LMFDB - Embedded newform 97.2.h.a.79.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,2,Mod(8,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.8"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	97.h (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.774548899606$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			79.7
Character	$\chi$	$=$	97.79
Dual form			97.2.h.a.70.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.904642 - 2.18400i) q^{2} +(0.396451 - 0.164215i) q^{3} +(-2.53726 - 2.53726i) q^{4} +(0.587356 + 0.879041i) q^{5} -1.01440i q^{6} +(-1.01849 + 1.52427i) q^{7} +(-3.46868 + 1.43678i) q^{8} +(-1.99111 + 1.99111i) q^{9} +(2.45117 - 0.487568i) q^{10} +(1.87132 - 0.775124i) q^{11} +(-1.42256 - 0.589242i) q^{12} +(1.05257 - 0.703303i) q^{13} +(2.40764 + 3.60329i) q^{14} +(0.377210 + 0.252044i) q^{15} +1.69892i q^{16} +(-4.56750 + 3.05190i) q^{17} +(2.54734 + 6.14983i) q^{18} +(-1.52343 - 2.27998i) q^{19} +(0.740079 - 3.72063i) q^{20} +(-0.153471 + 0.771551i) q^{21} -4.78816i q^{22} +(7.33474 + 1.45897i) q^{23} +(-1.13922 + 1.13922i) q^{24} +(1.48569 - 3.58678i) q^{25} +(-0.583817 - 2.93504i) q^{26} +(-0.955053 + 2.30570i) q^{27} +(6.45164 - 1.28331i) q^{28} +(-5.05785 - 1.00607i) q^{29} +(0.891703 - 0.595817i) q^{30} +(0.527749 + 1.27410i) q^{31} +(-3.22694 - 1.33664i) q^{32} +(0.614597 - 0.614597i) q^{33} +(2.53340 + 12.7363i) q^{34} -1.93811 q^{35} +10.1039 q^{36} +(-0.620545 - 3.11969i) q^{37} +(-6.35763 + 1.26461i) q^{38} +(0.301798 - 0.451673i) q^{39} +(-3.30034 - 2.20522i) q^{40} +(-2.03747 + 10.2431i) q^{41} +(1.54623 + 1.03316i) q^{42} +(-0.738574 - 0.738574i) q^{43} +(-6.71470 - 2.78132i) q^{44} +(-2.91976 - 0.580777i) q^{45} +(9.82170 - 14.6992i) q^{46} +(-6.51992 - 6.51992i) q^{47} +(0.278988 + 0.673537i) q^{48} +(1.39269 + 3.36225i) q^{49} +(-6.48950 - 6.48950i) q^{50} +(-1.30962 + 1.95998i) q^{51} +(-4.45510 - 0.886174i) q^{52} +(-12.7053 - 5.26272i) q^{53} +(4.17167 + 4.17167i) q^{54} +(1.78049 + 1.18969i) q^{55} +(1.34277 - 6.75056i) q^{56} +(-0.978374 - 0.653729i) q^{57} +(-6.77279 + 10.1362i) q^{58} +(5.32278 - 1.05877i) q^{59} +(-0.317579 - 1.59658i) q^{60} +4.56051 q^{61} +3.26005 q^{62} +(-1.00708 - 5.06292i) q^{63} +(-8.24108 + 8.24108i) q^{64} +(1.23646 + 0.512160i) q^{65} +(-0.786289 - 1.89827i) q^{66} +(12.7282 - 8.50469i) q^{67} +(19.3324 + 3.84545i) q^{68} +(3.14745 - 0.626067i) q^{69} +(-1.75330 + 4.23283i) q^{70} +(0.424284 + 2.13302i) q^{71} +(4.04576 - 9.76733i) q^{72} +(5.79670 - 5.79670i) q^{73} +(-7.37477 - 1.46693i) q^{74} -1.66595i q^{75} +(-1.91955 + 9.65025i) q^{76} +(-0.724409 + 3.64185i) q^{77} +(-0.713434 - 1.06773i) q^{78} +(1.37881 + 3.32873i) q^{79} +(-1.49342 + 0.997869i) q^{80} -7.37665i q^{81} +(20.5276 + 13.7161i) q^{82} +(8.16638 + 12.2219i) q^{83} +(2.34702 - 1.56823i) q^{84} +(-5.36549 - 2.22246i) q^{85} +(-2.28119 + 0.944900i) q^{86} +(-2.17040 + 0.431719i) q^{87} +(-5.37732 + 5.37732i) q^{88} +(5.26086 - 2.17912i) q^{89} +(-3.90976 + 5.85136i) q^{90} +2.32071i q^{91} +(-14.9084 - 22.3119i) q^{92} +(0.418453 + 0.418453i) q^{93} +(-20.1377 + 8.34130i) q^{94} +(1.10940 - 2.67832i) q^{95} -1.49882 q^{96} +(-9.79663 - 1.01294i) q^{97} +8.60304 q^{98} +(-2.18264 + 5.26936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{4} - 8 q^{5} - 8 q^{7} - 8 q^{8} - 32 q^{9} + 8 q^{10} - 8 q^{11} - 16 q^{12} - 8 q^{13} + 16 q^{14} - 40 q^{15} - 16 q^{17} + 56 q^{18} + 32 q^{19} - 16 q^{20} - 8 q^{21} + 24 q^{24}+ \cdots + 80 q^{99}+O(q^{100}) $ 56 * q - 8 * q^2 - 8 * q^4 - 8 * q^5 - 8 * q^7 - 8 * q^8 - 32 * q^9 + 8 * q^10 - 8 * q^11 - 16 * q^12 - 8 * q^13 + 16 * q^14 - 40 * q^15 - 16 * q^17 + 56 * q^18 + 32 * q^19 - 16 * q^20 - 8 * q^21 + 24 * q^24 - 48 * q^26 - 48 * q^28 - 24 * q^29 + 32 * q^30 + 16 * q^31 + 88 * q^32 - 16 * q^33 - 8 * q^34 + 48 * q^35 - 8 * q^36 - 32 * q^37 - 8 * q^38 - 24 * q^39 - 56 * q^40 + 8 * q^41 + 40 * q^42 - 80 * q^44 + 64 * q^45 - 8 * q^46 - 56 * q^47 - 24 * q^48 + 80 * q^49 + 88 * q^50 - 8 * q^51 + 24 * q^52 + 8 * q^53 + 24 * q^54 - 8 * q^55 - 8 * q^56 - 8 * q^57 + 56 * q^58 - 32 * q^59 - 40 * q^60 + 32 * q^61 - 80 * q^62 - 8 * q^63 + 24 * q^64 - 16 * q^65 + 56 * q^66 + 104 * q^67 + 24 * q^68 + 72 * q^69 - 88 * q^70 + 32 * q^71 + 104 * q^72 + 40 * q^73 - 24 * q^74 - 88 * q^76 - 8 * q^77 + 40 * q^78 - 88 * q^79 + 120 * q^80 - 112 * q^82 + 16 * q^83 + 32 * q^84 + 96 * q^85 + 80 * q^86 - 168 * q^87 - 48 * q^88 - 152 * q^90 - 48 * q^92 - 56 * q^93 + 24 * q^94 - 128 * q^95 - 32 * q^96 + 32 * q^97 - 136 * q^98 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{5}{16}\right)$

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 $

$2$	0.904642	−	2.18400i	0.639678	−	1.54432i	−0.187430	−	0.982278i	$-0.560016\pi$
$2$	0.904642	−	2.18400i	0.639678	−	1.54432i	0.827109	−	0.562042i	$-0.189984\pi$
$3$	0.396451	−	0.164215i	0.228891	−	0.0948098i	−0.265290	−	0.964169i	$-0.585468\pi$
$3$	0.396451	−	0.164215i	0.228891	−	0.0948098i	0.494181	+	0.869359i	$0.335468\pi$
$4$	−2.53726	−	2.53726i	−1.26863	−	1.26863i
$5$	0.587356	+	0.879041i	0.262674	+	0.393119i	0.939239	−	0.343264i	$-0.111532\pi$
$5$	0.587356	+	0.879041i	0.262674	+	0.393119i	−0.676565	+	0.736382i	$0.736532\pi$
$6$		−	1.01440i		−	0.414129i
$7$	−1.01849	+	1.52427i	−0.384952	+	0.576121i	−0.972452	−	0.233103i	$-0.925112\pi$
$7$	−1.01849	+	1.52427i	−0.384952	+	0.576121i	0.587500	+	0.809224i	$0.300112\pi$
$8$	−3.46868	+	1.43678i	−1.22637	+	0.507977i
$9$	−1.99111	+	1.99111i	−0.663705	+	0.663705i
$10$	2.45117	−	0.487568i	0.775128	−	0.154183i
$11$	1.87132	−	0.775124i	0.564223	−	0.233709i	−0.0822946	−	0.996608i	$-0.526225\pi$
$11$	1.87132	−	0.775124i	0.564223	−	0.233709i	0.646517	+	0.762899i	$0.276225\pi$
$12$	−1.42256	−	0.589242i	−0.410656	−	0.170099i
$13$	1.05257	−	0.703303i	0.291930	−	0.195061i	−0.400978	−	0.916088i	$-0.631329\pi$
$13$	1.05257	−	0.703303i	0.291930	−	0.195061i	0.692907	+	0.721027i	$0.256329\pi$
$14$	2.40764	+	3.60329i	0.643470	+	0.963021i
$15$	0.377210	+	0.252044i	0.0973952	+	0.0650774i
$16$			1.69892i			0.424729i
$17$	−4.56750	+	3.05190i	−1.10778	+	0.740195i	−0.968240	−	0.250021i	$-0.919562\pi$
$17$	−4.56750	+	3.05190i	−1.10778	+	0.740195i	−0.139540	+	0.990216i	$0.544562\pi$
$18$	2.54734	+	6.14983i	0.600415	+	1.44953i
$19$	−1.52343	−	2.27998i	−0.349500	−	0.523063i	0.614518	−	0.788903i	$-0.289351\pi$
$19$	−1.52343	−	2.27998i	−0.349500	−	0.523063i	−0.964017	+	0.265840i	$0.914351\pi$
$20$	0.740079	−	3.72063i	0.165487	−	0.831958i
$21$	−0.153471	+	0.771551i	−0.0334901	+	0.168366i
$22$		−	4.78816i		−	1.02084i
$23$	7.33474	+	1.45897i	1.52940	+	0.304216i	0.886861	−	0.462037i	$-0.152881\pi$
$23$	7.33474	+	1.45897i	1.52940	+	0.304216i	0.642539	+	0.766253i	$0.277881\pi$
$24$	−1.13922	+	1.13922i	−0.232543	+	0.232543i
$25$	1.48569	−	3.58678i	0.297138	−	0.717356i
$26$	−0.583817	−	2.93504i	−0.114496	−	0.575609i
$27$	−0.955053	+	2.30570i	−0.183800	+	0.443733i
$28$	6.45164	−	1.28331i	1.21925	−	0.242523i
$29$	−5.05785	−	1.00607i	−0.939219	−	0.186822i	−0.298336	−	0.954461i	$-0.596432\pi$
$29$	−5.05785	−	1.00607i	−0.939219	−	0.186822i	−0.640883	+	0.767639i	$0.721432\pi$
$30$	0.891703	−	0.595817i	0.162802	−	0.108781i
$31$	0.527749	+	1.27410i	0.0947865	+	0.228835i	0.964160	−	0.265320i	$-0.0854776\pi$
$31$	0.527749	+	1.27410i	0.0947865	+	0.228835i	−0.869374	+	0.494155i	$0.835478\pi$
$32$	−3.22694	−	1.33664i	−0.570447	−	0.236287i
$33$	0.614597	−	0.614597i	0.106988	−	0.106988i
$34$	2.53340	+	12.7363i	0.434475	+	2.18425i
$35$	−1.93811			−0.327601
$36$	10.1039			1.68399
$37$	−0.620545	−	3.11969i	−0.102017	−	0.512874i	−0.997676	−	0.0681330i	$-0.978296\pi$
$37$	−0.620545	−	3.11969i	−0.102017	−	0.512874i	0.895659	−	0.444741i	$-0.146704\pi$
$38$	−6.35763	+	1.26461i	−1.03134	+	0.205147i
$39$	0.301798	−	0.451673i	0.0483264	−	0.0723256i
$40$	−3.30034	−	2.20522i	−0.521829	−	0.348675i
$41$	−2.03747	+	10.2431i	−0.318199	+	1.59970i	0.408511	+	0.912753i	$0.366048\pi$
$41$	−2.03747	+	10.2431i	−0.318199	+	1.59970i	−0.726711	+	0.686943i	$0.758952\pi$
$42$	1.54623	+	1.03316i	0.238588	+	0.159420i
$43$	−0.738574	−	0.738574i	−0.112632	−	0.112632i	0.648545	−	0.761176i	$-0.275378\pi$
$43$	−0.738574	−	0.738574i	−0.112632	−	0.112632i	−0.761176	+	0.648545i	$0.775378\pi$
$44$	−6.71470	−	2.78132i	−1.01228	−	0.419300i
$45$	−2.91976	−	0.580777i	−0.435252	−	0.0865771i
$46$	9.82170	−	14.6992i	1.44813	−	2.16728i
$47$	−6.51992	−	6.51992i	−0.951028	−	0.951028i	0.0478275	−	0.998856i	$-0.484770\pi$
$47$	−6.51992	−	6.51992i	−0.951028	−	0.951028i	−0.998856	+	0.0478275i	$0.984770\pi$
$48$	0.278988	+	0.673537i	0.0402685	+	0.0972167i
$49$	1.39269	+	3.36225i	0.198956	+	0.480322i
$50$	−6.48950	−	6.48950i	−0.917754	−	0.917754i
$51$	−1.30962	+	1.95998i	−0.183383	+	0.274452i
$52$	−4.45510	−	0.886174i	−0.617811	−	0.122890i
$53$	−12.7053	−	5.26272i	−1.74521	−	0.722890i	−0.998320	−	0.0579437i	$-0.981546\pi$
$53$	−12.7053	−	5.26272i	−1.74521	−	0.722890i	−0.746891	−	0.664946i	$-0.768454\pi$
$54$	4.17167	+	4.17167i	0.567693	+	0.567693i
$55$	1.78049	+	1.18969i	0.240082	+	0.160417i
$56$	1.34277	−	6.75056i	0.179435	−	0.902082i
$57$	−0.978374	−	0.653729i	−0.129589	−	0.0865885i
$58$	−6.77279	+	10.1362i	−0.889311	+	1.33095i
$59$	5.32278	−	1.05877i	0.692967	−	0.137840i	0.163973	−	0.986465i	$-0.447569\pi$
$59$	5.32278	−	1.05877i	0.692967	−	0.137840i	0.528995	+	0.848625i	$0.322569\pi$
