LMFDB - Embedded newform 950.2.u.c.499.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			499.1
Root			$-0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	950.499
Dual form			950.2.u.c.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342020 - 0.939693i) q^{2} +(-1.85083 - 0.326352i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(0.326352 + 1.85083i) q^{6} +(-2.65366 + 1.53209i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.500000 + 0.181985i) q^{9} +O(q^{10})$	\(q+(-0.342020 - 0.939693i) q^{2} +(-1.85083 - 0.326352i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(0.326352 + 1.85083i) q^{6} +(-2.65366 + 1.53209i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.500000 + 0.181985i) q^{9} +(2.17365 - 3.76487i) q^{11} +(1.62760 - 0.939693i) q^{12} +(-5.67128 + 1.00000i) q^{13} +(2.34730 + 1.96962i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-0.705990 - 1.93969i) q^{17} -0.532089i q^{18} +(-4.34002 - 0.405223i) q^{19} +(5.41147 - 1.96962i) q^{21} +(-4.28125 - 0.754900i) q^{22} +(4.98724 + 5.94356i) q^{23} +(-1.43969 - 1.20805i) q^{24} +(2.87939 + 4.98724i) q^{26} +(4.01676 + 2.31908i) q^{27} +(1.04801 - 2.87939i) q^{28} +(3.87939 + 1.41198i) q^{29} +(4.22668 + 7.32083i) q^{31} +(-0.984808 + 0.173648i) q^{32} +(-5.25173 + 6.25877i) q^{33} +(-1.58125 + 1.32683i) q^{34} +(-0.500000 + 0.181985i) q^{36} -4.00000i q^{37} +(1.10359 + 4.21688i) q^{38} +10.8229 q^{39} +(-0.0248149 + 0.140732i) q^{41} +(-3.70167 - 4.41147i) q^{42} +(6.99811 - 8.34002i) q^{43} +(0.754900 + 4.28125i) q^{44} +(3.87939 - 6.71929i) q^{46} +(2.01352 - 5.53209i) q^{47} +(-0.642788 + 1.76604i) q^{48} +(1.19459 - 2.06910i) q^{49} +(0.673648 + 3.82045i) q^{51} +(3.70167 - 4.41147i) q^{52} +(3.25519 + 3.87939i) q^{53} +(0.805407 - 4.56769i) q^{54} -3.06418 q^{56} +(7.90041 + 2.16637i) q^{57} -4.12836i q^{58} +(7.19119 - 2.61738i) q^{59} +(-6.94356 + 5.82634i) q^{61} +(5.43372 - 6.47565i) q^{62} +(-1.60565 + 0.283119i) q^{63} +(0.500000 + 0.866025i) q^{64} +(7.67752 + 2.79439i) q^{66} +(2.15830 - 5.92989i) q^{67} +(1.78763 + 1.03209i) q^{68} +(-7.29086 - 12.6281i) q^{69} +(4.34730 + 3.64781i) q^{71} +(0.342020 + 0.407604i) q^{72} +(-2.07407 - 0.365715i) q^{73} +(-3.75877 + 1.36808i) q^{74} +(3.58512 - 2.47929i) q^{76} +13.3209i q^{77} +(-3.70167 - 10.1702i) q^{78} +(0.0641778 - 0.363970i) q^{79} +(-7.90033 - 6.62916i) q^{81} +(0.140732 - 0.0248149i) q^{82} +(0.652739 - 0.376859i) q^{83} +(-2.87939 + 4.98724i) q^{84} +(-10.2306 - 3.72362i) q^{86} +(-6.71929 - 3.87939i) q^{87} +(3.76487 - 2.17365i) q^{88} +(-0.308811 - 1.75135i) q^{89} +(13.5175 - 11.3426i) q^{91} +(-7.64090 - 1.34730i) q^{92} +(-5.43372 - 14.9290i) q^{93} -5.88713 q^{94} +1.87939 q^{96} +(3.65279 + 10.0360i) q^{97} +(-2.35289 - 0.414878i) q^{98} +(1.77197 - 1.48686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^6 + 6 * q^9	$ 12 q + 6 q^{6} + 6 q^{9} + 24 q^{11} + 24 q^{14} - 12 q^{19} + 24 q^{21} - 6 q^{24} + 12 q^{26} + 24 q^{29} + 24 q^{31} - 24 q^{34} - 6 q^{36} + 48 q^{39} + 54 q^{41} + 12 q^{44} + 24 q^{46} + 6 q^{49} + 6 q^{51} + 18 q^{54} - 6 q^{59} - 24 q^{61} + 6 q^{64} + 42 q^{66} - 24 q^{69} + 48 q^{71} - 36 q^{79} - 66 q^{81} - 12 q^{84} - 48 q^{86} - 96 q^{89} + 72 q^{91} + 48 q^{94} + 66 q^{99}+O(q^{100}) $ 12 * q + 6 * q^6 + 6 * q^9 + 24 * q^11 + 24 * q^14 - 12 * q^19 + 24 * q^21 - 6 * q^24 + 12 * q^26 + 24 * q^29 + 24 * q^31 - 24 * q^34 - 6 * q^36 + 48 * q^39 + 54 * q^41 + 12 * q^44 + 24 * q^46 + 6 * q^49 + 6 * q^51 + 18 * q^54 - 6 * q^59 - 24 * q^61 + 6 * q^64 + 42 * q^66 - 24 * q^69 + 48 * q^71 - 36 * q^79 - 66 * q^81 - 12 * q^84 - 48 * q^86 - 96 * q^89 + 72 * q^91 + 48 * q^94 + 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.342020	−	0.939693i	−0.241845	−	0.664463i
$2$	−0.342020	−	0.939693i	−0.241845	−	0.664463i
$3$	−1.85083	−	0.326352i	−1.06858	−	0.188419i	−0.388419	−	0.921483i	$-0.626979\pi$
$3$	−1.85083	−	0.326352i	−1.06858	−	0.188419i	−0.680160	+	0.733064i	$0.738090\pi$
$4$	−0.766044	+	0.642788i	−0.383022	+	0.321394i
$5$		0			0
$5$		0			0
$6$	0.326352	+	1.85083i	0.133233	+	0.755599i
$7$	−2.65366	+	1.53209i	−1.00299	+	0.579075i	−0.909131	−	0.416511i	$-0.863253\pi$
$7$	−2.65366	+	1.53209i	−1.00299	+	0.579075i	−0.0938567	+	0.995586i	$0.529920\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	0.500000	+	0.181985i	0.166667	+	0.0606617i
$10$		0			0
$11$	2.17365	−	3.76487i	0.655380	−	1.13515i	−0.326419	−	0.945225i	$-0.605842\pi$
$11$	2.17365	−	3.76487i	0.655380	−	1.13515i	0.981798	−	0.189926i	$-0.0608247\pi$
$12$	1.62760	−	0.939693i	0.469846	−	0.271266i
$13$	−5.67128	+	1.00000i	−1.57293	+	0.277350i	−0.890978	−	0.454046i	$-0.849980\pi$
$13$	−5.67128	+	1.00000i	−1.57293	+	0.277350i	−0.681953	+	0.731396i	$0.738869\pi$
$14$	2.34730	+	1.96962i	0.627341	+	0.526402i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.705990	−	1.93969i	−0.171228	−	0.470445i	0.824162	−	0.566354i	$-0.191646\pi$
$17$	−0.705990	−	1.93969i	−0.171228	−	0.470445i	−0.995390	+	0.0959092i	$0.969424\pi$
$18$		−	0.532089i		−	0.125415i
$19$	−4.34002	−	0.405223i	−0.995669	−	0.0929645i
$19$	−4.34002	−	0.405223i	−0.995669	−	0.0929645i
$20$		0			0
$21$	5.41147	−	1.96962i	1.18088	−	0.429805i
$22$	−4.28125	−	0.754900i	−0.912766	−	0.160945i
$23$	4.98724	+	5.94356i	1.03991	+	1.23932i	0.970341	+	0.241742i	$0.0777186\pi$
$23$	4.98724	+	5.94356i	1.03991	+	1.23932i	0.0695711	+	0.997577i	$0.477837\pi$
$24$	−1.43969	−	1.20805i	−0.293876	−	0.246591i
$25$		0			0
$26$	2.87939	+	4.98724i	0.564694	+	0.978079i
$27$	4.01676	+	2.31908i	0.773026	+	0.446307i
$28$	1.04801	−	2.87939i	0.198055	−	0.544153i
$29$	3.87939	+	1.41198i	0.720384	+	0.262198i	0.676089	−	0.736820i	$-0.263674\pi$
$29$	3.87939	+	1.41198i	0.720384	+	0.262198i	0.0442951	+	0.999018i	$0.485896\pi$
$30$		0			0
$31$	4.22668	+	7.32083i	0.759134	+	1.31486i	0.943292	+	0.331963i	$0.107711\pi$
$31$	4.22668	+	7.32083i	0.759134	+	1.31486i	−0.184158	+	0.982897i	$0.558956\pi$
$32$	−0.984808	+	0.173648i	−0.174091	+	0.0306970i
$33$	−5.25173	+	6.25877i	−0.914209	+	1.08951i
$34$	−1.58125	+	1.32683i	−0.271182	+	0.227549i
$35$		0			0
$36$	−0.500000	+	0.181985i	−0.0833333	+	0.0303309i
$37$		−	4.00000i		−	0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$	1.10359	+	4.21688i	0.179026	+	0.684068i
$39$	10.8229			1.73306
$40$		0			0
$41$	−0.0248149	+	0.140732i	−0.00387544	+	0.0219787i	−0.986684	−	0.162648i	$-0.947997\pi$
$41$	−0.0248149	+	0.140732i	−0.00387544	+	0.0219787i	0.982809	+	0.184627i	$0.0591076\pi$
$42$	−3.70167	−	4.41147i	−0.571180	−	0.680705i
$43$	6.99811	−	8.34002i	1.06720	−	1.27184i	0.106484	−	0.994314i	$-0.466041\pi$
$43$	6.99811	−	8.34002i	1.06720	−	1.27184i	0.960718	−	0.277527i	$-0.0895148\pi$
$44$	0.754900	+	4.28125i	0.113805	+	0.645423i
$45$		0			0
$46$	3.87939	−	6.71929i	0.571984	−	0.990706i
$47$	2.01352	−	5.53209i	0.293701	−	0.806938i	−0.701816	−	0.712358i	$-0.747627\pi$
$47$	2.01352	−	5.53209i	0.293701	−	0.806938i	0.995517	−	0.0945797i	$-0.0301507\pi$
$48$	−0.642788	+	1.76604i	−0.0927784	+	0.254907i
$49$	1.19459	−	2.06910i	0.170656	−	0.295585i
$50$		0			0
$51$	0.673648	+	3.82045i	0.0943296	+	0.534970i
$52$	3.70167	−	4.41147i	0.513329	−	0.611761i
$53$	3.25519	+	3.87939i	0.447135	+	0.532875i	0.941784	−	0.336218i	$-0.109148\pi$
$53$	3.25519	+	3.87939i	0.447135	+	0.532875i	−0.494649	+	0.869093i	$0.664703\pi$
$54$	0.805407	−	4.56769i	0.109602	−	0.621584i
$55$		0			0
$56$	−3.06418			−0.409468
$57$	7.90041	+	2.16637i	1.04644	+	0.286943i
$58$		−	4.12836i		−	0.542080i
$59$	7.19119	−	2.61738i	0.936213	−	0.340754i	0.171544	−	0.985177i	$-0.445125\pi$
$59$	7.19119	−	2.61738i	0.936213	−	0.340754i	0.764669	+	0.644423i	$0.222902\pi$
$60$		0			0
$61$	−6.94356	+	5.82634i	−0.889032	+	0.745987i	−0.968016	−	0.250889i	$-0.919277\pi$
$61$	−6.94356	+	5.82634i	−0.889032	+	0.745987i	0.0789836	+	0.996876i	$0.474833\pi$
$62$	5.43372	−	6.47565i	0.690083	−	0.822409i
$63$	−1.60565	+	0.283119i	−0.202292	+	0.0356696i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	7.67752	+	2.79439i	0.945037	+	0.343965i
$67$	2.15830	−	5.92989i	0.263679	−	0.724452i	−0.735233	−	0.677814i	$-0.762927\pi$
$67$	2.15830	−	5.92989i	0.263679	−	0.724452i	0.998912	−	0.0466373i	$-0.0148505\pi$
$68$	1.78763	+	1.03209i	0.216782	+	0.125159i
$69$	−7.29086	−	12.6281i	−0.877716	−	1.52025i
$70$		0			0
$71$	4.34730	+	3.64781i	0.515929	+	0.432916i	0.863210	−	0.504845i	$-0.168450\pi$
