LMFDB - Embedded newform 525.2.z.a.64.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(64,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("525.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.z (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.7
Character	$\chi$	$=$	525.64
Dual form			525.2.z.a.484.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.158974 + 0.218810i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.595429 - 1.83254i) q^{4} +(-0.756459 - 2.10423i) q^{5} +(-0.0835778 - 0.257226i) q^{6} -1.00000i q^{7} +(1.01009 - 0.328197i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.158974 + 0.218810i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.595429 - 1.83254i) q^{4} +(-0.756459 - 2.10423i) q^{5} +(-0.0835778 - 0.257226i) q^{6} -1.00000i q^{7} +(1.01009 - 0.328197i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.340167 - 0.500039i) q^{10} +(2.65577 - 1.92953i) q^{11} +(-1.13257 + 1.55885i) q^{12} +(-2.38467 + 3.28222i) q^{13} +(0.218810 - 0.158974i) q^{14} +(0.0691931 + 2.23500i) q^{15} +(-2.88532 - 2.09631i) q^{16} +(-2.37847 + 0.772812i) q^{17} +0.270463i q^{18} +(0.114574 + 0.352624i) q^{19} +(-4.30650 + 0.133325i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(0.844398 + 0.274362i) q^{22} +(-5.04249 - 6.94039i) q^{23} -1.06207 q^{24} +(-3.85554 + 3.18352i) q^{25} -1.09728 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-1.83254 - 0.595429i) q^{28} +(1.45653 - 4.48273i) q^{29} +(-0.478039 + 0.370448i) q^{30} +(1.10051 + 3.38703i) q^{31} -3.08873i q^{32} +(-3.12204 + 1.01441i) q^{33} +(-0.547215 - 0.397575i) q^{34} +(-2.10423 + 0.756459i) q^{35} +(1.55885 - 1.13257i) q^{36} +(3.35068 - 4.61181i) q^{37} +(-0.0589430 + 0.0811281i) q^{38} +(3.28222 - 2.38467i) q^{39} +(-1.45469 - 1.87719i) q^{40} +(-2.67111 - 1.94067i) q^{41} +(-0.257226 + 0.0835778i) q^{42} +9.75390i q^{43} +(-1.95462 - 6.01571i) q^{44} +(0.624846 - 2.14699i) q^{45} +(0.716997 - 2.20669i) q^{46} +(8.45686 + 2.74780i) q^{47} +(2.09631 + 2.88532i) q^{48} -1.00000 q^{49} +(-1.30952 - 0.337531i) q^{50} +2.50087 q^{51} +(4.59490 + 6.32434i) q^{52} +(-4.07394 - 1.32370i) q^{53} +(0.0835778 - 0.257226i) q^{54} +(-6.06914 - 4.12873i) q^{55} +(-0.328197 - 1.01009i) q^{56} -0.370771i q^{57} +(1.21242 - 0.393938i) q^{58} +(0.774946 + 0.563031i) q^{59} +(4.13693 + 1.20398i) q^{60} +(5.00813 - 3.63862i) q^{61} +(-0.566161 + 0.779254i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-5.09479 + 3.70158i) q^{64} +(8.71044 + 2.53503i) q^{65} +(-0.718288 - 0.521867i) q^{66} +(6.87203 - 2.23286i) q^{67} +4.81880i q^{68} +(2.65099 + 8.15892i) q^{69} +(-0.500039 - 0.340167i) q^{70} +(2.77937 - 8.55403i) q^{71} +(1.01009 + 0.328197i) q^{72} +(-6.50548 - 8.95402i) q^{73} +1.54178 q^{74} +(4.65060 - 1.83628i) q^{75} +0.714419 q^{76} +(-1.92953 - 2.65577i) q^{77} +(1.04358 + 0.339079i) q^{78} +(0.686427 - 2.11261i) q^{79} +(-2.22848 + 7.65713i) q^{80} +(0.309017 + 0.951057i) q^{81} -0.892982i q^{82} +(-11.1327 + 3.61724i) q^{83} +(1.55885 + 1.13257i) q^{84} +(3.42539 + 4.42024i) q^{85} +(-2.13425 + 1.55062i) q^{86} +(-2.77048 + 3.81324i) q^{87} +(2.04929 - 2.82061i) q^{88} +(12.4881 - 9.07311i) q^{89} +(0.569117 - 0.204594i) q^{90} +(3.28222 + 2.38467i) q^{91} +(-15.7210 + 5.10807i) q^{92} -3.56133i q^{93} +(0.743180 + 2.28727i) q^{94} +(0.655330 - 0.507836i) q^{95} +(-0.954471 + 2.93756i) q^{96} +(11.3135 + 3.67597i) q^{97} +(-0.158974 - 0.218810i) q^{98} +3.28271 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.158974	+	0.218810i	0.112412	+	0.154722i	0.861516	−	0.507731i	$-0.169516\pi$
$2$	0.158974	+	0.218810i	0.112412	+	0.154722i	−0.749104	+	0.662453i	$0.769516\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	0.595429	−	1.83254i	0.297715	−	0.916271i
$5$	−0.756459	−	2.10423i	−0.338299	−	0.941039i
$5$	−0.756459	−	2.10423i	−0.338299	−	0.941039i
$6$	−0.0835778	−	0.257226i	−0.0341205	−	0.105012i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.01009	−	0.328197i	0.357120	−	0.116035i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	0.340167	−	0.500039i	0.107570	−	0.158126i
$11$	2.65577	−	1.92953i	0.800744	−	0.581775i	−0.110388	−	0.993889i	$-0.535209\pi$
$11$	2.65577	−	1.92953i	0.800744	−	0.581775i	0.911132	+	0.412114i	$0.135209\pi$
$12$	−1.13257	+	1.55885i	−0.326946	+	0.450002i
$13$	−2.38467	+	3.28222i	−0.661389	+	0.910324i	−0.999526	−	0.0307729i	$-0.990203\pi$
$13$	−2.38467	+	3.28222i	−0.661389	+	0.910324i	0.338137	+	0.941097i	$0.390203\pi$
$14$	0.218810	−	0.158974i	0.0584793	−	0.0424877i
$15$	0.0691931	+	2.23500i	0.0178656	+	0.577074i
$16$	−2.88532	−	2.09631i	−0.721329	−	0.524076i
$17$	−2.37847	+	0.772812i	−0.576864	+	0.187434i	−0.582895	−	0.812547i	$-0.698080\pi$
$17$	−2.37847	+	0.772812i	−0.576864	+	0.187434i	0.00603136	+	0.999982i	$0.498080\pi$
$18$			0.270463i			0.0637489i
$19$	0.114574	+	0.352624i	0.0262852	+	0.0808974i	0.963339	−	0.268289i	$-0.0864581\pi$
$19$	0.114574	+	0.352624i	0.0262852	+	0.0808974i	−0.937053	+	0.349186i	$0.886458\pi$
$20$	−4.30650	+	0.133325i	−0.962963	+	0.0298123i
$21$	−0.309017	+	0.951057i	−0.0674330	+	0.207538i
$22$	0.844398	+	0.274362i	0.180026	+	0.0584941i
$23$	−5.04249	−	6.94039i	−1.05143	−	1.44717i	−0.887561	−	0.460690i	$-0.847602\pi$
$23$	−5.04249	−	6.94039i	−1.05143	−	1.44717i	−0.163871	−	0.986482i	$-0.552398\pi$
$24$	−1.06207			−0.216794
$25$	−3.85554	+	3.18352i	−0.771108	+	0.636704i
$26$	−1.09728			−0.215195
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	−1.83254	−	0.595429i	−0.346318	−	0.112526i
$29$	1.45653	−	4.48273i	0.270470	−	0.832422i	−0.719912	−	0.694065i	$-0.755818\pi$
$29$	1.45653	−	4.48273i	0.270470	−	0.832422i	0.990382	−	0.138357i	$-0.0441821\pi$
$30$	−0.478039	+	0.370448i	−0.0872775	+	0.0676342i
$31$	1.10051	+	3.38703i	0.197658	+	0.608328i	0.999935	+	0.0113770i	$0.00362150\pi$
$31$	1.10051	+	3.38703i	0.197658	+	0.608328i	−0.802277	+	0.596951i	$0.796378\pi$
$32$		−	3.08873i		−	0.546016i
$33$	−3.12204	+	1.01441i	−0.543478	+	0.176587i
$34$	−0.547215	−	0.397575i	−0.0938465	−	0.0681835i
$35$	−2.10423	+	0.756459i	−0.355679	+	0.127865i
$36$	1.55885	−	1.13257i	0.259809	−	0.188762i
$37$	3.35068	−	4.61181i	0.550848	−	0.758177i	−0.439279	−	0.898351i	$-0.644766\pi$
$37$	3.35068	−	4.61181i	0.550848	−	0.758177i	0.990127	+	0.140174i	$0.0447661\pi$
$38$	−0.0589430	+	0.0811281i	−0.00956183	+	0.0131607i
$39$	3.28222	−	2.38467i	0.525576	−	0.381853i
$40$	−1.45469	−	1.87719i	−0.230007	−	0.296809i
$41$	−2.67111	−	1.94067i	−0.417157	−	0.303082i	0.359336	−	0.933208i	$-0.383003\pi$
$41$	−2.67111	−	1.94067i	−0.417157	−	0.303082i	−0.776493	+	0.630126i	$0.783003\pi$
$42$	−0.257226	+	0.0835778i	−0.0396908	+	0.0128963i
$43$			9.75390i			1.48746i	0.668483	+	0.743728i	$0.266944\pi$
$43$			9.75390i			1.48746i	−0.668483	+	0.743728i	$0.733056\pi$
$44$	−1.95462	−	6.01571i	−0.294670	−	0.906902i
$45$	0.624846	−	2.14699i	0.0931465	−	0.320054i
$46$	0.716997	−	2.20669i	0.105715	−	0.325359i
$47$	8.45686	+	2.74780i	1.23356	+	0.400808i	0.852003	−	0.523537i	$-0.175388\pi$
$47$	8.45686	+	2.74780i	1.23356	+	0.400808i	0.381558	+	0.924345i	$0.375388\pi$
$48$	2.09631	+	2.88532i	0.302576	+	0.416460i
$49$	−1.00000			−0.142857
$50$	−1.30952	−	0.337531i	−0.185194	−	0.0477340i
$51$	2.50087			0.350192
$52$	4.59490	+	6.32434i	0.637199	+	0.877029i
$53$	−4.07394	−	1.32370i	−0.559599	−	0.181825i	0.0155419	−	0.999879i	$-0.495053\pi$
$53$	−4.07394	−	1.32370i	−0.559599	−	0.181825i	−0.575141	+	0.818055i	$0.695053\pi$
$54$	0.0835778	−	0.257226i	0.0113735	−	0.0350040i
$55$	−6.06914	−	4.12873i	−0.818363	−	0.556718i
$56$	−0.328197	−	1.01009i	−0.0438572	−	0.134979i
$57$		−	0.370771i		−	0.0491098i
$58$	1.21242	−	0.393938i	0.159198	−	0.0517265i
$59$	0.774946	+	0.563031i	0.100889	+	0.0733004i	0.637086	−	0.770793i	$-0.280140\pi$
$59$	0.774946	+	0.563031i	0.100889	+	0.0733004i	−0.536197	+	0.844093i	$0.680140\pi$
$60$	4.13693	+	1.20398i	0.534075	+	0.155434i
$61$	5.00813	−	3.63862i	0.641225	−	0.465877i	−0.219046	−	0.975715i	$-0.570294\pi$
$61$	5.00813	−	3.63862i	0.641225	−	0.465877i	0.860271	+	0.509837i	$0.170294\pi$
$62$	−0.566161	+	0.779254i	−0.0719025	+	0.0989653i
$63$	0.587785	−	0.809017i	0.0740540	−	0.101927i
$64$	−5.09479	+	3.70158i	−0.636849	+	0.462698i
$65$	8.71044	+	2.53503i	1.08040	+	0.314431i
$66$	−0.718288	−	0.521867i	−0.0884152	−	0.0642374i
$67$	6.87203	−	2.23286i	0.839552	−	0.272787i	0.142489	−	0.989796i	$-0.454490\pi$
$67$	6.87203	−	2.23286i	0.839552	−	0.272787i	0.697063	+	0.717009i	$0.254490\pi$
$68$			4.81880i			0.584366i
$69$	2.65099	+	8.15892i	0.319142	+	0.982219i
$70$	−0.500039	−	0.340167i	−0.0597661	−	0.0406578i
$71$	2.77937	−	8.55403i	0.329851	−	1.01518i	−0.639352	−	0.768914i	$-0.720797\pi$
$71$	2.77937	−	8.55403i	0.329851	−	1.01518i	0.969203	−	0.246263i	$-0.0792027\pi$
$72$	1.01009	+	0.328197i	0.119040	+	0.0386784i
$73$	−6.50548	−	8.95402i	−0.761409	−	1.04799i	−0.997096	−	0.0761601i	$-0.975734\pi$
$73$	−6.50548	−	8.95402i	−0.761409	−	1.04799i	0.235687	−	0.971829i	$-0.424266\pi$
