LMFDB - Embedded newform 207.3.j.c.10.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,3,Mod(10,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("207.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	207.j (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.64034147226$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			10.6
Character	$\chi$	$=$	207.10
Dual form			207.3.j.c.145.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.718657 + 0.829374i) q^{2} +(0.397865 - 2.76721i) q^{4} +(4.86076 + 2.21983i) q^{5} +(2.07875 - 7.07956i) q^{7} +(6.27382 - 4.03194i) q^{8} +O(q^{10})$	\(q+(0.718657 + 0.829374i) q^{2} +(0.397865 - 2.76721i) q^{4} +(4.86076 + 2.21983i) q^{5} +(2.07875 - 7.07956i) q^{7} +(6.27382 - 4.03194i) q^{8} +(1.65214 + 5.62668i) q^{10} +(-10.0553 - 8.71297i) q^{11} +(-17.3029 + 5.08058i) q^{13} +(7.36551 - 3.36371i) q^{14} +(-2.87700 - 0.844763i) q^{16} +(30.2920 - 4.35534i) q^{17} +(29.7987 + 4.28440i) q^{19} +(8.07668 - 12.5676i) q^{20} -14.6012i q^{22} +(15.5474 + 16.9493i) q^{23} +(2.32777 + 2.68639i) q^{25} +(-16.6485 - 10.6994i) q^{26} +(-18.7636 - 8.56905i) q^{28} +(4.53399 + 31.5346i) q^{29} +(-11.7411 + 7.54555i) q^{31} +(-13.7591 - 30.1283i) q^{32} +(25.3818 + 21.9934i) q^{34} +(25.8197 - 29.7975i) q^{35} +(-60.2758 + 27.5271i) q^{37} +(17.8616 + 27.7933i) q^{38} +(39.4457 - 5.67144i) q^{40} +(3.19522 - 6.99656i) q^{41} +(19.3523 - 30.1128i) q^{43} +(-28.1113 + 24.3586i) q^{44} +(-2.88410 + 25.0753i) q^{46} -39.0101 q^{47} +(-4.57753 - 2.94180i) q^{49} +(-0.555155 + 3.86118i) q^{50} +(7.17484 + 49.9021i) q^{52} +(-27.4890 + 93.6188i) q^{53} +(-29.5350 - 64.6727i) q^{55} +(-15.5027 - 52.7972i) q^{56} +(-22.8956 + 26.4229i) q^{58} +(-12.8663 + 3.77788i) q^{59} +(-3.69653 - 5.75192i) q^{61} +(-14.6959 - 4.31511i) q^{62} +(10.1171 - 22.1534i) q^{64} +(-95.3830 - 13.7140i) q^{65} +(-1.90072 + 1.64698i) q^{67} -85.5574i q^{68} +43.2688 q^{70} +(65.1402 + 75.1758i) q^{71} +(8.23397 - 57.2685i) q^{73} +(-66.1479 - 30.2087i) q^{74} +(23.7117 - 80.7547i) q^{76} +(-82.5864 + 53.0751i) q^{77} +(-14.5051 - 49.3997i) q^{79} +(-12.1092 - 10.4926i) q^{80} +(8.09903 - 2.37809i) q^{82} +(-51.3058 + 23.4306i) q^{83} +(156.910 + 46.0730i) q^{85} +(38.8824 - 5.59045i) q^{86} +(-98.2153 - 14.1212i) q^{88} +(-39.9848 + 62.2176i) q^{89} +133.058i q^{91} +(53.0882 - 36.2794i) q^{92} +(-28.0349 - 32.3540i) q^{94} +(135.333 + 86.9735i) q^{95} +(1.71968 + 0.785353i) q^{97} +(-0.849820 - 5.91063i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 24 q^{4}+O(q^{10}) $ 80 * q - 24 * q^4	$ 80 q - 24 q^{4} - 16 q^{13} + 224 q^{16} + 66 q^{19} - 44 q^{25} - 528 q^{28} - 22 q^{31} - 242 q^{34} - 352 q^{37} - 110 q^{40} - 88 q^{43} + 336 q^{46} + 40 q^{49} + 530 q^{52} + 442 q^{55} - 618 q^{58} - 308 q^{61} - 312 q^{64} - 22 q^{67} - 400 q^{70} + 46 q^{73} + 2354 q^{76} + 1540 q^{79} + 1676 q^{82} + 1118 q^{85} + 528 q^{88} - 674 q^{94} - 792 q^{97}+O(q^{100}) $ 80 * q - 24 * q^4 - 16 * q^13 + 224 * q^16 + 66 * q^19 - 44 * q^25 - 528 * q^28 - 22 * q^31 - 242 * q^34 - 352 * q^37 - 110 * q^40 - 88 * q^43 + 336 * q^46 + 40 * q^49 + 530 * q^52 + 442 * q^55 - 618 * q^58 - 308 * q^61 - 312 * q^64 - 22 * q^67 - 400 * q^70 + 46 * q^73 + 2354 * q^76 + 1540 * q^79 + 1676 * q^82 + 1118 * q^85 + 528 * q^88 - 674 * q^94 - 792 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{3}{22}\right)$	$1$

Coefficient data

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

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

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

$2$	0.718657	+	0.829374i	0.359328	+	0.414687i	0.906415	−	0.422389i	$-0.138808\pi$
$2$	0.718657	+	0.829374i	0.359328	+	0.414687i	−0.547086	+	0.837076i	$0.684263\pi$
$3$		0			0
$3$		0			0
$4$	0.397865	−	2.76721i	0.0994664	−	0.691804i
$5$	4.86076	+	2.21983i	0.972151	+	0.443967i	0.837207	−	0.546887i	$-0.184187\pi$
$5$	4.86076	+	2.21983i	0.972151	+	0.443967i	0.134944	+	0.990853i	$0.456914\pi$
$6$		0			0
$7$	2.07875	−	7.07956i	0.296964	−	1.01137i	−0.666939	−	0.745112i	$-0.732396\pi$
$7$	2.07875	−	7.07956i	0.296964	−	1.01137i	0.963903	−	0.266253i	$-0.0857858\pi$
$8$	6.27382	−	4.03194i	0.784227	−	0.503992i
$9$		0			0
$10$	1.65214	+	5.62668i	0.165214	+	0.562668i
$11$	−10.0553	−	8.71297i	−0.914119	−	0.792088i	0.0644688	−	0.997920i	$-0.479465\pi$
$11$	−10.0553	−	8.71297i	−0.914119	−	0.792088i	−0.978587	+	0.205831i	$0.934010\pi$
$12$		0			0
$13$	−17.3029	+	5.08058i	−1.33099	+	0.390814i	−0.868446	−	0.495783i	$-0.834881\pi$
$13$	−17.3029	+	5.08058i	−1.33099	+	0.390814i	−0.462543	+	0.886597i	$0.653063\pi$
$14$	7.36551	−	3.36371i	0.526108	−	0.240265i
$15$		0			0
$16$	−2.87700	−	0.844763i	−0.179812	−	0.0527977i
$17$	30.2920	−	4.35534i	1.78188	−	0.256196i	0.828939	−	0.559338i	$-0.188945\pi$
$17$	30.2920	−	4.35534i	1.78188	−	0.256196i	0.952945	+	0.303142i	$0.0980356\pi$
$18$		0			0
$19$	29.7987	+	4.28440i	1.56835	+	0.225495i	0.871017	−	0.491252i	$-0.163461\pi$
$19$	29.7987	+	4.28440i	1.56835	+	0.225495i	0.697333	+	0.716747i	$0.254370\pi$
$20$	8.07668	−	12.5676i	0.403834	−	0.628378i
$21$		0			0
$22$		−	14.6012i		−	0.663693i
$23$	15.5474	+	16.9493i	0.675973	+	0.736927i
$23$	15.5474	+	16.9493i	0.675973	+	0.736927i
$24$		0			0
$25$	2.32777	+	2.68639i	0.0931108	+	0.107456i
$26$	−16.6485	−	10.6994i	−0.640328	−	0.411514i
$27$		0			0
$28$	−18.7636	−	8.56905i	−0.670128	−	0.306037i
$29$	4.53399	+	31.5346i	0.156344	+	1.08740i	0.905298	+	0.424777i	$0.139647\pi$
$29$	4.53399	+	31.5346i	0.156344	+	1.08740i	−0.748954	+	0.662622i	$0.769444\pi$
$30$		0			0
$31$	−11.7411	+	7.54555i	−0.378745	+	0.243405i	−0.716137	−	0.697959i	$-0.754092\pi$
$31$	−11.7411	+	7.54555i	−0.378745	+	0.243405i	0.337392	+	0.941364i	$0.390455\pi$
$32$	−13.7591	−	30.1283i	−0.429972	−	0.941508i
$33$		0			0
$34$	25.3818	+	21.9934i	0.746523	+	0.646866i
$35$	25.8197	−	29.7975i	0.737706	−	0.851358i
$36$		0			0
$37$	−60.2758	+	27.5271i	−1.62908	+	0.743974i	−0.999458	−	0.0329296i	$-0.989516\pi$
$37$	−60.2758	+	27.5271i	−1.62908	+	0.743974i	−0.629619	+	0.776904i	$0.716789\pi$
$38$	17.8616	+	27.7933i	0.470043	+	0.731401i
$39$		0			0
$40$	39.4457	−	5.67144i	0.986143	−	0.141786i
$41$	3.19522	−	6.99656i	0.0779322	−	0.170648i	−0.866655	−	0.498907i	$-0.833735\pi$
$41$	3.19522	−	6.99656i	0.0779322	−	0.170648i	0.944588	+	0.328260i	$0.106462\pi$
$42$		0			0
$43$	19.3523	−	30.1128i	0.450054	−	0.700297i	−0.539894	−	0.841733i	$-0.681536\pi$
$43$	19.3523	−	30.1128i	0.450054	−	0.700297i	0.989947	+	0.141436i	$0.0451720\pi$
$44$	−28.1113	+	24.3586i	−0.638894	+	0.553605i
$45$		0			0
$46$	−2.88410	+	25.0753i	−0.0626979	+	0.545116i
$47$	−39.0101			−0.830003			−0.415002	−	0.909821i	$-0.636219\pi$
$47$	−39.0101			−0.830003			−0.415002	+	0.909821i	$0.636219\pi$
$48$		0			0
$49$	−4.57753	−	2.94180i	−0.0934189	−	0.0600367i
$50$	−0.555155	+	3.86118i	−0.0111031	+	0.0772237i
$51$		0			0
$52$	7.17484	+	49.9021i	0.137978	+	0.959656i
$53$	−27.4890	+	93.6188i	−0.518660	+	1.76639i	0.115625	+	0.993293i	$0.463113\pi$
$53$	−27.4890	+	93.6188i	−0.518660	+	1.76639i	−0.634284	+	0.773100i	$0.718705\pi$
$54$		0			0
$55$	−29.5350	−	64.6727i	−0.537001	−	1.17587i
$56$	−15.5027	−	52.7972i	−0.276833	−	0.942808i
$57$		0			0
$58$	−22.8956	+	26.4229i	−0.394751	+	0.455567i
$59$	−12.8663	+	3.77788i	−0.218073	+	0.0640319i	−0.388944	−	0.921261i	$-0.627160\pi$
$59$	−12.8663	+	3.77788i	−0.218073	+	0.0640319i	0.170871	+	0.985293i	$0.445342\pi$
$60$		0			0
$61$	−3.69653	−	5.75192i	−0.0605989	−	0.0942937i	0.809632	−	0.586938i	$-0.199667\pi$
$61$	−3.69653	−	5.75192i	−0.0605989	−	0.0942937i	−0.870231	+	0.492644i	$0.836030\pi$
$62$	−14.6959	−	4.31511i	−0.237031	−	0.0695985i
$63$		0			0
$64$	10.1171	−	22.1534i	0.158080	−	0.346146i
