LMFDB - Embedded newform 224.2.x.b.27.14

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			27.14
Character	$\chi$	$=$	224.27
Dual form			224.2.x.b.83.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.242331 - 1.39330i) q^{2} +(1.25862 + 3.03857i) q^{3} +(-1.88255 + 0.675278i) q^{4} +(0.824079 - 1.98950i) q^{5} +(3.92863 - 2.48997i) q^{6} +(2.64443 + 0.0837494i) q^{7} +(1.39706 + 2.45931i) q^{8} +(-5.52747 + 5.52747i) q^{9} +O(q^{10})$	\(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} +(2.64443 + 0.0837494i) 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} +(-0.524139 - 3.70476i) 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} +(3.07384 + 8.14068i) 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} +(-5.03482 + 1.62806i) 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} +(2.34584 - 5.19208i) 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} +(10.5975 - 6.25551i) 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} +(3.48846 + 6.62047i) 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} +(-7.80257 - 2.01024i) 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} +(-1.62691 - 0.735054i) 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} +(-11.2839 - 13.2496i) 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} +(3.03594 + 8.04030i) 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} +(-1.07577 - 9.84087i) 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	$0.273339\pi$
$3$	1.25862	+	3.03857i	0.726663	+	1.75432i	0.0732556	+	0.997313i	$0.476661\pi$
$4$	−1.88255	+	0.675278i	−0.941276	+	0.337639i
$5$	0.824079	−	1.98950i	0.368540	−	0.889733i	−0.625451	−	0.780264i	$-0.715085\pi$
$5$	0.824079	−	1.98950i	0.368540	−	0.889733i	0.993990	−	0.109469i	$-0.0349152\pi$
$6$	3.92863	−	2.48997i	1.60386	−	1.01652i
$7$	2.64443	+	0.0837494i	0.999499	+	0.0316543i
$7$	2.64443	+	0.0837494i	0.999499	+	0.0316543i
$8$	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	$0.0237429\pi$
$13$	1.24310	+	3.00110i	0.344773	+	0.832356i	−0.652446	+	0.757835i	$0.726257\pi$
$14$	−0.524139	−	3.70476i	−0.140082	−	0.990140i
$15$	7.08245			1.82868
$16$	3.08800	−	2.54249i	0.772000	−	0.635623i
$17$	−2.68128			−0.650307			−0.325153	−	0.945661i	$-0.605416\pi$
$17$	−2.68128			−0.650307			−0.325153	+	0.945661i	$0.605416\pi$
$18$	9.04089	+	6.36193i	2.13096	+	1.49952i
$19$	4.54495	−	1.88258i	1.04268	−	0.431894i	0.205409	−	0.978676i	$-0.434147\pi$
$19$	4.54495	−	1.88258i	1.04268	−	0.431894i	0.837275	+	0.546782i	$0.184147\pi$
$20$	−0.207903	+	4.30183i	−0.0464886	+	0.961918i
$21$	3.07384	+	8.14068i	0.670767	+	1.77644i
$22$	−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
$28$	−5.03482	+	1.62806i	−0.951492	+	0.307674i
$29$	−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	$-0.359657\pi$
$31$	4.75214			0.853510			0.426755	+	0.904367i	$0.359657\pi$
$32$	−4.29076	−	3.68637i	−0.758507	−	0.651665i
$33$		−	2.21924i		−	0.386321i
$34$	0.649758	+	3.73582i	0.111433	+	0.640688i
$35$	2.34584	−	5.19208i	0.396519	−	0.877621i
$36$	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	0.392156	−	0.919899i	$-0.371729\pi$
$41$	−3.37920	−	3.37920i	−0.527742	−	0.527742i	−0.919899	+	0.392156i	$0.871729\pi$
$42$	10.5975	−	6.25551i	1.63523	−	0.965247i
$43$	−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	$0.0705649\pi$
$47$			3.01477i			0.439750i	−0.975528	+	0.219875i	$0.929435\pi$
$48$	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
$56$	3.48846	+	6.62047i	0.466166	+	0.884697i
$57$	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	0.242886	−	0.970055i	$-0.421906\pi$
$59$	−2.08390	−	0.863180i	−0.271301	−	0.112376i	−0.514186	+	0.857678i	$0.671906\pi$
$60$	−13.3331	+	4.78262i	−1.72129	+	0.617434i
