LMFDB - Embedded newform 425.2.p.a.16.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(16,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("425.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.p (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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$42$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			16.14
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.17358 - 0.852653i) q^{2} +(1.92956 - 0.626952i) q^{3} +(0.0322299 + 0.0991936i) q^{4} +(1.60043 - 1.56161i) q^{5} +(-2.79906 - 0.909470i) q^{6} +3.65292i q^{7} +(-0.849779 + 2.61535i) q^{8} +(0.903084 - 0.656129i) q^{9} +(-3.20974 + 0.468058i) q^{10} +(3.79333 - 5.22107i) q^{11} +(0.124379 + 0.171193i) q^{12} +(1.74978 - 1.27129i) q^{13} +(3.11468 - 4.28699i) q^{14} +(2.10907 - 4.01661i) q^{15} +(3.39603 - 2.46736i) q^{16} +(2.85120 - 2.97837i) q^{17} -1.61929 q^{18} +(-0.831011 + 2.55759i) q^{19} +(0.206483 + 0.108422i) q^{20} +(2.29021 + 7.04854i) q^{21} +(-8.90352 + 2.89293i) q^{22} +(0.0562594 - 0.0774344i) q^{23} +5.57925i q^{24} +(0.122747 - 4.99849i) q^{25} -3.13747 q^{26} +(-2.24641 + 3.09191i) q^{27} +(-0.362347 + 0.117734i) q^{28} +(-6.98725 + 2.27030i) q^{29} +(-5.89993 + 2.91550i) q^{30} +(-9.39777 - 3.05352i) q^{31} -0.589409 q^{32} +(4.04610 - 12.4526i) q^{33} +(-5.88561 + 1.06426i) q^{34} +(5.70444 + 5.84625i) q^{35} +(0.0941902 + 0.0684332i) q^{36} +(-0.293460 - 0.403913i) q^{37} +(3.15599 - 2.29296i) q^{38} +(2.57927 - 3.55006i) q^{39} +(2.72415 + 5.51271i) q^{40} +(4.80652 + 6.61561i) q^{41} +(3.32222 - 10.2248i) q^{42} +5.69452 q^{43} +(0.640155 + 0.207999i) q^{44} +(0.420705 - 2.46035i) q^{45} +(-0.132049 + 0.0429054i) q^{46} +(1.22147 + 3.75930i) q^{47} +(5.00592 - 6.89006i) q^{48} -6.34386 q^{49} +(-4.40603 + 5.76145i) q^{50} +(3.63426 - 7.53451i) q^{51} +(0.182499 + 0.132593i) q^{52} +(-1.76396 - 5.42891i) q^{53} +(5.27266 - 1.71319i) q^{54} +(-2.08232 - 14.2797i) q^{55} +(-9.55368 - 3.10418i) q^{56} +5.45603i q^{57} +(10.1358 + 3.29334i) q^{58} +(1.43016 - 1.03907i) q^{59} +(0.466398 + 0.0797509i) q^{60} +(-1.04964 + 1.44470i) q^{61} +(8.42541 + 11.5966i) q^{62} +(2.39679 + 3.29890i) q^{63} +(-6.10034 - 4.43215i) q^{64} +(0.815140 - 4.76709i) q^{65} +(-15.3662 + 11.1642i) q^{66} +(-4.37751 + 13.4726i) q^{67} +(0.387329 + 0.186828i) q^{68} +(0.0600082 - 0.184686i) q^{69} +(-1.70978 - 11.7249i) q^{70} +(-7.83664 + 2.54628i) q^{71} +(0.948586 + 2.91945i) q^{72} +(5.62201 - 7.73803i) q^{73} +0.724242i q^{74} +(-2.89697 - 9.72185i) q^{75} -0.280480 q^{76} +(19.0722 + 13.8567i) q^{77} +(-6.05394 + 1.96704i) q^{78} +(-0.462956 + 0.150424i) q^{79} +(1.58205 - 9.25210i) q^{80} +(-3.43094 + 10.5593i) q^{81} -11.8622i q^{82} +(-0.827740 + 2.54752i) q^{83} +(-0.625357 + 0.454348i) q^{84} +(-0.0879099 - 9.21913i) q^{85} +(-6.68296 - 4.85545i) q^{86} +(-12.0590 + 8.76135i) q^{87} +(10.4314 + 14.3576i) q^{88} +(11.1673 + 8.11352i) q^{89} +(-2.59156 + 2.52870i) q^{90} +(4.64393 + 6.39182i) q^{91} +(0.00949423 + 0.00308486i) q^{92} -20.0480 q^{93} +(1.77189 - 5.45332i) q^{94} +(2.66398 + 5.39096i) q^{95} +(-1.13730 + 0.369531i) q^{96} +(-8.57447 + 2.78601i) q^{97} +(7.44500 + 5.40911i) q^{98} -7.20398i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) $ 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.17358	−	0.852653i	−0.829844	−	0.602917i	0.0896714	−	0.995971i	$-0.471418\pi$
$2$	−1.17358	−	0.852653i	−0.829844	−	0.602917i	−0.919515	+	0.393055i	$0.871418\pi$
$3$	1.92956	−	0.626952i	1.11403	−	0.361971i	0.306545	−	0.951856i	$-0.400827\pi$
$3$	1.92956	−	0.626952i	1.11403	−	0.361971i	0.807487	+	0.589885i	$0.200827\pi$
$4$	0.0322299	+	0.0991936i	0.0161150	+	0.0495968i
$5$	1.60043	−	1.56161i	0.715734	−	0.698373i
$5$	1.60043	−	1.56161i	0.715734	−	0.698373i
$6$	−2.79906	−	0.909470i	−1.14271	−	0.371289i
$7$			3.65292i			1.38068i	0.723487	+	0.690338i	$0.242538\pi$
$7$			3.65292i			1.38068i	−0.723487	+	0.690338i	$0.757462\pi$
$8$	−0.849779	+	2.61535i	−0.300442	+	0.924666i
$9$	0.903084	−	0.656129i	0.301028	−	0.218710i
$10$	−3.20974	+	0.468058i	−1.01501	+	0.148013i
$11$	3.79333	−	5.22107i	1.14373	−	1.57421i	0.384856	−	0.922976i	$-0.374251\pi$
$11$	3.79333	−	5.22107i	1.14373	−	1.57421i	0.758876	−	0.651236i	$-0.225749\pi$
$12$	0.124379	+	0.171193i	0.0359052	+	0.0494193i
$13$	1.74978	−	1.27129i	0.485302	−	0.352592i	−0.318073	−	0.948066i	$-0.603036\pi$
$13$	1.74978	−	1.27129i	0.485302	−	0.352592i	0.803375	+	0.595474i	$0.203036\pi$
$14$	3.11468	−	4.28699i	0.832433	−	1.14575i
$15$	2.10907	−	4.01661i	0.544560	−	1.03709i
$16$	3.39603	−	2.46736i	0.849006	−	0.616839i
$17$	2.85120	−	2.97837i	0.691517	−	0.722360i
$17$	2.85120	−	2.97837i	0.691517	−	0.722360i
$18$	−1.61929			−0.381670
$19$	−0.831011	+	2.55759i	−0.190647	+	0.586751i	−1.00000		0.000571575i	$-0.999818\pi$
$19$	−0.831011	+	2.55759i	−0.190647	+	0.586751i	0.809353	+	0.587323i	$0.199818\pi$
$20$	0.206483	+	0.108422i	0.0461711	+	0.0242438i
$21$	2.29021	+	7.04854i	0.499765	+	1.53812i
$22$	−8.90352	+	2.89293i	−1.89824	+	0.616775i
$23$	0.0562594	−	0.0774344i	0.0117309	−	0.0161462i	−0.803111	−	0.595829i	$-0.796824\pi$
$23$	0.0562594	−	0.0774344i	0.0117309	−	0.0161462i	0.814842	+	0.579683i	$0.196824\pi$
$24$			5.57925i			1.13886i
$25$	0.122747	−	4.99849i	0.0245494	−	0.999699i
$26$	−3.13747			−0.615309
$27$	−2.24641	+	3.09191i	−0.432321	+	0.595039i
$28$	−0.362347	+	0.117734i	−0.0684771	+	0.0222496i
$29$	−6.98725	+	2.27030i	−1.29750	+	0.421583i	−0.874711	−	0.484645i	$-0.838949\pi$
$29$	−6.98725	+	2.27030i	−1.29750	+	0.421583i	−0.422789	+	0.906228i	$0.638949\pi$
$30$	−5.89993	+	2.91550i	−1.07718	+	0.532295i
$31$	−9.39777	−	3.05352i	−1.68789	−	0.548428i	−0.701473	−	0.712696i	$-0.747474\pi$
$31$	−9.39777	−	3.05352i	−1.68789	−	0.548428i	−0.986416	+	0.164267i	$0.947474\pi$
$32$	−0.589409			−0.104194
$33$	4.04610	−	12.4526i	0.704335	−	2.16772i
$34$	−5.88561	+	1.06426i	−1.00937	+	0.182519i
$35$	5.70444	+	5.84625i	0.964227	+	0.988196i
$36$	0.0941902	+	0.0684332i	0.0156984	+	0.0114055i
$37$	−0.293460	−	0.403913i	−0.0482445	−	0.0664029i	0.784213	−	0.620492i	$-0.213067\pi$
$37$	−0.293460	−	0.403913i	−0.0482445	−	0.0664029i	−0.832458	+	0.554089i	$0.813067\pi$
$38$	3.15599	−	2.29296i	0.511969	−	0.371967i
$39$	2.57927	−	3.55006i	0.413014	−	0.568465i
$40$	2.72415	+	5.51271i	0.430726	+	0.871636i
$41$	4.80652	+	6.61561i	0.750653	+	1.03318i	0.997934	+	0.0642413i	$0.0204627\pi$
$41$	4.80652	+	6.61561i	0.750653	+	1.03318i	−0.247282	+	0.968944i	$0.579537\pi$
$42$	3.32222	−	10.2248i	0.512630	−	1.57771i
$43$	5.69452			0.868407			0.434203	−	0.900815i	$-0.357030\pi$
$43$	5.69452			0.868407			0.434203	+	0.900815i	$0.357030\pi$
$44$	0.640155	+	0.207999i	0.0965071	+	0.0313570i
$45$	0.420705	−	2.46035i	0.0627149	−	0.366768i
$46$	−0.132049	+	0.0429054i	−0.0194696	+	0.00632606i
$47$	1.22147	+	3.75930i	0.178170	+	0.548351i	0.999764	−	0.0217222i	$-0.00691495\pi$
$47$	1.22147	+	3.75930i	0.178170	+	0.548351i	−0.821594	+	0.570073i	$0.806915\pi$
$48$	5.00592	−	6.89006i	0.722543	−	0.994495i
$49$	−6.34386			−0.906266
$50$	−4.40603	+	5.76145i	−0.623107	+	0.814792i
