LMFDB - Embedded newform 91.2.i.a.83.2

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			83.2
Root			$-0.626770 - 0.626770i$ of defining polynomial
Character	$\chi$	$=$	91.83
Dual form			91.2.i.a.34.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45161 + 1.45161i) q^{2} +1.81964i q^{3} -2.21432i q^{4} +(2.01464 + 2.01464i) q^{5} +(-2.64141 - 2.64141i) q^{6} +(-2.38948 - 1.13594i) q^{7} +(0.311108 + 0.311108i) q^{8} -0.311108 q^{9} +O(q^{10})$	\(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} +(-2.38948 - 1.13594i) 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} +(2.06702 - 4.34801i) 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} +(-2.51534 + 5.29108i) 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} +(0.743387 + 0.353401i) 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} +(13.9759 + 6.64405i) 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} +(-9.62789 - 4.57703i) 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} +(6.77519 + 6.71541i) 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} +(-14.2953 - 1.46522i) 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 $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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	−0.0267996	+	0.999641i	$0.508532\pi$
$2$	−1.45161	+	1.45161i	−1.02644	+	1.02644i	−0.999641	+	0.0267996i	$0.991468\pi$
$3$			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	$-0.0301402\pi$
$5$	2.01464	+	2.01464i	0.900973	+	0.900973i	−0.0945469	+	0.995520i	$0.530140\pi$
$6$	−2.64141	−	2.64141i	−1.07835	−	1.07835i
$7$	−2.38948	−	1.13594i	−0.903140	−	0.429347i
$7$	−2.38948	−	1.13594i	−0.903140	−	0.429347i
$8$	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	0.771904	−	0.635739i	$-0.219305\pi$
$11$	0.451606	+	0.451606i	0.136164	+	0.136164i	−0.635739	+	0.771904i	$0.719305\pi$
$12$	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	$-0.324180\pi$
$17$	4.32672			1.04938			0.524692	+	0.851292i	$0.324180\pi$
$18$	0.451606	−	0.451606i	0.106445	−	0.106445i
$19$	3.40251	+	3.40251i	0.780588	+	0.780588i	0.979930	−	0.199342i	$-0.0638803\pi$
$19$	3.40251	+	3.40251i	0.780588	+	0.780588i	−0.199342	+	0.979930i	$0.563880\pi$
$20$	4.46105	−	4.46105i	0.997522	−	0.997522i
$21$	2.06702	−	4.34801i	0.451060	−	0.948814i
$22$	−1.31111			−0.279529
$23$			0.933323i			0.194611i	0.995255	+	0.0973057i	$0.0310225\pi$
$23$			0.933323i			0.194611i	−0.995255	+	0.0973057i	$0.968978\pi$
$24$	−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
$28$	−2.51534	+	5.29108i	−0.475355	+	0.999920i
$29$	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	$-0.494898\pi$
$31$	−5.47781	−	5.47781i	−0.983843	−	0.983843i	−0.999872	+	0.0160282i	$0.994898\pi$
$32$	−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	0.860815	−	0.508919i	$-0.169955\pi$
$37$	2.14050	+	2.14050i	0.351896	+	0.351896i	−0.508919	+	0.860815i	$0.669955\pi$
$38$	−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	$-0.314402\pi$
$41$	−1.81964	−	1.81964i	−0.284181	−	0.284181i	−0.834774	+	0.550593i	$0.814402\pi$
$42$	3.31111	+	9.31209i	0.510915	+	1.43689i
$43$		−	10.4795i		−	1.59811i	−0.601259	−	0.799054i	$-0.705334\pi$
$43$		−	10.4795i		−	1.59811i	0.601259	−	0.799054i	$-0.294666\pi$
$44$	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	$-0.958641\pi$
$47$	−5.90958	+	5.90958i	−0.862002	+	0.862002i	0.129569	+	0.991570i	$0.458641\pi$
$48$			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	$-0.742508\pi$
$59$	0.255657	−	0.255657i	0.0332837	−	0.0332837i	0.723553	+	0.690269i	$0.242508\pi$
$60$	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
$63$	0.743387	+	0.353401i	0.0936580	+	0.0445244i
$64$		−	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	−0.104961	−	0.994476i	$-0.533472\pi$
$67$	7.28100	−	7.28100i	0.889515	−	0.889515i	0.994476	+	0.104961i	$0.0334718\pi$
$68$		−	9.58075i		−	1.16184i
$69$	−1.69832			−0.204453
$70$	13.9759	+	6.64405i	1.67044	+	0.794116i
$71$	5.56914	−	5.56914i	0.660935	−	0.660935i	−0.294665	−	0.955600i	$-0.595208\pi$
$71$	5.56914	−	5.56914i	0.660935	−	0.660935i	0.955600	+	0.294665i	$0.0952082\pi$