$74$	1.54178			0.179228
$75$	4.65060	−	1.83628i	0.537005	−	0.212035i
$76$	0.714419			0.0819495
$77$	−1.92953	−	2.65577i	−0.219890	−	0.302653i
$78$	1.04358	+	0.339079i	0.118162	+	0.0383931i
$79$	0.686427	−	2.11261i	0.0772291	−	0.237687i	−0.904987	−	0.425438i	$-0.860120\pi$
$79$	0.686427	−	2.11261i	0.0772291	−	0.237687i	0.982217	+	0.187752i	$0.0601200\pi$
$80$	−2.22848	+	7.65713i	−0.249152	+	0.856093i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	0.892982i		−	0.0986133i
$83$	−11.1327	+	3.61724i	−1.22198	+	0.397044i	−0.847801	−	0.530314i	$-0.822074\pi$
$83$	−11.1327	+	3.61724i	−1.22198	+	0.397044i	−0.374175	+	0.927358i	$0.622074\pi$
$84$	1.55885	+	1.13257i	0.170085	+	0.123574i
$85$	3.42539	+	4.42024i	0.371535	+	0.479442i
$86$	−2.13425	+	1.55062i	−0.230142	+	0.167208i
$87$	−2.77048	+	3.81324i	−0.297027	+	0.408822i
$88$	2.04929	−	2.82061i	0.218455	−	0.300678i
$89$	12.4881	−	9.07311i	1.32373	−	0.961748i	0.323855	−	0.946107i	$-0.395021\pi$
$89$	12.4881	−	9.07311i	1.32373	−	0.961748i	0.999878	−	0.0156410i	$-0.00497888\pi$
$90$	0.569117	−	0.204594i	0.0599901	−	0.0215661i
$91$	3.28222	+	2.38467i	0.344070	+	0.249982i
$92$	−15.7210	+	5.10807i	−1.63903	+	0.532553i
$93$		−	3.56133i		−	0.369293i
$94$	0.743180	+	2.28727i	0.0766532	+	0.235914i
$95$	0.655330	−	0.507836i	0.0672354	−	0.0521029i
$96$	−0.954471	+	2.93756i	−0.0974153	+	0.299813i
$97$	11.3135	+	3.67597i	1.14871	+	0.373238i	0.820657	−	0.571421i	$-0.193608\pi$
$97$	11.3135	+	3.67597i	1.14871	+	0.373238i	0.328052	+	0.944660i	$0.393608\pi$
$98$	−0.158974	−	0.218810i	−0.0160588	−	0.0221031i
$99$	3.28271			0.329925
$100$	3.53824	+	8.96100i	0.353824	+	0.896100i
$101$	6.41165			0.637983			0.318992	−	0.947758i	$-0.396656\pi$
$101$	6.41165			0.637983			0.318992	+	0.947758i	$0.396656\pi$
$102$	0.397575	+	0.547215i	0.0393658	+	0.0541823i
$103$	−3.53975	−	1.15013i	−0.348782	−	0.113326i	0.129387	−	0.991594i	$-0.458699\pi$
$103$	−3.53975	−	1.15013i	−0.348782	−	0.113326i	−0.478168	+	0.878268i	$0.658699\pi$
$104$	−1.33151	+	4.09797i	−0.130566	+	0.401839i
$105$	2.23500	−	0.0691931i	0.218113	−	0.00675255i
$106$	−0.358013	−	1.10185i	−0.0347733	−	0.107021i
$107$			13.8366i			1.33763i	0.743428	+	0.668816i	$0.233199\pi$
$107$			13.8366i			1.33763i	−0.743428	+	0.668816i	$0.766801\pi$
$108$	−1.83254	+	0.595429i	−0.176337	+	0.0572952i
$109$	3.55407	+	2.58218i	0.340418	+	0.247328i	0.744838	−	0.667245i	$-0.232527\pi$
$109$	3.55407	+	2.58218i	0.340418	+	0.247328i	−0.404420	+	0.914573i	$0.632527\pi$
$110$	−0.0614333	−	1.98435i	−0.00585743	−	0.189200i
$111$	−4.61181	+	3.35068i	−0.437734	+	0.318032i
$112$	−2.09631	+	2.88532i	−0.198082	+	0.272637i
$113$	4.88256	−	6.72026i	0.459312	−	0.632189i	−0.515054	−	0.857158i	$-0.672228\pi$
$113$	4.88256	−	6.72026i	0.459312	−	0.632189i	0.974366	+	0.224969i	$0.0722280\pi$
$114$	0.0811281	−	0.0589430i	0.00759835	−	0.00552052i
$115$	−10.7897	+	15.8607i	−1.00615	+	1.47901i
$116$	−7.34754	−	5.33830i	−0.682202	−	0.495649i
$117$	−3.85848	+	1.25370i	−0.356717	+	0.115904i
$118$			0.259073i			0.0238496i
$119$	0.772812	+	2.37847i	0.0708435	+	0.218034i
$120$	0.803412	+	2.23483i	0.0733411	+	0.204012i
$121$	−0.0691632	+	0.212862i	−0.00628756	+	0.0193511i
$122$	1.59233	+	0.517379i	0.144163	+	0.0468413i
$123$	1.94067	+	2.67111i	0.174985	+	0.240846i
$124$	6.86215			0.616240
$125$	9.61541	+	5.70473i	0.860028	+	0.510247i
$126$	0.270463			0.0240948
$127$	12.8146	+	17.6378i	1.13711	+	1.56510i	0.773797	+	0.633434i	$0.218355\pi$
$127$	12.8146	+	17.6378i	1.13711	+	1.56510i	0.363315	+	0.931666i	$0.381645\pi$
$128$	−7.49500	−	2.43527i	−0.662471	−	0.215250i
$129$	3.01412	−	9.27651i	0.265378	−	0.816751i
$130$	0.830049	+	2.30893i	0.0728001	+	0.202507i
$131$	−5.77774	−	17.7820i	−0.504803	−	1.55362i	−0.801101	−	0.598529i	$-0.795752\pi$
$131$	−5.77774	−	17.7820i	−0.504803	−	1.55362i	0.296298	−	0.955095i	$-0.404248\pi$
$132$			6.32529i			0.550546i
$133$	0.352624	−	0.114574i	0.0305764	−	0.00993486i
$134$	1.58105	+	1.14870i	0.136582	+	0.0992324i
$135$	−1.25772	+	1.84882i	−0.108247	+	0.159121i
$136$	−2.14883	+	1.56122i	−0.184261	+	0.133873i
$137$	7.17956	−	9.88182i	0.613392	−	0.844261i	−0.383460	−	0.923558i	$-0.625267\pi$
$137$	7.17956	−	9.88182i	0.613392	−	0.844261i	0.996851	+	0.0792967i	$0.0252674\pi$
$138$	−1.36381	+	1.87712i	−0.116095	+	0.159791i
$139$	−9.31402	+	6.76703i	−0.790005	+	0.573972i	−0.907965	−	0.419046i	$-0.862365\pi$
$139$	−9.31402	+	6.76703i	−0.790005	+	0.573972i	0.117960	+	0.993018i	$0.462365\pi$
$140$	0.133325	+	4.30650i	0.0112680	+	0.363966i
$141$	−7.19384	−	5.22663i	−0.605830	−	0.440162i
$142$	2.31355	−	0.751719i	0.194149	−	0.0630829i
$143$			13.3181i			1.11372i
$144$	−1.10209	−	3.39189i	−0.0918411	−	0.282658i
$145$	−10.5345	+	0.326136i	−0.874842	+	0.0270841i
$146$	0.925021	−	2.84692i	0.0765553	−	0.235613i
$147$	0.951057	+	0.309017i	0.0784418	+	0.0254873i
$148$	−6.45625	−	8.88627i	−0.530701	−	0.730447i
$149$	10.3502			0.847919			0.423959	−	0.905681i	$-0.360640\pi$
$149$	10.3502			0.847919			0.423959	+	0.905681i	$0.360640\pi$
$150$	1.14112	+	0.725674i	0.0931722	+	0.0592510i
$151$	20.3689			1.65759			0.828797	−	0.559549i	$-0.189026\pi$
$151$	20.3689			1.65759			0.828797	+	0.559549i	$0.189026\pi$
$152$	0.231460	+	0.318578i	0.0187739	+	0.0258401i
$153$	−2.37847	−	0.772812i	−0.192288	−	0.0624781i
$154$	0.274362	−	0.844398i	0.0221087	−	0.0680436i
$155$	6.29459	−	4.87788i	0.505593	−	0.391800i
$156$	−2.41568	−	7.43471i	−0.193410	−	0.595253i
$157$		−	12.2181i		−	0.975114i	−0.873091	−	0.487557i	$-0.837888\pi$
$157$		−	12.2181i		−	0.975114i	0.873091	−	0.487557i	$-0.162112\pi$
$158$	0.571383	−	0.185654i	0.0454568	−	0.0147698i
$159$	3.46550	+	2.51783i	0.274832	+	0.199677i
$160$	−6.49939	+	2.33650i	−0.513822	+	0.184716i
$161$	−6.94039	+	5.04249i	−0.546980	+	0.397404i
$162$	−0.158974	+	0.218810i	−0.0124902	+	0.0171913i
$163$	9.95997	−	13.7087i	0.780125	−	1.07375i	−0.215143	−	0.976583i	$-0.569022\pi$
$163$	9.95997	−	13.7087i	0.780125	−	1.07375i	0.995268	−	0.0971679i	$-0.0309784\pi$
$164$	−5.14682	+	3.73939i	−0.401899	+	0.291997i
$165$	4.49625	+	5.80212i	0.350033	+	0.451695i
$166$	−2.56131	−	1.86090i	−0.198796	−	0.144434i
$167$	0.515073	−	0.167357i	0.0398576	−	0.0129505i	−0.289020	−	0.957323i	$-0.593330\pi$
$167$	0.515073	−	0.167357i	0.0398576	−	0.0129505i	0.328878	+	0.944372i	$0.393330\pi$
$168$			1.06207i			0.0819404i
$169$	−1.06908	−	3.29030i	−0.0822371	−	0.253100i
$170$	−0.422642	+	1.45221i	−0.0324152	+	0.111380i
$171$	−0.114574	+	0.352624i	−0.00876172	+	0.0269658i
$172$	17.8744	+	5.80776i	1.36291	+	0.442837i
$173$	4.82507	+	6.64114i	0.366843	+	0.504916i	0.952039	−	0.305975i	$-0.0989825\pi$
$173$	4.82507	+	6.64114i	0.366843	+	0.504916i	−0.585196	+	0.810892i	$0.698982\pi$
$174$	−1.27481			−0.0966430
$175$	3.18352	+	3.85554i	0.240652	+	0.291451i
$176$	−11.7076			−0.882495
$177$	−0.563031	−	0.774946i	−0.0423200	−	0.0582485i
$178$	3.97057	+	1.29012i	0.297607	+	0.0966982i
$179$	−1.14772	+	3.53231i	−0.0857843	+	0.264017i	−0.984743	−	0.174017i	$-0.944325\pi$
$179$	−1.14772	+	3.53231i	−0.0857843	+	0.264017i	0.898958	+	0.438034i	$0.144325\pi$
$180$	−3.56240	−	2.42344i	−0.265526	−	0.180632i
$181$	−5.97207	−	18.3802i	−0.443901	−	1.36619i	−0.883685	−	0.468083i	$-0.844945\pi$
$181$	−5.97207	−	18.3802i	−0.443901	−	1.36619i	0.439784	−	0.898104i	$-0.355055\pi$
$182$			1.09728i			0.0813360i
$183$	−5.88741	+	1.91293i	−0.435210	+	0.141408i
$184$	−7.37118	−	5.35548i	−0.543411	−	0.394811i
$185$	−12.2389	−	3.56194i	−0.899825	−	0.261879i
$186$	0.779254	−	0.566161i	0.0571377	−	0.0415129i
$187$	−4.82550	+	6.64173i	−0.352876	+	0.485692i
$188$	10.0709	−	13.8614i	0.734498	−	1.01095i
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	0.215300	+	0.0626595i	0.0156195	+	0.00454579i
$191$	4.33368	+	3.14860i	0.313574	+	0.227825i	0.733428	−	0.679767i	$-0.237919\pi$
$191$	4.33368	+	3.14860i	0.313574	+	0.227825i	−0.419855	+	0.907591i	$0.637919\pi$
$192$	5.98928	−	1.94604i	0.432239	−	0.140443i
$193$		−	15.9559i		−	1.14853i	−0.818670	−	0.574264i	$-0.805288\pi$
$193$		−	15.9559i		−	1.14853i	0.818670	−	0.574264i	$-0.194712\pi$
$194$	0.994216	+	3.05988i	0.0713805	+	0.219687i
$195$	−7.50075	−	5.10263i	−0.537140	−	0.365407i
$196$	−0.595429	+	1.83254i	−0.0425307	+	0.130896i
$197$	−12.0932	−	3.92933i	−0.861607	−	0.279953i	−0.155307	−	0.987866i	$-0.549637\pi$
$197$	−12.0932	−	3.92933i	−0.861607	−	0.279953i	−0.706300	+	0.707913i	$0.749637\pi$
$198$	0.521867	+	0.718288i	0.0370875	+	0.0510465i
$199$	4.83717			0.342898			0.171449	−	0.985193i	$-0.445155\pi$
$199$	4.83717			0.342898			0.171449	+	0.985193i	$0.445155\pi$
$200$	−2.84961	+	4.48102i	−0.201498	+	0.316856i
$201$	−7.22568			−0.509660
$202$	1.01929	+	1.40293i	0.0717169	+	0.0987098i
$203$	−4.48273	−	1.45653i	−0.314626	−	0.102228i
$204$	1.48909	−	4.58295i	0.104257	−	0.320871i
$205$	−2.06304	+	7.08866i	−0.144089	+	0.495093i
$206$	−0.311069	−	0.957373i	−0.0216732	−	0.0667033i
$207$		−	8.57880i		−	0.596268i
