LMFDB - Embedded newform 260.2.o.a.27.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(27,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("260.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.7
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23527 + 0.688553i) q^{2} +(-1.59413 - 1.59413i) q^{3} +(1.05179 - 1.70110i) q^{4} +(1.94514 - 1.10291i) q^{5} +(3.06682 + 0.871538i) q^{6} +(0.0942377 - 0.0942377i) q^{7} +(-0.127946 + 2.82553i) q^{8} +2.08249i q^{9} +O(q^{10})$	\(q+(-1.23527 + 0.688553i) q^{2} +(-1.59413 - 1.59413i) q^{3} +(1.05179 - 1.70110i) q^{4} +(1.94514 - 1.10291i) q^{5} +(3.06682 + 0.871538i) q^{6} +(0.0942377 - 0.0942377i) q^{7} +(-0.127946 + 2.82553i) q^{8} +2.08249i q^{9} +(-1.64337 + 2.70173i) q^{10} -2.08771i q^{11} +(-4.38846 + 1.03508i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(-0.0515214 + 0.181297i) q^{14} +(-4.85899 - 1.34262i) q^{15} +(-1.78748 - 3.57840i) q^{16} +(-3.21214 - 3.21214i) q^{17} +(-1.43390 - 2.57244i) q^{18} +3.07287 q^{19} +(0.169716 - 4.46891i) q^{20} -0.300454 q^{21} +(1.43750 + 2.57889i) q^{22} +(-4.44667 - 4.44667i) q^{23} +(4.70822 - 4.30030i) q^{24} +(2.56717 - 4.29065i) q^{25} +(0.386588 - 1.36035i) q^{26} +(-1.46263 + 1.46263i) q^{27} +(-0.0611896 - 0.259426i) q^{28} +0.0603882i q^{29} +(6.92664 - 1.68717i) q^{30} -3.95313i q^{31} +(4.67194 + 3.18951i) q^{32} +(-3.32808 + 3.32808i) q^{33} +(6.17959 + 1.75613i) q^{34} +(0.0793699 - 0.287242i) q^{35} +(3.54252 + 2.19034i) q^{36} +(-3.14507 - 3.14507i) q^{37} +(-3.79583 + 2.11584i) q^{38} +2.25444 q^{39} +(2.86744 + 5.63718i) q^{40} -8.79014 q^{41} +(0.371142 - 0.206878i) q^{42} +(6.26368 + 6.26368i) q^{43} +(-3.55140 - 2.19583i) q^{44} +(2.29680 + 4.05074i) q^{45} +(8.55462 + 2.43108i) q^{46} +(5.57941 - 5.57941i) q^{47} +(-2.85495 + 8.55389i) q^{48} +6.98224i q^{49} +(-0.216808 + 7.06774i) q^{50} +10.2411i q^{51} +(0.459132 + 1.94659i) q^{52} +(-3.86564 + 3.86564i) q^{53} +(0.799646 - 2.81385i) q^{54} +(-2.30256 - 4.06090i) q^{55} +(0.254214 + 0.278329i) q^{56} +(-4.89855 - 4.89855i) q^{57} +(-0.0415805 - 0.0745958i) q^{58} -5.43037 q^{59} +(-7.39457 + 6.85347i) q^{60} +12.0751 q^{61} +(2.72194 + 4.88319i) q^{62} +(0.196249 + 0.196249i) q^{63} +(-7.96726 - 0.723032i) q^{64} +(-0.595547 + 2.15530i) q^{65} +(1.81952 - 6.40264i) q^{66} +(5.51319 - 5.51319i) q^{67} +(-8.84266 + 2.08568i) q^{68} +14.1771i q^{69} +(0.0997379 + 0.409472i) q^{70} +1.82705i q^{71} +(-5.88414 - 0.266446i) q^{72} +(10.5349 - 10.5349i) q^{73} +(6.05056 + 1.71947i) q^{74} +(-10.9322 + 2.74745i) q^{75} +(3.23201 - 5.22726i) q^{76} +(-0.196741 - 0.196741i) q^{77} +(-2.78484 + 1.55230i) q^{78} -7.53432 q^{79} +(-7.42356 - 4.98906i) q^{80} +10.9107 q^{81} +(10.8582 - 6.05248i) q^{82} +(10.7812 + 10.7812i) q^{83} +(-0.316014 + 0.511102i) q^{84} +(-9.79078 - 2.70536i) q^{85} +(-12.0502 - 3.42446i) q^{86} +(0.0962666 - 0.0962666i) q^{87} +(5.89889 + 0.267115i) q^{88} -2.38303i q^{89} +(-5.62632 - 3.42229i) q^{90} +0.133272i q^{91} +(-12.2412 + 2.88727i) q^{92} +(-6.30180 + 6.30180i) q^{93} +(-3.05036 + 10.7338i) q^{94} +(5.97718 - 3.38911i) q^{95} +(-2.36318 - 12.5322i) q^{96} +(8.89152 + 8.89152i) q^{97} +(-4.80764 - 8.62496i) q^{98} +4.34763 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 - 12 * q^8	$ 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) $ 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.23527	+	0.688553i	−0.873468	+	0.486881i
$2$	−1.23527	+	0.688553i	−0.873468	+	0.486881i
$3$	−1.59413	−	1.59413i	−0.920370	−	0.920370i	0.0766851	−	0.997055i	$-0.475566\pi$
$3$	−1.59413	−	1.59413i	−0.920370	−	0.920370i	−0.997055	+	0.0766851i	$0.975566\pi$
$4$	1.05179	−	1.70110i	0.525894	−	0.850550i
$5$	1.94514	−	1.10291i	0.869895	−	0.493238i
$5$	1.94514	−	1.10291i	0.869895	−	0.493238i
$6$	3.06682	+	0.871538i	1.25202	+	0.355804i
$7$	0.0942377	−	0.0942377i	0.0356185	−	0.0356185i	−0.689073	−	0.724692i	$-0.741982\pi$
$7$	0.0942377	−	0.0942377i	0.0356185	−	0.0356185i	0.724692	+	0.689073i	$0.241982\pi$
$8$	−0.127946	+	2.82553i	−0.0452358	+	0.998976i
$9$			2.08249i			0.694163i
$10$	−1.64337	+	2.70173i	−0.519678	+	0.854362i
$11$		−	2.08771i		−	0.629469i	−0.949180	−	0.314734i	$-0.898085\pi$
$11$		−	2.08771i		−	0.629469i	0.949180	−	0.314734i	$-0.101915\pi$
$12$	−4.38846	+	1.03508i	−1.26684	+	0.298803i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$14$	−0.0515214	+	0.181297i	−0.0137697	+	0.0484536i
$15$	−4.85899	−	1.34262i	−1.25459	−	0.346664i
$16$	−1.78748	−	3.57840i	−0.446870	−	0.894599i
$17$	−3.21214	−	3.21214i	−0.779058	−	0.779058i	0.200612	−	0.979671i	$-0.435707\pi$
$17$	−3.21214	−	3.21214i	−0.779058	−	0.779058i	−0.979671	+	0.200612i	$0.935707\pi$
$18$	−1.43390	−	2.57244i	−0.337974	−	0.606329i
$19$	3.07287			0.704965			0.352483	−	0.935818i	$-0.385338\pi$
$19$	3.07287			0.704965			0.352483	+	0.935818i	$0.385338\pi$
$20$	0.169716	−	4.46891i	0.0379496	−	0.999280i
$21$	−0.300454			−0.0655644
$22$	1.43750	+	2.57889i	0.306476	+	0.549821i
$23$	−4.44667	−	4.44667i	−0.927196	−	0.927196i	0.0703283	−	0.997524i	$-0.477595\pi$
$23$	−4.44667	−	4.44667i	−0.927196	−	0.927196i	−0.997524	+	0.0703283i	$0.977595\pi$
$24$	4.70822	−	4.30030i	0.961062	−	0.877794i
$25$	2.56717	−	4.29065i	0.513433	−	0.858129i
$26$	0.386588	−	1.36035i	0.0758161	−	0.266786i
$27$	−1.46263	+	1.46263i	−0.281484	+	0.281484i
$28$	−0.0611896	−	0.259426i	−0.0115637	−	0.0490269i
$29$			0.0603882i			0.0112138i	0.999984	+	0.00560691i	$0.00178474\pi$
$29$			0.0603882i			0.0112138i	−0.999984	+	0.00560691i	$0.998215\pi$
$30$	6.92664	−	1.68717i	1.26463	−	0.308034i
$31$		−	3.95313i		−	0.710004i	−0.934866	−	0.355002i	$-0.884480\pi$
$31$		−	3.95313i		−	0.710004i	0.934866	−	0.355002i	$-0.115520\pi$
$32$	4.67194	+	3.18951i	0.825890	+	0.563831i
$33$	−3.32808	+	3.32808i	−0.579344	+	0.579344i
$34$	6.17959	+	1.75613i	1.05979	+	0.301174i
$35$	0.0793699	−	0.287242i	0.0134160	−	0.0485527i
$36$	3.54252	+	2.19034i	0.590420	+	0.365056i
$37$	−3.14507	−	3.14507i	−0.517047	−	0.517047i	0.399630	−	0.916677i	$-0.369139\pi$
$37$	−3.14507	−	3.14507i	−0.517047	−	0.517047i	−0.916677	+	0.399630i	$0.869139\pi$
$38$	−3.79583	+	2.11584i	−0.615765	+	0.343234i
$39$	2.25444			0.360999
$40$	2.86744	+	5.63718i	0.453382	+	0.891316i
$41$	−8.79014			−1.37279			−0.686394	−	0.727230i	$-0.740808\pi$
$41$	−8.79014			−1.37279			−0.686394	+	0.727230i	$0.740808\pi$
$42$	0.371142	−	0.206878i	0.0572684	−	0.0319220i
$43$	6.26368	+	6.26368i	0.955202	+	0.955202i	0.999039	−	0.0438365i	$-0.0139581\pi$
$43$	6.26368	+	6.26368i	0.955202	+	0.955202i	−0.0438365	+	0.999039i	$0.513958\pi$
$44$	−3.55140	−	2.19583i	−0.535394	−	0.331034i
$45$	2.29680	+	4.05074i	0.342387	+	0.603848i
$46$	8.55462	+	2.43108i	1.26131	+	0.358442i
$47$	5.57941	−	5.57941i	0.813840	−	0.813840i	−0.171367	−	0.985207i	$-0.554818\pi$
$47$	5.57941	−	5.57941i	0.813840	−	0.813840i	0.985207	+	0.171367i	$0.0548185\pi$
$48$	−2.85495	+	8.55389i	−0.412076	+	1.23465i
$49$			6.98224i			0.997463i