$71$	4.34730	+	3.64781i	0.515929	+	0.432916i	−0.347281	+	0.937761i	$0.612895\pi$
$72$	0.342020	+	0.407604i	0.0403075	+	0.0480366i
$73$	−2.07407	−	0.365715i	−0.242752	−	0.0428037i	0.0509484	−	0.998701i	$-0.483776\pi$
$73$	−2.07407	−	0.365715i	−0.242752	−	0.0428037i	−0.293700	+	0.955898i	$0.594887\pi$
$74$	−3.75877	+	1.36808i	−0.436948	+	0.159036i
$75$		0			0
$76$	3.58512	−	2.47929i	0.411242	−	0.284395i
$77$			13.3209i			1.51806i
$78$	−3.70167	−	10.1702i	−0.419131	−	1.15155i
$79$	0.0641778	−	0.363970i	0.00722056	−	0.0409499i	−0.980985	−	0.194086i	$-0.937826\pi$
$79$	0.0641778	−	0.363970i	0.00722056	−	0.0409499i	0.988205	+	0.153136i	$0.0489372\pi$
$80$		0			0
$81$	−7.90033	−	6.62916i	−0.877814	−	0.736574i
$82$	0.140732	−	0.0248149i	0.0155413	−	0.00274035i
$83$	0.652739	−	0.376859i	0.0716474	−	0.0413657i	−0.463748	−	0.885967i	$-0.653496\pi$
$83$	0.652739	−	0.376859i	0.0716474	−	0.0413657i	0.535396	+	0.844601i	$0.320162\pi$
$84$	−2.87939	+	4.98724i	−0.314167	+	0.544153i
$85$		0			0
$86$	−10.2306	−	3.72362i	−1.10319	−	0.401528i
$87$	−6.71929	−	3.87939i	−0.720384	−	0.415914i
$88$	3.76487	−	2.17365i	0.401336	−	0.231712i
$89$	−0.308811	−	1.75135i	−0.0327339	−	0.185643i	0.964057	−	0.265697i	$-0.0856020\pi$
$89$	−0.308811	−	1.75135i	−0.0327339	−	0.185643i	−0.996791	+	0.0800536i	$0.974491\pi$
$90$		0			0
$91$	13.5175	−	11.3426i	1.41702	−	1.18902i
$92$	−7.64090	−	1.34730i	−0.796619	−	0.140465i
$93$	−5.43372	−	14.9290i	−0.563450	−	1.54807i
$94$	−5.88713			−0.607211
$95$		0			0
$96$	1.87939			0.191814
$97$	3.65279	+	10.0360i	0.370885	+	1.01900i	0.975020	+	0.222116i	$0.0712963\pi$
$97$	3.65279	+	10.0360i	0.370885	+	1.01900i	−0.604136	+	0.796882i	$0.706481\pi$
$98$	−2.35289	−	0.414878i	−0.237678	−	0.0419090i
$99$	1.77197	−	1.48686i	0.178090	−	0.149435i
$100$		0			0
$101$	−0.898986	−	5.09840i	−0.0894524	−	0.507310i	−0.996307	−	0.0858656i	$-0.972634\pi$
$101$	−0.898986	−	5.09840i	−0.0894524	−	0.507310i	0.906854	−	0.421444i	$-0.138477\pi$
$102$	3.35965	−	1.93969i	0.332655	−	0.192058i
$103$	15.4182	+	8.90167i	1.51920	+	0.877108i	0.999744	+	0.0226079i	$0.00719693\pi$
$103$	15.4182	+	8.90167i	1.51920	+	0.877108i	0.519451	+	0.854500i	$0.326136\pi$
$104$	−5.41147	−	1.96962i	−0.530639	−	0.193137i
$105$		0			0
$106$	2.53209	−	4.38571i	0.245938	−	0.425977i
$107$	−4.12122	+	2.37939i	−0.398413	+	0.230024i	−0.685799	−	0.727791i	$-0.740547\pi$
$107$	−4.12122	+	2.37939i	−0.398413	+	0.230024i	0.287386	+	0.957815i	$0.407214\pi$
$108$	−4.56769	+	0.805407i	−0.439526	+	0.0775004i
$109$	14.1480	+	11.8715i	1.35513	+	1.13709i	0.977454	+	0.211149i	$0.0677206\pi$
$109$	14.1480	+	11.8715i	1.35513	+	1.13709i	0.377675	+	0.925938i	$0.376724\pi$
$110$		0			0
$111$	−1.30541	+	7.40333i	−0.123904	+	0.702693i
$112$	1.04801	+	2.87939i	0.0990277	+	0.272076i
$113$		−	2.58853i		−	0.243508i	−0.992560	−	0.121754i	$-0.961148\pi$
$113$		−	2.58853i		−	0.243508i	0.992560	−	0.121754i	$-0.0388519\pi$
$114$	−0.666374	−	8.16490i	−0.0624117	−	0.764713i
$115$		0			0
$116$	−3.87939	+	1.41198i	−0.360192	+	0.131099i
$117$	−3.01763	−	0.532089i	−0.278980	−	0.0491916i
$118$	−4.91906	−	5.86231i	−0.452836	−	0.539669i
$119$	4.84524	+	4.06564i	0.444162	+	0.372696i
$120$		0			0
$121$	−3.94949	−	6.84072i	−0.359045	−	0.621884i
$122$	7.84981	+	4.53209i	0.710688	+	0.410316i
$123$	0.0918566	−	0.252374i	0.00828243	−	0.0227558i
$124$	−7.94356	−	2.89122i	−0.713353	−	0.259639i
$125$		0			0
$126$	0.815207	+	1.41198i	0.0726245	+	0.125789i
$127$	10.6585	−	1.87939i	0.945791	−	0.166768i	0.320578	−	0.947222i	$-0.396123\pi$
$127$	10.6585	−	1.87939i	0.945791	−	0.166768i	0.625213	+	0.780454i	$0.285012\pi$
$128$	0.642788	−	0.766044i	0.0568149	−	0.0677094i
$129$	−15.6741	+	13.1521i	−1.38003	+	1.15798i
$130$		0			0
$131$	−6.95084	+	2.52990i	−0.607297	+	0.221038i	−0.627320	−	0.778761i	$-0.715848\pi$
$131$	−6.95084	+	2.52990i	−0.607297	+	0.221038i	0.0200229	+	0.999800i	$0.493626\pi$
$132$		−	8.17024i		−	0.711129i
$133$	12.1378	−	5.57398i	1.05248	−	0.483325i
$134$	−6.31046			−0.545141
$135$		0			0
$136$	0.358441	−	2.03282i	0.0307360	−	0.174313i
$137$	−5.21983	−	6.22075i	−0.445960	−	0.531475i	0.495496	−	0.868610i	$-0.334986\pi$
$137$	−5.21983	−	6.22075i	−0.445960	−	0.531475i	−0.941456	+	0.337136i	$0.890542\pi$
$138$	−9.37295	+	11.1702i	−0.797878	+	0.950874i
$139$	2.57145	+	14.5834i	0.218108	+	1.23695i	0.875432	+	0.483342i	$0.160577\pi$
$139$	2.57145	+	14.5834i	0.218108	+	1.23695i	−0.657324	+	0.753608i	$0.728312\pi$
$140$		0			0
$141$	−5.53209	+	9.58186i	−0.465886	+	0.806938i
$142$	1.94096	−	5.33275i	0.162882	−	0.447514i
$143$	−8.56250	+	23.5253i	−0.716032	+	1.96728i
$144$	0.266044	−	0.460802i	0.0221704	−	0.0384002i
$145$		0			0
$146$	0.365715	+	2.07407i	0.0302668	+	0.171651i
$147$	−2.88624	+	3.43969i	−0.238053	+	0.283701i
$148$	2.57115	+	3.06418i	0.211347	+	0.251874i
$149$	0.822948	−	4.66717i	0.0674185	−	0.382350i	−0.932364	−	0.361520i	$-0.882258\pi$
$149$	0.822948	−	4.66717i	0.0674185	−	0.382350i	0.999783	−	0.0208299i	$-0.00663085\pi$
$150$		0			0
$151$	0.453363			0.0368942			0.0184471	−	0.999830i	$-0.494128\pi$
$151$	0.453363			0.0368942			0.0184471	+	0.999830i	$0.494128\pi$
$152$	−3.55596	−	2.52094i	−0.288426	−	0.204476i
$153$		−	1.09833i		−	0.0887944i
$154$	12.5175	−	4.55601i	1.00869	−	0.367134i
$155$		0			0
$156$	−8.29086	+	6.95686i	−0.663800	+	0.556994i
$157$	−8.39749	+	10.0077i	−0.670193	+	0.798705i	−0.988810	−	0.149179i	$-0.952337\pi$
$157$	−8.39749	+	10.0077i	−0.670193	+	0.798705i	0.318617	+	0.947883i	$0.396781\pi$
$158$	−0.363970	+	0.0641778i	−0.0289559	+	0.00510571i
$159$	−4.75877	−	8.24243i	−0.377395	−	0.653667i
$160$		0			0
$161$	−22.3405	−	8.13127i	−1.76068	−	0.640834i
$162$	−3.52730	+	9.69119i	−0.277131	+	0.761412i
$163$	5.09170	+	2.93969i	0.398812	+	0.230254i	0.685971	−	0.727628i	$-0.259377\pi$
$163$	5.09170	+	2.93969i	0.398812	+	0.230254i	−0.287159	+	0.957883i	$0.592711\pi$
$164$	−0.0714517	−	0.123758i	−0.00557944	−	0.00966388i
$165$		0			0
$166$	−0.577382	−	0.484481i	−0.0448135	−	0.0376030i
$167$	14.2876	+	17.0273i	1.10561	+	1.31762i	0.943697	+	0.330810i	$0.107322\pi$
$167$	14.2876	+	17.0273i	1.10561	+	1.31762i	0.161913	+	0.986805i	$0.448234\pi$
$168$	5.67128	+	1.00000i	0.437549	+	0.0771517i
$169$	18.9474	−	6.89630i	1.45749	−	0.530485i
$170$		0			0
$171$	−2.09627	−	0.992431i	−0.160306	−	0.0758931i
$172$			10.8871i			0.830136i
$173$	−7.24827	−	19.9145i	−0.551076	−	1.51407i	−0.832244	−	0.554410i	$-0.812944\pi$
$173$	−7.24827	−	19.9145i	−0.551076	−	1.51407i	0.281168	−	0.959659i	$-0.409278\pi$
$174$	−1.34730	+	7.64090i	−0.102138	+	0.579255i
$175$		0			0
$176$	−3.33022	−	2.79439i	−0.251025	−	0.210635i
$177$	−14.1639	+	2.49747i	−1.06462	+	0.187722i
$178$	−1.54011	+	0.889185i	−0.115436	+	0.0666473i
$179$	1.88666	−	3.26779i	0.141016	−	0.244246i	−0.786864	−	0.617127i	$-0.788297\pi$
$179$	1.88666	−	3.26779i	0.141016	−	0.244246i	0.927879	+	0.372881i	$0.121630\pi$
$180$		0			0
$181$	−8.79561	−	3.20134i	−0.653772	−	0.237954i	−0.00622701	−	0.999981i	$-0.501982\pi$
$181$	−8.79561	−	3.20134i	−0.653772	−	0.237954i	−0.647545	+	0.762027i	$0.724204\pi$
$182$	−15.2818	−	8.82295i	−1.13276	−	0.654000i
$183$	14.7528	−	8.51754i	1.09056	−	0.629635i
$184$	1.34730	+	7.64090i	0.0993240	+	0.563294i
$185$		0			0
$186$	−12.1702	+	10.2120i	−0.892366	+	0.748784i
$187$	−8.83726	−	1.55825i	−0.646245	−	0.113950i
$188$	2.01352	+	5.53209i	0.146851	+	0.403469i
$189$	−14.2121			−1.03378
$190$		0			0
$191$	18.7101			1.35381			0.676907	−	0.736069i	$-0.263320\pi$
$191$	18.7101			1.35381			0.676907	+	0.736069i	$0.263320\pi$
$192$	−0.642788	−	1.76604i	−0.0463892	−	0.127453i
$193$	−11.7545	−	2.07263i	−0.846107	−	0.149191i	−0.266244	−	0.963906i	$-0.585783\pi$
$193$	−11.7545	−	2.07263i	−0.846107	−	0.149191i	−0.579863	+	0.814714i	$0.696894\pi$
$194$	8.18139	−	6.86500i	0.587389	−	0.492878i
$195$		0			0
$196$	0.414878	+	2.35289i	0.0296341	+	0.168063i
$197$	2.58110	−	1.49020i	0.183896	−	0.106172i	−0.405226	−	0.914217i	$-0.632807\pi$
$197$	2.58110	−	1.49020i	0.183896	−	0.106172i	0.589122	+	0.808044i	$0.299474\pi$
$198$	−2.00324	−	1.15657i	−0.142364	−	0.0821941i
$199$	−22.7246	−	8.27109i	−1.61091	−	0.586322i	−0.629287	−	0.777173i	$-0.716653\pi$
$199$	−22.7246	−	8.27109i	−1.61091	−	0.586322i	−0.981619	+	0.190851i	$0.938875\pi$
$200$		0			0
$201$	−5.92989	+	10.2709i	−0.418262	+	0.724452i
$202$	−4.48346	+	2.58853i	−0.315455	+	0.182128i
