LMFDB - Embedded newform 370.2.c.a.369.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(369,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(2))

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("370.369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.c (of order $2$, degree $1$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 19x^{8} + 103x^{6} + 210x^{4} + 140x^{2} + 16 $ x^10 + 19x^8 + 103x^6 + 210x^4 + 140x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			369.1
Root			$-3.40359i$ of defining polynomial
Character	$\chi$	$=$	370.369
Dual form			370.2.c.a.369.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.40359i q^{3} +1.00000 q^{4} +(-1.28269 - 1.83159i) q^{5} +3.40359i q^{6} -2.06225i q^{7} -1.00000 q^{8} -8.58443 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.40359i q^{3} +1.00000 q^{4} +(-1.28269 - 1.83159i) q^{5} +3.40359i q^{6} -2.06225i q^{7} -1.00000 q^{8} -8.58443 q^{9} +(1.28269 + 1.83159i) q^{10} +3.77719 q^{11} -3.40359i q^{12} -2.88351 q^{13} +2.06225i q^{14} +(-6.23397 + 4.36575i) q^{15} +1.00000 q^{16} +5.80724 q^{17} +8.58443 q^{18} -0.157282i q^{19} +(-1.28269 - 1.83159i) q^{20} -7.01905 q^{21} -3.77719 q^{22} +5.41883 q^{23} +3.40359i q^{24} +(-1.70942 + 4.69871i) q^{25} +2.88351 q^{26} +19.0071i q^{27} -2.06225i q^{28} -4.29061i q^{29} +(6.23397 - 4.36575i) q^{30} +0.425694i q^{31} -1.00000 q^{32} -12.8560i q^{33} -5.80724 q^{34} +(-3.77719 + 2.64522i) q^{35} -8.58443 q^{36} +(-4.80724 + 3.72698i) q^{37} +0.157282i q^{38} +9.81429i q^{39} +(1.28269 + 1.83159i) q^{40} +0.923733 q^{41} +7.01905 q^{42} -10.8263 q^{43} +3.77719 q^{44} +(11.0112 + 15.7231i) q^{45} -5.41883 q^{46} -0.676445i q^{47} -3.40359i q^{48} +2.74713 q^{49} +(1.70942 - 4.69871i) q^{50} -19.7655i q^{51} -2.88351 q^{52} -9.87810i q^{53} -19.0071i q^{54} +(-4.84496 - 6.91824i) q^{55} +2.06225i q^{56} -0.535322 q^{57} +4.29061i q^{58} -8.47192i q^{59} +(-6.23397 + 4.36575i) q^{60} +1.23904i q^{61} -0.425694i q^{62} +17.7032i q^{63} +1.00000 q^{64} +(3.69865 + 5.28140i) q^{65} +12.8560i q^{66} -6.45516i q^{67} +5.80724 q^{68} -18.4435i q^{69} +(3.77719 - 2.64522i) q^{70} -3.28329 q^{71} +8.58443 q^{72} +0.980489i q^{73} +(4.80724 - 3.72698i) q^{74} +(15.9925 + 5.81815i) q^{75} -0.157282i q^{76} -7.78950i q^{77} -9.81429i q^{78} +8.04725i q^{79} +(-1.28269 - 1.83159i) q^{80} +38.9391 q^{81} -0.923733 q^{82} +11.9496i q^{83} -7.01905 q^{84} +(-7.44889 - 10.6365i) q^{85} +10.8263 q^{86} -14.6035 q^{87} -3.77719 q^{88} -7.65857i q^{89} +(-11.0112 - 15.7231i) q^{90} +5.94652i q^{91} +5.41883 q^{92} +1.44889 q^{93} +0.676445i q^{94} +(-0.288075 + 0.201743i) q^{95} +3.40359i q^{96} +13.9571 q^{97} -2.74713 q^{98} -32.4250 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9	$ 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9} + 3 q^{10} - 2 q^{13} - 10 q^{15} + 10 q^{16} + 18 q^{17} + 8 q^{18} - 3 q^{20} - 12 q^{21} + 10 q^{23} + 5 q^{25} + 2 q^{26} + 10 q^{30} - 10 q^{32} - 18 q^{34} - 8 q^{36} - 8 q^{37} + 3 q^{40} - 4 q^{41} + 12 q^{42} - 10 q^{43} + 20 q^{45} - 10 q^{46} - 8 q^{49} - 5 q^{50} - 2 q^{52} + 5 q^{55} + 12 q^{57} - 10 q^{60} + 10 q^{64} + 2 q^{65} + 18 q^{68} - 20 q^{71} + 8 q^{72} + 8 q^{74} + 25 q^{75} - 3 q^{80} + 58 q^{81} + 4 q^{82} - 12 q^{84} - 28 q^{85} + 10 q^{86} - 10 q^{87} - 20 q^{90} + 10 q^{92} - 32 q^{93} + 2 q^{95} + 2 q^{97} + 8 q^{98} - 82 q^{99}+O(q^{100}) $ 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9 + 3 * q^10 - 2 * q^13 - 10 * q^15 + 10 * q^16 + 18 * q^17 + 8 * q^18 - 3 * q^20 - 12 * q^21 + 10 * q^23 + 5 * q^25 + 2 * q^26 + 10 * q^30 - 10 * q^32 - 18 * q^34 - 8 * q^36 - 8 * q^37 + 3 * q^40 - 4 * q^41 + 12 * q^42 - 10 * q^43 + 20 * q^45 - 10 * q^46 - 8 * q^49 - 5 * q^50 - 2 * q^52 + 5 * q^55 + 12 * q^57 - 10 * q^60 + 10 * q^64 + 2 * q^65 + 18 * q^68 - 20 * q^71 + 8 * q^72 + 8 * q^74 + 25 * q^75 - 3 * q^80 + 58 * q^81 + 4 * q^82 - 12 * q^84 - 28 * q^85 + 10 * q^86 - 10 * q^87 - 20 * q^90 + 10 * q^92 - 32 * q^93 + 2 * q^95 + 2 * q^97 + 8 * q^98 - 82 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	3.40359i		−	1.96506i	−0.186094	−	0.982532i	$-0.559583\pi$
$3$		−	3.40359i		−	1.96506i	0.186094	−	0.982532i	$-0.440417\pi$
$4$	1.00000			0.500000
$5$	−1.28269	−	1.83159i	−0.573636	−	0.819110i
$5$	−1.28269	−	1.83159i	−0.573636	−	0.819110i
$6$			3.40359i			1.38951i
$7$		−	2.06225i		−	0.779457i	−0.920930	−	0.389728i	$-0.872569\pi$
$7$		−	2.06225i		−	0.779457i	0.920930	−	0.389728i	$-0.127431\pi$
$8$	−1.00000			−0.353553
$9$	−8.58443			−2.86148
$10$	1.28269	+	1.83159i	0.405622	+	0.579198i
$11$	3.77719			1.13886			0.569432	−	0.822038i	$-0.307163\pi$
$11$	3.77719			1.13886			0.569432	+	0.822038i	$0.307163\pi$
$12$		−	3.40359i		−	0.982532i
$13$	−2.88351			−0.799742			−0.399871	−	0.916571i	$-0.630945\pi$
$13$	−2.88351			−0.799742			−0.399871	+	0.916571i	$0.630945\pi$
$14$			2.06225i			0.551159i
$15$	−6.23397	+	4.36575i	−1.60960	+	1.12723i
$16$	1.00000			0.250000
$17$	5.80724			1.40846			0.704232	−	0.709970i	$-0.251292\pi$
$17$	5.80724			1.40846			0.704232	+	0.709970i	$0.251292\pi$
$18$	8.58443			2.02337
$19$		−	0.157282i		−	0.0360829i	−0.999837	−	0.0180414i	$-0.994257\pi$
$19$		−	0.157282i		−	0.0360829i	0.999837	−	0.0180414i	$-0.00574308\pi$
$20$	−1.28269	−	1.83159i	−0.286818	−	0.409555i
$21$	−7.01905			−1.53168
$22$	−3.77719			−0.805299
$23$	5.41883			1.12990			0.564952	−	0.825124i	$-0.308895\pi$
$23$	5.41883			1.12990			0.564952	+	0.825124i	$0.308895\pi$
$24$			3.40359i			0.694755i
$25$	−1.70942	+	4.69871i	−0.341883	+	0.939742i
$26$	2.88351			0.565503
$27$			19.0071i			3.65792i
$28$		−	2.06225i		−	0.389728i
$29$		−	4.29061i		−	0.796746i	−0.917223	−	0.398373i	$-0.869575\pi$
$29$		−	4.29061i		−	0.796746i	0.917223	−	0.398373i	$-0.130425\pi$
$30$	6.23397	−	4.36575i	1.13816	−	0.797073i
$31$			0.425694i			0.0764569i	0.999269	+	0.0382285i	$0.0121715\pi$
$31$			0.425694i			0.0764569i	−0.999269	+	0.0382285i	$0.987829\pi$
$32$	−1.00000			−0.176777
$33$		−	12.8560i		−	2.23794i
$34$	−5.80724			−0.995934
$35$	−3.77719	+	2.64522i	−0.638461	+	0.447125i
$36$	−8.58443			−1.43074
$37$	−4.80724	+	3.72698i	−0.790306	+	0.612713i
$37$	−4.80724	+	3.72698i	−0.790306	+	0.612713i
$38$			0.157282i			0.0255144i
$39$			9.81429i			1.57154i
$40$	1.28269	+	1.83159i	0.202811	+	0.289599i
$41$	0.923733			0.144263			0.0721314	−	0.997395i	$-0.477020\pi$
$41$	0.923733			0.144263			0.0721314	+	0.997395i	$0.477020\pi$
$42$	7.01905			1.08306
$43$	−10.8263			−1.65099			−0.825497	−	0.564406i	$-0.809105\pi$
$43$	−10.8263			−1.65099			−0.825497	+	0.564406i	$0.809105\pi$
$44$	3.77719			0.569432
$45$	11.0112	+	15.7231i	1.64145	+	2.34386i
$46$	−5.41883			−0.798963
$47$		−	0.676445i		−	0.0986697i	−0.998782	−	0.0493348i	$-0.984290\pi$
$47$		−	0.676445i		−	0.0986697i	0.998782	−	0.0493348i	$-0.0157101\pi$
$48$		−	3.40359i		−	0.491266i
$49$	2.74713			0.392447
$50$	1.70942	−	4.69871i	0.241748	−	0.664498i
$51$		−	19.7655i		−	2.76772i
$52$	−2.88351			−0.399871
$53$		−	9.87810i		−	1.35686i	−0.734664	−	0.678431i	$-0.762660\pi$
$53$		−	9.87810i		−	1.35686i	0.734664	−	0.678431i	$-0.237340\pi$
$54$		−	19.0071i		−	2.58654i
$55$	−4.84496	−	6.91824i	−0.653294	−	0.932856i
$56$			2.06225i			0.275580i
$57$	−0.535322			−0.0709052
