LMFDB - Embedded newform 55.3.f.a.12.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,3,Mod(12,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("55.12");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	55.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.49864145398$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 212 x^{16} - 792 x^{15} + 1480 x^{14} + 148 x^{13} + \cdots + 38416 $ x^20 - 4x^19 + 8x^18 + 4x^17 + 212x^16 - 792x^15 + 1480x^14 + 148x^13 + 11654x^12 - 43032x^11 + 79360x^10 - 4948x^9 + 109988x^8 - 423032x^7 + 812488x^6 - 86868x^5 - 87295x^4 + 20876x^3 + 561800x^2 + 207760*x + 38416
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.10
Root			$-2.27868 + 2.27868i$ of defining polynomial
Character	$\chi$	$=$	55.12
Dual form			55.3.f.a.23.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.27868 + 2.27868i) q^{2} +(-1.69843 + 1.69843i) q^{3} +6.38475i q^{4} +(2.55248 - 4.29940i) q^{5} -7.74034 q^{6} +(-3.30878 - 3.30878i) q^{7} +(-5.43407 + 5.43407i) q^{8} +3.23068i q^{9} +(15.6132 - 3.98068i) q^{10} +3.31662 q^{11} +(-10.8440 - 10.8440i) q^{12} +(7.65935 - 7.65935i) q^{13} -15.0793i q^{14} +(2.96703 + 11.6374i) q^{15} +0.773991 q^{16} +(-19.8139 - 19.8139i) q^{17} +(-7.36168 + 7.36168i) q^{18} +17.4895i q^{19} +(27.4506 + 16.2969i) q^{20} +11.2395 q^{21} +(7.55752 + 7.55752i) q^{22} +(-11.7334 + 11.7334i) q^{23} -18.4588i q^{24} +(-11.9697 - 21.9483i) q^{25} +34.9064 q^{26} +(-20.7729 - 20.7729i) q^{27} +(21.1258 - 21.1258i) q^{28} +14.2026i q^{29} +(-19.7571 + 33.2789i) q^{30} -44.6924 q^{31} +(23.5000 + 23.5000i) q^{32} +(-5.63305 + 5.63305i) q^{33} -90.2989i q^{34} +(-22.6714 + 5.78020i) q^{35} -20.6271 q^{36} +(-2.84977 - 2.84977i) q^{37} +(-39.8529 + 39.8529i) q^{38} +26.0177i q^{39} +(9.49291 + 37.2336i) q^{40} +61.2271 q^{41} +(25.6111 + 25.6111i) q^{42} +(-10.2480 + 10.2480i) q^{43} +21.1758i q^{44} +(13.8900 + 8.24624i) q^{45} -53.4734 q^{46} +(58.6916 + 58.6916i) q^{47} +(-1.31457 + 1.31457i) q^{48} -27.1039i q^{49} +(22.7379 - 77.2881i) q^{50} +67.3049 q^{51} +(48.9030 + 48.9030i) q^{52} +(-45.5877 + 45.5877i) q^{53} -94.6697i q^{54} +(8.46561 - 14.2595i) q^{55} +35.9603 q^{56} +(-29.7047 - 29.7047i) q^{57} +(-32.3632 + 32.3632i) q^{58} +3.71455i q^{59} +(-74.3020 + 18.9437i) q^{60} -15.3228 q^{61} +(-101.840 - 101.840i) q^{62} +(10.6896 - 10.6896i) q^{63} +104.002i q^{64} +(-13.3803 - 52.4809i) q^{65} -25.6718 q^{66} +(-23.6682 - 23.6682i) q^{67} +(126.507 - 126.507i) q^{68} -39.8568i q^{69} +(-64.8320 - 38.4896i) q^{70} +66.4871 q^{71} +(-17.5557 - 17.5557i) q^{72} +(93.3093 - 93.3093i) q^{73} -12.9874i q^{74} +(57.6073 + 16.9478i) q^{75} -111.666 q^{76} +(-10.9740 - 10.9740i) q^{77} +(-59.2860 + 59.2860i) q^{78} +57.1583i q^{79} +(1.97559 - 3.32770i) q^{80} +41.4866 q^{81} +(139.517 + 139.517i) q^{82} +(45.3490 - 45.3490i) q^{83} +71.7612i q^{84} +(-135.762 + 34.6133i) q^{85} -46.7036 q^{86} +(-24.1221 - 24.1221i) q^{87} +(-18.0228 + 18.0228i) q^{88} +114.906i q^{89} +(12.8603 + 50.4413i) q^{90} -50.6863 q^{91} +(-74.9150 - 74.9150i) q^{92} +(75.9069 - 75.9069i) q^{93} +267.479i q^{94} +(75.1944 + 44.6415i) q^{95} -79.8260 q^{96} +(-31.9248 - 31.9248i) q^{97} +(61.7610 - 61.7610i) q^{98} +10.7150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 8 q^{6} + 12 q^{8} + 12 q^{10} - 16 q^{12} + 4 q^{13} - 20 q^{15} - 16 q^{16} + 24 q^{17} - 24 q^{18} - 8 q^{20} - 64 q^{21} - 86 q^{23} + 90 q^{25} + 96 q^{26} - 50 q^{27}+ \cdots + 620 q^{98}+O(q^{100}) $ 20 * q - 4 * q^2 - 2 * q^3 - 8 * q^5 - 8 * q^6 + 12 * q^8 + 12 * q^10 - 16 * q^12 + 4 * q^13 - 20 * q^15 - 16 * q^16 + 24 * q^17 - 24 * q^18 - 8 * q^20 - 64 * q^21 - 86 * q^23 + 90 * q^25 + 96 * q^26 - 50 * q^27 + 76 * q^28 - 56 * q^30 - 40 * q^31 + 184 * q^32 - 22 * q^33 - 60 * q^35 - 168 * q^36 - 126 * q^37 + 184 * q^38 + 64 * q^40 - 56 * q^41 + 32 * q^42 - 24 * q^43 + 278 * q^45 + 168 * q^46 + 156 * q^47 + 8 * q^48 - 352 * q^50 + 304 * q^51 - 100 * q^52 - 52 * q^53 + 66 * q^55 + 216 * q^56 - 80 * q^57 - 344 * q^58 - 224 * q^60 - 120 * q^61 - 540 * q^62 + 388 * q^63 - 56 * q^65 - 242 * q^67 + 204 * q^68 + 112 * q^70 - 204 * q^71 + 612 * q^72 - 228 * q^73 - 116 * q^75 - 504 * q^76 - 880 * q^78 + 640 * q^80 + 152 * q^81 + 256 * q^82 + 464 * q^83 - 532 * q^85 - 128 * q^86 + 496 * q^87 - 264 * q^88 - 112 * q^90 - 96 * q^91 - 168 * q^92 + 346 * q^93 + 508 * q^95 - 112 * q^96 + 290 * q^97 + 620 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	2.27868	+	2.27868i	1.13934	+	1.13934i	0.988569	+	0.150770i	$0.0481753\pi$
$2$	2.27868	+	2.27868i	1.13934	+	1.13934i	0.150770	+	0.988569i	$0.451825\pi$
$3$	−1.69843	+	1.69843i	−0.566143	+	0.566143i	−0.931046	−	0.364903i	$-0.881102\pi$
$3$	−1.69843	+	1.69843i	−0.566143	+	0.566143i	0.364903	+	0.931046i	$0.381102\pi$
$4$			6.38475i			1.59619i
$5$	2.55248	−	4.29940i	0.510496	−	0.859880i
$5$	2.55248	−	4.29940i	0.510496	−	0.859880i
$6$	−7.74034			−1.29006
$7$	−3.30878	−	3.30878i	−0.472684	−	0.472684i	0.430098	−	0.902782i	$-0.358479\pi$
$7$	−3.30878	−	3.30878i	−0.472684	−	0.472684i	−0.902782	+	0.430098i	$0.858479\pi$
$8$	−5.43407	+	5.43407i	−0.679259	+	0.679259i
$9$			3.23068i			0.358964i
$10$	15.6132	−	3.98068i	1.56132	−	0.398068i
$11$	3.31662			0.301511
$11$	3.31662			0.301511
$12$	−10.8440	−	10.8440i	−0.903670	−	0.903670i
$13$	7.65935	−	7.65935i	0.589180	−	0.589180i	−0.348229	−	0.937409i	$-0.613217\pi$
$13$	7.65935	−	7.65935i	0.589180	−	0.589180i	0.937409	+	0.348229i	$0.113217\pi$
$14$		−	15.0793i		−	1.07709i
$15$	2.96703	+	11.6374i	0.197802	+	0.775829i
$16$	0.773991			0.0483744
$17$	−19.8139	−	19.8139i	−1.16552	−	1.16552i	−0.983248	−	0.182274i	$-0.941654\pi$
$17$	−19.8139	−	19.8139i	−1.16552	−	1.16552i	−0.182274	−	0.983248i	$-0.558346\pi$
$18$	−7.36168	+	7.36168i	−0.408982	+	0.408982i
$19$			17.4895i			0.920499i	0.887789	+	0.460250i	$0.152240\pi$
$19$			17.4895i			0.920499i	−0.887789	+	0.460250i	$0.847760\pi$
$20$	27.4506	+	16.2969i	1.37253	+	0.814846i
$21$	11.2395			0.535213
$22$	7.55752	+	7.55752i	0.343524	+	0.343524i
$23$	−11.7334	+	11.7334i	−0.510149	+	0.510149i	−0.914572	−	0.404423i	$-0.867472\pi$
$23$	−11.7334	+	11.7334i	−0.510149	+	0.510149i	0.404423	+	0.914572i	$0.367472\pi$
$24$		−	18.4588i		−	0.769115i
$25$	−11.9697	−	21.9483i	−0.478789	−	0.877930i
$26$	34.9064			1.34255
$27$	−20.7729	−	20.7729i	−0.769368	−	0.769368i
$28$	21.1258	−	21.1258i	0.754491	−	0.754491i
$29$			14.2026i			0.489745i	0.969555	+	0.244873i	$0.0787461\pi$
$29$			14.2026i			0.489745i	−0.969555	+	0.244873i	$0.921254\pi$
$30$	−19.7571	+	33.2789i	−0.658569	+	1.10930i
$31$	−44.6924			−1.44169			−0.720846	−	0.693096i	$-0.756246\pi$
$31$	−44.6924			−1.44169			−0.720846	+	0.693096i	$0.756246\pi$
$32$	23.5000	+	23.5000i	0.734374	+	0.734374i
$33$	−5.63305	+	5.63305i	−0.170699	+	0.170699i
$34$		−	90.2989i		−	2.65585i
$35$	−22.6714	+	5.78020i	−0.647754	+	0.165148i
$36$	−20.6271			−0.572974
$37$	−2.84977	−	2.84977i	−0.0770207	−	0.0770207i	0.667547	−	0.744568i	$-0.267344\pi$
$37$	−2.84977	−	2.84977i	−0.0770207	−	0.0770207i	−0.744568	+	0.667547i	$0.767344\pi$
$38$	−39.8529	+	39.8529i	−1.04876	+	1.04876i
$39$			26.0177i			0.667121i
$40$	9.49291	+	37.2336i	0.237323	+	0.930840i
$41$	61.2271			1.49334			0.746672	−	0.665192i	$-0.231650\pi$
$41$	61.2271			1.49334			0.746672	+	0.665192i	$0.231650\pi$
$42$	25.6111	+	25.6111i	0.609789	+	0.609789i
$43$	−10.2480	+	10.2480i	−0.238325	+	0.238325i	−0.816156	−	0.577832i	$-0.803899\pi$
$43$	−10.2480	+	10.2480i	−0.238325	+	0.238325i	0.577832	+	0.816156i	$0.303899\pi$
$44$			21.1758i			0.481268i
$45$	13.8900	+	8.24624i	0.308666	+	0.183250i
$46$	−53.4734			−1.16247
$47$	58.6916	+	58.6916i	1.24876	+	1.24876i	0.956269	+	0.292489i	$0.0944835\pi$
$47$	58.6916	+	58.6916i	1.24876	+	1.24876i	0.292489	+	0.956269i	$0.405516\pi$
$48$	−1.31457	+	1.31457i	−0.0273868	+	0.0273868i
$49$		−	27.1039i		−	0.553141i
$50$	22.7379	−	77.2881i	0.454758	−	1.54576i
$51$	67.3049			1.31970
$52$	48.9030	+	48.9030i	0.940442	+	0.940442i
$53$	−45.5877	+	45.5877i	−0.860145	+	0.860145i	−0.991355	−	0.131210i	$-0.958114\pi$
$53$	−45.5877	+	45.5877i	−0.860145	+	0.860145i	0.131210	+	0.991355i	$0.458114\pi$
$54$		−	94.6697i		−	1.75314i
$55$	8.46561	−	14.2595i	0.153920	−	0.259264i
$56$	35.9603			0.642149
$57$	−29.7047	−	29.7047i	−0.521134	−	0.521134i
$58$	−32.3632	+	32.3632i	−0.557986	+	0.557986i
