LMFDB - Embedded newform 3150.2.m.d.1457.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1457,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("3150.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	3150.1457
Dual form			3150.2.m.d.2843.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +0.828427i q^{11} +(-0.585786 + 0.585786i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(4.41421 - 4.41421i) q^{17} +7.07107i q^{19} +(-0.585786 - 0.585786i) q^{22} +(-0.828427 - 0.828427i) q^{23} -0.828427i q^{26} +(-0.707107 + 0.707107i) q^{28} -8.82843 q^{29} -3.17157 q^{31} +(0.707107 - 0.707107i) q^{32} +6.24264i q^{34} +(8.07107 + 8.07107i) q^{37} +(-5.00000 - 5.00000i) q^{38} -0.828427i q^{41} +(3.58579 - 3.58579i) q^{43} +0.828427 q^{44} +1.17157 q^{46} +(3.58579 - 3.58579i) q^{47} +1.00000i q^{49} +(0.585786 + 0.585786i) q^{52} +(0.828427 + 0.828427i) q^{53} -1.00000i q^{56} +(6.24264 - 6.24264i) q^{58} -8.00000 q^{59} +9.41421 q^{61} +(2.24264 - 2.24264i) q^{62} +1.00000i q^{64} +(-2.41421 - 2.41421i) q^{67} +(-4.41421 - 4.41421i) q^{68} +3.75736i q^{71} +(-6.00000 + 6.00000i) q^{73} -11.4142 q^{74} +7.07107 q^{76} +(0.585786 - 0.585786i) q^{77} +9.31371i q^{79} +(0.585786 + 0.585786i) q^{82} +(1.65685 + 1.65685i) q^{83} +5.07107i q^{86} +(-0.585786 + 0.585786i) q^{88} +9.31371 q^{89} +0.828427 q^{91} +(-0.828427 + 0.828427i) q^{92} +5.07107i q^{94} +(0.242641 + 0.242641i) q^{97} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * q	$ 4 q - 8 q^{13} + 4 q^{14} - 4 q^{16} + 12 q^{17} - 8 q^{22} + 8 q^{23} - 24 q^{29} - 24 q^{31} + 4 q^{37} - 20 q^{38} + 20 q^{43} - 8 q^{44} + 16 q^{46} + 20 q^{47} + 8 q^{52} - 8 q^{53} + 8 q^{58} - 32 q^{59} + 32 q^{61} - 8 q^{62} - 4 q^{67} - 12 q^{68} - 24 q^{73} - 40 q^{74} + 8 q^{77} + 8 q^{82} - 16 q^{83} - 8 q^{88} - 8 q^{89} - 8 q^{91} + 8 q^{92} - 16 q^{97}+O(q^{100}) $ 4 * q - 8 * q^13 + 4 * q^14 - 4 * q^16 + 12 * q^17 - 8 * q^22 + 8 * q^23 - 24 * q^29 - 24 * q^31 + 4 * q^37 - 20 * q^38 + 20 * q^43 - 8 * q^44 + 16 * q^46 + 20 * q^47 + 8 * q^52 - 8 * q^53 + 8 * q^58 - 32 * q^59 + 32 * q^61 - 8 * q^62 - 4 * q^67 - 12 * q^68 - 24 * q^73 - 40 * q^74 + 8 * q^77 + 8 * q^82 - 16 * q^83 - 8 * q^88 - 8 * q^89 - 8 * q^91 + 8 * q^92 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$			0.828427i			0.249780i	0.992171	+	0.124890i	$0.0398578\pi$
$11$			0.828427i			0.249780i	−0.992171	+	0.124890i	$0.960142\pi$
$12$		0			0
$13$	−0.585786	+	0.585786i	−0.162468	+	0.162468i	−0.783659	−	0.621191i	$-0.786649\pi$
$13$	−0.585786	+	0.585786i	−0.162468	+	0.162468i	0.621191	+	0.783659i	$0.286649\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.41421	−	4.41421i	1.07060	−	1.07060i	0.0732936	−	0.997310i	$-0.476649\pi$
$17$	4.41421	−	4.41421i	1.07060	−	1.07060i	0.997310	−	0.0732936i	$-0.0233510\pi$
$18$		0			0
$19$			7.07107i			1.62221i	0.584898	+	0.811107i	$0.301135\pi$
$19$			7.07107i			1.62221i	−0.584898	+	0.811107i	$0.698865\pi$
$20$		0			0
$21$		0			0
$22$	−0.585786	−	0.585786i	−0.124890	−	0.124890i
$23$	−0.828427	−	0.828427i	−0.172739	−	0.172739i	0.615443	−	0.788182i	$-0.288977\pi$
$23$	−0.828427	−	0.828427i	−0.172739	−	0.172739i	−0.788182	+	0.615443i	$0.788977\pi$
$24$		0			0
$25$		0			0
$26$		−	0.828427i		−	0.162468i
$27$		0			0
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	−8.82843			−1.63940			−0.819699	−	0.572795i	$-0.805859\pi$
$29$	−8.82843			−1.63940			−0.819699	+	0.572795i	$0.805859\pi$
$30$		0			0
$31$	−3.17157			−0.569631			−0.284816	−	0.958582i	$-0.591932\pi$
$31$	−3.17157			−0.569631			−0.284816	+	0.958582i	$0.591932\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$			6.24264i			1.07060i
$35$		0			0
$36$		0			0
$37$	8.07107	+	8.07107i	1.32688	+	1.32688i	0.908081	+	0.418794i	$0.137547\pi$
$37$	8.07107	+	8.07107i	1.32688	+	1.32688i	0.418794	+	0.908081i	$0.362453\pi$
$38$	−5.00000	−	5.00000i	−0.811107	−	0.811107i
$39$		0			0
$40$		0			0
$41$		−	0.828427i		−	0.129379i	−0.997905	−	0.0646893i	$-0.979394\pi$
$41$		−	0.828427i		−	0.129379i	0.997905	−	0.0646893i	$-0.0206056\pi$
$42$		0			0
$43$	3.58579	−	3.58579i	0.546827	−	0.546827i	−0.378694	−	0.925522i	$-0.623627\pi$
$43$	3.58579	−	3.58579i	0.546827	−	0.546827i	0.925522	+	0.378694i	$0.123627\pi$
$44$	0.828427			0.124890
$45$		0			0
$46$	1.17157			0.172739
$47$	3.58579	−	3.58579i	0.523041	−	0.523041i	−0.395448	−	0.918488i	$-0.629411\pi$
$47$	3.58579	−	3.58579i	0.523041	−	0.523041i	0.918488	+	0.395448i	$0.129411\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		0			0
$52$	0.585786	+	0.585786i	0.0812340	+	0.0812340i
$53$	0.828427	+	0.828427i	0.113793	+	0.113793i	0.761711	−	0.647917i	$-0.224360\pi$
$53$	0.828427	+	0.828427i	0.113793	+	0.113793i	−0.647917	+	0.761711i	$0.724360\pi$
$54$		0			0
$55$		0			0
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	6.24264	−	6.24264i	0.819699	−	0.819699i
$59$	−8.00000			−1.04151			−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000			−1.04151			−0.520756	+	0.853706i	$0.674350\pi$
$60$		0			0
$61$	9.41421			1.20537			0.602683	−	0.797981i	$-0.294098\pi$
$61$	9.41421			1.20537			0.602683	+	0.797981i	$0.294098\pi$
$62$	2.24264	−	2.24264i	0.284816	−	0.284816i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−2.41421	−	2.41421i	−0.294943	−	0.294943i	0.544086	−	0.839029i	$-0.316876\pi$
$67$	−2.41421	−	2.41421i	−0.294943	−	0.294943i	−0.839029	+	0.544086i	$0.816876\pi$
$68$	−4.41421	−	4.41421i	−0.535302	−	0.535302i
$69$		0			0
$70$		0			0
$71$			3.75736i			0.445917i	0.974828	+	0.222958i	$0.0715714\pi$
$71$			3.75736i			0.445917i	−0.974828	+	0.222958i	$0.928429\pi$
$72$		0			0
$73$	−6.00000	+	6.00000i	−0.702247	+	0.702247i	−0.964892	−	0.262646i	$-0.915405\pi$
$73$	−6.00000	+	6.00000i	−0.702247	+	0.702247i	0.262646	+	0.964892i	$0.415405\pi$
$74$	−11.4142			−1.32688
$75$		0			0
$76$	7.07107			0.811107
$77$	0.585786	−	0.585786i	0.0667566	−	0.0667566i
$78$		0			0
$79$			9.31371i			1.04787i	0.851757	+	0.523937i	$0.175537\pi$
$79$			9.31371i			1.04787i	−0.851757	+	0.523937i	$0.824463\pi$
$80$		0			0
$81$		0			0
$82$	0.585786	+	0.585786i	0.0646893	+	0.0646893i
$83$	1.65685	+	1.65685i	0.181863	+	0.181863i	0.792167	−	0.610304i	$-0.208953\pi$
