LMFDB - Embedded newform 78.3.f.a.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,3,Mod(31,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("78.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	78.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:	$2.12534606201$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
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			73.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	78.73
Dual form			78.3.f.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(1.26795 + 1.26795i) q^{5} +(1.73205 + 1.73205i) q^{6} +(0.732051 - 0.732051i) q^{7} +(-2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(1.26795 + 1.26795i) q^{5} +(1.73205 + 1.73205i) q^{6} +(0.732051 - 0.732051i) q^{7} +(-2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +2.53590i q^{10} +(-1.73205 + 1.73205i) q^{11} +3.46410i q^{12} +(-3.92820 - 12.3923i) q^{13} +1.46410 q^{14} +(2.19615 + 2.19615i) q^{15} -4.00000 q^{16} +5.32051i q^{17} +(3.00000 + 3.00000i) q^{18} +(-14.7321 - 14.7321i) q^{19} +(-2.53590 + 2.53590i) q^{20} +(1.26795 - 1.26795i) q^{21} -3.46410 q^{22} +5.32051i q^{23} +(-3.46410 + 3.46410i) q^{24} -21.7846i q^{25} +(8.46410 - 16.3205i) q^{26} +5.19615 q^{27} +(1.46410 + 1.46410i) q^{28} +4.14359 q^{29} +4.39230i q^{30} +(-24.9808 - 24.9808i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-3.00000 + 3.00000i) q^{33} +(-5.32051 + 5.32051i) q^{34} +1.85641 q^{35} +6.00000i q^{36} +(-3.14359 + 3.14359i) q^{37} -29.4641i q^{38} +(-6.80385 - 21.4641i) q^{39} -5.07180 q^{40} +(44.4449 + 44.4449i) q^{41} +2.53590 q^{42} +37.1769i q^{43} +(-3.46410 - 3.46410i) q^{44} +(3.80385 + 3.80385i) q^{45} +(-5.32051 + 5.32051i) q^{46} +(-30.8038 + 30.8038i) q^{47} -6.92820 q^{48} +47.9282i q^{49} +(21.7846 - 21.7846i) q^{50} +9.21539i q^{51} +(24.7846 - 7.85641i) q^{52} +57.7128 q^{53} +(5.19615 + 5.19615i) q^{54} -4.39230 q^{55} +2.92820i q^{56} +(-25.5167 - 25.5167i) q^{57} +(4.14359 + 4.14359i) q^{58} +(-66.6218 + 66.6218i) q^{59} +(-4.39230 + 4.39230i) q^{60} +103.426 q^{61} -49.9615i q^{62} +(2.19615 - 2.19615i) q^{63} -8.00000i q^{64} +(10.7321 - 20.6936i) q^{65} -6.00000 q^{66} +(46.6936 + 46.6936i) q^{67} -10.6410 q^{68} +9.21539i q^{69} +(1.85641 + 1.85641i) q^{70} +(-26.9090 - 26.9090i) q^{71} +(-6.00000 + 6.00000i) q^{72} +(5.67949 - 5.67949i) q^{73} -6.28719 q^{74} -37.7321i q^{75} +(29.4641 - 29.4641i) q^{76} +2.53590i q^{77} +(14.6603 - 28.2679i) q^{78} +4.21024 q^{79} +(-5.07180 - 5.07180i) q^{80} +9.00000 q^{81} +88.8897i q^{82} +(-109.799 - 109.799i) q^{83} +(2.53590 + 2.53590i) q^{84} +(-6.74613 + 6.74613i) q^{85} +(-37.1769 + 37.1769i) q^{86} +7.17691 q^{87} -6.92820i q^{88} +(-19.5167 + 19.5167i) q^{89} +7.60770i q^{90} +(-11.9474 - 6.19615i) q^{91} -10.6410 q^{92} +(-43.2679 - 43.2679i) q^{93} -61.6077 q^{94} -37.3590i q^{95} +(-6.92820 - 6.92820i) q^{96} +(4.03332 + 4.03332i) q^{97} +(-47.9282 + 47.9282i) q^{98} +(-5.19615 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 12 q^{5} - 4 q^{7} - 8 q^{8} + 12 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 12 * q^5 - 4 * q^7 - 8 * q^8 + 12 * q^9	$ 4 q + 4 q^{2} + 12 q^{5} - 4 q^{7} - 8 q^{8} + 12 q^{9} + 12 q^{13} - 8 q^{14} - 12 q^{15} - 16 q^{16} + 12 q^{18} - 52 q^{19} - 24 q^{20} + 12 q^{21} + 20 q^{26} - 8 q^{28} + 72 q^{29} + 4 q^{31} - 16 q^{32} - 12 q^{33} + 48 q^{34} - 48 q^{35} - 68 q^{37} - 48 q^{39} - 48 q^{40} + 60 q^{41} + 24 q^{42} + 36 q^{45} + 48 q^{46} - 144 q^{47} + 4 q^{50} + 16 q^{52} + 120 q^{53} + 24 q^{55} - 12 q^{57} + 72 q^{58} - 24 q^{59} + 24 q^{60} + 192 q^{61} - 12 q^{63} + 36 q^{65} - 24 q^{66} - 28 q^{67} + 96 q^{68} - 48 q^{70} + 24 q^{71} - 24 q^{72} + 92 q^{73} - 136 q^{74} + 104 q^{76} + 24 q^{78} - 288 q^{79} - 48 q^{80} + 36 q^{81} - 72 q^{83} + 24 q^{84} + 264 q^{85} - 24 q^{86} - 96 q^{87} + 12 q^{89} - 124 q^{91} + 96 q^{92} - 180 q^{93} - 288 q^{94} - 164 q^{97} - 164 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 12 * q^5 - 4 * q^7 - 8 * q^8 + 12 * q^9 + 12 * q^13 - 8 * q^14 - 12 * q^15 - 16 * q^16 + 12 * q^18 - 52 * q^19 - 24 * q^20 + 12 * q^21 + 20 * q^26 - 8 * q^28 + 72 * q^29 + 4 * q^31 - 16 * q^32 - 12 * q^33 + 48 * q^34 - 48 * q^35 - 68 * q^37 - 48 * q^39 - 48 * q^40 + 60 * q^41 + 24 * q^42 + 36 * q^45 + 48 * q^46 - 144 * q^47 + 4 * q^50 + 16 * q^52 + 120 * q^53 + 24 * q^55 - 12 * q^57 + 72 * q^58 - 24 * q^59 + 24 * q^60 + 192 * q^61 - 12 * q^63 + 36 * q^65 - 24 * q^66 - 28 * q^67 + 96 * q^68 - 48 * q^70 + 24 * q^71 - 24 * q^72 + 92 * q^73 - 136 * q^74 + 104 * q^76 + 24 * q^78 - 288 * q^79 - 48 * q^80 + 36 * q^81 - 72 * q^83 + 24 * q^84 + 264 * q^85 - 24 * q^86 - 96 * q^87 + 12 * q^89 - 124 * q^91 + 96 * q^92 - 180 * q^93 - 288 * q^94 - 164 * q^97 - 164 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$			2.00000i			0.500000i
$5$	1.26795	+	1.26795i	0.253590	+	0.253590i	0.822441	−	0.568851i	$-0.192612\pi$
$5$	1.26795	+	1.26795i	0.253590	+	0.253590i	−0.568851	+	0.822441i	$0.692612\pi$
$6$	1.73205	+	1.73205i	0.288675	+	0.288675i
$7$	0.732051	−	0.732051i	0.104579	−	0.104579i	−0.652881	−	0.757460i	$-0.726440\pi$
$7$	0.732051	−	0.732051i	0.104579	−	0.104579i	0.757460	+	0.652881i	$0.226440\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	3.00000			0.333333
$10$			2.53590i			0.253590i
$11$	−1.73205	+	1.73205i	−0.157459	+	0.157459i	−0.781440	−	0.623981i	$-0.785514\pi$
$11$	−1.73205	+	1.73205i	−0.157459	+	0.157459i	0.623981	+	0.781440i	$0.285514\pi$
$12$			3.46410i			0.288675i
$13$	−3.92820	−	12.3923i	−0.302169	−	0.953254i
$13$	−3.92820	−	12.3923i	−0.302169	−	0.953254i
$14$	1.46410			0.104579
$15$	2.19615	+	2.19615i	0.146410	+	0.146410i
$16$	−4.00000			−0.250000
$17$			5.32051i			0.312971i	0.987680	+	0.156486i	$0.0500165\pi$
$17$			5.32051i			0.312971i	−0.987680	+	0.156486i	$0.949984\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$	−14.7321	−	14.7321i	−0.775371	−	0.775371i	0.203669	−	0.979040i	$-0.434713\pi$
$19$	−14.7321	−	14.7321i	−0.775371	−	0.775371i	−0.979040	+	0.203669i	$0.934713\pi$
$20$	−2.53590	+	2.53590i	−0.126795	+	0.126795i
$21$	1.26795	−	1.26795i	0.0603785	−	0.0603785i
$22$	−3.46410			−0.157459
$23$			5.32051i			0.231326i	0.993288	+	0.115663i	$0.0368993\pi$
$23$			5.32051i			0.231326i	−0.993288	+	0.115663i	$0.963101\pi$
$24$	−3.46410	+	3.46410i	−0.144338	+	0.144338i
$25$		−	21.7846i		−	0.871384i
$26$	8.46410	−	16.3205i	0.325542	−	0.627712i
$27$	5.19615			0.192450
$28$	1.46410	+	1.46410i	0.0522893	+	0.0522893i
$29$	4.14359			0.142883			0.0714413	−	0.997445i	$-0.477240\pi$
$29$	4.14359			0.142883			0.0714413	+	0.997445i	$0.477240\pi$
$30$			4.39230i			0.146410i
$31$	−24.9808	−	24.9808i	−0.805831	−	0.805831i	0.178169	−	0.984000i	$-0.442983\pi$
$31$	−24.9808	−	24.9808i	−0.805831	−	0.805831i	−0.984000	+	0.178169i	$0.942983\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−3.00000	+	3.00000i	−0.0909091	+	0.0909091i
$34$	−5.32051	+	5.32051i	−0.156486	+	0.156486i
$35$	1.85641			0.0530402
$36$			6.00000i			0.166667i
$37$	−3.14359	+	3.14359i	−0.0849620	+	0.0849620i	−0.748311	−	0.663349i	$-0.769135\pi$
$37$	−3.14359	+	3.14359i	−0.0849620	+	0.0849620i	0.663349	+	0.748311i	$0.269135\pi$
$38$		−	29.4641i		−	0.775371i
$39$	−6.80385	−	21.4641i	−0.174458	−	0.550362i
$40$	−5.07180			−0.126795
$41$	44.4449	+	44.4449i	1.08402	+	1.08402i	0.996130	+	0.0878910i	$0.0280127\pi$
$41$	44.4449	+	44.4449i	1.08402	+	1.08402i	0.0878910	+	0.996130i	$0.471987\pi$
$42$	2.53590			0.0603785
$43$			37.1769i			0.864579i	0.901735	+	0.432290i	$0.142294\pi$
$43$			37.1769i			0.864579i	−0.901735	+	0.432290i	$0.857706\pi$
$44$	−3.46410	−	3.46410i	−0.0787296	−	0.0787296i
$45$	3.80385	+	3.80385i	0.0845299	+	0.0845299i
$46$	−5.32051	+	5.32051i	−0.115663	+	0.115663i
$47$	−30.8038	+	30.8038i	−0.655401	+	0.655401i	−0.954288	−	0.298887i	$-0.903385\pi$
$47$	−30.8038	+	30.8038i	−0.655401	+	0.655401i	0.298887	+	0.954288i	$0.403385\pi$
$48$	−6.92820			−0.144338
$49$			47.9282i			0.978127i
$50$	21.7846	−	21.7846i	0.435692	−	0.435692i
$51$			9.21539i			0.180694i
$52$	24.7846	−	7.85641i	0.476627	−	0.151085i
$53$	57.7128			1.08892			0.544460	−	0.838786i	$-0.316734\pi$
$53$	57.7128			1.08892			0.544460	+	0.838786i	$0.316734\pi$
$54$	5.19615	+	5.19615i	0.0962250	+	0.0962250i
$55$	−4.39230			−0.0798601
$56$			2.92820i			0.0522893i
$57$	−25.5167	−	25.5167i	−0.447661	−	0.447661i
$58$	4.14359	+	4.14359i	0.0714413	+	0.0714413i
