LMFDB - Embedded newform 273.2.cd.e.44.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(44,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("273.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cd (of order $12$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			44.2
Character	$\chi$	$=$	273.44
Dual form			273.2.cd.e.242.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.42391 + 0.649484i) q^{2} +(-1.28483 - 1.16155i) q^{3} +(3.72144 - 2.14858i) q^{4} +(3.58252 - 0.959933i) q^{5} +(3.86873 + 1.98102i) q^{6} +(1.55291 - 2.14207i) q^{7} +(-4.07612 + 4.07612i) q^{8} +(0.301593 + 2.98480i) q^{9} +O(q^{10})$	\(q+(-2.42391 + 0.649484i) q^{2} +(-1.28483 - 1.16155i) q^{3} +(3.72144 - 2.14858i) q^{4} +(3.58252 - 0.959933i) q^{5} +(3.86873 + 1.98102i) q^{6} +(1.55291 - 2.14207i) q^{7} +(-4.07612 + 4.07612i) q^{8} +(0.301593 + 2.98480i) q^{9} +(-8.06023 + 4.65358i) q^{10} +(-2.52674 - 0.677038i) q^{11} +(-7.27712 - 1.56209i) q^{12} +(3.59741 - 0.242118i) q^{13} +(-2.37286 + 6.20077i) q^{14} +(-5.71795 - 2.92793i) q^{15} +(2.93561 - 5.08463i) q^{16} +(-0.358785 - 0.621434i) q^{17} +(-2.66961 - 7.03900i) q^{18} +(1.19661 + 4.46581i) q^{19} +(11.2697 - 11.2697i) q^{20} +(-4.48336 + 0.948423i) q^{21} +6.56431 q^{22} +(2.80909 - 4.86549i) q^{23} +(9.97177 - 0.502509i) q^{24} +(7.58284 - 4.37795i) q^{25} +(-8.56254 + 2.92333i) q^{26} +(3.07951 - 4.18529i) q^{27} +(1.17665 - 11.3081i) q^{28} +1.19958i q^{29} +(15.7614 + 3.38331i) q^{30} +(-3.93812 - 1.05522i) q^{31} +(-0.829338 + 3.09513i) q^{32} +(2.46003 + 3.80482i) q^{33} +(1.27327 + 1.27327i) q^{34} +(3.50707 - 9.16470i) q^{35} +(7.53544 + 10.4598i) q^{36} +(-5.34024 + 1.43091i) q^{37} +(-5.80094 - 10.0475i) q^{38} +(-4.90331 - 3.86750i) q^{39} +(-10.6900 + 18.5156i) q^{40} +(3.34101 + 3.34101i) q^{41} +(10.2513 - 5.21076i) q^{42} -4.83534i q^{43} +(-10.8578 + 2.90934i) q^{44} +(3.94567 + 10.4036i) q^{45} +(-3.64892 + 13.6179i) q^{46} +(-0.235612 - 0.879316i) q^{47} +(-9.67784 + 3.12304i) q^{48} +(-2.17695 - 6.65288i) q^{49} +(-15.5367 + 15.5367i) q^{50} +(-0.260849 + 1.21519i) q^{51} +(12.8674 - 8.63035i) q^{52} +(2.40005 - 1.38567i) q^{53} +(-4.74616 + 12.1448i) q^{54} -9.70201 q^{55} +(2.40151 + 15.0612i) q^{56} +(3.64983 - 7.12775i) q^{57} +(-0.779109 - 2.90768i) q^{58} +(-8.51651 - 2.28199i) q^{59} +(-27.5699 + 1.38934i) q^{60} +(5.31781 - 9.21071i) q^{61} +10.2310 q^{62} +(6.86201 + 3.98909i) q^{63} +3.70150i q^{64} +(12.6554 - 4.32067i) q^{65} +(-8.43405 - 7.62479i) q^{66} +(-3.15045 - 0.844160i) q^{67} +(-2.67040 - 1.54176i) q^{68} +(-9.26073 + 2.98843i) q^{69} +(-2.54850 + 24.4922i) q^{70} +(7.32763 + 7.32763i) q^{71} +(-13.3958 - 10.9371i) q^{72} +(-1.53552 + 5.73065i) q^{73} +(12.0149 - 6.93680i) q^{74} +(-14.8279 - 3.18292i) q^{75} +(14.0483 + 14.0483i) q^{76} +(-5.37406 + 4.36109i) q^{77} +(14.3970 + 6.18984i) q^{78} +(-1.74363 + 3.02006i) q^{79} +(5.63598 - 21.0338i) q^{80} +(-8.81808 + 1.80039i) q^{81} +(-10.2682 - 5.92837i) q^{82} +(-1.93496 - 1.93496i) q^{83} +(-14.6468 + 13.1623i) q^{84} +(-1.88189 - 1.88189i) q^{85} +(3.14048 + 11.7204i) q^{86} +(1.39338 - 1.54126i) q^{87} +(13.0590 - 7.53962i) q^{88} +(-2.74480 - 10.2437i) q^{89} +(-16.3209 - 22.6547i) q^{90} +(5.06782 - 8.08191i) q^{91} -24.1422i q^{92} +(3.83414 + 5.93011i) q^{93} +(1.14220 + 1.97835i) q^{94} +(8.57375 + 14.8502i) q^{95} +(4.66072 - 3.01341i) q^{96} +(-13.6182 + 13.6182i) q^{97} +(9.59767 + 14.7121i) q^{98} +(1.25878 - 7.74601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.42391	+	0.649484i	−1.71396	+	0.459254i	−0.976390	−	0.216015i	$-0.930694\pi$
$2$	−2.42391	+	0.649484i	−1.71396	+	0.459254i	−0.737571	+	0.675270i	$0.764027\pi$
$3$	−1.28483	−	1.16155i	−0.741799	−	0.670622i
$3$	−1.28483	−	1.16155i	−0.741799	−	0.670622i
$4$	3.72144	−	2.14858i	1.86072	−	1.07429i
$5$	3.58252	−	0.959933i	1.60215	−	0.429295i	0.656459	−	0.754361i	$-0.272053\pi$
$5$	3.58252	−	0.959933i	1.60215	−	0.429295i	0.945691	+	0.325066i	$0.105387\pi$
$6$	3.86873	+	1.98102i	1.57940	+	0.808746i
$7$	1.55291	−	2.14207i	0.586944	−	0.809627i
$7$	1.55291	−	2.14207i	0.586944	−	0.809627i
$8$	−4.07612	+	4.07612i	−1.44113	+	1.44113i
$9$	0.301593	+	2.98480i	0.100531	+	0.994934i
$10$	−8.06023	+	4.65358i	−2.54887	+	1.47159i
$11$	−2.52674	−	0.677038i	−0.761841	−	0.204135i	−0.143077	−	0.989712i	$-0.545700\pi$
$11$	−2.52674	−	0.677038i	−0.761841	−	0.204135i	−0.618764	+	0.785577i	$0.712366\pi$
$12$	−7.27712	−	1.56209i	−2.10072	−	0.450936i
$13$	3.59741	−	0.242118i	0.997743	−	0.0671514i
$13$	3.59741	−	0.242118i	0.997743	−	0.0671514i
$14$	−2.37286	+	6.20077i	−0.634174	+	1.65723i
$15$	−5.71795	−	2.92793i	−1.47637	−	0.755988i
$16$	2.93561	−	5.08463i	0.733903	−	1.27116i
$17$	−0.358785	−	0.621434i	−0.0870182	−	0.150720i	0.819231	−	0.573463i	$-0.194401\pi$
$17$	−0.358785	−	0.621434i	−0.0870182	−	0.150720i	−0.906249	+	0.422743i	$0.861067\pi$
$18$	−2.66961	−	7.03900i	−0.629234	−	1.65911i
$19$	1.19661	+	4.46581i	0.274521	+	1.02453i	0.956162	+	0.292840i	$0.0946002\pi$
$19$	1.19661	+	4.46581i	0.274521	+	1.02453i	−0.681640	+	0.731687i	$0.738733\pi$
$20$	11.2697	−	11.2697i	2.51997	−	2.51997i
$21$	−4.48336	+	0.948423i	−0.978349	+	0.206963i
$22$	6.56431			1.39952
$23$	2.80909	−	4.86549i	0.585736	−	1.01452i	−0.409048	−	0.912513i	$-0.634139\pi$
$23$	2.80909	−	4.86549i	0.585736	−	1.01452i	0.994783	−	0.102011i	$-0.0325276\pi$
$24$	9.97177	−	0.502509i	2.03548	−	0.102574i
$25$	7.58284	−	4.37795i	1.51657	−	0.875590i
$26$	−8.56254	+	2.92333i	−1.67925	+	0.573313i
$27$	3.07951	−	4.18529i	0.592651	−	0.805459i
$28$	1.17665	−	11.3081i	0.222366	−	2.13704i
$29$			1.19958i			0.222757i	0.993778	+	0.111378i	$0.0355266\pi$
$29$			1.19958i			0.222757i	−0.993778	+	0.111378i	$0.964473\pi$
$30$	15.7614	+	3.38331i	2.87763	+	0.617705i
$31$	−3.93812	−	1.05522i	−0.707307	−	0.189522i	−0.112806	−	0.993617i	$-0.535984\pi$
$31$	−3.93812	−	1.05522i	−0.707307	−	0.189522i	−0.594501	+	0.804095i	$0.702650\pi$
$32$	−0.829338	+	3.09513i	−0.146608	+	0.547147i
$33$	2.46003	+	3.80482i	0.428236	+	0.662335i
$34$	1.27327	+	1.27327i	0.218365	+	0.218365i
$35$	3.50707	−	9.16470i	0.592804	−	1.54912i
$36$	7.53544	+	10.4598i	1.25591	+	1.74330i
$37$	−5.34024	+	1.43091i	−0.877930	+	0.235241i	−0.669514	−	0.742800i	$-0.733497\pi$
$37$	−5.34024	+	1.43091i	−0.877930	+	0.235241i	−0.208416	+	0.978040i	$0.566831\pi$
$38$	−5.80094	−	10.0475i	−0.941037	−	1.62992i
$39$	−4.90331	−	3.86750i	−0.785158	−	0.619296i
$40$	−10.6900	+	18.5156i	−1.69023	+	2.92757i
$41$	3.34101	+	3.34101i	0.521779	+	0.521779i	0.918108	−	0.396330i	$-0.129716\pi$
$41$	3.34101	+	3.34101i	0.521779	+	0.521779i	−0.396330	+	0.918108i	$0.629716\pi$
$42$	10.2513	−	5.21076i	1.58180	−	0.804037i
$43$		−	4.83534i		−	0.737383i	−0.929552	−	0.368691i	$-0.879806\pi$
$43$		−	4.83534i		−	0.737383i	0.929552	−	0.368691i	$-0.120194\pi$
$44$	−10.8578	+	2.90934i	−1.63687	+	0.438599i
$45$	3.94567	+	10.4036i	0.588186	+	1.55088i
$46$	−3.64892	+	13.6179i	−0.538003	+	2.00786i
$47$	−0.235612	−	0.879316i	−0.0343675	−	0.128261i	0.946611	−	0.322379i	$-0.104482\pi$
$47$	−0.235612	−	0.879316i	−0.0343675	−	0.128261i	−0.980978	+	0.194117i	$0.937816\pi$
$48$	−9.67784	+	3.12304i	−1.39688	+	0.450771i
$49$	−2.17695	−	6.65288i	−0.310993	−	0.950412i
$50$	−15.5367	+	15.5367i	−2.19722	+	2.19722i
$51$	−0.260849	+	1.21519i	−0.0365262	+	0.170160i
$52$	12.8674	−	8.63035i	1.78438	−	1.19681i
$53$	2.40005	−	1.38567i	0.329672	−	0.190336i	−0.326024	−	0.945362i	$-0.605709\pi$
$53$	2.40005	−	1.38567i	0.329672	−	0.190336i	0.655695	+	0.755026i	$0.272376\pi$
$54$	−4.74616	+	12.1448i	−0.645870	+	1.65270i
$55$	−9.70201			−1.30822
$56$	2.40151	+	15.0612i	0.320915	+	2.01264i
$57$	3.64983	−	7.12775i	0.483431	−	0.944093i
$58$	−0.779109	−	2.90768i	−0.102302	−	0.381797i
$59$	−8.51651	−	2.28199i	−1.10875	−	0.297090i	−0.342430	−	0.939543i	$-0.611250\pi$
$59$	−8.51651	−	2.28199i	−1.10875	−	0.297090i	−0.766325	+	0.642453i	$0.777917\pi$
$60$	−27.5699	+	1.38934i	−3.55926	+	0.179362i
$61$	5.31781	−	9.21071i	0.680876	−	1.17931i	−0.293838	−	0.955855i	$-0.594933\pi$
$61$	5.31781	−	9.21071i	0.680876	−	1.17931i	0.974714	−	0.223456i	$-0.0717339\pi$
$62$	10.2310			1.29934
$63$	6.86201	+	3.98909i	0.864532	+	0.502578i
$64$			3.70150i			0.462688i
$65$	12.6554	−	4.32067i	1.56971	−	0.535913i
$66$	−8.43405	−	7.62479i	−1.03816	−	0.938547i
$67$	−3.15045	−	0.844160i	−0.384888	−	0.103131i	0.0611861	−	0.998126i	$-0.480512\pi$
$67$	−3.15045	−	0.844160i	−0.384888	−	0.103131i	−0.446074	+	0.894996i	$0.647178\pi$
$68$	−2.67040	−	1.54176i	−0.323833	−	0.186965i
$69$	−9.26073	+	2.98843i	−1.11486	+	0.359765i
$70$	−2.54850	+	24.4922i	−0.304604	+	2.92737i
$71$	7.32763	+	7.32763i	0.869629	+	0.869629i	0.992431	−	0.122802i	$-0.0391880\pi$
$71$	7.32763	+	7.32763i	0.869629	+	0.869629i	−0.122802	+	0.992431i	$0.539188\pi$
$72$	−13.3958	−	10.9371i	−1.57870	−	1.28895i
$73$	−1.53552	+	5.73065i	−0.179719	+	0.670722i	0.815980	+	0.578080i	$0.196198\pi$
$73$	−1.53552	+	5.73065i	−0.179719	+	0.670722i	−0.995699	+	0.0926420i	$0.970469\pi$
$74$	12.0149	−	6.93680i	1.39670	−	0.806386i
