LMFDB - Embedded newform 425.3.u.f.401.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(126,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.126"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.u (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,0,16,0,-16,0,0,16,0,-96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			401.7
Character	$\chi$	$=$	425.401
Dual form			425.3.u.f.301.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.116200 + 0.280533i) q^{2} +(-4.44521 - 2.97019i) q^{3} +(2.76323 + 2.76323i) q^{4} +(1.34977 - 0.901888i) q^{6} +(-2.10407 - 0.418526i) q^{7} +(-2.21840 + 0.918890i) q^{8} +(7.49367 + 18.0913i) q^{9} +(-3.66996 - 5.49249i) q^{11} +(-4.07581 - 20.4905i) q^{12} +(9.67560 - 9.67560i) q^{13} +(0.361904 - 0.541628i) q^{14} +14.9021i q^{16} +(-0.398523 + 16.9953i) q^{17} -5.94598 q^{18} +(4.71303 - 11.3783i) q^{19} +(8.10993 + 8.10993i) q^{21} +(1.96727 - 0.391315i) q^{22} +(1.56321 - 1.04450i) q^{23} +(12.5905 + 2.50441i) q^{24} +(1.59001 + 3.83863i) q^{26} +(11.0369 - 55.4861i) q^{27} +(-4.65755 - 6.97052i) q^{28} +(-5.73848 - 28.8493i) q^{29} +(27.7949 - 41.5980i) q^{31} +(-13.0541 - 5.40719i) q^{32} +35.3157i q^{33} +(-4.72144 - 2.08666i) q^{34} +(-29.2838 + 70.6973i) q^{36} +(-39.7482 - 26.5589i) q^{37} +(2.64432 + 2.64432i) q^{38} +(-71.7485 + 14.2717i) q^{39} +(-74.0482 - 14.7291i) q^{41} +(-3.21748 + 1.33272i) q^{42} +(-12.5935 - 30.4033i) q^{43} +(5.03606 - 25.3180i) q^{44} +(0.111372 + 0.559903i) q^{46} +(24.9678 - 24.9678i) q^{47} +(44.2621 - 66.2429i) q^{48} +(-41.0181 - 16.9903i) q^{49} +(52.2509 - 74.3641i) q^{51} +53.4719 q^{52} +(-10.3638 + 25.0205i) q^{53} +(14.2832 + 9.54371i) q^{54} +(5.05224 - 1.00495i) q^{56} +(-54.7460 + 36.5801i) q^{57} +(8.75998 + 1.74247i) q^{58} +(69.9951 - 28.9929i) q^{59} +(11.8582 - 59.6151i) q^{61} +(8.43982 + 12.6311i) q^{62} +(-8.19554 - 41.2018i) q^{63} +(-39.1157 + 39.1157i) q^{64} +(-9.90722 - 4.10371i) q^{66} -88.5032i q^{67} +(-48.0632 + 45.8608i) q^{68} -10.0512 q^{69} +(26.4277 + 17.6584i) q^{71} +(-33.2479 - 33.2479i) q^{72} +(42.8431 - 8.52203i) q^{73} +(12.0694 - 8.06452i) q^{74} +(44.4639 - 18.4176i) q^{76} +(5.42312 + 13.0926i) q^{77} +(4.33354 - 21.7862i) q^{78} +(23.2131 + 34.7408i) q^{79} +(-89.2469 + 89.2469i) q^{81} +(12.7364 - 19.0614i) q^{82} +(-87.2086 - 36.1230i) q^{83} +44.8192i q^{84} +9.99249 q^{86} +(-60.1792 + 145.285i) q^{87} +(13.1884 + 8.81222i) q^{88} +(62.4827 + 62.4827i) q^{89} +(-24.4077 + 16.3087i) q^{91} +(7.20571 + 1.43331i) q^{92} +(-247.108 + 102.356i) q^{93} +(4.10301 + 9.90555i) q^{94} +(41.9678 + 62.8093i) q^{96} +(1.86699 + 9.38597i) q^{97} +(9.53265 - 9.53265i) q^{98} +(71.8649 - 107.553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{4} - 16 q^{6} + 16 q^{9} - 96 q^{11} + 16 q^{14} + 16 q^{19} + 224 q^{21} + 160 q^{24} + 288 q^{26} + 176 q^{29} + 48 q^{31} - 48 q^{34} - 144 q^{36} - 336 q^{41} + 48 q^{44} - 224 q^{46}+ \cdots + 1664 q^{99}+O(q^{100}) $ 128 * q + 16 * q^4 - 16 * q^6 + 16 * q^9 - 96 * q^11 + 16 * q^14 + 16 * q^19 + 224 * q^21 + 160 * q^24 + 288 * q^26 + 176 * q^29 + 48 * q^31 - 48 * q^34 - 144 * q^36 - 336 * q^41 + 48 * q^44 - 224 * q^46 + 48 * q^49 - 16 * q^51 - 512 * q^54 - 16 * q^56 - 272 * q^59 - 16 * q^61 - 688 * q^64 - 80 * q^66 - 448 * q^69 + 192 * q^71 - 704 * q^74 + 496 * q^76 - 304 * q^79 + 128 * q^81 - 2496 * q^86 + 256 * q^89 - 1632 * q^91 + 1296 * q^94 - 1728 * q^96 + 1664 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{16}\right)$

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 $

$2$	−0.116200	+	0.280533i	−0.0581002	+	0.140266i	−0.950264	−	0.311446i	$-0.899187\pi$
$2$	−0.116200	+	0.280533i	−0.0581002	+	0.140266i	0.892164	+	0.451712i	$0.149187\pi$
$3$	−4.44521	−	2.97019i	−1.48174	−	0.990064i	−0.993061	−	0.117598i	$-0.962481\pi$
$3$	−4.44521	−	2.97019i	−1.48174	−	0.990064i	−0.488675	−	0.872466i	$-0.662519\pi$
$4$	2.76323	+	2.76323i	0.690808	+	0.690808i
$5$		0			0
$5$		0			0
$6$	1.34977	−	0.901888i	0.224962	−	0.150315i
$7$	−2.10407	−	0.418526i	−0.300582	−	0.0597894i	0.0424954	−	0.999097i	$-0.486469\pi$
$7$	−2.10407	−	0.418526i	−0.300582	−	0.0597894i	−0.343077	+	0.939307i	$0.611469\pi$
$8$	−2.21840	+	0.918890i	−0.277300	+	0.114861i
$9$	7.49367	+	18.0913i	0.832630	+	2.01015i
$10$		0			0
$11$	−3.66996	−	5.49249i	−0.333633	−	0.499317i	0.626286	−	0.779593i	$-0.284574\pi$
$11$	−3.66996	−	5.49249i	−0.333633	−	0.499317i	−0.959919	+	0.280276i	$0.909574\pi$
$12$	−4.07581	−	20.4905i	−0.339651	−	1.70754i
$13$	9.67560	−	9.67560i	0.744277	−	0.744277i	−0.229121	−	0.973398i	$-0.573585\pi$
$13$	9.67560	−	9.67560i	0.744277	−	0.744277i	0.973398	+	0.229121i	$0.0735851\pi$
$14$	0.361904	−	0.541628i	0.0258503	−	0.0386877i
$15$		0			0
$16$			14.9021i			0.931380i
$17$	−0.398523	+	16.9953i	−0.0234425	+	0.999725i
$17$	−0.398523	+	16.9953i	−0.0234425	+	0.999725i
$18$	−5.94598			−0.330332
$19$	4.71303	−	11.3783i	0.248054	−	0.598856i	−0.749985	−	0.661455i	$-0.769939\pi$
$19$	4.71303	−	11.3783i	0.248054	−	0.598856i	0.998039	+	0.0625996i	$0.0199391\pi$
$20$		0			0
$21$	8.10993	+	8.10993i	0.386187	+	0.386187i
$22$	1.96727	−	0.391315i	0.0894215	−	0.0177871i
$23$	1.56321	−	1.04450i	0.0679656	−	0.0454132i	−0.521123	−	0.853481i	$-0.674487\pi$
$23$	1.56321	−	1.04450i	0.0679656	−	0.0454132i	0.589089	+	0.808068i	$0.299487\pi$
$24$	12.5905	+	2.50441i	0.524605	+	0.104350i
$25$		0			0
$26$	1.59001	+	3.83863i	0.0611544	+	0.147640i
$27$	11.0369	−	55.4861i	0.408773	−	2.05504i
$28$	−4.65755	−	6.97052i	−0.166341	−	0.248947i
$29$	−5.73848	−	28.8493i	−0.197879	−	0.994803i	−0.944239	−	0.329261i	$-0.893200\pi$
$29$	−5.73848	−	28.8493i	−0.197879	−	0.994803i	0.746360	−	0.665542i	$-0.231800\pi$
$30$		0			0
$31$	27.7949	−	41.5980i	0.896609	−	1.34187i	−0.0428037	−	0.999084i	$-0.513629\pi$
$31$	27.7949	−	41.5980i	0.896609	−	1.34187i	0.939413	−	0.342787i	$-0.111371\pi$
$32$	−13.0541	−	5.40719i	−0.407941	−	0.168975i
$33$			35.3157i			1.07017i
$34$	−4.72144	−	2.08666i	−0.138866	−	0.0613725i
$35$		0			0
$36$	−29.2838	+	70.6973i	−0.813438	+	1.96381i
$37$	−39.7482	−	26.5589i	−1.07428	−	0.717809i	−0.113056	−	0.993589i	$-0.536064\pi$
$37$	−39.7482	−	26.5589i	−1.07428	−	0.717809i	−0.961221	+	0.275780i	$0.911064\pi$
$38$	2.64432	+	2.64432i	0.0695873	+	0.0695873i
$39$	−71.7485	+	14.2717i	−1.83970	+	0.365940i
$40$		0			0
$41$	−74.0482	−	14.7291i	−1.80605	−	0.359247i	−0.826897	−	0.562353i	$-0.809896\pi$
$41$	−74.0482	−	14.7291i	−1.80605	−	0.359247i	−0.979157	+	0.203106i	$0.934896\pi$
$42$	−3.21748	+	1.33272i	−0.0766067	+	0.0317315i
$43$	−12.5935	−	30.4033i	−0.292871	−	0.707053i	0.707129	−	0.707085i	$-0.249990\pi$
$43$	−12.5935	−	30.4033i	−0.292871	−	0.707053i	−1.00000		3.12334e-5i	$0.999990\pi$
$44$	5.03606	−	25.3180i	0.114456	−	0.575408i
$45$		0			0
$46$	0.111372	+	0.559903i	0.00242112	+	0.0121718i
$47$	24.9678	−	24.9678i	0.531230	−	0.531230i	−0.389709	−	0.920938i	$-0.627424\pi$
$47$	24.9678	−	24.9678i	0.531230	−	0.531230i	0.920938	+	0.389709i	$0.127424\pi$
$48$	44.2621	−	66.2429i	0.922126	−	1.38006i
$49$	−41.0181	−	16.9903i	−0.837105	−	0.346740i
$50$		0			0
$51$	52.2509	−	74.3641i	1.02453	−	1.45812i
$52$	53.4719			1.02830
$53$	−10.3638	+	25.0205i	−0.195544	+	0.472085i	−0.990989	−	0.133940i	$-0.957237\pi$
$53$	−10.3638	+	25.0205i	−0.195544	+	0.472085i	0.795445	+	0.606025i	$0.207237\pi$
$54$	14.2832	+	9.54371i	0.264503	+	0.176735i
$55$		0			0
$56$	5.05224	−	1.00495i	0.0902186	−	0.0179456i
$57$	−54.7460	+	36.5801i	−0.960456	+	0.641756i
$58$	8.75998	+	1.74247i	0.151034	+	0.0300426i
$59$	69.9951	−	28.9929i	1.18636	−	0.491405i	0.299790	−	0.954005i	$-0.403083\pi$
$59$	69.9951	−	28.9929i	1.18636	−	0.491405i	0.886567	+	0.462600i	$0.153083\pi$
$60$		0			0
$61$	11.8582	−	59.6151i	0.194397	−	0.977297i	−0.753191	−	0.657802i	$-0.771487\pi$
$61$	11.8582	−	59.6151i	0.194397	−	0.977297i	0.947588	−	0.319496i	$-0.103513\pi$
$62$	8.43982	+	12.6311i	0.136126	+	0.203727i
$63$	−8.19554	−	41.2018i	−0.130088	−	0.653996i
$64$	−39.1157	+	39.1157i	−0.611183	+	0.611183i
$65$		0			0
$66$	−9.90722	−	4.10371i	−0.150109	−	0.0621774i
$67$		−	88.5032i		−	1.32094i	−0.750851	−	0.660472i	$-0.770356\pi$
$67$		−	88.5032i		−	1.32094i	0.750851	−	0.660472i	$-0.229644\pi$
$68$	−48.0632	+	45.8608i	−0.706812	+	0.674424i
$69$	−10.0512			−0.145669
$70$		0			0
