LMFDB - Embedded newform 231.2.s.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(8,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("231.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.s (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.1
Character	$\chi$	$=$	231.8
Dual form			231.2.s.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24267 + 1.62939i) q^{2} +(1.07372 - 1.35909i) q^{3} +(1.75661 - 5.40628i) q^{4} +(0.476086 - 0.655276i) q^{5} +(-0.193509 + 4.79750i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(3.15622 + 9.71386i) q^{8} +(-0.694246 - 2.91857i) q^{9} +O(q^{10})$	\(q+(-2.24267 + 1.62939i) q^{2} +(1.07372 - 1.35909i) q^{3} +(1.75661 - 5.40628i) q^{4} +(0.476086 - 0.655276i) q^{5} +(-0.193509 + 4.79750i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(3.15622 + 9.71386i) q^{8} +(-0.694246 - 2.91857i) q^{9} +2.24530i q^{10} +(-2.36906 - 2.32111i) q^{11} +(-5.46151 - 8.19221i) q^{12} +(-1.09704 - 1.50995i) q^{13} +(2.63642 - 0.856624i) q^{14} +(-0.379395 - 1.35063i) q^{15} +(-13.7084 - 9.95972i) q^{16} +(-3.37944 - 2.45531i) q^{17} +(6.31246 + 5.41418i) q^{18} +(2.67826 - 0.870219i) q^{19} +(-2.70631 - 3.72491i) q^{20} +(-1.44115 + 0.960772i) q^{21} +(9.09502 + 1.34535i) q^{22} +1.65622i q^{23} +(16.5909 + 6.14039i) q^{24} +(1.34236 + 4.13135i) q^{25} +(4.92061 + 1.59880i) q^{26} +(-4.71202 - 2.19018i) q^{27} +(-3.34126 + 4.59885i) q^{28} +(1.60946 - 4.95341i) q^{29} +(3.05156 + 2.41082i) q^{30} +(5.40322 - 3.92567i) q^{31} +26.5442 q^{32} +(-5.69831 + 0.727538i) q^{33} +11.5796 q^{34} +(-0.655276 + 0.476086i) q^{35} +(-16.9981 - 1.37348i) q^{36} +(-1.12129 + 3.45097i) q^{37} +(-4.58852 + 6.31555i) q^{38} +(-3.23007 - 0.130286i) q^{39} +(7.86789 + 2.55643i) q^{40} +(-0.885423 - 2.72505i) q^{41} +(1.66655 - 4.50290i) q^{42} -2.68617i q^{43} +(-16.7101 + 8.73052i) q^{44} +(-2.24299 - 0.934564i) q^{45} +(-2.69864 - 3.71435i) q^{46} +(10.2469 - 3.32942i) q^{47} +(-28.2551 + 7.93695i) q^{48} +(0.809017 + 0.587785i) q^{49} +(-9.74206 - 7.07802i) q^{50} +(-6.96556 + 1.95665i) q^{51} +(-10.0903 + 3.27853i) q^{52} +(2.05261 + 2.82517i) q^{53} +(14.1362 - 2.76588i) q^{54} +(-2.64884 + 0.447340i) q^{55} -10.2138i q^{56} +(1.69300 - 4.57436i) q^{57} +(4.46157 + 13.7313i) q^{58} +(-2.61461 - 0.849537i) q^{59} +(-7.96830 - 0.321404i) q^{60} +(-4.92684 + 6.78121i) q^{61} +(-5.72118 + 17.6080i) q^{62} +(-0.241619 + 2.99025i) q^{63} +(-32.1130 + 23.3315i) q^{64} -1.51172 q^{65} +(11.5940 - 10.9164i) q^{66} -4.13041 q^{67} +(-19.2104 + 13.9572i) q^{68} +(2.25095 + 1.77832i) q^{69} +(0.693835 - 2.13541i) q^{70} +(5.27422 - 7.25934i) q^{71} +(26.1593 - 15.9555i) q^{72} +(14.1884 + 4.61010i) q^{73} +(-3.10832 - 9.56641i) q^{74} +(7.05619 + 2.61153i) q^{75} -16.0080i q^{76} +(1.53585 + 2.93959i) q^{77} +(7.45628 - 4.97088i) q^{78} +(-5.55936 - 7.65180i) q^{79} +(-13.0527 + 4.24109i) q^{80} +(-8.03604 + 4.05241i) q^{81} +(6.42590 + 4.66869i) q^{82} +(13.1751 + 9.57228i) q^{83} +(2.66267 + 9.47896i) q^{84} +(-3.21781 + 1.04553i) q^{85} +(4.37684 + 6.02420i) q^{86} +(-5.00401 - 7.50598i) q^{87} +(15.0697 - 30.3387i) q^{88} +10.7874i q^{89} +(6.55305 - 1.55879i) q^{90} +(0.576750 + 1.77505i) q^{91} +(8.95398 + 2.90933i) q^{92} +(0.466217 - 11.5585i) q^{93} +(-17.5555 + 24.1630i) q^{94} +(0.704847 - 2.16930i) q^{95} +(28.5010 - 36.0759i) q^{96} +(-4.52367 + 3.28664i) q^{97} -2.77209 q^{98} +(-5.12960 + 8.52568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−2.24267	+	1.62939i	−1.58581	+	1.15216i	−0.676175	+	0.736741i	$0.736364\pi$
$2$	−2.24267	+	1.62939i	−1.58581	+	1.15216i	−0.909632	+	0.415415i	$0.863636\pi$
$3$	1.07372	−	1.35909i	0.619913	−	0.784670i
$3$	1.07372	−	1.35909i	0.619913	−	0.784670i
$4$	1.75661	−	5.40628i	0.878303	−	2.70314i
$5$	0.476086	−	0.655276i	0.212912	−	0.293048i	−0.689182	−	0.724589i	$-0.742030\pi$
$5$	0.476086	−	0.655276i	0.212912	−	0.293048i	0.902094	+	0.431540i	$0.142030\pi$
$6$	−0.193509	+	4.79750i	−0.0789996	+	1.95857i
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$8$	3.15622	+	9.71386i	1.11589	+	3.43437i
$9$	−0.694246	−	2.91857i	−0.231415	−	0.972855i
$10$			2.24530i			0.710026i
$11$	−2.36906	−	2.32111i	−0.714298	−	0.699841i
$11$	−2.36906	−	2.32111i	−0.714298	−	0.699841i
$12$	−5.46151	−	8.19221i	−1.57660	−	2.36489i
$13$	−1.09704	−	1.50995i	−0.304265	−	0.418785i	0.629317	−	0.777149i	$-0.283335\pi$
$13$	−1.09704	−	1.50995i	−0.304265	−	0.418785i	−0.933582	+	0.358364i	$0.883335\pi$
$14$	2.63642	−	0.856624i	0.704612	−	0.228942i
$15$	−0.379395	−	1.35063i	−0.0979593	−	0.348730i
$16$	−13.7084	−	9.95972i	−3.42709	−	2.48993i
$17$	−3.37944	−	2.45531i	−0.819635	−	0.595500i	0.0969731	−	0.995287i	$-0.469084\pi$
$17$	−3.37944	−	2.45531i	−0.819635	−	0.595500i	−0.916608	+	0.399787i	$0.869084\pi$
$18$	6.31246	+	5.41418i	1.48786	+	1.27613i
$19$	2.67826	−	0.870219i	0.614434	−	0.199642i	0.0147668	−	0.999891i	$-0.495299\pi$
$19$	2.67826	−	0.870219i	0.614434	−	0.199642i	0.599668	+	0.800249i	$0.295299\pi$
$20$	−2.70631	−	3.72491i	−0.605148	−	0.832915i
$21$	−1.44115	+	0.960772i	−0.314485	+	0.209658i
$22$	9.09502	+	1.34535i	1.93907	+	0.286830i
$23$			1.65622i			0.345346i	0.984979	+	0.172673i	$0.0552403\pi$
$23$			1.65622i			0.345346i	−0.984979	+	0.172673i	$0.944760\pi$
$24$	16.5909	+	6.14039i	3.38660	+	1.25340i
$25$	1.34236	+	4.13135i	0.268471	+	0.826270i
$26$	4.92061	+	1.59880i	0.965011	+	0.313551i
$27$	−4.71202	−	2.19018i	−0.906828	−	0.421501i
$28$	−3.34126	+	4.59885i	−0.631439	+	0.869101i
$29$	1.60946	−	4.95341i	0.298869	−	0.919825i	−0.683025	−	0.730395i	$-0.739336\pi$
$29$	1.60946	−	4.95341i	0.298869	−	0.919825i	0.981894	−	0.189430i	$-0.0606640\pi$
$30$	3.05156	+	2.41082i	0.557136	+	0.440154i
$31$	5.40322	−	3.92567i	0.970448	−	0.705071i	0.0148941	−	0.999889i	$-0.495259\pi$
$31$	5.40322	−	3.92567i	0.970448	−	0.705071i	0.955554	+	0.294818i	$0.0952589\pi$
$32$	26.5442			4.69239
$33$	−5.69831	+	0.727538i	−0.991948	+	0.126648i
$34$	11.5796			1.98589
$35$	−0.655276	+	0.476086i	−0.110762	+	0.0804732i
$36$	−16.9981	−	1.37348i	−2.83301	−	0.228913i
$37$	−1.12129	+	3.45097i	−0.184339	+	0.567336i	−0.999936	−	0.0112833i	$-0.996408\pi$
$37$	−1.12129	+	3.45097i	−0.184339	+	0.567336i	0.815598	+	0.578619i	$0.196408\pi$
$38$	−4.58852	+	6.31555i	−0.744356	+	1.02452i
$39$	−3.23007	−	0.130286i	−0.517226	−	0.0208625i
$40$	7.86789	+	2.55643i	1.24402	+	0.404207i
$41$	−0.885423	−	2.72505i	−0.138280	−	0.425582i	0.857806	−	0.513974i	$-0.171827\pi$
$41$	−0.885423	−	2.72505i	−0.138280	−	0.425582i	−0.996086	+	0.0883921i	$0.971827\pi$
$42$	1.66655	−	4.50290i	0.257154	−	0.694812i
$43$		−	2.68617i		−	0.409638i	−0.978800	−	0.204819i	$-0.934339\pi$
$43$		−	2.68617i		−	0.409638i	0.978800	−	0.204819i	$-0.0656605\pi$
$44$	−16.7101	+	8.73052i	−2.51914	+	1.31617i
$45$	−2.24299	−	0.934564i	−0.334365	−	0.139317i
$46$	−2.69864	−	3.71435i	−0.397892	−	0.547652i
$47$	10.2469	−	3.32942i	1.49466	−	0.485646i	0.556207	−	0.831044i	$-0.312256\pi$
$47$	10.2469	−	3.32942i	1.49466	−	0.485646i	0.938456	+	0.345398i	$0.112256\pi$
$48$	−28.2551	+	7.93695i	−4.07828	+	1.14560i
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	−9.74206	−	7.07802i	−1.37774	−	1.00098i
$51$	−6.96556	+	1.95665i	−0.975373	+	0.273985i
$52$	−10.0903	+	3.27853i	−1.39927	+	0.454650i
$53$	2.05261	+	2.82517i	0.281948	+	0.388068i	0.926378	−	0.376596i	$-0.122905\pi$
$53$	2.05261	+	2.82517i	0.281948	+	0.388068i	−0.644430	+	0.764663i	$0.722905\pi$
$54$	14.1362	−	2.76588i	1.92369	−	0.376389i
$55$	−2.64884	+	0.447340i	−0.357170	+	0.0603193i
$56$		−	10.2138i		−	1.36487i
$57$	1.69300	−	4.57436i	0.224243	−	0.605889i
$58$	4.46157	+	13.7313i	0.585833	+	1.80301i
$59$	−2.61461	−	0.849537i	−0.340393	−	0.110600i	0.133832	−	0.991004i	$-0.457272\pi$
$59$	−2.61461	−	0.849537i	−0.340393	−	0.110600i	−0.474225	+	0.880404i	$0.657272\pi$
$60$	−7.96830	−	0.321404i	−1.02870	−	0.0414931i
$61$	−4.92684	+	6.78121i	−0.630817	+	0.868245i	−0.998084	−	0.0618703i	$-0.980293\pi$
$61$	−4.92684	+	6.78121i	−0.630817	+	0.868245i	0.367267	+	0.930116i	$0.380293\pi$
$62$	−5.72118	+	17.6080i	−0.726590	+	2.23621i
$63$	−0.241619	+	2.99025i	−0.0304411	+	0.376737i
$64$	−32.1130	+	23.3315i	−4.01413	+	2.91644i
$65$	−1.51172			−0.187506
$66$	11.5940	−	10.9164i	1.42712	−	1.34372i
$67$	−4.13041			−0.504610			−0.252305	−	0.967648i	$-0.581189\pi$
$67$	−4.13041			−0.504610			−0.252305	+	0.967648i	$0.581189\pi$
$68$	−19.2104	+	13.9572i	−2.32960	+	1.69256i
$69$	2.25095	+	1.77832i	0.270983	+	0.214084i
$70$	0.693835	−	2.13541i	0.0829292	−	0.255230i
$71$	5.27422	−	7.25934i	0.625935	−	0.861525i	−0.371834	−	0.928299i	$-0.621271\pi$
$71$	5.27422	−	7.25934i	0.625935	−	0.861525i	0.997768	+	0.0667744i	$0.0212708\pi$
$72$	26.1593	−	15.9555i	3.08291	−	1.88037i
$73$	14.1884	+	4.61010i	1.66063	+	0.539572i	0.981004	−	0.193986i	$-0.0621417\pi$
$73$	14.1884	+	4.61010i	1.66063	+	0.539572i	0.679627	+	0.733558i	$0.262142\pi$
$74$	−3.10832	−	9.56641i	−0.361334	−	1.11207i