$75$	−14.8279	−	3.18292i	−1.71218	−	0.367532i
$76$	14.0483	+	14.0483i	1.61145	+	1.61145i
$77$	−5.37406	+	4.36109i	−0.612431	+	0.496992i
$78$	14.3970	+	6.18984i	1.63014	+	0.700862i
$79$	−1.74363	+	3.02006i	−0.196174	+	0.339784i	−0.947285	−	0.320393i	$-0.896185\pi$
$79$	−1.74363	+	3.02006i	−0.196174	+	0.339784i	0.751111	+	0.660176i	$0.229518\pi$
$80$	5.63598	−	21.0338i	0.630122	−	2.35165i
$81$	−8.81808	+	1.80039i	−0.979787	+	0.200044i
$82$	−10.2682	−	5.92837i	−1.13394	−	0.654679i
$83$	−1.93496	−	1.93496i	−0.212390	−	0.212390i	0.592892	−	0.805282i	$-0.297986\pi$
$83$	−1.93496	−	1.93496i	−0.212390	−	0.212390i	−0.805282	+	0.592892i	$0.797986\pi$
$84$	−14.6468	+	13.1623i	−1.59810	+	1.43613i
$85$	−1.88189	−	1.88189i	−0.204120	−	0.204120i
$86$	3.14048	+	11.7204i	0.338646	+	1.26385i
$87$	1.39338	−	1.54126i	0.149386	−	0.165241i
$88$	13.0590	−	7.53962i	1.39209	−	0.803726i
$89$	−2.74480	−	10.2437i	−0.290948	−	1.08583i	−0.944382	−	0.328849i	$-0.893339\pi$
$89$	−2.74480	−	10.2437i	−0.290948	−	1.08583i	0.653435	−	0.756983i	$-0.273327\pi$
$90$	−16.3209	−	22.6547i	−1.72037	−	2.38801i
$91$	5.06782	−	8.08191i	0.531252	−	0.847214i
$92$		−	24.1422i		−	2.51700i
$93$	3.83414	+	5.93011i	0.397582	+	0.614924i
$94$	1.14220	+	1.97835i	0.117809	+	0.204052i
$95$	8.57375	+	14.8502i	0.879649	+	1.52360i
$96$	4.66072	−	3.01341i	0.475683	−	0.307555i
$97$	−13.6182	+	13.6182i	−1.38272	+	1.38272i	−0.542975	+	0.839749i	$0.682702\pi$
$97$	−13.6182	+	13.6182i	−1.38272	+	1.38272i	−0.839749	+	0.542975i	$0.817298\pi$
$98$	9.59767	+	14.7121i	0.969511	+	1.48614i
$99$	1.25878	−	7.74601i	0.126512	−	0.778504i
$100$	18.8127	−	32.5846i	1.88127	−	3.25846i
$101$	8.22476	+	14.2457i	0.818394	+	1.41750i	0.906865	+	0.421421i	$0.138469\pi$
$101$	8.22476	+	14.2457i	0.818394	+	1.41750i	−0.0884712	+	0.996079i	$0.528198\pi$
$102$	−0.156971	−	3.11492i	−0.0155424	−	0.308423i
$103$	−1.66310	−	0.960190i	−0.163870	−	0.0946103i	0.415822	−	0.909446i	$-0.363494\pi$
$103$	−1.66310	−	0.960190i	−0.163870	−	0.0946103i	−0.579692	+	0.814836i	$0.696827\pi$
$104$	−13.6766	+	15.6504i	−1.34110	+	1.53465i
$105$	−15.1513	+	7.70146i	−1.47861	+	0.751586i
$106$	−4.91752	+	4.91752i	−0.477632	+	0.477632i
$107$	6.59999	+	3.81051i	0.638045	+	0.368375i	0.783861	−	0.620936i	$-0.213247\pi$
$107$	6.59999	+	3.81051i	0.638045	+	0.368375i	−0.145816	+	0.989312i	$0.546581\pi$
$108$	2.46780	−	22.1919i	0.237464	−	2.13541i
$109$	15.5683	+	4.17150i	1.49117	+	0.399557i	0.910131	−	0.414320i	$-0.135980\pi$
$109$	15.5683	+	4.17150i	1.49117	+	0.399557i	0.581037	+	0.813877i	$0.302647\pi$
$110$	23.5168	−	6.30130i	2.24224	−	0.600805i
$111$	8.52340	+	4.36448i	0.809005	+	0.414258i
$112$	−6.33291	−	14.1843i	−0.598404	−	1.34029i
$113$		−	9.44516i		−	0.888526i	−0.895897	−	0.444263i	$-0.853466\pi$
$113$		−	9.44516i		−	0.888526i	0.895897	−	0.444263i	$-0.146534\pi$
$114$	−4.21748	+	19.6475i	−0.395003	+	1.84016i
$115$	5.39307	−	20.1272i	0.502907	−	1.87687i
$116$	2.57740	+	4.46418i	0.239305	+	0.414489i
$117$	1.80763	+	10.6645i	0.167115	+	0.985937i
$118$	22.1253			2.03680
$119$	−1.88832	−	0.196486i	−0.173102	−	0.0180119i
$120$	35.2417	−	11.3725i	3.21711	−	1.03816i
$121$	−3.60024	−	2.07860i	−0.327294	−	0.188963i
$122$	−6.90766	+	25.7797i	−0.625390	+	2.33399i
$123$	−0.411884	−	8.17341i	−0.0371383	−	0.736971i
$124$	−16.9227	+	4.53443i	−1.51970	+	0.407203i
$125$	9.85018	−	9.85018i	0.881027	−	0.881027i
$126$	−19.2237	−	5.21241i	−1.71259	−	0.464359i
$127$			5.13993i			0.456095i	0.973650	+	0.228048i	$0.0732342\pi$
$127$			5.13993i			0.456095i	−0.973650	+	0.228048i	$0.926766\pi$
$128$	−4.06274	−	15.1624i	−0.359099	−	1.34018i
$129$	−5.61650	+	6.21261i	−0.494505	+	0.546990i
$130$	−27.8693	+	18.6924i	−2.44430	+	1.63943i
$131$	8.70090	+	5.02346i	0.760201	+	0.438902i	0.829368	−	0.558703i	$-0.188701\pi$
$131$	8.70090	+	5.02346i	0.760201	+	0.438902i	−0.0691670	+	0.997605i	$0.522034\pi$
$132$	17.3298	+	8.87389i	1.50837	+	0.772373i
$133$	11.4243	+	4.37177i	0.990614	+	0.379080i
$134$	8.18466			0.707047
$135$	7.01479	−	17.9500i	0.603737	−	1.54489i
$136$	3.99550	+	1.07059i	0.342611	+	0.0918023i
$137$	−4.27489	−	1.14545i	−0.365228	−	0.0978626i	0.0715375	−	0.997438i	$-0.477209\pi$
$137$	−4.27489	−	1.14545i	−0.365228	−	0.0978626i	−0.436766	+	0.899575i	$0.643876\pi$
$138$	20.5062	−	13.2584i	1.74560	−	1.12863i
$139$	−2.12187			−0.179975			−0.0899875	−	0.995943i	$-0.528683\pi$
$139$	−2.12187			−0.179975			−0.0899875	+	0.995943i	$0.528683\pi$
$140$	−6.63968	−	41.6412i	−0.561156	−	3.51932i
$141$	−0.718649	+	1.40345i	−0.0605212	+	0.118192i
$142$	−22.5207	−	13.0023i	−1.88989	−	1.09113i
$143$	−9.25366	−	1.82382i	−0.773830	−	0.152515i
$144$	16.0620	+	7.22873i	1.33850	+	0.602395i
$145$	1.15152	+	4.29752i	0.0956284	+	0.356890i
$146$		−	14.8879i		−	1.23213i
$147$	−4.93065	+	11.0765i	−0.406673	+	0.913574i
$148$	−16.7990	+	16.7990i	−1.38087	+	1.38087i
$149$	−16.0468	+	4.29972i	−1.31460	+	0.352247i	−0.846954	−	0.531667i	$-0.821566\pi$
$149$	−16.0468	+	4.29972i	−1.31460	+	0.352247i	−0.467650	+	0.883914i	$0.654899\pi$
$150$	38.0087	−	1.91538i	3.10340	−	0.156390i
$151$	−2.70205	+	10.0842i	−0.219890	+	0.820640i	0.764498	+	0.644626i	$0.222987\pi$
$151$	−2.70205	+	10.0842i	−0.219890	+	0.820640i	−0.984388	+	0.176014i	$0.943680\pi$
$152$	−23.0807	−	13.3257i	−1.87209	−	1.08085i
$153$	1.74665	−	1.25832i	0.141208	−	0.101729i
$154$	10.1938	−	14.0612i	0.821438	−	1.13309i
$155$	−15.1213			−1.21457
$156$	−26.5570	−	3.85756i	−2.12626	−	0.308852i
$157$	−0.902803	−	1.56370i	−0.0720516	−	0.124797i	0.827749	−	0.561099i	$-0.189621\pi$
$157$	−0.902803	−	1.56370i	−0.0720516	−	0.124797i	−0.899800	+	0.436302i	$0.856288\pi$
$158$	2.26492	−	8.45281i	0.180188	−	0.672470i
$159$	−4.69319	−	1.00743i	−0.372194	−	0.0798942i
$160$			11.8845i			0.939550i
$161$	−6.05997	−	13.5729i	−0.477592	−	1.06970i
$162$	20.2049	−	10.0912i	1.58745	−	0.792838i
$163$	8.58348	−	2.29994i	0.672310	−	0.180145i	0.0935151	−	0.995618i	$-0.470190\pi$
$163$	8.58348	−	2.29994i	0.672310	−	0.180145i	0.578795	+	0.815473i	$0.303523\pi$
$164$	19.6118	+	5.25497i	1.53143	+	0.410345i
$165$	12.4655	+	11.2694i	0.970435	+	0.877321i
$166$	5.94690	+	3.43345i	0.461569	+	0.266487i
$167$	−15.1062	+	15.1062i	−1.16895	+	1.16895i	−0.186495	+	0.982456i	$0.559713\pi$
$167$	−15.1062	+	15.1062i	−1.16895	+	1.16895i	−0.982456	+	0.186495i	$0.940287\pi$
$168$	14.4088	−	22.1406i	1.11167	−	1.70819i
$169$	12.8828	−	1.74199i	0.990981	−	0.134000i
$170$	5.78378	+	3.33927i	0.443596	+	0.256110i
$171$	−12.9687	+	4.91850i	−0.991739	+	0.376127i
$172$	−10.3891	−	17.9945i	−0.792162	−	1.37206i
$173$	−6.29273	+	10.8993i	−0.478428	+	0.828661i	−0.999694	−	0.0247331i	$-0.992126\pi$
$173$	−6.29273	+	10.8993i	−0.478428	+	0.828661i	0.521267	+	0.853394i	$0.325460\pi$
$174$	−2.37639	+	4.64086i	−0.180154	+	0.351822i
$175$	2.39755	−	23.0415i	0.181238	−	1.74178i
$176$	−10.8600	+	10.8600i	−0.818605	+	0.818605i
$177$	8.29164	+	12.8243i	0.623238	+	0.963937i
$178$	13.3063	+	23.0471i	0.997347	+	1.72746i
$179$	2.00334	+	3.46988i	0.149736	+	0.259351i	0.931130	−	0.364687i	$-0.118824\pi$
$179$	2.00334	+	3.46988i	0.149736	+	0.259351i	−0.781394	+	0.624039i	$0.785491\pi$
$180$	37.0365	+	30.2388i	2.76054	+	2.25387i
$181$		−	4.67555i		−	0.347531i	−0.984787	−	0.173766i	$-0.944407\pi$
$181$		−	4.67555i		−	0.347531i	0.984787	−	0.173766i	$-0.0555935\pi$
$182$	−7.03485	+	22.8813i	−0.521458	+	1.69607i
$183$	−17.5312	+	5.65732i	−1.29595	+	0.418201i
$184$	8.38212	+	31.2825i	0.617938	+	2.30618i
$185$	−17.7579	+	10.2525i	−1.30559	+	0.753782i
$186$	−13.1451	−	11.8838i	−0.963846	−	0.871364i
$187$	0.485823	+	1.81312i	0.0355269	+	0.132588i
$188$	−2.76610	−	2.76610i	−0.201738	−	0.201738i
$189$	−4.18300	−	13.0959i	−0.304269	−	0.952586i
$190$	−30.4269	−	30.4269i	−2.20740	−	2.20740i
$191$	13.1603	+	7.59811i	0.952247	+	0.549780i	0.893778	−	0.448509i	$-0.148045\pi$
$191$	13.1603	+	7.59811i	0.952247	+	0.549780i	0.0584690	+	0.998289i	$0.481378\pi$
$192$	4.29949	−	4.75581i	0.310289	−	0.343221i
$193$	−0.511449	+	1.90875i	−0.0368149	+	0.137395i	−0.981887	−	0.189466i	$-0.939324\pi$
$193$	−0.511449	+	1.90875i	−0.0368149	+	0.137395i	0.945072	+	0.326861i	$0.105991\pi$
$194$	24.1645	−	41.8542i	1.73491	−	3.00496i
$195$	−21.2787	−	9.14855i	−1.52380	−	0.655141i
$196$	−22.3956	−	20.0810i	−1.59969	−	1.43436i
$197$	14.6269	+	14.6269i	1.04213	+	1.04213i	0.999073	+	0.0430522i	$0.0137082\pi$
$197$	14.6269	+	14.6269i	1.04213	+	1.04213i	0.0430522	+	0.999073i	$0.486292\pi$
$198$	1.97975	+	19.5932i	0.140695	+	1.39243i
$199$	−6.35018	+	3.66628i	−0.450152	+	0.259895i	−0.707894	−	0.706318i	$-0.750355\pi$
$199$	−6.35018	+	3.66628i	−0.450152	+	0.259895i	0.257742	+	0.966214i	$0.417021\pi$
$200$	−13.0635	+	48.7537i	−0.923729	+	3.44740i
$201$	3.06726	+	4.74401i	0.216348	+	0.334617i
$202$	−29.1884	−	29.1884i	−2.05369	−	2.05369i
$203$	2.56959	+	1.86284i	0.180350	+	0.130746i
$204$	1.64019	+	5.08271i	0.114836	+	0.355861i
$205$	15.1764	+	8.76209i	1.05997	+	0.611971i
$206$	4.65482	+	1.24726i	0.324317	+	0.0869004i
$207$	15.3697	+	6.91718i	1.06827	+	0.480777i
$208$	9.32954	−	19.0023i	0.646887	−	1.31757i
$209$		−	12.0941i		−	0.836566i