$60$	−0.317579	−	1.59658i	−0.0409993	−	0.206117i
$61$	4.56051			0.583914			0.291957	−	0.956431i	$-0.405694\pi$
$61$	4.56051			0.583914			0.291957	+	0.956431i	$0.405694\pi$
$62$	3.26005			0.414027
$63$	−1.00708	−	5.06292i	−0.126880	−	0.637868i
$64$	−8.24108	+	8.24108i	−1.03013	+	1.03013i
$65$	1.23646	+	0.512160i	0.153364	+	0.0635257i
$66$	−0.786289	−	1.89827i	−0.0967855	−	0.233661i
$67$	12.7282	−	8.50469i	1.55499	−	1.03901i	0.580593	−	0.814194i	$-0.302821\pi$
$67$	12.7282	−	8.50469i	1.55499	−	1.03901i	0.974400	−	0.224819i	$-0.0721792\pi$
$68$	19.3324	+	3.84545i	2.34440	+	0.466330i
$69$	3.14745	−	0.626067i	0.378909	−	0.0753696i
$70$	−1.75330	+	4.23283i	−0.209559	+	0.505920i
$71$	0.424284	+	2.13302i	0.0503532	+	0.253143i	0.997761	−	0.0668876i	$-0.0213069\pi$
$71$	0.424284	+	2.13302i	0.0503532	+	0.253143i	−0.947407	+	0.320030i	$0.896307\pi$
$72$	4.04576	−	9.76733i	0.476797	−	1.15109i
$73$	5.79670	−	5.79670i	0.678452	−	0.678452i	−0.281197	−	0.959650i	$-0.590732\pi$
$73$	5.79670	−	5.79670i	0.678452	−	0.678452i	0.959650	+	0.281197i	$0.0907316\pi$
$74$	−7.37477	−	1.46693i	−0.857299	−	0.170527i
$75$		−	1.66595i		−	0.192368i
$76$	−1.91955	+	9.65025i	−0.220188	+	1.10696i
$77$	−0.724409	+	3.64185i	−0.0825540	+	0.415027i
$78$	−0.713434	−	1.06773i	−0.0807805	−	0.120897i
$79$	1.37881	+	3.32873i	0.155128	+	0.374512i	0.982268	−	0.187485i	$-0.0600334\pi$
$79$	1.37881	+	3.32873i	0.155128	+	0.374512i	−0.827140	+	0.561996i	$0.810033\pi$
$80$	−1.49342	+	0.997869i	−0.166969	+	0.111565i
$81$		−	7.37665i		−	0.819627i
$82$	20.5276	+	13.7161i	2.26690	+	1.51469i
$83$	8.16638	+	12.2219i	0.896377	+	1.34152i	0.939534	+	0.342455i	$0.111258\pi$
$83$	8.16638	+	12.2219i	0.896377	+	1.34152i	−0.0431572	+	0.999068i	$0.513742\pi$
$84$	2.34702	−	1.56823i	0.256081	−	0.171108i
$85$	−5.36549	−	2.22246i	−0.581969	−	0.241060i
$86$	−2.28119	+	0.944900i	−0.245987	+	0.101891i
$87$	−2.17040	+	0.431719i	−0.232691	+	0.0462852i
$88$	−5.37732	+	5.37732i	−0.573224	+	0.573224i
$89$	5.26086	−	2.17912i	0.557650	−	0.230986i	−0.0860144	−	0.996294i	$-0.527413\pi$
$89$	5.26086	−	2.17912i	0.557650	−	0.230986i	0.643665	+	0.765308i	$0.277413\pi$
$90$	−3.90976	+	5.85136i	−0.412124	+	0.616788i
$91$			2.32071i			0.243276i
$92$	−14.9084	−	22.3119i	−1.55430	−	2.32618i
$93$	0.418453	+	0.418453i	0.0433916	+	0.0433916i
$94$	−20.1377	+	8.34130i	−2.07704	+	0.860340i
$95$	1.10940	−	2.67832i	0.113822	−	0.274790i
$96$	−1.49882			−0.152973
$97$	−9.79663	−	1.01294i	−0.994697	−	0.102848i
$97$	−9.79663	−	1.01294i	−0.994697	−	0.102848i
$98$	8.60304			0.869038
$99$	−2.18264	+	5.26936i	−0.219364	+	0.529591i
$100$	−12.8702	+	5.33100i	−1.28702	+	0.533100i
$101$	3.99728	+	3.99728i	0.397745	+	0.397745i	0.877437	−	0.479692i	$-0.159252\pi$
$101$	3.99728	+	3.99728i	0.397745	+	0.397745i	−0.479692	+	0.877437i	$0.659252\pi$
$102$	3.09586	+	4.63329i	0.306536	+	0.458764i
$103$		−	15.7188i		−	1.54882i	−0.632682	−	0.774412i	$-0.718046\pi$
$103$		−	15.7188i		−	1.54882i	0.632682	−	0.774412i	$-0.281954\pi$
$104$	−2.64054	+	3.95184i	−0.258926	+	0.387510i
$105$	−0.768366	+	0.318268i	−0.0749849	+	0.0310598i
$106$	−22.9875	+	22.9875i	−2.23275	+	2.23275i
$107$	13.4962	−	2.68457i	1.30473	−	0.259527i	0.506688	−	0.862130i	$-0.330870\pi$
$107$	13.4962	−	2.68457i	1.30473	−	0.259527i	0.798041	+	0.602603i	$0.205870\pi$
$108$	8.27339	−	3.42695i	0.796107	−	0.329758i
$109$	3.77713	+	1.56454i	0.361784	+	0.149856i	0.556168	−	0.831070i	$-0.312271\pi$
$109$	3.77713	+	1.56454i	0.361784	+	0.149856i	−0.194385	+	0.980925i	$0.562271\pi$
$110$	4.20899	−	2.81235i	0.401311	−	0.268147i
$111$	−0.758317	−	1.13490i	−0.0719762	−	0.107720i
$112$	−2.58961	−	1.73032i	−0.244696	−	0.163500i
$113$			7.54899i			0.710149i	0.934838	+	0.355075i	$0.115545\pi$
$113$			7.54899i			0.710149i	−0.934838	+	0.355075i	$0.884455\pi$
$114$	−2.31282	+	1.54538i	−0.216616	+	0.144738i
$115$	3.02561	+	7.30447i	0.282140	+	0.681145i
$116$	10.2804	+	15.3857i	0.954512	+	1.42853i
$117$	−0.695425	+	3.49614i	−0.0642921	+	0.323218i
$118$	2.50287	−	12.5828i	0.230407	−	1.15834i
$119$		−	10.0704i		−	0.923155i
$120$	−1.67055	−	0.332293i	−0.152500	−	0.0303341i
$121$	−4.87717	+	4.87717i	−0.443379	+	0.443379i
$122$	4.12563	−	9.96015i	0.373517	−	0.901750i
$123$	0.874310	+	4.39545i	0.0788339	+	0.396325i
$124$	1.89368	−	4.57176i	0.170058	−	0.410556i
$125$	9.21005	−	1.83199i	0.823772	−	0.163858i
$126$	−11.9685	−	2.38068i	−1.06624	−	0.212087i
$127$	9.08000	−	6.06706i	0.805720	−	0.538365i	−0.0831434	−	0.996538i	$-0.526496\pi$
$127$	9.08000	−	6.06706i	0.805720	−	0.538365i	0.888863	+	0.458173i	$0.151496\pi$
$128$	7.86999	+	18.9998i	0.695616	+	1.67936i
$129$	−0.414094	−	0.171523i	−0.0364589	−	0.0151018i
$130$	2.23711	−	2.23711i	0.196208	−	0.196208i
$131$	1.98568	+	9.98271i	0.173490	+	0.872193i	0.965243	+	0.261353i	$0.0841685\pi$
$131$	1.98568	+	9.98271i	0.173490	+	0.872193i	−0.791753	+	0.610841i	$0.790831\pi$
$132$	−3.11879			−0.271455
$133$	5.02691			0.435888
$134$	−7.05980	−	35.4920i	−0.609874	−	3.06604i
$135$	−2.58776	+	0.514738i	−0.222719	+	0.0443016i
$136$	11.4583	−	17.1486i	0.982541	−	1.47048i
$137$	−9.00464	−	6.01671i	−0.769319	−	0.514042i	0.107883	−	0.994164i	$-0.465593\pi$
$137$	−9.00464	−	6.01671i	−0.769319	−	0.514042i	−0.877202	+	0.480121i	$0.840593\pi$
$138$	1.47999	−	7.44039i	0.125985	−	0.633368i
$139$	0.592049	+	0.395594i	0.0502169	+	0.0335539i	0.580425	−	0.814313i	$-0.302886\pi$
$139$	0.592049	+	0.395594i	0.0502169	+	0.0335539i	−0.530208	+	0.847867i	$0.677886\pi$
$140$	4.91749	+	4.91749i	0.415604	+	0.415604i
$141$	−3.65550	−	1.51416i	−0.307849	−	0.127515i
$142$	5.04233	+	1.00298i	0.423143	+	0.0841684i
$143$	1.42454	−	2.13197i	0.119126	−	0.178284i
$144$	−3.38274	−	3.38274i	−0.281895	−	0.281895i
$145$	−2.08638	−	5.03697i	−0.173265	−	0.418298i
$146$	−7.41605	−	17.9039i	−0.613756	−	1.48174i
$147$	1.10427	+	1.10427i	0.0910784	+	0.0910784i
$148$	−6.34098	+	9.48995i	−0.521225	+	0.780069i
$149$	−14.0346	−	2.79166i	−1.14976	−	0.228702i	−0.416817	−	0.908990i	$-0.636854\pi$
$149$	−14.0346	−	2.79166i	−1.14976	−	0.228702i	−0.732944	+	0.680289i	$0.761854\pi$
$150$	−3.63844	−	1.50709i	−0.297078	−	0.123054i
$151$	−7.14658	−	7.14658i	−0.581581	−	0.581581i	0.353757	−	0.935337i	$-0.384904\pi$
$151$	−7.14658	−	7.14658i	−0.581581	−	0.581581i	−0.935337	+	0.353757i	$0.884904\pi$
$152$	8.56013	+	5.71970i	0.694318	+	0.463929i
$153$	3.01772	−	15.1711i	0.243968	−	1.22651i
$154$	7.29846	+	4.87668i	0.588127	+	0.392974i
$155$	−0.810008	+	1.21226i	−0.0650614	+	0.0973713i
$156$	−1.91175	+	0.380271i	−0.153063	+	0.0304461i
$157$	0.0826996	+	0.415759i	0.00660015	+	0.0331812i	0.983945	−	0.178472i	$-0.0571153\pi$
$157$	0.0826996	+	0.415759i	0.00660015	+	0.0331812i	−0.977345	+	0.211653i	$0.932115\pi$
$158$	8.51728			0.677598
$159$	−5.90126			−0.468000
$160$	−0.720399	−	3.62169i	−0.0569526	−	0.286320i
$161$	−9.69421	+	9.69421i	−0.764011	+	0.764011i
$162$	−16.1106	−	6.67322i	−1.26577	−	0.524298i
$163$	−3.76091	−	9.07965i	−0.294578	−	0.711173i	−0.999997	−	0.00238318i	$-0.999241\pi$
$163$	−3.76091	−	9.07965i	−0.294578	−	0.711173i	0.705420	−	0.708790i	$-0.250759\pi$
$164$	31.1589	−	20.8197i	2.43310	−	1.62575i
$165$	0.901243	+	0.179268i	0.0701617	+	0.0139560i
$166$	34.0802	−	6.77897i	2.64513	−	0.526150i
$167$	−4.73980	+	11.4429i	−0.366776	+	0.885477i	0.627498	+	0.778618i	$0.284079\pi$
$167$	−4.73980	+	11.4429i	−0.366776	+	0.885477i	−0.994274	+	0.106858i	$0.965921\pi$
$168$	−0.576203	−	2.89677i	−0.0444550	−	0.223491i
$169$	−4.36162	+	10.5299i	−0.335509	+	0.809991i
$170$	−9.70770	+	9.70770i	−0.744547	+	0.744547i
$171$	7.57303	+	1.50637i	0.579124	+	0.115195i
$172$			3.74791i			0.285775i
$173$	−3.57468	+	17.9711i	−0.271778	+	1.36632i	0.567839	+	0.823140i	$0.307780\pi$
$173$	−3.57468	+	17.9711i	−0.271778	+	1.36632i	−0.839617	+	0.543180i	$0.817220\pi$
$174$	−1.02056	+	5.13070i	−0.0773685	+	0.388957i
$175$	3.95407	+	5.91769i	0.298900	+	0.447335i
$176$	1.31687	+	3.17921i	0.0992629	+	0.239642i
$177$	1.93636	−	1.29383i	0.145545	−	0.0972504i
$178$		−	13.4610i		−	1.00895i
$179$	1.45998	+	0.975525i	0.109124	+	0.0729142i	0.608935	−	0.793220i	$-0.291597\pi$
$179$	1.45998	+	0.975525i	0.109124	+	0.0729142i	−0.499811	+	0.866135i	$0.666597\pi$
$180$	5.93461	+	8.88178i	0.442340	+	0.662009i
$181$	−2.67875	+	1.78988i	−0.199110	+	0.133041i	−0.651128	−	0.758968i	$-0.725704\pi$
$181$	−2.67875	+	1.78988i	−0.199110	+	0.133041i	0.452018	+	0.892009i	$0.350704\pi$
$182$	5.06842	+	2.09941i	0.375696	+	0.155618i
$183$	1.80802	−	0.748906i	0.133653	−	0.0553607i
$184$	−27.5381	+	5.47767i	−2.03014	+	0.403819i
$185$	2.37785	−	2.37785i	0.174823	−	0.174823i
$186$	1.29245	−	0.535351i	0.0947671	−	0.0392538i
$187$	−6.18162	+	9.25145i	−0.452045	+	0.676533i
$188$			33.0855i			2.41301i
$189$	−2.54181	−	3.80409i	−0.184890	−	0.276707i
$190$	−4.84584	−	4.84584i	−0.351554	−	0.351554i
$191$	−21.0243	+	8.70854i	−1.52126	+	0.630128i	−0.977844	−	0.209334i	$-0.932870\pi$
$191$	−21.0243	+	8.70854i	−1.52126	+	0.630128i	−0.543419	+	0.839462i	$0.682870\pi$
$192$	−1.91387	+	4.62049i	−0.138122	+	0.333455i
$193$	0.260716			0.0187668			0.00938338	−	0.999956i	$-0.497013\pi$
$193$	0.260716			0.0187668			0.00938338	+	0.999956i	$0.497013\pi$
$194$	−11.0747	+	20.4795i	−0.795117	+	1.47034i
$195$	0.574302			0.0411266
$196$	4.99729	−	12.0645i	0.356949	−	0.861752i