$61$	−5.36260	+	2.22126i	−0.686611	+	0.284403i	−0.698587	−	0.715525i	$-0.746188\pi$
$61$	−5.36260	+	2.22126i	−0.686611	+	0.284403i	0.0119767	+	0.999928i	$0.496188\pi$
$62$	−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
$70$	−7.80257	−	2.01024i	−0.932586	−	0.240270i
$71$	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	0.457835	−	0.889037i	$-0.348625\pi$
$73$	−3.68420	−	3.68420i	−0.431203	−	0.431203i	−0.889037	+	0.457835i	$0.848625\pi$
$74$	−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
$77$	−1.62691	−	0.735054i	−0.185403	−	0.0837672i
$78$	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	−0.600547	−	0.799589i	$-0.705050\pi$
$83$	−4.18900	+	1.73514i	−0.459803	+	0.190457i	0.140744	+	0.990046i	$0.455050\pi$
$84$	−11.2839	−	13.2496i	−1.23117	−	1.44564i
$85$	−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	−0.751815	−	0.659374i	$-0.770821\pi$
$89$	−0.872091	+	0.872091i	−0.0924415	+	0.0924415i	0.659374	+	0.751815i	$0.270821\pi$
$90$	20.1075	−	12.7441i	2.11952	−	1.34335i
$91$	3.03594	+	8.04030i	0.318253	+	0.842853i
$92$	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	$0.302331\pi$
$97$			16.0201i			1.62660i	−0.581845	+	0.813300i	$0.697669\pi$
$98$	−1.07577	−	9.84087i	−0.108670	−	0.994078i
$99$	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	−0.949123	−	0.314906i	$-0.898027\pi$
$101$	−0.555956	+	1.34220i	−0.0553197	+	0.133554i	0.893803	+	0.448459i	$0.148027\pi$
$102$	−10.5338	+	6.67631i	−1.04300	+	0.661053i
$103$	4.23866	+	4.23866i	0.417647	+	0.417647i	0.884392	−	0.466745i	$-0.154573\pi$
$103$	4.23866	+	4.23866i	0.417647	+	0.417647i	−0.466745	+	0.884392i	$0.654573\pi$
$104$	−5.64396	+	7.24990i	−0.553436	+	0.710911i
$105$	18.7290	+	0.593151i	1.82776	+	0.0578856i
$106$	−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
$112$	8.37892	−	6.46481i	0.791733	−	0.610867i
$113$			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
$119$	−7.09045	−	0.224556i	−0.649981	−	0.0205850i
$120$	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
$126$	23.3752	+	17.5808i	2.08242	+	1.56622i
$127$		−	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	0.989817	−	0.142346i	$-0.0454647\pi$
$131$	2.16614	+	5.22953i	0.189257	+	0.456906i	−0.800560	+	0.599252i	$0.795465\pi$
$132$	1.49861	+	4.17784i	0.130437	+	0.363634i
$133$	12.1765	−	4.59771i	1.05583	−	0.398672i
$134$	−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	−0.974622	−	0.223859i	$-0.928135\pi$
$139$	−1.49929	+	3.61960i	−0.127168	+	0.307011i	0.847454	+	0.530869i	$0.178135\pi$
$140$	−0.910061	+	11.3584i	−0.0769142	+	0.959964i
$141$	−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
$147$	7.44677	+	21.7849i	0.614199	+	1.79679i
$148$	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
$154$	−0.629898	+	2.44489i	−0.0507586	+	0.197015i
$155$	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	−0.949813	−	0.312819i	$-0.898727\pi$
$157$	−17.5449	+	7.26734i	−1.40024	+	0.579996i	−0.450423	+	0.892815i	$0.648727\pi$
$158$	−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	0.999485	−	0.0320865i	$-0.0102152\pi$
$167$	12.5015	+	12.5015i	0.967399	+	0.967399i	−0.0320865	+	0.999485i	$0.510215\pi$
$168$	−15.7261	+	18.9326i	−1.21330	+	1.46068i
$169$	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	$-0.998107\pi$
$173$	−3.90765	−	9.43391i	−0.297093	−	0.717247i	0.702889	−	0.711300i	$-0.251893\pi$
$174$	−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	0.422829	−	0.906210i	$-0.361037\pi$
$181$	1.09010	+	0.451534i	0.0810264	+	0.0335623i	−0.341802	+	0.939772i	$0.611037\pi$
$182$	10.4668	−	6.17838i	0.775853	−	0.457972i
$183$	−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
$189$	−38.1984	−	17.2584i	−2.77852	−	1.25537i
$190$	−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
