LMFDB - Embedded newform 930.2.be.b.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.10
Character	$\chi$	$=$	930.37
Dual form			930.2.be.b.553.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-2.06875 - 0.848677i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.339513 - 1.26708i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-2.06875 - 0.848677i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.339513 - 1.26708i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.862725 - 2.06294i) q^{10} +(4.94046 + 2.85238i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-6.23462 + 1.67056i) q^{13} +(1.13603 - 0.655888i) q^{14} +(1.35519 - 1.77861i) q^{15} -1.00000 q^{16} +(-6.57827 - 1.76264i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-4.15840 + 2.40085i) q^{19} +(0.848677 - 2.06875i) q^{20} +(1.13603 + 0.655888i) q^{21} +(1.47650 + 5.51037i) q^{22} +(-1.66519 - 1.66519i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.55949 + 3.51141i) q^{25} +(-5.58981 - 3.22728i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.26708 + 0.339513i) q^{28} -7.52743 q^{29} +(2.21593 - 0.299401i) q^{30} +(4.04515 - 3.82580i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.03387 + 4.03387i) q^{33} +(-3.40516 - 5.89791i) q^{34} +(-1.77771 + 2.33314i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.36785 - 0.634463i) q^{37} +(-4.63809 - 1.24277i) q^{38} -6.45456i q^{39} +(2.06294 - 0.862725i) q^{40} +(0.748561 - 1.29655i) q^{41} +(0.339513 + 1.26708i) q^{42} +(1.59099 - 5.93764i) q^{43} +(-2.85238 + 4.94046i) q^{44} +(1.36726 + 1.76935i) q^{45} -2.35494i q^{46} +(-0.556857 - 0.556857i) q^{47} +(0.258819 - 0.965926i) q^{48} +(4.57196 + 2.63962i) q^{49} +(0.0339997 + 4.99988i) q^{50} +(3.40516 - 5.89791i) q^{51} +(-1.67056 - 6.23462i) q^{52} +(-11.3438 + 3.03956i) q^{53} +1.00000 q^{54} +(-7.79986 - 10.0937i) q^{55} +(0.655888 + 1.13603i) q^{56} +(-1.24277 - 4.63809i) q^{57} +(-5.32270 - 5.32270i) q^{58} +(-8.97763 + 5.18324i) q^{59} +(1.77861 + 1.35519i) q^{60} -1.06457i q^{61} +(5.56560 + 0.155106i) q^{62} +(-0.927565 + 0.927565i) q^{63} -1.00000i q^{64} +(14.3157 + 1.83520i) q^{65} -5.70476 q^{66} +(7.40809 - 1.98499i) q^{67} +(1.76264 - 6.57827i) q^{68} +(2.03944 - 1.17747i) q^{69} +(-2.90681 + 0.392747i) q^{70} +(-6.75775 + 11.7048i) q^{71} +(0.965926 - 0.258819i) q^{72} +(9.69353 - 2.59737i) q^{73} +(-1.22569 - 2.12296i) q^{74} +(-4.31303 + 2.52939i) q^{75} +(-2.40085 - 4.15840i) q^{76} +(5.29154 - 5.29154i) q^{77} +(4.56406 - 4.56406i) q^{78} +(4.40821 + 7.63525i) q^{79} +(2.06875 + 0.848677i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.44611 - 0.387484i) q^{82} +(10.1233 - 2.71253i) q^{83} +(-0.655888 + 1.13603i) q^{84} +(12.1129 + 9.22930i) q^{85} +(5.32355 - 3.07355i) q^{86} +(1.94824 - 7.27094i) q^{87} +(-5.51037 + 1.47650i) q^{88} +6.21779 q^{89} +(-0.284326 + 2.21792i) q^{90} +8.46693i q^{91} +(1.66519 - 1.66519i) q^{92} +(2.64848 + 4.89751i) q^{93} -0.787514i q^{94} +(10.6403 - 1.43764i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-5.21180 - 5.21180i) q^{97} +(1.36637 + 5.09936i) q^{98} +(-2.85238 - 4.94046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{7}+O(q^{10}) $ 64 * q + 4 * q^7	$ 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$			1.00000i			0.500000i
$5$	−2.06875	−	0.848677i	−0.925175	−	0.379540i
$5$	−2.06875	−	0.848677i	−0.925175	−	0.379540i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	0.339513	−	1.26708i	0.128324	−	0.478910i	−0.871613	−	0.490195i	$-0.836925\pi$
$7$	0.339513	−	1.26708i	0.128324	−	0.478910i	0.999936	+	0.0112848i	$0.00359214\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−0.862725	−	2.06294i	−0.272818	−	0.652358i
$11$	4.94046	+	2.85238i	1.48961	+	0.860025i	0.999929	−	0.0118795i	$-0.00378145\pi$
$11$	4.94046	+	2.85238i	1.48961	+	0.860025i	0.489677	+	0.871904i	$0.337115\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	−6.23462	+	1.67056i	−1.72917	+	0.463331i	−0.979993	−	0.199034i	$-0.936219\pi$
$13$	−6.23462	+	1.67056i	−1.72917	+	0.463331i	−0.749181	+	0.662365i	$0.769553\pi$
$14$	1.13603	−	0.655888i	0.303617	−	0.175293i
$15$	1.35519	−	1.77861i	0.349909	−	0.459235i
$16$	−1.00000			−0.250000
$17$	−6.57827	−	1.76264i	−1.59546	−	0.427503i	−0.651796	−	0.758395i	$-0.725984\pi$
$17$	−6.57827	−	1.76264i	−1.59546	−	0.427503i	−0.943669	+	0.330891i	$0.892651\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	−4.15840	+	2.40085i	−0.954003	+	0.550794i	−0.894322	−	0.447424i	$-0.852342\pi$
$19$	−4.15840	+	2.40085i	−0.954003	+	0.550794i	−0.0596805	+	0.998218i	$0.519008\pi$
$20$	0.848677	−	2.06875i	0.189770	−	0.462588i
$21$	1.13603	+	0.655888i	0.247902	+	0.143126i
$22$	1.47650	+	5.51037i	0.314791	+	1.17482i
$23$	−1.66519	−	1.66519i	−0.347216	−	0.347216i	0.511855	−	0.859072i	$-0.328958\pi$
$23$	−1.66519	−	1.66519i	−0.347216	−	0.347216i	−0.859072	+	0.511855i	$0.828958\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	3.55949	+	3.51141i	0.711899	+	0.702282i
$26$	−5.58981	−	3.22728i	−1.09625	−	0.632922i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.26708	+	0.339513i	0.239455	+	0.0641618i
$29$	−7.52743			−1.39781			−0.698905	−	0.715215i	$-0.746329\pi$
$29$	−7.52743			−1.39781			−0.698905	+	0.715215i	$0.746329\pi$
$30$	2.21593	−	0.299401i	0.404572	−	0.0546630i
$31$	4.04515	−	3.82580i	0.726531	−	0.687134i
$31$	4.04515	−	3.82580i	0.726531	−	0.687134i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−4.03387	+	4.03387i	−0.702207	+	0.702207i
$34$	−3.40516	−	5.89791i	−0.583981	−	1.01148i
$35$	−1.77771	+	2.33314i	−0.300488	+	0.394372i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−2.36785	−	0.634463i	−0.389272	−	0.104305i	0.0588742	−	0.998265i	$-0.481249\pi$
$37$	−2.36785	−	0.634463i	−0.389272	−	0.104305i	−0.448146	+	0.893960i	$0.647916\pi$
$38$	−4.63809	−	1.24277i	−0.752398	−	0.201604i
$39$		−	6.45456i		−	1.03356i
$40$	2.06294	−	0.862725i	0.326179	−	0.136409i
$41$	0.748561	−	1.29655i	0.116906	−	0.202486i	−0.801634	−	0.597815i	$-0.796036\pi$
$41$	0.748561	−	1.29655i	0.116906	−	0.202486i	0.918540	+	0.395328i	$0.129369\pi$
$42$	0.339513	+	1.26708i	0.0523879	+	0.195514i
$43$	1.59099	−	5.93764i	0.242623	−	0.905482i	−0.731940	−	0.681369i	$-0.761385\pi$
$43$	1.59099	−	5.93764i	0.242623	−	0.905482i	0.974563	−	0.224113i	$-0.0719485\pi$
$44$	−2.85238	+	4.94046i	−0.430012	+	0.744803i
$45$	1.36726	+	1.76935i	0.203818	+	0.263760i
$46$		−	2.35494i		−	0.347216i
$47$	−0.556857	−	0.556857i	−0.0812259	−	0.0812259i	0.665327	−	0.746552i	$-0.268292\pi$
$47$	−0.556857	−	0.556857i	−0.0812259	−	0.0812259i	−0.746552	+	0.665327i	$0.768292\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	4.57196	+	2.63962i	0.653137	+	0.377089i
$50$	0.0339997	+	4.99988i	0.00480829	+	0.707090i
$51$	3.40516	−	5.89791i	0.476818	−	0.825873i
$52$	−1.67056	−	6.23462i	−0.231665	−	0.864587i
$53$	−11.3438	+	3.03956i	−1.55819	+	0.417515i	−0.932089	−	0.362228i	$-0.882016\pi$
$53$	−11.3438	+	3.03956i	−1.55819	+	0.417515i	−0.626099	+	0.779743i	$0.715349\pi$
$54$	1.00000			0.136083
$55$	−7.79986	−	10.0937i	−1.05173	−	1.36104i
$56$	0.655888	+	1.13603i	0.0876467	+	0.151809i
$57$	−1.24277	−	4.63809i	−0.164609	−	0.614330i
$58$	−5.32270	−	5.32270i	−0.698905	−	0.698905i
$59$	−8.97763	+	5.18324i	−1.16879	+	0.674800i	−0.953394	−	0.301727i	$-0.902437\pi$
$59$	−8.97763	+	5.18324i	−1.16879	+	0.674800i	−0.215394	+	0.976527i	$0.569103\pi$
$60$	1.77861	+	1.35519i	0.229618	+	0.174955i
$61$		−	1.06457i		−	0.136304i	−0.997675	−	0.0681521i	$-0.978290\pi$
$61$		−	1.06457i		−	0.136304i	0.997675	−	0.0681521i	$-0.0217103\pi$
$62$	5.56560	+	0.155106i	0.706832	+	0.0196984i
$63$	−0.927565	+	0.927565i	−0.116862	+	0.116862i
$64$		−	1.00000i		−	0.125000i
$65$	14.3157	+	1.83520i	1.77564	+	0.227629i
$66$	−5.70476			−0.702207
$67$	7.40809	−	1.98499i	0.905042	−	0.242505i	0.223862	−	0.974621i	$-0.428134\pi$
$67$	7.40809	−	1.98499i	0.905042	−	0.242505i	0.681180	+	0.732116i	$0.261467\pi$
$68$	1.76264	−	6.57827i	0.213752	−	0.797732i
$69$	2.03944	−	1.17747i	0.245519	−	0.141751i
$70$	−2.90681	+	0.392747i	−0.347430	+	0.0469423i
$71$	−6.75775	+	11.7048i	−0.801998	+	1.38910i	0.116301	+	0.993214i	$0.462896\pi$
$71$	−6.75775	+	11.7048i	−0.801998	+	1.38910i	−0.918299	+	0.395887i	$0.870437\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	9.69353	−	2.59737i	1.13454	−	0.304000i	0.357788	−	0.933803i	$-0.383531\pi$
$73$	9.69353	−	2.59737i	1.13454	−	0.304000i	0.776755	+	0.629803i	$0.216865\pi$
$74$	−1.22569	−	2.12296i	−0.142483	−	0.246789i
$75$	−4.31303	+	2.52939i	−0.498025	+	0.292068i
$76$	−2.40085	−	4.15840i	−0.275397	−	0.477001i
$77$	5.29154	−	5.29154i	0.603026	−	0.603026i
$78$	4.56406	−	4.56406i	0.516778	−	0.516778i
$79$	4.40821	+	7.63525i	0.495963	+	0.859032i	0.999989	−	0.00465578i	$-0.00148199\pi$
$79$	4.40821	+	7.63525i	0.495963	+	0.859032i	−0.504027	+	0.863688i	$0.668149\pi$
$80$	2.06875	+	0.848677i	0.231294	+	0.0948850i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.44611	−	0.387484i	0.159696	−	0.0427904i
