LMFDB - Embedded newform 224.2.x.b.27.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(27,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4]))

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

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

chi := DirichletCharacter("224.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.x (of order $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			27.13
Character	$\chi$	$=$	224.27
Dual form			224.2.x.b.83.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.242331 - 1.39330i) q^{2} +(-1.25862 - 3.03857i) q^{3} +(-1.88255 + 0.675278i) q^{4} +(-0.824079 + 1.98950i) q^{5} +(-3.92863 + 2.48997i) q^{6} +(-0.0837494 - 2.64443i) q^{7} +(1.39706 + 2.45931i) q^{8} +(-5.52747 + 5.52747i) q^{9} +O(q^{10})$	\(q+(-0.242331 - 1.39330i) q^{2} +(-1.25862 - 3.03857i) q^{3} +(-1.88255 + 0.675278i) q^{4} +(-0.824079 + 1.98950i) q^{5} +(-3.92863 + 2.48997i) q^{6} +(-0.0837494 - 2.64443i) q^{7} +(1.39706 + 2.45931i) q^{8} +(-5.52747 + 5.52747i) q^{9} +(2.97167 + 0.666069i) q^{10} +(-0.623399 - 0.258220i) q^{11} +(4.42129 + 4.87035i) q^{12} +(-1.24310 - 3.00110i) q^{13} +(-3.66417 + 0.757514i) q^{14} +7.08245 q^{15} +(3.08800 - 2.54249i) q^{16} +2.68128 q^{17} +(9.04089 + 6.36193i) q^{18} +(-4.54495 + 1.88258i) q^{19} +(0.207903 - 4.30183i) q^{20} +(-7.92987 + 3.58280i) q^{21} +(-0.208709 + 0.931155i) q^{22} +(-0.871276 - 0.871276i) q^{23} +(5.71442 - 7.34041i) q^{24} +(0.256515 + 0.256515i) q^{25} +(-3.88019 + 2.45926i) q^{26} +(14.6369 + 6.06280i) q^{27} +(1.94339 + 4.92171i) q^{28} +(-2.60571 - 6.29073i) q^{29} +(-1.71630 - 9.86795i) q^{30} -4.75214 q^{31} +(-4.29076 - 3.68637i) q^{32} +2.21924i q^{33} +(-0.649758 - 3.73582i) q^{34} +(5.33011 + 2.01260i) q^{35} +(6.67317 - 14.1383i) q^{36} +(-5.97522 - 2.47502i) q^{37} +(3.72438 + 5.87626i) q^{38} +(-7.55448 + 7.55448i) q^{39} +(-6.04410 + 0.752795i) q^{40} +(3.37920 + 3.37920i) q^{41} +(6.91355 + 10.1804i) q^{42} +(-11.8871 - 4.92381i) q^{43} +(1.34795 + 0.0651453i) q^{44} +(-6.44185 - 15.5520i) q^{45} +(-1.00281 + 1.42508i) q^{46} -3.01477i q^{47} +(-11.6121 - 6.18308i) q^{48} +(-6.98597 + 0.442938i) q^{49} +(0.295240 - 0.419564i) q^{50} +(-3.37471 - 8.14727i) q^{51} +(4.36677 + 4.81029i) q^{52} +(1.62665 - 3.92708i) q^{53} +(4.90030 - 21.8627i) q^{54} +(1.02746 - 1.02746i) q^{55} +(6.38646 - 3.90040i) q^{56} +(11.4407 + 11.4407i) q^{57} +(-8.13341 + 5.15496i) q^{58} +(2.08390 + 0.863180i) q^{59} +(-13.3331 + 4.78262i) q^{60} +(5.36260 - 2.22126i) q^{61} +(1.15159 + 6.62114i) q^{62} +(15.0799 + 14.1541i) q^{63} +(-4.09643 + 6.87163i) q^{64} +6.99512 q^{65} +(3.09206 - 0.537792i) q^{66} +(6.52791 - 2.70395i) q^{67} +(-5.04765 + 1.81061i) q^{68} +(-1.55083 + 3.74404i) q^{69} +(1.51249 - 7.91414i) q^{70} +(9.16414 - 9.16414i) q^{71} +(-21.3160 - 5.87155i) q^{72} +(3.68420 + 3.68420i) q^{73} +(-2.00045 + 8.92502i) q^{74} +(0.456585 - 1.10229i) q^{75} +(7.28484 - 6.61317i) q^{76} +(-0.630635 + 1.67016i) q^{77} +(12.3563 + 8.69495i) q^{78} +5.81800 q^{79} +(2.51354 + 8.23880i) q^{80} -28.6549i q^{81} +(3.88934 - 5.52711i) q^{82} +(4.18900 - 1.73514i) q^{83} +(12.5090 - 12.0997i) q^{84} +(-2.20959 + 5.33442i) q^{85} +(-3.97971 + 17.7555i) q^{86} +(-15.8352 + 15.8352i) q^{87} +(-0.235884 - 1.89388i) q^{88} +(0.872091 - 0.872091i) q^{89} +(-20.1075 + 12.7441i) q^{90} +(-7.83209 + 3.53862i) q^{91} +(2.22858 + 1.05187i) q^{92} +(5.98113 + 14.4397i) q^{93} +(-4.20047 + 0.730573i) q^{94} -10.5936i q^{95} +(-5.80088 + 17.6775i) q^{96} -16.0201i q^{97} +(2.31006 + 9.62619i) q^{98} +(4.87313 - 2.01852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9	$ 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{11} - 20 q^{14} - 16 q^{15} + 16 q^{16} - 16 q^{18} - 4 q^{21} + 32 q^{22} - 48 q^{23} - 8 q^{25} - 24 q^{28} - 8 q^{29} + 16 q^{30} - 8 q^{32} + 20 q^{35} + 32 q^{36} - 8 q^{37} - 8 q^{39} + 16 q^{42} + 32 q^{43} - 144 q^{44} - 8 q^{46} + 16 q^{50} - 32 q^{51} - 32 q^{53} + 64 q^{56} - 8 q^{57} - 72 q^{58} - 88 q^{60} + 112 q^{64} - 16 q^{65} - 64 q^{67} - 40 q^{70} + 56 q^{71} - 8 q^{72} - 168 q^{74} + 52 q^{77} + 192 q^{78} - 16 q^{79} - 24 q^{84} - 48 q^{85} - 8 q^{86} - 96 q^{88} - 52 q^{91} - 8 q^{92} - 32 q^{93} + 88 q^{98} + 16 q^{99}+O(q^{100}) $ 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^11 - 20 * q^14 - 16 * q^15 + 16 * q^16 - 16 * q^18 - 4 * q^21 + 32 * q^22 - 48 * q^23 - 8 * q^25 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 8 * q^32 + 20 * q^35 + 32 * q^36 - 8 * q^37 - 8 * q^39 + 16 * q^42 + 32 * q^43 - 144 * q^44 - 8 * q^46 + 16 * q^50 - 32 * q^51 - 32 * q^53 + 64 * q^56 - 8 * q^57 - 72 * q^58 - 88 * q^60 + 112 * q^64 - 16 * q^65 - 64 * q^67 - 40 * q^70 + 56 * q^71 - 8 * q^72 - 168 * q^74 + 52 * q^77 + 192 * q^78 - 16 * q^79 - 24 * q^84 - 48 * q^85 - 8 * q^86 - 96 * q^88 - 52 * q^91 - 8 * q^92 - 32 * q^93 + 88 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	−0.242331	−	1.39330i	−0.171354	−	0.985210i
$2$	−0.242331	−	1.39330i	−0.171354	−	0.985210i
$3$	−1.25862	−	3.03857i	−0.726663	−	1.75432i	−0.653407	−	0.757006i	$-0.726661\pi$
$3$	−1.25862	−	3.03857i	−0.726663	−	1.75432i	−0.0732556	−	0.997313i	$-0.523339\pi$
$4$	−1.88255	+	0.675278i	−0.941276	+	0.337639i
$5$	−0.824079	+	1.98950i	−0.368540	+	0.889733i	0.625451	+	0.780264i	$0.284915\pi$
$5$	−0.824079	+	1.98950i	−0.368540	+	0.889733i	−0.993990	+	0.109469i	$0.965085\pi$
$6$	−3.92863	+	2.48997i	−1.60386	+	1.01652i
$7$	−0.0837494	−	2.64443i	−0.0316543	−	0.999499i
$7$	−0.0837494	−	2.64443i	−0.0316543	−	0.999499i
$8$	1.39706	+	2.45931i	0.493937	+	0.869498i
$9$	−5.52747	+	5.52747i	−1.84249	+	1.84249i
$10$	2.97167	+	0.666069i	0.939724	+	0.210629i
$11$	−0.623399	−	0.258220i	−0.187962	−	0.0778564i	0.286717	−	0.958015i	$-0.407436\pi$
$11$	−0.623399	−	0.258220i	−0.187962	−	0.0778564i	−0.474679	+	0.880159i	$0.657436\pi$
$12$	4.42129	+	4.87035i	1.27632	+	1.40595i
$13$	−1.24310	−	3.00110i	−0.344773	−	0.832356i	−0.997219	−	0.0745212i	$-0.976257\pi$
$13$	−1.24310	−	3.00110i	−0.344773	−	0.832356i	0.652446	−	0.757835i	$-0.273743\pi$
$14$	−3.66417	+	0.757514i	−0.979292	+	0.202454i
$15$	7.08245			1.82868
$16$	3.08800	−	2.54249i	0.772000	−	0.635623i
$17$	2.68128			0.650307			0.325153	−	0.945661i	$-0.394584\pi$
$17$	2.68128			0.650307			0.325153	+	0.945661i	$0.394584\pi$
$18$	9.04089	+	6.36193i	2.13096	+	1.49952i
$19$	−4.54495	+	1.88258i	−1.04268	+	0.431894i	−0.837275	−	0.546782i	$-0.815853\pi$
$19$	−4.54495	+	1.88258i	−1.04268	+	0.431894i	−0.205409	+	0.978676i	$0.565853\pi$
$20$	0.207903	−	4.30183i	0.0464886	−	0.961918i
$21$	−7.92987	+	3.58280i	−1.73044	+	0.781831i
$22$	−0.208709	+	0.931155i	−0.0444968	+	0.198523i
$23$	−0.871276	−	0.871276i	−0.181674	−	0.181674i	0.610411	−	0.792085i	$-0.291004\pi$
$23$	−0.871276	−	0.871276i	−0.181674	−	0.181674i	−0.792085	+	0.610411i	$0.791004\pi$
$24$	5.71442	−	7.34041i	1.16645	−	1.49835i
$25$	0.256515	+	0.256515i	0.0513031	+	0.0513031i
$26$	−3.88019	+	2.45926i	−0.760967	+	0.482301i
$27$	14.6369	+	6.06280i	2.81687	+	1.16679i
$28$	1.94339	+	4.92171i	0.367265	+	0.930116i
$29$	−2.60571	−	6.29073i	−0.483867	−	1.16816i	−0.957758	−	0.287576i	$-0.907151\pi$
$29$	−2.60571	−	6.29073i	−0.483867	−	1.16816i	0.473891	−	0.880584i	$-0.342849\pi$
$30$	−1.71630	−	9.86795i	−0.313352	−	1.80163i
$31$	−4.75214			−0.853510			−0.426755	−	0.904367i	$-0.640343\pi$
$31$	−4.75214			−0.853510			−0.426755	+	0.904367i	$0.640343\pi$
$32$	−4.29076	−	3.68637i	−0.758507	−	0.651665i
$33$			2.21924i			0.386321i
$34$	−0.649758	−	3.73582i	−0.111433	−	0.640688i
$35$	5.33011	+	2.01260i	0.900953	+	0.340191i
$36$	6.67317	−	14.1383i	1.11220	−	2.35639i
$37$	−5.97522	−	2.47502i	−0.982319	−	0.406890i	−0.167035	−	0.985951i	$-0.553419\pi$
$37$	−5.97522	−	2.47502i	−0.982319	−	0.406890i	−0.815284	+	0.579061i	$0.803419\pi$
$38$	3.72438	+	5.87626i	0.604174	+	0.953256i
$39$	−7.55448	+	7.55448i	−1.20969	+	1.20969i
$40$	−6.04410	+	0.752795i	−0.955656	+	0.119027i
$41$	3.37920	+	3.37920i	0.527742	+	0.527742i	0.919899	−	0.392156i	$-0.128271\pi$
$41$	3.37920	+	3.37920i	0.527742	+	0.527742i	−0.392156	+	0.919899i	$0.628271\pi$
$42$	6.91355	+	10.1804i	1.06678	+	1.57087i
$43$	−11.8871	−	4.92381i	−1.81277	−	0.750874i	−0.980505	−	0.196496i	$-0.937044\pi$
$43$	−11.8871	−	4.92381i	−1.81277	−	0.750874i	−0.832265	−	0.554378i	$-0.812956\pi$
$44$	1.34795	+	0.0651453i	0.203211	+	0.00982103i
$45$	−6.44185	−	15.5520i	−0.960295	−	2.31836i
$46$	−1.00281	+	1.42508i	−0.147856	+	0.210117i
$47$		−	3.01477i		−	0.439750i	−0.975528	−	0.219875i	$-0.929435\pi$
$47$		−	3.01477i		−	0.439750i	0.975528	−	0.219875i	$-0.0705649\pi$
$48$	−11.6121	−	6.18308i	−1.67607	−	0.892451i
$49$	−6.98597	+	0.442938i	−0.997996	+	0.0632769i
$50$	0.295240	−	0.419564i	0.0417533	−	0.0593353i
$51$	−3.37471	−	8.14727i	−0.472554	−	1.14085i
$52$	4.36677	+	4.81029i	0.605563	+	0.667068i
$53$	1.62665	−	3.92708i	0.223437	−	0.539425i	−0.771915	−	0.635726i	$-0.780701\pi$
$53$	1.62665	−	3.92708i	0.223437	−	0.539425i	0.995352	+	0.0963004i	$0.0307010\pi$
$54$	4.90030	−	21.8627i	0.666847	−	2.97514i
$55$	1.02746	−	1.02746i	0.138543	−	0.138543i
$56$	6.38646	−	3.90040i	0.853427	−	0.521212i
$57$	11.4407	+	11.4407i	1.51536	+	1.51536i
$58$	−8.13341	+	5.15496i	−1.06797	+	0.676880i
$59$	2.08390	+	0.863180i	0.271301	+	0.112376i	0.514186	−	0.857678i	$-0.328094\pi$
$59$	2.08390	+	0.863180i	0.271301	+	0.112376i	−0.242886	+	0.970055i	$0.578094\pi$
