	0.0291492i
$724$	−1.78513	−	1.29697i	−0.0663439	−	0.0482016i
$725$	−2.76419	+	8.50730i	−0.102659	+	0.315953i
$726$	−4.43414	−	13.6469i	−0.164567	−	0.506484i
$727$	11.5620	−	8.40026i	0.428809	−	0.311548i	−0.352363	−	0.935863i	$-0.614622\pi$
$727$	11.5620	−	8.40026i	0.428809	−	0.311548i	0.781173	+	0.624315i	$0.214622\pi$
$728$	−7.02379	−	21.6170i	−0.260319	−	0.801180i
$729$	6.47496	+	19.9279i	0.239813	+	0.738070i
$730$	12.8448	−	9.33230i	0.475408	−	0.345404i
$731$	−3.09778	−	9.53399i	−0.114576	−	0.352628i
$732$	−5.43492	+	16.7270i	−0.200880	+	0.618246i
$733$	21.4403	+	15.5773i	0.791916	+	0.575361i	0.908531	−	0.417816i	$-0.137204\pi$
$733$	21.4403	+	15.5773i	0.791916	+	0.575361i	−0.116615	+	0.993177i	$0.537204\pi$
$734$	−7.33938	+	22.5883i	−0.270902	+	0.833749i
$735$	−9.58881	+	6.96668i	−0.353689	+	0.256970i
$736$	−4.36407	+	3.17068i	−0.160862	+	0.116873i
$737$	0.269527	+	0.195823i	0.00992815	+	0.00721322i
$738$	4.11584			0.151506
$739$	−45.6940			−1.68088			−0.840440	−	0.541905i	$-0.817703\pi$
$739$	−45.6940			−1.68088			−0.840440	+	0.541905i	$0.817703\pi$
$740$	8.89167	+	6.46017i	0.326864	+	0.237481i
$741$	23.7146	+	72.9862i	0.871179	+	2.68121i
$742$	4.64267	−	14.2887i	0.170438	−	0.524553i
$743$	18.3304			0.672478			0.336239	−	0.941777i	$-0.390845\pi$
$743$	18.3304			0.672478			0.336239	+	0.941777i	$0.390845\pi$
$744$	8.56888	+	5.95367i	0.314150	+	0.218272i
$745$	−17.0418			−0.624365
$746$	−6.87502	+	21.1591i	−0.251712	+	0.774691i
$747$	0.426286	+	1.31197i	0.0155970	+	0.0480025i
$748$	5.24275	+	3.80908i	0.191694	+	0.139274i
$749$	−54.0121			−1.97356
$750$	−1.87403			−0.0684300
$751$	33.3000	+	24.1939i	1.21514	+	0.882848i	0.995687	−	0.0927764i	$-0.0295742\pi$
$751$	33.3000	+	24.1939i	1.21514	+	0.882848i	0.219449	+	0.975624i	$0.429574\pi$
$752$	−0.664894	+	0.483074i	−0.0242462	+	0.0176159i
$753$	−5.13161	+	3.72833i	−0.187006	+	0.135868i
$754$	−17.2120	+	52.9730i	−0.626823	+	1.92916i
$755$	−7.02634	−	5.10494i	−0.255715	−	0.185788i
$756$	−5.25941	+	16.1868i	−0.191283	+	0.588708i
$757$	−2.96843	−	9.13588i	−0.107889	−	0.332049i	0.882508	−	0.470297i	$-0.155853\pi$
$757$	−2.96843	−	9.13588i	−0.107889	−	0.332049i	−0.990398	+	0.138247i	$0.955853\pi$
$758$	27.8708	−	20.2493i	1.01231	−	0.735489i
$759$	5.71177	+	17.5790i	0.207324	+	0.638078i
$760$	2.03225	+	6.25461i	0.0737174	+	0.226879i
$761$	26.8533	−	19.5100i	0.973430	−	0.707238i	0.0171990	−	0.999852i	$-0.494525\pi$
$761$	26.8533	−	19.5100i	0.973430	−	0.707238i	0.956231	+	0.292614i	$0.0945251\pi$
$762$	0.955691	+	2.94131i	0.0346210	+	0.106553i
$763$	−15.4552	+	47.5662i	−0.559515	+	1.72201i
$764$	−14.9038	−	10.8283i	−0.539201	−	0.391752i
$765$	0.560754	−	1.72582i	0.0202741	−	0.0623973i
$766$	17.6436	−	12.8188i	0.637489	−	0.463163i
$767$	−17.2461	+	12.5301i	−0.622722	+	0.452434i
