LMFDB - Embedded newform 312.2.bt.d.115.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(19,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$312 = 2^{3} \cdot 3 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	312.bt (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.11
Character	$\chi$	$=$	312.115
Dual form			312.2.bt.d.19.11

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13656 - 0.841559i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.583557 - 1.91297i) q^{4} +(0.00433170 - 0.00433170i) q^{5} +(1.29709 + 0.563514i) q^{6} +(1.57369 - 0.421669i) q^{7} +(-0.946628 - 2.66531i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.00127787 - 0.00856863i) q^{10} +(3.23180 + 0.865959i) q^{11} +(1.94846 - 0.451111i) q^{12} +(-3.04585 - 1.92946i) q^{13} +(1.43374 - 1.80361i) q^{14} +(0.00591721 + 0.00158551i) q^{15} +(-3.31892 - 2.23266i) q^{16} +(4.80624 + 2.77488i) q^{17} +(0.160529 + 1.40507i) q^{18} +(-3.45861 + 0.926732i) q^{19} +(-0.00575862 - 0.0108142i) q^{20} +(1.15202 + 1.15202i) q^{21} +(4.40191 - 1.73554i) q^{22} +(-2.76176 - 4.78352i) q^{23} +(1.83492 - 2.15246i) q^{24} +4.99996i q^{25} +(-5.08556 + 0.370304i) q^{26} -1.00000 q^{27} +(0.111697 - 3.25650i) q^{28} +(-1.51783 + 0.876322i) q^{29} +(0.00805959 - 0.00317764i) q^{30} +(0.487954 - 0.487954i) q^{31} +(-5.65108 + 0.255510i) q^{32} +(0.865959 + 3.23180i) q^{33} +(7.79783 - 0.890900i) q^{34} +(0.00499021 - 0.00864330i) q^{35} +(1.36490 + 1.46186i) q^{36} +(-3.01169 + 11.2398i) q^{37} +(-3.15103 + 3.96392i) q^{38} +(0.148038 - 3.60251i) q^{39} +(-0.0156458 - 0.00744482i) q^{40} +(1.29226 - 4.82278i) q^{41} +(2.27884 + 0.339853i) q^{42} +(-9.33754 - 5.39103i) q^{43} +(3.54250 - 5.67701i) q^{44} +(0.00158551 + 0.00591721i) q^{45} +(-7.16454 - 3.11259i) q^{46} +(2.87499 + 2.87499i) q^{47} +(0.274077 - 3.99060i) q^{48} +(-3.76348 + 2.17284i) q^{49} +(4.20776 + 5.68278i) q^{50} +5.54977i q^{51} +(-5.46843 + 4.70067i) q^{52} +3.71872i q^{53} +(-1.13656 + 0.841559i) q^{54} +(0.0177503 - 0.0102481i) q^{55} +(-2.61358 - 3.79522i) q^{56} +(-2.53188 - 2.53188i) q^{57} +(-0.987640 + 2.27334i) q^{58} +(0.772342 + 2.88242i) q^{59} +(0.00648607 - 0.0103942i) q^{60} +(-1.81829 - 1.04979i) q^{61} +(0.143949 - 0.965233i) q^{62} +(-0.421669 + 1.57369i) q^{63} +(-6.20779 + 5.04612i) q^{64} +(-0.0215515 + 0.00483585i) q^{65} +(3.70397 + 2.94440i) q^{66} +(0.133225 - 0.497203i) q^{67} +(8.11299 - 7.57490i) q^{68} +(2.76176 - 4.78352i) q^{69} +(-0.00160215 - 0.0140232i) q^{70} +(-0.569550 - 2.12559i) q^{71} +(2.78154 + 0.512853i) q^{72} +(-1.36174 + 1.36174i) q^{73} +(6.03597 + 15.3093i) q^{74} +(-4.33009 + 2.49998i) q^{75} +(-0.245485 + 7.15703i) q^{76} +5.45101 q^{77} +(-2.86347 - 4.21907i) q^{78} -12.6705i q^{79} +(-0.0240478 + 0.00470537i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.58992 - 6.56891i) q^{82} +(-3.55694 - 3.55694i) q^{83} +(2.87606 - 1.53152i) q^{84} +(0.0328391 - 0.00879922i) q^{85} +(-15.1496 + 1.73084i) q^{86} +(-1.51783 - 0.876322i) q^{87} +(-0.751264 - 9.43351i) q^{88} +(14.4893 + 3.88239i) q^{89} +(0.00678171 + 0.00539099i) q^{90} +(-5.60682 - 1.75203i) q^{91} +(-10.7624 + 2.49172i) q^{92} +(0.666558 + 0.178604i) q^{93} +(5.68708 + 0.848136i) q^{94} +(-0.0109673 + 0.0189960i) q^{95} +(-3.04682 - 4.76622i) q^{96} +(4.71000 - 1.26204i) q^{97} +(-2.44886 + 5.63677i) q^{98} +(-2.36584 + 2.36584i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$56 q + 28 q^{3} - 12 q^{8} - 28 q^{9} - 28 q^{14} + 12 q^{16} - 8 q^{19} - 4 q^{20} + 10 q^{22} - 6 q^{24} + 34 q^{26} - 56 q^{27} - 14 q^{28} - 30 q^{32} + 56 q^{34} - 28 q^{40} + 40 q^{41} - 14 q^{42}+ \cdots + 4 q^{98}+O(q^{100})$ 56 * q + 28 * q^3 - 12 * q^8 - 28 * q^9 - 28 * q^14 + 12 * q^16 - 8 * q^19 - 4 * q^20 + 10 * q^22 - 6 * q^24 + 34 * q^26 - 56 * q^27 - 14 * q^28 - 30 * q^32 + 56 * q^34 - 28 * q^40 + 40 * q^41 - 14 * q^42 - 44 * q^44 - 18 * q^46 - 12 * q^48 + 24 * q^49 - 72 * q^50 + 32 * q^52 - 54 * q^56 - 16 * q^57 - 16 * q^58 + 32 * q^59 - 20 * q^60 + 48 * q^65 + 20 * q^66 - 24 * q^67 - 26 * q^68 + 64 * q^70 + 6 * q^72 + 44 * q^73 - 6 * q^74 - 12 * q^75 + 6 * q^76 + 32 * q^78 - 4 * q^80 - 28 * q^81 - 30 * q^82 + 40 * q^83 + 2 * q^84 - 28 * q^86 + 126 * q^88 - 68 * q^89 - 72 * q^91 + 52 * q^92 + 34 * q^94 - 4 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$ .

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.13656	−	0.841559i	0.803672	−	0.595072i
$2$	1.13656	−	0.841559i	0.803672	−	0.595072i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.583557	−	1.91297i	0.291779	−	0.956486i
$5$	0.00433170	−	0.00433170i	0.00193719	−	0.00193719i	−0.706138	−	0.708075i	$-0.749564\pi$
$5$	0.00433170	−	0.00433170i	0.00193719	−	0.00193719i	0.708075	+	0.706138i	$0.249564\pi$
$6$	1.29709	+	0.563514i	0.529536	+	0.230054i
$7$	1.57369	−	0.421669i	0.594800	−	0.159376i	0.0511537	−	0.998691i	$-0.483710\pi$
$7$	1.57369	−	0.421669i	0.594800	−	0.159376i	0.543646	+	0.839315i	$0.317043\pi$
$8$	−0.946628	−	2.66531i	−0.334684	−	0.942331i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.00127787	−	0.00856863i	0.000404099	−	0.00270964i
$11$	3.23180	+	0.865959i	0.974426	+	0.261097i	0.710695	−	0.703500i	$-0.248380\pi$
$11$	3.23180	+	0.865959i	0.974426	+	0.261097i	0.263730	+	0.964596i	$0.415047\pi$
$12$	1.94846	−	0.451111i	0.562472	−	0.130224i
$13$	−3.04585	−	1.92946i	−0.844766	−	0.535136i
$13$	−3.04585	−	1.92946i	−0.844766	−	0.535136i
$14$	1.43374	−	1.80361i	0.383184	−	0.482035i
$15$	0.00591721	+	0.00158551i	0.00152782	+	0.000409377i
$16$	−3.31892	−	2.23266i	−0.829730	−	0.558164i
$17$	4.80624	+	2.77488i	1.16568	+	0.673008i	0.952660	−	0.304039i	$-0.0983352\pi$
$17$	4.80624	+	2.77488i	1.16568	+	0.673008i	0.213025	+	0.977047i	$0.431669\pi$
$18$	0.160529	+	1.40507i	0.0378371	+	0.331179i
$19$	−3.45861	+	0.926732i	−0.793460	+	0.212607i	−0.632711	−	0.774388i	$-0.718058\pi$
$19$	−3.45861	+	0.926732i	−0.793460	+	0.212607i	−0.160749	+	0.986995i	$0.551391\pi$
$20$	−0.00575862	−	0.0108142i	−0.00128767	−	0.00241813i
$21$	1.15202	+	1.15202i	0.251392	+	0.251392i
$22$	4.40191	−	1.73554i	0.938490	−	0.370017i
$23$	−2.76176	−	4.78352i	−0.575868	−	0.997432i	−0.995947	−	0.0899447i	$-0.971331\pi$
$23$	−2.76176	−	4.78352i	−0.575868	−	0.997432i	0.420079	−	0.907488i	$-0.362002\pi$
$24$	1.83492	−	2.15246i	0.374550	−	0.439369i
$25$			4.99996i			0.999992i
$26$	−5.08556	+	0.370304i	−0.997359	+	0.0726227i
$27$	−1.00000			−0.192450
$28$	0.111697	−	3.25650i	0.0211088	−	0.615420i
$29$	−1.51783	+	0.876322i	−0.281855	+	0.162729i	−0.634263	−	0.773118i	$-0.718696\pi$
$29$	−1.51783	+	0.876322i	−0.281855	+	0.162729i	0.352408	+	0.935846i	$0.385363\pi$
$30$	0.00805959	−	0.00317764i	0.00147147	−	0.000580156i
$31$	0.487954	−	0.487954i	0.0876391	−	0.0876391i	−0.661928	−	0.749567i	$-0.730262\pi$
$31$	0.487954	−	0.487954i	0.0876391	−	0.0876391i	0.749567	+	0.661928i	$0.230262\pi$
$32$	−5.65108	+	0.255510i	−0.998979	+	0.0451682i
$33$	0.865959	+	3.23180i	0.150744	+	0.562585i
$34$	7.79783	−	0.890900i	1.33732	−	0.152788i
$35$	0.00499021	−	0.00864330i	0.000843500	−	0.00146098i
$36$	1.36490	+	1.46186i	0.227484	+	0.243644i
$37$	−3.01169	+	11.2398i	−0.495119	+	1.84781i	0.0342404	+	0.999414i	$0.489099\pi$
$37$	−3.01169	+	11.2398i	−0.495119	+	1.84781i	−0.529360	+	0.848397i	$0.677568\pi$
$38$	−3.15103	+	3.96392i	−0.511165	+	0.643032i
$39$	0.148038	−	3.60251i	0.0237050	−	0.576863i
$40$	−0.0156458	−	0.00744482i	−0.00247382	−	0.00117713i
$41$	1.29226	−	4.82278i	0.201817	−	0.753191i	−0.788579	−	0.614933i	$-0.789183\pi$
$41$	1.29226	−	4.82278i	0.201817	−	0.753191i	0.990396	−	0.138258i	$-0.0441504\pi$
$42$	2.27884	+	0.339853i	0.351633	+	0.0524404i
$43$	−9.33754	−	5.39103i	−1.42396	−	0.822125i	−0.427327	−	0.904097i	$-0.640545\pi$
$43$	−9.33754	−	5.39103i	−1.42396	−	0.822125i	−0.996635	+	0.0819721i	$0.973878\pi$
$44$	3.54250	−	5.67701i	0.534052	−	0.855842i
$45$	0.00158551	+	0.00591721i	0.000236354	+	0.000882085i
$46$	−7.16454	−	3.11259i	−1.05635	−	0.458926i
$47$	2.87499	+	2.87499i	0.419360	+	0.419360i	0.884983	−	0.465623i	$-0.154170\pi$
$47$	2.87499	+	2.87499i	0.419360	+	0.419360i	−0.465623	+	0.884983i	$0.654170\pi$
$48$	0.274077	−	3.99060i	0.0395595	−	0.575993i
$49$	−3.76348	+	2.17284i	−0.537640	+	0.310406i
$50$	4.20776	+	5.68278i	0.595068	+	0.803666i
$51$			5.54977i			0.777123i
$52$	−5.46843	+	4.70067i	−0.758335	+	0.651866i
$53$			3.71872i			0.510805i	0.966835	+	0.255402i	$0.0822080\pi$
$53$			3.71872i			0.510805i	−0.966835	+	0.255402i	$0.917792\pi$
$54$	−1.13656	+	0.841559i	−0.154667	+	0.114522i
$55$	0.0177503	−	0.0102481i	0.00239345	−	0.00138186i
$56$	−2.61358	−	3.79522i	−0.349255	−	0.507157i
$57$	−2.53188	−	2.53188i	−0.335356	−	0.335356i
$58$	−0.987640	+	2.27334i	−0.129683	+	0.298505i
$59$	0.772342	+	2.88242i	0.100550	+	0.375259i	0.997802	−	0.0662595i	$-0.0211065\pi$
$59$	0.772342	+	2.88242i	0.100550	+	0.375259i	−0.897252	+	0.441519i	$0.854440\pi$
$60$	0.00648607	−	0.0103942i	0.000837348	−	0.00134189i
$61$	−1.81829	−	1.04979i	−0.232808	−	0.134412i	0.379059	−	0.925373i	$-0.376248\pi$
$61$	−1.81829	−	1.04979i	−0.232808	−	0.134412i	−0.611867	+	0.790961i	$0.709581\pi$