$65$	−95.3830	−	13.7140i	−1.46743	−	0.210985i
$66$		0			0
$67$	−1.90072	+	1.64698i	−0.0283689	+	0.0245818i	−0.668930	−	0.743326i	$-0.733247\pi$
$67$	−1.90072	+	1.64698i	−0.0283689	+	0.0245818i	0.640561	+	0.767907i	$0.278702\pi$
$68$		−	85.5574i		−	1.25820i
$69$		0			0
$70$	43.2688			0.618126
$71$	65.1402	+	75.1758i	0.917468	+	1.05881i	0.998072	+	0.0620678i	$0.0197695\pi$
$71$	65.1402	+	75.1758i	0.917468	+	1.05881i	−0.0806044	+	0.996746i	$0.525685\pi$
$72$		0			0
$73$	8.23397	−	57.2685i	0.112794	−	0.784501i	−0.852386	−	0.522914i	$-0.824845\pi$
$73$	8.23397	−	57.2685i	0.112794	−	0.784501i	0.965180	−	0.261587i	$-0.0842458\pi$
$74$	−66.1479	−	30.2087i	−0.893890	−	0.408226i
$75$		0			0
$76$	23.7117	−	80.7547i	0.311996	−	1.06256i
$77$	−82.5864	+	53.0751i	−1.07255	+	0.689286i
$78$		0			0
$79$	−14.5051	−	49.3997i	−0.183608	−	0.625313i	−0.998928	−	0.0463009i	$-0.985257\pi$
$79$	−14.5051	−	49.3997i	−0.183608	−	0.625313i	0.815319	−	0.579012i	$-0.196561\pi$
$80$	−12.1092	−	10.4926i	−0.151364	−	0.131158i
$81$		0			0
$82$	8.09903	−	2.37809i	0.0987687	−	0.0290011i
$83$	−51.3058	+	23.4306i	−0.618142	+	0.282296i	−0.699772	−	0.714367i	$-0.746715\pi$
$83$	−51.3058	+	23.4306i	−0.618142	+	0.282296i	0.0816295	+	0.996663i	$0.473988\pi$
$84$		0			0
$85$	156.910	+	46.0730i	1.84600	+	0.542036i
$86$	38.8824	−	5.59045i	0.452121	−	0.0650052i
$87$		0			0
$88$	−98.2153	−	14.1212i	−1.11608	−	0.160469i
$89$	−39.9848	+	62.2176i	−0.449268	+	0.699074i	−0.989834	−	0.142227i	$-0.954574\pi$
$89$	−39.9848	+	62.2176i	−0.449268	+	0.699074i	0.540566	+	0.841301i	$0.318210\pi$
$90$		0			0
$91$			133.058i			1.46217i
$92$	53.0882	−	36.2794i	0.577045	−	0.394341i
$93$		0			0
$94$	−28.0349	−	32.3540i	−0.298244	−	0.344192i
$95$	135.333	+	86.9735i	1.42456	+	0.915510i
$96$		0			0
$97$	1.71968	+	0.785353i	0.0177287	+	0.00809642i	0.424260	−	0.905541i	$-0.360534\pi$
$97$	1.71968	+	0.785353i	0.0177287	+	0.00809642i	−0.406531	+	0.913637i	$0.633262\pi$
$98$	−0.849820	−	5.91063i	−0.00867163	−	0.0603125i
$99$		0			0
$100$	8.35996	−	5.37262i	0.0835996	−	0.0537262i
$101$	−9.39095	−	20.5633i	−0.0929797	−	0.203597i	0.857428	−	0.514604i	$-0.172061\pi$
$101$	−9.39095	−	20.5633i	−0.0929797	−	0.203597i	−0.950408	+	0.311007i	$0.899334\pi$
$102$		0			0
$103$	22.7166	+	19.6841i	0.220550	+	0.191108i	0.758127	−	0.652107i	$-0.226115\pi$
$103$	22.7166	+	19.6841i	0.220550	+	0.191108i	−0.537577	+	0.843215i	$0.680660\pi$
$104$	−88.0704	+	101.639i	−0.846831	+	0.977295i
$105$		0			0
$106$	−97.4002	+	44.4812i	−0.918870	+	0.419634i
$107$	48.1181	+	74.8732i	0.449702	+	0.699749i	0.989897	−	0.141791i	$-0.0452860\pi$
$107$	48.1181	+	74.8732i	0.449702	+	0.699749i	−0.540195	+	0.841540i	$0.681650\pi$
$108$		0			0
$109$	−176.142	+	25.3254i	−1.61598	+	0.232343i	−0.890197	−	0.455576i	$-0.849433\pi$
$109$	−176.142	+	25.3254i	−1.61598	+	0.232343i	−0.725787	+	0.687919i	$0.758524\pi$
$110$	32.4123	−	70.9731i	0.294658	−	0.645210i
$111$		0			0
$112$	−11.9611	+	18.6118i	−0.106796	+	0.166177i
$113$	98.7667	−	85.5818i	0.874041	−	0.757361i	−0.0972486	−	0.995260i	$-0.531004\pi$
$113$	98.7667	−	85.5818i	0.874041	−	0.757361i	0.971290	+	0.237899i	$0.0764587\pi$
$114$		0			0
$115$	37.9473	+	116.899i	0.329977	+	1.01651i
$116$	89.0668			0.767817
$117$		0			0
$118$	−12.3797	−	7.95596i	−0.104913	−	0.0674234i
$119$	32.1356	−	223.508i	0.270047	−	1.87822i
$120$		0			0
$121$	7.97319	+	55.4548i	0.0658942	+	0.458304i
$122$	2.11395	−	7.19946i	0.0173275	−	0.0590120i
$123$		0			0
$124$	16.2088	+	35.4923i	0.130716	+	0.286228i
$125$	−32.2856	−	109.955i	−0.258285	−	0.879638i
$126$		0			0
$127$	34.4979	−	39.8127i	0.271637	−	0.313486i	−0.603498	−	0.797365i	$-0.706227\pi$
$127$	34.4979	−	39.8127i	0.271637	−	0.313486i	0.875135	+	0.483878i	$0.160772\pi$
$128$	−101.475	+	29.7957i	−0.792771	+	0.232779i
$129$		0			0
$130$	−57.1736	−	88.9639i	−0.439797	−	0.684338i
$131$	11.8776	+	3.48758i	0.0906688	+	0.0266228i	0.326752	−	0.945110i	$-0.394046\pi$
$131$	11.8776	+	3.48758i	0.0906688	+	0.0266228i	−0.236084	+	0.971733i	$0.575864\pi$
$132$		0			0
$133$	92.2755	−	202.055i	0.693801	−	1.51921i
$134$	−2.73193	−	0.392792i	−0.0203875	−	0.00293128i
$135$		0			0
$136$	172.486	−	149.460i	1.26828	−	1.09897i
$137$		−	10.6717i		−	0.0778959i	−0.999241	−	0.0389480i	$-0.987599\pi$
$137$		−	10.6717i		−	0.0778959i	0.999241	−	0.0389480i	$-0.0124007\pi$
$138$		0			0
$139$	104.984			0.755280			0.377640	−	0.925952i	$-0.376736\pi$
$139$	104.984			0.755280			0.377640	+	0.925952i	$0.376736\pi$
$140$	−72.1834	−	83.3041i	−0.515596	−	0.595029i
$141$		0			0
$142$	−15.5354	+	108.051i	−0.109404	+	0.760924i
$143$	218.253	+	99.6726i	1.52624	+	0.697011i
$144$		0			0
$145$	−47.9629	+	163.346i	−0.330778	+	1.12653i
$146$	53.4145	−	34.3274i	0.365852	−	0.235119i
$147$		0			0
$148$	52.1916	+	177.748i	0.352646	+	1.20100i
$149$	108.975	+	94.4273i	0.731375	+	0.633740i	0.938781	−	0.344515i	$-0.111957\pi$
$149$	108.975	+	94.4273i	0.731375	+	0.633740i	−0.207406	+	0.978255i	$0.566502\pi$
$150$		0			0
$151$	−61.5866	+	18.0835i	−0.407858	+	0.119758i	−0.479225	−	0.877692i	$-0.659082\pi$
$151$	−61.5866	+	18.0835i	−0.407858	+	0.119758i	0.0713667	+	0.997450i	$0.477264\pi$
$152$	204.226	−	93.2668i	1.34359	−	0.613597i
$153$		0			0
$154$	−103.370	−	30.3523i	−0.671236	−	0.197093i
$155$	−73.8205	+	10.6138i	−0.476261	+	0.0684760i
$156$		0			0
$157$	−97.3222	−	13.9928i	−0.619887	−	0.0891263i	−0.174786	−	0.984607i	$-0.555923\pi$
$157$	−97.3222	−	13.9928i	−0.619887	−	0.0891263i	−0.445101	+	0.895480i	$0.646832\pi$
$158$	30.5467	−	47.5316i	0.193333	−	0.300833i
$159$		0			0
$160$		−	176.989i		−	1.10618i
$161$	152.313	−	74.8352i	0.946042	−	0.464815i
$162$		0			0
$163$	54.3760	+	62.7533i	0.333595	+	0.384989i	0.897621	−	0.440768i	$-0.145294\pi$
$163$	54.3760	+	62.7533i	0.333595	+	0.384989i	−0.564026	+	0.825757i	$0.690748\pi$
$164$	−18.0897	−	11.6256i	−0.110303	−	0.0708875i
$165$		0			0
$166$	−56.3040	−	25.7132i	−0.339181	−	0.154899i
$167$	13.8152	+	96.0871i	0.0827260	+	0.575372i	0.988455	+	0.151515i	$0.0484151\pi$
$167$	13.8152	+	96.0871i	0.0827260	+	0.575372i	−0.905729	+	0.423857i	$0.860676\pi$
$168$		0			0
$169$	131.405	−	84.4488i	0.777544	−	0.499697i
$170$	74.5529	+	163.248i	0.438547	+	0.960283i
$171$		0			0
$172$	−75.6289	−	65.5328i	−0.439703	−	0.381005i
$173$	45.4388	−	52.4392i	0.262652	−	0.303117i	−0.609071	−	0.793116i	$-0.708457\pi$
$173$	45.4388	−	52.4392i	0.262652	−	0.303117i	0.871723	+	0.489999i	$0.163003\pi$
$174$		0			0
$175$	23.8573	−	10.8953i	0.136327	−	0.0622586i
$176$	21.5687	+	33.5616i	0.122549	+	0.190691i
$177$		0			0
$178$	−80.3371	+	11.5507i	−0.451332	+	0.0648917i
$179$	−0.794691	+	1.74013i	−0.00443961	+	0.00972140i	−0.911839	−	0.410548i	$-0.865337\pi$
$179$	−0.794691	+	1.74013i	−0.00443961	+	0.00972140i	0.907399	+	0.420270i	$0.138065\pi$
$180$		0			0
$181$	41.0574	−	63.8865i	0.226836	−	0.352964i	−0.709115	−	0.705092i	$-0.750905\pi$
$181$	41.0574	−	63.8865i	0.226836	−	0.352964i	0.935952	+	0.352128i	$0.114542\pi$
$182$	−110.355	+	95.6229i	−0.606345	+	0.525401i
$183$		0			0
$184$	165.880	+	43.6509i	0.901521	+	0.237233i
$185$	−354.092			−1.91401
$186$		0			0
$187$	−342.544	−	220.139i	−1.83178	−	1.17722i
$188$	−15.5208	+	107.949i	−0.0825574	+	0.574199i
$189$		0			0
$190$	25.1247	+	174.746i	0.132235	+	0.919716i
$191$	67.0012	−	228.185i	0.350792	−	1.19469i	−0.575476	−	0.817819i	$-0.695183\pi$
$191$	67.0012	−	228.185i	0.350792	−	1.19469i	0.926267	−	0.376867i	$-0.122999\pi$
$192$		0			0
$193$	85.7016	+	187.660i	0.444050	+	0.972333i	0.990837	+	0.135062i	$0.0431233\pi$
$193$	85.7016	+	187.660i	0.444050	+	0.972333i	−0.546787	+	0.837271i	$0.684149\pi$
$194$	0.584511	+	1.99066i	0.00301294	+	0.0102611i
$195$		0			0
$196$	−9.96183	+	11.4966i	−0.0508257	+	0.0586559i
$197$	−133.978	+	39.3396i	−0.680093	+	0.199693i	−0.603493	−	0.797368i	$-0.706225\pi$