$72$	−0.0967881	−	0.0967881i	−0.0114066	−	0.0114066i
$73$	8.86144	−	8.86144i	1.03715	−	1.03715i	0.0378706	−	0.999283i	$-0.487943\pi$
$73$	8.86144	−	8.86144i	1.03715	−	1.03715i	0.999283	−	0.0378706i	$-0.0120575\pi$
$74$	−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	$-0.358518\pi$
$83$	−4.30785	−	4.30785i	−0.472848	−	0.472848i	−0.902835	+	0.429987i	$0.858518\pi$
$84$	−9.62789	−	4.57703i	−1.05049	−	0.499395i
$85$	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	$-0.888197\pi$
$89$	−5.61214	+	5.61214i	−0.594885	+	0.594885i	0.344062	+	0.938947i	$0.388197\pi$
$90$	1.81964			0.191807
$91$	6.77519	+	6.71541i	0.710233	+	0.703967i
$92$	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	$-0.244588\pi$
$97$	0.236784	+	0.236784i	0.0240417	+	0.0240417i	−0.694984	+	0.719025i	$0.744588\pi$
$98$	−14.2953	−	1.46522i	−1.44404	−	0.148009i
$99$	−0.140498	−	0.140498i	−0.0141206	−	0.0141206i
$100$	6.90321			0.690321
$101$	−9.21955			−0.917380			−0.458690	−	0.888596i	$-0.651681\pi$
$101$	−9.21955			−0.917380			−0.458690	+	0.888596i	$0.651681\pi$
$102$	−11.4286	−	11.4286i	−1.13160	−	1.13160i
$103$	2.50708			0.247030			0.123515	−	0.992343i	$-0.460583\pi$
$103$	2.50708			0.247030			0.123515	+	0.992343i	$0.460583\pi$
$104$	−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	−0.856320	−	0.516446i	$-0.827255\pi$
$109$	−3.54839	+	3.54839i	−0.339875	+	0.339875i	0.516446	+	0.856320i	$0.327255\pi$
$110$	−2.64141	−	2.64141i	−0.251848	−	0.251848i
$111$	−3.89495	+	3.89495i	−0.369692	+	0.369692i
$112$	−8.42395	−	4.00469i	−0.795989	−	0.378408i
$113$	−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
$119$	−10.3386	−	4.91492i	−0.947741	−	0.450550i
$120$	−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	$0.210231\pi$
$127$			13.8272i			1.22696i	−0.789709	+	0.613481i	$0.789769\pi$
$128$	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	0.802185	−	0.597075i	$-0.203671\pi$
$137$	2.40075	+	2.40075i	0.205110	+	0.205110i	−0.597075	+	0.802185i	$0.703671\pi$
$138$	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	−0.591153	−	0.806559i	$-0.701327\pi$
$149$	2.62936	−	2.62936i	0.215406	−	0.215406i	0.806559	+	0.591153i	$0.201327\pi$
$150$	8.23467	−	8.23467i	0.672358	−	0.672358i
$151$	−4.78346	−	4.78346i	−0.389272	−	0.389272i	0.485156	−	0.874428i	$-0.338763\pi$
$151$	−4.78346	−	4.78346i	−0.389272	−	0.389272i	−0.874428	+	0.485156i	$0.838763\pi$
$152$			2.11709i			0.171719i
$153$	−1.34608			−0.108824
$154$	3.13287	+	1.48935i	0.252454	+	0.120015i
$155$		−	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
$161$	1.06020	−	2.23016i	0.0835557	−	0.175761i
$162$	14.2788	−	14.2788i	1.12185	−	1.12185i
$163$	10.4494	+	10.4494i	0.818459	+	0.818459i	0.985885	−	0.167426i	$-0.0535455\pi$
$163$	10.4494	+	10.4494i	0.818459	+	0.818459i	−0.167426	+	0.985885i	$0.553545\pi$
$164$	−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	0.303180	−	0.952933i	$-0.401952\pi$
$167$	16.2326	−	16.2326i	1.25611	−	1.25611i	0.952933	−	0.303180i	$-0.0980483\pi$
$168$	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	$-0.684111\pi$
$173$	−14.3810			−1.09337			−0.546685	+	0.837338i	$0.684111\pi$
$174$	−16.7250	−	16.7250i	−1.26792	−	1.26792i
$175$	3.54134	−	7.44929i	0.267700	−	0.563113i
$176$	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	$0.0490990\pi$
$179$			4.11108i			0.307276i	−0.988127	+	0.153638i	$0.950901\pi$
$180$	−1.38787	+	1.38787i	−0.103446	+	0.103446i
$181$	−21.5760			−1.60373			−0.801867	−	0.597502i	$-0.796160\pi$
$181$	−21.5760			−1.60373			−0.801867	+	0.597502i	$0.796160\pi$
$182$	−19.5830	+	0.0867758i	−1.45159	+	0.00643225i
$183$	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
$189$	5.55798	−	11.6913i	0.404284	−	0.850419i
$190$	−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	0.896174	−	0.443703i	$-0.146336\pi$
$193$	6.28592	+	6.28592i	0.452470	+	0.452470i	−0.443703	+	0.896174i	$0.646336\pi$
$194$	−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	−0.813367	−	0.581751i	$-0.802368\pi$
$197$	−3.25088	+	3.25088i	−0.231616	+	0.231616i	0.581751	+	0.813367i	$0.302368\pi$
