LMFDB - Embedded newform 1216.2.i.q.577.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(577,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1216.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.i (of order $3$, degree $2$, 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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.41342275584.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} + 2x^{5} + 81x^{4} - 8x^{3} + 208x^{2} + 128x + 256 $ x^8 - 2x^7 + 13x^6 + 2x^5 + 81x^4 - 8x^3 + 208x^2 + 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 608)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.4
Root			$-0.564469 - 0.977689i$ of defining polynomial
Character	$\chi$	$=$	1216.577
Dual form			1216.2.i.q.961.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20711 + 2.09077i) q^{3} +(1.27158 + 2.20243i) q^{5} +5.01077 q^{7} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(1.20711 + 2.09077i) q^{3} +(1.27158 + 2.20243i) q^{5} +5.01077 q^{7} +(-1.41421 + 2.44949i) q^{9} -3.54315 q^{11} +(-2.36275 + 4.09240i) q^{13} +(-3.06986 + 5.31715i) q^{15} +(-1.18040 - 2.04452i) q^{17} +(-4.31473 + 0.618970i) q^{19} +(6.04854 + 10.4764i) q^{21} +(-1.88751 + 3.26926i) q^{23} +(-0.733811 + 1.27100i) q^{25} +0.414214 q^{27} +(5.15341 - 8.92597i) q^{29} -1.35392 q^{31} +(-4.27696 - 7.40792i) q^{33} +(6.37158 + 11.0359i) q^{35} +7.83920 q^{37} -11.4084 q^{39} +(-0.628938 - 1.08935i) q^{41} +(-0.0213173 - 0.0369226i) q^{43} -7.19312 q^{45} +(1.94092 - 3.36177i) q^{47} +18.1079 q^{49} +(2.84974 - 4.93590i) q^{51} +(3.59462 - 6.22606i) q^{53} +(-4.50539 - 7.80356i) q^{55} +(-6.50246 - 8.27394i) q^{57} +(-3.33605 - 5.77820i) q^{59} +(-3.55685 + 6.16065i) q^{61} +(-7.08630 + 12.2738i) q^{63} -12.0177 q^{65} +(-3.46498 + 6.00153i) q^{67} -9.11370 q^{69} +(2.31737 + 4.01380i) q^{71} +(-0.967622 - 1.67597i) q^{73} -3.54315 q^{75} -17.7539 q^{77} +(6.11839 + 10.5974i) q^{79} +(4.74264 + 8.21449i) q^{81} +4.47840 q^{83} +(3.00194 - 5.19952i) q^{85} +24.8829 q^{87} +(1.64802 - 2.85446i) q^{89} +(-11.8392 + 20.5061i) q^{91} +(-1.63433 - 2.83073i) q^{93} +(-6.84974 - 8.71584i) q^{95} +(0.343663 + 0.595242i) q^{97} +(5.01077 - 8.67891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 2 q^{5} + 8 q^{7}+O(q^{10}) $ 8 * q + 4 * q^3 - 2 * q^5 + 8 * q^7	$ 8 q + 4 q^{3} - 2 q^{5} + 8 q^{7} - 4 q^{11} - 2 q^{13} - 2 q^{15} - 2 q^{17} + 2 q^{19} + 8 q^{21} - 2 q^{23} - 2 q^{25} - 8 q^{27} + 10 q^{29} - 24 q^{31} - 6 q^{33} + 4 q^{35} + 8 q^{37} + 12 q^{39} + 8 q^{41} - 18 q^{43} - 16 q^{45} + 6 q^{47} + 32 q^{49} + 18 q^{51} + 10 q^{53} - 20 q^{55} + 10 q^{57} - 8 q^{59} - 18 q^{61} - 8 q^{63} - 36 q^{65} + 4 q^{67} - 52 q^{69} + 6 q^{71} - 4 q^{75} - 16 q^{77} - 14 q^{79} + 4 q^{81} - 4 q^{83} + 22 q^{85} + 60 q^{87} - 2 q^{89} - 40 q^{91} + 16 q^{93} - 50 q^{95} - 12 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 2 * q^5 + 8 * q^7 - 4 * q^11 - 2 * q^13 - 2 * q^15 - 2 * q^17 + 2 * q^19 + 8 * q^21 - 2 * q^23 - 2 * q^25 - 8 * q^27 + 10 * q^29 - 24 * q^31 - 6 * q^33 + 4 * q^35 + 8 * q^37 + 12 * q^39 + 8 * q^41 - 18 * q^43 - 16 * q^45 + 6 * q^47 + 32 * q^49 + 18 * q^51 + 10 * q^53 - 20 * q^55 + 10 * q^57 - 8 * q^59 - 18 * q^61 - 8 * q^63 - 36 * q^65 + 4 * q^67 - 52 * q^69 + 6 * q^71 - 4 * q^75 - 16 * q^77 - 14 * q^79 + 4 * q^81 - 4 * q^83 + 22 * q^85 + 60 * q^87 - 2 * q^89 - 40 * q^91 + 16 * q^93 - 50 * q^95 - 12 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$2$		0			0
$3$	1.20711	+	2.09077i	0.696923	+	1.20711i	0.969528	+	0.244981i	$0.0787816\pi$
$3$	1.20711	+	2.09077i	0.696923	+	1.20711i	−0.272605	+	0.962126i	$0.587885\pi$
$4$		0			0
$5$	1.27158	+	2.20243i	0.568666	+	0.984958i	0.996698	+	0.0811950i	$0.0258737\pi$
$5$	1.27158	+	2.20243i	0.568666	+	0.984958i	−0.428032	+	0.903763i	$0.640793\pi$
$6$		0			0
$7$	5.01077			1.89389			0.946947	−	0.321389i	$-0.104150\pi$
$7$	5.01077			1.89389			0.946947	+	0.321389i	$0.104150\pi$
$8$		0			0
$9$	−1.41421	+	2.44949i	−0.471405	+	0.816497i
$10$		0			0
$11$	−3.54315			−1.06830			−0.534150	−	0.845390i	$-0.679368\pi$
$11$	−3.54315			−1.06830			−0.534150	+	0.845390i	$0.679368\pi$
$12$		0			0
$13$	−2.36275	+	4.09240i	−0.655309	+	1.13503i	0.326508	+	0.945195i	$0.394128\pi$
$13$	−2.36275	+	4.09240i	−0.655309	+	1.13503i	−0.981816	+	0.189833i	$0.939205\pi$
$14$		0			0
$15$	−3.06986	+	5.31715i	−0.792633	+	1.37288i
$16$		0			0
$17$	−1.18040	−	2.04452i	−0.286290	−	0.495868i	0.686631	−	0.727006i	$-0.259089\pi$
$17$	−1.18040	−	2.04452i	−0.286290	−	0.495868i	−0.972921	+	0.231137i	$0.925755\pi$
$18$		0			0
$19$	−4.31473	+	0.618970i	−0.989866	+	0.142001i
$19$	−4.31473	+	0.618970i	−0.989866	+	0.142001i
$20$		0			0
$21$	6.04854	+	10.4764i	1.31990	+	2.28613i
$22$		0			0
$23$	−1.88751	+	3.26926i	−0.393573	+	0.681688i	−0.992918	−	0.118803i	$-0.962094\pi$
$23$	−1.88751	+	3.26926i	−0.393573	+	0.681688i	0.599345	+	0.800491i	$0.295428\pi$
$24$		0			0
$25$	−0.733811	+	1.27100i	−0.146762	+	0.254200i
$26$		0			0
$27$	0.414214			0.0797154
$28$		0			0
$29$	5.15341	−	8.92597i	0.956964	−	1.65751i	0.227157	−	0.973858i	$-0.427057\pi$