$59$			3.71455i			0.0629584i	0.999504	+	0.0314792i	$0.0100218\pi$
$59$			3.71455i			0.0629584i	−0.999504	+	0.0314792i	$0.989978\pi$
$60$	−74.3020	+	18.9437i	−1.23837	+	0.315729i
$61$	−15.3228			−0.251193			−0.125596	−	0.992081i	$-0.540084\pi$
$61$	−15.3228			−0.251193			−0.125596	+	0.992081i	$0.540084\pi$
$62$	−101.840	−	101.840i	−1.64258	−	1.64258i
$63$	10.6896	−	10.6896i	0.169677	−	0.169677i
$64$			104.002i			1.62503i
$65$	−13.3803	−	52.4809i	−0.205851	−	0.807399i
$66$	−25.6718			−0.388967
$67$	−23.6682	−	23.6682i	−0.353257	−	0.353257i	0.508063	−	0.861320i	$-0.330362\pi$
$67$	−23.6682	−	23.6682i	−0.353257	−	0.353257i	−0.861320	+	0.508063i	$0.830362\pi$
$68$	126.507	−	126.507i	1.86039	−	1.86039i
$69$		−	39.8568i		−	0.577635i
$70$	−64.8320	−	38.4896i	−0.926172	−	0.549851i
$71$	66.4871			0.936438			0.468219	−	0.883613i	$-0.344896\pi$
$71$	66.4871			0.936438			0.468219	+	0.883613i	$0.344896\pi$
$72$	−17.5557	−	17.5557i	−0.243830	−	0.243830i
$73$	93.3093	−	93.3093i	1.27821	−	1.27821i	0.336541	−	0.941669i	$-0.390743\pi$
$73$	93.3093	−	93.3093i	1.27821	−	1.27821i	0.941669	−	0.336541i	$-0.109257\pi$
$74$		−	12.9874i		−	0.175505i
$75$	57.6073	+	16.9478i	0.768097	+	0.225971i
$76$	−111.666			−1.46929
$77$	−10.9740	−	10.9740i	−0.142519	−	0.142519i
$78$	−59.2860	+	59.2860i	−0.760077	+	0.760077i
$79$			57.1583i			0.723523i	0.932271	+	0.361762i	$0.117825\pi$
$79$			57.1583i			0.723523i	−0.932271	+	0.361762i	$0.882175\pi$
$80$	1.97559	−	3.32770i	0.0246949	−	0.0415962i
$81$	41.4866			0.512180
$82$	139.517	+	139.517i	1.70143	+	1.70143i
$83$	45.3490	−	45.3490i	0.546373	−	0.546373i	−0.379017	−	0.925390i	$-0.623738\pi$
$83$	45.3490	−	45.3490i	0.546373	−	0.546373i	0.925390	+	0.379017i	$0.123738\pi$
$84$			71.7612i			0.854300i
$85$	−135.762	+	34.6133i	−1.59720	+	0.407216i
$86$	−46.7036			−0.543065
$87$	−24.1221	−	24.1221i	−0.277266	−	0.277266i
$88$	−18.0228	+	18.0228i	−0.204804	+	0.204804i
$89$			114.906i			1.29107i	0.763729	+	0.645537i	$0.223366\pi$
$89$			114.906i			1.29107i	−0.763729	+	0.645537i	$0.776634\pi$
$90$	12.8603	+	50.4413i	0.142892	+	0.560459i
$91$	−50.6863			−0.556992
$92$	−74.9150	−	74.9150i	−0.814294	−	0.814294i
$93$	75.9069	−	75.9069i	0.816203	−	0.816203i
$94$			267.479i			2.84552i
$95$	75.1944	+	44.6415i	0.791519	+	0.469911i
$96$	−79.8260			−0.831521
$97$	−31.9248	−	31.9248i	−0.329121	−	0.329121i	0.523131	−	0.852252i	$-0.324764\pi$
$97$	−31.9248	−	31.9248i	−0.329121	−	0.329121i	−0.852252	+	0.523131i	$0.824764\pi$
$98$	61.7610	−	61.7610i	0.630215	−	0.630215i
$99$			10.7150i			0.108232i
$100$	140.134	−	76.4236i	1.40134	−	0.764236i
$101$	109.388			1.08305			0.541523	−	0.840686i	$-0.317848\pi$
$101$	109.388			1.08305			0.541523	+	0.840686i	$0.317848\pi$
$102$	153.366	+	153.366i	1.50359	+	1.50359i
$103$	−28.7421	+	28.7421i	−0.279050	+	0.279050i	−0.832730	−	0.553680i	$-0.813223\pi$
$103$	−28.7421	+	28.7421i	−0.279050	+	0.279050i	0.553680	+	0.832730i	$0.313223\pi$
$104$			83.2429i			0.800412i
$105$	28.6885	−	48.3230i	0.273224	−	0.460219i
$106$	−207.759			−1.95999
$107$	−53.4385	−	53.4385i	−0.499425	−	0.499425i	0.411834	−	0.911259i	$-0.364888\pi$
$107$	−53.4385	−	53.4385i	−0.499425	−	0.499425i	−0.911259	+	0.411834i	$0.864888\pi$
$108$	132.630	−	132.630i	1.22806	−	1.22806i
$109$		−	97.4174i		−	0.893738i	−0.894600	−	0.446869i	$-0.852539\pi$
$109$		−	97.4174i		−	0.893738i	0.894600	−	0.446869i	$-0.147461\pi$
$110$	51.7832	−	13.2024i	0.470757	−	0.120022i
$111$	9.68025			0.0872095
$112$	−2.56097	−	2.56097i	−0.0228658	−	0.0228658i
$113$	−109.416	+	109.416i	−0.968280	+	0.968280i	−0.999512	−	0.0312321i	$-0.990057\pi$
$113$	−109.416	+	109.416i	−0.968280	+	0.968280i	0.0312321	+	0.999512i	$0.490057\pi$
$114$		−	135.375i		−	1.18750i
$115$	20.4974	+	80.3961i	0.178238	+	0.699096i
$116$	−90.6801			−0.781725
$117$	24.7449	+	24.7449i	0.211495	+	0.211495i
$118$	−8.46425	+	8.46425i	−0.0717310	+	0.0717310i
$119$			131.120i			1.10185i
$120$	−79.3617	−	47.1156i	−0.661347	−	0.392630i
$121$	11.0000			0.0909091
$122$	−34.9156	−	34.9156i	−0.286194	−	0.286194i
$123$	−103.990	+	103.990i	−0.845446	+	0.845446i
$124$		−	285.350i		−	2.30121i
$125$	−124.917	−	4.55981i	−0.999334	−	0.0364785i
$126$	48.7164			0.386638
$127$	−3.94652	−	3.94652i	−0.0310749	−	0.0310749i	0.691399	−	0.722474i	$-0.256995\pi$
$127$	−3.94652	−	3.94652i	−0.0310749	−	0.0310749i	−0.722474	+	0.691399i	$0.756995\pi$
$128$	−142.987	+	142.987i	−1.11708	+	1.11708i
$129$		−	34.8108i		−	0.269852i
$130$	89.0977	−	150.077i	0.685367	−	1.15443i
$131$	−165.435			−1.26286			−0.631430	−	0.775433i	$-0.717532\pi$
$131$	−165.435			−1.26286			−0.631430	+	0.775433i	$0.717532\pi$
$132$	−35.9656	−	35.9656i	−0.272467	−	0.272467i
$133$	57.8690	−	57.8690i	0.435105	−	0.435105i
$134$		−	107.864i		−	0.804958i
$135$	−142.334	+	36.2888i	−1.05432	+	0.268806i
$136$	215.340			1.58338
$137$	47.3215	+	47.3215i	0.345412	+	0.345412i	0.858397	−	0.512985i	$-0.171460\pi$
$137$	47.3215	+	47.3215i	0.345412	+	0.345412i	−0.512985	+	0.858397i	$0.671460\pi$
$138$	90.8208	−	90.8208i	0.658122	−	0.658122i
$139$		−	157.241i		−	1.13123i	−0.824670	−	0.565614i	$-0.808639\pi$
$139$		−	157.241i		−	1.13123i	0.824670	−	0.565614i	$-0.191361\pi$
$140$	−36.9051	−	144.751i	−0.263608	−	1.03394i
$141$	−199.367			−1.41395
$142$	151.503	+	151.503i	1.06692	+	1.06692i
$143$	25.4032	−	25.4032i	0.177645	−	0.177645i
$144$			2.50052i			0.0173647i
$145$	61.0627	+	36.2518i	0.421122	+	0.250013i
$146$	425.244			2.91263
$147$	46.0340	+	46.0340i	0.313157	+	0.313157i
$148$	18.1950	−	18.1950i	0.122939	−	0.122939i
$149$			91.9814i			0.617325i	0.951172	+	0.308663i	$0.0998814\pi$
$149$			91.9814i			0.617325i	−0.951172	+	0.308663i	$0.900119\pi$
$150$	92.6497	+	169.887i	0.617665	+	1.13258i
$151$	178.745			1.18374			0.591870	−	0.806034i	$-0.298390\pi$
$151$	178.745			1.18374			0.591870	+	0.806034i	$0.298390\pi$
$152$	−95.0391	−	95.0391i	−0.625257	−	0.625257i
$153$	64.0123	−	64.0123i	0.418381	−	0.418381i
$154$		−	50.0124i		−	0.324756i
$155$	−114.076	+	192.151i	−0.735977	+	1.23968i
$156$	−166.116			−1.06485
$157$	−85.3500	−	85.3500i	−0.543631	−	0.543631i	0.380961	−	0.924591i	$-0.375593\pi$
$157$	−85.3500	−	85.3500i	−0.543631	−	0.543631i	−0.924591	+	0.380961i	$0.875593\pi$
$158$	−130.245	+	130.245i	−0.824338	+	0.824338i
$159$		−	154.855i		−	0.973930i
$160$	161.019	−	41.0527i	1.00637	−	0.256579i
$161$	77.6468			0.482278
$162$	94.5346	+	94.5346i	0.583547	+	0.583547i
$163$	34.8150	−	34.8150i	0.213589	−	0.213589i	−0.592201	−	0.805790i	$-0.701741\pi$
$163$	34.8150	−	34.8150i	0.213589	−	0.213589i	0.805790	+	0.592201i	$0.201741\pi$
$164$			390.920i			2.38366i
$165$	9.84051	+	38.5970i	0.0596395	+	0.233921i
$166$	206.671			1.24501
$167$	−8.73842	−	8.73842i	−0.0523259	−	0.0523259i	0.680460	−	0.732786i	$-0.261780\pi$
$167$	−8.73842	−	8.73842i	−0.0523259	−	0.0523259i	−0.732786	+	0.680460i	$0.761780\pi$
$168$	−61.0761	+	61.0761i	−0.363548	+	0.363548i
$169$			51.6688i			0.305733i
$170$	−388.231	−	230.486i	−2.28371	−	1.35580i
$171$	−56.5029			−0.330427
$172$	−65.4306	−	65.4306i	−0.380411	−	0.380411i
$173$	40.7527	−	40.7527i	0.235565	−	0.235565i	−0.579446	−	0.815011i	$-0.696731\pi$
$173$	40.7527	−	40.7527i	0.235565	−	0.235565i	0.815011	+	0.579446i	$0.196731\pi$
$174$		−	109.933i		−	0.631799i
$175$	−33.0168	+	112.227i	−0.188668	+	0.641299i
$176$	2.56704			0.0145854
$177$	−6.30889	−	6.30889i	−0.0356435	−	0.0356435i
$178$	−261.833	+	261.833i	−1.47097	+	1.47097i
$179$		−	299.550i		−	1.67346i	−0.547613	−	0.836732i	$-0.684463\pi$
$179$		−	299.550i		−	1.67346i	0.547613	−	0.836732i	$-0.315537\pi$
$180$	−52.6501	+	88.6841i	−0.292501	+	0.492689i
$181$	−204.042			−1.12730			−0.563651	−	0.826013i	$-0.690604\pi$
$181$	−204.042			−1.12730			−0.563651	+	0.826013i	$0.690604\pi$
$182$	−115.498	−	115.498i	−0.634602	−	0.634602i
$183$	26.0246	−	26.0246i	0.142211	−	0.142211i
$184$		−	127.521i		−	0.693047i
$185$	−19.5263	+	4.97833i	−0.105547	+	0.0269099i
$186$	345.935			1.85986
$187$	−65.7152	−	65.7152i	−0.351418	−	0.351418i
$188$	−374.731	+	374.731i	−1.99325	+	1.99325i
$189$			137.466i			0.727335i
$190$	69.6200	+	273.067i	0.366421	+	1.43720i
$191$	68.1555			0.356835			0.178418	−	0.983955i	$-0.442902\pi$
$191$	68.1555			0.356835			0.178418	+	0.983955i	$0.442902\pi$
$192$	−176.640	−	176.640i	−0.919998	−	0.919998i
$193$	56.3440	−	56.3440i	0.291938	−	0.291938i	−0.545908	−	0.837845i	$-0.683815\pi$
$193$	56.3440	−	56.3440i	0.291938	−	0.291938i	0.837845	+	0.545908i	$0.183815\pi$