$83$	10.1233	−	2.71253i	1.11118	−	0.297739i	0.343868	−	0.939018i	$-0.388263\pi$
$83$	10.1233	−	2.71253i	1.11118	−	0.297739i	0.767308	+	0.641279i	$0.221596\pi$
$84$	−0.655888	+	1.13603i	−0.0715632	+	0.123951i
$85$	12.1129	+	9.22930i	1.31383	+	1.00106i
$86$	5.32355	−	3.07355i	0.574053	−	0.331430i
$87$	1.94824	−	7.27094i	0.208874	−	0.779527i
$88$	−5.51037	+	1.47650i	−0.587408	+	0.157395i
$89$	6.21779			0.659085			0.329542	−	0.944141i	$-0.393106\pi$
$89$	6.21779			0.659085			0.329542	+	0.944141i	$0.393106\pi$
$90$	−0.284326	+	2.21792i	−0.0299706	+	0.233789i
$91$			8.46693i			0.887576i
$92$	1.66519	−	1.66519i	0.173608	−	0.173608i
$93$	2.64848	+	4.89751i	0.274634	+	0.507848i
$94$		−	0.787514i		−	0.0812259i
$95$	10.6403	−	1.43764i	1.09167	−	0.147499i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−5.21180	−	5.21180i	−0.529178	−	0.529178i	0.391149	−	0.920327i	$-0.372078\pi$
$97$	−5.21180	−	5.21180i	−0.529178	−	0.529178i	−0.920327	+	0.391149i	$0.872078\pi$
$98$	1.36637	+	5.09936i	0.138024	+	0.515113i
$99$	−2.85238	−	4.94046i	−0.286675	−	0.496535i
$100$	−3.51141	+	3.55949i	−0.351141	+	0.355949i
$101$	−18.2636			−1.81730			−0.908649	−	0.417560i	$-0.862885\pi$
$101$	−18.2636			−1.81730			−0.908649	+	0.417560i	$0.862885\pi$
$102$	6.57827	−	1.76264i	0.651346	−	0.174528i
$103$	1.60762	+	5.99973i	0.158404	+	0.591171i	0.998790	+	0.0491825i	$0.0156616\pi$
$103$	1.60762	+	5.99973i	0.158404	+	0.591171i	−0.840386	+	0.541988i	$0.817672\pi$
$104$	3.22728	−	5.58981i	0.316461	−	0.548126i
$105$	−1.79353	−	2.32099i	−0.175031	−	0.226506i
$106$	−10.1706	−	5.87197i	−0.987852	−	0.570337i
$107$	−4.84945	+	18.0984i	−0.468814	+	1.74964i	0.175110	+	0.984549i	$0.443972\pi$
$107$	−4.84945	+	18.0984i	−0.468814	+	1.74964i	−0.643924	+	0.765089i	$0.722695\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			10.4683i			1.00268i	0.865250	+	0.501340i	$0.167159\pi$
$109$			10.4683i			1.00268i	−0.865250	+	0.501340i	$0.832841\pi$
$110$	1.62201	−	12.6527i	0.154653	−	1.20639i
$111$	1.22569	−	2.12296i	0.116337	−	0.201502i
$112$	−0.339513	+	1.26708i	−0.0320809	+	0.119728i
$113$	−1.40405	−	5.24000i	−0.132082	−	0.492938i	0.867911	−	0.496720i	$-0.165463\pi$
$113$	−1.40405	−	5.24000i	−0.132082	−	0.492938i	−0.999993	+	0.00378284i	$0.998796\pi$
$114$	2.40085	−	4.15840i	0.224861	−	0.389470i
$115$	2.03166	+	4.85808i	0.189454	+	0.453019i
$116$		−	7.52743i		−	0.698905i
$117$	6.23462	+	1.67056i	0.576391	+	0.154444i
$118$	−10.0132	−	2.68304i	−0.921794	−	0.246994i
$119$	−4.46681	+	7.73674i	−0.409472	+	0.709226i
$120$	0.299401	+	2.21593i	0.0273315	+	0.202286i
$121$	10.7721	+	18.6579i	0.979284	+	1.69617i
$122$	0.752764	−	0.752764i	0.0681521	−	0.0681521i
$123$	1.05862	+	1.05862i	0.0954530	+	0.0954530i
$124$	3.82580	+	4.04515i	0.343567	+	0.363265i
$125$	−4.38367	−	10.2851i	−0.392087	−	0.919928i
$126$	−1.31178			−0.116862
$127$	−3.32198	−	0.890123i	−0.294778	−	0.0789856i	0.108399	−	0.994107i	$-0.465428\pi$
$127$	−3.32198	−	0.890123i	−0.294778	−	0.0789856i	−0.403177	+	0.915122i	$0.632094\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	5.32355	+	3.07355i	0.468712	+	0.270611i
$130$	8.82503	+	11.4204i	0.774006	+	1.00164i
$131$	−1.86698	−	3.23370i	−0.163119	−	0.282530i	0.772867	−	0.634568i	$-0.218822\pi$
$131$	−1.86698	−	3.23370i	−0.163119	−	0.282530i	−0.935986	+	0.352038i	$0.885489\pi$
$132$	−4.03387	−	4.03387i	−0.351104	−	0.351104i
$133$	1.63024	+	6.08414i	0.141360	+	0.527562i
$134$	6.64191	+	3.83471i	0.573774	+	0.331268i
$135$	−2.06294	+	0.862725i	−0.177549	+	0.0742516i
$136$	5.89791	−	3.40516i	0.505742	−	0.291990i
$137$	1.00942	+	3.76721i	0.0862407	+	0.321855i	0.995546	−	0.0942745i	$-0.0300531\pi$
$137$	1.00942	+	3.76721i	0.0862407	+	0.321855i	−0.909306	+	0.416129i	$0.863386\pi$
$138$	2.27469	+	0.609502i	0.193635	+	0.0518843i
$139$	−9.25427			−0.784937			−0.392469	−	0.919765i	$-0.628379\pi$
$139$	−9.25427			−0.784937			−0.392469	+	0.919765i	$0.628379\pi$
$140$	−2.33314	−	1.77771i	−0.197186	−	0.150244i
$141$	0.682007	−	0.393757i	0.0574354	−	0.0331603i
$142$	−13.0550	+	3.49807i	−1.09555	+	0.293552i
$143$	−35.5670	−	9.53015i	−2.97426	−	0.796952i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	15.5724	+	6.38836i	1.29322	+	0.530525i
$146$	8.69098	+	5.01774i	0.719271	+	0.415271i
$147$	−3.73299	+	3.73299i	−0.307892	+	0.307892i
$148$	0.634463	−	2.36785i	0.0521526	−	0.194636i
$149$	11.0872	−	6.40121i	0.908300	−	0.524407i	0.0284165	−	0.999596i	$-0.490954\pi$
$149$	11.0872	−	6.40121i	0.908300	−	0.524407i	0.879884	+	0.475189i	$0.157620\pi$
$150$	−4.83832	−	1.26122i	−0.395047	−	0.102979i
$151$			5.60934i			0.456482i	0.973605	+	0.228241i	$0.0732973\pi$
$151$			5.60934i			0.456482i	−0.973605	+	0.228241i	$0.926703\pi$
$152$	1.24277	−	4.63809i	0.100802	−	0.376199i
$153$	4.81563	+	4.81563i	0.389320	+	0.389320i
$154$	7.48336			0.603026
$155$	−11.6153	+	4.48161i	−0.932963	+	0.359972i
$156$	6.45456			0.516778
$157$	−15.0304	−	15.0304i	−1.19956	−	1.19956i	−0.974298	−	0.225262i	$-0.927676\pi$
$157$	−15.0304	−	15.0304i	−1.19956	−	1.19956i	−0.225262	−	0.974298i	$-0.572324\pi$
$158$	−2.28186	+	8.51601i	−0.181535	+	0.677497i
$159$		−	11.7439i		−	0.931356i
$160$	0.862725	+	2.06294i	0.0682044	+	0.163089i
$161$	−2.67528	+	1.54457i	−0.210842	+	0.121730i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	−3.74874	+	3.74874i	−0.293624	+	0.293624i	−0.838510	−	0.544886i	$-0.816573\pi$
$163$	−3.74874	+	3.74874i	−0.293624	+	0.293624i	0.544886	+	0.838510i	$0.316573\pi$
$164$	1.29655	+	0.748561i	0.101243	+	0.0584528i
$165$	11.7686	−	4.92164i	0.916180	−	0.383149i
$166$	9.07630	+	5.24020i	0.704457	+	0.406719i
$167$	5.56351	+	1.49074i	0.430518	+	0.115357i	0.467569	−	0.883957i	$-0.345130\pi$
$167$	5.56351	+	1.49074i	0.430518	+	0.115357i	−0.0370515	+	0.999313i	$0.511797\pi$
$168$	−1.26708	+	0.339513i	−0.0977572	+	0.0261940i
$169$	24.8214	−	14.3307i	1.90934	−	1.10236i
$170$	2.03902	+	15.0912i	0.156386	+	1.15744i
$171$	4.80171			0.367196
$172$	5.93764	+	1.59099i	0.452741	+	0.121312i
$173$	6.08489	+	22.7091i	0.462625	+	1.72654i	0.664644	+	0.747160i	$0.268583\pi$
$173$	6.08489	+	22.7091i	0.462625	+	1.72654i	−0.202019	+	0.979382i	$0.564750\pi$
$174$	6.51895	−	3.76372i	0.494200	−	0.285327i
$175$	5.65772	−	3.31799i	0.427684	−	0.250816i
$176$	−4.94046	−	2.85238i	−0.372402	−	0.215006i
$177$	−2.68304	−	10.0132i	−0.201670	−	0.752642i
$178$	4.39664	+	4.39664i	0.329542	+	0.329542i
$179$	−3.06873	−	5.31520i	−0.229368	−	0.397277i	0.728253	−	0.685308i	$-0.240333\pi$
$179$	−3.06873	−	5.31520i	−0.229368	−	0.397277i	−0.957621	+	0.288031i	$0.906999\pi$
$180$	−1.76935	+	1.36726i	−0.131880	+	0.101909i
$181$	2.62141	+	1.51347i	0.194848	+	0.112496i	0.594250	−	0.804280i	$-0.297449\pi$
$181$	2.62141	+	1.51347i	0.194848	+	0.112496i	−0.399402	+	0.916776i	$0.630782\pi$
$182$	−5.98703	+	5.98703i	−0.443788	+	0.443788i
$183$	1.02830	+	0.275531i	0.0760138	+	0.0203678i
$184$	2.35494			0.173608
$185$	4.36005	+	3.32209i	0.320557	+	0.244245i
$186$	−1.59030	+	5.33582i	−0.116607	+	0.391241i
$187$	−27.4720	−	27.4720i	−2.00895	−	2.00895i
$188$	0.556857	−	0.556857i	0.0406129	−	0.0406129i
$189$	−0.655888	−	1.13603i	−0.0477088	−	0.0826341i
$190$	8.54036	+	6.50724i	0.619583	+	0.472085i
$191$	−3.81653	+	6.61042i	−0.276154	+	0.478313i	−0.970426	−	0.241400i	$-0.922393\pi$
$191$	−3.81653	+	6.61042i	−0.276154	+	0.478313i	0.694271	+	0.719713i	$0.255727\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	13.3120	+	3.56695i	0.958221	+	0.256754i	0.703847	−	0.710352i	$-0.251464\pi$
$193$	13.3120	+	3.56695i	0.958221	+	0.256754i	0.254374	+	0.967106i	$0.418131\pi$
$194$		−	7.37059i		−	0.529178i
$195$	−5.47784	+	13.3529i	−0.392276	+	0.956221i
$196$	−2.63962	+	4.57196i	−0.188544	+	0.326569i
$197$	1.42019	+	5.30021i	0.101184	+	0.377624i	0.997884	−	0.0650141i	$-0.0207092\pi$
$197$	1.42019	+	5.30021i	0.101184	+	0.377624i	−0.896700	+	0.442638i	$0.854043\pi$
$198$	1.47650	−	5.51037i	0.104930	−	0.391605i
$199$	3.49946	−	6.06124i	0.248070	−	0.429670i	−0.714920	−	0.699206i	$-0.753537\pi$
$199$	3.49946	−	6.06124i	0.248070	−	0.429670i	0.962990	+	0.269536i	$0.0868704\pi$
$200$	−4.99988	+	0.0339997i	−0.353545	+	0.00240414i
$201$			7.66942i			0.540959i
$202$	−12.9143	−	12.9143i	−0.908649	−	0.908649i
$203$	−2.55566	+	9.53785i	−0.179372	+	0.669426i
$204$	5.89791	+	3.40516i	0.412937	+	0.238409i
$205$	−2.64894	+	2.04695i	−0.185010	+	0.142965i
$206$	−3.10569	+	5.37921i	−0.216383	+	0.374787i
$207$	0.609502	+	2.27469i	0.0423634	+	0.158102i
$208$	6.23462	−	1.67056i	0.432293	−	0.115833i
$209$	−27.3926			−1.89478
$210$	0.372972	−	2.90941i	0.0257375	−	0.200768i
$211$	6.07869	+	10.5286i	0.418475	+	0.724819i	0.995786	−	0.0917046i	$-0.0292316\pi$
$211$	6.07869	+	10.5286i	0.418475	+	0.724819i	−0.577312	+	0.816524i	$0.695898\pi$
$212$	−3.03956	−	11.3438i	−0.208758	−	0.779094i
$213$	−9.55691	−	9.55691i	−0.654829	−	0.654829i
$214$	−16.2266	+	9.36842i	−1.10923	+	0.640412i