$29$	5.15341	−	8.92597i	0.956964	−	1.65751i	0.729807	−	0.683653i	$-0.239610\pi$
$30$		0			0
$31$	−1.35392			−0.243171			−0.121586	−	0.992581i	$-0.538798\pi$
$31$	−1.35392			−0.243171			−0.121586	+	0.992581i	$0.538798\pi$
$32$		0			0
$33$	−4.27696	−	7.40792i	−0.744524	−	1.28955i
$34$		0			0
$35$	6.37158	+	11.0359i	1.07699	+	1.86541i
$36$		0			0
$37$	7.83920			1.28876			0.644378	−	0.764707i	$-0.277116\pi$
$37$	7.83920			1.28876			0.644378	+	0.764707i	$0.277116\pi$
$38$		0			0
$39$	−11.4084			−1.82680
$40$		0			0
$41$	−0.628938	−	1.08935i	−0.0982237	−	0.170128i	0.812726	−	0.582646i	$-0.197983\pi$
$41$	−0.628938	−	1.08935i	−0.0982237	−	0.170128i	−0.910949	+	0.412518i	$0.864649\pi$
$42$		0			0
$43$	−0.0213173	−	0.0369226i	−0.00325085	−	0.00563064i	0.864395	−	0.502813i	$-0.167701\pi$
$43$	−0.0213173	−	0.0369226i	−0.00325085	−	0.00563064i	−0.867646	+	0.497182i	$0.834368\pi$
$44$		0			0
$45$	−7.19312			−1.07229
$46$		0			0
$47$	1.94092	−	3.36177i	0.283112	−	0.490364i	−0.689038	−	0.724726i	$-0.741967\pi$
$47$	1.94092	−	3.36177i	0.283112	−	0.490364i	0.972150	+	0.234361i	$0.0752999\pi$
$48$		0			0
$49$	18.1079			2.58684
$50$		0			0
$51$	2.84974	−	4.93590i	0.399044	−	0.691165i
$52$		0			0
$53$	3.59462	−	6.22606i	0.493759	−	0.855215i	−0.506216	−	0.862407i	$-0.668956\pi$
$53$	3.59462	−	6.22606i	0.493759	−	0.855215i	0.999974	+	0.00719210i	$0.00228934\pi$
$54$		0			0
$55$	−4.50539	−	7.80356i	−0.607506	−	1.05223i
$56$		0			0
$57$	−6.50246	−	8.27394i	−0.861272	−	1.09591i
$58$		0			0
$59$	−3.33605	−	5.77820i	−0.434316	−	0.752258i	0.562923	−	0.826509i	$-0.309677\pi$
$59$	−3.33605	−	5.77820i	−0.434316	−	0.752258i	−0.997240	+	0.0742515i	$0.976343\pi$
$60$		0			0
$61$	−3.55685	+	6.16065i	−0.455408	+	0.788790i	−0.998712	−	0.0507464i	$-0.983840\pi$
$61$	−3.55685	+	6.16065i	−0.455408	+	0.788790i	0.543303	+	0.839536i	$0.317173\pi$
$62$		0			0
$63$	−7.08630	+	12.2738i	−0.892790	+	1.54636i
$64$		0			0
$65$	−12.0177			−1.49061
$66$		0			0
$67$	−3.46498	+	6.00153i	−0.423315	+	0.733203i	−0.996261	−	0.0863896i	$-0.972467\pi$
$67$	−3.46498	+	6.00153i	−0.423315	+	0.733203i	0.572946	+	0.819593i	$0.305800\pi$
$68$		0			0
$69$	−9.11370			−1.09716
$70$		0			0
$71$	2.31737	+	4.01380i	0.275021	+	0.476350i	0.970140	−	0.242544i	$-0.0779819\pi$
$71$	2.31737	+	4.01380i	0.275021	+	0.476350i	−0.695120	+	0.718894i	$0.744649\pi$
$72$		0			0
$73$	−0.967622	−	1.67597i	−0.113252	−	0.196157i	0.803828	−	0.594862i	$-0.202793\pi$
$73$	−0.967622	−	1.67597i	−0.113252	−	0.196157i	−0.917079	+	0.398704i	$0.869460\pi$
$74$		0			0
$75$	−3.54315			−0.409128
$76$		0			0
$77$	−17.7539			−2.02325
$78$		0			0
$79$	6.11839	+	10.5974i	0.688373	+	1.19230i	0.972364	+	0.233470i	$0.0750082\pi$
$79$	6.11839	+	10.5974i	0.688373	+	1.19230i	−0.283991	+	0.958827i	$0.591659\pi$
$80$		0			0
$81$	4.74264	+	8.21449i	0.526960	+	0.912722i
$82$		0			0
$83$	4.47840			0.491568			0.245784	−	0.969325i	$-0.420955\pi$
$83$	4.47840			0.491568			0.245784	+	0.969325i	$0.420955\pi$
$84$		0			0
$85$	3.00194	−	5.19952i	0.325606	−	0.563967i
$86$		0			0
$87$	24.8829			2.66772
$88$		0			0
$89$	1.64802	−	2.85446i	0.174690	−	0.302572i	−0.765364	−	0.643598i	$-0.777441\pi$
$89$	1.64802	−	2.85446i	0.174690	−	0.302572i	0.940054	+	0.341026i	$0.110774\pi$
$90$		0			0
$91$	−11.8392	+	20.5061i	−1.24109	+	2.14962i
$92$		0			0
$93$	−1.63433	−	2.83073i	−0.169472	−	0.293533i
$94$		0			0
$95$	−6.84974	−	8.71584i	−0.702769	−	0.894226i
$96$		0			0
$97$	0.343663	+	0.595242i	0.0348937	+	0.0604377i	0.882945	−	0.469477i	$-0.155557\pi$
$97$	0.343663	+	0.595242i	0.0348937	+	0.0604377i	−0.848051	+	0.529914i	$0.822224\pi$
$98$		0			0
$99$	5.01077	−	8.67891i	0.503602	−	0.872264i
$100$		0			0
$101$	7.22894	−	12.5209i	0.719307	−	1.24588i	−0.241968	−	0.970284i	$-0.577793\pi$
$101$	7.22894	−	12.5209i	0.719307	−	1.24588i	0.961275	−	0.275591i	$-0.0888737\pi$
$102$		0			0
$103$	−12.7432			−1.25562			−0.627810	−	0.778366i	$-0.716049\pi$
$103$	−12.7432			−1.25562			−0.627810	+	0.778366i	$0.716049\pi$
$104$		0			0
$105$	−15.3824	+	26.6430i	−1.50116	+	2.60009i
$106$		0			0
$107$	−12.1942			−1.17885			−0.589427	−	0.807822i	$-0.700646\pi$
$107$	−12.1942			−1.17885			−0.589427	+	0.807822i	$0.700646\pi$
$108$		0			0
$109$	3.93330	+	6.81267i	0.376742	+	0.652536i	0.990586	−	0.136891i	$-0.0437111\pi$
$109$	3.93330	+	6.81267i	0.376742	+	0.652536i	−0.613844	+	0.789427i	$0.710378\pi$
$110$		0			0
$111$	9.46275	+	16.3900i	0.898165	+	1.55567i
$112$		0			0
$113$	−3.00389			−0.282582			−0.141291	−	0.989968i	$-0.545125\pi$
$113$	−3.00389			−0.282582			−0.141291	+	0.989968i	$0.545125\pi$
$114$		0			0
$115$	−9.60045			−0.895246
$116$		0			0
$117$	−6.68286	−	11.5751i	−0.617831	−	1.07011i
$118$		0			0
$119$	−5.91473	−	10.2446i	−0.542202	−	0.939122i
$120$		0			0
$121$	1.55393			0.141266
$122$		0			0
$123$	1.51839	−	2.62993i	0.136909	−	0.237133i
$124$		0			0
$125$	8.98337			0.803497
$126$		0			0
$127$	−0.553696	+	0.959029i	−0.0491325	+	0.0851001i	−0.889546	−	0.456846i	$-0.848979\pi$
$127$	−0.553696	+	0.959029i	−0.0491325	+	0.0851001i	0.840413	+	0.541946i	$0.182312\pi$
$128$		0			0
$129$	0.0514644	−	0.0891390i	0.00453119	−	0.00784825i
$130$		0			0