$51$	3.63426	−	7.53451i	0.508899	−	1.05504i
$52$	0.182499	+	0.132593i	0.0253081	+	0.0183874i
$53$	−1.76396	−	5.42891i	−0.242299	−	0.745719i	−0.996069	−	0.0885806i	$-0.971767\pi$
$53$	−1.76396	−	5.42891i	−0.242299	−	0.745719i	0.753770	−	0.657138i	$-0.228233\pi$
$54$	5.27266	−	1.71319i	0.717518	−	0.233136i
$55$	−2.08232	−	14.2797i	−0.280780	−	1.92547i
$56$	−9.55368	−	3.10418i	−1.27666	−	0.414813i
$57$			5.45603i			0.722669i
$58$	10.1358	+	3.29334i	1.33090	+	0.432436i
$59$	1.43016	−	1.03907i	0.186191	−	0.135276i	−0.490785	−	0.871281i	$-0.663290\pi$
$59$	1.43016	−	1.03907i	0.186191	−	0.135276i	0.676976	+	0.736005i	$0.263290\pi$
$60$	0.466398	+	0.0797509i	0.0602117	+	0.0102958i
$61$	−1.04964	+	1.44470i	−0.134392	+	0.184975i	−0.870909	−	0.491444i	$-0.836469\pi$
$61$	−1.04964	+	1.44470i	−0.134392	+	0.184975i	0.736517	+	0.676419i	$0.236469\pi$
$62$	8.42541	+	11.5966i	1.07003	+	1.47277i
$63$	2.39679	+	3.29890i	0.301967	+	0.415622i
$64$	−6.10034	−	4.43215i	−0.762542	−	0.554019i
$65$	0.815140	−	4.76709i	0.101106	−	0.591284i
$66$	−15.3662	+	11.1642i	−1.89144	+	1.37421i
$67$	−4.37751	+	13.4726i	−0.534798	+	1.64594i	0.209286	+	0.977855i	$0.432886\pi$
$67$	−4.37751	+	13.4726i	−0.534798	+	1.64594i	−0.744084	+	0.668086i	$0.767114\pi$
$68$	0.387329	+	0.186828i	0.0469705	+	0.0226562i
$69$	0.0600082	−	0.184686i	0.00722414	−	0.0222336i
$70$	−1.70978	−	11.7249i	−0.204358	−	1.40140i
$71$	−7.83664	+	2.54628i	−0.930038	+	0.302188i	−0.734578	−	0.678524i	$-0.762620\pi$
$71$	−7.83664	+	2.54628i	−0.930038	+	0.302188i	−0.195460	+	0.980712i	$0.562620\pi$
$72$	0.948586	+	2.91945i	0.111792	+	0.344060i
$73$	5.62201	−	7.73803i	0.658007	−	0.905668i	−0.341407	−	0.939916i	$-0.610903\pi$
$73$	5.62201	−	7.73803i	0.658007	−	0.905668i	0.999413	+	0.0342472i	$0.0109034\pi$
$74$			0.724242i			0.0841915i
$75$	−2.89697	−	9.72185i	−0.334513	−	1.12258i
$76$	−0.280480			−0.0321732
$77$	19.0722	+	13.8567i	2.17348	+	1.57912i
$78$	−6.05394	+	1.96704i	−0.685474	+	0.222724i
$79$	−0.462956	+	0.150424i	−0.0520866	+	0.0169240i	−0.334944	−	0.942238i	$-0.608718\pi$
$79$	−0.462956	+	0.150424i	−0.0520866	+	0.0169240i	0.282858	+	0.959162i	$0.408718\pi$
$80$	1.58205	−	9.25210i	0.176878	−	1.03442i
$81$	−3.43094	+	10.5593i	−0.381216	+	1.17326i
$82$		−	11.8622i		−	1.30996i
$83$	−0.827740	+	2.54752i	−0.0908563	+	0.279627i	−0.986152	−	0.165846i	$-0.946964\pi$
$83$	−0.827740	+	2.54752i	−0.0908563	+	0.279627i	0.895295	+	0.445473i	$0.146964\pi$
$84$	−0.625357	+	0.454348i	−0.0682320	+	0.0495734i
$85$	−0.0879099	−	9.21913i	−0.00953516	−	0.999955i
$86$	−6.68296	−	4.85545i	−0.720642	−	0.523577i
$87$	−12.0590	+	8.76135i	−1.29286	+	0.939315i
$88$	10.4314	+	14.3576i	1.11200	+	1.53053i
$89$	11.1673	+	8.11352i	1.18373	+	0.860032i	0.992588	−	0.121530i	$-0.0387802\pi$
$89$	11.1673	+	8.11352i	1.18373	+	0.860032i	0.191144	+	0.981562i	$0.438780\pi$
$90$	−2.59156	+	2.52870i	−0.273174	+	0.266548i
$91$	4.64393	+	6.39182i	0.486816	+	0.670045i
$92$	0.00949423	+	0.00308486i	0.000989842	+	0.000321619i
$93$	−20.0480			−2.07888
$94$	1.77189	−	5.45332i	0.182757	−	0.562467i
$95$	2.66398	+	5.39096i	0.273319	+	0.553100i
$96$	−1.13730	+	0.369531i	−0.116075	+	0.0377151i
$97$	−8.57447	+	2.78601i	−0.870605	+	0.282877i	−0.710051	−	0.704150i	$-0.751328\pi$
$97$	−8.57447	+	2.78601i	−0.870605	+	0.282877i	−0.160554	+	0.987027i	$0.551328\pi$
$98$	7.44500	+	5.40911i	0.752059	+	0.546403i
$99$		−	7.20398i		−	0.724028i
$100$	0.499775	−	0.148925i	0.0499775	−	0.0148925i
$101$	9.59646			0.954883			0.477442	−	0.878663i	$-0.341564\pi$
$101$	9.59646			0.954883			0.477442	+	0.878663i	$0.341564\pi$
$102$	−10.6894	+	5.74355i	−1.05841	+	0.568696i
$103$	1.32047	+	4.06399i	0.130110	+	0.400437i	0.994797	−	0.101873i	$-0.0324836\pi$
$103$	1.32047	+	4.06399i	0.130110	+	0.400437i	−0.864688	+	0.502310i	$0.832484\pi$
$104$	1.83794	+	5.65661i	0.180225	+	0.554676i
$105$	14.6724	+	7.70427i	1.43188	+	0.751860i
$106$	−2.55884	+	7.87529i	−0.248536	+	0.764916i
$107$		−	0.940056i		−	0.0908786i	−0.998967	−	0.0454393i	$-0.985531\pi$
$107$		−	0.940056i		−	0.0908786i	0.998967	−	0.0454393i	$-0.0144688\pi$
$108$	−0.379100	−	0.123177i	−0.0364789	−	0.0118527i
$109$	−4.57074	−	6.29108i	−0.437797	−	0.602576i	0.531923	−	0.846792i	$-0.321469\pi$
$109$	−4.57074	−	6.29108i	−0.437797	−	0.602576i	−0.969721	+	0.244216i	$0.921469\pi$
$110$	−9.73183	+	18.5338i	−0.927894	+	1.76713i
$111$	−0.819483	−	0.595389i	−0.0777819	−	0.0565119i
$112$	9.01307	+	12.4054i	0.851655	+	1.17220i
$113$	7.94525	+	10.9357i	0.747426	+	1.02874i	0.998157	+	0.0606870i	$0.0193292\pi$
$113$	7.94525	+	10.9357i	0.747426	+	1.02874i	−0.250731	+	0.968057i	$0.580671\pi$
$114$	4.65210	−	6.40306i	0.435709	−	0.599702i
$115$	−0.0308832	−	0.211783i	−0.00287987	−	0.0197489i
$116$	−0.450397	−	0.619919i	−0.0418184	−	0.0575580i
$117$	0.746069	−	2.29617i	0.0689741	−	0.212281i
$118$	−2.56437			−0.236070
$119$	10.8798	+	10.4152i	0.997345	+	0.954761i
$120$	8.71261	+	8.92919i	0.795349	+	0.815120i
$121$	−9.47104	−	29.1489i	−0.861004	−	2.64990i
$122$	2.46366	−	0.800492i	0.223049	−	0.0724731i
$123$	13.4222	+	9.75176i	1.21023	+	0.879287i
$124$		−	1.03061i		−	0.0925518i
$125$	−7.60925	−	8.19142i	−0.680592	−	0.732663i
$126$		−	5.91514i		−	0.526963i
$127$	2.00210	+	1.45461i	0.177658	+	0.129076i	0.673060	−	0.739588i	$-0.264979\pi$
$127$	2.00210	+	1.45461i	0.177658	+	0.129076i	−0.495402	+	0.868664i	$0.664979\pi$
$128$	3.74439	+	11.5241i	0.330961	+	1.01859i
$129$	10.9879	−	3.57020i	0.967433	−	0.314338i
$130$	−5.02130	+	4.89951i	−0.440397	+	0.429715i
$131$	2.71652	+	0.882650i	0.237343	+	0.0771175i	0.425274	−	0.905065i	$-0.360178\pi$
$131$	2.71652	+	0.882650i	0.237343	+	0.0771175i	−0.187930	+	0.982182i	$0.560178\pi$
$132$	1.36562			0.118862
$133$	−9.34268	−	3.03562i	−0.810113	−	0.263222i
$134$	16.6248	−	12.0786i	1.43616	−	1.04343i
$135$	1.23315	+	8.45640i	0.106133	+	0.727811i
$136$	5.36659	+	9.98784i	0.460181	+	0.856450i
$137$	14.7157	−	10.6916i	1.25725	−	0.913445i	0.258630	−	0.965976i	$-0.416729\pi$
$137$	14.7157	−	10.6916i	1.25725	−	0.913445i	0.998619	+	0.0525314i	$0.0167290\pi$
$138$	−0.227898	+	0.165577i	−0.0193999	+	0.0140949i
$139$	−3.57911	+	4.92622i	−0.303576	+	0.417836i	−0.933364	−	0.358930i	$-0.883142\pi$
$139$	−3.57911	+	4.92622i	−0.303576	+	0.417836i	0.629788	+	0.776767i	$0.283142\pi$
$140$	−0.396056	+	0.754268i	−0.0334729	+	0.0637473i
$141$	4.71381	+	6.48800i	0.396974	+	0.546388i
$142$	11.3680	+	3.69368i	0.953981	+	0.309967i
$143$		−	13.9582i		−	1.16724i
$144$	1.44799	−	4.45646i	0.120666	−	0.371372i
$145$	−7.63728	+	14.5448i	−0.634242	+	1.20788i
$146$	−13.1957	+	4.28755i	−1.09209	+	0.354840i
$147$	−12.2409	+	3.97730i	−1.00961	+	0.328042i
$148$	0.0306074	−	0.0421274i	0.00251591	−	0.00346285i
$149$	−18.7767			−1.53825			−0.769123	−	0.639101i	$-0.779307\pi$
$149$	−18.7767			−1.53825			−0.769123	+	0.639101i	$0.779307\pi$
$150$	−4.88955	+	13.8794i	−0.399230	+	1.13325i
$151$	−0.994179			−0.0809051			−0.0404526	−	0.999181i	$-0.512880\pi$
$151$	−0.994179			−0.0809051			−0.0404526	+	0.999181i	$0.512880\pi$
$152$	−5.98282	−	4.34677i	−0.485271	−	0.352570i
$153$	0.620678	−	4.56047i	0.0501788	−	0.368692i
$154$	−10.5677	−	32.5239i	−0.851566	−	2.62085i