$215$	−8.33051	+	10.9333i	−0.568136	+	0.745645i
$216$			1.00000i			0.0680414i
$217$	−3.47421	−	6.42443i	−0.235845	−	0.436119i
$218$	−7.40220	+	7.40220i	−0.501340	+	0.501340i
$219$			10.0355i			0.678135i
$220$	10.0937	−	7.79986i	0.680519	−	0.525867i
$221$	43.9576			2.95691
$222$	2.36785	−	0.634463i	0.158920	−	0.0425824i
$223$	−2.24600	+	8.38218i	−0.150403	+	0.561312i	0.849052	+	0.528309i	$0.177174\pi$
$223$	−2.24600	+	8.38218i	−0.150403	+	0.561312i	−0.999455	+	0.0330031i	$0.989493\pi$
$224$	−1.13603	+	0.655888i	−0.0759043	+	0.0438233i
$225$	−1.32691	−	4.82072i	−0.0884604	−	0.321381i
$226$	2.71242	−	4.69805i	0.180428	−	0.312510i
$227$	18.8000	−	5.03746i	1.24780	−	0.334348i	0.426315	−	0.904575i	$-0.359811\pi$
$227$	18.8000	−	5.03746i	1.24780	−	0.334348i	0.821487	+	0.570227i	$0.193145\pi$
$228$	4.63809	−	1.24277i	0.307165	−	0.0823047i
$229$	1.90113	+	3.29286i	0.125630	+	0.217598i	0.921979	−	0.387240i	$-0.126571\pi$
$229$	1.90113	+	3.29286i	0.125630	+	0.217598i	−0.796349	+	0.604838i	$0.793238\pi$
$230$	−1.99858	+	4.87179i	−0.131783	+	0.321236i
$231$	3.74168	+	6.48078i	0.246185	+	0.426404i
$232$	5.32270	−	5.32270i	0.349452	−	0.349452i
$233$	−13.3013	+	13.3013i	−0.871395	+	0.871395i	−0.992625	−	0.121230i	$-0.961316\pi$
$233$	−13.3013	+	13.3013i	−0.871395	+	0.871395i	0.121230	+	0.992625i	$0.461316\pi$
$234$	3.22728	+	5.58981i	0.210974	+	0.365417i
$235$	0.679408	+	1.62459i	0.0443197	+	0.105977i
$236$	−5.18324	−	8.97763i	−0.337400	−	0.584394i
$237$	−8.51601	+	2.28186i	−0.553174	+	0.148223i
$238$	−8.62921	+	2.31219i	−0.559349	+	0.149877i
$239$	11.3728	−	19.6984i	0.735648	−	1.27418i	−0.218790	−	0.975772i	$-0.570211\pi$
$239$	11.3728	−	19.6984i	0.735648	−	1.27418i	0.954438	−	0.298408i	$-0.0964558\pi$
$240$	−1.35519	+	1.77861i	−0.0874773	+	0.114809i
$241$	1.01656	−	0.586910i	0.0654822	−	0.0378062i	−0.466901	−	0.884309i	$-0.654630\pi$
$241$	1.01656	−	0.586910i	0.0654822	−	0.0378062i	0.532384	+	0.846503i	$0.321296\pi$
$242$	−5.57606	+	20.8102i	−0.358443	+	1.33773i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	1.06457			0.0681521
$245$	−7.21808	−	9.34085i	−0.461146	−	0.596765i
$246$			1.49712i			0.0954530i
$247$	21.9153	−	21.9153i	1.39444	−	1.39444i
$248$	−0.155106	+	5.56560i	−0.00984922	+	0.353416i
$249$			10.4804i			0.664169i
$250$	4.17295	−	10.3724i	0.263921	−	0.656008i
$251$	2.30537	−	1.33101i	0.145514	−	0.0840124i	−0.425475	−	0.904970i	$-0.639893\pi$
$251$	2.30537	−	1.33101i	0.145514	−	0.0840124i	0.570989	+	0.820958i	$0.306560\pi$
$252$	−0.927565	−	0.927565i	−0.0584311	−	0.0584311i
$253$	−3.47706	−	12.9766i	−0.218601	−	0.815831i
$254$	−1.71959	−	2.97841i	−0.107896	−	0.186882i
$255$	−12.0499	+	9.31146i	−0.754592	+	0.583106i
$256$	1.00000			0.0625000
$257$	9.27449	−	2.48509i	0.578527	−	0.155016i	0.0423225	−	0.999104i	$-0.486524\pi$
$257$	9.27449	−	2.48509i	0.578527	−	0.155016i	0.536204	+	0.844088i	$0.319858\pi$
$258$	1.59099	+	5.93764i	0.0990505	+	0.369662i
$259$	−1.60783	+	2.78484i	−0.0999056	+	0.173042i
$260$	−1.83520	+	14.3157i	−0.113814	+	0.887821i
$261$	6.51895	+	3.76372i	0.403513	+	0.232968i
$262$	0.966420	−	3.60673i	0.0597056	−	0.222824i
$263$	−8.62782	−	8.62782i	−0.532014	−	0.532014i	0.389157	−	0.921171i	$-0.372766\pi$
$263$	−8.62782	−	8.62782i	−0.532014	−	0.532014i	−0.921171	+	0.389157i	$0.872766\pi$
$264$		−	5.70476i		−	0.351104i
$265$	26.0471	+	3.33911i	1.60006	+	0.205120i
$266$	−3.14938	+	5.45489i	−0.193101	+	0.334461i
$267$	−1.60928	+	6.00593i	−0.0984865	+	0.367557i
$268$	1.98499	+	7.40809i	0.121253	+	0.452521i
$269$	9.61731	−	16.6577i	0.586378	−	1.01564i	−0.408324	−	0.912837i	$-0.633887\pi$
$269$	9.61731	−	16.6577i	0.586378	−	1.01564i	0.994702	−	0.102799i	$-0.0327799\pi$
$270$	−2.06875	−	0.848677i	−0.125900	−	0.0516489i
$271$		−	21.4117i		−	1.30067i	−0.759648	−	0.650334i	$-0.774629\pi$
$271$		−	21.4117i		−	1.30067i	0.759648	−	0.650334i	$-0.225371\pi$
$272$	6.57827	+	1.76264i	0.398866	+	0.106876i
$273$	−8.17843	−	2.19140i	−0.494981	−	0.132630i
$274$	−1.95005	+	3.37759i	−0.117807	+	0.204048i
$275$	7.56968	+	27.5010i	0.456469	+	1.65837i
$276$	1.17747	+	2.03944i	0.0708753	+	0.122760i
$277$	8.60786	−	8.60786i	0.517196	−	0.517196i	−0.399526	−	0.916722i	$-0.630825\pi$
$277$	8.60786	−	8.60786i	0.517196	−	0.517196i	0.916722	+	0.399526i	$0.130825\pi$
$278$	−6.54376	−	6.54376i	−0.392469	−	0.392469i
$279$	−5.41610	+	1.29066i	−0.324254	+	0.0772700i
$280$	−0.392747	−	2.90681i	−0.0234711	−	0.173715i
$281$	−6.98812			−0.416876			−0.208438	−	0.978036i	$-0.566838\pi$
$281$	−6.98812			−0.416876			−0.208438	+	0.978036i	$0.566838\pi$
$282$	0.760680	+	0.203824i	0.0452979	+	0.0121375i
$283$	−12.0927	+	12.0927i	−0.718839	+	0.718839i	−0.968367	−	0.249529i	$-0.919724\pi$
$283$	−12.0927	+	12.0927i	−0.718839	+	0.718839i	0.249529	+	0.968367i	$0.419724\pi$
$284$	−11.7048	−	6.75775i	−0.694551	−	0.400999i
$285$	−1.36525	+	10.6498i	−0.0808705	+	0.630839i
$286$	−18.4108	−	31.8885i	−1.08866	−	1.88561i
$287$	−1.38868	−	1.38868i	−0.0819711	−	0.0819711i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	25.4443	+	14.6903i	1.49672	+	0.864133i
$290$	6.49411	+	15.5286i	0.381347	+	0.911872i
$291$	6.38312	−	3.68530i	0.374185	−	0.216036i
$292$	2.59737	+	9.69353i	0.152000	+	0.567271i
$293$	−6.85533	−	1.83688i	−0.400493	−	0.107312i	0.0529499	−	0.998597i	$-0.483138\pi$
$293$	−6.85533	−	1.83688i	−0.400493	−	0.107312i	−0.453443	+	0.891285i	$0.649804\pi$
$294$	−5.27924			−0.307892
$295$	22.9714	−	3.10374i	1.33745	−	0.180706i
$296$	2.12296	−	1.22569i	0.123394	−	0.0712417i
$297$	5.51037	−	1.47650i	0.319744	−	0.0856752i
$298$	12.3662	+	3.31351i	0.716354	+	0.191946i
$299$	13.1637	+	7.60004i	0.761274	+	0.439522i
$300$	−2.52939	−	4.31303i	−0.146034	−	0.249013i
$301$	−6.98330	−	4.03181i	−0.402511	−	0.232390i
$302$	−3.96640	+	3.96640i	−0.228241	+	0.228241i
$303$	4.72697	−	17.6413i	0.271558	−	1.01347i
$304$	4.15840	−	2.40085i	0.238501	−	0.137698i
$305$	−0.903476	+	2.20233i	−0.0517329	+	0.126105i
$306$			6.81033i			0.389320i
$307$	−0.170999	+	0.638175i	−0.00975940	+	0.0364226i	−0.970634	−	0.240562i	$-0.922668\pi$
$307$	−0.170999	+	0.638175i	−0.00975940	+	0.0364226i	0.960874	+	0.276984i	$0.0893350\pi$
$308$	5.29154	+	5.29154i	0.301513	+	0.301513i
$309$	−6.21137			−0.353353
$310$	−11.3822	−	5.04428i	−0.646467	−	0.286496i
$311$	−8.03734			−0.455756			−0.227878	−	0.973690i	$-0.573179\pi$
$311$	−8.03734			−0.455756			−0.227878	+	0.973690i	$0.573179\pi$
$312$	4.56406	+	4.56406i	0.258389	+	0.258389i
$313$	5.09414	−	19.0116i	0.287938	−	1.07460i	−0.658728	−	0.752381i	$-0.728905\pi$
$313$	5.09414	−	19.0116i	0.287938	−	1.07460i	0.946666	−	0.322217i	$-0.104428\pi$
$314$		−	21.2563i		−	1.19956i
$315$	2.70611	−	1.13170i	0.152472	−	0.0637642i
$316$	−7.63525	+	4.40821i	−0.429516	+	0.247981i
$317$	−2.61889	+	9.77383i	−0.147092	+	0.548953i	0.852562	+	0.522626i	$0.175048\pi$
$317$	−2.61889	+	9.77383i	−0.147092	+	0.548953i	−0.999653	+	0.0263268i	$0.991619\pi$
$318$	8.30423	−	8.30423i	0.465678	−	0.465678i
$319$	−37.1890	−	21.4711i	−2.08219	−	1.20215i
$320$	−0.848677	+	2.06875i	−0.0474425	+	0.115647i
$321$	−16.2266	−	9.36842i	−0.905679	−	0.522894i
$322$	−2.98389	−	0.799531i	−0.166286	−	0.0445561i
$323$	31.5869	−	8.46369i	1.75754	−	0.470932i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−28.0581	−	15.9460i	−1.55639	−	0.884523i
$326$	−5.30151			−0.293624
$327$	−10.1116	−	2.70939i	−0.559172	−	0.149830i
$328$	0.387484	+	1.44611i	0.0213952	+	0.0798480i
$329$	−0.894641	+	0.516521i	−0.0493231	+	0.0284767i
$330$	11.8017	+	4.84150i	0.649665	+	0.266516i
$331$	−4.41520	−	2.54912i	−0.242681	−	0.140112i	0.373727	−	0.927539i	$-0.378080\pi$
$331$	−4.41520	−	2.54912i	−0.242681	−	0.140112i	−0.616408	+	0.787427i	$0.711413\pi$
$332$	2.71253	+	10.1233i	0.148869	+	0.555588i
$333$	1.73339	+	1.73339i	0.0949890	+	0.0949890i
$334$	2.87989	+	4.98811i	0.157580	+	0.272937i
$335$	−17.0101	−	2.18062i	−0.929363	−	0.119140i
$336$	−1.13603	−	0.655888i	−0.0619756	−	0.0357816i
$337$	−20.3569	+	20.3569i	−1.10891	+	1.10891i	−0.115618	+	0.993294i	$0.536885\pi$
$337$	−20.3569	+	20.3569i	−1.10891	+	1.10891i	−0.993294	+	0.115618i	$0.963115\pi$
$338$	27.6847	+	7.41810i	1.50585	+	0.403491i
$339$	5.42485			0.294637
$340$	−9.22930	+	12.1129i	−0.500529	+	0.656915i
$341$	30.8976	−	7.36292i	1.67320	−	0.398725i
$342$	3.39532	+	3.39532i	0.183598	+	0.183598i
$343$	11.3898	−	11.3898i	0.614992	−	0.614992i
$344$	3.07355	+	5.32355i	0.165715	+	0.287026i
$345$	−5.21838	+	0.705071i	−0.280948	+	0.0379598i
$346$	−11.7551	+	20.3604i	−0.631958	+	1.09458i
$347$	−2.22937	−	0.597359i	−0.119679	−	0.0320679i	0.198482	−	0.980104i	$-0.436399\pi$
$347$	−2.22937	−	0.597359i	−0.119679	−	0.0320679i	−0.318161	+	0.948037i	$0.603065\pi$
$348$	7.27094	+	1.94824i	0.389763	+	0.104437i
$349$			30.8299i			1.65028i	0.564925	+	0.825142i	$0.308905\pi$
$349$			30.8299i			1.65028i	−0.564925	+	0.825142i	$0.691095\pi$
$350$	6.34679	+	1.65444i	0.339250	+	0.0884337i
$351$	−3.22728	+	5.58981i	−0.172259	+	0.298362i
