LMFDB - Embedded newform 2310.2.g.b.1121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2310,2,Mod(1121,2310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2310, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2310.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2310.g (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:	$18.4454428669$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.3
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2310.1121
Dual form			2310.2.g.b.1121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.292893 - 1.70711i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(-0.292893 - 1.70711i) q^{6} -1.00000i q^{7} +1.00000 q^{8} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.292893 - 1.70711i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(-0.292893 - 1.70711i) q^{6} -1.00000i q^{7} +1.00000 q^{8} +(-2.82843 + 1.00000i) q^{9} -1.00000i q^{10} +(-3.00000 + 1.41421i) q^{11} +(-0.292893 - 1.70711i) q^{12} +6.24264i q^{13} -1.00000i q^{14} +(-1.70711 + 0.292893i) q^{15} +1.00000 q^{16} -4.58579 q^{17} +(-2.82843 + 1.00000i) q^{18} -2.82843i q^{19} -1.00000i q^{20} +(-1.70711 + 0.292893i) q^{21} +(-3.00000 + 1.41421i) q^{22} -0.828427i q^{23} +(-0.292893 - 1.70711i) q^{24} -1.00000 q^{25} +6.24264i q^{26} +(2.53553 + 4.53553i) q^{27} -1.00000i q^{28} -6.82843 q^{29} +(-1.70711 + 0.292893i) q^{30} -5.41421 q^{31} +1.00000 q^{32} +(3.29289 + 4.70711i) q^{33} -4.58579 q^{34} -1.00000 q^{35} +(-2.82843 + 1.00000i) q^{36} -2.82843 q^{37} -2.82843i q^{38} +(10.6569 - 1.82843i) q^{39} -1.00000i q^{40} -11.0711 q^{41} +(-1.70711 + 0.292893i) q^{42} +0.828427i q^{43} +(-3.00000 + 1.41421i) q^{44} +(1.00000 + 2.82843i) q^{45} -0.828427i q^{46} +0.585786i q^{47} +(-0.292893 - 1.70711i) q^{48} -1.00000 q^{49} -1.00000 q^{50} +(1.34315 + 7.82843i) q^{51} +6.24264i q^{52} -13.3137i q^{53} +(2.53553 + 4.53553i) q^{54} +(1.41421 + 3.00000i) q^{55} -1.00000i q^{56} +(-4.82843 + 0.828427i) q^{57} -6.82843 q^{58} +13.8995i q^{59} +(-1.70711 + 0.292893i) q^{60} +2.58579i q^{61} -5.41421 q^{62} +(1.00000 + 2.82843i) q^{63} +1.00000 q^{64} +6.24264 q^{65} +(3.29289 + 4.70711i) q^{66} +13.3137 q^{67} -4.58579 q^{68} +(-1.41421 + 0.242641i) q^{69} -1.00000 q^{70} -11.3137i q^{71} +(-2.82843 + 1.00000i) q^{72} -4.58579i q^{73} -2.82843 q^{74} +(0.292893 + 1.70711i) q^{75} -2.82843i q^{76} +(1.41421 + 3.00000i) q^{77} +(10.6569 - 1.82843i) q^{78} +10.0000i q^{79} -1.00000i q^{80} +(7.00000 - 5.65685i) q^{81} -11.0711 q^{82} -16.0000 q^{83} +(-1.70711 + 0.292893i) q^{84} +4.58579i q^{85} +0.828427i q^{86} +(2.00000 + 11.6569i) q^{87} +(-3.00000 + 1.41421i) q^{88} -7.65685i q^{89} +(1.00000 + 2.82843i) q^{90} +6.24264 q^{91} -0.828427i q^{92} +(1.58579 + 9.24264i) q^{93} +0.585786i q^{94} -2.82843 q^{95} +(-0.292893 - 1.70711i) q^{96} +3.65685 q^{97} -1.00000 q^{98} +(7.07107 - 7.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^8	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{8} - 12 q^{11} - 4 q^{12} - 4 q^{15} + 4 q^{16} - 24 q^{17} - 4 q^{21} - 12 q^{22} - 4 q^{24} - 4 q^{25} - 4 q^{27} - 16 q^{29} - 4 q^{30} - 16 q^{31} + 4 q^{32} + 16 q^{33} - 24 q^{34} - 4 q^{35} + 20 q^{39} - 16 q^{41} - 4 q^{42} - 12 q^{44} + 4 q^{45} - 4 q^{48} - 4 q^{49} - 4 q^{50} + 28 q^{51} - 4 q^{54} - 8 q^{57} - 16 q^{58} - 4 q^{60} - 16 q^{62} + 4 q^{63} + 4 q^{64} + 8 q^{65} + 16 q^{66} + 8 q^{67} - 24 q^{68} - 4 q^{70} + 4 q^{75} + 20 q^{78} + 28 q^{81} - 16 q^{82} - 64 q^{83} - 4 q^{84} + 8 q^{87} - 12 q^{88} + 4 q^{90} + 8 q^{91} + 12 q^{93} - 4 q^{96} - 8 q^{97} - 4 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^8 - 12 * q^11 - 4 * q^12 - 4 * q^15 + 4 * q^16 - 24 * q^17 - 4 * q^21 - 12 * q^22 - 4 * q^24 - 4 * q^25 - 4 * q^27 - 16 * q^29 - 4 * q^30 - 16 * q^31 + 4 * q^32 + 16 * q^33 - 24 * q^34 - 4 * q^35 + 20 * q^39 - 16 * q^41 - 4 * q^42 - 12 * q^44 + 4 * q^45 - 4 * q^48 - 4 * q^49 - 4 * q^50 + 28 * q^51 - 4 * q^54 - 8 * q^57 - 16 * q^58 - 4 * q^60 - 16 * q^62 + 4 * q^63 + 4 * q^64 + 8 * q^65 + 16 * q^66 + 8 * q^67 - 24 * q^68 - 4 * q^70 + 4 * q^75 + 20 * q^78 + 28 * q^81 - 16 * q^82 - 64 * q^83 - 4 * q^84 + 8 * q^87 - 12 * q^88 + 4 * q^90 + 8 * q^91 + 12 * q^93 - 4 * q^96 - 8 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2310\mathbb{Z}\right)^\times$.

$n$	$211$	$661$	$1387$	$1541$
$\chi(n)$	$-1$	$1$	$1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.292893	−	1.70711i	−0.169102	−	0.985599i
$3$	−0.292893	−	1.70711i	−0.169102	−	0.985599i
$4$	1.00000			0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.292893	−	1.70711i	−0.119573	−	0.696923i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.00000			0.353553
$9$	−2.82843	+	1.00000i	−0.942809	+	0.333333i
$10$		−	1.00000i		−	0.316228i
$11$	−3.00000	+	1.41421i	−0.904534	+	0.426401i
$11$	−3.00000	+	1.41421i	−0.904534	+	0.426401i
$12$	−0.292893	−	1.70711i	−0.0845510	−	0.492799i
$13$			6.24264i			1.73140i	0.500566	+	0.865699i	$0.333125\pi$
$13$			6.24264i			1.73140i	−0.500566	+	0.865699i	$0.666875\pi$
$14$		−	1.00000i		−	0.267261i
$15$	−1.70711	+	0.292893i	−0.440773	+	0.0756247i
$16$	1.00000			0.250000
$17$	−4.58579			−1.11222			−0.556108	−	0.831110i	$-0.687706\pi$
$17$	−4.58579			−1.11222			−0.556108	+	0.831110i	$0.687706\pi$
$18$	−2.82843	+	1.00000i	−0.666667	+	0.235702i
$19$		−	2.82843i		−	0.648886i	−0.945905	−	0.324443i	$-0.894823\pi$
$19$		−	2.82843i		−	0.648886i	0.945905	−	0.324443i	$-0.105177\pi$
$20$		−	1.00000i		−	0.223607i
$21$	−1.70711	+	0.292893i	−0.372521	+	0.0639145i
$22$	−3.00000	+	1.41421i	−0.639602	+	0.301511i
$23$		−	0.828427i		−	0.172739i	−0.996263	−	0.0863695i	$-0.972473\pi$
$23$		−	0.828427i		−	0.172739i	0.996263	−	0.0863695i	$-0.0275266\pi$
$24$	−0.292893	−	1.70711i	−0.0597866	−	0.348462i
$25$	−1.00000			−0.200000
$26$			6.24264i			1.22428i
$27$	2.53553	+	4.53553i	0.487964	+	0.872864i
$28$		−	1.00000i		−	0.188982i
$29$	−6.82843			−1.26801			−0.634004	−	0.773330i	$-0.718590\pi$
$29$	−6.82843			−1.26801			−0.634004	+	0.773330i	$0.718590\pi$
$30$	−1.70711	+	0.292893i	−0.311674	+	0.0534747i
$31$	−5.41421			−0.972421			−0.486211	−	0.873842i	$-0.661621\pi$
$31$	−5.41421			−0.972421			−0.486211	+	0.873842i	$0.661621\pi$
$32$	1.00000			0.176777
$33$	3.29289	+	4.70711i	0.573219	+	0.819402i
$34$	−4.58579			−0.786456
$35$	−1.00000			−0.169031
$36$	−2.82843	+	1.00000i	−0.471405	+	0.166667i
$37$	−2.82843			−0.464991			−0.232495	−	0.972598i	$-0.574689\pi$
$37$	−2.82843			−0.464991			−0.232495	+	0.972598i	$0.574689\pi$
$38$		−	2.82843i		−	0.458831i
$39$	10.6569	−	1.82843i	1.70646	−	0.292783i
$40$		−	1.00000i		−	0.158114i
$41$	−11.0711			−1.72901			−0.864505	−	0.502624i	$-0.832368\pi$
$41$	−11.0711			−1.72901			−0.864505	+	0.502624i	$0.832368\pi$
$42$	−1.70711	+	0.292893i	−0.263412	+	0.0451944i
$43$			0.828427i			0.126334i	0.998003	+	0.0631670i	$0.0201201\pi$
$43$			0.828427i			0.126334i	−0.998003	+	0.0631670i	$0.979880\pi$
$44$	−3.00000	+	1.41421i	−0.452267	+	0.213201i
$45$	1.00000	+	2.82843i	0.149071	+	0.421637i
$46$		−	0.828427i		−	0.122145i
$47$			0.585786i			0.0854457i	0.999087	+	0.0427229i	$0.0136033\pi$
$47$			0.585786i			0.0854457i	−0.999087	+	0.0427229i	$0.986397\pi$
$48$	−0.292893	−	1.70711i	−0.0422755	−	0.246400i
$49$	−1.00000			−0.142857
$50$	−1.00000			−0.141421
$51$	1.34315	+	7.82843i	0.188078	+	1.09620i
$52$			6.24264i			0.865699i
$53$		−	13.3137i		−	1.82878i	−0.404836	−	0.914389i	$-0.632671\pi$
$53$		−	13.3137i		−	1.82878i	0.404836	−	0.914389i	$-0.367329\pi$
$54$	2.53553	+	4.53553i	0.345042	+	0.617208i
$55$	1.41421	+	3.00000i	0.190693	+	0.404520i
$56$		−	1.00000i		−	0.133631i
$57$	−4.82843	+	0.828427i	−0.639541	+	0.109728i
$58$	−6.82843			−0.896616