$59$	−66.6218	+	66.6218i	−1.12918	+	1.12918i	−0.138872	+	0.990310i	$0.544348\pi$
$59$	−66.6218	+	66.6218i	−1.12918	+	1.12918i	−0.990310	+	0.138872i	$0.955652\pi$
$60$	−4.39230	+	4.39230i	−0.0732051	+	0.0732051i
$61$	103.426			1.69550			0.847751	−	0.530394i	$-0.177956\pi$
$61$	103.426			1.69550			0.847751	+	0.530394i	$0.177956\pi$
$62$		−	49.9615i		−	0.805831i
$63$	2.19615	−	2.19615i	0.0348596	−	0.0348596i
$64$		−	8.00000i		−	0.125000i
$65$	10.7321	−	20.6936i	0.165108	−	0.318363i
$66$	−6.00000			−0.0909091
$67$	46.6936	+	46.6936i	0.696919	+	0.696919i	0.963745	−	0.266826i	$-0.0859748\pi$
$67$	46.6936	+	46.6936i	0.696919	+	0.696919i	−0.266826	+	0.963745i	$0.585975\pi$
$68$	−10.6410			−0.156486
$69$			9.21539i			0.133556i
$70$	1.85641	+	1.85641i	0.0265201	+	0.0265201i
$71$	−26.9090	−	26.9090i	−0.379000	−	0.379000i	0.491742	−	0.870741i	$-0.336360\pi$
$71$	−26.9090	−	26.9090i	−0.379000	−	0.379000i	−0.870741	+	0.491742i	$0.836360\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	5.67949	−	5.67949i	0.0778013	−	0.0778013i	−0.667135	−	0.744937i	$-0.732480\pi$
$73$	5.67949	−	5.67949i	0.0778013	−	0.0778013i	0.744937	+	0.667135i	$0.232480\pi$
$74$	−6.28719			−0.0849620
$75$		−	37.7321i		−	0.503094i
$76$	29.4641	−	29.4641i	0.387686	−	0.387686i
$77$			2.53590i			0.0329337i
$78$	14.6603	−	28.2679i	0.187952	−	0.362410i
$79$	4.21024			0.0532941			0.0266471	−	0.999645i	$-0.491517\pi$
$79$	4.21024			0.0532941			0.0266471	+	0.999645i	$0.491517\pi$
$80$	−5.07180	−	5.07180i	−0.0633975	−	0.0633975i
$81$	9.00000			0.111111
$82$			88.8897i			1.08402i
$83$	−109.799	−	109.799i	−1.32288	−	1.32288i	−0.911438	−	0.411438i	$-0.865027\pi$
$83$	−109.799	−	109.799i	−1.32288	−	1.32288i	−0.411438	−	0.911438i	$-0.634973\pi$
$84$	2.53590	+	2.53590i	0.0301893	+	0.0301893i
$85$	−6.74613	+	6.74613i	−0.0793663	+	0.0793663i
$86$	−37.1769	+	37.1769i	−0.432290	+	0.432290i
$87$	7.17691			0.0824933
$88$		−	6.92820i		−	0.0787296i
$89$	−19.5167	+	19.5167i	−0.219288	+	0.219288i	−0.808198	−	0.588910i	$-0.799557\pi$
$89$	−19.5167	+	19.5167i	−0.219288	+	0.219288i	0.588910	+	0.808198i	$0.299557\pi$
$90$			7.60770i			0.0845299i
$91$	−11.9474	−	6.19615i	−0.131291	−	0.0680896i
$92$	−10.6410			−0.115663
$93$	−43.2679	−	43.2679i	−0.465247	−	0.465247i
$94$	−61.6077			−0.655401
$95$		−	37.3590i		−	0.393252i
$96$	−6.92820	−	6.92820i	−0.0721688	−	0.0721688i
$97$	4.03332	+	4.03332i	0.0415806	+	0.0415806i	0.727591	−	0.686011i	$-0.240640\pi$
$97$	4.03332	+	4.03332i	0.0415806	+	0.0415806i	−0.686011	+	0.727591i	$0.740640\pi$
$98$	−47.9282	+	47.9282i	−0.489063	+	0.489063i
$99$	−5.19615	+	5.19615i	−0.0524864	+	0.0524864i
$100$	43.5692			0.435692
$101$		−	111.464i		−	1.10360i	−0.833975	−	0.551802i	$-0.813940\pi$
$101$		−	111.464i		−	1.10360i	0.833975	−	0.551802i	$-0.186060\pi$
$102$	−9.21539	+	9.21539i	−0.0903470	+	0.0903470i
$103$		−	71.3205i		−	0.692432i	−0.938155	−	0.346216i	$-0.887466\pi$
$103$		−	71.3205i		−	0.692432i	0.938155	−	0.346216i	$-0.112534\pi$
$104$	32.6410	+	16.9282i	0.313856	+	0.162771i
$105$	3.21539			0.0306228
$106$	57.7128	+	57.7128i	0.544460	+	0.544460i
$107$	−116.536			−1.08912			−0.544560	−	0.838722i	$-0.683303\pi$
$107$	−116.536			−1.08912			−0.544560	+	0.838722i	$0.683303\pi$
$108$			10.3923i			0.0962250i
$109$	−109.315	−	109.315i	−1.00289	−	1.00289i	−0.999996	−	0.00289735i	$-0.999078\pi$
$109$	−109.315	−	109.315i	−1.00289	−	1.00289i	−0.00289735	−	0.999996i	$-0.500922\pi$
$110$	−4.39230	−	4.39230i	−0.0399300	−	0.0399300i
$111$	−5.44486	+	5.44486i	−0.0490528	+	0.0490528i
$112$	−2.92820	+	2.92820i	−0.0261447	+	0.0261447i
$113$	148.277			1.31218			0.656092	−	0.754681i	$-0.272208\pi$
$113$	148.277			1.31218			0.656092	+	0.754681i	$0.272208\pi$
$114$		−	51.0333i		−	0.447661i
$115$	−6.74613	+	6.74613i	−0.0586620	+	0.0586620i
$116$			8.28719i			0.0714413i
$117$	−11.7846	−	37.1769i	−0.100723	−	0.317751i
$118$	−133.244			−1.12918
$119$	3.89488	+	3.89488i	0.0327301	+	0.0327301i
$120$	−8.78461			−0.0732051
$121$			115.000i			0.950413i
$122$	103.426	+	103.426i	0.847751	+	0.847751i
$123$	76.9808	+	76.9808i	0.625860	+	0.625860i
$124$	49.9615	−	49.9615i	0.402916	−	0.402916i
$125$	59.3205	−	59.3205i	0.474564	−	0.474564i
$126$	4.39230			0.0348596
$127$			70.0385i			0.551484i	0.961232	+	0.275742i	$0.0889236\pi$
$127$			70.0385i			0.551484i	−0.961232	+	0.275742i	$0.911076\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			64.3923i			0.499165i
$130$	31.4256	−	9.96152i	0.241736	−	0.0766271i
$131$	238.890			1.82359			0.911793	−	0.410650i	$-0.134698\pi$
$131$	238.890			1.82359			0.911793	+	0.410650i	$0.134698\pi$
$132$	−6.00000	−	6.00000i	−0.0454545	−	0.0454545i
$133$	−21.5692			−0.162175
$134$			93.3872i			0.696919i
$135$	6.58846	+	6.58846i	0.0488034	+	0.0488034i
$136$	−10.6410	−	10.6410i	−0.0782428	−	0.0782428i
$137$	−91.9474	+	91.9474i	−0.671149	+	0.671149i	−0.957981	−	0.286832i	$-0.907398\pi$
$137$	−91.9474	+	91.9474i	−0.671149	+	0.671149i	0.286832	+	0.957981i	$0.407398\pi$
$138$	−9.21539	+	9.21539i	−0.0667782	+	0.0667782i
$139$	139.138			1.00100			0.500498	−	0.865738i	$-0.333150\pi$
$139$	139.138			1.00100			0.500498	+	0.865738i	$0.333150\pi$
$140$			3.71281i			0.0265201i
$141$	−53.3538	+	53.3538i	−0.378396	+	0.378396i
$142$		−	53.8179i		−	0.379000i
$143$	28.2679	+	14.6603i	0.197678	+	0.102519i
$144$	−12.0000			−0.0833333
$145$	5.25387	+	5.25387i	0.0362336	+	0.0362336i
$146$	11.3590			0.0778013
$147$			83.0141i			0.564722i
$148$	−6.28719	−	6.28719i	−0.0424810	−	0.0424810i
$149$	126.224	+	126.224i	0.847143	+	0.847143i	0.989776	−	0.142633i	$-0.0455567\pi$
$149$	126.224	+	126.224i	0.847143	+	0.847143i	−0.142633	+	0.989776i	$0.545557\pi$
$150$	37.7321	−	37.7321i	0.251547	−	0.251547i
$151$	124.406	−	124.406i	0.823883	−	0.823883i	−0.162779	−	0.986663i	$-0.552046\pi$
$151$	124.406	−	124.406i	0.823883	−	0.823883i	0.986663	+	0.162779i	$0.0520458\pi$
$152$	58.9282			0.387686
$153$			15.9615i			0.104324i
$154$	−2.53590	+	2.53590i	−0.0164669	+	0.0164669i
$155$		−	63.3487i		−	0.408701i
$156$	42.9282	−	13.6077i	0.275181	−	0.0872288i
$157$	−268.785			−1.71200			−0.856002	−	0.516973i	$-0.827059\pi$
$157$	−268.785			−1.71200			−0.856002	+	0.516973i	$0.827059\pi$
$158$	4.21024	+	4.21024i	0.0266471	+	0.0266471i
$159$	99.9615			0.628689
$160$		−	10.1436i		−	0.0633975i
$161$	3.89488	+	3.89488i	0.0241918	+	0.0241918i
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	−46.4449	+	46.4449i	−0.284938	+	0.284938i	−0.835075	−	0.550137i	$-0.814576\pi$
$163$	−46.4449	+	46.4449i	−0.284938	+	0.284938i	0.550137	+	0.835075i	$0.314576\pi$
$164$	−88.8897	+	88.8897i	−0.542011	+	0.542011i
$165$	−7.60770			−0.0461072
$166$		−	219.597i		−	1.32288i
$167$	−119.512	+	119.512i	−0.715638	+	0.715638i	−0.967709	−	0.252071i	$-0.918888\pi$
$167$	−119.512	+	119.512i	−0.715638	+	0.715638i	0.252071	+	0.967709i	$0.418888\pi$
$168$			5.07180i			0.0301893i
$169$	−138.138	+	97.3590i	−0.817387	+	0.576089i
$170$	−13.4923			−0.0793663
$171$	−44.1962	−	44.1962i	−0.258457	−	0.258457i
$172$	−74.3538			−0.432290
$173$		−	242.603i		−	1.40233i	−0.713001	−	0.701163i	$-0.752664\pi$
$173$		−	242.603i		−	1.40233i	0.713001	−	0.701163i	$-0.247336\pi$
$174$	7.17691	+	7.17691i	0.0412466	+	0.0412466i
$175$	−15.9474	−	15.9474i	−0.0911282	−	0.0911282i
$176$	6.92820	−	6.92820i	0.0393648	−	0.0393648i
$177$	−115.392	+	115.392i	−0.651934	+	0.651934i
$178$	−39.0333			−0.219288
$179$			26.7180i			0.149262i	0.997211	+	0.0746312i	$0.0237780\pi$
$179$			26.7180i			0.149262i	−0.997211	+	0.0746312i	$0.976222\pi$
$180$	−7.60770	+	7.60770i	−0.0422650	+	0.0422650i
$181$		−	256.144i		−	1.41516i	−0.706634	−	0.707579i	$-0.749787\pi$
$181$		−	256.144i		−	1.41516i	0.706634	−	0.707579i	$-0.250213\pi$
$182$	−5.75129	−	18.1436i	−0.0316005	−	0.0996901i
$183$	179.138			0.978899
$184$	−10.6410	−	10.6410i	−0.0578316	−	0.0578316i
$185$	−7.97183			−0.0430910
$186$		−	86.5359i		−	0.465247i
$187$	−9.21539	−	9.21539i	−0.0492802	−	0.0492802i
$188$	−61.6077	−	61.6077i	−0.327701	−	0.327701i
$189$	3.80385	−	3.80385i	0.0201262	−	0.0201262i
$190$	37.3590	−	37.3590i	0.196626	−	0.196626i
$191$	−129.282			−0.676869			−0.338435	−	0.940990i	$-0.609897\pi$
$191$	−129.282			−0.676869			−0.338435	+	0.940990i	$0.609897\pi$
$192$		−	13.8564i		−	0.0721688i
$193$	−160.282	+	160.282i	−0.830477	+	0.830477i	−0.987582	−	0.157105i	$-0.949784\pi$
$193$	−160.282	+	160.282i	−0.830477	+	0.830477i	0.157105	+	0.987582i	$0.449784\pi$
$194$			8.06664i			0.0415806i
