LMFDB - Embedded newform 825.2.cb.a.169.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(169,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("825.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.cb (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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.15
Character	$\chi$	$=$	825.169
Dual form			825.2.cb.a.454.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.42855 - 0.464164i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.207274 + 0.150593i) q^{4} +(-1.19097 - 1.89251i) q^{5} +1.50207 q^{6} +(4.03713 - 1.31174i) q^{7} +(1.53958 + 2.11906i) q^{8} +(0.809017 - 0.587785i) q^{9} +(0.822929 + 3.25635i) q^{10} +(0.298062 + 3.30320i) q^{11} +(-0.243665 - 0.0791716i) q^{12} +(-0.623267 - 0.857854i) q^{13} -6.37611 q^{14} +(1.71750 + 1.43185i) q^{15} +(-1.37413 - 4.22913i) q^{16} +4.54852i q^{17} +(-1.42855 + 0.464164i) q^{18} +(0.838749 - 0.609387i) q^{19} +(0.0381416 - 0.571620i) q^{20} +(-3.43419 + 2.49508i) q^{21} +(1.10743 - 4.85714i) q^{22} +(-4.25799 + 1.38351i) q^{23} +(-2.11906 - 1.53958i) q^{24} +(-2.16317 + 4.50785i) q^{25} +(0.492184 + 1.51479i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(1.03433 + 0.336075i) q^{28} +(7.06541 + 5.13332i) q^{29} +(-1.78892 - 2.84267i) q^{30} +(0.518636 + 1.59620i) q^{31} +1.44075i q^{32} +(-1.30422 - 3.04943i) q^{33} +(2.11126 - 6.49779i) q^{34} +(-7.29060 - 6.07805i) q^{35} +0.256205 q^{36} -7.44406i q^{37} +(-1.48105 + 0.481222i) q^{38} +(0.857854 + 0.623267i) q^{39} +(2.17673 - 5.43741i) q^{40} +(7.87262 + 5.71979i) q^{41} +(6.06404 - 1.97033i) q^{42} +6.16231i q^{43} +(-0.435660 + 0.729554i) q^{44} +(-2.07590 - 0.831035i) q^{45} +6.72493 q^{46} +(-1.88396 + 0.612137i) q^{47} +(2.61375 + 3.59751i) q^{48} +(8.91464 - 6.47687i) q^{49} +(5.18258 - 5.43562i) q^{50} +(-1.40557 - 4.32590i) q^{51} -0.271671i q^{52} -9.55636i q^{53} +(1.21520 - 0.882893i) q^{54} +(5.89636 - 4.49811i) q^{55} +(8.99516 + 6.53537i) q^{56} +(-0.609387 + 0.838749i) q^{57} +(-7.71059 - 10.6127i) q^{58} +6.18756 q^{59} +(0.140366 + 0.555429i) q^{60} +(8.19988 + 5.95756i) q^{61} -2.52098i q^{62} +(2.49508 - 3.43419i) q^{63} +(-2.07951 + 6.40007i) q^{64} +(-0.881201 + 2.20122i) q^{65} +(0.447709 + 4.96163i) q^{66} +(1.25773 - 1.73111i) q^{67} +(-0.684977 + 0.942790i) q^{68} +(3.62206 - 2.63158i) q^{69} +(7.59377 + 12.0668i) q^{70} +(-2.19449 + 6.75393i) q^{71} +(2.49110 + 0.809407i) q^{72} +(4.77315 + 6.56967i) q^{73} +(-3.45527 + 10.6342i) q^{74} +(0.664297 - 4.95567i) q^{75} +0.265620 q^{76} +(5.53627 + 12.9445i) q^{77} +(-0.936189 - 1.28855i) q^{78} +13.9684 q^{79} +(-6.36711 + 7.63732i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-8.59151 - 11.8252i) q^{82} -14.3063i q^{83} -1.08756 q^{84} +(8.60811 - 5.41716i) q^{85} +(2.86032 - 8.80317i) q^{86} +(-8.30588 - 2.69874i) q^{87} +(-6.54078 + 5.71717i) q^{88} +(-1.86413 - 5.73720i) q^{89} +(2.57980 + 2.15074i) q^{90} +(-3.64150 - 2.64570i) q^{91} +(-1.09092 - 0.354461i) q^{92} +(-0.986504 - 1.35781i) q^{93} +2.97547 q^{94} +(-2.15220 - 0.861576i) q^{95} +(-0.445216 - 1.37023i) q^{96} +5.91852i q^{97} +(-15.7413 + 5.11467i) q^{98} +(2.18271 + 2.49715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 60 q^{4} + 6 q^{5} - 16 q^{6} + 10 q^{7} + 60 q^{9} + 8 q^{10} + 4 q^{11} - 20 q^{12} - 64 q^{16} - 24 q^{19} - 44 q^{20} + 8 q^{21} - 40 q^{22} + 40 q^{23} - 12 q^{24} + 4 q^{25} + 40 q^{26} + 30 q^{28}+ \cdots - 4 q^{99}+O(q^{100}) $ 240 * q + 60 * q^4 + 6 * q^5 - 16 * q^6 + 10 * q^7 + 60 * q^9 + 8 * q^10 + 4 * q^11 - 20 * q^12 - 64 * q^16 - 24 * q^19 - 44 * q^20 + 8 * q^21 - 40 * q^22 + 40 * q^23 - 12 * q^24 + 4 * q^25 + 40 * q^26 + 30 * q^28 + 4 * q^30 - 2 * q^31 + 30 * q^35 + 240 * q^36 - 16 * q^39 + 68 * q^40 - 6 * q^41 - 10 * q^42 + 26 * q^44 + 4 * q^45 - 48 * q^46 - 40 * q^47 + 40 * q^48 + 58 * q^49 - 78 * q^50 + 16 * q^51 - 4 * q^54 - 10 * q^55 - 40 * q^57 + 60 * q^58 - 24 * q^59 + 8 * q^60 + 28 * q^61 - 10 * q^63 + 44 * q^64 + 60 * q^65 + 8 * q^66 - 40 * q^67 - 250 * q^68 + 2 * q^69 - 44 * q^70 - 16 * q^71 + 22 * q^74 + 20 * q^75 - 168 * q^76 - 30 * q^77 + 172 * q^79 - 118 * q^80 - 60 * q^81 + 40 * q^82 + 96 * q^84 + 40 * q^85 - 72 * q^86 - 40 * q^87 - 100 * q^88 + 2 * q^90 - 30 * q^91 + 100 * q^92 + 56 * q^94 - 122 * q^95 + 28 * q^96 - 140 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	−1.42855	−	0.464164i	−1.01014	−	0.328214i	−0.243228	−	0.969969i	$-0.578206\pi$
$2$	−1.42855	−	0.464164i	−1.01014	−	0.328214i	−0.766909	+	0.641755i	$0.778206\pi$
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	0.207274	+	0.150593i	0.103637	+	0.0752967i
$5$	−1.19097	−	1.89251i	−0.532619	−	0.846355i
$5$	−1.19097	−	1.89251i	−0.532619	−	0.846355i
$6$	1.50207			0.613216
$7$	4.03713	−	1.31174i	1.52589	−	0.495792i	0.578450	−	0.815718i	$-0.303658\pi$
$7$	4.03713	−	1.31174i	1.52589	−	0.495792i	0.947443	+	0.319926i	$0.103658\pi$
$8$	1.53958	+	2.11906i	0.544325	+	0.749199i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	0.822929	+	3.25635i	0.260233	+	1.02975i
$11$	0.298062	+	3.30320i	0.0898690	+	0.995954i
$11$	0.298062	+	3.30320i	0.0898690	+	0.995954i
$12$	−0.243665	−	0.0791716i	−0.0703401	−	0.0228549i
$13$	−0.623267	−	0.857854i	−0.172863	−	0.237926i	0.713791	−	0.700359i	$-0.246977\pi$
$13$	−0.623267	−	0.857854i	−0.172863	−	0.237926i	−0.886654	+	0.462433i	$0.846977\pi$
$14$	−6.37611			−1.70409
$15$	1.71750	+	1.43185i	0.443456	+	0.369702i
$16$	−1.37413	−	4.22913i	−0.343532	−	1.05728i
$17$			4.54852i			1.10318i	0.834116	+	0.551589i	$0.185978\pi$
$17$			4.54852i			1.10318i	−0.834116	+	0.551589i	$0.814022\pi$
$18$	−1.42855	+	0.464164i	−0.336713	+	0.109405i
$19$	0.838749	−	0.609387i	0.192422	−	0.139803i	−0.487403	−	0.873177i	$-0.662056\pi$
$19$	0.838749	−	0.609387i	0.192422	−	0.139803i	0.679825	+	0.733374i	$0.262056\pi$
$20$	0.0381416	−	0.571620i	0.00852872	−	0.127818i
$21$	−3.43419	+	2.49508i	−0.749402	+	0.544472i
$22$	1.10743	−	4.85714i	0.236106	−	1.03555i
$23$	−4.25799	+	1.38351i	−0.887852	+	0.288481i	−0.717214	−	0.696853i	$-0.754583\pi$
$23$	−4.25799	+	1.38351i	−0.887852	+	0.288481i	−0.170638	+	0.985334i	$0.554583\pi$
$24$	−2.11906	−	1.53958i	−0.432550	−	0.314266i
$25$	−2.16317	+	4.50785i	−0.432634	+	0.901570i
$26$	0.492184	+	1.51479i	0.0965251	+	0.297074i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	1.03433	+	0.336075i	0.195470	+	0.0635122i
$29$	7.06541	+	5.13332i	1.31201	+	0.953233i	0.999995	+	0.00315687i	$0.00100486\pi$
$29$	7.06541	+	5.13332i	1.31201	+	0.953233i	0.312018	+	0.950076i	$0.398995\pi$
$30$	−1.78892	−	2.84267i	−0.326611	−	0.518999i
$31$	0.518636	+	1.59620i	0.0931498	+	0.286685i	0.986767	−	0.162144i	$-0.0518410\pi$
$31$	0.518636	+	1.59620i	0.0931498	+	0.286685i	−0.893617	+	0.448830i	$0.851841\pi$
$32$			1.44075i			0.254691i
$33$	−1.30422	−	3.04943i	−0.227036	−	0.530837i
$34$	2.11126	−	6.49779i	0.362078	−	1.11436i
$35$	−7.29060	−	6.07805i	−1.23234	−	1.02738i
$36$	0.256205			0.0427008
$37$		−	7.44406i		−	1.22380i	−0.790937	−	0.611898i	$-0.790406\pi$
$37$		−	7.44406i		−	1.22380i	0.790937	−	0.611898i	$-0.209594\pi$
$38$	−1.48105	+	0.481222i	−0.240258	+	0.0780646i
$39$	0.857854	+	0.623267i	0.137366	+	0.0998026i
$40$	2.17673	−	5.43741i	0.344171	−	0.859730i
$41$	7.87262	+	5.71979i	1.22950	+	0.893281i	0.996852	−	0.0792805i	$-0.0252623\pi$
$41$	7.87262	+	5.71979i	1.22950	+	0.893281i	0.232644	+	0.972562i	$0.425262\pi$
$42$	6.06404	−	1.97033i	0.935702	−	0.304028i
$43$			6.16231i			0.939743i	0.882735	+	0.469872i	$0.155700\pi$
$43$			6.16231i			0.939743i	−0.882735	+	0.469872i	$0.844300\pi$
$44$	−0.435660	+	0.729554i	−0.0656783	+	0.109984i
$45$	−2.07590	−	0.831035i	−0.309458	−	0.123883i
$46$	6.72493			0.991537
$47$	−1.88396	+	0.612137i	−0.274804	+	0.0892894i	−0.443177	−	0.896434i	$-0.646149\pi$
$47$	−1.88396	+	0.612137i	−0.274804	+	0.0892894i	0.168373	+	0.985723i	$0.446149\pi$
$48$	2.61375	+	3.59751i	0.377262	+	0.519256i
$49$	8.91464	−	6.47687i	1.27352	−	0.925267i
$50$	5.18258	−	5.43562i	0.732928	−	0.768713i
$51$	−1.40557	−	4.32590i	−0.196819	−	0.605747i
$52$		−	0.271671i		−	0.0376739i
$53$		−	9.55636i		−	1.31267i	−0.754471	−	0.656334i	$-0.772106\pi$
$53$		−	9.55636i		−	1.31267i	0.754471	−	0.656334i	$-0.227894\pi$
$54$	1.21520	−	0.882893i	0.165367	−	0.120146i
$55$	5.89636	−	4.49811i	0.795065	−	0.606525i
$56$	8.99516	+	6.53537i	1.20203	+	0.873325i
$57$	−0.609387	+	0.838749i	−0.0807152	+	0.111095i
$58$	−7.71059	−	10.6127i	−1.01245	−	1.39352i
$59$	6.18756			0.805552			0.402776	−	0.915299i	$-0.368045\pi$
$59$	6.18756			0.805552			0.402776	+	0.915299i	$0.368045\pi$
$60$	0.140366	+	0.555429i	0.0181211	+	0.0717056i
$61$	8.19988	+	5.95756i	1.04989	+	0.762787i	0.972191	−	0.234190i	$-0.0752437\pi$
$61$	8.19988	+	5.95756i	1.04989	+	0.762787i	0.0776957	+	0.996977i	$0.475244\pi$
$62$		−	2.52098i		−	0.320165i
$63$	2.49508	−	3.43419i	0.314351	−	0.432667i
$64$	−2.07951	+	6.40007i	−0.259939	+	0.800009i
$65$	−0.881201	+	2.20122i	−0.109300	+	0.273027i
$66$	0.447709	+	4.96163i	0.0551091	+	0.610735i
$67$	1.25773	−	1.73111i	0.153656	−	0.211489i	−0.725249	−	0.688487i	$-0.758275\pi$
$67$	1.25773	−	1.73111i	0.153656	−	0.211489i	0.878904	+	0.476998i	$0.158275\pi$