$58$			4.29061i			0.563385i
$59$		−	8.47192i		−	1.10295i	−0.834192	−	0.551475i	$-0.814065\pi$
$59$		−	8.47192i		−	1.10295i	0.834192	−	0.551475i	$-0.185935\pi$
$60$	−6.23397	+	4.36575i	−0.804802	+	0.563616i
$61$			1.23904i			0.158643i	0.996849	+	0.0793215i	$0.0252754\pi$
$61$			1.23904i			0.158643i	−0.996849	+	0.0793215i	$0.974725\pi$
$62$		−	0.425694i		−	0.0540632i
$63$			17.7032i			2.23040i
$64$	1.00000			0.125000
$65$	3.69865	+	5.28140i	0.458761	+	0.655077i
$66$			12.8560i			1.58246i
$67$		−	6.45516i		−	0.788623i	−0.918977	−	0.394312i	$-0.870983\pi$
$67$		−	6.45516i		−	0.788623i	0.918977	−	0.394312i	$-0.129017\pi$
$68$	5.80724			0.704232
$69$		−	18.4435i		−	2.22033i
$70$	3.77719	−	2.64522i	0.451460	−	0.316165i
$71$	−3.28329			−0.389655			−0.194828	−	0.980838i	$-0.562415\pi$
$71$	−3.28329			−0.389655			−0.194828	+	0.980838i	$0.562415\pi$
$72$	8.58443			1.01168
$73$			0.980489i			0.114758i	0.998352	+	0.0573788i	$0.0182743\pi$
$73$			0.980489i			0.114758i	−0.998352	+	0.0573788i	$0.981726\pi$
$74$	4.80724	−	3.72698i	0.558831	−	0.433253i
$75$	15.9925	+	5.81815i	1.84665	+	0.671822i
$76$		−	0.157282i		−	0.0180414i
$77$		−	7.78950i		−	0.887696i
$78$		−	9.81429i		−	1.11125i
$79$			8.04725i			0.905387i	0.891666	+	0.452693i	$0.149537\pi$
$79$			8.04725i			0.905387i	−0.891666	+	0.452693i	$0.850463\pi$
$80$	−1.28269	−	1.83159i	−0.143409	−	0.204778i
$81$	38.9391			4.32657
$82$	−0.923733			−0.102009
$83$			11.9496i			1.31164i	0.754916	+	0.655821i	$0.227677\pi$
$83$			11.9496i			1.31164i	−0.754916	+	0.655821i	$0.772323\pi$
$84$	−7.01905			−0.765841
$85$	−7.44889	−	10.6365i	−0.807945	−	1.15369i
$86$	10.8263			1.16743
$87$	−14.6035			−1.56566
$88$	−3.77719			−0.402649
$89$		−	7.65857i		−	0.811807i	−0.913916	−	0.405903i	$-0.866957\pi$
$89$		−	7.65857i		−	0.811807i	0.913916	−	0.405903i	$-0.133043\pi$
$90$	−11.0112	−	15.7231i	−1.16068	−	1.65736i
$91$			5.94652i			0.623364i
$92$	5.41883			0.564952
$93$	1.44889			0.150243
$94$			0.676445i			0.0697700i
$95$	−0.288075	+	0.201743i	−0.0295558	+	0.0206984i
$96$			3.40359i			0.347378i
$97$	13.9571			1.41712			0.708562	−	0.705649i	$-0.249344\pi$
$97$	13.9571			1.41712			0.708562	+	0.705649i	$0.249344\pi$
$98$	−2.74713			−0.277502
$99$	−32.4250			−3.25883
$100$	−1.70942	+	4.69871i	−0.170942	+	0.469871i
$101$	−8.38279			−0.834119			−0.417059	−	0.908879i	$-0.636939\pi$
$101$	−8.38279			−0.834119			−0.417059	+	0.908879i	$0.636939\pi$
$102$			19.7655i			1.95707i
$103$	13.4727			1.32751			0.663753	−	0.747951i	$-0.268962\pi$
$103$	13.4727			1.32751			0.663753	+	0.747951i	$0.268962\pi$
$104$	2.88351			0.282751
$105$	9.00326	+	12.8560i	0.878628	+	1.25462i
$106$			9.87810i			0.959446i
$107$			1.89614i			0.183306i	0.995791	+	0.0916532i	$0.0292151\pi$
$107$			1.89614i			0.183306i	−0.995791	+	0.0916532i	$0.970785\pi$
$108$			19.0071i			1.82896i
$109$		−	17.2044i		−	1.64789i	−0.566672	−	0.823943i	$-0.691769\pi$
$109$		−	17.2044i		−	1.64789i	0.566672	−	0.823943i	$-0.308231\pi$
$110$	4.84496	+	6.91824i	0.461949	+	0.659629i
$111$	12.6851	+	16.3619i	1.20402	+	1.55300i
$112$		−	2.06225i		−	0.194864i
$113$	−1.17098			−0.110157			−0.0550783	−	0.998482i	$-0.517541\pi$
$113$	−1.17098			−0.110157			−0.0550783	+	0.998482i	$0.517541\pi$
$114$	0.535322			0.0501375
$115$	−6.95068	−	9.92506i	−0.648154	−	0.925516i
$116$		−	4.29061i		−	0.398373i
$117$	24.7533			2.28844
$118$			8.47192i			0.779903i
$119$		−	11.9760i		−	1.09784i
$120$	6.23397	−	4.36575i	0.569081	−	0.398537i
$121$	3.26714			0.297012
$122$		−	1.23904i		−	0.112178i
$123$		−	3.14401i		−	0.283486i
$124$			0.425694i			0.0382285i
$125$	10.7987	−	2.89605i	0.965869	−	0.259030i
$126$		−	17.7032i		−	1.57713i
$127$		−	16.1128i		−	1.42978i	−0.699236	−	0.714891i	$-0.746476\pi$
$127$		−	16.1128i		−	1.42978i	0.699236	−	0.714891i	$-0.253524\pi$
$128$	−1.00000			−0.0883883
$129$			36.8483i			3.24431i
$130$	−3.69865	−	5.28140i	−0.324393	−	0.463209i
$131$			9.64715i			0.842875i	0.906857	+	0.421438i	$0.138474\pi$
$131$			9.64715i			0.842875i	−0.906857	+	0.421438i	$0.861526\pi$
$132$		−	12.8560i		−	1.11897i
$133$	−0.324354			−0.0281250
$134$			6.45516i			0.557641i
$135$	34.8132	−	24.3802i	2.99624	−	2.09832i
$136$	−5.80724			−0.497967
$137$			2.53592i			0.216658i	0.994115	+	0.108329i	$0.0345501\pi$
$137$			2.53592i			0.216658i	−0.994115	+	0.108329i	$0.965450\pi$
$138$			18.4435i			1.57001i
$139$	7.56000			0.641230			0.320615	−	0.947210i	$-0.396110\pi$
$139$	7.56000			0.641230			0.320615	+	0.947210i	$0.396110\pi$
$140$	−3.77719	+	2.64522i	−0.319231	+	0.223562i
$141$	−2.30234			−0.193892
$142$	3.28329			0.275528
$143$	−10.8916			−0.910798
$144$	−8.58443			−0.715369
$145$	−7.85862	+	5.50352i	−0.652623	+	0.457042i
$146$		−	0.980489i		−	0.0811458i
$147$		−	9.35011i		−	0.771184i
$148$	−4.80724	+	3.72698i	−0.395153	+	0.306356i
$149$	6.72596			0.551012			0.275506	−	0.961299i	$-0.411155\pi$
$149$	6.72596			0.551012			0.275506	+	0.961299i	$0.411155\pi$
$150$	−15.9925	−	5.81815i	−1.30578	−	0.475050i
$151$	−15.8051			−1.28620			−0.643101	−	0.765781i	$-0.722353\pi$
$151$	−15.8051			−1.28620			−0.643101	+	0.765781i	$0.722353\pi$
$152$			0.157282i			0.0127572i
$153$	−49.8519			−4.03028
$154$			7.78950i			0.627696i
$155$	0.779696	−	0.546033i	0.0626267	−	0.0438585i
$156$			9.81429i			0.785772i
$157$		−	8.50755i		−	0.678976i	−0.940610	−	0.339488i	$-0.889746\pi$
$157$		−	8.50755i		−	0.678976i	0.940610	−	0.339488i	$-0.110254\pi$
$158$		−	8.04725i		−	0.640205i
$159$	−33.6210			−2.66632
$160$	1.28269	+	1.83159i	0.101405	+	0.144800i
$161$		−	11.1750i		−	0.880712i
$162$	−38.9391			−3.05935
$163$	−5.41321			−0.423995			−0.211998	−	0.977270i	$-0.567997\pi$
$163$	−5.41321			−0.423995			−0.211998	+	0.977270i	$0.567997\pi$
$164$	0.923733			0.0721314
$165$	−23.5469	+	16.4902i	−1.83312	+	1.28376i
$166$		−	11.9496i		−	0.927471i
$167$	2.08165			0.161083			0.0805415	−	0.996751i	$-0.474335\pi$
$167$	2.08165			0.161083			0.0805415	+	0.996751i	$0.474335\pi$
$168$	7.01905			0.541532
$169$	−4.68537			−0.360413
$170$	7.44889	+	10.6365i	0.571304	+	0.815780i
$171$			1.35017i			0.103250i
$172$	−10.8263			−0.825497
$173$		−	12.3562i		−	0.939423i	−0.882820	−	0.469712i	$-0.844358\pi$
$173$		−	12.3562i		−	0.939423i	0.882820	−	0.469712i	$-0.155642\pi$
$174$	14.6035			1.10709
$175$	9.68991	+	3.52524i	0.732489	+	0.266483i
$176$	3.77719			0.284716
$177$	−28.8349			−2.16737
$178$			7.65857i			0.574034i
$179$			13.4571i			1.00583i	0.864336	+	0.502915i	$0.167739\pi$
$179$			13.4571i			1.00583i	−0.864336	+	0.502915i	$0.832261\pi$
$180$	11.0112	+	15.7231i	0.820723	+	1.17193i
$181$	−3.66608			−0.272498			−0.136249	−	0.990675i	$-0.543505\pi$
$181$	−3.66608			−0.272498			−0.136249	+	0.990675i	$0.543505\pi$
$182$		−	5.94652i		−	0.440785i
$183$	4.21719			0.311744
$184$	−5.41883			−0.399482
$185$	12.9925	+	4.02432i	0.955227	+	0.295874i
$186$	−1.44889			−0.106238
$187$	21.9350			1.60405
$188$		−	0.676445i		−	0.0493348i
$189$	39.1974			2.85119
$190$	0.288075	−	0.201743i	0.0208991	−	0.0146360i
$191$		−	18.5540i		−	1.34252i	−0.741221	−	0.671261i	$-0.765753\pi$
$191$		−	18.5540i		−	1.34252i	0.741221	−	0.671261i	$-0.234247\pi$
$192$		−	3.40359i		−	0.245633i
$193$	4.89778			0.352550			0.176275	−	0.984341i	$-0.443595\pi$
