LMFDB - Embedded newform 250.2.e.c.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(49,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("250.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.e (of order $10$, degree $4$, 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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			149.1
Root			$0.644389 - 0.983224i$ of defining polynomial
Character	$\chi$	$=$	250.149
Dual form			250.2.e.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)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(-0.792578 + 1.09089i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.09089 - 0.792578i) q^{6} +0.833366i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.365190 + 1.12394i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.792578 + 1.09089i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.09089 - 0.792578i) q^{6} +0.833366i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.365190 + 1.12394i) q^{9} +(0.257524 - 0.792578i) q^{11} +(-1.28242 + 0.416683i) q^{12} +(-4.34038 + 1.41027i) q^{13} +(0.257524 - 0.792578i) q^{14} +(0.309017 + 0.951057i) q^{16} +(3.20425 + 4.41027i) q^{17} -1.18178i q^{18} +(-7.00116 + 5.08664i) q^{19} +(-0.909110 - 0.660507i) q^{21} +(-0.489840 + 0.674207i) q^{22} +(3.35741 + 1.09089i) q^{23} +1.34841 q^{24} +4.56375 q^{26} +(-5.36279 - 1.74248i) q^{27} +(-0.489840 + 0.674207i) q^{28} +(2.64518 + 1.92183i) q^{29} +(-4.85599 + 3.52808i) q^{31} -1.00000i q^{32} +(0.660507 + 0.909110i) q^{33} +(-1.68458 - 5.18459i) q^{34} +(-0.365190 + 1.12394i) q^{36} +(6.95685 - 2.26042i) q^{37} +(8.23036 - 2.67421i) q^{38} +(1.90163 - 5.85263i) q^{39} +(0.576909 + 1.77554i) q^{41} +(0.660507 + 0.909110i) q^{42} -1.63877i q^{43} +(0.674207 - 0.489840i) q^{44} +(-2.85599 - 2.07500i) q^{46} +(0.489840 - 0.674207i) q^{47} +(-1.28242 - 0.416683i) q^{48} +6.30550 q^{49} -7.35074 q^{51} +(-4.34038 - 1.41027i) q^{52} +(3.77782 - 5.19972i) q^{53} +(4.56186 + 3.31439i) q^{54} +(0.674207 - 0.489840i) q^{56} -11.6691i q^{57} +(-1.92183 - 2.64518i) q^{58} +(-4.18178 - 12.8702i) q^{59} +(1.81832 - 5.59621i) q^{61} +(5.70855 - 1.85482i) q^{62} +(-0.936652 + 0.304337i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-0.347249 - 1.06872i) q^{66} +(0.881621 + 1.21345i) q^{67} +5.45140i q^{68} +(-3.85105 + 2.79795i) q^{69} +(1.91027 + 1.38790i) q^{71} +(0.694633 - 0.956080i) q^{72} +(-3.16703 - 1.02903i) q^{73} -7.31486 q^{74} -8.65392 q^{76} +(0.660507 + 0.214612i) q^{77} +(-3.61712 + 4.97854i) q^{78} +(4.18178 + 3.03824i) q^{79} +(3.28304 - 2.38527i) q^{81} -1.86692i q^{82} +(7.25068 + 9.97971i) q^{83} +(-0.347249 - 1.06872i) q^{84} +(-0.506408 + 1.55856i) q^{86} +(-4.19302 + 1.36239i) q^{87} +(-0.792578 + 0.257524i) q^{88} +(2.16491 - 6.66290i) q^{89} +(-1.17527 - 3.61712i) q^{91} +(2.07500 + 2.85599i) q^{92} -8.09363i q^{93} +(-0.674207 + 0.489840i) q^{94} +(1.09089 + 0.792578i) q^{96} +(-6.51864 + 8.97214i) q^{97} +(-5.99689 - 1.94851i) q^{98} +0.984855 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 6 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 - 6 * q^6 + 2 * q^9	$ 16 q + 4 q^{4} - 6 q^{6} + 2 q^{9} + 2 q^{11} + 2 q^{14} - 4 q^{16} - 40 q^{19} - 38 q^{21} - 4 q^{24} + 44 q^{26} + 30 q^{29} - 18 q^{31} + 2 q^{34} - 2 q^{36} + 24 q^{39} - 18 q^{41} - 2 q^{44} + 14 q^{46} + 8 q^{49} + 52 q^{51} + 50 q^{54} - 2 q^{56} - 20 q^{59} + 12 q^{61} + 4 q^{64} - 52 q^{66} - 86 q^{69} - 18 q^{71} - 48 q^{74} - 20 q^{76} + 20 q^{79} - 34 q^{81} - 52 q^{84} - 46 q^{86} + 30 q^{89} + 2 q^{91} + 2 q^{94} - 6 q^{96} + 84 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 6 * q^6 + 2 * q^9 + 2 * q^11 + 2 * q^14 - 4 * q^16 - 40 * q^19 - 38 * q^21 - 4 * q^24 + 44 * q^26 + 30 * q^29 - 18 * q^31 + 2 * q^34 - 2 * q^36 + 24 * q^39 - 18 * q^41 - 2 * q^44 + 14 * q^46 + 8 * q^49 + 52 * q^51 + 50 * q^54 - 2 * q^56 - 20 * q^59 + 12 * q^61 + 4 * q^64 - 52 * q^66 - 86 * q^69 - 18 * q^71 - 48 * q^74 - 20 * q^76 + 20 * q^79 - 34 * q^81 - 52 * q^84 - 46 * q^86 + 30 * q^89 + 2 * q^91 + 2 * q^94 - 6 * q^96 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	−0.792578	+	1.09089i	−0.457595	+	0.629826i	−0.974008	−	0.226514i	$-0.927267\pi$
$3$	−0.792578	+	1.09089i	−0.457595	+	0.629826i	0.516413	+	0.856340i	$0.327267\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$		0			0
$5$		0			0
$6$	1.09089	−	0.792578i	0.445354	−	0.323569i
$7$			0.833366i			0.314983i	0.987520	+	0.157491i	$0.0503406\pi$
$7$			0.833366i			0.314983i	−0.987520	+	0.157491i	$0.949659\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	0.365190	+	1.12394i	0.121730	+	0.374646i
$10$		0			0
$11$	0.257524	−	0.792578i	0.0776465	−	0.238971i	−0.904698	−	0.426054i	$-0.859903\pi$
$11$	0.257524	−	0.792578i	0.0776465	−	0.238971i	0.982344	+	0.187083i	$0.0599033\pi$
$12$	−1.28242	+	0.416683i	−0.370202	+	0.120286i
$13$	−4.34038	+	1.41027i	−1.20380	+	0.391140i	−0.841159	−	0.540787i	$-0.818126\pi$
$13$	−4.34038	+	1.41027i	−1.20380	+	0.391140i	−0.362645	+	0.931927i	$0.618126\pi$
$14$	0.257524	−	0.792578i	0.0688262	−	0.211825i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	3.20425	+	4.41027i	0.777145	+	1.06965i	0.995591	+	0.0937997i	$0.0299013\pi$
$17$	3.20425	+	4.41027i	0.777145	+	1.06965i	−0.218446	+	0.975849i	$0.570099\pi$
$18$		−	1.18178i		−	0.278548i
$19$	−7.00116	+	5.08664i	−1.60618	+	1.16696i	−0.732062	+	0.681238i	$0.761442\pi$
$19$	−7.00116	+	5.08664i	−1.60618	+	1.16696i	−0.874116	+	0.485718i	$0.838558\pi$
$20$		0			0
$21$	−0.909110	−	0.660507i	−0.198384	−	0.144134i
$22$	−0.489840	+	0.674207i	−0.104434	+	0.143741i
$23$	3.35741	+	1.09089i	0.700069	+	0.227466i	0.637361	−	0.770566i	$-0.280026\pi$
$23$	3.35741	+	1.09089i	0.700069	+	0.227466i	0.0627085	+	0.998032i	$0.480026\pi$
$24$	1.34841			0.275244
$25$		0			0
$26$	4.56375			0.895024
$27$	−5.36279	−	1.74248i	−1.03207	−	0.335340i
$28$	−0.489840	+	0.674207i	−0.0925711	+	0.127413i
$29$	2.64518	+	1.92183i	0.491197	+	0.356876i	0.805645	−	0.592399i	$-0.201819\pi$
$29$	2.64518	+	1.92183i	0.491197	+	0.356876i	−0.314447	+	0.949275i	$0.601819\pi$
$30$		0			0
$31$	−4.85599	+	3.52808i	−0.872161	+	0.633662i	−0.931166	−	0.364596i	$-0.881207\pi$
$31$	−4.85599	+	3.52808i	−0.872161	+	0.633662i	0.0590050	+	0.998258i	$0.481207\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.660507	+	0.909110i	0.114980	+	0.158256i
$34$	−1.68458	−	5.18459i	−0.288902	−	0.889150i
$35$		0			0
$36$	−0.365190	+	1.12394i	−0.0608650	+	0.187323i
$37$	6.95685	−	2.26042i	1.14370	−	0.371610i	0.324932	−	0.945737i	$-0.394658\pi$
$37$	6.95685	−	2.26042i	1.14370	−	0.371610i	0.818766	+	0.574127i	$0.194658\pi$
$38$	8.23036	−	2.67421i	1.33514	−	0.433814i
$39$	1.90163	−	5.85263i	0.304505	−	0.937171i
$40$		0			0
$41$	0.576909	+	1.77554i	0.0900981	+	0.277293i	0.985945	−	0.167069i	$-0.0534303\pi$
$41$	0.576909	+	1.77554i	0.0900981	+	0.277293i	−0.895847	+	0.444362i	$0.853430\pi$
$42$	0.660507	+	0.909110i	0.101918	+	0.140279i
$43$		−	1.63877i		−	0.249910i	−0.992162	−	0.124955i	$-0.960121\pi$
$43$		−	1.63877i		−	0.249910i	0.992162	−	0.124955i	$-0.0398787\pi$
$44$	0.674207	−	0.489840i	0.101641	−	0.0738462i
$45$		0			0
$46$	−2.85599	−	2.07500i	−0.421092	−	0.305941i
$47$	0.489840	−	0.674207i	0.0714505	−	0.0983432i	−0.771796	−	0.635870i	$-0.780641\pi$
$47$	0.489840	−	0.674207i	0.0714505	−	0.0983432i	0.843247	+	0.537527i	$0.180641\pi$
$48$	−1.28242	−	0.416683i	−0.185101	−	0.0601430i
$49$	6.30550			0.900786
$50$		0			0
$51$	−7.35074			−1.02931
$52$	−4.34038	−	1.41027i	−0.601902	−	0.195570i
$53$	3.77782	−	5.19972i	0.518923	−	0.714237i	−0.466469	−	0.884538i	$-0.654474\pi$
$53$	3.77782	−	5.19972i	0.518923	−	0.714237i	0.985392	+	0.170301i	$0.0544740\pi$
$54$	4.56186	+	3.31439i	0.620791	+	0.451031i
$55$		0			0
$56$	0.674207	−	0.489840i	0.0900947	−	0.0654576i
$57$		−	11.6691i		−	1.54560i
$58$	−1.92183	−	2.64518i	−0.252349	−	0.347329i
$59$	−4.18178	−	12.8702i	−0.544421	−	1.67556i	−0.722362	−	0.691515i	$-0.756943\pi$
$59$	−4.18178	−	12.8702i	−0.544421	−	1.67556i	0.177940	−	0.984041i	$-0.443057\pi$
$60$		0			0
$61$	1.81832	−	5.59621i	0.232812	−	0.716521i	−0.764592	−	0.644514i	$-0.777060\pi$
$61$	1.81832	−	5.59621i	0.232812	−	0.716521i	0.997404	−	0.0720066i	$-0.0229403\pi$
$62$	5.70855	−	1.85482i	0.724987	−	0.235563i