$194$		−	145.493i		−	0.749962i
$195$	111.861	+	66.4096i	0.573644	+	0.340562i
$196$	173.051			0.882916
$197$	61.2935	+	61.2935i	0.311134	+	0.311134i	0.845349	−	0.534215i	$-0.179393\pi$
$197$	61.2935	+	61.2935i	0.311134	+	0.311134i	−0.534215	+	0.845349i	$0.679393\pi$
$198$	−24.4159	+	24.4159i	−0.123313	+	0.123313i
$199$		−	291.772i		−	1.46619i	−0.680125	−	0.733096i	$-0.738075\pi$
$199$		−	291.772i		−	1.46619i	0.680125	−	0.733096i	$-0.261925\pi$
$200$	184.313	+	54.2241i	0.921563	+	0.271120i
$201$	80.3975			0.399988
$202$	249.259	+	249.259i	1.23396	+	1.23396i
$203$	46.9934	−	46.9934i	0.231494	−	0.231494i
$204$			429.725i			2.10649i
$205$	156.281	−	263.240i	0.762346	−	1.28410i
$206$	−130.988			−0.635864
$207$	−37.9070	−	37.9070i	−0.183125	−	0.183125i
$208$	5.92826	−	5.92826i	0.0285013	−	0.0285013i
$209$			58.0061i			0.277541i
$210$	175.484	−	44.7407i	0.835640	−	0.213051i
$211$	−93.8771			−0.444915			−0.222458	−	0.974942i	$-0.571408\pi$
$211$	−93.8771			−0.444915			−0.222458	+	0.974942i	$0.571408\pi$
$212$	−291.066	−	291.066i	−1.37295	−	1.37295i
$213$	−112.924	+	112.924i	−0.530158	+	0.530158i
$214$		−	243.538i		−	1.13803i
$215$	17.9024	+	70.2178i	0.0832670	+	0.326594i
$216$	225.763			1.04520
$217$	147.878	+	147.878i	0.681464	+	0.681464i
$218$	221.983	−	221.983i	1.01827	−	1.01827i
$219$			316.958i			1.44730i
$220$	91.0433	+	54.0508i	0.413833	+	0.245685i
$221$	−303.523			−1.37341
$222$	22.0582	+	22.0582i	0.0993611	+	0.0993611i
$223$	−158.088	+	158.088i	−0.708915	+	0.708915i	−0.966307	−	0.257392i	$-0.917137\pi$
$223$	−158.088	+	158.088i	−0.708915	+	0.708915i	0.257392	+	0.966307i	$0.417137\pi$
$224$		−	155.513i		−	0.694253i
$225$	70.9078	−	38.6703i	0.315146	−	0.171868i
$226$	−498.646			−2.20640
$227$	158.917	+	158.917i	0.700076	+	0.700076i	0.964427	−	0.264351i	$-0.0851576\pi$
$227$	158.917	+	158.917i	0.700076	+	0.700076i	−0.264351	+	0.964427i	$0.585158\pi$
$228$	189.657	−	189.657i	0.831828	−	0.831828i
$229$		−	43.6426i		−	0.190579i	−0.995450	−	0.0952895i	$-0.969622\pi$
$229$		−	43.6426i		−	0.190579i	0.995450	−	0.0952895i	$-0.0303777\pi$
$230$	−136.490	+	229.904i	−0.593434	+	0.999582i
$231$	37.2771			0.161373
$232$	−77.1780	−	77.1780i	−0.332664	−	0.332664i
$233$	231.736	−	231.736i	0.994574	−	0.994574i	−0.00541090	−	0.999985i	$-0.501722\pi$
$233$	231.736	−	231.736i	0.994574	−	0.994574i	0.999985	+	0.00541090i	$0.00172235\pi$
$234$			112.771i			0.481929i
$235$	402.148	−	102.530i	1.71127	−	0.436297i
$236$	−23.7164			−0.100493
$237$	−97.0793	−	97.0793i	−0.409617	−	0.409617i
$238$	−298.780	+	298.780i	−1.25538	+	1.25538i
$239$		−	203.850i		−	0.852930i	−0.904504	−	0.426465i	$-0.859759\pi$
$239$		−	203.850i		−	0.852930i	0.904504	−	0.426465i	$-0.140241\pi$
$240$	2.29645	+	9.00727i	0.00956855	+	0.0375303i
$241$	96.8670			0.401938			0.200969	−	0.979598i	$-0.435591\pi$
$241$	96.8670			0.401938			0.200969	+	0.979598i	$0.435591\pi$
$242$	25.0655	+	25.0655i	0.103576	+	0.103576i
$243$	116.494	−	116.494i	0.479401	−	0.479401i
$244$		−	97.8320i		−	0.400951i
$245$	−116.531	−	69.1821i	−0.475635	−	0.282376i
$246$	−473.919			−1.92650
$247$	133.958	+	133.958i	0.542340	+	0.542340i
$248$	242.862	−	242.862i	0.979282	−	0.979282i
$249$			154.044i			0.618650i
$250$	−274.255	−	295.036i	−1.09702	−	1.18014i
$251$	−165.654			−0.659978			−0.329989	−	0.943985i	$-0.607045\pi$
$251$	−165.654			−0.659978			−0.329989	+	0.943985i	$0.607045\pi$
$252$	68.2505	+	68.2505i	0.270835	+	0.270835i
$253$	−38.9154	+	38.9154i	−0.153816	+	0.153816i
$254$		−	17.9857i		−	0.0708098i
$255$	171.794	−	289.371i	0.673703	−	1.13479i
$256$	−235.634			−0.920445
$257$	168.525	+	168.525i	0.655740	+	0.655740i	0.954369	−	0.298629i	$-0.0965295\pi$
$257$	168.525	+	168.525i	0.655740	+	0.655740i	−0.298629	+	0.954369i	$0.596529\pi$
$258$	79.3227	−	79.3227i	0.307452	−	0.307452i
$259$			18.8585i			0.0728128i
$260$	335.077	−	85.4298i	1.28876	−	0.328576i
$261$	−45.8841			−0.175801
$262$	−376.972	−	376.972i	−1.43883	−	1.43883i
$263$	−50.7899	+	50.7899i	−0.193117	+	0.193117i	−0.797042	−	0.603924i	$-0.793603\pi$
$263$	−50.7899	+	50.7899i	−0.193117	+	0.193117i	0.603924	+	0.797042i	$0.293603\pi$
$264$		−	61.2208i		−	0.231897i
$265$	79.6382	+	312.361i	0.300522	+	1.17872i
$266$	263.729			0.991464
$267$	−195.159	−	195.159i	−0.730933	−	0.730933i
$268$	151.115	−	151.115i	0.563864	−	0.563864i
$269$			256.648i			0.954081i	0.878881	+	0.477041i	$0.158291\pi$
$269$			256.648i			0.954081i	−0.878881	+	0.477041i	$0.841709\pi$
$270$	−407.023	−	241.642i	−1.50749	−	0.894971i
$271$	−215.163			−0.793958			−0.396979	−	0.917828i	$-0.629941\pi$
$271$	−215.163			−0.793958			−0.396979	+	0.917828i	$0.629941\pi$
$272$	−15.3358	−	15.3358i	−0.0563815	−	0.0563815i
$273$	86.0870	−	86.0870i	0.315337	−	0.315337i
$274$			215.661i			0.787083i
$275$	−39.6991	−	72.7941i	−0.144360	−	0.264706i
$276$	254.476			0.922013
$277$	73.9418	+	73.9418i	0.266938	+	0.266938i	0.827865	−	0.560927i	$-0.189555\pi$
$277$	73.9418	+	73.9418i	0.266938	+	0.266938i	−0.560927	+	0.827865i	$0.689555\pi$
$278$	358.301	−	358.301i	1.28885	−	1.28885i
$279$		−	144.387i		−	0.517516i
$280$	91.7880	−	154.608i	0.327814	−	0.552171i
$281$	190.836			0.679133			0.339566	−	0.940582i	$-0.389720\pi$
$281$	190.836			0.679133			0.339566	+	0.940582i	$0.389720\pi$
$282$	−454.293	−	454.293i	−1.61097	−	1.61097i
$283$	−87.1090	+	87.1090i	−0.307806	+	0.307806i	−0.844058	−	0.536252i	$-0.819840\pi$
$283$	−87.1090	+	87.1090i	−0.307806	+	0.307806i	0.536252	+	0.844058i	$0.319840\pi$
$284$			424.503i			1.49473i
$285$	−203.533	+	51.8918i	−0.714150	+	0.182076i
$286$	115.771			0.404795
$287$	−202.587	−	202.587i	−0.705879	−	0.705879i
$288$	−75.9208	+	75.9208i	−0.263614	+	0.263614i
$289$			496.179i			1.71688i
$290$	56.5360	+	221.749i	0.194952	+	0.764650i
$291$	108.444			0.372660
$292$	595.756	+	595.756i	2.04026	+	2.04026i
$293$	−317.484	+	317.484i	−1.08356	+	1.08356i	−0.0873871	+	0.996174i	$0.527852\pi$
$293$	−317.484	+	317.484i	−1.08356	+	1.08356i	−0.996174	+	0.0873871i	$0.972148\pi$
$294$			209.793i			0.713583i
$295$	15.9703	+	9.48129i	0.0541367	+	0.0321400i
$296$	30.9717			0.104634
$297$	−68.8960	−	68.8960i	−0.231973	−	0.231973i
$298$	−209.596	+	209.596i	−0.703343	+	0.703343i
$299$			179.741i			0.601140i
$300$	−108.208	+	367.808i	−0.360692	+	1.22603i
$301$	67.8166			0.225304
$302$	407.302	+	407.302i	1.34868	+	1.34868i
$303$	−185.787	+	185.787i	−0.613159	+	0.613159i
$304$			13.5367i			0.0445286i
$305$	−39.1110	+	65.8787i	−0.128233	+	0.215996i
$306$	291.727			0.953355
$307$	−263.140	−	263.140i	−0.857132	−	0.857132i	0.133867	−	0.990999i	$-0.457261\pi$
$307$	−263.140	−	263.140i	−0.857132	−	0.857132i	−0.990999	+	0.133867i	$0.957261\pi$
$308$	70.0662	−	70.0662i	0.227488	−	0.227488i
$309$		−	97.6328i		−	0.315964i
$310$	−697.793	+	177.906i	−2.25095	+	0.573891i
$311$	301.613			0.969816			0.484908	−	0.874565i	$-0.338853\pi$
$311$	301.613			0.969816			0.484908	+	0.874565i	$0.338853\pi$
$312$	−141.382	−	141.382i	−0.453148	−	0.453148i
$313$	98.0189	−	98.0189i	0.313159	−	0.313159i	−0.532973	−	0.846132i	$-0.678925\pi$
$313$	98.0189	−	98.0189i	0.313159	−	0.313159i	0.846132	+	0.532973i	$0.178925\pi$
$314$		−	388.971i		−	1.23876i
$315$	−18.6740	−	73.2440i	−0.0592824	−	0.232521i
$316$	−364.941			−1.15488
$317$	232.617	+	232.617i	0.733806	+	0.733806i	0.971372	−	0.237565i	$-0.0763493\pi$
$317$	232.617	+	232.617i	0.733806	+	0.733806i	−0.237565	+	0.971372i	$0.576349\pi$
$318$	352.864	−	352.864i	1.10964	−	1.10964i
$319$			47.1047i			0.147664i
$320$	447.145	+	265.462i	1.39733	+	0.829569i
$321$	181.523			0.565492
$322$	176.932	+	176.932i	0.549479	+	0.549479i
$323$	346.535	−	346.535i	1.07286	−	1.07286i
$324$			264.881i			0.817535i
$325$	−259.789	−	76.4291i	−0.799352	−	0.235166i
$326$	158.664			0.486701
$327$	165.457	+	165.457i	0.505983	+	0.505983i
$328$	−332.713	+	332.713i	−1.01437	+	1.01437i
$329$		−	388.396i		−	1.18053i
$330$	−65.5267	+	110.373i	−0.198566	+	0.334465i
$331$	124.210			0.375256			0.187628	−	0.982240i	$-0.439920\pi$
$331$	124.210			0.375256			0.187628	+	0.982240i	$0.439920\pi$
$332$	289.542	+	289.542i	0.872113	+	0.872113i
$333$	9.20668	−	9.20668i	0.0276477	−	0.0276477i
$334$		−	39.8241i		−	0.119234i
$335$	−162.172	+	41.3466i	−0.484095	+	0.123423i
$336$	8.69925			0.0258906
$337$	248.427	+	248.427i	0.737171	+	0.737171i	0.972030	−	0.234858i	$-0.0754626\pi$
