LMFDB - Embedded newform 287.2.f.a.50.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(50,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("287.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			50.6
Character	$\chi$	$=$	287.50
Dual form			287.2.f.a.155.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.43253i q^{2} +(-1.43055 - 1.43055i) q^{3} -0.0521511 q^{4} -4.15342i q^{5} +(-2.04931 + 2.04931i) q^{6} +(0.707107 + 0.707107i) q^{7} -2.79036i q^{8} +1.09294i q^{9} +O(q^{10})$	\(q-1.43253i q^{2} +(-1.43055 - 1.43055i) q^{3} -0.0521511 q^{4} -4.15342i q^{5} +(-2.04931 + 2.04931i) q^{6} +(0.707107 + 0.707107i) q^{7} -2.79036i q^{8} +1.09294i q^{9} -5.94992 q^{10} +(4.11227 + 4.11227i) q^{11} +(0.0746047 + 0.0746047i) q^{12} +(0.0880909 + 0.0880909i) q^{13} +(1.01295 - 1.01295i) q^{14} +(-5.94167 + 5.94167i) q^{15} -4.10158 q^{16} +(-2.13938 + 2.13938i) q^{17} +1.56567 q^{18} +(0.297969 - 0.297969i) q^{19} +0.216606i q^{20} -2.02310i q^{21} +(5.89096 - 5.89096i) q^{22} +4.16948 q^{23} +(-3.99174 + 3.99174i) q^{24} -12.2509 q^{25} +(0.126193 - 0.126193i) q^{26} +(-2.72815 + 2.72815i) q^{27} +(-0.0368764 - 0.0368764i) q^{28} +(5.55922 + 5.55922i) q^{29} +(8.51164 + 8.51164i) q^{30} -0.142422 q^{31} +0.294937i q^{32} -11.7656i q^{33} +(3.06473 + 3.06473i) q^{34} +(2.93691 - 2.93691i) q^{35} -0.0569978i q^{36} -2.46114 q^{37} +(-0.426850 - 0.426850i) q^{38} -0.252036i q^{39} -11.5895 q^{40} +(5.98107 - 2.28622i) q^{41} -2.89816 q^{42} -3.03490i q^{43} +(-0.214459 - 0.214459i) q^{44} +4.53942 q^{45} -5.97292i q^{46} +(3.23660 - 3.23660i) q^{47} +(5.86751 + 5.86751i) q^{48} +1.00000i q^{49} +17.5499i q^{50} +6.12097 q^{51} +(-0.00459404 - 0.00459404i) q^{52} +(-2.33870 - 2.33870i) q^{53} +(3.90816 + 3.90816i) q^{54} +(17.0800 - 17.0800i) q^{55} +(1.97308 - 1.97308i) q^{56} -0.852517 q^{57} +(7.96376 - 7.96376i) q^{58} +3.83254 q^{59} +(0.309865 - 0.309865i) q^{60} +10.6646i q^{61} +0.204024i q^{62} +(-0.772822 + 0.772822i) q^{63} -7.78066 q^{64} +(0.365879 - 0.365879i) q^{65} -16.8546 q^{66} +(0.401432 - 0.401432i) q^{67} +(0.111571 - 0.111571i) q^{68} +(-5.96465 - 5.96465i) q^{69} +(-4.20723 - 4.20723i) q^{70} +(-9.25416 - 9.25416i) q^{71} +3.04968 q^{72} -14.6784i q^{73} +3.52567i q^{74} +(17.5255 + 17.5255i) q^{75} +(-0.0155394 + 0.0155394i) q^{76} +5.81562i q^{77} -0.361051 q^{78} +(4.00501 + 4.00501i) q^{79} +17.0356i q^{80} +11.0843 q^{81} +(-3.27509 - 8.56808i) q^{82} +6.87081 q^{83} +0.105507i q^{84} +(8.88575 + 8.88575i) q^{85} -4.34760 q^{86} -15.9054i q^{87} +(11.4747 - 11.4747i) q^{88} +(-10.4608 - 10.4608i) q^{89} -6.50287i q^{90} +0.124579i q^{91} -0.217443 q^{92} +(0.203742 + 0.203742i) q^{93} +(-4.63653 - 4.63653i) q^{94} +(-1.23759 - 1.23759i) q^{95} +(0.421921 - 0.421921i) q^{96} +(-5.89322 + 5.89322i) q^{97} +1.43253 q^{98} +(-4.49444 + 4.49444i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.43253i		−	1.01295i	−0.862254	−	0.506477i	$-0.830948\pi$
$2$		−	1.43253i		−	1.01295i	0.862254	−	0.506477i	$-0.169052\pi$
$3$	−1.43055	−	1.43055i	−0.825927	−	0.825927i	0.161023	−	0.986951i	$-0.448521\pi$
$3$	−1.43055	−	1.43055i	−0.825927	−	0.825927i	−0.986951	+	0.161023i	$0.948521\pi$
$4$	−0.0521511			−0.0260756
$5$		−	4.15342i		−	1.85747i	−0.370748	−	0.928734i	$-0.620899\pi$
$5$		−	4.15342i		−	1.85747i	0.370748	−	0.928734i	$-0.379101\pi$
$6$	−2.04931	+	2.04931i	−0.836626	+	0.836626i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		−	2.79036i		−	0.986541i
$9$			1.09294i			0.364312i
$10$	−5.94992			−1.88153
$11$	4.11227	+	4.11227i	1.23990	+	1.23990i	0.960043	+	0.279852i	$0.0902854\pi$
$11$	4.11227	+	4.11227i	1.23990	+	1.23990i	0.279852	+	0.960043i	$0.409715\pi$
$12$	0.0746047	+	0.0746047i	0.0215365	+	0.0215365i
$13$	0.0880909	+	0.0880909i	0.0244320	+	0.0244320i	0.719217	−	0.694785i	$-0.244501\pi$
$13$	0.0880909	+	0.0880909i	0.0244320	+	0.0244320i	−0.694785	+	0.719217i	$0.744501\pi$
$14$	1.01295	−	1.01295i	0.270723	−	0.270723i
$15$	−5.94167	+	5.94167i	−1.53413	+	1.53413i
$16$	−4.10158			−1.02540
$17$	−2.13938	+	2.13938i	−0.518876	+	0.518876i	−0.917231	−	0.398355i	$-0.869581\pi$
$17$	−2.13938	+	2.13938i	−0.518876	+	0.518876i	0.398355	+	0.917231i	$0.369581\pi$
$18$	1.56567			0.369031
$19$	0.297969	−	0.297969i	0.0683587	−	0.0683587i	−0.672101	−	0.740460i	$-0.734608\pi$
$19$	0.297969	−	0.297969i	0.0683587	−	0.0683587i	0.740460	+	0.672101i	$0.234608\pi$
$20$			0.216606i			0.0484345i
$21$		−	2.02310i		−	0.441477i
$22$	5.89096	−	5.89096i	1.25596	−	1.25596i
$23$	4.16948			0.869397			0.434699	−	0.900576i	$-0.356855\pi$
$23$	4.16948			0.869397			0.434699	+	0.900576i	$0.356855\pi$
$24$	−3.99174	+	3.99174i	−0.814811	+	0.814811i
$25$	−12.2509			−2.45018
$26$	0.126193	−	0.126193i	0.0247485	−	0.0247485i
$27$	−2.72815	+	2.72815i	−0.525032	+	0.525032i
$28$	−0.0368764	−	0.0368764i	−0.00696899	−	0.00696899i
$29$	5.55922	+	5.55922i	1.03232	+	1.03232i	0.999460	+	0.0328605i	$0.0104617\pi$
$29$	5.55922	+	5.55922i	1.03232	+	1.03232i	0.0328605	+	0.999460i	$0.489538\pi$
$30$	8.51164	+	8.51164i	1.55401	+	1.55401i
$31$	−0.142422			−0.0255798			−0.0127899	−	0.999918i	$-0.504071\pi$
$31$	−0.142422			−0.0255798			−0.0127899	+	0.999918i	$0.504071\pi$
$32$			0.294937i			0.0521379i
$33$		−	11.7656i		−	2.04813i
$34$	3.06473	+	3.06473i	0.525597	+	0.525597i
$35$	2.93691	−	2.93691i	0.496429	−	0.496429i
$36$		−	0.0569978i		−	0.00949964i
$37$	−2.46114			−0.404610			−0.202305	−	0.979323i	$-0.564843\pi$
$37$	−2.46114			−0.404610			−0.202305	+	0.979323i	$0.564843\pi$
$38$	−0.426850	−	0.426850i	−0.0692442	−	0.0692442i
$39$		−	0.252036i		−	0.0403581i
$40$	−11.5895			−1.83247
$41$	5.98107	−	2.28622i	0.934086	−	0.357048i
$41$	5.98107	−	2.28622i	0.934086	−	0.357048i
$42$	−2.89816			−0.447196
$43$		−	3.03490i		−	0.462818i	−0.972857	−	0.231409i	$-0.925666\pi$
$43$		−	3.03490i		−	0.462818i	0.972857	−	0.231409i	$-0.0743336\pi$
$44$	−0.214459	−	0.214459i	−0.0323310	−	0.0323310i
$45$	4.53942			0.676697
$46$		−	5.97292i		−	0.880659i
$47$	3.23660	−	3.23660i	0.472106	−	0.472106i	−0.430489	−	0.902596i	$-0.641659\pi$
$47$	3.23660	−	3.23660i	0.472106	−	0.472106i	0.902596	+	0.430489i	$0.141659\pi$
$48$	5.86751	+	5.86751i	0.846902	+	0.846902i
$49$			1.00000i			0.142857i
$50$			17.5499i			2.48192i
$51$	6.12097			0.857107
$52$	−0.00459404	−	0.00459404i	−0.000637078	−	0.000637078i
$53$	−2.33870	−	2.33870i	−0.321244	−	0.321244i	0.528000	−	0.849244i	$-0.322942\pi$
$53$	−2.33870	−	2.33870i	−0.321244	−	0.321244i	−0.849244	+	0.528000i	$0.822942\pi$
$54$	3.90816	+	3.90816i	0.531833	+	0.531833i
$55$	17.0800	−	17.0800i	2.30306	−	2.30306i
$56$	1.97308	−	1.97308i	0.263664	−	0.263664i
$57$	−0.852517			−0.112919
$58$	7.96376	−	7.96376i	1.04569	−	1.04569i
$59$	3.83254			0.498954			0.249477	−	0.968381i	$-0.419741\pi$
$59$	3.83254			0.498954			0.249477	+	0.968381i	$0.419741\pi$
$60$	0.309865	−	0.309865i	0.0400034	−	0.0400034i
$61$			10.6646i			1.36546i	0.730672	+	0.682729i	$0.239207\pi$
$61$			10.6646i			1.36546i	−0.730672	+	0.682729i	$0.760793\pi$
$62$			0.204024i			0.0259111i
$63$	−0.772822	+	0.772822i	−0.0973664	+	0.0973664i
$64$	−7.78066			−0.972582
$65$	0.365879	−	0.365879i	0.0453817	−	0.0453817i
$66$	−16.8546			−2.07466
$67$	0.401432	−	0.401432i	0.0490427	−	0.0490427i	−0.682160	−	0.731203i	$-0.738959\pi$
$67$	0.401432	−	0.401432i	0.0490427	−	0.0490427i	0.731203	+	0.682160i	$0.238959\pi$
$68$	0.111571	−	0.111571i	0.0135300	−	0.0135300i
$69$	−5.96465	−	5.96465i	−0.718059	−	0.718059i
$70$	−4.20723	−	4.20723i	−0.502860	−	0.502860i
$71$	−9.25416	−	9.25416i	−1.09827	−	1.09827i	−0.994614	−	0.103653i	$-0.966947\pi$
$71$	−9.25416	−	9.25416i	−1.09827	−	1.09827i	−0.103653	−	0.994614i	$-0.533053\pi$
$72$	3.04968			0.359408
$73$		−	14.6784i		−	1.71798i	−0.511991	−	0.858991i	$-0.671092\pi$
$73$		−	14.6784i		−	1.71798i	0.511991	−	0.858991i	$-0.328908\pi$
$74$			3.52567i			0.409851i
$75$	17.5255	+	17.5255i	2.02367	+	2.02367i