$208$	13.7611	−	4.47124i	0.954158	−	0.310025i
$209$	0.984681	+	0.715412i	0.0681118	+	0.0494861i
$210$	0.370448	+	0.478039i	0.0255633	+	0.0329878i
$211$	−19.9615	+	14.5029i	−1.37421	+	0.998418i	−0.376810	+	0.926291i	$0.622979\pi$
$211$	−19.9615	+	14.5029i	−1.37421	+	0.998418i	−0.997395	+	0.0721278i	$0.977021\pi$
$212$	−4.85149	+	6.67750i	−0.333201	+	0.458612i
$213$	−5.28668	+	7.27650i	−0.362238	+	0.498577i
$214$	−3.02757	+	2.19966i	−0.206961	+	0.150366i
$215$	20.5244	−	7.37842i	1.39975	−	0.503204i
$216$	−0.859232	−	0.624269i	−0.0584633	−	0.0424761i
$217$	3.38703	−	1.10051i	0.229927	−	0.0747077i
$218$			1.18817i			0.0804727i
$219$	3.42013	+	10.5261i	0.231111	+	0.711287i
$220$	−11.1798	+	8.66360i	−0.753743	+	0.584100i
$221$	3.13533	−	9.64956i	0.210905	−	0.649100i
$222$	−1.46632	−	0.476436i	−0.0984130	−	0.0319763i
$223$	13.7528	+	18.9291i	0.920957	+	1.26759i	0.963284	+	0.268485i	$0.0865231\pi$
$223$	13.7528	+	18.9291i	0.920957	+	1.26759i	−0.0423264	+	0.999104i	$0.513477\pi$
$224$	−3.08873			−0.206375
$225$	−4.99042	+	0.309293i	−0.332695	+	0.0206195i
$226$	2.24666			0.149446
$227$	−5.95960	−	8.20268i	−0.395552	−	0.544431i	0.564068	−	0.825728i	$-0.309235\pi$
$227$	−5.95960	−	8.20268i	−0.395552	−	0.544431i	−0.959621	+	0.281297i	$0.909235\pi$
$228$	−0.679453	−	0.220768i	−0.0449979	−	0.0146207i
$229$	6.64218	−	20.4425i	0.438928	−	1.35088i	−0.450080	−	0.892988i	$-0.648605\pi$
$229$	6.64218	−	20.4425i	0.438928	−	1.35088i	0.889008	−	0.457892i	$-0.151395\pi$
$230$	−5.18576	+	0.160545i	−0.341939	+	0.0105860i
$231$	1.01441	+	3.12204i	0.0667435	+	0.205415i
$232$		−	5.00598i		−	0.328659i
$233$	5.95132	−	1.93370i	0.389884	−	0.126681i	−0.107514	−	0.994204i	$-0.534289\pi$
$233$	5.95132	−	1.93370i	0.389884	−	0.126681i	0.497398	+	0.867523i	$0.334289\pi$
$234$	−0.887720	−	0.644967i	−0.0580321	−	0.0421628i
$235$	−0.615270	−	19.8738i	−0.0401358	−	1.29642i
$236$	1.49320	−	1.08488i	0.0971993	−	0.0706194i
$237$	−1.30566	+	1.79709i	−0.0848119	+	0.116734i
$238$	−0.397575	+	0.547215i	−0.0257709	+	0.0354707i
$239$	6.09078	−	4.42521i	0.393980	−	0.286243i	−0.373105	−	0.927789i	$-0.621707\pi$
$239$	6.09078	−	4.42521i	0.393980	−	0.286243i	0.767084	+	0.641546i	$0.221707\pi$
$240$	4.48559	−	6.59373i	0.289544	−	0.425623i
$241$	−8.99544	−	6.53557i	−0.579447	−	0.420993i	0.259078	−	0.965856i	$-0.416581\pi$
$241$	−8.99544	−	6.53557i	−0.579447	−	0.420993i	−0.838525	+	0.544864i	$0.816581\pi$
$242$	−0.0575715	+	0.0187061i	−0.00370084	+	0.00120247i
$243$		−	1.00000i		−	0.0641500i
$244$	−3.68594	−	11.3441i	−0.235968	−	0.726235i
$245$	0.756459	+	2.10423i	0.0483284	+	0.134434i
$246$	−0.275947	+	0.849276i	−0.0175937	+	0.0541479i
$247$	−1.43061	−	0.464834i	−0.0910276	−	0.0295767i
$248$	2.22323	+	3.06001i	0.141175	+	0.194311i
$249$	11.7056			0.741815
$250$	0.280355	+	3.01085i	0.0177312	+	0.190423i
$251$	−1.80748			−0.114087			−0.0570436	−	0.998372i	$-0.518167\pi$
$251$	−1.80748			−0.114087			−0.0570436	+	0.998372i	$0.518167\pi$
$252$	−1.13257	−	1.55885i	−0.0713454	−	0.0981986i
$253$	−26.7834	−	8.70244i	−1.68386	−	0.547118i
$254$	−1.82212	+	5.60791i	−0.114330	+	0.351872i
$255$	−1.89181	−	5.26240i	−0.118469	−	0.329544i
$256$	3.23342	+	9.95145i	0.202089	+	0.621965i
$257$		−	6.46839i		−	0.403487i	−0.979438	−	0.201743i	$-0.935339\pi$
$257$		−	6.46839i		−	0.403487i	0.979438	−	0.201743i	$-0.0646607\pi$
$258$	2.50896	−	0.815209i	0.156201	−	0.0507527i
$259$	−4.61181	−	3.35068i	−0.286564	−	0.208201i
$260$	9.83200	−	14.4528i	0.609755	−	0.896326i
$261$	3.81324	−	2.77048i	0.236034	−	0.171488i
$262$	2.97237	−	4.09111i	0.183634	−	0.252750i
$263$	0.493919	−	0.679822i	0.0304564	−	0.0419196i	−0.793517	−	0.608548i	$-0.791752\pi$
$263$	0.493919	−	0.679822i	0.0304564	−	0.0419196i	0.823974	+	0.566628i	$0.191752\pi$
$264$	−2.82061	+	2.04929i	−0.173597	+	0.126125i
$265$	0.296395	+	9.57382i	0.0182074	+	0.588115i
$266$	0.0811281	+	0.0589430i	0.00497429	+	0.00361403i
$267$	−14.6806	+	4.77002i	−0.898438	+	0.291920i
$268$		−	13.9228i		−	0.850470i
$269$	3.21757	+	9.90267i	0.196179	+	0.603777i	0.999961	+	0.00885253i	$0.00281788\pi$
$269$	3.21757	+	9.90267i	0.196179	+	0.603777i	−0.803782	+	0.594924i	$0.797182\pi$
$270$	−0.604485	+	0.0187142i	−0.0367878	+	0.00113891i
$271$	−6.14166	+	18.9021i	−0.373079	+	1.14822i	0.571686	+	0.820473i	$0.306290\pi$
$271$	−6.14166	+	18.9021i	−0.373079	+	1.14822i	−0.944765	+	0.327748i	$0.893710\pi$
$272$	8.48269	+	2.75619i	0.514339	+	0.167119i
$273$	−2.38467	−	3.28222i	−0.144327	−	0.198649i
$274$	3.30360			0.199578
$275$	−4.09673	+	15.8941i	−0.247042	+	0.958448i
$276$	16.5301			0.994992
$277$	−6.19414	−	8.52550i	−0.372170	−	0.512247i	0.581319	−	0.813675i	$-0.302537\pi$
$277$	−6.19414	−	8.52550i	−0.372170	−	0.512247i	−0.953489	+	0.301428i	$0.902537\pi$
$278$	−2.96138	−	0.962212i	−0.177612	−	0.0577096i
$279$	−1.10051	+	3.38703i	−0.0658860	+	0.202776i
$280$	−1.87719	+	1.45469i	−0.112183	+	0.0869345i
$281$	8.31603	+	25.5941i	0.496093	+	1.52682i	0.815247	+	0.579114i	$0.196601\pi$
$281$	8.31603	+	25.5941i	0.496093	+	1.52682i	−0.319154	+	0.947703i	$0.603399\pi$
$282$		−	2.40498i		−	0.143215i
$283$	−14.9699	+	4.86400i	−0.889866	+	0.289135i	−0.718048	−	0.695994i	$-0.754964\pi$
$283$	−14.9699	+	4.86400i	−0.889866	+	0.289135i	−0.171818	+	0.985129i	$0.554964\pi$
$284$	−14.0207	−	10.1866i	−0.831976	−	0.604466i
$285$	−0.780185	+	0.280473i	−0.0462142	+	0.0166138i
$286$	−2.91413	+	2.11724i	−0.172316	+	0.125195i
$287$	−1.94067	+	2.67111i	−0.114554	+	0.157671i
$288$	1.81551	−	2.49884i	0.106980	−	0.147245i
$289$	−8.69341	+	6.31613i	−0.511377	+	0.371537i
$290$	−1.74608	−	2.25320i	−0.102533	−	0.132312i
$291$	−9.62382	−	6.99211i	−0.564158	−	0.409885i
$292$	−20.2822	+	6.59008i	−1.18692	+	0.385655i
$293$			27.9963i			1.63556i	0.575531	+	0.817780i	$0.304796\pi$
$293$			27.9963i			1.63556i	−0.575531	+	0.817780i	$0.695204\pi$
$294$	0.0835778	+	0.257226i	0.00487436	+	0.0150017i
$295$	0.598531	−	2.05657i	0.0348478	−	0.119738i
$296$	1.87089	−	5.75802i	0.108743	−	0.334678i
$297$	−3.12204	−	1.01441i	−0.181159	−	0.0588622i
$298$	1.64541	+	2.26472i	0.0953162	+	0.131191i
$299$	34.8046			2.01280
$300$	−0.595960	−	9.61580i	−0.0344078	−	0.555168i
$301$	9.75390			0.562205
$302$	3.23813	+	4.45690i	0.186333	+	0.256466i
$303$	−6.09784	−	1.98131i	−0.350312	−	0.113823i
$304$	0.408624	−	1.25761i	0.0234362	−	0.0721291i
$305$	−11.4449	−	7.78577i	−0.655334	−	0.445812i
$306$	−0.209017	−	0.643289i	−0.0119487	−	0.0367744i
$307$		−	14.4567i		−	0.825088i	−0.910938	−	0.412544i	$-0.864640\pi$
$307$		−	14.4567i		−	0.825088i	0.910938	−	0.412544i	$-0.135360\pi$
$308$	−6.01571	+	1.95462i	−0.342777	+	0.111375i
$309$	3.01109	+	2.18769i	0.171295	+	0.124453i
$310$	2.06800	+	0.601858i	0.117455	+	0.0341832i
$311$	−1.86825	+	1.35736i	−0.105939	+	0.0769689i	−0.639493	−	0.768797i	$-0.720856\pi$
$311$	−1.86825	+	1.35736i	−0.105939	+	0.0769689i	0.533555	+	0.845766i	$0.320856\pi$
$312$	2.53269	−	3.48594i	0.143385	−	0.197353i
$313$	0.580196	−	0.798572i	0.0327946	−	0.0451380i	−0.792305	−	0.610125i	$-0.791119\pi$
$313$	0.580196	−	0.798572i	0.0327946	−	0.0451380i	0.825099	+	0.564988i	$0.191119\pi$
$314$	2.67345	−	1.94237i	0.150871	−	0.109614i
$315$	−2.14699	−	0.624846i	−0.120969	−	0.0352061i
$316$	−3.46272	−	2.51581i	−0.194793	−	0.141526i
$317$	0.533698	−	0.173409i	0.0299755	−	0.00973962i	−0.293991	−	0.955808i	$-0.594984\pi$
$317$	0.533698	−	0.173409i	0.0299755	−	0.00973962i	0.323966	+	0.946069i	$0.394984\pi$
$318$			1.15856i			0.0649686i
$319$	−4.78136	−	14.7155i	−0.267705	−	0.823910i
$320$	11.6430	+	7.92050i	0.650862	+	0.442769i
$321$	4.27574	−	13.1594i	0.238648	−	0.734484i
$322$	−2.20669	−	0.716997i	−0.122974	−	0.0399567i
$323$	−0.545024	−	0.750161i	−0.0303259	−	0.0417401i
$324$	1.92685			0.107047
$325$	−1.25481	−	20.2464i	−0.0696046	−	1.12307i
$326$	4.58298			0.253828
$327$	−2.58218	−	3.55407i	−0.142795	−	0.196541i
$328$	−3.33498	−	1.08360i	−0.184143	−	0.0598318i
$329$	2.74780	−	8.45686i	0.151491	−	0.466242i
$330$	−0.554771	+	1.90621i	−0.0305391	+	0.104934i
$331$	6.43465	+	19.8038i	0.353681	+	1.08852i	0.956771	+	0.290844i	$0.0939360\pi$
$331$	6.43465	+	19.8038i	0.353681	+	1.08852i	−0.603090	+	0.797673i	$0.706064\pi$
$332$			22.5550i			1.23787i
$333$	5.42151	−	1.76156i	0.297097	−	0.0965326i
$334$	0.118503	+	0.0860974i	0.00648419	+	0.00471104i
$335$	−9.89685	−	12.7712i	−0.540722	−	0.697768i
$336$	2.88532	−	2.09631i	0.157407	−	0.114363i
$337$	3.50963	−	4.83060i	0.191182	−	0.263139i	−0.702656	−	0.711530i	$-0.748003\pi$
$337$	3.50963	−	4.83060i	0.191182	−	0.263139i	0.893838	+	0.448391i	$0.148003\pi$
$338$	0.549992	−	0.756999i	0.0299156	−	0.0411753i
$339$	−6.72026	+	4.88256i	−0.364995	+	0.265184i
$340$	10.1399	−	3.64522i	0.549911	−	0.197690i
$341$	9.45808	+	6.87169i	0.512184	+	0.372123i
$342$	−0.0953719	+	0.0309882i	−0.00515712	+	0.00167565i
$343$			1.00000i			0.0539949i
$344$	3.20120	+	9.85229i	0.172597	+	0.531200i
$345$	15.1629	−	11.7502i	0.816341	−	0.632608i
$346$	−0.686082	+	2.11154i	−0.0368840	+	0.113517i
