LMFDB - Embedded newform 368.2.j.c.277.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(93,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("368.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.221124989353984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 2 x^{10} + 2 x^{9} + 12 x^{8} - 8 x^{7} - 14 x^{6} - 16 x^{5} + 48 x^{4} + 16 x^{3} + \cdots + 64 $ x^12 - 2x^11 - 2x^10 + 2x^9 + 12x^8 - 8x^7 - 14x^6 - 16x^5 + 48x^4 + 16x^3 - 32x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.6
Root			$-0.518742 + 1.31564i$ of defining polynomial
Character	$\chi$	$=$	368.277
Dual form			368.2.j.c.93.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38463 + 0.287766i) q^{2} +(0.339667 - 0.339667i) q^{3} +(1.83438 + 0.796898i) q^{4} +(1.46929 + 1.46929i) q^{5} +(0.568056 - 0.372567i) q^{6} -2.63128i q^{7} +(2.31061 + 1.63128i) q^{8} +2.76925i q^{9} +(1.61161 + 2.45723i) q^{10} +(-2.99062 - 2.99062i) q^{11} +(0.893758 - 0.352399i) q^{12} +(-0.749580 + 0.749580i) q^{13} +(0.757193 - 3.64334i) q^{14} +0.998138 q^{15} +(2.72991 + 2.92363i) q^{16} -3.64954 q^{17} +(-0.796898 + 3.83438i) q^{18} +(1.76925 - 1.76925i) q^{19} +(1.52436 + 3.86611i) q^{20} +(-0.893758 - 0.893758i) q^{21} +(-3.28029 - 5.00149i) q^{22} +1.00000i q^{23} +(1.33893 - 0.230747i) q^{24} -0.682370i q^{25} +(-1.25359 + 0.822185i) q^{26} +(1.95962 + 1.95962i) q^{27} +(2.09686 - 4.82677i) q^{28} +(0.0790494 - 0.0790494i) q^{29} +(1.38205 + 0.287231i) q^{30} -2.07656 q^{31} +(2.93858 + 4.83371i) q^{32} -2.03163 q^{33} +(-5.05325 - 1.05022i) q^{34} +(3.86611 - 3.86611i) q^{35} +(-2.20681 + 5.07987i) q^{36} +(-3.64475 - 3.64475i) q^{37} +(2.95889 - 1.94062i) q^{38} +0.509215i q^{39} +(0.998138 + 5.79178i) q^{40} -1.90098i q^{41} +(-0.980327 - 1.49471i) q^{42} +(6.84422 + 6.84422i) q^{43} +(-3.10272 - 7.86915i) q^{44} +(-4.06884 + 4.06884i) q^{45} +(-0.287766 + 1.38463i) q^{46} -8.55356 q^{47} +(1.92032 + 0.0658004i) q^{48} +0.0763717 q^{49} +(0.196363 - 0.944828i) q^{50} +(-1.23963 + 1.23963i) q^{51} +(-1.97236 + 0.777677i) q^{52} +(-6.62218 - 6.62218i) q^{53} +(2.14943 + 3.27726i) q^{54} -8.78817i q^{55} +(4.29235 - 6.07987i) q^{56} -1.20191i q^{57} +(0.132202 - 0.0867061i) q^{58} +(-5.45162 - 5.45162i) q^{59} +(1.83097 + 0.795414i) q^{60} +(2.13515 - 2.13515i) q^{61} +(-2.87525 - 0.597563i) q^{62} +7.28668 q^{63} +(2.67786 + 7.53851i) q^{64} -2.20270 q^{65} +(-2.81304 - 0.584634i) q^{66} +(3.51996 - 3.51996i) q^{67} +(-6.69465 - 2.90831i) q^{68} +(0.339667 + 0.339667i) q^{69} +(6.46566 - 4.24059i) q^{70} +1.61740i q^{71} +(-4.51742 + 6.39867i) q^{72} +14.4563i q^{73} +(-3.99778 - 6.09545i) q^{74} +(-0.231779 - 0.231779i) q^{75} +(4.65540 - 1.83557i) q^{76} +(-7.86915 + 7.86915i) q^{77} +(-0.146535 + 0.705073i) q^{78} -12.5492 q^{79} +(-0.284631 + 8.30669i) q^{80} -6.97652 q^{81} +(0.547039 - 2.63215i) q^{82} +(1.26143 - 1.26143i) q^{83} +(-0.927259 - 2.35173i) q^{84} +(-5.36224 - 5.36224i) q^{85} +(7.50715 + 11.4462i) q^{86} -0.0537009i q^{87} +(-2.03163 - 11.7887i) q^{88} +12.3891i q^{89} +(-6.80469 + 4.46295i) q^{90} +(1.97236 + 1.97236i) q^{91} +(-0.796898 + 1.83438i) q^{92} +(-0.705337 + 0.705337i) q^{93} +(-11.8435 - 2.46143i) q^{94} +5.19909 q^{95} +(2.63999 + 0.643712i) q^{96} +7.54694 q^{97} +(0.105746 + 0.0219772i) q^{98} +(8.28178 - 8.28178i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26}+ \cdots + 36 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8 - 6 * q^10 - 4 * q^11 - 8 * q^12 + 18 * q^13 - 2 * q^14 + 8 * q^16 - 8 * q^17 - 4 * q^18 - 8 * q^19 - 32 * q^20 + 8 * q^21 - 34 * q^22 + 12 * q^24 - 14 * q^26 + 14 * q^27 + 12 * q^28 + 2 * q^29 - 30 * q^30 + 20 * q^31 - 8 * q^32 - 36 * q^33 + 10 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 24 * q^38 - 14 * q^42 + 20 * q^43 + 4 * q^44 - 20 * q^45 - 2 * q^46 - 16 * q^47 - 12 * q^48 + 52 * q^49 + 6 * q^50 - 4 * q^51 - 16 * q^53 + 16 * q^54 + 28 * q^56 + 14 * q^58 + 8 * q^59 + 48 * q^60 + 12 * q^61 - 44 * q^62 - 4 * q^63 + 24 * q^64 - 52 * q^65 + 34 * q^66 - 4 * q^67 - 16 * q^68 + 2 * q^69 + 28 * q^70 + 8 * q^72 - 26 * q^74 - 46 * q^75 - 8 * q^76 - 12 * q^77 - 44 * q^78 - 4 * q^79 + 4 * q^80 + 48 * q^81 - 6 * q^82 + 28 * q^83 + 12 * q^84 - 8 * q^85 + 44 * q^86 - 36 * q^88 + 4 * q^90 - 4 * q^92 - 14 * q^93 + 48 * q^95 + 32 * q^96 + 36 * q^97 - 2 * q^98 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.38463	+	0.287766i	0.979079	+	0.203482i
$2$	1.38463	+	0.287766i	0.979079	+	0.203482i
$3$	0.339667	−	0.339667i	0.196107	−	0.196107i	−0.602222	−	0.798329i	$-0.705718\pi$
$3$	0.339667	−	0.339667i	0.196107	−	0.196107i	0.798329	+	0.602222i	$0.205718\pi$
$4$	1.83438	+	0.796898i	0.917191	+	0.398449i
$5$	1.46929	+	1.46929i	0.657087	+	0.657087i	0.954690	−	0.297603i	$-0.0961872\pi$
$5$	1.46929	+	1.46929i	0.657087	+	0.657087i	−0.297603	+	0.954690i	$0.596187\pi$
$6$	0.568056	−	0.372567i	0.231908	−	0.152100i
$7$		−	2.63128i		−	0.994530i	−0.867599	−	0.497265i	$-0.834338\pi$
$7$		−	2.63128i		−	0.994530i	0.867599	−	0.497265i	$-0.165662\pi$
$8$	2.31061	+	1.63128i	0.816925	+	0.576744i
$9$			2.76925i			0.923084i
$10$	1.61161	+	2.45723i	0.509635	+	0.777045i
$11$	−2.99062	−	2.99062i	−0.901705	−	0.901705i	0.0938784	−	0.995584i	$-0.470074\pi$
$11$	−2.99062	−	2.99062i	−0.901705	−	0.901705i	−0.995584	+	0.0938784i	$0.970074\pi$
$12$	0.893758	−	0.352399i	0.258006	−	0.101729i
$13$	−0.749580	+	0.749580i	−0.207896	+	0.207896i	−0.803373	−	0.595477i	$-0.796963\pi$
$13$	−0.749580	+	0.749580i	−0.207896	+	0.207896i	0.595477	+	0.803373i	$0.296963\pi$
$14$	0.757193	−	3.64334i	0.202368	−	0.973723i
$15$	0.998138			0.257718
$16$	2.72991	+	2.92363i	0.682477	+	0.730907i
$17$	−3.64954			−0.885144			−0.442572	−	0.896733i	$-0.645934\pi$
$17$	−3.64954			−0.885144			−0.442572	+	0.896733i	$0.645934\pi$
$18$	−0.796898	+	3.83438i	−0.187831	+	0.903772i
$19$	1.76925	−	1.76925i	0.405894	−	0.405894i	−0.474410	−	0.880304i	$-0.657338\pi$
$19$	1.76925	−	1.76925i	0.405894	−	0.405894i	0.880304	+	0.474410i	$0.157338\pi$
$20$	1.52436	+	3.86611i	0.340858	+	0.864489i
$21$	−0.893758	−	0.893758i	−0.195034	−	0.195034i
$22$	−3.28029	−	5.00149i	−0.699360	−	1.06632i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	1.33893	−	0.230747i	0.273308	−	0.0471010i
$25$		−	0.682370i		−	0.136474i
$26$	−1.25359	+	0.822185i	−0.245850	+	0.161244i
$27$	1.95962	+	1.95962i	0.377130	+	0.377130i
$28$	2.09686	−	4.82677i	0.396269	−	0.912173i
$29$	0.0790494	−	0.0790494i	0.0146791	−	0.0146791i	−0.699729	−	0.714408i	$-0.746696\pi$
$29$	0.0790494	−	0.0790494i	0.0146791	−	0.0146791i	0.714408	+	0.699729i	$0.246696\pi$
$30$	1.38205	+	0.287231i	0.252326	+	0.0524409i
$31$	−2.07656			−0.372960			−0.186480	−	0.982459i	$-0.559708\pi$
$31$	−2.07656			−0.372960			−0.186480	+	0.982459i	$0.559708\pi$
$32$	2.93858	+	4.83371i	0.519473	+	0.854487i
$33$	−2.03163			−0.353661
$34$	−5.05325	−	1.05022i	−0.866626	−	0.180110i
$35$	3.86611	−	3.86611i	0.653492	−	0.653492i
$36$	−2.20681	+	5.07987i	−0.367802	+	0.846644i
$37$	−3.64475	−	3.64475i	−0.599193	−	0.599193i	0.340905	−	0.940098i	$-0.389267\pi$
