LMFDB - Embedded newform 770.2.w.b.139.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(139,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

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

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

chi := DirichletCharacter("770.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.w (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.1
Character	$\chi$	$=$	770.139
Dual form			770.2.w.b.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.968385 + 2.98038i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.19353 - 0.434105i) q^{5} +(-2.53526 + 1.84198i) q^{6} +(-2.64551 - 0.0356561i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-5.51786 - 4.00896i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.968385 + 2.98038i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.19353 - 0.434105i) q^{5} +(-2.53526 + 1.84198i) q^{6} +(-2.64551 - 0.0356561i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-5.51786 - 4.00896i) q^{9} +(-1.51944 - 1.64052i) q^{10} +(1.99266 + 2.65128i) q^{11} -3.13376 q^{12} +(-0.261648 + 0.360127i) q^{13} +(-2.11931 - 1.58384i) q^{14} +(3.41797 - 6.11716i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.40581 + 1.93493i) q^{17} +(-2.10763 - 6.48663i) q^{18} +(2.40499 - 7.40179i) q^{19} +(-0.264979 - 2.22031i) q^{20} +(2.66814 - 7.85011i) q^{21} +(0.0537105 + 3.31619i) q^{22} -1.99676i q^{23} +(-2.53526 - 1.84198i) q^{24} +(4.62311 + 1.90444i) q^{25} +(-0.423355 + 0.137556i) q^{26} +(9.68585 - 7.03718i) q^{27} +(-0.783597 - 2.52705i) q^{28} +(-4.85697 + 1.57812i) q^{29} +(6.36078 - 2.93985i) q^{30} +(-3.27281 + 4.50464i) q^{31} -1.00000 q^{32} +(-9.83150 + 3.37143i) q^{33} +2.39171i q^{34} +(5.78752 + 1.22664i) q^{35} +(2.10763 - 6.48663i) q^{36} +(-7.85036 + 2.55074i) q^{37} +(6.29634 - 4.57456i) q^{38} +(-0.819942 - 1.12855i) q^{39} +(1.09069 - 1.95202i) q^{40} +(-0.708641 + 2.18097i) q^{41} +(6.77275 - 4.78257i) q^{42} -8.65607 q^{43} +(-1.90575 + 2.71442i) q^{44} +(10.3633 + 11.1891i) q^{45} +(1.17366 - 1.61541i) q^{46} +(2.97808 - 9.16558i) q^{47} +(-0.968385 - 2.98038i) q^{48} +(6.99746 + 0.188657i) q^{49} +(2.62077 + 4.25812i) q^{50} +(-7.12820 + 2.31609i) q^{51} +(-0.423355 - 0.137556i) q^{52} +(-1.53124 + 2.10758i) q^{53} +11.9724 q^{54} +(-3.22002 - 6.68068i) q^{55} +(0.851419 - 2.50501i) q^{56} +(19.7312 + 14.3356i) q^{57} +(-4.85697 - 1.57812i) q^{58} +(-2.33250 + 0.757874i) q^{59} +(6.87398 + 1.36038i) q^{60} +(-2.33434 + 1.69600i) q^{61} +(-5.29552 + 1.72062i) q^{62} +(14.4546 + 10.8025i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.730264 - 0.676366i) q^{65} +(-9.93553 - 3.05127i) q^{66} -14.0855i q^{67} +(-1.40581 + 1.93493i) q^{68} +(5.95110 + 1.93363i) q^{69} +(3.96120 + 4.39419i) q^{70} +(-0.978851 + 0.711177i) q^{71} +(5.51786 - 4.00896i) q^{72} +(-9.12734 + 2.96565i) q^{73} +(-7.85036 - 2.55074i) q^{74} +(-10.1529 + 11.9344i) q^{75} +7.78270 q^{76} +(-5.17707 - 7.08505i) q^{77} -1.39497i q^{78} +(-0.689124 + 0.948498i) q^{79} +(2.02976 - 0.938124i) q^{80} +(5.27096 + 16.2223i) q^{81} +(-1.85525 + 1.34792i) q^{82} +(-2.06359 - 2.84029i) q^{83} +(8.29040 + 0.111738i) q^{84} +(-2.24372 - 4.85459i) q^{85} +(-7.00291 - 5.08791i) q^{86} -16.0038i q^{87} +(-3.13729 + 1.07584i) q^{88} +5.49098i q^{89} +(1.80727 + 15.1435i) q^{90} +(0.705033 - 0.943392i) q^{91} +(1.89903 - 0.617032i) q^{92} +(-10.2562 - 14.1165i) q^{93} +(7.79671 - 5.66464i) q^{94} +(-8.48855 + 15.1920i) q^{95} +(0.968385 - 2.98038i) q^{96} +(-4.32302 - 3.14086i) q^{97} +(5.55017 + 4.26563i) q^{98} +(-0.366330 - 22.6179i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.968385	+	2.98038i	−0.559097	+	1.72072i	0.125773	+	0.992059i	$0.459859\pi$
$3$	−0.968385	+	2.98038i	−0.559097	+	1.72072i	−0.684870	+	0.728665i	$0.740141\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.19353	−	0.434105i	−0.980974	−	0.194137i
$5$	−2.19353	−	0.434105i	−0.980974	−	0.194137i
$6$	−2.53526	+	1.84198i	−1.03502	+	0.751984i
$7$	−2.64551	−	0.0356561i	−0.999909	−	0.0134767i
$7$	−2.64551	−	0.0356561i	−0.999909	−	0.0134767i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−5.51786	−	4.00896i	−1.83929	−	1.33632i
$10$	−1.51944	−	1.64052i	−0.480489	−	0.518778i
$11$	1.99266	+	2.65128i	0.600810	+	0.799392i
$11$	1.99266	+	2.65128i	0.600810	+	0.799392i
$12$	−3.13376			−0.904638
$13$	−0.261648	+	0.360127i	−0.0725681	+	0.0998814i	−0.843758	−	0.536724i	$-0.819662\pi$
$13$	−0.261648	+	0.360127i	−0.0725681	+	0.0998814i	0.771190	+	0.636605i	$0.219662\pi$
$14$	−2.11931	−	1.58384i	−0.566408	−	0.423299i
$15$	3.41797	−	6.11716i	0.882517	−	1.57944i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.40581	+	1.93493i	0.340959	+	0.469290i	0.944721	−	0.327875i	$-0.106332\pi$
$17$	1.40581	+	1.93493i	0.340959	+	0.469290i	−0.603762	+	0.797164i	$0.706332\pi$
$18$	−2.10763	−	6.48663i	−0.496774	−	1.52891i
$19$	2.40499	−	7.40179i	0.551742	−	1.69809i	−0.152654	−	0.988280i	$-0.548782\pi$
$19$	2.40499	−	7.40179i	0.551742	−	1.69809i	0.704396	−	0.709807i	$-0.251218\pi$
$20$	−0.264979	−	2.22031i	−0.0592510	−	0.496477i
$21$	2.66814	−	7.85011i	0.582236	−	1.71303i
$22$	0.0537105	+	3.31619i	0.0114511	+	0.707014i
$23$		−	1.99676i		−	0.416353i	−0.978091	−	0.208176i	$-0.933247\pi$
$23$		−	1.99676i		−	0.416353i	0.978091	−	0.208176i	$-0.0667528\pi$
$24$	−2.53526	−	1.84198i	−0.517509	−	0.375992i
$25$	4.62311	+	1.90444i	0.924621	+	0.380888i
$26$	−0.423355	+	0.137556i	−0.0830268	+	0.0269770i
$27$	9.68585	−	7.03718i	1.86404	−	1.35431i
$28$	−0.783597	−	2.52705i	−0.148086	−	0.477567i
$29$	−4.85697	+	1.57812i	−0.901916	+	0.293050i	−0.723028	−	0.690819i	$-0.757250\pi$
$29$	−4.85697	+	1.57812i	−0.901916	+	0.293050i	−0.178888	+	0.983869i	$0.557250\pi$
$30$	6.36078	−	2.93985i	1.16131	−	0.536742i
$31$	−3.27281	+	4.50464i	−0.587814	+	0.809057i	−0.994525	−	0.104500i	$-0.966676\pi$
$31$	−3.27281	+	4.50464i	−0.587814	+	0.809057i	0.406711	+	0.913557i	$0.366676\pi$
$32$	−1.00000			−0.176777
$33$	−9.83150	+	3.37143i	−1.71144	+	0.586890i
$34$			2.39171i			0.410174i
$35$	5.78752	+	1.22664i	0.978269	+	0.207340i
$36$	2.10763	−	6.48663i	0.351272	−	1.08111i
$37$	−7.85036	+	2.55074i	−1.29059	+	0.419338i	−0.872298	−	0.488974i	$-0.837371\pi$
$37$	−7.85036	+	2.55074i	−1.29059	+	0.419338i	−0.418292	+	0.908312i	$0.637371\pi$
$38$	6.29634	−	4.57456i	1.02140	−	0.742091i
$39$	−0.819942	−	1.12855i	−0.131296	−	0.180713i
$40$	1.09069	−	1.95202i	0.172454	−	0.308642i
$41$	−0.708641	+	2.18097i	−0.110671	+	0.340611i	−0.991020	−	0.133717i	$-0.957309\pi$
$41$	−0.708641	+	2.18097i	−0.110671	+	0.340611i	0.880348	+	0.474328i	$0.157309\pi$
$42$	6.77275	−	4.78257i	1.04506	−	0.737967i
$43$	−8.65607			−1.32004			−0.660019	−	0.751249i	$-0.729452\pi$
$43$	−8.65607			−1.32004			−0.660019	+	0.751249i	$0.729452\pi$
$44$	−1.90575	+	2.71442i	−0.287303	+	0.409215i
$45$	10.3633	+	11.1891i	1.54486	+	1.66797i
$46$	1.17366	−	1.61541i	0.173047	−	0.238179i
$47$	2.97808	−	9.16558i	0.434397	−	1.33694i	−0.459305	−	0.888278i	$-0.651902\pi$
$47$	2.97808	−	9.16558i	0.434397	−	1.33694i	0.893703	−	0.448659i	$-0.148098\pi$
$48$	−0.968385	−	2.98038i	−0.139774	−	0.430181i
$49$	6.99746	+	0.188657i	0.999637	+	0.0269510i
$50$	2.62077	+	4.25812i	0.370633	+	0.602189i
$51$	−7.12820	+	2.31609i	−0.998148	+	0.324318i
$52$	−0.423355	−	0.137556i	−0.0587088	−	0.0190756i
$53$	−1.53124	+	2.10758i	−0.210333	+	0.289498i	−0.901129	−	0.433552i	$-0.857260\pi$
$53$	−1.53124	+	2.10758i	−0.210333	+	0.289498i	0.690796	+	0.723050i	$0.257260\pi$
$54$	11.9724			1.62923
$55$	−3.22002	−	6.68068i	−0.434187	−	0.900823i
$56$	0.851419	−	2.50501i	0.113776	−	0.334746i
$57$	19.7312	+	14.3356i	2.61346	+	1.89879i
$58$	−4.85697	−	1.57812i	−0.637751	−	0.207218i
$59$	−2.33250	+	0.757874i	−0.303665	+	0.0986667i	−0.456886	−	0.889525i	$-0.651035\pi$
$59$	−2.33250	+	0.757874i	−0.303665	+	0.0986667i	0.153221	+	0.988192i	$0.451035\pi$
$60$	6.87398	+	1.36038i	0.887427	+	0.175624i
$61$	−2.33434	+	1.69600i	−0.298882	+	0.217150i	−0.727111	−	0.686520i	$-0.759137\pi$
$61$	−2.33434	+	1.69600i	−0.298882	+	0.217150i	0.428230	+	0.903670i	$0.359137\pi$
$62$	−5.29552	+	1.72062i	−0.672532	+	0.218519i
$63$	14.4546	+	10.8025i	1.82111	+	1.36099i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.730264	−	0.676366i	0.0905781	−	0.0838929i
$66$	−9.93553	−	3.05127i	−1.22298	−	0.375585i
$67$		−	14.0855i		−	1.72082i	−0.509601	−	0.860411i	$-0.670207\pi$
$67$		−	14.0855i		−	1.72082i	0.509601	−	0.860411i	$-0.329793\pi$
$68$	−1.40581	+	1.93493i	−0.170479	+	0.234645i
$69$	5.95110	+	1.93363i	0.716428	+	0.232782i
$70$	3.96120	+	4.39419i	0.473454	+	0.525206i
$71$	−0.978851	+	0.711177i	−0.116168	+	0.0844012i	−0.644353	−	0.764729i	$-0.722873\pi$
$71$	−0.978851	+	0.711177i	−0.116168	+	0.0844012i	0.528184	+	0.849130i	$0.322873\pi$
$72$	5.51786	−	4.00896i	0.650286	−	0.472460i
$73$	−9.12734	+	2.96565i	−1.06827	+	0.347103i	−0.789815	−	0.613345i	$-0.789824\pi$
$73$	−9.12734	+	2.96565i	−1.06827	+	0.347103i	−0.278459	+	0.960448i	$0.589824\pi$
$74$	−7.85036	−	2.55074i	−0.912585	−	0.296517i