$203$	−12.4578	+	2.19665i	−0.874368	+	0.154175i
$204$	−2.97178	−	2.49362i	−0.208066	−	0.174588i
$205$		0			0
$206$	3.09152	−	17.5329i	0.215396	−	1.22157i
$207$	1.41198	+	3.87939i	0.0981394	+	0.269636i
$208$			5.75877i			0.399299i
$209$	−10.9593	+	15.4588i	−0.758070	+	1.06931i
$210$		0			0
$211$	−12.2947	+	4.47492i	−0.846404	+	0.308066i	−0.728573	−	0.684968i	$-0.759816\pi$
$211$	−12.2947	+	4.47492i	−0.846404	+	0.308066i	−0.117831	+	0.993034i	$0.537594\pi$
$212$	−4.98724	−	0.879385i	−0.342525	−	0.0603964i
$213$	−6.85565	−	8.17024i	−0.469741	−	0.559816i
$214$	3.64543	+	3.05888i	0.249196	+	0.209101i
$215$		0			0
$216$	2.31908	+	4.01676i	0.157793	+	0.273306i
$217$	−22.4323	−	12.9513i	−1.52280	−	0.879192i
$218$	6.31672	−	17.3550i	0.427822	−	1.17543i
$219$	3.71941	+	1.35375i	0.251334	+	0.0914782i
$220$		0			0
$221$	5.94356	+	10.2946i	0.399807	+	0.692487i
$222$	7.40333	−	1.30541i	0.496879	−	0.0876132i
$223$	−1.76070	+	2.09833i	−0.117906	+	0.140514i	−0.821769	−	0.569821i	$-0.807012\pi$
$223$	−1.76070	+	2.09833i	−0.117906	+	0.140514i	0.703863	+	0.710336i	$0.251457\pi$
$224$	2.34730	−	1.96962i	0.156835	−	0.131600i
$225$		0			0
$226$	−2.43242	+	0.885328i	−0.161802	+	0.0588911i
$227$			24.2422i			1.60901i	0.593947	+	0.804504i	$0.297569\pi$
$227$			24.2422i			1.60901i	−0.593947	+	0.804504i	$0.702431\pi$
$228$	−7.44459	+	3.41875i	−0.493030	+	0.226412i
$229$	15.6750			1.03583			0.517916	−	0.855431i	$-0.326708\pi$
$229$	15.6750			1.03583			0.517916	+	0.855431i	$0.326708\pi$
$230$		0			0
$231$	4.34730	−	24.6547i	0.286031	−	1.62216i
$232$	2.65366	+	3.16250i	0.174221	+	0.207629i
$233$	−16.9902	+	20.2481i	−1.11306	+	1.32650i	−0.173223	+	0.984883i	$0.555418\pi$
$233$	−16.9902	+	20.2481i	−1.11306	+	1.32650i	−0.939840	+	0.341614i	$0.889026\pi$
$234$	0.532089	+	3.01763i	0.0347837	+	0.197268i
$235$		0			0
$236$	−3.82635	+	6.62744i	−0.249074	+	0.431409i
$237$	−0.237565	+	0.652704i	−0.0154315	+	0.0423977i
$238$	2.16328	−	5.94356i	0.140225	−	0.385264i
$239$	−6.87939	+	11.9154i	−0.444990	+	0.770746i	−0.998052	−	0.0623946i	$-0.980126\pi$
$239$	−6.87939	+	11.9154i	−0.444990	+	0.770746i	0.553061	+	0.833141i	$0.313460\pi$
$240$		0			0
$241$	2.24257	+	12.7183i	0.144457	+	0.819256i	0.967802	+	0.251714i	$0.0809943\pi$
$241$	2.24257	+	12.7183i	0.144457	+	0.819256i	−0.823345	+	0.567542i	$0.807895\pi$
$242$	−5.07737	+	6.05097i	−0.326386	+	0.388971i
$243$	3.51471	+	4.18866i	0.225468	+	0.268703i
$244$	1.57398	−	8.92647i	0.100764	−	0.571459i
$245$		0			0
$246$	−0.268571			−0.0171234
$247$	25.0187	−	2.04189i	1.59190	−	0.129922i
$248$			8.45336i			0.536789i
$249$	−1.33110	+	0.484481i	−0.0843550	+	0.0307027i
$250$		0			0
$251$	13.9231	−	11.6829i	0.878817	−	0.737415i	−0.0871182	−	0.996198i	$-0.527766\pi$
$251$	13.9231	−	11.6829i	0.878817	−	0.737415i	0.965936	+	0.258783i	$0.0833213\pi$
$252$	1.04801	−	1.24897i	0.0660185	−	0.0786777i
$253$	33.2172	−	5.85710i	2.08835	−	0.368233i
$254$	−5.41147	−	9.37295i	−0.339546	−	0.588111i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−2.38479	+	6.55216i	−0.148759	+	0.408712i	−0.991582	−	0.129478i	$-0.958670\pi$
$257$	−2.38479	+	6.55216i	−0.148759	+	0.408712i	0.842823	+	0.538191i	$0.180892\pi$
$258$	17.7198	+	10.2306i	1.10319	+	0.636926i
$259$	6.12836	+	10.6146i	0.380797	+	0.659561i
$260$		0			0
$261$	1.68273	+	1.41198i	0.104159	+	0.0873994i
$262$	4.75465	+	5.66637i	0.293743	+	0.350070i
$263$	−10.1834	−	1.79561i	−0.627935	−	0.110722i	−0.149381	−	0.988780i	$-0.547728\pi$
$263$	−10.1834	−	1.79561i	−0.627935	−	0.110722i	−0.478554	+	0.878058i	$0.658839\pi$
$264$	−7.67752	+	2.79439i	−0.472519	+	0.171983i
$265$		0			0
$266$	−9.38919	−	9.49935i	−0.575688	−	0.582443i
$267$			3.34224i			0.204542i
$268$	2.15830	+	5.92989i	0.131839	+	0.362226i
$269$	1.81521	−	10.2946i	0.110675	−	0.627670i	−0.878126	−	0.478430i	$-0.841206\pi$
$269$	1.81521	−	10.2946i	0.110675	−	0.627670i	0.988801	−	0.149240i	$-0.0476828\pi$
$270$		0			0
$271$	−14.7023	−	12.3367i	−0.893103	−	0.749403i	0.0757270	−	0.997129i	$-0.475872\pi$
$271$	−14.7023	−	12.3367i	−0.893103	−	0.749403i	−0.968830	+	0.247726i	$0.920317\pi$
$272$	−2.03282	+	0.358441i	−0.123258	+	0.0217337i
$273$	−28.7204	+	16.5817i	−1.73824	+	1.00357i
$274$	−4.06031	+	7.03266i	−0.245292	+	0.424858i
$275$		0			0
$276$	13.7023	+	4.98724i	0.824784	+	0.300197i
$277$	25.6741	+	14.8229i	1.54261	+	0.890625i	0.998673	+	0.0514966i	$0.0163991\pi$
$277$	25.6741	+	14.8229i	1.54261	+	0.890625i	0.543934	+	0.839128i	$0.316934\pi$
$278$	12.8245	−	7.40420i	0.769159	−	0.444074i
$279$	0.781059	+	4.42961i	0.0467608	+	0.265194i
$280$		0			0
$281$	−13.4552	+	11.2902i	−0.802668	+	0.673519i	−0.948846	−	0.315740i	$-0.897747\pi$
$281$	−13.4552	+	11.2902i	−0.802668	+	0.673519i	0.146177	+	0.989258i	$0.453303\pi$
$282$	10.8961	+	1.92127i	0.648853	+	0.114410i
$283$	−1.90814	−	5.24257i	−0.113427	−	0.311639i	0.869970	−	0.493105i	$-0.164138\pi$
$283$	−1.90814	−	5.24257i	−0.113427	−	0.311639i	−0.983397	+	0.181466i	$0.941916\pi$
$284$	−5.67499			−0.336749
$285$		0			0
$286$	25.0351			1.48036
$287$	−0.149764	−	0.411474i	−0.00884031	−	0.0242885i
$288$	−0.524005	−	0.0923963i	−0.0308773	−	0.00544450i
$289$	9.75877	−	8.18858i	0.574045	−	0.481681i
$290$		0			0
$291$	−3.48545	−	19.7670i	−0.204321	−	1.15876i
$292$	1.82391	−	1.05303i	0.106736	−	0.0616241i
$293$	17.7903	+	10.2713i	1.03932	+	0.600053i	0.919641	−	0.392759i	$-0.128479\pi$
$293$	17.7903	+	10.2713i	1.03932	+	0.600053i	0.119681	+	0.992812i	$0.461813\pi$
$294$	4.21941	+	1.53574i	0.246081	+	0.0895661i
$295$		0			0
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	17.4620	−	10.0817i	1.01325	−	0.585001i
$298$	−4.66717	+	0.822948i	−0.270362	+	0.0476721i
$299$	−34.2276	−	28.7204i	−1.97943	−	1.66094i
$300$		0			0
$301$	−5.79292	+	32.8533i	−0.333898	+	1.89363i
$302$	−0.155059	−	0.426022i	−0.00892266	−	0.0245148i
$303$			9.72967i			0.558955i
$304$	−1.15270	+	4.20372i	−0.0661121	+	0.241100i
$305$		0			0
$306$	−1.03209	+	0.375650i	−0.0590006	+	0.0214745i
$307$	−1.39003	−	0.245100i	−0.0793332	−	0.0139886i	0.133841	−	0.991003i	$-0.457269\pi$
$307$	−1.39003	−	0.245100i	−0.0793332	−	0.0139886i	−0.213174	+	0.977014i	$0.568380\pi$
$308$	−8.56250	−	10.2044i	−0.487894	−	0.581449i
$309$	−25.6313	−	21.5073i	−1.45812	−	1.22350i
$310$		0			0
$311$	5.22668	+	9.05288i	0.296378	+	0.513342i	0.975304	−	0.220865i	$-0.0708879\pi$
$311$	5.22668	+	9.05288i	0.296378	+	0.513342i	−0.678927	+	0.734206i	$0.737555\pi$
$312$	9.37295	+	5.41147i	0.530639	+	0.306364i
$313$	11.4411	−	31.4342i	0.646691	−	1.77677i	0.0170834	−	0.999854i	$-0.494562\pi$
$313$	11.4411	−	31.4342i	0.646691	−	1.77677i	0.629607	−	0.776914i	$-0.283216\pi$
$314$	12.2763	+	4.46821i	0.692792	+	0.252156i
$315$		0			0
$316$	0.184793	+	0.320070i	0.0103954	+	0.0180053i
$317$	3.68642	−	0.650015i	0.207050	−	0.0365085i	−0.0691611	−	0.997606i	$-0.522032\pi$
$317$	3.68642	−	0.650015i	0.207050	−	0.0365085i	0.276211	+	0.961097i	$0.410921\pi$
$318$	−6.11776	+	7.29086i	−0.343067	+	0.408851i
$319$	13.7483	−	11.5362i	0.769759	−	0.645905i
$320$		0			0
$321$	8.40420	−	3.05888i	0.469077	−	0.170730i
$322$			23.7743i			1.32489i
$323$	2.27801	+	8.70439i	0.126752	+	0.484325i
$324$	10.3131			0.572953
$325$		0			0
$326$	1.02094	−	5.79006i	0.0565449	−	0.320682i
$327$	−22.3112	−	26.5895i	−1.23381	−	1.47040i
$328$	−0.0918566	+	0.109470i	−0.00507193	+	0.00604449i
$329$	3.13247	+	17.7651i	0.172699	+	0.979424i
$330$		0			0
$331$	2.52094	−	4.36640i	0.138564	−	0.239999i	−0.788389	−	0.615176i	$-0.789085\pi$
$331$	2.52094	−	4.36640i	0.138564	−	0.239999i	0.926953	+	0.375177i	$0.122418\pi$
$332$	−0.257787	+	0.708263i	−0.0141479	+	0.0388710i
$333$	0.727940	−	2.00000i	0.0398909	−	0.109599i
$334$	11.1138	−	19.2497i	0.608120	−	1.05330i
$335$		0			0
$336$	−1.00000	−	5.67128i	−0.0545545	−	0.309394i
$337$	1.74578	−	2.08054i	0.0950986	−	0.113334i	−0.716396	−	0.697694i	$-0.754210\pi$
$337$	1.74578	−	2.08054i	0.0950986	−	0.113334i	0.811495	+	0.584359i	$0.198654\pi$
$338$	−12.9608	−	15.4461i	−0.704975	−	0.840156i
$339$	−0.844770	+	4.79093i	−0.0458816	+	0.260208i
$340$		0			0
$341$	36.7493			1.99008
$342$	−0.215615	+	2.30928i	−0.0116591	+	0.124871i
$343$		−	14.1284i		−	0.762859i
$344$	10.2306	−	3.72362i	0.551594	−	0.200764i
$345$		0			0
$346$	−16.2344	+	13.6223i	−0.872768	+	0.732339i
$347$	7.68540	−	9.15910i	0.412574	−	0.491686i	−0.519237	−	0.854630i	$-0.673784\pi$