$155$	−19.8089	+	9.78871i	−1.59109	+	0.786248i
$156$	0.435273	+	0.141429i	0.0348497	+	0.0113234i
$157$	−1.02264			−0.0816157			−0.0408078	−	0.999167i	$-0.512993\pi$
$157$	−1.02264			−0.0816157			−0.0408078	+	0.999167i	$0.512993\pi$
$158$	0.671573	+	0.218207i	0.0534275	+	0.0173597i
$159$	−6.80734	−	9.36950i	−0.539857	−	0.743050i
$160$	−0.943307	+	0.920427i	−0.0745750	+	0.0727661i
$161$	0.282862	+	0.205511i	0.0222926	+	0.0161966i
$162$	13.0299	−	9.46680i	1.02373	−	0.743782i
$163$	0.121142	+	0.166738i	0.00948859	+	0.0130599i	0.813735	−	0.581236i	$-0.197431\pi$
$163$	0.121142	+	0.166738i	0.00948859	+	0.0130599i	−0.804246	+	0.594296i	$0.797431\pi$
$164$	−0.501312	+	0.689997i	−0.0391459	+	0.0538797i
$165$	−12.9706	−	26.2479i	−1.00976	−	2.04340i
$166$	3.14357	−	2.28394i	0.243988	−	0.177268i
$167$	8.98546	+	2.91955i	0.695316	+	0.225922i	0.635288	−	0.772275i	$-0.280881\pi$
$167$	8.98546	+	2.91955i	0.695316	+	0.225922i	0.0600272	+	0.998197i	$0.480881\pi$
$168$	−20.3806			−1.57240
$169$	−2.57167	+	7.91478i	−0.197821	+	0.608829i
$170$	−7.75755	+	10.8943i	−0.594977	+	0.835555i
$171$	0.927636	+	2.85497i	0.0709381	+	0.218325i
$172$	0.183534	+	0.564860i	0.0139944	+	0.0430702i
$173$	−10.6689	+	14.6845i	−0.811144	+	1.11644i	0.180002	+	0.983666i	$0.442389\pi$
$173$	−10.6689	+	14.6845i	−0.811144	+	1.11644i	−0.991146	+	0.132777i	$0.957611\pi$
$174$	21.6225			1.63920
$175$	18.2591	+	0.448385i	1.38026	+	0.0338947i
$176$		−	27.0904i		−	2.04201i
$177$	2.10814	−	2.90160i	0.158457	−	0.218098i
$178$	−6.18766	−	19.0437i	−0.463785	−	1.42738i
$179$	0.473492	+	1.45726i	0.0353905	+	0.108921i	0.967191	−	0.254050i	$-0.0817627\pi$
$179$	0.473492	+	1.45726i	0.0353905	+	0.108921i	−0.931801	+	0.362970i	$0.881763\pi$
$180$	0.257611	−	0.0375659i	0.0192012	−	0.00280000i
$181$	−19.7831	−	6.42791i	−1.47046	−	0.477782i	−0.539215	−	0.842168i	$-0.681279\pi$
$181$	−19.7831	−	6.42791i	−1.47046	−	0.477782i	−0.931248	+	0.364386i	$0.881279\pi$
$182$		−	11.4609i		−	0.849542i
$183$	−1.11958	+	3.44571i	−0.0827618	+	0.254715i
$184$	0.154710	+	0.212940i	0.0114054	+	0.0156982i
$185$	−1.10042	−	0.188164i	−0.0809042	−	0.0138341i
$186$	23.5278	+	17.0940i	1.72514	+	1.25339i
$187$	−4.73474	−	26.1842i	−0.346238	−	1.91478i
$188$	−0.333531	+	0.242324i	−0.0243252	+	0.0176733i
$189$	−11.2945	−	8.20596i	−0.821556	−	0.596896i
$190$	1.47023	−	8.59815i	0.106662	−	0.623775i
$191$	9.01063	−	6.54661i	0.651986	−	0.473696i	−0.211961	−	0.977278i	$-0.567985\pi$
$191$	9.01063	−	6.54661i	0.651986	−	0.473696i	0.863947	+	0.503582i	$0.167985\pi$
$192$	−14.5497	−	4.72749i	−1.05004	−	0.341177i
$193$			24.5408i			1.76648i	0.468917	+	0.883242i	$0.344644\pi$
$193$			24.5408i			1.76648i	−0.468917	+	0.883242i	$0.655356\pi$
$194$	12.4383	+	4.04145i	0.893017	+	0.290159i
$195$	−1.41587	−	9.70944i	−0.101393	−	0.695307i
$196$	−0.204462	−	0.629270i	−0.0146044	−	0.0449479i
$197$	−2.51439	+	0.816976i	−0.179143	+	0.0582071i	−0.397215	−	0.917726i	$-0.630023\pi$
$197$	−2.51439	+	0.816976i	−0.179143	+	0.0582071i	0.218072	+	0.975933i	$0.430023\pi$
$198$	−6.14250	+	8.45442i	−0.436528	+	0.600830i
$199$		−	3.94316i		−	0.279523i	−0.990185	−	0.139761i	$-0.955366\pi$
$199$		−	3.94316i		−	0.279523i	0.990185	−	0.139761i	$-0.0446336\pi$
$200$	12.9685	+	4.56864i	0.917012	+	0.323052i
$201$			28.7407i			2.02721i
$202$	−11.2622	−	8.18245i	−0.792404	−	0.575715i
$203$	−8.29322	−	25.5239i	−0.582070	−	1.79143i
$204$	0.864507	+	0.117659i	0.0605276	+	0.00823777i
$205$	18.0235	+	3.08190i	1.25882	+	0.215249i
$206$	1.91550	−	5.89530i	0.133459	−	0.410745i
$207$		−	0.106843i		−	0.00742612i
$208$	2.80557	−	8.63467i	0.194532	−	0.598707i
$209$	10.2011	+	14.0405i	0.705622	+	0.971205i
$210$	−10.6501	−	21.5520i	−0.734926	−	1.48723i
$211$	−11.8329	+	16.2866i	−0.814613	+	1.12122i	0.175982	+	0.984393i	$0.443690\pi$
$211$	−11.8329	+	16.2866i	−0.814613	+	1.12122i	−0.990595	+	0.136825i	$0.956310\pi$
$212$	0.481661	−	0.349947i	0.0330806	−	0.0240345i
$213$	−13.5249	+	9.82640i	−0.926710	+	0.673294i
$214$	−0.801541	+	1.10323i	−0.0547922	+	0.0754151i
$215$	9.11368	−	8.89263i	0.621548	−	0.606472i
$216$	−6.17749	−	8.50259i	−0.420325	−	0.578528i
$217$	11.1543	−	34.3293i	0.757202	−	2.33043i
$218$			11.2803i			0.764000i
$219$	5.99663	−	18.4557i	0.405215	−	1.24712i
$220$	1.34934	−	0.666785i	0.0909723	−	0.0449547i
$221$	1.20260	−	8.83619i	0.0808957	−	0.594386i
$222$	0.454065	+	1.39747i	0.0304749	+	0.0937920i
$223$	17.8156	+	12.9438i	1.19302	+	0.866781i	0.993580	−	0.113129i	$-0.0360874\pi$
$223$	17.8156	+	12.9438i	1.19302	+	0.866781i	0.199441	+	0.979910i	$0.436087\pi$
$224$		−	2.15307i		−	0.143858i
$225$	−3.16881	−	4.59460i	−0.211254	−	0.306307i
$226$		−	19.6084i		−	1.30433i
$227$	2.35587	−	3.24257i	0.156364	−	0.215217i	−0.723646	−	0.690171i	$-0.757535\pi$
$227$	2.35587	−	3.24257i	0.156364	−	0.215217i	0.880011	+	0.474954i	$0.157535\pi$
$228$	−0.541203	+	0.175847i	−0.0358420	+	0.0116458i
$229$	−0.200889	−	0.618273i	−0.0132751	−	0.0408566i	0.944200	−	0.329374i	$-0.106838\pi$
$229$	−0.200889	−	0.618273i	−0.0132751	−	0.0408566i	−0.957475	+	0.288517i	$0.906838\pi$
$230$	−0.144334	+	0.274877i	−0.00951710	+	0.0181248i
$231$	45.4884	+	14.7801i	2.99292	+	0.972459i
$232$		−	20.2034i		−	1.32642i
$233$	−7.16487	−	2.32801i	−0.469386	−	0.152513i	0.0647672	−	0.997900i	$-0.479370\pi$
$233$	−7.16487	−	2.32801i	−0.469386	−	0.152513i	−0.534153	+	0.845388i	$0.679370\pi$
$234$	−2.83340	+	2.05859i	−0.185225	+	0.134574i
$235$	7.82544	+	4.10904i	0.510476	+	0.268044i
$236$	0.149164	+	0.108374i	0.00970972	+	0.00705452i
$237$	−0.798994	+	0.580503i	−0.0519002	+	0.0377077i
$238$	−3.88766	−	21.4997i	−0.251999	−	1.39362i
$239$	−0.414276	−	0.300989i	−0.0267973	−	0.0194694i	0.574306	−	0.818641i	$-0.305272\pi$
$239$	−0.414276	−	0.300989i	−0.0267973	−	0.0194694i	−0.601103	+	0.799171i	$0.705272\pi$
$240$	−2.74797	−	18.8444i	−0.177380	−	1.21640i
$241$	0.138737	+	0.190955i	0.00893682	+	0.0123005i	0.813462	−	0.581618i	$-0.197580\pi$
$241$	0.138737	+	0.190955i	0.00893682	+	0.0123005i	−0.804525	+	0.593919i	$0.797580\pi$
$242$	−13.7389	+	42.2839i	−0.883169	+	2.71811i
$243$			11.0605i			0.709530i
$244$	−0.177135	−	0.0575546i	−0.0113399	−	0.00368456i
$245$	−10.1529	+	9.90664i	−0.648645	+	0.632912i
$246$	−7.43705	−	22.8889i	−0.474169	−	1.45934i
$247$	1.79735	+	5.53168i	0.114363	+	0.351972i
$248$	15.9721	−	21.9836i	1.01423	−	1.39596i
$249$			5.43455i			0.344401i
$250$	1.94560	+	16.1013i	0.123050	+	1.01834i
$251$	−2.27493			−0.143592			−0.0717961	−	0.997419i	$-0.522873\pi$
$251$	−2.27493			−0.143592			−0.0717961	+	0.997419i	$0.522873\pi$
$252$	−0.249981	+	0.344070i	−0.0157473	+	0.0216743i
$253$	−0.190880	−	0.587468i	−0.0120005	−	0.0369338i
$254$	−1.10934	−	3.41420i	−0.0696062	−	0.214226i
$255$	−5.94958	−	17.7337i	−0.372577	−	1.11053i
$256$	0.771452	−	2.37428i	0.0482157	−	0.148393i
$257$	−6.73321			−0.420006			−0.210003	−	0.977701i	$-0.567347\pi$
$257$	−6.73321			−0.420006			−0.210003	+	0.977701i	$0.567347\pi$
$258$	−15.9393	−	5.17900i	−0.992338	−	0.322430i
$259$	1.47546	−	1.07199i	0.0916809	−	0.0666101i
$260$	0.499136	−	0.0727862i	0.0309551	−	0.00451401i
$261$	−4.82047	+	6.63481i	−0.298380	+	0.410684i