$75$	−10.1529	+	11.9344i	−1.17236	+	1.37807i
$76$	7.78270			0.892737
$77$	−5.17707	−	7.08505i	−0.589982	−	0.807416i
$78$		−	1.39497i		−	0.157949i
$79$	−0.689124	+	0.948498i	−0.0775325	+	0.106714i	−0.846022	−	0.533148i	$-0.821009\pi$
$79$	−0.689124	+	0.948498i	−0.0775325	+	0.106714i	0.768489	+	0.639863i	$0.221009\pi$
$80$	2.02976	−	0.938124i	0.226934	−	0.104885i
$81$	5.27096	+	16.2223i	0.585662	+	1.80248i
$82$	−1.85525	+	1.34792i	−0.204878	+	0.148852i
$83$	−2.06359	−	2.84029i	−0.226509	−	0.311762i	0.680603	−	0.732652i	$-0.261718\pi$
$83$	−2.06359	−	2.84029i	−0.226509	−	0.311762i	−0.907112	+	0.420890i	$0.861718\pi$
$84$	8.29040	+	0.111738i	0.904556	+	0.0121916i
$85$	−2.24372	−	4.85459i	−0.243365	−	0.526554i
$86$	−7.00291	−	5.08791i	−0.755143	−	0.548644i
$87$		−	16.0038i		−	1.71579i
$88$	−3.13729	+	1.07584i	−0.334436	+	0.114685i
$89$			5.49098i			0.582043i	0.956717	+	0.291021i	$0.0939950\pi$
$89$			5.49098i			0.582043i	−0.956717	+	0.291021i	$0.906005\pi$
$90$	1.80727	+	15.1435i	0.190503	+	1.59627i
$91$	0.705033	−	0.943392i	0.0739076	−	0.0988943i
$92$	1.89903	−	0.617032i	0.197988	−	0.0643300i
$93$	−10.2562	−	14.1165i	−1.06352	−	1.46381i
$94$	7.79671	−	5.66464i	0.804169	−	0.584263i
$95$	−8.48855	+	15.1920i	−0.870907	+	1.55867i
$96$	0.968385	−	2.98038i	0.0988354	−	0.304184i
$97$	−4.32302	−	3.14086i	−0.438936	−	0.318906i	0.346276	−	0.938133i	$-0.387446\pi$
$97$	−4.32302	−	3.14086i	−0.438936	−	0.318906i	−0.785212	+	0.619227i	$0.787446\pi$
$98$	5.55017	+	4.26563i	0.560652	+	0.430894i
$99$	−0.366330	−	22.6179i	−0.0368175	−	2.27318i
$100$	−0.382611	+	4.98534i	−0.0382611	+	0.498534i
$101$	−11.5788	−	8.41251i	−1.15214	−	0.837076i	−0.163373	−	0.986564i	$-0.552237\pi$
$101$	−11.5788	−	8.41251i	−1.15214	−	0.837076i	−0.988763	+	0.149488i	$0.952237\pi$
$102$	−7.12820	−	2.31609i	−0.705797	−	0.229327i
$103$	5.69282	+	17.5207i	0.560930	+	1.72637i	0.679744	+	0.733450i	$0.262091\pi$
$103$	5.69282	+	17.5207i	0.560930	+	1.72637i	−0.118813	+	0.992917i	$0.537909\pi$
$104$	−0.261648	−	0.360127i	−0.0256567	−	0.0353134i
$105$	−9.26040	+	16.0612i	−0.903723	+	1.56741i
$106$	−2.47761	+	0.805023i	−0.240646	+	0.0781907i
$107$	−2.58000	+	7.94041i	−0.249418	+	0.767629i	0.745461	+	0.666549i	$0.232229\pi$
$107$	−2.58000	+	7.94041i	−0.249418	+	0.767629i	−0.994878	+	0.101079i	$0.967771\pi$
$108$	9.68585	+	7.03718i	0.932021	+	0.677153i
$109$			14.3158i			1.37121i	0.727975	+	0.685604i	$0.240462\pi$
$109$			14.3158i			1.37121i	−0.727975	+	0.685604i	$0.759538\pi$
$110$	1.32176	−	7.29746i	0.126025	−	0.695786i
$111$		−	25.8672i		−	2.45520i
$112$	2.16122	−	1.52615i	0.204216	−	0.144207i
$113$	11.9052	+	3.86822i	1.11994	+	0.363892i	0.809746	−	0.586781i	$-0.199605\pi$
$113$	11.9052	+	3.86822i	1.11994	+	0.363892i	0.310197	+	0.950672i	$0.399605\pi$
$114$	7.53665	+	23.1954i	0.705872	+	2.17245i
$115$	−0.866802	+	4.37994i	−0.0808297	+	0.408431i
$116$	−3.00177	−	4.13158i	−0.278707	−	0.383608i
$117$	2.88747	−	0.938197i	0.266947	−	0.0867363i
$118$	−2.33250	−	0.757874i	−0.214724	−	0.0697679i
$119$	−3.65009	−	5.16901i	−0.334604	−	0.473842i
$120$	4.76156	+	5.14099i	0.434669	+	0.469306i
$121$	−3.05861	+	10.5662i	−0.278056	+	0.960565i
$122$	−2.88540			−0.261232
$123$	−5.81390	−	4.22404i	−0.524222	−	0.380869i
$124$	−5.29552	−	1.72062i	−0.475552	−	0.154516i
$125$	−9.31417	−	6.18435i	−0.833085	−	0.553145i
$126$	5.34448	+	17.2356i	0.476124	+	1.53547i
$127$	−6.26217	+	4.54973i	−0.555678	+	0.403723i	−0.829874	−	0.557950i	$-0.811588\pi$
$127$	−6.26217	+	4.54973i	−0.555678	+	0.403723i	0.274197	+	0.961674i	$0.411588\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	8.38241	−	25.7984i	0.738030	−	2.27142i
$130$	0.988354	−	0.117953i	0.0866844	−	0.0103452i
$131$	20.7090			1.80935			0.904675	−	0.426101i	$-0.140113\pi$
$131$	20.7090			1.80935			0.904675	+	0.426101i	$0.140113\pi$
$132$	−6.24452	−	8.30849i	−0.543516	−	0.723161i
$133$	−6.62634	+	19.4958i	−0.574576	+	1.69050i
$134$	8.27927	−	11.3954i	0.715220	−	0.984415i
$135$	−24.3010	+	11.2316i	−2.09150	+	0.966659i
$136$	−2.27465	+	0.739078i	−0.195049	+	0.0633754i
$137$	−2.28506	−	3.14511i	−0.195226	−	0.268705i	0.700170	−	0.713976i	$-0.253107\pi$
$137$	−2.28506	−	3.14511i	−0.195226	−	0.268705i	−0.895396	+	0.445271i	$0.853107\pi$
$138$	3.67798	+	5.06231i	0.313091	+	0.430932i
$139$	−5.60393	−	17.2471i	−0.475319	−	1.46288i	−0.845527	−	0.533933i	$-0.820714\pi$
$139$	−5.60393	−	17.2471i	−0.475319	−	1.46288i	0.370208	−	0.928949i	$-0.379286\pi$
$140$	0.621836	+	5.88331i	0.0525547	+	0.497230i
$141$	24.4330	+	17.7516i	2.05763	+	1.49496i
$142$	−1.20993			−0.101535
$143$	−1.47618	+	0.0239088i	−0.123444	+	0.00199935i
$144$	6.82045			0.568371
$145$	11.3389	−	1.35322i	0.941648	−	0.112379i
$146$	−9.12734	−	2.96565i	−0.755384	−	0.245439i
$147$	−7.33850	+	20.6724i	−0.605269	+	1.70503i
$148$	−4.85179	−	6.67791i	−0.398814	−	0.548921i
$149$	−3.86344	−	5.31757i	−0.316505	−	0.435632i	0.620891	−	0.783897i	$-0.286771\pi$
$149$	−3.86344	−	5.31757i	−0.316505	−	0.435632i	−0.937396	+	0.348265i	$0.886771\pi$
$150$	−15.2287	+	3.68740i	−1.24342	+	0.301075i
$151$	−6.09421	−	1.98013i	−0.495940	−	0.161141i	0.0503585	−	0.998731i	$-0.483964\pi$
$151$	−6.09421	−	1.98013i	−0.495940	−	0.161141i	−0.546299	+	0.837591i	$0.683964\pi$
$152$	6.29634	+	4.57456i	0.510700	+	0.371046i
$153$		−	16.3125i		−	1.31879i
$154$	−0.0238494	−	8.77493i	−0.00192184	−	0.707104i
$155$	9.13448	−	8.46030i	0.733699	−	0.679547i
$156$	0.819942	−	1.12855i	0.0656479	−	0.0903565i
$157$	−2.54618	+	7.83633i	−0.203207	+	0.625407i	0.796575	+	0.604539i	$0.206643\pi$
$157$	−2.54618	+	7.83633i	−0.203207	+	0.625407i	−0.999782	+	0.0208675i	$0.993357\pi$
$158$	−1.11503	+	0.362294i	−0.0887067	+	0.0288226i
$159$	−4.79855	−	6.60464i	−0.380550	−	0.523782i
$160$	2.19353	+	0.434105i	0.173413	+	0.0343190i
$161$	−0.0711965	+	5.28244i	−0.00561107	+	0.416315i
$162$	−5.27096	+	16.2223i	−0.414125	+	1.27455i
$163$	−12.1589	+	16.7353i	−0.952362	+	1.31081i	−0.00189150	+	0.999998i	$0.500602\pi$
$163$	−12.1589	+	16.7353i	−0.952362	+	1.31081i	−0.950470	+	0.310815i	$0.899398\pi$
$164$	−2.29321			−0.179070
$165$	23.0292	−	3.12741i	1.79282	−	0.243468i
$166$		−	3.51079i		−	0.272490i
$167$	−4.38081	+	6.02967i	−0.338997	+	0.466590i	−0.944148	−	0.329521i	$-0.893113\pi$
$167$	−4.38081	+	6.02967i	−0.338997	+	0.466590i	0.605151	+	0.796111i	$0.293113\pi$
$168$	6.64139	+	4.96337i	0.512395	+	0.382932i
$169$	3.95599	+	12.1753i	0.304307	+	0.936560i
$170$	1.03825	−	5.24627i	0.0796302	−	0.402370i
$171$	−42.9438	+	31.2005i	−3.28400	+	2.38596i
$172$	−2.67487	−	8.23241i	−0.203957	−	0.627716i
$173$	−21.4062	−	6.95530i	−1.62748	−	0.528802i	−0.653793	−	0.756673i	$-0.726823\pi$
$173$	−21.4062	−	6.95530i	−1.62748	−	0.528802i	−0.973691	+	0.227872i	$0.926823\pi$
$174$	9.40683	−	12.9474i	0.713130	−	0.981539i
$175$	−12.1626	−	5.20306i	−0.919404	−	0.393314i
$176$	−3.17048	−	0.973677i	−0.238984	−	0.0733937i
$177$		−	7.68564i		−	0.577688i
$178$	−3.22752	+	4.44229i	−0.241913	+	0.332964i
$179$	1.63580	−	5.03446i	0.122265	−	0.376294i	−0.871128	−	0.491057i	$-0.836611\pi$
$179$	1.63580	−	5.03446i	0.122265	−	0.376294i	0.993393	+	0.114763i	$0.0366109\pi$
$180$	−7.43903	+	13.3137i	−0.554472	+	0.992341i
$181$	11.3219	+	15.5833i	0.841554	+	1.15830i	0.985661	+	0.168737i	$0.0539690\pi$
$181$	11.3219	+	15.5833i	0.841554	+	1.15830i	−0.144107	+	0.989562i	$0.546031\pi$
$182$	1.12490	−	0.348812i	0.0833828	−	0.0258557i
$183$	−2.79418	−	8.59960i	−0.206552	−	0.635701i
$184$	1.89903	+	0.617032i	0.139998	+	0.0454882i
$185$	18.3272	−	2.18723i	1.34745	−	0.160808i
$186$		−	17.4489i		−	1.27942i
$187$	−2.32875	+	7.58286i	−0.170295	+	0.554514i
$188$	9.63726			0.702870
$189$	−25.8749	+	18.2716i	−1.88212	+	1.32906i
$190$	−15.7970	+	7.30114i	−1.14604	+	0.529680i
$191$	−0.0412070	−	0.126822i	−0.00298163	−	0.00917653i	0.949555	−	0.313602i	$-0.101536\pi$
$191$	−0.0412070	−	0.126822i	−0.00298163	−	0.00917653i	−0.952536	+	0.304425i	$0.901536\pi$
$192$	2.53526	−	1.84198i	0.182967	−	0.132933i
$193$	6.76583	−	4.91566i	0.487015	−	0.353837i	−0.317020	−	0.948419i	$-0.602682\pi$
$193$	6.76583	−	4.91566i	0.487015	−	0.353837i	0.804035	+	0.594582i	$0.202682\pi$
$194$	−1.65125	−	5.08202i	−0.118553	−	0.364868i
$195$	1.30865	+	2.83145i	0.0937146	+	0.202764i
$196$	1.98291	+	6.71328i	0.141636	+	0.479520i
$197$	3.28818			0.234273			0.117136	−	0.993116i	$-0.462629\pi$
$197$	3.28818			0.234273			0.117136	+	0.993116i	$0.462629\pi$
$198$	12.9981	−	18.5136i	0.923735	−	1.31570i
$199$		−	2.31978i		−	0.164445i	−0.996614	−	0.0822224i	$-0.973798\pi$
$199$		−	2.31978i		−	0.164445i	0.996614	−	0.0822224i	$-0.0262018\pi$
$200$	−3.23985	+	3.80833i	−0.229092	+	0.269290i
$201$	41.9803	+	13.6402i	2.96106	+	0.962107i
$202$	−4.42272	−	13.6117i	−0.311181	−	0.957718i
$203$	12.9054	−	4.00176i	0.905783	−	0.280869i
$204$	−4.40547	−	6.06361i	−0.308445	−	0.424538i
$205$	2.50119	−	4.47640i	0.174691	−	0.312645i
$206$	−5.69282	+	17.5207i	−0.396638	+	1.22073i
$207$	−8.00492	+	11.0178i	−0.556380	+	0.765792i
$208$		−	0.445142i		−	0.0308650i
$209$	24.4166	−	8.37295i	1.68893	−	0.579169i