$50$	−0.216808	+	7.06774i	−0.0306613	+	0.999530i
$51$			10.2411i			1.43404i
$52$	0.459132	+	1.94659i	0.0636702	+	0.269943i
$53$	−3.86564	+	3.86564i	−0.530987	+	0.530987i	−0.920866	−	0.389879i	$-0.872517\pi$
$53$	−3.86564	+	3.86564i	−0.530987	+	0.530987i	0.389879	+	0.920866i	$0.372517\pi$
$54$	0.799646	−	2.81385i	0.108818	−	0.382916i
$55$	−2.30256	−	4.06090i	−0.310478	−	0.547571i
$56$	0.254214	+	0.278329i	0.0339708	+	0.0371933i
$57$	−4.89855	−	4.89855i	−0.648829	−	0.648829i
$58$	−0.0415805	−	0.0745958i	−0.00545979	−	0.00979491i
$59$	−5.43037			−0.706974			−0.353487	−	0.935439i	$-0.615004\pi$
$59$	−5.43037			−0.706974			−0.353487	+	0.935439i	$0.615004\pi$
$60$	−7.39457	+	6.85347i	−0.954635	+	0.884780i
$61$	12.0751			1.54606			0.773030	−	0.634370i	$-0.218740\pi$
$61$	12.0751			1.54606			0.773030	+	0.634370i	$0.218740\pi$
$62$	2.72194	+	4.88319i	0.345687	+	0.620166i
$63$	0.196249	+	0.196249i	0.0247250	+	0.0247250i
$64$	−7.96726	−	0.723032i	−0.995907	−	0.0903790i
$65$	−0.595547	+	2.15530i	−0.0738685	+	0.267332i
$66$	1.81952	−	6.40264i	0.223967	−	0.788110i
$67$	5.51319	−	5.51319i	0.673543	−	0.673543i	−0.284988	−	0.958531i	$-0.591990\pi$
$67$	5.51319	−	5.51319i	0.673543	−	0.673543i	0.958531	+	0.284988i	$0.0919897\pi$
$68$	−8.84266	+	2.08568i	−1.07233	+	0.252926i
$69$			14.1771i			1.70673i
$70$	0.0997379	+	0.409472i	0.0119210	+	0.0489412i
$71$			1.82705i			0.216831i	0.994106	+	0.108415i	$0.0345777\pi$
$71$			1.82705i			0.216831i	−0.994106	+	0.108415i	$0.965422\pi$
$72$	−5.88414	−	0.266446i	−0.693452	−	0.0314010i
$73$	10.5349	−	10.5349i	1.23301	−	1.23301i	0.270213	−	0.962800i	$-0.412906\pi$
$73$	10.5349	−	10.5349i	1.23301	−	1.23301i	0.962800	−	0.270213i	$-0.0870942\pi$
$74$	6.05056	+	1.71947i	0.703364	+	0.199884i
$75$	−10.9322	+	2.74745i	−1.26235	+	0.317248i
$76$	3.23201	−	5.22726i	0.370737	−	0.599608i
$77$	−0.196741	−	0.196741i	−0.0224207	−	0.0224207i
$78$	−2.78484	+	1.55230i	−0.315321	+	0.175763i
$79$	−7.53432			−0.847677			−0.423839	−	0.905738i	$-0.639318\pi$
$79$	−7.53432			−0.847677			−0.423839	+	0.905738i	$0.639318\pi$
$80$	−7.42356	−	4.98906i	−0.829980	−	0.557794i
$81$	10.9107			1.21230
$82$	10.8582	−	6.05248i	1.19909	−	0.668384i
$83$	10.7812	+	10.7812i	1.18339	+	1.18339i	0.978861	+	0.204524i	$0.0655648\pi$
$83$	10.7812	+	10.7812i	1.18339	+	1.18339i	0.204524	+	0.978861i	$0.434435\pi$
$84$	−0.316014	+	0.511102i	−0.0344799	+	0.0557658i
$85$	−9.79078	−	2.70536i	−1.06196	−	0.293438i
$86$	−12.0502	−	3.42446i	−1.29941	−	0.369270i
$87$	0.0962666	−	0.0962666i	0.0103209	−	0.0103209i
$88$	5.89889	+	0.267115i	0.628824	+	0.0284745i
$89$		−	2.38303i		−	0.252600i	−0.991992	−	0.126300i	$-0.959690\pi$
$89$		−	2.38303i		−	0.252600i	0.991992	−	0.126300i	$-0.0403103\pi$
$90$	−5.62632	−	3.42229i	−0.593066	−	0.360741i
$91$			0.133272i			0.0139707i
$92$	−12.2412	+	2.88727i	−1.27623	+	0.301019i
$93$	−6.30180	+	6.30180i	−0.653466	+	0.653466i
$94$	−3.05036	+	10.7338i	−0.314621	+	1.10711i
$95$	5.97718	−	3.38911i	0.613245	−	0.347715i
$96$	−2.36318	−	12.5322i	−0.241191	−	1.27906i
$97$	8.89152	+	8.89152i	0.902797	+	0.902797i	0.995677	−	0.0928800i	$-0.0296073\pi$
$97$	8.89152	+	8.89152i	0.902797	+	0.902797i	−0.0928800	+	0.995677i	$0.529607\pi$
$98$	−4.80764	−	8.62496i	−0.485645	−	0.871252i
$99$	4.34763			0.436954
$100$	−4.59870	−	8.87986i	−0.459870	−	0.887986i
$101$	8.50140			0.845921			0.422960	−	0.906148i	$-0.360991\pi$
$101$	8.50140			0.845921			0.422960	+	0.906148i	$0.360991\pi$
$102$	−7.05156	−	12.6506i	−0.698208	−	1.25259i
$103$	8.61228	+	8.61228i	0.848593	+	0.848593i	0.989958	−	0.141364i	$-0.0451489\pi$
$103$	8.61228	+	8.61228i	0.848593	+	0.848593i	−0.141364	+	0.989958i	$0.545149\pi$
$104$	−1.90748	−	2.08842i	−0.187044	−	0.204787i
$105$	−0.584426	+	0.331374i	−0.0570341	+	0.0323388i
$106$	2.11341	−	7.43682i	0.205273	−	0.722327i
$107$	7.38762	−	7.38762i	0.714188	−	0.714188i	−0.253221	−	0.967409i	$-0.581490\pi$
$107$	7.38762	−	7.38762i	0.714188	−	0.714188i	0.967409	+	0.253221i	$0.0814899\pi$
$108$	0.949703	+	4.02646i	0.0913852	+	0.387446i
$109$		−	1.01282i		−	0.0970107i	−0.998823	−	0.0485053i	$-0.984554\pi$
$109$		−	1.01282i		−	0.0970107i	0.998823	−	0.0485053i	$-0.0154458\pi$
$110$	5.64043	+	3.43087i	0.537794	+	0.327121i
$111$			10.0273i			0.951749i
$112$	−0.505668	−	0.168772i	−0.0477811	−	0.0159474i
$113$	9.77168	−	9.77168i	0.919243	−	0.919243i	−0.0777317	−	0.996974i	$-0.524768\pi$
$113$	9.77168	−	9.77168i	0.919243	−	0.919243i	0.996974	+	0.0777317i	$0.0247677\pi$
$114$	9.42395	+	2.67812i	0.882634	+	0.250829i
$115$	−13.5537	−	3.74513i	−1.26389	−	0.349235i
$116$	0.102726	+	0.0635157i	0.00953791	+	0.00589728i
$117$	−1.47254	−	1.47254i	−0.136137	−	0.136137i
$118$	6.70798	−	3.73910i	0.617520	−	0.344212i
$119$	−0.605409			−0.0554977
$120$	4.41532	−	13.5575i	0.403061	−	1.23762i
$121$	6.64146			0.603769
$122$	−14.9160	+	8.31436i	−1.35043	+	0.752747i
$123$	14.0126	+	14.0126i	1.26347	+	1.26347i
$124$	−6.72467	−	4.15786i	−0.603894	−	0.373387i
$125$	0.261300	−	11.1773i	0.0233714	−	0.999727i
$126$	−0.377548	−	0.107293i	−0.0336347	−	0.00955839i
$127$	−3.24550	+	3.24550i	−0.287992	+	0.287992i	−0.836286	−	0.548294i	$-0.815277\pi$
$127$	−3.24550	+	3.24550i	−0.287992	+	0.287992i	0.548294	+	0.836286i	$0.315277\pi$
$128$	10.3396	−	4.59274i	0.913898	−	0.405945i
$129$		−	19.9702i		−	1.75828i
$130$	−0.748378	−	3.07245i	−0.0656371	−	0.269471i
$131$			6.82654i			0.596438i	0.954498	+	0.298219i	$0.0963925\pi$
$131$			6.82654i			0.596438i	−0.954498	+	0.298219i	$0.903607\pi$
$132$	2.16096	+	9.16183i	0.188087	+	0.797435i
$133$	0.289580	−	0.289580i	0.0251098	−	0.0251098i
$134$	−3.01416	+	10.6064i	−0.260383	+	0.916254i
$135$	−1.23187	+	4.45818i	−0.106023	+	0.383699i
$136$	9.48698	−	8.66502i	0.813502	−	0.743019i
$137$	−15.3560	−	15.3560i	−1.31195	−	1.31195i	−0.919975	−	0.391978i	$-0.871791\pi$
$137$	−15.3560	−	15.3560i	−1.31195	−	1.31195i	−0.391978	−	0.919975i	$-0.628209\pi$
$138$	−9.76171	−	17.5126i	−0.830972	−	1.49077i
$139$	−13.8537			−1.17505			−0.587527	−	0.809204i	$-0.699898\pi$
$139$	−13.8537			−1.17505			−0.587527	+	0.809204i	$0.699898\pi$
$140$	−0.405146	−	0.437134i	−0.0342411	−	0.0369445i
$141$	−17.7886			−1.49807
$142$	−1.25802	−	2.25690i	−0.105571	−	0.189395i
$143$	1.47623	+	1.47623i	0.123449	+	0.123449i
$144$	7.45197	−	3.72241i	0.620997	−	0.310201i
$145$	0.0666029	+	0.117464i	0.00553107	+	0.00975484i
$146$	−5.75960	+	20.2672i	−0.476668	+	1.67733i
$147$	11.1306	−	11.1306i	0.918035	−	0.918035i
$148$	−8.65803	+	2.04213i	−0.711686	+	0.167862i
$149$		−	0.756913i		−	0.0620087i	−0.999519	−	0.0310044i	$-0.990129\pi$
$149$		−	0.756913i		−	0.0620087i	0.999519	−	0.0310044i	$-0.00987057\pi$
$150$	11.6125	−	10.9213i	0.948157	−	0.891718i
$151$		−	0.572673i		−	0.0466035i	−0.999728	−	0.0233017i	$-0.992582\pi$
$151$		−	0.572673i		−	0.0466035i	0.999728	−	0.0233017i	$-0.00741784\pi$
$152$	−0.393162	+	8.68250i	−0.0318897	+	0.704244i
$153$	6.68924	−	6.68924i	0.540793	−	0.540793i
$154$	0.378495	+	0.107562i	0.0305000	+	0.00866757i