$71$	26.4277	+	17.6584i	0.372221	+	0.248710i	0.727585	−	0.686018i	$-0.240643\pi$
$71$	26.4277	+	17.6584i	0.372221	+	0.248710i	−0.355363	+	0.934728i	$0.615643\pi$
$72$	−33.2479	−	33.2479i	−0.461776	−	0.461776i
$73$	42.8431	−	8.52203i	0.586892	−	0.116740i	0.107293	−	0.994227i	$-0.465782\pi$
$73$	42.8431	−	8.52203i	0.586892	−	0.116740i	0.479600	+	0.877487i	$0.340782\pi$
$74$	12.0694	−	8.06452i	0.163100	−	0.108980i
$75$		0			0
$76$	44.4639	−	18.4176i	0.585052	−	0.242336i
$77$	5.42312	+	13.0926i	0.0704301	+	0.170033i
$78$	4.33354	−	21.7862i	0.0555582	−	0.279310i
$79$	23.2131	+	34.7408i	0.293836	+	0.439757i	0.948788	−	0.315914i	$-0.102311\pi$
$79$	23.2131	+	34.7408i	0.293836	+	0.439757i	−0.654952	+	0.755671i	$0.727311\pi$
$80$		0			0
$81$	−89.2469	+	89.2469i	−1.10181	+	1.10181i
$82$	12.7364	−	19.0614i	0.155322	−	0.232456i
$83$	−87.2086	−	36.1230i	−1.05071	−	0.435217i	−0.210562	−	0.977580i	$-0.567529\pi$
$83$	−87.2086	−	36.1230i	−1.05071	−	0.435217i	−0.840144	+	0.542364i	$0.817529\pi$
$84$			44.8192i			0.533562i
$85$		0			0
$86$	9.99249			0.116192
$87$	−60.1792	+	145.285i	−0.691715	+	1.66995i
$88$	13.1884	+	8.81222i	0.149868	+	0.100139i
$89$	62.4827	+	62.4827i	0.702053	+	0.702053i	0.964851	−	0.262798i	$-0.0846453\pi$
$89$	62.4827	+	62.4827i	0.702053	+	0.702053i	−0.262798	+	0.964851i	$0.584645\pi$
$90$		0			0
$91$	−24.4077	+	16.3087i	−0.268216	+	0.179216i
$92$	7.20571	+	1.43331i	0.0783230	+	0.0155794i
$93$	−247.108	+	102.356i	−2.65708	+	1.10060i
$94$	4.10301	+	9.90555i	0.0436491	+	0.105378i
$95$		0			0
$96$	41.9678	+	62.8093i	0.437165	+	0.654263i
$97$	1.86699	+	9.38597i	0.0192473	+	0.0967626i	0.989215	−	0.146472i	$-0.0467917\pi$
$97$	1.86699	+	9.38597i	0.0192473	+	0.0967626i	−0.969968	+	0.243234i	$0.921792\pi$
$98$	9.53265	−	9.53265i	0.0972720	−	0.0972720i
$99$	71.8649	−	107.553i	0.725908	−	1.08640i
$100$		0			0
$101$			8.14676i			0.0806610i	0.999186	+	0.0403305i	$0.0128411\pi$
$101$			8.14676i			0.0806610i	−0.999186	+	0.0403305i	$0.987159\pi$
$102$	14.7900	+	23.2992i	0.145000	+	0.228424i
$103$	102.475			0.994907			0.497454	−	0.867491i	$-0.334268\pi$
$103$	102.475			0.994907			0.497454	+	0.867491i	$0.334268\pi$
$104$	−12.5735	+	30.3551i	−0.120899	+	0.291876i
$105$		0			0
$106$	−5.81479	−	5.81479i	−0.0548565	−	0.0548565i
$107$	−12.8048	+	2.54704i	−0.119671	+	0.0238041i	−0.254563	−	0.967056i	$-0.581932\pi$
$107$	−12.8048	+	2.54704i	−0.119671	+	0.0238041i	0.134891	+	0.990860i	$0.456932\pi$
$108$	183.818	−	122.823i	1.70202	−	1.13725i
$109$	14.1717	+	2.81893i	0.130016	+	0.0258618i	0.259669	−	0.965698i	$-0.416386\pi$
$109$	14.1717	+	2.81893i	0.130016	+	0.0258618i	−0.129653	+	0.991559i	$0.541386\pi$
$110$		0			0
$111$	97.8041	+	236.120i	0.881118	+	2.12721i
$112$	6.23691	−	31.3551i	0.0556867	−	0.279956i
$113$	79.4316	+	118.878i	0.702934	+	1.05202i	0.995406	+	0.0957415i	$0.0305222\pi$
$113$	79.4316	+	118.878i	0.702934	+	1.05202i	−0.292472	+	0.956274i	$0.594478\pi$
$114$	−3.90041	−	19.6087i	−0.0342141	−	0.172006i
$115$		0			0
$116$	63.8605	−	95.5740i	0.550521	−	0.823914i
$117$	247.550	+	102.539i	2.11581	+	0.876399i
$118$			23.0049i			0.194957i
$119$	7.95151	−	35.5926i	0.0668194	−	0.299097i
$120$		0			0
$121$	29.6059	−	71.4750i	0.244677	−	0.590702i
$122$	15.3461	+	10.2539i	0.125787	+	0.0840485i
$123$	285.411	+	285.411i	2.32042	+	2.32042i
$124$	191.749	−	38.1412i	1.54636	−	0.307590i
$125$		0			0
$126$	12.5108	+	2.48855i	0.0992918	+	0.0197504i
$127$	−29.6298	+	12.2731i	−0.233306	+	0.0966384i	−0.496274	−	0.868166i	$-0.665299\pi$
$127$	−29.6298	+	12.2731i	−0.233306	+	0.0966384i	0.262968	+	0.964805i	$0.415299\pi$
$128$	−28.0567	−	67.7349i	−0.219193	−	0.529179i
$129$	−34.3231	+	172.554i	−0.266071	+	1.33763i
$130$		0			0
$131$	−24.5534	−	123.438i	−0.187431	−	0.942278i	−0.953929	−	0.300032i	$-0.903003\pi$
$131$	−24.5534	−	123.438i	−0.187431	−	0.942278i	0.766498	−	0.642246i	$-0.221997\pi$
$132$	−97.5856	+	97.5856i	−0.739285	+	0.739285i
$133$	−14.6786	+	21.9681i	−0.110366	+	0.165174i
$134$	24.8281	+	10.2841i	0.185284	+	0.0767471i
$135$		0			0
$136$	−14.7328	−	38.0686i	−0.108329	−	0.279916i
$137$	−3.84544			−0.0280689			−0.0140345	−	0.999902i	$-0.504467\pi$
$137$	−3.84544			−0.0280689			−0.0140345	+	0.999902i	$0.504467\pi$
$138$	1.16795	−	2.81968i	0.00846341	−	0.0204325i
$139$	−148.938	−	99.5172i	−1.07150	−	0.715951i	−0.110881	−	0.993834i	$-0.535367\pi$
$139$	−148.938	−	99.5172i	−1.07150	−	0.715951i	−0.960615	+	0.277883i	$0.910367\pi$
$140$		0			0
$141$	−185.146	+	36.8279i	−1.31309	+	0.261191i
$142$	−8.02468	+	5.36192i	−0.0565118	+	0.0377600i
$143$	−88.6522	−	17.6340i	−0.619946	−	0.123315i
$144$	−269.599	+	111.671i	−1.87221	+	0.775496i
$145$		0			0
$146$	−2.58768	+	13.0092i	−0.0177239	+	0.0891039i
$147$	131.870	+	197.357i	0.897073	+	1.34257i
$148$	−36.4451	−	183.222i	−0.246251	−	1.23799i
$149$	−62.0836	+	62.0836i	−0.416669	+	0.416669i	−0.884054	−	0.467385i	$-0.845196\pi$
$149$	−62.0836	+	62.0836i	−0.416669	+	0.416669i	0.467385	+	0.884054i	$0.345196\pi$
$150$		0			0
$151$	−81.3591	−	33.7000i	−0.538802	−	0.223179i	0.0966516	−	0.995318i	$-0.469187\pi$
$151$	−81.3591	−	33.7000i	−0.538802	−	0.223179i	−0.635453	+	0.772139i	$0.719187\pi$
$152$			29.5722i			0.194554i
$153$	−310.454	+	120.148i	−2.02911	+	0.785279i
$154$	−4.30306			−0.0279420
$155$		0			0
$156$	−237.693	−	158.822i	−1.52368	−	1.01809i
$157$	120.763	+	120.763i	0.769190	+	0.769190i	0.977964	−	0.208774i	$-0.0669474\pi$
$157$	120.763	+	120.763i	0.769190	+	0.769190i	−0.208774	+	0.977964i	$0.566947\pi$
$158$	−12.4433	+	2.47513i	−0.0787550	+	0.0156653i
$159$	120.385	−	80.4387i	0.757139	−	0.505904i
$160$		0			0
$161$	−3.72626	+	1.54347i	−0.0231445	+	0.00958675i
$162$	−14.6661	−	35.4072i	−0.0905317	−	0.218563i
$163$	37.9067	−	190.570i	0.232556	−	1.16914i	−0.671261	−	0.741221i	$-0.734247\pi$
$163$	37.9067	−	190.570i	0.232556	−	1.16914i	0.903818	−	0.427918i	$-0.140753\pi$
$164$	−163.912	−	245.312i	−0.999466	−	1.49581i
$165$		0			0
$166$	20.2674	−	20.2674i	0.122093	−	0.122093i
$167$	−165.394	+	247.530i	−0.990385	+	1.48222i	−0.118230	+	0.992986i	$0.537722\pi$
$167$	−165.394	+	247.530i	−0.990385	+	1.48222i	−0.872155	+	0.489230i	$0.837278\pi$
$168$	−25.4432	−	10.5389i	−0.151447	−	0.0627316i
$169$		−	18.2346i		−	0.107897i
$170$		0			0
$171$	241.166			1.41033
$172$	49.2127	−	118.810i	0.286120	−	0.690756i
$173$	56.3529	+	37.6538i	0.325740	+	0.217652i	0.707677	−	0.706536i	$-0.249743\pi$
$173$	56.3529	+	37.6538i	0.325740	+	0.217652i	−0.381938	+	0.924188i	$0.624743\pi$
$174$	−33.7645	−	33.7645i	−0.194049	−	0.194049i
$175$		0			0
$176$	81.8495	−	54.6901i	0.465054	−	0.310739i
$177$	−397.257	−	79.0194i	−2.24439	−	0.446437i
$178$	−24.7890	+	10.2679i	−0.139264	+	0.0576850i
$179$	−25.4676	−	61.4842i	−0.142277	−	0.343487i	0.836638	−	0.547757i	$-0.184518\pi$
$179$	−25.4676	−	61.4842i	−0.142277	−	0.343487i	−0.978915	+	0.204270i	$0.934518\pi$
$180$		0			0
$181$	128.248	+	191.936i	0.708551	+	1.06042i	0.994758	+	0.102253i	$0.0326053\pi$
$181$	128.248	+	191.936i	0.708551	+	1.06042i	−0.286208	+	0.958168i	$0.592395\pi$
$182$	−1.73894	−	8.74222i	−0.00955459	−	0.0480342i
$183$	−229.781	+	229.781i	−1.25563	+	1.25563i
$184$	−2.50803	+	3.75354i	−0.0136306	+	0.0203997i
$185$		0			0
$186$		−	81.2157i		−	0.436643i
$187$	94.8092	−	60.1833i	0.507001	−	0.321836i
$188$	137.984			0.733955
$189$	−46.4447	+	112.127i	−0.245739	+	0.593267i
$190$		0			0
$191$	−170.119	−	170.119i	−0.890677	−	0.890677i	0.103910	−	0.994587i	$-0.466865\pi$
$191$	−170.119	−	170.119i	−0.890677	−	0.890677i	−0.994587	+	0.103910i	$0.966865\pi$
$192$	290.058	−	57.6962i	1.51072	−	0.300501i
$193$	225.040	−	150.367i	1.16601	−	0.779103i	0.186889	−	0.982381i	$-0.440160\pi$
$193$	225.040	−	150.367i	1.16601	−	0.779103i	0.979121	+	0.203278i	$0.0651595\pi$
$194$	−2.85002	−	0.566903i	−0.0146908	−	0.00292218i
$195$		0			0
$196$	−66.3946	−	160.291i	−0.338748	−	0.817809i
$197$	27.0338	−	135.908i	0.137227	−	0.689889i	−0.849511	−	0.527571i	$-0.823103\pi$
$197$	27.0338	−	135.908i	0.137227	−	0.689889i	0.986739	−	0.162318i	$-0.0518970\pi$
$198$	21.8215	+	32.6582i	0.110210	+	0.164940i
$199$	−2.68533	−	13.5001i	−0.0134941	−	0.0678397i	0.973451	−	0.228893i	$-0.0735107\pi$
$199$	−2.68533	−	13.5001i	−0.0134941	−	0.0678397i	−0.986946	+	0.161054i	$0.948511\pi$
$200$		0			0