$768$	1.51612	+	1.10153i	0.0547084	+	0.0397480i
$769$	6.43665			0.232112			0.116056	−	0.993243i	$-0.462975\pi$
$769$	6.43665			0.232112			0.116056	+	0.993243i	$0.462975\pi$
$770$	−6.67427			−0.240524
$771$	−26.0685	−	18.9399i	−0.938836	−	0.682104i
$772$	1.58072	+	4.86497i	0.0568915	+	0.175094i
$773$	12.5320	−	38.5696i	0.450745	−	1.38725i	−0.425314	−	0.905046i	$-0.639836\pi$
$773$	12.5320	−	38.5696i	0.450745	−	1.38725i	0.876059	−	0.482205i	$-0.160164\pi$
$774$	−1.44814			−0.0520525
$775$	−5.56653	+	0.117415i	−0.199956	+	0.00421767i
$776$	−5.70820			−0.204913
$777$	23.2333	−	71.5048i	0.833491	−	2.56522i
$778$	4.60410	+	14.1700i	0.165065	+	0.508018i
$779$	42.7705	+	31.0746i	1.53241	+	1.11336i
$780$	−11.6692			−0.417823
$781$	3.44598			0.123307
$782$	15.4673	+	11.2377i	0.553110	+	0.401858i
$783$	33.7420	−	24.5150i	1.20584	−	0.876095i
$784$	−5.11667	+	3.71748i	−0.182738	+	0.132767i
$785$	3.21117	−	9.88296i	0.114612	−	0.352738i
$786$	−1.19301	−	0.866775i	−0.0425534	−	0.0309169i
$787$	−14.3376	+	44.1265i	−0.511079	+	1.57294i	0.279227	+	0.960225i	$0.409922\pi$
$787$	−14.3376	+	44.1265i	−0.511079	+	1.57294i	−0.790305	+	0.612713i	$0.790078\pi$
$788$	1.46842	+	4.51934i	0.0523104	+	0.160995i
$789$	−31.8334	+	23.1283i	−1.13330	+	0.823390i
$790$	1.56376	+	4.81276i	0.0556361	+	0.171230i
$791$	16.2065	+	49.8783i	0.576235	+	1.77347i
$792$	0.757359	−	0.550254i	0.0269116	−	0.0195524i
$793$	−18.0584	−	55.5780i	−0.641272	−	1.97363i
$794$	4.93727	−	15.1954i	0.175217	−	0.539263i
$795$	−6.24013	−	4.53372i	−0.221315	−	0.160794i
$796$	2.59836	−	7.99693i	0.0920964	−	0.283444i
$797$	−10.2183	+	7.42403i	−0.361951	+	0.262973i	−0.753865	−	0.657029i	$-0.771813\pi$
$797$	−10.2183	+	7.42403i	−0.361951	+	0.262973i	0.391914	+	0.920002i	$0.371813\pi$
$798$	36.3961	−	26.4433i	1.28841	−	0.936084i
$799$	2.35655	+	1.71213i	0.0833686	+	0.0605709i
$800$	−1.00000			−0.0353553
$801$	5.19968			0.183722
$802$	−27.3961	−	19.9045i	−0.967391	−	0.702851i
$803$	−8.97077	−	27.6092i	−0.316572	−	0.974308i
$804$	0.105518	−	0.324751i	0.00372133	−	0.0114531i
$805$	−19.6907			−0.694004
$806$	−34.6615	+	0.731116i	−1.22090	+	0.0257525i
$807$	13.7635			0.484497
$808$	−4.66234	+	14.3492i	−0.164021	+	0.504804i
$809$	0.765212	+	2.35508i	0.0269034	+	0.0828003i	0.963607	−	0.267324i	$-0.0861394\pi$
$809$	0.765212	+	2.35508i	0.0269034	+	0.0828003i	−0.936703	+	0.350124i	$0.886139\pi$
$810$	8.31172	+	6.03882i	0.292044	+	0.212182i
$811$	−17.4043			−0.611147			−0.305573	−	0.952169i	$-0.598848\pi$
$811$	−17.4043			−0.611147			−0.305573	+	0.952169i	$0.598848\pi$
$812$	32.6521			1.14587
$813$	−2.26706	−	1.64712i	−0.0795093	−	0.0577669i
$814$	16.2578	−	11.8120i	0.569834	−	0.414009i
$815$	5.15983	−	3.74884i	0.180741	−	0.131316i
$816$	2.05250	−	6.31694i	0.0718518	−	0.221137i
$817$	−15.0486	−	10.9335i	−0.526485	−	0.382514i