$131$	0.196333	+	0.340059i	0.0171537	+	0.0297111i	0.874475	−	0.485071i	$-0.161206\pi$
$131$	0.196333	+	0.340059i	0.0171537	+	0.0297111i	−0.857321	+	0.514782i	$0.827873\pi$
$132$		0			0
$133$	−21.6201	+	3.10152i	−1.87470	+	0.268936i
$134$		0			0
$135$	0.526704	+	0.912278i	0.0453315	+	0.0785164i
$136$		0			0
$137$	10.7534	−	18.6255i	0.918726	−	1.59128i	0.117374	−	0.993088i	$-0.462552\pi$
$137$	10.7534	−	18.6255i	0.918726	−	1.59128i	0.801352	−	0.598193i	$-0.204114\pi$
$138$		0			0
$139$	8.87920	−	15.3792i	0.753124	−	1.30445i	−0.193178	−	0.981164i	$-0.561880\pi$
$139$	8.87920	−	15.3792i	0.753124	−	1.30445i	0.946302	−	0.323285i	$-0.104787\pi$
$140$		0			0
$141$	9.37158			0.789229
$142$		0			0
$143$	8.37158	−	14.5000i	0.700067	−	1.21255i
$144$		0			0
$145$	26.2118			2.17677
$146$		0			0
$147$	21.8581	+	37.8594i	1.80283	+	3.12259i
$148$		0			0
$149$	1.03971	+	1.80083i	0.0851763	+	0.147530i	0.905466	−	0.424418i	$-0.139521\pi$
$149$	1.03971	+	1.80083i	0.0851763	+	0.147530i	−0.820290	+	0.571948i	$0.806188\pi$
$150$		0			0
$151$	−7.94602			−0.646638			−0.323319	−	0.946290i	$-0.604799\pi$
$151$	−7.94602			−0.646638			−0.323319	+	0.946290i	$0.604799\pi$
$152$		0			0
$153$	6.67737			0.539833
$154$		0			0
$155$	−1.72161	−	2.98192i	−0.138283	−	0.239513i
$156$		0			0
$157$	−10.8525	−	18.7971i	−0.866123	−	1.50017i	−0.865928	−	0.500169i	$-0.833271\pi$
$157$	−10.8525	−	18.7971i	−0.866123	−	1.50017i	−0.000195692	−	1.00000i	$-0.500062\pi$
$158$		0			0
$159$	17.3563			1.37645
$160$		0			0
$161$	−9.45788	+	16.3815i	−0.745386	+	1.29105i
$162$		0			0
$163$	11.2216			0.878940			0.439470	−	0.898257i	$-0.355166\pi$
$163$	11.2216			0.878940			0.439470	+	0.898257i	$0.355166\pi$
$164$		0			0
$165$	10.8770	−	18.8395i	0.846771	−	1.46665i
$166$		0			0
$167$	−1.96345	+	3.40079i	−0.151936	+	0.263161i	−0.931939	−	0.362615i	$-0.881884\pi$
$167$	−1.96345	+	3.40079i	−0.151936	+	0.263161i	0.780003	+	0.625776i	$0.215217\pi$
$168$		0			0
$169$	−4.66517	−	8.08031i	−0.358859	−	0.621562i
$170$		0			0
$171$	4.58579	−	11.4442i	0.350684	−	0.875163i
$172$		0			0
$173$	5.59462	+	9.69016i	0.425351	+	0.736729i	0.996453	−	0.0841497i	$-0.0268174\pi$
$173$	5.59462	+	9.69016i	0.425351	+	0.736729i	−0.571102	+	0.820879i	$0.693484\pi$
$174$		0			0
$175$	−3.67696	+	6.36868i	−0.277952	+	0.481427i
$176$		0			0
$177$	8.05393	−	13.9498i	0.605370	−	1.04853i
$178$		0			0
$179$	−8.68425			−0.649092			−0.324546	−	0.945870i	$-0.605211\pi$
$179$	−8.68425			−0.649092			−0.324546	+	0.945870i	$0.605211\pi$
$180$		0			0
$181$	−4.63627	+	8.03025i	−0.344611	+	0.596884i	−0.985283	−	0.170931i	$-0.945323\pi$
$181$	−4.63627	+	8.03025i	−0.344611	+	0.596884i	0.640672	+	0.767815i	$0.278656\pi$
$182$		0			0
$183$	−17.1740			−1.26954
$184$		0			0
$185$	9.96814	+	17.2653i	0.732872	+	1.26937i
$186$		0			0
$187$	4.18235	+	7.24404i	0.305843	+	0.529736i
$188$		0			0
$189$	2.07553			0.150973
$190$		0			0
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		0			0
$193$	10.7770	+	18.6662i	0.775743	+	1.34363i	0.934376	+	0.356288i	$0.115958\pi$
$193$	10.7770	+	18.6662i	0.775743	+	1.34363i	−0.158633	+	0.987338i	$0.550709\pi$
$194$		0			0
$195$	−14.5066	−	25.1262i	−1.03884	−	1.79932i
$196$		0			0
$197$	−5.81765			−0.414491			−0.207245	−	0.978289i	$-0.566450\pi$
$197$	−5.81765			−0.414491			−0.207245	+	0.978289i	$0.566450\pi$
$198$		0			0
$199$	−2.67817	+	4.63873i	−0.189851	+	0.328831i	−0.945200	−	0.326491i	$-0.894134\pi$
$199$	−2.67817	+	4.63873i	−0.189851	+	0.328831i	0.755350	+	0.655322i	$0.227467\pi$
$200$		0			0
$201$	−16.7304			−1.18007
$202$		0			0
$203$	25.8226	−	44.7260i	1.81239	−	3.13915i
$204$		0			0
$205$	1.59949	−	2.77039i	0.111713	−	0.193492i
$206$		0			0
$207$	−5.33868	−	9.24687i	−0.371064	−	0.642702i
$208$		0			0
$209$	15.2877	−	2.19310i	1.05747	−	0.151700i
$210$		0			0
$211$	−3.66740	−	6.35212i	−0.252474	−	0.437298i	0.711732	−	0.702451i	$-0.247911\pi$
$211$	−3.66740	−	6.35212i	−0.252474	−	0.437298i	−0.964206	+	0.265153i	$0.914578\pi$
$212$		0			0
$213$	−5.59462	+	9.69016i	−0.383337	+	0.663959i
$214$		0			0
$215$	0.0542131	−	0.0938998i	0.00369730	−	0.00640391i
$216$		0			0
$217$	−6.78418			−0.460540
$218$		0			0
$219$	2.33605	−	4.04615i	0.157855	−	0.273413i
$220$		0			0
$221$	11.1560			0.750433
$222$		0			0
$223$	−5.48407	−	9.49869i	−0.367240	−	0.636079i	0.621893	−	0.783103i	$-0.286364\pi$
$223$	−5.48407	−	9.49869i	−0.367240	−	0.636079i	−0.989133	+	0.147023i	$0.953031\pi$
$224$		0			0
$225$	−2.07553	−	3.59492i	−0.138369	−	0.239662i
$226$		0			0
$227$	−20.8646			−1.38483			−0.692417	−	0.721497i	$-0.743454\pi$
$227$	−20.8646			−1.38483			−0.692417	+	0.721497i	$0.743454\pi$
$228$		0			0
$229$	6.67737			0.441253			0.220626	−	0.975358i	$-0.429190\pi$
$229$	6.67737			0.441253			0.220626	+	0.975358i	$0.429190\pi$
$230$		0			0
$231$	−21.4309	−	37.1194i	−1.41005	−	2.44228i
$232$		0			0
$233$	−3.16132	−	5.47556i	−0.207105	−	0.358716i	0.743697	−	0.668517i	$-0.233071\pi$
$233$	−3.16132	−	5.47556i	−0.207105	−	0.358716i	−0.950801	+	0.309801i	$0.899737\pi$
$234$		0			0
$235$	9.87210			0.643985
$236$		0			0
$237$	−14.7711	+	25.5843i	−0.959487	+	1.66188i