$59$			13.8995i			1.80956i	0.425879	+	0.904780i	$0.359965\pi$
$59$			13.8995i			1.80956i	−0.425879	+	0.904780i	$0.640035\pi$
$60$	−1.70711	+	0.292893i	−0.220387	+	0.0378124i
$61$			2.58579i			0.331076i	0.986203	+	0.165538i	$0.0529361\pi$
$61$			2.58579i			0.331076i	−0.986203	+	0.165538i	$0.947064\pi$
$62$	−5.41421			−0.687606
$63$	1.00000	+	2.82843i	0.125988	+	0.356348i
$64$	1.00000			0.125000
$65$	6.24264			0.774304
$66$	3.29289	+	4.70711i	0.405327	+	0.579405i
$67$	13.3137			1.62653			0.813264	−	0.581895i	$-0.197688\pi$
$67$	13.3137			1.62653			0.813264	+	0.581895i	$0.197688\pi$
$68$	−4.58579			−0.556108
$69$	−1.41421	+	0.242641i	−0.170251	+	0.0292105i
$70$	−1.00000			−0.119523
$71$		−	11.3137i		−	1.34269i	−0.741145	−	0.671345i	$-0.765717\pi$
$71$		−	11.3137i		−	1.34269i	0.741145	−	0.671345i	$-0.234283\pi$
$72$	−2.82843	+	1.00000i	−0.333333	+	0.117851i
$73$		−	4.58579i		−	0.536726i	−0.963318	−	0.268363i	$-0.913517\pi$
$73$		−	4.58579i		−	0.536726i	0.963318	−	0.268363i	$-0.0864826\pi$
$74$	−2.82843			−0.328798
$75$	0.292893	+	1.70711i	0.0338204	+	0.197120i
$76$		−	2.82843i		−	0.324443i
$77$	1.41421	+	3.00000i	0.161165	+	0.341882i
$78$	10.6569	−	1.82843i	1.20665	−	0.207029i
$79$			10.0000i			1.12509i	0.826767	+	0.562544i	$0.190177\pi$
$79$			10.0000i			1.12509i	−0.826767	+	0.562544i	$0.809823\pi$
$80$		−	1.00000i		−	0.111803i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$	−11.0711			−1.22259
$83$	−16.0000			−1.75623			−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000			−1.75623			−0.878114	+	0.478451i	$0.841198\pi$
$84$	−1.70711	+	0.292893i	−0.186261	+	0.0319573i
$85$			4.58579i			0.497398i
$86$			0.828427i			0.0893316i
$87$	2.00000	+	11.6569i	0.214423	+	1.24975i
$88$	−3.00000	+	1.41421i	−0.319801	+	0.150756i
$89$		−	7.65685i		−	0.811625i	−0.913956	−	0.405812i	$-0.866989\pi$
$89$		−	7.65685i		−	0.811625i	0.913956	−	0.405812i	$-0.133011\pi$
$90$	1.00000	+	2.82843i	0.105409	+	0.298142i
$91$	6.24264			0.654407
$92$		−	0.828427i		−	0.0863695i
$93$	1.58579	+	9.24264i	0.164438	+	0.958417i
$94$			0.585786i			0.0604193i
$95$	−2.82843			−0.290191
$96$	−0.292893	−	1.70711i	−0.0298933	−	0.174231i
$97$	3.65685			0.371297			0.185649	−	0.982616i	$-0.440561\pi$
$97$	3.65685			0.371297			0.185649	+	0.982616i	$0.440561\pi$
$98$	−1.00000			−0.101015
$99$	7.07107	−	7.00000i	0.710669	−	0.703526i
$100$	−1.00000			−0.100000
$101$	16.7279			1.66449			0.832245	−	0.554408i	$-0.187055\pi$
$101$	16.7279			1.66449			0.832245	+	0.554408i	$0.187055\pi$
$102$	1.34315	+	7.82843i	0.132991	+	0.775130i
$103$	−5.75736			−0.567289			−0.283645	−	0.958929i	$-0.591544\pi$
$103$	−5.75736			−0.567289			−0.283645	+	0.958929i	$0.591544\pi$
$104$			6.24264i			0.612141i
$105$	0.292893	+	1.70711i	0.0285835	+	0.166597i
$106$		−	13.3137i		−	1.29314i
$107$	14.4853			1.40035			0.700173	−	0.713974i	$-0.253106\pi$
$107$	14.4853			1.40035			0.700173	+	0.713974i	$0.253106\pi$
$108$	2.53553	+	4.53553i	0.243982	+	0.436432i
$109$			4.48528i			0.429612i	0.976657	+	0.214806i	$0.0689119\pi$
$109$			4.48528i			0.429612i	−0.976657	+	0.214806i	$0.931088\pi$
$110$	1.41421	+	3.00000i	0.134840	+	0.286039i
$111$	0.828427	+	4.82843i	0.0786308	+	0.458294i
$112$		−	1.00000i		−	0.0944911i
$113$			0.485281i			0.0456514i	0.999739	+	0.0228257i	$0.00726628\pi$
$113$			0.485281i			0.0456514i	−0.999739	+	0.0228257i	$0.992734\pi$
$114$	−4.82843	+	0.828427i	−0.452224	+	0.0775893i
$115$	−0.828427			−0.0772512
$116$	−6.82843			−0.634004
$117$	−6.24264	−	17.6569i	−0.577132	−	1.63238i
$118$			13.8995i			1.27955i
$119$			4.58579i			0.420378i
$120$	−1.70711	+	0.292893i	−0.155837	+	0.0267374i
$121$	7.00000	−	8.48528i	0.636364	−	0.771389i
$122$			2.58579i			0.234106i
$123$	3.24264	+	18.8995i	0.292379	+	1.70411i
$124$	−5.41421			−0.486211
$125$			1.00000i			0.0894427i
$126$	1.00000	+	2.82843i	0.0890871	+	0.251976i
$127$			21.6569i			1.92174i	0.277008	+	0.960868i	$0.410657\pi$
$127$			21.6569i			1.92174i	−0.277008	+	0.960868i	$0.589343\pi$
$128$	1.00000			0.0883883
$129$	1.41421	−	0.242641i	0.124515	−	0.0213633i
$130$	6.24264			0.547516
$131$	12.4853			1.09084			0.545422	−	0.838162i	$-0.316369\pi$
$131$	12.4853			1.09084			0.545422	+	0.838162i	$0.316369\pi$
$132$	3.29289	+	4.70711i	0.286610	+	0.409701i
$133$	−2.82843			−0.245256
$134$	13.3137			1.15013
$135$	4.53553	−	2.53553i	0.390357	−	0.218224i
$136$	−4.58579			−0.393228
$137$			0.343146i			0.0293169i	0.999893	+	0.0146585i	$0.00466610\pi$
$137$			0.343146i			0.0293169i	−0.999893	+	0.0146585i	$0.995334\pi$
$138$	−1.41421	+	0.242641i	−0.120386	+	0.0206549i
$139$		−	15.3137i		−	1.29889i	−0.760408	−	0.649446i	$-0.775001\pi$
$139$		−	15.3137i		−	1.29889i	0.760408	−	0.649446i	$-0.224999\pi$
$140$	−1.00000			−0.0845154
$141$	1.00000	−	0.171573i	0.0842152	−	0.0144490i
$142$		−	11.3137i		−	0.949425i
$143$	−8.82843	−	18.7279i	−0.738270	−	1.56611i
$144$	−2.82843	+	1.00000i	−0.235702	+	0.0833333i
$145$			6.82843i			0.567070i
$146$		−	4.58579i		−	0.379522i
$147$	0.292893	+	1.70711i	0.0241574	+	0.140800i
$148$	−2.82843			−0.232495
$149$	7.31371			0.599162			0.299581	−	0.954071i	$-0.403153\pi$
$149$	7.31371			0.599162			0.299581	+	0.954071i	$0.403153\pi$
$150$	0.292893	+	1.70711i	0.0239146	+	0.139385i
$151$		−	0.343146i		−	0.0279248i	−0.999903	−	0.0139624i	$-0.995555\pi$
$151$		−	0.343146i		−	0.0279248i	0.999903	−	0.0139624i	$-0.00444452\pi$
$152$		−	2.82843i		−	0.229416i
$153$	12.9706	−	4.58579i	1.04861	−	0.370739i
$154$	1.41421	+	3.00000i	0.113961	+	0.241747i
$155$			5.41421i			0.434880i
$156$	10.6569	−	1.82843i	0.853231	−	0.146391i
$157$	−12.1421			−0.969048			−0.484524	−	0.874778i	$-0.661007\pi$
$157$	−12.1421			−0.969048			−0.484524	+	0.874778i	$0.661007\pi$
$158$			10.0000i			0.795557i
$159$	−22.7279	+	3.89949i	−1.80244	+	0.309250i
$160$		−	1.00000i		−	0.0790569i
$161$	−0.828427			−0.0652892
$162$	7.00000	−	5.65685i	0.549972	−	0.444444i
$163$	−21.3137			−1.66942			−0.834709	−	0.550691i	$-0.814364\pi$
$163$	−21.3137			−1.66942			−0.834709	+	0.550691i	$0.814364\pi$
$164$	−11.0711			−0.864505
$165$	4.70711	−	3.29289i	0.366448	−	0.256351i
$166$	−16.0000			−1.24184
$167$	−14.8284			−1.14746			−0.573729	−	0.819045i	$-0.694504\pi$
$167$	−14.8284			−1.14746			−0.573729	+	0.819045i	$0.694504\pi$
$168$	−1.70711	+	0.292893i	−0.131706	+	0.0225972i
$169$	−25.9706			−1.99774
$170$			4.58579i			0.351714i
$171$	2.82843	+	8.00000i	0.216295	+	0.611775i
$172$			0.828427i			0.0631670i
$173$	−8.58579			−0.652765			−0.326383	−	0.945238i	$-0.605830\pi$
$173$	−8.58579			−0.652765			−0.326383	+	0.945238i	$0.605830\pi$
$174$	2.00000	+	11.6569i	0.151620	+	0.883704i
$175$			1.00000i			0.0755929i
$176$	−3.00000	+	1.41421i	−0.226134	+	0.106600i
$177$	23.7279	−	4.07107i	1.78350	−	0.306000i
$178$		−	7.65685i		−	0.573905i
$179$		−	22.1421i		−	1.65498i	−0.561480	−	0.827490i	$-0.689768\pi$
$179$		−	22.1421i		−	1.65498i	0.561480	−	0.827490i	$-0.310232\pi$
$180$	1.00000	+	2.82843i	0.0745356	+	0.210819i
$181$	−9.31371			−0.692283			−0.346141	−	0.938182i	$-0.612508\pi$
$181$	−9.31371			−0.692283			−0.346141	+	0.938182i	$0.612508\pi$
$182$	6.24264			0.462735
$183$	4.41421	−	0.757359i	0.326308	−	0.0559856i
$184$		−	0.828427i		−	0.0610725i
$185$			2.82843i			0.207950i
$186$	1.58579	+	9.24264i	0.116276	+	0.677703i
$187$	13.7574	−	6.48528i	1.00604	−	0.474251i
$188$			0.585786i			0.0427229i
$189$	4.53553	−	2.53553i	0.329912	−	0.184433i
$190$	−2.82843			−0.205196
$191$		−	4.48528i		−	0.324544i	−0.986746	−	0.162272i	$-0.948118\pi$
$191$		−	4.48528i		−	0.324544i	0.986746	−	0.162272i	$-0.0518821\pi$
$192$	−0.292893	−	1.70711i	−0.0211377	−	0.123200i
$193$			2.48528i			0.178894i	0.995992	+	0.0894472i	$0.0285100\pi$
$193$			2.48528i			0.178894i	−0.995992	+	0.0894472i	$0.971490\pi$
