LMFDB - Embedded newform 310.2.b.b.249.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(249,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("310.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.b (of order $2$, degree $1$, 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:	$8$
Coefficient field:	8.0.2058981376.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 18x^{4} - 34x^{3} + 32x^{2} - 8x + 1 $ x^8 - 2x^7 + 2x^6 + 18x^4 - 34x^3 + 32x^2 - 8x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			249.1
Root			$0.148421 + 0.148421i$ of defining polynomial
Character	$\chi$	$=$	310.249
Dual form			310.2.b.b.249.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.78165i q^{3} -1.00000 q^{4} +(-0.264435 - 2.22038i) q^{5} -1.78165 q^{6} -1.70316i q^{7} +1.00000i q^{8} -0.174289 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.78165i q^{3} -1.00000 q^{4} +(-0.264435 - 2.22038i) q^{5} -1.78165 q^{6} -1.70316i q^{7} +1.00000i q^{8} -0.174289 q^{9} +(-2.22038 + 0.264435i) q^{10} -0.955942 q^{11} +1.78165i q^{12} +3.25278i q^{13} -1.70316 q^{14} +(-3.95594 + 0.471131i) q^{15} +1.00000 q^{16} -0.825711i q^{17} +0.174289i q^{18} -0.877447 q^{19} +(0.264435 + 2.22038i) q^{20} -3.03444 q^{21} +0.955942i q^{22} -0.580605i q^{23} +1.78165 q^{24} +(-4.86015 + 1.17429i) q^{25} +3.25278 q^{26} -5.03444i q^{27} +1.70316i q^{28} +3.83339 q^{29} +(0.471131 + 3.95594i) q^{30} +1.00000 q^{31} -1.00000i q^{32} +1.70316i q^{33} -0.825711 q^{34} +(-3.78165 + 0.450374i) q^{35} +0.174289 q^{36} -2.21835i q^{37} +0.877447i q^{38} +5.79533 q^{39} +(2.22038 - 0.264435i) q^{40} +3.33128 q^{41} +3.03444i q^{42} +7.87383i q^{43} +0.955942 q^{44} +(0.0460880 + 0.386987i) q^{45} -0.580605 q^{46} -11.7720i q^{47} -1.78165i q^{48} +4.09925 q^{49} +(1.17429 + 4.86015i) q^{50} -1.47113 q^{51} -3.25278i q^{52} -2.19505i q^{53} -5.03444 q^{54} +(0.252784 + 2.12255i) q^{55} +1.70316 q^{56} +1.56331i q^{57} -3.83339i q^{58} +0.464055 q^{59} +(3.95594 - 0.471131i) q^{60} +2.77565 q^{61} -1.00000i q^{62} +0.296842i q^{63} -1.00000 q^{64} +(7.22241 - 0.860149i) q^{65} +1.70316 q^{66} -14.5977i q^{67} +0.825711i q^{68} -1.03444 q^{69} +(0.450374 + 3.78165i) q^{70} +8.37594 q^{71} -0.174289i q^{72} +12.9981i q^{73} -2.21835 q^{74} +(2.09218 + 8.65910i) q^{75} +0.877447 q^{76} +1.62812i q^{77} -5.79533i q^{78} -1.56331 q^{79} +(-0.264435 - 2.22038i) q^{80} -9.49249 q^{81} -3.33128i q^{82} -9.44843i q^{83} +3.03444 q^{84} +(-1.83339 + 0.218347i) q^{85} +7.87383 q^{86} -6.82977i q^{87} -0.955942i q^{88} +13.5787 q^{89} +(0.386987 - 0.0460880i) q^{90} +5.54001 q^{91} +0.580605i q^{92} -1.78165i q^{93} -11.7720 q^{94} +(0.232027 + 1.94826i) q^{95} -1.78165 q^{96} +10.6535i q^{97} -4.09925i q^{98} +0.166610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6}+O(q^{10}) $ 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6	$ 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{10} + 12 q^{11} - 12 q^{14} - 12 q^{15} + 8 q^{16} - 4 q^{19} + 2 q^{20} + 12 q^{21} - 4 q^{24} - 4 q^{25} + 8 q^{26} + 8 q^{29} + 4 q^{30} + 8 q^{31} - 8 q^{34} - 12 q^{35} + 8 q^{39} - 2 q^{40} - 8 q^{41} - 12 q^{44} - 18 q^{45} + 8 q^{50} - 12 q^{51} - 4 q^{54} - 16 q^{55} + 12 q^{56} + 12 q^{60} - 8 q^{64} + 12 q^{66} + 28 q^{69} + 20 q^{70} + 24 q^{71} - 36 q^{74} - 20 q^{75} + 4 q^{76} + 24 q^{79} - 2 q^{80} - 32 q^{81} - 12 q^{84} + 8 q^{85} + 8 q^{86} + 24 q^{89} + 6 q^{90} - 28 q^{91} - 20 q^{94} + 4 q^{96} + 24 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^10 + 12 * q^11 - 12 * q^14 - 12 * q^15 + 8 * q^16 - 4 * q^19 + 2 * q^20 + 12 * q^21 - 4 * q^24 - 4 * q^25 + 8 * q^26 + 8 * q^29 + 4 * q^30 + 8 * q^31 - 8 * q^34 - 12 * q^35 + 8 * q^39 - 2 * q^40 - 8 * q^41 - 12 * q^44 - 18 * q^45 + 8 * q^50 - 12 * q^51 - 4 * q^54 - 16 * q^55 + 12 * q^56 + 12 * q^60 - 8 * q^64 + 12 * q^66 + 28 * q^69 + 20 * q^70 + 24 * q^71 - 36 * q^74 - 20 * q^75 + 4 * q^76 + 24 * q^79 - 2 * q^80 - 32 * q^81 - 12 * q^84 + 8 * q^85 + 8 * q^86 + 24 * q^89 + 6 * q^90 - 28 * q^91 - 20 * q^94 + 4 * q^96 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$251$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	1.78165i		−	1.02864i	−0.857599	−	0.514319i	$-0.828045\pi$
$3$		−	1.78165i		−	1.02864i	0.857599	−	0.514319i	$-0.171955\pi$
$4$	−1.00000			−0.500000
$5$	−0.264435	−	2.22038i	−0.118259	−	0.992983i
$5$	−0.264435	−	2.22038i	−0.118259	−	0.992983i
$6$	−1.78165			−0.727357
$7$		−	1.70316i		−	0.643733i	−0.946785	−	0.321867i	$-0.895690\pi$
$7$		−	1.70316i		−	0.643733i	0.946785	−	0.321867i	$-0.104310\pi$
$8$			1.00000i			0.353553i
$9$	−0.174289			−0.0580963
$10$	−2.22038	+	0.264435i	−0.702145	+	0.0836216i
$11$	−0.955942			−0.288228			−0.144114	−	0.989561i	$-0.546033\pi$
$11$	−0.955942			−0.288228			−0.144114	+	0.989561i	$0.546033\pi$
$12$			1.78165i			0.514319i
$13$			3.25278i			0.902160i	0.892484	+	0.451080i	$0.148961\pi$
$13$			3.25278i			0.902160i	−0.892484	+	0.451080i	$0.851039\pi$
$14$	−1.70316			−0.455188
$15$	−3.95594	+	0.471131i	−1.02142	+	0.121645i
$16$	1.00000			0.250000
$17$		−	0.825711i		−	0.200264i	−0.994974	−	0.100132i	$-0.968073\pi$
$17$		−	0.825711i		−	0.200264i	0.994974	−	0.100132i	$-0.0319266\pi$
$18$			0.174289i			0.0410803i
$19$	−0.877447			−0.201300			−0.100650	−	0.994922i	$-0.532092\pi$
$19$	−0.877447			−0.201300			−0.100650	+	0.994922i	$0.532092\pi$
$20$	0.264435	+	2.22038i	0.0591294	+	0.496491i
$21$	−3.03444			−0.662169
$22$			0.955942i			0.203808i
$23$		−	0.580605i		−	0.121065i	−0.998166	−	0.0605323i	$-0.980720\pi$
$23$		−	0.580605i		−	0.121065i	0.998166	−	0.0605323i	$-0.0192798\pi$
$24$	1.78165			0.363678
$25$	−4.86015	+	1.17429i	−0.972030	+	0.234858i
$26$	3.25278			0.637923
$27$		−	5.03444i		−	0.968878i
$28$			1.70316i			0.321867i
$29$	3.83339			0.711843			0.355921	−	0.934516i	$-0.384167\pi$
$29$	3.83339			0.711843			0.355921	+	0.934516i	$0.384167\pi$
$30$	0.471131	+	3.95594i	0.0860163	+	0.722253i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$		−	1.00000i		−	0.176777i
$33$			1.70316i			0.296482i
$34$	−0.825711			−0.141608
$35$	−3.78165	+	0.450374i	−0.639216	+	0.0761271i
$36$	0.174289			0.0290482
$37$		−	2.21835i		−	0.364694i	−0.983234	−	0.182347i	$-0.941631\pi$
$37$		−	2.21835i		−	0.364694i	0.983234	−	0.182347i	$-0.0583694\pi$
$38$			0.877447i			0.142341i
$39$	5.79533			0.927996
$40$	2.22038	−	0.264435i	0.351072	−	0.0418108i
$41$	3.33128			0.520258			0.260129	−	0.965574i	$-0.416235\pi$
$41$	3.33128			0.520258			0.260129	+	0.965574i	$0.416235\pi$
$42$			3.03444i			0.468224i
$43$			7.87383i			1.20075i	0.799719	+	0.600374i	$0.204982\pi$
$43$			7.87383i			1.20075i	−0.799719	+	0.600374i	$0.795018\pi$
$44$	0.955942			0.144114
$45$	0.0460880	+	0.386987i	0.00687040	+	0.0576887i
$46$	−0.580605			−0.0856056
$47$		−	11.7720i		−	1.71713i	−0.512707	−	0.858564i	$-0.671357\pi$
$47$		−	11.7720i		−	1.71713i	0.512707	−	0.858564i	$-0.328643\pi$
$48$		−	1.78165i		−	0.257160i
$49$	4.09925			0.585607
$50$	1.17429	+	4.86015i	0.166070	+	0.687329i
$51$	−1.47113			−0.206000
$52$		−	3.25278i		−	0.451080i
$53$		−	2.19505i		−	0.301513i	−0.988571	−	0.150756i	$-0.951829\pi$
$53$		−	2.19505i		−	0.301513i	0.988571	−	0.150756i	$-0.0481709\pi$
$54$	−5.03444			−0.685100
