LMFDB - Embedded newform 145.2.e.a.133.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [145,2,Mod(12,145)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(145, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("145.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	145.e (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:	$1.15783082931$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			133.13
Character	$\chi$	$=$	145.133
Dual form			145.2.e.a.12.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.73482i q^{2} +1.63186 q^{3} -5.47925 q^{4} +(0.903087 + 2.04559i) q^{5} +4.46285i q^{6} +(1.05887 - 1.05887i) q^{7} -9.51511i q^{8} -0.337028 q^{9} +O(q^{10})$	\(q+2.73482i q^{2} +1.63186 q^{3} -5.47925 q^{4} +(0.903087 + 2.04559i) q^{5} +4.46285i q^{6} +(1.05887 - 1.05887i) q^{7} -9.51511i q^{8} -0.337028 q^{9} +(-5.59432 + 2.46978i) q^{10} +(1.15733 - 1.15733i) q^{11} -8.94137 q^{12} +(-1.53095 + 1.53095i) q^{13} +(2.89582 + 2.89582i) q^{14} +(1.47371 + 3.33812i) q^{15} +15.0636 q^{16} -7.16970i q^{17} -0.921711i q^{18} +(1.87609 + 1.87609i) q^{19} +(-4.94824 - 11.2083i) q^{20} +(1.72793 - 1.72793i) q^{21} +(3.16509 + 3.16509i) q^{22} +(4.16994 + 4.16994i) q^{23} -15.5273i q^{24} +(-3.36887 + 3.69469i) q^{25} +(-4.18686 - 4.18686i) q^{26} -5.44557 q^{27} +(-5.80180 + 5.80180i) q^{28} +(1.03600 - 5.28457i) q^{29} +(-9.12915 + 4.03034i) q^{30} +(-0.504388 + 0.504388i) q^{31} +22.1661i q^{32} +(1.88860 - 1.88860i) q^{33} +19.6078 q^{34} +(3.12226 + 1.20976i) q^{35} +1.84666 q^{36} +4.74574 q^{37} +(-5.13076 + 5.13076i) q^{38} +(-2.49829 + 2.49829i) q^{39} +(19.4640 - 8.59298i) q^{40} +(2.38277 + 2.38277i) q^{41} +(4.72557 + 4.72557i) q^{42} -8.05942 q^{43} +(-6.34129 + 6.34129i) q^{44} +(-0.304366 - 0.689421i) q^{45} +(-11.4040 + 11.4040i) q^{46} -1.86671 q^{47} +24.5818 q^{48} +4.75760i q^{49} +(-10.1043 - 9.21325i) q^{50} -11.7000i q^{51} +(8.38843 - 8.38843i) q^{52} +(-5.39552 - 5.39552i) q^{53} -14.8927i q^{54} +(3.41259 + 1.32225i) q^{55} +(-10.0753 - 10.0753i) q^{56} +(3.06152 + 3.06152i) q^{57} +(14.4524 + 2.83326i) q^{58} -3.57926i q^{59} +(-8.07483 - 18.2904i) q^{60} +(-0.867739 + 0.867739i) q^{61} +(-1.37941 - 1.37941i) q^{62} +(-0.356868 + 0.356868i) q^{63} -30.4931 q^{64} +(-4.51426 - 1.74911i) q^{65} +(5.16498 + 5.16498i) q^{66} +(-7.09185 - 7.09185i) q^{67} +39.2845i q^{68} +(6.80476 + 6.80476i) q^{69} +(-3.30847 + 8.53882i) q^{70} -3.30380i q^{71} +3.20686i q^{72} -11.7385i q^{73} +12.9787i q^{74} +(-5.49753 + 6.02922i) q^{75} +(-10.2795 - 10.2795i) q^{76} -2.45092i q^{77} +(-6.83238 - 6.83238i) q^{78} +(-2.01731 - 2.01731i) q^{79} +(13.6038 + 30.8140i) q^{80} -7.87533 q^{81} +(-6.51644 + 6.51644i) q^{82} +(-5.28177 - 5.28177i) q^{83} +(-9.46773 + 9.46773i) q^{84} +(14.6663 - 6.47486i) q^{85} -22.0411i q^{86} +(1.69060 - 8.62369i) q^{87} +(-11.0121 - 11.0121i) q^{88} +(10.1661 + 10.1661i) q^{89} +(1.88544 - 0.832385i) q^{90} +3.24214i q^{91} +(-22.8481 - 22.8481i) q^{92} +(-0.823091 + 0.823091i) q^{93} -5.10511i q^{94} +(-2.14343 + 5.53198i) q^{95} +36.1721i q^{96} -6.05786 q^{97} -13.0112 q^{98} +(-0.390052 + 0.390052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 4 q^{3} - 22 q^{4} - 4 q^{7} + 10 q^{9}+O(q^{10}) $ 26 * q - 4 * q^3 - 22 * q^4 - 4 * q^7 + 10 * q^9	$ 26 q - 4 q^{3} - 22 q^{4} - 4 q^{7} + 10 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 14 q^{13} + 4 q^{14} - 10 q^{15} + 6 q^{16} - 20 q^{20} + 16 q^{21} + 8 q^{22} - 4 q^{23} + 10 q^{25} + 6 q^{26} - 4 q^{27} + 8 q^{28} + 16 q^{30} + 8 q^{31} + 32 q^{34} + 16 q^{35} - 22 q^{36} + 16 q^{37} + 8 q^{38} + 16 q^{39} + 32 q^{40} - 6 q^{41} + 4 q^{42} + 12 q^{43} - 44 q^{45} - 32 q^{46} - 36 q^{47} + 4 q^{48} - 46 q^{50} + 26 q^{52} + 14 q^{53} + 46 q^{55} - 32 q^{56} + 12 q^{57} + 58 q^{58} - 14 q^{60} + 18 q^{61} - 28 q^{62} - 60 q^{63} - 30 q^{64} - 18 q^{65} + 20 q^{66} - 32 q^{67} - 12 q^{69} + 32 q^{70} + 2 q^{75} + 20 q^{76} + 56 q^{78} - 4 q^{79} + 12 q^{80} - 86 q^{81} - 58 q^{82} - 60 q^{83} - 76 q^{84} + 8 q^{85} - 12 q^{87} - 68 q^{88} + 46 q^{89} + 6 q^{90} + 28 q^{92} + 8 q^{93} + 20 q^{95} - 8 q^{97} + 34 q^{98} - 36 q^{99}+O(q^{100}) $ 26 * q - 4 * q^3 - 22 * q^4 - 4 * q^7 + 10 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 14 * q^13 + 4 * q^14 - 10 * q^15 + 6 * q^16 - 20 * q^20 + 16 * q^21 + 8 * q^22 - 4 * q^23 + 10 * q^25 + 6 * q^26 - 4 * q^27 + 8 * q^28 + 16 * q^30 + 8 * q^31 + 32 * q^34 + 16 * q^35 - 22 * q^36 + 16 * q^37 + 8 * q^38 + 16 * q^39 + 32 * q^40 - 6 * q^41 + 4 * q^42 + 12 * q^43 - 44 * q^45 - 32 * q^46 - 36 * q^47 + 4 * q^48 - 46 * q^50 + 26 * q^52 + 14 * q^53 + 46 * q^55 - 32 * q^56 + 12 * q^57 + 58 * q^58 - 14 * q^60 + 18 * q^61 - 28 * q^62 - 60 * q^63 - 30 * q^64 - 18 * q^65 + 20 * q^66 - 32 * q^67 - 12 * q^69 + 32 * q^70 + 2 * q^75 + 20 * q^76 + 56 * q^78 - 4 * q^79 + 12 * q^80 - 86 * q^81 - 58 * q^82 - 60 * q^83 - 76 * q^84 + 8 * q^85 - 12 * q^87 - 68 * q^88 + 46 * q^89 + 6 * q^90 + 28 * q^92 + 8 * q^93 + 20 * q^95 - 8 * q^97 + 34 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/145\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$			2.73482i			1.93381i	0.255136	+	0.966905i	$0.417880\pi$
$2$			2.73482i			1.93381i	−0.255136	+	0.966905i	$0.582120\pi$
$3$	1.63186			0.942156			0.471078	−	0.882092i	$-0.343865\pi$
$3$	1.63186			0.942156			0.471078	+	0.882092i	$0.343865\pi$
$4$	−5.47925			−2.73962
$5$	0.903087	+	2.04559i	0.403873	+	0.914815i
$5$	0.903087	+	2.04559i	0.403873	+	0.914815i
$6$			4.46285i			1.82195i
$7$	1.05887	−	1.05887i	0.400215	−	0.400215i	−0.478094	−	0.878309i	$-0.658672\pi$
$7$	1.05887	−	1.05887i	0.400215	−	0.400215i	0.878309	+	0.478094i	$0.158672\pi$
$8$		−	9.51511i		−	3.36410i
$9$	−0.337028			−0.112343
$10$	−5.59432	+	2.46978i	−1.76908	+	0.781013i
$11$	1.15733	−	1.15733i	0.348948	−	0.348948i	−0.510770	−	0.859717i	$-0.670640\pi$
$11$	1.15733	−	1.15733i	0.348948	−	0.348948i	0.859717	+	0.510770i	$0.170640\pi$
$12$	−8.94137			−2.58115
$13$	−1.53095	+	1.53095i	−0.424608	+	0.424608i	−0.886787	−	0.462179i	$-0.847068\pi$
$13$	−1.53095	+	1.53095i	−0.424608	+	0.424608i	0.462179	+	0.886787i	$0.347068\pi$
$14$	2.89582	+	2.89582i	0.773939	+	0.773939i
$15$	1.47371	+	3.33812i	0.380511	+	0.861898i
$16$	15.0636			3.76591
$17$		−	7.16970i		−	1.73891i	−0.494015	−	0.869453i	$-0.664471\pi$
$17$		−	7.16970i		−	1.73891i	0.494015	−	0.869453i	$-0.335529\pi$
$18$		−	0.921711i		−	0.217249i
$19$	1.87609	+	1.87609i	0.430404	+	0.430404i	0.888766	−	0.458362i	$-0.151564\pi$
$19$	1.87609	+	1.87609i	0.430404	+	0.430404i	−0.458362	+	0.888766i	$0.651564\pi$
$20$	−4.94824	−	11.2083i	−1.10646	−	2.50625i
$21$	1.72793	−	1.72793i	0.377064	−	0.377064i
$22$	3.16509	+	3.16509i	0.674799	+	0.674799i
$23$	4.16994	+	4.16994i	0.869492	+	0.869492i	0.992416	−	0.122924i	$-0.0392271\pi$
$23$	4.16994	+	4.16994i	0.869492	+	0.869492i	−0.122924	+	0.992416i	$0.539227\pi$
$24$		−	15.5273i		−	3.16951i
$25$	−3.36887	+	3.69469i	−0.673774	+	0.738938i
$26$	−4.18686	−	4.18686i	−0.821111	−	0.821111i
$27$	−5.44557			−1.04800
$28$	−5.80180	+	5.80180i	−1.09644	+	1.09644i
$29$	1.03600	−	5.28457i	0.192380	−	0.981321i
$29$	1.03600	−	5.28457i	0.192380	−	0.981321i
$30$	−9.12915	+	4.03034i	−1.66675	+	0.735836i
$31$	−0.504388	+	0.504388i	−0.0905907	+	0.0905907i	−0.750950	−	0.660359i	$-0.770404\pi$
$31$	−0.504388	+	0.504388i	−0.0905907	+	0.0905907i	0.660359	+	0.750950i	$0.270404\pi$
$32$			22.1661i			3.91846i
$33$	1.88860	−	1.88860i	0.328763	−	0.328763i
$34$	19.6078			3.36272
$35$	3.12226	+	1.20976i	0.527758	+	0.204487i
$36$	1.84666			0.307777
$37$	4.74574			0.780194			0.390097	−	0.920774i	$-0.372441\pi$
$37$	4.74574			0.780194			0.390097	+	0.920774i	$0.372441\pi$
$38$	−5.13076	+	5.13076i	−0.832320	+	0.832320i
$39$	−2.49829	+	2.49829i	−0.400047	+	0.400047i
$40$	19.4640	−	8.59298i	3.07753	−	1.35867i
$41$	2.38277	+	2.38277i	0.372126	+	0.372126i	0.868251	−	0.496125i	$-0.165244\pi$
$41$	2.38277	+	2.38277i	0.372126	+	0.372126i	−0.496125	+	0.868251i	$0.665244\pi$
$42$	4.72557	+	4.72557i	0.729171	+	0.729171i
$43$	−8.05942			−1.22905			−0.614525	−	0.788897i	$-0.710652\pi$
$43$	−8.05942			−1.22905			−0.614525	+	0.788897i	$0.710652\pi$
$44$	−6.34129	+	6.34129i	−0.955985	+	0.955985i
$45$	−0.304366	−	0.689421i	−0.0453721	−	0.102773i
$46$	−11.4040	+	11.4040i	−1.68143	+	1.68143i
$47$	−1.86671			−0.272287			−0.136144	−	0.990689i	$-0.543471\pi$
$47$	−1.86671			−0.272287			−0.136144	+	0.990689i	$0.543471\pi$
$48$	24.5818			3.54807
$49$			4.75760i			0.679657i
$50$	−10.1043	−	9.21325i	−1.42897	−	1.30295i
$51$		−	11.7000i		−	1.63832i
$52$	8.38843	−	8.38843i	1.16327	−	1.16327i