$210$	−16.9323	+	7.55062i	−1.16844	+	0.521042i
$211$	−1.51276	+	2.08213i	−0.104142	+	0.143340i	−0.857907	−	0.513804i	$-0.828236\pi$
$211$	−1.51276	+	2.08213i	−0.104142	+	0.143340i	0.753765	+	0.657144i	$0.228236\pi$
$212$	−2.47761	−	0.805023i	−0.170163	−	0.0552892i
$213$	−1.17167	−	3.60604i	−0.0802818	−	0.247082i
$214$	−6.75452	+	4.90744i	−0.461729	+	0.335466i
$215$	18.9873	+	3.75764i	1.29492	+	0.256269i
$216$	3.69966	+	11.3864i	0.251730	+	0.774746i
$217$	8.81888	−	11.8004i	0.598664	−	0.801062i
$218$	−8.41463	+	11.5817i	−0.569911	+	0.784415i
$219$		−	30.0748i		−	2.03227i
$220$	5.35867	−	5.12686i	0.361281	−	0.345653i
$221$	−1.06465			−0.0716160
$222$	15.2043	−	20.9270i	1.02045	−	1.40453i
$223$	1.32208	−	4.06895i	0.0885331	−	0.272477i	−0.896981	−	0.442068i	$-0.854245\pi$
$223$	1.32208	−	4.06895i	0.0885331	−	0.272477i	0.985514	+	0.169592i	$0.0542449\pi$
$224$	2.64551	+	0.0356561i	0.176761	+	0.00238237i
$225$	−17.8748	−	29.0423i	−1.19166	−	1.93615i
$226$	7.35779	+	10.1271i	0.489433	+	0.673647i
$227$	−5.63539	+	1.83105i	−0.374034	+	0.121531i	−0.490001	−	0.871722i	$-0.663003\pi$
$227$	−5.63539	+	1.83105i	−0.374034	+	0.121531i	0.115967	+	0.993253i	$0.463003\pi$
$228$	−7.53665	+	23.1954i	−0.499127	+	1.53615i
$229$	−8.22790	+	11.3247i	−0.543715	+	0.748360i	−0.989143	−	0.146958i	$-0.953052\pi$
$229$	−8.22790	+	11.3247i	−0.543715	+	0.748360i	0.445428	+	0.895318i	$0.353052\pi$
$230$	−3.27572	+	3.03395i	−0.215995	+	0.200053i
$231$	26.1296	−	8.56859i	1.71920	−	0.563772i
$232$		−	5.10692i		−	0.335285i
$233$	10.7751	+	7.82854i	0.705898	+	0.512865i	0.881848	−	0.471534i	$-0.156300\pi$
$233$	10.7751	+	7.82854i	0.705898	+	0.512865i	−0.175950	+	0.984399i	$0.556300\pi$
$234$	2.88747	+	0.938197i	0.188760	+	0.0613318i
$235$	−10.5113	+	18.8121i	−0.685682	+	1.22717i
$236$	−1.44156	−	1.98414i	−0.0938377	−	0.129156i
$237$	−2.15955	−	2.97236i	−0.140278	−	0.193076i
$238$	0.0852789	−	6.32729i	0.00552781	−	0.410137i
$239$	17.7669	+	5.77282i	1.14925	+	0.373413i	0.820860	−	0.571130i	$-0.193495\pi$
$239$	17.7669	+	5.77282i	1.14925	+	0.373413i	0.328387	+	0.944543i	$0.393495\pi$
$240$	0.830379	+	6.95792i	0.0536007	+	0.449132i
$241$	−6.26612			−0.403636			−0.201818	−	0.979423i	$-0.564685\pi$
$241$	−6.26612			−0.403636			−0.201818	+	0.979423i	$0.564685\pi$
$242$	−8.68513	+	6.75044i	−0.558302	+	0.433935i
$243$	−17.5360			−1.12493
$244$	−2.33434	−	1.69600i	−0.149441	−	0.108575i
$245$	−15.2672	−	3.45145i	−0.975386	−	0.220505i
$246$	−2.22071	−	6.83465i	−0.141587	−	0.435761i
$247$	2.03633	+	2.80276i	0.129568	+	0.178336i
$248$	−3.27281	−	4.50464i	−0.207824	−	0.286045i
$249$	10.4635	−	3.39980i	0.663097	−	0.215453i
$250$	−3.90026	−	10.4780i	−0.246674	−	0.662685i
$251$	−0.535441	+	0.736972i	−0.0337968	+	0.0465173i	−0.825581	−	0.564284i	$-0.809152\pi$
$251$	−0.535441	+	0.736972i	−0.0337968	+	0.0465173i	0.791784	+	0.610801i	$0.209152\pi$
$252$	−5.80706	+	17.0853i	−0.365810	+	1.07627i
$253$	5.29397	−	3.97886i	0.332829	−	0.250149i
$254$	−7.74046			−0.485680
$255$	16.6413	−	1.98602i	1.04212	−	0.124370i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	5.01334	+	15.4295i	0.312724	+	0.962465i	0.976681	+	0.214695i	$0.0688756\pi$
$257$	5.01334	+	15.4295i	0.312724	+	0.962465i	−0.663957	+	0.747770i	$0.731124\pi$
$258$	21.9454	−	15.9443i	1.36626	−	0.992648i
$259$	20.8592	−	6.46809i	1.29612	−	0.401907i
$260$	0.868926	+	0.485514i	0.0538885	+	0.0301103i
$261$	33.1267	+	10.7635i	2.05049	+	0.666245i
$262$	16.7539	+	12.1724i	1.03506	+	0.752015i
$263$	17.3262			1.06838			0.534189	−	0.845365i	$-0.320617\pi$
$263$	17.3262			1.06838			0.534189	+	0.845365i	$0.320617\pi$
$264$	−0.168316	−	10.3921i	−0.0103591	−	0.639592i
$265$	4.27373	−	3.95830i	0.262533	−	0.243157i
$266$	−16.8201	+	11.8775i	−1.03131	+	0.728259i
$267$	−16.3652	−	5.31738i	−1.00153	−	0.325418i
$268$	13.3961	−	4.35267i	0.818299	−	0.265882i
$269$	9.57259	+	13.1755i	0.583651	+	0.803326i	0.994090	−	0.108562i	$-0.0346245\pi$
$269$	9.57259	+	13.1755i	0.583651	+	0.803326i	−0.410439	+	0.911888i	$0.634624\pi$
$270$	−26.2617	−	5.19726i	−1.59824	−	0.316295i
$271$	0.830793	+	2.55692i	0.0504671	+	0.155322i	0.973114	−	0.230324i	$-0.0739787\pi$
$271$	0.830793	+	2.55692i	0.0504671	+	0.155322i	−0.922647	+	0.385646i	$0.873979\pi$
$272$	−2.27465	−	0.739078i	−0.137921	−	0.0448132i
$273$	2.12892	+	3.01483i	0.128848	+	0.182466i
$274$		−	3.88757i		−	0.234857i
$275$	4.16307	+	16.0521i	0.251043	+	0.967976i
$276$			6.25736i			0.376649i
$277$	−19.6757	−	14.2952i	−1.18220	−	0.858918i	−0.189782	−	0.981826i	$-0.560778\pi$
$277$	−19.6757	−	14.2952i	−1.18220	−	0.858918i	−0.992418	+	0.122908i	$0.960778\pi$
$278$	5.60393	−	17.2471i	0.336101	−	1.03441i
$279$	36.1178	−	11.7354i	2.16232	−	0.702579i
$280$	−2.95505	+	5.12520i	−0.176598	+	0.306289i
$281$	−8.59824	−	11.8345i	−0.512928	−	0.705985i	0.471482	−	0.881876i	$-0.343719\pi$
$281$	−8.59824	−	11.8345i	−0.512928	−	0.705985i	−0.984410	+	0.175891i	$0.943719\pi$
$282$	9.33258	+	28.7227i	0.555747	+	1.71041i
$283$	21.8330	+	7.09397i	1.29784	+	0.421693i	0.874828	−	0.484433i	$-0.160974\pi$
$283$	21.8330	+	7.09397i	1.29784	+	0.421693i	0.423008	+	0.906126i	$0.360974\pi$
$284$	−0.978851	−	0.711177i	−0.0580841	−	0.0422006i
$285$	−37.0578	−	40.0108i	−2.19511	−	2.37004i
$286$	−1.20830	−	0.848331i	−0.0714485	−	0.0501629i
$287$	1.95248	−	5.74452i	0.115251	−	0.339088i
$288$	5.51786	+	4.00896i	0.325143	+	0.236230i
$289$	3.48563	−	10.7277i	0.205037	−	0.631039i
$290$	9.96881	+	5.57009i	0.585389	+	0.327087i
$291$	13.5473	−	9.84270i	0.794158	−	0.576989i
$292$	−5.64100	−	7.76418i	−0.330115	−	0.454364i
$293$	−9.36367	+	3.04244i	−0.547032	+	0.177741i	−0.569478	−	0.822007i	$-0.692855\pi$
$293$	−9.36367	+	3.04244i	−0.547032	+	0.177741i	0.0224462	+	0.999748i	$0.492855\pi$
$294$	−18.0879	+	12.4109i	−1.05491	+	0.723816i
$295$	5.44538	−	0.649868i	0.317043	−	0.0378368i
$296$		−	8.25435i		−	0.479775i
$297$	37.9582	+	11.6572i	2.20256	+	0.676421i
$298$		−	6.57288i		−	0.380757i
$299$	0.719087	+	0.522447i	0.0415859	+	0.0302139i
$300$	−14.4877	−	5.96805i	−0.836448	−	0.344566i
$301$	22.8997	+	0.308642i	1.31992	+	0.0177898i
$302$	−3.76643	−	5.18405i	−0.216734	−	0.298308i
$303$	36.2853	−	26.3628i	2.08453	−	1.51450i
$304$	2.40499	+	7.40179i	0.137935	+	0.424522i
$305$	5.85667	−	2.70686i	0.335352	−	0.154995i
$306$	9.58825	−	13.1971i	0.548124	−	0.754428i
$307$			19.2709i			1.09985i	0.835214	+	0.549925i	$0.185344\pi$
$307$			19.2709i			1.09985i	−0.835214	+	0.549925i	$0.814656\pi$
$308$	5.13848	−	7.11309i	0.292792	−	0.405306i
$309$	−57.7312			−3.28422
$310$	12.3628	−	1.47541i	0.702159	−	0.0837977i
$311$	−14.9525	−	4.85837i	−0.847880	−	0.275493i	−0.147322	−	0.989089i	$-0.547065\pi$
$311$	−14.9525	−	4.85837i	−0.847880	−	0.275493i	−0.700558	+	0.713596i	$0.747065\pi$
$312$	1.32669	−	0.431069i	0.0751092	−	0.0244045i
$313$	−23.1159	+	16.7947i	−1.30659	+	0.949290i	−0.999997	−	0.00255201i	$-0.999188\pi$
$313$	−23.1159	+	16.7947i	−1.30659	+	0.949290i	−0.306589	+	0.951842i	$0.599188\pi$
$314$	−6.66598	+	4.84312i	−0.376183	+	0.273313i
$315$	−27.0171	−	29.9703i	−1.52224	−	1.68864i
$316$	−1.11503	−	0.362294i	−0.0627251	−	0.0203806i
$317$	4.93114	−	6.78713i	0.276960	−	0.381203i	−0.647764	−	0.761841i	$-0.724296\pi$
$317$	4.93114	−	6.78713i	0.276960	−	0.381203i	0.924724	+	0.380638i	$0.124296\pi$
$318$		−	8.16378i		−	0.457802i
$319$	−13.8623	−	9.73253i	−0.776142	−	0.544917i
$320$	1.51944	+	1.64052i	0.0849392	+	0.0917078i
$321$	−21.1670	−	15.3787i	−1.18143	−	0.858358i
$322$	−3.16254	+	4.23174i	−0.176242	+	0.235826i
$323$	17.7029	−	5.75202i	0.985016	−	0.320051i
$324$	−13.7995	+	10.0260i	−0.766641	+	0.556997i
$325$	−1.89547	+	1.16661i	−0.105142	+	0.0647122i
$326$	−19.6736	+	6.39233i	−1.08962	+	0.354039i
$327$	−42.6666	−	13.8632i	−2.35947	−	0.766638i
$328$	−1.85525	−	1.34792i	−0.102439	−	0.0744262i
$329$	−8.20535	+	24.1415i	−0.452376	+	1.33096i
$330$	20.4693	+	11.0061i	1.12680	+	0.605866i
$331$	−20.8293			−1.14488			−0.572441	−	0.819946i	$-0.694003\pi$
$331$	−20.8293			−1.14488			−0.572441	+	0.819946i	$0.694003\pi$
$332$	2.06359	−	2.84029i	0.113254	−	0.155881i
$333$	53.5430	+	17.3972i	2.93414	+	0.953358i
$334$	−7.08830	+	2.30313i	−0.387855	+	0.126022i
$335$	−6.11459	+	30.8970i	−0.334076	+	1.68808i
$336$	2.45560	+	7.91916i	0.133964	+	0.432026i
$337$	−3.31374	−	10.1987i	−0.180511	−	0.555556i	0.819331	−	0.573321i	$-0.194345\pi$
$337$	−3.31374	−	10.1987i	−0.180511	−	0.555556i	−0.999842	+	0.0177646i	$0.994345\pi$
$338$	−3.95599	+	12.1753i	−0.215177	+	0.662248i
$339$	−23.0576	+	31.7360i	−1.25231	+	1.72366i
$340$	3.92364	−	3.63405i	0.212789	−	0.197084i
$341$	−18.4647	+	0.299062i	−0.999918	+	0.0161951i
$342$	−53.0815			−2.87032
$343$	−18.5051	−	0.748596i	−0.999183	−	0.0404204i
$344$	2.67487	−	8.23241i	0.144220	−	0.443862i
$345$	−12.2145	−	6.82487i	−0.657606	−	0.367439i
$346$	−13.2298	−	18.2092i	−0.711237	−	0.978933i
$347$	8.00292	−	5.81446i	0.429619	−	0.312137i	−0.351877	−	0.936046i	$-0.614457\pi$
$347$	8.00292	−	5.81446i	0.429619	−	0.312137i	0.781497	+	0.623909i	$0.214457\pi$
$348$	15.2206	−	4.94546i	0.815908	−	0.265105i
