LMFDB - Embedded newform 702.2.g.d.451.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(451,702)] 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("702.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,6] 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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	12.0.157365759791601.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{10} + 11x^{8} - 6x^{7} - 17x^{6} - 12x^{5} + 44x^{4} + 16x^{2} - 96x + 64 $ x^12 - 3x^11 + x^10 + 11x^8 - 6x^7 - 17x^6 - 12x^5 + 44x^4 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.5
Root			$-0.681625 - 1.23911i$ of defining polynomial
Character	$\chi$	$=$	702.451
Dual form			702.2.g.d.523.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.57078 + 2.72066i) q^{5} +4.02018 q^{7} -1.00000 q^{8} +(-1.57078 + 2.72066i) q^{10} +(1.49829 + 2.59511i) q^{11} +(2.80413 - 2.26647i) q^{13} +(2.01009 + 3.48158i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.17039 - 5.49127i) q^{17} +(-1.48533 - 2.57267i) q^{19} -3.14155 q^{20} +(-1.49829 + 2.59511i) q^{22} -3.02477 q^{23} +(-2.43467 + 4.21697i) q^{25} +(3.36488 + 1.29521i) q^{26} +(-2.01009 + 3.48158i) q^{28} +(1.89875 + 3.28873i) q^{29} +(-0.230655 - 0.399506i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.17039 - 5.49127i) q^{34} +(6.31480 + 10.9376i) q^{35} +(-4.64449 + 8.04449i) q^{37} +(1.48533 - 2.57267i) q^{38} +(-1.57078 - 2.72066i) q^{40} +7.57892 q^{41} -9.14352 q^{43} -2.99658 q^{44} +(-1.51239 - 2.61953i) q^{46} +(2.83067 - 4.90286i) q^{47} +9.16187 q^{49} -4.86934 q^{50} +(0.560753 + 3.56168i) q^{52} -8.87131 q^{53} +(-4.70695 + 8.15268i) q^{55} -4.02018 q^{56} +(-1.89875 + 3.28873i) q^{58} +(3.93589 - 6.81717i) q^{59} -10.3844 q^{61} +(0.230655 - 0.399506i) q^{62} +1.00000 q^{64} +(10.5709 + 4.06898i) q^{65} -2.58869 q^{67} +6.34077 q^{68} +(-6.31480 + 10.9376i) q^{70} +(-4.36317 - 7.55723i) q^{71} +8.41835 q^{73} -9.28897 q^{74} +2.97066 q^{76} +(6.02340 + 10.4328i) q^{77} +(-1.27731 + 2.21237i) q^{79} +(1.57078 - 2.72066i) q^{80} +(3.78946 + 6.56354i) q^{82} +(-1.60132 + 2.77357i) q^{83} +(9.95993 - 17.2511i) q^{85} +(-4.57176 - 7.91852i) q^{86} +(-1.49829 - 2.59511i) q^{88} +(-2.17120 + 3.76062i) q^{89} +(11.2731 - 9.11161i) q^{91} +(1.51239 - 2.61953i) q^{92} +5.66134 q^{94} +(4.66624 - 8.08217i) q^{95} +10.6714 q^{97} +(4.58094 + 7.93441i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} - q^{5} + 10 q^{7} - 12 q^{8} + q^{10} - 8 q^{11} + 8 q^{13} + 5 q^{14} - 6 q^{16} - 3 q^{17} - 7 q^{19} + 2 q^{20} + 8 q^{22} + 2 q^{23} - 13 q^{25} + q^{26} - 5 q^{28} - q^{29}+ \cdots + 3 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 - q^5 + 10 * q^7 - 12 * q^8 + q^10 - 8 * q^11 + 8 * q^13 + 5 * q^14 - 6 * q^16 - 3 * q^17 - 7 * q^19 + 2 * q^20 + 8 * q^22 + 2 * q^23 - 13 * q^25 + q^26 - 5 * q^28 - q^29 - 14 * q^31 + 6 * q^32 + 3 * q^34 + 5 * q^35 - 7 * q^37 + 7 * q^38 + q^40 + 18 * q^41 + 16 * q^43 + 16 * q^44 + q^46 + 13 * q^47 + 6 * q^49 - 26 * q^50 - 7 * q^52 + 12 * q^53 - 20 * q^55 - 10 * q^56 + q^58 - 4 * q^59 - 56 * q^61 + 14 * q^62 + 12 * q^64 + 7 * q^65 - 8 * q^67 + 6 * q^68 - 5 * q^70 + 13 * q^71 + 54 * q^73 - 14 * q^74 + 14 * q^76 + 4 * q^77 - 6 * q^79 - q^80 + 9 * q^82 - 30 * q^83 - 9 * q^85 + 8 * q^86 + 8 * q^88 - 3 * q^89 - 12 * q^91 - q^92 + 26 * q^94 + 21 * q^95 + 48 * q^97 + 3 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.57078	+	2.72066i	0.702472	+	1.21672i	0.967596	+	0.252503i	$0.0812537\pi$
$5$	1.57078	+	2.72066i	0.702472	+	1.21672i	−0.265124	+	0.964214i	$0.585413\pi$
$6$		0			0
$7$	4.02018			1.51949			0.759743	−	0.650223i	$-0.225325\pi$
$7$	4.02018			1.51949			0.759743	+	0.650223i	$0.225325\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.57078	+	2.72066i	−0.496723	+	0.860349i
$11$	1.49829	+	2.59511i	0.451751	+	0.782456i	0.998495	−	0.0548441i	$-0.0174662\pi$
$11$	1.49829	+	2.59511i	0.451751	+	0.782456i	−0.546744	+	0.837300i	$0.684133\pi$
$12$		0			0
$13$	2.80413	−	2.26647i	0.777725	−	0.628604i
$13$	2.80413	−	2.26647i	0.777725	−	0.628604i
$14$	2.01009	+	3.48158i	0.537220	+	0.930492i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.17039	−	5.49127i	−0.768932	−	1.33183i	−0.938143	−	0.346249i	$-0.887455\pi$
$17$	−3.17039	−	5.49127i	−0.768932	−	1.33183i	0.169211	−	0.985580i	$-0.445878\pi$
$18$		0			0
$19$	−1.48533	−	2.57267i	−0.340758	−	0.590211i	0.643815	−	0.765181i	$-0.277350\pi$
$19$	−1.48533	−	2.57267i	−0.340758	−	0.590211i	−0.984574	+	0.174970i	$0.944017\pi$
$20$	−3.14155			−0.702472
$21$		0			0
$22$	−1.49829	+	2.59511i	−0.319436	+	0.553280i
$23$	−3.02477			−0.630709			−0.315355	−	0.948974i	$-0.602123\pi$
$23$	−3.02477			−0.630709			−0.315355	+	0.948974i	$0.602123\pi$
$24$		0			0
$25$	−2.43467	+	4.21697i	−0.486934	+	0.843394i
$26$	3.36488	+	1.29521i	0.659907	+	0.254012i
$27$		0			0
$28$	−2.01009	+	3.48158i	−0.379872	+	0.657957i
$29$	1.89875	+	3.28873i	0.352588	+	0.610701i	0.986702	−	0.162539i	$-0.0519683\pi$
$29$	1.89875	+	3.28873i	0.352588	+	0.610701i	−0.634114	+	0.773240i	$0.718635\pi$
$30$		0			0
$31$	−0.230655	−	0.399506i	−0.0414269	−	0.0717534i	0.844569	−	0.535447i	$-0.179857\pi$
$31$	−0.230655	−	0.399506i	−0.0414269	−	0.0717534i	−0.885995	+	0.463694i	$0.846524\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	3.17039	−	5.49127i	0.543717	−	0.941745i
$35$	6.31480	+	10.9376i	1.06740	+	1.84879i
$36$		0			0
$37$	−4.64449	+	8.04449i	−0.763549	+	1.32251i	0.177462	+	0.984128i	$0.443211\pi$
$37$	−4.64449	+	8.04449i	−0.763549	+	1.32251i	−0.941010	+	0.338378i	$0.890122\pi$
$38$	1.48533	−	2.57267i	0.240952	−	0.417342i
$39$		0			0
$40$	−1.57078	−	2.72066i	−0.248361	−	0.430175i
$41$	7.57892			1.18363			0.591814	−	0.806075i	$-0.298412\pi$
$41$	7.57892			1.18363			0.591814	+	0.806075i	$0.298412\pi$
$42$		0			0
$43$	−9.14352			−1.39437			−0.697187	−	0.716889i	$-0.745565\pi$
$43$	−9.14352			−1.39437			−0.697187	+	0.716889i	$0.745565\pi$
$44$	−2.99658			−0.451751
$45$		0			0
$46$	−1.51239	−	2.61953i	−0.222989	−	0.386229i
$47$	2.83067	−	4.90286i	0.412895	−	0.715156i	−0.582309	−	0.812967i	$-0.697851\pi$
$47$	2.83067	−	4.90286i	0.412895	−	0.715156i	0.995205	+	0.0978112i	$0.0311841\pi$
$48$		0			0
$49$	9.16187			1.30884
$50$	−4.86934			−0.688629
$51$		0			0
$52$	0.560753	+	3.56168i	0.0777624	+	0.493916i
$53$	−8.87131			−1.21857			−0.609284	−	0.792952i	$-0.708543\pi$
$53$	−8.87131			−1.21857			−0.609284	+	0.792952i	$0.708543\pi$
$54$		0			0
$55$	−4.70695	+	8.15268i	−0.634685	+	1.09931i
$56$	−4.02018			−0.537220
$57$		0			0
$58$	−1.89875	+	3.28873i	−0.249318	+	0.431831i
$59$	3.93589	−	6.81717i	0.512410	−	0.887520i	−0.487487	−	0.873130i	$-0.662086\pi$
$59$	3.93589	−	6.81717i	0.512410	−	0.887520i	0.999896	−	0.0143894i	$-0.00458043\pi$
$60$		0			0
$61$	−10.3844			−1.32959			−0.664795	−	0.747026i	$-0.731481\pi$
$61$	−10.3844			−1.32959			−0.664795	+	0.747026i	$0.731481\pi$
$62$	0.230655	−	0.399506i	0.0292932	−	0.0507373i
$63$		0			0
$64$	1.00000			0.125000
$65$	10.5709	+	4.06898i	1.31116	+	0.504695i
$66$		0			0
$67$	−2.58869			−0.316259			−0.158129	−	0.987418i	$-0.550546\pi$
$67$	−2.58869			−0.316259			−0.158129	+	0.987418i	$0.550546\pi$