$198$	0.407896			0.0289879
$199$	6.20116			0.439589			0.219794	−	0.975546i	$-0.429461\pi$
$199$	6.20116			0.439589			0.219794	+	0.975546i	$0.429461\pi$
$200$	−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
$203$	−15.1299	−	7.19263i	−1.06191	−	0.504824i
$204$	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
$210$	−12.0898	+	25.4312i	−0.834276	+	1.75492i
$211$	−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	$-0.211005\pi$
$223$	2.58074	+	2.58074i	0.172819	+	0.172819i	−0.615398	+	0.788217i	$0.711005\pi$
$224$	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	$-0.329308\pi$
$227$	−5.25403	−	5.25403i	−0.348722	−	0.348722i	−0.859633	+	0.510911i	$0.829308\pi$
$228$	13.7096	+	13.7096i	0.907943	+	0.907943i
$229$	0.729224	−	0.729224i	0.0481885	−	0.0481885i	−0.682602	−	0.730790i	$-0.739152\pi$
$229$	0.729224	−	0.729224i	0.0481885	−	0.0481885i	0.730790	+	0.682602i	$0.239152\pi$
$230$		−	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	$0.298491\pi$
$233$			24.6128i			1.61244i	−0.591615	+	0.806221i	$0.701509\pi$
$234$	−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	−0.885924	−	0.463830i	$-0.846475\pi$
$239$	−6.52543	+	6.52543i	−0.422095	+	0.422095i	0.463830	+	0.885924i	$0.346475\pi$
$240$	−12.9240	+	12.9240i	−0.834238	+	0.834238i
$241$	−20.1563	+	20.1563i	−1.29838	+	1.29838i	−0.368920	+	0.929461i	$0.620272\pi$
$241$	−20.1563	+	20.1563i	−1.29838	+	1.29838i	−0.929461	+	0.368920i	$0.879728\pi$
$242$	15.3756	+	15.3756i	0.988379	+	0.988379i
$243$		−	3.22051i		−	0.206596i
$244$	−17.2493			−1.10427
$245$	−2.03353	+	19.8400i	−0.129918	+	1.26753i
$246$			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	$-0.349327\pi$
$251$	14.4448			0.911747			0.455873	+	0.890045i	$0.349327\pi$
$252$	0.782543	−	1.64610i	0.0492956	−	0.103694i
$253$	−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	$-0.650754\pi$
$257$	−14.6237			−0.912201			−0.456101	+	0.889928i	$0.650754\pi$
$258$	−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
$266$	23.6038	+	11.2211i	1.44724	+	0.688009i
$267$	−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	$-0.702871\pi$
$271$	3.43438	−	3.43438i	0.208624	−	0.208624i	0.803682	+	0.595059i	$0.202871\pi$
$272$	15.2535			0.924882
$273$	−12.2197	+	12.3284i	−0.739568	+	0.746151i
$274$	−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	$-0.943292\pi$
$277$		−	5.89877i		−	0.354423i	0.984173	−	0.177211i	$-0.0567076\pi$
$278$	4.85104	+	4.85104i	0.290946	+	0.290946i
$279$	1.70419	+	1.70419i	0.102027	+	0.102027i
$280$	1.42395	−	2.99531i	0.0850973	−	0.179004i
$281$	9.23729	+	9.23729i	0.551050	+	0.551050i	0.926744	−	0.375694i	$-0.122595\pi$
$281$	9.23729	+	9.23729i	0.551050	+	0.551050i	−0.375694	+	0.926744i	$0.622595\pi$
$282$	31.2192			1.85908
$283$	−8.32721			−0.495001			−0.247501	−	0.968888i	$-0.579609\pi$
$283$	−8.32721			−0.495001			−0.247501	+	0.968888i	$0.579609\pi$
$284$	−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	$-0.971024\pi$
$293$	−15.4903	+	15.4903i	−0.904955	+	0.904955i	0.0909047	+	0.995860i	$0.471024\pi$
$294$	2.66618	−	26.0123i	0.155495	−	1.51707i
$295$	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
$301$	−11.9041	+	25.0406i	−0.686142	+	1.44331i
$302$	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	$-0.675123\pi$
$307$	5.77526	−	5.77526i	0.329611	−	0.329611i	0.852439	+	0.522827i	$0.175123\pi$
$308$	−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	$-0.523718\pi$
$311$	−2.62562			−0.148885			−0.0744426	+	0.997225i	$0.523718\pi$
$312$	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	−0.674143	−	0.738601i	$-0.735487\pi$
$317$	1.14764	−	1.14764i	0.0644581	−	0.0644581i	0.738601	+	0.674143i	$0.235487\pi$
$318$	−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	−0.782378	−	0.622803i	$-0.785994\pi$
$331$	−2.90321	+	2.90321i	−0.159575	+	0.159575i	0.622803	+	0.782378i	$0.285994\pi$
$332$	−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
$336$	7.28711	−	15.3286i	0.397545	−	0.836244i
$337$			4.47304i			0.243662i	0.992551	+	0.121831i	$0.0388766\pi$