$37$	−3.64475	−	3.64475i	−0.599193	−	0.599193i	−0.940098	+	0.340905i	$0.889267\pi$
$38$	2.95889	−	1.94062i	0.479995	−	0.314811i
$39$			0.509215i			0.0815397i
$40$	0.998138	+	5.79178i	0.157820	+	0.915761i
$41$		−	1.90098i		−	0.296884i	−0.988921	−	0.148442i	$-0.952574\pi$
$41$		−	1.90098i		−	0.296884i	0.988921	−	0.148442i	$-0.0474258\pi$
$42$	−0.980327	−	1.49471i	−0.151268	−	0.230639i
$43$	6.84422	+	6.84422i	1.04373	+	1.04373i	0.998999	+	0.0447348i	$0.0142443\pi$
$43$	6.84422	+	6.84422i	1.04373	+	1.04373i	0.0447348	+	0.998999i	$0.485756\pi$
$44$	−3.10272	−	7.86915i	−0.467752	−	1.18632i
$45$	−4.06884	+	4.06884i	−0.606546	+	0.606546i
$46$	−0.287766	+	1.38463i	−0.0424288	+	0.204152i
$47$	−8.55356			−1.24767			−0.623833	−	0.781558i	$-0.714425\pi$
$47$	−8.55356			−1.24767			−0.623833	+	0.781558i	$0.714425\pi$
$48$	1.92032	+	0.0658004i	0.277174	+	0.00949746i
$49$	0.0763717			0.0109102
$50$	0.196363	−	0.944828i	0.0277700	−	0.133619i
$51$	−1.23963	+	1.23963i	−0.173583	+	0.173583i
$52$	−1.97236	+	0.777677i	−0.273516	+	0.107844i
$53$	−6.62218	−	6.62218i	−0.909627	−	0.909627i	0.0866152	−	0.996242i	$-0.472395\pi$
$53$	−6.62218	−	6.62218i	−0.909627	−	0.909627i	−0.996242	+	0.0866152i	$0.972395\pi$
$54$	2.14943	+	3.27726i	0.292501	+	0.445979i
$55$		−	8.78817i		−	1.18500i
$56$	4.29235	−	6.07987i	0.573589	−	0.812456i
$57$		−	1.20191i		−	0.159197i
$58$	0.132202	−	0.0867061i	0.0173589	−	0.0113851i
$59$	−5.45162	−	5.45162i	−0.709741	−	0.709741i	0.256740	−	0.966481i	$-0.417352\pi$
$59$	−5.45162	−	5.45162i	−0.709741	−	0.709741i	−0.966481	+	0.256740i	$0.917352\pi$
$60$	1.83097	+	0.795414i	0.236377	+	0.102688i
$61$	2.13515	−	2.13515i	0.273379	−	0.273379i	−0.557080	−	0.830459i	$-0.688078\pi$
$61$	2.13515	−	2.13515i	0.273379	−	0.273379i	0.830459	+	0.557080i	$0.188078\pi$
$62$	−2.87525	−	0.597563i	−0.365158	−	0.0758905i
$63$	7.28668			0.918035
$64$	2.67786	+	7.53851i	0.334732	+	0.942313i
$65$	−2.20270			−0.273212
$66$	−2.81304	−	0.584634i	−0.346262	−	0.0719635i
$67$	3.51996	−	3.51996i	0.430031	−	0.430031i	−0.458608	−	0.888639i	$-0.651652\pi$
$67$	3.51996	−	3.51996i	0.430031	−	0.430031i	0.888639	+	0.458608i	$0.151652\pi$
$68$	−6.69465	−	2.90831i	−0.811846	−	0.352685i
$69$	0.339667	+	0.339667i	0.0408911	+	0.0408911i
$70$	6.46566	−	4.24059i	0.772794	−	0.506847i
$71$			1.61740i			0.191950i	0.995384	+	0.0959749i	$0.0305968\pi$
$71$			1.61740i			0.191950i	−0.995384	+	0.0959749i	$0.969403\pi$
$72$	−4.51742	+	6.39867i	−0.532384	+	0.754091i
$73$			14.4563i			1.69198i	0.533199	+	0.845990i	$0.320990\pi$
$73$			14.4563i			1.69198i	−0.533199	+	0.845990i	$0.679010\pi$
$74$	−3.99778	−	6.09545i	−0.464732	−	0.708582i
$75$	−0.231779	−	0.231779i	−0.0267635	−	0.0267635i
$76$	4.65540	−	1.83557i	0.534011	−	0.210554i
$77$	−7.86915	+	7.86915i	−0.896773	+	0.896773i
$78$	−0.146535	+	0.705073i	−0.0165918	+	0.0798338i
$79$	−12.5492			−1.41190			−0.705950	−	0.708262i	$-0.749480\pi$
$79$	−12.5492			−1.41190			−0.705950	+	0.708262i	$0.749480\pi$
$80$	−0.284631	+	8.30669i	−0.0318228	+	0.928716i
$81$	−6.97652			−0.775169
$82$	0.547039	−	2.63215i	0.0604104	−	0.290673i
$83$	1.26143	−	1.26143i	0.138460	−	0.138460i	−0.634480	−	0.772940i	$-0.718786\pi$
$83$	1.26143	−	1.26143i	0.138460	−	0.138460i	0.772940	+	0.634480i	$0.218786\pi$
$84$	−0.927259	−	2.35173i	−0.101172	−	0.256594i
$85$	−5.36224	−	5.36224i	−0.581616	−	0.581616i
$86$	7.50715	+	11.4462i	0.809517	+	1.23428i
$87$		−	0.0537009i		−	0.00575734i
$88$	−2.03163	−	11.7887i	−0.216572	−	1.25668i
$89$			12.3891i			1.31324i	0.754222	+	0.656620i	$0.228014\pi$
$89$			12.3891i			1.31324i	−0.754222	+	0.656620i	$0.771986\pi$
$90$	−6.80469	+	4.46295i	−0.717278	+	0.470436i
$91$	1.97236	+	1.97236i	0.206759	+	0.206759i
$92$	−0.796898	+	1.83438i	−0.0830823	+	0.191247i
$93$	−0.705337	+	0.705337i	−0.0731400	+	0.0731400i
$94$	−11.8435	−	2.46143i	−1.22156	−	0.253877i
$95$	5.19909			0.533416
$96$	2.63999	+	0.643712i	0.269443	+	0.0656986i
$97$	7.54694			0.766276			0.383138	−	0.923691i	$-0.374843\pi$
$97$	7.54694			0.766276			0.383138	+	0.923691i	$0.374843\pi$
$98$	0.105746	+	0.0219772i	0.0106820	+	0.00222003i
$99$	8.28178	−	8.28178i	0.832350	−	0.832350i
$100$	0.543779	−	1.25173i	0.0543779	−	0.125173i
$101$	−3.11433	−	3.11433i	−0.309888	−	0.309888i	0.534978	−	0.844866i	$-0.320320\pi$
$101$	−3.11433	−	3.11433i	−0.309888	−	0.309888i	−0.844866	+	0.534978i	$0.820320\pi$
$102$	−2.07314	+	1.35970i	−0.205272	+	0.134630i
$103$		−	3.73367i		−	0.367890i	−0.982937	−	0.183945i	$-0.941113\pi$
$103$		−	3.73367i		−	0.367890i	0.982937	−	0.183945i	$-0.0588868\pi$
$104$	−2.95476	+	0.509215i	−0.289739	+	0.0499327i
$105$		−	2.62638i		−	0.256308i
$106$	−7.26361	−	11.0749i	−0.705504	−	1.07569i
$107$	0.0709721	+	0.0709721i	0.00686113	+	0.00686113i	0.710529	−	0.703668i	$-0.248456\pi$
$107$	0.0709721	+	0.0709721i	0.00686113	+	0.00686113i	−0.703668	+	0.710529i	$0.748456\pi$
$108$	2.03308	+	5.15632i	0.195633	+	0.496167i
$109$	2.51118	−	2.51118i	0.240527	−	0.240527i	−0.576541	−	0.817068i	$-0.695598\pi$
$109$	2.51118	−	2.51118i	0.240527	−	0.240527i	0.817068	+	0.576541i	$0.195598\pi$
$110$	2.52894	−	12.1683i	0.241125	−	1.16021i
$111$	−2.47600			−0.235011
$112$	7.69288	−	7.18315i	0.726909	−	0.678744i
$113$	18.1520			1.70760			0.853799	−	0.520603i	$-0.174293\pi$
$113$	18.1520			1.70760			0.853799	+	0.520603i	$0.174293\pi$
$114$	0.345870	−	1.66420i	0.0323937	−	0.155867i
$115$	−1.46929	+	1.46929i	−0.137012	+	0.137012i
$116$	0.208001	−	0.0820124i	0.0193124	−	0.00761466i
$117$	−2.07578	−	2.07578i	−0.191906	−	0.191906i
$118$	−5.97967	−	9.11726i	−0.550473	−	0.839311i
$119$			9.60296i			0.880302i
$120$	2.30631	+	1.62824i	0.210536	+	0.148637i
$121$			6.88759i			0.626145i
$122$	3.57082	−	2.34197i	0.323287	−	0.212032i
$123$	−0.645701	−	0.645701i	−0.0582209	−	0.0582209i
$124$	−3.80919	−	1.65480i	−0.342076	−	0.148606i
$125$	8.34905	−	8.34905i	0.746762	−	0.746762i
$126$	10.0893	+	2.09686i	0.898829	+	0.186803i
$127$	12.4430			1.10414			0.552068	−	0.833799i	$-0.313839\pi$
$127$	12.4430			1.10414			0.552068	+	0.833799i	$0.313839\pi$
$128$	1.53851	+	11.2086i	0.135986	+	0.990711i
$129$	4.64951			0.409366
$130$	−3.04992	−	0.633864i	−0.267496	−	0.0555935i
$131$	8.15929	−	8.15929i	0.712880	−	0.712880i	−0.254257	−	0.967137i	$-0.581831\pi$
$131$	8.15929	−	8.15929i	0.712880	−	0.712880i	0.967137	+	0.254257i	$0.0818308\pi$
$132$	−3.72678	−	1.61900i	−0.324374	−	0.140916i
$133$	−4.65540	−	4.65540i	−0.403674	−	0.403674i
$134$	5.88675	−	3.86090i	0.508538	−	0.333531i
$135$			5.75851i			0.495614i
$136$	−8.43268	−	5.95342i	−0.723096	−	0.510502i
$137$			19.1721i			1.63798i	0.573806	+	0.818991i	$0.305466\pi$
$137$			19.1721i			1.63798i	−0.573806	+	0.818991i	$0.694534\pi$
$138$	0.372567	+	0.568056i	0.0317150	+	0.0483562i
$139$	−3.90522	−	3.90522i	−0.331237	−	0.331237i	0.521819	−	0.853056i	$-0.325253\pi$
$139$	−3.90522	−	3.90522i	−0.331237	−	0.331237i	−0.853056	+	0.521819i	$0.825253\pi$
$140$	10.1728	−	4.01103i	0.859760	−	0.338994i
$141$	−2.90536	+	2.90536i	−0.244676	+	0.244676i
$142$	−0.465433	+	2.23949i	−0.0390582	+	0.187934i
$143$	4.48342			0.374922