$68$	6.34077			0.768932
$69$		0			0
$70$	−6.31480	+	10.9376i	−0.754763	+	1.30729i
$71$	−4.36317	−	7.55723i	−0.517813	−	0.896878i	−0.999786	−	0.0206923i	$-0.993413\pi$
$71$	−4.36317	−	7.55723i	−0.517813	−	0.896878i	0.481973	−	0.876186i	$-0.339920\pi$
$72$		0			0
$73$	8.41835			0.985294			0.492647	−	0.870229i	$-0.336029\pi$
$73$	8.41835			0.985294			0.492647	+	0.870229i	$0.336029\pi$
$74$	−9.28897			−1.07982
$75$		0			0
$76$	2.97066			0.340758
$77$	6.02340	+	10.4328i	0.686430	+	1.18893i
$78$		0			0
$79$	−1.27731	+	2.21237i	−0.143709	+	0.248911i	−0.928890	−	0.370355i	$-0.879236\pi$
$79$	−1.27731	+	2.21237i	−0.143709	+	0.248911i	0.785182	+	0.619265i	$0.212569\pi$
$80$	1.57078	−	2.72066i	0.175618	−	0.304179i
$81$		0			0
$82$	3.78946	+	6.56354i	0.418476	+	0.724821i
$83$	−1.60132	+	2.77357i	−0.175768	+	0.304439i	−0.940427	−	0.339996i	$-0.889574\pi$
$83$	−1.60132	+	2.77357i	−0.175768	+	0.304439i	0.764659	+	0.644435i	$0.222908\pi$
$84$		0			0
$85$	9.95993	−	17.2511i	1.08031	−	1.87115i
$86$	−4.57176	−	7.91852i	−0.492986	−	0.853876i
$87$		0			0
$88$	−1.49829	−	2.59511i	−0.159718	−	0.276640i
$89$	−2.17120	+	3.76062i	−0.230146	+	0.398625i	−0.957851	−	0.287265i	$-0.907254\pi$
$89$	−2.17120	+	3.76062i	−0.230146	+	0.398625i	0.727705	+	0.685891i	$0.240587\pi$
$90$		0			0
$91$	11.2731	−	9.11161i	1.18174	−	0.955156i
$92$	1.51239	−	2.61953i	0.157677	−	0.273105i
$93$		0			0
$94$	5.66134			0.583922
$95$	4.66624	−	8.08217i	0.478746	−	0.829213i
$96$		0			0
$97$	10.6714			1.08352			0.541759	−	0.840534i	$-0.317758\pi$
$97$	10.6714			1.08352			0.541759	+	0.840534i	$0.317758\pi$
$98$	4.58094	+	7.93441i	0.462744	+	0.801497i
$99$		0			0
$100$	−2.43467	−	4.21697i	−0.243467	−	0.421697i
$101$	−3.54741	−	6.14429i	−0.352980	−	0.611380i	0.633790	−	0.773505i	$-0.281498\pi$
$101$	−3.54741	−	6.14429i	−0.352980	−	0.611380i	−0.986770	+	0.162125i	$0.948165\pi$
$102$		0			0
$103$	−7.15427	−	12.3916i	−0.704931	−	1.22098i	−0.966716	−	0.255850i	$-0.917645\pi$
$103$	−7.15427	−	12.3916i	−0.704931	−	1.22098i	0.261785	−	0.965126i	$-0.415689\pi$
$104$	−2.80413	+	2.26647i	−0.274967	+	0.222245i
$105$		0			0
$106$	−4.43566	−	7.68278i	−0.430829	−	0.746218i
$107$	−1.33003	+	2.30368i	−0.128579	+	0.222705i	−0.923126	−	0.384497i	$-0.874375\pi$
$107$	−1.33003	+	2.30368i	−0.128579	+	0.222705i	0.794547	+	0.607202i	$0.207708\pi$
$108$		0			0
$109$	−3.36602			−0.322407			−0.161203	−	0.986921i	$-0.551537\pi$
$109$	−3.36602			−0.322407			−0.161203	+	0.986921i	$0.551537\pi$
$110$	−9.41390			−0.897580
$111$		0			0
$112$	−2.01009	−	3.48158i	−0.189936	−	0.328978i
$113$	−1.93078	+	3.34421i	−0.181633	+	0.314597i	−0.942437	−	0.334385i	$-0.891472\pi$
$113$	−1.93078	+	3.34421i	−0.181633	+	0.314597i	0.760804	+	0.648982i	$0.224805\pi$
$114$		0			0
$115$	−4.75124	−	8.22939i	−0.443055	−	0.767395i
$116$	−3.79749			−0.352588
$117$		0			0
$118$	7.87179			0.724657
$119$	−12.7455	−	22.0759i	−1.16838	−	2.02370i
$120$		0			0
$121$	1.01026	−	1.74982i	0.0918419	−	0.159075i
$122$	−5.19221	−	8.99317i	−0.470081	−	0.814204i
$123$		0			0
$124$	0.461310			0.0414269
$125$	0.410478			0.0367143
$126$		0			0
$127$	0.546824	−	0.947126i	0.0485228	−	0.0840439i	−0.840744	−	0.541433i	$-0.817882\pi$
$127$	0.546824	−	0.947126i	0.0485228	−	0.0840439i	0.889267	+	0.457389i	$0.151215\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	1.76163	+	11.1892i	0.154505	+	0.981357i
$131$	−1.20573	−	2.08838i	−0.105345	−	0.182462i	0.808534	−	0.588449i	$-0.200261\pi$
$131$	−1.20573	−	2.08838i	−0.105345	−	0.182462i	−0.913879	+	0.405987i	$0.866928\pi$
$132$		0			0
$133$	−5.97130	−	10.3426i	−0.517778	−	0.896817i
$134$	−1.29434	−	2.24187i	−0.111814	−	0.193668i
$135$		0			0
$136$	3.17039	+	5.49127i	0.271858	+	0.470873i
$137$	13.2290			1.13023			0.565114	−	0.825013i	$-0.308832\pi$
$137$	13.2290			1.13023			0.565114	+	0.825013i	$0.308832\pi$
$138$		0			0
$139$	−0.873653	+	1.51321i	−0.0741023	+	0.128349i	−0.900696	−	0.434451i	$-0.856942\pi$
$139$	−0.873653	+	1.51321i	−0.0741023	+	0.128349i	0.826593	+	0.562800i	$0.190276\pi$
$140$	−12.6296			−1.06740
$141$		0			0
$142$	4.36317	−	7.55723i	0.366149	−	0.634189i
$143$	10.0831	+	3.88121i	0.843193	+	0.324563i
$144$		0			0
$145$	−5.96501	+	10.3317i	−0.495367	+	0.858001i
$146$	4.20918	+	7.29051i	0.348354	+	0.603367i
$147$		0			0
$148$	−4.64449	−	8.04449i	−0.381774	−	0.661253i
$149$	−6.06449	+	10.5040i	−0.496822	+	0.860521i	−0.999993	−	0.00366565i	$-0.998833\pi$
$149$	−6.06449	+	10.5040i	−0.496822	+	0.860521i	0.503171	+	0.864187i	$0.332167\pi$
$150$		0			0
$151$	2.86476	−	4.96191i	0.233131	−	0.403795i	−0.725597	−	0.688120i	$-0.758436\pi$
$151$	2.86476	−	4.96191i	0.233131	−	0.403795i	0.958728	+	0.284325i	$0.0917696\pi$
$152$	1.48533	+	2.57267i	0.120476	+	0.208671i
$153$		0			0
$154$	−6.02340	+	10.4328i	−0.485379	+	0.840701i
$155$	0.724614	−	1.25507i	0.0582024	−	0.100810i
$156$		0			0
$157$	10.3752	+	17.9704i	0.828034	+	1.43420i	0.899578	+	0.436760i	$0.143874\pi$
$157$	10.3752	+	17.9704i	0.828034	+	1.43420i	−0.0715438	+	0.997437i	$0.522793\pi$
$158$	−2.55462			−0.203235
$159$		0			0
$160$	3.14155			0.248361
$161$	−12.1601			−0.958354
$162$		0			0
$163$	−4.68645	−	8.11717i	−0.367071	−	0.635786i	0.622035	−	0.782989i	$-0.286306\pi$
$163$	−4.68645	−	8.11717i	−0.367071	−	0.635786i	−0.989106	+	0.147204i	$0.952973\pi$
$164$	−3.78946	+	6.56354i	−0.295907	+	0.512526i
$165$		0			0
$166$	−3.20265			−0.248574
$167$	3.48176			0.269427			0.134713	−	0.990885i	$-0.456989\pi$
$167$	3.48176			0.269427			0.134713	+	0.990885i	$0.456989\pi$
$168$		0			0
$169$	2.72627	−	12.7109i	0.209713	−	0.977763i
$170$	19.9199			1.52778
$171$		0			0
$172$	4.57176	−	7.91852i	0.348594	−	0.603782i
$173$	−18.1300			−1.37840			−0.689199	−	0.724572i	$-0.742038\pi$
$173$	−18.1300			−1.37840			−0.689199	+	0.724572i	$0.742038\pi$
$174$		0			0
$175$	−9.78782	+	16.9530i	−0.739889	+	1.28153i
$176$	1.49829	−	2.59511i	0.112938	−	0.195614i
$177$		0			0
$178$	−4.34239			−0.325476
$179$	12.9184	−	22.3753i	0.965565	−	1.67241i	0.257474	−	0.966285i	$-0.417110\pi$
$179$	12.9184	−	22.3753i	0.965565	−	1.67241i	0.708090	−	0.706122i	$-0.249557\pi$
$180$		0			0
$181$	15.0772			1.12068			0.560339	−	0.828264i	$-0.310671\pi$
$181$	15.0772			1.12068			0.560339	+	0.828264i	$0.310671\pi$
$182$	13.5274	+	5.20699i	1.00272	+	0.385968i
$183$		0			0
$184$	3.02477			0.222989
$185$	−29.1818			−2.14549
$186$		0			0
$187$	9.50031	−	16.4550i	0.694732	−	1.20331i
$188$	2.83067	+	4.90286i	0.206448	+	0.357578i
$189$		0			0
$190$	9.33248			0.677050
$191$	13.2688			0.960098			0.480049	−	0.877242i	$-0.340619\pi$
$191$	13.2688			0.960098			0.480049	+	0.877242i	$0.340619\pi$
$192$		0			0
$193$	−2.70649			−0.194818			−0.0974089	−	0.995244i	$-0.531055\pi$
$193$	−2.70649			−0.194818			−0.0974089	+	0.995244i	$0.531055\pi$
$194$	5.33571	+	9.24172i	0.383082	+	0.663517i
$195$		0			0
$196$	−4.58094	+	7.93441i	−0.327210	+	0.566744i
$197$	−5.03966	+	8.72894i	−0.359061	+	0.621911i	−0.987804	−	0.155701i	$-0.950236\pi$
$197$	−5.03966	+	8.72894i	−0.359061	+	0.621911i	0.628743	+	0.777613i	$0.283570\pi$
$198$		0			0
$199$	−3.83413	−	6.64091i	−0.271795	−	0.470762i	0.697527	−	0.716559i	$-0.254284\pi$