$818$	−6.91421	+	21.2798i	−0.241750	+	0.744029i
$819$	3.59616	+	11.0678i	0.125660	+	0.386741i
$820$	−6.50354	+	4.72510i	−0.227114	+	0.165008i
$821$	0.600130	+	1.84701i	0.0209447	+	0.0644611i	0.960983	−	0.276609i	$-0.0892107\pi$
$821$	0.600130	+	1.84701i	0.0209447	+	0.0644611i	−0.940038	+	0.341070i	$0.889211\pi$
$822$	−8.93072	−	27.4859i	−0.311494	−	0.958681i
$823$	33.0122	−	23.9848i	1.15073	−	0.836057i	0.162155	−	0.986765i	$-0.448155\pi$
$823$	33.0122	−	23.9848i	1.15073	−	0.836057i	0.988578	+	0.150708i	$0.0481554\pi$
$824$	−1.59236	−	4.90078i	−0.0554725	−	0.170727i
$825$	−1.05886	+	3.25882i	−0.0368646	+	0.113458i
$826$	10.1101	+	7.34542i	0.351775	+	0.255580i
$827$	7.86323	−	24.2005i	0.273431	−	0.841535i	−0.716199	−	0.697896i	$-0.754120\pi$
$827$	7.86323	−	24.2005i	0.273431	−	0.841535i	0.989630	−	0.143639i	$-0.0458803\pi$
$828$	2.23439	−	1.62338i	0.0776503	−	0.0564162i
$829$	−33.7217	+	24.5003i	−1.17120	+	0.850929i	−0.991152	−	0.132728i	$-0.957626\pi$
$829$	−33.7217	+	24.5003i	−1.17120	+	0.850929i	−0.180051	+	0.983657i	$0.557626\pi$
$830$	−2.17976	−	1.58369i	−0.0756607	−	0.0549707i
$831$	−17.9368			−0.622222
$832$	−6.22677			−0.215875
$833$	18.1347	+	13.1757i	0.628331	+	0.456509i
$834$	−2.06198	−	6.34614i	−0.0714007	−	0.219749i
$835$	−1.90983	+	5.87785i	−0.0660924	+	0.203411i
$836$	12.0246			0.415881
$837$	21.3194	+	14.8128i	0.736906	+	0.512004i
$838$	−19.7399			−0.681905
$839$	−9.06758	+	27.9071i	−0.313048	+	0.963461i	0.663503	+	0.748174i	$0.269069\pi$
$839$	−9.06758	+	27.9071i	−0.313048	+	0.963461i	−0.976551	+	0.215288i	$0.930931\pi$
$840$	2.11391	+	6.50593i	0.0729367	+	0.224476i
$841$	−41.2718	−	29.9858i	−1.42317	−	1.03399i
$842$	8.08830			0.278741
$843$	9.57829			0.329894
$844$	9.03443	+	6.56390i	0.310978	+	0.225939i
$845$	20.8506	−	15.1488i	0.717281	−	0.521135i
$846$	0.340423	−	0.247332i	0.0117040	−	0.00850345i
$847$	8.63692	−	26.5817i	0.296768	−	0.913359i
$848$	−3.32979	−	2.41923i	−0.114345	−	0.0830768i
$849$	−6.61428	+	20.3567i	−0.227002	+	0.698639i
$850$	1.09523	+	3.37078i	0.0375661	+	0.115617i
$851$	47.9642	−	34.8480i	1.64419	−	1.19457i
$852$	−1.09143	−	3.35906i	−0.0373916	−	0.115080i
$853$	−16.5273	−	50.8658i	−0.565884	−	1.74161i	−0.665310	−	0.746567i	$-0.731701\pi$
$853$	−16.5273	−	50.8658i	−0.565884	−	1.74161i	0.0994259	−	0.995045i	$-0.468299\pi$
$854$	−27.7152	+	20.1363i	−0.948394	+	0.689049i
$855$	−1.04050	−	3.20234i	−0.0355844	−	0.109518i
$856$	−4.57243	+	14.0725i	−0.156282	+	0.480988i
$857$	−16.6880	−	12.1245i	−0.570051	−	0.414166i	0.265073	−	0.964228i	$-0.414604\pi$
$857$	−16.6880	−	12.1245i	−0.570051	−	0.414166i	−0.835124	+	0.550062i	$0.814604\pi$
$858$	−6.59326	+	20.2920i	−0.225090	+	0.692756i
$859$	−35.4410	+	25.7494i	−1.20923	+	0.878558i	−0.995161	−	0.0982600i	$-0.968672\pi$
$859$	−35.4410	+	25.7494i	−1.20923	+	0.878558i	−0.214071	+	0.976818i	$0.568672\pi$