$155$	−4.35996	−	7.68941i	−0.350200	−	0.617628i
$156$	2.37119	−	3.83502i	0.189847	−	0.307048i
$157$	5.93253	+	5.93253i	0.473467	+	0.473467i	0.903035	−	0.429567i	$-0.141334\pi$
$157$	5.93253	+	5.93253i	0.473467	+	0.473467i	−0.429567	+	0.903035i	$0.641334\pi$
$158$	9.30693	−	5.18778i	0.740419	−	0.412718i
$159$	12.3247			0.977409
$160$	12.6053	+	1.05132i	0.996540	+	0.0831139i
$161$	−0.838088			−0.0660506
$162$	−13.4777	+	7.51260i	−1.05891	+	0.590246i
$163$	−7.64242	−	7.64242i	−0.598601	−	0.598601i	0.341339	−	0.939940i	$-0.389119\pi$
$163$	−7.64242	−	7.64242i	−0.598601	−	0.598601i	−0.939940	+	0.341339i	$0.889119\pi$
$164$	−9.24537	+	14.9529i	−0.721942	+	1.16763i
$165$	−2.80301	+	10.1442i	−0.218214	+	0.789723i
$166$	−20.7411	−	5.89425i	−1.60982	−	0.457483i
$167$	−12.9350	+	12.9350i	−1.00094	+	1.00094i	−0.000941800		1.00000i	$0.500300\pi$
$167$	−12.9350	+	12.9350i	−1.00094	+	1.00094i	−1.00000		0.000941800i	$0.999700\pi$
$168$	0.0384419	−	0.848942i	0.00296586	−	0.0654973i
$169$		−	1.00000i		−	0.0769231i
$170$	13.9571	−	3.39962i	1.07046	−	0.260739i
$171$			6.39922i			0.489361i
$172$	17.2432	−	4.06708i	1.31478	−	0.310112i
$173$	−14.9245	+	14.9245i	−1.13469	+	1.13469i	−0.145303	+	0.989387i	$0.546416\pi$
$173$	−14.9245	+	14.9245i	−1.13469	+	1.13469i	−0.989387	+	0.145303i	$0.953584\pi$
$174$	−0.0526306	+	0.185200i	−0.00398992	+	0.0140400i
$175$	−0.162417	−	0.646264i	−0.0122775	−	0.0488530i
$176$	−7.47065	+	3.73174i	−0.563122	+	0.281291i
$177$	8.65671	+	8.65671i	0.650678	+	0.650678i
$178$	1.64084	+	2.94368i	0.122986	+	0.220638i
$179$	19.4084			1.45065			0.725324	−	0.688408i	$-0.241690\pi$
$179$	19.4084			1.45065			0.725324	+	0.688408i	$0.241690\pi$
$180$	9.30646	+	0.353431i	0.693663	+	0.0263432i
$181$	2.31305			0.171927			0.0859637	−	0.996298i	$-0.472603\pi$
$181$	2.31305			0.171927			0.0859637	+	0.996298i	$0.472603\pi$
$182$	−0.0917650	−	0.164627i	−0.00680207	−	0.0122030i
$183$	−19.2493	−	19.2493i	−1.42295	−	1.42295i
$184$	13.1332	−	11.9953i	0.968189	−	0.884304i
$185$	−9.58636	−	2.64888i	−0.704803	−	0.194749i
$186$	3.44531	−	12.1236i	0.252622	−	0.888942i
$187$	−6.70602	+	6.70602i	−0.490393	+	0.490393i
$188$	−3.62277	−	15.3595i	−0.264218	−	1.12021i
$189$			0.275670i			0.0200520i
$190$	−5.04985	+	8.30207i	−0.366355	+	0.602296i
$191$		−	11.2217i		−	0.811974i	−0.913879	−	0.405987i	$-0.866928\pi$
$191$		−	11.2217i		−	0.811974i	0.913879	−	0.405987i	$-0.133072\pi$
$192$	11.5482	+	13.8534i	0.833421	+	0.999786i
$193$	3.78263	−	3.78263i	0.272280	−	0.272280i	−0.557738	−	0.830017i	$-0.688330\pi$
$193$	3.78263	−	3.78263i	0.272280	−	0.272280i	0.830017	+	0.557738i	$0.188330\pi$
$194$	−17.1057	−	4.86115i	−1.22812	−	0.349010i
$195$	4.38520	−	2.48645i	0.314031	−	0.178058i
$196$	11.8775	+	7.34384i	0.848392	+	0.524560i
$197$	10.5230	+	10.5230i	0.749733	+	0.749733i	0.974429	−	0.224696i	$-0.0721388\pi$
$197$	10.5230	+	10.5230i	0.749733	+	0.749733i	−0.224696	+	0.974429i	$0.572139\pi$
$198$	−5.37051	+	2.99358i	−0.381665	+	0.212744i
$199$	−26.8755			−1.90515			−0.952576	−	0.304301i	$-0.901577\pi$
$199$	−26.8755			−1.90515			−0.952576	+	0.304301i	$0.901577\pi$
$200$	11.7949	+	7.80258i	0.834025	+	0.551726i
$201$	−17.5774			−1.23982
$202$	−10.5015	+	5.85366i	−0.738885	+	0.411862i
$203$	0.00569084	+	0.00569084i	0.000399419	+	0.000399419i
$204$	17.4212	+	10.7715i	1.21973	+	0.754156i
$205$	−17.0981	+	9.69475i	−1.19418	+	0.677111i
$206$	−16.5685	−	4.70849i	−1.15438	−	0.328056i
$207$	9.26015	−	9.26015i	0.643625	−	0.643625i
$208$	3.79425	+	1.26637i	0.263084	+	0.0878068i
$209$		−	6.41527i		−	0.443753i
$210$	0.493755	−	0.811745i	0.0340724	−	0.0560157i
$211$			15.1096i			1.04019i	0.854108	+	0.520095i	$0.174103\pi$
$211$			15.1096i			1.04019i	−0.854108	+	0.520095i	$0.825897\pi$
$212$	2.51000	+	10.6417i	0.172388	+	0.730874i
$213$	2.91255	−	2.91255i	0.199565	−	0.199565i
$214$	−4.03894	+	14.2125i	−0.276096	+	0.971545i
$215$	19.0920	+	5.27547i	1.30207	+	0.359784i
$216$	−3.94557	−	4.31985i	−0.268462	−	0.293929i
$217$	−0.372534	−	0.372534i	−0.0252893	−	0.0252893i
$218$	0.697381	+	1.25111i	0.0472326	+	0.0847358i
$219$	−33.5879			−2.26966
$220$	−9.32980	−	0.354317i	−0.629015	−	0.0238881i
$221$	4.54265			0.305572
$222$	−6.90433	−	12.3864i	−0.463388	−	0.831322i
$223$	14.4646	+	14.4646i	0.968622	+	0.968622i	0.999522	−	0.0309000i	$-0.00983736\pi$
$223$	14.4646	+	14.4646i	0.968622	+	0.968622i	−0.0309000	+	0.999522i	$0.509837\pi$
$224$	0.740845	−	0.139700i	0.0494998	−	0.00933413i
$225$	8.93522	+	5.34610i	0.595681	+	0.356406i
$226$	−5.34235	+	18.7990i	−0.355368	+	1.25049i
$227$	13.3452	−	13.3452i	0.885752	−	0.885752i	−0.108360	−	0.994112i	$-0.534560\pi$
$227$	13.3452	−	13.3452i	0.885752	−	0.885752i	0.994112	+	0.108360i	$0.0345600\pi$
$228$	−13.4852	+	3.18068i	−0.893077	+	0.210646i
$229$			10.2433i			0.676897i	0.940985	+	0.338448i	$0.109902\pi$
$229$			10.2433i			0.676897i	−0.940985	+	0.338448i	$0.890098\pi$
$230$	19.3212	−	4.70621i	1.27400	−	0.310318i
$231$			0.627261i			0.0412707i
$232$	−0.170629	−	0.00772644i	−0.0112023	−	0.000507266i
$233$	5.58926	−	5.58926i	0.366165	−	0.366165i	−0.499912	−	0.866076i	$-0.666634\pi$
$233$	5.58926	−	5.58926i	0.366165	−	0.366165i	0.866076	+	0.499912i	$0.166634\pi$
$234$	2.83291	+	0.805064i	0.185193	+	0.0526287i
$235$	4.69915	−	17.0063i	0.306539	−	1.10937i
$236$	−5.71160	+	9.23761i	−0.371794	+	0.601317i
$237$	12.0107	+	12.0107i	0.780177	+	0.780177i
$238$	0.747844	−	0.416856i	0.0484755	−	0.0270208i
$239$	16.4914			1.06674			0.533369	−	0.845883i	$-0.320926\pi$
$239$	16.4914			1.06674			0.533369	+	0.845883i	$0.320926\pi$
$240$	3.88092	+	19.7873i	0.250512	+	1.27727i
$241$	15.4546			0.995520			0.497760	−	0.867315i	$-0.334156\pi$
$241$	15.4546			0.995520			0.497760	+	0.867315i	$0.334156\pi$
$242$	−8.20401	+	4.57300i	−0.527373	+	0.293964i
$243$	−13.0052	−	13.0052i	−0.834282	−	0.834282i
$244$	12.7005	−	20.5410i	0.813064	−	1.31500i
$245$	7.70080	+	13.5815i	0.491986	+	0.867687i
$246$	−26.9578	−	7.66094i	−1.71877	−	0.488443i
$247$	−2.17285	+	2.17285i	−0.138255	+	0.138255i
$248$	11.1697	+	0.505788i	0.709277	+	0.0321176i
$249$		−	34.3731i		−	2.17831i
$250$	7.37338	+	13.9869i	0.466334	+	0.884609i
$251$			4.89967i			0.309264i	0.987972	+	0.154632i	$0.0494193\pi$
$251$			4.89967i			0.309264i	−0.987972	+	0.154632i	$0.950581\pi$
$252$	0.540251	−	0.127427i	0.0340326	−	0.00802712i
$253$	−9.28337	+	9.28337i	−0.583640	+	0.583640i
$254$	1.77437	−	6.24377i	0.111334	−	0.391769i
$255$	11.2951	+	19.9205i	0.707324	+	1.24747i
$256$	−9.60982	+	12.7926i	−0.600614	+	0.799539i
$257$	4.80358	+	4.80358i	0.299639	+	0.299639i	0.840872	−	0.541233i	$-0.182042\pi$
$257$	4.80358	+	4.80358i	0.299639	+	0.299639i	−0.541233	+	0.840872i	$0.682042\pi$
$258$	13.7506	+	24.6686i	0.856072	+	1.53580i
$259$	−0.592768			−0.0368328
$260$	3.03999	+	3.28001i	0.188532	+	0.203417i
$261$	−0.125758			−0.00778421
$262$	−4.70044	−	8.43263i	−0.290394	−	0.520969i
$263$	−2.65042	−	2.65042i	−0.163432	−	0.163432i	0.620653	−	0.784085i	$-0.286867\pi$