$60$	−13.3331	+	4.78262i	−1.72129	+	0.617434i
$61$	5.36260	−	2.22126i	0.686611	−	0.284403i	−0.0119767	−	0.999928i	$-0.503812\pi$
$61$	5.36260	−	2.22126i	0.686611	−	0.284403i	0.698587	+	0.715525i	$0.253812\pi$
$62$	1.15159	+	6.62114i	0.146252	+	0.840886i
$63$	15.0799	+	14.1541i	1.89989	+	1.78325i
$64$	−4.09643	+	6.87163i	−0.512053	+	0.858954i
$65$	6.99512			0.867638
$66$	3.09206	−	0.537792i	0.380607	−	0.0661976i
$67$	6.52791	−	2.70395i	0.797511	−	0.330340i	0.0535518	−	0.998565i	$-0.482946\pi$
$67$	6.52791	−	2.70395i	0.797511	−	0.330340i	0.743959	+	0.668225i	$0.232946\pi$
$68$	−5.04765	+	1.81061i	−0.612118	+	0.219569i
$69$	−1.55083	+	3.74404i	−0.186698	+	0.450729i
$70$	1.51249	−	7.91414i	0.180778	−	0.945921i
$71$	9.16414	−	9.16414i	1.08758	−	1.08758i	0.0918067	−	0.995777i	$-0.470736\pi$
$71$	9.16414	−	9.16414i	1.08758	−	1.08758i	0.995777	−	0.0918067i	$-0.0292642\pi$
$72$	−21.3160	−	5.87155i	−2.51212	−	0.691969i
$73$	3.68420	+	3.68420i	0.431203	+	0.431203i	0.889037	−	0.457835i	$-0.151375\pi$
$73$	3.68420	+	3.68420i	0.431203	+	0.431203i	−0.457835	+	0.889037i	$0.651375\pi$
$74$	−2.00045	+	8.92502i	−0.232548	+	1.03751i
$75$	0.456585	−	1.10229i	0.0527219	−	0.127282i
$76$	7.28484	−	6.61317i	0.835629	−	0.758582i
$77$	−0.630635	+	1.67016i	−0.0718676	+	0.190332i
$78$	12.3563	+	8.69495i	1.39908	+	0.984509i
$79$	5.81800			0.654576			0.327288	−	0.944925i	$-0.393865\pi$
$79$	5.81800			0.654576			0.327288	+	0.944925i	$0.393865\pi$
$80$	2.51354	+	8.23880i	0.281022	+	0.921126i
$81$		−	28.6549i		−	3.18387i
$82$	3.88934	−	5.52711i	0.429506	−	0.610367i
$83$	4.18900	−	1.73514i	0.459803	−	0.190457i	−0.140744	−	0.990046i	$-0.544950\pi$
$83$	4.18900	−	1.73514i	0.459803	−	0.190457i	0.600547	+	0.799589i	$0.294950\pi$
$84$	12.5090	−	12.0997i	1.36484	−	1.32018i
$85$	−2.20959	+	5.33442i	−0.239664	+	0.578599i
$86$	−3.97971	+	17.7555i	−0.429143	+	1.91462i
$87$	−15.8352	+	15.8352i	−1.69772	+	1.69772i
$88$	−0.235884	−	1.89388i	−0.0251453	−	0.201889i
$89$	0.872091	−	0.872091i	0.0924415	−	0.0924415i	−0.659374	−	0.751815i	$-0.729179\pi$
$89$	0.872091	−	0.872091i	0.0924415	−	0.0924415i	0.751815	+	0.659374i	$0.229179\pi$
$90$	−20.1075	+	12.7441i	−2.11952	+	1.34335i
$91$	−7.83209	+	3.53862i	−0.821026	+	0.370948i
$92$	2.22858	+	1.05187i	0.232345	+	0.109665i
$93$	5.98113	+	14.4397i	0.620214	+	1.49733i
$94$	−4.20047	+	0.730573i	−0.433246	+	0.0753528i
$95$		−	10.5936i		−	1.08688i
$96$	−5.80088	+	17.6775i	−0.592050	+	1.80420i
$97$		−	16.0201i		−	1.62660i	−0.581845	−	0.813300i	$-0.697669\pi$
$97$		−	16.0201i		−	1.62660i	0.581845	−	0.813300i	$-0.302331\pi$
$98$	2.31006	+	9.62619i	0.233352	+	0.972392i
$99$	4.87313	−	2.01852i	0.489768	−	0.202869i
$100$	−0.656122	−	0.309684i	−0.0656122	−	0.0309684i
$101$	0.555956	−	1.34220i	0.0553197	−	0.133554i	−0.893803	−	0.448459i	$-0.851973\pi$
$101$	0.555956	−	1.34220i	0.0553197	−	0.133554i	0.949123	+	0.314906i	$0.101973\pi$
$102$	−10.5338	+	6.67631i	−1.04300	+	0.661053i
$103$	−4.23866	−	4.23866i	−0.417647	−	0.417647i	0.466745	−	0.884392i	$-0.345427\pi$
$103$	−4.23866	−	4.23866i	−0.417647	−	0.417647i	−0.884392	+	0.466745i	$0.845427\pi$
$104$	5.64396	−	7.24990i	0.553436	−	0.710911i
$105$	−0.593151	−	18.7290i	−0.0578856	−	1.82776i
$106$	−5.86577	−	1.31475i	−0.569734	−	0.127700i
$107$	7.88751	+	3.26711i	0.762514	+	0.315844i	0.729836	−	0.683622i	$-0.239596\pi$
$107$	7.88751	+	3.26711i	0.762514	+	0.315844i	0.0326782	+	0.999466i	$0.489596\pi$
$108$	−31.6488	−	1.52956i	−3.04540	−	0.147182i
$109$	−4.75970	+	1.97153i	−0.455897	+	0.188839i	−0.598801	−	0.800898i	$-0.704356\pi$
$109$	−4.75970	+	1.97153i	−0.455897	+	0.188839i	0.142904	+	0.989737i	$0.454356\pi$
$110$	−1.68054	−	1.18257i	−0.160234	−	0.112754i
$111$			21.2712i			2.01897i
$112$	−6.98205	−	7.95305i	−0.659741	−	0.751493i
$113$			10.2261i			0.961993i	0.876723	+	0.480996i	$0.159725\pi$
$113$			10.2261i			0.961993i	−0.876723	+	0.480996i	$0.840275\pi$
$114$	13.1679	−	18.7128i	1.23328	−	1.75261i
$115$	2.45141	−	1.01541i	0.228595	−	0.0946872i
$116$	9.15337	+	10.0830i	0.849869	+	0.936187i
$117$	23.4597	+	9.71733i	2.16885	+	0.898368i
$118$	0.697672	−	3.11267i	0.0642259	−	0.286544i
$119$	−0.224556	−	7.09045i	−0.0205850	−	0.649981i
$120$	9.89463	+	17.4179i	0.903252	+	1.59003i
$121$	−7.45623	−	7.45623i	−0.677839	−	0.677839i
$122$	−4.39440	−	6.93341i	−0.397850	−	0.627722i
$123$	6.01482	−	14.5210i	0.542338	−	1.30932i
$124$	8.94615	−	3.20902i	0.803388	−	0.288178i
$125$	−10.6692	+	4.41935i	−0.954286	+	0.395278i
$126$	16.0665	−	24.4408i	1.43132	−	2.17736i
$127$		−	3.43170i		−	0.304514i	−0.988341	−	0.152257i	$-0.951346\pi$
$127$		−	3.43170i		−	0.304514i	0.988341	−	0.152257i	$-0.0486542\pi$
$128$	10.5669	+	4.04233i	0.933992	+	0.357295i
$129$			42.3171i			3.72581i
$130$	−1.69513	−	9.74627i	−0.148673	−	0.854805i
$131$	−2.16614	−	5.22953i	−0.189257	−	0.456906i	0.800560	−	0.599252i	$-0.204535\pi$
$131$	−2.16614	−	5.22953i	−0.189257	−	0.456906i	−0.989817	+	0.142346i	$0.954535\pi$
$132$	−1.49861	−	4.17784i	−0.130437	−	0.363634i
$133$	5.35898	+	11.8611i	0.464683	+	1.02849i
$134$	−5.34932	−	8.44006i	−0.462111	−	0.729110i
$135$	−24.1239	+	24.1239i	−2.07626	+	2.07626i
$136$	3.74592	+	6.59411i	0.321210	+	0.565440i
$137$	−6.07189	+	6.07189i	−0.518757	+	0.518757i	−0.917195	−	0.398438i	$-0.869552\pi$
$137$	−6.07189	+	6.07189i	−0.518757	+	0.518757i	0.398438	+	0.917195i	$0.369552\pi$
$138$	5.59237	+	1.25347i	0.476054	+	0.106703i
$139$	1.49929	−	3.61960i	0.127168	−	0.307011i	−0.847454	−	0.530869i	$-0.821865\pi$
$139$	1.49929	−	3.61960i	0.127168	−	0.307011i	0.974622	+	0.223859i	$0.0718654\pi$
$140$	−11.3933	−	0.189510i	−0.962907	−	0.0160165i
$141$	−9.16060	+	3.79444i	−0.771461	+	0.319550i
$142$	−14.9891	−	10.5476i	−1.25786	−	0.885136i
$143$			2.19188i			0.183294i
$144$	−3.01528	+	31.1224i	−0.251273	+	2.59353i
$145$	14.6627			1.21767
$146$	4.24038	−	6.02597i	0.350937	−	0.498713i
$147$	10.1386	+	20.6699i	0.836215	+	1.70482i
$148$	12.9200	+	0.624411i	1.06202	+	0.0513263i
$149$	−0.328004	+	0.791871i	−0.0268711	+	0.0648726i	−0.936746	−	0.350011i	$-0.886178\pi$
$149$	−0.328004	+	0.791871i	−0.0268711	+	0.0648726i	0.909874	+	0.414884i	$0.136178\pi$
$150$	−1.64647	−	0.369039i	−0.134434	−	0.0301319i
$151$	5.36290	+	5.36290i	0.436427	+	0.436427i	0.890808	−	0.454381i	$-0.150139\pi$
$151$	5.36290	+	5.36290i	0.436427	+	0.436427i	−0.454381	+	0.890808i	$0.650139\pi$
$152$	−10.9794	−	8.54737i	−0.890551	−	0.693284i
$153$	−14.8207	+	14.8207i	−1.19818	+	1.19818i
$154$	2.47985	+	0.473931i	0.199832	+	0.0381904i
$155$	3.91614	−	9.45440i	0.314552	−	0.759396i
$156$	9.12032	−	19.3231i	0.730210	−	1.54708i
$157$	17.5449	−	7.26734i	1.40024	−	0.579996i	0.450423	−	0.892815i	$-0.351273\pi$
$157$	17.5449	−	7.26734i	1.40024	−	0.579996i	0.949813	+	0.312819i	$0.101273\pi$
$158$	−1.40988	−	8.10620i	−0.112164	−	0.644895i
$159$	−13.9800			−1.10869
$160$	10.8700	−	5.49862i	0.859348	−	0.434704i
$161$	−2.23106	+	2.37699i	−0.175832	+	0.187333i
$162$	−39.9247	+	6.94396i	−3.13678	+	0.545569i
$163$	−14.6269	+	6.05865i	−1.14567	+	0.474550i	−0.873078	−	0.487581i	$-0.837879\pi$
$163$	−14.6269	+	6.05865i	−1.14567	+	0.474550i	−0.272587	+	0.962131i	$0.587879\pi$
$164$	−8.64341	−	4.07961i	−0.674937	−	0.318564i
$165$	−4.41519	−	1.82883i	−0.343722	−	0.142374i
$166$	−3.43269	−	5.41605i	−0.266429	−	0.420367i
$167$	−12.5015	−	12.5015i	−0.967399	−	0.967399i	0.0320865	−	0.999485i	$-0.489785\pi$
$167$	−12.5015	−	12.5015i	−0.967399	−	0.967399i	−0.999485	+	0.0320865i	$0.989785\pi$
$168$	−19.8897	−	14.4966i	−1.53453	−	1.11844i
$169$	1.73106	−	1.73106i	0.133158	−	0.133158i
$170$	7.96788	+	1.78592i	0.611109	+	0.136974i
$171$	14.7162	−	35.5280i	1.12538	−	2.71690i
$172$	25.7031	+	1.24221i	1.95984	+	0.0947174i
$173$	3.90765	+	9.43391i	0.297093	+	0.717247i	0.999982	+	0.00594710i	$0.00189303\pi$
$173$	3.90765	+	9.43391i	0.297093	+	0.717247i	−0.702889	+	0.711300i	$0.748107\pi$
$174$	25.9006	+	18.2258i	1.96352	+	1.38170i
$175$	0.656853	−	0.699819i	0.0496534	−	0.0529013i
$176$	−2.58158	+	0.787603i	−0.194594	+	0.0593678i
$177$		−	7.41849i		−	0.557608i
$178$	−1.42642	−	1.00375i	−0.106914	−	0.0752340i
$179$	0.689085	+	1.66360i	0.0515046	+	0.124343i	0.947538	−	0.319644i	$-0.103563\pi$
$179$	0.689085	+	1.66360i	0.0515046	+	0.124343i	−0.896033	+	0.443988i	$0.853563\pi$
$180$	22.6291	+	24.9274i	1.68667	+	1.85798i
$181$	−1.09010	−	0.451534i	−0.0810264	−	0.0335623i	0.341802	−	0.939772i	$-0.388963\pi$
$181$	−1.09010	−	0.451534i	−0.0810264	−	0.0335623i	−0.422829	+	0.906210i	$0.638963\pi$
$182$	6.82831	+	10.0549i	0.506148	+	0.745319i
$183$	−13.4989	−	13.4989i	−0.997869	−	0.997869i
$184$	0.925512	−	3.35997i	0.0682296	−	0.247700i
$185$	9.84811	−	9.84811i	0.724047	−	0.724047i
$186$	18.6694	−	11.8327i	1.36891	−	0.867614i
$187$	−1.67151	−	0.692362i	−0.122233	−	0.0506305i
$188$	2.03581	+	5.67546i	0.148477	+	0.413926i
$189$	14.8068	−	39.2139i	1.07703	−	2.85239i
$190$	−14.7600	+	2.56716i	−1.07081	+	0.186241i
$191$			4.49592i			0.325313i	0.986683	+	0.162657i	$0.0520063\pi$
$191$			4.49592i			0.325313i	−0.986683	+	0.162657i	$0.947994\pi$
$192$	26.0358	+	3.79853i	1.87897	+	0.274136i
$193$	12.6862			0.913170			0.456585	−	0.889680i	$-0.349072\pi$
$193$	12.6862			0.913170			0.456585	+	0.889680i	$0.349072\pi$
$194$	−22.3208	+	3.88218i	−1.60254	+	0.278724i
$195$	−8.80418	−	21.2552i	−0.630480	−	1.52211i
$196$	12.8523	−	5.55133i	0.918025	−	0.396523i