$76$	−0.0155394	+	0.0155394i	−0.00178249	+	0.00178249i
$77$			5.81562i			0.662752i
$78$	−0.361051			−0.0408809
$79$	4.00501	+	4.00501i	0.450599	+	0.450599i	0.895553	−	0.444954i	$-0.146780\pi$
$79$	4.00501	+	4.00501i	0.450599	+	0.450599i	−0.444954	+	0.895553i	$0.646780\pi$
$80$			17.0356i			1.90464i
$81$	11.0843			1.23159
$82$	−3.27509	−	8.56808i	−0.361673	−	0.946186i
$83$	6.87081			0.754169			0.377085	−	0.926179i	$-0.376927\pi$
$83$	6.87081			0.754169			0.377085	+	0.926179i	$0.376927\pi$
$84$			0.105507i			0.0115118i
$85$	8.88575	+	8.88575i	0.963795	+	0.963795i
$86$	−4.34760			−0.468813
$87$		−	15.9054i		−	1.70524i
$88$	11.4747	−	11.4747i	1.22321	−	1.22321i
$89$	−10.4608	−	10.4608i	−1.10884	−	1.10884i	−0.993303	−	0.115536i	$-0.963141\pi$
$89$	−10.4608	−	10.4608i	−1.10884	−	1.10884i	−0.115536	−	0.993303i	$-0.536859\pi$
$90$		−	6.50287i		−	0.685463i
$91$			0.124579i			0.0130595i
$92$	−0.217443			−0.0226700
$93$	0.203742	+	0.203742i	0.0211270	+	0.0211270i
$94$	−4.63653	−	4.63653i	−0.478222	−	0.478222i
$95$	−1.23759	−	1.23759i	−0.126974	−	0.126974i
$96$	0.421921	−	0.421921i	0.0430621	−	0.0430621i
$97$	−5.89322	+	5.89322i	−0.598366	+	0.598366i	−0.939877	−	0.341512i	$-0.889061\pi$
$97$	−5.89322	+	5.89322i	−0.598366	+	0.598366i	0.341512	+	0.939877i	$0.389061\pi$
$98$	1.43253			0.144708
$99$	−4.49444	+	4.49444i	−0.451708	+	0.451708i
$100$	0.638899			0.0638899
$101$	−4.34956	+	4.34956i	−0.432797	+	0.432797i	−0.889579	−	0.456782i	$-0.849002\pi$
$101$	−4.34956	+	4.34956i	−0.432797	+	0.432797i	0.456782	+	0.889579i	$0.349002\pi$
$102$		−	8.76849i		−	0.868210i
$103$			17.9682i			1.77046i	0.465153	+	0.885230i	$0.345999\pi$
$103$			17.9682i			1.77046i	−0.465153	+	0.885230i	$0.654001\pi$
$104$	0.245805	−	0.245805i	0.0241032	−	0.0241032i
$105$	−8.40279			−0.820029
$106$	−3.35026	+	3.35026i	−0.325406	+	0.325406i
$107$	−1.31915			−0.127527			−0.0637634	−	0.997965i	$-0.520310\pi$
$107$	−1.31915			−0.127527			−0.0637634	+	0.997965i	$0.520310\pi$
$108$	0.142276	−	0.142276i	0.0136905	−	0.0136905i
$109$	−11.1130	+	11.1130i	−1.06443	+	1.06443i	−0.0666545	+	0.997776i	$0.521233\pi$
$109$	−11.1130	+	11.1130i	−1.06443	+	1.06443i	−0.997776	+	0.0666545i	$0.978767\pi$
$110$	−24.4676	−	24.4676i	−2.33290	−	2.33290i
$111$	3.52078	+	3.52078i	0.334178	+	0.334178i
$112$	−2.90026	−	2.90026i	−0.274049	−	0.274049i
$113$	6.73616			0.633684			0.316842	−	0.948478i	$-0.397377\pi$
$113$	6.73616			0.633684			0.316842	+	0.948478i	$0.397377\pi$
$114$			1.22126i			0.114381i
$115$		−	17.3176i		−	1.61488i
$116$	−0.289919	−	0.289919i	−0.0269183	−	0.0269183i
$117$	−0.0962776	+	0.0962776i	−0.00890087	+	0.00890087i
$118$		−	5.49024i		−	0.505417i
$119$	−3.02554			−0.277351
$120$	16.5794	+	16.5794i	1.51348	+	1.51348i
$121$			22.8215i			2.07468i
$122$	15.2773			1.38315
$123$	−11.8268	−	5.28566i	−1.06638	−	0.476592i
$124$	0.00742747			0.000667006
$125$			30.1161i			2.69367i
$126$	1.10709	+	1.10709i	0.0986277	+	0.0986277i
$127$	−11.2681			−0.999879			−0.499939	−	0.866060i	$-0.666644\pi$
$127$	−11.2681			−0.999879			−0.499939	+	0.866060i	$0.666644\pi$
$128$			11.7359i			1.03732i
$129$	−4.34157	+	4.34157i	−0.382254	+	0.382254i
$130$	−0.524133	−	0.524133i	−0.0459695	−	0.0459695i
$131$		−	6.39425i		−	0.558668i	−0.960194	−	0.279334i	$-0.909886\pi$
$131$		−	6.39425i		−	0.558668i	0.960194	−	0.279334i	$-0.0901137\pi$
$132$			0.613589i			0.0534060i
$133$	0.421391			0.0365393
$134$	−0.575065	−	0.575065i	−0.0496780	−	0.0496780i
$135$	11.3311	+	11.3311i	0.975230	+	0.975230i
$136$	5.96963	+	5.96963i	0.511892	+	0.511892i
$137$	0.198346	−	0.198346i	0.0169459	−	0.0169459i	−0.698583	−	0.715529i	$-0.746186\pi$
$137$	0.198346	−	0.198346i	0.0169459	−	0.0169459i	0.715529	+	0.698583i	$0.246186\pi$
$138$	−8.54455	+	8.54455i	−0.727361	+	0.727361i
$139$	13.7360			1.16507			0.582535	−	0.812805i	$-0.302061\pi$
$139$	13.7360			1.16507			0.582535	+	0.812805i	$0.302061\pi$
$140$	−0.153163	+	0.153163i	−0.0129447	+	0.0129447i
$141$	−9.26021			−0.779851
$142$	−13.2569	+	13.2569i	−1.11249	+	1.11249i
$143$			0.724506i			0.0605863i
$144$		−	4.48277i		−	0.373564i
$145$	23.0898	−	23.0898i	1.91750	−	1.91750i
$146$	−21.0274			−1.74024
$147$	1.43055	−	1.43055i	0.117990	−	0.117990i
$148$	0.128351			0.0105504
$149$	−4.00217	+	4.00217i	−0.327870	+	0.327870i	−0.851776	−	0.523906i	$-0.824474\pi$
$149$	−4.00217	+	4.00217i	−0.327870	+	0.327870i	0.523906	+	0.851776i	$0.324474\pi$
$150$	25.1059	−	25.1059i	2.04989	−	2.04989i
$151$	14.0384	+	14.0384i	1.14243	+	1.14243i	0.988004	+	0.154426i	$0.0493527\pi$
$151$	14.0384	+	14.0384i	1.14243	+	1.14243i	0.154426	+	0.988004i	$0.450647\pi$
$152$	−0.831439	−	0.831439i	−0.0674386	−	0.0674386i
$153$	−2.33820	−	2.33820i	−0.189033	−	0.189033i
$154$	8.33107			0.671337
$155$			0.591539i			0.0475136i
$156$			0.0131440i			0.00105236i
$157$	−4.71266	−	4.71266i	−0.376111	−	0.376111i	0.493586	−	0.869697i	$-0.335686\pi$
$157$	−4.71266	−	4.71266i	−0.376111	−	0.376111i	−0.869697	+	0.493586i	$0.835686\pi$
$158$	5.73731	−	5.73731i	0.456436	−	0.456436i
$159$			6.69123i			0.530649i
$160$	1.22500			0.0968445
$161$	2.94827	+	2.94827i	0.232356	+	0.232356i
$162$		−	15.8786i		−	1.24754i
$163$	11.1478			0.873160			0.436580	−	0.899666i	$-0.356190\pi$
$163$	11.1478			0.873160			0.436580	+	0.899666i	$0.356190\pi$
$164$	−0.311920	+	0.119229i	−0.0243568	+	0.00931022i
$165$	−48.8675			−3.80433
$166$		−	9.84266i		−	0.763939i
$167$	−5.42711	−	5.42711i	−0.419962	−	0.419962i	0.465229	−	0.885191i	$-0.345972\pi$
$167$	−5.42711	−	5.42711i	−0.419962	−	0.419962i	−0.885191	+	0.465229i	$0.845972\pi$
$168$	−5.64517			−0.435535
$169$		−	12.9845i		−	0.998806i
$170$	12.7291	−	12.7291i	0.976279	−	0.976279i
$171$	0.325661	+	0.325661i	0.0249039	+	0.0249039i
$172$			0.158273i			0.0120682i
$173$			17.7239i			1.34752i	0.738949	+	0.673762i	$0.235323\pi$
$173$			17.7239i			1.34752i	−0.738949	+	0.673762i	$0.764677\pi$
$174$	−22.7851			−1.72733
$175$	−8.66271	−	8.66271i	−0.654839	−	0.654839i
$176$	−16.8668	−	16.8668i	−1.27138	−	1.27138i
$177$	−5.48263	−	5.48263i	−0.412100	−	0.412100i
$178$	−14.9854	+	14.9854i	−1.12320	+	1.12320i
$179$	−4.86959	+	4.86959i	−0.363970	+	0.363970i	−0.865272	−	0.501302i	$-0.832854\pi$
$179$	−4.86959	+	4.86959i	−0.363970	+	0.363970i	0.501302	+	0.865272i	$0.332854\pi$
$180$	−0.236736			−0.0176453
$181$	−9.00704	+	9.00704i	−0.669488	+	0.669488i	−0.957597	−	0.288110i	$-0.906973\pi$
$181$	−9.00704	+	9.00704i	−0.669488	+	0.669488i	0.288110	+	0.957597i	$0.406973\pi$
$182$	0.178464			0.0132286
$183$	15.2562	−	15.2562i	1.12777	−	1.12777i
$184$		−	11.6343i		−	0.857696i
$185$			10.2222i			0.751549i
$186$	0.291867	−	0.291867i	0.0214007	−	0.0214007i
$187$	−17.5954			−1.28670
$188$	−0.168792	+	0.168792i	−0.0123104	+	0.0123104i
$189$	−3.85818			−0.280642
$190$	−1.77289	+	1.77289i	−0.128619	+	0.128619i
$191$	18.5553	−	18.5553i	1.34262	−	1.34262i	0.449171	−	0.893446i	$-0.351719\pi$
$191$	18.5553	−	18.5553i	1.34262	−	1.34262i	0.893446	−	0.449171i	$-0.148281\pi$
$192$	11.1306	+	11.1306i	0.803282	+	0.803282i
$193$	−7.64828	−	7.64828i	−0.550535	−	0.550535i	0.376060	−	0.926595i	$-0.377279\pi$
$193$	−7.64828	−	7.64828i	−0.550535	−	0.550535i	−0.926595	+	0.376060i	$0.877279\pi$
$194$	8.44223	+	8.44223i	0.606117	+	0.606117i
$195$	−1.04681			−0.0749639
$196$		−	0.0521511i		−	0.00372508i
$197$		−	26.1648i		−	1.86417i	−0.362243	−	0.932084i	$-0.617989\pi$
$197$		−	26.1648i		−	1.86417i	0.362243	−	0.932084i	$-0.382011\pi$
$198$	6.43844	+	6.43844i	0.457560	+	0.457560i
$199$	1.77145	−	1.77145i	0.125575	−	0.125575i	−0.641526	−	0.767101i	$-0.721698\pi$
$199$	1.77145	−	1.77145i	0.125575	−	0.125575i	0.767101	+	0.641526i	$0.221698\pi$
$200$			34.1845i			2.41721i
$201$	−1.14854			−0.0810114
$202$	6.23088	+	6.23088i	0.438404	+	0.438404i
$203$			7.86192i			0.551798i
$204$	−0.319215			−0.0223496
$205$	−9.49564	−	24.8419i	−0.663204	−	1.73503i
$206$	25.7401			1.79339
$207$			4.55698i			0.316732i