$196$	−13.4506	+	3.88362i	−0.960754	+	0.277401i
$197$	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	0.918255	−	0.395990i	$-0.129598\pi$
$199$	7.36746	+	7.36746i	0.522265	+	0.522265i	−0.395990	+	0.918255i	$0.629598\pi$
$200$	−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
$203$	−6.36375	−	16.8536i	−0.446648	−	1.18289i
$204$	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
$210$	−3.71218	−	26.2388i	−0.256165	−	1.81065i
$211$	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
$217$	12.5667	+	0.397989i	0.853082	+	0.0270173i
$218$	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	$-0.180965\pi$
$223$	25.1684			1.68540			0.842700	+	0.538383i	$0.180965\pi$
$224$	−11.0379	−	10.1077i	−0.737499	−	0.675348i
$225$	−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	$-0.688646\pi$
$227$	−11.3017	−	27.2846i	−0.750118	−	1.81095i	−0.191559	−	0.981481i	$-0.561354\pi$
$228$	−29.2634	−	13.8121i	−1.93802	−	0.914727i
$229$	2.33071	−	5.62684i	0.154018	−	0.371832i	−0.827971	−	0.560771i	$-0.810505\pi$
$229$	2.33071	−	5.62684i	0.154018	−	0.371832i	0.981989	+	0.188939i	$0.0605048\pi$
$230$	2.00882	+	3.16948i	0.132457	+	0.208989i
$231$	0.185860	−	5.86862i	0.0122287	−	0.386127i
$232$	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
$238$	1.40536	+	9.93352i	0.0910962	+	0.643894i
$239$	−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	$-0.858192\pi$
$241$	−28.0178			−1.80479			−0.902394	+	0.430912i	$0.858192\pi$
$242$	−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
$245$	6.63822	−	13.5336i	0.424101	−	0.864630i
$246$	−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	0.0122529	−	0.999925i	$-0.496100\pi$
$251$	−10.8704	−	4.50269i	−0.686137	−	0.284207i	−0.698390	+	0.715718i	$0.746100\pi$
$252$	18.8308	−	36.8289i	1.18623	−	2.32000i
$253$	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	$0.182678\pi$
$257$			17.4070i			1.08582i	−0.839791	+	0.542910i	$0.817322\pi$
$258$	−58.9602	+	10.2547i	−3.67070	+	0.638432i
$259$	−15.5937	−	7.04541i	−0.968947	−	0.437781i
$260$	−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
$266$	−9.35671	−	15.8513i	−0.573697	−	0.971903i
$267$	−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	$-0.910535\pi$
$269$	−7.83216	−	18.9085i	−0.477535	−	1.15287i	0.483226	−	0.875496i	$-0.339465\pi$
$270$	39.4577	+	27.7658i	2.40132	+	1.68977i
$271$			0.819802i			0.0497994i	0.999690	+	0.0248997i	$0.00792664\pi$
$271$			0.819802i			0.0497994i	−0.999690	+	0.0248997i	$0.992073\pi$
$272$	−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
$280$	16.0462	−	1.48452i	0.958945	−	0.0887170i
$281$	−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	0.745388	−	0.666630i	$-0.232264\pi$
$283$	13.4762	+	5.58204i	0.801079	+	0.331818i	0.0556903	+	0.998448i	$0.482264\pi$
$284$	−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	$0.268130\pi$
$293$	−5.69443	+	13.7476i	−0.332672	+	0.803141i	−0.998378	+	0.0569272i	$0.981870\pi$
$294$	28.5482	−	15.6547i	1.66496	−	0.913001i
$295$	−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
$301$	−31.0223	−	14.0162i	−1.78809	−	0.807880i
$302$	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	−0.0186633	−	0.999826i	$-0.505941\pi$
$307$	11.8291	−	4.89978i	0.675123	−	0.279645i	0.693787	+	0.720181i	$0.255941\pi$
$308$	3.55910	+	0.285162i	0.202799	+	0.0162486i
$309$	−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	−0.586799	−	0.809733i	$-0.699612\pi$
$311$	3.93148	−	3.93148i	0.222934	−	0.222934i	0.809733	+	0.586799i	$0.199612\pi$
$312$	−29.1329	−	8.02473i	−1.64933	−	0.454311i
$313$	−2.30964	+	2.30964i	−0.130548	+	0.130548i	−0.769362	−	0.638813i	$-0.779426\pi$
$313$	−2.30964	+	2.30964i	−0.130548	+	0.130548i	0.638813	+	0.769362i	$0.279426\pi$