$193$	4.89778			0.352550			0.176275	+	0.984341i	$0.443595\pi$
$194$	−13.9571			−1.00206
$195$	17.9757	−	12.5887i	1.28727	−	0.901494i
$196$	2.74713			0.196224
$197$			14.7803i			1.05305i	0.850158	+	0.526527i	$0.176506\pi$
$197$			14.7803i			1.05305i	−0.850158	+	0.526527i	$0.823494\pi$
$198$	32.4250			2.30434
$199$			12.3298i			0.874039i	0.899452	+	0.437019i	$0.143966\pi$
$199$			12.3298i			0.874039i	−0.899452	+	0.437019i	$0.856034\pi$
$200$	1.70942	−	4.69871i	0.120874	−	0.332249i
$201$	−21.9707			−1.54970
$202$	8.38279			0.589811
$203$	−8.84831			−0.621029
$204$		−	19.7655i		−	1.38386i
$205$	−1.18486	−	1.69190i	−0.0827544	−	0.118167i
$206$	−13.4727			−0.938689
$207$	−46.5176			−3.23320
$208$	−2.88351			−0.199935
$209$		−	0.594082i		−	0.0410935i
$210$	−9.00326	−	12.8560i	−0.621284	−	0.887148i
$211$	14.1805			0.976224			0.488112	−	0.872781i	$-0.337686\pi$
$211$	14.1805			0.976224			0.488112	+	0.872781i	$0.337686\pi$
$212$		−	9.87810i		−	0.678431i
$213$			11.1750i			0.765697i
$214$		−	1.89614i		−	0.129617i
$215$	13.8868	+	19.8293i	0.947070	+	1.35235i
$216$		−	19.0071i		−	1.29327i
$217$	0.877887			0.0595949
$218$			17.2044i			1.16523i
$219$	3.33718			0.225506
$220$	−4.84496	−	6.91824i	−0.326647	−	0.466428i
$221$	−16.7452			−1.12641
$222$	−12.6851	−	16.3619i	−0.851370	−	1.09814i
$223$			7.29071i			0.488222i	0.969747	+	0.244111i	$0.0784962\pi$
$223$			7.29071i			0.488222i	−0.969747	+	0.244111i	$0.921504\pi$
$224$			2.06225i			0.137790i
$225$	14.6744	−	40.3358i	0.978291	−	2.68905i
$226$	1.17098			0.0778925
$227$	26.3807			1.75095			0.875473	−	0.483267i	$-0.160550\pi$
$227$	26.3807			1.75095			0.875473	+	0.483267i	$0.160550\pi$
$228$	−0.535322			−0.0354526
$229$	−19.5925			−1.29471			−0.647354	−	0.762190i	$-0.724124\pi$
$229$	−19.5925			−1.29471			−0.647354	+	0.762190i	$0.724124\pi$
$230$	6.95068	+	9.92506i	0.458314	+	0.654439i
$231$	−26.5123			−1.74438
$232$			4.29061i			0.281692i
$233$			3.69983i			0.242384i	0.992629	+	0.121192i	$0.0386717\pi$
$233$			3.69983i			0.242384i	−0.992629	+	0.121192i	$0.961328\pi$
$234$	−24.7533			−1.61817
$235$	−1.23897	+	0.867669i	−0.0808213	+	0.0566005i
$236$		−	8.47192i		−	0.551475i
$237$	27.3896			1.77914
$238$			11.9760i			0.776287i
$239$		−	8.68397i		−	0.561719i	−0.959749	−	0.280860i	$-0.909380\pi$
$239$		−	8.68397i		−	0.561719i	0.959749	−	0.280860i	$-0.0906195\pi$
$240$	−6.23397	+	4.36575i	−0.402401	+	0.281808i
$241$			27.5610i			1.77536i	0.460464	+	0.887678i	$0.347683\pi$
$241$			27.5610i			1.77536i	−0.460464	+	0.887678i	$0.652317\pi$
$242$	−3.26714			−0.210020
$243$		−	75.5116i		−	4.84407i
$244$			1.23904i			0.0793215i
$245$	−3.52371	−	5.03161i	−0.225122	−	0.321457i
$246$			3.14401i			0.200455i
$247$			0.453523i			0.0288570i
$248$		−	0.425694i		−	0.0270316i
$249$	40.6716			2.57746
$250$	−10.7987	+	2.89605i	−0.682973	+	0.183162i
$251$			20.4512i			1.29087i	0.763816	+	0.645434i	$0.223324\pi$
$251$			20.4512i			1.29087i	−0.763816	+	0.645434i	$0.776676\pi$
$252$			17.7032i			1.11520i
$253$	20.4679			1.28681
$254$			16.1128i			1.01101i
$255$	−36.2022	+	25.3530i	−2.26707	+	1.58766i
$256$	1.00000			0.0625000
$257$	22.8951			1.42815			0.714077	−	0.700067i	$-0.246847\pi$
$257$	22.8951			1.42815			0.714077	+	0.700067i	$0.246847\pi$
$258$		−	36.8483i		−	2.29407i
$259$	7.68597	+	9.91373i	0.477583	+	0.616009i
$260$	3.69865	+	5.28140i	0.229380	+	0.327538i
$261$			36.8324i			2.27987i
$262$		−	9.64715i		−	0.596003i
$263$			22.1600i			1.36644i	0.730212	+	0.683221i	$0.239421\pi$
$263$			22.1600i			1.36644i	−0.730212	+	0.683221i	$0.760579\pi$
$264$			12.8560i			0.791232i
$265$	−18.0926	+	12.6705i	−1.11142	+	0.778345i
$266$	0.324354			0.0198874
$267$	−26.0666			−1.59525
$268$		−	6.45516i		−	0.394312i
$269$	23.9657			1.46121			0.730607	−	0.682798i	$-0.239237\pi$
$269$	23.9657			1.46121			0.730607	+	0.682798i	$0.239237\pi$
$270$	−34.8132	+	24.3802i	−2.11866	+	1.48373i
$271$	9.82713			0.596956			0.298478	−	0.954417i	$-0.403521\pi$
$271$	9.82713			0.596956			0.298478	+	0.954417i	$0.403521\pi$
$272$	5.80724			0.352116
$273$	20.2395			1.22495
$274$		−	2.53592i		−	0.153201i
$275$	−6.45678	+	17.7479i	−0.389359	+	1.07024i
$276$		−	18.4435i		−	1.11017i
$277$	−0.807608			−0.0485245			−0.0242622	−	0.999706i	$-0.507724\pi$
$277$	−0.807608			−0.0485245			−0.0242622	+	0.999706i	$0.507724\pi$
$278$	−7.56000			−0.453418
$279$		−	3.65434i		−	0.218780i
$280$	3.77719	−	2.64522i	0.225730	−	0.158082i
$281$			1.03833i			0.0619414i	0.999520	+	0.0309707i	$0.00985986\pi$
$281$			1.03833i			0.0619414i	−0.999520	+	0.0309707i	$0.990140\pi$
$282$	2.30234			0.137102
$283$	6.26151			0.372208			0.186104	−	0.982530i	$-0.440414\pi$
$283$	6.26151			0.372208			0.186104	+	0.982530i	$0.440414\pi$
$284$	−3.28329			−0.194828
$285$	0.686652	+	0.980489i	0.0406738	+	0.0580791i
$286$	10.8916			0.644031
$287$		−	1.90497i		−	0.112447i
$288$	8.58443			0.505842
$289$	16.7241			0.983769
$290$	7.85862	−	5.50352i	0.461474	−	0.323178i
$291$		−	47.5041i		−	2.78474i
$292$			0.980489i			0.0573788i
$293$		−	4.84496i		−	0.283045i	−0.989935	−	0.141523i	$-0.954800\pi$
$293$		−	4.84496i		−	0.283045i	0.989935	−	0.141523i	$-0.0451998\pi$
$294$			9.35011i			0.545309i
$295$	−15.5170	+	10.8668i	−0.903437	+	0.632692i
$296$	4.80724	−	3.72698i	0.279415	−	0.216627i
$297$			71.7934i			4.16588i
$298$	−6.72596			−0.389624
$299$	−15.6253			−0.903632
$300$	15.9925	+	5.81815i	0.923327	+	0.335911i
$301$			22.3265i			1.28688i
$302$	15.8051			0.909483
$303$			28.5316i			1.63910i
$304$		−	0.157282i		−	0.00902072i
$305$	2.26941	−	1.58931i	0.129946	−	0.0910034i
$306$	49.8519			2.84984
$307$		−	2.87515i		−	0.164093i	−0.996628	−	0.0820467i	$-0.973854\pi$
$307$		−	2.87515i		−	0.164093i	0.996628	−	0.0820467i	$-0.0261457\pi$
$308$		−	7.78950i		−	0.443848i
$309$		−	45.8556i		−	2.60864i
$310$	−0.779696	+	0.546033i	−0.0442837	+	0.0310126i
$311$			6.07102i			0.344256i	0.985075	+	0.172128i	$0.0550643\pi$
$311$			6.07102i			0.344256i	−0.985075	+	0.172128i	$0.944936\pi$
$312$		−	9.81429i		−	0.555625i
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$			8.50755i			0.480109i
$315$	32.4250	−	22.7077i	1.82694	−	1.27944i
$316$			8.04725i			0.452693i
$317$		−	25.5691i		−	1.43610i	−0.695989	−	0.718052i	$-0.745034\pi$
$317$		−	25.5691i		−	1.43610i	0.695989	−	0.718052i	$-0.254966\pi$
$318$	33.6210			1.88537
$319$		−	16.2064i		−	0.907386i
$320$	−1.28269	−	1.83159i	−0.0717045	−	0.102389i
$321$	6.45367			0.360209
$322$			11.1750i			0.622757i
$323$		−	0.913372i		−	0.0508214i
$324$	38.9391			2.16329
$325$	4.92912	−	13.5488i	0.273418	−	0.751551i
$326$	5.41321			0.299810
$327$	−58.5569			−3.23820
$328$	−0.923733			−0.0510046
$329$	−1.39500			−0.0769087
$330$	23.5469	−	16.4902i	1.29621	−	0.907758i
$331$			16.8578i			0.926589i	0.886204	+	0.463295i	$0.153333\pi$
$331$			16.8578i			0.926589i	−0.886204	+	0.463295i	$0.846667\pi$
$332$			11.9496i			0.655821i
$333$	41.2674	−	31.9940i	2.26144	−	1.75326i
$334$	−2.08165			−0.113903
$335$	−11.8232	+	8.27996i	−0.645969	+	0.452383i
$336$	−7.01905			−0.382921
$337$		−	14.7105i		−	0.801334i	−0.916224	−	0.400667i	$-0.868779\pi$
$337$		−	14.7105i		−	0.801334i	0.916224	−	0.400667i	$-0.131221\pi$
$338$	4.68537			0.254851
$339$			3.98554i			0.216465i
$340$	−7.44889	−	10.6365i	−0.403973	−	0.576843i