$68$	−0.684977	+	0.942790i	−0.0830657	+	0.114330i
$69$	3.62206	−	2.63158i	0.436045	−	0.316805i
$70$	7.59377	+	12.0668i	0.907629	+	1.44226i
$71$	−2.19449	+	6.75393i	−0.260438	+	0.801545i	0.732272	+	0.681012i	$0.238460\pi$
$71$	−2.19449	+	6.75393i	−0.260438	+	0.801545i	−0.992709	+	0.120532i	$0.961540\pi$
$72$	2.49110	+	0.809407i	0.293579	+	0.0953896i
$73$	4.77315	+	6.56967i	0.558655	+	0.768922i	0.991155	−	0.132712i	$-0.0423685\pi$
$73$	4.77315	+	6.56967i	0.558655	+	0.768922i	−0.432500	+	0.901634i	$0.642368\pi$
$74$	−3.45527	+	10.6342i	−0.401667	+	1.23620i
$75$	0.664297	−	4.95567i	0.0767064	−	0.572232i
$76$	0.265620			0.0304687
$77$	5.53627	+	12.9445i	0.630917	+	1.47516i
$78$	−0.936189	−	1.28855i	−0.106003	−	0.145900i
$79$	13.9684			1.57157			0.785785	−	0.618499i	$-0.212259\pi$
$79$	13.9684			1.57157			0.785785	+	0.618499i	$0.212259\pi$
$80$	−6.36711	+	7.63732i	−0.711865	+	0.853878i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−8.59151	−	11.8252i	−0.948774	−	1.30587i
$83$		−	14.3063i		−	1.57032i	−0.619290	−	0.785162i	$-0.712580\pi$
$83$		−	14.3063i		−	1.57032i	0.619290	−	0.785162i	$-0.287420\pi$
$84$	−1.08756			−0.118663
$85$	8.60811	−	5.41716i	0.933681	−	0.587574i
$86$	2.86032	−	8.80317i	0.308437	−	0.949270i
$87$	−8.30588	−	2.69874i	−0.890484	−	0.289336i
$88$	−6.54078	+	5.71717i	−0.697250	+	0.609452i
$89$	−1.86413	−	5.73720i	−0.197597	−	0.608142i	−0.999936	−	0.0112738i	$-0.996411\pi$
$89$	−1.86413	−	5.73720i	−0.197597	−	0.608142i	0.802339	−	0.596869i	$-0.203589\pi$
$90$	2.57980	+	2.15074i	0.271935	+	0.226708i
$91$	−3.64150	−	2.64570i	−0.381732	−	0.277345i
$92$	−1.09092	−	0.354461i	−0.113736	−	0.0369551i
$93$	−0.986504	−	1.35781i	−0.102296	−	0.140798i
$94$	2.97547			0.306896
$95$	−2.15220	−	0.861576i	−0.220811	−	0.0883958i
$96$	−0.445216	−	1.37023i	−0.0454397	−	0.139849i
$97$			5.91852i			0.600934i	0.953792	+	0.300467i	$0.0971426\pi$
$97$			5.91852i			0.600934i	−0.953792	+	0.300467i	$0.902857\pi$
$98$	−15.7413	+	5.11467i	−1.59012	+	0.516660i
$99$	2.18271	+	2.49715i	0.219371	+	0.250973i
$100$	−1.12722	+	0.608600i	−0.112722	+	0.0608600i
$101$	−8.06261	−	5.85783i	−0.802259	−	0.582875i	0.109317	−	0.994007i	$-0.465134\pi$
$101$	−8.06261	−	5.85783i	−0.802259	−	0.582875i	−0.911576	+	0.411132i	$0.865134\pi$
$102$			6.83219i			0.676487i
$103$	0.829402	−	1.14157i	0.0817234	−	0.112483i	−0.766198	−	0.642605i	$-0.777854\pi$
$103$	0.829402	−	1.14157i	0.0817234	−	0.112483i	0.847921	+	0.530122i	$0.177854\pi$
$104$	0.858267	−	2.64148i	0.0841600	−	0.259018i
$105$	8.81199	+	3.52765i	0.859962	+	0.344264i
$106$	−4.43572	+	13.6517i	−0.430835	+	1.32597i
$107$	−8.32415	−	2.70468i	−0.804726	−	0.261471i	−0.122363	−	0.992485i	$-0.539047\pi$
$107$	−8.32415	−	2.70468i	−0.804726	−	0.261471i	−0.682362	+	0.731014i	$0.739047\pi$
$108$	−0.243665	+	0.0791716i	−0.0234467	+	0.00761829i
$109$	2.88733	−	8.88628i	0.276556	−	0.851152i	−0.712248	−	0.701928i	$-0.752323\pi$
$109$	2.88733	−	8.88628i	0.276556	−	0.851152i	0.988804	−	0.149223i	$-0.0476773\pi$
$110$	−10.5111	+	3.68890i	−1.00219	+	0.351722i
$111$	2.30034	+	7.07972i	0.218339	+	0.671978i
$112$	−11.0951	−	15.2710i	−1.04839	−	1.44298i
$113$	−0.142300	+	0.195860i	−0.0133865	+	0.0184249i	−0.815658	−	0.578535i	$-0.803625\pi$
$113$	−0.142300	+	0.195860i	−0.0133865	+	0.0184249i	0.802271	+	0.596960i	$0.203625\pi$
$114$	1.25986	−	0.915339i	0.117996	−	0.0857294i
$115$	7.68944	+	6.41056i	0.717044	+	0.597788i
$116$	0.691431	+	2.12801i	0.0641978	+	0.197580i
$117$	−1.00847	−	0.327671i	−0.0932328	−	0.0302932i
$118$	−8.83925	−	2.87205i	−0.813719	−	0.264393i
$119$	5.96650	+	18.3630i	0.546948	+	1.68333i
$120$	−0.389939	+	5.84393i	−0.0355964	+	0.533475i
$121$	−10.8223	+	1.96912i	−0.983847	+	0.179011i
$122$	−8.94865	−	12.3168i	−0.810173	−	1.11511i
$123$	−9.25482	−	3.00707i	−0.834479	−	0.271139i
$124$	−0.132877	+	0.408953i	−0.0119327	+	0.0367251i
$125$	11.1074	−	1.27490i	0.993477	−	0.114031i
$126$	−5.15838	+	3.74778i	−0.459545	+	0.333879i
$127$	7.92052	−	10.9017i	0.702833	−	0.967366i	−0.297089	−	0.954850i	$-0.596016\pi$
$127$	7.92052	−	10.9017i	0.702833	−	0.967366i	0.999922	−	0.0125166i	$-0.00398425\pi$
$128$	7.63507	−	10.5088i	0.674851	−	0.928853i
$129$	−1.90426	−	5.86070i	−0.167661	−	0.516006i
$130$	2.28057	−	2.73553i	0.200019	−	0.239922i
$131$	−3.11771	−	2.26515i	−0.272396	−	0.197907i	0.443198	−	0.896424i	$-0.353844\pi$
$131$	−3.11771	−	2.26515i	−0.272396	−	0.197907i	−0.715594	+	0.698517i	$0.753844\pi$
$132$	0.188893	−	0.828474i	0.0164410	−	0.0721094i
$133$	2.58678	−	3.56040i	0.224302	−	0.308726i
$134$	−2.60025	+	1.88919i	−0.224627	+	0.163201i
$135$	2.23111	+	0.148872i	0.192023	+	0.0128128i
$136$	−9.63857	+	7.00283i	−0.826501	+	0.600488i
$137$	12.0953	−	3.92999i	1.03337	−	0.335762i	0.257248	−	0.966346i	$-0.417184\pi$
$137$	12.0953	−	3.92999i	1.03337	−	0.335762i	0.776121	+	0.630584i	$0.217184\pi$
$138$	−6.39579	+	2.07812i	−0.544446	+	0.176901i
$139$	−5.94842	+	4.32178i	−0.504538	+	0.366568i	−0.810748	−	0.585396i	$-0.800939\pi$
$139$	−5.94842	+	4.32178i	−0.504538	+	0.366568i	0.306210	+	0.951964i	$0.400939\pi$
$140$	−0.595836	−	2.35774i	−0.0503574	−	0.199265i
$141$	1.60260	−	1.16435i	0.134963	−	0.0980563i
$142$	6.26987	−	8.62973i	0.526156	−	0.724191i
$143$	2.64789	−	2.31447i	0.221428	−	0.193546i
$144$	−3.59751	−	2.61375i	−0.299793	−	0.217812i
$145$	1.30014	−	19.4850i	0.107971	−	1.61814i
$146$	−3.76927	−	11.6006i	−0.311947	−	0.960075i
$147$	−6.47687	+	8.91464i	−0.534203	+	0.735267i
$148$	1.12103	−	1.54296i	0.0921478	−	0.126831i
$149$	13.5920	−	9.87518i	1.11350	−	0.809006i	0.130290	−	0.991476i	$-0.458409\pi$
$149$	13.5920	−	9.87518i	1.11350	−	0.809006i	0.983212	+	0.182470i	$0.0584091\pi$
$150$	−3.24923	+	6.77109i	−0.265298	+	0.552857i
$151$	−1.35633	+	4.17435i	−0.110376	+	0.339704i	−0.990955	−	0.134197i	$-0.957155\pi$
$151$	−1.35633	+	4.17435i	−0.110376	+	0.339704i	0.880578	+	0.473901i	$0.157155\pi$
$152$	2.58265	+	0.839153i	0.209480	+	0.0680643i
$153$	2.67355	+	3.67983i	0.216144	+	0.297497i
$154$	−1.90047	−	21.0616i	−0.153145	−	1.69719i
$155$	2.40313	−	2.88255i	0.193024	−	0.231532i
$156$	0.0839508	+	0.258374i	0.00672145	+	0.0206865i
$157$	6.45974	+	2.09890i	0.515543	+	0.167510i	0.555222	−	0.831702i	$-0.312633\pi$
$157$	6.45974	+	2.09890i	0.515543	+	0.167510i	−0.0396786	+	0.999212i	$0.512633\pi$
$158$	−19.9546	−	6.48364i	−1.58750	−	0.515811i
$159$	2.95308	+	9.08864i	0.234194	+	0.720776i
$160$	2.72663	−	1.71589i	0.215559	−	0.135653i
$161$	−15.3753	+	11.1708i	−1.21174	+	0.880381i
$162$	−0.882893	+	1.21520i	−0.0693666	+	0.0954749i
$163$	9.30697	+	12.8099i	0.728978	+	1.00335i	0.999178	+	0.0405481i	$0.0129104\pi$
$163$	9.30697	+	12.8099i	0.728978	+	1.00335i	−0.270199	+	0.962804i	$0.587090\pi$
$164$	0.770426	+	2.37113i	0.0601602	+	0.185154i
$165$	−4.21778	+	6.10003i	−0.328353	+	0.474887i
$166$	−6.64049	+	20.4373i	−0.515402	+	1.58624i
$167$	−12.3472	+	4.01184i	−0.955452	+	0.310445i	−0.744929	−	0.667144i	$-0.767517\pi$
$167$	−12.3472	+	4.01184i	−0.955452	+	0.310445i	−0.210523	+	0.977589i	$0.567517\pi$
$168$	−10.5744	−	3.43585i	−0.815836	−	0.265081i
$169$	3.66977	−	11.2944i	0.282290	−	0.868799i
$170$	−14.8116	+	3.74311i	−1.13600	+	0.287084i
$171$	0.320374	−	0.986008i	0.0244996	−	0.0754019i
$172$	−0.928003	+	1.27729i	−0.0707595	+	0.0973922i
$173$			23.0124i			1.74960i	0.484482	+	0.874801i	$0.339008\pi$
$173$			23.0124i			1.74960i	−0.484482	+	0.874801i	$0.660992\pi$
$174$	10.6127	+	7.71059i	0.804548	+	0.584538i
$175$	−2.81987	+	21.0363i	−0.213162	+	1.59019i
$176$	13.5601	−	5.79956i	1.02213	−	0.437159i
$177$	−5.88472	+	1.91206i	−0.442323	+	0.143719i
$178$			9.06115i			0.679162i
$179$	2.40832	+	7.41205i	0.180006	+	0.554003i	0.999827	−	0.0186181i	$-0.00592667\pi$
$179$	2.40832	+	7.41205i	0.180006	+	0.554003i	−0.819820	+	0.572621i	$0.805927\pi$
$180$	−0.305133	−	0.484869i	−0.0227432	−	0.0361400i
$181$	8.12073			0.603609			0.301805	−	0.953370i	$-0.402411\pi$
$181$	8.12073			0.603609			0.301805	+	0.953370i	$0.402411\pi$
$182$	3.97402	+	5.46977i	0.294574	+	0.405446i
$183$	−9.63953	−	3.13207i	−0.712575	−	0.231530i
$184$	−9.48726	−	6.89290i	−0.699410	−	0.508151i
$185$	−14.0879	+	8.86567i	−1.03577	+	0.651817i
$186$	0.779026	+	2.39759i	0.0571209	+	0.175800i
$187$	−15.0247	+	1.35574i	−1.09871	+	0.0991416i
$188$	−0.482681	−	0.156832i	−0.0352031	−	0.0114382i
$189$	−1.31174	+	4.03713i	−0.0954153	+	0.293658i
$190$	2.67461	+	2.22978i	0.194036	+	0.161765i
$191$	−4.41424			−0.319403			−0.159702	−	0.987165i	$-0.551053\pi$
$191$	−4.41424			−0.319403			−0.159702	+	0.987165i	$0.551053\pi$
$192$		−	6.72944i		−	0.485655i
$193$	−4.94358	−	6.80426i	−0.355847	−	0.489781i	0.593139	−	0.805100i	$-0.297889\pi$
$193$	−4.94358	−	6.80426i	−0.355847	−	0.489781i	−0.948986	+	0.315319i	$0.897889\pi$
$194$	2.74716	−	8.45490i	0.197235	−	0.607026i
$195$	0.157858	−	2.36579i	0.0113045	−	0.169418i
$196$	2.82315			0.201653
$197$	−15.8935	−	21.8755i	−1.13237	−	1.55857i	−0.783497	−	0.621396i	$-0.786566\pi$
$197$	−15.8935	−	21.8755i	−1.13237	−	1.55857i	−0.348869	−	0.937172i	$-0.613434\pi$
$198$	−1.95903	−	4.58044i	−0.139222	−	0.325518i
$199$	4.88511			0.346296			0.173148	−	0.984896i	$-0.444606\pi$
$199$	4.88511			0.346296			0.173148	+	0.984896i	$0.444606\pi$