$352$	−1.47650	−	5.51037i	−0.0786977	−	0.293704i
$353$	−1.89320	+	7.06551i	−0.100765	+	0.376059i	−0.997830	−	0.0658384i	$-0.979028\pi$
$353$	−1.89320	+	7.06551i	−0.100765	+	0.376059i	0.897066	+	0.441897i	$0.145694\pi$
$354$	5.18324	−	8.97763i	0.275486	−	0.477156i
$355$	23.9137	−	18.4792i	1.26921	−	0.980772i
$356$			6.21779i			0.329542i
$357$	−6.31702	−	6.31702i	−0.334332	−	0.334332i
$358$	1.58849	−	5.92834i	0.0839545	−	0.313322i
$359$	6.36378	+	3.67413i	0.335867	+	0.193913i	0.658443	−	0.752631i	$-0.271215\pi$
$359$	6.36378	+	3.67413i	0.335867	+	0.193913i	−0.322576	+	0.946544i	$0.604549\pi$
$360$	−2.21792	−	0.284326i	−0.116895	−	0.0149853i
$361$	2.02820	−	3.51294i	0.106747	−	0.184892i
$362$	0.783431	+	2.92380i	0.0411762	+	0.153672i
$363$	−20.8102	+	5.57606i	−1.09225	+	0.292667i
$364$	−8.46693			−0.443788
$365$	−22.2579	−	2.85335i	−1.16503	−	0.149351i
$366$	0.532285	+	0.921944i	0.0278230	+	0.0481908i
$367$	1.76084	+	6.57154i	0.0919150	+	0.343031i	0.996534	−	0.0831904i	$-0.0265110\pi$
$367$	1.76084	+	6.57154i	0.0919150	+	0.343031i	−0.904619	+	0.426222i	$0.859844\pi$
$368$	1.66519	+	1.66519i	0.0868041	+	0.0868041i
$369$	−1.29655	+	0.748561i	−0.0674955	+	0.0389685i
$370$	0.733946	+	5.43209i	0.0381560	+	0.282401i
$371$			15.4054i			0.799810i
$372$	−4.89751	+	2.64848i	−0.253924	+	0.137317i
$373$	−15.2670	+	15.2670i	−0.790498	+	0.790498i	−0.981575	−	0.191077i	$-0.938802\pi$
$373$	−15.2670	+	15.2670i	−0.790498	+	0.790498i	0.191077	+	0.981575i	$0.438802\pi$
$374$		−	38.8513i		−	2.00895i
$375$	11.0692	−	1.57231i	0.571613	−	0.0811939i
$376$	0.787514			0.0406129
$377$	46.9307	−	12.5751i	2.41706	−	0.647648i
$378$	0.339513	−	1.26708i	0.0174626	−	0.0651715i
$379$	18.1505	−	10.4792i	0.932328	−	0.538280i	0.0447812	−	0.998997i	$-0.485741\pi$
$379$	18.1505	−	10.4792i	0.932328	−	0.538280i	0.887547	+	0.460717i	$0.152408\pi$
$380$	1.43764	+	10.6403i	0.0737493	+	0.545834i
$381$	1.71959	−	2.97841i	0.0880970	−	0.152589i
$382$	−7.37297	+	1.97558i	−0.377234	+	0.101080i
$383$	−20.3337	+	5.44840i	−1.03900	+	0.278400i	−0.737700	−	0.675128i	$-0.764088\pi$
$383$	−20.3337	+	5.44840i	−1.03900	+	0.278400i	−0.301303	+	0.953528i	$0.597422\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−15.4377	+	6.45608i	−0.786778	+	0.329033i
$386$	6.89081	+	11.9352i	0.350733	+	0.607488i
$387$	−4.34666	+	4.34666i	−0.220953	+	0.220953i
$388$	5.21180	−	5.21180i	0.264589	−	0.264589i
$389$	−10.5622	−	18.2943i	−0.535524	−	0.927556i	−0.999138	−	0.0415179i	$-0.986781\pi$
$389$	−10.5622	−	18.2943i	−0.535524	−	0.927556i	0.463613	−	0.886038i	$-0.346553\pi$
$390$	−13.3153	+	5.56851i	−0.674249	+	0.281972i
$391$	8.01894	+	13.8892i	0.405535	+	0.702408i
$392$	−5.09936	+	1.36637i	−0.257557	+	0.0690121i
$393$	3.60673	−	0.966420i	0.181935	−	0.0487494i
$394$	−2.74359	+	4.75204i	−0.138220	+	0.239404i
$395$	−2.63965	−	19.5366i	−0.132815	−	0.982993i
$396$	4.94046	−	2.85238i	0.248268	−	0.143337i
$397$	3.34212	−	12.4730i	0.167736	−	0.626000i	−0.829939	−	0.557854i	$-0.811625\pi$
$397$	3.34212	−	12.4730i	0.167736	−	0.626000i	0.997675	−	0.0681463i	$-0.0217085\pi$
$398$	6.76043	−	1.81145i	0.338870	−	0.0907999i
$399$	−6.29876			−0.315333
$400$	−3.55949	−	3.51141i	−0.177975	−	0.175571i
$401$		−	30.1179i		−	1.50401i	−0.659155	−	0.752007i	$-0.729086\pi$
$401$		−	30.1179i		−	1.50401i	0.659155	−	0.752007i	$-0.270914\pi$
$402$	−5.42310	+	5.42310i	−0.270480	+	0.270480i
$403$	−18.8288	+	30.6101i	−0.937928	+	1.52480i
$404$		−	18.2636i		−	0.908649i
$405$	−0.299401	−	2.21593i	−0.0148774	−	0.110111i
$406$	−8.55140	+	4.93715i	−0.424399	+	0.245027i
$407$	−9.88855	−	9.88855i	−0.490157	−	0.490157i
$408$	1.76264	+	6.57827i	0.0872638	+	0.325673i
$409$	2.47551	+	4.28771i	0.122406	+	0.212013i	0.920716	−	0.390233i	$-0.127606\pi$
$409$	2.47551	+	4.28771i	0.122406	+	0.212013i	−0.798310	+	0.602247i	$0.794272\pi$
$410$	−3.32049	−	0.425671i	−0.163987	−	0.0210224i
$411$	−3.90010			−0.192378
$412$	−5.99973	+	1.60762i	−0.295585	+	0.0792019i
$413$	3.51955	+	13.1351i	0.173186	+	0.646338i
$414$	−1.17747	+	2.03944i	−0.0578694	+	0.100233i
$415$	−23.2447	−	2.97985i	−1.14104	−	0.146275i
$416$	5.58981	+	3.22728i	0.274063	+	0.158230i
$417$	2.39518	−	8.93894i	0.117293	−	0.437742i
$418$	−19.3695	−	19.3695i	−0.947392	−	0.947392i
$419$			33.4588i			1.63457i	0.576232	+	0.817286i	$0.304522\pi$
$419$			33.4588i			1.63457i	−0.576232	+	0.817286i	$0.695478\pi$
$420$	2.32099	−	1.79353i	0.113253	−	0.0875154i
$421$	7.88878	−	13.6638i	0.384475	−	0.665931i	−0.607221	−	0.794533i	$-0.707716\pi$
$421$	7.88878	−	13.6638i	0.384475	−	0.665931i	0.991696	+	0.128602i	$0.0410490\pi$
$422$	−3.14656	+	11.7431i	−0.153172	+	0.571647i
$423$	0.203824	+	0.760680i	0.00991025	+	0.0369855i
$424$	5.87197	−	10.1706i	0.285168	−	0.493926i
$425$	−17.2259	−	29.3731i	−0.835581	−	1.42481i
$426$		−	13.5155i		−	0.654829i
$427$	−1.34889	−	0.361435i	−0.0652775	−	0.0174910i
$428$	−18.0984	−	4.84945i	−0.874819	−	0.234407i
$429$	18.4108	−	31.8885i	0.888884	−	1.53959i
$430$	−13.6216	+	1.84045i	−0.656890	+	0.0887544i
$431$	−4.56886	−	7.91349i	−0.220074	−	0.381180i	0.734756	−	0.678331i	$-0.237297\pi$
$431$	−4.56886	−	7.91349i	−0.220074	−	0.381180i	−0.954830	+	0.297152i	$0.903963\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	−25.1526	−	25.1526i	−1.20876	−	1.20876i	−0.971430	−	0.237328i	$-0.923728\pi$
$433$	−25.1526	−	25.1526i	−1.20876	−	1.20876i	−0.237328	−	0.971430i	$-0.576272\pi$
$434$	2.08612	−	6.99939i	0.100137	−	0.335982i
$435$	−10.2011	+	13.3884i	−0.489106	+	0.641923i
$436$	−10.4683			−0.501340
$437$	10.9224	+	2.92665i	0.522490	+	0.140001i
$438$	−7.09616	+	7.09616i	−0.339068	+	0.339068i
$439$	16.0958	+	9.29294i	0.768213	+	0.443528i	0.832237	−	0.554420i	$-0.187060\pi$
$439$	16.0958	+	9.29294i	0.768213	+	0.443528i	−0.0640239	+	0.997948i	$0.520393\pi$
$440$	12.6527	+	1.62201i	0.603193	+	0.0773264i
$441$	−2.63962	−	4.57196i	−0.125696	−	0.217712i
$442$	31.0827	+	31.0827i	1.47846	+	1.47846i
$443$	−8.17846	−	30.5224i	−0.388570	−	1.45016i	−0.832461	−	0.554083i	$-0.813069\pi$
$443$	−8.17846	−	30.5224i	−0.388570	−	1.45016i	0.443891	−	0.896081i	$-0.353598\pi$
$444$	2.12296	+	1.22569i	0.100751	+	0.0581686i
$445$	−12.8631	−	5.27690i	−0.609769	−	0.250149i
$446$	−7.51526	+	4.33894i	−0.355858	+	0.205455i
$447$	3.31351	+	12.3662i	0.156724	+	0.584901i
$448$	−1.26708	−	0.339513i	−0.0598638	−	0.0160405i
$449$	−16.2891			−0.768731			−0.384365	−	0.923181i	$-0.625580\pi$
$449$	−16.2891			−0.768731			−0.384365	+	0.923181i	$0.625580\pi$
$450$	2.47050	−	4.34703i	0.116460	−	0.204921i
$451$	7.39648	−	4.27036i	0.348286	−	0.201083i
$452$	5.24000	−	1.40405i	0.246469	−	0.0660411i
$453$	−5.41821	−	1.45180i	−0.254569	−	0.0682117i
$454$	16.8557	+	9.73162i	0.791075	+	0.456727i
$455$	7.18569	−	17.5160i	0.336871	−	0.821163i
$456$	4.15840	+	2.40085i	0.194735	+	0.112430i
$457$	−4.63151	+	4.63151i	−0.216653	+	0.216653i	−0.807086	−	0.590433i	$-0.798957\pi$
$457$	−4.63151	+	4.63151i	−0.216653	+	0.216653i	0.590433	+	0.807086i	$0.298957\pi$
$458$	−0.984098	+	3.67270i	−0.0459839	+	0.171614i
$459$	−5.89791	+	3.40516i	−0.275291	+	0.158939i
$460$	−4.85808	+	2.03166i	−0.226509	+	0.0947268i
$461$			29.8714i			1.39125i	0.718406	+	0.695624i	$0.244872\pi$
$461$			29.8714i			1.39125i	−0.718406	+	0.695624i	$0.755128\pi$
$462$	−1.93684	+	7.22837i	−0.0901098	+	0.336294i
$463$	−7.81660	−	7.81660i	−0.363268	−	0.363268i	0.501747	−	0.865015i	$-0.332691\pi$
$463$	−7.81660	−	7.81660i	−0.363268	−	0.363268i	−0.865015	+	0.501747i	$0.832691\pi$
$464$	7.52743			0.349452
$465$	−1.32265	−	12.3794i	−0.0613362	−	0.574083i
$466$	−18.8108			−0.871395
$467$	−24.8525	−	24.8525i	−1.15004	−	1.15004i	−0.986545	−	0.163492i	$-0.947724\pi$
$467$	−24.8525	−	24.8525i	−1.15004	−	1.15004i	−0.163492	−	0.986545i	$-0.552276\pi$
$468$	−1.67056	+	6.23462i	−0.0772218	+	0.288196i
$469$		−	10.0606i		−	0.464553i
$470$	−0.668346	+	1.62917i	−0.0308285	+	0.0751482i
$471$	18.4085	−	10.6281i	0.848217	−	0.489718i
$472$	2.68304	−	10.0132i	0.123497	−	0.460897i
$473$	24.7966	−	24.7966i	1.14015	−	1.14015i
$474$	−7.63525	−	4.40821i	−0.350698	−	0.202476i
$475$	−23.2322	−	6.05603i	−1.06597	−	0.277870i
$476$	−7.73674	−	4.46681i	−0.354613	−	0.204736i
$477$	11.3438	+	3.03956i	0.519396	+	0.139172i
$478$	21.9707	−	5.88702i	1.00491	−	0.269266i
$479$	−18.5845	+	10.7298i	−0.849146	+	0.490255i	−0.860363	−	0.509682i	$-0.829763\pi$
$479$	−18.5845	+	10.7298i	−0.849146	+	0.490255i	0.0112164	+	0.999937i	$0.496430\pi$
$480$	−2.21593	+	0.299401i	−0.101143	+	0.0136657i
$481$	15.8226			0.721447
$482$	1.13382	+	0.303807i	0.0516442	+	0.0138380i
$483$	−0.799531	−	2.98389i	−0.0363799	−	0.135772i
$484$	−18.6579	+	10.7721i	−0.848085	+	0.489642i
$485$	6.35880	+	15.2051i	0.288738	+	0.690426i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	1.09707	+	4.09432i	0.0497130	+	0.185532i	0.986317	−	0.164857i	$-0.0527162\pi$
$487$	1.09707	+	4.09432i	0.0497130	+	0.185532i	−0.936604	+	0.350388i	$0.886050\pi$
$488$	0.752764	+	0.752764i	0.0340760	+	0.0340760i
