LMFDB - Embedded newform 91.2.i.a.34.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(34,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("91.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 35x^{8} + 295x^{4} + 169 $ x^12 + 35x^8 + 295x^4 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.2
Root			$0.626770 - 0.626770i$ of defining polynomial
Character	$\chi$	$=$	91.34
Dual form			91.2.i.a.83.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45161 - 1.45161i) q^{2} +1.81964i q^{3} +2.21432i q^{4} +(-2.01464 + 2.01464i) q^{5} +(2.64141 - 2.64141i) q^{6} +(-1.13594 + 2.38948i) q^{7} +(0.311108 - 0.311108i) q^{8} -0.311108 q^{9} +O(q^{10})$	\(q+(-1.45161 - 1.45161i) q^{2} +1.81964i q^{3} +2.21432i q^{4} +(-2.01464 + 2.01464i) q^{5} +(2.64141 - 2.64141i) q^{6} +(-1.13594 + 2.38948i) q^{7} +(0.311108 - 0.311108i) q^{8} -0.311108 q^{9} +5.84892 q^{10} +(0.451606 - 0.451606i) q^{11} -4.02928 q^{12} +(3.40251 - 1.19288i) q^{13} +(5.11753 - 1.81964i) q^{14} +(-3.66593 - 3.66593i) q^{15} +3.52543 q^{16} -4.32672 q^{17} +(0.451606 + 0.451606i) q^{18} +(-3.40251 + 3.40251i) q^{19} +(-4.46105 - 4.46105i) q^{20} +(-4.34801 - 2.06702i) q^{21} -1.31111 q^{22} -0.933323i q^{23} +(0.566106 + 0.566106i) q^{24} -3.11753i q^{25} +(-6.67068 - 3.20751i) q^{26} +4.89283i q^{27} +(-5.29108 - 2.51534i) q^{28} +6.33185 q^{29} +10.6430i q^{30} +(5.47781 - 5.47781i) q^{31} +(-5.73975 - 5.73975i) q^{32} +(0.821763 + 0.821763i) q^{33} +(6.28070 + 6.28070i) q^{34} +(-2.52543 - 7.10246i) q^{35} -0.688892i q^{36} +(2.14050 - 2.14050i) q^{37} +9.87820 q^{38} +(2.17061 + 6.19135i) q^{39} +1.25354i q^{40} +(1.81964 - 1.81964i) q^{41} +(3.31111 + 9.31209i) q^{42} +10.4795i q^{43} +(1.00000 + 1.00000i) q^{44} +(0.626770 - 0.626770i) q^{45} +(-1.35482 + 1.35482i) q^{46} +(5.90958 + 5.90958i) q^{47} +6.41503i q^{48} +(-4.41926 - 5.42864i) q^{49} +(-4.52543 + 4.52543i) q^{50} -7.87310i q^{51} +(2.64141 + 7.53424i) q^{52} +3.36196 q^{53} +(7.10246 - 7.10246i) q^{54} +1.81964i q^{55} +(0.389986 + 1.09679i) q^{56} +(-6.19135 - 6.19135i) q^{57} +(-9.19135 - 9.19135i) q^{58} +(-0.255657 - 0.255657i) q^{59} +(8.11753 - 8.11753i) q^{60} -7.78989i q^{61} -15.9032 q^{62} +(0.353401 - 0.743387i) q^{63} +9.61285i q^{64} +(-4.45161 + 9.25803i) q^{65} -2.38575i q^{66} +(7.28100 + 7.28100i) q^{67} -9.58075i q^{68} +1.69832 q^{69} +(-6.64405 + 13.9759i) q^{70} +(5.56914 + 5.56914i) q^{71} +(-0.0967881 + 0.0967881i) q^{72} +(-8.86144 - 8.86144i) q^{73} -6.21432 q^{74} +5.67280 q^{75} +(-7.53424 - 7.53424i) q^{76} +(0.566106 + 1.59210i) q^{77} +(5.83654 - 12.1383i) q^{78} -13.7971 q^{79} +(-7.10246 + 7.10246i) q^{80} -9.83654 q^{81} -5.28281 q^{82} +(4.30785 - 4.30785i) q^{83} +(4.57703 - 9.62789i) q^{84} +(8.71678 - 8.71678i) q^{85} +(15.2121 - 15.2121i) q^{86} +11.5217i q^{87} -0.280996i q^{88} +(5.61214 + 5.61214i) q^{89} -1.81964 q^{90} +(-1.01470 + 9.48527i) q^{91} +2.06668 q^{92} +(9.96767 + 9.96767i) q^{93} -17.1568i q^{94} -13.7096i q^{95} +(10.4443 - 10.4443i) q^{96} +(-0.236784 + 0.236784i) q^{97} +(-1.46522 + 14.2953i) q^{98} +(-0.140498 + 0.140498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - 8 * q^7 + 4 * q^8 - 4 * q^9	$ 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9} - 8 q^{11} + 8 q^{14} - 4 q^{15} + 16 q^{16} - 8 q^{18} - 16 q^{22} - 20 q^{28} - 4 q^{29} - 16 q^{32} - 4 q^{35} + 12 q^{37} + 40 q^{39} + 40 q^{42} + 12 q^{44} + 24 q^{46} - 28 q^{50} - 12 q^{53} - 8 q^{57} - 44 q^{58} + 44 q^{60} + 20 q^{63} - 40 q^{65} + 60 q^{67} + 4 q^{70} - 28 q^{72} - 48 q^{74} + 44 q^{78} - 4 q^{79} - 92 q^{81} - 4 q^{84} + 12 q^{85} + 36 q^{86} - 32 q^{91} + 24 q^{92} - 28 q^{93} - 28 q^{98} + 12 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - 8 * q^7 + 4 * q^8 - 4 * q^9 - 8 * q^11 + 8 * q^14 - 4 * q^15 + 16 * q^16 - 8 * q^18 - 16 * q^22 - 20 * q^28 - 4 * q^29 - 16 * q^32 - 4 * q^35 + 12 * q^37 + 40 * q^39 + 40 * q^42 + 12 * q^44 + 24 * q^46 - 28 * q^50 - 12 * q^53 - 8 * q^57 - 44 * q^58 + 44 * q^60 + 20 * q^63 - 40 * q^65 + 60 * q^67 + 4 * q^70 - 28 * q^72 - 48 * q^74 + 44 * q^78 - 4 * q^79 - 92 * q^81 - 4 * q^84 + 12 * q^85 + 36 * q^86 - 32 * q^91 + 24 * q^92 - 28 * q^93 - 28 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.45161	−	1.45161i	−1.02644	−	1.02644i	−0.999641	−	0.0267996i	$-0.991468\pi$
$2$	−1.45161	−	1.45161i	−1.02644	−	1.02644i	−0.0267996	−	0.999641i	$-0.508532\pi$
$3$			1.81964i			1.05057i	0.850926	+	0.525286i	$0.176042\pi$
$3$			1.81964i			1.05057i	−0.850926	+	0.525286i	$0.823958\pi$
$4$			2.21432i			1.10716i
$5$	−2.01464	+	2.01464i	−0.900973	+	0.900973i	−0.995520	−	0.0945469i	$-0.969860\pi$
$5$	−2.01464	+	2.01464i	−0.900973	+	0.900973i	0.0945469	+	0.995520i	$0.469860\pi$
$6$	2.64141	−	2.64141i	1.07835	−	1.07835i
$7$	−1.13594	+	2.38948i	−0.429347	+	0.903140i
$7$	−1.13594	+	2.38948i	−0.429347	+	0.903140i
$8$	0.311108	−	0.311108i	0.109993	−	0.109993i
$9$	−0.311108			−0.103703
$10$	5.84892			1.84959
$11$	0.451606	−	0.451606i	0.136164	−	0.136164i	−0.635739	−	0.771904i	$-0.719305\pi$
$11$	0.451606	−	0.451606i	0.136164	−	0.136164i	0.771904	+	0.635739i	$0.219305\pi$
$12$	−4.02928			−1.16315
$13$	3.40251	−	1.19288i	0.943685	−	0.330844i
$13$	3.40251	−	1.19288i	0.943685	−	0.330844i
$14$	5.11753	−	1.81964i	1.36772	−	0.486321i
$15$	−3.66593	−	3.66593i	−0.946538	−	0.946538i
$16$	3.52543			0.881357
$17$	−4.32672			−1.04938			−0.524692	−	0.851292i	$-0.675820\pi$
$17$	−4.32672			−1.04938			−0.524692	+	0.851292i	$0.675820\pi$
$18$	0.451606	+	0.451606i	0.106445	+	0.106445i
$19$	−3.40251	+	3.40251i	−0.780588	+	0.780588i	−0.979930	−	0.199342i	$-0.936120\pi$
$19$	−3.40251	+	3.40251i	−0.780588	+	0.780588i	0.199342	+	0.979930i	$0.436120\pi$
$20$	−4.46105	−	4.46105i	−0.997522	−	0.997522i
$21$	−4.34801	−	2.06702i	−0.948814	−	0.451060i
$22$	−1.31111			−0.279529
$23$		−	0.933323i		−	0.194611i	−0.995255	−	0.0973057i	$-0.968978\pi$
$23$		−	0.933323i		−	0.194611i	0.995255	−	0.0973057i	$-0.0310225\pi$
$24$	0.566106	+	0.566106i	0.115556	+	0.115556i
$25$		−	3.11753i		−	0.623506i
$26$	−6.67068	−	3.20751i	−1.30823	−	0.629045i
$27$			4.89283i			0.941625i
$28$	−5.29108	−	2.51534i	−0.999920	−	0.475355i
$29$	6.33185			1.17580			0.587898	−	0.808935i	$-0.299956\pi$
$29$	6.33185			1.17580			0.587898	+	0.808935i	$0.299956\pi$
$30$			10.6430i			1.94313i
$31$	5.47781	−	5.47781i	0.983843	−	0.983843i	−0.0160282	−	0.999872i	$-0.505102\pi$
$31$	5.47781	−	5.47781i	0.983843	−	0.983843i	0.999872	+	0.0160282i	$0.00510215\pi$
$32$	−5.73975	−	5.73975i	−1.01465	−	1.01465i
$33$	0.821763	+	0.821763i	0.143050	+	0.143050i
$34$	6.28070	+	6.28070i	1.07713	+	1.07713i
$35$	−2.52543	−	7.10246i	−0.426875	−	1.20053i
$36$		−	0.688892i		−	0.114815i
$37$	2.14050	−	2.14050i	0.351896	−	0.351896i	−0.508919	−	0.860815i	$-0.669955\pi$
$37$	2.14050	−	2.14050i	0.351896	−	0.351896i	0.860815	+	0.508919i	$0.169955\pi$
$38$	9.87820			1.60246
$39$	2.17061	+	6.19135i	0.347576	+	0.991410i
$40$			1.25354i			0.198202i
$41$	1.81964	−	1.81964i	0.284181	−	0.284181i	−0.550593	−	0.834774i	$-0.685598\pi$
$41$	1.81964	−	1.81964i	0.284181	−	0.284181i	0.834774	+	0.550593i	$0.185598\pi$
$42$	3.31111	+	9.31209i	0.510915	+	1.43689i
$43$			10.4795i			1.59811i	0.601259	+	0.799054i	$0.294666\pi$
$43$			10.4795i			1.59811i	−0.601259	+	0.799054i	$0.705334\pi$
$44$	1.00000	+	1.00000i	0.150756	+	0.150756i
$45$	0.626770	−	0.626770i	0.0934333	−	0.0934333i
$46$	−1.35482	+	1.35482i	−0.199757	+	0.199757i
$47$	5.90958	+	5.90958i	0.862002	+	0.862002i	0.991570	−	0.129569i	$-0.0413593\pi$
$47$	5.90958	+	5.90958i	0.862002	+	0.862002i	−0.129569	+	0.991570i	$0.541359\pi$
$48$			6.41503i			0.925929i
$49$	−4.41926	−	5.42864i	−0.631323	−	0.775520i
$50$	−4.52543	+	4.52543i	−0.639992	+	0.639992i
$51$		−	7.87310i		−	1.10245i
$52$	2.64141	+	7.53424i	0.366297	+	1.04481i
$53$	3.36196			0.461801			0.230901	−	0.972977i	$-0.425833\pi$
$53$	3.36196			0.461801			0.230901	+	0.972977i	$0.425833\pi$
$54$	7.10246	−	7.10246i	0.966522	−	0.966522i
$55$			1.81964i			0.245361i
$56$	0.389986	+	1.09679i	0.0521141	+	0.146564i
$57$	−6.19135	−	6.19135i	−0.820065	−	0.820065i
$58$	−9.19135	−	9.19135i	−1.20688	−	1.20688i
$59$	−0.255657	−	0.255657i	−0.0332837	−	0.0332837i	0.690269	−	0.723553i	$-0.257492\pi$
$59$	−0.255657	−	0.255657i	−0.0332837	−	0.0332837i	−0.723553	+	0.690269i	$0.757492\pi$
$60$	8.11753	−	8.11753i	1.04797	−	1.04797i
$61$		−	7.78989i		−	0.997394i	−0.866776	−	0.498697i	$-0.833812\pi$
$61$		−	7.78989i		−	0.997394i	0.866776	−	0.498697i	$-0.166188\pi$