$349$	−0.191524	+	0.589451i	−0.0102521	+	0.0315526i	−0.956052	−	0.293198i	$-0.905280\pi$
$349$	−0.191524	+	0.589451i	−0.0102521	+	0.0315526i	0.945800	+	0.324751i	$0.105280\pi$
$350$	−6.78145	−	11.3583i	−0.362484	−	0.607129i
$351$			5.32940i			0.284462i
$352$	−1.99266	−	2.65128i	−0.106209	−	0.141314i
$353$	31.3359			1.66784			0.833922	−	0.551883i	$-0.186090\pi$
$353$	31.3359			1.66784			0.833922	+	0.551883i	$0.186090\pi$
$354$	4.51751	−	6.21781i	0.240103	−	0.330473i
$355$	2.45586	−	1.13506i	0.130344	−	0.0602428i
$356$	−5.22223	+	1.69681i	−0.276778	+	0.0899305i
$357$	18.9403	−	5.87309i	1.00243	−	0.310837i
$358$	4.28257	−	3.11147i	0.226341	−	0.164446i
$359$	23.5967	−	7.66704i	1.24539	−	0.404651i	0.389122	−	0.921186i	$-0.372779\pi$
$359$	23.5967	−	7.66704i	1.24539	−	0.404651i	0.856266	+	0.516536i	$0.172779\pi$
$360$	−13.8439	+	6.39842i	−0.729636	+	0.337227i
$361$	−33.6312	−	24.4345i	−1.77006	−	1.28603i
$362$			19.2621i			1.01239i
$363$	−28.5294	−	19.3480i	−1.49741	−	1.01551i
$364$	1.11509	+	0.379002i	0.0584464	+	0.0198651i
$365$	21.3084	−	2.54301i	1.11533	−	0.133107i
$366$	2.79418	−	8.59960i	0.146054	−	0.449508i
$367$	−3.99547	−	12.2968i	−0.208562	−	0.641887i	−0.999548	−	0.0300536i	$-0.990432\pi$
$367$	−3.99547	−	12.2968i	−0.208562	−	0.641887i	0.790986	−	0.611834i	$-0.209568\pi$
$368$	1.17366	+	1.61541i	0.0611815	+	0.0842091i
$369$	12.6536	−	9.19339i	0.658721	−	0.478589i
$370$	16.1127	+	9.00298i	0.837658	+	0.468043i
$371$	4.12607	−	5.52102i	0.214215	−	0.286637i
$372$	10.2562	−	14.1165i	0.531759	−	0.731904i
$373$	−0.692597			−0.0358613			−0.0179307	−	0.999839i	$-0.505708\pi$
$373$	−0.692597			−0.0358613			−0.0179307	+	0.999839i	$0.505708\pi$
$374$	−6.34109	+	4.76586i	−0.327890	+	0.246437i
$375$	27.4514	−	21.7710i	1.41759	−	1.12425i
$376$	7.79671	+	5.66464i	0.402085	+	0.292132i
$377$	0.702489	−	2.16204i	0.0361800	−	0.111351i
$378$	−31.6730	−	0.426888i	−1.62908	−	0.0219567i
$379$	−23.1147	+	16.7938i	−1.18732	+	0.862638i	−0.992978	−	0.118296i	$-0.962257\pi$
$379$	−23.1147	+	16.7938i	−1.18732	+	0.862638i	−0.194341	+	0.980934i	$0.562257\pi$
$380$	−17.0716	−	3.37851i	−0.875752	−	0.173314i
$381$	−7.49575	−	23.0695i	−0.384019	−	1.18189i
$382$	0.0412070	−	0.126822i	0.00210833	−	0.00648878i
$383$	−12.4475	−	9.04364i	−0.636037	−	0.462108i	0.222449	−	0.974944i	$-0.428595\pi$
$383$	−12.4475	−	9.04364i	−0.636037	−	0.462108i	−0.858487	+	0.512836i	$0.828595\pi$
$384$	3.13376			0.159919
$385$	8.28038	+	17.7886i	0.422007	+	0.906592i
$386$	8.36302			0.425667
$387$	47.7630	+	34.7018i	2.42793	+	1.76399i
$388$	1.65125	−	5.08202i	0.0838294	−	0.258000i
$389$	6.99895	+	21.5405i	0.354861	+	1.09215i	0.956090	+	0.293073i	$0.0946778\pi$
$389$	6.99895	+	21.5405i	0.354861	+	1.09215i	−0.601229	+	0.799076i	$0.705322\pi$
$390$	−0.605562	+	3.05990i	−0.0306638	+	0.154944i
$391$	3.86359	−	2.80706i	0.195390	−	0.141959i
$392$	−2.34176	+	6.59668i	−0.118277	+	0.333183i
$393$	−20.0543	+	61.7206i	−1.01160	+	3.11339i
$394$	2.66019	+	1.93274i	0.134018	+	0.0973701i
$395$	1.92336	−	1.78140i	0.0967746	−	0.0896320i
$396$	21.3977	−	7.33772i	1.07527	−	0.368734i
$397$	17.4287			0.874723			0.437361	−	0.899286i	$-0.355913\pi$
$397$	17.4287			0.874723			0.437361	+	0.899286i	$0.355913\pi$
$398$	1.36353	−	1.87674i	0.0683477	−	0.0940725i
$399$	−51.6880	−	38.6284i	−2.58764	−	1.93384i
$400$	−4.85957	+	1.17667i	−0.242979	+	0.0588335i
$401$	25.0691	−	18.2138i	1.25189	−	0.909552i	0.253561	−	0.967320i	$-0.418398\pi$
$401$	25.0691	−	18.2138i	1.25189	−	0.909552i	0.998330	+	0.0577678i	$0.0183983\pi$
$402$	25.9452	+	35.7105i	1.29403	+	1.78108i
$403$	−0.765920	−	2.35726i	−0.0381532	−	0.117423i
$404$	4.42272	−	13.6117i	0.220038	−	0.677209i
$405$	−4.51978	−	37.8722i	−0.224590	−	1.88189i
$406$	12.7929	+	4.34812i	0.634900	+	0.215794i
$407$	−22.4058	−	15.7308i	−1.11062	−	0.779745i
$408$		−	7.49503i		−	0.371059i
$409$	19.9968	+	14.5285i	0.988779	+	0.718390i	0.959653	−	0.281186i	$-0.0907278\pi$
$409$	19.9968	+	14.5285i	0.988779	+	0.718390i	0.0291253	+	0.999576i	$0.490728\pi$
$410$	4.65467	−	2.15132i	0.229878	−	0.106246i
$411$	11.5865	−	3.76467i	0.571517	−	0.185697i
$412$	−14.9040	+	10.8284i	−0.734268	+	0.533477i
$413$	6.19766	−	1.92180i	0.304967	−	0.0945654i
$414$	−12.9522	+	4.20844i	−0.636568	+	0.206833i
$415$	3.29356	+	7.12606i	0.161674	+	0.349805i
$416$	0.261648	−	0.360127i	0.0128283	−	0.0176567i
$417$	56.8298			2.78297
$418$	24.6749	+	7.57784i	1.20689	+	0.370644i
$419$			18.1989i			0.889076i	0.895760	+	0.444538i	$0.146632\pi$
$419$			18.1989i			0.889076i	−0.895760	+	0.444538i	$0.853368\pi$
$420$	−18.1367	−	3.84400i	−0.884980	−	0.187568i
$421$	−6.69750	+	20.6128i	−0.326416	+	1.00460i	0.644381	+	0.764704i	$0.277115\pi$
$421$	−6.69750	+	20.6128i	−0.326416	+	1.00460i	−0.970797	+	0.239901i	$0.922885\pi$
$422$	−2.44769	+	0.795303i	−0.119152	+	0.0387148i
$423$	−53.1771	+	38.6354i	−2.58556	+	1.87852i
$424$	−1.53124	−	2.10758i	−0.0743638	−	0.102353i
$425$	2.81425	+	11.6227i	0.136511	+	0.563782i
$426$	1.17167	−	3.60604i	0.0567678	−	0.174713i
$427$	6.23599	−	4.40355i	0.301781	−	0.213102i
$428$	−8.34904			−0.403566
$429$	1.35825	−	4.42272i	0.0655769	−	0.213531i
$430$	13.1524	+	14.2005i	0.634264	+	0.684807i
$431$	−4.00046	+	5.50616i	−0.192695	+	0.265222i	−0.894422	−	0.447224i	$-0.852413\pi$
$431$	−4.00046	+	5.50616i	−0.192695	+	0.265222i	0.701727	+	0.712446i	$0.252413\pi$
$432$	−3.69966	+	11.3864i	−0.178000	+	0.547828i
$433$	−3.75360	−	11.5524i	−0.180386	−	0.555172i	0.819452	−	0.573148i	$-0.194278\pi$
$433$	−3.75360	−	11.5524i	−0.180386	−	0.555172i	−0.999838	+	0.0179756i	$0.994278\pi$
$434$	14.0707	−	4.36310i	0.675416	−	0.209435i
$435$	−6.94734	+	35.1048i	−0.333100	+	1.68315i
$436$	−13.6152	+	4.42383i	−0.652048	+	0.211863i
$437$	−14.7796	−	4.80218i	−0.707003	−	0.229719i
$438$	17.6775	−	24.3311i	0.844666	−	1.16258i
$439$	−17.8678			−0.852785			−0.426392	−	0.904538i	$-0.640216\pi$
$439$	−17.8678			−0.852785			−0.426392	+	0.904538i	$0.640216\pi$
$440$	7.34874	−	0.997973i	0.350338	−	0.0475765i
$441$	−37.8547	−	29.0935i	−1.80260	−	1.38540i
$442$	−0.861319	−	0.625785i	−0.0409688	−	0.0297656i
$443$	32.6283	+	10.6016i	1.55022	+	0.503696i	0.954173	−	0.299255i	$-0.0967381\pi$
$443$	32.6283	+	10.6016i	1.55022	+	0.503696i	0.596045	+	0.802951i	$0.296738\pi$
$444$	24.6011	−	7.99339i	1.16752	−	0.379350i
$445$	2.38366	−	12.0446i	0.112996	−	0.570969i
$446$	3.46125	−	2.51475i	0.163895	−	0.119077i
$447$	19.5897	−	6.36508i	0.926561	−	0.301058i
$448$	2.11931	+	1.58384i	0.100128	+	0.0748293i
$449$	−1.28163	−	0.931157i	−0.0604838	−	0.0439440i	0.557133	−	0.830424i	$-0.311902\pi$
$449$	−1.28163	−	0.931157i	−0.0604838	−	0.0439440i	−0.617616	+	0.786480i	$0.711902\pi$
$450$	2.60958	−	34.0023i	0.123017	−	1.60288i
$451$	−7.19446	+	2.46713i	−0.338774	+	0.116173i
$452$			12.5178i			0.588789i
$453$	11.8031	−	16.2456i	0.554558	−	0.763283i
$454$	−5.63539	−	1.83105i	−0.264482	−	0.0859354i
$455$	−1.95604	+	1.76330i	−0.0917005	+	0.0826646i
$456$	−19.7312	+	14.3356i	−0.923998	+	0.671324i
$457$	−23.4465	+	17.0349i	−1.09678	+	0.796859i	−0.980532	−	0.196360i	$-0.937088\pi$
$457$	−23.4465	+	17.0349i	−1.09678	+	0.796859i	−0.116251	+	0.993220i	$0.537088\pi$
$458$	−13.3130	+	4.32566i	−0.622077	+	0.202125i
$459$	27.2329	+	8.84851i	1.27112	+	0.413013i
$460$	−4.43343	+	0.529098i	−0.206710	+	0.0246693i
$461$	−24.8649			−1.15808			−0.579038	−	0.815301i	$-0.696572\pi$
$461$	−24.8649			−1.15808			−0.579038	+	0.815301i	$0.696572\pi$
$462$	26.1757	+	8.42643i	1.21781	+	0.392033i
$463$		−	10.6100i		−	0.493091i	−0.969131	−	0.246545i	$-0.920705\pi$
$463$		−	10.6100i		−	0.493091i	0.969131	−	0.246545i	$-0.0792954\pi$
$464$	3.00177	−	4.13158i	0.139354	−	0.191804i
$465$	16.3692	+	35.4171i	0.759105	+	1.64243i
$466$	4.11571	+	12.6668i	0.190656	+	0.586780i
$467$	12.7532	−	9.26575i	0.590148	−	0.428768i	−0.252220	−	0.967670i	$-0.581161\pi$
$467$	12.7532	−	9.26575i	0.590148	−	0.428768i	0.842368	+	0.538902i	$0.181161\pi$
$468$	1.78456	+	2.45623i	0.0824911	+	0.113539i
$469$	−0.502235	+	37.2634i	−0.0231910	+	1.72067i
$470$	−19.5613	+	9.04095i	−0.902297	+	0.417028i
$471$	−20.8896	−	15.1772i	−0.962540	−	0.699327i
$472$		−	2.45253i		−	0.112887i
$473$	−17.2486	−	22.9497i	−0.793092	−	1.05523i
$474$		−	3.67404i		−	0.168754i
$475$	25.2148	−	29.6391i	1.15693	−	1.35994i
$476$	3.78808	−	5.06876i	0.173626	−	0.232326i
$477$	16.8984	−	5.49062i	0.773724	−	0.251398i
$478$	10.9806	+	15.1134i	0.502239	+	0.691273i
$479$	23.4211	−	17.0164i	1.07014	−	0.777500i	0.0942000	−	0.995553i	$-0.469971\pi$
$479$	23.4211	−	17.0164i	1.07014	−	0.777500i	0.975937	+	0.218053i	$0.0699707\pi$
$480$	−3.41797	+	6.11716i	−0.156008	+	0.279209i
$481$	1.13544	−	3.49452i	0.0517716	−	0.159337i
$482$	−5.06939	−	3.68313i	−0.230905	−	0.167762i
$483$	−15.6748	−	5.32763i	−0.713226	−	0.242416i
$484$	−10.9942	+	0.356228i	−0.499738	+	0.0161922i
$485$	8.11920	+	8.76620i	0.368674	+	0.398053i
$486$	−14.1869	−	10.3074i	−0.643531	−	0.467553i
$487$	−40.4796	−	13.1526i	−1.83431	−	0.596003i	−0.998926	−	0.0463317i	$-0.985247\pi$