$210$	31.7233	−	28.5081i	2.18912	−	1.96725i
$211$	12.5260			0.862325			0.431163	−	0.902274i	$-0.358104\pi$
$211$	12.5260			0.862325			0.431163	+	0.902274i	$0.358104\pi$
$212$	5.95443	−	10.3134i	0.408952	−	0.708325i
$213$	−0.903358	−	17.9262i	−0.0618971	−	1.22828i
$214$	−18.4726	−	4.94972i	−1.26276	−	0.338356i
$215$	−4.64160	−	17.3227i	−0.316555	−	1.18140i
$216$	4.50731	+	29.6122i	0.306683	+	2.01486i
$217$	−8.37589	+	6.79709i	−0.568592	+	0.461416i
$218$	−40.4453			−2.73930
$219$	8.62934	−	5.57934i	0.583117	−	0.377017i
$220$	−36.1055	+	20.8455i	−2.43423	+	1.40540i
$221$	−1.44116	−	2.14869i	−0.0969429	−	0.144536i
$222$	−23.4946	−	5.04329i	−1.57685	−	0.338483i
$223$	−3.17920	+	3.17920i	−0.212895	+	0.212895i	−0.805496	−	0.592601i	$-0.798101\pi$
$223$	−3.17920	+	3.17920i	−0.212895	+	0.212895i	0.592601	+	0.805496i	$0.298101\pi$
$224$	5.34211	+	6.58296i	0.356935	+	0.439842i
$225$	15.3543	+	21.3129i	1.02362	+	1.42086i
$226$	6.13448	+	22.8942i	0.408059	+	1.52290i
$227$	2.93970	−	10.9711i	0.195115	−	0.728179i	−0.797122	−	0.603818i	$-0.793645\pi$
$227$	2.93970	−	10.9711i	0.195115	−	0.728179i	0.992237	−	0.124361i	$-0.0396880\pi$
$228$	−1.73188	−	34.3674i	−0.114697	−	2.27604i
$229$	17.7017	−	4.74317i	1.16976	−	0.313437i	0.378905	−	0.925436i	$-0.376301\pi$
$229$	17.7017	−	4.74317i	1.16976	−	0.313437i	0.790859	+	0.611998i	$0.209634\pi$
$230$			52.2892i			3.44785i
$231$	11.9704	+	0.638986i	0.787595	+	0.0420422i
$232$	−4.88965	−	4.88965i	−0.321021	−	0.321021i
$233$	−2.40978	+	4.17387i	−0.157870	+	0.273439i	−0.934100	−	0.357010i	$-0.883796\pi$
$233$	−2.40978	+	4.17387i	−0.157870	+	0.273439i	0.776230	+	0.630449i	$0.217129\pi$
$234$	−11.3080	−	24.6758i	−0.739225	−	1.61311i
$235$	−1.68817	−	2.92399i	−0.110124	−	0.190740i
$236$	−36.5967	+	9.80607i	−2.38225	+	0.638321i
$237$	5.74824	−	1.85496i	0.373388	−	0.120492i
$238$	4.70472	−	0.750168i	0.304962	−	0.0486262i
$239$	12.6692	+	12.6692i	0.819500	+	0.819500i	0.986036	−	0.166535i	$-0.0532579\pi$
$239$	12.6692	+	12.6692i	0.819500	+	0.819500i	−0.166535	+	0.986036i	$0.553258\pi$
$240$	−31.6731	+	20.4784i	−2.04449	+	1.32188i
$241$	−3.25905	+	12.1629i	−0.209934	+	0.783484i	0.777955	+	0.628320i	$0.216257\pi$
$241$	−3.25905	+	12.1629i	−0.209934	+	0.783484i	−0.987889	+	0.155164i	$0.950410\pi$
$242$	10.0767	+	2.70003i	0.647752	+	0.173565i
$243$	13.4210	+	7.92946i	0.860959	+	0.508675i
$244$		−	45.7029i		−	2.92583i
$245$	−14.1853	−	21.7443i	−0.906265	−	1.38920i
$246$	6.30687	+	19.5441i	0.402111	+	1.24608i
$247$	5.38595	+	15.7756i	0.342700	+	1.00378i
$248$	20.3535	−	11.7511i	1.29245	−	0.746194i
$249$	0.238545	+	4.73367i	0.0151172	+	0.299984i
$250$	−17.4784	+	30.2734i	−1.10543	+	1.91466i
$251$	−18.7701			−1.18476			−0.592379	−	0.805660i	$-0.701811\pi$
$251$	−18.7701			−1.18476			−0.592379	+	0.805660i	$0.701811\pi$
$252$	34.1075	+	0.101615i	2.14857	+	0.00640112i
$253$	−10.3920	+	10.3920i	−0.653337	+	0.653337i
$254$	−3.33830	−	12.4587i	−0.209464	−	0.781729i
$255$	0.232002	+	4.60383i	0.0145285	+	0.288303i
$256$	15.9939	+	27.7023i	0.999620	+	1.73139i
$257$	−5.88351	+	10.1905i	−0.367003	+	0.635668i	−0.989095	−	0.147276i	$-0.952950\pi$
$257$	−5.88351	+	10.1905i	−0.367003	+	0.635668i	0.622092	+	0.782944i	$0.286283\pi$
$258$	9.57889	−	18.7066i	0.596356	−	1.16462i
$259$	−5.22778	+	13.6613i	−0.324838	+	0.848869i
$260$	37.8130	−	43.2702i	2.34506	−	2.68350i
$261$	−3.58052	+	0.361786i	−0.221628	+	0.0223940i
$262$	−24.3528	−	6.52532i	−1.50452	−	0.403136i
$263$	12.2786	−	7.08907i	0.757133	−	0.437131i	−0.0711324	−	0.997467i	$-0.522661\pi$
$263$	12.2786	−	7.08907i	0.757133	−	0.437131i	0.828265	+	0.560336i	$0.189328\pi$
$264$	−25.5363	−	5.48156i	−1.57165	−	0.337367i
$265$	7.26806	−	7.26806i	0.446474	−	0.446474i
$266$	−30.5309	−	3.17684i	−1.87197	−	0.194785i
$267$	−8.37201	+	16.3497i	−0.512359	+	1.00059i
$268$	−13.5380	+	3.62748i	−0.826962	+	0.221584i
$269$	2.26549	−	1.30798i	0.138129	−	0.0797490i	−0.429343	−	0.903142i	$-0.641255\pi$
$269$	2.26549	−	1.30798i	0.138129	−	0.0797490i	0.567472	+	0.823393i	$0.307921\pi$
$270$	−5.34497	+	48.0651i	−0.325284	+	2.92515i
$271$	−22.9213	+	6.14174i	−1.39237	+	0.373084i	−0.875598	−	0.483040i	$-0.839533\pi$
$271$	−22.9213	+	6.14174i	−1.39237	+	0.373084i	−0.516770	+	0.856124i	$0.672866\pi$
$272$	−4.21302			−0.255452
$273$	−15.8989	+	4.49737i	−0.962243	+	0.272193i
$274$	11.1059			0.670931
$275$	−22.1239	+	5.92808i	−1.33412	+	0.357477i
$276$	−28.0424	+	31.0187i	−1.68795	+	1.86710i
$277$	1.85506	−	1.07102i	0.111460	−	0.0643514i	−0.443234	−	0.896406i	$-0.646169\pi$
$277$	1.85506	−	1.07102i	0.111460	−	0.0643514i	0.554694	+	0.832055i	$0.312835\pi$
$278$	5.14323	−	1.37812i	0.308470	−	0.0826544i
$279$	1.96190	−	12.0728i	0.117456	−	0.722777i
$280$	23.0612	+	51.6517i	1.37817	+	3.08678i
$281$	−10.3426	+	10.3426i	−0.616987	+	0.616987i	−0.944758	−	0.327770i	$-0.893703\pi$
$281$	−10.3426	+	10.3426i	−0.616987	+	0.616987i	0.327770	+	0.944758i	$0.393703\pi$
$282$	0.830421	−	3.86858i	0.0494508	−	0.230371i
$283$	−0.330377	+	0.190743i	−0.0196389	+	0.0113385i	−0.509787	−	0.860300i	$-0.670276\pi$
$283$	−0.330377	+	0.190743i	−0.0196389	+	0.0113385i	0.490148	+	0.871639i	$0.336943\pi$
$284$	43.0133	+	11.5254i	2.55237	+	0.683906i
$285$	6.23341	−	29.0389i	0.369235	−	1.72011i
$286$	23.6145	−	1.58934i	1.39636	−	0.0939794i
$287$	12.3450	−	1.96841i	0.728701	−	0.116191i
$288$	−9.48848	−	1.54194i	−0.559114	−	0.0908596i
$289$	8.24255	−	14.2765i	0.484856	−	0.839795i
$290$	−5.58235	−	9.66891i	−0.327807	−	0.567778i
$291$	33.3155	−	1.67887i	1.95299	−	0.0984173i
$292$	6.59838	+	24.6255i	0.386141	+	1.44110i
$293$	9.54534	−	9.54534i	0.557645	−	0.557645i	−0.370992	−	0.928636i	$-0.620982\pi$
$293$	9.54534	−	9.54534i	0.557645	−	0.557645i	0.928636	+	0.370992i	$0.120982\pi$
$294$	4.75744	−	30.0508i	0.277459	−	1.75260i
$295$	−32.7011			−1.90393
$296$	15.9349	−	27.6000i	0.926197	−	1.60422i
$297$	−10.6147	+	8.49020i	−0.615928	+	0.492651i
$298$	36.1033	−	20.8443i	2.09141	−	1.20748i
$299$	8.92743	−	18.1833i	0.516287	−	1.05157i
$300$	−62.0200	+	20.0138i	−3.58072	+	1.15550i
$301$	−10.3577	−	7.50884i	−0.597005	−	0.432802i
$302$		−	26.1981i		−	1.50753i
$303$	5.97968	−	27.8568i	0.343524	−	1.60033i
$304$	26.2198	+	7.02557i	1.50381	+	0.402944i
$305$	10.2095	−	38.1023i	0.584593	−	2.18173i
$306$	−3.41646	+	4.18448i	−0.195306	+	0.239211i
$307$	22.5415	+	22.5415i	1.28651	+	1.28651i	0.936892	+	0.349620i	$0.113689\pi$
$307$	22.5415	+	22.5415i	1.28651	+	1.28651i	0.349620	+	0.936892i	$0.386311\pi$
$308$	−10.6291	+	27.7761i	−0.605652	+	1.58269i
$309$	1.02149	+	3.16546i	0.0581107	+	0.180077i
$310$	36.6527	−	9.82105i	2.08173	−	0.557798i
$311$	5.70705	+	9.88490i	0.323617	+	0.560522i	0.981232	−	0.192833i	$-0.0617677\pi$
$311$	5.70705	+	9.88490i	0.323617	+	0.560522i	−0.657614	+	0.753355i	$0.728434\pi$
$312$	35.7509	−	4.22208i	2.02400	−	0.239028i
$313$	10.4355	−	18.0749i	0.589852	−	1.02165i	−0.404400	−	0.914582i	$-0.632519\pi$
$313$	10.4355	−	18.0749i	0.589852	−	1.02165i	0.994251	−	0.107071i	$-0.0341472\pi$
$314$	3.20391	+	3.20391i	0.180807	+	0.180807i
$315$	28.4125	+	7.70391i	1.60086	+	0.434066i
$316$			14.9853i			0.842991i
$317$	2.30184	−	0.616776i	0.129284	−	0.0346416i	−0.193597	−	0.981081i	$-0.562015\pi$
$317$	2.30184	−	0.616776i	0.129284	−	0.0346416i	0.322881	+	0.946440i	$0.395349\pi$
$318$	12.0302	−	0.606238i	0.674617	−	0.0339961i
$319$	0.812163	−	3.03103i	0.0454724	−	0.169705i
$320$	3.55319	+	13.2607i	0.198629	+	0.741295i
$321$	−4.05379	−	12.5621i	−0.226260	−	0.701148i
$322$	23.5042	+	28.9637i	1.30984	+	1.61408i
$323$	2.34588	−	2.34588i	0.130528	−	0.130528i
$324$	−28.9477	+	25.6464i	−1.60821	+	1.42480i
$325$	26.2186	−	17.5852i	1.45435	−	0.975454i
$326$	−19.3118	+	11.1497i	−1.06958	+	0.617523i
$327$	−15.1572	−	23.4430i	−0.838195	−	1.29640i
$328$	−27.2368			−1.50390
$329$	−2.24944	−	0.860799i	−0.124016	−	0.0474574i
$330$	−37.5344	−	19.2198i	−2.06620	−	1.05802i
$331$	2.10669	+	7.86228i	0.115794	+	0.432150i	0.999345	−	0.0361852i	$-0.0115206\pi$
$331$	2.10669	+	7.86228i	0.115794	+	0.432150i	−0.883551	+	0.468335i	$0.844854\pi$
$332$	−11.3583	−	3.04344i	−0.623367	−	0.167031i
$333$	−5.88157	−	15.5080i	−0.322308	−	0.849833i
$334$	26.8048	−	46.4272i	1.46669	−	2.54038i
$335$	−12.0969			−0.660922
$336$	−8.33902	+	25.5804i	−0.454931	+	1.39553i
$337$		−	17.1778i		−	0.935733i	−0.883799	−	0.467867i	$-0.845023\pi$
$337$		−	17.1778i		−	0.935733i	0.883799	−	0.467867i	$-0.154977\pi$
$338$	−30.0952	+	12.5896i	−1.63696	+	0.684783i
$339$	−10.9710	+	12.1355i	−0.595865	+	0.659107i
$340$	−11.0467	−	2.95996i	−0.599093	−	0.160527i
$341$	9.23619	+	5.33252i	0.500168	+	0.288772i
$342$	28.2404	−	20.3449i	1.52706	−	1.10013i
$343$	−17.6316	−	5.66813i	−0.952015	−	0.306050i
$344$	19.7095	+	19.7095i	1.06266	+	1.06266i
$345$	−30.3080	+	19.5958i	−1.63173	+	1.05500i
$346$	8.17406	−	30.5060i	0.439440	−	1.64001i
$347$	8.99067	−	5.19077i	0.482645	−	0.278655i	−0.238873	−	0.971051i	$-0.576778\pi$
$347$	8.99067	−	5.19077i	0.482645	−	0.278655i	0.721518	+	0.692396i	$0.243445\pi$
$348$	1.87385	−	8.72951i	0.100449	−	0.467951i