$489$	−2.65076	−	4.59125i	−0.119871	−	0.207623i
$490$	1.50103	−	11.7089i	0.0678095	−	0.528956i
$491$	−8.23789	−	4.75615i	−0.371771	−	0.214642i	0.302461	−	0.953162i	$-0.402192\pi$
$491$	−8.23789	−	4.75615i	−0.371771	−	0.214642i	−0.674232	+	0.738520i	$0.735525\pi$
$492$	−1.05862	+	1.05862i	−0.0477265	+	0.0477265i
$493$	49.5175	+	13.2682i	2.23016	+	0.597568i
$494$	30.9929			1.39444
$495$	1.70801	+	12.6414i	0.0767694	+	0.568187i
$496$	−4.04515	+	3.82580i	−0.181633	+	0.171783i
$497$	12.5365	+	12.5365i	0.562340	+	0.562340i
$498$	−7.41077	+	7.41077i	−0.332084	+	0.332084i
$499$	−8.53758	−	14.7875i	−0.382195	−	0.661980i	0.609181	−	0.793031i	$-0.291498\pi$
$499$	−8.53758	−	14.7875i	−0.382195	−	0.661980i	−0.991376	+	0.131051i	$0.958165\pi$
$500$	10.2851	−	4.38367i	0.459964	−	0.196043i
$501$	−2.87989	+	4.98811i	−0.128664	+	0.222852i
$502$	2.57131	+	0.688980i	0.114763	+	0.0307507i
$503$	−37.9825	−	10.1774i	−1.69356	−	0.453787i	−0.722252	−	0.691630i	$-0.756893\pi$
$503$	−37.9825	−	10.1774i	−1.69356	−	0.453787i	−0.971304	+	0.237843i	$0.923560\pi$
$504$		−	1.31178i		−	0.0584311i
$505$	37.7830	+	15.4999i	1.68132	+	0.689737i
$506$	6.71717	−	11.6345i	0.298615	−	0.517216i
$507$	7.41810	+	27.6847i	0.329449	+	1.22952i
$508$	0.890123	−	3.32198i	0.0394928	−	0.147389i
$509$	0.845498	−	1.46445i	0.0374760	−	0.0649104i	−0.846679	−	0.532104i	$-0.821402\pi$
$509$	0.845498	−	1.46445i	0.0374760	−	0.0649104i	0.884155	+	0.467194i	$0.154735\pi$
$510$	−15.1047	−	1.93635i	−0.668849	−	0.0857432i
$511$		−	13.1643i		−	0.582354i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.24277	+	4.63809i	−0.0548698	+	0.204777i
$514$	8.31528	+	4.80083i	0.366771	+	0.211756i
$515$	1.76606	−	13.7763i	0.0778217	−	0.607057i
$516$	−3.07355	+	5.32355i	−0.135306	+	0.234356i
$517$	−1.16276	−	4.33950i	−0.0511383	−	0.190851i
$518$	−3.10609	+	0.832274i	−0.136474	+	0.0365680i
$519$	−23.5102			−1.03198
$520$	−11.4204	+	8.82503i	−0.500818	+	0.387003i
$521$	−6.45038	−	11.1724i	−0.282596	−	0.489471i	0.689427	−	0.724355i	$-0.257862\pi$
$521$	−6.45038	−	11.1724i	−0.282596	−	0.489471i	−0.972023	+	0.234884i	$0.924529\pi$
$522$	1.94824	+	7.27094i	0.0852723	+	0.318241i
$523$	8.60833	+	8.60833i	0.376416	+	0.376416i	0.869807	−	0.493391i	$-0.164243\pi$
$523$	8.60833	+	8.60833i	0.376416	+	0.376416i	−0.493391	+	0.869807i	$0.664243\pi$
$524$	3.23370	−	1.86698i	0.141265	−	0.0815594i
$525$	1.74060	+	6.32370i	0.0759662	+	0.275989i
$526$		−	12.2016i		−	0.532014i
$527$	−33.3536	+	18.0370i	−1.45291	+	0.785703i
$528$	4.03387	−	4.03387i	0.175552	−	0.175552i
$529$		−	17.4543i		−	0.758881i
$530$	16.0570	+	20.7792i	0.697471	+	0.902591i
$531$	10.3665			0.449867
$532$	−6.08414	+	1.63024i	−0.263781	+	0.0706799i
$533$	−2.50104	+	9.33399i	−0.108332	+	0.404300i
$534$	−5.38477	+	3.10890i	−0.233022	+	0.134535i
$535$	25.3920	−	33.3255i	1.09779	−	1.44079i
$536$	−3.83471	+	6.64191i	−0.165634	+	0.286887i
$537$	5.92834	−	1.58849i	0.255827	−	0.0685486i
$538$	18.5792	−	4.97829i	0.801007	−	0.214629i
$539$	15.0584	+	26.0819i	0.648611	+	1.12343i
$540$	−0.862725	−	2.06294i	−0.0371258	−	0.0887746i
$541$	15.3360	+	26.5627i	0.659346	+	1.14202i	0.980785	+	0.195091i	$0.0625002\pi$
$541$	15.3360	+	26.5627i	0.659346	+	1.14202i	−0.321439	+	0.946930i	$0.604167\pi$
$542$	15.1404	−	15.1404i	0.650334	−	0.650334i
$543$	−2.14037	+	2.14037i	−0.0918522	+	0.0918522i
$544$	3.40516	+	5.89791i	0.145995	+	0.252871i
$545$	8.88420	−	21.6563i	0.380557	−	0.927655i
$546$	−4.23347	−	7.33258i	−0.181176	−	0.313805i
$547$	1.91459	−	0.513012i	0.0818618	−	0.0219348i	−0.217656	−	0.976026i	$-0.569841\pi$
$547$	1.91459	−	0.513012i	0.0818618	−	0.0219348i	0.299517	+	0.954091i	$0.403174\pi$
$548$	−3.76721	+	1.00942i	−0.160927	+	0.0431203i
$549$	−0.532285	+	0.921944i	−0.0227174	+	0.0393476i
$550$	−14.0936	+	24.7987i	−0.600953	+	1.05742i
$551$	31.3021	−	18.0723i	1.33351	−	0.769905i
$552$	−0.609502	+	2.27469i	−0.0259421	+	0.0968174i
$553$	11.1711	−	2.99329i	0.475043	−	0.127287i
$554$	12.1733			0.517196
$555$	−4.33735	+	3.35166i	−0.184110	+	0.142270i
$556$		−	9.25427i		−	0.392469i
$557$	−0.166418	+	0.166418i	−0.00705138	+	0.00705138i	−0.710624	−	0.703572i	$-0.751587\pi$
$557$	−0.166418	+	0.166418i	−0.00705138	+	0.00705138i	0.703572	+	0.710624i	$0.251587\pi$
$558$	−4.74240	−	2.91713i	−0.200762	−	0.123492i
$559$			39.6768i			1.67815i
$560$	1.77771	−	2.33314i	0.0751219	−	0.0985930i
$561$	33.6462	−	19.4256i	1.42054	−	0.820151i
$562$	−4.94134	−	4.94134i	−0.208438	−	0.208438i
$563$	10.0543	+	37.5233i	0.423740	+	1.58142i	0.766659	+	0.642055i	$0.221918\pi$
$563$	10.0543	+	37.5233i	0.423740	+	1.58142i	−0.342919	+	0.939365i	$0.611415\pi$
$564$	0.393757	+	0.682007i	0.0165802	+	0.0287177i
$565$	−1.54243	+	12.0319i	−0.0648903	+	0.506184i
$566$	−17.1017			−0.718839
$567$	1.26708	−	0.339513i	0.0532123	−	0.0142582i
$568$	−3.49807	−	13.0550i	−0.146776	−	0.547775i
$569$	13.7654	−	23.8423i	0.577075	−	0.999523i	−0.418738	−	0.908107i	$-0.637527\pi$
$569$	13.7654	−	23.8423i	0.577075	−	0.999523i	0.995813	−	0.0914159i	$-0.0291393\pi$
$570$	−8.49592	+	6.56516i	−0.355855	+	0.274984i
$571$	−15.2670	−	8.81441i	−0.638905	−	0.368872i	0.145288	−	0.989389i	$-0.453589\pi$
$571$	−15.2670	−	8.81441i	−0.638905	−	0.368872i	−0.784192	+	0.620518i	$0.786923\pi$
$572$	9.53015	−	35.5670i	0.398476	−	1.48713i
$573$	−5.39739	−	5.39739i	−0.225479	−	0.225479i
$574$		−	1.96389i		−	0.0819711i
$575$	−0.0800672	−	11.7744i	−0.00333903	−	0.491027i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−6.91822	+	25.8191i	−0.288009	+	1.07486i	0.658603	+	0.752490i	$0.271148\pi$
$577$	−6.91822	+	25.8191i	−0.288009	+	1.07486i	−0.946612	+	0.322374i	$0.895519\pi$
$578$	7.60424	+	28.3794i	0.316295	+	1.18043i
$579$	−6.89081	+	11.9352i	−0.286372	+	0.496011i
$580$	−6.38836	+	15.5724i	−0.265262	+	0.646609i
$581$		−	13.7479i		−	0.570361i
$582$	7.11945	+	1.90765i	0.295111	+	0.0790746i
$583$	−64.7135	−	17.3399i	−2.68016	−	0.718147i
$584$	−5.01774	+	8.69098i	−0.207636	+	0.359635i
$585$	−11.4801	−	8.74717i	−0.474645	−	0.361651i
$586$	−3.54858	−	6.14632i	−0.146590	−	0.253902i
$587$	−15.4582	+	15.4582i	−0.638026	+	0.638026i	−0.950068	−	0.312042i	$-0.898987\pi$
$587$	−15.4582	+	15.4582i	−0.638026	+	0.638026i	0.312042	+	0.950068i	$0.398987\pi$
$588$	−3.73299	−	3.73299i	−0.153946	−	0.153946i
$589$	−7.63618	+	25.6210i	−0.314643	+	1.05570i
$590$	18.4379	+	14.0486i	0.759077	+	0.578370i
$591$	−5.48718			−0.225712
$592$	2.36785	+	0.634463i	0.0973180	+	0.0260763i
$593$	−19.9590	+	19.9590i	−0.819616	+	0.819616i	−0.986052	−	0.166436i	$-0.946774\pi$
$593$	−19.9590	+	19.9590i	−0.819616	+	0.819616i	0.166436	+	0.986052i	$0.446774\pi$
$594$	4.94046	+	2.85238i	0.202710	+	0.117035i
$595$	15.8067	−	12.2145i	0.648013	−	0.500747i
$596$	6.40121	+	11.0872i	0.262204	+	0.454150i
$597$	4.94898	+	4.94898i	0.202548	+	0.202548i
$598$	3.93407	+	14.6821i	0.160876	+	0.600398i
$599$	−11.1465	−	6.43546i	−0.455436	−	0.262946i	0.254687	−	0.967023i	$-0.418027\pi$
$599$	−11.1465	−	6.43546i	−0.455436	−	0.262946i	−0.710123	+	0.704078i	$0.751361\pi$
$600$	1.26122	−	4.83832i	0.0514893	−	0.197523i
$601$	−33.0345	+	19.0725i	−1.34750	+	0.777981i	−0.987895	−	0.155122i	$-0.950423\pi$
$601$	−33.0345	+	19.0725i	−1.34750	+	0.777981i	−0.359608	+	0.933103i	$0.617090\pi$
$602$	−2.08702	−	7.78886i	−0.0850605	−	0.317450i
$603$	−7.40809	−	1.98499i	−0.301681	−	0.0808351i
$604$	−5.60934			−0.228241
$605$	−6.45038	−	47.7406i	−0.262245	−	1.94093i
$606$	15.8168	−	9.13181i	0.642512	−	0.370954i
$607$	−20.2370	+	5.42249i	−0.821395	+	0.220092i	−0.644956	−	0.764220i	$-0.723124\pi$
$607$	−20.2370	+	5.42249i	−0.821395	+	0.220092i	−0.176439	+	0.984312i	$0.556458\pi$
$608$	4.63809	+	1.24277i	0.188100	+	0.0504011i
$609$	−8.55140	−	4.93715i	−0.346520	−	0.200064i
$610$	−2.19614	+	0.918431i	−0.0889191	+	0.0371862i
$611$	4.40206	+	2.54153i	0.178088	+	0.102819i
$612$	−4.81563	+	4.81563i	−0.194660	+	0.194660i
$613$	8.74247	−	32.6273i	0.353105	−	1.31781i	−0.529748	−	0.848155i	$-0.677713\pi$
$613$	8.74247	−	32.6273i	0.353105	−	1.31781i	0.882853	−	0.469650i	$-0.155620\pi$
$614$	−0.572172	+	0.330344i	−0.0230910	+	0.0133316i
$615$	−1.29160	−	3.08847i	−0.0520825	−	0.124539i
$616$			7.48336i			0.301513i
$617$	0.834210	−	3.11331i	0.0335840	−	0.125337i	−0.947099	−	0.320942i	$-0.896000\pi$
$617$	0.834210	−	3.11331i	0.0335840	−	0.125337i	0.980683	+	0.195605i	$0.0626671\pi$
$618$	−4.39210	−	4.39210i	−0.176676	−	0.176676i
$619$	−1.26734			−0.0509386			−0.0254693	−	0.999676i	$-0.508108\pi$
$619$	−1.26734			−0.0509386			−0.0254693	+	0.999676i	$0.508108\pi$
$620$	−4.48161	−	11.6153i	−0.179986	−	0.466482i
$621$	−2.35494			−0.0945004
$622$	−5.68326	−	5.68326i	−0.227878	−	0.227878i
$623$	2.11102	−	7.87843i	0.0845762	−	0.315643i
$624$			6.45456i			0.258389i
$625$	0.339989	+	24.9977i	0.0135996	+	0.999908i
$626$	17.0453	−	9.84112i	0.681268	−	0.393330i
$627$	7.08972	−	26.4592i	0.283136	−	1.05668i
$628$	15.0304	−	15.0304i	0.599780	−	0.599780i