$487$	−40.4796	−	13.1526i	−1.83431	−	0.596003i	−0.835381	−	0.549671i	$-0.814753\pi$
$488$	−0.891638	−	2.74418i	−0.0403626	−	0.124223i
$489$	−38.1032	−	52.4446i	−1.72309	−	2.37162i
$490$	−10.3227	−	11.7661i	−0.466333	−	0.531539i
$491$	−18.7987	+	6.10808i	−0.848375	+	0.275654i	−0.700765	−	0.713392i	$-0.747158\pi$
$491$	−18.7987	+	6.10808i	−0.848375	+	0.275654i	−0.147610	+	0.989046i	$0.547158\pi$
$492$	2.22071	−	6.83465i	0.100117	−	0.308130i
$493$	−9.88153	−	7.17935i	−0.445042	−	0.323342i
$494$			3.46441i			0.155871i
$495$	−9.01498	+	49.7720i	−0.405193	+	2.23708i
$496$		−	5.56804i		−	0.250012i
$497$	2.61492	−	1.84652i	0.117295	−	0.0828280i
$498$	10.4635	+	3.39980i	0.468881	+	0.152349i
$499$	−4.85756	−	14.9500i	−0.217454	−	0.669256i	−0.998970	−	0.0453703i	$-0.985553\pi$
$499$	−4.85756	−	14.9500i	−0.217454	−	0.669256i	0.781516	−	0.623885i	$-0.214447\pi$
$500$	3.00342	−	10.7694i	0.134317	−	0.481621i
$501$	−13.7284	−	18.8955i	−0.613340	−	0.844190i
$502$	−0.866362	+	0.281498i	−0.0386676	+	0.0125639i
$503$	24.9467	+	8.10567i	1.11232	+	0.361414i	0.806831	−	0.590783i	$-0.201181\pi$
$503$	24.9467	+	8.10567i	1.11232	+	0.361414i	0.305487	+	0.952196i	$0.401181\pi$
$504$	−14.7405	+	10.4090i	−0.656594	+	0.463654i
$505$	21.7465	+	23.4795i	0.967708	+	1.04482i
$506$	6.62163	−	0.107247i	0.294367	−	0.00476770i
$507$	−40.1179			−1.78170
$508$	−6.26217	−	4.54973i	−0.277839	−	0.201862i
$509$	1.44262	+	0.468736i	0.0639430	+	0.0207763i	0.340814	−	0.940131i	$-0.389297\pi$
$509$	1.44262	+	0.468736i	0.0639430	+	0.0207763i	−0.276871	+	0.960907i	$0.589297\pi$
$510$	14.6305	+	8.17479i	0.647848	+	0.361986i
$511$	24.2522	−	7.52022i	1.07285	−	0.332675i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−28.7934	−	88.6169i	−1.27126	−	3.91253i
$514$	−5.01334	+	15.4295i	−0.221129	+	0.680566i
$515$	−4.88153	−	40.9034i	−0.215106	−	1.80242i
$516$	27.1260			1.19416
$517$	30.2349	−	10.3682i	1.32973	−	0.455991i
$518$	20.6773	+	7.02791i	0.908506	+	0.308789i
$519$	41.4589	−	57.0633i	1.81984	−	2.50480i
$520$	0.417598	+	0.903531i	0.0183129	+	0.0396225i
$521$	−21.4980	+	6.98514i	−0.941846	+	0.306024i	−0.739398	−	0.673268i	$-0.764890\pi$
$521$	−21.4980	+	6.98514i	−0.941846	+	0.306024i	−0.202448	+	0.979293i	$0.564890\pi$
$522$	20.4734	+	28.1792i	0.896097	+	1.23337i
$523$	−2.45466	−	3.37855i	−0.107335	−	0.147733i	0.751970	−	0.659197i	$-0.229104\pi$
$523$	−2.45466	−	3.37855i	−0.107335	−	0.147733i	−0.859305	+	0.511463i	$0.829104\pi$
$524$	6.39942	+	19.6954i	0.279560	+	0.860397i
$525$	27.2851	−	31.2106i	1.19082	−	1.36214i
$526$	14.0172	+	10.1841i	0.611177	+	0.444046i
$527$	−13.3171			−0.580103
$528$	5.97218	−	8.50635i	0.259906	−	0.370191i
$529$	19.0130			0.826650
$530$	5.78416	−	0.690298i	0.251248	−	0.0299846i
$531$	15.9087	+	5.16904i	0.690377	+	0.224317i
$532$	−20.5892	−	0.277501i	−0.892656	−	0.0120312i
$533$	−0.600014	−	0.825848i	−0.0259895	−	0.0357715i
$534$	−10.1143	−	13.9211i	−0.437687	−	0.602424i
$535$	9.10626	−	16.2975i	0.393698	−	0.704603i
$536$	13.3961	+	4.35267i	0.578625	+	0.188007i
$537$	13.4205	+	9.75060i	0.579139	+	0.420769i
$538$			16.2859i			0.702133i
$539$	13.4434	+	18.9282i	0.579047	+	0.815294i
$540$	−18.1913	−	19.6409i	−0.782828	−	0.845210i
$541$	21.2218	−	29.2093i	0.912396	−	1.25581i	−0.0539457	−	0.998544i	$-0.517180\pi$
$541$	21.2218	−	29.2093i	0.912396	−	1.25581i	0.966342	−	0.257262i	$-0.0828202\pi$
$542$	−0.830793	+	2.55692i	−0.0356856	+	0.109829i
$543$	−57.4083	+	18.6531i	−2.46363	+	0.800480i
$544$	−1.40581	−	1.93493i	−0.0602736	−	0.0829595i
$545$	6.21456	−	31.4021i	0.266203	−	1.34512i
$546$	−0.0497391	+	3.69040i	−0.00212864	+	0.157935i
$547$	6.81189	−	20.9648i	0.291255	−	0.896392i	−0.693198	−	0.720747i	$-0.743799\pi$
$547$	6.81189	−	20.9648i	0.291255	−	0.896392i	0.984454	−	0.175645i	$-0.0562011\pi$
$548$	2.28506	−	3.14511i	0.0976128	−	0.134353i
$549$	19.6797			0.839911
$550$	−6.06717	+	15.4334i	−0.258705	+	0.658082i
$551$			39.7456i			1.69322i
$552$	−3.67798	+	5.06231i	−0.156545	+	0.215466i
$553$	1.85690	−	2.48469i	0.0789636	−	0.105660i
$554$	−7.51546	−	23.1302i	−0.319301	−	0.982708i
$555$	−11.2291	+	56.7403i	−0.476647	+	2.40849i
$556$	14.6713	−	10.6593i	0.622201	−	0.452055i
$557$	−6.56255	−	20.1974i	−0.278064	−	0.855793i	−0.988392	−	0.151923i	$-0.951454\pi$
$557$	−6.56255	−	20.1974i	−0.278064	−	0.855793i	0.710328	−	0.703871i	$-0.248546\pi$
$558$	36.1178	+	11.7354i	1.52899	+	0.496799i
$559$	2.26484	−	3.11729i	0.0957926	−	0.131847i
$560$	−5.40320	+	2.40944i	−0.228327	+	0.101818i
$561$	−20.3447	−	14.2837i	−0.858954	−	0.603058i
$562$		−	14.6282i		−	0.617053i
$563$	4.68474	−	6.44799i	0.197438	−	0.271750i	−0.698806	−	0.715311i	$-0.746285\pi$
$563$	4.68474	−	6.44799i	0.197438	−	0.271750i	0.896244	+	0.443561i	$0.146285\pi$
$564$	−9.33258	+	28.7227i	−0.392973	+	1.20945i
$565$	−24.4351	−	13.6531i	−1.02799	−	0.574391i
$566$	13.4935	+	18.5722i	0.567175	+	0.780650i
$567$	−13.3659	−	43.1043i	−0.561317	−	1.81021i
$568$	−0.373888	−	1.15071i	−0.0156880	−	0.0482827i
$569$	4.43717	+	1.44172i	0.186016	+	0.0604402i	0.400544	−	0.916278i	$-0.368821\pi$
$569$	4.43717	+	1.44172i	0.186016	+	0.0604402i	−0.214528	+	0.976718i	$0.568821\pi$
$570$	−6.46259	−	54.1514i	−0.270688	−	2.26815i
$571$			9.38461i			0.392734i	0.980530	+	0.196367i	$0.0629144\pi$
$571$			9.38461i			0.392734i	−0.980530	+	0.196367i	$0.937086\pi$
$572$	−0.478902	−	1.39654i	−0.0200239	−	0.0583922i
$573$	0.417883			0.0174573
$574$	4.95614	−	3.49978i	0.206865	−	0.146078i
$575$	3.80270	−	9.23122i	0.158584	−	0.384969i
$576$	2.10763	+	6.48663i	0.0878181	+	0.270276i
$577$	−12.3366	+	8.96309i	−0.513581	+	0.373138i	−0.814180	−	0.580612i	$-0.802813\pi$
$577$	−12.3366	+	8.96309i	−0.513581	+	0.373138i	0.300600	+	0.953750i	$0.402813\pi$
$578$	9.12550	−	6.63006i	0.379571	−	0.275774i
$579$	8.09862	+	24.9250i	0.336567	+	1.03585i
$580$	4.79092	+	10.3658i	0.198932	+	0.430417i
$581$	5.35798	+	7.58760i	0.222286	+	0.314787i
$582$	16.7454			0.694119
$583$	−8.63904	+	0.139922i	−0.357792	+	0.00579496i
$584$		−	9.59705i		−	0.397129i
$585$	−6.74102	+	0.804493i	−0.278707	+	0.0332617i
$586$	−9.36367	−	3.04244i	−0.386810	−	0.125682i
$587$	8.78638	+	27.0417i	0.362653	+	1.11613i	0.951438	+	0.307841i	$0.0996065\pi$
$587$	8.78638	+	27.0417i	0.362653	+	1.11613i	−0.588785	+	0.808290i	$0.700394\pi$
$588$	−21.9283	−	0.591206i	−0.904310	−	0.0243809i
$589$	25.4713	+	35.0582i	1.04953	+	1.44455i
$590$	4.78739	+	2.67496i	0.197094	+	0.110126i
$591$	−3.18422	+	9.80002i	−0.130981	+	0.403119i
$592$	4.85179	−	6.67791i	0.199407	−	0.274461i
$593$		−	8.41197i		−	0.345438i	−0.984971	−	0.172719i	$-0.944745\pi$
$593$		−	8.41197i		−	0.345438i	0.984971	−	0.172719i	$-0.0552553\pi$
$594$	23.8569	+	31.7421i	0.978859	+	1.30240i
$595$	5.76268	+	12.9229i	0.236247	+	0.529786i
$596$	3.86344	−	5.31757i	0.158253	−	0.217816i
$597$	6.91383	+	2.24644i	0.282964	+	0.0919406i
$598$	0.274667	+	0.845338i	0.0112320	+	0.0345684i
$599$	−6.25087	+	4.54153i	−0.255404	+	0.185562i	−0.708118	−	0.706094i	$-0.750456\pi$
$599$	−6.25087	+	4.54153i	−0.255404	+	0.185562i	0.452715	+	0.891656i	$0.350456\pi$
$600$	−8.21286	−	13.3439i	−0.335289	−	0.544763i
$601$	1.64119	+	5.05106i	0.0669455	+	0.206037i	0.978933	−	0.204180i	$-0.0654529\pi$
$601$	1.64119	+	5.05106i	0.0669455	+	0.206037i	−0.911988	+	0.410217i	$0.865453\pi$
$602$	18.3449	+	13.7098i	0.747681	+	0.558771i
$603$	−56.4683	+	77.7220i	−2.29957	+	3.16508i
$604$		−	6.40784i		−	0.260731i
$605$	11.2960	−	21.8495i	0.459247	−	0.888309i
$606$	44.8510			1.82195
$607$	10.4381	−	14.3669i	0.423671	−	0.583132i	−0.542815	−	0.839852i	$-0.682642\pi$
$607$	10.4381	−	14.3669i	0.423671	−	0.583132i	0.966486	+	0.256720i	$0.0826417\pi$
$608$	−2.40499	+	7.40179i	−0.0975351	+	0.300182i
$609$	−0.570634	+	42.3384i	−0.0231233	+	1.71564i
$610$	6.32920	+	1.25257i	0.256262	+	0.0507149i
$611$	2.52157	+	3.47064i	0.102012	+	0.140407i
$612$	15.5141	−	5.04084i	0.627121	−	0.203764i
$613$	−1.07558	+	3.31030i	−0.0434423	+	0.133702i	−0.970425	−	0.241402i	$-0.922393\pi$
$613$	−1.07558	+	3.31030i	−0.0434423	+	0.133702i	0.926983	+	0.375104i	$0.122393\pi$
$614$	−11.3272	+	15.5905i	−0.457127	+	0.629181i
$615$	10.9193	+	11.7894i	0.440307	+	0.475394i
$616$	8.33809	−	2.73429i	0.335951	−	0.110167i
$617$		−	31.8872i		−	1.28373i	−0.766818	−	0.641865i	$-0.778161\pi$
$617$		−	31.8872i		−	1.28373i	0.766818	−	0.641865i	$-0.221839\pi$
$618$	−46.7056	−	33.9336i	−1.87877	−	1.36501i
$619$	16.0172	+	5.20430i	0.643785	+	0.209178i	0.612672	−	0.790338i	$-0.290095\pi$
$619$	16.0172	+	5.20430i	0.643785	+	0.209178i	0.0311130	+	0.999516i	$0.490095\pi$
$620$	10.8689	+	6.07303i	0.436507	+	0.243899i
$621$	−14.0515	−	19.3403i	−0.563869	−	0.776099i
$622$	−9.24117	−	12.7194i	−0.370537	−	0.510000i
$623$	0.195787	−	14.5264i	0.00784403	−	0.581990i
$624$	1.32669	+	0.431069i	0.0531102	+	0.0172566i
$625$	17.7462	+	17.6088i	0.709849	+	0.704354i
$626$	−28.5728			−1.14200
$627$	1.30995	+	80.8789i	0.0523144	+	3.22999i
$628$	−8.23960			−0.328796
$629$	−15.9716	−	11.6041i	−0.636830	−	0.462684i
$630$	−4.24120	−	40.1268i	−0.168973	−	1.59869i