$208$	−0.361312	−	0.361312i	−0.0250525	−	0.0250525i
$209$	2.45065			0.169515
$210$			12.0373i			0.830651i
$211$	5.07293	−	5.07293i	0.349235	−	0.349235i	−0.510589	−	0.859825i	$-0.670573\pi$
$211$	5.07293	−	5.07293i	0.349235	−	0.349235i	0.859825	+	0.510589i	$0.170573\pi$
$212$	0.121966	+	0.121966i	0.00837663	+	0.00837663i
$213$			26.4770i			1.81418i
$214$			1.88972i			0.129179i
$215$	−12.6052			−0.859669
$216$	7.61251	+	7.61251i	0.517966	+	0.517966i
$217$	−0.100708	−	0.100708i	−0.00683648	−	0.00683648i
$218$	15.9197	+	15.9197i	1.07822	+	1.07822i
$219$	−20.9982	+	20.9982i	−1.41893	+	1.41893i
$220$	−0.890740	+	0.890740i	−0.0600537	+	0.0600537i
$221$	−0.376920			−0.0253544
$222$	5.04364	−	5.04364i	0.338507	−	0.338507i
$223$	4.27550			0.286309			0.143154	−	0.989700i	$-0.454275\pi$
$223$	4.27550			0.286309			0.143154	+	0.989700i	$0.454275\pi$
$224$	−0.208552	+	0.208552i	−0.0139344	+	0.0139344i
$225$		−	13.3895i		−	0.892631i
$226$		−	9.64977i		−	0.641893i
$227$	−13.5841	+	13.5841i	−0.901606	+	0.901606i	−0.995575	−	0.0939691i	$-0.970045\pi$
$227$	−13.5841	+	13.5841i	−0.901606	+	0.901606i	0.0939691	+	0.995575i	$0.470045\pi$
$228$	0.0444597			0.00294442
$229$	−6.33841	+	6.33841i	−0.418854	+	0.418854i	−0.884809	−	0.465955i	$-0.845711\pi$
$229$	−6.33841	+	6.33841i	−0.418854	+	0.418854i	0.465955	+	0.884809i	$0.345711\pi$
$230$	−24.8081			−1.63580
$231$	8.31953	−	8.31953i	0.547385	−	0.547385i
$232$	15.5122	−	15.5122i	1.01843	−	1.01843i
$233$	18.2005	+	18.2005i	1.19235	+	1.19235i	0.976405	+	0.215948i	$0.0692840\pi$
$233$	18.2005	+	18.2005i	1.19235	+	1.19235i	0.215948	+	0.976405i	$0.430716\pi$
$234$	0.137921	+	0.137921i	0.00901617	+	0.00901617i
$235$	−13.4430	−	13.4430i	−0.876922	−	0.876922i
$236$	−0.199871			−0.0130105
$237$		−	11.4587i		−	0.744324i
$238$			4.33419i			0.280943i
$239$	−3.01746	−	3.01746i	−0.195183	−	0.195183i	0.602748	−	0.797931i	$-0.294072\pi$
$239$	−3.01746	−	3.01746i	−0.195183	−	0.195183i	−0.797931	+	0.602748i	$0.794072\pi$
$240$	24.3703	−	24.3703i	1.57309	−	1.57309i
$241$		−	21.0717i		−	1.35735i	−0.734440	−	0.678674i	$-0.762555\pi$
$241$		−	21.0717i		−	1.35735i	0.734440	−	0.678674i	$-0.237445\pi$
$242$	32.6925			2.10155
$243$	−7.67218	−	7.67218i	−0.492171	−	0.492171i
$244$		−	0.556169i		−	0.0356051i
$245$	4.15342			0.265352
$246$	−7.57188	+	16.9422i	−0.482766	+	1.08020i
$247$	0.0524966			0.00334028
$248$			0.397408i			0.0252355i
$249$	−9.82902	−	9.82902i	−0.622889	−	0.622889i
$250$	43.1424			2.72856
$251$			13.0830i			0.825790i	0.910779	+	0.412895i	$0.135482\pi$
$251$			13.0830i			0.825790i	−0.910779	+	0.412895i	$0.864518\pi$
$252$	0.0403035	−	0.0403035i	0.00253888	−	0.00253888i
$253$	17.1460	+	17.1460i	1.07796	+	1.07796i
$254$			16.1419i			1.01283i
$255$		−	25.4230i		−	1.59205i
$256$	1.25078			0.0781740
$257$	17.9482	+	17.9482i	1.11958	+	1.11958i	0.991803	+	0.127773i	$0.0407829\pi$
$257$	17.9482	+	17.9482i	1.11958	+	1.11958i	0.127773	+	0.991803i	$0.459217\pi$
$258$	6.21945	+	6.21945i	0.387206	+	0.387206i
$259$	−1.74029	−	1.74029i	−0.108136	−	0.108136i
$260$	−0.0190810	+	0.0190810i	−0.00118335	+	0.00118335i
$261$	−6.07586	+	6.07586i	−0.376087	+	0.376087i
$262$	−9.15997			−0.565905
$263$	14.1137	−	14.1137i	0.870289	−	0.870289i	−0.122215	−	0.992504i	$-0.539000\pi$
$263$	14.1137	−	14.1137i	0.870289	−	0.870289i	0.992504	+	0.122215i	$0.0389997\pi$
$264$	−32.8302			−2.02056
$265$	−9.71359	+	9.71359i	−0.596701	+	0.596701i
$266$		−	0.603657i		−	0.0370126i
$267$			29.9293i			1.83164i
$268$	−0.0209351	+	0.0209351i	−0.00127882	+	0.00127882i
$269$	9.00838			0.549251			0.274625	−	0.961551i	$-0.411446\pi$
$269$	9.00838			0.549251			0.274625	+	0.961551i	$0.411446\pi$
$270$	16.2322	−	16.2322i	0.987863	−	0.987863i
$271$	6.58820			0.400205			0.200102	−	0.979775i	$-0.435873\pi$
$271$	6.58820			0.400205			0.200102	+	0.979775i	$0.435873\pi$
$272$	8.77484	−	8.77484i	0.532053	−	0.532053i
$273$	0.178217	−	0.178217i	0.0107862	−	0.0107862i
$274$	−0.284138	−	0.284138i	−0.0171654	−	0.0171654i
$275$	−50.3791	−	50.3791i	−3.03797	−	3.03797i
$276$	0.311063	+	0.311063i	0.0187238	+	0.0187238i
$277$	6.02204			0.361829			0.180915	−	0.983499i	$-0.442094\pi$
$277$	6.02204			0.361829			0.180915	+	0.983499i	$0.442094\pi$
$278$		−	19.6773i		−	1.18016i
$279$		−	0.155658i		−	0.00931901i
$280$	−8.19504	−	8.19504i	−0.489747	−	0.489747i
$281$	5.64609	−	5.64609i	0.336818	−	0.336818i	−0.518351	−	0.855168i	$-0.673454\pi$
$281$	5.64609	−	5.64609i	0.336818	−	0.336818i	0.855168	+	0.518351i	$0.173454\pi$
$282$			13.2656i			0.789953i
$283$	18.2168			1.08288			0.541439	−	0.840740i	$-0.317880\pi$
$283$	18.2168			1.08288			0.541439	+	0.840740i	$0.317880\pi$
$284$	0.482615	+	0.482615i	0.0286379	+	0.0286379i
$285$			3.54086i			0.209743i
$286$	1.03788			0.0613711
$287$	5.84586	+	2.61265i	0.345070	+	0.154220i
$288$	−0.322347			−0.0189945
$289$			7.84611i			0.461536i
$290$	−33.0769	−	33.0769i	−1.94234	−	1.94234i
$291$	16.8611			0.988413
$292$			0.765497i			0.0447973i
$293$	11.1337	−	11.1337i	0.650437	−	0.650437i	−0.302662	−	0.953098i	$-0.597875\pi$
$293$	11.1337	−	11.1337i	0.650437	−	0.650437i	0.953098	+	0.302662i	$0.0978752\pi$
$294$	−2.04931	−	2.04931i	−0.119518	−	0.119518i
$295$		−	15.9182i		−	0.926791i
$296$			6.86747i			0.399164i
$297$	−22.4377			−1.30197
$298$	5.73324	+	5.73324i	0.332118	+	0.332118i
$299$	0.367293	+	0.367293i	0.0212411	+	0.0212411i
$300$	−0.913976	−	0.913976i	−0.0527684	−	0.0527684i
$301$	2.14600	−	2.14600i	0.123693	−	0.123693i
$302$	20.1105	−	20.1105i	1.15723	−	1.15723i
$303$	12.4445			0.714918
$304$	−1.22214	+	1.22214i	−0.0700947	+	0.0700947i
$305$	44.2945			2.53629
$306$	−3.34955	+	3.34955i	−0.191481	+	0.191481i
$307$			25.5666i			1.45916i	0.683895	+	0.729580i	$0.260285\pi$
$307$			25.5666i			1.45916i	−0.683895	+	0.729580i	$0.739715\pi$
$308$		−	0.303291i		−	0.0172816i
$309$	25.7044	−	25.7044i	1.46227	−	1.46227i
$310$	0.847399			0.0481290
$311$	−17.2681	+	17.2681i	−0.979186	+	0.979186i	−0.999788	−	0.0206022i	$-0.993442\pi$
$311$	−17.2681	+	17.2681i	−0.979186	+	0.979186i	0.0206022	+	0.999788i	$0.493442\pi$
$312$	−0.703272			−0.0398149
$313$	−1.93346	+	1.93346i	−0.109286	+	0.109286i	−0.759635	−	0.650350i	$-0.774622\pi$
$313$	−1.93346	+	1.93346i	−0.109286	+	0.109286i	0.650350	+	0.759635i	$0.274622\pi$
$314$	−6.75104	+	6.75104i	−0.380983	+	0.380983i
$315$	3.20986	+	3.20986i	0.180855	+	0.180855i
$316$	−0.208866	−	0.208866i	−0.0117496	−	0.0117496i
$317$	−13.5786	−	13.5786i	−0.762650	−	0.762650i	0.214150	−	0.976801i	$-0.431302\pi$
$317$	−13.5786	−	13.5786i	−0.762650	−	0.762650i	−0.976801	+	0.214150i	$0.931302\pi$
$318$	9.58541			0.537523
$319$			45.7220i			2.55994i
$320$			32.3164i			1.80654i
$321$	1.88710	+	1.88710i	0.105328	+	0.105328i
$322$	4.22349	−	4.22349i	0.235366	−	0.235366i
$323$			1.27494i			0.0709393i
$324$	−0.578059			−0.0321144
$325$	−1.07919	−	1.07919i	−0.0598629	−	0.0598629i
$326$		−	15.9695i		−	0.884470i
$327$	31.7953			1.75828
$328$	−6.37937	−	16.6893i	−0.352242	−	0.921514i
$329$	4.57724			0.252351
$330$			70.0043i			3.85361i
$331$	12.4254	+	12.4254i	0.682960	+	0.682960i	0.960666	−	0.277706i	$-0.0895742\pi$
$331$	12.4254	+	12.4254i	0.682960	+	0.682960i	−0.277706	+	0.960666i	$0.589574\pi$
$332$	−0.358320			−0.0196654
$333$		−	2.68987i		−	0.147404i
$334$	−7.77451	+	7.77451i	−0.425402	+	0.425402i
$335$	−1.66732	−	1.66732i	−0.0910952	−	0.0910952i
$336$			8.29791i			0.452688i
$337$		−	9.49981i		−	0.517488i	−0.965946	−	0.258744i	$-0.916691\pi$
$337$		−	9.49981i		−	0.517488i	0.965946	−	0.258744i	$-0.0833086\pi$
$338$	−18.6007			−1.01174
$339$	−9.63640	−	9.63640i	−0.523377	−	0.523377i
$340$	−0.463402	−	0.463402i	−0.0251315	−	0.0251315i
$341$	−0.585677	−	0.585677i	−0.0317162	−	0.0317162i
$342$	0.466520	−	0.466520i	0.0252265	−	0.0252265i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−8.46846			−0.456589
$345$	−24.7737	+	24.7737i	−1.33377	+	1.33377i
$346$	25.3901			1.36498