$200$	−12.8828	+	2.35633i	−0.910949	+	0.166618i
$201$	−0.661226	+	2.03505i	−0.0466393	+	0.143541i
$202$	8.79885	+	12.1106i	0.619085	+	0.852097i
$203$	35.2576	+	11.4559i	2.47460	+	0.804045i
$204$	0.360114	−	1.10832i	0.0252130	−	0.0775977i
$205$	1.44868	−	21.7111i	0.101180	−	1.51637i
$206$	−1.71472	+	1.24582i	−0.119470	+	0.0868002i
$207$	−2.63158	+	3.62206i	−0.182908	+	0.251751i
$208$	−2.77152	+	3.81468i	−0.192171	+	0.264500i
$209$	2.26293	+	2.58892i	0.156530	+	0.179080i
$210$	−10.9510	−	9.12964i	−0.755688	−	0.630005i
$211$	−4.28963	+	13.2021i	−0.295310	+	0.908871i	0.687807	+	0.725893i	$0.258573\pi$
$211$	−4.28963	+	13.2021i	−0.295310	+	0.908871i	−0.983117	+	0.182977i	$0.941427\pi$
$212$	1.43912	−	1.98079i	0.0988395	−	0.136041i
$213$		−	7.10151i		−	0.486587i
$214$	10.6361	+	7.72754i	0.727066	+	0.528244i
$215$	11.6622	−	7.33914i	0.795356	−	0.500525i
$216$	−2.61930			−0.178221
$217$	4.18760	+	5.76374i	0.284273	+	0.391268i
$218$	−8.24939	+	11.3543i	−0.558719	+	0.769011i
$219$	−6.56967	−	4.77315i	−0.443937	−	0.322539i
$220$	1.89955	−	0.0443885i	0.128067	−	0.00299267i
$221$	3.90197	−	2.83494i	0.262475	−	0.190699i
$222$		−	11.1815i		−	0.750452i
$223$			22.4959i			1.50644i	0.657771	+	0.753218i	$0.271499\pi$
$223$			22.4959i			1.50644i	−0.657771	+	0.753218i	$0.728501\pi$
$224$	1.88989	+	5.81650i	0.126274	+	0.388631i
$225$	0.899604	+	4.91841i	0.0599736	+	0.327894i
$226$	0.294194	−	0.213745i	0.0195695	−	0.0142181i
$227$	−7.07887	−	9.74323i	−0.469841	−	0.646681i	0.506672	−	0.862139i	$-0.330876\pi$
$227$	−7.07887	−	9.74323i	−0.469841	−	0.646681i	−0.976513	+	0.215458i	$0.930876\pi$
$228$	−0.252620	+	0.0820812i	−0.0167302	+	0.00543596i
$229$	−6.97038			−0.460616			−0.230308	−	0.973118i	$-0.573973\pi$
$229$	−6.97038			−0.460616			−0.230308	+	0.973118i	$0.573973\pi$
$230$	−8.00920	−	12.7270i	−0.528111	−	0.839192i
$231$	−9.26537	−	10.6001i	−0.609617	−	0.697438i
$232$			22.8752i			1.50183i
$233$	−26.8229	+	8.71527i	−1.75722	+	0.570957i	−0.996907	−	0.0785958i	$-0.974956\pi$
$233$	−26.8229	+	8.71527i	−1.75722	+	0.570957i	−0.760317	+	0.649552i	$0.774956\pi$
$234$	1.28855	+	0.936189i	0.0842354	+	0.0612006i
$235$	3.40222	+	2.83638i	0.221937	+	0.185025i
$236$	1.28252	+	0.931806i	0.0834850	+	0.0606554i
$237$	−13.2848	+	4.31648i	−0.862938	+	0.280386i
$238$		−	29.0019i		−	1.87991i
$239$	11.6758			0.755247			0.377623	−	0.925959i	$-0.376741\pi$
$239$	11.6758			0.755247			0.377623	+	0.925959i	$0.376741\pi$
$240$	3.69542	−	9.23107i	0.238538	−	0.595863i
$241$	−1.60328	+	4.93439i	−0.103276	+	0.317852i	−0.989322	−	0.145746i	$-0.953442\pi$
$241$	−1.60328	+	4.93439i	−0.103276	+	0.317852i	0.886046	+	0.463598i	$0.153442\pi$
$242$	16.3742	+	2.21035i	1.05257	+	0.142087i
$243$			1.00000i			0.0641500i
$244$	0.802452	+	2.46969i	0.0513717	+	0.158106i
$245$	−22.8746	−	9.15726i	−1.46141	−	0.585036i
$246$	11.8252	+	8.59151i	0.753947	+	0.547775i
$247$	−1.04553	−	0.339713i	−0.0665254	−	0.0216154i
$248$	−2.58395	+	3.55650i	−0.164081	+	0.225838i
$249$	4.42090	+	13.6061i	0.280163	+	0.862254i
$250$	−16.4593	−	3.33440i	−1.04098	−	0.210886i
$251$	16.8570	+	12.2473i	1.06400	+	0.773044i	0.974825	−	0.222972i	$-0.0715757\pi$
$251$	16.8570	+	12.2473i	1.06400	+	0.773044i	0.0891788	+	0.996016i	$0.471576\pi$
$252$	1.03433	−	0.336075i	0.0651568	−	0.0211707i
$253$	−5.83914	−	13.6526i	−0.367104	−	0.858334i
$254$	−16.3750	+	11.8972i	−1.02746	+	0.746494i
$255$	−6.51281	+	7.81208i	−0.407848	+	0.489212i
$256$	−4.89643	+	3.55746i	−0.306027	+	0.222341i
$257$	−15.9500	+	5.18247i	−0.994934	+	0.323274i	−0.760840	−	0.648940i	$-0.775213\pi$
$257$	−15.9500	+	5.18247i	−0.994934	+	0.323274i	−0.234095	+	0.972214i	$0.575213\pi$
$258$			9.25620i			0.576266i
$259$	−9.76470	−	30.0527i	−0.606749	−	1.86738i
$260$	−0.514139	+	0.323552i	−0.0318855	+	0.0200658i
$261$	8.73332			0.540579
$262$	3.40241	+	4.68301i	0.210202	+	0.289318i
$263$	13.5736	+	4.41034i	0.836987	+	0.271953i	0.695985	−	0.718056i	$-0.254968\pi$
$263$	13.5736	+	4.41034i	0.836987	+	0.271953i	0.141001	+	0.990009i	$0.454968\pi$
$264$	4.45395	−	7.45857i	0.274122	−	0.459043i
$265$	−18.0855	+	11.3814i	−1.11098	+	0.699151i
$266$	−5.34796	+	3.88552i	−0.327904	+	0.238236i
$267$	3.54579	+	4.88036i	0.216999	+	0.298673i
$268$	0.521388	−	0.169409i	0.0318489	−	0.0103483i
$269$	−18.5522			−1.13114			−0.565572	−	0.824699i	$-0.691345\pi$
$269$	−18.5522			−1.13114			−0.565572	+	0.824699i	$0.691345\pi$
$270$	−3.11815	−	1.24827i	−0.189764	−	0.0759673i
$271$	6.31378	+	4.58723i	0.383535	+	0.278654i	0.762801	−	0.646633i	$-0.223824\pi$
$271$	6.31378	+	4.58723i	0.383535	+	0.278654i	−0.379266	+	0.925288i	$0.623824\pi$
$272$	19.2363	−	6.25025i	1.16637	−	0.378977i
$273$	4.28083	+	1.39093i	0.259088	+	0.0841828i
$274$	−19.1029			−1.15405
$275$	−15.5351	−	5.80178i	−0.936802	−	0.349861i
$276$	1.14706			0.0690448
$277$	2.86049	+	0.929428i	0.171870	+	0.0558439i	0.393688	−	0.919244i	$-0.371199\pi$
$277$	2.86049	+	0.929428i	0.171870	+	0.0558439i	−0.221818	+	0.975088i	$0.571199\pi$
$278$	10.5036	−	3.41284i	0.629966	−	0.204688i
$279$	1.35781	+	0.986504i	0.0812897	+	0.0590605i
$280$	1.65525	−	24.8069i	0.0989200	−	1.48249i
$281$	8.08897			0.482548			0.241274	−	0.970457i	$-0.422435\pi$
$281$	8.08897			0.482548			0.241274	+	0.970457i	$0.422435\pi$
$282$	−2.82984	+	0.919471i	−0.168515	+	0.0547537i
$283$	17.1316	+	23.5797i	1.01837	+	1.40167i	0.913341	+	0.407196i	$0.133493\pi$
$283$	17.1316	+	23.5797i	1.01837	+	1.40167i	0.105029	+	0.994469i	$0.466507\pi$
$284$	−1.47196	+	1.06944i	−0.0873446	+	0.0634596i
$285$	2.31310	+	0.154343i	0.137016	+	0.00914247i
$286$	−4.85694	+	2.07728i	−0.287197	+	0.122832i
$287$	39.2857	+	12.7647i	2.31896	+	0.753476i
$288$	0.846851	+	1.16559i	0.0499012	+	0.0686831i
$289$	−3.68906			−0.217004
$290$	−10.9015	+	27.2318i	−0.640161	+	1.59911i
$291$	−1.82892	−	5.62884i	−0.107213	−	0.329969i
$292$			2.08053i			0.121754i
$293$	0.633363	−	0.205792i	0.0370015	−	0.0120225i	−0.290458	−	0.956888i	$-0.593808\pi$
$293$	0.633363	−	0.205792i	0.0370015	−	0.0120225i	0.327459	+	0.944865i	$0.393808\pi$
$294$	13.3904	−	9.72869i	0.780943	−	0.567389i
$295$	−7.36921	−	11.7100i	−0.429052	−	0.681783i
$296$	15.7744	−	11.4608i	0.916867	−	0.666143i
$297$	−2.84754	−	1.70044i	−0.165231	−	0.0986694i
$298$	−24.0006	+	7.79826i	−1.39032	+	0.451741i
$299$	3.84071	+	2.79044i	0.222114	+	0.161375i
$300$	0.883983	−	0.927144i	0.0510368	−	0.0535287i
$301$	8.08337	+	24.8780i	0.465918	+	1.43395i
$302$	3.87517	−	5.33371i	0.222991	−	0.306921i
$303$	9.47816	+	3.07964i	0.544506	+	0.176921i
$304$	−3.72972	−	2.70980i	−0.213914	−	0.155418i
$305$	1.50890	−	22.6136i	0.0863996	−	1.29485i
$306$	−2.11126	−	6.49779i	−0.120693	−	0.371454i
$307$		−	18.4534i		−	1.05319i	−0.850116	−	0.526596i	$-0.823468\pi$
$307$		−	18.4534i		−	1.05319i	0.850116	−	0.526596i	$-0.176532\pi$
$308$	−0.801829	+	3.51678i	−0.0456885	+	0.200387i
$309$	−0.436042	+	1.34200i	−0.0248056	+	0.0763437i
$310$	−4.77097	+	3.00242i	−0.270973	+	0.170526i
$311$	6.57392			0.372773			0.186386	−	0.982477i	$-0.440322\pi$
$311$	6.57392			0.372773			0.186386	+	0.982477i	$0.440322\pi$
$312$			2.77741i			0.157240i
$313$	2.17683	−	0.707294i	0.123042	−	0.0399786i	−0.246849	−	0.969054i	$-0.579395\pi$
$313$	2.17683	−	0.707294i	0.123042	−	0.0399786i	0.369891	+	0.929075i	$0.379395\pi$
$314$	−8.25383	−	5.99676i	−0.465790	−	0.338417i
$315$	−9.47081	−	0.631944i	−0.533619	−	0.0356060i
$316$	2.89529	+	2.10355i	0.162873	+	0.118334i
$317$	24.6701	−	8.01581i	1.38561	−	0.450212i	0.481102	−	0.876665i	$-0.340237\pi$
$317$	24.6701	−	8.01581i	1.38561	−	0.450212i	0.904510	+	0.426452i	$0.140237\pi$
$318$		−	14.3543i		−	0.804949i
$319$	−14.8505	+	24.8685i	−0.831467	+	1.39237i
$320$	14.5888	−	3.68682i	0.815540	−	0.206099i
$321$	8.75253			0.488519
$322$	27.1494	−	8.82138i	1.51298	−	0.491596i
$323$	2.77181	+	3.81507i	0.154228	+	0.212276i
$324$	0.207274	−	0.150593i	0.0115152	−	0.00836630i
$325$	5.21531	−	0.953909i	0.289293	−	0.0529133i
$326$	−7.34956	−	22.6196i	−0.407054	−	1.25278i
$327$			9.34359i			0.516702i
$328$			25.4886i			1.40737i
$329$	−6.80285	+	4.94256i	−0.375053	+	0.272492i
$330$	8.85672	−	6.75646i	0.487547	−	0.371931i
$331$	−20.7098	−	15.0465i	−1.13831	−	0.827031i	−0.151428	−	0.988468i	$-0.548387\pi$
$331$	−20.7098	−	15.0465i	−1.13831	−	0.827031i	−0.986883	+	0.161437i	$0.948387\pi$
$332$	2.15444	−	2.96533i	0.118240	−	0.162744i
$333$	−4.37551	−	6.02237i	−0.239776	−	0.330024i
$334$	19.5007			1.06703
$335$	−4.77406	−	0.318551i	−0.260835	−	0.0174043i
$336$	15.2710	+	11.0951i	0.833104	+	0.605285i
$337$			3.67755i			0.200329i	0.994971	+	0.100164i	$0.0319369\pi$
$337$			3.67755i			0.200329i	−0.994971	+	0.100164i	$0.968063\pi$
$338$	−10.4849	+	14.4312i	−0.570304	+	0.784956i
$339$	0.0748117	−	0.230247i	0.00406322	−	0.0125053i
$340$	2.60003	+	0.173488i	0.141006	+	0.00940871i
$341$	−5.11798	+	2.18893i	−0.277154	+	0.118537i
$342$	−0.915339	+	1.25986i	−0.0494959	+	0.0681252i
$343$	10.0280	−	13.8024i	0.541461	−	0.745258i
$344$	−13.0583	+	9.48739i	−0.704055	+	0.511526i
$345$	−9.29407	−	3.72064i	−0.500376	−	0.200313i
$346$	10.6815	−	32.8744i	0.574243	−	1.76734i
$347$	29.1175	+	9.46084i	1.56311	+	0.507885i	0.957636	−	0.287982i	$-0.0929843\pi$