$62$	−15.9032			−2.01971
$63$	0.353401	−	0.743387i	0.0445244	−	0.0936580i
$64$			9.61285i			1.20161i
$65$	−4.45161	+	9.25803i	−0.552154	+	1.14832i
$66$		−	2.38575i		−	0.293666i
$67$	7.28100	+	7.28100i	0.889515	+	0.889515i	0.994476	−	0.104961i	$-0.0334718\pi$
$67$	7.28100	+	7.28100i	0.889515	+	0.889515i	−0.104961	+	0.994476i	$0.533472\pi$
$68$		−	9.58075i		−	1.16184i
$69$	1.69832			0.204453
$70$	−6.64405	+	13.9759i	−0.794116	+	1.67044i
$71$	5.56914	+	5.56914i	0.660935	+	0.660935i	0.955600	−	0.294665i	$-0.0952082\pi$
$71$	5.56914	+	5.56914i	0.660935	+	0.660935i	−0.294665	+	0.955600i	$0.595208\pi$
$72$	−0.0967881	+	0.0967881i	−0.0114066	+	0.0114066i
$73$	−8.86144	−	8.86144i	−1.03715	−	1.03715i	−0.999283	−	0.0378706i	$-0.987943\pi$
$73$	−8.86144	−	8.86144i	−1.03715	−	1.03715i	−0.0378706	−	0.999283i	$-0.512057\pi$
$74$	−6.21432			−0.722400
$75$	5.67280			0.655039
$76$	−7.53424	−	7.53424i	−0.864236	−	0.864236i
$77$	0.566106	+	1.59210i	0.0645137	+	0.181437i
$78$	5.83654	−	12.1383i	0.660857	−	1.37439i
$79$	−13.7971			−1.55229			−0.776145	−	0.630554i	$-0.782828\pi$
$79$	−13.7971			−1.55229			−0.776145	+	0.630554i	$0.782828\pi$
$80$	−7.10246	+	7.10246i	−0.794079	+	0.794079i
$81$	−9.83654			−1.09295
$82$	−5.28281			−0.583389
$83$	4.30785	−	4.30785i	0.472848	−	0.472848i	−0.429987	−	0.902835i	$-0.641482\pi$
$83$	4.30785	−	4.30785i	0.472848	−	0.472848i	0.902835	+	0.429987i	$0.141482\pi$
$84$	4.57703	−	9.62789i	0.499395	−	1.05049i
$85$	8.71678	−	8.71678i	0.945468	−	0.945468i
$86$	15.2121	−	15.2121i	1.64036	−	1.64036i
$87$			11.5217i			1.23526i
$88$		−	0.280996i		−	0.0299543i
$89$	5.61214	+	5.61214i	0.594885	+	0.594885i	0.938947	−	0.344062i	$-0.111803\pi$
$89$	5.61214	+	5.61214i	0.594885	+	0.594885i	−0.344062	+	0.938947i	$0.611803\pi$
$90$	−1.81964			−0.191807
$91$	−1.01470	+	9.48527i	−0.106370	+	0.994327i
$92$	2.06668			0.215466
$93$	9.96767	+	9.96767i	1.03360	+	1.03360i
$94$		−	17.1568i		−	1.76959i
$95$		−	13.7096i		−	1.40658i
$96$	10.4443	−	10.4443i	1.06597	−	1.06597i
$97$	−0.236784	+	0.236784i	−0.0240417	+	0.0240417i	−0.719025	−	0.694984i	$-0.755412\pi$
$97$	−0.236784	+	0.236784i	−0.0240417	+	0.0240417i	0.694984	+	0.719025i	$0.255412\pi$
$98$	−1.46522	+	14.2953i	−0.148009	+	1.44404i
$99$	−0.140498	+	0.140498i	−0.0141206	+	0.0141206i
$100$	6.90321			0.690321
$101$	9.21955			0.917380			0.458690	−	0.888596i	$-0.348319\pi$
$101$	9.21955			0.917380			0.458690	+	0.888596i	$0.348319\pi$
$102$	−11.4286	+	11.4286i	−1.13160	+	1.13160i
$103$	−2.50708			−0.247030			−0.123515	−	0.992343i	$-0.539417\pi$
$103$	−2.50708			−0.247030			−0.123515	+	0.992343i	$0.539417\pi$
$104$	0.687433	−	1.42966i	0.0674084	−	0.140190i
$105$	12.9240	−	4.59538i	1.26125	−	0.448463i
$106$	−4.88025	−	4.88025i	−0.474011	−	0.474011i
$107$	2.88247			0.278659			0.139329	−	0.990246i	$-0.455505\pi$
$107$	2.88247			0.278659			0.139329	+	0.990246i	$0.455505\pi$
$108$	−10.8343			−1.04253
$109$	−3.54839	−	3.54839i	−0.339875	−	0.339875i	0.516446	−	0.856320i	$-0.327255\pi$
$109$	−3.54839	−	3.54839i	−0.339875	−	0.339875i	−0.856320	+	0.516446i	$0.827255\pi$
$110$	2.64141	−	2.64141i	0.251848	−	0.251848i
$111$	3.89495	+	3.89495i	0.369692	+	0.369692i
$112$	−4.00469	+	8.42395i	−0.378408	+	0.795989i
$113$	−16.3526			−1.53832			−0.769161	−	0.639055i	$-0.779326\pi$
$113$	−16.3526			−1.53832			−0.769161	+	0.639055i	$0.779326\pi$
$114$			17.9748i			1.68350i
$115$	1.88031	+	1.88031i	0.175340	+	0.175340i
$116$			14.0207i			1.30179i
$117$	−1.05855	+	0.371113i	−0.0978626	+	0.0343094i
$118$			0.742226i			0.0683274i
$119$	4.91492	−	10.3386i	0.450550	−	0.947741i
$120$	−2.28100			−0.208226
$121$			10.5921i			0.962919i
$122$	−11.3079	+	11.3079i	−1.02377	+	1.02377i
$123$	3.31111	+	3.31111i	0.298553	+	0.298553i
$124$	12.1296	+	12.1296i	1.08927	+	1.08927i
$125$	−3.79249	−	3.79249i	−0.339211	−	0.339211i
$126$	−1.59210	+	0.566106i	−0.141836	+	0.0504327i
$127$		−	13.8272i		−	1.22696i	−0.789709	−	0.613481i	$-0.789769\pi$
$127$		−	13.8272i		−	1.22696i	0.789709	−	0.613481i	$-0.210231\pi$
$128$	2.47457	−	2.47457i	0.218723	−	0.218723i
$129$	−19.0690			−1.67893
$130$	19.9010	−	6.97703i	1.74543	−	0.611926i
$131$			12.8301i			1.12097i	0.828166	+	0.560483i	$0.189385\pi$
$131$			12.8301i			1.12097i	−0.828166	+	0.560483i	$0.810615\pi$
$132$	−1.81964	+	1.81964i	−0.158380	+	0.158380i
$133$	−4.26517	−	11.9953i	−0.369838	−	1.04012i
$134$		−	21.1383i		−	1.82607i
$135$	−9.85728	−	9.85728i	−0.848379	−	0.848379i
$136$	−1.34608	+	1.34608i	−0.115425	+	0.115425i
$137$	2.40075	−	2.40075i	0.205110	−	0.205110i	−0.597075	−	0.802185i	$-0.703671\pi$
$137$	2.40075	−	2.40075i	0.205110	−	0.205110i	0.802185	+	0.597075i	$0.203671\pi$
$138$	−2.46529	−	2.46529i	−0.209859	−	0.209859i
$139$		−	3.34184i		−	0.283451i	−0.989906	−	0.141726i	$-0.954735\pi$
$139$		−	3.34184i		−	0.283451i	0.989906	−	0.141726i	$-0.0452651\pi$
$140$	15.7271	−	5.59210i	1.32918	−	0.472619i
$141$	−10.7533	+	10.7533i	−0.905595	+	0.905595i
$142$		−	16.1684i		−	1.35682i
$143$	0.997882	−	2.07530i	0.0834471	−	0.173545i
$144$	−1.09679			−0.0913990
$145$	−12.7564	+	12.7564i	−1.05936	+	1.05936i
$146$			25.7266i			2.12915i
$147$	9.87820	−	8.04149i	0.814740	−	0.663251i
$148$	4.73975	+	4.73975i	0.389605	+	0.389605i
$149$	2.62936	+	2.62936i	0.215406	+	0.215406i	0.806559	−	0.591153i	$-0.201327\pi$
$149$	2.62936	+	2.62936i	0.215406	+	0.215406i	−0.591153	+	0.806559i	$0.701327\pi$
$150$	−8.23467	−	8.23467i	−0.672358	−	0.672358i
$151$	−4.78346	+	4.78346i	−0.389272	+	0.389272i	−0.874428	−	0.485156i	$-0.838763\pi$
$151$	−4.78346	+	4.78346i	−0.389272	+	0.389272i	0.485156	+	0.874428i	$0.338763\pi$
$152$			2.11709i			0.171719i
$153$	1.34608			0.108824
$154$	1.48935	−	3.13287i	0.120015	−	0.252454i
$155$			22.0716i			1.77283i
$156$	−13.7096	+	4.80642i	−1.09765	+	0.384822i
$157$		−	3.42542i		−	0.273379i	−0.990614	−	0.136689i	$-0.956354\pi$
$157$		−	3.42542i		−	0.273379i	0.990614	−	0.136689i	$-0.0436462\pi$
$158$	20.0279	+	20.0279i	1.59333	+	1.59333i
$159$			6.11758i			0.485156i
$160$	23.1270			1.82835
$161$	2.23016	+	1.06020i	0.175761	+	0.0835557i
$162$	14.2788	+	14.2788i	1.12185	+	1.12185i
$163$	10.4494	−	10.4494i	0.818459	−	0.818459i	−0.167426	−	0.985885i	$-0.553545\pi$
$163$	10.4494	−	10.4494i	0.818459	−	0.818459i	0.985885	+	0.167426i	$0.0535455\pi$
$164$	4.02928	+	4.02928i	0.314634	+	0.314634i
$165$	−3.31111			−0.257769
$166$	−12.5066			−0.970701
$167$	−16.2326	−	16.2326i	−1.25611	−	1.25611i	−0.952933	−	0.303180i	$-0.901952\pi$
$167$	−16.2326	−	16.2326i	−1.25611	−	1.25611i	−0.303180	−	0.952933i	$-0.598048\pi$
$168$	−1.99576	+	0.709636i	−0.153977	+	0.0547496i
$169$	10.1541	−	8.11753i	0.781084	−	0.624426i
$170$	−25.3067			−1.94093
$171$	1.05855	−	1.05855i	0.0809491	−	0.0809491i
$172$	−23.2050			−1.76936
$173$	14.3810			1.09337			0.546685	−	0.837338i	$-0.315889\pi$
$173$	14.3810			1.09337			0.546685	+	0.837338i	$0.315889\pi$
$174$	16.7250	−	16.7250i	1.26792	−	1.26792i
$175$	7.44929	+	3.54134i	0.563113	+	0.267700i
$176$	1.59210	−	1.59210i	0.120009	−	0.120009i
$177$	0.465205	−	0.465205i	0.0349669	−	0.0349669i
$178$		−	16.2932i		−	1.22123i
$179$		−	4.11108i		−	0.307276i	−0.988127	−	0.153638i	$-0.950901\pi$
$179$		−	4.11108i		−	0.307276i	0.988127	−	0.153638i	$-0.0490990\pi$
$180$	1.38787	+	1.38787i	0.103446	+	0.103446i
$181$	21.5760			1.60373			0.801867	−	0.597502i	$-0.203840\pi$
$181$	21.5760			1.60373			0.801867	+	0.597502i	$0.203840\pi$
$182$	15.2418	−	12.2959i	1.12980	−	0.911435i
$183$	14.1748			1.04783
$184$	−0.290364	−	0.290364i	−0.0214059	−	0.0214059i
$185$			8.62466i			0.634097i
$186$		−	28.9382i		−	2.12186i
$187$	−1.95397	+	1.95397i	−0.142889	+	0.142889i
$188$	−13.0857	+	13.0857i	−0.954373	+	0.954373i
$189$	−11.6913	−	5.55798i	−0.850419	−	0.404284i
$190$	−19.9010	+	19.9010i	−1.44377	+	1.44377i
$191$	10.3017			0.745408			0.372704	−	0.927950i	$-0.378431\pi$
$191$	10.3017			0.745408			0.372704	+	0.927950i	$0.378431\pi$
$192$	−17.4920			−1.26237
$193$	6.28592	−	6.28592i	0.452470	−	0.452470i	−0.443703	−	0.896174i	$-0.646336\pi$
$193$	6.28592	−	6.28592i	0.452470	−	0.452470i	0.896174	+	0.443703i	$0.146336\pi$
$194$	0.687433			0.0493548
$195$	−16.8463	−	8.10034i	−1.20639	−	0.580078i
$196$	12.0207	−	9.78566i	0.858625	−	0.698976i
$197$	−3.25088	−	3.25088i	−0.231616	−	0.231616i	0.581751	−	0.813367i	$-0.302368\pi$
$197$	−3.25088	−	3.25088i	−0.231616	−	0.231616i	−0.813367	+	0.581751i	$0.802368\pi$
$198$	0.407896			0.0289879
$199$	−6.20116			−0.439589			−0.219794	−	0.975546i	$-0.570539\pi$