$347$	7.68540	−	9.15910i	0.412574	−	0.491686i	0.931811	+	0.362944i	$0.118228\pi$
$348$	7.64090	−	1.34730i	0.409595	−	0.0722227i
$349$	−8.53714	−	14.7868i	−0.456983	−	0.791517i	0.541817	−	0.840496i	$-0.317737\pi$
$349$	−8.53714	−	14.7868i	−0.456983	−	0.791517i	−0.998800	+	0.0489792i	$0.984403\pi$
$350$		0			0
$351$	−25.0993	−	9.13538i	−1.33970	−	0.487611i
$352$	−1.48686	+	4.08512i	−0.0792501	+	0.217738i
$353$	−3.35375	−	1.93629i	−0.178502	−	0.103058i	0.408087	−	0.912943i	$-0.366196\pi$
$353$	−3.35375	−	1.93629i	−0.178502	−	0.103058i	−0.586589	+	0.809885i	$0.699529\pi$
$354$	7.19119	+	12.4555i	0.382207	+	0.662003i
$355$		0			0
$356$	1.36231	+	1.14311i	0.0722023	+	0.0605850i
$357$	−7.64090	−	9.10607i	−0.404399	−	0.481944i
$358$	−3.71599	−	0.655230i	−0.196396	−	0.0346300i
$359$	−22.1780	+	8.07213i	−1.17051	+	0.426031i	−0.852841	−	0.522171i	$-0.825122\pi$
$359$	−22.1780	+	8.07213i	−1.17051	+	0.426031i	−0.317669	+	0.948202i	$0.602900\pi$
$360$		0			0
$361$	18.6716	+	3.51735i	0.982715	+	0.185124i
$362$			9.36009i			0.491955i
$363$	5.07737	+	13.9500i	0.266493	+	0.732183i
$364$	−3.06418	+	17.3778i	−0.160607	+	0.910845i
$365$		0			0
$366$	−13.0496	−	10.9499i	−0.682115	−	0.572363i
$367$	10.0570	−	1.77332i	0.524971	−	0.0925665i	0.0951187	−	0.995466i	$-0.469677\pi$
$367$	10.0570	−	1.77332i	0.524971	−	0.0925665i	0.429852	+	0.902899i	$0.358566\pi$
$368$	6.71929	−	3.87939i	0.350267	−	0.202227i
$369$	−0.0380187	+	0.0658503i	−0.00197917	+	0.00342803i
$370$		0			0
$371$	−14.5817	−	5.30731i	−0.757045	−	0.275542i
$372$	13.7587	+	7.94356i	0.713353	+	0.411855i
$373$	−19.3726	+	11.1848i	−1.00308	+	0.579127i	−0.909157	−	0.416453i	$-0.863273\pi$
$373$	−19.3726	+	11.1848i	−1.00308	+	0.579127i	−0.0939195	+	0.995580i	$0.529940\pi$
$374$	1.55825	+	8.83726i	0.0805751	+	0.456964i
$375$		0			0
$376$	4.50980	−	3.78417i	0.232575	−	0.195154i
$377$	−23.4131	−	4.12836i	−1.20583	−	0.212621i
$378$	4.86084	+	13.3550i	0.250014	+	0.686909i
$379$	25.4783			1.30873			0.654367	−	0.756177i	$-0.272935\pi$
$379$	25.4783			1.30873			0.654367	+	0.756177i	$0.272935\pi$
$380$		0			0
$381$	−20.3405			−1.04207
$382$	−6.39922	−	17.5817i	−0.327413	−	0.899559i
$383$	14.4579	+	2.54933i	0.738766	+	0.130264i	0.530354	−	0.847777i	$-0.322059\pi$
$383$	14.4579	+	2.54933i	0.738766	+	0.130264i	0.208413	+	0.978041i	$0.433170\pi$
$384$	−1.43969	+	1.20805i	−0.0734690	+	0.0616478i
$385$		0			0
$386$	2.07263	+	11.7545i	0.105494	+	0.598288i
$387$	5.01681	−	2.89646i	0.255019	−	0.147235i
$388$	−9.24919	−	5.34002i	−0.469556	−	0.271099i
$389$	−27.0060	−	9.82938i	−1.36926	−	0.498369i	−0.450354	−	0.892850i	$-0.648702\pi$
$389$	−27.0060	−	9.82938i	−1.36926	−	0.498369i	−0.918904	+	0.394481i	$0.870924\pi$
$390$		0			0
$391$	8.00774	−	13.8698i	0.404969	−	0.701427i
$392$	2.06910	−	1.19459i	0.104505	−	0.0603360i
$393$	13.6905	−	2.41400i	0.690593	−	0.121770i
$394$	−2.28312	−	1.91576i	−0.115022	−	0.0965148i
$395$		0			0
$396$	−0.401674	+	2.27801i	−0.0201849	+	0.114474i
$397$	−7.12187	−	19.5672i	−0.357436	−	0.982048i	−0.979916	−	0.199412i	$-0.936097\pi$
$397$	−7.12187	−	19.5672i	−0.357436	−	0.982048i	0.622479	−	0.782636i	$-0.286125\pi$
$398$			24.1830i			1.21219i
$399$	−24.2841	+	6.35532i	−1.21572	+	0.318164i
$400$		0			0
$401$	−6.97906	+	2.54017i	−0.348517	+	0.126850i	−0.510347	−	0.859969i	$-0.670483\pi$
$401$	−6.97906	+	2.54017i	−0.348517	+	0.126850i	0.161829	+	0.986819i	$0.448261\pi$
$402$	11.6796	+	2.05943i	0.582526	+	0.102715i
$403$	−31.2915	−	37.2918i	−1.55874	−	1.85764i
$404$	3.96585	+	3.32774i	0.197308	+	0.165561i
$405$		0			0
$406$	6.32501	+	10.9552i	0.313905	+	0.543699i
$407$	−15.0595	−	8.69459i	−0.746471	−	0.430975i
$408$	−1.32683	+	3.64543i	−0.0656878	+	0.180476i
$409$	19.7729	+	7.19675i	0.977707	+	0.355856i	0.780948	−	0.624596i	$-0.214736\pi$
$409$	19.7729	+	7.19675i	0.977707	+	0.355856i	0.196759	+	0.980452i	$0.436958\pi$
$410$		0			0
$411$	7.63088	+	13.2171i	0.376404	+	0.651950i
$412$	−17.5329	+	3.09152i	−0.863783	+	0.152308i
$413$	−15.0729	+	17.9632i	−0.741688	+	0.883909i
$414$	3.16250	−	2.65366i	0.155429	−	0.130420i
$415$		0			0
$416$	5.41147	−	1.96962i	0.265319	−	0.0965683i
$417$		−	27.8307i		−	1.36287i
$418$	18.2748	+	5.01114i	0.893851	+	0.245103i
$419$	18.9162			0.924118			0.462059	−	0.886849i	$-0.347111\pi$
$419$	18.9162			0.924118			0.462059	+	0.886849i	$0.347111\pi$
$420$		0			0
$421$	1.26352	−	7.16577i	0.0615801	−	0.349238i	−0.938413	−	0.345516i	$-0.887704\pi$
$421$	1.26352	−	7.16577i	0.0615801	−	0.349238i	0.999993	−	0.00372244i	$-0.00118489\pi$
$422$	8.41009	+	10.0228i	0.409397	+	0.487900i
$423$	2.01352	−	2.39961i	0.0979005	−	0.116673i
$424$	0.879385	+	4.98724i	0.0427067	+	0.242202i
$425$		0			0
$426$	−5.33275	+	9.23659i	−0.258373	+	0.447514i
$427$	9.49935	−	26.0993i	0.459706	−	1.26303i
$428$	1.62760	−	4.47178i	0.0786728	−	0.216152i
$429$	23.5253	−	40.7470i	1.13581	−	1.96728i
$430$		0			0
$431$	2.47565	+	14.0401i	0.119248	+	0.676289i	0.984559	+	0.175053i	$0.0560098\pi$
$431$	2.47565	+	14.0401i	0.119248	+	0.676289i	−0.865311	+	0.501235i	$0.832879\pi$
$432$	2.98135	−	3.55303i	0.143440	−	0.170945i
$433$	4.85738	+	5.78880i	0.233431	+	0.278192i	0.870026	−	0.493006i	$-0.164102\pi$
$433$	4.85738	+	5.78880i	0.233431	+	0.278192i	−0.636595	+	0.771198i	$0.719658\pi$
$434$	−4.49794	+	25.5091i	−0.215908	+	1.22448i
$435$		0			0
$436$	−18.4688			−0.884497
$437$	−19.2363	−	27.8161i	−0.920196	−	1.33063i
$438$		−	3.95811i		−	0.189126i
$439$	5.72193	−	2.08261i	0.273093	−	0.0993977i	−0.201844	−	0.979418i	$-0.564693\pi$
$439$	5.72193	−	2.08261i	0.273093	−	0.0993977i	0.474937	+	0.880020i	$0.342471\pi$
$440$		0			0
$441$	0.973841	−	0.817150i	0.0463734	−	0.0389119i
$442$	7.64090	−	9.10607i	0.363440	−	0.433131i
$443$	26.8543	−	4.73514i	1.27589	−	0.224973i	0.505654	−	0.862736i	$-0.331251\pi$
$443$	26.8543	−	4.73514i	1.27589	−	0.224973i	0.770232	+	0.637763i	$0.220140\pi$
$444$	−3.75877	−	6.51038i	−0.178383	−	0.308969i
$445$		0			0
$446$	2.57398	+	0.936851i	0.121881	+	0.0443612i
$447$	−3.04628	+	8.36959i	−0.144084	+	0.395868i
$448$	−2.65366	−	1.53209i	−0.125373	−	0.0723844i
$449$	19.8464	+	34.3750i	0.936610	+	1.62226i	0.771737	+	0.635942i	$0.219388\pi$
$449$	19.8464	+	34.3750i	0.936610	+	1.62226i	0.164874	+	0.986315i	$0.447278\pi$
$450$		0			0
$451$	0.475900	+	0.399328i	0.0224093	+	0.0188036i
$452$	1.66387	+	1.98293i	0.0782620	+	0.0932690i
$453$	−0.839100	−	0.147956i	−0.0394243	−	0.00695157i
$454$	22.7802	−	8.29131i	1.06913	−	0.389130i
$455$		0			0
$456$	5.75877	+	5.82634i	0.269679	+	0.272843i
$457$		−	6.93676i		−	0.324488i	−0.986751	−	0.162244i	$-0.948127\pi$
$457$		−	6.93676i		−	0.324488i	0.986751	−	0.162244i	$-0.0518731\pi$
$458$	−5.36116	−	14.7297i	−0.250511	−	0.688272i
$459$	1.66250	−	9.42853i	0.0775990	−	0.440086i
$460$		0			0
$461$	20.5817	+	17.2701i	0.958586	+	0.804349i	0.980723	−	0.195406i	$-0.0626023\pi$
$461$	20.5817	+	17.2701i	0.958586	+	0.804349i	−0.0221363	+	0.999755i	$0.507047\pi$
$462$	−24.6547	+	4.34730i	−1.14704	+	0.202255i
$463$	−13.0547	+	7.53714i	−0.606704	+	0.350281i	−0.771674	−	0.636018i	$-0.780580\pi$
$463$	−13.0547	+	7.53714i	−0.606704	+	0.350281i	0.164970	+	0.986299i	$0.447247\pi$
$464$	2.06418	−	3.57526i	0.0958270	−	0.165977i
$465$		0			0
$466$	24.8380	+	9.04028i	1.15060	+	0.418783i
$467$	18.5110	+	10.6873i	0.856586	+	0.494550i	0.862868	−	0.505430i	$-0.168666\pi$
$467$	18.5110	+	10.6873i	0.856586	+	0.494550i	−0.00628157	+	0.999980i	$0.502000\pi$
$468$	2.65366	−	1.53209i	0.122665	−	0.0708208i
$469$	3.35773	+	19.0426i	0.155045	+	0.879306i
$470$		0			0
$471$	18.8084	−	15.7821i	0.866645	−	0.727202i
$472$	7.53644	+	1.32888i	0.346893	+	0.0611666i
$473$	−16.1877	−	44.4752i	−0.744310	−	2.04497i
$474$	0.694593			0.0319037
$475$		0			0
$476$	−6.32501			−0.289906
$477$	0.921605	+	2.53209i	0.0421974	+	0.115936i
$478$	13.5497	+	2.38919i	0.619751	+	0.109279i
$479$	5.00774	−	4.20199i	0.228810	−	0.191994i	−0.521174	−	0.853450i	$-0.674506\pi$
$479$	5.00774	−	4.20199i	0.228810	−	0.191994i	0.749984	+	0.661456i	$0.230061\pi$
$480$		0			0
$481$	4.00000	+	22.6851i	0.182384	+	1.03435i
$482$	11.1843	−	6.45723i	0.509429	−	0.294119i
$483$	38.6949	+	22.3405i	1.76068	+	1.01653i
$484$	7.42262	+	2.70161i	0.337392	+	0.122801i
$485$		0			0
$486$	2.73396	−	4.73535i	0.124015	−	0.214800i
$487$	−15.2818	+	8.82295i	−0.692484	+	0.399806i	−0.804542	−	0.593896i	$-0.797589\pi$
$487$	−15.2818	+	8.82295i	−0.692484	+	0.399806i	0.112058	+	0.993702i	$0.464256\pi$