$629$	14.4580	+	8.34734i	0.576479	+	0.332830i
$630$	2.71374	+	1.11327i	0.108118	+	0.0443539i
$631$	−30.3847	−	17.5426i	−1.20960	−	0.698360i	−0.246925	−	0.969035i	$-0.579420\pi$
$631$	−30.3847	−	17.5426i	−1.20960	−	0.698360i	−0.962671	+	0.270674i	$0.912753\pi$
$632$	−8.51601	−	2.28186i	−0.338749	−	0.0907674i
$633$	−11.7431	+	3.14656i	−0.466748	+	0.125065i
$634$	−8.76298	+	5.05931i	−0.348022	+	0.200931i
$635$	6.11694	+	4.66074i	0.242744	+	0.184956i
$636$	11.7439			0.465678
$637$	−32.9141	−	8.81931i	−1.30410	−	0.349434i
$638$	−11.1143	−	41.4790i	−0.440018	−	1.64217i
$639$	11.7048	−	6.75775i	0.463034	−	0.267333i
$640$	−2.06294	+	0.862725i	−0.0815447	+	0.0341022i
$641$	−23.7173	−	13.6932i	−0.936777	−	0.540849i	−0.0478286	−	0.998856i	$-0.515230\pi$
$641$	−23.7173	−	13.6932i	−0.936777	−	0.540849i	−0.888949	+	0.458007i	$0.848563\pi$
$642$	−4.84945	−	18.0984i	−0.191393	−	0.714287i
$643$	−6.01249	−	6.01249i	−0.237109	−	0.237109i	0.578543	−	0.815652i	$-0.303622\pi$
$643$	−6.01249	−	6.01249i	−0.237109	−	0.237109i	−0.815652	+	0.578543i	$0.803622\pi$
$644$	−1.54457	−	2.67528i	−0.0608648	−	0.105421i
$645$	−8.40466	−	10.8764i	−0.330933	−	0.428258i
$646$	28.3201	+	16.3506i	1.11424	+	0.643306i
$647$	−2.53385	+	2.53385i	−0.0996159	+	0.0996159i	−0.755158	−	0.655542i	$-0.772440\pi$
$647$	−2.53385	+	2.53385i	−0.0996159	+	0.0996159i	0.655542	+	0.755158i	$0.272440\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	−59.1382			−2.32138
$650$	−8.56460	−	31.1156i	−0.335931	−	1.22045i
$651$	7.10471	−	1.69306i	0.278456	−	0.0663563i
$652$	−3.74874	−	3.74874i	−0.146812	−	0.146812i
$653$	12.8222	−	12.8222i	0.501772	−	0.501772i	−0.410216	−	0.911988i	$-0.634547\pi$
$653$	12.8222	−	12.8222i	0.501772	−	0.501772i	0.911988	+	0.410216i	$0.134547\pi$
$654$	−5.23414	−	9.06580i	−0.204671	−	0.354501i
$655$	1.11795	+	8.27421i	0.0436820	+	0.323300i
$656$	−0.748561	+	1.29655i	−0.0292264	+	0.0506216i
$657$	−9.69353	−	2.59737i	−0.378181	−	0.101333i
$658$	−0.997842	−	0.267371i	−0.0388999	−	0.0104232i
$659$		−	48.8287i		−	1.90210i	−0.309040	−	0.951049i	$-0.600008\pi$
$659$		−	48.8287i		−	1.90210i	0.309040	−	0.951049i	$-0.399992\pi$
$660$	4.92164	+	11.7686i	0.191574	+	0.458090i
$661$	−3.20212	+	5.54624i	−0.124548	+	0.215724i	−0.921556	−	0.388245i	$-0.873081\pi$
$661$	−3.20212	+	5.54624i	−0.124548	+	0.215724i	0.797008	+	0.603969i	$0.206415\pi$
$662$	−1.31952	−	4.92451i	−0.0512846	−	0.191397i
$663$	−11.3771	+	42.4598i	−0.441849	+	1.64900i
$664$	−5.24020	+	9.07630i	−0.203359	+	0.352229i
$665$	1.79090	−	13.9701i	0.0694482	−	0.541739i
$666$			2.45138i			0.0949890i
$667$	12.5346	+	12.5346i	0.485342	+	0.485342i
$668$	−1.49074	+	5.56351i	−0.0576784	+	0.215259i
$669$	−7.51526	−	4.33894i	−0.290557	−	0.167753i
$670$	−10.4861	−	13.5699i	−0.405112	−	0.524252i
$671$	3.03656	−	5.25947i	0.117225	−	0.203040i
$672$	−0.339513	−	1.26708i	−0.0130970	−	0.0488786i
$673$	−27.8596	+	7.46495i	−1.07391	+	0.287753i	−0.752097	−	0.659052i	$-0.770958\pi$
$673$	−27.8596	+	7.46495i	−1.07391	+	0.287753i	−0.321810	+	0.946804i	$0.604291\pi$
$674$	−28.7890			−1.10891
$675$	4.99988	−	0.0339997i	0.192446	−	0.00130865i
$676$	14.3307	+	24.8214i	0.551179	+	0.954671i
$677$	−1.80945	−	6.75297i	−0.0695429	−	0.259538i	0.922398	−	0.386242i	$-0.126227\pi$
$677$	−1.80945	−	6.75297i	−0.0695429	−	0.259538i	−0.991941	+	0.126704i	$0.959560\pi$
$678$	3.83594	+	3.83594i	0.147319	+	0.147319i
$679$	−8.37322	+	4.83428i	−0.321335	+	0.185523i
$680$	−15.0912	+	2.03902i	−0.578722	+	0.0781929i
$681$			19.4632i			0.745833i
$682$	27.0542	+	16.6415i	1.03596	+	0.637236i
$683$	14.0707	−	14.0707i	0.538400	−	0.538400i	−0.384659	−	0.923059i	$-0.625681\pi$
$683$	14.0707	−	14.0707i	0.538400	−	0.538400i	0.923059	+	0.384659i	$0.125681\pi$
$684$			4.80171i			0.183598i
$685$	1.10890	−	8.65011i	0.0423690	−	0.330504i
$686$	16.1076			0.614992
$687$	−3.67270	+	0.984098i	−0.140122	+	0.0375457i
$688$	−1.59099	+	5.93764i	−0.0606558	+	0.226371i
$689$	65.6465	−	37.9010i	2.50093	−	1.44391i
$690$	−4.18851	−	3.19139i	−0.159454	−	0.121494i
$691$	8.22812	−	14.2515i	0.313012	−	0.542153i	−0.666001	−	0.745951i	$-0.731995\pi$
$691$	8.22812	−	14.2515i	0.313012	−	0.542153i	0.979013	+	0.203798i	$0.0653285\pi$
$692$	−22.7091	+	6.08489i	−0.863271	+	0.231313i
$693$	−7.22837	+	1.93684i	−0.274583	+	0.0735743i
$694$	−1.15401	−	1.99880i	−0.0438056	−	0.0758735i
$695$	19.1448	+	7.85389i	0.726204	+	0.297915i
$696$	3.76372	+	6.51895i	0.142663	+	0.247100i
$697$	−7.20958	+	7.20958i	−0.273082	+	0.273082i
$698$	−21.8000	+	21.8000i	−0.825142	+	0.825142i
$699$	−9.40542	−	16.2907i	−0.355746	−	0.616169i
$700$	3.31799	+	5.65772i	0.125408	+	0.213842i
$701$	5.61318	+	9.72232i	0.212007	+	0.367207i	0.952343	−	0.305031i	$-0.0986667\pi$
$701$	5.61318	+	9.72232i	0.212007	+	0.367207i	−0.740336	+	0.672237i	$0.765333\pi$
$702$	−6.23462	+	1.67056i	−0.235311	+	0.0630513i
$703$	11.3697	−	3.04651i	0.428817	−	0.114901i
$704$	2.85238	−	4.94046i	0.107503	−	0.186201i
$705$	−1.74508	+	0.235783i	−0.0657235	+	0.00888009i
$706$	−6.33476	+	3.65738i	−0.238412	+	0.137647i
$707$	−6.20073	+	23.1414i	−0.233202	+	0.870323i
$708$	10.0132	−	2.68304i	0.376321	−	0.100835i
$709$	−27.9162			−1.04842			−0.524208	−	0.851590i	$-0.675638\pi$
$709$	−27.9162			−1.04842			−0.524208	+	0.851590i	$0.675638\pi$
$710$	29.9763	+	3.84281i	1.12499	+	0.144218i
$711$		−	8.81642i		−	0.330642i
$712$	−4.39664	+	4.39664i	−0.164771	+	0.164771i
$713$	−13.1066	−	0.365264i	−0.490848	−	0.0136792i
$714$		−	8.93362i		−	0.334332i
$715$	65.4914	+	49.9005i	2.44924	+	1.86617i
$716$	5.31520	−	3.06873i	0.198638	−	0.114684i
$717$	16.0836	+	16.0836i	0.600654	+	0.600654i
$718$	1.90187	+	7.09787i	0.0709771	+	0.264890i
$719$	2.71296	+	4.69898i	0.101176	+	0.175242i	0.912170	−	0.409813i	$-0.134406\pi$
$719$	2.71296	+	4.69898i	0.101176	+	0.175242i	−0.810993	+	0.585055i	$0.801073\pi$
$720$	−1.36726	−	1.76935i	−0.0509546	−	0.0659399i
$721$	8.14793			0.303445
$722$	3.91818	−	1.04987i	0.145819	−	0.0390722i
$723$	0.303807	+	1.13382i	0.0112987	+	0.0421673i
$724$	−1.51347	+	2.62141i	−0.0562478	+	0.0974240i
$725$	−26.7939	−	26.4319i	−0.995099	−	0.981657i
$726$	−18.6579	−	10.7721i	−0.692459	−	0.399791i
$727$	11.0189	−	41.1231i	0.408669	−	1.52517i	−0.388519	−	0.921441i	$-0.627013\pi$
$727$	11.0189	−	41.1231i	0.408669	−	1.52517i	0.797188	−	0.603731i	$-0.206320\pi$
$728$	−5.98703	−	5.98703i	−0.221894	−	0.221894i
$729$		−	1.00000i		−	0.0370370i
$730$	−13.7211	−	17.7563i	−0.507840	−	0.657191i
$731$	−20.9319	+	36.2551i	−0.774194	+	1.34094i
$732$	−0.275531	+	1.02830i	−0.0101839	+	0.0380069i
$733$	−1.81418	−	6.77061i	−0.0670083	−	0.250078i	0.924294	−	0.381680i	$-0.124655\pi$
$733$	−1.81418	−	6.77061i	−0.0670083	−	0.250078i	−0.991303	+	0.131602i	$0.957988\pi$
$734$	−3.40168	+	5.89188i	−0.125558	+	0.217473i
$735$	10.8907	−	4.55454i	0.401711	−	0.167997i
$736$			2.35494i			0.0868041i
$737$	42.2614	+	11.3239i	1.55672	+	0.417121i
$738$	−1.44611	−	0.387484i	−0.0532320	−	0.0142635i
$739$	−11.1753	+	19.3562i	−0.411091	+	0.712030i	−0.995009	−	0.0997821i	$-0.968185\pi$
$739$	−11.1753	+	19.3562i	−0.411091	+	0.712030i	0.583918	+	0.811812i	$0.301519\pi$
$740$	−3.32209	+	4.36005i	−0.122122	+	0.160278i
$741$	15.4965	+	26.8406i	0.569276	+	0.986016i
$742$	−10.8933	+	10.8933i	−0.399905	+	0.399905i
$743$	23.7473	+	23.7473i	0.871206	+	0.871206i	0.992604	−	0.121398i	$-0.0387378\pi$
$743$	23.7473	+	23.7473i	0.871206	+	0.871206i	−0.121398	+	0.992604i	$0.538738\pi$
$744$	−5.33582	−	1.59030i	−0.195621	−	0.0583034i
$745$	−28.3693	+	3.83306i	−1.03937	+	0.140432i
$746$	−21.5909			−0.790498
$747$	−10.1233	−	2.71253i	−0.370392	−	0.0992462i
$748$	27.4720	−	27.4720i	1.00448	−	1.00448i
$749$	21.2856	+	12.2893i	0.777760	+	0.449040i
$750$	8.93892	+	6.71533i	0.326403	+	0.245209i
$751$	11.4907	+	19.9025i	0.419302	+	0.726252i	0.995869	−	0.0907973i	$-0.0289415\pi$
$751$	11.4907	+	19.9025i	0.419302	+	0.726252i	−0.576567	+	0.817050i	$0.695608\pi$
$752$	0.556857	+	0.556857i	0.0203065	+	0.0203065i
$753$	0.688980	+	2.57131i	0.0251078	+	0.0937036i
$754$	42.0769	+	24.2931i	1.53235	+	0.884704i
$755$	4.76052	−	11.6043i	0.173253	−	0.422325i
$756$	1.13603	−	0.655888i	0.0413170	−	0.0238544i
$757$	9.72166	+	36.2817i	0.353340	+	1.31868i	0.882561	+	0.470198i	$0.155818\pi$
$757$	9.72166	+	36.2817i	0.353340	+	1.31868i	−0.529221	+	0.848484i	$0.677516\pi$
$758$	20.2442	+	5.42443i	0.735304	+	0.197024i
$759$	13.4343			0.487636
$760$	−6.50724	+	8.54036i	−0.236042	+	0.309792i
$761$	−31.8614	+	18.3952i	−1.15497	+	0.666825i	−0.950094	−	0.311963i	$-0.899014\pi$
$761$	−31.8614	+	18.3952i	−1.15497	+	0.666825i	−0.204880	+	0.978787i	$0.565680\pi$
$762$	3.32198	−	0.890123i	0.120343	−	0.0322458i
$763$	13.2641	+	3.55412i	0.480194	+	0.128668i
$764$	−6.61042	−	3.81653i	−0.239157	−	0.138077i
$765$	−5.87544	−	14.0493i	−0.212427	−	0.507952i
$766$	−18.2307	−	10.5255i	−0.658702	−	0.380302i
$767$	47.3132	−	47.3132i	1.70838	−	1.70838i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	21.7850	−	12.5776i	0.785586	−	0.453558i	−0.0528202	−	0.998604i	$-0.516821\pi$