$199$	−6.20116			−0.439589			−0.219794	+	0.975546i	$0.570539\pi$
$200$	−0.969888	−	0.969888i	−0.0685815	−	0.0685815i
$201$	−13.2488	+	13.2488i	−0.934500	+	0.934500i
$202$	−13.3832	−	13.3832i	−0.941636	−	0.941636i
$203$	−7.19263	+	15.1299i	−0.504824	+	1.06191i
$204$	17.4336			1.22059
$205$			7.33185i			0.512079i
$206$	3.63929	+	3.63929i	0.253561	+	0.253561i
$207$			0.290364i			0.0201817i
$208$	11.9953	−	4.20540i	0.831724	−	0.291592i
$209$			3.07318i			0.212577i
$210$	−25.4312	−	12.0898i	−1.75492	−	0.834276i
$211$	−9.55554			−0.657830			−0.328915	−	0.944359i	$-0.606683\pi$
$211$	−9.55554			−0.657830			−0.328915	+	0.944359i	$0.606683\pi$
$212$			7.44446i			0.511288i
$213$	−10.1339	+	10.1339i	−0.694360	+	0.694360i
$214$	−4.18421	−	4.18421i	−0.286027	−	0.286027i
$215$	−21.1124	−	21.1124i	−1.43985	−	1.43985i
$216$	1.52220	+	1.52220i	0.103572	+	0.103572i
$217$	6.86665	+	19.3116i	0.466138	+	1.31096i
$218$			10.3017i			0.697722i
$219$	16.1247	−	16.1247i	1.08960	−	1.08960i
$220$	−4.02928			−0.271654
$221$	−14.7217	+	5.16124i	−0.990289	+	0.347183i
$222$		−	11.3079i		−	0.758934i
$223$	−2.58074	+	2.58074i	−0.172819	+	0.172819i	−0.788217	−	0.615398i	$-0.788995\pi$
$223$	−2.58074	+	2.58074i	−0.172819	+	0.172819i	0.615398	+	0.788217i	$0.288995\pi$
$224$	20.2351	−	7.19500i	1.35201	−	0.480736i
$225$			0.969888i			0.0646592i
$226$	23.7375	+	23.7375i	1.57900	+	1.57900i
$227$	5.25403	−	5.25403i	0.348722	−	0.348722i	−0.510911	−	0.859633i	$-0.670692\pi$
$227$	5.25403	−	5.25403i	0.348722	−	0.348722i	0.859633	+	0.510911i	$0.170692\pi$
$228$	13.7096	−	13.7096i	0.907943	−	0.907943i
$229$	−0.729224	−	0.729224i	−0.0481885	−	0.0481885i	0.682602	−	0.730790i	$-0.260848\pi$
$229$	−0.729224	−	0.729224i	−0.0481885	−	0.0481885i	−0.730790	+	0.682602i	$0.760848\pi$
$230$		−	5.45893i		−	0.359952i
$231$	−2.89706	+	1.03011i	−0.190613	+	0.0677764i
$232$	1.96989	−	1.96989i	0.129330	−	0.129330i
$233$		−	24.6128i		−	1.61244i	−0.591615	−	0.806221i	$-0.701509\pi$
$233$		−	24.6128i		−	1.61244i	0.591615	−	0.806221i	$-0.298491\pi$
$234$	2.07530	+	0.997882i	0.135667	+	0.0652336i
$235$	−23.8113			−1.55328
$236$	0.566106	−	0.566106i	0.0368503	−	0.0368503i
$237$		−	25.1057i		−	1.63079i
$238$	−22.1421	+	7.87310i	−1.43526	+	0.510337i
$239$	−6.52543	−	6.52543i	−0.422095	−	0.422095i	0.463830	−	0.885924i	$-0.346475\pi$
$239$	−6.52543	−	6.52543i	−0.422095	−	0.422095i	−0.885924	+	0.463830i	$0.846475\pi$
$240$	−12.9240	−	12.9240i	−0.834238	−	0.834238i
$241$	20.1563	+	20.1563i	1.29838	+	1.29838i	0.929461	+	0.368920i	$0.120272\pi$
$241$	20.1563	+	20.1563i	1.29838	+	1.29838i	0.368920	+	0.929461i	$0.379728\pi$
$242$	15.3756	−	15.3756i	0.988379	−	0.988379i
$243$		−	3.22051i		−	0.206596i
$244$	17.2493			1.10427
$245$	19.8400	+	2.03353i	1.26753	+	0.129918i
$246$		−	9.61285i		−	0.612893i
$247$	−7.51828	+	15.6358i	−0.478377	+	0.994883i
$248$		−	3.40838i		−	0.216432i
$249$	7.83876	+	7.83876i	0.496761	+	0.496761i
$250$			11.0104i			0.696359i
$251$	−14.4448			−0.911747			−0.455873	−	0.890045i	$-0.650673\pi$
$251$	−14.4448			−0.911747			−0.455873	+	0.890045i	$0.650673\pi$
$252$	1.64610	+	0.782543i	0.103694	+	0.0492956i
$253$	−0.421494	−	0.421494i	−0.0264991	−	0.0264991i
$254$	−20.0716	+	20.0716i	−1.25940	+	1.25940i
$255$	15.8614	+	15.8614i	0.993282	+	0.993282i
$256$	12.0415			0.752593
$257$	14.6237			0.912201			0.456101	−	0.889928i	$-0.349246\pi$
$257$	14.6237			0.912201			0.456101	+	0.889928i	$0.349246\pi$
$258$	27.6806	+	27.6806i	1.72332	+	1.72332i
$259$	2.68320	+	7.54617i	0.166726	+	0.468896i
$260$	−20.5002	−	9.85728i	−1.27137	−	0.611322i
$261$	−1.96989			−0.121933
$262$	18.6242	−	18.6242i	1.15061	−	1.15061i
$263$	−2.61729			−0.161389			−0.0806946	−	0.996739i	$-0.525714\pi$
$263$	−2.61729			−0.161389			−0.0806946	+	0.996739i	$0.525714\pi$
$264$	0.511313			0.0314692
$265$	−6.77314	+	6.77314i	−0.416071	+	0.416071i
$266$	−11.2211	+	23.6038i	−0.688009	+	1.44724i
$267$	−10.2121	+	10.2121i	−0.624970	+	0.624970i
$268$	−16.1225	+	16.1225i	−0.984836	+	0.984836i
$269$		−	9.82340i		−	0.598944i	−0.954105	−	0.299472i	$-0.903190\pi$
$269$		−	9.82340i		−	0.598944i	0.954105	−	0.299472i	$-0.0968104\pi$
$270$			28.6178i			1.74162i
$271$	−3.43438	−	3.43438i	−0.208624	−	0.208624i	0.595059	−	0.803682i	$-0.297129\pi$
$271$	−3.43438	−	3.43438i	−0.208624	−	0.208624i	−0.803682	+	0.595059i	$0.797129\pi$
$272$	−15.2535			−0.924882
$273$	−17.2598	−	1.84640i	−1.04461	−	0.111749i
$274$	−6.96989			−0.421066
$275$	−1.40790	−	1.40790i	−0.0848993	−	0.0848993i
$276$			3.76062i			0.226363i
$277$			5.89877i			0.354423i	0.984173	+	0.177211i	$0.0567076\pi$
$277$			5.89877i			0.354423i	−0.984173	+	0.177211i	$0.943292\pi$
$278$	−4.85104	+	4.85104i	−0.290946	+	0.290946i
$279$	−1.70419	+	1.70419i	−0.102027	+	0.102027i
$280$	−2.99531	−	1.42395i	−0.179004	−	0.0850973i
$281$	9.23729	−	9.23729i	0.551050	−	0.551050i	−0.375694	−	0.926744i	$-0.622595\pi$
$281$	9.23729	−	9.23729i	0.551050	−	0.551050i	0.926744	+	0.375694i	$0.122595\pi$
$282$	31.2192			1.85908
$283$	8.32721			0.495001			0.247501	−	0.968888i	$-0.420391\pi$
$283$	8.32721			0.495001			0.247501	+	0.968888i	$0.420391\pi$
$284$	−12.3319	+	12.3319i	−0.731761	+	0.731761i
$285$	24.9467			1.47771
$286$	−4.46105	+	1.56399i	−0.263788	+	0.0924806i
$287$	2.28100	+	6.41503i	0.134643	+	0.378667i
$288$	1.78568	+	1.78568i	0.105222	+	0.105222i
$289$	1.72054			0.101208
$290$	37.0345			2.17474
$291$	−0.430862	−	0.430862i	−0.0252576	−	0.0252576i
$292$	19.6221	−	19.6221i	1.14829	−	1.14829i
$293$	15.4903	+	15.4903i	0.904955	+	0.904955i	0.995860	−	0.0909047i	$-0.0289759\pi$
$293$	15.4903	+	15.4903i	0.904955	+	0.904955i	−0.0909047	+	0.995860i	$0.528976\pi$
$294$	−26.0123	−	2.66618i	−1.51707	−	0.155495i
$295$	1.03011			0.0599754
$296$		−	1.33185i		−	0.0774123i
$297$	2.20963	+	2.20963i	0.128216	+	0.128216i
$298$		−	7.63359i		−	0.442202i
$299$	−1.11334	−	3.17564i	−0.0643860	−	0.183652i
$300$			12.5614i			0.725232i
$301$	−25.0406	−	11.9041i	−1.44331	−	0.686142i
$302$	13.8874			0.799130
$303$			16.7763i			0.963774i
$304$	−11.9953	+	11.9953i	−0.687977	+	0.687977i
$305$	15.6938	+	15.6938i	0.898625	+	0.898625i
$306$	−1.95397	−	1.95397i	−0.111701	−	0.111701i
$307$	−5.77526	−	5.77526i	−0.329611	−	0.329611i	0.522827	−	0.852439i	$-0.324877\pi$
$307$	−5.77526	−	5.77526i	−0.329611	−	0.329611i	−0.852439	+	0.522827i	$0.824877\pi$
$308$	−3.52543	+	1.25354i	−0.200880	+	0.0714270i
$309$		−	4.56199i		−	0.259523i
$310$	32.0393	−	32.0393i	1.81971	−	1.81971i
$311$	2.62562			0.148885			0.0744426	−	0.997225i	$-0.476282\pi$
$311$	2.62562			0.148885			0.0744426	+	0.997225i	$0.476282\pi$
$312$	2.60147	+	1.25088i	0.147279	+	0.0708174i
$313$		−	19.8489i		−	1.12193i	−0.827840	−	0.560964i	$-0.810431\pi$
$313$		−	19.8489i		−	1.12193i	0.827840	−	0.560964i	$-0.189569\pi$
$314$	−4.97237	+	4.97237i	−0.280607	+	0.280607i
$315$	0.785680	+	2.20963i	0.0442681	+	0.124499i
$316$		−	30.5511i		−	1.71863i
$317$	1.14764	+	1.14764i	0.0644581	+	0.0644581i	0.738601	−	0.674143i	$-0.235487\pi$
$317$	1.14764	+	1.14764i	0.0644581	+	0.0644581i	−0.674143	+	0.738601i	$0.735487\pi$
$318$	8.88031	−	8.88031i	0.497983	−	0.497983i
$319$	2.85950	−	2.85950i	0.160101	−	0.160101i
$320$	−19.3664	−	19.3664i	−1.08262	−	1.08262i
$321$			5.24507i			0.292751i
$322$	−1.69832	−	4.77631i	−0.0946435	−	0.266173i
$323$	14.7217	−	14.7217i	0.819137	−	0.819137i
$324$		−	21.7812i		−	1.21007i
$325$	−3.71883	−	10.6074i	−0.206283	−	0.588394i
$326$	−30.3368			−1.68020
$327$	6.45682	−	6.45682i	0.357063	−	0.357063i
$328$		−	1.13221i		−	0.0625159i
$329$	−20.8338	+	7.40790i	−1.14861	+	0.408411i
$330$	4.80642	+	4.80642i	0.264585	+	0.264585i
$331$	−2.90321	−	2.90321i	−0.159575	−	0.159575i	0.622803	−	0.782378i	$-0.285994\pi$
$331$	−2.90321	−	2.90321i	−0.159575	−	0.159575i	−0.782378	+	0.622803i	$0.785994\pi$
$332$	9.53896	+	9.53896i	0.523518	+	0.523518i
$333$	−0.665926	+	0.665926i	−0.0364925	+	0.0364925i
$334$			47.1266i			2.57865i
$335$	−29.3371			−1.60286
$336$	−15.3286	−	7.28711i	−0.836244	−	0.397545i
$337$		−	4.47304i		−	0.243662i	−0.992551	−	0.121831i	$-0.961123\pi$
$337$		−	4.47304i		−	0.243662i	0.992551	−	0.121831i	$-0.0388766\pi$
$338$	−26.5232	−	2.95629i	−1.44267	−	0.160801i
$339$		−	29.7559i		−	1.61612i
$340$	19.3017	+	19.3017i	1.04678	+	1.04678i
$341$		−	4.94762i		−	0.267929i
$342$	−3.07318			−0.166179
$343$	17.9917	−	4.39312i	0.971459	−	0.237206i
$344$	3.26025	+	3.26025i	0.175781	+	0.175781i
$345$	−3.42149	+	3.42149i	−0.184207	+	0.184207i