$197$	11.0548	+	4.57904i	0.787620	+	0.326243i	0.739986	−	0.672622i	$-0.234832\pi$
$197$	11.0548	+	4.57904i	0.787620	+	0.326243i	0.0476337	+	0.998865i	$0.484832\pi$
$198$	−3.99330	−	6.30057i	−0.283792	−	0.447762i
$199$	−7.36746	−	7.36746i	−0.522265	−	0.522265i	0.395990	−	0.918255i	$-0.370402\pi$
$199$	−7.36746	−	7.36746i	−0.522265	−	0.522265i	−0.918255	+	0.395990i	$0.870402\pi$
$200$	−0.272483	+	0.989219i	−0.0192675	+	0.0699484i
$201$	−16.4323	−	16.4323i	−1.15904	−	1.15904i
$202$	−2.00480	−	0.449356i	−0.141057	−	0.0316166i
$203$	−16.4171	+	7.41744i	−1.15226	+	0.520602i
$204$	11.8547	+	13.0588i	0.829997	+	0.914298i
$205$	−9.50765	+	3.93820i	−0.664043	+	0.275056i
$206$	−4.87855	+	6.93286i	−0.339904	+	0.483035i
$207$	9.63192			0.669465
$208$	−11.4690	−	6.10684i	−0.795230	−	0.423433i
$209$	3.31944			0.229611
$210$	−25.9513	+	5.36506i	−1.79081	+	0.370224i
$211$	6.69674	+	16.1673i	0.461022	+	1.11301i	0.967978	+	0.251034i	$0.0807707\pi$
$211$	6.69674	+	16.1673i	0.461022	+	1.11301i	−0.506956	+	0.861972i	$0.669229\pi$
$212$	−0.410380	+	8.49136i	−0.0281850	+	0.583189i
$213$	−39.3800	−	16.3117i	−2.69828	−	1.11766i
$214$	2.64067	−	11.7814i	0.180512	−	0.805357i
$215$	19.5919	−	19.5919i	1.33615	−	1.33615i
$216$	5.53835	+	44.4668i	0.376837	+	3.02558i
$217$	0.397989	+	12.5667i	0.0270173	+	0.853082i
$218$	3.90035	+	6.15391i	0.264165	+	0.416795i
$219$	6.55770	−	15.8317i	0.443128	−	1.06981i
$220$	−1.24043	+	2.62807i	−0.0836295	+	0.177184i
$221$	−3.33310	−	8.04681i	−0.224208	−	0.541287i
$222$	29.6371	−	5.15468i	1.98911	−	0.345959i
$223$	−25.1684			−1.68540			−0.842700	−	0.538383i	$-0.819035\pi$
$223$	−25.1684			−1.68540			−0.842700	+	0.538383i	$0.819035\pi$
$224$	−9.38899	+	11.6553i	−0.627328	+	0.778755i
$225$	−2.83576			−0.189051
$226$	14.2480	−	2.47811i	0.947764	−	0.164841i
$227$	11.3017	+	27.2846i	0.750118	+	1.81095i	0.558560	+	0.829464i	$0.311354\pi$
$227$	11.3017	+	27.2846i	0.750118	+	1.81095i	0.191559	+	0.981481i	$0.438646\pi$
$228$	−29.2634	−	13.8121i	−1.93802	−	0.914727i
$229$	−2.33071	+	5.62684i	−0.154018	+	0.371832i	−0.981989	−	0.188939i	$-0.939495\pi$
$229$	−2.33071	+	5.62684i	−0.154018	+	0.371832i	0.827971	+	0.560771i	$0.189495\pi$
$230$	−2.00882	−	3.16948i	−0.132457	−	0.208989i
$231$	5.86862	−	0.185860i	0.386127	−	0.0122287i
$232$	11.8305	−	15.1968i	0.776712	−	0.997718i
$233$	−5.98323	+	5.98323i	−0.391974	+	0.391974i	−0.875391	−	0.483416i	$-0.839396\pi$
$233$	−5.98323	+	5.98323i	−0.391974	+	0.391974i	0.483416	+	0.875391i	$0.339396\pi$
$234$	7.85411	−	35.0412i	0.513439	−	2.29071i
$235$	5.99790	+	2.48441i	0.391260	+	0.162065i
$236$	−4.50594	−	0.217768i	−0.293311	−	0.0141755i
$237$	−7.32263	−	17.6784i	−0.475656	−	1.14834i
$238$	−9.82469	+	2.03111i	−0.636840	+	0.131657i
$239$	−15.7731			−1.02028			−0.510138	−	0.860092i	$-0.670406\pi$
$239$	−15.7731			−1.02028			−0.510138	+	0.860092i	$0.670406\pi$
$240$	21.8706	−	18.0071i	1.41174	−	1.16235i
$241$	28.0178			1.80479			0.902394	−	0.430912i	$-0.141808\pi$
$241$	28.0178			1.80479			0.902394	+	0.430912i	$0.141808\pi$
$242$	−8.58186	+	12.1956i	−0.551663	+	0.783963i
$243$	−43.1592	+	17.8771i	−2.76866	+	1.14682i
$244$	−8.59540	+	7.80289i	−0.550264	+	0.499529i
$245$	4.87577	−	14.2636i	0.311501	−	0.911270i
$246$	−21.6897	−	4.86152i	−1.38289	−	0.309959i
$247$	11.2996	+	11.2996i	0.718979	+	0.718979i
$248$	−6.63904	−	11.6870i	−0.421580	−	0.742125i
$249$	−10.5447	−	10.5447i	−0.668243	−	0.668243i
$250$	8.74295	+	13.7945i	0.552953	+	0.872440i
$251$	10.8704	+	4.50269i	0.686137	+	0.284207i	0.698390	−	0.715718i	$-0.253900\pi$
$251$	10.8704	+	4.50269i	0.686137	+	0.284207i	−0.0122529	+	0.999925i	$0.503900\pi$
$252$	−37.9467	−	16.4626i	−2.39041	−	1.03705i
$253$	0.318172	+	0.768134i	0.0200033	+	0.0482922i
$254$	−4.78138	+	0.831608i	−0.300010	+	0.0521797i
$255$	18.9900			1.18920
$256$	3.07147	−	15.7024i	0.191967	−	0.981401i
$257$		−	17.4070i		−	1.08582i	−0.839791	−	0.542910i	$-0.817322\pi$
$257$		−	17.4070i		−	1.08582i	0.839791	−	0.542910i	$-0.182678\pi$
$258$	58.9602	−	10.2547i	3.67070	−	0.638432i
$259$	−6.04457	+	16.0083i	−0.375591	+	0.994707i
$260$	−13.1687	+	4.72365i	−0.816686	+	0.292948i
$261$	49.1748	+	20.3689i	3.04385	+	1.26080i
$262$	−6.76136	+	4.28535i	−0.417718	+	0.264750i
$263$	0.439018	−	0.439018i	0.0270710	−	0.0270710i	−0.693442	−	0.720513i	$-0.743907\pi$
$263$	0.439018	−	0.439018i	0.0270710	−	0.0270710i	0.720513	+	0.693442i	$0.243907\pi$
$264$	−5.45781	+	3.10042i	−0.335905	+	0.190818i
$265$	6.47244	+	6.47244i	0.397599	+	0.397599i
$266$	15.2274	−	10.3410i	0.933653	−	0.634046i
$267$	−3.74754	−	1.55228i	−0.229346	−	0.0949981i
$268$	−10.4632	+	9.49847i	−0.639142	+	0.580212i
$269$	7.83216	+	18.9085i	0.477535	+	1.15287i	0.960761	+	0.277377i	$0.0894650\pi$
$269$	7.83216	+	18.9085i	0.477535	+	1.15287i	−0.483226	+	0.875496i	$0.660535\pi$
$270$	39.4577	+	27.7658i	2.40132	+	1.68977i
$271$		−	0.819802i		−	0.0497994i	−0.999690	−	0.0248997i	$-0.992073\pi$
$271$		−	0.819802i		−	0.0497994i	0.999690	−	0.0248997i	$-0.00792664\pi$
$272$	8.27980	−	6.81714i	0.502036	−	0.413350i
$273$	20.6099	+	19.3446i	1.24737	+	1.17079i
$274$	9.93136	+	6.98854i	0.599975	+	0.422193i
$275$	−0.0936740	−	0.226149i	−0.00564875	−	0.0136373i
$276$	0.391253	−	8.09559i	0.0235506	−	0.487297i
$277$	11.8718	−	28.6611i	0.713308	−	1.72208i	0.0217422	−	0.999764i	$-0.493079\pi$
$277$	11.8718	−	28.6611i	0.713308	−	1.72208i	0.691566	−	0.722314i	$-0.256921\pi$
$278$	−5.40651	−	1.21181i	−0.324261	−	0.0726796i
$279$	26.2673	−	26.2673i	1.57258	−	1.57258i
$280$	2.49690	+	15.9201i	0.149218	+	0.951410i
$281$	−0.733988	−	0.733988i	−0.0437861	−	0.0437861i	0.684875	−	0.728661i	$-0.259857\pi$
$281$	−0.733988	−	0.733988i	−0.0437861	−	0.0437861i	−0.728661	+	0.684875i	$0.759857\pi$
$282$	7.50668	+	11.8439i	0.447016	+	0.705295i
$283$	−13.4762	−	5.58204i	−0.801079	−	0.331818i	−0.0556903	−	0.998448i	$-0.517736\pi$
$283$	−13.4762	−	5.58204i	−0.801079	−	0.331818i	−0.745388	+	0.666630i	$0.767736\pi$
$284$	−11.0636	+	23.4403i	−0.656505	+	1.39093i
$285$	−32.1894	+	13.3333i	−1.90674	+	0.789796i
$286$	3.05394	−	0.531160i	0.180583	−	0.0314082i
$287$	8.65303	−	9.21904i	0.510772	−	0.544183i
$288$	44.0934	−	3.34075i	2.59823	−	0.196855i
$289$	−9.81072			−0.577101
$290$	−3.55324	−	20.4295i	−0.208653	−	1.19966i
$291$	−48.6783	+	20.1632i	−2.85357	+	1.18199i
$292$	−9.42355	−	4.44783i	−0.551471	−	0.260290i
$293$	5.69443	−	13.7476i	0.332672	−	0.803141i	−0.665706	−	0.746214i	$-0.731870\pi$
$293$	5.69443	−	13.7476i	0.332672	−	0.803141i	0.998378	−	0.0569272i	$-0.0181303\pi$
$294$	26.3424	−	19.1350i	1.53632	−	1.11597i
$295$	−3.43460	+	3.43460i	−0.199970	+	0.199970i
$296$	−2.26092	−	18.1527i	−0.131413	−	1.05510i
$297$	−7.55909	−	7.55909i	−0.438623	−	0.438623i
$298$	1.18280	+	0.265112i	0.0685176	+	0.0153575i
$299$	−1.53171	+	3.69787i	−0.0885810	+	0.213853i
$300$	−0.115190	+	2.38345i	−0.00665050	+	0.137608i
$301$	−12.0251	+	31.8470i	−0.693116	+	1.83563i
$302$	6.17251	−	8.77171i	0.355188	−	0.504755i
$303$	−4.77810			−0.274494
$304$	−9.24837	+	17.3689i	−0.530430	+	0.996176i
$305$			12.4994i			0.715714i
$306$	24.2412	+	17.0581i	1.38578	+	0.975149i
$307$	−11.8291	+	4.89978i	−0.675123	+	0.279645i	−0.693787	−	0.720181i	$-0.744059\pi$
$307$	−11.8291	+	4.89978i	−0.675123	+	0.279645i	0.0186633	+	0.999826i	$0.494059\pi$
$308$	0.0593817	−	3.57001i	0.00338359	−	0.203420i
$309$	−7.54461	+	18.2143i	−0.429198	+	1.03618i
$310$	−14.1218	−	3.16525i	−0.802064	−	0.179774i
$311$	−3.93148	+	3.93148i	−0.222934	+	0.222934i	−0.809733	−	0.586799i	$-0.800388\pi$
$311$	−3.93148	+	3.93148i	−0.222934	+	0.222934i	0.586799	+	0.809733i	$0.300388\pi$
$312$	−29.1329	−	8.02473i	−1.64933	−	0.454311i
$313$	2.30964	−	2.30964i	0.130548	−	0.130548i	−0.638813	−	0.769362i	$-0.720574\pi$
$313$	2.30964	−	2.30964i	0.130548	−	0.130548i	0.769362	+	0.638813i	$0.220574\pi$
$314$	−14.3772	−	22.6841i	−0.811354	−	1.28014i
$315$	−40.5866	+	18.3375i	−2.28680	+	1.03320i
$316$	−10.9527	+	3.92877i	−0.616136	+	0.221010i
$317$	2.05636	+	4.96449i	0.115497	+	0.278834i	0.971048	−	0.238884i	$-0.0767816\pi$
$317$	2.05636	+	4.96449i	0.115497	+	0.278834i	−0.855551	+	0.517718i	$0.826782\pi$
$318$	3.38779	+	19.4783i	0.189978	+	1.09229i
$319$			4.59448i			0.257242i
$320$	−10.2954	−	13.8126i	−0.575528	−	0.772149i
$321$		−	28.0788i		−	1.56721i
$322$	3.85251	+	2.53250i	0.214692	+	0.141131i
$323$	−12.1863	+	5.04773i	−0.678064	+	0.280863i
$324$	19.3500	+	53.9443i	1.07500	+	2.99690i
$325$	0.450955	−	1.08870i	0.0250145	−	0.0603904i
$326$	11.9860	+	18.9114i	0.663846	+	1.04740i
$327$	11.9813	+	11.9813i	0.662566	+	0.662566i
$328$	−3.58955	+	13.0315i	−0.198200	+	0.719542i
$329$	−7.97234	+	0.252485i	−0.439529	+	0.0139200i
$330$	−1.47817	+	6.59486i	−0.0813705	+	0.363035i
$331$	−7.57759	−	3.13874i	−0.416502	−	0.172521i	0.164584	−	0.986363i	$-0.447372\pi$
$331$	−7.57759	−	3.13874i	−0.416502	−	0.172521i	−0.581086	+	0.813842i	$0.697372\pi$
$332$	−6.71431	+	6.09524i	−0.368496	+	0.334520i
$333$	46.7084	−	19.3473i	2.55961	−	1.06022i
$334$	−14.3888	+	20.4479i	−0.787323	+	1.11886i
$335$			15.2156i			0.831315i
$336$	−15.3782	+	31.2253i	−0.838949	+	1.70348i
$337$		−	3.17787i		−	0.173110i	−0.996247	−	0.0865549i	$-0.972414\pi$
$337$		−	3.17787i		−	0.173110i	0.996247	−	0.0865549i	$-0.0275858\pi$
$338$	−2.83137	−	1.99239i	−0.154006	−	0.108372i
$339$	31.0728	−	12.8708i	1.68764	−	0.699045i
$340$	0.557448	−	11.5344i	0.0302319	−	0.625541i