$337$	248.427	+	248.427i	0.737171	+	0.737171i	−0.234858	+	0.972030i	$0.575463\pi$
$338$	−117.737	+	117.737i	−0.348333	+	0.348333i
$339$		−	371.669i		−	1.09637i
$340$	−220.997	−	866.808i	−0.649992	−	2.54943i
$341$	−148.228			−0.434686
$342$	−128.752	−	128.752i	−0.376468	−	0.376468i
$343$	−251.811	+	251.811i	−0.734144	+	0.734144i
$344$		−	111.376i		−	0.323768i
$345$	−171.360	−	101.734i	−0.496697	−	0.294880i
$346$	185.724			0.536776
$347$	194.711	+	194.711i	0.561127	+	0.561127i	0.929628	−	0.368501i	$-0.120129\pi$
$347$	194.711	+	194.711i	0.561127	+	0.561127i	−0.368501	+	0.929628i	$0.620129\pi$
$348$	154.014	−	154.014i	0.442568	−	0.442568i
$349$			23.5545i			0.0674914i	0.999430	+	0.0337457i	$0.0107436\pi$
$349$			23.5545i			0.0674914i	−0.999430	+	0.0337457i	$0.989256\pi$
$350$	−330.965	+	180.495i	−0.945613	+	0.515700i
$351$	−318.214			−0.906593
$352$	77.9406	+	77.9406i	0.221422	+	0.221422i
$353$	−60.4688	+	60.4688i	−0.171300	+	0.171300i	−0.787550	−	0.616251i	$-0.788651\pi$
$353$	−60.4688	+	60.4688i	−0.171300	+	0.171300i	0.616251	+	0.787550i	$0.288651\pi$
$354$		−	28.7519i		−	0.0812200i
$355$	169.707	−	285.855i	0.478047	−	0.805224i
$356$	−733.643			−2.06080
$357$	−222.697	−	222.697i	−0.623802	−	0.623802i
$358$	682.578	−	682.578i	1.90664	−	1.90664i
$359$		−	502.684i		−	1.40024i	−0.714028	−	0.700118i	$-0.753131\pi$
$359$		−	502.684i		−	1.40024i	0.714028	−	0.700118i	$-0.246869\pi$
$360$	−120.290	+	30.6686i	−0.334138	+	0.0851904i
$361$	55.1177			0.152681
$362$	−464.945	−	464.945i	−1.28438	−	1.28438i
$363$	−18.6827	+	18.6827i	−0.0514675	+	0.0514675i
$364$		−	323.619i		−	0.889063i
$365$	−163.004	−	639.344i	−0.446587	−	1.75163i
$366$	118.603			0.324053
$367$	−402.334	−	402.334i	−1.09628	−	1.09628i	−0.994842	−	0.101437i	$-0.967656\pi$
$367$	−402.334	−	402.334i	−1.09628	−	1.09628i	−0.101437	−	0.994842i	$-0.532344\pi$
$368$	−9.08157	+	9.08157i	−0.0246782	+	0.0246782i
$369$			197.805i			0.536058i
$370$	−55.8381	−	33.1500i	−0.150914	−	0.0895947i
$371$	301.680			0.813153
$372$	484.646	+	484.646i	1.30281	+	1.30281i
$373$	−129.594	+	129.594i	−0.347437	+	0.347437i	−0.859154	−	0.511717i	$-0.829010\pi$
$373$	−129.594	+	129.594i	−0.347437	+	0.347437i	0.511717	+	0.859154i	$0.329010\pi$
$374$		−	299.487i		−	0.800769i
$375$	219.907	−	204.418i	0.586418	−	0.545114i
$376$	−637.869			−1.69646
$377$	108.783	+	108.783i	0.288548	+	0.288548i
$378$	−313.242	+	313.242i	−0.828681	+	0.828681i
$379$			308.983i			0.815260i	0.913147	+	0.407630i	$0.133645\pi$
$379$			308.983i			0.815260i	−0.913147	+	0.407630i	$0.866355\pi$
$380$	−285.025	+	480.097i	−0.750066	+	1.26341i
$381$	13.4058			0.0351857
$382$	155.305	+	155.305i	0.406556	+	0.406556i
$383$	−137.024	+	137.024i	−0.357765	+	0.357765i	−0.862989	−	0.505223i	$-0.831410\pi$
$383$	−137.024	+	137.024i	−0.357765	+	0.357765i	0.505223	+	0.862989i	$0.331410\pi$
$384$		−	485.705i		−	1.26486i
$385$	−75.1925	+	19.1707i	−0.195305	+	0.0497941i
$386$	256.780			0.665232
$387$	−33.1079	−	33.1079i	−0.0855500	−	0.0855500i
$388$	203.832	−	203.832i	0.525339	−	0.525339i
$389$			219.114i			0.563275i	0.959521	+	0.281637i	$0.0908775\pi$
$389$			219.114i			0.563275i	−0.959521	+	0.281637i	$0.909122\pi$
$390$	103.568	+	406.220i	0.265559	+	1.04159i
$391$	464.970			1.18918
$392$	147.284	+	147.284i	0.375726	+	0.375726i
$393$	280.979	−	280.979i	0.714959	−	0.714959i
$394$			279.336i			0.708975i
$395$	245.747	+	145.895i	0.622143	+	0.369355i
$396$	−68.4123			−0.172758
$397$	447.147	+	447.147i	1.12631	+	1.12631i	0.990772	+	0.135542i	$0.0432777\pi$
$397$	447.147	+	447.147i	1.12631	+	1.12631i	0.135542	+	0.990772i	$0.456722\pi$
$398$	664.855	−	664.855i	1.67049	−	1.67049i
$399$			196.573i			0.492663i
$400$	−9.26445	−	16.9878i	−0.0231611	−	0.0424694i
$401$	−697.196			−1.73864			−0.869321	−	0.494247i	$-0.835444\pi$
$401$	−697.196			−1.73864			−0.869321	+	0.494247i	$0.835444\pi$
$402$	183.200	+	183.200i	0.455722	+	0.455722i
$403$	−342.315	+	342.315i	−0.849416	+	0.849416i
$404$			698.412i			1.72874i
$405$	105.894	−	178.368i	0.261466	−	0.440414i
$406$	214.166			0.527501
$407$	−9.45161	−	9.45161i	−0.0232226	−	0.0232226i
$408$	−365.740	+	365.740i	−0.896421	+	0.896421i
$409$		−	37.7115i		−	0.0922043i	−0.998937	−	0.0461021i	$-0.985320\pi$
$409$		−	37.7115i		−	0.0922043i	0.998937	−	0.0461021i	$-0.0146800\pi$
$410$	955.953	−	243.725i	2.33159	−	0.594452i
$411$	−160.744			−0.391105
$412$	−183.511	−	183.511i	−0.445415	−	0.445415i
$413$	12.2906	−	12.2906i	0.0297594	−	0.0297594i
$414$		−	172.756i		−	0.417284i
$415$	−79.2212	−	310.726i	−0.190894	−	0.748736i
$416$	359.989			0.865357
$417$	267.062	+	267.062i	0.640437	+	0.640437i
$418$	−132.177	+	132.177i	−0.316213	+	0.316213i
$419$		−	486.001i		−	1.15991i	−0.814650	−	0.579953i	$-0.803071\pi$
$419$		−	486.001i		−	1.15991i	0.814650	−	0.579953i	$-0.196929\pi$
$420$	308.530	+	183.169i	0.734596	+	0.436116i
$421$	−388.904			−0.923762			−0.461881	−	0.886942i	$-0.652825\pi$
$421$	−388.904			−0.923762			−0.461881	+	0.886942i	$0.652825\pi$
$422$	−213.916	−	213.916i	−0.506909	−	0.506909i
$423$	−189.614	+	189.614i	−0.448260	+	0.448260i
$424$		−	495.453i		−	1.16852i
$425$	−197.714	+	672.046i	−0.465208	+	1.58129i
$426$	−514.633			−1.20806
$427$	50.6997	+	50.6997i	0.118735	+	0.118735i
$428$	341.191	−	341.191i	0.797175	−	0.797175i
$429$			86.2910i			0.201144i
$430$	−119.210	+	200.797i	−0.277232	+	0.466971i
$431$	504.929			1.17153			0.585764	−	0.810482i	$-0.300795\pi$
$431$	504.929			1.17153			0.585764	+	0.810482i	$0.300795\pi$
$432$	−16.0781	−	16.0781i	−0.0372177	−	0.0372177i
$433$	150.370	−	150.370i	0.347274	−	0.347274i	−0.511819	−	0.859093i	$-0.671028\pi$
$433$	150.370	−	150.370i	0.347274	−	0.347274i	0.859093	+	0.511819i	$0.171028\pi$
$434$			673.931i			1.55284i
$435$	−165.282	+	42.1395i	−0.379958	+	0.0968725i
$436$	621.985			1.42657
$437$	−205.212	−	205.212i	−0.469592	−	0.469592i
$438$	−722.246	+	722.246i	−1.64896	+	1.64896i
$439$		−	210.919i		−	0.480454i	−0.970717	−	0.240227i	$-0.922778\pi$
$439$		−	210.919i		−	0.480454i	0.970717	−	0.240227i	$-0.0772219\pi$
$440$	31.4844	+	123.490i	0.0715555	+	0.280659i
$441$	87.5640			0.198558
$442$	−691.630	−	691.630i	−1.56477	−	1.56477i
$443$	−442.849	+	442.849i	−0.999660	+	0.999660i	−1.00000		0.000339697i	$-0.999892\pi$
$443$	−442.849	+	442.849i	−0.999660	+	0.999660i	0.000339697		1.00000i	$0.499892\pi$
$444$			61.8060i			0.139203i
$445$	494.026	+	293.294i	1.11017	+	0.659088i
$446$	−720.463			−1.61539
$447$	−156.224	−	156.224i	−0.349494	−	0.349494i
$448$	344.119	−	344.119i	0.768123	−	0.768123i
$449$		−	641.685i		−	1.42914i	−0.699563	−	0.714571i	$-0.746622\pi$
$449$		−	641.685i		−	1.42914i	0.699563	−	0.714571i	$-0.253378\pi$
$450$	249.693	+	73.4588i	0.554874	+	0.163242i
$451$	203.067			0.450260
$452$	−698.591	−	698.591i	−1.54556	−	1.54556i
$453$	−303.585	+	303.585i	−0.670166	+	0.670166i
$454$			724.243i			1.59525i
$455$	−129.376	+	217.921i	−0.284342	+	0.478946i
$456$	322.834			0.707970
$457$	−103.709	−	103.709i	−0.226934	−	0.226934i	0.584477	−	0.811411i	$-0.301300\pi$
$457$	−103.709	−	103.709i	−0.226934	−	0.226934i	−0.811411	+	0.584477i	$0.801300\pi$
$458$	99.4474	−	99.4474i	0.217134	−	0.217134i
$459$			823.185i			1.79343i
$460$	−513.309	+	130.871i	−1.11589	+	0.284502i
$461$	−800.040			−1.73544			−0.867722	−	0.497050i	$-0.834417\pi$
$461$	−800.040			−1.73544			−0.867722	+	0.497050i	$0.834417\pi$
$462$	84.9425	+	84.9425i	0.183858	+	0.183858i
$463$	252.447	−	252.447i	0.545242	−	0.545242i	−0.379819	−	0.925061i	$-0.624014\pi$
$463$	252.447	−	252.447i	0.545242	−	0.545242i	0.925061	+	0.379819i	$0.124014\pi$
$464$			10.9927i			0.0236911i
$465$	−132.604	−	520.105i	−0.285169	−	1.11851i
$466$	1056.10			2.26631
$467$	80.1036	+	80.1036i	0.171528	+	0.171528i	0.787650	−	0.616122i	$-0.211297\pi$
$467$	80.1036	+	80.1036i	0.171528	+	0.171528i	−0.616122	+	0.787650i	$0.711297\pi$
$468$	−157.990	+	157.990i	−0.337585	+	0.337585i
$469$			156.626i			0.333957i
$470$	1150.00	+	682.733i	2.44680	+	1.45262i
$471$	289.922			0.615545
$472$	−20.1851	−	20.1851i	−0.0427651	−	0.0427651i
$473$	−33.9886	+	33.9886i	−0.0718576	+	0.0718576i
$474$		−	442.425i		−	0.933386i
$475$	383.864	−	209.344i	0.808134	−	0.440725i
$476$	−837.166			−1.75875
$477$	−147.279	−	147.279i	−0.308761	−	0.308761i
$478$	464.509	−	464.509i	0.971776	−	0.971776i
$479$		−	411.116i		−	0.858280i	−0.903238	−	0.429140i	$-0.858817\pi$
$479$		−	411.116i		−	0.858280i	0.903238	−	0.429140i	$-0.141183\pi$