$144$	−8.09627	+	7.55981i	−0.674689	+	0.629984i
$145$	0.232293			0.0192909
$146$	−4.16003	+	20.0165i	−0.344287	+	1.65658i
$147$	0.0259409	−	0.0259409i	0.00213957	−	0.00213957i
$148$	−3.78137	−	9.59035i	−0.310826	−	0.788322i
$149$	3.78869	+	3.78869i	0.310382	+	0.310382i	0.845057	−	0.534676i	$-0.179566\pi$
$149$	3.78869	+	3.78869i	0.310382	+	0.310382i	−0.534676	+	0.845057i	$0.679566\pi$
$150$	−0.254229	−	0.387625i	−0.0207577	−	0.0316494i
$151$			7.90187i			0.643045i	0.946902	+	0.321523i	$0.104195\pi$
$151$			7.90187i			0.643045i	−0.946902	+	0.321523i	$0.895805\pi$
$152$	6.97420	−	1.20191i	0.565683	−	0.0974880i
$153$		−	10.1065i		−	0.817062i
$154$	−13.1603	+	8.63136i	−1.06049	+	0.695535i
$155$	−3.05106	−	3.05106i	−0.245067	−	0.245067i
$156$	−0.405792	+	0.934095i	−0.0324894	+	0.0747874i
$157$	5.73125	−	5.73125i	0.457404	−	0.457404i	−0.440399	−	0.897802i	$-0.645163\pi$
$157$	5.73125	−	5.73125i	0.457404	−	0.457404i	0.897802	+	0.440399i	$0.145163\pi$
$158$	−17.3760	−	3.61125i	−1.38236	−	0.287295i
$159$	−4.49867			−0.356768
$160$	−2.78449	+	11.4198i	−0.220134	+	0.902811i
$161$	2.63128			0.207374
$162$	−9.65988	−	2.00761i	−0.758952	−	0.157733i
$163$	15.0985	−	15.0985i	1.18261	−	1.18261i	0.203542	−	0.979066i	$-0.434755\pi$
$163$	15.0985	−	15.0985i	1.18261	−	1.18261i	0.979066	−	0.203542i	$-0.0652454\pi$
$164$	1.51489	−	3.48713i	0.118293	−	0.272299i
$165$	−2.98505	−	2.98505i	−0.232386	−	0.232386i
$166$	2.10960	−	1.38361i	0.163737	−	0.107389i
$167$			24.8170i			1.92040i	0.279316	+	0.960199i	$0.409892\pi$
$167$			24.8170i			1.92040i	−0.279316	+	0.960199i	$0.590108\pi$
$168$	−0.607160	−	3.52310i	−0.0468434	−	0.271813i
$169$			11.8763i			0.913558i
$170$	−5.88162	−	8.96777i	−0.451100	−	0.687796i
$171$	4.89951	+	4.89951i	0.374675	+	0.374675i
$172$	7.10076	+	18.0091i	0.541428	+	1.37318i
$173$	−15.3500	+	15.3500i	−1.16704	+	1.16704i	−0.184143	+	0.982899i	$0.558951\pi$
$173$	−15.3500	+	15.3500i	−1.16704	+	1.16704i	−0.982899	+	0.184143i	$0.941049\pi$
$174$	0.0154533	−	0.0743557i	0.00117151	−	0.00563689i
$175$	−1.79551			−0.135728
$176$	0.579344	−	16.9076i	0.0436697	−	1.27446i
$177$	−3.70347			−0.278370
$178$	−3.56516	+	17.1542i	−0.267220	+	1.28576i
$179$	4.97599	−	4.97599i	0.371923	−	0.371923i	−0.496254	−	0.868177i	$-0.665292\pi$
$179$	4.97599	−	4.97599i	0.371923	−	0.371923i	0.868177	+	0.496254i	$0.165292\pi$
$180$	−10.7062	+	4.22135i	−0.797996	+	0.314641i
$181$	−6.45355	−	6.45355i	−0.479688	−	0.479688i	0.425344	−	0.905032i	$-0.360153\pi$
$181$	−6.45355	−	6.45355i	−0.479688	−	0.479688i	−0.905032	+	0.425344i	$0.860153\pi$
$182$	2.16340	+	3.29855i	0.160362	+	0.244505i
$183$		−	1.45048i		−	0.107223i
$184$	−1.63128	+	2.31061i	−0.120259	+	0.170341i
$185$		−	10.7104i		−	0.787443i
$186$	−1.17960	+	0.773656i	−0.0864925	+	0.0567272i
$187$	10.9144	+	10.9144i	0.798139	+	0.798139i
$188$	−15.6905	−	6.81631i	−1.14435	−	0.497131i
$189$	5.15632	−	5.15632i	0.375067	−	0.375067i
$190$	7.19880	+	1.49612i	0.522256	+	0.108540i
$191$	−8.83309			−0.639140			−0.319570	−	0.947563i	$-0.603538\pi$
$191$	−8.83309			−0.639140			−0.319570	+	0.947563i	$0.603538\pi$
$192$	3.47016	+	1.65100i	0.250437	+	0.119151i
$193$	25.7203			1.85139			0.925693	−	0.378276i	$-0.123483\pi$
$193$	25.7203			1.85139			0.925693	+	0.378276i	$0.123483\pi$
$194$	10.4497	+	2.17176i	0.750244	+	0.155923i
$195$	−0.748185	+	0.748185i	−0.0535786	+	0.0535786i
$196$	0.140095	+	0.0608604i	0.0100068	+	0.00434717i
$197$	13.6056	+	13.6056i	0.969360	+	0.969360i	0.999544	−	0.0301846i	$-0.00960950\pi$
$197$	13.6056	+	13.6056i	0.969360	+	0.969360i	−0.0301846	+	0.999544i	$0.509610\pi$
$198$	13.8504	−	9.08395i	0.984304	−	0.645568i
$199$		−	18.1665i		−	1.28779i	−0.765113	−	0.643896i	$-0.777317\pi$
$199$		−	18.1665i		−	1.28779i	0.765113	−	0.643896i	$-0.222683\pi$
$200$	1.11314	−	1.57669i	0.0787106	−	0.111489i
$201$		−	2.39123i		−	0.168664i
$202$	−3.41599	−	5.20839i	−0.240348	−	0.366461i
$203$	−0.208001	−	0.208001i	−0.0145988	−	0.0145988i
$204$	−3.26181	+	1.28609i	−0.228372	+	0.0900445i
$205$	2.79310	−	2.79310i	0.195078	−	0.195078i
$206$	1.07443	−	5.16974i	0.0748588	−	0.360193i
$207$	−2.76925			−0.192476
$208$	−4.23778	−	0.145209i	−0.293837	−	0.0100684i
$209$	−10.5823			−0.731994
$210$	0.755784	−	3.63656i	0.0521540	−	0.250946i
$211$	14.8891	−	14.8891i	1.02501	−	1.02501i	0.0253303	−	0.999679i	$-0.491936\pi$
$211$	14.8891	−	14.8891i	1.02501	−	1.02501i	0.999679	−	0.0253303i	$-0.00806373\pi$
$212$	−6.87040	−	17.4248i	−0.471861	−	1.19674i
$213$	0.549376	+	0.549376i	0.0376426	+	0.0376426i
$214$	0.0778465	+	0.118693i	0.00532147	+	0.00811370i
$215$			20.1123i			1.37165i
$216$	1.33124	+	7.72462i	0.0905793	+	0.525594i
$217$			5.46400i			0.370920i
$218$	4.19968	−	2.75441i	0.284438	−	0.186552i
$219$	4.91032	+	4.91032i	0.331808	+	0.331808i
$220$	7.00328	−	16.1209i	0.472161	−	1.08687i
$221$	2.73563	−	2.73563i	0.184018	−	0.184018i
$222$	−3.42833	−	0.712509i	−0.230095	−	0.0478205i
$223$	−13.1617			−0.881375			−0.440687	−	0.897661i	$-0.645265\pi$
$223$	−13.1617			−0.881375			−0.440687	+	0.897661i	$0.645265\pi$
$224$	12.7188	−	7.73223i	0.849813	−	0.516631i
$225$	1.88966			0.125977
$226$	25.1338	+	5.22354i	1.67187	+	0.347465i
$227$	−20.0761	+	20.0761i	−1.33250	+	1.33250i	−0.429373	+	0.903127i	$0.641266\pi$
$227$	−20.0761	+	20.0761i	−1.33250	+	1.33250i	−0.903127	+	0.429373i	$0.858734\pi$
$228$	0.957802	−	2.20477i	0.0634320	−	0.146014i
$229$	8.36396	+	8.36396i	0.552706	+	0.552706i	0.927221	−	0.374515i	$-0.122191\pi$
$229$	8.36396	+	8.36396i	0.552706	+	0.552706i	−0.374515	+	0.927221i	$0.622191\pi$
$230$	−2.45723	+	1.61161i	−0.162025	+	0.106266i
$231$			5.34578i			0.351726i
$232$	0.311604	−	0.0537009i	0.0204578	−	0.00352564i
$233$		−	3.94663i		−	0.258552i	−0.991609	−	0.129276i	$-0.958735\pi$
$233$		−	3.94663i		−	0.258552i	0.991609	−	0.129276i	$-0.0412653\pi$
$234$	−2.27684	−	3.47152i	−0.148842	−	0.226940i
$235$	−12.5677	−	12.5677i	−0.819824	−	0.819824i
$236$	−5.65597	−	14.3447i	−0.368172	−	0.933763i
$237$	−4.26256	+	4.26256i	−0.276883	+	0.276883i
$238$	−2.76341	+	13.2965i	−0.179125	+	0.861885i
$239$	11.4254			0.739050			0.369525	−	0.929221i	$-0.379520\pi$
$239$	11.4254			0.739050			0.369525	+	0.929221i	$0.379520\pi$
$240$	2.72483	+	2.91819i	0.175887	+	0.188368i
$241$	7.33232			0.472316			0.236158	−	0.971715i	$-0.424112\pi$
$241$	7.33232			0.472316			0.236158	+	0.971715i	$0.424112\pi$
$242$	−1.98202	+	9.53674i	−0.127409	+	0.613045i
$243$	−8.24856	+	8.24856i	−0.529146	+	0.529146i
$244$	5.61819	−	2.21519i	0.359668	−	0.141813i
$245$	0.112212	+	0.112212i	0.00716897	+	0.00716897i
$246$	−0.708244	−	1.07987i	−0.0451560	−	0.0688497i
$247$			2.65240i			0.168768i
$248$	−4.79811	−	3.38744i	−0.304681	−	0.215103i
$249$		−	0.856931i		−	0.0543058i
$250$	13.9629	−	9.15774i	0.883091	−	0.579187i
$251$	8.12841	+	8.12841i	0.513061	+	0.513061i	0.915463	−	0.402402i	$-0.131825\pi$
$251$	8.12841	+	8.12841i	0.513061	+	0.513061i	−0.402402	+	0.915463i	$0.631825\pi$
$252$	13.3665	+	5.80674i	0.842013	+	0.365790i
$253$	2.99062	−	2.99062i	0.188019	−	0.188019i
$254$	17.2289	+	3.58067i	1.08104	+	0.224671i