$347$	3.89774	+	1.26645i	0.209242	+	0.0679867i	0.411762	−	0.911291i	$-0.364913\pi$
$347$	3.89774	+	1.26645i	0.209242	+	0.0679867i	−0.202521	+	0.979278i	$0.564913\pi$
$348$	5.33830	+	7.34754i	0.286163	+	0.393869i
$349$	−25.1783			−1.34776			−0.673882	−	0.738839i	$-0.735374\pi$
$349$	−25.1783			−1.34776			−0.673882	+	0.738839i	$0.735374\pi$
$350$	−0.337531	+	1.30952i	−0.0180418	+	0.0699966i
$351$	4.05705			0.216549
$352$	−5.95980	−	8.20296i	−0.317658	−	0.437219i
$353$	−20.9683	−	6.81303i	−1.11603	−	0.362621i	−0.307780	−	0.951457i	$-0.599586\pi$
$353$	−20.9683	−	6.81303i	−1.11603	−	0.362621i	−0.808252	+	0.588837i	$0.799586\pi$
$354$	0.0800580	−	0.246393i	0.00425503	−	0.0130956i
$355$	−20.1021	+	0.622339i	−1.06691	+	0.0330303i
$356$	−9.19110	−	28.2873i	−0.487128	−	1.49922i
$357$		−	2.50087i		−	0.132360i
$358$	−0.955360	+	0.310415i	−0.0504923	+	0.0164060i
$359$	−14.7116	−	10.6886i	−0.776446	−	0.564121i	0.127464	−	0.991843i	$-0.459316\pi$
$359$	−14.7116	−	10.6886i	−0.776446	−	0.564121i	−0.903910	+	0.427722i	$0.859316\pi$
$360$	−0.0734878	−	2.37372i	−0.00387315	−	0.125106i
$361$	15.2601	−	11.0871i	0.803164	−	0.583532i
$362$	3.07235	−	4.22872i	0.161479	−	0.222257i
$363$	0.131556	−	0.181072i	0.00690491	−	0.00950379i
$364$	6.32434	−	4.59490i	0.331486	−	0.240838i
$365$	−13.9202	+	20.4624i	−0.728615	+	1.07105i
$366$	−1.35452	−	0.984113i	−0.0708017	−	0.0514404i
$367$	35.1868	−	11.4329i	1.83674	−	0.596792i	0.838048	−	0.545597i	$-0.183697\pi$
$367$	35.1868	−	11.4329i	1.83674	−	0.596792i	0.998689	−	0.0511947i	$-0.0163029\pi$
$368$			30.5958i			1.59492i
$369$	−1.02027	−	3.14008i	−0.0531133	−	0.163466i
$370$	−1.16629	−	3.24426i	−0.0606327	−	0.168661i
$371$	−1.32370	+	4.07394i	−0.0687232	+	0.211508i
$372$	−6.52630	−	2.12052i	−0.338373	−	0.109944i
$373$	−9.00460	−	12.3938i	−0.466240	−	0.641725i	0.509548	−	0.860442i	$-0.329813\pi$
$373$	−9.00460	−	12.3938i	−0.466240	−	0.641725i	−0.975788	+	0.218717i	$0.929813\pi$
$374$	−2.22041			−0.114814
$375$	−7.38194	−	8.39684i	−0.381202	−	0.433611i
$376$	9.44400			0.487037
$377$	11.2400	+	15.4705i	0.578888	+	0.796771i
$378$	−0.257226	−	0.0835778i	−0.0132303	−	0.00429878i
$379$	2.86160	−	8.80709i	0.146990	−	0.452390i	−0.850271	−	0.526345i	$-0.823562\pi$
$379$	2.86160	−	8.80709i	0.146990	−	0.452390i	0.997262	+	0.0739550i	$0.0235621\pi$
$380$	−0.540428	−	1.50330i	−0.0277234	−	0.0771177i
$381$	−6.73703	−	20.7345i	−0.345149	−	1.06226i
$382$			1.44880i			0.0741269i
$383$	6.43481	−	2.09080i	0.328803	−	0.106835i	−0.139963	−	0.990157i	$-0.544698\pi$
$383$	6.43481	−	2.09080i	0.328803	−	0.106835i	0.468767	+	0.883322i	$0.344698\pi$
$384$	6.37563	+	4.63217i	0.325355	+	0.236384i
$385$	−4.12873	+	6.06914i	−0.210420	+	0.309312i
$386$	3.49130	−	2.53657i	0.177702	−	0.129108i
$387$	−5.73320	+	7.89107i	−0.291435	+	0.401126i
$388$	13.4727	−	18.5436i	0.683975	−	0.941411i
$389$	−19.8473	+	14.4199i	−1.00630	+	0.731118i	−0.963429	−	0.267962i	$-0.913650\pi$
$389$	−19.8473	+	14.4199i	−1.00630	+	0.731118i	−0.0428686	+	0.999081i	$0.513650\pi$
$390$	−0.0759244	−	2.45242i	−0.00384458	−	0.124183i
$391$	17.3570	+	12.6106i	0.877783	+	0.637747i
$392$	−1.01009	+	0.328197i	−0.0510171	+	0.0165765i
$393$			18.6971i			0.943146i
$394$	−1.06274	−	3.27078i	−0.0535401	−	0.164779i
$395$	−4.96466	+	0.153700i	−0.249799	+	0.00773350i
$396$	1.95462	−	6.01571i	0.0982234	−	0.302301i
$397$	−27.0078	−	8.77536i	−1.35548	−	0.440423i	−0.460950	−	0.887426i	$-0.652491\pi$
$397$	−27.0078	−	8.77536i	−1.35548	−	0.440423i	−0.894532	+	0.447003i	$0.852491\pi$
$398$	0.768986	+	1.05842i	0.0385458	+	0.0530537i
$399$	−0.370771			−0.0185617
$400$	17.7981	−	1.10308i	0.889905	−	0.0551538i
$401$	−26.1328			−1.30501			−0.652505	−	0.757785i	$-0.726282\pi$
$401$	−26.1328			−1.30501			−0.652505	+	0.757785i	$0.726282\pi$
$402$	−1.14870	−	1.58105i	−0.0572919	−	0.0788555i
$403$	−13.7413	−	4.46483i	−0.684505	−	0.222409i
$404$	3.81768	−	11.7496i	0.189937	−	0.584566i
$405$	1.76748	−	1.36968i	0.0878268	−	0.0680598i
$406$	−0.393938	−	1.21242i	−0.0195508	−	0.0601712i
$407$		−	18.7131i		−	0.927575i
$408$	2.52610	−	0.820780i	0.125061	−	0.0406347i
$409$	−3.94082	−	2.86317i	−0.194861	−	0.141575i	0.486077	−	0.873916i	$-0.338428\pi$
$409$	−3.94082	−	2.86317i	−0.194861	−	0.141575i	−0.680938	+	0.732341i	$0.738428\pi$
$410$	−1.87904	+	0.675504i	−0.0927990	+	0.0333607i
$411$	−9.88182	+	7.17956i	−0.487434	+	0.354142i
$412$	−4.21534	+	5.80192i	−0.207675	+	0.285840i
$413$	0.563031	−	0.774946i	0.0277049	−	0.0381326i
$414$	1.87712	−	1.36381i	0.0922556	−	0.0670276i
$415$	16.0330	+	20.6895i	0.787027	+	1.01561i
$416$	10.1379	+	7.36561i	0.497051	+	0.361129i
$417$	10.9493	−	3.55764i	0.536189	−	0.174218i
$418$			0.329190i			0.0161012i
$419$	11.3251	+	34.8550i	0.553267	+	1.70278i	0.700477	+	0.713675i	$0.252970\pi$
$419$	11.3251	+	34.8550i	0.553267	+	1.70278i	−0.147211	+	0.989105i	$0.547030\pi$
$420$	1.20398	−	4.13693i	0.0587484	−	0.201861i
$421$	−11.0316	+	33.9519i	−0.537649	+	1.65471i	0.200205	+	0.979754i	$0.435839\pi$
$421$	−11.0316	+	33.9519i	−0.537649	+	1.65471i	−0.737854	+	0.674960i	$0.764161\pi$
$422$	−6.34673	−	2.06218i	−0.308954	−	0.100385i
$423$	5.22663	+	7.19384i	0.254127	+	0.349776i
$424$	−4.54947			−0.220942
$425$	6.71003	−	10.5515i	0.325484	−	0.511824i
$426$	−2.43261			−0.117861
$427$	−3.63862	−	5.00813i	−0.176085	−	0.242360i
$428$	25.3561	+	8.23870i	1.22563	+	0.398232i
$429$	4.11552	−	12.6663i	0.198699	−	0.611533i
$430$	4.87733	+	3.31796i	0.235206	+	0.160006i
$431$	8.51676	+	26.2119i	0.410238	+	1.26258i	0.916442	+	0.400168i	$0.131048\pi$
$431$	8.51676	+	26.2119i	0.410238	+	1.26258i	−0.506204	+	0.862414i	$0.668952\pi$
$432$			3.56645i			0.171591i
$433$	15.5701	−	5.05904i	0.748252	−	0.243122i	0.0900231	−	0.995940i	$-0.471306\pi$
$433$	15.5701	−	5.05904i	0.748252	−	0.243122i	0.658229	+	0.752818i	$0.271306\pi$
$434$	0.779254	+	0.566161i	0.0374054	+	0.0271766i
$435$	10.1197	+	2.94516i	0.485201	+	0.141210i
$436$	6.84816	−	4.97548i	0.327967	−	0.238282i
$437$	1.86961	−	2.57329i	0.0894354	−	0.123097i
$438$	−1.75949	+	2.42174i	−0.0840719	+	0.115715i
$439$	−17.7100	+	12.8670i	−0.845250	+	0.614110i	−0.923832	−	0.382797i	$-0.874961\pi$
$439$	−17.7100	+	12.8670i	−0.845250	+	0.614110i	0.0785819	+	0.996908i	$0.474961\pi$
$440$	−7.48541	−	2.17850i	−0.356853	−	0.103856i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	2.60985	−	0.847993i	0.124138	−	0.0403349i
$443$			19.9833i			0.949435i	0.880138	+	0.474718i	$0.157450\pi$
$443$			19.9833i			0.949435i	−0.880138	+	0.474718i	$0.842550\pi$
$444$	3.39425	+	10.4464i	0.161084	+	0.495766i
$445$	−28.5386	−	19.4143i	−1.35286	−	0.920326i
$446$	−1.95553	+	6.01850i	−0.0925970	+	0.284984i
$447$	−9.84359	−	3.19838i	−0.465586	−	0.151278i
$448$	3.70158	+	5.09479i	0.174883	+	0.240706i
$449$	20.7894			0.981115			0.490557	−	0.871409i	$-0.336793\pi$
$449$	20.7894			0.981115			0.490557	+	0.871409i	$0.336793\pi$
$450$	−0.861026	−	1.04278i	−0.0405892	−	0.0491573i
$451$	−10.8384			−0.510362
$452$	−9.40795	−	12.9489i	−0.442513	−	0.609067i
$453$	−19.3719	−	6.29432i	−0.910173	−	0.295733i
$454$	0.847401	−	2.60803i	0.0397705	−	0.122401i
$455$	2.53503	−	8.71044i	0.118844	−	0.408352i
$456$	−0.121686	−	0.374511i	−0.00569847	−	0.0175381i
$457$			22.9355i			1.07288i	0.843939	+	0.536440i	$0.180231\pi$
$457$			22.9355i			1.07288i	−0.843939	+	0.536440i	$0.819769\pi$
$458$	5.52896	−	1.79647i	0.258351	−	0.0839434i
$459$	2.02325	+	1.46998i	0.0944371	+	0.0686126i
$460$	22.6408	+	29.2165i	1.05563	+	1.36223i
$461$	3.05007	−	2.21600i	0.142056	−	0.103210i	−0.514488	−	0.857498i	$-0.672018\pi$
$461$	3.05007	−	2.21600i	0.142056	−	0.103210i	0.656543	+	0.754288i	$0.272018\pi$
$462$	−0.521867	+	0.718288i	−0.0242794	+	0.0334178i
$463$	10.6929	−	14.7175i	0.496940	−	0.683979i	−0.484709	−	0.874675i	$-0.661074\pi$
$463$	10.6929	−	14.7175i	0.496940	−	0.683979i	0.981649	+	0.190696i	$0.0610745\pi$
$464$	−13.5997	+	9.88077i	−0.631351	+	0.458703i
$465$	−7.49385	+	2.69400i	−0.347519	+	0.124931i
$466$	1.36922	+	0.994796i	0.0634279	+	0.0460830i
$467$	−18.3454	+	5.96079i	−0.848925	+	0.275832i	−0.700996	−	0.713166i	$-0.747261\pi$
$467$	−18.3454	+	5.96079i	−0.848925	+	0.275832i	−0.147929	+	0.988998i	$0.547261\pi$
$468$			7.81732i			0.361356i
$469$	−2.23286	−	6.87203i	−0.103104	−	0.317321i
$470$	4.25076	−	3.29405i	0.196073	−	0.151943i
$471$	−3.77561	+	11.6201i	−0.173971	+	0.535428i
$472$	0.967549	+	0.314376i	0.0445350	+	0.0144703i
$473$	18.8204	+	25.9041i	0.865364	+	1.19107i
$474$	−0.600787			−0.0275951
$475$	−1.56433	−	0.994805i	−0.0717765	−	0.0456448i
$476$	4.81880			0.220869
$477$	−2.51783	−	3.46550i	−0.115284	−	0.158674i
$478$	1.93656	+	0.629225i	0.0885760	+	0.0287801i
$479$	−3.49095	+	10.7440i	−0.159506	+	0.490908i	−0.998590	−	0.0530943i	$-0.983092\pi$
$479$	−3.49095	+	10.7440i	−0.159506	+	0.490908i	0.839084	+	0.544002i	$0.183092\pi$
$480$	6.90331	−	0.213719i	0.315092	−	0.00975489i
$481$	7.14671	+	21.9953i	0.325862	+	1.00290i
$482$		−	3.00728i		−	0.136978i
$483$	8.15892	−	2.65099i	0.371244	−	0.120624i