$53$	−5.39552	−	5.39552i	−0.741132	−	0.741132i	0.231664	−	0.972796i	$-0.425583\pi$
$53$	−5.39552	−	5.39552i	−0.741132	−	0.741132i	−0.972796	+	0.231664i	$0.925583\pi$
$54$		−	14.8927i		−	2.02663i
$55$	3.41259	+	1.32225i	0.460153	+	0.178292i
$56$	−10.0753	−	10.0753i	−1.34636	−	1.34636i
$57$	3.06152	+	3.06152i	0.405508	+	0.405508i
$58$	14.4524	+	2.83326i	1.89769	+	0.372026i
$59$		−	3.57926i		−	0.465979i	−0.972479	−	0.232990i	$-0.925149\pi$
$59$		−	3.57926i		−	0.465979i	0.972479	−	0.232990i	$-0.0748509\pi$
$60$	−8.07483	−	18.2904i	−1.04246	−	2.36128i
$61$	−0.867739	+	0.867739i	−0.111103	+	0.111103i	−0.760473	−	0.649370i	$-0.775033\pi$
$61$	−0.867739	+	0.867739i	−0.111103	+	0.111103i	0.649370	+	0.760473i	$0.275033\pi$
$62$	−1.37941	−	1.37941i	−0.175185	−	0.175185i
$63$	−0.356868	+	0.356868i	−0.0449612	+	0.0449612i
$64$	−30.4931			−3.81164
$65$	−4.51426	−	1.74911i	−0.559926	−	0.216950i
$66$	5.16498	+	5.16498i	0.635765	+	0.635765i
$67$	−7.09185	−	7.09185i	−0.866408	−	0.866408i	0.125665	−	0.992073i	$-0.459894\pi$
$67$	−7.09185	−	7.09185i	−0.866408	−	0.866408i	−0.992073	+	0.125665i	$0.959894\pi$
$68$			39.2845i			4.76395i
$69$	6.80476	+	6.80476i	0.819197	+	0.819197i
$70$	−3.30847	+	8.53882i	−0.395438	+	1.02058i
$71$		−	3.30380i		−	0.392089i	−0.980595	−	0.196044i	$-0.937190\pi$
$71$		−	3.30380i		−	0.392089i	0.980595	−	0.196044i	$-0.0628096\pi$
$72$			3.20686i			0.377932i
$73$		−	11.7385i		−	1.37389i	−0.726708	−	0.686946i	$-0.758951\pi$
$73$		−	11.7385i		−	1.37389i	0.726708	−	0.686946i	$-0.241049\pi$
$74$			12.9787i			1.50875i
$75$	−5.49753	+	6.02922i	−0.634800	+	0.696195i
$76$	−10.2795	−	10.2795i	−1.17914	−	1.17914i
$77$		−	2.45092i		−	0.279308i
$78$	−6.83238	−	6.83238i	−0.773615	−	0.773615i
$79$	−2.01731	−	2.01731i	−0.226966	−	0.226966i	0.584458	−	0.811424i	$-0.301307\pi$
$79$	−2.01731	−	2.01731i	−0.226966	−	0.226966i	−0.811424	+	0.584458i	$0.801307\pi$
$80$	13.6038	+	30.8140i	1.52095	+	3.44511i
$81$	−7.87533			−0.875036
$82$	−6.51644	+	6.51644i	−0.719621	+	0.719621i
$83$	−5.28177	−	5.28177i	−0.579749	−	0.579749i	0.355085	−	0.934834i	$-0.384452\pi$
$83$	−5.28177	−	5.28177i	−0.579749	−	0.579749i	−0.934834	+	0.355085i	$0.884452\pi$
$84$	−9.46773	+	9.46773i	−1.03301	+	1.03301i
$85$	14.6663	−	6.47486i	1.59078	−	0.702297i
$86$		−	22.0411i		−	2.37675i
$87$	1.69060	−	8.62369i	0.181251	−	0.924557i
$88$	−11.0121	−	11.0121i	−1.17390	−	1.17390i
$89$	10.1661	+	10.1661i	1.07760	+	1.07760i	0.996724	+	0.0808784i	$0.0257725\pi$
$89$	10.1661	+	10.1661i	1.07760	+	1.07760i	0.0808784	+	0.996724i	$0.474227\pi$
$90$	1.88544	−	0.832385i	0.198743	−	0.0877411i
$91$			3.24214i			0.339869i
$92$	−22.8481	−	22.8481i	−2.38208	−	2.38208i
$93$	−0.823091	+	0.823091i	−0.0853506	+	0.0853506i
$94$		−	5.10511i		−	0.526552i
$95$	−2.14343	+	5.53198i	−0.219912	+	0.567569i
$96$			36.1721i			3.69180i
$97$	−6.05786			−0.615082			−0.307541	−	0.951535i	$-0.599506\pi$
$97$	−6.05786			−0.615082			−0.307541	+	0.951535i	$0.599506\pi$
$98$	−13.0112			−1.31433
$99$	−0.390052	+	0.390052i	−0.0392017	+	0.0392017i
$100$	18.4589	−	20.2441i	1.84589	−	2.02441i
$101$	3.69493	−	3.69493i	0.367659	−	0.367659i	−0.498964	−	0.866623i	$-0.666286\pi$
$101$	3.69493	−	3.69493i	0.367659	−	0.367659i	0.866623	+	0.498964i	$0.166286\pi$
$102$	31.9973			3.16820
$103$	0.333704	+	0.333704i	0.0328808	+	0.0328808i	0.723356	−	0.690475i	$-0.242599\pi$
$103$	0.333704	+	0.333704i	0.0328808	+	0.0328808i	−0.690475	+	0.723356i	$0.742599\pi$
$104$	14.5671	+	14.5671i	1.42842	+	1.42842i
$105$	5.09510	+	1.97416i	0.497230	+	0.192658i
$106$	14.7558	−	14.7558i	1.43321	−	1.43321i
$107$	−8.38671	+	8.38671i	−0.810774	+	0.810774i	−0.984750	−	0.173976i	$-0.944338\pi$
$107$	−8.38671	+	8.38671i	−0.810774	+	0.810774i	0.173976	+	0.984750i	$0.444338\pi$
$108$	29.8376			2.87112
$109$	1.22995			0.117808			0.0589040	−	0.998264i	$-0.481239\pi$
$109$	1.22995			0.117808			0.0589040	+	0.998264i	$0.481239\pi$
$110$	−3.61612	+	9.33281i	−0.344783	+	0.889849i
$111$	7.74438			0.735064
$112$	15.9504	−	15.9504i	1.50717	−	1.50717i
$113$		−	0.155786i		−	0.0146552i	−0.999973	−	0.00732758i	$-0.997668\pi$
$113$		−	0.155786i		−	0.0146552i	0.999973	−	0.00732758i	$-0.00233246\pi$
$114$	−8.37270	+	8.37270i	−0.784175	+	0.784175i
$115$	−4.76416	+	12.2958i	−0.444260	+	1.14659i
$116$	−5.67647	+	28.9555i	−0.527047	+	2.68845i
$117$	0.515972	−	0.515972i	0.0477016	−	0.0477016i
$118$	9.78863			0.901116
$119$	−7.59176	−	7.59176i	−0.695936	−	0.695936i
$120$	31.7626	−	14.0225i	2.89951	−	1.28008i
$121$			8.32118i			0.756471i
$122$	−2.37311	−	2.37311i	−0.214851	−	0.214851i
$123$	3.88835	+	3.88835i	0.350600	+	0.350600i
$124$	2.76366	−	2.76366i	0.248184	−	0.248184i
$125$	−10.6002	−	3.55469i	−0.948110	−	0.317941i
$126$	−0.975971	−	0.975971i	−0.0869464	−	0.0869464i
$127$			18.5247i			1.64380i	0.569634	+	0.821899i	$0.307085\pi$
$127$			18.5247i			1.64380i	−0.569634	+	0.821899i	$0.692915\pi$
$128$		−	39.0610i		−	3.45253i
$129$	−13.1519			−1.15796
$130$	4.78350	−	12.3457i	0.419541	−	1.08279i
$131$	4.58794	+	4.58794i	0.400850	+	0.400850i	0.878533	−	0.477682i	$-0.158523\pi$
$131$	4.58794	+	4.58794i	0.400850	+	0.400850i	−0.477682	+	0.878533i	$0.658523\pi$
$132$	−10.3481	+	10.3481i	−0.900687	+	0.900687i
$133$	3.97306			0.344508
$134$	19.3949	−	19.3949i	1.67547	−	1.67547i
$135$	−4.91782	−	11.1394i	−0.423259	−	0.958726i
$136$	−68.2205			−5.84986
$137$			2.71664i			0.232098i	0.993243	+	0.116049i	$0.0370230\pi$
$137$			2.71664i			0.232098i	−0.993243	+	0.116049i	$0.962977\pi$
$138$	−18.6098	+	18.6098i	−1.58417	+	1.58417i
$139$			12.0322i			1.02056i	0.860009	+	0.510279i	$0.170458\pi$
$139$			12.0322i			1.02056i	−0.860009	+	0.510279i	$0.829542\pi$
$140$	−17.1076	−	6.62857i	−1.44586	−	0.560216i
$141$	−3.04621			−0.256537
$142$	9.03529			0.758225
$143$			3.54362i			0.296332i
$144$	−5.07687			−0.423072
$145$	11.7457	−	2.65321i	0.975424	−	0.220337i
$146$	32.1028			2.65685
$147$			7.76374i			0.640342i
$148$	−26.0031			−2.13744
$149$	9.07657			0.743581			0.371791	−	0.928317i	$-0.378744\pi$
$149$	9.07657			0.743581			0.371791	+	0.928317i	$0.378744\pi$
$150$	−16.4888	−	15.0347i	−1.34631	−	1.22758i
$151$			14.6422i			1.19156i	0.803146	+	0.595782i	$0.203158\pi$
$151$			14.6422i			1.19156i	−0.803146	+	0.595782i	$0.796842\pi$
$152$	17.8512	−	17.8512i	1.44792	−	1.44792i
$153$			2.41639i			0.195353i
$154$	6.70282			0.540129
$155$	−1.48728	−	0.576264i	−0.119461	−	0.0462866i
$156$	13.6888	−	13.6888i	1.09598	−	1.09598i
$157$	1.37029			0.109361			0.0546805	−	0.998504i	$-0.482586\pi$
$157$	1.37029			0.109361			0.0546805	+	0.998504i	$0.482586\pi$
$158$	5.51699	−	5.51699i	0.438908	−	0.438908i
$159$	−8.80475	−	8.80475i	−0.698262	−	0.698262i
$160$	−45.3428	+	20.0179i	−3.58466	+	1.58256i
$161$	8.83083			0.695967
$162$		−	21.5376i		−	1.69215i
$163$			2.81205i			0.220257i	0.993917	+	0.110128i	$0.0351262\pi$
$163$			2.81205i			0.220257i	−0.993917	+	0.110128i	$0.964874\pi$
$164$	−13.0558	−	13.0558i	−1.01948	−	1.01948i
$165$	5.56887	+	2.15773i	0.433536	+	0.167979i
$166$	14.4447	−	14.4447i	1.12113	−	1.12113i
$167$	−5.01507	−	5.01507i	−0.388078	−	0.388078i	0.485923	−	0.874001i	$-0.338483\pi$
$167$	−5.01507	−	5.01507i	−0.388078	−	0.388078i	−0.874001	+	0.485923i	$0.838483\pi$
$168$	−16.4414	−	16.4414i	−1.26848	−	1.26848i
$169$			8.31241i			0.639416i
$170$	17.7076	+	40.1096i	1.35811	+	3.07626i
$171$	−0.632294	−	0.632294i	−0.0483527	−	0.0483527i
$172$	44.1595			3.36713
$173$	11.8741	−	11.8741i	0.902767	−	0.902767i	−0.0929073	−	0.995675i	$-0.529616\pi$
$173$	11.8741	−	11.8741i	0.902767	−	0.902767i	0.995675	+	0.0929073i	$0.0296160\pi$
$174$	23.5843	+	4.62349i	1.78792	+	0.350506i
$175$	0.345002	+	7.47938i	0.0260797	+	0.565388i
$176$	17.4336	−	17.4336i	1.31411	−	1.31411i
$177$		−	5.84085i		−	0.439025i
$178$	−27.8024	+	27.8024i	−2.08388	+	2.08388i
$179$	0.831099			0.0621193			0.0310596	−	0.999518i	$-0.490112\pi$
$179$	0.831099			0.0621193			0.0310596	+	0.999518i	$0.490112\pi$
$180$	1.66769	+	3.77751i	0.124303	+	0.281559i
$181$	−16.5277			−1.22849			−0.614245	−	0.789115i	$-0.710540\pi$
$181$	−16.5277			−1.22849			−0.614245	+	0.789115i	$0.710540\pi$
$182$	−8.86667			−0.657242
$183$	−1.41603	+	1.41603i	−0.104676	+	0.104676i
$184$	39.6774	−	39.6774i	2.92506	−	2.92506i
$185$	4.28581	+	9.70783i	0.315099	+	0.713734i
$186$	−2.25101	−	2.25101i	−0.165052	−	0.165052i
$187$	−8.29769	−	8.29769i	−0.606787	−	0.606787i
$188$	10.2282			0.745965
$189$	−5.76614	+	5.76614i	−0.419425	+	0.419425i
$190$	−15.1290	−	5.86191i	−1.09757	−	0.425268i
$191$	1.92415	−	1.92415i	0.139227	−	0.139227i	−0.634058	−	0.773285i	$-0.718612\pi$