$337$			4.47304i			0.243662i	−0.992551	+	0.121831i	$0.961123\pi$
$338$	−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
$343$	−4.39312	−	17.9917i	−0.237206	−	0.971459i
$344$	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	$-0.897557\pi$
$349$	−11.8133	+	11.8133i	−0.632351	+	0.632351i	0.316306	+	0.948657i	$0.397557\pi$
$350$	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	$-0.284932\pi$
$353$	−2.91007	−	2.91007i	−0.154887	−	0.154887i	−0.780297	+	0.625410i	$0.784932\pi$
$354$	−1.35059			−0.0717829
$355$	22.4396			1.19097
$356$	12.4271	+	12.4271i	0.658633	+	0.658633i
$357$	8.94340	−	18.8126i	0.473335	−	0.995671i
$358$	−5.96767	−	5.96767i	−0.315401	−	0.315401i
$359$	3.52320	+	3.52320i	0.185948	+	0.185948i	0.793942	−	0.607994i	$-0.208026\pi$
$359$	3.52320	+	3.52320i	0.185948	+	0.185948i	−0.607994	+	0.793942i	$0.708026\pi$
$360$		−	0.389986i		−	0.0205541i
$361$			4.15410i			0.218637i
$362$	31.3199	−	31.3199i	1.64614	−	1.64614i
$363$	19.2739			1.01162
$364$	14.8701	−	15.0024i	0.779404	−	0.786342i
$365$	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
$371$	−8.03335	−	3.81900i	−0.417071	−	0.198273i
$372$	−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	−0.895745	−	0.444569i	$-0.853357\pi$
$379$	−8.78346	+	8.78346i	−0.451176	+	0.451176i	0.444569	+	0.895745i	$0.353357\pi$
$380$	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	$-0.473859\pi$
$383$	−17.8990	−	17.8990i	−0.914596	−	0.914596i	−0.996630	+	0.0820333i	$0.973859\pi$
$384$	−4.50284	+	4.50284i	−0.229785	+	0.229785i
$385$	2.06702	−	4.34801i	0.105345	−	0.221595i
$386$	−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	$-0.901042\pi$
$389$		−	12.0667i		−	0.611805i	0.952063	−	0.305902i	$-0.0989581\pi$
$390$	−12.6957	+	36.2127i	−0.642873	+	1.83370i
$391$			4.03823i			0.204222i
$392$	−0.314025	+	3.06376i	−0.0158607	+	0.154743i
$393$	−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	$-0.660466\pi$
$397$	7.82177	−	7.82177i	0.392563	−	0.392563i	0.875600	+	0.483037i	$0.160466\pi$
$398$	−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	0.113723	−	0.993512i	$-0.463722\pi$
$401$	−17.6178	−	17.6178i	−0.879789	−	0.879789i	−0.993512	+	0.113723i	$0.963722\pi$
$402$	−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	0.977665	+	0.210169i	$0.0674013\pi$
$409$	24.0225	+	24.0225i	1.18783	+	1.18783i	0.210169	+	0.977665i	$0.432599\pi$
$410$	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	0.365989	−	0.930619i	$-0.380731\pi$
$421$	26.6042	−	26.6042i	1.29661	−	1.29661i	0.930619	−	0.365989i	$-0.119269\pi$
$422$	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
$427$	−8.84888	+	18.6138i	−0.428228	+	0.900786i
$428$		−	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	−0.813425	−	0.581670i	$-0.802399\pi$
$431$	−4.81135	+	4.81135i	−0.231754	+	0.231754i	0.581670	+	0.813425i	$0.302399\pi$
$432$			17.2493i			0.829908i
$433$	8.34704			0.401133			0.200567	−	0.979680i	$-0.435722\pi$
$433$	8.34704			0.401133			0.200567	+	0.979680i	$0.435722\pi$
$434$	−38.0005	−	18.0652i	−1.82408	−	0.867157i
$435$	−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	$-0.481581\pi$
$439$	2.42350			0.115667			0.0578336	+	0.998326i	$0.481581\pi$
$440$	−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
$448$	−10.9197	+	22.9697i	−0.515905	+	1.08522i
$449$	−24.7447	−	24.7447i	−1.16777	−	1.16777i	−0.982730	−	0.185043i	$-0.940758\pi$
$449$	−24.7447	−	24.7447i	−1.16777	−	1.16777i	−0.185043	−	0.982730i	$-0.559242\pi$
$450$	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
$455$	0.120433	+	27.1787i	0.00564600	+	1.27416i
$456$	−3.85236			−0.180403
$457$	−2.84521	+	2.84521i	−0.133093	+	0.133093i	−0.770515	−	0.637422i	$-0.780001\pi$
$457$	−2.84521	+	2.84521i	−0.133093	+	0.133093i	0.637422	+	0.770515i	$0.280001\pi$
$458$			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	$-0.224964\pi$
$461$	2.38575	+	2.38575i	0.111115	+	0.111115i	−0.649363	+	0.760479i	$0.724964\pi$
$462$	−2.71008	+	5.70071i	−0.126084	+	0.265221i
$463$	17.5899	+	17.5899i	0.817471	+	0.817471i	0.985741	−	0.168270i	$-0.0538180\pi$