$349$	−1.14175	−	1.14175i	−0.0611163	−	0.0611163i	0.675888	−	0.737004i	$-0.263760\pi$
$349$	−1.14175	−	1.14175i	−0.0611163	−	0.0611163i	−0.737004	+	0.675888i	$0.763760\pi$
$350$	9.15366	+	57.4077i	0.489284	+	3.06857i
$351$	10.0649	−	15.8018i	0.537226	−	0.843438i
$352$	4.19105	−	7.25911i	0.223384	−	0.386912i
$353$	2.65621	−	9.91309i	0.141376	−	0.527621i	−0.858514	−	0.512789i	$-0.828612\pi$
$353$	2.65621	−	9.91309i	0.141376	−	0.527621i	0.999890	−	0.0148314i	$-0.00472114\pi$
$354$	−28.4274	−	25.6997i	−1.51090	−	1.36593i
$355$	33.2854	+	19.2173i	1.76660	+	1.01995i
$356$	−32.2240	−	32.2240i	−1.70787	−	1.70787i
$357$	2.19795	+	2.44583i	0.116328	+	0.129447i
$358$	−7.10954	−	7.10954i	−0.375751	−	0.375751i
$359$	−7.24828	−	27.0510i	−0.382550	−	1.42769i	−0.841993	−	0.539488i	$-0.818618\pi$
$359$	−7.24828	−	27.0510i	−0.382550	−	1.42769i	0.459444	−	0.888207i	$-0.348049\pi$
$360$	−58.4894	−	26.3233i	−3.08266	−	1.38736i
$361$	−2.05710	+	1.18767i	−0.108268	+	0.0625087i
$362$	3.03670	+	11.3331i	0.159605	+	0.595655i
$363$	2.21130	+	6.85251i	0.116063	+	0.359664i
$364$	1.49500	−	40.9650i	0.0783595	−	2.14715i
$365$			22.0042i			1.15175i
$366$	38.8197	−	25.0991i	2.02914	−	1.31195i
$367$	5.92235	+	10.2578i	0.309144	+	0.535453i	0.978175	−	0.207781i	$-0.0666242\pi$
$367$	5.92235	+	10.2578i	0.309144	+	0.535453i	−0.669031	+	0.743234i	$0.733291\pi$
$368$	−16.4928	−	28.5664i	−0.859747	−	1.48913i
$369$	−8.96464	+	10.9799i	−0.466680	+	0.571590i
$370$	36.3847	−	36.3847i	1.89155	−	1.89155i
$371$	0.758851	−	7.29289i	0.0393976	−	0.378628i
$372$	27.0098	+	13.8306i	1.40039	+	0.717085i
$373$	−13.3628	+	23.1451i	−0.691902	+	1.19841i	0.279313	+	0.960200i	$0.409893\pi$
$373$	−13.3628	+	23.1451i	−0.691902	+	1.19841i	−0.971214	+	0.238208i	$0.923440\pi$
$374$	−2.35518	−	4.07929i	−0.121783	−	0.210935i
$375$	−24.0973	+	1.21434i	−1.24438	+	0.0627083i
$376$	4.54458	+	2.62382i	0.234369	+	0.135313i
$377$	0.290440	+	4.31539i	0.0149584	+	0.222254i
$378$	18.6448	+	29.0264i	0.958984	+	1.49296i
$379$	8.27837	−	8.27837i	0.425231	−	0.425231i	−0.461769	−	0.887000i	$-0.652785\pi$
$379$	8.27837	−	8.27837i	0.425231	−	0.425231i	0.887000	+	0.461769i	$0.152785\pi$
$380$	63.8135	+	36.8427i	3.27356	+	1.88999i
$381$	5.97030	−	6.60395i	0.305868	−	0.338331i
$382$	−36.8342	−	9.86971i	−1.88460	−	0.504978i
$383$	−4.88230	+	1.30821i	−0.249474	+	0.0668463i	−0.381389	−	0.924415i	$-0.624554\pi$
$383$	−4.88230	+	1.30821i	−0.249474	+	0.0668463i	0.131915	+	0.991261i	$0.457887\pi$
$384$	−12.3919	+	24.2002i	−0.632373	+	1.23496i
$385$	−15.0663	+	20.7824i	−0.767851	+	1.05917i
$386$		−	4.95882i		−	0.252397i
$387$	14.4325	−	1.45831i	0.733647	−	0.0741299i
$388$	−21.4197	+	79.9394i	−1.08742	+	4.05831i
$389$	6.23093	+	10.7923i	0.315921	+	0.547191i	0.979633	−	0.200797i	$-0.0643533\pi$
$389$	6.23093	+	10.7923i	0.315921	+	0.547191i	−0.663712	+	0.747988i	$0.731020\pi$
$390$	57.5195	+	8.35504i	2.91261	+	0.423074i
$391$	−4.03144			−0.203879
$392$	35.9915	+	18.2445i	1.81785	+	0.921484i
$393$	−5.34418	−	16.5609i	−0.269578	−	0.835385i
$394$	−44.9542	−	25.9543i	−2.26476	−	1.30756i
$395$	−3.34754	+	12.4932i	−0.168433	+	0.628601i
$396$	−11.9584	−	31.5309i	−0.600934	−	1.58449i
$397$	−32.1566	+	8.61633i	−1.61389	+	0.432441i	−0.949200	−	0.314674i	$-0.898105\pi$
$397$	−32.1566	+	8.61633i	−1.61389	+	0.432441i	−0.664694	+	0.747116i	$0.731438\pi$
$398$	13.0111	−	13.0111i	0.652185	−	0.652185i
$399$	−9.60031	−	18.8869i	−0.480616	−	0.945529i
$400$		−	51.4079i		−	2.57040i
$401$	−1.74637	−	6.51755i	−0.0872097	−	0.325471i	0.908514	−	0.417855i	$-0.137218\pi$
$401$	−1.74637	−	6.51755i	−0.0872097	−	0.325471i	−0.995723	+	0.0923840i	$0.970551\pi$
$402$	−10.5159	−	9.50691i	−0.524486	−	0.474161i
$403$	−14.4225	−	2.84256i	−0.718437	−	0.141598i
$404$	61.2160	+	35.3431i	3.04561	+	1.75838i
$405$	−29.8627	+	14.9147i	−1.48389	+	0.741118i
$406$	−7.43834	−	2.84644i	−0.369159	−	0.141267i
$407$	14.4622			0.716864
$408$	−3.89000	−	6.01651i	−0.192584	−	0.297862i
$409$	21.3966	+	5.73320i	1.05799	+	0.283488i	0.745551	−	0.666449i	$-0.232186\pi$
$409$	21.3966	+	5.73320i	1.05799	+	0.283488i	0.312442	+	0.949937i	$0.398853\pi$
$410$	−42.4770	−	11.3817i	−2.09779	−	0.562101i
$411$	4.16201	+	6.43722i	0.205297	+	0.317525i
$412$	−8.25217			−0.406555
$413$	−18.1135	+	14.6993i	−0.891309	+	0.723303i
$414$	−41.7473	−	6.78421i	−2.05177	−	0.333426i
$415$	−8.78948	−	5.07461i	−0.431459	−	0.249103i
$416$	−2.23409	+	11.3353i	−0.109535	+	0.555757i
$417$	2.72626	+	2.46467i	0.133505	+	0.120695i
$418$	7.85492	+	29.3150i	0.384197	+	1.43384i
$419$			19.3975i			0.947628i	0.880625	+	0.473814i	$0.157123\pi$
$419$			19.3975i			0.947628i	−0.880625	+	0.473814i	$0.842877\pi$
$420$	−39.8375	+	61.2143i	−1.94387	+	2.98695i
$421$	18.5575	−	18.5575i	0.904435	−	0.904435i	−0.0913811	−	0.995816i	$-0.529128\pi$
$421$	18.5575	−	18.5575i	0.904435	−	0.904435i	0.995816	+	0.0913811i	$0.0291281\pi$
$422$	−30.3619	+	8.13544i	−1.47799	+	0.396027i
$423$	2.55353	−	0.968451i	0.124157	−	0.0470877i
$424$	−4.13473	+	15.4310i	−0.200800	+	0.749398i
$425$	−5.44122	−	3.14149i	−0.263938	−	0.152385i
$426$	13.8324	+	42.8647i	0.670184	+	2.07680i
$427$	−11.4720	−	25.6945i	−0.555167	−	1.24345i
$428$	32.7487			1.58297
$429$	9.77095	+	13.0919i	0.471746	+	0.632083i
$430$	22.5016	+	38.9740i	1.08512	+	1.87949i
$431$	−0.947166	+	3.53487i	−0.0456234	+	0.170269i	−0.984978	−	0.172677i	$-0.944758\pi$
$431$	−0.947166	+	3.53487i	−0.0456234	+	0.170269i	0.939355	+	0.342946i	$0.111425\pi$
$432$	−12.2404	−	27.9445i	−0.588917	−	1.34448i
$433$			12.2523i			0.588807i	0.955681	+	0.294403i	$0.0951209\pi$
$433$			12.2523i			0.588807i	−0.955681	+	0.294403i	$0.904879\pi$
$434$	15.8878	−	21.9155i	0.762638	−	1.05198i
$435$	3.51229	−	6.85915i	0.168401	−	0.328871i
$436$	66.8992	−	17.9256i	3.20389	−	0.858480i
$437$	25.0897	+	6.72277i	1.20020	+	0.321594i
$438$	−17.2930	+	19.1284i	−0.826293	+	0.913991i
$439$	−32.7391	−	18.9019i	−1.56255	−	0.902140i	−0.996998	−	0.0774293i	$-0.975329\pi$
$439$	−32.7391	−	18.9019i	−1.56255	−	0.902140i	−0.565555	−	0.824711i	$-0.691338\pi$
$440$	39.5466	−	39.5466i	1.88531	−	1.88531i
$441$	19.2010	−	8.50424i	0.914333	−	0.404964i
$442$	4.88877	+	4.27221i	0.232535	+	0.203208i
$443$	−23.7495	−	13.7118i	−1.12837	−	0.651467i	−0.184849	−	0.982767i	$-0.559179\pi$
$443$	−23.7495	−	13.7118i	−1.12837	−	0.651467i	−0.943525	+	0.331300i	$0.892513\pi$
$444$	41.0968	−	2.07100i	1.95037	−	0.0982852i
$445$	−19.6666	−	34.0635i	−0.932285	−	1.61476i
$446$	5.64125	−	9.77093i	0.267121	−	0.462667i
$447$	25.6118	+	13.1147i	1.21140	+	0.620306i
$448$	7.92889	+	5.74809i	0.374605	+	0.271572i
$449$	−21.3150	+	21.3150i	−1.00592	+	1.00592i	−0.00593671	+	0.999982i	$0.501890\pi$
$449$	−21.3150	+	21.3150i	−1.00592	+	1.00592i	−0.999982	+	0.00593671i	$0.998110\pi$
$450$	−51.0597	−	41.6881i	−2.40698	−	1.96520i
$451$	−6.17989	−	10.7039i	−0.290999	−	0.504026i
$452$	−20.2936	−	35.1496i	−0.954533	−	1.65330i
$453$	15.1850	−	9.81793i	0.713453	−	0.461287i
$454$			28.5023i			1.33768i
$455$	10.3975	−	33.8183i	0.487440	−	1.58543i
$456$	14.1764	+	43.9307i	0.663872	+	2.05724i
$457$	−4.17516	−	15.5819i	−0.195306	−	0.728890i	−0.992188	−	0.124755i	$-0.960185\pi$
$457$	−4.17516	−	15.5819i	−0.195306	−	0.728890i	0.796882	−	0.604135i	$-0.206481\pi$
$458$	−39.8268	+	22.9940i	−1.86098	+	1.07444i
$459$	−3.70576	−	0.412091i	−0.172970	−	0.0192347i
$460$	−23.1749	−	86.4898i	−1.08053	−	4.03261i
$461$	0.939708	+	0.939708i	0.0437665	+	0.0437665i	0.728651	−	0.684885i	$-0.240147\pi$
$461$	0.939708	+	0.939708i	0.0437665	+	0.0437665i	−0.684885	+	0.728651i	$0.740147\pi$
$462$	−29.4302	+	6.22574i	−1.36921	+	0.289648i
$463$	−28.7736	−	28.7736i	−1.33722	−	1.33722i	−0.898740	−	0.438483i	$-0.855516\pi$
$463$	−28.7736	−	28.7736i	−1.33722	−	1.33722i	−0.438483	−	0.898740i	$-0.644484\pi$
$464$	6.09943	+	3.52151i	0.283159	+	0.163482i
$465$	19.4284	+	17.5642i	0.900969	+	0.814520i
$466$	3.13023	−	11.6822i	0.145005	−	0.541167i
$467$	−13.7213	+	23.7659i	−0.634945	+	1.09976i	0.351582	+	0.936157i	$0.385644\pi$
$467$	−13.7213	+	23.7659i	−0.634945	+	1.09976i	−0.986527	+	0.163600i	$0.947689\pi$
$468$	29.6406	+	35.8037i	1.37014	+	1.65503i
$469$	−6.70061	+	5.43758i	−0.309405	+	0.251084i
$470$	5.99105	+	5.99105i	0.276347	+	0.276347i
$471$	−0.656369	+	3.05775i	−0.0302439	+	0.140894i
$472$	44.0160	−	25.4127i	2.02600	−	1.16971i
$473$	−3.27371	+	12.2177i	−0.150525	+	0.561769i
$474$	−12.7284	+	8.22963i	−0.584636	+	0.377999i
$475$	28.6248	+	28.6248i	1.31340	+	1.31340i
$476$	−7.44944	+	3.32599i	−0.341444	+	0.152446i
$477$	4.85978	+	6.74576i	0.222514	+	0.308867i
$478$	−38.9373	−	22.4805i	−1.78095	−	1.02823i
$479$	9.97919	+	2.67392i	0.455961	+	0.122174i	0.479487	−	0.877549i	$-0.340823\pi$
$479$	9.97919	+	2.67392i	0.455961	+	0.122174i	−0.0235263	+	0.999723i	$0.507489\pi$
$480$	13.8044	−	15.2696i	0.630083	−	0.696957i
$481$	−18.8646	+	6.44055i	−0.860151	+	0.293664i
$482$		−	31.5985i		−	1.43927i
$483$	−7.97961	+	24.4779i	−0.363085	+	1.11378i
$484$	−17.8641			−0.812005
$485$	−35.7150	+	61.8602i	−1.62174	+	2.80893i
$486$	−37.6814	−	10.5035i	−1.70926	−	0.476450i