$195$	18.5885	−	35.8423i	0.0953254	−	0.183807i
$196$	−95.8564			−0.489063
$197$	−109.268	−	109.268i	−0.554660	−	0.554660i	0.373122	−	0.927782i	$-0.378287\pi$
$197$	−109.268	−	109.268i	−0.554660	−	0.554660i	−0.927782	+	0.373122i	$0.878287\pi$
$198$	−10.3923			−0.0524864
$199$		−	25.1000i		−	0.126130i	−0.998009	−	0.0630652i	$-0.979912\pi$
$199$		−	25.1000i		−	0.126130i	0.998009	−	0.0630652i	$-0.0200876\pi$
$200$	43.5692	+	43.5692i	0.217846	+	0.217846i
$201$	80.8756	+	80.8756i	0.402366	+	0.402366i
$202$	111.464	−	111.464i	0.551802	−	0.551802i
$203$	3.03332	−	3.03332i	0.0149425	−	0.0149425i
$204$	−18.4308			−0.0903470
$205$			112.708i			0.549793i
$206$	71.3205	−	71.3205i	0.346216	−	0.346216i
$207$			15.9615i			0.0771088i
$208$	15.7128	+	49.5692i	0.0755424	+	0.238314i
$209$	51.0333			0.244179
$210$	3.21539	+	3.21539i	0.0153114	+	0.0153114i
$211$	206.718			0.979706			0.489853	−	0.871805i	$-0.337050\pi$
$211$	206.718			0.979706			0.489853	+	0.871805i	$0.337050\pi$
$212$			115.426i			0.544460i
$213$	−46.6077	−	46.6077i	−0.218815	−	0.218815i
$214$	−116.536	−	116.536i	−0.544560	−	0.544560i
$215$	−47.1384	+	47.1384i	−0.219249	+	0.219249i
$216$	−10.3923	+	10.3923i	−0.0481125	+	0.0481125i
$217$	−36.5744			−0.168546
$218$		−	218.631i		−	1.00289i
$219$	9.83717	−	9.83717i	0.0449186	−	0.0449186i
$220$		−	8.78461i		−	0.0399300i
$221$	65.9334	−	20.9000i	0.298341	−	0.0945703i
$222$	−10.8897			−0.0490528
$223$	139.412	+	139.412i	0.625164	+	0.625164i	0.946847	−	0.321683i	$-0.104249\pi$
$223$	139.412	+	139.412i	0.625164	+	0.625164i	−0.321683	+	0.946847i	$0.604249\pi$
$224$	−5.85641			−0.0261447
$225$		−	65.3538i		−	0.290461i
$226$	148.277	+	148.277i	0.656092	+	0.656092i
$227$	−97.3679	−	97.3679i	−0.428934	−	0.428934i	0.459331	−	0.888265i	$-0.348089\pi$
$227$	−97.3679	−	97.3679i	−0.428934	−	0.428934i	−0.888265	+	0.459331i	$0.848089\pi$
$228$	51.0333	−	51.0333i	0.223830	−	0.223830i
$229$	204.177	−	204.177i	0.891602	−	0.891602i	−0.103072	−	0.994674i	$-0.532867\pi$
$229$	204.177	−	204.177i	0.891602	−	0.891602i	0.994674	+	0.103072i	$0.0328671\pi$
$230$	−13.4923			−0.0586620
$231$			4.39230i			0.0190143i
$232$	−8.28719	+	8.28719i	−0.0357206	+	0.0357206i
$233$			231.962i			0.995543i	0.867308	+	0.497772i	$0.165848\pi$
$233$			231.962i			0.995543i	−0.867308	+	0.497772i	$0.834152\pi$
$234$	25.3923	−	48.9615i	0.108514	−	0.209237i
$235$	−78.1154			−0.332406
$236$	−133.244	−	133.244i	−0.564591	−	0.564591i
$237$	7.29234			0.0307694
$238$			7.78976i			0.0327301i
$239$	139.981	+	139.981i	0.585694	+	0.585694i	0.936462	−	0.350769i	$-0.114080\pi$
$239$	139.981	+	139.981i	0.585694	+	0.585694i	−0.350769	+	0.936462i	$0.614080\pi$
$240$	−8.78461	−	8.78461i	−0.0366025	−	0.0366025i
$241$	53.4589	−	53.4589i	0.221821	−	0.221821i	−0.587444	−	0.809265i	$-0.699866\pi$
$241$	53.4589	−	53.4589i	0.221821	−	0.221821i	0.809265	+	0.587444i	$0.199866\pi$
$242$	−115.000	+	115.000i	−0.475207	+	0.475207i
$243$	15.5885			0.0641500
$244$			206.851i			0.847751i
$245$	−60.7705	+	60.7705i	−0.248043	+	0.248043i
$246$			153.962i			0.625860i
$247$	−124.694	+	240.435i	−0.504832	+	0.973419i
$248$	99.9230			0.402916
$249$	−190.177	−	190.177i	−0.763763	−	0.763763i
$250$	118.641			0.474564
$251$		−	421.377i		−	1.67879i	−0.543520	−	0.839396i	$-0.682909\pi$
$251$		−	421.377i		−	1.67879i	0.543520	−	0.839396i	$-0.317091\pi$
$252$	4.39230	+	4.39230i	0.0174298	+	0.0174298i
$253$	−9.21539	−	9.21539i	−0.0364245	−	0.0364245i
$254$	−70.0385	+	70.0385i	−0.275742	+	0.275742i
$255$	−11.6846	+	11.6846i	−0.0458221	+	0.0458221i
$256$	16.0000			0.0625000
$257$			249.664i			0.971455i	0.874110	+	0.485728i	$0.161445\pi$
$257$			249.664i			0.971455i	−0.874110	+	0.485728i	$0.838555\pi$
$258$	−64.3923	+	64.3923i	−0.249583	+	0.249583i
$259$			4.60254i			0.0177704i
$260$	41.3872	+	21.4641i	0.159181	+	0.0825542i
$261$	12.4308			0.0476275
$262$	238.890	+	238.890i	0.911793	+	0.911793i
$263$	−94.8897			−0.360797			−0.180399	−	0.983594i	$-0.557739\pi$
$263$	−94.8897			−0.360797			−0.180399	+	0.983594i	$0.557739\pi$
$264$		−	12.0000i		−	0.0454545i
$265$	73.1769	+	73.1769i	0.276139	+	0.276139i
$266$	−21.5692	−	21.5692i	−0.0810873	−	0.0810873i
$267$	−33.8038	+	33.8038i	−0.126606	+	0.126606i
$268$	−93.3872	+	93.3872i	−0.348460	+	0.348460i
$269$	−208.774			−0.776113			−0.388056	−	0.921636i	$-0.626853\pi$
$269$	−208.774			−0.776113			−0.388056	+	0.921636i	$0.626853\pi$
$270$			13.1769i			0.0488034i
$271$	381.047	−	381.047i	1.40608	−	1.40608i	0.627307	−	0.778772i	$-0.284157\pi$
$271$	381.047	−	381.047i	1.40608	−	1.40608i	0.778772	−	0.627307i	$-0.215843\pi$
$272$		−	21.2820i		−	0.0782428i
$273$	−20.6936	−	10.7321i	−0.0758006	−	0.0393115i
$274$	−183.895			−0.671149
$275$	37.7321	+	37.7321i	0.137207	+	0.137207i
$276$	−18.4308			−0.0667782
$277$			68.7846i			0.248320i	0.992262	+	0.124160i	$0.0396236\pi$
$277$			68.7846i			0.248320i	−0.992262	+	0.124160i	$0.960376\pi$
$278$	139.138	+	139.138i	0.500498	+	0.500498i
$279$	−74.9423	−	74.9423i	−0.268610	−	0.268610i
$280$	−3.71281	+	3.71281i	−0.0132600	+	0.0132600i
$281$	69.6218	−	69.6218i	0.247764	−	0.247764i	−0.572288	−	0.820053i	$-0.693944\pi$
$281$	69.6218	−	69.6218i	0.247764	−	0.247764i	0.820053	+	0.572288i	$0.193944\pi$
$282$	−106.708			−0.378396
$283$			425.808i			1.50462i	0.658809	+	0.752310i	$0.271061\pi$
$283$			425.808i			1.50462i	−0.658809	+	0.752310i	$0.728939\pi$
$284$	53.8179	−	53.8179i	0.189500	−	0.189500i
$285$		−	64.7077i		−	0.227044i
$286$	13.6077	+	42.9282i	0.0475794	+	0.150099i
$287$	65.0718			0.226731
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$	260.692			0.902049
$290$			10.5077i			0.0362336i
$291$	6.98592	+	6.98592i	0.0240066	+	0.0240066i
$292$	11.3590	+	11.3590i	0.0389006	+	0.0389006i
$293$	306.042	−	306.042i	1.04451	−	1.04451i	0.0455508	−	0.998962i	$-0.485496\pi$
$293$	306.042	−	306.042i	1.04451	−	1.04451i	0.998962	−	0.0455508i	$-0.0145043\pi$
$294$	−83.0141	+	83.0141i	−0.282361	+	0.282361i
$295$	−168.946			−0.572699
$296$		−	12.5744i		−	0.0424810i
$297$	−9.00000	+	9.00000i	−0.0303030	+	0.0303030i
$298$			252.449i			0.847143i
$299$	65.9334	−	20.9000i	0.220513	−	0.0698998i
$300$	75.4641			0.251547
$301$	27.2154	+	27.2154i	0.0904166	+	0.0904166i
$302$	248.813			0.823883
$303$		−	193.061i		−	0.637167i
$304$	58.9282	+	58.9282i	0.193843	+	0.193843i
$305$	131.138	+	131.138i	0.429962	+	0.429962i
$306$	−15.9615	+	15.9615i	−0.0521618	+	0.0521618i
$307$	246.512	−	246.512i	0.802969	−	0.802969i	−0.180589	−	0.983559i	$-0.557801\pi$
$307$	246.512	−	246.512i	0.802969	−	0.802969i	0.983559	+	0.180589i	$0.0578005\pi$
$308$	−5.07180			−0.0164669
$309$		−	123.531i		−	0.399776i
$310$	63.3487	−	63.3487i	0.204351	−	0.204351i
$311$			313.377i			1.00764i	0.863808	+	0.503821i	$0.168073\pi$
$311$			313.377i			1.00764i	−0.863808	+	0.503821i	$0.831927\pi$
$312$	56.5359	+	29.3205i	0.181205	+	0.0939760i
$313$	−262.841			−0.839747			−0.419874	−	0.907583i	$-0.637926\pi$
$313$	−262.841			−0.839747			−0.419874	+	0.907583i	$0.637926\pi$
$314$	−268.785	−	268.785i	−0.856002	−	0.856002i
$315$	5.56922			0.0176801
$316$			8.42047i			0.0266471i
$317$	−148.981	−	148.981i	−0.469971	−	0.469971i	0.431934	−	0.901905i	$-0.357831\pi$
$317$	−148.981	−	148.981i	−0.469971	−	0.469971i	−0.901905	+	0.431934i	$0.857831\pi$
$318$	99.9615	+	99.9615i	0.314344	+	0.314344i
$319$	−7.17691	+	7.17691i	−0.0224982	+	0.0224982i
$320$	10.1436	−	10.1436i	0.0316987	−	0.0316987i
$321$	−201.846			−0.628804
$322$			7.78976i			0.0241918i
$323$	78.3820	−	78.3820i	0.242669	−	0.242669i
$324$			18.0000i			0.0555556i
$325$	−269.962	+	85.5744i	−0.830651	+	0.263306i
$326$	−92.8897			−0.284938
$327$	−189.340	−	189.340i	−0.579021	−	0.579021i
$328$	−177.779			−0.542011
$329$			45.1000i			0.137082i
$330$	−7.60770	−	7.60770i	−0.0230536	−	0.0230536i
$331$	−295.870	−	295.870i	−0.893869	−	0.893869i	0.101016	−	0.994885i	$-0.467791\pi$
$331$	−295.870	−	295.870i	−0.893869	−	0.893869i	−0.994885	+	0.101016i	$0.967791\pi$
$332$	219.597	−	219.597i	0.661438	−	0.661438i
$333$	−9.43078	+	9.43078i	−0.0283207	+	0.0283207i
$334$	−239.023			−0.715638
$335$			118.410i			0.353463i
$336$	−5.07180	+	5.07180i	−0.0150946	+	0.0150946i
$337$		−	48.9385i		−	0.145218i	−0.997360	−	0.0726091i	$-0.976867\pi$
$337$		−	48.9385i		−	0.145218i	0.997360	−	0.0726091i	$-0.0231325\pi$
$338$	−235.497	−	40.7795i	−0.696738	−	0.120649i
$339$	256.823			0.757590
$340$	−13.4923	−	13.4923i	−0.0396831	−	0.0396831i
$341$	86.5359			0.253771