$341$	2.96248	+	1.22710i	0.160427	+	0.0664512i
$342$	−53.0673	−	11.8945i	−2.86955	−	0.643180i
$343$	1.75639	+	18.4368i	0.0948361	+	0.995493i
$344$	−4.49789	−	36.1130i	−0.242510	−	1.94708i
$345$	−6.17077	−	6.17077i	−0.332223	−	0.332223i
$346$	12.1973	−	7.73065i	0.655730	−	0.415602i
$347$	−3.90004	+	9.41553i	−0.209365	+	0.505452i	−0.993324	−	0.115361i	$-0.963197\pi$
$347$	−3.90004	+	9.41553i	−0.209365	+	0.505452i	0.783959	+	0.620813i	$0.213197\pi$
$348$	19.1175	−	40.5039i	1.02480	−	2.17123i
$349$	−19.8320	+	8.21468i	−1.06158	+	0.439722i	−0.844013	−	0.536323i	$-0.819813\pi$
$349$	−19.8320	+	8.21468i	−1.06158	+	0.439722i	−0.217570	+	0.976045i	$0.569813\pi$
$350$	−1.13423	−	0.745603i	−0.0606272	−	0.0398541i
$351$		−	51.4635i		−	2.74692i
$352$	1.72296	+	3.40605i	0.0918341	+	0.181543i
$353$		−	8.47471i		−	0.451063i	−0.974236	−	0.225532i	$-0.927588\pi$
$353$		−	8.47471i		−	0.451063i	0.974236	−	0.225532i	$-0.0724119\pi$
$354$	−10.3362	+	1.79773i	−0.549361	+	0.0955483i
$355$	10.6801	+	25.7841i	0.566842	+	1.36848i
$356$	−1.05285	+	2.23066i	−0.0558011	+	0.118225i
$357$	−21.2622	+	9.60649i	−1.12532	+	0.508430i
$358$	2.15090	−	1.36324i	0.113679	−	0.0720495i
$359$	16.7952	−	16.7952i	0.886414	−	0.886414i	−0.107762	−	0.994177i	$-0.534369\pi$
$359$	16.7952	−	16.7952i	0.886414	−	0.886414i	0.994177	+	0.107762i	$0.0343685\pi$
$360$	29.2476	−	37.5697i	1.54148	−	1.98010i
$361$	3.67747	−	3.67747i	0.193551	−	0.193551i
$362$	−0.364956	+	1.62825i	−0.0191817	+	0.0855791i
$363$	−13.2717	+	32.0408i	−0.696585	+	1.68171i
$364$	12.3547	−	11.9505i	0.647565	−	0.626375i
$365$	−10.3658	+	4.29365i	−0.542570	+	0.224740i
$366$	−15.5368	+	22.0792i	−0.812121	+	1.15410i
$367$			0.399698i			0.0208641i	0.999946	+	0.0104320i	$0.00332068\pi$
$367$			0.399698i			0.0208641i	−0.999946	+	0.0104320i	$0.996679\pi$
$368$	−4.90571	−	0.475288i	−0.255728	−	0.0247761i
$369$	−37.3569			−1.94472
$370$	−16.1078	−	11.3348i	−0.837406	−	0.589270i
$371$	−10.5211	−	3.97266i	−0.546228	−	0.206250i
$372$	−21.0106	−	23.1446i	−1.08935	−	1.19999i
$373$	2.30682	−	5.56916i	0.119443	−	0.288360i	−0.852839	−	0.522175i	$-0.825121\pi$
$373$	2.30682	−	5.56916i	0.119443	−	0.288360i	0.972281	+	0.233815i	$0.0751209\pi$
$374$	−0.559607	+	2.49669i	−0.0289366	+	0.129101i
$375$	26.8570	+	26.8570i	1.38689	+	1.38689i
$376$	7.41426	−	4.21183i	0.382361	−	0.217208i
$377$	−15.6400	+	15.6400i	−0.805500	+	0.805500i
$378$	−58.2248	−	11.1275i	−2.99476	−	0.572337i
$379$	4.69148	−	11.3262i	0.240985	−	0.581790i	−0.756396	−	0.654114i	$-0.773042\pi$
$379$	4.69148	−	11.3262i	0.240985	−	0.581790i	0.997381	+	0.0723241i	$0.0230416\pi$
$380$	7.15363	+	19.9430i	0.366973	+	1.02305i
$381$	−10.4275	+	4.31920i	−0.534215	+	0.221279i
$382$	6.26415	−	1.08950i	0.320502	−	0.0557437i
$383$	24.8644			1.27051			0.635255	−	0.772303i	$-0.280895\pi$
$383$	24.8644			1.27051			0.635255	+	0.772303i	$0.280895\pi$
$384$	−1.01679	−	37.1960i	−0.0518878	−	1.89815i
$385$	−2.80309	−	2.63099i	−0.142859	−	0.134088i
$386$	−3.07425	−	17.6756i	−0.156475	−	0.899664i
$387$	92.9220	−	38.4896i	4.72349	−	1.95653i
$388$	10.8181	+	30.1587i	0.549203	+	1.53108i
$389$	−27.6691	−	11.4609i	−1.40288	−	0.581091i	−0.452380	−	0.891825i	$-0.649425\pi$
$389$	−27.6691	−	11.4609i	−1.40288	−	0.581091i	−0.950497	+	0.310735i	$0.899425\pi$
$390$	−27.4812	+	17.4176i	−1.39157	+	0.881975i
$391$	−2.33614	−	2.33614i	−0.118144	−	0.118144i
$392$	−10.8492	−	16.5619i	−0.547966	−	0.836501i
$393$	−13.1639	+	13.1639i	−0.664033	+	0.664033i
$394$	3.70104	−	16.5122i	0.186456	−	0.831874i
$395$	−4.79449	+	11.5749i	−0.241237	+	0.582398i
$396$	−7.81086	+	7.09068i	−0.392510	+	0.356320i
$397$	−5.84792	−	14.1181i	−0.293499	−	0.708569i	−1.00000		0.000856758i	$-0.999727\pi$
$397$	−5.84792	−	14.1181i	−0.293499	−	0.708569i	0.706501	−	0.707712i	$-0.250273\pi$
$398$	−8.47969	+	12.0504i	−0.425049	+	0.604033i
$399$	29.2960	−	31.2123i	1.46663	−	1.56257i
$400$	1.44431	+	0.139931i	0.0722154	+	0.00699655i
$401$			25.4029i			1.26856i	0.773103	+	0.634281i	$0.218704\pi$
$401$			25.4029i			1.26856i	−0.773103	+	0.634281i	$0.781296\pi$
$402$	−18.9130	+	26.8771i	−0.943294	+	1.34051i
$403$	5.90737	+	14.2617i	0.294267	+	0.710424i
$404$	−0.140260	+	2.90218i	−0.00697818	+	0.144389i
$405$	57.0090	+	23.6139i	2.83280	+	1.17338i
$406$	14.3131	+	21.0765i	0.710346	+	1.04601i
$407$	3.08585	+	3.08585i	0.152960	+	0.152960i
$408$	15.3220	−	19.6817i	0.758551	−	0.974390i
$409$	−15.1589	+	15.1589i	−0.749562	+	0.749562i	−0.974397	−	0.224835i	$-0.927816\pi$
$409$	−15.1589	+	15.1589i	−0.749562	+	0.749562i	0.224835	+	0.974397i	$0.427816\pi$
$410$	7.79108	+	12.2926i	0.384774	+	0.607090i
$411$	26.0921	+	10.8077i	1.28703	+	0.533104i
$412$	10.8418	+	5.11721i	0.534135	+	0.252107i
$413$	2.10809	−	5.58301i	0.103732	−	0.274722i
$414$	−2.33411	−	13.4201i	−0.114715	−	0.659563i
$415$			9.76393i			0.479293i
$416$	−5.72935	+	17.4595i	−0.280905	+	0.856025i
$417$	−12.8855			−0.631003
$418$	−0.804404	−	4.62497i	−0.0393447	−	0.226215i
$419$	−12.8383	−	30.9945i	−0.627194	−	1.51418i	−0.843095	−	0.537765i	$-0.819269\pi$
$419$	−12.8383	−	30.9945i	−0.627194	−	1.51418i	0.215900	−	0.976415i	$-0.430731\pi$
$420$	13.7639	+	34.8578i	0.671611	+	1.70089i
$421$	−11.9570	−	4.95276i	−0.582749	−	0.241383i	0.0717787	−	0.997421i	$-0.477132\pi$
$421$	−11.9570	−	4.95276i	−0.582749	−	0.241383i	−0.654528	+	0.756038i	$0.727132\pi$
$422$	20.9031	−	13.2484i	1.01755	−	0.644922i
$423$	16.6641	+	16.6641i	0.810235	+	0.810235i
$424$	11.9304	−	1.48594i	0.579393	−	0.0721636i
$425$	0.687790	+	0.687790i	0.0333627	+	0.0333627i
$426$	−13.1841	+	58.8209i	−0.638772	+	2.84988i
$427$	−6.32308	−	13.9950i	−0.305995	−	0.677264i
$428$	−17.0549	−	0.824246i	−0.824377	−	0.0398414i
$429$	6.66018	−	2.75874i	0.321556	−	0.133193i
$430$	−32.0450	−	22.5496i	−1.54535	−	1.08744i
$431$	−37.7600			−1.81883			−0.909417	−	0.415885i	$-0.863472\pi$
$431$	−37.7600			−1.81883			−0.909417	+	0.415885i	$0.863472\pi$
$432$	60.6133	−	18.4922i	2.91626	−	0.889709i
$433$	24.2606			1.16589			0.582945	−	0.812512i	$-0.301900\pi$
$433$	24.2606			1.16589			0.582945	+	0.812512i	$0.301900\pi$
$434$	17.4127	−	3.59981i	0.835835	−	0.172797i
$435$	−18.4548	−	44.5538i	−0.884839	−	2.13619i
$436$	7.62905	−	6.92563i	0.365365	−	0.331678i
$437$	5.60016	+	2.31966i	0.267892	+	0.110965i
$438$	−23.6474	−	5.30031i	−1.12991	−	0.253259i
$439$	3.09504	−	3.09504i	0.147718	−	0.147718i	−0.629380	−	0.777098i	$-0.716691\pi$
$439$	3.09504	−	3.09504i	0.147718	−	0.147718i	0.777098	+	0.629380i	$0.216691\pi$
$440$	3.96227	+	1.09142i	0.188894	+	0.0520313i
$441$	36.1665	−	41.0631i	1.72221	−	1.95539i
$442$	−10.4039	+	6.59398i	−0.494862	+	0.313644i
$443$	1.34081	−	3.23699i	0.0637036	−	0.153794i	−0.888822	−	0.458253i	$-0.848476\pi$
$443$	1.34081	−	3.23699i	0.0637036	−	0.153794i	0.952526	+	0.304459i	$0.0984755\pi$
$444$	−14.3640	−	40.0441i	−0.681685	−	1.90041i
$445$	1.01636	+	2.45370i	0.0481799	+	0.116317i
$446$	6.09908	+	35.0670i	0.288800	+	1.66047i
$447$	2.81899			0.133334
$448$	18.5146	+	10.2572i	0.874732	+	0.484607i
$449$	28.9280			1.36519			0.682597	−	0.730795i	$-0.260850\pi$
$449$	28.9280			1.36519			0.682597	+	0.730795i	$0.260850\pi$
$450$	0.687194	+	3.95106i	0.0323946	+	0.186255i
$451$	−1.23401	−	2.97917i	−0.0581073	−	0.140283i
$452$	−6.90548	−	19.2512i	−0.324806	−	0.905500i
$453$	9.54571	−	23.0454i	0.448497	−	1.08277i
$454$	35.2769	−	22.3585i	1.65563	−	1.04934i
$455$	−0.585837	−	18.4981i	−0.0274645	−	0.867203i
$456$	−12.1529	+	44.1197i	−0.569111	+	2.06609i
$457$	8.25491	−	8.25491i	0.386149	−	0.386149i	−0.487163	−	0.873311i	$-0.661968\pi$
$457$	8.25491	−	8.25491i	0.386149	−	0.386149i	0.873311	+	0.487163i	$0.161968\pi$
$458$	8.40466	+	1.88382i	0.392724	+	0.0880250i
$459$	39.2456	+	16.2561i	1.83183	+	0.758768i
$460$	−3.92922	+	3.56694i	−0.183201	+	0.166309i
$461$	7.76886	+	18.7557i	0.361832	+	0.873540i	0.995032	+	0.0995519i	$0.0317409\pi$
$461$	7.76886	+	18.7557i	0.361832	+	0.873540i	−0.633200	+	0.773988i	$0.718259\pi$
$462$	−1.68111	−	8.13169i	−0.0782122	−	0.378321i
$463$	12.5010			0.580969			0.290484	−	0.956880i	$-0.406184\pi$
$463$	12.5010			0.580969			0.290484	+	0.956880i	$0.406184\pi$
$464$	−24.0405	−	12.8008i	−1.11605	−	0.594261i
$465$	−33.6568			−1.56080
$466$	9.78633	+	6.88649i	0.453343	+	0.319010i
$467$	33.4570	−	13.8584i	1.54821	−	0.641288i	0.565216	−	0.824943i	$-0.308793\pi$
$467$	33.4570	−	13.8584i	1.54821	−	0.641288i	0.982991	+	0.183655i	$0.0587928\pi$
$468$	−50.7260	−	2.45154i	−2.34481	−	0.113323i
$469$	−7.69710	−	17.0361i	−0.355419	−	0.786654i
$470$	2.00804	−	8.95890i	0.0926242	−	0.413243i
$471$	−44.1646	−	44.1646i	−2.03500	−	2.03500i
$472$	0.788513	+	6.33088i	0.0362943	+	0.291402i
$473$	6.13900	+	6.13900i	0.282271	+	0.282271i
$474$	−22.8568	+	14.4866i	−1.04985	+	0.665393i
$475$	−1.64876	−	0.682939i	−0.0756504	−	0.0313354i
$476$	5.21077	+	13.1965i	0.238835	+	0.604861i
$477$	12.7156	+	30.6981i	0.582205	+	1.40557i
$478$	3.82231	+	21.9766i	0.174828	+	1.00519i
$479$	−18.5273			−0.846535			−0.423267	−	0.906005i	$-0.639117\pi$
$479$	−18.5273			−0.846535			−0.423267	+	0.906005i	$0.639117\pi$
$480$	−30.3891	−	26.1086i	−1.38707	−	1.19169i
$481$			21.0089i			0.957925i
$482$	−6.78959	−	39.0372i	−0.309257	−	1.77809i
$483$	10.0307	+	3.78750i	0.456413	+	0.172337i
$484$	19.0718	+	9.00170i	0.866898	+	0.409168i
$485$	31.8721	+	13.2019i	1.44724	+	0.599466i
$486$	35.3669	+	55.8014i	1.60428	+	2.53120i