$341$			1.60793i			0.0870741i
$342$		−	1.35017i		−	0.0730090i
$343$		−	20.1010i		−	1.08535i
$344$	10.8263			0.583715
$345$	−33.7808	+	23.6573i	−1.81870	+	1.27366i
$346$			12.3562i			0.664273i
$347$	3.26296			0.175165			0.0875824	−	0.996157i	$-0.472086\pi$
$347$	3.26296			0.175165			0.0875824	+	0.996157i	$0.472086\pi$
$348$	−14.6035			−0.782829
$349$	−17.2097			−0.921213			−0.460607	−	0.887604i	$-0.652368\pi$
$349$	−17.2097			−0.921213			−0.460607	+	0.887604i	$0.652368\pi$
$350$	−9.68991	−	3.52524i	−0.517948	−	0.188432i
$351$		−	54.8072i		−	2.92539i
$352$	−3.77719			−0.201325
$353$	−4.88641			−0.260077			−0.130039	−	0.991509i	$-0.541510\pi$
$353$	−4.88641			−0.260077			−0.130039	+	0.991509i	$0.541510\pi$
$354$	28.8349			1.53256
$355$	4.21144	+	6.01363i	0.223520	+	0.319170i
$356$		−	7.65857i		−	0.405903i
$357$	−40.7613			−2.15732
$358$		−	13.4571i		−	0.711229i
$359$	3.39107			0.178974			0.0894870	−	0.995988i	$-0.471477\pi$
$359$	3.39107			0.178974			0.0894870	+	0.995988i	$0.471477\pi$
$360$	−11.0112	−	15.7231i	−0.580339	−	0.828681i
$361$	18.9753			0.998698
$362$	3.66608			0.192685
$363$		−	11.1200i		−	0.583649i
$364$			5.94652i			0.311682i
$365$	1.79585	−	1.25766i	0.0939991	−	0.0658291i
$366$	−4.21719			−0.220436
$367$			9.25169i			0.482934i	0.970409	+	0.241467i	$0.0776286\pi$
$367$			9.25169i			0.482934i	−0.970409	+	0.241467i	$0.922371\pi$
$368$	5.41883			0.282476
$369$	−7.92972			−0.412805
$370$	−12.9925	−	4.02432i	−0.675448	−	0.209214i
$371$	−20.3711			−1.05761
$372$	1.44889			0.0751214
$373$			11.4101i			0.590792i	0.955375	+	0.295396i	$0.0954515\pi$
$373$			11.4101i			0.590792i	−0.955375	+	0.295396i	$0.904548\pi$
$374$	−21.9350			−1.13423
$375$	−9.85695	−	36.7545i	−0.509011	−	1.89799i
$376$			0.676445i			0.0348850i
$377$			12.3720i			0.637191i
$378$	−39.1974			−2.01610
$379$	36.3643			1.86791			0.933954	−	0.357394i	$-0.116335\pi$
$379$	36.3643			1.86791			0.933954	+	0.357394i	$0.116335\pi$
$380$	−0.288075	+	0.201743i	−0.0147779	+	0.0103492i
$381$	−54.8415			−2.80961
$382$			18.5540i			0.949307i
$383$	−13.6526			−0.697615			−0.348807	−	0.937194i	$-0.613413\pi$
$383$	−13.6526			−0.697615			−0.348807	+	0.937194i	$0.613413\pi$
$384$			3.40359i			0.173689i
$385$	−14.2671	+	9.99151i	−0.727121	+	0.509214i
$386$	−4.89778			−0.249290
$387$	92.9376			4.72428
$388$	13.9571			0.708562
$389$			2.36833i			0.120079i	0.998196	+	0.0600396i	$0.0191227\pi$
$389$			2.36833i			0.120079i	−0.998196	+	0.0600396i	$0.980877\pi$
$390$	−17.9757	+	12.5887i	−0.910236	+	0.637453i
$391$	31.4685			1.59143
$392$	−2.74713			−0.138751
$393$	32.8349			1.65630
$394$		−	14.7803i		−	0.744621i
$395$	14.7392	−	10.3221i	0.741611	−	0.519362i
$396$	−32.4250			−1.62942
$397$		−	34.4978i		−	1.73140i	−0.500567	−	0.865698i	$-0.666875\pi$
$397$		−	34.4978i		−	1.73140i	0.500567	−	0.865698i	$-0.333125\pi$
$398$		−	12.3298i		−	0.618039i
$399$			1.10397i			0.0552675i
$400$	−1.70942	+	4.69871i	−0.0854708	+	0.234936i
$401$		−	29.0777i		−	1.45207i	−0.687658	−	0.726035i	$-0.741361\pi$
$401$		−	29.0777i		−	1.45207i	0.687658	−	0.726035i	$-0.258639\pi$
$402$	21.9707			1.09580
$403$		−	1.22749i		−	0.0611458i
$404$	−8.38279			−0.417059
$405$	−49.9468	−	71.3204i	−2.48188	−	3.54394i
$406$	8.84831			0.439134
$407$	−18.1579	+	14.0775i	−0.900051	+	0.697797i
$408$			19.7655i			0.978537i
$409$		−	16.4980i		−	0.815773i	−0.913033	−	0.407887i	$-0.866266\pi$
$409$		−	16.4980i		−	0.815773i	0.913033	−	0.407887i	$-0.133734\pi$
$410$	1.18486	+	1.69190i	0.0585162	+	0.0835568i
$411$	8.63124			0.425748
$412$	13.4727			0.663753
$413$	−17.4712			−0.859702
$414$	46.5176			2.28621
$415$	21.8868	−	15.3277i	1.07438	−	0.752405i
$416$	2.88351			0.141376
$417$		−	25.7311i		−	1.26006i
$418$			0.594082i			0.0290575i
$419$	22.9409			1.12074			0.560368	−	0.828244i	$-0.310660\pi$
$419$	22.9409			1.12074			0.560368	+	0.828244i	$0.310660\pi$
$420$	9.00326	+	12.8560i	0.439314	+	0.627308i
$421$			1.72030i			0.0838422i	0.999121	+	0.0419211i	$0.0133478\pi$
$421$			1.72030i			0.0838422i	−0.999121	+	0.0419211i	$0.986652\pi$
$422$	−14.1805			−0.690294
$423$			5.80690i			0.282341i
$424$			9.87810i			0.479723i
$425$	−9.92699	+	27.2866i	−0.481530	+	1.32359i
$426$		−	11.1750i		−	0.541430i
$427$	2.55521			0.123655
$428$			1.89614i			0.0916532i
$429$			37.0704i			1.78978i
$430$	−13.8868	−	19.8293i	−0.669680	−	0.956253i
$431$		−	2.55447i		−	0.123045i	−0.998106	−	0.0615223i	$-0.980404\pi$
$431$		−	2.55447i		−	0.123045i	0.998106	−	0.0615223i	$-0.0195955\pi$
$432$			19.0071i			0.914480i
$433$			30.0446i			1.44385i	0.691970	+	0.721926i	$0.256743\pi$
$433$			30.0446i			1.44385i	−0.691970	+	0.721926i	$0.743257\pi$
$434$	−0.877887			−0.0421399
$435$	18.7317	+	26.7475i	0.898118	+	1.28245i
$436$		−	17.2044i		−	0.823943i
$437$		−	0.852283i		−	0.0407702i
$438$	−3.33718			−0.159457
$439$			38.4265i			1.83400i	0.398889	+	0.916999i	$0.369396\pi$
$439$			38.4265i			1.83400i	−0.398889	+	0.916999i	$0.630604\pi$
$440$	4.84496	+	6.91824i	0.230974	+	0.329814i
$441$	−23.5825			−1.12298
$442$	16.7452			0.796490
$443$		−	1.00809i		−	0.0478957i	−0.999713	−	0.0239479i	$-0.992376\pi$
$443$		−	1.00809i		−	0.0478957i	0.999713	−	0.0239479i	$-0.00762357\pi$
$444$	12.6851	+	16.3619i	0.602010	+	0.776501i
$445$	−14.0273	+	9.82357i	−0.664959	+	0.465682i
$446$		−	7.29071i		−	0.345225i
$447$		−	22.8924i		−	1.08277i
$448$		−	2.06225i		−	0.0974321i
$449$		−	32.1157i		−	1.51563i	−0.652468	−	0.757817i	$-0.726266\pi$
$449$		−	32.1157i		−	1.51563i	0.652468	−	0.757817i	$-0.273734\pi$
$450$	−14.6744	+	40.3358i	−0.691756	+	1.90145i
$451$	3.48911			0.164296
$452$	−1.17098			−0.0550783
$453$			53.7942i			2.52747i
$454$	−26.3807			−1.23811
$455$	10.8916	−	7.62753i	0.510604	−	0.357584i
$456$	0.535322			0.0250688
$457$	7.85884			0.367621			0.183810	−	0.982962i	$-0.441157\pi$
$457$	7.85884			0.367621			0.183810	+	0.982962i	$0.441157\pi$
$458$	19.5925			0.915496
$459$			110.379i			5.15205i
$460$	−6.95068	−	9.92506i	−0.324077	−	0.462758i
$461$		−	16.7952i		−	0.782233i	−0.920341	−	0.391116i	$-0.872089\pi$
$461$		−	16.7952i		−	0.782233i	0.920341	−	0.391116i	$-0.127911\pi$
$462$	26.5123			1.23346
$463$	−2.46094			−0.114370			−0.0571848	−	0.998364i	$-0.518212\pi$
$463$	−2.46094			−0.114370			−0.0571848	+	0.998364i	$0.518212\pi$
$464$		−	4.29061i		−	0.199187i
$465$	−1.85847	−	2.65376i	−0.0861847	−	0.123065i
$466$		−	3.69983i		−	0.171391i
$467$	−7.57699			−0.350621			−0.175311	−	0.984513i	$-0.556093\pi$
$467$	−7.57699			−0.350621			−0.175311	+	0.984513i	$0.556093\pi$
$468$	24.7533			1.14422
$469$	−13.3121			−0.614698
$470$	1.23897	−	0.867669i	0.0571493	−	0.0400226i
$471$	−28.9562			−1.33423
$472$			8.47192i			0.389952i
$473$	−40.8929			−1.88026
$474$	−27.3896			−1.25804
$475$	0.739021	+	0.268860i	0.0339086	+	0.0123361i
$476$		−	11.9760i		−	0.548918i
$477$			84.7979i			3.88263i
$478$			8.68397i			0.397195i
$479$			12.6993i			0.580246i	0.956989	+	0.290123i	$0.0936962\pi$
$479$			12.6993i			0.580246i	−0.956989	+	0.290123i	$0.906304\pi$
$480$	6.23397	−	4.36575i	0.284540	−	0.199268i
$481$	13.8617	−	10.7468i	0.632041	−	0.490012i
$482$		−	27.5610i		−	1.25537i
$483$	−38.0351			−1.73066
$484$	3.26714			0.148506
$485$	−17.9026	−	25.5635i	−0.812913	−	1.16078i
$486$			75.5116i			3.42527i