$83$	1.65685	+	1.65685i	0.181863	+	0.181863i	−0.610304	+	0.792167i	$0.708953\pi$
$84$		0			0
$85$		0			0
$86$			5.07107i			0.546827i
$87$		0			0
$88$	−0.585786	+	0.585786i	−0.0624450	+	0.0624450i
$89$	9.31371			0.987251			0.493626	−	0.869675i	$-0.335671\pi$
$89$	9.31371			0.987251			0.493626	+	0.869675i	$0.335671\pi$
$90$		0			0
$91$	0.828427			0.0868428
$92$	−0.828427	+	0.828427i	−0.0863695	+	0.0863695i
$93$		0			0
$94$			5.07107i			0.523041i
$95$		0			0
$96$		0			0
$97$	0.242641	+	0.242641i	0.0246364	+	0.0246364i	0.719318	−	0.694681i	$-0.244455\pi$
$97$	0.242641	+	0.242641i	0.0246364	+	0.0246364i	−0.694681	+	0.719318i	$0.744455\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$		0			0
$100$		0			0
$101$			15.6569i			1.55792i	0.627077	+	0.778958i	$0.284251\pi$
$101$			15.6569i			1.55792i	−0.627077	+	0.778958i	$0.715749\pi$
$102$		0			0
$103$	0.585786	−	0.585786i	0.0577193	−	0.0577193i	−0.677658	−	0.735377i	$-0.737005\pi$
$103$	0.585786	−	0.585786i	0.0577193	−	0.0577193i	0.735377	+	0.677658i	$0.237005\pi$
$104$	−0.828427			−0.0812340
$105$		0			0
$106$	−1.17157			−0.113793
$107$	−5.07107	+	5.07107i	−0.490239	+	0.490239i	−0.908381	−	0.418143i	$-0.862681\pi$
$107$	−5.07107	+	5.07107i	−0.490239	+	0.490239i	0.418143	+	0.908381i	$0.362681\pi$
$108$		0			0
$109$			8.14214i			0.779875i	0.920841	+	0.389938i	$0.127503\pi$
$109$			8.14214i			0.779875i	−0.920841	+	0.389938i	$0.872497\pi$
$110$		0			0
$111$		0			0
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	2.58579	+	2.58579i	0.243250	+	0.243250i	0.818193	−	0.574943i	$-0.194976\pi$
$113$	2.58579	+	2.58579i	0.243250	+	0.243250i	−0.574943	+	0.818193i	$0.694976\pi$
$114$		0			0
$115$		0			0
$116$			8.82843i			0.819699i
$117$		0			0
$118$	5.65685	−	5.65685i	0.520756	−	0.520756i
$119$	−6.24264			−0.572262
$120$		0			0
$121$	10.3137			0.937610
$122$	−6.65685	+	6.65685i	−0.602683	+	0.602683i
$123$		0			0
$124$			3.17157i			0.284816i
$125$		0			0
$126$		0			0
$127$	6.82843	+	6.82843i	0.605925	+	0.605925i	0.941879	−	0.335954i	$-0.109059\pi$
$127$	6.82843	+	6.82843i	0.605925	+	0.605925i	−0.335954	+	0.941879i	$0.609059\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	6.00000i		−	0.524222i	−0.965038	−	0.262111i	$-0.915581\pi$
$131$		−	6.00000i		−	0.524222i	0.965038	−	0.262111i	$-0.0844187\pi$
$132$		0			0
$133$	5.00000	−	5.00000i	0.433555	−	0.433555i
$134$	3.41421			0.294943
$135$		0			0
$136$	6.24264			0.535302
$137$	13.0711	−	13.0711i	1.11674	−	1.11674i	0.124520	−	0.992217i	$-0.460261\pi$
$137$	13.0711	−	13.0711i	1.11674	−	1.11674i	0.992217	−	0.124520i	$-0.0397389\pi$
$138$		0			0
$139$			8.24264i			0.699132i	0.936912	+	0.349566i	$0.113671\pi$
$139$			8.24264i			0.699132i	−0.936912	+	0.349566i	$0.886329\pi$
$140$		0			0
$141$		0			0
$142$	−2.65685	−	2.65685i	−0.222958	−	0.222958i
$143$	−0.485281	−	0.485281i	−0.0405813	−	0.0405813i
$144$		0			0
$145$		0			0
$146$		−	8.48528i		−	0.702247i
$147$		0			0
$148$	8.07107	−	8.07107i	0.663438	−	0.663438i
$149$	−17.3137			−1.41839			−0.709197	−	0.705010i	$-0.750942\pi$
$149$	−17.3137			−1.41839			−0.709197	+	0.705010i	$0.750942\pi$
$150$		0			0
$151$	9.31371			0.757939			0.378969	−	0.925409i	$-0.376279\pi$
$151$	9.31371			0.757939			0.378969	+	0.925409i	$0.376279\pi$
$152$	−5.00000	+	5.00000i	−0.405554	+	0.405554i
$153$		0			0
$154$			0.828427i			0.0667566i
$155$		0			0
$156$		0			0
$157$	5.41421	+	5.41421i	0.432101	+	0.432101i	0.889343	−	0.457241i	$-0.151162\pi$
$157$	5.41421	+	5.41421i	0.432101	+	0.432101i	−0.457241	+	0.889343i	$0.651162\pi$
$158$	−6.58579	−	6.58579i	−0.523937	−	0.523937i
$159$		0			0
$160$		0			0
$161$			1.17157i			0.0923329i
$162$		0			0
$163$	−14.8995	+	14.8995i	−1.16702	+	1.16702i	−0.184114	+	0.982905i	$0.558941\pi$
$163$	−14.8995	+	14.8995i	−1.16702	+	1.16702i	−0.982905	+	0.184114i	$0.941059\pi$
$164$	−0.828427			−0.0646893
$165$		0			0
$166$	−2.34315			−0.181863
$167$	12.8995	−	12.8995i	0.998193	−	0.998193i	−0.00180548	−	0.999998i	$-0.500575\pi$
$167$	12.8995	−	12.8995i	0.998193	−	0.998193i	0.999998	+	0.00180548i	$0.000574703\pi$
$168$		0			0
$169$			12.3137i			0.947208i
$170$		0			0
$171$		0			0
$172$	−3.58579	−	3.58579i	−0.273414	−	0.273414i
$173$	8.00000	+	8.00000i	0.608229	+	0.608229i	0.942483	−	0.334254i	$-0.108484\pi$
$173$	8.00000	+	8.00000i	0.608229	+	0.608229i	−0.334254	+	0.942483i	$0.608484\pi$
$174$		0			0
$175$		0			0
$176$		−	0.828427i		−	0.0624450i
$177$		0			0
$178$	−6.58579	+	6.58579i	−0.493626	+	0.493626i
$179$	−9.31371			−0.696139			−0.348070	−	0.937469i	$-0.613163\pi$
$179$	−9.31371			−0.696139			−0.348070	+	0.937469i	$0.613163\pi$
$180$		0			0
$181$	3.07107			0.228271			0.114135	−	0.993465i	$-0.463590\pi$
$181$	3.07107			0.228271			0.114135	+	0.993465i	$0.463590\pi$
$182$	−0.585786	+	0.585786i	−0.0434214	+	0.0434214i
$183$		0			0
$184$		−	1.17157i		−	0.0863695i
$185$		0			0
$186$		0			0
$187$	3.65685	+	3.65685i	0.267416	+	0.267416i
$188$	−3.58579	−	3.58579i	−0.261520	−	0.261520i
$189$		0			0
$190$		0			0
$191$			10.5858i			0.765961i	0.923757	+	0.382980i	$0.125102\pi$
$191$			10.5858i			0.765961i	−0.923757	+	0.382980i	$0.874898\pi$
$192$		0			0
$193$	6.00000	−	6.00000i	0.431889	−	0.431889i	−0.457381	−	0.889271i	$-0.651213\pi$
$193$	6.00000	−	6.00000i	0.431889	−	0.431889i	0.889271	+	0.457381i	$0.151213\pi$
$194$	−0.343146			−0.0246364
$195$		0			0
$196$	1.00000			0.0714286
$197$	8.82843	−	8.82843i	0.628999	−	0.628999i	−0.318817	−	0.947816i	$-0.603286\pi$
$197$	8.82843	−	8.82843i	0.628999	−	0.628999i	0.947816	+	0.318817i	$0.103286\pi$
$198$		0			0
$199$			11.6569i			0.826332i	0.910656	+	0.413166i	$0.135577\pi$
$199$			11.6569i			0.826332i	−0.910656	+	0.413166i	$0.864423\pi$
$200$		0			0
$201$		0			0
$202$	−11.0711	−	11.0711i	−0.778958	−	0.778958i
$203$	6.24264	+	6.24264i	0.438147	+	0.438147i
$204$		0			0
$205$		0			0
$206$			0.828427i			0.0577193i
$207$		0			0
$208$	0.585786	−	0.585786i	0.0406170	−	0.0406170i
$209$	−5.85786			−0.405197
$210$		0			0
$211$	20.4853			1.41026			0.705132	−	0.709076i	$-0.250888\pi$
$211$	20.4853			1.41026			0.705132	+	0.709076i	$0.250888\pi$
$212$	0.828427	−	0.828427i	0.0568966	−	0.0568966i
$213$		0			0
$214$		−	7.17157i		−	0.490239i
$215$		0			0
$216$		0			0