$347$	−1.41128	+	1.41128i	−0.0757616	+	0.0757616i	−0.743972	−	0.668211i	$-0.767061\pi$
$347$	−1.41128	+	1.41128i	−0.0757616	+	0.0757616i	0.668211	+	0.743972i	$0.267061\pi$
$348$			0.829487i			0.0444652i
$349$		−	8.37303i		−	0.448198i	−0.974566	−	0.224099i	$-0.928056\pi$
$349$		−	8.37303i		−	0.448198i	0.974566	−	0.224099i	$-0.0719439\pi$
$350$	−12.4096	+	12.4096i	−0.663322	+	0.663322i
$351$	−0.480650			−0.0256552
$352$	−1.21286	+	1.21286i	−0.0646456	+	0.0646456i
$353$	−1.47542			−0.0785289			−0.0392644	−	0.999229i	$-0.512501\pi$
$353$	−1.47542			−0.0785289			−0.0392644	+	0.999229i	$0.512501\pi$
$354$	−7.85405	+	7.85405i	−0.417438	+	0.417438i
$355$	−38.4364	+	38.4364i	−2.03999	+	2.03999i
$356$	0.545541	+	0.545541i	0.0289136	+	0.0289136i
$357$	4.32818	+	4.32818i	0.229072	+	0.229072i
$358$	6.97584	+	6.97584i	0.368685	+	0.368685i
$359$	−32.1445			−1.69652			−0.848262	−	0.529577i	$-0.822351\pi$
$359$	−32.1445			−1.69652			−0.848262	+	0.529577i	$0.822351\pi$
$360$		−	12.6666i		−	0.667589i
$361$			18.8224i			0.990654i
$362$	12.9029	+	12.9029i	0.678160	+	0.678160i
$363$	32.6472	−	32.6472i	1.71353	−	1.71353i
$364$		−	0.00649695i		−	0.000340533i
$365$	−60.9658			−3.19109
$366$	−21.8550	−	21.8550i	−1.14238	−	1.14238i
$367$			21.3714i			1.11558i	0.829983	+	0.557789i	$0.188350\pi$
$367$			21.3714i			1.11558i	−0.829983	+	0.557789i	$0.811650\pi$
$368$	−17.1015			−0.891476
$369$	2.49869	+	6.53692i	0.130077	+	0.340299i
$370$	14.6436			0.761284
$371$		−	3.30741i		−	0.171712i
$372$	−0.0106254	−	0.0106254i	−0.000550899	−	0.000550899i
$373$	5.20849			0.269685			0.134843	−	0.990867i	$-0.456947\pi$
$373$	5.20849			0.269685			0.134843	+	0.990867i	$0.456947\pi$
$374$			25.2060i			1.30337i
$375$	43.0826	−	43.0826i	2.22478	−	2.22478i
$376$	−9.03126	−	9.03126i	−0.465752	−	0.465752i
$377$			0.979432i			0.0504433i
$378$			5.52697i			0.284277i
$379$	−10.4977			−0.539232			−0.269616	−	0.962968i	$-0.586897\pi$
$379$	−10.4977			−0.539232			−0.269616	+	0.962968i	$0.586897\pi$
$380$	0.0645417	+	0.0645417i	0.00331092	+	0.00331092i
$381$	16.1195	+	16.1195i	0.825827	+	0.825827i
$382$	−26.5811	−	26.5811i	−1.36001	−	1.36001i
$383$	−5.32815	+	5.32815i	−0.272256	+	0.272256i	−0.830008	−	0.557752i	$-0.811664\pi$
$383$	−5.32815	+	5.32815i	−0.272256	+	0.272256i	0.557752	+	0.830008i	$0.311664\pi$
$384$	16.7888	−	16.7888i	0.856750	−	0.856750i
$385$	24.1547			1.23104
$386$	−10.9564	+	10.9564i	−0.557667	+	0.557667i
$387$	3.31695			0.168610
$388$	0.307338	−	0.307338i	0.0156027	−	0.0156027i
$389$		−	6.45167i		−	0.327113i	−0.986534	−	0.163556i	$-0.947703\pi$
$389$		−	6.45167i		−	0.327113i	0.986534	−	0.163556i	$-0.0522965\pi$
$390$			1.49960i			0.0759350i
$391$	−8.92010	+	8.92010i	−0.451109	+	0.451109i
$392$	2.79036			0.140934
$393$	−9.14728	+	9.14728i	−0.461419	+	0.461419i
$394$	−37.4820			−1.88832
$395$	16.6345	−	16.6345i	0.836973	−	0.836973i
$396$	0.234390	−	0.234390i	0.0117786	−	0.0117786i
$397$	0.473294	+	0.473294i	0.0237539	+	0.0237539i	0.718884	−	0.695130i	$-0.244653\pi$
$397$	0.473294	+	0.473294i	0.0237539	+	0.0237539i	−0.695130	+	0.718884i	$0.744653\pi$
$398$	−2.53766	−	2.53766i	−0.127202	−	0.127202i
$399$	−0.602821	−	0.602821i	−0.0301788	−	0.0301788i
$400$	50.2482			2.51241
$401$		−	16.5371i		−	0.825824i	−0.910771	−	0.412912i	$-0.864512\pi$
$401$		−	16.5371i		−	0.825824i	0.910771	−	0.412912i	$-0.135488\pi$
$402$			1.64532i			0.0820609i
$403$	−0.0125461	−	0.0125461i	−0.000624965	−	0.000624965i
$404$	0.226834	−	0.226834i	0.0112854	−	0.0112854i
$405$		−	46.0378i		−	2.28764i
$406$	11.2625			0.558946
$407$	−10.1209	−	10.1209i	−0.501673	−	0.501673i
$408$		−	17.0797i		−	0.845571i
$409$	−28.0847			−1.38870			−0.694349	−	0.719639i	$-0.744307\pi$
$409$	−28.0847			−1.38870			−0.694349	+	0.719639i	$0.744307\pi$
$410$	−35.5869	+	13.6028i	−1.75751	+	0.671795i
$411$	−0.567488			−0.0279921
$412$		−	0.937062i		−	0.0461658i
$413$	2.71001	+	2.71001i	0.133351	+	0.133351i
$414$	6.52802			0.320835
$415$		−	28.5374i		−	1.40084i
$416$	−0.0259812	+	0.0259812i	−0.00127383	+	0.00127383i
$417$	−19.6500	−	19.6500i	−0.962264	−	0.962264i
$418$		−	3.51064i		−	0.171711i
$419$			12.3845i			0.605020i	0.953146	+	0.302510i	$0.0978246\pi$
$419$			12.3845i			0.605020i	−0.953146	+	0.302510i	$0.902175\pi$
$420$	0.438215			0.0213827
$421$	−13.4828	−	13.4828i	−0.657112	−	0.657112i	0.297584	−	0.954696i	$-0.403819\pi$
$421$	−13.4828	−	13.4828i	−0.657112	−	0.657112i	−0.954696	+	0.297584i	$0.903819\pi$
$422$	−7.26715	−	7.26715i	−0.353759	−	0.353759i
$423$	3.53739	+	3.53739i	0.171994	+	0.171994i
$424$	−6.52580	+	6.52580i	−0.316921	+	0.316921i
$425$	26.2094	−	26.2094i	1.27134	−	1.27134i
$426$	37.9292			1.83768
$427$	−7.54099	+	7.54099i	−0.364934	+	0.364934i
$428$	0.0687950			0.00332533
$429$	1.03644	−	1.03644i	0.0500398	−	0.0500398i
$430$			18.0574i			0.870805i
$431$			1.33652i			0.0643778i	0.999482	+	0.0321889i	$0.0102478\pi$
$431$			1.33652i			0.0643778i	−0.999482	+	0.0321889i	$0.989752\pi$
$432$	11.1897	−	11.1897i	0.538366	−	0.538366i
$433$	−34.3058			−1.64863			−0.824315	−	0.566131i	$-0.808440\pi$
$433$	−34.3058			−1.64863			−0.824315	+	0.566131i	$0.808440\pi$
$434$	−0.144267	+	0.144267i	−0.00692504	+	0.00692504i
$435$	−66.0621			−3.16743
$436$	0.579554	−	0.579554i	0.0277556	−	0.0277556i
$437$	1.24238	−	1.24238i	0.0594309	−	0.0594309i
$438$	30.0806	+	30.0806i	1.43731	+	1.43731i
$439$	−6.91629	−	6.91629i	−0.330096	−	0.330096i	0.522527	−	0.852623i	$-0.324990\pi$
$439$	−6.91629	−	6.91629i	−0.330096	−	0.330096i	−0.852623	+	0.522527i	$0.824990\pi$
$440$	−47.6593	−	47.6593i	−2.27207	−	2.27207i
$441$	−1.09294			−0.0520445
$442$			0.539950i			0.0256828i
$443$			32.6829i			1.55281i	0.630235	+	0.776405i	$0.282959\pi$
$443$			32.6829i			1.55281i	−0.630235	+	0.776405i	$0.717041\pi$
$444$	−0.183613	−	0.183613i	−0.00871388	−	0.00871388i
$445$	−43.4480	+	43.4480i	−2.05963	+	2.05963i
$446$		−	6.12479i		−	0.290017i
$447$	11.4506			0.541594
$448$	−5.50176	−	5.50176i	−0.259934	−	0.259934i
$449$		−	41.8033i		−	1.97282i	−0.164300	−	0.986410i	$-0.552537\pi$
$449$		−	41.8033i		−	1.97282i	0.164300	−	0.986410i	$-0.447463\pi$
$450$	−19.1809			−0.904194
$451$	33.9973	+	15.1942i	1.60087	+	0.715467i
$452$	−0.351298			−0.0165237
$453$		−	40.1653i		−	1.88713i
$454$	19.4596	+	19.4596i	0.913285	+	0.913285i
$455$	0.517430			0.0242575
$456$			2.37883i			0.111399i
$457$	1.86448	−	1.86448i	0.0872168	−	0.0872168i	−0.662152	−	0.749369i	$-0.730357\pi$
$457$	1.86448	−	1.86448i	0.0872168	−	0.0872168i	0.749369	+	0.662152i	$0.230357\pi$
$458$	9.07999	+	9.07999i	0.424280	+	0.424280i
$459$		−	11.6731i		−	0.544853i
$460$			0.903134i			0.0421088i
$461$	14.2517			0.663768			0.331884	−	0.943320i	$-0.392316\pi$
$461$	14.2517			0.663768			0.331884	+	0.943320i	$0.392316\pi$
$462$	−11.9180	−	11.9180i	−0.554476	−	0.554476i
$463$	17.4521	+	17.4521i	0.811069	+	0.811069i	0.984794	−	0.173725i	$-0.0555804\pi$
$463$	17.4521	+	17.4521i	0.811069	+	0.811069i	−0.173725	+	0.984794i	$0.555580\pi$
$464$	−22.8016	−	22.8016i	−1.05854	−	1.05854i
$465$	0.846225	−	0.846225i	0.0392427	−	0.0392427i
$466$	26.0728	−	26.0728i	1.20780	−	1.20780i
$467$	−9.10181			−0.421182			−0.210591	−	0.977574i	$-0.567539\pi$
$467$	−9.10181			−0.421182			−0.210591	+	0.977574i	$0.567539\pi$
$468$	0.00502099	−	0.00502099i	0.000232095	−	0.000232095i
$469$	0.567711			0.0262144
$470$	−19.2575	+	19.2575i	−0.888281	+	0.888281i
$471$			13.4834i			0.621281i
$472$		−	10.6942i		−	0.492238i
$473$	12.4803	−	12.4803i	0.573846	−	0.573846i
$474$	−16.4150			−0.753966
$475$	−3.65039	+	3.65039i	−0.167491	+	0.167491i
$476$	0.157785			0.00723208
$477$	2.55604	−	2.55604i	0.117033	−	0.117033i
$478$	−4.32261	+	4.32261i	−0.197712	+	0.197712i
$479$	26.2334	+	26.2334i	1.19864	+	1.19864i	0.974575	+	0.224061i	$0.0719315\pi$
$479$	26.2334	+	26.2334i	1.19864	+	1.19864i	0.224061	+	0.974575i	$0.428069\pi$
$480$	−1.75242	−	1.75242i	−0.0799865	−	0.0799865i
$481$	−0.216804	−	0.216804i	−0.00988542	−	0.00988542i