$55$	0.252784	+	2.12255i	0.0340854	+	0.286205i
$56$	1.70316			0.227594
$57$			1.56331i			0.207065i
$58$		−	3.83339i		−	0.503349i
$59$	0.464055			0.0604148			0.0302074	−	0.999544i	$-0.490383\pi$
$59$	0.464055			0.0604148			0.0302074	+	0.999544i	$0.490383\pi$
$60$	3.95594	−	0.471131i	0.510710	−	0.0608227i
$61$	2.77565			0.355386			0.177693	−	0.984086i	$-0.443137\pi$
$61$	2.77565			0.355386			0.177693	+	0.984086i	$0.443137\pi$
$62$		−	1.00000i		−	0.127000i
$63$			0.296842i			0.0373985i
$64$	−1.00000			−0.125000
$65$	7.22241	−	0.860149i	0.895829	−	0.106688i
$66$	1.70316			0.209644
$67$		−	14.5977i		−	1.78340i	−0.452629	−	0.891699i	$-0.649514\pi$
$67$		−	14.5977i		−	1.78340i	0.452629	−	0.891699i	$-0.350486\pi$
$68$			0.825711i			0.100132i
$69$	−1.03444			−0.124532
$70$	0.450374	+	3.78165i	0.0538300	+	0.451994i
$71$	8.37594			0.994041			0.497021	−	0.867739i	$-0.334427\pi$
$71$	8.37594			0.994041			0.497021	+	0.867739i	$0.334427\pi$
$72$		−	0.174289i		−	0.0205402i
$73$			12.9981i			1.52131i	0.649158	+	0.760654i	$0.275122\pi$
$73$			12.9981i			1.52131i	−0.649158	+	0.760654i	$0.724878\pi$
$74$	−2.21835			−0.257878
$75$	2.09218	+	8.65910i	0.241584	+	0.999867i
$76$	0.877447			0.100650
$77$			1.62812i			0.185542i
$78$		−	5.79533i		−	0.656192i
$79$	−1.56331			−0.175886			−0.0879429	−	0.996126i	$-0.528029\pi$
$79$	−1.56331			−0.175886			−0.0879429	+	0.996126i	$0.528029\pi$
$80$	−0.264435	−	2.22038i	−0.0295647	−	0.248246i
$81$	−9.49249			−1.05472
$82$		−	3.33128i		−	0.367878i
$83$		−	9.44843i		−	1.03710i	−0.855047	−	0.518550i	$-0.826472\pi$
$83$		−	9.44843i		−	1.03710i	0.855047	−	0.518550i	$-0.173528\pi$
$84$	3.03444			0.331084
$85$	−1.83339	+	0.218347i	−0.198859	+	0.0236830i
$86$	7.87383			0.849057
$87$		−	6.82977i		−	0.732228i
$88$		−	0.955942i		−	0.101904i
$89$	13.5787			1.43934			0.719668	−	0.694319i	$-0.244294\pi$
$89$	13.5787			1.43934			0.719668	+	0.694319i	$0.244294\pi$
$90$	0.386987	−	0.0460880i	0.0407920	−	0.00485811i
$91$	5.54001			0.580750
$92$			0.580605i			0.0605323i
$93$		−	1.78165i		−	0.184749i
$94$	−11.7720			−1.21419
$95$	0.232027	+	1.94826i	0.0238055	+	0.199888i
$96$	−1.78165			−0.181839
$97$			10.6535i			1.08170i	0.841118	+	0.540852i	$0.181898\pi$
$97$			10.6535i			1.08170i	−0.841118	+	0.540852i	$0.818102\pi$
$98$		−	4.09925i		−	0.414087i
$99$	0.166610			0.0167450
$100$	4.86015	−	1.17429i	0.486015	−	0.117429i
$101$	12.3800			1.23186			0.615928	−	0.787802i	$-0.288781\pi$
$101$	12.3800			1.23186			0.615928	+	0.787802i	$0.288781\pi$
$102$			1.47113i			0.145664i
$103$			0.103473i			0.0101955i	0.999987	+	0.00509773i	$0.00162266\pi$
$103$			0.103473i			0.0101955i	−0.999987	+	0.00509773i	$0.998377\pi$
$104$	−3.25278			−0.318962
$105$	0.802410	+	6.73760i	0.0783072	+	0.657522i
$106$	−2.19505			−0.213202
$107$		−	0.168287i		−	0.0162689i	−0.999967	−	0.00813445i	$-0.997411\pi$
$107$		−	0.168287i		−	0.0162689i	0.999967	−	0.00813445i	$-0.00258931\pi$
$108$			5.03444i			0.484439i
$109$	−17.1307			−1.64082			−0.820411	−	0.571775i	$-0.806255\pi$
$109$	−17.1307			−1.64082			−0.820411	+	0.571775i	$0.806255\pi$
$110$	2.12255	−	0.252784i	0.202377	−	0.0241020i
$111$	−3.95232			−0.375138
$112$		−	1.70316i		−	0.160933i
$113$			12.5847i			1.18387i	0.805987	+	0.591933i	$0.201635\pi$
$113$			12.5847i			1.18387i	−0.805987	+	0.591933i	$0.798365\pi$
$114$	1.56331			0.146417
$115$	−1.28916	+	0.153532i	−0.120215	+	0.0143169i
$116$	−3.83339			−0.355921
$117$		−	0.566925i		−	0.0524122i
$118$		−	0.464055i		−	0.0427197i
$119$	−1.40632			−0.128917
$120$	−0.471131	−	3.95594i	−0.0430082	−	0.361126i
$121$	−10.0862			−0.916925
$122$		−	2.77565i		−	0.251296i
$123$		−	5.93519i		−	0.535158i
$124$	−1.00000			−0.0898027
$125$	3.89256	+	10.4808i	0.348161	+	0.937435i
$126$	0.296842			0.0264448
$127$			10.9981i			0.975920i	0.872866	+	0.487960i	$0.162259\pi$
$127$			10.9981i			0.975920i	−0.872866	+	0.487960i	$0.837741\pi$
$128$			1.00000i			0.0883883i
$129$	14.0284			1.23513
$130$	−0.860149	−	7.22241i	−0.0754400	−	0.633447i
$131$	−5.62812			−0.491731			−0.245866	−	0.969304i	$-0.579072\pi$
$131$	−5.62812			−0.491731			−0.245866	+	0.969304i	$0.579072\pi$
$132$		−	1.70316i		−	0.148241i
$133$			1.49443i			0.129584i
$134$	−14.5977			−1.26105
$135$	−11.1784	+	1.33128i	−0.962079	+	0.114578i
$136$	0.825711			0.0708041
$137$			9.70722i			0.829344i	0.909971	+	0.414672i	$0.136104\pi$
$137$			9.70722i			0.829344i	−0.909971	+	0.414672i	$0.863896\pi$
$138$			1.03444i			0.0880572i
$139$	−5.92963			−0.502944			−0.251472	−	0.967865i	$-0.580915\pi$
$139$	−5.92963			−0.502944			−0.251472	+	0.967865i	$0.580915\pi$
$140$	3.78165	−	0.450374i	0.319608	−	0.0380635i
$141$	−20.9737			−1.76630
$142$		−	8.37594i		−	0.702893i
$143$		−	3.10947i		−	0.260027i
$144$	−0.174289			−0.0145241
$145$	−1.01368	−	8.51157i	−0.0841816	−	0.706847i
$146$	12.9981			1.07573
$147$		−	7.30345i		−	0.602378i
$148$			2.21835i			0.182347i
$149$	−0.452051			−0.0370334			−0.0185167	−	0.999829i	$-0.505894\pi$
$149$	−0.452051			−0.0370334			−0.0185167	+	0.999829i	$0.505894\pi$
$150$	8.65910	−	2.09218i	0.707013	−	0.170825i
$151$	13.6322			1.10937			0.554686	−	0.832060i	$-0.312839\pi$
$151$	13.6322			1.10937			0.554686	+	0.832060i	$0.312839\pi$
$152$		−	0.877447i		−	0.0711704i
$153$			0.143912i			0.0116346i
$154$	1.62812			0.131198
$155$	−0.264435	−	2.22038i	−0.0212399	−	0.178345i
$156$	−5.79533			−0.463998
$157$		−	9.56331i		−	0.763235i	−0.924320	−	0.381617i	$-0.875367\pi$
$157$		−	9.56331i		−	0.763235i	0.924320	−	0.381617i	$-0.124633\pi$
$158$			1.56331i			0.124370i
$159$	−3.91081			−0.310147
$160$	−2.22038	+	0.264435i	−0.175536	+	0.0209054i
$161$	−0.988863			−0.0779333
$162$			9.49249i			0.745800i
$163$			14.2725i			1.11791i	0.829199	+	0.558953i	$0.188797\pi$
$163$			14.2725i			1.11791i	−0.829199	+	0.558953i	$0.811203\pi$
$164$	−3.33128			−0.260129
$165$	3.78165	−	0.450374i	0.294401	−	0.0350616i
$166$	−9.44843			−0.733341
$167$			3.52287i			0.272608i	0.990667	+	0.136304i	$0.0435223\pi$
$167$			3.52287i			0.272608i	−0.990667	+	0.136304i	$0.956478\pi$
$168$		−	3.03444i		−	0.234112i
$169$	2.41939			0.186107
$170$	0.218347	+	1.83339i	0.0167464	+	0.140615i
$171$	0.152929			0.0116948
$172$		−	7.87383i		−	0.600374i
$173$		−	10.1570i		−	0.772222i	−0.922452	−	0.386111i	$-0.873818\pi$
$173$		−	10.1570i		−	0.772222i	0.922452	−	0.386111i	$-0.126182\pi$
$174$	−6.82977			−0.517764
$175$	2.00000	+	8.27760i	0.151186	+	0.625728i
$176$	−0.955942			−0.0720569
$177$		−	0.826785i		−	0.0621450i
$178$		−	13.5787i		−	1.01776i
$179$	−16.3044			−1.21865			−0.609323	−	0.792922i	$-0.708559\pi$
$179$	−16.3044			−1.21865			−0.609323	+	0.792922i	$0.708559\pi$
$180$	−0.0460880	−	0.386987i	−0.00343520	−	0.0288443i
$181$	−24.5466			−1.82454			−0.912268	−	0.409595i	$-0.865670\pi$
$181$	−24.5466			−1.82454			−0.912268	+	0.409595i	$0.865670\pi$
$182$		−	5.54001i		−	0.410653i
$183$		−	4.94525i		−	0.365563i
$184$	0.580605			0.0428028
$185$	−4.92557	+	0.586608i	−0.362135	+	0.0431282i
$186$	−1.78165			−0.130637
$187$			0.789332i			0.0577217i
$188$			11.7720i			0.858564i
$189$	−8.57444			−0.623699
$190$	1.94826	−	0.232027i	0.141342	−	0.0168330i
$191$	0.737596			0.0533706			0.0266853	−	0.999644i	$-0.491505\pi$
$191$	0.737596			0.0533706			0.0266853	+	0.999644i	$0.491505\pi$