$262$	−2.43545	−	3.35211i	−0.150462	−	0.207094i
$263$	0.664622	−	0.482876i	0.0409824	−	0.0297754i	−0.567106	−	0.823645i	$-0.691937\pi$
$263$	0.664622	−	0.482876i	0.0409824	−	0.0297754i	0.608088	+	0.793870i	$0.291937\pi$
$264$	29.1297	+	21.1639i	1.79281	+	1.30255i
$265$	−11.3009	−	5.93397i	−0.694211	−	0.364521i
$266$	8.37602	+	11.5286i	0.513566	+	0.706864i
$267$	26.6348	+	8.65417i	1.63002	+	0.529626i
$268$	−1.47748			−0.0902516
$269$	−21.2053	−	6.89001i	−1.29291	−	0.420091i	−0.419799	−	0.907617i	$-0.637899\pi$
$269$	−21.2053	−	6.89001i	−1.29291	−	0.420091i	−0.873109	+	0.487526i	$0.837899\pi$
$270$	5.76318	−	10.9757i	0.350736	−	0.667959i
$271$	1.29221	+	3.97701i	0.0784962	+	0.241586i	0.982602	−	0.185721i	$-0.0594621\pi$
$271$	1.29221	+	3.97701i	0.0784962	+	0.241586i	−0.904106	+	0.427308i	$0.859462\pi$
$272$	2.33404	−	17.1495i	0.141522	−	1.03984i
$273$	12.9681	+	9.42188i	0.784865	+	0.570238i
$274$	−26.3863			−1.59405
$275$	−25.6319	−	19.6018i	−1.54566	−	1.18203i
$276$	0.0202538			0.00121913
$277$	5.74845	−	7.91206i	0.345391	−	0.475390i	−0.600615	−	0.799538i	$-0.705078\pi$
$277$	5.74845	−	7.91206i	0.345391	−	0.475390i	0.946006	+	0.324148i	$0.105078\pi$
$278$	8.40071	−	2.72956i	0.503841	−	0.163708i
$279$	−10.4905	+	3.40857i	−0.628049	+	0.204065i
$280$	−20.1375	+	9.95111i	−1.20345	+	0.594692i
$281$	8.53065	−	26.2546i	0.508896	−	1.56622i	−0.285225	−	0.958461i	$-0.592068\pi$
$281$	8.53065	−	26.2546i	0.508896	−	1.56622i	0.794121	−	0.607760i	$-0.207932\pi$
$282$		−	11.6334i		−	0.692759i
$283$	1.39163	+	0.452169i	0.0827240	+	0.0268787i	0.350087	−	0.936717i	$-0.386152\pi$
$283$	1.39163	+	0.452169i	0.0827240	+	0.0268787i	−0.267363	+	0.963596i	$0.586152\pi$
$284$	−0.505149	−	0.695278i	−0.0299751	−	0.0412572i
$285$	8.52019	+	8.73199i	0.504692	+	0.517238i
$286$	−11.9015	+	16.3810i	−0.703748	+	0.968626i
$287$	−24.1663	+	17.5579i	−1.42649	+	1.03641i
$288$	−0.532286	+	0.386728i	−0.0313652	+	0.0227882i
$289$	−0.741346	−	16.9838i	−0.0436086	−	0.999049i
$290$	21.3646	−	10.5575i	1.25457	−	0.619957i
$291$	−14.7983	+	10.7516i	−0.867489	+	0.630268i
$292$	0.948760	+	0.308271i	0.0555220	+	0.0180402i
$293$	6.68146			0.390335			0.195168	−	0.980770i	$-0.437475\pi$
$293$	6.68146			0.390335			0.195168	+	0.980770i	$0.437475\pi$
$294$	17.7568	+	5.76955i	1.03560	+	0.336487i
$295$	0.666245	−	3.89632i	0.0387903	−	0.226853i
$296$	1.30575	−	0.424264i	0.0758952	−	0.0246598i
$297$	7.62174	+	23.4573i	0.442258	+	1.36113i
$298$	22.0359	+	16.0100i	1.27650	+	0.927434i
$299$		−	0.207015i		−	0.0119720i
$300$	0.870976	−	0.600695i	0.0502858	−	0.0346812i
$301$			20.8017i			1.19899i
$302$	1.16674	+	0.847690i	0.0671386	+	0.0487791i
$303$	18.5170	−	6.01652i	1.06377	−	0.345640i
$304$	3.48835	+	10.7360i	0.200071	+	0.615754i
$305$	0.576191	+	3.95127i	0.0329926	+	0.226249i
$306$	−4.61691	+	4.82284i	−0.263931	+	0.275703i
$307$	−24.8943			−1.42079			−0.710397	−	0.703802i	$-0.751484\pi$
$307$	−24.8943			−1.42079			−0.710397	+	0.703802i	$0.751484\pi$
$308$	−0.759805	+	2.33844i	−0.0432939	+	0.133245i
$309$	5.09585	+	7.01384i	0.289893	+	0.399003i
$310$	31.5936	+	5.40230i	1.79440	+	0.306830i
$311$	−0.556240	+	0.765598i	−0.0315415	+	0.0434131i	−0.824496	−	0.565867i	$-0.808542\pi$
$311$	−0.556240	+	0.765598i	−0.0315415	+	0.0434131i	0.792955	+	0.609280i	$0.208542\pi$
$312$	7.09285	+	9.76246i	0.401553	+	0.552691i
$313$	−12.1500	−	16.7230i	−0.686756	−	0.945238i	0.313234	−	0.949676i	$-0.398588\pi$
$313$	−12.1500	−	16.7230i	−0.686756	−	0.945238i	−0.999990	+	0.00443746i	$0.998588\pi$
$314$	1.20015	+	0.871959i	0.0677283	+	0.0492075i
$315$	8.98749	+	1.53680i	0.506388	+	0.0865890i
$316$	−0.0298421	−	0.0410741i	−0.00167875	−	0.00231060i
$317$	−18.2988	−	5.94563i	−1.02776	−	0.333940i	−0.253857	−	0.967242i	$-0.581699\pi$
$317$	−18.2988	−	5.94563i	−1.02776	−	0.333940i	−0.773905	+	0.633302i	$0.781699\pi$
$318$			16.8001i			0.942104i
$319$	−14.6516	+	45.0929i	−0.820331	+	2.52472i
$320$	−16.6844	+	2.43300i	−0.932689	+	0.136009i
$321$	−0.589370	−	1.81389i	−0.0328954	−	0.101242i
$322$	−0.156730	−	0.482366i	−0.00873424	−	0.0268812i
$323$	5.24806	+	9.76725i	0.292010	+	0.543464i
$324$	−1.15800			−0.0643332
$325$	−6.13976	−	8.90231i	−0.340572	−	0.493812i
$326$		−	0.298972i		−	0.0165585i
$327$	−12.7637	−	9.27339i	−0.705836	−	0.512820i
$328$	−21.3866	+	6.94894i	−1.18088	+	0.383691i
$329$	−13.7324	+	4.46194i	−0.757094	+	0.245995i
$330$	−7.15837	+	41.8634i	−0.394055	+	2.30451i
$331$	2.21173	−	6.80702i	0.121568	−	0.374148i	−0.871692	−	0.490054i	$-0.836977\pi$
$331$	2.21173	−	6.80702i	0.121568	−	0.374148i	0.993260	+	0.115906i	$0.0369772\pi$
$332$	−0.279376			−0.0153327
$333$	−0.530038	−	0.172220i	−0.0290459	−	0.00943759i
$334$	−8.05575	−	11.0878i	−0.440791	−	0.606697i
$335$	14.0331	+	28.3979i	0.766708	+	1.55154i
$336$	25.1689	+	18.2863i	1.37307	+	0.997597i
$337$	−8.39475	−	11.5544i	−0.457291	−	0.629408i	0.516653	−	0.856195i	$-0.327178\pi$
$337$	−8.39475	−	11.5544i	−0.457291	−	0.629408i	−0.973944	+	0.226787i	$0.927178\pi$
$338$	9.76660	−	7.09585i	0.531233	−	0.385964i
$339$	22.1870	+	16.1198i	1.20503	+	0.875507i
$340$	0.911645	−	0.305852i	0.0494409	−	0.0165872i
$341$	−51.5915	+	37.4834i	−2.79384	+	2.02984i
$342$	1.34565	−	4.14148i	0.0727643	−	0.223945i
$343$			2.39683i			0.129417i
$344$	−4.83909	+	14.8932i	−0.260906	+	0.802986i
$345$	−0.192369	−	0.389287i	−0.0103568	−	0.0209585i
$346$	25.0416	−	8.13651i	1.34624	−	0.437421i
$347$	17.1466	−	5.57126i	0.920477	−	0.299081i	0.189815	−	0.981820i	$-0.439211\pi$
$347$	17.1466	−	5.57126i	0.920477	−	0.299081i	0.730663	+	0.682739i	$0.239211\pi$
$348$	−1.25773	−	0.913794i	−0.0674213	−	0.0489845i
$349$	19.4211			1.03959			0.519795	−	0.854291i	$-0.326008\pi$
$349$	19.4211			1.03959			0.519795	+	0.854291i	$0.326008\pi$
$350$	−21.0462	−	16.0949i	−1.12496	−	0.860309i
$351$			8.26601i			0.441207i
$352$	−2.23582	+	3.07734i	−0.119170	+	0.164023i
$353$	2.25444	+	6.93846i	0.119992	+	0.369297i	0.992955	−	0.118488i	$-0.0378048\pi$
$353$	2.25444	+	6.93846i	0.119992	+	0.369297i	−0.872964	+	0.487785i	$0.837805\pi$
$354$	−4.94812	+	1.60774i	−0.262989	+	0.0854504i
$355$	−8.56570	+	16.3129i	−0.454620	+	0.865800i
$356$	−0.444888	+	1.36922i	−0.0235790	+	0.0725687i
$357$	27.5230	+	13.2757i	1.45667	+	0.702624i
$358$	0.686857	−	2.11393i	0.0363015	−	0.111725i
$359$	28.5016	−	20.7076i	1.50425	−	1.09290i	0.535606	−	0.844468i	$-0.320083\pi$
$359$	28.5016	−	20.7076i	1.50425	−	1.09290i	0.968648	−	0.248437i	$-0.0799169\pi$
$360$	6.07718	+	3.19105i	0.320296	+	0.168183i
$361$	9.52064	+	6.91715i	0.501086	+	0.364061i
$362$	17.7362	+	24.4117i	0.932192	+	1.28305i
$363$	−36.5499	−	50.3066i	−1.91837	−	2.64041i
$364$	−0.484354	+	0.666656i	−0.0253870	+	0.0349423i
$365$	−3.08616	−	21.1636i	−0.161537	−	1.10775i
$366$	4.25191	−	3.08919i	0.222251	−	0.161475i
$367$	4.54805	+	1.47775i	0.237406	+	0.0771379i	0.425304	−	0.905051i	$-0.360167\pi$
$367$	4.54805	+	1.47775i	0.237406	+	0.0771379i	−0.187898	+	0.982189i	$0.560167\pi$
$368$		−	0.401781i		−	0.0209443i
$369$	8.68139	+	2.82076i	0.451935	+	0.146843i
$370$	1.13098	+	1.15910i	0.0587971	+	0.0602587i
$371$	19.8314	−	6.44362i	1.02960	−	0.334536i