$62$	0.143949	−	0.965233i	0.0182816	−	0.122585i
$63$	−0.421669	+	1.57369i	−0.0531254	+	0.198267i
$64$	−6.20779	+	5.04612i	−0.775974	+	0.630765i
$65$	−0.0215515	+	0.00483585i	−0.00267314	+	0.000599813i
$66$	3.70397	+	2.94440i	0.455927	+	0.362430i
$67$	0.133225	−	0.497203i	0.0162760	−	0.0607430i	−0.957310	−	0.289063i	$-0.906656\pi$
$67$	0.133225	−	0.497203i	0.0162760	−	0.0607430i	0.973586	+	0.228320i	$0.0733231\pi$
$68$	8.11299	−	7.57490i	0.983845	−	0.918591i
$69$	2.76176	−	4.78352i	0.332477	−	0.575868i
$70$	−0.00160215	−	0.0140232i	−0.000191493	−	0.00167610i
$71$	−0.569550	−	2.12559i	−0.0675932	−	0.252261i	0.923859	−	0.382734i	$-0.125017\pi$
$71$	−0.569550	−	2.12559i	−0.0675932	−	0.252261i	−0.991452	+	0.130472i	$0.958351\pi$
$72$	2.78154	+	0.512853i	0.327808	+	0.0604403i
$73$	−1.36174	+	1.36174i	−0.159380	+	0.159380i	−0.782292	−	0.622912i	$-0.785949\pi$
$73$	−1.36174	+	1.36174i	−0.159380	+	0.159380i	0.622912	+	0.782292i	$0.285949\pi$
$74$	6.03597	+	15.3093i	0.701667	+	1.77967i
$75$	−4.33009	+	2.49998i	−0.499996	+	0.288673i
$76$	−0.245485	+	7.15703i	−0.0281591	+	0.820967i
$77$	5.45101			0.621200
$78$	−2.86347	−	4.21907i	−0.324224	−	0.477715i
$79$		−	12.6705i		−	1.42555i	−0.701394	−	0.712774i	$-0.747439\pi$
$79$		−	12.6705i		−	1.42555i	0.701394	−	0.712774i	$-0.252561\pi$
$80$	−0.0240478	+	0.00470537i	−0.00268862	+	0.000526076i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.58992	−	6.56891i	−0.286008	−	0.725415i
$83$	−3.55694	−	3.55694i	−0.390425	−	0.390425i	0.484414	−	0.874839i	$-0.339033\pi$
$83$	−3.55694	−	3.55694i	−0.390425	−	0.390425i	−0.874839	+	0.484414i	$0.839033\pi$
$84$	2.87606	−	1.53152i	0.313804	−	0.167102i
$85$	0.0328391	−	0.00879922i	0.00356190	−	0.000954409i
$86$	−15.1496	+	1.73084i	−1.63362	+	0.186641i
$87$	−1.51783	−	0.876322i	−0.162729	−	0.0939516i
$88$	−0.751264	−	9.43351i	−0.0800850	−	1.00562i
$89$	14.4893	+	3.88239i	1.53586	+	0.411532i	0.924925	−	0.380149i	$-0.124127\pi$
$89$	14.4893	+	3.88239i	1.53586	+	0.411532i	0.610934	+	0.791682i	$0.290794\pi$
$90$	0.00678171	+	0.00539099i	0.000714855	+	0.000568260i
$91$	−5.60682	−	1.75203i	−0.587754	−	0.183663i
$92$	−10.7624	+	2.49172i	−1.12206	+	0.259780i
$93$	0.666558	+	0.178604i	0.0691188	+	0.0185203i
$94$	5.68708	+	0.848136i	0.586577	+	0.0874786i
$95$	−0.0109673	+	0.0189960i	−0.00112522	+	0.00194895i
$96$	−3.04682	−	4.76622i	−0.310965	−	0.486451i
$97$	4.71000	−	1.26204i	0.478228	−	0.128141i	−0.0116495	−	0.999932i	$-0.503708\pi$
$97$	4.71000	−	1.26204i	0.478228	−	0.128141i	0.489877	+	0.871791i	$0.337042\pi$
$98$	−2.44886	+	5.63677i	−0.247372	+	0.569399i
$99$	−2.36584	+	2.36584i	−0.237776	+	0.237776i
$100$	9.56479	+	2.91776i	0.956479	+	0.291776i
$101$	7.89450	+	13.6737i	0.785532	+	1.36058i	0.928681	+	0.370880i	$0.120944\pi$
$101$	7.89450	+	13.6737i	0.785532	+	1.36058i	−0.143149	+	0.989701i	$0.545723\pi$
$102$	4.67046	+	6.30767i	0.462444	+	0.624552i
$103$	14.3782			1.41673			0.708363	−	0.705848i	$-0.249434\pi$
$103$	14.3782			1.41673			0.708363	+	0.705848i	$0.249434\pi$
$104$	−2.25933	+	9.94462i	−0.221546	+	0.975150i
$105$	0.00998042			0.000973990
$106$	3.12952	+	4.22656i	0.303966	+	0.410520i
$107$	−2.19013	−	3.79342i	−0.211728	−	0.366724i	0.740527	−	0.672026i	$-0.234576\pi$
$107$	−2.19013	−	3.79342i	−0.211728	−	0.366724i	−0.952255	+	0.305302i	$0.901242\pi$
$108$	−0.583557	+	1.91297i	−0.0561528	+	0.184076i
$109$	−8.41638	+	8.41638i	−0.806143	+	0.806143i	−0.984048	−	0.177905i	$-0.943068\pi$
$109$	−8.41638	+	8.41638i	−0.806143	+	0.806143i	0.177905	+	0.984048i	$0.443068\pi$
$110$	0.0115499	−	0.0265855i	0.00110124	−	0.00253483i
$111$	−11.2398	+	3.01169i	−1.06683	+	0.285857i
$112$	−6.16440	−	2.11403i	−0.582481	−	0.199757i
$113$	4.02349	−	6.96890i	0.378498	−	0.655579i	−0.612346	−	0.790590i	$-0.709774\pi$
$113$	4.02349	−	6.96890i	0.378498	−	0.655579i	0.990844	+	0.135012i	$0.0431072\pi$
$114$	−5.00837	−	0.746918i	−0.469077	−	0.0699553i
$115$	−0.0326839	−	0.00875762i	−0.00304779	−	0.000816652i
$116$	0.790636	+	3.41496i	0.0734087	+	0.317071i
$117$	3.19388	−	1.67305i	0.295275	−	0.154674i
$118$	3.30354	+	2.62609i	0.304116	+	0.241751i
$119$	8.73362	+	2.34017i	0.800610	+	0.214523i
$120$	−0.00137551	−	0.0172721i	−0.000125566	−	0.00157672i
$121$	0.168393	+	0.0972215i	0.0153084	+	0.00883832i
$122$	−2.95006	+	0.337043i	−0.267086	+	0.0305145i
$123$	4.82278	−	1.29226i	0.434855	−	0.116519i
$124$	−0.648693	−	1.21819i	−0.0582544	−	0.109397i
$125$	0.0433168	+	0.0433168i	0.00387437	+	0.00387437i
$126$	0.845100	+	2.14346i	0.0752875	+	0.190955i
$127$	−1.91208	−	3.31182i	−0.169670	−	0.293877i	0.768634	−	0.639689i	$-0.220937\pi$
$127$	−1.91208	−	3.31182i	−0.169670	−	0.293877i	−0.938304	+	0.345812i	$0.887603\pi$
$128$	−2.80895	+	10.9595i	−0.248278	+	0.968689i
$129$		−	10.7821i		−	0.949308i
$130$	−0.0204250	+	0.0236331i	−0.00179139	+	0.00207276i
$131$	10.1296			0.885025			0.442513	−	0.896762i	$-0.354087\pi$
$131$	10.1296			0.885025			0.442513	+	0.896762i	$0.354087\pi$
$132$	6.68769	+	0.229387i	0.582088	+	0.0199656i
$133$	−5.05201	+	2.91678i	−0.438065	+	0.252917i
$134$	−0.267006	−	0.677219i	−0.0230658	−	0.0585028i
$135$	−0.00433170	+	0.00433170i	−0.000372813	+	0.000372813i
$136$	2.84621	−	15.4369i	0.244061	−	1.32370i
$137$	−4.42582	−	16.5174i	−0.378123	−	1.41117i	−0.848728	−	0.528830i	$-0.822631\pi$
$137$	−4.42582	−	16.5174i	−0.378123	−	1.41117i	0.470605	−	0.882344i	$-0.344036\pi$
$138$	−0.886688	−	7.76096i	−0.0754799	−	0.660657i
$139$	8.51425	−	14.7471i	0.722169	−	1.25083i	−0.237959	−	0.971275i	$-0.576478\pi$
$139$	8.51425	−	14.7471i	0.722169	−	1.25083i	0.960129	−	0.279559i	$-0.0901882\pi$
$140$	−0.0136223	−	0.0145900i	−0.00115130	−	0.00123308i
$141$	−1.05232	+	3.92730i	−0.0886211	+	0.330739i
$142$	−2.43614	−	1.93656i	−0.204436	−	0.162513i
$143$	−8.17275	−	8.87322i	−0.683439	−	0.742016i
$144$	3.59300	−	1.75794i	0.299417	−	0.146495i
$145$	−0.00277884	+	0.0103708i	−0.000230770	+	0.000861245i
$146$	−0.401721	+	2.69369i	−0.0332467	+	0.222932i
$147$	−3.76348	−	2.17284i	−0.310406	−	0.179213i
$148$	19.7439	+	12.3203i	1.62294	+	1.01273i
$149$	−3.12545	−	11.6643i	−0.256047	−	0.955580i	−0.967505	−	0.252852i	$-0.918632\pi$
$149$	−3.12545	−	11.6643i	−0.256047	−	0.955580i	0.711458	−	0.702728i	$-0.248035\pi$
$150$	−2.81755	+	6.48542i	−0.230052	+	0.529532i
$151$	1.75767	+	1.75767i	0.143037	+	0.143037i	0.774999	−	0.631962i	$-0.217750\pi$
$151$	1.75767	+	1.75767i	0.143037	+	0.143037i	−0.631962	+	0.774999i	$0.717750\pi$
$152$	5.74405	+	8.34101i	0.465904	+	0.676545i
$153$	−4.80624	+	2.77488i	−0.388561	+	0.224336i
$154$	6.19543	−	4.58735i	0.499242	−	0.369659i
$155$		−	0.00422734i		−	0.000339548i
$156$	−6.80511	−	2.38546i	−0.544845	−	0.190990i
$157$		−	23.1742i		−	1.84950i	−0.380570	−	0.924752i	$-0.624272\pi$
$157$		−	23.1742i		−	1.84950i	0.380570	−	0.924752i	$-0.375728\pi$
$158$	−10.6630	−	14.4009i	−0.848303	−	1.14567i
$159$	−3.22050	+	1.85936i	−0.255402	+	0.147457i
$160$	−0.0233720	+	0.0255856i	−0.00184772	+	0.00202272i
$161$	−6.36323	−	6.36323i	−0.501493	−	0.501493i
$162$	−1.29709	−	0.563514i	−0.101909	−	0.0442739i
$163$	−2.24703	−	8.38602i	−0.176001	−	0.656844i	−0.996379	−	0.0850226i	$-0.972904\pi$
$163$	−2.24703	−	8.38602i	−0.176001	−	0.656844i	0.820378	−	0.571821i	$-0.193763\pi$
$164$	−8.47173	−	5.28642i	−0.661531	−	0.412800i
$165$	0.0177503	+	0.0102481i	0.00138186	+	0.000797815i
$166$	−7.03607	−	1.04932i	−0.546105	−	0.0814428i
$167$	−6.23234	+	23.2594i	−0.482273	+	1.79987i	0.109764	+	0.993958i	$0.464990\pi$
$167$	−6.23234	+	23.2594i	−0.482273	+	1.79987i	−0.592037	+	0.805910i	$0.701676\pi$
$168$	1.97996	−	4.16104i	0.152758	−	0.321031i
$169$	5.55437	+	11.7537i	0.427259	+	0.904129i
$170$	0.0299187	−	0.0376369i	0.00229466	−	0.00288662i
$171$	0.926732	−	3.45861i	0.0708690	−	0.264487i
$172$	−15.7619	+	14.7165i	−1.20183	+	1.12212i
$173$	5.71509	−	9.89883i	0.434510	−	0.752594i	−0.562745	−	0.826630i	$-0.690255\pi$
$173$	5.71509	−	9.89883i	0.434510	−	0.752594i	0.997256	+	0.0740365i	$0.0235881\pi$
$174$	−2.46259	+	0.281351i	−0.186689	+	0.0213291i
$175$	2.10833	+	7.86840i	0.159375	+	0.594795i
$176$	−8.79272	−	10.0896i	−0.662776	−	0.760529i
$177$	−2.11008	+	2.11008i	−0.158603	+	0.158603i
$178$	19.7352	−	7.78099i	1.47922	−	0.583210i
$179$	16.6433	−	9.60904i	1.24398	−	0.718214i	0.274080	−	0.961707i	$-0.411627\pi$
$179$	16.6433	−	9.60904i	1.24398	−	0.718214i	0.969903	+	0.243493i	$0.0782934\pi$
$180$	0.0122447		0.000419991i	0.000912665		3.13043e-5i
$181$	−9.90437			−0.736186			−0.368093	−	0.929789i	$-0.619989\pi$
$181$	−9.90437			−0.736186			−0.368093	+	0.929789i	$0.619989\pi$
$182$	−7.84695	+	2.72717i	−0.581655	+	0.202151i
$183$		−	2.09958i		−	0.155205i
$184$	−10.1352	+	11.8892i	−0.747177	+	0.876482i
$185$	0.0356416	+	0.0617331i	0.00262043	+	0.00453871i
$186$	0.907891	−	0.357953i	0.0665698	−	0.0262464i
$187$	13.1299	+	13.1299i	0.960153	+	0.960153i
$188$	7.17748	−	3.82205i	0.523472	−	0.278751i
$189$	−1.57369	+	0.421669i	−0.114469	+	0.0306719i
$190$	0.00352115	+	0.0308198i	0.000255451	+	0.00223590i
$191$	−7.28556	−	4.20632i	−0.527165	−	0.304359i	0.212696	−	0.977118i	$-0.431775\pi$