$192$			1.78165i			0.128580i
$193$			7.88452i			0.567540i	0.958892	+	0.283770i	$0.0915853\pi$
$193$			7.88452i			0.567540i	−0.958892	+	0.283770i	$0.908415\pi$
$194$	10.6535			0.764880
$195$	−1.53249	−	12.8678i	−0.109744	−	0.921484i
$196$	−4.09925			−0.292804
$197$			22.9236i			1.63324i	0.577175	+	0.816620i	$0.304155\pi$
$197$			22.9236i			1.63324i	−0.577175	+	0.816620i	$0.695845\pi$
$198$		−	0.166610i		−	0.0118405i
$199$	25.4144			1.80158			0.900791	−	0.434253i	$-0.142988\pi$
$199$	25.4144			1.80158			0.900791	+	0.434253i	$0.142988\pi$
$200$	−1.17429	−	4.86015i	−0.0830348	−	0.343664i
$201$	−26.0081			−1.83447
$202$		−	12.3800i		−	0.871054i
$203$		−	6.52887i		−	0.458237i
$204$	1.47113			0.103000
$205$	−0.880906	−	7.39670i	−0.0615251	−	0.516608i
$206$	0.103473			0.00720927
$207$			0.101193i			0.00703341i
$208$			3.25278i			0.225540i
$209$	0.838789			0.0580203
$210$	6.73760	−	0.802410i	0.464938	−	0.0553716i
$211$	−19.4672			−1.34018			−0.670090	−	0.742280i	$-0.733745\pi$
$211$	−19.4672			−1.34018			−0.670090	+	0.742280i	$0.733745\pi$
$212$			2.19505i			0.150756i
$213$		−	14.9230i		−	1.02251i
$214$	−0.168287			−0.0115039
$215$	17.4829	−	2.08211i	1.19232	−	0.141999i
$216$	5.03444			0.342550
$217$		−	1.70316i		−	0.115618i
$218$			17.1307i			1.16024i
$219$	23.1580			1.56488
$220$	−0.252784	−	2.12255i	−0.0170427	−	0.143102i
$221$	2.68586			0.180670
$222$			3.95232i			0.265263i
$223$		−	6.10932i		−	0.409110i	−0.978855	−	0.204555i	$-0.934425\pi$
$223$		−	6.10932i		−	0.409110i	0.978855	−	0.204555i	$-0.0655747\pi$
$224$	−1.70316			−0.113797
$225$	0.847071	−	0.204666i	0.0564714	−	0.0136444i
$226$	12.5847			0.837120
$227$			7.11849i			0.472471i	0.971696	+	0.236235i	$0.0759137\pi$
$227$			7.11849i			0.472471i	−0.971696	+	0.236235i	$0.924086\pi$
$228$		−	1.56331i		−	0.103533i
$229$	8.45444			0.558685			0.279342	−	0.960192i	$-0.409884\pi$
$229$	8.45444			0.558685			0.279342	+	0.960192i	$0.409884\pi$
$230$	0.153532	+	1.28916i	0.0101236	+	0.0850049i
$231$	2.90075			0.190855
$232$			3.83339i			0.251674i
$233$			10.8298i			0.709482i	0.934965	+	0.354741i	$0.115431\pi$
$233$			10.8298i			0.709482i	−0.934965	+	0.354741i	$0.884569\pi$
$234$	−0.566925			−0.0370610
$235$	−26.1384	+	3.11293i	−1.70508	+	0.203065i
$236$	−0.464055			−0.0302074
$237$			2.78527i			0.180923i
$238$			1.40632i			0.0911580i
$239$	21.3263			1.37949			0.689743	−	0.724055i	$-0.257724\pi$
$239$	21.3263			1.37949			0.689743	+	0.724055i	$0.257724\pi$
$240$	−3.95594	+	0.471131i	−0.255355	+	0.0304114i
$241$	21.1967			1.36540			0.682700	−	0.730699i	$-0.260806\pi$
$241$	21.1967			1.36540			0.682700	+	0.730699i	$0.260806\pi$
$242$			10.0862i			0.648364i
$243$			1.80902i			0.116048i
$244$	−2.77565			−0.177693
$245$	−1.08398	−	9.10189i	−0.0692532	−	0.581498i
$246$	−5.93519			−0.378414
$247$		−	2.85415i		−	0.181605i
$248$			1.00000i			0.0635001i
$249$	−16.8338			−1.06680
$250$	10.4808	−	3.89256i	0.662867	−	0.246187i
$251$	10.4847			0.661785			0.330893	−	0.943668i	$-0.392650\pi$
$251$	10.4847			0.661785			0.330893	+	0.943668i	$0.392650\pi$
$252$		−	0.296842i		−	0.0186993i
$253$			0.555025i			0.0348941i
$254$	10.9981			0.690080
$255$	0.389018	+	3.26647i	0.0243612	+	0.204554i
$256$	1.00000			0.0625000
$257$			21.2421i			1.32505i	0.749042	+	0.662523i	$0.230514\pi$
$257$			21.2421i			1.32505i	−0.749042	+	0.662523i	$0.769486\pi$
$258$		−	14.0284i		−	0.873372i
$259$	−3.77820			−0.234766
$260$	−7.22241	+	0.860149i	−0.447915	+	0.0533442i
$261$	−0.668118			−0.0413555
$262$			5.62812i			0.347706i
$263$		−	12.4164i		−	0.765627i	−0.923826	−	0.382813i	$-0.874955\pi$
$263$		−	12.4164i		−	0.765627i	0.923826	−	0.382813i	$-0.125045\pi$
$264$	−1.70316			−0.104822
$265$	−4.87383	+	0.580446i	−0.299397	+	0.0356565i
$266$	1.49443			0.0916295
$267$		−	24.1925i		−	1.48056i
$268$			14.5977i			0.891699i
$269$	28.2477			1.72229			0.861145	−	0.508359i	$-0.169748\pi$
$269$	28.2477			1.72229			0.861145	+	0.508359i	$0.169748\pi$
$270$	1.33128	+	11.1784i	0.0810191	+	0.680293i
$271$	−2.68992			−0.163401			−0.0817005	−	0.996657i	$-0.526035\pi$
$271$	−2.68992			−0.163401			−0.0817005	+	0.996657i	$0.526035\pi$
$272$		−	0.825711i		−	0.0500661i
$273$		−	9.87037i		−	0.597382i
$274$	9.70722			0.586435
$275$	4.64602	−	1.12255i	0.280166	−	0.0676925i
$276$	1.03444			0.0622658
$277$		−	1.39777i		−	0.0839839i	−0.999118	−	0.0419919i	$-0.986630\pi$
$277$		−	1.39777i		−	0.0839839i	0.999118	−	0.0419919i	$-0.0133704\pi$
$278$			5.92963i			0.355635i
$279$	−0.174289			−0.0104344
$280$	−0.450374	−	3.78165i	−0.0269150	−	0.225997i
$281$	−1.89653			−0.113137			−0.0565687	−	0.998399i	$-0.518016\pi$
$281$	−1.89653			−0.113137			−0.0565687	+	0.998399i	$0.518016\pi$
$282$			20.9737i			1.24896i
$283$			28.1116i			1.67106i	0.549444	+	0.835530i	$0.314839\pi$
$283$			28.1116i			1.67106i	−0.549444	+	0.835530i	$0.685161\pi$
$284$	−8.37594			−0.497021
$285$	3.47113	−	0.413392i	0.205612	−	0.0244873i
$286$	−3.10947			−0.183867
$287$		−	5.67370i		−	0.334908i
$288$			0.174289i			0.0102701i
$289$	16.3182			0.959894
$290$	−8.51157	+	1.01368i	−0.499817	+	0.0595254i
$291$	18.9809			1.11268
$292$		−	12.9981i		−	0.760654i
$293$		−	33.6636i		−	1.96665i	−0.181860	−	0.983324i	$-0.558212\pi$
$293$		−	33.6636i		−	1.96665i	0.181860	−	0.983324i	$-0.441788\pi$
$294$	−7.30345			−0.425946
$295$	−0.122712	−	1.03038i	−0.00714458	−	0.0599908i
$296$	2.21835			0.128939
$297$			4.81263i			0.279257i
$298$			0.452051i			0.0261866i
$299$	1.88858			0.109220
$300$	−2.09218	−	8.65910i	−0.120792	−	0.499933i
$301$	13.4104			0.772961
$302$		−	13.6322i		−	0.784444i
$303$		−	22.0569i		−	1.26713i
$304$	−0.877447			−0.0503251
$305$	−0.733978	−	6.16299i	−0.0420275	−	0.352892i
$306$	0.143912			0.00822692
$307$			9.69700i			0.553437i	0.960951	+	0.276718i	$0.0892469\pi$
$307$			9.69700i			0.553437i	−0.960951	+	0.276718i	$0.910753\pi$
$308$		−	1.62812i		−	0.0927708i
$309$	0.184352			0.0104874
$310$	−2.22038	+	0.264435i	−0.126109	+	0.0150189i
$311$	11.3444			0.643280			0.321640	−	0.946862i	$-0.395766\pi$
$311$	11.3444			0.643280			0.321640	+	0.946862i	$0.395766\pi$
$312$			5.79533i			0.328096i
$313$		−	6.22002i		−	0.351576i	−0.984428	−	0.175788i	$-0.943753\pi$
$313$		−	6.22002i		−	0.351576i	0.984428	−	0.175788i	$-0.0562474\pi$
$314$	−9.56331			−0.539689
$315$	0.659101	−	0.0784952i	0.0371361	−	0.00442271i
$316$	1.56331			0.0879429
$317$		−	26.7326i		−	1.50145i	−0.660612	−	0.750727i	$-0.729703\pi$
$317$		−	26.7326i		−	1.50145i	0.660612	−	0.750727i	$-0.270297\pi$
$318$			3.91081i			0.219307i
$319$	−3.66450			−0.205173
$320$	0.264435	+	2.22038i	0.0147823	+	0.124123i
$321$	−0.299829			−0.0167348
$322$			0.988863i			0.0551072i
$323$			0.724518i			0.0403132i
$324$	9.49249			0.527361
$325$	−3.81971	−	15.8090i	−0.211879	−	0.876926i
$326$	14.2725			0.790479
$327$			30.5209i			1.68781i
$328$			3.33128i			0.183939i
$329$	−20.0496			−1.10537
$330$	−0.450374	−	3.78165i	−0.0247923	−	0.208173i
$331$	16.8184			0.924421			0.462211	−	0.886770i	$-0.347056\pi$
$331$	16.8184			0.924421			0.462211	+	0.886770i	$0.347056\pi$
$332$			9.44843i			0.518550i
$333$			0.386633i			0.0211874i
$334$	3.52287			0.192763
$335$	−32.4125	+	3.86015i	−1.77088	+	0.210902i
$336$	−3.03444			−0.165542
$337$			25.8023i			1.40554i	0.711418	+	0.702769i	$0.248053\pi$