$487$	−0.307533	+	0.307533i	−0.0139356	+	0.0139356i	−0.714040	−	0.700105i	$-0.753137\pi$
$487$	−0.307533	+	0.307533i	−0.0139356	+	0.0139356i	0.700105	+	0.714040i	$0.253137\pi$
$488$	12.9547	+	10.0851i	0.586430	+	0.456529i
$489$	36.8193	+	36.8193i	1.66503	+	1.66503i
$490$	−21.0550	−	3.33687i	−0.951169	−	0.150744i
$491$	36.5287	+	15.1307i	1.64852	+	0.682838i	0.997116	−	0.0758970i	$-0.0241820\pi$
$491$	36.5287	+	15.1307i	1.64852	+	0.682838i	0.651400	+	0.758735i	$0.274182\pi$
$492$	−1.51745	+	31.3983i	−0.0684120	+	1.41554i
$493$	−6.98663	−	16.8672i	−0.314662	−	0.759662i
$494$	13.0055	−	18.4820i	0.585145	−	0.831545i
$495$			11.3585i			0.510528i
$496$	−14.6746	+	12.0823i	−0.658909	+	0.542510i
$497$	−25.0014	−	23.4664i	−1.12147	−	1.05261i
$498$	−12.1366	+	17.2472i	−0.543854	+	0.772866i
$499$	11.4771	+	27.7082i	0.513786	+	1.24039i	0.941665	+	0.336552i	$0.109261\pi$
$499$	11.4771	+	27.7082i	0.513786	+	1.24039i	−0.427879	+	0.903836i	$0.640739\pi$
$500$	17.1011	−	15.5244i	0.764785	−	0.694270i
$501$	−22.2522	+	53.7215i	−0.994154	+	2.40010i
$502$	3.63933	−	16.2369i	0.162431	−	0.724688i
$503$	21.5299	−	21.5299i	0.959969	−	0.959969i	−0.0392600	−	0.999229i	$-0.512500\pi$
$503$	21.5299	−	21.5299i	0.959969	−	0.959969i	0.999229	+	0.0392600i	$0.0125000\pi$
$504$	−13.7417	+	56.8604i	−0.612103	+	2.53276i
$505$	2.21215	+	2.21215i	0.0984395	+	0.0984395i
$506$	0.993136	−	0.629450i	0.0441503	−	0.0279825i
$507$	−7.43868	−	3.08120i	−0.330364	−	0.136841i
$508$	2.31735	+	6.46035i	0.102816	+	0.286632i
$509$	12.7961	−	5.30030i	0.567176	−	0.234932i	−0.0806214	−	0.996745i	$-0.525690\pi$
$509$	12.7961	−	5.30030i	0.567176	−	0.234932i	0.647797	+	0.761813i	$0.275690\pi$
$510$	−4.60188	−	26.4588i	−0.203775	−	1.17161i
$511$	9.43403	−	10.0511i	0.417337	−	0.444636i
$512$	−22.6224	−	0.474290i	−0.999780	−	0.0209609i
$513$	−77.9377			−3.44103
$514$	−24.2531	+	4.21826i	−1.06976	+	0.186060i
$515$	11.9258	−	4.93983i	0.525514	−	0.217675i
$516$	−28.5758	−	79.6640i	−1.25798	−	3.50701i
$517$	−0.778475	+	1.87941i	−0.0342373	+	0.0826562i
$518$	23.7691	+	4.54258i	1.04435	+	0.199589i
$519$	23.7474	−	23.7474i	1.04239	−	1.04239i
$520$	9.77262	+	17.2032i	0.428558	+	0.754409i
$521$	−26.1575	−	26.1575i	−1.14598	−	1.14598i	−0.987336	−	0.158645i	$-0.949287\pi$
$521$	−26.1575	−	26.1575i	−1.14598	−	1.14598i	−0.158645	−	0.987336i	$-0.550713\pi$
$522$	16.4633	−	73.4511i	0.720579	−	3.21487i
$523$	7.83184	−	18.9077i	0.342463	−	0.826778i	−0.655003	−	0.755626i	$-0.727333\pi$
$523$	7.83184	−	18.9077i	0.342463	−	0.826778i	0.997466	−	0.0711514i	$-0.0226673\pi$
$524$	7.60926	+	8.38210i	0.332412	+	0.366174i
$525$	−2.95317	−	1.11509i	−0.128887	−	0.0486665i
$526$	−0.718070	−	0.505295i	−0.0313094	−	0.0220319i
$527$	−12.7418			−0.555043
$528$	5.64241	+	6.85302i	0.245554	+	0.298239i
$529$		−	21.4818i		−	0.933989i
$530$	7.44956	−	10.5865i	0.323588	−	0.459849i
$531$	−16.2899	+	6.74750i	−0.706922	+	0.292817i
$532$	−18.0981	−	18.7104i	−0.784653	−	0.811198i
$533$	5.94065	−	14.3420i	0.257318	−	0.621221i
$534$	−1.25464	+	5.59760i	−0.0542938	+	0.242232i
$535$	−12.9999	+	12.9999i	−0.562033	+	0.562033i
$536$	15.7698	+	12.2766i	0.681149	+	0.530267i
$537$	4.18767	−	4.18767i	0.180711	−	0.180711i
$538$	24.4472	−	15.4946i	1.05399	−	0.668022i
$539$	4.46943	+	1.52779i	0.192512	+	0.0658067i
$540$	29.1242	−	61.7049i	1.25330	−	2.65535i
$541$	−8.04425	−	19.4205i	−0.345849	−	0.834954i	−0.997101	−	0.0760921i	$-0.975756\pi$
$541$	−8.04425	−	19.4205i	−0.345849	−	0.834954i	0.651251	−	0.758862i	$-0.274244\pi$
$542$	−1.14223	+	0.198663i	−0.0490628	+	0.00853332i
$543$			3.88065i			0.166535i
$544$	−11.5047	−	9.88421i	−0.493262	−	0.423782i
$545$		−	11.0941i		−	0.475221i
$546$	21.9583	−	33.4036i	0.939729	−	1.42954i
$547$	−18.9194	+	7.83669i	−0.808937	+	0.335073i	−0.748530	−	0.663101i	$-0.769240\pi$
$547$	−18.9194	+	7.83669i	−0.808937	+	0.335073i	−0.0604073	+	0.998174i	$0.519240\pi$
$548$	7.33043	−	15.5309i	0.313141	−	0.663446i
$549$	−17.3637	+	41.9196i	−0.741063	+	1.78909i
$550$	−0.292392	+	0.185319i	−0.0124677	+	0.00790201i
$551$	23.6856	+	23.6856i	1.00904	+	1.00904i
$552$	−11.3744	+	1.41668i	−0.484125	+	0.0602980i
$553$	−0.487254	−	15.3853i	−0.0207202	−	0.654248i
$554$	−42.8103	−	9.59548i	−1.81884	−	0.407673i
$555$	−42.3192	−	17.5292i	−1.79635	−	0.744072i
$556$	−0.378249	+	7.82653i	−0.0160413	+	0.331919i
$557$	−2.22340	+	0.920962i	−0.0942085	+	0.0390224i	−0.429290	−	0.903167i	$-0.641236\pi$
$557$	−2.22340	+	0.920962i	−0.0942085	+	0.0390224i	0.335081	+	0.942189i	$0.391236\pi$
$558$	−42.9636	−	30.2328i	−1.81879	−	1.27986i
$559$			41.7953i			1.76775i
$560$	21.5764	−	7.33686i	0.911769	−	0.310039i
$561$			5.95042i			0.251227i
$562$	−0.844795	+	1.20053i	−0.0356355	+	0.0506414i
$563$	−16.9952	+	7.03966i	−0.716264	+	0.296686i	−0.710894	−	0.703299i	$-0.751709\pi$
$563$	−16.9952	+	7.03966i	−0.716264	+	0.296686i	−0.00537035	+	0.999986i	$0.501709\pi$
$564$	14.6830	−	13.3292i	0.618265	−	0.561260i
$565$	−20.3449	−	8.42714i	−0.855917	−	0.354532i
$566$	−4.51172	+	20.1291i	−0.189642	+	0.846089i
$567$	−75.7757	+	2.39983i	−3.18228	+	0.100783i
$568$	35.3404	+	9.73459i	1.48285	+	0.408454i
$569$	−10.3726	−	10.3726i	−0.434843	−	0.434843i	0.455429	−	0.890272i	$-0.349486\pi$
$569$	−10.3726	−	10.3726i	−0.434843	−	0.434843i	−0.890272	+	0.455429i	$0.849486\pi$
$570$	26.3777	+	41.6183i	1.10484	+	1.74320i
$571$	4.51061	−	10.8896i	0.188763	−	0.455715i	−0.800959	−	0.598719i	$-0.795676\pi$
$571$	4.51061	−	10.8896i	0.188763	−	0.455715i	0.989722	+	0.143005i	$0.0456764\pi$
$572$	−1.48013	−	4.12632i	−0.0618872	−	0.172530i
$573$	13.6612	−	5.65864i	0.570703	−	0.236393i
$574$	−14.9418	−	9.82218i	−0.623657	−	0.409970i
$575$		−	0.446992i		−	0.0186408i
$576$	−15.3399	−	60.6257i	−0.639161	−	2.52607i
$577$		−	23.0622i		−	0.960093i	−0.877243	−	0.480046i	$-0.840620\pi$
$577$		−	23.0622i		−	0.960093i	0.877243	−	0.480046i	$-0.159380\pi$
$578$	2.37744	+	13.6692i	0.0988886	+	0.568566i
$579$	−15.9670	−	38.5478i	−0.663567	−	1.60199i
$580$	−27.6034	+	9.90143i	−1.14617	+	0.411134i
$581$	−4.93928	−	10.9322i	−0.204916	−	0.453544i
$582$	39.8896	+	62.9372i	1.65348	+	2.60883i
$583$	−2.02810	+	2.02810i	−0.0839954	+	0.0839954i
$584$	−3.91353	+	14.2076i	−0.161943	+	0.587916i
$585$	−38.6653	+	38.6653i	−1.59861	+	1.59861i
$586$	−20.5344	−	4.60256i	−0.848267	−	0.190130i
$587$	−5.83675	+	14.0912i	−0.240908	+	0.581604i	−0.997374	−	0.0724299i	$-0.976925\pi$
$587$	−5.83675	+	14.0912i	−0.240908	+	0.581604i	0.756465	+	0.654034i	$0.226925\pi$
$588$	−33.0443	−	32.0658i	−1.36272	−	1.32237i
$589$	21.5983	−	8.94629i	0.889941	−	0.368626i
$590$	5.61773	+	3.95311i	0.231278	+	0.162747i
$591$		−	39.3540i		−	1.61881i
$592$	−24.7442	+	7.54909i	−1.01698	+	0.310266i
$593$	−23.0448			−0.946335			−0.473168	−	0.880972i	$-0.656890\pi$
$593$	−23.0448			−0.946335			−0.473168	+	0.880972i	$0.656890\pi$
$594$	−8.70025	+	12.3638i	−0.356975	+	0.507295i
$595$	14.2915	+	5.39634i	0.585896	+	0.221228i
$596$	0.0827506	−	1.71223i	0.00338960	−	0.0701357i
$597$	−13.1137	+	31.6594i	−0.536709	+	1.29573i
$598$	5.52341	+	1.23802i	0.225869	+	0.0506262i
$599$	−15.8621	−	15.8621i	−0.648108	−	0.648108i	0.304427	−	0.952536i	$-0.401535\pi$
$599$	−15.8621	−	15.8621i	−0.648108	−	0.648108i	−0.952536	+	0.304427i	$0.901535\pi$
$600$	3.34876	−	0.417090i	0.136713	−	0.0170276i
$601$	7.79999	−	7.79999i	0.318168	−	0.318168i	−0.529895	−	0.848063i	$-0.677769\pi$
$601$	7.79999	−	7.79999i	0.318168	−	0.318168i	0.848063	+	0.529895i	$0.177769\pi$
$602$	47.2864	+	9.03703i	1.92725	+	0.368322i
$603$	−21.1368	+	51.0288i	−0.860759	+	2.07806i
$604$	−13.7174	−	6.47449i	−0.558153	−	0.263443i
$605$	20.9787	−	8.68967i	0.852906	−	0.353285i
$606$	1.15788	+	6.65730i	0.0470357	+	0.270435i
$607$	31.8826			1.29408			0.647038	−	0.762458i	$-0.276007\pi$
$607$	31.8826			1.29408			0.647038	+	0.762458i	$0.276007\pi$
$608$	26.4412	+	8.67669i	1.07233	+	0.351886i
$609$	43.2013	+	40.5489i	1.75061	+	1.64313i
$610$	17.4154	−	3.02900i	0.705128	−	0.122640i
$611$	−9.04764	+	3.74766i	−0.366028	+	0.151614i
$612$	17.8927	−	37.9089i	0.723268	−	1.53238i
$613$	16.6544	+	6.89848i	0.672665	+	0.278627i	0.692757	−	0.721171i	$-0.256396\pi$
$613$	16.6544	+	6.89848i	0.672665	+	0.278627i	−0.0200918	+	0.999798i	$0.506396\pi$
$614$	9.69341	+	15.2941i	0.391194	+	0.617220i
$615$	23.9330	+	23.9330i	0.965072	+	0.965072i
$616$	−4.98848	+	0.782389i	−0.200991	+	0.0315233i
$617$	−20.2465	+	20.2465i	−0.815093	+	0.815093i	−0.985392	−	0.170300i	$-0.945526\pi$
$617$	−20.2465	+	20.2465i	−0.815093	+	0.815093i	0.170300	+	0.985392i	$0.445526\pi$
$618$	27.2062	+	6.09799i	1.09439	+	0.245297i
$619$	−14.1434	+	34.1451i	−0.568469	+	1.37241i	0.334376	+	0.942440i	$0.391475\pi$
$619$	−14.1434	+	34.1451i	−0.568469	+	1.37241i	−0.902845	+	0.429966i	$0.858525\pi$
$620$	−0.987986	+	20.4429i	−0.0396785	+	0.821006i
$621$	−7.47040	−	18.0351i	−0.299777	−	0.723726i
$622$	6.43045	+	4.52500i	0.257837	+	0.181436i
$623$	−2.37922	−	2.23314i	−0.0953214	−	0.0894690i
$624$	−4.12103	+	42.5354i	−0.164973	+	1.70278i
$625$		−	23.0546i		−	0.922182i
$626$	−3.77771	−	2.65831i	−0.150988	−	0.106248i
$627$	−4.17791	−	10.0864i	−0.166850	−	0.402810i
$628$	−28.1217	+	25.5288i	−1.12218	+	1.01871i
$629$	−16.0212	−	6.63622i	−0.638809	−	0.264603i
$630$	35.3849	+	52.1055i	1.40977	+	2.07593i
$631$	−4.35670	−	4.35670i	−0.173437	−	0.173437i	0.615050	−	0.788488i	$-0.289136\pi$
$631$	−4.35670	−	4.35670i	−0.173437	−	0.173437i	−0.788488	+	0.615050i	$0.789136\pi$