$199$	−3.83413	−	6.64091i	−0.271795	−	0.470762i	−0.969321	+	0.245797i	$0.920950\pi$
$200$	2.43467	−	4.21697i	0.172157	−	0.298185i
$201$		0			0
$202$	3.54741	−	6.14429i	0.249595	−	0.432311i
$203$	7.63331	+	13.2213i	0.535753	+	0.927952i
$204$		0			0
$205$	11.9048	+	20.6197i	0.831466	+	1.44014i
$206$	7.15427	−	12.3916i	0.498462	−	0.863361i
$207$		0			0
$208$	−3.36488	−	1.29521i	−0.233313	−	0.0898069i
$209$	4.45091	−	7.70920i	0.307876	−	0.533257i
$210$		0			0
$211$	25.5744			1.76061			0.880306	−	0.474407i	$-0.157338\pi$
$211$	25.5744			1.76061			0.880306	+	0.474407i	$0.157338\pi$
$212$	4.43566	−	7.68278i	0.304642	−	0.527656i
$213$		0			0
$214$	−2.66006			−0.181838
$215$	−14.3624	−	24.8764i	−0.979509	−	1.69656i
$216$		0			0
$217$	−0.927276	−	1.60609i	−0.0629476	−	0.109028i
$218$	−1.68301	−	2.91506i	−0.113988	−	0.197433i
$219$		0			0
$220$	−4.70695	−	8.15268i	−0.317343	−	0.549653i
$221$	−21.3359	−	8.21265i	−1.43521	−	0.552443i
$222$		0			0
$223$	−4.19073	−	7.25855i	−0.280632	−	0.486068i	0.690909	−	0.722942i	$-0.257211\pi$
$223$	−4.19073	−	7.25855i	−0.280632	−	0.486068i	−0.971540	+	0.236874i	$0.923877\pi$
$224$	2.01009	−	3.48158i	0.134305	−	0.232623i
$225$		0			0
$226$	−3.86156			−0.256867
$227$	12.1487			0.806336			0.403168	−	0.915126i	$-0.367909\pi$
$227$	12.1487			0.806336			0.403168	+	0.915126i	$0.367909\pi$
$228$		0			0
$229$	14.6317	+	25.3428i	0.966889	+	1.67470i	0.704452	+	0.709752i	$0.251193\pi$
$229$	14.6317	+	25.3428i	0.966889	+	1.67470i	0.262437	+	0.964949i	$0.415474\pi$
$230$	4.75124	−	8.22939i	0.313288	−	0.542630i
$231$		0			0
$232$	−1.89875	−	3.28873i	−0.124659	−	0.215915i
$233$	−7.95483			−0.521139			−0.260569	−	0.965455i	$-0.583910\pi$
$233$	−7.95483			−0.521139			−0.260569	+	0.965455i	$0.583910\pi$
$234$		0			0
$235$	17.7854			1.16019
$236$	3.93589	+	6.81717i	0.256205	+	0.443760i
$237$		0			0
$238$	12.7455	−	22.0759i	0.826170	−	1.43097i
$239$	5.97440	+	10.3480i	0.386452	+	0.669354i	0.991969	−	0.126478i	$-0.0403673\pi$
$239$	5.97440	+	10.3480i	0.386452	+	0.669354i	−0.605518	+	0.795832i	$0.707034\pi$
$240$		0			0
$241$	−22.8116			−1.46942			−0.734711	−	0.678381i	$-0.762682\pi$
$241$	−22.8116			−1.46942			−0.734711	+	0.678381i	$0.762682\pi$
$242$	2.02052			0.129884
$243$		0			0
$244$	5.19221	−	8.99317i	0.332397	−	0.575729i
$245$	14.3912	+	24.9264i	0.919423	+	1.59249i
$246$		0			0
$247$	−9.99592	−	3.84764i	−0.636025	−	0.244819i
$248$	0.230655	+	0.399506i	0.0146466	+	0.0253687i
$249$		0			0
$250$	0.205239	+	0.355485i	0.0129805	+	0.0224828i
$251$	10.4930	+	18.1744i	0.662310	+	1.14716i	0.980007	+	0.198963i	$0.0637573\pi$
$251$	10.4930	+	18.1744i	0.662310	+	1.14716i	−0.317697	+	0.948192i	$0.602909\pi$
$252$		0			0
$253$	−4.53199	−	7.84963i	−0.284923	−	0.493502i
$254$	1.09365			0.0686215
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.975729			−0.0608643			−0.0304322	−	0.999537i	$-0.509688\pi$
$257$	−0.975729			−0.0608643			−0.0304322	+	0.999537i	$0.509688\pi$
$258$		0			0
$259$	−18.6717	+	32.3403i	−1.16020	+	2.00953i
$260$	−8.80931	+	7.12022i	−0.546330	+	0.441577i
$261$		0			0
$262$	1.20573	−	2.08838i	0.0744900	−	0.129020i
$263$	−7.28367	−	12.6157i	−0.449130	−	0.777917i	0.549199	−	0.835691i	$-0.314933\pi$
$263$	−7.28367	−	12.6157i	−0.449130	−	0.777917i	−0.998330	+	0.0577747i	$0.981599\pi$
$264$		0			0
$265$	−13.9348	−	24.1358i	−0.856010	−	1.48265i
$266$	5.97130	−	10.3426i	0.366124	−	0.634145i
$267$		0			0
$268$	1.29434	−	2.24187i	0.0790646	−	0.136944i
$269$	4.42368	+	7.66203i	0.269716	+	0.467162i	0.968789	−	0.247889i	$-0.0797367\pi$
$269$	4.42368	+	7.66203i	0.269716	+	0.467162i	−0.699072	+	0.715051i	$0.746403\pi$
$270$		0			0
$271$	−8.99631	+	15.5821i	−0.546487	+	0.946544i	0.452025	+	0.892006i	$0.350702\pi$
$271$	−8.99631	+	15.5821i	−0.546487	+	0.946544i	−0.998512	+	0.0545380i	$0.982631\pi$
$272$	−3.17039	+	5.49127i	−0.192233	+	0.332957i
$273$		0			0
$274$	6.61449	+	11.4566i	0.399596	+	0.692121i
$275$	−14.5914			−0.879892
$276$		0			0
$277$	12.6936			0.762682			0.381341	−	0.924435i	$-0.375462\pi$
$277$	12.6936			0.762682			0.381341	+	0.924435i	$0.375462\pi$
$278$	−1.74731			−0.104796
$279$		0			0
$280$	−6.31480	−	10.9376i	−0.377382	−	0.653644i
$281$	−4.31980	+	7.48212i	−0.257698	+	0.446346i	−0.965625	−	0.259940i	$-0.916297\pi$
$281$	−4.31980	+	7.48212i	−0.257698	+	0.446346i	0.707927	+	0.706286i	$0.249631\pi$
$282$		0			0
$283$	−25.0134			−1.48689			−0.743447	−	0.668795i	$-0.766810\pi$
$283$	−25.0134			−1.48689			−0.743447	+	0.668795i	$0.766810\pi$
$284$	8.72634			0.517813
$285$		0			0
$286$	1.68034	+	10.6728i	0.0993606	+	0.631099i
$287$	30.4686			1.79851
$288$		0			0
$289$	−11.6027	+	20.0965i	−0.682512	+	1.18215i
$290$	−11.9300			−0.700555
$291$		0			0
$292$	−4.20918	+	7.29051i	−0.246323	+	0.426645i
$293$	0.226316	−	0.391990i	0.0132215	−	0.0229003i	−0.859339	−	0.511406i	$-0.829125\pi$
$293$	0.226316	−	0.391990i	0.0132215	−	0.0229003i	0.872560	+	0.488506i	$0.162458\pi$
$294$		0			0
$295$	24.7296			1.43981
$296$	4.64449	−	8.04449i	0.269955	−	0.467576i
$297$		0			0
$298$	−12.1290			−0.702613
$299$	−8.48185	+	6.85555i	−0.490518	+	0.396467i
$300$		0			0
$301$	−36.7586			−2.11873
$302$	5.72952			0.329697
$303$		0			0
$304$	−1.48533	+	2.57267i	−0.0851896	+	0.147553i
$305$	−16.3116	−	28.2525i	−0.933999	−	1.61773i
$306$		0			0
$307$	−19.2631			−1.09940			−0.549701	−	0.835362i	$-0.685258\pi$
$307$	−19.2631			−1.09940			−0.549701	+	0.835362i	$0.685258\pi$
$308$	−12.0468			−0.686430
$309$		0			0
$310$	1.44923			0.0823107
$311$	−0.687943	−	1.19155i	−0.0390097	−	0.0675667i	0.845861	−	0.533403i	$-0.179087\pi$
$311$	−0.687943	−	1.19155i	−0.0390097	−	0.0675667i	−0.884871	+	0.465836i	$0.845754\pi$
$312$		0			0
$313$	−1.64786	+	2.85418i	−0.0931426	+	0.161328i	−0.908832	−	0.417163i	$-0.863025\pi$
$313$	−1.64786	+	2.85418i	−0.0931426	+	0.161328i	0.815689	+	0.578490i	$0.196358\pi$
$314$	−10.3752	+	17.9704i	−0.585509	+	1.01413i
$315$		0			0
$316$	−1.27731	−	2.21237i	−0.0718543	−	0.124455i
$317$	3.48925	−	6.04356i	0.195976	−	0.339440i	−0.751244	−	0.660025i	$-0.770546\pi$
$317$	3.48925	−	6.04356i	0.195976	−	0.339440i	0.947220	+	0.320584i	$0.103879\pi$
$318$		0			0
$319$	−5.68974	+	9.85492i	−0.318564	+	0.551770i
$320$	1.57078	+	2.72066i	0.0878090	+	0.152090i
$321$		0			0
$322$	−6.08007	−	10.5310i	−0.338829	−	0.586869i
$323$	−9.41815	+	16.3127i	−0.524040	+	0.907663i
$324$		0			0
$325$	2.73050	+	17.3430i	0.151461	+	0.962018i
$326$	4.68645	−	8.11717i	0.259558	−	0.449568i
$327$		0			0
$328$	−7.57892			−0.418476
$329$	11.3798	−	19.7104i	0.627389	−	1.08667i
$330$		0			0
$331$	22.0265			1.21069			0.605344	−	0.795964i	$-0.293035\pi$
$331$	22.0265			1.21069			0.605344	+	0.795964i	$0.293035\pi$
$332$	−1.60132	−	2.77357i	−0.0878840	−	0.152220i
$333$		0			0
$334$	1.74088	+	3.01529i	0.0952567	+	0.164989i
$335$	−4.06625	−	7.04295i	−0.222163	−	0.384797i
$336$		0			0
$337$	9.24184	+	16.0073i	0.503435	+	0.871975i	0.999992	+	0.00397115i	$0.00126406\pi$
$337$	9.24184	+	16.0073i	0.503435	+	0.871975i	−0.496557	+	0.868004i	$0.665403\pi$
$338$	12.3711	−	3.99444i	0.672900	−	0.217269i
$339$		0			0
$340$	9.95993	+	17.2511i	0.540153	+	0.935573i
$341$	0.691176	−	1.19715i	0.0374293	−	0.0648294i
$342$		0			0