$346$	−20.8756	−	20.8756i	−1.12228	−	1.12228i
$347$	8.81135			0.473018			0.236509	−	0.971629i	$-0.423997\pi$
$347$	8.81135			0.473018			0.236509	+	0.971629i	$0.423997\pi$
$348$	−25.5128			−1.36763
$349$	11.8133	+	11.8133i	0.632351	+	0.632351i	0.948657	−	0.316306i	$-0.102443\pi$
$349$	11.8133	+	11.8133i	0.632351	+	0.632351i	−0.316306	+	0.948657i	$0.602443\pi$
$350$	−5.67280	−	15.9541i	−0.303224	−	0.852781i
$351$	5.83654	+	16.6479i	0.311531	+	0.888598i
$352$	−5.18421			−0.276319
$353$	2.91007	−	2.91007i	0.154887	−	0.154887i	−0.625410	−	0.780297i	$-0.715068\pi$
$353$	2.91007	−	2.91007i	0.154887	−	0.154887i	0.780297	+	0.625410i	$0.215068\pi$
$354$	−1.35059			−0.0717829
$355$	−22.4396			−1.19097
$356$	−12.4271	+	12.4271i	−0.658633	+	0.658633i
$357$	18.8126	+	8.94340i	0.995671	+	0.473335i
$358$	−5.96767	+	5.96767i	−0.315401	+	0.315401i
$359$	3.52320	−	3.52320i	0.185948	−	0.185948i	−0.607994	−	0.793942i	$-0.708026\pi$
$359$	3.52320	−	3.52320i	0.185948	−	0.185948i	0.793942	+	0.607994i	$0.208026\pi$
$360$		−	0.389986i		−	0.0205541i
$361$		−	4.15410i		−	0.218637i
$362$	−31.3199	−	31.3199i	−1.64614	−	1.64614i
$363$	−19.2739			−1.01162
$364$	−21.0034	−	2.24687i	−1.10088	−	0.117768i
$365$	35.7052			1.86890
$366$	−20.5763	−	20.5763i	−1.07554	−	1.07554i
$367$			19.8112i			1.03414i	0.855944	+	0.517068i	$0.172976\pi$
$367$			19.8112i			1.03414i	−0.855944	+	0.517068i	$0.827024\pi$
$368$		−	3.29036i		−	0.171522i
$369$	−0.566106	+	0.566106i	−0.0294703	+	0.0294703i
$370$	12.5196	−	12.5196i	0.650863	−	0.650863i
$371$	−3.81900	+	8.03335i	−0.198273	+	0.417071i
$372$	−22.0716	+	22.0716i	−1.14436	+	1.14436i
$373$	−24.5368			−1.27047			−0.635234	−	0.772320i	$-0.719096\pi$
$373$	−24.5368			−1.27047			−0.635234	+	0.772320i	$0.719096\pi$
$374$	5.67280			0.293334
$375$	6.90099	−	6.90099i	0.356366	−	0.356366i
$376$	3.67704			0.189629
$377$	21.5442	−	7.55311i	1.10958	−	0.389005i
$378$	8.90321	+	25.0392i	0.457932	+	1.28788i
$379$	−8.78346	−	8.78346i	−0.451176	−	0.451176i	0.444569	−	0.895745i	$-0.353357\pi$
$379$	−8.78346	−	8.78346i	−0.451176	−	0.451176i	−0.895745	+	0.444569i	$0.853357\pi$
$380$	30.3575			1.55731
$381$	25.1605			1.28901
$382$	−14.9541	−	14.9541i	−0.765117	−	0.765117i
$383$	17.8990	−	17.8990i	0.914596	−	0.914596i	−0.0820333	−	0.996630i	$-0.526141\pi$
$383$	17.8990	−	17.8990i	0.914596	−	0.914596i	0.996630	+	0.0820333i	$0.0261414\pi$
$384$	4.50284	+	4.50284i	0.229785	+	0.229785i
$385$	−4.34801	−	2.06702i	−0.221595	−	0.105345i
$386$	−18.2494			−0.928868
$387$		−	3.26025i		−	0.165728i
$388$	−0.524315	−	0.524315i	−0.0266181	−	0.0266181i
$389$			12.0667i			0.611805i	0.952063	+	0.305902i	$0.0989581\pi$
$389$			12.0667i			0.611805i	−0.952063	+	0.305902i	$0.901042\pi$
$390$	12.6957	+	36.2127i	0.642873	+	1.83370i
$391$			4.03823i			0.204222i
$392$	−3.06376	−	0.314025i	−0.154743	−	0.0158607i
$393$	−23.3461			−1.17766
$394$			9.43801i			0.475480i
$395$	27.7961	−	27.7961i	1.39857	−	1.39857i
$396$	−0.311108	−	0.311108i	−0.0156338	−	0.0156338i
$397$	−7.82177	−	7.82177i	−0.392563	−	0.392563i	0.483037	−	0.875600i	$-0.339534\pi$
$397$	−7.82177	−	7.82177i	−0.392563	−	0.392563i	−0.875600	+	0.483037i	$0.839534\pi$
$398$	9.00164	+	9.00164i	0.451212	+	0.451212i
$399$	21.8272	−	7.76110i	1.09273	−	0.388541i
$400$		−	10.9906i		−	0.549532i
$401$	−17.6178	+	17.6178i	−0.879789	+	0.879789i	−0.993512	−	0.113723i	$-0.963722\pi$
$401$	−17.6178	+	17.6178i	−0.879789	+	0.879789i	0.113723	+	0.993512i	$0.463722\pi$
$402$	38.4642			1.91842
$403$	12.1039	−	25.1726i	0.602940	−	1.25394i
$404$			20.4150i			1.01569i
$405$	19.8171	−	19.8171i	0.984717	−	0.984717i
$406$	32.4035	−	11.5217i	1.60816	−	0.571813i
$407$		−	1.93332i		−	0.0958313i
$408$	−2.44938	−	2.44938i	−0.121263	−	0.121263i
$409$	−24.0225	+	24.0225i	−1.18783	+	1.18783i	−0.210169	+	0.977665i	$0.567401\pi$
$409$	−24.0225	+	24.0225i	−1.18783	+	1.18783i	−0.977665	+	0.210169i	$0.932599\pi$
$410$	10.6430	−	10.6430i	0.525618	−	0.525618i
$411$	4.36851	+	4.36851i	0.215483	+	0.215483i
$412$		−	5.55147i		−	0.273501i
$413$	0.901299	−	0.320476i	0.0443500	−	0.0157696i
$414$	0.421494	−	0.421494i	0.0207153	−	0.0207153i
$415$			17.3575i			0.852047i
$416$	−26.3763	−	12.6827i	−1.29321	−	0.621822i
$417$	6.08097			0.297786
$418$	4.46105	−	4.46105i	0.218197	−	0.218197i
$419$		−	19.6899i		−	0.961912i	−0.876745	−	0.480956i	$-0.840290\pi$
$419$		−	19.6899i		−	0.961912i	0.876745	−	0.480956i	$-0.159710\pi$
$420$	10.1756	+	28.6178i	0.496521	+	1.39640i
$421$	26.6042	+	26.6042i	1.29661	+	1.29661i	0.930619	+	0.365989i	$0.119269\pi$
$421$	26.6042	+	26.6042i	1.29661	+	1.29661i	0.365989	+	0.930619i	$0.380731\pi$
$422$	13.8709	+	13.8709i	0.675224	+	0.675224i
$423$	−1.83852	−	1.83852i	−0.0893918	−	0.0893918i
$424$	1.04593	−	1.04593i	0.0507950	−	0.0507950i
$425$			13.4887i			0.654298i
$426$	29.4207			1.42544
$427$	18.6138	+	8.84888i	0.900786	+	0.428228i
$428$			6.38271i			0.308520i
$429$	3.77631	+	1.81579i	0.182322	+	0.0876673i
$430$			61.2937i			2.95585i
$431$	−4.81135	−	4.81135i	−0.231754	−	0.231754i	0.581670	−	0.813425i	$-0.302399\pi$
$431$	−4.81135	−	4.81135i	−0.231754	−	0.231754i	−0.813425	+	0.581670i	$0.802399\pi$
$432$			17.2493i			0.829908i
$433$	−8.34704			−0.401133			−0.200567	−	0.979680i	$-0.564278\pi$
$433$	−8.34704			−0.401133			−0.200567	+	0.979680i	$0.564278\pi$
$434$	18.0652	−	38.0005i	0.867157	−	1.82408i
$435$	−23.2121	−	23.2121i	−1.11293	−	1.11293i
$436$	7.85728	−	7.85728i	0.376295	−	0.376295i
$437$	3.17564	+	3.17564i	0.151911	+	0.151911i
$438$	−46.8134			−2.23683
$439$	−2.42350			−0.115667			−0.0578336	−	0.998326i	$-0.518419\pi$
$439$	−2.42350			−0.115667			−0.0578336	+	0.998326i	$0.518419\pi$
$440$	0.566106	+	0.566106i	0.0269880	+	0.0269880i
$441$	1.37487	+	1.68889i	0.0654698	+	0.0804234i
$442$	28.8622	+	13.8780i	1.37283	+	0.660110i
$443$	13.7763			0.654532			0.327266	−	0.944932i	$-0.393873\pi$
$443$	13.7763			0.654532			0.327266	+	0.944932i	$0.393873\pi$
$444$	−8.62466	+	8.62466i	−0.409308	+	0.409308i
$445$	−22.6128			−1.07195
$446$	7.49245			0.354778
$447$	−4.78450	+	4.78450i	−0.226299	+	0.226299i
$448$	−22.9697	−	10.9197i	−1.08522	−	0.515905i
$449$	−24.7447	+	24.7447i	−1.16777	+	1.16777i	−0.185043	+	0.982730i	$0.559242\pi$
$449$	−24.7447	+	24.7447i	−1.16777	+	1.16777i	−0.982730	+	0.185043i	$0.940758\pi$
$450$	1.40790	−	1.40790i	0.0663688	−	0.0663688i
$451$		−	1.64353i		−	0.0773906i
$452$		−	36.2099i		−	1.70317i
$453$	−8.70419	−	8.70419i	−0.408959	−	0.408959i
$454$	−15.2535			−0.715885
$455$	−17.0651	−	21.1536i	−0.800026	−	0.991698i
$456$	−3.85236			−0.180403
$457$	−2.84521	−	2.84521i	−0.133093	−	0.133093i	0.637422	−	0.770515i	$-0.280001\pi$
$457$	−2.84521	−	2.84521i	−0.133093	−	0.133093i	−0.770515	+	0.637422i	$0.780001\pi$
$458$			2.11709i			0.0989252i
$459$		−	21.1699i		−	0.988127i
$460$	−4.16360	+	4.16360i	−0.194129	+	0.194129i
$461$	−2.38575	+	2.38575i	−0.111115	+	0.111115i	−0.760479	−	0.649363i	$-0.775036\pi$
$461$	−2.38575	+	2.38575i	−0.111115	+	0.111115i	0.649363	+	0.760479i	$0.275036\pi$
$462$	5.70071	+	2.71008i	0.265221	+	0.126084i
$463$	17.5899	−	17.5899i	0.817471	−	0.817471i	−0.168270	−	0.985741i	$-0.553818\pi$
$463$	17.5899	−	17.5899i	0.817471	−	0.817471i	0.985741	+	0.168270i	$0.0538180\pi$
$464$	22.3225			1.03630
$465$	−40.1625			−1.86249
$466$	−35.7282	+	35.7282i	−1.65507	+	1.65507i
$467$	−21.4287			−0.991602			−0.495801	−	0.868436i	$-0.665126\pi$
$467$	−21.4287			−0.991602			−0.495801	+	0.868436i	$0.665126\pi$
$468$	−0.821763	−	2.34396i	−0.0379860	−	0.108350i
$469$	−25.6686	+	9.12701i	−1.18527	+	0.421446i
$470$	34.5647	+	34.5647i	1.59435	+	1.59435i
$471$	6.23306			0.287204
$472$	−0.159074			−0.00732196
$473$	4.73260	+	4.73260i	0.217605	+	0.217605i
$474$	−36.4436	+	36.4436i	−1.67391	+	1.67391i
$475$	10.6074	+	10.6074i	0.486702	+	0.486702i
$476$	22.8930	+	10.8832i	1.04930	+	0.498830i
$477$	−1.04593			−0.0478900
$478$			18.9447i			0.866510i
$479$	4.61425	+	4.61425i	0.210831	+	0.210831i	0.804620	−	0.593790i	$-0.202369\pi$
$479$	4.61425	+	4.61425i	0.210831	+	0.210831i	−0.593790	+	0.804620i	$0.702369\pi$
$480$			42.0830i			1.92082i
$481$	4.72971	−	9.83641i	0.215656	−	0.448501i
$482$		−	58.5180i		−	2.66542i
$483$	−1.92919	+	4.05810i	−0.0877814	+	0.184650i
$484$	−23.4543			−1.06610
$485$		−	0.954067i		−	0.0433220i
$486$	−4.67492	+	4.67492i	−0.212059	+	0.212059i
$487$	9.62867	+	9.62867i	0.436317	+	0.436317i	0.890770	−	0.454454i	$-0.150166\pi$
$487$	9.62867	+	9.62867i	0.436317	+	0.436317i	−0.454454	+	0.890770i	$0.650166\pi$