$75$	7.05619	+	2.61153i	0.814778	+	0.301554i
$76$		−	16.0080i		−	1.83625i
$77$	1.53585	+	2.93959i	0.175026	+	0.334997i
$78$	7.45628	−	4.97088i	0.844257	−	0.562841i
$79$	−5.55936	−	7.65180i	−0.625477	−	0.860895i	0.372260	−	0.928128i	$-0.378583\pi$
$79$	−5.55936	−	7.65180i	−0.625477	−	0.860895i	−0.997737	+	0.0672333i	$0.978583\pi$
$80$	−13.0527	+	4.24109i	−1.45934	+	0.474168i
$81$	−8.03604	+	4.05241i	−0.892894	+	0.450267i
$82$	6.42590	+	4.66869i	0.709622	+	0.515570i
$83$	13.1751	+	9.57228i	1.44616	+	1.05069i	0.986710	+	0.162488i	$0.0519520\pi$
$83$	13.1751	+	9.57228i	1.44616	+	1.05069i	0.459446	+	0.888206i	$0.348048\pi$
$84$	2.66267	+	9.47896i	0.290521	+	1.03424i
$85$	−3.21781	+	1.04553i	−0.349020	+	0.113404i
$86$	4.37684	+	6.02420i	0.471966	+	0.649606i
$87$	−5.00401	−	7.50598i	−0.536486	−	0.804725i
$88$	15.0697	−	30.3387i	1.60643	−	3.23411i
$89$			10.7874i			1.14347i	0.820439	+	0.571733i	$0.193729\pi$
$89$			10.7874i			1.14347i	−0.820439	+	0.571733i	$0.806271\pi$
$90$	6.55305	−	1.55879i	0.690752	−	0.164311i
$91$	0.576750	+	1.77505i	0.0604598	+	0.186076i
$92$	8.95398	+	2.90933i	0.933517	+	0.303318i
$93$	0.466217	−	11.5585i	0.0483445	−	1.19856i
$94$	−17.5555	+	24.1630i	−1.81071	+	2.49223i
$95$	0.704847	−	2.16930i	0.0723158	−	0.222565i
$96$	28.5010	−	36.0759i	2.90887	−	3.68198i
$97$	−4.52367	+	3.28664i	−0.459309	+	0.333708i	−0.793260	−	0.608883i	$-0.791618\pi$
$97$	−4.52367	+	3.28664i	−0.459309	+	0.333708i	0.333951	+	0.942590i	$0.391618\pi$
$98$	−2.77209			−0.280024
$99$	−5.12960	+	8.52568i	−0.515544	+	0.856863i
$100$	24.6932			2.46932
$101$	4.67034	−	3.39320i	0.464716	−	0.337636i	−0.330662	−	0.943749i	$-0.607272\pi$
$101$	4.67034	−	3.39320i	0.464716	−	0.337636i	0.795379	+	0.606113i	$0.207272\pi$
$102$	12.4333	−	15.7378i	1.23108	−	1.55827i
$103$	−1.10838	+	3.41126i	−0.109212	+	0.336121i	−0.990696	−	0.136094i	$-0.956545\pi$
$103$	−1.10838	+	3.41126i	−0.109212	+	0.336121i	0.881484	+	0.472214i	$0.156545\pi$
$104$	11.2049	−	15.4223i	1.09873	−	1.51228i
$105$	−0.0565405	+	1.40176i	−0.00551778	+	0.136798i
$106$	−9.20665	−	2.99142i	−0.894229	−	0.290553i
$107$	0.840291	+	2.58615i	0.0812340	+	0.250012i	0.983422	−	0.181330i	$-0.0580402\pi$
$107$	0.840291	+	2.58615i	0.0812340	+	0.250012i	−0.902188	+	0.431342i	$0.858040\pi$
$108$	−20.1179	+	21.6272i	−1.93584	+	2.08108i
$109$			4.49322i			0.430373i	0.976573	+	0.215186i	$0.0690359\pi$
$109$			4.49322i			0.430373i	−0.976573	+	0.215186i	$0.930964\pi$
$110$	5.21159	−	5.31925i	0.496905	−	0.507170i
$111$	3.48623	+	5.22931i	0.330898	+	0.496344i
$112$	9.95972	+	13.7084i	0.941105	+	1.29532i
$113$	−3.78927	+	1.23121i	−0.356464	+	0.115822i	−0.481774	−	0.876295i	$-0.660007\pi$
$113$	−3.78927	+	1.23121i	−0.356464	+	0.115822i	0.125310	+	0.992118i	$0.460007\pi$
$114$	3.65661	+	13.0173i	0.342473	+	1.21919i
$115$	1.08528	+	0.788503i	0.101203	+	0.0735282i
$116$	−23.9523	−	17.4024i	−2.22392	−	1.61577i
$117$	−3.64527	+	4.25007i	−0.337005	+	0.392919i
$118$	7.24793	−	2.35500i	0.667226	−	0.216795i
$119$	2.45531	+	3.37944i	0.225078	+	0.309793i
$120$	11.9223	−	7.94827i	1.08836	−	0.725574i
$121$	0.224891	+	10.9977i	0.0204446	+	0.999791i
$122$		−	23.2358i		−	2.10367i
$123$	−4.65429	−	1.72258i	−0.419663	−	0.155320i
$124$	−11.7319	−	36.1072i	−1.05356	−	3.24252i
$125$	7.19786	+	2.33873i	0.643796	+	0.209182i
$126$	−4.33043	−	7.09984i	−0.385786	−	0.632504i
$127$	1.44518	−	1.98911i	0.128239	−	0.176505i	−0.740070	−	0.672530i	$-0.765208\pi$
$127$	1.44518	−	1.98911i	0.128239	−	0.176505i	0.868308	+	0.496025i	$0.165208\pi$
$128$	17.5975	−	54.1596i	1.55542	−	4.78708i
$129$	−3.65075	−	2.88420i	−0.321431	−	0.253940i
$130$	3.39029	−	2.46319i	0.297348	−	0.216036i
$131$	−12.6026			−1.10109			−0.550546	−	0.834805i	$-0.685580\pi$
$131$	−12.6026			−1.10109			−0.550546	+	0.834805i	$0.685580\pi$
$132$	−6.07640	+	32.0846i	−0.528883	+	2.79261i
$133$	−2.81609			−0.244186
$134$	9.26314	−	6.73006i	0.800213	−	0.581389i
$135$	−3.67850	+	2.04496i	−0.316595	+	0.176002i
$136$	13.1842	−	40.5769i	1.13054	−	3.47944i
$137$	−3.93045	+	5.40980i	−0.335801	+	0.462190i	−0.943209	−	0.332200i	$-0.892209\pi$
$137$	−3.93045	+	5.40980i	−0.335801	+	0.462190i	0.607408	+	0.794390i	$0.292209\pi$
$138$	−7.94572	−	0.320493i	−0.676385	−	0.0272822i
$139$	2.83277	+	0.920423i	0.240272	+	0.0780692i	0.426678	−	0.904404i	$-0.359684\pi$
$139$	2.83277	+	0.920423i	0.240272	+	0.0780692i	−0.186405	+	0.982473i	$0.559684\pi$
$140$	1.42279	+	4.37890i	0.120248	+	0.370084i
$141$	6.47733	−	17.5013i	0.545490	−	1.47388i
$142$			24.8741i			2.08739i
$143$	−0.905800	+	6.12352i	−0.0757468	+	0.512074i
$144$	−19.5511	+	46.9233i	−1.62926	+	3.91027i
$145$	−2.47961	−	3.41289i	−0.205920	−	0.283425i
$146$	−39.3317	+	12.7796i	−3.25511	+	1.05765i
$147$	1.66751	−	0.468409i	0.137534	−	0.0386337i
$148$	16.6872	+	12.1240i	1.37168	+	0.996586i
$149$	5.64463	+	4.10106i	0.462426	+	0.335972i	0.794482	−	0.607287i	$-0.207742\pi$
$149$	5.64463	+	4.10106i	0.462426	+	0.335972i	−0.332056	+	0.943260i	$0.607742\pi$
$150$	−20.0799	+	5.64051i	−1.63952	+	0.460545i
$151$	16.9106	−	5.49460i	1.37617	−	0.447144i	0.474760	−	0.880115i	$-0.342535\pi$
$151$	16.9106	−	5.49460i	1.37617	−	0.447144i	0.901408	+	0.432971i	$0.142535\pi$
$152$	16.9064	+	23.2696i	1.37129	+	1.88742i
$153$	−4.81981	+	11.5677i	−0.389659	+	0.935194i
$154$	−8.23415	−	4.09002i	−0.663526	−	0.329583i
$155$		−	5.40956i		−	0.434506i
$156$	−6.37833	+	17.2338i	−0.510675	+	1.37981i
$157$	1.32884	+	4.08974i	0.106053	+	0.326397i	0.989976	−	0.141235i	$-0.0451073\pi$
$157$	1.32884	+	4.08974i	0.106053	+	0.326397i	−0.883923	+	0.467632i	$0.845107\pi$
$158$	24.9356	+	8.10207i	1.98377	+	0.644566i
$159$	6.04359	+	0.243770i	0.479288	+	0.0193322i
$160$	12.6373	−	17.3937i	0.999066	−	1.37510i
$161$	0.511800	−	1.57516i	0.0403355	−	0.124140i
$162$	11.4192	−	22.1821i	0.897179	−	1.74279i
$163$	7.21544	−	5.24233i	0.565157	−	0.410611i	−0.268186	−	0.963367i	$-0.586424\pi$
$163$	7.21544	−	5.24233i	0.565157	−	0.410611i	0.833343	+	0.552757i	$0.186424\pi$
$164$	−16.2877			−1.27186
$165$	−2.23614	+	4.08033i	−0.174084	+	0.317653i
$166$	−45.1444			−3.50389
$167$	7.10004	−	5.15848i	0.549418	−	0.399175i	−0.278153	−	0.960537i	$-0.589722\pi$
$167$	7.10004	−	5.15848i	0.549418	−	0.399175i	0.827571	+	0.561361i	$0.189722\pi$
$168$	−13.8814	−	10.9667i	−1.07097	−	0.846101i
$169$	2.94078	−	9.05078i	0.226213	−	0.696214i
$170$	5.51290	−	7.58785i	0.422820	−	0.581962i
$171$	−4.39916	−	7.21252i	−0.336412	−	0.551555i
$172$	−14.5222	−	4.71855i	−1.10731	−	0.359786i
$173$	1.82550	+	5.61832i	0.138790	+	0.427153i	0.996160	−	0.0875479i	$-0.0279031\pi$
$173$	1.82550	+	5.61832i	0.138790	+	0.427153i	−0.857370	+	0.514701i	$0.827903\pi$
$174$	23.4526	+	8.67992i	1.77793	+	0.658023i
$175$		−	4.34396i		−	0.328372i
$176$	9.35836	+	55.4138i	0.705413	+	4.17698i
$177$	−3.96195	+	2.64132i	−0.297799	+	0.198534i
$178$	−17.5770	−	24.1927i	−1.31745	−	1.81332i
$179$	11.2075	−	3.64154i	0.837689	−	0.272182i	0.141409	−	0.989951i	$-0.454837\pi$
$179$	11.2075	−	3.64154i	0.837689	−	0.272182i	0.696281	+	0.717770i	$0.254837\pi$
$180$	−8.99255	+	10.4845i	−0.670265	+	0.781471i
$181$	−15.5729	−	11.3144i	−1.15752	−	0.840989i	−0.168060	−	0.985777i	$-0.553750\pi$
$181$	−15.5729	−	11.3144i	−1.15752	−	0.840989i	−0.989463	+	0.144787i	$0.953750\pi$
$182$	−4.18572	−	3.04110i	−0.310266	−	0.225422i
$183$	3.92622	+	13.9771i	0.290235	+	1.03322i
$184$	−16.0883	+	5.22740i	−1.18604	+	0.385369i
$185$	1.72751	+	2.37771i	0.127009	+	0.174813i
$186$	17.7879	+	26.6816i	1.30427	+	1.95639i
$187$	2.30706	+	13.6608i	0.168709	+	0.998979i
$188$		−	61.2460i		−	4.46682i
$189$	3.80459	+	3.53908i	0.276743	+	0.257430i
$190$	1.95390	+	6.01349i	0.141751	+	0.436264i
$191$	−1.50202	−	0.488035i	−0.108682	−	0.0353130i	0.254171	−	0.967159i	$-0.418197\pi$
$191$	−1.50202	−	0.488035i	−0.108682	−	0.0353130i	−0.362853	+	0.931846i	$0.618197\pi$
$192$	−2.77087	+	68.6960i	−0.199971	+	4.95770i
$193$	0.406739	−	0.559828i	0.0292777	−	0.0402973i	−0.794127	−	0.607752i	$-0.792072\pi$
$193$	0.406739	−	0.559828i	0.0292777	−	0.0402973i	0.823405	+	0.567454i	$0.192072\pi$
$194$	4.78987	−	14.7417i	0.343892	−	1.05839i
$195$	−1.62317	+	2.05456i	−0.116237	+	0.147130i
$196$	4.59885	−	3.34126i	0.328489	−	0.238662i
$197$	−21.7819			−1.55190			−0.775949	−	0.630796i	$-0.782728\pi$
$197$	−21.7819			−1.55190			−0.775949	+	0.630796i	$0.782728\pi$
$198$	−2.38770	−	27.4784i	−0.169686	−	1.95281i
$199$	23.1966			1.64436			0.822182	−	0.569224i	$-0.192756\pi$
$199$	23.1966			1.64436			0.822182	+	0.569224i	$0.192756\pi$
$200$	−35.8946	+	26.0789i	−2.53813	+	1.84406i
$201$	−4.43491	+	5.61359i	−0.312814	+	0.395952i
$202$	−4.94517	+	15.2197i	−0.347941	+	1.07085i
$203$	−3.06138	+	4.21362i	−0.214866	+	0.295738i
$204$	−1.65757	+	41.0948i	−0.116053	+	2.87721i
$205$	−2.20720	−	0.717162i	−0.154157	−	0.0500888i
$206$	−3.07254	−	9.45631i	−0.214074	−	0.658853i
$207$	4.83379	−	1.14982i	0.335971	−	0.0799183i
$208$			31.6252i			2.19281i