$191$	−7.28556	−	4.20632i	−0.527165	−	0.304359i	−0.739861	+	0.672760i	$0.765109\pi$
$192$	−7.47396	−	2.85304i	−0.539387	−	0.205901i
$193$	−3.79409	−	1.01662i	−0.273105	−	0.0731782i	0.119667	−	0.992814i	$-0.461817\pi$
$193$	−3.79409	−	1.01662i	−0.273105	−	0.0731782i	−0.392772	+	0.919636i	$0.628484\pi$
$194$	4.29113	−	5.39813i	0.308085	−	0.387563i
$195$	−0.0149637	−	0.0162462i	−0.00107157	−	0.00116342i
$196$	1.96039	+	8.46740i	0.140028	+	0.604815i
$197$	15.3987	+	4.12608i	1.09711	+	0.293971i	0.761589	−	0.648060i	$-0.224420\pi$
$197$	15.3987	+	4.12608i	1.09711	+	0.293971i	0.335525	+	0.942031i	$0.391086\pi$
$198$	−0.697937	+	4.67993i	−0.0496002	+	0.332588i
$199$	6.41779	−	11.1159i	0.454945	−	0.787988i	−0.543740	−	0.839254i	$-0.682992\pi$
$199$	6.41779	−	11.1159i	0.454945	−	0.787988i	0.998685	+	0.0512659i	$0.0163256\pi$
$200$	13.3265	−	4.73311i	0.942323	−	0.334681i
$201$	0.497203	−	0.133225i	0.0350700	−	0.00939697i
$202$	20.4798	+	8.89732i	1.44095	+	0.626013i
$203$	−2.01909	+	2.01909i	−0.141712	+	0.141712i
$204$	10.6165	+	3.23861i	0.743307	+	0.226748i
$205$	−0.0152931	−	0.0264885i	−0.00106812	−	0.00185004i
$206$	16.3417	−	12.1001i	1.13858	−	0.843054i
$207$	5.52353			0.383912
$208$	5.80111	+	13.2041i	0.402234	+	0.915537i
$209$	−11.9801			−0.828679
$210$	0.0113434	−	0.00839911i	0.000782768	−	0.000579594i
$211$	−2.73940	−	4.74478i	−0.188588	−	0.326644i	0.756192	−	0.654350i	$-0.227058\pi$
$211$	−2.73940	−	4.74478i	−0.188588	−	0.326644i	−0.944780	+	0.327706i	$0.893724\pi$
$212$	7.11380	+	2.17008i	0.488578	+	0.149042i
$213$	1.55604	−	1.55604i	0.106618	−	0.106618i
$214$	−5.68162	−	2.46834i	−0.388387	−	0.168732i
$215$	−0.0637997	+	0.0170951i	−0.00435111	+	0.00116588i
$216$	0.946628	+	2.66531i	0.0644099	+	0.181352i
$217$	0.562134	−	0.973645i	0.0381601	−	0.0660953i
$218$	−2.48288	+	16.6486i	−0.168162	+	1.12759i
$219$	−1.86017	−	0.498432i	−0.125699	−	0.0336809i
$220$	−0.00924607	−	0.0399361i	−0.000623370	−	0.00269249i
$221$	−9.28504	−	17.7253i	−0.624580	−	1.19233i
$222$	−10.2402	+	12.8819i	−0.687279	+	0.864579i
$223$	13.8516	+	3.71152i	0.927572	+	0.248542i	0.690819	−	0.723028i	$-0.257250\pi$
$223$	13.8516	+	3.71152i	0.927572	+	0.248542i	0.236753	+	0.971570i	$0.423917\pi$
$224$	−8.78532	+	2.78498i	−0.586994	+	0.186079i
$225$	−4.33009	−	2.49998i	−0.288673	−	0.166665i
$226$	−1.29178	−	11.3066i	−0.0859277	−	0.752104i
$227$	−9.25409	+	2.47963i	−0.614215	+	0.164579i	−0.552497	−	0.833515i	$-0.686325\pi$
$227$	−9.25409	+	2.47963i	−0.614215	+	0.164579i	−0.0617186	+	0.998094i	$0.519658\pi$
$228$	−6.32091	+	3.36592i	−0.418613	+	0.222913i
$229$	17.2631	+	17.2631i	1.14078	+	1.14078i	0.988309	+	0.152467i	$0.0487217\pi$
$229$	17.2631	+	17.2631i	1.14078	+	1.14078i	0.152467	+	0.988309i	$0.451278\pi$
$230$	−0.0445174	+	0.0175518i	−0.00293539	+	0.00115733i
$231$	2.72551	+	4.72071i	0.179325	+	0.310600i
$232$	3.77250	+	3.21595i	0.247677	+	0.211138i
$233$		−	11.8549i		−	0.776641i	−0.921524	−	0.388320i	$-0.873055\pi$
$233$		−	11.8549i		−	0.776641i	0.921524	−	0.388320i	$-0.126945\pi$
$234$	2.22208	−	4.58937i	0.145262	−	0.300017i
$235$	0.0249071			0.00162476
$236$	5.96470	+	0.204588i	0.388269	+	0.0133176i
$237$	10.9730	−	6.33527i	0.712774	−	0.411520i
$238$	11.8957	−	4.69011i	0.771085	−	0.304015i
$239$	−8.19428	+	8.19428i	−0.530044	+	0.530044i	−0.920585	−	0.390541i	$-0.872288\pi$
$239$	−8.19428	+	8.19428i	−0.530044	+	0.530044i	0.390541	+	0.920585i	$0.372288\pi$
$240$	−0.0160988	−	0.0184733i	−0.00103918	−	0.00119245i
$241$	5.54758	+	20.7038i	0.357351	+	1.33365i	0.877500	+	0.479576i	$0.159210\pi$
$241$	5.54758	+	20.7038i	0.357351	+	1.33365i	−0.520149	+	0.854075i	$0.674124\pi$
$242$	0.273207	−	0.0312138i	0.0175624	−	0.00200650i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.06929	+	2.86572i	−0.196491	+	0.183459i
$245$	−0.00689014	+	0.0257143i	−0.000440195	+	0.00164283i
$246$	4.39388	−	5.52739i	0.280144	−	0.352413i
$247$	12.3225	+	3.85057i	0.784062	+	0.245006i
$248$	−1.76246	−	0.838639i	−0.111916	−	0.0532537i
$249$	1.30193	−	4.85887i	0.0825066	−	0.307919i
$250$	0.0856860	+	0.0127787i	0.00541926	+	0.000808196i
$251$	6.73491	+	3.88840i	0.425104	+	0.245434i	0.697259	−	0.716820i	$-0.254403\pi$
$251$	6.73491	+	3.88840i	0.425104	+	0.245434i	−0.272155	+	0.962254i	$0.587736\pi$
$252$	2.76436	+	1.72498i	0.174138	+	0.108664i
$253$	−4.78315	−	17.8510i	−0.300714	−	1.12228i
$254$	−4.96030	−	2.15497i	−0.311237	−	0.135215i
$255$	0.0240399	+	0.0240399i	0.00150544	+	0.00150544i
$256$	6.03049	+	14.8200i	0.376905	+	0.926252i
$257$	−13.3396	+	7.70163i	−0.832103	+	0.480415i	−0.854572	−	0.519333i	$-0.826180\pi$
$257$	−13.3396	+	7.70163i	−0.832103	+	0.480415i	0.0224694	+	0.999748i	$0.492847\pi$
$258$	−9.07374	−	12.2545i	−0.564907	−	0.762933i
$259$			18.9579i			1.17799i
$260$	−0.00332570	+	0.0440494i	−0.000206251	+	0.00273183i
$261$		−	1.75264i		−	0.108486i
$262$	11.5129	−	8.52464i	0.711271	−	0.526654i
$263$	−17.8675	+	10.3158i	−1.10176	+	0.636101i	−0.936683	−	0.350180i	$-0.886120\pi$
$263$	−17.8675	+	10.3158i	−1.10176	+	0.636101i	−0.165077	+	0.986281i	$0.552787\pi$
$264$	7.79403	−	5.36737i	0.479689	−	0.330339i
$265$	0.0161084	+	0.0161084i	0.000989528	+	0.000989528i
$266$	−3.28730	+	7.56668i	−0.201557	+	0.463943i
$267$	3.88239	+	14.4893i	0.237598	+	0.886729i
$268$	−0.873390	−	0.545002i	−0.0533508	−	0.0332913i
$269$	−13.8319	−	7.98587i	−0.843348	−	0.486907i	0.0150527	−	0.999887i	$-0.495208\pi$
$269$	−13.8319	−	7.98587i	−0.843348	−	0.486907i	−0.858401	+	0.512979i	$0.828542\pi$
$270$	−0.00127787	+	0.00856863i	−7.77690e−5	+	0.000521470i
$271$	−6.02478	+	22.4848i	−0.365979	+	1.36585i	0.500109	+	0.865962i	$0.333293\pi$
$271$	−6.02478	+	22.4848i	−0.365979	+	1.36585i	−0.866088	+	0.499891i	$0.833373\pi$
$272$	−9.75617	−	19.9403i	−0.591555	−	1.20906i
$273$	−1.28610	−	5.73166i	−0.0778385	−	0.346896i
$274$	−18.9306	−	15.0485i	−1.14364	−	0.909111i
$275$	−4.32976	+	16.1589i	−0.261095	+	0.974418i
$276$	−7.53909	−	8.07463i	−0.453800	−	0.486036i
$277$	−3.01247	+	5.21776i	−0.181002	+	0.313505i	−0.942222	−	0.334989i	$-0.891267\pi$
$277$	−3.01247	+	5.21776i	−0.181002	+	0.313505i	0.761220	+	0.648494i	$0.224601\pi$
$278$	−2.73357	−	23.9263i	−0.163949	−	1.43500i
$279$	0.178604	+	0.666558i	0.0106927	+	0.0399058i
$280$	−0.0277610	−	0.00511849i	−0.00165904	−	0.000305888i
$281$	−20.3774	+	20.3774i	−1.21561	+	1.21561i	−0.246461	+	0.969153i	$0.579268\pi$
$281$	−20.3774	+	20.3774i	−1.21561	+	1.21561i	−0.969153	+	0.246461i	$0.920732\pi$
$282$	2.10903	+	5.34922i	0.125591	+	0.318541i
$283$	6.85490	−	3.95768i	0.407482	−	0.235260i	−0.282225	−	0.959348i	$-0.591073\pi$
$283$	6.85490	−	3.95768i	0.407482	−	0.235260i	0.689707	+	0.724088i	$0.257739\pi$
$284$	−4.39856	−	0.150870i	−0.261007	−	0.00895250i
$285$	−0.0219347			−0.00129930
$286$	−16.7562	−	3.20713i	−0.990814	−	0.189642i
$287$		−	8.13447i		−	0.480163i
$288$	2.60426	−	5.02173i	0.153458	−	0.295909i
$289$	6.89996	+	11.9511i	0.405880	+	0.703005i
$290$	0.00556928	+	0.0141256i	0.000327039	+	0.000829483i
$291$	3.44796	+	3.44796i	0.202123	+	0.202123i
$292$	1.81032	+	3.39963i	0.105941	+	0.198948i
$293$	−1.74094	+	0.466483i	−0.101707	+	0.0272522i	−0.309313	−	0.950960i	$-0.600099\pi$
$293$	−1.74094	+	0.466483i	−0.101707	+	0.0272522i	0.207607	+	0.978212i	$0.433433\pi$
$294$	−6.10601	+	0.697610i	−0.356110	+	0.0406854i
$295$	0.0158313	+	0.00914022i	0.000921735	+	0.000532164i
$296$	32.8085	−	2.61280i	1.90696	−	0.151866i
$297$	−3.23180	−	0.865959i	−0.187528	−	0.0502481i
$298$	−13.3685	−	10.6270i	−0.774417	−	0.615607i
$299$	−0.817691	+	19.8986i	−0.0472883	+	1.15076i
$300$	2.25554	+	9.74223i	0.130223	+	0.562468i
$301$	−16.9676	−	4.54647i	−0.977999	−	0.262054i
$302$	3.47689	+	0.518523i	0.200073	+	0.0298377i
$303$	−7.89450	+	13.6737i	−0.453527	+	0.785532i
$304$	13.5479	+	4.64614i	0.777027	+	0.266474i
$305$	−0.0124236	+	0.00332890i	−0.000711375	+	0.000190612i
$306$	−3.12737	+	7.19857i	−0.178780	+	0.411515i
$307$	14.6289	−	14.6289i	0.834914	−	0.834914i	−0.153270	−	0.988184i	$-0.548980\pi$
$307$	14.6289	−	14.6289i	0.834914	−	0.834914i	0.988184	+	0.153270i	$0.0489804\pi$
$308$	3.18098	−	10.4276i	0.181253	−	0.594169i
$309$	7.18910	+	12.4519i	0.408974	+	0.708363i
$310$	−0.00355755	−	0.00480464i	−0.000202055	−	0.000272885i
$311$	25.6430			1.45408			0.727040	−	0.686595i	$-0.240895\pi$
$311$	25.6430			1.45408			0.727040	+	0.686595i	$0.240895\pi$
$312$	−9.74196	+	3.01567i	−0.551530	+	0.170729i
$313$	−19.4022			−1.09668			−0.548340	−	0.836256i	$-0.684740\pi$
$313$	−19.4022			−1.09668			−0.548340	+	0.836256i	$0.684740\pi$
$314$	−19.5025	−	26.3390i	−1.10059	−	1.48640i
$315$	0.00499021	+	0.00864330i	0.000281167	+	0.000486995i
$316$	−24.2384	−	7.39399i	−1.36352	−	0.415944i
$317$	−11.2646	+	11.2646i	−0.632682	+	0.632682i	−0.948740	−	0.316058i	$-0.897641\pi$
$317$	−11.2646	+	11.2646i	−0.632682	+	0.632682i	0.316058	+	0.948740i	$0.397641\pi$
$318$	−2.09555	+	4.82352i	−0.117513	+	0.270490i
$319$	−5.66420	+	1.51772i	−0.317134	+	0.0849759i
$320$	−0.00503200	+	0.0487485i	−0.000281297	+	0.00272513i
$321$	2.19013	−	3.79342i	0.122241	−	0.211728i
$322$	−12.5873	−	1.87719i	−0.701460	−	0.104612i