$263$	−2.65042	−	2.65042i	−0.163432	−	0.163432i	−0.784085	+	0.620653i	$0.786867\pi$
$264$	−8.97778	−	9.82941i	−0.552544	−	0.604958i
$265$	−3.25576	+	11.7827i	−0.200000	+	0.723805i
$266$	−0.158319	+	0.557101i	−0.00970714	+	0.0341581i
$267$	−3.79885	+	3.79885i	−0.232486	+	0.232486i
$268$	−3.57977	−	15.1772i	−0.218669	−	0.927094i
$269$			22.6452i			1.38070i	0.723475	+	0.690351i	$0.242544\pi$
$269$			22.6452i			1.38070i	−0.723475	+	0.690351i	$0.757456\pi$
$270$	−1.54800	−	6.35527i	−0.0942082	−	0.386770i
$271$		−	26.9231i		−	1.63546i	−0.575602	−	0.817730i	$-0.695232\pi$
$271$		−	26.9231i		−	1.63546i	0.575602	−	0.817730i	$-0.304768\pi$
$272$	−5.75267	+	17.2359i	−0.348807	+	1.04508i
$273$	0.212453	−	0.212453i	0.0128582	−	0.0128582i
$274$	29.5423	+	8.39540i	1.78471	+	0.507185i
$275$	−8.95763	−	5.35950i	−0.540165	−	0.323190i
$276$	24.1167	+	14.9113i	1.45166	+	0.897558i
$277$	−5.20649	−	5.20649i	−0.312828	−	0.312828i	0.533176	−	0.846004i	$-0.320998\pi$
$277$	−5.20649	−	5.20649i	−0.312828	−	0.312828i	−0.846004	+	0.533176i	$0.820998\pi$
$278$	17.1131	−	9.53900i	1.02637	−	0.572111i
$279$	8.23235			0.492858
$280$	0.801455	+	0.261014i	0.0478961	+	0.0155985i
$281$	−9.45951			−0.564307			−0.282154	−	0.959369i	$-0.591049\pi$
$281$	−9.45951			−0.564307			−0.282154	+	0.959369i	$0.591049\pi$
$282$	21.9737	−	12.2484i	1.30852	−	0.729380i
$283$	3.21144	+	3.21144i	0.190900	+	0.190900i	0.796085	−	0.605185i	$-0.206901\pi$
$283$	3.21144	+	3.21144i	0.190900	+	0.190900i	−0.605185	+	0.796085i	$0.706901\pi$
$284$	3.10800	+	1.92167i	0.184426	+	0.114030i
$285$	−14.9311	−	4.12571i	−0.884440	−	0.244386i
$286$	−2.84002	−	0.807084i	−0.167934	−	0.0477238i
$287$	−0.828362	+	0.828362i	−0.0488966	+	0.0488966i
$288$	−6.64212	+	9.72926i	−0.391391	+	0.573302i
$289$			3.63568i			0.213863i
$290$	−0.163153	−	0.0992399i	−0.00958066	−	0.00582757i
$291$		−	28.3485i		−	1.66182i
$292$	−6.84041	−	29.0013i	−0.400305	−	1.69717i
$293$	8.77038	−	8.77038i	0.512371	−	0.512371i	−0.402881	−	0.915252i	$-0.631991\pi$
$293$	8.77038	−	8.77038i	0.512371	−	0.512371i	0.915252	+	0.402881i	$0.131991\pi$
$294$	−6.08529	+	21.4133i	−0.354901	+	1.24885i
$295$	−10.5629	+	5.98923i	−0.614993	+	0.348706i
$296$	9.28890	−	8.48410i	0.539906	−	0.493128i
$297$	3.05355	+	3.05355i	0.177185	+	0.177185i
$298$	0.521175	+	0.934992i	0.0301908	+	0.0541627i
$299$	6.28855			0.363676
$300$	−6.82472	+	21.4866i	−0.394025	+	1.24053i
$301$	1.18055			0.0680457
$302$	0.394316	+	0.707406i	0.0226903	+	0.0407066i
$303$	−13.5523	−	13.5523i	−0.778560	−	0.778560i
$304$	−5.49270	−	10.9960i	−0.315028	−	0.630661i
$305$	23.4878	−	13.3178i	1.34491	−	0.762575i
$306$	−3.65713	+	12.8689i	−0.209064	+	0.735668i
$307$	14.7552	−	14.7552i	0.842126	−	0.842126i	−0.147009	−	0.989135i	$-0.546965\pi$
$307$	14.7552	−	14.7552i	0.842126	−	0.842126i	0.989135	+	0.147009i	$0.0469646\pi$
$308$	−0.541606	+	0.127746i	−0.0308609	+	0.00727901i
$309$		−	27.4582i		−	1.56204i
$310$	10.6803	+	6.49644i	0.606600	+	0.368973i
$311$			12.7852i			0.724982i	0.931987	+	0.362491i	$0.118074\pi$
$311$			12.7852i			0.724982i	−0.931987	+	0.362491i	$0.881926\pi$
$312$	−0.288447	+	6.36998i	−0.0163301	+	0.360629i
$313$	−22.1230	+	22.1230i	−1.25047	+	1.25047i	−0.294954	+	0.955511i	$0.595304\pi$
$313$	−22.1230	+	22.1230i	−1.25047	+	1.25047i	−0.955511	+	0.294954i	$0.904696\pi$
$314$	−11.4131	−	3.24342i	−0.644081	−	0.183037i
$315$	0.598177	+	0.165287i	0.0337035	+	0.00931286i
$316$	−7.92451	+	12.8166i	−0.445789	+	0.720992i
$317$	−3.78179	−	3.78179i	−0.212407	−	0.212407i	0.592882	−	0.805289i	$-0.297990\pi$
$317$	−3.78179	−	3.78179i	−0.212407	−	0.212407i	−0.805289	+	0.592882i	$0.797990\pi$
$318$	−15.2243	+	8.48618i	−0.853736	+	0.475882i
$319$	0.126073			0.00705874
$320$	−16.2949	+	7.38079i	−0.910913	+	0.412599i
$321$	−23.5536			−1.31463
$322$	1.03527	−	0.577068i	0.0576931	−	0.0321588i
$323$	−9.87049	−	9.87049i	−0.549209	−	0.549209i
$324$	11.4758	−	18.5602i	0.637542	−	1.03112i
$325$	1.21868	+	4.84921i	0.0676004	+	0.268986i
$326$	14.7027	+	4.17825i	0.814306	+	0.231412i
$327$	−1.61457	+	1.61457i	−0.0892857	+	0.0892857i
$328$	1.12466	−	24.8368i	0.0620992	−	1.37138i
$329$		−	1.05158i		−	0.0579755i
$330$	−3.52232	−	14.4608i	−0.193898	−	0.796042i
$331$		−	14.0262i		−	0.770949i	−0.922718	−	0.385474i	$-0.874038\pi$
$331$		−	14.0262i		−	0.770949i	0.922718	−	0.385474i	$-0.125962\pi$
$332$	29.6793	−	7.00033i	1.62886	−	0.384193i
$333$	6.54957	−	6.54957i	0.358914	−	0.358914i
$334$	7.07180	−	24.8847i	0.386952	−	1.36163i
$335$	4.64338	−	16.8045i	0.253695	−	0.918128i
$336$	0.537055	+	1.07514i	0.0292988	+	0.0586538i
$337$	−18.0690	−	18.0690i	−0.984283	−	0.984283i	0.0155953	−	0.999878i	$-0.495036\pi$
$337$	−18.0690	−	18.0690i	−0.984283	−	0.984283i	−0.999878	+	0.0155953i	$0.995036\pi$
$338$	0.688553	+	1.23527i	0.0374524	+	0.0671899i
$339$	−31.1546			−1.69209
$340$	−14.8999	+	13.8096i	−0.808062	+	0.748932i
$341$	−8.25300			−0.446925
$342$	−4.40620	−	7.90477i	−0.238260	−	0.427441i
$343$	1.31765	+	1.31765i	0.0711466	+	0.0711466i
$344$	−18.4996	+	16.8968i	−0.997434	+	0.911015i
$345$	15.6361	+	27.5766i	0.841821	+	1.48467i
$346$	8.15950	−	28.7122i	0.438657	−	1.54358i
$347$	8.63601	−	8.63601i	0.463605	−	0.463605i	−0.436230	−	0.899835i	$-0.643687\pi$
$347$	8.63601	−	8.63601i	0.463605	−	0.463605i	0.899835	+	0.436230i	$0.143687\pi$
$348$	−0.0625069	−	0.265011i	−0.00335072	−	0.0142061i
$349$			13.6417i			0.730224i	0.930964	+	0.365112i	$0.118969\pi$
$349$			13.6417i			0.730224i	−0.930964	+	0.365112i	$0.881031\pi$
$350$	0.645616	+	0.686479i	0.0345096	+	0.0366938i
$351$		−	2.06847i		−	0.110407i
$352$	6.65878	−	9.75366i	0.354914	−	0.519872i
$353$	−5.16802	+	5.16802i	−0.275066	+	0.275066i	−0.831136	−	0.556070i	$-0.812309\pi$
$353$	−5.16802	+	5.16802i	−0.275066	+	0.275066i	0.556070	+	0.831136i	$0.312309\pi$
$354$	−16.6540	−	4.73278i	−0.885149	−	0.251544i
$355$	2.01508	+	3.55388i	0.106949	+	0.188620i
$356$	−4.05377	−	2.50644i	−0.214849	−	0.132841i
$357$	0.965099	+	0.965099i	0.0510785	+	0.0510785i
$358$	−23.9746	+	13.3637i	−1.26710	+	0.706293i
$359$	19.8311			1.04665			0.523323	−	0.852135i	$-0.324692\pi$
$359$	19.8311			1.04665			0.523323	+	0.852135i	$0.324692\pi$
$360$	−11.7394	+	5.97141i	−0.618718	+	0.314721i
$361$	−9.55746			−0.503024
$362$	−2.85724	+	1.59266i	−0.150173	+	0.0837081i
$363$	−10.5873	−	10.5873i	−0.555691	−	0.555691i
$364$	0.226709	+	0.140174i	0.0118828	+	0.00734712i
$365$	8.87280	−	32.1109i	0.464423	−	1.68076i
$366$	37.0322	+	10.5239i	1.93571	+	0.550094i
$367$	−16.2512	+	16.2512i	−0.848307	+	0.848307i	−0.989922	−	0.141615i	$-0.954770\pi$
$367$	−16.2512	+	16.2512i	−0.848307	+	0.848307i	0.141615	+	0.989922i	$0.454770\pi$
$368$	−7.96361	+	23.8603i	−0.415132	+	1.24380i
$369$		−	18.3054i		−	0.952939i
$370$	13.6656	−	3.32864i	0.710443	−	0.173048i
$371$			0.728578i			0.0378259i
$372$	4.09183	+	17.3482i	0.212151	+	0.899460i
$373$	−1.04006	+	1.04006i	−0.0538523	+	0.0538523i	−0.733520	−	0.679668i	$-0.762124\pi$
$373$	−1.04006	+	1.04006i	−0.0538523	+	0.0538523i	0.679668	+	0.733520i	$0.262124\pi$