$191$	1.92415	−	1.92415i	0.139227	−	0.139227i	0.773285	+	0.634058i	$0.218612\pi$
$192$	−49.7606			−3.59116
$193$	5.17863			0.372766			0.186383	−	0.982477i	$-0.440323\pi$
$193$	5.17863			0.372766			0.186383	+	0.982477i	$0.440323\pi$
$194$		−	16.5672i		−	1.18945i
$195$	−7.36665	−	2.85430i	−0.527537	−	0.204401i
$196$		−	26.0680i		−	1.86200i
$197$	12.4638	−	12.4638i	0.888007	−	0.888007i	−0.106324	−	0.994332i	$-0.533908\pi$
$197$	12.4638	−	12.4638i	0.888007	−	0.888007i	0.994332	+	0.106324i	$0.0339081\pi$
$198$	−1.06672	−	1.06672i	−0.0758087	−	0.0758087i
$199$			8.92943i			0.632990i	0.948594	+	0.316495i	$0.102506\pi$
$199$			8.92943i			0.632990i	−0.948594	+	0.316495i	$0.897494\pi$
$200$	35.1554	+	32.0552i	2.48586	+	2.26664i
$201$	−11.5729	−	11.5729i	−0.816291	−	0.816291i
$202$	10.1050	+	10.1050i	0.710983	+	0.710983i
$203$	−4.49868	−	6.69265i	−0.315746	−	0.469732i
$204$			64.1069i			4.48838i
$205$	−2.72232	+	7.02601i	−0.190135	+	0.490718i
$206$	−0.912621	+	0.912621i	−0.0635853	+	0.0635853i
$207$	−1.40539	−	1.40539i	−0.0976811	−	0.0976811i
$208$	−23.0616	+	23.0616i	−1.59904	+	1.59904i
$209$	4.34250			0.300377
$210$	−5.39897	+	13.9342i	−0.372564	+	0.961549i
$211$	6.16024	+	6.16024i	0.424088	+	0.424088i	0.886609	−	0.462520i	$-0.153055\pi$
$211$	6.16024	+	6.16024i	0.424088	+	0.424088i	−0.462520	+	0.886609i	$0.653055\pi$
$212$	29.5634	+	29.5634i	2.03042	+	2.03042i
$213$		−	5.39134i		−	0.369409i
$214$	−22.9362	−	22.9362i	−1.56788	−	1.56788i
$215$	−7.27836	−	16.4863i	−0.496380	−	1.12435i
$216$			51.8152i			3.52558i
$217$			1.06816i			0.0725115i
$218$			3.36370i			0.227819i
$219$		−	19.1557i		−	1.29442i
$220$	−18.6984	−	7.24493i	−1.26065	−	0.488453i
$221$	10.9764	+	10.9764i	0.738354	+	0.738354i
$222$			21.1795i			1.42148i
$223$	11.3717	+	11.3717i	0.761509	+	0.761509i	0.976595	−	0.215086i	$-0.0690033\pi$
$223$	11.3717	+	11.3717i	0.761509	+	0.761509i	−0.215086	+	0.976595i	$0.569003\pi$
$224$	23.4710	+	23.4710i	1.56822	+	1.56822i
$225$	1.13540	−	1.24521i	0.0756935	−	0.0830143i
$226$	0.426048			0.0283403
$227$	−19.9481	+	19.9481i	−1.32400	+	1.32400i	−0.413497	+	0.910506i	$0.635693\pi$
$227$	−19.9481	+	19.9481i	−1.32400	+	1.32400i	−0.910506	+	0.413497i	$0.864307\pi$
$228$	−16.7748	−	16.7748i	−1.11094	−	1.11094i
$229$	0.344302	−	0.344302i	0.0227521	−	0.0227521i	−0.695639	−	0.718391i	$-0.744879\pi$
$229$	0.344302	−	0.344302i	0.0227521	−	0.0227521i	0.718391	+	0.695639i	$0.244879\pi$
$230$	−33.6268	−	13.0291i	−2.21729	−	0.859115i
$231$		−	3.99956i		−	0.263152i
$232$	−50.2833	−	9.85762i	−3.30126	−	0.647184i
$233$	−11.1619	−	11.1619i	−0.731241	−	0.731241i	0.239625	−	0.970866i	$-0.422976\pi$
$233$	−11.1619	−	11.1619i	−0.731241	−	0.731241i	−0.970866	+	0.239625i	$0.922976\pi$
$234$	1.41109	+	1.41109i	0.0922459	+	0.0922459i
$235$	−1.68580	−	3.81852i	−0.109970	−	0.249093i
$236$			19.6116i			1.27661i
$237$	−3.29198	−	3.29198i	−0.213837	−	0.213837i
$238$	20.7621	−	20.7621i	1.34581	−	1.34581i
$239$		−	12.4300i		−	0.804031i	−0.915633	−	0.402016i	$-0.868310\pi$
$239$		−	12.4300i		−	0.804031i	0.915633	−	0.402016i	$-0.131690\pi$
$240$	22.1995	+	50.2842i	1.43297	+	3.24583i
$241$		−	1.15975i		−	0.0747058i	−0.999302	−	0.0373529i	$-0.988107\pi$
$241$		−	1.15975i		−	0.0747058i	0.999302	−	0.0373529i	$-0.0118926\pi$
$242$	−22.7569			−1.46287
$243$	3.48526			0.223579
$244$	4.75455	−	4.75455i	0.304379	−	0.304379i
$245$	−9.73208	+	4.29652i	−0.621760	+	0.274495i
$246$	−10.6339	+	10.6339i	−0.677995	+	0.677995i
$247$	−5.74438			−0.365506
$248$	4.79931	+	4.79931i	0.304756	+	0.304756i
$249$	−8.61911	−	8.61911i	−0.546214	−	0.546214i
$250$	9.72145	−	28.9896i	0.614838	−	1.83347i
$251$	−17.5113	+	17.5113i	−1.10531	+	1.10531i	−0.111547	+	0.993759i	$0.535580\pi$
$251$	−17.5113	+	17.5113i	−1.10531	+	1.10531i	−0.993759	+	0.111547i	$0.964420\pi$
$252$	1.95537	−	1.95537i	0.123177	−	0.123177i
$253$	9.65198			0.606815
$254$	−50.6616			−3.17879
$255$	23.9333	−	10.5661i	1.49876	−	0.661673i
$256$	45.8385			2.86491
$257$	12.6288	−	12.6288i	0.787765	−	0.787765i	−0.193362	−	0.981127i	$-0.561939\pi$
$257$	12.6288	−	12.6288i	0.787765	−	0.787765i	0.981127	+	0.193362i	$0.0619392\pi$
$258$		−	35.9680i		−	2.23927i
$259$	5.02511	−	5.02511i	0.312245	−	0.312245i
$260$	24.7348	+	9.58380i	1.53398	+	0.594362i
$261$	−0.349160	+	1.78105i	−0.0216124	+	0.110244i
$262$	−12.5472	+	12.5472i	−0.775168	+	0.775168i
$263$	28.1945			1.73855			0.869275	−	0.494329i	$-0.164586\pi$
$263$	28.1945			1.73855			0.869275	+	0.494329i	$0.164586\pi$
$264$	−17.9702	−	17.9702i	−1.10599	−	1.10599i
$265$	6.16439	−	15.9096i	0.378676	−	0.977322i
$266$			10.8656i			0.666213i
$267$	16.5896	+	16.5896i	1.01527	+	1.01527i
$268$	38.8580	+	38.8580i	2.37363	+	2.37363i
$269$	11.0679	−	11.0679i	0.674824	−	0.674824i	−0.284000	−	0.958824i	$-0.591662\pi$
$269$	11.0679	−	11.0679i	0.674824	−	0.674824i	0.958824	+	0.284000i	$0.0916617\pi$
$270$	30.4642	−	13.4494i	1.85399	−	0.818502i
$271$	2.17997	+	2.17997i	0.132424	+	0.132424i	0.770212	−	0.637788i	$-0.220150\pi$
$271$	2.17997	+	2.17997i	0.132424	+	0.132424i	−0.637788	+	0.770212i	$0.720150\pi$
$272$		−	108.002i		−	6.54857i
$273$			5.29072i			0.320209i
$274$	−7.42953			−0.448834
$275$	0.377083	+	8.17486i	0.0227389	+	0.492962i
$276$	−37.2850	−	37.2850i	−2.24429	−	2.24429i
$277$	18.6295	−	18.6295i	1.11934	−	1.11934i	0.127503	−	0.991838i	$-0.459304\pi$
$277$	18.6295	−	18.6295i	1.11934	−	1.11934i	0.991838	−	0.127503i	$-0.0406962\pi$
$278$	−32.9059			−1.97357
$279$	0.169993	−	0.169993i	0.0101772	−	0.0101772i
$280$	11.5110	−	29.7087i	0.687914	−	1.77543i
$281$	21.6535			1.29174			0.645871	−	0.763447i	$-0.276494\pi$
$281$	21.6535			1.29174			0.645871	+	0.763447i	$0.276494\pi$
$282$		−	8.33084i		−	0.496094i
$283$	4.61797	−	4.61797i	0.274510	−	0.274510i	−0.556403	−	0.830913i	$-0.687819\pi$
$283$	4.61797	−	4.61797i	0.274510	−	0.274510i	0.830913	+	0.556403i	$0.187819\pi$
$284$			18.1023i			1.07417i
$285$	−3.49779	+	9.02742i	−0.207191	+	0.534738i
$286$	−9.69115			−0.573050
$287$	5.04607			0.297860
$288$		−	7.47061i		−	0.440210i
$289$	−34.4045			−2.02380
$290$	7.25605	+	32.1223i	0.426090	+	1.88628i
$291$	−9.88558			−0.579503
$292$			64.3183i			3.76395i
$293$	−9.80441			−0.572780			−0.286390	−	0.958113i	$-0.592455\pi$
$293$	−9.80441			−0.572780			−0.286390	+	0.958113i	$0.592455\pi$
$294$	−21.2324			−1.23830
$295$	7.32169	−	3.23238i	0.426285	−	0.188196i
$296$		−	45.1562i		−	2.62465i
$297$	−6.30231	+	6.30231i	−0.365697	+	0.365697i
$298$			24.8228i			1.43795i
$299$	−12.7679			−0.738387
$300$	30.1223	−	33.0356i	1.73911	−	1.90731i
$301$	−8.53386	+	8.53386i	−0.491884	+	0.491884i
$302$	−40.0438			−2.30426
$303$	6.02961	−	6.02961i	0.346392	−	0.346392i
$304$	28.2607	+	28.2607i	1.62086	+	1.62086i
$305$	−2.55868	−	0.991393i	−0.146510	−	0.0567670i
$306$	−6.60839			−0.377777
$307$		−	0.488133i		−	0.0278592i	−0.999903	−	0.0139296i	$-0.995566\pi$
$307$		−	0.488133i		−	0.0278592i	0.999903	−	0.0139296i	$-0.00443407\pi$
$308$			13.4292i			0.765198i
$309$	0.544559	+	0.544559i	0.0309789	+	0.0309789i
$310$	1.57598	−	4.06743i	0.0895096	−	0.231015i
$311$	7.27332	−	7.27332i	0.412432	−	0.412432i	−0.470153	−	0.882585i	$-0.655801\pi$
$311$	7.27332	−	7.27332i	0.412432	−	0.412432i	0.882585	+	0.470153i	$0.155801\pi$
$312$	23.7715	+	23.7715i	1.34580	+	1.34580i
$313$	−19.2967	−	19.2967i	−1.09071	−	1.09071i	−0.995452	−	0.0952605i	$-0.969632\pi$
$313$	−19.2967	−	19.2967i	−1.09071	−	1.09071i	−0.0952605	−	0.995452i	$-0.530368\pi$
$314$			3.74750i			0.211483i
$315$	−1.05229	−	0.407723i	−0.0592898	−	0.0229726i
$316$	11.0534	+	11.0534i	0.621800	+	0.621800i
$317$	−2.65586			−0.149168			−0.0745839	−	0.997215i	$-0.523763\pi$
$317$	−2.65586			−0.149168			−0.0745839	+	0.997215i	$0.523763\pi$
$318$	24.0794	−	24.0794i	1.35031	−	1.35031i
$319$	−4.91700	−	7.31497i	−0.275299	−	0.409560i
$320$	−27.5379	−	62.3764i	−1.53942	−	3.48695i
$321$	−13.6860	+	13.6860i	−0.763875	+	0.763875i
$322$			24.1507i			1.34587i
$323$	13.4510	−	13.4510i	0.748433	−	0.748433i
$324$	43.1509			2.39727
$325$	−0.498815	−	10.8139i	−0.0276693	−	0.599849i
$326$	−7.69045			−0.425935
$327$	2.00711			0.110994
$328$	22.6723	−	22.6723i	1.25187	−	1.25187i
$329$	−1.97660	+	1.97660i	−0.108973	+	0.108973i
$330$	−5.90100	+	15.2299i	−0.324839	+	0.838376i
$331$	−13.7951	−	13.7951i	−0.758248	−	0.758248i	0.217756	−	0.976003i	$-0.430126\pi$
$331$	−13.7951	−	13.7951i	−0.758248	−	0.758248i	−0.976003	+	0.217756i	$0.930126\pi$
$332$	28.9401	+	28.9401i	1.58829	+	1.58829i
$333$	−1.59945			−0.0876491
$334$	13.7153	−	13.7153i	0.750469	−	0.750469i
$335$	8.10245	−	20.9116i	0.442684	−	1.14252i
$336$	26.0289	−	26.0289i	1.41999	−	1.41999i