$63$	−0.936652	+	0.304337i	−0.118007	+	0.0383428i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$		0			0
$66$	−0.347249	−	1.06872i	−0.0427434	−	0.131551i
$67$	0.881621	+	1.21345i	0.107707	+	0.148246i	0.859468	−	0.511190i	$-0.170795\pi$
$67$	0.881621	+	1.21345i	0.107707	+	0.148246i	−0.751761	+	0.659436i	$0.770795\pi$
$68$			5.45140i			0.661079i
$69$	−3.85105	+	2.79795i	−0.463612	+	0.336834i
$70$		0			0
$71$	1.91027	+	1.38790i	0.226708	+	0.164713i	0.695341	−	0.718680i	$-0.255253\pi$
$71$	1.91027	+	1.38790i	0.226708	+	0.164713i	−0.468633	+	0.883393i	$0.655253\pi$
$72$	0.694633	−	0.956080i	0.0818632	−	0.112675i
$73$	−3.16703	−	1.02903i	−0.370672	−	0.120439i	0.117756	−	0.993043i	$-0.462430\pi$
$73$	−3.16703	−	1.02903i	−0.370672	−	0.120439i	−0.488429	+	0.872604i	$0.662430\pi$
$74$	−7.31486			−0.850335
$75$		0			0
$76$	−8.65392			−0.992672
$77$	0.660507	+	0.214612i	0.0752718	+	0.0244573i
$78$	−3.61712	+	4.97854i	−0.409559	+	0.563709i
$79$	4.18178	+	3.03824i	0.470487	+	0.341829i	0.797631	−	0.603146i	$-0.206086\pi$
$79$	4.18178	+	3.03824i	0.470487	+	0.341829i	−0.327144	+	0.944974i	$0.606086\pi$
$80$		0			0
$81$	3.28304	−	2.38527i	0.364782	−	0.265030i
$82$		−	1.86692i		−	0.206167i
$83$	7.25068	+	9.97971i	0.795866	+	1.09542i	0.993353	+	0.115110i	$0.0367220\pi$
$83$	7.25068	+	9.97971i	0.795866	+	1.09542i	−0.197487	+	0.980306i	$0.563278\pi$
$84$	−0.347249	−	1.06872i	−0.0378880	−	0.116607i
$85$		0			0
$86$	−0.506408	+	1.55856i	−0.0546074	+	0.168064i
$87$	−4.19302	+	1.36239i	−0.449539	+	0.146064i
$88$	−0.792578	+	0.257524i	−0.0844891	+	0.0274522i
$89$	2.16491	−	6.66290i	0.229480	−	0.706266i	−0.768326	−	0.640058i	$-0.778910\pi$
$89$	2.16491	−	6.66290i	0.229480	−	0.706266i	0.997806	−	0.0662073i	$-0.0210899\pi$
$90$		0			0
$91$	−1.17527	−	3.61712i	−0.123202	−	0.379178i
$92$	2.07500	+	2.85599i	0.216333	+	0.297757i
$93$		−	8.09363i		−	0.839270i
$94$	−0.674207	+	0.489840i	−0.0695391	+	0.0505231i
$95$		0			0
$96$	1.09089	+	0.792578i	0.111338	+	0.0808921i
$97$	−6.51864	+	8.97214i	−0.661867	+	0.910982i	−0.999541	−	0.0302807i	$-0.990360\pi$
$97$	−6.51864	+	8.97214i	−0.661867	+	0.910982i	0.337674	+	0.941263i	$0.390360\pi$
$98$	−5.99689	−	1.94851i	−0.605777	−	0.196829i
$99$	0.984855			0.0989816
$100$		0			0
$101$	12.7085			1.26454			0.632272	−	0.774746i	$-0.282122\pi$
$101$	12.7085			1.26454			0.632272	+	0.774746i	$0.282122\pi$
$102$	6.99097	+	2.27150i	0.692209	+	0.224912i
$103$	4.12340	−	5.67537i	0.406291	−	0.559211i	−0.556018	−	0.831170i	$-0.687672\pi$
$103$	4.12340	−	5.67537i	0.406291	−	0.559211i	0.962309	+	0.271959i	$0.0876715\pi$
$104$	3.69215	+	2.68250i	0.362045	+	0.263041i
$105$		0			0
$106$	−5.19972	+	3.77782i	−0.505042	+	0.366934i
$107$			10.7700i			1.04118i	0.853807	+	0.520589i	$0.174288\pi$
$107$			10.7700i			1.04118i	−0.853807	+	0.520589i	$0.825712\pi$
$108$	−3.31439	−	4.56186i	−0.318927	−	0.438965i
$109$	3.28655	+	10.1150i	0.314795	+	0.968838i	0.975839	+	0.218491i	$0.0701136\pi$
$109$	3.28655	+	10.1150i	0.314795	+	0.968838i	−0.661044	+	0.750347i	$0.729886\pi$
$110$		0			0
$111$	−3.04798	+	9.38071i	−0.289301	+	0.890378i
$112$	−0.792578	+	0.257524i	−0.0748916	+	0.0243337i
$113$	−1.65651	+	0.538232i	−0.155831	+	0.0506326i	−0.385894	−	0.922543i	$-0.626107\pi$
$113$	−1.65651	+	0.538232i	−0.155831	+	0.0506326i	0.230063	+	0.973176i	$0.426107\pi$
$114$	−3.60594	+	11.0979i	−0.337727	+	1.03942i
$115$		0			0
$116$	1.01037	+	3.10959i	0.0938103	+	0.288718i
$117$	−3.17013	−	4.36331i	−0.293078	−	0.403388i
$118$			13.5325i			1.24577i
$119$	−3.67537	+	2.67031i	−0.336921	+	0.244787i
$120$		0			0
$121$	8.33733	+	6.05742i	0.757939	+	0.550675i
$122$	−3.45865	+	4.76042i	−0.313131	+	0.430988i
$123$	−2.39417	−	0.777913i	−0.215875	−	0.0701420i
$124$	−6.00233			−0.539025
$125$		0			0
$126$	0.984855			0.0877378
$127$	−5.38938	−	1.75112i	−0.478230	−	0.155386i	0.0599756	−	0.998200i	$-0.480898\pi$
$127$	−5.38938	−	1.75112i	−0.478230	−	0.155386i	−0.538206	+	0.842813i	$0.680898\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	1.78772	+	1.29885i	0.157400	+	0.114358i
$130$		0			0
$131$	13.3281	−	9.68345i	1.16448	−	0.846047i	0.174145	−	0.984720i	$-0.444284\pi$
$131$	13.3281	−	9.68345i	1.16448	−	0.846047i	0.990338	+	0.138673i	$0.0442838\pi$
$132$			1.12372i			0.0978074i
$133$	−4.23903	−	5.83453i	−0.367571	−	0.505918i
$134$	−0.463496	−	1.42649i	−0.0400399	−	0.123230i
$135$		0			0
$136$	1.68458	−	5.18459i	0.144451	−	0.444575i
$137$	−2.75164	+	0.894062i	−0.235088	+	0.0763849i	−0.424192	−	0.905572i	$-0.639442\pi$
$137$	−2.75164	+	0.894062i	−0.235088	+	0.0763849i	0.189104	+	0.981957i	$0.439442\pi$
$138$	4.52718	−	1.47097i	0.385379	−	0.125217i
$139$	−1.54184	+	4.74531i	−0.130778	+	0.402492i	−0.994909	−	0.100774i	$-0.967868\pi$
$139$	−1.54184	+	4.74531i	−0.130778	+	0.402492i	0.864132	+	0.503266i	$0.167868\pi$
$140$		0			0
$141$	0.347249	+	1.06872i	0.0292437	+	0.0900027i
$142$	−1.38790	−	1.91027i	−0.116470	−	0.160307i
$143$			3.80327i			0.318045i
$144$	−0.956080	+	0.694633i	−0.0796733	+	0.0578861i
$145$		0			0
$146$	2.69403	+	1.95733i	0.222960	+	0.161990i
$147$	−4.99760	+	6.87861i	−0.412195	+	0.567338i
$148$	6.95685	+	2.26042i	0.571849	+	0.185805i
$149$	−2.00579			−0.164320			−0.0821602	−	0.996619i	$-0.526182\pi$
$149$	−2.00579			−0.164320			−0.0821602	+	0.996619i	$0.526182\pi$
$150$		0			0
$151$	−1.96971			−0.160293			−0.0801463	−	0.996783i	$-0.525539\pi$
$151$	−1.96971			−0.160293			−0.0801463	+	0.996783i	$0.525539\pi$
$152$	8.23036	+	2.67421i	0.667571	+	0.216907i
$153$	−3.78672	+	5.21197i	−0.306138	+	0.421363i
$154$	−0.561861	−	0.408216i	−0.0452760	−	0.0328950i
$155$		0			0
$156$	4.97854	−	3.61712i	0.398603	−	0.289602i
$157$		−	7.78467i		−	0.621284i	−0.950527	−	0.310642i	$-0.899456\pi$
$157$		−	7.78467i		−	0.621284i	0.950527	−	0.310642i	$-0.100544\pi$
$158$	−3.03824	−	4.18178i	−0.241709	−	0.332685i
$159$	2.67811	+	8.24237i	0.212388	+	0.653662i
$160$		0			0
$161$	−0.909110	+	2.79795i	−0.0716479	+	0.220510i
$162$	−3.85944	+	1.25401i	−0.303226	+	0.0985242i
$163$	−13.4060	+	4.35589i	−1.05004	+	0.341180i	−0.782685	−	0.622418i	$-0.786151\pi$
$163$	−13.4060	+	4.35589i	−1.05004	+	0.341180i	−0.267358	+	0.963597i	$0.586151\pi$
$164$	−0.576909	+	1.77554i	−0.0450490	+	0.138647i
$165$		0			0
$166$	−3.81191	−	11.7319i	−0.295862	−	0.910568i
$167$	−4.79406	−	6.59846i	−0.370976	−	0.510604i	0.582190	−	0.813053i	$-0.302196\pi$
$167$	−4.79406	−	6.59846i	−0.370976	−	0.510604i	−0.953166	+	0.302448i	$0.902196\pi$
$168$			1.12372i			0.0866970i
$169$	6.33280	−	4.60105i	0.487139	−	0.353927i
$170$		0			0
$171$	−8.27383	−	6.01129i	−0.632716	−	0.459695i
$172$	0.963245	−	1.32579i	0.0734467	−	0.101091i
$173$	−2.38084	−	0.773580i	−0.181012	−	0.0588142i	0.217109	−	0.976147i	$-0.430337\pi$
$173$	−2.38084	−	0.773580i	−0.181012	−	0.0588142i	−0.398120	+	0.917333i	$0.630337\pi$
$174$	4.40880			0.334230
$175$		0			0
$176$	0.833366			0.0628173
$177$	17.3544	+	5.63877i	1.30443	+	0.423836i
$178$	−4.11790	+	5.66780i	−0.308649	+	0.424820i
$179$	−16.2067	−	11.7749i	−1.21135	−	0.880096i	−0.215995	−	0.976394i	$-0.569300\pi$
$179$	−16.2067	−	11.7749i	−1.21135	−	0.880096i	−0.995352	+	0.0962986i	$0.969300\pi$
$180$		0			0
$181$	−6.37367	+	4.63074i	−0.473751	+	0.344201i	−0.798902	−	0.601462i	$-0.794585\pi$
$181$	−6.37367	+	4.63074i	−0.473751	+	0.344201i	0.325150	+	0.945662i	$0.394585\pi$
$182$			3.80327i			0.281917i
$183$	4.66369	+	6.41901i	0.344750	+	0.474507i
$184$	−1.09089	−	3.35741i	−0.0804215	−	0.247512i
$185$		0			0
$186$	−2.50107	+	7.69750i	−0.183387	+	0.564408i
$187$	4.32066	−	1.40387i	0.315958	−	0.102661i
$188$	0.792578	−	0.257524i	0.0578047	−	0.0187819i
$189$	1.45212	−	4.46916i	0.105626	−	0.325084i
$190$		0			0
$191$	−1.63013	−	5.01702i	−0.117952	−	0.363019i	0.874599	−	0.484847i	$-0.161125\pi$
$191$	−1.63013	−	5.01702i	−0.117952	−	0.363019i	−0.992551	+	0.121827i	$0.961125\pi$
$192$	−0.792578	−	1.09089i	−0.0571994	−	0.0787282i
$193$		−	13.4461i		−	0.967873i	−0.875103	−	0.483937i	$-0.839207\pi$
$193$		−	13.4461i		−	0.967873i	0.875103	−	0.483937i	$-0.160793\pi$
$194$	8.97214	−	6.51864i	0.644162	−	0.468011i
$195$		0			0
$196$	5.10126	+	3.70628i	0.364376	+	0.264734i
$197$	3.19672	−	4.39991i	0.227757	−	0.313480i	−0.679810	−	0.733388i	$-0.737938\pi$
$197$	3.19672	−	4.39991i	0.227757	−	0.313480i	0.907567	+	0.419908i	$0.137938\pi$
$198$	−0.936652	−	0.304337i	−0.0665650	−	0.0216283i