$769$	21.7850	−	12.5776i	0.785586	−	0.453558i	0.838406	+	0.545046i	$0.183488\pi$
$770$	−15.4812	−	6.35096i	−0.557905	−	0.228873i
$771$			9.60166i			0.345795i
$772$	−3.56695	+	13.3120i	−0.128377	+	0.479110i
$773$	6.95187	+	6.95187i	0.250042	+	0.250042i	0.820988	−	0.570946i	$-0.193423\pi$
$773$	6.95187	+	6.95187i	0.250042	+	0.250042i	−0.570946	+	0.820988i	$0.693423\pi$
$774$	−6.14710			−0.220953
$775$	27.8326	+	0.586281i	0.999778	+	0.0210598i
$776$	7.37059			0.264589
$777$	−2.27381	−	2.27381i	−0.0815726	−	0.0815726i
$778$	5.46739	−	20.4046i	0.196016	−	0.731540i
$779$			7.18874i			0.257563i
$780$	−13.3529	−	5.47784i	−0.478110	−	0.196138i
$781$	−66.7729	+	38.5513i	−2.38932	+	1.37948i
$782$	−4.15091	+	15.4914i	−0.148436	+	0.553972i
$783$	−5.32270	+	5.32270i	−0.190218	+	0.190218i
$784$	−4.57196	−	2.63962i	−0.163284	−	0.0942722i
$785$	18.3383	+	43.8503i	0.654522	+	1.56508i
$786$	3.23370	+	1.86698i	0.115342	+	0.0665930i
$787$	−1.38883	−	0.372136i	−0.0495065	−	0.0132652i	0.233981	−	0.972241i	$-0.424825\pi$
$787$	−1.38883	−	0.372136i	−0.0495065	−	0.0132652i	−0.283487	+	0.958976i	$0.591491\pi$
$788$	−5.30021	+	1.42019i	−0.188812	+	0.0505921i
$789$	10.5669	−	6.10079i	0.376191	−	0.217194i
$790$	11.9480	−	15.6810i	0.425089	−	0.557904i
$791$	−7.11618			−0.253022
$792$	5.51037	+	1.47650i	0.195803	+	0.0524651i
$793$	1.77843	+	6.63719i	0.0631539	+	0.235694i
$794$	11.1830	−	6.45648i	0.396868	−	0.229132i
$795$	−9.96682	+	24.2954i	−0.353487	+	0.861667i
$796$	6.06124	+	3.49946i	0.214835	+	0.124035i
$797$	11.2743	+	42.0761i	0.399355	+	1.49041i	0.814235	+	0.580535i	$0.197157\pi$
$797$	11.2743	+	42.0761i	0.399355	+	1.49041i	−0.414880	+	0.909876i	$0.636177\pi$
$798$	−4.45390	−	4.45390i	−0.157666	−	0.157666i
$799$	2.68161	+	4.64469i	0.0948687	+	0.164317i
$800$	−0.0339997	−	4.99988i	−0.00120207	−	0.176773i
$801$	−5.38477	−	3.10890i	−0.190261	−	0.109847i
$802$	21.2965	−	21.2965i	0.752007	−	0.752007i
$803$	55.2993	+	14.8174i	1.95147	+	0.522894i
$804$	−7.66942			−0.270480
$805$	6.84535	−	0.924895i	0.241267	−	0.0325983i
$806$	−34.9586	+	8.33066i	−1.23136	+	0.293435i
$807$	13.6009	+	13.6009i	0.478775	+	0.478775i
$808$	12.9143	−	12.9143i	0.454325	−	0.454325i
$809$	−17.6139	−	30.5081i	−0.619271	−	1.07261i	−0.989619	−	0.143715i	$-0.954095\pi$
$809$	−17.6139	−	30.5081i	−0.619271	−	1.07261i	0.370348	−	0.928893i	$-0.379238\pi$
$810$	1.35519	−	1.77861i	0.0476166	−	0.0624940i
$811$	−12.6087	+	21.8389i	−0.442751	+	0.766868i	−0.997893	−	0.0648883i	$-0.979331\pi$
$811$	−12.6087	+	21.8389i	−0.442751	+	0.766868i	0.555141	+	0.831756i	$0.312664\pi$
$812$	−9.53785	−	2.55566i	−0.334713	−	0.0896860i
$813$	20.6821	+	5.54176i	0.725354	+	0.194358i
$814$		−	13.9845i		−	0.490157i
$815$	10.9367	−	4.57375i	0.383095	−	0.160211i
$816$	−3.40516	+	5.89791i	−0.119205	+	0.206468i
$817$	7.63945	+	28.5108i	0.267271	+	0.997468i
$818$	−1.28142	+	4.78232i	−0.0448037	+	0.167210i
$819$	4.23347	−	7.33258i	0.147929	−	0.256221i
$820$	−2.04695	−	2.64894i	−0.0714825	−	0.0925049i
$821$		−	18.2029i		−	0.635285i	−0.948211	−	0.317642i	$-0.897109\pi$
$821$		−	18.2029i		−	0.635285i	0.948211	−	0.317642i	$-0.102891\pi$
$822$	−2.75779	−	2.75779i	−0.0961890	−	0.0961890i
$823$	5.24722	−	19.5829i	0.182907	−	0.682617i	−0.812162	−	0.583432i	$-0.801710\pi$
$823$	5.24722	−	19.5829i	0.182907	−	0.682617i	0.995069	−	0.0991855i	$-0.0316237\pi$
$824$	−5.37921	−	3.10569i	−0.187394	−	0.108192i
$825$	−28.5231	+	0.193960i	−0.993048	+	0.00675283i
$826$	−6.79924	+	11.7766i	−0.236576	+	0.409762i
$827$	10.1426	+	37.8528i	0.352694	+	1.31627i	0.883362	+	0.468692i	$0.155274\pi$
$827$	10.1426	+	37.8528i	0.352694	+	1.31627i	−0.530668	+	0.847580i	$0.678059\pi$
$828$	−2.27469	+	0.609502i	−0.0790511	+	0.0211817i
$829$	−5.77711			−0.200647			−0.100324	−	0.994955i	$-0.531988\pi$
$829$	−5.77711			−0.200647			−0.100324	+	0.994955i	$0.531988\pi$
$830$	−14.3294	−	18.5435i	−0.497380	−	0.643656i
$831$	6.08667	+	10.5424i	0.211144	+	0.365713i
$832$	1.67056	+	6.23462i	0.0579163	+	0.216147i
$833$	−25.4229	−	25.4229i	−0.880850	−	0.880850i
$834$	8.01443	−	4.62714i	0.277517	−	0.160225i
$835$	−10.2444	−	7.80560i	−0.354522	−	0.270124i
$836$		−	27.3926i		−	0.947392i
$837$	0.155106	−	5.56560i	0.00536123	−	0.192375i
$838$	−23.6590	+	23.6590i	−0.817286	+	0.817286i
$839$			7.93867i			0.274073i	0.990566	+	0.137037i	$0.0437578\pi$
$839$			7.93867i			0.274073i	−0.990566	+	0.137037i	$0.956242\pi$
$840$	2.90941	+	0.372972i	0.100384	+	0.0128688i
$841$	27.6623			0.953871
$842$	15.2399	−	4.08353i	0.525203	−	0.140728i
$843$	1.80866	−	6.75000i	0.0622935	−	0.232482i
$844$	−10.5286	+	6.07869i	−0.362410	+	0.209237i
$845$	−63.5116	+	8.58124i	−2.18486	+	0.295204i
$846$	−0.393757	+	0.682007i	−0.0135376	+	0.0234479i
$847$	27.2983	−	7.31455i	0.937979	−	0.251331i
$848$	11.3438	−	3.03956i	0.389547	−	0.104379i
$849$	−8.55086	−	14.8105i	−0.293465	−	0.508296i
$850$	8.58935	−	32.9505i	0.294612	−	1.13019i
$851$	2.88642	+	4.99943i	0.0989452	+	0.171378i
$852$	9.55691	−	9.55691i	0.327414	−	0.327414i
$853$	−10.0343	+	10.0343i	−0.343569	+	0.343569i	−0.857707	−	0.514138i	$-0.828112\pi$
$853$	−10.0343	+	10.0343i	−0.343569	+	0.343569i	0.514138	+	0.857707i	$0.328112\pi$
$854$	−0.698238	−	1.20938i	−0.0238932	−	0.0413843i
$855$	−9.93356	−	4.07510i	−0.339720	−	0.139365i
$856$	−9.36842	−	16.2266i	−0.320206	−	0.554613i
$857$	−18.4920	+	4.95491i	−0.631673	+	0.169256i	−0.560429	−	0.828203i	$-0.689364\pi$
$857$	−18.4920	+	4.95491i	−0.631673	+	0.169256i	−0.0712445	+	0.997459i	$0.522697\pi$
$858$	35.5670	−	9.53015i	1.21424	−	0.325354i
$859$	−12.1123	+	20.9791i	−0.413265	+	0.715796i	−0.995245	−	0.0974072i	$-0.968945\pi$
$859$	−12.1123	+	20.9791i	−0.413265	+	0.715796i	0.581979	+	0.813204i	$0.302278\pi$
$860$	−10.9333	−	8.33051i	−0.372822	−	0.284068i
$861$	1.70078	−	0.981944i	0.0579623	−	0.0334646i
$862$	2.36501	−	8.82635i	0.0805527	−	0.300627i
$863$	0.737022	−	0.197484i	0.0250885	−	0.00672244i	−0.246253	−	0.969206i	$-0.579199\pi$
$863$	0.737022	−	0.197484i	0.0250885	−	0.00672244i	0.271341	+	0.962483i	$0.412533\pi$
$864$	−1.00000			−0.0340207
$865$	6.68456	−	52.1437i	0.227282	−	1.77294i
$866$		−	35.5712i		−	1.20876i
$867$	−20.7752	+	20.7752i	−0.705562	+	0.705562i
$868$	6.42443	−	3.47421i	0.218059	−	0.117922i
$869$			50.2956i			1.70616i
$870$	−16.6803	+	2.25372i	−0.565515	+	0.0764084i
$871$	−42.8706	+	24.7514i	−1.45262	+	0.838668i
$872$	−7.40220	−	7.40220i	−0.250670	−	0.250670i
$873$	1.90765	+	7.11945i	0.0645642	+	0.240957i
$874$	5.65386	+	9.79277i	0.191245	+	0.331245i
$875$	−14.5203	+	2.06252i	−0.490877	+	0.0697260i
$876$	−10.0355			−0.339068
$877$	32.7264	−	8.76900i	1.10509	−	0.296108i	0.340255	−	0.940333i	$-0.389487\pi$
$877$	32.7264	−	8.76900i	1.10509	−	0.296108i	0.764836	+	0.644225i	$0.222820\pi$
$878$	4.81038	+	17.9526i	0.162342	+	0.605870i
$879$	3.54858	−	6.14632i	0.119691	−	0.207310i
$880$	7.79986	+	10.0937i	0.262933	+	0.340260i
$881$	18.0658	+	10.4303i	0.608654	+	0.351406i	0.772438	−	0.635090i	$-0.219037\pi$
$881$	18.0658	+	10.4303i	0.608654	+	0.351406i	−0.163785	+	0.986496i	$0.552370\pi$
$882$	1.36637	−	5.09936i	0.0460080	−	0.171704i
$883$	23.2452	+	23.2452i	0.782265	+	0.782265i	0.980213	−	0.197948i	$-0.0634276\pi$
$883$	23.2452	+	23.2452i	0.782265	+	0.782265i	−0.197948	+	0.980213i	$0.563428\pi$
$884$			43.9576i			1.47846i
$885$	−2.94746	+	22.9920i	−0.0990778	+	0.772867i
$886$	15.7996	−	27.3657i	0.530797	−	0.919367i
$887$	2.00112	−	7.46827i	0.0671909	−	0.250760i	−0.924158	−	0.382009i	$-0.875232\pi$
$887$	2.00112	−	7.46827i	0.0671909	−	0.250760i	0.991349	+	0.131249i	$0.0418989\pi$
$888$	0.634463	+	2.36785i	0.0212912	+	0.0794598i
$889$	−2.25571	+	3.90701i	−0.0756541	+	0.131037i
$890$	−5.36425	−	12.8269i	−0.179810	−	0.429959i
$891$			5.70476i			0.191117i
$892$	−8.38218	−	2.24600i	−0.280656	−	0.0752016i
$893$	3.65256	+	0.978702i	0.122228	+	0.0327510i
$894$	−6.40121	+	11.0872i	−0.214088	+	0.370812i
$895$	1.83757	+	13.6002i	0.0614231	+	0.454605i
$896$	−0.655888	−	1.13603i	−0.0219117	−	0.0379521i
$897$	−10.7481	+	10.7481i	−0.358868	+	0.358868i
$898$	−11.5181	−	11.5181i	−0.384365	−	0.384365i
$899$	−30.4496	+	28.7985i	−1.01555	+	0.960482i
$900$	4.82072	−	1.32691i	0.160691	−	0.0442302i
$901$	79.9801			2.66452
$902$	8.24970	+	2.21050i	0.274685	+	0.0736016i
$903$	5.70184	−	5.70184i	0.189745	−	0.189745i
$904$	4.69805	+	2.71242i	0.156255	+	0.0902138i
$905$	−4.13861	−	5.35574i	−0.137572	−	0.178031i
$906$	−2.80467	−	4.85783i	−0.0931789	−	0.161391i
$907$	−40.2472	−	40.2472i	−1.33639	−	1.33639i	−0.899531	−	0.436856i	$-0.856092\pi$
$907$	−40.2472	−	40.2472i	−1.33639	−	1.33639i	−0.436856	−	0.899531i	$-0.643908\pi$
$908$	5.03746	+	18.8000i	0.167174	+	0.623901i
$909$	15.8168	+	9.13181i	0.524609	+	0.302883i
$910$	17.4667	−	7.30464i	0.579017	−	0.242146i
$911$	24.9180	−	14.3864i	0.825569	−	0.476642i	−0.0267642	−	0.999642i	$-0.508520\pi$
$911$	24.9180	−	14.3864i	0.825569	−	0.476642i	0.852333	+	0.522999i	$0.175187\pi$