$201$	−262.872	+	393.415i	−1.30782	+	1.95729i
$202$	−2.28543	−	0.946658i	−0.0113140	−	0.00468642i
$203$			63.1027i			0.310851i
$204$	349.866	−	61.1038i	1.71503	−	0.299528i
$205$		0			0
$206$	−11.9077	+	28.7477i	−0.0578043	+	0.139552i
$207$	30.6106	+	20.4534i	0.147877	+	0.0988086i
$208$	144.187	+	144.187i	0.693205	+	0.693205i
$209$	−79.7916	+	15.8715i	−0.381778	+	0.0759404i
$210$		0			0
$211$	299.532	+	59.5806i	1.41958	+	0.282373i	0.844427	−	0.535671i	$-0.179941\pi$
$211$	299.532	+	59.5806i	1.41958	+	0.282373i	0.575156	+	0.818044i	$0.304941\pi$
$212$	−97.7751	+	40.4998i	−0.461203	+	0.191037i
$213$	−65.0277	−	156.991i	−0.305295	−	0.737046i
$214$	0.773400	−	3.88815i	0.00361402	−	0.0181689i
$215$		0			0
$216$	26.5014	+	133.232i	0.122692	+	0.616813i
$217$	−75.8923	+	75.8923i	−0.349734	+	0.349734i
$218$	−2.43756	+	3.64807i	−0.0111815	+	0.0167343i
$219$	−215.759	−	89.3702i	−0.985200	−	0.408083i
$220$		0			0
$221$	160.584	+	168.296i	0.726625	+	0.761520i
$222$	−77.6042			−0.349569
$223$	8.52903	−	20.5909i	0.0382468	−	0.0923359i	−0.903602	−	0.428373i	$-0.859087\pi$
$223$	8.52903	−	20.5909i	0.0382468	−	0.0923359i	0.941849	+	0.336037i	$0.109087\pi$
$224$	25.2037	+	16.8406i	0.112517	+	0.0751812i
$225$		0			0
$226$	−42.5791	+	8.46951i	−0.188403	+	0.0374757i
$227$	113.145	−	75.6008i	0.498434	−	0.333043i	−0.280810	−	0.959763i	$-0.590603\pi$
$227$	113.145	−	75.6008i	0.498434	−	0.333043i	0.779244	+	0.626720i	$0.215603\pi$
$228$	−252.355	−	50.1966i	−1.10682	−	0.220160i
$229$	149.301	−	61.8425i	0.651970	−	0.270055i	−0.0320854	−	0.999485i	$-0.510215\pi$
$229$	149.301	−	61.8425i	0.651970	−	0.270055i	0.684055	+	0.729431i	$0.260215\pi$
$230$		0			0
$231$	14.7806	−	74.3069i	0.0639851	−	0.321675i
$232$	39.2395	+	58.7261i	0.169136	+	0.253130i
$233$	−30.0835	−	151.240i	−0.129114	−	0.649099i	−0.990088	−	0.140450i	$-0.955145\pi$
$233$	−30.0835	−	151.240i	−0.129114	−	0.649099i	0.860974	−	0.508649i	$-0.169855\pi$
$234$	−57.5309	+	57.5309i	−0.245859	+	0.245859i
$235$		0			0
$236$	273.527	+	113.298i	1.15901	+	0.480078i
$237$		−	223.377i		−	0.942520i
$238$	9.06092	+	6.36653i	0.0380711	+	0.0267501i
$239$	−24.6360			−0.103079			−0.0515397	−	0.998671i	$-0.516413\pi$
$239$	−24.6360			−0.103079			−0.0515397	+	0.998671i	$0.516413\pi$
$240$		0			0
$241$	−211.730	−	141.474i	−0.878548	−	0.587027i	0.0324336	−	0.999474i	$-0.489674\pi$
$241$	−211.730	−	141.474i	−0.878548	−	0.587027i	−0.910982	+	0.412447i	$0.864674\pi$
$242$	16.6108	+	16.6108i	0.0686399	+	0.0686399i
$243$	162.427	−	32.3087i	0.668423	−	0.132958i
$244$	197.497	−	131.963i	0.809415	−	0.540834i
$245$		0			0
$246$	−113.232	+	46.9023i	−0.460293	+	0.190660i
$247$	−64.4901	−	155.693i	−0.261094	−	0.630336i
$248$	−23.4361	+	117.821i	−0.0945004	+	0.475086i
$249$	280.368	+	419.601i	1.12598	+	1.68514i
$250$		0			0
$251$	−58.8552	+	58.8552i	−0.234483	+	0.234483i	−0.814561	−	0.580078i	$-0.803022\pi$
$251$	−58.8552	+	58.8552i	−0.234483	+	0.234483i	0.580078	+	0.814561i	$0.303022\pi$
$252$	91.2038	−	136.496i	0.361920	−	0.541651i
$253$	−11.4738	−	4.75262i	−0.0453512	−	0.0187851i
$254$		−	9.73828i		−	0.0383397i
$255$		0			0
$256$	−199.010			−0.777381
$257$	22.7940	−	55.0296i	0.0886926	−	0.214123i	−0.873309	−	0.487167i	$-0.838030\pi$
$257$	22.7940	−	55.0296i	0.0886926	−	0.214123i	0.962002	+	0.273044i	$0.0880304\pi$
$258$	−44.4187	−	29.6796i	−0.172165	−	0.115037i
$259$	72.5176	+	72.5176i	0.279991	+	0.279991i
$260$		0			0
$261$	478.920	−	320.004i	1.83494	−	1.22607i
$262$	37.4816	+	7.45556i	0.143060	+	0.0284563i
$263$	−413.855	+	171.424i	−1.57359	+	0.651803i	−0.987382	−	0.158357i	$-0.949380\pi$
$263$	−413.855	+	171.424i	−1.57359	+	0.651803i	−0.586209	+	0.810160i	$0.699380\pi$
$264$	−32.4513	−	78.3443i	−0.122922	−	0.296759i
$265$		0			0
$266$	−4.45712	−	6.67055i	−0.0167561	−	0.0250773i
$267$	−92.1629	−	463.334i	−0.345179	−	1.73533i
$268$	244.555	−	244.555i	0.912518	−	0.912518i
$269$	−249.394	+	373.244i	−0.927115	+	1.38753i	−0.00526195	+	0.999986i	$0.501675\pi$
$269$	−249.394	+	373.244i	−0.927115	+	1.38753i	−0.921853	+	0.387540i	$0.873325\pi$
$270$		0			0
$271$			130.751i			0.482478i	0.970466	+	0.241239i	$0.0775537\pi$
$271$			130.751i			0.482478i	−0.970466	+	0.241239i	$0.922446\pi$
$272$	−253.266	−	5.93882i	−0.931125	−	0.0218339i
$273$	156.937			0.574861
$274$	0.446842	−	1.07877i	0.00163081	−	0.00393712i
$275$		0			0
$276$	−27.7737	−	27.7737i	−0.100629	−	0.100629i
$277$	−364.857	+	72.5746i	−1.31717	+	0.262002i	−0.803151	−	0.595775i	$-0.796845\pi$
$277$	−364.857	+	72.5746i	−1.31717	+	0.262002i	−0.514022	+	0.857777i	$0.671845\pi$
$278$	45.2245	−	30.2180i	0.162678	−	0.108698i
$279$	960.849	+	191.125i	3.44390	+	0.685035i
$280$		0			0
$281$	−135.694	−	327.595i	−0.482898	−	1.16582i	−0.958227	−	0.286010i	$-0.907671\pi$
$281$	−135.694	−	327.595i	−0.482898	−	1.16582i	0.475329	−	0.879808i	$-0.342329\pi$
$282$	11.1826	−	56.2190i	0.0396548	−	0.199358i
$283$	139.027	+	208.069i	0.491263	+	0.735227i	0.991421	−	0.130707i	$-0.0417248\pi$
$283$	139.027	+	208.069i	0.491263	+	0.735227i	−0.500158	+	0.865934i	$0.666725\pi$
$284$	24.2316	+	121.820i	0.0853224	+	0.428944i
$285$		0			0
$286$	15.2484	−	22.8208i	0.0533159	−	0.0797929i
$287$	149.638	+	61.9822i	0.521388	+	0.215966i
$288$		−	276.686i		−	0.960715i
$289$	−288.682	−	13.5461i	−0.998901	−	0.0468721i
$290$		0			0
$291$	19.5790	−	47.2679i	0.0672818	−	0.162433i
$292$	141.934	+	94.8372i	0.486075	+	0.324785i
$293$	1.31220	+	1.31220i	0.00447848	+	0.00447848i	0.709342	−	0.704864i	$-0.248992\pi$
$293$	1.31220	+	1.31220i	0.00447848	+	0.00447848i	−0.704864	+	0.709342i	$0.748992\pi$
$294$	−70.6884	+	14.0608i	−0.240437	+	0.0478259i
$295$		0			0
$296$	112.582	+	22.3940i	0.380345	+	0.0756553i
$297$	−345.261	+	143.012i	−1.16250	+	0.481522i
$298$	−10.2023	−	24.6306i	−0.0342360	−	0.0826531i
$299$	5.01880	−	25.2312i	0.0167853	−	0.0843853i
$300$		0			0
$301$	13.7730	+	69.2414i	0.0457574	+	0.230038i
$302$	18.9079	−	18.9079i	0.0626090	−	0.0626090i
$303$	24.1975	−	36.2141i	0.0798596	−	0.119518i
$304$	169.560	+	70.2340i	0.557762	+	0.231033i
$305$		0			0
$306$	2.36961	−	101.054i	0.00774382	−	0.330241i
$307$	493.288			1.60680			0.803401	−	0.595438i	$-0.203022\pi$
$307$	493.288			1.60680			0.803401	+	0.595438i	$0.203022\pi$
$308$	−21.1925	+	51.1631i	−0.0688067	+	0.166114i
$309$	−455.525	−	304.372i	−1.47419	−	0.985022i
$310$		0			0
$311$	311.842	−	62.0293i	1.00271	−	0.199451i	0.333678	−	0.942687i	$-0.391710\pi$
$311$	311.842	−	62.0293i	1.00271	−	0.199451i	0.669029	+	0.743236i	$0.266710\pi$
$312$	146.052	−	97.5891i	0.468117	−	0.312786i
$313$	−163.744	−	32.5707i	−0.523144	−	0.104060i	−0.0735477	−	0.997292i	$-0.523432\pi$
$313$	−163.744	−	32.5707i	−0.523144	−	0.104060i	−0.449596	+	0.893232i	$0.648432\pi$
$314$	−47.9106	+	19.8452i	−0.152582	+	0.0632013i
$315$		0			0
$316$	−31.8538	+	160.140i	−0.100803	+	0.506772i
$317$	−50.1758	−	75.0934i	−0.158283	−	0.236888i	0.743848	−	0.668348i	$-0.232998\pi$
$317$	−50.1758	−	75.0934i	−0.158283	−	0.236888i	−0.902132	+	0.431461i	$0.857998\pi$
$318$	8.57690	+	43.1190i	0.0269714	+	0.135594i
$319$	−137.394	+	137.394i	−0.430703	+	0.430703i
$320$		0			0
$321$	64.4854	+	26.7107i	0.200889	+	0.0832110i
$322$		−	1.22469i		−	0.00380338i
$323$	191.499	+	84.6340i	0.592876	+	0.262025i
$324$	−493.219			−1.52228
$325$		0			0
$326$	49.0562	+	32.7783i	0.150479	+	0.100547i
$327$	−54.6235	−	54.6235i	−0.167044	−	0.167044i
$328$	177.803	−	35.3672i	0.542081	−	0.107827i
$329$	−62.9837	+	42.0844i	−0.191440	+	0.127916i
$330$		0			0
$331$	−401.574	+	166.337i	−1.21321	+	0.502530i	−0.895246	−	0.445572i	$-0.853000\pi$
$331$	−401.574	+	166.337i	−1.21321	+	0.502530i	−0.317968	+	0.948102i	$0.603000\pi$
$332$	−141.161	−	340.794i	−0.425185	−	1.02649i
$333$	182.626	−	918.123i	0.548426	−	2.75712i
$334$	−50.2214	−	75.1616i	−0.150363	−	0.225035i
$335$		0			0
$336$	−120.855	+	120.855i	−0.359687	+	0.359687i
$337$	181.045	−	270.954i	0.537227	−	0.804016i	−0.459213	−	0.888326i	$-0.651869\pi$
$337$	181.045	−	270.954i	0.537227	−	0.804016i	0.996440	+	0.0843097i	$0.0268685\pi$
$338$	5.11540	+	2.11887i	0.0151343	+	0.00626884i
$339$		−	764.363i		−	2.25476i
$340$		0			0
$341$	−330.483			−0.969158
$342$	−28.0236	+	67.6549i	−0.0819402	+	0.197821i
$343$	166.598	+	111.317i	0.485708	+	0.324540i
$344$	55.8746	+	55.8746i	0.162426	+	0.162426i
$345$		0			0