$337$			25.8023i			1.40554i	−0.711418	+	0.702769i	$0.751947\pi$
$338$		−	2.41939i		−	0.131598i
$339$	22.4215			1.21777
$340$	1.83339	−	0.218347i	0.0994295	−	0.0118415i
$341$	−0.955942			−0.0517672
$342$		−	0.152929i		−	0.00826948i
$343$		−	18.9038i		−	1.02071i
$344$	−7.87383			−0.424528
$345$	0.273541	+	2.29684i	0.0147270	+	0.123658i
$346$	−10.1570			−0.546043
$347$			10.7167i			0.575302i	0.957735	+	0.287651i	$0.0928742\pi$
$347$			10.7167i			0.575302i	−0.957735	+	0.287651i	$0.907126\pi$
$348$			6.82977i			0.366114i
$349$	22.8896			1.22525			0.612627	−	0.790372i	$-0.290113\pi$
$349$	22.8896			1.22525			0.612627	+	0.790372i	$0.290113\pi$
$350$	8.27760	−	2.00000i	0.442456	−	0.106904i
$351$	16.3759			0.874083
$352$			0.955942i			0.0509519i
$353$		−	17.0708i		−	0.908588i	−0.890852	−	0.454294i	$-0.849892\pi$
$353$		−	17.0708i		−	0.908588i	0.890852	−	0.454294i	$-0.150108\pi$
$354$	−0.826785			−0.0439431
$355$	−2.21489	−	18.5977i	−0.117554	−	0.987066i
$356$	−13.5787			−0.719668
$357$			2.50557i			0.132609i
$358$			16.3044i			0.861712i
$359$	−26.4044			−1.39357			−0.696785	−	0.717280i	$-0.745387\pi$
$359$	−26.4044			−1.39357			−0.696785	+	0.717280i	$0.745387\pi$
$360$	−0.386987	+	0.0460880i	−0.0203960	+	0.00242905i
$361$	−18.2301			−0.959478
$362$			24.5466i			1.29014i
$363$			17.9701i			0.943184i
$364$	−5.54001			−0.290375
$365$	28.8606	−	3.43714i	1.51063	−	0.179908i
$366$	−4.94525			−0.258492
$367$			26.6161i			1.38935i	0.719324	+	0.694674i	$0.244451\pi$
$367$			26.6161i			1.38935i	−0.719324	+	0.694674i	$0.755549\pi$
$368$		−	0.580605i		−	0.0302662i
$369$	−0.580605			−0.0302251
$370$	0.586608	+	4.92557i	0.0304963	+	0.256068i
$371$	−3.73851			−0.194094
$372$			1.78165i			0.0923744i
$373$		−	6.38000i		−	0.330344i	−0.986265	−	0.165172i	$-0.947182\pi$
$373$		−	6.38000i		−	0.330344i	0.986265	−	0.165172i	$-0.0528179\pi$
$374$	0.789332			0.0408154
$375$	18.6732	−	6.93519i	0.964281	−	0.358131i
$376$	11.7720			0.607096
$377$			12.4692i			0.642196i
$378$			8.57444i			0.441022i
$379$	−31.8593			−1.63650			−0.818250	−	0.574863i	$-0.805056\pi$
$379$	−31.8593			−1.63650			−0.818250	+	0.574863i	$0.805056\pi$
$380$	−0.232027	−	1.94826i	−0.0119028	−	0.0999438i
$381$	19.5947			1.00387
$382$		−	0.737596i		−	0.0377387i
$383$			8.45789i			0.432178i	0.976374	+	0.216089i	$0.0693302\pi$
$383$			8.45789i			0.432178i	−0.976374	+	0.216089i	$0.930670\pi$
$384$	1.78165			0.0909196
$385$	3.61504	−	0.430532i	0.184240	−	0.0219419i
$386$	7.88452			0.401312
$387$		−	1.37232i		−	0.0697591i
$388$		−	10.6535i		−	0.540852i
$389$	−6.99866			−0.354846			−0.177423	−	0.984135i	$-0.556776\pi$
$389$	−6.99866			−0.354846			−0.177423	+	0.984135i	$0.556776\pi$
$390$	−12.8678	+	1.53249i	−0.651588	+	0.0776005i
$391$	−0.479412			−0.0242449
$392$			4.09925i			0.207043i
$393$			10.0274i			0.505813i
$394$	22.9236			1.15488
$395$	0.413392	+	3.47113i	0.0208000	+	0.174652i
$396$	−0.166610			−0.00837248
$397$		−	6.59489i		−	0.330988i	−0.986211	−	0.165494i	$-0.947078\pi$
$397$		−	6.59489i		−	0.330988i	0.986211	−	0.165494i	$-0.0529218\pi$
$398$		−	25.4144i		−	1.27391i
$399$	2.66256			0.133295
$400$	−4.86015	+	1.17429i	−0.243007	+	0.0587145i
$401$	−7.20661			−0.359881			−0.179940	−	0.983678i	$-0.557590\pi$
$401$	−7.20661			−0.359881			−0.179940	+	0.983678i	$0.557590\pi$
$402$			26.0081i			1.29717i
$403$			3.25278i			0.162033i
$404$	−12.3800			−0.615928
$405$	2.51014	+	21.0769i	0.124730	+	1.04732i
$406$	−6.52887			−0.324022
$407$			2.12061i			0.105115i
$408$		−	1.47113i		−	0.0728318i
$409$	9.43368			0.466465			0.233233	−	0.972421i	$-0.425070\pi$
$409$	9.43368			0.466465			0.233233	+	0.972421i	$0.425070\pi$
$410$	−7.39670	+	0.880906i	−0.365297	+	0.0435048i
$411$	17.2949			0.853095
$412$		−	0.103473i		−	0.00509773i
$413$		−	0.790359i		−	0.0388910i
$414$	0.101193			0.00497337
$415$	−20.9791	+	2.49849i	−1.02982	+	0.122646i
$416$	3.25278			0.159481
$417$			10.5645i			0.517348i
$418$		−	0.838789i		−	0.0410265i
$419$	−36.3221			−1.77445			−0.887225	−	0.461336i	$-0.847370\pi$
$419$	−36.3221			−1.77445			−0.887225	+	0.461336i	$0.847370\pi$
$420$	−0.802410	−	6.73760i	−0.0391536	−	0.328761i
$421$	−3.14197			−0.153130			−0.0765652	−	0.997065i	$-0.524395\pi$
$421$	−3.14197			−0.153130			−0.0765652	+	0.997065i	$0.524395\pi$
$422$			19.4672i			0.947651i
$423$			2.05174i			0.0997588i
$424$	2.19505			0.106601
$425$	0.969623	+	4.01308i	0.0470336	+	0.194663i
$426$	−14.9230			−0.723023
$427$		−	4.72737i		−	0.228774i
$428$			0.168287i			0.00813445i
$429$	−5.54001			−0.267474
$430$	−2.08211	−	17.4829i	−0.100408	−	0.843099i
$431$	−12.3436			−0.594571			−0.297286	−	0.954789i	$-0.596081\pi$
$431$	−12.3436			−0.594571			−0.297286	+	0.954789i	$0.596081\pi$
$432$		−	5.03444i		−	0.242219i
$433$		−	2.32706i		−	0.111831i	−0.998435	−	0.0559157i	$-0.982192\pi$
$433$		−	2.32706i		−	0.111831i	0.998435	−	0.0559157i	$-0.0178078\pi$
$434$	−1.70316			−0.0817542
$435$	−15.1647	+	1.80603i	−0.727090	+	0.0865924i
$436$	17.1307			0.820411
$437$			0.509451i			0.0243703i
$438$		−	23.1580i		−	1.10653i
$439$	6.15592			0.293806			0.146903	−	0.989151i	$-0.453070\pi$
$439$	6.15592			0.293806			0.146903	+	0.989151i	$0.453070\pi$
$440$	−2.12255	+	0.252784i	−0.101189	+	0.0120510i
$441$	−0.714455			−0.0340217
$442$		−	2.68586i		−	0.127753i
$443$		−	8.85415i		−	0.420673i	−0.977629	−	0.210337i	$-0.932544\pi$
$443$		−	8.85415i		−	0.420673i	0.977629	−	0.210337i	$-0.0674560\pi$
$444$	3.95232			0.187569
$445$	−3.59067	−	30.1498i	−0.170214	−	1.42924i
$446$	−6.10932			−0.289284
$447$			0.805397i			0.0380940i
$448$			1.70316i			0.0804667i
$449$	−31.4641			−1.48488			−0.742441	−	0.669912i	$-0.766332\pi$
$449$	−31.4641			−1.48488			−0.742441	+	0.669912i	$0.766332\pi$
$450$	−0.204666	−	0.847071i	−0.00964803	−	0.0399313i
$451$	−3.18451			−0.149953
$452$		−	12.5847i		−	0.591933i
$453$		−	24.2878i		−	1.14114i
$454$	7.11849			0.334087
$455$	−1.46497	−	12.3009i	−0.0686788	−	0.576675i
$456$	−1.56331			−0.0732086
$457$		−	33.8296i		−	1.58248i	−0.611504	−	0.791241i	$-0.709435\pi$
$457$		−	33.8296i		−	1.58248i	0.611504	−	0.791241i	$-0.290565\pi$
$458$		−	8.45444i		−	0.395050i
$459$	−4.15699			−0.194032
$460$	1.28916	−	0.153532i	0.0601075	−	0.00715847i
$461$	−5.37340			−0.250264			−0.125132	−	0.992140i	$-0.539935\pi$
$461$	−5.37340			−0.250264			−0.125132	+	0.992140i	$0.539935\pi$
$462$		−	2.90075i		−	0.134955i
$463$			27.6191i			1.28357i	0.766885	+	0.641784i	$0.221806\pi$
$463$			27.6191i			1.28357i	−0.766885	+	0.641784i	$0.778194\pi$
$464$	3.83339			0.177961
$465$	−3.95594	+	0.471131i	−0.183452	+	0.0218482i
$466$	10.8298			0.501680
$467$		−	17.1794i		−	0.794969i	−0.917609	−	0.397484i	$-0.869883\pi$
$467$		−	17.1794i		−	0.794969i	0.917609	−	0.397484i	$-0.130117\pi$
$468$			0.566925i			0.0262061i
$469$	−24.8623			−1.14803
$470$	3.11293	+	26.1384i	0.143589	+	1.20567i
$471$	−17.0385			−0.785093
$472$			0.464055i			0.0213599i
$473$		−	7.52693i		−	0.346089i
$474$	2.78527			0.127932
$475$	4.26452	−	1.03038i	0.195670	−	0.0472769i
$476$	1.40632			0.0644584
$477$			0.382572i			0.0175168i
$478$		−	21.3263i		−	0.975443i
$479$	−34.8397			−1.59187			−0.795933	−	0.605385i	$-0.793019\pi$
$479$	−34.8397			−1.59187			−0.795933	+	0.605385i	$0.793019\pi$