$199$	17.4090			1.23409			0.617045	−	0.786927i	$-0.288329\pi$
$199$	17.4090			1.23409			0.617045	+	0.786927i	$0.288329\pi$
$200$		0			0
$201$	−2.02249			−0.142655
$202$	−12.0865	−	3.92715i	−0.850404	−	0.276313i
$203$	−1.60159	+	2.20440i	−0.112410	+	0.154719i
$204$	−5.94688	−	4.32066i	−0.416365	−	0.302507i
$205$		0			0
$206$	−5.67537	+	4.12340i	−0.395422	+	0.287291i
$207$			4.17191i			0.289968i
$208$	−2.68250	−	3.69215i	−0.185998	−	0.256004i
$209$	2.22859	+	6.85890i	0.154155	+	0.474440i
$210$		0			0
$211$	−0.0834142	+	0.256723i	−0.00574247	+	0.0176735i	−0.953887	−	0.300167i	$-0.902958\pi$
$211$	−0.0834142	+	0.256723i	−0.00574247	+	0.0176735i	0.948144	+	0.317840i	$0.102958\pi$
$212$	6.11264	−	1.98612i	0.419818	−	0.136407i
$213$	−3.02808	+	0.983884i	−0.207481	+	0.0674146i
$214$	3.32812	−	10.2429i	0.227506	−	0.700191i
$215$		0			0
$216$	1.74248	+	5.36279i	0.118560	+	0.364892i
$217$	−2.94018	−	4.04681i	−0.199593	−	0.274716i
$218$		−	10.6355i		−	0.720328i
$219$	3.63267	−	2.63929i	0.245473	−	0.178347i
$220$		0			0
$221$	−20.1274	−	14.6234i	−1.35391	−	0.983676i
$222$	5.79760	−	7.97971i	0.389109	−	0.535563i
$223$	22.0372	+	7.16032i	1.47572	+	0.479491i	0.932831	−	0.360313i	$-0.117330\pi$
$223$	22.0372	+	7.16032i	1.47572	+	0.479491i	0.542889	+	0.839804i	$0.317330\pi$
$224$	0.833366			0.0556816
$225$		0			0
$226$	1.74176			0.115860
$227$	0.240287	+	0.0780741i	0.0159484	+	0.00518196i	0.316980	−	0.948432i	$-0.397331\pi$
$227$	0.240287	+	0.0780741i	0.0159484	+	0.00518196i	−0.301032	+	0.953614i	$0.597331\pi$
$228$	6.85890	−	9.44047i	0.454242	−	0.625210i
$229$	−17.0625	−	12.3966i	−1.12752	−	0.819191i	−0.142187	−	0.989840i	$-0.545414\pi$
$229$	−17.0625	−	12.3966i	−1.12752	−	0.819191i	−0.985332	+	0.170649i	$0.945414\pi$
$230$		0			0
$231$	−0.757621	+	0.550444i	−0.0498478	+	0.0362166i
$232$		−	3.26962i		−	0.214661i
$233$	8.58610	+	11.8178i	0.562494	+	0.774207i	0.991641	−	0.129028i	$-0.0411857\pi$
$233$	8.58610	+	11.8178i	0.562494	+	0.774207i	−0.429147	+	0.903235i	$0.641186\pi$
$234$	1.66663	+	5.12937i	0.108951	+	0.335318i
$235$		0			0
$236$	4.18178	−	12.8702i	0.272211	−	0.837778i
$237$	−6.62877	+	2.15382i	−0.430585	+	0.139906i
$238$	4.32066	−	1.40387i	0.280067	−	0.0909992i
$239$	−1.79793	+	5.53346i	−0.116298	+	0.357930i	−0.992216	−	0.124532i	$-0.960257\pi$
$239$	−1.79793	+	5.53346i	−0.116298	+	0.357930i	0.875917	+	0.482461i	$0.160257\pi$
$240$		0			0
$241$	4.24254	+	13.0572i	0.273286	+	0.841087i	0.989668	+	0.143379i	$0.0457968\pi$
$241$	4.24254	+	13.0572i	0.273286	+	0.841087i	−0.716382	+	0.697708i	$0.754203\pi$
$242$	−6.05742	−	8.33733i	−0.389386	−	0.535944i
$243$		−	11.4444i		−	0.734157i
$244$	4.76042	−	3.45865i	0.304754	−	0.221417i
$245$		0			0
$246$	2.03660	+	1.47968i	0.129849	+	0.0943408i
$247$	23.2141	−	31.9515i	1.47708	−	2.03303i
$248$	5.70855	+	1.85482i	0.362494	+	0.117781i
$249$	−16.6335			−1.05410
$250$		0			0
$251$	−15.8938			−1.00320			−0.501602	−	0.865098i	$-0.667256\pi$
$251$	−15.8938			−1.00320			−0.501602	+	0.865098i	$0.667256\pi$
$252$	−0.936652	−	0.304337i	−0.0590036	−	0.0191714i
$253$	1.72923	−	2.38008i	0.108716	−	0.149634i
$254$	4.58448	+	3.33082i	0.287656	+	0.208994i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$			2.31253i			0.144252i	0.997396	+	0.0721259i	$0.0229783\pi$
$257$			2.31253i			0.144252i	−0.997396	+	0.0721259i	$0.977022\pi$
$258$	−1.29885	−	1.78772i	−0.0808631	−	0.111298i
$259$	1.88375	+	5.79760i	0.117051	+	0.360245i
$260$		0			0
$261$	−1.19403	+	3.67485i	−0.0739088	+	0.227468i
$262$	−15.6681	+	5.09089i	−0.967981	+	0.314516i
$263$	20.4090	−	6.63129i	1.25847	−	0.408903i	0.397524	−	0.917592i	$-0.369870\pi$
$263$	20.4090	−	6.63129i	1.25847	−	0.408903i	0.860951	+	0.508689i	$0.169870\pi$
$264$	0.347249	−	1.06872i	0.0213717	−	0.0657754i
$265$		0			0
$266$	2.22859	+	6.85890i	0.136644	+	0.420546i
$267$	5.55263	+	7.64254i	0.339815	+	0.467716i
$268$			1.49990i			0.0916212i
$269$	17.3020	−	12.5706i	1.05492	−	0.766445i	0.0817787	−	0.996651i	$-0.473940\pi$
$269$	17.3020	−	12.5706i	1.05492	−	0.766445i	0.973142	+	0.230206i	$0.0739399\pi$
$270$		0			0
$271$	21.1400	+	15.3591i	1.28417	+	0.933001i	0.999670	−	0.0256766i	$-0.00817402\pi$
$271$	21.1400	+	15.3591i	1.28417	+	0.933001i	0.284495	+	0.958677i	$0.408174\pi$
$272$	−3.20425	+	4.41027i	−0.194286	+	0.267412i
$273$	4.87738	+	1.58476i	0.295192	+	0.0959139i
$274$	2.89324			0.174787
$275$		0			0
$276$	−4.76016			−0.286528
$277$	17.7342	+	5.76220i	1.06555	+	0.346217i	0.788752	−	0.614712i	$-0.210728\pi$
$277$	17.7342	+	5.76220i	1.06555	+	0.346217i	0.276795	+	0.960929i	$0.410728\pi$
$278$	2.93276	−	4.03660i	0.175895	−	0.242099i
$279$	−5.73871	−	4.16941i	−0.343567	−	0.249616i
$280$		0			0
$281$	−11.9886	+	8.71023i	−0.715180	+	0.519609i	−0.884841	−	0.465894i	$-0.845733\pi$
$281$	−11.9886	+	8.71023i	−0.715180	+	0.519609i	0.169661	+	0.985503i	$0.445733\pi$
$282$		−	1.12372i		−	0.0669167i
$283$	−9.27523	−	12.7663i	−0.551355	−	0.758875i	0.438840	−	0.898565i	$-0.355389\pi$
$283$	−9.27523	−	12.7663i	−0.551355	−	0.758875i	−0.990195	+	0.139690i	$0.955389\pi$
$284$	0.729660	+	2.24566i	0.0432974	+	0.133256i
$285$		0			0
$286$	1.17527	−	3.61712i	0.0694955	−	0.213885i
$287$	−1.47968	+	0.480776i	−0.0873426	+	0.0283793i
$288$	1.12394	−	0.365190i	0.0662288	−	0.0215190i
$289$	−3.93000	+	12.0953i	−0.231177	+	0.711489i
$290$		0			0
$291$	−4.62108	−	14.2222i	−0.270893	−	0.833722i
$292$	−1.95733	−	2.69403i	−0.114544	−	0.157656i
$293$			18.4003i			1.07496i	0.843277	+	0.537479i	$0.180623\pi$
$293$			18.4003i			1.07496i	−0.843277	+	0.537479i	$0.819377\pi$
$294$	6.87861	−	4.99760i	0.401169	−	0.291466i
$295$		0			0
$296$	−5.91785	−	4.29957i	−0.343968	−	0.249907i
$297$	−2.76210	+	3.80170i	−0.160273	+	0.220597i
$298$	1.90761	+	0.619822i	0.110505	+	0.0359053i
$299$	−16.1109			−0.931718
$300$		0			0
$301$	1.36569			0.0787173
$302$	1.87330	+	0.608674i	0.107797	+	0.0350252i
$303$	−10.0725	+	13.8636i	−0.578649	+	0.796443i
$304$	−7.00116	−	5.08664i	−0.401544	−	0.291739i
$305$		0			0
$306$	5.21197	−	3.78672i	0.297949	−	0.216472i
$307$			34.1179i			1.94721i	0.228237	+	0.973606i	$0.426704\pi$
$307$			34.1179i			1.94721i	−0.228237	+	0.973606i	$0.573296\pi$
$308$	0.408216	+	0.561861i	0.0232603	+	0.0320150i
$309$	2.92309	+	8.99635i	0.166289	+	0.511784i
$310$		0			0
$311$	−4.02893	+	12.3998i	−0.228460	+	0.703127i	0.769462	+	0.638692i	$0.220524\pi$
$311$	−4.02893	+	12.3998i	−0.228460	+	0.703127i	−0.997922	+	0.0644345i	$0.979476\pi$
$312$	−5.85263	+	1.90163i	−0.331340	+	0.107659i
$313$	−3.31217	+	1.07619i	−0.187215	+	0.0608298i	−0.401124	−	0.916024i	$-0.631380\pi$
$313$	−3.31217	+	1.07619i	−0.187215	+	0.0608298i	0.213909	+	0.976854i	$0.431380\pi$
$314$	−2.40559	+	7.40366i	−0.135756	+	0.417813i
$315$		0			0
$316$	1.59730	+	4.91598i	0.0898550	+	0.276545i
$317$	2.83333	+	3.89975i	0.159136	+	0.219032i	0.881138	−	0.472859i	$-0.156778\pi$
$317$	2.83333	+	3.89975i	0.159136	+	0.219032i	−0.722002	+	0.691891i	$0.756778\pi$
$318$		−	8.66654i		−	0.485995i
$319$	2.20440	−	1.60159i	0.123423	−	0.0896719i
$320$		0			0
$321$	−11.7489	−	8.53609i	−0.655761	−	0.476438i
$322$	1.72923	−	2.38008i	0.0963662	−	0.132637i
$323$	−44.8670	−	14.5782i	−2.49647	−	0.811151i
$324$	4.05806			0.225448
$325$		0			0
$326$	14.0960			0.780703
$327$	−13.6392	−	4.43163i	−0.754248	−	0.245070i
$328$	1.09735	−	1.51037i	0.0605908	−	0.0833961i
$329$	0.561861	+	0.408216i	0.0309764	+	0.0225057i
$330$		0			0
$331$	−6.92796	+	5.03346i	−0.380795	+	0.276664i	−0.761673	−	0.647961i	$-0.775622\pi$
$331$	−6.92796	+	5.03346i	−0.380795	+	0.276664i	0.380878	+	0.924625i	$0.375622\pi$
$332$			12.3356i			0.677004i
$333$	5.08114	+	6.99359i	0.278445	+	0.383246i
$334$	2.52039	+	7.75696i	0.137910	+	0.424442i
$335$		0			0
$336$	0.347249	−	1.06872i	0.0189440	−	0.0583036i
$337$	−13.9531	+	4.53365i	−0.760076	+	0.246964i	−0.663311	−	0.748344i	$-0.730849\pi$
$337$	−13.9531	+	4.53365i	−0.760076	+	0.246964i	−0.0967646	+	0.995307i	$0.530849\pi$
$338$	−7.44466	+	2.41892i	−0.404936	+	0.131572i
$339$	0.725760	−	2.23366i	0.0394179	−	0.121316i
$340$		0			0
$341$	1.54574	+	4.75731i	0.0837068	+	0.257623i
$342$	6.01129	+	8.27383i	0.325053	+	0.447398i
$343$			11.0883i			0.598715i
$344$	−1.32579	+	0.963245i	−0.0714820	+	0.0519347i
$345$		0			0
$346$	2.02526	+	1.47144i	0.108879	+	0.0791049i