$197$	−133.978	+	39.3396i	−0.680093	+	0.199693i	−0.0766005	+	0.997062i	$0.524407\pi$
$198$		0			0
$199$	4.56426	+	7.10212i	0.0229360	+	0.0356891i	0.852532	−	0.522675i	$-0.175066\pi$
$199$	4.56426	+	7.10212i	0.0229360	+	0.0356891i	−0.829596	+	0.558364i	$0.811429\pi$
$200$	25.4354	+	7.46850i	0.127177	+	0.0373425i
$201$		0			0
$202$	10.3058	−	22.5666i	0.0510189	−	0.111716i
$203$	232.676	+	33.4537i	1.14619	+	0.164797i
$204$		0			0
$205$	31.0624	−	26.9157i	0.151524	−	0.131296i
$206$			32.9867i			0.160130i
$207$		0			0
$208$	54.0722			0.259963
$209$	−262.305	−	302.716i	−1.25505	−	1.44840i
$210$		0			0
$211$	52.3052	−	363.791i	0.247892	−	1.72413i	−0.362463	−	0.931998i	$-0.618064\pi$
$211$	52.3052	−	363.791i	0.247892	−	1.72413i	0.610355	−	0.792128i	$-0.291027\pi$
$212$	248.126	+	113.316i	1.17041	+	0.534507i
$213$		0			0
$214$	−27.5175	+	93.7160i	−0.128586	+	0.437925i
$215$	160.912	−	103.412i	0.748429	−	0.480986i
$216$		0			0
$217$	29.0124	+	98.8071i	0.133698	+	0.455332i
$218$	−147.590	−	127.888i	−0.677019	−	0.586640i
$219$		0			0
$220$	−190.714	+	55.9988i	−0.866883	+	0.254540i
$221$	−502.011	+	229.261i	−2.27155	+	1.03738i
$222$		0			0
$223$	304.587	+	89.4347i	1.36586	+	0.401053i	0.880825	−	0.473442i	$-0.156989\pi$
$223$	304.587	+	89.4347i	1.36586	+	0.401053i	0.485035	+	0.874495i	$0.338807\pi$
$224$	−241.896	+	34.7795i	−1.07989	+	0.155265i
$225$		0			0
$226$	141.959	+	20.4106i	0.628136	+	0.0903123i
$227$	−124.426	+	193.611i	−0.548133	+	0.852911i	−0.999217	−	0.0395702i	$-0.987401\pi$
$227$	−124.426	+	193.611i	−0.548133	+	0.852911i	0.451084	+	0.892482i	$0.351037\pi$
$228$		0			0
$229$		−	225.147i		−	0.983177i	−0.870828	−	0.491588i	$-0.836416\pi$
$229$		−	225.147i		−	0.983177i	0.870828	−	0.491588i	$-0.163584\pi$
$230$	−69.6820	+	115.483i	−0.302965	+	0.502099i
$231$		0			0
$232$	155.591	+	179.561i	0.670650	+	0.773971i
$233$	25.5088	+	16.3935i	0.109480	+	0.0703585i	0.594235	−	0.804291i	$-0.297455\pi$
$233$	25.5088	+	16.3935i	0.109480	+	0.0703585i	−0.484755	+	0.874650i	$0.661091\pi$
$234$		0			0
$235$	−189.619	−	86.5960i	−0.806888	−	0.368494i
$236$	5.33516	+	37.1068i	0.0226066	+	0.157232i
$237$		0			0
$238$	208.466	−	133.973i	0.875908	−	0.562912i
$239$	−142.738	−	312.552i	−0.597229	−	1.30775i	−0.930974	−	0.365086i	$-0.881039\pi$
$239$	−142.738	−	312.552i	−0.597229	−	1.30775i	0.333744	−	0.942664i	$-0.391688\pi$
$240$		0			0
$241$	40.1408	+	34.7822i	0.166559	+	0.144324i	0.734152	−	0.678985i	$-0.237580\pi$
$241$	40.1408	+	34.7822i	0.166559	+	0.144324i	−0.567593	+	0.823309i	$0.692125\pi$
$242$	−40.2628	+	46.4657i	−0.166375	+	0.192007i
$243$		0			0
$244$	−17.3875	+	7.94061i	−0.0712603	+	0.0325435i
$245$	−15.7199	−	24.4607i	−0.0641630	−	0.0998396i
$246$		0			0
$247$	−537.369	+	77.2621i	−2.17558	+	0.312802i
$248$	−43.2383	+	94.6788i	−0.174348	+	0.381769i
$249$		0			0
$250$	67.9913	−	105.797i	0.271965	−	0.423186i
$251$	40.2150	−	34.8465i	0.160219	−	0.138831i	−0.571062	−	0.820907i	$-0.693468\pi$
$251$	40.2150	−	34.8465i	0.160219	−	0.138831i	0.731281	+	0.682076i	$0.238923\pi$
$252$		0			0
$253$	−8.65463	−	305.894i	−0.0342080	−	1.20907i
$254$	57.8118			0.227606
$255$		0			0
$256$	−179.589	−	115.415i	−0.701521	−	0.450840i
$257$	−22.1395	+	153.984i	−0.0861459	+	0.599158i	0.900325	+	0.435219i	$0.143329\pi$
$257$	−22.1395	+	153.984i	−0.0861459	+	0.599158i	−0.986470	+	0.163939i	$0.947580\pi$
$258$		0			0
$259$	69.5812	+	483.948i	0.268653	+	1.86853i
$260$	−75.8992	+	258.489i	−0.291920	+	0.994188i
$261$		0			0
$262$	5.64342	+	12.3574i	0.0215398	+	0.0471655i
$263$	63.5131	+	216.306i	0.241495	+	0.822456i	0.987649	+	0.156683i	$0.0500799\pi$
$263$	63.5131	+	216.306i	0.241495	+	0.822456i	−0.746154	+	0.665773i	$0.768102\pi$
$264$		0			0
$265$	−341.435	+	394.037i	−1.28844	+	1.48693i
$266$	233.894	−	68.6774i	0.879300	−	0.258186i
$267$		0			0
$268$	3.80132	+	5.91497i	0.0141840	+	0.0220708i
$269$	−308.754	−	90.6584i	−1.14779	−	0.337020i	−0.348110	−	0.937454i	$-0.613177\pi$
$269$	−308.754	−	90.6584i	−1.14779	−	0.337020i	−0.799675	+	0.600433i	$0.794995\pi$
$270$		0			0
$271$	−167.464	+	366.695i	−0.617948	+	1.35312i	0.299054	+	0.954236i	$0.403329\pi$
$271$	−167.464	+	366.695i	−0.617948	+	1.35312i	−0.917002	+	0.398881i	$0.869398\pi$
$272$	−90.8294	−	13.0593i	−0.333932	−	0.0480121i
$273$		0			0
$274$	8.85087	−	7.66932i	0.0323024	−	0.0279902i
$275$		−	47.2943i		−	0.171979i
$276$		0			0
$277$	229.063			0.826943			0.413471	−	0.910517i	$-0.364316\pi$
$277$	229.063			0.826943			0.413471	+	0.910517i	$0.364316\pi$
$278$	75.4474	+	87.0710i	0.271394	+	0.313205i
$279$		0			0
$280$	41.8463	−	291.048i	0.149451	−	1.03946i
$281$	−129.668	−	59.2174i	−0.461452	−	0.210738i	0.171103	−	0.985253i	$-0.445267\pi$
$281$	−129.668	−	59.2174i	−0.461452	−	0.210738i	−0.632556	+	0.774515i	$0.717994\pi$
$282$		0			0
$283$	−96.0771	+	327.209i	−0.339495	+	1.15621i	0.596033	+	0.802960i	$0.296743\pi$
$283$	−96.0771	+	327.209i	−0.339495	+	1.15621i	−0.935528	+	0.353254i	$0.885075\pi$
$284$	233.945	−	150.347i	0.823749	−	0.529391i
$285$		0			0
$286$	74.1828	+	252.643i	0.259380	+	0.883369i
$287$	−42.8905	−	37.1648i	−0.149444	−	0.129494i
$288$		0			0
$289$	621.345	−	182.443i	2.14998	−	0.631292i
$290$	−169.944	+	77.6109i	−0.586014	+	0.267624i
$291$		0			0
$292$	−155.198	−	45.5703i	−0.531501	−	0.156063i
$293$	167.700	−	24.1116i	0.572355	−	0.0822922i	0.149941	−	0.988695i	$-0.452092\pi$
$293$	167.700	−	24.1116i	0.572355	−	0.0822922i	0.422414	+	0.906403i	$0.361183\pi$
$294$		0			0
$295$	−70.9261	−	10.1976i	−0.240427	−	0.0345683i
$296$	−267.172	+	415.728i	−0.902609	+	1.40449i
$297$		0			0
$298$			158.242i			0.531013i
$299$	−355.126	−	214.282i	−1.18771	−	0.716662i
$300$		0			0
$301$	−172.957	−	199.603i	−0.574607	−	0.663131i
$302$	−59.2576	−	38.0825i	−0.196217	−	0.126101i
$303$		0			0
$304$	−82.1114	−	37.4990i	−0.270103	−	0.123352i
$305$	−5.19965	−	36.1643i	−0.0170480	−	0.118572i
$306$		0			0
$307$	415.836	−	267.242i	1.35452	−	0.870495i	0.356552	−	0.934275i	$-0.383952\pi$
$307$	415.836	−	267.242i	1.35452	−	0.870495i	0.997964	+	0.0637807i	$0.0203158\pi$
$308$	114.012	+	249.651i	0.370168	+	0.810555i
$309$		0			0
$310$	−61.8544	−	53.5971i	−0.199530	−	0.172894i
$311$	361.925	−	417.684i	1.16375	−	1.34304i	0.235145	−	0.971960i	$-0.424444\pi$
$311$	361.925	−	417.684i	1.16375	−	1.34304i	0.928603	−	0.371075i	$-0.121011\pi$
$312$		0			0
$313$	−418.338	+	191.049i	−1.33654	+	0.610379i	−0.950103	−	0.311935i	$-0.899023\pi$
$313$	−418.338	+	191.049i	−1.33654	+	0.610379i	−0.386441	+	0.922314i	$0.626296\pi$
$314$	−58.3360	−	90.7726i	−0.185783	−	0.289085i
$315$		0			0
$316$	−142.471	+	20.4842i	−0.450857	+	0.0648234i
$317$	70.6986	−	154.808i	0.223024	−	0.488354i	−0.764735	−	0.644346i	$-0.777130\pi$
$317$	70.6986	−	154.808i	0.223024	−	0.488354i	0.987758	+	0.155991i	$0.0498572\pi$
$318$		0			0
$319$	229.169	−	356.594i	0.718398	−	1.11785i
$320$	98.3535	−	85.2238i	0.307355	−	0.266324i
$321$		0			0
$322$	171.527	+	72.5434i	0.532692	+	0.225290i
$323$	921.322			2.85239
$324$		0			0
$325$	−53.9255	−	34.6558i	−0.165925	−	0.106633i
$326$	−12.9682	+	90.1961i	−0.0397799	+	0.276675i
$327$		0			0
$328$	−8.16345	−	56.7781i	−0.0248886	−	0.173104i
$329$	−81.0922	+	276.175i	−0.246481	+	0.839436i
$330$		0			0
$331$	−219.808	−	481.312i	−0.664072	−	1.45411i	−0.878678	−	0.477414i	$-0.841574\pi$
$331$	−219.808	−	481.312i	−0.664072	−	1.45411i	0.214606	−	0.976701i	$-0.431153\pi$
$332$	44.4246	+	151.296i	0.133809	+	0.455712i
$333$		0			0
$334$	−69.7638	+	80.5117i	−0.208874	+	0.241053i
$335$	−12.8949	+	3.78630i	−0.0384924	+	0.0113024i
$336$		0			0
$337$	49.5828	+	77.1523i	0.147130	+	0.228939i	0.906994	−	0.421143i	$-0.138371\pi$
$337$	49.5828	+	77.1523i	0.147130	+	0.228939i	−0.759864	+	0.650082i	$0.774735\pi$