$342$		−	88.3923i		−	0.258457i
$343$	70.9564	+	70.9564i	0.206870	+	0.206870i
$344$	−74.3538	−	74.3538i	−0.216145	−	0.216145i
$345$	−11.6846	+	11.6846i	−0.0338685	+	0.0338685i
$346$	242.603	−	242.603i	0.701163	−	0.701163i
$347$	−552.133			−1.59116			−0.795581	−	0.605847i	$-0.792834\pi$
$347$	−552.133			−1.59116			−0.795581	+	0.605847i	$0.792834\pi$
$348$			14.3538i			0.0412466i
$349$	189.210	−	189.210i	0.542150	−	0.542150i	−0.382009	−	0.924159i	$-0.624768\pi$
$349$	189.210	−	189.210i	0.542150	−	0.542150i	0.924159	+	0.382009i	$0.124768\pi$
$350$		−	31.8949i		−	0.0911282i
$351$	−20.4115	−	64.3923i	−0.0581525	−	0.183454i
$352$	13.8564			0.0393648
$353$	−51.8705	−	51.8705i	−0.146942	−	0.146942i	0.629809	−	0.776750i	$-0.283133\pi$
$353$	−51.8705	−	51.8705i	−0.146942	−	0.146942i	−0.776750	+	0.629809i	$0.783133\pi$
$354$	−230.785			−0.651934
$355$		−	68.2384i		−	0.192221i
$356$	−39.0333	−	39.0333i	−0.109644	−	0.109644i
$357$	6.74613	+	6.74613i	0.0188967	+	0.0188967i
$358$	−26.7180	+	26.7180i	−0.0746312	+	0.0746312i
$359$	−205.119	+	205.119i	−0.571363	+	0.571363i	−0.932509	−	0.361146i	$-0.882385\pi$
$359$	−205.119	+	205.119i	−0.571363	+	0.571363i	0.361146	+	0.932509i	$0.382385\pi$
$360$	−15.2154			−0.0422650
$361$			73.0666i			0.202401i
$362$	256.144	−	256.144i	0.707579	−	0.707579i
$363$			199.186i			0.548721i
$364$	12.3923	−	23.8949i	0.0340448	−	0.0656453i
$365$	14.4026			0.0394592
$366$	179.138	+	179.138i	0.489449	+	0.489449i
$367$	−351.292			−0.957200			−0.478600	−	0.878033i	$-0.658856\pi$
$367$	−351.292			−0.957200			−0.478600	+	0.878033i	$0.658856\pi$
$368$		−	21.2820i		−	0.0578316i
$369$	133.335	+	133.335i	0.361340	+	0.361340i
$370$	−7.97183	−	7.97183i	−0.0215455	−	0.0215455i
$371$	42.2487	−	42.2487i	0.113878	−	0.113878i
$372$	86.5359	−	86.5359i	0.232623	−	0.232623i
$373$	−131.836			−0.353447			−0.176724	−	0.984261i	$-0.556550\pi$
$373$	−131.836			−0.353447			−0.176724	+	0.984261i	$0.556550\pi$
$374$		−	18.4308i		−	0.0492802i
$375$	102.746	−	102.746i	0.273990	−	0.273990i
$376$		−	123.215i		−	0.327701i
$377$	−16.2769	−	51.3487i	−0.0431747	−	0.136203i
$378$	7.60770			0.0201262
$379$	−24.7987	−	24.7987i	−0.0654319	−	0.0654319i	0.673634	−	0.739065i	$-0.264733\pi$
$379$	−24.7987	−	24.7987i	−0.0654319	−	0.0654319i	−0.739065	+	0.673634i	$0.764733\pi$
$380$	74.7180			0.196626
$381$			121.310i			0.318399i
$382$	−129.282	−	129.282i	−0.338435	−	0.338435i
$383$	174.555	+	174.555i	0.455758	+	0.455758i	0.897260	−	0.441502i	$-0.145554\pi$
$383$	174.555	+	174.555i	0.455758	+	0.455758i	−0.441502	+	0.897260i	$0.645554\pi$
$384$	13.8564	−	13.8564i	0.0360844	−	0.0360844i
$385$	−3.21539	+	3.21539i	−0.00835166	+	0.00835166i
$386$	−320.564			−0.830477
$387$			111.531i			0.288193i
$388$	−8.06664	+	8.06664i	−0.0207903	+	0.0207903i
$389$			644.305i			1.65631i	0.560498	+	0.828156i	$0.310610\pi$
$389$			644.305i			1.65631i	−0.560498	+	0.828156i	$0.689390\pi$
$390$	54.4308	−	17.2539i	0.139566	−	0.0442407i
$391$	−28.3078			−0.0723985
$392$	−95.8564	−	95.8564i	−0.244532	−	0.244532i
$393$	413.769			1.05285
$394$		−	218.536i		−	0.554660i
$395$	5.33836	+	5.33836i	0.0135148	+	0.0135148i
$396$	−10.3923	−	10.3923i	−0.0262432	−	0.0262432i
$397$	432.692	−	432.692i	1.08990	−	1.08990i	0.0943673	−	0.995537i	$-0.469917\pi$
$397$	432.692	−	432.692i	1.08990	−	1.08990i	0.995537	−	0.0943673i	$-0.0300828\pi$
$398$	25.1000	−	25.1000i	0.0630652	−	0.0630652i
$399$	−37.3590			−0.0936315
$400$			87.1384i			0.217846i
$401$	−274.550	+	274.550i	−0.684663	+	0.684663i	−0.961047	−	0.276384i	$-0.910864\pi$
$401$	−274.550	+	274.550i	−0.684663	+	0.684663i	0.276384	+	0.961047i	$0.410864\pi$
$402$			161.751i			0.402366i
$403$	−211.440	+	407.699i	−0.524664	+	1.01166i
$404$	222.928			0.551802
$405$	11.4115	+	11.4115i	0.0281766	+	0.0281766i
$406$	6.06664			0.0149425
$407$		−	10.8897i		−	0.0267561i
$408$	−18.4308	−	18.4308i	−0.0451735	−	0.0451735i
$409$	76.1872	+	76.1872i	0.186277	+	0.186277i	0.794084	−	0.607808i	$-0.207951\pi$
$409$	76.1872	+	76.1872i	0.186277	+	0.186277i	−0.607808	+	0.794084i	$0.707951\pi$
$410$	−112.708	+	112.708i	−0.274897	+	0.274897i
$411$	−159.258	+	159.258i	−0.387488	+	0.387488i
$412$	142.641			0.346216
$413$			97.5411i			0.236177i
$414$	−15.9615	+	15.9615i	−0.0385544	+	0.0385544i
$415$		−	278.438i		−	0.670936i
$416$	−33.8564	+	65.2820i	−0.0813856	+	0.156928i
$417$	240.995			0.577925
$418$	51.0333	+	51.0333i	0.122089	+	0.122089i
$419$	76.8231			0.183349			0.0916743	−	0.995789i	$-0.470778\pi$
$419$	76.8231			0.183349			0.0916743	+	0.995789i	$0.470778\pi$
$420$			6.43078i			0.0153114i
$421$	117.756	+	117.756i	0.279707	+	0.279707i	0.832992	−	0.553285i	$-0.186626\pi$
$421$	117.756	+	117.756i	0.279707	+	0.279707i	−0.553285	+	0.832992i	$0.686626\pi$
$422$	206.718	+	206.718i	0.489853	+	0.489853i
$423$	−92.4115	+	92.4115i	−0.218467	+	0.218467i
$424$	−115.426	+	115.426i	−0.272230	+	0.272230i
$425$	115.905			0.272718
$426$		−	93.2154i		−	0.218815i
$427$	75.7128	−	75.7128i	0.177313	−	0.177313i
$428$		−	233.072i		−	0.544560i
$429$	48.9615	+	25.3923i	0.114129	+	0.0591895i
$430$	−94.2769			−0.219249
$431$	362.478	+	362.478i	0.841017	+	0.841017i	0.988991	−	0.147975i	$-0.0472754\pi$
$431$	362.478	+	362.478i	0.841017	+	0.841017i	−0.147975	+	0.988991i	$0.547275\pi$
$432$	−20.7846			−0.0481125
$433$			197.292i			0.455641i	0.973703	+	0.227820i	$0.0731599\pi$
$433$			197.292i			0.455641i	−0.973703	+	0.227820i	$0.926840\pi$
$434$	−36.5744	−	36.5744i	−0.0842728	−	0.0842728i
$435$	9.09996	+	9.09996i	0.0209195	+	0.0209195i
$436$	218.631	−	218.631i	0.501447	−	0.501447i
$437$	78.3820	−	78.3820i	0.179364	−	0.179364i
$438$	19.6743			0.0449186
$439$		−	272.238i		−	0.620133i	−0.950715	−	0.310067i	$-0.899649\pi$
$439$		−	272.238i		−	0.620133i	0.950715	−	0.310067i	$-0.100351\pi$
$440$	8.78461	−	8.78461i	0.0199650	−	0.0199650i
$441$			143.785i			0.326042i
$442$	86.8334	+	45.0333i	0.196456	+	0.101885i
$443$	74.7358			0.168704			0.0843519	−	0.996436i	$-0.473118\pi$
$443$	74.7358			0.168704			0.0843519	+	0.996436i	$0.473118\pi$
$444$	−10.8897	−	10.8897i	−0.0245264	−	0.0245264i
$445$	−49.4923			−0.111219
$446$			278.823i			0.625164i
$447$	218.627	+	218.627i	0.489098	+	0.489098i
$448$	−5.85641	−	5.85641i	−0.0130723	−	0.0130723i
$449$	516.224	−	516.224i	1.14972	−	1.14972i	0.163113	−	0.986607i	$-0.447847\pi$
$449$	516.224	−	516.224i	1.14972	−	1.14972i	0.986607	−	0.163113i	$-0.0521534\pi$
$450$	65.3538	−	65.3538i	0.145231	−	0.145231i
$451$	−153.962			−0.341378
$452$			296.554i			0.656092i
$453$	215.478	−	215.478i	0.475669	−	0.475669i
$454$		−	194.736i		−	0.428934i
$455$	−7.29234	−	23.0052i	−0.0160271	−	0.0505608i
$456$	102.067			0.223830
$457$	−50.9615	−	50.9615i	−0.111513	−	0.111513i	0.649149	−	0.760662i	$-0.275125\pi$
$457$	−50.9615	−	50.9615i	−0.111513	−	0.111513i	−0.760662	+	0.649149i	$0.775125\pi$
$458$	408.354			0.891602
$459$			27.6462i			0.0602313i
$460$	−13.4923	−	13.4923i	−0.0293310	−	0.0293310i
$461$	202.550	+	202.550i	0.439371	+	0.439371i	0.891800	−	0.452429i	$-0.149443\pi$
$461$	202.550	+	202.550i	0.439371	+	0.439371i	−0.452429	+	0.891800i	$0.649443\pi$
$462$	−4.39230	+	4.39230i	−0.00950715	+	0.00950715i
$463$	−223.247	+	223.247i	−0.482176	+	0.482176i	−0.905826	−	0.423650i	$-0.860749\pi$
$463$	−223.247	+	223.247i	−0.482176	+	0.482176i	0.423650	+	0.905826i	$0.360749\pi$
$464$	−16.5744			−0.0357206
$465$		−	109.723i		−	0.235964i
$466$	−231.962	+	231.962i	−0.497772	+	0.497772i
$467$		−	161.818i		−	0.346505i	−0.984877	−	0.173253i	$-0.944572\pi$
$467$		−	161.818i		−	0.346505i	0.984877	−	0.173253i	$-0.0554277\pi$
$468$	74.3538	−	23.5692i	0.158876	−	0.0503616i
$469$	68.3641			0.145766
$470$	−78.1154	−	78.1154i	−0.166203	−	0.166203i
$471$	−465.549			−0.988426
$472$		−	266.487i		−	0.564591i
$473$	−64.3923	−	64.3923i	−0.136136	−	0.136136i
$474$	7.29234	+	7.29234i	0.0153847	+	0.0153847i
$475$	−320.932	+	320.932i	−0.675646	+	0.675646i
$476$	−7.78976	+	7.78976i	−0.0163651	+	0.0163651i
$477$	173.138			0.362974
$478$			279.962i			0.585694i
$479$	−89.1295	+	89.1295i	−0.186074	+	0.186074i	−0.793996	−	0.607922i	$-0.792003\pi$
$479$	−89.1295	+	89.1295i	−0.186074	+	0.186074i	0.607922	+	0.793996i	$0.292003\pi$
$480$		−	17.5692i		−	0.0366025i
$481$	51.3050	+	26.6077i	0.106663	+	0.0553175i
$482$	106.918			0.221821
$483$	6.74613	+	6.74613i	0.0139672	+	0.0139672i
$484$	−230.000			−0.475207
$485$			10.2281i			0.0210888i
$486$	15.5885	+	15.5885i	0.0320750	+	0.0320750i