$217$	2.24264	+	2.24264i	0.152240	+	0.152240i
$218$	−5.75736	−	5.75736i	−0.389938	−	0.389938i
$219$		0			0
$220$		0			0
$221$			5.17157i			0.347878i
$222$		0			0
$223$	−11.8995	+	11.8995i	−0.796849	+	0.796849i	−0.982597	−	0.185748i	$-0.940529\pi$
$223$	−11.8995	+	11.8995i	−0.796849	+	0.796849i	0.185748	+	0.982597i	$0.440529\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	−3.65685			−0.243250
$227$	−15.6569	+	15.6569i	−1.03918	+	1.03918i	−0.0399815	+	0.999200i	$0.512730\pi$
$227$	−15.6569	+	15.6569i	−1.03918	+	1.03918i	−0.999200	+	0.0399815i	$0.987270\pi$
$228$		0			0
$229$			19.0711i			1.26025i	0.776493	+	0.630126i	$0.216997\pi$
$229$			19.0711i			1.26025i	−0.776493	+	0.630126i	$0.783003\pi$
$230$		0			0
$231$		0			0
$232$	−6.24264	−	6.24264i	−0.409849	−	0.409849i
$233$	−2.58579	−	2.58579i	−0.169401	−	0.169401i	0.617315	−	0.786716i	$-0.288220\pi$
$233$	−2.58579	−	2.58579i	−0.169401	−	0.169401i	−0.786716	+	0.617315i	$0.788220\pi$
$234$		0			0
$235$		0			0
$236$			8.00000i			0.520756i
$237$		0			0
$238$	4.41421	−	4.41421i	0.286131	−	0.286131i
$239$	17.2132			1.11343			0.556715	−	0.830704i	$-0.312062\pi$
$239$	17.2132			1.11343			0.556715	+	0.830704i	$0.312062\pi$
$240$		0			0
$241$	3.65685			0.235559			0.117779	−	0.993040i	$-0.462422\pi$
$241$	3.65685			0.235559			0.117779	+	0.993040i	$0.462422\pi$
$242$	−7.29289	+	7.29289i	−0.468805	+	0.468805i
$243$		0			0
$244$		−	9.41421i		−	0.602683i
$245$		0			0
$246$		0			0
$247$	−4.14214	−	4.14214i	−0.263558	−	0.263558i
$248$	−2.24264	−	2.24264i	−0.142408	−	0.142408i
$249$		0			0
$250$		0			0
$251$			26.9706i			1.70237i	0.524868	+	0.851183i	$0.324115\pi$
$251$			26.9706i			1.70237i	−0.524868	+	0.851183i	$0.675885\pi$
$252$		0			0
$253$	0.686292	−	0.686292i	0.0431468	−	0.0431468i
$254$	−9.65685			−0.605925
$255$		0			0
$256$	1.00000			0.0625000
$257$	−12.8995	+	12.8995i	−0.804648	+	0.804648i	−0.983818	−	0.179170i	$-0.942659\pi$
$257$	−12.8995	+	12.8995i	−0.804648	+	0.804648i	0.179170	+	0.983818i	$0.442659\pi$
$258$		0			0
$259$		−	11.4142i		−	0.709245i
$260$		0			0
$261$		0			0
$262$	4.24264	+	4.24264i	0.262111	+	0.262111i
$263$	22.0000	+	22.0000i	1.35658	+	1.35658i	0.878099	+	0.478479i	$0.158812\pi$
$263$	22.0000	+	22.0000i	1.35658	+	1.35658i	0.478479	+	0.878099i	$0.341188\pi$
$264$		0			0
$265$		0			0
$266$			7.07107i			0.433555i
$267$		0			0
$268$	−2.41421	+	2.41421i	−0.147472	+	0.147472i
$269$	−1.31371			−0.0800982			−0.0400491	−	0.999198i	$-0.512751\pi$
$269$	−1.31371			−0.0800982			−0.0400491	+	0.999198i	$0.512751\pi$
$270$		0			0
$271$	12.8284			0.779271			0.389636	−	0.920969i	$-0.372601\pi$
$271$	12.8284			0.779271			0.389636	+	0.920969i	$0.372601\pi$
$272$	−4.41421	+	4.41421i	−0.267651	+	0.267651i
$273$		0			0
$274$			18.4853i			1.11674i
$275$		0			0
$276$		0			0
$277$	−3.92893	−	3.92893i	−0.236067	−	0.236067i	0.579153	−	0.815219i	$-0.303384\pi$
$277$	−3.92893	−	3.92893i	−0.236067	−	0.236067i	−0.815219	+	0.579153i	$0.803384\pi$
$278$	−5.82843	−	5.82843i	−0.349566	−	0.349566i
$279$		0			0
$280$		0			0
$281$		−	27.0711i		−	1.61492i	−0.589919	−	0.807462i	$-0.700840\pi$
$281$		−	27.0711i		−	1.61492i	0.589919	−	0.807462i	$-0.299160\pi$
$282$		0			0
$283$	−18.0000	+	18.0000i	−1.06999	+	1.06999i	−0.0726300	+	0.997359i	$0.523139\pi$
$283$	−18.0000	+	18.0000i	−1.06999	+	1.06999i	−0.997359	+	0.0726300i	$0.976861\pi$
$284$	3.75736			0.222958
$285$		0			0
$286$	0.686292			0.0405813
$287$	−0.585786	+	0.585786i	−0.0345779	+	0.0345779i
$288$		0			0
$289$		−	21.9706i		−	1.29239i
$290$		0			0
$291$		0			0
$292$	6.00000	+	6.00000i	0.351123	+	0.351123i
$293$	5.51472	+	5.51472i	0.322173	+	0.322173i	0.849600	−	0.527427i	$-0.176843\pi$
$293$	5.51472	+	5.51472i	0.322173	+	0.322173i	−0.527427	+	0.849600i	$0.676843\pi$
$294$		0			0
$295$		0			0
$296$			11.4142i			0.663438i
$297$		0			0
$298$	12.2426	−	12.2426i	0.709197	−	0.709197i
$299$	0.970563			0.0561291
$300$		0			0
$301$	−5.07107			−0.292291
$302$	−6.58579	+	6.58579i	−0.378969	+	0.378969i
$303$		0			0
$304$		−	7.07107i		−	0.405554i
$305$		0			0
$306$		0			0
$307$	−24.4853	−	24.4853i	−1.39745	−	1.39745i	−0.807279	−	0.590169i	$-0.799061\pi$
$307$	−24.4853	−	24.4853i	−1.39745	−	1.39745i	−0.590169	−	0.807279i	$-0.700939\pi$
$308$	−0.585786	−	0.585786i	−0.0333783	−	0.0333783i
$309$		0			0
$310$		0			0
$311$		−	16.0000i		−	0.907277i	−0.891186	−	0.453638i	$-0.850126\pi$
$311$		−	16.0000i		−	0.907277i	0.891186	−	0.453638i	$-0.149874\pi$
$312$		0			0
$313$	−8.34315	+	8.34315i	−0.471582	+	0.471582i	−0.902426	−	0.430844i	$-0.858216\pi$
$313$	−8.34315	+	8.34315i	−0.471582	+	0.471582i	0.430844	+	0.902426i	$0.358216\pi$
$314$	−7.65685			−0.432101
$315$		0			0
$316$	9.31371			0.523937
$317$	3.75736	−	3.75736i	0.211034	−	0.211034i	−0.593672	−	0.804707i	$-0.702323\pi$
$317$	3.75736	−	3.75736i	0.211034	−	0.211034i	0.804707	+	0.593672i	$0.202323\pi$
$318$		0			0
$319$		−	7.31371i		−	0.409489i
$320$		0			0
$321$		0			0
$322$	−0.828427	−	0.828427i	−0.0461664	−	0.0461664i
$323$	31.2132	+	31.2132i	1.73675	+	1.73675i
$324$		0			0
$325$		0			0
$326$		−	21.0711i		−	1.16702i
$327$		0			0
$328$	0.585786	−	0.585786i	0.0323446	−	0.0323446i
$329$	−5.07107			−0.279577
$330$		0			0
$331$	−30.1421			−1.65676			−0.828381	−	0.560165i	$-0.810738\pi$
$331$	−30.1421			−1.65676			−0.828381	+	0.560165i	$0.810738\pi$
$332$	1.65685	−	1.65685i	0.0909317	−	0.0909317i
$333$		0			0
$334$			18.2426i			0.998193i
$335$		0			0
$336$		0			0
$337$	−18.4853	−	18.4853i	−1.00696	−	1.00696i	−0.999976	−	0.00698181i	$-0.997778\pi$
$337$	−18.4853	−	18.4853i	−1.00696	−	1.00696i	−0.00698181	−	0.999976i	$-0.502222\pi$
$338$	−8.70711	−	8.70711i	−0.473604	−	0.473604i
$339$		0			0
$340$		0			0
$341$		−	2.62742i		−	0.142283i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	5.07107			0.273414
$345$		0			0
$346$	−11.3137			−0.608229
$347$	−9.17157	+	9.17157i	−0.492356	+	0.492356i	−0.909048	−	0.416692i	$-0.863189\pi$
$347$	−9.17157	+	9.17157i	−0.492356	+	0.492356i	0.416692	+	0.909048i	$0.363189\pi$
$348$		0			0
$349$			16.7279i			0.895425i	0.894178	+	0.447713i	$0.147761\pi$
$349$			16.7279i			0.895425i	−0.894178	+	0.447713i	$0.852239\pi$
$350$		0			0
$351$		0			0
$352$	0.585786	+	0.585786i	0.0312225	+	0.0312225i