$372$	−0.646145	−	1.98863i	−0.0335011	−	0.103106i
$373$	−24.9214	−	18.1065i	−1.29038	−	0.937518i	−0.290570	−	0.956854i	$-0.593845\pi$
$373$	−24.9214	−	18.1065i	−1.29038	−	0.937518i	−0.999813	+	0.0193358i	$0.993845\pi$
$374$	−16.7695	+	34.7663i	−0.867130	+	1.79772i
$375$	−19.8181	−	11.0352i	−1.02340	−	0.569855i
$376$	−10.8699			−0.560571
$377$	−9.33996	+	12.8553i	−0.481032	+	0.662084i
$378$	6.25816	+	19.2606i	0.321885	+	0.990660i
$379$	19.2956	−	6.26953i	0.991151	−	0.322044i	0.231827	−	0.972757i	$-0.425530\pi$
$379$	19.2956	−	6.26953i	0.991151	−	0.322044i	0.759324	+	0.650713i	$0.225530\pi$
$380$	−0.448888	+	0.438000i	−0.0230275	+	0.0224689i
$381$	4.77515	+	1.55154i	0.244638	+	0.0794878i
$382$	−16.1566			−0.826646
$383$	−4.80036	+	14.7740i	−0.245287	+	0.754916i	0.750302	+	0.661095i	$0.229908\pi$
$383$	−4.80036	+	14.7740i	−0.245287	+	0.754916i	−0.995589	+	0.0938208i	$0.970092\pi$
$384$	14.4501	+	19.8888i	0.737402	+	1.01495i
$385$	52.1625	−	7.60657i	2.65845	−	0.387666i
$386$	20.9248	−	28.8005i	1.06504	−	1.46591i
$387$	5.14264	−	3.73634i	0.261415	−	0.189929i
$388$	−0.552709	−	0.760739i	−0.0280596	−	0.0386207i
$389$	−17.8861	−	12.9950i	−0.906862	−	0.658874i	0.0333569	−	0.999444i	$-0.489380\pi$
$389$	−17.8861	−	12.9950i	−0.906862	−	0.658874i	−0.940219	+	0.340569i	$0.889380\pi$
$390$	−6.61715	+	12.6020i	−0.335072	+	0.638128i
$391$	−0.0702215	−	0.388342i	−0.00355125	−	0.0196393i
$392$	5.39088	−	16.5914i	0.272280	−	0.837993i
$393$	5.79507			0.292322
$394$	3.64743	+	1.18512i	0.183755	+	0.0597056i
$395$	−0.506026	+	0.963699i	−0.0254609	+	0.0484890i
$396$	0.714589	−	0.232184i	0.0359094	−	0.0116677i
$397$	−11.0102	+	3.57744i	−0.552587	+	0.179546i	−0.571983	−	0.820266i	$-0.693826\pi$
$397$	−11.0102	+	3.57744i	−0.552587	+	0.179546i	0.0193960	+	0.999812i	$0.493826\pi$
$398$	−3.36214	+	4.62759i	−0.168529	+	0.231960i
$399$	−19.9305			−0.997771
$400$	−11.9162	−	17.2779i	−0.595811	−	0.863894i
$401$		−	32.3000i		−	1.61299i	−0.591243	−	0.806494i	$-0.701363\pi$
$401$		−	32.3000i		−	1.61299i	0.591243	−	0.806494i	$-0.298637\pi$
$402$	24.5058	−	33.7294i	1.22224	−	1.68227i
$403$	−20.3260	+	6.60430i	−1.01251	+	0.328984i
$404$	0.309293	+	0.951907i	0.0153879	+	0.0473592i
$405$	10.9986	+	22.2573i	0.546525	+	1.10597i
$406$	−12.0303	+	37.0255i	−0.597054	+	1.83754i
$407$	−3.22205			−0.159711
$408$	16.6171	+	15.9075i	0.822667	+	0.787541i
$409$	7.51173	−	5.45759i	0.371431	−	0.269860i	−0.386373	−	0.922343i	$-0.626272\pi$
$409$	7.51173	−	5.45759i	0.371431	−	0.269860i	0.757804	+	0.652482i	$0.226272\pi$
$410$	−18.5242	−	18.9846i	−0.914843	−	0.937585i
$411$	21.6918	−	29.8562i	1.06998	−	1.47270i
$412$	−0.360563	+	0.261964i	−0.0177637	+	0.0129061i
$413$	3.79566	+	5.22428i	0.186772	+	0.257070i
$414$	−0.0911002	+	0.125389i	−0.00447733	+	0.00616252i
$415$	2.65350	+	5.36974i	0.130255	+	0.263590i
$416$	−1.03134	+	0.749310i	−0.0505654	+	0.0367379i
$417$	−3.81760	+	11.7494i	−0.186949	+	0.575369i
$418$		−	25.1756i		−	1.23138i
$419$	−31.1450	−	10.1196i	−1.52153	−	0.494376i	−0.575322	−	0.817927i	$-0.695123\pi$
$419$	−31.1450	−	10.1196i	−1.52153	−	0.494376i	−0.946211	+	0.323551i	$0.895123\pi$
$420$	−0.291324	+	1.70372i	−0.0142152	+	0.0831328i
$421$	−6.47318	−	19.9224i	−0.315484	−	0.970959i	−0.975555	−	0.219756i	$-0.929474\pi$
$421$	−6.47318	−	19.9224i	−0.315484	−	0.970959i	0.660071	−	0.751203i	$-0.270526\pi$
$422$	27.7737	−	9.02422i	1.35200	−	0.439292i
$423$	3.56968	+	2.59352i	0.173564	+	0.126101i
$424$	15.6975			0.762338
$425$	−14.5374	−	14.6173i	−0.705166	−	0.709042i
$426$	24.2510			1.17496
$427$	−5.27739	−	3.83425i	−0.255391	−	0.185552i
$428$	0.0932475	−	0.0302979i	0.00450729	−	0.00146451i
$429$	−8.75110	−	26.9331i	−0.422507	−	1.30034i
$430$	−18.2779	+	2.66537i	−0.881440	+	0.128535i
$431$	26.2222	+	8.52010i	1.26308	+	0.410399i	0.862590	−	0.505903i	$-0.168841\pi$
$431$	26.2222	+	8.52010i	1.26308	+	0.410399i	0.400488	+	0.916302i	$0.368841\pi$
$432$			16.0429i			0.771865i
$433$	9.02906	−	27.7886i	0.433909	−	1.33543i	−0.460291	−	0.887768i	$-0.652255\pi$
$433$	9.02906	−	27.7886i	0.433909	−	1.33543i	0.894200	−	0.447667i	$-0.147745\pi$
$434$	−42.3614	+	30.7774i	−2.03341	+	1.47736i
$435$	−5.61770	+	32.8533i	−0.269348	+	1.57520i
$436$	0.476720	−	0.656149i	0.0228308	−	0.0314238i
$437$	0.151293	+	0.208237i	0.00723733	+	0.00996134i
$438$	−22.7739	+	16.5462i	−1.08818	+	0.790607i
$439$	−5.66224	+	7.79341i	−0.270244	+	0.371959i	−0.922472	−	0.386064i	$-0.873834\pi$
$439$	−5.66224	+	7.79341i	−0.270244	+	0.371959i	0.652228	+	0.758023i	$0.273834\pi$
$440$	39.1158	+	6.68855i	1.86477	+	0.318864i
$441$	−5.72904	+	4.16239i	−0.272811	+	0.198209i
$442$	−8.94555	+	9.34454i	−0.425496	+	0.444474i
$443$	−11.7799			−0.559682			−0.279841	−	0.960046i	$-0.590282\pi$
$443$	−11.7799			−0.559682			−0.279841	+	0.960046i	$0.590282\pi$
$444$	0.0326469	−	0.100477i	0.00154935	−	0.00476842i
$445$	30.5426	−	4.45386i	1.44786	−	0.211133i
$446$	−9.87140	−	30.3811i	−0.467425	−	1.43858i
$447$	−36.2308	+	11.7721i	−1.71366	+	0.556801i
$448$	16.1903	−	22.2841i	0.764921	−	1.05282i
$449$		−	32.8820i		−	1.55180i	−0.630859	−	0.775898i	$-0.717297\pi$
$449$		−	32.8820i		−	1.55180i	0.630859	−	0.775898i	$-0.282703\pi$
$450$	−0.198763	+	8.09401i	−0.00936976	+	0.381555i
$451$	52.7733			2.48500
$452$	−0.828676	+	1.14057i	−0.0389776	+	0.0536481i
$453$	−1.91833	+	0.623303i	−0.0901309	+	0.0292853i
$454$	−5.52958	+	1.79667i	−0.259516	+	0.0843218i
$455$	17.4138	+	2.97765i	0.816372	+	0.139594i
$456$	−14.2694	−	4.63642i	−0.668227	−	0.217120i
$457$	−28.5424			−1.33516			−0.667579	−	0.744539i	$-0.732669\pi$
$457$	−28.5424			−1.33516			−0.667579	+	0.744539i	$0.732669\pi$
$458$	−0.291413	+	0.896878i	−0.0136169	+	0.0419084i
$459$	2.80391	+	15.5063i	0.130875	+	0.723772i
$460$	0.0200122	−	0.00988918i	0.000933073	−	0.000461086i
$461$	1.85076	+	1.34466i	0.0861985	+	0.0626269i	0.630050	−	0.776555i	$-0.283034\pi$
$461$	1.85076	+	1.34466i	0.0861985	+	0.0626269i	−0.543851	+	0.839182i	$0.683034\pi$
$462$	−40.7819	−	56.1314i	−1.89734	−	2.61147i
$463$	−1.48804	+	1.08112i	−0.0691549	+	0.0502440i	−0.621826	−	0.783156i	$-0.713609\pi$
$463$	−1.48804	+	1.08112i	−0.0691549	+	0.0502440i	0.552671	+	0.833400i	$0.313609\pi$
$464$	−18.1273	+	24.9500i	−0.841537	+	1.15828i
$465$	−32.0854	+	31.3071i	−1.48792	+	1.45183i
$466$	6.42354	+	8.84124i	0.297565	+	0.409563i
$467$	4.16421	−	12.8161i	0.192697	−	0.593060i	−0.807299	−	0.590143i	$-0.799071\pi$
$467$	4.16421	−	12.8161i	0.192697	−	0.593060i	0.999996	−	0.00291712i	$-0.000928550\pi$
$468$	0.251811			0.0116399
$469$	−49.2144	−	15.9907i	−2.27251	−	0.738383i
$470$	−5.68017	−	11.4947i	−0.262007	−	0.530209i
$471$	−1.97325	+	0.641148i	−0.0909225	+	0.0295425i
$472$	1.50222	+	4.62336i	0.0691453	+	0.212807i
$473$	21.6012	−	29.7315i	0.993225	−	1.36706i
$474$	1.43265			0.0658037
$475$	12.6821	+	4.46774i	0.581894	+	0.204994i
$476$	−0.682468	+	1.41488i	−0.0312809	+	0.0648511i
$477$	−5.15507	−	3.74538i	−0.236035	−	0.171489i
$478$	0.229545	+	0.706467i	0.0104991	+	0.0323130i
$479$	2.23620	−	0.726586i	0.102175	−	0.0331986i	−0.257484	−	0.966283i	$-0.582893\pi$
$479$	2.23620	−	0.726586i	0.102175	−	0.0331986i	0.359658	+	0.933084i	$0.382893\pi$