$323$	−19.1945	−	5.14315i	−1.06801	−	0.286172i
$324$	−1.94846	+	0.451111i	−0.108248	+	0.0250617i
$325$	9.64723	−	15.2291i	0.535132	−	0.844760i
$326$	−9.61122	−	7.64025i	−0.532316	−	0.423154i
$327$	−11.4970	−	3.08061i	−0.635785	−	0.170358i
$328$	−14.0775	+	1.12110i	−0.777300	+	0.0619024i
$329$	5.73663	+	3.31205i	0.316271	+	0.182599i
$330$	0.0287987	−	0.00329025i	0.00158532	−	0.000181122i
$331$	−3.11057	+	0.833475i	−0.170972	+	0.0458119i	−0.343290	−	0.939230i	$-0.611541\pi$
$331$	−3.11057	+	0.833475i	−0.170972	+	0.0458119i	0.172317	+	0.985042i	$0.444875\pi$
$332$	−8.88001	+	4.72865i	−0.487354	+	0.259518i
$333$	−8.22810	−	8.22810i	−0.450897	−	0.450897i
$334$	12.4907	+	31.6807i	0.683461	+	1.73349i
$335$	−0.00157664	−	0.00273082i	−8.61411e−5	−	0.000149201i
$336$	−1.25140	−	6.39554i	−0.0682696	−	0.348905i
$337$		−	14.3103i		−	0.779534i	−0.920914	−	0.389767i	$-0.872556\pi$
$337$		−	14.3103i		−	0.779534i	0.920914	−	0.389767i	$-0.127444\pi$
$338$	16.2043	+	8.68449i	0.881398	+	0.472374i
$339$	8.04699			0.437052
$340$	0.00233085	−	0.0679552i	0.000126408	−	0.00368539i
$341$	1.99952	−	1.15442i	0.108280	−	0.0625155i
$342$	−1.85733	−	4.71083i	−0.100433	−	0.254733i
$343$	−13.0705	+	13.0705i	−0.705740	+	0.705740i
$344$	−5.52961	+	29.9908i	−0.298137	+	1.61699i
$345$	−0.00875762	−	0.0326839i	−0.000471494	−	0.00175964i
$346$	−1.83488	−	16.0602i	−0.0986437	−	0.863404i
$347$	0.895267	−	1.55065i	0.0480604	−	0.0832431i	−0.840994	−	0.541044i	$-0.818029\pi$
$347$	0.895267	−	1.55065i	0.0480604	−	0.0832431i	0.889055	+	0.457801i	$0.151363\pi$
$348$	−2.56212	+	2.39219i	−0.137344	+	0.128235i
$349$	2.69383	−	10.0535i	0.144197	−	0.538151i	−0.855593	−	0.517650i	$-0.826807\pi$
$349$	2.69383	−	10.0535i	0.144197	−	0.538151i	0.999790	−	0.0205016i	$-0.00652631\pi$
$350$	9.01798	+	7.16866i	0.482031	+	0.383181i
$351$	3.04585	+	1.92946i	0.162575	+	0.102987i
$352$	−18.4844	−	4.06785i	−0.985224	−	0.216817i
$353$	−2.28519	+	8.52844i	−0.121628	+	0.453923i	−0.999697	−	0.0246115i	$-0.992165\pi$
$353$	−2.28519	+	8.52844i	−0.121628	+	0.453923i	0.878069	+	0.478534i	$0.158832\pi$
$354$	−0.622485	+	4.17400i	−0.0330847	+	0.221845i
$355$	−0.0116745	−	0.00674030i	−0.000619620	−	0.000357738i
$356$	15.8822	−	25.4520i	0.841756	−	1.34895i
$357$	2.34017	+	8.73362i	0.123855	+	0.462232i
$358$	10.8297	−	24.9277i	0.572365	−	1.31747i
$359$	−6.93284	−	6.93284i	−0.365901	−	0.365901i	0.500079	−	0.865980i	$-0.333304\pi$
$359$	−6.93284	−	6.93284i	−0.365901	−	0.365901i	−0.865980	+	0.500079i	$0.833304\pi$
$360$	0.0142703	−	0.00982728i	0.000752112	−	0.000517943i
$361$	−5.35132	+	3.08959i	−0.281648	+	0.162610i
$362$	−11.2570	+	8.33511i	−0.591652	+	0.438084i
$363$			0.194443i			0.0102056i
$364$	−6.62349	+	9.70327i	−0.347165	+	0.508590i
$365$			0.0117973i			0.000617499i
$366$	−1.76692	−	2.38630i	−0.0923582	−	0.124734i
$367$	−12.8657	+	7.42801i	−0.671583	+	0.387739i	−0.796676	−	0.604406i	$-0.793410\pi$
$367$	−12.8657	+	7.42801i	−0.671583	+	0.387739i	0.125093	+	0.992145i	$0.460077\pi$
$368$	−1.51387	+	22.0422i	−0.0789159	+	1.14903i
$369$	3.53052	+	3.53052i	0.183791	+	0.183791i
$370$	0.0924611	+	0.0401691i	0.00480682	+	0.00208829i
$371$	1.56807	+	5.85211i	0.0814101	+	0.303827i
$372$	0.730638	−	1.17088i	0.0378818	−	0.0607073i
$373$	18.4652	+	10.6609i	0.956090	+	0.551999i	0.894967	−	0.446131i	$-0.147199\pi$
$373$	18.4652	+	10.6609i	0.956090	+	0.551999i	0.0611226	+	0.998130i	$0.480532\pi$
$374$	25.9725	+	3.87339i	1.34301	+	0.200288i
$375$	−0.0158551	+	0.0591719i	−0.000818751	+	0.00305562i
$376$	4.94119	−	10.3843i	0.254823	−	0.535528i
$377$	6.31392	+	0.259458i	0.325183	+	0.0133627i
$378$	−1.43374	+	1.80361i	−0.0737437	+	0.0927676i
$379$	−6.98578	+	26.0713i	−0.358835	+	1.33919i	0.516753	+	0.856134i	$0.327141\pi$
$379$	−6.98578	+	26.0713i	−0.358835	+	1.33919i	−0.875589	+	0.483058i	$0.839526\pi$
$380$	0.0299387	+	0.0320654i	0.00153582	+	0.00164492i
$381$	1.91208	−	3.31182i	0.0979590	−	0.169670i
$382$	−11.8204	+	1.35047i	−0.604783	+	0.0690963i
$383$	−5.60173	−	20.9059i	−0.286235	−	1.06824i	−0.947932	−	0.318473i	$-0.896830\pi$
$383$	−5.60173	−	20.9059i	−0.286235	−	1.06824i	0.661697	−	0.749771i	$-0.269837\pi$
$384$	−10.8956	+	3.04711i	−0.556016	+	0.155497i
$385$	0.0236121	−	0.0236121i	0.00120339	−	0.00120339i
$386$	−5.16778	+	2.03749i	−0.263033	+	0.103706i
$387$	9.33754	−	5.39103i	0.474654	−	0.274042i
$388$	0.334306	−	9.74656i	0.0169718	−	0.494807i
$389$	25.5925			1.29759			0.648797	−	0.760962i	$-0.275273\pi$
$389$	25.5925			1.29759			0.648797	+	0.760962i	$0.275273\pi$
$390$	−0.0306794	−	0.00587204i	−0.00155351	−	0.000297342i
$391$		−	30.6543i		−	1.55025i
$392$	9.35392	+	7.97397i	0.472445	+	0.402746i
$393$	5.06479	+	8.77247i	0.255485	+	0.442513i
$394$	20.9740	−	8.26939i	1.05665	−	0.416606i
$395$	−0.0548849	−	0.0548849i	−0.00276156	−	0.00276156i
$396$	3.14519	+	5.90640i	0.158052	+	0.296808i
$397$	−7.13276	+	1.91122i	−0.357983	+	0.0959212i	−0.433328	−	0.901236i	$-0.642661\pi$
$397$	−7.13276	+	1.91122i	−0.357983	+	0.0959212i	0.0753451	+	0.997158i	$0.475994\pi$
$398$	−2.06048	−	18.0349i	−0.103283	−	0.904009i
$399$	−5.05201	−	2.91678i	−0.252917	−	0.146022i
$400$	11.1632	−	16.5945i	0.558160	−	0.829724i
$401$	−0.0510228	−	0.0136715i	−0.00254796	−	0.000682723i	0.257545	−	0.966266i	$-0.417086\pi$
$401$	−0.0510228	−	0.0136715i	−0.00254796	−	0.000682723i	−0.260093	+	0.965584i	$0.583753\pi$
$402$	0.452986	−	0.569844i	0.0225929	−	0.0284212i
$403$	−2.42772	+	0.544746i	−0.120933	+	0.0271357i
$404$	30.7642	−	7.12258i	1.53058	−	0.354362i
$405$	−0.00591721	−	0.00158551i	−0.000294028	−	7.87847e-5i
$406$	−0.595641	+	3.99400i	−0.0295612	+	0.198219i
$407$	−19.4664	+	33.7168i	−0.964914	+	1.67128i
$408$	14.7919	−	5.25357i	0.732307	−	0.260090i
$409$	9.42392	−	2.52513i	0.465983	−	0.124860i	−0.0181853	−	0.999835i	$-0.505789\pi$
$409$	9.42392	−	2.52513i	0.465983	−	0.124860i	0.484168	+	0.874975i	$0.339122\pi$
$410$	−0.0396733	−	0.0172358i	−0.00195932	−	0.000851215i
$411$	12.0916	−	12.0916i	0.596432	−	0.596432i
$412$	8.39050	−	27.5051i	0.413370	−	1.35508i
$413$	2.43086	+	4.21037i	0.119615	+	0.207179i
$414$	6.27785	−	4.64838i	0.308539	−	0.228455i
$415$	−0.0308152			−0.00151266
$416$	17.7053	+	10.1253i	0.868075	+	0.496433i
$417$	17.0285			0.833889
$418$	−13.6161	+	10.0819i	−0.665986	+	0.493123i
$419$	4.74183	+	8.21309i	0.231654	+	0.401236i	0.958295	−	0.285781i	$-0.0922531\pi$
$419$	4.74183	+	8.21309i	0.231654	+	0.401236i	−0.726641	+	0.687017i	$0.758920\pi$
$420$	0.00582415	−	0.0190923i	0.000284189	−	0.000931607i
$421$	−15.6320	+	15.6320i	−0.761859	+	0.761859i	−0.976658	−	0.214799i	$-0.931090\pi$
$421$	−15.6320	+	15.6320i	−0.761859	+	0.761859i	0.214799	+	0.976658i	$0.431090\pi$
$422$	−7.10651	−	3.08738i	−0.345940	−	0.150291i
$423$	−3.92730	+	1.05232i	−0.190952	+	0.0511654i
$424$	9.91154	−	3.52024i	0.481347	−	0.170958i
$425$	−13.8743	+	24.0310i	−0.673003	+	1.16568i
$426$	0.459041	−	3.07804i	0.0222406	−	0.149132i
$427$	−3.30409	−	0.885327i	−0.159896	−	0.0428440i
$428$	−8.53478	+	1.97598i	−0.412544	+	0.0955128i
$429$	3.59806	−	11.5144i	0.173716	−	0.555921i
$430$	−0.0581260	+	0.0731209i	−0.00280308	+	0.00352620i
$431$	37.8715	+	10.1476i	1.82421	+	0.488795i	0.997293	−	0.0735317i	$-0.0234270\pi$
$431$	37.8715	+	10.1476i	1.82421	+	0.488795i	0.826915	+	0.562327i	$0.190094\pi$
$432$	3.31892	+	2.23266i	0.159682	+	0.107419i
$433$	−5.12070	−	2.95644i	−0.246085	−	0.142077i	0.371885	−	0.928279i	$-0.378712\pi$
$433$	−5.12070	−	2.95644i	−0.246085	−	0.142077i	−0.617970	+	0.786201i	$0.712045\pi$
$434$	−0.180478	−	1.57968i	−0.00866321	−	0.0758270i
$435$	−0.0103708	+	0.00277884i	−0.000497240	+	0.000133235i
$436$	11.1889	+	21.0117i	0.535849	+	1.00628i
$437$	13.9849	+	13.9849i	0.668989	+	0.668989i
$438$	−2.53367	+	0.998946i	−0.121063	+	0.0477315i
$439$	−3.69569	−	6.40112i	−0.176385	−	0.305509i	0.764254	−	0.644915i	$-0.223107\pi$
$439$	−3.69569	−	6.40112i	−0.176385	−	0.305509i	−0.940640	+	0.339406i	$0.889774\pi$
$440$	−0.0441174	−	0.0376089i	−0.00210321	−	0.00179293i
$441$		−	4.34569i		−	0.206938i
$442$	−25.4700	−	12.3321i	−1.21148	−	0.586576i
$443$	−27.3664			−1.30022			−0.650109	−	0.759841i	$-0.725277\pi$
$443$	−27.3664			−1.30022			−0.650109	+	0.759841i	$0.725277\pi$
$444$	−0.797778	+	23.2589i	−0.0378609	+	1.10382i
$445$	0.0795804	−	0.0459458i	0.00377247	−	0.00217804i
$446$	18.8667	−	7.43855i	0.893364	−	0.352226i
$447$	8.53889	−	8.53889i	0.403876	−	0.403876i
$448$	−7.64135	+	10.5587i	−0.361020	+	0.498850i
$449$	4.34105	+	16.2010i	0.204867	+	0.764573i	0.989490	+	0.144600i	$0.0461897\pi$
$449$	4.34105	+	16.2010i	0.204867	+	0.764573i	−0.784623	+	0.619973i	$0.787144\pi$
$450$	−7.02531	+	0.802640i	−0.331176	+	0.0378368i
$451$	8.35266	−	14.4672i	0.393311	−	0.681235i
$452$	−10.9834	−	11.7636i	−0.516614	−	0.553312i
$453$	−0.643353	+	2.40103i	−0.0302274	+	0.112810i
$454$	−8.43112	+	10.6061i	−0.395692	+	0.497770i
$455$	−0.0318763	+	0.0166978i	−0.00149438	+	0.000782803i
$456$	−4.35150	+	9.14500i	−0.203778	+	0.428254i
$457$	7.41678	−	27.6798i	0.346942	−	1.29481i	−0.543385	−	0.839484i	$-0.682858\pi$
$457$	7.41678	−	27.6798i	0.346942	−	1.29481i	0.890327	−	0.455322i	$-0.150476\pi$