$487$	−527.440	−	527.440i	−1.08304	−	1.08304i	−0.996225	−	0.0868139i	$-0.972331\pi$
$487$	−527.440	−	527.440i	−1.08304	−	1.08304i	−0.0868139	−	0.996225i	$-0.527669\pi$
$488$	−206.851	+	206.851i	−0.423876	+	0.423876i
$489$	−80.4449	+	80.4449i	−0.164509	+	0.164509i
$490$	−121.541			−0.248043
$491$		−	700.726i		−	1.42714i	−0.700584	−	0.713570i	$-0.747077\pi$
$491$		−	700.726i		−	1.42714i	0.700584	−	0.713570i	$-0.252923\pi$
$492$	−153.962	+	153.962i	−0.312930	+	0.312930i
$493$			22.0460i			0.0447181i
$494$	−365.128	+	115.741i	−0.739126	+	0.234293i
$495$	−13.1769			−0.0266200
$496$	99.9230	+	99.9230i	0.201458	+	0.201458i
$497$	−39.3975			−0.0792705
$498$		−	380.354i		−	0.763763i
$499$	279.065	+	279.065i	0.559249	+	0.559249i	0.929094	−	0.369845i	$-0.120589\pi$
$499$	279.065	+	279.065i	0.559249	+	0.559249i	−0.369845	+	0.929094i	$0.620589\pi$
$500$	118.641	+	118.641i	0.237282	+	0.237282i
$501$	−207.000	+	207.000i	−0.413174	+	0.413174i
$502$	421.377	−	421.377i	0.839396	−	0.839396i
$503$	−23.9821			−0.0476782			−0.0238391	−	0.999716i	$-0.507589\pi$
$503$	−23.9821			−0.0476782			−0.0238391	+	0.999716i	$0.507589\pi$
$504$			8.78461i			0.0174298i
$505$	141.331	−	141.331i	0.279863	−	0.279863i
$506$		−	18.4308i		−	0.0364245i
$507$	−239.263	+	168.631i	−0.471919	+	0.332605i
$508$	−140.077			−0.275742
$509$	−287.678	−	287.678i	−0.565183	−	0.565183i	0.365592	−	0.930775i	$-0.380866\pi$
$509$	−287.678	−	287.678i	−0.565183	−	0.565183i	−0.930775	+	0.365592i	$0.880866\pi$
$510$	−23.3693			−0.0458221
$511$		−	8.31535i		−	0.0162727i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−76.5500	−	76.5500i	−0.149220	−	0.149220i
$514$	−249.664	+	249.664i	−0.485728	+	0.485728i
$515$	90.4308	−	90.4308i	0.175594	−	0.175594i
$516$	−128.785			−0.249583
$517$		−	106.708i		−	0.206398i
$518$	−4.60254	+	4.60254i	−0.00888521	+	0.00888521i
$519$		−	420.200i		−	0.809634i
$520$	19.9230	+	62.8513i	0.0383136	+	0.120868i
$521$	−921.349			−1.76842			−0.884212	−	0.467086i	$-0.845304\pi$
$521$	−921.349			−1.76842			−0.884212	+	0.467086i	$0.845304\pi$
$522$	12.4308	+	12.4308i	0.0238138	+	0.0238138i
$523$	−558.677			−1.06822			−0.534108	−	0.845416i	$-0.679352\pi$
$523$	−558.677			−1.06822			−0.534108	+	0.845416i	$0.679352\pi$
$524$			477.779i			0.911793i
$525$	−27.6218	−	27.6218i	−0.0526129	−	0.0526129i
$526$	−94.8897	−	94.8897i	−0.180399	−	0.180399i
$527$	132.910	−	132.910i	0.252202	−	0.252202i
$528$	12.0000	−	12.0000i	0.0227273	−	0.0227273i
$529$	500.692			0.946488
$530$			146.354i			0.276139i
$531$	−199.865	+	199.865i	−0.376394	+	0.376394i
$532$		−	43.1384i		−	0.0810873i
$533$	376.186	−	725.363i	0.705790	−	1.36091i
$534$	−67.6077			−0.126606
$535$	−147.762	−	147.762i	−0.276190	−	0.276190i
$536$	−186.774			−0.348460
$537$			46.2769i			0.0861767i
$538$	−208.774	−	208.774i	−0.388056	−	0.388056i
$539$	−83.0141	−	83.0141i	−0.154015	−	0.154015i
$540$	−13.1769	+	13.1769i	−0.0244017	+	0.0244017i
$541$	−101.756	+	101.756i	−0.188090	+	0.188090i	−0.794870	−	0.606780i	$-0.792461\pi$
$541$	−101.756	+	101.756i	−0.188090	+	0.188090i	0.606780	+	0.794870i	$0.292461\pi$
$542$	762.095			1.40608
$543$		−	443.654i		−	0.817042i
$544$	21.2820	−	21.2820i	0.0391214	−	0.0391214i
$545$		−	277.213i		−	0.508647i
$546$	−9.96152	−	31.4256i	−0.0182445	−	0.0575561i
$547$	301.800			0.551737			0.275868	−	0.961195i	$-0.411035\pi$
$547$	301.800			0.551737			0.275868	+	0.961195i	$0.411035\pi$
$548$	−183.895	−	183.895i	−0.335575	−	0.335575i
$549$	310.277			0.565167
$550$			75.4641i			0.137207i
$551$	−61.0436	−	61.0436i	−0.110787	−	0.110787i
$552$	−18.4308	−	18.4308i	−0.0333891	−	0.0333891i
$553$	3.08211	−	3.08211i	0.00557343	−	0.00557343i
$554$	−68.7846	+	68.7846i	−0.124160	+	0.124160i
$555$	−13.8076			−0.0248786
$556$			278.277i			0.500498i
$557$	−285.258	+	285.258i	−0.512132	+	0.512132i	−0.915179	−	0.403047i	$-0.867951\pi$
$557$	−285.258	+	285.258i	−0.512132	+	0.512132i	0.403047	+	0.915179i	$0.367951\pi$
$558$		−	149.885i		−	0.268610i
$559$	460.708	−	146.038i	0.824164	−	0.261250i
$560$	−7.42563			−0.0132600
$561$	−15.9615	−	15.9615i	−0.0284519	−	0.0284519i
$562$	139.244			0.247764
$563$		−	863.174i		−	1.53317i	−0.642143	−	0.766585i	$-0.721955\pi$
$563$		−	863.174i		−	1.53317i	0.642143	−	0.766585i	$-0.278045\pi$
$564$	−106.708	−	106.708i	−0.189198	−	0.189198i
$565$	188.008	+	188.008i	0.332757	+	0.332757i
$566$	−425.808	+	425.808i	−0.752310	+	0.752310i
$567$	6.58846	−	6.58846i	0.0116199	−	0.0116199i
$568$	107.636			0.189500
$569$		−	317.223i		−	0.557510i	−0.960362	−	0.278755i	$-0.910078\pi$
$569$		−	317.223i		−	0.557510i	0.960362	−	0.278755i	$-0.0899217\pi$
$570$	64.7077	−	64.7077i	0.113522	−	0.113522i
$571$			73.2539i			0.128290i	0.997941	+	0.0641452i	$0.0204321\pi$
$571$			73.2539i			0.128290i	−0.997941	+	0.0641452i	$0.979568\pi$
$572$	−29.3205	+	56.5359i	−0.0512596	+	0.0988390i
$573$	−223.923			−0.390791
$574$	65.0718	+	65.0718i	0.113365	+	0.113365i
$575$	115.905			0.201574
$576$		−	24.0000i		−	0.0416667i
$577$	−81.6410	−	81.6410i	−0.141492	−	0.141492i	0.632813	−	0.774305i	$-0.281900\pi$
$577$	−81.6410	−	81.6410i	−0.141492	−	0.141492i	−0.774305	+	0.632813i	$0.781900\pi$
$578$	260.692	+	260.692i	0.451025	+	0.451025i
$579$	−277.617	+	277.617i	−0.479476	+	0.479476i
$580$	−10.5077	+	10.5077i	−0.0181168	+	0.0181168i
$581$	−160.756			−0.276689
$582$			13.9718i			0.0240066i
$583$	−99.9615	+	99.9615i	−0.171461	+	0.171461i
$584$			22.7180i			0.0389006i
$585$	32.1962	−	62.0807i	0.0550362	−	0.106121i
$586$	612.084			1.04451
$587$	382.219	+	382.219i	0.651140	+	0.651140i	0.953268	−	0.302128i	$-0.0976968\pi$
$587$	382.219	+	382.219i	0.651140	+	0.651140i	−0.302128	+	0.953268i	$0.597697\pi$
$588$	−166.028			−0.282361
$589$			736.036i			1.24964i
$590$	−168.946	−	168.946i	−0.286349	−	0.286349i
$591$	−189.258	−	189.258i	−0.320233	−	0.320233i
$592$	12.5744	−	12.5744i	0.0212405	−	0.0212405i
$593$	171.355	−	171.355i	0.288963	−	0.288963i	−0.547707	−	0.836670i	$-0.684499\pi$
$593$	171.355	−	171.355i	0.288963	−	0.288963i	0.836670	+	0.547707i	$0.184499\pi$
$594$	−18.0000			−0.0303030
$595$			9.87703i			0.0166000i
$596$	−252.449	+	252.449i	−0.423572	+	0.423572i
$597$		−	43.4744i		−	0.0728215i
$598$	86.8334	+	45.0333i	0.145206	+	0.0753066i
$599$	−109.608			−0.182984			−0.0914922	−	0.995806i	$-0.529164\pi$
$599$	−109.608			−0.182984			−0.0914922	+	0.995806i	$0.529164\pi$
$600$	75.4641	+	75.4641i	0.125774	+	0.125774i
$601$	779.108			1.29635			0.648176	−	0.761491i	$-0.275532\pi$
$601$	779.108			1.29635			0.648176	+	0.761491i	$0.275532\pi$
$602$			54.4308i			0.0904166i
$603$	140.081	+	140.081i	0.232306	+	0.232306i
$604$	248.813	+	248.813i	0.411942	+	0.411942i
$605$	−145.814	+	145.814i	−0.241015	+	0.241015i
$606$	193.061	−	193.061i	0.318583	−	0.318583i
$607$	1144.40			1.88534			0.942669	−	0.333730i	$-0.108307\pi$
$607$	1144.40			1.88534			0.942669	+	0.333730i	$0.108307\pi$
$608$			117.856i			0.193843i
$609$	5.25387	−	5.25387i	0.00862704	−	0.00862704i
$610$			262.277i			0.429962i
$611$	502.734	+	260.727i	0.822806	+	0.426722i
$612$	−31.9230			−0.0521618
$613$	292.349	+	292.349i	0.476915	+	0.476915i	0.904144	−	0.427229i	$-0.140510\pi$
$613$	292.349	+	292.349i	0.476915	+	0.476915i	−0.427229	+	0.904144i	$0.640510\pi$
$614$	493.023			0.802969
$615$			195.215i			0.317423i
$616$	−5.07180	−	5.07180i	−0.00823344	−	0.00823344i
$617$	−369.391	−	369.391i	−0.598689	−	0.598689i	0.341275	−	0.939964i	$-0.389141\pi$
$617$	−369.391	−	369.391i	−0.598689	−	0.598689i	−0.939964	+	0.341275i	$0.889141\pi$
$618$	123.531	−	123.531i	0.199888	−	0.199888i
$619$	−446.070	+	446.070i	−0.720631	+	0.720631i	−0.968734	−	0.248103i	$-0.920193\pi$
$619$	−446.070	+	446.070i	−0.720631	+	0.720631i	0.248103	+	0.968734i	$0.420193\pi$
$620$	126.697			0.204351
$621$			27.6462i			0.0445188i
$622$	−313.377	+	313.377i	−0.503821	+	0.503821i
$623$			28.5744i			0.0458658i
$624$	27.2154	+	85.8564i	0.0436144	+	0.137590i
$625$	−394.184			−0.630695
$626$	−262.841	−	262.841i	−0.419874	−	0.419874i
$627$	88.3923			0.140977
$628$		−	537.569i		−	0.856002i
$629$	−16.7255	−	16.7255i	−0.0265906	−	0.0265906i
$630$	5.56922	+	5.56922i	0.00884003	+	0.00884003i
$631$	−604.406	+	604.406i	−0.957855	+	0.957855i	−0.999147	−	0.0412923i	$-0.986853\pi$
$631$	−604.406	+	604.406i	−0.957855	+	0.957855i	0.0412923	+	0.999147i	$0.486853\pi$
$632$	−8.42047	+	8.42047i	−0.0133235	+	0.0133235i
$633$	358.046			0.565634
$634$		−	297.962i		−	0.469971i
$635$	−88.8052	+	88.8052i	−0.139851	+	0.139851i