$338$	164.475	+	48.2941i	0.486612	+	0.142882i
$339$		0			0
$340$	189.923	−	415.874i	0.558598	−	1.22316i
$341$	183.805	+	26.4271i	0.539016	+	0.0774988i
$342$		0			0
$343$	242.894	−	210.469i	0.708146	−	0.613612i
$344$		−	266.949i		−	0.776015i
$345$		0			0
$346$	76.1466			0.220077
$347$	−377.876	−	436.092i	−1.08898	−	1.25675i	−0.964374	−	0.264544i	$-0.914779\pi$
$347$	−377.876	−	436.092i	−1.08898	−	1.25675i	−0.124606	−	0.992206i	$-0.539767\pi$
$348$		0			0
$349$	33.6847	−	234.283i	0.0965179	−	0.671297i	−0.882916	−	0.469531i	$-0.844423\pi$
$349$	33.6847	−	234.283i	0.0965179	−	0.671297i	0.979434	−	0.201766i	$-0.0646679\pi$
$350$	26.1815	+	11.9567i	0.0748042	+	0.0341619i
$351$		0			0
$352$	−124.155	+	422.832i	−0.352712	+	1.20123i
$353$	−42.3300	+	27.2038i	−0.119915	+	0.0770647i	−0.599223	−	0.800582i	$-0.704524\pi$
$353$	−42.3300	+	27.2038i	−0.119915	+	0.0770647i	0.479308	+	0.877647i	$0.340888\pi$
$354$		0			0
$355$	149.753	+	510.011i	0.421839	+	1.43665i
$356$	156.261	+	135.401i	0.438935	+	0.380340i
$357$		0			0
$358$	−2.01433	+	0.591460i	−0.00562662	+	0.00165212i
$359$	43.9433	−	20.0682i	0.122405	−	0.0559004i	−0.353271	−	0.935521i	$-0.614931\pi$
$359$	43.9433	−	20.0682i	0.122405	−	0.0559004i	0.475676	+	0.879621i	$0.342203\pi$
$360$		0			0
$361$	523.227	+	153.633i	1.44938	+	0.425577i
$362$	82.4920	−	11.8606i	0.227879	−	0.0327640i
$363$		0			0
$364$	368.200	+	52.9391i	1.01154	+	0.145437i
$365$	167.150	−	260.090i	0.457945	−	0.712576i
$366$		0			0
$367$		−	1.29054i		−	0.00351647i	−0.999998	−	0.00175823i	$-0.999440\pi$
$367$		−	1.29054i		−	0.00351647i	0.999998	−	0.00175823i	$-0.000559664\pi$
$368$	−30.4116	−	61.8970i	−0.0826402	−	0.168198i
$369$		0			0
$370$	−254.470	−	293.674i	−0.687758	−	0.793715i
$371$	605.637	+	389.219i	1.63245	+	1.04911i
$372$		0			0
$373$	−611.510	−	279.267i	−1.63944	−	0.748706i	−0.639637	−	0.768677i	$-0.720915\pi$
$373$	−611.510	−	279.267i	−1.63944	−	0.748706i	−0.999801	+	0.0199705i	$0.993643\pi$
$374$	−63.5934	−	442.302i	−0.170036	−	1.18262i
$375$		0			0
$376$	−244.743	+	157.286i	−0.650911	+	0.418315i
$377$	−238.665	−	522.603i	−0.633063	−	1.38621i
$378$		0			0
$379$	−364.833	−	316.130i	−0.962621	−	0.834116i	0.0235712	−	0.999722i	$-0.492496\pi$
$379$	−364.833	−	316.130i	−0.962621	−	0.834116i	−0.986192	+	0.165607i	$0.947042\pi$
$380$	294.519	−	339.893i	0.775049	−	0.894455i
$381$		0			0
$382$	237.402	−	108.418i	0.621470	−	0.283816i
$383$	−21.3547	−	33.2286i	−0.0557565	−	0.0867588i	0.812256	−	0.583301i	$-0.198239\pi$
$383$	−21.3547	−	33.2286i	−0.0557565	−	0.0867588i	−0.868013	+	0.496542i	$0.834603\pi$
$384$		0			0
$385$	−519.250	+	74.6569i	−1.34870	+	0.193914i
$386$	−94.0506	+	205.942i	−0.243654	+	0.533529i
$387$		0			0
$388$	2.85744	−	4.44627i	0.00736454	−	0.0114595i
$389$	−359.683	+	311.667i	−0.924634	+	0.801200i	−0.980354	−	0.197247i	$-0.936800\pi$
$389$	−359.683	+	311.667i	−0.924634	+	0.801200i	0.0557201	+	0.998446i	$0.482255\pi$
$390$		0			0
$391$	544.782	+	445.715i	1.39330	+	1.13994i
$392$	−40.5797			−0.103520
$393$		0			0
$394$	−128.912	−	82.8465i	−0.327187	−	0.210270i
$395$	39.1535	−	272.319i	0.0991228	−	0.689414i
$396$		0			0
$397$	80.6577	+	560.987i	0.203168	+	1.41306i	0.794807	+	0.606862i	$0.207572\pi$
$397$	80.6577	+	560.987i	0.203168	+	1.41306i	−0.591639	+	0.806203i	$0.701519\pi$
$398$	−2.61018	+	8.88946i	−0.00655825	+	0.0223353i
$399$		0			0
$400$	−4.42763	−	9.69516i	−0.0110691	−	0.0242379i
$401$	1.59006	+	5.41524i	0.00396523	+	0.0135043i	0.961452	−	0.274973i	$-0.0886691\pi$
$401$	1.59006	+	5.41524i	0.00396523	+	0.0135043i	−0.957487	+	0.288478i	$0.906851\pi$
$402$		0			0
$403$	164.819	−	190.211i	0.408980	−	0.471988i
$404$	−60.6394	+	17.8053i	−0.150098	+	0.0440726i
$405$		0			0
$406$	139.468	+	217.017i	0.343518	+	0.534525i
$407$	845.934	+	248.389i	2.07846	+	0.610292i
$408$		0			0
$409$	64.1224	−	140.408i	0.156778	−	0.343297i	−0.814901	−	0.579600i	$-0.803209\pi$
$409$	64.1224	−	140.408i	0.156778	−	0.343297i	0.971679	+	0.236304i	$0.0759360\pi$
$410$	44.6464	+	6.41918i	0.108894	+	0.0156565i
$411$		0			0
$412$	63.5082	−	55.0302i	0.154146	−	0.133568i
$413$			98.9408i			0.239566i
$414$		0			0
$415$	−301.397			−0.726257
$416$	391.141	+	451.401i	0.940243	+	1.08510i
$417$		0			0
$418$	62.5576	−	435.098i	0.149659	−	1.04090i
$419$	−292.767	−	133.702i	−0.698729	−	0.319099i	0.0341894	−	0.999415i	$-0.489115\pi$
$419$	−292.767	−	133.702i	−0.698729	−	0.319099i	−0.732918	+	0.680317i	$0.761842\pi$
$420$		0			0
$421$	73.0964	−	248.944i	0.173626	−	0.591315i	−0.825992	−	0.563681i	$-0.809385\pi$
$421$	73.0964	−	248.944i	0.173626	−	0.591315i	0.999618	−	0.0276337i	$-0.00879719\pi$
$422$	339.308	−	218.060i	0.804047	−	0.516730i
$423$		0			0
$424$	205.004	+	698.181i	0.483501	+	1.64665i
$425$	82.2130	+	71.2380i	0.193442	+	0.167619i
$426$		0			0
$427$	−48.4052	+	14.2130i	−0.113361	+	0.0332858i
$428$	226.335	−	103.364i	0.528819	−	0.241504i
$429$		0			0
$430$	201.408	+	59.1387i	0.468390	+	0.137532i
$431$	−110.547	+	15.8942i	−0.256489	+	0.0368775i	−0.269360	−	0.963040i	$-0.586812\pi$
$431$	−110.547	+	15.8942i	−0.256489	+	0.0368775i	0.0128709	+	0.999917i	$0.495903\pi$
$432$		0			0
$433$	−348.348	−	50.0849i	−0.804499	−	0.115669i	−0.272216	−	0.962236i	$-0.587757\pi$
$433$	−348.348	−	50.0849i	−0.804499	−	0.115669i	−0.532283	+	0.846567i	$0.678666\pi$
$434$	−61.0981	+	95.0705i	−0.140779	+	0.219056i
$435$		0			0
$436$			497.500i			1.14105i
$437$	390.673	+	571.678i	0.893989	+	1.30819i
$438$		0			0
$439$	−60.9655	−	70.3579i	−0.138874	−	0.160269i	0.682052	−	0.731303i	$-0.261088\pi$
$439$	−60.9655	−	70.3579i	−0.138874	−	0.160269i	−0.820926	+	0.571035i	$0.806542\pi$
$440$	−446.054	−	286.661i	−1.01376	−	0.651503i
$441$		0			0
$442$	−550.917	−	251.595i	−1.24642	−	0.569220i
$443$	27.7847	+	193.247i	0.0627194	+	0.436223i	0.996851	+	0.0792947i	$0.0252668\pi$
$443$	27.7847	+	193.247i	0.0627194	+	0.436223i	−0.934132	+	0.356928i	$0.883824\pi$
$444$		0			0
$445$	−332.469	+	213.665i	−0.747122	+	0.480146i
$446$	144.719	+	316.889i	0.324481	+	0.710514i
$447$		0			0
$448$	−135.805	−	117.676i	−0.303136	−	0.262669i
$449$	−285.566	+	329.560i	−0.636004	+	0.733987i	−0.978663	−	0.205472i	$-0.934127\pi$
$449$	−285.566	+	329.560i	−0.636004	+	0.733987i	0.342659	+	0.939460i	$0.388672\pi$
$450$		0			0
$451$	−93.0897	+	42.5127i	−0.206407	+	0.0942631i
$452$	−197.527	−	307.359i	−0.437007	−	0.679997i
$453$		0			0
$454$	−249.996	+	35.9439i	−0.550651	+	0.0791717i
$455$	−295.366	+	646.762i	−0.649156	+	1.42145i
$456$		0			0
$457$	−63.3086	+	98.5101i	−0.138531	+	0.215558i	−0.903586	−	0.428406i	$-0.859075\pi$
$457$	−63.3086	+	98.5101i	−0.138531	+	0.215558i	0.765055	+	0.643964i	$0.222712\pi$
$458$	186.732	−	161.804i	0.407711	−	0.353283i
$459$		0			0
$460$	338.583	−	58.4983i	0.736049	−	0.127170i
$461$	−449.862			−0.975840			−0.487920	−	0.872888i	$-0.662244\pi$
$461$	−449.862			−0.975840			−0.487920	+	0.872888i	$0.662244\pi$
$462$		0			0
$463$	426.367	+	274.010i	0.920880	+	0.591814i	0.912913	−	0.408155i	$-0.133828\pi$
$463$	426.367	+	274.010i	0.920880	+	0.591814i	0.00796728	+	0.999968i	$0.497464\pi$
$464$	13.5950	−	94.5550i	0.0292995	−	0.203782i
$465$		0			0
$466$	4.73573	+	32.9377i	0.0101625	+	0.0706818i
$467$	181.147	−	616.931i	0.387896	−	1.32105i	−0.501992	−	0.864872i	$-0.667399\pi$
$467$	181.147	−	616.931i	0.387896	−	1.32105i	0.889888	−	0.456179i	$-0.150783\pi$
$468$		0			0
$469$	7.70879	+	16.8799i	0.0164366	+	0.0359912i
$470$	−64.4503	−	219.498i	−0.137128	−	0.467016i
$471$		0			0
$472$	−65.4885	+	75.5778i	−0.138747	+	0.160122i
$473$	−456.965	+	134.177i	−0.966100	+	0.283672i
$474$		0			0
$475$	57.8549	+	90.0239i	0.121800	+	0.189524i
$476$	−605.709	−	177.852i	−1.27250	−	0.373639i
$477$		0			0
$478$	156.643	−	343.001i	0.327706	−	0.717575i