$353$	−21.3848	−	21.3848i	−1.13820	−	1.13820i	−0.988773	−	0.149424i	$-0.952258\pi$
$353$	−21.3848	−	21.3848i	−1.13820	−	1.13820i	−0.149424	−	0.988773i	$-0.547742\pi$
$354$		0			0
$355$		0			0
$356$		−	9.31371i		−	0.493626i
$357$		0			0
$358$	6.58579	−	6.58579i	0.348070	−	0.348070i
$359$	−4.72792			−0.249530			−0.124765	−	0.992186i	$-0.539818\pi$
$359$	−4.72792			−0.249530			−0.124765	+	0.992186i	$0.539818\pi$
$360$		0			0
$361$	−31.0000			−1.63158
$362$	−2.17157	+	2.17157i	−0.114135	+	0.114135i
$363$		0			0
$364$		−	0.828427i		−	0.0434214i
$365$		0			0
$366$		0			0
$367$	20.0000	+	20.0000i	1.04399	+	1.04399i	0.998987	+	0.0450047i	$0.0143303\pi$
$367$	20.0000	+	20.0000i	1.04399	+	1.04399i	0.0450047	+	0.998987i	$0.485670\pi$
$368$	0.828427	+	0.828427i	0.0431847	+	0.0431847i
$369$		0			0
$370$		0			0
$371$		−	1.17157i		−	0.0608250i
$372$		0			0
$373$	−2.75736	+	2.75736i	−0.142771	+	0.142771i	−0.774880	−	0.632109i	$-0.782190\pi$
$373$	−2.75736	+	2.75736i	−0.142771	+	0.142771i	0.632109	+	0.774880i	$0.282190\pi$
$374$	−5.17157			−0.267416
$375$		0			0
$376$	5.07107			0.261520
$377$	5.17157	−	5.17157i	0.266350	−	0.266350i
$378$		0			0
$379$			5.65685i			0.290573i	0.989390	+	0.145287i	$0.0464104\pi$
$379$			5.65685i			0.290573i	−0.989390	+	0.145287i	$0.953590\pi$
$380$		0			0
$381$		0			0
$382$	−7.48528	−	7.48528i	−0.382980	−	0.382980i
$383$	−3.24264	−	3.24264i	−0.165691	−	0.165691i	0.619391	−	0.785082i	$-0.287379\pi$
$383$	−3.24264	−	3.24264i	−0.165691	−	0.165691i	−0.785082	+	0.619391i	$0.787379\pi$
$384$		0			0
$385$		0			0
$386$			8.48528i			0.431889i
$387$		0			0
$388$	0.242641	−	0.242641i	0.0123182	−	0.0123182i
$389$	−17.3137			−0.877840			−0.438920	−	0.898526i	$-0.644639\pi$
$389$	−17.3137			−0.877840			−0.438920	+	0.898526i	$0.644639\pi$
$390$		0			0
$391$	−7.31371			−0.369870
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$		0			0
$394$			12.4853i			0.628999i
$395$		0			0
$396$		0			0
$397$	22.5858	+	22.5858i	1.13355	+	1.13355i	0.989583	+	0.143965i	$0.0459854\pi$
$397$	22.5858	+	22.5858i	1.13355	+	1.13355i	0.143965	+	0.989583i	$0.454015\pi$
$398$	−8.24264	−	8.24264i	−0.413166	−	0.413166i
$399$		0			0
$400$		0			0
$401$		−	16.9289i		−	0.845391i	−0.906272	−	0.422695i	$-0.861084\pi$
$401$		−	16.9289i		−	0.845391i	0.906272	−	0.422695i	$-0.138916\pi$
$402$		0			0
$403$	1.85786	−	1.85786i	0.0925468	−	0.0925468i
$404$	15.6569			0.778958
$405$		0			0
$406$	−8.82843			−0.438147
$407$	−6.68629	+	6.68629i	−0.331427	+	0.331427i
$408$		0			0
$409$		−	14.6863i		−	0.726190i	−0.931752	−	0.363095i	$-0.881720\pi$
$409$		−	14.6863i		−	0.726190i	0.931752	−	0.363095i	$-0.118280\pi$
$410$		0			0
$411$		0			0
$412$	−0.585786	−	0.585786i	−0.0288596	−	0.0288596i
$413$	5.65685	+	5.65685i	0.278356	+	0.278356i
$414$		0			0
$415$		0			0
$416$			0.828427i			0.0406170i
$417$		0			0
$418$	4.14214	−	4.14214i	0.202598	−	0.202598i
$419$	20.0000			0.977064			0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000			0.977064			0.488532	+	0.872546i	$0.337533\pi$
$420$		0			0
$421$	−0.142136			−0.00692727			−0.00346363	−	0.999994i	$-0.501103\pi$
$421$	−0.142136			−0.00692727			−0.00346363	+	0.999994i	$0.501103\pi$
$422$	−14.4853	+	14.4853i	−0.705132	+	0.705132i
$423$		0			0
$424$			1.17157i			0.0568966i
$425$		0			0
$426$		0			0
$427$	−6.65685	−	6.65685i	−0.322148	−	0.322148i
$428$	5.07107	+	5.07107i	0.245119	+	0.245119i
$429$		0			0
$430$		0			0
$431$			29.2132i			1.40715i	0.710621	+	0.703575i	$0.248414\pi$
$431$			29.2132i			1.40715i	−0.710621	+	0.703575i	$0.751586\pi$
$432$		0			0
$433$	15.7574	−	15.7574i	0.757250	−	0.757250i	−0.218571	−	0.975821i	$-0.570139\pi$
$433$	15.7574	−	15.7574i	0.757250	−	0.757250i	0.975821	+	0.218571i	$0.0701394\pi$
$434$	−3.17157			−0.152240
$435$		0			0
$436$	8.14214			0.389938
$437$	5.85786	−	5.85786i	0.280220	−	0.280220i
$438$		0			0
$439$		−	13.7990i		−	0.658590i	−0.944227	−	0.329295i	$-0.893189\pi$
$439$		−	13.7990i		−	0.658590i	0.944227	−	0.329295i	$-0.106811\pi$
$440$		0			0
$441$		0			0
$442$	−3.65685	−	3.65685i	−0.173939	−	0.173939i
$443$	7.51472	+	7.51472i	0.357035	+	0.357035i	0.862719	−	0.505684i	$-0.168760\pi$
$443$	7.51472	+	7.51472i	0.357035	+	0.357035i	−0.505684	+	0.862719i	$0.668760\pi$
$444$		0			0
$445$		0			0
$446$		−	16.8284i		−	0.796849i
$447$		0			0
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	23.7574			1.12118			0.560590	−	0.828094i	$-0.310575\pi$
$449$	23.7574			1.12118			0.560590	+	0.828094i	$0.310575\pi$
$450$		0			0
$451$	0.686292			0.0323162
$452$	2.58579	−	2.58579i	0.121625	−	0.121625i
$453$		0			0
$454$		−	22.1421i		−	1.03918i
$455$		0			0
$456$		0			0
$457$	24.4853	+	24.4853i	1.14537	+	1.14537i	0.987452	+	0.157921i	$0.0504793\pi$
$457$	24.4853	+	24.4853i	1.14537	+	1.14537i	0.157921	+	0.987452i	$0.449521\pi$
$458$	−13.4853	−	13.4853i	−0.630126	−	0.630126i
$459$		0			0
$460$		0			0
$461$		−	14.6863i		−	0.684009i	−0.939698	−	0.342004i	$-0.888894\pi$
$461$		−	14.6863i		−	0.684009i	0.939698	−	0.342004i	$-0.111106\pi$
$462$		0			0
$463$	22.4853	−	22.4853i	1.04498	−	1.04498i	0.0460401	−	0.998940i	$-0.485340\pi$
$463$	22.4853	−	22.4853i	1.04498	−	1.04498i	0.998940	−	0.0460401i	$-0.0146602\pi$
$464$	8.82843			0.409849
$465$		0			0
$466$	3.65685			0.169401
$467$	1.65685	−	1.65685i	0.0766701	−	0.0766701i	−0.667732	−	0.744402i	$-0.732735\pi$
$467$	1.65685	−	1.65685i	0.0766701	−	0.0766701i	0.744402	+	0.667732i	$0.232735\pi$
$468$		0			0
$469$			3.41421i			0.157654i
$470$		0			0
$471$		0			0
$472$	−5.65685	−	5.65685i	−0.260378	−	0.260378i
$473$	2.97056	+	2.97056i	0.136587	+	0.136587i
$474$		0			0
$475$		0			0
$476$			6.24264i			0.286131i
$477$		0			0
$478$	−12.1716	+	12.1716i	−0.556715	+	0.556715i
$479$	1.65685			0.0757036			0.0378518	−	0.999283i	$-0.487949\pi$
$479$	1.65685			0.0757036			0.0378518	+	0.999283i	$0.487949\pi$
$480$		0			0
$481$	−9.45584			−0.431149
$482$	−2.58579	+	2.58579i	−0.117779	+	0.117779i
$483$		0			0
$484$		−	10.3137i		−	0.468805i
$485$		0			0
$486$		0			0
$487$	−20.0000	−	20.0000i	−0.906287	−	0.906287i	0.0896838	−	0.995970i	$-0.471414\pi$
$487$	−20.0000	−	20.0000i	−0.906287	−	0.906287i	−0.995970	+	0.0896838i	$0.971414\pi$