$631$	−6.19656	−	19.0711i	−0.246681	−	0.759207i	−0.995355	−	0.0962685i	$-0.969309\pi$
$631$	−6.19656	−	19.0711i	−0.246681	−	0.759207i	0.748674	−	0.662938i	$-0.230691\pi$
$632$	−0.689124	−	0.948498i	−0.0274119	−	0.0377292i
$633$	−4.74062	−	6.52490i	−0.188423	−	0.259341i
$634$	7.97875	−	2.59245i	0.316877	−	0.102959i
$635$	15.7113	−	7.26151i	0.623483	−	0.288164i
$636$	4.79855	−	6.60464i	0.190275	−	0.261891i
$637$	−1.89881	+	2.47061i	−0.0752336	+	0.0978893i
$638$	−5.49423	−	16.0219i	−0.217519	−	0.634312i
$639$	8.25224			0.326454
$640$	0.264979	+	2.22031i	0.0104742	+	0.0877655i
$641$	−9.46008	+	29.1151i	−0.373651	+	1.14998i	0.570734	+	0.821135i	$0.306659\pi$
$641$	−9.46008	+	29.1151i	−0.373651	+	1.14998i	−0.944384	+	0.328843i	$0.893341\pi$
$642$	−8.08509	−	24.8833i	−0.319093	−	0.982067i
$643$	−7.52409	+	5.46657i	−0.296721	+	0.215581i	−0.726178	−	0.687507i	$-0.758705\pi$
$643$	−7.52409	+	5.46657i	−0.296721	+	0.215581i	0.429457	+	0.903087i	$0.358705\pi$
$644$	−5.04590	+	1.56465i	−0.198836	+	0.0616560i
$645$	−29.5862	+	52.9506i	−1.16496	+	2.08493i
$646$	17.7029	+	5.75202i	0.696512	+	0.226310i
$647$	−20.2910	−	14.7423i	−0.797722	−	0.579579i	0.112523	−	0.993649i	$-0.464107\pi$
$647$	−20.2910	−	14.7423i	−0.797722	−	0.579579i	−0.910245	+	0.414070i	$0.864107\pi$
$648$	−17.0572			−0.670069
$649$	−6.65721	−	4.67392i	−0.261318	−	0.183467i
$650$	−2.21918	−	0.170316i	−0.0870436	−	0.00668035i
$651$	26.6296	+	37.7109i	1.04369	+	1.47801i
$652$	−19.6736	−	6.39233i	−0.770477	−	0.250343i
$653$	−23.1457	+	7.52048i	−0.905760	+	0.294299i	−0.724612	−	0.689157i	$-0.757981\pi$
$653$	−23.1457	+	7.52048i	−0.905760	+	0.294299i	−0.181148	+	0.983456i	$0.557981\pi$
$654$	−26.3694	−	36.2944i	−1.03113	−	1.41922i
$655$	−45.4256	−	8.98986i	−1.77493	−	0.351263i
$656$	−0.708641	−	2.18097i	−0.0276678	−	0.0851527i
$657$	62.2525	+	20.2271i	2.42870	+	0.789133i
$658$	−20.8283	+	14.7079i	−0.811970	+	0.573373i
$659$		−	11.3492i		−	0.442103i	−0.975262	−	0.221051i	$-0.929051\pi$
$659$		−	11.3492i		−	0.442103i	0.975262	−	0.221051i	$-0.0709489\pi$
$660$	10.0908	+	20.9356i	0.392782	+	0.814919i
$661$			48.5500i			1.88837i	0.329409	+	0.944187i	$0.393150\pi$
$661$			48.5500i			1.88837i	−0.329409	+	0.944187i	$0.606850\pi$
$662$	−16.8513	−	12.2432i	−0.654943	−	0.475844i
$663$	1.03099	−	3.17306i	0.0400403	−	0.123231i
$664$	3.33896	−	1.08489i	0.129577	−	0.0421021i
$665$	22.9982	−	39.8879i	0.891833	−	1.54679i
$666$	33.0914	+	45.5464i	1.28226	+	1.76489i
$667$	3.15113	+	9.69819i	0.122012	+	0.375515i
$668$	−7.08830	−	2.30313i	−0.274255	−	0.0891107i
$669$	10.8467	+	7.88061i	0.419359	+	0.304682i
$670$	−23.1076	+	21.4021i	−0.892724	+	0.826835i
$671$	−9.14811	−	2.80945i	−0.353159	−	0.108458i
$672$	−2.66814	+	7.85011i	−0.102926	+	0.302824i
$673$	12.5477	+	9.11646i	0.483680	+	0.351414i	0.802748	−	0.596318i	$-0.203370\pi$
$673$	12.5477	+	9.11646i	0.483680	+	0.351414i	−0.319069	+	0.947732i	$0.603370\pi$
$674$	3.31374	−	10.1987i	0.127641	−	0.392837i
$675$	58.1806	−	14.0875i	2.23937	−	0.542229i
$676$	−10.3569	+	7.52474i	−0.398343	+	0.289413i
$677$	−14.7490	−	20.3003i	−0.566851	−	0.780203i	0.425326	−	0.905040i	$-0.360159\pi$
$677$	−14.7490	−	20.3003i	−0.566851	−	0.780203i	−0.992177	+	0.124837i	$0.960159\pi$
$678$	−37.3079	+	12.1221i	−1.43280	+	0.465545i
$679$	11.3246	+	8.46332i	0.434599	+	0.324792i
$680$	5.31034	−	0.633751i	0.203642	−	0.0243032i
$681$		−	18.5688i		−	0.711557i
$682$	−15.1140	−	10.6113i	−0.578746	−	0.406328i
$683$		−	0.388940i		−	0.0148824i	−0.999972	−	0.00744118i	$-0.997631\pi$
$683$		−	0.388940i		−	0.0148824i	0.999972	−	0.00744118i	$-0.00236862\pi$
$684$	−42.9438	−	31.2005i	−1.64200	−	1.19298i
$685$	3.64702	+	7.89084i	0.139346	+	0.301493i
$686$	−14.5309	−	11.4827i	−0.554794	−	0.438410i
$687$	−25.7843	−	35.4890i	−0.983731	−	1.35399i
$688$	7.00291	−	5.08791i	0.266983	−	0.193975i
$689$	−0.358350	−	1.10289i	−0.0136520	−	0.0420166i
$690$	−5.87018	−	12.7009i	−0.223474	−	0.483516i
$691$	5.57008	−	7.66656i	0.211896	−	0.291650i	−0.689818	−	0.723983i	$-0.742310\pi$
$691$	5.57008	−	7.66656i	0.211896	−	0.291650i	0.901714	+	0.432333i	$0.142310\pi$
$692$		−	22.5078i		−	0.855619i
$693$	0.162664	+	59.8490i	0.00617908	+	2.27347i
$694$	9.89215			0.375501
$695$	4.80531	+	40.2647i	0.182276	+	1.52733i
$696$	15.2206	+	4.94546i	0.576934	+	0.187457i
$697$	−5.21625	+	1.69486i	−0.197580	+	0.0641975i
$698$	−0.501417	+	0.364300i	−0.0189789	+	0.0137890i
$699$	−33.7665	+	24.5328i	−1.27716	+	0.927914i
$700$	1.18996	−	13.1751i	0.0449762	−	0.497973i
$701$	37.4416	+	12.1655i	1.41415	+	0.459485i	0.913738	−	0.406304i	$-0.133183\pi$
$701$	37.4416	+	12.1655i	1.41415	+	0.459485i	0.500410	+	0.865789i	$0.333183\pi$
$702$	−3.13254	+	4.31158i	−0.118230	+	0.162730i
$703$			64.2412i			2.42290i
$704$	−0.0537105	−	3.31619i	−0.00202429	−	0.124984i
$705$	−45.8884	−	49.5451i	−1.72826	−	1.86598i
$706$	25.3513	+	18.4188i	0.954109	+	0.693201i
$707$	30.3320	+	22.6682i	1.14075	+	0.852527i
$708$	7.30948	−	2.37499i	0.274707	−	0.0892577i
$709$	−31.7642	+	23.0780i	−1.19293	+	0.866714i	−0.993571	−	0.113212i	$-0.963886\pi$
$709$	−31.7642	+	23.0780i	−1.19293	+	0.866714i	−0.199359	+	0.979927i	$0.563886\pi$
$710$	2.65400	+	0.525235i	0.0996030	+	0.0197117i
$711$	7.60498	−	2.47101i	0.285209	−	0.0926700i
$712$	−5.22223	−	1.69681i	−0.195711	−	0.0635905i
$713$	8.99467	+	6.53501i	0.336853	+	0.244738i
$714$	18.7752	+	6.38141i	0.702642	+	0.238818i
$715$	3.24841	+	0.588370i	0.121484	+	0.0220038i
$716$	5.29355			0.197829
$717$	−34.4104	+	47.3619i	−1.28508	+	1.76876i
$718$	23.5967	+	7.66704i	0.880622	+	0.286131i
$719$	1.95319	−	0.634629i	0.0728416	−	0.0236677i	−0.272370	−	0.962193i	$-0.587807\pi$
$719$	1.95319	−	0.634629i	0.0728416	−	0.0236677i	0.345211	+	0.938525i	$0.387807\pi$
$720$	−14.9608	−	2.96079i	−0.557557	−	0.110342i
$721$	−14.4357	−	46.5542i	−0.537614	−	1.73377i
$722$	−12.8460	−	39.5358i	−0.478077	−	1.47137i
$723$	6.06801	−	18.6754i	0.225672	−	0.694546i
$724$	−11.3219	+	15.5833i	−0.420777	+	0.579150i
$725$	−25.4597	−	1.95396i	−0.945550	−	0.0725683i
$726$	−11.7083	−	32.4220i	−0.434537	−	1.20329i
$727$	17.8284			0.661221			0.330610	−	0.943767i	$-0.392745\pi$
$727$	17.8284			0.661221			0.330610	+	0.943767i	$0.392745\pi$
$728$	0.679352	+	0.962050i	0.0251784	+	0.0356560i
$729$	1.16870	−	3.59690i	0.0432854	−	0.133219i
$730$	18.7336	+	10.4674i	0.693363	+	0.387418i
$731$	−12.1688	−	16.7489i	−0.450079	−	0.619481i
$732$	7.31526	−	5.31485i	0.270380	−	0.196442i
$733$	−7.04649	+	2.28954i	−0.260268	+	0.0845662i	−0.436245	−	0.899828i	$-0.643692\pi$
$733$	−7.04649	+	2.28954i	−0.260268	+	0.0845662i	0.175976	+	0.984394i	$0.443692\pi$
$734$	3.99547	−	12.2968i	0.147475	−	0.453883i
$735$	25.0712	−	42.1598i	0.924764	−	1.55509i
$736$			1.99676i			0.0736015i
$737$	37.3447	−	28.0677i	1.37561	−	1.03389i
$738$	15.6407			0.575743
$739$	−18.3997	+	25.3250i	−0.676843	+	0.931594i	−0.999891	−	0.0147884i	$-0.995293\pi$
$739$	−18.3997	+	25.3250i	−0.676843	+	0.931594i	0.323048	+	0.946383i	$0.395293\pi$
$740$	7.74361	+	16.7544i	0.284661	+	0.615902i
$741$	−10.3253	+	3.35488i	−0.379308	+	0.123245i
$742$	6.58324	−	2.04136i	0.241678	−	0.0749405i
$743$	−9.25162	+	6.72170i	−0.339409	+	0.246595i	−0.744412	−	0.667720i	$-0.767270\pi$
$743$	−9.25162	+	6.72170i	−0.339409	+	0.246595i	0.405003	+	0.914315i	$0.367270\pi$
$744$	16.5949	−	5.39200i	0.608398	−	0.197680i
$745$	6.16618	+	13.3414i	0.225911	+	0.488790i
$746$	−0.560323	−	0.407099i	−0.0205149	−	0.0149049i
$747$			23.9452i			0.876108i
$748$	−7.93135	+	0.128460i	−0.289999	+	0.00469695i
$749$	7.10853	−	20.9145i	0.259740	−	0.764197i
$750$	35.0053	−	1.47755i	1.27821	−	0.0539523i
$751$	−10.7651	+	33.1314i	−0.392822	+	1.20898i	0.537822	+	0.843058i	$0.319247\pi$
$751$	−10.7651	+	33.1314i	−0.392822	+	1.20898i	−0.930644	+	0.365925i	$0.880753\pi$
$752$	2.97808	+	9.16558i	0.108599	+	0.334234i
$753$	−1.67794	−	2.30949i	−0.0611477	−	0.0841626i
$754$	1.83914	−	1.33621i	0.0669776	−	0.0486620i
$755$	12.5082	+	6.98899i	0.455221	+	0.254355i
$756$	−25.3731	−	18.9623i	−0.922811	−	0.689652i
$757$	−12.0937	+	16.6456i	−0.439555	+	0.604995i	−0.970113	−	0.242653i	$-0.921982\pi$
$757$	−12.0937	+	16.6456i	−0.439555	+	0.604995i	0.530558	+	0.847648i	$0.321982\pi$
$758$	−28.5713			−1.03776
$759$	6.73192	+	19.6311i	0.244353	+	0.712565i
$760$	−11.8253	−	12.7677i	−0.428950	−	0.463132i
$761$	21.1301	+	15.3519i	0.765965	+	0.556506i	0.900734	−	0.434371i	$-0.143029\pi$
$761$	21.1301	+	15.3519i	0.765965	+	0.556506i	−0.134769	+	0.990877i	$0.543029\pi$
$762$	7.49575	−	23.0695i	0.271542	−	0.835721i
$763$	0.510446	−	37.8727i	0.0184794	−	1.37108i
$764$	0.107881	−	0.0783804i	0.00390301	−	0.00283570i
$765$	−7.08134	+	35.7819i	−0.256026	+	1.29370i
$766$	−4.75452	−	14.6329i	−0.171788	−	0.528709i
$767$	0.337361	−	1.03829i	0.0121814	−	0.0374905i
$768$	2.53526	+	1.84198i	0.0914835	+	0.0664666i
$769$	11.2259			0.404817			0.202409	−	0.979301i	$-0.435123\pi$
$769$	11.2259			0.404817			0.202409	+	0.979301i	$0.435123\pi$
$770$	−3.75692	+	19.2584i	−0.135390	+	0.694024i
$771$	−50.8406			−1.83098
$772$	6.76583	+	4.91566i	0.243507	+	0.176919i