$347$	13.5115	−	18.5970i	0.725337	−	0.998340i	−0.273993	−	0.961732i	$-0.588344\pi$
$347$	13.5115	−	18.5970i	0.725337	−	0.998340i	0.999330	−	0.0366088i	$-0.0116555\pi$
$348$	−4.19302	−	1.36239i	−0.224769	−	0.0730320i
$349$	−3.55023			−0.190040			−0.0950198	−	0.995475i	$-0.530291\pi$
$349$	−3.55023			−0.190040			−0.0950198	+	0.995475i	$0.530291\pi$
$350$		0			0
$351$	25.7339			1.37357
$352$	−0.792578	−	0.257524i	−0.0422445	−	0.0137261i
$353$	−3.31576	+	4.56375i	−0.176480	+	0.242904i	−0.888089	−	0.459672i	$-0.847967\pi$
$353$	−3.31576	+	4.56375i	−0.176480	+	0.242904i	0.711609	+	0.702576i	$0.247967\pi$
$354$	−14.7625	−	10.7256i	−0.784618	−	0.570058i
$355$		0			0
$356$	5.66780	−	4.11790i	0.300393	−	0.218248i
$357$		−	6.12586i		−	0.324215i
$358$	11.7749	+	16.2067i	0.622322	+	0.856552i
$359$	5.22442	+	16.0791i	0.275734	+	0.848623i	0.989024	+	0.147754i	$0.0472043\pi$
$359$	5.22442	+	16.0791i	0.275734	+	0.848623i	−0.713290	+	0.700869i	$0.752796\pi$
$360$		0			0
$361$	17.2710	−	53.1548i	0.909002	−	2.79762i
$362$	7.49270	−	2.43453i	0.393808	−	0.127956i
$363$	−13.2160	+	4.29413i	−0.693658	+	0.225383i
$364$	1.17527	−	3.61712i	0.0616011	−	0.189589i
$365$		0			0
$366$	−2.45184	−	7.54600i	−0.128160	−	0.394436i
$367$	−7.41393	−	10.2044i	−0.387004	−	0.532665i	0.570419	−	0.821354i	$-0.306781\pi$
$367$	−7.41393	−	10.2044i	−0.387004	−	0.532665i	−0.957423	+	0.288688i	$0.906781\pi$
$368$			3.53019i			0.184024i
$369$	−1.78492	+	1.29682i	−0.0929193	+	0.0675099i
$370$		0			0
$371$	4.33327	+	3.14830i	0.224972	+	0.163452i
$372$	4.75731	−	6.54788i	0.246655	−	0.339492i
$373$	12.6011	+	4.09435i	0.652460	+	0.211997i	0.616499	−	0.787356i	$-0.288551\pi$
$373$	12.6011	+	4.09435i	0.652460	+	0.211997i	0.0359616	+	0.999353i	$0.488551\pi$
$374$	−4.54301			−0.234913
$375$		0			0
$376$	−0.833366			−0.0429776
$377$	−14.1914	−	4.61106i	−0.730894	−	0.237482i
$378$	−2.76210	+	3.80170i	−0.142067	+	0.195538i
$379$	18.0702	+	13.1288i	0.928203	+	0.674379i	0.945552	−	0.325470i	$-0.105523\pi$
$379$	18.0702	+	13.1288i	0.928203	+	0.674379i	−0.0173488	+	0.999849i	$0.505523\pi$
$380$		0			0
$381$	6.18178	−	4.49133i	0.316702	−	0.230098i
$382$			5.27521i			0.269903i
$383$	−14.3143	−	19.7019i	−0.731425	−	1.00672i	−0.999066	−	0.0432012i	$-0.986244\pi$
$383$	−14.3143	−	19.7019i	−0.731425	−	1.00672i	0.267642	−	0.963519i	$-0.413756\pi$
$384$	0.416683	+	1.28242i	0.0212638	+	0.0654431i
$385$		0			0
$386$	−4.15508	+	12.7880i	−0.211488	+	0.650893i
$387$	1.84188	−	0.598463i	0.0936279	−	0.0304216i
$388$	−10.5474	+	3.42705i	−0.535462	+	0.173982i
$389$	−9.30500	+	28.6378i	−0.471782	+	1.45200i	0.378467	+	0.925615i	$0.376452\pi$
$389$	−9.30500	+	28.6378i	−0.471782	+	1.45200i	−0.850249	+	0.526381i	$0.823548\pi$
$390$		0			0
$391$	5.94688	+	18.3026i	0.300746	+	0.925602i
$392$	−3.70628	−	5.10126i	−0.187195	−	0.257652i
$393$			22.2144i			1.12057i
$394$	−4.39991	+	3.19672i	−0.221664	+	0.161048i
$395$		0			0
$396$	0.796764	+	0.578883i	0.0400389	+	0.0290900i
$397$	−20.7902	+	28.6152i	−1.04343	+	1.43616i	−0.149059	+	0.988828i	$0.547624\pi$
$397$	−20.7902	+	28.6152i	−1.04343	+	1.43616i	−0.894370	+	0.447328i	$0.852376\pi$
$398$	−16.5569	−	5.37968i	−0.829924	−	0.269659i
$399$	9.72459			0.486839
$400$		0			0
$401$	−5.66794			−0.283043			−0.141522	−	0.989935i	$-0.545199\pi$
$401$	−5.66794			−0.283043			−0.141522	+	0.989935i	$0.545199\pi$
$402$	1.92350	+	0.624984i	0.0959356	+	0.0311714i
$403$	16.1013	−	22.1615i	0.802061	−	1.10394i
$404$	10.2814	+	7.46988i	0.511519	+	0.371640i
$405$		0			0
$406$	2.20440	−	1.60159i	0.109403	−	0.0794856i
$407$		−	6.09595i		−	0.302165i
$408$	4.32066	+	5.94688i	0.213904	+	0.294414i
$409$	−5.98493	−	18.4197i	−0.295936	−	0.910797i	−0.982906	−	0.184111i	$-0.941060\pi$
$409$	−5.98493	−	18.4197i	−0.295936	−	0.910797i	0.686970	−	0.726686i	$-0.258940\pi$
$410$		0			0
$411$	1.20557	−	3.71035i	0.0594662	−	0.183018i
$412$	6.67180	−	2.16780i	0.328696	−	0.106800i
$413$	10.7256	−	3.48495i	0.527771	−	0.171483i
$414$	1.28919	−	3.96772i	0.0633603	−	0.195003i
$415$		0			0
$416$	1.41027	+	4.34038i	0.0691444	+	0.212805i
$417$	−3.95458	−	5.44301i	−0.193657	−	0.266545i
$418$		−	7.21188i		−	0.352744i
$419$	18.5906	−	13.5068i	0.908209	−	0.659853i	−0.0323520	−	0.999477i	$-0.510300\pi$
$419$	18.5906	−	13.5068i	0.908209	−	0.659853i	0.940561	+	0.339624i	$0.110300\pi$
$420$		0			0
$421$	8.19306	+	5.95261i	0.399305	+	0.290112i	0.769258	−	0.638938i	$-0.220626\pi$
$421$	8.19306	+	5.95261i	0.399305	+	0.290112i	−0.369953	+	0.929051i	$0.620626\pi$
$422$	0.158663	−	0.218381i	0.00772361	−	0.0106306i
$423$	0.936652	+	0.304337i	0.0455416	+	0.0147974i
$424$	−6.42721			−0.312133
$425$		0			0
$426$	3.18392			0.154261
$427$	4.66369	+	1.51532i	0.225692	+	0.0733316i
$428$	−6.33047	+	8.71314i	−0.305995	+	0.421165i
$429$	−4.14895	−	3.01439i	−0.200313	−	0.145536i
$430$		0			0
$431$	23.0589	−	16.7533i	1.11071	−	0.806978i	0.127935	−	0.991783i	$-0.459165\pi$
$431$	23.0589	−	16.7533i	1.11071	−	0.806978i	0.982775	+	0.184804i	$0.0591651\pi$
$432$		−	5.63877i		−	0.271295i
$433$	−9.33971	−	12.8550i	−0.448838	−	0.617772i	0.523309	−	0.852143i	$-0.324697\pi$
$433$	−9.33971	−	12.8550i	−0.448838	−	0.617772i	−0.972147	+	0.234370i	$0.924697\pi$
$434$	1.54574	+	4.75731i	0.0741981	+	0.228358i
$435$		0			0
$436$	−3.28655	+	10.1150i	−0.157397	+	0.484419i
$437$	−29.0548	+	9.44047i	−1.38988	+	0.451599i
$438$	−4.27046	+	1.38756i	−0.204051	+	0.0663000i
$439$	−0.910550	+	2.80238i	−0.0434582	+	0.133751i	−0.970431	−	0.241377i	$-0.922401\pi$
$439$	−0.910550	+	2.80238i	−0.0434582	+	0.133751i	0.926973	+	0.375127i	$0.122401\pi$
$440$		0			0
$441$	2.30271	+	7.08700i	0.109653	+	0.337476i
$442$	14.6234	+	20.1274i	0.695564	+	0.957362i
$443$		−	5.27327i		−	0.250541i	−0.992123	−	0.125270i	$-0.960020\pi$
$443$		−	5.27327i		−	0.250541i	0.992123	−	0.125270i	$-0.0399798\pi$
$444$	−7.97971	+	5.79760i	−0.378700	+	0.275142i
$445$		0			0
$446$	−18.7460	−	13.6197i	−0.887647	−	0.644914i
$447$	1.58974	−	2.18809i	0.0751922	−	0.103493i
$448$	−0.792578	−	0.257524i	−0.0374458	−	0.0121669i
$449$	6.81659			0.321695			0.160847	−	0.986979i	$-0.448577\pi$
$449$	6.81659			0.321695			0.160847	+	0.986979i	$0.448577\pi$
$450$		0			0
$451$	1.55583			0.0732609
$452$	−1.65651	−	0.538232i	−0.0779156	−	0.0253163i
$453$	1.56115	−	2.14874i	0.0733491	−	0.100956i
$454$	−0.204401	−	0.148506i	−0.00959300	−	0.00696972i
$455$		0			0
$456$	−9.44047	+	6.85890i	−0.442090	+	0.321198i
$457$		−	4.17712i		−	0.195397i	−0.995216	−	0.0976987i	$-0.968852\pi$
$457$		−	4.17712i		−	0.195397i	0.995216	−	0.0976987i	$-0.0311482\pi$
$458$	12.3966	+	17.0625i	0.579255	+	0.797277i
$459$	−9.49893	−	29.2347i	−0.443372	−	1.36456i
$460$		0			0
$461$	−11.5678	+	35.6020i	−0.538766	+	1.65815i	0.196601	+	0.980484i	$0.437010\pi$
$461$	−11.5678	+	35.6020i	−0.538766	+	1.65815i	−0.735367	+	0.677669i	$0.762990\pi$
$462$	0.890637	−	0.289386i	0.0414362	−	0.0134634i
$463$	13.1995	−	4.28879i	0.613434	−	0.199317i	0.0142111	−	0.999899i	$-0.495476\pi$
$463$	13.1995	−	4.28879i	0.613434	−	0.199317i	0.599223	+	0.800582i	$0.295476\pi$
$464$	−1.01037	+	3.10959i	−0.0469052	+	0.144359i
$465$		0			0
$466$	−4.51398	−	13.8926i	−0.209106	−	0.643562i
$467$	8.14705	+	11.2134i	0.377000	+	0.518896i	0.954787	−	0.297292i	$-0.0960833\pi$
$467$	8.14705	+	11.2134i	0.377000	+	0.518896i	−0.577786	+	0.816188i	$0.696083\pi$
$468$		−	5.39334i		−	0.249307i
$469$	−1.01125	+	0.734713i	−0.0466950	+	0.0339259i
$470$		0			0
$471$	8.49222	+	6.16996i	0.391301	+	0.284297i
$472$	−7.95422	+	10.9480i	−0.366123	+	0.503924i
$473$	−1.29885	−	0.422023i	−0.0597213	−	0.0194046i
$474$	6.96990			0.320138
$475$		0			0
$476$	−4.54301			−0.208228
$477$	7.22379	+	2.34715i	0.330755	+	0.107469i
$478$	3.41986	−	4.70704i	0.156421	−	0.215295i
$479$	23.2976	+	16.9267i	1.06450	+	0.773401i	0.974915	−	0.222578i	$-0.0714473\pi$
$479$	23.2976	+	16.9267i	1.06450	+	0.773401i	0.0895806	+	0.995980i	$0.471447\pi$
$480$		0			0
$481$	−27.0076	+	19.6221i	−1.23144	+	0.894692i
$482$		−	13.7291i		−	0.625345i
$483$	−2.33172	−	3.20933i	−0.106097	−	0.146030i
$484$	3.18458	+	9.80111i	0.144753	+	0.445505i
$485$		0			0
$486$	−3.53650	+	10.8842i	−0.160419	+	0.493719i
$487$	37.0449	−	12.0366i	1.67866	−	0.545430i	0.694011	−	0.719964i	$-0.255842\pi$
$487$	37.0449	−	12.0366i	1.67866	−	0.545430i	0.984651	+	0.174534i	$0.0558418\pi$
$488$	−5.59621	+	1.81832i	−0.253328	+	0.0823114i