$860$	2.28825	−	1.66251i	0.0780285	−	0.0566910i
$861$	44.4891	+	32.3232i	1.51618	+	1.10157i
$862$	32.8863			1.12011
$863$	−40.1113			−1.36540			−0.682701	−	0.730697i	$-0.739195\pi$
$863$	−40.1113			−1.36540			−0.682701	+	0.730697i	$0.739195\pi$
$864$	3.77212	+	2.74061i	0.128330	+	0.0932373i
$865$	−3.96623	−	12.2068i	−0.134856	−	0.415044i
$866$	2.32813	−	7.16525i	0.0791131	−	0.243485i
$867$	8.31759			0.282480
$868$	6.68666	+	19.1924i	0.226960	+	0.651434i
$869$	9.25263			0.313874
$870$	5.18018	−	15.9429i	0.175624	−	0.540516i
$871$	0.350600	+	1.07904i	0.0118796	+	0.0365618i
$872$	11.0847	+	8.05349i	0.375375	+	0.272726i
$873$	2.92258			0.0989143
$874$	35.4755			1.19998
$875$	−2.95314	−	2.14558i	−0.0998343	−	0.0725339i
$876$	−24.0716	+	17.4890i	−0.813303	+	0.590899i
$877$	−4.07387	+	2.95984i	−0.137565	+	0.0999468i	−0.654440	−	0.756114i	$-0.727095\pi$
$877$	−4.07387	+	2.95984i	−0.137565	+	0.0999468i	0.516875	+	0.856061i	$0.327095\pi$
$878$	3.17444	−	9.76991i	0.107132	−	0.329719i
$879$	4.52196	+	3.28540i	0.152522	+	0.110814i
$880$	−0.565015	+	1.73894i	−0.0190467	+	0.0586196i
$881$	−6.41078	−	19.7304i	−0.215985	−	0.664733i	−0.999082	−	0.0428336i	$-0.986361\pi$
$881$	−6.41078	−	19.7304i	−0.215985	−	0.664733i	0.783098	−	0.621899i	$-0.213639\pi$
$882$	2.61972	−	1.90334i	0.0882104	−	0.0640886i
$883$	−12.5728	−	38.6952i	−0.423110	−	1.30220i	−0.904793	−	0.425852i	$-0.859974\pi$
$883$	−12.5728	−	38.6952i	−0.423110	−	1.30220i	0.481683	−	0.876345i	$-0.340026\pi$
$884$	6.81976	+	20.9891i	0.229373	+	0.705938i
$885$	5.19046	−	3.77109i	0.174476	−	0.126764i
$886$	1.41941	+	4.36848i	0.0476859	+	0.146762i
$887$	16.2555	−	50.0294i	0.545807	−	1.67982i	−0.173256	−	0.984877i	$-0.555429\pi$
$887$	16.2555	−	50.0294i	0.545807	−	1.67982i	0.719063	−	0.694944i	$-0.244571\pi$
$888$	−16.6633	−	12.1066i	−0.559183	−	0.406270i
$889$	−1.86152	+	5.72916i	−0.0624332	+	0.192150i
$890$	−8.21614	+	5.96937i	−0.275406	+	0.200094i
$891$	15.1974	−	11.0415i	0.509131	−	0.369905i
$892$	1.50599	+	1.09416i	0.0504242	+	0.0366353i
$893$	5.40492			0.180869
$894$	31.9370			1.06813
$895$	−11.4200	−	8.29709i	−0.381727	−	0.277341i
$896$	1.12800	+	3.47162i	0.0376838	+	0.115979i
$897$	−19.4516	+	59.8660i	−0.649471	+	1.99887i
$898$	15.2141			0.507702
$899$	14.3880	−	47.6806i	0.479868	−	1.59024i
$900$	0.511996			0.0170665
$901$	−4.50780	+	13.8736i	−0.150177	+	0.462196i
$902$	4.54205	+	13.9790i	0.151234	+	0.465450i
$903$	−15.6533	−	11.3728i	−0.520909	−	0.378463i
$904$	14.3674			0.477854
$905$	−2.20654			−0.0733480
$906$	13.1676	+	9.56682i	0.437464	+	0.317836i
$907$	−2.35134	+	1.70835i	−0.0780748	+	0.0567247i	−0.626138	−	0.779712i	$-0.715365\pi$
$907$	−2.35134	+	1.70835i	−0.0780748	+	0.0567247i	0.548063	+	0.836437i	$0.315365\pi$
$908$	−2.42746	+	1.76366i	−0.0805583	+	0.0585290i