$374$	3.66630	−	12.9012i	0.189580	−	0.667105i
$375$	−18.2346	+	17.4015i	−0.941629	+	0.898608i
$376$	15.0509	+	16.4787i	0.776192	+	0.849822i
$377$	−0.0427009	−	0.0427009i	−0.00219921	−	0.00219921i
$378$	−0.189813	−	0.340527i	−0.00976295	−	0.0175148i
$379$	2.91119			0.149538			0.0747690	−	0.997201i	$-0.476178\pi$
$379$	2.91119			0.149538			0.0747690	+	0.997201i	$0.476178\pi$
$380$	0.521514	−	13.7324i	0.0267531	−	0.704457i
$381$	10.3475			0.530118
$382$	7.72674	+	13.8618i	0.395334	+	0.709233i
$383$	1.22555	+	1.22555i	0.0626229	+	0.0626229i	0.737725	−	0.675102i	$-0.235900\pi$
$383$	1.22555	+	1.22555i	0.0626229	+	0.0626229i	−0.675102	+	0.737725i	$0.735900\pi$
$384$	−23.8040	−	9.16118i	−1.21474	−	0.467504i
$385$	−0.599678	−	0.165701i	−0.0305624	−	0.00844492i
$386$	−2.06803	+	7.27712i	−0.105260	+	0.370395i
$387$	−13.0440	+	13.0440i	−0.663066	+	0.663066i
$388$	24.4774	−	5.77336i	1.24265	−	0.293098i
$389$			30.1820i			1.53029i	0.643860	+	0.765144i	$0.277332\pi$
$389$			30.1820i			1.53029i	−0.643860	+	0.765144i	$0.722668\pi$
$390$	−3.70486	+	6.09088i	−0.187603	+	0.308424i
$391$			28.5667i			1.44468i
$392$	−19.7285	−	0.893351i	−0.996442	−	0.0451210i
$393$	10.8824	−	10.8824i	0.548943	−	0.548943i
$394$	−20.2444	−	5.75312i	−1.01990	−	0.289838i
$395$	−14.6553	+	8.30970i	−0.737390	+	0.418106i
$396$	4.57279	−	7.39576i	0.229791	−	0.371651i
$397$	−25.8661	−	25.8661i	−1.29818	−	1.29818i	−0.929593	−	0.368588i	$-0.879841\pi$
$397$	−25.8661	−	25.8661i	−1.29818	−	1.29818i	−0.368588	−	0.929593i	$-0.620159\pi$
$398$	33.1985	−	18.5052i	1.66409	−	0.927582i
$399$	−0.923256			−0.0462206
$400$	−19.9424	−	1.51689i	−0.997120	−	0.0758444i
$401$	−4.32311			−0.215886			−0.107943	−	0.994157i	$-0.534426\pi$
$401$	−4.32311			−0.215886			−0.107943	+	0.994157i	$0.534426\pi$
$402$	21.7129	−	12.1030i	1.08294	−	0.603643i
$403$	2.79529	+	2.79529i	0.139243	+	0.139243i
$404$	8.94167	−	14.4617i	0.444865	−	0.719498i
$405$	21.2229	−	12.0336i	1.05457	−	0.597952i
$406$	−0.0109482	−	0.00311129i	−0.000543349	−	0.000154410i
$407$	−6.56600	+	6.56600i	−0.325465	+	0.325465i
$408$	−28.9366	−	1.31031i	−1.43258	−	0.0648701i
$409$		−	15.2460i		−	0.753868i	−0.926240	−	0.376934i	$-0.876978\pi$
$409$		−	15.2460i		−	0.753868i	0.926240	−	0.376934i	$-0.123022\pi$
$410$	14.4454	−	23.7486i	0.713408	−	1.17286i
$411$			48.9589i			2.41496i
$412$	23.7087	−	5.59205i	1.16804	−	0.275501i
$413$	−0.511746	+	0.511746i	−0.0251814	+	0.0251814i
$414$	−5.06268	+	17.8149i	−0.248817	+	0.875554i
$415$	32.8616	+	9.08023i	1.61311	+	0.445731i
$416$	−5.55889	+	1.04823i	−0.272547	+	0.0513939i
$417$	22.0845	+	22.0845i	1.08148	+	1.08148i
$418$	4.41725	+	7.92460i	0.216055	+	0.387605i
$419$	12.3653			0.604086			0.302043	−	0.953294i	$-0.402331\pi$
$419$	12.3653			0.604086			0.302043	+	0.953294i	$0.402331\pi$
$420$	−0.0509917	+	1.34270i	−0.00248814	+	0.0655172i
$421$	4.28664			0.208918			0.104459	−	0.994529i	$-0.466689\pi$
$421$	4.28664			0.208918			0.104459	+	0.994529i	$0.466689\pi$
$422$	−10.4038	−	18.6645i	−0.506448	−	0.908573i
$423$	11.6190	+	11.6190i	0.564937	+	0.564937i
$424$	−10.4279	−	11.4171i	−0.506424	−	0.554463i
$425$	−22.0283	+	5.53606i	−1.06853	+	0.268538i
$426$	−1.59234	+	5.60324i	−0.0771493	+	0.271478i
$427$	1.13793	−	1.13793i	0.0550683	−	0.0550683i
$428$	−4.79686	−	20.3373i	−0.231865	−	0.983040i
$429$		−	4.70661i		−	0.227237i
$430$	−27.2163	+	6.62926i	−1.31249	+	0.319692i
$431$			2.48796i			0.119841i	0.998203	+	0.0599203i	$0.0190847\pi$
$431$			2.48796i			0.119841i	−0.998203	+	0.0599203i	$0.980915\pi$
$432$	7.84830	+	2.61945i	0.377601	+	0.126028i
$433$	24.3736	−	24.3736i	1.17132	−	1.17132i	0.189423	−	0.981896i	$-0.439338\pi$
$433$	24.3736	−	24.3736i	1.17132	−	1.17132i	0.981896	−	0.189423i	$-0.0606617\pi$
$434$	0.716690	+	0.203671i	0.0344022	+	0.00977652i
$435$	0.0810787	−	0.293426i	0.00388743	−	0.0140687i
$436$	−1.72291	−	1.06527i	−0.0825124	−	0.0510174i
$437$	−13.6641	−	13.6641i	−0.653641	−	0.653641i
$438$	41.4901	−	23.1270i	1.98248	−	1.10505i
$439$	−10.8728			−0.518932			−0.259466	−	0.965752i	$-0.583547\pi$
$439$	−10.8728			−0.518932			−0.259466	+	0.965752i	$0.583547\pi$
$440$	11.7688	−	5.98639i	0.561056	−	0.285390i
$441$	−14.5404			−0.692401
$442$	−5.61140	+	3.12786i	−0.266907	+	0.148777i
$443$	−10.5626	−	10.5626i	−0.501843	−	0.501843i	0.410167	−	0.912010i	$-0.365470\pi$
$443$	−10.5626	−	10.5626i	−0.501843	−	0.501843i	−0.912010	+	0.410167i	$0.865470\pi$
$444$	17.0574	+	10.5466i	0.809510	+	0.500519i
$445$	−2.62827	−	4.63533i	−0.124592	−	0.219736i
$446$	−27.8274	−	7.90806i	−1.31766	−	0.374458i
$447$	−1.20662	+	1.20662i	−0.0570710	+	0.0570710i
$448$	−0.818953	+	0.682679i	−0.0386919	+	0.0322536i
$449$			4.27598i			0.201796i	0.994897	+	0.100898i	$0.0321716\pi$
$449$			4.27598i			0.201796i	−0.994897	+	0.100898i	$0.967828\pi$
$450$	−14.7185	−	0.451500i	−0.693836	−	0.0212839i
$451$			18.3513i			0.864127i
$452$	−6.34486	−	26.9004i	−0.298437	−	1.26529i
$453$	−0.912914	+	0.912914i	−0.0428924	+	0.0428924i
$454$	−7.29605	+	25.6738i	−0.342421	+	1.20493i
$455$	0.146988	+	0.259233i	0.00689088	+	0.0121531i
$456$	14.4678	−	13.2143i	0.677515	−	0.618814i
$457$	21.4651	+	21.4651i	1.00409	+	1.00409i	0.999992	+	0.00410307i	$0.00130605\pi$
$457$	21.4651	+	21.4651i	1.00409	+	1.00409i	0.00410307	+	0.999992i	$0.498694\pi$
$458$	−7.05306	−	12.6533i	−0.329568	−	0.591248i
$459$	9.39635			0.438584
$460$	−20.6265	+	19.1171i	−0.961714	+	0.891341i
$461$	−0.993976			−0.0462941			−0.0231470	−	0.999732i	$-0.507369\pi$
$461$	−0.993976			−0.0462941			−0.0231470	+	0.999732i	$0.507369\pi$
$462$	−0.431902	−	0.774837i	−0.0200939	−	0.0360487i
$463$	6.21086	+	6.21086i	0.288643	+	0.288643i	0.836544	−	0.547900i	$-0.184573\pi$
$463$	6.21086	+	6.21086i	0.288643	+	0.288643i	−0.547900	+	0.836544i	$0.684573\pi$
$464$	0.216093	−	0.107943i	0.0100319	−	0.00501112i
$465$	−5.30757	+	19.2082i	−0.246133	+	0.890761i
$466$	−3.05575	+	10.7528i	−0.141555	+	0.498112i
$467$	1.63295	−	1.63295i	0.0755640	−	0.0755640i	−0.668315	−	0.743879i	$-0.732984\pi$
$467$	1.63295	−	1.63295i	0.0755640	−	0.0755640i	0.743879	+	0.668315i	$0.232984\pi$
$468$	−4.05374	+	0.956138i	−0.187384	+	0.0441975i
$469$		−	1.03910i		−	0.0479812i
$470$	5.90505	+	24.2431i	0.272380	+	1.11825i
$471$		−	18.9144i		−	0.871530i
$472$	0.694795	−	15.3437i	0.0319805	−	0.706251i
$473$	13.0768	−	13.0768i	0.601270	−	0.601270i
$474$	−23.1064	−	6.56645i	−1.06131	−	0.301607i
$475$	7.88858	−	13.1846i	0.361953	−	0.604951i
$476$	−0.636762	+	1.02986i	−0.0291859	+	0.0472036i
$477$	−8.05015	−	8.05015i	−0.368591	−	0.368591i
$478$	−20.3713	+	11.3552i	−0.931761	+	0.519374i
$479$	17.0521			0.779128			0.389564	−	0.920999i	$-0.372626\pi$
$479$	17.0521			0.779128			0.389564	+	0.920999i	$0.372626\pi$
$480$	−18.4186	−	21.7705i	−0.840690	−	0.993681i
$481$	4.44780			0.202802
$482$	−19.0906	+	10.6413i	−0.869555	+	0.484699i
$483$	1.33602	+	1.33602i	0.0607910	+	0.0607910i
$484$	6.98542	−	11.2978i	0.317519	−	0.513536i