$314$	14.3772	+	22.6841i	0.811354	+	1.28014i
$315$	15.7325	+	41.6656i	0.886428	+	2.34759i
$316$	−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
$322$	−2.77120	+	3.68454i	−0.154433	+	0.205332i
$323$	−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
$329$	−0.252485	+	7.97234i	−0.0139200	+	0.439529i
$330$	−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
$336$	30.1896	+	17.3232i	1.64698	+	0.945058i
$337$		−	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
$343$	18.4368	+	1.75639i	0.995493	+	0.0948361i
$344$	−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	0.217570	−	0.976045i	$-0.430187\pi$
$349$	19.8320	−	8.21468i	1.06158	−	0.439722i	0.844013	+	0.536323i	$0.180187\pi$
$350$	0.815879	−	1.08478i	0.0436106	−	0.0579838i
$351$		−	51.4635i		−	2.74692i
$352$	1.72296	+	3.40605i	0.0918341	+	0.181543i
$353$			8.47471i			0.451063i	0.974236	+	0.225532i	$0.0724119\pi$
$353$			8.47471i			0.451063i	−0.974236	+	0.225532i	$0.927588\pi$
$354$	−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
$357$	−8.24184	−	21.8275i	−0.436204	−	1.15523i
$358$	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
$364$	−11.1448	−	13.0862i	−0.584144	−	0.685902i
$365$	−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	$-0.996679\pi$
$367$		−	0.399698i		−	0.0208641i	0.999946	−	0.0104320i	$-0.00332068\pi$
$368$	−4.90571	−	0.475288i	−0.255728	−	0.0247761i
$369$	37.3569			1.94472
$370$	16.1078	+	11.3348i	0.837406	+	0.589270i
$371$	4.63044	−	10.2486i	0.240400	−	0.532082i
$372$	−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
$378$	−14.7895	+	57.4040i	−0.760689	+	2.95254i
$379$	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	$-0.719105\pi$
$383$	−24.8644			−1.27051			−0.635255	+	0.772303i	$0.719105\pi$
$384$	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
$392$	8.67052	+	17.7995i	0.437928	+	0.899010i
$393$	−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	$0.000272715\pi$
$397$	5.84792	+	14.1181i	0.293499	+	0.708569i	−0.706501	+	0.707712i	$0.749727\pi$
$398$	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
$406$	−21.9399	+	12.9507i	−1.08886	+	0.642734i
$407$	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	−0.224835	−	0.974397i	$-0.572184\pi$
$409$	15.1589	−	15.1589i	0.749562	−	0.749562i	0.974397	+	0.224835i	$0.0721843\pi$
$410$	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
$413$	−5.43843	−	2.45714i	−0.267608	−	0.120908i
$414$	−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	$0.180731\pi$
$419$	12.8383	+	30.9945i	0.627194	+	1.51418i	−0.215900	+	0.976415i	$0.569269\pi$
$420$	−35.6589	+	11.5307i	−1.73997	+	0.562638i
$421$	−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
$427$	−14.3670	+	5.42485i	−0.695269	+	0.262527i
$428$	−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	$-0.698100\pi$
$433$	−24.2606			−1.16589			−0.582945	+	0.812512i	$0.698100\pi$
$434$	−2.49078	−	17.6056i	−0.119561	−	0.845094i
$435$	−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	−0.777098	−	0.629380i	$-0.783309\pi$
$439$	−3.09504	+	3.09504i	−0.147718	+	0.147718i	0.629380	+	0.777098i	$0.283309\pi$
$440$	−3.96227	−	1.09142i	−0.188894	−	0.0520313i
$441$	−41.0631	+	36.1665i	−1.95539	+	1.72221i
$442$	−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
$448$	−11.4082	+	17.8284i	−0.538986	+	0.842314i
$449$	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
$455$	18.4981	+	0.585837i	0.867203	+	0.0274645i
$456$	−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	$-0.968259\pi$
$461$	−7.76886	−	18.7557i	−0.361832	−	0.873540i	0.633200	−	0.773988i	$-0.281741\pi$
$462$	−8.22177	+	1.16319i	−0.382512	+	0.0541165i
$463$	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	−0.982991	−	0.183655i	$-0.941207\pi$