$197$	11.9350	−	4.94363i	0.850332	−	0.352219i	0.0854129	−	0.996346i	$-0.472779\pi$
$197$	11.9350	−	4.94363i	0.850332	−	0.352219i	0.764919	+	0.644127i	$0.222779\pi$
$198$	9.53377	+	9.53377i	0.677535	+	0.677535i
$199$	−8.36751	−	12.5229i	−0.593157	−	0.887722i	0.406507	−	0.913648i	$-0.366747\pi$
$199$	−8.36751	−	12.5229i	−0.593157	−	0.887722i	−0.999664	+	0.0259253i	$0.991747\pi$
$200$			14.5760i			1.03068i
$201$	3.64949	−	5.46185i	0.257415	−	0.385249i
$202$	12.3462	−	5.11395i	0.868674	−	0.359816i
$203$	6.68487	−	6.68487i	0.469186	−	0.469186i
$204$	8.29583	−	1.65014i	0.580824	−	0.115533i
$205$	−10.2008	+	4.22530i	−0.712454	+	0.295108i
$206$	−34.3299	−	14.2199i	−2.39188	−	0.990749i
$207$	−17.5093	+	11.6993i	−1.21698	+	0.813160i
$208$	1.19485	+	1.78823i	0.0828482	+	0.123991i
$209$	−4.61809	−	3.08571i	−0.319440	−	0.213443i
$210$			1.96603i			0.135669i
$211$	−9.16228	+	6.12204i	−0.630757	+	0.421458i	−0.829433	−	0.558607i	$-0.811336\pi$
$211$	−9.16228	+	6.12204i	−0.630757	+	0.421458i	0.198675	+	0.980065i	$0.436336\pi$
$212$	18.8838	+	45.5896i	1.29695	+	3.13111i
$213$	0.518482	+	0.775963i	0.0355258	+	0.0531681i
$214$	6.34616	−	31.9043i	0.433815	−	2.18093i
$215$	0.215431	−	1.08304i	0.0146922	−	0.0738629i
$216$		−	9.36996i		−	0.637545i
$217$	−2.47958	−	0.493219i	−0.168325	−	0.0334819i
$218$	6.83390	−	6.83390i	0.462850	−	0.462850i
$219$	1.34620	−	3.25001i	0.0909678	−	0.219616i
$220$	−1.49903	−	7.53612i	−0.101064	−	0.508085i
$221$	−2.66119	+	6.42467i	−0.179011	+	0.432170i
$222$	−3.16463	+	0.629483i	−0.212396	+	0.0422482i
$223$	−3.17917	−	0.632376i	−0.212893	−	0.0423470i	0.0874915	−	0.996165i	$-0.472115\pi$
$223$	−3.17917	−	0.632376i	−0.212893	−	0.0423470i	−0.300384	+	0.953818i	$0.597115\pi$
$224$	5.32400	−	3.55738i	0.355725	−	0.237688i
$225$	4.18350	+	10.0999i	0.278900	+	0.673324i
$226$	16.4870	+	6.82913i	1.09670	+	0.454267i
$227$	−2.16809	+	2.16809i	−0.143901	+	0.143901i	−0.775387	−	0.631486i	$-0.782445\pi$
$227$	−2.16809	+	2.16809i	−0.143901	+	0.143901i	0.631486	+	0.775387i	$0.282445\pi$
$228$	0.823710	+	4.14107i	0.0545515	+	0.274249i
$229$	7.66542			0.506545			0.253272	−	0.967395i	$-0.418493\pi$
$229$	7.66542			0.506545			0.253272	+	0.967395i	$0.418493\pi$
$230$	18.6900			1.23239
$231$	0.310855	+	1.56277i	0.0204528	+	0.102823i
$232$	18.9896	−	3.77726i	1.24673	−	0.247989i
$233$	11.3544	−	16.9931i	0.743853	−	1.11325i	−0.245737	−	0.969337i	$-0.579030\pi$
$233$	11.3544	−	16.9931i	0.743853	−	1.11325i	0.989590	−	0.143918i	$-0.0459702\pi$
$234$	7.00645	+	4.68156i	0.458026	+	0.306043i
$235$	1.90176	−	9.56079i	0.124057	−	0.623677i
$236$	−16.1916	−	10.8189i	−1.05399	−	0.704251i
$237$	1.09326	+	1.09326i	0.0710148	+	0.0710148i
$238$	−21.9938	−	9.11014i	−1.42565	−	0.590522i
$239$	1.59195	+	0.316659i	0.102975	+	0.0204830i	0.246309	−	0.969191i	$-0.420782\pi$
$239$	1.59195	+	0.316659i	0.102975	+	0.0204830i	−0.143334	+	0.989674i	$0.545782\pi$
$240$	−0.428201	+	0.640848i	−0.0276403	+	0.0413666i
$241$	17.4740	+	17.4740i	1.12560	+	1.12560i	0.990884	+	0.134714i	$0.0430116\pi$
$241$	17.4740	+	17.4740i	1.12560	+	1.12560i	0.134714	+	0.990884i	$0.456988\pi$
$242$	6.23964	+	15.0638i	0.401099	+	0.968340i
$243$	−4.07652	−	9.84159i	−0.261509	−	0.631338i
$244$	−11.5712	−	11.5712i	−0.740770	−	0.740770i
$245$	−2.13755	+	3.19907i	−0.136563	+	0.204381i
$246$	10.3906	+	2.06682i	0.662481	+	0.131776i
$247$	−3.20703	−	1.32840i	−0.204059	−	0.0845239i
$248$	−3.66119	−	3.66119i	−0.232486	−	0.232486i
$249$	5.24459	+	3.50432i	0.332362	+	0.222077i
$250$	4.33073	−	21.7720i	0.273899	−	1.37698i
$251$	7.04096	+	4.70462i	0.444422	+	0.296953i	0.757573	−	0.652750i	$-0.226385\pi$
$251$	7.04096	+	4.70462i	0.444422	+	0.296953i	−0.313152	+	0.949703i	$0.601385\pi$
$252$	−10.2907	+	15.4012i	−0.648255	+	0.970183i
$253$	14.8565	−	2.95514i	0.934020	−	0.185788i
$254$	−5.03631	−	25.3192i	−0.316006	−	1.58867i
$255$	−2.49212			−0.156062
$256$	25.3059			1.58162
$257$	5.69646	+	28.6380i	0.355335	+	1.78639i	0.582811	+	0.812608i	$0.301953\pi$
$257$	5.69646	+	28.6380i	0.355335	+	1.78639i	−0.227475	+	0.973784i	$0.573047\pi$
$258$	−0.749213	+	0.749213i	−0.0466440	+	0.0466440i
$259$	5.38728	+	2.23148i	0.334749	+	0.138658i
$260$	−1.83775	−	4.43671i	−0.113972	−	0.275153i
$261$	12.0739	−	8.06755i	0.747358	−	0.499369i
$262$	23.5986	+	4.69404i	1.45792	+	0.289999i
$263$	−10.4418	+	2.07700i	−0.643867	+	0.128073i	−0.506215	−	0.862407i	$-0.668956\pi$
$263$	−10.4418	+	2.07700i	−0.643867	+	0.128073i	−0.137653	+	0.990481i	$0.543956\pi$
$264$	−1.24881	+	3.01488i	−0.0768587	+	0.185553i
$265$	−2.83641	−	14.2596i	−0.174239	−	0.875960i
$266$	4.54755	−	10.9788i	0.278828	−	0.673151i
$267$	1.72783	−	1.72783i	0.105741	−	0.105741i
$268$	−53.8733	−	10.7161i	−3.29083	−	0.654588i
$269$			14.4291i			0.879760i	0.898057	+	0.439880i	$0.144979\pi$
$269$			14.4291i			0.879760i	−0.898057	+	0.439880i	$0.855021\pi$
$270$	−1.21681	+	6.11732i	−0.0740528	+	0.372289i
$271$	−2.15154	+	10.8165i	−0.130697	+	0.657056i	0.858778	+	0.512348i	$0.171224\pi$
$271$	−2.15154	+	10.8165i	−0.130697	+	0.657056i	−0.989474	+	0.144708i	$0.953776\pi$
$272$	−5.18493	−	7.75980i	−0.314383	−	0.470507i
$273$	0.381095	+	0.920046i	0.0230649	+	0.0556837i
$274$	−21.2865	+	14.2232i	−1.28596	+	0.859253i
$275$		−	7.86359i		−	0.474192i
$276$	−9.57439	−	6.39740i	−0.576311	−	0.385079i
$277$	−8.66885	−	12.9738i	−0.520860	−	0.779523i	0.474027	−	0.880510i	$-0.342800\pi$
$277$	−8.66885	−	12.9738i	−0.520860	−	0.779523i	−0.994888	+	0.100987i	$0.967800\pi$
$278$	1.39957	−	0.935163i	0.0839406	−	0.0560873i
$279$	−3.58768	−	1.48607i	−0.214789	−	0.0889685i
$280$	6.72270	−	2.78463i	0.401758	−	0.166414i
$281$	13.9935	−	2.78347i	0.834780	−	0.166048i	0.240847	−	0.970563i	$-0.422575\pi$
$281$	13.9935	−	2.78347i	0.834780	−	0.166048i	0.593932	+	0.804515i	$0.297575\pi$
$282$	−6.61384	+	6.61384i	−0.393848	+	0.393848i
$283$	−12.3986	+	5.13568i	−0.737022	+	0.305284i	−0.719434	−	0.694561i	$-0.755599\pi$
$283$	−12.3986	+	5.13568i	−0.737022	+	0.305284i	−0.0175878	+	0.999845i	$0.505599\pi$
$284$	4.33550	−	6.48854i	0.257265	−	0.385024i
$285$		−	1.24400i		−	0.0736883i
$286$	−3.36753	−	5.03986i	−0.199126	−	0.298013i
$287$	−13.5381	−	13.5381i	−0.799128	−	0.799128i
$288$	9.08660	−	3.76379i	0.535433	−	0.221784i
$289$	5.04229	−	12.1732i	0.296605	−	0.716068i
$290$	−12.8882			−0.756819
$291$	−4.05022	+	1.20718i	−0.237428	+	0.0707660i
$292$	−29.4155			−1.72141
$293$	10.1005	−	24.3847i	0.590077	−	1.42457i	−0.293351	−	0.956005i	$-0.594770\pi$
$293$	10.1005	−	24.3847i	0.590077	−	1.42457i	0.883428	−	0.468567i	$-0.155230\pi$
$294$	3.41068	−	1.41275i	0.198915	−	0.0823933i
$295$	4.05707	+	4.05707i	0.236212	+	0.236212i
$296$	6.63477	+	9.92964i	0.385638	+	0.577148i
$297$			5.05498i			0.293320i
$298$	−18.7933	+	28.1262i	−1.08867	+	1.62930i
$299$	8.74641	−	3.62288i	0.505818	−	0.209517i
$300$	−4.22696	+	4.22696i	−0.244044	+	0.244044i
$301$	1.87802	−	0.373561i	0.108247	−	0.0215317i
$302$	−22.0732	+	9.14303i	−1.27017	+	0.526122i
$303$	2.24114	+	0.928312i	0.128750	+	0.0533301i
$304$	3.87350	−	2.58819i	0.222160	−	0.148443i
$305$	2.67864	+	4.00888i	0.153379	+	0.229548i
$306$	−30.4037	−	20.3151i	−1.73806	−	1.16134i
$307$			30.0254i			1.71364i	0.515616	+	0.856820i	$0.327563\pi$
$307$			30.0254i			1.71364i	−0.515616	+	0.856820i	$0.672437\pi$
$308$	11.0783	−	7.40230i	0.631246	−	0.421785i
$309$	−2.58128	−	6.23175i	−0.146844	−	0.354512i
$310$	1.91481	+	2.86572i	0.108754	+	0.162762i
$311$	1.75080	−	8.80186i	0.0992787	−	0.499108i	−0.898866	−	0.438223i	$-0.855608\pi$
$311$	1.75080	−	8.80186i	0.0992787	−	0.499108i	0.998145	−	0.0608844i	$-0.0193921\pi$
$312$	−0.397890	+	2.00033i	−0.0225261	+	0.113246i
$313$		−	21.4497i		−	1.21241i	−0.795310	−	0.606203i	$-0.792692\pi$
$313$		−	21.4497i		−	1.21241i	0.795310	−	0.606203i	$-0.207308\pi$
$314$	0.982831	+	0.195497i	0.0554643	+	0.0110325i
$315$	3.85900	−	3.85900i	0.217430	−	0.217430i
$316$	4.94747	−	11.9443i	0.278317	−	0.671917i
$317$	1.11986	+	5.62991i	0.0628975	+	0.316207i	0.999407	−	0.0344352i	$-0.0109632\pi$
$317$	1.11986	+	5.62991i	0.0628975	+	0.316207i	−0.936509	+	0.350642i	$0.885963\pi$
$318$	−5.33853	+	12.8883i	−0.299370	+	0.722742i
$319$	−10.2447	+	2.03779i	−0.573590	+	0.114094i
$320$	−12.0847	−	2.40379i	−0.675554	−	0.134376i
$321$	4.90974	−	3.28059i	0.274035	−	0.183104i
$322$	12.4024	+	29.9419i	0.691156	+	1.66860i
$323$	13.9166	+	5.76443i	0.774338	+	0.320741i
$324$	−18.7165	+	18.7165i	−1.03980	+	1.03980i
$325$	−0.958801	−	4.82022i	−0.0531847	−	0.267378i
$326$	−23.2322			−1.28671
$327$	1.75437			0.0970168
$328$	−7.64964	−	38.4573i	−0.422381	−	2.12345i
$329$	16.5786	−	3.29769i	0.914007	−	0.181807i
$330$	1.20682	−	1.80614i	0.0664335	−	0.0994248i
$331$	23.2646	+	15.5449i	1.27874	+	0.854426i	0.994542	−	0.104339i	$-0.0332728\pi$
$331$	23.2646	+	15.5449i	1.27874	+	0.854426i	0.284198	+	0.958766i	$0.408273\pi$
$332$	10.2898	−	51.7303i	0.564725	−	2.83907i
$333$	7.44723	+	4.97608i	0.408106	+	0.272688i
$334$	20.7034	+	20.7034i	1.13284	+	1.13284i
$335$	14.9519	+	6.19329i	0.816912	+	0.338376i
$336$	−1.31080	−	0.260734i	−0.0715100	−	0.0142242i
$337$	−0.677949	+	1.01462i	−0.0369302	+	0.0552700i	−0.849475	−	0.527628i	$-0.823081\pi$
$337$	−0.677949	+	1.01462i	−0.0369302	+	0.0552700i	0.812545	+	0.582898i	$0.198081\pi$
$338$	19.0515	+	19.0515i	1.03627	+	1.03627i
$339$	1.23966	+	2.99280i	0.0673291	+	0.162547i
$340$	7.97469	+	19.2526i	0.432488	+	1.04412i