$773$	9.80515	−	30.1771i	0.352667	−	1.08540i	−0.604684	−	0.796466i	$-0.706700\pi$
$773$	9.80515	−	30.1771i	0.352667	−	1.08540i	0.957350	−	0.288930i	$-0.0932996\pi$
$774$	18.2438	+	56.1488i	0.655761	+	2.01823i
$775$	−23.7094	+	14.5926i	−0.851665	+	0.524180i
$776$	4.32302	−	3.14086i	0.155187	−	0.112750i
$777$	−0.922321	+	68.4319i	−0.0330881	+	2.45498i
$778$	−6.99895	+	21.5405i	−0.250924	+	0.772266i
$779$	14.4388	+	10.4904i	0.517325	+	0.375859i
$780$	−2.28847	+	2.11957i	−0.0819405	+	0.0758927i
$781$	−3.83605	−	1.17808i	−0.137265	−	0.0421550i
$782$	4.77566			0.170777
$783$	−35.9383	+	49.4648i	−1.28433	+	1.76773i
$784$	−5.77195	+	3.96038i	−0.206141	+	0.141442i
$785$	8.98689	−	16.0839i	0.320756	−	0.574058i
$786$	−52.5027	+	38.1455i	−1.87271	+	1.36060i
$787$	3.07718	+	4.23537i	0.109689	+	0.150975i	0.860332	−	0.509734i	$-0.170256\pi$
$787$	3.07718	+	4.23537i	0.109689	+	0.150975i	−0.750643	+	0.660708i	$0.770256\pi$
$788$	1.01610	+	3.12724i	0.0361971	+	0.111403i
$789$	−16.7784	+	51.6386i	−0.597327	+	1.83838i
$790$	2.60311	−	0.310663i	0.0926145	−	0.0110529i
$791$	−31.3573	−	10.6579i	−1.11494	−	0.378952i
$792$	21.6241	+	6.64092i	0.768379	+	0.235975i
$793$		−	1.28441i		−	0.0456109i
$794$	14.1001	+	10.2444i	0.500395	+	0.363558i
$795$	7.65864	+	16.5705i	0.271624	+	0.587696i
$796$	2.20624	−	0.716851i	0.0781981	−	0.0254081i
$797$	−13.7297	+	9.97523i	−0.486332	+	0.353341i	−0.803772	−	0.594937i	$-0.797177\pi$
$797$	−13.7297	+	9.97523i	−0.486332	+	0.353341i	0.317440	+	0.948278i	$0.397177\pi$
$798$	−19.1112	−	61.6325i	−0.676530	−	2.18177i
$799$	21.9214	−	7.12269i	0.775523	−	0.251983i
$800$	−4.62311	−	1.90444i	−0.163451	−	0.0673321i
$801$	22.0131	−	30.2984i	0.777795	−	1.07054i
$802$	30.9871			1.09419
$803$	−26.0505	−	18.2896i	−0.919301	−	0.645427i
$804$			44.1407i			1.55672i
$805$	2.44931	−	11.5563i	0.0863267	−	0.407305i
$806$	0.765920	−	2.35726i	0.0269784	−	0.0830309i
$807$	−48.5381	+	15.7710i	−1.70862	+	0.555165i
$808$	11.5788	−	8.41251i	0.407342	−	0.295951i
$809$	−20.1511	−	27.7356i	−0.708475	−	0.975132i	−0.999829	−	0.0185165i	$-0.994106\pi$
$809$	−20.1511	−	27.7356i	−0.708475	−	0.975132i	0.291354	−	0.956615i	$-0.405894\pi$
$810$	18.6042	−	33.2960i	0.653684	−	1.16990i
$811$	15.4323	−	47.4957i	0.541901	−	1.66780i	−0.186344	−	0.982485i	$-0.559664\pi$
$811$	15.4323	−	47.4957i	0.541901	−	1.66780i	0.728245	−	0.685317i	$-0.240336\pi$
$812$	7.79390	+	11.0372i	0.273512	+	0.387329i
$813$	−8.42512			−0.295482
$814$	−8.88037	−	25.8963i	−0.311257	−	0.907664i
$815$	33.9358	−	31.4312i	1.18872	−	1.10099i
$816$	4.40547	−	6.06361i	0.154222	−	0.212269i
$817$	−20.8177	+	64.0704i	−0.728320	+	2.24154i
$818$	7.63810	+	23.5077i	0.267060	+	0.821926i
$819$	−7.67229	+	2.37905i	−0.268092	+	0.0831309i
$820$	5.03022	+	0.995494i	0.175663	+	0.0347642i
$821$	9.39877	−	3.05385i	0.328019	−	0.106580i	−0.140378	−	0.990098i	$-0.544832\pi$
$821$	9.39877	−	3.05385i	0.328019	−	0.106580i	0.468397	+	0.883518i	$0.344832\pi$
$822$	11.5865	+	3.76467i	0.404124	+	0.131308i
$823$	0.169540	−	0.233352i	0.00590979	−	0.00813413i	−0.806052	−	0.591845i	$-0.798400\pi$
$823$	0.169540	−	0.233352i	0.00590979	−	0.00813413i	0.811962	+	0.583711i	$0.198400\pi$
$824$	−18.4224			−0.641773
$825$	−51.8728	−	3.13703i	−1.80598	−	0.109217i
$826$	6.14362	+	2.08813i	0.213764	+	0.0726554i
$827$	−5.89886	−	4.28577i	−0.205123	−	0.149031i	0.480481	−	0.877005i	$-0.340462\pi$
$827$	−5.89886	−	4.28577i	−0.205123	−	0.149031i	−0.685605	+	0.727974i	$0.740462\pi$
$828$	−12.9522	−	4.20844i	−0.450121	−	0.146253i
$829$	−37.9894	+	12.3435i	−1.31943	+	0.428708i	−0.882298	−	0.470691i	$-0.844005\pi$
$829$	−37.9894	+	12.3435i	−1.31943	+	0.428708i	−0.437129	+	0.899399i	$0.644005\pi$
$830$	−1.52405	+	7.70101i	−0.0529006	+	0.267306i
$831$	61.6590	−	44.7979i	2.13893	−	1.55402i
$832$	0.423355	−	0.137556i	0.0146772	−	0.00476891i
$833$	9.47206	+	13.8048i	0.328187	+	0.478309i
$834$	45.9763	+	33.4037i	1.59203	+	1.15668i
$835$	12.2269	−	11.3245i	0.423130	−	0.391901i
$836$	15.5083	+	20.6341i	0.536365	+	0.713647i
$837$			66.6626i			2.30420i
$838$	−10.6971	+	14.7232i	−0.369524	+	0.508606i
$839$	−4.01705	−	1.30522i	−0.138684	−	0.0450611i	0.238853	−	0.971056i	$-0.423229\pi$
$839$	−4.01705	−	1.30522i	−0.138684	−	0.0450611i	−0.377536	+	0.925995i	$0.623229\pi$
$840$	−12.4134	−	13.7703i	−0.428304	−	0.475122i
$841$	−2.36185	+	1.71598i	−0.0814431	+	0.0591718i
$842$	−17.5343	+	12.7394i	−0.604271	+	0.439028i
$843$	43.5976	−	14.1657i	1.50158	−	0.487893i
$844$	−2.44769	−	0.795303i	−0.0842530	−	0.0273755i
$845$	−3.39222	−	28.4241i	−0.116696	−	0.977819i
$846$	−65.7305			−2.25986
$847$	8.46834	−	27.8440i	0.290976	−	0.956730i
$848$		−	2.60511i		−	0.0894598i
$849$	−42.2855	+	58.2010i	−1.45123	+	1.99745i
$850$	−4.55486	+	11.0571i	−0.156230	+	0.379256i
$851$	5.09320	+	15.6753i	0.174593	+	0.537341i
$852$	3.06748	−	2.22866i	0.105090	−	0.0763526i
$853$	−0.0698111	−	0.0960867i	−0.00239029	−	0.00328995i	0.807820	−	0.589429i	$-0.200647\pi$
$853$	−0.0698111	−	0.0960867i	−0.00239029	−	0.00328995i	−0.810210	+	0.586139i	$0.800647\pi$
$854$	7.63336	+	0.102882i	0.261208	+	0.00352055i
$855$	107.743	−	49.7970i	3.68472	−	1.70302i
$856$	−6.75452	−	4.90744i	−0.230865	−	0.167733i
$857$			15.4855i			0.528975i	0.964389	+	0.264488i	$0.0852029\pi$
$857$			15.4855i			0.528975i	−0.964389	+	0.264488i	$0.914797\pi$
$858$	3.69846	−	2.77970i	0.126263	−	0.0948973i
$859$		−	6.75391i		−	0.230440i	−0.993340	−	0.115220i	$-0.963243\pi$
$859$		−	6.75391i		−	0.230440i	0.993340	−	0.115220i	$-0.0367574\pi$
$860$	2.29367	+	19.2192i	0.0782136	+	0.655369i
$861$	15.2301	+	11.3821i	0.519041	+	0.387899i
$862$	−6.47287	+	2.10316i	−0.220467	+	0.0716341i
$863$	−12.6337	−	17.3888i	−0.430056	−	0.591921i	0.537910	−	0.843002i	$-0.319214\pi$
$863$	−12.6337	−	17.3888i	−0.430056	−	0.591921i	−0.967966	+	0.251081i	$0.919214\pi$
$864$	−9.68585	+	7.03718i	−0.329519	+	0.239410i
$865$	43.9357	+	24.5492i	1.49386	+	0.834697i
$866$	3.75360	−	11.5524i	0.127552	−	0.392566i
$867$	28.5971	+	20.7770i	0.971209	+	0.705625i
$868$	13.9480	+	4.74073i	0.473426	+	0.160911i
$869$	−3.88793	+	0.0629706i	−0.131889	+	0.00213613i
$870$	−26.2546	+	24.3169i	−0.890115	+	0.824419i
$871$	5.07259	+	3.68545i	0.171878	+	0.124877i
$872$	−13.6152	−	4.42383i	−0.461067	−	0.149810i
$873$	11.2623	+	34.6616i	0.381169	+	1.17312i
$874$	−9.13428	−	12.5723i	−0.308972	−	0.425263i
$875$	24.4202	+	16.6929i	0.825555	+	0.564322i
$876$	28.6029	−	9.29364i	0.966402	−	0.314003i
$877$	−7.10375	+	21.8631i	−0.239876	+	0.738264i	0.756561	+	0.653924i	$0.226878\pi$
$877$	−7.10375	+	21.8631i	−0.239876	+	0.738264i	−0.996437	+	0.0843401i	$0.973122\pi$
$878$	−14.4554	−	10.5024i	−0.487845	−	0.354440i
$879$		−	30.8536i		−	1.04067i
$880$	6.53185	+	3.51211i	0.220189	+	0.118393i
$881$			3.91869i			0.132024i	0.997819	+	0.0660120i	$0.0210276\pi$
$881$			3.91869i			0.132024i	−0.997819	+	0.0660120i	$0.978972\pi$
$882$	−13.5243	−	45.7875i	−0.455388	−	1.54175i
$883$	18.9531	+	6.15824i	0.637823	+	0.207241i	0.610038	−	0.792373i	$-0.291154\pi$
$883$	18.9531	+	6.15824i	0.637823	+	0.207241i	0.0277858	+	0.999614i	$0.491154\pi$
$884$	−0.328995	−	1.01254i	−0.0110653	−	0.0340555i
$885$	−3.33637	+	16.8586i	−0.112151	+	0.566697i
$886$	20.1654	+	27.7553i	0.677470	+	0.932458i
$887$	1.54712	−	0.502691i	0.0519474	−	0.0168787i	−0.282928	−	0.959141i	$-0.591306\pi$
$887$	1.54712	−	0.502691i	0.0519474	−	0.0168787i	0.334875	+	0.942262i	$0.391306\pi$
$888$	24.6011	+	7.99339i	0.825560	+	0.268241i
$889$	16.7289	−	11.8131i	0.561068	−	0.396198i
$890$	9.00806	−	8.34321i	0.301951	−	0.279665i
$891$	−32.5068	+	46.3004i	−1.08902	+	1.55112i
$892$	4.27834			0.143250
$893$	−60.6795	−	44.0862i	−2.03056	−	1.47529i
$894$	19.5897	+	6.36508i	0.655177	+	0.212880i
$895$	−5.77365	+	10.3331i	−0.192992	+	0.345398i
$896$	0.783597	+	2.52705i	0.0261781	+	0.0844228i
$897$	−2.25345	+	1.63722i	−0.0752404	+	0.0546653i
$898$	−0.489538	−	1.50664i	−0.0163361	−	0.0502774i
$899$	8.78706	−	27.0438i	0.293065	−	0.901960i
$900$	22.0972	−	25.9745i	0.736574	−	0.865818i
$901$	−6.23066			−0.207573
$902$	−7.27059	−	2.23285i	−0.242084	−	0.0743457i
$903$	−23.0956	+	67.9511i	−0.768574	+	2.26127i
$904$	−7.35779	+	10.1271i	−0.244717	+	0.336823i
$905$	−18.0702	−	39.0973i	−0.600673	−	1.29964i
$906$	19.0978	−	6.20525i	0.634482	−	0.206156i
$907$	−0.673304	−	0.926723i	−0.0223567	−	0.0307713i	0.797692	−	0.603065i	$-0.206054\pi$
$907$	−0.673304	−	0.926723i	−0.0223567	−	0.0307713i	−0.820049	+	0.572293i	$0.806054\pi$
$908$	−3.48286	−	4.79375i	−0.115583	−	0.159086i
$909$	30.1649	+	92.8381i	1.00051	+	3.07924i
$910$	−2.61891	+	0.276805i	−0.0868159	+	0.00917601i
$911$	46.5269	+	33.8037i	1.54150	+	1.11997i	0.949384	+	0.314118i	$0.101709\pi$
$911$	46.5269	+	33.8037i	1.54150	+	1.11997i	0.592120	+	0.805850i	$0.298291\pi$
$912$	−24.3891			−0.807604
$913$	3.41838	−	11.1309i	0.113132	−	0.368379i
$914$	−28.9815			−0.958623
$915$	2.39598	+	20.0764i	0.0792086	+	0.663706i
$916$	−13.3130	−	4.32566i	−0.439875	−	0.142924i
$917$	−54.7858	−	0.738400i	−1.80919	−	0.0243841i
$918$	16.8309	+	23.1657i	0.555502	+	0.764582i