$488$	−8.92647	+	1.57398i	−0.404082	+	0.0712506i
$489$	−8.46451	−	7.10257i	−0.382778	−	0.321189i
$490$		0			0
$491$	2.53549	−	14.3795i	0.114425	−	0.648937i	−0.872608	−	0.488421i	$-0.837573\pi$
$491$	2.53549	−	14.3795i	0.114425	−	0.648937i	0.987033	−	0.160516i	$-0.0513159\pi$
$492$	0.0918566	+	0.252374i	0.00414121	+	0.0113779i
$493$		−	8.52166i		−	0.383796i
$494$	−10.4757	−	22.8115i	−0.471322	−	1.02634i
$495$		0			0
$496$	7.94356	−	2.89122i	0.356677	−	0.129820i
$497$	−17.1250	−	3.01960i	−0.768161	−	0.135448i
$498$	0.910526	+	1.08512i	0.0408016	+	0.0486255i
$499$	10.0248	+	8.41182i	0.448772	+	0.376565i	0.838980	−	0.544162i	$-0.183152\pi$
$499$	10.0248	+	8.41182i	0.448772	+	0.376565i	−0.390208	+	0.920727i	$0.627597\pi$
$500$		0			0
$501$	−20.8871	−	36.1776i	−0.933168	−	1.61629i
$502$	−15.7403	−	9.08765i	−0.702523	−	0.405602i
$503$	−9.80418	+	26.9368i	−0.437147	+	1.20105i	0.504193	+	0.863591i	$0.331790\pi$
$503$	−9.80418	+	26.9368i	−0.437147	+	1.20105i	−0.941340	+	0.337460i	$0.890432\pi$
$504$	−1.53209	−	0.557635i	−0.0682447	−	0.0248390i
$505$		0			0
$506$	−16.8648	−	29.2108i	−0.749733	−	1.29858i
$507$	−37.3192	+	6.58037i	−1.65740	+	0.292245i
$508$	−6.95686	+	8.29086i	−0.308661	+	0.367847i
$509$	−18.1361	+	15.2180i	−0.803868	+	0.674526i	−0.949136	−	0.314867i	$-0.898040\pi$
$509$	−18.1361	+	15.2180i	−0.803868	+	0.674526i	0.145268	+	0.989392i	$0.453596\pi$
$510$		0			0
$511$	6.06418	−	2.20718i	0.268263	−	0.0976399i
$512$			1.00000i			0.0441942i
$513$	−16.4931	−	11.6925i	−0.728188	−	0.516238i
$514$	6.97266			0.307551
$515$		0			0
$516$	3.55303	−	20.1503i	0.156414	−	0.887065i
$517$	−16.4509	−	19.6054i	−0.723510	−	0.862246i
$518$	7.87846	−	9.38919i	0.346160	−	0.412537i
$519$	6.91622	+	39.2238i	0.303588	+	1.72174i
$520$		0			0
$521$	20.3812	−	35.3013i	0.892916	−	1.54658i	0.0565541	−	0.998400i	$-0.481989\pi$
$521$	20.3812	−	35.3013i	0.892916	−	1.54658i	0.836362	−	0.548177i	$-0.184678\pi$
$522$	0.751299	−	2.06418i	0.0328835	−	0.0903466i
$523$	11.9055	−	32.7101i	0.520591	−	1.43031i	−0.349274	−	0.937021i	$-0.613572\pi$
$523$	11.9055	−	32.7101i	0.520591	−	1.43031i	0.869864	−	0.493291i	$-0.164206\pi$
$524$	3.69846	−	6.40593i	0.161568	−	0.279844i
$525$		0			0
$526$	1.79561	+	10.1834i	0.0782922	+	0.444017i
$527$	11.2162	−	13.3669i	0.488584	−	0.582271i
$528$	5.25173	+	6.25877i	0.228552	+	0.272378i
$529$	−6.45946	+	36.6334i	−0.280846	+	1.59276i
$530$		0			0
$531$	4.07192			0.176706
$532$	−5.71518	+	12.0719i	−0.247785	+	0.523384i
$533$		−	0.822948i		−	0.0356458i
$534$	3.14068	−	1.14311i	0.135911	−	0.0494674i
$535$		0			0
$536$	4.83409	−	4.05629i	0.208801	−	0.175205i
$537$	−4.55834	+	5.43242i	−0.196707	+	0.234426i
$538$	−10.2946	+	1.81521i	−0.443830	+	0.0782592i
$539$	−5.19325	−	8.99497i	−0.223689	−	0.387441i
$540$		0			0
$541$	19.1138	+	6.95686i	0.821767	+	0.299099i	0.718475	−	0.695552i	$-0.244840\pi$
$541$	19.1138	+	6.95686i	0.821767	+	0.299099i	0.103291	+	0.994651i	$0.467063\pi$
$542$	−6.56423	+	18.0351i	−0.281958	+	0.774673i
$543$	15.2344	+	8.79561i	0.653772	+	0.377456i
$544$	1.03209	+	1.78763i	0.0442504	+	0.0766440i
$545$		0			0
$546$	25.4047	+	21.3170i	1.08722	+	0.912285i
$547$	−10.1269	−	12.0688i	−0.432995	−	0.516023i	0.504789	−	0.863243i	$-0.331570\pi$
$547$	−10.1269	−	12.0688i	−0.432995	−	0.516023i	−0.937784	+	0.347220i	$0.887126\pi$
$548$	7.99724	+	1.41013i	0.341625	+	0.0602378i
$549$	−4.53209	+	1.64955i	−0.193425	+	0.0704009i
$550$		0			0
$551$	−16.2645	−	7.70004i	−0.692889	−	0.328033i
$552$		−	14.5817i		−	0.620639i
$553$	0.387329	+	1.06418i	0.0164709	+	0.0452534i
$554$	5.14796	−	29.1955i	0.218716	−	1.24040i
$555$		0			0
$556$	−11.3439	−	9.51866i	−0.481088	−	0.403681i
$557$	31.6555	−	5.58172i	1.34129	−	0.236505i	0.543482	−	0.839421i	$-0.317106\pi$
$557$	31.6555	−	5.58172i	1.34129	−	0.236505i	0.797805	+	0.602916i	$0.205995\pi$
$558$	3.89533	−	2.24897i	0.164903	−	0.0952065i
$559$	−31.3482	+	54.2967i	−1.32589	+	2.29651i
$560$		0			0
$561$	15.8478	+	5.76811i	0.669093	+	0.243530i
$562$	15.2113	+	8.78224i	0.641649	+	0.370456i
$563$	−2.62095	+	1.51320i	−0.110460	+	0.0637739i	−0.554212	−	0.832376i	$-0.686980\pi$
$563$	−2.62095	+	1.51320i	−0.110460	+	0.0637739i	0.443752	+	0.896149i	$0.353647\pi$
$564$	−1.92127	−	10.8961i	−0.0809002	−	0.458808i
$565$		0			0
$566$	−4.27379	+	3.58613i	−0.179641	+	0.150736i
$567$	31.1212	+	5.48751i	1.30697	+	0.230454i
$568$	1.94096	+	5.33275i	0.0814409	+	0.223757i
$569$	0.132474			0.00555361			0.00277681	−	0.999996i	$-0.499116\pi$
$569$	0.132474			0.00555361			0.00277681	+	0.999996i	$0.499116\pi$
$570$		0			0
$571$	27.3969			1.14653			0.573263	−	0.819372i	$-0.305677\pi$
$571$	27.3969			1.14653			0.573263	+	0.819372i	$0.305677\pi$
$572$	−8.56250	−	23.5253i	−0.358016	−	0.983641i
$573$	−34.6292	−	6.10607i	−1.44666	−	0.255085i
$574$	−0.335437	+	0.281465i	−0.0140009	+	0.0117481i
$575$		0			0
$576$	0.0923963	+	0.524005i	0.00384984	+	0.0218336i
$577$	16.8834	−	9.74763i	0.702864	−	0.405799i	−0.105549	−	0.994414i	$-0.533660\pi$
$577$	16.8834	−	9.74763i	0.702864	−	0.405799i	0.808413	+	0.588615i	$0.200327\pi$
$578$	−11.0324	−	6.36959i	−0.458889	−	0.264940i
$579$	21.0792	+	7.67220i	0.876021	+	0.318846i
$580$		0			0
$581$	−1.15476	+	2.00011i	−0.0479076	+	0.0829785i
$582$	−17.3828	+	10.0360i	−0.720540	+	0.416004i
$583$	21.6810	−	3.82295i	0.897936	−	0.158330i
$584$	−1.61334	−	1.35375i	−0.0667605	−	0.0560187i
$585$		0			0
$586$	3.56717	−	20.2304i	0.147358	−	0.835711i
$587$	12.7917	+	35.1450i	0.527972	+	1.45059i	0.861455	+	0.507834i	$0.169554\pi$
$587$	12.7917	+	35.1450i	0.527972	+	1.45059i	−0.333483	+	0.942756i	$0.608224\pi$
$588$		−	4.49020i		−	0.185173i
$589$	−15.3773	−	33.4853i	−0.633612	−	1.37974i
$590$		0			0
$591$	−5.26352	+	1.91576i	−0.216512	+	0.0788040i
$592$	−3.93923	−	0.694593i	−0.161901	−	0.0285476i
$593$	−9.23222	−	11.0025i	−0.379122	−	0.451820i	0.542415	−	0.840111i	$-0.317510\pi$
$593$	−9.23222	−	11.0025i	−0.379122	−	0.451820i	−0.921537	+	0.388291i	$0.873066\pi$
$594$	−15.4461	−	12.9608i	−0.633761	−	0.531788i
$595$		0			0
$596$	2.36959	+	4.10424i	0.0970620	+	0.168116i
$597$	39.3602	+	22.7246i	1.61091	+	0.930057i
$598$	−15.2818	+	41.9864i	−0.624919	+	1.71695i
$599$	5.40198	+	1.96616i	0.220719	+	0.0803351i	0.450013	−	0.893022i	$-0.351419\pi$
$599$	5.40198	+	1.96616i	0.220719	+	0.0803351i	−0.229294	+	0.973357i	$0.573642\pi$
$600$		0			0
$601$	18.0385	+	31.2436i	0.735805	+	1.27445i	0.954369	+	0.298629i	$0.0965294\pi$
$601$	18.0385	+	31.2436i	0.735805	+	1.27445i	−0.218564	+	0.975823i	$0.570137\pi$
$602$	32.8533	−	5.79292i	1.33900	−	0.236102i
$603$	2.15830	−	2.57217i	0.0878929	−	0.104747i
$604$	−0.347296	+	0.291416i	−0.0141313	+	0.0118576i
$605$		0			0
$606$	9.14290	−	3.32774i	0.371405	−	0.135180i
$607$			6.49256i			0.263525i	0.991281	+	0.131763i	$0.0420636\pi$
$607$			6.49256i			0.263525i	−0.991281	+	0.131763i	$0.957936\pi$
$608$	4.34445	−	0.354570i	0.176191	−	0.0143797i
$609$	23.7743			0.963381
$610$		0			0
$611$	−5.88713	+	33.3876i	−0.238168	+	1.35072i
$612$	0.705990	+	0.841367i	0.0285380	+	0.0340102i
$613$	0.692791	−	0.825637i	0.0279816	−	0.0333471i	−0.751872	−	0.659309i	$-0.770849\pi$
$613$	0.692791	−	0.825637i	0.0279816	−	0.0333471i	0.779854	+	0.625962i	$0.215293\pi$
$614$	0.245100	+	1.39003i	0.00989143	+	0.0560971i
$615$		0			0
$616$	−6.66044	+	11.5362i	−0.268357	+	0.464808i
$617$	−5.89777	+	16.2040i	−0.237435	+	0.652348i	0.762550	+	0.646929i	$0.223947\pi$
$617$	−5.89777	+	16.2040i	−0.237435	+	0.652348i	−0.999985	+	0.00541866i	$0.998275\pi$
$618$	−11.4438	+	31.4415i	−0.460336	+	1.26476i
$619$	−12.5865	+	21.8004i	−0.505893	+	0.876232i	0.494084	+	0.869414i	$0.335504\pi$
$619$	−12.5865	+	21.8004i	−0.505893	+	0.876232i	−0.999977	+	0.00681784i	$0.997830\pi$
$620$		0			0
$621$	6.24897	+	35.4397i	0.250763	+	1.42215i
$622$	6.71929	−	8.00774i	0.269419	−	0.321081i
$623$	3.50271	+	4.17436i	0.140333	+	0.167242i
$624$	1.87939	−	10.6585i	0.0752356	−	0.426682i
$625$		0			0
$626$	−33.4516			−1.33700
$627$	25.3288	−	25.0351i	1.01154	−	0.999805i
$628$		−	13.0642i		−	0.521317i
$629$	−7.75877	+	2.82396i	−0.309362	+	0.112599i
$630$		0			0
$631$	19.0838	−	16.0132i	0.759713	−	0.637475i	−0.178339	−	0.983969i	$-0.557072\pi$
$631$	19.0838	−	16.0132i	0.759713	−	0.637475i	0.938052	+	0.346494i	$0.112628\pi$
$632$	0.237565	−	0.283119i	0.00944982	−	0.0112619i
$633$	24.2159	−	4.26991i	0.962495	−	0.169714i