$341$	1.97517	+	1.97517i	0.106961	+	0.106961i
$342$	10.1408	−	15.1768i	0.548351	−	0.820665i
$343$	−19.1294	−	3.80508i	−1.03289	−	0.205455i
$344$	3.62305	+	1.50072i	0.195342	+	0.0809132i
$345$	2.39901	+	2.39901i	0.129158	+	0.129158i
$346$	36.0151	+	24.0645i	1.93618	+	1.29372i
$347$	0.402254	−	2.02227i	0.0215941	−	0.108561i	−0.968485	−	0.249072i	$-0.919874\pi$
$347$	0.402254	−	2.02227i	0.0215941	−	0.108561i	0.990079	+	0.140511i	$0.0448745\pi$
$348$	6.60225	+	4.41148i	0.353918	+	0.236480i
$349$	−6.64216	+	9.94069i	−0.355547	+	0.532113i	−0.965527	−	0.260304i	$-0.916177\pi$
$349$	−6.64216	+	9.94069i	−0.355547	+	0.532113i	0.609980	+	0.792417i	$0.291177\pi$
$350$	16.5012	−	3.28230i	0.882028	−	0.175446i
$351$	0.616350	+	3.09860i	0.0328983	+	0.165391i
$352$	−7.07468			−0.377082
$353$	−16.9597			−0.902671			−0.451336	−	0.892354i	$-0.649052\pi$
$353$	−16.9597			−0.902671			−0.451336	+	0.892354i	$0.649052\pi$
$354$	−1.07402	−	5.39945i	−0.0570834	−	0.286978i
$355$	−1.62580	+	1.62580i	−0.0862887	+	0.0862887i
$356$	−18.8772	−	7.81918i	−1.00049	−	0.414416i
$357$	−1.65372	−	3.99243i	−0.0875241	−	0.211302i
$358$	3.45130	−	2.30609i	0.182407	−	0.121880i
$359$	−17.9103	−	3.56258i	−0.945269	−	0.188026i	−0.301691	−	0.953406i	$-0.597551\pi$
$359$	−17.9103	−	3.56258i	−0.945269	−	0.188026i	−0.643579	+	0.765380i	$0.722551\pi$
$360$	10.9622	−	2.18051i	0.577758	−	0.114923i
$361$	4.39353	−	10.6069i	0.231238	−	0.558259i
$362$	1.48579	+	7.46959i	0.0780916	+	0.392593i
$363$	−1.13265	+	2.73447i	−0.0594489	+	0.143522i
$364$	5.88823	−	5.88823i	0.308627	−	0.308627i
$365$	8.50026	+	1.69081i	0.444924	+	0.0885009i
$366$		−	4.62620i		−	0.241816i
$367$	7.05622	−	35.4740i	0.368331	−	1.85173i	−0.139433	−	0.990231i	$-0.544528\pi$
$367$	7.05622	−	35.4740i	0.368331	−	1.85173i	0.507765	−	0.861496i	$-0.330472\pi$
$368$	−2.47867	+	12.4611i	−0.129210	+	0.649581i
$369$	−16.3383	−	24.4519i	−0.850536	−	1.27292i
$370$	−3.04212	−	7.34433i	−0.158152	−	0.381814i
$371$	20.9620	−	14.0064i	1.08829	−	0.727175i
$372$		−	2.12345i		−	0.110096i
$373$	−8.76267	−	5.85503i	−0.453714	−	0.303162i	0.307635	−	0.951504i	$-0.400462\pi$
$373$	−8.76267	−	5.85503i	−0.453714	−	0.303162i	−0.761349	+	0.648343i	$0.775462\pi$
$374$	14.6130	+	21.8699i	0.755620	+	1.13087i
$375$	3.35049	−	2.23873i	0.173019	−	0.115607i
$376$	31.9832	+	13.2479i	1.64941	+	0.683207i
$377$	−6.03130	+	2.49825i	−0.310628	+	0.128666i
$378$	−10.6076	+	2.10997i	−0.545594	+	0.108525i
$379$	−16.0695	+	16.0695i	−0.825433	+	0.825433i	−0.986881	−	0.161449i	$-0.948383\pi$
$379$	−16.0695	+	16.0695i	−0.825433	+	0.825433i	0.161449	+	0.986881i	$0.448383\pi$
$380$	−9.61042	+	3.98077i	−0.493004	+	0.204209i
$381$	2.60347	−	3.89637i	0.133380	−	0.199617i
$382$			53.7951i			2.75240i
$383$	−6.08084	−	9.10062i	−0.310717	−	0.465020i	0.642940	−	0.765916i	$-0.277714\pi$
$383$	−6.08084	−	9.10062i	−0.310717	−	0.465020i	−0.953657	+	0.300896i	$0.902714\pi$
$384$	6.24013	+	6.24013i	0.318440	+	0.318440i
$385$	−3.62682	+	1.50228i	−0.184840	+	0.0765632i
$386$	0.235855	−	0.569403i	0.0120047	−	0.0289819i
$387$	2.94117			0.149508
$388$	22.2865	+	27.4267i	1.13143	+	1.39238i
$389$	12.0964			0.613310			0.306655	−	0.951821i	$-0.400790\pi$
$389$	12.0964			0.613310			0.306655	+	0.951821i	$0.400790\pi$
$390$	0.519538	−	1.25427i	0.0263078	−	0.0635127i
$391$	−37.9540	+	15.7211i	−1.91942	+	0.795049i
$392$	−9.66161	−	9.66161i	−0.487985	−	0.487985i
$393$	2.42654	+	3.63157i	0.122403	+	0.183189i
$394$		−	30.5382i		−	1.53849i
$395$	−2.11624	+	3.16718i	−0.106480	+	0.159358i
$396$	18.9077	−	7.83181i	0.950146	−	0.393563i
$397$	−6.01400	+	6.01400i	−0.301834	+	0.301834i	−0.841731	−	0.539897i	$-0.818463\pi$
$397$	−6.01400	+	6.01400i	−0.301834	+	0.301834i	0.539897	+	0.841731i	$0.318463\pi$
$398$	−34.9195	+	6.94593i	−1.75036	+	0.348168i
$399$	1.99292	−	0.825496i	0.0997709	−	0.0413265i
$400$	6.09364	+	2.52407i	0.304682	+	0.126203i
$401$	5.14866	−	3.44022i	0.257112	−	0.171796i	−0.420334	−	0.907370i	$-0.638087\pi$
$401$	5.14866	−	3.44022i	0.257112	−	0.171796i	0.677445	+	0.735573i	$0.263087\pi$
$402$	−8.62720	−	12.9115i	−0.430285	−	0.643968i
$403$	1.45157	+	0.969908i	0.0723078	+	0.0483145i
$404$		−	20.2843i		−	1.00918i
$405$	6.48437	−	4.33272i	0.322211	−	0.215295i
$406$	−8.55234	−	20.6472i	−0.424445	−	1.02470i
$407$	−3.57938	−	5.35692i	−0.177423	−	0.265533i
$408$	1.72660	−	8.68019i	0.0854793	−	0.429733i
$409$	−2.29572	+	11.5414i	−0.113516	+	0.570684i	0.881602	+	0.471993i	$0.156465\pi$
$409$	−2.29572	+	11.5414i	−0.113516	+	0.570684i	−0.995118	+	0.0986905i	$0.968535\pi$
$410$			26.1009i			1.28903i
$411$	−4.55794	−	0.906630i	−0.224826	−	0.0447208i
$412$	−39.8828	+	39.8828i	−1.96488	+	1.96488i
$413$	−3.80733	+	9.19171i	−0.187347	+	0.452295i
$414$	9.71169	+	48.8239i	0.477303	+	2.39957i
$415$	−5.94693	+	14.3572i	−0.291923	+	0.704766i
$416$	−4.33663	+	0.862610i	−0.212621	+	0.0422929i
$417$	0.299681	+	0.0596102i	0.0146754	+	0.00291913i
$418$	−10.9169	+	7.29444i	−0.533963	+	0.356783i
$419$	−9.47986	−	22.8864i	−0.463121	−	1.11807i	−0.967109	−	0.254363i	$-0.918134\pi$
$419$	−9.47986	−	22.8864i	−0.463121	−	1.11807i	0.503988	−	0.863711i	$-0.331866\pi$
$420$	2.75707	+	1.14202i	0.134531	+	0.0557247i
$421$	13.8000	−	13.8000i	0.672569	−	0.672569i	−0.285738	−	0.958308i	$-0.592239\pi$
$421$	13.8000	−	13.8000i	0.672569	−	0.672569i	0.958308	+	0.285738i	$0.0922388\pi$
$422$	5.08194	+	25.5487i	0.247385	+	1.24369i
$423$	25.9638			1.26240
$424$	51.6321			2.50748
$425$	4.16061	+	20.9168i	0.201819	+	1.01461i
$426$	2.16374	−	0.430395i	0.104834	−	0.0208527i
$427$	−4.64482	+	6.95147i	−0.224779	+	0.336405i
$428$	−41.0549	−	27.4320i	−1.98446	−	1.32597i
$429$	0.214657	−	1.07915i	0.0103637	−	0.0521020i
$430$	−2.17048	−	1.45027i	−0.104670	−	0.0699380i
$431$	−12.8517	−	12.8517i	−0.619042	−	0.619042i	0.326244	−	0.945286i	$-0.394217\pi$
$431$	−12.8517	−	12.8517i	−0.619042	−	0.619042i	−0.945286	+	0.326244i	$0.894217\pi$
$432$	−3.91720	−	1.62256i	−0.188466	−	0.0780653i
$433$	22.4864	+	4.47283i	1.08063	+	0.214951i	0.703132	−	0.711060i	$-0.251784\pi$
$433$	22.4864	+	4.47283i	1.08063	+	0.214951i	0.377498	+	0.926010i	$0.376784\pi$
$434$	−3.32032	+	4.96921i	−0.159381	+	0.238530i
$435$	−1.65430	−	1.65430i	−0.0793174	−	0.0793174i
$436$	−5.61392	−	13.5532i	−0.268858	−	0.649081i
$437$	−7.84757	−	18.9457i	−0.375400	−	0.906296i
$438$	−5.88020	−	5.88020i	−0.280967	−	0.280967i
$439$	9.89024	−	14.8018i	0.472035	−	0.706451i	−0.516693	−	0.856171i	$-0.672837\pi$
$439$	9.89024	−	14.8018i	0.472035	−	0.706451i	0.988728	+	0.149720i	$0.0478371\pi$
$440$	−7.88529	−	1.56848i	−0.375916	−	0.0747744i
$441$	−9.46763	−	3.92162i	−0.450840	−	0.186744i
$442$	11.6240	+	11.6240i	0.552900	+	0.552900i
$443$	1.47578	+	0.986088i	0.0701167	+	0.0468504i	0.590134	−	0.807305i	$-0.299075\pi$
$443$	1.47578	+	0.986088i	0.0701167	+	0.0468504i	−0.520018	+	0.854155i	$0.674075\pi$
$444$	−0.955492	+	4.80358i	−0.0453457	+	0.227968i
$445$	5.00554	+	3.34459i	0.237285	+	0.158549i
$446$	−4.25712	+	6.37123i	−0.201580	+	0.301686i
$447$	−6.02247	+	1.19794i	−0.284853	+	0.0566608i
$448$	−4.16822	−	20.9551i	−0.196930	−	0.990034i
$449$	−9.65284			−0.455546			−0.227773	−	0.973714i	$-0.573144\pi$
$449$	−9.65284			−0.455546			−0.227773	+	0.973714i	$0.573144\pi$
$450$	25.8427			1.21823
$451$	4.12689	+	20.7473i	0.194328	+	0.976951i
$452$	19.1537	−	19.1537i	0.900916	−	0.900916i
$453$	−4.00685	−	1.65969i	−0.188258	−	0.0779791i
$454$	2.77376	+	6.69645i	0.130179	+	0.314280i
$455$	−2.03999	+	1.36308i	−0.0956364	+	0.0639022i
$456$	4.33293	+	0.861874i	0.202908	+	0.0403610i
$457$	−20.0714	+	3.99245i	−0.938900	+	0.186759i	−0.640741	−	0.767757i	$-0.721373\pi$
$457$	−20.0714	+	3.99245i	−0.938900	+	0.186759i	−0.298159	+	0.954516i	$0.596373\pi$
$458$	6.93446	−	16.7413i	0.324026	−	0.782268i
$459$	−2.67458	−	13.4460i	−0.124839	−	0.627606i
$460$	10.8566	−	26.2101i	0.506191	−	1.22205i
$461$	−26.4448	+	26.4448i	−1.23166	+	1.23166i	−0.268328	+	0.963328i	$0.586471\pi$
$461$	−26.4448	+	26.4448i	−1.23166	+	1.23166i	−0.963328	+	0.268328i	$0.913529\pi$
$462$	3.69431	+	0.734843i	0.171875	+	0.0341880i
$463$			28.8345i			1.34005i	0.742338	+	0.670026i	$0.233717\pi$
$463$			28.8345i			1.34005i	−0.742338	+	0.670026i	$0.766283\pi$
$464$	1.70923	−	8.59286i	0.0793489	−	0.398914i
$465$	−0.122056	+	0.613618i	−0.00566022	+	0.0284559i
$466$	−26.8412	−	40.1707i	−1.24339	−	1.86087i
$467$	−16.0152	−	38.6641i	−0.741094	−	1.78916i	−0.601373	−	0.798969i	$-0.705379\pi$
$467$	−16.0152	−	38.6641i	−0.741094	−	1.78916i	−0.139721	−	0.990191i	$-0.544621\pi$
$468$	10.6351	−	7.10614i	0.491607	−	0.328481i
$469$			28.0631i			1.29583i
$470$	−19.1603	−	12.8025i	−0.883801	−	0.590537i
$471$	0.101060	+	0.151247i	0.00465661	+	0.00696912i
$472$	−16.9418	+	11.3202i	−0.779812	+	0.521053i
$473$	−1.95459	−	0.809618i	−0.0898722	−	0.0372263i
$474$	3.37668	−	1.39867i	0.155096	−	0.0642429i
$475$	−10.4411	+	2.07687i	−0.479072	+	0.0952934i
$476$	−25.5513	+	25.5513i	−1.17114	+	1.17114i
$477$	35.7764	−	14.8191i	1.63809	−	0.678519i
$478$	2.13173	−	3.19036i	0.0975031	−	0.145924i
$479$			19.1195i			0.873593i	0.899560	+	0.436797i	$0.143887\pi$
$479$			19.1195i			0.873593i	−0.899560	+	0.436797i	$0.856113\pi$
$480$	−0.880341	−	1.31752i	−0.0401819	−	0.0601364i
$481$	−2.84725	−	2.84725i	−0.129824	−	0.129824i
$482$	53.9709	−	22.3555i	2.45831	−	1.01826i
$483$	−2.25134	+	5.43522i	−0.102440	+	0.247311i