$467$	−33.4570	+	13.8584i	−1.54821	+	0.641288i	−0.565216	+	0.824943i	$0.691207\pi$
$468$	50.7260	+	2.45154i	2.34481	+	0.113323i
$469$	17.4890	−	6.60368i	0.807568	−	0.304930i
$470$	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
$476$	13.4998	−	4.36529i	0.618761	−	0.200083i
$477$	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	$-0.360883\pi$
$479$	18.5273			0.846535			0.423267	+	0.906005i	$0.360883\pi$
$480$	−30.3891	−	26.1086i	−1.38707	−	1.19169i
$481$		−	21.0089i		−	0.957925i
$482$	6.78959	+	39.0372i	0.309257	+	1.77809i
$483$	4.41462	−	9.77095i	0.200872	−	0.444594i
$484$	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
$490$	−20.4650	−	5.96940i	−0.924513	−	0.269670i
$491$	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	−0.999229	−	0.0392600i	$-0.987500\pi$
$503$	−21.5299	+	21.5299i	−0.959969	+	0.959969i	0.0392600	+	0.999229i	$0.487500\pi$
$504$	−55.8769	−	17.3121i	−2.48895	−	0.771141i
$505$	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	−0.647797	−	0.761813i	$-0.724310\pi$
$509$	−12.7961	+	5.30030i	−0.567176	+	0.234932i	0.0806214	+	0.996745i	$0.474310\pi$
$510$	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
$518$	−6.03751	+	23.4340i	−0.265273	+	1.02963i
$519$	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	$0.0507125\pi$
$521$	26.1575	+	26.1575i	1.14598	+	1.14598i	0.158645	+	0.987336i	$0.449287\pi$
$522$	16.4633	−	73.4511i	0.720579	−	3.21487i
$523$	−7.83184	+	18.9077i	−0.342463	+	0.826778i	0.655003	+	0.755626i	$0.272667\pi$
$523$	−7.83184	+	18.9077i	−0.342463	+	0.826778i	−0.997466	+	0.0711514i	$0.977333\pi$
$524$	−7.60926	−	8.38210i	−0.332412	−	0.366174i
$525$	−1.29972	+	2.87670i	−0.0567245	+	0.125549i
$526$	−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
$532$	−19.8181	+	16.8779i	−0.859223	+	0.731751i
$533$	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
$539$	−4.24067	−	2.08005i	−0.182659	−	0.0895940i
$540$	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
$546$	31.9472	+	24.0280i	1.36721	+	1.02830i
$547$	−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
$553$	15.3853	+	0.487254i	0.654248	+	0.0207202i
$554$	−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
$560$	−5.95687	−	21.9974i	−0.251724	−	0.929560i
$561$			5.95042i			0.251227i
$562$	−0.844795	+	1.20053i	−0.0356355	+	0.0506414i
$563$	16.9952	−	7.03966i	0.716264	−	0.296686i	0.00537035	−	0.999986i	$-0.498291\pi$
$563$	16.9952	−	7.03966i	0.716264	−	0.296686i	0.710894	+	0.703299i	$0.248291\pi$
$564$	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
$567$	2.39983	−	75.7757i	0.100783	−	3.18228i
$568$	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
$574$	−10.7480	+	14.2903i	−0.448611	+	0.596466i
$575$		−	0.446992i		−	0.0186408i
$576$	−15.3399	−	60.6257i	−0.639161	−	2.52607i
$577$			23.0622i			0.960093i	0.877243	+	0.480046i	$0.159380\pi$
$577$			23.0622i			0.960093i	−0.877243	+	0.480046i	$0.840620\pi$
$578$	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
$581$	−11.2228	+	4.23763i	−0.465601	+	0.175806i
$582$	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	−0.756465	−	0.654034i	$-0.773075\pi$
$587$	5.83675	−	14.0912i	0.240908	−	0.581604i	0.997374	+	0.0724299i	$0.0230754\pi$
$588$	−28.7298	−	35.9825i	−1.18480	−	1.48389i
$589$	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	$-0.343110\pi$
$593$	23.0448			0.946335			0.473168	+	0.880972i	$0.343110\pi$
$594$	8.70025	−	12.3638i	0.356975	−	0.507295i
$595$	−6.28985	+	13.9214i	−0.257859	+	0.570723i
$596$	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	−0.848063	−	0.529895i	$-0.822231\pi$
$601$	−7.79999	+	7.79999i	−0.318168	+	0.318168i	0.529895	+	0.848063i	$0.322231\pi$
$602$	−12.0110	+	46.6198i	−0.489534	+	1.90008i
$603$	−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	$-0.723993\pi$