$488$	−2.42350	−	2.42350i	−0.109707	−	0.109707i
$489$	19.0142	+	19.0142i	0.859850	+	0.859850i
$490$	−25.8479	−	31.7517i	−1.16769	−	1.43439i
$491$		−	9.21924i		−	0.416059i	−0.978123	−	0.208029i	$-0.933295\pi$
$491$		−	9.21924i		−	0.416059i	0.978123	−	0.208029i	$-0.0667049\pi$
$492$	−7.33185	+	7.33185i	−0.330545	+	0.330545i
$493$	−27.3962			−1.23386
$494$	33.6106	−	11.7835i	1.51221	−	0.530163i
$495$		−	0.566106i		−	0.0254446i
$496$	19.3116	−	19.3116i	0.867117	−	0.867117i
$497$	−19.6336	+	6.98113i	−0.880687	+	0.313147i
$498$		−	22.7576i		−	1.01979i
$499$	−6.65947	−	6.65947i	−0.298119	−	0.298119i	0.542158	−	0.840277i	$-0.317608\pi$
$499$	−6.65947	−	6.65947i	−0.298119	−	0.298119i	−0.840277	+	0.542158i	$0.817608\pi$
$500$	8.39779	−	8.39779i	0.375561	−	0.375561i
$501$	29.5375	−	29.5375i	1.31964	−	1.31964i
$502$	20.9681	+	20.9681i	0.935854	+	0.935854i
$503$		−	1.81069i		−	0.0807346i	−0.999185	−	0.0403673i	$-0.987147\pi$
$503$		−	1.81069i		−	0.0807346i	0.999185	−	0.0403673i	$-0.0128528\pi$
$504$	−0.121328	−	0.341219i	−0.00540436	−	0.0151991i
$505$	−18.5741	+	18.5741i	−0.826535	+	0.826535i
$506$			1.22369i			0.0543996i
$507$	14.7710	+	18.4769i	0.656004	+	0.820586i
$508$	30.6178			1.35844
$509$	−22.2864	+	22.2864i	−0.987827	+	0.987827i	−0.999927	−	0.0121000i	$-0.996148\pi$
$509$	−22.2864	+	22.2864i	−0.987827	+	0.987827i	0.0121000	+	0.999927i	$0.496148\pi$
$510$		−	46.0491i		−	2.03909i
$511$	31.2404	−	11.1082i	1.38199	−	0.491396i
$512$	−22.4286	−	22.4286i	−0.991215	−	0.991215i
$513$	−16.6479	−	16.6479i	−0.735022	−	0.735022i
$514$	−21.2278	−	21.2278i	−0.936320	−	0.936320i
$515$	5.05086	−	5.05086i	0.222567	−	0.222567i
$516$		−	42.2248i		−	1.85884i
$517$	5.33761			0.234748
$518$	7.05912	−	14.8490i	0.310160	−	0.652428i
$519$			26.1684i			1.14866i
$520$	1.49532	+	4.26517i	0.0655739	+	0.187040i
$521$		−	15.8744i		−	0.695472i	−0.937592	−	0.347736i	$-0.886951\pi$
$521$		−	15.8744i		−	0.695472i	0.937592	−	0.347736i	$-0.113049\pi$
$522$	2.85950	+	2.85950i	0.125157	+	0.125157i
$523$		−	3.90795i		−	0.170883i	−0.996343	−	0.0854413i	$-0.972770\pi$
$523$		−	3.90795i		−	0.170883i	0.996343	−	0.0854413i	$-0.0272300\pi$
$524$	−28.4098			−1.24109
$525$	−6.44399	+	13.5551i	−0.281239	+	0.591591i
$526$	3.79928	+	3.79928i	0.165656	+	0.165656i
$527$	−23.7010	+	23.7010i	−1.03243	+	1.03243i
$528$	2.89706	+	2.89706i	0.126079	+	0.126079i
$529$	22.1289			0.962126
$530$	19.6639			0.854143
$531$	0.0795368	+	0.0795368i	0.00345160	+	0.00345160i
$532$	26.5614	−	9.44446i	1.15158	−	0.409469i
$533$	4.02074	−	8.36196i	0.174158	−	0.362197i
$534$	29.6479			1.28299
$535$	−5.80713	+	5.80713i	−0.251064	+	0.251064i
$536$	4.53035			0.195681
$537$	7.48070			0.322816
$538$	−14.2597	+	14.2597i	−0.614780	+	0.614780i
$539$	−4.44737	−	0.455841i	−0.191562	−	0.0196345i
$540$	21.8272	−	21.8272i	0.939292	−	0.939292i
$541$	8.57406	−	8.57406i	0.368628	−	0.368628i	−0.498349	−	0.866977i	$-0.666060\pi$
$541$	8.57406	−	8.57406i	0.368628	−	0.368628i	0.866977	+	0.498349i	$0.166060\pi$
$542$			9.97073i			0.428280i
$543$			39.2607i			1.68484i
$544$	24.8343	+	24.8343i	1.06476	+	1.06476i
$545$	14.2975			0.612436
$546$	22.3742	+	27.7347i	0.957529	+	1.18694i
$547$	−4.72546			−0.202046			−0.101023	−	0.994884i	$-0.532212\pi$
$547$	−4.72546			−0.202046			−0.101023	+	0.994884i	$0.532212\pi$
$548$	5.31603	+	5.31603i	0.227090	+	0.227090i
$549$			2.42350i			0.103432i
$550$			4.08742i			0.174288i
$551$	−21.5442	+	21.5442i	−0.917812	+	0.917812i
$552$	0.528360	−	0.528360i	0.0224885	−	0.0224885i
$553$	15.6727	−	32.9678i	0.666470	−	1.40193i
$554$	8.56268	−	8.56268i	0.363794	−	0.363794i
$555$	−15.6938			−0.666165
$556$	7.39991			0.313826
$557$	−23.8415	+	23.8415i	−1.01019	+	1.01019i	−0.0102475	+	0.999947i	$0.503262\pi$
$557$	−23.8415	+	23.8415i	−1.01019	+	1.01019i	−0.999947	+	0.0102475i	$0.996738\pi$
$558$	4.94762			0.209450
$559$	12.5007	+	35.6565i	0.528725	+	1.50811i
$560$	−8.90321	−	25.0392i	−0.376229	−	1.05810i
$561$	−3.55554	−	3.55554i	−0.150115	−	0.150115i
$562$	−26.8178			−1.13124
$563$	−41.2776			−1.73965			−0.869823	−	0.493365i	$-0.835767\pi$
$563$	−41.2776			−1.73965			−0.869823	+	0.493365i	$0.835767\pi$
$564$	−23.8113	−	23.8113i	−1.00264	−	1.00264i
$565$	32.9446	−	32.9446i	1.38599	−	1.38599i
$566$	−12.0878	−	12.0878i	−0.508089	−	0.508089i
$567$	11.1738	−	23.5042i	0.469254	−	0.987085i
$568$	3.46520			0.145397
$569$		−	43.5402i		−	1.82530i	−0.408742	−	0.912650i	$-0.634032\pi$
$569$		−	43.5402i		−	1.82530i	0.408742	−	0.912650i	$-0.365968\pi$
$570$	−36.2127	−	36.2127i	−1.51678	−	1.51678i
$571$			21.2701i			0.890126i	0.895499	+	0.445063i	$0.146819\pi$
$571$			21.2701i			0.890126i	−0.895499	+	0.445063i	$0.853181\pi$
$572$	4.59538	+	2.20963i	0.192143	+	0.0923893i
$573$			18.7455i			0.783105i
$574$	6.00098	−	12.6232i	0.250476	−	0.526882i
$575$	−2.90967			−0.121341
$576$		−	2.99063i		−	0.124610i
$577$	8.73703	−	8.73703i	0.363727	−	0.363727i	−0.501456	−	0.865183i	$-0.667202\pi$
$577$	8.73703	−	8.73703i	0.363727	−	0.363727i	0.865183	+	0.501456i	$0.167202\pi$
$578$	−2.49754	−	2.49754i	−0.103884	−	0.103884i
$579$	11.4381	+	11.4381i	0.475353	+	0.475353i
$580$	−28.2467	−	28.2467i	−1.17288	−	1.17288i
$581$	5.40006	+	15.1870i	0.224032	+	0.630064i
$582$			1.25088i			0.0518508i
$583$	1.51828	−	1.51828i	0.0628808	−	0.0628808i
$584$	−5.51373			−0.228160
$585$	1.38493	−	2.88025i	0.0572598	−	0.119083i
$586$		−	44.9717i		−	1.85776i
$587$	−30.6931	+	30.6931i	−1.26684	+	1.26684i	−0.319131	+	0.947711i	$0.603391\pi$
$587$	−30.6931	+	30.6931i	−1.26684	+	1.26684i	−0.947711	+	0.319131i	$0.896609\pi$
$588$	17.8064	+	21.8735i	0.734325	+	0.902047i
$589$			37.2766i			1.53595i
$590$	−1.49532	−	1.49532i	−0.0615612	−	0.0615612i
$591$	5.91546	−	5.91546i	0.243329	−	0.243329i
$592$	7.54617	−	7.54617i	0.310146	−	0.310146i
$593$	−5.18036	−	5.18036i	−0.212732	−	0.212732i	0.592695	−	0.805427i	$-0.298064\pi$
$593$	−5.18036	−	5.18036i	−0.212732	−	0.212732i	−0.805427	+	0.592695i	$0.798064\pi$
$594$		−	6.41503i		−	0.263212i
$595$	10.9268	+	30.7304i	0.447956	+	1.25982i
$596$	−5.82225	+	5.82225i	−0.238488	+	0.238488i
$597$		−	11.2839i		−	0.461820i
$598$	−2.99365	+	6.22591i	−0.122419	+	0.254596i
$599$	−18.5254			−0.756928			−0.378464	−	0.925616i	$-0.623548\pi$
$599$	−18.5254			−0.756928			−0.378464	+	0.925616i	$0.623548\pi$
$600$	1.76485	−	1.76485i	0.0720498	−	0.0720498i
$601$			30.9807i			1.26373i	0.775079	+	0.631864i	$0.217710\pi$
$601$			30.9807i			1.26373i	−0.775079	+	0.631864i	$0.782290\pi$
$602$	19.0690	+	53.6291i	0.777193	+	2.18576i
$603$	−2.26517	−	2.26517i	−0.0922451	−	0.0922451i
$604$	−10.5921	−	10.5921i	−0.430987	−	0.430987i
$605$	−21.3393	−	21.3393i	−0.867564	−	0.867564i
$606$	24.3526	−	24.3526i	0.989257	−	0.989257i
$607$		−	29.4674i		−	1.19605i	−0.801479	−	0.598023i	$-0.795953\pi$
$607$		−	29.4674i		−	1.19605i	0.801479	−	0.598023i	$-0.204047\pi$
$608$	39.0591			1.58405
$609$	−27.5310	−	13.0880i	−1.11561	−	0.530354i
$610$		−	45.5625i		−	1.84477i
$611$	27.1568	+	13.0580i	1.09865	+	0.528270i
$612$			2.98065i			0.120485i
$613$	13.9398	+	13.9398i	0.563022	+	0.563022i	0.930165	−	0.367142i	$-0.119664\pi$
$613$	13.9398	+	13.9398i	0.563022	+	0.563022i	−0.367142	+	0.930165i	$0.619664\pi$
$614$			16.7668i			0.676653i
$615$	−13.3414			−0.537976
$616$	0.671436	+	0.319196i	0.0270529	+	0.0128608i
$617$	−27.7052	−	27.7052i	−1.11537	−	1.11537i	−0.992412	−	0.122957i	$-0.960762\pi$
$617$	−27.7052	−	27.7052i	−1.11537	−	1.11537i	−0.122957	−	0.992412i	$-0.539238\pi$
$618$	−6.62222	+	6.62222i	−0.266385	+	0.266385i
$619$	4.58642	+	4.58642i	0.184344	+	0.184344i	0.793246	−	0.608902i	$-0.208390\pi$
$619$	4.58642	+	4.58642i	0.184344	+	0.184344i	−0.608902	+	0.793246i	$0.708390\pi$
$620$	−48.8736			−1.96281
$621$	4.56659			0.183251
$622$	−3.81137	−	3.81137i	−0.152822	−	0.152822i
$623$	−19.7852	+	7.03503i	−0.792677	+	0.281853i
$624$	7.65233	+	21.8272i	0.306338	+	0.873786i
$625$	30.8687			1.23475
$626$	−28.8128	+	28.8128i	−1.15159	+	1.15159i
$627$	−5.59210			−0.223327
$628$	7.58498			0.302674
$629$	−9.26134	+	9.26134i	−0.369274	+	0.369274i
$630$	2.06702	−	4.34801i	0.0823519	−	0.173229i
$631$	11.1175	−	11.1175i	0.442582	−	0.442582i	−0.450297	−	0.892879i	$-0.648682\pi$
$631$	11.1175	−	11.1175i	0.442582	−	0.442582i	0.892879	+	0.450297i	$0.148682\pi$
$632$	−4.29237	+	4.29237i	−0.170741	+	0.170741i
$633$		−	17.3877i		−	0.691099i
$634$		−	3.33185i		−	0.132325i
$635$	27.8567	+	27.8567i	1.10546	+	1.10546i
$636$	−13.5463			−0.537145
$637$	−21.5123	−	13.1994i	−0.852347	−	0.522977i