$482$	−30.1859			−1.37493
$483$		−	8.43528i		−	0.383819i
$484$		−	1.19017i		−	0.0540984i
$485$	24.4770	+	24.4770i	1.11144	+	1.11144i
$486$	−10.9907	+	10.9907i	−0.498546	+	0.498546i
$487$			1.65413i			0.0749558i	0.999297	+	0.0374779i	$0.0119324\pi$
$487$			1.65413i			0.0749558i	−0.999297	+	0.0374779i	$0.988068\pi$
$488$	29.7580			1.34708
$489$	−15.9474	−	15.9474i	−0.721166	−	0.721166i
$490$		−	5.94992i		−	0.268790i
$491$	−0.0361489			−0.00163138			−0.000815688	−	1.00000i	$-0.500260\pi$
$491$	−0.0361489			−0.00163138			−0.000815688		1.00000i	$0.500260\pi$
$492$	0.616779	+	0.275653i	0.0278065	+	0.0124274i
$493$	−23.7865			−1.07129
$494$		−	0.0752032i		−	0.00338355i
$495$	18.6673	+	18.6673i	0.839034	+	0.839034i
$496$	0.584156			0.0262294
$497$		−	13.0874i		−	0.587048i
$498$	−14.0804	+	14.0804i	−0.630958	+	0.630958i
$499$	22.3457	+	22.3457i	1.00033	+	1.00033i	1.00000		0.000332119i	$0.000105717\pi$
$499$	22.3457	+	22.3457i	1.00033	+	1.00033i	0.000332119		1.00000i	$0.499894\pi$
$500$		−	1.57059i		−	0.0702389i
$501$			15.5275i			0.693716i
$502$	18.7418			0.836487
$503$	−17.2456	−	17.2456i	−0.768945	−	0.768945i	0.208975	−	0.977921i	$-0.432987\pi$
$503$	−17.2456	−	17.2456i	−0.768945	−	0.768945i	−0.977921	+	0.208975i	$0.932987\pi$
$504$	2.15645	+	2.15645i	0.0960559	+	0.0960559i
$505$	18.0655	+	18.0655i	0.803906	+	0.803906i
$506$	24.5622	−	24.5622i	1.09193	−	1.09193i
$507$	−18.5749	+	18.5749i	−0.824941	+	0.824941i
$508$	0.587642			0.0260724
$509$	11.1940	−	11.1940i	0.496166	−	0.496166i	−0.414076	−	0.910242i	$-0.635895\pi$
$509$	11.1940	−	11.1940i	0.496166	−	0.496166i	0.910242	+	0.414076i	$0.135895\pi$
$510$	−36.4193			−1.61267
$511$	10.3792	−	10.3792i	0.459150	−	0.459150i
$512$			21.6801i			0.958132i
$513$			1.62581i			0.0717811i
$514$	25.7114	−	25.7114i	1.13408	−	1.13408i
$515$	74.6296			3.28857
$516$	0.226418	−	0.226418i	0.00996749	−	0.00996749i
$517$	26.6195			1.17072
$518$	−2.49303	+	2.49303i	−0.109537	+	0.109537i
$519$	25.3549	−	25.3549i	1.11296	−	1.11296i
$520$	−1.02093	−	1.02093i	−0.0447708	−	0.0447708i
$521$	−12.0417	−	12.0417i	−0.527558	−	0.527558i	0.392286	−	0.919843i	$-0.371685\pi$
$521$	−12.0417	−	12.0417i	−0.527558	−	0.527558i	−0.919843	+	0.392286i	$0.871685\pi$
$522$	8.70388	+	8.70388i	0.380958	+	0.380958i
$523$	−32.9133			−1.43920			−0.719599	−	0.694390i	$-0.755674\pi$
$523$	−32.9133			−1.43920			−0.719599	+	0.694390i	$0.755674\pi$
$524$			0.333467i			0.0145676i
$525$			24.7848i			1.08170i
$526$	−20.2184	−	20.2184i	−0.881563	−	0.881563i
$527$	0.304695	−	0.304695i	0.0132727	−	0.0132727i
$528$			48.2575i			2.10014i
$529$	−5.61541			−0.244148
$530$	13.9150	+	13.9150i	0.604431	+	0.604431i
$531$			4.18872i			0.181775i
$532$	−0.0219760			−0.000952782
$533$	0.728273	+	0.325483i	0.0315450	+	0.0140982i
$534$	42.8747			1.85537
$535$			5.47898i			0.236877i
$536$	−1.12014	−	1.12014i	−0.0483826	−	0.0483826i
$537$	13.9324			0.601225
$538$		−	12.9048i		−	0.556366i
$539$	−4.11227	+	4.11227i	−0.177128	+	0.177128i
$540$	−0.590932	−	0.590932i	−0.0254297	−	0.0254297i
$541$		−	21.2163i		−	0.912161i	−0.889939	−	0.456080i	$-0.849253\pi$
$541$		−	21.2163i		−	0.912161i	0.889939	−	0.456080i	$-0.150747\pi$
$542$		−	9.43782i		−	0.405389i
$543$	25.7700			1.10590
$544$	−0.630981	−	0.630981i	−0.0270531	−	0.0270531i
$545$	46.1569	+	46.1569i	1.97714	+	1.97714i
$546$	−0.255301	−	0.255301i	−0.0109259	−	0.0109259i
$547$	−14.5235	+	14.5235i	−0.620981	+	0.620981i	−0.945782	−	0.324801i	$-0.894703\pi$
$547$	−14.5235	+	14.5235i	−0.620981	+	0.620981i	0.324801	+	0.945782i	$0.394703\pi$
$548$	−0.0103440	+	0.0103440i	−0.000441873	+	0.000441873i
$549$	−11.6557			−0.497453
$550$	−72.1697	+	72.1697i	−3.07732	+	3.07732i
$551$	3.31294			0.141136
$552$	−16.6435	+	16.6435i	−0.708394	+	0.708394i
$553$			5.66394i			0.240855i
$554$		−	8.62678i		−	0.366517i
$555$	14.6233	−	14.6233i	0.620725	−	0.620725i
$556$	−0.716347			−0.0303799
$557$	−30.5354	+	30.5354i	−1.29383	+	1.29383i	−0.361424	+	0.932402i	$0.617709\pi$
$557$	−30.5354	+	30.5354i	−1.29383	+	1.29383i	−0.932402	+	0.361424i	$0.882291\pi$
$558$	−0.222985			−0.00943972
$559$	0.267347	−	0.267347i	0.0113076	−	0.0113076i
$560$	−12.0460	+	12.0460i	−0.509036	+	0.509036i
$561$	25.1711	+	25.1711i	1.06272	+	1.06272i
$562$	−8.08822	−	8.08822i	−0.341181	−	0.341181i
$563$	−24.1769	−	24.1769i	−1.01893	−	1.01893i	−0.999817	−	0.0191160i	$-0.993915\pi$
$563$	−24.1769	−	24.1769i	−1.01893	−	1.01893i	−0.0191160	−	0.999817i	$-0.506085\pi$
$564$	0.482931			0.0203350
$565$		−	27.9781i		−	1.17705i
$566$		−	26.0962i		−	1.09691i
$567$	7.83778	+	7.83778i	0.329156	+	0.329156i
$568$	−25.8224	+	25.8224i	−1.08348	+	1.08348i
$569$		−	15.6165i		−	0.654679i	−0.944907	−	0.327339i	$-0.893848\pi$
$569$		−	15.6165i		−	0.654679i	0.944907	−	0.327339i	$-0.106152\pi$
$570$	5.07241			0.212460
$571$	1.18896	+	1.18896i	0.0497566	+	0.0497566i	0.731547	−	0.681791i	$-0.238799\pi$
$571$	1.18896	+	1.18896i	0.0497566	+	0.0497566i	−0.681791	+	0.731547i	$0.738799\pi$
$572$		−	0.0377838i		−	0.00157982i
$573$	−53.0886			−2.21781
$574$	3.74271	−	8.37438i	0.156218	−	0.349540i
$575$	−51.0800			−2.13018
$576$		−	8.50376i		−	0.354323i
$577$	8.88143	+	8.88143i	0.369739	+	0.369739i	0.867382	−	0.497643i	$-0.165801\pi$
$577$	8.88143	+	8.88143i	0.369739	+	0.369739i	−0.497643	+	0.867382i	$0.665801\pi$
$578$	11.2398			0.467515
$579$			21.8825i			0.909404i
$580$	−1.20416	+	1.20416i	−0.0499999	+	0.0499999i
$581$	4.85840	+	4.85840i	0.201560	+	0.201560i
$582$		−	24.1540i		−	1.00122i
$583$		−	19.2347i		−	0.796619i
$584$	−40.9581			−1.69486
$585$	0.399882	+	0.399882i	0.0165331	+	0.0165331i
$586$	−15.9494	−	15.9494i	−0.658862	−	0.658862i
$587$	11.6442	+	11.6442i	0.480609	+	0.480609i	0.905326	−	0.424717i	$-0.139626\pi$
$587$	11.6442	+	11.6442i	0.480609	+	0.480609i	−0.424717	+	0.905326i	$0.639626\pi$
$588$	−0.0746047	+	0.0746047i	−0.00307665	+	0.00307665i
$589$	−0.0424373	+	0.0424373i	−0.00174860	+	0.00174860i
$590$	−22.8033			−0.938796
$591$	−37.4300	+	37.4300i	−1.53967	+	1.53967i
$592$	10.0946			0.414885
$593$	13.8522	−	13.8522i	0.568841	−	0.568841i	−0.362963	−	0.931804i	$-0.618235\pi$
$593$	13.8522	−	13.8522i	0.568841	−	0.568841i	0.931804	+	0.362963i	$0.118235\pi$
$594$			32.1428i			1.31884i
$595$			12.5663i			0.515170i
$596$	0.208718	−	0.208718i	0.00854940	−	0.00854940i
$597$	−5.06829			−0.207431
$598$	0.526160	−	0.526160i	0.0215163	−	0.0215163i
$599$	−10.6534			−0.435288			−0.217644	−	0.976028i	$-0.569837\pi$
$599$	−10.6534			−0.435288			−0.217644	+	0.976028i	$0.569837\pi$
$600$	48.9025	−	48.9025i	1.99644	−	1.99644i
$601$	25.5159	−	25.5159i	1.04081	−	1.04081i	0.0416837	−	0.999131i	$-0.486728\pi$
$601$	25.5159	−	25.5159i	1.04081	−	1.04081i	0.999131	−	0.0416837i	$-0.0132722\pi$
$602$	−3.07421	−	3.07421i	−0.125296	−	0.125296i
$603$	0.438739	+	0.438739i	0.0178668	+	0.0178668i
$604$	−0.732119	−	0.732119i	−0.0297895	−	0.0297895i
$605$	94.7872			3.85365
$606$		−	17.8272i		−	0.724179i
$607$		−	9.89410i		−	0.401589i	−0.979633	−	0.200794i	$-0.935648\pi$
$607$		−	9.89410i		−	0.401589i	0.979633	−	0.200794i	$-0.0643523\pi$
$608$	0.0878819	+	0.0878819i	0.00356408	+	0.00356408i
$609$	11.2469	−	11.2469i	0.455745	−	0.455745i
$610$		−	63.4533i		−	2.56915i
$611$	0.570229			0.0230690
$612$	0.121940	+	0.121940i	0.00492913	+	0.00492913i
$613$			13.7993i			0.557347i	0.960386	+	0.278674i	$0.0898947\pi$
$613$			13.7993i			0.557347i	−0.960386	+	0.278674i	$0.910105\pi$
$614$	36.6249			1.47806
$615$	−21.9536	+	49.1215i	−0.885254	+	1.98077i
$616$	16.2277			0.653832
$617$			31.8748i			1.28323i	0.767026	+	0.641616i	$0.221736\pi$
$617$			31.8748i			1.28323i	−0.767026	+	0.641616i	$0.778264\pi$
$618$	−36.8224	−	36.8224i	−1.48121	−	1.48121i
$619$	9.40831			0.378152			0.189076	−	0.981962i	$-0.439451\pi$
$619$	9.40831			0.378152			0.189076	+	0.981962i	$0.439451\pi$
$620$		−	0.0308494i		−	0.00123894i
$621$	−11.3750	+	11.3750i	−0.456462	+	0.456462i
$622$	24.7372	+	24.7372i	0.991870	+	0.991870i