$238$		0			0
$239$	15.0648			0.974458			0.487229	−	0.873274i	$-0.338008\pi$
$239$	15.0648			0.974458			0.487229	+	0.873274i	$0.338008\pi$
$240$		0			0
$241$	−8.46814	+	14.6672i	−0.545481	+	0.944800i	0.453096	+	0.891462i	$0.350320\pi$
$241$	−8.46814	+	14.6672i	−0.545481	+	0.944800i	−0.998576	+	0.0533385i	$0.983014\pi$
$242$		0			0
$243$	−10.8284	+	18.7554i	−0.694644	+	1.20316i
$244$		0			0
$245$	23.0255	+	39.8813i	1.47105	+	2.54793i
$246$		0			0
$247$	7.66155	−	19.1201i	0.487493	−	1.21658i
$248$		0			0
$249$	5.40590	+	9.36330i	0.342585	+	0.593375i
$250$		0			0
$251$	−8.61686	+	14.9248i	−0.543891	+	0.942047i	0.454785	+	0.890601i	$0.349716\pi$
$251$	−8.61686	+	14.9248i	−0.543891	+	0.942047i	−0.998676	+	0.0514458i	$0.983617\pi$
$252$		0			0
$253$	6.68773	−	11.5835i	0.420454	−	0.728248i
$254$		0			0
$255$	14.4947			0.907691
$256$		0			0
$257$	−4.86081	+	8.41916i	−0.303209	+	0.525173i	−0.976861	−	0.213876i	$-0.931391\pi$
$257$	−4.86081	+	8.41916i	−0.303209	+	0.525173i	0.673652	+	0.739049i	$0.264725\pi$
$258$		0			0
$259$	39.2805			2.44077
$260$		0			0
$261$	14.5760	+	25.2465i	0.902235	+	1.56272i
$262$		0			0
$263$	−6.45667	−	11.1833i	−0.398135	−	0.689591i	0.595361	−	0.803459i	$-0.297009\pi$
$263$	−6.45667	−	11.1833i	−0.398135	−	0.689591i	−0.993496	+	0.113868i	$0.963676\pi$
$264$		0			0
$265$	18.2833			1.12313
$266$		0			0
$267$	7.95737			0.486983
$268$		0			0
$269$	12.5559	+	21.7474i	0.765545	+	1.32596i	0.939958	+	0.341290i	$0.110864\pi$
$269$	12.5559	+	21.7474i	0.765545	+	1.32596i	−0.174413	+	0.984673i	$0.555803\pi$
$270$		0			0
$271$	11.3277	+	19.6202i	0.688111	+	1.19184i	0.972448	+	0.233119i	$0.0748930\pi$
$271$	11.3277	+	19.6202i	0.688111	+	1.19184i	−0.284338	+	0.958724i	$0.591774\pi$
$272$		0			0
$273$	−57.1647			−3.45977
$274$		0			0
$275$	2.60000	−	4.50334i	0.156786	−	0.271561i
$276$		0			0
$277$	−25.4628			−1.52991			−0.764956	−	0.644083i	$-0.777239\pi$
$277$	−25.4628			−1.52991			−0.764956	+	0.644083i	$0.777239\pi$
$278$		0			0
$279$	1.91473	−	3.31641i	0.114632	−	0.198548i
$280$		0			0
$281$	4.82652	−	8.35978i	0.287926	−	0.498703i	−0.685388	−	0.728178i	$-0.740368\pi$
$281$	4.82652	−	8.35978i	0.287926	−	0.498703i	0.973315	+	0.229475i	$0.0737009\pi$
$282$		0			0
$283$	−10.7292	−	18.5835i	−0.637783	−	1.10467i	−0.985918	−	0.167228i	$-0.946518\pi$
$283$	−10.7292	−	18.5835i	−0.637783	−	1.10467i	0.348135	−	0.937444i	$-0.386815\pi$
$284$		0			0
$285$	9.95444	−	24.8422i	0.589650	−	1.47152i
$286$		0			0
$287$	−3.15147	−	5.45850i	−0.186025	−	0.322205i
$288$		0			0
$289$	5.71330	−	9.89572i	0.336076	−	0.582101i
$290$		0			0
$291$	−0.829676	+	1.43704i	−0.0486365	+	0.0842408i
$292$		0			0
$293$	2.56081			0.149604			0.0748021	−	0.997198i	$-0.476167\pi$
$293$	2.56081			0.149604			0.0748021	+	0.997198i	$0.476167\pi$
$294$		0			0
$295$	8.48407	−	14.6948i	0.493962	−	0.855567i
$296$		0			0
$297$	−1.46762			−0.0851600
$298$		0			0
$299$	−8.91942	−	15.4489i	−0.515824	−	0.893433i
$300$		0			0
$301$	−0.106816	−	0.185011i	−0.00615677	−	0.0106638i
$302$		0			0
$303$	34.9044			2.00521
$304$		0			0
$305$	−18.0912			−1.03590
$306$		0			0
$307$	3.08952	+	5.35120i	0.176328	+	0.305409i	0.940620	−	0.339461i	$-0.110245\pi$
$307$	3.08952	+	5.35120i	0.176328	+	0.305409i	−0.764292	+	0.644870i	$0.776911\pi$
$308$		0			0
$309$	−15.3824	−	26.6430i	−0.875071	−	1.51567i
$310$		0			0
$311$	8.21282			0.465706			0.232853	−	0.972512i	$-0.425194\pi$
$311$	8.21282			0.465706			0.232853	+	0.972512i	$0.425194\pi$
$312$		0			0
$313$	9.28579	−	16.0835i	0.524864	−	0.909091i	−0.474717	−	0.880139i	$-0.657449\pi$
$313$	9.28579	−	16.0835i	0.524864	−	0.909091i	0.999581	−	0.0289525i	$-0.00921717\pi$
$314$		0			0
$315$	−36.0431			−2.03080
$316$		0			0
$317$	0.572494	−	0.991589i	0.0321545	−	0.0556932i	−0.849500	−	0.527588i	$-0.823096\pi$
$317$	0.572494	−	0.991589i	0.0321545	−	0.0556932i	0.881655	+	0.471895i	$0.156430\pi$
$318$		0			0
$319$	−18.2593	+	31.6261i	−1.02233	+	1.77072i
$320$		0			0
$321$	−14.7196	−	25.4952i	−0.821571	−	1.42300i
$322$		0			0
$323$	6.35861	+	8.09090i	0.353803	+	0.450190i
$324$		0			0
$325$	−3.46762	−	6.00610i	−0.192349	−	0.333158i
$326$		0			0
$327$	−9.49583	+	16.4473i	−0.525120	+	0.909535i
$328$		0			0
$329$	9.72550	−	16.8451i	0.536184	−	0.928698i
$330$		0			0
$331$	−8.47062			−0.465587			−0.232794	−	0.972526i	$-0.574787\pi$
$331$	−8.47062			−0.465587			−0.232794	+	0.972526i	$0.574787\pi$
$332$		0			0
$333$	−11.0863	+	19.2020i	−0.607526	+	1.05227i
$334$		0			0
$335$	−17.6240			−0.962900
$336$		0			0
$337$	−7.29657	−	12.6380i	−0.397469	−	0.688437i	0.595944	−	0.803026i	$-0.296778\pi$
$337$	−7.29657	−	12.6380i	−0.397469	−	0.688437i	−0.993413	+	0.114589i	$0.963445\pi$
$338$		0			0
$339$	−3.62601	−	6.28044i	−0.196938	−	0.341107i
$340$		0			0
$341$	4.79714			0.259780
$342$		0			0
$343$	55.6589			3.00530
$344$		0			0
$345$	−11.5888	−	20.0723i	−0.623918	−	1.08066i
$346$		0			0
$347$	−9.15370	−	15.8547i	−0.491396	−	0.851123i	0.508555	−	0.861030i	$-0.330180\pi$
$347$	−9.15370	−	15.8547i	−0.491396	−	0.851123i	−0.999951	+	0.00990637i	$0.996847\pi$
$348$		0			0
$349$	16.8931			0.904265			0.452133	−	0.891951i	$-0.350663\pi$