$484$	0.348898	+	0.253489i	0.0158590	+	0.0115222i
$485$	−0.823099	−	26.5868i	−0.0373750	−	1.20725i
$486$	0.218810	−	0.158974i	0.00992540	−	0.00721123i
$487$	9.57981	−	13.1855i	0.434102	−	0.597491i	−0.534786	−	0.844987i	$-0.679608\pi$
$487$	9.57981	−	13.1855i	0.434102	−	0.597491i	0.968889	+	0.247497i	$0.0796079\pi$
$488$	3.86446	−	5.31898i	0.174936	−	0.240779i
$489$	−13.7087	+	9.95997i	−0.619930	+	0.450406i
$490$	−0.340167	+	0.500039i	−0.0153672	+	0.0225894i
$491$	28.2270	+	20.5081i	1.27387	+	0.925519i	0.999350	−	0.0360633i	$-0.0114818\pi$
$491$	28.2270	+	20.5081i	1.27387	+	0.925519i	0.274518	+	0.961582i	$0.411482\pi$
$492$	6.05045	−	1.96591i	0.272776	−	0.0886302i
$493$			11.7877i			0.530890i
$494$	−0.125721	−	0.386928i	−0.00565643	−	0.0174087i
$495$	−2.48323	−	6.90757i	−0.111613	−	0.310472i
$496$	3.92492	−	12.0797i	0.176234	−	0.542393i
$497$	−8.55403	−	2.77937i	−0.383701	−	0.124672i
$498$	1.86090	+	2.56131i	0.0833889	+	0.114775i
$499$	10.5424			0.471944			0.235972	−	0.971760i	$-0.424173\pi$
$499$	10.5424			0.471944			0.235972	+	0.971760i	$0.424173\pi$
$500$	16.1795	−	14.2239i	0.723567	−	0.636111i
$501$	−0.541580			−0.0241960
$502$	−0.287343	−	0.395494i	−0.0128248	−	0.0176518i
$503$	35.5637	+	11.5553i	1.58571	+	0.515227i	0.963519	−	0.267642i	$-0.0862443\pi$
$503$	35.5637	+	11.5553i	1.58571	+	0.515227i	0.622187	+	0.782869i	$0.286244\pi$
$504$	0.328197	−	1.01009i	0.0146191	−	0.0449929i
$505$	−4.85015	−	13.4916i	−0.215829	−	0.600367i
$506$	−2.35369	−	7.24392i	−0.104634	−	0.322032i
$507$			3.45962i			0.153647i
$508$	39.9522	−	12.9813i	1.77259	−	0.575950i
$509$	−9.61821	−	6.98804i	−0.426320	−	0.309739i	0.353856	−	0.935300i	$-0.384870\pi$
$509$	−9.61821	−	6.98804i	−0.426320	−	0.309739i	−0.780176	+	0.625561i	$0.784870\pi$
$510$	0.850715	−	1.25053i	0.0376703	−	0.0553745i
$511$	−8.95402	+	6.50548i	−0.396103	+	0.287785i
$512$	−10.9278	+	15.0408i	−0.482944	+	0.664715i
$513$	0.217933	−	0.299960i	0.00962200	−	0.0132435i
$514$	1.41535	−	1.02831i	0.0624282	−	0.0453567i
$515$	0.257531	+	8.31846i	0.0113482	+	0.366555i
$516$	−15.2049	−	11.0470i	−0.669358	−	0.486317i
$517$	27.7614	−	9.02024i	1.22095	−	0.396710i
$518$		−	1.54178i		−	0.0677419i
$519$	−2.53669	−	7.80713i	−0.111348	−	0.342695i
$520$	9.63030	−	0.298144i	0.422317	−	0.0130745i
$521$	3.63157	−	11.1768i	0.159102	−	0.489665i	−0.839452	−	0.543435i	$-0.817124\pi$
$521$	3.63157	−	11.1768i	0.159102	−	0.489665i	0.998553	+	0.0537695i	$0.0171236\pi$
$522$	1.21242	+	0.393938i	0.0530660	+	0.0172422i
$523$	−3.28045	−	4.51516i	−0.143444	−	0.197434i	0.731250	−	0.682110i	$-0.238938\pi$
$523$	−3.28045	−	4.51516i	−0.143444	−	0.197434i	−0.874694	+	0.484676i	$0.838938\pi$
$524$	−36.0266			−1.57383
$525$	−1.83628	−	4.65060i	−0.0801419	−	0.202969i
$526$	0.227272			0.00990953
$527$	−5.23507	−	7.20546i	−0.228043	−	0.313875i
$528$	11.1346	+	3.61785i	0.484571	+	0.157447i
$529$	−15.6350	+	48.1194i	−0.679781	+	2.09215i
$530$	−2.04772	+	1.58685i	−0.0889474	+	0.0689282i
$531$	0.296003	+	0.911003i	0.0128454	+	0.0395342i
$532$		−	0.714419i		−	0.0309740i
$533$	12.7394	−	4.13929i	0.551806	−	0.179293i
$534$	−3.37757	−	2.45395i	−0.146162	−	0.106193i
$535$	29.1153	−	10.4668i	1.25876	−	0.452519i
$536$	6.20854	−	4.51077i	0.268168	−	0.194835i
$537$	2.18309	−	3.00476i	0.0942071	−	0.129665i
$538$	−1.65529	+	2.27831i	−0.0713645	+	0.0982248i
$539$	−2.65577	+	1.92953i	−0.114392	+	0.0831107i
$540$	2.63916	+	3.40567i	0.113571	+	0.146557i
$541$	32.4102	+	23.5474i	1.39342	+	1.01238i	0.995480	+	0.0949718i	$0.0302761\pi$
$541$	32.4102	+	23.5474i	1.39342	+	1.01238i	0.397944	+	0.917410i	$0.369724\pi$
$542$	−5.11233	+	1.66110i	−0.219593	+	0.0713502i
$543$			19.3260i			0.829360i
$544$	2.38701	+	7.34646i	0.102342	+	0.314977i
$545$	2.74499	−	9.43189i	0.117583	−	0.404018i
$546$	0.339079	−	1.04358i	0.0145112	−	0.0446610i
$547$	10.9558	+	3.55975i	0.468435	+	0.152204i	0.533717	−	0.845663i	$-0.320795\pi$
$547$	10.9558	+	3.55975i	0.468435	+	0.152204i	−0.0652822	+	0.997867i	$0.520795\pi$
$548$	−13.8339	−	19.0408i	−0.590957	−	0.813382i
$549$	6.19039			0.264199
$550$	−4.12905	+	1.63035i	−0.176063	+	0.0695183i
$551$	1.74760			0.0744502
$552$	5.35548	+	7.37118i	0.227944	+	0.313738i
$553$	−2.11261	−	0.686427i	−0.0898371	−	0.0291899i
$554$	0.880751	−	2.71067i	0.0374195	−	0.115165i
$555$	10.5392	+	7.16965i	0.447365	+	0.304335i
$556$	6.85504	+	21.0976i	0.290718	+	0.894739i
$557$			31.9773i			1.35492i	0.735559	+	0.677461i	$0.236920\pi$
$557$			31.9773i			1.35492i	−0.735559	+	0.677461i	$0.763080\pi$
$558$	−0.916068	+	0.297648i	−0.0387802	+	0.0126005i
$559$	−32.0144	−	23.2598i	−1.35407	−	0.983787i
$560$	7.65713	+	2.22848i	0.323573	+	0.0941704i
$561$	6.64173	−	4.82550i	0.280414	−	0.203733i
$562$	−4.27820	+	5.88844i	−0.180465	+	0.248389i
$563$	−1.10002	+	1.51405i	−0.0463603	+	0.0638094i	−0.831568	−	0.555423i	$-0.812556\pi$
$563$	−1.10002	+	1.51405i	−0.0463603	+	0.0638094i	0.785208	+	0.619233i	$0.212556\pi$
$564$	−13.8614	+	10.0709i	−0.583672	+	0.424063i
$565$	−17.8344	−	5.19041i	−0.750299	−	0.218362i
$566$	−3.44412	−	2.50230i	−0.144767	−	0.105179i
$567$	0.951057	−	0.309017i	0.0399406	−	0.0129775i
$568$		−	9.55251i		−	0.400814i
$569$	5.08187	+	15.6404i	0.213043	+	0.655679i	0.999287	+	0.0377624i	$0.0120230\pi$
$569$	5.08187	+	15.6404i	0.213043	+	0.655679i	−0.786244	+	0.617916i	$0.787977\pi$
$570$	−0.185400	−	0.126124i	−0.00776554	−	0.00528275i
$571$	−9.50811	+	29.2630i	−0.397902	+	1.22462i	0.528776	+	0.848761i	$0.322651\pi$
$571$	−9.50811	+	29.2630i	−0.397902	+	1.22462i	−0.926678	+	0.375855i	$0.877349\pi$
$572$	24.4060	+	7.92999i	1.02047	+	0.331570i
$573$	−3.14860	−	4.33368i	−0.131535	−	0.181042i
$574$	−0.892982			−0.0372723
$575$	41.5364	+	10.7061i	1.73219	+	0.446475i
$576$	−6.29751			−0.262396
$577$	6.67840	+	9.19202i	0.278025	+	0.382669i	0.925079	−	0.379776i	$-0.123999\pi$
$577$	6.67840	+	9.19202i	0.278025	+	0.382669i	−0.647053	+	0.762445i	$0.723999\pi$
$578$	−2.76406	−	0.898097i	−0.114970	−	0.0373559i
$579$	−4.93063	+	15.1749i	−0.204910	+	0.630649i
$580$	−5.67488	+	19.4991i	−0.235637	+	0.809656i
$581$	3.61724	+	11.1327i	0.150069	+	0.461864i
$582$		−	3.21735i		−	0.133363i
$583$	−13.3736	+	4.34533i	−0.553876	+	0.179965i
$584$	−9.50979	−	6.90927i	−0.393518	−	0.285908i
$585$	5.55684	+	7.17075i	0.229747	+	0.296474i
$586$	−6.12585	+	4.45069i	−0.253057	+	0.183856i
$587$	20.2163	−	27.8254i	0.834418	−	1.14848i	−0.152667	−	0.988278i	$-0.548786\pi$
$587$	20.2163	−	27.8254i	0.834418	−	1.14848i	0.987085	−	0.160200i	$-0.0512139\pi$
$588$	1.13257	−	1.55885i	0.0467066	−	0.0642861i
$589$	−1.06826	+	0.776134i	−0.0440167	+	0.0319800i
$590$	0.545149	−	0.195978i	0.0224434	−	0.00806829i
$591$	10.2871	+	7.47403i	0.423155	+	0.307440i
$592$	−19.3355	+	6.28249i	−0.794685	+	0.258209i
$593$		−	12.1372i		−	0.498415i	−0.968450	−	0.249208i	$-0.919830\pi$
$593$		−	12.1372i		−	0.498415i	0.968450	−	0.249208i	$-0.0801701\pi$
$594$	−0.274362	−	0.844398i	−0.0112572	−	0.0346461i
$595$	4.42024	−	3.42539i	0.181212	−	0.140427i
$596$	6.16279	−	18.9671i	0.252438	−	0.776924i
$597$	−4.60042	−	1.49477i	−0.188283	−	0.0611768i
$598$	5.53304	+	7.61557i	0.226263	+	0.311424i
$599$	11.1321			0.454846			0.227423	−	0.973796i	$-0.426970\pi$
$599$	11.1321			0.454846			0.227423	+	0.973796i	$0.426970\pi$
$600$	4.09485	−	3.38112i	0.167172	−	0.138034i
$601$	−9.38741			−0.382920			−0.191460	−	0.981500i	$-0.561322\pi$
$601$	−9.38741			−0.382920			−0.191460	+	0.981500i	$0.561322\pi$
$602$	1.55062	+	2.13425i	0.0631986	+	0.0869854i
$603$	6.87203	+	2.23286i	0.279851	+	0.0909290i
$604$	12.1282	−	37.3268i	0.493490	−	1.51881i
$605$	0.500230	−	0.0154866i	0.0203372	−	0.000629619i
$606$	−0.535872	−	1.64924i	−0.0217683	−	0.0669959i
$607$			5.23971i			0.212673i	0.994330	+	0.106337i	$0.0339121\pi$
$607$			5.23971i			0.212673i	−0.994330	+	0.106337i	$0.966088\pi$
$608$	1.08916	−	0.353890i	0.0441713	−	0.0143521i
$609$	3.81324	+	2.77048i	0.154520	+	0.112266i
$610$	−0.115848	−	3.74200i	−0.00469055	−	0.151509i
$611$	−29.1857	+	21.2047i	−1.18073	+	0.857849i
$612$	−2.83242	+	3.89849i	−0.114494	+	0.157587i
$613$	8.23723	−	11.3376i	0.332699	−	0.457920i	−0.609593	−	0.792715i	$-0.708667\pi$
$613$	8.23723	−	11.3376i	0.332699	−	0.457920i	0.942291	+	0.334795i	$0.108667\pi$
$614$	3.16327	−	2.29825i	0.127659	−	0.0927497i
$615$	4.15258	−	6.10420i	0.167448	−	0.246145i
$616$	−2.82061	−	2.04929i	−0.113646	−	0.0825684i
$617$	3.28524	−	1.06744i	0.132259	−	0.0429735i	−0.242140	−	0.970241i	$-0.577849\pi$
$617$	3.28524	−	1.06744i	0.132259	−	0.0429735i	0.374399	+	0.927268i	$0.377849\pi$
$618$			1.00664i			0.0404931i
$619$	1.03614	+	3.18893i	0.0416462	+	0.128174i	0.969718	−	0.244228i	$-0.0785344\pi$
$619$	1.03614	+	3.18893i	0.0416462	+	0.128174i	−0.928072	+	0.372402i	$0.878534\pi$
$620$	−5.19094	−	14.4395i	−0.208473	−	0.579905i
$621$	−2.65099	+	8.15892i	−0.106381	+	0.327406i
$622$	−0.594007	−	0.193005i	−0.0238175	−	0.00773878i
$623$	−9.07311	−	12.4881i	−0.363507	−	0.500324i
$624$	−14.4692			−0.579233