$479$	−437.215	−	62.8620i	−0.912766	−	0.131236i	−0.330099	−	0.943946i	$-0.607082\pi$
$479$	−437.215	−	62.8620i	−0.912766	−	0.131236i	−0.582668	+	0.812710i	$0.697991\pi$
$480$		0			0
$481$	903.091	−	782.533i	1.87753	−	1.62689i
$482$			58.2882i			0.120930i
$483$		0			0
$484$	156.628			0.323611
$485$	6.61561	+	7.63482i	0.0136404	+	0.0157419i
$486$		0			0
$487$	89.9279	−	625.462i	0.184657	−	1.28432i	−0.660917	−	0.750459i	$-0.729833\pi$
$487$	89.9279	−	625.462i	0.184657	−	1.28432i	0.845574	−	0.533858i	$-0.179258\pi$
$488$	−46.3827	−	21.1823i	−0.0950466	−	0.0434063i
$489$		0			0
$490$	8.98984	−	30.6166i	0.0183466	−	0.0624828i
$491$	−115.699	+	74.3555i	−0.235640	+	0.151437i	−0.653132	−	0.757244i	$-0.726546\pi$
$491$	−115.699	+	74.3555i	−0.235640	+	0.151437i	0.417492	+	0.908681i	$0.362909\pi$
$492$		0			0
$493$	274.687	+	935.499i	0.557175	+	1.89756i
$494$	−450.263	−	390.155i	−0.911464	−	0.789788i
$495$		0			0
$496$	40.1533	−	11.7901i	0.0809543	−	0.0237703i
$497$	667.621	−	304.892i	1.34330	−	0.613466i
$498$		0			0
$499$	38.1930	+	11.2145i	0.0765390	+	0.0224739i	0.319778	−	0.947493i	$-0.396392\pi$
$499$	38.1930	+	11.2145i	0.0765390	+	0.0224739i	−0.243239	+	0.969966i	$0.578210\pi$
$500$	−317.114	+	45.5941i	−0.634227	+	0.0911881i
$501$		0			0
$502$	57.8015	+	8.31061i	0.115143	+	0.0165550i
$503$	−28.3510	+	44.1150i	−0.0563638	+	0.0877037i	−0.868292	−	0.496054i	$-0.834782\pi$
$503$	−28.3510	+	44.1150i	−0.0563638	+	0.0877037i	0.811928	+	0.583758i	$0.198418\pi$
$504$		0			0
$505$		−	120.800i		−	0.239207i
$506$	247.481	−	227.011i	0.489093	−	0.448638i
$507$		0			0
$508$	−96.4448	−	111.303i	−0.189852	−	0.219101i
$509$	−203.480	−	130.769i	−0.399764	−	0.256913i	0.325276	−	0.945619i	$-0.394543\pi$
$509$	−203.480	−	130.769i	−0.399764	−	0.256913i	−0.725041	+	0.688706i	$0.758179\pi$
$510$		0			0
$511$	−388.320	−	177.340i	−0.759921	−	0.347044i
$512$	26.8633	+	186.838i	0.0524673	+	0.364918i
$513$		0			0
$514$	−143.621	+	92.2995i	−0.279418	+	0.179571i
$515$	66.7247	+	146.107i	0.129562	+	0.283702i
$516$		0			0
$517$	392.259	+	339.894i	0.758721	+	0.657436i
$518$	−351.369	+	405.501i	−0.678319	+	0.782821i
$519$		0			0
$520$	−653.710	+	298.539i	−1.25713	+	0.574114i
$521$	0.164585	+	0.256099i	0.000315902	+	0.000491553i	0.841411	−	0.540395i	$-0.181725\pi$
$521$	0.164585	+	0.256099i	0.000315902	+	0.000491553i	−0.841096	+	0.540887i	$0.818089\pi$
$522$		0			0
$523$	−124.369	+	17.8816i	−0.237800	+	0.0341905i	−0.260184	−	0.965559i	$-0.583783\pi$
$523$	−124.369	+	17.8816i	−0.237800	+	0.0341905i	0.0223843	+	0.999749i	$0.492874\pi$
$524$	14.3766	−	31.4803i	0.0274362	−	0.0600769i
$525$		0			0
$526$	−133.754	+	208.126i	−0.254286	+	0.395676i
$527$	−322.799	+	279.707i	−0.612521	+	0.530752i
$528$		0			0
$529$	−45.5587	+	527.035i	−0.0861222	+	0.996285i
$530$	−572.179			−1.07958
$531$		0			0
$532$	−522.417	−	335.737i	−0.981986	−	0.631084i
$533$	−19.7399	+	137.294i	−0.0370355	+	0.257587i
$534$		0			0
$535$	67.6842	+	470.754i	0.126513	+	0.879914i
$536$	−5.28423	+	17.9964i	−0.00985863	+	0.0335754i
$537$		0			0
$538$	−146.699	−	321.225i	−0.272674	−	0.597073i
$539$	20.3966	+	69.4645i	0.0378416	+	0.128877i
$540$		0			0
$541$	−306.844	+	354.117i	−0.567179	+	0.654559i	−0.964798	−	0.262991i	$-0.915291\pi$
$541$	−306.844	+	354.117i	−0.567179	+	0.654559i	0.397619	+	0.917550i	$0.369836\pi$
$542$	−424.476	+	124.638i	−0.783167	+	0.229958i
$543$		0			0
$544$	−548.010	−	852.721i	−1.00737	−	1.56750i
$545$	−912.403	−	267.906i	−1.67413	−	0.491570i
$546$		0			0
$547$	80.0673	−	175.323i	0.146375	−	0.320517i	−0.822216	−	0.569176i	$-0.807262\pi$
$547$	80.0673	−	175.323i	0.146375	−	0.320517i	0.968591	+	0.248658i	$0.0799897\pi$
$548$	−29.5310	−	4.24592i	−0.0538887	−	0.00774803i
$549$		0			0
$550$	39.2246	−	33.9883i	0.0713175	−	0.0617970i
$551$			959.113i			1.74068i
$552$		0			0
$553$	−379.880			−0.686945
$554$	164.618	+	189.979i	0.297144	+	0.342923i
$555$		0			0
$556$	41.7695	−	290.513i	0.0751250	−	0.522506i
$557$	163.784	+	74.7977i	0.294047	+	0.134287i	0.556976	−	0.830528i	$-0.311961\pi$
$557$	163.784	+	74.7977i	0.294047	+	0.134287i	−0.262930	+	0.964815i	$0.584689\pi$
$558$		0			0
$559$	−181.860	+	619.358i	−0.325331	+	1.10798i
$560$	−99.4551	+	63.9159i	−0.177598	+	0.114136i
$561$		0			0
$562$	−44.0735	−	150.100i	−0.0784225	−	0.267083i
$563$	597.233	+	517.506i	1.06081	+	0.919193i	0.996893	−	0.0787627i	$-0.0250970\pi$
$563$	597.233	+	517.506i	1.06081	+	0.919193i	0.0639117	+	0.997956i	$0.479642\pi$
$564$		0			0
$565$	670.058	−	196.747i	1.18594	−	0.348224i
$566$	−340.425	+	155.467i	−0.601457	+	0.274676i
$567$		0			0
$568$	711.782	+	208.998i	1.25314	+	0.367954i
$569$	409.074	−	58.8160i	0.718935	−	0.103367i	0.226869	−	0.973925i	$-0.427151\pi$
$569$	409.074	−	58.8160i	0.718935	−	0.103367i	0.492066	+	0.870558i	$0.336242\pi$
$570$		0			0
$571$	252.515	+	36.3062i	0.442233	+	0.0635836i	0.359835	−	0.933016i	$-0.382833\pi$
$571$	252.515	+	36.3062i	0.442233	+	0.0635836i	0.0823983	+	0.996599i	$0.473742\pi$
$572$	362.651	−	564.295i	0.634005	−	0.986530i
$573$		0			0
$574$		−	62.2810i		−	0.108503i
$575$	−9.34177	+	81.2204i	−0.0162466	+	0.141253i
$576$		0			0
$577$	−397.587	−	458.840i	−0.689059	−	0.795217i	0.298172	−	0.954512i	$-0.403623\pi$
$577$	−397.587	−	458.840i	−0.689059	−	0.795217i	−0.987231	+	0.159296i	$0.949078\pi$
$578$	597.848	+	384.214i	1.03434	+	0.664729i
$579$		0			0
$580$	432.932	+	197.713i	0.746435	+	0.340885i
$581$	59.2264	+	411.928i	0.101939	+	0.708999i
$582$		0			0
$583$	1092.11	−	701.855i	1.87326	−	1.20387i
$584$	−179.245	−	392.491i	−0.306926	−	0.672074i
$585$		0			0
$586$	140.516	+	121.758i	0.239789	+	0.207778i
$587$	−334.476	+	386.006i	−0.569806	+	0.657591i	−0.965381	−	0.260842i	$-0.916000\pi$
$587$	−334.476	+	386.006i	−0.569806	+	0.657591i	0.395575	+	0.918434i	$0.370545\pi$
$588$		0			0
$589$	−382.197	+	174.544i	−0.648892	+	0.296339i
$590$	−42.5139	−	66.1529i	−0.0720574	−	0.112124i
$591$		0			0
$592$	196.667	−	28.2765i	0.332208	−	0.0477644i
$593$	279.912	−	612.922i	0.472027	−	1.03360i	−0.512552	−	0.858656i	$-0.671300\pi$
$593$	279.912	−	612.922i	0.472027	−	1.03360i	0.984579	−	0.174939i	$-0.0559729\pi$
$594$		0			0
$595$	652.353	−	1015.08i	1.09639	−	1.70602i
$596$	304.658	−	263.988i	0.511171	−	0.442932i
$597$		0			0
$598$	−77.4940	−	448.528i	−0.129589	−	0.750047i
$599$	−211.026			−0.352298			−0.176149	−	0.984364i	$-0.556364\pi$
$599$	−211.026			−0.352298			−0.176149	+	0.984364i	$0.556364\pi$
$600$		0			0
$601$	−855.272	−	549.650i	−1.42308	−	0.914558i	−0.999964	−	0.00848334i	$-0.997300\pi$
$601$	−855.272	−	549.650i	−1.42308	−	0.914558i	−0.423117	−	0.906075i	$-0.639064\pi$
$602$	41.2488	−	286.891i	0.0685196	−	0.476564i
$603$		0			0
$604$	25.5376	+	177.618i	0.0422808	+	0.294070i
$605$	−84.3446	+	287.251i	−0.139413	+	0.474796i
$606$		0			0
$607$	40.4700	+	88.6169i	0.0666721	+	0.145992i	0.940034	−	0.341079i	$-0.110793\pi$
$607$	40.4700	+	88.6169i	0.0666721	+	0.145992i	−0.873362	+	0.487071i	$0.838065\pi$
$608$	−280.922	−	956.731i	−0.462042	−	1.57357i
$609$		0			0
$610$	26.2570	−	30.3022i	0.0430443	−	0.0496757i
$611$	674.987	−	198.194i	1.10473	−	0.324377i
$612$		0			0
$613$	342.542	+	533.005i	0.558796	+	0.869503i	0.999605	−	0.0280977i	$-0.00894496\pi$
$613$	342.542	+	533.005i	0.558796	+	0.869503i	−0.440810	+	0.897601i	$0.645309\pi$
$614$	520.487	+	152.829i	0.847699	+	0.248907i
$615$		0			0
$616$	−304.137	+	665.966i	−0.493728	+	1.08111i
$617$	−116.455	−	16.7437i	−0.188743	−	0.0271372i	0.0472948	−	0.998881i	$-0.484940\pi$
$617$	−116.455	−	16.7437i	−0.188743	−	0.0271372i	−0.236038	+	0.971744i	$0.575849\pi$
$618$		0			0
$619$	−414.208	+	358.913i	−0.669156	+	0.579827i	−0.921769	−	0.387741i	$-0.873256\pi$
$619$	−414.208	+	358.913i	−0.669156	+	0.579827i	0.252613	+	0.967568i	$0.418710\pi$