$349$	16.8931			0.904265			0.452133	+	0.891951i	$0.350663\pi$
$350$		0			0
$351$	−0.978683	+	1.69513i	−0.0522382	+	0.0904793i
$352$		0			0
$353$	3.70395			0.197141			0.0985707	−	0.995130i	$-0.468573\pi$
$353$	3.70395			0.197141			0.0985707	+	0.995130i	$0.468573\pi$
$354$		0			0
$355$	−5.89341	+	10.2077i	−0.312790	+	0.541768i
$356$		0			0
$357$	14.2794	−	24.7327i	0.755747	−	1.30899i
$358$		0			0
$359$	−15.8175	−	27.3967i	−0.834814	−	1.44594i	−0.894181	−	0.447705i	$-0.852242\pi$
$359$	−15.8175	−	27.3967i	−0.834814	−	1.44594i	0.0593669	−	0.998236i	$-0.481092\pi$
$360$		0			0
$361$	18.2338	−	5.34137i	0.959671	−	0.281125i
$362$		0			0
$363$	1.87575	+	3.24890i	0.0984515	+	0.170523i
$364$		0			0
$365$	2.46081	−	4.26225i	0.128805	−	0.223096i
$366$		0			0
$367$	3.14092	−	5.44024i	0.163955	−	0.283978i	−0.772329	−	0.635223i	$-0.780908\pi$
$367$	3.14092	−	5.44024i	0.163955	−	0.283978i	0.936284	+	0.351245i	$0.114242\pi$
$368$		0			0
$369$	3.55781			0.185212
$370$		0			0
$371$	18.0118	−	31.1974i	0.935126	−	1.61969i
$372$		0			0
$373$	−15.7941			−0.817790			−0.408895	−	0.912582i	$-0.634086\pi$
$373$	−15.7941			−0.817790			−0.408895	+	0.912582i	$0.634086\pi$
$374$		0			0
$375$	10.8439	+	18.7822i	0.559976	+	0.969907i
$376$		0			0
$377$	24.3524	+	42.1797i	1.25421	+	2.17236i
$378$		0			0
$379$	21.8372			1.12170			0.560852	−	0.827916i	$-0.310474\pi$
$379$	21.8372			1.12170			0.560852	+	0.827916i	$0.310474\pi$
$380$		0			0
$381$	−2.67348			−0.136966
$382$		0			0
$383$	1.27960	+	2.21633i	0.0653845	+	0.113249i	0.896865	−	0.442305i	$-0.145839\pi$
$383$	1.27960	+	2.21633i	0.0653845	+	0.113249i	−0.831480	+	0.555555i	$0.812506\pi$
$384$		0			0
$385$	−22.5755	−	39.1019i	−1.15055	−	1.99282i
$386$		0			0
$387$	0.120589			0.00612987
$388$		0			0
$389$	−3.78774	+	6.56055i	−0.192046	+	0.332633i	−0.945928	−	0.324376i	$-0.894846\pi$
$389$	−3.78774	+	6.56055i	−0.192046	+	0.332633i	0.753882	+	0.657010i	$0.228179\pi$
$390$		0			0
$391$	8.91209			0.450704
$392$		0			0
$393$	−0.473991	+	0.820976i	−0.0239097	+	0.0414127i
$394$		0			0
$395$	−15.5600	+	26.9507i	−0.782909	+	1.35604i
$396$		0			0
$397$	−9.61576	−	16.6550i	−0.482601	−	0.835889i	0.517199	−	0.855865i	$-0.326975\pi$
$397$	−9.61576	−	16.6550i	−0.482601	−	0.835889i	−0.999800	+	0.0199755i	$0.993641\pi$
$398$		0			0
$399$	−32.5824	−	41.4588i	−1.63116	−	2.07554i
$400$		0			0
$401$	−16.5270	−	28.6257i	−0.825321	−	1.42950i	−0.901674	−	0.432417i	$-0.857661\pi$
$401$	−16.5270	−	28.6257i	−0.825321	−	1.42950i	0.0763524	−	0.997081i	$-0.475673\pi$
$402$		0			0
$403$	3.19897	−	5.54078i	0.159352	−	0.276006i
$404$		0			0
$405$	−12.0613	+	20.8907i	−0.599329	+	1.03807i
$406$		0			0
$407$	−27.7755			−1.37678
$408$		0			0
$409$	10.3607	−	17.9453i	0.512306	−	0.887340i	−0.487592	−	0.873071i	$-0.662125\pi$
$409$	10.3607	−	17.9453i	0.512306	−	0.887340i	0.999898	−	0.0142685i	$-0.00454196\pi$
$410$		0			0
$411$	51.9221			2.56113
$412$		0			0
$413$	−16.7162	−	28.9532i	−0.822549	−	1.42470i
$414$		0			0
$415$	5.69462	+	9.86337i	0.279538	+	0.484174i
$416$		0			0
$417$	42.8726			2.09948
$418$		0			0
$419$	24.7725			1.21021			0.605107	−	0.796144i	$-0.293130\pi$
$419$	24.7725			1.21021			0.605107	+	0.796144i	$0.293130\pi$
$420$		0			0
$421$	4.71765	+	8.17121i	0.229924	+	0.398240i	0.957785	−	0.287484i	$-0.0928188\pi$
$421$	4.71765	+	8.17121i	0.229924	+	0.398240i	−0.727861	+	0.685724i	$0.759485\pi$
$422$		0			0
$423$	5.48974	+	9.50852i	0.266920	+	0.462320i
$424$		0			0
$425$	3.46477			0.168066
$426$		0			0
$427$	−17.8226	+	30.8696i	−0.862495	+	1.49388i
$428$		0			0
$429$	40.4216			1.95157
$430$		0			0
$431$	−11.3821	+	19.7144i	−0.548258	+	0.949610i	0.450137	+	0.892960i	$0.351375\pi$
$431$	−11.3821	+	19.7144i	−0.548258	+	0.949610i	−0.998394	+	0.0566502i	$0.981958\pi$
$432$		0			0
$433$	1.50831	−	2.61247i	0.0724849	−	0.125547i	−0.827505	−	0.561458i	$-0.810240\pi$
$433$	1.50831	−	2.61247i	0.0724849	−	0.125547i	0.899990	+	0.435911i	$0.143574\pi$
$434$		0			0
$435$	31.6405	+	54.8029i	1.51704	+	2.62760i
$436$		0			0
$437$	6.12052	−	15.2743i	0.292784	−	0.730668i
$438$		0			0
$439$	16.9738	+	29.3995i	0.810116	+	1.40316i	0.912782	+	0.408446i	$0.133929\pi$
$439$	16.9738	+	29.3995i	0.810116	+	1.40316i	−0.102667	+	0.994716i	$0.532737\pi$
$440$		0			0
$441$	−25.6084	+	44.3550i	−1.21945	+	2.11214i
$442$		0			0
$443$	5.14681	−	8.91454i	0.244532	−	0.423543i	−0.717468	−	0.696592i	$-0.754699\pi$
$443$	5.14681	−	8.91454i	0.244532	−	0.423543i	0.962000	+	0.273049i	$0.0880322\pi$
$444$		0			0
$445$	8.38235			0.397362
$446$		0			0
$447$	−2.51008	+	4.34758i	−0.118723	+	0.205634i
$448$		0			0
$449$	−32.6607			−1.54136			−0.770678	−	0.637225i	$-0.780082\pi$
$449$	−32.6607			−1.54136			−0.770678	+	0.637225i	$0.780082\pi$
$450$		0			0
$451$	2.22842	+	3.85974i	0.104932	+	0.181748i
$452$		0			0
$453$	−9.59169	−	16.6133i	−0.450657	−	0.780561i
$454$		0			0
$455$	−60.2178			−2.82305
$456$		0			0
$457$	−41.7597			−1.95343			−0.976717	−	0.214530i	$-0.931178\pi$
$457$	−41.7597			−1.95343			−0.976717	+	0.214530i	$0.931178\pi$
$458$		0			0
$459$	−0.488939	−	0.846867i	−0.0228217	−	0.0395284i
$460$		0			0