$463$	17.5899	+	17.5899i	0.817471	+	0.817471i	−0.168270	+	0.985741i	$0.553818\pi$
$464$	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	$-0.334874\pi$
$467$	21.4287			0.991602			0.495801	+	0.868436i	$0.334874\pi$
$468$	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
$476$	−10.8832	+	22.8930i	−0.498830	+	1.04930i
$477$	−1.04593			−0.0478900
$478$		−	18.9447i		−	0.866510i
$479$	−4.61425	+	4.61425i	−0.210831	+	0.210831i	−0.804620	−	0.593790i	$-0.797631\pi$
$479$	−4.61425	+	4.61425i	−0.210831	+	0.210831i	0.593790	+	0.804620i	$0.297631\pi$
$480$		−	42.0830i		−	1.92082i
$481$	−4.72971	−	9.83641i	−0.215656	−	0.448501i
$482$		−	58.5180i		−	2.66542i
$483$	4.05810	+	1.92919i	0.184650	+	0.0877814i
$484$	−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	−0.454454	−	0.890770i	$-0.650166\pi$
$487$	9.62867	−	9.62867i	0.436317	−	0.436317i	0.890770	+	0.454454i	$0.150166\pi$
$488$	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	$0.0667049\pi$
$491$			9.21924i			0.416059i	−0.978123	+	0.208029i	$0.933295\pi$
$492$	−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	−0.840277	−	0.542158i	$-0.817608\pi$
$499$	−6.65947	+	6.65947i	−0.298119	+	0.298119i	0.542158	+	0.840277i	$0.317608\pi$
$500$	−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	$-0.00385163\pi$
$509$	22.2864	+	22.2864i	0.987827	+	0.987827i	−0.0121000	+	0.999927i	$0.503852\pi$
$510$		−	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
$518$	14.8490	+	7.05912i	0.652428	+	0.310160i
$519$		−	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
$525$	13.5551	+	6.44399i	0.591591	+	0.281239i
$526$	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
$539$	−0.455841	+	4.44737i	−0.0196345	+	0.191562i
$540$	21.8272	+	21.8272i	0.939292	+	0.939292i
$541$	8.57406	+	8.57406i	0.368628	+	0.368628i	0.866977	−	0.498349i	$-0.166060\pi$
$541$	8.57406	+	8.57406i	0.368628	+	0.368628i	−0.498349	+	0.866977i	$0.666060\pi$
$542$			9.97073i			0.428280i
$543$		−	39.2607i		−	1.68484i
$544$	−24.8343	+	24.8343i	−1.06476	+	1.06476i
$545$	−14.2975			−0.612436
$546$	−0.157901	−	35.6342i	−0.00675754	−	1.52500i
$547$	−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
$553$	32.9678	+	15.6727i	1.40193	+	0.666470i
$554$	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	−0.999947	−	0.0102475i	$-0.996738\pi$
$557$	−23.8415	−	23.8415i	−1.01019	−	1.01019i	−0.0102475	−	0.999947i	$-0.503262\pi$
$558$	−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	$-0.164233\pi$
$563$	41.2776			1.73965			0.869823	+	0.493365i	$0.164233\pi$
$564$	−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
$567$	23.5042	+	11.1738i	0.987085	+	0.469254i
$568$	3.46520			0.145397
$569$			43.5402i			1.82530i	0.408742	+	0.912650i	$0.365968\pi$
$569$			43.5402i			1.82530i	−0.408742	+	0.912650i	$0.634032\pi$
$570$	36.2127	−	36.2127i	1.51678	−	1.51678i
$571$		−	21.2701i		−	0.890126i	−0.895499	−	0.445063i	$-0.853181\pi$
$571$		−	21.2701i		−	0.890126i	0.895499	−	0.445063i	$-0.146819\pi$
$572$	−4.59538	+	2.20963i	−0.192143	+	0.0923893i
$573$			18.7455i			0.783105i
$574$	−12.6232	−	6.00098i	−0.526882	−	0.250476i
$575$	−2.90967			−0.121341
$576$			2.99063i			0.124610i
$577$	−8.73703	−	8.73703i	−0.363727	−	0.363727i	0.501456	−	0.865183i	$-0.332798\pi$
$577$	−8.73703	−	8.73703i	−0.363727	−	0.363727i	−0.865183	+	0.501456i	$0.832798\pi$
$578$	−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	0.947711	+	0.319131i	$0.103391\pi$
$587$	30.6931	+	30.6931i	1.26684	+	1.26684i	0.319131	+	0.947711i	$0.396609\pi$
$588$	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	$-0.701936\pi$
$593$	5.18036	−	5.18036i	0.212732	−	0.212732i	0.805427	+	0.592695i	$0.201936\pi$
$594$		−	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
$609$	13.0880	−	27.5310i	0.530354	−	1.11561i
$610$			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	−0.367142	−	0.930165i	$-0.619664\pi$
$613$	13.9398	−	13.9398i	0.563022	−	0.563022i	0.930165	+	0.367142i	$0.119664\pi$
$614$			16.7668i			0.676653i
$615$	13.3414			0.537976
$616$	0.319196	−	0.671436i	0.0128608	−	0.0270529i
$617$	−27.7052	+	27.7052i	−1.11537	+	1.11537i	−0.122957	+	0.992412i	$0.539238\pi$