$255$	−3.64275			−0.228118
$256$	−1.09521	+	15.9625i	−0.0684503	+	0.997655i
$257$	−11.6453			−0.726417			−0.363208	−	0.931708i	$-0.618319\pi$
$257$	−11.6453			−0.726417			−0.363208	+	0.931708i	$0.618319\pi$
$258$	6.43783	+	1.33797i	0.400802	+	0.0832985i
$259$	−9.59035	+	9.59035i	−0.595915	+	0.595915i
$260$	−4.04060	−	1.75533i	−0.250587	−	0.108861i
$261$	0.218908	+	0.218908i	0.0135500	+	0.0135500i
$262$	13.6455	−	8.94960i	0.843024	−	0.552908i
$263$			15.1470i			0.934002i	0.884257	+	0.467001i	$0.154666\pi$
$263$			15.1470i			0.934002i	−0.884257	+	0.467001i	$0.845334\pi$
$264$	−4.69430	−	3.31415i	−0.288914	−	0.203972i
$265$		−	19.4598i		−	1.19541i
$266$	−5.10632	−	7.78565i	−0.313089	−	0.477369i
$267$	4.20816	+	4.20816i	0.257535	+	0.257535i
$268$	9.26199	−	3.65190i	0.565766	−	0.223075i
$269$	14.2175	−	14.2175i	0.866859	−	0.866859i	−0.125264	−	0.992123i	$-0.539978\pi$
$269$	14.2175	−	14.2175i	0.866859	−	0.866859i	0.992123	+	0.125264i	$0.0399779\pi$
$270$	−1.65711	+	7.97339i	−0.100848	+	0.485245i
$271$	−29.2477			−1.77667			−0.888335	−	0.459196i	$-0.848137\pi$
$271$	−29.2477			−1.77667			−0.888335	+	0.459196i	$0.848137\pi$
$272$	−9.96291	−	10.6699i	−0.604090	−	0.646958i
$273$	1.33989			0.0810936
$274$	−5.51708	+	26.5462i	−0.333299	+	1.60371i
$275$	−2.04071	+	2.04071i	−0.123059	+	0.123059i
$276$	0.352399	+	0.893758i	0.0212119	+	0.0537979i
$277$	18.1466	+	18.1466i	1.09033	+	1.09033i	0.995493	+	0.0948326i	$0.0302316\pi$
$277$	18.1466	+	18.1466i	1.09033	+	1.09033i	0.0948326	+	0.995493i	$0.469768\pi$
$278$	−4.28348	−	6.53106i	−0.256906	−	0.391707i
$279$		−	5.75051i		−	0.344274i
$280$	15.2398	−	2.62638i	0.910752	−	0.156956i
$281$		−	7.80937i		−	0.465868i	−0.972493	−	0.232934i	$-0.925167\pi$
$281$		−	7.80937i		−	0.465868i	0.972493	−	0.232934i	$-0.0748326\pi$
$282$	−4.85890	+	3.18677i	−0.289344	+	0.189770i
$283$	6.93643	+	6.93643i	0.412328	+	0.412328i	0.882549	−	0.470221i	$-0.155826\pi$
$283$	6.93643	+	6.93643i	0.412328	+	0.412328i	−0.470221	+	0.882549i	$0.655826\pi$
$284$	−1.28890	+	2.96692i	−0.0764822	+	0.176055i
$285$	1.76596	−	1.76596i	0.104606	−	0.104606i
$286$	6.20786	+	1.29018i	0.367078	+	0.0762897i
$287$	−5.00202			−0.295260
$288$	−13.3858	+	8.13767i	−0.788764	+	0.479517i
$289$	−3.68085			−0.216520
$290$	0.321639	+	0.0668461i	0.0188873	+	0.00392534i
$291$	2.56345	−	2.56345i	0.150272	−	0.150272i
$292$	−11.5202	+	26.5183i	−0.674167	+	1.55187i
$293$	−17.8367	−	17.8367i	−1.04203	−	1.04203i	−0.999077	−	0.0429542i	$-0.986323\pi$
$293$	−17.8367	−	17.8367i	−1.04203	−	1.04203i	−0.0429542	−	0.999077i	$-0.513677\pi$
$294$	0.0433834	−	0.0284536i	0.00253017	−	0.00165945i
$295$		−	16.0200i		−	0.932723i
$296$	−2.47600	−	14.3672i	−0.143915	−	0.835077i
$297$		−	11.7210i		−	0.680120i
$298$	4.15566	+	6.33618i	0.240731	+	0.367045i
$299$	−0.749580	−	0.749580i	−0.0433494	−	0.0433494i
$300$	−0.240466	−	0.609874i	−0.0138833	−	0.0352111i
$301$	18.0091	−	18.0091i	1.03802	−	1.03802i
$302$	−2.27389	+	10.9411i	−0.130848	+	0.629592i
$303$	−2.11567			−0.121542
$304$	10.0025	+	0.342740i	0.573685	+	0.0196575i
$305$	6.27433			0.359267
$306$	2.90831	−	13.9937i	0.166257	−	0.799969i
$307$	−7.49984	+	7.49984i	−0.428038	+	0.428038i	−0.887960	−	0.459921i	$-0.847878\pi$
$307$	−7.49984	+	7.49984i	−0.428038	+	0.428038i	0.459921	+	0.887960i	$0.347878\pi$
$308$	−20.7059	+	8.16411i	−1.17983	+	0.465193i
$309$	−1.26821	−	1.26821i	−0.0721457	−	0.0721457i
$310$	−3.34659	−	5.10258i	−0.190074	−	0.289807i
$311$		−	11.2453i		−	0.637660i	−0.947812	−	0.318830i	$-0.896710\pi$
$311$		−	11.2453i		−	0.637660i	0.947812	−	0.318830i	$-0.103290\pi$
$312$	−0.830672	+	1.17660i	−0.0470275	+	0.0666118i
$313$		−	32.0265i		−	1.81025i	−0.425149	−	0.905123i	$-0.639778\pi$
$313$		−	32.0265i		−	1.81025i	0.425149	−	0.905123i	$-0.360222\pi$
$314$	9.58491	−	6.28638i	0.540908	−	0.354761i
$315$	10.7062	+	10.7062i	0.603229	+	0.603229i
$316$	−23.0201	−	10.0005i	−1.29498	−	0.562570i
$317$	3.70621	−	3.70621i	0.208162	−	0.208162i	−0.595324	−	0.803486i	$-0.702976\pi$
$317$	3.70621	−	3.70621i	0.208162	−	0.208162i	0.803486	+	0.595324i	$0.202976\pi$
$318$	−6.22898	−	1.29457i	−0.349304	−	0.0725956i
$319$	−0.472813			−0.0264724
$320$	−7.14170	+	15.0108i	−0.399233	+	0.839130i
$321$	0.0482137			0.00269103
$322$	3.64334	+	0.757193i	0.203035	+	0.0421967i
$323$	−6.45696	+	6.45696i	−0.359275	+	0.359275i
$324$	−12.7976	−	5.55957i	−0.710978	−	0.308865i
$325$	0.511492	+	0.511492i	0.0283724	+	0.0283724i
$326$	25.2507	−	16.5610i	1.39851	−	0.917228i
$327$		−	1.70593i		−	0.0943381i
$328$	3.10103	−	4.39244i	0.171226	−	0.242532i
$329$			22.5068i			1.24084i
$330$	−3.27418	−	4.99218i	−0.180238	−	0.274810i
$331$	−12.6447	−	12.6447i	−0.695018	−	0.695018i	0.268314	−	0.963332i	$-0.413534\pi$
$331$	−12.6447	−	12.6447i	−0.695018	−	0.695018i	−0.963332	+	0.268314i	$0.913534\pi$
$332$	3.31917	−	1.30871i	0.182163	−	0.0718249i
$333$	10.0932	−	10.0932i	0.553106	−	0.553106i
$334$	−7.14150	+	34.3623i	−0.390766	+	1.88022i
$335$	10.3437			0.565136
$336$	0.173139	−	5.05289i	0.00944551	−	0.275658i
$337$	−7.17715			−0.390964			−0.195482	−	0.980707i	$-0.562627\pi$
$337$	−7.17715			−0.390964			−0.195482	+	0.980707i	$0.562627\pi$
$338$	−3.41759	+	16.4442i	−0.185892	+	0.894446i
$339$	6.16564	−	6.16564i	0.334871	−	0.334871i
$340$	−5.56323	−	14.1095i	−0.301709	−	0.765197i
$341$	6.21018	+	6.21018i	0.336300	+	0.336300i
$342$	5.37408	+	8.19390i	0.290597	+	0.443076i
$343$		−	18.6199i		−	1.00538i
$344$	4.64951	+	26.9792i	0.250685	+	1.45462i
$345$			0.998138i			0.0537380i
$346$	−25.6713	+	16.8369i	−1.38010	+	0.905155i
$347$	−6.56460	−	6.56460i	−0.352406	−	0.352406i	0.508598	−	0.861004i	$-0.330164\pi$
$347$	−6.56460	−	6.56460i	−0.352406	−	0.352406i	−0.861004	+	0.508598i	$0.830164\pi$
$348$	0.0427941	−	0.0985079i	0.00229400	−	0.00528058i
$349$	16.2157	−	16.2157i	0.868005	−	0.868005i	−0.124246	−	0.992251i	$-0.539651\pi$
$349$	16.2157	−	16.2157i	0.868005	−	0.868005i	0.992251	+	0.124246i	$0.0396513\pi$
$350$	−2.48611	−	0.516686i	−0.132888	−	0.0276181i
$351$	−2.93779			−0.156808
$352$	5.66760	−	23.2440i	0.302084	−	1.23891i
$353$	−30.8325			−1.64105			−0.820523	−	0.571613i	$-0.806318\pi$
$353$	−30.8325			−1.64105			−0.820523	+	0.571613i	$0.806318\pi$
$354$	−5.12792	−	1.06573i	−0.272546	−	0.0566431i
$355$	−2.37643	+	2.37643i	−0.126128	+	0.126128i
$356$	−9.87282	+	22.7263i	−0.523259	+	1.20449i
$357$	3.26181	+	3.26181i	0.172633	+	0.172633i
$358$	8.32181	−	5.45797i	0.439821	−	0.288462i
$359$			6.97708i			0.368236i	0.982904	+	0.184118i	$0.0589429\pi$
$359$			6.97708i			0.368236i	−0.982904	+	0.184118i	$0.941057\pi$
$360$	−16.0389	+	2.76410i	−0.845325	+	0.145681i
$361$			12.7395i			0.670499i
$362$	−7.07864	−	10.7929i	−0.372045	−	0.567260i
$363$	2.33949	+	2.33949i	0.122791	+	0.122791i
$364$	2.04629	+	5.18982i	0.107255	+	0.272020i
$365$	−21.2405	+	21.2405i	−1.11178	+	1.11178i
$366$	0.417400	−	2.00838i	0.0218178	−	0.104979i
$367$	−29.5172			−1.54079			−0.770394	−	0.637569i	$-0.779940\pi$
$367$	−29.5172			−1.54079			−0.770394	+	0.637569i	$0.779940\pi$
$368$	−2.92363	+	2.72991i	−0.152405	+	0.142306i