$489$	5.87354	−	18.0769i	0.265611	−	0.817466i
$490$		0			0
$491$	−7.26403	−	22.3564i	−0.327821	−	1.00893i	−0.970151	−	0.242501i	$-0.922032\pi$
$491$	−7.26403	−	22.3564i	−0.327821	−	1.00893i	0.642330	−	0.766428i	$-0.277968\pi$
$492$	−1.47968	−	2.03660i	−0.0667090	−	0.0918171i
$493$			17.8240i			0.802753i
$494$	−31.9515	+	23.2141i	−1.43757	+	1.04445i
$495$		0			0
$496$	−4.85599	−	3.52808i	−0.218040	−	0.158416i
$497$	−1.15662	+	1.59196i	−0.0518817	+	0.0714091i
$498$	15.8194	+	5.14003i	0.708884	+	0.230330i
$499$	−28.2651			−1.26532			−0.632660	−	0.774430i	$-0.718037\pi$
$499$	−28.2651			−1.26532			−0.632660	+	0.774430i	$0.718037\pi$
$500$		0			0
$501$	10.9979			0.491348
$502$	15.1159	+	4.91144i	0.674654	+	0.219208i
$503$	4.05821	−	5.58565i	0.180947	−	0.249052i	−0.708903	−	0.705306i	$-0.750809\pi$
$503$	4.05821	−	5.58565i	0.180947	−	0.249052i	0.889849	+	0.456255i	$0.150809\pi$
$504$	0.796764	+	0.578883i	0.0354907	+	0.0257855i
$505$		0			0
$506$	−2.38008	+	1.72923i	−0.105808	+	0.0768737i
$507$			10.5551i			0.468768i
$508$	−3.33082	−	4.58448i	−0.147781	−	0.203403i
$509$	−10.3641	−	31.8975i	−0.459382	−	1.41383i	−0.865913	−	0.500195i	$-0.833262\pi$
$509$	−10.3641	−	31.8975i	−0.459382	−	1.41383i	0.406531	−	0.913637i	$-0.366738\pi$
$510$		0			0
$511$	0.857557	−	2.63929i	0.0379361	−	0.116755i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	46.4091	−	15.0792i	2.04901	−	0.665765i
$514$	0.714612	−	2.19935i	0.0315202	−	0.0970091i
$515$		0			0
$516$	0.682847	+	2.10159i	0.0300607	+	0.0925173i
$517$	−0.408216	−	0.561861i	−0.0179533	−	0.0247106i
$518$		−	6.09595i		−	0.267841i
$519$	2.73089	−	1.98411i	0.119873	−	0.0870926i
$520$		0			0
$521$	−0.997861	−	0.724989i	−0.0437171	−	0.0317623i	0.565712	−	0.824603i	$-0.308601\pi$
$521$	−0.997861	−	0.724989i	−0.0437171	−	0.0317623i	−0.609429	+	0.792840i	$0.708601\pi$
$522$	2.27118	−	3.12602i	0.0994071	−	0.136822i
$523$	21.9033	+	7.11681i	0.957764	+	0.311196i	0.745867	−	0.666095i	$-0.232036\pi$
$523$	21.9033	+	7.11681i	0.957764	+	0.311196i	0.211898	+	0.977292i	$0.432036\pi$
$524$	16.4745			0.719690
$525$		0			0
$526$	−21.4593			−0.935671
$527$	−31.1196	−	10.1114i	−1.35559	−	0.440458i
$528$	−0.660507	+	0.909110i	−0.0287449	+	0.0395639i
$529$	−8.52520	−	6.19392i	−0.370661	−	0.269301i
$530$		0			0
$531$	12.9382	−	9.40013i	0.561469	−	0.407931i
$532$		−	7.21188i		−	0.312674i
$533$	−5.00801	−	6.89294i	−0.216921	−	0.298566i
$534$	−2.91919	−	8.98434i	−0.126326	−	0.388791i
$535$		0			0
$536$	0.463496	−	1.42649i	0.0200200	−	0.0616151i
$537$	25.6902	−	8.34725i	1.10861	−	0.360210i
$538$	−20.3397	+	6.60877i	−0.876907	+	0.284924i
$539$	1.62382	−	4.99760i	0.0699428	−	0.215262i
$540$		0			0
$541$	−8.27238	−	25.4598i	−0.355657	−	1.09460i	−0.955627	−	0.294578i	$-0.904821\pi$
$541$	−8.27238	−	25.4598i	−0.355657	−	1.09460i	0.599970	−	0.800023i	$-0.295179\pi$
$542$	−15.3591	−	21.1400i	−0.659731	−	0.908042i
$543$		−	10.6232i		−	0.455885i
$544$	4.41027	−	3.20425i	0.189089	−	0.137381i
$545$		0			0
$546$	−4.14895	−	3.01439i	−0.177559	−	0.129004i
$547$	−3.77763	+	5.19947i	−0.161520	+	0.222313i	−0.882104	−	0.471054i	$-0.843874\pi$
$547$	−3.77763	+	5.19947i	−0.161520	+	0.222313i	0.720584	+	0.693367i	$0.243874\pi$
$548$	−2.75164	−	0.894062i	−0.117544	−	0.0381924i
$549$	6.95383			0.296782
$550$		0			0
$551$	−28.2950			−1.20541
$552$	4.52718	+	1.47097i	0.192690	+	0.0626087i
$553$	−2.53197	+	3.48495i	−0.107670	+	0.148195i
$554$	−15.0856	−	10.9604i	−0.640928	−	0.465661i
$555$		0			0
$556$	−4.03660	+	2.93276i	−0.171190	+	0.124377i
$557$		−	44.0843i		−	1.86791i	−0.357386	−	0.933957i	$-0.616332\pi$
$557$		−	44.0843i		−	1.86791i	0.357386	−	0.933957i	$-0.383668\pi$
$558$	4.16941	+	5.73871i	0.176505	+	0.242939i
$559$	2.31112	+	7.11289i	0.0977498	+	0.300843i
$560$		0			0
$561$	−1.89299	+	5.82604i	−0.0799223	+	0.245975i
$562$	14.0934	−	4.57924i	0.594496	−	0.193164i
$563$	−19.0952	+	6.20440i	−0.804766	+	0.261484i	−0.682379	−	0.730998i	$-0.739055\pi$
$563$	−19.0952	+	6.20440i	−0.804766	+	0.261484i	−0.122387	+	0.992483i	$0.539055\pi$
$564$	−0.347249	+	1.06872i	−0.0146218	+	0.0450014i
$565$		0			0
$566$	4.87628	+	15.0076i	0.204965	+	0.630818i
$567$	1.98780	+	2.73597i	0.0834797	+	0.114900i
$568$		−	2.36123i		−	0.0990750i
$569$	−24.2170	+	17.5947i	−1.01523	+	0.737609i	−0.965300	−	0.261144i	$-0.915900\pi$
$569$	−24.2170	+	17.5947i	−1.01523	+	0.737609i	−0.0499312	+	0.998753i	$0.515900\pi$
$570$		0			0
$571$	11.5201	+	8.36985i	0.482102	+	0.350267i	0.802139	−	0.597138i	$-0.203695\pi$
$571$	11.5201	+	8.36985i	0.482102	+	0.350267i	−0.320037	+	0.947405i	$0.603695\pi$
$572$	−2.23551	+	3.07691i	−0.0934712	+	0.128652i
$573$	6.76503	+	2.19809i	0.282613	+	0.0918265i
$574$	1.55583			0.0649389
$575$		0			0
$576$	−1.18178			−0.0492408
$577$	17.3177	+	5.62687i	0.720946	+	0.234250i	0.646433	−	0.762970i	$-0.276260\pi$
$577$	17.3177	+	5.62687i	0.720946	+	0.234250i	0.0745128	+	0.997220i	$0.476260\pi$
$578$	7.47531	−	10.2889i	0.310932	−	0.427961i
$579$	14.6682	+	10.6571i	0.609591	+	0.442894i
$580$		0			0
$581$	−8.31675	+	6.04247i	−0.345037	+	0.250684i
$582$			14.9541i			0.619869i
$583$	−3.14830	−	4.33327i	−0.130389	−	0.179466i
$584$	1.02903	+	3.16703i	0.0425815	+	0.131052i
$585$		0			0
$586$	5.68601	−	17.4998i	0.234887	−	0.722908i
$587$	4.91155	−	1.59586i	0.202721	−	0.0658681i	−0.205896	−	0.978574i	$-0.566011\pi$
$587$	4.91155	−	1.59586i	0.202721	−	0.0658681i	0.408618	+	0.912706i	$0.366011\pi$
$588$	−8.08629	+	2.62739i	−0.333473	+	0.108352i
$589$	16.0515	−	49.4014i	0.661389	−	2.03555i
$590$		0			0
$591$	2.26616	+	6.97454i	0.0932176	+	0.286894i
$592$	4.29957	+	5.91785i	0.176711	+	0.243222i
$593$		−	35.6286i		−	1.46309i	−0.681793	−	0.731546i	$-0.738799\pi$
$593$		−	35.6286i		−	1.46309i	0.681793	−	0.731546i	$-0.261201\pi$
$594$	3.80170	−	2.76210i	0.155986	−	0.113330i
$595$		0			0
$596$	−1.62271	−	1.17897i	−0.0664690	−	0.0482925i
$597$	−13.7980	+	18.9913i	−0.564714	+	0.777262i
$598$	15.3224	+	4.97854i	0.626579	+	0.203588i
$599$	31.8284			1.30047			0.650236	−	0.759733i	$-0.274670\pi$
$599$	31.8284			1.30047			0.650236	+	0.759733i	$0.274670\pi$
$600$		0			0
$601$	−12.6378			−0.515508			−0.257754	−	0.966211i	$-0.582982\pi$
$601$	−12.6378			−0.515508			−0.257754	+	0.966211i	$0.582982\pi$
$602$	−1.29885	−	0.422023i	−0.0529373	−	0.0172004i
$603$	−1.04188	+	1.43403i	−0.0424287	+	0.0583981i
$604$	−1.59353	−	1.15777i	−0.0648397	−	0.0471088i
$605$		0			0
$606$	13.8636	−	10.0725i	0.563170	−	0.409167i
$607$		−	34.9481i		−	1.41850i	−0.704957	−	0.709250i	$-0.749034\pi$
$607$		−	34.9481i		−	1.41850i	0.704957	−	0.709250i	$-0.250966\pi$
$608$	5.08664	+	7.00116i	0.206291	+	0.283935i
$609$	−1.13537	−	3.49432i	−0.0460076	−	0.141597i
$610$		0			0
$611$	−1.17527	+	3.61712i	−0.0475465	+	0.146333i
$612$	−6.12704	+	1.99080i	−0.247671	+	0.0804732i
$613$	−6.77418	+	2.20106i	−0.273606	+	0.0889001i	−0.442607	−	0.896716i	$-0.645946\pi$
$613$	−6.77418	+	2.20106i	−0.273606	+	0.0889001i	0.169000	+	0.985616i	$0.445946\pi$
$614$	10.5430	−	32.4480i	0.425481	−	1.30950i
$615$		0			0
$616$	−0.214612	−	0.660507i	−0.00864696	−	0.0266126i
$617$	−9.45572	−	13.0147i	−0.380673	−	0.523951i	0.575090	−	0.818090i	$-0.304967\pi$
$617$	−9.45572	−	13.0147i	−0.380673	−	0.523951i	−0.955763	+	0.294139i	$0.904967\pi$
$618$		−	9.45932i		−	0.380510i
$619$	−0.607103	+	0.441086i	−0.0244015	+	0.0177287i	−0.599919	−	0.800061i	$-0.704801\pi$
$619$	−0.607103	+	0.441086i	−0.0244015	+	0.0177287i	0.575518	+	0.817789i	$0.304801\pi$
$620$		0			0
$621$	−16.1043	−	11.7004i	−0.646241	−	0.469522i
$622$	7.66348	−	10.5479i	0.307278	−	0.422931i
$623$	5.55263	+	1.80416i	0.222461	+	0.0722821i
$624$	6.15382			0.246350
$625$		0			0
$626$	3.48262			0.139194
$627$	−9.24864	−	3.00507i	−0.369355	−	0.120011i
$628$	4.57571	−	6.29793i	0.182591	−	0.251315i
$629$	32.2606	+	23.4387i	1.28631	+	0.934561i
$630$		0			0
$631$	12.4391	−	9.03753i	0.495192	−	0.359778i	−0.311985	−	0.950087i	$-0.600994\pi$
$631$	12.4391	−	9.03753i	0.495192	−	0.359778i	0.807178	+	0.590309i	$0.200994\pi$
$632$		−	5.16896i		−	0.205610i
$633$	−0.213944	−	0.294468i	−0.00850350	−	0.0117041i
$634$	−1.48957	−	4.58443i	−0.0591585	−	0.182071i
$635$		0			0
$636$	−2.67811	+	8.24237i	−0.106194	+	0.326831i
$637$	−27.3683	+	8.89249i	−1.08437	+	0.352333i
$638$	−2.59143	+	0.842006i	−0.102596	+	0.0333353i