$625$	4.73039	−	24.5484i	0.189216	−	0.981936i
$626$	0.266972			0.0106703
$627$	−0.715412	−	0.984681i	−0.0285708	−	0.0393244i
$628$	−22.3903	−	7.27504i	−0.893469	−	0.290306i
$629$	−4.40542	+	13.5585i	−0.175656	+	0.540613i
$630$	−0.204594	−	0.569117i	−0.00815124	−	0.0226741i
$631$	−4.41395	−	13.5847i	−0.175717	−	0.540800i	0.823949	−	0.566664i	$-0.191766\pi$
$631$	−4.41395	−	13.5847i	−0.175717	−	0.540800i	−0.999665	+	0.0258640i	$0.991766\pi$
$632$		−	2.35920i		−	0.0938440i
$633$	23.4661	−	7.62461i	0.932695	−	0.303051i
$634$	0.122788	+	0.0892106i	0.00487653	+	0.00354301i
$635$	27.4202	−	40.3071i	1.08814	−	1.59954i
$636$	6.67750	−	4.85149i	0.264780	−	0.192374i
$637$	2.38467	−	3.28222i	0.0944841	−	0.130046i
$638$	2.45978	−	3.38560i	0.0973836	−	0.134037i
$639$	7.27650	−	5.28668i	0.287854	−	0.209138i
$640$	0.545291	+	17.6134i	0.0215545	+	0.696229i
$641$	−32.2135	−	23.4044i	−1.27235	−	0.924420i	−0.273061	−	0.961997i	$-0.588036\pi$
$641$	−32.2135	−	23.4044i	−1.27235	−	0.924420i	−0.999294	+	0.0375768i	$0.988036\pi$
$642$	3.55913	−	1.15643i	0.140468	−	0.0456407i
$643$			36.7255i			1.44831i	0.689635	+	0.724157i	$0.257771\pi$
$643$			36.7255i			1.44831i	−0.689635	+	0.724157i	$0.742229\pi$
$644$	5.10807	+	15.7210i	0.201286	+	0.619495i
$645$	−21.7999	+	0.674902i	−0.858371	+	0.0265742i
$646$	0.0774975	−	0.238513i	0.00304910	−	0.00938416i
$647$	−47.3364	−	15.3805i	−1.86099	−	0.604671i	−0.994405	−	0.105632i	$-0.966313\pi$
$647$	−47.3364	−	15.3805i	−1.86099	−	0.604671i	−0.866580	−	0.499039i	$-0.833687\pi$
$648$	0.624269	+	0.859232i	0.0245236	+	0.0337538i
$649$	3.14446			0.123431
$650$	4.23062	−	3.49322i	0.165939	−	0.137015i
$651$	−3.56133			−0.139580
$652$	−19.1914	−	26.4147i	−0.751592	−	1.03448i
$653$	−12.6464	−	4.10908i	−0.494893	−	0.160801i	0.0509278	−	0.998702i	$-0.483782\pi$
$653$	−12.6464	−	4.10908i	−0.494893	−	0.160801i	−0.545821	+	0.837902i	$0.683782\pi$
$654$	0.367163	−	1.13001i	0.0143572	−	0.0441870i
$655$	−33.0468	+	25.6090i	−1.29125	+	1.00063i
$656$	3.63875	+	11.1989i	0.142069	+	0.437244i
$657$		−	11.0678i		−	0.431795i
$658$	2.28727	−	0.743180i	0.0891672	−	0.0289722i
$659$	−22.8352	−	16.5908i	−0.889534	−	0.646284i	0.0462224	−	0.998931i	$-0.485282\pi$
$659$	−22.8352	−	16.5908i	−0.889534	−	0.646284i	−0.935757	+	0.352647i	$0.885282\pi$
$660$	13.3098	−	4.78482i	0.518085	−	0.186249i
$661$	30.3664	−	22.0625i	1.18112	−	0.858131i	0.188819	−	0.982012i	$-0.439534\pi$
$661$	30.3664	−	22.0625i	1.18112	−	0.858131i	0.992297	+	0.123880i	$0.0395339\pi$
$662$	−3.31032	+	4.55627i	−0.128659	+	0.177084i
$663$	−5.96376	+	8.20841i	−0.231613	+	0.318788i
$664$	−10.0579	+	7.30747i	−0.390321	+	0.283585i
$665$	−0.507836	−	0.655330i	−0.0196930	−	0.0254126i
$666$	1.24733	+	0.906236i	0.0483329	+	0.0351159i
$667$	−38.4564	+	12.4953i	−1.48904	+	0.483818i
$668$		−	1.04354i		−	0.0403759i
$669$	−7.23029	−	22.2525i	−0.279539	−	0.860333i
$670$	1.22112	−	4.19583i	0.0471762	−	0.162099i
$671$	6.27961	−	19.3266i	0.242422	−	0.746097i
$672$	2.93756	+	0.954471i	0.113319	+	0.0368195i
$673$	−20.9043	−	28.7723i	−0.805800	−	1.10909i	−0.991958	−	0.126569i	$-0.959603\pi$
$673$	−20.9043	−	28.7723i	−0.805800	−	1.10909i	0.186157	−	0.982520i	$-0.440397\pi$
$674$	1.61492			0.0622045
$675$	4.84175	+	1.24797i	0.186359	+	0.0480344i
$676$	−6.66617			−0.256391
$677$	−18.6713	−	25.6989i	−0.717598	−	0.987688i	−0.999600	−	0.0282747i	$-0.990999\pi$
$677$	−18.6713	−	25.6989i	−0.717598	−	0.987688i	0.282003	−	0.959414i	$-0.409001\pi$
$678$	−2.13670	−	0.694256i	−0.0820595	−	0.0266627i
$679$	3.67597	−	11.3135i	0.141071	−	0.434171i
$680$	4.91065	+	3.34063i	0.188315	+	0.128107i
$681$	3.13315	+	9.64283i	0.120062	+	0.369514i
$682$			3.16194i			0.121077i
$683$	−35.7464	+	11.6147i	−1.36780	+	0.444425i	−0.898639	−	0.438688i	$-0.855443\pi$
$683$	−35.7464	+	11.6147i	−1.36780	+	0.444425i	−0.469160	+	0.883113i	$0.655443\pi$
$684$	0.577977	+	0.419925i	0.0220995	+	0.0160562i
$685$	−26.2246	−	7.63224i	−1.00199	−	0.291613i
$686$	−0.218810	+	0.158974i	−0.00835419	+	0.00606967i
$687$	−12.6342	+	17.3895i	−0.482024	+	0.663449i
$688$	20.4471	−	28.1431i	0.779540	−	1.07295i
$689$	14.0597	−	10.2150i	0.535632	−	0.389159i
$690$	4.98156	+	1.44980i	0.189645	+	0.0551929i
$691$	16.0123	+	11.6336i	0.609137	+	0.442564i	0.849110	−	0.528215i	$-0.177139\pi$
$691$	16.0123	+	11.6336i	0.609137	+	0.442564i	−0.239973	+	0.970780i	$0.577139\pi$
$692$	15.0432	−	4.88782i	0.571855	−	0.185807i
$693$		−	3.28271i		−	0.124700i
$694$	0.342529	+	1.05420i	0.0130022	+	0.0400167i
$695$	21.2850	+	14.4798i	0.807388	+	0.549251i
$696$	−1.54693	+	4.76097i	−0.0586364	+	0.180464i
$697$	7.85293	+	2.55157i	0.297451	+	0.0966476i
$698$	−4.00271	−	5.50925i	−0.151505	−	0.208528i
$699$	−6.25758			−0.236684
$700$	8.96100	−	3.53824i	0.338694	−	0.133733i
$701$	−26.9888			−1.01935			−0.509676	−	0.860366i	$-0.670235\pi$
$701$	−26.9888			−1.01935			−0.509676	+	0.860366i	$0.670235\pi$
$702$	0.644967	+	0.887720i	0.0243427	+	0.0335049i
$703$	2.01014	+	0.653133i	0.0758137	+	0.0246334i
$704$	−6.38827	+	19.6611i	−0.240767	+	0.741005i
$705$	−5.55617	+	19.0912i	−0.209258	+	0.719016i
$706$	−1.84268	−	5.67117i	−0.0693500	−	0.213437i
$707$		−	6.41165i		−	0.241135i
$708$	−1.75537	+	0.570353i	−0.0659707	+	0.0214352i
$709$	31.1250	+	22.6136i	1.16892	+	0.849272i	0.990880	−	0.134750i	$-0.0430232\pi$
$709$	31.1250	+	22.6136i	1.16892	+	0.849272i	0.178044	+	0.984023i	$0.443023\pi$
$710$	−3.33190	−	4.29960i	−0.125044	−	0.161361i
$711$	1.79709	−	1.30566i	0.0673961	−	0.0489662i
$712$	9.63627	−	13.2632i	0.361135	−	0.497059i
$713$	17.9580	−	24.7171i	0.672532	−	0.925661i
$714$	0.547215	−	0.397575i	0.0204790	−	0.0148789i
$715$	28.0243	−	10.0746i	1.04805	−	0.376769i
$716$	5.78972	+	4.20648i	0.216372	+	0.157203i
$717$	−7.16014	+	2.32647i	−0.267400	+	0.0868836i
$718$		−	4.91824i		−	0.183547i
$719$	−4.39450	−	13.5249i	−0.163887	−	0.504393i	0.835065	−	0.550151i	$-0.185430\pi$
$719$	−4.39450	−	13.5249i	−0.163887	−	0.504393i	−0.998953	+	0.0457577i	$0.985430\pi$
$720$	−6.30363	+	4.88488i	−0.234922	+	0.182049i
$721$	−1.15013	+	3.53975i	−0.0428332	+	0.131827i
$722$	4.85193	+	1.57649i	0.180570	+	0.0586708i
$723$	6.53557	+	8.99544i	0.243060	+	0.334544i
$724$	−37.2384			−1.38395
$725$	8.65517	+	21.9202i	0.321445	+	0.814097i
$726$	0.0605343			0.00224664
$727$	16.6728	+	22.9481i	0.618359	+	0.851098i	0.997232	−	0.0743508i	$-0.0236885\pi$
$727$	16.6728	+	22.9481i	0.618359	+	0.851098i	−0.378874	+	0.925448i	$0.623688\pi$
$728$	4.09797	+	1.33151i	0.151881	+	0.0493491i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−6.69031	+	0.207125i	−0.247619	+	0.00766603i
$731$	−7.53793	−	23.1994i	−0.278800	−	0.858059i
$732$			11.9279i			0.440869i
$733$	29.8294	−	9.69214i	1.10177	−	0.357988i	0.298988	−	0.954257i	$-0.403351\pi$
$733$	29.8294	−	9.69214i	1.10177	−	0.357988i	0.802784	+	0.596269i	$0.203351\pi$
$734$	8.09543	+	5.88167i	0.298808	+	0.217096i
$735$	−0.0691931	−	2.23500i	−0.00255222	−	0.0824391i
$736$	−21.4370	+	15.5749i	−0.790179	+	0.574099i
$737$	13.9422	−	19.1897i	0.513566	−	0.706863i
$738$	0.524881	−	0.722437i	0.0193212	−	0.0265933i
$739$	−27.2956	+	19.8314i	−1.00408	+	0.729510i	−0.962960	−	0.269644i	$-0.913094\pi$
$739$	−27.2956	+	19.8314i	−1.00408	+	0.729510i	−0.0411246	+	0.999154i	$0.513094\pi$
$740$	−13.8148	+	20.3075i	−0.507843	+	0.746519i
$741$	1.21695	+	0.884166i	0.0447058	+	0.0324807i
$742$	−1.10185	+	0.358013i	−0.0404503	+	0.0131431i
$743$		−	27.7052i		−	1.01641i	−0.861237	−	0.508203i	$-0.830310\pi$
$743$		−	27.7052i		−	1.01641i	0.861237	−	0.508203i	$-0.169690\pi$
$744$	−1.16882	−	3.59726i	−0.0428510	−	0.131882i
$745$	−7.82947	−	21.7791i	−0.286850	−	0.797924i
$746$	1.28037	−	3.94058i	0.0468778	−	0.144275i
$747$	−11.1327	−	3.61724i	−0.407325	−	0.132348i
$748$	9.29802	+	12.7976i	0.339969	+	0.467927i
$749$	13.8366			0.505577
$750$	0.663771	−	2.95012i	0.0242375	−	0.107723i
$751$	−26.3652			−0.962081			−0.481041	−	0.876698i	$-0.659741\pi$
$751$	−26.3652			−0.962081			−0.481041	+	0.876698i	$0.659741\pi$
$752$	−18.6405	−	25.6565i	−0.679749	−	0.935594i
$753$	1.71902	+	0.558542i	0.0626444	+	0.0203544i
$754$	−1.59822	+	4.91882i	−0.0582038	+	0.179133i
$755$	−15.4082	−	42.8607i	−0.560762	−	1.55986i
$756$	0.595429	+	1.83254i	0.0216556	+	0.0666489i
$757$		−	1.58230i		−	0.0575095i	−0.999586	−	0.0287548i	$-0.990846\pi$
$757$		−	1.58230i		−	0.0575095i	0.999586	−	0.0287548i	$-0.00915419\pi$
$758$	2.38200	−	0.773957i	0.0865180	−	0.0281114i
$759$	22.7833	+	16.5530i	0.826981	+	0.600837i
$760$	0.495270	−	0.728036i	0.0179653	−	0.0264087i
$761$	14.6886	−	10.6719i	0.532461	−	0.386855i	−0.288817	−	0.957384i	$-0.593262\pi$
$761$	14.6886	−	10.6719i	0.532461	−	0.386855i	0.821277	+	0.570529i	$0.193262\pi$
$762$	3.46588	−	4.77038i	0.125556	−	0.172813i
$763$	2.58218	−	3.55407i	0.0934813	−	0.128666i
$764$	8.35034	−	6.06688i	0.302105	−	0.219492i
$765$	0.173043	+	5.58944i	0.00625638	+	0.202087i
$766$	1.48046	+	1.07561i	0.0534911	+	0.0388635i
$767$	−3.69598	+	1.20090i	−0.133454	+	0.0433619i