$337$	16.3087			0.888389			0.444195	−	0.895930i	$-0.353490\pi$
$337$	16.3087			0.888389			0.444195	+	0.895930i	$0.353490\pi$
$338$	−22.7329			−1.23651
$339$		−	0.254222i		−	0.0138074i
$340$	−80.3600	+	35.4773i	−4.35813	+	1.92403i
$341$			1.16748i			0.0632228i
$342$	1.72921	−	1.72921i	0.0935051	−	0.0935051i
$343$	12.4497	+	12.4497i	0.672223	+	0.672223i
$344$			76.6863i			4.13465i
$345$	−7.77445	+	20.0650i	−0.418562	+	1.08027i
$346$	32.4734	+	32.4734i	1.74578	+	1.74578i
$347$	3.15980	+	3.15980i	0.169627	+	0.169627i	0.786815	−	0.617188i	$-0.211728\pi$
$347$	3.15980	+	3.15980i	0.169627	+	0.169627i	−0.617188	+	0.786815i	$0.711728\pi$
$348$	−9.26322	+	47.2513i	−0.496561	+	2.53294i
$349$			17.3855i			0.930627i	0.885146	+	0.465313i	$0.154058\pi$
$349$			17.3855i			0.930627i	−0.885146	+	0.465313i	$0.845942\pi$
$350$	−20.4548	+	0.943519i	−1.09335	+	0.0504332i
$351$	8.33687	−	8.33687i	0.444989	−	0.444989i
$352$	25.6535	+	25.6535i	1.36734	+	1.36734i
$353$	−9.60586	+	9.60586i	−0.511268	+	0.511268i	−0.914915	−	0.403647i	$-0.867742\pi$
$353$	−9.60586	+	9.60586i	−0.511268	+	0.511268i	0.403647	+	0.914915i	$0.367742\pi$
$354$	15.9737			0.848992
$355$	6.75821	−	2.98362i	0.358689	−	0.158354i
$356$	−55.7024	−	55.7024i	−2.95222	−	2.95222i
$357$	−12.3887	−	12.3887i	−0.655680	−	0.655680i
$358$			2.27291i			0.120127i
$359$	16.6718	+	16.6718i	0.879906	+	0.879906i	0.993524	−	0.113618i	$-0.0362440\pi$
$359$	16.6718	+	16.6718i	0.879906	+	0.879906i	−0.113618	+	0.993524i	$0.536244\pi$
$360$	−6.55992	+	2.89607i	−0.345738	+	0.152636i
$361$		−	11.9606i		−	0.629505i
$362$		−	45.2002i		−	2.37567i
$363$			13.5790i			0.712713i
$364$		−	17.7645i		−	0.931112i
$365$	24.0122	−	10.6009i	1.25686	−	0.554878i
$366$	−3.87259	−	3.87259i	−0.202423	−	0.202423i
$367$			5.52771i			0.288544i	0.989538	+	0.144272i	$0.0460840\pi$
$367$			5.52771i			0.288544i	−0.989538	+	0.144272i	$0.953916\pi$
$368$	62.8145	+	62.8145i	3.27443	+	3.27443i
$369$	−0.803059	−	0.803059i	−0.0418056	−	0.0418056i
$370$	−26.5492	+	11.7209i	−1.38023	+	0.609342i
$371$	−11.4263			−0.593224
$372$	4.50992	−	4.50992i	0.233828	−	0.233828i
$373$	−0.505639	−	0.505639i	−0.0261810	−	0.0261810i	0.693895	−	0.720076i	$-0.255893\pi$
$373$	−0.505639	−	0.505639i	−0.0261810	−	0.0261810i	−0.720076	+	0.693895i	$0.755893\pi$
$374$	22.6927	−	22.6927i	1.17341	−	1.17341i
$375$	−17.2981	−	5.80077i	−0.893268	−	0.299550i
$376$			17.7619i			0.916003i
$377$	6.50434	+	9.67645i	0.334991	+	0.498363i
$378$	−15.7694	−	15.7694i	−0.811088	−	0.811088i
$379$	−21.9491	−	21.9491i	−1.12745	−	1.12745i	−0.990590	−	0.136859i	$-0.956299\pi$
$379$	−21.9491	−	21.9491i	−1.12745	−	1.12745i	−0.136859	−	0.990590i	$-0.543701\pi$
$380$	11.7444	−	30.3111i	0.602475	−	1.55492i
$381$			30.2297i			1.54871i
$382$	5.26221	+	5.26221i	0.269238	+	0.269238i
$383$	−8.19179	+	8.19179i	−0.418581	+	0.418581i	−0.884714	−	0.466134i	$-0.845647\pi$
$383$	−8.19179	+	8.19179i	−0.418581	+	0.418581i	0.466134	+	0.884714i	$0.345647\pi$
$384$		−	63.7421i		−	3.25282i
$385$	5.01357	−	2.21339i	0.255515	−	0.112805i
$386$			14.1626i			0.720859i
$387$	2.71625			0.138075
$388$	33.1925			1.68509
$389$	−1.00500	+	1.00500i	−0.0509555	+	0.0509555i	−0.732125	−	0.681170i	$-0.761472\pi$
$389$	−1.00500	+	1.00500i	−0.0509555	+	0.0509555i	0.681170	+	0.732125i	$0.261472\pi$
$390$	7.80601	−	20.1465i	0.395273	−	1.02016i
$391$	29.8972	−	29.8972i	1.51197	−	1.51197i
$392$	45.2691			2.28643
$393$	7.48688	+	7.48688i	0.377663	+	0.377663i
$394$	34.0862	+	34.0862i	1.71724	+	1.71724i
$395$	2.30479	−	5.94841i	0.115966	−	0.299297i
$396$	2.13719	−	2.13719i	0.107398	−	0.107398i
$397$	−9.25008	+	9.25008i	−0.464248	+	0.464248i	−0.900045	−	0.435797i	$-0.856467\pi$
$397$	−9.25008	+	9.25008i	−0.464248	+	0.464248i	0.435797	+	0.900045i	$0.356467\pi$
$398$	−24.4204			−1.22408
$399$	6.48348			0.324580
$400$	−50.7474	+	55.6555i	−2.53737	+	2.78277i
$401$	−9.92342			−0.495552			−0.247776	−	0.968817i	$-0.579700\pi$
$401$	−9.92342			−0.495552			−0.247776	+	0.968817i	$0.579700\pi$
$402$	31.6499	−	31.6499i	1.57855	−	1.57855i
$403$		−	1.54438i		−	0.0769311i
$404$	−20.2454	+	20.2454i	−1.00725	+	1.00725i
$405$	−7.11211	−	16.1097i	−0.353403	−	0.800497i
$406$	18.3032	−	12.3031i	0.908373	−	0.610592i
$407$	5.49238	−	5.49238i	0.272247	−	0.272247i
$408$	−111.326			−5.51148
$409$	−1.32729	−	1.32729i	−0.0656305	−	0.0656305i	0.673530	−	0.739160i	$-0.264777\pi$
$409$	−1.32729	−	1.32729i	−0.0656305	−	0.0656305i	−0.739160	+	0.673530i	$0.764777\pi$
$410$	−19.2149	−	7.44505i	−0.948955	−	0.367685i
$411$			4.43318i			0.218673i
$412$	−1.82845	−	1.82845i	−0.0900811	−	0.0900811i
$413$	−3.78996	−	3.78996i	−0.186492	−	0.186492i
$414$	3.84348	−	3.84348i	0.188897	−	0.188897i
$415$	6.03443	−	15.5742i	0.296219	−	0.764509i
$416$	−33.9352	−	33.9352i	−1.66381	−	1.66381i
$417$			19.6349i			0.961525i
$418$			11.8760i			0.580872i
$419$	−13.3122			−0.650345			−0.325172	−	0.945655i	$-0.605422\pi$
$419$	−13.3122			−0.650345			−0.325172	+	0.945655i	$0.605422\pi$
$420$	−27.9173	−	10.8169i	−1.36222	−	0.527811i
$421$	6.09719	+	6.09719i	0.297159	+	0.297159i	0.839900	−	0.542741i	$-0.182614\pi$
$421$	6.09719	+	6.09719i	0.297159	+	0.297159i	−0.542741	+	0.839900i	$0.682614\pi$
$422$	−16.8471	+	16.8471i	−0.820106	+	0.820106i
$423$	0.629133			0.0305895
$424$	−51.3390	+	51.3390i	−2.49324	+	2.49324i
$425$	26.4898	+	24.1538i	1.28494	+	1.17163i
$426$	14.7443			0.714366
$427$			1.83764i			0.0889297i
$428$	45.9528	−	45.9528i	2.22121	−	2.22121i
$429$			5.78269i			0.279191i
$430$	45.0870	−	19.9050i	2.17429	−	0.959904i
$431$	−7.97468			−0.384127			−0.192063	−	0.981383i	$-0.561518\pi$
$431$	−7.97468			−0.384127			−0.192063	+	0.981383i	$0.561518\pi$
$432$	−82.0301			−3.94667
$433$			27.9015i			1.34086i	0.741973	+	0.670430i	$0.233890\pi$
$433$			27.9015i			1.34086i	−0.741973	+	0.670430i	$0.766110\pi$
$434$	−2.92123			−0.140223
$435$	19.1673	−	4.32967i	0.919001	−	0.207592i
$436$	−6.73921			−0.322750
$437$			15.6463i			0.748466i
$438$	52.3873			2.50316
$439$	23.0891			1.10198			0.550991	−	0.834511i	$-0.314250\pi$
$439$	23.0891			1.10198			0.550991	+	0.834511i	$0.314250\pi$
$440$	12.5814	−	32.4711i	0.599793	−	1.54800i
$441$		−	1.60344i		−	0.0763544i
$442$	−30.0185	+	30.0185i	−1.42784	+	1.42784i
$443$		−	13.1208i		−	0.623388i	−0.950183	−	0.311694i	$-0.899104\pi$
$443$		−	13.1208i		−	0.623388i	0.950183	−	0.311694i	$-0.100896\pi$
$444$	−42.4334			−2.01380
$445$	−11.6148	+	29.9765i	−0.550593	+	1.42102i
$446$	−31.0997	+	31.0997i	−1.47261	+	1.47261i
$447$	14.8117			0.700569
$448$	−32.2882	+	32.2882i	−1.52547	+	1.52547i
$449$	−14.1942	−	14.1942i	−0.669865	−	0.669865i	0.287819	−	0.957685i	$-0.407070\pi$
$449$	−14.1942	−	14.1942i	−0.669865	−	0.669865i	−0.957685	+	0.287819i	$0.907070\pi$
$450$	3.40544	+	3.10512i	0.160534	+	0.146377i
$451$	5.51529			0.259705
$452$			0.853592i			0.0401496i
$453$			23.8940i			1.12264i
$454$	−54.5545	−	54.5545i	−2.56037	−	2.56037i
$455$	−6.63209	+	2.92794i	−0.310917	+	0.137264i
$456$	29.1307	−	29.1307i	1.36417	−	1.36417i
$457$	−20.5601	−	20.5601i	−0.961761	−	0.961761i	0.0375345	−	0.999295i	$-0.488050\pi$
$457$	−20.5601	−	20.5601i	−0.961761	−	0.961761i	−0.999295	+	0.0375345i	$0.988050\pi$
$458$	0.941604	+	0.941604i	0.0439983	+	0.0439983i
$459$			39.0431i			1.82237i
$460$	26.1040	−	67.3717i	1.21711	−	3.14122i
$461$	10.9719	+	10.9719i	0.511014	+	0.511014i	0.914837	−	0.403823i	$-0.132319\pi$
$461$	10.9719	+	10.9719i	0.511014	+	0.511014i	−0.403823	+	0.914837i	$0.632319\pi$
$462$	10.9381			0.508885
$463$	−19.5635	+	19.5635i	−0.909193	+	0.909193i	−0.996207	−	0.0870140i	$-0.972268\pi$
$463$	−19.5635	+	19.5635i	−0.909193	+	0.909193i	0.0870140	+	0.996207i	$0.472268\pi$
$464$	15.6059	−	79.6049i	0.724484	−	3.69557i
$465$	−2.42703	−	0.940383i	−0.112551	−	0.0436092i
$466$	30.5258	−	30.5258i	1.41408	−	1.41408i
$467$			38.4099i			1.77740i	0.458491	+	0.888699i	$0.348390\pi$
$467$			38.4099i			1.77740i	−0.458491	+	0.888699i	$0.651610\pi$
$468$	−2.82714	+	2.82714i	−0.130684	+	0.130684i
$469$	−15.0187			−0.693498
$470$	10.4430	−	4.61036i	0.481698	−	0.212660i
$471$	2.23612			0.103035
$472$	−34.0570			−1.56760
$473$	−9.32739	+	9.32739i	−0.428874	+	0.428874i
$474$	9.00297	−	9.00297i	0.413520	−	0.413520i
$475$	−13.2519	+	0.611270i	−0.608037	+	0.0280470i
$476$	41.5971	+	41.5971i	1.90660	+	1.90660i
$477$	1.81844	+	1.81844i	0.0832608	+	0.0832608i
$478$	33.9939			1.55484
$479$	14.9920	−	14.9920i	0.685002	−	0.685002i	−0.276121	−	0.961123i	$-0.589049\pi$
$479$	14.9920	−	14.9920i	0.685002	−	0.685002i	0.961123	+	0.276121i	$0.0890491\pi$
$480$	−73.9932	+	32.6665i	−3.37731	+	1.49102i
$481$	−7.26547	+	7.26547i	−0.331277	+	0.331277i
$482$	3.17170			0.144467