$623$		−	14.7938i		−	0.592700i
$624$			1.03375i			0.0413830i
$625$	63.8305			2.55322
$626$	2.76975	+	2.76975i	0.110701	+	0.110701i
$627$	−3.50578	−	3.50578i	−0.140007	−	0.140007i
$628$	0.245770	+	0.245770i	0.00980731	+	0.00980731i
$629$	5.26532	−	5.26532i	0.209942	−	0.209942i
$630$	4.59823	−	4.59823i	0.183198	−	0.183198i
$631$	−29.6917			−1.18201			−0.591004	−	0.806669i	$-0.701268\pi$
$631$	−29.6917			−1.18201			−0.591004	+	0.806669i	$0.701268\pi$
$632$	11.1754	−	11.1754i	0.444534	−	0.444534i
$633$	−14.5142			−0.576886
$634$	−19.4518	+	19.4518i	−0.772530	+	0.772530i
$635$			46.8010i			1.85724i
$636$		−	0.348955i		−	0.0138370i
$637$	−0.0880909	+	0.0880909i	−0.00349029	+	0.00349029i
$638$	65.4982			2.59310
$639$	10.1142	−	10.1142i	0.400111	−	0.400111i
$640$	48.7443			1.92679
$641$	−2.15118	+	2.15118i	−0.0849667	+	0.0849667i	−0.748313	−	0.663346i	$-0.769136\pi$
$641$	−2.15118	+	2.15118i	−0.0849667	+	0.0849667i	0.663346	+	0.748313i	$0.269136\pi$
$642$	2.70334	−	2.70334i	0.106692	−	0.106692i
$643$	−10.6815	−	10.6815i	−0.421238	−	0.421238i	0.464392	−	0.885630i	$-0.346273\pi$
$643$	−10.6815	−	10.6815i	−0.421238	−	0.421238i	−0.885630	+	0.464392i	$0.846273\pi$
$644$	−0.153756	−	0.153756i	−0.00605882	−	0.00605882i
$645$	18.0324	+	18.0324i	0.710024	+	0.710024i
$646$	1.82639			0.0718583
$647$		−	19.4327i		−	0.763977i	−0.924167	−	0.381988i	$-0.875239\pi$
$647$		−	19.4327i		−	0.763977i	0.924167	−	0.381988i	$-0.124761\pi$
$648$		−	30.9292i		−	1.21501i
$649$	15.7604	+	15.7604i	0.618651	+	0.618651i
$650$	−1.54598	+	1.54598i	−0.0606384	+	0.0606384i
$651$			0.288134i			0.0112929i
$652$	−0.581368			−0.0227681
$653$	−31.9084	−	31.9084i	−1.24867	−	1.24867i	−0.956306	−	0.292367i	$-0.905557\pi$
$653$	−31.9084	−	31.9084i	−1.24867	−	1.24867i	−0.292367	−	0.956306i	$-0.594443\pi$
$654$		−	45.5478i		−	1.78106i
$655$	−26.5580			−1.03771
$656$	−24.5319	+	9.37712i	−0.957808	+	0.366115i
$657$	16.0426			0.625881
$658$		−	6.55705i		−	0.255620i
$659$	18.3736	+	18.3736i	0.715734	+	0.715734i	0.967729	−	0.251995i	$-0.0810865\pi$
$659$	18.3736	+	18.3736i	0.715734	+	0.715734i	−0.251995	+	0.967729i	$0.581087\pi$
$660$	2.54849			0.0992000
$661$		−	14.9586i		−	0.581820i	−0.956750	−	0.290910i	$-0.906042\pi$
$661$		−	14.9586i		−	0.581820i	0.956750	−	0.290910i	$-0.0939581\pi$
$662$	17.7997	−	17.7997i	0.691807	−	0.691807i
$663$	0.539201	+	0.539201i	0.0209409	+	0.0209409i
$664$		−	19.1720i		−	0.744019i
$665$		−	1.75022i		−	0.0678705i
$666$	−3.85333			−0.149314
$667$	23.1791	+	23.1791i	0.897497	+	0.897497i
$668$	0.283030	+	0.283030i	0.0109507	+	0.0109507i
$669$	−6.11631	−	6.11631i	−0.236470	−	0.236470i
$670$	−2.38849	+	2.38849i	−0.0922753	+	0.0922753i
$671$	−43.8556	+	43.8556i	−1.69302	+	1.69302i
$672$	0.596687			0.0230177
$673$	−18.0756	+	18.0756i	−0.696763	+	0.696763i	−0.963711	−	0.266948i	$-0.913985\pi$
$673$	−18.0756	+	18.0756i	−0.696763	+	0.696763i	0.266948	+	0.963711i	$0.413985\pi$
$674$	−13.6088			−0.524191
$675$	33.4223	−	33.4223i	1.28643	−	1.28643i
$676$			0.677155i			0.0260444i
$677$			10.1264i			0.389189i	0.980884	+	0.194595i	$0.0623392\pi$
$677$			10.1264i			0.389189i	−0.980884	+	0.194595i	$0.937661\pi$
$678$	−13.8045	+	13.8045i	−0.530157	+	0.530157i
$679$	−8.33427			−0.319840
$680$	24.7944	−	24.7944i	0.950822	−	0.950822i
$681$	38.8653			1.48932
$682$	−0.839002	+	0.839002i	−0.0321271	+	0.0321271i
$683$	25.9248	−	25.9248i	0.991987	−	0.991987i	−0.00798159	−	0.999968i	$-0.502541\pi$
$683$	25.9248	−	25.9248i	0.991987	−	0.991987i	0.999968	+	0.00798159i	$0.00254065\pi$
$684$	−0.0169836	−	0.0169836i	−0.000649383	−	0.000649383i
$685$	−0.823817	−	0.823817i	−0.0314764	−	0.0314764i
$686$	1.01295	+	1.01295i	0.0386748	+	0.0386748i
$687$	18.1348			0.691886
$688$			12.4479i			0.474572i
$689$		−	0.412035i		−	0.0156973i
$690$	35.4891	+	35.4891i	1.35105	+	1.35105i
$691$	21.2595	−	21.2595i	0.808748	−	0.808748i	−0.175696	−	0.984444i	$-0.556218\pi$
$691$	21.2595	−	21.2595i	0.808748	−	0.808748i	0.984444	+	0.175696i	$0.0562176\pi$
$692$		−	0.924321i		−	0.0351374i
$693$	−6.35610			−0.241448
$694$	2.02171	+	2.02171i	0.0767430	+	0.0767430i
$695$		−	57.0514i		−	2.16408i
$696$	−44.3819			−1.68229
$697$	−7.90469	+	17.6869i	−0.299411	+	0.669938i
$698$	−11.9946			−0.454004
$699$		−	52.0733i		−	1.96959i
$700$	0.451770	+	0.451770i	0.0170753	+	0.0170753i
$701$	−12.4755			−0.471193			−0.235596	−	0.971851i	$-0.575704\pi$
$701$	−12.4755			−0.471193			−0.235596	+	0.971851i	$0.575704\pi$
$702$			0.688547i			0.0259875i
$703$	−0.733344	+	0.733344i	−0.0276586	+	0.0276586i
$704$	−31.9961	−	31.9961i	−1.20590	−	1.20590i
$705$			38.4616i			1.44855i
$706$			2.11359i			0.0795461i
$707$	−6.15120			−0.231340
$708$	0.285925	+	0.285925i	0.0107457	+	0.0107457i
$709$	13.3457	+	13.3457i	0.501207	+	0.501207i	0.911813	−	0.410606i	$-0.134683\pi$
$709$	13.3457	+	13.3457i	0.501207	+	0.501207i	−0.410606	+	0.911813i	$0.634683\pi$
$710$	55.0615	+	55.0615i	2.06642	+	2.06642i
$711$	−4.37722	+	4.37722i	−0.164159	+	0.164159i
$712$	−29.1893	+	29.1893i	−1.09391	+	1.09391i
$713$	−0.593826			−0.0222390
$714$	6.20026	−	6.20026i	0.232039	−	0.232039i
$715$	3.00918			0.112537
$716$	0.253954	−	0.253954i	0.00949072	−	0.00949072i
$717$			8.63324i			0.322414i
$718$			46.0481i			1.71850i
$719$	9.12821	−	9.12821i	0.340425	−	0.340425i	−0.516102	−	0.856527i	$-0.672617\pi$
$719$	9.12821	−	9.12821i	0.340425	−	0.340425i	0.856527	+	0.516102i	$0.172617\pi$
$720$	−18.6188			−0.693882
$721$	−12.7054	+	12.7054i	−0.473175	+	0.473175i
$722$	26.9638			1.00349
$723$	−30.1441	+	30.1441i	−1.12107	+	1.12107i
$724$	0.469727	−	0.469727i	0.0174573	−	0.0174573i
$725$	−68.1055	−	68.1055i	−2.52938	−	2.52938i
$726$	−46.7682	−	46.7682i	−1.73573	−	1.73573i
$727$	−7.16412	−	7.16412i	−0.265703	−	0.265703i	0.561663	−	0.827366i	$-0.310162\pi$
$727$	−7.16412	−	7.16412i	−0.265703	−	0.265703i	−0.827366	+	0.561663i	$0.810162\pi$
$728$	0.347621			0.0128837
$729$		−	11.3021i		−	0.418595i
$730$			87.3355i			3.23243i
$731$	6.49280	+	6.49280i	0.240145	+	0.240145i
$732$	−0.795627	+	0.795627i	−0.0294072	+	0.0294072i
$733$			24.0714i			0.889098i	0.895755	+	0.444549i	$0.146636\pi$
$733$			24.0714i			0.889098i	−0.895755	+	0.444549i	$0.853364\pi$
$734$	30.6152			1.13003
$735$	−5.94167	−	5.94167i	−0.219162	−	0.219162i
$736$			1.22973i			0.0453286i
$737$	3.30159			0.121616
$738$	9.36436	−	3.57946i	0.344707	−	0.131762i
$739$	6.93712			0.255186			0.127593	−	0.991827i	$-0.459275\pi$
$739$	6.93712			0.255186			0.127593	+	0.991827i	$0.459275\pi$
$740$		−	0.533098i		−	0.0195971i
$741$	−0.0750990	−	0.0750990i	−0.00275883	−	0.00275883i
$742$	−4.73798			−0.173937
$743$			11.4319i			0.419395i	0.977766	+	0.209697i	$0.0672479\pi$
$743$			11.4319i			0.419395i	−0.977766	+	0.209697i	$0.932752\pi$
$744$	0.568512	−	0.568512i	0.0208427	−	0.0208427i
$745$	16.6227	+	16.6227i	0.609008	+	0.609008i
$746$		−	7.46133i		−	0.273179i
$747$			7.50935i			0.274753i
$748$	0.917620			0.0335515
$749$	−0.932778	−	0.932778i	−0.0340830	−	0.0340830i
$750$	−61.7172	−	61.7172i	−2.25359	−	2.25359i
$751$	−5.90700	−	5.90700i	−0.215550	−	0.215550i	0.591070	−	0.806620i	$-0.298706\pi$
$751$	−5.90700	−	5.90700i	−0.215550	−	0.215550i	−0.806620	+	0.591070i	$0.798706\pi$
$752$	−13.2752	+	13.2752i	−0.484096	+	0.484096i
$753$	18.7158	−	18.7158i	0.682043	−	0.682043i
$754$	1.40307			0.0510968
$755$	58.3075	−	58.3075i	2.12203	−	2.12203i
$756$	0.201209			0.00731788
$757$	−9.87616	+	9.87616i	−0.358955	+	0.358955i	−0.863428	−	0.504473i	$-0.831687\pi$
$757$	−9.87616	+	9.87616i	−0.358955	+	0.358955i	0.504473	+	0.863428i	$0.331687\pi$
$758$			15.0384i			0.546218i
$759$		−	49.0564i		−	1.78064i
$760$	−3.45332	+	3.45332i	−0.125265	+	0.125265i
$761$	9.95825			0.360986			0.180493	−	0.983576i	$-0.442231\pi$
$761$	9.95825			0.360986			0.180493	+	0.983576i	$0.442231\pi$
$762$	23.0917	−	23.0917i	0.836525	−	0.836525i
$763$	−15.7161			−0.568962
$764$	−0.967682	+	0.967682i	−0.0350095	+	0.0350095i