$768$		−	10.4636i		−	0.377572i
$769$	14.2017	+	43.7082i	0.512125	+	1.57616i	0.788453	+	0.615095i	$0.210882\pi$
$769$	14.2017	+	43.7082i	0.512125	+	1.57616i	−0.276328	+	0.961063i	$0.589118\pi$
$770$	−1.98435	+	0.0614333i	−0.0715110	+	0.00221390i
$771$	−1.99884	+	6.15180i	−0.0719865	+	0.221552i
$772$	−29.2398	−	9.50059i	−1.05236	−	0.341934i
$773$	5.98600	+	8.23903i	0.215302	+	0.296337i	0.902984	−	0.429675i	$-0.141372\pi$
$773$	5.98600	+	8.23903i	0.215302	+	0.296337i	−0.687682	+	0.726012i	$0.741372\pi$
$774$	−2.63807			−0.0948236
$775$	−15.0258	−	9.55533i	−0.539741	−	0.343237i
$776$	12.6340			0.453536
$777$	3.35068	+	4.61181i	0.120205	+	0.165448i
$778$	−6.31043	−	2.05038i	−0.226240	−	0.0735098i
$779$	0.378287	−	1.16425i	0.0135535	−	0.0417135i
$780$	−13.8170	+	10.7072i	−0.494726	+	0.383379i
$781$	−9.12388	−	28.0804i	−0.326478	−	1.00480i
$782$			5.80265i			0.207502i
$783$	−4.48273	+	1.45653i	−0.160200	+	0.0520521i
$784$	2.88532	+	2.09631i	0.103047	+	0.0748681i
$785$	−25.7097	+	9.24252i	−0.917620	+	0.329880i
$786$	−4.09111	+	2.97237i	−0.145925	+	0.106021i
$787$	−1.95627	+	2.69258i	−0.0697336	+	0.0959801i	−0.842459	−	0.538760i	$-0.818893\pi$
$787$	−1.95627	+	2.69258i	−0.0697336	+	0.0959801i	0.772726	+	0.634740i	$0.218893\pi$
$788$	−14.4013	+	19.8217i	−0.513026	+	0.706120i
$789$	−0.679822	+	0.493919i	−0.0242023	+	0.0175840i
$790$	−0.822885	−	1.06188i	−0.0292769	−	0.0377800i
$791$	−6.72026	−	4.88256i	−0.238945	−	0.173604i
$792$	3.31583	−	1.07738i	0.117823	−	0.0382829i
$793$			25.1147i			0.891849i
$794$	−2.37342	−	7.30462i	−0.0842294	−	0.259231i
$795$	2.67658	−	9.19683i	0.0949287	−	0.326178i
$796$	2.88019	−	8.86432i	0.102086	−	0.314187i
$797$	16.3787	+	5.32176i	0.580163	+	0.188507i	0.584374	−	0.811485i	$-0.301340\pi$
$797$	16.3787	+	5.32176i	0.580163	+	0.188507i	−0.00421037	+	0.999991i	$0.501340\pi$
$798$	−0.0589430	−	0.0811281i	−0.00208656	−	0.00287191i
$799$	−22.2379			−0.786721
$800$	9.83305	+	11.9087i	0.347651	+	0.421037i
$801$	15.4361			0.545408
$802$	−4.15445	−	5.71811i	−0.146699	−	0.201913i
$803$	−34.5541	−	11.2273i	−1.21939	−	0.396203i
$804$	−4.30238	+	13.2414i	−0.151733	+	0.466987i
$805$	15.8607	+	10.7897i	0.559015	+	0.380288i
$806$	−1.20757	−	3.71653i	−0.0425350	−	0.130909i
$807$		−	10.4123i		−	0.366530i
$808$	6.47633	−	2.10429i	0.227837	−	0.0740286i
$809$	−23.6622	−	17.1916i	−0.831917	−	0.604423i	0.0881841	−	0.996104i	$-0.471894\pi$
$809$	−23.6622	−	17.1916i	−0.831917	−	0.604423i	−0.920101	+	0.391681i	$0.871894\pi$
$810$	0.580683	+	0.168998i	0.0204031	+	0.00593798i
$811$	27.1918	−	19.7560i	0.954832	−	0.693726i	0.00288716	−	0.999996i	$-0.499081\pi$
$811$	27.1918	−	19.7560i	0.954832	−	0.693726i	0.951945	+	0.306270i	$0.0990810\pi$
$812$	−5.33830	+	7.34754i	−0.187338	+	0.257848i
$813$	11.6821	−	16.0791i	0.409710	−	0.563918i
$814$	4.09461	−	2.97491i	0.143516	−	0.104271i
$815$	−36.3806	−	10.5880i	−1.27436	−	0.370880i
$816$	−7.21581	−	5.24259i	−0.252604	−	0.183527i
$817$	−3.43946	+	1.11755i	−0.120331	+	0.0390980i
$818$		−	1.31746i		−	0.0460639i
$819$	1.25370	+	3.85848i	0.0438077	+	0.134826i
$820$	11.7619	+	8.00139i	0.410743	+	0.279421i
$821$	−7.36426	+	22.6649i	−0.257014	+	0.791009i	0.736412	+	0.676534i	$0.236519\pi$
$821$	−7.36426	+	22.6649i	−0.257014	+	0.791009i	−0.993426	+	0.114475i	$0.963481\pi$
$822$	−3.14191	−	1.02087i	−0.109587	−	0.0356069i
$823$	23.7767	+	32.7258i	0.828803	+	1.14075i	0.988145	+	0.153526i	$0.0490628\pi$
$823$	23.7767	+	32.7258i	0.828803	+	1.14075i	−0.159342	+	0.987223i	$0.550937\pi$
$824$	−3.95293			−0.137707
$825$	8.80776	−	13.8502i	0.306647	−	0.482202i
$826$	0.259073			0.00901431
$827$	−15.6779	−	21.5788i	−0.545173	−	0.750367i	0.444174	−	0.895941i	$-0.353497\pi$
$827$	−15.6779	−	21.5788i	−0.545173	−	0.750367i	−0.989347	+	0.145574i	$0.953497\pi$
$828$	−15.7210	−	5.10807i	−0.546343	−	0.177518i
$829$	9.48540	−	29.1931i	0.329441	−	1.01392i	−0.639954	−	0.768413i	$-0.721047\pi$
$829$	9.48540	−	29.1931i	0.329441	−	1.01392i	0.969396	−	0.245504i	$-0.0789533\pi$
$830$	−1.97823	+	6.79726i	−0.0686654	+	0.235936i
$831$	3.25645	+	10.0223i	0.112965	+	0.347671i
$832$		−	25.5493i		−	0.885762i
$833$	2.37847	−	0.772812i	0.0824091	−	0.0267763i
$834$	2.51910	+	1.83024i	0.0872294	+	0.0633759i
$835$	−0.741789	−	0.957232i	−0.0256707	−	0.0331264i
$836$	1.89733	−	1.37849i	0.0656206	−	0.0476761i
$837$	2.09330	−	2.88118i	0.0723550	−	0.0995881i
$838$	−5.82621	+	8.01910i	−0.201263	+	0.277015i
$839$	−17.2569	+	12.5379i	−0.595773	+	0.432855i	−0.844376	−	0.535751i	$-0.820029\pi$
$839$	−17.2569	+	12.5379i	−0.595773	+	0.432855i	0.248603	+	0.968606i	$0.420029\pi$
$840$	2.23483	−	0.803412i	0.0771091	−	0.0277203i
$841$	5.48808	+	3.98733i	0.189244	+	0.137494i
$842$	−9.18275	+	2.98366i	−0.316458	+	0.102824i
$843$		−	26.9112i		−	0.926872i
$844$	14.6915	+	45.2157i	0.505701	+	1.55639i
$845$	−6.11482	+	4.73857i	−0.210356	+	0.163012i
$846$	−0.743180	+	2.28727i	−0.0255511	+	0.0786381i
$847$	0.212862	+	0.0691632i	0.00731404	+	0.00237648i
$848$	8.97972	+	12.3595i	0.308365	+	0.424428i
$849$	15.7403			0.540204
$850$	3.37550	−	0.209204i	0.115779	−	0.00717563i
$851$	−48.9035			−1.67639
$852$	10.1866	+	14.0207i	0.348989	+	0.480342i
$853$	6.51336	+	2.11632i	0.223013	+	0.0724614i	0.418392	−	0.908266i	$-0.362594\pi$
$853$	6.51336	+	2.11632i	0.223013	+	0.0724614i	−0.195379	+	0.980728i	$0.562594\pi$
$854$	0.517379	−	1.59233i	0.0177043	−	0.0544884i
$855$	0.828671	−	0.0256548i	0.0283400	−	0.000877374i
$856$	4.54113	+	13.9762i	0.155213	+	0.477695i
$857$			10.0264i			0.342496i	0.985228	+	0.171248i	$0.0547800\pi$
$857$			10.0264i			0.342496i	−0.985228	+	0.171248i	$0.945220\pi$
$858$	3.42576	−	1.11310i	0.116954	−	0.0380005i
$859$	−41.8447	−	30.4020i	−1.42772	−	1.03730i	−0.990435	−	0.137980i	$-0.955939\pi$
$859$	−41.8447	−	30.4020i	−1.42772	−	1.03730i	−0.437288	−	0.899322i	$-0.644061\pi$
$860$	−1.30043	−	42.0052i	−0.0443445	−	1.43237i
$861$	2.67111	−	1.94067i	0.0910311	−	0.0661380i
$862$	−4.38147	+	6.03057i	−0.149233	+	0.205402i
$863$	10.2479	−	14.1050i	0.348841	−	0.480138i	−0.598157	−	0.801379i	$-0.704100\pi$
$863$	10.2479	−	14.1050i	0.348841	−	0.480138i	0.946998	+	0.321241i	$0.104100\pi$
$864$	−2.49884	+	1.81551i	−0.0850122	+	0.0617650i
$865$	10.3245	−	15.1768i	0.351043	−	0.516026i
$866$	3.58222	+	2.60263i	0.121729	+	0.0884410i
$867$	10.2197	−	3.32059i	0.347080	−	0.112773i
$868$		−	6.86215i		−	0.232917i
$869$	−2.25334	−	6.93507i	−0.0764394	−	0.235256i
$870$	0.964340	+	2.68249i	0.0326942	+	0.0909448i
$871$	−9.05881	+	27.8801i	−0.306946	+	0.944683i
$872$	4.43739	+	1.44180i	0.150269	+	0.0488254i
$873$	6.99211	+	9.62382i	0.236647	+	0.325717i
$874$	0.860281			0.0290994
$875$	5.70473	−	9.61541i	0.192855	−	0.325060i
$876$	21.3259			0.720537
$877$	2.54904	+	3.50845i	0.0860748	+	0.118472i	0.849883	−	0.526972i	$-0.176673\pi$
$877$	2.54904	+	3.50845i	0.0860748	+	0.118472i	−0.763808	+	0.645443i	$0.776673\pi$
$878$	−5.63086	−	1.82958i	−0.190032	−	0.0617453i
$879$	8.65133	−	26.6260i	0.291802	−	0.898074i
$880$	8.85633	+	24.6355i	0.298547	+	0.830462i
$881$	8.20228	+	25.2440i	0.276342	+	0.850492i	0.988861	+	0.148840i	$0.0475539\pi$
$881$	8.20228	+	25.2440i	0.276342	+	0.850492i	−0.712520	+	0.701652i	$0.752446\pi$
$882$		−	0.270463i		−	0.00910698i
$883$	25.2715	−	8.21121i	0.850454	−	0.276329i	0.148818	−	0.988865i	$-0.452453\pi$
$883$	25.2715	−	8.21121i	0.850454	−	0.276329i	0.701636	+	0.712535i	$0.252453\pi$
$884$	−15.8164	−	11.4913i	−0.531962	−	0.386493i
$885$	−1.20475	+	1.77096i	−0.0404973	+	0.0595302i
$886$	−4.37254	+	3.17683i	−0.146898	+	0.106728i
$887$	15.7360	−	21.6588i	0.528364	−	0.727231i	−0.458516	−	0.888686i	$-0.651619\pi$
$887$	15.7360	−	21.6588i	0.528364	−	0.727231i	0.986880	+	0.161455i	$0.0516188\pi$
$888$	−3.55865	+	4.89806i	−0.119421	+	0.164368i
$889$	17.6378	−	12.8146i	0.591552	−	0.429788i
$890$	−0.288874	−	9.33089i	−0.00968308	−	0.312772i
$891$	2.65577	+	1.92953i	0.0889716	+	0.0646416i
$892$	42.8773	−	13.9317i	1.43564	−	0.466467i
$893$			3.29692i			0.110327i
$894$	−0.865044	−	2.66233i	−0.0289314	−	0.0890417i
$895$	8.30097	−	0.256989i	0.277471	−	0.00859020i
$896$	−2.43527	+	7.49500i	−0.0813568	+	0.250390i
$897$	−33.1011	−	10.7552i	−1.10521	−	0.359106i
$898$	3.30499	+	4.54893i	0.110289	+	0.151800i
$899$	16.7861			0.559847
$900$	−2.40465	+	9.32933i	−0.0801551	+	0.310978i
$901$	10.7127			0.356892
$902$	−1.72303	−	2.37155i	−0.0573707	−	0.0789640i
$903$	−9.27651	−	3.01412i	−0.308703	−	0.100304i
$904$	2.72624	−	8.39050i	0.0906734	−	0.279064i
$905$	−34.1584	+	26.4704i	−1.13546	+	0.879907i
$906$	−1.70238	−	5.23940i	−0.0565579	−	0.174067i
$907$		−	8.70881i		−	0.289171i	−0.989492	−	0.144586i	$-0.953815\pi$
$907$		−	8.70881i		−	0.289171i	0.989492	−	0.144586i	$-0.0461849\pi$
$908$	−18.5803	+	6.03710i	−0.616608	+	0.200348i
$909$	5.18713	+	3.76867i	0.172046	+	0.124999i
$910$	2.30893	−	0.830049i	0.0765404	−	0.0275159i
$911$	36.6980	−	26.6627i	1.21586	−	0.883374i	0.220110	−	0.975475i	$-0.429358\pi$
$911$	36.6980	−	26.6627i	1.21586	−	0.883374i	0.995750	+	0.0921009i	$0.0293582\pi$