$607$	−31.8826			−1.29408			−0.647038	+	0.762458i	$0.723993\pi$
$608$	−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
$616$	−0.465165	−	5.02799i	−0.0187420	−	0.202583i
$617$	−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	$-0.608525\pi$
$619$	14.1434	−	34.1451i	0.568469	−	1.37241i	0.902845	−	0.429966i	$-0.141475\pi$
$620$	−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
$630$	54.2401	−	32.0170i	2.16098	−	1.27559i
$631$	−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
$637$	7.35494	+	21.5162i	0.291413	+	0.852504i
$638$	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	0.997419	−	0.0718033i	$-0.0228754\pi$
$643$	6.12039	+	14.7759i	0.241365	+	0.582706i	−0.756054	+	0.654509i	$0.772875\pi$
$644$	5.80521	+	2.96823i	0.228757	+	0.116965i
$645$	−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	0.833213	−	0.552952i	$-0.186499\pi$
$647$	7.12879	+	7.12879i	0.280262	+	0.280262i	−0.552952	+	0.833213i	$0.686499\pi$
$648$	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
$651$	14.6073	+	38.6857i	0.572506	+	1.51621i
$652$	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
$658$	11.1690	−	1.58016i	0.435414	−	0.0616010i
$659$	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	0.242562	−	0.970136i	$-0.422012\pi$
$661$	−6.99080	−	2.89568i	−0.271911	−	0.112629i	−0.514473	+	0.857507i	$0.672012\pi$
$662$	−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
$665$	0.887208	−	28.0140i	0.0344045	−	1.08634i
$666$	−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
$672$	16.8205	−	46.2611i	0.648864	−	1.78456i
$673$	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	$-0.723495\pi$
$677$	9.12470	−	22.0290i	0.350691	−	0.846642i	0.996535	−	0.0831730i	$-0.0265054\pi$
$678$	25.4627	+	40.1746i	0.977890	+	1.54290i
$679$	−1.34168	+	42.3641i	−0.0514889	+	1.62578i
$680$	−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
$686$	−2.02064	−	26.1135i	−0.0771482	−	0.997020i
$687$	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	−0.858069	−	0.513534i	$-0.828336\pi$
$691$	−28.9600	+	11.9956i	−1.10169	+	0.456336i	−0.243623	+	0.969870i	$0.578336\pi$
$692$	13.7269	+	15.1211i	0.521817	+	0.574816i
$693$	13.0557	−	4.92969i	0.495944	−	0.187264i
$694$	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
$700$	−1.70913	−	0.873886i	−0.0645991	−	0.0330298i
$701$	−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
$707$	−1.58259	+	3.50278i	−0.0595195	+	0.131736i
$708$	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
$714$	−28.4149	+	16.7728i	−1.06340	+	0.627706i
$715$	−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	$0.0985609\pi$
$719$			16.3413i			0.609428i	−0.952444	+	0.304714i	$0.901439\pi$
$720$	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	$-0.476438\pi$
$727$	28.8831	−	28.8831i	1.07122	−	1.07122i	0.997262	−	0.0739549i	$-0.0235621\pi$
$728$	−15.5322	+	18.6991i	−0.575662	+	0.693036i
$729$	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	0.0284180	−	0.999596i	$-0.490953\pi$
$733$	20.4499	−	8.47062i	0.755334	−	0.312869i	0.726916	+	0.686727i	$0.240953\pi$
$734$	−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
$742$	−15.4015	−	3.96802i	−0.565406	−	0.145670i
$743$	−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
$749$	20.5843	+	9.30021i	0.752134	+	0.339822i
$750$	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
$756$	83.5647	+	6.69537i	3.03922	+	0.243508i
$757$	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	−0.0508495	−	0.998706i	$-0.516193\pi$
$761$	26.1478	−	26.1478i	0.947857	−	0.947857i	0.998706	+	0.0508495i	$0.0161929\pi$
$762$	−8.54482	−	13.4819i	−0.309546	−	0.488397i
$763$	−12.7518	+	4.81495i	−0.461646	+	0.174313i