$487$	21.6658	+	5.80535i	0.981773	+	0.263065i	0.713791	−	0.700359i	$-0.246977\pi$
$487$	21.6658	+	5.80535i	0.981773	+	0.263065i	0.267982	+	0.963424i	$0.413643\pi$
$488$	15.8680	+	59.2201i	0.718309	+	2.68077i
$489$	−13.6998	−	7.01513i	−0.619528	−	0.317235i
$490$	48.5064	+	43.4932i	2.19130	+	1.96482i
$491$	10.5715			0.477083			0.238542	−	0.971132i	$-0.423331\pi$
$491$	10.5715			0.477083			0.238542	+	0.971132i	$0.423331\pi$
$492$	−19.0940	−	29.5319i	−0.860824	−	1.33140i
$493$	0.745462	−	0.430392i	0.0335739	−	0.0193839i
$494$	−23.3011	−	34.7406i	−1.04836	−	1.56305i
$495$	−2.92606	−	28.9586i	−0.131517	−	1.30159i
$496$	−16.9262	+	16.9262i	−0.760008	+	0.760008i
$497$	27.0754	−	4.31718i	1.21450	−	0.193652i
$498$	−3.65265	−	11.3190i	−0.163679	−	0.507218i
$499$	2.11971	+	7.91086i	0.0948912	+	0.354139i	0.997003	−	0.0773638i	$-0.0246503\pi$
$499$	2.11971	+	7.91086i	0.0948912	+	0.354139i	−0.902112	+	0.431502i	$0.857984\pi$
$500$	15.4930	−	57.8208i	0.692869	−	2.58582i
$501$	36.9555	−	1.86231i	1.65105	−	0.0832017i
$502$	45.4969	−	12.1909i	2.03063	−	0.544105i
$503$			11.3010i			0.503885i	0.967742	+	0.251943i	$0.0810694\pi$
$503$			11.3010i			0.503885i	−0.967742	+	0.251943i	$0.918931\pi$
$504$	−44.2304	+	11.7104i	−1.97018	+	0.521622i
$505$	43.1402	+	43.1402i	1.91972	+	1.91972i
$506$	18.4397	−	31.9386i	0.819746	−	1.41984i
$507$	−18.5756	−	12.7258i	−0.824972	−	0.565174i
$508$	11.0435	+	19.1280i	0.489978	+	0.848666i
$509$	−10.5043	+	2.81462i	−0.465595	+	0.124756i	−0.483987	−	0.875075i	$-0.660812\pi$
$509$	−10.5043	+	2.81462i	−0.465595	+	0.124756i	0.0183923	+	0.999831i	$0.494145\pi$
$510$	−3.55246	−	11.0086i	−0.157306	−	0.487468i
$511$	9.89095	+	12.1884i	0.437550	+	0.539182i
$512$	−34.5607	−	34.5607i	−1.52738	−	1.52738i
$513$	22.3757	+	8.74433i	0.987910	+	0.386072i
$514$	7.64249	−	28.5222i	0.337096	−	1.25806i
$515$	−6.87979	−	1.84344i	−0.303160	−	0.0812315i
$516$	−7.55323	+	35.1874i	−0.332513	+	1.54904i
$517$			2.38132i			0.104730i
$518$	3.79889	−	36.5090i	0.166914	−	1.60411i
$519$	20.7453	−	6.69449i	0.910616	−	0.293855i
$520$	−33.9733	+	69.1965i	−1.48983	+	3.03447i
$521$	−30.7947	+	17.7793i	−1.34914	+	0.778926i	−0.988128	−	0.153635i	$-0.950902\pi$
$521$	−30.7947	+	17.7793i	−1.34914	+	0.778926i	−0.361012	+	0.932561i	$0.617569\pi$
$522$	8.44386	−	3.20242i	0.369578	−	0.140166i
$523$	9.50808	−	16.4685i	0.415759	−	0.720116i	−0.579748	−	0.814796i	$-0.696849\pi$
$523$	9.50808	−	16.4685i	0.415759	−	0.720116i	0.995508	+	0.0946792i	$0.0301825\pi$
$524$	43.1732			1.88603
$525$	−29.8444	+	26.8197i	−1.30252	+	1.17051i
$526$	−25.1580	+	25.1580i	−1.09694	+	1.09694i
$527$	0.757192	+	2.82588i	0.0329838	+	0.123097i
$528$	26.5678	−	1.33884i	1.15622	−	0.0582654i
$529$	−4.28196	−	7.41658i	−0.186172	−	0.322460i
$530$	−12.8966	+	22.3376i	−0.560193	+	0.970283i
$531$	4.24277	−	26.1083i	0.184121	−	1.13300i
$532$	51.9080	−	8.27674i	2.25050	−	0.358842i
$533$	12.8279	+	11.2101i	0.555639	+	0.485563i
$534$	9.67411	−	45.0676i	0.418640	−	1.95027i
$535$	27.3024	+	7.31566i	1.18039	+	0.316283i
$536$	16.2825	−	9.40071i	0.703297	−	0.406049i
$537$	1.45649	−	6.78520i	0.0628524	−	0.292803i
$538$	−4.64182	+	4.64182i	−0.200123	+	0.200123i
$539$	0.996339	+	18.2840i	0.0429154	+	0.787548i
$540$	−12.4618	−	81.8717i	−0.536270	−	3.52320i
$541$	14.0981	−	3.77756i	0.606123	−	0.162410i	0.0573115	−	0.998356i	$-0.481747\pi$
$541$	14.0981	−	3.77756i	0.606123	−	0.162410i	0.548811	+	0.835946i	$0.315081\pi$
$542$	51.5701	−	29.7740i	2.21513	−	1.27890i
$543$	−5.43090	+	6.00731i	−0.233062	+	0.257798i
$544$	2.22098	−	0.595109i	0.0952236	−	0.0255151i
$545$	59.7779			2.56060
$546$	35.6164	−	21.2273i	1.52424	−	0.908443i
$547$	−14.8115			−0.633294			−0.316647	−	0.948543i	$-0.602557\pi$
$547$	−14.8115			−0.633294			−0.316647	+	0.948543i	$0.602557\pi$
$548$	−18.3698	+	4.92219i	−0.784721	+	0.210265i
$549$	29.0960	+	13.0947i	1.24179	+	0.558869i
$550$	49.7761	−	28.7382i	2.12246	−	1.22540i
$551$	−5.35711	+	1.43543i	−0.228220	+	0.0611515i
$552$	25.5666	−	49.9291i	1.08819	−	2.12512i
$553$	3.76149	+	8.42487i	0.159955	+	0.358262i
$554$	−3.80089	+	3.80089i	−0.161484	+	0.161484i
$555$	34.7248	+	7.45394i	1.47399	+	0.316402i
$556$	−7.89644	+	4.55901i	−0.334884	+	0.193345i
$557$	−27.4039	−	7.34285i	−1.16114	−	0.311127i	−0.373719	−	0.927542i	$-0.621918\pi$
$557$	−27.4039	−	7.34285i	−1.16114	−	0.311127i	−0.787421	+	0.616415i	$0.788584\pi$
$558$	3.08559	+	30.5375i	0.130624	+	1.29275i
$559$	−1.17072	−	17.3947i	−0.0495163	−	0.735718i
$560$	−36.3037	−	44.7362i	−1.53411	−	1.89045i
$561$	1.48183	−	2.89386i	0.0625628	−	0.122179i
$562$	18.3521	−	31.7868i	0.774138	−	1.34085i
$563$	2.87990	+	4.98814i	0.121373	+	0.210225i	0.920310	−	0.391191i	$-0.127937\pi$
$563$	2.87990	+	4.98814i	0.121373	+	0.210225i	−0.798936	+	0.601416i	$0.794603\pi$
$564$	0.341007	+	6.76694i	0.0143590	+	0.284939i
$565$	−9.06671	−	33.8374i	−0.381440	−	1.42355i
$566$	0.676918	−	0.676918i	0.0284530	−	0.0284530i
$567$	−9.83710	+	21.6848i	−0.413119	+	0.910677i
$568$	−59.7366			−2.50649
$569$	13.6368	−	23.6197i	0.571686	−	0.990189i	−0.424707	−	0.905331i	$-0.639623\pi$
$569$	13.6368	−	23.6197i	0.571686	−	0.990189i	0.996393	−	0.0848585i	$-0.0270438\pi$
$570$	3.75107	+	74.4360i	0.157115	+	3.11778i
$571$	−19.1573	+	11.0605i	−0.801707	+	0.462866i	−0.844068	−	0.536237i	$-0.819845\pi$
$571$	−19.1573	+	11.0605i	−0.801707	+	0.462866i	0.0423609	+	0.999102i	$0.486512\pi$
$572$	−38.3556	+	13.0950i	−1.60373	+	0.547528i
$573$	−8.08321	−	25.0487i	−0.337681	−	1.04642i
$574$	−28.6446	+	12.7891i	−1.19560	+	0.533807i
$575$		−	49.1922i		−	2.05146i
$576$	−11.0482	+	1.11635i	−0.460344	+	0.0465145i
$577$	−25.4078	−	6.80800i	−1.05774	−	0.283421i	−0.312294	−	0.949986i	$-0.601097\pi$
$577$	−25.4078	−	6.80800i	−1.05774	−	0.283421i	−0.745447	+	0.666565i	$0.767764\pi$
$578$	−10.7068	+	39.9583i	−0.445344	+	1.66205i
$579$	2.87424	−	1.85835i	0.119449	−	0.0772306i
$580$	13.5189	+	13.5189i	0.561341	+	0.561341i
$581$	−7.14966	+	1.14001i	−0.296618	+	0.0472957i
$582$	−79.6632	+	25.7073i	−3.30215	+	1.06560i
$583$	−7.00245	+	1.87630i	−0.290012	+	0.0777084i
$584$	−17.0999	−	29.6178i	−0.707597	−	1.22559i
$585$	16.7131	+	36.4707i	0.691002	+	1.50788i
$586$	−16.9375	+	29.3366i	−0.699680	+	1.21188i
$587$	10.0075	+	10.0075i	0.413052	+	0.413052i	0.882801	−	0.469748i	$-0.155655\pi$
$587$	10.0075	+	10.0075i	0.413052	+	0.413052i	−0.469748	+	0.882801i	$0.655655\pi$
$588$	5.44955	+	51.8144i	0.224736	+	2.13679i
$589$		−	18.8496i		−	0.776683i
$590$	79.2644	−	21.2388i	3.26326	−	0.874389i
$591$	−1.80322	−	35.7831i	−0.0741747	−	1.47192i
$592$	−8.40121	+	31.3538i	−0.345288	+	1.28863i
$593$	3.76514	+	14.0517i	0.154616	+	0.577034i	0.999138	+	0.0415135i	$0.0132180\pi$
$593$	3.76514	+	14.0517i	0.154616	+	0.577034i	−0.844522	+	0.535521i	$0.820115\pi$
$594$	20.2148	−	27.4735i	0.829425	−	1.12725i
$595$	−6.95355	+	1.10874i	−0.285068	+	0.0454540i
$596$	−50.4789	+	50.4789i	−2.06770	+	2.06770i
$597$	12.4175	+	2.66551i	0.508214	+	0.109092i
$598$	−9.82951	+	49.8728i	−0.401959	+	2.03945i
$599$	−4.28171	+	2.47204i	−0.174946	+	0.101005i	−0.584916	−	0.811094i	$-0.698872\pi$
$599$	−4.28171	+	2.47204i	−0.174946	+	0.101005i	0.409970	+	0.912099i	$0.365539\pi$
$600$	73.4143	−	47.4664i	2.99713	−	1.93781i
$601$	−14.4246			−0.588392			−0.294196	−	0.955745i	$-0.595052\pi$
$601$	−14.4246			−0.588392			−0.294196	+	0.955745i	$0.595052\pi$
$602$	29.9829	+	11.4736i	1.22201	+	0.467629i
$603$	1.56950	−	9.65805i	0.0639148	−	0.393306i
$604$	11.6111	+	43.3333i	0.472450	+	1.76321i
$605$	−14.8932	−	3.99063i	−0.605496	−	0.162242i
$606$	3.59838	+	71.4061i	0.146174	+	2.90067i
$607$	−12.9626	+	22.4520i	−0.526138	+	0.911297i	0.473399	+	0.880848i	$0.343027\pi$
$607$	−12.9626	+	22.4520i	−0.526138	+	0.911297i	−0.999536	+	0.0304489i	$0.990306\pi$
$608$	−14.8147			−0.600814
$609$	−1.13771	−	5.37816i	−0.0461024	−	0.217934i
$610$			98.9873i			4.00788i
$611$	−1.06049	−	3.10622i	−0.0429029	−	0.125664i
$612$	3.79646	−	8.43560i	0.153463	−	0.340989i
$613$	−9.97821	−	2.67365i	−0.403016	−	0.107988i	0.0516164	−	0.998667i	$-0.483563\pi$
$613$	−9.97821	−	2.67365i	−0.403016	−	0.107988i	−0.454632	+	0.890679i	$0.650229\pi$
$614$	−69.2788	−	39.9982i	−2.79587	−	1.61419i
$615$	−9.32150	−	28.8860i	−0.375879	−	1.16480i
$616$	4.12902	−	39.6817i	0.166363	−	1.59882i
$617$	−21.0842	−	21.0842i	−0.848818	−	0.848818i	0.141168	−	0.989986i	$-0.454914\pi$
$617$	−21.0842	−	21.0842i	−0.848818	−	0.848818i	−0.989986	+	0.141168i	$0.954914\pi$
$618$	−4.53192	−	7.00933i	−0.182300	−	0.281957i
$619$	−3.41253	+	12.7357i	−0.137161	+	0.511893i	0.862818	+	0.505514i	$0.168697\pi$
$619$	−3.41253	+	12.7357i	−0.137161	+	0.511893i	−0.999980	+	0.00637874i	$0.997970\pi$
$620$	−56.2732	+	32.4893i	−2.25998	+	1.30480i
$621$	−11.7129	−	26.7401i	−0.470021	−	1.07304i
$622$	−20.2535	−	20.2535i	−0.812089	−	0.812089i
$623$	−26.2052	−	10.0280i	−1.04989	−	0.401763i
$624$	−34.0590	+	13.5780i	−1.36345	+	0.543556i
$625$	3.94317	−	6.82976i	0.157727	−	0.273191i
$626$	−13.5554	+	50.5896i	−0.541784	+	2.02197i
$627$	−14.0479	+	15.5389i	−0.561020	+	0.620564i
$628$	−6.71947	−	3.87949i	−0.268136	−	0.154808i