$480$	0.471131	+	3.95594i	0.0215041	+	0.180563i
$481$	7.21580			0.329012
$482$		−	21.1967i		−	0.965483i
$483$			1.76181i			0.0801652i
$484$	10.0862			0.458462
$485$	23.6549	−	2.81717i	1.07411	−	0.127921i
$486$	1.80902			0.0820586
$487$		−	13.3051i		−	0.602913i	−0.953480	−	0.301456i	$-0.902527\pi$
$487$		−	13.3051i		−	0.602913i	0.953480	−	0.301456i	$-0.0974728\pi$
$488$			2.77565i			0.125648i
$489$	25.4286			1.14992
$490$	−9.10189	+	1.08398i	−0.411181	+	0.0489694i
$491$	−26.6006			−1.20047			−0.600235	−	0.799824i	$-0.704926\pi$
$491$	−26.6006			−1.20047			−0.600235	+	0.799824i	$0.704926\pi$
$492$			5.93519i			0.267579i
$493$		−	3.16527i		−	0.142557i
$494$	−2.85415			−0.128414
$495$	−0.0440575	−	0.369938i	−0.00198024	−	0.0166275i
$496$	1.00000			0.0449013
$497$		−	14.2656i		−	0.639897i
$498$			16.8338i			0.754342i
$499$	−39.5505			−1.77052			−0.885262	−	0.465093i	$-0.846021\pi$
$499$	−39.5505			−1.77052			−0.885262	+	0.465093i	$0.846021\pi$
$500$	−3.89256	−	10.4808i	−0.174080	−	0.468717i
$501$	6.27653			0.280415
$502$		−	10.4847i		−	0.467953i
$503$		−	16.0689i		−	0.716476i	−0.933630	−	0.358238i	$-0.883378\pi$
$503$		−	16.0689i		−	0.716476i	0.933630	−	0.358238i	$-0.116622\pi$
$504$	−0.296842			−0.0132224
$505$	−3.27370	−	27.4883i	−0.145678	−	1.22321i
$506$	0.555025			0.0246739
$507$		−	4.31052i		−	0.191437i
$508$		−	10.9981i		−	0.487960i
$509$	0.724989			0.0321346			0.0160673	−	0.999871i	$-0.494885\pi$
$509$	0.724989			0.0321346			0.0160673	+	0.999871i	$0.494885\pi$
$510$	3.26647	−	0.389018i	0.144642	−	0.0172260i
$511$	22.1378			0.979316
$512$		−	1.00000i		−	0.0441942i
$513$			4.41745i			0.195035i
$514$	21.2421			0.936948
$515$	0.229748	−	0.0273617i	0.0101239	−	0.00120570i
$516$	−14.0284			−0.617567
$517$			11.2534i			0.494923i
$518$			3.77820i			0.166004i
$519$	−18.0962			−0.794337
$520$	0.860149	+	7.22241i	0.0377200	+	0.316724i
$521$	−39.6677			−1.73787			−0.868936	−	0.494924i	$-0.835196\pi$
$521$	−39.6677			−1.73787			−0.868936	+	0.494924i	$0.835196\pi$
$522$			0.668118i			0.0292427i
$523$			34.9084i			1.52644i	0.646139	+	0.763220i	$0.276383\pi$
$523$			34.9084i			1.52644i	−0.646139	+	0.763220i	$0.723617\pi$
$524$	5.62812			0.245866
$525$	14.7478	−	3.56331i	0.643648	−	0.155515i
$526$	−12.4164			−0.541380
$527$		−	0.825711i		−	0.0359685i
$528$			1.70316i			0.0741204i
$529$	22.6629			0.985343
$530$	0.580446	+	4.87383i	0.0252130	+	0.211706i
$531$	−0.0808797			−0.00350988
$532$		−	1.49443i		−	0.0647918i
$533$			10.8359i			0.469356i
$534$	−24.1925			−1.04691
$535$	−0.373660	+	0.0445009i	−0.0161547	+	0.00192394i
$536$	14.5977			0.630527
$537$			29.0487i			1.25354i
$538$		−	28.2477i		−	1.21784i
$539$	−3.91865			−0.168788
$540$	11.1784	−	1.33128i	0.481040	−	0.0572891i
$541$	23.4224			1.00701			0.503503	−	0.863993i	$-0.332044\pi$
$541$	23.4224			1.00701			0.503503	+	0.863993i	$0.332044\pi$
$542$			2.68992i			0.115542i
$543$			43.7336i			1.87679i
$544$	−0.825711			−0.0354021
$545$	4.52994	+	38.0366i	0.194041	+	1.62931i
$546$	−9.87037			−0.422413
$547$		−	12.2797i		−	0.525042i	−0.964926	−	0.262521i	$-0.915446\pi$
$547$		−	12.2797i		−	0.525042i	0.964926	−	0.262521i	$-0.0845539\pi$
$548$		−	9.70722i		−	0.414672i
$549$	−0.483766			−0.0206466
$550$	−1.12255	−	4.64602i	−0.0478658	−	0.198107i
$551$	−3.36360			−0.143294
$552$		−	1.03444i		−	0.0440286i
$553$			2.66256i			0.113224i
$554$	−1.39777			−0.0593856
$555$	1.04513	+	8.77565i	0.0443634	+	0.372506i
$556$	5.92963			0.251472
$557$			0.750071i			0.0317815i	0.999874	+	0.0158908i	$0.00505840\pi$
$557$			0.750071i			0.0317815i	−0.999874	+	0.0158908i	$0.994942\pi$
$558$			0.174289i			0.00737824i
$559$	−25.6119			−1.08327
$560$	−3.78165	+	0.450374i	−0.159804	+	0.0190318i
$561$	1.40632			0.0593747
$562$			1.89653i			0.0800002i
$563$			28.2765i			1.19171i	0.803091	+	0.595857i	$0.203187\pi$
$563$			28.2765i			1.19171i	−0.803091	+	0.595857i	$0.796813\pi$
$564$	20.9737			0.883151
$565$	27.9427	−	3.32782i	1.17556	−	0.140002i
$566$	28.1116			1.18162
$567$			16.1672i			0.678959i
$568$			8.37594i			0.351447i
$569$	22.2340			0.932097			0.466049	−	0.884759i	$-0.345677\pi$
$569$	22.2340			0.932097			0.466049	+	0.884759i	$0.345677\pi$
$570$	−0.413392	−	3.47113i	−0.0173151	−	0.145390i
$571$	40.2237			1.68331			0.841654	−	0.540017i	$-0.181582\pi$
$571$	40.2237			1.68331			0.841654	+	0.540017i	$0.181582\pi$
$572$			3.10947i			0.130014i
$573$		−	1.31414i		−	0.0548990i
$574$	−5.67370			−0.236815
$575$	0.681799	+	2.82183i	0.0284330	+	0.117678i
$576$	0.174289			0.00726204
$577$		−	3.52693i		−	0.146828i	−0.997302	−	0.0734140i	$-0.976611\pi$
$577$		−	3.52693i		−	0.146828i	0.997302	−	0.0734140i	$-0.0233894\pi$
$578$		−	16.3182i		−	0.678748i
$579$	14.0475			0.583794
$580$	1.01368	+	8.51157i	0.0420908	+	0.353424i
$581$	−16.0922			−0.667616
$582$		−	18.9809i		−	0.786784i
$583$			2.09834i			0.0869043i
$584$	−12.9981			−0.537864
$585$	−1.25879	+	0.149914i	−0.0520444	+	0.00619820i
$586$	−33.6636			−1.39063
$587$			23.1539i			0.955663i	0.878452	+	0.477831i	$0.158577\pi$
$587$			23.1539i			0.955663i	−0.878452	+	0.477831i	$0.841423\pi$
$588$			7.30345i			0.301189i
$589$	−0.877447			−0.0361546
$590$	−1.03038	+	0.122712i	−0.0424199	+	0.00505198i
$591$	40.8420			1.68001
$592$		−	2.21835i		−	0.0911735i
$593$			12.1206i			0.497734i	0.968538	+	0.248867i	$0.0800582\pi$
$593$			12.1206i			0.497734i	−0.968538	+	0.248867i	$0.919942\pi$
$594$	4.81263			0.197465
$595$	0.371879	+	3.12255i	0.0152455	+	0.128012i
$596$	0.452051			0.0185167
$597$		−	45.2797i		−	1.85318i
$598$		−	1.88858i		−	0.0772300i
$599$	−22.9719			−0.938606			−0.469303	−	0.883037i	$-0.655495\pi$
$599$	−22.9719			−0.938606			−0.469303	+	0.883037i	$0.655495\pi$
$600$	−8.65910	+	2.09218i	−0.353506	+	0.0854127i
$601$	0.778036			0.0317367			0.0158684	−	0.999874i	$-0.494949\pi$
$601$	0.778036			0.0317367			0.0158684	+	0.999874i	$0.494949\pi$
$602$		−	13.4104i		−	0.546566i
$603$			2.54423i			0.103609i
$604$	−13.6322			−0.554686
$605$	2.66713	+	22.3951i	0.108434	+	0.910491i
$606$	−22.0569			−0.895999
$607$			17.9354i			0.727974i	0.931404	+	0.363987i	$0.118585\pi$
$607$			17.9354i			0.727974i	−0.931404	+	0.363987i	$0.881415\pi$
$608$			0.877447i			0.0355852i
$609$	−11.6322			−0.471360
$610$	−6.16299	+	0.733978i	−0.249532	+	0.0297179i
$611$	38.2919			1.54912
$612$		−	0.143912i		−	0.00581731i
$613$			29.4758i			1.19052i	0.803535	+	0.595258i	$0.202950\pi$
$613$			29.4758i			1.19052i	−0.803535	+	0.595258i	$0.797050\pi$
$614$	9.69700			0.391339
$615$	−13.1784	+	1.56947i	−0.531402	+	0.0632871i
$616$	−1.62812			−0.0655989
$617$		−	35.0111i		−	1.40950i	−0.709458	−	0.704748i	$-0.751060\pi$
$617$		−	35.0111i		−	1.40950i	0.709458	−	0.704748i	$-0.248940\pi$
$618$		−	0.184352i		−	0.00741573i
$619$	33.3896			1.34204			0.671021	−	0.741438i	$-0.265856\pi$
$619$	33.3896			1.34204			0.671021	+	0.741438i	$0.265856\pi$
$620$	0.264435	+	2.22038i	0.0106199	+	0.0891725i
$621$	−2.92302			−0.117297
$622$		−	11.3444i		−	0.454867i
$623$		−	23.1266i		−	0.926548i
$624$	5.79533			0.231999
$625$	22.2421	−	11.4144i	0.889684	−	0.456578i
$626$	−6.22002			−0.248602
$627$		−	1.49443i		−	0.0596818i
$628$			9.56331i			0.381617i
$629$	−1.83171			−0.0730352
$630$	−0.0784952	−	0.659101i	−0.00312733	−	0.0262592i