$638$	−8.30174			−0.328669
$639$	−1.73260	−	1.73260i	−0.0685407	−	0.0685407i
$640$			9.97073i			0.394128i
$641$		−	22.3590i		−	0.883129i	−0.897229	−	0.441565i	$-0.854424\pi$
$641$		−	22.3590i		−	0.883129i	0.897229	−	0.441565i	$-0.145576\pi$
$642$	7.61377	−	7.61377i	0.300492	−	0.300492i
$643$	−5.69880	+	5.69880i	−0.224739	+	0.224739i	−0.810491	−	0.585752i	$-0.800799\pi$
$643$	−5.69880	+	5.69880i	−0.224739	+	0.224739i	0.585752	+	0.810491i	$0.300799\pi$
$644$	−2.34763	+	4.93829i	−0.0925096	+	0.194596i
$645$	38.4170	−	38.4170i	1.51267	−	1.51267i
$646$	−42.7402			−1.68159
$647$	7.73510			0.304098			0.152049	−	0.988373i	$-0.451413\pi$
$647$	7.73510			0.304098			0.152049	+	0.988373i	$0.451413\pi$
$648$	−3.06022	+	3.06022i	−0.120217	+	0.120217i
$649$	−0.230912			−0.00906410
$650$	−9.99952	+	20.7961i	−0.392214	+	0.815689i
$651$	−35.1403	+	12.4949i	−1.37726	+	0.489712i
$652$	23.1383	+	23.1383i	0.906165	+	0.906165i
$653$	21.3921			0.837137			0.418568	−	0.908185i	$-0.362532\pi$
$653$	21.3921			0.837137			0.418568	+	0.908185i	$0.362532\pi$
$654$	−18.7455			−0.733007
$655$	−25.8479	−	25.8479i	−1.00996	−	1.00996i
$656$	6.41503	−	6.41503i	0.250465	−	0.250465i
$657$	2.75686	+	2.75686i	0.107555	+	0.107555i
$658$	40.9958	+	19.4891i	1.59818	+	0.759766i
$659$	−1.68445			−0.0656167			−0.0328084	−	0.999462i	$-0.510445\pi$
$659$	−1.68445			−0.0656167			−0.0328084	+	0.999462i	$0.510445\pi$
$660$		−	7.33185i		−	0.285392i
$661$	−23.4056	−	23.4056i	−0.910372	−	0.910372i	0.0859290	−	0.996301i	$-0.472614\pi$
$661$	−23.4056	−	23.4056i	−0.910372	−	0.910372i	−0.996301	+	0.0859290i	$0.972614\pi$
$662$			8.42864i			0.327588i
$663$	−9.39163	−	26.7883i	−0.364741	−	1.04037i
$664$		−	2.68041i		−	0.104020i
$665$	32.7589	+	15.5734i	1.27034	+	0.603910i
$666$	1.93332			0.0749148
$667$		−	5.90967i		−	0.228823i
$668$	35.9441	−	35.9441i	1.39072	−	1.39072i
$669$	−4.69604	−	4.69604i	−0.181559	−	0.181559i
$670$	42.5860	+	42.5860i	1.64524	+	1.64524i
$671$	−3.51796	−	3.51796i	−0.135809	−	0.135809i
$672$	13.0923	+	36.8206i	0.505048	+	1.42039i
$673$			26.2464i			1.01173i	0.862614	+	0.505863i	$0.168826\pi$
$673$			26.2464i			1.01173i	−0.862614	+	0.505863i	$0.831174\pi$
$674$	−6.49309	+	6.49309i	−0.250105	+	0.250105i
$675$	15.2535			0.587109
$676$	17.9748	+	22.4844i	0.691339	+	0.864785i
$677$			36.7658i			1.41303i	0.707700	+	0.706513i	$0.249733\pi$
$677$			36.7658i			1.41303i	−0.707700	+	0.706513i	$0.750267\pi$
$678$	−43.1939	+	43.1939i	−1.65885	+	1.65885i
$679$	−0.296818	−	0.834764i	−0.0113908	−	0.0320353i
$680$		−	5.42372i		−	0.207990i
$681$	9.56046	+	9.56046i	0.366358	+	0.366358i
$682$	−7.18200	+	7.18200i	−0.275013	+	0.275013i
$683$	−14.5812	+	14.5812i	−0.557934	+	0.557934i	−0.928719	−	0.370785i	$-0.879089\pi$
$683$	−14.5812	+	14.5812i	−0.557934	+	0.557934i	0.370785	+	0.928719i	$0.379089\pi$
$684$	2.34396	+	2.34396i	0.0896235	+	0.0896235i
$685$			9.67329i			0.369597i
$686$	−32.4939	−	19.7397i	−1.24062	−	0.753667i
$687$	1.32693	−	1.32693i	0.0506255	−	0.0506255i
$688$			36.9447i			1.40850i
$689$	11.4391	−	4.01040i	0.435795	−	0.152784i
$690$	9.93332			0.378155
$691$	30.4663	−	30.4663i	1.15899	−	1.15899i	0.174299	−	0.984693i	$-0.444234\pi$
$691$	30.4663	−	30.4663i	1.15899	−	1.15899i	0.984693	−	0.174299i	$-0.0557658\pi$
$692$			31.8442i			1.21054i
$693$	−0.176120	−	0.495316i	−0.00669024	−	0.0188155i
$694$	−12.7906	−	12.7906i	−0.485525	−	0.485525i
$695$	6.73260	+	6.73260i	0.255382	+	0.255382i
$696$	3.58450	+	3.58450i	0.135870	+	0.135870i
$697$	−7.87310	+	7.87310i	−0.298215	+	0.298215i
$698$		−	34.2965i		−	1.29814i
$699$	44.7866			1.69399
$700$	−7.84166	+	16.4951i	−0.296387	+	0.623457i
$701$		−	17.7368i		−	0.669911i	−0.942234	−	0.334955i	$-0.891279\pi$
$701$		−	17.7368i		−	0.669911i	0.942234	−	0.334955i	$-0.108721\pi$
$702$	15.6938	−	32.6385i	0.592325	−	1.23186i
$703$			14.5661i			0.549371i
$704$	4.34122	+	4.34122i	0.163616	+	0.163616i
$705$		−	43.3282i		−	1.63183i
$706$	−8.44854			−0.317965
$707$	−10.4729	+	22.0300i	−0.393874	+	0.828522i
$708$	1.03011	+	1.03011i	0.0387140	+	0.0387140i
$709$	19.2422	−	19.2422i	0.722656	−	0.722656i	−0.246489	−	0.969146i	$-0.579277\pi$
$709$	19.2422	−	19.2422i	0.722656	−	0.722656i	0.969146	+	0.246489i	$0.0792770\pi$
$710$	32.5734	+	32.5734i	1.22246	+	1.22246i
$711$	4.29237			0.160977
$712$	3.49196			0.130867
$713$	−5.11257	−	5.11257i	−0.191467	−	0.191467i
$714$	−14.3262	−	40.2908i	−0.536146	−	1.50785i
$715$	2.17061	+	6.19135i	0.0811762	+	0.231543i
$716$	9.10324			0.340204
$717$	11.8740	−	11.8740i	0.443441	−	0.443441i
$718$	−10.2286			−0.381728
$719$	42.3551			1.57958			0.789789	−	0.613379i	$-0.210190\pi$
$719$	42.3551			1.57958			0.789789	+	0.613379i	$0.210190\pi$
$720$	2.20963	−	2.20963i	0.0823481	−	0.0823481i
$721$	2.84790	−	5.99062i	0.106061	−	0.223102i
$722$	−6.03011	+	6.03011i	−0.224418	+	0.224418i
$723$	−36.6773	+	36.6773i	−1.36404	+	1.36404i
$724$			47.7762i			1.77559i
$725$		−	19.7397i		−	0.733116i
$726$	27.9781	+	27.9781i	1.03836	+	1.03836i
$727$	23.2484			0.862234			0.431117	−	0.902296i	$-0.358120\pi$
$727$	23.2484			0.862234			0.431117	+	0.902296i	$0.358120\pi$
$728$	2.63526	+	3.26662i	0.0976693	+	0.121069i
$729$	−23.6494			−0.875904
$730$	−51.8299	−	51.8299i	−1.91831	−	1.91831i
$731$		−	45.3419i		−	1.67703i
$732$			31.3876i			1.16012i
$733$	24.1280	−	24.1280i	0.891188	−	0.891188i	−0.103447	−	0.994635i	$-0.532987\pi$
$733$	24.1280	−	24.1280i	0.891188	−	0.891188i	0.994635	+	0.103447i	$0.0329873\pi$
$734$	28.7580	−	28.7580i	1.06148	−	1.06148i
$735$	−3.70030	+	36.1017i	−0.136488	+	1.33163i
$736$	−5.35704	+	5.35704i	−0.197463	+	0.197463i
$737$	6.57628			0.242240
$738$	1.64353			0.0604990
$739$	4.46590	−	4.46590i	0.164281	−	0.164281i	−0.620179	−	0.784460i	$-0.712940\pi$
$739$	4.46590	−	4.46590i	0.164281	−	0.164281i	0.784460	+	0.620179i	$0.212940\pi$
$740$	−19.0977			−0.702047
$741$	−28.4516	−	13.6806i	−1.04520	−	0.502570i
$742$	17.2050	−	6.11758i	0.631614	−	0.224583i
$743$	10.0114	+	10.0114i	0.367282	+	0.367282i	0.866485	−	0.499203i	$-0.166374\pi$
$743$	10.0114	+	10.0114i	0.367282	+	0.367282i	−0.499203	+	0.866485i	$0.666374\pi$
$744$	6.20204			0.227378
$745$	−10.5944			−0.388149
$746$	35.6178	+	35.6178i	1.30406	+	1.30406i
$747$	−1.34021	+	1.34021i	−0.0490356	+	0.0490356i
$748$	−4.32672	−	4.32672i	−0.158201	−	0.158201i
$749$	−3.27432	+	6.88761i	−0.119641	+	0.251668i
$750$	−20.0350			−0.731576
$751$			8.16686i			0.298013i	0.988836	+	0.149006i	$0.0476075\pi$
$751$			8.16686i			0.298013i	−0.988836	+	0.149006i	$0.952392\pi$
$752$	20.8338	+	20.8338i	0.759731	+	0.759731i
$753$		−	26.2844i		−	0.957856i
$754$	−42.2378	−	20.3095i	−1.53821	−	0.739628i
$755$		−	19.2739i		−	0.701448i
$756$	12.3071	−	25.8884i	0.447607	−	0.941550i
$757$	10.5210			0.382392			0.191196	−	0.981552i	$-0.438763\pi$
$757$	10.5210			0.382392			0.191196	+	0.981552i	$0.438763\pi$
$758$			25.5002i			0.926210i
$759$	0.766970	−	0.766970i	0.0278393	−	0.0278393i
$760$	−4.26517	−	4.26517i	−0.154714	−	0.154714i
$761$	5.95138	+	5.95138i	0.215737	+	0.215737i	0.806699	−	0.590962i	$-0.201252\pi$
$761$	5.95138	+	5.95138i	0.215737	+	0.215737i	−0.590962	+	0.806699i	$0.701252\pi$
$762$	−36.5232	−	36.5232i	−1.32310	−	1.32310i
$763$	12.5096	−	4.44805i	0.452878	−	0.161030i
$764$			22.8113i			0.825286i
$765$	−2.71186	+	2.71186i	−0.0980475	+	0.0980475i
$766$	−51.9646			−1.87756
$767$	−1.17484	−	0.564907i	−0.0424210	−	0.0203976i
$768$			21.9112i			0.790653i
$769$	9.73800	−	9.73800i	0.351161	−	0.351161i	−0.509380	−	0.860541i	$-0.670125\pi$
$769$	9.73800	−	9.73800i	0.351161	−	0.351161i	0.860541	+	0.509380i	$0.170125\pi$
$770$	3.31111	+	9.31209i	0.119324	+	0.335584i
$771$			26.6099i			0.958333i
$772$	13.9190	+	13.9190i	0.500957	+	0.500957i
$773$	−16.0246	+	16.0246i	−0.576364	+	0.576364i	−0.933899	−	0.357536i	$-0.883617\pi$
$773$	−16.0246	+	16.0246i	−0.576364	+	0.576364i	0.357536	+	0.933899i	$0.383617\pi$
$774$	−4.73260	+	4.73260i	−0.170110	+	0.170110i
$775$	−17.0772	−	17.0772i	−0.613433	−	0.613433i
$776$			0.147331i			0.00528886i
$777$	−13.7314	+	4.88247i	−0.492610	+	0.175158i
$778$	17.5161	−	17.5161i	0.627981	−	0.627981i
$779$			12.3827i			0.443657i
$780$	17.9367	−	37.3032i	0.642239	−	1.33567i
$781$	5.03011			0.179992
$782$	5.86192	−	5.86192i	0.209622	−	0.209622i
$783$			30.9807i			1.10716i
$784$	−15.5798	−	19.1383i	−0.556421	−	0.683510i
$785$	6.90099	+	6.90099i	0.246307	+	0.246307i
$786$	33.8894	+	33.8894i	1.20879	+	1.20879i
$787$	−17.9844	−	17.9844i	−0.641075	−	0.641075i	0.309745	−	0.950820i	$-0.399756\pi$