$480$	−203.754	+	343.204i	−0.424488	+	0.715009i
$481$	−43.6547			−0.0907582
$482$	220.729	+	220.729i	0.457944	+	0.457944i
$483$	−131.878	+	131.878i	−0.273039	+	0.273039i
$484$			70.2322i			0.145108i
$485$	−218.745	+	55.7702i	−0.451020	+	0.114990i
$486$	530.907			1.09240
$487$	−212.163	−	212.163i	−0.435652	−	0.435652i	0.454894	−	0.890546i	$-0.349677\pi$
$487$	−212.163	−	212.163i	−0.435652	−	0.435652i	−0.890546	+	0.454894i	$0.849677\pi$
$488$	83.2650	−	83.2650i	0.170625	−	0.170625i
$489$			118.262i			0.241844i
$490$	−107.892	−	423.179i	−0.220187	−	0.863631i
$491$	113.699			0.231566			0.115783	−	0.993275i	$-0.463062\pi$
$491$	113.699			0.231566			0.115783	+	0.993275i	$0.463062\pi$
$492$	−663.949	−	663.949i	−1.34949	−	1.34949i
$493$	281.409	−	281.409i	0.570809	−	0.570809i
$494$			610.495i			1.23582i
$495$	46.0679	+	27.3497i	0.0930664	+	0.0552519i
$496$	−34.5915			−0.0697410
$497$	−219.991	−	219.991i	−0.442639	−	0.442639i
$498$	−351.017	+	351.017i	−0.704853	+	0.704853i
$499$			343.023i			0.687421i	0.939076	+	0.343711i	$0.111684\pi$
$499$			343.023i			0.687421i	−0.939076	+	0.343711i	$0.888316\pi$
$500$	29.1133	−	797.562i	0.0582265	−	1.59512i
$501$	29.6832			0.0592479
$502$	−377.473	−	377.473i	−0.751939	−	0.751939i
$503$	−625.342	+	625.342i	−1.24323	+	1.24323i	−0.284571	+	0.958655i	$0.591851\pi$
$503$	−625.342	+	625.342i	−1.24323	+	1.24323i	−0.958655	+	0.284571i	$0.908149\pi$
$504$			116.176i			0.230509i
$505$	279.209	−	470.301i	0.552890	−	0.931290i
$506$	−177.351			−0.350497
$507$	−87.7559	−	87.7559i	−0.173088	−	0.173088i
$508$	25.1975	−	25.1975i	0.0496014	−	0.0496014i
$509$			106.269i			0.208780i	0.994536	+	0.104390i	$0.0332890\pi$
$509$			106.269i			0.208780i	−0.994536	+	0.104390i	$0.966711\pi$
$510$	1050.85	−	267.919i	2.06048	−	0.525332i
$511$	−617.481			−1.20838
$512$	35.0124	+	35.0124i	0.0683837	+	0.0683837i
$513$	363.308	−	363.308i	0.708203	−	0.708203i
$514$			768.029i			1.49422i
$515$	50.2103	+	196.937i	0.0974957	+	0.382403i
$516$	222.258			0.430733
$517$	194.658	+	194.658i	0.376515	+	0.376515i
$518$	−42.9725	+	42.9725i	−0.0829585	+	0.0829585i
$519$			138.431i			0.266726i
$520$	357.895	+	212.476i	0.688259	+	0.408607i
$521$	483.272			0.927586			0.463793	−	0.885944i	$-0.346488\pi$
$521$	483.272			0.927586			0.463793	+	0.885944i	$0.346488\pi$
$522$	−104.555	−	104.555i	−0.200297	−	0.200297i
$523$	−224.917	+	224.917i	−0.430052	+	0.430052i	−0.888646	−	0.458594i	$-0.848353\pi$
$523$	−224.917	+	224.917i	−0.430052	+	0.430052i	0.458594	+	0.888646i	$0.348353\pi$
$524$		−	1056.26i		−	2.01576i
$525$	−134.533	−	246.687i	−0.256254	−	0.469880i
$526$	−231.468			−0.440052
$527$	885.530	+	885.530i	1.68032	+	1.68032i
$528$	−4.35993	+	4.35993i	−0.00825744	+	0.00825744i
$529$			253.653i			0.479495i
$530$	−530.301	+	893.241i	−1.00057	+	1.68536i
$531$	−12.0005			−0.0225998
$532$	369.479	+	369.479i	0.694509	+	0.694509i
$533$	468.960	−	468.960i	0.879849	−	0.879849i
$534$		−	889.409i		−	1.66556i
$535$	−366.154	+	93.3530i	−0.684400	+	0.174492i
$536$	257.229			0.479906
$537$	508.764	+	508.764i	0.947420	+	0.947420i
$538$	−584.818	+	584.818i	−1.08702	+	1.08702i
$539$		−	89.8934i		−	0.166778i
$540$	−231.695	−	908.765i	−0.429064	−	1.68290i
$541$	507.591			0.938246			0.469123	−	0.883133i	$-0.344570\pi$
$541$	507.591			0.938246			0.469123	+	0.883133i	$0.344570\pi$
$542$	−490.286	−	490.286i	−0.904587	−	0.904587i
$543$	346.550	−	346.550i	0.638214	−	0.638214i
$544$		−	931.251i		−	1.71186i
$545$	−418.837	−	248.656i	−0.768507	−	0.456249i
$546$	392.329			0.718551
$547$	−224.439	−	224.439i	−0.410309	−	0.410309i	0.471537	−	0.881846i	$-0.343699\pi$
$547$	−224.439	−	224.439i	−0.410309	−	0.410309i	−0.881846	+	0.471537i	$0.843699\pi$
$548$	−302.136	+	302.136i	−0.551342	+	0.551342i
$549$		−	49.5029i		−	0.0901693i
$550$	75.4130	−	256.336i	0.137115	−	0.466065i
$551$	−248.396			−0.450810
$552$	216.585	+	216.585i	0.392364	+	0.392364i
$553$	189.125	−	189.125i	0.341997	−	0.341997i
$554$			336.979i			0.608265i
$555$	24.7086	−	41.6193i	0.0445200	−	0.0749897i
$556$	1003.94			1.80565
$557$	40.3442	+	40.3442i	0.0724312	+	0.0724312i	0.742394	−	0.669963i	$-0.233690\pi$
$557$	40.3442	+	40.3442i	0.0724312	+	0.0724312i	−0.669963	+	0.742394i	$0.733690\pi$
$558$	329.011	−	329.011i	0.589626	−	0.589626i
$559$			156.985i			0.280832i
$560$	−17.5475	+	4.47382i	−0.0313347	+	0.00798896i
$561$	223.225			0.397906
$562$	434.854	+	434.854i	0.773762	+	0.773762i
$563$	−75.8838	+	75.8838i	−0.134785	+	0.134785i	−0.771280	−	0.636496i	$-0.780383\pi$
$563$	−75.8838	+	75.8838i	−0.134785	+	0.134785i	0.636496	+	0.771280i	$0.280383\pi$
$564$		−	1272.91i		−	2.25693i
$565$	191.141	+	749.703i	0.338302	+	1.32691i
$566$	−396.987			−0.701390
$567$	−137.270	−	137.270i	−0.242099	−	0.242099i
$568$	−361.295	+	361.295i	−0.636084	+	0.636084i
$569$		−	940.148i		−	1.65228i	−0.563464	−	0.826141i	$-0.690532\pi$
$569$		−	940.148i		−	1.65228i	0.563464	−	0.826141i	$-0.309468\pi$
$570$	−582.030	−	345.541i	−1.02111	−	0.606212i
$571$	−77.9393			−0.136496			−0.0682481	−	0.997668i	$-0.521741\pi$
$571$	−77.9393			−0.136496			−0.0682481	+	0.997668i	$0.521741\pi$
$572$	162.193	+	162.193i	0.283554	+	0.283554i
$573$	−115.757	+	115.757i	−0.202020	+	0.202020i
$574$		−	923.263i		−	1.60847i
$575$	397.974	+	117.083i	0.692129	+	0.203622i
$576$	−335.996			−0.583327
$577$	−500.861	−	500.861i	−0.868043	−	0.868043i	0.124213	−	0.992256i	$-0.460359\pi$
$577$	−500.861	−	500.861i	−0.868043	−	0.868043i	−0.992256	+	0.124213i	$0.960359\pi$
$578$	−1130.63	+	1130.63i	−1.95611	+	1.95611i
$579$			191.393i			0.330557i
$580$	−231.459	+	389.870i	−0.399067	+	0.672190i
$581$	−300.100			−0.516523
$582$	247.109	+	247.109i	0.424586	+	0.424586i
$583$	−151.197	+	151.197i	−0.259343	+	0.259343i
$584$			1014.10i			1.73647i
$585$	169.549	−	43.2275i	0.289827	−	0.0738931i
$586$	−1446.89			−2.46909
$587$	−101.416	−	101.416i	−0.172771	−	0.172771i	0.615425	−	0.788196i	$-0.288984\pi$
$587$	−101.416	−	101.416i	−0.172771	−	0.172771i	−0.788196	+	0.615425i	$0.788984\pi$
$588$	−293.916	+	293.916i	−0.499856	+	0.499856i
$589$		−	781.648i		−	1.32708i
$590$	14.7864	+	57.9960i	0.0250617	+	0.0982984i
$591$	−208.205			−0.352293
$592$	−2.20569	−	2.20569i	−0.00372583	−	0.00372583i
$593$	597.297	−	597.297i	1.00725	−	1.00725i	0.00727231	−	0.999974i	$-0.497685\pi$
$593$	597.297	−	597.297i	1.00725	−	1.00725i	0.999974	−	0.00727231i	$-0.00231487\pi$
$594$		−	313.984i		−	0.528592i
$595$	563.736	+	334.680i	0.947456	+	0.562487i
$596$	−587.278			−0.985366
$597$	495.554	+	495.554i	0.830074	+	0.830074i
$598$	−409.572	+	409.572i	−0.684902	+	0.684902i
$599$			347.771i			0.580585i	0.956938	+	0.290293i	$0.0937527\pi$
$599$			347.771i			0.580585i	−0.956938	+	0.290293i	$0.906247\pi$
$600$	−405.138	+	220.946i	−0.675230	+	0.368244i
$601$	−192.174			−0.319757			−0.159878	−	0.987137i	$-0.551110\pi$
$601$	−192.174			−0.319757			−0.159878	+	0.987137i	$0.551110\pi$
$602$	154.532	+	154.532i	0.256698	+	0.256698i
$603$	76.4644	−	76.4644i	0.126807	−	0.126807i
$604$			1141.24i			1.88947i
$605$	28.0773	−	47.2934i	0.0464087	−	0.0781709i
$606$	−846.698			−1.39719
$607$	−74.3868	−	74.3868i	−0.122548	−	0.122548i	0.643173	−	0.765721i	$-0.277618\pi$
$607$	−74.3868	−	74.3868i	−0.122548	−	0.122548i	−0.765721	+	0.643173i	$0.777618\pi$
$608$	−411.002	+	411.002i	−0.675991	+	0.675991i
$609$			159.630i			0.262118i
$610$	−239.238	+	60.9950i	−0.392193	+	0.0999918i
$611$	899.079			1.47149
$612$	408.702	+	408.702i	0.667814	+	0.667814i
$613$	599.202	−	599.202i	0.977491	−	0.977491i	−0.0222612	−	0.999752i	$-0.507087\pi$
$613$	599.202	−	599.202i	0.977491	−	0.977491i	0.999752	+	0.0222612i	$0.00708655\pi$
$614$		−	1199.22i		−	1.95313i
$615$	181.663	+	712.526i	0.295386	+	1.15858i
$616$	119.267			0.193615
$617$	−95.9908	−	95.9908i	−0.155577	−	0.155577i	0.625027	−	0.780603i	$-0.285088\pi$
$617$	−95.9908	−	95.9908i	−0.155577	−	0.155577i	−0.780603	+	0.625027i	$0.785088\pi$
$618$	222.474	−	222.474i	0.359990	−	0.359990i
$619$		−	349.611i		−	0.564800i	−0.959297	−	0.282400i	$-0.908869\pi$
$619$		−	349.611i		−	0.564800i	0.959297	−	0.282400i	$-0.0911305\pi$
$620$	−1226.83	−	728.349i	−1.97876	−	1.17476i
$621$	487.476			0.784985
$622$	687.279	+	687.279i	1.10495	+	1.10495i
$623$	380.198	−	380.198i	0.610270	−	0.610270i
$624$			20.1375i			0.0322716i
$625$	−338.452	+	525.429i	−0.541523	+	0.840686i
$626$	446.707			0.713590