$485$	27.1019	+	7.48872i	1.23063	+	0.340045i
$486$	25.0197	+	7.11016i	1.13491	+	0.322523i
$487$	−8.69411	+	8.69411i	−0.393968	+	0.393968i	−0.876099	−	0.482131i	$-0.839863\pi$
$487$	−8.69411	+	8.69411i	−0.393968	+	0.393968i	0.482131	+	0.876099i	$0.339863\pi$
$488$	−1.54496	+	34.1186i	−0.0699372	+	1.54448i
$489$			24.3660i			1.10187i
$490$	−18.8641	−	11.4744i	−0.852195	−	0.518359i
$491$		−	28.2356i		−	1.27425i	−0.770759	−	0.637127i	$-0.780123\pi$
$491$		−	28.2356i		−	1.27425i	0.770759	−	0.637127i	$-0.219877\pi$
$492$	38.5751	−	9.09854i	1.73910	−	0.410194i
$493$	0.193975	−	0.193975i	0.00873621	−	0.00873621i
$494$	1.18793	−	4.18018i	0.0534477	−	0.188075i
$495$	8.45677	−	4.79506i	0.380104	−	0.215522i
$496$	−14.1459	+	7.06615i	−0.635168	+	0.317280i
$497$	0.172177	+	0.172177i	0.00772319	+	0.00772319i
$498$	23.6677	+	42.4601i	1.06058	+	1.90268i
$499$	21.6541			0.969373			0.484686	−	0.874688i	$-0.338934\pi$
$499$	21.6541			0.969373			0.484686	+	0.874688i	$0.338934\pi$
$500$	−18.7388	−	12.2006i	−0.838027	−	0.545629i
$501$	41.2401			1.84247
$502$	−3.37368	−	6.05242i	−0.150575	−	0.270133i
$503$	−24.6105	−	24.6105i	−1.09733	−	1.09733i	−0.994722	−	0.102604i	$-0.967283\pi$
$503$	−24.6105	−	24.6105i	−1.09733	−	1.09733i	−0.102604	−	0.994722i	$-0.532717\pi$
$504$	−0.579616	+	0.529398i	−0.0258182	+	0.0235813i
$505$	16.5364	−	9.37630i	0.735862	−	0.417240i
$506$	5.07538	−	17.8596i	0.225628	−	0.793955i
$507$	−1.59413	+	1.59413i	−0.0707977	+	0.0707977i
$508$	2.10734	+	8.93450i	0.0934980	+	0.396404i
$509$			9.64884i			0.427677i	0.976869	+	0.213839i	$0.0685966\pi$
$509$			9.64884i			0.427677i	−0.976869	+	0.213839i	$0.931403\pi$
$510$	−27.6688	−	16.8299i	−1.22519	−	0.745241i
$511$		−	1.98556i		−	0.0878362i
$512$	3.06233	−	22.4192i	0.135337	−	0.990800i
$513$	−4.49448	+	4.49448i	−0.198436	+	0.198436i
$514$	−9.24124	−	2.62620i	−0.407614	−	0.115837i
$515$	26.2507	+	7.25353i	1.15675	+	0.319629i
$516$	−33.9713	−	21.0044i	−1.49550	−	0.924669i
$517$	−11.6482	−	11.6482i	−0.512287	−	0.512287i
$518$	0.732229	−	0.408153i	0.0321723	−	0.0179332i
$519$	47.5832			2.08867
$520$	−6.01367	−	1.95850i	−0.263717	−	0.0858859i
$521$	−14.6649			−0.642481			−0.321241	−	0.946998i	$-0.604100\pi$
$521$	−14.6649			−0.642481			−0.321241	+	0.946998i	$0.604100\pi$
$522$	0.155345	−	0.0865909i	0.00679926	−	0.00378998i
$523$	11.9835	+	11.9835i	0.524002	+	0.524002i	0.918778	−	0.394776i	$-0.129178\pi$
$523$	11.9835	+	11.9835i	0.524002	+	0.524002i	−0.394776	+	0.918778i	$0.629178\pi$
$524$	11.6126	+	7.18008i	0.507300	+	0.313663i
$525$	−0.771315	+	1.28914i	−0.0336629	+	0.0562627i
$526$	5.09894	+	1.44903i	0.222324	+	0.0631808i
$527$	−12.6980	+	12.6980i	−0.553134	+	0.553134i
$528$	17.8581	+	5.96030i	0.777172	+	0.259389i
$529$			16.5458i			0.719383i
$530$	−4.09126	−	16.7966i	−0.177713	−	0.729597i
$531$		−	11.3087i		−	0.490755i
$532$	−0.188028	−	0.797182i	−0.00815203	−	0.0345622i
$533$	6.21556	−	6.21556i	0.269226	−	0.269226i
$534$	2.07690	−	7.30832i	0.0898762	−	0.316262i
$535$	6.22208	−	22.5179i	0.269004	−	0.973533i
$536$	14.8723	+	16.2831i	0.642385	+	0.703322i
$537$	−30.9394	−	30.9394i	−1.33513	−	1.33513i
$538$	−15.5924	−	27.9730i	−0.672237	−	1.20600i
$539$	14.5769			0.627871
$540$	6.28814	+	6.78461i	0.270599	+	0.291963i
$541$	−27.1382			−1.16676			−0.583381	−	0.812199i	$-0.698270\pi$
$541$	−27.1382			−1.16676			−0.583381	+	0.812199i	$0.698270\pi$
$542$	18.5380	+	33.2573i	0.796274	+	1.42852i
$543$	−3.68729	−	3.68729i	−0.158237	−	0.158237i
$544$	−4.76176	−	25.2521i	−0.204159	−	1.08267i
$545$	−1.11705	−	1.97008i	−0.0478493	−	0.0843891i
$546$	−0.116152	+	0.408722i	−0.00497084	+	0.0174917i
$547$	−5.39191	+	5.39191i	−0.230541	+	0.230541i	−0.812919	−	0.582377i	$-0.802123\pi$
$547$	−5.39191	+	5.39191i	−0.230541	+	0.230541i	0.582377	+	0.812919i	$0.302123\pi$
$548$	−42.2734	+	9.97083i	−1.80583	+	0.425933i
$549$			25.1463i			1.07322i
$550$	14.7554	+	0.452633i	0.629173	+	0.0193003i
$551$			0.185565i			0.00790535i
$552$	−40.0579	−	1.81391i	−1.70498	−	0.0772051i
$553$	−0.710017	+	0.710017i	−0.0301930	+	0.0301930i
$554$	10.0164	+	2.84648i	0.425555	+	0.120935i
$555$	11.0592	+	19.5045i	0.469438	+	0.827921i
$556$	−14.5711	+	23.5665i	−0.617954	+	0.999442i
$557$	−0.668452	−	0.668452i	−0.0283232	−	0.0283232i	0.692803	−	0.721127i	$-0.256375\pi$
$557$	−0.668452	−	0.668452i	−0.0283232	−	0.0283232i	−0.721127	+	0.692803i	$0.756375\pi$
$558$	−10.1692	+	5.66841i	−0.430496	+	0.239963i
$559$	−8.85818			−0.374661
$560$	−1.16974	+	0.229422i	−0.0494304	+	0.00969486i
$561$	21.3805			0.902686
$562$	11.6851	−	6.51338i	0.492904	−	0.274750i
$563$	14.4182	+	14.4182i	0.607655	+	0.607655i	0.942333	−	0.334677i	$-0.108627\pi$
$563$	14.4182	+	14.4182i	0.607655	+	0.607655i	−0.334677	+	0.942333i	$0.608627\pi$
$564$	−18.7098	+	30.2601i	−0.787826	+	1.27418i
$565$	8.23001	−	29.7846i	0.346239	−	1.25305i
$566$	−6.17824	−	1.75575i	−0.259691	−	0.0737997i
$567$	1.02820	−	1.02820i	0.0431803	−	0.0431803i
$568$	−5.16239	−	0.233764i	−0.216609	−	0.00980852i
$569$			20.5835i			0.862906i	0.902135	+	0.431453i	$0.141999\pi$
$569$			20.5835i			0.862906i	−0.902135	+	0.431453i	$0.858001\pi$
$570$	21.2847	−	5.18446i	0.891517	−	0.217153i
$571$		−	0.606956i		−	0.0254003i	−0.999919	−	0.0127002i	$-0.995957\pi$
$571$		−	0.606956i		−	0.0254003i	0.999919	−	0.0127002i	$-0.00404270\pi$
$572$	4.06391	−	0.958536i	0.169921	−	0.0400784i
$573$	−17.8888	+	17.8888i	−0.747316	+	0.747316i
$574$	0.452880	−	1.59362i	0.0189028	−	0.0665165i
$575$	−30.4945	+	7.66375i	−1.27171	+	0.319601i
$576$	1.50571	−	16.5917i	0.0627377	−	0.691322i
$577$	20.2057	+	20.2057i	0.841174	+	0.841174i	0.989012	−	0.147838i	$-0.0472314\pi$
$577$	20.2057	+	20.2057i	0.841174	+	0.841174i	−0.147838	+	0.989012i	$0.547231\pi$
$578$	−2.50336	−	4.49105i	−0.104126	−	0.186803i
$579$	−12.0600			−0.501196
$580$	0.269870	+	0.0102488i	0.0112057	+	0.000425559i
$581$	2.03198			0.0843008
$582$	19.5194	+	35.0180i	0.809106	+	1.45154i
$583$	8.07034	+	8.07034i	0.334239	+	0.334239i
$584$	28.4187	+	31.1145i	1.17598	+	1.28753i
$585$	−4.48839	−	1.24022i	−0.185572	−	0.0512768i
$586$	−4.79492	+	16.8727i	−0.198076	+	0.697003i
$587$	−27.3636	+	27.3636i	−1.12942	+	1.12942i	−0.139147	+	0.990272i	$0.544436\pi$
$587$	−27.3636	+	27.3636i	−1.12942	+	1.12942i	−0.990272	+	0.139147i	$0.955564\pi$
$588$	−7.22721	−	30.6413i	−0.298045	−	1.26362i
$589$		−	12.1475i		−	0.500528i
$590$	8.92409	−	14.6714i	0.367399	−	0.604012i
$591$		−	33.5500i		−	1.38006i
$592$	−5.63255	+	16.8761i	−0.231496	+	0.693602i
$593$	−22.7433	+	22.7433i	−0.933954	+	0.933954i	−0.997950	−	0.0639961i	$-0.979615\pi$
$593$	−22.7433	+	22.7433i	−0.933954	+	0.933954i	0.0639961	+	0.997950i	$0.479615\pi$
$594$	−5.87450	−	1.66943i	−0.241034	−	0.0684976i
$595$	−1.17761	+	0.667713i	−0.0482772	+	0.0273736i
$596$	−1.28758	−	0.796112i	−0.0527415	−	0.0326100i
$597$	42.8429	+	42.8429i	1.75345	+	1.75345i
$598$	−7.76806	+	4.33000i	−0.317660	+	0.177067i
$599$	−10.1945			−0.416534			−0.208267	−	0.978072i	$-0.566782\pi$