$209$	−8.36483	−	4.15493i	−0.578607	−	0.287403i
$210$	−2.15722	−	3.23581i	−0.148862	−	0.223292i
$211$	−4.69416	−	6.46096i	−0.323159	−	0.444791i	0.616269	−	0.787536i	$-0.288643\pi$
$211$	−4.69416	−	6.46096i	−0.323159	−	0.444791i	−0.939428	+	0.342745i	$0.888643\pi$
$212$	18.8793	−	6.13426i	1.29664	−	0.421302i
$213$	−4.20305	−	14.9626i	−0.287988	−	1.02522i
$214$	−6.09835	−	4.43071i	−0.416875	−	0.302877i
$215$	−1.76018	−	1.27885i	−0.120044	−	0.0872167i
$216$	6.40294	−	52.6846i	0.435665	−	3.58473i
$217$	−6.35187	+	2.06385i	−0.431193	+	0.140103i
$218$	−7.32123	−	10.0768i	−0.495857	−	0.682488i
$219$	21.5000	−	14.3334i	1.45283	−	0.968561i
$220$	−2.23453	+	15.1062i	−0.150652	+	1.01846i
$221$			7.79636i			0.524440i
$222$	−16.3391	−	6.04718i	−1.09661	−	0.405860i
$223$	−6.89290	−	21.2142i	−0.461583	−	1.42061i	−0.863230	−	0.504811i	$-0.831562\pi$
$223$	−6.89290	−	21.2142i	−0.461583	−	1.42061i	0.401647	−	0.915795i	$-0.368438\pi$
$224$	−25.2450	−	8.20260i	−1.68675	−	0.548059i
$225$	11.1257	−	6.78593i	0.741712	−	0.452395i
$226$	6.49195	−	8.93540i	0.431838	−	0.594374i
$227$	2.01610	−	6.20492i	0.133813	−	0.411835i	−0.861590	−	0.507604i	$-0.830531\pi$
$227$	2.01610	−	6.20492i	0.133813	−	0.411835i	0.995404	+	0.0957695i	$0.0305312\pi$
$228$	−21.7563	−	17.1882i	−1.44085	−	1.13831i
$229$	1.14416	−	0.831278i	0.0756079	−	0.0549324i	−0.549339	−	0.835599i	$-0.685121\pi$
$229$	1.14416	−	0.831278i	0.0756079	−	0.0549324i	0.624947	+	0.780667i	$0.285121\pi$
$230$	−3.71871			−0.245204
$231$	5.64423	+	1.06894i	0.371363	+	0.0703313i
$232$	53.1965			3.49252
$233$	10.9568	−	7.96056i	0.717802	−	0.521514i	−0.167879	−	0.985808i	$-0.553692\pi$
$233$	10.9568	−	7.96056i	0.717802	−	0.521514i	0.885681	+	0.464294i	$0.153692\pi$
$234$	1.25010	−	15.4711i	0.0817213	−	1.01138i
$235$	2.69671	−	8.29963i	0.175914	−	0.541408i
$236$	−9.18566	+	12.6430i	−0.597936	+	0.822988i
$237$	−16.3687	−	0.660236i	−1.06326	−	0.0428869i
$238$	−11.0129	−	3.57830i	−0.713859	−	0.231947i
$239$	−5.71339	−	17.5840i	−0.369569	−	1.13742i	−0.947070	−	0.321026i	$-0.895972\pi$
$239$	−5.71339	−	17.5840i	−0.369569	−	1.13742i	0.577502	−	0.816389i	$-0.304028\pi$
$240$	−8.25097	+	22.2936i	−0.532598	+	1.43904i
$241$			13.7496i			0.885688i	0.896599	+	0.442844i	$0.146030\pi$
$241$			13.7496i			0.885688i	−0.896599	+	0.442844i	$0.853970\pi$
$242$	−18.4240	−	24.2978i	−1.18434	−	1.56192i
$243$	−3.12089	+	15.2729i	−0.200205	+	0.979754i
$244$	28.0066	+	38.5478i	1.79294	+	2.46777i
$245$	0.770323	−	0.250293i	0.0492141	−	0.0159906i
$246$	13.2448	−	3.72050i	0.844457	−	0.237210i
$247$	−4.25215	−	3.08937i	−0.270558	−	0.196572i
$248$	55.1872	+	40.0959i	3.50439	+	2.54609i
$249$	27.1560	−	7.62819i	1.72094	−	0.483417i
$250$	−19.9531	+	6.48317i	−1.26195	+	0.410031i
$251$	12.6854	+	17.4600i	0.800698	+	1.10207i	0.992693	+	0.120670i	$0.0385043\pi$
$251$	12.6854	+	17.4600i	0.800698	+	1.10207i	−0.191995	+	0.981396i	$0.561496\pi$
$252$	15.7417	+	6.55895i	0.991634	+	0.413175i
$253$	3.84427	−	3.92368i	0.241687	−	0.246680i
$254$			6.81569i			0.427654i
$255$	−2.03406	+	5.49589i	−0.127378	+	0.344166i
$256$	24.2498	+	74.6332i	1.51561	+	4.66457i
$257$	−11.7649	−	3.82263i	−0.733872	−	0.238449i	−0.0818446	−	0.996645i	$-0.526081\pi$
$257$	−11.7649	−	3.82263i	−0.733872	−	0.238449i	−0.652027	+	0.758196i	$0.726081\pi$
$258$	12.8869	+	0.519798i	0.802305	+	0.0323612i
$259$	2.13282	−	2.93557i	0.132527	−	0.182408i
$260$	−2.65549	+	8.17277i	−0.164687	+	0.506854i
$261$	−15.5742	−	1.25843i	−0.964019	−	0.0778948i
$262$	28.2634	−	20.5346i	1.74612	−	1.26863i
$263$	3.26707			0.201456			0.100728	−	0.994914i	$-0.467883\pi$
$263$	3.26707			0.201456			0.100728	+	0.994914i	$0.467883\pi$
$264$	−25.0523	−	53.0563i	−1.54186	−	3.26539i
$265$	2.82849			0.173753
$266$	6.31555	−	4.58852i	0.387231	−	0.281340i
$267$	14.6611	+	11.5827i	0.897245	+	0.708850i
$268$	−7.25550	+	22.3301i	−0.443200	+	1.36403i
$269$	2.94916	−	4.05918i	0.179814	−	0.247492i	−0.709590	−	0.704615i	$-0.751120\pi$
$269$	2.94916	−	4.05918i	0.179814	−	0.247492i	0.889404	+	0.457122i	$0.151120\pi$
$270$	4.91761	−	10.5799i	0.299276	−	0.643871i
$271$	28.8945	+	9.38839i	1.75522	+	0.570304i	0.996687	−	0.0813355i	$-0.0259185\pi$
$271$	28.8945	+	9.38839i	1.75522	+	0.570304i	0.758529	+	0.651640i	$0.225919\pi$
$272$	21.8725	+	67.3166i	1.32621	+	4.08167i
$273$	3.03172	+	1.12206i	0.183488	+	0.0679100i
$274$		−	18.5366i		−	1.11984i
$275$	6.40919	−	12.9032i	0.386489	−	0.778090i
$276$	13.5681	−	9.04546i	0.816704	−	0.544472i
$277$	−14.7170	−	20.2562i	−0.884258	−	1.21708i	−0.975223	−	0.221223i	$-0.928995\pi$
$277$	−14.7170	−	20.2562i	−0.884258	−	1.21708i	0.0909651	−	0.995854i	$-0.471005\pi$
$278$	−7.85270	+	2.55150i	−0.470974	+	0.153029i
$279$	−15.2085	−	13.0443i	−0.910509	−	0.780940i
$280$	−6.69283	−	4.86262i	−0.399973	−	0.290597i
$281$	−4.42055	−	3.21171i	−0.263708	−	0.191595i	0.448072	−	0.893997i	$-0.352111\pi$
$281$	−4.42055	−	3.21171i	−0.263708	−	0.191595i	−0.711780	+	0.702402i	$0.752111\pi$
$282$	13.9900	+	49.8038i	0.833094	+	2.96577i
$283$	−10.8331	+	3.51989i	−0.643961	+	0.209236i	−0.612750	−	0.790277i	$-0.709937\pi$
$283$	−10.8331	+	3.51989i	−0.643961	+	0.209236i	−0.0312115	+	0.999513i	$0.509937\pi$
$284$	−29.9813	−	41.2657i	−1.77906	−	2.44867i
$285$	−2.19146	−	3.28717i	−0.129811	−	0.194715i
$286$	−7.94622	−	15.2089i	−0.469870	−	0.899323i
$287$			2.86529i			0.169133i
$288$	−18.4282	−	77.4709i	−1.08589	−	4.56501i
$289$	0.138797	+	0.427172i	0.00816450	+	0.0251278i
$290$	11.1219	+	3.61372i	0.653099	+	0.212205i
$291$	−0.390325	+	9.67700i	−0.0228813	+	0.567276i
$292$	49.8470	−	68.6085i	2.91707	−	4.01501i
$293$	−1.13746	+	3.50076i	−0.0664514	+	0.204516i	−0.978769	−	0.204967i	$-0.934291\pi$
$293$	−1.13746	+	3.50076i	−0.0664514	+	0.204516i	0.912317	+	0.409484i	$0.134291\pi$
$294$	−2.97645	+	3.76752i	−0.173590	+	0.219726i
$295$	−1.80146	+	1.30884i	−0.104885	+	0.0762034i
$296$	−37.0613			−2.15414
$297$	6.07940	+	16.1258i	0.352762	+	0.935713i
$298$	−19.3413			−1.12041
$299$	2.50081	−	1.81694i	0.144626	−	0.105077i
$300$	26.5136	−	33.5603i	1.53076	−	1.93760i
$301$	−0.830073	+	2.55470i	−0.0478446	+	0.147251i
$302$	−28.9721	+	39.8767i	−1.66716	+	2.29464i
$303$	0.402981	−	9.99076i	0.0231506	−	0.573954i
$304$	−45.3817	−	14.7454i	−2.60282	−	0.845707i
$305$	2.09797	+	6.45688i	0.120129	+	0.369720i
$306$	−8.03912	−	33.7959i	−0.459566	−	1.93198i
$307$			28.4104i			1.62147i	0.585415	+	0.810734i	$0.300932\pi$
$307$			28.4104i			1.62147i	−0.585415	+	0.810734i	$0.699068\pi$
$308$	18.5901	−	3.13952i	1.05927	−	0.178891i
$309$	3.44610	+	5.16913i	0.196042	+	0.294061i
$310$	8.81430	+	12.1318i	0.500619	+	0.689043i
$311$	1.75844	−	0.571351i	0.0997119	−	0.0323984i	−0.258736	−	0.965948i	$-0.583306\pi$
$311$	1.75844	−	0.571351i	0.0997119	−	0.0323984i	0.358448	+	0.933550i	$0.383306\pi$
$312$	−8.92926	−	31.7877i	−0.505520	−	1.79962i
$313$	−4.51828	−	3.28273i	−0.255389	−	0.185551i	0.452723	−	0.891651i	$-0.350453\pi$
$313$	−4.51828	−	3.28273i	−0.255389	−	0.185551i	−0.708112	+	0.706101i	$0.750453\pi$
$314$	−9.64395	−	7.00674i	−0.544240	−	0.395413i
$315$	1.84441	+	1.58194i	0.103921	+	0.0891324i
$316$	−51.1334	+	16.6142i	−2.87648	+	0.934624i
$317$	−4.13456	−	5.69073i	−0.232220	−	0.319623i	0.676966	−	0.736015i	$-0.263295\pi$
$317$	−4.13456	−	5.69073i	−0.232220	−	0.319623i	−0.909185	+	0.416392i	$0.863295\pi$
$318$	−13.9510	+	9.30071i	−0.782332	+	0.521558i
$319$	−15.3103	+	7.99919i	−0.857213	+	0.447869i
$320$			32.1507i			1.79728i
$321$	4.41704	+	1.63477i	0.246535	+	0.0912441i
$322$	1.41876	+	4.36649i	0.0790642	+	0.243335i
$323$	−11.1877	−	3.63509i	−0.622499	−	0.202262i
$324$	7.79226	+	50.5635i	0.432904	+	2.80909i
$325$	4.76551	−	6.55916i	0.264343	−	0.363837i
$326$	−7.64004	+	23.5136i	−0.423142	+	1.30230i
$327$	6.10669	+	4.82447i	0.337701	+	0.266794i
$328$	23.6762	−	17.2018i	1.30730	−	0.949808i
$329$	−10.7742			−0.594002
$330$	−1.63354	−	12.7944i	−0.0899234	−	0.704308i
$331$	−27.5753			−1.51568			−0.757838	−	0.652443i	$-0.773744\pi$
$331$	−27.5753			−1.51568			−0.757838	+	0.652443i	$0.773744\pi$
$332$	74.8938	−	54.4136i	4.11033	−	2.98633i
$333$	10.8503	+	0.876730i	0.594595	+	0.0480445i
$334$	−7.51785	+	23.1375i	−0.411358	+	1.26603i
$335$	−1.96643	+	2.70656i	−0.107437	+	0.147875i
$336$	29.3249	+	1.18283i	1.59980	+	0.0645285i
$337$	3.77626	+	1.22698i	0.205706	+	0.0668380i	0.410058	−	0.912060i	$-0.365509\pi$
$337$	3.77626	+	1.22698i	0.205706	+	0.0668380i	−0.204352	+	0.978898i	$0.565509\pi$
$338$	8.15210	+	25.0896i	0.443416	+	1.36469i
$339$	−2.39529	+	6.47192i	−0.130095	+	0.351507i
$340$			19.2329i			1.04305i
$341$	−21.9125	−	3.24133i	−1.18663	−	0.175528i
$342$	21.6179	+	9.00734i	1.16896	+	0.487061i
$343$	−0.587785	−	0.809017i	−0.0317374	−	0.0436828i
$344$	26.0931	−	8.47817i	1.40685	−	0.457112i
$345$	2.23693	−	0.628361i	0.120432	−	0.0338298i
$346$	−13.2485	−	9.62557i	−0.712241	−	0.517474i
$347$	−7.01523	−	5.09686i	−0.376597	−	0.273614i	0.383344	−	0.923606i	$-0.374772\pi$