$787$	−17.9844	−	17.9844i	−0.641075	−	0.641075i	−0.950820	+	0.309745i	$0.899756\pi$
$788$	7.19850	−	7.19850i	0.256436	−	0.256436i
$789$		−	4.76254i		−	0.169551i
$790$	−80.6979			−2.87110
$791$	18.5756	−	39.0743i	0.660474	−	1.38932i
$792$			0.0874201i			0.00310634i
$793$	−9.29237	−	26.5052i	−0.329982	−	0.941226i
$794$			22.7082i			0.805886i
$795$	−12.3247	−	12.3247i	−0.437112	−	0.437112i
$796$		−	13.7314i		−	0.486695i
$797$	43.9698			1.55749			0.778745	−	0.627341i	$-0.215857\pi$
$797$	43.9698			1.55749			0.778745	+	0.627341i	$0.215857\pi$
$798$	−42.9505	−	20.4184i	−1.52043	−	0.722803i
$799$	−25.5691	−	25.5691i	−0.904571	−	0.904571i
$800$	−17.8938	+	17.8938i	−0.632643	+	0.632643i
$801$	−1.74598	−	1.74598i	−0.0616912	−	0.0616912i
$802$	51.1481			1.80610
$803$	−8.00376			−0.282447
$804$	−29.3371	−	29.3371i	−1.03464	−	1.03464i
$805$	−6.62889	+	2.35704i	−0.233638	+	0.0830748i
$806$	−54.1109	+	18.9706i	−1.90597	+	0.668210i
$807$	17.8751			0.629234
$808$	2.86827	−	2.86827i	0.100906	−	0.100906i
$809$	12.0509			0.423686			0.211843	−	0.977304i	$-0.432054\pi$
$809$	12.0509			0.423686			0.211843	+	0.977304i	$0.432054\pi$
$810$	−57.5331			−2.02151
$811$	−1.07742	+	1.07742i	−0.0378333	+	0.0378333i	−0.725770	−	0.687937i	$-0.758517\pi$
$811$	−1.07742	+	1.07742i	−0.0378333	+	0.0378333i	0.687937	+	0.725770i	$0.258517\pi$
$812$	−33.5023	−	15.9268i	−1.17570	−	0.558920i
$813$	6.24935	−	6.24935i	0.219174	−	0.219174i
$814$	−2.80642	+	2.80642i	−0.0983651	+	0.0983651i
$815$			42.1034i			1.47482i
$816$		−	27.7560i		−	0.971656i
$817$	−35.6565	−	35.6565i	−1.24746	−	1.24746i
$818$	69.7423			2.43848
$819$	0.315681	−	2.95094i	0.0110308	−	0.103114i
$820$	−16.2351			−0.566953
$821$	−34.1847	−	34.1847i	−1.19305	−	1.19305i	−0.976205	−	0.216848i	$-0.930422\pi$
$821$	−34.1847	−	34.1847i	−1.19305	−	1.19305i	−0.216848	−	0.976205i	$-0.569578\pi$
$822$		−	12.6827i		−	0.442361i
$823$			4.71609i			0.164393i	0.996616	+	0.0821963i	$0.0261934\pi$
$823$			4.71609i			0.164393i	−0.996616	+	0.0821963i	$0.973807\pi$
$824$	−0.779972	+	0.779972i	−0.0271716	+	0.0271716i
$825$	2.56187	−	2.56187i	0.0891929	−	0.0891929i
$826$	−1.77354	−	0.843127i	−0.0617092	−	0.0293361i
$827$	24.0939	−	24.0939i	0.837826	−	0.837826i	−0.150746	−	0.988572i	$-0.548168\pi$
$827$	24.0939	−	24.0939i	0.837826	−	0.837826i	0.988572	+	0.150746i	$0.0481677\pi$
$828$	−0.642959			−0.0223444
$829$	−12.4689			−0.433061			−0.216531	−	0.976276i	$-0.569474\pi$
$829$	−12.4689			−0.433061			−0.216531	+	0.976276i	$0.569474\pi$
$830$	25.1963	−	25.1963i	0.874575	−	0.874575i
$831$	−10.7337			−0.372347
$832$	11.4669	+	32.7078i	0.397544	+	1.13394i
$833$	19.1209	+	23.4882i	0.662501	+	0.813819i
$834$	−8.82717	−	8.82717i	−0.305660	−	0.305660i
$835$	65.4055			2.26345
$836$	−6.80501			−0.235356
$837$	26.8020	+	26.8020i	0.926412	+	0.926412i
$838$	−28.5819	+	28.5819i	−0.987346	+	0.987346i
$839$	−26.1454	−	26.1454i	−0.902640	−	0.902640i	0.0930239	−	0.995664i	$-0.470347\pi$
$839$	−26.1454	−	26.1454i	−0.902640	−	0.902640i	−0.995664	+	0.0930239i	$0.970347\pi$
$840$	2.59108	−	5.45040i	0.0894009	−	0.188057i
$841$	11.0923			0.382495
$842$		−	77.2375i		−	2.66178i
$843$	16.8086	+	16.8086i	0.578918	+	0.578918i
$844$		−	21.1590i		−	0.728323i
$845$	−4.10294	+	36.8107i	−0.141145	+	1.26633i
$846$			5.33761i			0.183511i
$847$	−25.3097	−	12.0320i	−0.869650	−	0.413426i
$848$	11.8524			0.407012
$849$			15.1526i			0.520035i
$850$	19.5803	−	19.5803i	0.671598	−	0.671598i
$851$	−1.99778	−	1.99778i	−0.0684829	−	0.0684829i
$852$	−22.4396	−	22.4396i	−0.768768	−	0.768768i
$853$	−15.4396	−	15.4396i	−0.528641	−	0.528641i	0.391526	−	0.920167i	$-0.371947\pi$
$853$	−15.4396	−	15.4396i	−0.528641	−	0.528641i	−0.920167	+	0.391526i	$0.871947\pi$
$854$	−14.1748	−	39.8650i	−0.485053	−	1.36415i
$855$			4.26517i			0.145866i
$856$	0.896758	−	0.896758i	0.0306506	−	0.0306506i
$857$	35.9311			1.22738			0.613691	−	0.789546i	$-0.289684\pi$
$857$	35.9311			1.22738			0.613691	+	0.789546i	$0.289684\pi$
$858$	−2.84590	−	8.11753i	−0.0971575	−	0.277128i
$859$			6.05104i			0.206459i	0.994658	+	0.103229i	$0.0329176\pi$
$859$			6.05104i			0.206459i	−0.994658	+	0.103229i	$0.967082\pi$
$860$	46.7496	−	46.7496i	1.59415	−	1.59415i
$861$	−11.6731	+	4.15060i	−0.397817	+	0.141452i
$862$			13.9684i			0.475764i
$863$	−11.8524	−	11.8524i	−0.403459	−	0.403459i	0.475991	−	0.879450i	$-0.342089\pi$
$863$	−11.8524	−	11.8524i	−0.403459	−	0.403459i	−0.879450	+	0.475991i	$0.842089\pi$
$864$	28.0836	−	28.0836i	0.955424	−	0.955424i
$865$	−28.9726	+	28.9726i	−0.985098	+	0.985098i
$866$	12.1166	+	12.1166i	0.411739	+	0.411739i
$867$			3.13076i			0.106326i
$868$	−42.7621	+	15.2050i	−1.45144	+	0.516090i
$869$	−6.23083	+	6.23083i	−0.211367	+	0.211367i
$870$			67.3896i			2.28472i
$871$	33.4590	+	16.0883i	1.13371	+	0.545132i
$872$	−2.20787			−0.0747678
$873$	0.0736653	−	0.0736653i	0.00249319	−	0.00249319i
$874$		−	9.21955i		−	0.311856i
$875$	13.3702	−	4.75404i	0.451994	−	0.160716i
$876$	35.7052	+	35.7052i	1.20637	+	1.20637i
$877$	29.7741	+	29.7741i	1.00540	+	1.00540i	0.999985	+	0.00541422i	$0.00172341\pi$
$877$	29.7741	+	29.7741i	1.00540	+	1.00540i	0.00541422	+	0.999985i	$0.498277\pi$
$878$	3.51796	+	3.51796i	0.118725	+	0.118725i
$879$	−28.1869	+	28.1869i	−0.950721	+	0.950721i
$880$			6.41503i			0.216251i
$881$	18.8928			0.636516			0.318258	−	0.948004i	$-0.396902\pi$
$881$	18.8928			0.636516			0.318258	+	0.948004i	$0.396902\pi$
$882$	0.455841	−	4.44737i	0.0153490	−	0.149751i
$883$			7.28391i			0.245123i	0.992461	+	0.122562i	$0.0391109\pi$
$883$			7.28391i			0.245123i	−0.992461	+	0.122562i	$0.960889\pi$
$884$	−11.4286	−	32.5986i	−0.384387	−	1.09641i
$885$			1.87444i			0.0630085i
$886$	−19.9978	−	19.9978i	−0.671838	−	0.671838i
$887$			36.5520i			1.22730i	0.789580	+	0.613648i	$0.210298\pi$
$887$			36.5520i			1.22730i	−0.789580	+	0.613648i	$0.789702\pi$
$888$	2.42350			0.0813272
$889$	33.0398	+	15.7069i	1.10812	+	0.526792i
$890$	32.8249	+	32.8249i	1.10029	+	1.10029i
$891$	−4.44224	+	4.44224i	−0.148821	+	0.148821i
$892$	−5.71459	−	5.71459i	−0.191339	−	0.191339i
$893$	−40.2148			−1.34574
$894$	13.8904			0.464565
$895$	8.28233	+	8.28233i	0.276848	+	0.276848i
$896$	3.10197	+	8.72393i	0.103630	+	0.291446i
$897$	5.77854	−	2.02588i	0.192940	−	0.0676422i
$898$	71.8390			2.39730
$899$	34.6847	−	34.6847i	1.15680	−	1.15680i
$900$	−2.14764			−0.0715881
$901$	−14.5463			−0.484607
$902$	−2.38575	+	2.38575i	−0.0794368	+	0.0794368i
$903$	21.6613	−	45.5650i	0.720842	−	1.51631i
$904$	−5.08742	+	5.08742i	−0.169205	+	0.169205i
$905$	−43.4679	+	43.4679i	−1.44492	+	1.44492i
$906$			25.2701i			0.839544i
$907$			8.45875i			0.280868i	0.990090	+	0.140434i	$0.0448498\pi$
$907$			8.45875i			0.280868i	−0.990090	+	0.140434i	$0.955150\pi$
$908$	11.6341	+	11.6341i	0.386091	+	0.386091i
$909$	−2.86827			−0.0951347
$910$	−5.93491	+	55.4786i	−0.196740	+	1.83910i
$911$	−11.0973			−0.367669			−0.183834	−	0.982957i	$-0.558851\pi$
$911$	−11.0973			−0.367669			−0.183834	+	0.982957i	$0.558851\pi$
$912$	−21.8272	−	21.8272i	−0.722770	−	0.722770i
$913$		−	3.89090i		−	0.128770i
$914$			8.26025i			0.273225i
$915$	−28.5572	+	28.5572i	−0.944071	+	0.944071i
$916$	1.61474	−	1.61474i	0.0533524	−	0.0533524i
$917$	−30.6572	−	14.5742i	−1.01239	−	0.481283i
$918$	−30.7304	+	30.7304i	−1.01425	+	1.01425i
$919$	−30.7225			−1.01344			−0.506722	−	0.862110i	$-0.669143\pi$
$919$	−30.7225			−1.01344			−0.506722	+	0.862110i	$0.669143\pi$
$920$	1.16996			0.0385724
$921$	10.5089	−	10.5089i	0.346281	−	0.346281i
$922$	6.92634			0.228107
$923$	25.5923	+	12.3057i	0.842381	+	0.405048i
$924$	−2.28100	−	6.41503i	−0.0750393	−	0.211039i
$925$	−6.67307	−	6.67307i	−0.219409	−	0.219409i
$926$	−51.0672			−1.67817
$927$	0.779972			0.0256176
$928$	−36.3432	−	36.3432i	−1.19302	−	1.19302i
$929$	−24.7606	+	24.7606i	−0.812370	+	0.812370i	−0.984989	−	0.172619i	$-0.944777\pi$
$929$	−24.7606	+	24.7606i	−0.812370	+	0.812370i	0.172619	+	0.984989i	$0.444777\pi$
$930$	58.3001	+	58.3001i	1.91174	+	1.91174i
$931$	33.5075	+	3.43441i	1.09817	+	0.112558i
$932$	54.5007			1.78523
$933$			4.77770i			0.156415i
$934$	31.1060	+	31.1060i	1.01782	+	1.01782i
$935$		−	7.87310i		−	0.257478i
$936$	−0.213866	+	0.444778i	−0.00699043	+	0.0145380i
$937$		−	18.9594i		−	0.619376i	−0.950838	−	0.309688i	$-0.899775\pi$
$937$		−	18.9594i		−	0.619376i	0.950838	−	0.309688i	$-0.100225\pi$
$938$	50.5096	+	24.0119i	1.64920	+	0.784016i
$939$	36.1180			1.17867
$940$		−	52.7259i		−	1.71973i