$346$	−17.1114	+	11.4335i	−0.0494548	+	0.0330447i
$347$	182.204	+	36.2426i	0.525083	+	0.104445i	0.450512	−	0.892770i	$-0.351241\pi$
$347$	182.204	+	36.2426i	0.525083	+	0.104445i	0.0745707	+	0.997216i	$0.476241\pi$
$348$	−567.746	+	235.168i	−1.63145	+	0.675771i
$349$	118.699	+	286.566i	0.340113	+	0.821105i	0.997704	+	0.0677297i	$0.0215756\pi$
$349$	118.699	+	286.566i	0.340113	+	0.821105i	−0.657591	+	0.753375i	$0.728424\pi$
$350$		0			0
$351$	−430.073	−	643.649i	−1.22528	−	1.83376i
$352$	18.2092	+	91.5437i	0.0517306	+	0.260067i
$353$	−216.640	+	216.640i	−0.613710	+	0.613710i	−0.943911	−	0.330201i	$-0.892884\pi$
$353$	−216.640	+	216.640i	−0.613710	+	0.613710i	0.330201	+	0.943911i	$0.392884\pi$
$354$	68.3290	−	102.262i	0.193020	−	0.288874i
$355$		0			0
$356$			345.308i			0.969967i
$357$	−141.063	+	134.599i	−0.395134	+	0.377028i
$358$	20.2077			0.0564460
$359$	19.7227	−	47.6147i	0.0549378	−	0.132632i	−0.894027	−	0.448012i	$-0.852132\pi$
$359$	19.7227	−	47.6147i	0.0549378	−	0.132632i	0.948965	+	0.315381i	$0.102132\pi$
$360$		0			0
$361$	148.013	+	148.013i	0.410010	+	0.410010i
$362$	−68.7468	+	13.6746i	−0.189908	+	0.0377751i
$363$	−343.899	+	229.786i	−0.947380	+	0.633019i
$364$	−112.509	−	22.3794i	−0.309090	−	0.0614817i
$365$		0			0
$366$	−37.7604	−	91.1616i	−0.103170	−	0.249075i
$367$	8.58594	−	43.1645i	0.0233949	−	0.117614i	−0.967323	−	0.253546i	$-0.918403\pi$
$367$	8.58594	−	43.1645i	0.0233949	−	0.117614i	0.990718	+	0.135932i	$0.0434029\pi$
$368$	15.5653	+	23.2951i	0.0422970	+	0.0633019i
$369$	−288.424	−	1450.01i	−0.781637	−	3.92956i
$370$		0			0
$371$	32.2780	−	48.3074i	0.0870026	−	0.130209i
$372$	−965.649	−	399.985i	−2.59583	−	1.07523i
$373$			173.156i			0.464226i	0.972689	+	0.232113i	$0.0745639\pi$
$373$			173.156i			0.464226i	−0.972689	+	0.232113i	$0.925436\pi$
$374$	5.86653	+	33.5904i	0.0156859	+	0.0898139i
$375$		0			0
$376$	−32.4458	+	78.3311i	−0.0862920	+	0.208327i
$377$	−334.657	−	223.611i	−0.887686	−	0.593133i
$378$	−26.0585	−	26.0585i	−0.0689379	−	0.0689379i
$379$	−262.544	+	52.2233i	−0.692729	+	0.137792i	−0.528885	−	0.848694i	$-0.677390\pi$
$379$	−262.544	+	52.2233i	−0.692729	+	0.137792i	−0.163845	+	0.986486i	$0.552390\pi$
$380$		0			0
$381$	168.164	+	33.4499i	0.441376	+	0.0877951i
$382$	67.4920	−	27.9561i	0.176681	−	0.0731835i
$383$	−252.268	−	609.029i	−0.658664	−	1.59016i	−0.799869	−	0.600175i	$-0.795098\pi$
$383$	−252.268	−	609.029i	−0.658664	−	1.59016i	0.141205	−	0.989980i	$-0.454902\pi$
$384$	−76.4678	+	384.430i	−0.199135	+	1.00112i
$385$		0			0
$386$	16.0331	+	80.6038i	0.0415365	+	0.208818i
$387$	455.665	−	455.665i	1.17743	−	1.17743i
$388$	−20.7767	+	31.0945i	−0.0535482	+	0.0801405i
$389$	−16.8059	−	6.96124i	−0.0432029	−	0.0178952i	0.360977	−	0.932575i	$-0.382443\pi$
$389$	−16.8059	−	6.96124i	−0.0432029	−	0.0178952i	−0.404180	+	0.914679i	$0.632443\pi$
$390$		0			0
$391$	17.1287	+	26.9835i	0.0438074	+	0.0690116i
$392$	106.607			0.271956
$393$	−257.491	+	621.638i	−0.655193	+	1.58178i
$394$	34.9853	+	23.3764i	0.0887952	+	0.0593311i
$395$		0			0
$396$	495.774	−	98.6156i	1.25196	−	0.249029i
$397$	−305.188	+	203.920i	−0.768736	+	0.513653i	−0.877012	−	0.480468i	$-0.840467\pi$
$397$	−305.188	+	203.920i	−0.768736	+	0.513653i	0.108276	+	0.994121i	$0.465467\pi$
$398$	4.09925	+	0.815392i	0.0102996	+	0.00204872i
$399$	130.499	−	54.0546i	0.327066	−	0.135475i
$400$		0			0
$401$	−60.1594	+	302.442i	−0.150023	+	0.754219i	0.830377	+	0.557202i	$0.188125\pi$
$401$	−60.1594	+	302.442i	−0.150023	+	0.754219i	−0.980400	+	0.197016i	$0.936875\pi$
$402$	−79.8200	−	119.459i	−0.198557	−	0.297162i
$403$	−133.553	−	671.418i	−0.331398	−	1.66605i
$404$	−22.5114	+	22.5114i	−0.0557213	+	0.0557213i
$405$		0			0
$406$	−17.7024	−	7.33256i	−0.0436019	−	0.0180605i
$407$			315.787i			0.775890i
$408$	−47.5808	+	212.982i	−0.116620	+	0.522014i
$409$	91.6025			0.223967			0.111983	−	0.993710i	$-0.464280\pi$
$409$	91.6025			0.223967			0.111983	+	0.993710i	$0.464280\pi$
$410$		0			0
$411$	17.0938	+	11.4217i	0.0415907	+	0.0277900i
$412$	283.163	+	283.163i	0.687290	+	0.687290i
$413$	−159.409	+	31.7084i	−0.385978	+	0.0767758i
$414$	−9.29481	+	6.21059i	−0.0224512	+	0.0150014i
$415$		0			0
$416$	−178.624	+	73.9886i	−0.429385	+	0.177857i
$417$	366.475	+	884.749i	0.878837	+	2.12170i
$418$	4.81933	−	24.2284i	0.0115295	−	0.0579628i
$419$	−71.2015	−	106.561i	−0.169932	−	0.254321i	0.736722	−	0.676195i	$-0.236372\pi$
$419$	−71.2015	−	106.561i	−0.169932	−	0.254321i	−0.906654	+	0.421874i	$0.861372\pi$
$420$		0			0
$421$	157.702	−	157.702i	0.374588	−	0.374588i	−0.494557	−	0.869145i	$-0.664670\pi$
$421$	157.702	−	157.702i	0.374588	−	0.374588i	0.869145	+	0.494557i	$0.164670\pi$
$422$	−51.5201	+	77.1052i	−0.122085	+	0.182714i
$423$	638.801	+	264.600i	1.51017	+	0.625532i
$424$		−	65.0286i		−	0.153369i
$425$		0			0
$426$	51.5973			0.121120
$427$	−49.9010	+	120.472i	−0.116864	+	0.282135i
$428$	−42.4208	−	28.3447i	−0.0991141	−	0.0662259i
$429$	341.701	+	341.701i	0.796506	+	0.796506i
$430$		0			0
$431$	−348.736	+	233.018i	−0.809133	+	0.540646i	−0.889936	−	0.456085i	$-0.849251\pi$
$431$	−348.736	+	233.018i	−0.809133	+	0.540646i	0.0808033	+	0.996730i	$0.474251\pi$
$432$	826.858	+	164.472i	1.91402	+	0.380723i
$433$	694.649	−	287.733i	1.60427	−	0.664511i	0.612259	−	0.790657i	$-0.290261\pi$
$433$	694.649	−	287.733i	1.60427	−	0.664511i	0.992012	+	0.126147i	$0.0402610\pi$
$434$	−12.4715	−	30.1090i	−0.0287363	−	0.0693755i
$435$		0			0
$436$	31.3704	+	46.9491i	0.0719505	+	0.107682i
$437$	−4.51718	−	22.7094i	−0.0103368	−	0.0519665i
$438$	50.1425	−	50.1425i	0.114481	−	0.114481i
$439$	−208.517	+	312.068i	−0.474982	+	0.710860i	−0.989163	−	0.146821i	$-0.953096\pi$
$439$	−208.517	+	312.068i	−0.474982	+	0.710860i	0.514181	+	0.857681i	$0.328096\pi$
$440$		0			0
$441$		−	869.392i		−	1.97141i
$442$	−65.8725	+	25.4930i	−0.149033	+	0.0576765i
$443$	357.099			0.806092			0.403046	−	0.915180i	$-0.367951\pi$
$443$	357.099			0.806092			0.403046	+	0.915180i	$0.367951\pi$
$444$	−382.199	+	922.709i	−0.860808	+	2.07817i
$445$		0			0
$446$	4.78534	+	4.78534i	0.0107295	+	0.0107295i
$447$	460.375	−	91.5743i	1.02992	−	0.204864i
$448$	98.6731	−	65.9313i	0.220253	−	0.147168i
$449$	154.177	+	30.6676i	0.343378	+	0.0683021i	0.363767	−	0.931490i	$-0.381491\pi$
$449$	154.177	+	30.6676i	0.343378	+	0.0683021i	−0.0203891	+	0.999792i	$0.506491\pi$
$450$		0			0
$451$	190.855	+	460.764i	0.423181	+	1.02165i
$452$	−108.999	+	547.975i	−0.241148	+	1.21233i
$453$	261.562	+	391.456i	0.577400	+	0.864141i
$454$	8.06105	+	40.5256i	0.0177556	+	0.0892635i
$455$		0			0
$456$	87.8352	−	131.455i	0.192621	−	0.288278i
$457$	158.906	+	65.8210i	0.347716	+	0.144029i	0.549704	−	0.835359i	$-0.314740\pi$
$457$	158.906	+	65.8210i	0.347716	+	0.144029i	−0.201989	+	0.979388i	$0.564740\pi$
$458$			49.0699i			0.107140i
$459$	938.605	+	209.688i	2.04489	+	0.456836i
$460$		0			0
$461$	−206.066	+	497.487i	−0.446997	+	1.07915i	0.526444	+	0.850210i	$0.323525\pi$
$461$	−206.066	+	497.487i	−0.446997	+	1.07915i	−0.973441	+	0.228937i	$0.926475\pi$
$462$	19.1280	+	12.7809i	0.0414026	+	0.0276643i
$463$	−153.031	−	153.031i	−0.330522	−	0.330522i	0.522263	−	0.852785i	$-0.325088\pi$
$463$	−153.031	−	153.031i	−0.330522	−	0.330522i	−0.852785	+	0.522263i	$0.825088\pi$
$464$	429.915	−	85.5153i	0.926540	−	0.184300i
$465$		0			0
$466$	45.9235	+	9.13475i	0.0985483	+	0.0196025i
$467$	217.434	−	90.0641i	0.465597	−	0.192857i	−0.137536	−	0.990497i	$-0.543918\pi$
$467$	217.434	−	90.0641i	0.465597	−	0.192857i	0.603134	+	0.797640i	$0.293918\pi$
$468$	400.701	+	967.377i	0.856198	+	2.06704i
$469$	−37.0409	+	186.217i	−0.0789785	+	0.397052i
$470$		0			0
$471$	−178.127	−	895.504i	−0.378189	−	1.90128i
$472$	−128.636	+	128.636i	−0.272533	+	0.272533i
$473$	−120.772	+	180.748i	−0.255332	+	0.382132i
$474$	62.6646	+	25.9565i	0.132204	+	0.0547606i
$475$		0			0
$476$	120.322	−	76.3787i	0.252778	−	0.160460i
$477$	−530.317			−1.11178
$478$	2.86271	−	6.91119i	0.00598893	−	0.0144586i
$479$	474.069	+	316.763i	0.989706	+	0.661300i	0.941315	−	0.337528i	$-0.109591\pi$
$479$	474.069	+	316.763i	0.989706	+	0.661300i	0.0483902	+	0.998829i	$0.484591\pi$
$480$		0			0
$481$	−641.562	+	127.615i	−1.33381	+	0.265311i
$482$	64.2911	−	42.9579i	0.133384	−	0.0891243i
$483$	21.1484	+	4.20667i	0.0437855	+	0.00870947i