$634$	−1.87164	−	3.24178i	−0.0743325	−	0.128748i
$635$		0			0
$636$	8.94356	+	3.25519i	0.354635	+	0.129077i
$637$	−4.70578	+	12.9290i	−0.186450	+	0.512266i
$638$	−15.5427	−	8.97359i	−0.615342	−	0.355268i
$639$	1.50980	+	2.61505i	0.0597268	+	0.103450i
$640$		0			0
$641$	−11.5587	−	9.69891i	−0.456542	−	0.383084i	0.385315	−	0.922785i	$-0.374093\pi$
$641$	−11.5587	−	9.69891i	−0.456542	−	0.383084i	−0.841857	+	0.539701i	$0.818537\pi$
$642$	−5.74881	−	6.85117i	−0.226887	−	0.270394i
$643$	12.3929	+	2.18520i	0.488728	+	0.0861760i	0.412582	−	0.910921i	$-0.364627\pi$
$643$	12.3929	+	2.18520i	0.488728	+	0.0861760i	0.0761467	+	0.997097i	$0.475738\pi$
$644$	22.3405	−	8.13127i	0.880339	−	0.320417i
$645$		0			0
$646$	7.40033	−	5.11770i	0.291162	−	0.201353i
$647$		−	27.7161i		−	1.08963i	−0.838556	−	0.544815i	$-0.816600\pi$
$647$		−	27.7161i		−	1.08963i	0.838556	−	0.544815i	$-0.183400\pi$
$648$	−3.52730	−	9.69119i	−0.138566	−	0.380706i
$649$	5.77703	−	32.7631i	0.226768	−	1.28607i
$650$		0			0
$651$	37.2918	+	31.2915i	1.46158	+	1.22641i
$652$	−5.79006	+	1.02094i	−0.226756	+	0.0399833i
$653$	10.4263	−	6.01960i	0.408011	−	0.235565i	−0.281924	−	0.959437i	$-0.590973\pi$
$653$	10.4263	−	6.01960i	0.408011	−	0.235565i	0.689935	+	0.723872i	$0.257639\pi$
$654$	−17.3550	+	30.0598i	−0.678636	+	1.17543i
$655$		0			0
$656$	0.134285	+	0.0488759i	0.00524296	+	0.00190828i
$657$	−0.970481	−	0.560307i	−0.0378621	−	0.0218597i
$658$	15.6224	−	9.01960i	0.609025	−	0.351621i
$659$	−6.09223	−	34.5508i	−0.237320	−	1.34591i	−0.837673	−	0.546172i	$-0.816084\pi$
$659$	−6.09223	−	34.5508i	−0.237320	−	1.34591i	0.600353	−	0.799735i	$-0.295027\pi$
$660$		0			0
$661$	−16.3746	+	13.7400i	−0.636900	+	0.534422i	−0.903064	−	0.429505i	$-0.858688\pi$
$661$	−16.3746	+	13.7400i	−0.636900	+	0.534422i	0.266165	+	0.963928i	$0.414243\pi$
$662$	−4.96529	−	0.875515i	−0.192982	−	0.0340279i
$663$	−7.64090	−	20.9932i	−0.296748	−	0.815308i
$664$	0.753718			0.0292499
$665$		0			0
$666$	−2.12836			−0.0824721
$667$	10.9552	+	30.0993i	0.424188	+	1.16545i
$668$	−21.8899	−	3.85978i	−0.846947	−	0.149340i
$669$	3.94356	−	3.30904i	0.152467	−	0.127935i
$670$		0			0
$671$	6.84255	+	38.8060i	0.264154	+	1.49809i
$672$	−4.98724	+	2.87939i	−0.192387	+	0.111075i
$673$	−2.17150	−	1.25372i	−0.0837053	−	0.0483273i	0.457563	−	0.889177i	$-0.348722\pi$
$673$	−2.17150	−	1.25372i	−0.0837053	−	0.0483273i	−0.541268	+	0.840850i	$0.682056\pi$
$674$	−2.55216	−	0.928909i	−0.0983054	−	0.0357802i
$675$		0			0
$676$	−10.0817	+	17.4620i	−0.387758	+	0.671617i
$677$	14.1173	−	8.15064i	0.542573	−	0.313255i	−0.203548	−	0.979065i	$-0.565247\pi$
$677$	14.1173	−	8.15064i	0.542573	−	0.313255i	0.746121	+	0.665810i	$0.231914\pi$
$678$	4.79093	−	0.844770i	0.183995	−	0.0324432i
$679$	−25.0692	−	21.0356i	−0.962069	−	0.807272i
$680$		0			0
$681$	7.91147	−	44.8682i	0.303168	−	1.71935i
$682$	−12.5690	−	34.5330i	−0.481292	−	1.32234i
$683$			42.2181i			1.61543i	0.589572	+	0.807716i	$0.299296\pi$
$683$			42.2181i			1.61543i	−0.589572	+	0.807716i	$0.700704\pi$
$684$	2.24376	−	0.587208i	0.0857921	−	0.0224525i
$685$		0			0
$686$	−13.2763	+	4.83218i	−0.506892	+	0.184494i
$687$	−29.0118	−	5.11556i	−1.10687	−	0.195171i
$688$	−6.99811	−	8.34002i	−0.266800	−	0.317960i
$689$	−22.3405	−	18.7459i	−0.851105	−	0.714162i
$690$		0			0
$691$	−9.44862	−	16.3655i	−0.359442	−	0.622572i	0.628425	−	0.777870i	$-0.283700\pi$
$691$	−9.44862	−	16.3655i	−0.359442	−	0.622572i	−0.987868	+	0.155298i	$0.950366\pi$
$692$	18.3533	+	10.5963i	0.697687	+	0.402810i
$693$	−2.42420	+	6.66044i	−0.0920879	+	0.253009i
$694$	−11.2353	−	4.08931i	−0.426486	−	0.155228i
$695$		0			0
$696$	−3.87939	−	6.71929i	−0.147048	−	0.254694i
$697$	0.290497	−	0.0512224i	0.0110033	−	0.00194019i
$698$	−10.9751	+	13.0797i	−0.415415	+	0.495072i
$699$	38.0540	−	31.9311i	1.43933	−	1.20774i
$700$		0			0
$701$	−18.0300	+	6.56239i	−0.680985	+	0.247858i	−0.659270	−	0.751906i	$-0.729135\pi$
$701$	−18.0300	+	6.56239i	−0.680985	+	0.247858i	−0.0217145	+	0.999764i	$0.506912\pi$
$702$			26.7101i			1.00811i
$703$	−1.62089	+	17.3601i	−0.0611331	+	0.654748i
$704$	4.34730			0.163845
$705$		0			0
$706$	−0.672466	+	3.81374i	−0.0253086	+	0.143532i
$707$	10.1968	+	12.1521i	0.383490	+	0.457026i
$708$	9.24481	−	11.0175i	0.347441	−	0.414065i
$709$	3.48246	+	19.7500i	0.130786	+	0.741727i	0.977702	+	0.209999i	$0.0673461\pi$
$709$	3.48246	+	19.7500i	0.130786	+	0.741727i	−0.846915	+	0.531728i	$0.821543\pi$
$710$		0			0
$711$	0.0983261	−	0.170306i	0.00368752	−	0.00638696i
$712$	0.608239	−	1.67112i	0.0227947	−	0.0626279i
$713$	−22.4323	+	61.6323i	−0.840097	+	2.30815i
$714$	−5.94356	+	10.2946i	−0.222432	+	0.385264i
$715$		0			0
$716$	0.655230	+	3.71599i	0.0244871	+	0.138873i
$717$	16.6212	−	19.8084i	0.620731	−	0.739758i
$718$	15.1706	+	18.0797i	0.566163	+	0.674727i
$719$	4.88444	−	27.7010i	0.182159	−	1.03307i	−0.747393	−	0.664382i	$-0.768695\pi$
$719$	4.88444	−	27.7010i	0.182159	−	1.03307i	0.929552	−	0.368692i	$-0.120194\pi$
$720$		0			0
$721$	−54.5526			−2.03165
$722$	−3.08083	−	18.7486i	−0.114657	−	0.697749i
$723$		−	24.2713i		−	0.902658i
$724$	8.79561	−	3.20134i	0.326886	−	0.118977i
$725$		0			0
$726$	11.3721	−	9.54233i	0.422059	−	0.354149i
$727$	−19.8226	+	23.6236i	−0.735178	+	0.876151i	−0.996011	−	0.0892329i	$-0.971558\pi$
$727$	−19.8226	+	23.6236i	−0.735178	+	0.876151i	0.260833	+	0.965384i	$0.416003\pi$
$728$	17.3778	−	3.06418i	0.644065	−	0.113566i
$729$	10.3316	+	17.8948i	0.382651	+	0.662770i
$730$		0			0
$731$	−21.1177	−	7.68621i	−0.781066	−	0.284285i
$732$	−5.82634	+	16.0077i	−0.215348	+	0.591663i
$733$	−26.9837	−	15.5790i	−0.996665	−	0.575425i	−0.0894049	−	0.995995i	$-0.528497\pi$
$733$	−26.9837	−	15.5790i	−0.996665	−	0.575425i	−0.907260	+	0.420571i	$0.861830\pi$
$734$	−5.10607	−	8.84397i	−0.188468	−	0.326437i
$735$		0			0
$736$	−5.94356	−	4.98724i	−0.219083	−	0.183832i
$737$	−17.6339	−	21.0152i	−0.649552	−	0.774106i
$738$	0.0748822	+	0.0132037i	0.00275645	+	0.000486037i
$739$	39.6724	−	14.4396i	1.45937	−	0.531168i	0.514179	−	0.857683i	$-0.328097\pi$
$739$	39.6724	−	14.4396i	1.45937	−	0.531168i	0.945192	+	0.326515i	$0.105874\pi$
$740$		0			0
$741$	−46.9718	−	4.38571i	−1.72555	−	0.161113i
$742$			15.5175i			0.569667i
$743$	12.8844	+	35.3996i	0.472683	+	1.29869i	0.915588	+	0.402117i	$0.131726\pi$
$743$	12.8844	+	35.3996i	0.472683	+	1.29869i	−0.442905	+	0.896568i	$0.646052\pi$
$744$	2.75877	−	15.6458i	0.101141	−	0.573602i
$745$		0			0
$746$	17.1361	+	14.3789i	0.627397	+	0.526449i
$747$	0.394952	−	0.0696407i	0.0144505	−	0.00254802i
$748$	7.77136	−	4.48680i	0.284149	−	0.164054i
$749$	7.29086	−	12.6281i	0.266402	−	0.461422i
$750$		0			0
$751$	−24.6186	−	8.96042i	−0.898344	−	0.326970i	−0.148755	−	0.988874i	$-0.547527\pi$
$751$	−24.6186	−	8.96042i	−0.898344	−	0.326970i	−0.749589	+	0.661904i	$0.769749\pi$
$752$	−5.09840	−	2.94356i	−0.185920	−	0.107341i
$753$	−29.5820	+	17.0792i	−1.07803	+	0.622400i
$754$	4.12836	+	23.4131i	0.150346	+	0.852654i
$755$		0			0
$756$	10.8871	−	9.13538i	0.395961	−	0.332251i
$757$	5.07504	+	0.894867i	0.184456	+	0.0325245i	0.265113	−	0.964217i	$-0.414591\pi$
$757$	5.07504	+	0.894867i	0.184456	+	0.0325245i	−0.0806572	+	0.996742i	$0.525702\pi$
$758$	−8.71411	−	23.9418i	−0.316511	−	0.869606i
$759$	−63.3911			−2.30095
$760$		0			0
$761$	3.84018			0.139207			0.0696033	−	0.997575i	$-0.477827\pi$
$761$	3.84018			0.139207			0.0696033	+	0.997575i	$0.477827\pi$
$762$	6.95686	+	19.1138i	0.252020	+	0.692420i
$763$	−55.7321	−	9.82707i	−2.01764	−	0.355764i
$764$	−14.3327	+	12.0266i	−0.518541	+	0.435107i
$765$		0			0
$766$	−2.54933	−	14.4579i	−0.0921109	−	0.522387i
$767$	−38.1659	+	22.0351i	−1.37809	+	0.795641i
$768$	1.62760	+	0.939693i	0.0587308	+	0.0339082i
$769$	20.8268	+	7.58034i	0.751034	+	0.273354i	0.689041	−	0.724722i	$-0.258032\pi$
$769$	20.8268	+	7.58034i	0.751034	+	0.273354i	0.0619934	+	0.998077i	$0.480254\pi$
$770$		0			0
$771$	6.55216	−	11.3487i	0.235970	−	0.408712i
$772$	10.3367	−	5.96791i	0.372027	−	0.214790i
$773$	42.0478	−	7.41416i	1.51235	−	0.266669i	0.644931	−	0.764240i	$-0.276886\pi$
$773$	42.0478	−	7.41416i	1.51235	−	0.266669i	0.867423	+	0.497572i	$0.165775\pi$
$774$	−4.43763	−	3.72362i	−0.159507	−	0.133843i
$775$		0			0
$776$	−1.85457	+	10.5178i	−0.0665752	+	0.377567i
$777$	−7.87846	−	21.6459i	−0.282638	−	0.776542i
$778$			28.7392i			1.03035i
$779$	0.164725	−	0.600726i	0.00590190	−	0.0215233i