$480$	−1.24310	+	2.36743i	−0.0567397	+	0.108058i
$481$	−1.02698	−	0.333687i	−0.0468263	−	0.0152148i
$482$		−	0.342394i		−	0.0155956i
$483$	0.674645	+	0.219205i	0.0306974	+	0.00997420i
$484$	2.58613	−	1.87893i	0.117551	−	0.0854060i
$485$	−9.37216	+	17.8488i	−0.425568	+	0.810472i
$486$	9.43076	−	12.9803i	0.427788	−	0.588799i
$487$	5.37489	+	7.39791i	0.243560	+	0.335231i	0.913243	−	0.407416i	$-0.133570\pi$
$487$	5.37489	+	7.39791i	0.243560	+	0.335231i	−0.669683	+	0.742647i	$0.733570\pi$
$488$	−2.88644	−	3.97285i	−0.130663	−	0.179842i
$489$	0.338288	+	0.245781i	0.0152979	+	0.0111146i
$490$	20.3621	−	2.96929i	0.919867	−	0.134139i
$491$	19.2336	−	13.9740i	0.867999	−	0.630638i	−0.0620504	−	0.998073i	$-0.519764\pi$
$491$	19.2336	−	13.9740i	0.867999	−	0.630638i	0.930049	+	0.367435i	$0.119764\pi$
$492$	−0.534717	+	1.64569i	−0.0241069	+	0.0741934i
$493$	−13.1603	+	27.2837i	−0.592708	+	1.22879i
$494$	2.60727	−	8.02436i	0.117307	−	0.361033i
$495$	−11.2498	−	11.5295i	−0.505642	−	0.518211i
$496$	−39.4492	+	12.8178i	−1.77132	+	0.575537i
$497$	−9.30137	−	28.6267i	−0.417223	−	1.28408i
$498$	4.63379	−	6.37786i	0.207645	−	0.285799i
$499$			26.5198i			1.18719i	0.804764	+	0.593595i	$0.202292\pi$
$499$			26.5198i			1.18719i	−0.804764	+	0.593595i	$0.797708\pi$
$500$	0.567290	−	1.01880i	0.0253700	−	0.0455620i
$501$	19.1684			0.856381
$502$	2.66980	+	1.93972i	0.119159	+	0.0865741i
$503$	−20.7303	+	6.73569i	−0.924319	+	0.300329i	−0.732237	−	0.681050i	$-0.761524\pi$
$503$	−20.7303	+	6.73569i	−0.924319	+	0.300329i	−0.192081	+	0.981379i	$0.561524\pi$
$504$	−10.6645	+	3.46511i	−0.475036	+	0.154348i
$505$	15.3585	−	14.9859i	0.683442	−	0.666865i
$506$	−0.276894	+	0.852193i	−0.0123095	+	0.0378846i
$507$			16.8844i			0.749860i
$508$	−0.0797606	+	0.245478i	−0.00353880	+	0.0108913i
$509$	13.0464	−	9.47874i	0.578270	−	0.420138i	−0.259830	−	0.965654i	$-0.583667\pi$
$509$	13.0464	−	9.47874i	0.578270	−	0.420138i	0.838100	+	0.545517i	$0.183667\pi$
$510$	−8.13845	+	25.8848i	−0.360377	+	1.14620i
$511$	28.2665	+	20.5368i	1.25043	+	0.908494i
$512$	16.6761	−	12.1159i	0.736987	−	0.535452i
$513$	−6.04106	−	8.31480i	−0.266719	−	0.367108i
$514$	7.90194	+	5.74109i	0.348540	+	0.253229i
$515$	8.45969	+	4.44207i	0.372778	+	0.195741i
$516$	0.708281	+	0.974865i	0.0311803	+	0.0429160i
$517$	24.2610	+	7.88289i	1.06700	+	0.346689i
$518$	−2.64560			−0.116241
$519$	−11.3799	+	35.0236i	−0.499520	+	1.53736i
$520$	11.7749	+	6.18285i	0.516364	+	0.271136i
$521$	4.73567	−	1.53871i	0.207474	−	0.0674123i	−0.203436	−	0.979088i	$-0.565211\pi$
$521$	4.73567	−	1.53871i	0.207474	−	0.0674123i	0.410910	+	0.911676i	$0.365211\pi$
$522$	11.3144	−	3.67627i	0.495217	−	0.160906i
$523$	21.9163	+	15.9231i	0.958333	+	0.696270i	0.952763	−	0.303715i	$-0.0982270\pi$
$523$	21.9163	+	15.9231i	0.958333	+	0.696270i	0.00556991	+	0.999984i	$0.498227\pi$
$524$			0.297909i			0.0130142i
$525$	35.5132	−	10.5824i	1.54992	−	0.461854i
$526$	−1.19171			−0.0519610
$527$	−35.8894	+	19.2838i	−1.56337	+	0.840017i
$528$	−16.9844	−	52.2726i	−0.739150	−	2.27487i
$529$	7.10456	+	21.8656i	0.308894	+	0.950678i
$530$	8.20290	+	16.5997i	0.356311	+	0.721047i
$531$	0.609791	−	1.87674i	0.0264627	−	0.0814437i
$532$		−	1.02457i		−	0.0444208i
$533$	16.8207	+	5.46539i	0.728587	+	0.236732i
$534$	−23.8789	−	32.8666i	−1.03334	−	1.42227i
$535$	−1.46800	−	1.50449i	−0.0634672	−	0.0650449i
$536$	−31.5157	−	22.8975i	−1.36127	−	0.989020i
$537$	1.82726	+	2.51501i	0.0788522	+	0.108531i
$538$	19.0112	+	26.1667i	0.819631	+	1.12813i
$539$	−24.0644	+	33.1217i	−1.03653	+	1.42665i
$540$	−0.799077	+	0.394870i	−0.0343868	+	0.0169925i
$541$	20.7307	+	28.5333i	0.891281	+	1.22674i	0.973167	+	0.230102i	$0.0739058\pi$
$541$	20.7307	+	28.5333i	0.891281	+	1.22674i	−0.0818855	+	0.996642i	$0.526094\pi$
$542$	1.87451	−	5.76913i	0.0805169	−	0.247806i
$543$	−42.2026			−1.81109
$544$	−1.68052	+	1.75548i	−0.0720517	+	0.0752654i
$545$	−17.1394	−	2.93072i	−0.734170	−	0.125538i
$546$	−7.18547	−	22.1146i	−0.307510	−	0.946417i
$547$	22.6762	−	7.36794i	0.969564	−	0.315031i	0.218924	−	0.975742i	$-0.429745\pi$
$547$	22.6762	−	7.36794i	0.969564	−	0.315031i	0.750640	+	0.660711i	$0.229745\pi$
$548$	1.53483	+	1.11512i	0.0655645	+	0.0476354i
$549$			1.99339i			0.0850757i
$550$	13.3674	+	44.8593i	0.569988	+	1.91281i
$551$		−	19.7572i		−	0.841683i
$552$	0.432026	+	0.313885i	0.0183882	+	0.0133598i
$553$	−0.549486	−	1.69114i	−0.0233665	−	0.0719148i
$554$	−13.4925	+	4.38397i	−0.573241	+	0.186257i
$555$	−2.24129	+	0.326835i	−0.0951375	+	0.0138734i
$556$	−0.604004	−	0.196253i	−0.0256155	−	0.00832297i
$557$	16.1543			0.684478			0.342239	−	0.939613i	$-0.388815\pi$
$557$	16.1543			0.684478			0.342239	+	0.939613i	$0.388815\pi$
$558$	15.2177	+	4.94453i	0.644217	+	0.209319i
$559$	9.96417	−	7.23939i	0.421440	−	0.306194i
$560$	33.7972	+	5.77910i	1.42819	+	0.244212i
$561$	−25.5522	−	47.5556i	−1.07882	−	2.00780i
$562$	−32.3975	+	23.5381i	−1.36660	+	0.992897i
$563$	−16.9673	+	12.3275i	−0.715087	+	0.519541i	−0.884811	−	0.465951i	$-0.845712\pi$
$563$	−16.9673	+	12.3275i	−0.715087	+	0.519541i	0.169724	+	0.985492i	$0.445712\pi$
$564$	−0.491642	+	0.676687i	−0.0207019	+	0.0284937i
$565$	29.7931	+	5.09443i	1.25341	+	0.214324i
$566$	−1.24764	−	1.71724i	−0.0524424	−	0.0721808i
$567$	−38.5725	−	12.5330i	−1.61989	−	0.526335i
$568$		−	22.6593i		−	0.950765i
$569$	2.44032	−	7.51053i	0.102303	−	0.314858i	−0.886785	−	0.462183i	$-0.847066\pi$
$569$	2.44032	−	7.51053i	0.102303	−	0.314858i	0.989088	+	0.147325i	$0.0470664\pi$
$570$	−2.55374	−	17.5124i	−0.106964	−	0.733514i
$571$	−30.1282	+	9.78923i	−1.26082	+	0.409667i	−0.861788	−	0.507269i	$-0.830655\pi$
$571$	−30.1282	+	9.78923i	−1.26082	+	0.409667i	−0.399036	+	0.916935i	$0.630655\pi$
$572$	1.38456	−	0.449871i	0.0578913	−	0.0188100i
$573$	13.2821	−	18.2813i	0.554870	−	0.763713i
$574$	43.3318			1.80863
$575$	−0.380150	−	0.290717i	−0.0158533	−	0.0121237i
$576$	−8.41718			−0.350716
$577$	11.1705	+	8.11582i	0.465033	+	0.337866i	0.795502	−	0.605950i	$-0.207207\pi$
$577$	11.1705	+	8.11582i	0.465033	+	0.337866i	−0.330469	+	0.943817i	$0.607207\pi$
$578$	−13.6113	+	20.5639i	−0.566155	+	0.855347i
$579$	15.3859	+	47.3529i	0.639416	+	1.96792i
$580$	−1.68890	−	0.288791i	−0.0701278	−	0.0119914i
$581$	−9.30591	−	3.02367i	−0.386074	−	0.125443i
$582$	26.5342			1.09988
$583$	−35.0360	−	11.3839i	−1.45104	−	0.471473i
$584$	15.4602	+	21.2792i	0.639748	+	0.880538i
$585$	−2.39168	−	4.83992i	−0.0988840	−	0.200106i
$586$	−7.84121	−	5.69697i	−0.323917	−	0.235340i
$587$	14.1568	−	10.2855i	0.584312	−	0.424527i	−0.255964	−	0.966686i	$-0.582393\pi$
$587$	14.1568	−	10.2855i	0.584312	−	0.424527i	0.840276	+	0.542159i	$0.182393\pi$
$588$	−0.789045	−	1.08603i	−0.0325397	−	0.0447870i
$589$	15.6193	−	21.4981i	0.643582	−	0.885815i
$590$	−4.10410	+	4.00455i	−0.168963	+	0.164865i
$591$	−4.33947	+	3.15281i	−0.178502	+	0.129689i
$592$	−1.99320	−	0.647628i	−0.0819198	−	0.0266174i
$593$	15.4700			0.635278			0.317639	−	0.948212i	$-0.397110\pi$
$593$	15.4700			0.635278			0.317639	+	0.948212i	$0.397110\pi$
$594$	11.0563	−	34.0276i	0.453643	−	1.39617i
$595$	33.6768	−	0.321128i	1.38061	−	0.0131650i