$484$	279.310	−	115.694i	0.577086	−	0.239037i
$485$		0			0
$486$	−9.81042	+	49.3203i	−0.0201861	+	0.101482i
$487$	−367.228	−	549.596i	−0.754062	−	1.12853i	−0.987723	−	0.156216i	$-0.950070\pi$
$487$	−367.228	−	549.596i	−0.754062	−	1.12853i	0.233661	−	0.972318i	$-0.424930\pi$
$488$	28.4736	+	143.146i	0.0583475	+	0.293333i
$489$	−734.531	+	734.531i	−1.50211	+	1.50211i
$490$		0			0
$491$	−573.097	−	237.385i	−1.16720	−	0.483472i	−0.286937	−	0.957949i	$-0.592637\pi$
$491$	−573.097	−	237.385i	−1.16720	−	0.483472i	−0.880268	+	0.474478i	$0.842637\pi$
$492$			1577.32i			3.20593i
$493$	492.590	−	86.0302i	0.999168	−	0.174504i
$494$	51.1707			0.103584
$495$		0			0
$496$	619.897	+	414.202i	1.24979	+	0.835084i
$497$	−48.2153	−	48.2153i	−0.0970127	−	0.0970127i
$498$	−150.291	+	29.8947i	−0.301788	+	0.0600294i
$499$	137.147	−	91.6387i	0.274844	−	0.183645i	−0.410508	−	0.911857i	$-0.634649\pi$
$499$	137.147	−	91.6387i	0.274844	−	0.183645i	0.685351	+	0.728212i	$0.259649\pi$
$500$		0			0
$501$	1470.42	−	609.070i	2.93498	−	1.21571i
$502$	−9.67181	−	23.3498i	−0.0192666	−	0.0465136i
$503$	−59.8169	+	300.720i	−0.118920	+	0.597853i	0.874661	+	0.484735i	$0.161084\pi$
$503$	−59.8169	+	300.720i	−0.118920	+	0.597853i	−0.993582	+	0.113118i	$0.963916\pi$
$504$	56.0408	+	83.8710i	0.111192	+	0.166411i
$505$		0			0
$506$	2.66653	−	2.66653i	0.00526983	−	0.00526983i
$507$	−54.1603	+	81.0566i	−0.106825	+	0.159875i
$508$	−115.787	−	47.9607i	−0.227928	−	0.0944109i
$509$		−	562.728i		−	1.10556i	−0.833328	−	0.552778i	$-0.813568\pi$
$509$		−	562.728i		−	1.10556i	0.833328	−	0.552778i	$-0.186432\pi$
$510$		0			0
$511$	−93.7117			−0.183389
$512$	135.352	−	326.768i	0.264359	−	0.638219i
$513$	−579.318	−	387.088i	−1.12927	−	0.754557i
$514$	12.7889	+	12.7889i	0.0248812	+	0.0248812i
$515$		0			0
$516$	−571.649	+	381.964i	−1.10785	+	0.740240i
$517$	−228.766	−	45.5044i	−0.442488	−	0.0880163i
$518$	−28.7701	+	11.9170i	−0.0555408	+	0.0230057i
$519$	−138.661	−	334.758i	−0.267170	−	0.645006i
$520$		0			0
$521$	320.835	+	480.163i	0.615806	+	0.921619i	0.999999	−	0.00163417i	$-0.000520173\pi$
$521$	320.835	+	480.163i	0.615806	+	0.921619i	−0.384193	+	0.923253i	$0.625520\pi$
$522$	34.1209	+	171.537i	0.0653656	+	0.328615i
$523$	249.718	−	249.718i	0.477472	−	0.477472i	−0.426850	−	0.904322i	$-0.640377\pi$
$523$	249.718	−	249.718i	0.477472	−	0.477472i	0.904322	+	0.426850i	$0.140377\pi$
$524$	273.242	−	408.936i	0.521454	−	0.780412i
$525$		0			0
$526$		−	136.019i		−	0.258592i
$527$	695.895	+	488.961i	1.32048	+	0.927820i
$528$	−526.278			−0.996739
$529$	−201.087	+	485.467i	−0.380126	+	0.917706i
$530$		0			0
$531$	1049.04	+	1049.04i	1.97559	+	1.97559i
$532$	−101.264	+	20.1426i	−0.190345	+	0.0378620i
$533$	−858.974	+	573.948i	−1.61158	+	1.07683i
$534$	140.690	+	27.9849i	0.263464	+	0.0524063i
$535$		0			0
$536$	81.3247	+	196.335i	0.151725	+	0.366297i
$537$	−69.4112	+	348.954i	−0.129257	+	0.649821i
$538$	−75.7276	−	113.334i	−0.140758	−	0.210659i
$539$	57.2162	+	287.645i	0.106153	+	0.533665i
$540$		0			0
$541$	487.484	−	729.572i	0.901080	−	1.34856i	−0.0359647	−	0.999353i	$-0.511450\pi$
$541$	487.484	−	729.572i	0.901080	−	1.34856i	0.937045	−	0.349209i	$-0.113550\pi$
$542$	−36.6801	−	15.1934i	−0.0676754	−	0.0280321i
$543$		−	1234.12i		−	2.27277i
$544$	97.0993	−	219.704i	0.178491	−	0.403868i
$545$		0			0
$546$	−18.2361	+	44.0260i	−0.0333995	+	0.0806336i
$547$	380.643	+	254.337i	0.695873	+	0.464968i	0.852525	−	0.522686i	$-0.175070\pi$
$547$	380.643	+	254.337i	0.695873	+	0.464968i	−0.156652	+	0.987654i	$0.550070\pi$
$548$	−10.6258	−	10.6258i	−0.0193902	−	0.0193902i
$549$	1167.38	−	232.206i	2.12637	−	0.422962i
$550$		0			0
$551$	−355.300	−	70.6736i	−0.644828	−	0.128264i
$552$	22.2975	−	9.23591i	0.0403940	−	0.0167317i
$553$	−34.3020	−	82.8124i	−0.0620290	−	0.149751i
$554$	22.0370	−	110.787i	0.0397780	−	0.199977i
$555$		0			0
$556$	−136.561	−	686.539i	−0.245613	−	1.23478i
$557$	−374.871	+	374.871i	−0.673018	+	0.673018i	−0.958411	−	0.285393i	$-0.907876\pi$
$557$	−374.871	+	374.871i	−0.673018	+	0.673018i	0.285393	+	0.958411i	$0.407876\pi$
$558$	−165.268	+	247.341i	−0.296179	+	0.443263i
$559$	−416.020	−	172.321i	−0.744221	−	0.308266i
$560$		0			0
$561$	−600.203	−	14.0741i	−1.06988	−	0.0250876i
$562$	107.669			0.191582
$563$	125.291	−	302.480i	0.222542	−	0.537265i	−0.772692	−	0.634782i	$-0.781090\pi$
$563$	125.291	−	302.480i	0.222542	−	0.537265i	0.995234	+	0.0975170i	$0.0310900\pi$
$564$	−613.366	−	409.838i	−1.08753	−	0.726663i
$565$		0			0
$566$	−74.5253	+	14.8240i	−0.131670	+	0.0261908i
$567$	225.134	−	150.430i	0.397062	−	0.265308i
$568$	−74.8533	−	14.8892i	−0.131784	−	0.0262135i
$569$	−261.743	+	108.417i	−0.460005	+	0.190540i	−0.600637	−	0.799522i	$-0.705086\pi$
$569$	−261.743	+	108.417i	−0.460005	+	0.190540i	0.140633	+	0.990062i	$0.455086\pi$
$570$		0			0
$571$	−170.415	+	856.733i	−0.298450	+	1.50041i	0.482545	+	0.875871i	$0.339712\pi$
$571$	−170.415	+	856.733i	−0.298450	+	1.50041i	−0.780995	+	0.624538i	$0.785288\pi$
$572$	−196.240	−	293.694i	−0.343076	−	0.513450i
$573$	250.928	+	1261.50i	0.437921	+	2.20158i
$574$	−34.7761	+	34.7761i	−0.0605855	+	0.0605855i
$575$		0			0
$576$	−1000.77	−	414.535i	−1.73746	−	0.719678i
$577$		−	801.517i		−	1.38911i	−0.719439	−	0.694555i	$-0.755601\pi$
$577$		−	801.517i		−	1.38911i	0.719439	−	0.694555i	$-0.244399\pi$
$578$	37.3451	−	79.4108i	0.0646110	−	0.137389i
$579$	−1446.97			−2.49908
$580$		0			0
$581$	168.375	+	112.504i	0.289802	+	0.193639i
$582$	10.9851	+	10.9851i	0.0188747	+	0.0188747i
$583$	175.460	−	34.9011i	0.300960	−	0.0598647i
$584$	−87.2122	+	58.2734i	−0.149336	+	0.0997831i
$585$		0			0
$586$	−0.520591	+	0.215636i	−0.000888381	+	0.000367979i
$587$	−100.076	−	241.606i	−0.170488	−	0.411594i	0.815423	−	0.578865i	$-0.196504\pi$
$587$	−100.076	−	241.606i	−0.170488	−	0.411594i	−0.985911	+	0.167271i	$0.946504\pi$
$588$	−180.957	+	909.730i	−0.307749	+	1.54716i
$589$	−342.315	−	512.310i	−0.581179	−	0.869796i
$590$		0			0
$591$	−523.844	+	523.844i	−0.886369	+	0.886369i
$592$	395.783	−	592.332i	0.668553	−	1.00056i
$593$	133.678	+	55.3714i	0.225427	+	0.0933751i	0.492538	−	0.870291i	$-0.336069\pi$
$593$	133.678	+	55.3714i	0.225427	+	0.0933751i	−0.267111	+	0.963666i	$0.586069\pi$
$594$		−	113.475i		−	0.191036i
$595$		0			0
$596$	−343.103			−0.575676
$597$	−28.1610	+	67.9867i	−0.0471709	+	0.113881i
$598$	6.49499	+	4.33981i	0.0108612	+	0.00725721i
$599$	2.96833	+	2.96833i	0.00495547	+	0.00495547i	0.709580	−	0.704625i	$-0.248885\pi$
$599$	2.96833	+	2.96833i	0.00495547	+	0.00495547i	−0.704625	+	0.709580i	$0.748885\pi$
$600$		0			0
$601$	91.4982	−	61.1372i	0.152243	−	0.101726i	−0.477115	−	0.878841i	$-0.658318\pi$
$601$	91.4982	−	61.1372i	0.152243	−	0.101726i	0.629359	+	0.777115i	$0.283318\pi$
$602$	−21.0249	−	4.18211i	−0.0349251	−	0.00694703i
$603$	1601.14	−	663.214i	2.65529	−	1.09986i
$604$	−131.693	−	317.935i	−0.218035	−	0.526382i
$605$		0			0
$606$	7.34747	+	10.9963i	0.0121245	+	0.0181457i
$607$	113.239	+	569.290i	0.186555	+	0.937875i	0.954693	+	0.297591i	$0.0961832\pi$
$607$	113.239	+	569.290i	0.186555	+	0.937875i	−0.768138	+	0.640284i	$0.778817\pi$
$608$	−123.049	+	123.049i	−0.202383	+	0.202383i
$609$	187.427	−	280.504i	0.307762	−	0.460598i
$610$		0			0
$611$		−	483.157i		−	0.790764i
$612$	−1189.85	−	525.862i	−1.94420	−	0.859251i
$613$	−32.4493			−0.0529353			−0.0264676	−	0.999650i	$-0.508426\pi$
$613$	−32.4493			−0.0529353			−0.0264676	+	0.999650i	$0.508426\pi$
$614$	−57.3203	+	138.383i	−0.0933556	+	0.225380i
$615$		0			0
$616$	−24.0612	−	24.0612i	−0.0390605	−	0.0390605i
$617$	150.267	−	29.8900i	0.243545	−	0.0484440i	−0.0718085	−	0.997418i	$-0.522877\pi$
$617$	150.267	−	29.8900i	0.243545	−	0.0484440i	0.315353	+	0.948974i	$0.397877\pi$
$618$	138.318	−	92.4214i	0.223816	−	0.149549i
$619$	143.212	+	28.4867i	0.231361	+	0.0460205i	0.309409	−	0.950929i	$-0.399869\pi$
$619$	143.212	+	28.4867i	0.231361	+	0.0460205i	−0.0780483	+	0.996950i	$0.524869\pi$
$620$		0			0
$621$	−40.7024	−	98.2644i	−0.0655434	−	0.158236i
$622$	−18.8350	+	94.6897i	−0.0302813	+	0.152234i
$623$	−105.317	−	157.619i	−0.169049	−	0.253000i
$624$	−212.677	−	1069.20i	−0.340829	−	1.71346i
$625$		0			0
$626$	28.1643	−	42.1508i	0.0449909	−	0.0673336i
$627$	401.832	+	166.444i	0.640880	+	0.265461i
$628$			667.391i			1.06272i