$194$	3.65685			0.262547
$195$	−1.82843	−	10.6569i	−0.130936	−	0.763153i
$196$	−1.00000			−0.0714286
$197$	0.828427			0.0590230			0.0295115	−	0.999564i	$-0.490605\pi$
$197$	0.828427			0.0590230			0.0295115	+	0.999564i	$0.490605\pi$
$198$	7.07107	−	7.00000i	0.502519	−	0.497468i
$199$	16.7279			1.18581			0.592905	−	0.805272i	$-0.297981\pi$
$199$	16.7279			1.18581			0.592905	+	0.805272i	$0.297981\pi$
$200$	−1.00000			−0.0707107
$201$	−3.89949	−	22.7279i	−0.275049	−	1.60310i
$202$	16.7279			1.17697
$203$			6.82843i			0.479262i
$204$	1.34315	+	7.82843i	0.0940390	+	0.548100i
$205$			11.0711i			0.773237i
$206$	−5.75736			−0.401134
$207$	0.828427	+	2.34315i	0.0575797	+	0.162860i
$208$			6.24264i			0.432849i
$209$	4.00000	+	8.48528i	0.276686	+	0.586939i
$210$	0.292893	+	1.70711i	0.0202116	+	0.117802i
$211$		−	9.65685i		−	0.664805i	−0.943138	−	0.332403i	$-0.892141\pi$
$211$		−	9.65685i		−	0.664805i	0.943138	−	0.332403i	$-0.107859\pi$
$212$		−	13.3137i		−	0.914389i
$213$	−19.3137	+	3.31371i	−1.32335	+	0.227052i
$214$	14.4853			0.990193
$215$	0.828427			0.0564983
$216$	2.53553	+	4.53553i	0.172521	+	0.308604i
$217$			5.41421i			0.367541i
$218$			4.48528i			0.303782i
$219$	−7.82843	+	1.34315i	−0.528996	+	0.0907614i
$220$	1.41421	+	3.00000i	0.0953463	+	0.202260i
$221$		−	28.6274i		−	1.92569i
$222$	0.828427	+	4.82843i	0.0556004	+	0.324063i
$223$	−17.5563			−1.17566			−0.587830	−	0.808984i	$-0.700018\pi$
$223$	−17.5563			−1.17566			−0.587830	+	0.808984i	$0.700018\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	2.82843	−	1.00000i	0.188562	−	0.0666667i
$226$			0.485281i			0.0322804i
$227$	−26.1421			−1.73511			−0.867557	−	0.497337i	$-0.834311\pi$
$227$	−26.1421			−1.73511			−0.867557	+	0.497337i	$0.834311\pi$
$228$	−4.82843	+	0.828427i	−0.319770	+	0.0548639i
$229$	3.17157			0.209583			0.104792	−	0.994494i	$-0.466582\pi$
$229$	3.17157			0.209583			0.104792	+	0.994494i	$0.466582\pi$
$230$	−0.828427			−0.0546249
$231$	4.70711	−	3.29289i	0.309705	−	0.216656i
$232$	−6.82843			−0.448308
$233$	−13.3137			−0.872210			−0.436105	−	0.899896i	$-0.643642\pi$
$233$	−13.3137			−0.872210			−0.436105	+	0.899896i	$0.643642\pi$
$234$	−6.24264	−	17.6569i	−0.408094	−	1.15426i
$235$	0.585786			0.0382125
$236$			13.8995i			0.904780i
$237$	17.0711	−	2.92893i	1.10889	−	0.190255i
$238$			4.58579i			0.297252i
$239$	13.3137			0.861192			0.430596	−	0.902545i	$-0.358303\pi$
$239$	13.3137			0.861192			0.430596	+	0.902545i	$0.358303\pi$
$240$	−1.70711	+	0.292893i	−0.110193	+	0.0189062i
$241$			9.89949i			0.637683i	0.947808	+	0.318841i	$0.103294\pi$
$241$			9.89949i			0.637683i	−0.947808	+	0.318841i	$0.896706\pi$
$242$	7.00000	−	8.48528i	0.449977	−	0.545455i
$243$	−11.7071	−	10.2929i	−0.751011	−	0.660289i
$244$			2.58579i			0.165538i
$245$			1.00000i			0.0638877i
$246$	3.24264	+	18.8995i	0.206743	+	1.20499i
$247$	17.6569			1.12348
$248$	−5.41421			−0.343803
$249$	4.68629	+	27.3137i	0.296982	+	1.73094i
$250$			1.00000i			0.0632456i
$251$			7.07107i			0.446322i	0.974782	+	0.223161i	$0.0716375\pi$
$251$			7.07107i			0.446322i	−0.974782	+	0.223161i	$0.928362\pi$
$252$	1.00000	+	2.82843i	0.0629941	+	0.178174i
$253$	1.17157	+	2.48528i	0.0736562	+	0.156248i
$254$			21.6569i			1.35887i
$255$	7.82843	−	1.34315i	0.490235	−	0.0841110i
$256$	1.00000			0.0625000
$257$		−	22.0000i		−	1.37232i	−0.727450	−	0.686161i	$-0.759294\pi$
$257$		−	22.0000i		−	1.37232i	0.727450	−	0.686161i	$-0.240706\pi$
$258$	1.41421	−	0.242641i	0.0880451	−	0.0151061i
$259$			2.82843i			0.175750i
$260$	6.24264			0.387152
$261$	19.3137	−	6.82843i	1.19549	−	0.422669i
$262$	12.4853			0.771343
$263$	−15.1716			−0.935519			−0.467760	−	0.883856i	$-0.654939\pi$
$263$	−15.1716			−0.935519			−0.467760	+	0.883856i	$0.654939\pi$
$264$	3.29289	+	4.70711i	0.202664	+	0.289702i
$265$	−13.3137			−0.817855
$266$	−2.82843			−0.173422
$267$	−13.0711	+	2.24264i	−0.799936	+	0.137247i
$268$	13.3137			0.813264
$269$		−	5.51472i		−	0.336238i	−0.985767	−	0.168119i	$-0.946231\pi$
$269$		−	5.51472i		−	0.336238i	0.985767	−	0.168119i	$-0.0537693\pi$
$270$	4.53553	−	2.53553i	0.276024	−	0.154308i
$271$		−	1.17157i		−	0.0711680i	−0.999367	−	0.0355840i	$-0.988671\pi$
$271$		−	1.17157i		−	0.0711680i	0.999367	−	0.0355840i	$-0.0113291\pi$
$272$	−4.58579			−0.278054
$273$	−1.82843	−	10.6569i	−0.110661	−	0.644982i
$274$			0.343146i			0.0207302i
$275$	3.00000	−	1.41421i	0.180907	−	0.0852803i
$276$	−1.41421	+	0.242641i	−0.0851257	+	0.0146053i
$277$			9.79899i			0.588764i	0.955688	+	0.294382i	$0.0951138\pi$
$277$			9.79899i			0.588764i	−0.955688	+	0.294382i	$0.904886\pi$
$278$		−	15.3137i		−	0.918455i
$279$	15.3137	−	5.41421i	0.916808	−	0.324140i
$280$	−1.00000			−0.0597614
$281$	8.48528			0.506189			0.253095	−	0.967442i	$-0.418552\pi$
$281$	8.48528			0.506189			0.253095	+	0.967442i	$0.418552\pi$
$282$	1.00000	−	0.171573i	0.0595491	−	0.0102170i
$283$			15.7990i			0.939152i	0.882892	+	0.469576i	$0.155593\pi$
$283$			15.7990i			0.939152i	−0.882892	+	0.469576i	$0.844407\pi$
$284$		−	11.3137i		−	0.671345i
$285$	0.828427	+	4.82843i	0.0490718	+	0.286011i
$286$	−8.82843	−	18.7279i	−0.522036	−	1.10741i
$287$			11.0711i			0.653504i
$288$	−2.82843	+	1.00000i	−0.166667	+	0.0589256i
$289$	4.02944			0.237026
$290$			6.82843i			0.400979i
$291$	−1.07107	−	6.24264i	−0.0627871	−	0.365950i
$292$		−	4.58579i		−	0.268363i
$293$	−7.41421			−0.433143			−0.216571	−	0.976267i	$-0.569487\pi$
$293$	−7.41421			−0.433143			−0.216571	+	0.976267i	$0.569487\pi$
$294$	0.292893	+	1.70711i	0.0170819	+	0.0995605i
$295$	13.8995			0.809260
$296$	−2.82843			−0.164399
$297$	−14.0208	−	10.0208i	−0.813570	−	0.581467i
$298$	7.31371			0.423672
$299$	5.17157			0.299080
$300$	0.292893	+	1.70711i	0.0169102	+	0.0985599i
$301$	0.828427			0.0477497
$302$		−	0.343146i		−	0.0197458i
$303$	−4.89949	−	28.5563i	−0.281469	−	1.64052i
$304$		−	2.82843i		−	0.162221i
$305$	2.58579			0.148062
$306$	12.9706	−	4.58579i	0.741478	−	0.262152i
$307$			4.68629i			0.267461i	0.991018	+	0.133730i	$0.0426956\pi$
$307$			4.68629i			0.267461i	−0.991018	+	0.133730i	$0.957304\pi$
$308$	1.41421	+	3.00000i	0.0805823	+	0.170941i
$309$	1.68629	+	9.82843i	0.0959298	+	0.559120i
$310$			5.41421i			0.307507i
$311$			28.7279i			1.62901i	0.580156	+	0.814506i	$0.302992\pi$
$311$			28.7279i			1.62901i	−0.580156	+	0.814506i	$0.697008\pi$
$312$	10.6569	−	1.82843i	0.603326	−	0.103514i
$313$	−11.1716			−0.631455			−0.315727	−	0.948850i	$-0.602248\pi$
$313$	−11.1716			−0.631455			−0.315727	+	0.948850i	$0.602248\pi$
$314$	−12.1421			−0.685220
$315$	2.82843	−	1.00000i	0.159364	−	0.0563436i
$316$			10.0000i			0.562544i
$317$		−	14.8284i		−	0.832847i	−0.909171	−	0.416424i	$-0.863283\pi$
$317$		−	14.8284i		−	0.832847i	0.909171	−	0.416424i	$-0.136717\pi$
$318$	−22.7279	+	3.89949i	−1.27452	+	0.218673i
$319$	20.4853	−	9.65685i	1.14696	−	0.540680i
$320$		−	1.00000i		−	0.0559017i
$321$	−4.24264	−	24.7279i	−0.236801	−	1.38018i
$322$	−0.828427			−0.0461664
$323$			12.9706i			0.721701i
$324$	7.00000	−	5.65685i	0.388889	−	0.314270i
$325$		−	6.24264i		−	0.346279i
$326$	−21.3137			−1.18046
$327$	7.65685	−	1.31371i	0.423425	−	0.0726482i
$328$	−11.0711			−0.611297
$329$	0.585786			0.0322955
$330$	4.70711	−	3.29289i	0.259118	−	0.181268i
$331$	24.9706			1.37251			0.686253	−	0.727363i	$-0.259254\pi$
$331$	24.9706			1.37251			0.686253	+	0.727363i	$0.259254\pi$
$332$	−16.0000			−0.878114
$333$	8.00000	−	2.82843i	0.438397	−	0.154997i
$334$	−14.8284			−0.811375
$335$		−	13.3137i		−	0.727406i
$336$	−1.70711	+	0.292893i	−0.0931303	+	0.0159786i
$337$		−	10.0000i		−	0.544735i	−0.962193	−	0.272367i	$-0.912193\pi$
$337$		−	10.0000i		−	0.544735i	0.962193	−	0.272367i	$-0.0878066\pi$