$487$	−10.8489			−0.491611			−0.245806	−	0.969319i	$-0.579052\pi$
$487$	−10.8489			−0.491611			−0.245806	+	0.969319i	$0.579052\pi$
$488$		−	1.23904i		−	0.0560888i
$489$			18.4243i			0.833178i
$490$	3.52371	+	5.03161i	0.159185	+	0.227305i
$491$	−17.5266			−0.790965			−0.395482	−	0.918474i	$-0.629423\pi$
$491$	−17.5266			−0.790965			−0.395482	+	0.918474i	$0.629423\pi$
$492$		−	3.14401i		−	0.141743i
$493$		−	24.9166i		−	1.12219i
$494$		−	0.453523i		−	0.0204050i
$495$	41.5912	+	59.3892i	1.86938	+	2.66934i
$496$			0.425694i			0.0191142i
$497$			6.77096i			0.303719i
$498$	−40.6716			−1.82254
$499$		−	32.4860i		−	1.45427i	−0.686494	−	0.727135i	$-0.740851\pi$
$499$		−	32.4860i		−	1.45427i	0.686494	−	0.727135i	$-0.259149\pi$
$500$	10.7987	−	2.89605i	0.482935	−	0.129515i
$501$		−	7.08508i		−	0.316538i
$502$		−	20.4512i		−	0.912782i
$503$	18.1375			0.808712			0.404356	−	0.914602i	$-0.367496\pi$
$503$	18.1375			0.808712			0.404356	+	0.914602i	$0.367496\pi$
$504$		−	17.7032i		−	0.788565i
$505$	10.7525	+	15.3538i	0.478481	+	0.683235i
$506$	−20.4679			−0.909911
$507$			15.9471i			0.708235i
$508$		−	16.1128i		−	0.714891i
$509$	−15.2070			−0.674037			−0.337018	−	0.941498i	$-0.609418\pi$
$509$	−15.2070			−0.674037			−0.337018	+	0.941498i	$0.609418\pi$
$510$	36.2022	−	25.3530i	1.60306	−	1.12265i
$511$	2.02201			0.0894485
$512$	−1.00000			−0.0441942
$513$	2.98947			0.131988
$514$	−22.8951			−1.00986
$515$	−17.2813	−	24.6765i	−0.761506	−	1.08737i
$516$			36.8483i			1.62215i
$517$		−	2.55506i		−	0.112371i
$518$	−7.68597	−	9.91373i	−0.337702	−	0.435584i
$519$	−42.0554			−1.84603
$520$	−3.69865	−	5.28140i	−0.162196	−	0.231605i
$521$	21.5850			0.945657			0.472829	−	0.881154i	$-0.343233\pi$
$521$	21.5850			0.945657			0.472829	+	0.881154i	$0.343233\pi$
$522$		−	36.8324i		−	1.61211i
$523$	6.64279			0.290469			0.145234	−	0.989397i	$-0.453606\pi$
$523$	6.64279			0.290469			0.145234	+	0.989397i	$0.453606\pi$
$524$			9.64715i			0.421438i
$525$	11.9985	−	32.9805i	0.523657	−	1.43939i
$526$		−	22.1600i		−	0.966220i
$527$			2.47211i			0.107687i
$528$		−	12.8560i		−	0.559485i
$529$	6.36374			0.276684
$530$	18.0926	−	12.6705i	0.785892	−	0.550373i
$531$			72.7266i			3.15606i
$532$	−0.324354			−0.0140625
$533$	−2.66359			−0.115373
$534$	26.0666			1.12801
$535$	3.47294	−	2.43215i	0.150148	−	0.105151i
$536$			6.45516i			0.278820i
$537$	45.8024			1.97652
$538$	−23.9657			−1.03323
$539$	10.3764			0.446944
$540$	34.8132	−	24.3802i	1.49812	−	1.04916i
$541$		−	12.3214i		−	0.529737i	−0.964285	−	0.264868i	$-0.914671\pi$
$541$		−	12.3214i		−	0.529737i	0.964285	−	0.264868i	$-0.0853286\pi$
$542$	−9.82713			−0.422112
$543$			12.4778i			0.535475i
$544$	−5.80724			−0.248983
$545$	−31.5114	+	22.0680i	−1.34980	+	0.945287i
$546$	−20.2395			−0.866171
$547$	−38.2186			−1.63411			−0.817054	−	0.576561i	$-0.804394\pi$
$547$	−38.2186			−1.63411			−0.817054	+	0.576561i	$0.804394\pi$
$548$			2.53592i			0.108329i
$549$		−	10.6365i		−	0.453953i
$550$	6.45678	−	17.7479i	0.275318	−	0.756774i
$551$	−0.674834			−0.0287489
$552$			18.4435i			0.785007i
$553$	16.5954			0.705710
$554$	0.807608			0.0343120
$555$	13.6971	−	44.2211i	0.581411	−	1.87708i
$556$	7.56000			0.320615
$557$	32.9212			1.39492			0.697458	−	0.716626i	$-0.254315\pi$
$557$	32.9212			1.39492			0.697458	+	0.716626i	$0.254315\pi$
$558$			3.65434i			0.154701i
$559$	31.2177			1.32037
$560$	−3.77719	+	2.64522i	−0.159615	+	0.111781i
$561$		−	74.6579i		−	3.15206i
$562$		−	1.03833i		−	0.0437992i
$563$	5.39047			0.227181			0.113591	−	0.993528i	$-0.463765\pi$
$563$	5.39047			0.227181			0.113591	+	0.993528i	$0.463765\pi$
$564$	−2.30234			−0.0969461
$565$	1.50200	+	2.14475i	0.0631898	+	0.0902304i
$566$	−6.26151			−0.263191
$567$		−	80.3022i		−	3.37238i
$568$	3.28329			0.137764
$569$			2.18118i			0.0914399i	0.998954	+	0.0457200i	$0.0145582\pi$
$569$			2.18118i			0.0914399i	−0.998954	+	0.0457200i	$0.985442\pi$
$570$	−0.686652	−	0.980489i	−0.0287607	−	0.0410682i
$571$	41.7356			1.74658			0.873291	−	0.487200i	$-0.161982\pi$
$571$	41.7356			1.74658			0.873291	+	0.487200i	$0.161982\pi$
$572$	−10.8916			−0.455399
$573$	−63.1503			−2.63814
$574$			1.90497i			0.0795118i
$575$	−9.26304	+	25.4615i	−0.386295	+	1.06182i
$576$	−8.58443			−0.357685
$577$	−27.9657			−1.16423			−0.582114	−	0.813107i	$-0.697774\pi$
$577$	−27.9657			−1.16423			−0.582114	+	0.813107i	$0.697774\pi$
$578$	−16.7241			−0.695630
$579$		−	16.6700i		−	0.692783i
$580$	−7.85862	+	5.50352i	−0.326312	+	0.228521i
$581$	24.6431			1.02237
$582$			47.5041i			1.96911i
$583$		−	37.3114i		−	1.54528i
$584$		−	0.980489i		−	0.0405729i
$585$	−31.7508	−	45.3378i	−1.31273	−	1.87449i
$586$			4.84496i			0.200143i
$587$	−19.4024			−0.800825			−0.400412	−	0.916335i	$-0.631133\pi$
$587$	−19.4024			−0.800825			−0.400412	+	0.916335i	$0.631133\pi$
$588$		−	9.35011i		−	0.385592i
$589$	0.0669539			0.00275879
$590$	15.5170	−	10.8668i	0.638827	−	0.447381i
$591$	50.3061			2.06932
$592$	−4.80724	+	3.72698i	−0.197576	+	0.153178i
$593$		−	12.5182i		−	0.514061i	−0.966403	−	0.257030i	$-0.917256\pi$
$593$		−	12.5182i		−	0.514061i	0.966403	−	0.257030i	$-0.0827440\pi$
$594$		−	71.7934i		−	2.94572i
$595$	−21.9350	+	15.3615i	−0.899249	+	0.629759i
$596$	6.72596			0.275506
$597$	41.9657			1.71754
$598$	15.6253			0.638964
$599$	11.7177			0.478771			0.239386	−	0.970925i	$-0.423054\pi$
$599$	11.7177			0.478771			0.239386	+	0.970925i	$0.423054\pi$
$600$	−15.9925	−	5.81815i	−0.652891	−	0.237525i
$601$	1.37239			0.0559808			0.0279904	−	0.999608i	$-0.491089\pi$
$601$	1.37239			0.0559808			0.0279904	+	0.999608i	$0.491089\pi$
$602$		−	22.3265i		−	0.909961i
$603$			55.4139i			2.25663i
$604$	−15.8051			−0.643101
$605$	−4.19072	−	5.98404i	−0.170377	−	0.243286i
$606$		−	28.5316i		−	1.15902i
$607$	24.6378			1.00002			0.500008	−	0.866021i	$-0.333330\pi$
$607$	24.6378			1.00002			0.500008	+	0.866021i	$0.333330\pi$
$608$			0.157282i			0.00637861i
$609$			30.1160i			1.22036i
$610$	−2.26941	+	1.58931i	−0.0918858	+	0.0643491i
$611$			1.95054i			0.0789102i
$612$	−49.8519			−2.01514
$613$			27.6733i			1.11771i	0.829264	+	0.558857i	$0.188760\pi$
$613$			27.6733i			1.11771i	−0.829264	+	0.558857i	$0.811240\pi$
$614$			2.87515i			0.116032i
$615$	−5.75852	+	4.03279i	−0.232206	+	0.162618i
$616$			7.78950i			0.313848i
$617$		−	17.9433i		−	0.722371i	−0.932494	−	0.361185i	$-0.882372\pi$
$617$		−	17.9433i		−	0.722371i	0.932494	−	0.361185i	$-0.117628\pi$
$618$			45.8556i			1.84458i
$619$	−25.1044			−1.00903			−0.504515	−	0.863403i	$-0.668329\pi$
$619$	−25.1044			−1.00903			−0.504515	+	0.863403i	$0.668329\pi$
$620$	0.779696	−	0.546033i	0.0313133	−	0.0219292i
$621$			102.996i			4.13310i
$622$		−	6.07102i		−	0.243426i
$623$	−15.7939			−0.632768
$624$			9.81429i			0.392886i
$625$	−19.1558	−	16.0641i	−0.766232	−	0.642564i
$626$	10.0000			0.399680
$627$	−2.02201			−0.0807514
$628$		−	8.50755i		−	0.339488i
$629$	−27.9168	+	21.6435i	−1.11312	+	0.862983i
$630$	−32.4250	+	22.7077i	−1.29184	+	0.904698i
$631$			47.8987i			1.90682i	0.301679	+	0.953409i	$0.402453\pi$
$631$			47.8987i			1.90682i	−0.301679	+	0.953409i	$0.597547\pi$
$632$		−	8.04725i		−	0.320102i
$633$		−	48.2645i		−	1.91834i
$634$			25.5691i			1.01548i
$635$	−29.5120	+	20.6677i	−1.17115	+	0.820175i