$629$	467.218	−	664.950i	0.742795	−	1.05715i
$630$		0			0
$631$	144.897	−	349.813i	0.229631	−	0.554379i	−0.766501	−	0.642243i	$-0.778004\pi$
$631$	144.897	−	349.813i	0.229631	−	0.554379i	0.996133	+	0.0878637i	$0.0280040\pi$
$632$	−83.4187	−	55.7386i	−0.131992	−	0.0881940i
$633$	−1154.52	−	1154.52i	−1.82388	−	1.82388i
$634$	26.8966	−	5.35007i	0.0424237	−	0.00843859i
$635$		0			0
$636$	554.923	+	110.381i	0.872520	+	0.173555i
$637$	−561.266	+	232.484i	−0.881109	+	0.364967i
$638$	−22.5783	−	54.5089i	−0.0353892	−	0.0854371i
$639$	−121.424	+	610.439i	−0.190022	+	0.955304i
$640$		0			0
$641$	45.3274	+	227.876i	0.0707136	+	0.355502i	0.999900	−	0.0141089i	$-0.00449115\pi$
$641$	45.3274	+	227.876i	0.0707136	+	0.355502i	−0.929187	+	0.369610i	$0.879491\pi$
$642$	−14.9865	+	14.9865i	−0.0233434	+	0.0233434i
$643$	−143.286	+	214.442i	−0.222839	+	0.333502i	−0.925997	−	0.377532i	$-0.876773\pi$
$643$	−143.286	+	214.442i	−0.222839	+	0.333502i	0.703158	+	0.711034i	$0.251773\pi$
$644$	−14.5615	−	6.03156i	−0.0226110	−	0.00936577i
$645$		0			0
$646$	−45.9949	+	43.8872i	−0.0711995	+	0.0679369i
$647$	175.220			0.270820			0.135410	−	0.990790i	$-0.456765\pi$
$647$	175.220			0.270820			0.135410	+	0.990790i	$0.456765\pi$
$648$	115.977	−	279.993i	0.178977	−	0.432088i
$649$	−416.123	−	278.044i	−0.641175	−	0.428419i
$650$		0			0
$651$	562.772	−	111.942i	0.864473	−	0.171954i
$652$	631.333	−	421.843i	0.968302	−	0.646999i
$653$	852.370	+	169.547i	1.30531	+	0.259643i	0.798282	−	0.602284i	$-0.205743\pi$
$653$	852.370	+	169.547i	1.30531	+	0.259643i	0.507032	+	0.861927i	$0.330743\pi$
$654$	21.6710	−	8.97641i	0.0331360	−	0.0137254i
$655$		0			0
$656$	219.494	−	1103.47i	0.334595	−	1.68212i
$657$	475.227	+	711.228i	0.723329	+	1.08254i
$658$	−4.48731	−	22.5592i	−0.00681961	−	0.0342845i
$659$	−795.445	+	795.445i	−1.20705	+	1.20705i	−0.235070	+	0.971978i	$0.575532\pi$
$659$	−795.445	+	795.445i	−1.20705	+	1.20705i	−0.971978	+	0.235070i	$0.924468\pi$
$660$		0			0
$661$	66.2141	+	27.4268i	0.100173	+	0.0414929i	0.432207	−	0.901774i	$-0.357735\pi$
$661$	66.2141	+	27.4268i	0.100173	+	0.0414929i	−0.332034	+	0.943267i	$0.607735\pi$
$662$		−	131.983i		−	0.199370i
$663$	−213.958	−	1225.08i	−0.322712	−	1.84778i
$664$	226.656			0.341350
$665$		0			0
$666$	236.342	+	157.919i	0.354868	+	0.237115i
$667$	−39.1036	−	39.1036i	−0.0586261	−	0.0586261i
$668$	−1141.01	+	226.960i	−1.70809	+	0.339761i
$669$	−99.0722	+	66.1979i	−0.148090	+	0.0989506i
$670$		0			0
$671$	−370.955	+	153.654i	−0.552838	+	0.228993i
$672$	−62.0160	−	149.720i	−0.0922857	−	0.222797i
$673$	−59.5700	+	299.478i	−0.0885141	+	0.444990i	0.910958	+	0.412499i	$0.135344\pi$
$673$	−59.5700	+	299.478i	−0.0885141	+	0.444990i	−0.999472	+	0.0324911i	$0.989656\pi$
$674$	54.9738	+	82.2741i	0.0815635	+	0.122068i
$675$		0			0
$676$	50.3864	−	50.3864i	0.0745361	−	0.0745361i
$677$	−231.305	+	346.173i	−0.341662	+	0.511333i	−0.962018	−	0.272987i	$-0.911988\pi$
$677$	−231.305	+	346.173i	−0.341662	+	0.511333i	0.620356	+	0.784321i	$0.286988\pi$
$678$	214.429	+	88.8194i	0.316267	+	0.131002i
$679$		−	20.5301i		−	0.0302358i
$680$		0			0
$681$	−727.500			−1.06828
$682$	38.4022	−	92.7112i	0.0563083	−	0.135940i
$683$	208.782	+	139.504i	0.305684	+	0.204251i	0.698945	−	0.715175i	$-0.253653\pi$
$683$	208.782	+	139.504i	0.305684	+	0.204251i	−0.393261	+	0.919427i	$0.628653\pi$
$684$	666.397	+	666.397i	0.974264	+	0.974264i
$685$		0			0
$686$	−50.5868	+	33.8010i	−0.0737417	+	0.0492726i
$687$	−847.358	−	168.550i	−1.23342	−	0.245342i
$688$	453.073	−	187.669i	0.658536	−	0.272774i
$689$	141.812	+	342.365i	0.205823	+	0.496901i
$690$		0			0
$691$	−247.207	−	369.971i	−0.357752	−	0.535414i	0.608318	−	0.793693i	$-0.291844\pi$
$691$	−247.207	−	369.971i	−0.357752	−	0.535414i	−0.966070	+	0.258279i	$0.916844\pi$
$692$	51.6700	+	259.762i	0.0746676	+	0.375379i
$693$	−196.223	+	196.223i	−0.283150	+	0.283150i
$694$	−31.3394	+	46.9027i	−0.0451576	+	0.0675832i
$695$		0			0
$696$		−	377.599i		−	0.542527i
$697$	279.836	−	1252.60i	0.401486	−	1.79714i
$698$	−94.1839			−0.134934
$699$	−315.485	+	761.647i	−0.451337	+	1.08962i
$700$		0			0
$701$	532.113	+	532.113i	0.759077	+	0.759077i	0.976154	−	0.217078i	$-0.0696525\pi$
$701$	532.113	+	532.113i	0.759077	+	0.759077i	−0.217078	+	0.976154i	$0.569653\pi$
$702$	230.539	−	45.8571i	0.328404	−	0.0653235i
$703$	−489.529	+	327.093i	−0.696343	+	0.465281i
$704$	358.396	+	71.2893i	0.509085	+	0.101263i
$705$		0			0
$706$	−35.6009	−	85.9481i	−0.0504262	−	0.121740i
$707$	3.40963	−	17.1414i	0.00482268	−	0.0242452i
$708$	−879.365	−	1316.06i	−1.24204	−	1.85884i
$709$	−82.6803	−	415.662i	−0.116615	−	0.586265i	−0.994263	−	0.106959i	$-0.965888\pi$
$709$	−82.6803	−	415.662i	−0.116615	−	0.586265i	0.877648	−	0.479306i	$-0.159112\pi$
$710$		0			0
$711$	−454.556	+	680.291i	−0.639319	+	0.956809i
$712$	−196.026	−	81.1967i	−0.275318	−	0.114040i
$713$		−	94.0582i		−	0.131919i
$714$	−21.3678	−	55.2132i	−0.0299269	−	0.0773295i
$715$		0			0
$716$	99.5222	−	240.268i	0.138998	−	0.335570i
$717$	109.512	+	73.1735i	0.152736	+	0.102055i
$718$	11.0657	+	11.0657i	0.0154118	+	0.0154118i
$719$	45.5078	−	9.05206i	0.0632932	−	0.0125898i	−0.163342	−	0.986569i	$-0.552227\pi$
$719$	45.5078	−	9.05206i	0.0632932	−	0.0125898i	0.226635	+	0.973980i	$0.427227\pi$
$720$		0			0
$721$	−215.616	−	42.8886i	−0.299051	−	0.0594849i
$722$	−58.7218	+	24.3234i	−0.0813322	+	0.0336889i
$723$	520.981	+	1257.76i	0.720582	+	1.73964i
$724$	−175.986	+	884.742i	−0.243075	+	1.22202i
$725$		0			0
$726$	−24.5012	−	123.176i	−0.0337483	−	0.169664i
$727$	350.335	−	350.335i	0.481892	−	0.481892i	−0.423844	−	0.905735i	$-0.639319\pi$
$727$	350.335	−	350.335i	0.481892	−	0.481892i	0.905735	+	0.423844i	$0.139319\pi$
$728$	39.1600	−	58.6070i	0.0537912	−	0.0805042i
$729$	231.476	+	95.8805i	0.317525	+	0.131523i
$730$		0			0
$731$	521.733	−	201.914i	0.713725	−	0.276216i
$732$	−1269.87			−1.73480
$733$	380.396	−	918.356i	0.518957	−	1.25287i	−0.419587	−	0.907715i	$-0.637825\pi$
$733$	380.396	−	918.356i	0.518957	−	1.25287i	0.938544	−	0.345159i	$-0.112175\pi$
$734$	11.1114	+	7.42437i	0.0151381	+	0.0101149i
$735$		0			0
$736$	−26.0541	+	5.18249i	−0.0353996	+	0.00704143i
$737$	−486.103	+	324.804i	−0.659570	+	0.440711i
$738$	440.289	+	87.5789i	0.596598	+	0.118671i
$739$	144.114	−	59.6940i	0.195012	−	0.0807768i	−0.283040	−	0.959108i	$-0.591343\pi$
$739$	144.114	−	59.6940i	0.195012	−	0.0807768i	0.478052	+	0.878331i	$0.341343\pi$
$740$		0			0
$741$	−175.766	+	883.635i	−0.237201	+	1.19249i
$742$	9.80109	+	14.6684i	0.0132090	+	0.0197687i
$743$	161.000	+	809.400i	0.216689	+	1.08937i	0.923979	+	0.382444i	$0.124917\pi$
$743$	161.000	+	809.400i	0.216689	+	1.08937i	−0.707290	+	0.706923i	$0.750083\pi$
$744$	454.130	−	454.130i	0.610390	−	0.610390i
$745$		0			0
$746$	−48.5760	−	20.1208i	−0.0651152	−	0.0269716i
$747$		−	1848.41i		−	2.47445i
$748$	428.280	+	95.6792i	0.572567	+	0.127913i
$749$	28.0083			0.0373943
$750$		0			0
$751$	−17.3029	−	11.5614i	−0.0230398	−	0.0153947i	0.543997	−	0.839087i	$-0.316910\pi$
$751$	−17.3029	−	11.5614i	−0.0230398	−	0.0153947i	−0.567037	+	0.823692i	$0.691910\pi$
$752$	372.072	+	372.072i	0.494777	+	0.494777i
$753$	436.435	−	86.8123i	0.579595	−	0.115289i
$754$	101.618	−	67.8987i	0.134771	−	0.0900513i
$755$		0			0
$756$	−438.171	+	181.497i	−0.579592	+	0.240075i
$757$	−112.139	−	270.728i	−0.148136	−	0.357632i	0.832341	−	0.554263i	$-0.187000\pi$
$757$	−112.139	−	270.728i	−0.148136	−	0.357632i	−0.980478	+	0.196631i	$0.937000\pi$
$758$	15.8574	−	79.7207i	0.0209201	−	0.105172i
$759$	36.8874	+	55.2059i	0.0486000	+	0.0727351i
$760$		0			0
$761$	526.662	−	526.662i	0.692066	−	0.692066i	−0.270620	−	0.962686i	$-0.587229\pi$
$761$	526.662	−	526.662i	0.692066	−	0.692066i	0.962686	+	0.270620i	$0.0872288\pi$
$762$	−28.9246	+	43.2887i	−0.0379587	+	0.0568093i
$763$	−28.6385	−	11.8625i	−0.0375341	−	0.0155471i
$764$		−	940.158i		−	1.23057i
$765$		0			0
$766$	200.166			0.261314
$767$	396.721	−	957.768i	0.517237	−	1.24872i
$768$	884.639	+	591.097i	1.15187	+	0.769658i
$769$	777.888	+	777.888i	1.01156	+	1.01156i	0.999932	+	0.0116255i	$0.00370060\pi$
$769$	777.888	+	777.888i	1.01156	+	1.01156i	0.0116255	+	0.999932i	$0.496299\pi$
$770$		0			0
$771$	−264.773	+	176.915i	−0.343415	+	0.229462i
$772$	1037.34	+	206.339i	1.34370	+	0.267278i