$631$	−26.4183			−1.05170			−0.525849	−	0.850578i	$-0.676252\pi$
$631$	−26.4183			−1.05170			−0.525849	+	0.850578i	$0.676252\pi$
$632$		−	1.56331i		−	0.0621850i
$633$			34.6839i			1.37856i
$634$	−26.7326			−1.06169
$635$	24.4198	−	2.90827i	0.969072	−	0.115411i
$636$	3.91081			0.155074
$637$			13.3340i			0.528312i
$638$			3.66450i			0.145079i
$639$	−1.45983			−0.0577502
$640$	2.22038	−	0.264435i	0.0877681	−	0.0104527i
$641$	−2.92690			−0.115606			−0.0578029	−	0.998328i	$-0.518409\pi$
$641$	−2.92690			−0.115606			−0.0578029	+	0.998328i	$0.518409\pi$
$642$			0.299829i			0.0118333i
$643$			27.5173i			1.08518i	0.839999	+	0.542588i	$0.182556\pi$
$643$			27.5173i			1.08518i	−0.839999	+	0.542588i	$0.817444\pi$
$644$	0.988863			0.0389667
$645$	−3.70960	−	31.1484i	−0.146066	−	1.22647i
$646$	0.724518			0.0285058
$647$			30.6922i			1.20663i	0.797501	+	0.603317i	$0.206155\pi$
$647$			30.6922i			1.20663i	−0.797501	+	0.603317i	$0.793845\pi$
$648$		−	9.49249i		−	0.372900i
$649$	−0.443610			−0.0174132
$650$	−15.8090	+	3.81971i	−0.620081	+	0.149821i
$651$	−3.03444			−0.118929
$652$		−	14.2725i		−	0.558953i
$653$		−	4.28376i		−	0.167637i	−0.996481	−	0.0838183i	$-0.973288\pi$
$653$		−	4.28376i		−	0.167637i	0.996481	−	0.0838183i	$-0.0267115\pi$
$654$	30.5209			1.19346
$655$	1.48827	+	12.4966i	0.0581515	+	0.488281i
$656$	3.33128			0.130065
$657$		−	2.26542i		−	0.0883824i
$658$			20.0496i			0.781616i
$659$	30.9818			1.20688			0.603440	−	0.797408i	$-0.293796\pi$
$659$	30.9818			1.20688			0.603440	+	0.797408i	$0.293796\pi$
$660$	−3.78165	+	0.450374i	−0.147201	+	0.0175308i
$661$	1.90394			0.0740548			0.0370274	−	0.999314i	$-0.488211\pi$
$661$	1.90394			0.0740548			0.0370274	+	0.999314i	$0.488211\pi$
$662$		−	16.8184i		−	0.653665i
$663$		−	4.78527i		−	0.185845i
$664$	9.44843			0.366670
$665$	3.31820	−	0.395179i	0.128674	−	0.0153244i
$666$	0.386633			0.0149817
$667$		−	2.22569i		−	0.0861789i
$668$		−	3.52287i		−	0.136304i
$669$	−10.8847			−0.420826
$670$	3.86015	+	32.4125i	0.149131	+	1.25220i
$671$	−2.65336			−0.102432
$672$			3.03444i			0.117056i
$673$			0.392900i			0.0151452i	0.999971	+	0.00757259i	$0.00241045\pi$
$673$			0.392900i			0.0151452i	−0.999971	+	0.00757259i	$0.997590\pi$
$674$	25.8023			0.993866
$675$	5.91188	+	24.4681i	0.227549	+	0.941778i
$676$	−2.41939			−0.0930536
$677$			2.91836i			0.112162i	0.998426	+	0.0560808i	$0.0178604\pi$
$677$			2.91836i			0.112162i	−0.998426	+	0.0560808i	$0.982140\pi$
$678$		−	22.4215i		−	0.861093i
$679$	18.1447			0.696328
$680$	−0.218347	−	1.83339i	−0.00837321	−	0.0703073i
$681$	12.6827			0.486002
$682$			0.955942i			0.0366049i
$683$		−	5.34118i		−	0.204375i	−0.994765	−	0.102187i	$-0.967416\pi$
$683$		−	5.34118i		−	0.204375i	0.994765	−	0.102187i	$-0.0325841\pi$
$684$	−0.152929			−0.00584740
$685$	21.5537	−	2.56692i	0.823524	−	0.0980771i
$686$	−18.9038			−0.721750
$687$		−	15.0629i		−	0.574684i
$688$			7.87383i			0.300187i
$689$	7.14001			0.272013
$690$	2.29684	−	0.273541i	0.0874393	−	0.0104135i
$691$	16.5402			0.629218			0.314609	−	0.949221i	$-0.398127\pi$
$691$	16.5402			0.629218			0.314609	+	0.949221i	$0.398127\pi$
$692$			10.1570i			0.386111i
$693$		−	0.283764i		−	0.0107793i
$694$	10.7167			0.406800
$695$	1.56800	+	13.1660i	0.0594776	+	0.499415i
$696$	6.82977			0.258882
$697$		−	2.75067i		−	0.104189i
$698$		−	22.8896i		−	0.866385i
$699$	19.2949			0.729800
$700$	−2.00000	−	8.27760i	−0.0755929	−	0.312864i
$701$	−47.1762			−1.78182			−0.890911	−	0.454178i	$-0.849933\pi$
$701$	−47.1762			−1.78182			−0.890911	+	0.454178i	$0.849933\pi$
$702$		−	16.3759i		−	0.618070i
$703$			1.94648i			0.0734130i
$704$	0.955942			0.0360284
$705$	5.54617	+	46.5695i	0.208881	+	1.75391i
$706$	−17.0708			−0.642469
$707$		−	21.0851i		−	0.792987i
$708$			0.826785i			0.0310725i
$709$	−5.85548			−0.219907			−0.109954	−	0.993937i	$-0.535070\pi$
$709$	−5.85548			−0.219907			−0.109954	+	0.993937i	$0.535070\pi$
$710$	−18.5977	+	2.21489i	−0.697961	+	0.0831233i
$711$	0.272467			0.0102183
$712$			13.5787i			0.508882i
$713$		−	0.580605i		−	0.0217438i
$714$	2.50557			0.0937685
$715$	−6.90421	+	0.822253i	−0.258203	+	0.0307505i
$716$	16.3044			0.609323
$717$		−	37.9961i		−	1.41899i
$718$			26.4044i			0.985403i
$719$	18.6099			0.694033			0.347017	−	0.937859i	$-0.387195\pi$
$719$	18.6099			0.694033			0.347017	+	0.937859i	$0.387195\pi$
$720$	0.0460880	+	0.386987i	0.00171760	+	0.0144222i
$721$	0.176230			0.00656315
$722$			18.2301i			0.678454i
$723$		−	37.7652i		−	1.40450i
$724$	24.5466			0.912268
$725$	−18.6308	+	4.50151i	−0.691932	+	0.167182i
$726$	17.9701			0.666932
$727$			48.9359i			1.81493i	0.420125	+	0.907466i	$0.361986\pi$
$727$			48.9359i			1.81493i	−0.420125	+	0.907466i	$0.638014\pi$
$728$			5.54001i			0.205326i
$729$	−25.2544			−0.935349
$730$	−3.43714	−	28.8606i	−0.127214	−	1.06818i
$731$	6.50151			0.240467
$732$			4.94525i			0.182782i
$733$		−	31.0966i		−	1.14858i	−0.818653	−	0.574289i	$-0.805279\pi$
$733$		−	31.0966i		−	1.14858i	0.818653	−	0.574289i	$-0.194721\pi$
$734$	26.6161			0.982418
$735$	−16.2164	+	1.93128i	−0.598151	+	0.0712365i
$736$	−0.580605			−0.0214014
$737$			13.9546i			0.514024i
$738$			0.580605i			0.0213724i
$739$	45.6033			1.67755			0.838773	−	0.544482i	$-0.183274\pi$
$739$	45.6033			1.67755			0.838773	+	0.544482i	$0.183274\pi$
$740$	4.92557	−	0.586608i	0.181067	−	0.0215641i
$741$	−5.08510			−0.186806
$742$			3.73851i			0.137245i
$743$		−	27.7165i		−	1.01682i	−0.861115	−	0.508411i	$-0.830233\pi$
$743$		−	27.7165i		−	1.01682i	0.861115	−	0.508411i	$-0.169767\pi$
$744$	1.78165			0.0653186
$745$	0.119538	+	1.00372i	0.00437953	+	0.0367736i
$746$	−6.38000			−0.233588
$747$			1.64676i			0.0602517i
$748$		−	0.789332i		−	0.0288608i
$749$	−0.286619			−0.0104728
$750$	−6.93519	−	18.6732i	−0.253237	−	0.681850i
$751$	−18.2200			−0.664858			−0.332429	−	0.943128i	$-0.607868\pi$
$751$	−18.2200			−0.664858			−0.332429	+	0.943128i	$0.607868\pi$
$752$		−	11.7720i		−	0.429282i
$753$		−	18.6800i		−	0.680738i
$754$	12.4692			0.454101
$755$	−3.60482	−	30.2686i	−0.131193	−	1.10159i
$756$	8.57444			0.311850
$757$		−	50.7928i		−	1.84610i	−0.384686	−	0.923048i	$-0.625690\pi$
$757$		−	50.7928i		−	1.84610i	0.384686	−	0.923048i	$-0.374310\pi$
$758$			31.8593i			1.15718i
$759$	0.988863			0.0358935
$760$	−1.94826	+	0.232027i	−0.0706710	+	0.00841652i
$761$	−33.5287			−1.21541			−0.607707	−	0.794161i	$-0.707911\pi$
$761$	−33.5287			−1.21541			−0.607707	+	0.794161i	$0.707911\pi$
$762$		−	19.5947i		−	0.709842i
$763$			29.1762i			1.05625i
$764$	−0.737596			−0.0266853
$765$	0.319540	−	0.0380554i	0.0115530	−	0.00137590i
$766$	8.45789			0.305596
$767$			1.50947i			0.0545038i
$768$		−	1.78165i		−	0.0642899i
$769$	17.9712			0.648060			0.324030	−	0.946047i	$-0.394962\pi$
$769$	17.9712			0.648060			0.324030	+	0.946047i	$0.394962\pi$
$770$	−0.430532	−	3.61504i	−0.0155153	−	0.130277i
$771$	37.8460			1.36299
$772$		−	7.88452i		−	0.283770i
$773$			0.150179i			0.00540156i	0.999996	+	0.00270078i	$0.000859686\pi$
$773$			0.150179i			0.00540156i	−0.999996	+	0.00270078i	$0.999140\pi$
$774$	−1.37232			−0.0493271
$775$	−4.86015	+	1.17429i	−0.174582	+	0.0421817i
$776$	−10.6535			−0.382440
$777$			6.73143i			0.241489i
$778$			6.99866i			0.250914i
$779$	−2.92302			−0.104728