$483$	14.4107			0.655709
$484$		−	45.5938i		−	2.07245i
$485$	−5.47077	−	12.3919i	−0.248415	−	0.562687i
$486$			9.53156i			0.432360i
$487$	28.0848	−	28.0848i	1.27264	−	1.27264i	0.327945	−	0.944697i	$-0.393644\pi$
$487$	28.0848	−	28.0848i	1.27264	−	1.27264i	0.944697	−	0.327945i	$-0.106356\pi$
$488$	8.25663	+	8.25663i	0.373760	+	0.373760i
$489$			4.58888i			0.207516i
$490$	−11.7502	−	26.6155i	−0.530821	−	1.20237i
$491$	25.3582	+	25.3582i	1.14440	+	1.14440i	0.987636	+	0.156764i	$0.0501062\pi$
$491$	25.3582	+	25.3582i	1.14440	+	1.14440i	0.156764	+	0.987636i	$0.449894\pi$
$492$	−21.3052	−	21.3052i	−0.960513	−	0.960513i
$493$	−37.8888	−	7.42777i	−1.70643	−	0.334530i
$494$		−	15.7098i		−	0.706820i
$495$	−1.15014	−	0.445635i	−0.0516948	−	0.0200298i
$496$	−7.59792	+	7.59792i	−0.341156	+	0.341156i
$497$	−3.49829	−	3.49829i	−0.156920	−	0.156920i
$498$	23.5717	−	23.5717i	1.05627	−	1.05627i
$499$	4.79875			0.214821			0.107411	−	0.994215i	$-0.465744\pi$
$499$	4.79875			0.214821			0.107411	+	0.994215i	$0.465744\pi$
$500$	58.0811	+	19.4770i	2.59746	+	0.871039i
$501$	−8.18390	−	8.18390i	−0.365630	−	0.365630i
$502$	−47.8904	−	47.8904i	−2.13745	−	2.13745i
$503$		−	35.2896i		−	1.57348i	−0.617282	−	0.786742i	$-0.711766\pi$
$503$		−	35.2896i		−	1.57348i	0.617282	−	0.786742i	$-0.288234\pi$
$504$	3.39564	+	3.39564i	0.151254	+	0.151254i
$505$	10.8951	+	4.22146i	0.484828	+	0.187853i
$506$			26.3964i			1.17346i
$507$			13.5647i			0.602429i
$508$		−	101.501i		−	4.50339i
$509$			30.1303i			1.33550i	0.744384	+	0.667752i	$0.232743\pi$
$509$			30.1303i			1.33550i	−0.744384	+	0.667752i	$0.767257\pi$
$510$	28.8963	+	65.4533i	1.27955	+	2.89832i
$511$	−12.4296	−	12.4296i	−0.549852	−	0.549852i
$512$			47.2382i			2.08765i
$513$	−10.2164	−	10.2164i	−0.451063	−	0.451063i
$514$	34.5376	+	34.5376i	1.52339	+	1.52339i
$515$	−0.381257	+	0.983985i	−0.0168002	+	0.0433596i
$516$	72.0622			3.17236
$517$	−2.16040	+	2.16040i	−0.0950141	+	0.0950141i
$518$	13.7428	+	13.7428i	0.603823	+	0.603823i
$519$	19.3768	−	19.3768i	0.850548	−	0.850548i
$520$	−16.6430	+	42.9537i	−0.729842	+	1.88365i
$521$		−	25.2836i		−	1.10769i	−0.832619	−	0.553847i	$-0.813159\pi$
$521$		−	25.2836i		−	1.10769i	0.832619	−	0.553847i	$-0.186841\pi$
$522$	−4.87085	−	0.954889i	−0.213191	−	0.0417943i
$523$	−3.79891	−	3.79891i	−0.166115	−	0.166115i	0.619155	−	0.785269i	$-0.287475\pi$
$523$	−3.79891	−	3.79891i	−0.166115	−	0.166115i	−0.785269	+	0.619155i	$0.787475\pi$
$524$	−25.1384	−	25.1384i	−1.09818	−	1.09818i
$525$	0.562996	+	12.2053i	0.0245711	+	0.532683i
$526$			77.1070i			3.36203i
$527$	3.61631	+	3.61631i	0.157529	+	0.157529i
$528$	28.4492	−	28.4492i	1.23809	−	1.23809i
$529$			11.7768i			0.512033i
$530$	43.5100	+	16.8585i	1.88996	+	0.732287i
$531$			1.20631i			0.0523494i
$532$	−21.7694			−0.943822
$533$	−7.29578			−0.316015
$534$	−45.3697	+	45.3697i	−1.96334	+	1.96334i
$535$	−24.7297	−	9.58183i	−1.06916	−	0.414259i
$536$	−67.4798	+	67.4798i	−2.91468	+	2.91468i
$537$	1.35624			0.0585260
$538$	30.2688	+	30.2688i	1.30498	+	1.30498i
$539$	5.50610	+	5.50610i	0.237165	+	0.237165i
$540$	26.9459	+	61.0355i	1.15957	+	2.62655i
$541$	−4.49423	+	4.49423i	−0.193222	+	0.193222i	−0.797087	−	0.603865i	$-0.793627\pi$
$541$	−4.49423	+	4.49423i	−0.193222	+	0.193222i	0.603865	+	0.797087i	$0.293627\pi$
$542$	−5.96182	+	5.96182i	−0.256082	+	0.256082i
$543$	−26.9708			−1.15743
$544$	158.924			6.81383
$545$	1.11075	+	2.51598i	0.0475795	+	0.107773i
$546$	−14.4692			−0.619224
$547$	5.45211	−	5.45211i	0.233115	−	0.233115i	−0.580876	−	0.813992i	$-0.697290\pi$
$547$	5.45211	−	5.45211i	0.233115	−	0.233115i	0.813992	+	0.580876i	$0.197290\pi$
$548$		−	14.8851i		−	0.635862i
$549$	0.292452	−	0.292452i	0.0124816	−	0.0124816i
$550$	−22.3568	+	1.03125i	−0.953296	+	0.0439728i
$551$	11.8579	−	7.97071i	0.505165	−	0.339563i
$552$	64.7481	−	64.7481i	2.75586	−	2.75586i
$553$	−4.27214			−0.181670
$554$	50.9485	+	50.9485i	2.16459	+	2.16459i
$555$	6.99385	+	15.8418i	0.296873	+	0.672448i
$556$		−	65.9274i		−	2.79595i
$557$	−32.1374	−	32.1374i	−1.36170	−	1.36170i	−0.871746	−	0.489958i	$-0.837012\pi$
$557$	−32.1374	−	32.1374i	−1.36170	−	1.36170i	−0.489958	−	0.871746i	$-0.662988\pi$
$558$	0.464900	+	0.464900i	0.0196808	+	0.0196808i
$559$	12.3385	−	12.3385i	0.521864	−	0.521864i
$560$	47.0326	+	18.2234i	1.98749	+	0.770078i
$561$	−13.5407	−	13.5407i	−0.571688	−	0.571688i
$562$			59.2186i			2.49798i
$563$			2.60063i			0.109603i	0.998497	+	0.0548017i	$0.0174527\pi$
$563$			2.60063i			0.109603i	−0.998497	+	0.0548017i	$0.982547\pi$
$564$	16.6909			0.702815
$565$	0.318675	−	0.140689i	0.0134068	−	0.00591882i
$566$	12.6293	+	12.6293i	0.530850	+	0.530850i
$567$	−8.33894	+	8.33894i	−0.350202	+	0.350202i
$568$	−31.4360			−1.31903
$569$	16.3628	−	16.3628i	0.685965	−	0.685965i	−0.275372	−	0.961338i	$-0.588801\pi$
$569$	16.3628	−	16.3628i	0.685965	−	0.685965i	0.961338	+	0.275372i	$0.0888012\pi$
$570$	−24.6884	−	9.56582i	−1.03408	−	0.400668i
$571$	−10.3466			−0.432992			−0.216496	−	0.976284i	$-0.569463\pi$
$571$	−10.3466			−0.432992			−0.216496	+	0.976284i	$0.569463\pi$
$572$		−	19.4163i		−	0.811838i
$573$	3.13995	−	3.13995i	0.131173	−	0.131173i
$574$			13.8001i			0.576005i
$575$	−29.4546	+	1.35866i	−1.22834	+	0.0566599i
$576$	10.2770			0.428210
$577$	23.3309			0.971278			0.485639	−	0.874159i	$-0.338587\pi$
$577$	23.3309			0.971278			0.485639	+	0.874159i	$0.338587\pi$
$578$		−	94.0903i		−	3.91364i
$579$	8.45081			0.351204
$580$	−64.3573	+	14.5376i	−2.67229	+	0.603640i
$581$	−11.1854			−0.464048
$582$		−	27.0353i		−	1.12065i
$583$	−12.4888			−0.517233
$584$	−111.694			−4.62191
$585$	1.52143	+	0.589499i	0.0629035	+	0.0243728i
$586$		−	26.8133i		−	1.10765i
$587$	−26.1594	+	26.1594i	−1.07971	+	1.07971i	−0.0831773	+	0.996535i	$0.526507\pi$
$587$	−26.1594	+	26.1594i	−1.07971	+	1.07971i	−0.996535	+	0.0831773i	$0.973493\pi$
$588$		−	42.5394i		−	1.75430i
$589$	−1.89255			−0.0779812
$590$	8.83998	+	20.0235i	0.363936	+	0.824355i
$591$	20.3392	−	20.3392i	0.836641	−	0.836641i
$592$	71.4881			2.93814
$593$	−10.3930	+	10.3930i	−0.426790	+	0.426790i	−0.887533	−	0.460743i	$-0.847583\pi$
$593$	−10.3930	+	10.3930i	−0.426790	+	0.426790i	0.460743	+	0.887533i	$0.347583\pi$
$594$	−17.2357	−	17.2357i	−0.707189	−	0.707189i
$595$	8.67361	−	22.3857i	0.355583	−	0.917722i
$596$	−49.7327			−2.03713
$597$			14.5716i			0.596375i
$598$		−	34.9179i		−	1.42790i
$599$	11.0108	+	11.0108i	0.449891	+	0.449891i	0.895318	−	0.445427i	$-0.146948\pi$
$599$	11.0108	+	11.0108i	0.449891	+	0.449891i	−0.445427	+	0.895318i	$0.646948\pi$
$600$	57.3687	+	52.3096i	2.34207	+	2.13553i
$601$	4.22053	−	4.22053i	0.172159	−	0.172159i	−0.615768	−	0.787927i	$-0.711154\pi$
$601$	4.22053	−	4.22053i	0.172159	−	0.172159i	0.787927	+	0.615768i	$0.211154\pi$
$602$	−23.3386	−	23.3386i	−0.951210	−	0.951210i
$603$	2.39015	+	2.39015i	0.0973345	+	0.0973345i
$604$		−	80.2282i		−	3.26444i
$605$	−17.0217	+	7.51475i	−0.692031	+	0.305518i
$606$	16.4899	+	16.4899i	0.669857	+	0.669857i
$607$	−48.6467			−1.97451			−0.987254	−	0.159154i	$-0.949123\pi$
$607$	−48.6467			−1.97451			−0.987254	+	0.159154i	$0.949123\pi$
$608$	−41.5856	+	41.5856i	−1.68652	+	1.68652i
$609$	−7.34123	−	10.9215i	−0.297482	−	0.442561i
$610$	2.71128	−	6.99753i	0.109777	−	0.283322i
$611$	2.85783	−	2.85783i	0.115615	−	0.115615i
$612$		−	13.2400i		−	0.535195i
$613$	14.0319	−	14.0319i	0.566744	−	0.566744i	−0.364471	−	0.931215i	$-0.618750\pi$
$613$	14.0319	−	14.0319i	0.566744	−	0.566744i	0.931215	+	0.364471i	$0.118750\pi$
$614$	1.33496			0.0538744
$615$	−4.44244	+	11.4655i	−0.179137	+	0.462332i
$616$	−23.3208			−0.939620
$617$	35.2664			1.41977			0.709885	−	0.704318i	$-0.248747\pi$
$617$	35.2664			1.41977			0.709885	+	0.704318i	$0.248747\pi$
$618$	−1.48927	+	1.48927i	−0.0599072	+	0.0599072i
$619$	9.65826	−	9.65826i	0.388198	−	0.388198i	−0.485846	−	0.874044i	$-0.661488\pi$
$619$	9.65826	−	9.65826i	0.388198	−	0.388198i	0.874044	+	0.485846i	$0.161488\pi$
$620$	8.14915	+	3.15749i	0.327278	+	0.126808i
$621$	−22.7077	−	22.7077i	−0.911228	−	0.911228i
$622$	19.8912	+	19.8912i	0.797566	+	0.797566i
$623$	21.5291			0.862544
$624$	−37.6334	+	37.6334i	−1.50654	+	1.50654i
$625$	−2.30146	−	24.8938i	−0.0920584	−	0.995754i
$626$	52.7730	−	52.7730i	2.10923	−	2.10923i
$627$	7.08636			0.283002
$628$	−7.50815			−0.299608
$629$		−	34.0255i		−	1.35669i
$630$	1.11505	−	2.87782i	0.0444246	−	0.114655i
$631$		−	24.9743i		−	0.994212i	−0.867690	−	0.497106i	$-0.834396\pi$
$631$		−	24.9743i		−	0.994212i	0.867690	−	0.497106i	$-0.165604\pi$
$632$	−19.1950	+	19.1950i	−0.763535	+	0.763535i
$633$	10.0527	+	10.0527i	0.399557	+	0.399557i