$773$	596.572	−	247.108i	0.771762	−	0.319674i	0.0381759	−	0.999271i	$-0.487845\pi$
$773$	596.572	−	247.108i	0.771762	−	0.319674i	0.733586	+	0.679597i	$0.237845\pi$
$774$	74.8804	+	180.777i	0.0967447	+	0.233562i
$775$		0			0
$776$	−12.7664	−	19.1062i	−0.0164515	−	0.0246214i
$777$	−106.964	−	537.747i	−0.137663	−	0.692081i
$778$	3.90571	−	3.90571i	0.00502020	−	0.00502020i
$779$	−516.583	+	773.121i	−0.663136	+	0.992453i
$780$		0			0
$781$		−	209.960i		−	0.268834i
$782$	−9.56012	+	1.66966i	−0.0122252	+	0.00213512i
$783$	−1664.07			−2.12525
$784$	253.191	−	611.256i	0.322947	−	0.779663i
$785$		0			0
$786$	−144.469	−	144.469i	−0.183803	−	0.183803i
$787$	−1462.32	+	290.874i	−1.85810	+	0.369599i	−0.991575	−	0.129537i	$-0.958651\pi$
$787$	−1462.32	+	290.874i	−1.85810	+	0.369599i	−0.866524	+	0.499135i	$0.833651\pi$
$788$	450.246	−	300.845i	0.571378	−	0.381783i
$789$	2348.83	+	467.212i	2.97697	+	0.592157i
$790$		0			0
$791$	−117.376	−	283.372i	−0.148390	−	0.358245i
$792$	−60.5951	+	304.632i	−0.0765089	+	0.384636i
$793$	−462.077	−	691.547i	−0.582695	−	0.872065i
$794$	−21.7433	−	109.311i	−0.0273845	−	0.137671i
$795$		0			0
$796$	29.8837	−	44.7241i	0.0375423	−	0.0561860i
$797$	471.706	+	195.387i	0.591852	+	0.245153i	0.658447	−	0.752627i	$-0.271214\pi$
$797$	471.706	+	195.387i	0.591852	+	0.245153i	−0.0665952	+	0.997780i	$0.521214\pi$
$798$			42.8905i			0.0537475i
$799$	414.386	+	434.286i	0.518630	+	0.543537i
$800$		0			0
$801$	−662.170	+	1598.62i	−0.826679	+	1.99578i
$802$	−77.8542	−	52.0205i	−0.0970751	−	0.0648635i
$803$	−204.040	−	204.040i	−0.254097	−	0.254097i
$804$	−1813.47	+	360.722i	−2.25556	+	0.448659i
$805$		0			0
$806$	203.874	+	40.5530i	0.252945	+	0.0503139i
$807$	2217.22	−	918.401i	2.74748	−	1.13804i
$808$	−7.48598	−	18.0727i	−0.00926482	−	0.0223673i
$809$	49.4862	−	248.784i	0.0611696	−	0.307520i	−0.938073	−	0.346438i	$-0.887391\pi$
$809$	49.4862	−	248.784i	0.0611696	−	0.307520i	0.999242	+	0.0389179i	$0.0123911\pi$
$810$		0			0
$811$	93.1315	+	468.204i	0.114835	+	0.577316i	0.994763	+	0.102209i	$0.0325909\pi$
$811$	93.1315	+	468.204i	0.114835	+	0.577316i	−0.879928	+	0.475108i	$0.842409\pi$
$812$	−174.367	+	174.367i	−0.214738	+	0.214738i
$813$	388.357	−	581.217i	0.477684	−	0.714904i
$814$	−88.5886	−	36.6946i	−0.108831	−	0.0450794i
$815$		0			0
$816$	1108.18	+	778.648i	1.35806	+	0.954225i
$817$	−405.290			−0.496071
$818$	−10.6442	+	25.6975i	−0.0130125	+	0.0314150i
$819$	−477.949	−	319.355i	−0.583576	−	0.389933i
$820$		0			0
$821$	745.074	−	148.204i	0.907520	−	0.180517i	0.280805	−	0.959765i	$-0.409399\pi$
$821$	745.074	−	148.204i	0.907520	−	0.180517i	0.626716	+	0.779248i	$0.284399\pi$
$822$	−5.19046	+	3.46816i	−0.00631443	+	0.00421917i
$823$	−511.327	−	101.709i	−0.621296	−	0.123584i	−0.125602	−	0.992081i	$-0.540086\pi$
$823$	−511.327	−	101.709i	−0.621296	−	0.123584i	−0.495694	+	0.868497i	$0.665086\pi$
$824$	−227.331	+	94.1637i	−0.275887	+	0.114276i
$825$		0			0
$826$	9.62814	−	48.4040i	0.0116563	−	0.0586004i
$827$	−11.9567	−	17.8944i	−0.0144579	−	0.0216378i	0.824170	−	0.566342i	$-0.191642\pi$
$827$	−11.9567	−	17.8944i	−0.0144579	−	0.0216378i	−0.838628	+	0.544704i	$0.816642\pi$
$828$	28.0669	+	141.102i	0.0338972	+	0.170413i
$829$	459.219	−	459.219i	0.553943	−	0.553943i	−0.373633	−	0.927577i	$-0.621888\pi$
$829$	459.219	−	459.219i	0.553943	−	0.553943i	0.927577	+	0.373633i	$0.121888\pi$
$830$		0			0
$831$	1837.43	+	761.086i	2.21110	+	0.915868i
$832$			756.936i			0.909778i
$833$	305.102	−	690.346i	0.366269	−	0.828746i
$834$	−290.786			−0.348664
$835$		0			0
$836$	−264.339	−	176.626i	−0.316195	−	0.211275i
$837$	−2001.34	−	2001.34i	−2.39109	−	2.39109i
$838$	38.1674	−	7.59196i	0.0455458	−	0.00905962i
$839$	659.294	−	440.526i	0.785810	−	0.525061i	−0.0967235	−	0.995311i	$-0.530836\pi$
$839$	659.294	−	440.526i	0.785810	−	0.525061i	0.882533	+	0.470250i	$0.155836\pi$
$840$		0			0
$841$	−22.3682	+	9.26521i	−0.0265971	+	0.0110169i
$842$	25.9155	+	62.5655i	0.0307785	+	0.0743058i
$843$	−369.831	+	1859.27i	−0.438708	+	2.20553i
$844$	663.041	+	992.311i	0.785594	+	1.17572i
$845$		0			0
$846$	−148.458	+	148.458i	−0.175482	+	0.175482i
$847$	−92.2071	+	137.998i	−0.108863	+	0.162925i
$848$	−372.858	−	154.443i	−0.439691	−	0.182126i
$849$		−	1337.85i		−	1.57579i
$850$		0			0
$851$	−89.8757			−0.105612
$852$	254.115	−	613.489i	0.298257	−	0.720057i
$853$	−1340.48	−	895.677i	−1.57148	−	1.05003i	−0.967447	−	0.253075i	$-0.918558\pi$
$853$	−1340.48	−	895.677i	−1.57148	−	1.05003i	−0.604037	−	0.796956i	$-0.706442\pi$
$854$	−27.9977	−	27.9977i	−0.0327842	−	0.0327842i
$855$		0			0
$856$	26.0658	−	17.4166i	0.0304507	−	0.0203465i
$857$	−717.863	−	142.792i	−0.837647	−	0.166618i	−0.242415	−	0.970173i	$-0.577940\pi$
$857$	−717.863	−	142.792i	−0.837647	−	0.166618i	−0.595232	+	0.803554i	$0.702940\pi$
$858$	−135.564	+	56.1525i	−0.158000	+	0.0654458i
$859$	−313.269	−	756.298i	−0.364690	−	0.880440i	−0.994601	−	0.103773i	$-0.966909\pi$
$859$	−313.269	−	756.298i	−0.364690	−	0.880440i	0.629911	−	0.776667i	$-0.283091\pi$
$860$		0			0
$861$	−481.074	−	719.978i	−0.558739	−	0.836212i
$862$	−24.8459	−	124.909i	−0.0288236	−	0.144906i
$863$	776.208	−	776.208i	0.899430	−	0.899430i	−0.0959560	−	0.995386i	$-0.530591\pi$
$863$	776.208	−	776.208i	0.899430	−	0.899430i	0.995386	+	0.0959560i	$0.0305908\pi$
$864$	−444.100	+	664.643i	−0.514005	+	0.769262i
$865$		0			0
$866$			228.307i			0.263633i
$867$	1243.02	+	917.657i	1.43370	+	1.05843i
$868$	−419.416			−0.483198
$869$	105.622	−	254.995i	0.121545	−	0.293435i
$870$		0			0
$871$	−856.322	−	856.322i	−0.983148	−	0.983148i
$872$	−34.0288	+	6.76875i	−0.0390239	+	0.00776233i
$873$	−155.814	+	104.112i	−0.178481	+	0.119257i
$874$	6.89562	+	1.37162i	0.00788973	+	0.00156936i
$875$		0			0
$876$	−349.241	−	843.142i	−0.398677	−	0.962490i
$877$	43.1465	−	216.912i	0.0491979	−	0.247334i	−0.948359	−	0.317200i	$-0.897257\pi$
$877$	43.1465	−	216.912i	0.0491979	−	0.247334i	0.997556	+	0.0698660i	$0.0222572\pi$
$878$	−63.3154	−	94.7582i	−0.0721132	−	0.107925i
$879$	−1.93551	−	9.73045i	−0.00220194	−	0.0110699i
$880$		0			0
$881$	−659.231	+	986.609i	−0.748276	+	1.11987i	0.240527	+	0.970643i	$0.422680\pi$
$881$	−659.231	+	986.609i	−0.748276	+	1.11987i	−0.988802	+	0.149231i	$0.952320\pi$
$882$	243.893	+	101.024i	0.276523	+	0.114539i
$883$			1451.19i			1.64348i	0.569861	+	0.821741i	$0.306997\pi$
$883$			1451.19i			1.64348i	−0.569861	+	0.821741i	$0.693003\pi$
$884$	−21.3098	+	908.772i	−0.0241061	+	1.02802i
$885$		0			0
$886$	−41.4950	+	100.178i	−0.0468341	+	0.113068i
$887$	−895.845	−	598.585i	−1.00997	−	0.674842i	−0.0636182	−	0.997974i	$-0.520264\pi$
$887$	−895.845	−	598.585i	−1.00997	−	0.674842i	−0.946354	+	0.323133i	$0.895264\pi$
$888$	−433.936	−	433.936i	−0.488667	−	0.488667i
$889$	67.4799	−	13.4226i	0.0759054	−	0.0150985i
$890$		0			0
$891$	817.720	+	162.655i	0.917756	+	0.182553i
$892$	80.4651	−	33.3297i	0.0902075	−	0.0373652i
$893$	−166.416	−	401.764i	−0.186356	−	0.449904i
$894$	−27.8062	+	139.791i	−0.0311031	+	0.156366i
$895$		0			0
$896$	30.6845	+	154.262i	0.0342461	+	0.172167i
$897$	−97.2511	+	97.2511i	−0.108418	+	0.108418i
$898$	−26.5187	+	39.6880i	−0.0295308	+	0.0441960i
$899$	−1359.57	−	563.153i	−1.51232	−	0.626422i
$900$		0			0
$901$	−421.101	−	186.108i	−0.467371	−	0.206557i
$902$	−151.437			−0.167890
$903$	144.437	−	348.701i	0.159952	−	0.386158i
$904$	−285.446	−	190.729i	−0.315759	−	0.210984i
$905$		0			0
$906$	−140.210	+	27.8895i	−0.154757	+	0.0307831i
$907$	−1304.29	+	871.497i	−1.43802	+	0.960857i	−0.440002	+	0.897997i	$0.645022\pi$
$907$	−1304.29	+	871.497i	−1.43802	+	0.960857i	−0.998022	+	0.0628601i	$0.979978\pi$
$908$	521.547	+	103.742i	0.574391	+	0.114254i
$909$	−147.386	+	61.0492i	−0.162141	+	0.0671608i
$910$		0			0
$911$	195.704	−	983.872i	0.214824	−	1.07999i	−0.711334	−	0.702854i	$-0.751909\pi$
$911$	195.704	−	983.872i	0.214824	−	1.07999i	0.926158	−	0.377137i	$-0.123091\pi$
$912$	−545.120	−	815.830i	−0.597719	−	0.894550i
$913$	121.647	+	611.562i	0.133239	+	0.669838i
$914$	−36.9299	+	36.9299i	−0.0404047	+	0.0404047i
$915$		0			0
$916$	583.438	+	241.668i	0.636941	+	0.263830i
$917$			270.000i			0.294438i
$918$	−167.891	+	238.944i	−0.182887	+	0.260287i
$919$	−806.204			−0.877263			−0.438631	−	0.898667i	$-0.644537\pi$
$919$	−806.204			−0.877263			−0.438631	+	0.898667i	$0.644537\pi$