$620$			208.500i			0.336290i
$621$		0			0
$622$	606.517			0.975107
$623$	357.355	+	412.410i	0.573603	+	0.661974i
$624$		0			0
$625$	99.7954	−	694.092i	0.159673	−	1.11055i
$626$	−459.093	−	209.661i	−0.733375	−	0.334921i
$627$		0			0
$628$	−77.4423	+	263.744i	−0.123316	+	0.419975i
$629$	−1705.99	+	1096.37i	−2.71222	+	1.74304i
$630$		0			0
$631$	−19.0915	−	65.0196i	−0.0302559	−	0.103042i	0.942981	−	0.332847i	$-0.108009\pi$
$631$	−19.0915	−	65.0196i	−0.0302559	−	0.103042i	−0.973237	+	0.229805i	$0.926191\pi$
$632$	−290.179	−	251.441i	−0.459143	−	0.397850i
$633$		0			0
$634$	179.202	−	52.6185i	0.282653	−	0.0829944i
$635$	256.064	−	116.940i	0.403250	−	0.184158i
$636$		0			0
$637$	94.1504	+	27.6450i	0.147803	+	0.0433988i
$638$	460.444	−	66.2018i	0.721699	−	0.103765i
$639$		0			0
$640$	−559.385	−	80.4275i	−0.874040	−	0.125668i
$641$	650.539	−	1012.26i	1.01488	−	1.57919i	0.217184	−	0.976131i	$-0.430313\pi$
$641$	650.539	−	1012.26i	1.01488	−	1.57919i	0.797698	−	0.603057i	$-0.206051\pi$
$642$		0			0
$643$		−	457.000i		−	0.710731i	−0.934727	−	0.355365i	$-0.884356\pi$
$643$		−	457.000i		−	0.710731i	0.934727	−	0.355365i	$-0.115644\pi$
$644$	−146.485	−	451.256i	−0.227461	−	0.700708i
$645$		0			0
$646$	662.115	+	764.121i	1.02495	+	1.18285i
$647$	−1030.69	−	662.384i	−1.59303	−	1.02378i	−0.970475	−	0.241202i	$-0.922458\pi$
$647$	−1030.69	−	662.384i	−1.59303	−	1.02378i	−0.622555	−	0.782576i	$-0.713905\pi$
$648$		0			0
$649$	162.291	+	74.1158i	0.250063	+	0.114200i
$650$	−10.0113	−	69.6301i	−0.0154020	−	0.107123i
$651$		0			0
$652$	195.286	−	125.503i	0.299519	−	0.192489i
$653$	415.471	+	909.754i	0.636249	+	1.39319i	0.903090	+	0.429451i	$0.141293\pi$
$653$	415.471	+	909.754i	0.636249	+	1.39319i	−0.266841	+	0.963741i	$0.585980\pi$
$654$		0			0
$655$	49.9923	+	43.3186i	0.0763242	+	0.0661353i
$656$	−15.1031	+	17.4299i	−0.0230230	+	0.0265699i
$657$		0			0
$658$	−287.329	+	131.219i	−0.436671	+	0.199421i
$659$	311.819	+	485.199i	0.473169	+	0.736266i	0.993014	−	0.117995i	$-0.0376466\pi$
$659$	311.819	+	485.199i	0.473169	+	0.736266i	−0.519845	+	0.854261i	$0.674010\pi$
$660$		0			0
$661$	−1146.15	+	164.791i	−1.73396	+	0.249306i	−0.935648	−	0.352934i	$-0.885184\pi$
$661$	−1146.15	+	164.791i	−1.73396	+	0.249306i	−0.798315	+	0.602240i	$0.794275\pi$
$662$	241.221	−	528.201i	0.364383	−	0.797887i
$663$		0			0
$664$	−227.413	+	353.861i	−0.342489	+	0.532923i
$665$	897.057	−	777.305i	1.34896	−	1.16888i
$666$		0			0
$667$	−463.998	+	567.127i	−0.695649	+	0.850266i
$668$	271.390			0.406273
$669$		0			0
$670$	−12.4073	−	7.97368i	−0.0185184	−	0.0119010i
$671$	−12.9465	+	90.0451i	−0.0192944	+	0.134195i
$672$		0			0
$673$	67.2571	+	467.783i	0.0999363	+	0.695072i	0.976772	+	0.214282i	$0.0687411\pi$
$673$	67.2571	+	467.783i	0.0999363	+	0.695072i	−0.876836	+	0.480790i	$0.840350\pi$
$674$	−28.3551	+	96.5687i	−0.0420699	+	0.143277i
$675$		0			0
$676$	−181.407	−	397.225i	−0.268353	−	0.587611i
$677$	259.134	+	882.528i	0.382767	+	1.30359i	0.895509	+	0.445043i	$0.146812\pi$
$677$	259.134	+	882.528i	0.382767	+	1.30359i	−0.512742	+	0.858543i	$0.671370\pi$
$678$		0			0
$679$	9.13474	−	10.5420i	0.0134532	−	0.0155258i
$680$	1170.19	−	343.599i	1.72087	−	0.505292i
$681$		0			0
$682$	110.174	+	171.435i	0.161546	+	0.251371i
$683$	459.820	+	135.015i	0.673236	+	0.197680i	0.600444	−	0.799667i	$-0.294991\pi$
$683$	459.820	+	135.015i	0.673236	+	0.197680i	0.0727925	+	0.997347i	$0.476809\pi$
$684$		0			0
$685$	23.6895	−	51.8727i	0.0345832	−	0.0757266i
$686$	349.115	+	50.1952i	0.508914	+	0.0731708i
$687$		0			0
$688$	−81.1147	+	70.2863i	−0.117899	+	0.102160i
$689$		−	1759.53i		−	2.55375i
$690$		0			0
$691$	44.7442			0.0647528			0.0323764	−	0.999476i	$-0.489692\pi$
$691$	44.7442			0.0647528			0.0323764	+	0.999476i	$0.489692\pi$
$692$	−127.032	−	146.603i	−0.183572	−	0.211854i
$693$		0			0
$694$	90.1204	−	626.801i	0.129857	−	0.903172i
$695$	510.301	+	233.047i	0.734246	+	0.335319i
$696$		0			0
$697$	66.3174	−	225.856i	0.0951469	−	0.324041i
$698$	218.516	−	140.432i	0.313060	−	0.201191i
$699$		0			0
$700$	−20.6575	−	70.3531i	−0.0295108	−	0.100504i
$701$	461.432	+	399.833i	0.658248	+	0.570375i	0.918624	−	0.395132i	$-0.129301\pi$
$701$	461.432	+	399.833i	0.658248	+	0.570375i	−0.260376	+	0.965507i	$0.583847\pi$
$702$		0			0
$703$	−1914.08	+	562.023i	−2.72273	+	0.799464i
$704$	−294.752	+	134.609i	−0.418682	+	0.191206i
$705$		0			0
$706$	−52.9829	−	15.5572i	−0.0750466	−	0.0220357i
$707$	−165.101	+	23.7379i	−0.233523	+	0.0335755i
$708$		0			0
$709$	383.213	+	55.0977i	0.540498	+	0.0777118i	0.407157	−	0.913358i	$-0.366520\pi$
$709$	383.213	+	55.0977i	0.540498	+	0.0777118i	0.133341	+	0.991070i	$0.457429\pi$
$710$	−315.369	+	490.724i	−0.444182	+	0.691161i
$711$		0			0
$712$			551.558i			0.774661i
$713$	−310.435	−	81.6902i	−0.435393	−	0.114573i
$714$		0			0
$715$	839.616	+	968.968i	1.17429	+	1.35520i
$716$	4.49913	+	2.89142i	0.00628371	+	0.00403829i
$717$		0			0
$718$	48.2242	+	22.0233i	0.0671647	+	0.0306731i
$719$	−150.493	−	1046.70i	−0.209308	−	1.45577i	−0.775421	−	0.631444i	$-0.782463\pi$
$719$	−150.493	−	1046.70i	−0.209308	−	1.45577i	0.566113	−	0.824328i	$-0.308447\pi$
$720$		0			0
$721$	186.577	−	119.906i	0.258775	−	0.166305i
$722$	248.601	+	544.361i	0.344323	+	0.753962i
$723$		0			0
$724$	−160.452	−	139.033i	−0.221619	−	0.192034i
$725$	−74.1600	+	85.5853i	−0.102290	+	0.118049i
$726$		0			0
$727$	80.1084	−	36.5843i	0.110190	−	0.0503222i	−0.359557	−	0.933123i	$-0.617072\pi$
$727$	80.1084	−	36.5843i	0.110190	−	0.0503222i	0.469747	+	0.882801i	$0.344345\pi$
$728$	536.481	+	834.781i	0.736924	+	1.14668i
$729$		0			0
$730$	335.836	−	48.2859i	0.460049	−	0.0661450i
$731$	455.070	−	996.463i	0.622530	−	1.36315i
$732$		0			0
$733$	239.267	−	372.306i	0.326421	−	0.507921i	−0.638794	−	0.769378i	$-0.720566\pi$
$733$	239.267	−	372.306i	0.326421	−	0.507921i	0.965215	+	0.261456i	$0.0842028\pi$
$734$	1.07034	−	0.927458i	0.00145823	−	0.00126357i
$735$		0			0
$736$	296.735	−	701.623i	0.403173	−	0.953292i
$737$	33.4624			0.0454035
$738$		0			0
$739$	−337.304	−	216.772i	−0.456432	−	0.293331i	0.292151	−	0.956372i	$-0.405629\pi$
$739$	−337.304	−	216.772i	−0.456432	−	0.293331i	−0.748583	+	0.663041i	$0.769266\pi$
$740$	−140.881	+	979.847i	−0.190379	+	1.32412i
$741$		0			0
$742$	112.437	+	782.015i	0.151532	+	1.05393i
$743$	−39.8702	+	135.785i	−0.0536611	+	0.182753i	−0.981963	−	0.189076i	$-0.939451\pi$
$743$	−39.8702	+	135.785i	−0.0536611	+	0.182753i	0.928301	+	0.371829i	$0.121269\pi$
$744$		0			0
$745$	320.088	+	700.894i	0.429648	+	0.940798i
$746$	−207.849	−	707.868i	−0.278618	−	0.948885i
$747$		0			0
$748$	−745.459	+	860.306i	−0.996604	+	1.15014i
$749$	630.094	−	185.012i	0.841247	−	0.247012i
$750$		0			0
$751$	−289.753	−	450.865i	−0.385824	−	0.600353i	0.592965	−	0.805229i	$-0.297957\pi$
$751$	−289.753	−	450.865i	−0.385824	−	0.600353i	−0.978788	+	0.204875i	$0.934321\pi$
$752$	112.232	+	32.9543i	0.149245	+	0.0438223i
$753$		0			0
$754$	261.915	−	573.515i	0.347368	−	0.760629i
$755$	−339.500	−	48.8127i	−0.449668	−	0.0646525i
$756$		0			0
$757$	486.222	−	421.313i	0.642301	−	0.556557i	−0.271643	−	0.962398i	$-0.587567\pi$
$757$	486.222	−	421.313i	0.642301	−	0.556557i	0.913943	+	0.405842i	$0.133022\pi$
$758$		−	529.772i		−	0.698908i
$759$		0			0
$760$	1199.73			1.57859
$761$	901.010	+	1039.82i	1.18398	+	1.36639i	0.915107	+	0.403212i	$0.132106\pi$
$761$	901.010	+	1039.82i	1.18398	+	1.36639i	0.268874	+	0.963175i	$0.413348\pi$
$762$		0			0
$763$	−186.862	+	1299.65i	−0.244904	+	1.70335i
$764$	−604.780	−	276.194i	−0.791596	−	0.361510i
$765$		0			0
$766$	12.2122	−	41.5910i	0.0159429	−	0.0542964i
$767$	203.430	−	130.736i	0.265228	−	0.170452i
$768$		0			0
$769$	−228.694	−	778.860i	−0.297391	−	1.01282i	−0.963665	−	0.267115i	$-0.913930\pi$