$632$	8.12811	+	14.3083i	0.323319	+	0.569153i
$633$	40.6970	−	40.6970i	1.61756	−	1.61756i
$634$	6.41869	−	4.06817i	0.254919	−	0.161568i
$635$	6.82738	+	2.82799i	0.270936	+	0.112226i
$636$	26.3181	−	9.44040i	1.04358	−	0.374336i
$637$	10.0135	+	20.4150i	0.396751	+	0.808872i
$638$	6.40148	−	1.11339i	0.253437	−	0.0440794i
$639$			101.309i			4.00773i
$640$	−16.7502	+	17.6917i	−0.662110	+	0.699326i
$641$	−5.51270			−0.217739			−0.108869	−	0.994056i	$-0.534723\pi$
$641$	−5.51270			−0.217739			−0.108869	+	0.994056i	$0.534723\pi$
$642$	−39.1221	+	6.80437i	−1.54403	+	0.268547i
$643$	−6.12039	−	14.7759i	−0.241365	−	0.582706i	0.756054	−	0.654509i	$-0.227125\pi$
$643$	−6.12039	−	14.7759i	−0.241365	−	0.582706i	−0.997419	+	0.0718033i	$0.977125\pi$
$644$	2.59495	−	5.98140i	0.102255	−	0.235700i
$645$	−84.1900	−	34.8726i	−3.31498	−	1.37311i
$646$	9.98611	+	15.7559i	0.392898	+	0.619908i
$647$	−7.12879	−	7.12879i	−0.280262	−	0.280262i	0.552952	−	0.833213i	$-0.313501\pi$
$647$	−7.12879	−	7.12879i	−0.280262	−	0.280262i	−0.833213	+	0.552952i	$0.813501\pi$
$648$	70.4712	−	40.0327i	2.76837	−	1.57263i
$649$	−1.07621	−	1.07621i	−0.0422450	−	0.0422450i
$650$	−1.62617	−	0.364488i	−0.0637835	−	0.0142964i
$651$	37.6838	−	17.0260i	1.47695	−	0.667300i
$652$	23.4446	−	21.2829i	0.918160	−	0.833504i
$653$	36.0059	−	14.9141i	1.40902	−	0.583635i	0.456944	−	0.889496i	$-0.348944\pi$
$653$	36.0059	−	14.9141i	1.40902	−	0.583635i	0.952076	+	0.305860i	$0.0989440\pi$
$654$	13.7900	−	19.5969i	0.539233	−	0.766300i
$655$	12.1892			0.476273
$656$	19.0265	+	1.84338i	0.742862	+	0.0719718i
$657$	−40.7286			−1.58897
$658$	2.28373	+	11.0466i	0.0890292	+	0.430643i
$659$	12.9689	+	31.3096i	0.505196	+	1.21965i	0.946620	+	0.322352i	$0.104473\pi$
$659$	12.9689	+	31.3096i	0.505196	+	1.21965i	−0.441424	+	0.897299i	$0.645527\pi$
$660$	9.54680	+	0.461388i	0.371609	+	0.0179595i
$661$	6.99080	+	2.89568i	0.271911	+	0.112629i	0.514473	−	0.857507i	$-0.327988\pi$
$661$	6.99080	+	2.89568i	0.271911	+	0.112629i	−0.242562	+	0.970136i	$0.577988\pi$
$662$	−2.53691	+	11.3184i	−0.0985999	+	0.439904i
$663$	−20.2557	+	20.2557i	−0.786666	+	0.786666i
$664$	10.1196	+	7.87796i	0.392715	+	0.305724i
$665$	−28.0140	+	0.887208i	−1.08634	+	0.0344045i
$666$	−38.2754	−	60.3903i	−1.48314	−	2.34008i
$667$	−3.21068	+	7.75126i	−0.124318	+	0.300130i
$668$	31.9768	+	15.0928i	1.23722	+	0.583957i
$669$	31.6774	+	76.4759i	1.22472	+	2.95673i
$670$	21.1998	−	3.68720i	0.819020	−	0.142449i
$671$	−3.91662			−0.151199
$672$	47.2327	+	13.8595i	1.82204	+	0.534642i
$673$	28.3567			1.09307			0.546536	−	0.837436i	$-0.315946\pi$
$673$	28.3567			1.09307			0.546536	+	0.837436i	$0.315946\pi$
$674$	−4.42772	+	0.770097i	−0.170549	+	0.0296630i
$675$	2.19939	+	5.30979i	0.0846544	+	0.204374i
$676$	−2.08986	+	4.42775i	−0.0803793	+	0.170298i
$677$	−9.12470	+	22.0290i	−0.350691	+	0.846642i	0.645845	+	0.763469i	$0.276505\pi$
$677$	−9.12470	+	22.0290i	−0.350691	+	0.846642i	−0.996535	+	0.0831730i	$0.973495\pi$
$678$	−25.4627	−	40.1746i	−0.977890	−	1.54290i
$679$	−42.3641	+	1.34168i	−1.62578	+	0.0514889i
$680$	−16.2059	+	2.01846i	−0.621470	+	0.0774042i
$681$	68.6819	−	68.6819i	2.63189	−	2.63189i
$682$	0.991813	−	4.42498i	0.0379785	−	0.169441i
$683$	7.72775	+	3.20094i	0.295694	+	0.122481i	0.525599	−	0.850733i	$-0.323841\pi$
$683$	7.72775	+	3.20094i	0.295694	+	0.122481i	−0.229904	+	0.973213i	$0.573841\pi$
$684$	−3.71269	+	76.8209i	−0.141958	+	2.93732i
$685$	−7.07633	−	17.0838i	−0.270373	−	0.652737i
$686$	25.2623	−	6.91498i	0.964519	−	0.264015i
$687$	20.0310			0.764231
$688$	−49.2262	+	15.0182i	−1.87673	+	0.572564i
$689$	−13.8076			−0.526029
$690$	−7.10235	+	10.0931i	−0.270382	+	0.384237i
$691$	28.9600	−	11.9956i	1.10169	−	0.456336i	0.243623	−	0.969870i	$-0.421664\pi$
$691$	28.9600	−	11.9956i	1.10169	−	0.456336i	0.858069	+	0.513534i	$0.171664\pi$
$692$	−13.7269	−	15.1211i	−0.521817	−	0.574816i
$693$	−5.74594	−	12.7176i	−0.218270	−	0.483101i
$694$	14.0637	+	3.15224i	0.533852	+	0.119657i
$695$	5.96568	+	5.96568i	0.226291	+	0.226291i
$696$	−61.0666	−	16.8210i	−2.31472	−	0.637597i
$697$	9.06058	+	9.06058i	0.343194	+	0.343194i
$698$	16.2514	+	25.6412i	0.615125	+	0.970533i
$699$	25.7111	+	10.6499i	0.972482	+	0.402815i
$700$	−0.763987	+	1.76100i	−0.0288760	+	0.0665597i
$701$	−3.06015	−	7.38785i	−0.115580	−	0.279035i	0.855494	−	0.517812i	$-0.173253\pi$
$701$	−3.06015	−	7.38785i	−0.115580	−	0.279035i	−0.971074	+	0.238777i	$0.923253\pi$
$702$	−71.7039	+	12.4712i	−2.70629	+	0.470695i
$703$	31.8165			1.19998
$704$	4.32810	−	3.22599i	0.163122	−	0.121584i
$705$		−	21.3520i		−	0.804162i
$706$	−11.8078	+	2.05368i	−0.444392	+	0.0772914i
$707$	−3.59590	−	1.35778i	−0.135238	−	0.0510644i
$708$	5.00955	+	13.9657i	0.188270	+	0.524863i
$709$	−0.607077	−	0.251460i	−0.0227993	−	0.00944377i	0.371255	−	0.928531i	$-0.378928\pi$
$709$	−0.607077	−	0.251460i	−0.0227993	−	0.00944377i	−0.394054	+	0.919087i	$0.628928\pi$
$710$	33.3367	−	21.1289i	1.25111	−	0.792952i
$711$	−32.1588	+	32.1588i	−1.20605	+	1.20605i
$712$	3.36311	+	0.926378i	0.126038	+	0.0347175i
$713$	4.14043	+	4.14043i	0.155060	+	0.155060i
$714$	18.5372	+	27.2966i	0.693737	+	1.02155i
$715$	−4.36075	−	1.80628i	−0.163083	−	0.0675511i
$716$	−2.42063	−	2.66648i	−0.0904631	−	0.0996512i
$717$	19.8523	+	47.9277i	0.741397	+	1.78989i
$718$	−27.4706	−	19.3306i	−1.02519	−	0.721413i
$719$		−	16.3413i		−	0.609428i	−0.952444	−	0.304714i	$-0.901439\pi$
$719$		−	16.3413i		−	0.609428i	0.952444	−	0.304714i	$-0.0985609\pi$
$720$	−59.4333	−	31.6462i	−2.21495	−	1.17939i
$721$	−10.8538	+	11.5638i	−0.404217	+	0.430658i
$722$	−6.01497	−	4.23264i	−0.223854	−	0.157523i
$723$	−35.2637	−	85.1342i	−1.31147	−	3.16617i
$724$	2.35708	+	0.113916i	0.0876001	+	0.00423364i
$725$	0.945265	−	2.28207i	0.0351063	−	0.0847540i
$726$	47.8585	+	10.7270i	1.77620	+	0.398116i
$727$	−28.8831	+	28.8831i	−1.07122	+	1.07122i	−0.0739549	+	0.997262i	$0.523562\pi$
$727$	−28.8831	+	28.8831i	−1.07122	+	1.07122i	−0.997262	+	0.0739549i	$0.976438\pi$
$728$	−19.6445	−	14.3179i	−0.728073	−	0.530655i
$729$	47.8556	+	47.8556i	1.77243	+	1.77243i
$730$	8.49429	+	13.4021i	0.314388	+	0.496035i
$731$	−31.8727	−	13.2021i	−1.17886	−	0.488298i
$732$	34.5279	+	16.2969i	1.27619	+	0.602350i
$733$	−20.4499	+	8.47062i	−0.755334	+	0.312869i	−0.726916	−	0.686727i	$-0.759047\pi$
$733$	−20.4499	+	8.47062i	−0.755334	+	0.312869i	−0.0284180	+	0.999596i	$0.509047\pi$
$734$	0.556898	−	0.0968592i	0.0205555	−	0.00357514i
$735$	−49.4778	+	3.13709i	−1.82502	+	0.115713i
$736$	0.526590	+	6.95029i	0.0194104	+	0.256191i
$737$	−4.76771			−0.175621
$738$	9.05273	+	52.0492i	0.333236	+	1.91596i
$739$	24.7778	−	10.2633i	0.911465	−	0.377541i	0.122848	−	0.992426i	$-0.460797\pi$
$739$	24.7778	−	10.2633i	0.911465	−	0.377541i	0.788617	+	0.614884i	$0.210797\pi$
$740$	−11.8894	+	25.1898i	−0.437061	+	0.925994i
$741$	20.1128	−	48.5567i	0.738864	−	1.78377i
$742$	−2.98551	+	15.6217i	−0.109601	+	0.573491i
$743$	−14.7349	+	14.7349i	−0.540573	+	0.540573i	−0.923697	−	0.383124i	$-0.874848\pi$
$743$	−14.7349	+	14.7349i	−0.540573	+	0.540573i	0.383124	+	0.923697i	$0.374848\pi$
$744$	−27.1557	+	34.8826i	−0.995578	+	1.27886i
$745$	−1.30513	−	1.30513i	−0.0478162	−	0.0478162i
$746$	−8.31850	−	1.86451i	−0.304562	−	0.0682644i
$747$	−13.5637	+	32.7456i	−0.496268	+	1.19810i
$748$	3.61424	+	0.174673i	0.132150	+	0.00638668i
$749$	7.97906	−	21.1315i	0.291549	−	0.772130i
$750$	30.9115	−	43.9280i	1.12873	−	1.60403i
$751$	−16.7817			−0.612375			−0.306187	−	0.951971i	$-0.599053\pi$
$751$	−16.7817			−0.612375			−0.306187	+	0.951971i	$0.599053\pi$
$752$	−7.66503	−	9.30961i	−0.279515	−	0.339487i
$753$		−	38.6978i		−	1.41023i
$754$	25.5812	+	18.0011i	0.931612	+	0.655561i
$755$	−15.0890	+	6.25006i	−0.549144	+	0.227463i
$756$	−1.39423	+	83.8209i	−0.0507078	+	3.04854i
$757$	11.3417	−	27.3812i	0.412220	−	0.995186i	−0.572321	−	0.820030i	$-0.693957\pi$
$757$	11.3417	−	27.3812i	0.412220	−	0.995186i	0.984541	−	0.175157i	$-0.0560432\pi$
$758$	−16.9177	−	3.79193i	−0.614479	−	0.137729i
$759$	1.93357	−	1.93357i	0.0701843	−	0.0701843i
$760$	26.0530	−	14.7999i	0.945040	−	0.536850i
$761$	−26.1478	+	26.1478i	−0.947857	+	0.947857i	−0.998706	−	0.0508495i	$-0.983807\pi$
$761$	−26.1478	+	26.1478i	−0.947857	+	0.947857i	0.0508495	+	0.998706i	$0.483807\pi$
$762$	8.54482	+	13.4819i	0.309546	+	0.488397i
$763$	5.61219	+	12.4216i	0.203175	+	0.449691i
$764$	−3.03600	−	8.46380i	−0.109838	−	0.306209i
$765$	−17.2724	−	41.6993i	−0.624486	−	1.50764i
$766$	−6.02541	−	34.6434i	−0.217707	−	1.25172i
$767$		−	7.32702i		−	0.264563i
$768$	−51.5787	+	10.4304i	−1.86119	+	0.376376i
$769$			0.182902i			0.00659561i	0.999995	+	0.00329780i	$0.00104973\pi$
$769$			0.182902i			0.00659561i	−0.999995	+	0.00329780i	$0.998950\pi$
$770$	−2.98648	+	4.54311i	−0.107625	+	0.163722i
$771$	−52.8925	+	21.9088i	−1.90488	+	0.789025i
$772$	−23.8824	+	8.56669i	−0.859545	+	0.308322i
$773$	17.4127	−	42.0379i	0.626290	−	1.51200i	−0.217911	−	0.975969i	$-0.569924\pi$
$773$	17.4127	−	42.0379i	0.626290	−	1.51200i	0.844200	−	0.536028i	$-0.180076\pi$
$774$	−76.1453	−	120.141i	−2.73699	−	4.31837i
$775$	−1.21900	−	1.21900i	−0.0437877	−	0.0437877i
$776$	39.3985	−	22.3812i	1.41432	−	0.803437i
$777$	56.2501	−	1.78145i	2.01796	−	0.0639092i
$778$	−9.26336	+	41.3285i	−0.332108	+	1.48170i
$779$	−21.7199	−	8.99668i	−0.778197	−	0.322340i
$780$	30.9275	+	34.0687i	1.10738	+	1.21985i