$347$	29.1175	+	9.46084i	1.56311	+	0.507885i	0.605472	+	0.795866i	$0.292984\pi$
$348$	−1.31518	−	1.81019i	−0.0705011	−	0.0970364i
$349$	5.68868	−	17.5080i	0.304508	−	0.937180i	−0.675352	−	0.737495i	$-0.736008\pi$
$349$	5.68868	−	17.5080i	0.304508	−	0.937180i	0.979860	−	0.199684i	$-0.0639916\pi$
$350$	13.7926	−	28.7425i	0.737247	−	1.53635i
$351$	1.06037			0.0565981
$352$	−4.75909	+	0.429432i	−0.253660	+	0.0228888i
$353$	1.40264	+	1.93057i	0.0746552	+	0.102754i	0.844712	−	0.535222i	$-0.179772\pi$
$353$	1.40264	+	1.93057i	0.0746552	+	0.102754i	−0.770056	+	0.637976i	$0.779772\pi$
$354$	9.29413			0.493978
$355$	15.3954	−	3.89066i	0.817105	−	0.206495i
$356$	0.477599	−	1.46990i	0.0253127	−	0.0779045i
$357$	−11.3489	−	15.6205i	−0.600650	−	0.826724i
$358$		−	11.7063i		−	0.618700i
$359$	34.1511			1.80243			0.901213	−	0.433377i	$-0.142678\pi$
$359$	34.1511			1.80243			0.901213	+	0.433377i	$0.142678\pi$
$360$	−1.43502	−	5.67841i	−0.0756322	−	0.299278i
$361$	−5.53918	+	17.0478i	−0.291536	+	0.897254i
$362$	−11.6009	−	3.76935i	−0.609728	−	0.198113i
$363$	9.68415	−	5.21702i	0.508286	−	0.273823i
$364$	−0.356362	−	1.09677i	−0.0186785	−	0.0574864i
$365$	6.74847	−	16.8575i	0.353231	−	0.882363i
$366$	12.3168	+	8.94865i	0.643807	+	0.467754i
$367$	−18.5954	−	6.04203i	−0.970675	−	0.315391i	−0.219586	−	0.975593i	$-0.570471\pi$
$367$	−18.5954	−	6.04203i	−0.970675	−	0.315391i	−0.751088	+	0.660202i	$0.770471\pi$
$368$	11.7020	+	16.1065i	0.610011	+	0.839608i
$369$	9.73109			0.506580
$370$	24.2405	−	6.12594i	1.26020	−	0.318472i
$371$	−12.5355	−	38.5803i	−0.650810	−	2.00299i
$372$		−	0.429999i		−	0.0222944i
$373$	−8.08610	+	2.62733i	−0.418683	+	0.136038i	−0.510779	−	0.859712i	$-0.670643\pi$
$373$	−8.08610	+	2.62733i	−0.418683	+	0.136038i	0.0920967	+	0.995750i	$0.470643\pi$
$374$	22.0928	+	5.03718i	1.14239	+	0.260467i
$375$	−10.1698	+	4.64488i	−0.525167	+	0.239861i
$376$	−4.19768	−	3.04979i	−0.216479	−	0.157281i
$377$		−	9.26051i		−	0.476941i
$378$	3.74778	−	5.15838i	0.192765	−	0.265319i
$379$	−7.93933	+	24.4347i	−0.407816	+	1.25513i	0.510705	+	0.859756i	$0.329384\pi$
$379$	−7.93933	+	24.4347i	−0.407816	+	1.25513i	−0.918521	+	0.395373i	$0.870616\pi$
$380$	−0.316346	−	0.502689i	−0.0162282	−	0.0257874i
$381$	−4.16407	+	12.8157i	−0.213332	+	0.656567i
$382$	6.30597	+	2.04893i	0.322641	+	0.104833i
$383$	25.2685	−	8.21024i	1.29116	−	0.419523i	0.418663	−	0.908142i	$-0.362499\pi$
$383$	25.2685	−	8.21024i	1.29116	−	0.419523i	0.872498	+	0.488618i	$0.162499\pi$
$384$	−4.01399	+	12.3538i	−0.204838	+	0.630428i
$385$	17.9040	−	25.8940i	0.912473	−	1.31968i
$386$	3.90386	+	12.0149i	0.198701	+	0.611540i
$387$	3.62211	+	4.98541i	0.184122	+	0.253423i
$388$	−0.891289	+	1.22675i	−0.0452484	+	0.0622790i
$389$	16.2363	−	11.7964i	0.823215	−	0.598101i	−0.0944168	−	0.995533i	$-0.530099\pi$
$389$	16.2363	−	11.7964i	0.823215	−	0.598101i	0.917632	+	0.397432i	$0.130099\pi$
$390$	−1.32362	+	3.30638i	−0.0670242	+	0.167425i
$391$	−6.29290	−	19.3676i	−0.318246	−	0.979460i
$392$	27.4497	+	8.91894i	1.38642	+	0.450475i
$393$	3.66509	+	1.19086i	0.184879	+	0.0600710i
$394$	12.5508	+	38.6275i	0.632302	+	1.94603i
$395$	−16.6360	−	26.4354i	−0.837048	−	1.33011i
$396$	0.0763648	+	0.846297i	0.00383748	+	0.0425280i
$397$	−8.57638	−	11.8044i	−0.430436	−	0.592444i	0.537617	−	0.843189i	$-0.319325\pi$
$397$	−8.57638	−	11.8044i	−0.430436	−	0.592444i	−0.968053	+	0.250745i	$0.919325\pi$
$398$	−6.97863	−	2.26749i	−0.349807	−	0.113659i
$399$	−1.35995	+	4.18550i	−0.0680827	+	0.209537i
$400$	22.0367	+	2.95397i	1.10184	+	0.147699i
$401$	0.410783	−	0.298451i	0.0205135	−	0.0149039i	−0.577481	−	0.816404i	$-0.695964\pi$
$401$	0.410783	−	0.298451i	0.0205135	−	0.0149039i	0.597995	+	0.801500i	$0.295964\pi$
$402$	1.88919	−	2.60025i	0.0942242	−	0.129689i
$403$	1.04605	−	1.43977i	0.0521077	−	0.0717201i
$404$	−0.789019	−	2.42835i	−0.0392551	−	0.120815i
$405$	−2.16791	+	0.547865i	−0.107724	+	0.0272236i
$406$	−45.0498	−	32.7306i	−2.23578	−	1.62439i
$407$	24.5893	−	2.21879i	1.21884	−	0.109981i
$408$	7.00283	−	9.63857i	0.346692	−	0.477180i
$409$	−13.1596	+	9.56098i	−0.650699	+	0.472760i	−0.863509	−	0.504333i	$-0.831738\pi$
$409$	−13.1596	+	9.56098i	−0.650699	+	0.472760i	0.212810	+	0.977094i	$0.431738\pi$
$410$	−12.1470	+	30.3430i	−0.599899	+	1.49853i
$411$	−10.2889	+	7.47529i	−0.507512	+	0.368729i
$412$	0.343827	−	0.111716i	0.0169391	−	0.00550386i
$413$	24.9800	−	8.11650i	1.22919	−	0.399387i
$414$	5.44058	−	3.95281i	0.267390	−	0.194270i
$415$	−27.0749	+	17.0384i	−1.32905	+	0.836384i
$416$	1.23595	−	0.897972i	0.0605975	−	0.0440267i
$417$	4.32178	−	5.94842i	0.211638	−	0.291295i
$418$	−2.03102	−	4.74878i	−0.0993405	−	0.232270i
$419$	−27.2327	−	19.7857i	−1.33040	−	0.966595i	−0.999739	−	0.0228475i	$-0.992727\pi$
$419$	−27.2327	−	19.7857i	−1.33040	−	0.966595i	−0.330666	−	0.943748i	$-0.607273\pi$
$420$	1.29526	+	2.05822i	0.0632020	+	0.100431i
$421$	0.567965	+	1.74802i	0.0276809	+	0.0851932i	0.963943	−	0.266110i	$-0.0857385\pi$
$421$	0.567965	+	1.74802i	0.0276809	+	0.0851932i	−0.936262	+	0.351303i	$0.885739\pi$
$422$	12.2559	−	16.8688i	0.596608	−	0.821160i
$423$	−1.16435	+	1.60260i	−0.0566128	+	0.0779209i
$424$	20.2505	−	14.7128i	0.983449	−	0.714518i
$425$	−20.5040	−	9.83923i	−0.994592	−	0.477273i
$426$	−3.29627	+	10.1449i	−0.159705	+	0.491520i
$427$	40.9188	+	13.2953i	1.98020	+	0.643405i
$428$	−1.31807	−	1.81417i	−0.0637115	−	0.0876913i
$429$	−1.80309	+	3.01944i	−0.0870538	+	0.145780i
$430$	−20.0666	+	5.07114i	−0.967699	+	0.244552i
$431$	0.509596	+	1.56838i	0.0245464	+	0.0755460i	0.962579	−	0.271000i	$-0.0873544\pi$
$431$	0.509596	+	1.56838i	0.0245464	+	0.0755460i	−0.938033	+	0.346546i	$0.887354\pi$
$432$	4.22913	+	1.37413i	0.203474	+	0.0661127i
$433$	−10.5024	−	3.41244i	−0.504714	−	0.163991i	0.0455832	−	0.998961i	$-0.485485\pi$
$433$	−10.5024	−	3.41244i	−0.504714	−	0.163991i	−0.550297	+	0.834969i	$0.685485\pi$
$434$	−3.30688	−	10.1775i	−0.158735	−	0.488537i
$435$	4.78468	+	18.9331i	0.229408	+	0.907772i
$436$	1.93668	−	1.40708i	0.0927503	−	0.0673871i
$437$	−2.72830	+	3.75518i	−0.130512	+	0.179634i
$438$	7.16959	+	9.86809i	0.342576	+	0.471515i
$439$	11.0450	+	33.9929i	0.527147	+	1.62239i	0.760030	+	0.649888i	$0.225184\pi$
$439$	11.0450	+	33.9929i	0.527147	+	1.62239i	−0.232883	+	0.972505i	$0.574816\pi$
$440$	18.6097	+	5.56949i	0.887182	+	0.265515i
$441$	3.40509	−	10.4798i	0.162147	−	0.499038i
$442$	−6.89004	+	2.23871i	−0.327726	+	0.106484i
$443$	19.6823	+	6.39516i	0.935133	+	0.303843i	0.736660	−	0.676263i	$-0.236402\pi$
$443$	19.6823	+	6.39516i	0.935133	+	0.303843i	0.198473	+	0.980106i	$0.436402\pi$
$444$	−0.589358	+	1.81386i	−0.0279697	+	0.0860819i
$445$	−8.63758	+	10.3607i	−0.409460	+	0.491146i
$446$	10.4418	−	32.1365i	0.494433	−	1.52171i
$447$	−9.87518	+	13.5920i	−0.467080	+	0.642880i
$448$			28.5657i			1.34960i
$449$	−28.2419	−	20.5189i	−1.33282	−	0.968347i	−0.999676	−	0.0254701i	$-0.991892\pi$
$449$	−28.2419	−	20.5189i	−1.33282	−	0.968347i	−0.333140	−	0.942877i	$-0.608108\pi$
$450$	0.997818	−	7.44375i	0.0470376	−	0.350902i
$451$	−16.5471	+	27.7097i	−0.779173	+	1.30480i
$452$	−0.0589903	+	0.0191671i	−0.00277467	+	0.000901545i
$453$		−	4.38917i		−	0.206221i
$454$	5.59007	+	17.2045i	0.262355	+	0.807445i
$455$	−0.670091	+	10.0425i	−0.0314144	+	0.470800i
$456$	−2.71556			−0.127168
$457$	−20.8335	−	28.6749i	−0.974550	−	1.34135i	−0.939715	−	0.341960i	$-0.888909\pi$
$457$	−20.8335	−	28.6749i	−0.974550	−	1.34135i	−0.0348354	−	0.999393i	$-0.511091\pi$
$458$	9.95754	+	3.23540i	0.465285	+	0.151180i
$459$	−3.67983	−	2.67355i	−0.171760	−	0.124791i
$460$	0.628433	+	2.48672i	0.0293008	+	0.115944i
$461$	−7.41753	−	22.8288i	−0.345469	−	1.06324i	−0.961332	−	0.275391i	$-0.911193\pi$
$461$	−7.41753	−	22.8288i	−0.345469	−	1.06324i	0.615864	−	0.787853i	$-0.288807\pi$
$462$	8.31585	+	19.4435i	0.386888	+	0.904593i
$463$	−29.2067	−	9.48984i	−1.35735	−	0.441030i	−0.462193	−	0.886779i	$-0.652937\pi$
$463$	−29.2067	−	9.48984i	−1.35735	−	0.441030i	−0.895158	+	0.445749i	$0.852937\pi$
$464$	12.0007	−	36.9343i	0.557118	−	1.71463i
$465$	−1.39476	+	3.48408i	−0.0646805	+	0.161570i
$466$	42.3631			1.96243
$467$		−	9.61490i		−	0.444924i	−0.974941	−	0.222462i	$-0.928591\pi$
$467$		−	9.61490i		−	0.444924i	0.974941	−	0.222462i	$-0.0714094\pi$
$468$	−0.159684	−	0.219786i	−0.00738139	−	0.0101596i
$469$	2.80683	−	8.63855i	0.129608	−	0.398891i
$470$	−3.54370	−	5.63110i	−0.163459	−	0.259743i
$471$	−6.79217			−0.312967
$472$	9.52627	+	13.1118i	0.438482	+	0.603519i
$473$	−20.3554	+	1.83675i	−0.935941	+	0.0844538i
$474$	20.9815			0.963713
$475$	0.932665	+	5.09916i	0.0427936	+	0.233965i
$476$	−1.52864	+	4.70468i	−0.0700653	+	0.215639i
$477$	−5.61709	−	7.73126i	−0.257189	−	0.353990i
$478$	−16.6795	−	5.41950i	−0.762903	−	0.247882i
$479$	−11.1959	+	34.4574i	−0.511554	+	1.57440i	0.277913	+	0.960606i	$0.410357\pi$
$479$	−11.1959	+	34.4574i	−0.511554	+	1.57440i	−0.789466	+	0.613794i	$0.789643\pi$
$480$	−2.06294	+	2.47449i	−0.0941599	+	0.112944i
$481$	−6.38591	+	4.63964i	−0.291173	+	0.211549i
$482$	4.58073	−	6.30484i	0.208647	−	0.287177i
$483$	11.1708	−	15.3753i	0.508288	−	0.699599i
$484$	−2.53972	−	1.22162i	−0.115442	−	0.0555283i
$485$	11.2008	−	7.04879i	0.508604	−	0.320069i