$343$	8.69112			0.469276
$344$	9.14352			0.492986
$345$		0			0
$346$	−9.06500	−	15.7010i	−0.487338	−	0.844093i
$347$	0.691691	−	1.19804i	0.0371319	−	0.0643144i	−0.846862	−	0.531812i	$-0.821511\pi$
$347$	0.691691	−	1.19804i	0.0371319	−	0.0643144i	0.883994	+	0.467498i	$0.154844\pi$
$348$		0			0
$349$	9.17110	+	15.8848i	0.490918	+	0.850294i	0.999945	−	0.0104557i	$-0.00332822\pi$
$349$	9.17110	+	15.8848i	0.490918	+	0.850294i	−0.509028	+	0.860750i	$0.669995\pi$
$350$	−19.5756			−1.04636
$351$		0			0
$352$	2.99658			0.159718
$353$	12.6367	+	21.8874i	0.672585	+	1.16495i	0.977169	+	0.212465i	$0.0681493\pi$
$353$	12.6367	+	21.8874i	0.672585	+	1.16495i	−0.304584	+	0.952486i	$0.598517\pi$
$354$		0			0
$355$	13.7071	−	23.7414i	0.727498	−	1.26006i
$356$	−2.17120	−	3.76062i	−0.115073	−	0.199313i
$357$		0			0
$358$	25.8367			1.36551
$359$	−23.0239			−1.21516			−0.607579	−	0.794260i	$-0.707859\pi$
$359$	−23.0239			−1.21516			−0.607579	+	0.794260i	$0.707859\pi$
$360$		0			0
$361$	5.08758	−	8.81195i	0.267768	−	0.463787i
$362$	7.53859	+	13.0572i	0.396219	+	0.686272i
$363$		0			0
$364$	2.25433	+	14.3186i	0.118159	+	0.750499i
$365$	13.2233	+	22.9035i	0.692141	+	1.19882i
$366$		0			0
$367$	−14.3965	−	24.9355i	−0.751491	−	1.30162i	−0.947100	−	0.320938i	$-0.896002\pi$
$367$	−14.3965	−	24.9355i	−0.751491	−	1.30162i	0.195609	−	0.980682i	$-0.437332\pi$
$368$	1.51239	+	2.61953i	0.0788386	+	0.136553i
$369$		0			0
$370$	−14.5909	−	25.2722i	−0.758544	−	1.31384i
$371$	−35.6643			−1.85160
$372$		0			0
$373$	2.01216	−	3.48517i	0.104186	−	0.180455i	−0.809219	−	0.587506i	$-0.800110\pi$
$373$	2.01216	−	3.48517i	0.104186	−	0.180455i	0.913405	+	0.407051i	$0.133443\pi$
$374$	19.0006			0.982499
$375$		0			0
$376$	−2.83067	+	4.90286i	−0.145981	+	0.252846i
$377$	12.7781	+	4.91856i	0.658106	+	0.253319i
$378$		0			0
$379$	4.44801	−	7.70419i	0.228479	−	0.395737i	−0.728878	−	0.684643i	$-0.759958\pi$
$379$	4.44801	−	7.70419i	0.228479	−	0.395737i	0.957358	+	0.288906i	$0.0932914\pi$
$380$	4.66624	+	8.08217i	0.239373	+	0.414606i
$381$		0			0
$382$	6.63441	+	11.4911i	0.339446	+	0.587937i
$383$	−5.70111	+	9.87461i	−0.291313	+	0.504569i	−0.974120	−	0.226029i	$-0.927425\pi$
$383$	−5.70111	+	9.87461i	−0.291313	+	0.504569i	0.682807	+	0.730598i	$0.260759\pi$
$384$		0			0
$385$	−18.9228	+	32.7753i	−0.964395	+	1.67038i
$386$	−1.35325	−	2.34389i	−0.0688785	−	0.119301i
$387$		0			0
$388$	−5.33571	+	9.24172i	−0.270880	+	0.469177i
$389$	−10.8697	+	18.8269i	−0.551118	+	0.954564i	0.447076	+	0.894496i	$0.352465\pi$
$389$	−10.8697	+	18.8269i	−0.551118	+	0.954564i	−0.998194	+	0.0600684i	$0.980868\pi$
$390$		0			0
$391$	9.58970	+	16.6099i	0.484972	+	0.839996i
$392$	−9.16187			−0.462744
$393$		0			0
$394$	−10.0793			−0.507788
$395$	−8.02547			−0.403805
$396$		0			0
$397$	−18.5668	−	32.1586i	−0.931839	−	1.61399i	−0.780176	−	0.625560i	$-0.784870\pi$
$397$	−18.5668	−	32.1586i	−0.931839	−	1.61399i	−0.151663	−	0.988432i	$-0.548463\pi$
$398$	3.83413	−	6.64091i	0.192188	−	0.332879i
$399$		0			0
$400$	4.86934			0.243467
$401$	−11.0795			−0.553282			−0.276641	−	0.960973i	$-0.589221\pi$
$401$	−11.0795			−0.553282			−0.276641	+	0.960973i	$0.589221\pi$
$402$		0			0
$403$	−1.55225	−	0.597495i	−0.0773233	−	0.0297633i
$404$	7.09482			0.352980
$405$		0			0
$406$	−7.63331	+	13.2213i	−0.378835	+	0.656161i
$407$	−27.8351			−1.37974
$408$		0			0
$409$	7.31902	−	12.6769i	0.361902	−	0.626833i	−0.626372	−	0.779525i	$-0.715461\pi$
$409$	7.31902	−	12.6769i	0.361902	−	0.626833i	0.988274	+	0.152692i	$0.0487941\pi$
$410$	−11.9048	+	20.6197i	−0.587935	+	1.01833i
$411$		0			0
$412$	14.3085			0.704931
$413$	15.8230	−	27.4063i	0.778600	−	1.34857i
$414$		0			0
$415$	−10.0613			−0.493888
$416$	−0.560753	−	3.56168i	−0.0274932	−	0.174626i
$417$		0			0
$418$	8.90182			0.435402
$419$	31.5703			1.54231			0.771155	−	0.636647i	$-0.219679\pi$
$419$	31.5703			1.54231			0.771155	+	0.636647i	$0.219679\pi$
$420$		0			0
$421$	−5.65501	+	9.79476i	−0.275608	+	0.477367i	−0.970288	−	0.241951i	$-0.922213\pi$
$421$	−5.65501	+	9.79476i	−0.275608	+	0.477367i	0.694680	+	0.719319i	$0.255546\pi$
$422$	12.7872	+	22.1480i	0.622470	+	1.07815i
$423$		0			0
$424$	8.87131			0.430829
$425$	30.8754			1.49768
$426$		0			0
$427$	−41.7473			−2.02029
$428$	−1.33003	−	2.30368i	−0.0642894	−	0.111352i
$429$		0			0
$430$	14.3624	−	24.8764i	0.692617	−	1.19965i
$431$	−10.7106	+	18.5512i	−0.515910	+	0.893582i	0.483920	+	0.875112i	$0.339213\pi$
$431$	−10.7106	+	18.5512i	−0.515910	+	0.893582i	−0.999829	+	0.0184695i	$0.994121\pi$
$432$		0			0
$433$	−6.26037	−	10.8433i	−0.300854	−	0.521095i	0.675475	−	0.737383i	$-0.263938\pi$
$433$	−6.26037	−	10.8433i	−0.300854	−	0.521095i	−0.976330	+	0.216288i	$0.930605\pi$
$434$	0.927276	−	1.60609i	0.0445107	−	0.0770947i
$435$		0			0
$436$	1.68301	−	2.91506i	0.0806017	−	0.139606i
$437$	4.49279	+	7.78174i	0.214919	+	0.372251i
$438$		0			0
$439$	−1.26334	−	2.18817i	−0.0602961	−	0.104436i	0.834302	−	0.551308i	$-0.185871\pi$
$439$	−1.26334	−	2.18817i	−0.0602961	−	0.104436i	−0.894598	+	0.446872i	$0.852538\pi$
$440$	4.70695	−	8.15268i	0.224395	−	0.388664i
$441$		0			0
$442$	−3.55561	−	22.5838i	−0.169123	−	1.07420i
$443$	−1.18489	+	2.05229i	−0.0562958	+	0.0975071i	−0.892800	−	0.450454i	$-0.851262\pi$
$443$	−1.18489	+	2.05229i	−0.0562958	+	0.0975071i	0.836504	+	0.547961i	$0.184596\pi$
$444$		0			0
$445$	−13.6418			−0.646685
$446$	4.19073	−	7.25855i	0.198437	−	0.343702i
$447$		0			0
$448$	4.02018			0.189936
$449$	−7.28629	−	12.6202i	−0.343861	−	0.595585i	0.641285	−	0.767303i	$-0.278402\pi$
$449$	−7.28629	−	12.6202i	−0.343861	−	0.595585i	−0.985146	+	0.171718i	$0.945068\pi$
$450$		0			0
$451$	11.3554	+	19.6681i	0.534705	+	0.926137i
$452$	−1.93078	−	3.34421i	−0.0908164	−	0.157299i
$453$		0			0
$454$	6.07434	+	10.5211i	0.285083	+	0.493778i
$455$	42.4971	+	16.3580i	1.99230	+	0.766876i
$456$		0			0
$457$	11.2003	+	19.3994i	0.523926	+	0.907466i	0.999612	+	0.0278511i	$0.00886643\pi$
$457$	11.2003	+	19.3994i	0.523926	+	0.907466i	−0.475686	+	0.879615i	$0.657800\pi$
$458$	−14.6317	+	25.3428i	−0.683694	+	1.18419i
$459$		0			0
$460$	9.50248			0.443055
$461$	−11.8483			−0.551833			−0.275916	−	0.961182i	$-0.588981\pi$
$461$	−11.8483			−0.551833			−0.275916	+	0.961182i	$0.588981\pi$
$462$		0			0
$463$	4.25273	+	7.36594i	0.197641	+	0.342324i	0.947763	−	0.318975i	$-0.103339\pi$
$463$	4.25273	+	7.36594i	0.197641	+	0.342324i	−0.750122	+	0.661299i	$0.770005\pi$
$464$	1.89875	−	3.28873i	0.0881471	−	0.152675i
$465$		0			0
$466$	−3.97742	−	6.88909i	−0.184250	−	0.319131i
$467$	−5.05659			−0.233991			−0.116996	−	0.993132i	$-0.537326\pi$
$467$	−5.05659			−0.233991			−0.116996	+	0.993132i	$0.537326\pi$
$468$		0			0
$469$	−10.4070			−0.480551
$470$	8.89269	+	15.4026i	0.410189	+	0.710468i
$471$		0			0
$472$	−3.93589	+	6.81717i	−0.181164	+	0.313786i
$473$	−13.6996	−	23.7285i	−0.629910	−	1.09104i
$474$		0			0
$475$	14.4652			0.663707
$476$	25.4911			1.16838
$477$		0			0
$478$	−5.97440	+	10.3480i	−0.273262	+	0.473305i
$479$	13.8291	+	23.9527i	0.631869	+	1.09443i	0.987169	+	0.159676i	$0.0510451\pi$
$479$	13.8291	+	23.9527i	0.631869	+	1.09443i	−0.355301	+	0.934752i	$0.615622\pi$
$480$		0			0