$639$	−0.862297	+	2.65388i	−0.0341120	+	0.104986i
$640$		0			0
$641$	2.92140	+	8.99114i	0.115388	+	0.355129i	0.992028	−	0.126019i	$-0.0402200\pi$
$641$	2.92140	+	8.99114i	0.115388	+	0.355129i	−0.876639	+	0.481148i	$0.840220\pi$
$642$	8.53609	+	11.7489i	0.336893	+	0.463693i
$643$			32.8334i			1.29482i	0.762141	+	0.647411i	$0.224148\pi$
$643$			32.8334i			1.29482i	−0.762141	+	0.647411i	$0.775852\pi$
$644$	−2.38008	+	1.72923i	−0.0937883	+	0.0681412i
$645$		0			0
$646$	38.1661	+	27.7293i	1.50163	+	1.09100i
$647$	−10.5026	+	14.4556i	−0.412901	+	0.568309i	−0.963923	−	0.266182i	$-0.914238\pi$
$647$	−10.5026	+	14.4556i	−0.412901	+	0.568309i	0.551022	+	0.834490i	$0.314238\pi$
$648$	−3.85944	−	1.25401i	−0.151613	−	0.0492621i
$649$	−11.2775			−0.442682
$650$		0			0
$651$	6.74495			0.264355
$652$	−13.4060	−	4.35589i	−0.525021	−	0.170590i
$653$	−18.7881	+	25.8596i	−0.735235	+	1.01196i	0.263644	+	0.964620i	$0.415076\pi$
$653$	−18.7881	+	25.8596i	−0.735235	+	1.01196i	−0.998879	+	0.0473435i	$0.984924\pi$
$654$	11.6022	+	8.42947i	0.453681	+	0.329618i
$655$		0			0
$656$	−1.51037	+	1.09735i	−0.0589700	+	0.0428442i
$657$		−	3.93534i		−	0.153532i
$658$	−0.408216	−	0.561861i	−0.0159139	−	0.0219036i
$659$	3.52244	+	10.8410i	0.137215	+	0.422304i	0.995928	−	0.0901527i	$-0.0287355\pi$
$659$	3.52244	+	10.8410i	0.137215	+	0.422304i	−0.858713	+	0.512457i	$0.828736\pi$
$660$		0			0
$661$	2.26642	−	6.97531i	0.0881533	−	0.271308i	−0.897256	−	0.441511i	$-0.854442\pi$
$661$	2.26642	−	6.97531i	0.0881533	−	0.271308i	0.985409	+	0.170203i	$0.0544425\pi$
$662$	8.14431	−	2.64625i	0.316537	−	0.102849i
$663$	31.9050	−	10.3666i	1.23909	−	0.402604i
$664$	3.81191	−	11.7319i	0.147931	−	0.455284i
$665$		0			0
$666$	−2.67131	−	8.22146i	−0.103511	−	0.318575i
$667$	6.78445	+	9.33799i	0.262695	+	0.361568i
$668$		−	8.15615i		−	0.315571i
$669$	−25.2773	+	18.3651i	−0.977278	+	0.710034i
$670$		0			0
$671$	−3.96717	−	2.88232i	−0.153151	−	0.111271i
$672$	−0.660507	+	0.909110i	−0.0254796	+	0.0350697i
$673$	−31.1595	−	10.1243i	−1.20111	−	0.390264i	−0.360940	−	0.932589i	$-0.617544\pi$
$673$	−31.1595	−	10.1243i	−1.20111	−	0.390264i	−0.840169	+	0.542325i	$0.817544\pi$
$674$	14.6712			0.565113
$675$		0			0
$676$	7.82777			0.301068
$677$	30.9879	+	10.0686i	1.19096	+	0.386967i	0.836428	−	0.548076i	$-0.184640\pi$
$677$	30.9879	+	10.0686i	1.19096	+	0.386967i	0.354534	+	0.935043i	$0.384640\pi$
$678$	−1.38048	+	1.90006i	−0.0530169	+	0.0729715i
$679$	−7.47707	−	5.43241i	−0.286944	−	0.208477i
$680$		0			0
$681$	−0.275617	+	0.200247i	−0.0105617	+	0.00767349i
$682$		−	5.00214i		−	0.191542i
$683$	2.55652	+	3.51875i	0.0978227	+	0.134641i	0.855123	−	0.518426i	$-0.173482\pi$
$683$	2.55652	+	3.51875i	0.0978227	+	0.134641i	−0.757300	+	0.653067i	$0.773482\pi$
$684$	−3.16032	−	9.72648i	−0.120838	−	0.371901i
$685$		0			0
$686$	3.42649	−	10.5456i	0.130824	−	0.402635i
$687$	27.0467	−	8.78799i	1.03189	−	0.335283i
$688$	1.55856	−	0.506408i	0.0594197	−	0.0193066i
$689$	−9.06413	+	27.8965i	−0.345316	+	1.06277i
$690$		0			0
$691$	−6.26053	−	19.2679i	−0.238162	−	0.732987i	−0.996686	−	0.0813423i	$-0.974079\pi$
$691$	−6.26053	−	19.2679i	−0.238162	−	0.732987i	0.758524	−	0.651645i	$-0.225921\pi$
$692$	−1.47144	−	2.02526i	−0.0559356	−	0.0769888i
$693$			0.820744i			0.0311775i
$694$	−18.5970	+	13.5115i	−0.705933	+	0.512891i
$695$		0			0
$696$	3.56680	+	2.59143i	0.135199	+	0.0982278i
$697$	−5.98208	+	8.23362i	−0.226587	+	0.311871i
$698$	3.37647	+	1.09708i	0.127801	+	0.0415252i
$699$	−19.6970			−0.745010
$700$		0			0
$701$	12.5964			0.475758			0.237879	−	0.971295i	$-0.423548\pi$
$701$	12.5964			0.475758			0.237879	+	0.971295i	$0.423548\pi$
$702$	−24.4744	−	7.95222i	−0.923727	−	0.300137i
$703$	−37.2081	+	51.2126i	−1.40333	+	1.93152i
$704$	0.674207	+	0.489840i	0.0254101	+	0.0184615i
$705$		0			0
$706$	4.56375	−	3.31576i	0.171759	−	0.124790i
$707$			10.5908i			0.398310i
$708$	10.7256	+	14.7625i	0.403092	+	0.554808i
$709$	−9.10924	−	28.0354i	−0.342105	−	1.05289i	−0.963116	−	0.269088i	$-0.913278\pi$
$709$	−9.10924	−	28.0354i	−0.342105	−	1.05289i	0.621011	−	0.783802i	$-0.286722\pi$
$710$		0			0
$711$	−1.88765	+	5.80960i	−0.0707926	+	0.217877i
$712$	−6.66290	+	2.16491i	−0.249703	+	0.0811333i
$713$	−20.1523	+	6.54788i	−0.754710	+	0.245220i
$714$	−1.89299	+	5.82604i	−0.0708435	+	0.218034i
$715$		0			0
$716$	−6.19042	−	19.0522i	−0.231347	−	0.712012i
$717$	−4.61139	−	6.34704i	−0.172216	−	0.237034i
$718$		−	16.9066i		−	0.630948i
$719$	−24.3987	+	17.7267i	−0.909919	+	0.661095i	−0.940994	−	0.338422i	$-0.890107\pi$
$719$	−24.3987	+	17.7267i	−0.909919	+	0.661095i	0.0310756	+	0.999517i	$0.490107\pi$
$720$		0			0
$721$	4.72966	+	3.43630i	0.176142	+	0.127974i
$722$	−32.8515	+	45.2162i	−1.22261	+	1.68277i
$723$	−17.6065	−	5.72069i	−0.654792	−	0.212755i
$724$	−7.87829			−0.292794
$725$		0			0
$726$	13.8961			0.515732
$727$	−5.65626	−	1.83783i	−0.209779	−	0.0681614i	0.202242	−	0.979336i	$-0.435177\pi$
$727$	−5.65626	−	1.83783i	−0.209779	−	0.0681614i	−0.412021	+	0.911174i	$0.635177\pi$
$728$	−2.23551	+	3.07691i	−0.0828533	+	0.114038i
$729$	22.3337	+	16.2264i	0.827173	+	0.600976i
$730$		0			0
$731$	7.22743	−	5.25103i	0.267316	−	0.194216i
$732$			7.93434i			0.293261i
$733$	−5.98148	−	8.23281i	−0.220931	−	0.304086i	0.684136	−	0.729355i	$-0.260180\pi$
$733$	−5.98148	−	8.23281i	−0.220931	−	0.304086i	−0.905067	+	0.425269i	$0.860180\pi$
$734$	3.89773	+	11.9960i	0.143868	+	0.442780i
$735$		0			0
$736$	1.09089	−	3.35741i	0.0402107	−	0.123756i
$737$	1.18879	−	0.386261i	0.0437896	−	0.0142281i
$738$	2.09830	−	0.681780i	0.0772396	−	0.0250967i
$739$	−11.2234	+	34.5422i	−0.412861	+	1.27066i	0.501289	+	0.865280i	$0.332859\pi$
$739$	−11.2234	+	34.5422i	−0.412861	+	1.27066i	−0.914150	+	0.405376i	$0.867141\pi$
$740$		0			0
$741$	16.4566	+	50.6482i	0.604548	+	1.86061i
$742$	−3.14830	−	4.33327i	−0.115578	−	0.159079i
$743$			2.84832i			0.104495i	0.998634	+	0.0522473i	$0.0166384\pi$
$743$			2.84832i			0.104495i	−0.998634	+	0.0522473i	$0.983362\pi$
$744$	−6.54788	+	4.75731i	−0.240057	+	0.174412i
$745$		0			0
$746$	−10.7191	−	7.78791i	−0.392455	−	0.285136i
$747$	−8.56871	+	11.7938i	−0.313513	+	0.431513i
$748$	4.32066	+	1.40387i	0.157979	+	0.0513305i
$749$	−8.97537			−0.327953
$750$		0			0
$751$	−31.5502			−1.15128			−0.575641	−	0.817702i	$-0.695248\pi$
$751$	−31.5502			−1.15128			−0.575641	+	0.817702i	$0.695248\pi$
$752$	0.792578	+	0.257524i	0.0289023	+	0.00939094i
$753$	12.5970	−	17.3383i	0.459062	−	0.631844i
$754$	12.0719	+	8.77076i	0.439633	+	0.319412i
$755$		0			0
$756$	3.80170	−	2.76210i	0.138266	−	0.100456i
$757$			45.6446i			1.65898i	0.558520	+	0.829491i	$0.311369\pi$
$757$			45.6446i			1.65898i	−0.558520	+	0.829491i	$0.688631\pi$
$758$	−13.1288	−	18.0702i	−0.476858	−	0.656339i
$759$	1.22586	+	3.77280i	0.0444958	+	0.136944i
$760$		0			0
$761$	2.80550	−	8.63445i	0.101699	−	0.312998i	−0.887242	−	0.461304i	$-0.847382\pi$
$761$	2.80550	−	8.63445i	0.101699	−	0.312998i	0.988942	+	0.148305i	$0.0473818\pi$
$762$	−7.26712	+	2.36123i	−0.263260	+	0.0855383i
$763$	−8.42947	+	2.73890i	−0.305167	+	0.0991549i
$764$	1.63013	−	5.01702i	0.0589760	−	0.181510i
$765$		0			0
$766$	7.52545	+	23.1610i	0.271906	+	0.836840i
$767$	36.3010	+	49.9641i	1.31075	+	1.80410i
$768$		−	1.34841i		−	0.0486567i
$769$	−20.5964	+	14.9641i	−0.742724	+	0.539621i	−0.893563	−	0.448938i	$-0.851802\pi$
$769$	−20.5964	+	14.9641i	−0.742724	+	0.539621i	0.150839	+	0.988558i	$0.451802\pi$
$770$		0			0
$771$	−2.52272	−	1.83286i	−0.0908535	−	0.0660089i
$772$	7.90343	−	10.8781i	0.284451	−	0.391513i
$773$	16.3128	+	5.30034i	0.586729	+	0.190640i	0.587313	−	0.809360i	$-0.300186\pi$
$773$	16.3128	+	5.30034i	0.586729	+	0.190640i	−0.000583568		1.00000i	$0.500186\pi$
$774$	−1.93667			−0.0696120
$775$		0			0
$776$	11.0902			0.398114
$777$	−7.81756	−	2.54008i	−0.280453	−	0.0911249i
$778$	17.6992	−	24.3608i	0.634546	−	0.873377i
$779$	−13.0706	−	9.49635i	−0.468303	−	0.340242i
$780$		0			0
$781$	1.59196	−	1.15662i	0.0569647	−	0.0413873i
$782$		−	19.2445i		−	0.688182i
$783$	−10.8368	−	14.9156i	−0.387275	−	0.533038i
$784$	1.94851	+	5.99689i	0.0695895	+	0.214175i
$785$		0			0
$786$	6.86463	−	21.1271i	0.244853	−	0.753580i
$787$	10.7211	−	3.48351i	0.382168	−	0.124174i	−0.111632	−	0.993750i	$-0.535608\pi$
$787$	10.7211	−	3.48351i	0.382168	−	0.124174i	0.493799	+	0.869576i	$0.335608\pi$