$486$	0.464164	−	1.42855i	0.0210549	−	0.0648004i
$487$	12.7302	−	17.5216i	0.576860	−	0.793979i	−0.416487	−	0.909142i	$-0.636739\pi$
$487$	12.7302	−	17.5216i	0.576860	−	0.793979i	0.993347	+	0.115163i	$0.0367389\pi$
$488$			26.5482i			1.20178i
$489$	−12.8099	−	9.30697i	−0.579286	−	0.420876i
$490$	28.4271	+	23.6992i	1.28420	+	1.07062i
$491$	−24.9817			−1.12741			−0.563705	−	0.825976i	$-0.690624\pi$
$491$	−24.9817			−1.12741			−0.563705	+	0.825976i	$0.690624\pi$
$492$	−1.46544	−	2.01700i	−0.0660670	−	0.0909335i
$493$	−23.3490	+	32.1372i	−1.05159	+	1.44738i
$494$	1.33591	+	0.970594i	0.0601054	+	0.0436691i
$495$	2.12633	−	7.10484i	0.0955715	−	0.319339i
$496$	6.03785	−	4.38676i	0.271107	−	0.196971i
$497$			30.1451i			1.35219i
$498$		−	21.4891i		−	0.962948i
$499$	−6.15072	−	18.9300i	−0.275344	−	0.847421i	−0.989128	−	0.147056i	$-0.953020\pi$
$499$	−6.15072	−	18.9300i	−0.275344	−	0.847421i	0.713784	−	0.700366i	$-0.246980\pi$
$500$	2.49427	+	1.40845i	0.111547	+	0.0629878i
$501$	10.5031	−	7.63096i	0.469245	−	0.340926i
$502$	−18.3963	−	25.3203i	−0.821067	−	1.13010i
$503$	−40.4365	+	13.1386i	−1.80297	+	0.585821i	−0.999949	−	0.0101257i	$-0.996777\pi$
$503$	−40.4365	+	13.1386i	−1.80297	+	0.585821i	−0.803024	+	0.595947i	$0.796777\pi$
$504$	11.1186			0.495263
$505$	−1.48364	+	22.2350i	−0.0660213	+	0.989447i
$506$	2.00444	+	22.2138i	0.0891084	+	0.987524i
$507$			11.8756i			0.527415i
$508$	3.28344	−	1.06685i	0.145679	−	0.0473340i
$509$	−13.8465	−	10.0601i	−0.613736	−	0.445905i	0.236992	−	0.971512i	$-0.423838\pi$
$509$	−13.8465	−	10.0601i	−0.613736	−	0.445905i	−0.850728	+	0.525606i	$0.823838\pi$
$510$	12.9300	−	8.13694i	0.572548	−	0.360310i
$511$	27.8875	+	20.2615i	1.23367	+	0.896316i
$512$	−16.0616	+	5.21872i	−0.709828	+	0.230637i
$513$			1.03675i			0.0457737i
$514$	25.1909			1.11112
$515$	−3.14823	−	0.210067i	−0.138728	−	0.00925667i
$516$	0.487880	−	1.50154i	0.0214777	−	0.0661016i
$517$	−2.58355	−	6.04067i	−0.113624	−	0.265668i
$518$			47.4642i			2.08546i
$519$	−7.11123	−	21.8861i	−0.312148	−	0.960694i
$520$	−6.02118	+	1.52165i	−0.264046	+	0.0667286i
$521$	24.7418	+	17.9760i	1.08396	+	0.787541i	0.978369	−	0.206869i	$-0.0663273\pi$
$521$	24.7418	+	17.9760i	1.08396	+	0.787541i	0.105589	+	0.994410i	$0.466327\pi$
$522$	−12.4760	−	4.05369i	−0.546059	−	0.177425i
$523$	6.59851	−	9.08207i	0.288533	−	0.397131i	−0.640004	−	0.768372i	$-0.721067\pi$
$523$	6.59851	−	9.08207i	0.288533	−	0.397131i	0.928537	+	0.371240i	$0.121067\pi$
$524$	−0.305104	−	0.939014i	−0.0133285	−	0.0410210i
$525$	−3.81872	−	20.8781i	−0.166663	−	0.911195i
$526$	−17.3435	−	12.6008i	−0.756213	−	0.549421i
$527$	−7.26034	+	2.35903i	−0.316265	+	0.102761i
$528$	−11.1043	+	9.70601i	−0.483251	+	0.422400i
$529$	−2.39099	+	1.73716i	−0.103956	+	0.0755286i
$530$	31.1189	−	7.86421i	1.35172	−	0.341599i
$531$	5.00584	−	3.63696i	0.217235	−	0.157831i
$532$	1.07234	−	0.348426i	0.0464920	−	0.0151062i
$533$		−	10.3185i		−	0.446944i
$534$	−2.80005	−	8.61766i	−0.121170	−	0.372923i
$535$	4.79520	+	18.9747i	0.207315	+	0.820349i
$536$	5.60470			0.242086
$537$	−4.58090	−	6.30507i	−0.197680	−	0.272084i
$538$	26.5027	+	8.61125i	1.14261	+	0.371257i
$539$	24.0515	+	27.5164i	1.03597	+	1.18521i
$540$	0.440031	+	0.366847i	0.0189359	+	0.0157866i
$541$	31.5496	−	22.9221i	1.35642	−	0.985499i	0.357759	−	0.933814i	$-0.383541\pi$
$541$	31.5496	−	22.9221i	1.35642	−	0.985499i	0.998663	−	0.0516847i	$-0.0164591\pi$
$542$	−6.89032	−	9.48372i	−0.295965	−	0.407361i
$543$	−7.72327	+	2.50944i	−0.331437	+	0.107691i
$544$	−6.55328			−0.280970
$545$	−20.2561	+	5.11902i	−0.867676	+	0.219275i
$546$	−5.46977	−	3.97402i	−0.234084	−	0.170072i
$547$	−7.11082	+	2.31045i	−0.304037	+	0.0987875i	−0.457062	−	0.889435i	$-0.651098\pi$
$547$	−7.11082	+	2.31045i	−0.304037	+	0.0987875i	0.153025	+	0.988222i	$0.451098\pi$
$548$	3.09887	+	1.00688i	0.132377	+	0.0430119i
$549$	10.1356			0.432577
$550$	19.4997	+	15.4990i	0.831470	+	0.660878i
$551$	9.05428			0.385725
$552$	11.1529	+	3.62381i	0.474701	+	0.154240i
$553$	56.3924	−	18.3230i	2.39805	−	0.779173i
$554$	−3.65494	−	2.65547i	−0.155284	−	0.112820i
$555$	10.6588	−	12.7852i	0.452440	−	0.542700i
$556$	−1.88378			−0.0798902
$557$	−17.9946	+	5.84679i	−0.762455	+	0.247737i	−0.664332	−	0.747438i	$-0.731284\pi$
$557$	−17.9946	+	5.84679i	−0.762455	+	0.247737i	−0.0981230	+	0.995174i	$0.531284\pi$
$558$	−1.48180	−	2.03952i	−0.0627294	−	0.0863396i
$559$	5.28636	−	3.84076i	0.223589	−	0.162447i
$560$	−15.6867	+	39.1849i	−0.662882	+	1.65586i
$561$	13.8704	−	5.93227i	0.585608	−	0.250461i
$562$	−11.5555	−	3.75461i	−0.487440	−	0.158379i
$563$	7.44636	+	10.2490i	0.313827	+	0.431946i	0.936570	−	0.350481i	$-0.113982\pi$
$563$	7.44636	+	10.2490i	0.313827	+	0.431946i	−0.622743	+	0.782426i	$0.713982\pi$
$564$	0.507521			0.0213705
$565$	0.540142	+	0.0360412i	0.0227239	+	0.00151626i
$566$	−13.5286	−	41.6366i	−0.568648	−	1.75012i
$567$		−	4.24489i		−	0.178269i
$568$	−17.6906	+	5.74801i	−0.742279	+	0.241181i
$569$	−26.6453	+	19.3590i	−1.11703	+	0.811570i	−0.983756	−	0.179510i	$-0.942549\pi$
$569$	−26.6453	+	19.3590i	−1.11703	+	0.811570i	−0.133273	+	0.991079i	$0.542549\pi$
$570$	−3.23274	−	1.29414i	−0.135405	−	0.0542058i
$571$	−1.32702	+	0.964139i	−0.0555342	+	0.0403480i	−0.615206	−	0.788366i	$-0.710927\pi$
$571$	−1.32702	+	0.964139i	−0.0555342	+	0.0403480i	0.559672	+	0.828714i	$0.310927\pi$
$572$	0.897384	−	0.0809746i	0.0375215	−	0.00338572i
$573$	4.19819	−	1.36408i	0.175382	−	0.0569851i
$574$	−50.1967	−	36.4700i	−2.09517	−	1.52223i
$575$	2.97413	−	22.1871i	0.124030	−	0.925267i
$576$	2.07951	+	6.40007i	0.0866462	+	0.266670i
$577$	−21.5993	+	29.7289i	−0.899192	+	1.23763i	0.0715325	+	0.997438i	$0.477211\pi$
$577$	−21.5993	+	29.7289i	−0.899192	+	1.23763i	−0.970725	+	0.240194i	$0.922789\pi$
$578$	5.27001	+	1.71233i	0.219203	+	0.0712235i
$579$	6.80426	+	4.94358i	0.282775	+	0.205448i
$580$	3.20379	−	3.84293i	0.133030	−	0.159569i
$581$	−18.7662	−	57.7566i	−0.778555	−	2.39615i
$582$			8.89001i			0.368503i
$583$	31.5666	−	2.84839i	1.30736	−	0.117968i
$584$	−6.57284	+	20.2291i	−0.271986	+	0.837087i
$585$	0.580937	+	2.29878i	0.0240188	+	0.0950428i
$586$	−1.00031			−0.0413225
$587$		−	5.22789i		−	0.215778i	−0.994163	−	0.107889i	$-0.965591\pi$
$587$		−	5.22789i		−	0.215778i	0.994163	−	0.107889i	$-0.0344091\pi$
$588$	−2.68497	+	0.872400i	−0.110726	+	0.0359772i
$589$	1.40771	+	1.02276i	0.0580035	+	0.0421420i
$590$	5.09193	+	20.1489i	0.209631	+	0.829516i
$591$	21.8755	+	15.8935i	0.899839	+	0.653772i
$592$	−31.4819	+	10.2291i	−1.29390	+	0.420413i
$593$		−	32.9555i		−	1.35332i	−0.736296	−	0.676660i	$-0.763427\pi$
$593$		−	32.9555i		−	1.35332i	0.736296	−	0.676660i	$-0.236573\pi$
$594$	3.27858	+	3.75089i	0.134522	+	0.153901i
$595$	27.6462	−	33.1614i	1.13338	−	1.35949i
$596$	4.30441			0.176315
$597$	−4.64602	+	1.50958i	−0.190149	+	0.0617831i
$598$	−4.19143	−	5.76900i	−0.171400	−	0.235912i
$599$	−14.8232	+	10.7697i	−0.605658	+	0.440036i	−0.847883	−	0.530184i	$-0.822123\pi$
$599$	−14.8232	+	10.7697i	−0.605658	+	0.440036i	0.242225	+	0.970220i	$0.422123\pi$
$600$	11.5241	−	6.22200i	0.470469	−	0.254012i
$601$	5.35935	+	16.4944i	0.218612	+	0.672819i	0.998877	+	0.0473705i	$0.0150841\pi$
$601$	5.35935	+	16.4944i	0.218612	+	0.672819i	−0.780265	+	0.625449i	$0.784916\pi$
$602$		−	39.2916i		−	1.60140i
$603$		−	2.13977i		−	0.0871383i
$604$	−0.909761	+	0.660980i	−0.0370177	+	0.0268949i
$605$	16.6156	+	18.1362i	0.675522	+	0.737340i
$606$	−12.1106	−	8.79885i	−0.491958	−	0.357429i
$607$	−4.89357	+	6.73542i	−0.198624	+	0.273382i	−0.896698	−	0.442644i	$-0.854041\pi$
$607$	−4.89357	+	6.73542i	−0.198624	+	0.273382i	0.698074	+	0.716026i	$0.254041\pi$
$608$	0.877974	+	1.20843i	0.0356065	+	0.0490082i
$609$	−37.0720			−1.50223
$610$	−12.6520	+	31.6043i	−0.512264	+	1.27962i
$611$	1.69934	+	1.23464i	0.0687478	+	0.0499482i
$612$			1.16535i			0.0471066i
$613$	14.4947	−	19.9502i	0.585434	−	0.805780i	−0.408844	−	0.912604i	$-0.634068\pi$
$613$	14.4947	−	19.9502i	0.585434	−	0.805780i	0.994278	+	0.106824i	$0.0340681\pi$
$614$	−8.56542	+	26.3616i	−0.345672	+	1.06387i
$615$	5.33132	+	21.0962i	0.214980	+	0.850679i
$616$	−18.9065	+	31.6608i	−0.761766	+	1.27565i
$617$	1.18202	−	1.62691i	0.0475862	−	0.0654968i	−0.784561	−	0.620052i	$-0.787112\pi$
$617$	1.18202	−	1.62691i	0.0475862	−	0.0654968i	0.832147	+	0.554555i	$0.187112\pi$
$618$	1.24582	−	1.71472i	0.0501141	−	0.0689762i
$619$	4.82187	−	3.50329i	0.193807	−	0.140809i	−0.486650	−	0.873597i	$-0.661781\pi$
$619$	4.82187	−	3.50329i	0.193807	−	0.140809i	0.680457	+	0.732788i	$0.261781\pi$
$620$	0.932200	−	0.235581i	0.0374381	−	0.00946117i
$621$	1.38351	−	4.25799i	0.0555181	−	0.170867i
$622$	−9.39117	−	3.05138i	−0.376552	−	0.122349i
$623$	−15.0515	−	20.7166i	−0.603025	−	0.829992i
$624$	1.45708	−	4.48442i	0.0583297	−	0.179520i
$625$	−15.6414	−	19.5025i	−0.625655	−	0.780100i
$626$	−3.43801			−0.137410
$627$	−2.95219	−	1.76293i	−0.117899	−	0.0704046i
$628$	1.02286	+	1.40784i	0.0408164	+	0.0561789i
$629$	33.8595			1.35007
$630$	13.2362	+	5.29877i	0.527343	+	0.211108i
$631$	−3.72112	+	11.4524i	−0.148135	+	0.455914i	−0.997401	−	0.0720523i	$-0.977045\pi$
$631$	−3.72112	+	11.4524i	−0.148135	+	0.455914i	0.849266	+	0.527966i	$0.177045\pi$