$765$	−9.71155	+	9.71155i	−0.351122	+	0.351122i
$766$	7.63275	+	7.63275i	0.275782	+	0.275782i
$767$	0.337612	+	0.337612i	0.0121904	+	0.0121904i
$768$	−1.78931	−	1.78931i	−0.0645660	−	0.0645660i
$769$	15.3336			0.552944			0.276472	−	0.961022i	$-0.410835\pi$
$769$	15.3336			0.552944			0.276472	+	0.961022i	$0.410835\pi$
$770$		−	34.6025i		−	1.24699i
$771$		−	51.3515i		−	1.84938i
$772$	0.398866	+	0.398866i	0.0143555	+	0.0143555i
$773$	−3.63777	+	3.63777i	−0.130842	+	0.130842i	−0.769495	−	0.638653i	$-0.779492\pi$
$773$	−3.63777	+	3.63777i	−0.130842	+	0.130842i	0.638653	+	0.769495i	$0.279492\pi$
$774$		−	4.75164i		−	0.170794i
$775$	1.74480			0.0626751
$776$	16.4442	+	16.4442i	0.590312	+	0.590312i
$777$			4.97914i			0.178626i
$778$	−9.24223			−0.331350
$779$	1.10095	−	2.46339i	0.0394456	−	0.0882602i
$780$	0.0545925			0.00195473
$781$		−	76.1111i		−	2.72347i
$782$	12.7783	+	12.7783i	0.456953	+	0.456953i
$783$	−30.3327			−1.08400
$784$		−	4.10158i		−	0.146485i
$785$	−19.5737	+	19.5737i	−0.698614	+	0.698614i
$786$	13.1038	+	13.1038i	0.467396	+	0.467396i
$787$		−	23.1861i		−	0.826496i	−0.910619	−	0.413248i	$-0.864394\pi$
$787$		−	23.1861i		−	0.826496i	0.910619	−	0.413248i	$-0.135606\pi$
$788$			1.36453i			0.0486092i
$789$	−40.3807			−1.43759
$790$	−23.8295	−	23.8295i	−0.847815	−	0.847815i
$791$	4.76318	+	4.76318i	0.169359	+	0.169359i
$792$	12.5411	+	12.5411i	0.445629	+	0.445629i
$793$	−0.939451	+	0.939451i	−0.0333609	+	0.0333609i
$794$	0.678009	−	0.678009i	0.0240616	−	0.0240616i
$795$	27.7915			0.985663
$796$	−0.0923832	+	0.0923832i	−0.00327444	+	0.00327444i
$797$	−32.1655			−1.13936			−0.569681	−	0.821866i	$-0.692933\pi$
$797$	−32.1655			−1.13936			−0.569681	+	0.821866i	$0.692933\pi$
$798$	−0.863561	+	0.863561i	−0.0305697	+	0.0305697i
$799$			13.8486i			0.489929i
$800$		−	3.61325i		−	0.127748i
$801$	11.4329	−	11.4329i	0.403963	−	0.403963i
$802$	−23.6899			−0.836521
$803$	60.3617	−	60.3617i	2.13012	−	2.13012i
$804$	0.0598974			0.00211242
$805$	12.2454	−	12.2454i	0.431594	−	0.431594i
$806$	−0.0179727	+	0.0179727i	−0.000633060	+	0.000633060i
$807$	−12.8869	−	12.8869i	−0.453641	−	0.453641i
$808$	12.1368	+	12.1368i	0.426972	+	0.426972i
$809$	11.3034	+	11.3034i	0.397406	+	0.397406i	0.877317	−	0.479911i	$-0.159331\pi$
$809$	11.3034	+	11.3034i	0.397406	+	0.397406i	−0.479911	+	0.877317i	$0.659331\pi$
$810$	−65.9506			−2.31727
$811$		−	18.6875i		−	0.656207i	−0.944642	−	0.328103i	$-0.893591\pi$
$811$		−	18.6875i		−	0.656207i	0.944642	−	0.328103i	$-0.106409\pi$
$812$		−	0.410008i		−	0.0143885i
$813$	−9.42474	−	9.42474i	−0.330540	−	0.330540i
$814$	−14.4985	+	14.4985i	−0.508172	+	0.508172i
$815$		−	46.3013i		−	1.62187i
$816$	−25.1057			−0.878874
$817$	−0.904306	−	0.904306i	−0.0316376	−	0.0316376i
$818$			40.2322i			1.40669i
$819$	−0.136157			−0.00475772
$820$	0.495208	+	1.29553i	0.0172934	+	0.0452420i
$821$	22.9781			0.801940			0.400970	−	0.916091i	$-0.368673\pi$
$821$	22.9781			0.801940			0.400970	+	0.916091i	$0.368673\pi$
$822$			0.812946i			0.0283547i
$823$	−16.2925	−	16.2925i	−0.567921	−	0.567921i	0.363624	−	0.931546i	$-0.381539\pi$
$823$	−16.2925	−	16.2925i	−0.567921	−	0.567921i	−0.931546	+	0.363624i	$0.881539\pi$
$824$	50.1377			1.74663
$825$			144.139i			5.01829i
$826$	3.88218	−	3.88218i	0.135078	−	0.135078i
$827$	−1.14263	−	1.14263i	−0.0397331	−	0.0397331i	0.686961	−	0.726694i	$-0.258944\pi$
$827$	−1.14263	−	1.14263i	−0.0397331	−	0.0397331i	−0.726694	+	0.686961i	$0.758944\pi$
$828$		−	0.237651i		−	0.00825896i
$829$			15.3278i			0.532357i	0.963924	+	0.266178i	$0.0857610\pi$
$829$			15.3278i			0.532357i	−0.963924	+	0.266178i	$0.914239\pi$
$830$	−40.8807			−1.41899
$831$	−8.61482	−	8.61482i	−0.298845	−	0.298845i
$832$	−0.685405	−	0.685405i	−0.0237621	−	0.0237621i
$833$	−2.13938	−	2.13938i	−0.0741251	−	0.0741251i
$834$	−28.1493	+	28.1493i	−0.974729	+	0.974729i
$835$	−22.5411	+	22.5411i	−0.780066	+	0.780066i
$836$	−0.127804			−0.00442021
$837$	0.388548	−	0.388548i	0.0134302	−	0.0134302i
$838$	17.7411			0.612858
$839$	−6.07101	+	6.07101i	−0.209595	+	0.209595i	−0.804095	−	0.594501i	$-0.797350\pi$
$839$	−6.07101	+	6.07101i	−0.209595	+	0.209595i	0.594501	+	0.804095i	$0.297350\pi$
$840$			23.4468i			0.808991i
$841$			32.8098i			1.13137i
$842$	−19.3146	+	19.3146i	−0.665624	+	0.665624i
$843$	−16.1540			−0.556374
$844$	−0.264559	+	0.264559i	−0.00910650	+	0.00910650i
$845$	−53.9300			−1.85525
$846$	5.06743	−	5.06743i	0.174222	−	0.174222i
$847$	−16.1372	+	16.1372i	−0.554482	+	0.554482i
$848$	9.59235	+	9.59235i	0.329403	+	0.329403i
$849$	−26.0601	−	26.0601i	−0.894379	−	0.894379i
$850$	−37.5458	−	37.5458i	−1.28781	−	1.28781i
$851$	−10.2617			−0.351766
$852$		−	1.38081i		−	0.0473057i
$853$		−	5.18075i		−	0.177385i	−0.996059	−	0.0886927i	$-0.971731\pi$
$853$		−	5.18075i		−	0.177385i	0.996059	−	0.0886927i	$-0.0282689\pi$
$854$	10.8027	+	10.8027i	0.369661	+	0.369661i
$855$	1.35261	−	1.35261i	0.0462582	−	0.0462582i
$856$			3.68089i			0.125810i
$857$	−12.3561			−0.422077			−0.211038	−	0.977478i	$-0.567685\pi$
$857$	−12.3561			−0.422077			−0.211038	+	0.977478i	$0.567685\pi$
$858$	−1.48474	−	1.48474i	−0.0506881	−	0.0506881i
$859$			41.2801i			1.40846i	0.709973	+	0.704229i	$0.248707\pi$
$859$			41.2801i			1.40846i	−0.709973	+	0.704229i	$0.751293\pi$
$860$	0.657377			0.0224164
$861$	−4.62525	−	12.1003i	−0.157628	−	0.412377i
$862$	1.91461			0.0652118
$863$		−	4.92150i		−	0.167530i	−0.996486	−	0.0837649i	$-0.973306\pi$
$863$		−	4.92150i		−	0.167530i	0.996486	−	0.0837649i	$-0.0266945\pi$
$864$	−0.804631	−	0.804631i	−0.0273741	−	0.0273741i
$865$	73.6149			2.50298
$866$			49.1442i			1.66999i
$867$	11.2242	−	11.2242i	0.381195	−	0.381195i
$868$	0.00525201	+	0.00525201i	0.000178265	+	0.000178265i
$869$			32.9394i			1.11739i
$870$			94.6361i			3.20846i
$871$	0.0707250			0.00239642
$872$	31.0092	+	31.0092i	1.05010	+	1.05010i
$873$	−6.44091	−	6.44091i	−0.217992	−	0.217992i
$874$	−1.77974	−	1.77974i	−0.0602007	−	0.0602007i
$875$	−21.2953	+	21.2953i	−0.719913	+	0.719913i
$876$	1.09508	−	1.09508i	0.0369993	−	0.0369993i
$877$	−4.36785			−0.147492			−0.0737459	−	0.997277i	$-0.523495\pi$
$877$	−4.36785			−0.147492			−0.0737459	+	0.997277i	$0.523495\pi$
$878$	−9.90781	+	9.90781i	−0.334372	+	0.334372i
$879$	−31.8545			−1.07443
$880$	−70.0550	+	70.0550i	−2.36155	+	2.36155i
$881$		−	28.0131i		−	0.943785i	−0.881656	−	0.471893i	$-0.843571\pi$
$881$		−	28.0131i		−	0.943785i	0.881656	−	0.471893i	$-0.156429\pi$
$882$			1.56567i			0.0527187i
$883$	4.02532	−	4.02532i	0.135463	−	0.135463i	−0.636124	−	0.771587i	$-0.719463\pi$
$883$	4.02532	−	4.02532i	0.135463	−	0.135463i	0.771587	+	0.636124i	$0.219463\pi$
$884$	0.0196568			0.000661129
$885$	−22.7717	+	22.7717i	−0.765462	+	0.765462i
$886$	46.8193			1.57292
$887$	−3.40590	+	3.40590i	−0.114359	+	0.114359i	−0.761971	−	0.647612i	$-0.775768\pi$
$887$	−3.40590	+	3.40590i	−0.114359	+	0.114359i	0.647612	+	0.761971i	$0.275768\pi$
$888$	9.82425	−	9.82425i	0.329680	−	0.329680i
$889$	−7.96772	−	7.96772i	−0.267229	−	0.267229i
$890$	62.2407	+	62.2407i	2.08631	+	2.08631i
$891$	45.5816	+	45.5816i	1.52704	+	1.52704i
$892$	−0.222972			−0.00746566
$893$		−	1.92881i		−	0.0645451i
$894$		−	16.4033i		−	0.548610i
$895$	20.2255	+	20.2255i	0.676062	+	0.676062i
$896$	−8.29855	+	8.29855i	−0.277235	+	0.277235i
$897$		−	1.05086i		−	0.0350872i
$898$	−59.8846			−1.99838
$899$	−0.791755	−	0.791755i	−0.0264065	−	0.0264065i
$900$			0.698276i			0.0232759i
$901$	10.0067			0.333372
$902$	21.7662	−	48.7023i	0.724735	−	1.62161i
$903$	−6.13991			−0.204323
$904$		−	18.7963i		−	0.625155i
$905$	37.4100	+	37.4100i	1.24355	+	1.24355i
$906$	−57.5381			−1.91157
$907$			0.676544i			0.0224643i	0.999937	+	0.0112321i	$0.00357538\pi$
$907$			0.676544i			0.0224643i	−0.999937	+	0.0112321i	$0.996425\pi$
$908$	0.708424	−	0.708424i	0.0235099	−	0.0235099i
$909$	−4.75379	−	4.75379i	−0.157673	−	0.157673i
$910$		−	0.741236i		−	0.0245717i