$788$	5.17240	−	1.68061i	0.184259	−	0.0598694i
$789$	−8.94173	+	27.5198i	−0.318334	+	0.979731i
$790$		0			0
$791$	−0.448544	−	1.38048i	−0.0159484	−	0.0490841i
$792$	−0.578883	−	0.796764i	−0.0205697	−	0.0283118i
$793$			26.8540i			0.953613i
$794$	28.6152	−	20.7902i	1.01552	−	0.737816i
$795$		0			0
$796$	14.0842	+	10.2328i	0.499200	+	0.362690i
$797$	15.6770	−	21.5775i	0.555307	−	0.764315i	−0.435413	−	0.900231i	$-0.643398\pi$
$797$	15.6770	−	21.5775i	0.555307	−	0.764315i	0.990720	+	0.135916i	$0.0433977\pi$
$798$	−9.24864	−	3.00507i	−0.327398	−	0.106378i
$799$	4.54301			0.160720
$800$		0			0
$801$	8.27929			0.292534
$802$	5.39053	+	1.75149i	0.190346	+	0.0618472i
$803$	−1.63117	+	2.24511i	−0.0575628	+	0.0792284i
$804$	−1.63623	−	1.18879i	−0.0577053	−	0.0419254i
$805$		0			0
$806$	−22.1615	+	16.1013i	−0.780605	+	0.567143i
$807$			28.8378i			1.01514i
$808$	−7.46988	−	10.2814i	−0.262789	−	0.361699i
$809$	−3.39121	−	10.4371i	−0.119229	−	0.366948i	0.873577	−	0.486686i	$-0.161794\pi$
$809$	−3.39121	−	10.4371i	−0.119229	−	0.366948i	−0.992805	+	0.119738i	$0.961794\pi$
$810$		0			0
$811$	−3.04882	+	9.38329i	−0.107058	+	0.329492i	−0.990208	−	0.139599i	$-0.955419\pi$
$811$	−3.04882	+	9.38329i	−0.107058	+	0.329492i	0.883150	+	0.469091i	$0.155419\pi$
$812$	−2.59143	+	0.842006i	−0.0909413	+	0.0295486i
$813$	−33.5102	+	10.8881i	−1.17526	+	0.381864i
$814$	−1.88375	+	5.79760i	−0.0660255	+	0.203206i
$815$		0			0
$816$	−2.27150	−	6.99097i	−0.0795186	−	0.244733i
$817$	8.33584	+	11.4733i	0.291634	+	0.401400i
$818$			19.3676i			0.677174i
$819$	3.63623	−	2.64187i	0.127060	−	0.0923146i
$820$		0			0
$821$	1.85904	+	1.35067i	0.0648808	+	0.0471387i	0.619753	−	0.784797i	$-0.287233\pi$
$821$	1.85904	+	1.35067i	0.0648808	+	0.0471387i	−0.554872	+	0.831936i	$0.687233\pi$
$822$	−2.29312	+	3.15621i	−0.0799818	+	0.110086i
$823$	0.765985	+	0.248884i	0.0267006	+	0.00867554i	0.322337	−	0.946625i	$-0.395532\pi$
$823$	0.765985	+	0.248884i	0.0267006	+	0.00867554i	−0.295636	+	0.955301i	$0.595532\pi$
$824$	−7.01515			−0.244384
$825$		0			0
$826$	−11.2775			−0.392396
$827$	−34.6701	−	11.2650i	−1.20560	−	0.391722i	−0.363780	−	0.931485i	$-0.618514\pi$
$827$	−34.6701	−	11.2650i	−1.20560	−	0.391722i	−0.841817	+	0.539762i	$0.818514\pi$
$828$	−2.45219	+	3.37515i	−0.0852194	+	0.117294i
$829$	23.9231	+	17.3811i	0.830883	+	0.603672i	0.919809	−	0.392367i	$-0.128344\pi$
$829$	23.9231	+	17.3811i	0.830883	+	0.603672i	−0.0889263	+	0.996038i	$0.528344\pi$
$830$		0			0
$831$	−20.3417	+	14.7791i	−0.705646	+	0.512682i
$832$		−	4.56375i		−	0.158219i
$833$	20.2044	+	27.8090i	0.700042	+	0.963525i
$834$	2.07904	+	6.39864i	0.0719914	+	0.221567i
$835$		0			0
$836$	−2.22859	+	6.85890i	−0.0770775	+	0.237220i
$837$	32.1892	−	10.4589i	1.11262	−	0.361513i
$838$	−21.8545	+	7.10097i	−0.754953	+	0.245299i
$839$	13.4507	−	41.3969i	0.464369	−	1.42918i	−0.395405	−	0.918507i	$-0.629396\pi$
$839$	13.4507	−	41.3969i	0.464369	−	1.42918i	0.859774	−	0.510674i	$-0.170604\pi$
$840$		0			0
$841$	−5.65797	−	17.4135i	−0.195103	−	0.600464i
$842$	−5.95261	−	8.19306i	−0.205140	−	0.282351i
$843$		−	19.9818i		−	0.688209i
$844$	−0.218381	+	0.158663i	−0.00751699	+	0.00546141i
$845$		0			0
$846$	−0.796764	−	0.578883i	−0.0273933	−	0.0199024i
$847$	−5.04805	+	6.94804i	−0.173453	+	0.238738i
$848$	6.11264	+	1.98612i	0.209909	+	0.0682035i
$849$	21.2779			0.730257
$850$		0			0
$851$	25.8229			0.885197
$852$	−3.02808	−	0.983884i	−0.103740	−	0.0337073i
$853$	29.7458	−	40.9415i	1.01848	−	1.40181i	0.105208	−	0.994450i	$-0.466449\pi$
$853$	29.7458	−	40.9415i	1.01848	−	1.40181i	0.913267	−	0.407361i	$-0.133551\pi$
$854$	−3.96717	−	2.88232i	−0.135754	−	0.0986308i
$855$		0			0
$856$	8.71314	−	6.33047i	0.297809	−	0.216371i
$857$		−	34.1589i		−	1.16684i	−0.812169	−	0.583422i	$-0.801713\pi$
$857$		−	34.1589i		−	1.16684i	0.812169	−	0.583422i	$-0.198287\pi$
$858$	3.01439	+	4.14895i	0.102909	+	0.141643i
$859$	−3.39523	−	10.4494i	−0.115844	−	0.356530i	0.876278	−	0.481805i	$-0.160019\pi$
$859$	−3.39523	−	10.4494i	−0.115844	−	0.356530i	−0.992122	+	0.125275i	$0.960019\pi$
$860$		0			0
$861$	0.648286	−	1.99522i	0.0220935	−	0.0679968i
$862$	−27.1074	+	8.80773i	−0.923282	+	0.299993i
$863$	44.0415	−	14.3100i	1.49919	−	0.487117i	0.559410	−	0.828891i	$-0.311028\pi$
$863$	44.0415	−	14.3100i	1.49919	−	0.487117i	0.939782	+	0.341774i	$0.111028\pi$
$864$	−1.74248	+	5.36279i	−0.0592802	+	0.182446i
$865$		0			0
$866$	4.91018	+	15.1120i	0.166855	+	0.513526i
$867$	−10.0798	−	13.8737i	−0.342328	−	0.471175i
$868$		−	5.00214i		−	0.169784i
$869$	3.48495	−	2.53197i	0.118219	−	0.0858911i
$870$		0			0
$871$	−5.53786	−	4.02349i	−0.187643	−	0.136331i
$872$	6.25140	−	8.60431i	0.211699	−	0.291379i
$873$	−12.4647	−	4.05002i	−0.421865	−	0.137072i
$874$	30.5500			1.03337
$875$		0			0
$876$	4.49023			0.151711
$877$	−19.9505	−	6.48231i	−0.673681	−	0.218892i	−0.0478541	−	0.998854i	$-0.515238\pi$
$877$	−19.9505	−	6.48231i	−0.673681	−	0.218892i	−0.625827	+	0.779962i	$0.715238\pi$
$878$	1.73197	−	2.38385i	0.0584511	−	0.0804511i
$879$	−20.0727	−	14.5837i	−0.677037	−	0.491896i
$880$		0			0
$881$	41.1491	−	29.8966i	1.38635	−	1.00724i	0.390094	−	0.920775i	$-0.372442\pi$
$881$	41.1491	−	29.8966i	1.38635	−	1.00724i	0.996255	−	0.0864666i	$-0.0275576\pi$
$882$		−	7.45171i		−	0.250912i
$883$	28.8540	+	39.7141i	0.971014	+	1.33649i	0.941533	+	0.336920i	$0.109385\pi$
$883$	28.8540	+	39.7141i	0.971014	+	1.33649i	0.0294804	+	0.999565i	$0.490615\pi$
$884$	−7.68797	−	23.6611i	−0.258574	−	0.795810i
$885$		0			0
$886$	−1.62953	+	5.01518i	−0.0547451	+	0.168488i
$887$	−35.1599	+	11.4242i	−1.18056	+	0.383586i	−0.832573	−	0.553915i	$-0.813133\pi$
$887$	−35.1599	+	11.4242i	−1.18056	+	0.383586i	−0.347982	+	0.937501i	$0.613133\pi$
$888$	9.38071	−	3.04798i	0.314796	−	0.102283i
$889$	1.45932	−	4.49133i	0.0489440	−	0.150634i
$890$		0			0
$891$	−1.04505	−	3.21633i	−0.0350104	−	0.107751i
$892$	13.6197	+	18.7460i	0.456023	+	0.627662i
$893$			7.21188i			0.241336i
$894$	−2.18809	+	1.58974i	−0.0731807	+	0.0531689i
$895$		0			0
$896$	0.674207	+	0.489840i	0.0225237	+	0.0163644i
$897$	12.7691	−	17.5752i	0.426349	−	0.586820i
$898$	−6.48297	−	2.10644i	−0.216339	−	0.0702929i
$899$	−19.6253			−0.654542
$900$		0			0
$901$	35.0373			1.16726
$902$	−1.47968	−	0.480776i	−0.0492679	−	0.0160081i
$903$	−1.08242	+	1.48982i	−0.0360207	+	0.0495782i
$904$	1.40911	+	1.02378i	0.0468663	+	0.0340504i
$905$		0			0
$906$	−2.14874	+	1.56115i	−0.0713870	+	0.0518657i
$907$		−	44.9718i		−	1.49326i	−0.665237	−	0.746632i	$-0.731670\pi$
$907$		−	44.9718i		−	1.49326i	0.665237	−	0.746632i	$-0.268330\pi$
$908$	0.148506	+	0.204401i	0.00492834	+	0.00678327i
$909$	4.64102	+	14.2836i	0.153933	+	0.473757i
$910$		0			0
$911$	−8.32785	+	25.6305i	−0.275914	+	0.849176i	0.713062	+	0.701101i	$0.247308\pi$
$911$	−8.32785	+	25.6305i	−0.275914	+	0.849176i	−0.988976	+	0.148075i	$0.952692\pi$
$912$	11.0979	−	3.60594i	0.367489	−	0.119405i
$913$	9.77692	−	3.17671i	0.323569	−	0.105134i
$914$	−1.29080	+	3.97268i	−0.0426959	+	0.131404i
$915$		0			0
$916$	−6.51728	−	20.0581i	−0.215337	−	0.662739i
$917$	8.06985	+	11.1072i	0.266490	+	0.366792i
$918$			30.7392i			1.01454i
$919$	25.8087	−	18.7511i	0.851350	−	0.618542i	−0.0741679	−	0.997246i	$-0.523630\pi$
$919$	25.8087	−	18.7511i	0.851350	−	0.618542i	0.925518	+	0.378704i	$0.123630\pi$
$920$		0			0
$921$	−37.2189	−	27.0411i	−1.22640	−	0.891034i
$922$	22.0033	−	30.2849i	0.724639	−	0.997380i
$923$	−10.2486	−	3.32998i	−0.337338	−	0.109608i
$924$	−0.936471			−0.0308076
$925$		0			0
$926$	−13.8788			−0.456086
$927$	7.88460	+	2.56186i	0.258964	+	0.0841426i
$928$	1.92183	−	2.64518i	0.0630873	−	0.0868322i
$929$	−5.06070	−	3.67681i	−0.166036	−	0.120632i	0.501664	−	0.865062i	$-0.332721\pi$
$929$	−5.06070	−	3.67681i	−0.166036	−	0.120632i	−0.667700	+	0.744430i	$0.732721\pi$
$930$		0			0
$931$	−44.1459	+	32.0738i	−1.44682	+	1.05118i
$932$			14.6075i			0.478486i
$933$	−10.3335	−	14.2229i	−0.338305	−	0.465637i
$934$	−4.28316	−	13.1822i	−0.140149	−	0.431335i
$935$		0			0
$936$	−1.66663	+	5.12937i	−0.0544756	+	0.167659i
$937$	−29.4062	+	9.55466i	−0.960660	+	0.312137i	−0.747040	−	0.664780i	$-0.768525\pi$
$937$	−29.4062	+	9.55466i	−0.960660	+	0.312137i	−0.213620	+	0.976917i	$0.568525\pi$
$938$	1.18879	−	0.386261i	0.0388154	−	0.0126119i