$369$	5.26431			0.274049
$370$	3.08209	−	14.8299i	0.160230	−	0.770969i
$371$	−17.4248	+	17.4248i	−0.904651	+	0.904651i
$372$	−1.85594	+	0.731775i	−0.0962259	+	0.0379408i
$373$	−24.5447	−	24.5447i	−1.27087	−	1.27087i	−0.945630	−	0.325244i	$-0.894554\pi$
$373$	−24.5447	−	24.5447i	−1.27087	−	1.27087i	−0.325244	−	0.945630i	$-0.605446\pi$
$374$	11.9716	+	18.2531i	0.619034	+	0.943847i
$375$		−	5.67179i		−	0.292890i
$376$	−19.7640	−	13.9532i	−1.01925	−	0.719584i
$377$			0.118508i			0.00610346i
$378$	8.62339	−	5.65576i	0.443539	−	0.290901i
$379$	−21.9729	−	21.9729i	−1.12867	−	1.12867i	−0.990393	−	0.138279i	$-0.955843\pi$
$379$	−21.9729	−	21.9729i	−1.12867	−	1.12867i	−0.138279	−	0.990393i	$-0.544157\pi$
$380$	9.53712	+	4.14315i	0.489244	+	0.212539i
$381$	4.22647	−	4.22647i	0.216529	−	0.216529i
$382$	−12.2305	−	2.54187i	−0.625769	−	0.130053i
$383$	10.3368			0.528184			0.264092	−	0.964497i	$-0.414928\pi$
$383$	10.3368			0.528184			0.264092	+	0.964497i	$0.414928\pi$
$384$	4.32977	+	3.28461i	0.220953	+	0.167617i
$385$	−23.1241			−1.17852
$386$	35.6130	+	7.40143i	1.81265	+	0.376723i
$387$	−18.9534	+	18.9534i	−0.963454	+	0.963454i
$388$	13.8440	+	6.01414i	0.702821	+	0.305322i
$389$	−22.5187	−	22.5187i	−1.14174	−	1.14174i	−0.988131	−	0.153612i	$-0.950909\pi$
$389$	−22.5187	−	22.5187i	−1.14174	−	1.14174i	−0.153612	−	0.988131i	$-0.549091\pi$
$390$	−1.25126	+	0.820654i	−0.0633600	+	0.0415554i
$391$		−	3.64954i		−	0.184565i
$392$	0.176465	+	0.124584i	0.00891285	+	0.00629242i
$393$		−	5.54288i		−	0.279601i
$394$	14.9235	+	22.7539i	0.751833	+	1.14633i
$395$	−18.4385	−	18.4385i	−0.927740	−	0.927740i
$396$	21.7917	−	8.59221i	1.09507	−	0.431775i
$397$	−5.33488	+	5.33488i	−0.267750	+	0.267750i	−0.828193	−	0.560443i	$-0.810631\pi$
$397$	−5.33488	+	5.33488i	−0.267750	+	0.267750i	0.560443	+	0.828193i	$0.310631\pi$
$398$	5.22772	−	25.1539i	0.262042	−	1.26085i
$399$	−3.16257			−0.158326
$400$	1.99500	−	1.86281i	0.0997499	−	0.0931404i
$401$	10.1801			0.508370			0.254185	−	0.967156i	$-0.418193\pi$
$401$	10.1801			0.508370			0.254185	+	0.967156i	$0.418193\pi$
$402$	0.688114	−	3.31095i	0.0343200	−	0.165135i
$403$	1.55655	−	1.55655i	0.0775370	−	0.0775370i
$404$	−3.23107	−	8.19468i	−0.160752	−	0.407700i
$405$	−10.2505	−	10.2505i	−0.509353	−	0.509353i
$406$	−0.228148	−	0.347859i	−0.0113228	−	0.0172640i
$407$			21.8001i			1.08059i
$408$	−4.88648	+	0.842121i	−0.241917	+	0.0416912i
$409$			15.1443i			0.748838i	0.927260	+	0.374419i	$0.122158\pi$
$409$			15.1443i			0.748838i	−0.927260	+	0.374419i	$0.877842\pi$
$410$	4.67116	−	3.06364i	0.230692	−	0.151302i
$411$	6.51212	+	6.51212i	0.321219	+	0.321219i
$412$	2.97536	−	6.84898i	0.146585	−	0.337425i
$413$	−14.3447	+	14.3447i	−0.705859	+	0.705859i
$414$	−3.83438	−	0.796898i	−0.188450	−	0.0391654i
$415$	3.70681			0.181960
$416$	−5.82596	−	1.42055i	−0.285641	−	0.0696482i
$417$	−2.65295			−0.129915
$418$	−14.6526	−	3.04524i	−0.716680	−	0.148947i
$419$	−14.4452	+	14.4452i	−0.705696	+	0.705696i	−0.965627	−	0.259931i	$-0.916300\pi$
$419$	−14.4452	+	14.4452i	−0.705696	+	0.705696i	0.259931	+	0.965627i	$0.416300\pi$
$420$	2.09296	−	4.81778i	0.102126	−	0.235084i
$421$	9.41803	+	9.41803i	0.459007	+	0.459007i	0.898329	−	0.439323i	$-0.144782\pi$
$421$	9.41803	+	9.41803i	0.459007	+	0.459007i	−0.439323	+	0.898329i	$0.644782\pi$
$422$	24.9005	−	16.3313i	1.21214	−	0.794994i
$423$		−	23.6870i		−	1.15170i
$424$	−4.49867	−	26.1039i	−0.218475	−	1.26772i
$425$			2.49034i			0.120799i
$426$	0.602589	+	0.918773i	0.0291955	+	0.0445147i
$427$	−5.61819	−	5.61819i	−0.271883	−	0.271883i
$428$	0.0736324	+	0.186747i	0.00355915	+	0.00902678i
$429$	1.52287	−	1.52287i	0.0735248	−	0.0735248i
$430$	−5.78764	+	27.8480i	−0.279105	+	1.34295i
$431$	21.0570			1.01428			0.507139	−	0.861864i	$-0.330703\pi$
$431$	21.0570			1.01428			0.507139	+	0.861864i	$0.330703\pi$
$432$	−0.379619	+	11.0788i	−0.0182644	+	0.533029i
$433$	11.2435			0.540329			0.270165	−	0.962814i	$-0.412922\pi$
$433$	11.2435			0.540329			0.270165	+	0.962814i	$0.412922\pi$
$434$	−1.57235	+	7.56559i	−0.0754754	+	0.363160i
$435$	0.0789022	−	0.0789022i	0.00378307	−	0.00378307i
$436$	6.60762	−	2.60531i	0.316447	−	0.124772i
$437$	1.76925	+	1.76925i	0.0846348	+	0.0846348i
$438$	5.38593	+	8.21198i	0.257350	+	0.392384i
$439$		−	1.55838i		−	0.0743776i	−0.999308	−	0.0371888i	$-0.988160\pi$
$439$		−	1.55838i		−	0.0743776i	0.999308	−	0.0371888i	$-0.0118403\pi$
$440$	14.3360	−	20.3061i	0.683440	−	0.968054i
$441$			0.211493i			0.0100711i
$442$	4.57504	−	3.00060i	0.217612	−	0.142724i
$443$	−9.91757	−	9.91757i	−0.471198	−	0.471198i	0.431104	−	0.902302i	$-0.358124\pi$
$443$	−9.91757	−	9.91757i	−0.471198	−	0.471198i	−0.902302	+	0.431104i	$0.858124\pi$
$444$	−4.54193	−	1.97312i	−0.215550	−	0.0936401i
$445$	−18.2031	+	18.2031i	−0.862912	+	0.862912i
$446$	−18.2241	−	3.78750i	−0.862935	−	0.179343i
$447$	2.57378			0.121736
$448$	19.8359	−	7.04619i	0.937159	−	0.332901i
$449$	8.61435			0.406536			0.203268	−	0.979123i	$-0.434844\pi$
$449$	8.61435			0.406536			0.203268	+	0.979123i	$0.434844\pi$
$450$	2.61647	+	0.543779i	0.123342	+	0.0256340i
$451$	−5.68512	+	5.68512i	−0.267702	+	0.267702i
$452$	33.2977	+	14.4653i	1.56619	+	0.680390i
$453$	2.68400	+	2.68400i	0.126105	+	0.126105i
$454$	−33.5752	+	22.0207i	−1.57576	+	1.03348i
$455$			5.79593i			0.271717i
$456$	1.96065	−	2.77715i	0.0918161	−	0.130052i
$457$			13.8329i			0.647078i	0.946215	+	0.323539i	$0.104873\pi$
$457$			13.8329i			0.647078i	−0.946215	+	0.323539i	$0.895127\pi$
$458$	9.17410	+	13.9878i	0.428677	+	0.653608i
$459$	−7.15173	−	7.15173i	−0.333814	−	0.333814i
$460$	−3.86611	+	1.52436i	−0.180258	+	0.0710739i
$461$	−14.5907	+	14.5907i	−0.679558	+	0.679558i	−0.959900	−	0.280343i	$-0.909552\pi$
$461$	−14.5907	+	14.5907i	−0.679558	+	0.679558i	0.280343	+	0.959900i	$0.409552\pi$
$462$	−1.53833	+	7.40190i	−0.0715698	+	0.344368i
$463$	14.9968			0.696958			0.348479	−	0.937317i	$-0.386698\pi$
$463$	14.9968			0.696958			0.348479	+	0.937317i	$0.386698\pi$
$464$	0.446908	+	0.0153135i	0.0207472	+	0.000710910i
$465$	−2.07269			−0.0961187
$466$	1.13571	−	5.46460i	0.0526106	−	0.253143i
$467$	−12.7424	+	12.7424i	−0.589647	+	0.589647i	−0.937536	−	0.347889i	$-0.886899\pi$
$467$	−12.7424	+	12.7424i	−0.589647	+	0.589647i	0.347889	+	0.937536i	$0.386899\pi$
$468$	−2.15359	−	5.46195i	−0.0995495	−	0.252479i
$469$	−9.26199	−	9.26199i	−0.427679	−	0.427679i
$470$	−13.7850	−	21.0181i	−0.635854	−	0.969492i
$471$		−	3.89343i		−	0.179400i
$472$	−3.70347	−	21.4897i	−0.170466	−	0.989144i
$473$		−	40.9369i		−	1.88228i
$474$	−7.12867	+	4.67543i	−0.327431	+	0.214750i
$475$	−1.20729	−	1.20729i	−0.0553941	−	0.0553941i
$476$	−7.65258	+	17.6155i	−0.350755	+	0.807405i
$477$	18.3385	−	18.3385i	0.839662	−	0.839662i
$478$	15.8200	+	3.28786i	0.723588	+	0.150383i
$479$	−10.2952			−0.470400			−0.235200	−	0.971947i	$-0.575574\pi$
$479$	−10.2952			−0.470400			−0.235200	+	0.971947i	$0.575574\pi$
$480$	2.93311	+	4.82471i	0.133878	+	0.220217i
$481$	5.46406			0.249140
$482$	10.1525	+	2.10999i	0.462435	+	0.0961076i