$629$	2.80522	+	2.80522i	0.111851	+	0.111851i
$630$	−73.8729	−	0.220086i	−2.94317	−	0.00876842i
$631$	12.2359	+	12.2359i	0.487104	+	0.487104i	0.907391	−	0.420287i	$-0.138071\pi$
$631$	12.2359	+	12.2359i	0.487104	+	0.487104i	−0.420287	+	0.907391i	$0.638071\pi$
$632$	−5.20288	−	19.4174i	−0.206959	−	0.772383i
$633$	−16.0938	−	14.5496i	−0.639672	−	0.578295i
$634$	−5.17886	+	2.99002i	−0.205679	+	0.118749i
$635$	4.93399	+	18.4139i	0.195799	+	0.730733i
$636$	−19.6300	+	6.33458i	−0.778379	+	0.251183i
$637$	−9.44218	−	23.4061i	−0.374113	−	0.927383i
$638$			7.87443i			0.311752i
$639$	−19.6616	+	24.0815i	−0.777799	+	0.952648i
$640$	−29.1097	−	50.4195i	−1.15066	−	1.99300i
$641$	−20.3458	−	35.2400i	−0.803612	−	1.39190i	−0.917224	−	0.398372i	$-0.869575\pi$
$641$	−20.3458	−	35.2400i	−0.803612	−	1.39190i	0.113612	−	0.993525i	$-0.463758\pi$
$642$	17.9849	+	27.8165i	0.709806	+	1.09783i
$643$	−17.8828	+	17.8828i	−0.705229	+	0.705229i	−0.965528	−	0.260299i	$-0.916179\pi$
$643$	−17.8828	+	17.8828i	−0.705229	+	0.705229i	0.260299	+	0.965528i	$0.416179\pi$
$644$	−51.7143	−	37.4906i	−2.03783	−	1.47734i
$645$	−14.1575	+	27.6482i	−0.557452	+	1.08865i
$646$	−4.16259	+	7.20981i	−0.163775	+	0.283666i
$647$	7.90638	+	13.6943i	0.310832	+	0.538377i	0.978543	−	0.206044i	$-0.0660591\pi$
$647$	7.90638	+	13.6943i	0.310832	+	0.538377i	−0.667711	+	0.744421i	$0.732726\pi$
$648$	28.6050	−	43.2822i	1.12371	−	1.70029i
$649$	19.9740	+	11.5320i	0.784049	+	0.452671i
$650$	−52.1301	+	59.6535i	−2.04471	+	2.33980i
$651$	18.6568	+	0.995908i	0.731217	+	0.0390327i
$652$	27.0014	−	27.0014i	1.05746	−	1.05746i
$653$	−43.4808	−	25.1036i	−1.70153	−	0.982381i	−0.944212	−	0.329340i	$-0.893174\pi$
$653$	−43.4808	−	25.1036i	−1.70153	−	0.982381i	−0.757322	−	0.653041i	$-0.773493\pi$
$654$	51.9655	+	46.9794i	2.03201	+	1.83704i
$655$	35.9933	+	9.64438i	1.40637	+	0.376837i
$656$	26.7958	−	7.17990i	1.04620	−	0.280328i
$657$	−17.5680	−	2.85491i	−0.685391	−	0.111381i
$658$	6.01152	+	0.625519i	0.234353	+	0.0243853i
$659$		−	41.1531i		−	1.60310i	−0.597930	−	0.801548i	$-0.704010\pi$
$659$		−	41.1531i		−	1.60310i	0.597930	−	0.801548i	$-0.295990\pi$
$660$	70.6027	+	15.1554i	2.74821	+	0.589923i
$661$	3.36505	−	12.5585i	0.130885	−	0.488470i	−0.869096	−	0.494644i	$-0.835299\pi$
$661$	3.36505	−	12.5585i	0.130885	−	0.488470i	0.999981	+	0.00617374i	$0.00196518\pi$
$662$	−10.2129	−	17.6892i	−0.396934	−	0.687509i
$663$	−0.644164	+	4.43469i	−0.0250172	+	0.172229i
$664$	15.7743			0.612162
$665$	45.1244	+	4.69535i	1.74985	+	0.182078i
$666$	24.3286	+	33.7700i	0.942713	+	1.30856i
$667$	5.83655	+	3.36973i	0.225992	+	0.130477i
$668$	−23.7600	+	88.6736i	−0.919303	+	3.43088i
$669$	7.77755	−	0.391936i	0.300698	−	0.0151531i
$670$	29.3217	−	7.85672i	1.13280	−	0.303532i
$671$	−19.6727	+	19.6727i	−0.759458	+	0.759458i
$672$	0.782725	−	14.6631i	0.0301943	−	0.565643i
$673$		−	50.2523i		−	1.93709i	−0.248847	−	0.968543i	$-0.580052\pi$
$673$		−	50.2523i		−	1.93709i	0.248847	−	0.968543i	$-0.419948\pi$
$674$	11.1567	+	41.6373i	0.429740	+	1.60381i
$675$	5.02839	−	45.2183i	0.193543	−	1.74045i
$676$	44.1997	−	34.1623i	1.69999	−	1.31394i
$677$	32.2713	+	18.6318i	1.24029	+	0.716080i	0.969152	−	0.246462i	$-0.0792680\pi$
$677$	32.2713	+	18.6318i	1.24029	+	0.716080i	0.271134	+	0.962542i	$0.412601\pi$
$678$	18.7110	−	36.5407i	0.718592	−	1.40334i
$679$	8.02339	+	50.3192i	0.307910	+	1.93107i
$680$	15.3416			0.588325
$681$	−16.5206	+	10.6814i	−0.633069	+	0.409314i
$682$	−25.8510	−	6.92677i	−0.989888	−	0.265240i
$683$	41.3864	+	11.0895i	1.58361	+	0.424326i	0.940040	−	0.341064i	$-0.110787\pi$
$683$	41.3864	+	11.0895i	1.58361	+	0.424326i	0.643567	+	0.765390i	$0.277454\pi$
$684$	−37.6944	+	46.1681i	−1.44128	+	1.76528i
$685$	−16.4144			−0.627162
$686$	46.4186	+	2.28759i	1.77227	+	0.0873406i
$687$	−28.2532	−	14.4673i	−1.07793	−	0.551962i
$688$	−24.5859	−	14.1947i	−0.937330	−	0.541168i
$689$	8.29846	−	5.56591i	0.316146	−	0.212044i
$690$	60.7367	−	67.1829i	2.31221	−	2.55761i
$691$	12.4091	+	46.3114i	0.472064	+	1.76177i	0.632335	+	0.774695i	$0.282097\pi$
$691$	12.4091	+	46.3114i	0.472064	+	1.76177i	−0.160270	+	0.987073i	$0.551237\pi$
$692$			54.0817i			2.05588i
$693$	−14.6378	−	14.7252i	−0.556043	−	0.559366i
$694$	−18.4212	+	18.4212i	−0.699261	+	0.699261i
$695$	−7.60165	+	2.03686i	−0.288347	+	0.0772624i
$696$	0.602801	+	11.9620i	0.0228491	+	0.453417i
$697$	0.877514	−	3.27493i	0.0332382	−	0.124047i
$698$	3.50903	+	2.02594i	0.132819	+	0.0766830i
$699$	7.94433	−	2.56363i	0.300482	−	0.0969656i
$700$	−40.5842	−	90.8992i	−1.53394	−	3.43567i
$701$	6.76669			0.255574			0.127787	−	0.991802i	$-0.459213\pi$
$701$	6.76669			0.255574			0.127787	+	0.991802i	$0.459213\pi$
$702$	−14.1334	+	44.8391i	−0.533431	+	1.69234i
$703$	−12.7804	−	22.1362i	−0.482021	−	0.834884i
$704$	2.50606	−	9.35274i	0.0944506	−	0.352495i
$705$	−1.22736	+	5.71774i	−0.0462249	+	0.215343i
$706$			25.7536i			0.969249i
$707$	43.2876	+	4.50423i	1.62800	+	0.169399i
$708$	58.4110	+	29.9099i	2.19522	+	1.12408i
$709$	44.6938	−	11.9757i	1.67851	−	0.449755i	0.711125	−	0.703066i	$-0.248186\pi$
$709$	44.6938	−	11.9757i	1.67851	−	0.449755i	0.967385	+	0.253311i	$0.0815195\pi$
$710$	−93.1620	−	24.9627i	−3.49631	−	0.936833i
$711$	−9.54016	−	4.29357i	−0.357784	−	0.161021i
$712$	52.9428	+	30.5665i	1.98412	+	1.14553i
$713$	−16.1967	+	16.1967i	−0.606570	+	0.606570i
$714$	−6.91614	−	4.50094i	−0.258830	−	0.168443i
$715$	−34.9021	+	2.34903i	−1.30527	+	0.0878487i
$716$	14.9106	+	8.60865i	0.557236	+	0.321720i
$717$	−1.56187	−	30.9937i	−0.0583291	−	1.15748i
$718$	35.1383	+	60.8614i	1.31135	+	2.27133i
$719$	17.7507	−	30.7452i	0.661990	−	1.14660i	−0.318101	−	0.948057i	$-0.603045\pi$
$719$	17.7507	−	30.7452i	0.661990	−	1.14660i	0.980092	−	0.198544i	$-0.0636214\pi$
$720$	64.4814	+	10.4786i	2.40308	+	0.390516i
$721$	−4.63943	+	2.07139i	−0.172782	+	0.0771426i
$722$	4.21484	−	4.21484i	0.156860	−	0.156860i
$723$	18.3152	−	11.8418i	0.681150	−	0.440401i
$724$	−10.0458	−	17.3998i	−0.373349	−	0.646659i
$725$	5.25171	+	9.09623i	0.195044	+	0.337826i
$726$	−9.81059	−	15.1737i	−0.364105	−	0.563147i
$727$		−	11.8237i		−	0.438518i	−0.975667	−	0.219259i	$-0.929636\pi$
$727$		−	11.8237i		−	0.438518i	0.975667	−	0.219259i	$-0.0703640\pi$
$728$	12.2858	+	53.5999i	0.455342	+	1.98654i
$729$	−8.03329	−	25.7772i	−0.297529	−	0.954713i
$730$	−14.2913	−	53.3360i	−0.528947	−	1.97406i
$731$	−3.00485	+	1.73485i	−0.111138	+	0.0641657i
$732$	−53.0863	+	58.7206i	−1.96213	+	2.17038i
$733$	1.34969	+	5.03711i	0.0498519	+	0.186050i	0.986362	−	0.164591i	$-0.0526304\pi$
$733$	1.34969	+	5.03711i	0.0498519	+	0.186050i	−0.936510	+	0.350641i	$0.885964\pi$
$734$	−21.0175	−	21.0175i	−0.775770	−	0.775770i
$735$	−7.03146	+	44.4148i	−0.259359	+	1.63827i
$736$	12.7296	+	12.7296i	0.469221	+	0.469221i
$737$	7.38884	+	4.26595i	0.272171	+	0.157138i
$738$	14.5982	−	32.4366i	0.537367	−	1.19401i
$739$	−4.85016	+	18.1010i	−0.178416	+	0.665858i	0.817529	+	0.575888i	$0.195344\pi$
$739$	−4.85016	+	18.1010i	−0.178416	+	0.665858i	−0.995945	+	0.0899695i	$0.971323\pi$
$740$	−44.0567	+	76.3085i	−1.61956	+	2.80516i
$741$	11.4042	−	26.5251i	0.418943	−	0.974425i
$742$	2.89723	+	18.1701i	0.106361	+	0.667047i
$743$	−34.5937	−	34.5937i	−1.26912	−	1.26912i	−0.946543	−	0.322578i	$-0.895450\pi$
$743$	−34.5937	−	34.5937i	−1.26912	−	1.26912i	−0.322578	−	0.946543i	$-0.604550\pi$
$744$	−39.8003	−	8.54343i	−1.45915	−	0.313217i
$745$	−53.3604	+	30.8077i	−1.95497	+	1.12871i
$746$	17.3579	−	64.7806i	0.635518	−	2.37178i
$747$	5.19191	−	6.35906i	0.189962	−	0.232666i
$748$	5.70358	+	5.70358i	0.208544	+	0.208544i
$749$	18.4116	−	8.22029i	0.672744	−	0.300363i
$750$	57.6210	−	18.5943i	2.10402	−	0.678967i
$751$	−7.42934	−	4.28933i	−0.271100	−	0.156520i	0.358287	−	0.933611i	$-0.383361\pi$
$751$	−7.42934	−	4.28933i	−0.271100	−	0.156520i	−0.629388	+	0.777092i	$0.716694\pi$
$752$	−5.16266	−	1.38333i	−0.188263	−	0.0504449i
$753$	24.1164	+	21.8024i	0.878852	+	0.794525i
$754$	−3.50678	−	10.2715i	−0.127709	−	0.374065i
$755$			38.7206i			1.40919i
$756$	−43.7044	−	39.7481i	−1.58951	−	1.44563i
$757$	40.1392			1.45889			0.729443	−	0.684042i	$-0.239779\pi$
$757$	40.1392			1.45889			0.729443	+	0.684042i	$0.239779\pi$
$758$	−14.6893	+	25.4427i	−0.533541	+	0.924120i
$759$	25.4227	−	1.28113i	0.922787	−	0.0465022i
$760$	−95.4788	−	25.5835i	−3.46338	−	0.928010i
$761$	−3.29654	−	12.3028i	−0.119499	−	0.445978i	0.880085	−	0.474817i	$-0.157486\pi$
$761$	−3.29654	−	12.3028i	−0.119499	−	0.445978i	−0.999584	+	0.0288391i	$0.990819\pi$
$762$	−10.1823	+	19.8850i	−0.368865	+	0.720357i
$763$	33.1117	−	26.8704i	1.19873	−	0.972773i
$764$	65.3005			2.36249
$765$	5.04950	−	6.18463i	0.182565	−	0.223606i
$766$	10.9846	−	6.34195i	0.396889	−	0.229144i
$767$	−31.1899	−	6.14727i	−1.12620	−	0.221965i
$768$	11.6281	−	54.1706i	0.419594	−	1.95471i
$769$	−13.5525	+	13.5525i	−0.488714	+	0.488714i	−0.907900	−	0.419186i	$-0.862316\pi$
$769$	−13.5525	+	13.5525i	−0.488714	+	0.488714i	0.419186	+	0.907900i	$0.362316\pi$
$770$	23.0215	−	60.1600i	0.829639	−	2.16801i
$771$	19.3962	−	6.25914i	0.698536	−	0.225417i