$458$	34.1485	+	5.09270i	1.59565	+	0.237966i
$459$	−4.80624	−	2.77488i	−0.224336	−	0.129520i
$460$	−0.0358260	+	0.0574128i	−0.00167040	+	0.00267688i
$461$	−9.47325	−	35.3546i	−0.441213	−	1.64663i	−0.725745	−	0.687963i	$-0.758505\pi$
$461$	−9.47325	−	35.3546i	−0.441213	−	1.64663i	0.284532	−	0.958666i	$-0.408162\pi$
$462$	7.07047	+	3.07172i	0.328948	+	0.142909i
$463$	9.62736	+	9.62736i	0.447422	+	0.447422i	0.894497	−	0.447075i	$-0.147534\pi$
$463$	9.62736	+	9.62736i	0.447422	+	0.447422i	−0.447075	+	0.894497i	$0.647534\pi$
$464$	6.99410	+	0.480359i	0.324693	+	0.0223001i
$465$	0.00366098	−	0.00211367i	0.000169774	−	9.80190e-5i
$466$	−9.97660	−	13.4739i	−0.462157	−	0.624165i
$467$			26.0667i			1.20622i	0.797658	+	0.603110i	$0.206072\pi$
$467$			26.0667i			1.20622i	−0.797658	+	0.603110i	$0.793928\pi$
$468$	−1.33668	−	7.08613i	−0.0617883	−	0.327557i
$469$		−	0.838620i		−	0.0387239i
$470$	0.0283086	−	0.0209608i	0.00130578	−	0.000966850i
$471$	20.0695	−	11.5871i	0.924752	−	0.533906i
$472$	6.95143	−	4.78711i	0.319966	−	0.220345i
$473$	−25.5087	−	25.5087i	−1.17289	−	1.17289i
$474$	7.14003	−	16.4349i	0.327952	−	0.754879i
$475$	−4.63363	−	17.2929i	−0.212605	−	0.793454i
$476$	9.57324	−	15.3416i	0.438789	−	0.703179i
$477$	−3.22050	−	1.85936i	−0.147457	−	0.0851342i
$478$	−2.41736	+	16.2093i	−0.110567	+	0.741396i
$479$	8.72017	−	32.5441i	0.398435	−	1.48698i	−0.417415	−	0.908716i	$-0.637064\pi$
$479$	8.72017	−	32.5441i	0.398435	−	1.48698i	0.815850	−	0.578263i	$-0.196269\pi$
$480$	−0.0338437	−	0.00744794i	−0.00154475	−	0.000339951i
$481$	30.8599	−	28.4238i	1.40709	−	1.29601i
$482$	23.7287	+	18.8626i	1.08081	+	0.859170i
$483$	2.32910	−	8.69233i	0.105978	−	0.395515i
$484$	0.284249	−	0.265396i	0.0129204	−	0.0120635i
$485$	0.0149355	−	0.0258691i	0.000678186	−	0.00117465i
$486$	−0.160529	−	1.40507i	−0.00728175	−	0.0637354i
$487$	−6.44555	−	24.0551i	−0.292076	−	1.09004i	−0.943512	−	0.331338i	$-0.892500\pi$
$487$	−6.44555	−	24.0551i	−0.292076	−	1.09004i	0.651436	−	0.758703i	$-0.274167\pi$
$488$	−1.07677	+	5.84006i	−0.0487432	+	0.264367i
$489$	6.13899	−	6.13899i	0.277615	−	0.277615i
$490$	0.0138091	+	0.0350245i	0.000623829	+	0.00158224i
$491$	31.9925	−	18.4709i	1.44380	−	0.833578i	0.445699	−	0.895183i	$-0.352955\pi$
$491$	31.9925	−	18.4709i	1.44380	−	0.833578i	0.998101	+	0.0616050i	$0.0196219\pi$
$492$	0.342311	−	9.97994i	0.0154326	−	0.449931i
$493$	−9.72677			−0.438072
$494$	17.2458	−	5.99369i	0.775925	−	0.269669i
$495$			0.0204962i			0.000921238i
$496$	−2.70892	+	0.530047i	−0.121634	+	0.0237998i
$497$	−1.79259	−	3.10486i	−0.0804088	−	0.139272i
$498$	−2.60930	−	6.61808i	−0.116926	−	0.296563i
$499$	−15.6264	−	15.6264i	−0.699534	−	0.699534i	0.264776	−	0.964310i	$-0.414702\pi$
$499$	−15.6264	−	15.6264i	−0.699534	−	0.699534i	−0.964310	+	0.264776i	$0.914702\pi$
$500$	0.108142	−	0.0575860i	0.00483624	−	0.00257532i
$501$	−23.2594	+	6.23234i	−1.03915	+	0.278441i
$502$	10.9270	−	1.24840i	0.487695	−	0.0557190i
$503$	−29.7238	−	17.1610i	−1.32532	−	0.765173i	−0.340747	−	0.940155i	$-0.610680\pi$
$503$	−29.7238	−	17.1610i	−1.32532	−	0.765173i	−0.984572	+	0.174982i	$0.944013\pi$
$504$	4.59355	−	0.365820i	0.204613	−	0.0162949i
$505$	0.0934268	+	0.0250336i	0.00415744	+	0.00111398i
$506$	−20.4590	−	16.2635i	−0.909513	−	0.722999i
$507$	−7.40180	+	10.6871i	−0.328726	+	0.474629i
$508$	−7.45124	+	1.72512i	−0.330595	+	0.0765399i
$509$	10.3675	+	2.77797i	0.459533	+	0.123131i	0.481156	−	0.876635i	$-0.340217\pi$
$509$	10.3675	+	2.77797i	0.459533	+	0.123131i	−0.0216237	+	0.999766i	$0.506884\pi$
$510$	0.0475539	+	0.00709191i	0.00210572	+	0.000314035i
$511$	−1.56876	+	2.71717i	−0.0693977	+	0.120200i
$512$	19.3260	+	11.7689i	0.854095	+	0.520117i
$513$	3.45861	−	0.926732i	0.152701	−	0.0409162i
$514$	−8.67996	+	19.9795i	−0.382857	+	0.881257i
$515$	0.0622820	−	0.0622820i	0.00274447	−	0.00274447i
$516$	−20.6258	−	6.29195i	−0.908000	−	0.276988i
$517$	6.80177	+	11.7810i	0.299141	+	0.518128i
$518$	15.9542	+	21.5469i	0.700987	+	0.946716i
$519$	11.4302			0.501729
$520$	0.0332903	+	0.0528638i	0.00145988	+	0.00231823i
$521$	36.1876			1.58541			0.792704	−	0.609607i	$-0.208673\pi$
$521$	36.1876			1.58541			0.792704	+	0.609607i	$0.208673\pi$
$522$	−1.47495	−	1.99199i	−0.0645570	−	0.0871872i
$523$	5.07033	+	8.78207i	0.221710	+	0.384013i	0.955327	−	0.295550i	$-0.0955028\pi$
$523$	5.07033	+	8.78207i	0.221710	+	0.384013i	−0.733617	+	0.679563i	$0.762170\pi$
$524$	5.91119	−	19.3776i	0.258231	−	0.846514i
$525$	−5.76007	+	5.76007i	−0.251390	+	0.251390i
$526$	−11.6262	+	26.7612i	−0.506928	+	1.16684i
$527$	3.69924	−	0.991208i	0.161141	−	0.0431777i
$528$	4.34146	−	12.6595i	0.188938	−	0.550934i
$529$	−3.75469	+	6.50332i	−0.163247	+	0.282753i
$530$	0.0318643	+	0.00475205i	0.00138410	+	0.000206416i
$531$	−2.88242	−	0.772342i	−0.125086	−	0.0335168i
$532$	2.63158	+	11.3665i	0.114094	+	0.492799i
$533$	−13.2414	+	12.1961i	−0.573548	+	0.528271i
$534$	16.6062	+	13.2007i	0.718619	+	0.571251i
$535$	−0.0259190	−	0.00694496i	−0.00112057	−	0.000300257i
$536$	−1.45132	+	0.115579i	−0.0626873	+	0.00499227i
$537$	16.6433	+	9.60904i	0.718214	+	0.414661i
$538$	−22.4415	+	2.56393i	−0.967521	+	0.110539i
$539$	−14.0444	+	3.76319i	−0.604936	+	0.162092i
$540$	0.00575862	+	0.0108142i	0.000247812	+	0.000465369i
$541$	16.6100	+	16.6100i	0.714119	+	0.714119i	0.967394	−	0.253276i	$-0.0815079\pi$
$541$	16.6100	+	16.6100i	0.714119	+	0.714119i	−0.253276	+	0.967394i	$0.581508\pi$
$542$	12.0747	+	30.6256i	0.518654	+	1.31548i
$543$	−4.95218	−	8.57743i	−0.212519	−	0.368093i
$544$	−27.8695	−	14.4531i	−1.19489	−	0.619669i
$545$			0.0729144i			0.00312331i
$546$	−6.28527	−	5.43207i	−0.268985	−	0.232471i
$547$	31.5052			1.34706			0.673532	−	0.739158i	$-0.264776\pi$
$547$	31.5052			1.34706			0.673532	+	0.739158i	$0.264776\pi$
$548$	−34.1800	−	1.17237i	−1.46010	−	0.0500811i
$549$	1.81829	−	1.04979i	0.0776026	−	0.0448039i
$550$	8.67761	+	22.0094i	0.370015	+	0.938483i
$551$	4.43748	−	4.43748i	0.189043	−	0.189043i
$552$	−15.3639	−	2.83276i	−0.653933	−	0.120570i
$553$	−5.34278	−	19.9395i	−0.227198	−	0.847915i
$554$	0.967180	+	8.46549i	0.0410915	+	0.359664i
$555$	−0.0356416	+	0.0617331i	−0.00151290	+	0.00262043i
$556$	−23.2423	−	24.8933i	−0.985692	−	1.05571i
$557$	3.98647	−	14.8777i	0.168912	−	0.630389i	−0.828596	−	0.559846i	$-0.810860\pi$
$557$	3.98647	−	14.8777i	0.168912	−	0.630389i	0.997509	−	0.0705430i	$-0.0224732\pi$
$558$	0.763942	+	0.607280i	0.0323402	+	0.0257082i
$559$	18.0389	+	34.4367i	0.762966	+	1.45652i
$560$	−0.0358596	+	0.0175450i	−0.00151535	+	0.000741412i
$561$	−4.80587	+	17.9358i	−0.202904	+	0.757248i
$562$	−6.01145	+	40.3090i	−0.253578	+	1.70033i
$563$	−36.0452	−	20.8107i	−1.51912	−	0.877067i	−0.999746	−	0.0225229i	$-0.992830\pi$
$563$	−36.0452	−	20.8107i	−1.51912	−	0.877067i	−0.519379	−	0.854544i	$-0.673837\pi$
$564$	6.89873	+	4.30486i	0.290489	+	0.181267i
$565$	−0.0127586	−	0.0476157i	−0.000536758	−	0.00200321i
$566$	4.46042	−	10.2670i	0.187485	−	0.431553i
$567$	−1.15202	−	1.15202i	−0.0483804	−	0.0483804i
$568$	−5.12621	+	3.53017i	−0.215091	+	0.148123i
$569$	−1.73040	+	0.999049i	−0.0725423	+	0.0418823i	−0.535832	−	0.844324i	$-0.680002\pi$
$569$	−1.73040	+	0.999049i	−0.0725423	+	0.0418823i	0.463290	+	0.886207i	$0.346669\pi$
$570$	−0.0249302	+	0.0184593i	−0.00104421	+	0.000773176i
$571$		−	42.3453i		−	1.77210i	−0.463592	−	0.886049i	$-0.653440\pi$
$571$		−	42.3453i		−	1.77210i	0.463592	−	0.886049i	$-0.346560\pi$
$572$	−21.7435	+	10.4562i	−0.909140	+	0.437196i
$573$		−	8.41264i		−	0.351443i
$574$	−6.84564	−	9.24535i	−0.285731	−	0.385893i
$575$	23.9174	−	13.8087i	0.997425	−	0.575863i
$576$	−1.26617	−	7.89916i	−0.0527572	−	0.329132i
$577$	−17.1186	−	17.1186i	−0.712659	−	0.712659i	0.254432	−	0.967091i	$-0.418111\pi$
$577$	−17.1186	−	17.1186i	−0.712659	−	0.712659i	−0.967091	+	0.254432i	$0.918111\pi$
$578$	17.8998	+	7.77645i	0.744533	+	0.323458i
$579$	−1.01662	−	3.79409i	−0.0422495	−	0.157677i
$580$	0.0182174	+	0.0113678i	0.000756435	+	0.000472021i
$581$	−7.09739	−	4.09768i	−0.294449	−	0.170000i
$582$	6.82048	+	1.01717i	0.282718	+	0.0421629i
$583$	−3.22026	+	12.0182i	−0.133369	+	0.497741i
$584$	4.91853	+	2.34041i	0.203530	+	0.0968467i
$585$	0.00658779	−	0.0210821i	0.000272372	−	0.000871637i
$586$	−1.58611	+	1.99529i	−0.0655218	+	0.0824246i
$587$	1.99421	−	7.44249i	0.0823098	−	0.307185i	−0.912481	−	0.409118i	$-0.865836\pi$
$587$	1.99421	−	7.44249i	0.0823098	−	0.307185i	0.994791	+	0.101934i	$0.0325030\pi$
$588$	−6.35279	+	5.93145i	−0.261985	+	0.244609i
$589$	−1.23544	+	2.13985i	−0.0509054	+	0.0881708i
$590$	0.0256854	−	0.00293454i	0.00105745	−	0.000120813i
$591$	4.12608	+	15.3987i	0.169724	+	0.633419i
$592$	35.0902	−	30.5799i	1.44220	−	1.25683i
$593$	11.8828	−	11.8828i	0.487967	−	0.487967i	−0.419697	−	0.907664i	$-0.637864\pi$
$593$	11.8828	−	11.8828i	0.487967	−	0.487967i	0.907664	+	0.419697i	$0.137864\pi$
$594$	−4.40191	+	1.73554i	−0.180613	+	0.0712099i
$595$	0.0479683	−	0.0276945i	0.00196651	−	0.00113536i
$596$	−24.1374	−	0.827911i	−0.988708	−	0.0339126i
$597$	12.8356			0.525325
$598$	15.8165	+	23.3041i	0.646783	+	0.952978i