$483$	0.893758	−	0.893758i	0.0406674	−	0.0406674i
$484$	−5.48871	+	12.6345i	−0.249487	+	0.574294i
$485$	11.0887	+	11.0887i	0.503510	+	0.503510i
$486$	−13.7948	+	9.04752i	−0.625746	+	0.410404i
$487$		−	10.8868i		−	0.493327i	−0.969101	−	0.246663i	$-0.920666\pi$
$487$		−	10.8868i		−	0.493327i	0.969101	−	0.246663i	$-0.0793342\pi$
$488$	8.41655	−	1.45048i	0.380999	−	0.0656602i
$489$		−	10.2569i		−	0.463835i
$490$	0.123081	+	0.187663i	0.00556024	+	0.00847774i
$491$	28.6304	+	28.6304i	1.29207	+	1.29207i	0.933505	+	0.358565i	$0.116734\pi$
$491$	28.6304	+	28.6304i	1.29207	+	1.29207i	0.358565	+	0.933505i	$0.383266\pi$
$492$	−0.669904	−	1.69902i	−0.0302016	−	0.0765977i
$493$	−0.288494	+	0.288494i	−0.0129931	+	0.0129931i
$494$	−0.763270	+	3.67258i	−0.0343411	+	0.165237i
$495$	24.3367			1.09385
$496$	−5.66880	−	6.07108i	−0.254537	−	0.272599i
$497$	4.25582			0.190900
$498$	0.246596	−	1.18653i	0.0110502	−	0.0531696i
$499$	14.0373	−	14.0373i	0.628398	−	0.628398i	−0.319267	−	0.947665i	$-0.603437\pi$
$499$	14.0373	−	14.0373i	0.628398	−	0.628398i	0.947665	+	0.319267i	$0.103437\pi$
$500$	21.9687	−	8.66200i	0.982470	−	0.387377i
$501$	8.42952	+	8.42952i	0.376603	+	0.376603i
$502$	8.91573	+	13.5939i	0.397928	+	0.606725i
$503$		−	19.8160i		−	0.883550i	−0.897126	−	0.441775i	$-0.854349\pi$
$503$		−	19.8160i		−	0.883550i	0.897126	−	0.441775i	$-0.145651\pi$
$504$	16.8367	+	11.8866i	0.749966	+	0.529471i
$505$		−	9.15172i		−	0.407246i
$506$	5.00149	−	3.28029i	0.222343	−	0.145827i
$507$	4.03397	+	4.03397i	0.179155	+	0.179155i
$508$	22.8252	+	9.91579i	1.01270	+	0.439942i
$509$	−3.76825	+	3.76825i	−0.167025	+	0.167025i	−0.785670	−	0.618645i	$-0.787682\pi$
$509$	−3.76825	+	3.76825i	−0.167025	+	0.167025i	0.618645	+	0.785670i	$0.287682\pi$
$510$	−5.04384	−	1.04826i	−0.223345	−	0.0464177i
$511$	38.0385			1.68272
$512$	−6.10991	+	21.7869i	−0.270023	+	0.962854i
$513$	6.93414			0.306150
$514$	−16.1245	−	3.35114i	−0.711219	−	0.147812i
$515$	5.48585	−	5.48585i	0.241736	−	0.241736i
$516$	8.52897	+	3.70518i	0.375467	+	0.163112i
$517$	25.5804	+	25.5804i	1.12503	+	1.12503i
$518$	−16.0388	+	10.5193i	−0.704706	+	0.462190i
$519$			10.4278i			0.457730i
$520$	−5.08959	−	3.59322i	−0.223193	−	0.157573i
$521$		−	39.7301i		−	1.74061i	−0.492517	−	0.870303i	$-0.663923\pi$
$521$		−	39.7301i		−	1.74061i	0.492517	−	0.870303i	$-0.336077\pi$
$522$	0.240111	+	0.366100i	0.0105094	+	0.0160237i
$523$	7.97407	+	7.97407i	0.348682	+	0.348682i	0.859618	−	0.510937i	$-0.170701\pi$
$523$	7.97407	+	7.97407i	0.348682	+	0.348682i	−0.510937	+	0.859618i	$0.670701\pi$
$524$	21.4694	−	8.46512i	0.937893	−	0.369801i
$525$	−0.609874	+	0.609874i	−0.0266171	+	0.0266171i
$526$	−4.35879	+	20.9729i	−0.190052	+	0.914461i
$527$	7.57848			0.330124
$528$	−5.54615	−	5.93972i	−0.241365	−	0.258493i
$529$	−1.00000			−0.0434783
$530$	5.59988	−	26.9446i	0.243243	−	1.17040i
$531$	15.0969	−	15.0969i	0.655151	−	0.655151i
$532$	−4.82990	−	12.2497i	−0.209403	−	0.531090i
$533$	1.42494	+	1.42494i	0.0617210	+	0.0617210i
$534$	4.61576	+	7.03769i	0.199743	+	0.304551i
$535$			0.208557i			0.00901672i
$536$	13.8753	−	2.39123i	0.599321	−	0.103285i
$537$		−	3.38036i		−	0.145873i
$538$	23.7773	−	15.5947i	1.02511	−	0.672334i
$539$	−0.228399	−	0.228399i	−0.00983782	−	0.00983782i
$540$	−4.58895	+	10.5633i	−0.197477	+	0.454572i
$541$	20.3483	−	20.3483i	0.874843	−	0.874843i	−0.118152	−	0.992995i	$-0.537697\pi$
$541$	20.3483	−	20.3483i	0.874843	−	0.874843i	0.992995	+	0.118152i	$0.0376971\pi$
$542$	−40.4971	−	8.41650i	−1.73950	−	0.361519i
$543$	−4.38411			−0.188140
$544$	−10.7245	−	17.6408i	−0.459808	−	0.756344i
$545$	7.37931			0.316095
$546$	1.85524	+	0.385574i	0.0793971	+	0.0165011i
$547$	9.56242	−	9.56242i	0.408860	−	0.408860i	−0.472481	−	0.881341i	$-0.656642\pi$
$547$	9.56242	−	9.56242i	0.408860	−	0.408860i	0.881341	+	0.472481i	$0.156642\pi$
$548$	−15.2782	+	35.1689i	−0.652652	+	1.50234i
$549$	5.91278	+	5.91278i	0.252351	+	0.252351i
$550$	−3.41287	+	2.23837i	−0.145525	+	0.0954445i
$551$		−	0.279717i		−	0.0119163i
$552$	0.230747	+	1.33893i	0.00982124	+	0.0569886i
$553$			33.0205i			1.40418i
$554$	19.9043	+	30.3483i	0.845654	+	1.28938i
$555$	−3.63796	−	3.63796i	−0.154423	−	0.154423i
$556$	−4.05160	−	10.2757i	−0.171826	−	0.435788i
$557$	−31.7035	+	31.7035i	−1.34332	+	1.34332i	−0.450591	+	0.892731i	$0.648787\pi$
$557$	−31.7035	+	31.7035i	−1.34332	+	1.34332i	−0.892731	+	0.450591i	$0.851213\pi$
$558$	1.65480	−	7.96230i	0.0700534	−	0.337071i
$559$	−10.2606			−0.433977
$560$	21.8572	+	0.748945i	0.923636	+	0.0316487i
$561$	7.41451			0.313041
$562$	2.24727	−	10.8131i	0.0947955	−	0.456121i
$563$	−4.75332	+	4.75332i	−0.200329	+	0.200329i	−0.800141	−	0.599812i	$-0.795242\pi$
$563$	−4.75332	+	4.75332i	−0.200329	+	0.200329i	0.599812	+	0.800141i	$0.295242\pi$
$564$	−7.64481	+	3.01426i	−0.321905	+	0.126923i
$565$	26.6706	+	26.6706i	1.12204	+	1.12204i
$566$	7.60830	+	11.6004i	0.319801	+	0.487603i
$567$			18.3572i			0.770929i
$568$	−2.63843	+	3.73718i	−0.110706	+	0.156809i
$569$		−	9.29390i		−	0.389621i	−0.980841	−	0.194810i	$-0.937591\pi$
$569$		−	9.29390i		−	0.389621i	0.980841	−	0.194810i	$-0.0624091\pi$
$570$	2.95338	−	1.93701i	0.123703	−	0.0811324i
$571$	−7.99665	−	7.99665i	−0.334649	−	0.334649i	0.519700	−	0.854349i	$-0.326044\pi$
$571$	−7.99665	−	7.99665i	−0.334649	−	0.334649i	−0.854349	+	0.519700i	$0.826044\pi$
$572$	8.22430	+	3.57283i	0.343875	+	0.149387i
$573$	−3.00031	+	3.00031i	−0.125340	+	0.125340i
$574$	−6.92593	−	1.43941i	−0.289083	−	0.0600799i
$575$	0.682370			0.0284568
$576$	−20.8760	+	7.41567i	−0.869835	+	0.308986i
$577$	−25.4622			−1.06001			−0.530003	−	0.847996i	$-0.677809\pi$
$577$	−25.4622			−1.06001			−0.530003	+	0.847996i	$0.677809\pi$
$578$	−5.09660	−	1.05922i	−0.211990	−	0.0440579i
$579$	8.73632	−	8.73632i	0.363069	−	0.363069i
$580$	0.426114	+	0.185114i	0.0176934	+	0.00768643i
$581$	−3.31917	−	3.31917i	−0.137702	−	0.137702i
$582$	4.28709	−	2.81174i	0.177706	−	0.116550i
$583$			39.6088i			1.64043i
$584$	−23.5822	+	33.4029i	−0.975839	+	1.38222i
$585$		−	6.09984i		−	0.252197i
$586$	−19.5644	−	29.8300i	−0.808197	−	1.23226i
$587$	−7.76960	−	7.76960i	−0.320686	−	0.320686i	0.528344	−	0.849030i	$-0.322813\pi$
$587$	−7.76960	−	7.76960i	−0.320686	−	0.320686i	−0.849030	+	0.528344i	$0.822813\pi$
$588$	0.0682578	−	0.0269133i	0.00281490	−	0.00110988i
$589$	−3.67395	+	3.67395i	−0.151383	+	0.151383i
$590$	4.61003	−	22.1818i	0.189792	−	0.913209i
$591$	9.24275			0.380196
$592$	0.706062	−	20.6057i	0.0290190	−	0.846890i
$593$	38.0898			1.56416			0.782081	−	0.623177i	$-0.214158\pi$
$593$	38.0898			1.56416			0.782081	+	0.623177i	$0.214158\pi$
$594$	3.37290	−	16.2292i	0.138392	−	0.665891i
$595$	−14.1095	+	14.1095i	−0.578435	+	0.578435i
$596$	3.93070	+	9.96910i	0.161008	+	0.408350i
$597$	−6.17057	−	6.17057i	−0.252545	−	0.252545i
$598$	−0.822185	−	1.25359i	−0.0336216	−	0.0512632i
$599$			12.2577i			0.500836i	0.968138	+	0.250418i	$0.0805680\pi$
$599$			12.2577i			0.500836i	−0.968138	+	0.250418i	$0.919432\pi$
$600$	−0.157455	−	0.913646i	−0.00642807	−	0.0372994i