$347$	−7.01523	−	5.09686i	−0.376597	−	0.273614i	−0.759941	+	0.649992i	$0.774772\pi$
$348$	−49.3695	+	13.8680i	−2.64648	+	0.743404i
$349$	−17.6947	+	5.74935i	−0.947175	+	0.307756i	−0.741567	−	0.670879i	$-0.765917\pi$
$349$	−17.6947	+	5.74935i	−0.947175	+	0.307756i	−0.205608	+	0.978635i	$0.565917\pi$
$350$	7.07802	+	9.74206i	0.378336	+	0.520735i
$351$	1.86222	+	9.51763i	0.0993979	+	0.508014i
$352$	−62.8847	−	61.6119i	−3.35177	−	3.28393i
$353$			17.4425i			0.928371i	0.885738	+	0.464185i	$0.153653\pi$
$353$			17.4425i			0.928371i	−0.885738	+	0.464185i	$0.846347\pi$
$354$	4.58161	−	12.3792i	0.243510	−	0.657947i
$355$	−2.24589	−	6.91213i	−0.119199	−	0.366858i
$356$	58.3199	+	18.9493i	3.09095	+	1.00431i
$357$	7.22928	+	0.291595i	0.382614	+	0.0154328i
$358$	−19.2012	+	26.4283i	−1.01482	+	1.39678i
$359$	0.969576	−	2.98405i	0.0511723	−	0.157492i	−0.922205	−	0.386702i	$-0.873614\pi$
$359$	0.969576	−	2.98405i	0.0511723	−	0.157492i	0.973377	+	0.229210i	$0.0736142\pi$
$360$	1.99886	−	24.7377i	0.105349	−	1.30379i
$361$	−8.95554	+	6.50658i	−0.471344	+	0.342452i
$362$	53.3604			2.80456
$363$	15.1883	+	11.5028i	0.797180	+	0.603741i
$364$	10.6095			0.556091
$365$	9.77580	−	7.10253i	0.511689	−	0.371764i
$366$	−31.5795	−	24.9487i	−1.65069	−	1.30409i
$367$	−5.70383	+	17.5546i	−0.297737	+	0.916341i	0.684551	+	0.728965i	$0.259998\pi$
$367$	−5.70383	+	17.5546i	−0.297737	+	0.916341i	−0.982288	+	0.187376i	$0.940002\pi$
$368$	16.4955	−	22.7041i	0.859887	−	1.18353i
$369$	−7.33854	+	4.47602i	−0.382029	+	0.233012i
$370$	−7.74846	−	2.51763i	−0.402823	−	0.130885i
$371$	−1.07912	−	3.32119i	−0.0560252	−	0.172428i
$372$	−61.6697	−	22.8243i	−3.19742	−	1.18338i
$373$		−	15.2883i		−	0.791597i	−0.918337	−	0.395798i	$-0.870468\pi$
$373$		−	15.2883i		−	0.791597i	0.918337	−	0.395798i	$-0.129532\pi$
$374$	−27.4328	−	26.8776i	−1.41852	−	1.38981i
$375$	10.9070	−	7.27140i	0.563237	−	0.375493i
$376$	64.6830	+	89.0285i	3.33577	+	4.59130i
$377$	−9.24505	+	3.00390i	−0.476144	+	0.154709i
$378$	−14.2990	−	1.73781i	−0.735461	−	0.0893831i
$379$	−2.55183	−	1.85401i	−0.131079	−	0.0952341i	0.520314	−	0.853975i	$-0.325815\pi$
$379$	−2.55183	−	1.85401i	−0.131079	−	0.0952341i	−0.651393	+	0.758741i	$0.725815\pi$
$380$	−10.4897	−	7.62119i	−0.538109	−	0.390959i
$381$	−1.15167	−	4.09988i	−0.0590017	−	0.210043i
$382$	4.16373	−	1.35288i	0.213035	−	0.0692193i
$383$	16.7904	+	23.1100i	0.857951	+	1.18087i	0.982054	+	0.188599i	$0.0603945\pi$
$383$	16.7904	+	23.1100i	0.857951	+	1.18087i	−0.124103	+	0.992269i	$0.539605\pi$
$384$	−54.7129	−	82.0689i	−2.79206	−	4.18806i
$385$	2.65743	+	0.393092i	0.135435	+	0.0200338i
$386$			1.91825i			0.0976363i
$387$	−7.83977	+	1.86487i	−0.398518	+	0.0947965i
$388$	9.82217	+	30.2295i	0.498645	+	1.53467i
$389$	11.3221	+	3.67879i	0.574055	+	0.186522i	0.581636	−	0.813449i	$-0.302413\pi$
$389$	11.3221	+	3.67879i	0.574055	+	0.186522i	−0.00758034	+	0.999971i	$0.502413\pi$
$390$	0.292531	−	7.25248i	0.0148129	−	0.367244i
$391$	4.06653	−	5.59710i	0.205653	−	0.283057i
$392$	−3.15622	+	9.71386i	−0.159413	+	0.490624i
$393$	−13.5316	+	17.1280i	−0.682581	+	0.863994i
$394$	48.8496	−	35.4913i	2.46101	−	1.78803i
$395$	−7.66077			−0.385455
$396$	37.0815	+	42.7083i	1.86341	+	2.14617i
$397$	−10.2808			−0.515980			−0.257990	−	0.966148i	$-0.583060\pi$
$397$	−10.2808			−0.515980			−0.257990	+	0.966148i	$0.583060\pi$
$398$	−52.0224	+	37.7965i	−2.60765	+	1.89457i
$399$	−3.02369	+	3.82731i	−0.151374	+	0.191605i
$400$	22.7455	−	70.0036i	1.13728	−	3.50018i
$401$	−15.2101	+	20.9349i	−0.759555	+	1.04544i	0.237696	+	0.971340i	$0.423608\pi$
$401$	−15.2101	+	20.9349i	−0.759555	+	1.04544i	−0.997251	+	0.0740977i	$0.976392\pi$
$402$	0.799270	−	19.8156i	0.0398640	−	0.988314i
$403$	−11.8551	−	3.85197i	−0.590546	−	0.191880i
$404$	−10.1406	−	31.2097i	−0.504516	−	1.55274i
$405$	−1.17040	+	7.19512i	−0.0581577	+	0.357528i
$406$		−	14.4379i		−	0.716543i
$407$	10.6665	−	5.57292i	0.528718	−	0.276240i
$408$	−40.9915	−	61.4868i	−2.02938	−	3.04405i
$409$	16.1573	+	22.2386i	0.798926	+	1.09963i	0.992939	+	0.118628i	$0.0378496\pi$
$409$	16.1573	+	22.2386i	0.798926	+	1.09963i	−0.194013	+	0.980999i	$0.562150\pi$
$410$	6.11856	−	1.98804i	0.302174	−	0.0981823i
$411$	3.13219	+	11.1504i	0.154500	+	0.550011i
$412$	16.4952	+	11.9845i	0.812660	+	0.590432i
$413$	2.22412	+	1.61592i	0.109442	+	0.0795140i
$414$	−8.96707	+	10.4548i	−0.440707	+	0.513827i
$415$	12.5450	−	4.07611i	0.615808	−	0.200088i
$416$	−29.1201	−	40.0804i	−1.42773	−	1.96510i
$417$	4.29254	−	2.86171i	0.210207	−	0.140139i
$418$	25.5296	−	4.31147i	1.24869	−	0.210881i
$419$		−	29.8519i		−	1.45836i	−0.684322	−	0.729180i	$-0.739902\pi$
$419$		−	29.8519i		−	1.45836i	0.684322	−	0.729180i	$-0.260098\pi$
$420$	7.47899	+	2.76801i	0.364937	+	0.135065i
$421$	−8.13626	−	25.0408i	−0.396537	−	1.22042i	−0.927758	−	0.373183i	$-0.878267\pi$
$421$	−8.13626	−	25.0408i	−0.396537	−	1.22042i	0.531221	−	0.847233i	$-0.321733\pi$
$422$	21.0549	+	6.84115i	1.02494	+	0.333022i
$423$	−16.8310	−	27.5948i	−0.818351	−	1.34170i
$424$	−20.9649	+	28.8557i	−1.01814	+	1.40135i
$425$	5.60732	−	17.2575i	0.271995	−	0.837114i
$426$	33.8061	+	26.7078i	1.63791	+	1.29400i
$427$	6.78121	−	4.92684i	0.328166	−	0.238426i
$428$	15.4575			0.747166
$429$	7.34983	+	7.80601i	0.354853	+	0.376878i
$430$	6.03126			0.290853
$431$	4.45872	−	3.23945i	0.214769	−	0.156039i	−0.475200	−	0.879878i	$-0.657624\pi$
$431$	4.45872	−	3.23945i	0.214769	−	0.156039i	0.689969	+	0.723839i	$0.257624\pi$
$432$	42.7805	+	76.9542i	2.05828	+	3.70246i
$433$	11.2869	−	34.7374i	0.542412	−	1.66937i	−0.184652	−	0.982804i	$-0.559116\pi$
$433$	11.2869	−	34.7374i	0.542412	−	1.66937i	0.727064	−	0.686570i	$-0.240884\pi$
$434$	10.8823	−	14.9782i	0.522368	−	0.718978i
$435$	−7.30082	−	0.294481i	−0.350048	−	0.0141193i
$436$	24.2916	+	7.89282i	1.16336	+	0.377997i
$437$	1.44127	+	4.43578i	0.0689455	+	0.212192i
$438$	−24.8626	+	67.1770i	−1.18798	+	3.20984i
$439$		−	0.238703i		−	0.0113927i	−0.999984	−	0.00569633i	$-0.998187\pi$
$439$		−	0.238703i		−	0.0113927i	0.999984	−	0.00569633i	$-0.00181321\pi$
$440$	−12.7057	−	24.3186i	−0.605722	−	1.15934i
$441$	1.15383	−	2.76924i	0.0549444	−	0.131868i
$442$	−12.7034	−	17.4847i	−0.604237	−	0.831661i
$443$	15.5490	−	5.05217i	0.738754	−	0.240036i	0.0846188	−	0.996413i	$-0.473033\pi$
$443$	15.5490	−	5.05217i	0.738754	−	0.240036i	0.654135	+	0.756378i	$0.273033\pi$
$444$	34.3950	−	9.66166i	1.63232	−	0.458522i
$445$	7.06875	+	5.13575i	0.335091	+	0.243458i
$446$	50.0248	+	36.3451i	2.36874	+	1.72099i
$447$	11.6345	−	3.26816i	0.550291	−	0.154578i
$448$	37.7511	−	12.2661i	1.78357	−	0.579518i
$449$	19.9244	+	27.4236i	0.940291	+	1.29420i	0.955708	+	0.294318i	$0.0950925\pi$
$449$	19.9244	+	27.4236i	0.940291	+	1.29420i	−0.0154168	+	0.999881i	$0.504908\pi$
$450$	−13.8943	+	33.3467i	−0.654982	+	1.57198i
$451$	−4.22753	+	8.51098i	−0.199066	+	0.400766i
$452$			22.6486i			1.06530i
$453$	10.6897	−	28.8827i	0.502244	−	1.35703i
$454$	5.58882	+	17.2006i	0.262296	+	0.807264i
$455$	1.43773	+	0.467147i	0.0674019	+	0.0219002i
$456$	49.7782	+	2.00782i	2.33108	+	0.0940247i
$457$	−19.2379	+	26.4788i	−0.899913	+	1.23862i	0.0705827	+	0.997506i	$0.477514\pi$
$457$	−19.2379	+	26.4788i	−0.899913	+	1.23862i	−0.970496	+	0.241118i	$0.922486\pi$
$458$	−1.21148	+	3.72856i	−0.0566089	+	0.174224i
$459$	10.5464	+	18.9710i	0.492264	+	0.885492i
$460$	6.16927	−	4.48224i	0.287644	−	0.208985i
$461$	9.13287			0.425360			0.212680	−	0.977122i	$-0.431781\pi$
$461$	9.13287			0.425360			0.212680	+	0.977122i	$0.431781\pi$
$462$	−14.3999	+	6.79940i	−0.669943	+	0.316337i
$463$	−28.2846			−1.31450			−0.657248	−	0.753675i	$-0.728279\pi$
$463$	−28.2846			−1.31450			−0.657248	+	0.753675i	$0.728279\pi$
$464$	−71.3977	+	51.8734i	−3.31455	+	2.40816i
$465$	−7.35207	−	5.80835i	−0.340944	−	0.269356i
$466$	−11.6015	+	35.7058i	−0.537430	+	1.65404i
$467$	1.25932	−	1.73330i	0.0582743	−	0.0802077i	−0.778885	−	0.627166i	$-0.784215\pi$
$467$	1.25932	−	1.73330i	0.0582743	−	0.0802077i	0.837160	+	0.546959i	$0.184215\pi$
$468$	16.5737	+	27.1730i	0.766121	+	1.25607i
$469$	3.92825	+	1.27637i	0.181390	+	0.0589371i
$470$	7.47554	+	23.0073i	0.344821	+	1.06125i
$471$	6.98513	+	2.58523i	0.321858	+	0.119121i
$472$		−	28.0793i		−	1.29245i
$473$	−6.23491	+	6.36371i	−0.286681	+	0.292604i
$474$	37.7853	−	25.1904i	1.73554	−	1.15703i
$475$	7.19035	+	9.89667i	0.329916	+	0.454090i
$476$	22.5832	−	7.33772i	1.03510	−	0.336324i
$477$	6.82044	−	7.95204i	0.312286	−	0.364099i
$478$	41.4646	+	30.1258i	1.89654	+	1.37792i
$479$	2.04349	+	1.48469i	0.0933696	+	0.0678370i	0.633491	−	0.773750i	$-0.281622\pi$
$479$	2.04349	+	1.48469i	0.0933696	+	0.0678370i	−0.540121	+	0.841587i	$0.681622\pi$
$480$	−10.0707	−	35.8512i	−0.459663	−	1.63638i
$481$	6.44090	−	2.09277i	0.293680	−	0.0954223i
$482$	−22.4035	−	30.8357i	−1.02045	−	1.40453i
$483$	−1.59125	−	2.38686i	−0.0724044	−	0.108606i
$484$	59.8516	+	18.1028i	2.72053	+	0.822854i
$485$			4.52897i			0.205650i
$486$	−17.8864	−	39.3371i	−0.811343	−	1.78437i