$338$	−25.9706			−1.41261
$339$	0.828427	−	0.142136i	0.0449940	−	0.00771975i
$340$			4.58579i			0.248699i
$341$	16.2426	−	7.65685i	0.879588	−	0.414642i
$342$	2.82843	+	8.00000i	0.152944	+	0.432590i
$343$			1.00000i			0.0539949i
$344$			0.828427i			0.0446658i
$345$	0.242641	+	1.41421i	0.0130633	+	0.0761387i
$346$	−8.58579			−0.461575
$347$	8.68629			0.466305			0.233152	−	0.972440i	$-0.425096\pi$
$347$	8.68629			0.466305			0.233152	+	0.972440i	$0.425096\pi$
$348$	2.00000	+	11.6569i	0.107211	+	0.624873i
$349$		−	10.5858i		−	0.566644i	−0.959025	−	0.283322i	$-0.908563\pi$
$349$		−	10.5858i		−	0.566644i	0.959025	−	0.283322i	$-0.0914365\pi$
$350$			1.00000i			0.0534522i
$351$	−28.3137	+	15.8284i	−1.51127	+	0.844859i
$352$	−3.00000	+	1.41421i	−0.159901	+	0.0753778i
$353$		−	30.4853i		−	1.62257i	−0.584652	−	0.811284i	$-0.698769\pi$
$353$		−	30.4853i		−	1.62257i	0.584652	−	0.811284i	$-0.301231\pi$
$354$	23.7279	−	4.07107i	1.26112	−	0.216375i
$355$	−11.3137			−0.600469
$356$		−	7.65685i		−	0.405812i
$357$	7.82843	−	1.34315i	0.414324	−	0.0710868i
$358$		−	22.1421i		−	1.17025i
$359$	20.9706			1.10678			0.553392	−	0.832921i	$-0.313333\pi$
$359$	20.9706			1.10678			0.553392	+	0.832921i	$0.313333\pi$
$360$	1.00000	+	2.82843i	0.0527046	+	0.149071i
$361$	11.0000			0.578947
$362$	−9.31371			−0.489518
$363$	−16.5355	−	9.46447i	−0.867890	−	0.496756i
$364$	6.24264			0.327203
$365$	−4.58579			−0.240031
$366$	4.41421	−	0.757359i	0.230735	−	0.0395878i
$367$	2.24264			0.117065			0.0585324	−	0.998286i	$-0.481358\pi$
$367$	2.24264			0.117065			0.0585324	+	0.998286i	$0.481358\pi$
$368$		−	0.828427i		−	0.0431847i
$369$	31.3137	−	11.0711i	1.63013	−	0.576337i
$370$			2.82843i			0.147043i
$371$	−13.3137			−0.691213
$372$	1.58579	+	9.24264i	0.0822192	+	0.479209i
$373$		−	7.17157i		−	0.371330i	−0.982613	−	0.185665i	$-0.940556\pi$
$373$		−	7.17157i		−	0.371330i	0.982613	−	0.185665i	$-0.0594439\pi$
$374$	13.7574	−	6.48528i	0.711376	−	0.335346i
$375$	1.70711	−	0.292893i	0.0881546	−	0.0151249i
$376$			0.585786i			0.0302096i
$377$		−	42.6274i		−	2.19542i
$378$	4.53553	−	2.53553i	0.233283	−	0.130414i
$379$	−28.4853			−1.46319			−0.731595	−	0.681739i	$-0.761224\pi$
$379$	−28.4853			−1.46319			−0.731595	+	0.681739i	$0.761224\pi$
$380$	−2.82843			−0.145095
$381$	36.9706	−	6.34315i	1.89406	−	0.324969i
$382$		−	4.48528i		−	0.229487i
$383$			22.7279i			1.16134i	0.814138	+	0.580671i	$0.197210\pi$
$383$			22.7279i			1.16134i	−0.814138	+	0.580671i	$0.802790\pi$
$384$	−0.292893	−	1.70711i	−0.0149466	−	0.0871154i
$385$	3.00000	−	1.41421i	0.152894	−	0.0720750i
$386$			2.48528i			0.126497i
$387$	−0.828427	−	2.34315i	−0.0421113	−	0.119109i
$388$	3.65685			0.185649
$389$			24.0000i			1.21685i	0.793612	+	0.608424i	$0.208198\pi$
$389$			24.0000i			1.21685i	−0.793612	+	0.608424i	$0.791802\pi$
$390$	−1.82843	−	10.6569i	−0.0925860	−	0.539631i
$391$			3.79899i			0.192123i
$392$	−1.00000			−0.0505076
$393$	−3.65685	−	21.3137i	−0.184464	−	1.07513i
$394$	0.828427			0.0417356
$395$	10.0000			0.503155
$396$	7.07107	−	7.00000i	0.355335	−	0.351763i
$397$	−8.14214			−0.408642			−0.204321	−	0.978904i	$-0.565499\pi$
$397$	−8.14214			−0.408642			−0.204321	+	0.978904i	$0.565499\pi$
$398$	16.7279			0.838495
$399$	0.828427	+	4.82843i	0.0414732	+	0.241724i
$400$	−1.00000			−0.0500000
$401$			26.3431i			1.31551i	0.753230	+	0.657757i	$0.228495\pi$
$401$			26.3431i			1.31551i	−0.753230	+	0.657757i	$0.771505\pi$
$402$	−3.89949	−	22.7279i	−0.194489	−	1.13357i
$403$		−	33.7990i		−	1.68365i
$404$	16.7279			0.832245
$405$	−5.65685	−	7.00000i	−0.281091	−	0.347833i
$406$			6.82843i			0.338889i
$407$	8.48528	−	4.00000i	0.420600	−	0.198273i
$408$	1.34315	+	7.82843i	0.0664956	+	0.387565i
$409$			12.9289i			0.639295i	0.947537	+	0.319647i	$0.103564\pi$
$409$			12.9289i			0.639295i	−0.947537	+	0.319647i	$0.896436\pi$
$410$			11.0711i			0.546761i
$411$	0.585786	−	0.100505i	0.0288947	−	0.00495755i
$412$	−5.75736			−0.283645
$413$	13.8995			0.683949
$414$	0.828427	+	2.34315i	0.0407150	+	0.115159i
$415$			16.0000i			0.785409i
$416$			6.24264i			0.306071i
$417$	−26.1421	+	4.48528i	−1.28019	+	0.219645i
$418$	4.00000	+	8.48528i	0.195646	+	0.415029i
$419$		−	3.75736i		−	0.183559i	−0.995779	−	0.0917795i	$-0.970745\pi$
$419$		−	3.75736i		−	0.183559i	0.995779	−	0.0917795i	$-0.0292555\pi$
$420$	0.292893	+	1.70711i	0.0142917	+	0.0832983i
$421$	14.3431			0.699042			0.349521	−	0.936929i	$-0.386344\pi$
$421$	14.3431			0.699042			0.349521	+	0.936929i	$0.386344\pi$
$422$		−	9.65685i		−	0.470088i
$423$	−0.585786	−	1.65685i	−0.0284819	−	0.0805590i
$424$		−	13.3137i		−	0.646571i
$425$	4.58579			0.222443
$426$	−19.3137	+	3.31371i	−0.935752	+	0.160550i
$427$	2.58579			0.125135
$428$	14.4853			0.700173
$429$	−29.3848	+	20.5563i	−1.41871	+	0.992470i
$430$	0.828427			0.0399503
$431$	−23.3137			−1.12298			−0.561491	−	0.827483i	$-0.689772\pi$
$431$	−23.3137			−1.12298			−0.561491	+	0.827483i	$0.689772\pi$
$432$	2.53553	+	4.53553i	0.121991	+	0.218216i
$433$	11.4558			0.550533			0.275266	−	0.961368i	$-0.411234\pi$
$433$	11.4558			0.550533			0.275266	+	0.961368i	$0.411234\pi$
$434$			5.41421i			0.259891i
$435$	11.6569	−	2.00000i	0.558903	−	0.0958927i
$436$			4.48528i			0.214806i
$437$	−2.34315			−0.112088
$438$	−7.82843	+	1.34315i	−0.374057	+	0.0641780i
$439$		−	23.7990i		−	1.13586i	−0.823076	−	0.567932i	$-0.807744\pi$
$439$		−	23.7990i		−	1.13586i	0.823076	−	0.567932i	$-0.192256\pi$
$440$	1.41421	+	3.00000i	0.0674200	+	0.143019i
$441$	2.82843	−	1.00000i	0.134687	−	0.0476190i
$442$		−	28.6274i		−	1.36167i
$443$		−	28.3431i		−	1.34662i	−0.739359	−	0.673312i	$-0.764871\pi$
$443$		−	28.3431i		−	1.34662i	0.739359	−	0.673312i	$-0.235129\pi$
$444$	0.828427	+	4.82843i	0.0393154	+	0.229147i
$445$	−7.65685			−0.362970
$446$	−17.5563			−0.831317
$447$	−2.14214	−	12.4853i	−0.101320	−	0.590534i
$448$		−	1.00000i		−	0.0472456i
$449$		−	2.68629i		−	0.126774i	−0.997989	−	0.0633870i	$-0.979810\pi$
$449$		−	2.68629i		−	0.126774i	0.997989	−	0.0633870i	$-0.0201902\pi$
$450$	2.82843	−	1.00000i	0.133333	−	0.0471405i
$451$	33.2132	−	15.6569i	1.56395	−	0.737252i
$452$			0.485281i			0.0228257i
$453$	−0.585786	+	0.100505i	−0.0275226	+	0.00472214i
$454$	−26.1421			−1.22691
$455$		−	6.24264i		−	0.292660i
$456$	−4.82843	+	0.828427i	−0.226112	+	0.0387947i
$457$			19.1716i			0.896808i	0.893831	+	0.448404i	$0.148007\pi$
$457$			19.1716i			0.896808i	−0.893831	+	0.448404i	$0.851993\pi$
$458$	3.17157			0.148198
$459$	−11.6274	−	20.7990i	−0.542721	−	0.970814i
$460$	−0.828427			−0.0386256
$461$	−33.2132			−1.54689			−0.773447	−	0.633862i	$-0.781469\pi$
$461$	−33.2132			−1.54689			−0.773447	+	0.633862i	$0.781469\pi$
$462$	4.70711	−	3.29289i	0.218994	−	0.153199i
$463$	12.6274			0.586846			0.293423	−	0.955983i	$-0.405206\pi$
$463$	12.6274			0.586846			0.293423	+	0.955983i	$0.405206\pi$
$464$	−6.82843			−0.317002
$465$	9.24264	−	1.58579i	0.428617	−	0.0735391i
$466$	−13.3137			−0.616746
$467$			42.5269i			1.96791i	0.178415	+	0.983955i	$0.442903\pi$
$467$			42.5269i			1.96791i	−0.178415	+	0.983955i	$0.557097\pi$
$468$	−6.24264	−	17.6569i	−0.288566	−	0.816188i
$469$		−	13.3137i		−	0.614770i
$470$	0.585786			0.0270203
$471$	3.55635	+	20.7279i	0.163868	+	0.955092i
$472$			13.8995i			0.639776i
$473$	−1.17157	−	2.48528i	−0.0538690	−	0.114273i
$474$	17.0711	−	2.92893i	0.784100	−	0.134530i
$475$			2.82843i			0.129777i
$476$			4.58579i			0.210189i
$477$	13.3137	+	37.6569i	0.609593	+	1.72419i
$478$	13.3137			0.608955
$479$	−8.48528			−0.387702			−0.193851	−	0.981031i	$-0.562098\pi$
$479$	−8.48528			−0.387702			−0.193851	+	0.981031i	$0.562098\pi$
$480$	−1.70711	+	0.292893i	−0.0779184	+	0.0133687i
$481$		−	17.6569i		−	0.805083i
$482$			9.89949i			0.450910i