$601$		−	12.6119i		−	0.514452i	−0.966351	−	0.257226i	$-0.917192\pi$
$601$		−	12.6119i		−	0.514452i	0.966351	−	0.257226i	$-0.0828085\pi$
$602$	30.1182	−	19.7534i	1.22753	−	0.805089i
$603$	9.74765	+	9.74765i	0.396955	+	0.396955i
$604$	−6.29698	+	14.4950i	−0.256221	+	0.589795i
$605$	−10.1199	+	10.1199i	−0.411431	+	0.411431i
$606$	−2.92941	−	0.608819i	−0.118999	−	0.0247316i
$607$	−15.2647			−0.619576			−0.309788	−	0.950806i	$-0.600258\pi$
$607$	−15.2647			−0.619576			−0.309788	+	0.950806i	$0.600258\pi$
$608$	13.7511	+	3.35296i	0.557683	+	0.135980i
$609$	−0.141302			−0.00572585
$610$	8.68760	+	1.80554i	0.351751	+	0.0731042i
$611$	6.41158	−	6.41158i	0.259385	−	0.259385i
$612$	8.05385	−	18.5392i	0.325558	−	0.749402i
$613$	19.9931	+	19.9931i	0.807512	+	0.807512i	0.984257	−	0.176745i	$-0.0565567\pi$
$613$	19.9931	+	19.9931i	0.807512	+	0.807512i	−0.176745	+	0.984257i	$0.556557\pi$
$614$	−12.5427	+	8.22627i	−0.506181	+	0.331985i
$615$		−	1.89744i		−	0.0765124i
$616$	−31.0193	+	5.34578i	−1.24980	+	0.215388i
$617$			13.3767i			0.538527i	0.963067	+	0.269264i	$0.0867803\pi$
$617$			13.3767i			0.538527i	−0.963067	+	0.269264i	$0.913220\pi$
$618$	−1.39104	−	2.12094i	−0.0559560	−	0.0853166i
$619$	15.5329	+	15.5329i	0.624318	+	0.624318i	0.946633	−	0.322314i	$-0.104461\pi$
$619$	15.5329	+	15.5329i	0.624318	+	0.624318i	−0.322314	+	0.946633i	$0.604461\pi$
$620$	−3.16543	−	8.02820i	−0.127127	−	0.322420i
$621$	−1.95962	+	1.95962i	−0.0786370	+	0.0786370i
$622$	3.23600	−	15.5705i	0.129752	−	0.624319i
$623$	32.5991			1.30606
$624$	−1.48876	+	1.39011i	−0.0595979	+	0.0556490i
$625$	21.1225			0.844901
$626$	9.21616	−	44.3448i	0.368352	−	1.77237i
$627$	−3.59446	+	3.59446i	−0.143549	+	0.143549i
$628$	15.0805	−	5.94608i	0.601778	−	0.237274i
$629$	13.3017	+	13.3017i	0.530372	+	0.530372i
$630$	11.7433	+	17.9050i	0.467862	+	0.713354i
$631$		−	14.6461i		−	0.583054i	−0.956563	−	0.291527i	$-0.905837\pi$
$631$		−	14.6461i		−	0.583054i	0.956563	−	0.291527i	$-0.0941633\pi$
$632$	−28.9964	−	20.4713i	−1.15342	−	0.814305i
$633$		−	10.1147i		−	0.402022i
$634$	6.19824	−	4.06520i	0.246164	−	0.161450i
$635$	18.2824	+	18.2824i	0.725513	+	0.725513i
$636$	−8.25228	−	3.58498i	−0.327224	−	0.142154i
$637$	−0.0572467	+	0.0572467i	−0.00226820	+	0.00226820i
$638$	−0.654669	−	0.136060i	−0.0259186	−	0.00538665i
$639$	−4.47898			−0.177186
$640$	−14.2082	+	18.7292i	−0.561628	+	0.740337i
$641$	−25.9309			−1.02421			−0.512104	−	0.858924i	$-0.671134\pi$
$641$	−25.9309			−1.02421			−0.512104	+	0.858924i	$0.671134\pi$
$642$	0.0667580	+	0.0138743i	0.00263473	+	0.000547574i
$643$	−27.2600	+	27.2600i	−1.07503	+	1.07503i	−0.0780842	+	0.996947i	$0.524880\pi$
$643$	−27.2600	+	27.2600i	−1.07503	+	1.07503i	−0.996947	+	0.0780842i	$0.975120\pi$
$644$	4.82677	+	2.09686i	0.190201	+	0.0826279i
$645$	6.83148	+	6.83148i	0.268989	+	0.268989i
$646$	−10.7986	+	7.08239i	−0.424864	+	0.278653i
$647$		−	32.0376i		−	1.25953i	−0.776787	−	0.629763i	$-0.783152\pi$
$647$		−	32.0376i		−	1.25953i	0.776787	−	0.629763i	$-0.216848\pi$
$648$	−16.1200	−	11.3807i	−0.633255	−	0.447074i
$649$			32.6074i			1.27995i
$650$	0.561035	+	0.855415i	0.0220056	+	0.0335521i
$651$	1.85594	+	1.85594i	0.0727399	+	0.0727399i
$652$	39.7284	−	15.6645i	1.55589	−	0.613468i
$653$	22.7295	−	22.7295i	0.889473	−	0.889473i	−0.105000	−	0.994472i	$-0.533484\pi$
$653$	22.7295	−	22.7295i	0.889473	−	0.889473i	0.994472	+	0.105000i	$0.0334841\pi$
$654$	0.490909	−	2.36207i	0.0191961	−	0.0923644i
$655$	23.9767			0.936848
$656$	5.55777	−	5.18951i	0.216994	−	0.202616i
$657$	−40.0331			−1.56184
$658$	−6.47670	+	31.1635i	−0.252488	+	1.21488i
$659$	26.7819	−	26.7819i	1.04327	−	1.04327i	0.0442537	−	0.999020i	$-0.485909\pi$
$659$	26.7819	−	26.7819i	1.04327	−	1.04327i	0.999020	−	0.0442537i	$-0.0140910\pi$
$660$	−3.09694	−	7.85450i	−0.120548	−	0.305736i
$661$	17.8416	+	17.8416i	0.693957	+	0.693957i	0.963100	−	0.269143i	$-0.0867405\pi$
$661$	17.8416	+	17.8416i	0.693957	+	0.693957i	−0.269143	+	0.963100i	$0.586741\pi$
$662$	−13.8695	−	21.1470i	−0.539054	−	0.821901i
$663$		−	1.85840i		−	0.0721743i
$664$	4.97241	−	0.856931i	0.192967	−	0.0332554i
$665$		−	13.6803i		−	0.530498i
$666$	16.8798	−	11.0709i	0.654081	−	0.428987i
$667$	0.0790494	+	0.0790494i	0.00306080	+	0.00306080i
$668$	−19.7766	+	45.5239i	−0.765181	+	1.76137i
$669$	−4.47060	+	4.47060i	−0.172844	+	0.172844i
$670$	14.3221	+	2.97656i	0.553312	+	0.114995i
$671$	−12.7709			−0.493014
$672$	1.69379	−	6.94655i	0.0653392	−	0.267969i
$673$	−14.7037			−0.566784			−0.283392	−	0.959004i	$-0.591460\pi$
$673$	−14.7037			−0.566784			−0.283392	+	0.959004i	$0.591460\pi$
$674$	−9.93767	−	2.06534i	−0.382785	−	0.0795540i
$675$	1.33719	−	1.33719i	0.0514684	−	0.0514684i
$676$	−9.46416	+	21.7856i	−0.364006	+	0.837907i
$677$	−26.5869	−	26.5869i	−1.02182	−	1.02182i	−0.999757	−	0.0220606i	$-0.992977\pi$
$677$	−26.5869	−	26.5869i	−1.02182	−	1.02182i	−0.0220606	−	0.999757i	$-0.507023\pi$
$678$	10.3114	−	6.76284i	0.396006	−	0.259725i
$679$		−	19.8581i		−	0.762084i
$680$	−3.64275	−	21.1374i	−0.139693	−	0.810581i
$681$			13.6384i			0.522625i
$682$	6.81170	+	10.3859i	0.260834	+	0.397695i
$683$	3.64714	+	3.64714i	0.139554	+	0.139554i	0.773433	−	0.633879i	$-0.218538\pi$
$683$	3.64714	+	3.64714i	0.139554	+	0.139554i	−0.633879	+	0.773433i	$0.718538\pi$
$684$	5.08316	+	12.8920i	0.194359	+	0.492937i
$685$	−28.1694	+	28.1694i	−1.07630	+	1.07630i
$686$	5.35818	−	25.7816i	0.204576	−	0.984347i
$687$	5.68192			0.216779
$688$	−1.32586	+	38.6940i	−0.0505481	+	1.47520i
$689$	9.92772			0.378216
$690$	−0.287231	+	1.38205i	−0.0109347	+	0.0526137i
$691$	26.3238	−	26.3238i	1.00141	−	1.00141i	0.00140609	−	0.999999i	$-0.499552\pi$
$691$	26.3238	−	26.3238i	1.00141	−	1.00141i	0.999999	−	0.00140609i	$-0.000447571\pi$
$692$	−40.3903	+	15.9254i	−1.53541	+	0.605394i
$693$	−21.7917	−	21.7917i	−0.827797	−	0.827797i
$694$	−7.20045	−	10.9786i	−0.273325	−	0.416741i
$695$		−	11.4758i		−	0.435302i
$696$	0.0876011	−	0.124082i	0.00332051	−	0.00470331i
$697$			6.93772i			0.262785i
$698$	27.1190	−	17.7863i	1.02647	−	0.673222i
$699$	−1.34054	−	1.34054i	−0.0507038	−	0.0507038i
$700$	−3.29364	−	1.43084i	−0.124488	−	0.0540805i
$701$	4.09012	−	4.09012i	0.154482	−	0.154482i	−0.625635	−	0.780116i	$-0.715160\pi$
$701$	4.09012	−	4.09012i	0.154482	−	0.154482i	0.780116	+	0.625635i	$0.215160\pi$
$702$	−4.06774	−	0.845397i	−0.153527	−	0.0319075i
$703$	−12.8970			−0.486418
$704$	14.5363	−	30.5532i	0.547859	−	1.15152i
$705$	−8.53764			−0.321546
$706$	−42.6914	−	8.87255i	−1.60671	−	0.333923i
$707$	−8.19468	+	8.19468i	−0.308193	+	0.308193i
$708$	−6.79358	−	2.95129i	−0.255318	−	0.110916i
$709$	35.5748	+	35.5748i	1.33604	+	1.33604i	0.899860	+	0.436178i	$0.143668\pi$
$709$	35.5748	+	35.5748i	1.33604	+	1.33604i	0.436178	+	0.899860i	$0.356332\pi$
$710$	−3.97432	+	2.60661i	−0.149154	+	0.0978243i
$711$		−	34.7520i		−	1.30330i
$712$	−20.2100	+	28.6263i	−0.757403	+	1.07282i
$713$		−	2.07656i		−	0.0777676i
$714$	3.57775	+	5.45502i	0.133894	+	0.204149i
$715$	6.58744	+	6.58744i	0.246356	+	0.246356i
$716$	13.0932	−	5.16251i	0.489317	−	0.192932i