$909$	2.38710	−	7.34674i	0.0791752	−	0.243676i
$910$	−18.3885	−	13.3600i	−0.609574	−	0.442881i
$911$	6.30722	−	19.4116i	0.208967	−	0.643136i	−0.790560	−	0.612385i	$-0.790210\pi$
$911$	6.30722	−	19.4116i	0.208967	−	0.643136i	0.999527	−	0.0307506i	$-0.00978975\pi$
$912$	−3.80850	−	11.7213i	−0.126112	−	0.388133i
$913$	−3.98554	+	2.89566i	−0.131902	+	0.0958324i
$914$	−8.79269	−	27.0611i	−0.290836	−	0.895103i
$915$	5.43492	+	16.7270i	0.179673	+	0.552976i
$916$	−12.2745	+	8.91793i	−0.405560	+	0.294657i
$917$	−0.887605	−	2.73177i	−0.0293113	−	0.0902109i
$918$	5.10663	−	15.7166i	0.168544	−	0.518724i
$919$	30.4959	+	22.1566i	1.00597	+	0.730879i	0.963360	−	0.268213i	$-0.0864331\pi$
$919$	30.4959	+	22.1566i	1.00597	+	0.730879i	0.0426087	+	0.999092i	$0.486433\pi$
$920$	−1.66693	+	5.13027i	−0.0549569	+	0.169140i
$921$	39.7945	−	28.9124i	1.31127	−	0.952695i
$922$	4.80342	−	3.48989i	0.158192	−	0.114933i
$923$	9.49413	+	6.89789i	0.312503	+	0.227047i
$924$	12.5078			0.411477
$925$	10.9907			0.361372
$926$	−31.8439	−	23.1359i	−1.04645	−	0.760293i
$927$	0.815282	+	2.50918i	0.0267774	+	0.0824123i
$928$	2.76419	−	8.50730i	0.0907389	−	0.279266i
$929$	−53.0190			−1.73950			−0.869748	−	0.493497i	$-0.835719\pi$
$929$	−53.0190			−1.73950			−0.869748	+	0.493497i	$0.835719\pi$
$930$	10.4318	−	0.220039i	0.342074	−	0.00721538i
$931$	41.5934			1.36317
$932$	7.05369	−	21.7090i	0.231051	−	0.711103i
$933$	−6.22562	−	19.1605i	−0.203818	−	0.627286i
$934$	15.8515	+	11.5168i	0.518676	+	0.376840i
$935$	6.48039			0.211931
$936$	3.18808			0.104206
$937$	−20.1962	−	14.6734i	−0.659780	−	0.479358i	0.206809	−	0.978381i	$-0.433692\pi$
$937$	−20.1962	−	14.6734i	−0.659780	−	0.479358i	−0.866589	+	0.499023i	$0.833692\pi$
$938$	0.538085	−	0.390942i	0.0175691	−	0.0127647i
$939$	2.26038	−	1.64226i	0.0737648	−	0.0535932i
$940$	−0.253967	+	0.781630i	−0.00828349	+	0.0254940i
$941$	12.1036	+	8.79376i	0.394565	+	0.286668i	0.767324	−	0.641260i	$-0.221588\pi$
$941$	12.1036	+	8.79376i	0.394565	+	0.286668i	−0.372758	+	0.927928i	$0.621588\pi$
$942$	−6.01783	+	18.5210i	−0.196072	+	0.603446i
$943$	13.4001	+	41.2413i	0.436368	+	1.34300i
$944$	2.76968	−	2.01229i	0.0901453	−	0.0654944i
$945$	5.25941	+	16.1868i	0.171089	+	0.526556i
$946$	−1.59810	−	4.91846i	−0.0519588	−	0.159913i
$947$	8.00574	−	5.81651i	0.260152	−	0.189011i	−0.450062	−	0.892997i	$-0.648598\pi$
$947$	8.00574	−	5.81651i	0.260152	−	0.189011i	0.710214	+	0.703986i	$0.248598\pi$
$948$	−2.93054	−	9.01926i	−0.0951794	−	0.292932i
$949$	30.5503	−	94.0241i	0.991704	−	3.05215i
$950$	5.32049	+	3.86556i	0.172620	+	0.125415i
$951$	8.07777	−	24.8608i	0.261940	−	0.806167i
$952$	10.4666	−	7.60446i	0.339226	−	0.246462i
$953$	−14.9427	+	10.8565i	−0.484040	+	0.351676i	−0.802888	−	0.596130i	$-0.796704\pi$