$939$	1.45115	−	4.46618i	0.0473565	−	0.145748i
$940$		0			0
$941$	−7.92136	−	24.3794i	−0.258229	−	0.794747i	−0.993176	−	0.116623i	$-0.962793\pi$
$941$	−7.92136	−	24.3794i	−0.258229	−	0.794747i	0.734947	−	0.678124i	$-0.237207\pi$
$942$	−6.16996	−	8.49222i	−0.201028	−	0.276691i
$943$			6.59058i			0.214619i
$944$	10.9480	−	7.95422i	0.356328	−	0.258888i
$945$		0			0
$946$	1.10487	+	0.802735i	0.0359224	+	0.0260992i
$947$	26.5751	−	36.5775i	0.863575	−	1.18861i	−0.117130	−	0.993117i	$-0.537370\pi$
$947$	26.5751	−	36.5775i	0.863575	−	1.18861i	0.980705	−	0.195492i	$-0.0626304\pi$
$948$	−6.62877	−	2.15382i	−0.215293	−	0.0699528i
$949$	15.1973			0.493325
$950$		0			0
$951$	−6.49984			−0.210772
$952$	4.32066	+	1.40387i	0.140033	+	0.0454996i
$953$	−12.1107	+	16.6690i	−0.392304	+	0.539961i	−0.958792	−	0.284110i	$-0.908302\pi$
$953$	−12.1107	+	16.6690i	−0.392304	+	0.539961i	0.566487	+	0.824070i	$0.308302\pi$
$954$	−6.14492	−	4.46455i	−0.198949	−	0.144545i
$955$		0			0
$956$	−4.70704	+	3.41986i	−0.152237	+	0.110606i
$957$			3.67414i			0.118768i
$958$	−16.9267	−	23.2976i	−0.546877	−	0.752712i
$959$	−0.745080	−	2.29312i	−0.0240599	−	0.0740488i
$960$		0			0
$961$	1.55373	−	4.78188i	0.0501202	−	0.154254i
$962$	31.7493	−	10.3160i	1.02364	−	0.332600i
$963$	−12.1049	+	3.93311i	−0.390074	+	0.126743i
$964$	−4.24254	+	13.0572i	−0.136643	+	0.420544i
$965$		0			0
$966$	1.22586	+	3.77280i	0.0394413	+	0.121388i
$967$	−30.0333	−	41.3373i	−0.965806	−	1.32932i	−0.944137	−	0.329553i	$-0.893102\pi$
$967$	−30.0333	−	41.3373i	−0.965806	−	1.32932i	−0.0216692	−	0.999765i	$-0.506898\pi$
$968$		−	10.3055i		−	0.331231i
$969$	51.4638	−	37.3906i	1.65325	−	1.20116i
$970$		0			0
$971$	−11.8229	−	8.58982i	−0.379414	−	0.275661i	0.381690	−	0.924291i	$-0.375342\pi$
$971$	−11.8229	−	8.58982i	−0.379414	−	0.275661i	−0.761104	+	0.648630i	$0.775342\pi$
$972$	6.72683	−	9.25869i	0.215763	−	0.296973i
$973$	−3.95458	−	1.28492i	−0.126778	−	0.0411927i
$974$	−38.9513			−1.24808
$975$		0			0
$976$	5.88420			0.188349
$977$	49.6981	+	16.1479i	1.58998	+	0.516616i	0.964603	−	0.263705i	$-0.0849446\pi$
$977$	49.6981	+	16.1479i	1.58998	+	0.516616i	0.625379	+	0.780322i	$0.284945\pi$
$978$	−11.1721	+	15.3771i	−0.357246	+	0.491707i
$979$	−4.72335	−	3.43171i	−0.150959	−	0.109678i
$980$		0			0
$981$	−10.1684	+	7.38777i	−0.324652	+	0.235873i
$982$			23.5069i			0.750135i
$983$	−17.4037	−	23.9541i	−0.555090	−	0.764016i	0.435602	−	0.900140i	$-0.356536\pi$
$983$	−17.4037	−	23.9541i	−0.555090	−	0.764016i	−0.990692	+	0.136123i	$0.956536\pi$
$984$	0.777913	+	2.39417i	0.0247989	+	0.0763233i
$985$		0			0
$986$	5.50792	−	16.9516i	0.175408	−	0.539850i
$987$	−0.890637	+	0.289386i	−0.0283493	+	0.00921124i
$988$	37.5613	−	12.2044i	1.19498	−	0.388274i
$989$	1.78772	−	5.50203i	0.0568461	−	0.174954i
$990$		0			0
$991$	4.59673	+	14.1473i	0.146020	+	0.449403i	0.997141	−	0.0755666i	$-0.0240765\pi$
$991$	4.59673	+	14.1473i	0.146020	+	0.449403i	−0.851121	+	0.524970i	$0.824077\pi$
$992$	3.52808	+	4.85599i	0.112017	+	0.154178i
$993$		−	11.5471i		−	0.366435i
$994$	1.59196	−	1.15662i	0.0504938	−	0.0366859i
$995$		0			0
$996$	−13.4568	−	9.77692i	−0.426394	−	0.309794i
$997$	18.0888	−	24.8971i	0.572879	−	0.788500i	−0.420013	−	0.907518i	$-0.637974\pi$
$997$	18.0888	−	24.8971i	0.572879	−	0.788500i	0.992892	+	0.119018i	$0.0379745\pi$
$998$	26.8817	+	8.73440i	0.850926	+	0.276483i
$999$	−41.2468			−1.30499

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.e.c.149.1		16
5.2	odd	4		50.2.d.b.21.2	✓	8
5.3	odd	4		250.2.d.d.101.1		8
5.4	even	2	inner	250.2.e.c.149.4		16
15.2	even	4		450.2.h.e.271.2		8
20.7	even	4		400.2.u.d.321.1		8
25.6	even	5	inner	250.2.e.c.99.4		16
25.8	odd	20		250.2.d.d.151.1		8
25.9	even	10		1250.2.b.e.1249.7		8
25.12	odd	20		1250.2.a.l.1.2		4
25.13	odd	20		1250.2.a.f.1.3		4
25.16	even	5		1250.2.b.e.1249.2		8
25.17	odd	20		50.2.d.b.31.2	yes	8
25.19	even	10	inner	250.2.e.c.99.1		16
75.17	even	20		450.2.h.e.181.2		8
100.63	even	20		10000.2.a.x.1.2		4
100.67	even	20		400.2.u.d.81.1		8
100.87	even	20		10000.2.a.t.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.21.2	✓	8	5.2	odd	4
50.2.d.b.31.2	yes	8	25.17	odd	20
250.2.d.d.101.1		8	5.3	odd	4
250.2.d.d.151.1		8	25.8	odd	20
250.2.e.c.99.1		16	25.19	even	10	inner
250.2.e.c.99.4		16	25.6	even	5	inner
250.2.e.c.149.1		16	1.1	even	1	trivial
250.2.e.c.149.4		16	5.4	even	2	inner
400.2.u.d.81.1		8	100.67	even	20
400.2.u.d.321.1		8	20.7	even	4
450.2.h.e.181.2		8	75.17	even	20
450.2.h.e.271.2		8	15.2	even	4
1250.2.a.f.1.3		4	25.13	odd	20
1250.2.a.l.1.2		4	25.12	odd	20
1250.2.b.e.1249.2		8	25.16	even	5
1250.2.b.e.1249.7		8	25.9	even	10
10000.2.a.t.1.3		4	100.87	even	20
10000.2.a.x.1.2		4	100.63	even	20

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.792578 + 1.09089i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.09089 - 0.792578i) q^{6} +0.833366i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.365190 + 1.12394i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.792578 + 1.09089i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.09089 - 0.792578i) q^{6} +0.833366i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.365190 + 1.12394i) q^{9} +(0.257524 - 0.792578i) q^{11} +(-1.28242 + 0.416683i) q^{12} +(-4.34038 + 1.41027i) q^{13} +(0.257524 - 0.792578i) q^{14} +(0.309017 + 0.951057i) q^{16} +(3.20425 + 4.41027i) q^{17} -1.18178i q^{18} +(-7.00116 + 5.08664i) q^{19} +(-0.909110 - 0.660507i) q^{21} +(-0.489840 + 0.674207i) q^{22} +(3.35741 + 1.09089i) q^{23} +1.34841 q^{24} +4.56375 q^{26} +(-5.36279 - 1.74248i) q^{27} +(-0.489840 + 0.674207i) q^{28} +(2.64518 + 1.92183i) q^{29} +(-4.85599 + 3.52808i) q^{31} -1.00000i q^{32} +(0.660507 + 0.909110i) q^{33} +(-1.68458 - 5.18459i) q^{34} +(-0.365190 + 1.12394i) q^{36} +(6.95685 - 2.26042i) q^{37} +(8.23036 - 2.67421i) q^{38} +(1.90163 - 5.85263i) q^{39} +(0.576909 + 1.77554i) q^{41} +(0.660507 + 0.909110i) q^{42} -1.63877i q^{43} +(0.674207 - 0.489840i) q^{44} +(-2.85599 - 2.07500i) q^{46} +(0.489840 - 0.674207i) q^{47} +(-1.28242 - 0.416683i) q^{48} +6.30550 q^{49} -7.35074 q^{51} +(-4.34038 - 1.41027i) q^{52} +(3.77782 - 5.19972i) q^{53} +(4.56186 + 3.31439i) q^{54} +(0.674207 - 0.489840i) q^{56} -11.6691i q^{57} +(-1.92183 - 2.64518i) q^{58} +(-4.18178 - 12.8702i) q^{59} +(1.81832 - 5.59621i) q^{61} +(5.70855 - 1.85482i) q^{62} +(-0.936652 + 0.304337i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-0.347249 - 1.06872i) q^{66} +(0.881621 + 1.21345i) q^{67} +5.45140i q^{68} +(-3.85105 + 2.79795i) q^{69} +(1.91027 + 1.38790i) q^{71} +(0.694633 - 0.956080i) q^{72} +(-3.16703 - 1.02903i) q^{73} -7.31486 q^{74} -8.65392 q^{76} +(0.660507 + 0.214612i) q^{77} +(-3.61712 + 4.97854i) q^{78} +(4.18178 + 3.03824i) q^{79} +(3.28304 - 2.38527i) q^{81} -1.86692i q^{82} +(7.25068 + 9.97971i) q^{83} +(-0.347249 - 1.06872i) q^{84} +(-0.506408 + 1.55856i) q^{86} +(-4.19302 + 1.36239i) q^{87} +(-0.792578 + 0.257524i) q^{88} +(2.16491 - 6.66290i) q^{89} +(-1.17527 - 3.61712i) q^{91} +(2.07500 + 2.85599i) q^{92} -8.09363i q^{93} +(-0.674207 + 0.489840i) q^{94} +(1.09089 + 0.792578i) q^{96} +(-6.51864 + 8.97214i) q^{97} +(-5.99689 - 1.94851i) q^{98} +0.984855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 6 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 - 6 * q^6 + 2 * q^9	\( 16 q + 4 q^{4} - 6 q^{6} + 2 q^{9} + 2 q^{11} + 2 q^{14} - 4 q^{16} - 40 q^{19} - 38 q^{21} - 4 q^{24} + 44 q^{26} + 30 q^{29} - 18 q^{31} + 2 q^{34} - 2 q^{36} + 24 q^{39} - 18 q^{41} - 2 q^{44} + 14 q^{46} + 8 q^{49} + 52 q^{51} + 50 q^{54} - 2 q^{56} - 20 q^{59} + 12 q^{61} + 4 q^{64} - 52 q^{66} - 86 q^{69} - 18 q^{71} - 48 q^{74} - 20 q^{76} + 20 q^{79} - 34 q^{81} - 52 q^{84} - 46 q^{86} + 30 q^{89} + 2 q^{91} + 2 q^{94} - 6 q^{96} + 84 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 6 * q^6 + 2 * q^9 + 2 * q^11 + 2 * q^14 - 4 * q^16 - 40 * q^19 - 38 * q^21 - 4 * q^24 + 44 * q^26 + 30 * q^29 - 18 * q^31 + 2 * q^34 - 2 * q^36 + 24 * q^39 - 18 * q^41 - 2 * q^44 + 14 * q^46 + 8 * q^49 + 52 * q^51 + 50 * q^54 - 2 * q^56 - 20 * q^59 + 12 * q^61 + 4 * q^64 - 52 * q^66 - 86 * q^69 - 18 * q^71 - 48 * q^74 - 20 * q^76 + 20 * q^79 - 34 * q^81 - 52 * q^84 - 46 * q^86 + 30 * q^89 + 2 * q^91 + 2 * q^94 - 6 * q^96 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more