$780$		0			0
$781$	23.1830	−	8.43794i	0.829554	−	0.301933i
$782$	−15.7722	−	2.78106i	−0.564012	−	0.0994505i
$783$	12.3081	+	14.6682i	0.439854	+	0.524198i
$784$	−1.83022	−	1.53574i	−0.0653651	−	0.0548478i
$785$		0			0
$786$	−6.95084	−	12.0392i	−0.247928	−	0.429424i
$787$	−20.1252	−	11.6193i	−0.717385	−	0.414182i	0.0964046	−	0.995342i	$-0.469266\pi$
$787$	−20.1252	−	11.6193i	−0.717385	−	0.414182i	−0.813789	+	0.581160i	$0.802599\pi$
$788$	−1.01936	+	2.80066i	−0.0363131	+	0.0997694i
$789$	18.2618	+	6.64674i	0.650136	+	0.236630i
$790$		0			0
$791$	3.96585	+	6.86906i	0.141009	+	0.244236i
$792$	2.27801	−	0.401674i	0.0809454	−	0.0142729i
$793$	33.5526	−	39.9864i	1.19149	−	1.41996i
$794$	−15.9513	+	13.3847i	−0.566091	+	0.475006i
$795$		0			0
$796$	22.7246	−	8.27109i	0.805453	−	0.293161i
$797$		−	26.8331i		−	0.950476i	−0.879857	−	0.475238i	$-0.842362\pi$
$797$		−	26.8331i		−	0.950476i	0.879857	−	0.475238i	$-0.157638\pi$
$798$	14.2777	+	20.6459i	0.505425	+	0.730857i
$799$	−12.1521			−0.429909
$800$		0			0
$801$	0.164315	−	0.931876i	0.00580578	−	0.0329262i
$802$	4.77396	+	5.68938i	0.168574	+	0.200899i
$803$	−5.88517	+	7.01367i	−0.207683	+	0.247507i
$804$	−2.05943	−	11.6796i	−0.0726305	−	0.411908i
$805$		0			0
$806$	−24.3405	+	42.1590i	−0.857357	+	1.48499i
$807$	−6.71929	+	18.4611i	−0.236530	+	0.649862i
$808$	1.77066	−	4.86484i	0.0622915	−	0.171144i
$809$	1.99391	−	3.45355i	0.0701021	−	0.121420i	−0.828844	−	0.559480i	$-0.811001\pi$
$809$	1.99391	−	3.45355i	0.0701021	−	0.121420i	0.898946	+	0.438060i	$0.144334\pi$
$810$		0			0
$811$	−1.41828	−	8.04347i	−0.0498026	−	0.282445i	0.949728	−	0.313076i	$-0.101359\pi$
$811$	−1.41828	−	8.04347i	−0.0498026	−	0.282445i	−0.999531	+	0.0306312i	$0.990248\pi$
$812$	8.13127	−	9.69047i	0.285352	−	0.340069i
$813$	23.1855	+	27.6313i	0.813149	+	0.969074i
$814$	−3.01960	+	17.1250i	−0.105837	+	0.600231i
$815$		0			0
$816$	3.87939			0.135806
$817$	−33.7515	+	33.3601i	−1.18082	+	1.16712i
$818$		−	21.0419i		−	0.735712i
$819$	8.82295	−	3.21129i	0.308299	−	0.112212i
$820$		0			0
$821$	40.4466	−	33.9387i	1.41159	−	1.18447i	0.455928	−	0.890017i	$-0.349307\pi$
$821$	40.4466	−	33.9387i	1.41159	−	1.18447i	0.955666	−	0.294452i	$-0.0951371\pi$
$822$	9.81007	−	11.6912i	0.342166	−	0.407777i
$823$	0.779953	−	0.137527i	0.0271875	−	0.00479388i	−0.160038	−	0.987111i	$-0.551162\pi$
$823$	0.779953	−	0.137527i	0.0271875	−	0.00479388i	0.187225	+	0.982317i	$0.440051\pi$
$824$	8.90167	+	15.4182i	0.310105	+	0.537117i
$825$		0			0
$826$	22.0351	+	8.02011i	0.766699	+	0.279055i
$827$	−5.62505	+	15.4547i	−0.195602	+	0.537413i	−0.998256	−	0.0590324i	$-0.981198\pi$
$827$	−5.62505	+	15.4547i	−0.195602	+	0.537413i	0.802654	+	0.596445i	$0.203421\pi$
$828$	−3.57526	−	2.06418i	−0.124249	−	0.0717351i
$829$	10.9855	+	19.0274i	0.381541	+	0.660848i	0.991283	−	0.131752i	$-0.0420603\pi$
$829$	10.9855	+	19.0274i	0.381541	+	0.660848i	−0.609742	+	0.792600i	$0.708727\pi$
$830$		0			0
$831$	−42.6810	−	35.8136i	−1.48059	−	1.24236i
$832$	−3.70167	−	4.41147i	−0.128332	−	0.152940i
$833$	−4.85678	−	0.856381i	−0.168277	−	0.0296719i
$834$	−26.1523	+	9.51866i	−0.905580	+	0.329604i
$835$		0			0
$836$	−1.54142	−	18.8866i	−0.0533112	−	0.653208i
$837$			39.2080i			1.35523i
$838$	−6.46973	−	17.7754i	−0.223493	−	0.614042i
$839$	5.38919	−	30.5636i	0.186055	−	1.05517i	−0.738537	−	0.674213i	$-0.764483\pi$
$839$	5.38919	−	30.5636i	0.186055	−	1.05517i	0.924592	−	0.380959i	$-0.124406\pi$
$840$		0			0
$841$	−9.15935	−	7.68561i	−0.315840	−	0.265021i
$842$	−7.16577	+	1.26352i	−0.246949	+	0.0435437i
$843$	28.5879	−	16.5052i	0.984619	−	0.568470i
$844$	6.54189	−	11.3309i	0.225181	−	0.390025i
$845$		0			0
$846$	−2.94356	−	1.07137i	−0.101202	−	0.0368344i
$847$	20.9612	+	12.1019i	0.720235	+	0.415828i
$848$	4.38571	−	2.53209i	0.150606	−	0.0869523i
$849$	1.82073	+	10.3259i	0.0624872	+	0.354382i
$850$		0			0
$851$	23.7743	−	19.9490i	0.814971	−	0.683842i
$852$	10.5035	+	1.85204i	0.359843	+	0.0634500i
$853$	14.8991	+	40.9350i	0.510136	+	1.40159i	0.881095	+	0.472939i	$0.156807\pi$
$853$	14.8991	+	40.9350i	0.510136	+	1.40159i	−0.370959	+	0.928649i	$0.620971\pi$
$854$	−27.7743			−0.950415
$855$		0			0
$856$	−4.75877			−0.162651
$857$	10.7636	+	29.5727i	0.367677	+	1.01018i	0.976243	+	0.216680i	$0.0695229\pi$
$857$	10.7636	+	29.5727i	0.367677	+	1.01018i	−0.608566	+	0.793503i	$0.708255\pi$
$858$	−46.3358	−	8.17024i	−1.58188	−	0.278928i
$859$	13.2069	−	11.0819i	0.450614	−	0.378110i	−0.389049	−	0.921217i	$-0.627196\pi$
$859$	13.2069	−	11.0819i	0.450614	−	0.378110i	0.839664	+	0.543107i	$0.182752\pi$
$860$		0			0
$861$	0.142903	+	0.810446i	0.00487014	+	0.0276199i
$862$	12.3467	−	7.12836i	0.420529	−	0.242793i
$863$	4.13819	+	2.38919i	0.140866	+	0.0813288i	0.568776	−	0.822492i	$-0.307417\pi$
$863$	4.13819	+	2.38919i	0.140866	+	0.0813288i	−0.427911	+	0.903821i	$0.640750\pi$
$864$	−4.35844	−	1.58634i	−0.148277	−	0.0539685i
$865$		0			0
$866$	3.77837	−	6.54433i	0.128394	−	0.222385i
$867$	−20.7342	+	11.9709i	−0.704171	+	0.406553i
$868$	25.5091	−	4.49794i	0.865835	−	0.152670i
$869$	−1.23080	−	1.03276i	−0.0417520	−	0.0350341i
$870$		0			0
$871$	−6.31046	+	35.7884i	−0.213822	+	1.21264i
$872$	6.31672	+	17.3550i	0.213911	+	0.587716i
$873$			5.68273i			0.192331i
$874$	−19.5594	+	27.5899i	−0.661608	+	0.933241i
$875$		0			0
$876$	−3.71941	+	1.35375i	−0.125667	+	0.0457391i
$877$	54.4097	+	9.59390i	1.83729	+	0.323963i	0.981218	−	0.192901i	$-0.0617896\pi$
$877$	54.4097	+	9.59390i	1.83729	+	0.323963i	0.856068	+	0.516864i	$0.172901\pi$
$878$	−3.91403	−	4.66456i	−0.132092	−	0.157421i
$879$	−29.5749	−	24.8163i	−0.997537	−	0.837033i
$880$		0			0
$881$	23.3778	+	40.4915i	0.787618	+	1.36419i	0.927423	+	0.374015i	$0.122019\pi$
$881$	23.3778	+	40.4915i	0.787618	+	1.36419i	−0.139805	+	0.990179i	$0.544648\pi$
$882$	−1.10094	−	0.635630i	−0.0370707	−	0.0214028i
$883$	−0.955234	+	2.62449i	−0.0321462	+	0.0883210i	−0.954727	−	0.297482i	$-0.903853\pi$
$883$	−0.955234	+	2.62449i	−0.0321462	+	0.0883210i	0.922581	+	0.385803i	$0.126075\pi$
$884$	−11.1702	−	4.06564i	−0.375696	−	0.136742i
$885$		0			0
$886$	−13.6343	−	23.6153i	−0.458053	−	0.793371i
$887$	−29.3605	+	5.17705i	−0.985830	+	0.173828i	−0.643247	−	0.765659i	$-0.722413\pi$
$887$	−29.3605	+	5.17705i	−0.985830	+	0.173828i	−0.342583	+	0.939487i	$0.611302\pi$
$888$	−4.83218	+	5.75877i	−0.162157	+	0.193252i
$889$	−25.4047	+	21.3170i	−0.852045	+	0.714951i
$890$		0			0
$891$	−42.1305	+	15.3342i	−1.41142	+	0.513716i
$892$		−	2.73917i		−	0.0917142i
$893$	−10.9804	+	23.1935i	−0.367446	+	0.776140i
$894$	8.90673			0.297885
$895$		0			0
$896$	−0.532089	+	3.01763i	−0.0177758	+	0.100812i
$897$	53.9767	+	64.3269i	1.80223	+	2.14781i
$898$	25.5141	−	30.4065i	0.851415	−	1.01468i
$899$	6.06006	+	34.3683i	0.202114	+	1.14625i
$900$		0			0
$901$	5.22668	−	9.05288i	0.174126	−	0.301595i
$902$	0.212478	−	0.583778i	0.00707474	−	0.0194377i
$903$	21.4435	−	58.9154i	0.713593	−	1.96058i
$904$	1.29426	−	2.24173i	0.0430465	−	0.0745588i
$905$		0			0
$906$	0.147956	+	0.839100i	0.00491551	+	0.0278772i
$907$	−20.7398	+	24.7167i	−0.688653	+	0.820705i	−0.991192	−	0.132432i	$-0.957721\pi$
$907$	−20.7398	+	24.7167i	−0.688653	+	0.820705i	0.302539	+	0.953137i	$0.402166\pi$
$908$	−15.5826	−	18.5706i	−0.517125	−	0.616286i
$909$	0.478340	−	2.71280i	0.0158655	−	0.0899780i
$910$		0			0
$911$	−55.2336			−1.82997			−0.914985	−	0.403487i	$-0.867798\pi$
$911$	−55.2336			−1.82997			−0.914985	+	0.403487i	$0.867798\pi$
$912$	3.50535	−	7.40420i	0.116074	−	0.245178i
$913$		−	3.27664i		−	0.108441i
$914$	−6.51842	+	2.37251i	−0.215610	+	0.0784757i
$915$		0			0
$916$	−12.0077	+	10.0757i	−0.396747	+	0.332910i
$917$	14.5691	−	17.3628i	0.481114	−	0.573369i
$918$	−9.42853	+	1.66250i	−0.311188	+	0.0548708i
$919$	−2.04963	−	3.55006i	−0.0676111	−	0.117106i	0.830238	−	0.557409i	$-0.188204\pi$
$919$	−2.04963	−	3.55006i	−0.0676111	−	0.117106i	−0.897849	+	0.440303i	$0.854871\pi$
$920$		0			0
$921$	2.49273	+	0.907278i	0.0821381	+	0.0298958i
$922$	9.18923	−	25.2472i	0.302631	−	0.831473i
$923$	−28.3026	−	16.3405i	−0.931590	−	0.537854i
$924$	12.5175	+	21.6810i	0.411797	+	0.713253i
$925$		0			0
$926$	11.5476	+	9.68956i	0.379477	+	0.318419i
$927$	6.08910	+	7.25671i	0.199992	+	0.238342i
$928$	−4.06564	−	0.716881i	−0.133461	−	0.0235328i
$929$	−5.84389	+	2.12700i	−0.191732	+	0.0697847i	−0.436102	−	0.899897i	$-0.643641\pi$