$483$	0.242641	+	1.41421i	0.0110405	+	0.0643489i
$484$	7.00000	−	8.48528i	0.318182	−	0.385695i
$485$		−	3.65685i		−	0.166049i
$486$	−11.7071	−	10.2929i	−0.531045	−	0.466895i
$487$	−10.9706			−0.497124			−0.248562	−	0.968616i	$-0.579958\pi$
$487$	−10.9706			−0.497124			−0.248562	+	0.968616i	$0.579958\pi$
$488$			2.58579i			0.117053i
$489$	6.24264	+	36.3848i	0.282302	+	1.64538i
$490$			1.00000i			0.0451754i
$491$	−37.9411			−1.71226			−0.856130	−	0.516761i	$-0.827137\pi$
$491$	−37.9411			−1.71226			−0.856130	+	0.516761i	$0.827137\pi$
$492$	3.24264	+	18.8995i	0.146190	+	0.852055i
$493$	31.3137			1.41030
$494$	17.6569			0.794419
$495$	−7.00000	−	7.07107i	−0.314627	−	0.317821i
$496$	−5.41421			−0.243105
$497$	−11.3137			−0.507489
$498$	4.68629	+	27.3137i	0.209998	+	1.22396i
$499$	2.82843			0.126618			0.0633089	−	0.997994i	$-0.479835\pi$
$499$	2.82843			0.126618			0.0633089	+	0.997994i	$0.479835\pi$
$500$			1.00000i			0.0447214i
$501$	4.34315	+	25.3137i	0.194037	+	1.13093i
$502$			7.07107i			0.315597i
$503$	−29.4558			−1.31337			−0.656686	−	0.754164i	$-0.728042\pi$
$503$	−29.4558			−1.31337			−0.656686	+	0.754164i	$0.728042\pi$
$504$	1.00000	+	2.82843i	0.0445435	+	0.125988i
$505$		−	16.7279i		−	0.744383i
$506$	1.17157	+	2.48528i	0.0520828	+	0.110484i
$507$	7.60660	+	44.3345i	0.337821	+	1.96897i
$508$			21.6569i			0.960868i
$509$		−	24.3431i		−	1.07899i	−0.841988	−	0.539495i	$-0.818615\pi$
$509$		−	24.3431i		−	1.07899i	0.841988	−	0.539495i	$-0.181385\pi$
$510$	7.82843	−	1.34315i	0.346649	−	0.0594755i
$511$	−4.58579			−0.202863
$512$	1.00000			0.0441942
$513$	12.8284	−	7.17157i	0.566389	−	0.316633i
$514$		−	22.0000i		−	0.970378i
$515$			5.75736i			0.253700i
$516$	1.41421	−	0.242641i	0.0622573	−	0.0106817i
$517$	−0.828427	−	1.75736i	−0.0364342	−	0.0772886i
$518$			2.82843i			0.124274i
$519$	2.51472	+	14.6569i	0.110384	+	0.643364i
$520$	6.24264			0.273758
$521$		−	12.6274i		−	0.553217i	−0.960983	−	0.276609i	$-0.910789\pi$
$521$		−	12.6274i		−	0.553217i	0.960983	−	0.276609i	$-0.0892105\pi$
$522$	19.3137	−	6.82843i	0.845338	−	0.298872i
$523$		−	44.2843i		−	1.93642i	−0.250147	−	0.968208i	$-0.580479\pi$
$523$		−	44.2843i		−	1.93642i	0.250147	−	0.968208i	$-0.419521\pi$
$524$	12.4853			0.545422
$525$	1.70711	−	0.292893i	0.0745042	−	0.0127829i
$526$	−15.1716			−0.661512
$527$	24.8284			1.08154
$528$	3.29289	+	4.70711i	0.143305	+	0.204851i
$529$	22.3137			0.970161
$530$	−13.3137			−0.578311
$531$	−13.8995	−	39.3137i	−0.603187	−	1.70607i
$532$	−2.82843			−0.122628
$533$		−	69.1127i		−	2.99360i
$534$	−13.0711	+	2.24264i	−0.565640	+	0.0970486i
$535$		−	14.4853i		−	0.626253i
$536$	13.3137			0.575065
$537$	−37.7990	+	6.48528i	−1.63115	+	0.279861i
$538$		−	5.51472i		−	0.237756i
$539$	3.00000	−	1.41421i	0.129219	−	0.0609145i
$540$	4.53553	−	2.53553i	0.195178	−	0.109112i
$541$		−	10.6274i		−	0.456908i	−0.973555	−	0.228454i	$-0.926633\pi$
$541$		−	10.6274i		−	0.456908i	0.973555	−	0.228454i	$-0.0733671\pi$
$542$		−	1.17157i		−	0.0503234i
$543$	2.72792	+	15.8995i	0.117066	+	0.682313i
$544$	−4.58579			−0.196614
$545$	4.48528			0.192128
$546$	−1.82843	−	10.6569i	−0.0782495	−	0.456071i
$547$			7.31371i			0.312712i	0.987701	+	0.156356i	$0.0499746\pi$
$547$			7.31371i			0.312712i	−0.987701	+	0.156356i	$0.950025\pi$
$548$			0.343146i			0.0146585i
$549$	−2.58579	−	7.31371i	−0.110359	−	0.312141i
$550$	3.00000	−	1.41421i	0.127920	−	0.0603023i
$551$			19.3137i			0.822792i
$552$	−1.41421	+	0.242641i	−0.0601929	+	0.0103275i
$553$	10.0000			0.425243
$554$			9.79899i			0.416319i
$555$	4.82843	−	0.828427i	0.204955	−	0.0351648i
$556$		−	15.3137i		−	0.649446i
$557$	30.4853			1.29170			0.645851	−	0.763463i	$-0.276503\pi$
$557$	30.4853			1.29170			0.645851	+	0.763463i	$0.276503\pi$
$558$	15.3137	−	5.41421i	0.648281	−	0.229202i
$559$	−5.17157			−0.218734
$560$	−1.00000			−0.0422577
$561$	−15.1005	−	21.5858i	−0.637544	−	0.911353i
$562$	8.48528			0.357930
$563$	−15.7990			−0.665848			−0.332924	−	0.942954i	$-0.608035\pi$
$563$	−15.7990			−0.665848			−0.332924	+	0.942954i	$0.608035\pi$
$564$	1.00000	−	0.171573i	0.0421076	−	0.00722452i
$565$	0.485281			0.0204159
$566$			15.7990i			0.664081i
$567$	−5.65685	−	7.00000i	−0.237566	−	0.293972i
$568$		−	11.3137i		−	0.474713i
$569$	6.82843			0.286263			0.143131	−	0.989704i	$-0.454283\pi$
$569$	6.82843			0.286263			0.143131	+	0.989704i	$0.454283\pi$
$570$	0.828427	+	4.82843i	0.0346990	+	0.202241i
$571$		−	12.6863i		−	0.530905i	−0.964124	−	0.265452i	$-0.914479\pi$
$571$		−	12.6863i		−	0.530905i	0.964124	−	0.265452i	$-0.0855213\pi$
$572$	−8.82843	−	18.7279i	−0.369135	−	0.783054i
$573$	−7.65685	+	1.31371i	−0.319870	+	0.0548810i
$574$			11.0711i			0.462097i
$575$			0.828427i			0.0345478i
$576$	−2.82843	+	1.00000i	−0.117851	+	0.0416667i
$577$	13.3137			0.554257			0.277128	−	0.960833i	$-0.410617\pi$
$577$	13.3137			0.554257			0.277128	+	0.960833i	$0.410617\pi$
$578$	4.02944			0.167602
$579$	4.24264	−	0.727922i	0.176318	−	0.0302514i
$580$			6.82843i			0.283535i
$581$			16.0000i			0.663792i
$582$	−1.07107	−	6.24264i	−0.0443972	−	0.258766i
$583$	18.8284	+	39.9411i	0.779794	+	1.65419i
$584$		−	4.58579i		−	0.189761i
$585$	−17.6569	+	6.24264i	−0.730021	+	0.258101i
$586$	−7.41421			−0.306278
$587$			26.9289i			1.11148i	0.831357	+	0.555738i	$0.187564\pi$
$587$			26.9289i			1.11148i	−0.831357	+	0.555738i	$0.812436\pi$
$588$	0.292893	+	1.70711i	0.0120787	+	0.0703999i
$589$			15.3137i			0.630990i
$590$	13.8995			0.572233
$591$	−0.242641	−	1.41421i	−0.00998090	−	0.0581730i
$592$	−2.82843			−0.116248
$593$	−34.7279			−1.42610			−0.713052	−	0.701111i	$-0.752688\pi$
$593$	−34.7279			−1.42610			−0.713052	+	0.701111i	$0.752688\pi$
$594$	−14.0208	−	10.0208i	−0.575281	−	0.411159i
$595$	4.58579			0.187999
$596$	7.31371			0.299581
$597$	−4.89949	−	28.5563i	−0.200523	−	1.16873i
$598$	5.17157			0.211481
$599$		−	14.3431i		−	0.586045i	−0.956106	−	0.293023i	$-0.905339\pi$
$599$		−	14.3431i		−	0.586045i	0.956106	−	0.293023i	$-0.0946611\pi$
$600$	0.292893	+	1.70711i	0.0119573	+	0.0696923i
$601$		−	11.7574i		−	0.479593i	−0.970823	−	0.239796i	$-0.922919\pi$
$601$		−	11.7574i		−	0.479593i	0.970823	−	0.239796i	$-0.0770807\pi$
$602$	0.828427			0.0337642
$603$	−37.6569	+	13.3137i	−1.53351	+	0.542176i
$604$		−	0.343146i		−	0.0139624i
$605$	−8.48528	−	7.00000i	−0.344976	−	0.284590i
$606$	−4.89949	−	28.5563i	−0.199028	−	1.16002i
$607$			11.7990i			0.478906i	0.970908	+	0.239453i	$0.0769681\pi$
$607$			11.7990i			0.478906i	−0.970908	+	0.239453i	$0.923032\pi$
$608$		−	2.82843i		−	0.114708i
$609$	11.6569	−	2.00000i	0.472360	−	0.0810441i
$610$	2.58579			0.104695
$611$	−3.65685			−0.147940
$612$	12.9706	−	4.58579i	0.524304	−	0.185369i
$613$		−	21.3137i		−	0.860853i	−0.902626	−	0.430426i	$-0.858363\pi$
$613$		−	21.3137i		−	0.860853i	0.902626	−	0.430426i	$-0.141637\pi$
$614$			4.68629i			0.189123i
$615$	18.8995	−	3.24264i	0.762101	−	0.130756i
$616$	1.41421	+	3.00000i	0.0569803	+	0.120873i
$617$		−	10.0000i		−	0.402585i	−0.979531	−	0.201292i	$-0.935486\pi$
$617$		−	10.0000i		−	0.402585i	0.979531	−	0.201292i	$-0.0645141\pi$
$618$	1.68629	+	9.82843i	0.0678326	+	0.395357i
$619$	−0.0416306			−0.00167327			−0.000836637	−	1.00000i	$-0.500266\pi$
$619$	−0.0416306			−0.00167327			−0.000836637		1.00000i	$0.500266\pi$
$620$			5.41421i			0.217440i
$621$	3.75736	−	2.10051i	0.150778	−	0.0842904i
$622$			28.7279i			1.15188i
$623$	−7.65685			−0.306765
$624$	10.6569	−	1.82843i	0.426616	−	0.0731957i
$625$	1.00000			0.0400000
$626$	−11.1716			−0.446506
$627$	13.3137	−	9.31371i	0.531698	−	0.371954i
$628$	−12.1421			−0.484524
$629$	12.9706			0.517170
$630$	2.82843	−	1.00000i	0.112687	−	0.0398410i
$631$	12.2843			0.489029			0.244515	−	0.969646i	$-0.421371\pi$