$772$	2.19777	+	8.20220i	0.0790996	+	0.295204i
$773$	6.54075	−	24.4104i	0.235254	−	0.877981i	−0.742780	−	0.669536i	$-0.766493\pi$
$773$	6.54075	−	24.4104i	0.235254	−	0.877981i	0.978034	−	0.208445i	$-0.0668403\pi$
$774$	−34.0360	+	12.9085i	−1.22340	+	0.463986i
$775$	−34.4818	+	9.23937i	−1.23862	+	0.331888i
$776$		−	111.019i		−	3.98536i
$777$	22.5851	−	11.4801i	0.810235	−	0.411846i
$778$	−22.1126	−	22.1126i	−0.792775	−	0.792775i
$779$	−10.9224	+	18.9182i	−0.391337	+	0.677816i
$780$	−98.8440	+	11.6732i	−3.53918	+	0.417967i
$781$	−13.5539	−	23.4761i	−0.484998	−	0.840041i
$782$	9.77183	−	2.61836i	0.349440	−	0.0936322i
$783$	5.02060	+	3.69412i	0.179422	+	0.132017i
$784$	−40.2182	−	8.46130i	−1.43636	−	0.302189i
$785$	−4.73536	−	4.73536i	−0.169012	−	0.169012i
$786$	23.7098	+	36.6710i	0.845701	+	1.30801i
$787$	2.69803	−	10.0692i	0.0961745	−	0.358928i	−0.901020	−	0.433777i	$-0.857181\pi$
$787$	2.69803	−	10.0692i	0.0961745	−	0.358928i	0.997195	+	0.0748487i	$0.0238474\pi$
$788$	85.8604	+	23.0062i	3.05865	+	0.819562i
$789$	−24.0103	−	5.15400i	−0.854790	−	0.183487i
$790$		−	32.4565i		−	1.15475i
$791$	−20.2322	−	14.6675i	−0.719375	−	0.521515i
$792$	26.4428	+	36.7046i	0.939603	+	1.30424i
$793$	16.9003	−	34.4223i	0.600146	−	1.22237i
$794$	72.3484	−	41.7704i	2.56755	−	1.48238i
$795$	−17.7805	+	0.896015i	−0.630609	+	0.0317784i
$796$	−15.7546	+	27.2877i	−0.558406	+	0.967187i
$797$	−13.6252			−0.482629			−0.241315	−	0.970447i	$-0.577579\pi$
$797$	−13.6252			−0.482629			−0.241315	+	0.970447i	$0.577579\pi$
$798$	35.5370	+	39.5449i	1.25800	+	1.39987i
$799$	−0.461903	+	0.461903i	−0.0163410	+	0.0163410i
$800$	7.26161	+	27.1007i	0.256737	+	0.958154i
$801$	29.7477	−	11.2821i	1.05108	−	0.398634i
$802$	8.46609	+	14.6637i	0.298948	+	0.517793i
$803$	7.75974	−	13.4403i	0.273835	−	0.474297i
$804$	21.6075	+	11.0643i	0.762039	+	0.390209i
$805$	−34.7390	−	42.8081i	−1.22439	−	1.50879i
$806$	36.8051	−	2.47710i	1.29640	−	0.0872522i
$807$	−4.43006	−	0.950947i	−0.155946	−	0.0334749i
$808$	−91.5924	−	24.5421i	−3.22221	−	0.863388i
$809$	−16.7268	+	9.65721i	−0.588082	+	0.339529i	−0.764339	−	0.644815i	$-0.776934\pi$
$809$	−16.7268	+	9.65721i	−0.588082	+	0.339529i	0.176257	+	0.984344i	$0.443601\pi$
$810$	62.6975	−	55.5472i	2.20297	−	1.95173i
$811$	10.0317	−	10.0317i	0.352261	−	0.352261i	−0.508690	−	0.860950i	$-0.669870\pi$
$811$	10.0317	−	10.0317i	0.352261	−	0.352261i	0.860950	+	0.508690i	$0.169870\pi$
$812$	13.5651	+	1.41149i	0.476040	+	0.0495337i
$813$	36.5840	+	18.7332i	1.28306	+	0.657000i
$814$	−35.0550	+	9.39296i	−1.22868	+	0.329223i
$815$	28.5427	−	16.4791i	0.999807	−	0.577239i
$816$	5.41303	+	4.89364i	0.189494	+	0.171312i
$817$	21.5937	−	5.78602i	0.755468	−	0.202427i
$818$	−55.5869			−1.94355
$819$	25.6513	+	12.6890i	0.896329	+	0.443389i
$820$	75.3041			2.62973
$821$	23.2528	−	6.23056i	0.811527	−	0.217448i	0.170888	−	0.985290i	$-0.445336\pi$
$821$	23.2528	−	6.23056i	0.811527	−	0.217448i	0.640639	+	0.767842i	$0.278670\pi$
$822$	−14.2692	−	12.9001i	−0.497696	−	0.449941i
$823$	−28.2187	+	16.2921i	−0.983642	+	0.567906i	−0.903368	−	0.428867i	$-0.858913\pi$
$823$	−28.2187	+	16.2921i	−0.983642	+	0.567906i	−0.0802743	+	0.996773i	$0.525580\pi$
$824$	10.6928	−	2.86514i	0.372503	−	0.0998119i
$825$	35.3113	+	18.0815i	1.22938	+	0.629516i
$826$	34.3586	−	47.3941i	1.19549	−	1.64905i
$827$	31.4756	−	31.4756i	1.09451	−	1.09451i	0.0994736	−	0.995040i	$-0.468284\pi$
$827$	31.4756	−	31.4756i	1.09451	−	1.09451i	0.995040	−	0.0994736i	$-0.0317159\pi$
$828$	72.0596	−	7.28112i	2.50424	−	0.253036i
$829$	3.27464	−	1.89061i	0.113733	−	0.0656638i	−0.442054	−	0.896988i	$-0.645750\pi$
$829$	3.27464	−	1.89061i	0.113733	−	0.0656638i	0.555787	+	0.831324i	$0.312417\pi$
$830$	24.6008	+	6.59175i	0.853905	+	0.228803i
$831$	−3.62749	−	0.778669i	−0.125836	−	0.0270117i
$832$	0.896199	+	13.3158i	0.0310701	+	0.461643i
$833$	−3.35327	+	3.73979i	−0.116184	+	0.129576i
$834$	−8.20895	−	4.20347i	−0.284253	−	0.145554i
$835$	−39.6172	+	68.6191i	−1.37101	+	2.37466i
$836$	−25.9851	−	45.0075i	−0.898714	−	1.55662i
$837$	−16.5438	+	13.2326i	−0.571839	+	0.457386i
$838$	−12.5983	−	47.0176i	−0.435202	−	1.62420i
$839$	37.1220	−	37.1220i	1.28159	−	1.28159i	0.341835	−	0.939760i	$-0.388952\pi$
$839$	37.1220	−	37.1220i	1.28159	−	1.28159i	0.939760	−	0.341835i	$-0.111048\pi$
$840$	30.3664	−	93.1506i	1.04774	−	3.21400i
$841$	27.5610			0.950379
$842$	−32.9288	+	57.0343i	−1.13480	+	1.96553i
$843$	25.3020	−	1.27505i	0.871446	−	0.0439149i
$844$	46.6148	−	26.9131i	1.60455	−	0.926386i
$845$	44.4805	−	18.6073i	1.53018	−	0.640111i
$846$	−5.56051	+	4.00591i	−0.191174	+	0.137726i
$847$	−10.0433	+	4.48410i	−0.345093	+	0.154075i
$848$		−	16.2711i		−	0.558753i
$849$	0.646037	+	0.138677i	0.0221719	+	0.00475937i
$850$	15.2294	+	4.08069i	0.522363	+	0.139967i
$851$	−8.03912	+	30.0024i	−0.275578	+	1.02847i
$852$	−41.8776	−	64.7704i	−1.43470	−	2.21900i
$853$	−15.8451	−	15.8451i	−0.542525	−	0.542525i	0.381744	−	0.924268i	$-0.375324\pi$
$853$	−15.8451	−	15.8451i	−0.542525	−	0.542525i	−0.924268	+	0.381744i	$0.875324\pi$
$854$	44.4951	+	54.8303i	1.52259	+	1.87625i
$855$	−41.7390	+	30.0697i	−1.42745	+	1.02836i
$856$	−42.4345	+	11.3703i	−1.45038	+	0.388628i
$857$	−15.0832	−	26.1248i	−0.515232	−	0.892408i	−0.999844	−	0.0176784i	$-0.994373\pi$
$857$	−15.0832	−	26.1248i	−0.515232	−	0.892408i	0.484612	−	0.874729i	$-0.338961\pi$
$858$	−32.1868	−	25.3875i	−1.09884	−	0.866715i
$859$	−0.361074	+	0.625398i	−0.0123197	+	0.0213383i	−0.872120	−	0.489293i	$-0.837255\pi$
$859$	−0.361074	+	0.625398i	−0.0123197	+	0.0213383i	0.859800	+	0.510631i	$0.170588\pi$
$860$	−54.4926	−	54.4926i	−1.85818	−	1.85818i
$861$	−18.1477	−	11.8103i	−0.618470	−	0.402493i
$862$		−	9.18337i		−	0.312787i
$863$	−0.947765	+	0.253953i	−0.0322623	+	0.00864466i	−0.274914	−	0.961469i	$-0.588649\pi$
$863$	−0.947765	+	0.253953i	−0.0322623	+	0.00864466i	0.242652	+	0.970113i	$0.421983\pi$
$864$	10.4001	+	13.0025i	0.353818	+	0.442354i
$865$	−12.0812	+	45.0876i	−0.410773	+	1.53303i
$866$	−7.95765	−	29.6984i	−0.270412	−	1.00919i
$867$	−27.1732	+	8.76879i	−0.922851	+	0.297804i
$868$	−16.5663	+	43.2912i	−0.562298	+	1.46940i
$869$	6.45041	−	6.45041i	0.218815	−	0.218815i
$870$	−4.05856	+	18.9071i	−0.137598	+	0.641011i
$871$	−11.5378	−	2.27401i	−0.390945	−	0.0770520i
$872$	−80.4617	+	46.4546i	−2.72478	+	1.57315i
$873$	−44.7549	−	36.5406i	−1.51473	−	1.23671i
$874$	−65.1815			−2.20480
$875$	−5.80338	−	36.3962i	−0.196190	−	1.23042i
$876$	20.1260	−	39.3040i	0.679994	−	1.32796i
$877$	−10.0700	−	37.5816i	−0.340038	−	1.26904i	−0.898303	−	0.439377i	$-0.855199\pi$
$877$	−10.0700	−	37.5816i	−0.340038	−	1.26904i	0.558264	−	0.829663i	$-0.311467\pi$
$878$	91.6331	+	24.5530i	3.09247	+	0.828624i
$879$	−23.3516	+	1.17676i	−0.787629	+	0.0396911i
$880$	−28.4813	+	49.3311i	−0.960106	+	1.66295i
$881$	−3.32018			−0.111860			−0.0559299	−	0.998435i	$-0.517812\pi$
$881$	−3.32018			−0.111860			−0.0559299	+	0.998435i	$0.517812\pi$
$882$	−41.0180	+	33.0842i	−1.38115	+	1.11400i
$883$		−	0.699202i		−	0.0235300i	−0.999931	−	0.0117650i	$-0.996255\pi$
$883$		−	0.699202i		−	0.0235300i	0.999931	−	0.0117650i	$-0.00374500\pi$
$884$	−9.97982	−	4.89978i	−0.335658	−	0.164797i
$885$	42.0155	+	37.9840i	1.41233	+	1.27682i
$886$	66.4722	+	17.8112i	2.23318	+	0.598378i
$887$	23.8997	+	13.7985i	0.802475	+	0.463309i	0.844336	−	0.535814i	$-0.179995\pi$
$887$	23.8997	+	13.7985i	0.802475	+	0.463309i	−0.0418610	+	0.999123i	$0.513329\pi$
$888$	−52.5326	+	16.9522i	−1.76288	+	0.568880i
$889$	11.0101	+	7.98184i	0.369267	+	0.267702i
$890$	69.7936	+	69.7936i	2.33949	+	2.33949i
$891$	23.5000	+	1.42106i	0.787278	+	0.0476072i
$892$	−5.00046	+	18.6620i	−0.167428	+	0.624849i
$893$	3.64492	−	2.10440i	0.121973	−	0.0704210i
$894$	−70.5984	−	15.1545i	−2.36116	−	0.506842i
$895$	10.5078	+	10.5078i	0.351238	+	0.351238i
$896$	−38.7879	−	14.8431i	−1.29581	−	0.495872i
$897$	−32.5911	+	12.9928i	−1.08819	+	0.433817i
$898$	37.8219	−	65.5095i	1.26213	−	2.18608i
$899$	1.26582	−	4.72410i	0.0422174	−	0.157558i
$900$	102.932	+	46.3250i	3.43108	+	1.54417i
$901$	−1.72220	−	0.994314i	−0.0573749	−	0.0331254i
$902$	21.9315	+	21.9315i	0.730238	+	0.730238i
$903$	4.58595	+	21.6786i	0.152611	+	0.721417i
$904$	38.4996	+	38.4996i	1.28048	+	1.28048i
$905$	−4.48822	−	16.7502i	−0.149193	−	0.556797i
$906$	−30.4304	+	33.6602i	−1.01098	+	1.11828i
$907$	19.0984	−	11.0265i	0.634152	−	0.366128i	−0.148206	−	0.988956i	$-0.547350\pi$
$907$	19.0984	−	11.0265i	0.634152	−	0.366128i	0.782358	+	0.622829i	$0.214017\pi$
$908$	−12.6324	−	47.1446i	−0.419219	−	1.56455i
$909$	−40.0401	+	28.8457i	−1.32804	+	0.956751i
$910$	−3.23801	+	88.7255i	−0.107339	+	2.94122i
$911$			53.8941i			1.78559i	0.450464	+	0.892795i	$0.351259\pi$
$911$			53.8941i			1.78559i	−0.450464	+	0.892795i	$0.648741\pi$
$912$	−25.5275	−	39.4823i	−0.845300	−	1.30739i
$913$	3.57911	+	6.19920i	0.118451	+	0.205164i
$914$	20.2404	+	35.0574i	0.669492	+	1.15959i
$915$	−57.3753	+	37.0962i	−1.89677	+	1.22636i
$916$	55.6850	−	55.6850i	1.83988	−	1.83988i
$917$	24.2723	−	10.8370i	0.801543	−	0.357868i
$918$	9.25007	−	1.40796i	0.305298	−	0.0464698i