$627$	−98.5192	−	98.5192i	−0.157128	−	0.157128i
$628$	544.938	−	544.938i	0.867736	−	0.867736i
$629$			112.930i			0.179539i
$630$	124.348	−	209.451i	0.197377	−	0.332463i
$631$	249.068			0.394720			0.197360	−	0.980331i	$-0.436763\pi$
$631$	249.068			0.394720			0.197360	+	0.980331i	$0.436763\pi$
$632$	−310.602	−	310.602i	−0.491460	−	0.491460i
$633$	159.444	−	159.444i	0.251886	−	0.251886i
$634$			1060.12i			1.67211i
$635$	−27.0411	+	6.89426i	−0.0425843	+	0.0108571i
$636$	988.709			1.55457
$637$	−207.598	−	207.598i	−0.325900	−	0.325900i
$638$	−107.337	+	107.337i	−0.168239	+	0.168239i
$639$			214.798i			0.336148i
$640$	249.787	+	979.727i	0.390292	+	1.53082i
$641$	1112.98			1.73632			0.868159	−	0.496287i	$-0.165304\pi$
$641$	1112.98			1.73632			0.868159	+	0.496287i	$0.165304\pi$
$642$	413.632	+	413.632i	0.644287	+	0.644287i
$643$	−396.093	+	396.093i	−0.616008	+	0.616008i	−0.944505	−	0.328497i	$-0.893458\pi$
$643$	−396.093	+	396.093i	−0.616008	+	0.616008i	0.328497	+	0.944505i	$0.393458\pi$
$644$			495.755i			0.769806i
$645$	−149.666	−	88.8539i	−0.232040	−	0.137758i
$646$	1579.28			2.44471
$647$	190.770	+	190.770i	0.294854	+	0.294854i	0.838994	−	0.544140i	$-0.183144\pi$
$647$	190.770	+	190.770i	0.294854	+	0.294854i	−0.544140	+	0.838994i	$0.683144\pi$
$648$	−225.441	+	225.441i	−0.347903	+	0.347903i
$649$			12.3198i			0.0189827i
$650$	−417.819	−	766.134i	−0.642799	−	1.17867i
$651$	−502.319			−0.771612
$652$	222.285	+	222.285i	0.340928	+	0.340928i
$653$	41.7823	−	41.7823i	0.0639851	−	0.0639851i	−0.674390	−	0.738375i	$-0.735593\pi$
$653$	41.7823	−	41.7823i	0.0639851	−	0.0639851i	0.738375	+	0.674390i	$0.235593\pi$
$654$			754.044i			1.15297i
$655$	−422.268	+	711.270i	−0.644684	+	1.08591i
$656$	47.3892			0.0722397
$657$	301.453	+	301.453i	0.458832	+	0.458832i
$658$	885.029	−	885.029i	1.34503	−	1.34503i
$659$		−	690.184i		−	1.04732i	−0.851927	−	0.523660i	$-0.824566\pi$
$659$		−	690.184i		−	1.04732i	0.851927	−	0.523660i	$-0.175434\pi$
$660$	−246.432	+	62.8292i	−0.373382	+	0.0951957i
$661$	−658.583			−0.996344			−0.498172	−	0.867078i	$-0.665995\pi$
$661$	−658.583			−0.996344			−0.498172	+	0.867078i	$0.665995\pi$
$662$	283.034	+	283.034i	0.427544	+	0.427544i
$663$	515.512	−	515.512i	0.777544	−	0.777544i
$664$			492.859i			0.742258i
$665$	−101.093	−	396.511i	−0.152019	−	0.596257i
$666$	41.9581			0.0630002
$667$	−166.645	−	166.645i	−0.249843	−	0.249843i
$668$	55.7926	−	55.7926i	0.0835219	−	0.0835219i
$669$		−	537.002i		−	0.802694i
$670$	−463.753	−	275.322i	−0.692168	−	0.410928i
$671$	−50.8198			−0.0757375
$672$	264.127	+	264.127i	0.393046	+	0.393046i
$673$	−901.911	+	901.911i	−1.34014	+	1.34014i	−0.444216	+	0.895920i	$0.646518\pi$
$673$	−901.911	+	901.911i	−1.34014	+	1.34014i	−0.895920	+	0.444216i	$0.853482\pi$
$674$			1132.17i			1.67978i
$675$	−207.284	+	704.576i	−0.307087	+	1.04382i
$676$	−329.893			−0.488007
$677$	−485.397	−	485.397i	−0.716982	−	0.716982i	0.251004	−	0.967986i	$-0.419239\pi$
$677$	−485.397	−	485.397i	−0.716982	−	0.716982i	−0.967986	+	0.251004i	$0.919239\pi$
$678$	846.915	−	846.915i	1.24914	−	1.24914i
$679$			211.264i			0.311141i
$680$	549.651	−	925.833i	0.808310	−	1.36152i
$681$	−539.819			−0.792686
$682$	−337.764	−	337.764i	−0.495255	−	0.495255i
$683$	713.724	−	713.724i	1.04498	−	1.04498i	0.0460448	−	0.998939i	$-0.485338\pi$
$683$	713.724	−	713.724i	1.04498	−	1.04498i	0.998939	−	0.0460448i	$-0.0146617\pi$
$684$		−	360.757i		−	0.527423i
$685$	324.241	−	82.6670i	0.473345	−	0.120682i
$686$	−1147.59			−1.67288
$687$	74.1238	+	74.1238i	0.107895	+	0.107895i
$688$	−7.93183	+	7.93183i	−0.0115288	+	0.0115288i
$689$			698.344i			1.01356i
$690$	−158.657	−	622.293i	−0.229938	−	0.901875i
$691$	−1319.75			−1.90991			−0.954954	−	0.296754i	$-0.904096\pi$
$691$	−1319.75			−1.90991			−0.954954	+	0.296754i	$0.904096\pi$
$692$	260.195	+	260.195i	0.376005	+	0.376005i
$693$	35.4535	−	35.4535i	0.0511594	−	0.0511594i
$694$			887.368i			1.27863i
$695$	−676.041	−	401.353i	−0.972721	−	0.577487i
$696$	262.163			0.376670
$697$	−1213.15	−	1213.15i	−1.74053	−	1.74053i
$698$	−53.6731	+	53.6731i	−0.0768955	+	0.0768955i
$699$			787.174i			1.12614i
$700$	−716.543	−	210.804i	−1.02363	−	0.301149i
$701$	−1276.93			−1.82159			−0.910795	−	0.412859i	$-0.864530\pi$
$701$	−1276.93			−1.82159			−0.910795	+	0.412859i	$0.864530\pi$
$702$	−725.108	−	725.108i	−1.03292	−	1.03292i
$703$	49.8410	−	49.8410i	0.0708975	−	0.0708975i
$704$			344.935i			0.489964i
$705$	−508.880	+	857.159i	−0.721816	+	1.21583i
$706$	−275.578			−0.390337
$707$	−361.940	−	361.940i	−0.511938	−	0.511938i
$708$	40.2807	−	40.2807i	0.0568936	−	0.0568936i
$709$		−	746.781i		−	1.05329i	−0.850086	−	0.526644i	$-0.823450\pi$
$709$		−	746.781i		−	1.05329i	0.850086	−	0.526644i	$-0.176550\pi$
$710$	1038.08	−	264.664i	1.46208	−	0.372766i
$711$	−184.660			−0.259719
$712$	−624.405	−	624.405i	−0.876974	−	0.876974i
$713$	524.396	−	524.396i	0.735478	−	0.735478i
$714$		−	1014.91i		−	1.42144i
$715$	−44.3774	−	174.060i	−0.0620663	−	0.243440i
$716$	1912.55			2.67116
$717$	346.225	+	346.225i	0.482880	+	0.482880i
$718$	1145.46	−	1145.46i	1.59534	−	1.59534i
$719$			135.949i			0.189080i	0.995521	+	0.0945402i	$0.0301381\pi$
$719$			135.949i			0.189080i	−0.995521	+	0.0945402i	$0.969862\pi$
$720$	10.7507	+	6.38251i	0.0149316	+	0.00886460i
$721$	190.203			0.263804
$722$	125.596	+	125.596i	0.173955	+	0.173955i
$723$	−164.522	+	164.522i	−0.227554	+	0.227554i
$724$		−	1302.75i		−	1.79938i
$725$	311.723	−	170.001i	0.429962	−	0.234484i
$726$	−85.1438			−0.117278
$727$	192.127	+	192.127i	0.264273	+	0.264273i	0.826788	−	0.562514i	$-0.190166\pi$
$727$	192.127	+	192.127i	0.264273	+	0.264273i	−0.562514	+	0.826788i	$0.690166\pi$
$728$	275.433	−	275.433i	0.378342	−	0.378342i
$729$			769.094i			1.05500i
$730$	1085.43	−	1828.29i	1.48688	−	2.50451i
$731$	406.103			0.555545
$732$	166.161	+	166.161i	0.226995	+	0.226995i
$733$	−288.677	+	288.677i	−0.393830	+	0.393830i	−0.876050	−	0.482220i	$-0.839830\pi$
$733$	−288.677	+	288.677i	−0.393830	+	0.393830i	0.482220	+	0.876050i	$0.339830\pi$
$734$		−	1833.58i		−	2.49807i
$735$	315.420	−	80.4180i	0.429142	−	0.109412i
$736$	−551.471			−0.749281
$737$	−78.4985	−	78.4985i	−0.106511	−	0.106511i
$738$	−450.734	+	450.734i	−0.610751	+	0.610751i
$739$			135.495i			0.183349i	0.995789	+	0.0916746i	$0.0292220\pi$
$739$			135.495i			0.183349i	−0.995789	+	0.0916746i	$0.970778\pi$
$740$	−31.7854	−	124.670i	−0.0429532	−	0.168473i
$741$	−455.036			−0.614084
$742$	687.431	+	687.431i	0.926457	+	0.926457i
$743$	−350.021	+	350.021i	−0.471091	+	0.471091i	−0.902268	−	0.431177i	$-0.858099\pi$
$743$	−350.021	+	350.021i	−0.471091	+	0.471091i	0.431177	+	0.902268i	$0.358099\pi$
$744$			824.967i			1.10883i
$745$	395.465	+	234.781i	0.530826	+	0.315142i
$746$	−590.605			−0.791696
$747$	146.508	+	146.508i	0.196128	+	0.196128i
$748$	419.575	−	419.575i	0.560929	−	0.560929i
$749$			353.633i			0.472140i
$750$	966.899	+	35.2945i	1.28920	+	0.0470594i
$751$	1143.86			1.52311			0.761556	−	0.648099i	$-0.224436\pi$
$751$	1143.86			1.52311			0.761556	+	0.648099i	$0.224436\pi$
$752$	45.4268	+	45.4268i	0.0604080	+	0.0604080i
$753$	281.352	−	281.352i	0.373642	−	0.373642i
$754$			495.761i			0.657509i
$755$	456.242	−	768.495i	0.604294	−	1.01787i
$756$	−877.688			−1.16096
$757$	−99.4207	−	99.4207i	−0.131335	−	0.131335i	0.638383	−	0.769719i	$-0.279603\pi$
$757$	−99.4207	−	99.4207i	−0.131335	−	0.131335i	−0.769719	+	0.638383i	$0.779603\pi$
$758$	−704.074	+	704.074i	−0.928857	+	0.928857i
$759$		−	132.190i		−	0.174163i
$760$	−651.197	+	166.026i	−0.856838	+	0.218456i
$761$	−782.950			−1.02884			−0.514421	−	0.857537i	$-0.671993\pi$
$761$	−782.950			−1.02884			−0.514421	+	0.857537i	$0.671993\pi$
$762$	30.5474	+	30.5474i	0.0400884	+	0.0400884i
$763$	−322.333	+	322.333i	−0.422455	+	0.422455i
$764$			435.156i			0.569576i
$765$	−111.825	−	438.604i	−0.146176	−	0.573339i
$766$	−624.467			−0.815231
$767$	28.4510	+	28.4510i	0.0370939	+	0.0370939i
$768$	400.208	−	400.208i	0.521104	−	0.521104i
$769$			1060.55i			1.37913i	0.724224	+	0.689565i	$0.242198\pi$
$769$			1060.55i			1.37913i	−0.724224	+	0.689565i	$0.757802\pi$
$770$	−215.023	−	127.656i	−0.279251	−	0.165786i
$771$	−572.456			−0.742485
$772$	359.742	+	359.742i	0.465987	+	0.465987i
$773$	−599.585	+	599.585i	−0.775660	+	0.775660i	−0.979090	−	0.203429i	$-0.934791\pi$
$773$	−599.585	+	599.585i	−0.775660	+	0.775660i	0.203429	+	0.979090i	$0.434791\pi$