$461$	−3.84700	−	6.66319i	−0.179172	−	0.310336i	0.762425	−	0.647077i	$-0.224009\pi$
$461$	−3.84700	−	6.66319i	−0.179172	−	0.310336i	−0.941597	+	0.336741i	$0.890675\pi$
$462$		0			0
$463$	−2.88045			−0.133866			−0.0669328	−	0.997757i	$-0.521321\pi$
$463$	−2.88045			−0.133866			−0.0669328	+	0.997757i	$0.521321\pi$
$464$		0			0
$465$	4.15634	−	7.19899i	0.192746	−	0.333845i
$466$		0			0
$467$	13.2431			0.612818			0.306409	−	0.951900i	$-0.400873\pi$
$467$	13.2431			0.612818			0.306409	+	0.951900i	$0.400873\pi$
$468$		0			0
$469$	−17.3622	+	30.0723i	−0.801714	+	1.38861i
$470$		0			0
$471$	26.2002	−	45.3801i	1.20724	−	2.09101i
$472$		0			0
$473$	0.0755303	+	0.130822i	0.00347289	+	0.00601522i
$474$		0			0
$475$	2.37948	−	5.93822i	0.109178	−	0.272464i
$476$		0			0
$477$	10.1671	+	17.6100i	0.465520	+	0.806304i
$478$		0			0
$479$	−6.32814	+	10.9607i	−0.289140	+	0.500805i	−0.973605	−	0.228241i	$-0.926703\pi$
$479$	−6.32814	+	10.9607i	−0.289140	+	0.500805i	0.684465	+	0.729046i	$0.260036\pi$
$480$		0			0
$481$	−18.5221	+	32.0812i	−0.844533	+	1.46277i
$482$		0			0
$483$	−45.6667			−2.07791
$484$		0			0
$485$	−0.873987	+	1.51379i	−0.0396857	+	0.0687377i
$486$		0			0
$487$	2.01459			0.0912896			0.0456448	−	0.998958i	$-0.485466\pi$
$487$	2.01459			0.0912896			0.0456448	+	0.998958i	$0.485466\pi$
$488$		0			0
$489$	13.5456	+	23.4617i	0.612554	+	1.06097i
$490$		0			0
$491$	−9.11151	−	15.7816i	−0.411197	−	0.712213i	0.583824	−	0.811880i	$-0.301556\pi$
$491$	−9.11151	−	15.7816i	−0.411197	−	0.712213i	−0.995021	+	0.0996666i	$0.968222\pi$
$492$		0			0
$493$	−24.3324			−1.09588
$494$		0			0
$495$	25.4863			1.14552
$496$		0			0
$497$	11.6118	+	20.1122i	0.520860	+	0.902156i
$498$		0			0
$499$	−22.0723	−	38.2304i	−0.988093	−	1.71143i	−0.627293	−	0.778783i	$-0.715837\pi$
$499$	−22.0723	−	38.2304i	−0.988093	−	1.71143i	−0.360799	−	0.932643i	$-0.617496\pi$
$500$		0			0
$501$	−9.48036			−0.423551
$502$		0			0
$503$	3.27432	−	5.67130i	0.145995	−	0.252871i	−0.783749	−	0.621078i	$-0.786695\pi$
$503$	3.27432	−	5.67130i	0.145995	−	0.252871i	0.929744	+	0.368207i	$0.120028\pi$
$504$		0			0
$505$	36.7686			1.63618
$506$		0			0
$507$	11.2627	−	19.5076i	0.500194	−	0.866362i
$508$		0			0
$509$	2.87747	−	4.98392i	0.127542	−	0.220908i	−0.795182	−	0.606371i	$-0.792625\pi$
$509$	2.87747	−	4.98392i	0.127542	−	0.220908i	0.922724	+	0.385462i	$0.125958\pi$
$510$		0			0
$511$	−4.84853	−	8.39790i	−0.214486	−	0.371501i
$512$		0			0
$513$	−1.78722	+	0.256386i	−0.0789076	+	0.0113197i
$514$		0			0
$515$	−16.2039	−	28.0660i	−0.714029	−	1.23673i
$516$		0			0
$517$	−6.87697	+	11.9113i	−0.302449	+	0.523856i
$518$		0			0
$519$	−13.5066	+	23.3941i	−0.592874	+	1.02689i
$520$		0			0
$521$	15.0087			0.657545			0.328772	−	0.944409i	$-0.393365\pi$
$521$	15.0087			0.657545			0.328772	+	0.944409i	$0.393365\pi$
$522$		0			0
$523$	−5.98257	+	10.3621i	−0.261600	+	0.453104i	−0.966667	−	0.256036i	$-0.917583\pi$
$523$	−5.98257	+	10.3621i	−0.261600	+	0.453104i	0.705068	+	0.709140i	$0.250917\pi$
$524$		0			0
$525$	−17.7539			−0.774845
$526$		0			0
$527$	1.59817	+	2.76811i	0.0696174	+	0.120581i
$528$		0			0
$529$	4.37462	+	7.57706i	0.190201	+	0.329437i
$530$		0			0
$531$	18.8715			0.818954
$532$		0			0
$533$	5.94409			0.257467
$534$		0			0
$535$	−15.5058	−	26.8568i	−0.670374	−	1.16112i
$536$		0			0
$537$	−10.4828	−	18.1568i	−0.452367	−	0.783523i
$538$		0			0
$539$	−64.1589			−2.76352
$540$		0			0
$541$	14.9343	−	25.8670i	0.642077	−	1.11211i	−0.342891	−	0.939375i	$-0.611406\pi$
$541$	14.9343	−	25.8670i	0.642077	−	1.11211i	0.984968	−	0.172735i	$-0.0552605\pi$
$542$		0			0
$543$	−22.3859			−0.960670
$544$		0			0
$545$	−10.0030	+	17.3257i	−0.428481	+	0.742150i
$546$		0			0
$547$	2.97811	−	5.15823i	0.127335	−	0.220550i	−0.795308	−	0.606205i	$-0.792691\pi$
$547$	2.97811	−	5.15823i	0.127335	−	0.220550i	0.922643	+	0.385655i	$0.126024\pi$
$548$		0			0
$549$	−10.0603	−	17.4249i	−0.429363	−	0.743678i
$550$		0			0
$551$	−16.7107	+	41.7029i	−0.711898	+	1.77660i
$552$		0			0
$553$	30.6579	+	53.1010i	1.30371	+	2.25809i
$554$		0			0
$555$	−24.0652	+	41.6822i	−1.02151	+	1.76931i
$556$		0			0
$557$	1.64171	−	2.84353i	0.0695616	−	0.120484i	−0.829147	−	0.559031i	$-0.811173\pi$
$557$	1.64171	−	2.84353i	0.0695616	−	0.120484i	0.898708	+	0.438547i	$0.144507\pi$
$558$		0			0
$559$	0.201469			0.00852125
$560$		0			0
$561$	−10.0971	+	17.4887i	−0.426299	+	0.738371i
$562$		0			0
$563$	−42.1804			−1.77769			−0.888846	−	0.458206i	$-0.848492\pi$
$563$	−42.1804			−1.77769			−0.888846	+	0.458206i	$0.848492\pi$
$564$		0			0
$565$	−3.81967	−	6.61586i	−0.160695	−	0.278331i
$566$		0			0
$567$	23.7643	+	41.1610i	0.998007	+	1.72860i
$568$		0			0
$569$	−30.1852			−1.26543			−0.632715	−	0.774384i	$-0.718060\pi$
$569$	−30.1852			−1.26543			−0.632715	+	0.774384i	$0.718060\pi$
$570$		0			0
$571$	16.2254			0.679010			0.339505	−	0.940604i	$-0.389740\pi$
$571$	16.2254			0.679010			0.339505	+	0.940604i	$0.389740\pi$
$572$		0			0
$573$	9.65685	+	16.7262i	0.403421	+	0.698745i
$574$		0			0
$575$	−2.77015	−	4.79804i	−0.115523	−	0.200092i
$576$		0			0
$577$	40.9118			1.70318			0.851589	−	0.524209i	$-0.175639\pi$