$631$	12.2843			0.489029			0.244515	+	0.969646i	$0.421371\pi$
$632$			10.0000i			0.397779i
$633$	−16.4853	+	2.82843i	−0.655231	+	0.112420i
$634$		−	14.8284i		−	0.588912i
$635$	21.6569			0.859426
$636$	−22.7279	+	3.89949i	−0.901221	+	0.154625i
$637$		−	6.24264i		−	0.247342i
$638$	20.4853	−	9.65685i	0.811020	−	0.382319i
$639$	11.3137	+	32.0000i	0.447563	+	1.26590i
$640$		−	1.00000i		−	0.0395285i
$641$		−	22.2843i		−	0.880176i	−0.897955	−	0.440088i	$-0.854947\pi$
$641$		−	22.2843i		−	0.880176i	0.897955	−	0.440088i	$-0.145053\pi$
$642$	−4.24264	−	24.7279i	−0.167444	−	0.975933i
$643$	11.4142			0.450133			0.225066	−	0.974343i	$-0.427740\pi$
$643$	11.4142			0.450133			0.225066	+	0.974343i	$0.427740\pi$
$644$	−0.828427			−0.0326446
$645$	−0.242641	−	1.41421i	−0.00955397	−	0.0556846i
$646$			12.9706i			0.510320i
$647$			25.7574i			1.01263i	0.862350	+	0.506313i	$0.168992\pi$
$647$			25.7574i			1.01263i	−0.862350	+	0.506313i	$0.831008\pi$
$648$	7.00000	−	5.65685i	0.274986	−	0.222222i
$649$	−19.6569	−	41.6985i	−0.771599	−	1.63681i
$650$		−	6.24264i		−	0.244857i
$651$	9.24264	−	1.58579i	0.362248	−	0.0621519i
$652$	−21.3137			−0.834709
$653$			30.1421i			1.17955i	0.807567	+	0.589776i	$0.200784\pi$
$653$			30.1421i			1.17955i	−0.807567	+	0.589776i	$0.799216\pi$
$654$	7.65685	−	1.31371i	0.299407	−	0.0513701i
$655$		−	12.4853i		−	0.487840i
$656$	−11.0711			−0.432253
$657$	4.58579	+	12.9706i	0.178909	+	0.506030i
$658$	0.585786			0.0228363
$659$	17.9411			0.698887			0.349444	−	0.936957i	$-0.386371\pi$
$659$	17.9411			0.698887			0.349444	+	0.936957i	$0.386371\pi$
$660$	4.70711	−	3.29289i	0.183224	−	0.128176i
$661$	−51.2548			−1.99358			−0.996791	−	0.0800482i	$-0.974493\pi$
$661$	−51.2548			−1.99358			−0.996791	+	0.0800482i	$0.974493\pi$
$662$	24.9706			0.970508
$663$	−48.8701	+	8.38478i	−1.89796	+	0.325638i
$664$	−16.0000			−0.620920
$665$			2.82843i			0.109682i
$666$	8.00000	−	2.82843i	0.309994	−	0.109599i
$667$			5.65685i			0.219034i
$668$	−14.8284			−0.573729
$669$	5.14214	+	29.9706i	0.198806	+	1.15873i
$670$		−	13.3137i		−	0.514353i
$671$	−3.65685	−	7.75736i	−0.141171	−	0.299470i
$672$	−1.70711	+	0.292893i	−0.0658531	+	0.0112986i
$673$			6.97056i			0.268695i	0.990934	+	0.134348i	$0.0428939\pi$
$673$			6.97056i			0.268695i	−0.990934	+	0.134348i	$0.957106\pi$
$674$		−	10.0000i		−	0.385186i
$675$	−2.53553	−	4.53553i	−0.0975927	−	0.174573i
$676$	−25.9706			−0.998868
$677$	29.3553			1.12822			0.564109	−	0.825701i	$-0.309220\pi$
$677$	29.3553			1.12822			0.564109	+	0.825701i	$0.309220\pi$
$678$	0.828427	−	0.142136i	0.0318156	−	0.00545869i
$679$		−	3.65685i		−	0.140337i
$680$			4.58579i			0.175857i
$681$	7.65685	+	44.6274i	0.293411	+	1.71013i
$682$	16.2426	−	7.65685i	0.621963	−	0.293196i
$683$			50.2843i			1.92407i	0.272919	+	0.962037i	$0.412011\pi$
$683$			50.2843i			1.92407i	−0.272919	+	0.962037i	$0.587989\pi$
$684$	2.82843	+	8.00000i	0.108148	+	0.305888i
$685$	0.343146			0.0131109
$686$			1.00000i			0.0381802i
$687$	−0.928932	−	5.41421i	−0.0354410	−	0.206565i
$688$			0.828427i			0.0315835i
$689$	83.1127			3.16634
$690$	0.242641	+	1.41421i	0.00923717	+	0.0538382i
$691$	43.3553			1.64931			0.824657	−	0.565633i	$-0.191368\pi$
$691$	43.3553			1.64931			0.824657	+	0.565633i	$0.191368\pi$
$692$	−8.58579			−0.326383
$693$	−7.00000	−	7.07107i	−0.265908	−	0.268608i
$694$	8.68629			0.329727
$695$	−15.3137			−0.580882
$696$	2.00000	+	11.6569i	0.0758098	+	0.441852i
$697$	50.7696			1.92303
$698$		−	10.5858i		−	0.400678i
$699$	3.89949	+	22.7279i	0.147492	+	0.859649i
$700$			1.00000i			0.0377964i
$701$	−10.1421			−0.383063			−0.191532	−	0.981486i	$-0.561345\pi$
$701$	−10.1421			−0.383063			−0.191532	+	0.981486i	$0.561345\pi$
$702$	−28.3137	+	15.8284i	−1.06863	+	0.597405i
$703$			8.00000i			0.301726i
$704$	−3.00000	+	1.41421i	−0.113067	+	0.0533002i
$705$	−0.171573	−	1.00000i	−0.00646181	−	0.0376622i
$706$		−	30.4853i		−	1.14733i
$707$		−	16.7279i		−	0.629118i
$708$	23.7279	−	4.07107i	0.891750	−	0.153000i
$709$	−12.6274			−0.474233			−0.237116	−	0.971481i	$-0.576202\pi$
$709$	−12.6274			−0.474233			−0.237116	+	0.971481i	$0.576202\pi$
$710$	−11.3137			−0.424596
$711$	−10.0000	−	28.2843i	−0.375029	−	1.06074i
$712$		−	7.65685i		−	0.286953i
$713$			4.48528i			0.167975i
$714$	7.82843	−	1.34315i	0.292972	−	0.0502660i
$715$	−18.7279	+	8.82843i	−0.700385	+	0.330164i
$716$		−	22.1421i		−	0.827490i
$717$	−3.89949	−	22.7279i	−0.145629	−	0.848790i
$718$	20.9706			0.782614
$719$			29.6985i			1.10757i	0.832661	+	0.553783i	$0.186816\pi$
$719$			29.6985i			1.10757i	−0.832661	+	0.553783i	$0.813184\pi$
$720$	1.00000	+	2.82843i	0.0372678	+	0.105409i
$721$			5.75736i			0.214415i
$722$	11.0000			0.409378
$723$	16.8995	−	2.89949i	0.628499	−	0.107833i
$724$	−9.31371			−0.346141
$725$	6.82843			0.253601
$726$	−16.5355	−	9.46447i	−0.613691	−	0.351259i
$727$	26.0416			0.965831			0.482915	−	0.875667i	$-0.339578\pi$
$727$	26.0416			0.965831			0.482915	+	0.875667i	$0.339578\pi$
$728$	6.24264			0.231368
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$	−4.58579			−0.169728
$731$		−	3.79899i		−	0.140511i
$732$	4.41421	−	0.757359i	0.163154	−	0.0279928i
$733$		−	39.2132i		−	1.44837i	−0.689604	−	0.724186i	$-0.742216\pi$
$733$		−	39.2132i		−	1.44837i	0.689604	−	0.724186i	$-0.257784\pi$
$734$	2.24264			0.0827774
$735$	1.70711	−	0.292893i	0.0629676	−	0.0108035i
$736$		−	0.828427i		−	0.0305362i
$737$	−39.9411	+	18.8284i	−1.47125	+	0.693554i
$738$	31.3137	−	11.0711i	1.15267	−	0.407532i
$739$			26.6274i			0.979505i	0.871861	+	0.489753i	$0.162913\pi$
$739$			26.6274i			0.979505i	−0.871861	+	0.489753i	$0.837087\pi$
$740$			2.82843i			0.103975i
$741$	−5.17157	−	30.1421i	−0.189982	−	1.10730i
$742$	−13.3137			−0.488762
$743$	11.4558			0.420274			0.210137	−	0.977672i	$-0.432609\pi$
$743$	11.4558			0.420274			0.210137	+	0.977672i	$0.432609\pi$
$744$	1.58579	+	9.24264i	0.0581378	+	0.338852i
$745$		−	7.31371i		−	0.267954i
$746$		−	7.17157i		−	0.262570i
$747$	45.2548	−	16.0000i	1.65579	−	0.585409i
$748$	13.7574	−	6.48528i	0.503019	−	0.237125i
$749$		−	14.4853i		−	0.529281i
$750$	1.70711	−	0.292893i	0.0623347	−	0.0106949i
$751$	39.7990			1.45229			0.726143	−	0.687544i	$-0.241311\pi$
$751$	39.7990			1.45229			0.726143	+	0.687544i	$0.241311\pi$
$752$			0.585786i			0.0213614i
$753$	12.0711	−	2.07107i	0.439894	−	0.0754739i
$754$		−	42.6274i		−	1.55240i
$755$	−0.343146			−0.0124884
$756$	4.53553	−	2.53553i	0.164956	−	0.0922165i
$757$	−45.3137			−1.64695			−0.823477	−	0.567349i	$-0.807969\pi$
$757$	−45.3137			−1.64695			−0.823477	+	0.567349i	$0.807969\pi$
$758$	−28.4853			−1.03463
$759$	3.89949	−	2.72792i	0.141543	−	0.0990173i
$760$	−2.82843			−0.102598
$761$	−19.7574			−0.716204			−0.358102	−	0.933683i	$-0.616576\pi$
$761$	−19.7574			−0.716204			−0.358102	+	0.933683i	$0.616576\pi$
$762$	36.9706	−	6.34315i	1.33930	−	0.229788i
$763$	4.48528			0.162378
$764$		−	4.48528i		−	0.162272i
$765$	−4.58579	−	12.9706i	−0.165799	−	0.468952i
$766$			22.7279i			0.821193i
$767$	−86.7696			−3.13307
$768$	−0.292893	−	1.70711i	−0.0105689	−	0.0615999i
$769$			43.7574i			1.57793i	0.614438	+	0.788965i	$0.289383\pi$
$769$			43.7574i			1.57793i	−0.614438	+	0.788965i	$0.710617\pi$
$770$	3.00000	−	1.41421i	0.108112	−	0.0509647i
$771$	−37.5563	+	6.44365i	−1.35256	+	0.232062i
$772$			2.48528i			0.0894472i
$773$			20.1421i			0.724462i	0.932088	+	0.362231i	$0.117985\pi$
$773$			20.1421i			0.724462i	−0.932088	+	0.362231i	$0.882015\pi$
$774$	−0.828427	−	2.34315i	−0.0297772	−	0.0842226i
$775$	5.41421			0.194484
$776$	3.65685			0.131273
$777$	4.82843	−	0.828427i	0.173219	−	0.0297197i
$778$			24.0000i			0.860442i
$779$			31.3137i			1.12193i
$780$	−1.82843	−	10.6569i	−0.0654682	−	0.381577i