$636$	−33.6210			−1.33316
$637$	−7.92138			−0.313856
$638$			16.2064i			0.641619i
$639$	28.1852			1.11499
$640$	1.28269	+	1.83159i	0.0507027	+	0.0723998i
$641$	−19.4541			−0.768390			−0.384195	−	0.923252i	$-0.625521\pi$
$641$	−19.4541			−0.768390			−0.384195	+	0.923252i	$0.625521\pi$
$642$	−6.45367			−0.254706
$643$	26.0553			1.02752			0.513760	−	0.857934i	$-0.328252\pi$
$643$	26.0553			1.02752			0.513760	+	0.857934i	$0.328252\pi$
$644$		−	11.1750i		−	0.440356i
$645$	67.4908	−	47.2649i	2.65745	−	1.86105i
$646$			0.913372i			0.0359362i
$647$	14.7320			0.579176			0.289588	−	0.957151i	$-0.406482\pi$
$647$	14.7320			0.579176			0.289588	+	0.957151i	$0.406482\pi$
$648$	−38.9391			−1.52967
$649$		−	32.0000i		−	1.25611i
$650$	−4.92912	+	13.5488i	−0.193336	+	0.531427i
$651$		−	2.98797i		−	0.117108i
$652$	−5.41321			−0.211998
$653$	−30.5877			−1.19699			−0.598494	−	0.801127i	$-0.704234\pi$
$653$	−30.5877			−1.19699			−0.598494	+	0.801127i	$0.704234\pi$
$654$	58.5569			2.28976
$655$	17.6696	−	12.3743i	0.690408	−	0.483504i
$656$	0.923733			0.0360657
$657$		−	8.41694i		−	0.328376i
$658$	1.39500			0.0543827
$659$	29.3533			1.14344			0.571720	−	0.820448i	$-0.306276\pi$
$659$	29.3533			1.14344			0.571720	+	0.820448i	$0.306276\pi$
$660$	−23.5469	+	16.4902i	−0.916561	+	0.641882i
$661$		−	16.7963i		−	0.653299i	−0.945145	−	0.326650i	$-0.894080\pi$
$661$		−	16.7963i		−	0.653299i	0.945145	−	0.326650i	$-0.105920\pi$
$662$		−	16.8578i		−	0.655198i
$663$			56.9940i			2.21346i
$664$		−	11.9496i		−	0.463735i
$665$	0.416045	+	0.594082i	0.0161335	+	0.0230375i
$666$	−41.2674	+	31.9940i	−1.59908	+	1.23974i
$667$		−	23.2501i		−	0.900247i
$668$	2.08165			0.0805415
$669$	24.8146			0.959388
$670$	11.8232	−	8.27996i	0.456769	−	0.319883i
$671$			4.68009i			0.180673i
$672$	7.01905			0.270766
$673$		−	21.2015i		−	0.817259i	−0.912700	−	0.408629i	$-0.866007\pi$
$673$		−	21.2015i		−	0.817259i	0.912700	−	0.408629i	$-0.133993\pi$
$674$			14.7105i			0.566628i
$675$	−89.3089	−	32.4911i	−3.43750	−	1.25058i
$676$	−4.68537			−0.180207
$677$			45.9734i			1.76690i	0.468526	+	0.883450i	$0.344785\pi$
$677$			45.9734i			1.76690i	−0.468526	+	0.883450i	$0.655215\pi$
$678$		−	3.98554i		−	0.153064i
$679$		−	28.7829i		−	1.10459i
$680$	7.44889	+	10.6365i	0.285652	+	0.407890i
$681$		−	89.7890i		−	3.44072i
$682$		−	1.60793i		−	0.0615707i
$683$	3.06580			0.117309			0.0586547	−	0.998278i	$-0.481319\pi$
$683$	3.06580			0.117309			0.0586547	+	0.998278i	$0.481319\pi$
$684$			1.35017i			0.0516251i
$685$	4.64476	−	3.25280i	0.177467	−	0.124283i
$686$			20.1010i			0.767460i
$687$			66.6848i			2.54418i
$688$	−10.8263			−0.412749
$689$			28.4836i			1.08514i
$690$	33.7808	−	23.6573i	1.28601	−	0.900617i
$691$	8.43426			0.320854			0.160427	−	0.987048i	$-0.448713\pi$
$691$	8.43426			0.320854			0.160427	+	0.987048i	$0.448713\pi$
$692$		−	12.3562i		−	0.469712i
$693$			66.8684i			2.54012i
$694$	−3.26296			−0.123860
$695$	−9.69713	−	13.8468i	−0.367833	−	0.525238i
$696$	14.6035			0.553543
$697$	5.36434			0.203189
$698$	17.2097			0.651396
$699$	12.5927			0.476300
$700$	9.68991	+	3.52524i	0.366244	+	0.133242i
$701$			20.3110i			0.767136i	0.923513	+	0.383568i	$0.125305\pi$
$701$			20.3110i			0.767136i	−0.923513	+	0.383568i	$0.874695\pi$
$702$			54.8072i			2.06856i
$703$	0.586186	+	0.756091i	0.0221084	+	0.0285165i
$704$	3.77719			0.142358
$705$	2.95319	+	4.21694i	0.111224	+	0.158819i
$706$	4.88641			0.183902
$707$			17.2874i			0.650159i
$708$	−28.8349			−1.08368
$709$		−	23.8789i		−	0.896790i	−0.893836	−	0.448395i	$-0.851996\pi$
$709$		−	23.8789i		−	0.896790i	0.893836	−	0.448395i	$-0.148004\pi$
$710$	−4.21144	−	6.01363i	−0.158053	−	0.225688i
$711$		−	69.0811i		−	2.59074i
$712$			7.65857i			0.287017i
$713$			2.30677i			0.0863890i
$714$	40.7613			1.52545
$715$	13.9705	+	19.9488i	0.522466	+	0.746044i
$716$			13.4571i			0.502915i
$717$	−29.5567			−1.10381
$718$	−3.39107			−0.126554
$719$	14.6971			0.548110			0.274055	−	0.961714i	$-0.411635\pi$
$719$	14.6971			0.548110			0.274055	+	0.961714i	$0.411635\pi$
$720$	11.0112	+	15.7231i	0.410362	+	0.585966i
$721$		−	27.7841i		−	1.03473i
$722$	−18.9753			−0.706186
$723$	93.8062			3.48869
$724$	−3.66608			−0.136249
$725$	20.1603	+	7.33444i	0.748736	+	0.272394i
$726$			11.1200i			0.412702i
$727$	5.61569			0.208274			0.104137	−	0.994563i	$-0.466792\pi$
$727$	5.61569			0.208274			0.104137	+	0.994563i	$0.466792\pi$
$728$		−	5.94652i		−	0.220393i
$729$	−140.193			−5.19233
$730$	−1.79585	+	1.25766i	−0.0664674	+	0.0465482i
$731$	−62.8709			−2.32536
$732$	4.21719			0.155872
$733$			16.7565i			0.618917i	0.950913	+	0.309459i	$0.100148\pi$
$733$			16.7565i			0.618917i	−0.950913	+	0.309459i	$0.899852\pi$
$734$		−	9.25169i		−	0.341486i
$735$	−17.1255	+	11.9933i	−0.631684	+	0.442379i
$736$	−5.41883			−0.199741
$737$		−	24.3823i		−	0.898135i
$738$	7.92972			0.291897
$739$	−13.2106			−0.485960			−0.242980	−	0.970031i	$-0.578125\pi$
$739$	−13.2106			−0.485960			−0.242980	+	0.970031i	$0.578125\pi$
$740$	12.9925	+	4.02432i	0.477614	+	0.147937i
$741$	1.54361			0.0567058
$742$	20.3711			0.747847
$743$		−	23.0799i		−	0.846721i	−0.905961	−	0.423360i	$-0.860850\pi$
$743$		−	23.0799i		−	0.846721i	0.905961	−	0.423360i	$-0.139150\pi$
$744$	−1.44889			−0.0531188
$745$	−8.62731	−	12.3192i	−0.316080	−	0.451340i
$746$		−	11.4101i		−	0.417753i
$747$		−	102.581i		−	3.75323i
$748$	21.9350			0.802024
$749$	3.91030			0.142879
$750$	9.85695	+	36.7545i	0.359925	+	1.34209i
$751$	25.0437			0.913856			0.456928	−	0.889504i	$-0.348950\pi$
$751$	25.0437			0.913856			0.456928	+	0.889504i	$0.348950\pi$
$752$		−	0.676445i		−	0.0246674i
$753$	69.6075			2.53664
$754$		−	12.3720i		−	0.450562i
$755$	20.2731	+	28.9484i	0.737812	+	1.05354i
$756$	39.1974			1.42560
$757$	−33.5882			−1.22078			−0.610392	−	0.792099i	$-0.708988\pi$
$757$	−33.5882			−1.22078			−0.610392	+	0.792099i	$0.708988\pi$
$758$	−36.3643			−1.32081
$759$		−	69.6645i		−	2.52866i
$760$	0.288075	−	0.201743i	0.0104496	−	0.00731800i
$761$	−14.8529			−0.538416			−0.269208	−	0.963082i	$-0.586762\pi$
$761$	−14.8529			−0.538416			−0.269208	+	0.963082i	$0.586762\pi$
$762$	54.8415			1.98670
$763$	−35.4798			−1.28446
$764$		−	18.5540i		−	0.671261i
$765$	63.9445	+	91.3080i	2.31192	+	3.30125i
$766$	13.6526			0.493288
$767$			24.4289i			0.882075i
$768$		−	3.40359i		−	0.122816i
$769$			8.80892i			0.317658i	0.987306	+	0.158829i	$0.0507718\pi$
$769$			8.80892i			0.317658i	−0.987306	+	0.158829i	$0.949228\pi$
$770$	14.2671	−	9.99151i	0.514152	−	0.360069i
$771$		−	77.9254i		−	2.80641i
$772$	4.89778			0.176275
$773$		−	38.8401i		−	1.39698i	−0.715619	−	0.698491i	$-0.753855\pi$
$773$		−	38.8401i		−	1.39698i	0.715619	−	0.698491i	$-0.246145\pi$
$774$	−92.9376			−3.34057
$775$	−2.00021	−	0.727688i	−0.0718498	−	0.0261393i
$776$	−13.9571			−0.501029
$777$	33.7423	−	26.1599i	1.21050	−	0.938481i
$778$		−	2.36833i		−	0.0849089i
$779$		−	0.145286i		−	0.00520542i
$780$	17.9757	−	12.5887i	0.643634	−	0.450747i
$781$	−12.4016			−0.443764
$782$	−31.4685			−1.12531
$783$	81.5521			2.91443
$784$	2.74713			0.0981118
$785$	−15.5823	+	10.9125i	−0.556156	+	0.389485i
$786$	−32.8349			−1.17118
$787$			34.2645i			1.22140i	0.791864	+	0.610698i	$0.209111\pi$
$787$			34.2645i			1.22140i	−0.791864	+	0.610698i	$0.790889\pi$