$596$	−0.605172	−	1.86253i	−0.0247888	−	0.0762921i
$597$	−2.47217	−	7.60856i	−0.101179	−	0.311398i
$598$	−0.176512	+	0.242948i	−0.00721812	+	0.00993489i
$599$	−13.0028			−0.531279			−0.265639	−	0.964072i	$-0.585583\pi$
$599$	−13.0028			−0.531279			−0.265639	+	0.964072i	$0.585583\pi$
$600$	27.8878	+	0.684835i	1.13852	+	0.0279583i
$601$			33.0671i			1.34883i	0.738351	+	0.674417i	$0.235605\pi$
$601$			33.0671i			1.34883i	−0.738351	+	0.674417i	$0.764395\pi$
$602$	17.7366	−	24.4123i	0.722890	−	0.994973i
$603$	4.88650	+	15.0391i	0.198994	+	0.612440i
$604$	−0.0320423	−	0.0986161i	−0.00130378	−	0.00401263i
$605$	−60.6769	−	31.8606i	−2.46687	−	1.29532i
$606$	−26.8611	−	8.72769i	−1.09116	−	0.354538i
$607$		−	6.18978i		−	0.251235i	−0.992079	−	0.125618i	$-0.959909\pi$
$607$		−	6.18978i		−	0.251235i	0.992079	−	0.125618i	$-0.0400913\pi$
$608$	0.489805	−	1.50747i	0.0198642	−	0.0611358i
$609$	−32.0045	−	44.0505i	−1.29689	−	1.78502i
$610$	2.69286	−	5.12841i	0.109031	−	0.207643i
$611$	6.91647	+	5.02511i	0.279811	+	0.203294i
$612$	0.472374	−	0.0854165i	0.0190946	−	0.00345276i
$613$	−25.2480	+	18.3437i	−1.01976	+	0.740896i	−0.966233	−	0.257671i	$-0.917045\pi$
$613$	−25.2480	+	18.3437i	−1.01976	+	0.740896i	−0.0535230	+	0.998567i	$0.517045\pi$
$614$	29.2154	+	21.2262i	1.17904	+	0.856620i
$615$	36.7097	−	5.35316i	1.48028	−	0.215860i
$616$	−52.4474	+	38.1053i	−2.11317	+	1.53530i
$617$	−23.1823	−	7.53240i	−0.933286	−	0.303243i	−0.197380	−	0.980327i	$-0.563243\pi$
$617$	−23.1823	−	7.53240i	−0.933286	−	0.303243i	−0.735906	+	0.677084i	$0.763243\pi$
$618$		−	12.5763i		−	0.505892i
$619$	−0.282342	−	0.0917386i	−0.0113483	−	0.00368728i	0.303337	−	0.952883i	$-0.401899\pi$
$619$	−0.282342	−	0.0917386i	−0.0113483	−	0.00368728i	−0.314686	+	0.949196i	$0.601899\pi$
$620$	−1.60942	−	1.64942i	−0.0646357	−	0.0662424i
$621$	0.113039	+	0.347898i	0.00453610	+	0.0139607i
$622$	1.30558	−	0.424209i	0.0523490	−	0.0170092i
$623$	−29.6381	+	40.7933i	−1.18742	+	1.63435i
$624$		−	18.4201i		−	0.737393i
$625$	−24.9699	−	1.22710i	−0.998795	−	0.0490839i
$626$			29.9854i			1.19846i
$627$	28.4863	+	20.6965i	1.13763	+	0.826539i
$628$	−0.0329597	−	0.101439i	−0.00131523	−	0.00404788i
$629$	−2.03971	−	0.277604i	−0.0813287	−	0.0110688i
$630$	−9.23715	−	9.46676i	−0.368017	−	0.377165i
$631$	10.1925	−	31.3691i	0.405755	−	1.24879i	−0.514508	−	0.857486i	$-0.672025\pi$
$631$	10.1925	−	31.3691i	0.405755	−	1.24879i	0.920263	−	0.391300i	$-0.127975\pi$
$632$		−	1.33862i		−	0.0532474i
$633$	−12.6214	+	38.8447i	−0.501656	+	1.54394i
$634$	16.4054	+	22.5802i	0.651543	+	0.896773i
$635$	5.47576	−	0.798500i	0.217299	−	0.0316875i
$636$	0.709994	−	0.977223i	0.0281531	−	0.0387494i
$637$	−11.1004	+	8.06489i	−0.439812	+	0.319542i
$638$	55.6434	−	40.4273i	2.20294	−	1.60053i
$639$	−5.40646	+	7.44136i	−0.213876	+	0.294376i
$640$	23.9887	+	12.5962i	0.948238	+	0.497907i
$641$	−23.2195	−	31.9589i	−0.917116	−	1.26230i	−0.964677	−	0.263434i	$-0.915145\pi$
$641$	−23.2195	−	31.9589i	−0.917116	−	1.26230i	0.0475614	−	0.998868i	$-0.484855\pi$
$642$	−0.854952	+	2.63127i	−0.0337423	+	0.103848i
$643$			2.51183i			0.0990569i	0.998773	+	0.0495284i	$0.0157718\pi$
$643$			2.51183i			0.0990569i	−0.998773	+	0.0495284i	$0.984228\pi$
$644$	−0.0112688	+	0.0346817i	−0.000444052	+	0.00136665i
$645$	12.0102	−	22.8727i	0.472899	−	0.900612i
$646$	2.16907	−	15.9374i	0.0853409	−	0.627048i
$647$	−2.66807	−	8.21148i	−0.104893	−	0.322827i	0.884813	−	0.465947i	$-0.154286\pi$
$647$	−2.66807	−	8.21148i	−0.104893	−	0.322827i	−0.989705	+	0.143121i	$0.954286\pi$
$648$	−24.7009	−	17.9462i	−0.970341	−	0.704994i
$649$		−	11.4085i		−	0.447824i
$650$	−0.385115	+	15.6826i	−0.0151054	+	0.615123i
$651$		−	73.2338i		−	2.87026i
$652$	−0.0126349	+	0.0173905i	−0.000494822	+	0.000681064i
$653$	14.5652	−	4.73252i	0.569980	−	0.185198i	−0.00982692	−	0.999952i	$-0.503128\pi$
$653$	14.5652	−	4.73252i	0.569980	−	0.185198i	0.579807	+	0.814754i	$0.303128\pi$
$654$	7.07222	+	21.7661i	0.276546	+	0.851120i
$655$	5.72595	−	2.82952i	0.223731	−	0.110559i
$656$	32.6462	+	10.6074i	1.27462	+	0.414149i
$657$		−	10.6769i		−	0.416544i
$658$	19.9206	+	6.47258i	0.776585	+	0.252328i
$659$	−11.9971	+	8.71642i	−0.467342	+	0.339543i	−0.796404	−	0.604765i	$-0.793267\pi$
$659$	−11.9971	+	8.71642i	−0.467342	+	0.339543i	0.329063	+	0.944308i	$0.393267\pi$
$660$	2.18559	−	2.13257i	0.0850738	−	0.0830103i
$661$	−11.6391	−	8.45629i	−0.452708	−	0.328912i	0.337956	−	0.941162i	$-0.390264\pi$
$661$	−11.6391	−	8.45629i	−0.452708	−	0.328912i	−0.790664	+	0.612250i	$0.790264\pi$
$662$	−8.39967	+	6.10271i	−0.326462	+	0.237189i
$663$	−3.21938	−	17.8039i	−0.125030	−	0.691448i
$664$	−5.95927	−	4.32966i	−0.231264	−	0.168023i
$665$	−19.6928	+	9.73133i	−0.763652	+	0.377365i
$666$	0.475197	+	0.654052i	0.0184135	+	0.0253440i
$667$	−0.217299	+	0.668779i	−0.00841387	+	0.0258952i
$668$			0.985397i			0.0381261i
$669$	42.4914	+	13.8063i	1.64281	+	0.533783i
$670$	7.74471	−	45.2924i	0.299204	−	1.74980i
$671$	3.56127	+	10.9605i	0.137481	+	0.423124i
$672$	−1.34987	−	4.15447i	−0.0520723	−	0.160262i
$673$	20.9002	−	28.7667i	0.805645	−	1.10887i	−0.186336	−	0.982486i	$-0.559661\pi$
$673$	20.9002	−	28.7667i	0.805645	−	1.10887i	0.991981	−	0.126389i	$-0.0403387\pi$
$674$			20.7178i			0.798019i
$675$	15.1792	+	11.6082i	0.584247	+	0.446799i
$676$	−0.867980			−0.0333838
$677$	14.5895	−	20.0807i	0.560720	−	0.771766i	−0.430697	−	0.902496i	$-0.641732\pi$
$677$	14.5895	−	20.0807i	0.560720	−	0.771766i	0.991418	+	0.130731i	$0.0417324\pi$
$678$	−12.2935	−	37.8356i	−0.472131	−	1.45307i
$679$	−10.1771	−	31.3219i	−0.390561	−	1.20202i
$680$	24.1860	+	7.60430i	0.927489	+	0.291612i
$681$	2.51285	−	7.73376i	0.0962926	−	0.296358i
$682$	92.5069			3.54227
$683$	17.8560	+	5.80177i	0.683241	+	0.221998i	0.630014	−	0.776584i	$-0.283049\pi$
$683$	17.8560	+	5.80177i	0.683241	+	0.221998i	0.0532272	+	0.998582i	$0.483049\pi$
$684$	−0.253297	+	0.184031i	−0.00968505	+	0.00703660i
$685$	6.85536	−	40.0914i	0.261930	−	1.53181i
$686$	2.04367	−	2.81287i	0.0780275	−	0.107396i
$687$	−0.775255	−	1.06705i	−0.0295778	−	0.0407104i
$688$	19.3388	−	14.0504i	0.737283	−	0.535667i
$689$	−9.98827	−	7.25690i	−0.380523	−	0.276466i
$690$	−0.106167	+	0.620882i	−0.00404170	+	0.0236366i
$691$	−4.56535	−	6.28366i	−0.173674	−	0.239042i	0.713302	−	0.700856i	$-0.247199\pi$
$691$	−4.56535	−	6.28366i	−0.173674	−	0.239042i	−0.886977	+	0.461814i	$0.847199\pi$
$692$	−1.80047	−	0.585008i	−0.0684436	−	0.0222387i
$693$	26.3156			0.999647
$694$	−24.8732	−	8.08179i	−0.944173	−	0.306780i
$695$	1.96473	+	13.4732i	0.0745263	+	0.511069i
$696$	−12.6665	−	38.9836i	−0.480124	−	1.47767i
$697$	33.4081	+	4.54682i	1.26542	+	0.172223i
$698$	−22.7922	−	16.5595i	−0.862697	−	0.626786i
$699$	−15.2846			−0.578117
$700$	0.544014	+	1.82564i	0.0205618	+	0.0690027i
$701$	5.37135			0.202873			0.101437	−	0.994842i	$-0.467656\pi$
$701$	5.37135			0.202873			0.101437	+	0.994842i	$0.467656\pi$
$702$	7.04804	−	9.70079i	0.266011	−	0.366133i
$703$	1.27691	−	0.414894i	0.0481597	−	0.0156480i
$704$	−46.2812	+	15.0377i	−1.74429	+	0.566753i
$705$	17.6758	+	3.02245i	0.665711	+	0.113832i
$706$	3.27034	−	10.0651i	0.123081	−	0.378804i