$781$	16.0000	+	33.9411i	0.572525	+	1.21451i
$782$			3.79899i			0.135852i
$783$	−17.3137	−	30.9706i	−0.618741	−	1.10680i
$784$	−1.00000			−0.0357143
$785$			12.1421i			0.433371i
$786$	−3.65685	−	21.3137i	−0.130436	−	0.760235i
$787$			49.1716i			1.75278i	0.481605	+	0.876389i	$0.340054\pi$
$787$			49.1716i			1.75278i	−0.481605	+	0.876389i	$0.659946\pi$
$788$	0.828427			0.0295115
$789$	4.44365	+	25.8995i	0.158198	+	0.922046i
$790$	10.0000			0.355784
$791$	0.485281			0.0172546
$792$	7.07107	−	7.00000i	0.251259	−	0.248734i
$793$	−16.1421			−0.573224
$794$	−8.14214			−0.288954
$795$	3.89949	+	22.7279i	0.138301	+	0.806076i
$796$	16.7279			0.592905
$797$			10.4853i			0.371408i	0.982606	+	0.185704i	$0.0594565\pi$
$797$			10.4853i			0.371408i	−0.982606	+	0.185704i	$0.940543\pi$
$798$	0.828427	+	4.82843i	0.0293260	+	0.170924i
$799$		−	2.68629i		−	0.0950342i
$800$	−1.00000			−0.0353553
$801$	7.65685	+	21.6569i	0.270542	+	0.765207i
$802$			26.3431i			0.930209i
$803$	6.48528	+	13.7574i	0.228861	+	0.485487i
$804$	−3.89949	−	22.7279i	−0.137525	−	0.801552i
$805$			0.828427i			0.0291982i
$806$		−	33.7990i		−	1.19052i
$807$	−9.41421	+	1.61522i	−0.331396	+	0.0568586i
$808$	16.7279			0.588486
$809$	−16.6863			−0.586659			−0.293329	−	0.956011i	$-0.594763\pi$
$809$	−16.6863			−0.586659			−0.293329	+	0.956011i	$0.594763\pi$
$810$	−5.65685	−	7.00000i	−0.198762	−	0.245955i
$811$		−	10.8284i		−	0.380238i	−0.981761	−	0.190119i	$-0.939113\pi$
$811$		−	10.8284i		−	0.380238i	0.981761	−	0.190119i	$-0.0608873\pi$
$812$			6.82843i			0.239631i
$813$	−2.00000	+	0.343146i	−0.0701431	+	0.0120346i
$814$	8.48528	−	4.00000i	0.297409	−	0.140200i
$815$			21.3137i			0.746587i
$816$	1.34315	+	7.82843i	0.0470195	+	0.274050i
$817$	2.34315			0.0819763
$818$			12.9289i			0.452050i
$819$	−17.6569	+	6.24264i	−0.616980	+	0.218136i
$820$			11.0711i			0.386618i
$821$	−34.6274			−1.20851			−0.604253	−	0.796793i	$-0.706528\pi$
$821$	−34.6274			−1.20851			−0.604253	+	0.796793i	$0.706528\pi$
$822$	0.585786	−	0.100505i	0.0204316	−	0.00350552i
$823$	18.7696			0.654265			0.327133	−	0.944978i	$-0.393918\pi$
$823$	18.7696			0.654265			0.327133	+	0.944978i	$0.393918\pi$
$824$	−5.75736			−0.200567
$825$	−3.29289	−	4.70711i	−0.114644	−	0.163880i
$826$	13.8995			0.483625
$827$	−11.0294			−0.383531			−0.191766	−	0.981441i	$-0.561421\pi$
$827$	−11.0294			−0.383531			−0.191766	+	0.981441i	$0.561421\pi$
$828$	0.828427	+	2.34315i	0.0287898	+	0.0814299i
$829$	36.4264			1.26514			0.632571	−	0.774503i	$-0.282000\pi$
$829$	36.4264			1.26514			0.632571	+	0.774503i	$0.282000\pi$
$830$			16.0000i			0.555368i
$831$	16.7279	−	2.87006i	0.580285	−	0.0995612i
$832$			6.24264i			0.216425i
$833$	4.58579			0.158888
$834$	−26.1421	+	4.48528i	−0.905228	+	0.155313i
$835$			14.8284i			0.513159i
$836$	4.00000	+	8.48528i	0.138343	+	0.293470i
$837$	−13.7279	−	24.5563i	−0.474506	−	0.848792i
$838$		−	3.75736i		−	0.129796i
$839$			20.4437i			0.705793i	0.935662	+	0.352897i	$0.114803\pi$
$839$			20.4437i			0.705793i	−0.935662	+	0.352897i	$0.885197\pi$
$840$	0.292893	+	1.70711i	0.0101058	+	0.0589008i
$841$	17.6274			0.607842
$842$	14.3431			0.494297
$843$	−2.48528	−	14.4853i	−0.0855976	−	0.498900i
$844$		−	9.65685i		−	0.332403i
$845$			25.9706i			0.893415i
$846$	−0.585786	−	1.65685i	−0.0201398	−	0.0569638i
$847$	−8.48528	−	7.00000i	−0.291558	−	0.240523i
$848$		−	13.3137i		−	0.457195i
$849$	26.9706	−	4.62742i	0.925627	−	0.158813i
$850$	4.58579			0.157291
$851$			2.34315i			0.0803220i
$852$	−19.3137	+	3.31371i	−0.661677	+	0.113526i
$853$		−	12.5858i		−	0.430929i	−0.976512	−	0.215465i	$-0.930873\pi$
$853$		−	12.5858i		−	0.430929i	0.976512	−	0.215465i	$-0.0691266\pi$
$854$	2.58579			0.0884838
$855$	8.00000	−	2.82843i	0.273594	−	0.0967302i
$856$	14.4853			0.495097
$857$	47.0122			1.60591			0.802953	−	0.596042i	$-0.203261\pi$
$857$	47.0122			1.60591			0.802953	+	0.596042i	$0.203261\pi$
$858$	−29.3848	+	20.5563i	−1.00318	+	0.701782i
$859$	−9.41421			−0.321209			−0.160604	−	0.987019i	$-0.551344\pi$
$859$	−9.41421			−0.321209			−0.160604	+	0.987019i	$0.551344\pi$
$860$	0.828427			0.0282491
$861$	18.8995	−	3.24264i	0.644093	−	0.110509i
$862$	−23.3137			−0.794068
$863$			28.3431i			0.964812i	0.875948	+	0.482406i	$0.160237\pi$
$863$			28.3431i			0.964812i	−0.875948	+	0.482406i	$0.839763\pi$
$864$	2.53553	+	4.53553i	0.0862606	+	0.154302i
$865$			8.58579i			0.291925i
$866$	11.4558			0.389285
$867$	−1.18019	−	6.87868i	−0.0400815	−	0.233612i
$868$			5.41421i			0.183770i
$869$	−14.1421	−	30.0000i	−0.479739	−	1.01768i
$870$	11.6569	−	2.00000i	0.395204	−	0.0678064i
$871$			83.1127i			2.81617i
$872$			4.48528i			0.151891i
$873$	−10.3431	+	3.65685i	−0.350062	+	0.123766i
$874$	−2.34315			−0.0792581
$875$	1.00000			0.0338062
$876$	−7.82843	+	1.34315i	−0.264498	+	0.0453807i
$877$		−	52.6274i		−	1.77710i	−0.458778	−	0.888551i	$-0.651713\pi$
$877$		−	52.6274i		−	1.77710i	0.458778	−	0.888551i	$-0.348287\pi$
$878$		−	23.7990i		−	0.803177i
$879$	2.17157	+	12.6569i	0.0732453	+	0.426905i
$880$	1.41421	+	3.00000i	0.0476731	+	0.101130i
$881$			28.6274i			0.964482i	0.876039	+	0.482241i	$0.160177\pi$
$881$			28.6274i			0.964482i	−0.876039	+	0.482241i	$0.839823\pi$
$882$	2.82843	−	1.00000i	0.0952381	−	0.0336718i
$883$	−37.1127			−1.24894			−0.624471	−	0.781048i	$-0.714685\pi$
$883$	−37.1127			−1.24894			−0.624471	+	0.781048i	$0.714685\pi$
$884$		−	28.6274i		−	0.962844i
$885$	−4.07107	−	23.7279i	−0.136847	−	0.797605i
$886$		−	28.3431i		−	0.952207i
$887$	15.0294			0.504639			0.252320	−	0.967644i	$-0.418807\pi$
$887$	15.0294			0.504639			0.252320	+	0.967644i	$0.418807\pi$
$888$	0.828427	+	4.82843i	0.0278002	+	0.162031i
$889$	21.6569			0.726348
$890$	−7.65685			−0.256658
$891$	−13.0000	+	26.8701i	−0.435516	+	0.900181i
$892$	−17.5563			−0.587830
$893$	1.65685			0.0554445
$894$	−2.14214	−	12.4853i	−0.0716437	−	0.417570i
$895$	−22.1421			−0.740130
$896$		−	1.00000i		−	0.0334077i
$897$	−1.51472	−	8.82843i	−0.0505750	−	0.294773i
$898$		−	2.68629i		−	0.0896427i
$899$	36.9706			1.23304
$900$	2.82843	−	1.00000i	0.0942809	−	0.0333333i
$901$			61.0538i			2.03400i
$902$	33.2132	−	15.6569i	1.10588	−	0.521316i
$903$	−0.242641	−	1.41421i	−0.00807458	−	0.0470621i
$904$			0.485281i			0.0161402i
$905$			9.31371i			0.309598i
$906$	−0.585786	+	0.100505i	−0.0194615	+	0.00333906i
$907$	−35.6569			−1.18397			−0.591983	−	0.805950i	$-0.701655\pi$
$907$	−35.6569			−1.18397			−0.591983	+	0.805950i	$0.701655\pi$
$908$	−26.1421			−0.867557
$909$	−47.3137	+	16.7279i	−1.56930	+	0.554830i
$910$		−	6.24264i		−	0.206942i
$911$			45.2548i			1.49936i	0.661801	+	0.749680i	$0.269792\pi$
$911$			45.2548i			1.49936i	−0.661801	+	0.749680i	$0.730208\pi$
$912$	−4.82843	+	0.828427i	−0.159885	+	0.0274320i
$913$	48.0000	−	22.6274i	1.58857	−	0.748858i
$914$			19.1716i			0.634139i
$915$	−0.757359	−	4.41421i	−0.0250375	−	0.145929i
$916$	3.17157			0.104792
$917$		−	12.4853i		−	0.412300i
$918$	−11.6274	−	20.7990i	−0.383762	−	0.686469i
$919$			23.3137i			0.769048i	0.923115	+	0.384524i	$0.125634\pi$
$919$			23.3137i			0.769048i	−0.923115	+	0.384524i	$0.874366\pi$
$920$	−0.828427			−0.0273124
$921$	8.00000	−	1.37258i	0.263609	−	0.0452281i
$922$	−33.2132			−1.09382
$923$	70.6274			2.32473
$924$	4.70711	−	3.29289i	0.154852	−	0.108328i
$925$	2.82843			0.0929981
$926$	12.6274			0.414963
$927$	16.2843	−	5.75736i	0.534846	−	0.189096i
$928$	−6.82843			−0.224154
$929$			28.6274i			0.939235i	0.882870	+	0.469618i	$0.155608\pi$
$929$			28.6274i			0.939235i	−0.882870	+	0.469618i	$0.844392\pi$
$930$	9.24264	−	1.58579i	0.303078	−	0.0520000i
$931$			2.82843i			0.0926980i
$932$	−13.3137			−0.436105
$933$	49.0416	−	8.41421i	1.60555	−	0.275469i
$934$			42.5269i			1.39152i