$481$	5.20882	+	33.0843i	0.237502	+	1.50852i
$482$	−11.4058	−	19.7554i	−0.519519	−	0.899833i
$483$		0			0
$484$	1.01026	+	1.74982i	0.0459209	+	0.0795374i
$485$	16.7624	+	29.0333i	0.761142	+	1.31834i
$486$		0			0
$487$	7.82813	+	13.5587i	0.354726	+	0.614404i	0.987071	−	0.160283i	$-0.0512407\pi$
$487$	7.82813	+	13.5587i	0.354726	+	0.614404i	−0.632345	+	0.774687i	$0.717907\pi$
$488$	10.3844			0.470081
$489$		0			0
$490$	−14.3912	+	24.9264i	−0.650130	+	1.12606i
$491$	−23.3362			−1.05315			−0.526575	−	0.850129i	$-0.676524\pi$
$491$	−23.3362			−1.05315			−0.526575	+	0.850129i	$0.676524\pi$
$492$		0			0
$493$	12.0395	−	20.8531i	0.542233	−	0.939175i
$494$	−1.66581	−	10.5805i	−0.0749482	−	0.476041i
$495$		0			0
$496$	−0.230655	+	0.399506i	−0.0103567	+	0.0179384i
$497$	−17.5407	−	30.3815i	−0.786810	−	1.36279i
$498$		0			0
$499$	−6.18709	−	10.7164i	−0.276972	−	0.479730i	0.693659	−	0.720304i	$-0.255998\pi$
$499$	−6.18709	−	10.7164i	−0.276972	−	0.479730i	−0.970631	+	0.240574i	$0.922664\pi$
$500$	−0.205239	+	0.355485i	−0.00917858	+	0.0158978i
$501$		0			0
$502$	−10.4930	+	18.1744i	−0.468324	+	0.811161i
$503$	−0.944092	−	1.63521i	−0.0420950	−	0.0729106i	0.844210	−	0.536012i	$-0.180070\pi$
$503$	−0.944092	−	1.63521i	−0.0420950	−	0.0729106i	−0.886305	+	0.463101i	$0.846737\pi$
$504$		0			0
$505$	11.1444	−	19.3026i	0.495918	−	0.858954i
$506$	4.53199	−	7.84963i	0.201471	−	0.348959i
$507$		0			0
$508$	0.546824	+	0.947126i	0.0242614	+	0.0420219i
$509$	41.2032			1.82630			0.913150	−	0.407623i	$-0.133642\pi$
$509$	41.2032			1.82630			0.913150	+	0.407623i	$0.133642\pi$
$510$		0			0
$511$	33.8433			1.49714
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−0.487865	−	0.845006i	−0.0215188	−	0.0372716i
$515$	22.4755	−	38.9287i	0.990389	−	1.71540i
$516$		0			0
$517$	16.9646			0.746104
$518$	−37.3434			−1.64077
$519$		0			0
$520$	−10.5709	−	4.06898i	−0.463567	−	0.178436i
$521$	−1.41291			−0.0619006			−0.0309503	−	0.999521i	$-0.509853\pi$
$521$	−1.41291			−0.0619006			−0.0309503	+	0.999521i	$0.509853\pi$
$522$		0			0
$523$	−4.54206	+	7.86707i	−0.198610	+	0.344003i	−0.948078	−	0.318038i	$-0.896976\pi$
$523$	−4.54206	+	7.86707i	−0.198610	+	0.344003i	0.749468	+	0.662041i	$0.230309\pi$
$524$	2.41145			0.105345
$525$		0			0
$526$	7.28367	−	12.6157i	0.317583	−	0.550070i
$527$	−1.46253	+	2.53318i	−0.0637089	+	0.110347i
$528$		0			0
$529$	−13.8507			−0.602206
$530$	13.9348	−	24.1358i	0.605291	−	1.04839i
$531$		0			0
$532$	11.9426			0.517778
$533$	21.2523	−	17.1774i	0.920537	−	0.744034i
$534$		0			0
$535$	−8.35670			−0.361292
$536$	2.58869			0.111814
$537$		0			0
$538$	−4.42368	+	7.66203i	−0.190718	+	0.330334i
$539$	13.7271	+	23.7761i	0.591269	+	1.02411i
$540$		0			0
$541$	27.7980			1.19513			0.597564	−	0.801821i	$-0.296135\pi$
$541$	27.7980			1.19513			0.597564	+	0.801821i	$0.296135\pi$
$542$	−17.9926			−0.772850
$543$		0			0
$544$	−6.34077			−0.271858
$545$	−5.28727	−	9.15782i	−0.226482	−	0.392278i
$546$		0			0
$547$	2.59556	−	4.49564i	0.110978	−	0.192220i	−0.805187	−	0.593021i	$-0.797935\pi$
$547$	2.59556	−	4.49564i	0.110978	−	0.192220i	0.916165	+	0.400801i	$0.131268\pi$
$548$	−6.61449	+	11.4566i	−0.282557	+	0.489403i
$549$		0			0
$550$	−7.29568	−	12.6365i	−0.311089	−	0.538821i
$551$	5.64053	−	9.76969i	0.240295	−	0.416203i
$552$		0			0
$553$	−5.13502	+	8.89411i	−0.218363	+	0.378216i
$554$	6.34678	+	10.9929i	0.269649	+	0.467045i
$555$		0			0
$556$	−0.873653	−	1.51321i	−0.0370511	−	0.0641745i
$557$	−16.5669	+	28.6947i	−0.701961	+	1.21583i	0.265816	+	0.964024i	$0.414359\pi$
$557$	−16.5669	+	28.6947i	−0.701961	+	1.21583i	−0.967777	+	0.251809i	$0.918975\pi$
$558$		0			0
$559$	−25.6396	+	20.7235i	−1.08444	+	0.876510i
$560$	6.31480	−	10.9376i	0.266849	−	0.462196i
$561$		0			0
$562$	−8.63961			−0.364440
$563$	−3.10107	+	5.37122i	−0.130695	+	0.226370i	−0.923945	−	0.382526i	$-0.875054\pi$
$563$	−3.10107	+	5.37122i	−0.130695	+	0.226370i	0.793250	+	0.608896i	$0.208387\pi$
$564$		0			0
$565$	−12.1313			−0.510368
$566$	−12.5067	−	21.6623i	−0.525696	−	0.910533i
$567$		0			0
$568$	4.36317	+	7.55723i	0.183075	+	0.317094i
$569$	1.65741	+	2.87072i	0.0694822	+	0.120347i	0.898674	−	0.438618i	$-0.144532\pi$
$569$	1.65741	+	2.87072i	0.0694822	+	0.120347i	−0.829191	+	0.558965i	$0.811199\pi$
$570$		0			0
$571$	−18.8940	−	32.7253i	−0.790688	−	1.36951i	−0.925542	−	0.378646i	$-0.876390\pi$
$571$	−18.8940	−	32.7253i	−0.790688	−	1.36951i	0.134854	−	0.990865i	$-0.456943\pi$
$572$	−8.40279	+	6.79164i	−0.351338	+	0.283973i
$573$		0			0
$574$	15.2343	+	26.3866i	0.635868	+	1.10136i
$575$	7.36433	−	12.7554i	0.307114	−	0.531936i
$576$		0			0
$577$	−11.3971			−0.474469			−0.237235	−	0.971452i	$-0.576241\pi$
$577$	−11.3971			−0.474469			−0.237235	+	0.971452i	$0.576241\pi$
$578$	−23.2054			−0.965218
$579$		0			0
$580$	−5.96501	−	10.3317i	−0.247683	−	0.429000i
$581$	−6.43761	+	11.1503i	−0.267077	+	0.462591i
$582$		0			0
$583$	−13.2918	−	23.0221i	−0.550490	−	0.953476i
$584$	−8.41835			−0.348354
$585$		0			0
$586$	0.452631			0.0186980
$587$	−21.0137	−	36.3968i	−0.867328	−	1.50226i	−0.864717	−	0.502260i	$-0.832502\pi$
$587$	−21.0137	−	36.3968i	−0.867328	−	1.50226i	−0.00261117	−	0.999997i	$-0.500831\pi$
$588$		0			0
$589$	−0.685198	+	1.18680i	−0.0282331	+	0.0489012i
$590$	12.3648	+	21.4165i	0.509051	+	0.881703i
$591$		0			0
$592$	9.28897			0.381774
$593$	−22.9349			−0.941825			−0.470913	−	0.882180i	$-0.656075\pi$
$593$	−22.9349			−0.941825			−0.470913	+	0.882180i	$0.656075\pi$
$594$		0			0
$595$	40.0407	−	69.3526i	1.64151	−	2.84318i
$596$	−6.06449	−	10.5040i	−0.248411	−	0.430261i
$597$		0			0
$598$	−10.1780	−	3.91773i	−0.416210	−	0.160208i
$599$	−11.3919	−	19.7314i	−0.465462	−	0.806204i	0.533760	−	0.845636i	$-0.320778\pi$
$599$	−11.3919	−	19.7314i	−0.465462	−	0.806204i	−0.999222	+	0.0394321i	$0.987445\pi$
$600$		0			0
$601$	1.41180	+	2.44531i	0.0575886	+	0.0997463i	0.893382	−	0.449297i	$-0.148326\pi$
$601$	1.41180	+	2.44531i	0.0575886	+	0.0997463i	−0.835794	+	0.549043i	$0.814992\pi$
$602$	−18.3793	−	31.8339i	−0.749085	−	1.29745i
$603$		0			0
$604$	2.86476	+	4.96191i	0.116565	+	0.201897i
$605$	6.34757			0.258065
$606$		0			0
$607$	1.73492	−	3.00497i	0.0704182	−	0.121968i	−0.828666	−	0.559743i	$-0.810900\pi$
$607$	1.73492	−	3.00497i	0.0704182	−	0.121968i	0.899085	+	0.437775i	$0.144233\pi$
$608$	−2.97066			−0.120476
$609$		0			0
$610$	16.3116	−	28.2525i	0.660437	−	1.14391i
$611$	−3.17461	−	20.1639i	−0.128431	−	0.815743i
$612$		0			0
$613$	8.72739	−	15.1163i	0.352496	−	0.610541i	−0.634190	−	0.773177i	$-0.718666\pi$
$613$	8.72739	−	15.1163i	0.352496	−	0.610541i	0.986686	+	0.162636i	$0.0519997\pi$
$614$	−9.63153	−	16.6823i	−0.388697	−	0.673243i
$615$		0			0
$616$	−6.02340	−	10.4328i	−0.242690	−	0.420351i
$617$	−3.87473	+	6.71123i	−0.155991	+	0.270184i	−0.933419	−	0.358787i	$-0.883190\pi$
$617$	−3.87473	+	6.71123i	−0.155991	+	0.270184i	0.777429	+	0.628971i	$0.216524\pi$
$618$		0			0
$619$	−12.9978	+	22.5128i	−0.522425	+	0.904867i	0.477235	+	0.878776i	$0.341639\pi$
$619$	−12.9978	+	22.5128i	−0.522425	+	0.904867i	−0.999660	+	0.0260907i	$0.991694\pi$
$620$	0.724614	+	1.25507i	0.0291012	+	0.0504048i
$621$		0			0