$780$	1.53249	+	12.8678i	0.0548718	+	0.460742i
$781$	−8.00692			−0.286510
$782$			0.479412i			0.0171437i
$783$		−	19.2990i		−	0.689689i
$784$	4.09925			0.146402
$785$	−21.2341	+	2.52887i	−0.757879	+	0.0902592i
$786$	10.0274			0.357664
$787$			5.57471i			0.198717i	0.995052	+	0.0993584i	$0.0316790\pi$
$787$			5.57471i			0.198717i	−0.995052	+	0.0993584i	$0.968321\pi$
$788$		−	22.9236i		−	0.816620i
$789$	−22.1217			−0.787553
$790$	3.47113	−	0.413392i	0.123497	−	0.0147078i
$791$	21.4337			0.762094
$792$			0.166610i			0.00592024i
$793$			9.02859i			0.320615i
$794$	−6.59489			−0.234044
$795$	1.03415	+	8.68348i	0.0366777	+	0.307971i
$796$	−25.4144			−0.900791
$797$		−	47.8848i		−	1.69617i	−0.529863	−	0.848083i	$-0.677757\pi$
$797$		−	47.8848i		−	1.69617i	0.529863	−	0.848083i	$-0.322243\pi$
$798$		−	2.66256i		−	0.0942536i
$799$	−9.72030			−0.343879
$800$	1.17429	+	4.86015i	0.0415174	+	0.171832i
$801$	−2.36661			−0.0836201
$802$			7.20661i			0.254474i
$803$		−	12.4254i		−	0.438483i
$804$	26.0081			0.917236
$805$	0.261490	+	2.19565i	0.00921630	+	0.0773864i
$806$	3.25278			0.114574
$807$		−	50.3276i		−	1.77161i
$808$			12.3800i			0.435527i
$809$	−29.6523			−1.04252			−0.521260	−	0.853398i	$-0.674538\pi$
$809$	−29.6523			−1.04252			−0.521260	+	0.853398i	$0.674538\pi$
$810$	21.0769	−	2.51014i	0.740567	−	0.0881974i
$811$	−42.9299			−1.50747			−0.753737	−	0.657176i	$-0.771751\pi$
$811$	−42.9299			−1.50747			−0.753737	+	0.657176i	$0.771751\pi$
$812$			6.52887i			0.229118i
$813$			4.79251i			0.168081i
$814$	2.12061			0.0743274
$815$	31.6903	−	3.77413i	1.11006	−	0.132202i
$816$	−1.47113			−0.0514999
$817$		−	6.90887i		−	0.241711i
$818$		−	9.43368i		−	0.329841i
$819$	−0.965562			−0.0337395
$820$	0.880906	+	7.39670i	0.0307626	+	0.258304i
$821$	−25.6725			−0.895977			−0.447989	−	0.894039i	$-0.647859\pi$
$821$	−25.6725			−0.895977			−0.447989	+	0.894039i	$0.647859\pi$
$822$		−	17.2949i		−	0.603229i
$823$		−	22.0212i		−	0.767611i	−0.923414	−	0.383805i	$-0.874613\pi$
$823$		−	22.0212i		−	0.767611i	0.923414	−	0.383805i	$-0.125387\pi$
$824$	−0.103473			−0.00360464
$825$	−2.00000	−	8.27760i	−0.0696311	−	0.288189i
$826$	−0.790359			−0.0275001
$827$			13.3944i			0.465770i	0.972504	+	0.232885i	$0.0748165\pi$
$827$			13.3944i			0.465770i	−0.972504	+	0.232885i	$0.925184\pi$
$828$		−	0.101193i		−	0.00351671i
$829$	−29.4008			−1.02113			−0.510565	−	0.859839i	$-0.670564\pi$
$829$	−29.4008			−1.02113			−0.510565	+	0.859839i	$0.670564\pi$
$830$	2.49849	+	20.9791i	0.0867239	+	0.728195i
$831$	−2.49034			−0.0863890
$832$		−	3.25278i		−	0.112770i
$833$		−	3.38480i		−	0.117276i
$834$	10.5645			0.365820
$835$	7.82209	−	0.931568i	0.270695	−	0.0322382i
$836$	−0.838789			−0.0290101
$837$		−	5.03444i		−	0.174016i
$838$			36.3221i			1.25473i
$839$	−4.62547			−0.159689			−0.0798445	−	0.996807i	$-0.525442\pi$
$839$	−4.62547			−0.159689			−0.0798445	+	0.996807i	$0.525442\pi$
$840$	−6.73760	+	0.802410i	−0.232469	+	0.0276858i
$841$	−14.3051			−0.493280
$842$			3.14197i			0.108279i
$843$			3.37895i			0.116377i
$844$	19.4672			0.670090
$845$	−0.639772	−	5.37197i	−0.0220088	−	0.184801i
$846$	2.05174			0.0705401
$847$			17.1784i			0.590255i
$848$		−	2.19505i		−	0.0753782i
$849$	50.0851			1.71892
$850$	4.01308	−	0.969623i	0.137647	−	0.0332578i
$851$	−1.28798			−0.0441515
$852$			14.9230i			0.511254i
$853$			37.8444i			1.29577i	0.761739	+	0.647884i	$0.224346\pi$
$853$			37.8444i			1.29577i	−0.761739	+	0.647884i	$0.775654\pi$
$854$	−4.72737			−0.161767
$855$	−0.0404398	−	0.339561i	−0.00138301	−	0.0116127i
$856$	0.168287			0.00575193
$857$		−	45.2178i		−	1.54461i	−0.635252	−	0.772305i	$-0.719104\pi$
$857$		−	45.2178i		−	1.54461i	0.635252	−	0.772305i	$-0.280896\pi$
$858$			5.54001i			0.189133i
$859$	−12.8751			−0.439291			−0.219646	−	0.975580i	$-0.570490\pi$
$859$	−12.8751			−0.439291			−0.219646	+	0.975580i	$0.570490\pi$
$860$	−17.4829	+	2.08211i	−0.596161	+	0.0709995i
$861$	−10.1086			−0.344499
$862$			12.3436i			0.420425i
$863$			4.67207i			0.159039i	0.996833	+	0.0795196i	$0.0253386\pi$
$863$			4.67207i			0.159039i	−0.996833	+	0.0795196i	$0.974661\pi$
$864$	−5.03444			−0.171275
$865$	−22.5523	+	2.68586i	−0.766803	+	0.0913220i
$866$	−2.32706			−0.0790767
$867$		−	29.0734i		−	0.987384i
$868$			1.70316i			0.0578090i
$869$	1.49443			0.0506951
$870$	1.80603	+	15.1647i	0.0612301	+	0.514130i
$871$	47.4833			1.60891
$872$		−	17.1307i		−	0.580118i
$873$		−	1.85680i		−	0.0628430i
$874$	0.509451			0.0172324
$875$	17.8505	−	6.62964i	0.603458	−	0.224123i
$876$	−23.1580			−0.782438
$877$			18.8734i			0.637309i	0.947871	+	0.318654i	$0.103231\pi$
$877$			18.8734i			0.637309i	−0.947871	+	0.318654i	$0.896769\pi$
$878$		−	6.15592i		−	0.207752i
$879$	−59.9769			−2.02297
$880$	0.252784	+	2.12255i	0.00852136	+	0.0715512i
$881$	−49.2241			−1.65840			−0.829200	−	0.558952i	$-0.811204\pi$
$881$	−49.2241			−1.65840			−0.829200	+	0.558952i	$0.811204\pi$
$882$			0.714455i			0.0240569i
$883$		−	38.5429i		−	1.29707i	−0.761185	−	0.648535i	$-0.775382\pi$
$883$		−	38.5429i		−	1.29707i	0.761185	−	0.648535i	$-0.224618\pi$
$884$	−2.68586			−0.0903352
$885$	−1.83577	+	0.218631i	−0.0617089	+	0.00734918i
$886$	−8.85415			−0.297461
$887$		−	8.42044i		−	0.282731i	−0.989957	−	0.141365i	$-0.954851\pi$
$887$		−	8.42044i		−	0.282731i	0.989957	−	0.141365i	$-0.0451492\pi$
$888$		−	3.95232i		−	0.132631i
$889$	18.7314			0.628232
$890$	−30.1498	+	3.59067i	−1.01062	+	0.120359i
$891$	9.07427			0.304000
$892$			6.10932i			0.204555i
$893$			10.3293i			0.345658i
$894$	0.805397			0.0269365
$895$	4.31144	+	36.2018i	0.144115	+	1.21009i
$896$	1.70316			0.0568985
$897$		−	3.36480i		−	0.112347i
$898$			31.4641i			1.04997i
$899$	3.83339			0.127851
$900$	−0.847071	+	0.204666i	−0.0282357	+	0.00682219i
$901$	−1.81247			−0.0603822
$902$			3.18451i			0.106033i
$903$		−	23.8926i		−	0.795097i
$904$	−12.5847			−0.418560
$905$	6.49097	+	54.5027i	0.215767	+	1.81173i
$906$	−24.2878			−0.806909
$907$			42.0772i			1.39715i	0.715537	+	0.698575i	$0.246182\pi$
$907$			42.0772i			1.39715i	−0.715537	+	0.698575i	$0.753818\pi$
$908$		−	7.11849i		−	0.236235i
$909$	−2.15770			−0.0715663
$910$	−12.3009	+	1.46497i	−0.407771	+	0.0485633i
$911$	−24.0042			−0.795296			−0.397648	−	0.917538i	$-0.630173\pi$
$911$	−24.0042			−0.795296			−0.397648	+	0.917538i	$0.630173\pi$
$912$			1.56331i			0.0517663i
$913$			9.03216i			0.298921i
$914$	−33.8296			−1.11898
$915$	−10.9803	+	1.30769i	−0.362998	+	0.0432311i
$916$	−8.45444			−0.279342
$917$			9.58558i			0.316544i
$918$			4.15699i			0.137201i
$919$	−16.5137			−0.544736			−0.272368	−	0.962193i	$-0.587807\pi$
$919$	−16.5137			−0.544736			−0.272368	+	0.962193i	$0.587807\pi$
$920$	−0.153532	−	1.28916i	−0.00506181	−	0.0425024i
$921$	17.2767			0.569286
$922$			5.37340i			0.176963i
$923$			27.2451i			0.896784i
$924$	−2.90075			−0.0954276
$925$	2.60498	+	10.7815i	0.0856512	+	0.354493i
$926$	27.6191			0.907620
$927$		−	0.0180341i		−	0.000592318i
$928$		−	3.83339i		−	0.125837i
$929$	32.9470			1.08096			0.540479	−	0.841358i	$-0.318243\pi$
$929$	32.9470			1.08096			0.540479	+	0.841358i	$0.318243\pi$
$930$	0.471131	+	3.95594i	0.0154490	+	0.129720i
$931$	−3.59688			−0.117883
$932$		−	10.8298i		−	0.354741i
$933$		−	20.2117i		−	0.661702i