$912$	1.24277	+	4.63809i	0.0411523	+	0.153583i
$913$	57.7509	+	15.4743i	1.91128	+	0.512125i
$914$	−6.54994			−0.216653
$915$	−1.89345	−	1.44270i	−0.0625957	−	0.0476941i
$916$	−3.29286	+	1.90113i	−0.108799	+	0.0628151i
$917$	−4.73122	+	1.26773i	−0.156239	+	0.0418640i
$918$	−6.57827	−	1.76264i	−0.217115	−	0.0581759i
$919$	46.5838	+	26.8951i	1.53666	+	0.887189i	0.999031	+	0.0440050i	$0.0140118\pi$
$919$	46.5838	+	26.8951i	1.53666	+	0.887189i	0.537625	+	0.843184i	$0.319322\pi$
$920$	−4.87179	−	1.99858i	−0.160618	−	0.0658913i
$921$	−0.572172	−	0.330344i	−0.0188537	−	0.0108852i
$922$	−21.1223	+	21.1223i	−0.695624	+	0.695624i
$923$	22.5785	−	84.2641i	0.743181	−	2.77359i
$924$	−6.48078	+	3.74168i	−0.213202	+	0.123092i
$925$	−6.20048	−	10.5729i	−0.203871	−	0.347633i
$926$		−	11.0543i		−	0.363268i
$927$	1.60762	−	5.99973i	0.0528012	−	0.197057i
$928$	5.32270	+	5.32270i	0.174726	+	0.174726i
$929$	41.6442			1.36630			0.683151	−	0.730277i	$-0.260609\pi$
$929$	41.6442			1.36630			0.683151	+	0.730277i	$0.260609\pi$
$930$	7.81834	−	9.68884i	0.256373	−	0.317710i
$931$	−25.3494			−0.830793
$932$	−13.3013	−	13.3013i	−0.435697	−	0.435697i
$933$	2.08022	−	7.76348i	0.0681032	−	0.254165i
$934$		−	35.1467i		−	1.15004i
$935$	33.5180	+	80.1477i	1.09615	+	2.62111i
$936$	−5.58981	+	3.22728i	−0.182709	+	0.105487i
$937$	−1.72626	+	6.44250i	−0.0563946	+	0.210467i	−0.988374	−	0.152045i	$-0.951414\pi$
$937$	−1.72626	+	6.44250i	−0.0563946	+	0.210467i	0.931979	+	0.362512i	$0.118081\pi$
$938$	7.11389	−	7.11389i	0.232277	−	0.232277i
$939$	17.0453	+	9.84112i	0.556253	+	0.321153i
$940$	−1.62459	+	0.679408i	−0.0529883	+	0.0221599i
$941$	18.6861	+	10.7884i	0.609149	+	0.351692i	0.772632	−	0.634854i	$-0.218940\pi$
$941$	18.6861	+	10.7884i	0.609149	+	0.351692i	−0.163483	+	0.986546i	$0.552273\pi$
$942$	20.5320	+	5.50153i	0.668968	+	0.179249i
$943$	−3.40549	+	0.912499i	−0.110898	+	0.0297151i
$944$	8.97763	−	5.18324i	0.292197	−	0.168700i
$945$	0.392747	+	2.90681i	0.0127761	+	0.0945584i
$946$	35.0677			1.14015
$947$	−21.5759	−	5.78124i	−0.701122	−	0.187865i	−0.109389	−	0.993999i	$-0.534889\pi$
$947$	−21.5759	−	5.78124i	−0.701122	−	0.187865i	−0.591733	+	0.806134i	$0.701556\pi$
$948$	−2.28186	−	8.51601i	−0.0741113	−	0.276587i
$949$	−56.0965	+	32.3873i	−1.82097	+	1.05134i
$950$	−12.1454	−	20.7099i	−0.394048	−	0.671918i
$951$	−8.76298	−	5.05931i	−0.284159	−	0.164059i
$952$	−2.31219	−	8.62921i	−0.0749385	−	0.279674i
$953$	31.4648	+	31.4648i	1.01925	+	1.01925i	0.999811	+	0.0194347i	$0.00618664\pi$
$953$	31.4648	+	31.4648i	1.01925	+	1.01925i	0.0194347	+	0.999811i	$0.493813\pi$
$954$	5.87197	+	10.1706i	0.190112	+	0.329284i
$955$	13.5056	−	10.4363i	0.437030	−	0.337712i
$956$	19.6984	+	11.3728i	0.637090	+	0.367824i
$957$	30.3647	−	30.3647i	0.981552	−	0.981552i
$958$	−20.7283	−	5.55413i	−0.669701	−	0.179446i
$959$	5.11606			0.165206
$960$	−1.77861	−	1.35519i	−0.0574044	−	0.0437387i
$961$	1.72651	−	30.9519i	0.0556940	−	0.998448i
$962$	11.1882	+	11.1882i	0.360723	+	0.360723i
$963$	13.2489	−	13.2489i	0.426941	−	0.426941i
$964$	0.586910	+	1.01656i	0.0189031	+	0.0327411i
$965$	−24.5121	−	18.6768i	−0.789073	−	0.601226i
$966$	1.54457	−	2.67528i	0.0496959	−	0.0860758i
$967$	−9.70059	−	2.59927i	−0.311950	−	0.0835867i	0.0994474	−	0.995043i	$-0.468292\pi$
$967$	−9.70059	−	2.59927i	−0.311950	−	0.0835867i	−0.411397	+	0.911456i	$0.634959\pi$
$968$	−20.8102	−	5.57606i	−0.668864	−	0.179221i
$969$			32.7012i			1.05051i
$970$	−6.25525	+	15.2479i	−0.200844	+	0.489582i
$971$	−18.0250	+	31.2202i	−0.578450	+	1.00190i	0.417207	+	0.908811i	$0.363009\pi$
$971$	−18.0250	+	31.2202i	−0.578450	+	1.00190i	−0.995657	+	0.0930934i	$0.970324\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	−3.14194	+	11.7259i	−0.100726	+	0.375915i
$974$	−2.11938	+	3.67087i	−0.0679092	+	0.117622i
$975$	22.6646	−	22.9750i	0.725848	−	0.735788i
$976$			1.06457i			0.0340760i
$977$	30.5171	+	30.5171i	0.976329	+	0.976329i	0.999726	−	0.0233976i	$-0.00744835\pi$
$977$	30.5171	+	30.5171i	0.976329	+	0.976329i	−0.0233976	+	0.999726i	$0.507448\pi$
$978$	1.37213	−	5.12087i	0.0438760	−	0.163747i
$979$	30.7188	+	17.7355i	0.981777	+	0.566829i
$980$	9.34085	−	7.21808i	0.298383	−	0.230573i
$981$	5.23414	−	9.06580i	0.167113	−	0.289449i
$982$	−2.46196	−	9.18817i	−0.0785644	−	0.293206i
$983$	28.2622	−	7.57283i	0.901424	−	0.241536i	0.221796	−	0.975093i	$-0.428808\pi$
$983$	28.2622	−	7.57283i	0.901424	−	0.241536i	0.679628	+	0.733557i	$0.262141\pi$
$984$	−1.49712			−0.0477265
$985$	1.56015	−	12.1701i	0.0497105	−	0.387772i
$986$	25.6321	+	44.3962i	0.816294	+	1.41386i
$987$	−0.267371	−	0.997842i	−0.00851051	−	0.0317617i
$988$	21.9153	+	21.9153i	0.697218	+	0.697218i
$989$	−12.5366	+	7.23802i	−0.398641	+	0.230156i
$990$	−7.73104	+	10.1465i	−0.245709	+	0.322478i
$991$			3.77362i			0.119873i	0.998202	+	0.0599366i	$0.0190898\pi$
$991$			3.77362i			0.119873i	−0.998202	+	0.0599366i	$0.980910\pi$
$992$	−5.56560	−	0.155106i	−0.176708	−	0.00492461i
$993$	3.60499	−	3.60499i	0.114401	−	0.114401i
$994$			17.7293i			0.562340i
$995$	−12.3836	+	9.56930i	−0.392585	+	0.303367i
$996$	−10.4804			−0.332084
$997$	−41.8959	+	11.2260i	−1.32686	+	0.355530i	−0.851542	−	0.524286i	$-0.824332\pi$
$997$	−41.8959	+	11.2260i	−1.32686	+	0.355530i	−0.475315	+	0.879816i	$0.657666\pi$
$998$	4.41938	−	16.4933i	0.139893	−	0.522087i
$999$	−2.12296	+	1.22569i	−0.0671673	+	0.0387791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.b.37.10	yes	64
5.3	odd	4		930.2.be.a.223.14	✓	64
31.26	odd	6		930.2.be.a.367.14	yes	64
155.88	even	12	inner	930.2.be.b.553.10	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.14	✓	64	5.3	odd	4
930.2.be.a.367.14	yes	64	31.26	odd	6
930.2.be.b.37.10	yes	64	1.1	even	1	trivial
930.2.be.b.553.10	yes	64	155.88	even	12	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-2.06875 - 0.848677i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.339513 - 1.26708i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-2.06875 - 0.848677i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.339513 - 1.26708i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.862725 - 2.06294i) q^{10} +(4.94046 + 2.85238i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-6.23462 + 1.67056i) q^{13} +(1.13603 - 0.655888i) q^{14} +(1.35519 - 1.77861i) q^{15} -1.00000 q^{16} +(-6.57827 - 1.76264i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-4.15840 + 2.40085i) q^{19} +(0.848677 - 2.06875i) q^{20} +(1.13603 + 0.655888i) q^{21} +(1.47650 + 5.51037i) q^{22} +(-1.66519 - 1.66519i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.55949 + 3.51141i) q^{25} +(-5.58981 - 3.22728i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.26708 + 0.339513i) q^{28} -7.52743 q^{29} +(2.21593 - 0.299401i) q^{30} +(4.04515 - 3.82580i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.03387 + 4.03387i) q^{33} +(-3.40516 - 5.89791i) q^{34} +(-1.77771 + 2.33314i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.36785 - 0.634463i) q^{37} +(-4.63809 - 1.24277i) q^{38} -6.45456i q^{39} +(2.06294 - 0.862725i) q^{40} +(0.748561 - 1.29655i) q^{41} +(0.339513 + 1.26708i) q^{42} +(1.59099 - 5.93764i) q^{43} +(-2.85238 + 4.94046i) q^{44} +(1.36726 + 1.76935i) q^{45} -2.35494i q^{46} +(-0.556857 - 0.556857i) q^{47} +(0.258819 - 0.965926i) q^{48} +(4.57196 + 2.63962i) q^{49} +(0.0339997 + 4.99988i) q^{50} +(3.40516 - 5.89791i) q^{51} +(-1.67056 - 6.23462i) q^{52} +(-11.3438 + 3.03956i) q^{53} +1.00000 q^{54} +(-7.79986 - 10.0937i) q^{55} +(0.655888 + 1.13603i) q^{56} +(-1.24277 - 4.63809i) q^{57} +(-5.32270 - 5.32270i) q^{58} +(-8.97763 + 5.18324i) q^{59} +(1.77861 + 1.35519i) q^{60} -1.06457i q^{61} +(5.56560 + 0.155106i) q^{62} +(-0.927565 + 0.927565i) q^{63} -1.00000i q^{64} +(14.3157 + 1.83520i) q^{65} -5.70476 q^{66} +(7.40809 - 1.98499i) q^{67} +(1.76264 - 6.57827i) q^{68} +(2.03944 - 1.17747i) q^{69} +(-2.90681 + 0.392747i) q^{70} +(-6.75775 + 11.7048i) q^{71} +(0.965926 - 0.258819i) q^{72} +(9.69353 - 2.59737i) q^{73} +(-1.22569 - 2.12296i) q^{74} +(-4.31303 + 2.52939i) q^{75} +(-2.40085 - 4.15840i) q^{76} +(5.29154 - 5.29154i) q^{77} +(4.56406 - 4.56406i) q^{78} +(4.40821 + 7.63525i) q^{79} +(2.06875 + 0.848677i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.44611 - 0.387484i) q^{82} +(10.1233 - 2.71253i) q^{83} +(-0.655888 + 1.13603i) q^{84} +(12.1129 + 9.22930i) q^{85} +(5.32355 - 3.07355i) q^{86} +(1.94824 - 7.27094i) q^{87} +(-5.51037 + 1.47650i) q^{88} +6.21779 q^{89} +(-0.284326 + 2.21792i) q^{90} +8.46693i q^{91} +(1.66519 - 1.66519i) q^{92} +(2.64848 + 4.89751i) q^{93} -0.787514i q^{94} +(10.6403 - 1.43764i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-5.21180 - 5.21180i) q^{97} +(1.36637 + 5.09936i) q^{98} +(-2.85238 - 4.94046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{7}+O(q^{10}) \) 64 * q + 4 * q^7	\( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more