$774$		−	150.884i		−	0.194941i
$775$	534.956	+	980.921i	0.690265	+	1.26570i
$776$	346.963			0.447117
$777$	−32.0299	−	32.0299i	−0.0412225	−	0.0412225i
$778$	−499.290	+	499.290i	−0.641761	+	0.641761i
$779$			1070.83i			1.37462i
$780$	−424.009	+	714.202i	−0.543601	+	0.915643i
$781$	220.513			0.282347
$782$	1059.52	+	1059.52i	1.35488	+	1.35488i
$783$	295.030	−	295.030i	0.376794	−	0.376794i
$784$		−	20.9782i		−	0.0267579i
$785$	−584.808	+	149.100i	−0.744979	+	0.189936i
$786$	1280.52			1.62916
$787$	−10.9757	−	10.9757i	−0.0139462	−	0.0139462i	0.700099	−	0.714046i	$-0.253139\pi$
$787$	−10.9757	−	10.9757i	−0.0139462	−	0.0139462i	−0.714046	+	0.700099i	$0.753139\pi$
$788$	−391.343	+	391.343i	−0.496628	+	0.496628i
$789$		−	172.526i		−	0.218664i
$790$	227.529	+	892.426i	0.288011	+	1.12965i
$791$	724.066			0.915380
$792$	−58.2258	−	58.2258i	−0.0735174	−	0.0735174i
$793$	−117.362	+	117.362i	−0.147998	+	0.147998i
$794$			2037.81i			2.56651i
$795$	−665.783	−	395.264i	−0.837463	−	0.497187i
$796$	1862.89			2.34032
$797$	291.068	+	291.068i	0.365205	+	0.365205i	0.865725	−	0.500520i	$-0.166858\pi$
$797$	291.068	+	291.068i	0.365205	+	0.365205i	−0.500520	+	0.865725i	$0.666858\pi$
$798$	−447.926	+	447.926i	−0.561310	+	0.561310i
$799$		−	2325.82i		−	2.91091i
$800$	234.495	−	797.071i	0.293119	−	0.996339i
$801$	−371.223			−0.463450
$802$	−1588.68	−	1588.68i	−1.98090	−	1.98090i
$803$	309.472	−	309.472i	0.385395	−	0.385395i
$804$			513.318i			0.638455i
$805$	198.192	−	333.835i	0.246201	−	0.414702i
$806$	−1560.05			−1.93555
$807$	−435.898	−	435.898i	−0.540146	−	0.540146i
$808$	−594.420	+	594.420i	−0.735669	+	0.735669i
$809$			934.080i			1.15461i	0.816528	+	0.577305i	$0.195896\pi$
$809$			934.080i			1.15461i	−0.816528	+	0.577305i	$0.804104\pi$
$810$	647.740	−	165.145i	0.799679	−	0.203882i
$811$	247.443			0.305109			0.152554	−	0.988295i	$-0.451250\pi$
$811$	247.443			0.305109			0.152554	+	0.988295i	$0.451250\pi$
$812$	300.041	+	300.041i	0.369508	+	0.369508i
$813$	365.438	−	365.438i	0.449494	−	0.449494i
$814$		−	43.0743i		−	0.0529169i
$815$	−60.8192	−	238.548i	−0.0746248	−	0.292697i
$816$	52.0934			0.0638399
$817$	−179.232	−	179.232i	−0.219378	−	0.219378i
$818$	85.9325	−	85.9325i	0.105052	−	0.105052i
$819$		−	163.751i		−	0.199940i
$820$	1680.72	+	997.814i	2.04966	+	1.21685i
$821$	−958.912			−1.16798			−0.583990	−	0.811761i	$-0.698509\pi$
$821$	−958.912			−1.16798			−0.583990	+	0.811761i	$0.698509\pi$
$822$	−366.285	−	366.285i	−0.445602	−	0.445602i
$823$	−841.533	+	841.533i	−1.02252	+	1.02252i	−0.0227782	+	0.999741i	$0.507251\pi$
$823$	−841.533	+	841.533i	−1.02252	+	1.02252i	−0.999741	+	0.0227782i	$0.992749\pi$
$824$		−	312.373i		−	0.379094i
$825$	191.062	+	56.2096i	0.231590	+	0.0681329i
$826$	56.0128			0.0678121
$827$	501.948	+	501.948i	0.606951	+	0.606951i	0.942148	−	0.335197i	$-0.108803\pi$
$827$	501.948	+	501.948i	0.606951	+	0.606951i	−0.335197	+	0.942148i	$0.608803\pi$
$828$	242.026	−	242.026i	0.292302	−	0.292302i
$829$			219.411i			0.264670i	0.991205	+	0.132335i	$0.0422474\pi$
$829$			219.411i			0.264670i	−0.991205	+	0.132335i	$0.957753\pi$
$830$	527.524	−	888.563i	0.635571	−	1.07056i
$831$	−251.170			−0.302250
$832$	796.585	+	796.585i	0.957434	+	0.957434i
$833$	−537.033	+	537.033i	−0.644697	+	0.644697i
$834$			1217.10i			1.45935i
$835$	−59.8746	+	15.2654i	−0.0717061	+	0.0182819i
$836$	−370.354			−0.443007
$837$	928.393	+	928.393i	1.10919	+	1.10919i
$838$	1107.44	−	1107.44i	1.32153	−	1.32153i
$839$			1101.77i			1.31320i	0.754241	+	0.656598i	$0.228005\pi$
$839$			1101.77i			1.31320i	−0.754241	+	0.656598i	$0.771995\pi$
$840$	106.695	+	418.486i	0.127018	+	0.498198i
$841$	639.286			0.760150
$842$	−886.187	−	886.187i	−1.05248	−	1.05248i
$843$	−324.122	+	324.122i	−0.384486	+	0.384486i
$844$		−	599.381i		−	0.710168i
$845$	222.145	+	131.884i	0.262894	+	0.156075i
$846$	−864.138			−1.02144
$847$	−36.3966	−	36.3966i	−0.0429712	−	0.0429712i
$848$	−35.2845	+	35.2845i	−0.0416090	+	0.0416090i
$849$		−	295.897i		−	0.348524i
$850$	−1981.90	+	1080.85i	−2.33165	+	1.27159i
$851$	66.8751			0.0785841
$852$	−720.988	−	720.988i	−0.846230	−	0.846230i
$853$	1045.69	−	1045.69i	1.22589	−	1.22589i	0.260387	−	0.965504i	$-0.416150\pi$
$853$	1045.69	−	1045.69i	1.22589	−	1.22589i	0.965504	−	0.260387i	$-0.0838501\pi$
$854$			231.057i			0.270558i
$855$	−144.222	+	242.929i	−0.168681	+	0.284127i
$856$	580.777			0.678478
$857$	−1006.72	−	1006.72i	−1.17471	−	1.17471i	−0.981074	−	0.193632i	$-0.937973\pi$
$857$	−1006.72	−	1006.72i	−1.17471	−	1.17471i	−0.193632	−	0.981074i	$-0.562027\pi$
$858$	−196.629	+	196.629i	−0.229172	+	0.229172i
$859$		−	1366.58i		−	1.59090i	−0.606021	−	0.795448i	$-0.707235\pi$
$859$		−	1366.58i		−	1.59090i	0.606021	−	0.795448i	$-0.292765\pi$
$860$	−448.323	+	114.302i	−0.521305	+	0.132910i
$861$	688.160			0.799257
$862$	1150.57	+	1150.57i	1.33477	+	1.33477i
$863$	947.174	−	947.174i	1.09754	−	1.09754i	0.102838	−	0.994698i	$-0.467208\pi$
$863$	947.174	−	947.174i	1.09754	−	1.09754i	0.994698	−	0.102838i	$-0.0327924\pi$
$864$		−	976.326i		−	1.13001i
$865$	−71.1918	−	279.232i	−0.0823027	−	0.322812i
$866$	685.288			0.791325
$867$	−842.725	−	842.725i	−0.972001	−	0.972001i
$868$	−944.161	+	944.161i	−1.08774	+	1.08774i
$869$			189.573i			0.218150i
$870$	−472.647	−	280.602i	−0.543272	−	0.322531i
$871$	−362.566			−0.416264
$872$	529.373	+	529.373i	0.607079	+	0.607079i
$873$	103.139	−	103.139i	0.118143	−	0.118143i
$874$		−	935.223i		−	1.07005i
$875$	398.235	+	428.410i	0.455126	+	0.489612i
$876$	−2023.70			−2.31016
$877$	−87.0484	−	87.0484i	−0.0992570	−	0.0992570i	0.655735	−	0.754992i	$-0.272359\pi$
$877$	−87.0484	−	87.0484i	−0.0992570	−	0.0992570i	−0.754992	+	0.655735i	$0.772359\pi$
$878$	480.617	−	480.617i	0.547400	−	0.547400i
$879$		−	1078.45i		−	1.22690i
$880$	6.55231	−	11.0367i	0.00744580	−	0.0125417i
$881$	868.490			0.985800			0.492900	−	0.870086i	$-0.335937\pi$
$881$	868.490			0.985800			0.492900	+	0.870086i	$0.335937\pi$
$882$	199.530	+	199.530i	0.226225	+	0.226225i
$883$	608.328	−	608.328i	0.688934	−	0.688934i	−0.273063	−	0.961996i	$-0.588037\pi$
$883$	608.328	−	608.328i	0.688934	−	0.688934i	0.961996	+	0.273063i	$0.0880366\pi$
$884$		−	1937.92i		−	2.19221i
$885$	−43.2278	+	11.0212i	−0.0488449	+	0.0124533i
$886$	−2018.22			−2.27790
$887$	495.738	+	495.738i	0.558892	+	0.558892i	0.928992	−	0.370100i	$-0.120676\pi$
$887$	495.738	+	495.738i	0.558892	+	0.558892i	−0.370100	+	0.928992i	$0.620676\pi$
$888$	−52.6032	+	52.6032i	−0.0592378	+	0.0592378i
$889$			26.1163i			0.0293772i
$890$	457.402	+	1794.05i	0.513935	+	2.01578i
$891$	137.595			0.154428
$892$	−1009.35	−	1009.35i	−1.13156	−	1.13156i
$893$	−1026.49	+	1026.49i	−1.14948	+	1.14948i
$894$		−	711.968i		−	0.796385i
$895$	−1287.89	−	764.595i	−1.43898	−	0.854296i
$896$	946.224			1.05605
$897$	−305.277	−	305.277i	−0.340331	−	0.340331i
$898$	1462.19	−	1462.19i	1.62828	−	1.62828i
$899$		−	634.749i		−	0.706061i
$900$	246.900	+	452.728i	0.274334	+	0.503031i
$901$	1806.54			2.00504
$902$	462.725	+	462.725i	0.512999	+	0.512999i
$903$	−115.182	+	115.182i	−0.127554	+	0.127554i
$904$		−	1189.14i		−	1.31543i
$905$	−520.812	+	877.257i	−0.575483	+	0.969345i
$906$	−1383.55			−1.52709
$907$	163.744	+	163.744i	0.180534	+	0.180534i	0.791588	−	0.611055i	$-0.209254\pi$
$907$	163.744	+	163.744i	0.180534	+	0.180534i	−0.611055	+	0.791588i	$0.709254\pi$
$908$	−1014.65	+	1014.65i	−1.11745	+	1.11745i
$909$			353.396i			0.388775i
$910$	−791.376	+	201.766i	−0.869644	+	0.221720i
$911$	1750.93			1.92199			0.960995	−	0.276566i	$-0.0891963\pi$
$911$	1750.93			1.92199			0.960995	+	0.276566i	$0.0891963\pi$
$912$	−22.9911	−	22.9911i	−0.0252096	−	0.0252096i
$913$	150.405	−	150.405i	0.164738	−	0.164738i
$914$		−	472.638i		−	0.517109i
$915$	−45.4630	−	178.318i	−0.0496864	−	0.194883i
$916$	278.647			0.304200
$917$	547.388	+	547.388i	0.596933	+	0.596933i
$918$	−1875.77	+	1875.77i	−2.04333	+	2.04333i
$919$			1637.39i			1.78170i	0.454293	+	0.890852i	$0.349892\pi$
$919$			1637.39i			1.78170i	−0.454293	+	0.890852i	$0.650108\pi$
$920$	−548.263	−	325.494i	−0.595938	−	0.353797i
$921$	893.848			0.970519
$922$	−1823.03	−	1823.03i	−1.97726	−	1.97726i
$923$	509.247	−	509.247i	0.551731	−	0.551731i
$924$			238.005i			0.257581i
$925$	−28.4365	+	96.6583i	−0.0307422	+	0.104495i
$926$	1150.49			1.24243
$927$	−92.8565	−	92.8565i	−0.100169	−	0.100169i