$934$	−17.1794			−0.562128
$935$	1.75262	−	0.208727i	0.0573166	−	0.00682609i
$936$	0.566925			0.0185305
$937$		−	29.1552i		−	0.952458i	−0.879321	−	0.476229i	$-0.842003\pi$
$937$		−	29.1552i		−	0.952458i	0.879321	−	0.476229i	$-0.157997\pi$
$938$			24.8623i			0.811782i
$939$	−11.0819			−0.361645
$940$	26.1384	−	3.11293i	0.852539	−	0.101533i
$941$	54.1322			1.76466			0.882330	−	0.470632i	$-0.155974\pi$
$941$	54.1322			1.76466			0.882330	+	0.470632i	$0.155974\pi$
$942$			17.0385i			0.555144i
$943$		−	1.93416i		−	0.0629849i
$944$	0.464055			0.0151037
$945$	2.26738	+	19.0385i	0.0737579	+	0.619322i
$946$	−7.52693			−0.244722
$947$			26.2992i			0.854610i	0.904108	+	0.427305i	$0.140537\pi$
$947$			26.2992i			0.854610i	−0.904108	+	0.427305i	$0.859463\pi$
$948$		−	2.78527i		−	0.0904614i
$949$	−42.2799			−1.37246
$950$	−1.03038	−	4.26452i	−0.0334298	−	0.138359i
$951$	−47.6283			−1.54445
$952$		−	1.40632i		−	0.0455790i
$953$			41.8116i			1.35441i	0.735794	+	0.677205i	$0.236809\pi$
$953$			41.8116i			1.35441i	−0.735794	+	0.677205i	$0.763191\pi$
$954$	0.382572			0.0123862
$955$	−0.195046	−	1.63774i	−0.00631154	−	0.0529961i
$956$	−21.3263			−0.689743
$957$			6.52887i			0.211048i
$958$			34.8397i			1.12562i
$959$	16.5329			0.533876
$960$	3.95594	−	0.471131i	0.127677	−	0.0152057i
$961$	1.00000			0.0322581
$962$		−	7.21580i		−	0.232647i
$963$			0.0293306i			0.000945164i
$964$	−21.1967			−0.682700
$965$	17.5066	−	2.08494i	0.563558	−	0.0671166i
$966$	1.76181			0.0566853
$967$		−	49.4561i		−	1.59040i	−0.606347	−	0.795200i	$-0.707366\pi$
$967$		−	49.4561i		−	1.59040i	0.606347	−	0.795200i	$-0.292634\pi$
$968$		−	10.0862i		−	0.324182i
$969$	1.29084			0.0414677
$970$	−2.81717	−	23.6549i	−0.0904537	−	0.759512i
$971$	−33.6211			−1.07895			−0.539476	−	0.842001i	$-0.681378\pi$
$971$	−33.6211			−1.07895			−0.539476	+	0.842001i	$0.681378\pi$
$972$		−	1.80902i		−	0.0580242i
$973$			10.0991i			0.323762i
$974$	−13.3051			−0.426324
$975$	−28.1662	+	6.80540i	−0.902040	+	0.217947i
$976$	2.77565			0.0888464
$977$			12.3528i			0.395202i	0.980283	+	0.197601i	$0.0633150\pi$
$977$			12.3528i			0.395202i	−0.980283	+	0.197601i	$0.936685\pi$
$978$		−	25.4286i		−	0.813117i
$979$	−12.9804			−0.414856
$980$	1.08398	+	9.10189i	0.0346266	+	0.290749i
$981$	2.98569			0.0953257
$982$			26.6006i			0.848860i
$983$		−	17.7619i		−	0.566518i	−0.959043	−	0.283259i	$-0.908584\pi$
$983$		−	17.7619i		−	0.566518i	0.959043	−	0.283259i	$-0.0914156\pi$
$984$	5.93519			0.189207
$985$	50.8991	−	6.06180i	1.62178	−	0.193145i
$986$	−3.16527			−0.100803
$987$			35.7215i			1.13703i
$988$			2.85415i			0.0908025i
$989$	4.57159			0.145368
$990$	−0.369938	+	0.0440575i	−0.0117574	+	0.00140024i
$991$	11.4671			0.364263			0.182132	−	0.983274i	$-0.441700\pi$
$991$	11.4671			0.364263			0.182132	+	0.983274i	$0.441700\pi$
$992$		−	1.00000i		−	0.0317500i
$993$		−	29.9645i		−	0.950895i
$994$	−14.2656			−0.452476
$995$	−6.72046	−	56.4296i	−0.213053	−	1.78894i
$996$	16.8338			0.533400
$997$		−	56.2534i		−	1.78156i	−0.454432	−	0.890782i	$-0.650158\pi$
$997$		−	56.2534i		−	1.78156i	0.454432	−	0.890782i	$-0.349842\pi$
$998$			39.5505i			1.25195i
$999$	−11.1681			−0.353344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.b.b.249.1	✓	8
3.2	odd	2		2790.2.d.l.559.6		8
4.3	odd	2		2480.2.d.e.1489.7		8
5.2	odd	4		1550.2.a.q.1.1		4
5.3	odd	4		1550.2.a.n.1.4		4
5.4	even	2	inner	310.2.b.b.249.8	yes	8
15.14	odd	2		2790.2.d.l.559.2		8
20.19	odd	2		2480.2.d.e.1489.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.b.b.249.1	✓	8	1.1	even	1	trivial
310.2.b.b.249.8	yes	8	5.4	even	2	inner
1550.2.a.n.1.4		4	5.3	odd	4
1550.2.a.q.1.1		4	5.2	odd	4
2480.2.d.e.1489.2		8	20.19	odd	2
2480.2.d.e.1489.7		8	4.3	odd	2
2790.2.d.l.559.2		8	15.14	odd	2
2790.2.d.l.559.6		8	3.2	odd	2

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.78165i q^{3} -1.00000 q^{4} +(-0.264435 - 2.22038i) q^{5} -1.78165 q^{6} -1.70316i q^{7} +1.00000i q^{8} -0.174289 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.78165i q^{3} -1.00000 q^{4} +(-0.264435 - 2.22038i) q^{5} -1.78165 q^{6} -1.70316i q^{7} +1.00000i q^{8} -0.174289 q^{9} +(-2.22038 + 0.264435i) q^{10} -0.955942 q^{11} +1.78165i q^{12} +3.25278i q^{13} -1.70316 q^{14} +(-3.95594 + 0.471131i) q^{15} +1.00000 q^{16} -0.825711i q^{17} +0.174289i q^{18} -0.877447 q^{19} +(0.264435 + 2.22038i) q^{20} -3.03444 q^{21} +0.955942i q^{22} -0.580605i q^{23} +1.78165 q^{24} +(-4.86015 + 1.17429i) q^{25} +3.25278 q^{26} -5.03444i q^{27} +1.70316i q^{28} +3.83339 q^{29} +(0.471131 + 3.95594i) q^{30} +1.00000 q^{31} -1.00000i q^{32} +1.70316i q^{33} -0.825711 q^{34} +(-3.78165 + 0.450374i) q^{35} +0.174289 q^{36} -2.21835i q^{37} +0.877447i q^{38} +5.79533 q^{39} +(2.22038 - 0.264435i) q^{40} +3.33128 q^{41} +3.03444i q^{42} +7.87383i q^{43} +0.955942 q^{44} +(0.0460880 + 0.386987i) q^{45} -0.580605 q^{46} -11.7720i q^{47} -1.78165i q^{48} +4.09925 q^{49} +(1.17429 + 4.86015i) q^{50} -1.47113 q^{51} -3.25278i q^{52} -2.19505i q^{53} -5.03444 q^{54} +(0.252784 + 2.12255i) q^{55} +1.70316 q^{56} +1.56331i q^{57} -3.83339i q^{58} +0.464055 q^{59} +(3.95594 - 0.471131i) q^{60} +2.77565 q^{61} -1.00000i q^{62} +0.296842i q^{63} -1.00000 q^{64} +(7.22241 - 0.860149i) q^{65} +1.70316 q^{66} -14.5977i q^{67} +0.825711i q^{68} -1.03444 q^{69} +(0.450374 + 3.78165i) q^{70} +8.37594 q^{71} -0.174289i q^{72} +12.9981i q^{73} -2.21835 q^{74} +(2.09218 + 8.65910i) q^{75} +0.877447 q^{76} +1.62812i q^{77} -5.79533i q^{78} -1.56331 q^{79} +(-0.264435 - 2.22038i) q^{80} -9.49249 q^{81} -3.33128i q^{82} -9.44843i q^{83} +3.03444 q^{84} +(-1.83339 + 0.218347i) q^{85} +7.87383 q^{86} -6.82977i q^{87} -0.955942i q^{88} +13.5787 q^{89} +(0.386987 - 0.0460880i) q^{90} +5.54001 q^{91} +0.580605i q^{92} -1.78165i q^{93} -11.7720 q^{94} +(0.232027 + 1.94826i) q^{95} -1.78165 q^{96} +10.6535i q^{97} -4.09925i q^{98} +0.166610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6}+O(q^{10}) \) 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6	\( 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{10} + 12 q^{11} - 12 q^{14} - 12 q^{15} + 8 q^{16} - 4 q^{19} + 2 q^{20} + 12 q^{21} - 4 q^{24} - 4 q^{25} + 8 q^{26} + 8 q^{29} + 4 q^{30} + 8 q^{31} - 8 q^{34} - 12 q^{35} + 8 q^{39} - 2 q^{40} - 8 q^{41} - 12 q^{44} - 18 q^{45} + 8 q^{50} - 12 q^{51} - 4 q^{54} - 16 q^{55} + 12 q^{56} + 12 q^{60} - 8 q^{64} + 12 q^{66} + 28 q^{69} + 20 q^{70} + 24 q^{71} - 36 q^{74} - 20 q^{75} + 4 q^{76} + 24 q^{79} - 2 q^{80} - 32 q^{81} - 12 q^{84} + 8 q^{85} + 8 q^{86} + 24 q^{89} + 6 q^{90} - 28 q^{91} - 20 q^{94} + 4 q^{96} + 24 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^10 + 12 * q^11 - 12 * q^14 - 12 * q^15 + 8 * q^16 - 4 * q^19 + 2 * q^20 + 12 * q^21 - 4 * q^24 - 4 * q^25 + 8 * q^26 + 8 * q^29 + 4 * q^30 + 8 * q^31 - 8 * q^34 - 12 * q^35 + 8 * q^39 - 2 * q^40 - 8 * q^41 - 12 * q^44 - 18 * q^45 + 8 * q^50 - 12 * q^51 - 4 * q^54 - 16 * q^55 + 12 * q^56 + 12 * q^60 - 8 * q^64 + 12 * q^66 + 28 * q^69 + 20 * q^70 + 24 * q^71 - 36 * q^74 - 20 * q^75 + 4 * q^76 + 24 * q^79 - 2 * q^80 - 32 * q^81 - 12 * q^84 + 8 * q^85 + 8 * q^86 + 24 * q^89 + 6 * q^90 - 28 * q^91 - 20 * q^94 + 4 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more