$577$	40.9118			1.70318			0.851589	+	0.524209i	$0.175639\pi$
$578$		0			0
$579$	−26.0179	+	45.0643i	−1.08127	+	1.87281i
$580$		0			0
$581$	22.4402			0.930977
$582$		0			0
$583$	−12.7363	+	22.0599i	−0.527482	+	0.913626i
$584$		0			0
$585$	16.9955	−	29.4371i	0.702679	−	1.21708i
$586$		0			0
$587$	20.7257	+	35.8980i	0.855442	+	1.48167i	0.876234	+	0.481886i	$0.160048\pi$
$587$	20.7257	+	35.8980i	0.855442	+	1.48167i	−0.0207917	+	0.999784i	$0.506619\pi$
$588$		0			0
$589$	5.84179	−	0.838035i	0.240707	−	0.0345306i
$590$		0			0
$591$	−7.02253	−	12.1634i	−0.288868	−	0.500334i
$592$		0			0
$593$	−16.8182	+	29.1299i	−0.690640	+	1.19622i	0.280989	+	0.959711i	$0.409338\pi$
$593$	−16.8182	+	29.1299i	−0.690640	+	1.19622i	−0.971629	+	0.236512i	$0.923996\pi$
$594$		0			0
$595$	15.0421	−	26.0536i	0.616664	−	1.06809i
$596$		0			0
$597$	−12.9314			−0.529245
$598$		0			0
$599$	6.86539	−	11.8912i	0.280512	−	0.485861i	−0.690999	−	0.722856i	$-0.742829\pi$
$599$	6.86539	−	11.8912i	0.280512	−	0.485861i	0.971511	+	0.236995i	$0.0761624\pi$
$600$		0			0
$601$	−29.7060			−1.21173			−0.605867	−	0.795566i	$-0.707174\pi$
$601$	−29.7060			−1.21173			−0.605867	+	0.795566i	$0.707174\pi$
$602$		0			0
$603$	−9.80045	−	16.9749i	−0.399105	−	0.691271i
$604$		0			0
$605$	1.97593	+	3.42242i	0.0803331	+	0.139141i
$606$		0			0
$607$	26.5597			1.07802			0.539012	−	0.842298i	$-0.318798\pi$
$607$	26.5597			1.07802			0.539012	+	0.842298i	$0.318798\pi$
$608$		0			0
$609$	124.682			5.05239
$610$		0			0
$611$	9.17180	+	15.8860i	0.371051	+	0.642680i
$612$		0			0
$613$	5.40092	+	9.35467i	0.218141	+	0.377832i	0.954240	−	0.299043i	$-0.0966673\pi$
$613$	5.40092	+	9.35467i	0.218141	+	0.377832i	−0.736099	+	0.676874i	$0.763334\pi$
$614$		0			0
$615$	7.72300			0.311421
$616$		0			0
$617$	6.03869	−	10.4593i	0.243108	−	0.421076i	−0.718490	−	0.695538i	$-0.755166\pi$
$617$	6.03869	−	10.4593i	0.243108	−	0.421076i	0.961598	+	0.274461i	$0.0884996\pi$
$618$		0			0
$619$	−24.3647			−0.979300			−0.489650	−	0.871919i	$-0.662875\pi$
$619$	−24.3647			−0.979300			−0.489650	+	0.871919i	$0.662875\pi$
$620$		0			0
$621$	−0.781832	+	1.35417i	−0.0313738	+	0.0543411i
$622$		0			0
$623$	8.25788	−	14.3031i	0.330845	−	0.573040i
$624$		0			0
$625$	15.0921	+	26.1403i	0.603684	+	1.04561i
$626$		0			0
$627$	23.0392	+	29.3158i	0.920097	+	1.17076i
$628$		0			0
$629$	−9.25341	−	16.0274i	−0.368958	−	0.639054i
$630$		0			0
$631$	−7.23066	+	12.5239i	−0.287848	+	0.498567i	−0.973296	−	0.229555i	$-0.926273\pi$
$631$	−7.23066	+	12.5239i	−0.287848	+	0.498567i	0.685448	+	0.728122i	$0.259606\pi$
$632$		0			0
$633$	8.85388	−	15.3354i	0.351910	−	0.609526i
$634$		0			0
$635$	−2.81626			−0.111760
$636$		0			0
$637$	−42.7843	+	74.1046i	−1.69518	+	2.93613i
$638$		0			0
$639$	−13.1090			−0.518584
$640$		0			0
$641$	11.6931	+	20.2531i	0.461850	+	0.799948i	0.999053	−	0.0435047i	$-0.0138523\pi$
$641$	11.6931	+	20.2531i	0.461850	+	0.799948i	−0.537203	+	0.843453i	$0.680519\pi$
$642$		0			0
$643$	18.2668	+	31.6391i	0.720373	+	1.24772i	0.960850	+	0.277068i	$0.0893628\pi$
$643$	18.2668	+	31.6391i	0.720373	+	1.24772i	−0.240477	+	0.970655i	$0.577304\pi$
$644$		0			0
$645$	0.261764			0.0103069
$646$		0			0
$647$	32.4841			1.27708			0.638541	−	0.769587i	$-0.279538\pi$
$647$	32.4841			1.27708			0.638541	+	0.769587i	$0.279538\pi$
$648$		0			0
$649$	11.8201	+	20.4730i	0.463980	+	0.803637i
$650$		0			0
$651$	−8.18923	−	14.1842i	−0.320961	−	0.555921i
$652$		0			0
$653$	−32.4383			−1.26941			−0.634704	−	0.772756i	$-0.718878\pi$
$653$	−32.4383			−1.26941			−0.634704	+	0.772756i	$0.718878\pi$
$654$		0			0
$655$	−0.499305	+	0.864822i	−0.0195095	+	0.0337914i
$656$		0			0
$657$	5.47369			0.213549
$658$		0			0
$659$	−14.3071	+	24.7805i	−0.557324	+	0.965313i	0.440395	+	0.897804i	$0.354838\pi$
$659$	−14.3071	+	24.7805i	−0.557324	+	0.965313i	−0.997719	+	0.0675087i	$0.978495\pi$
$660$		0			0
$661$	22.9613	−	39.7702i	0.893092	−	1.54688i	0.0569438	−	0.998377i	$-0.481864\pi$
$661$	22.9613	−	39.7702i	0.893092	−	1.54688i	0.836148	−	0.548503i	$-0.184802\pi$
$662$		0			0
$663$	13.4665	+	23.3246i	0.522994	+	0.905852i
$664$		0			0
$665$	−34.3225	−	43.6731i	−1.33097	−	1.69357i
$666$		0			0
$667$	19.4542	+	33.6957i	0.753271	+	1.30470i
$668$		0			0
$669$	13.2397	−	22.9319i	0.511877	−	0.886597i
$670$		0			0
$671$	12.6025	−	21.8281i	0.486513	−	0.842665i
$672$		0			0
$673$	−20.2246			−0.779602			−0.389801	−	0.920899i	$-0.627456\pi$
$673$	−20.2246			−0.779602			−0.389801	+	0.920899i	$0.627456\pi$
$674$		0			0
$675$	−0.303954	+	0.526464i	−0.0116992	+	0.0202636i
$676$		0			0
$677$	−14.9031			−0.572774			−0.286387	−	0.958114i	$-0.592454\pi$
$677$	−14.9031			−0.572774			−0.286387	+	0.958114i	$0.592454\pi$
$678$		0			0
$679$	1.72202	+	2.98262i	0.0660850	+	0.114463i
$680$		0			0
$681$	−25.1858	−	43.6232i	−0.965124	−	1.67164i
$682$		0			0
$683$	−15.5805			−0.596172			−0.298086	−	0.954539i	$-0.596348\pi$
$683$	−15.5805			−0.596172			−0.298086	+	0.954539i	$0.596348\pi$
$684$		0			0
$685$	54.6951			2.08979
$686$		0			0
$687$	8.06029	+	13.9608i	0.307519	+	0.532639i
$688$		0			0
$689$	16.9864	+	29.4212i	0.647129	+	1.12086i