$636$			199.923i			0.314344i
$637$	593.941	−	188.272i	0.932403	−	0.295560i
$638$	−14.3538			−0.0224982
$639$	−80.7269	−	80.7269i	−0.126333	−	0.126333i
$640$	20.2872			0.0316987
$641$			1213.91i			1.89378i	0.321565	+	0.946888i	$0.395791\pi$
$641$			1213.91i			1.89378i	−0.321565	+	0.946888i	$0.604209\pi$
$642$	−201.846	−	201.846i	−0.314402	−	0.314402i
$643$	413.804	+	413.804i	0.643552	+	0.643552i	0.951427	−	0.307875i	$-0.0996178\pi$
$643$	413.804	+	413.804i	0.643552	+	0.643552i	−0.307875	+	0.951427i	$0.599618\pi$
$644$	−7.78976	+	7.78976i	−0.0120959	+	0.0120959i
$645$	−81.6462	+	81.6462i	−0.126583	+	0.126583i
$646$	156.764			0.242669
$647$		−	117.913i		−	0.182245i	−0.995840	−	0.0911227i	$-0.970954\pi$
$647$		−	117.913i		−	0.182245i	0.995840	−	0.0911227i	$-0.0290455\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$		−	230.785i		−	0.355600i
$650$	−355.536	−	184.387i	−0.546978	−	0.283673i
$651$	−63.3487			−0.0973098
$652$	−92.8897	−	92.8897i	−0.142469	−	0.142469i
$653$	−1088.62			−1.66711			−0.833553	−	0.552439i	$-0.813697\pi$
$653$	−1088.62			−1.66711			−0.833553	+	0.552439i	$0.813697\pi$
$654$		−	378.679i		−	0.579021i
$655$	302.900	+	302.900i	0.462443	+	0.462443i
$656$	−177.779	−	177.779i	−0.271005	−	0.271005i
$657$	17.0385	−	17.0385i	0.0259338	−	0.0259338i
$658$	−45.1000	+	45.1000i	−0.0685410	+	0.0685410i
$659$	1222.68			1.85535			0.927676	−	0.373387i	$-0.121804\pi$
$659$	1222.68			1.85535			0.927676	+	0.373387i	$0.121804\pi$
$660$		−	15.2154i		−	0.0230536i
$661$	−667.851	+	667.851i	−1.01036	+	1.01036i	−0.0104193	+	0.999946i	$0.503317\pi$
$661$	−667.851	+	667.851i	−1.01036	+	1.01036i	−0.999946	+	0.0104193i	$0.996683\pi$
$662$		−	591.741i		−	0.893869i
$663$	114.200	−	36.1999i	0.172247	−	0.0546002i
$664$	439.195			0.661438
$665$	−27.3487	−	27.3487i	−0.0411258	−	0.0411258i
$666$	−18.8616			−0.0283207
$667$			22.0460i			0.0330525i
$668$	−239.023	−	239.023i	−0.357819	−	0.357819i
$669$	241.468	+	241.468i	0.360939	+	0.360939i
$670$	−118.410	+	118.410i	−0.176732	+	0.176732i
$671$	−179.138	+	179.138i	−0.266972	+	0.266972i
$672$	−10.1436			−0.0150946
$673$		−	411.779i		−	0.611857i	−0.952055	−	0.305928i	$-0.901033\pi$
$673$		−	411.779i		−	0.611857i	0.952055	−	0.305928i	$-0.0989668\pi$
$674$	48.9385	−	48.9385i	0.0726091	−	0.0726091i
$675$		−	113.196i		−	0.167698i
$676$	−194.718	−	276.277i	−0.288044	−	0.408694i
$677$	−948.600			−1.40118			−0.700591	−	0.713563i	$-0.747080\pi$
$677$	−948.600			−1.40118			−0.700591	+	0.713563i	$0.747080\pi$
$678$	256.823	+	256.823i	0.378795	+	0.378795i
$679$	5.90519			0.00869690
$680$		−	26.9845i		−	0.0396831i
$681$	−168.646	−	168.646i	−0.247645	−	0.247645i
$682$	86.5359	+	86.5359i	0.126885	+	0.126885i
$683$	101.809	−	101.809i	0.149061	−	0.149061i	−0.628637	−	0.777699i	$-0.716387\pi$
$683$	101.809	−	101.809i	0.149061	−	0.149061i	0.777699	+	0.628637i	$0.216387\pi$
$684$	88.3923	−	88.3923i	0.129229	−	0.129229i
$685$	−233.169			−0.340393
$686$			141.913i			0.206870i
$687$	353.645	−	353.645i	0.514767	−	0.514767i
$688$		−	148.708i		−	0.216145i
$689$	−226.708	−	715.195i	−0.329039	−	1.03802i
$690$	−23.3693			−0.0338685
$691$	−111.135	−	111.135i	−0.160832	−	0.160832i	0.622103	−	0.782935i	$-0.286278\pi$
$691$	−111.135	−	111.135i	−0.160832	−	0.160832i	−0.782935	+	0.622103i	$0.786278\pi$
$692$	485.205			0.701163
$693$			7.60770i			0.0109779i
$694$	−552.133	−	552.133i	−0.795581	−	0.795581i
$695$	176.420	+	176.420i	0.253842	+	0.253842i
$696$	−14.3538	+	14.3538i	−0.0206233	+	0.0206233i
$697$	−236.469	+	236.469i	−0.339267	+	0.339267i
$698$	378.420			0.542150
$699$			401.769i			0.574777i
$700$	31.8949	−	31.8949i	0.0455641	−	0.0455641i
$701$			779.520i			1.11201i	0.831178	+	0.556006i	$0.187667\pi$
$701$			779.520i			1.11201i	−0.831178	+	0.556006i	$0.812333\pi$
$702$	43.9808	−	84.8038i	0.0626507	−	0.120803i
$703$	92.6232			0.131754
$704$	13.8564	+	13.8564i	0.0196824	+	0.0196824i
$705$	−135.300			−0.191915
$706$		−	103.741i		−	0.146942i
$707$	−81.5974	−	81.5974i	−0.115414	−	0.115414i
$708$	−230.785	−	230.785i	−0.325967	−	0.325967i
$709$	43.0179	−	43.0179i	0.0606740	−	0.0606740i	−0.676119	−	0.736793i	$-0.736339\pi$
$709$	43.0179	−	43.0179i	0.0606740	−	0.0606740i	0.736793	+	0.676119i	$0.236339\pi$
$710$	68.2384	−	68.2384i	0.0961104	−	0.0961104i
$711$	12.6307			0.0177647
$712$		−	78.0666i		−	0.109644i
$713$	132.910	−	132.910i	0.186410	−	0.186410i
$714$			13.4923i			0.0188967i
$715$	17.2539	+	54.4308i	0.0241313	+	0.0761270i
$716$	−53.4359			−0.0746312
$717$	242.454	+	242.454i	0.338150	+	0.338150i
$718$	−410.238			−0.571363
$719$			335.290i			0.466328i	0.972437	+	0.233164i	$0.0749078\pi$
$719$			335.290i			0.466328i	−0.972437	+	0.233164i	$0.925092\pi$
$720$	−15.2154	−	15.2154i	−0.0211325	−	0.0211325i
$721$	−52.2102	−	52.2102i	−0.0724136	−	0.0724136i
$722$	−73.0666	+	73.0666i	−0.101200	+	0.101200i
$723$	92.5936	−	92.5936i	0.128069	−	0.128069i
$724$	512.287			0.707579
$725$		−	90.2666i		−	0.124506i
$726$	−199.186	+	199.186i	−0.274361	+	0.274361i
$727$		−	537.577i		−	0.739445i	−0.929142	−	0.369723i	$-0.879453\pi$
$727$		−	537.577i		−	0.739445i	0.929142	−	0.369723i	$-0.120547\pi$
$728$	36.2872	−	11.5026i	0.0498450	−	0.0158002i
$729$	27.0000			0.0370370
$730$	14.4026	+	14.4026i	0.0197296	+	0.0197296i
$731$	−197.800			−0.270588
$732$			358.277i			0.489449i
$733$	−479.946	−	479.946i	−0.654770	−	0.654770i	0.299368	−	0.954138i	$-0.403224\pi$
$733$	−479.946	−	479.946i	−0.654770	−	0.654770i	−0.954138	+	0.299368i	$0.903224\pi$
$734$	−351.292	−	351.292i	−0.478600	−	0.478600i
$735$	−105.258	+	105.258i	−0.143208	+	0.143208i
$736$	21.2820	−	21.2820i	0.0289158	−	0.0289158i
$737$	−161.751			−0.219473
$738$			266.669i			0.361340i
$739$	512.788	−	512.788i	0.693895	−	0.693895i	−0.269192	−	0.963087i	$-0.586757\pi$
$739$	512.788	−	512.788i	0.693895	−	0.693895i	0.963087	+	0.269192i	$0.0867565\pi$
$740$		−	15.9437i		−	0.0215455i
$741$	−215.976	+	416.445i	−0.291465	+	0.562004i
$742$	84.4974			0.113878
$743$	801.509	+	801.509i	1.07875	+	1.07875i	0.996622	+	0.0821246i	$0.0261705\pi$
$743$	801.509	+	801.509i	1.07875	+	1.07875i	0.0821246	+	0.996622i	$0.473829\pi$
$744$	173.072			0.232623
$745$			320.092i			0.429654i
$746$	−131.836	−	131.836i	−0.176724	−	0.176724i
$747$	−329.396	−	329.396i	−0.440959	−	0.440959i
$748$	18.4308	−	18.4308i	0.0246401	−	0.0246401i
$749$	−85.3102	+	85.3102i	−0.113899	+	0.113899i
$750$	205.492			0.273990
$751$		−	1384.43i		−	1.84345i	−0.387849	−	0.921723i	$-0.626782\pi$
$751$		−	1384.43i		−	1.84345i	0.387849	−	0.921723i	$-0.373218\pi$
$752$	123.215	−	123.215i	0.163850	−	0.163850i
$753$		−	729.846i		−	0.969251i
$754$	35.0718	−	67.6256i	0.0465143	−	0.0896891i
$755$	315.482			0.417857
$756$	7.60770	+	7.60770i	0.0100631	+	0.0100631i
$757$	−125.836			−0.166230			−0.0831148	−	0.996540i	$-0.526487\pi$
$757$	−125.836			−0.166230			−0.0831148	+	0.996540i	$0.526487\pi$
$758$		−	49.5974i		−	0.0654319i
$759$	−15.9615	−	15.9615i	−0.0210297	−	0.0210297i
$760$	74.7180	+	74.7180i	0.0983131	+	0.0983131i
$761$	−3.55514	+	3.55514i	−0.00467166	+	0.00467166i	−0.709439	−	0.704767i	$-0.751051\pi$
$761$	−3.55514	+	3.55514i	−0.00467166	+	0.00467166i	0.704767	+	0.709439i	$0.251051\pi$
$762$	−121.310	+	121.310i	−0.159200	+	0.159200i
$763$	−160.049			−0.209762
$764$		−	258.564i		−	0.338435i
$765$	−20.2384	+	20.2384i	−0.0264554	+	0.0264554i
$766$			349.110i			0.455758i
$767$	1087.30	+	563.894i	1.41760	+	0.735194i
$768$	27.7128			0.0360844
$769$	−958.405	−	958.405i	−1.24630	−	1.24630i	−0.957342	−	0.288959i	$-0.906691\pi$
$769$	−958.405	−	958.405i	−1.24630	−	1.24630i	−0.288959	−	0.957342i	$-0.593309\pi$
$770$	−6.43078			−0.00835166
$771$			432.431i			0.560870i
$772$	−320.564	−	320.564i	−0.415238	−	0.415238i
$773$	76.8165	+	76.8165i	0.0993746	+	0.0993746i	0.755046	−	0.655672i	$-0.227614\pi$
$773$	76.8165	+	76.8165i	0.0993746	+	0.0993746i	−0.655672	+	0.755046i	$0.727614\pi$
$774$	−111.531	+	111.531i	−0.144097	+	0.144097i
$775$	−544.196	+	544.196i	−0.702189	+	0.702189i
$776$	−16.1333			−0.0207903
$777$			7.97183i			0.0102598i
$778$	−644.305	+	644.305i	−0.828156	+	0.828156i
$779$		−	1309.53i		−	1.68104i
$780$	71.6846	+	37.1769i	0.0919034	+	0.0476627i
$781$	93.2154			0.119354
$782$	−28.3078	−	28.3078i	−0.0361992	−	0.0361992i
$783$	21.5307			0.0274978
$784$		−	191.713i		−	0.244532i
$785$	−340.805	−	340.805i	−0.434147	−	0.434147i
$786$	413.769	+	413.769i	0.526424	+	0.526424i