$769$	−228.694	−	778.860i	−0.297391	−	1.01282i	0.666273	−	0.745708i	$-0.267888\pi$
$770$	−435.081	−	377.000i	−0.565040	−	0.489610i
$771$		0			0
$772$	553.394	−	162.491i	0.716832	−	0.210481i
$773$	349.779	−	159.739i	0.452495	−	0.206648i	−0.176113	−	0.984370i	$-0.556352\pi$
$773$	349.779	−	159.739i	0.452495	−	0.206648i	0.628608	+	0.777722i	$0.283625\pi$
$774$		0			0
$775$	−47.6009	−	13.9769i	−0.0614205	−	0.0180347i
$776$	13.9555	−	2.00649i	0.0179839	−	0.00258569i
$777$		0			0
$778$	−516.977	−	74.3300i	−0.664494	−	0.0955399i
$779$	125.189	−	194.798i	0.160705	−	0.250062i
$780$		0			0
$781$		−	1323.48i		−	1.69460i
$782$	21.8462	+	772.144i	0.0279363	+	0.987397i
$783$		0			0
$784$	10.6844	+	12.3305i	0.0136281	+	0.0157277i
$785$	−441.998	−	284.055i	−0.563055	−	0.361853i
$786$		0			0
$787$	−663.192	−	302.870i	−0.842684	−	0.384841i	−0.0531790	−	0.998585i	$-0.516935\pi$
$787$	−663.192	−	302.870i	−0.842684	−	0.384841i	−0.789505	+	0.613744i	$0.789663\pi$
$788$	55.5558	+	386.399i	0.0705022	+	0.490354i
$789$		0			0
$790$	253.992	−	163.231i	0.321509	−	0.206621i
$791$	−400.571	−	877.127i	−0.506410	−	1.10888i
$792$		0			0
$793$	93.1837	+	80.7441i	0.117508	+	0.101821i
$794$	−407.303	+	470.052i	−0.512976	+	0.592005i
$795$		0			0
$796$	21.4691	−	9.80459i	0.0269712	−	0.0123173i
$797$	448.066	+	697.204i	0.562190	+	0.874785i	0.999702	−	0.0244278i	$-0.00777638\pi$
$797$	448.066	+	697.204i	0.562190	+	0.874785i	−0.437511	+	0.899213i	$0.644140\pi$
$798$		0			0
$799$	−1181.70	+	169.902i	−1.47897	+	0.212644i
$800$	48.9082	−	107.094i	0.0611352	−	0.133867i
$801$		0			0
$802$	−3.34856	+	5.21046i	−0.00417526	+	0.00649683i
$803$	−581.774	+	504.110i	−0.724501	+	0.627784i
$804$		0			0
$805$	906.476	−	25.6468i	1.12606	−	0.0318594i
$806$	276.205			0.342686
$807$		0			0
$808$	−141.827	−	91.1467i	−0.175529	−	0.112805i
$809$	36.3898	−	253.097i	0.0449813	−	0.312852i	−0.954892	−	0.296952i	$-0.904030\pi$
$809$	36.3898	−	253.097i	0.0449813	−	0.312852i	0.999874	−	0.0158993i	$-0.00506113\pi$
$810$		0			0
$811$	−162.096	−	1127.40i	−0.199872	−	1.39014i	−0.804652	−	0.593747i	$-0.797648\pi$
$811$	−162.096	−	1127.40i	−0.199872	−	1.39014i	0.604780	−	0.796393i	$-0.293261\pi$
$812$	185.147	−	630.554i	0.228014	−	0.776544i
$813$		0			0
$814$	401.929	+	880.102i	0.493771	+	1.08121i
$815$	125.007	+	425.734i	0.153383	+	0.522373i
$816$		0			0
$817$	705.688	−	814.407i	0.863755	−	0.996827i
$818$	162.533	−	47.7240i	0.198696	−	0.0583423i
$819$		0			0
$820$	−62.1229	−	96.6651i	−0.0757596	−	0.117884i
$821$	−4.96255	−	1.45714i	−0.00604452	−	0.00177483i	0.278709	−	0.960376i	$-0.410094\pi$
$821$	−4.96255	−	1.45714i	−0.00604452	−	0.00177483i	−0.284753	+	0.958601i	$0.591912\pi$
$822$		0			0
$823$	246.020	−	538.709i	0.298931	−	0.654567i	−0.699249	−	0.714878i	$-0.746482\pi$
$823$	246.020	−	538.709i	0.298931	−	0.654567i	0.998180	+	0.0603112i	$0.0192093\pi$
$824$	221.885	+	31.9023i	0.269278	+	0.0387163i
$825$		0			0
$826$	−82.0590	+	71.1045i	−0.0993450	+	0.0860829i
$827$			1221.72i			1.47729i	0.674097	+	0.738643i	$0.264533\pi$
$827$			1221.72i			1.47729i	−0.674097	+	0.738643i	$0.735467\pi$
$828$		0			0
$829$	591.345			0.713323			0.356662	−	0.934234i	$-0.383915\pi$
$829$	591.345			0.713323			0.356662	+	0.934234i	$0.383915\pi$
$830$	−216.601	−	249.971i	−0.260965	−	0.301170i
$831$		0			0
$832$	−62.5029	+	434.717i	−0.0751237	+	0.522497i
$833$	−151.475	−	69.1764i	−0.181843	−	0.0830449i
$834$		0			0
$835$	−146.145	+	497.724i	−0.175024	+	0.596076i
$836$	−942.042	+	605.413i	−1.12684	+	0.724179i
$837$		0			0
$838$	−99.5100	−	338.900i	−0.118747	−	0.404415i
$839$	−669.203	−	579.868i	−0.797620	−	0.691141i	0.157449	−	0.987527i	$-0.449673\pi$
$839$	−669.203	−	579.868i	−0.797620	−	0.691141i	−0.955068	+	0.296386i	$0.904219\pi$
$840$		0			0
$841$	−166.938	+	49.0173i	−0.198499	+	0.0582846i
$842$	258.999	−	118.281i	0.307599	−	0.140476i
$843$		0			0
$844$	−985.876	−	289.479i	−1.16810	−	0.342985i
$845$	826.190	−	118.788i	0.977739	−	0.140578i
$846$		0			0
$847$	409.170	+	58.8297i	0.483081	+	0.0694566i
$848$	158.171	−	246.120i	0.186523	−	0.290235i
$849$		0			0
$850$			119.381i			0.140448i
$851$	−1403.70	−	593.661i	−1.64947	−	0.697604i
$852$		0			0
$853$	−748.264	−	863.542i	−0.877214	−	1.01236i	−0.999802	−	0.0199013i	$-0.993665\pi$
$853$	−748.264	−	863.542i	−0.877214	−	1.01236i	0.122588	−	0.992458i	$-0.460881\pi$
$854$	−46.5746	−	29.9317i	−0.0545370	−	0.0350488i
$855$		0			0
$856$	603.768	+	275.732i	0.705336	+	0.322116i
$857$	52.9406	+	368.210i	0.0617744	+	0.429650i	0.997115	+	0.0759024i	$0.0241838\pi$
$857$	52.9406	+	368.210i	0.0617744	+	0.429650i	−0.935341	+	0.353748i	$0.884907\pi$
$858$		0			0
$859$	−748.132	+	480.795i	−0.870933	+	0.559715i	−0.898038	−	0.439918i	$-0.855008\pi$
$859$	−748.132	+	480.795i	−0.870933	+	0.559715i	0.0271047	+	0.999633i	$0.491371\pi$
$860$	−222.142	−	486.423i	−0.258304	−	0.565608i
$861$		0			0
$862$	−92.6274	−	80.2621i	−0.107456	−	0.0931115i
$863$	243.898	−	281.474i	0.282617	−	0.326157i	−0.596637	−	0.802512i	$-0.703497\pi$
$863$	243.898	−	281.474i	0.282617	−	0.326157i	0.879253	+	0.476354i	$0.158042\pi$
$864$		0			0
$865$	337.273	−	154.028i	0.389911	−	0.178067i
$866$	−208.803	−	324.905i	−0.241113	−	0.375178i
$867$		0			0
$868$	284.963	−	40.9716i	0.328299	−	0.0472023i
$869$	−284.565	+	623.111i	−0.327463	+	0.717044i
$870$		0			0
$871$	24.5202	−	38.1542i	0.0281518	−	0.0438051i
$872$	−1002.97	+	869.082i	−1.15020	+	0.996653i
$873$		0			0
$874$	−193.375	+	734.855i	−0.221253	+	0.840795i
$875$	−845.544			−0.966337
$876$		0			0
$877$	250.866	+	161.222i	0.286050	+	0.183833i	0.675795	−	0.737090i	$-0.263800\pi$
$877$	250.866	+	161.222i	0.286050	+	0.183833i	−0.389745	+	0.920923i	$0.627437\pi$
$878$	14.5398	−	101.126i	0.0165601	−	0.115178i
$879$		0			0
$880$	30.3392	+	211.013i	0.0344763	+	0.239788i
$881$	297.482	−	1013.13i	0.337664	−	1.14998i	−0.599293	−	0.800530i	$-0.704551\pi$
$881$	297.482	−	1013.13i	0.337664	−	1.14998i	0.936956	−	0.349447i	$-0.113630\pi$
$882$		0			0
$883$	334.427	+	732.292i	0.378739	+	0.829323i	0.998991	+	0.0449199i	$0.0143033\pi$
$883$	334.427	+	732.292i	0.378739	+	0.829323i	−0.620252	+	0.784403i	$0.712969\pi$
$884$	434.681	+	1480.39i	0.491721	+	1.67465i
$885$		0			0
$886$	−140.306	+	161.922i	−0.158359	+	0.182756i
$887$	−952.295	+	279.619i	−1.07361	+	0.315241i	−0.770321	−	0.637656i	$-0.779904\pi$
$887$	−952.295	+	279.619i	−1.07361	+	0.315241i	−0.303292	+	0.952898i	$0.598086\pi$
$888$		0			0
$889$	−210.144	−	326.991i	−0.236383	−	0.367818i
$890$	−416.140	−	122.190i	−0.467572	−	0.137292i
$891$		0			0
$892$	368.670	−	807.274i	0.413307	−	0.905016i
$893$	−1162.45	−	167.135i	−1.30174	−	0.187161i
$894$		0			0
$895$	−7.72560	+	6.69427i	−0.00863195	+	0.00747963i
$896$			780.334i			0.870908i
$897$		0			0
$898$	−478.553			−0.532909
$899$	−291.180	−	336.039i	−0.323893	−	0.373792i
$900$		0			0
$901$	−424.955	+	2955.63i	−0.471649	+	3.28039i
$902$	−102.158	−	46.6542i	−0.113258	−	0.0517231i
$903$		0			0
$904$	274.584	−	935.146i	0.303743	−	1.03445i
$905$	341.387	−	219.396i	0.377224	−	0.242427i
$906$		0			0
$907$	75.9138	+	258.539i	0.0836977	+	0.285048i	0.990697	−	0.136083i	$-0.0434514\pi$
$907$	75.9138	+	258.539i	0.0836977	+	0.285048i	−0.907000	+	0.421131i	$0.861633\pi$
$908$	486.258	+	421.345i	0.535526	+	0.464036i
$909$		0			0
$910$	−748.674	+	219.831i	−0.822719	+	0.241572i
$911$	−31.8137	+	14.5288i	−0.0349218	+	0.0159482i	−0.432799	−	0.901490i	$-0.642474\pi$
$911$	−31.8137	+	14.5288i	−0.0349218	+	0.0159482i	0.397878	+	0.917439i	$0.369747\pi$
$912$		0			0
$913$	720.045	+	211.424i	0.788659	+	0.231571i
$914$	−127.199	+	18.2884i	−0.139167	+	0.0200092i
$915$		0			0
$916$	−623.031	−	89.5784i	−0.680165	−	0.0977930i