$764$	−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	$-0.998950\pi$
$769$		−	0.182902i		−	0.00659561i	0.999995	−	0.00329780i	$-0.00104973\pi$
$770$	4.34503	+	3.26797i	0.156584	+	0.117769i
$771$	−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	$0.430076\pi$
$773$	−17.4127	+	42.0379i	−0.626290	+	1.51200i	−0.844200	+	0.536028i	$0.819924\pi$
$774$	−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
$777$	1.78145	−	56.2501i	0.0639092	−	2.01796i
$778$	−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
$784$	22.6988	−	16.3940i	0.810673	−	0.585499i
$785$			40.8945i			1.45959i
$786$	21.5313	+	15.1512i	0.767997	+	0.540427i
$787$	7.61027	−	3.15228i	0.271277	−	0.112367i	−0.242898	−	0.970052i	$-0.578098\pi$
$787$	7.61027	−	3.15228i	0.271277	−	0.112367i	0.514175	+	0.857685i	$0.328098\pi$
$788$	−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
$791$	−0.856432	+	27.0422i	−0.0304512	+	0.961511i
$792$	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	0.321474	−	0.946918i	$-0.395822\pi$
$797$	34.3958	−	14.2472i	1.21836	−	0.504663i	0.896889	+	0.442256i	$0.145822\pi$
$798$	36.3886	−	48.3817i	1.28814	−	1.71269i
$799$		−	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
$805$	−6.56761	+	2.47986i	−0.231478	+	0.0874037i
$806$	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	$0.423981\pi$
$811$	−17.5923	+	42.4717i	−0.617751	+	1.49138i	−0.854309	+	0.519765i	$0.826019\pi$
$812$	23.3609	+	27.4305i	0.819809	+	0.962620i
$813$	−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
$819$	−61.2236	−	27.6615i	−2.13933	−	0.966571i
$820$	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
$826$	−2.10563	+	8.17279i	−0.0732641	+	0.284368i
$827$	−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	−0.932187	−	0.361976i	$-0.882102\pi$
$829$	−38.4490	+	15.9261i	−1.33539	+	0.553136i	−0.403200	+	0.915112i	$0.632102\pi$
$830$	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	0.616969	−	0.786987i	$-0.288360\pi$
$839$	−4.92466	−	4.92466i	−0.170018	−	0.170018i	−0.786987	+	0.616969i	$0.788360\pi$
$840$	24.7069	+	46.8891i	0.852468	+	1.61783i
$841$	−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	−0.205869	−	0.978580i	$-0.566002\pi$
$853$	−30.4737	−	12.6226i	−1.04340	−	0.432191i	−0.837531	+	0.546389i	$0.816002\pi$
$854$	11.0400	+	18.7029i	0.377781	+	0.640001i
$855$	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	−0.840069	−	0.542480i	$-0.817486\pi$
$857$	−8.71179	+	8.71179i	−0.297589	+	0.297589i	0.542480	+	0.840069i	$0.317486\pi$
$858$	−5.45771	−	8.61108i	−0.186323	−	0.293977i
$859$	24.6028	+	10.1908i	0.839436	+	0.347706i	0.760631	−	0.649184i	$-0.224890\pi$
$859$	24.6028	+	10.1908i	0.839436	+	0.347706i	0.0788051	+	0.996890i	$0.474890\pi$
$860$	23.6527	−	50.1127i	0.806552	−	1.70883i
$861$	17.1219	−	37.8961i	0.583511	−	1.29150i
$862$	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
$868$	−23.9262	+	7.73677i	−0.812107	+	0.262603i
$869$	−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
$875$	28.5841	−	10.7931i	0.966320	−	0.364873i
$876$	−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	$-0.328096\pi$
$881$	30.5234			1.02836			0.514180	+	0.857683i	$0.328096\pi$
$882$	60.3415	+	48.4488i	2.03180	+	1.63136i
$883$	−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	−0.237886	−	0.971293i	$-0.576454\pi$
$887$	21.8427	−	21.8427i	0.733407	−	0.733407i	0.971293	+	0.237886i	$0.0764544\pi$
$888$	52.3125	−	29.7172i	1.75549	−	0.997245i
$889$	0.287403	−	9.07488i	0.00963919	−	0.304362i
$890$	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
$896$	27.6049	+	11.5746i	0.922214	+	0.386681i
$897$	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
$903$	3.54403	−	111.904i	0.117938	−	3.72394i
$904$	−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