$781$	−8.07929	+	3.34655i	−0.289100	+	0.119749i
$782$	−2.68882	+	3.82105i	−0.0961518	+	0.136641i
$783$		−	107.875i		−	3.85512i
$784$	−20.4465	+	19.1296i	−0.730232	+	0.683199i
$785$			40.8945i			1.45959i
$786$	21.5313	+	15.1512i	0.767997	+	0.540427i
$787$	−7.61027	+	3.15228i	−0.271277	+	0.112367i	−0.514175	−	0.857685i	$-0.671902\pi$
$787$	−7.61027	+	3.15228i	−0.271277	+	0.112367i	0.242898	+	0.970052i	$0.421902\pi$
$788$	−23.9033	−	1.15523i	−0.851520	−	0.0411532i
$789$	−1.88654	−	0.781432i	−0.0671627	−	0.0278197i
$790$	17.2892	+	3.87519i	0.615121	+	0.137873i
$791$	27.0422	−	0.856432i	0.961511	−	0.0304512i
$792$	11.7722	+	9.16455i	0.418308	+	0.325648i
$793$	−13.3325	−	13.3325i	−0.473450	−	0.473450i
$794$	−18.2536	+	11.5692i	−0.647797	+	0.410574i
$795$	11.5207	−	27.8133i	0.408595	−	0.986436i
$796$	18.8447	+	8.89454i	0.667933	+	0.315258i
$797$	−34.3958	+	14.2472i	−1.21836	+	0.504663i	−0.896889	−	0.442256i	$-0.854178\pi$
$797$	−34.3958	+	14.2472i	−1.21836	+	0.504663i	−0.321474	+	0.946918i	$0.604178\pi$
$798$	−50.5873	−	33.2543i	−1.79077	−	1.17719i
$799$		−	8.08345i		−	0.285972i
$800$	−0.155035	−	2.04626i	−0.00548132	−	0.0723461i
$801$			9.64093i			0.340645i
$802$	35.3938	−	6.15592i	1.24980	−	0.217373i
$803$	−1.34539	−	3.24806i	−0.0474778	−	0.114622i
$804$	42.0310	+	19.8382i	1.48232	+	0.699641i
$805$	−2.89047	−	6.39753i	−0.101876	−	0.225483i
$806$	18.4392	−	11.6868i	0.649493	−	0.411649i
$807$	47.5972	−	47.5972i	1.67550	−	1.67550i
$808$	4.07759	−	0.507865i	0.143449	−	0.0178666i
$809$	9.80000	−	9.80000i	0.344550	−	0.344550i	−0.513525	−	0.858075i	$-0.671661\pi$
$809$	9.80000	−	9.80000i	0.344550	−	0.344550i	0.858075	+	0.513525i	$0.171661\pi$
$810$	19.0861	−	85.1528i	0.670617	−	2.99196i
$811$	17.5923	−	42.4717i	0.617751	−	1.49138i	−0.236558	−	0.971617i	$-0.576019\pi$
$811$	17.5923	−	42.4717i	0.617751	−	1.49138i	0.854309	−	0.519765i	$-0.173981\pi$
$812$	25.8973	−	25.0498i	0.908816	−	0.879077i
$813$	−2.49103	+	1.03182i	−0.0873641	+	0.0361874i
$814$	3.55170	−	5.04729i	0.124487	−	0.176908i
$815$		−	34.0930i		−	1.19423i
$816$	−31.1355	−	16.5786i	−1.08996	−	0.580367i
$817$	63.2959			2.21444
$818$	24.7944	+	17.4474i	0.866916	+	0.610035i
$819$	23.7320	−	62.8513i	0.829264	−	2.19620i
$820$	15.2393	−	13.8342i	0.532178	−	0.483110i
$821$	1.02804	−	2.48190i	0.0358787	−	0.0866189i	−0.904924	−	0.425572i	$-0.860073\pi$
$821$	1.02804	−	2.48190i	0.0358787	−	0.0866189i	0.940803	+	0.338953i	$0.110073\pi$
$822$	8.73540	−	38.9730i	0.304682	−	1.35934i
$823$	37.1905	+	37.1905i	1.29638	+	1.29638i	0.930768	+	0.365611i	$0.119140\pi$
$823$	37.1905	+	37.1905i	1.29638	+	1.29638i	0.365611	+	0.930768i	$0.380860\pi$
$824$	4.50250	−	16.3458i	0.156852	−	0.569434i
$825$	−0.569270	+	0.569270i	−0.0198194	+	0.0198194i
$826$	−8.28965	−	1.58426i	−0.288434	−	0.0551234i
$827$	−10.7657	+	25.9908i	−0.374361	+	0.903787i	0.618639	+	0.785675i	$0.287684\pi$
$827$	−10.7657	+	25.9908i	−0.374361	+	0.903787i	−0.993000	+	0.118112i	$0.962316\pi$
$828$	−18.1326	+	6.50422i	−0.630151	+	0.226037i
$829$	38.4490	−	15.9261i	1.33539	−	0.553136i	0.403200	−	0.915112i	$-0.367898\pi$
$829$	38.4490	−	15.9261i	1.33539	−	0.553136i	0.932187	+	0.361976i	$0.117898\pi$
$830$	13.6041	−	2.36610i	0.472204	−	0.0821287i
$831$	−102.031			−3.53941
$832$	25.7147	+	3.75170i	0.891498	+	0.130067i
$833$	−18.7314	+	1.18764i	−0.649003	+	0.0411494i
$834$	3.12255	+	17.9533i	0.108125	+	0.621670i
$835$	35.1741	−	14.5696i	1.21725	−	0.504202i
$836$	−6.24902	+	2.24155i	−0.216127	+	0.0775255i
$837$	−69.5565	−	28.8113i	−2.40423	−	0.995863i
$838$	−40.0734	+	25.3986i	−1.38431	+	0.877379i
$839$	4.92466	+	4.92466i	0.170018	+	0.170018i	0.786987	−	0.616969i	$-0.211640\pi$
$839$	4.92466	+	4.92466i	0.170018	+	0.170018i	−0.616969	+	0.786987i	$0.711640\pi$
$840$	45.2318	−	27.6244i	1.56065	−	0.953131i
$841$	−12.2775	+	12.2775i	−0.423362	+	0.423362i
$842$	−4.00310	+	17.8599i	−0.137956	+	0.615492i
$843$	−1.30647	+	3.15409i	−0.0449971	+	0.108632i
$844$	−23.5244	−	25.9137i	−0.809743	−	0.891986i
$845$	2.01742	+	4.87048i	0.0694013	+	0.167550i
$846$	19.1798	−	27.2562i	0.659414	−	0.937088i
$847$	−19.0930	+	20.3419i	−0.656043	+	0.698956i
$848$	−4.96147	−	16.2625i	−0.170378	−	0.558458i
$849$			47.9741i			1.64647i
$850$	0.791623	−	1.12497i	0.0271524	−	0.0385861i
$851$	3.04964	+	7.36249i	0.104540	+	0.252383i
$852$	85.1499	+	4.11522i	2.91719	+	0.140985i
$853$	30.4737	+	12.6226i	1.04340	+	0.432191i	0.837531	−	0.546389i	$-0.183998\pi$
$853$	30.4737	+	12.6226i	1.04340	+	0.432191i	0.205869	+	0.978580i	$0.433998\pi$
$854$	−17.9669	+	12.2013i	−0.614813	+	0.417521i
$855$	58.5559	+	58.5559i	2.00257	+	2.00257i
$856$	2.98450	+	23.9622i	0.102008	+	0.819011i
$857$	8.71179	−	8.71179i	0.297589	−	0.297589i	−0.542480	−	0.840069i	$-0.682514\pi$
$857$	8.71179	−	8.71179i	0.297589	−	0.297589i	0.840069	+	0.542480i	$0.182514\pi$
$858$	−5.45771	−	8.61108i	−0.186323	−	0.293977i
$859$	−24.6028	−	10.1908i	−0.839436	−	0.347706i	−0.0788051	−	0.996890i	$-0.525110\pi$
$859$	−24.6028	−	10.1908i	−0.839436	−	0.347706i	−0.760631	+	0.649184i	$0.775110\pi$
$860$	−23.6527	+	50.1127i	−0.806552	+	1.70883i
$861$	−38.9036	−	14.6896i	−1.32583	−	0.500620i
$862$	9.15042	+	52.6109i	0.311664	+	1.79193i
$863$			17.7600i			0.604556i	0.953220	+	0.302278i	$0.0977472\pi$
$863$			17.7600i			0.604556i	−0.953220	+	0.302278i	$0.902253\pi$
$864$	−40.4537	−	79.9711i	−1.37626	−	2.72067i
$865$	−21.9890			−0.747649
$866$	−5.87909	−	33.8022i	−0.199780	−	1.14865i
$867$	12.3479	+	29.8106i	0.419358	+	1.01242i
$868$	−9.23524	−	23.3887i	−0.313464	−	0.793863i
$869$	−3.62694	−	1.50233i	−0.123035	−	0.0509629i
$870$	−57.6045	+	36.5097i	−1.95297	+	1.23780i
$871$	−16.2297	−	16.2297i	−0.549921	−	0.549921i
$872$	−11.4982	−	8.95123i	−0.389379	−	0.303127i
$873$	88.5509	+	88.5509i	2.99700	+	2.99700i
$874$	1.87489	−	8.36481i	0.0634189	−	0.282944i
$875$	12.5802	+	27.8439i	0.425288	+	0.941296i
$876$	−1.65441	+	34.2322i	−0.0558975	+	1.15660i
$877$	−45.4844	+	18.8403i	−1.53590	+	0.636190i	−0.980699	−	0.195526i	$-0.937359\pi$
$877$	−45.4844	+	18.8403i	−1.53590	+	0.636190i	−0.555201	+	0.831716i	$0.687359\pi$
$878$	−5.06233	−	3.56228i	−0.170845	−	0.120221i
$879$	−48.9400			−1.65071
$880$	0.560488	−	5.78511i	0.0188940	−	0.195016i
$881$	−30.5234			−1.02836			−0.514180	−	0.857683i	$-0.671904\pi$
$881$	−30.5234			−1.02836			−0.514180	+	0.857683i	$0.671904\pi$
$882$	−65.9774	−	40.4397i	−2.22157	−	1.36168i
$883$	−13.5867	−	32.8013i	−0.457230	−	1.10385i	−0.969514	−	0.245035i	$-0.921200\pi$
$883$	−13.5867	−	32.8013i	−0.457230	−	1.10385i	0.512284	−	0.858816i	$-0.328800\pi$
$884$	11.7086	+	12.8978i	0.393801	+	0.433799i
$885$	14.7591	+	6.11343i	0.496122	+	0.205501i
$886$	−4.83501	−	1.08372i	−0.162435	−	0.0364082i
$887$	−21.8427	+	21.8427i	−0.733407	+	0.733407i	−0.971293	−	0.237886i	$-0.923546\pi$
$887$	−21.8427	+	21.8427i	−0.733407	+	0.733407i	0.237886	+	0.971293i	$0.423546\pi$
$888$	−52.3125	+	29.7172i	−1.75549	+	0.997245i
$889$	−9.07488	+	0.287403i	−0.304362	+	0.00963919i
$890$	3.17244	−	2.01069i	0.106340	−	0.0673986i
$891$	−7.39927	+	17.8634i	−0.247885	+	0.598447i
$892$	47.3808	−	16.9957i	1.58643	−	0.569057i
$893$	5.67555	+	13.7020i	0.189925	+	0.458520i
$894$	−0.683128	−	3.92769i	−0.0228472	−	0.131361i
$895$	−3.87759			−0.129614
$896$	9.80467	−	28.2819i	0.327551	−	0.944834i
$897$	13.1641			0.439536
$898$	−7.01014	−	40.3052i	−0.233932	−	1.34500i
$899$	12.3827	+	29.8944i	0.412985	+	0.997035i
$900$	5.33847	−	1.91493i	0.177949	−	0.0638310i
$901$	4.36150	−	10.5296i	0.145303	−	0.350792i
$902$	−3.85182	+	2.44129i	−0.128252	+	0.0812860i
$903$	111.904	−	3.54403i	3.72394	−	0.117938i
$904$	−25.1492	+	14.2865i	−0.836451	+	0.475163i
$905$	1.79666	−	1.79666i	0.0597229	−	0.0597229i
$906$	−34.4223	−	7.71540i	−1.14360	−	0.256327i
$907$	−44.2914	−	18.3461i	−1.47067	−	0.609172i	−0.503660	−	0.863902i	$-0.668014\pi$
$907$	−44.2914	−	18.3461i	−1.47067	−	0.609172i	−0.967012	+	0.254730i	$0.918014\pi$
$908$	−39.7007	−	43.7330i	−1.31751	−	1.45133i
$909$	4.34593	+	10.4920i	0.144145	+	0.347997i
$910$	−25.6313	+	5.29890i	−0.849670	+	0.175657i
$911$	28.0080			0.927946			0.463973	−	0.885849i	$-0.346423\pi$
$911$	28.0080			0.927946			0.463973	+	0.885849i	$0.346423\pi$
$912$	64.4168	+	6.24100i	2.13305	+	0.206660i
$913$	−3.05947			−0.101254
$914$	−13.5020	−	9.50112i	−0.446605	−	0.314269i
$915$	37.9803	−	15.7320i	1.25559	−	0.520083i
$916$	0.588006	−	12.1667i	0.0194283	−	0.401999i
$917$	−13.6477	+	6.16617i	−0.450686	+	0.203625i
$918$	13.1391	−	58.6202i	0.433655	−	1.93475i
$919$	−11.0504	−	11.0504i	−0.364520	−	0.364520i	0.500954	−	0.865474i	$-0.332983\pi$
$919$	−11.0504	−	11.0504i	−0.364520	−	0.364520i	−0.865474	+	0.500954i	$0.832983\pi$
$920$	5.92198	+	4.61019i	0.195242	+	0.151993i
$921$	29.7767	+	29.7767i	0.981174	+	0.981174i
$922$	24.2496	−	15.3694i	0.798618	−	0.506165i
$923$	−38.8945	−	16.1106i	−1.28023	−	0.530287i
$924$	−10.9225	+	4.31284i	−0.359323	+	0.141882i
$925$	−0.897855	−	2.16761i	−0.0295213	−	0.0712707i
$926$	−3.02937	−	17.4175i	−0.0995513	−	0.572376i
$927$	46.8581			1.53902
$928$	−12.0095	+	36.5976i	−0.394232	+	1.20138i
$929$		−	3.46522i		−	0.113690i	−0.998383	−	0.0568451i	$-0.981896\pi$
$929$		−	3.46522i		−	0.113690i	0.998383	−	0.0568451i	$-0.0181041\pi$
$930$	8.15609	+	46.8939i	0.267449	+	1.53771i
$931$	30.9171	−	15.1648i	1.01327	−	0.497006i
$932$	7.22339	−	15.3041i	0.236610	−	0.501302i
$933$	16.8943	+	6.99786i	0.553096	+	0.229100i