$717$	3.88084	−	3.88084i	0.144933	−	0.144933i
$718$	−2.00777	+	9.66065i	−0.0749292	+	0.360532i
$719$	9.02570			0.336602			0.168301	−	0.985736i	$-0.446172\pi$
$719$	9.02570			0.336602			0.168301	+	0.985736i	$0.446172\pi$
$720$	−23.0033	−	0.788217i	−0.857283	−	0.0293751i
$721$	−9.82434			−0.365878
$722$	−3.66600	+	17.6394i	−0.136434	+	0.656472i
$723$	2.49054	−	2.49054i	0.0926243	−	0.0926243i
$724$	−6.69545	−	16.9811i	−0.248834	−	0.631097i
$725$	−0.0539409	−	0.0539409i	−0.00200332	−	0.00200332i
$726$	2.56609	+	3.91254i	0.0952365	+	0.145208i
$727$			13.8698i			0.514401i	0.966358	+	0.257200i	$0.0828001\pi$
$727$			13.8698i			0.514401i	−0.966358	+	0.257200i	$0.917200\pi$
$728$	1.33989	+	7.77481i	0.0496595	+	0.288154i
$729$		−	15.3260i		−	0.567631i
$730$	−35.5224	+	23.2978i	−1.31474	+	0.862291i
$731$	−24.9783	−	24.9783i	−0.923855	−	0.923855i
$732$	1.15589	−	2.66074i	0.0427228	−	0.0983437i
$733$	−3.11508	+	3.11508i	−0.115058	+	0.115058i	−0.762292	−	0.647234i	$-0.775926\pi$
$733$	−3.11508	+	3.11508i	−0.115058	+	0.115058i	0.647234	+	0.762292i	$0.275926\pi$
$734$	−40.8703	−	8.49407i	−1.50855	−	0.313522i
$735$	0.0762295			0.00281177
$736$	−4.83371	+	2.93858i	−0.178173	+	0.108318i
$737$	−21.0537			−0.775523
$738$	7.28910	+	1.51489i	0.268315	+	0.0557639i
$739$	−16.6142	+	16.6142i	−0.611165	+	0.611165i	−0.943250	−	0.332085i	$-0.892248\pi$
$739$	−16.6142	+	16.6142i	−0.611165	+	0.611165i	0.332085	+	0.943250i	$0.392248\pi$
$740$	8.53508	−	19.6469i	0.313756	−	0.722236i
$741$	0.900930	+	0.900930i	0.0330965	+	0.0330965i
$742$	−29.1411	+	19.1126i	−1.06980	+	0.701645i
$743$			34.8345i			1.27796i	0.769225	+	0.638978i	$0.220642\pi$
$743$			34.8345i			1.27796i	−0.769225	+	0.638978i	$0.779358\pi$
$744$	−2.78036	+	0.479159i	−0.101933	+	0.0175668i
$745$			11.1334i			0.407895i
$746$	−26.9221	−	41.0483i	−0.985687	−	1.50289i
$747$	3.49322	+	3.49322i	0.127810	+	0.127810i
$748$	11.3235	+	28.7188i	0.414028	+	1.05006i
$749$	0.186747	−	0.186747i	0.00682360	−	0.00682360i
$750$	1.63215	−	7.85331i	0.0595977	−	0.286762i
$751$	−13.9840			−0.510284			−0.255142	−	0.966904i	$-0.582122\pi$
$751$	−13.9840			−0.510284			−0.255142	+	0.966904i	$0.582122\pi$
$752$	−23.3504	−	25.0074i	−0.851503	−	0.911927i
$753$	5.52190			0.201229
$754$	−0.0341025	+	0.164089i	−0.00124194	+	0.00597577i
$755$	−11.6101	+	11.6101i	−0.422536	+	0.422536i
$756$	13.5677	−	5.34959i	0.493453	−	0.194563i
$757$	−8.30456	−	8.30456i	−0.301834	−	0.301834i	0.539897	−	0.841731i	$-0.318463\pi$
$757$	−8.30456	−	8.30456i	−0.301834	−	0.301834i	−0.841731	+	0.539897i	$0.818463\pi$
$758$	−24.1012	−	36.7473i	−0.875395	−	1.33472i
$759$		−	2.03163i		−	0.0737434i
$760$	12.0131	+	8.48117i	0.435761	+	0.307644i
$761$		−	29.3207i		−	1.06288i	−0.847097	−	0.531438i	$-0.821652\pi$
$761$		−	29.3207i		−	1.06288i	0.847097	−	0.531438i	$-0.178348\pi$
$762$	7.06831	−	4.63584i	0.256058	−	0.167939i
$763$	−6.60762	−	6.60762i	−0.239212	−	0.239212i
$764$	−16.2033	−	7.03907i	−0.586213	−	0.254665i
$765$	14.8494	−	14.8494i	0.536881	−	0.536881i
$766$	14.3126	+	2.97457i	0.517134	+	0.107476i
$767$	8.17286			0.295105
$768$	5.04992	+	5.79393i	0.182223	+	0.209070i
$769$	−44.4923			−1.60443			−0.802216	−	0.597034i	$-0.796346\pi$
$769$	−44.4923			−1.60443			−0.802216	+	0.597034i	$0.796346\pi$

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38463 + 0.287766i) q^{2} +(0.339667 - 0.339667i) q^{3} +(1.83438 + 0.796898i) q^{4} +(1.46929 + 1.46929i) q^{5} +(0.568056 - 0.372567i) q^{6} -2.63128i q^{7} +(2.31061 + 1.63128i) q^{8} +2.76925i q^{9} +(1.61161 + 2.45723i) q^{10} +(-2.99062 - 2.99062i) q^{11} +(0.893758 - 0.352399i) q^{12} +(-0.749580 + 0.749580i) q^{13} +(0.757193 - 3.64334i) q^{14} +0.998138 q^{15} +(2.72991 + 2.92363i) q^{16} -3.64954 q^{17} +(-0.796898 + 3.83438i) q^{18} +(1.76925 - 1.76925i) q^{19} +(1.52436 + 3.86611i) q^{20} +(-0.893758 - 0.893758i) q^{21} +(-3.28029 - 5.00149i) q^{22} +1.00000i q^{23} +(1.33893 - 0.230747i) q^{24} -0.682370i q^{25} +(-1.25359 + 0.822185i) q^{26} +(1.95962 + 1.95962i) q^{27} +(2.09686 - 4.82677i) q^{28} +(0.0790494 - 0.0790494i) q^{29} +(1.38205 + 0.287231i) q^{30} -2.07656 q^{31} +(2.93858 + 4.83371i) q^{32} -2.03163 q^{33} +(-5.05325 - 1.05022i) q^{34} +(3.86611 - 3.86611i) q^{35} +(-2.20681 + 5.07987i) q^{36} +(-3.64475 - 3.64475i) q^{37} +(2.95889 - 1.94062i) q^{38} +0.509215i q^{39} +(0.998138 + 5.79178i) q^{40} -1.90098i q^{41} +(-0.980327 - 1.49471i) q^{42} +(6.84422 + 6.84422i) q^{43} +(-3.10272 - 7.86915i) q^{44} +(-4.06884 + 4.06884i) q^{45} +(-0.287766 + 1.38463i) q^{46} -8.55356 q^{47} +(1.92032 + 0.0658004i) q^{48} +0.0763717 q^{49} +(0.196363 - 0.944828i) q^{50} +(-1.23963 + 1.23963i) q^{51} +(-1.97236 + 0.777677i) q^{52} +(-6.62218 - 6.62218i) q^{53} +(2.14943 + 3.27726i) q^{54} -8.78817i q^{55} +(4.29235 - 6.07987i) q^{56} -1.20191i q^{57} +(0.132202 - 0.0867061i) q^{58} +(-5.45162 - 5.45162i) q^{59} +(1.83097 + 0.795414i) q^{60} +(2.13515 - 2.13515i) q^{61} +(-2.87525 - 0.597563i) q^{62} +7.28668 q^{63} +(2.67786 + 7.53851i) q^{64} -2.20270 q^{65} +(-2.81304 - 0.584634i) q^{66} +(3.51996 - 3.51996i) q^{67} +(-6.69465 - 2.90831i) q^{68} +(0.339667 + 0.339667i) q^{69} +(6.46566 - 4.24059i) q^{70} +1.61740i q^{71} +(-4.51742 + 6.39867i) q^{72} +14.4563i q^{73} +(-3.99778 - 6.09545i) q^{74} +(-0.231779 - 0.231779i) q^{75} +(4.65540 - 1.83557i) q^{76} +(-7.86915 + 7.86915i) q^{77} +(-0.146535 + 0.705073i) q^{78} -12.5492 q^{79} +(-0.284631 + 8.30669i) q^{80} -6.97652 q^{81} +(0.547039 - 2.63215i) q^{82} +(1.26143 - 1.26143i) q^{83} +(-0.927259 - 2.35173i) q^{84} +(-5.36224 - 5.36224i) q^{85} +(7.50715 + 11.4462i) q^{86} -0.0537009i q^{87} +(-2.03163 - 11.7887i) q^{88} +12.3891i q^{89} +(-6.80469 + 4.46295i) q^{90} +(1.97236 + 1.97236i) q^{91} +(-0.796898 + 1.83438i) q^{92} +(-0.705337 + 0.705337i) q^{93} +(-11.8435 - 2.46143i) q^{94} +5.19909 q^{95} +(2.63999 + 0.643712i) q^{96} +7.54694 q^{97} +(0.105746 + 0.0219772i) q^{98} +(8.28178 - 8.28178i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26}+ \cdots + 36 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8 - 6 * q^10 - 4 * q^11 - 8 * q^12 + 18 * q^13 - 2 * q^14 + 8 * q^16 - 8 * q^17 - 4 * q^18 - 8 * q^19 - 32 * q^20 + 8 * q^21 - 34 * q^22 + 12 * q^24 - 14 * q^26 + 14 * q^27 + 12 * q^28 + 2 * q^29 - 30 * q^30 + 20 * q^31 - 8 * q^32 - 36 * q^33 + 10 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 24 * q^38 - 14 * q^42 + 20 * q^43 + 4 * q^44 - 20 * q^45 - 2 * q^46 - 16 * q^47 - 12 * q^48 + 52 * q^49 + 6 * q^50 - 4 * q^51 - 16 * q^53 + 16 * q^54 + 28 * q^56 + 14 * q^58 + 8 * q^59 + 48 * q^60 + 12 * q^61 - 44 * q^62 - 4 * q^63 + 24 * q^64 - 52 * q^65 + 34 * q^66 - 4 * q^67 - 16 * q^68 + 2 * q^69 + 28 * q^70 + 8 * q^72 - 26 * q^74 - 46 * q^75 - 8 * q^76 - 12 * q^77 - 44 * q^78 - 4 * q^79 + 4 * q^80 + 48 * q^81 - 6 * q^82 + 28 * q^83 + 12 * q^84 - 8 * q^85 + 44 * q^86 - 36 * q^88 + 4 * q^90 - 4 * q^92 - 14 * q^93 + 48 * q^95 + 32 * q^96 + 36 * q^97 - 2 * q^98 + 36 * q^99

Introduction

L-functions

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