$929$	−5.84389	+	2.12700i	−0.191732	+	0.0697847i	0.244370	+	0.969682i	$0.421419\pi$
$930$		0			0
$931$	−6.02300	+	8.49584i	−0.197396	+	0.278440i
$932$		−	26.4320i		−	0.865809i
$933$	−6.71929	−	18.4611i	−0.219980	−	0.604389i
$934$	3.71167	−	21.0499i	0.121449	−	0.688774i
$935$		0			0
$936$	−2.34730	−	1.96962i	−0.0767238	−	0.0643789i
$937$	−41.1320	+	7.25268i	−1.34372	+	0.236935i	−0.798823	−	0.601566i	$-0.794544\pi$
$937$	−41.1320	+	7.25268i	−1.34372	+	0.236935i	−0.544900	+	0.838501i	$0.683433\pi$
$938$	16.7458	−	9.66819i	0.546769	−	0.315677i
$939$	−31.4342	+	54.4457i	−1.02582	+	1.77677i
$940$		0			0
$941$	−0.610815	−	0.222318i	−0.0199120	−	0.00724737i	0.332045	−	0.943264i	$-0.392261\pi$
$941$	−0.610815	−	0.222318i	−0.0199120	−	0.00724737i	−0.351957	+	0.936016i	$0.614484\pi$
$942$	−21.2632	−	12.2763i	−0.692792	−	0.399984i
$943$	−0.960210	+	0.554378i	−0.0312687	+	0.0180530i
$944$	−1.32888	−	7.53644i	−0.0432513	−	0.245290i
$945$		0			0
$946$	−36.2565	+	30.4229i	−1.17880	+	0.989132i
$947$	21.9877	+	3.87702i	0.714504	+	0.125986i	0.519071	−	0.854731i	$-0.326278\pi$
$947$	21.9877	+	3.87702i	0.714504	+	0.125986i	0.195432	+	0.980717i	$0.437389\pi$
$948$	−0.237565	−	0.652704i	−0.00771574	−	0.0211988i
$949$	12.1284			0.393703
$950$		0			0
$951$	−7.03508			−0.228128
$952$	2.16328	+	5.94356i	0.0701123	+	0.192632i
$953$	0.365379	+	0.0644262i	0.0118358	+	0.00208697i	0.179563	−	0.983746i	$-0.442532\pi$
$953$	0.365379	+	0.0644262i	0.0118358	+	0.00208697i	−0.167727	+	0.985833i	$0.553643\pi$
$954$	2.06418	−	1.73205i	0.0668302	−	0.0560772i
$955$		0			0
$956$	−2.38919	−	13.5497i	−0.0772718	−	0.438230i
$957$	−29.2108	+	16.8648i	−0.944250	+	0.545163i
$958$	−5.66133	−	3.26857i	−0.182909	−	0.105603i
$959$	23.3824	+	8.51049i	0.755056	+	0.274818i
$960$		0			0
$961$	−20.2297	+	35.0388i	−0.652570	+	1.13028i
$962$	19.9490	−	11.5175i	0.643180	−	0.371340i
$963$	−2.49362	+	0.439693i	−0.0803558	+	0.0141689i
$964$	−9.89306	−	8.30126i	−0.318634	−	0.267366i
$965$		0			0
$966$	7.75877	−	44.0022i	0.249634	−	1.41575i
$967$	−0.495671	−	1.36184i	−0.0159397	−	0.0437940i	0.931468	−	0.363824i	$-0.118529\pi$
$967$	−0.495671	−	1.36184i	−0.0159397	−	0.0437940i	−0.947407	+	0.320030i	$0.896307\pi$
$968$		−	7.89899i		−	0.253883i
$969$	−1.37551	−	16.8538i	−0.0441879	−	0.541422i
$970$		0			0
$971$	4.86262	−	1.76985i	0.156049	−	0.0567971i	−0.262815	−	0.964846i	$-0.584651\pi$
$971$	4.86262	−	1.76985i	0.156049	−	0.0567971i	0.418863	+	0.908049i	$0.362429\pi$
$972$	−5.38484	−	0.949493i	−0.172719	−	0.0304550i
$973$	−29.1669	−	34.7597i	−0.935046	−	1.11434i
$974$	13.5175	+	11.3426i	0.433130	+	0.363439i
$975$		0			0
$976$	4.53209	+	7.84981i	0.145069	+	0.251266i
$977$	−27.5580	−	15.9106i	−0.881657	−	0.509025i	−0.0104528	−	0.999945i	$-0.503327\pi$
$977$	−27.5580	−	15.9106i	−0.881657	−	0.509025i	−0.871204	+	0.490920i	$0.836661\pi$
$978$	−3.77920	+	10.3833i	−0.120845	+	0.332020i
$979$	−7.26486	−	2.64419i	−0.232186	−	0.0845088i
$980$		0			0
$981$	4.91353	+	8.51049i	0.156877	+	0.271719i
$982$	−14.3795	+	2.53549i	−0.458868	+	0.0809108i
$983$	14.7055	−	17.5253i	0.469031	−	0.558970i	−0.478725	−	0.877965i	$-0.658901\pi$
$983$	14.7055	−	17.5253i	0.469031	−	0.558970i	0.947756	+	0.318995i	$0.103345\pi$
$984$	0.205737	−	0.172634i	0.00655866	−	0.00550337i
$985$		0			0
$986$	−8.00774	+	2.91458i	−0.255018	+	0.0928191i
$987$		−	33.9026i		−	1.07913i
$988$	−17.8529	+	17.6459i	−0.567978	+	0.561391i
$989$	84.4707			2.68601
$990$		0			0
$991$	−3.24030	+	18.3766i	−0.102931	+	0.583753i	0.889095	+	0.457723i	$0.151335\pi$
$991$	−3.24030	+	18.3766i	−0.102931	+	0.583753i	−0.992026	+	0.126030i	$0.959776\pi$
$992$	−5.43372	−	6.47565i	−0.172521	−	0.205602i
$993$	−6.09083	+	7.25877i	−0.193287	+	0.230350i
$994$	3.01960	+	17.1250i	0.0957759	+	0.543172i
$995$		0			0
$996$	0.708263	−	1.22675i	0.0224422	−	0.0388710i
$997$	−4.78892	+	13.1575i	−0.151667	+	0.416701i	−0.992137	−	0.125157i	$-0.960057\pi$
$997$	−4.78892	+	13.1575i	−0.151667	+	0.416701i	0.840470	+	0.541858i	$0.182279\pi$
$998$	4.47584	−	12.2973i	0.141680	−	0.389263i
$999$	9.27631	−	16.0670i	0.293490	−	0.508339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.c.499.1		12
5.2	odd	4		950.2.l.c.651.1		6
5.3	odd	4		190.2.k.a.81.1	yes	6
5.4	even	2	inner	950.2.u.c.499.2		12
19.4	even	9	inner	950.2.u.c.99.2		12
95.4	even	18	inner	950.2.u.c.99.1		12
95.23	odd	36		190.2.k.a.61.1	✓	6
95.42	odd	36		950.2.l.c.251.1		6
95.78	even	36		3610.2.a.w.1.1		3
95.93	odd	36		3610.2.a.x.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.a.61.1	✓	6	95.23	odd	36
190.2.k.a.81.1	yes	6	5.3	odd	4
950.2.l.c.251.1		6	95.42	odd	36
950.2.l.c.651.1		6	5.2	odd	4
950.2.u.c.99.1		12	95.4	even	18	inner
950.2.u.c.99.2		12	19.4	even	9	inner
950.2.u.c.499.1		12	1.1	even	1	trivial
950.2.u.c.499.2		12	5.4	even	2	inner
3610.2.a.w.1.1		3	95.78	even	36
3610.2.a.x.1.3		3	95.93	odd	36

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.342020 - 0.939693i) q^{2} +(-1.85083 - 0.326352i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(0.326352 + 1.85083i) q^{6} +(-2.65366 + 1.53209i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.500000 + 0.181985i) q^{9} +O(q^{10})\)	\(q+(-0.342020 - 0.939693i) q^{2} +(-1.85083 - 0.326352i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(0.326352 + 1.85083i) q^{6} +(-2.65366 + 1.53209i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.500000 + 0.181985i) q^{9} +(2.17365 - 3.76487i) q^{11} +(1.62760 - 0.939693i) q^{12} +(-5.67128 + 1.00000i) q^{13} +(2.34730 + 1.96962i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-0.705990 - 1.93969i) q^{17} -0.532089i q^{18} +(-4.34002 - 0.405223i) q^{19} +(5.41147 - 1.96962i) q^{21} +(-4.28125 - 0.754900i) q^{22} +(4.98724 + 5.94356i) q^{23} +(-1.43969 - 1.20805i) q^{24} +(2.87939 + 4.98724i) q^{26} +(4.01676 + 2.31908i) q^{27} +(1.04801 - 2.87939i) q^{28} +(3.87939 + 1.41198i) q^{29} +(4.22668 + 7.32083i) q^{31} +(-0.984808 + 0.173648i) q^{32} +(-5.25173 + 6.25877i) q^{33} +(-1.58125 + 1.32683i) q^{34} +(-0.500000 + 0.181985i) q^{36} -4.00000i q^{37} +(1.10359 + 4.21688i) q^{38} +10.8229 q^{39} +(-0.0248149 + 0.140732i) q^{41} +(-3.70167 - 4.41147i) q^{42} +(6.99811 - 8.34002i) q^{43} +(0.754900 + 4.28125i) q^{44} +(3.87939 - 6.71929i) q^{46} +(2.01352 - 5.53209i) q^{47} +(-0.642788 + 1.76604i) q^{48} +(1.19459 - 2.06910i) q^{49} +(0.673648 + 3.82045i) q^{51} +(3.70167 - 4.41147i) q^{52} +(3.25519 + 3.87939i) q^{53} +(0.805407 - 4.56769i) q^{54} -3.06418 q^{56} +(7.90041 + 2.16637i) q^{57} -4.12836i q^{58} +(7.19119 - 2.61738i) q^{59} +(-6.94356 + 5.82634i) q^{61} +(5.43372 - 6.47565i) q^{62} +(-1.60565 + 0.283119i) q^{63} +(0.500000 + 0.866025i) q^{64} +(7.67752 + 2.79439i) q^{66} +(2.15830 - 5.92989i) q^{67} +(1.78763 + 1.03209i) q^{68} +(-7.29086 - 12.6281i) q^{69} +(4.34730 + 3.64781i) q^{71} +(0.342020 + 0.407604i) q^{72} +(-2.07407 - 0.365715i) q^{73} +(-3.75877 + 1.36808i) q^{74} +(3.58512 - 2.47929i) q^{76} +13.3209i q^{77} +(-3.70167 - 10.1702i) q^{78} +(0.0641778 - 0.363970i) q^{79} +(-7.90033 - 6.62916i) q^{81} +(0.140732 - 0.0248149i) q^{82} +(0.652739 - 0.376859i) q^{83} +(-2.87939 + 4.98724i) q^{84} +(-10.2306 - 3.72362i) q^{86} +(-6.71929 - 3.87939i) q^{87} +(3.76487 - 2.17365i) q^{88} +(-0.308811 - 1.75135i) q^{89} +(13.5175 - 11.3426i) q^{91} +(-7.64090 - 1.34730i) q^{92} +(-5.43372 - 14.9290i) q^{93} -5.88713 q^{94} +1.87939 q^{96} +(3.65279 + 10.0360i) q^{97} +(-2.35289 - 0.414878i) q^{98} +(1.77197 - 1.48686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^6 + 6 * q^9	\( 12 q + 6 q^{6} + 6 q^{9} + 24 q^{11} + 24 q^{14} - 12 q^{19} + 24 q^{21} - 6 q^{24} + 12 q^{26} + 24 q^{29} + 24 q^{31} - 24 q^{34} - 6 q^{36} + 48 q^{39} + 54 q^{41} + 12 q^{44} + 24 q^{46} + 6 q^{49} + 6 q^{51} + 18 q^{54} - 6 q^{59} - 24 q^{61} + 6 q^{64} + 42 q^{66} - 24 q^{69} + 48 q^{71} - 36 q^{79} - 66 q^{81} - 12 q^{84} - 48 q^{86} - 96 q^{89} + 72 q^{91} + 48 q^{94} + 66 q^{99}+O(q^{100}) \) 12 * q + 6 * q^6 + 6 * q^9 + 24 * q^11 + 24 * q^14 - 12 * q^19 + 24 * q^21 - 6 * q^24 + 12 * q^26 + 24 * q^29 + 24 * q^31 - 24 * q^34 - 6 * q^36 + 48 * q^39 + 54 * q^41 + 12 * q^44 + 24 * q^46 + 6 * q^49 + 6 * q^51 + 18 * q^54 - 6 * q^59 - 24 * q^61 + 6 * q^64 + 42 * q^66 - 24 * q^69 + 48 * q^71 - 36 * q^79 - 66 * q^81 - 12 * q^84 - 48 * q^86 - 96 * q^89 + 72 * q^91 + 48 * q^94 + 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more