$632$	21.5056	+	29.5999i	0.855445	+	1.17742i
$633$		−	13.8815i		−	0.551741i
$634$	−38.9631			−1.54742
$635$	−30.0646	−	2.00607i	−1.19308	−	0.0796086i
$636$	−0.756593	+	2.32855i	−0.0300008	+	0.0923331i
$637$	−11.1124	−	3.61064i	−0.440290	−	0.143059i
$638$	32.7577	−	28.6329i	1.29689	−	1.13359i
$639$	2.19449	+	6.75393i	0.0868125	+	0.267182i
$640$	−28.9811	−	1.93378i	−1.14558	−	0.0764392i
$641$	26.5502	+	19.2898i	1.04867	+	0.761902i	0.971959	−	0.235151i	$-0.0755585\pi$
$641$	26.5502	+	19.2898i	1.04867	+	0.761902i	0.0767098	+	0.997053i	$0.475559\pi$
$642$	−12.5034	−	4.06261i	−0.493471	−	0.160338i
$643$	−5.75764	−	7.92471i	−0.227059	−	0.312520i	0.680253	−	0.732977i	$-0.261870\pi$
$643$	−5.75764	−	7.92471i	−0.227059	−	0.312520i	−0.907312	+	0.420457i	$0.861870\pi$
$644$	−4.86914			−0.191871
$645$	−8.82351	+	10.5838i	−0.347425	+	0.416735i
$646$	−2.18885	−	6.73659i	−0.0861192	−	0.265048i
$647$			26.1490i			1.02802i	0.857783	+	0.514012i	$0.171842\pi$
$647$			26.1490i			1.02802i	−0.857783	+	0.514012i	$0.828158\pi$
$648$	2.49110	−	0.809407i	0.0978596	−	0.0317965i
$649$	1.84428	+	20.4388i	0.0723941	+	0.802293i
$650$	−7.89310	−	1.05805i	−0.309593	−	0.0415002i
$651$	−5.76374	−	4.18760i	−0.225899	−	0.164125i
$652$			4.05674i			0.158874i
$653$	1.07657	−	1.48177i	0.0421294	−	0.0579862i	−0.787433	−	0.616401i	$-0.788590\pi$
$653$	1.07657	−	1.48177i	0.0421294	−	0.0579862i	0.829562	+	0.558415i	$0.188590\pi$
$654$	4.33696	−	13.3478i	0.169589	−	0.521940i
$655$	−0.573707	+	8.59803i	−0.0224166	+	0.335953i
$656$	13.3718	−	41.1540i	0.522079	−	1.60680i
$657$	7.72311	+	2.50939i	0.301307	+	0.0979007i
$658$	12.0124	−	3.90305i	0.468291	−	0.152157i
$659$	−11.7951	+	36.3015i	−0.459471	+	1.41411i	0.406334	+	0.913725i	$0.366807\pi$
$659$	−11.7951	+	36.3015i	−0.459471	+	1.41411i	−0.865805	+	0.500381i	$0.833193\pi$
$660$	−1.79286	+	0.629208i	−0.0697870	+	0.0244919i
$661$	2.14808	+	6.61112i	0.0835507	+	0.257143i	0.984101	−	0.177609i	$-0.0568362\pi$
$661$	2.14808	+	6.61112i	0.0835507	+	0.257143i	−0.900550	+	0.434752i	$0.856836\pi$
$662$	22.6009	+	31.1074i	0.878408	+	1.20902i
$663$	−2.83494	+	3.90197i	−0.110100	+	0.151540i
$664$	30.3159	−	22.0258i	1.17649	−	0.854767i
$665$	−9.81886	−	0.655168i	−0.380759	−	0.0254063i
$666$	3.45527	+	10.6342i	0.133889	+	0.412068i
$667$	−37.1864	−	12.0826i	−1.43986	−	0.467840i
$668$	−3.16340	−	1.02785i	−0.122396	−	0.0397688i
$669$	−6.95161	−	21.3948i	−0.268765	−	0.827173i
$670$	6.67213	+	2.67102i	0.257767	+	0.103190i
$671$	−17.2350	+	28.8616i	−0.665348	+	1.11419i
$672$	−3.59479	−	4.94781i	−0.138672	−	0.190866i
$673$	8.19508	+	2.66274i	0.315897	+	0.102641i	0.462674	−	0.886528i	$-0.346890\pi$
$673$	8.19508	+	2.66274i	0.315897	+	0.102641i	−0.146777	+	0.989170i	$0.546890\pi$
$674$	1.70699	−	5.25356i	0.0657506	−	0.202360i
$675$	−2.37544	−	4.39969i	−0.0914309	−	0.169344i
$676$	2.46151	−	1.78839i	0.0946734	−	0.0687843i
$677$	−6.17935	+	8.50514i	−0.237492	+	0.326879i	−0.911082	−	0.412226i	$-0.864751\pi$
$677$	−6.17935	+	8.50514i	−0.237492	+	0.326879i	0.673590	+	0.739105i	$0.264751\pi$
$678$	−0.213745	+	0.294194i	−0.00820881	+	0.0112985i
$679$	7.76358	+	23.8938i	0.297939	+	0.916961i
$680$	24.7322	+	9.90090i	0.948436	+	0.379682i
$681$	9.74323	+	7.07887i	0.373362	+	0.271263i
$682$	8.32731	−	0.751408i	0.318869	−	0.0287729i
$683$	15.5877	−	21.4546i	0.596446	−	0.820938i	−0.398931	−	0.916981i	$-0.630619\pi$
$683$	15.5877	−	21.4546i	0.596446	−	0.820938i	0.995377	+	0.0960434i	$0.0306188\pi$
$684$	0.214891	−	0.156128i	0.00821658	−	0.00596969i
$685$	−21.8427	−	18.2099i	−0.834566	−	0.695764i
$686$	−20.7321	+	15.0627i	−0.791554	+	0.575098i
$687$	6.62922	−	2.15397i	0.252921	−	0.0821789i
$688$	26.0612	−	8.46779i	0.993574	−	0.322832i
$689$	−8.19796	+	5.95616i	−0.312317	+	0.226912i
$690$	11.5501	+	9.62910i	0.439703	+	0.366573i
$691$	−22.8013	+	16.5661i	−0.867402	+	0.630204i	−0.929888	−	0.367842i	$-0.880097\pi$
$691$	−22.8013	+	16.5661i	−0.867402	+	0.630204i	0.0624868	+	0.998046i	$0.480097\pi$
$692$	−3.46552	+	4.76988i	−0.131739	+	0.181323i
$693$	12.0875	+	7.21817i	0.459167	+	0.274196i
$694$	−37.2044	−	27.0306i	−1.41226	−	1.02607i
$695$	15.2634	+	6.11031i	0.578974	+	0.231777i
$696$	−7.06881	−	21.7556i	−0.267943	−	0.824643i
$697$	−26.0166	+	35.8088i	−0.985449	+	1.35635i
$698$	−16.2531	+	22.3705i	−0.615190	+	0.846737i
$699$	22.8169	−	16.5774i	0.863014	−	0.627016i
$700$	−3.75241	+	3.93562i	−0.141828	+	0.148753i
$701$	12.0077	−	36.9559i	0.453524	−	1.39580i	−0.419335	−	0.907831i	$-0.637737\pi$
$701$	12.0077	−	36.9559i	0.453524	−	1.39580i	0.872859	−	0.487972i	$-0.162263\pi$
$702$	−1.51479	−	0.492184i	−0.0571719	−	0.0185763i
$703$	−4.53631	−	6.24370i	−0.171090	−	0.235485i
$704$	−21.7606	−	4.96143i	−0.820132	−	0.186991i
$705$	−4.11220	−	1.64621i	−0.154874	−	0.0619999i
$706$	−1.10764	−	3.40898i	−0.0416867	−	0.128299i
$707$	−40.2338	−	13.0727i	−1.51315	−	0.491651i
$708$	−1.50769	−	0.489879i	−0.0566626	−	0.0184108i
$709$	2.26115	+	6.95911i	0.0849194	+	0.261355i	0.984496	−	0.175409i	$-0.0561247\pi$
$709$	2.26115	+	6.95911i	0.0849194	+	0.261355i	−0.899576	+	0.436764i	$0.856125\pi$
$710$	−23.7991	−	1.58800i	−0.893163	−	0.0595967i
$711$	11.3007	−	8.21043i	0.423809	−	0.307915i
$712$	9.28747	−	12.7831i	0.348063	−	0.479067i
$713$	−4.41669	−	6.07906i	−0.165406	−	0.227662i
$714$	8.96208	+	27.5824i	0.335397	+	1.03225i
$715$	−7.53372	−	2.25469i	−0.281745	−	0.0843205i
$716$	−0.617024	+	1.89900i	−0.0230593	+	0.0709691i
$717$	−11.1044	+	3.60803i	−0.414700	+	0.134744i
$718$	−48.7865	−	15.8517i	−1.82070	−	0.591581i
$719$	−12.6133	+	38.8199i	−0.470399	+	1.44774i	0.381666	+	0.924301i	$0.375351\pi$
$719$	−12.6133	+	38.8199i	−0.470399	+	1.44774i	−0.852064	+	0.523437i	$0.824649\pi$
$720$	−0.661998	+	9.92122i	−0.0246712	+	0.369742i
$721$	1.85095	−	5.69665i	0.0689331	−	0.212154i
$722$	15.8260	−	21.7826i	0.588982	−	0.810664i
$723$		−	5.18832i		−	0.192956i
$724$	1.68322	+	1.22293i	0.0625562	+	0.0454498i
$725$	−38.4239	+	20.7455i	−1.42703	+	0.770469i
$726$	−16.2558	+	2.95775i	−0.603311	+	0.109772i
$727$	44.8778	−	14.5817i	1.66442	−	0.540804i	0.682632	−	0.730763i	$-0.260835\pi$
$727$	44.8778	−	14.5817i	1.66442	−	0.540804i	0.981792	+	0.189959i	$0.0608354\pi$
$728$		−	11.7898i		−	0.436959i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−17.4652	+	20.9494i	−0.646416	+	0.775372i
$731$	−28.0294			−1.03670
$732$	−1.52635	−	2.10085i	−0.0564157	−	0.0776495i
$733$	15.4309	+	5.01381i	0.569955	+	0.185189i	0.579795	−	0.814762i	$-0.303132\pi$
$733$	15.4309	+	5.01381i	0.569955	+	0.185189i	−0.00984080	+	0.999952i	$0.503132\pi$
$734$	23.7600	+	17.2627i	0.876999	+	0.637177i
$735$	24.5848	+	1.64043i	0.906824	+	0.0605082i
$736$	−1.99328	−	6.13470i	−0.0734734	−	0.226128i
$737$	6.09310	+	3.63855i	0.224442	+	0.134028i
$738$	−13.9014	−	4.51682i	−0.511716	−	0.166267i
$739$	−5.55666	+	17.1016i	−0.204405	+	0.629094i	0.795332	+	0.606174i	$0.207296\pi$
$739$	−5.55666	+	17.1016i	−0.204405	+	0.629094i	−0.999737	+	0.0229201i	$0.992704\pi$
$740$	−4.25518	−	0.283928i	−0.156423	−	0.0104374i
$741$	1.09933			0.0403851
$742$			60.9324i			2.23690i
$743$	23.3291	+	32.1097i	0.855861	+	1.17799i	0.982541	+	0.186048i	$0.0595680\pi$
$743$	23.3291	+	32.1097i	0.855861	+	1.17799i	−0.126680	+	0.991944i	$0.540432\pi$
$744$	1.35846	−	4.18091i	0.0498036	−	0.153280i
$745$	−34.8766	−	13.9619i	−1.27778	−	0.511526i
$746$	12.7709			0.467577
$747$	−8.40905	−	11.5741i	−0.307671	−	0.423473i
$748$	−3.31840	−	1.98161i	−0.121333	−	0.0724549i
$749$	−37.1535			−1.35756
$750$	16.6841	−	1.91499i	0.609216	−	0.0699254i
$751$	9.34859	−	28.7720i	0.341135	−	1.04991i	−0.622486	−	0.782631i	$-0.713877\pi$
$751$	9.34859	−	28.7720i	0.341135	−	1.04991i	0.963621	−	0.267274i	$-0.0861229\pi$
$752$	5.17761	+	7.12637i	0.188808	+	0.259872i
$753$	−19.8166	−	6.43880i	−0.722156	−	0.234643i
$754$	−4.29840	+	13.2291i	−0.156538	+	0.481776i
$755$	9.51534	−	2.40467i	0.346299	−	0.0875150i
$756$	−0.879856	+	0.639253i	−0.0320000	+	0.0232494i
$757$	23.0683	−	31.7507i	0.838430	−	1.15400i	−0.147865	−	0.989008i	$-0.547240\pi$
$757$	23.0683	−	31.7507i	0.838430	−	1.15400i	0.986295	−	0.164992i	$-0.0527599\pi$
$758$	22.6835	−	31.2211i	0.823901	−	1.13400i
$759$	9.77225	+	11.1800i	0.354710	+	0.405810i
$760$	−1.48776	−	5.88709i	−0.0539666	−	0.213547i
$761$	5.82484	−	17.9270i	0.211150	−	0.649854i	−0.788254	−	0.615350i	$-0.789015\pi$
$761$	5.82484	−	17.9270i	0.211150	−	0.649854i	0.999405	−	0.0345041i	$-0.0109852\pi$
$762$	11.8972	−	16.3750i	0.430988	−	0.593205i
$763$		−	39.6625i		−	1.43588i
$764$	−0.914957	−	0.664755i	−0.0331020	−	0.0240500i
$765$	3.77998	−	9.44230i	0.136666	−	0.341387i
$766$	−39.9082			−1.44194
$767$	−3.85650	−	5.30802i	−0.139250	−	0.191662i
$768$	3.55746	−	4.89643i	0.128369	−	0.176685i
$769$	9.32613	+	6.77583i	0.336309	+	0.244343i	0.743103	−	0.669177i	$-0.233353\pi$
$769$	9.32613	+	6.77583i	0.336309	+	0.244343i	−0.406794	+	0.913520i	$0.633353\pi$
$770$	−37.5958	+	28.6804i	−1.35486	+	1.03357i
$771$	13.5679	−	9.85765i	0.488636	−	0.355014i
$772$		−	2.15482i		−	0.0775536i
$773$			29.9161i			1.07601i	0.842942	+	0.538004i	$0.180821\pi$
$773$			29.9161i			1.07601i	−0.842942	+	0.538004i	$0.819179\pi$
$774$	−2.86032	−	8.80317i	−0.102812	−	0.316423i