$622$	0.687943	−	1.19155i	0.0275840	−	0.0477769i
$623$	−8.72861	+	15.1184i	−0.349704	+	0.605705i
$624$		0			0
$625$	12.8181	+	22.2016i	0.512725	+	0.888065i
$626$	−3.29572			−0.131723
$627$		0			0
$628$	−20.7505			−0.828034
$629$	58.8993			2.34847
$630$		0			0
$631$	−5.26229	−	9.11456i	−0.209489	−	0.362845i	0.742065	−	0.670328i	$-0.233847\pi$
$631$	−5.26229	−	9.11456i	−0.209489	−	0.362845i	−0.951554	+	0.307483i	$0.900513\pi$
$632$	1.27731	−	2.21237i	0.0508087	−	0.0880032i
$633$		0			0
$634$	6.97851			0.277152
$635$	3.43575			0.136344
$636$		0			0
$637$	25.6911	−	20.7651i	1.01792	−	0.822742i
$638$	−11.3795			−0.450518
$639$		0			0
$640$	−1.57078	+	2.72066i	−0.0620903	+	0.107544i
$641$	15.8320			0.625327			0.312664	−	0.949864i	$-0.398779\pi$
$641$	15.8320			0.625327			0.312664	+	0.949864i	$0.398779\pi$
$642$		0			0
$643$	9.92261	−	17.1865i	0.391310	−	0.677768i	−0.601313	−	0.799014i	$-0.705356\pi$
$643$	9.92261	−	17.1865i	0.391310	−	0.677768i	0.992623	+	0.121246i	$0.0386889\pi$
$644$	6.08007	−	10.5310i	0.239588	−	0.414979i
$645$		0			0
$646$	−18.8363			−0.741104
$647$	−21.9195	+	37.9657i	−0.861745	+	1.49259i	0.00849831	+	0.999964i	$0.497295\pi$
$647$	−21.9195	+	37.9657i	−0.861745	+	1.49259i	−0.870243	+	0.492622i	$0.836038\pi$
$648$		0			0
$649$	23.5884			0.925927
$650$	−13.6542	+	11.0362i	−0.535564	+	0.432875i
$651$		0			0
$652$	9.37290			0.367071
$653$	4.49652			0.175962			0.0879811	−	0.996122i	$-0.471958\pi$
$653$	4.49652			0.175962			0.0879811	+	0.996122i	$0.471958\pi$
$654$		0			0
$655$	3.78785	−	6.56074i	0.148003	−	0.256349i
$656$	−3.78946	−	6.56354i	−0.147954	−	0.256263i
$657$		0			0
$658$	22.7596			0.887262
$659$	16.8978			0.658243			0.329122	−	0.944288i	$-0.393247\pi$
$659$	16.8978			0.658243			0.329122	+	0.944288i	$0.393247\pi$
$660$		0			0
$661$	−9.05347			−0.352139			−0.176070	−	0.984378i	$-0.556338\pi$
$661$	−9.05347			−0.352139			−0.176070	+	0.984378i	$0.556338\pi$
$662$	11.0133	+	19.0756i	0.428043	+	0.741392i
$663$		0			0
$664$	1.60132	−	2.77357i	0.0621434	−	0.107635i
$665$	18.7591	−	32.4918i	0.727448	−	1.25998i
$666$		0			0
$667$	−5.74328	−	9.94765i	−0.222381	−	0.385175i
$668$	−1.74088	+	3.01529i	−0.0673567	+	0.116665i
$669$		0			0
$670$	4.06625	−	7.04295i	0.157093	−	0.272093i
$671$	−15.5589	−	26.9487i	−0.600643	−	1.04034i
$672$		0			0
$673$	13.8076	+	23.9154i	0.532243	+	0.921872i	0.999291	+	0.0376400i	$0.0119840\pi$
$673$	13.8076	+	23.9154i	0.532243	+	0.921872i	−0.467049	+	0.884232i	$0.654683\pi$
$674$	−9.24184	+	16.0073i	−0.355982	+	0.616580i
$675$		0			0
$676$	9.64485	+	8.71648i	0.370956	+	0.335249i
$677$	−0.347911	+	0.602599i	−0.0133713	+	0.0231598i	−0.872634	−	0.488375i	$-0.837590\pi$
$677$	−0.347911	+	0.602599i	−0.0133713	+	0.0231598i	0.859262	+	0.511535i	$0.170923\pi$
$678$		0			0
$679$	42.9011			1.64639
$680$	−9.95993	+	17.2511i	−0.381946	+	0.661550i
$681$		0			0
$682$	1.38235			0.0529330
$683$	−6.83583	−	11.8400i	−0.261566	−	0.453045i	0.705093	−	0.709115i	$-0.250905\pi$
$683$	−6.83583	−	11.8400i	−0.261566	−	0.453045i	−0.966658	+	0.256070i	$0.917572\pi$
$684$		0			0
$685$	20.7798	+	35.9916i	0.793954	+	1.37517i
$686$	4.34556	+	7.52673i	0.165914	+	0.287372i
$687$		0			0
$688$	4.57176	+	7.91852i	0.174297	+	0.301891i
$689$	−24.8763	+	20.1065i	−0.947711	+	0.765998i
$690$		0			0
$691$	−19.5341	−	33.8340i	−0.743111	−	1.28711i	−0.951072	−	0.308969i	$-0.900016\pi$
$691$	−19.5341	−	33.8340i	−0.743111	−	1.28711i	0.207961	−	0.978137i	$-0.433317\pi$
$692$	9.06500	−	15.7010i	0.344600	−	0.596864i
$693$		0			0
$694$	1.38338			0.0525125
$695$	−5.48925			−0.208219
$696$		0			0
$697$	−24.0281	−	41.6179i	−0.910129	−	1.57639i
$698$	−9.17110	+	15.8848i	−0.347131	+	0.601249i
$699$		0			0
$700$	−9.78782	−	16.9530i	−0.369945	−	0.640763i
$701$	−52.6941			−1.99023			−0.995114	−	0.0987285i	$-0.968522\pi$
$701$	−52.6941			−1.99023			−0.995114	+	0.0987285i	$0.968522\pi$
$702$		0			0
$703$	27.5944			1.04074
$704$	1.49829	+	2.59511i	0.0564689	+	0.0978070i
$705$		0			0
$706$	−12.6367	+	21.8874i	−0.475589	+	0.823745i
$707$	−14.2612	−	24.7012i	−0.536349	−	0.928983i
$708$		0			0
$709$	41.0873			1.54306			0.771532	−	0.636190i	$-0.219491\pi$
$709$	41.0873			1.54306			0.771532	+	0.636190i	$0.219491\pi$
$710$	27.4142			1.02884
$711$		0			0
$712$	2.17120	−	3.76062i	0.0813690	−	0.140935i
$713$	0.697679	+	1.20842i	0.0261283	+	0.0452555i
$714$		0			0
$715$	5.27887	+	33.5293i	0.197419	+	1.25392i
$716$	12.9184	+	22.3753i	0.482782	+	0.836203i
$717$		0			0
$718$	−11.5120	−	19.9393i	−0.429623	−	0.744129i
$719$	−2.50717	−	4.34255i	−0.0935018	−	0.161950i	0.815481	−	0.578785i	$-0.196473\pi$
$719$	−2.50717	−	4.34255i	−0.0935018	−	0.161950i	−0.908982	+	0.416835i	$0.863139\pi$
$720$		0			0
$721$	−28.7615	−	49.8163i	−1.07113	−	1.85526i
$722$	10.1752			0.378681
$723$		0			0
$724$	−7.53859	+	13.0572i	−0.280169	+	0.485268i
$725$	−18.4913			−0.686749
$726$		0			0
$727$	−3.80214	+	6.58550i	−0.141013	+	0.244243i	−0.927879	−	0.372883i	$-0.878369\pi$
$727$	−3.80214	+	6.58550i	−0.141013	+	0.244243i	0.786865	+	0.617125i	$0.211703\pi$
$728$	−11.2731	+	9.11161i	−0.417809	+	0.337699i
$729$		0			0
$730$	−13.2233	+	22.9035i	−0.489418	+	0.847696i
$731$	28.9885	+	50.2096i	1.07218	+	1.85707i
$732$		0			0
$733$	7.46870	+	12.9362i	0.275863	+	0.477808i	0.970352	−	0.241694i	$-0.0777031\pi$
$733$	7.46870	+	12.9362i	0.275863	+	0.477808i	−0.694490	+	0.719503i	$0.744370\pi$
$734$	14.3965	−	24.9355i	0.531384	−	0.920385i
$735$		0			0
$736$	−1.51239	+	2.61953i	−0.0557473	+	0.0965572i
$737$	−3.87860	−	6.71794i	−0.142870	−	0.247458i
$738$		0			0
$739$	3.54416	−	6.13866i	0.130374	−	0.225814i	−0.793447	−	0.608640i	$-0.791716\pi$
$739$	3.54416	−	6.13866i	0.130374	−	0.225814i	0.923821	+	0.382825i	$0.125049\pi$
$740$	14.5909	−	25.2722i	0.536372	−	0.929023i
$741$		0			0
$742$	−17.8321	−	30.8862i	−0.654639	−	1.13387i
$743$	10.7089			0.392870			0.196435	−	0.980517i	$-0.437064\pi$
$743$	10.7089			0.392870			0.196435	+	0.980517i	$0.437064\pi$
$744$		0			0
$745$	−38.1038			−1.39601
$746$	4.02432			0.147341
$747$		0			0
$748$	9.50031	+	16.4550i	0.347366	+	0.601655i
$749$	−5.34696	+	9.26120i	−0.195374	+	0.338397i
$750$		0			0
$751$	21.3917			0.780596			0.390298	−	0.920689i	$-0.372372\pi$
$751$	21.3917			0.780596			0.390298	+	0.920689i	$0.372372\pi$
$752$	−5.66134			−0.206448
$753$		0			0
$754$	2.12946	+	13.5255i	0.0775502	+	0.492568i
$755$	17.9996			0.655072
$756$		0			0
$757$	17.2139	−	29.8154i	0.625650	−	1.08366i	−0.362764	−	0.931881i	$-0.618167\pi$
$757$	17.2139	−	29.8154i	0.625650	−	1.08366i	0.988415	−	0.151777i	$-0.0484997\pi$
$758$	8.89603			0.323118
$759$		0			0
$760$	−4.66624	+	8.08217i	−0.169262	+	0.293171i
$761$	−3.75556	+	6.50483i	−0.136139	+	0.235800i	−0.926032	−	0.377445i	$-0.876803\pi$
$761$	−3.75556	+	6.50483i	−0.136139	+	0.235800i	0.789893	+	0.613245i	$0.210136\pi$
$762$		0			0
$763$	−13.5320			−0.489893
$764$	−6.63441	+	11.4911i	−0.240024	+	0.415735i
$765$		0			0
$766$	−11.4022			−0.411979
$767$	−4.41413	−	28.0368i	−0.159385	−	1.01235i
$768$		0			0
$769$	28.8412			1.04004			0.520020	−	0.854154i	$-0.325925\pi$
$769$	28.8412			1.04004			0.520020	+	0.854154i	$0.325925\pi$
$770$	−37.8456			−1.36386
$771$		0			0