$953$	−14.9427	+	10.8565i	−0.484040	+	0.351676i	0.318848	+	0.947806i	$0.396704\pi$
$954$	1.70484	+	1.23864i	0.0551962	+	0.0401024i
$955$	−18.4221			−0.596126
$956$	−20.0577			−0.648713
$957$	−24.7969	−	18.0160i	−0.801570	−	0.582375i
$958$	2.33046	+	7.17241i	0.0752937	+	0.231730i
$959$	17.3954	−	53.5377i	0.561728	−	1.72882i
$960$	1.87403			0.0604841
$961$	30.9724	−	1.30719i	0.999111	−	0.0421673i
$962$	68.4366			2.20649
$963$	2.34107	−	7.20506i	0.0754398	−	0.232180i
$964$	0.135893	+	0.418234i	0.00437680	+	0.0134704i
$965$	4.13839	+	3.00672i	0.133220	+	0.0967897i
$966$	36.9009			1.18727
$967$	−39.4622			−1.26902			−0.634510	−	0.772915i	$-0.718798\pi$
$967$	−39.4622			−1.26902			−0.634510	+	0.772915i	$0.718798\pi$
$968$	−6.19453	−	4.50059i	−0.199100	−	0.144654i
$969$	−35.3389	+	25.6752i	−1.13525	+	0.824806i
$970$	−4.61803	+	3.35520i	−0.148276	+	0.107729i
$971$	−11.4029	+	35.0944i	−0.365935	+	1.12623i	0.583458	+	0.812143i	$0.301699\pi$
$971$	−11.4029	+	35.0944i	−0.365935	+	1.12623i	−0.949393	+	0.314089i	$0.898301\pi$
$972$	−4.26006	−	3.09511i	−0.136641	−	0.0992759i
$973$	4.01638	−	12.3611i	0.128759	−	0.396280i
$974$	0.261479	+	0.804749i	0.00837832	+	0.0257858i
$975$	−9.44056	+	6.85897i	−0.302340	+	0.219663i
$976$	2.90012	+	8.92565i	0.0928306	+	0.285703i
$977$	−10.8631	−	33.4330i	−0.347540	−	1.06962i	−0.960210	−	0.279279i	$-0.909905\pi$
$977$	−10.8631	−	33.4330i	−0.347540	−	1.06962i	0.612670	−	0.790339i	$-0.290095\pi$
$978$	−9.66969	+	7.02544i	−0.309203	+	0.224649i
$979$	5.73813	+	17.6601i	0.183391	+	0.564420i
$980$	−1.95440	+	6.01501i	−0.0624309	+	0.192142i
$981$	−5.67531	−	4.12336i	−0.181199	−	0.131649i
$982$	−0.962849	+	2.96334i	−0.0307257	+	0.0945641i
$983$	27.0782	−	19.6734i	0.863659	−	0.627485i	−0.0652190	−	0.997871i	$-0.520775\pi$
$983$	27.0782	−	19.6734i	0.863659	−	0.627485i	0.928878	+	0.370386i	$0.120775\pi$
$984$	12.1878	−	8.85499i	0.388534	−	0.282287i
$985$	3.84438	+	2.79311i	0.122492	+	0.0889957i
$986$	−31.7036			−1.00965
$987$	5.62210			0.178953
$988$	33.1295	+	24.0700i	1.05399	+	0.765768i
$989$	−4.71478	−	14.5106i	−0.149921	−	0.461410i
$990$	0.289286	−	0.890329i	0.00919410	−	0.0282965i
$991$	−11.8203			−0.375483			−0.187741	−	0.982218i	$-0.560117\pi$
$991$	−11.8203			−0.375483			−0.187741	+	0.982218i	$0.560117\pi$
$992$	5.56653	−	0.117415i	0.176737	−	0.00372793i
$993$	33.6402			1.06754
$994$	2.12590	−	6.54285i	0.0674295	−	0.207527i
$995$	−2.59836	−	7.99693i	−0.0823735	−	0.253520i
$996$	4.08495	+	2.96789i	0.129436	+	0.0940411i
$997$	56.2299			1.78082			0.890410	−	0.455159i	$-0.150418\pi$
$997$	56.2299			1.78082			0.890410	+	0.455159i	$0.150418\pi$
$998$	−13.6109			−0.430847
$999$	−41.4583	−	30.1212i	−1.31168	−	0.952993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.h.e.101.1	✓	8
31.2	even	5		9610.2.a.ba.1.2		4
31.4	even	5	inner	310.2.h.e.221.1	yes	8