$484$	24.7493			1.12497
$485$	−4.86370	−	9.20659i	−0.220849	−	0.418050i
$486$	−25.1818			−1.14227
$487$	10.4237	−	25.1650i	0.472342	−	1.14033i	−0.490784	−	0.871281i	$-0.663290\pi$
$487$	10.4237	−	25.1650i	0.472342	−	1.14033i	0.963126	−	0.269052i	$-0.0867104\pi$
$488$	−15.8190	+	6.55244i	−0.716092	+	0.296615i
$489$	−2.98204	−	2.98204i	−0.134852	−	0.134852i
$490$	5.05305	+	7.56242i	0.228273	+	0.341635i
$491$			7.57555i			0.341880i	0.985281	+	0.170940i	$0.0546804\pi$
$491$			7.57555i			0.341880i	−0.985281	+	0.170940i	$0.945320\pi$
$492$	8.93405	−	13.3708i	0.402778	−	0.602800i
$493$	26.1721	−	10.8408i	1.17873	−	0.488247i
$494$	−5.80243	+	5.80243i	−0.261064	+	0.261064i
$495$	−5.91397	+	1.17636i	−0.265813	+	0.0528735i
$496$	−2.16459	+	0.896602i	−0.0971929	+	0.0402586i
$497$	−3.68343	−	1.52573i	−0.165224	−	0.0684382i
$498$	12.3979	−	8.28402i	0.555563	−	0.371216i
$499$	−16.4350	−	24.5967i	−0.735731	−	1.10110i	−0.990952	−	0.134217i	$-0.957148\pi$
$499$	−16.4350	−	24.5967i	−0.735731	−	1.10110i	0.255221	−	0.966883i	$-0.417852\pi$
$500$	−28.0165	−	18.7200i	−1.25294	−	0.837186i
$501$			5.31489i			0.237452i
$502$	16.6444	−	11.1215i	0.742878	−	0.496375i
$503$	−6.24197	−	15.0695i	−0.278316	−	0.671914i	0.721473	−	0.692442i	$-0.243465\pi$
$503$	−6.24197	−	15.0695i	−0.278316	−	0.671914i	−0.999789	+	0.0205282i	$0.993465\pi$
$504$	10.7675	+	16.1147i	0.479624	+	0.717808i
$505$	−1.16595	+	5.86160i	−0.0518839	+	0.260838i
$506$	6.98578	−	35.1199i	0.310556	−	1.56127i
$507$			4.89083i			0.217209i
$508$	−38.4320	−	7.64461i	−1.70515	−	0.339175i
$509$	29.5552	−	29.5552i	1.31001	−	1.31001i	0.388608	−	0.921403i	$-0.372956\pi$
$509$	29.5552	−	29.5552i	1.31001	−	1.31001i	0.921403	−	0.388608i	$-0.127044\pi$
$510$	−2.25447	+	5.44278i	−0.0998297	+	0.241010i
$511$	2.93189	+	14.7396i	0.129699	+	0.652042i
$512$	7.15277	−	17.2683i	0.316111	−	0.763159i
$513$	6.71192	−	1.33508i	0.296338	−	0.0589454i
$514$	67.6987	+	13.4661i	2.98606	+	0.593964i
$515$	13.8175	−	9.23256i	0.608872	−	0.406835i
$516$	0.615464	+	1.48586i	0.0270943	+	0.0654114i
$517$	−17.2546	−	7.14708i	−0.758855	−	0.314328i
$518$	9.74711	−	9.74711i	0.428263	−	0.428263i
$519$	1.53395	+	7.71169i	0.0673329	+	0.338505i
$520$	−5.02476			−0.220350
$521$	1.72704			0.0756631			0.0378316	−	0.999284i	$-0.487955\pi$
$521$	1.72704			0.0756631			0.0378316	+	0.999284i	$0.487955\pi$
$522$	−6.69693	−	33.6677i	−0.293117	−	1.47360i
$523$	−24.2760	+	4.82880i	−1.06152	+	0.211149i	−0.694813	−	0.719190i	$-0.744513\pi$
$523$	−24.2760	+	4.82880i	−1.06152	+	0.211149i	−0.366702	+	0.930339i	$0.619513\pi$
$524$	20.2905	−	30.3669i	0.886396	−	1.32659i
$525$	2.53937	+	1.69675i	0.110827	+	0.0740524i
$526$	−4.90990	+	24.6838i	−0.214082	+	1.07626i
$527$	−6.29892	−	4.20880i	−0.274385	−	0.183338i
$528$	1.04415	+	1.04415i	0.0454408	+	0.0454408i
$529$	30.4206	+	12.6006i	1.32264	+	0.547854i
$530$	−33.7089	−	6.70511i	−1.46422	−	0.291251i
$531$	−8.49014	+	12.7064i	−0.368441	+	0.551410i
$532$	−12.7546	−	12.7546i	−0.552981	−	0.552981i
$533$	5.05940	+	12.2145i	0.219147	+	0.529067i
$534$	−2.21051	−	5.33664i	−0.0956581	−	0.230939i
$535$	10.2869	+	10.2869i	0.444743	+	0.444743i
$536$	−31.9307	+	47.7876i	−1.37919	+	2.06411i
$537$	0.739005	+	0.146997i	0.0318904	+	0.00634340i
$538$	31.5132	+	13.0532i	1.35863	+	0.562763i
$539$	5.21233	+	5.21233i	0.224511	+	0.224511i
$540$	7.87185	+	5.25980i	0.338750	+	0.226346i
$541$	−8.34246	+	41.9404i	−0.358670	+	1.80316i	0.206793	+	0.978385i	$0.433697\pi$
$541$	−8.34246	+	41.9404i	−0.358670	+	1.80316i	−0.565464	+	0.824773i	$0.691303\pi$
$542$	21.6769	+	14.4840i	0.931101	+	0.622142i
$543$	−0.768067	+	1.14949i	−0.0329609	+	0.0493295i
$544$	18.8183	−	3.74320i	0.806829	−	0.160488i
$545$	0.843228	+	4.23919i	0.0361199	+	0.181587i
$546$	2.35413			0.100748
$547$	34.6477			1.48143			0.740713	−	0.671821i	$-0.234488\pi$
$547$	34.6477			1.48143			0.740713	+	0.671821i	$0.234488\pi$
$548$	7.58116	+	38.1131i	0.323851	+	1.62811i
$549$	−9.08050	+	9.08050i	−0.387546	+	0.387546i
$550$	−17.1741	−	7.11373i	−0.732305	−	0.303330i
$551$	5.41148	+	13.0645i	0.230537	+	0.556565i
$552$	−10.0180	+	6.69381i	−0.426394	+	0.284908i
$553$	−6.47820	−	1.28859i	−0.275481	−	0.0547966i
$554$	−36.1771	+	7.19606i	−1.53702	+	0.305731i
$555$	0.552222	−	1.33318i	0.0234405	−	0.0565904i
$556$	−0.498456	−	2.50591i	−0.0211392	−	0.106274i
$557$	4.29706	−	10.3740i	0.182072	−	0.439561i	−0.806321	−	0.591478i	$-0.798545\pi$
$557$	4.29706	−	10.3740i	0.182072	−	0.439561i	0.988393	+	0.151917i	$0.0485446\pi$
$558$	−6.49114	+	6.49114i	−0.274792	+	0.274792i
$559$	−1.29684	−	0.257958i	−0.0548505	−	0.0109105i
$560$		−	3.29269i		−	0.139142i
$561$	−0.931479	+	4.68286i	−0.0393271	+	0.197711i
$562$	6.57997	−	33.0797i	0.277559	−	1.39538i
$563$	13.8203	+	20.6836i	0.582457	+	0.871708i	0.999305	−	0.0372677i	$-0.0118654\pi$
$563$	13.8203	+	20.6836i	0.582457	+	0.871708i	−0.416848	+	0.908976i	$0.636865\pi$
$564$	5.43314	+	13.1168i	0.228776	+	0.552315i
$565$	−6.63587	+	4.43395i	−0.279173	+	0.186537i
$566$			31.7245i			1.33348i
$567$	11.2440	+	7.51302i	0.472205	+	0.315517i
$568$	−4.53638	−	6.78917i	−0.190342	−	0.284867i
$569$	−16.2411	+	10.8520i	−0.680864	+	0.454939i	−0.847301	−	0.531113i	$-0.821774\pi$
$569$	−16.2411	+	10.8520i	−0.680864	+	0.454939i	0.166437	+	0.986052i	$0.446774\pi$
$570$	−2.71690	−	1.12538i	−0.113798	−	0.0471368i
$571$	35.0007	−	14.4978i	1.46473	−	0.606713i	0.499083	−	0.866554i	$-0.333670\pi$
$571$	35.0007	−	14.4978i	1.46473	−	0.606713i	0.965651	+	0.259841i	$0.0836702\pi$
$572$	−9.02379	+	1.79494i	−0.377304	+	0.0750504i
$573$	−6.90502	+	6.90502i	−0.288461	+	0.288461i
$574$	−41.8143	+	17.3200i	−1.74529	+	0.722924i
$575$	16.1302	−	24.1405i	0.672675	−	1.00673i
$576$		−	32.8178i		−	1.36741i
$577$	2.48939	+	3.72563i	0.103635	+	0.155100i	0.879663	−	0.475598i	$-0.157768\pi$
$577$	2.48939	+	3.72563i	0.103635	+	0.155100i	−0.776028	+	0.630699i	$0.782768\pi$
$578$	−22.0247	−	22.0247i	−0.916106	−	0.916106i
$579$	0.103361	−	0.0428136i	0.00429554	−	0.00177927i
$580$	−7.48641	+	18.0738i	−0.310856	+	0.750474i
$581$	−26.9468			−1.11794
$582$	−1.02753	+	9.93774i	−0.0425924	+	0.411933i
$583$	−27.8549			−1.15363
$584$	−11.7784	+	28.4355i	−0.487392	+	1.17667i
$585$	−3.48171	+	1.44217i	−0.143951	+	0.0596265i
$586$	−44.1189	−	44.1189i	−1.82254	−	1.82254i
$587$	9.24683	+	13.8389i	0.381658	+	0.571191i	0.971711	−	0.236173i	$-0.0758933\pi$
$587$	9.24683	+	13.8389i	0.381658	+	0.571191i	−0.590053	+	0.807364i	$0.700893\pi$
$588$		−	5.60362i		−	0.231090i
$589$	2.10093	−	3.14426i	0.0865673	−	0.129557i
$590$	12.5308	−	5.19044i	0.515886	−	0.213687i
$591$	3.91981	−	3.91981i	0.161240	−	0.161240i
$592$	5.30009	−	1.05425i	0.217833	−	0.0433296i
$593$	−14.2708	+	5.91115i	−0.586030	+	0.242742i	−0.655942	−	0.754812i	$-0.727728\pi$
$593$	−14.2708	+	5.91115i	−0.586030	+	0.242742i	0.0699115	+	0.997553i	$0.477728\pi$
$594$	11.0401	+	4.57295i	0.452980	+	0.187630i
$595$	8.85232	−	5.91493i	0.362910	−	0.242489i
$596$	28.5263	+	42.6927i	1.16848	+	1.74876i
$597$	−5.37375	−	3.59063i	−0.219933	−	0.146955i
$598$		−	22.3796i		−	0.915168i
$599$	12.0017	−	8.01931i	0.490378	−	0.327660i	−0.285676	−	0.958326i	$-0.592218\pi$
$599$	12.0017	−	8.01931i	0.490378	−	0.327660i	0.776054	+	0.630666i	$0.217218\pi$
$600$	2.39360	+	5.77867i	0.0977185	+	0.235913i
$601$	−14.5476	−	21.7720i	−0.593407	−	0.888097i	0.406264	−	0.913756i	$-0.366831\pi$
$601$	−14.5476	−	21.7720i	−0.593407	−	0.888097i	−0.999671	+	0.0256593i	$0.991831\pi$
$602$	0.883077	−	4.43953i	0.0359915	−	0.180942i
$603$	−8.40943	+	42.2770i	−0.342458	+	1.72165i
$604$			36.2655i			1.47562i
$605$	−7.15187	−	1.42260i	−0.290765	−	0.0578367i
$606$	4.05486	−	4.05486i	0.164718	−	0.164718i
$607$	14.3886	−	34.7370i	0.584014	−	1.40993i	−0.305133	−	0.952310i	$-0.598701\pi$
$607$	14.3886	−	34.7370i	0.584014	−	1.40993i	0.889146	−	0.457623i	$-0.151299\pi$
$608$	1.86851	+	9.39363i	0.0757781	+	0.380962i
$609$	1.55247	−	3.74798i	0.0629091	−	0.151876i
$610$	11.1786	−	2.22356i	0.452608	−	0.0900293i
$611$	−11.4481	−	2.27718i	−0.463142	−	0.0921247i
$612$	−46.1497	+	30.8363i	−1.86549	+	1.24648i
$613$	−12.2168	−	29.4939i	−0.493431	−	1.19125i	−0.952963	−	0.303086i	$-0.901983\pi$
$613$	−12.2168	−	29.4939i	−0.493431	−	1.19125i	0.459532	−	0.888161i	$-0.348017\pi$
$614$	65.5754	+	27.1622i	2.64641	+	1.09618i
$615$	−3.35025	+	3.35025i	−0.135095	+	0.135095i
$616$	−2.71978	−	13.6732i	−0.109583	−	0.550910i
$617$	−8.30489			−0.334342			−0.167171	−	0.985928i	$-0.553463\pi$
$617$	−8.30489			−0.334342			−0.167171	+	0.985928i	$0.553463\pi$
$618$	−15.9453			−0.641413
$619$	7.17665	+	36.0795i	0.288454	+	1.45016i	0.804683	+	0.593705i	$0.202336\pi$
$619$	7.17665	+	36.0795i	0.288454	+	1.45016i	−0.516229	+	0.856451i	$0.672664\pi$
$620$	5.13102	−	1.02062i	0.206067	−	0.0409893i
$621$	−10.3690	+	15.5183i	−0.416095	+	0.622730i
$622$	−17.6394	−	11.7863i	−0.707276	−	0.472586i
$623$	−2.03654	+	10.2384i	−0.0815924	+	0.410193i
$624$	0.767355	+	0.512730i	0.0307188	+	0.0205256i
$625$	−6.70603	−	6.70603i	−0.268241	−	0.268241i
$626$	−46.8460	−	19.4043i	−1.87234	−	0.775550i
$627$	−2.33757	−	0.464971i	−0.0933535	−	0.0185692i
$628$	0.845058	−	1.26472i	0.0337215	−	0.0504678i
$629$	12.3553	+	12.3553i	0.492639	+	0.492639i
$630$	−4.93704	−	11.9191i	−0.196696	−	0.474867i
$631$	7.13023	+	17.2139i	0.283850	+	0.685274i	0.999919	−	0.0127555i	$-0.00406033\pi$