$919$	21.1152	+	29.0626i	0.696528	+	0.958688i	0.999983	+	0.00584226i	$0.00185966\pi$
$919$	21.1152	+	29.0626i	0.696528	+	0.958688i	−0.303455	+	0.952846i	$0.598140\pi$
$920$	−3.89771	−	2.17785i	−0.128504	−	0.0718017i
$921$	−57.4347	−	18.6617i	−1.89254	−	0.614923i
$922$	−20.1162	−	14.6152i	−0.662490	−	0.481327i
$923$		−	0.538589i		−	0.0177279i
$924$	16.2237	+	22.2028i	0.533720	+	0.730420i
$925$	−41.1508	−	3.15820i	−1.35303	−	0.103841i
$926$	6.23643	−	8.58371i	0.204942	−	0.282078i
$927$	38.8276	−	119.499i	1.27527	−	3.92486i
$928$	4.85697	−	1.57812i	0.159438	−	0.0518045i
$929$	21.7677	+	29.9606i	0.714174	+	0.982976i	0.999697	+	0.0246044i	$0.00783263\pi$
$929$	21.7677	+	29.9606i	0.714174	+	0.982976i	−0.285523	+	0.958372i	$0.592167\pi$
$930$	−7.57465	+	38.2746i	−0.248382	+	1.25507i
$931$	18.2252	−	51.3400i	0.597307	−	1.68260i
$932$	−4.11571	+	12.6668i	−0.134814	+	0.414916i
$933$	28.9596	−	39.8595i	0.948095	−	1.30494i
$934$	15.7638			0.515809
$935$	8.39993	−	15.6223i	0.274707	−	0.510903i
$936$			3.03607i			0.0992370i
$937$	25.0321	−	34.4537i	0.817763	−	1.12555i	−0.172316	−	0.985042i	$-0.555125\pi$
$937$	25.0321	−	34.4537i	0.817763	−	1.12555i	0.990079	−	0.140513i	$-0.0448751\pi$
$938$	−22.3092	+	29.8515i	−0.728421	+	0.974687i
$939$	−27.6694	−	85.1578i	−0.902958	−	2.77902i
$940$	−21.1396	−	4.18358i	−0.689497	−	0.136453i
$941$	−5.34510	+	3.88344i	−0.174245	+	0.126597i	−0.671490	−	0.741014i	$-0.734345\pi$
$941$	−5.34510	+	3.88344i	−0.174245	+	0.126597i	0.497244	+	0.867611i	$0.334345\pi$
$942$	−7.97910	−	24.5572i	−0.259973	−	0.800115i
$943$	4.35488	+	1.41499i	0.141814	+	0.0460783i
$944$	1.44156	−	1.98414i	0.0469188	−	0.0645782i
$945$	64.6891	−	28.8467i	2.10434	−	0.938385i
$946$	−0.464922	−	28.7052i	−0.0151159	−	0.933286i
$947$		−	12.4849i		−	0.405703i	−0.979209	−	0.202852i	$-0.934979\pi$
$947$		−	12.4849i		−	0.405703i	0.979209	−	0.202852i	$-0.0650209\pi$
$948$	2.15955	−	2.97236i	0.0701389	−	0.0965379i
$949$	1.32014	−	4.06296i	0.0428534	−	0.131889i
$950$	37.8206	−	9.15767i	1.22706	−	0.297114i
$951$	15.4530	+	21.2692i	0.501098	+	0.689702i
$952$	6.04396	−	1.87413i	0.195886	−	0.0607410i
$953$	14.4670	+	44.5248i	0.468632	+	1.44230i	0.854357	+	0.519687i	$0.173951\pi$
$953$	14.4670	+	44.5248i	0.468632	+	1.44230i	−0.385725	+	0.922614i	$0.626049\pi$
$954$	16.8984	+	5.49062i	0.547105	+	0.177765i
$955$	0.0353345	+	0.296076i	0.00114340	+	0.00958078i
$956$			18.6813i			0.604195i
$957$	42.4307	−	31.8902i	1.37159	−	1.03086i
$958$	28.9501			0.935334
$959$	5.93300	+	8.40190i	0.191587	+	0.271312i
$960$	−6.36078	+	2.93985i	−0.205293	+	0.0948834i
$961$	−0.000944506	−	0.00290689i	−3.04679e−5	−	9.37706e-5i
$962$	2.97262	−	2.15973i	0.0958411	−	0.0696326i
$963$	46.0688	−	33.4710i	1.48455	−	1.07859i
$964$	−1.93634	−	5.95943i	−0.0623652	−	0.191940i
$965$	−16.9749	+	7.84555i	−0.546442	+	0.252557i
$966$	−9.54964	−	13.5235i	−0.307255	−	0.435113i
$967$	58.8296			1.89183			0.945916	−	0.324411i	$-0.105166\pi$
$967$	58.8296			1.89183			0.945916	+	0.324411i	$0.105166\pi$
$968$	−9.10390	−	6.17405i	−0.292611	−	0.198442i
$969$			58.3316i			1.87388i
$970$	1.41593	+	11.8643i	0.0454627	+	0.380941i
$971$	−49.9252	−	16.2217i	−1.60217	−	0.520578i	−0.634531	−	0.772898i	$-0.718807\pi$
$971$	−49.9252	−	16.2217i	−1.60217	−	0.520578i	−0.967644	+	0.252320i	$0.918807\pi$
$972$	−5.41891	−	16.6777i	−0.173812	−	0.534938i
$973$	14.2103	+	45.8273i	0.455561	+	1.46915i
$974$	−25.0178	−	34.4340i	−0.801622	−	1.10334i
$975$	−1.64142	−	6.77895i	−0.0525674	−	0.217100i
$976$	0.891638	−	2.74418i	0.0285406	−	0.0878391i
$977$	−14.5821	+	20.0706i	−0.466523	+	0.642114i	−0.975846	−	0.218462i	$-0.929896\pi$
$977$	−14.5821	+	20.0706i	−0.466523	+	0.642114i	0.509322	+	0.860576i	$0.329896\pi$
$978$		−	64.8250i		−	2.07288i
$979$	−14.5581	+	10.9417i	−0.465280	+	0.349697i
$980$	−1.43530	−	15.5865i	−0.0458489	−	0.497893i
$981$	57.3915	−	78.9927i	1.83237	−	2.52204i
$982$	−18.7987	−	6.10808i	−0.599892	−	0.194917i
$983$	−5.10173	−	15.7015i	−0.162720	−	0.500801i	0.836141	−	0.548514i	$-0.184806\pi$
$983$	−5.10173	−	15.7015i	−0.162720	−	0.500801i	−0.998861	+	0.0477138i	$0.984806\pi$
$984$	5.81390	−	4.22404i	0.185340	−	0.134658i
$985$	−7.21270	−	1.42741i	−0.229816	−	0.0454811i
$986$	−3.77441	−	11.6164i	−0.120202	−	0.369943i
$987$	−64.0049	−	47.8333i	−2.03730	−	1.52255i
$988$	−2.03633	+	2.80276i	−0.0647842	+	0.0891678i
$989$			17.2841i			0.549602i
$990$	−36.5485	+	34.9675i	−1.16159	+	1.11134i
$991$	−2.07778			−0.0660028			−0.0330014	−	0.999455i	$-0.510507\pi$
$991$	−2.07778			−0.0660028			−0.0330014	+	0.999455i	$0.510507\pi$
$992$	3.27281	−	4.50464i	0.103912	−	0.143022i
$993$	20.1708	−	62.0793i	0.640100	−	1.97003i
$994$	3.20087	+	0.0431412i	0.101526	+	0.00136836i
$995$	−1.00703	+	5.08849i	−0.0319249	+	0.161316i
$996$	6.46680	+	8.90078i	0.204908	+	0.282032i
$997$	−28.7631	+	9.34568i	−0.910935	+	0.295981i	−0.726743	−	0.686910i	$-0.758967\pi$
$997$	−28.7631	+	9.34568i	−0.910935	+	0.295981i	−0.184192	+	0.982890i	$0.558967\pi$
$998$	4.85756	−	14.9500i	0.153763	−	0.473235i
$999$	−58.0874	+	79.9504i	−1.83780	+	2.52952i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.w.b.139.1	yes	96
5.4	even	2		770.2.w.a.139.24	yes	96
7.6	odd	2	inner	770.2.w.b.139.24	yes	96
11.8	odd	10		770.2.w.a.349.1	yes	96
35.34	odd	2		770.2.w.a.139.1	✓	96
55.19	odd	10	inner	770.2.w.b.349.24	yes	96
77.41	even	10		770.2.w.a.349.24	yes	96
385.349	even	10	inner	770.2.w.b.349.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.w.a.139.1	✓	96	35.34	odd	2
770.2.w.a.139.24	yes	96	5.4	even	2
770.2.w.a.349.1	yes	96	11.8	odd	10
770.2.w.a.349.24	yes	96	77.41	even	10
770.2.w.b.139.1	yes	96	1.1	even	1	trivial
770.2.w.b.139.24	yes	96	7.6	odd	2	inner
770.2.w.b.349.1	yes	96	385.349	even	10	inner
770.2.w.b.349.24	yes	96	55.19	odd	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.968385 + 2.98038i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.19353 - 0.434105i) q^{5} +(-2.53526 + 1.84198i) q^{6} +(-2.64551 - 0.0356561i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-5.51786 - 4.00896i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.968385 + 2.98038i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.19353 - 0.434105i) q^{5} +(-2.53526 + 1.84198i) q^{6} +(-2.64551 - 0.0356561i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-5.51786 - 4.00896i) q^{9} +(-1.51944 - 1.64052i) q^{10} +(1.99266 + 2.65128i) q^{11} -3.13376 q^{12} +(-0.261648 + 0.360127i) q^{13} +(-2.11931 - 1.58384i) q^{14} +(3.41797 - 6.11716i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.40581 + 1.93493i) q^{17} +(-2.10763 - 6.48663i) q^{18} +(2.40499 - 7.40179i) q^{19} +(-0.264979 - 2.22031i) q^{20} +(2.66814 - 7.85011i) q^{21} +(0.0537105 + 3.31619i) q^{22} -1.99676i q^{23} +(-2.53526 - 1.84198i) q^{24} +(4.62311 + 1.90444i) q^{25} +(-0.423355 + 0.137556i) q^{26} +(9.68585 - 7.03718i) q^{27} +(-0.783597 - 2.52705i) q^{28} +(-4.85697 + 1.57812i) q^{29} +(6.36078 - 2.93985i) q^{30} +(-3.27281 + 4.50464i) q^{31} -1.00000 q^{32} +(-9.83150 + 3.37143i) q^{33} +2.39171i q^{34} +(5.78752 + 1.22664i) q^{35} +(2.10763 - 6.48663i) q^{36} +(-7.85036 + 2.55074i) q^{37} +(6.29634 - 4.57456i) q^{38} +(-0.819942 - 1.12855i) q^{39} +(1.09069 - 1.95202i) q^{40} +(-0.708641 + 2.18097i) q^{41} +(6.77275 - 4.78257i) q^{42} -8.65607 q^{43} +(-1.90575 + 2.71442i) q^{44} +(10.3633 + 11.1891i) q^{45} +(1.17366 - 1.61541i) q^{46} +(2.97808 - 9.16558i) q^{47} +(-0.968385 - 2.98038i) q^{48} +(6.99746 + 0.188657i) q^{49} +(2.62077 + 4.25812i) q^{50} +(-7.12820 + 2.31609i) q^{51} +(-0.423355 - 0.137556i) q^{52} +(-1.53124 + 2.10758i) q^{53} +11.9724 q^{54} +(-3.22002 - 6.68068i) q^{55} +(0.851419 - 2.50501i) q^{56} +(19.7312 + 14.3356i) q^{57} +(-4.85697 - 1.57812i) q^{58} +(-2.33250 + 0.757874i) q^{59} +(6.87398 + 1.36038i) q^{60} +(-2.33434 + 1.69600i) q^{61} +(-5.29552 + 1.72062i) q^{62} +(14.4546 + 10.8025i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.730264 - 0.676366i) q^{65} +(-9.93553 - 3.05127i) q^{66} -14.0855i q^{67} +(-1.40581 + 1.93493i) q^{68} +(5.95110 + 1.93363i) q^{69} +(3.96120 + 4.39419i) q^{70} +(-0.978851 + 0.711177i) q^{71} +(5.51786 - 4.00896i) q^{72} +(-9.12734 + 2.96565i) q^{73} +(-7.85036 - 2.55074i) q^{74} +(-10.1529 + 11.9344i) q^{75} +7.78270 q^{76} +(-5.17707 - 7.08505i) q^{77} -1.39497i q^{78} +(-0.689124 + 0.948498i) q^{79} +(2.02976 - 0.938124i) q^{80} +(5.27096 + 16.2223i) q^{81} +(-1.85525 + 1.34792i) q^{82} +(-2.06359 - 2.84029i) q^{83} +(8.29040 + 0.111738i) q^{84} +(-2.24372 - 4.85459i) q^{85} +(-7.00291 - 5.08791i) q^{86} -16.0038i q^{87} +(-3.13729 + 1.07584i) q^{88} +5.49098i q^{89} +(1.80727 + 15.1435i) q^{90} +(0.705033 - 0.943392i) q^{91} +(1.89903 - 0.617032i) q^{92} +(-10.2562 - 14.1165i) q^{93} +(7.79671 - 5.66464i) q^{94} +(-8.48855 + 15.1920i) q^{95} +(0.968385 - 2.98038i) q^{96} +(-4.32302 - 3.14086i) q^{97} +(5.55017 + 4.26563i) q^{98} +(-0.366330 - 22.6179i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

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