31.29	odd	10		9610.2.a.bh.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.h.e.101.1	✓	8	1.1	even	1	trivial
310.2.h.e.221.1	yes	8	31.4	even	5	inner
9610.2.a.ba.1.2		4	31.2	even	5
9610.2.a.bh.1.3		4	31.29	odd	10

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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.579108 - 1.78231i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} +1.87403 q^{6} +(2.95314 + 2.14558i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.414214 + 0.300944i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.579108 - 1.78231i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} +1.87403 q^{6} +(2.95314 + 2.14558i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.414214 + 0.300944i) q^{9} +(0.309017 - 0.951057i) q^{10} +(-1.47923 - 1.07472i) q^{11} +(-0.579108 + 1.78231i) q^{12} +(-1.92418 - 5.92201i) q^{13} +(-2.95314 + 2.14558i) q^{14} +(0.579108 + 1.78231i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.86735 - 2.08325i) q^{17} +(-0.158216 - 0.486937i) q^{18} +(2.03225 - 6.25461i) q^{19} +(0.809017 + 0.587785i) q^{20} +(2.11391 - 6.50593i) q^{21} +(1.47923 - 1.07472i) q^{22} +(4.36407 - 3.17068i) q^{23} +(-1.51612 - 1.10153i) q^{24} +1.00000 q^{25} +6.22677 q^{26} +(-3.77212 - 2.74061i) q^{27} +(-1.12800 - 3.47162i) q^{28} +(-2.76419 + 8.50730i) q^{29} -1.87403 q^{30} +(-5.56653 + 0.117415i) q^{31} -1.00000 q^{32} +(-1.05886 + 3.25882i) q^{33} +(1.09523 + 3.37078i) q^{34} +(-2.95314 - 2.14558i) q^{35} +0.511996 q^{36} +10.9907 q^{37} +(5.32049 + 3.86556i) q^{38} +(-9.44056 + 6.85897i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-2.48413 + 7.64537i) q^{41} +(5.53428 + 4.02089i) q^{42} +(0.874032 - 2.68999i) q^{43} +(0.565015 + 1.73894i) q^{44} +(0.414214 - 0.300944i) q^{45} +(1.66693 + 5.13027i) q^{46} +(0.253967 + 0.781630i) q^{47} +(1.51612 - 1.10153i) q^{48} +(1.95440 + 6.01501i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-5.37351 - 3.90409i) q^{51} +(-1.92418 + 5.92201i) q^{52} +(-3.32979 + 2.41923i) q^{53} +(3.77212 - 2.74061i) q^{54} +(1.47923 + 1.07472i) q^{55} +3.65028 q^{56} -12.3246 q^{57} +(-7.23674 - 5.25780i) q^{58} +(-1.05792 - 3.25595i) q^{59} +(0.579108 - 1.78231i) q^{60} +9.38499 q^{61} +(1.60848 - 5.33036i) q^{62} -1.86893 q^{63} +(0.309017 - 0.951057i) q^{64} +(1.92418 + 5.92201i) q^{65} +(-2.77212 - 2.01406i) q^{66} -0.182208 q^{67} -3.54424 q^{68} +(-8.17840 - 5.94196i) q^{69} +(2.95314 - 2.14558i) q^{70} +(-1.52473 + 1.10778i) q^{71} +(-0.158216 + 0.486937i) q^{72} +(12.8448 + 9.33230i) q^{73} +(-3.39631 + 10.4528i) q^{74} +(-0.579108 - 1.78231i) q^{75} +(-5.32049 + 3.86556i) q^{76} +(-2.06246 - 6.34761i) q^{77} +(-3.60597 - 11.0980i) q^{78} +(-4.09398 + 2.97445i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(-3.17479 + 9.77101i) q^{81} +(-6.50354 - 4.72510i) q^{82} +(0.832595 - 2.56246i) q^{83} +(-5.53428 + 4.02089i) q^{84} +(-2.86735 + 2.08325i) q^{85} +(2.28825 + 1.66251i) q^{86} +16.7634 q^{87} -1.82843 q^{88} +(-8.21614 - 5.96937i) q^{89} +(0.158216 + 0.486937i) q^{90} +(7.02379 - 21.6170i) q^{91} -5.39428 q^{92} +(3.43289 + 9.85328i) q^{93} -0.821854 q^{94} +(-2.03225 + 6.25461i) q^{95} +(0.579108 + 1.78231i) q^{96} +(-4.61803 - 3.35520i) q^{97} -6.32456 q^{98} +0.936148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} + 10 q^{7} + 2 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 + 10 * q^7 + 2 * q^8 + 8 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} + 10 q^{7} + 2 q^{8} + 8 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} - 14 q^{13} - 10 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 12 q^{18} - 4 q^{19} + 2 q^{20} + 22 q^{21} - 2 q^{22} + 18 q^{23} - 2 q^{24} + 8 q^{25} - 16 q^{26} - 22 q^{27} - 10 q^{28} + 2 q^{29} - 8 q^{30} + 2 q^{31} - 8 q^{32} - 26 q^{33} - 8 q^{34} - 10 q^{35} + 8 q^{36} + 40 q^{37} + 4 q^{38} - 22 q^{39} - 2 q^{40} + 12 q^{41} + 18 q^{42} + 2 q^{44} - 8 q^{45} + 12 q^{46} + 10 q^{47} + 2 q^{48} + 2 q^{50} + 2 q^{51} - 14 q^{52} - 36 q^{53} + 22 q^{54} - 2 q^{55} - 48 q^{57} - 2 q^{58} + 16 q^{59} - 2 q^{60} - 4 q^{61} - 2 q^{62} + 56 q^{63} - 2 q^{64} + 14 q^{65} - 14 q^{66} + 4 q^{67} - 12 q^{68} - 30 q^{69} + 10 q^{70} + 20 q^{71} + 12 q^{72} + 28 q^{73} + 10 q^{74} + 2 q^{75} - 4 q^{76} + 18 q^{77} - 18 q^{78} - 18 q^{79} + 2 q^{80} - 42 q^{81} - 2 q^{82} + 6 q^{83} - 18 q^{84} + 2 q^{85} - 8 q^{87} + 8 q^{88} - 28 q^{89} - 12 q^{90} - 18 q^{91} - 12 q^{92} + 38 q^{93} + 4 q^{95} - 2 q^{96} - 28 q^{97} - 40 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 + 10 * q^7 + 2 * q^8 + 8 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 - 14 * q^13 - 10 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 12 * q^18 - 4 * q^19 + 2 * q^20 + 22 * q^21 - 2 * q^22 + 18 * q^23 - 2 * q^24 + 8 * q^25 - 16 * q^26 - 22 * q^27 - 10 * q^28 + 2 * q^29 - 8 * q^30 + 2 * q^31 - 8 * q^32 - 26 * q^33 - 8 * q^34 - 10 * q^35 + 8 * q^36 + 40 * q^37 + 4 * q^38 - 22 * q^39 - 2 * q^40 + 12 * q^41 + 18 * q^42 + 2 * q^44 - 8 * q^45 + 12 * q^46 + 10 * q^47 + 2 * q^48 + 2 * q^50 + 2 * q^51 - 14 * q^52 - 36 * q^53 + 22 * q^54 - 2 * q^55 - 48 * q^57 - 2 * q^58 + 16 * q^59 - 2 * q^60 - 4 * q^61 - 2 * q^62 + 56 * q^63 - 2 * q^64 + 14 * q^65 - 14 * q^66 + 4 * q^67 - 12 * q^68 - 30 * q^69 + 10 * q^70 + 20 * q^71 + 12 * q^72 + 28 * q^73 + 10 * q^74 + 2 * q^75 - 4 * q^76 + 18 * q^77 - 18 * q^78 - 18 * q^79 + 2 * q^80 - 42 * q^81 - 2 * q^82 + 6 * q^83 - 18 * q^84 + 2 * q^85 - 8 * q^87 + 8 * q^88 - 28 * q^89 - 12 * q^90 - 18 * q^91 - 12 * q^92 + 38 * q^93 + 4 * q^95 - 2 * q^96 - 28 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more