$488$	6.65685	+	6.65685i	0.301342	+	0.301342i
$489$		0			0
$490$		0			0
$491$		−	10.9706i		−	0.495095i	−0.968876	−	0.247547i	$-0.920375\pi$
$491$		−	10.9706i		−	0.495095i	0.968876	−	0.247547i	$-0.0796246\pi$
$492$		0			0
$493$	−38.9706	+	38.9706i	−1.75515	+	1.75515i
$494$	5.85786			0.263558
$495$		0			0
$496$	3.17157			0.142408
$497$	2.65685	−	2.65685i	0.119176	−	0.119176i
$498$		0			0
$499$		−	24.0000i		−	1.07439i	−0.843459	−	0.537194i	$-0.819484\pi$
$499$		−	24.0000i		−	1.07439i	0.843459	−	0.537194i	$-0.180516\pi$
$500$		0			0
$501$		0			0
$502$	−19.0711	−	19.0711i	−0.851183	−	0.851183i
$503$	17.5858	+	17.5858i	0.784111	+	0.784111i	0.980522	−	0.196410i	$-0.0629285\pi$
$503$	17.5858	+	17.5858i	0.784111	+	0.784111i	−0.196410	+	0.980522i	$0.562928\pi$
$504$		0			0
$505$		0			0
$506$			0.970563i			0.0431468i
$507$		0			0
$508$	6.82843	−	6.82843i	0.302962	−	0.302962i
$509$	29.6569			1.31452			0.657258	−	0.753665i	$-0.271716\pi$
$509$	29.6569			1.31452			0.657258	+	0.753665i	$0.271716\pi$
$510$		0			0
$511$	8.48528			0.375367
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	18.2426i		−	0.804648i
$515$		0			0
$516$		0			0
$517$	2.97056	+	2.97056i	0.130645	+	0.130645i
$518$	8.07107	+	8.07107i	0.354622	+	0.354622i
$519$		0			0
$520$		0			0
$521$			26.9706i			1.18160i	0.806817	+	0.590801i	$0.201188\pi$
$521$			26.9706i			1.18160i	−0.806817	+	0.590801i	$0.798812\pi$
$522$		0			0
$523$	−26.2843	+	26.2843i	−1.14933	+	1.14933i	−0.162647	+	0.986684i	$0.552003\pi$
$523$	−26.2843	+	26.2843i	−1.14933	+	1.14933i	−0.986684	+	0.162647i	$0.947997\pi$
$524$	−6.00000			−0.262111
$525$		0			0
$526$	−31.1127			−1.35658
$527$	−14.0000	+	14.0000i	−0.609850	+	0.609850i
$528$		0			0
$529$		−	21.6274i		−	0.940322i
$530$		0			0
$531$		0			0
$532$	−5.00000	−	5.00000i	−0.216777	−	0.216777i
$533$	0.485281	+	0.485281i	0.0210199	+	0.0210199i
$534$		0			0
$535$		0			0
$536$		−	3.41421i		−	0.147472i
$537$		0			0
$538$	0.928932	−	0.928932i	0.0400491	−	0.0400491i
$539$	−0.828427			−0.0356829
$540$		0			0
$541$	26.4853			1.13869			0.569346	−	0.822098i	$-0.307197\pi$
$541$	26.4853			1.13869			0.569346	+	0.822098i	$0.307197\pi$
$542$	−9.07107	+	9.07107i	−0.389636	+	0.389636i
$543$		0			0
$544$		−	6.24264i		−	0.267651i
$545$		0			0
$546$		0			0
$547$	1.72792	+	1.72792i	0.0738806	+	0.0738806i	0.743082	−	0.669201i	$-0.233363\pi$
$547$	1.72792	+	1.72792i	0.0738806	+	0.0738806i	−0.669201	+	0.743082i	$0.733363\pi$
$548$	−13.0711	−	13.0711i	−0.558368	−	0.558368i
$549$		0			0
$550$		0			0
$551$		−	62.4264i		−	2.65945i
$552$		0			0
$553$	6.58579	−	6.58579i	0.280056	−	0.280056i
$554$	5.55635			0.236067
$555$		0			0
$556$	8.24264			0.349566
$557$	21.8995	−	21.8995i	0.927911	−	0.927911i	−0.0696594	−	0.997571i	$-0.522191\pi$
$557$	21.8995	−	21.8995i	0.927911	−	0.927911i	0.997571	+	0.0696594i	$0.0221913\pi$
$558$		0			0
$559$			4.20101i			0.177684i
$560$		0			0
$561$		0			0
$562$	19.1421	+	19.1421i	0.807462	+	0.807462i
$563$	−8.14214	−	8.14214i	−0.343150	−	0.343150i	0.514400	−	0.857550i	$-0.328015\pi$
$563$	−8.14214	−	8.14214i	−0.343150	−	0.343150i	−0.857550	+	0.514400i	$0.828015\pi$
$564$		0			0
$565$		0			0
$566$		−	25.4558i		−	1.06999i
$567$		0			0
$568$	−2.65685	+	2.65685i	−0.111479	+	0.111479i
$569$	−26.3848			−1.10611			−0.553054	−	0.833146i	$-0.686538\pi$
$569$	−26.3848			−1.10611			−0.553054	+	0.833146i	$0.686538\pi$
$570$		0			0
$571$	−24.9706			−1.04499			−0.522493	−	0.852644i	$-0.674998\pi$
$571$	−24.9706			−1.04499			−0.522493	+	0.852644i	$0.674998\pi$
$572$	−0.485281	+	0.485281i	−0.0202906	+	0.0202906i
$573$		0			0
$574$		−	0.828427i		−	0.0345779i
$575$		0			0
$576$		0			0
$577$	16.8284	+	16.8284i	0.700577	+	0.700577i	0.964534	−	0.263958i	$-0.0850279\pi$
$577$	16.8284	+	16.8284i	0.700577	+	0.700577i	−0.263958	+	0.964534i	$0.585028\pi$
$578$	15.5355	+	15.5355i	0.646193	+	0.646193i
$579$		0			0
$580$		0			0
$581$		−	2.34315i		−	0.0972101i
$582$		0			0
$583$	−0.686292	+	0.686292i	−0.0284233	+	0.0284233i
$584$	−8.48528			−0.351123
$585$		0			0
$586$	−7.79899			−0.322173
$587$	−14.0000	+	14.0000i	−0.577842	+	0.577842i	−0.934308	−	0.356466i	$-0.883981\pi$
$587$	−14.0000	+	14.0000i	−0.577842	+	0.577842i	0.356466	+	0.934308i	$0.383981\pi$
$588$		0			0
$589$		−	22.4264i		−	0.924064i
$590$		0			0
$591$		0			0
$592$	−8.07107	−	8.07107i	−0.331719	−	0.331719i
$593$	−11.5858	−	11.5858i	−0.475771	−	0.475771i	0.428005	−	0.903776i	$-0.359217\pi$
$593$	−11.5858	−	11.5858i	−0.475771	−	0.475771i	−0.903776	+	0.428005i	$0.859217\pi$
$594$		0			0
$595$		0			0
$596$			17.3137i			0.709197i
$597$		0			0
$598$	−0.686292	+	0.686292i	−0.0280645	+	0.0280645i
$599$	−19.0711			−0.779223			−0.389611	−	0.920979i	$-0.627391\pi$
$599$	−19.0711			−0.779223			−0.389611	+	0.920979i	$0.627391\pi$
$600$		0			0
$601$	−18.0000			−0.734235			−0.367118	−	0.930175i	$-0.619655\pi$
$601$	−18.0000			−0.734235			−0.367118	+	0.930175i	$0.619655\pi$
$602$	3.58579	−	3.58579i	0.146146	−	0.146146i
$603$		0			0
$604$		−	9.31371i		−	0.378969i
$605$		0			0
$606$		0			0
$607$	−24.3848	−	24.3848i	−0.989748	−	0.989748i	0.0102004	−	0.999948i	$-0.496753\pi$
$607$	−24.3848	−	24.3848i	−0.989748	−	0.989748i	−0.999948	+	0.0102004i	$0.996753\pi$
$608$	5.00000	+	5.00000i	0.202777	+	0.202777i
$609$		0			0
$610$		0			0
$611$			4.20101i			0.169955i
$612$		0			0
$613$	6.41421	−	6.41421i	0.259068	−	0.259068i	−0.565607	−	0.824675i	$-0.691358\pi$
$613$	6.41421	−	6.41421i	0.259068	−	0.259068i	0.824675	+	0.565607i	$0.191358\pi$
$614$	34.6274			1.39745
$615$		0			0
$616$	0.828427			0.0333783
$617$	27.4142	−	27.4142i	1.10365	−	1.10365i	0.109689	−	0.993966i	$-0.465015\pi$
$617$	27.4142	−	27.4142i	1.10365	−	1.10365i	0.993966	−	0.109689i	$-0.0349854\pi$
$618$		0			0
$619$		−	18.8701i		−	0.758452i	−0.925304	−	0.379226i	$-0.876190\pi$
$619$		−	18.8701i		−	0.758452i	0.925304	−	0.379226i	$-0.123810\pi$
$620$		0			0
$621$		0			0
$622$	11.3137	+	11.3137i	0.453638	+	0.453638i
$623$	−6.58579	−	6.58579i	−0.263854	−	0.263854i
$624$		0			0
$625$		0			0
$626$		−	11.7990i		−	0.471582i
$627$		0			0
$628$	5.41421	−	5.41421i	0.216051	−	0.216051i
$629$	71.2548			2.84112
$630$		0			0
$631$	−28.9706			−1.15330			−0.576650	−	0.816991i	$-0.695640\pi$