$788$			14.7803i			0.526527i
$789$	75.4234			2.68514
$790$	−14.7392	+	10.3221i	−0.524398	+	0.367245i
$791$			2.41485i			0.0858623i
$792$	32.4250			1.15217
$793$		−	3.57279i		−	0.126873i
$794$			34.4978i			1.22428i
$795$	43.1253	+	61.5798i	1.52950	+	2.18401i
$796$			12.3298i			0.437019i
$797$	34.0208			1.20508			0.602539	−	0.798089i	$-0.294156\pi$
$797$	34.0208			1.20508			0.602539	+	0.798089i	$0.294156\pi$
$798$		−	1.10397i		−	0.0390800i
$799$		−	3.92828i		−	0.138973i
$800$	1.70942	−	4.69871i	0.0604370	−	0.166125i
$801$			65.7445i			2.32297i
$802$			29.0777i			1.02677i
$803$			3.70349i			0.130693i
$804$	−21.9707			−0.774848
$805$	−20.4679	+	14.3340i	−0.721400	+	0.505208i
$806$			1.22749i			0.0432366i
$807$		−	81.5694i		−	2.87138i
$808$	8.38279			0.294905
$809$			23.0866i			0.811680i	0.913944	+	0.405840i	$0.133021\pi$
$809$			23.0866i			0.811680i	−0.913944	+	0.405840i	$0.866979\pi$
$810$	49.9468	+	71.3204i	1.75495	+	2.50594i
$811$	−14.0477			−0.493280			−0.246640	−	0.969107i	$-0.579327\pi$
$811$	−14.0477			−0.493280			−0.246640	+	0.969107i	$0.579327\pi$
$812$	−8.84831			−0.310515
$813$		−	33.4475i		−	1.17306i
$814$	18.1579	−	14.0775i	0.636432	−	0.493417i
$815$	6.94347	+	9.91476i	0.243219	+	0.347299i
$816$		−	19.7655i		−	0.691930i
$817$			1.70278i			0.0595726i
$818$			16.4980i			0.576839i
$819$		−	51.0474i		−	1.78374i
$820$	−1.18486	−	1.69190i	−0.0413772	−	0.0590836i
$821$	−5.87069			−0.204888			−0.102444	−	0.994739i	$-0.532666\pi$
$821$	−5.87069			−0.204888			−0.102444	+	0.994739i	$0.532666\pi$
$822$	−8.63124			−0.301049
$823$			36.6536i			1.27766i	0.769346	+	0.638832i	$0.220582\pi$
$823$			36.6536i			1.27766i	−0.769346	+	0.638832i	$0.779418\pi$
$824$	−13.4727			−0.469345
$825$	60.4066	+	21.9762i	2.10309	+	0.765115i
$826$	17.4712			0.607901
$827$	−31.2291			−1.08594			−0.542971	−	0.839751i	$-0.682701\pi$
$827$	−31.2291			−1.08594			−0.542971	+	0.839751i	$0.682701\pi$
$828$	−46.5176			−1.61660
$829$		−	5.76907i		−	0.200368i	−0.994969	−	0.100184i	$-0.968057\pi$
$829$		−	5.76907i		−	0.200368i	0.994969	−	0.100184i	$-0.0319431\pi$
$830$	−21.8868	+	15.3277i	−0.759701	+	0.532031i
$831$			2.74877i			0.0953536i
$832$	−2.88351			−0.0999677
$833$	15.9533			0.552747
$834$			25.7311i			0.890996i
$835$	−2.67011	−	3.81272i	−0.0924030	−	0.131945i
$836$		−	0.594082i		−	0.0205468i
$837$	−8.09122			−0.279673
$838$	−22.9409			−0.792480
$839$	−19.1631			−0.661582			−0.330791	−	0.943704i	$-0.607316\pi$
$839$	−19.1631			−0.661582			−0.330791	+	0.943704i	$0.607316\pi$
$840$	−9.00326	−	12.8560i	−0.310642	−	0.443574i
$841$	10.5907			0.365195
$842$		−	1.72030i		−	0.0592854i
$843$	3.53404			0.121719
$844$	14.1805			0.488112
$845$	6.00987	+	8.58166i	0.206746	+	0.295218i
$846$		−	5.80690i		−	0.199645i
$847$		−	6.73765i		−	0.231508i
$848$		−	9.87810i		−	0.339215i
$849$		−	21.3116i		−	0.731413i
$850$	9.92699	−	27.2866i	0.340493	−	0.935921i
$851$	−26.0496	+	20.1959i	−0.892970	+	0.692307i
$852$			11.1750i			0.382849i
$853$	30.1823			1.03342			0.516711	−	0.856160i	$-0.327156\pi$
$853$	30.1823			1.03342			0.516711	+	0.856160i	$0.327156\pi$
$854$	−2.55521			−0.0874376
$855$	2.47296	−	1.73185i	0.0845734	−	0.0592281i
$856$		−	1.89614i		−	0.0648086i
$857$	−13.4228			−0.458513			−0.229257	−	0.973366i	$-0.573630\pi$
$857$	−13.4228			−0.458513			−0.229257	+	0.973366i	$0.573630\pi$
$858$		−	37.0704i		−	1.26556i
$859$		−	25.1243i		−	0.857230i	−0.903487	−	0.428615i	$-0.859002\pi$
$859$		−	25.1243i		−	0.857230i	0.903487	−	0.428615i	$-0.140998\pi$
$860$	13.8868	+	19.8293i	0.473535	+	0.676173i
$861$	−6.48373			−0.220965
$862$			2.55447i			0.0870057i
$863$		−	6.80983i		−	0.231809i	−0.993260	−	0.115905i	$-0.963023\pi$
$863$		−	6.80983i		−	0.231809i	0.993260	−	0.115905i	$-0.0369767\pi$
$864$		−	19.0071i		−	0.646635i
$865$	−22.6314	+	15.8491i	−0.769491	+	0.538887i
$866$		−	30.0446i		−	1.02096i
$867$		−	56.9219i		−	1.93317i
$868$	0.877887			0.0297974
$869$			30.3960i			1.03111i
$870$	−18.7317	−	26.7475i	−0.635065	−	0.906826i
$871$			18.6135i			0.630695i
$872$			17.2044i			0.582616i
$873$	−119.813			−4.05507
$874$			0.852283i			0.0288289i
$875$	−5.97237	−	22.2697i	−0.201903	−	0.752853i
$876$	3.33718			0.112753
$877$			29.4096i			0.993090i	0.868011	+	0.496545i	$0.165398\pi$
$877$			29.4096i			0.993090i	−0.868011	+	0.496545i	$0.834602\pi$
$878$		−	38.4265i		−	1.29683i
$879$	−16.4903			−0.556202
$880$	−4.84496	−	6.91824i	−0.163323	−	0.233214i
$881$	50.5602			1.70342			0.851708	−	0.524016i	$-0.175567\pi$
$881$	50.5602			1.70342			0.851708	+	0.524016i	$0.175567\pi$
$882$	23.5825			0.794066
$883$	40.4904			1.36261			0.681305	−	0.732000i	$-0.261413\pi$
$883$	40.4904			1.36261			0.681305	+	0.732000i	$0.261413\pi$
$884$	−16.7452			−0.563203
$885$	36.9863	+	52.8137i	1.24328	+	1.77531i
$886$			1.00809i			0.0338674i
$887$		−	8.64379i		−	0.290230i	−0.989415	−	0.145115i	$-0.953645\pi$
$887$		−	8.64379i		−	0.290230i	0.989415	−	0.145115i	$-0.0463552\pi$
$888$	−12.6851	−	16.3619i	−0.425685	−	0.549069i
$889$	−33.2287			−1.11445
$890$	14.0273	−	9.82357i	0.470197	−	0.329287i
$891$	147.080			4.92738
$892$			7.29071i			0.244111i
$893$	−0.106392			−0.00356028
$894$			22.8924i			0.765637i
$895$	24.6478	−	17.2613i	0.823885	−	0.576980i
$896$			2.06225i			0.0688949i
$897$			53.1820i			1.77569i
$898$			32.1157i			1.07171i
$899$	1.82649			0.0609168
$900$	14.6744	−	40.3358i	0.489145	−	1.34453i
$901$		−	57.3645i		−	1.91109i
$902$	−3.48911			−0.116175
$903$	75.9903			2.52880
$904$	1.17098			0.0389462
$905$	4.70244	+	6.71474i	0.156314	+	0.223206i
$906$		−	53.7942i		−	1.78719i
$907$	−33.0245			−1.09656			−0.548281	−	0.836294i	$-0.684717\pi$
$907$	−33.0245			−1.09656			−0.548281	+	0.836294i	$0.684717\pi$
$908$	26.3807			0.875473
$909$	71.9615			2.38681
$910$	−10.8916	+	7.62753i	−0.361052	+	0.252850i
$911$		−	0.940972i		−	0.0311758i	−0.999879	−	0.0155879i	$-0.995038\pi$
$911$		−	0.940972i		−	0.0311758i	0.999879	−	0.0155879i	$-0.00496198\pi$
$912$	−0.535322			−0.0177263
$913$			45.1360i			1.49378i
$914$	−7.85884			−0.259947
$915$	−5.40935	−	7.72415i	−0.178827	−	0.255352i
$916$	−19.5925			−0.647354
$917$	19.8948			0.656985
$918$		−	110.379i		−	3.64305i
$919$			54.5548i			1.79960i	0.436306	+	0.899798i	$0.356287\pi$
$919$			54.5548i			1.79960i	−0.436306	+	0.899798i	$0.643713\pi$
$920$	6.95068	+	9.92506i	0.229157	+	0.327219i
$921$	−9.78583			−0.322454
$922$			16.7952i			0.553122i
$923$	9.46740			0.311623
$924$	−26.5123			−0.872189
$925$	−9.29445	−	28.9588i	−0.305600	−	0.952160i
$926$	2.46094			0.0808716
$927$	−115.656			−3.79863
$928$			4.29061i			0.140846i
$929$	−22.7416			−0.746128			−0.373064	−	0.927806i	$-0.621693\pi$
$929$	−22.7416			−0.746128			−0.373064	+	0.927806i	$0.621693\pi$
$930$	1.85847	+	2.65376i	0.0609418	+	0.0870204i
$931$		−	0.432073i		−	0.0141606i
$932$			3.69983i			0.121192i
$933$	20.6633			0.676485
$934$	7.57699			0.247927
$935$	−28.1358	−	40.1759i	−0.920140	−	1.31389i
$936$	−24.7533			−0.809087
$937$			43.2122i			1.41168i	0.708370	+	0.705841i	$0.249431\pi$
$937$			43.2122i			1.41168i	−0.708370	+	0.705841i	$0.750569\pi$
$938$	13.3121			0.434657
$939$			34.0359i			1.11072i
$940$	−1.23897	+	0.867669i	−0.0404107	+	0.0283002i
$941$	32.0847			1.04593			0.522966	−	0.852354i	$-0.324825\pi$