$787$	−486.883	+	486.883i	−0.618657	+	0.618657i	−0.945187	−	0.326530i	$-0.894121\pi$
$787$	−486.883	+	486.883i	−0.618657	+	0.618657i	0.326530	+	0.945187i	$0.394121\pi$
$788$	218.536	−	218.536i	0.277330	−	0.277330i
$789$	−164.354			−0.208307
$790$			10.6767i			0.0135148i
$791$	108.546	−	108.546i	0.137227	−	0.137227i
$792$		−	20.7846i		−	0.0262432i
$793$	−406.277	−	1281.68i	−0.512329	−	1.61624i
$794$	865.384			1.08990
$795$	126.746	+	126.746i	0.159429	+	0.159429i
$796$	50.1999			0.0630652
$797$			713.587i			0.895341i	0.894198	+	0.447671i	$0.147746\pi$
$797$			713.587i			0.895341i	−0.894198	+	0.447671i	$0.852254\pi$
$798$	−37.3590	−	37.3590i	−0.0468158	−	0.0468158i
$799$	−163.892	−	163.892i	−0.205122	−	0.205122i
$800$	−87.1384	+	87.1384i	−0.108923	+	0.108923i
$801$	−58.5500	+	58.5500i	−0.0730961	+	0.0730961i
$802$	−549.100			−0.684663
$803$			19.6743i			0.0245010i
$804$	−161.751	+	161.751i	−0.201183	+	0.201183i
$805$			9.87703i			0.0122696i
$806$	−619.138	+	196.259i	−0.768162	+	0.243498i
$807$	−361.608			−0.448089
$808$	222.928	+	222.928i	0.275901	+	0.275901i
$809$	−257.600			−0.318418			−0.159209	−	0.987245i	$-0.550894\pi$
$809$	−257.600			−0.318418			−0.159209	+	0.987245i	$0.550894\pi$
$810$			22.8231i			0.0281766i
$811$	−127.258	−	127.258i	−0.156914	−	0.156914i	0.624283	−	0.781198i	$-0.285391\pi$
$811$	−127.258	−	127.258i	−0.156914	−	0.156914i	−0.781198	+	0.624283i	$0.785391\pi$
$812$	6.06664	+	6.06664i	0.00747123	+	0.00747123i
$813$	659.993	−	659.993i	0.811800	−	0.811800i
$814$	10.8897	−	10.8897i	0.0133780	−	0.0133780i
$815$	−117.779			−0.144515
$816$		−	36.8616i		−	0.0451735i
$817$	547.692	−	547.692i	0.670370	−	0.670370i
$818$			152.374i			0.186277i
$819$	−35.8423	−	18.5885i	−0.0437635	−	0.0226965i
$820$	−225.415			−0.274897
$821$	1116.87	+	1116.87i	1.36038	+	1.36038i	0.873428	+	0.486953i	$0.161892\pi$
$821$	1116.87	+	1116.87i	1.36038	+	1.36038i	0.486953	+	0.873428i	$0.338108\pi$
$822$	−318.515			−0.387488
$823$		−	617.920i		−	0.750814i	−0.926860	−	0.375407i	$-0.877503\pi$
$823$		−	617.920i		−	0.750814i	0.926860	−	0.375407i	$-0.122497\pi$
$824$	142.641	+	142.641i	0.173108	+	0.173108i
$825$	65.3538	+	65.3538i	0.0792168	+	0.0792168i
$826$	−97.5411	+	97.5411i	−0.118088	+	0.118088i
$827$	349.847	−	349.847i	0.423032	−	0.423032i	−0.463214	−	0.886246i	$-0.653304\pi$
$827$	349.847	−	349.847i	0.423032	−	0.423032i	0.886246	+	0.463214i	$0.153304\pi$
$828$	−31.9230			−0.0385544
$829$			247.646i			0.298729i	0.988782	+	0.149364i	$0.0477227\pi$
$829$			247.646i			0.298729i	−0.988782	+	0.149364i	$0.952277\pi$
$830$	278.438	−	278.438i	0.335468	−	0.335468i
$831$			119.138i			0.143368i
$832$	−99.1384	+	31.4256i	−0.119157	+	0.0377712i
$833$	−255.002			−0.306125
$834$	240.995	+	240.995i	0.288963	+	0.288963i
$835$	−303.069			−0.362957
$836$			102.067i			0.122089i
$837$	−129.804	−	129.804i	−0.155082	−	0.155082i
$838$	76.8231	+	76.8231i	0.0916743	+	0.0916743i
$839$	−598.868	+	598.868i	−0.713788	+	0.713788i	−0.967325	−	0.253538i	$-0.918406\pi$
$839$	−598.868	+	598.868i	−0.713788	+	0.713788i	0.253538	+	0.967325i	$0.418406\pi$
$840$	−6.43078	+	6.43078i	−0.00765569	+	0.00765569i
$841$	−823.831			−0.979585
$842$			235.513i			0.279707i
$843$	120.588	−	120.588i	0.143047	−	0.143047i
$844$			413.436i			0.489853i
$845$	−298.599	−	51.7063i	−0.353371	−	0.0611909i
$846$	−184.823			−0.218467
$847$	84.1858	+	84.1858i	0.0993930	+	0.0993930i
$848$	−230.851			−0.272230
$849$			737.520i			0.868693i
$850$	115.905	+	115.905i	0.136359	+	0.136359i
$851$	−16.7255	−	16.7255i	−0.0196540	−	0.0196540i
$852$	93.2154	−	93.2154i	0.109408	−	0.109408i
$853$	−519.210	+	519.210i	−0.608687	+	0.608687i	−0.942603	−	0.333916i	$-0.891630\pi$
$853$	−519.210	+	519.210i	−0.608687	+	0.608687i	0.333916	+	0.942603i	$0.391630\pi$
$854$	151.426			0.177313
$855$		−	112.077i		−	0.131084i
$856$	233.072	−	233.072i	0.272280	−	0.272280i
$857$		−	226.756i		−	0.264593i	−0.991210	−	0.132297i	$-0.957765\pi$
$857$		−	226.756i		−	0.264593i	0.991210	−	0.132297i	$-0.0422351\pi$
$858$	23.5692	+	74.3538i	0.0274700	+	0.0866595i
$859$	950.656			1.10670			0.553350	−	0.832949i	$-0.313349\pi$
$859$	950.656			1.10670			0.553350	+	0.832949i	$0.313349\pi$
$860$	−94.2769	−	94.2769i	−0.109624	−	0.109624i
$861$	112.708			0.130903
$862$			724.956i			0.841017i
$863$	773.711	+	773.711i	0.896537	+	0.896537i	0.995128	−	0.0985910i	$-0.0314336\pi$
$863$	773.711	+	773.711i	0.896537	+	0.896537i	−0.0985910	+	0.995128i	$0.531434\pi$
$864$	−20.7846	−	20.7846i	−0.0240563	−	0.0240563i
$865$	307.608	−	307.608i	0.355616	−	0.355616i
$866$	−197.292	+	197.292i	−0.227820	+	0.227820i
$867$	451.532			0.520798
$868$		−	73.1487i		−	0.0842728i
$869$	−7.29234	+	7.29234i	−0.00839165	+	0.00839165i
$870$			18.1999i			0.0209195i
$871$	395.219	−	762.063i	0.453753	−	0.874929i
$872$	437.261			0.501447
$873$	12.1000	+	12.1000i	0.0138602	+	0.0138602i
$874$	156.764			0.179364
$875$		−	86.8513i		−	0.0992586i
$876$	19.6743	+	19.6743i	0.0224593	+	0.0224593i
$877$	646.713	+	646.713i	0.737415	+	0.737415i	0.972077	−	0.234662i	$-0.0753984\pi$
$877$	646.713	+	646.713i	0.737415	+	0.737415i	−0.234662	+	0.972077i	$0.575398\pi$
$878$	272.238	−	272.238i	0.310067	−	0.310067i
$879$	530.081	−	530.081i	0.603050	−	0.603050i
$880$	17.5692			0.0199650
$881$			783.997i			0.889895i	0.895557	+	0.444947i	$0.146778\pi$
$881$			783.997i			0.889895i	−0.895557	+	0.444947i	$0.853222\pi$
$882$	−143.785	+	143.785i	−0.163021	+	0.163021i
$883$			1089.81i			1.23421i	0.786881	+	0.617105i	$0.211695\pi$
$883$			1089.81i			1.23421i	−0.786881	+	0.617105i	$0.788305\pi$
$884$	41.8001	+	131.867i	0.0472852	+	0.149170i
$885$	−292.623			−0.330648
$886$	74.7358	+	74.7358i	0.0843519	+	0.0843519i
$887$	−1057.03			−1.19169			−0.595846	−	0.803099i	$-0.703183\pi$
$887$	−1057.03			−1.19169			−0.595846	+	0.803099i	$0.703183\pi$
$888$		−	21.7795i		−	0.0245264i
$889$	51.2717	+	51.2717i	0.0576735	+	0.0576735i
$890$	−49.4923	−	49.4923i	−0.0556093	−	0.0556093i
$891$	−15.5885	+	15.5885i	−0.0174955	+	0.0174955i
$892$	−278.823	+	278.823i	−0.312582	+	0.312582i
$893$	907.608			1.01636
$894$			437.254i			0.489098i
$895$	−33.8770	+	33.8770i	−0.0378514	+	0.0378514i
$896$		−	11.7128i		−	0.0130723i
$897$	114.200	−	36.1999i	0.127313	−	0.0403567i
$898$	1032.45			1.14972
$899$	−103.510	−	103.510i	−0.115139	−	0.115139i
$900$	130.708			0.145231
$901$			307.061i			0.340801i
$902$	−153.962	−	153.962i	−0.170689	−	0.170689i
$903$	47.1384	+	47.1384i	0.0522020	+	0.0522020i
$904$	−296.554	+	296.554i	−0.328046	+	0.328046i
$905$	324.777	−	324.777i	0.358870	−	0.358870i
$906$	430.956			0.475669
$907$		−	546.669i		−	0.602722i	−0.953510	−	0.301361i	$-0.902559\pi$
$907$		−	546.669i		−	0.602722i	0.953510	−	0.301361i	$-0.0974410\pi$
$908$	194.736	−	194.736i	0.214467	−	0.214467i
$909$		−	334.392i		−	0.367868i
$910$	15.7128	−	30.2975i	0.0172668	−	0.0332940i
$911$	724.743			0.795547			0.397774	−	0.917484i	$-0.369783\pi$
$911$	724.743			0.795547			0.397774	+	0.917484i	$0.369783\pi$
$912$	102.067	+	102.067i	0.111915	+	0.111915i
$913$	380.354			0.416598
$914$		−	101.923i		−	0.111513i
$915$	227.138	+	227.138i	0.248239	+	0.248239i
$916$	408.354	+	408.354i	0.445801	+	0.445801i
$917$	174.879	−	174.879i	0.190708	−	0.190708i
$918$	−27.6462	+	27.6462i	−0.0301157	+	0.0301157i
$919$	−941.108			−1.02406			−0.512028	−	0.858969i	$-0.671106\pi$
$919$	−941.108			−1.02406			−0.512028	+	0.858969i	$0.671106\pi$
$920$		−	26.9845i		−	0.0293310i
$921$	426.970	−	426.970i	0.463594	−	0.463594i
$922$			405.100i			0.439371i
$923$	−227.760	+	439.168i	−0.246761	+	0.475805i
$924$	−8.78461			−0.00950715
$925$	68.4820	+	68.4820i	0.0740345	+	0.0740345i
$926$	−446.495			−0.482176
$927$		−	213.962i		−	0.230811i
$928$	−16.5744	−	16.5744i	−0.0178603	−	0.0178603i
$929$	−260.130	−	260.130i	−0.280010	−	0.280010i	0.553103	−	0.833113i	$-0.313444\pi$
$929$	−260.130	−	260.130i	−0.280010	−	0.280010i	−0.833113	+	0.553103i	$0.813444\pi$
$930$	109.723	−	109.723i	0.117982	−	0.117982i
$931$	706.081	−	706.081i	0.758411	−	0.758411i
$932$	−463.923			−0.497772
$933$			542.785i			0.581763i
$934$	161.818	−	161.818i	0.173253	−	0.173253i
$935$		−	23.3693i		−	0.0249939i
$936$	97.9230	+	50.7846i	0.104619	+	0.0542571i
$937$	1387.56			1.48085			0.740426	−	0.672138i	$-0.234624\pi$
$937$	1387.56			1.48085			0.740426	+	0.672138i	$0.234624\pi$
$938$	68.3641	+	68.3641i	0.0728829	+	0.0728829i
$939$	−455.254			−0.484828
$940$		−	156.231i		−	0.166203i