$941$	−32.7842	+	32.7842i	−1.06874	+	1.06874i	−0.0712788	+	0.997456i	$0.522708\pi$
$941$	−32.7842	+	32.7842i	−1.06874	+	1.06874i	−0.997456	+	0.0712788i	$0.977292\pi$
$942$	−9.04794	−	9.04794i	−0.294798	−	0.294798i
$943$	−1.69832	−	1.69832i	−0.0553048	−	0.0553048i
$944$	−0.901299	−	0.901299i	−0.0293348	−	0.0293348i
$945$	34.7511	−	12.3565i	1.13045	−	0.401957i
$946$		−	13.7397i		−	0.446718i
$947$	−29.9748	+	29.9748i	−0.974050	+	0.974050i	−0.999672	−	0.0256213i	$-0.991844\pi$
$947$	−29.9748	+	29.9748i	−0.974050	+	0.974050i	0.0256213	+	0.999672i	$0.491844\pi$
$948$	55.5921			1.80555
$949$	−40.7217	−	19.5805i	−1.32188	−	0.635610i
$950$		−	30.7956i		−	0.999141i
$951$	−2.08830	+	2.08830i	−0.0677179	+	0.0677179i
$952$	−1.68736	−	4.74550i	−0.0546877	−	0.153802i
$953$			41.0785i			1.33066i	0.746548	+	0.665332i	$0.231710\pi$
$953$			41.0785i			1.33066i	−0.746548	+	0.665332i	$0.768290\pi$
$954$	1.51828	+	1.51828i	0.0491562	+	0.0491562i
$955$	−20.7543	+	20.7543i	−0.671593	+	0.671593i
$956$	14.4494	−	14.4494i	0.467326	−	0.467326i
$957$	5.20328	+	5.20328i	0.168198	+	0.168198i
$958$		−	13.3962i		−	0.432810i
$959$	3.00944	+	8.46367i	0.0971797	+	0.273306i
$960$	35.2400	−	35.2400i	1.13737	−	1.13737i
$961$		−	29.0128i		−	0.935895i
$962$	−21.1443	+	7.41291i	−0.681718	+	0.239002i
$963$	−0.896758			−0.0288976
$964$	−44.6325	+	44.6325i	−1.43752	+	1.43752i
$965$			25.3277i			0.815327i
$966$	8.69119	−	3.09033i	0.279635	−	0.0994299i
$967$	−43.8412	−	43.8412i	−1.40984	−	1.40984i	−0.760492	−	0.649347i	$-0.775042\pi$
$967$	−43.8412	−	43.8412i	−1.40984	−	1.40984i	−0.649347	−	0.760492i	$-0.724958\pi$
$968$	3.29529	+	3.29529i	0.105915	+	0.105915i
$969$	26.7883	+	26.7883i	0.860563	+	0.860563i
$970$	−1.38493	+	1.38493i	−0.0444674	+	0.0444674i
$971$			44.2843i			1.42115i	0.703621	+	0.710575i	$0.251565\pi$
$971$			44.2843i			1.42115i	−0.703621	+	0.710575i	$0.748435\pi$
$972$	7.13125			0.228735
$973$	7.98528	+	3.79615i	0.255996	+	0.121699i
$974$		−	27.9541i		−	0.895706i
$975$	19.3017	−	6.76694i	0.618150	−	0.216716i
$976$		−	27.4627i		−	0.879060i
$977$	7.01207	+	7.01207i	0.224336	+	0.224336i	0.810321	−	0.585986i	$-0.199292\pi$
$977$	7.01207	+	7.01207i	0.224336	+	0.224336i	−0.585986	+	0.810321i	$0.699292\pi$
$978$		−	55.2022i		−	1.76517i
$979$	5.06895			0.162004
$980$	−4.50289	+	43.9320i	−0.143839	+	1.40336i
$981$	1.10393	+	1.10393i	0.0352459	+	0.0352459i
$982$	−13.3827	+	13.3827i	−0.427059	+	0.427059i
$983$	−31.8034	−	31.8034i	−1.01437	−	1.01437i	−0.999895	−	0.0144754i	$-0.995392\pi$
$983$	−31.8034	−	31.8034i	−1.01437	−	1.01437i	−0.0144754	−	0.999895i	$-0.504608\pi$
$984$	2.06022			0.0656775
$985$	13.0987			0.417360
$986$	39.7684	+	39.7684i	1.26649	+	1.26649i
$987$	−13.4797	−	37.9101i	−0.429065	−	1.20669i
$988$	−34.6227	−	16.6479i	−1.10149	−	0.529640i
$989$	9.78076			0.311010
$990$	−0.821763	+	0.821763i	−0.0261173	+	0.0261173i
$991$	42.1367			1.33852			0.669259	−	0.743029i	$-0.266612\pi$
$991$	42.1367			1.33852			0.669259	+	0.743029i	$0.266612\pi$
$992$	−62.8825			−1.99652
$993$	5.28281	−	5.28281i	0.167645	−	0.167645i
$994$	38.6341	+	18.3664i	1.22540	+	0.582546i
$995$	12.4931	−	12.4931i	0.396058	−	0.396058i
$996$	−17.3575	+	17.3575i	−0.549994	+	0.549994i
$997$		−	27.7314i		−	0.878261i	−0.898423	−	0.439131i	$-0.855287\pi$
$997$		−	27.7314i		−	0.878261i	0.898423	−	0.439131i	$-0.144713\pi$
$998$			19.3339i			0.612003i
$999$	10.4731	+	10.4731i	0.331354	+	0.331354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.i.a.34.2	yes	12
3.2	odd	2		819.2.y.h.307.6		12
7.2	even	3		637.2.bc.a.619.1		24
7.3	odd	6		637.2.bc.a.411.5		24
7.4	even	3		637.2.bc.a.411.6		24
7.5	odd	6		637.2.bc.a.619.2		24
7.6	odd	2	inner	91.2.i.a.34.1	✓	12
13.5	odd	4	inner	91.2.i.a.83.2	yes	12
21.20	even	2		819.2.y.h.307.5		12
39.5	even	4		819.2.y.h.811.5		12
91.5	even	12		637.2.bc.a.31.6		24
91.18	odd	12		637.2.bc.a.460.2		24
91.31	even	12		637.2.bc.a.460.1		24
91.44	odd	12		637.2.bc.a.31.5		24
91.83	even	4	inner	91.2.i.a.83.1	yes	12
273.83	odd	4		819.2.y.h.811.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.1	✓	12	7.6	odd	2	inner
91.2.i.a.34.2	yes	12	1.1	even	1	trivial
91.2.i.a.83.1	yes	12	91.83	even	4	inner
91.2.i.a.83.2	yes	12	13.5	odd	4	inner
637.2.bc.a.31.5		24	91.44	odd	12
637.2.bc.a.31.6		24	91.5	even	12
637.2.bc.a.411.5		24	7.3	odd	6
637.2.bc.a.411.6		24	7.4	even	3
637.2.bc.a.460.1		24	91.31	even	12
637.2.bc.a.460.2		24	91.18	odd	12
637.2.bc.a.619.1		24	7.2	even	3
637.2.bc.a.619.2		24	7.5	odd	6
819.2.y.h.307.5		12	21.20	even	2
819.2.y.h.307.6		12	3.2	odd	2
819.2.y.h.811.5		12	39.5	even	4
819.2.y.h.811.6		12	273.83	odd	4

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.45161 - 1.45161i) q^{2} +1.81964i q^{3} +2.21432i q^{4} +(-2.01464 + 2.01464i) q^{5} +(2.64141 - 2.64141i) q^{6} +(-1.13594 + 2.38948i) q^{7} +(0.311108 - 0.311108i) q^{8} -0.311108 q^{9} +O(q^{10})\)	\(q+(-1.45161 - 1.45161i) q^{2} +1.81964i q^{3} +2.21432i q^{4} +(-2.01464 + 2.01464i) q^{5} +(2.64141 - 2.64141i) q^{6} +(-1.13594 + 2.38948i) q^{7} +(0.311108 - 0.311108i) q^{8} -0.311108 q^{9} +5.84892 q^{10} +(0.451606 - 0.451606i) q^{11} -4.02928 q^{12} +(3.40251 - 1.19288i) q^{13} +(5.11753 - 1.81964i) q^{14} +(-3.66593 - 3.66593i) q^{15} +3.52543 q^{16} -4.32672 q^{17} +(0.451606 + 0.451606i) q^{18} +(-3.40251 + 3.40251i) q^{19} +(-4.46105 - 4.46105i) q^{20} +(-4.34801 - 2.06702i) q^{21} -1.31111 q^{22} -0.933323i q^{23} +(0.566106 + 0.566106i) q^{24} -3.11753i q^{25} +(-6.67068 - 3.20751i) q^{26} +4.89283i q^{27} +(-5.29108 - 2.51534i) q^{28} +6.33185 q^{29} +10.6430i q^{30} +(5.47781 - 5.47781i) q^{31} +(-5.73975 - 5.73975i) q^{32} +(0.821763 + 0.821763i) q^{33} +(6.28070 + 6.28070i) q^{34} +(-2.52543 - 7.10246i) q^{35} -0.688892i q^{36} +(2.14050 - 2.14050i) q^{37} +9.87820 q^{38} +(2.17061 + 6.19135i) q^{39} +1.25354i q^{40} +(1.81964 - 1.81964i) q^{41} +(3.31111 + 9.31209i) q^{42} +10.4795i q^{43} +(1.00000 + 1.00000i) q^{44} +(0.626770 - 0.626770i) q^{45} +(-1.35482 + 1.35482i) q^{46} +(5.90958 + 5.90958i) q^{47} +6.41503i q^{48} +(-4.41926 - 5.42864i) q^{49} +(-4.52543 + 4.52543i) q^{50} -7.87310i q^{51} +(2.64141 + 7.53424i) q^{52} +3.36196 q^{53} +(7.10246 - 7.10246i) q^{54} +1.81964i q^{55} +(0.389986 + 1.09679i) q^{56} +(-6.19135 - 6.19135i) q^{57} +(-9.19135 - 9.19135i) q^{58} +(-0.255657 - 0.255657i) q^{59} +(8.11753 - 8.11753i) q^{60} -7.78989i q^{61} -15.9032 q^{62} +(0.353401 - 0.743387i) q^{63} +9.61285i q^{64} +(-4.45161 + 9.25803i) q^{65} -2.38575i q^{66} +(7.28100 + 7.28100i) q^{67} -9.58075i q^{68} +1.69832 q^{69} +(-6.64405 + 13.9759i) q^{70} +(5.56914 + 5.56914i) q^{71} +(-0.0967881 + 0.0967881i) q^{72} +(-8.86144 - 8.86144i) q^{73} -6.21432 q^{74} +5.67280 q^{75} +(-7.53424 - 7.53424i) q^{76} +(0.566106 + 1.59210i) q^{77} +(5.83654 - 12.1383i) q^{78} -13.7971 q^{79} +(-7.10246 + 7.10246i) q^{80} -9.83654 q^{81} -5.28281 q^{82} +(4.30785 - 4.30785i) q^{83} +(4.57703 - 9.62789i) q^{84} +(8.71678 - 8.71678i) q^{85} +(15.2121 - 15.2121i) q^{86} +11.5217i q^{87} -0.280996i q^{88} +(5.61214 + 5.61214i) q^{89} -1.81964 q^{90} +(-1.01470 + 9.48527i) q^{91} +2.06668 q^{92} +(9.96767 + 9.96767i) q^{93} -17.1568i q^{94} -13.7096i q^{95} +(10.4443 - 10.4443i) q^{96} +(-0.236784 + 0.236784i) q^{97} +(-1.46522 + 14.2953i) q^{98} +(-0.140498 + 0.140498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - 8 * q^7 + 4 * q^8 - 4 * q^9	\( 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9} - 8 q^{11} + 8 q^{14} - 4 q^{15} + 16 q^{16} - 8 q^{18} - 16 q^{22} - 20 q^{28} - 4 q^{29} - 16 q^{32} - 4 q^{35} + 12 q^{37} + 40 q^{39} + 40 q^{42} + 12 q^{44} + 24 q^{46} - 28 q^{50} - 12 q^{53} - 8 q^{57} - 44 q^{58} + 44 q^{60} + 20 q^{63} - 40 q^{65} + 60 q^{67} + 4 q^{70} - 28 q^{72} - 48 q^{74} + 44 q^{78} - 4 q^{79} - 92 q^{81} - 4 q^{84} + 12 q^{85} + 36 q^{86} - 32 q^{91} + 24 q^{92} - 28 q^{93} - 28 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 8 * q^7 + 4 * q^8 - 4 * q^9 - 8 * q^11 + 8 * q^14 - 4 * q^15 + 16 * q^16 - 8 * q^18 - 16 * q^22 - 20 * q^28 - 4 * q^29 - 16 * q^32 - 4 * q^35 + 12 * q^37 + 40 * q^39 + 40 * q^42 + 12 * q^44 + 24 * q^46 - 28 * q^50 - 12 * q^53 - 8 * q^57 - 44 * q^58 + 44 * q^60 + 20 * q^63 - 40 * q^65 + 60 * q^67 + 4 * q^70 - 28 * q^72 - 48 * q^74 + 44 * q^78 - 4 * q^79 - 92 * q^81 - 4 * q^84 + 12 * q^85 + 36 * q^86 - 32 * q^91 + 24 * q^92 - 28 * q^93 - 28 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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