$919$	−11.6653	+	20.2049i	−0.384803	+	0.666498i	−0.991742	−	0.128250i	$-0.959064\pi$
$919$	−11.6653	+	20.2049i	−0.384803	+	0.666498i	0.606939	+	0.794749i	$0.292397\pi$
$920$	60.0582	+	104.024i	1.98006	+	3.42957i
$921$	−2.77894	−	55.1452i	−0.0915693	−	1.81710i
$922$	−2.88809	−	1.66744i	−0.0951141	−	0.0549142i
$923$	28.1346	+	24.5864i	0.926063	+	0.809270i
$924$	45.9201	−	23.3414i	1.51066	−	0.767875i
$925$	−34.2297	+	34.2297i	−1.12546	+	1.12546i
$926$	88.4325	+	51.0565i	2.90607	+	1.67782i
$927$	2.36440	−	5.25360i	0.0776570	−	0.172551i
$928$	−3.71287	−	0.994859i	−0.121881	−	0.0326579i
$929$	−4.88038	+	1.30769i	−0.160120	+	0.0429041i	−0.337989	−	0.941150i	$-0.609747\pi$
$929$	−4.88038	+	1.30769i	−0.160120	+	0.0429041i	0.177868	+	0.984054i	$0.443080\pi$
$930$	−58.5002	−	29.9556i	−1.91830	−	0.982282i
$931$	27.1056	−	17.6828i	0.888349	−	0.579529i
$932$			20.7104i			0.678392i
$933$	4.14922	−	19.3295i	0.135839	−	0.632819i
$934$	17.8235	−	66.5182i	0.583203	−	2.17654i
$935$	3.48094	+	6.02916i	0.113839	+	0.197175i
$936$	−50.8381	−	36.1019i	−1.66170	−	1.18003i
$937$	3.32322			0.108565			0.0542824	−	0.998526i	$-0.482713\pi$
$937$	3.32322			0.108565			0.0542824	+	0.998526i	$0.482713\pi$
$938$	12.7100	−	17.5321i	0.414997	−	0.572444i
$939$	−34.4029	+	11.1018i	−1.12270	+	0.362293i
$940$	−12.5649	−	7.25432i	−0.409820	−	0.236610i
$941$	1.54347	−	5.76031i	0.0503157	−	0.187781i	−0.936194	−	0.351484i	$-0.885677\pi$
$941$	1.54347	−	5.76031i	0.0503157	−	0.187781i	0.986510	+	0.163703i	$0.0523439\pi$
$942$	−0.394982	−	7.83800i	−0.0128692	−	0.255376i
$943$	25.6409	−	6.87045i	0.834981	−	0.223733i
$944$	−36.6043	+	36.6043i	−1.19137	+	1.19137i
$945$	−27.5569	−	42.9009i	−0.896425	−	1.39557i
$946$		−	31.7407i		−	1.03198i
$947$	10.8784	+	40.5989i	0.353501	+	1.31929i	0.882360	+	0.470575i	$0.155954\pi$
$947$	10.8784	+	40.5989i	0.353501	+	1.31929i	−0.528858	+	0.848710i	$0.677380\pi$
$948$	17.4062	−	19.2536i	0.565328	−	0.625329i
$949$	−4.13642	+	20.9873i	−0.134274	+	0.681276i
$950$	−87.9752	−	50.7925i	−2.85429	−	1.64793i
$951$	−3.67390	−	1.88125i	−0.119134	−	0.0610038i
$952$	8.49792	−	6.89612i	0.275419	−	0.223504i
$953$	20.5810			0.666685			0.333342	−	0.942806i	$-0.391823\pi$
$953$	20.5810			0.666685			0.333342	+	0.942806i	$0.391823\pi$
$954$	−16.1609	−	13.1947i	−0.523229	−	0.427195i
$955$	54.4408	+	14.5874i	1.76166	+	0.472036i
$956$	74.3683	+	19.9269i	2.40524	+	0.644483i
$957$	−4.56420	+	2.95100i	−0.147540	+	0.0953924i
$958$	−25.9253			−0.837608
$959$	−9.09215	+	7.37834i	−0.293601	+	0.238259i
$960$	10.8377	−	21.1650i	0.349786	−	0.683097i
$961$	−12.4515	−	7.18887i	−0.401661	−	0.231899i
$962$	41.5430	−	27.8635i	1.33940	−	0.898357i
$963$	−9.38309	+	20.8489i	−0.302366	+	0.671846i
$964$	14.0046	+	52.2660i	0.451059	+	1.68338i
$965$			7.32910i			0.235932i
$966$	3.44383	−	64.5148i	0.110803	−	2.07573i
$967$	11.7578	−	11.7578i	0.378105	−	0.378105i	−0.492313	−	0.870418i	$-0.663849\pi$
$967$	11.7578	−	11.7578i	0.378105	−	0.378105i	0.870418	+	0.492313i	$0.163849\pi$
$968$	23.1476	−	6.20239i	0.743993	−	0.199352i
$969$	−5.73893	+	0.289203i	−0.184361	+	0.00929054i
$970$	46.3927	−	173.140i	1.48958	−	5.55918i
$971$	−16.1531	−	9.32600i	−0.518378	−	0.299286i	0.217893	−	0.975973i	$-0.430082\pi$
$971$	−16.1531	−	9.32600i	−0.518378	−	0.299286i	−0.736271	+	0.676687i	$0.763415\pi$
$972$	66.9826	+	0.672960i	2.14847	+	0.0215852i
$973$	−3.29508	+	4.54521i	−0.105635	+	0.145713i
$974$	−56.2865			−1.80353
$975$	−54.1127	−	7.86018i	−1.73299	−	0.251727i
$976$	−31.2221	−	54.0782i	−0.999394	−	1.73100i
$977$	−1.28449	+	4.79379i	−0.0410946	+	0.153367i	−0.983424	−	0.181319i	$-0.941963\pi$
$977$	−1.28449	+	4.79379i	−0.0410946	+	0.153367i	0.942330	+	0.334686i	$0.108630\pi$
$978$	37.7634	+	8.10619i	1.20754	+	0.259207i
$979$			27.7416i			0.886624i
$980$	−99.5092	−	50.4422i	−3.17870	−	1.61132i
$981$	−7.75583	+	47.7263i	−0.247624	+	1.52378i
$982$	−25.6242	+	6.86599i	−0.817702	+	0.219103i
$983$	−48.0531	−	12.8758i	−1.53266	−	0.410674i	−0.608772	−	0.793345i	$-0.708337\pi$
$983$	−48.0531	−	12.8758i	−1.53266	−	0.410674i	−0.923884	+	0.382671i	$0.875004\pi$
$984$	34.9947	+	31.6369i	1.11559	+	1.00855i
$985$	66.4421	+	38.3603i	2.11702	+	1.22226i
$986$	−1.52740	+	1.52740i	−0.0486422	+	0.0486422i
$987$	1.89030	+	3.71883i	0.0601688	+	0.118372i
$988$	53.9387	+	47.1360i	1.71602	+	1.49960i
$989$	−23.5263	−	13.5829i	−0.748092	−	0.431911i
$990$	25.9006	+	68.2925i	0.823176	+	2.17048i
$991$	−5.64881	−	9.78403i	−0.179440	−	0.310800i	0.762249	−	0.647284i	$-0.224095\pi$
$991$	−5.64881	−	9.78403i	−0.179440	−	0.310800i	−0.941689	+	0.336485i	$0.890762\pi$
$992$	6.53207	−	11.3139i	0.207393	−	0.359216i
$993$	6.42570	−	12.5488i	0.203913	−	0.398223i
$994$	−62.8244	+	28.0495i	−1.99267	+	0.889676i
$995$	−19.2302	+	19.2302i	−0.609640	+	0.609640i
$996$	11.0584	+	17.1036i	0.350398	+	0.541947i
$997$	29.7248	+	51.4849i	0.941394	+	1.63054i	0.762815	+	0.646617i	$0.223817\pi$
$997$	29.7248	+	51.4849i	0.941394	+	1.63054i	0.178579	+	0.983926i	$0.442850\pi$
$998$	−10.2759	−	17.7985i	−0.325279	−	0.563401i
$999$	−10.4565	+	26.7569i	−0.330829	+	0.846552i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cd.e.44.2	✓	112
3.2	odd	2	inner	273.2.cd.e.44.27	yes	112
7.4	even	3	inner	273.2.cd.e.200.27	yes	112
13.8	odd	4	inner	273.2.cd.e.86.2	yes	112
21.11	odd	6	inner	273.2.cd.e.200.2	yes	112
39.8	even	4	inner	273.2.cd.e.86.27	yes	112
91.60	odd	12	inner	273.2.cd.e.242.27	yes	112
273.242	even	12	inner	273.2.cd.e.242.2	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.e.44.2	✓	112	1.1	even	1	trivial
273.2.cd.e.44.27	yes	112	3.2	odd	2	inner
273.2.cd.e.86.2	yes	112	13.8	odd	4	inner
273.2.cd.e.86.27	yes	112	39.8	even	4	inner
273.2.cd.e.200.2	yes	112	21.11	odd	6	inner
273.2.cd.e.200.27	yes	112	7.4	even	3	inner
273.2.cd.e.242.2	yes	112	273.242	even	12	inner
273.2.cd.e.242.27	yes	112	91.60	odd	12	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.42391 + 0.649484i) q^{2} +(-1.28483 - 1.16155i) q^{3} +(3.72144 - 2.14858i) q^{4} +(3.58252 - 0.959933i) q^{5} +(3.86873 + 1.98102i) q^{6} +(1.55291 - 2.14207i) q^{7} +(-4.07612 + 4.07612i) q^{8} +(0.301593 + 2.98480i) q^{9} +O(q^{10})\)	\(q+(-2.42391 + 0.649484i) q^{2} +(-1.28483 - 1.16155i) q^{3} +(3.72144 - 2.14858i) q^{4} +(3.58252 - 0.959933i) q^{5} +(3.86873 + 1.98102i) q^{6} +(1.55291 - 2.14207i) q^{7} +(-4.07612 + 4.07612i) q^{8} +(0.301593 + 2.98480i) q^{9} +(-8.06023 + 4.65358i) q^{10} +(-2.52674 - 0.677038i) q^{11} +(-7.27712 - 1.56209i) q^{12} +(3.59741 - 0.242118i) q^{13} +(-2.37286 + 6.20077i) q^{14} +(-5.71795 - 2.92793i) q^{15} +(2.93561 - 5.08463i) q^{16} +(-0.358785 - 0.621434i) q^{17} +(-2.66961 - 7.03900i) q^{18} +(1.19661 + 4.46581i) q^{19} +(11.2697 - 11.2697i) q^{20} +(-4.48336 + 0.948423i) q^{21} +6.56431 q^{22} +(2.80909 - 4.86549i) q^{23} +(9.97177 - 0.502509i) q^{24} +(7.58284 - 4.37795i) q^{25} +(-8.56254 + 2.92333i) q^{26} +(3.07951 - 4.18529i) q^{27} +(1.17665 - 11.3081i) q^{28} +1.19958i q^{29} +(15.7614 + 3.38331i) q^{30} +(-3.93812 - 1.05522i) q^{31} +(-0.829338 + 3.09513i) q^{32} +(2.46003 + 3.80482i) q^{33} +(1.27327 + 1.27327i) q^{34} +(3.50707 - 9.16470i) q^{35} +(7.53544 + 10.4598i) q^{36} +(-5.34024 + 1.43091i) q^{37} +(-5.80094 - 10.0475i) q^{38} +(-4.90331 - 3.86750i) q^{39} +(-10.6900 + 18.5156i) q^{40} +(3.34101 + 3.34101i) q^{41} +(10.2513 - 5.21076i) q^{42} -4.83534i q^{43} +(-10.8578 + 2.90934i) q^{44} +(3.94567 + 10.4036i) q^{45} +(-3.64892 + 13.6179i) q^{46} +(-0.235612 - 0.879316i) q^{47} +(-9.67784 + 3.12304i) q^{48} +(-2.17695 - 6.65288i) q^{49} +(-15.5367 + 15.5367i) q^{50} +(-0.260849 + 1.21519i) q^{51} +(12.8674 - 8.63035i) q^{52} +(2.40005 - 1.38567i) q^{53} +(-4.74616 + 12.1448i) q^{54} -9.70201 q^{55} +(2.40151 + 15.0612i) q^{56} +(3.64983 - 7.12775i) q^{57} +(-0.779109 - 2.90768i) q^{58} +(-8.51651 - 2.28199i) q^{59} +(-27.5699 + 1.38934i) q^{60} +(5.31781 - 9.21071i) q^{61} +10.2310 q^{62} +(6.86201 + 3.98909i) q^{63} +3.70150i q^{64} +(12.6554 - 4.32067i) q^{65} +(-8.43405 - 7.62479i) q^{66} +(-3.15045 - 0.844160i) q^{67} +(-2.67040 - 1.54176i) q^{68} +(-9.26073 + 2.98843i) q^{69} +(-2.54850 + 24.4922i) q^{70} +(7.32763 + 7.32763i) q^{71} +(-13.3958 - 10.9371i) q^{72} +(-1.53552 + 5.73065i) q^{73} +(12.0149 - 6.93680i) q^{74} +(-14.8279 - 3.18292i) q^{75} +(14.0483 + 14.0483i) q^{76} +(-5.37406 + 4.36109i) q^{77} +(14.3970 + 6.18984i) q^{78} +(-1.74363 + 3.02006i) q^{79} +(5.63598 - 21.0338i) q^{80} +(-8.81808 + 1.80039i) q^{81} +(-10.2682 - 5.92837i) q^{82} +(-1.93496 - 1.93496i) q^{83} +(-14.6468 + 13.1623i) q^{84} +(-1.88189 - 1.88189i) q^{85} +(3.14048 + 11.7204i) q^{86} +(1.39338 - 1.54126i) q^{87} +(13.0590 - 7.53962i) q^{88} +(-2.74480 - 10.2437i) q^{89} +(-16.3209 - 22.6547i) q^{90} +(5.06782 - 8.08191i) q^{91} -24.1422i q^{92} +(3.83414 + 5.93011i) q^{93} +(1.14220 + 1.97835i) q^{94} +(8.57375 + 14.8502i) q^{95} +(4.66072 - 3.01341i) q^{96} +(-13.6182 + 13.6182i) q^{97} +(9.59767 + 14.7121i) q^{98} +(1.25878 - 7.74601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more