$941$	−61.6012	−	61.6012i	−0.0654635	−	0.0654635i	0.673617	−	0.739081i	$-0.264740\pi$
$941$	−61.6012	−	61.6012i	−0.0654635	−	0.0654635i	−0.739081	+	0.673617i	$0.764740\pi$
$942$	−465.549	−	465.549i	−0.494213	−	0.494213i
$943$	−236.469	+	236.469i	−0.250763	+	0.250763i
$944$	266.487	−	266.487i	0.282296	−	0.282296i
$945$	9.64617			0.0102076
$946$		−	128.785i		−	0.136136i
$947$	54.5064	−	54.5064i	0.0575569	−	0.0575569i	−0.677742	−	0.735299i	$-0.737042\pi$
$947$	54.5064	−	54.5064i	0.0575569	−	0.0575569i	0.735299	+	0.677742i	$0.237042\pi$
$948$			14.5847i			0.0153847i
$949$	−92.6922	−	48.0718i	−0.0976735	−	0.0506552i
$950$	−641.864			−0.675646
$951$	−258.042	−	258.042i	−0.271338	−	0.271338i
$952$	−15.5795			−0.0163651
$953$		−	1079.56i		−	1.13280i	−0.824131	−	0.566399i	$-0.808336\pi$
$953$		−	1079.56i		−	1.13280i	0.824131	−	0.566399i	$-0.191664\pi$
$954$	173.138	+	173.138i	0.181487	+	0.181487i
$955$	−163.923	−	163.923i	−0.171647	−	0.171647i
$956$	−279.962	+	279.962i	−0.292847	+	0.292847i
$957$	−12.4308	+	12.4308i	−0.0129893	+	0.0129893i
$958$	−178.259			−0.186074
$959$			134.620i			0.140376i
$960$	17.5692	−	17.5692i	0.0183013	−	0.0183013i
$961$			287.077i			0.298727i
$962$	24.6973	+	77.9127i	0.0256729	+	0.0809904i
$963$	−349.608			−0.363040
$964$	106.918	+	106.918i	0.110911	+	0.110911i
$965$	−406.459			−0.421201
$966$			13.4923i			0.0139672i
$967$	493.745	+	493.745i	0.510594	+	0.510594i	0.914709	−	0.404114i	$-0.132420\pi$
$967$	493.745	+	493.745i	0.510594	+	0.510594i	−0.404114	+	0.914709i	$0.632420\pi$
$968$	−230.000	−	230.000i	−0.237603	−	0.237603i
$969$	135.762	−	135.762i	0.140105	−	0.140105i
$970$	−10.2281	+	10.2281i	−0.0105444	+	0.0105444i
$971$	−1694.52			−1.74513			−0.872566	−	0.488497i	$-0.837545\pi$
$971$	−1694.52			−1.74513			−0.872566	+	0.488497i	$0.837545\pi$
$972$			31.1769i			0.0320750i
$973$	101.856	−	101.856i	0.104683	−	0.104683i
$974$		−	1054.88i		−	1.08304i
$975$	−467.587	+	148.219i	−0.479576	+	0.152020i
$976$	−413.703			−0.423876
$977$	−390.060	−	390.060i	−0.399243	−	0.399243i	0.478723	−	0.877966i	$-0.341100\pi$
$977$	−390.060	−	390.060i	−0.399243	−	0.399243i	−0.877966	+	0.478723i	$0.841100\pi$
$978$	−160.890			−0.164509
$979$		−	67.6077i		−	0.0690579i
$980$	−121.541	−	121.541i	−0.124021	−	0.124021i
$981$	−327.946	−	327.946i	−0.334298	−	0.334298i
$982$	700.726	−	700.726i	0.713570	−	0.713570i
$983$	−1123.12	+	1123.12i	−1.14254	+	1.14254i	−0.154559	+	0.987984i	$0.549396\pi$
$983$	−1123.12	+	1123.12i	−1.14254	+	1.14254i	−0.987984	+	0.154559i	$0.950604\pi$
$984$	−307.923			−0.312930
$985$		−	277.092i		−	0.281312i
$986$	−22.0460	+	22.0460i	−0.0223590	+	0.0223590i
$987$			78.1154i			0.0791443i
$988$	−480.869	−	249.387i	−0.486710	−	0.252416i
$989$	−197.800			−0.200000
$990$	−13.1769	−	13.1769i	−0.0133100	−	0.0133100i
$991$	610.985			0.616533			0.308267	−	0.951300i	$-0.400251\pi$
$991$	610.985			0.616533			0.308267	+	0.951300i	$0.400251\pi$
$992$			199.846i			0.201458i
$993$	−512.463	−	512.463i	−0.516075	−	0.516075i
$994$	−39.3975	−	39.3975i	−0.0396353	−	0.0396353i
$995$	31.8255	−	31.8255i	0.0319854	−	0.0319854i
$996$	380.354	−	380.354i	0.381881	−	0.381881i
$997$	−412.123			−0.413363			−0.206682	−	0.978408i	$-0.566266\pi$
$997$	−412.123			−0.413363			−0.206682	+	0.978408i	$0.566266\pi$
$998$			558.131i			0.559249i
$999$	−16.3346	+	16.3346i	−0.0163509	+	0.0163509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.3.f.a.73.2	yes	4
3.2	odd	2		234.3.i.b.73.2		4
4.3	odd	2		624.3.ba.a.385.1		4
13.5	odd	4	inner	78.3.f.a.31.2	✓	4
13.8	odd	4		1014.3.f.a.577.2		4
13.12	even	2		1014.3.f.a.775.2		4
39.5	even	4		234.3.i.b.109.2		4
52.31	even	4		624.3.ba.a.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.f.a.31.2	✓	4	13.5	odd	4	inner
78.3.f.a.73.2	yes	4	1.1	even	1	trivial
234.3.i.b.73.2		4	3.2	odd	2
234.3.i.b.109.2		4	39.5	even	4
624.3.ba.a.385.1		4	4.3	odd	2
624.3.ba.a.577.1		4	52.31	even	4
1014.3.f.a.577.2		4	13.8	odd	4
1014.3.f.a.775.2		4	13.12	even	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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	78.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(1.26795 + 1.26795i) q^{5} +(1.73205 + 1.73205i) q^{6} +(0.732051 - 0.732051i) q^{7} +(-2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(1.26795 + 1.26795i) q^{5} +(1.73205 + 1.73205i) q^{6} +(0.732051 - 0.732051i) q^{7} +(-2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +2.53590i q^{10} +(-1.73205 + 1.73205i) q^{11} +3.46410i q^{12} +(-3.92820 - 12.3923i) q^{13} +1.46410 q^{14} +(2.19615 + 2.19615i) q^{15} -4.00000 q^{16} +5.32051i q^{17} +(3.00000 + 3.00000i) q^{18} +(-14.7321 - 14.7321i) q^{19} +(-2.53590 + 2.53590i) q^{20} +(1.26795 - 1.26795i) q^{21} -3.46410 q^{22} +5.32051i q^{23} +(-3.46410 + 3.46410i) q^{24} -21.7846i q^{25} +(8.46410 - 16.3205i) q^{26} +5.19615 q^{27} +(1.46410 + 1.46410i) q^{28} +4.14359 q^{29} +4.39230i q^{30} +(-24.9808 - 24.9808i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-3.00000 + 3.00000i) q^{33} +(-5.32051 + 5.32051i) q^{34} +1.85641 q^{35} +6.00000i q^{36} +(-3.14359 + 3.14359i) q^{37} -29.4641i q^{38} +(-6.80385 - 21.4641i) q^{39} -5.07180 q^{40} +(44.4449 + 44.4449i) q^{41} +2.53590 q^{42} +37.1769i q^{43} +(-3.46410 - 3.46410i) q^{44} +(3.80385 + 3.80385i) q^{45} +(-5.32051 + 5.32051i) q^{46} +(-30.8038 + 30.8038i) q^{47} -6.92820 q^{48} +47.9282i q^{49} +(21.7846 - 21.7846i) q^{50} +9.21539i q^{51} +(24.7846 - 7.85641i) q^{52} +57.7128 q^{53} +(5.19615 + 5.19615i) q^{54} -4.39230 q^{55} +2.92820i q^{56} +(-25.5167 - 25.5167i) q^{57} +(4.14359 + 4.14359i) q^{58} +(-66.6218 + 66.6218i) q^{59} +(-4.39230 + 4.39230i) q^{60} +103.426 q^{61} -49.9615i q^{62} +(2.19615 - 2.19615i) q^{63} -8.00000i q^{64} +(10.7321 - 20.6936i) q^{65} -6.00000 q^{66} +(46.6936 + 46.6936i) q^{67} -10.6410 q^{68} +9.21539i q^{69} +(1.85641 + 1.85641i) q^{70} +(-26.9090 - 26.9090i) q^{71} +(-6.00000 + 6.00000i) q^{72} +(5.67949 - 5.67949i) q^{73} -6.28719 q^{74} -37.7321i q^{75} +(29.4641 - 29.4641i) q^{76} +2.53590i q^{77} +(14.6603 - 28.2679i) q^{78} +4.21024 q^{79} +(-5.07180 - 5.07180i) q^{80} +9.00000 q^{81} +88.8897i q^{82} +(-109.799 - 109.799i) q^{83} +(2.53590 + 2.53590i) q^{84} +(-6.74613 + 6.74613i) q^{85} +(-37.1769 + 37.1769i) q^{86} +7.17691 q^{87} -6.92820i q^{88} +(-19.5167 + 19.5167i) q^{89} +7.60770i q^{90} +(-11.9474 - 6.19615i) q^{91} -10.6410 q^{92} +(-43.2679 - 43.2679i) q^{93} -61.6077 q^{94} -37.3590i q^{95} +(-6.92820 - 6.92820i) q^{96} +(4.03332 + 4.03332i) q^{97} +(-47.9282 + 47.9282i) q^{98} +(-5.19615 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 12 q^{5} - 4 q^{7} - 8 q^{8} + 12 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 12 * q^5 - 4 * q^7 - 8 * q^8 + 12 * q^9	\( 4 q + 4 q^{2} + 12 q^{5} - 4 q^{7} - 8 q^{8} + 12 q^{9} + 12 q^{13} - 8 q^{14} - 12 q^{15} - 16 q^{16} + 12 q^{18} - 52 q^{19} - 24 q^{20} + 12 q^{21} + 20 q^{26} - 8 q^{28} + 72 q^{29} + 4 q^{31} - 16 q^{32} - 12 q^{33} + 48 q^{34} - 48 q^{35} - 68 q^{37} - 48 q^{39} - 48 q^{40} + 60 q^{41} + 24 q^{42} + 36 q^{45} + 48 q^{46} - 144 q^{47} + 4 q^{50} + 16 q^{52} + 120 q^{53} + 24 q^{55} - 12 q^{57} + 72 q^{58} - 24 q^{59} + 24 q^{60} + 192 q^{61} - 12 q^{63} + 36 q^{65} - 24 q^{66} - 28 q^{67} + 96 q^{68} - 48 q^{70} + 24 q^{71} - 24 q^{72} + 92 q^{73} - 136 q^{74} + 104 q^{76} + 24 q^{78} - 288 q^{79} - 48 q^{80} + 36 q^{81} - 72 q^{83} + 24 q^{84} + 264 q^{85} - 24 q^{86} - 96 q^{87} + 12 q^{89} - 124 q^{91} + 96 q^{92} - 180 q^{93} - 288 q^{94} - 164 q^{97} - 164 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 12 * q^5 - 4 * q^7 - 8 * q^8 + 12 * q^9 + 12 * q^13 - 8 * q^14 - 12 * q^15 - 16 * q^16 + 12 * q^18 - 52 * q^19 - 24 * q^20 + 12 * q^21 + 20 * q^26 - 8 * q^28 + 72 * q^29 + 4 * q^31 - 16 * q^32 - 12 * q^33 + 48 * q^34 - 48 * q^35 - 68 * q^37 - 48 * q^39 - 48 * q^40 + 60 * q^41 + 24 * q^42 + 36 * q^45 + 48 * q^46 - 144 * q^47 + 4 * q^50 + 16 * q^52 + 120 * q^53 + 24 * q^55 - 12 * q^57 + 72 * q^58 - 24 * q^59 + 24 * q^60 + 192 * q^61 - 12 * q^63 + 36 * q^65 - 24 * q^66 - 28 * q^67 + 96 * q^68 - 48 * q^70 + 24 * q^71 - 24 * q^72 + 92 * q^73 - 136 * q^74 + 104 * q^76 + 24 * q^78 - 288 * q^79 - 48 * q^80 + 36 * q^81 - 72 * q^83 + 24 * q^84 + 264 * q^85 - 24 * q^86 - 96 * q^87 + 12 * q^89 - 124 * q^91 + 96 * q^92 - 180 * q^93 - 288 * q^94 - 164 * q^97 - 164 * q^98

Introduction

L-functions

Modular forms

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