$599$			45.8502i			1.87339i	0.350151	+	0.936693i	$0.386130\pi$
$599$			45.8502i			1.87339i	−0.350151	+	0.936693i	$0.613870\pi$
$600$	10.7622	+	9.17451i	0.439366	+	0.374548i
$601$	12.4138	+	21.5013i	0.506368	+	0.877056i	0.999973	+	0.00736919i	$0.00234571\pi$
$601$	12.4138	+	21.5013i	0.506368	+	0.877056i	−0.493605	+	0.869686i	$0.664321\pi$
$602$	−23.1109	+	9.11192i	−0.941932	+	0.371374i
$603$	0.363977	+	0.363977i	0.0148223	+	0.0148223i
$604$	4.38808	−	2.33668i	0.178549	−	0.0950780i
$605$	0.00115056		0.000308292i	4.67769e−5		1.25338e-5i
$606$	2.53459	+	22.1847i	0.102961	+	0.901191i
$607$	−40.6484	−	23.4684i	−1.64987	−	0.952551i	−0.977123	−	0.212675i	$-0.931782\pi$
$607$	−40.6484	−	23.4684i	−1.64987	−	0.952551i	−0.672744	−	0.739876i	$-0.734884\pi$
$608$	19.3081	−	6.12075i	0.783047	−	0.248229i
$609$	−2.75812	−	0.739036i	−0.111765	−	0.0299473i
$610$	−0.0113188	+	0.0142387i	−0.000458284	+	0.000576509i
$611$	−3.20960	−	14.3039i	−0.129846	−	0.578675i
$612$	2.50356	+	10.8135i	0.101200	+	0.437110i
$613$	−7.13914	−	1.91293i	−0.288347	−	0.0772624i	0.111746	−	0.993737i	$-0.464356\pi$
$613$	−7.13914	−	1.91293i	−0.288347	−	0.0772624i	−0.400093	+	0.916474i	$0.631022\pi$
$614$	4.31560	−	28.9377i	0.174163	−	1.16783i
$615$	0.0152931	−	0.0264885i	0.000616679	−	0.00106812i
$616$	−5.16008	−	14.5287i	−0.207906	−	0.585376i
$617$	−3.43254	+	0.919746i	−0.138189	+	0.0370276i	−0.327250	−	0.944938i	$-0.606122\pi$
$617$	−3.43254	+	0.919746i	−0.138189	+	0.0370276i	0.189062	+	0.981965i	$0.439455\pi$
$618$	18.6499	+	8.10232i	0.750208	+	0.325923i
$619$	−16.7707	+	16.7707i	−0.674072	+	0.674072i	−0.958652	−	0.284580i	$-0.908146\pi$
$619$	−16.7707	+	16.7707i	−0.674072	+	0.674072i	0.284580	+	0.958652i	$0.408146\pi$
$620$	−0.00808678	−	0.00246689i	−0.000324773	−	9.90728e-5i
$621$	2.76176	+	4.78352i	0.110826	+	0.191956i
$622$	29.1449	−	21.5801i	1.16860	−	0.865283i
$623$	24.4387			0.979117
$624$	−8.53450	+	11.6259i	−0.341653	+	0.465410i
$625$	−24.9994			−0.999977
$626$	−22.0519	+	16.3281i	−0.881371	+	0.652603i
$627$	−5.99003	−	10.3750i	−0.239219	−	0.414339i
$628$	−44.3316	−	13.5235i	−1.76902	−	0.539646i
$629$	−45.6641	+	45.6641i	−1.82074	+	1.82074i
$630$	0.0129455	+	0.00562411i	0.000515763	+	0.000224070i
$631$	13.1022	−	3.51071i	0.521589	−	0.139759i	0.0115873	−	0.999933i	$-0.496312\pi$
$631$	13.1022	−	3.51071i	0.521589	−	0.139759i	0.510001	+	0.860174i	$0.329645\pi$
$632$	−33.7710	+	11.9943i	−1.34334	+	0.477107i
$633$	2.73940	−	4.74478i	0.108881	−	0.188588i
$634$	−3.32312	+	22.2828i	−0.131978	+	0.884961i
$635$	−0.0226284	−	0.00606326i	−0.000897980	−	0.000240613i
$636$	1.67755	+	7.24577i	0.0665193	+	0.287314i
$637$	15.6554	+	0.643326i	0.620289	+	0.0254895i
$638$	−5.16048	+	6.49174i	−0.204305	+	0.257011i
$639$	2.12559	+	0.569550i	0.0840871	+	0.0225311i
$640$	0.0353056	+	0.0596406i	0.00139558	+	0.00235750i
$641$	19.1888	+	11.0787i	0.757912	+	0.437581i	0.828546	−	0.559921i	$-0.189169\pi$
$641$	19.1888	+	11.0787i	0.757912	+	0.437581i	−0.0706333	+	0.997502i	$0.522502\pi$
$642$	−0.703161	−	6.15460i	−0.0277515	−	0.242903i
$643$	−23.0119	+	6.16601i	−0.907499	+	0.243164i	−0.682234	−	0.731134i	$-0.738991\pi$
$643$	−23.0119	+	6.16601i	−0.907499	+	0.243164i	−0.225265	+	0.974298i	$0.572325\pi$
$644$	−15.8860	+	8.45937i	−0.625996	+	0.333346i
$645$	−0.0467046	−	0.0467046i	−0.00183899	−	0.00183899i
$646$	−26.1440	+	10.3078i	−1.02862	+	0.405554i
$647$	−16.5037	−	28.5853i	−0.648829	−	1.12380i	−0.983403	−	0.181435i	$-0.941926\pi$
$647$	−16.5037	−	28.5853i	−0.648829	−	1.12380i	0.334574	−	0.942370i	$-0.391408\pi$
$648$	−1.83492	+	2.15246i	−0.0720823	+	0.0845566i
$649$			9.98424i			0.391916i
$650$	−1.85151	−	25.4276i	−0.0726221	−	0.997352i
$651$	1.12427			0.0440635
$652$	−17.3535	−	0.595223i	−0.679615	−	0.0233107i
$653$	6.90829	−	3.98850i	0.270342	−	0.156082i	−0.358701	−	0.933453i	$-0.616780\pi$
$653$	6.90829	−	3.98850i	0.270342	−	0.156082i	0.629043	+	0.777370i	$0.283447\pi$
$654$	−15.6596	+	6.17408i	−0.612338	+	0.241426i
$655$	0.0438783	−	0.0438783i	0.00171447	−	0.00171447i
$656$	−15.0565	+	13.1213i	−0.587858	+	0.512299i
$657$	−0.498432	−	1.86017i	−0.0194457	−	0.0725723i
$658$	9.30734	−	1.06336i	0.362838	−	0.0414541i
$659$	4.00689	−	6.94014i	0.156086	−	0.270350i	−0.777368	−	0.629046i	$-0.783446\pi$
$659$	4.00689	−	6.94014i	0.156086	−	0.270350i	0.933454	+	0.358697i	$0.116779\pi$
$660$	0.0299627	−	0.0279754i	0.00116630	−	0.00108894i
$661$	−4.42854	+	16.5276i	−0.172250	+	0.642847i	0.824753	+	0.565493i	$0.191314\pi$
$661$	−4.42854	+	16.5276i	−0.172250	+	0.642847i	−0.997004	+	0.0773545i	$0.975353\pi$
$662$	−2.83395	+	3.56503i	−0.110144	+	0.138559i
$663$	10.7081	−	16.9037i	0.415866	−	0.656487i
$664$	−6.11327	+	12.8475i	−0.237241	+	0.498578i
$665$	−0.00924918	+	0.0345184i	−0.000358668	+	0.00133857i
$666$	−16.2762	−	2.42733i	−0.630690	−	0.0940573i
$667$	8.38380	+	4.84039i	0.324622	+	0.187421i
$668$	40.8577	+	25.4955i	1.58083	+	0.986451i
$669$	3.71152	+	13.8516i	0.143496	+	0.535534i
$670$	−0.00409010	−	0.00177692i	−0.000158014	−	6.86483e-5i
$671$	−4.96727	−	4.96727i	−0.191759	−	0.191759i
$672$	−6.80452	−	6.21582i	−0.262490	−	0.239780i
$673$	−40.8080	+	23.5605i	−1.57303	+	0.908190i	−0.577237	+	0.816576i	$0.695869\pi$
$673$	−40.8080	+	23.5605i	−1.57303	+	0.908190i	−0.995795	+	0.0916142i	$0.970797\pi$
$674$	−12.0430	−	16.2646i	−0.463879	−	0.626490i
$675$		−	4.99996i		−	0.192449i
$676$	25.7257	−	3.76641i	0.989452	−	0.144862i
$677$			29.4037i			1.13008i	0.825065	+	0.565038i	$0.191138\pi$
$677$			29.4037i			1.13008i	−0.825065	+	0.565038i	$0.808862\pi$
$678$	9.14592	−	6.77201i	0.351247	−	0.260078i
$679$	6.87992	−	3.97212i	0.264027	−	0.152436i
$680$	−0.0545391	−	0.0791970i	−0.00209148	−	0.00303707i
$681$	−6.77446	−	6.77446i	−0.259598	−	0.259598i
$682$	1.30107	−	2.99479i	0.0498205	−	0.114676i
$683$	−6.46547	−	24.1295i	−0.247394	−	0.923288i	−0.972165	−	0.234298i	$-0.924721\pi$
$683$	−6.46547	−	24.1295i	−0.247394	−	0.923288i	0.724771	−	0.688990i	$-0.241946\pi$
$684$	−6.07543	−	3.79111i	−0.232300	−	0.144957i
$685$	−0.0907195	−	0.0523769i	−0.00346621	−	0.00200122i
$686$	−3.85587	+	25.8550i	−0.147218	+	0.987150i
$687$	−6.31872	+	23.5818i	−0.241074	+	0.899701i
$688$	18.9543	+	38.7399i	0.722624	+	1.47695i
$689$	7.17511	−	11.3266i	0.273350	−	0.431511i
$690$	−0.0374590	−	0.0297773i	−0.00142604	−	0.00113360i
$691$	−10.1307	+	37.8084i	−0.385391	+	1.43830i	0.452158	+	0.891938i	$0.350654\pi$
$691$	−10.1307	+	37.8084i	−0.385391	+	1.43830i	−0.837549	+	0.546362i	$0.816012\pi$
$692$	−15.6011	−	16.7093i	−0.593065	−	0.635194i
$693$	−2.72551	+	4.72071i	−0.103533	+	0.179325i
$694$	−0.287433	−	2.51583i	−0.0109108	−	0.0954996i
$695$	−0.0269989	−	0.100761i	−0.00102413	−	0.00382209i
$696$	−0.898848	+	4.87506i	−0.0340708	+	0.184788i
$697$	19.5936	−	19.5936i	0.742159	−	0.742159i
$698$	−5.39890	−	13.6935i	−0.204351	−	0.518305i
$699$	10.2666	−	5.92745i	0.388320	−	0.224197i
$700$	16.2824	+	0.558483i	0.615415	+	0.0211087i
$701$	−43.6308			−1.64791			−0.823956	−	0.566654i	$-0.808238\pi$
$701$	−43.6308			−1.64791			−0.823956	+	0.566654i	$0.808238\pi$
$702$	5.08556	−	0.370304i	0.191942	−	0.0139762i
$703$		−	41.6651i		−	1.57143i
$704$	−24.4321	+	10.9324i	−0.920819	+	0.412030i
$705$	0.0124536	+	0.0215702i	0.000469028	+	0.000812381i
$706$	4.57992	+	11.6162i	0.172368	+	0.437183i
$707$	18.1893	+	18.1893i	0.684078	+	0.684078i
$708$	2.80517	+	5.26787i	0.105425	+	0.197979i
$709$	47.8263	−	12.8150i	1.79615	−	0.481278i	0.802787	−	0.596265i	$-0.203349\pi$
$709$	47.8263	−	12.8150i	1.79615	−	0.481278i	0.993367	+	0.114987i	$0.0366827\pi$
$710$	−0.0189412	+	0.00216403i	−0.000710851	+	8.12146e-5i
$711$	10.9730	+	6.33527i	0.411520	+	0.237591i
$712$	−3.36817	−	42.2936i	−0.126227	−	1.58502i
$713$	−3.68175	−	0.986522i	−0.137883	−	0.0369455i
$714$	10.0096	+	7.95694i	0.374600	+	0.297781i
$715$	−0.0738379	−	0.00303422i	−0.00276138	−	0.000113473i
$716$	−8.66948	−	37.4457i	−0.323994	−	1.39941i
$717$	−11.1936	−	2.99931i	−0.418033	−	0.112011i
$718$	−13.7140	−	2.04523i	−0.511802	−	0.0763271i
$719$	10.6542	−	18.4536i	0.397334	−	0.688202i	−0.596062	−	0.802938i	$-0.703269\pi$
$719$	10.6542	−	18.4536i	0.397334	−	0.688202i	0.993396	+	0.114736i	$0.0366022\pi$
$720$	0.00794891	−	0.0231787i	0.000296238	−	0.000863817i
$721$	22.6268	−	6.06285i	0.842668	−	0.225792i
$722$	−3.48205	+	8.01497i	−0.129589	+	0.298286i
$723$	−15.1563	+	15.1563i	−0.563668	+	0.563668i
$724$	−5.77976	+	18.9468i	−0.214803	+	0.704151i
$725$	−4.38158	−	7.58911i	−0.162728	−	0.281853i
$726$	0.163635	+	0.220997i	0.00607307	+	0.00820197i
$727$	−38.5908			−1.43125			−0.715626	−	0.698484i	$-0.753859\pi$
$727$	−38.5908			−1.43125			−0.715626	+	0.698484i	$0.753859\pi$
$728$	0.637851	+	16.6025i	0.0236403	+	0.615328i
$729$	1.00000			0.0370370
$730$	0.00992813	+	0.0134084i	0.000367457	+	0.000496267i
$731$	−29.9190	−	51.8212i	−1.10659	−	1.91668i
$732$	−4.01643	−	1.22522i	−0.148452	−	0.0452855i
$733$	−2.88135	+	2.88135i	−0.106425	+	0.106425i	−0.758314	−	0.651889i	$-0.773977\pi$
$733$	−2.88135	+	2.88135i	−0.106425	+	0.106425i	0.651889	+	0.758314i	$0.273977\pi$
$734$	−8.37157	+	19.2696i	−0.309000	+	0.711255i