$617$	−27.7052	+	27.7052i	−1.11537	+	1.11537i	−0.992412	+	0.122957i	$0.960762\pi$
$618$	−6.62222	−	6.62222i	−0.266385	−	0.266385i
$619$	−4.58642	+	4.58642i	−0.184344	+	0.184344i	−0.793246	−	0.608902i	$-0.791610\pi$
$619$	−4.58642	+	4.58642i	−0.184344	+	0.184344i	0.608902	+	0.793246i	$0.291610\pi$
$620$	−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
$630$	−4.34801	−	2.06702i	−0.173229	−	0.0823519i
$631$	11.1175	+	11.1175i	0.442582	+	0.442582i	0.892879	−	0.450297i	$-0.148682\pi$
$631$	11.1175	+	11.1175i	0.442582	+	0.442582i	−0.450297	+	0.892879i	$0.648682\pi$
$632$	−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
$637$	−8.56087	−	23.7426i	−0.339194	−	0.940716i
$638$	−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	$0.145576\pi$
$641$			22.3590i			0.883129i	−0.897229	+	0.441565i	$0.854424\pi$
$642$	−7.61377	−	7.61377i	−0.300492	−	0.300492i
$643$	5.69880	+	5.69880i	0.224739	+	0.224739i	0.810491	−	0.585752i	$-0.199201\pi$
$643$	5.69880	+	5.69880i	0.224739	+	0.224739i	−0.585752	+	0.810491i	$0.699201\pi$
$644$	−4.93829	−	2.34763i	−0.194596	−	0.0925096i
$645$	38.4170	+	38.4170i	1.51267	+	1.51267i
$646$	−42.7402			−1.68159
$647$	−7.73510			−0.304098			−0.152049	−	0.988373i	$-0.548587\pi$
$647$	−7.73510			−0.304098			−0.152049	+	0.988373i	$0.548587\pi$
$648$	−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
$658$	−19.4891	+	40.9958i	−0.759766	+	1.59818i
$659$	−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	$-0.527386\pi$
$661$	23.4056	−	23.4056i	0.910372	−	0.910372i	0.996301	+	0.0859290i	$0.0273858\pi$
$662$		−	8.42864i		−	0.327588i
$663$	9.39163	−	26.7883i	0.364741	−	1.04037i
$664$		−	2.68041i		−	0.104020i
$665$	15.5734	−	32.7589i	0.603910	−	1.27034i
$666$	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	$-0.831174\pi$
$673$		−	26.2464i		−	1.01173i	0.862614	−	0.505863i	$-0.168826\pi$
$674$	−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	0.370785	−	0.928719i	$-0.379089\pi$
$683$	−14.5812	−	14.5812i	−0.557934	−	0.557934i	−0.928719	+	0.370785i	$0.879089\pi$
$684$	−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	−0.984693	−	0.174299i	$-0.944234\pi$
$691$	−30.4663	−	30.4663i	−1.15899	−	1.15899i	−0.174299	−	0.984693i	$-0.555766\pi$
$692$			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
$700$	−16.4951	−	7.84166i	−0.623457	−	0.296387i
$701$			17.7368i			0.669911i	0.942234	+	0.334955i	$0.108721\pi$
$701$			17.7368i			0.669911i	−0.942234	+	0.334955i	$0.891279\pi$
$702$	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
$707$	22.0300	+	10.4729i	0.828522	+	0.393874i
$708$	1.03011	−	1.03011i	0.0387140	−	0.0387140i
$709$	19.2422	+	19.2422i	0.722656	+	0.722656i	0.969146	−	0.246489i	$-0.0792770\pi$
$709$	19.2422	+	19.2422i	0.722656	+	0.722656i	−0.246489	+	0.969146i	$0.579277\pi$
$710$	−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	$-0.789810\pi$
$719$	−42.3551			−1.57958			−0.789789	+	0.613379i	$0.789810\pi$
$720$	−2.20963	−	2.20963i	−0.0823481	−	0.0823481i
$721$	−5.99062	−	2.84790i	−0.223102	−	0.106061i
$722$	−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	$-0.641880\pi$
$727$	−23.2484			−0.862234			−0.431117	+	0.902296i	$0.641880\pi$
$728$	0.0185978	+	4.19703i	0.000689279	+	0.155552i
$729$	−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	$-0.467013\pi$
$733$	−24.1280	−	24.1280i	−0.891188	−	0.891188i	−0.994635	+	0.103447i	$0.967013\pi$
$734$	−28.7580	−	28.7580i	−1.06148	−	1.06148i
$735$	−36.1017	−	3.70030i	−1.33163	−	0.136488i
$736$	−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	0.784460	−	0.620179i	$-0.212940\pi$
$739$	4.46590	+	4.46590i	0.164281	+	0.164281i	−0.620179	+	0.784460i	$0.712940\pi$
$740$	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	−0.499203	−	0.866485i	$-0.666374\pi$
$743$	10.0114	−	10.0114i	0.367282	−	0.367282i	0.866485	+	0.499203i	$0.166374\pi$
$744$	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
$749$	−6.88761	−	3.27432i	−0.251668	−	0.119641i
$750$	−20.0350			−0.731576
$751$		−	8.16686i		−	0.298013i	−0.988836	−	0.149006i	$-0.952392\pi$