$599$	−10.1945			−0.416534			−0.208267	+	0.978072i	$0.566782\pi$
$600$	−6.36426	−	31.2409i	−0.259820	−	1.27540i
$601$	−29.0983			−1.18694			−0.593471	−	0.804855i	$-0.702243\pi$
$601$	−29.0983			−1.18694			−0.593471	+	0.804855i	$0.702243\pi$
$602$	−1.45830	+	0.812871i	−0.0594358	+	0.0331301i
$603$	11.4811	+	11.4811i	0.467548	+	0.467548i
$604$	−0.974174	−	0.602331i	−0.0396386	−	0.0245085i
$605$	12.9186	−	7.32495i	0.525216	−	0.297802i
$606$	26.0723	+	7.40929i	1.05911	+	0.300982i
$607$	−33.7644	+	33.7644i	−1.37045	+	1.37045i	−0.510687	+	0.859767i	$0.670609\pi$
$607$	−33.7644	+	33.7644i	−1.37045	+	1.37045i	−0.859767	+	0.510687i	$0.829391\pi$
$608$	14.3563	+	9.80096i	0.582224	+	0.397481i
$609$		−	0.0181439i		−	0.000735227i
$610$	−19.8438	+	32.6237i	−0.803453	+	1.32090i
$611$			7.89047i			0.319214i
$612$	−4.34340	−	18.4147i	−0.175571	−	0.744372i
$613$	−22.7265	+	22.7265i	−0.917913	+	0.917913i	−0.996877	−	0.0789647i	$-0.974839\pi$
$613$	−22.7265	+	22.7265i	−0.917913	+	0.917913i	0.0789647	+	0.996877i	$0.474839\pi$
$614$	−8.06695	+	28.3865i	−0.325556	+	1.14559i
$615$	42.7112	+	11.8018i	1.72228	+	0.475896i
$616$	0.581070	−	0.530726i	0.0234120	−	0.0213835i
$617$	−6.40115	−	6.40115i	−0.257700	−	0.257700i	0.566418	−	0.824118i	$-0.308329\pi$
$617$	−6.40115	−	6.40115i	−0.257700	−	0.257700i	−0.824118	+	0.566418i	$0.808329\pi$
$618$	18.9064	+	33.9183i	0.760527	+	1.36439i
$619$	−18.4358			−0.740998			−0.370499	−	0.928833i	$-0.620813\pi$
$619$	−18.4358			−0.740998			−0.370499	+	0.928833i	$0.620813\pi$
$620$	−17.6662	−	0.670908i	−0.709492	−	0.0269443i
$621$	13.0077			0.521981
$622$	−8.80329	−	15.7932i	−0.352980	−	0.633249i
$623$	−0.224571	−	0.224571i	−0.00899724	−	0.00899724i
$624$	−4.02976	−	8.06727i	−0.161320	−	0.322949i
$625$	−11.8193	−	22.0296i	−0.472772	−	0.881185i
$626$	12.0950	−	42.5608i	0.483415	−	1.70107i
$627$	−10.2268	+	10.2268i	−0.408417	+	0.408417i
$628$	16.3316	−	3.85206i	0.651701	−	0.153714i
$629$			20.2048i			0.805619i
$630$	−0.852720	+	0.207703i	−0.0339732	+	0.00827509i
$631$		−	42.8895i		−	1.70740i	−0.520763	−	0.853701i	$-0.674352\pi$
$631$		−	42.8895i		−	1.70740i	0.520763	−	0.853701i	$-0.325648\pi$
$632$	0.963987	−	21.2885i	0.0383454	−	0.846810i
$633$	24.0867	−	24.0867i	0.957360	−	0.957360i
$634$	7.27551	+	2.06757i	0.288947	+	0.0821138i
$635$	−2.73346	+	9.89246i	−0.108474	+	0.392570i
$636$	12.9629	−	20.9655i	0.514014	−	0.831335i
$637$	−4.93719	−	4.93719i	−0.195619	−	0.195619i
$638$	−0.155735	+	0.0868081i	−0.00616559	+	0.00343677i
$639$	−3.80481			−0.150516
$640$	15.0466	−	20.3372i	0.594767	−	0.803898i
$641$	−0.421416			−0.0166449			−0.00832246	−	0.999965i	$-0.502649\pi$
$641$	−0.421416			−0.0166449			−0.00832246	+	0.999965i	$0.502649\pi$
$642$	29.0951	−	16.2179i	1.14829	−	0.640070i
$643$	28.3784	+	28.3784i	1.11914	+	1.11914i	0.991868	+	0.127268i	$0.0406208\pi$
$643$	28.3784	+	28.3784i	1.11914	+	1.11914i	0.127268	+	0.991868i	$0.459379\pi$
$644$	−0.881492	+	1.42567i	−0.0347356	+	0.0561793i
$645$	−22.0254	−	38.8449i	−0.867249	−	1.52952i
$646$	18.9891	+	5.39637i	0.747116	+	0.212317i
$647$	−18.8470	+	18.8470i	−0.740953	+	0.740953i	−0.972762	−	0.231808i	$-0.925536\pi$
$647$	−18.8470	+	18.8470i	−0.740953	+	0.740953i	0.231808	+	0.972762i	$0.425536\pi$
$648$	−1.39598	+	30.8286i	−0.0548394	+	1.21106i
$649$			11.3370i			0.445018i
$650$	−4.84434	−	5.15096i	−0.190011	−	0.202037i
$651$			1.18773i			0.0465510i
$652$	−21.0387	+	4.96231i	−0.823941	+	0.194339i
$653$	−0.597495	+	0.597495i	−0.0233818	+	0.0233818i	−0.718701	−	0.695319i	$-0.755263\pi$
$653$	−0.597495	+	0.597495i	−0.0233818	+	0.0233818i	0.695319	+	0.718701i	$0.255263\pi$
$654$	0.882712	−	3.10614i	0.0345168	−	0.121460i
$655$	7.52908	+	13.2786i	0.294185	+	0.518838i
$656$	15.7122	+	31.4546i	0.613458	+	1.22809i
$657$	21.9388	+	21.9388i	0.855912	+	0.855912i
$658$	0.724069	+	1.29899i	0.0282271	+	0.0506398i
$659$	42.0413			1.63770			0.818848	−	0.574010i	$-0.194613\pi$
$659$	42.0413			1.63770			0.818848	+	0.574010i	$0.194613\pi$
$660$	14.3081	+	15.4377i	0.556941	+	0.600913i
$661$	30.0939			1.17052			0.585258	−	0.810847i	$-0.300993\pi$
$661$	30.0939			1.17052			0.585258	+	0.810847i	$0.300993\pi$
$662$	9.65778	+	17.3261i	0.375360	+	0.673400i
$663$	−7.24157	−	7.24157i	−0.281239	−	0.281239i
$664$	−31.8419	+	29.0831i	−1.23571	+	1.12864i
$665$	0.243893	−	0.882657i	0.00945778	−	0.0342280i
$666$	−3.58077	+	12.6002i	−0.138752	+	0.488249i
$667$	0.268527	−	0.268527i	0.0103974	−	0.0103974i
$668$	8.39885	+	35.6086i	0.324961	+	1.37774i
$669$		−	46.1169i		−	1.78298i
$670$	5.83497	+	23.9553i	0.225424	+	0.925475i
$671$		−	25.2093i		−	0.973196i
$672$	−1.40370	−	0.958301i	−0.0541490	−	0.0369673i
$673$	−11.9962	+	11.9962i	−0.462419	+	0.462419i	−0.899448	−	0.437028i	$-0.856031\pi$
$673$	−11.9962	+	11.9962i	−0.462419	+	0.462419i	0.437028	+	0.899448i	$0.356031\pi$
$674$	34.7616	+	9.87866i	1.33897	+	0.380512i
$675$	2.52082	+	10.0305i	0.0970262	+	0.386072i
$676$	−1.70110	−	1.05179i	−0.0654269	−	0.0404534i
$677$	18.8444	+	18.8444i	0.724250	+	0.724250i	0.969468	−	0.245218i	$-0.0788596\pi$
$677$	18.8444	+	18.8444i	0.724250	+	0.724250i	−0.245218	+	0.969468i	$0.578860\pi$
$678$	38.4844	−	21.4516i	1.47798	−	0.823845i
$679$	1.67583			0.0643125
$680$	8.89678	−	27.3180i	0.341176	−	1.04760i
$681$	−42.5479			−1.63044
$682$	10.1947	−	5.68263i	0.390375	−	0.217599i
$683$	−3.30342	−	3.30342i	−0.126402	−	0.126402i	0.641076	−	0.767478i	$-0.278488\pi$
$683$	−3.30342	−	3.30342i	−0.126402	−	0.126402i	−0.767478	+	0.641076i	$0.778488\pi$
$684$	10.8857	+	6.73063i	0.416226	+	0.257352i
$685$	−46.8060	−	12.9333i	−1.78836	−	0.494156i
$686$	−2.53493	−	0.720384i	−0.0967842	−	0.0275044i
$687$	16.3291	−	16.3291i	0.622996	−	0.622996i
$688$	11.2177	−	33.6101i	0.427671	−	1.28137i
$689$		−	5.46684i		−	0.208270i
$690$	−38.3028	−	23.2982i	−1.45816	−	0.886948i
$691$		−	20.9759i		−	0.797959i	−0.916960	−	0.398980i	$-0.869364\pi$
$691$		−	20.9759i		−	0.797959i	0.916960	−	0.398980i	$-0.130636\pi$
$692$	9.69066	+	41.0855i	0.368384	+	1.56184i
$693$	0.409711	−	0.409711i	0.0155636	−	0.0155636i
$694$	−4.72146	+	16.6142i	−0.179224	+	0.630665i
$695$	−26.9474	+	15.2794i	−1.02217	+	0.579581i
$696$	0.259687	+	0.284321i	0.00984342	+	0.0107772i
$697$	28.2351	+	28.2351i	1.06948	+	1.06948i
$698$	−9.39304	−	16.8512i	−0.355532	−	0.637827i
$699$	−17.8200			−0.674014
$700$	−1.27019	−	0.403447i	−0.0480086	−	0.0152488i
$701$	22.5178			0.850485			0.425242	−	0.905080i	$-0.360189\pi$
$701$	22.5178			0.850485			0.425242	+	0.905080i	$0.360189\pi$
$702$	1.42425	+	2.55512i	0.0537550	+	0.0964370i
$703$	−9.66440	−	9.66440i	−0.364500	−	0.364500i
$704$	−1.50948	+	16.6333i	−0.0568907	+	0.626892i
$705$	−34.6013	+	19.6192i	−1.30316	+	0.738903i
$706$	2.82545	−	9.94236i	0.106337	−	0.374186i
$707$	0.801152	−	0.801152i	0.0301304	−	0.0301304i
$708$	23.8310	−	5.62090i	0.895622	−	0.211246i
$709$		−	30.7947i		−	1.15652i	−0.815853	−	0.578260i	$-0.803732\pi$
$709$		−	30.7947i		−	1.15652i	0.815853	−	0.578260i	$-0.196268\pi$
$710$	−4.93620	−	3.00251i	−0.185252	−	0.112682i