$487$	−6.28703	−	19.3495i	−0.284893	−	0.876809i	−0.986431	−	0.164177i	$-0.947503\pi$
$487$	−6.28703	−	19.3495i	−0.284893	−	0.876809i	0.701538	−	0.712632i	$-0.252497\pi$
$488$	−81.4220	−	26.4556i	−3.68580	−	1.19759i
$489$	0.622585	−	15.4352i	0.0281542	−	0.698005i
$490$	−1.31975	+	1.81648i	−0.0596204	+	0.0820604i
$491$	2.59388	−	7.98314i	0.117060	−	0.360274i	−0.875311	−	0.483560i	$-0.839343\pi$
$491$	2.59388	−	7.98314i	0.117060	−	0.360274i	0.992371	+	0.123286i	$0.0393433\pi$
$492$	−17.4885	+	22.1365i	−0.788441	+	0.997989i
$493$	−17.6012	+	12.7880i	−0.792719	+	0.575944i
$494$	14.5700			0.655534
$495$	3.14454	+	7.42026i	0.141337	+	0.333516i
$496$	−113.168			−5.08139
$497$	−7.25934	+	5.27422i	−0.325626	+	0.236581i
$498$	−48.4725	+	61.3553i	−2.17211	+	2.74940i
$499$	2.25777	−	6.94870i	0.101072	−	0.311066i	−0.887717	−	0.460390i	$-0.847710\pi$
$499$	2.25777	−	6.94870i	0.101072	−	0.311066i	0.988788	+	0.149324i	$0.0477096\pi$
$500$	25.2876	−	34.8054i	1.13090	−	1.55654i
$501$	0.612627	−	15.1884i	0.0273702	−	0.678566i
$502$	−56.8985	−	18.4874i	−2.53950	−	0.825135i
$503$	−7.21320	−	22.1999i	−0.321621	−	0.989847i	−0.972943	−	0.231045i	$-0.925785\pi$
$503$	−7.21320	−	22.1999i	−0.321621	−	0.989847i	0.651322	−	0.758801i	$-0.274215\pi$
$504$	−29.8095	+	7.09086i	−1.32782	+	0.315852i
$505$		−	4.67582i		−	0.208071i
$506$	−2.22820	+	15.0634i	−0.0990554	+	0.669648i
$507$	−9.14324	−	13.7148i	−0.406065	−	0.609095i
$508$	−8.21509	−	11.3071i	−0.364486	−	0.501672i
$509$	14.8392	−	4.82156i	0.657737	−	0.213712i	0.0389145	−	0.999243i	$-0.487610\pi$
$509$	14.8392	−	4.82156i	0.657737	−	0.213712i	0.618822	+	0.785531i	$0.287610\pi$
$510$	−4.39325	−	15.6398i	−0.194537	−	0.692540i
$511$	−12.0694	−	8.76894i	−0.533919	−	0.387915i
$512$	−83.8493	−	60.9201i	−3.70565	−	2.69231i
$513$	−14.5259	−	1.76539i	−0.641336	−	0.0779437i
$514$	32.6133	−	10.5967i	1.43851	−	0.467400i
$515$	1.70763	+	2.35035i	0.0752470	+	0.103569i
$516$	−22.0057	+	14.6706i	−0.968747	+	0.645835i
$517$	−32.0035	−	15.8966i	−1.40751	−	0.699131i
$518$			10.0587i			0.441955i
$519$	9.59587	+	3.55149i	0.421212	+	0.155893i
$520$	−4.77133	−	14.6846i	−0.209237	−	0.643964i
$521$	19.5407	+	6.34915i	0.856093	+	0.278161i	0.703996	−	0.710204i	$-0.251397\pi$
$521$	19.5407	+	6.34915i	0.856093	+	0.278161i	0.152097	+	0.988366i	$0.451397\pi$
$522$	36.9783	−	22.5543i	1.61850	−	0.987175i
$523$	12.2512	−	16.8623i	0.535707	−	0.737338i	−0.452279	−	0.891876i	$-0.649389\pi$
$523$	12.2512	−	16.8623i	0.535707	−	0.737338i	0.987987	+	0.154538i	$0.0493890\pi$
$524$	−22.1377	+	68.1330i	−0.967092	+	2.97640i
$525$	−5.90382	−	4.66420i	−0.257664	−	0.203562i
$526$	−7.32697	+	5.32335i	−0.319471	+	0.232109i
$527$	−27.8986			−1.21528
$528$	85.3606	+	46.7802i	3.71484	+	2.03585i
$529$	20.2569			0.880736
$530$	−6.34336	+	4.60872i	−0.275538	+	0.200190i
$531$	−0.664249	+	8.22069i	−0.0288259	+	0.356747i
$532$	−4.94675	+	15.2245i	−0.214469	+	0.660068i
$533$	−3.14335	+	4.32644i	−0.136153	+	0.187399i
$534$	−51.7528	−	2.08746i	−2.23956	−	0.0903334i
$535$	2.09469	+	0.680606i	0.0905614	+	0.0294252i
$536$	−13.0365	−	40.1222i	−0.563091	−	1.73302i
$537$	7.08457	−	19.1420i	0.305722	−	0.826039i
$538$			13.9087i			0.599649i
$539$	−0.552295	−	3.27032i	−0.0237890	−	0.140863i
$540$	4.59393	+	23.4791i	0.197691	+	1.01038i
$541$	7.85754	+	10.8150i	0.337822	+	0.464972i	0.943804	−	0.330506i	$-0.107219\pi$
$541$	7.85754	+	10.8150i	0.337822	+	0.464972i	−0.605982	+	0.795479i	$0.707219\pi$
$542$	−80.0982	+	26.0255i	−3.44051	+	1.11789i
$543$	−32.0981	+	9.01646i	−1.37746	+	0.386933i
$544$	−89.7044	−	65.1741i	−3.84605	−	2.79432i
$545$	2.94430	+	2.13916i	0.126120	+	0.0916315i
$546$	−8.62743	+	2.42347i	−0.369220	+	0.103715i
$547$	−25.4465	+	8.26809i	−1.08802	+	0.353518i	−0.797479	−	0.603346i	$-0.793834\pi$
$547$	−25.4465	+	8.26809i	−1.08802	+	0.353518i	−0.290536	+	0.956864i	$0.593834\pi$
$548$	22.3426	+	30.7520i	0.954429	+	1.31366i
$549$	23.2118	+	9.67147i	0.990658	+	0.412768i
$550$	6.65065	+	39.3806i	0.283585	+	1.67920i
$551$		−	14.6671i		−	0.624839i
$552$	−10.1698	+	27.4782i	−0.432857	+	1.16955i
$553$	2.92273	+	8.99523i	0.124287	+	0.382516i
$554$	66.0107	+	21.4482i	2.80453	+	0.911246i
$555$	5.08638	+	0.205161i	0.215905	+	0.00870859i
$556$	9.95212	−	13.6979i	0.422064	−	0.580921i
$557$	3.44896	−	10.6148i	0.146137	−	0.449764i	−0.851018	−	0.525136i	$-0.824014\pi$
$557$	3.44896	−	10.6148i	0.146137	−	0.449764i	0.997155	+	0.0753718i	$0.0240144\pi$
$558$	55.3619	+	4.47336i	2.34366	+	0.189372i
$559$	−4.05599	+	2.94685i	−0.171550	+	0.124638i
$560$	13.7244			0.579964
$561$	21.0434	+	11.5324i	0.888454	+	0.486899i
$562$	15.1470			0.638937
$563$	−35.1161	+	25.5134i	−1.47997	+	1.07526i	−0.502402	+	0.864634i	$0.667550\pi$
$563$	−35.1161	+	25.5134i	−1.47997	+	1.07526i	−0.977567	+	0.210626i	$0.932450\pi$
$564$	−83.2388	−	65.7611i	−3.50498	−	2.76904i
$565$	−0.997235	+	3.06917i	−0.0419540	+	0.129121i
$566$	18.5598	−	25.5453i	0.780126	−	1.07375i
$567$	8.89499	−	1.37079i	0.373555	−	0.0575679i
$568$	87.1628	+	28.3209i	3.65727	+	1.18832i
$569$	−10.4365	−	32.1204i	−0.437522	−	1.34656i	−0.890480	−	0.455023i	$-0.849631\pi$
$569$	−10.4365	−	32.1204i	−0.437522	−	1.34656i	0.452957	−	0.891532i	$-0.350369\pi$
$570$	10.2708	+	3.80128i	0.430197	+	0.159218i
$571$		−	0.923643i		−	0.0386533i	−0.999813	−	0.0193266i	$-0.993848\pi$
$571$		−	0.923643i		−	0.0386533i	0.999813	−	0.0193266i	$-0.00615224\pi$
$572$	31.5143	+	15.6536i	1.31768	+	0.654510i
$573$	−2.27603	+	1.51736i	−0.0950826	+	0.0633887i
$574$	−4.66869	−	6.42590i	−0.194867	−	0.268212i
$575$	−6.84242	+	2.22324i	−0.285349	+	0.0927154i
$576$	90.3888	+	77.5262i	3.76620	+	3.23026i
$577$	11.3123	+	8.21884i	0.470935	+	0.342155i	0.797806	−	0.602915i	$-0.205994\pi$
$577$	11.3123	+	8.21884i	0.470935	+	0.342155i	−0.326870	+	0.945069i	$0.605994\pi$
$578$	−1.00731	−	0.731851i	−0.0418984	−	0.0304410i
$579$	−0.324132	−	1.15389i	−0.0134705	−	0.0479542i
$580$	−22.8067	+	7.41035i	−0.946997	+	0.307698i
$581$	−9.57228	−	13.1751i	−0.397125	−	0.546596i
$582$	−14.8923	−	22.3383i	−0.617305	−	0.925953i
$583$	1.69479	−	11.4573i	0.0701909	−	0.474515i
$584$			152.375i			6.30532i
$585$	1.04951	+	4.41205i	0.0433917	+	0.182416i
$586$	−3.15316	−	9.70442i	−0.130256	−	0.400886i
$587$	−4.16362	−	1.35284i	−0.171851	−	0.0558378i	0.221828	−	0.975086i	$-0.428798\pi$
$587$	−4.16362	−	1.35284i	−0.171851	−	0.0558378i	−0.393679	+	0.919248i	$0.628798\pi$
$588$	0.396812	−	9.83783i	0.0163643	−	0.405705i
$589$	11.0550	−	15.2159i	0.455515	−	0.626962i
$590$	1.90746	−	5.87057i	0.0785291	−	0.241688i
$591$	−23.3877	+	29.6036i	−0.962042	+	1.21773i
$592$	49.7418	−	36.1395i	2.04437	−	1.48532i
$593$	−35.2848			−1.44897			−0.724487	−	0.689289i	$-0.757923\pi$
$593$	−35.2848			−1.44897			−0.724487	+	0.689289i	$0.757923\pi$
$594$	−39.9093	−	26.2591i	−1.63750	−	1.07742i
$595$	3.38340			0.138706
$596$	32.0869	−	23.3125i	1.31433	−	0.954916i
$597$	24.9067	−	31.5263i	1.01936	−	1.29028i
$598$	−2.64797	+	8.14961i	−0.108284	+	0.333262i
$599$	−26.2795	+	36.1707i	−1.07375	+	1.47789i	−0.207534	+	0.978228i	$0.566544\pi$
$599$	−26.2795	+	36.1707i	−1.07375	+	1.47789i	−0.866218	+	0.499666i	$0.833456\pi$
$600$	−3.09716	+	76.7854i	−0.126441	+	3.13475i
$601$	40.4360	+	13.1385i	1.64942	+	0.535929i	0.978614	−	0.205705i	$-0.0659487\pi$
$601$	40.4360	+	13.1385i	1.64942	+	0.535929i	0.670805	+	0.741634i	$0.265949\pi$
$602$	−2.30104	−	7.08187i	−0.0937834	−	0.288636i
$603$	2.86752	+	12.0549i	0.116774	+	0.490912i
$604$		−	101.075i		−	4.11270i
$605$	7.31359	+	5.08848i	0.297340	+	0.206876i
$606$	15.3751	+	23.0626i	0.624573	+	0.936854i
$607$	2.54269	+	3.49972i	0.103205	+	0.142049i	0.857496	−	0.514491i	$-0.172019\pi$
$607$	2.54269	+	3.49972i	0.103205	+	0.142049i	−0.754291	+	0.656540i	$0.772019\pi$
$608$	71.0921	−	23.0992i	2.88317	−	0.936797i
$609$	2.43962	+	8.68494i	0.0988586	+	0.351931i
$610$	−15.2258	−	11.0622i	−0.616476	−	0.447896i
$611$	−16.2685	−	11.8198i	−0.658154	−	0.478177i
$612$	54.0717	+	46.3771i	2.18572	+	1.87468i
$613$	46.8178	−	15.2120i	1.89095	−	0.614408i	0.912051	−	0.410077i	$-0.134498\pi$
$613$	46.8178	−	15.2120i	1.89095	−	0.614408i	0.978902	−	0.204331i	$-0.0655017\pi$
$614$	−46.2918	−	63.7152i	−1.86818	−	2.57133i
$615$	−3.34460	+	2.22975i	−0.134867	+	0.0899121i
$616$	−23.7073	+	24.1970i	−0.955193	+	0.974925i
$617$			38.5527i			1.55207i	0.630687	+	0.776037i	$0.282773\pi$
$617$			38.5527i			1.55207i	−0.630687	+	0.776037i	$0.717227\pi$
$618$	−16.1510	−	5.97758i	−0.649690	−	0.240454i
$619$	6.49478	+	19.9889i	0.261047	+	0.803421i	0.992578	+	0.121612i	$0.0388064\pi$
$619$	6.49478	+	19.9889i	0.261047	+	0.803421i	−0.731530	+	0.681809i	$0.761194\pi$
$620$	−29.2456	−	9.50246i	−1.17453	−	0.381628i
$621$	3.62742	−	7.80414i	0.145563	−	0.313169i
$622$	−3.01264	+	4.14654i	−0.120796	+	0.166261i
$623$	3.33350	−	10.2595i	0.133554	−	0.411037i
$624$	42.9815	+	33.9566i	1.72064	+	1.35935i
$625$	−12.6124	+	9.16342i	−0.504495	+	0.366537i