$911$		−	37.5297i		−	1.24341i	−0.783250	−	0.621707i	$-0.786440\pi$
$911$		−	37.5297i		−	1.24341i	0.783250	−	0.621707i	$-0.213560\pi$
$912$	3.49667			0.115786
$913$	28.2546	+	28.2546i	0.935091	+	0.935091i
$914$	−2.67093	−	2.67093i	−0.0883466	−	0.0883466i
$915$	−63.3654	−	63.3654i	−2.09479	−	2.09479i
$916$	0.330555	−	0.330555i	0.0109219	−	0.0109219i
$917$	4.52142	−	4.52142i	0.149310	−	0.149310i
$918$	−16.7221			−0.551911
$919$	2.75603	−	2.75603i	0.0909129	−	0.0909129i	−0.660188	−	0.751101i	$-0.729523\pi$
$919$	2.75603	−	2.75603i	0.0909129	−	0.0909129i	0.751101	+	0.660188i	$0.229523\pi$
$920$	−48.3224			−1.59314
$921$	36.5742	−	36.5742i	1.20516	−	1.20516i
$922$		−	20.4160i		−	0.672367i
$923$		−	1.63041i		−	0.0536657i
$924$	−0.433873	+	0.433873i	−0.0142734	+	0.0142734i
$925$	30.1513			0.991368
$926$	25.0007	−	25.0007i	0.821575	−	0.821575i
$927$	−19.6381			−0.645000
$928$	−1.63962	+	1.63962i	−0.0538231	+	0.0538231i
$929$	−23.4769	+	23.4769i	−0.770251	+	0.770251i	−0.978150	−	0.207899i	$-0.933338\pi$
$929$	−23.4769	+	23.4769i	−0.770251	+	0.770251i	0.207899	+	0.978150i	$0.433338\pi$
$930$	−1.21225	−	1.21225i	−0.0397511	−	0.0397511i
$931$	0.297969	+	0.297969i	0.00976553	+	0.00976553i
$932$	−0.949175	−	0.949175i	−0.0310913	−	0.0310913i
$933$	49.4058			1.61747
$934$			13.0386i			0.426638i
$935$			73.0811i			2.39001i
$936$	0.268649	+	0.268649i	0.00878107	+	0.00878107i
$937$	−20.1877	+	20.1877i	−0.659504	+	0.659504i	−0.955263	−	0.295759i	$-0.904428\pi$
$937$	−20.1877	+	20.1877i	−0.659504	+	0.659504i	0.295759	+	0.955263i	$0.404428\pi$
$938$		−	0.813264i		−	0.0265540i
$939$	5.53182			0.180524
$940$	0.701065	+	0.701065i	0.0228662	+	0.0228662i
$941$		−	27.3388i		−	0.891220i	−0.895227	−	0.445610i	$-0.852987\pi$
$941$		−	27.3388i		−	0.891220i	0.895227	−	0.445610i	$-0.147013\pi$
$942$	19.3154			0.629329
$943$	24.9380	−	9.53235i	0.812092	−	0.310416i
$944$	−15.7195			−0.511625
$945$			16.0247i			0.521282i
$946$	−17.8785	−	17.8785i	−0.581279	−	0.581279i
$947$	−48.8625			−1.58782			−0.793909	−	0.608037i	$-0.791957\pi$
$947$	−48.8625			−1.58782			−0.793909	+	0.608037i	$0.791957\pi$
$948$			0.597585i			0.0194087i
$949$	1.29304	−	1.29304i	0.0419737	−	0.0419737i
$950$	5.22931	+	5.22931i	0.169661	+	0.169661i
$951$			38.8497i			1.25979i
$952$			8.44234i			0.273618i
$953$	38.4568			1.24574			0.622870	−	0.782326i	$-0.285967\pi$
$953$	38.4568			1.24574			0.622870	+	0.782326i	$0.285967\pi$
$954$	−3.66162	−	3.66162i	−0.118549	−	0.118549i
$955$	−77.0682	−	77.0682i	−2.49387	−	2.49387i
$956$	0.157364	+	0.157364i	0.00508951	+	0.00508951i
$957$	65.4075	−	65.4075i	2.11432	−	2.11432i
$958$	37.5803	−	37.5803i	1.21416	−	1.21416i
$959$	0.280504			0.00905795
$960$	46.2301	−	46.2301i	1.49207	−	1.49207i
$961$	−30.9797			−0.999346
$962$	−0.310579	+	0.310579i	−0.0100135	+	0.0100135i
$963$		−	1.44174i		−	0.0464595i
$964$			1.09891i			0.0353936i
$965$	−31.7665	+	31.7665i	−1.02260	+	1.02260i
$966$	−12.0838			−0.388791
$967$	5.02847	−	5.02847i	0.161705	−	0.161705i	−0.621617	−	0.783322i	$-0.713524\pi$
$967$	5.02847	−	5.02847i	0.161705	−	0.161705i	0.783322	+	0.621617i	$0.213524\pi$
$968$	63.6801			2.04676
$969$	1.82386	−	1.82386i	0.0585907	−	0.0585907i
$970$	35.0642	−	35.0642i	1.12584	−	1.12584i
$971$	14.4248	+	14.4248i	0.462913	+	0.462913i	0.899609	−	0.436696i	$-0.143851\pi$
$971$	14.4248	+	14.4248i	0.462913	+	0.462913i	−0.436696	+	0.899609i	$0.643851\pi$
$972$	0.400113	+	0.400113i	0.0128336	+	0.0128336i
$973$	9.71281	+	9.71281i	0.311378	+	0.311378i
$974$	2.36960			0.0759268
$975$			3.08768i			0.0988848i
$976$		−	43.7416i		−	1.40013i
$977$	−19.5539	−	19.5539i	−0.625585	−	0.625585i	0.321369	−	0.946954i	$-0.395857\pi$
$977$	−19.5539	−	19.5539i	−0.625585	−	0.625585i	−0.946954	+	0.321369i	$0.895857\pi$
$978$	−22.8452	+	22.8452i	−0.730508	+	0.730508i
$979$		−	86.0349i		−	2.74969i
$980$	−0.216606			−0.00691921
$981$	−12.1458	−	12.1458i	−0.387785	−	0.387785i
$982$			0.0517845i			0.00165251i
$983$	18.9676			0.604972			0.302486	−	0.953154i	$-0.402184\pi$
$983$	18.9676			0.604972			0.302486	+	0.953154i	$0.402184\pi$
$984$	−14.7489	+	33.0009i	−0.470177	+	1.05203i
$985$	−108.674			−3.46263
$986$			34.0750i			1.08517i
$987$	−6.54796	−	6.54796i	−0.208424	−	0.208424i
$988$	−0.00273776			−8.70997e−5
$989$		−	12.6540i		−	0.402373i
$990$	26.7416	−	26.7416i	0.849902	−	0.849902i
$991$	32.0939	+	32.0939i	1.01950	+	1.01950i	0.999806	+	0.0196913i	$0.00626833\pi$
$991$	32.0939	+	32.0939i	1.01950	+	1.01950i	0.0196913	+	0.999806i	$0.493732\pi$
$992$		−	0.0420055i		−	0.00133368i
$993$		−	35.5501i		−	1.12815i
$994$	−18.7481			−0.594653
$995$	−7.35759	−	7.35759i	−0.233251	−	0.233251i
$996$	0.512595	+	0.512595i	0.0162422	+	0.0162422i
$997$	−2.97034	−	2.97034i	−0.0940717	−	0.0940717i	0.658505	−	0.752576i	$-0.271189\pi$
$997$	−2.97034	−	2.97034i	−0.0940717	−	0.0940717i	−0.752576	+	0.658505i	$0.771189\pi$
$998$	32.0110	−	32.0110i	1.01329	−	1.01329i
$999$	6.71436	−	6.71436i	0.212433	−	0.212433i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.f.a.50.6	✓	40
41.32	even	4	inner	287.2.f.a.155.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.f.a.50.6	✓	40	1.1	even	1	trivial
287.2.f.a.155.15	yes	40	41.32	even	4	inner

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.43253i q^{2} +(-1.43055 - 1.43055i) q^{3} -0.0521511 q^{4} -4.15342i q^{5} +(-2.04931 + 2.04931i) q^{6} +(0.707107 + 0.707107i) q^{7} -2.79036i q^{8} +1.09294i q^{9} +O(q^{10})\)	\(q-1.43253i q^{2} +(-1.43055 - 1.43055i) q^{3} -0.0521511 q^{4} -4.15342i q^{5} +(-2.04931 + 2.04931i) q^{6} +(0.707107 + 0.707107i) q^{7} -2.79036i q^{8} +1.09294i q^{9} -5.94992 q^{10} +(4.11227 + 4.11227i) q^{11} +(0.0746047 + 0.0746047i) q^{12} +(0.0880909 + 0.0880909i) q^{13} +(1.01295 - 1.01295i) q^{14} +(-5.94167 + 5.94167i) q^{15} -4.10158 q^{16} +(-2.13938 + 2.13938i) q^{17} +1.56567 q^{18} +(0.297969 - 0.297969i) q^{19} +0.216606i q^{20} -2.02310i q^{21} +(5.89096 - 5.89096i) q^{22} +4.16948 q^{23} +(-3.99174 + 3.99174i) q^{24} -12.2509 q^{25} +(0.126193 - 0.126193i) q^{26} +(-2.72815 + 2.72815i) q^{27} +(-0.0368764 - 0.0368764i) q^{28} +(5.55922 + 5.55922i) q^{29} +(8.51164 + 8.51164i) q^{30} -0.142422 q^{31} +0.294937i q^{32} -11.7656i q^{33} +(3.06473 + 3.06473i) q^{34} +(2.93691 - 2.93691i) q^{35} -0.0569978i q^{36} -2.46114 q^{37} +(-0.426850 - 0.426850i) q^{38} -0.252036i q^{39} -11.5895 q^{40} +(5.98107 - 2.28622i) q^{41} -2.89816 q^{42} -3.03490i q^{43} +(-0.214459 - 0.214459i) q^{44} +4.53942 q^{45} -5.97292i q^{46} +(3.23660 - 3.23660i) q^{47} +(5.86751 + 5.86751i) q^{48} +1.00000i q^{49} +17.5499i q^{50} +6.12097 q^{51} +(-0.00459404 - 0.00459404i) q^{52} +(-2.33870 - 2.33870i) q^{53} +(3.90816 + 3.90816i) q^{54} +(17.0800 - 17.0800i) q^{55} +(1.97308 - 1.97308i) q^{56} -0.852517 q^{57} +(7.96376 - 7.96376i) q^{58} +3.83254 q^{59} +(0.309865 - 0.309865i) q^{60} +10.6646i q^{61} +0.204024i q^{62} +(-0.772822 + 0.772822i) q^{63} -7.78066 q^{64} +(0.365879 - 0.365879i) q^{65} -16.8546 q^{66} +(0.401432 - 0.401432i) q^{67} +(0.111571 - 0.111571i) q^{68} +(-5.96465 - 5.96465i) q^{69} +(-4.20723 - 4.20723i) q^{70} +(-9.25416 - 9.25416i) q^{71} +3.04968 q^{72} -14.6784i q^{73} +3.52567i q^{74} +(17.5255 + 17.5255i) q^{75} +(-0.0155394 + 0.0155394i) q^{76} +5.81562i q^{77} -0.361051 q^{78} +(4.00501 + 4.00501i) q^{79} +17.0356i q^{80} +11.0843 q^{81} +(-3.27509 - 8.56808i) q^{82} +6.87081 q^{83} +0.105507i q^{84} +(8.88575 + 8.88575i) q^{85} -4.34760 q^{86} -15.9054i q^{87} +(11.4747 - 11.4747i) q^{88} +(-10.4608 - 10.4608i) q^{89} -6.50287i q^{90} +0.124579i q^{91} -0.217443 q^{92} +(0.203742 + 0.203742i) q^{93} +(-4.63653 - 4.63653i) q^{94} +(-1.23759 - 1.23759i) q^{95} +(0.421921 - 0.421921i) q^{96} +(-5.89322 + 5.89322i) q^{97} +1.43253 q^{98} +(-4.49444 + 4.49444i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Introduction

L-functions

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