$711$		−	15.6901i		−	0.588426i
$712$	6.73332	+	0.304899i	0.252342	+	0.0114266i
$713$	−17.5783	+	17.5783i	−0.658312	+	0.658312i
$714$	−1.85668	−	0.527637i	−0.0694846	−	0.0197463i
$715$	4.49965	+	1.24333i	0.168277	+	0.0464979i
$716$	20.4135	−	33.0155i	0.762888	−	1.23385i
$717$	−26.2893	−	26.2893i	−0.981793	−	0.981793i
$718$	−24.4968	+	13.6548i	−0.914211	+	0.509591i
$719$	−47.2247			−1.76118			−0.880592	−	0.473875i	$-0.842855\pi$
$719$	−47.2247			−1.76118			−0.880592	+	0.473875i	$0.842855\pi$
$720$	10.3897	−	15.4595i	0.387199	−	0.576141i
$721$	1.62320			0.0604512
$722$	11.8060	−	6.58082i	0.439376	−	0.244913i
$723$	−24.6366	−	24.6366i	−0.916247	−	0.916247i
$724$	2.43284	−	3.93472i	0.0904156	−	0.146233i
$725$	0.259105	+	0.155027i	0.00962290	+	0.00575755i
$726$	20.3682	+	5.78829i	0.755934	+	0.214823i
$727$	13.5916	−	13.5916i	0.504083	−	0.504083i	−0.408621	−	0.912704i	$-0.633990\pi$
$727$	13.5916	−	13.5916i	0.504083	−	0.504083i	0.912704	+	0.408621i	$0.133990\pi$
$728$	−0.376565	−	0.0170517i	−0.0139564	−	0.000631977i
$729$			8.73169i			0.323396i
$730$	11.1498	+	45.7750i	0.412671	+	1.69421i
$731$		−	40.2396i		−	1.48832i
$732$	−52.9911	+	12.4988i	−1.95861	+	0.461968i
$733$	6.55024	−	6.55024i	0.241939	−	0.241939i	−0.575713	−	0.817652i	$-0.695276\pi$
$733$	6.55024	−	6.55024i	0.241939	−	0.241939i	0.817652	+	0.575713i	$0.195276\pi$
$734$	8.88483	−	31.2645i	0.327945	−	1.15399i
$735$	9.37452	−	33.9266i	0.345784	−	1.25140i
$736$	−6.59187	−	34.9573i	−0.242980	−	1.28854i
$737$	−11.5099	−	11.5099i	−0.423974	−	0.423974i
$738$	12.6042	+	22.6121i	0.463967	+	0.832362i
$739$	−3.90879			−0.143787			−0.0718936	−	0.997412i	$-0.522904\pi$
$739$	−3.90879			−0.143787			−0.0718936	+	0.997412i	$0.522904\pi$
$740$	−14.5888	+	13.5213i	−0.536296	+	0.497052i
$741$	6.92760			0.254492
$742$	−0.501665	−	0.899991i	−0.0184167	−	0.0330397i
$743$	−26.9910	−	26.9910i	−0.990204	−	0.990204i	0.00974863	−	0.999952i	$-0.496897\pi$
$743$	−26.9910	−	26.9910i	−0.990204	−	0.990204i	−0.999952	+	0.00974863i	$0.996897\pi$
$744$	−16.9996	−	18.6122i	−0.623237	−	0.682357i
$745$	−0.834809	−	1.47230i	−0.0305850	−	0.0539410i
$746$	0.568620	−	2.00089i	0.0208186	−	0.0732579i
$747$	−22.4516	+	22.4516i	−0.821462	+	0.821462i
$748$	4.35429	+	18.4609i	0.159209	+	0.674998i
$749$		−	1.39238i		−	0.0508766i
$750$	10.5428	−	34.0510i	0.384968	−	1.24337i
$751$			3.54388i			0.129318i	0.997907	+	0.0646591i	$0.0205960\pi$
$751$			3.54388i			0.129318i	−0.997907	+	0.0646591i	$0.979404\pi$
$752$	−29.9384	−	9.99224i	−1.09174	−	0.364379i
$753$	7.81070	−	7.81070i	0.284638	−	0.284638i
$754$	0.0821491	+	0.0233453i	0.00299169	+	0.000850187i
$755$	−0.631608	−	1.11393i	−0.0229866	−	0.0405401i
$756$	0.468942	+	0.289946i	0.0170553	+	0.0105453i
$757$	−20.7879	−	20.7879i	−0.755551	−	0.755551i	0.219959	−	0.975509i	$-0.429408\pi$
$757$	−20.7879	−	20.7879i	−0.755551	−	0.755551i	−0.975509	+	0.219959i	$0.929408\pi$
$758$	−3.59611	+	2.00451i	−0.130617	+	0.0728072i
$759$	29.5978			1.07433
$760$	8.81128	+	17.3223i	0.319619	+	0.628347i
$761$	16.3149			0.591414			0.295707	−	0.955279i	$-0.404445\pi$
$761$	16.3149			0.591414			0.295707	+	0.955279i	$0.404445\pi$
$762$	−12.7819	+	7.12479i	−0.463041	+	0.258104i
$763$	−0.0954459	−	0.0954459i	−0.00345537	−	0.00345537i
$764$	−19.0892	−	11.8029i	−0.690624	−	0.427012i
$765$	5.63389	−	20.3892i	0.203694	−	0.737173i
$766$	−2.35775	−	0.670032i	−0.0851890	−	0.0242092i
$767$	3.83985	−	3.83985i	0.138649	−	0.138649i
$768$	35.7124	−	5.07380i	1.28866	−	0.183085i
$769$		−	34.6856i		−	1.25080i	−0.780306	−	0.625398i	$-0.784937\pi$
$769$		−	34.6856i		−	1.25080i	0.780306	−	0.625398i	$-0.215063\pi$
$770$	0.854858	−	0.208224i	0.0308070	−	0.00750387i
$771$		−	15.3150i		−	0.551557i
$772$	−2.45610	−	10.4132i	−0.0883971	−

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23527 + 0.688553i) q^{2} +(-1.59413 - 1.59413i) q^{3} +(1.05179 - 1.70110i) q^{4} +(1.94514 - 1.10291i) q^{5} +(3.06682 + 0.871538i) q^{6} +(0.0942377 - 0.0942377i) q^{7} +(-0.127946 + 2.82553i) q^{8} +2.08249i q^{9} +O(q^{10})\)	\(q+(-1.23527 + 0.688553i) q^{2} +(-1.59413 - 1.59413i) q^{3} +(1.05179 - 1.70110i) q^{4} +(1.94514 - 1.10291i) q^{5} +(3.06682 + 0.871538i) q^{6} +(0.0942377 - 0.0942377i) q^{7} +(-0.127946 + 2.82553i) q^{8} +2.08249i q^{9} +(-1.64337 + 2.70173i) q^{10} -2.08771i q^{11} +(-4.38846 + 1.03508i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(-0.0515214 + 0.181297i) q^{14} +(-4.85899 - 1.34262i) q^{15} +(-1.78748 - 3.57840i) q^{16} +(-3.21214 - 3.21214i) q^{17} +(-1.43390 - 2.57244i) q^{18} +3.07287 q^{19} +(0.169716 - 4.46891i) q^{20} -0.300454 q^{21} +(1.43750 + 2.57889i) q^{22} +(-4.44667 - 4.44667i) q^{23} +(4.70822 - 4.30030i) q^{24} +(2.56717 - 4.29065i) q^{25} +(0.386588 - 1.36035i) q^{26} +(-1.46263 + 1.46263i) q^{27} +(-0.0611896 - 0.259426i) q^{28} +0.0603882i q^{29} +(6.92664 - 1.68717i) q^{30} -3.95313i q^{31} +(4.67194 + 3.18951i) q^{32} +(-3.32808 + 3.32808i) q^{33} +(6.17959 + 1.75613i) q^{34} +(0.0793699 - 0.287242i) q^{35} +(3.54252 + 2.19034i) q^{36} +(-3.14507 - 3.14507i) q^{37} +(-3.79583 + 2.11584i) q^{38} +2.25444 q^{39} +(2.86744 + 5.63718i) q^{40} -8.79014 q^{41} +(0.371142 - 0.206878i) q^{42} +(6.26368 + 6.26368i) q^{43} +(-3.55140 - 2.19583i) q^{44} +(2.29680 + 4.05074i) q^{45} +(8.55462 + 2.43108i) q^{46} +(5.57941 - 5.57941i) q^{47} +(-2.85495 + 8.55389i) q^{48} +6.98224i q^{49} +(-0.216808 + 7.06774i) q^{50} +10.2411i q^{51} +(0.459132 + 1.94659i) q^{52} +(-3.86564 + 3.86564i) q^{53} +(0.799646 - 2.81385i) q^{54} +(-2.30256 - 4.06090i) q^{55} +(0.254214 + 0.278329i) q^{56} +(-4.89855 - 4.89855i) q^{57} +(-0.0415805 - 0.0745958i) q^{58} -5.43037 q^{59} +(-7.39457 + 6.85347i) q^{60} +12.0751 q^{61} +(2.72194 + 4.88319i) q^{62} +(0.196249 + 0.196249i) q^{63} +(-7.96726 - 0.723032i) q^{64} +(-0.595547 + 2.15530i) q^{65} +(1.81952 - 6.40264i) q^{66} +(5.51319 - 5.51319i) q^{67} +(-8.84266 + 2.08568i) q^{68} +14.1771i q^{69} +(0.0997379 + 0.409472i) q^{70} +1.82705i q^{71} +(-5.88414 - 0.266446i) q^{72} +(10.5349 - 10.5349i) q^{73} +(6.05056 + 1.71947i) q^{74} +(-10.9322 + 2.74745i) q^{75} +(3.23201 - 5.22726i) q^{76} +(-0.196741 - 0.196741i) q^{77} +(-2.78484 + 1.55230i) q^{78} -7.53432 q^{79} +(-7.42356 - 4.98906i) q^{80} +10.9107 q^{81} +(10.8582 - 6.05248i) q^{82} +(10.7812 + 10.7812i) q^{83} +(-0.316014 + 0.511102i) q^{84} +(-9.79078 - 2.70536i) q^{85} +(-12.0502 - 3.42446i) q^{86} +(0.0962666 - 0.0962666i) q^{87} +(5.89889 + 0.267115i) q^{88} -2.38303i q^{89} +(-5.62632 - 3.42229i) q^{90} +0.133272i q^{91} +(-12.2412 + 2.88727i) q^{92} +(-6.30180 + 6.30180i) q^{93} +(-3.05036 + 10.7338i) q^{94} +(5.97718 - 3.38911i) q^{95} +(-2.36318 - 12.5322i) q^{96} +(8.89152 + 8.89152i) q^{97} +(-4.80764 - 8.62496i) q^{98} +4.34763 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 - 12 * q^8	\( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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