$626$	15.4819			0.618780
$627$	−14.6284	+	6.90731i	−0.584203	+	0.275851i
$628$	24.4445			0.975443
$629$	12.2625	−	8.90925i	0.488939	−	0.355235i
$630$	−6.71401	−	0.542506i	−0.267493	−	0.0216140i
$631$	−5.21784	+	16.0589i	−0.207719	+	0.639293i	0.791872	+	0.610687i	$0.209107\pi$
$631$	−5.21784	+	16.0589i	−0.207719	+	0.639293i	−0.999591	+	0.0286056i	$0.990893\pi$
$632$	56.7820	−	78.1537i	2.25866	−	3.10879i
$633$	−13.8212	−	0.557484i	−0.549345	−	0.0221580i
$634$	18.5449	+	6.02560i	0.736511	+	0.239307i
$635$	−0.615390	−	1.89398i	−0.0244210	−	0.0751602i
$636$	11.9341	−	32.2451i	0.473218	−	1.27860i
$637$		−	1.86640i		−	0.0739495i
$638$	21.3021	−	42.8861i	0.843360	−	1.69788i
$639$	−24.8485	−	10.3534i	−0.982990	−	0.409573i
$640$	−27.1115	−	37.3158i	−1.07168	−	1.47504i
$641$	−21.6173	+	7.02390i	−0.853833	+	0.277427i	−0.703051	−	0.711140i	$-0.748179\pi$
$641$	−21.6173	+	7.02390i	−0.853833	+	0.277427i	−0.150783	+	0.988567i	$0.548179\pi$
$642$	−12.5697	+	3.53085i	−0.496085	+	0.139352i
$643$	−31.2766	−	22.7238i	−1.23343	−	0.896139i	−0.236287	−	0.971683i	$-0.575931\pi$
$643$	−31.2766	−	22.7238i	−1.23343	−	0.896139i	−0.997142	+	0.0755442i	$0.975931\pi$
$644$	−7.61671	−	5.53387i	−0.300140	−	0.218065i
$645$	−3.62802	+	1.01912i	−0.142853	+	0.0401278i
$646$	31.0132	−	10.0768i	1.22020	−	0.396467i
$647$	−1.10680	−	1.52338i	−0.0435127	−	0.0598901i	0.786706	−	0.617328i	$-0.211785\pi$
$647$	−1.10680	−	1.52338i	−0.0435127	−	0.0598901i	−0.830219	+	0.557437i	$0.811785\pi$
$648$	−64.7281	−	65.2707i	−2.54276	−	2.56408i
$649$	4.22229	+	8.08140i	0.165739	+	0.317223i
$650$			22.4749i			0.881538i
$651$	−4.01518	+	10.8488i	−0.157367	+	0.425196i
$652$	−15.6668	−	48.2174i	−0.613558	−	1.88834i
$653$	−24.2992	−	7.89528i	−0.950901	−	0.308966i	−0.207819	−	0.978167i	$-0.566637\pi$
$653$	−24.2992	−	7.89528i	−0.950901	−	0.308966i	−0.743081	+	0.669201i	$0.766637\pi$
$654$	−21.5563	−	0.869478i	−0.842916	−	0.0339993i
$655$	−5.99990	+	8.25816i	−0.234436	+	0.322673i
$656$	−15.0030	+	46.1746i	−0.585770	+	1.80282i
$657$	3.60461	−	44.6104i	0.140629	−	1.74042i
$658$	24.1630	−	17.5555i	0.941973	−	0.684383i
$659$	1.72159			0.0670636			0.0335318	−	0.999438i	$-0.489325\pi$
$659$	1.72159			0.0670636			0.0335318	+	0.999438i	$0.489325\pi$
$660$	18.1314	+	19.2567i	0.705763	+	0.749568i
$661$	16.8514			0.655443			0.327722	−	0.944774i	$-0.393719\pi$
$661$	16.8514			0.655443			0.327722	+	0.944774i	$0.393719\pi$
$662$	61.8423	−	44.9310i	2.40357	−	1.74629i
$663$	10.5960	+	8.37112i	0.411513	+	0.325107i
$664$	−51.4002	+	158.193i	−1.99471	+	6.13910i
$665$	−1.34070	+	1.84531i	−0.0519901	+	0.0715582i
$666$	−25.7623	+	15.7133i	−0.998267	+	0.608877i
$667$	8.20394	+	2.66562i	0.317658	+	0.103213i
$668$	−15.4162	−	47.4462i	−0.596471	−	1.83575i
$669$	−36.2330	−	13.4100i	−1.40085	−	0.518462i
$670$		−	9.27400i		−	0.358286i
$671$	27.4119	−	4.62936i	1.05823	−	0.178714i
$672$	−38.2541	+	25.5029i	−1.47569	+	0.983796i
$673$	0.265734	+	0.365751i	0.0102433	+	0.0140987i	0.814108	−	0.580714i	$-0.197226\pi$
$673$	0.265734	+	0.365751i	0.0102433	+	0.0140987i	−0.803865	+	0.594812i	$0.797226\pi$
$674$	−10.4681	+	3.40131i	−0.403218	+	0.131013i
$675$	2.72320	−	22.4070i	0.104816	−	0.862445i
$676$	−43.7652	−	31.7973i	−1.68328	−	1.22297i
$677$	7.54023	+	5.47829i	0.289794	+	0.210548i	0.723178	−	0.690662i	$-0.242681\pi$
$677$	7.54023	+	5.47829i	0.289794	+	0.210548i	−0.433384	+	0.901209i	$0.642681\pi$
$678$	−5.17347	−	18.4173i	−0.198686	−	0.707311i
$679$	5.31789	−	1.72789i	0.204082	−	0.0663103i
$680$	−20.3122	−	27.9574i	−0.778939	−	1.07212i
$681$	−6.26831	−	9.40241i	−0.240202	−	0.360301i
$682$	54.4239	−	28.4349i	2.08400	−	1.08883i
$683$		−	37.1103i		−	1.41999i	−0.704209	−	0.709993i	$-0.748698\pi$
$683$		−	37.1103i		−	1.41999i	0.704209	−	0.709993i	$-0.251302\pi$
$684$	−46.7205	+	11.1135i	−1.78640	+	0.424936i
$685$	1.67368	+	5.15105i	0.0639480	+	0.196812i
$686$	2.63642	+	0.856624i	0.100659	+	0.0327060i
$687$	0.0987235	−	2.44757i	0.00376654	−	0.0933806i
$688$	−26.7535	+	36.8231i	−1.01997	+	1.40387i
$689$	2.01407	−	6.19868i	0.0767300	−	0.236151i
$690$	−3.99286	+	5.05406i	−0.152005	+	0.192405i
$691$	−0.899931	+	0.653838i	−0.0342350	+	0.0248732i	−0.604771	−	0.796399i	$-0.706735\pi$
$691$	−0.899931	+	0.653838i	−0.0342350	+	0.0248732i	0.570536	+	0.821272i	$0.306735\pi$
$692$	33.5809			1.27655
$693$	7.51312	−	6.52327i	0.285400	−	0.247798i
$694$	24.0376			0.912456
$695$	1.95177	−	1.41805i	0.0740349	−	0.0537895i
$696$	57.1182	−	72.2988i	2.16506	−	2.74048i
$697$	−3.69861	+	11.3831i	−0.140095	+	0.431167i
$698$	30.3154	−	41.7255i	1.14745	−	1.57933i
$699$	0.945405	−	23.4386i	0.0357585	−	0.886531i
$700$	−23.4846	−	7.63062i	−0.887635	−	0.288410i
$701$	5.05567	+	15.5598i	0.190950	+	0.587684i	1.00000		5.58632e-5i	$-1.77818e-5\pi$
$701$	5.05567	+	15.5598i	0.190950	+	0.587684i	−0.809050	+	0.587740i	$0.800018\pi$
$702$	−19.6843	−	18.3106i	−0.742937	−	0.691090i
$703$			10.2184i			0.385393i
$704$	130.233	+	19.2642i	4.90833	+	0.726047i
$705$	−8.38442	−	12.5766i	−0.315775	−	0.473661i
$706$	−28.4207	−	39.1178i	−1.06963	−	1.47222i
$707$	−5.49032	+	1.78391i	−0.206485	+	0.0670909i
$708$	7.32010	+	26.0592i	0.275106	+	0.979364i
$709$	21.2206	+	15.4177i	0.796958	+	0.579024i	0.910020	−	0.414564i	$-0.136066\pi$
$709$	21.2206	+	15.4177i	0.796958	+	0.579024i	−0.113062	+	0.993588i	$0.536066\pi$
$710$	16.2994	+	11.8422i	0.611705	+	0.444430i
$711$	−18.4727	+	21.5376i	−0.692781	+	0.807723i
$712$	−104.788	+	34.0476i	−3.92709	+	1.27599i
$713$	6.50178	+	8.94893i	0.243493	+	0.335140i
$714$	−16.6880	+	11.1254i	−0.624533	+	0.416357i
$715$	3.58135	+	3.50887i	0.133935	+	0.131224i
$716$		−	66.9877i		−	2.50345i
$717$	−30.0328	−	11.1153i	−1.12160	−	0.415109i
$718$	2.68775	+	8.27206i	0.100306	+	0.308710i
$719$	7.88702	+	2.56265i	0.294136	+	0.0955706i	0.452368	−	0.891831i	$-0.350579\pi$
$719$	7.88702	+	2.56265i	0.294136	+	0.0955706i	−0.158232	+	0.987402i	$0.550579\pi$
$720$	21.4397	+	35.1509i	0.799010	+	1.31000i
$721$	2.10827	−	2.90179i	0.0785161	−	0.108068i
$722$	9.48253	−	29.1842i	0.352903	−	1.08612i
$723$	18.6869	+	14.7632i	0.694973	+	0.549049i
$724$	−88.5239	+	64.3164i	−3.28997	+	2.39030i
$725$	22.6247			0.840261
$726$	−52.8050	−	1.04924i	−1.95978	−	0.0389408i
$727$	42.7209			1.58443			0.792215	−	0.610242i	$-0.208928\pi$
$727$	42.7209			1.58443			0.792215	+	0.610242i	$0.208928\pi$
$728$	−15.4223	+	11.2049i	−0.571587	+	0.415282i
$729$	17.4062	+	20.6403i	0.644674	+	0.764457i
$730$	−10.3511	+	31.8573i	−0.383110	+	1.17909i
$731$	−6.59538	+	9.07776i	−0.243939	+	0.335753i
$732$	82.4611	+	3.32609i	3.04785	+	0.122936i
$733$	5.98375	+	1.94424i	0.221015	+	0.0718121i	0.417431	−	0.908709i	$-0.362930\pi$
$733$	5.98375	+	1.94424i	0.221015	+	0.0718121i	−0.196416	+	0.980521i	$0.562930\pi$
$734$	−15.8115	−	48.6629i	−0.583614	−	1.79618i
$735$	0.486941	−	1.31568i	0.0179611	−	0.0485297i
$736$			43.9630i			1.62050i
$737$	9.78518	+	9.58713i	0.360442	+	0.353147i
$738$	9.16471	−	21.9956i	0.337358	−	0.809670i
$739$	−11.0654	−	15.2302i	−0.407047	−	0.560252i	0.555448	−	0.831551i	$-0.312547\pi$
$739$	−11.0654	−	15.2302i	−0.407047	−	0.560252i	−0.962495	+	0.271299i	$0.912547\pi$
$740$	15.8891	−	5.16268i	0.584095	−	0.189784i
$741$	−8.76435	+	2.46193i	−0.321966	+	0.0904413i
$742$	7.83164	+	5.69002i	0.287509	+	0.208887i
$743$	−9.76404	−	7.09399i	−0.358208	−	0.260253i	0.394096	−	0.919069i	$-0.371058\pi$
$743$	−9.76404	−	7.09399i	−0.358208	−	0.260253i	−0.752304	+	0.658816i	$0.771058\pi$
$744$	113.750	−	31.9526i	4.17026	−	1.17144i
$745$	5.37465	−	1.74633i	0.196912	−	0.0639806i
$746$	24.9106	+	34.2865i	0.912043	+	1.25532i
$747$	18.7905	−	45.0979i	0.687510	−	1.65005i
$748$	77.9068	+	11.5241i	2.84855	+	0.421363i
$749$		−	2.71924i		−	0.0993588i
$750$	−12.6129	+	34.0792i	−0.460558	+	1.24440i
$751$	10.9022	+	33.5536i	0.397828	+	1.22439i	0.926737	+	0.375711i	$0.122601\pi$
$751$	10.9022	+	33.5536i	0.397828	+	1.22439i	−0.528909	+	0.848679i	$0.677399\pi$
$752$	−173.628	−	56.4153i	−6.33158	−	2.05725i
$753$	37.3503	+	1.50654i	1.36112	+	0.0549013i
$754$	15.8390	−	21.8006i	0.576824	−	0.793930i
$755$	4.45043	−	13.6970i	0.161968	−	0.498486i
$756$	25.8164	−	14.3519i	0.938934	−	0.521973i
$757$	26.5738	−	19.3070i	0.965840	−	0.701724i	0.0113404	−	0.999936i	$-0.496390\pi$
$757$	26.5738	−	19.3070i	0.965840	−	0.701724i	0.954500	+	0.298212i	$0.0963902\pi$
$758$	8.74382			0.317590
$759$	−1.20496	−	9.43765i	−0.0437374	−	0.342565i
$760$	23.2969			0.845067
$761$	−2.51408	+	1.82659i	−0.0911353	+	0.0662137i	−0.632420	−	0.774626i	$-0.717938\pi$
$761$	−2.51408	+	1.82659i	−0.0911353	+	0.0662137i	0.541284	+	0.840840i	$0.317938\pi$
$762$	9.26312	+	7.31815i	0.335568	+	0.265108i
$763$	1.38848	−	4.27331i	0.0502664	−	0.154704i
$764$	−5.27690	+	7.26304i	−0.190912	+	0.262767i
$765$	5.28539	+	8.66552i	0.191094	+	0.313303i
$766$	−75.3108	−	24.4700i	−2.72109	−	0.884135i
$767$	1.58558	+	4.87990i	0.0572519	+	0.176203i
$768$	127.471	+	47.1776i	4.59970	+	1.70237i