$631$	−28.9706			−1.15330			−0.576650	+	0.816991i	$0.695640\pi$
$632$	−6.58579	+	6.58579i	−0.261969	+	0.261969i
$633$		0			0
$634$			5.31371i			0.211034i
$635$		0			0
$636$		0			0
$637$	−0.585786	−	0.585786i	−0.0232097	−	0.0232097i
$638$	5.17157	+	5.17157i	0.204745	+	0.204745i
$639$		0			0
$640$		0			0
$641$			24.5269i			0.968755i	0.874859	+	0.484377i	$0.160954\pi$
$641$			24.5269i			0.968755i	−0.874859	+	0.484377i	$0.839046\pi$
$642$		0			0
$643$	28.1421	−	28.1421i	1.10982	−	1.10982i	0.116644	−	0.993174i	$-0.462786\pi$
$643$	28.1421	−	28.1421i	1.10982	−	1.10982i	0.993174	−	0.116644i	$-0.0372135\pi$
$644$	1.17157			0.0461664
$645$		0			0
$646$	−44.1421			−1.73675
$647$	−24.2132	+	24.2132i	−0.951919	+	0.951919i	−0.998896	−	0.0469767i	$-0.985041\pi$
$647$	−24.2132	+	24.2132i	−0.951919	+	0.951919i	0.0469767	+	0.998896i	$0.485041\pi$
$648$		0			0
$649$		−	6.62742i		−	0.260149i
$650$		0			0
$651$		0			0
$652$	14.8995	+	14.8995i	0.583509	+	0.583509i
$653$	5.41421	+	5.41421i	0.211875	+	0.211875i	0.805063	−	0.593189i	$-0.202131\pi$
$653$	5.41421	+	5.41421i	0.211875	+	0.211875i	−0.593189	+	0.805063i	$0.702131\pi$
$654$		0			0
$655$		0			0
$656$			0.828427i			0.0323446i
$657$		0			0
$658$	3.58579	−	3.58579i	0.139789	−	0.139789i
$659$	−21.7990			−0.849168			−0.424584	−	0.905389i	$-0.639580\pi$
$659$	−21.7990			−0.849168			−0.424584	+	0.905389i	$0.639580\pi$
$660$		0			0
$661$	−36.2426			−1.40968			−0.704838	−	0.709369i	$-0.748980\pi$
$661$	−36.2426			−1.40968			−0.704838	+	0.709369i	$0.748980\pi$
$662$	21.3137	−	21.3137i	0.828381	−	0.828381i
$663$		0			0
$664$			2.34315i			0.0909317i
$665$		0			0
$666$		0			0
$667$	7.31371	+	7.31371i	0.283188	+	0.283188i
$668$	−12.8995	−	12.8995i	−0.499096	−	0.499096i
$669$		0			0
$670$		0			0
$671$			7.79899i			0.301077i
$672$		0			0
$673$	25.7990	−	25.7990i	0.994478	−	0.994478i	−0.00550686	−	0.999985i	$-0.501753\pi$
$673$	25.7990	−	25.7990i	0.994478	−	0.994478i	0.999985	+	0.00550686i	$0.00175290\pi$
$674$	26.1421			1.00696
$675$		0			0
$676$	12.3137			0.473604
$677$	24.4853	−	24.4853i	0.941046	−	0.941046i	−0.0573106	−	0.998356i	$-0.518253\pi$
$677$	24.4853	−	24.4853i	0.941046	−	0.941046i	0.998356	+	0.0573106i	$0.0182525\pi$
$678$		0			0
$679$		−	0.343146i		−	0.0131687i
$680$		0			0
$681$		0			0
$682$	1.85786	+	1.85786i	0.0711413	+	0.0711413i
$683$	−15.8995	−	15.8995i	−0.608377	−	0.608377i	0.334145	−	0.942522i	$-0.391553\pi$
$683$	−15.8995	−	15.8995i	−0.608377	−	0.608377i	−0.942522	+	0.334145i	$0.891553\pi$
$684$		0			0
$685$		0			0
$686$			1.00000i			0.0381802i
$687$		0			0
$688$	−3.58579	+	3.58579i	−0.136707	+	0.136707i
$689$	−0.970563			−0.0369755
$690$		0			0
$691$	25.2132			0.959155			0.479578	−	0.877499i	$-0.340790\pi$
$691$	25.2132			0.959155			0.479578	+	0.877499i	$0.340790\pi$
$692$	8.00000	−	8.00000i	0.304114	−	0.304114i
$693$		0			0
$694$		−	12.9706i		−	0.492356i
$695$		0			0
$696$		0			0
$697$	−3.65685	−	3.65685i	−0.138513	−	0.138513i
$698$	−11.8284	−	11.8284i	−0.447713	−	0.447713i
$699$		0			0
$700$		0			0
$701$			9.51472i			0.359366i	0.983725	+	0.179683i	$0.0575072\pi$
$701$			9.51472i			0.359366i	−0.983725	+	0.179683i	$0.942493\pi$
$702$		0			0
$703$	−57.0711	+	57.0711i	−2.15248	+	2.15248i
$704$	−0.828427			−0.0312225
$705$		0			0
$706$	30.2426			1.13820
$707$	11.0711	−	11.0711i	0.416370	−	0.416370i
$708$		0			0
$709$		−	17.3137i		−	0.650230i	−0.945674	−	0.325115i	$-0.894597\pi$
$709$		−	17.3137i		−	0.650230i	0.945674	−	0.325115i	$-0.105403\pi$
$710$		0			0
$711$		0			0
$712$	6.58579	+	6.58579i	0.246813	+	0.246813i
$713$	2.62742	+	2.62742i	0.0983975	+	0.0983975i
$714$		0			0
$715$		0			0
$716$			9.31371i			0.348070i
$717$		0			0
$718$	3.34315	−	3.34315i	0.124765	−	0.124765i
$719$	45.4558			1.69522			0.847608	−	0.530622i	$-0.178042\pi$
$719$	45.4558			1.69522			0.847608	+	0.530622i	$0.178042\pi$
$720$		0			0
$721$	−0.828427			−0.0308522
$722$	21.9203	−	21.9203i	0.815789	−	0.815789i
$723$		0			0
$724$		−	3.07107i		−	0.114135i
$725$		0			0
$726$		0			0
$727$	1.75736	+	1.75736i	0.0651768	+	0.0651768i	0.738944	−	0.673767i	$-0.235325\pi$
$727$	1.75736	+	1.75736i	0.0651768	+	0.0651768i	−0.673767	+	0.738944i	$0.735325\pi$
$728$	0.585786	+	0.585786i	0.0217107	+	0.0217107i
$729$		0			0
$730$		0			0
$731$		−	31.6569i		−	1.17087i
$732$		0			0
$733$	4.72792	−	4.72792i	0.174630	−	0.174630i	−0.614380	−	0.789010i	$-0.710594\pi$
$733$	4.72792	−	4.72792i	0.174630	−	0.174630i	0.789010	+	0.614380i	$0.210594\pi$
$734$	−28.2843			−1.04399
$735$		0			0
$736$	−1.17157			−0.0431847
$737$	2.00000	−	2.00000i	0.0736709	−	0.0736709i
$738$		0			0
$739$		−	42.6274i		−	1.56807i	−0.620714	−	0.784037i	$-0.713157\pi$
$739$		−	42.6274i		−	1.56807i	0.620714	−	0.784037i	$-0.286843\pi$
$740$		0			0
$741$		0			0
$742$	0.828427	+	0.828427i	0.0304125	+	0.0304125i
$743$	10.1421	+	10.1421i	0.372079	+	0.372079i	0.868234	−	0.496155i	$-0.165255\pi$
$743$	10.1421	+	10.1421i	0.372079	+	0.372079i	−0.496155	+	0.868234i	$0.665255\pi$
$744$		0			0
$745$		0			0
$746$		−	3.89949i		−	0.142771i
$747$		0			0
$748$	3.65685	−	3.65685i	0.133708	−	0.133708i
$749$	7.17157			0.262044
$750$		0			0
$751$	11.0294			0.402470			0.201235	−	0.979543i	$-0.435505\pi$
$751$	11.0294			0.402470			0.201235	+	0.979543i	$0.435505\pi$
$752$	−3.58579	+	3.58579i	−0.130760	+	0.130760i
$753$		0			0
$754$			7.31371i			0.266350i
$755$		0			0
$756$		0			0
$757$	−9.92893	−	9.92893i	−0.360873	−	0.360873i	0.503261	−	0.864134i	$-0.332133\pi$
$757$	−9.92893	−	9.92893i	−0.360873	−	0.360873i	−0.864134	+	0.503261i	$0.832133\pi$
$758$	−4.00000	−	4.00000i	−0.145287	−	0.145287i
$759$		0			0
$760$		0			0
$761$		−	4.34315i		−	0.157439i	−0.996897	−	0.0787195i	$-0.974917\pi$
$761$		−	4.34315i		−	0.157439i	0.996897	−	0.0787195i	$-0.0250831\pi$
$762$		0			0
$763$	5.75736	−	5.75736i	0.208430	−	0.208430i
$764$	10.5858			0.382980
$765$		0			0
$766$	4.58579			0.165691
$767$	4.68629	−	4.68629i	0.169212	−	0.169212i
$768$		0			0
$769$		−	16.1421i		−	0.582100i	−0.956708	−	0.291050i	$-0.905995\pi$
$769$		−	16.1421i		−	0.582100i	0.956708	−	0.291050i	$-0.0940047\pi$
$770$		0			0
$771$		0			0
$772$	−6.00000	−	6.00000i	−0.215945	−	0.215945i
$773$	−35.9411	−	35.9411i	−1.29271	−	1.29271i	−0.933103	−	0.359610i	$-0.882910\pi$