$912$	−0.777248	+	1.06979i	−0.0257373	+	0.0354243i
$913$	−22.5864	+	31.0875i	−0.747500	+	1.02885i
$914$	−5.01852	+	3.64617i	−0.165998	+	0.120604i
$915$	8.47883	+	10.9414i	0.280301	+	0.361711i
$916$	−33.5069	−	24.3442i	−1.10710	−	0.804353i
$917$	−17.7820	+	5.77774i	−0.587215	+	0.190798i
$918$			0.676394i			0.0223243i
$919$	−5.29226	−	16.2879i	−0.174575	−	0.537288i	0.825038	−	0.565077i	$-0.191153\pi$
$919$	−5.29226	−	16.2879i	−0.174575	−	0.537288i	−0.999614	+	0.0277888i	$0.991153\pi$
$920$	−5.69314	+	19.5618i	−0.187697	+	0.644934i
$921$	−4.46737	+	13.7491i	−0.147205	+	0.453050i
$922$	0.969765	+	0.315096i	0.0319375	+	0.0103771i
$923$	21.4483	+	29.5211i	0.705980	+	0.971698i
$924$	6.32529			0.208087
$925$	1.76313	+	28.4480i	0.0579712	+	0.935364i
$926$	4.92022			0.161688
$927$	−2.18769	−	3.01109i	−0.0718530	−	0.0988972i
$928$	−13.8460	−	4.49883i	−0.454516	−	0.147681i
$929$	−13.9064	+	42.7994i	−0.456253	+	1.40420i	0.413404	+	0.910548i	$0.364340\pi$
$929$	−13.9064	+	42.7994i	−0.456253	+	1.40420i	−0.869657	+	0.493656i	$0.835660\pi$
$930$	−1.78080	−	1.21145i	−0.0583949	−	0.0397250i
$931$	−0.114574	−	0.352624i	−0.00375502	−	0.0115568i
$932$		−	12.0574i		−	0.394954i
$933$	2.19626	−	0.713607i	0.0719022	−	0.0233624i
$934$	−4.22073	−	3.06654i	−0.138106	−	0.100340i
$935$	17.6260	+	5.12975i	0.576432	+	0.167761i
$936$	−3.48594	+	2.53269i	−0.113942	+	0.0827835i
$937$	33.4691	−	46.0663i	1.09339	−	1.50492i	0.249518	−	0.968370i	$-0.419728\pi$
$937$	33.4691	−	46.0663i	1.09339	−	1.50492i	0.843869	−	0.536549i	$-0.180272\pi$
$938$	1.14870	−	1.58105i	0.0375063	−	0.0516230i
$939$	−0.798572	+	0.580196i	−0.0260604	+	0.0189340i
$940$	−36.7859	−	10.7059i	−1.19982	−	0.349188i
$941$	−14.2393	−	10.3454i	−0.464187	−	0.337252i	0.330985	−	0.943636i	$-0.392619\pi$
$941$	−14.2393	−	10.3454i	−0.464187	−	0.337252i	−0.795171	+	0.606385i	$0.792619\pi$
$942$	−3.14282	+	1.02117i	−0.102399	+	0.0332714i
$943$			28.3244i			0.922369i
$944$	−1.05568	−	3.24905i	−0.0343594	−	0.105747i
$945$	1.84882	+	1.25772i	0.0601422	+	0.0409136i
$946$	−2.67610	+	8.23618i	−0.0870074	+	0.267781i
$947$	−47.3729	−	15.3924i	−1.53941	−	0.500185i	−0.588198	−	0.808717i	$-0.700162\pi$
$947$	−47.3729	−	15.3924i	−1.53941	−	0.500185i	−0.951214	+	0.308532i	$0.900162\pi$
$948$	2.51581	+	3.46272i	0.0817099	+	0.112464i
$949$	44.9025			1.45760
$950$	−0.0310158	−	0.500439i	−0.00100629	−	0.0162364i
$951$	−0.561163			−0.0181970
$952$	1.56122	+	2.14883i	0.0505993	+	0.0696440i
$953$	−45.3396	−	14.7317i	−1.46869	−	0.477207i	−0.537980	−	0.842958i	$-0.680812\pi$
$953$	−45.3396	−	14.7317i	−1.46869	−	0.477207i	−0.930713	+	0.365751i	$0.880812\pi$
$954$	0.358013	−	1.10185i	0.0115911	−	0.0356738i
$955$	3.34712	−	11.5008i	0.108310	−	0.372158i
$956$	−4.48276	−	13.7965i	−0.144983	−	0.446211i
$957$			15.4728i			0.500165i
$958$	−2.90587	+	0.944175i	−0.0938844	+	0.0305049i
$959$	−9.88182	−	7.17956i	−0.319101	−	0.231840i
$960$	−8.62555	−	11.1307i	−0.278388	−	0.359242i
$961$	14.8187	−	10.7664i	0.478022	−	0.347303i
$962$	−3.67664	+	5.06046i	−0.118540	+	0.163156i
$963$	−8.13293	+	11.1940i	−0.262080	+	0.360722i
$964$	−17.3329	+	12.5931i	−0.558254	+	0.405595i
$965$	−33.5748	+	12.0700i	−1.08081	+	0.388545i
$966$	1.87712	+	1.36381i	0.0603954	+	0.0438799i
$967$	32.9772	−	10.7149i	1.06047	−	0.344569i	0.273703	−	0.961814i	$-0.411751\pi$
$967$	32.9772	−	10.7149i	1.06047	−	0.344569i	0.786771	+	0.617245i	$0.211751\pi$
$968$			0.237709i			0.00764026i
$969$	0.286536	+	0.881867i	0.00920486	+	0.0283296i
$970$	5.68660	−	4.40673i	0.182586	−	0.141492i
$971$	−16.0586	+	49.4233i	−0.515345	+	1.58607i	0.267308	+	0.963611i	$0.413866\pi$
$971$	−16.0586	+	49.4233i	−0.515345	+	1.58607i	−0.782653	+	0.622458i	$0.786134\pi$
$972$	−1.83254	−	0.595429i	−0.0587788	−	0.0190984i
$973$	6.76703	+	9.31402i	0.216941	+	0.298594i
$974$	4.40805			0.141243
$975$	−5.06308	+	19.6432i	−0.162148	+	0.629086i
$976$	−22.0777			−0.706690
$977$	−1.54772	−	2.13026i	−0.0495161	−	0.0681530i	0.783541	−	0.621340i	$-0.213411\pi$
$977$	−1.54772	−	2.13026i	−0.0495161	−	0.0681530i	−0.833057	+	0.553187i	$0.813411\pi$
$978$	−4.35868	−	1.41622i	−0.139375	−	0.0452857i
$979$	15.6586	−	48.1922i	0.500450	−	1.54023i
$980$	4.30650	−	0.133325i	0.137566	−	0.00425890i
$981$	1.35753	+	4.17806i	0.0433427	+	0.133395i
$982$			9.43661i			0.301134i
$983$	50.6429	−	16.4549i	1.61526	−	0.524829i	0.644440	−	0.764655i	$-0.277090\pi$
$983$	50.6429	−	16.4549i	1.61526	−	0.524829i	0.970816	+	0.239826i	$0.0770904\pi$
$984$	2.83690	+	2.06113i	0.0904372	+	0.0657064i
$985$	0.879830	+	28.4193i	0.0280337	+	0.905513i
$986$	−2.57925	+	1.87394i	−0.0821402	+	0.0596783i
$987$	−5.22663	+	7.19384i	−0.166365	+	0.228982i
$988$	−1.70366	+	2.34488i	−0.0542005	+	0.0746006i
$989$	67.6959	−	49.1839i	2.15260	−	1.56396i
$990$	1.11667	−	1.64148i	0.0354901	−	0.0521697i
$991$	8.52078	+	6.19071i	0.270671	+	0.196654i	0.714838	−	0.699290i	$-0.246500\pi$
$991$	8.52078	+	6.19071i	0.270671	+	0.196654i	−0.444167	+	0.895944i	$0.646500\pi$
$992$	10.4616	−	3.39919i	0.332157	−	0.107924i
$993$		−	20.8230i		−	0.660797i
$994$	−0.751719	−	2.31355i	−0.0238431	−	0.0733815i
$995$	−3.65912	−	10.1785i	−0.116002	−	0.322680i
$996$	6.96988	−	21.4511i	0.220849	−	0.679704i
$997$	22.6988	+	7.37527i	0.718877	+	0.233577i	0.645536	−	0.763730i	$-0.276634\pi$
$997$	22.6988	+	7.37527i	0.718877	+	0.233577i	0.0733408	+	0.997307i	$0.476634\pi$
$998$	1.67598	+	2.30679i	0.0530521	+	0.0730200i
$999$	−5.70051			−0.180356

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.a.64.7	✓	56
25.9	even	10	inner	525.2.z.a.484.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.a.64.7	✓	56	1.1	even	1	trivial
525.2.z.a.484.7	yes	56	25.9	even	10	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.158974 + 0.218810i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.595429 - 1.83254i) q^{4} +(-0.756459 - 2.10423i) q^{5} +(-0.0835778 - 0.257226i) q^{6} -1.00000i q^{7} +(1.01009 - 0.328197i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.158974 + 0.218810i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.595429 - 1.83254i) q^{4} +(-0.756459 - 2.10423i) q^{5} +(-0.0835778 - 0.257226i) q^{6} -1.00000i q^{7} +(1.01009 - 0.328197i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.340167 - 0.500039i) q^{10} +(2.65577 - 1.92953i) q^{11} +(-1.13257 + 1.55885i) q^{12} +(-2.38467 + 3.28222i) q^{13} +(0.218810 - 0.158974i) q^{14} +(0.0691931 + 2.23500i) q^{15} +(-2.88532 - 2.09631i) q^{16} +(-2.37847 + 0.772812i) q^{17} +0.270463i q^{18} +(0.114574 + 0.352624i) q^{19} +(-4.30650 + 0.133325i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(0.844398 + 0.274362i) q^{22} +(-5.04249 - 6.94039i) q^{23} -1.06207 q^{24} +(-3.85554 + 3.18352i) q^{25} -1.09728 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-1.83254 - 0.595429i) q^{28} +(1.45653 - 4.48273i) q^{29} +(-0.478039 + 0.370448i) q^{30} +(1.10051 + 3.38703i) q^{31} -3.08873i q^{32} +(-3.12204 + 1.01441i) q^{33} +(-0.547215 - 0.397575i) q^{34} +(-2.10423 + 0.756459i) q^{35} +(1.55885 - 1.13257i) q^{36} +(3.35068 - 4.61181i) q^{37} +(-0.0589430 + 0.0811281i) q^{38} +(3.28222 - 2.38467i) q^{39} +(-1.45469 - 1.87719i) q^{40} +(-2.67111 - 1.94067i) q^{41} +(-0.257226 + 0.0835778i) q^{42} +9.75390i q^{43} +(-1.95462 - 6.01571i) q^{44} +(0.624846 - 2.14699i) q^{45} +(0.716997 - 2.20669i) q^{46} +(8.45686 + 2.74780i) q^{47} +(2.09631 + 2.88532i) q^{48} -1.00000 q^{49} +(-1.30952 - 0.337531i) q^{50} +2.50087 q^{51} +(4.59490 + 6.32434i) q^{52} +(-4.07394 - 1.32370i) q^{53} +(0.0835778 - 0.257226i) q^{54} +(-6.06914 - 4.12873i) q^{55} +(-0.328197 - 1.01009i) q^{56} -0.370771i q^{57} +(1.21242 - 0.393938i) q^{58} +(0.774946 + 0.563031i) q^{59} +(4.13693 + 1.20398i) q^{60} +(5.00813 - 3.63862i) q^{61} +(-0.566161 + 0.779254i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-5.09479 + 3.70158i) q^{64} +(8.71044 + 2.53503i) q^{65} +(-0.718288 - 0.521867i) q^{66} +(6.87203 - 2.23286i) q^{67} +4.81880i q^{68} +(2.65099 + 8.15892i) q^{69} +(-0.500039 - 0.340167i) q^{70} +(2.77937 - 8.55403i) q^{71} +(1.01009 + 0.328197i) q^{72} +(-6.50548 - 8.95402i) q^{73} +1.54178 q^{74} +(4.65060 - 1.83628i) q^{75} +0.714419 q^{76} +(-1.92953 - 2.65577i) q^{77} +(1.04358 + 0.339079i) q^{78} +(0.686427 - 2.11261i) q^{79} +(-2.22848 + 7.65713i) q^{80} +(0.309017 + 0.951057i) q^{81} -0.892982i q^{82} +(-11.1327 + 3.61724i) q^{83} +(1.55885 + 1.13257i) q^{84} +(3.42539 + 4.42024i) q^{85} +(-2.13425 + 1.55062i) q^{86} +(-2.77048 + 3.81324i) q^{87} +(2.04929 - 2.82061i) q^{88} +(12.4881 - 9.07311i) q^{89} +(0.569117 - 0.204594i) q^{90} +(3.28222 + 2.38467i) q^{91} +(-15.7210 + 5.10807i) q^{92} -3.56133i q^{93} +(0.743180 + 2.28727i) q^{94} +(0.655330 - 0.507836i) q^{95} +(-0.954471 + 2.93756i) q^{96} +(11.3135 + 3.67597i) q^{97} +(-0.158974 - 0.218810i) q^{98} +3.28271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

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