$631$	7.13023	+	17.2139i	0.283850	+	0.685274i	−0.716069	+	0.698030i	$0.754060\pi$
$632$	−9.56529	−	9.56529i	−0.380487	−	0.380487i
$633$	−2.62706	+	3.93167i	−0.104416	+	0.156270i
$634$	13.3088	+	2.64728i	0.528559	+	0.105137i
$635$	10.6664	+	4.41816i	0.423283	+	0.175329i
$636$	14.9730	+	14.9730i	0.593719	+	0.593719i
$637$	3.83058	+	2.55951i	0.151773	+	0.101412i
$638$	−4.81721	+	24.2178i	−0.190715	+	0.958791i
$639$	−5.09188	−	3.40228i	−0.201432	−	0.134592i
$640$	−12.0791	+	18.0777i	−0.477470	+	0.714585i
$641$	30.9047	−	6.14732i	1.22066	−	0.242805i	0.457616	−	0.889150i	$-0.348703\pi$
$641$	30.9047	−	6.14732i	1.22066	−	0.242805i	0.763045	+	0.646345i	$0.223703\pi$
$642$	−2.72323	−	13.6906i	−0.107477	−	0.540326i
$643$	−5.25512			−0.207242			−0.103621	−	0.994617i	$-0.533043\pi$
$643$	−5.25512			−0.207242			−0.103621	+	0.994617i	$0.533043\pi$
$644$	49.1934			1.93849
$645$	−0.0924446	−	0.464750i	−0.00364000	−	0.0182995i
$646$	25.1790	−	25.1790i	0.990654	−	0.990654i
$647$	28.7175	+	11.8952i	1.12900	+	0.467648i	0.867442	−	0.497538i	$-0.165763\pi$
$647$	28.7175	+	11.8952i	1.12900	+	0.467648i	0.261561	+	0.965187i	$0.415763\pi$
$648$	10.5986	+	25.5873i	0.416352	+	1.00516i
$649$	9.13993	−	6.10710i	0.358774	−	0.239725i
$650$	−11.3947	−	2.26655i	−0.446938	−	0.0889015i
$651$	−1.06403	+	0.211648i	−0.0417025	+	0.00829514i
$652$	−13.4950	+	32.5798i	−0.528506	+	1.27593i
$653$	−0.389208	−	1.95668i	−0.0152309	−	0.0765708i	0.972422	−	0.233227i	$-0.0749285\pi$
$653$	−0.389208	−	1.95668i	−0.0152309	−	0.0765708i	−0.987653	+	0.156656i	$0.949929\pi$
$654$	1.58708	−	3.83154i	0.0620596	−	0.149825i
$655$	−7.60890	+	7.60890i	−0.297304	+	0.297304i
$656$	−17.4021	−	3.46149i	−0.679438	−	0.135149i
$657$			23.0838i			0.900584i
$658$	7.79554	−	39.1908i	0.303902	−	1.52782i
$659$	4.05126	−	20.3670i	0.157815	−	0.793388i	−0.818073	−	0.575114i	$-0.804958\pi$
$659$	4.05126	−	20.3670i	0.157815	−	0.793388i	0.975888	−	0.218273i	$-0.0700424\pi$
$660$	−1.83184	−	2.74154i	−0.0713042	−	0.106714i
$661$	0.504812	+	1.21872i	0.0196349	+	0.0474028i	0.933393	−	0.358856i	$-0.116833\pi$
$661$	0.504812	+	1.21872i	0.0196349	+	0.0474028i	−0.913758	+	0.406259i	$0.866833\pi$
$662$	54.9962	−	36.7473i	2.13749	−	1.42823i
$663$			2.98407i			0.115892i
$664$	−45.8867	−	30.6605i	−1.78075	−	1.18986i
$665$	2.95259	+	4.41886i	0.114496	+	0.171356i
$666$	17.6048	−	11.7632i	0.682173	−	0.455814i
$667$	−35.6302	−	14.7585i	−1.37961	−	0.571452i
$668$	41.0597	−	17.0075i	1.58865	−	0.658039i
$669$	−1.36423	+	0.271362i	−0.0527442	+	0.0104915i
$670$	27.0523	−	27.0523i	1.04512	−	1.04512i
$671$	8.53416	−	3.53496i	0.329457	−	0.136466i
$672$	1.52653	−	2.28461i	0.0588871	−	0.0881307i
$673$		−	2.95386i		−	0.113863i	−0.998378	−	0.0569314i	$-0.981868\pi$
$673$		−	2.95386i		−	0.113863i	0.998378	−	0.0569314i	$-0.0181316\pi$
$674$	1.60263	+	2.39851i	0.0617311	+	0.0923871i
$675$	6.85113	+	6.85113i	0.263700	+	0.263700i
$676$	37.7836	−	15.6505i	1.45322	−	0.601942i
$677$	−14.0226	+	33.8536i	−0.538933	+	1.30110i	0.386535	+	0.922275i	$0.373672\pi$
$677$	−14.0226	+	33.8536i	−0.538933	+	1.30110i	−0.925468	+	0.378825i	$0.876328\pi$
$678$	7.65773			0.294093
$679$	11.5217	−	13.9011i	0.442163	−	0.533474i
$680$	21.8044			0.836160
$681$	−0.503508	+	1.21557i	−0.0192945	+	0.0465809i
$682$	6.10059	−	2.52695i	0.233604	−	0.0967618i
$683$	−10.8125	−	10.8125i	−0.413730	−	0.413730i	0.469305	−	0.883036i	$-0.344504\pi$
$683$	−10.8125	−	10.8125i	−0.413730	−	0.413730i	−0.883036	+	0.469305i	$0.844504\pi$
$684$	−15.3927	−	23.0368i	−0.588554	−	0.880834i
$685$		−	11.4494i		−	0.437459i
$686$	−25.6156	+	38.3364i	−0.978008	+	1.46369i
$687$	3.03896	−	1.25878i	0.115944	−	0.0480254i
$688$	1.25478	−	1.25478i	0.0478379	−	0.0478379i
$689$	−17.0745	+	3.39633i	−0.650487	+	0.129390i
$690$	7.40969	−	3.06919i	0.282082	−	0.116842i
$691$	9.53153	+	3.94809i	0.362596	+	0.150192i	0.556541	−	0.830820i	$-0.312128\pi$
$691$	9.53153	+	3.94809i	0.362596	+	0.150192i	−0.193945	+	0.981012i	$0.562128\pi$
$692$	54.6673	−	36.5275i	2.07814	−	1.38857i
$693$	−5.80895	−	8.69372i	−0.220664	−	0.330247i
$694$	−4.05274	−	2.70795i	−0.153840	−	0.102792i
$695$			0.752790i			0.0285549i
$696$	6.90815	−	4.61588i	0.261853	−	0.174964i
$697$	−21.9547	−	53.0033i	−0.831593	−	2.00764i
$698$	15.7017	+	23.4992i	0.594317	+	0.889459i
$699$	1.71094	−	8.60150i	0.0647139	−	0.325339i
$700$	4.98220	−	25.0472i	0.188309	−	0.946696i
$701$		−	38.1415i		−	1.44058i	−0.693671	−	0.720292i	$-0.744008\pi$
$701$		−	38.1415i		−	1.44058i	0.693671	−	0.720292i	$-0.255992\pi$
$702$	7.32492	+	1.45702i	0.276461	+	0.0549915i
$703$	−6.16747	+	6.16747i	−0.232611	+	0.232611i
$704$	−9.03379	+	21.8095i	−0.340474	+	0.821977i
$705$	−0.816074	−	4.10268i	−0.0307351	−	0.154516i
$706$	−15.3424	+	37.0399i	−0.577419	+	1.39401i
$707$	−10.1641	+	2.02177i	−0.382262	+	0.0760366i
$708$	−8.19582	−	1.63025i	−0.308018	−	0.0612686i
$709$	−1.28488	+	0.858531i	−0.0482548	+	0.0322428i	−0.579464	−	0.814998i	$-0.696738\pi$
$709$	−1.28488	+	0.858531i	−0.0482548	+	0.0322428i	0.531209	+	0.847241i	$0.321738\pi$
$710$	2.07998	+	5.02152i	0.0780604	+	0.188454i
$711$	−9.37325	−	3.88253i	−0.351524	−	0.145606i
$712$	−15.1174	+	15.1174i	−0.566547	+	0.566547i
$713$	2.01203	+	10.1152i	0.0753511	+	0.378816i
$714$	−10.2155			−0.382305
$715$	2.71080			0.101378
$716$	−1.22918	−	6.17950i	−0.0459366	−	0.230939i
$717$	0.683131	−	0.135883i	0.0255120	−	0.00507465i
$718$	−23.9831	+	35.8932i	−0.895040	+	1.33952i
$719$	−31.3728	−	20.9626i	−1.17001	−	0.781775i	−0.190207	−	0.981744i	$-0.560916\pi$
$719$	−31.3728	−	20.9626i	−1.17001	−	0.781775i	−0.979802	+	0.199969i	$0.935916\pi$
$720$	0.986692	−	4.96043i	0.0367718	−	0.184864i
$721$	23.9598	+	16.0094i	0.892310	+	0.596223i
$722$	−19.1909	−	19.1909i	−0.714212	−	0.714212i
$723$	9.79708	+	4.05808i	0.364357	+	0.150922i
$724$	11.3381	+	2.25529i	0.421377	+	0.0838170i
$725$	−11.1229	+	16.6467i	−0.413096	+	0.618242i
$726$	4.94742	+	4.94742i	0.183616	+	0.183616i
$727$	5.62378	+	13.5770i	0.208575	+	0.503543i	0.993199	−	0.116428i	$-0.0371443\pi$
$727$	5.62378	+	13.5770i	0.208575	+	0.503543i	−0.784625	+	0.619971i	$0.787144\pi$
$728$	−3.33433	−	8.04980i	−0.123579	−	0.298345i
$729$	12.4160	+	12.4160i	0.459850	+	0.459850i
$730$	11.3824	−	17.0350i	0.421282	−	0.630493i
$731$	5.62749	+	1.11938i	0.208140	+	0.0414017i
$732$	−6.48758	−	2.68725i	−0.239788	−	0.0993234i
$733$	−14.2178	−	14.2178i	−0.525148	−	0.525148i	0.393974	−	0.919122i	$-0.371100\pi$
$733$	−14.2178	−	14.2178i	−0.525148	−	0.525148i	−0.919122	+	0.393974i	$0.871100\pi$
$734$	−71.0918	−	47.5020i	−2.62405	−	1.75333i
$735$	−0.322097	+	1.61929i	−0.0118807	+	0.0597285i
$736$	−21.7186	−	14.5119i	−0.800559	−	0.534917i
$737$	17.2262	−	25.7809i	0.634536	−	0.949650i
$738$	−68.1832	+	13.5625i	−2.50986	+	0.499242i
$739$	3.14768	+	15.8244i	0.115789	+	0.582111i	0.994498	+	0.104754i	$0.0334054\pi$
$739$	3.14768	+	15.8244i	0.115789	+	0.582111i	−0.878709	+	0.477358i	$0.841595\pi$
$740$	−12.0665			−0.443572
$741$	−1.48957			−0.0547209
$742$	−11.6268	−	58.4518i	−0.426833	−	2.14583i
$743$	−5.73777	+	5.73777i	−0.210498	+	0.210498i	−0.804479	−	0.593981i	$-0.797555\pi$
$743$	−5.73777	+	5.73777i	−0.210498	+	0.210498i	0.593981	+	0.804479i	$0.297555\pi$
$744$	−2.05271	−	0.850259i	−0.0752558	−	0.0311720i
$745$	−5.78934	−	13.9767i	−0.212105	−	0.512067i
$746$	−20.7144	+	13.8410i	−0.758410	+	0.506753i
$747$	−40.5953	−	8.07491i	−1.48530	−	0.295445i
$748$	39.1577	−	7.78895i	1.43175	−	0.284792i
$749$	−9.65371	+	23.3061i	−0.352739	+	0.851587i
$750$	−1.85838	−	9.34271i	−0.0678585	−	0.341148i
$751$	7.71306	−	18.6210i	0.281454	−	0.679489i	−0.718416	−	0.695613i	$-0.755133\pi$
$751$	7.71306	−	18.6210i	0.281454	−	0.679489i	0.999870	+	0.0161242i	$0.00513270\pi$
$752$	11.0768	−	11.0768i	0.403930	−	0.403930i
$753$	3.56397	+	0.708917i	0.129878	+	0.0258344i
$754$			15.4324i			0.562013i
$755$	2.08455	−	10.4797i	0.0758644	−	0.381396i
$756$	−3.20273	+	16.1012i	−0.116482	+	0.585595i
$757$	1.60979	+	2.40923i	0.0585089	+	0.0875648i	0.859571	−	0.511017i	$-0.170731\pi$
$757$	1.60979	+	2.40923i	0.0585089	+	0.0875648i	−0.801062	+	0.598582i	$0.795731\pi$
$758$	20.5586	+	49.6328i	0.746721	+	1.80274i
$759$	5.40459	−	3.61123i	0.196174	−	0.131079i
$760$			10.8842i			0.394812i
$761$	−37.1614	−	24.8304i	−1.34710	−	0.900103i	−0.347801	−	0.937568i	$-0.613071\pi$
$761$	−37.1614	−	24.8304i	−1.34710	−	0.900103i	−0.999298	+	0.0374660i	$0.988071\pi$
$762$	−6.15445	−	9.21079i	−0.222952	−	0.333672i
$763$	−6.23174	+	4.16392i	−0.225604	+	0.150744i
$764$	75.4399	+	31.2482i	2.72932	+	1.13052i
$765$	15.1085	−	6.25814i	0.546248	−	0.226263i
$766$	−25.3767	+	5.04775i	−0.916899	+	0.182382i
$767$	4.85795	−	4.85795i	0.175411	−	0.175411i
$768$	10.0325	−	4.15561i	0.362018	−	0.149953i
$769$	−10.0530	+	15.0454i	−0.362521	+	0.542550i	−0.967232	−	0.253894i	$-0.918288\pi$
$769$	−10.0530	+	15.0454i	−0.362521	+	0.542550i	0.604711	+	0.796445i	$0.293288\pi$
$770$			9.27999i			0.334428i
$771$	6.96117	+	10.4181i	0.250700	+	0.375200i
$772$	−0.661504	−	0.661504i	−0.0238081	−	0.0238081i
$773$	−6.03619	+	2.50027i	−0.217107	+	0.0899286i	−0.488586	−	0.872516i	$-0.662487\pi$
$773$	−6.03619	+	2.50027i	−0.217107	+	0.0899286i	0.271479	+	0.962444i	$0.412487\pi$
$774$	2.66071	−	6.42351i	0.0956371	−	0.230888i
$775$	5.35398			0.192321
$776$	35.4368	−	10.5620i	1.27211	−	0.379154i
$777$	2.50223			0.0897672