$935$	−6.48528	−	13.7574i	−0.212091	−	0.449914i
$936$	−6.24264	−	17.6569i	−0.204047	−	0.577132i
$937$			23.4142i			0.764909i	0.923974	+	0.382455i	$0.124921\pi$
$937$			23.4142i			0.764909i	−0.923974	+	0.382455i	$0.875079\pi$
$938$		−	13.3137i		−	0.434708i
$939$	3.27208	+	19.0711i	0.106780	+	0.622361i
$940$	0.585786			0.0191062
$941$	−28.0416			−0.914131			−0.457066	−	0.889433i	$-0.651100\pi$
$941$	−28.0416			−0.914131			−0.457066	+	0.889433i	$0.651100\pi$
$942$	3.55635	+	20.7279i	0.115872	+	0.675352i
$943$			9.17157i			0.298668i
$944$			13.8995i			0.452390i
$945$	−2.53553	−	4.53553i	−0.0824809	−	0.147541i
$946$	−1.17157	−	2.48528i	−0.0380911	−	0.0808035i
$947$		−	56.6274i		−	1.84014i	−0.391750	−	0.920072i	$-0.628130\pi$
$947$		−	56.6274i		−	1.84014i	0.391750	−	0.920072i	$-0.371870\pi$
$948$	17.0711	−	2.92893i	0.554443	−	0.0951273i
$949$	28.6274			0.929285
$950$			2.82843i			0.0917663i
$951$	−25.3137	+	4.34315i	−0.820853	+	0.140836i
$952$			4.58579i			0.148626i
$953$	−20.1421			−0.652468			−0.326234	−	0.945289i	$-0.605780\pi$
$953$	−20.1421			−0.652468			−0.326234	+	0.945289i	$0.605780\pi$
$954$	13.3137	+	37.6569i	0.431047	+	1.21919i
$955$	−4.48528			−0.145140
$956$	13.3137			0.430596
$957$	−22.4853	−	32.1421i	−0.726846	−	1.03901i
$958$	−8.48528			−0.274147
$959$	0.343146			0.0110808
$960$	−1.70711	+	0.292893i	−0.0550966	+	0.00945309i
$961$	−1.68629			−0.0543965
$962$		−	17.6569i		−	0.569280i
$963$	−40.9706	+	14.4853i	−1.32026	+	0.466782i
$964$			9.89949i			0.318841i
$965$	2.48528			0.0800040
$966$	0.242641	+	1.41421i	0.00780684	+	0.0455016i
$967$			34.4853i			1.10897i	0.832193	+	0.554486i	$0.187085\pi$
$967$			34.4853i			1.10897i	−0.832193	+	0.554486i	$0.812915\pi$
$968$	7.00000	−	8.48528i	0.224989	−	0.272727i
$969$	22.1421	−	3.79899i	0.711308	−	0.122041i
$970$		−	3.65685i		−	0.117415i
$971$		−	56.3259i		−	1.80758i	−0.427972	−	0.903792i	$-0.640772\pi$
$971$		−	56.3259i		−	1.80758i	0.427972	−	0.903792i	$-0.359228\pi$
$972$	−11.7071	−	10.2929i	−0.375506	−	0.330145i
$973$	−15.3137			−0.490935
$974$	−10.9706			−0.351520
$975$	−10.6569	+	1.82843i	−0.341292	+	0.0585565i
$976$			2.58579i			0.0827690i
$977$			57.7401i			1.84727i	0.383273	+	0.923635i	$0.374797\pi$
$977$			57.7401i			1.84727i	−0.383273	+	0.923635i	$0.625203\pi$
$978$	6.24264	+	36.3848i	0.199618	+	1.16346i
$979$	10.8284	+	22.9706i	0.346078	+	0.734142i
$980$			1.00000i			0.0319438i
$981$	−4.48528	−	12.6863i	−0.143204	−	0.405042i
$982$	−37.9411			−1.21075
$983$		−	1.75736i		−	0.0560511i	−0.999607	−	0.0280255i	$-0.991078\pi$
$983$		−	1.75736i		−	0.0560511i	0.999607	−	0.0280255i	$-0.00892197\pi$
$984$	3.24264	+	18.8995i	0.103372	+	0.602494i
$985$		−	0.828427i		−	0.0263959i
$986$	31.3137			0.997232
$987$	−0.171573	−	1.00000i	−0.00546122	−	0.0318304i
$988$	17.6569			0.561739
$989$	0.686292			0.0218228
$990$	−7.00000	−	7.07107i	−0.222475	−	0.224733i
$991$	12.4853			0.396608			0.198304	−	0.980141i	$-0.436457\pi$
$991$	12.4853			0.396608			0.198304	+	0.980141i	$0.436457\pi$
$992$	−5.41421			−0.171901
$993$	−7.31371	−	42.6274i	−0.232094	−	1.35274i
$994$	−11.3137			−0.358849
$995$		−	16.7279i		−	0.530311i
$996$	4.68629	+	27.3137i	0.148491	+	0.865468i
$997$			26.4437i			0.837479i	0.908106	+	0.418739i	$0.137528\pi$
$997$			26.4437i			0.837479i	−0.908106	+	0.418739i	$0.862472\pi$
$998$	2.82843			0.0895323
$999$	−7.17157	−	12.8284i	−0.226899	−	0.405873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2310.2.g.b.1121.3	yes	4
3.2	odd	2		2310.2.g.a.1121.4	yes	4
11.10	odd	2		2310.2.g.a.1121.3	✓	4
33.32	even	2	inner	2310.2.g.b.1121.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2310.2.g.a.1121.3	✓	4	11.10	odd	2
2310.2.g.a.1121.4	yes	4	3.2	odd	2
2310.2.g.b.1121.3	yes	4	1.1	even	1	trivial
2310.2.g.b.1121.4	yes	4	33.32	even	2	inner

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:	\( N \)	\(=\)	\( 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2310.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.292893 - 1.70711i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(-0.292893 - 1.70711i) q^{6} -1.00000i q^{7} +1.00000 q^{8} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.292893 - 1.70711i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(-0.292893 - 1.70711i) q^{6} -1.00000i q^{7} +1.00000 q^{8} +(-2.82843 + 1.00000i) q^{9} -1.00000i q^{10} +(-3.00000 + 1.41421i) q^{11} +(-0.292893 - 1.70711i) q^{12} +6.24264i q^{13} -1.00000i q^{14} +(-1.70711 + 0.292893i) q^{15} +1.00000 q^{16} -4.58579 q^{17} +(-2.82843 + 1.00000i) q^{18} -2.82843i q^{19} -1.00000i q^{20} +(-1.70711 + 0.292893i) q^{21} +(-3.00000 + 1.41421i) q^{22} -0.828427i q^{23} +(-0.292893 - 1.70711i) q^{24} -1.00000 q^{25} +6.24264i q^{26} +(2.53553 + 4.53553i) q^{27} -1.00000i q^{28} -6.82843 q^{29} +(-1.70711 + 0.292893i) q^{30} -5.41421 q^{31} +1.00000 q^{32} +(3.29289 + 4.70711i) q^{33} -4.58579 q^{34} -1.00000 q^{35} +(-2.82843 + 1.00000i) q^{36} -2.82843 q^{37} -2.82843i q^{38} +(10.6569 - 1.82843i) q^{39} -1.00000i q^{40} -11.0711 q^{41} +(-1.70711 + 0.292893i) q^{42} +0.828427i q^{43} +(-3.00000 + 1.41421i) q^{44} +(1.00000 + 2.82843i) q^{45} -0.828427i q^{46} +0.585786i q^{47} +(-0.292893 - 1.70711i) q^{48} -1.00000 q^{49} -1.00000 q^{50} +(1.34315 + 7.82843i) q^{51} +6.24264i q^{52} -13.3137i q^{53} +(2.53553 + 4.53553i) q^{54} +(1.41421 + 3.00000i) q^{55} -1.00000i q^{56} +(-4.82843 + 0.828427i) q^{57} -6.82843 q^{58} +13.8995i q^{59} +(-1.70711 + 0.292893i) q^{60} +2.58579i q^{61} -5.41421 q^{62} +(1.00000 + 2.82843i) q^{63} +1.00000 q^{64} +6.24264 q^{65} +(3.29289 + 4.70711i) q^{66} +13.3137 q^{67} -4.58579 q^{68} +(-1.41421 + 0.242641i) q^{69} -1.00000 q^{70} -11.3137i q^{71} +(-2.82843 + 1.00000i) q^{72} -4.58579i q^{73} -2.82843 q^{74} +(0.292893 + 1.70711i) q^{75} -2.82843i q^{76} +(1.41421 + 3.00000i) q^{77} +(10.6569 - 1.82843i) q^{78} +10.0000i q^{79} -1.00000i q^{80} +(7.00000 - 5.65685i) q^{81} -11.0711 q^{82} -16.0000 q^{83} +(-1.70711 + 0.292893i) q^{84} +4.58579i q^{85} +0.828427i q^{86} +(2.00000 + 11.6569i) q^{87} +(-3.00000 + 1.41421i) q^{88} -7.65685i q^{89} +(1.00000 + 2.82843i) q^{90} +6.24264 q^{91} -0.828427i q^{92} +(1.58579 + 9.24264i) q^{93} +0.585786i q^{94} -2.82843 q^{95} +(-0.292893 - 1.70711i) q^{96} +3.65685 q^{97} -1.00000 q^{98} +(7.07107 - 7.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^8	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{8} - 12 q^{11} - 4 q^{12} - 4 q^{15} + 4 q^{16} - 24 q^{17} - 4 q^{21} - 12 q^{22} - 4 q^{24} - 4 q^{25} - 4 q^{27} - 16 q^{29} - 4 q^{30} - 16 q^{31} + 4 q^{32} + 16 q^{33} - 24 q^{34} - 4 q^{35} + 20 q^{39} - 16 q^{41} - 4 q^{42} - 12 q^{44} + 4 q^{45} - 4 q^{48} - 4 q^{49} - 4 q^{50} + 28 q^{51} - 4 q^{54} - 8 q^{57} - 16 q^{58} - 4 q^{60} - 16 q^{62} + 4 q^{63} + 4 q^{64} + 8 q^{65} + 16 q^{66} + 8 q^{67} - 24 q^{68} - 4 q^{70} + 4 q^{75} + 20 q^{78} + 28 q^{81} - 16 q^{82} - 64 q^{83} - 4 q^{84} + 8 q^{87} - 12 q^{88} + 4 q^{90} + 8 q^{91} + 12 q^{93} - 4 q^{96} - 8 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^8 - 12 * q^11 - 4 * q^12 - 4 * q^15 + 4 * q^16 - 24 * q^17 - 4 * q^21 - 12 * q^22 - 4 * q^24 - 4 * q^25 - 4 * q^27 - 16 * q^29 - 4 * q^30 - 16 * q^31 + 4 * q^32 + 16 * q^33 - 24 * q^34 - 4 * q^35 + 20 * q^39 - 16 * q^41 - 4 * q^42 - 12 * q^44 + 4 * q^45 - 4 * q^48 - 4 * q^49 - 4 * q^50 + 28 * q^51 - 4 * q^54 - 8 * q^57 - 16 * q^58 - 4 * q^60 - 16 * q^62 + 4 * q^63 + 4 * q^64 + 8 * q^65 + 16 * q^66 + 8 * q^67 - 24 * q^68 - 4 * q^70 + 4 * q^75 + 20 * q^78 + 28 * q^81 - 16 * q^82 - 64 * q^83 - 4 * q^84 + 8 * q^87 - 12 * q^88 + 4 * q^90 + 8 * q^91 + 12 * q^93 - 4 * q^96 - 8 * q^97 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more