$735$	−0.0257143	+	0.00689014i	−0.000948488	+	0.000254147i
$736$	16.8292	+	26.3264i	0.620332	+	0.970403i
$737$	0.861114	−	1.49149i	0.0317196	−	0.0549399i
$738$	6.98380	+	1.04152i	0.257077	+	0.0383390i
$739$	−25.1494	−	6.73876i	−0.925136	−	0.247889i	−0.235357	−	0.971909i	$-0.575626\pi$
$739$	−25.1494	−	6.73876i	−0.925136	−	0.247889i	−0.689779	+	0.724020i	$0.742292\pi$
$740$	0.138893	−	0.0321566i	0.00510580	−	0.00118210i
$741$	2.82656	+	12.5969i	0.103836	+	0.462758i
$742$	6.70711	+	5.33168i	0.246226	+	0.195732i
$743$	21.0093	+	5.62943i	0.770756	+	0.206524i	0.622706	−	0.782456i	$-0.286033\pi$
$743$	21.0093	+	5.62943i	0.770756	+	0.206524i	0.148051	+	0.988980i	$0.452700\pi$
$744$	−0.154948	−	1.94566i	−0.00568066	−	0.0713312i
$745$	−0.0640649	−	0.0369879i	−0.00234716	−	0.00135513i
$746$	29.9586	−	3.42276i	1.09686	−	0.125316i
$747$	4.85887	−	1.30193i	0.177777	−	0.0476352i
$748$	32.7791	−	17.4551i	1.19852	−	0.638220i
$749$	−5.04617	−	5.04617i	−0.184383	−	0.184383i
$750$	0.0317763	+	0.0805956i	0.00116031	+	0.00294293i
$751$	2.57328	+	4.45706i	0.0939004	+	0.162640i	0.909149	−	0.416471i	$-0.136733\pi$
$751$	2.57328	+	4.45706i	0.0939004	+	0.162640i	−0.815249	+	0.579111i	$0.803400\pi$
$752$	−3.12300	−	15.9607i	−0.113884	−	0.582027i
$753$			7.77681i			0.283403i
$754$	7.39453	−	5.01865i	0.269293	−	0.182768i
$755$	0.0152274			0.000554182
$756$	−0.111697	+	3.25650i	−0.00406240	+	0.118438i
$757$	44.0303	−	25.4209i	1.60031	−	0.923939i	0.608885	−	0.793259i	$-0.291617\pi$
$757$	44.0303	−	25.4209i	1.60031	−	0.923939i	0.991425	−	0.130680i	$-0.0417162\pi$
$758$	14.0007	+	35.5106i	0.508530	+	1.28980i
$759$	13.0678	−	13.0678i	0.474332	−	0.474332i
$760$	0.0610122	+	0.0112493i	0.00221315	+	0.000408053i
$761$	9.04510	+	33.7568i	0.327885	+	1.22368i	0.911380	+	0.411565i	$0.135018\pi$
$761$	9.04510	+	33.7568i	0.327885	+	1.22368i	−0.583496	+	0.812116i	$0.698315\pi$
$762$	−0.613890	−	5.37323i	−0.0222389	−	0.194652i
$763$	−9.69586	+	16.7937i	−0.351014	+	0.607973i
$764$	−12.2981	+	11.4824i	−0.444930	+	0.415420i
$765$	−0.00879922	+	0.0328391i	−0.000318136	+	0.00118730i
$766$	−23.9603	−	19.0468i	−0.865721	−	0.688188i
$767$	3.20908	−	10.2696i	0.115873	−	0.370814i
$768$	−9.81928	+	12.6326i	−0.354323	+	0.455839i
$769$	11.4952	−	42.9007i	0.414528	−	1.54704i	−0.371251	−	0.928533i	$-0.621071\pi$
$769$	11.4952	−	42.9007i	0.414528	−	1.54704i	0.785779	−	0.618507i	$-0.212262\pi$
$770$	0.00696571	−	0.0467077i	0.000251027	−	0.00168323i
$771$	−13.3396	−	7.70163i	−0.480415	−	0.277368i
$772$	−4.15884	+	6.66474i	−0.149680	+	0.239869i
$773$	12.8446	+	47.9367i	0.461988	+	1.72416i	0.666687	+	0.745338i	$0.267712\pi$
$773$	12.8446	+	47.9367i	0.461988	+	1.72416i	−0.204699	+	0.978825i	$0.565621\pi$
$774$	6.07585	−	13.9853i	0.218392	−	0.502693i
$775$	2.43975	+	2.43975i	0.0876385	+	0.0876385i
$776$	−7.82235	−	11.3589i	−0.280806	−	0.407762i
$777$	−16.4180	+	9.47896i	−0.588994	+	0.340056i
$778$	29.0876	−	21.5376i	1.04284	−	0.772161i
$779$			17.8777i			0.640535i
$780$	−0.0398108	+	0.0191446i	−0.00142545	+	0.000685486i
$781$		−	7.36270i		−	0.263458i
$782$	−25.7974	−	34.8406i	−0.922513	−	1.24590i
$783$	1.51783	−	0.876322i	0.0542430	−	0.0313172i
$784$	17.3419	+	1.19105i	0.619354	+	0.0425376i
$785$	−0.100384	−	0.100384i	−0.00358285	−	0.00358285i
$786$	13.1390	+	5.70816i	0.468653	+	0.203603i
$787$	1.12108	+	4.18392i	0.0399621	+	0.149141i	0.983024	−	0.183476i	$-0.0587351\pi$
$787$	1.12108	+	4.18392i	0.0399621	+	0.149141i	−0.943062	+	0.332617i	$0.892068\pi$
$788$	16.8791	−	27.0495i	0.601293	−	0.963600i
$789$	−17.8675	−	10.3158i	−0.636101	−	0.367253i
$790$	−0.108569	−	0.0161914i	−0.00386272	−	0.000576063i
$791$	3.39317	−	12.6635i	0.120647	−	0.450261i
$792$	8.54529	+	4.06614i	0.303644	+	0.144484i
$793$	3.51270	+	6.70581i	0.124740	+	0.238130i
$794$	−6.49844	+	8.17486i	−0.230621	+	0.290115i
$795$	−0.00589607	+	0.0220044i	−0.000209112	+	0.000780416i
$796$	−17.5193	−	18.7638i	−0.620956	−	0.665066i
$797$	9.64544	−	16.7064i	0.341659	−	0.591771i	−0.643082	−	0.765797i	$-0.722345\pi$
$797$	9.64544	−	16.7064i	0.341659	−	0.591771i	0.984741	+	0.174027i	$0.0556779\pi$
$798$	−8.19658	+	0.936457i	−0.290156	+	0.0331502i
$799$	5.84012	+	21.7956i	0.206609	+	0.771074i
$800$	−1.27754	−	28.2552i	−0.0451679	−	0.998972i
$801$	−10.6069	+	10.6069i	−0.374776	+	0.374776i
$802$	−0.0694961	+	0.0274001i	−0.00245399	+	0.000967532i
$803$	−5.58010	+	3.22167i	−0.196917	+	0.113690i
$804$	0.0352904	−	1.02888i	0.00124460	−	0.0362858i
$805$	−0.0551272			−0.00194298
$806$	−2.30083	+	2.66221i	−0.0810431	+	0.0937723i
$807$		−	15.9717i		−	0.562232i
$808$	28.9715	−	33.9852i	1.01921	−	1.19559i
$809$	14.4841	+	25.0872i	0.509233	+	0.882018i	0.999943	+	0.0106948i	$0.00340432\pi$
$809$	14.4841	+	25.0872i	0.509233	+	0.882018i	−0.490709	+	0.871323i	$0.663262\pi$
$810$	−0.00805959	+	0.00317764i	−0.000283185	+	0.000111651i
$811$	35.5730	+	35.5730i	1.24914	+	1.24914i	0.956102	+	0.293033i	$0.0946647\pi$
$811$	35.5730	+	35.5730i	1.24914	+	1.24914i	0.293033	+	0.956102i	$0.405335\pi$
$812$	2.68420	+	5.04070i	0.0941970	+	0.176894i
$813$	−22.4848	+	6.02478i	−0.788576	+	0.211298i
$814$	6.24985	+	54.7035i	0.219057	+	1.91736i
$815$	−0.0460591	−	0.0265923i	−0.00161338	−	0.000931486i
$816$	12.3907	−	18.4192i	0.433762	−	0.644803i
$817$	37.2910	+	9.99209i	1.30465	+	0.349579i
$818$	8.58585	−	10.8008i	0.300197	−	0.377640i
$819$	4.32072	−	3.97963i	0.150978	−	0.139060i
$820$	−0.0595961	+	0.0137978i	−0.00208119	+	0.000481840i
$821$	12.8376	+	3.43981i	0.448034	+	0.120050i	0.475779	−	0.879565i	$-0.342166\pi$
$821$	12.8376	+	3.43981i	0.448034	+	0.120050i	−0.0277455	+	0.999615i	$0.508833\pi$
$822$	3.56707	−	23.9186i	0.124416	−	0.834256i
$823$	−11.2358	+	19.4610i	−0.391656	+	0.678367i	−0.992668	−	0.120872i	$-0.961431\pi$
$823$	−11.2358	+	19.4610i	−0.391656	+	0.678367i	0.601013	+	0.799240i	$0.294764\pi$
$824$	−13.6108	−	38.3224i	−0.474155	−	1.33502i
$825$	−16.1589	+	4.32976i	−0.562581	+	0.150743i
$826$	6.30610	+	2.73965i	0.219417	+	0.0953245i
$827$	2.97912	−	2.97912i	0.103594	−	0.103594i	−0.653410	−	0.757004i	$-0.726662\pi$
$827$	2.97912	−	2.97912i	0.103594	−	0.103594i	0.757004	+	0.653410i	$0.226662\pi$
$828$	3.22330	−	10.5664i	0.112017	−	0.367206i
$829$	7.48252	+	12.9601i	0.259879	+	0.450123i	0.966209	−	0.257759i	$-0.0829841\pi$
$829$	7.48252	+	12.9601i	0.259879	+	0.450123i	−0.706331	+	0.707882i	$0.749651\pi$
$830$	−0.0350235	+	0.0259328i	−0.00121568	+	0.000900141i
$831$	−6.02495			−0.209003
$832$	28.6443	−	3.39203i	0.993061	−	0.117597i
$833$	−24.1176			−0.835624
$834$	19.3540	−	14.3305i	0.670174	−	0.496224i
$835$	0.0737561	+	0.127749i	0.00255244	+	0.00442095i
$836$	−6.99105	+	22.9175i	−0.241791	+	0.792619i
$837$	−0.487954	+	0.487954i	−0.0168662	+	0.0168662i
$838$	12.3012	+	5.34418i	0.424938	+	0.184612i
$839$	−9.03430	+	2.42073i	−0.311899	+	0.0835730i	−0.411373	−	0.911467i	$-0.634951\pi$
$839$	−9.03430	+	2.42073i	−0.311899	+	0.0835730i	0.0994743	+	0.995040i	$0.468284\pi$
$840$	−0.00944775	−	0.0266010i	−0.000325978	−	0.000917820i
$841$	−12.9641	+	22.4545i	−0.447039	+	0.774294i
$842$	−4.61154	+	30.9221i	−0.158924	+	1.06565i
$843$	−27.8361	−	7.45865i	−0.958725	−	0.256889i
$844$	−10.6752	+	2.47154i	−0.367456	+	0.0850740i
$845$	0.0749732	+	0.0268535i	0.00257916	+	0.000923790i
$846$	−3.57805	+	4.50108i	−0.123016	+	0.154750i
$847$	0.305993	+	0.0819907i	0.0105141	+	0.00281723i
$848$	8.30262	−	12.3421i	0.285113	−	0.423830i
$849$	6.85490	+	3.95768i	0.235260	+	0.135827i
$850$	4.45447	+	38.9889i	0.152787	+	1.33731i
$851$	62.0833	−	16.6352i	2.12819	−	0.570247i
$852$	−2.06862	−	3.88470i	−0.0708699	−	0.133088i
$853$	−7.92636	−	7.92636i	−0.271393	−	0.271393i	0.558268	−	0.829661i	$-0.311466\pi$
$853$	−7.92636	−	7.92636i	−0.271393	−	0.271393i	−0.829661	+	0.558268i	$0.811466\pi$
$854$	−4.50036	+	1.77435i	−0.153999	+	0.0607171i
$855$	−0.0109673	−	0.0189960i	−0.000375075	−	0.000649649i
$856$	−8.03742	+	9.42835i	−0.274713	+	0.322254i
$857$		−	38.4399i		−	1.31308i	−0.754291	−	0.656541i	$-0.772019\pi$
$857$		−	38.4399i		−	1.31308i	0.754291	−	0.656541i	$-0.227981\pi$
$858$	−5.60064	−	16.1149i	−0.191203	−	0.550152i
$859$	1.82343			0.0622145			0.0311072	−	0.999516i	$-0.490097\pi$
$859$	1.82343			0.0622145			0.0311072	+	0.999516i	$0.490097\pi$
$860$	−0.00452837	+	0.132023i	−0.000154416	+	0.00450195i
$861$	7.04466	−	4.06724i	0.240081	−	0.138611i
$862$	51.5833	−	20.3377i	1.75693	−	0.692704i
$863$	25.6067	−	25.6067i	0.871661	−	0.871661i	−0.120993	−	0.992653i	$-0.538608\pi$
$863$	25.6067	−	25.6067i	0.871661	−	0.871661i	0.992653	+	0.120993i	$0.0386078\pi$
$864$	5.65108	−	0.255510i	0.192254	−	0.00869263i
$865$	−0.0181227	−	0.0676348i	−0.000616190	−	0.00229965i
$866$	−8.30802	+	0.949189i	−0.282318	+	0.0322548i
$867$	−6.89996	+	11.9511i	−0.234335	+	0.405880i
$868$	−1.53452	−	1.64352i	−0.0520849	−	0.0557848i
$869$	10.9722	−	40.9487i	0.372205	−	1.38909i
$870$	−0.00944848	+	0.0118859i	−0.000320334	+	0.000402971i
$871$	−1.36512	+	1.25735i	−0.0462552	+	0.0426037i
$872$	30.3995	+	14.4651i	1.02946	+	0.489850i
$873$	−1.26204	+	4.71000i	−0.0427136	+	0.159409i
$874$	27.6639	+	4.12563i	0.935745	+	0.139551i