$769$			7.26666i			0.262042i	0.991380	+	0.131021i	$0.0418256\pi$
$769$			7.26666i			0.262042i	−0.991380	+	0.131021i	$0.958174\pi$
$770$	−6.60025	+	3.44844i	−0.237856	+	0.124273i
$771$	−17.8275	+	11.8850i	−0.642041	+	0.428029i
$772$	−2.31211	−	3.18234i	−0.0832145	−	0.114535i
$773$	−13.4957	+	4.38503i	−0.485407	+	0.157718i	−0.541489	−	0.840708i	$-0.682139\pi$
$773$	−13.4957	+	4.38503i	−0.485407	+	0.157718i	0.0560817	+	0.998426i	$0.482139\pi$
$774$	14.5434	−	16.9564i	0.522752	−	0.609484i
$775$	23.4714	+	17.0529i	0.843116	+	0.612560i
$776$	−46.2037	−	33.5689i	−1.65862	−	1.20505i
$777$	−1.69965	−	6.05067i	−0.0609747	−	0.217067i
$778$	−31.3860	+	10.1979i	−1.12524	+	0.365614i
$779$	−4.74278	−	6.52788i	−0.169928	−	0.233886i
$780$	8.25627	+	12.3843i	0.295622	+	0.443430i
$781$	−29.3447	+	4.95576i	−1.05003	+	0.177331i
$782$			19.1784i			0.685819i
$783$	−18.4327	+	19.8155i	−0.658730	+	0.708149i
$784$	−5.23613	−	16.1152i	−0.187005	−	0.575542i
$785$	3.31255	+	1.07631i	0.118230	+	0.0384152i
$786$	2.43871	−	60.4609i	0.0869858	−	2.15657i
$787$	−10.1903	+	14.0257i	−0.363245	+	0.499964i	−0.951049	−	0.309039i	$-0.899993\pi$
$787$	−10.1903	+	14.0257i	−0.363245	+	0.499964i	0.587804	+	0.809003i	$0.299993\pi$
$788$	−38.2622	+	117.759i	−1.36304	+	4.19499i
$789$	3.50793	−	4.44025i	0.124886	−	0.158077i
$790$	17.1806	−	12.4824i	0.611258	−	0.444105i
$791$	3.98427			0.141664
$792$	−99.0074	−	22.9193i	−3.51808	−	0.814401i
$793$	15.6442			0.555543
$794$	23.0565	−	16.7515i	0.818245	−	0.594490i
$795$	3.03701	−	3.84416i	0.107711	−	0.136338i
$796$	40.7473	−	125.407i	1.44425	−	4.44494i
$797$	−9.28417	+	12.7786i	−0.328862	+	0.452640i	−0.941147	−	0.337997i	$-0.890251\pi$
$797$	−9.28417	+	12.7786i	−0.328862	+	0.452640i	0.612285	+	0.790637i	$0.290251\pi$
$798$	0.544937	−	13.5102i	0.0192906	−	0.478255i
$799$	−42.8035	−	13.9077i	−1.51428	−	0.492019i
$800$	35.6317	+	109.663i	1.25977	+	3.87718i
$801$	31.4839	−	7.48914i	1.11243	−	0.264616i
$802$		−	71.7332i		−	2.53299i
$803$	−22.9127	−	43.8545i	−0.808572	−	1.54759i
$804$	22.5582	+	33.8372i	0.795568	+	1.19335i
$805$	−0.788503	−	1.08528i	−0.0277911	−	0.0382511i
$806$	32.8635	−	10.6780i	1.15757	−	0.376117i
$807$	−2.35020	−	8.36660i	−0.0827311	−	0.294518i
$808$	47.7017	+	34.6573i	1.67814	+	1.21924i
$809$	31.1541	+	22.6348i	1.09532	+	0.795797i	0.980290	−	0.197565i	$-0.0633032\pi$
$809$	31.1541	+	22.6348i	1.09532	+	0.795797i	0.115031	+	0.993362i	$0.463303\pi$
$810$	−9.09886	−	18.0433i	−0.319701	−	0.633977i
$811$	24.5769	−	7.98553i	0.863013	−	0.280410i	0.156126	−	0.987737i	$-0.450099\pi$
$811$	24.5769	−	7.98553i	0.863013	−	0.280410i	0.706886	+	0.707327i	$0.250099\pi$
$812$	17.4024	+	23.9523i	0.610703	+	0.840561i
$813$	43.7843	−	29.1897i	1.53558	−	1.02373i
$814$	−14.8409	+	29.8781i	−0.520174	+	1.04723i
$815$		−	7.22390i		−	0.253042i
$816$	114.974	+	42.5526i	4.02490	+	1.48964i
$817$	−2.33756	−	7.19426i	−0.0817808	−	0.251695i
$818$	−72.4709	−	23.5472i	−2.53388	−	0.823309i
$819$	4.78020	−	2.91560i	0.167034	−	0.101879i
$820$	−7.75435	+	10.6729i	−0.270794	+	0.372716i
$821$	10.5214	−	32.3815i	0.367199	−	1.13012i	−0.581394	−	0.813622i	$-0.697493\pi$
$821$	10.5214	−	32.3815i	0.367199	−	1.13012i	0.948593	−	0.316499i	$-0.102507\pi$
$822$	−25.1930	−	19.9032i	−0.878705	−	0.694203i
$823$	−43.6699	+	31.7280i	−1.52224	+	1.10597i	−0.561871	+	0.827225i	$0.689918\pi$
$823$	−43.6699	+	31.7280i	−1.52224	+	1.10597i	−0.960365	+	0.278744i	$0.910082\pi$
$824$	−36.6348			−1.27623
$825$	−10.6549	−	22.5651i	−0.370955	−	0.785615i
$826$	−7.62093			−0.265166
$827$	−35.1619	+	25.5466i	−1.22270	+	0.888343i	−0.996321	−	0.0856966i	$-0.972688\pi$
$827$	−35.1619	+	25.5466i	−1.22270	+	0.888343i	−0.226378	+	0.974040i	$0.572688\pi$
$828$	2.27479	−	28.1526i	0.0790543	−	0.978369i
$829$	8.96048	−	27.5775i	0.311210	−	0.957807i	−0.666076	−	0.745884i	$-0.732027\pi$
$829$	8.96048	−	27.5775i	0.311210	−	0.957807i	0.977286	−	0.211923i	$-0.0679727\pi$
$830$	−21.4926	+	29.5821i	−0.746020	+	1.02681i
$831$	−43.3319	−	1.74781i	−1.50317	−	0.0606307i
$832$	70.4587	+	22.8934i	2.44272	+	0.793687i
$833$	−1.29083	−	3.97277i	−0.0447247	−	0.137648i
$834$	−4.96390	+	13.4121i	−0.171886	+	0.464423i
$835$		−	7.10837i		−	0.245995i
$836$	−37.1564	+	37.9240i	−1.28508	+	1.31163i
$837$	−34.0580	+	6.66379i	−1.17722	+	0.230334i
$838$	48.6405	+	66.9479i	1.68026	+	2.31268i
$839$	28.3254	−	9.20348i	0.977902	−	0.317739i	0.223900	−	0.974612i	$-0.428121\pi$
$839$	28.3254	−	9.20348i	0.977902	−	0.317739i	0.754002	+	0.656873i	$0.228121\pi$
$840$	−13.7950	+	3.87505i	−0.475972	+	0.133702i
$841$	1.51560	+	1.10114i	0.0522619	+	0.0379705i
$842$	59.0484	+	42.9012i	2.03494	+	1.47847i
$843$	−9.11144	+	2.55943i	−0.313815	+	0.0881515i
$844$	−43.1755	+	14.0286i	−1.48616	+	0.482883i
$845$	−4.53069	−	6.23596i	−0.155861	−	0.214524i
$846$	82.7092	+	34.4617i	2.84360	+	1.18482i
$847$	3.18459	−	10.5289i	0.109424	−	0.361778i
$848$		−	59.1720i		−	2.03197i
$849$	−6.84789	+	18.5025i	−0.235019	+	0.635005i
$850$	15.5440	+	47.8395i	0.533155	+	1.64088i
$851$	−5.71557	−	1.85710i	−0.195927	−	0.0636606i
$852$	−88.2752	−	3.56061i	−3.02426	−	0.121984i
$853$	−10.5281	+	14.4906i	−0.360474	+	0.496150i	−0.950281	−	0.311394i	$-0.899204\pi$
$853$	−10.5281	+	14.4906i	−0.360474	+	0.496150i	0.589807	+	0.807545i	$0.299204\pi$
$854$	−7.18025	+	22.0985i	−0.245703	+	0.756197i
$855$	−6.82057	−	0.551116i	−0.233259	−	0.0188478i
$856$	−22.4693	+	16.3249i	−0.767986	+	0.557975i
$857$	9.38008			0.320417			0.160209	−	0.987083i	$-0.448783\pi$
$857$	9.38008			0.320417			0.160209	+	0.987083i	$0.448783\pi$
$858$	−29.2023	−	5.53054i	−0.996951	−	0.188809i
$859$	20.6750			0.705421			0.352710	−	0.935733i	$-0.385260\pi$
$859$	20.6750			0.705421			0.352710	+	0.935733i	$0.385260\pi$
$860$	−10.0058	+	7.26961i	−0.341193	+	0.247892i
$861$	3.89418	+	3.07652i	0.132713	+	0.104848i
$862$	−4.72109	+	14.5300i	−0.160801	+	0.494894i
$863$	−18.0945	+	24.9050i	−0.615944	+	0.847775i	−0.997050	−	0.0767568i	$-0.975543\pi$
$863$	−18.0945	+	24.9050i	−0.615944	+	0.847775i	0.381105	+	0.924532i	$0.375543\pi$
$864$	−125.077	−	58.1366i	−4.25519	−	1.97785i
$865$	4.55064	+	1.47859i	0.154726	+	0.0502737i
$866$	31.2882	+	96.2953i	1.06322	+	3.27225i
$867$	0.729593	+	0.270027i	0.0247783	+	0.00917058i
$868$			37.9653i			1.28863i
$869$	−4.59022	+	31.0315i	−0.155713	+	1.05267i
$870$	16.8532	−	11.2355i	0.571376	−	0.380919i
$871$	4.53123	+	6.23671i	0.153535	+	0.211323i
$872$	−43.6465	+	14.1816i	−1.47806	+	0.480250i
$873$	12.7328	+	10.9209i	0.430940	+	0.369616i
$874$	−10.4599	−	7.59960i	−0.353813	−	0.257060i
$875$	−6.12287	−	4.44852i	−0.206991	−	0.150388i
$876$	−39.7233	−	141.413i	−1.34213	−	4.77790i
$877$	34.8852	−	11.3349i	1.17799	−	0.382752i	0.346371	−	0.938098i	$-0.387414\pi$
$877$	34.8852	−	11.3349i	1.17799	−	0.382752i	0.831620	+	0.555345i	$0.187414\pi$
$878$	0.388941	+	0.535332i	0.0131261	+	0.0180666i
$879$	3.53652	+	5.30475i	0.119284	+	0.178925i
$880$	40.7667	+	20.2494i	1.37425	+	0.682608i
$881$			39.8090i			1.34120i	0.741820	+	0.670599i	$0.233963\pi$
$881$			39.8090i			1.34120i	−0.741820	+	0.670599i	$0.766037\pi$
$882$	1.92451	+	8.09053i	0.0648018	+	0.272422i
$883$	17.1607	+	52.8152i	0.577503	+	1.77737i	0.627493	+	0.778622i	$0.284081\pi$
$883$	17.1607	+	52.8152i	0.577503	+	1.77737i	−0.0499899	+	0.998750i	$0.515919\pi$
$884$	42.1493	+	13.6951i	1.41763	+	0.460617i
$885$	−0.155439	+	3.85367i	−0.00522502	+	0.129540i
$886$	−26.6392	+	36.6658i	−0.894962	+	1.23181i
$887$	−8.87134	+	27.3032i	−0.297870	+	0.916751i	0.684372	+	0.729133i	$0.260077\pi$
$887$	−8.87134	+	27.3032i	−0.297870	+	0.916751i	−0.982242	+	0.187618i	$0.939923\pi$
$888$	−39.7935	+	50.3696i	−1.33538	+	1.69029i
$889$	−1.98911	+	1.44518i	−0.0667127	+	0.0484696i
$890$	−24.2210			−0.811891
$891$	28.4440	+	9.05215i	0.952908	+	0.303259i
$892$	−126.798			−4.24550
$893$	24.5465	−	17.8341i	0.821417	−	0.596795i
$894$	−20.7671	+	26.2865i	−0.694557	+	0.879153i
$895$	2.94952	−	9.07770i	0.0985917	−	0.303434i
$896$	−33.4725	+	46.0709i	−1.11824	+	1.53912i
$897$	0.215782	−	5.34971i	0.00720476	−	0.178622i
$898$	−89.3677	−	29.0373i	−2.98224	−	0.968988i
$899$	−10.7492	−	33.0826i	−0.358505	−	1.10337i
$900$	−17.1432	−	72.0687i	−0.571439	−	2.40229i
$901$		−	14.5873i		−	0.485973i
$902$	−4.38680	−	25.9756i	−0.146064	−	0.864894i
$903$	2.58080	+	3.87118i	0.0858837	+	0.128825i
$904$	−23.9196	−	32.9224i	−0.795553	−	1.09498i
$905$	−14.8280	+	4.81792i	−0.492901	+	0.160153i
$906$	23.0880	+	82.1921i	0.767047	+	2.73065i
$907$	23.5933	+	17.1416i	0.783404	+	0.569176i	0.905999	−	0.423281i	$-0.139122\pi$
$907$	23.5933	+	17.1416i	0.783404	+	0.569176i	−0.122595	+	0.992457i	$0.539122\pi$
$908$	−30.0040	−	21.7992i	−0.995718	−	0.723431i
$909$	−13.1457	−	11.2750i	−0.436014	−	0.373968i
$910$	−3.98552	+	1.29497i	−0.132119	+	0.0429280i
$911$	−10.2635	−	14.1265i	−0.340046	−	0.468033i	0.604409	−	0.796674i	$-0.293409\pi$
$911$	−10.2635	−	14.1265i	−0.340046	−	0.468033i	−0.944455	+	0.328641i	$0.893409\pi$
$912$	−68.7676	+	45.8453i	−2.27712	+	1.51809i