$778$	10.9429	−	26.4184i	0.392321	−	0.947147i
$779$	26.4579	−	10.9592i	0.947953	−	0.392655i
$780$	−1.45715	−	1.45715i	−0.0521744	−	0.0521744i
$781$	2.44732	+	3.66268i	0.0875721	+	0.131061i
$782$			97.1135i			3.47277i
$783$	7.15021	−	10.7010i	0.255528	−	0.382424i
$784$	−5.71219	+	2.36607i	−0.204007	+	0.0845024i
$785$	−0.316895	+	0.316895i	−0.0113105	+	0.0113105i
$786$	10.1265	−	2.01429i	0.361200	−	0.0718472i
$787$	−40.2222	+	16.6606i	−1.43377	+	0.593885i	−0.958278	−	0.285838i	$-0.907728\pi$
$787$	−40.2222	+	16.6606i	−1.43377	+	0.593885i	−0.475487	+	0.879723i	$0.657728\pi$
$788$	−42.8254	−	17.7389i	−1.52559	−	0.631921i
$789$	−3.79858	+	2.53813i	−0.135233	+	0.0903597i
$790$	5.00268	+	7.48703i	0.177987	+	0.266377i
$791$	−11.5067	−	7.68855i	−0.409132	−	0.273373i
$792$		−	21.4137i		−	0.760903i
$793$	4.80025	−	3.20742i	0.170462	−	0.113899i
$794$	7.69405	+	18.5751i	0.273052	+	0.659205i
$795$	−3.46614	−	5.18745i	−0.122931	−	0.183980i
$796$	−10.5432	+	53.0043i	−0.373694	+	1.87869i
$797$	−0.928847	+	4.66963i	−0.0329015	+	0.165407i	−0.993743	−	0.111692i	$-0.964373\pi$
$797$	−0.928847	+	4.66963i	−0.0329015	+	0.165407i	0.960841	+	0.277099i	$0.0893730\pi$
$798$		−	5.09932i		−	0.180514i
$799$	49.6779	+	9.88154i	1.75748	+	0.349584i
$800$	−9.58847	+	9.58847i	−0.339004	+	0.339004i
$801$	−6.13610	+	14.8139i	−0.216808	+	0.523422i
$802$	−2.85575	−	14.3568i	−0.100840	−	0.506957i
$803$	6.35429	−	15.3406i	0.224238	−	0.541359i
$804$	−23.1179	+	4.59843i	−0.815304	+	0.162174i
$805$	−14.2156	−	2.82765i	−0.501032	−	0.0996616i
$806$	3.43143	−	2.29281i	0.120867	−	0.0807607i
$807$	2.36949	+	5.72044i	0.0834098	+	0.201369i
$808$	−19.6085	−	8.12212i	−0.689825	−	0.285735i
$809$	−30.8503	+	30.8503i	−1.08464	+	1.08464i	−0.0885686	+	0.996070i	$0.528229\pi$
$809$	−30.8503	+	30.8503i	−1.08464	+	1.08464i	−0.996070	+	0.0885686i	$0.971771\pi$
$810$	−3.59662	−	18.0814i	−0.126372	−	0.635316i
$811$	46.2477			1.62398			0.811988	−	0.583674i	$-0.198386\pi$
$811$	46.2477			1.62398			0.811988	+	0.583674i	$0.198386\pi$
$812$	−33.9225			−1.19045
$813$	0.923258	+	4.64153i	0.0323801	+	0.162786i
$814$	−14.9376	+	2.97127i	−0.523562	+	0.104143i
$815$	5.77238	−	8.63898i	0.202198	−	0.302610i
$816$	−3.32985	−	2.22493i	−0.116568	−	0.0778883i
$817$	−0.558765	+	2.80910i	−0.0195487	+	0.0982781i
$818$	23.1295	+	15.4547i	0.808705	+	0.540359i
$819$	−4.62079	−	4.62079i	−0.161463	−	0.161463i
$820$	36.6027	+	15.1613i	1.27822	+	0.529457i
$821$	27.8355	+	5.53682i	0.971465	+	0.193236i	0.655218	−	0.755440i	$-0.272577\pi$
$821$	27.8355	+	5.53682i	0.971465	+	0.193236i	0.316248	+	0.948677i	$0.397577\pi$
$822$	−6.10338	+	9.13435i	−0.212880	+	0.318597i
$823$	10.9618	+	10.9618i	0.382106	+	0.382106i	0.871860	−	0.489754i	$-0.162914\pi$
$823$	10.9618	+	10.9618i	0.382106	+	0.382106i	−0.489754	+	0.871860i	$0.662914\pi$
$824$	22.5845	+	54.5237i	0.786767	+	1.89942i
$825$	−1.29132	−	3.11753i	−0.0449581	−	0.108538i
$826$	16.6304	+	16.6304i	0.578646	+	0.578646i
$827$	9.51329	−	14.2377i	0.330810	−	0.495092i	−0.628360	−	0.777923i	$-0.716274\pi$
$827$	9.51329	−	14.2377i	0.330810	−	0.495092i	0.959170	+	0.282831i	$0.0912736\pi$
$828$	74.1098	+	14.7414i	2.57549	+	0.512298i
$829$	−17.3528	−	7.18778i	−0.602689	−	0.249642i	0.0604098	−	0.998174i	$-0.480759\pi$
$829$	−17.3528	−	7.18778i	−0.602689	−	0.249642i	−0.663099	+	0.748532i	$0.730759\pi$
$830$	25.9762	+	25.9762i	0.901647	+	0.901647i
$831$	−5.56728	−	3.71994i	−0.193127	−	0.129043i
$832$	−2.87831	+	14.4703i	−0.0997876	+	0.501666i
$833$	−16.6224	−	11.1067i	−0.575931	−	0.384825i
$834$	0.401293	−	0.600577i	0.0138956	−	0.0207963i
$835$	−12.8427	+	2.55457i	−0.444440	+	0.0884046i
$836$	3.88805	+	19.5465i	0.134471	+	0.676031i
$837$	−3.44172			−0.118963
$838$	−58.5597			−2.02291
$839$	0.589132	+	2.96177i	0.0203391	+	0.102252i	0.989621	−	0.143699i	$-0.0458998\pi$
$839$	0.589132	+	2.96177i	0.0203391	+	0.102252i	−0.969282	+	0.245951i	$0.920900\pi$
$840$	2.20794	−	2.20794i	0.0761812	−	0.0761812i
$841$	−2.22286	−	0.920741i	−0.0766505	−	0.0317497i
$842$	−17.6551	−	42.6231i	−0.608434	−	1.46889i
$843$	5.09063	−	3.40145i	0.175331	−	0.117152i
$844$	38.7803	+	7.71388i	1.33487	+	0.265523i
$845$	−11.8180	+	2.35075i	−0.406552	+	0.0808683i
$846$	23.4879	−	56.7049i	0.807532	−	1.94956i
$847$	−2.46681	−	12.4015i	−0.0847605	−	0.426120i
$848$	8.94092	−	21.5853i	0.307033	−	0.741242i
$849$	−4.07209	+	4.07209i	−0.139754	+	0.139754i
$850$	49.4461	+	9.83544i	1.69599	+	0.337353i
$851$		−	23.7875i		−	0.815424i
$852$	0.653296	−	3.28434i	0.0223816	−	0.112520i
$853$	3.78683	−	19.0377i	0.129658	−	0.651837i	−0.860220	−	0.509922i	$-0.829674\pi$
$853$	3.78683	−	19.0377i	0.129658	−	0.651837i	0.989879	−	0.141915i	$-0.0453259\pi$
$854$	10.9801	+	16.4329i	0.375731	+	0.562321i
$855$	3.12391	+	7.54177i	0.106835	+	0.257923i
$856$	−42.9570	+	28.7030i	−1.46824	+	0.981047i
$857$		−	30.6788i		−	1.04797i	−0.851728	−	0.523984i	$-0.824445\pi$
$857$		−	30.6788i		−	1.04797i	0.851728	−	0.523984i	$-0.175555\pi$
$858$	−2.16268	−	1.44506i	−0.0738327	−	0.0493335i
$859$	−11.9646	−	17.9063i	−0.408228	−	0.610957i	0.569206	−	0.822195i	$-0.307250\pi$
$859$	−11.9646	−	17.9063i	−0.408228	−	0.610957i	−0.977435	+	0.211238i	$0.932250\pi$
$860$	−3.29456	+	2.20136i	−0.112344	+	0.0750657i
$861$	−7.59034	−	3.14402i	−0.258678	−	0.107148i
$862$	−39.6941	+	16.4418i	−1.35199	+	0.560012i
$863$	51.9496	−	10.3334i	1.76838	−	0.351753i	0.799767	−	0.600311i	$-0.204956\pi$
$863$	51.9496	−	10.3334i	1.76838	−	0.351753i	0.968617	+	0.248557i	$0.0799565\pi$
$864$	6.16379	−	6.16379i	0.209697	−	0.209697i
$865$	−17.8970	+	7.41316i	−0.608515	+	0.252055i
$866$	30.1108	−	45.0641i	1.02321	−	1.53134i
$867$		−	5.65408i		−	0.192023i
$868$	5.03991	+	7.54276i	0.171066	+	0.256018i
$869$	5.16037	+	5.16037i	0.175053	+	0.175053i
$870$	−5.10953	+	2.11644i	−0.173229	+	0.0717539i
$871$	7.41588	−	17.9035i	0.251278	−	0.606638i
$872$	−15.3496			−0.519802
$873$	21.5231	−	17.4893i	0.728446	−	0.591924i
$874$	−48.4766			−1.63975
$875$	−6.58786	+	15.9045i	−0.222710	+	0.537670i
$876$	−11.6618	+	4.83047i	−0.394015	+	0.163206i
$877$	30.5539	+	30.5539i	1.03173	+	1.03173i	0.999480	+	0.0322532i	$0.0102683\pi$
$877$	30.5539	+	30.5539i	1.03173	+	1.03173i	0.0322532	+	0.999480i	$0.489732\pi$
$878$	−23.3800	−	34.9906i	−0.789036	−	1.18088i
$879$		−	11.3260i		−	0.382017i
$880$	−2.02118	+	3.02491i	−0.0681340	+	0.101970i
$881$	−17.6380	+	7.30592i	−0.594241	+	0.246143i	−0.659474	−	0.751727i	$-0.729221\pi$
$881$	−17.6380	+	7.30592i	−0.594241	+	0.246143i	0.0652331	+	0.997870i	$0.479221\pi$
$882$	−17.1296	+	17.1296i	−0.576785	+	0.576785i
$883$	27.2040	−	5.41121i	0.915487	−	0.182102i	0.285204	−	0.958467i	$-0.407939\pi$
$883$	27.2040	−	5.41121i	0.915487	−	0.182102i	0.630283	+	0.776365i	$0.282939\pi$
$884$	23.0532	−	9.54894i	0.775362	−	0.321165i
$885$	2.27466	+	0.942196i	0.0764619	+	0.0316716i
$886$	3.48867	−	2.33106i	0.117204	−	0.0783133i
$887$	−12.1795	−	18.2279i	−0.408948	−	0.612034i	0.568633	−	0.822591i	$-0.307472\pi$
$887$	−12.1795	−	18.2279i	−0.408948	−	0.612034i	−0.977582	+	0.210557i	$0.932472\pi$
$888$	4.26096	+	2.84708i	0.142988	+	0.0955418i
$889$			20.0196i			0.671437i
$890$	11.8328	−	7.90643i	0.396636	−	0.265024i
$891$	−5.71782	−	13.8040i	−0.191554	−	0.462452i
$892$	6.46187	+	9.67088i	0.216360	+	0.323805i
$893$	−4.93262	+	24.7980i	−0.165064	+	0.829832i
$894$	−2.83187	+	14.2368i	−0.0947120	+	0.476149i
$895$			1.85636i			0.0620513i
$896$	−36.9764	−	7.35507i	−1.23530	−	0.245716i
$897$	2.87259	−	2.87259i	0.0959130	−	0.0959130i
$898$	−8.73236	+	21.0818i	−0.291403	+	0.703509i
$899$	−1.38744	−	6.97515i	−0.0462738	−	0.232634i
$900$	15.0113	−	36.2406i	0.500378	−	1.20802i
$901$	74.0928	−	14.7380i	2.46839	−	0.490993i
$902$	49.0454	+	9.75573i	1.63303	+	0.324830i
$903$	0.683197	−	0.456498i	0.0227354	−	0.0151913i
$904$	−10.8462	−	26.1851i	−0.360740	−	0.870902i
$905$	−3.14676	−	1.30343i	−0.104602	−	0.0433275i
$906$	−7.24953	+	7.24953i	−0.240849	+	0.240849i
$907$	1.10387	+	5.54954i	0.0366534	+	0.184269i	0.994775	−	0.102093i	$-0.0325539\pi$
$907$	1.10387	+	5.54954i	0.0366534	+	0.184269i	−0.958121	+	0.286362i	$0.907554\pi$
$908$	11.0020			0.365115
$909$	−15.9181			−0.527970
$910$	1.13150	+	5.68844i	0.0375089	+	0.188570i
$911$	−12.2254	+	2.43178i	−0.405045	+	0.0805685i	−0.393408	−	0.919364i	$-0.628704\pi$
$911$	−12.2254	+	2.43178i	−0.405045	+	0.0805685i	−0.0116367	+	0.999932i	$0.503704\pi$
$912$	1.11063	−	1.66218i	0.0367767	−	0.0550402i
$913$	24.7553	+	16.5410i	0.819282	+	0.547427i
$914$	−9.43792	+	47.4476i	−0.312179	+	1.56943i
$915$	1.72027	+	1.14945i	0.0568704	+	0.0379996i
$916$	−19.4491	−	19.4491i	−0.642618	−	0.642618i
$917$	−17.2388	−	7.14053i	−0.569274	−	0.235801i
$918$	−31.7856	−	6.32255i	−1.04908	−	0.208675i
$919$	16.4933	−	24.6840i	0.544065	−	0.814250i	−0.452944	−	0.891539i	$-0.649626\pi$
$919$	16.4933	−	24.6840i	0.544065	−	0.814250i	0.997009	+	0.0772886i	$0.0246263\pi$
$920$	−20.9898	−	20.9898i	−0.692013	−	0.692013i
$921$	4.93063	+	11.9036i	0.162470	+	0.392237i
$922$	33.8323	+	81.6784i	1.11421	+	2.68993i
$923$	1.94675	+	1.94675i	0.0640779	+	0.0640779i
$924$	3.17644	−	4.75388i	0.104497	−	0.156391i
$925$	−12.1116	−	2.40914i	−0.398226	−	0.0792121i
$926$	62.9744	+	26.0849i	2.06947	+	0.857202i
$927$	31.2980	+	31.2980i	1.02796	+	1.02796i
$928$	14.9766	+	10.0070i	0.491631	+	0.328497i
$929$	−2.95114	+	14.8364i	−0.0968236	+	0.486765i	0.901696	+	0.432371i	$0.142323\pi$