$751$		−	8.16686i		−	0.298013i	0.988836	−	0.149006i	$-0.0476075\pi$
$752$	−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
$756$	−25.8884	−	12.3071i	−0.941550	−	0.447607i
$757$	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	$-0.798748\pi$
$761$	−5.95138	+	5.95138i	−0.215737	+	0.215737i	0.590962	+	0.806699i	$0.298748\pi$
$762$	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	$-0.329875\pi$
$769$	−9.73800	−	9.73800i	−0.351161	−	0.351161i	−0.860541	+	0.509380i	$0.829875\pi$
$770$	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	$-0.116383\pi$
$773$	16.0246	+	16.0246i	0.576364	+	0.576364i	−0.357536	+	0.933899i	$0.616383\pi$
$774$	−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	$-0.600244\pi$
$787$	17.9844	−	17.9844i	0.641075	−	0.641075i	0.950820	+	0.309745i	$0.100244\pi$
$788$	7.19850	+	7.19850i	0.256436	+	0.256436i
$789$		−	4.76254i		−	0.169551i
$790$	80.6979			2.87110
$791$	39.0743	+	18.5756i	1.38932	+	0.660474i
$792$		−	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	$-0.784143\pi$
$797$	−43.9698			−1.55749			−0.778745	+	0.627341i	$0.784143\pi$
$798$	−20.4184	+	42.9505i	−0.722803	+	1.52043i
$799$	−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	$-0.241483\pi$
$811$	1.07742	+	1.07742i	0.0378333	+	0.0378333i	−0.687937	+	0.725770i	$0.741483\pi$
$812$	−15.9268	+	33.5023i	−0.558920	+	1.17570i
$813$	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
$819$	−2.10782	−	2.08922i	−0.0736530	−	0.0730032i
$820$	−16.2351			−0.566953
$821$	−34.1847	+	34.1847i	−1.19305	+	1.19305i	−0.216848	+	0.976205i	$0.569578\pi$
$821$	−34.1847	+	34.1847i	−1.19305	+	1.19305i	−0.976205	+	0.216848i	$0.930422\pi$
$822$		−	12.6827i		−	0.442361i
$823$		−	4.71609i		−	0.164393i	−0.996616	−	0.0821963i	$-0.973807\pi$
$823$		−	4.71609i		−	0.164393i	0.996616	−	0.0821963i	$-0.0261934\pi$
$824$	0.779972	+	0.779972i	0.0271716	+	0.0271716i
$825$	−2.56187	−	2.56187i	−0.0891929	−	0.0891929i
$826$	0.843127	−	1.77354i	0.0293361	−	0.0617092i
$827$	24.0939	+	24.0939i	0.837826	+	0.837826i	0.988572	−	0.150746i	$-0.0481677\pi$
$827$	24.0939	+	24.0939i	0.837826	+	0.837826i	−0.150746	+	0.988572i	$0.548168\pi$
$828$	−0.642959			−0.0223444
$829$	12.4689			0.433061			0.216531	−	0.976276i	$-0.430526\pi$
$829$	12.4689			0.433061			0.216531	+	0.976276i	$0.430526\pi$
$830$	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	$-0.529653\pi$
$839$	26.1454	−	26.1454i	0.902640	−	0.902640i	0.995664	+	0.0930239i	$0.0296533\pi$
$840$	5.45040	+	2.59108i	0.188057	+	0.0894009i
$841$	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
$847$	−12.0320	+	25.3097i	−0.413426	+	0.869650i
$848$	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	$-0.628053\pi$
$853$	15.4396	−	15.4396i	0.528641	−	0.528641i	0.920167	+	0.391526i	$0.128053\pi$
$854$	−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	$-0.710316\pi$
$857$	−35.9311			−1.22738			−0.613691	+	0.789546i	$0.710316\pi$
$858$	−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	−0.879450	−	0.475991i	$-0.842089\pi$
$863$	−11.8524	+	11.8524i	−0.403459	+	0.403459i	0.475991	+	0.879450i	$0.342089\pi$
$864$	−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	0.00541422	−	0.999985i	$-0.498277\pi$
$877$	29.7741	−	29.7741i	1.00540	−	1.00540i	0.999985	−	0.00541422i	$-0.00172341\pi$
$878$	−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	$-0.603098\pi$
$881$	−18.8928			−0.636516			−0.318258	+	0.948004i	$0.603098\pi$
$882$	4.44737	+	0.455841i	0.149751	+	0.0153490i
$883$		−	7.28391i		−	0.245123i	−0.992461	−	0.122562i	$-0.960889\pi$
$883$		−	7.28391i		−	0.245123i	0.992461	−	0.122562i	$-0.0391109\pi$
$884$	−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
$889$	15.7069	−	33.0398i	0.526792	−	1.10812i
$890$	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
$903$	−45.5650	−	21.6613i	−1.51631	−	0.720842i
$904$	−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	$-0.955150\pi$
$907$		−	8.45875i		−	0.280868i	0.990090	−	0.140434i	$-0.0448498\pi$
$908$	−11.6341	+	11.6341i	−0.386091	+	0.386091i
$909$	2.86827			0.0951347