$941$	32.0847			1.04593			0.522966	+	0.852354i	$0.324825\pi$
$942$	28.9562			0.943444
$943$	5.00555			0.163003
$944$		−	8.47192i		−	0.275737i
$945$	−50.2781	−	71.7934i	−1.63555	−	2.33544i
$946$	40.8929			1.32954
$947$	−8.26212			−0.268483			−0.134241	−	0.990949i	$-0.542860\pi$
$947$	−8.26212			−0.268483			−0.134241	+	0.990949i	$0.542860\pi$
$948$	27.3896			0.889571
$949$		−	2.82725i		−	0.0917764i
$950$	−0.739021	−	0.268860i	−0.0239770	−	0.00872296i
$951$	−87.0268			−2.82204
$952$			11.9760i			0.388144i
$953$		−	51.1883i		−	1.65815i	−0.559136	−	0.829076i	$-0.688867\pi$
$953$		−	51.1883i		−	1.65815i	0.559136	−	0.829076i	$-0.311133\pi$
$954$		−	84.7979i		−	2.74543i
$955$	−33.9833	+	23.7991i	−1.09967	+	0.770120i
$956$		−	8.68397i		−	0.280860i
$957$	−55.1601			−1.78307
$958$		−	12.6993i		−	0.410296i
$959$	5.22970			0.168876
$960$	−6.23397	+	4.36575i	−0.201201	+	0.140904i
$961$	30.8188			0.994154
$962$	−13.8617	+	10.7468i	−0.446920	+	0.346491i
$963$		−	16.2772i		−	0.524527i
$964$			27.5610i			0.887678i
$965$	−6.28233	−	8.97070i	−0.202235	−	0.288777i
$966$	38.0351			1.22376
$967$	1.84215			0.0592395			0.0296197	−	0.999561i	$-0.490570\pi$
$967$	1.84215			0.0592395			0.0296197	+	0.999561i	$0.490570\pi$
$968$	−3.26714			−0.105010
$969$	−3.10875			−0.0998673
$970$	17.9026	+	25.5635i	0.574817	+	0.820796i
$971$	52.6384			1.68925			0.844624	−	0.535361i	$-0.179824\pi$
$971$	52.6384			1.68925			0.844624	+	0.535361i	$0.179824\pi$
$972$		−	75.5116i		−	2.42203i
$973$		−	15.5906i		−	0.499811i
$974$	10.8489			0.347621
$975$	−46.1145	−	16.7767i	−1.47685	−	0.537284i
$976$			1.23904i			0.0396608i
$977$	−47.7629			−1.52807			−0.764035	−	0.645174i	$-0.776785\pi$
$977$	−47.7629			−1.52807			−0.764035	+	0.645174i	$0.776785\pi$
$978$		−	18.4243i		−	0.589146i
$979$		−	28.9278i		−	0.924538i
$980$	−3.52371	−	5.03161i	−0.112561	−	0.160729i
$981$			147.690i			4.71539i
$982$	17.5266			0.559297
$983$		−	34.6640i		−	1.10561i	−0.833310	−	0.552805i	$-0.813557\pi$
$983$		−	34.6640i		−	1.10561i	0.833310	−	0.552805i	$-0.186443\pi$
$984$			3.14401i			0.100227i
$985$	27.0714	−	18.9586i	0.862567	−	0.604070i
$986$			24.9166i			0.793507i
$987$			4.74800i			0.151131i
$988$			0.453523i			0.0144285i
$989$	−58.6659			−1.86547
$990$	−41.5912	−	59.3892i	−1.32185	−	1.88751i
$991$			45.9061i			1.45826i	0.684378	+	0.729128i	$0.260074\pi$
$991$			45.9061i			1.45826i	−0.684378	+	0.729128i	$0.739926\pi$
$992$		−	0.425694i		−	0.0135158i
$993$	57.3771			1.82081
$994$		−	6.77096i		−	0.214762i
$995$	22.5831	−	15.8153i	0.715934	−	0.501380i
$996$	40.6716			1.28873
$997$	−24.7232			−0.782993			−0.391496	−	0.920180i	$-0.628042\pi$
$997$	−24.7232			−0.782993			−0.391496	+	0.920180i	$0.628042\pi$
$998$			32.4860i			1.02832i
$999$	−70.8392	−	91.3718i	−2.24125	−	2.89088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.c.a.369.1	✓	10
3.2	odd	2		3330.2.e.d.739.6		10
5.2	odd	4		1850.2.d.i.1701.1		20
5.3	odd	4		1850.2.d.i.1701.20		20
5.4	even	2		370.2.c.b.369.10	yes	10
15.14	odd	2		3330.2.e.c.739.6		10
37.36	even	2		370.2.c.b.369.1	yes	10
111.110	odd	2		3330.2.e.c.739.5		10
185.73	odd	4		1850.2.d.i.1701.10		20
185.147	odd	4		1850.2.d.i.1701.11		20
185.184	even	2	inner	370.2.c.a.369.10	yes	10
555.554	odd	2		3330.2.e.d.739.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.c.a.369.1	✓	10	1.1	even	1	trivial
370.2.c.a.369.10	yes	10	185.184	even	2	inner
370.2.c.b.369.1	yes	10	37.36	even	2
370.2.c.b.369.10	yes	10	5.4	even	2
1850.2.d.i.1701.1		20	5.2	odd	4
1850.2.d.i.1701.10		20	185.73	odd	4
1850.2.d.i.1701.11		20	185.147	odd	4
1850.2.d.i.1701.20		20	5.3	odd	4
3330.2.e.c.739.5		10	111.110	odd	2
3330.2.e.c.739.6		10	15.14	odd	2
3330.2.e.d.739.5		10	555.554	odd	2
3330.2.e.d.739.6		10	3.2	odd	2

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.40359i q^{3} +1.00000 q^{4} +(-1.28269 - 1.83159i) q^{5} +3.40359i q^{6} -2.06225i q^{7} -1.00000 q^{8} -8.58443 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.40359i q^{3} +1.00000 q^{4} +(-1.28269 - 1.83159i) q^{5} +3.40359i q^{6} -2.06225i q^{7} -1.00000 q^{8} -8.58443 q^{9} +(1.28269 + 1.83159i) q^{10} +3.77719 q^{11} -3.40359i q^{12} -2.88351 q^{13} +2.06225i q^{14} +(-6.23397 + 4.36575i) q^{15} +1.00000 q^{16} +5.80724 q^{17} +8.58443 q^{18} -0.157282i q^{19} +(-1.28269 - 1.83159i) q^{20} -7.01905 q^{21} -3.77719 q^{22} +5.41883 q^{23} +3.40359i q^{24} +(-1.70942 + 4.69871i) q^{25} +2.88351 q^{26} +19.0071i q^{27} -2.06225i q^{28} -4.29061i q^{29} +(6.23397 - 4.36575i) q^{30} +0.425694i q^{31} -1.00000 q^{32} -12.8560i q^{33} -5.80724 q^{34} +(-3.77719 + 2.64522i) q^{35} -8.58443 q^{36} +(-4.80724 + 3.72698i) q^{37} +0.157282i q^{38} +9.81429i q^{39} +(1.28269 + 1.83159i) q^{40} +0.923733 q^{41} +7.01905 q^{42} -10.8263 q^{43} +3.77719 q^{44} +(11.0112 + 15.7231i) q^{45} -5.41883 q^{46} -0.676445i q^{47} -3.40359i q^{48} +2.74713 q^{49} +(1.70942 - 4.69871i) q^{50} -19.7655i q^{51} -2.88351 q^{52} -9.87810i q^{53} -19.0071i q^{54} +(-4.84496 - 6.91824i) q^{55} +2.06225i q^{56} -0.535322 q^{57} +4.29061i q^{58} -8.47192i q^{59} +(-6.23397 + 4.36575i) q^{60} +1.23904i q^{61} -0.425694i q^{62} +17.7032i q^{63} +1.00000 q^{64} +(3.69865 + 5.28140i) q^{65} +12.8560i q^{66} -6.45516i q^{67} +5.80724 q^{68} -18.4435i q^{69} +(3.77719 - 2.64522i) q^{70} -3.28329 q^{71} +8.58443 q^{72} +0.980489i q^{73} +(4.80724 - 3.72698i) q^{74} +(15.9925 + 5.81815i) q^{75} -0.157282i q^{76} -7.78950i q^{77} -9.81429i q^{78} +8.04725i q^{79} +(-1.28269 - 1.83159i) q^{80} +38.9391 q^{81} -0.923733 q^{82} +11.9496i q^{83} -7.01905 q^{84} +(-7.44889 - 10.6365i) q^{85} +10.8263 q^{86} -14.6035 q^{87} -3.77719 q^{88} -7.65857i q^{89} +(-11.0112 - 15.7231i) q^{90} +5.94652i q^{91} +5.41883 q^{92} +1.44889 q^{93} +0.676445i q^{94} +(-0.288075 + 0.201743i) q^{95} +3.40359i q^{96} +13.9571 q^{97} -2.74713 q^{98} -32.4250 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9	\( 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9} + 3 q^{10} - 2 q^{13} - 10 q^{15} + 10 q^{16} + 18 q^{17} + 8 q^{18} - 3 q^{20} - 12 q^{21} + 10 q^{23} + 5 q^{25} + 2 q^{26} + 10 q^{30} - 10 q^{32} - 18 q^{34} - 8 q^{36} - 8 q^{37} + 3 q^{40} - 4 q^{41} + 12 q^{42} - 10 q^{43} + 20 q^{45} - 10 q^{46} - 8 q^{49} - 5 q^{50} - 2 q^{52} + 5 q^{55} + 12 q^{57} - 10 q^{60} + 10 q^{64} + 2 q^{65} + 18 q^{68} - 20 q^{71} + 8 q^{72} + 8 q^{74} + 25 q^{75} - 3 q^{80} + 58 q^{81} + 4 q^{82} - 12 q^{84} - 28 q^{85} + 10 q^{86} - 10 q^{87} - 20 q^{90} + 10 q^{92} - 32 q^{93} + 2 q^{95} + 2 q^{97} + 8 q^{98} - 82 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9 + 3 * q^10 - 2 * q^13 - 10 * q^15 + 10 * q^16 + 18 * q^17 + 8 * q^18 - 3 * q^20 - 12 * q^21 + 10 * q^23 + 5 * q^25 + 2 * q^26 + 10 * q^30 - 10 * q^32 - 18 * q^34 - 8 * q^36 - 8 * q^37 + 3 * q^40 - 4 * q^41 + 12 * q^42 - 10 * q^43 + 20 * q^45 - 10 * q^46 - 8 * q^49 - 5 * q^50 - 2 * q^52 + 5 * q^55 + 12 * q^57 - 10 * q^60 + 10 * q^64 + 2 * q^65 + 18 * q^68 - 20 * q^71 + 8 * q^72 + 8 * q^74 + 25 * q^75 - 3 * q^80 + 58 * q^81 + 4 * q^82 - 12 * q^84 - 28 * q^85 + 10 * q^86 - 10 * q^87 - 20 * q^90 + 10 * q^92 - 32 * q^93 + 2 * q^95 + 2 * q^97 + 8 * q^98 - 82 * q^99

Introduction

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