$773$	−35.9411	−	35.9411i	−1.29271	−	1.29271i	−0.359610	−	0.933103i	$-0.617090\pi$
$774$		0			0
$775$		0			0
$776$			0.343146i			0.0123182i
$777$		0			0
$778$	12.2426	−	12.2426i	0.438920	−	0.438920i
$779$	5.85786			0.209880
$780$		0			0
$781$	−3.11270			−0.111381
$782$	5.17157	−	5.17157i	0.184935	−	0.184935i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$		0			0
$786$		0			0
$787$	12.6863	+	12.6863i	0.452217	+	0.452217i	0.896090	−	0.443872i	$-0.146396\pi$
$787$	12.6863	+	12.6863i	0.452217	+	0.452217i	−0.443872	+	0.896090i	$0.646396\pi$
$788$	−8.82843	−	8.82843i	−0.314500	−	0.314500i
$789$		0			0
$790$		0			0
$791$		−	3.65685i		−	0.130023i
$792$		0			0
$793$	−5.51472	+	5.51472i	−0.195833	+	0.195833i
$794$	−31.9411			−1.13355
$795$		0			0
$796$	11.6569			0.413166
$797$	35.7990	−	35.7990i	1.26807	−	1.26807i	0.320979	−	0.947086i	$-0.395988\pi$
$797$	35.7990	−	35.7990i	1.26807	−	1.26807i	0.947086	−	0.320979i	$-0.104012\pi$
$798$		0			0
$799$		−	31.6569i		−	1.11994i
$800$		0			0
$801$		0			0
$802$	11.9706	+	11.9706i	0.422695	+	0.422695i
$803$	−4.97056	−	4.97056i	−0.175407	−	0.175407i
$804$		0			0
$805$		0			0
$806$			2.62742i			0.0925468i
$807$		0			0
$808$	−11.0711	+	11.0711i	−0.389479	+	0.389479i
$809$	49.6985			1.74731			0.873653	−	0.486550i	$-0.161745\pi$
$809$	49.6985			1.74731			0.873653	+	0.486550i	$0.161745\pi$
$810$		0			0
$811$	−32.2426			−1.13219			−0.566096	−	0.824339i	$-0.691547\pi$
$811$	−32.2426			−1.13219			−0.566096	+	0.824339i	$0.691547\pi$
$812$	6.24264	−	6.24264i	0.219074	−	0.219074i
$813$		0			0
$814$		−	9.45584i		−	0.331427i
$815$		0			0
$816$		0			0
$817$	25.3553	+	25.3553i	0.887071	+	0.887071i
$818$	10.3848	+	10.3848i	0.363095	+	0.363095i
$819$		0			0
$820$		0			0
$821$		−	40.1421i		−	1.40097i	−0.713667	−	0.700485i	$-0.752967\pi$
$821$		−	40.1421i		−	1.40097i	0.713667	−	0.700485i	$-0.247033\pi$
$822$		0			0
$823$	37.3137	−	37.3137i	1.30067	−	1.30067i	0.372737	−	0.927937i	$-0.378419\pi$
$823$	37.3137	−	37.3137i	1.30067	−	1.30067i	0.927937	−	0.372737i	$-0.121581\pi$
$824$	0.828427			0.0288596
$825$		0			0
$826$	−8.00000			−0.278356
$827$	−10.8284	+	10.8284i	−0.376541	+	0.376541i	−0.869853	−	0.493311i	$-0.835786\pi$
$827$	−10.8284	+	10.8284i	−0.376541	+	0.376541i	0.493311	+	0.869853i	$0.335786\pi$
$828$		0			0
$829$		−	34.8701i		−	1.21109i	−0.795812	−	0.605544i	$-0.792956\pi$
$829$		−	34.8701i		−	1.21109i	0.795812	−	0.605544i	$-0.207044\pi$
$830$		0			0
$831$		0			0
$832$	−0.585786	−	0.585786i	−0.0203085	−	0.0203085i
$833$	4.41421	+	4.41421i	0.152943	+	0.152943i
$834$		0			0
$835$		0			0
$836$			5.85786i			0.202598i
$837$		0			0
$838$	−14.1421	+	14.1421i	−0.488532	+	0.488532i
$839$	21.1716			0.730924			0.365462	−	0.930826i	$-0.380911\pi$
$839$	21.1716			0.730924			0.365462	+	0.930826i	$0.380911\pi$
$840$		0			0
$841$	48.9411			1.68763
$842$	0.100505	−	0.100505i	0.00346363	−	0.00346363i
$843$		0			0
$844$		−	20.4853i		−	0.705132i
$845$		0			0
$846$		0			0
$847$	−7.29289	−	7.29289i	−0.250587	−	0.250587i
$848$	−0.828427	−	0.828427i	−0.0284483	−	0.0284483i
$849$		0			0
$850$		0			0
$851$		−	13.3726i		−	0.458406i
$852$		0			0
$853$	27.5563	−	27.5563i	0.943511	−	0.943511i	−0.0549762	−	0.998488i	$-0.517508\pi$
$853$	27.5563	−	27.5563i	0.943511	−	0.943511i	0.998488	+	0.0549762i	$0.0175083\pi$
$854$	9.41421			0.322148
$855$		0			0
$856$	−7.17157			−0.245119
$857$	−21.0416	+	21.0416i	−0.718768	+	0.718768i	−0.968353	−	0.249585i	$-0.919706\pi$
$857$	−21.0416	+	21.0416i	−0.718768	+	0.718768i	0.249585	+	0.968353i	$0.419706\pi$
$858$		0			0
$859$			40.7279i			1.38962i	0.719194	+	0.694809i	$0.244511\pi$
$859$			40.7279i			1.38962i	−0.719194	+	0.694809i	$0.755489\pi$
$860$		0			0
$861$		0			0
$862$	−20.6569	−	20.6569i	−0.703575	−	0.703575i
$863$	−26.6274	−	26.6274i	−0.906408	−	0.906408i	0.0895725	−	0.995980i	$-0.471450\pi$
$863$	−26.6274	−	26.6274i	−0.906408	−	0.906408i	−0.995980	+	0.0895725i	$0.971450\pi$
$864$		0			0
$865$		0			0
$866$			22.2843i			0.757250i
$867$		0			0
$868$	2.24264	−	2.24264i	0.0761202	−	0.0761202i
$869$	−7.71573			−0.261738
$870$		0			0
$871$	2.82843			0.0958376
$872$	−5.75736	+	5.75736i	−0.194969	+	0.194969i
$873$		0			0
$874$			8.28427i			0.280220i
$875$		0			0
$876$		0			0
$877$	−5.72792	−	5.72792i	−0.193418	−	0.193418i	0.603753	−	0.797171i	$-0.293671\pi$
$877$	−5.72792	−	5.72792i	−0.193418	−	0.193418i	−0.797171	+	0.603753i	$0.793671\pi$
$878$	9.75736	+	9.75736i	0.329295	+	0.329295i
$879$		0			0
$880$		0			0
$881$			25.5147i			0.859613i	0.902921	+	0.429806i	$0.141418\pi$
$881$			25.5147i			0.859613i	−0.902921	+	0.429806i	$0.858582\pi$
$882$		0			0
$883$	19.1005	−	19.1005i	0.642783	−	0.642783i	−0.308456	−	0.951239i	$-0.599812\pi$
$883$	19.1005	−	19.1005i	0.642783	−	0.642783i	0.951239	+	0.308456i	$0.0998121\pi$
$884$	5.17157			0.173939
$885$		0			0
$886$	−10.6274			−0.357035
$887$	−37.3848	+	37.3848i	−1.25526	+	1.25526i	−0.301927	+	0.953331i	$0.597630\pi$
$887$	−37.3848	+	37.3848i	−1.25526	+	1.25526i	−0.953331	+	0.301927i	$0.902370\pi$
$888$		0			0
$889$		−	9.65685i		−	0.323880i
$890$		0			0
$891$		0			0
$892$	11.8995	+	11.8995i	0.398425	+	0.398425i
$893$	25.3553	+	25.3553i	0.848484	+	0.848484i
$894$		0			0
$895$		0			0
$896$			1.00000i			0.0334077i
$897$		0			0
$898$	−16.7990	+	16.7990i	−0.560590	+	0.560590i
$899$	28.0000			0.933852
$900$		0			0
$901$	7.31371			0.243655
$902$	−0.485281	+	0.485281i	−0.0161581	+	0.0161581i
$903$		0			0
$904$			3.65685i			0.121625i
$905$		0			0
$906$		0			0
$907$	11.2426	+	11.2426i	0.373306	+	0.373306i	0.868680	−	0.495374i	$-0.164969\pi$
$907$	11.2426	+	11.2426i	0.373306	+	0.373306i	−0.495374	+	0.868680i	$0.664969\pi$
$908$	15.6569	+	15.6569i	0.519591	+	0.519591i
$909$		0			0
$910$		0			0
$911$		−	29.8995i		−	0.990614i	−0.868718	−	0.495307i	$-0.835055\pi$
$911$		−	29.8995i		−	0.990614i	0.868718	−	0.495307i	$-0.164945\pi$
$912$		0			0
$913$	−1.37258	+	1.37258i	−0.0454259	+	0.0454259i
$914$	−34.6274			−1.14537
$915$		0			0
$916$	19.0711			0.630126
$917$	−4.24264	+	4.24264i	−0.140104	+	0.140104i
$918$		0			0
$919$		−	8.68629i		−	0.286534i	−0.989684	−	0.143267i	$-0.954239\pi$
$919$		−	8.68629i		−	0.286534i	0.989684	−	0.143267i	$-0.0457608\pi$