$775$	−8.31731	−	1.11492i	−0.298767	−	0.0400490i
$776$	−12.5417	+	9.11205i	−0.450220	+	0.327104i
$777$	18.5736	+	25.5643i	0.666323	+	0.917115i
$778$	−28.6699	+	9.31541i	−1.02786	+	0.333974i
$779$	10.0887			0.361466
$780$	0.388992	−	0.466594i	0.0139281	−	0.0167067i
$781$	−22.9637	−	5.23575i	−0.821706	−	0.187350i
$782$			30.5885i			1.09384i
$783$	−8.30588	+	2.69874i	−0.296828	+	0.0964453i
$784$	−39.6414	−	28.8011i	−1.41576	−	1.02861i
$785$	−3.72119	−	14.7248i	−0.132815	−	0.525552i
$786$	−4.68301	−	3.40241i	−0.167038	−	0.121360i
$787$	4.10783	−	1.33472i	0.146428	−	0.0475775i	−0.234886	−	0.972023i	$-0.575472\pi$
$787$	4.10783	−	1.33472i	0.146428	−	0.0475775i	0.381314	+	0.924445i	$0.375472\pi$
$788$		−	6.92769i		−	0.246789i
$789$	−14.2722			−0.508103
$790$	11.4950	+	45.4861i	0.408975	+	1.61832i
$791$	−0.317568	+	0.977373i	−0.0112914	+	0.0347514i
$792$	−1.93114	+	8.46986i	−0.0686199	+	0.300964i
$793$		−	10.7474i		−	0.381653i
$794$	6.77262	+	20.8440i	0.240351	+	0.739725i
$795$	13.6833	−	16.4130i	0.485296	−	0.582110i
$796$	1.01256	+	0.735666i	0.0358891	+	0.0260750i
$797$	9.07956	+	2.95013i	0.321615	+	0.104499i	0.465375	−	0.885114i	$-0.345919\pi$
$797$	9.07956	+	2.95013i	0.321615	+	0.104499i	−0.143760	+	0.989613i	$0.545919\pi$
$798$	3.88552	−	5.34796i	0.137546	−	0.189316i
$799$	−2.78432	−	8.56926i	−0.0985022	−	0.303159i
$800$	−6.49468	−	3.11659i	−0.229622	−	0.110188i
$801$	−4.88036	−	3.54579i	−0.172439	−	0.125284i
$802$	−0.725354	+	0.235682i	−0.0256131	+	0.00832221i
$803$	−20.2783	+	17.7248i	−0.715605	+	0.625496i
$804$	−0.443519	+	0.322236i	−0.0156417	+	0.0113644i
$805$	39.4523	+	15.7937i	1.39051	+	0.556655i
$806$	−2.16263	+	1.57124i	−0.0761755	+	0.0553447i
$807$	17.6441	−	5.73293i	0.621103	−	0.201809i
$808$		−	26.1037i		−	0.918326i
$809$	−16.0720	−	49.4646i	−0.565062	−	1.73908i	−0.667766	−	0.744371i	$-0.732749\pi$
$809$	−16.0720	−	49.4646i	−0.565062	−	1.73908i	0.102704	−	0.994712i	$-0.467251\pi$
$810$	3.35127	+	0.223615i	0.117752	+	0.00785703i
$811$	23.5259			0.826106			0.413053	−	0.910707i	$-0.364462\pi$
$811$	23.5259			0.826106			0.413053	+	0.910707i	$0.364462\pi$
$812$	5.58280	+	7.68406i	0.195918	+	0.269658i
$813$	−7.42229	−	2.41165i	−0.260311	−	0.0845802i
$814$	−36.1569	−	8.24380i	−1.26730	−	0.288945i
$815$	13.1586	−	32.8698i	0.460925	−	1.15138i
$816$	−16.3634	+	11.8887i	−0.572832	+	0.416187i
$817$	3.75523	+	5.16863i	0.131379	+	0.180827i
$818$	23.2370	−	7.55015i	0.812462	−	0.263985i
$819$	−4.50114			−0.157282
$820$	3.56982	−	4.28199i	0.124664	−	0.149533i
$821$	−2.40077	−	1.74426i	−0.0837873	−	0.0608751i	0.545103	−	0.838369i	$-0.316491\pi$
$821$	−2.40077	−	1.74426i	−0.0837873	−	0.0608751i	−0.628890	+	0.777494i	$0.716491\pi$
$822$	18.1679	−	5.90311i	0.633679	−	0.205895i
$823$	−34.2632	−	11.1328i	−1.19434	−	0.388064i	−0.356663	−	0.934233i	$-0.616086\pi$
$823$	−34.2632	−	11.1328i	−1.19434	−	0.388064i	−0.837675	+	0.546169i	$0.816086\pi$
$824$	3.69599			0.128756
$825$	16.5676	+	0.717212i	0.576810	+	0.0249701i
$826$	−39.4526			−1.37273
$827$	−49.8360	−	16.1927i	−1.73297	−	0.563075i	−0.739094	−	0.673602i	$-0.764746\pi$
$827$	−49.8360	−	16.1927i	−1.73297	−	0.563075i	−0.993873	+	0.110527i	$0.964746\pi$
$828$	−1.09092	+	0.354461i	−0.0379120	+	0.0123184i
$829$	−12.8906	−	9.36556i	−0.447709	−	0.325279i	0.340982	−	0.940070i	$-0.389241\pi$
$829$	−12.8906	−	9.36556i	−0.447709	−	0.325279i	−0.788690	+	0.614791i	$0.789241\pi$
$830$	46.5864	−	11.7731i	1.61704	−	0.408650i
$831$	−3.00769			−0.104336
$832$	6.78641	−	2.20504i	0.235277	−	0.0764460i
$833$	29.4602	+	40.5485i	1.02073	+	1.40492i
$834$	−8.93492	+	6.49160i	−0.309391	+	0.224786i
$835$	22.2976	+	18.5891i	0.771639	+	0.643303i
$836$	0.0791713	+	0.877398i	0.00273820	+	0.0303455i
$837$	−1.59620	−	0.518636i	−0.0551726	−	0.0179267i
$838$	29.7195	+	40.9053i	1.02664	+	1.41305i
$839$	−51.8215			−1.78908			−0.894538	−	0.446992i	$-0.852495\pi$
$839$	−51.8215			−1.78908			−0.894538	+	0.446992i	$0.852495\pi$
$840$	6.09150	+	24.1042i	0.210177	+	0.831675i
$841$	14.6075	+	44.9573i	0.503707	+	1.55025i
$842$		−	2.76076i		−	0.0951421i
$843$	−7.69307	+	2.49963i	−0.264963	+	0.0860918i
$844$	−2.87728	+	2.09046i	−0.0990400	+	0.0719568i
$845$	−25.7453	+	6.50623i	−0.885666	+	0.223821i
$846$	2.40721	−	1.74894i	0.0827615	−	0.0601297i
$847$	−41.1081	+	22.1457i	−1.41249	+	0.760935i
$848$	−40.4151	+	13.1317i	−1.38786	+	0.450943i
$849$	−23.5797	−	17.1316i	−0.809252	−	0.587956i
$850$	24.7240	+	23.5731i	0.848028	+	0.808550i
$851$	10.2989	+	31.6967i	0.353042	+	1.08655i
$852$	1.06944	−	1.47196i	0.0366384	−	0.0504284i
$853$	−38.0597	−	12.3663i	−1.30314	−	0.423416i	−0.426467	−	0.904503i	$-0.640242\pi$
$853$	−38.0597	−	12.3663i	−1.30314	−	0.423416i	−0.876673	+	0.481087i	$0.840242\pi$
$854$	−52.2833	−	37.9861i	−1.78910	−	1.29986i
$855$	−2.24758	+	0.567999i	−0.0768658	+	0.0194252i
$856$	−7.08436	−	21.8034i	−0.242138	−	0.745226i
$857$			49.7527i			1.69952i	0.527169	+	0.849761i	$0.323254\pi$
$857$			49.7527i			1.69952i	−0.527169	+	0.849761i	$0.676746\pi$
$858$	3.97731	−	3.47649i	0.135783	−	0.118685i
$859$	9.15629	−	28.1801i	0.312408	−	0.961494i	−0.664400	−	0.747377i	$-0.731313\pi$
$859$	9.15629	−	28.1801i	0.312408	−	0.961494i	0.976808	−	0.214117i	$-0.0686873\pi$
$860$	3.52250	+	0.235040i	0.120116	+	0.00801481i
$861$	−41.3074			−1.40775
$862$		−	2.47704i		−	0.0843683i
$863$	10.2051	−	3.31585i	0.347386	−	0.112873i	−0.130127	−	0.991497i	$-0.541538\pi$
$863$	10.2051	−	3.31585i	0.347386	−	0.112873i	0.477513	+	0.878625i	$0.341538\pi$
$864$	−1.16559	−	0.846851i	−0.0396542	−	0.0288105i
$865$	43.5512	−	27.4071i	1.48078	−	0.931871i
$866$	13.4193	+	9.74968i	0.456006	+	0.331308i
$867$	3.50850	−	1.13998i	0.119155	−	0.0387158i
$868$			1.82530i			0.0619547i
$869$	4.16345	+	46.1406i	0.141235	+	1.56521i
$870$	1.95290	−	29.2677i	0.0662096	−	0.992269i
$871$	−2.26894			−0.0768801
$872$	23.2758	−	7.56277i	0.788219	−	0.256108i
$873$	3.47882	+	4.78818i	0.117740	+	0.162055i
$874$	5.64053	−	4.09808i	0.190794	−	0.138620i
$875$	43.1697	−	19.7170i	1.45940	−	0.666557i
$876$	−0.642918	−	1.97870i	−0.0217222	−	0.0668540i
$877$			22.3360i			0.754232i	0.926166	+	0.377116i	$0.123084\pi$
$877$			22.3360i			0.754232i	−0.926166	+	0.377116i	$0.876916\pi$
$878$		−	53.6872i		−	1.81186i
$879$	−0.538771	+	0.391440i	−0.0181723	+	0.0132029i
$880$	−27.1254	−	18.7555i	−0.914398	−	0.632247i
$881$	−17.9975	−	13.0760i	−0.606352	−	0.440540i	0.241776	−	0.970332i	$-0.422270\pi$
$881$	−17.9975	−	13.0760i	−0.606352	−	0.440540i	−0.848128	+	0.529792i	$0.822270\pi$
$882$	−9.72869	+	13.3904i	−0.327582	+	0.450878i
$883$	15.7024	+	21.6125i	0.528428	+	0.727318i	0.986890	−	0.161396i	$-0.0515995\pi$
$883$	15.7024	+	21.6125i	0.528428	+	0.727318i	−0.458462	+	0.888714i	$0.651600\pi$
$884$	1.23570			0.0415611
$885$	10.6271	+	8.85967i	0.357227	+	0.297815i
$886$	−25.1487	−	18.2716i	−0.844888	−	0.613847i
$887$		−	32.7619i		−	1.10004i	−0.835152	−	0.550019i	$-0.814621\pi$
$887$		−	32.7619i		−	1.10004i	0.835152	−	0.550019i	$-0.185379\pi$
$888$	−11.4608	+	15.7744i	−0.384598	+	0.529354i
$889$	17.6760	−	54.4012i	0.592834	−	1.82456i
$890$	17.1483	−	10.7916i	0.574812	−	0.361734i
$891$	3.23364	+	0.737273i	0.108331	+	0.0246996i
$892$	−3.38773	+	4.66281i	−0.113430	+	0.156122i
$893$	−1.20714	+	1.66149i	−0.0403956	+	0.0555997i
$894$	20.4161	−	14.8332i	0.682817	−	0.496096i
$895$	11.1591	−	13.3853i	0.373008	−	0.447422i
$896$	17.0390	−	52.4406i	0.569232	−	1.75192i
$897$	−4.51503	−	1.46702i	−0.150752	−	0.0489824i
$898$	30.8208	+	42.4212i	1.02850	+	1.41561i
$899$	−4.52941	+	13.9401i	−0.151064	+	0.464928i
$900$	−0.554215	+	1.15493i	−0.0184738	+	0.0384977i
$901$	43.4673			1.44811
$902$	36.5002	−	31.9042i	1.21533	−	1.06229i
$903$	−15.3755	−	21.1625i	−0.511664	−	0.704245i
$904$	−0.634121			−0.0210905
$905$	−9.67156	−	15.3685i	−0.321494	−	0.510868i
$906$	−2.03730	+	6.27015i	−0.0676846	+	0.208312i
$907$	14.0885	+	19.3911i	0.467800	+	0.643872i	0.976103	−	0.217306i	$-0.0697270\pi$
$907$	14.0885	+	19.3911i	0.467800	+	0.643872i	−0.508303	+	0.861178i	$0.669727\pi$
$908$		−	3.08555i		−	0.102398i
$909$	−9.96593			−0.330549
$910$	5.61863	−	14.0352i	0.186256	−	0.465263i
$911$	−9.31230	+	28.6603i	−0.308530	+	0.949558i	0.669806	+	0.742536i	$0.266377\pi$
$911$	−9.31230	+	28.6603i	−0.308530	+	0.949558i	−0.978336	+	0.207022i	$0.933623\pi$
$912$	4.38455	+	1.42463i	0.145187	+	0.0471741i
$913$	47.2568	−	4.26417i	1.56397	−	0.141123i
$914$	16.4519	+	50.6336i	0.544179	+	1.67481i
$915$	5.55294	+	21.9731i	0.183575	+	0.726408i
$916$	−1.44478	−	1.04969i	−0.0477368	−	0.0346828i
$917$	−15.5579	−	5.05507i	−0.513768	−	0.166933i
$918$	4.01586	+	5.52735i	0.132543	+	0.182430i
$919$	1.44243			0.0475814			0.0237907	−	0.999717i	$-0.492426\pi$
$919$	1.44243			0.0475814			0.0237907	+	0.999717i	$0.492426\pi$
$920$	−1.74580	+	26.1640i	−0.0575574	+	0.862600i
$921$	5.70242	+	17.5502i	0.187901	+	0.578300i
$922$			36.0550i			1.18741i
$923$	7.16164	−	2.32696i	0.235728	−	0.0765927i
$924$	−0.324160	−	3.59244i	−0.0106641	−	0.118183i
$925$	33.5567	+	16.1028i	1.10334	+	0.529456i
$926$	37.3184	+	27.1134i	1.22636	+	0.891003i
$927$		−	1.41106i		−	0.0463454i
$928$	−7.39583	+	10.1795i	−0.242780	+	0.334158i