$707$			35.0551i			1.31838i
$708$	0.355765	+	0.115595i	0.0133705	+	0.00434433i
$709$	−14.7024	−	20.2361i	−0.552160	−	0.759983i	0.438143	−	0.898905i	$-0.355636\pi$
$709$	−14.7024	−	20.2361i	−0.552160	−	0.759983i	−0.990303	+	0.138922i	$0.955636\pi$
$710$	23.9618	−	11.8409i	0.899269	−	0.444381i
$711$	−0.319391	+	0.439604i	−0.0119781	+	0.0164864i
$712$	−30.7094	+	22.3117i	−1.15089	+	0.836167i
$713$	−0.765160	+	0.555921i	−0.0286555	+	0.0208194i
$714$	−20.9808	−	39.0476i	−0.785185	−	1.46132i
$715$	−21.7972	−	22.3390i	−0.815169	−	0.835433i
$716$	−0.129290	+	0.0939347i	−0.00483180	+	0.00351051i
$717$	−0.988076	−	0.321045i	−0.0369004	−	0.0119897i
$718$	−51.1051			−1.90723
$719$	12.1492	+	3.94750i	0.453087	+	0.147217i	0.526666	−	0.850073i	$-0.323442\pi$
$719$	12.1492	+	3.94750i	0.453087	+	0.147217i	−0.0735787	+	0.997289i	$0.523442\pi$
$720$	−4.64185	−	9.39345i	−0.172992	−	0.350073i
$721$	−14.8454	+	4.82358i	−0.552873	+	0.179639i
$722$	−5.27527	−	16.2356i	−0.196325	−	0.604227i
$723$	0.387420	+	0.281477i	0.0144083	+	0.0104683i
$724$		−	2.16952i		−	0.0806297i
$725$	10.4904	+	35.2044i	0.389603	+	1.30746i
$726$			90.2030i			3.34775i
$727$	36.5654	+	26.5663i	1.35613	+	0.985290i	0.998680	+	0.0513593i	$0.0163554\pi$
$727$	36.5654	+	26.5663i	1.35613	+	0.985290i	0.357455	+	0.933930i	$0.383645\pi$
$728$	−20.6632	+	6.71387i	−0.765828	+	0.248832i
$729$	−3.35842	−	10.3362i	−0.124386	−	0.382821i
$730$	−14.4233	+	27.4685i	−0.533831	+	1.01665i
$731$	16.2362	−	16.9604i	0.600518	−	0.627303i
$732$	−0.377877			−0.0139667
$733$	−7.22395	+	22.2330i	−0.266823	+	0.821195i	0.724445	+	0.689332i	$0.242096\pi$
$733$	−7.22395	+	22.2330i	−0.266823	+	0.821195i	−0.991268	+	0.131863i	$0.957904\pi$
$734$	−4.07747	−	5.61216i	−0.150502	−	0.207149i
$735$	−13.3796	+	25.4808i	−0.493516	+	0.939875i
$736$	−0.0331598	+	0.0456405i	−0.00122229	+	0.00168233i
$737$	53.7361	+	73.9613i	1.97939	+	2.72440i
$738$	−7.78315	−	10.7126i	−0.286502	−	0.394336i
$739$	−4.99645	−	3.63013i	−0.183797	−	0.133537i	0.492082	−	0.870549i	$-0.336236\pi$
$739$	−4.99645	−	3.63013i	−0.183797	−	0.133537i	−0.675879	+	0.737012i	$0.736236\pi$
$740$	−0.0168017	−	0.115219i	−0.000617643	−	0.00423553i
$741$	6.93619	+	9.54685i	0.254807	+	0.350712i
$742$	−28.7678	−	9.34724i	−1.05610	−	0.343148i
$743$			43.6067i			1.59978i	0.600149	+	0.799888i	$0.295108\pi$
$743$			43.6067i			1.59978i	−0.600149	+	0.799888i	$0.704892\pi$
$744$	17.0364	−	52.4325i	0.624583	−	1.92227i
$745$	−30.0508	+	29.3219i	−1.10097	+	1.07427i
$746$	13.8087	+	42.4987i	0.505571	+	1.55599i
$747$	0.923985	+	2.84373i	0.0338068	+	0.104047i
$748$	2.44471	−	1.31357i	0.0893874	−	0.0480289i
$749$	3.43395			0.125474
$750$	13.8489	+	29.8486i	0.505690	+	1.08992i
$751$		−	18.0958i		−	0.660325i	−0.943924	−	0.330163i	$-0.892896\pi$
$751$		−	18.0958i		−	0.660325i	0.943924	−	0.330163i	$-0.107104\pi$
$752$	13.4237	+	9.75288i	0.489512	+	0.355651i
$753$	−4.38961	+	1.42627i	−0.159966	+	0.0519762i
$754$	21.9223	−	7.12299i	0.798363	−	0.259404i
$755$	−1.59111	+	1.55252i	−0.0579065	+	0.0565020i
$756$	0.449956	−	1.38482i	0.0163647	−	0.0503655i
$757$	1.68713			0.0613199			0.0306599	−	0.999530i	$-0.490239\pi$
$757$	1.68713			0.0613199			0.0306599	+	0.999530i	$0.490239\pi$
$758$	−27.9906	−	9.09471i	−1.01667	−	0.330335i
$759$	−0.736629	−	1.01388i	−0.0267379	−	0.0368016i
$760$	−16.3630	+	2.38613i	−0.593550	+	0.0865540i
$761$	5.82239	+	4.23022i	0.211062	+	0.153345i	0.688294	−	0.725432i	$-0.258360\pi$
$761$	5.82239	+	4.23022i	0.211062	+	0.153345i	−0.477232	+	0.878777i	$0.658360\pi$
$762$	−4.28108	−	5.89240i	−0.155087	−	0.213459i
$763$	22.9808	−	16.6966i	0.831963	−	0.604456i
$764$	0.939793	+	0.682800i	0.0340005	+	0.0247028i
$765$	−6.12833	−	8.26797i	−0.221570	−	0.298929i
$766$	18.2307	−	13.2454i	0.658701	−	0.478575i
$767$	1.18151	−	3.63630i	0.0426617	−	0.131299i
$768$		−	5.06499i		−	0.182767i
$769$	16.4657	−	50.6761i	0.593767	−	1.82743i	0.0329984	−	0.999455i	$-0.489494\pi$
$769$	16.4657	−	50.6761i	0.593767	−	1.82743i	0.560769	−	0.827972i	$-0.310506\pi$
$770$	−67.7024	−	35.5496i	−2.43983	−	1.28112i
$771$	−12.9921	+	4.22140i	−0.467901	+

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17358 - 0.852653i) q^{2} +(1.92956 - 0.626952i) q^{3} +(0.0322299 + 0.0991936i) q^{4} +(1.60043 - 1.56161i) q^{5} +(-2.79906 - 0.909470i) q^{6} +3.65292i q^{7} +(-0.849779 + 2.61535i) q^{8} +(0.903084 - 0.656129i) q^{9} +(-3.20974 + 0.468058i) q^{10} +(3.79333 - 5.22107i) q^{11} +(0.124379 + 0.171193i) q^{12} +(1.74978 - 1.27129i) q^{13} +(3.11468 - 4.28699i) q^{14} +(2.10907 - 4.01661i) q^{15} +(3.39603 - 2.46736i) q^{16} +(2.85120 - 2.97837i) q^{17} -1.61929 q^{18} +(-0.831011 + 2.55759i) q^{19} +(0.206483 + 0.108422i) q^{20} +(2.29021 + 7.04854i) q^{21} +(-8.90352 + 2.89293i) q^{22} +(0.0562594 - 0.0774344i) q^{23} +5.57925i q^{24} +(0.122747 - 4.99849i) q^{25} -3.13747 q^{26} +(-2.24641 + 3.09191i) q^{27} +(-0.362347 + 0.117734i) q^{28} +(-6.98725 + 2.27030i) q^{29} +(-5.89993 + 2.91550i) q^{30} +(-9.39777 - 3.05352i) q^{31} -0.589409 q^{32} +(4.04610 - 12.4526i) q^{33} +(-5.88561 + 1.06426i) q^{34} +(5.70444 + 5.84625i) q^{35} +(0.0941902 + 0.0684332i) q^{36} +(-0.293460 - 0.403913i) q^{37} +(3.15599 - 2.29296i) q^{38} +(2.57927 - 3.55006i) q^{39} +(2.72415 + 5.51271i) q^{40} +(4.80652 + 6.61561i) q^{41} +(3.32222 - 10.2248i) q^{42} +5.69452 q^{43} +(0.640155 + 0.207999i) q^{44} +(0.420705 - 2.46035i) q^{45} +(-0.132049 + 0.0429054i) q^{46} +(1.22147 + 3.75930i) q^{47} +(5.00592 - 6.89006i) q^{48} -6.34386 q^{49} +(-4.40603 + 5.76145i) q^{50} +(3.63426 - 7.53451i) q^{51} +(0.182499 + 0.132593i) q^{52} +(-1.76396 - 5.42891i) q^{53} +(5.27266 - 1.71319i) q^{54} +(-2.08232 - 14.2797i) q^{55} +(-9.55368 - 3.10418i) q^{56} +5.45603i q^{57} +(10.1358 + 3.29334i) q^{58} +(1.43016 - 1.03907i) q^{59} +(0.466398 + 0.0797509i) q^{60} +(-1.04964 + 1.44470i) q^{61} +(8.42541 + 11.5966i) q^{62} +(2.39679 + 3.29890i) q^{63} +(-6.10034 - 4.43215i) q^{64} +(0.815140 - 4.76709i) q^{65} +(-15.3662 + 11.1642i) q^{66} +(-4.37751 + 13.4726i) q^{67} +(0.387329 + 0.186828i) q^{68} +(0.0600082 - 0.184686i) q^{69} +(-1.70978 - 11.7249i) q^{70} +(-7.83664 + 2.54628i) q^{71} +(0.948586 + 2.91945i) q^{72} +(5.62201 - 7.73803i) q^{73} +0.724242i q^{74} +(-2.89697 - 9.72185i) q^{75} -0.280480 q^{76} +(19.0722 + 13.8567i) q^{77} +(-6.05394 + 1.96704i) q^{78} +(-0.462956 + 0.150424i) q^{79} +(1.58205 - 9.25210i) q^{80} +(-3.43094 + 10.5593i) q^{81} -11.8622i q^{82} +(-0.827740 + 2.54752i) q^{83} +(-0.625357 + 0.454348i) q^{84} +(-0.0879099 - 9.21913i) q^{85} +(-6.68296 - 4.85545i) q^{86} +(-12.0590 + 8.76135i) q^{87} +(10.4314 + 14.3576i) q^{88} +(11.1673 + 8.11352i) q^{89} +(-2.59156 + 2.52870i) q^{90} +(4.64393 + 6.39182i) q^{91} +(0.00949423 + 0.00308486i) q^{92} -20.0480 q^{93} +(1.77189 - 5.45332i) q^{94} +(2.66398 + 5.39096i) q^{95} +(-1.13730 + 0.369531i) q^{96} +(-8.57447 + 2.78601i) q^{97} +(7.44500 + 5.40911i) q^{98} -7.20398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) \) 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

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