$910$	−3.66641	−	25.9153i	−0.121540	−	0.859083i
$911$	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
$917$	5.29023	+	14.0105i	0.174699	+	0.462668i
$918$	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
$924$	3.61306	+	11.1735i	0.118861	+	0.367581i
$925$	−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	$0.0181041\pi$
$929$			3.46522i			0.113690i	−0.998383	+	0.0568451i	$0.981896\pi$
$930$	−8.15609	−	46.8939i	−0.267449	−	1.53771i
$931$	32.5848	−	11.1385i	1.06792	−	0.365051i
$932$	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	0.520011	−	0.854160i	$-0.325928\pi$
$937$	−10.2285	−	10.2285i	−0.334149	−	0.334149i	−0.854160	+	0.520011i	$0.825928\pi$
$938$	−13.4390	−	22.7671i	−0.438799	−	0.743373i
$939$	−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	$-0.848836\pi$
$941$	−17.9086	−	43.2352i	−0.583804	−	1.40943i	0.305536	−	0.952180i	$-0.401164\pi$
$942$	−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
$952$	−9.35356	−	17.7513i	−0.303151	−	0.575325i
$953$	−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
$966$	−14.6836	−	3.78307i	−0.472438	−	0.121718i
$967$	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	−0.830100	−	0.557615i	$-0.811717\pi$
$971$	4.71036	−	11.3718i	0.151163	−	0.364939i	0.981262	+	0.192676i	$0.0617166\pi$
$972$	−69.1773	+	62.7990i	−2.21886	+	2.01428i
$973$	−4.26790	+	9.44621i	−0.136823	+	0.302831i
$974$	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
$980$	−3.35785	+	29.9603i	−0.107263	+	0.957048i
$981$	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	−0.985363	−	0.170472i	$-0.945471\pi$
$983$	−25.5491	+	25.5491i	−0.814890	+	0.814890i	0.170472	+	0.985363i	$0.445471\pi$
$984$	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
$987$	−24.5423	+	9.26693i	−0.781190	+	0.294970i
$988$	−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
$994$	−38.7543	−	29.1477i	−1.22921	−	0.924509i
$995$	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	$-0.736532\pi$
$997$	10.1843	−	24.5872i	0.322542	−	0.778684i	0.999105	−	0.0422998i	$-0.0134684\pi$
$998$	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.27.14	yes	112
4.3	odd	2		896.2.x.b.783.1		112
7.6	odd	2	inner	224.2.x.b.27.13	✓	112
28.27	even	2		896.2.x.b.783.28		112
32.13	even	8		896.2.x.b.111.28		112
32.19	odd	8	inner	224.2.x.b.83.13	yes	112
224.13	odd	8		896.2.x.b.111.1		112
224.83	even	8	inner	224.2.x.b.83.14	yes	112

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.242331 - 1.39330i) q^{2} +(1.25862 + 3.03857i) q^{3} +(-1.88255 + 0.675278i) q^{4} +(0.824079 - 1.98950i) q^{5} +(3.92863 - 2.48997i) q^{6} +(2.64443 + 0.0837494i) q^{7} +(1.39706 + 2.45931i) q^{8} +(-5.52747 + 5.52747i) q^{9} +O(q^{10})\)	\(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} +(2.64443 + 0.0837494i) 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} +(-0.524139 - 3.70476i) 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} +(3.07384 + 8.14068i) 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} +(-5.03482 + 1.62806i) 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} +(2.34584 - 5.19208i) 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} +(10.5975 - 6.25551i) 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} +(3.48846 + 6.62047i) 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} +(-7.80257 - 2.01024i) 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} +(-1.62691 - 0.735054i) 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} +(-11.2839 - 13.2496i) 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} +(3.03594 + 8.04030i) 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} +(-1.07577 - 9.84087i) 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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