$928$	−333.761	+	333.761i	−0.359656	+	0.359656i
$929$		−	1639.43i		−	1.76473i	−0.470568	−	0.882364i	$-0.655951\pi$
$929$		−	1639.43i		−	1.76473i	0.470568	−	0.882364i	$-0.344049\pi$
$930$	882.991	−	1487.31i	0.949453	−	1.59926i
$931$	474.033			0.509166
$932$	1479.57	+	1479.57i	1.58753	+	1.58753i
$933$	−512.268	+	512.268i	−0.549055	+	0.549055i
$934$			365.061i			0.390857i
$935$	−450.273	+	114.799i	−0.481575	+	0.122780i
$936$	−268.931			−0.287319
$937$	−141.600	−	141.600i	−0.151121	−	0.151121i	0.627498	−	0.778618i	$-0.284079\pi$
$937$	−141.600	−	141.600i	−0.151121	−	0.151121i	−0.778618	+	0.627498i	$0.784079\pi$
$938$	−356.900	+	356.900i	−0.380491	+	0.380491i
$939$			332.956i			0.354586i
$940$	654.627	+	2567.61i	0.696412	+	2.73150i
$941$	1074.74			1.14212			0.571062	−	0.820907i	$-0.306531\pi$
$941$	1074.74			1.14212			0.571062	+	0.820907i	$0.306531\pi$
$942$	660.639	+	660.639i	0.701315	+	0.701315i
$943$	−718.405	+	718.405i	−0.761829	+	0.761829i
$944$			2.87502i			0.00304558i
$945$	591.023	+	350.880i	0.625421	+	0.371301i
$946$	−154.898			−0.163740
$947$	−1127.43	−	1127.43i	−1.19053	−	1.19053i	−0.976919	−	0.213609i	$-0.931478\pi$
$947$	−1127.43	−	1127.43i	−1.19053	−	1.19053i	−0.213609	−	0.976919i	$-0.568522\pi$
$948$	619.827	−	619.827i	0.653826	−	0.653826i
$949$		−	1429.38i		−	1.50619i
$950$	1351.73	+	397.674i	1.42287	+	0.418604i
$951$	−790.166			−0.830879
$952$	−712.514	−	712.514i	−0.748439	−	0.748439i
$953$	99.4706	−	99.4706i	0.104376	−	0.104376i	−0.652990	−	0.757366i	$-0.726486\pi$
$953$	99.4706	−	99.4706i	0.104376	−	0.104376i	0.757366	+	0.652990i	$0.226486\pi$
$954$		−	671.204i		−	0.703568i
$955$	173.965	−	293.028i	0.182163	−	0.306836i
$956$	1301.53			1.36144
$957$	−80.0040	−	80.0040i	−0.0835988	−	0.0835988i
$958$	936.801	−	936.801i	0.977871	−	0.977871i
$959$		−	313.153i		−	0.326541i
$960$	−1210.31	+	308.576i	−1.26074	+	0.321433i
$961$	1036.41			1.07847
$962$	−99.4750	−	99.4750i	−0.103404	−	0.103404i
$963$	172.643	−	172.643i	0.179276	−	0.179276i
$964$			618.472i			0.641568i
$965$	−98.4287	−	386.062i	−0.101999	−	0.400065i
$966$	−601.013			−0.622167
$967$	1260.15	+	1260.15i	1.30315	+	1.30315i	0.926256	+	0.376896i	$0.123008\pi$
$967$	1260.15	+	1260.15i	1.30315	+	1.30315i	0.376896	+	0.926256i	$0.376992\pi$
$968$	−59.7748	+	59.7748i	−0.0617508	+	0.0617508i
$969$			1177.13i			1.21479i
$970$	−625.531	−	371.367i	−0.644878	−	0.382852i
$971$	1148.23			1.18252			0.591261	−	0.806481i	$-0.298630\pi$
$971$	1148.23			1.18252			0.591261	+	0.806481i	$0.298630\pi$
$972$	743.787	+	743.787i	0.765213	+	0.765213i
$973$	−520.275	+	520.275i	−0.534713	+	0.534713i
$974$		−	966.900i		−	0.992711i
$975$	571.043	−	311.425i	0.585685	−	0.319410i
$976$	−11.8597			−0.0121513
$977$	145.709	+	145.709i	0.149139	+	0.149139i	0.777733	−	0.628594i	$-0.216369\pi$
$977$	145.709	+	145.709i	0.149139	+	0.149139i	−0.628594	+	0.777733i	$0.716369\pi$
$978$	−269.480	+	269.480i	−0.275542	+	0.275542i
$979$			381.099i			0.389274i
$980$	441.710	−	744.018i	0.450725	−	0.759202i
$981$	314.724			0.320820
$982$	259.083	+	259.083i	0.263832	+	0.263832i
$983$	−562.675	+	562.675i	−0.572406	+	0.572406i	−0.932800	−	0.360394i	$-0.882642\pi$
$983$	−562.675	+	562.675i	−0.572406	+	0.572406i	0.360394	+	0.932800i	$0.382642\pi$
$984$		−	1130.18i		−	1.14855i
$985$	419.975	−	107.075i	0.426371	−	0.108706i
$986$	1282.48			1.30069
$987$	659.663	+	659.663i	0.668351	+	0.668351i
$988$	−855.288	+	855.288i	−0.865676	+	0.865676i
$989$		−	240.487i		−	0.243162i
$990$	42.6528	+	167.295i	0.0430836	+	0.168985i
$991$	−1445.80			−1.45893			−0.729464	−	0.684019i	$-0.760231\pi$
$991$	−1445.80			−1.45893			−0.729464	+	0.684019i	$0.760231\pi$
$992$	−1050.27	−	1050.27i	−1.05874	−	1.05874i
$993$	−210.961	+	210.961i	−0.212449	+	0.212449i
$994$		−	1002.58i		−	1.00863i
$995$	−1254.45	−	744.742i	−1.26075	−	0.748484i
$996$	−983.532			−0.987482
$997$	273.932	+	273.932i	0.274757	+	0.274757i	0.831012	−	0.556255i	$-0.187762\pi$
$997$	273.932	+	273.932i	0.274757	+	0.274757i	−0.556255	+	0.831012i	$0.687762\pi$
$998$	−781.639	+	781.639i	−0.783206	+	0.783206i
$999$			118.396i			0.118515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.3.f.a.12.10	✓	20
3.2	odd	2		495.3.j.a.397.1		20
5.2	odd	4		275.3.f.b.243.1		20
5.3	odd	4	inner	55.3.f.a.23.10	yes	20
5.4	even	2		275.3.f.b.232.1		20
15.8	even	4		495.3.j.a.298.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.f.a.12.10	✓	20	1.1	even	1	trivial
55.3.f.a.23.10	yes	20	5.3	odd	4	inner
275.3.f.b.232.1		20	5.4	even	2
275.3.f.b.243.1		20	5.2	odd	4
495.3.j.a.298.1		20	15.8	even	4
495.3.j.a.397.1		20	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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.27868 + 2.27868i) q^{2} +(-1.69843 + 1.69843i) q^{3} +6.38475i q^{4} +(2.55248 - 4.29940i) q^{5} -7.74034 q^{6} +(-3.30878 - 3.30878i) q^{7} +(-5.43407 + 5.43407i) q^{8} +3.23068i q^{9} +(15.6132 - 3.98068i) q^{10} +3.31662 q^{11} +(-10.8440 - 10.8440i) q^{12} +(7.65935 - 7.65935i) q^{13} -15.0793i q^{14} +(2.96703 + 11.6374i) q^{15} +0.773991 q^{16} +(-19.8139 - 19.8139i) q^{17} +(-7.36168 + 7.36168i) q^{18} +17.4895i q^{19} +(27.4506 + 16.2969i) q^{20} +11.2395 q^{21} +(7.55752 + 7.55752i) q^{22} +(-11.7334 + 11.7334i) q^{23} -18.4588i q^{24} +(-11.9697 - 21.9483i) q^{25} +34.9064 q^{26} +(-20.7729 - 20.7729i) q^{27} +(21.1258 - 21.1258i) q^{28} +14.2026i q^{29} +(-19.7571 + 33.2789i) q^{30} -44.6924 q^{31} +(23.5000 + 23.5000i) q^{32} +(-5.63305 + 5.63305i) q^{33} -90.2989i q^{34} +(-22.6714 + 5.78020i) q^{35} -20.6271 q^{36} +(-2.84977 - 2.84977i) q^{37} +(-39.8529 + 39.8529i) q^{38} +26.0177i q^{39} +(9.49291 + 37.2336i) q^{40} +61.2271 q^{41} +(25.6111 + 25.6111i) q^{42} +(-10.2480 + 10.2480i) q^{43} +21.1758i q^{44} +(13.8900 + 8.24624i) q^{45} -53.4734 q^{46} +(58.6916 + 58.6916i) q^{47} +(-1.31457 + 1.31457i) q^{48} -27.1039i q^{49} +(22.7379 - 77.2881i) q^{50} +67.3049 q^{51} +(48.9030 + 48.9030i) q^{52} +(-45.5877 + 45.5877i) q^{53} -94.6697i q^{54} +(8.46561 - 14.2595i) q^{55} +35.9603 q^{56} +(-29.7047 - 29.7047i) q^{57} +(-32.3632 + 32.3632i) q^{58} +3.71455i q^{59} +(-74.3020 + 18.9437i) q^{60} -15.3228 q^{61} +(-101.840 - 101.840i) q^{62} +(10.6896 - 10.6896i) q^{63} +104.002i q^{64} +(-13.3803 - 52.4809i) q^{65} -25.6718 q^{66} +(-23.6682 - 23.6682i) q^{67} +(126.507 - 126.507i) q^{68} -39.8568i q^{69} +(-64.8320 - 38.4896i) q^{70} +66.4871 q^{71} +(-17.5557 - 17.5557i) q^{72} +(93.3093 - 93.3093i) q^{73} -12.9874i q^{74} +(57.6073 + 16.9478i) q^{75} -111.666 q^{76} +(-10.9740 - 10.9740i) q^{77} +(-59.2860 + 59.2860i) q^{78} +57.1583i q^{79} +(1.97559 - 3.32770i) q^{80} +41.4866 q^{81} +(139.517 + 139.517i) q^{82} +(45.3490 - 45.3490i) q^{83} +71.7612i q^{84} +(-135.762 + 34.6133i) q^{85} -46.7036 q^{86} +(-24.1221 - 24.1221i) q^{87} +(-18.0228 + 18.0228i) q^{88} +114.906i q^{89} +(12.8603 + 50.4413i) q^{90} -50.6863 q^{91} +(-74.9150 - 74.9150i) q^{92} +(75.9069 - 75.9069i) q^{93} +267.479i q^{94} +(75.1944 + 44.6415i) q^{95} -79.8260 q^{96} +(-31.9248 - 31.9248i) q^{97} +(61.7610 - 61.7610i) q^{98} +10.7150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 8 q^{6} + 12 q^{8} + 12 q^{10} - 16 q^{12} + 4 q^{13} - 20 q^{15} - 16 q^{16} + 24 q^{17} - 24 q^{18} - 8 q^{20} - 64 q^{21} - 86 q^{23} + 90 q^{25} + 96 q^{26} - 50 q^{27}+ \cdots + 620 q^{98}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 8 * q^5 - 8 * q^6 + 12 * q^8 + 12 * q^10 - 16 * q^12 + 4 * q^13 - 20 * q^15 - 16 * q^16 + 24 * q^17 - 24 * q^18 - 8 * q^20 - 64 * q^21 - 86 * q^23 + 90 * q^25 + 96 * q^26 - 50 * q^27 + 76 * q^28 - 56 * q^30 - 40 * q^31 + 184 * q^32 - 22 * q^33 - 60 * q^35 - 168 * q^36 - 126 * q^37 + 184 * q^38 + 64 * q^40 - 56 * q^41 + 32 * q^42 - 24 * q^43 + 278 * q^45 + 168 * q^46 + 156 * q^47 + 8 * q^48 - 352 * q^50 + 304 * q^51 - 100 * q^52 - 52 * q^53 + 66 * q^55 + 216 * q^56 - 80 * q^57 - 344 * q^58 - 224 * q^60 - 120 * q^61 - 540 * q^62 + 388 * q^63 - 56 * q^65 - 242 * q^67 + 204 * q^68 + 112 * q^70 - 204 * q^71 + 612 * q^72 - 228 * q^73 - 116 * q^75 - 504 * q^76 - 880 * q^78 + 640 * q^80 + 152 * q^81 + 256 * q^82 + 464 * q^83 - 532 * q^85 - 128 * q^86 + 496 * q^87 - 264 * q^88 - 112 * q^90 - 96 * q^91 - 168 * q^92 + 346 * q^93 + 508 * q^95 - 112 * q^96 + 290 * q^97 + 620 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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