$920$		0			0
$921$	−2192.77	−	1465.16i	−2.38086	−	1.59084i
$922$	−115.616	−	115.616i	−0.125397	−	0.125397i
$923$	426.560	−	84.8481i	0.462145	−	0.0919264i
$924$	246.169	−	164.485i	0.266417	−	0.178014i
$925$		0			0
$926$	60.7127	−	25.1480i	0.0655644	−	0.0271577i
$927$	767.918	+	1853.92i	0.828390	+	1.99991i
$928$	−81.0828	+	407.631i	−0.0873737	+	0.439257i
$929$	−523.957	−	784.157i	−0.564001	−	0.844087i	0.434394	−	0.900723i	$-0.356963\pi$
$929$	−523.957	−	784.157i	−0.564001	−	0.844087i	−0.998395	+	0.0566357i	$0.981963\pi$
$930$		0			0
$931$	−386.639	+	386.639i	−0.415295	+	0.415295i
$932$	334.783	−	501.039i	0.359210	−	0.537595i
$933$	−1570.44	−	650.498i	−1.68322	−	0.697211i
$934$			71.4628i			0.0765127i
$935$		0			0
$936$	−643.387			−0.687379
$937$	−409.745	+	989.212i	−0.437295	+	1.05572i	0.539585	+	0.841931i	$0.318581\pi$
$937$	−409.745	+	989.212i	−0.437295	+	1.05572i	−0.976879	+	0.213791i	$0.931419\pi$
$938$	−47.9358	−	32.0297i	−0.0511043	−	0.0341468i
$939$	631.135	+	631.135i	0.672135	+	0.672135i
$940$		0			0
$941$	1352.29	−	903.568i	1.43707	−	0.960221i	0.438979	−	0.898497i	$-0.355340\pi$
$941$	1352.29	−	903.568i	1.43707	−	0.960221i	0.998093	−	0.0617240i	$-0.0196599\pi$
$942$	271.917	+	54.0876i	0.288659	+	0.0574178i
$943$	−131.137	+	54.3189i	−0.139064	+	0.0576023i
$944$	432.055	+	1043.07i	0.457685	+	1.10495i
$945$		0			0
$946$	−36.6721	−	54.8836i	−0.0387654	−	0.0580165i
$947$	197.127	+	991.024i	0.208159	+	1.04649i	0.933631	+	0.358236i	$0.116622\pi$
$947$	197.127	+	991.024i	0.208159	+	1.04649i	−0.725472	+	0.688252i	$0.758378\pi$
$948$	617.243	−	617.243i	0.651100	−	0.651100i
$949$	332.077	−	496.989i	0.349924	−	0.523698i
$950$		0			0
$951$			482.838i			0.507716i
$952$	15.0661	+	86.2650i	0.0158257	+	0.0906145i
$953$	178.213			0.187002			0.0935009	−	0.995619i	$-0.470194\pi$
$953$	178.213			0.187002			0.0935009	+	0.995619i	$0.470194\pi$
$954$	61.6231	−	148.771i	0.0645944	−	0.155945i
$955$		0			0
$956$	−68.0748	−	68.0748i	−0.0712080	−	0.0712080i
$957$	1018.83	−	202.659i	1.06461	−	0.211765i
$958$	−143.949	+	96.1839i	−0.150260	+	0.100401i
$959$	8.09108	+	1.60942i	0.00843700	+	0.00167822i
$960$		0			0
$961$	−590.078	−	1424.58i	−0.614025	−	1.48239i
$962$	38.7497	−	194.808i	0.0402804	−	0.202503i
$963$	−142.035	−	212.570i	−0.147492	−	0.220737i
$964$	−194.135	−	975.983i	−0.201385	−	1.01243i
$965$		0			0
$966$	−3.63756	+	5.44399i	−0.00376559	+	0.00563560i
$967$	644.262	+	266.862i	0.666248	+	0.275969i	0.690065	−	0.723747i	$-0.257582\pi$
$967$	644.262	+	266.862i	0.666248	+	0.275969i	−0.0238171	+	0.999716i	$0.507582\pi$
$968$			185.764i			0.191905i
$969$	−599.874	−	945.004i	−0.619065	−	0.975237i
$970$		0			0
$971$	555.901	−	1342.06i	0.572503	−	1.38214i	−0.326914	−	0.945054i	$-0.606009\pi$
$971$	555.901	−	1342.06i	0.572503	−	1.38214i	0.899417	−	0.437091i	$-0.143991\pi$
$972$	538.099	+	359.546i	0.553600	+	0.369904i
$973$	271.726	+	271.726i	0.279266	+	0.279266i
$974$	196.852	−	39.1562i	0.202107	−	0.0402015i
$975$		0			0
$976$	888.390	+	176.712i	0.910236	+	0.181057i
$977$	947.460	−	392.451i	0.969765	−	0.401690i	0.159140	−	0.987256i	$-0.449128\pi$
$977$	947.460	−	392.451i	0.969765	−	0.401690i	0.810625	+	0.585566i	$0.199128\pi$
$978$	−120.707	−	291.413i	−0.123422	−	0.297968i
$979$	113.876	−	572.495i	0.116319	−	0.584775i
$980$		0			0
$981$	55.2001	+	277.510i	0.0562692	+	0.282884i
$982$	133.188	−	133.188i	0.135630	−	0.135630i
$983$	269.449	−	403.258i	0.274108	−	0.410232i	−0.668718	−	0.743516i	$-0.733157\pi$
$983$	269.449	−	403.258i	0.274108	−	0.410232i	0.942827	+	0.333284i	$0.108157\pi$
$984$	−895.417	−	370.894i	−0.909977	−	0.376925i
$985$		0			0
$986$	−33.1049	+	148.184i	−0.0335749	+	0.150288i
$987$	404.974			0.410308
$988$	252.014	−	608.417i	0.255075	−	0.615806i
$989$	−51.4426	−	34.3728i	−0.0520147	−	0.0347551i
$990$		0			0
$991$	1266.33	−	251.888i	1.27783	−	0.254175i	0.490896	−	0.871218i	$-0.336669\pi$
$991$	1266.33	−	251.888i	1.27783	−	0.254175i	0.786930	+	0.617043i	$0.211669\pi$
$992$	−587.766	+	392.732i	−0.592506	+	0.395900i
$993$	2279.13	+	453.348i	2.29520	+	0.456544i
$994$	19.1286	−	7.92333i	0.0192441	−	0.00797116i
$995$		0			0
$996$	−384.731	+	1934.18i	−0.386276	+	1.94194i
$997$	531.311	+	795.163i	0.532910	+	0.797556i	0.996056	−	0.0887260i	$-0.0282796\pi$
$997$	531.311	+	795.163i	0.532910	+	0.797556i	−0.463146	+	0.886282i	$0.653280\pi$
$998$	9.77110	+	49.1227i	0.00979068	+	0.0492211i
$999$	−1912.35	+	1912.35i	−1.91426	+	1.91426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.u.f.401.7		128
5.2	odd	4		85.3.p.a.44.7	yes	128
5.3	odd	4		85.3.p.a.44.10	yes	128
5.4	even	2	inner	425.3.u.f.401.10		128
17.12	odd	16	inner	425.3.u.f.301.7		128
85.12	even	16		85.3.p.a.29.10	yes	128
85.29	odd	16	inner	425.3.u.f.301.10		128
85.63	even	16		85.3.p.a.29.7	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.3.p.a.29.7	✓	128	85.63	even	16
85.3.p.a.29.10	yes	128	85.12	even	16
85.3.p.a.44.7	yes	128	5.2	odd	4
85.3.p.a.44.10	yes	128	5.3	odd	4
425.3.u.f.301.7		128	17.12	odd	16	inner
425.3.u.f.301.10		128	85.29	odd	16	inner
425.3.u.f.401.7		128	1.1	even	1	trivial
425.3.u.f.401.10		128	5.4	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.u (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.116200 + 0.280533i) q^{2} +(-4.44521 - 2.97019i) q^{3} +(2.76323 + 2.76323i) q^{4} +(1.34977 - 0.901888i) q^{6} +(-2.10407 - 0.418526i) q^{7} +(-2.21840 + 0.918890i) q^{8} +(7.49367 + 18.0913i) q^{9} +(-3.66996 - 5.49249i) q^{11} +(-4.07581 - 20.4905i) q^{12} +(9.67560 - 9.67560i) q^{13} +(0.361904 - 0.541628i) q^{14} +14.9021i q^{16} +(-0.398523 + 16.9953i) q^{17} -5.94598 q^{18} +(4.71303 - 11.3783i) q^{19} +(8.10993 + 8.10993i) q^{21} +(1.96727 - 0.391315i) q^{22} +(1.56321 - 1.04450i) q^{23} +(12.5905 + 2.50441i) q^{24} +(1.59001 + 3.83863i) q^{26} +(11.0369 - 55.4861i) q^{27} +(-4.65755 - 6.97052i) q^{28} +(-5.73848 - 28.8493i) q^{29} +(27.7949 - 41.5980i) q^{31} +(-13.0541 - 5.40719i) q^{32} +35.3157i q^{33} +(-4.72144 - 2.08666i) q^{34} +(-29.2838 + 70.6973i) q^{36} +(-39.7482 - 26.5589i) q^{37} +(2.64432 + 2.64432i) q^{38} +(-71.7485 + 14.2717i) q^{39} +(-74.0482 - 14.7291i) q^{41} +(-3.21748 + 1.33272i) q^{42} +(-12.5935 - 30.4033i) q^{43} +(5.03606 - 25.3180i) q^{44} +(0.111372 + 0.559903i) q^{46} +(24.9678 - 24.9678i) q^{47} +(44.2621 - 66.2429i) q^{48} +(-41.0181 - 16.9903i) q^{49} +(52.2509 - 74.3641i) q^{51} +53.4719 q^{52} +(-10.3638 + 25.0205i) q^{53} +(14.2832 + 9.54371i) q^{54} +(5.05224 - 1.00495i) q^{56} +(-54.7460 + 36.5801i) q^{57} +(8.75998 + 1.74247i) q^{58} +(69.9951 - 28.9929i) q^{59} +(11.8582 - 59.6151i) q^{61} +(8.43982 + 12.6311i) q^{62} +(-8.19554 - 41.2018i) q^{63} +(-39.1157 + 39.1157i) q^{64} +(-9.90722 - 4.10371i) q^{66} -88.5032i q^{67} +(-48.0632 + 45.8608i) q^{68} -10.0512 q^{69} +(26.4277 + 17.6584i) q^{71} +(-33.2479 - 33.2479i) q^{72} +(42.8431 - 8.52203i) q^{73} +(12.0694 - 8.06452i) q^{74} +(44.4639 - 18.4176i) q^{76} +(5.42312 + 13.0926i) q^{77} +(4.33354 - 21.7862i) q^{78} +(23.2131 + 34.7408i) q^{79} +(-89.2469 + 89.2469i) q^{81} +(12.7364 - 19.0614i) q^{82} +(-87.2086 - 36.1230i) q^{83} +44.8192i q^{84} +9.99249 q^{86} +(-60.1792 + 145.285i) q^{87} +(13.1884 + 8.81222i) q^{88} +(62.4827 + 62.4827i) q^{89} +(-24.4077 + 16.3087i) q^{91} +(7.20571 + 1.43331i) q^{92} +(-247.108 + 102.356i) q^{93} +(4.10301 + 9.90555i) q^{94} +(41.9678 + 62.8093i) q^{96} +(1.86699 + 9.38597i) q^{97} +(9.53265 - 9.53265i) q^{98} +(71.8649 - 107.553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{4} - 16 q^{6} + 16 q^{9} - 96 q^{11} + 16 q^{14} + 16 q^{19} + 224 q^{21} + 160 q^{24} + 288 q^{26} + 176 q^{29} + 48 q^{31} - 48 q^{34} - 144 q^{36} - 336 q^{41} + 48 q^{44} - 224 q^{46}+ \cdots + 1664 q^{99}+O(q^{100}) \) 128 * q + 16 * q^4 - 16 * q^6 + 16 * q^9 - 96 * q^11 + 16 * q^14 + 16 * q^19 + 224 * q^21 + 160 * q^24 + 288 * q^26 + 176 * q^29 + 48 * q^31 - 48 * q^34 - 144 * q^36 - 336 * q^41 + 48 * q^44 - 224 * q^46 + 48 * q^49 - 16 * q^51 - 512 * q^54 - 16 * q^56 - 272 * q^59 - 16 * q^61 - 688 * q^64 - 80 * q^66 - 448 * q^69 + 192 * q^71 - 704 * q^74 + 496 * q^76 - 304 * q^79 + 128 * q^81 - 2496 * q^86 + 256 * q^89 - 1632 * q^91 + 1296 * q^94 - 1728 * q^96 + 1664 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more