$929$	−2.95114	+	14.8364i	−0.0968236	+	0.486765i	−0.998520	+	0.0543944i	$0.982677\pi$
$930$	1.22972	+	0.821676i	0.0403242	+	0.0269438i
$931$	5.54420	−	8.29748i	0.181704	−	0.271939i
$932$	−71.9250	+	14.3068i	−2.35598	+	0.468634i
$933$	−0.751295	−	3.77701i	−0.0245963	−	0.123654i
$934$	−98.9303			−3.23710
$935$	−11.7632			−0.384698
$936$	−2.61096	−	13.1262i	−0.0853418	−	0.429042i
$937$	12.1405	−	12.1405i	0.396612	−	0.396612i	−0.480424	−	0.877036i	$-0.659517\pi$
$937$	12.1405	−	12.1405i	0.396612	−	0.396612i	0.877036	+	0.480424i	$0.159517\pi$
$938$	61.2898	+	25.3871i	2.00118	+	0.828917i
$939$	−3.52236	−	8.50374i	−0.114948	−	0.277509i
$940$	−29.0835	+	19.4329i	−0.948598	+	0.633833i
$941$	−1.68162	−	0.334495i	−0.0548192	−	0.0109042i	0.167605	−	0.985854i	$-0.446397\pi$
$941$	−1.68162	−	0.334495i	−0.0548192	−	0.0109042i	−0.222424	+	0.974950i	$0.571397\pi$
$942$	0.421748	−	0.0838908i	0.0137413	−	0.00273331i
$943$	−29.8886	+	72.1576i	−0.973308	+	2.34977i
$944$	1.79876	+	9.04297i	0.0585446	+	0.294323i
$945$	1.85100	−	4.46871i	0.0602131	−	0.145367i
$946$	−3.53641	+	3.53641i	−0.114979	+	0.114979i
$947$	−4.15763	−	0.827004i	−0.135105	−	0.0268740i	0.127075	−	0.991893i	$-0.459441\pi$
$947$	−4.15763	−	0.827004i	−0.135105	−	0.0268740i	−0.262179	+	0.965019i	$0.584441\pi$
$948$		−	5.54776i		−	0.180183i
$949$	2.02458	−	10.1783i	0.0657207	−	0.330400i
$950$	−4.90960	+	24.6822i	−0.159289	+	0.800798i
$951$	1.36849	+	2.04809i	0.0443762	+	0.0664137i
$952$	14.4690	+	34.9312i	0.468942	+	1.13213i
$953$	22.7500	−	15.2011i	0.736945	−	0.492411i	−0.129565	−	0.991571i	$-0.541358\pi$
$953$	22.7500	−	15.2011i	0.736945	−	0.492411i	0.866510	+	0.499160i	$0.166358\pi$
$954$		−	91.5416i		−	2.96377i
$955$	−20.0039	−	13.3662i	−0.647311	−	0.432519i
$956$	−3.23575	−	4.84264i	−0.104652	−	0.156622i
$957$	−3.72687	+	2.49021i	−0.120472	+	0.0804971i
$958$	41.7570	+	17.2963i	1.34911	+	0.558819i
$959$	18.3422	−	7.59760i	0.592301	−	0.245339i
$960$	−5.18572	+	1.03150i	−0.167369	+	0.0332917i
$961$	20.5755	−	20.5755i	0.663726	−	0.663726i
$962$	−8.79414	+	3.64265i	−0.283535	+	0.117444i
$963$	−21.5272	+	32.2178i	−0.693705	+	1.03820i
$964$		−	88.6721i		−	2.85594i
$965$	0.153133	+	0.229180i	0.00492953	+	0.00737756i
$966$	9.83385	+	9.83385i	0.316399	+	0.316399i
$967$	−3.23411	+	1.33961i	−0.104002	+	0.0430790i	−0.434078	−	0.900875i	$-0.642926\pi$
$967$	−3.23411	+	1.33961i	−0.104002	+	0.0430790i	0.330076	+	0.943954i	$0.392926\pi$
$968$	9.90997	−	23.9248i	0.318518	−	0.768971i
$969$	6.46384			0.207648
$970$	−24.5071	+	2.29365i	−0.786875	+	0.0736445i
$971$	36.9161			1.18469			0.592347	−	0.805683i	$-0.298201\pi$
$971$	36.9161			1.18469			0.592347	+	0.805683i	$0.298201\pi$
$972$	−14.6275	+	35.3138i	−0.469176	+	1.13269i
$973$	−1.20599	+	0.499536i	−0.0386622	+	0.0160144i
$974$	−45.5306	−	45.5306i	−1.45889	−	1.45889i
$975$	−1.17167	−	1.75353i	−0.0375235	−	0.0561579i
$976$			7.74793i			0.248005i
$977$	−16.2400	+	24.3049i	−0.519563	+	0.777582i	−0.994753	−	0.102302i	$-0.967379\pi$
$977$	−16.2400	+	24.3049i	−0.519563	+	0.777582i	0.475190	+	0.879883i	$0.342379\pi$
$978$	−9.21044	+	3.81509i	−0.294517	+	0.121993i
$979$	8.15564	−	8.15564i	0.260656	−	0.260656i
$980$	13.5404	−	2.69335i	0.432532	−	0.0860360i
$981$	−10.6359	+	4.40552i	−0.339577	+	0.140658i
$982$	16.5450	+	6.85316i	0.527972	+	0.218693i
$983$	−40.8442	+	27.2912i	−1.30273	+	0.870454i	−0.996668	−	0.0815592i	$-0.974010\pi$
$983$	−40.8442	+	27.2912i	−1.30273	+	0.870454i	−0.306058	+	0.952013i	$0.599010\pi$
$984$	−9.34799	−	13.9903i	−0.298003	−	0.445993i
$985$	11.3557	+	7.58766i	0.361824	+	0.241763i
$986$		−	66.9669i		−	2.13266i
$987$	6.03107	−	4.02983i	0.191971	−	0.128271i
$988$	4.76659	+	11.5076i	0.151645	+	0.366104i
$989$	−4.33969	−	6.49481i	−0.137994	−	0.206523i
$990$	−2.78085	+	13.9803i	−0.0883813	+	0.444323i
$991$	4.99251	−	25.0990i	0.158592	−	0.797297i	−0.816817	−	0.576897i	$-0.804264\pi$
$991$	4.99251	−	25.0990i	0.158592	−	0.797297i	0.975409	−	0.220401i	$-0.0707365\pi$
$992$		−	4.81685i		−	0.152935i
$993$	11.7760	+	2.34239i	0.373700	+	0.0743335i
$994$	−6.66437	+	6.66437i	−0.211381	+	0.211381i
$995$	6.09340	−	14.7108i	0.193174	−	0.466363i
$996$	−4.41551	−	22.1982i	−0.139911	−	0.703378i
$997$	12.6644	−	30.5746i	0.401086	−	0.968306i	−0.586318	−	0.810081i	$-0.699423\pi$
$997$	12.6644	−	30.5746i	0.401086	−	0.968306i	0.987403	−	0.158225i	$-0.0505771\pi$
$998$	−68.5869	+	13.6428i	−2.17108	+	0.431855i
$999$	7.78573	+	1.54868i	0.246330	+	0.0489980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.2.h.a.79.7	yes	56
3.2	odd	2		873.2.bh.b.370.1		56
97.19	odd	32		9409.2.a.n.1.4		56
97.70	even	16	inner	97.2.h.a.70.7	✓	56
97.78	odd	32		9409.2.a.n.1.3		56
291.167	odd	16		873.2.bh.b.361.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.2.h.a.70.7	✓	56	97.70	even	16	inner
97.2.h.a.79.7	yes	56	1.1	even	1	trivial
873.2.bh.b.361.1		56	291.167	odd	16
873.2.bh.b.370.1		56	3.2	odd	2
9409.2.a.n.1.3		56	97.78	odd	32
9409.2.a.n.1.4		56	97.19	odd	32

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:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	97.h (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.904642 - 2.18400i) q^{2} +(0.396451 - 0.164215i) q^{3} +(-2.53726 - 2.53726i) q^{4} +(0.587356 + 0.879041i) q^{5} -1.01440i q^{6} +(-1.01849 + 1.52427i) q^{7} +(-3.46868 + 1.43678i) q^{8} +(-1.99111 + 1.99111i) q^{9} +(2.45117 - 0.487568i) q^{10} +(1.87132 - 0.775124i) q^{11} +(-1.42256 - 0.589242i) q^{12} +(1.05257 - 0.703303i) q^{13} +(2.40764 + 3.60329i) q^{14} +(0.377210 + 0.252044i) q^{15} +1.69892i q^{16} +(-4.56750 + 3.05190i) q^{17} +(2.54734 + 6.14983i) q^{18} +(-1.52343 - 2.27998i) q^{19} +(0.740079 - 3.72063i) q^{20} +(-0.153471 + 0.771551i) q^{21} -4.78816i q^{22} +(7.33474 + 1.45897i) q^{23} +(-1.13922 + 1.13922i) q^{24} +(1.48569 - 3.58678i) q^{25} +(-0.583817 - 2.93504i) q^{26} +(-0.955053 + 2.30570i) q^{27} +(6.45164 - 1.28331i) q^{28} +(-5.05785 - 1.00607i) q^{29} +(0.891703 - 0.595817i) q^{30} +(0.527749 + 1.27410i) q^{31} +(-3.22694 - 1.33664i) q^{32} +(0.614597 - 0.614597i) q^{33} +(2.53340 + 12.7363i) q^{34} -1.93811 q^{35} +10.1039 q^{36} +(-0.620545 - 3.11969i) q^{37} +(-6.35763 + 1.26461i) q^{38} +(0.301798 - 0.451673i) q^{39} +(-3.30034 - 2.20522i) q^{40} +(-2.03747 + 10.2431i) q^{41} +(1.54623 + 1.03316i) q^{42} +(-0.738574 - 0.738574i) q^{43} +(-6.71470 - 2.78132i) q^{44} +(-2.91976 - 0.580777i) q^{45} +(9.82170 - 14.6992i) q^{46} +(-6.51992 - 6.51992i) q^{47} +(0.278988 + 0.673537i) q^{48} +(1.39269 + 3.36225i) q^{49} +(-6.48950 - 6.48950i) q^{50} +(-1.30962 + 1.95998i) q^{51} +(-4.45510 - 0.886174i) q^{52} +(-12.7053 - 5.26272i) q^{53} +(4.17167 + 4.17167i) q^{54} +(1.78049 + 1.18969i) q^{55} +(1.34277 - 6.75056i) q^{56} +(-0.978374 - 0.653729i) q^{57} +(-6.77279 + 10.1362i) q^{58} +(5.32278 - 1.05877i) q^{59} +(-0.317579 - 1.59658i) q^{60} +4.56051 q^{61} +3.26005 q^{62} +(-1.00708 - 5.06292i) q^{63} +(-8.24108 + 8.24108i) q^{64} +(1.23646 + 0.512160i) q^{65} +(-0.786289 - 1.89827i) q^{66} +(12.7282 - 8.50469i) q^{67} +(19.3324 + 3.84545i) q^{68} +(3.14745 - 0.626067i) q^{69} +(-1.75330 + 4.23283i) q^{70} +(0.424284 + 2.13302i) q^{71} +(4.04576 - 9.76733i) q^{72} +(5.79670 - 5.79670i) q^{73} +(-7.37477 - 1.46693i) q^{74} -1.66595i q^{75} +(-1.91955 + 9.65025i) q^{76} +(-0.724409 + 3.64185i) q^{77} +(-0.713434 - 1.06773i) q^{78} +(1.37881 + 3.32873i) q^{79} +(-1.49342 + 0.997869i) q^{80} -7.37665i q^{81} +(20.5276 + 13.7161i) q^{82} +(8.16638 + 12.2219i) q^{83} +(2.34702 - 1.56823i) q^{84} +(-5.36549 - 2.22246i) q^{85} +(-2.28119 + 0.944900i) q^{86} +(-2.17040 + 0.431719i) q^{87} +(-5.37732 + 5.37732i) q^{88} +(5.26086 - 2.17912i) q^{89} +(-3.90976 + 5.85136i) q^{90} +2.32071i q^{91} +(-14.9084 - 22.3119i) q^{92} +(0.418453 + 0.418453i) q^{93} +(-20.1377 + 8.34130i) q^{94} +(1.10940 - 2.67832i) q^{95} -1.49882 q^{96} +(-9.79663 - 1.01294i) q^{97} +8.60304 q^{98} +(-2.18264 + 5.26936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{4} - 8 q^{5} - 8 q^{7} - 8 q^{8} - 32 q^{9} + 8 q^{10} - 8 q^{11} - 16 q^{12} - 8 q^{13} + 16 q^{14} - 40 q^{15} - 16 q^{17} + 56 q^{18} + 32 q^{19} - 16 q^{20} - 8 q^{21} + 24 q^{24}+ \cdots + 80 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^4 - 8 * q^5 - 8 * q^7 - 8 * q^8 - 32 * q^9 + 8 * q^10 - 8 * q^11 - 16 * q^12 - 8 * q^13 + 16 * q^14 - 40 * q^15 - 16 * q^17 + 56 * q^18 + 32 * q^19 - 16 * q^20 - 8 * q^21 + 24 * q^24 - 48 * q^26 - 48 * q^28 - 24 * q^29 + 32 * q^30 + 16 * q^31 + 88 * q^32 - 16 * q^33 - 8 * q^34 + 48 * q^35 - 8 * q^36 - 32 * q^37 - 8 * q^38 - 24 * q^39 - 56 * q^40 + 8 * q^41 + 40 * q^42 - 80 * q^44 + 64 * q^45 - 8 * q^46 - 56 * q^47 - 24 * q^48 + 80 * q^49 + 88 * q^50 - 8 * q^51 + 24 * q^52 + 8 * q^53 + 24 * q^54 - 8 * q^55 - 8 * q^56 - 8 * q^57 + 56 * q^58 - 32 * q^59 - 40 * q^60 + 32 * q^61 - 80 * q^62 - 8 * q^63 + 24 * q^64 - 16 * q^65 + 56 * q^66 + 104 * q^67 + 24 * q^68 + 72 * q^69 - 88 * q^70 + 32 * q^71 + 104 * q^72 + 40 * q^73 - 24 * q^74 - 88 * q^76 - 8 * q^77 + 40 * q^78 - 88 * q^79 + 120 * q^80 - 112 * q^82 + 16 * q^83 + 32 * q^84 + 96 * q^85 + 80 * q^86 - 168 * q^87 - 48 * q^88 - 152 * q^90 - 48 * q^92 - 56 * q^93 + 24 * q^94 - 128 * q^95 - 32 * q^96 + 32 * q^97 - 136 * q^98 + 80 * q^99

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