$772$	1.35325	−	2.34389i	0.0487044	−	0.0843585i
$773$	9.56156	+	16.5611i	0.343905	+	0.595661i	0.985154	−	0.171671i	$-0.0549168\pi$
$773$	9.56156	+	16.5611i	0.343905	+	0.595661i	−0.641249	+	0.767333i	$0.721583\pi$
$774$		0			0
$775$	2.24628			0.0806886
$776$	−10.6714			−0.383082
$777$		0			0
$778$	−21.7395			−0.779398
$779$	−11.2572	−	19.4980i	−0.403331	−	0.698590i
$780$		0			0
$781$	13.0746	−	22.6458i	0.467845	−	0.810332i
$782$	−9.58970	+	16.6099i	−0.342927	+	0.593967i
$783$		0			0
$784$	−4.58094	−	7.93441i	−0.163605	−	0.283372i
$785$	−32.5943	+	56.4550i	−1.16334	+	2.01497i
$786$		0			0
$787$	−18.4036	+	31.8759i	−0.656016	+	1.13625i	0.325622	+	0.945500i	$0.394426\pi$
$787$	−18.4036	+	31.8759i	−0.656016	+	1.13625i	−0.981638	+	0.190753i	$0.938907\pi$
$788$	−5.03966	−	8.72894i	−0.179530	−	0.310956i
$789$		0			0
$790$	−4.01273	−	6.95026i	−0.142767	−	0.247279i
$791$	−7.76210	+	13.4443i	−0.275988	+	0.478026i
$792$		0			0
$793$	−29.1193	+	23.5359i	−1.03405	+	0.835786i
$794$	18.5668	−	32.1586i	0.658910	−	1.14127i
$795$		0			0
$796$	7.66827			0.271795
$797$	7.34753	−	12.7263i	0.260263	−	0.450788i	−0.706049	−	0.708163i	$-0.749524\pi$
$797$	7.34753	−	12.7263i	0.260263	−	0.450788i	0.966312	+	0.257375i	$0.0828575\pi$
$798$		0			0
$799$	−35.8973			−1.26995
$800$	2.43467	+	4.21697i	0.0860786	+	0.149092i
$801$		0			0
$802$	−5.53973	−	9.59509i	−0.195615	−	0.338814i
$803$	12.6131	+	21.8466i	0.445108	+	0.770949i
$804$		0			0
$805$	−19.1009	−	33.0837i	−0.673217	−	1.16605i
$806$	−0.258681	−	1.64304i	−0.00911165	−	0.0578736i
$807$		0			0
$808$	3.54741	+	6.14429i	0.124797	+	0.216155i
$809$	20.5898	−	35.6627i	0.723900	−	1.25383i	−0.235525	−	0.971868i	$-0.575681\pi$
$809$	20.5898	−	35.6627i	0.723900	−	1.25383i	0.959425	−	0.281964i	$-0.0909858\pi$
$810$		0			0
$811$	−30.4891			−1.07062			−0.535309	−	0.844656i	$-0.679805\pi$
$811$	−30.4891			−1.07062			−0.535309	+	0.844656i	$0.679805\pi$
$812$	−15.2666			−0.535753
$813$		0			0
$814$	−13.9176	−	24.1059i	−0.487810	−	0.844912i
$815$	14.7227	−	25.5005i	0.515714	−	0.893243i
$816$		0			0
$817$	13.5812	+	23.5233i	0.475145	+	0.822975i
$818$	14.6380			0.511807
$819$		0			0
$820$	−23.8096			−0.831466
$821$	−13.2168	−	22.8922i	−0.461269	−	0.798942i	0.537755	−	0.843101i	$-0.319272\pi$
$821$	−13.2168	−	22.8922i	−0.461269	−	0.798942i	−0.999025	+	0.0441593i	$0.985939\pi$
$822$		0			0
$823$	14.3719	−	24.8929i	0.500973	−	0.867711i	−0.499026	−	0.866587i	$-0.666309\pi$
$823$	14.3719	−	24.8929i	0.500973	−	0.867711i	0.999999	−	0.00112428i	$-0.000357870\pi$
$824$	7.15427	+	12.3916i	0.249231	+	0.431680i
$825$		0			0
$826$	31.6460			1.10111
$827$	3.66041			0.127285			0.0636425	−	0.997973i	$-0.479728\pi$
$827$	3.66041			0.127285			0.0636425	+	0.997973i	$0.479728\pi$
$828$		0			0
$829$	−20.5653	+	35.6201i	−0.714262	+	1.23714i	0.248982	+	0.968508i	$0.419904\pi$
$829$	−20.5653	+	35.6201i	−0.714262	+	1.23714i	−0.963244	+	0.268630i	$0.913429\pi$
$830$	−5.03064	−	8.71332i	−0.174616	−	0.302444i
$831$		0			0
$832$	2.80413	−	2.26647i	0.0972156	−	0.0785756i
$833$	−29.0467	−	50.3103i	−1.00641	−	1.74315i
$834$		0			0
$835$	5.46906	+	9.47269i	0.189265	+	0.327816i
$836$	4.45091	+	7.70920i	0.153938	+	0.266628i
$837$		0			0
$838$	15.7852	+	27.3407i	0.545289	+	0.944469i
$839$	−46.1887			−1.59461			−0.797306	−	0.603575i	$-0.793742\pi$
$839$	−46.1887			−1.59461			−0.797306	+	0.603575i	$0.793742\pi$
$840$		0			0
$841$	7.28952	−	12.6258i	0.251363	−	0.435373i
$842$	−11.3100			−0.389769
$843$		0			0
$844$	−12.7872	+	22.1480i	−0.440153	+	0.762367i
$845$	38.8645	−	12.5487i	1.33698	−	0.431690i
$846$		0			0
$847$	4.06143	−	7.03461i	0.139552	−	0.241712i
$848$	4.43566	+	7.68278i	0.152321	+	0.263828i
$849$		0			0
$850$	15.4377	+	26.7389i	0.529508	+	0.917135i
$851$	14.0485	−	24.3328i	0.481577	−	0.834116i
$852$		0			0
$853$	21.3359	−	36.9548i	0.730526	−	1.26531i	−0.226133	−	0.974096i	$-0.572608\pi$
$853$	21.3359	−	36.9548i	0.730526	−	1.26531i	0.956659	−	0.291211i	$-0.0940583\pi$
$854$	−20.8736	−	36.1542i	−0.714281	−	1.23717i
$855$		0			0
$856$	1.33003	−	2.30368i	0.0454594	−	0.0787381i
$857$	16.8359	−	29.1605i	0.575102	−	0.996105i	−0.420929	−	0.907094i	$-0.638296\pi$
$857$	16.8359	−	29.1605i	0.575102	−	0.996105i	0.996031	−	0.0890117i	$-0.0283709\pi$
$858$		0			0
$859$	21.7841	+	37.7312i	0.743265	+	1.28737i	0.951001	+	0.309188i	$0.100057\pi$
$859$	21.7841	+	37.7312i	0.743265	+	1.28737i	−0.207736	+	0.978185i	$0.566609\pi$
$860$	28.7248			0.979509
$861$		0			0
$862$	−21.4211			−0.729607
$863$	−14.4929			−0.493344			−0.246672	−	0.969099i	$-0.579337\pi$
$863$	−14.4929			−0.493344			−0.246672	+	0.969099i	$0.579337\pi$
$864$		0			0
$865$	−28.4782	−	49.3256i	−0.968286	−	1.67712i
$866$	6.26037	−	10.8433i	0.212736	−	0.368470i
$867$		0			0
$868$	1.85455			0.0629476
$869$	−7.65512			−0.259682
$870$		0			0
$871$	−7.25901	+	5.86717i	−0.245962	+	0.198802i
$872$	3.36602			0.113988
$873$		0			0
$874$	−4.49279	+	7.78174i	−0.151971	+	0.263221i
$875$	1.65020			0.0557869
$876$		0			0
$877$	−10.3587	+	17.9418i	−0.349789	+	0.605852i	−0.986212	−	0.165488i	$-0.947080\pi$
$877$	−10.3587	+	17.9418i	−0.349789	+	0.605852i	0.636423	+	0.771340i	$0.280413\pi$
$878$	1.26334	−	2.18817i	0.0426358	−	0.0738473i
$879$		0			0
$880$	9.41390			0.317343
$881$	−13.7696	+	23.8496i	−0.463908	+	0.803513i	−0.999152	−	0.0411853i	$-0.986887\pi$
$881$	−13.7696	+	23.8496i	−0.463908	+	0.803513i	0.535243	+	0.844698i	$0.320220\pi$
$882$		0			0
$883$	−47.7047			−1.60539			−0.802695	−	0.596390i	$-0.796601\pi$
$883$	−47.7047			−1.60539			−0.802695	+	0.596390i	$0.796601\pi$
$884$	17.7803	−	14.3711i	0.598018	−	0.483354i
$885$		0			0
$886$	−2.36978			−0.0796142
$887$	43.5135			1.46104			0.730520	−	0.682891i	$-0.239278\pi$
$887$	43.5135			1.46104			0.730520	+	0.682891i	$0.239278\pi$
$888$		0			0
$889$	2.19833	−	3.80762i	0.0737297	−	0.127704i
$890$	−6.82092	−	11.8142i	−0.228638	−	0.396012i
$891$		0			0
$892$	8.38145			0.280632
$893$	−16.8179			−0.562790
$894$		0			0
$895$	81.1674			2.71313
$896$	2.01009	+	3.48158i	0.0671524	+	0.116311i
$897$		0			0
$898$	7.28629	−	12.6202i	0.243147	−	0.421142i
$899$	0.875911	−	1.51712i	0.0292133	−	0.0505989i
$900$		0			0
$901$	28.1255	+	48.7148i	0.936996	+	1.62292i
$902$	−11.3554	+	19.6681i	−0.378094	+	0.654878i
$903$		0			0
$904$	1.93078	−	3.34421i	0.0642169	−	0.111227i
$905$	23.6828	+	41.0199i	0.787244	+	1.36355i
$906$		0			0
$907$	17.6660	+	30.5984i	0.586590	+	1.01600i	0.994675	+	0.103060i	$0.0328634\pi$
$907$	17.6660	+	30.5984i	0.586590	+	1.01600i	−0.408085	+	0.912944i	$0.633803\pi$
$908$	−6.07434	+	10.5211i	−0.201584	+	0.349154i
$909$		0			0
$910$	7.08209	+	44.9826i	0.234769	+	1.49116i
$911$	−1.65546	+	2.86734i	−0.0548478	+	0.0949991i	−0.892146	−	0.451748i	$-0.850801\pi$
$911$	−1.65546	+	2.86734i	−0.0548478	+	0.0949991i	0.837298	+	0.546747i	$0.184134\pi$
$912$		0			0
$913$	−9.59698			−0.317614
$914$	−11.2003	+	19.3994i	−0.370471	+	0.641675i
$915$		0			0
$916$	−29.2634			−0.966889
$917$	−4.84724	−	8.39566i	−0.160070	−	0.277249i
$918$		0			0
$919$	−0.206477	−	0.357628i	−0.00681104	−	0.0117971i	0.862600	−	0.505887i	$-0.168835\pi$
$919$	−0.206477	−	0.357628i	−0.00681104	−	0.0117971i	−0.869411	+	0.494090i	$0.835501\pi$