$634$		−	7.26329i		−	0.288462i
$635$	−37.8938	+	16.7294i	−1.50377	+	0.663885i
$636$	48.2434	+	48.2434i	1.91297	+	1.91297i
$637$	−7.28362	−	7.28362i	−0.288588	−	0.288588i
$638$	20.0051	−	13.4471i	0.792011	−	0.532376i
$639$			1.11347i			0.0440483i
$640$	79.9027	−	35.2754i	3.15843	−	1.39438i
$641$	30.8944	−	30.8944i	1.22026	−	1.22026i	0.252716	−	0.967540i	$-0.418676\pi$
$641$	30.8944	−	30.8944i	1.22026	−	1.22026i	0.967540	−	0.252716i	$-0.0813239\pi$
$642$	−37.4286	−	37.4286i	−1.47719	−	1.47719i
$643$	6.59143	−	6.59143i	0.259941	−	0.259941i	−0.565089	−	0.825030i	$-0.691158\pi$
$643$	6.59143	−	6.59143i	0.259941	−	0.259941i	0.825030	+	0.565089i	$0.191158\pi$
$644$	−48.3863			−1.90669
$645$	−11.8773	−	26.9033i	−0.467667	−	1.05932i
$646$	36.7860	+	36.7860i	1.44733	+	1.44733i
$647$	33.2521	+	33.2521i	1.30728	+	1.30728i	0.923373	+	0.383903i	$0.125420\pi$
$647$	33.2521	+	33.2521i	1.30728	+	1.30728i	0.383903	+	0.923373i	$0.374580\pi$
$648$			74.9346i			2.94371i
$649$	−4.14238	−	4.14238i	−0.162602	−	0.162602i
$650$	29.5742	−	1.36417i	1.15999	−	0.0535072i
$651$			1.74309i			0.0683171i
$652$		−	15.4079i		−	0.603420i
$653$			37.6967i			1.47519i	0.675245	+	0.737593i	$0.264038\pi$
$653$			37.6967i			1.47519i	−0.675245	+	0.737593i	$0.735962\pi$
$654$			5.48909i			0.214641i
$655$	−5.24173	+	13.5283i	−0.204811	+	0.528596i
$656$	35.8931	+	35.8931i	1.40139	+	1.40139i
$657$			3.95622i			0.154347i
$658$	−5.40564	−	5.40564i	−0.210734	−	0.210734i
$659$	−21.0129	−	21.0129i	−0.818548	−	0.818548i	0.167349	−	0.985898i	$-0.446479\pi$
$659$	−21.0129	−	21.0129i	−0.818548	−	0.818548i	−0.985898	+	0.167349i	$0.946479\pi$
$660$	−30.5132	−	11.8227i	−1.18772	−	0.460199i
$661$	−27.4749			−1.06865			−0.534325	−	0.845279i	$-0.679434\pi$
$661$	−27.4749			−1.06865			−0.534325	+	0.845279i	$0.679434\pi$
$662$	37.7271	−	37.7271i	1.46631	−	1.46631i
$663$	17.9120	+	17.9120i	0.695644	+	0.695644i
$664$	−50.2566	+	50.2566i	−1.95034	+	1.95034i
$665$	3.58802	+	8.12725i	0.139137	+	0.315161i
$666$		−	4.37420i		−	0.169497i
$667$	26.3564	−	17.7163i	1.02052	−	0.685978i
$668$	27.4788	+	27.4788i	1.06319	+	1.06319i
$669$	18.5571	+	18.5571i	0.717460	+	0.717460i
$670$	57.1894	+	22.1588i	2.20942	+	0.856068i
$671$			2.00852i			0.0775379i
$672$	38.3014	+	38.3014i	1.47751	+	1.47751i
$673$	1.01710	−	1.01710i	0.0392064	−	0.0392064i	−0.687232	−	0.726438i	$-0.741174\pi$
$673$	1.01710	−	1.01710i	0.0392064	−	0.0392064i	0.726438	+	0.687232i	$0.241174\pi$
$674$			44.6013i			1.71798i
$675$	18.3454	−	20.1197i	0.706115	−	0.774407i
$676$		−	45.5457i		−	1.75176i
$677$	−19.8563			−0.763140			−0.381570	−	0.924340i	$-0.624617\pi$
$677$	−19.8563			−0.763140			−0.381570	+	0.924340i	$0.624617\pi$
$678$	0.695252			0.0267010
$679$	−6.41447	+	6.41447i	−0.246165	+	0.246165i
$680$	−61.6090	−	139.551i	−2.36260	−	5.35154i
$681$	−32.5525	+	32.5525i	−1.24742	+	1.24742i
$682$	−3.19286			−0.122261
$683$	−29.7005	−	29.7005i	−1.13646	−	1.13646i	−0.989080	−	0.147379i	$-0.952916\pi$
$683$	−29.7005	−	29.7005i	−1.13646	−	1.13646i	−0.147379	−	0.989080i	$-0.547084\pi$
$684$	3.46450	+	3.46450i	0.132468	+	0.132468i
$685$	−5.55713	+	2.45336i	−0.212327	+	0.0937382i
$686$	−34.0478	+	34.0478i	−1.29995	+	1.29995i
$687$	0.561853	−	0.561853i	0.0214360	−	0.0214360i
$688$	−121.404			−4.62849
$689$	16.5205			0.629381
$690$	−54.8743	−	21.2617i	−2.08903	−	0.809421i
$691$	−26.7508			−1.01765			−0.508824	−	0.860871i	$-0.669920\pi$
$691$	−26.7508			−1.01765			−0.508824	+	0.860871i	$0.669920\pi$
$692$	−65.0608	+	65.0608i	−2.47324	+	2.47324i
$693$			0.826028i			0.0313782i
$694$	−8.64148	+	8.64148i	−0.328026	+	0.328026i
$695$	−24.6130	+	10.8661i	−0.933623	+	0.412176i
$696$	−82.0554	−	16.0863i	−3.11030	−	0.609748i
$697$	17.0837	−	17.0837i	0.647092	−	0.647092i
$698$	−47.5463			−1.79966
$699$	−18.2147	−	18.2147i	−0.688943	−	0.688943i
$700$	−1.89035	−	40.9813i	−0.0714486	−	1.54895i
$701$		−	1.02730i		−	0.0388005i	−0.999812	−	0.0194003i	$-0.993824\pi$
$701$		−	1.02730i		−	0.0388005i	0.999812	−	0.0194003i	$-0.00617568\pi$
$702$	22.7998	+	22.7998i	0.860525	+	0.860525i
$703$	8.90342	+	8.90342i	0.335799	+	0.335799i
$704$	−35.2906	+	35.2906i	−1.33006	+	1.33006i
$705$	−2.75099	−	6.23129i	−0.103608	−	0.234684i
$706$	−26.2703	−	26.2703i	−0.988696	−	0.988696i
$707$		−	7.82489i		−	0.294285i
$708$			32.0035i			1.20276i
$709$	32.8376			1.23324			0.616621	−	0.787260i	$-0.288501\pi$
$709$	32.8376			1.23324			0.616621	+	0.787260i	$0.288501\pi$
$710$	8.15966	+	18.4825i	0.306226	+	0.693636i
$711$	0.679891	+	0.679891i	0.0254979	+	0.0254979i
$712$	96.7314	−	96.7314i	3.62516	−	3.62516i
$713$	−4.20653			−0.157536
$714$	33.8809	−	33.8809i	1.26796	−	1.26796i
$715$	−7.24878	+	3.20019i	−0.271089	+	0.119680i
$716$	−4.55380			−0.170183
$717$		−	20.2841i		−	0.757523i
$718$	−45.5945	+	45.5945i	−1.70157	+	1.70157i
$719$		−	30.4349i		−	1.13503i	−0.823363	−	0.567515i	$-0.807905\pi$
$719$		−	30.4349i		−	1.13503i	0.823363	−	0.567515i	$-0.192095\pi$
$720$	−4.58485	−	10.3852i	−0.170867	−	0.387033i
$721$	0.706697			0.0263188
$722$	32.7101			1.21734
$723$		−	1.89255i		−	0.0703845i
$724$	90.5591			3.36560
$725$	16.0347	+	21.6307i	0.595515	+	0.803344i
$726$	−37.1362			−1.37825
$727$			1.37532i			0.0510077i	0.999675	+	0.0255038i	$0.00811900\pi$
$727$			1.37532i			0.0510077i	−0.999675	+	0.0255038i	$0.991881\pi$
$728$	30.8493			1.14335
$729$	29.3134			1.08568
$730$	28.9916	+	65.6691i	1.07303	+	2.43052i
$731$			57.7836i			2.13720i
$732$	7.75877	−	7.75877i	0.286772	−	0.286772i
$733$			8.23872i			0.304304i	0.988357	+	0.152152i	$0.0486203\pi$
$733$			8.23872i			0.304304i	−0.988357	+	0.152152i	$0.951380\pi$
$734$	−15.1173			−0.557990
$735$	−15.8814	+	7.01133i	−0.585795	+	0.258617i
$736$	−92.4314	+	92.4314i	−3.40707	+	3.40707i
$737$	−16.4152			−0.604662
$738$	2.19622	−	2.19622i	0.0808441	−	0.0808441i
$739$	30.5802	+	30.5802i	1.12491	+	1.12491i	0.990992	+	0.133918i	$0.0427558\pi$
$739$	30.5802	+	30.5802i	1.12491	+	1.12491i	0.133918	+	0.990992i	$0.457244\pi$
$740$	−23.4830	−	53.1916i	−0.863253	−	1.95536i
$741$	−9.37403			−0.344364
$742$		−	31.2489i		−	1.14718i
$743$			33.4069i			1.22558i	0.790245	+	0.612791i	$0.209953\pi$
$743$			33.4069i			1.22558i	−0.790245	+	0.612791i	$0.790047\pi$
$744$	7.83180	+	7.83180i	0.287128	+	0.287128i
$745$	8.19693	+	18.5669i	0.300312	+	0.680240i
$746$	1.38283	−	1.38283i	0.0506291	−	0.0506291i
$747$	1.78010	+	1.78010i	0.0651306	+	0.0651306i
$748$	45.4651	+	45.4651i	1.66237	+	1.66237i
$749$			17.7608i			0.648967i
$750$	15.8641	−	47.3071i	0.579273	−	1.72741i
$751$	6.72041	+	6.72041i	0.245231	+	0.245231i	0.819010	−	0.573779i	$-0.194523\pi$
$751$	6.72041	+	6.72041i	0.245231	+	0.245231i	−0.573779	+	0.819010i	$0.694523\pi$
$752$	−28.1194			−1.02541
$753$	−28.5761	+	28.5761i	−1.04137	+	1.04137i
$754$	−26.4634	+	17.7882i	−0.963739	+	0.647809i
$755$	−29.9519	+	13.2232i	−1.09006	+	0.481241i
$756$	31.5941	−	31.5941i	1.14907	−	1.14907i
$757$		−	43.4105i		−	1.57778i	−0.614532	−	0.788892i	$-0.710655\pi$
$757$		−	43.4105i		−	1.57778i	0.614532	−	0.788892i	$-0.289345\pi$
$758$	60.0269	−	60.0269i	2.18027	−	2.18027i
$759$	15.7507			0.571714
$760$	52.6374	+	20.3950i	1.90936	+	0.739805i
$761$	45.4580			1.64785			0.823925	−	0.566699i	$-0.191780\pi$
$761$	45.4580			1.64785			0.823925	+	0.566699i	$0.191780\pi$
$762$	−82.6728			−2.99492
$763$	1.30236	−	1.30236i	0.0471485	−	0.0471485i
$764$	−10.5429	+	10.5429i	−0.381429	+	0.381429i
$765$	−4.94294	+	2.18221i	−0.178712	+	0.0788979i
$766$	−22.4031	−	22.4031i	−0.809456	−	0.809456i
$767$	5.47965	+	5.47965i	0.197859	+	0.197859i
$768$	74.8021			2.69919
$769$	−35.2831	+	35.2831i	−1.27234	+	1.27234i	−0.327487	+	0.944856i	$0.606202\pi$
$769$	−35.2831	+	35.2831i	−1.27234	+	1.27234i	−0.944856	+	0.327487i	$0.893798\pi$
$770$	6.05323	+	13.7112i	0.218143	+	0.494118i
$771$	20.6085	−	20.6085i	0.742198	−	0.742198i
$772$	−28.3750			−1.02124
$773$	30.5826			1.09998			0.549990	−	0.835171i	$-0.314632\pi$
$773$	30.5826			1.09998			0.549990	+	0.835171i	$0.314632\pi$
$774$			7.42846i			0.267010i
$775$	−0.164340	−	3.56277i	−0.00590328	−	0.127979i
$776$			57.6412i			2.06920i
$777$	8.20028	−	8.20028i	0.294184	−	0.294184i
$778$	−2.74850	−	2.74850i	−0.0985384	−	0.0985384i
$779$			8.94056i			0.320329i
$780$	40.3637	+	15.6394i	1.44525	+	0.559981i
$781$	−3.82358	−	3.82358i	−0.136818	−	0.136818i
$782$	81.7635	+	81.7635i	2.92386	+	2.92386i
$783$	−5.64158	+	28.7775i	−0.201614	+	1.02842i
$784$			71.6667i			2.55953i
$785$	1.23749	+	2.80305i	0.0441679	+	0.100045i
$786$	−20.4753	+	20.4753i	−0.730329	+	0.730329i
$787$	−12.7850	−	12.7850i	−0.455735	−	0.455735i	0.441518	−	0.897253i	$-0.354440\pi$