$929$	−6.32376	+	19.4625i	−0.207476	+	0.638545i	0.792127	+	0.610357i	$0.208974\pi$
$929$	−6.32376	+	19.4625i	−0.207476	+	0.638545i	−0.999603	+	0.0281885i	$0.991026\pi$
$930$	3.60967	−	4.32978i	0.118366	−	0.141979i
$931$	3.53023	−	10.8649i	0.115699	−	0.356084i
$932$	−6.87214	−	2.23289i	−0.225105	−	0.0731409i
$933$	−6.25217	+	2.03145i	−0.204687	+	0.0665067i
$934$	−4.46289	+	13.7354i	−0.146030	+	0.449435i
$935$	20.4597	+	26.8197i	0.669105	+	0.877098i
$936$	−0.858267	−	2.64148i	−0.0280533	−	0.0863393i
$937$	−15.9080	−	21.8955i	−0.519692	−	0.715294i	0.465824	−	0.884877i	$-0.345758\pi$
$937$	−15.9080	−	21.8955i	−0.519692	−	0.715294i	−0.985516	+	0.169583i	$0.945758\pi$
$938$	−8.01941	+	11.0378i	−0.261843	+	0.360396i
$939$	−1.85172	+	1.34535i	−0.0604286	+	0.0439040i
$940$	0.278053	+	1.10026i	0.00906907	+	0.0358865i
$941$	−1.21496	−	3.73927i	−0.0396066	−	0.121897i	0.929298	−	0.369330i	$-0.120413\pi$
$941$	−1.21496	−	3.73927i	−0.0396066	−	0.121897i	−0.968905	+	0.247434i	$0.920413\pi$
$942$	9.70295	+	3.15268i	0.316139	+	0.102720i
$943$	−41.4349	−	13.4630i	−1.34931	−	0.438416i
$944$	−8.50250	−	26.1680i	−0.276733	−	0.851696i
$945$	9.20255	−	2.32563i	0.299359	−	0.0756526i
$946$	29.9312	+	6.82434i	0.973148	+	0.221879i
$947$	17.1157	+	23.5577i	0.556185	+	0.765523i	0.990835	−	0.135076i	$-0.0431280\pi$
$947$	17.1157	+	23.5577i	0.556185	+	0.765523i	−0.434650	+	0.900599i	$0.643128\pi$
$948$	−3.40362	−	1.10590i	−0.110544	−	0.0359181i
$949$	2.66087	−	8.18932i	0.0863756	−	0.265837i
$950$	1.03449	−	7.71732i	0.0335632	−	0.250383i
$951$	−20.9857	+	15.2470i	−0.680506	+	0.494417i
$952$	−29.7263	+	40.9147i	−0.963434	+	1.32605i
$953$	0.136620	−	0.188041i	0.00442555	−	0.00609125i	−0.806798	−	0.590827i	$-0.798802\pi$
$953$	0.136620	−	0.188041i	0.00442555	−	0.00609125i	0.811224	+	0.584735i	$0.198802\pi$
$954$	4.43572	+	13.6517i	0.143612	+	0.441992i
$955$	5.25724	+	8.35398i	0.170120	+	0.270329i
$956$	2.42010	+	1.75830i	0.0782715	+	0.0568676i
$957$	6.43884	−	28.2404i	0.208138	−	0.912883i
$958$	31.9878	−	44.0274i	1.03348	−	1.42246i
$959$	43.6751	−	31.7318i	1.41034	−	1.02467i
$960$	−12.7355	+	8.01457i	−0.411037	+	0.258669i
$961$	22.8007	−	16.5657i	0.735505	−	0.534376i
$962$	11.2762	−	3.66384i	0.363558	−	0.118127i
$963$	−8.32415	+	2.70468i	−0.268242	+	0.0871571i
$964$	−1.07540	+	0.781327i	−0.0346364	+	0.0251648i
$965$	−6.98944	+	17.4595i	−0.224998	+	0.562040i
$966$	−23.0947	+	16.7793i	−0.743059	+	0.539864i
$967$	0.369797	−	0.508982i	0.0118919	−	0.0163678i	−0.803030	−	0.595939i	$-0.796780\pi$
$967$	0.369797	−	0.508982i	0.0118919	−	0.0163678i	0.814922	+	0.579571i	$0.196780\pi$
$968$	−20.8345	−	19.9015i	−0.669647	−	0.639658i
$969$	−3.81507	−	2.77181i	−0.122558	−	0.0890433i
$970$	−19.2728	+	4.87052i	−0.618811	+	0.156383i
$971$	−4.81803	−	14.8284i	−0.154618	−	0.475865i	0.843504	−	0.537123i	$-0.180489\pi$
$971$	−4.81803	−	14.8284i	−0.154618	−	0.475865i	−0.998122	+	0.0612580i	$0.980489\pi$
$972$	−0.150593	+	0.207274i	−0.00483028	+	0.00664832i
$973$	−18.3455	+	25.2504i	−0.588129	+	0.809490i
$974$	−26.3186	+	19.1216i	−0.843302	+	0.612695i
$975$	−4.66528	+	2.51884i	−0.149408	+	0.0806674i
$976$	13.9276	−	42.8648i	0.445812	−	1.37207i
$977$	−19.5187	−	6.34201i	−0.624459	−	0.202899i	−0.0203398	−	0.999793i	$-0.506475\pi$
$977$	−19.5187	−	6.34201i	−0.624459	−	0.202899i	−0.604119	+	0.796894i	$0.706475\pi$
$978$	13.9797	+	19.2414i	0.447021	+	0.615272i
$979$	18.3955	−	7.86764i	0.587924	−	0.251451i
$980$	−3.36229	−	5.34283i	−0.107404	−	0.170670i
$981$	−2.88733	−	8.88628i	−0.0921853	−	0.283717i
$982$	35.6876	+	11.5956i	1.13884	+	0.370031i
$983$	−11.3934	−	3.70193i	−0.363392	−	0.118073i	0.121629	−	0.992576i	$-0.461188\pi$
$983$	−11.3934	−	3.70193i	−0.363392	−	0.118073i	−0.485021	+	0.874502i	$0.661188\pi$
$984$	−7.87642	−	24.2411i	−0.251091	−	0.772779i
$985$	−22.4709	+	56.1317i	−0.715982	+	1.78851i
$986$	48.2722	−	35.0718i	1.53730	−	1.11691i
$987$	4.94256	−	6.80285i	0.157323	−	0.216537i
$988$	−0.165552	−	0.227863i	−0.00526692	−	0.00724930i
$989$	−8.52558	−	26.2390i	−0.271098	−	0.834353i
$990$	−6.33538	+	9.16265i	−0.201352	+	0.291208i
$991$	6.52624	−	20.0857i	0.207313	−	0.638043i	−0.792298	−	0.610135i	$-0.791115\pi$
$991$	6.52624	−	20.0857i	0.207313	−	0.638043i	0.999610	−	0.0279083i	$-0.00888464\pi$
$992$	−2.29972	+	0.747224i	−0.0730162	+	0.0237244i
$993$	24.3458	+	7.91042i	0.772590	+	0.251030i
$994$	13.9923	−	43.0638i	0.443808	−	1.36590i
$995$	−5.81803	−	9.24511i	−0.184444	−	0.293090i
$996$	−1.13266	+	3.48596i	−0.0358896	+	0.110457i
$997$	12.6823	−	17.4557i	0.401653	−	0.552828i	−0.559505	−	0.828827i	$-0.689009\pi$
$997$	12.6823	−	17.4557i	0.401653	−	0.552828i	0.961158	+	0.275999i	$0.0890087\pi$
$998$			29.8973i			0.946384i
$999$	6.02237	+	4.37551i	0.190539	+	0.138435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.cb.a.169.15	yes	240
11.3	even	5		825.2.by.a.619.15	yes	240
25.4	even	10		825.2.by.a.4.15	✓	240
275.179	even	10	inner	825.2.cb.a.454.15	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.by.a.4.15	✓	240	25.4	even	10
825.2.by.a.619.15	yes	240	11.3	even	5
825.2.cb.a.169.15	yes	240	1.1	even	1	trivial
825.2.cb.a.454.15	yes	240	275.179	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.cb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42855 - 0.464164i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.207274 + 0.150593i) q^{4} +(-1.19097 - 1.89251i) q^{5} +1.50207 q^{6} +(4.03713 - 1.31174i) q^{7} +(1.53958 + 2.11906i) q^{8} +(0.809017 - 0.587785i) q^{9} +(0.822929 + 3.25635i) q^{10} +(0.298062 + 3.30320i) q^{11} +(-0.243665 - 0.0791716i) q^{12} +(-0.623267 - 0.857854i) q^{13} -6.37611 q^{14} +(1.71750 + 1.43185i) q^{15} +(-1.37413 - 4.22913i) q^{16} +4.54852i q^{17} +(-1.42855 + 0.464164i) q^{18} +(0.838749 - 0.609387i) q^{19} +(0.0381416 - 0.571620i) q^{20} +(-3.43419 + 2.49508i) q^{21} +(1.10743 - 4.85714i) q^{22} +(-4.25799 + 1.38351i) q^{23} +(-2.11906 - 1.53958i) q^{24} +(-2.16317 + 4.50785i) q^{25} +(0.492184 + 1.51479i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(1.03433 + 0.336075i) q^{28} +(7.06541 + 5.13332i) q^{29} +(-1.78892 - 2.84267i) q^{30} +(0.518636 + 1.59620i) q^{31} +1.44075i q^{32} +(-1.30422 - 3.04943i) q^{33} +(2.11126 - 6.49779i) q^{34} +(-7.29060 - 6.07805i) q^{35} +0.256205 q^{36} -7.44406i q^{37} +(-1.48105 + 0.481222i) q^{38} +(0.857854 + 0.623267i) q^{39} +(2.17673 - 5.43741i) q^{40} +(7.87262 + 5.71979i) q^{41} +(6.06404 - 1.97033i) q^{42} +6.16231i q^{43} +(-0.435660 + 0.729554i) q^{44} +(-2.07590 - 0.831035i) q^{45} +6.72493 q^{46} +(-1.88396 + 0.612137i) q^{47} +(2.61375 + 3.59751i) q^{48} +(8.91464 - 6.47687i) q^{49} +(5.18258 - 5.43562i) q^{50} +(-1.40557 - 4.32590i) q^{51} -0.271671i q^{52} -9.55636i q^{53} +(1.21520 - 0.882893i) q^{54} +(5.89636 - 4.49811i) q^{55} +(8.99516 + 6.53537i) q^{56} +(-0.609387 + 0.838749i) q^{57} +(-7.71059 - 10.6127i) q^{58} +6.18756 q^{59} +(0.140366 + 0.555429i) q^{60} +(8.19988 + 5.95756i) q^{61} -2.52098i q^{62} +(2.49508 - 3.43419i) q^{63} +(-2.07951 + 6.40007i) q^{64} +(-0.881201 + 2.20122i) q^{65} +(0.447709 + 4.96163i) q^{66} +(1.25773 - 1.73111i) q^{67} +(-0.684977 + 0.942790i) q^{68} +(3.62206 - 2.63158i) q^{69} +(7.59377 + 12.0668i) q^{70} +(-2.19449 + 6.75393i) q^{71} +(2.49110 + 0.809407i) q^{72} +(4.77315 + 6.56967i) q^{73} +(-3.45527 + 10.6342i) q^{74} +(0.664297 - 4.95567i) q^{75} +0.265620 q^{76} +(5.53627 + 12.9445i) q^{77} +(-0.936189 - 1.28855i) q^{78} +13.9684 q^{79} +(-6.36711 + 7.63732i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-8.59151 - 11.8252i) q^{82} -14.3063i q^{83} -1.08756 q^{84} +(8.60811 - 5.41716i) q^{85} +(2.86032 - 8.80317i) q^{86} +(-8.30588 - 2.69874i) q^{87} +(-6.54078 + 5.71717i) q^{88} +(-1.86413 - 5.73720i) q^{89} +(2.57980 + 2.15074i) q^{90} +(-3.64150 - 2.64570i) q^{91} +(-1.09092 - 0.354461i) q^{92} +(-0.986504 - 1.35781i) q^{93} +2.97547 q^{94} +(-2.15220 - 0.861576i) q^{95} +(-0.445216 - 1.37023i) q^{96} +5.91852i q^{97} +(-15.7413 + 5.11467i) q^{98} +(2.18271 + 2.49715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 60 q^{4} + 6 q^{5} - 16 q^{6} + 10 q^{7} + 60 q^{9} + 8 q^{10} + 4 q^{11} - 20 q^{12} - 64 q^{16} - 24 q^{19} - 44 q^{20} + 8 q^{21} - 40 q^{22} + 40 q^{23} - 12 q^{24} + 4 q^{25} + 40 q^{26} + 30 q^{28}+ \cdots - 4 q^{99}+O(q^{100}) \) 240 * q + 60 * q^4 + 6 * q^5 - 16 * q^6 + 10 * q^7 + 60 * q^9 + 8 * q^10 + 4 * q^11 - 20 * q^12 - 64 * q^16 - 24 * q^19 - 44 * q^20 + 8 * q^21 - 40 * q^22 + 40 * q^23 - 12 * q^24 + 4 * q^25 + 40 * q^26 + 30 * q^28 + 4 * q^30 - 2 * q^31 + 30 * q^35 + 240 * q^36 - 16 * q^39 + 68 * q^40 - 6 * q^41 - 10 * q^42 + 26 * q^44 + 4 * q^45 - 48 * q^46 - 40 * q^47 + 40 * q^48 + 58 * q^49 - 78 * q^50 + 16 * q^51 - 4 * q^54 - 10 * q^55 - 40 * q^57 + 60 * q^58 - 24 * q^59 + 8 * q^60 + 28 * q^61 - 10 * q^63 + 44 * q^64 + 60 * q^65 + 8 * q^66 - 40 * q^67 - 250 * q^68 + 2 * q^69 - 44 * q^70 - 16 * q^71 + 22 * q^74 + 20 * q^75 - 168 * q^76 - 30 * q^77 + 172 * q^79 - 118 * q^80 - 60 * q^81 + 40 * q^82 + 96 * q^84 + 40 * q^85 - 72 * q^86 - 40 * q^87 - 100 * q^88 + 2 * q^90 - 30 * q^91 + 100 * q^92 + 56 * q^94 - 122 * q^95 + 28 * q^96 - 140 * q^98 - 4 * q^99

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