$910$	−39.6276	−	39.2779i	−1.31364	−	1.30205i
$911$	−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
$917$	14.5742	−	30.6572i	0.481283	−	1.01239i
$918$	−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	$-0.0552228\pi$
$929$	24.7606	+	24.7606i	0.812370	+	0.812370i	−0.172619	+	0.984989i	$0.555223\pi$
$930$	−58.3001	+	58.3001i	−1.91174	+	1.91174i
$931$	−3.43441	+	33.5075i	−0.112558	+	1.09817i
$932$	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	$-0.100225\pi$
$938$	24.0119	−	50.5096i	0.784016	−	1.64920i
$939$	36.1180			1.17867
$940$			52.7259i			1.71973i
$941$	32.7842	+	32.7842i	1.06874	+	1.06874i	0.997456	+	0.0712788i	$0.0227080\pi$
$941$	32.7842	+	32.7842i	1.06874	+	1.06874i	0.0712788	+	0.997456i	$0.477292\pi$
$942$	−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	0.0256213	−	0.999672i	$-0.491844\pi$
$947$	−29.9748	−	29.9748i	−0.974050	−	0.974050i	−0.999672	+	0.0256213i	$0.991844\pi$
$948$	−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	$-0.768290\pi$
$953$		−	41.0785i		−	1.33066i	0.746548	−	0.665332i	$-0.231710\pi$
$954$	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	−0.649347	+	0.760492i	$0.724958\pi$
$967$	−43.8412	+	43.8412i	−1.40984	+	1.40984i	−0.760492	+	0.649347i	$0.775042\pi$
$968$	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
$973$	−3.79615	+	7.98528i	−0.121699	+	0.255996i
$974$			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	−0.585986	−	0.810321i	$-0.699292\pi$
$977$	7.01207	−	7.01207i	0.224336	−	0.224336i	0.810321	+	0.585986i	$0.199292\pi$
$978$		−	55.2022i		−	1.76517i
$979$	−5.06895			−0.162004
$980$	43.9320	+	4.50289i	1.40336	+	0.143839i
$981$	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	0.0144754	−	0.999895i	$-0.495392\pi$
$983$	31.8034	−	31.8034i	1.01437	−	1.01437i	0.999895	−	0.0144754i	$-0.00460781\pi$
$984$	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
$994$	18.3664	−	38.6341i	0.582546	−	1.22540i
$995$	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.83.2	yes	12
3.2	odd	2		819.2.y.h.811.5		12
7.2	even	3		637.2.bc.a.31.5		24
7.3	odd	6		637.2.bc.a.460.1		24
7.4	even	3		637.2.bc.a.460.2		24
7.5	odd	6		637.2.bc.a.31.6		24
7.6	odd	2	inner	91.2.i.a.83.1	yes	12
13.8	odd	4	inner	91.2.i.a.34.2	yes	12
21.20	even	2		819.2.y.h.811.6		12
39.8	even	4		819.2.y.h.307.6		12
91.34	even	4	inner	91.2.i.a.34.1	✓	12
91.47	even	12		637.2.bc.a.619.2		24
91.60	odd	12		637.2.bc.a.411.6		24
91.73	even	12		637.2.bc.a.411.5		24
91.86	odd	12		637.2.bc.a.619.1		24
273.125	odd	4		819.2.y.h.307.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.1	✓	12	91.34	even	4	inner
91.2.i.a.34.2	yes	12	13.8	odd	4	inner
91.2.i.a.83.1	yes	12	7.6	odd	2	inner
91.2.i.a.83.2	yes	12	1.1	even	1	trivial
637.2.bc.a.31.5		24	7.2	even	3
637.2.bc.a.31.6		24	7.5	odd	6
637.2.bc.a.411.5		24	91.73	even	12
637.2.bc.a.411.6		24	91.60	odd	12
637.2.bc.a.460.1		24	7.3	odd	6
637.2.bc.a.460.2		24	7.4	even	3
637.2.bc.a.619.1		24	91.86	odd	12
637.2.bc.a.619.2		24	91.47	even	12
819.2.y.h.307.5		12	273.125	odd	4
819.2.y.h.307.6		12	39.8	even	4
819.2.y.h.811.5		12	3.2	odd	2
819.2.y.h.811.6		12	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.45161 + 1.45161i) q^{2} +1.81964i q^{3} -2.21432i q^{4} +(2.01464 + 2.01464i) q^{5} +(-2.64141 - 2.64141i) q^{6} +(-2.38948 - 1.13594i) q^{7} +(0.311108 + 0.311108i) q^{8} -0.311108 q^{9} +O(q^{10})\)	\(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} +(-2.38948 - 1.13594i) 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} +(2.06702 - 4.34801i) 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} +(-2.51534 + 5.29108i) 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} +(0.743387 + 0.353401i) 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} +(13.9759 + 6.64405i) 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} +(-9.62789 - 4.57703i) 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} +(6.77519 + 6.71541i) 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} +(-14.2953 - 1.46522i) 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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