$787$	−12.7850	−	12.7850i	−0.455735	−	0.455735i	−0.897253	+	0.441518i	$0.854440\pi$
$788$	−68.2921	+	68.2921i	−2.43281	+	2.43281i
$789$	46.0096			1.63798
$790$	16.2678	+	6.30318i	0.578783	+	0.224257i
$791$	−0.164957	−	0.164957i	−0.00586521	−	0.00586521i
$792$	3.71139	+	3.71139i	0.131879	+	0.131879i
$793$		−	2.65692i		−	0.0943501i
$794$	−25.2973	−	25.2973i	−0.897768	−	0.897768i
$795$	10.0594	−	25.9623i	0.356772	−	0.920789i
$796$		−	48.9265i		−	1.73415i
$797$			12.6152i			0.446852i	0.974721	+	0.223426i	$0.0717241\pi$
$797$			12.6152i			0.446852i	−0.974721	+	0.223426i	$0.928276\pi$
$798$			17.7312i			0.627677i
$799$			13.3837i			0.473483i
$800$	−81.8970	−	74.6748i	−2.89550	−	2.64015i
$801$	−3.42625	−	3.42625i	−0.121061	−	0.121061i
$802$		−	27.1388i		−	0.958304i
$803$	−13.5853	−	13.5853i	−0.479417	−	0.479417i
$804$	63.4109	+	63.4109i	2.23633	+	2.23633i
$805$	7.97501	+	18.0643i	0.281082	+	0.636681i
$806$	4.22361			0.148770
$807$	18.0613	−	18.0613i	0.635789	−	0.635789i
$808$	−35.1577	−	35.1577i	−1.23684	−	1.23684i
$809$	26.7078	−	26.7078i	0.938996	−	0.938996i	−0.0592478	−	0.998243i	$-0.518870\pi$
$809$	26.7078	−	26.7078i	0.938996	−	0.938996i	0.998243	+	0.0592478i	$0.0188702\pi$
$810$	44.0571	−	19.4503i	1.54801	−	0.683415i
$811$		−	26.4437i		−	0.928564i	−0.885687	−	0.464282i	$-0.846312\pi$
$811$		−	26.4437i		−	0.928564i	0.885687	−	0.464282i	$-0.153688\pi$
$812$	24.6494	+	36.6707i	0.865024	+	1.28689i
$813$	3.55741	+	3.55741i	0.124764	+	0.124764i
$814$	15.0207	+	15.0207i	0.526474	+	0.526474i
$815$	−5.75230	+	2.53953i	−0.201494	+	0.0889557i
$816$		−	176.244i		−	6.16977i
$817$	−15.1202	−	15.1202i	−0.528988	−	0.528988i
$818$	3.62991	−	3.62991i	0.126917	−	0.126917i
$819$		−	1.09269i		−	0.0381818i
$820$	14.9162	−	38.4972i	0.520898	−	1.34438i
$821$		−	33.9341i		−	1.18431i	−0.805825	−	0.592154i	$-0.798278\pi$
$821$		−	33.9341i		−	1.18431i	0.805825	−	0.592154i	$-0.201722\pi$
$822$	−12.1240			−0.422872
$823$	6.03790			0.210468			0.105234	−	0.994447i	$-0.466441\pi$
$823$	6.03790			0.210468			0.105234	+	0.994447i	$0.466441\pi$
$824$	3.17523	−	3.17523i	0.110614	−	0.110614i
$825$	0.615347	+	13.3402i	0.0214236	+	0.464447i
$826$	10.3649	−	10.3649i	0.360640	−	0.360640i
$827$	−34.3817			−1.19557			−0.597784	−	0.801657i	$-0.703952\pi$
$827$	−34.3817			−1.19557			−0.597784	+	0.801657i	$0.703952\pi$
$828$	7.70046	+	7.70046i	0.267609	+	0.267609i
$829$	−22.3751	−	22.3751i	−0.777119	−	0.777119i	0.202221	−	0.979340i	$-0.435184\pi$
$829$	−22.3751	−	22.3751i	−0.777119	−	0.777119i	−0.979340	+	0.202221i	$0.935184\pi$
$830$	42.5927	+	16.5031i	1.47841	+	0.572830i
$831$	30.4008	−	30.4008i	1.05459	−	1.05459i
$832$	46.6833	−	46.6833i	1.61845	−	1.61845i
$833$	34.1105			1.18186
$834$	−53.6979			−1.85941
$835$	5.72973	−	14.7878i	0.198285	−	0.511754i
$836$	−23.7936			−0.822920
$837$	2.74668	−	2.74668i	0.0949391	−	0.0949391i
$838$		−	36.4065i		−	1.25764i
$839$	−7.70723	+	7.70723i	−0.266083	+	0.266083i	−0.827520	−	0.561437i	$-0.810249\pi$
$839$	−7.70723	+	7.70723i	−0.266083	+	0.266083i	0.561437	+	0.827520i	$0.310249\pi$
$840$	18.7844	−	48.4804i	0.648122	−	1.67273i
$841$	−26.8534	−	10.9496i	−0.925980	−	0.377572i
$842$	−16.6747	+	16.6747i	−0.574649	+	0.574649i
$843$	35.3356			1.21702
$844$	−33.7534	−	33.7534i	−1.16184	−	1.16184i
$845$	−17.0038	+	7.50683i	−0.584947	+	0.258243i
$846$			1.72057i			0.0591543i
$847$	8.81104	+	8.81104i	0.302751	+	0.302751i
$848$	−81.2762	−	81.2762i	−2.79104	−	2.79104i
$849$	7.53588	−	7.53588i	0.258631	−	0.258631i
$850$	−66.0562	+	72.4449i	−2.26571	+	2.48484i
$851$	19.7894	+	19.7894i	0.678373	+	0.678373i
$852$			29.5405i			1.01204i
$853$		−	11.7987i		−	0.403981i	−0.979388	−	0.201990i	$-0.935259\pi$
$853$		−	11.7987i		−	0.403981i	0.979388	−	0.201990i	$-0.0647410\pi$
$854$	−5.02562			−0.171973
$855$	0.722397	−	1.86443i	0.0247055	−	0.0637622i
$856$	79.8005	+	79.8005i	2.72753	+	2.72753i
$857$	9.84337	−	9.84337i	0.336243	−	0.336243i	−0.518708	−	0.854951i	$-0.673587\pi$
$857$	9.84337	−	9.84337i	0.336243	−	0.336243i	0.854951	+	0.518708i	$0.173587\pi$
$858$	−15.8146			−0.539902
$859$	−29.8718	+	29.8718i	−1.01921	+	1.01921i	−0.0194004	+	0.999812i	$0.506176\pi$
$859$	−29.8718	+	29.8718i	−1.01921	+	1.01921i	−0.999812	+	0.0194004i	$0.993824\pi$
$860$	39.8799	+	90.3322i	1.35989	+	3.08030i
$861$	8.23449			0.280631
$862$		−	21.8093i		−	0.742829i
$863$	−13.8824	+	13.8824i	−0.472561	+	0.472561i	−0.902742	−	0.430181i	$-0.858450\pi$
$863$	−13.8824	+	13.8824i	−0.472561	+	0.472561i	0.430181	+	0.902742i	$0.358450\pi$
$864$		−	120.707i		−	4.10654i
$865$	35.0127	+	13.5661i	1.19047	+	0.461262i
$866$	−76.3055			−2.59297
$867$	−56.1435			−1.90673
$868$		−	5.85271i		−	0.198654i
$869$	−4.66939			−0.158398
$870$	11.8409	+	52.4191i	0.401443	+	1.77717i
$871$	21.7145			0.735767
$872$		−	11.7031i		−	0.396318i
$873$	2.04167			0.0691000
$874$	−42.7899			−1.44739
$875$	−14.9882	+	7.46026i	−0.506692	+	0.252203i
$876$			104.959i			3.54622i
$877$	18.6332	−	18.6332i	0.629200	−	0.629200i	−0.318667	−	0.947867i	$-0.603235\pi$
$877$	18.6332	−	18.6332i	0.629200	−	0.629200i	0.947867	+	0.318667i	$0.103235\pi$
$878$			63.1446i			2.13103i
$879$	−15.9994			−0.539648
$880$	51.4060	+	19.9179i	1.73290	+	0.671432i
$881$	33.3971	−	33.3971i	1.12518	−	1.12518i	0.134226	−	0.990951i	$-0.457145\pi$
$881$	33.3971	−	33.3971i	1.12518	−	1.12518i	0.990951	−	0.134226i	$-0.0428547\pi$
$882$	4.38513			0.147655
$883$	12.9731	−	12.9731i	0.436580	−	0.436580i	−0.454279	−	0.890859i	$-0.650103\pi$
$883$	12.9731	−	12.9731i	0.436580	−	0.436580i	0.890859	+	0.454279i	$0.150103\pi$
$884$	−60.1425	−	60.1425i	−2.02281	−	2.02281i
$885$	11.9480	−	5.27480i	0.401627	−	0.177310i
$886$	35.8830			1.20551
$887$		−	11.7923i		−	0.395948i	−0.980207	−	0.197974i	$-0.936564\pi$
$887$		−	11.7923i		−	0.395948i	0.980207	−	0.197974i	$-0.0634362\pi$
$888$		−	73.6887i		−	2.47283i
$889$	19.6152	+	19.6152i	0.657872	+	0.657872i
$890$	−81.9803	−	31.7643i	−2.74799	−	1.06474i
$891$	−9.11434	+	9.11434i	−0.305342	+	0.305342i
$892$	−62.3086	−	62.3086i	−2.08625	−	2.08625i
$893$	−3.50211	−	3.50211i	−0.117194	−	0.117194i
$894$			40.5074i			1.35477i
$895$	0.750555	+	1.70009i	0.0250883	+	0.0568277i
$896$	−41.3604	−	41.3604i	−1.38175	−	1.38175i
$897$	−20.8354			−0.695675
$898$	38.8186	−	38.8186i	1.29539	−	1.29539i
$899$	2.14293	+	3.18802i	0.0714707	+	0.106326i
$900$	−6.22115	+	6.82283i	−0.207372	+	0.227428i
$901$	−38.6843	+	38.6843i	−1.28876	+	1.28876i
$902$			15.0833i			0.502220i
$903$	−13.9261	+	13.9261i	−0.463431	+	0.463431i
$904$	−1.48233			−0.0493014
$905$	−14.9259	−	33.8088i	−0.496154	−	1.12384i
$906$	−65.3459			−2.17097
$907$	37.1013			1.23193			0.615964	−	0.787775i	$-0.288767\pi$
$907$	37.1013			1.23193			0.615964	+	0.787775i	$0.288767\pi$
$908$	109.301	−	109.301i	3.62727	−	3.62727i
$909$	−1.24529	+	1.24529i	−0.0413038	+	0.0413038i
$910$	−8.00738	−	18.1376i	−0.265442	−	0.601255i
$911$	37.3064	+	37.3064i	1.23602	+	1.23602i	0.961616	+	0.274400i	$0.0884794\pi$
$911$	37.3064	+	37.3064i	1.23602	+	1.23602i	0.274400	+	0.961616i	$0.411521\pi$
$912$	46.1176	+	46.1176i	1.52711	+	1.52711i
$913$	−12.2255			−0.404604
$914$	56.2282	−	56.2282i	1.85986	−	1.85986i
$915$	−4.17541	−	1.61782i	−0.138035	−	0.0534833i
$916$	−1.88651	+	1.88651i	−0.0623322	+	0.0623322i
$917$	9.71605			0.320852
$918$	−106.776			−3.52413
$919$			38.7184i			1.27720i	0.769538	+	0.638601i	$0.220486\pi$
$919$			38.7184i			1.27720i	−0.769538	+	0.638601i	$0.779514\pi$
$920$	116.996	+	45.3315i	3.85724	+	1.49454i
$921$		−	0.796565i		−	0.0262477i
$922$	−30.0063	+	30.0063i	−0.988204	+	0.988204i
$923$	5.05794	+	5.05794i	0.166484	+	0.166484i
$924$			21.9146i			0.720936i
$925$	−15.9878	+	17.5340i	−0.525674	+	0.576515i
$926$	−53.5027	−	53.5027i	−1.75821	−	1.75821i
$927$	−0.112468	−	0.112468i	−0.00369392	−	0.00369392i
$928$	117.139	+	22.9640i	3.84526	+	0.753831i
$929$			25.0417i			0.821591i	0.911728	+	0.410795i	$0.134749\pi$
$929$			25.0417i			0.821591i	−0.911728	+	0.410795i	$0.865251\pi$
$930$	2.57178	−	6.63749i	0.0843320	−	0.217652i
$931$	−8.92567	+	8.92567i	−0.292527	+	0.292527i
$932$	61.1588	+	61.1588i	2.00332	+	2.00332i
$933$	11.8691	−	11.8691i	0.388575	−	0.388575i
$934$	−105.044			−3.43715
$935$	9.48013	−	24.4672i	0.310033	−	0.800163i
$936$	−4.90953	−	4.90953i	−0.160473	−	0.160473i
$937$	12.9733	+	12.9733i	0.423820	+	0.423820i	0.886517	−	0.462696i	$-0.153118\pi$
$937$	12.9733	+	12.9733i	0.423820	+	0.423820i	−0.462696	+	0.886517i	$0.653118\pi$
$938$		−	41.0734i		−	1.34109i
$939$	−31.4895	−	31.4895i	−1.02762	−	1.02762i
$940$	9.23692	+	20.9226i	0.301275	+	0.682420i
$941$			19.5452i			0.637155i	0.947897	+	0.318578i	$0.103205\pi$