$920$		0			0
$921$		0			0
$922$	10.3848	+	10.3848i	0.342004	+	0.342004i
$923$	−2.20101	−	2.20101i	−0.0724471	−	0.0724471i
$924$		0			0
$925$		0			0
$926$			31.7990i			1.04498i
$927$		0			0
$928$	−6.24264	+	6.24264i	−0.204925	+	0.204925i
$929$	−23.6569			−0.776156			−0.388078	−	0.921626i	$-0.626861\pi$
$929$	−23.6569			−0.776156			−0.388078	+	0.921626i	$0.626861\pi$
$930$		0			0
$931$	−7.07107			−0.231745
$932$	−2.58579	+	2.58579i	−0.0847003	+	0.0847003i
$933$		0			0
$934$			2.34315i			0.0766701i
$935$		0			0
$936$		0			0
$937$	16.9289	+	16.9289i	0.553044	+	0.553044i	0.927318	−	0.374274i	$-0.122108\pi$
$937$	16.9289	+	16.9289i	0.553044	+	0.553044i	−0.374274	+	0.927318i	$0.622108\pi$
$938$	−2.41421	−	2.41421i	−0.0788269	−	0.0788269i
$939$		0			0
$940$		0			0
$941$			13.3137i			0.434014i	0.976170	+	0.217007i	$0.0696295\pi$
$941$			13.3137i			0.434014i	−0.976170	+	0.217007i	$0.930370\pi$
$942$		0			0
$943$	−0.686292	+	0.686292i	−0.0223487	+	0.0223487i
$944$	8.00000			0.260378
$945$		0			0
$946$	−4.20101			−0.136587
$947$	8.58579	−	8.58579i	0.279001	−	0.279001i	−0.553709	−	0.832710i	$-0.686788\pi$
$947$	8.58579	−	8.58579i	0.279001	−	0.279001i	0.832710	+	0.553709i	$0.186788\pi$
$948$		0			0
$949$		−	7.02944i		−	0.228185i
$950$		0			0
$951$		0			0
$952$	−4.41421	−	4.41421i	−0.143065	−	0.143065i
$953$	−3.61522	−	3.61522i	−0.117109	−	0.117109i	0.646124	−	0.763233i	$-0.276389\pi$
$953$	−3.61522	−	3.61522i	−0.117109	−	0.117109i	−0.763233	+	0.646124i	$0.776389\pi$
$954$		0			0
$955$		0			0
$956$		−	17.2132i		−	0.556715i
$957$		0			0
$958$	−1.17157	+	1.17157i	−0.0378518	+	0.0378518i
$959$	−18.4853			−0.596921
$960$		0			0
$961$	−20.9411			−0.675520
$962$	6.68629	−	6.68629i	0.215575	−	0.215575i
$963$		0			0
$964$		−	3.65685i		−	0.117779i
$965$		0			0
$966$		0			0
$967$	−40.9706	−	40.9706i	−1.31752	−	1.31752i	−0.915730	−	0.401795i	$-0.868387\pi$
$967$	−40.9706	−	40.9706i	−1.31752	−	1.31752i	−0.401795	−	0.915730i	$-0.631613\pi$
$968$	7.29289	+	7.29289i	0.234402	+	0.234402i
$969$		0			0
$970$		0			0
$971$			24.3431i			0.781209i	0.920559	+	0.390604i	$0.127734\pi$
$971$			24.3431i			0.781209i	−0.920559	+	0.390604i	$0.872266\pi$
$972$		0			0
$973$	5.82843	−	5.82843i	0.186851	−	0.186851i
$974$	28.2843			0.906287
$975$		0			0
$976$	−9.41421			−0.301342
$977$	−1.61522	+	1.61522i	−0.0516756	+	0.0516756i	−0.732472	−	0.680797i	$-0.761634\pi$
$977$	−1.61522	+	1.61522i	−0.0516756	+	0.0516756i	0.680797	+	0.732472i	$0.261634\pi$
$978$		0			0
$979$			7.71573i			0.246596i
$980$		0			0
$981$		0			0
$982$	7.75736	+	7.75736i	0.247547	+	0.247547i
$983$	−24.4142	−	24.4142i	−0.778692	−	0.778692i	0.200916	−	0.979608i	$-0.435608\pi$
$983$	−24.4142	−	24.4142i	−0.778692	−	0.778692i	−0.979608	+	0.200916i	$0.935608\pi$
$984$		0			0
$985$		0			0
$986$		−	55.1127i		−	1.75515i
$987$		0			0
$988$	−4.14214	+	4.14214i	−0.131779	+	0.131779i
$989$	−5.94113			−0.188917
$990$		0			0
$991$	−23.3137			−0.740584			−0.370292	−	0.928915i	$-0.620742\pi$
$991$	−23.3137			−0.740584			−0.370292	+	0.928915i	$0.620742\pi$
$992$	−2.24264	+	2.24264i	−0.0712039	+	0.0712039i
$993$		0			0
$994$			3.75736i			0.119176i
$995$		0			0
$996$		0			0
$997$	36.5269	+	36.5269i	1.15682	+	1.15682i	0.985156	+	0.171663i	$0.0549141\pi$
$997$	36.5269	+	36.5269i	1.15682	+	1.15682i	0.171663	+	0.985156i	$0.445086\pi$
$998$	16.9706	+	16.9706i	0.537194	+	0.537194i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.m.d.1457.1	yes	4
3.2	odd	2		3150.2.m.c.1457.2	✓	4
5.2	odd	4		3150.2.m.e.2843.1	yes	4
5.3	odd	4		3150.2.m.c.2843.2	yes	4
5.4	even	2		3150.2.m.f.1457.2	yes	4
15.2	even	4		3150.2.m.f.2843.2	yes	4
15.8	even	4	inner	3150.2.m.d.2843.1	yes	4
15.14	odd	2		3150.2.m.e.1457.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.m.c.1457.2	✓	4	3.2	odd	2
3150.2.m.c.2843.2	yes	4	5.3	odd	4
3150.2.m.d.1457.1	yes	4	1.1	even	1	trivial
3150.2.m.d.2843.1	yes	4	15.8	even	4	inner
3150.2.m.e.1457.1	yes	4	15.14	odd	2
3150.2.m.e.2843.1	yes	4	5.2	odd	4
3150.2.m.f.1457.2	yes	4	5.4	even	2
3150.2.m.f.2843.2	yes	4	15.2	even	4

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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +0.828427i q^{11} +(-0.585786 + 0.585786i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(4.41421 - 4.41421i) q^{17} +7.07107i q^{19} +(-0.585786 - 0.585786i) q^{22} +(-0.828427 - 0.828427i) q^{23} -0.828427i q^{26} +(-0.707107 + 0.707107i) q^{28} -8.82843 q^{29} -3.17157 q^{31} +(0.707107 - 0.707107i) q^{32} +6.24264i q^{34} +(8.07107 + 8.07107i) q^{37} +(-5.00000 - 5.00000i) q^{38} -0.828427i q^{41} +(3.58579 - 3.58579i) q^{43} +0.828427 q^{44} +1.17157 q^{46} +(3.58579 - 3.58579i) q^{47} +1.00000i q^{49} +(0.585786 + 0.585786i) q^{52} +(0.828427 + 0.828427i) q^{53} -1.00000i q^{56} +(6.24264 - 6.24264i) q^{58} -8.00000 q^{59} +9.41421 q^{61} +(2.24264 - 2.24264i) q^{62} +1.00000i q^{64} +(-2.41421 - 2.41421i) q^{67} +(-4.41421 - 4.41421i) q^{68} +3.75736i q^{71} +(-6.00000 + 6.00000i) q^{73} -11.4142 q^{74} +7.07107 q^{76} +(0.585786 - 0.585786i) q^{77} +9.31371i q^{79} +(0.585786 + 0.585786i) q^{82} +(1.65685 + 1.65685i) q^{83} +5.07107i q^{86} +(-0.585786 + 0.585786i) q^{88} +9.31371 q^{89} +0.828427 q^{91} +(-0.828427 + 0.828427i) q^{92} +5.07107i q^{94} +(0.242641 + 0.242641i) q^{97} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q - 8 q^{13} + 4 q^{14} - 4 q^{16} + 12 q^{17} - 8 q^{22} + 8 q^{23} - 24 q^{29} - 24 q^{31} + 4 q^{37} - 20 q^{38} + 20 q^{43} - 8 q^{44} + 16 q^{46} + 20 q^{47} + 8 q^{52} - 8 q^{53} + 8 q^{58} - 32 q^{59} + 32 q^{61} - 8 q^{62} - 4 q^{67} - 12 q^{68} - 24 q^{73} - 40 q^{74} + 8 q^{77} + 8 q^{82} - 16 q^{83} - 8 q^{88} - 8 q^{89} - 8 q^{91} + 8 q^{92} - 16 q^{97}+O(q^{100}) \) 4 * q - 8 * q^13 + 4 * q^14 - 4 * q^16 + 12 * q^17 - 8 * q^22 + 8 * q^23 - 24 * q^29 - 24 * q^31 + 4 * q^37 - 20 * q^38 + 20 * q^43 - 8 * q^44 + 16 * q^46 + 20 * q^47 + 8 * q^52 - 8 * q^53 + 8 * q^58 - 32 * q^59 + 32 * q^61 - 8 * q^62 - 4 * q^67 - 12 * q^68 - 24 * q^73 - 40 * q^74 + 8 * q^77 + 8 * q^82 - 16 * q^83 - 8 * q^88 - 8 * q^89 - 8 * q^91 + 8 * q^92 - 16 * q^97

Introduction

L-functions

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