$934$	−27.4165	−	43.2573i	−0.897095	−	1.41542i
$935$	2.75491	−	2.75491i	0.0900953	−	0.0900953i
$936$	8.87676	+	71.2705i	0.290146	+	2.32955i
$937$	10.2285	+	10.2285i	0.334149	+	0.334149i	0.854160	−	0.520011i	$-0.174072\pi$
$937$	10.2285	+	10.2285i	0.334149	+	0.334149i	−0.520011	+	0.854160i	$0.674072\pi$
$938$	−21.8711	+	14.8527i	−0.714117	+	0.484958i
$939$	−9.92495	−	4.11105i	−0.323888	−	0.134159i
$940$	−12.9690	−	0.626781i	−0.423003	−	0.0204434i
$941$	17.9086	+	43.2352i	0.583804	+	1.40943i	0.889340	+	0.457246i	$0.151164\pi$
$941$	17.9086	+	43.2352i	0.583804	+	1.40943i	−0.305536	+	0.952180i	$0.598836\pi$
$942$	−50.8320	+	72.2369i	−1.65619	+	2.35360i
$943$		−	5.88843i		−	0.191754i
$944$	8.62971	−	2.63280i	0.280873	−	0.0856904i
$945$	65.8143	+	61.7735i	2.14094	+	2.00949i
$946$	7.06577	−	10.0411i	0.229728	−	0.326465i
$947$	4.53360	+	10.9451i	0.147322	+	0.355667i	0.980264	−	0.197694i	$-0.0633451\pi$
$947$	4.53360	+	10.9451i	0.147322	+	0.355667i	−0.832942	+	0.553361i	$0.813345\pi$
$948$	25.7231	+	28.3357i	0.835447	+	0.920300i
$949$	6.47684	−	15.6365i	0.210247	−	0.507581i
$950$	−0.551991	+	2.46271i	−0.0179090	+	0.0799009i
$951$	12.4968	−	12.4968i	0.405236	−	0.405236i
$952$	17.1239	−	10.4581i	0.554989	−	0.338948i
$953$	−23.1515	−	23.1515i	−0.749952	−	0.749952i	0.224518	−	0.974470i	$-0.427919\pi$
$953$	−23.1515	−	23.1515i	−0.749952	−	0.749952i	−0.974470	+	0.224518i	$0.927919\pi$
$954$	39.6901	−	25.1556i	1.28502	−	0.814444i
$955$	−8.94465	−	3.70499i	−0.289442	−	0.119891i
$956$	29.6937	−	10.6512i	0.960362	−	0.344485i
$957$	13.9607	−	5.78270i	0.451284	−	0.186928i
$958$	4.48974	+	25.8141i	0.145057	+	0.834014i
$959$	16.5652	+	15.5481i	0.534918	+	0.502076i
$960$	−29.0127	+	48.6680i	−0.936382	+	1.57075i
$961$	−8.41717			−0.271522
$962$	29.2717	−	5.09112i	0.943756	−	0.164144i
$963$	−61.6569	+	25.5391i	−1.98687	+	0.822987i
$964$	−52.7450	+	18.9198i	−1.69880	+	0.609367i
$965$	−10.4544	+	25.2392i	−0.336539	+	0.812478i
$966$	2.84635	−	14.8936i	0.0915800	−	0.479193i
$967$	13.5816	−	13.5816i	0.436755	−	0.436755i	−0.454163	−	0.890918i	$-0.650062\pi$
$967$	13.5816	−	13.5816i	0.436755	−	0.436755i	0.890918	+	0.454163i	$0.150062\pi$
$968$	7.92036	−	28.7540i	0.254570	−	0.924189i
$969$	30.6758	+	30.6758i	0.985448	+	0.985448i
$970$	10.6705	−	47.6066i	0.342610	−	1.52855i
$971$	−4.71036	+	11.3718i	−0.151163	+	0.364939i	−0.981262	−	0.192676i	$-0.938283\pi$
$971$	−4.71036	+	11.3718i	−0.151163	+	0.364939i	0.830100	+	0.557615i	$0.188283\pi$
$972$	69.1773	−	62.7990i	2.21886	−	2.01428i
$973$	−9.69734	−	3.66162i	−0.310882	−	0.117386i
$974$	0.503009	+	0.353959i	0.0161174	+	0.0113416i
$975$	−3.87568			−0.124121
$976$	10.9122	−	20.4936i	0.349290	−	0.655985i
$977$		−	16.3145i		−	0.521946i	−0.965346	−	0.260973i	$-0.915957\pi$
$977$		−	16.3145i		−	0.521946i	0.965346	−	0.260973i	$-0.0840434\pi$
$978$	42.3777	−	60.2226i	1.35509	−	1.92571i
$979$	−0.768853	+	0.318469i	−0.0245726	+	0.0101783i
$980$	0.453036	+	30.1445i	0.0144717	+	0.962932i
$981$	15.4115	−	37.2067i	0.492052	−	1.18792i
$982$	12.2295	−	54.5619i	0.390258	−	1.74114i
$983$	25.5491	−	25.5491i	0.814890	−	0.814890i	−0.170472	−	0.985363i	$-0.554529\pi$
$983$	25.5491	−	25.5491i	0.814890	−	0.814890i	0.985363	+	0.170472i	$0.0545293\pi$
$984$	44.1149	−	5.49452i	1.40633	−	0.175159i
$985$	−18.2200	+	18.2200i	−0.580538	+	0.580538i
$986$	−21.8080	+	13.8219i	−0.694507	+	0.440179i
$987$	10.8013	+	23.9067i	0.343810	+	0.760960i
$988$	−28.9026	−	13.6418i	−0.919513	−	0.434002i
$989$	6.06697	+	14.6470i	0.192919	+	0.465747i
$990$	15.8258	−	2.75252i	0.502977	−	0.0874810i
$991$		−	14.7714i		−	0.469227i	−0.972089	−	0.234614i	$-0.924617\pi$
$991$		−	14.7714i		−	0.469227i	0.972089	−	0.234614i	$-0.0753825\pi$
$992$	20.3903	+	17.5182i	0.647393	+	0.556202i
$993$			26.9755i			0.856042i
$994$	−26.6370	+	40.5210i	−0.844876	+	1.28525i
$995$	20.7290	−	8.58622i	0.657152	−	0.272201i
$996$	26.9716	+	12.7303i	0.854626	+	0.403376i
$997$	−10.1843	+	24.5872i	−0.322542	+	0.778684i	0.676563	+	0.736384i	$0.263468\pi$
$997$	−10.1843	+	24.5872i	−0.322542	+	0.778684i	−0.999105	+	0.0422998i	$0.986532\pi$
$998$	35.8244	−	22.7056i	1.13400	−	0.718732i
$999$	−72.4530	−	72.4530i	−2.29231	−	2.29231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.x.b.27.13	✓	112
4.3	odd	2		896.2.x.b.783.28		112
7.6	odd	2	inner	224.2.x.b.27.14	yes	112
28.27	even	2		896.2.x.b.783.1		112
32.13	even	8		896.2.x.b.111.1		112
32.19	odd	8	inner	224.2.x.b.83.14	yes	112
224.13	odd	8		896.2.x.b.111.28		112
224.83	even	8	inner	224.2.x.b.83.13	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.x.b.27.13	✓	112	1.1	even	1	trivial
224.2.x.b.27.14	yes	112	7.6	odd	2	inner
224.2.x.b.83.13	yes	112	224.83	even	8	inner
224.2.x.b.83.14	yes	112	32.19	odd	8	inner
896.2.x.b.111.1		112	32.13	even	8
896.2.x.b.111.28		112	224.13	odd	8
896.2.x.b.783.1		112	28.27	even	2
896.2.x.b.783.28		112	4.3	odd	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.242331 - 1.39330i) q^{2} +(-1.25862 - 3.03857i) q^{3} +(-1.88255 + 0.675278i) q^{4} +(-0.824079 + 1.98950i) q^{5} +(-3.92863 + 2.48997i) q^{6} +(-0.0837494 - 2.64443i) q^{7} +(1.39706 + 2.45931i) q^{8} +(-5.52747 + 5.52747i) q^{9} +O(q^{10})\)	\(q+(-0.242331 - 1.39330i) q^{2} +(-1.25862 - 3.03857i) q^{3} +(-1.88255 + 0.675278i) q^{4} +(-0.824079 + 1.98950i) q^{5} +(-3.92863 + 2.48997i) q^{6} +(-0.0837494 - 2.64443i) q^{7} +(1.39706 + 2.45931i) q^{8} +(-5.52747 + 5.52747i) q^{9} +(2.97167 + 0.666069i) q^{10} +(-0.623399 - 0.258220i) q^{11} +(4.42129 + 4.87035i) q^{12} +(-1.24310 - 3.00110i) q^{13} +(-3.66417 + 0.757514i) q^{14} +7.08245 q^{15} +(3.08800 - 2.54249i) q^{16} +2.68128 q^{17} +(9.04089 + 6.36193i) q^{18} +(-4.54495 + 1.88258i) q^{19} +(0.207903 - 4.30183i) q^{20} +(-7.92987 + 3.58280i) q^{21} +(-0.208709 + 0.931155i) q^{22} +(-0.871276 - 0.871276i) q^{23} +(5.71442 - 7.34041i) q^{24} +(0.256515 + 0.256515i) q^{25} +(-3.88019 + 2.45926i) q^{26} +(14.6369 + 6.06280i) q^{27} +(1.94339 + 4.92171i) q^{28} +(-2.60571 - 6.29073i) q^{29} +(-1.71630 - 9.86795i) q^{30} -4.75214 q^{31} +(-4.29076 - 3.68637i) q^{32} +2.21924i q^{33} +(-0.649758 - 3.73582i) q^{34} +(5.33011 + 2.01260i) q^{35} +(6.67317 - 14.1383i) q^{36} +(-5.97522 - 2.47502i) q^{37} +(3.72438 + 5.87626i) q^{38} +(-7.55448 + 7.55448i) q^{39} +(-6.04410 + 0.752795i) q^{40} +(3.37920 + 3.37920i) q^{41} +(6.91355 + 10.1804i) q^{42} +(-11.8871 - 4.92381i) q^{43} +(1.34795 + 0.0651453i) q^{44} +(-6.44185 - 15.5520i) q^{45} +(-1.00281 + 1.42508i) q^{46} -3.01477i q^{47} +(-11.6121 - 6.18308i) q^{48} +(-6.98597 + 0.442938i) q^{49} +(0.295240 - 0.419564i) q^{50} +(-3.37471 - 8.14727i) q^{51} +(4.36677 + 4.81029i) q^{52} +(1.62665 - 3.92708i) q^{53} +(4.90030 - 21.8627i) q^{54} +(1.02746 - 1.02746i) q^{55} +(6.38646 - 3.90040i) q^{56} +(11.4407 + 11.4407i) q^{57} +(-8.13341 + 5.15496i) q^{58} +(2.08390 + 0.863180i) q^{59} +(-13.3331 + 4.78262i) q^{60} +(5.36260 - 2.22126i) q^{61} +(1.15159 + 6.62114i) q^{62} +(15.0799 + 14.1541i) q^{63} +(-4.09643 + 6.87163i) q^{64} +6.99512 q^{65} +(3.09206 - 0.537792i) q^{66} +(6.52791 - 2.70395i) q^{67} +(-5.04765 + 1.81061i) q^{68} +(-1.55083 + 3.74404i) q^{69} +(1.51249 - 7.91414i) q^{70} +(9.16414 - 9.16414i) q^{71} +(-21.3160 - 5.87155i) q^{72} +(3.68420 + 3.68420i) q^{73} +(-2.00045 + 8.92502i) q^{74} +(0.456585 - 1.10229i) q^{75} +(7.28484 - 6.61317i) q^{76} +(-0.630635 + 1.67016i) q^{77} +(12.3563 + 8.69495i) q^{78} +5.81800 q^{79} +(2.51354 + 8.23880i) q^{80} -28.6549i q^{81} +(3.88934 - 5.52711i) q^{82} +(4.18900 - 1.73514i) q^{83} +(12.5090 - 12.0997i) q^{84} +(-2.20959 + 5.33442i) q^{85} +(-3.97971 + 17.7555i) q^{86} +(-15.8352 + 15.8352i) q^{87} +(-0.235884 - 1.89388i) q^{88} +(0.872091 - 0.872091i) q^{89} +(-20.1075 + 12.7441i) q^{90} +(-7.83209 + 3.53862i) q^{91} +(2.22858 + 1.05187i) q^{92} +(5.98113 + 14.4397i) q^{93} +(-4.20047 + 0.730573i) q^{94} -10.5936i q^{95} +(-5.80088 + 17.6775i) q^{96} -16.0201i q^{97} +(2.31006 + 9.62619i) q^{98} +(4.87313 - 2.01852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9	\( 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{11} - 20 q^{14} - 16 q^{15} + 16 q^{16} - 16 q^{18} - 4 q^{21} + 32 q^{22} - 48 q^{23} - 8 q^{25} - 24 q^{28} - 8 q^{29} + 16 q^{30} - 8 q^{32} + 20 q^{35} + 32 q^{36} - 8 q^{37} - 8 q^{39} + 16 q^{42} + 32 q^{43} - 144 q^{44} - 8 q^{46} + 16 q^{50} - 32 q^{51} - 32 q^{53} + 64 q^{56} - 8 q^{57} - 72 q^{58} - 88 q^{60} + 112 q^{64} - 16 q^{65} - 64 q^{67} - 40 q^{70} + 56 q^{71} - 8 q^{72} - 168 q^{74} + 52 q^{77} + 192 q^{78} - 16 q^{79} - 24 q^{84} - 48 q^{85} - 8 q^{86} - 96 q^{88} - 52 q^{91} - 8 q^{92} - 32 q^{93} + 88 q^{98} + 16 q^{99}+O(q^{100}) \) 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^11 - 20 * q^14 - 16 * q^15 + 16 * q^16 - 16 * q^18 - 4 * q^21 + 32 * q^22 - 48 * q^23 - 8 * q^25 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 8 * q^32 + 20 * q^35 + 32 * q^36 - 8 * q^37 - 8 * q^39 + 16 * q^42 + 32 * q^43 - 144 * q^44 - 8 * q^46 + 16 * q^50 - 32 * q^51 - 32 * q^53 + 64 * q^56 - 8 * q^57 - 72 * q^58 - 88 * q^60 + 112 * q^64 - 16 * q^65 - 64 * q^67 - 40 * q^70 + 56 * q^71 - 8 * q^72 - 168 * q^74 + 52 * q^77 + 192 * q^78 - 16 * q^79 - 24 * q^84 - 48 * q^85 - 8 * q^86 - 96 * q^88 - 52 * q^91 - 8 * q^92 - 32 * q^93 + 88 * q^98 + 16 * q^99

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