$941$			19.5452i			0.637155i	−0.947897	+	0.318578i	$0.896795\pi$
$942$			6.11540i			0.199250i
$943$			19.8720i			0.647121i
$944$		−	53.9166i		−	1.75484i
$945$	−17.0025	−	6.58783i	−0.553091	−	0.214302i
$946$	−25.5088	−	25.5088i	−0.829361	−	0.829361i
$947$		−	14.9594i		−	0.486115i	−0.970012	−	0.243058i	$-0.921850\pi$
$947$		−	14.9594i		−	0.486115i	0.970012	−	0.243058i	$-0.0781504\pi$
$948$	18.0376	+	18.0376i	0.585833	+	0.585833i
$949$	17.9711	+	17.9711i	0.583366	+	0.583366i
$950$	−1.67171	−	36.2415i	−0.0542376	−	1.17583i
$951$	−4.33399			−0.140539
$952$	−72.2365	+	72.2365i	−2.34120	+	2.34120i
$953$	−14.4711	−	14.4711i	−0.468765	−	0.468765i	0.432749	−	0.901514i	$-0.357544\pi$
$953$	−14.4711	−	14.4711i	−0.468765	−	0.468765i	−0.901514	+	0.432749i	$0.857544\pi$
$954$	−4.97311	+	4.97311i	−0.161011	+	0.161011i
$955$	5.67370	+	2.19835i	0.183597	+	0.0711369i
$956$			68.1071i			2.20274i
$957$	−8.02386	−	11.9370i	−0.259375	−	0.385869i
$958$	41.0004	+	41.0004i	1.32466	+	1.32466i
$959$	2.87657	+	2.87657i	0.0928892	+	0.0928892i
$960$	−44.9381	−	101.790i	−1.45037	−	3.28525i
$961$			30.4912i			0.983587i
$962$	−19.8698	−	19.8698i	−0.640626	−	0.640626i
$963$	2.82656	−	2.82656i	0.0910845	−	0.0910845i
$964$			6.35454i			0.204666i
$965$	4.67675	+	10.5933i	0.150550	+	0.341012i
$966$			39.4107i			1.26802i
$967$	49.4414			1.58993			0.794963	−	0.606657i	$-0.207490\pi$
$967$	49.4414			1.58993			0.794963	+	0.606657i	$0.207490\pi$
$968$	79.1770			2.54484
$969$	21.9501	−	21.9501i	0.705140	−	0.705140i
$970$	33.8896	−	14.9616i	1.08813	−	0.480387i
$971$	40.7685	−	40.7685i	1.30832	−	1.30832i	0.385701	−	0.922624i	$-0.373960\pi$
$971$	40.7685	−	40.7685i	1.30832	−	1.30832i	0.922624	−	0.385701i	$-0.126040\pi$
$972$	−19.0966			−0.612523
$973$	12.7405	+	12.7405i	0.408443	+	0.408443i
$974$	76.8068	+	76.8068i	2.46105	+	2.46105i
$975$	−0.813997	−	17.6468i	−0.0260688	−	0.565151i
$976$	−13.0713	+	13.0713i	−0.418402	+	0.418402i
$977$	−2.35368	+	2.35368i	−0.0753008	+	0.0753008i	−0.743754	−	0.668453i	$-0.766957\pi$
$977$	−2.35368	+	2.35368i	−0.0753008	+	0.0753008i	0.668453	+	0.743754i	$0.266957\pi$
$978$	−12.5498			−0.401297
$979$	23.5310			0.752054
$980$	53.3245	−	23.5417i	1.70339	−	0.752012i
$981$	−0.414528			−0.0132349
$982$	−69.3502	+	69.3502i	−2.21305	+	2.21305i
$983$			0.916231i			0.0292232i	0.999893	+	0.0146116i	$0.00465119\pi$
$983$			0.916231i			0.0292232i	−0.999893	+	0.0146116i	$0.995349\pi$
$984$	36.9980	−	36.9980i	1.17945	−	1.17945i
$985$	36.7516	+	14.2399i	1.17100	+	0.453721i
$986$	20.3136	−	103.619i	0.646918	−	3.29990i
$987$	−3.22554	+	3.22554i	−0.102670	+	0.102670i
$988$	31.4749			1.00135
$989$	−33.6073	−	33.6073i	−1.06865	−	1.06865i
$990$	1.21873	−	3.14542i	0.0387339	−	0.0999680i
$991$			11.2855i			0.358495i	0.983804	+	0.179248i	$0.0573663\pi$
$991$			11.2855i			0.358495i	−0.983804	+	0.179248i	$0.942634\pi$
$992$	−11.1803	−	11.1803i	−0.354976	−	0.354976i
$993$	−22.5117	−	22.5117i	−0.714387	−	0.714387i
$994$	9.56719	−	9.56719i	0.303453	−	0.303453i
$995$	−18.2659	+	8.06405i	−0.579069	+	0.255648i
$996$	47.2262	+	47.2262i	1.49642	+	1.49642i
$997$			45.0022i			1.42523i	0.701553	+	0.712617i	$0.252490\pi$
$997$			45.0022i			1.42523i	−0.701553	+	0.712617i	$0.747510\pi$
$998$			13.1237i			0.415424i
$999$	−25.8432			−0.817644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.2.e.a.133.13	yes	26
5.2	odd	4		145.2.j.a.17.1	yes	26
5.3	odd	4		725.2.j.c.307.13		26
5.4	even	2		725.2.e.c.568.1		26
29.12	odd	4		145.2.j.a.128.1	yes	26
145.12	even	4	inner	145.2.e.a.12.1	✓	26
145.99	odd	4		725.2.j.c.418.13		26
145.128	even	4		725.2.e.c.157.13		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.e.a.12.1	✓	26	145.12	even	4	inner
145.2.e.a.133.13	yes	26	1.1	even	1	trivial
145.2.j.a.17.1	yes	26	5.2	odd	4
145.2.j.a.128.1	yes	26	29.12	odd	4
725.2.e.c.157.13		26	145.128	even	4
725.2.e.c.568.1		26	5.4	even	2
725.2.j.c.307.13		26	5.3	odd	4
725.2.j.c.418.13		26	145.99	odd	4

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:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.73482i q^{2} +1.63186 q^{3} -5.47925 q^{4} +(0.903087 + 2.04559i) q^{5} +4.46285i q^{6} +(1.05887 - 1.05887i) q^{7} -9.51511i q^{8} -0.337028 q^{9} +O(q^{10})\)	\(q+2.73482i q^{2} +1.63186 q^{3} -5.47925 q^{4} +(0.903087 + 2.04559i) q^{5} +4.46285i q^{6} +(1.05887 - 1.05887i) q^{7} -9.51511i q^{8} -0.337028 q^{9} +(-5.59432 + 2.46978i) q^{10} +(1.15733 - 1.15733i) q^{11} -8.94137 q^{12} +(-1.53095 + 1.53095i) q^{13} +(2.89582 + 2.89582i) q^{14} +(1.47371 + 3.33812i) q^{15} +15.0636 q^{16} -7.16970i q^{17} -0.921711i q^{18} +(1.87609 + 1.87609i) q^{19} +(-4.94824 - 11.2083i) q^{20} +(1.72793 - 1.72793i) q^{21} +(3.16509 + 3.16509i) q^{22} +(4.16994 + 4.16994i) q^{23} -15.5273i q^{24} +(-3.36887 + 3.69469i) q^{25} +(-4.18686 - 4.18686i) q^{26} -5.44557 q^{27} +(-5.80180 + 5.80180i) q^{28} +(1.03600 - 5.28457i) q^{29} +(-9.12915 + 4.03034i) q^{30} +(-0.504388 + 0.504388i) q^{31} +22.1661i q^{32} +(1.88860 - 1.88860i) q^{33} +19.6078 q^{34} +(3.12226 + 1.20976i) q^{35} +1.84666 q^{36} +4.74574 q^{37} +(-5.13076 + 5.13076i) q^{38} +(-2.49829 + 2.49829i) q^{39} +(19.4640 - 8.59298i) q^{40} +(2.38277 + 2.38277i) q^{41} +(4.72557 + 4.72557i) q^{42} -8.05942 q^{43} +(-6.34129 + 6.34129i) q^{44} +(-0.304366 - 0.689421i) q^{45} +(-11.4040 + 11.4040i) q^{46} -1.86671 q^{47} +24.5818 q^{48} +4.75760i q^{49} +(-10.1043 - 9.21325i) q^{50} -11.7000i q^{51} +(8.38843 - 8.38843i) q^{52} +(-5.39552 - 5.39552i) q^{53} -14.8927i q^{54} +(3.41259 + 1.32225i) q^{55} +(-10.0753 - 10.0753i) q^{56} +(3.06152 + 3.06152i) q^{57} +(14.4524 + 2.83326i) q^{58} -3.57926i q^{59} +(-8.07483 - 18.2904i) q^{60} +(-0.867739 + 0.867739i) q^{61} +(-1.37941 - 1.37941i) q^{62} +(-0.356868 + 0.356868i) q^{63} -30.4931 q^{64} +(-4.51426 - 1.74911i) q^{65} +(5.16498 + 5.16498i) q^{66} +(-7.09185 - 7.09185i) q^{67} +39.2845i q^{68} +(6.80476 + 6.80476i) q^{69} +(-3.30847 + 8.53882i) q^{70} -3.30380i q^{71} +3.20686i q^{72} -11.7385i q^{73} +12.9787i q^{74} +(-5.49753 + 6.02922i) q^{75} +(-10.2795 - 10.2795i) q^{76} -2.45092i q^{77} +(-6.83238 - 6.83238i) q^{78} +(-2.01731 - 2.01731i) q^{79} +(13.6038 + 30.8140i) q^{80} -7.87533 q^{81} +(-6.51644 + 6.51644i) q^{82} +(-5.28177 - 5.28177i) q^{83} +(-9.46773 + 9.46773i) q^{84} +(14.6663 - 6.47486i) q^{85} -22.0411i q^{86} +(1.69060 - 8.62369i) q^{87} +(-11.0121 - 11.0121i) q^{88} +(10.1661 + 10.1661i) q^{89} +(1.88544 - 0.832385i) q^{90} +3.24214i q^{91} +(-22.8481 - 22.8481i) q^{92} +(-0.823091 + 0.823091i) q^{93} -5.10511i q^{94} +(-2.14343 + 5.53198i) q^{95} +36.1721i q^{96} -6.05786 q^{97} -13.0112 q^{98} +(-0.390052 + 0.390052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 4 q^{3} - 22 q^{4} - 4 q^{7} + 10 q^{9}+O(q^{10}) \) 26 * q - 4 * q^3 - 22 * q^4 - 4 * q^7 + 10 * q^9	\( 26 q - 4 q^{3} - 22 q^{4} - 4 q^{7} + 10 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 14 q^{13} + 4 q^{14} - 10 q^{15} + 6 q^{16} - 20 q^{20} + 16 q^{21} + 8 q^{22} - 4 q^{23} + 10 q^{25} + 6 q^{26} - 4 q^{27} + 8 q^{28} + 16 q^{30} + 8 q^{31} + 32 q^{34} + 16 q^{35} - 22 q^{36} + 16 q^{37} + 8 q^{38} + 16 q^{39} + 32 q^{40} - 6 q^{41} + 4 q^{42} + 12 q^{43} - 44 q^{45} - 32 q^{46} - 36 q^{47} + 4 q^{48} - 46 q^{50} + 26 q^{52} + 14 q^{53} + 46 q^{55} - 32 q^{56} + 12 q^{57} + 58 q^{58} - 14 q^{60} + 18 q^{61} - 28 q^{62} - 60 q^{63} - 30 q^{64} - 18 q^{65} + 20 q^{66} - 32 q^{67} - 12 q^{69} + 32 q^{70} + 2 q^{75} + 20 q^{76} + 56 q^{78} - 4 q^{79} + 12 q^{80} - 86 q^{81} - 58 q^{82} - 60 q^{83} - 76 q^{84} + 8 q^{85} - 12 q^{87} - 68 q^{88} + 46 q^{89} + 6 q^{90} + 28 q^{92} + 8 q^{93} + 20 q^{95} - 8 q^{97} + 34 q^{98} - 36 q^{99}+O(q^{100}) \) 26 * q - 4 * q^3 - 22 * q^4 - 4 * q^7 + 10 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 14 * q^13 + 4 * q^14 - 10 * q^15 + 6 * q^16 - 20 * q^20 + 16 * q^21 + 8 * q^22 - 4 * q^23 + 10 * q^25 + 6 * q^26 - 4 * q^27 + 8 * q^28 + 16 * q^30 + 8 * q^31 + 32 * q^34 + 16 * q^35 - 22 * q^36 + 16 * q^37 + 8 * q^38 + 16 * q^39 + 32 * q^40 - 6 * q^41 + 4 * q^42 + 12 * q^43 - 44 * q^45 - 32 * q^46 - 36 * q^47 + 4 * q^48 - 46 * q^50 + 26 * q^52 + 14 * q^53 + 46 * q^55 - 32 * q^56 + 12 * q^57 + 58 * q^58 - 14 * q^60 + 18 * q^61 - 28 * q^62 - 60 * q^63 - 30 * q^64 - 18 * q^65 + 20 * q^66 - 32 * q^67 - 12 * q^69 + 32 * q^70 + 2 * q^75 + 20 * q^76 + 56 * q^78 - 4 * q^79 + 12 * q^80 - 86 * q^81 - 58 * q^82 - 60 * q^83 - 76 * q^84 + 8 * q^85 - 12 * q^87 - 68 * q^88 + 46 * q^89 + 6 * q^90 + 28 * q^92 + 8 * q^93 + 20 * q^95 - 8 * q^97 + 34 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more