$917$	49.3811	−	76.8384i	0.0538507	−	0.0837933i
$918$		0			0
$919$		−	431.665i		−	0.469712i	−0.972030	−	0.234856i	$-0.924538\pi$
$919$		−	431.665i		−	0.469712i	0.972030	−	0.234856i	$-0.0754619\pi$
$920$	709.404	+	580.402i	0.771091	+	0.630872i
$921$		0			0
$922$	−323.297	−	373.104i	−0.350647	−	0.404668i
$923$	−1509.05	−	969.807i	−1.63494	−	1.05071i
$924$		0			0
$925$	−214.257	−	97.8478i	−0.231629	−	0.105781i
$926$	79.1553	+	550.537i	0.0854809	+	0.594533i
$927$		0			0
$928$	887.698	−	570.489i	0.956571	−	0.614751i
$929$	364.043	+	797.142i	0.391865	+	0.858065i	0.998031	+	0.0627264i	$0.0199795\pi$
$929$	364.043	+	797.142i	0.391865	+	0.858065i	−0.606166	+	0.795338i	$0.707293\pi$
$930$		0			0
$931$	−123.800	−	107.274i	−0.132976	−	0.115224i
$932$	55.5135	−	64.0660i	0.0595639	−	0.0687404i
$933$		0			0
$934$	641.850	−	293.123i	0.687205	−	0.313836i
$935$	−1176.35	−	1830.43i	−1.25813	−	1.95768i
$936$		0			0
$937$	802.462	−	115.377i	0.856416	−	0.123134i	0.299900	−	0.953971i	$-0.403047\pi$
$937$	802.462	−	115.377i	0.856416	−	0.123134i	0.556516	+	0.830837i	$0.312138\pi$
$938$	−8.45977	+	18.5243i	−0.00901895	+	0.0197487i
$939$		0			0
$940$	−315.072	+	490.262i	−0.335183	+	0.521556i
$941$	355.128	−	307.721i	0.377395	−	0.327014i	−0.445422	−	0.895321i	$-0.646947\pi$
$941$	355.128	−	307.721i	0.377395	−	0.327014i	0.822817	+	0.568306i	$0.192401\pi$
$942$		0			0
$943$	168.264	−	54.6213i	0.178435	−	0.0579229i
$944$	40.2077			0.0425929
$945$		0			0
$946$	−439.684	−	282.568i	−0.464782	−	0.298697i
$947$	−51.4354	+	357.741i	−0.0543141	+	0.377763i	0.944476	+	0.328581i	$0.106570\pi$
$947$	−51.4354	+	357.741i	−0.0543141	+	0.377763i	−0.998790	+	0.0491815i	$0.984339\pi$
$948$		0			0
$949$	148.486	+	1032.74i	0.156466	+	1.08824i
$950$	−33.0857	+	112.680i	−0.0348271	+	0.118610i
$951$		0			0
$952$	−699.557	−	1531.82i	−0.734829	−	1.60905i
$953$	−72.1360	−	245.673i	−0.0756936	−	0.257789i	0.912949	−	0.408073i	$-0.133799\pi$
$953$	−72.1360	−	245.673i	−0.0756936	−	0.257789i	−0.988643	+	0.150285i	$0.951981\pi$
$954$		0			0
$955$	832.209	−	960.421i	0.871423	−	1.00568i
$956$	−921.690	+	270.633i	−0.964111	+	0.283088i
$957$		0			0
$958$	−262.071	−	407.791i	−0.273561	−	0.425669i
$959$	−75.5512	−	22.1838i	−0.0787813	−	0.0231323i
$960$		0			0
$961$	−318.296	+	696.970i	−0.331213	+	0.725255i
$962$	1298.03	+	186.628i	1.34930	+	0.194000i
$963$		0			0
$964$	112.220	−	97.2395i	0.116411	−	0.100871i
$965$			1102.41i			1.14240i
$966$		0			0
$967$	65.2549			0.0674818			0.0337409	−	0.999431i	$-0.489258\pi$
$967$	65.2549			0.0674818			0.0337409	+	0.999431i	$0.489258\pi$
$968$	273.613	+	315.766i	0.282658	+	0.326204i
$969$		0			0
$970$	−1.57777	+	10.9736i	−0.00162657	+	0.0113130i
$971$	−144.193	−	65.8508i	−0.148500	−	0.0678175i	0.339779	−	0.940505i	$-0.389648\pi$
$971$	−144.193	−	65.8508i	−0.148500	−	0.0678175i	−0.488279	+	0.872688i	$0.662375\pi$
$972$		0			0
$973$	218.235	−	743.240i	0.224291	−	0.763864i
$974$	583.370	−	374.909i	0.598942	−	0.384917i
$975$		0			0
$976$	5.77591	+	19.6710i	0.00591794	+	0.0201547i
$977$	−623.117	−	539.934i	−0.637787	−	0.552645i	0.274814	−	0.961497i	$-0.411384\pi$
$977$	−623.117	−	539.934i	−0.637787	−	0.552645i	−0.912601	+	0.408852i	$0.865929\pi$
$978$		0			0
$979$	944.160	−	277.230i	0.964413	−	0.283177i
$980$	−73.9425	+	33.7684i	−0.0754515	+	0.0344575i
$981$		0			0
$982$	−144.817	−	42.5220i	−0.147471	−	0.0433015i
$983$	−1754.69	+	252.287i	−1.78504	+	0.256650i	−0.954052	−	0.299642i	$-0.903133\pi$
$983$	−1754.69	+	252.287i	−1.78504	+	0.256650i	−0.830987	+	0.556292i	$0.812224\pi$
$984$		0			0
$985$	−738.564	−	106.189i	−0.749811	−	0.107807i
$986$	−578.473	+	900.121i	−0.586687	+	0.912902i
$987$		0			0
$988$			1517.76i			1.53619i
$989$	811.268	−	140.166i	0.820292	−	0.141725i
$990$		0			0
$991$	76.8760	+	88.7197i	0.0775742	+	0.0895254i	0.793210	−	0.608948i	$-0.208408\pi$
$991$	76.8760	+	88.7197i	0.0775742	+	0.0895254i	−0.715636	+	0.698474i	$0.753863\pi$
$992$	388.881	+	249.919i	0.392018	+	0.251934i
$993$		0			0
$994$	732.660	+	334.595i	0.737083	+	0.336615i
$995$	6.42021	+	44.6536i	0.00645248	+	0.0448780i
$996$		0			0
$997$	−759.734	+	488.252i	−0.762020	+	0.489721i	−0.863023	−	0.505165i	$-0.831431\pi$
$997$	−759.734	+	488.252i	−0.762020	+	0.489721i	0.101002	+	0.994886i	$0.467795\pi$
$998$	18.1467	+	39.7356i	0.0181830	+	0.0398153i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.3.j.c.10.6	yes	80
3.2	odd	2	inner	207.3.j.c.10.3	✓	80
23.7	odd	22	inner	207.3.j.c.145.6	yes	80
69.53	even	22	inner	207.3.j.c.145.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.3.j.c.10.3	✓	80	3.2	odd	2	inner
207.3.j.c.10.6	yes	80	1.1	even	1	trivial
207.3.j.c.145.3	yes	80	69.53	even	22	inner
207.3.j.c.145.6	yes	80	23.7	odd	22	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	207.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.718657 + 0.829374i) q^{2} +(0.397865 - 2.76721i) q^{4} +(4.86076 + 2.21983i) q^{5} +(2.07875 - 7.07956i) q^{7} +(6.27382 - 4.03194i) q^{8} +O(q^{10})\)	\(q+(0.718657 + 0.829374i) q^{2} +(0.397865 - 2.76721i) q^{4} +(4.86076 + 2.21983i) q^{5} +(2.07875 - 7.07956i) q^{7} +(6.27382 - 4.03194i) q^{8} +(1.65214 + 5.62668i) q^{10} +(-10.0553 - 8.71297i) q^{11} +(-17.3029 + 5.08058i) q^{13} +(7.36551 - 3.36371i) q^{14} +(-2.87700 - 0.844763i) q^{16} +(30.2920 - 4.35534i) q^{17} +(29.7987 + 4.28440i) q^{19} +(8.07668 - 12.5676i) q^{20} -14.6012i q^{22} +(15.5474 + 16.9493i) q^{23} +(2.32777 + 2.68639i) q^{25} +(-16.6485 - 10.6994i) q^{26} +(-18.7636 - 8.56905i) q^{28} +(4.53399 + 31.5346i) q^{29} +(-11.7411 + 7.54555i) q^{31} +(-13.7591 - 30.1283i) q^{32} +(25.3818 + 21.9934i) q^{34} +(25.8197 - 29.7975i) q^{35} +(-60.2758 + 27.5271i) q^{37} +(17.8616 + 27.7933i) q^{38} +(39.4457 - 5.67144i) q^{40} +(3.19522 - 6.99656i) q^{41} +(19.3523 - 30.1128i) q^{43} +(-28.1113 + 24.3586i) q^{44} +(-2.88410 + 25.0753i) q^{46} -39.0101 q^{47} +(-4.57753 - 2.94180i) q^{49} +(-0.555155 + 3.86118i) q^{50} +(7.17484 + 49.9021i) q^{52} +(-27.4890 + 93.6188i) q^{53} +(-29.5350 - 64.6727i) q^{55} +(-15.5027 - 52.7972i) q^{56} +(-22.8956 + 26.4229i) q^{58} +(-12.8663 + 3.77788i) q^{59} +(-3.69653 - 5.75192i) q^{61} +(-14.6959 - 4.31511i) q^{62} +(10.1171 - 22.1534i) q^{64} +(-95.3830 - 13.7140i) q^{65} +(-1.90072 + 1.64698i) q^{67} -85.5574i q^{68} +43.2688 q^{70} +(65.1402 + 75.1758i) q^{71} +(8.23397 - 57.2685i) q^{73} +(-66.1479 - 30.2087i) q^{74} +(23.7117 - 80.7547i) q^{76} +(-82.5864 + 53.0751i) q^{77} +(-14.5051 - 49.3997i) q^{79} +(-12.1092 - 10.4926i) q^{80} +(8.09903 - 2.37809i) q^{82} +(-51.3058 + 23.4306i) q^{83} +(156.910 + 46.0730i) q^{85} +(38.8824 - 5.59045i) q^{86} +(-98.2153 - 14.1212i) q^{88} +(-39.9848 + 62.2176i) q^{89} +133.058i q^{91} +(53.0882 - 36.2794i) q^{92} +(-28.0349 - 32.3540i) q^{94} +(135.333 + 86.9735i) q^{95} +(1.71968 + 0.785353i) q^{97} +(-0.849820 - 5.91063i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 24 q^{4}+O(q^{10}) \) 80 * q - 24 * q^4	\( 80 q - 24 q^{4} - 16 q^{13} + 224 q^{16} + 66 q^{19} - 44 q^{25} - 528 q^{28} - 22 q^{31} - 242 q^{34} - 352 q^{37} - 110 q^{40} - 88 q^{43} + 336 q^{46} + 40 q^{49} + 530 q^{52} + 442 q^{55} - 618 q^{58} - 308 q^{61} - 312 q^{64} - 22 q^{67} - 400 q^{70} + 46 q^{73} + 2354 q^{76} + 1540 q^{79} + 1676 q^{82} + 1118 q^{85} + 528 q^{88} - 674 q^{94} - 792 q^{97}+O(q^{100}) \) 80 * q - 24 * q^4 - 16 * q^13 + 224 * q^16 + 66 * q^19 - 44 * q^25 - 528 * q^28 - 22 * q^31 - 242 * q^34 - 352 * q^37 - 110 * q^40 - 88 * q^43 + 336 * q^46 + 40 * q^49 + 530 * q^52 + 442 * q^55 - 618 * q^58 - 308 * q^61 - 312 * q^64 - 22 * q^67 - 400 * q^70 + 46 * q^73 + 2354 * q^76 + 1540 * q^79 + 1676 * q^82 + 1118 * q^85 + 528 * q^88 - 674 * q^94 - 792 * q^97

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