$875$	0.0864327	+	0.0499019i	0.00292196	+	0.00168699i
$876$	−2.03900	+	3.26760i	−0.0688916	+	0.110402i
$877$	−2.98286	−	11.1322i	−0.100724	−	0.375907i	0.897101	−	0.441826i	$-0.145669\pi$
$877$	−2.98286	−	11.1322i	−0.100724	−	0.375907i	−0.997825	+	0.0659183i	$0.979002\pi$
$878$	−9.58730	−	4.16514i	−0.323556	−	0.140567i
$879$	−1.27445	−	1.27445i	−0.0429863	−	0.0429863i
$880$	−0.0817923	−	0.00561754i	−0.00275722	−	0.000189367i
$881$	11.9623	−	6.90643i	0.403020	−	0.232684i	−0.284766	−	0.958597i	$-0.591916\pi$
$881$	11.9623	−	6.90643i	0.403020	−	0.232684i	0.687786	+	0.725913i	$0.258583\pi$
$882$	−3.65715	−	4.93916i	−0.123143	−	0.166310i
$883$			46.3198i			1.55879i	0.626536	+	0.779393i	$0.284472\pi$
$883$			46.3198i			1.55879i	−0.626536	+	0.779393i	$0.715528\pi$
$884$	−39.3264	+	7.41829i	−1.32269	+	0.249504i
$885$			0.0182804i			0.000614490i
$886$	−31.1037	+	23.0305i	−1.04495	+	0.773723i
$887$	−40.2976	+	23.2659i	−1.35306	+	0.781191i	−0.988677	−	0.150058i	$-0.952054\pi$
$887$	−40.2976	+	23.2659i	−1.35306	+	0.781191i	−0.364385	+	0.931248i	$0.618721\pi$
$888$	18.6670	+	27.1066i	0.626424	+	0.909639i
$889$	−4.40552	−	4.40552i	−0.147757	−	0.147757i
$890$	0.0517822	−	0.119192i	0.00173574	−	0.00399532i
$891$	−0.865959	−	3.23180i	−0.0290107	−	0.108270i
$892$	15.1832	−	24.3318i	0.508373	−	0.814690i
$893$	−12.6078	−	7.27912i	−0.421904	−	0.243586i
$894$	2.51902	−	16.8910i	0.0842486	−	0.564919i
$895$	0.0304705	−	0.113717i	0.00101852	−	0.00380115i
$896$	0.200856	+	18.4313i	0.00671014	+	0.615745i
$897$	−17.6415	+	9.24115i	−0.589033	+	0.308553i
$898$	18.5680	+	14.7602i	0.619622	+	0.492556i
$899$	−0.313029	+	1.16824i	−0.0104401	+	0.0389629i
$900$	−7.30925	+	6.82447i	−0.243642	+	0.227482i
$901$	−10.3190	+	17.8730i	−0.343776	+	0.595437i
$902$	−2.68169	−	23.4722i	−0.0892905	−	0.781538i
$903$	−4.54647	−	16.9676i	−0.151297	−	0.564648i
$904$	−22.3830	−	4.12692i	−0.744449	−	0.137259i
$905$	−0.0429027	+	0.0429027i	−0.00142613	+	0.00142613i
$906$	1.28939	+	3.27034i	0.0428372	+	0.108650i
$907$	−23.2692	+	13.4345i	−0.772642	+	0.446085i	−0.833816	−	0.552042i	$-0.813849\pi$
$907$	−23.2692	+	13.4345i	−0.772642	+	0.446085i	0.0611745	+	0.998127i	$0.480515\pi$
$908$	−0.656836	+	19.1498i	−0.0217979	+	0.635509i
$909$	−15.7890			−0.523688
$910$	−0.0221773	+	0.0458039i	−0.000735172	+	0.00151838i
$911$			34.1859i			1.13263i	0.824189	+	0.566315i	$0.191632\pi$
$911$			34.1859i			1.13263i	−0.824189	+	0.566315i	$0.808368\pi$
$912$	2.75029	+	14.0559i	0.0910713	+	0.465438i
$913$	−8.41517	−	14.5755i	−0.278502	−	0.482379i
$914$	−14.8645	−	37.7015i	−0.491675	−	1.24706i
$915$	−0.00909473	−	0.00909473i	−0.000300662	−	0.000300662i
$916$	43.0977	−	22.9498i	1.42399	−	0.758282i
$917$	15.9408	−	4.27133i	0.526413	−	0.141052i
$918$	−7.79783	+	0.890900i	−0.257367	+	0.0294041i
$919$	−12.0258	−	6.94309i	−0.396694	−	0.229031i	0.288362	−	0.957521i	$-0.406889\pi$
$919$	−12.0258	−	6.94309i	−0.396694	−	0.229031i	−0.685057	+	0.728490i	$0.740223\pi$
$920$	0.00759768	+	0.0954030i	0.000250488	+	0.00314534i
$921$	19.9834	+	5.35454i	0.658476	+	0.176438i
$922$	−40.5200	−	32.2105i	−1.33445	−	1.06080i
$923$	−2.36648	+	7.57315i	−0.0778936	+	0.249273i
$924$	10.6211	−	2.45901i	0.349408	−	0.0808955i
$925$	−56.1986	−	15.0584i	−1.84780	−	0.495116i
$926$	19.0441	+	2.84013i	0.625828	+	0.0933323i
$927$	−7.18910	+	12.4519i	−0.236121	+	0.408974i
$928$	8.35350	−	5.33999i	0.274217	−	0.175294i
$929$	26.6246	−	7.13405i	0.873526	−	0.234061i	0.205914	−	0.978570i	$-0.433983\pi$
$929$	26.6246	−	7.13405i	0.873526	−	0.234061i	0.667612	+	0.744510i	$0.267317\pi$
$930$	0.00238216	−	0.00548325i	7.81143e−5	−	0.000179803i
$931$	11.0028	−	11.0028i	0.360601	−	0.360601i
$932$	−22.6781	−	6.91802i	−0.742846	−	0.226607i
$933$	12.8215	+	22.2075i	0.419757	+	0.727040i
$934$	21.9366	+	29.6264i	0.717788	+	0.969406i
$935$	0.113749			0.00372000
$936$	−7.48263	−	6.92895i	−0.244577	−	0.226480i
$937$	28.0766			0.917224			0.458612	−	0.888637i	$-0.348347\pi$
$937$	28.0766			0.917224			0.458612	+	0.888637i	$0.348347\pi$
$938$	−0.705748	−	0.953146i	−0.0230435	−	0.0311213i
$939$	−9.70112	−	16.8028i	−0.316584	−	0.548340i
$940$	0.0145347	−	0.0476466i	0.000474071	−	0.00155406i
$941$	−4.25969	+	4.25969i	−0.138862	+	0.138862i	−0.773121	−	0.634259i	$-0.781305\pi$
$941$	−4.25969	+	4.25969i	−0.138862	+	0.138862i	0.634259	+	0.773121i	$0.281305\pi$
$942$	13.0590	−	30.0591i	0.425485	−	0.979379i
$943$	−26.6388	+	7.13783i	−0.867477	+	0.232440i
$944$	3.87211	−	11.2909i	0.126027	−	0.367488i
$945$	−0.00499021	+	0.00864330i	−0.000162332	+	0.000281167i
$946$	−50.4593	−	7.52520i	−1.64057	−	0.244666i
$947$	6.23584	+	1.67089i	0.202637	+	0.0542965i	0.358710	−	0.933449i	$-0.383217\pi$
$947$	6.23584	+	1.67089i	0.202637	+	0.0542965i	−0.156073	+	0.987746i	$0.549883\pi$
$948$	−5.71581	−	24.6881i	−0.185641	−	0.801831i
$949$	6.77508	−	1.52023i	0.219929	−	0.0493488i
$950$	−19.8194	−	15.7551i	−0.643027	−	0.511162i
$951$	−15.3877	−	4.12313i	−0.498981	−	0.133702i
$952$	−2.03021	−	25.4931i	−0.0657996	−	0.826236i
$953$	14.7203	+	8.49878i	0.476838	+	0.275302i	0.719098	−	0.694909i	$-0.244555\pi$
$953$	14.7203	+	8.49878i	0.476838	+	0.275302i	−0.242260	+	0.970211i	$0.577889\pi$
$954$	−5.22507	+	0.596963i	−0.169168	+	0.0193274i
$955$	−0.0497794	+	0.0133383i	−0.00161082	+	0.000431618i
$956$	10.8936	+	20.4573i	0.352324	+	0.661635i
$957$	−4.14648	−	4.14648i	−0.134037	−	0.134037i
$958$	−17.4768	−	44.3270i	−0.564649	−	1.43214i
$959$	−13.9297	−	24.1270i	−0.449815	−	0.779102i
$960$	−0.0447335	+	0.0200164i	−0.00144377	+	0.000646027i
$961$			30.5238i			0.984639i
$962$	11.1540	−	58.2758i	0.359619	−	1.87889i
$963$	4.38027			0.141152
$964$	42.8432	+	1.46952i	1.37989	+	0.0473299i
$965$	−0.0208386	+	0.0120312i	−0.000670817	+	0.000387297i
$966$	−4.66793	−	11.8395i	−0.150188	−	0.380929i
$967$	14.8731	−	14.8731i	0.478288	−	0.478288i	−0.426296	−	0.904584i	$-0.640182\pi$
$967$	14.8731	−	14.8731i	0.478288	−	0.478288i	0.904584	+	0.426296i	$0.140182\pi$
$968$	0.0997206	−	0.540852i	0.00320514	−	0.0173836i
$969$	−5.14315	−	19.1945i	−0.165222	−	0.616616i
$970$	−0.00479517	−	0.0419710i	−0.000153964	−	0.00134761i
$971$	−7.95576	+	13.7798i	−0.255313	+	0.442214i	−0.964980	−	0.262322i	$-0.915512\pi$
$971$	−7.95576	+	13.7798i	−0.255313	+	0.442214i	0.709668	+	0.704536i	$0.248845\pi$
$972$	−1.36490	−	1.46186i	−0.0437793	−	0.0468892i
$973$	7.18040	−	26.7976i	0.230193	−	0.859092i
$974$	−27.5696	−	21.9159i	−0.883387	−	0.702230i
$975$	18.0124	+	0.740183i	0.576859	+	0.0237048i
$976$	3.69093	+	7.54378i	0.118144	+	0.241470i
$977$	−2.13713	+	7.97588i	−0.0683729	+	0.255171i	−0.991649	−	0.128966i	$-0.958834\pi$
$977$	−2.13713	+	7.97588i	−0.0683729	+	0.255171i	0.923276	+	0.384137i	$0.125501\pi$
$978$	1.81104	−	12.1437i	0.0579106	−	0.388312i
$979$	43.4645	+	25.0942i	1.38913	+	0.802015i
$980$	0.0451700	+	0.0281864i	0.00144290	+	0.000900383i
$981$	−3.08061	−	11.4970i	−0.0983563	−	0.367071i
$982$	20.8172	−	47.9169i	0.664303	−	1.52909i
$983$	30.1467	+	30.1467i	0.961530	+	0.961530i	0.999287	−	0.0377570i	$-0.0120213\pi$
$983$	30.1467	+	30.1467i	0.961530	+	0.961530i	−0.0377570	+	0.999287i	$0.512021\pi$
$984$	−8.00965	−	11.6309i	−0.255338	−	0.370780i
$985$	0.0845755	−	0.0488297i	0.00269480	−	0.00155584i
$986$	−11.0551	+	8.18565i	−0.352066	+	0.260684i
$987$			6.62409i			0.210847i
$988$	14.5569	−	21.3256i	0.463117	−	0.678456i
$989$			59.5551i			1.89374i
$990$	0.0172488	+	0.0232953i	0.000548203	+	0.000740373i
$991$	−2.25938	+	1.30446i	−0.0717717	+	0.0414374i	−0.535456	−	0.844563i	$-0.679860\pi$
$991$	−2.25938	+	1.30446i	−0.0717717	+	0.0414374i	0.463685	+	0.886000i	$0.346527\pi$
$992$	−2.63279	+	2.88214i	−0.0835912	+	0.0915082i
$993$	−2.27710	−	2.27710i	−0.0722615	−	0.0722615i
$994$	−4.65032	−	2.02030i	−0.147499	−	0.0640802i
$995$	−0.0203509	−	0.0759508i	−0.000645168	−	0.00240780i
$996$	−8.53514	−	5.32599i	−0.270446	−	0.168760i
$997$	21.3384	+	12.3197i	0.675794	+	0.390170i	0.798268	−	0.602302i	$-0.205750\pi$
$997$	21.3384	+	12.3197i	0.675794	+	0.390170i	−0.122475	+	0.992472i	$0.539083\pi$
$998$	−30.9110	−	4.60988i	−0.978469	−	0.145923i
$999$	3.01169	−	11.2398i	0.0952858	−	0.355611i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bt.d.115.11	yes	56
3.2	odd	2		936.2.ed.e.739.4		56
8.3	odd	2	inner	312.2.bt.d.115.5	yes	56
13.6	odd	12	inner	312.2.bt.d.19.5	✓	56
24.11	even	2		936.2.ed.e.739.10		56
39.32	even	12		936.2.ed.e.19.10		56
104.19	even	12	inner	312.2.bt.d.19.11	yes	56
312.227	odd	12		936.2.ed.e.19.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.d.19.5	✓	56	13.6	odd	12	inner
312.2.bt.d.19.11	yes	56	104.19	even	12	inner
312.2.bt.d.115.5	yes	56	8.3	odd	2	inner
312.2.bt.d.115.11	yes	56	1.1	even	1	trivial
936.2.ed.e.19.4		56	312.227	odd	12
936.2.ed.e.19.10		56	39.32	even	12
936.2.ed.e.739.4		56	3.2	odd	2
936.2.ed.e.739.10		56	24.11	even	2

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

Newform invariants

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$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	312.2.bt.d.115.11

Level	$312$
Weight	$2$
Character	312.115
Analytic conductor	$2.491$
Analytic rank	$0$
Dimension	$56$
Inner twists	$4$