$913$	−8.99431	−	53.2582i	−0.297668	−	1.76259i
$914$		−	90.7293i		−	3.00106i
$915$	11.0281	+	4.08156i	0.364578	+	0.134932i
$916$	−2.48429	−	7.64585i	−0.0820831	−	0.252626i
$917$	11.9858	+	3.89441i	0.395805	+	0.128605i
$918$	−54.5634	−	25.3615i	−1.80086	−	0.837054i
$919$	24.6432	−	33.9185i	0.812904	−	1.11887i	−0.177965	−	0.984037i	$-0.556951\pi$
$919$	24.6432	−	33.9185i	0.812904	−	1.11887i	0.990869	−	0.134830i	$-0.0430487\pi$
$920$	−4.23401	+	13.0310i	−0.139591	+	0.429618i
$921$	38.6123	+	30.5049i	1.27232	+	1.00517i
$922$	−20.4820	+	14.8811i	−0.674539	+	0.490081i
$923$	−16.7473			−0.551243
$924$	15.6937	−	28.6366i	0.516285	−	0.942074i
$925$	−15.7623			−0.518262
$926$	63.4329	−	46.0867i	2.08454	−	1.51450i
$927$	10.7255	+	0.866639i	0.352270	+	0.0284642i
$928$	42.7218	−	131.484i	1.40241	−	4.31618i
$929$	−23.1333	+	31.8403i	−0.758980	+	1.04465i	0.238319	+	0.971187i	$0.423404\pi$
$929$	−23.1333	+	31.8403i	−0.758980	+	1.04465i	−0.997298	+	0.0734589i	$0.976596\pi$
$930$	25.9524	+	1.04680i	0.851012	+	0.0343258i
$931$	2.67826	+	0.870219i	0.0877764	+	0.0285203i
$932$	−23.7903	−	73.2189i	−0.779276	−	2.39836i
$933$	1.11155	−	3.00335i	0.0363907	−	0.0983251i
$934$			5.93915i			0.194335i
$935$	10.0500	+	4.99196i	0.328669	+	0.163255i
$936$	−52.7899	−	21.9955i	−1.72549	−	0.718944i
$937$	19.2107	+	26.4412i	0.627586	+	0.863798i	0.997878	−	0.0651178i	$-0.0207423\pi$
$937$	19.2107	+	26.4412i	0.627586	+	0.863798i	−0.370292	+	0.928915i	$0.620742\pi$
$938$	−10.8895	+	3.53820i	−0.355554	+	0.115526i
$939$	−9.31289	+	2.61602i	−0.303915	+	0.0853706i
$940$	−40.1330	−	29.1583i	−1.30899	−	0.951040i
$941$	23.3232	+	16.9453i	0.760313	+	0.552400i	0.899006	−	0.437936i	$-0.144290\pi$
$941$	23.3232	+	16.9453i	0.760313	+	0.552400i	−0.138693	+	0.990335i	$0.544290\pi$
$942$	−19.8777	+	5.58370i	−0.647650	+	0.181927i
$943$	4.51329	−	1.46646i	0.146973	−	0.0477544i
$944$	27.3809	+	37.6865i	0.891171	+	1.22659i
$945$	4.13038	−	0.808150i	0.134361	−	0.0262891i
$946$	3.61384	−	24.4308i	0.117496	−	0.794314i
$947$			23.1040i			0.750779i	0.926867	+	0.375390i	$0.122491\pi$
$947$			23.1040i			0.750779i	−0.926867	+	0.375390i	$0.877509\pi$
$948$	−32.3227	+	87.3338i	−1.04979	+	2.83647i
$949$	−8.60430	−	26.4813i	−0.279307	−	0.859620i
$950$	−32.2512	−	10.4790i	−1.04637	−	0.339985i
$951$	−12.1736	−	0.491024i	−0.394755	−	0.0159226i
$952$	−25.0779	+	34.5168i	−0.812780	+	1.11870i
$953$	−16.2021	+	49.8648i	−0.524836	+	1.61528i	0.239804	+	0.970821i	$0.422917\pi$
$953$	−16.2021	+	49.8648i	−0.524836	+	1.61528i	−0.764640	+	0.644458i	$0.777083\pi$
$954$	−2.33898	+	28.9470i	−0.0757272	+	0.937193i
$955$	−1.03489	+	0.751889i	−0.0334881	+	0.0243306i
$956$	−105.100			−3.39918
$957$	−5.56740	+	29.3970i	−0.179969	+	0.950269i
$958$	−7.00202			−0.226225
$959$	5.40980	−	3.93045i	0.174692	−	0.126921i
$960$	43.6956	+	34.5209i	1.41027	+	1.11416i
$961$	4.20440	−	12.9398i	0.135626	−	0.417413i
$962$	−11.0348	+	15.1882i	−0.355778	+	0.489686i
$963$	6.96447	−	4.24787i	0.224427	−	0.136886i
$964$	74.3340	+	24.1526i	2.39414	+	0.777902i
$965$	−0.173199	−	0.533053i	−0.00557548	−	0.0171596i
$966$	7.45779	+	2.76017i	0.239951	+	0.0888070i
$967$			50.9512i			1.63848i	0.573452	+	0.819239i	$0.305604\pi$
$967$			50.9512i			1.63848i	−0.573452	+	0.819239i	$0.694396\pi$
$968$	−106.120	+	36.8958i	−3.41084	+	1.18588i
$969$	−16.9529	+	11.3020i	−0.544604	+	0.363071i
$970$	−7.37948	−	10.1570i	−0.236941	−	0.326121i
$971$	−10.1293	+	3.29122i	−0.325066	+	0.105620i	−0.467004	−	0.884255i	$-0.654667\pi$
$971$	−10.1293	+	3.29122i	−0.325066	+	0.105620i	0.141938	+	0.989876i	$0.454667\pi$
$972$	77.0871	+	43.7008i	2.47257	+	1.40170i
$973$	−2.40970	−	1.75075i	−0.0772514	−	0.0561264i
$974$	45.6277	+	33.1505i	1.46201	+	1.06221i
$975$	−3.79765	−	13.5195i	−0.121622	−	0.432969i
$976$	135.078	−	43.8895i	4.32374	−	1.40487i
$977$	−25.3053	−	34.8298i	−0.809588	−	1.11430i	−0.991387	−	0.130967i	$-0.958192\pi$
$977$	−25.3053	−	34.8298i	−0.809588	−	1.11430i	0.181798	−	0.983336i	$-0.441808\pi$
$978$	23.7538	+	35.6306i	0.759564	+	1.13934i
$979$	25.0389	−	25.5561i	0.800245	−	0.816777i
$980$		−	4.60424i		−	0.147077i
$981$	13.1138	−	3.11940i	0.418690	−	0.0995949i
$982$	7.19047	+	22.1300i	0.229457	+	0.706197i
$983$	44.4786	+	14.4520i	1.41865	+	0.460946i	0.915172	−	0.403064i	$-0.132055\pi$
$983$	44.4786	+	14.4520i	1.41865	+	0.460946i	0.503475	+	0.864010i	$0.332055\pi$
$984$	2.04290	−	50.6479i	0.0651253	−	1.61460i
$985$	−10.3701	+	14.2732i	−0.330418	+	0.454781i
$986$	18.6370	−	57.3587i	0.593522	−	1.82667i
$987$	−11.5685	+	14.6431i	−0.368230	+	0.466096i
$988$	−24.1713	+	17.5615i	−0.768992	+	0.558706i
$989$	4.44889			0.141467
$990$	−19.1427	−	11.5175i	−0.608395	−	0.366050i
$991$	8.78805			0.279161			0.139581	−	0.990211i	$-0.455425\pi$
$991$	8.78805			0.279161			0.139581	+	0.990211i	$0.455425\pi$
$992$	143.424	−	104.204i	4.55372	−	3.30847i
$993$	−29.6082	+	37.4773i	−0.939587	+	1.18931i
$994$	7.68651	−	23.6567i	0.243801	−	0.750344i
$995$	11.0436	−	15.2002i	0.350105	−	0.481878i
$996$	6.46222	−	160.212i	0.204763	−	5.07652i
$997$	−7.59743	−	2.46856i	−0.240613	−	0.0781799i	0.186228	−	0.982507i	$-0.440374\pi$
$997$	−7.59743	−	2.46856i	−0.240613	−	0.0781799i	−0.426841	+	0.904327i	$0.640374\pi$
$998$	6.25874	+	19.2624i	0.198117	+	0.609742i
$999$	12.8418	−	13.8052i	0.406296	−	0.436777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.s.a.8.1	✓	96
3.2	odd	2	inner	231.2.s.a.8.24	yes	96
11.7	odd	10	inner	231.2.s.a.29.24	yes	96
33.29	even	10	inner	231.2.s.a.29.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.s.a.8.1	✓	96	1.1	even	1	trivial
231.2.s.a.8.24	yes	96	3.2	odd	2	inner
231.2.s.a.29.1	yes	96	33.29	even	10	inner
231.2.s.a.29.24	yes	96	11.7	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.24267 + 1.62939i) q^{2} +(1.07372 - 1.35909i) q^{3} +(1.75661 - 5.40628i) q^{4} +(0.476086 - 0.655276i) q^{5} +(-0.193509 + 4.79750i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(3.15622 + 9.71386i) q^{8} +(-0.694246 - 2.91857i) q^{9} +O(q^{10})\)	\(q+(-2.24267 + 1.62939i) q^{2} +(1.07372 - 1.35909i) q^{3} +(1.75661 - 5.40628i) q^{4} +(0.476086 - 0.655276i) q^{5} +(-0.193509 + 4.79750i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(3.15622 + 9.71386i) q^{8} +(-0.694246 - 2.91857i) q^{9} +2.24530i q^{10} +(-2.36906 - 2.32111i) q^{11} +(-5.46151 - 8.19221i) q^{12} +(-1.09704 - 1.50995i) q^{13} +(2.63642 - 0.856624i) q^{14} +(-0.379395 - 1.35063i) q^{15} +(-13.7084 - 9.95972i) q^{16} +(-3.37944 - 2.45531i) q^{17} +(6.31246 + 5.41418i) q^{18} +(2.67826 - 0.870219i) q^{19} +(-2.70631 - 3.72491i) q^{20} +(-1.44115 + 0.960772i) q^{21} +(9.09502 + 1.34535i) q^{22} +1.65622i q^{23} +(16.5909 + 6.14039i) q^{24} +(1.34236 + 4.13135i) q^{25} +(4.92061 + 1.59880i) q^{26} +(-4.71202 - 2.19018i) q^{27} +(-3.34126 + 4.59885i) q^{28} +(1.60946 - 4.95341i) q^{29} +(3.05156 + 2.41082i) q^{30} +(5.40322 - 3.92567i) q^{31} +26.5442 q^{32} +(-5.69831 + 0.727538i) q^{33} +11.5796 q^{34} +(-0.655276 + 0.476086i) q^{35} +(-16.9981 - 1.37348i) q^{36} +(-1.12129 + 3.45097i) q^{37} +(-4.58852 + 6.31555i) q^{38} +(-3.23007 - 0.130286i) q^{39} +(7.86789 + 2.55643i) q^{40} +(-0.885423 - 2.72505i) q^{41} +(1.66655 - 4.50290i) q^{42} -2.68617i q^{43} +(-16.7101 + 8.73052i) q^{44} +(-2.24299 - 0.934564i) q^{45} +(-2.69864 - 3.71435i) q^{46} +(10.2469 - 3.32942i) q^{47} +(-28.2551 + 7.93695i) q^{48} +(0.809017 + 0.587785i) q^{49} +(-9.74206 - 7.07802i) q^{50} +(-6.96556 + 1.95665i) q^{51} +(-10.0903 + 3.27853i) q^{52} +(2.05261 + 2.82517i) q^{53} +(14.1362 - 2.76588i) q^{54} +(-2.64884 + 0.447340i) q^{55} -10.2138i q^{56} +(1.69300 - 4.57436i) q^{57} +(4.46157 + 13.7313i) q^{58} +(-2.61461 - 0.849537i) q^{59} +(-7.96830 - 0.321404i) q^{60} +(-4.92684 + 6.78121i) q^{61} +(-5.72118 + 17.6080i) q^{62} +(-0.241619 + 2.99025i) q^{63} +(-32.1130 + 23.3315i) q^{64} -1.51172 q^{65} +(11.5940 - 10.9164i) q^{66} -4.13041 q^{67} +(-19.2104 + 13.9572i) q^{68} +(2.25095 + 1.77832i) q^{69} +(0.693835 - 2.13541i) q^{70} +(5.27422 - 7.25934i) q^{71} +(26.1593 - 15.9555i) q^{72} +(14.1884 + 4.61010i) q^{73} +(-3.10832 - 9.56641i) q^{74} +(7.05619 + 2.61153i) q^{75} -16.0080i q^{76} +(1.53585 + 2.93959i) q^{77} +(7.45628 - 4.97088i) q^{78} +(-5.55936 - 7.65180i) q^{79} +(-13.0527 + 4.24109i) q^{80} +(-8.03604 + 4.05241i) q^{81} +(6.42590 + 4.66869i) q^{82} +(13.1751 + 9.57228i) q^{83} +(2.66267 + 9.47896i) q^{84} +(-3.21781 + 1.04553i) q^{85} +(4.37684 + 6.02420i) q^{86} +(-5.00401 - 7.50598i) q^{87} +(15.0697 - 30.3387i) q^{88} +10.7874i q^{89} +(6.55305 - 1.55879i) q^{90} +(0.576750 + 1.77505i) q^{91} +(8.95398 + 2.90933i) q^{92} +(0.466217 - 11.5585i) q^{93} +(-17.5555 + 24.1630i) q^{94} +(0.704847 - 2.16930i) q^{95} +(28.5010 - 36.0759i) q^{96} +(-4.52367 + 3.28664i) q^{97} -2.77209 q^{98} +(-5.12960 + 8.52568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

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