$920$	4.75124	+	8.22939i	0.156644	+	0.271315i
$921$		0			0
$922$	−5.92417	−	10.2610i	−0.195102	−	0.337927i
$923$	−29.3631	−	11.3025i	−0.966498	−	0.372025i
$924$		0			0
$925$	−22.6156	−	39.1713i	−0.743596	−	1.28795i
$926$	−4.25273	+	7.36594i	−0.139753	+	0.242060i
$927$		0			0
$928$	3.79749			0.124659
$929$	18.2144			0.597594			0.298797	−	0.954317i	$-0.403415\pi$
$929$	18.2144			0.597594			0.298797	+	0.954317i	$0.403415\pi$
$930$		0			0
$931$	−13.6084	−	23.5705i	−0.445998	−	0.772491i
$932$	3.97742	−	6.88909i	0.130285	−	0.225660i
$933$		0			0
$934$	−2.52829	−	4.37913i	−0.0827283	−	0.143290i
$935$	59.6914			1.95212
$936$		0			0
$937$	−46.4192			−1.51645			−0.758224	−	0.651994i	$-0.773933\pi$
$937$	−46.4192			−1.51645			−0.758224	+	0.651994i	$0.773933\pi$
$938$	−5.20350	−	9.01273i	−0.169900	−	0.294276i
$939$		0			0
$940$	−8.89269	+	15.4026i	−0.290048	+	0.502377i
$941$	7.15817	+	12.3983i	0.233350	+	0.404174i	0.958792	−	0.284110i	$-0.0916979\pi$
$941$	7.15817	+	12.3983i	0.233350	+	0.404174i	−0.725442	+	0.688283i	$0.758365\pi$
$942$		0			0
$943$	−22.9245			−0.746525
$944$	−7.87179			−0.256205
$945$		0			0
$946$	13.6996	−	23.7285i	0.445414	−	0.771479i
$947$	−14.0513	−	24.3375i	−0.456605	−	0.790863i	0.542174	−	0.840266i	$-0.317601\pi$
$947$	−14.0513	−	24.3375i	−0.456605	−	0.790863i	−0.998779	+	0.0494030i	$0.984268\pi$
$948$		0			0
$949$	23.6061	−	19.0799i	0.766288	−	0.619360i
$950$	7.23258	+	12.5272i	0.234656	+	0.406436i
$951$		0			0
$952$	12.7455	+	22.0759i	0.413085	+	0.715485i
$953$	−25.9475	−	44.9423i	−0.840520	−	1.45582i	−0.889455	−	0.457022i	$-0.848916\pi$
$953$	−25.9475	−	44.9423i	−0.840520	−	1.45582i	0.0489349	−	0.998802i	$-0.484417\pi$
$954$		0			0
$955$	20.8423	+	36.1000i	0.674442	+	1.16817i
$956$	−11.9488			−0.386452
$957$		0			0
$958$	−13.8291	+	23.9527i	−0.446799	+	0.773878i
$959$	53.1830			1.71737
$960$		0			0
$961$	15.3936	−	26.6625i	0.496568	−	0.860080i
$962$	−26.0475	+	21.0531i	−0.839804	+	0.678780i
$963$		0			0
$964$	11.4058	−	19.7554i	0.367355	−	0.636278i
$965$	−4.25129	−	7.36346i	−0.136854	−	0.237038i
$966$		0			0
$967$	5.74440	+	9.94959i	0.184727	+	0.319957i	0.943485	−	0.331416i	$-0.107526\pi$
$967$	5.74440	+	9.94959i	0.184727	+	0.319957i	−0.758757	+	0.651373i	$0.774193\pi$
$968$	−1.01026	+	1.74982i	−0.0324710	+	0.0562414i
$969$		0			0
$970$	−16.7624	+	29.0333i	−0.538208	+	0.932204i
$971$	30.0430	+	52.0360i	0.964126	+	1.66992i	0.711945	+	0.702236i	$0.247815\pi$
$971$	30.0430	+	52.0360i	0.964126	+	1.66992i	0.252182	+	0.967680i	$0.418852\pi$
$972$		0			0
$973$	−3.51225	+	6.08339i	−0.112597	+	0.195024i
$974$	−7.82813	+	13.5587i	−0.250829	+	0.434449i
$975$		0			0
$976$	5.19221	+	8.99317i	0.166199	+	0.287865i
$977$	23.7895			0.761094			0.380547	−	0.924762i	$-0.375736\pi$
$977$	23.7895			0.761094			0.380547	+	0.924762i	$0.375736\pi$
$978$		0			0
$979$	−13.0123			−0.415875
$980$	−28.7825			−0.919423
$981$		0			0
$982$	−11.6681	−	20.2098i	−0.372345	−	0.644920i
$983$	13.6125	−	23.5776i	0.434173	−	0.752009i	−0.563055	−	0.826419i	$-0.690374\pi$
$983$	13.6125	−	23.5776i	0.434173	−	0.752009i	0.997228	+	0.0744104i	$0.0237075\pi$
$984$		0			0
$985$	−31.6647			−1.00892
$986$	24.0790			0.766833
$987$		0			0
$988$	8.33012	−	6.73290i	0.265016	−	0.214202i
$989$	27.6571			0.879444
$990$		0			0
$991$	−28.1292	+	48.7212i	−0.893554	+	1.54768i	−0.0579699	+	0.998318i	$0.518463\pi$
$991$	−28.1292	+	48.7212i	−0.893554	+	1.54768i	−0.835584	+	0.549363i	$0.814871\pi$
$992$	−0.461310			−0.0146466
$993$		0			0
$994$	17.5407	−	30.3815i	0.556359	−	0.963641i
$995$	12.0451	−	20.8628i	0.381856	−	0.661394i
$996$		0			0
$997$	26.9475			0.853435			0.426718	−	0.904385i	$-0.359670\pi$
$997$	26.9475			0.853435			0.426718	+	0.904385i	$0.359670\pi$
$998$	6.18709	−	10.7164i	0.195849	−	0.339220i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.g.d.451.5		12
3.2	odd	2		234.2.g.c.61.5	yes	12
9.4	even	3		702.2.f.c.685.5		12
9.5	odd	6		234.2.f.d.139.2	yes	12
13.3	even	3		702.2.f.c.289.5		12
39.29	odd	6		234.2.f.d.133.2	✓	12
117.68	odd	6		234.2.g.c.211.5	yes	12
117.94	even	3	inner	702.2.g.d.523.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.f.d.133.2	✓	12	39.29	odd	6
234.2.f.d.139.2	yes	12	9.5	odd	6
234.2.g.c.61.5	yes	12	3.2	odd	2
234.2.g.c.211.5	yes	12	117.68	odd	6
702.2.f.c.289.5		12	13.3	even	3
702.2.f.c.685.5		12	9.4	even	3
702.2.g.d.451.5		12	1.1	even	1	trivial
702.2.g.d.523.5		12	117.94	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.57078 + 2.72066i) q^{5} +4.02018 q^{7} -1.00000 q^{8} +(-1.57078 + 2.72066i) q^{10} +(1.49829 + 2.59511i) q^{11} +(2.80413 - 2.26647i) q^{13} +(2.01009 + 3.48158i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.17039 - 5.49127i) q^{17} +(-1.48533 - 2.57267i) q^{19} -3.14155 q^{20} +(-1.49829 + 2.59511i) q^{22} -3.02477 q^{23} +(-2.43467 + 4.21697i) q^{25} +(3.36488 + 1.29521i) q^{26} +(-2.01009 + 3.48158i) q^{28} +(1.89875 + 3.28873i) q^{29} +(-0.230655 - 0.399506i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.17039 - 5.49127i) q^{34} +(6.31480 + 10.9376i) q^{35} +(-4.64449 + 8.04449i) q^{37} +(1.48533 - 2.57267i) q^{38} +(-1.57078 - 2.72066i) q^{40} +7.57892 q^{41} -9.14352 q^{43} -2.99658 q^{44} +(-1.51239 - 2.61953i) q^{46} +(2.83067 - 4.90286i) q^{47} +9.16187 q^{49} -4.86934 q^{50} +(0.560753 + 3.56168i) q^{52} -8.87131 q^{53} +(-4.70695 + 8.15268i) q^{55} -4.02018 q^{56} +(-1.89875 + 3.28873i) q^{58} +(3.93589 - 6.81717i) q^{59} -10.3844 q^{61} +(0.230655 - 0.399506i) q^{62} +1.00000 q^{64} +(10.5709 + 4.06898i) q^{65} -2.58869 q^{67} +6.34077 q^{68} +(-6.31480 + 10.9376i) q^{70} +(-4.36317 - 7.55723i) q^{71} +8.41835 q^{73} -9.28897 q^{74} +2.97066 q^{76} +(6.02340 + 10.4328i) q^{77} +(-1.27731 + 2.21237i) q^{79} +(1.57078 - 2.72066i) q^{80} +(3.78946 + 6.56354i) q^{82} +(-1.60132 + 2.77357i) q^{83} +(9.95993 - 17.2511i) q^{85} +(-4.57176 - 7.91852i) q^{86} +(-1.49829 - 2.59511i) q^{88} +(-2.17120 + 3.76062i) q^{89} +(11.2731 - 9.11161i) q^{91} +(1.51239 - 2.61953i) q^{92} +5.66134 q^{94} +(4.66624 - 8.08217i) q^{95} +10.6714 q^{97} +(4.58094 + 7.93441i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} - q^{5} + 10 q^{7} - 12 q^{8} + q^{10} - 8 q^{11} + 8 q^{13} + 5 q^{14} - 6 q^{16} - 3 q^{17} - 7 q^{19} + 2 q^{20} + 8 q^{22} + 2 q^{23} - 13 q^{25} + q^{26} - 5 q^{28} - q^{29}+ \cdots + 3 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 - q^5 + 10 * q^7 - 12 * q^8 + q^10 - 8 * q^11 + 8 * q^13 + 5 * q^14 - 6 * q^16 - 3 * q^17 - 7 * q^19 + 2 * q^20 + 8 * q^22 + 2 * q^23 - 13 * q^25 + q^26 - 5 * q^28 - q^29 - 14 * q^31 + 6 * q^32 + 3 * q^34 + 5 * q^35 - 7 * q^37 + 7 * q^38 + q^40 + 18 * q^41 + 16 * q^43 + 16 * q^44 + q^46 + 13 * q^47 + 6 * q^49 - 26 * q^50 - 7 * q^52 + 12 * q^53 - 20 * q^55 - 10 * q^56 + q^58 - 4 * q^59 - 56 * q^61 + 14 * q^62 + 12 * q^64 + 7 * q^65 - 8 * q^67 + 6 * q^68 - 5 * q^70 + 13 * q^71 + 54 * q^73 - 14 * q^74 + 14 * q^76 + 4 * q^77 - 6 * q^79 - q^80 + 9 * q^82 - 30 * q^83 - 9 * q^85 + 8 * q^86 + 8 * q^88 - 3 * q^89 - 12 * q^91 - q^92 + 26 * q^94 + 21 * q^95 + 48 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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