$690$		0			0
$691$	9.65685			0.367364			0.183682	−	0.982986i	$-0.441198\pi$
$691$	9.65685			0.367364			0.183682	+	0.982986i	$0.441198\pi$
$692$		0			0
$693$	25.1079	−	43.4881i	0.953768	−	1.65198i
$694$		0			0
$695$	45.1623			1.71310
$696$		0			0
$697$	−1.48480	+	2.57175i	−0.0562409	+	0.0974120i
$698$		0			0
$699$	7.63209	−	13.2192i	0.288672	−	0.499995i
$700$		0			0
$701$	−23.1926	−	40.1708i	−0.875973	−	1.51723i	−0.855723	−	0.517435i	$-0.826887\pi$
$701$	−23.1926	−	40.1708i	−0.875973	−	1.51723i	−0.0202505	−	0.999795i	$-0.506446\pi$
$702$		0			0
$703$	−33.8240	+	4.85223i	−1.27570	+	0.183005i
$704$		0			0
$705$	11.9167	+	20.6403i	0.448808	+	0.777358i
$706$		0			0
$707$	36.2226	−	62.7394i	1.36229	−	2.35956i
$708$		0			0
$709$	8.42734	−	14.5966i	0.316495	−	0.548186i	−0.663259	−	0.748390i	$-0.730827\pi$
$709$	8.42734	−	14.5966i	0.316495	−	0.548186i	0.979754	+	0.200204i	$0.0641605\pi$
$710$		0			0
$711$	−34.6109			−1.29801
$712$		0			0
$713$	2.55554	−	4.42632i	0.0957056	−	0.165767i
$714$		0			0
$715$	42.5804			1.59242
$716$		0			0
$717$	18.1848	+	31.4969i	0.679123	+	1.17627i
$718$		0			0
$719$	−16.3444	−	28.3093i	−0.609544	−	1.05576i	−0.991316	−	0.131504i	$-0.958019\pi$
$719$	−16.3444	−	28.3093i	−0.609544	−	1.05576i	0.381772	−	0.924257i	$-0.375314\pi$
$720$		0			0
$721$	−63.8531			−2.37801
$722$		0			0
$723$	−40.8878			−1.52063
$724$		0			0
$725$	7.56326	+	13.0999i	0.280892	+	0.486520i
$726$		0			0
$727$	9.88710	+	17.1250i	0.366692	+	0.635130i	0.989046	−	0.147606i	$-0.0471568\pi$
$727$	9.88710	+	17.1250i	0.366692	+	0.635130i	−0.622354	+	0.782736i	$0.713824\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$		0			0
$731$	−0.0503259	+	0.0871671i	−0.00186137	+	0.00322399i
$732$		0			0
$733$	−16.8098			−0.620883			−0.310441	−	0.950593i	$-0.600477\pi$
$733$	−16.8098			−0.620883			−0.310441	+	0.950593i	$0.600477\pi$
$734$		0			0
$735$	−55.5885	+	96.2821i	−2.05041	+	3.55142i
$736$		0			0
$737$	12.2770	−	21.2643i	0.452228	−	0.783281i
$738$		0			0
$739$	12.2453	+	21.2094i	0.450450	+	0.780202i	0.998414	−	0.0562998i	$-0.0179303\pi$
$739$	12.2453	+	21.2094i	0.450450	+	0.780202i	−0.547964	+	0.836502i	$0.684597\pi$
$740$		0			0
$741$	49.2240	−	7.06143i	1.80829	−	0.259408i
$742$		0			0
$743$	−19.3753	−	33.5590i	−0.710810	−	1.23116i	−0.964553	−	0.263888i	$-0.914995\pi$
$743$	−19.3753	−	33.5590i	−0.710810	−	1.23116i	0.253743	−	0.967272i	$-0.418338\pi$
$744$		0			0
$745$	−2.64414	+	4.57978i	−0.0968737	+	0.167790i
$746$		0			0
$747$	−6.33341	+	10.9698i	−0.231727	+	0.401363i
$748$		0			0
$749$	−61.1021			−2.23262
$750$		0			0
$751$	−12.2321	+	21.1866i	−0.446356	+	0.773110i	−0.998146	−	0.0608726i	$-0.980612\pi$
$751$	−12.2321	+	21.1866i	−0.446356	+	0.773110i	0.551790	+	0.833983i	$0.313945\pi$
$752$		0			0
$753$	−41.6059			−1.51620
$754$		0			0
$755$	−10.1040	−	17.5006i	−0.367721	−	0.636911i
$756$		0			0
$757$	24.3593	+	42.1916i	0.885355	+	1.53348i	0.845307	+	0.534281i	$0.179418\pi$
$757$	24.3593	+	42.1916i	0.885355	+	1.53348i	0.0400479	+	0.999198i	$0.487249\pi$
$758$		0			0
$759$	32.2912			1.17210
$760$		0			0
$761$	−28.4609			−1.03171			−0.515853	−	0.856677i	$-0.672525\pi$
$761$	−28.4609			−1.03171			−0.515853	+	0.856677i	$0.672525\pi$
$762$		0			0
$763$	19.7089	+	34.1368i	0.713509	+	1.23583i
$764$		0			0
$765$	8.49078	+	14.7065i	0.306985	+	0.531713i
$766$		0			0
$767$	31.5290			1.13844
$768$		0			0
$769$	14.1751	−	24.5520i	0.511168	−	0.885369i	−0.488748	−	0.872425i	$-0.662546\pi$
$769$	14.1751	−	24.5520i	0.511168	−	0.885369i	0.999916	−	0.0129442i	$-0.00412039\pi$
$770$		0			0
$771$	−23.4700			−0.845253
$772$		0			0
$773$	−7.24499	+	12.5487i	−0.260584	+	0.451345i	−0.966397	−	0.257053i	$-0.917249\pi$
$773$	−7.24499	+	12.5487i	−0.260584	+	0.451345i	0.705813	+	0.708398i	$0.250582\pi$
$774$		0			0
$775$	0.993521	−	1.72083i	0.0356883	−	0.0618140i
$776$		0			0
$777$	47.4157	+	82.1264i	1.70103	+	2.94627i
$778$		0			0
$779$	3.38797	+	4.31097i	0.121387	+	0.154456i
$780$		0			0
$781$	−8.21078	−	14.2215i	−0.293805	−	0.508885i
$782$		0			0
$783$	2.13461	−	3.69726i	0.0762848	−	0.132129i
$784$		0			0
$785$	27.5995	−	47.8038i	0.985070	−	1.70619i
$786$		0			0
$787$	−5.37054			−0.191439			−0.0957196	−	0.995408i	$-0.530515\pi$
$787$	−5.37054			−0.191439			−0.0957196	+	0.995408i	$0.530515\pi$
$788$		0			0
$789$	15.5878	−	26.9988i	0.554940	−	0.961184i
$790$		0			0
$791$	−15.0518			−0.535180
$792$		0			0
$793$	−16.8079	−	29.1121i	−0.596866	−	1.03380i
$794$		0			0
$795$	22.0699	+	38.2262i	0.782739	+	1.35574i
$796$		0			0
$797$	32.2940			1.14391			0.571956	−	0.820284i	$-0.306185\pi$
$797$	32.2940			1.14391			0.571956	+	0.820284i	$0.306185\pi$
$798$		0			0
$799$	−9.16426			−0.324208
$800$		0			0
$801$	4.66132	+	8.07364i	0.164700	+	0.285268i
$802$		0			0
$803$	3.42843	+	5.93822i	0.120987	+	0.209555i
$804$		0			0
$805$	−48.1057			−1.69550
$806$		0			0
$807$	−30.3125	+	52.5029i	−1.06705	+	1.84819i
$808$		0			0
$809$	−22.2981			−0.783960			−0.391980	−	0.919974i	$-0.628210\pi$
$809$	−22.2981			−0.783960			−0.391980	+	0.919974i	$0.628210\pi$
$810$		0			0
$811$	−1.87575	+	3.24890i	−0.0658666	+	0.114084i	−0.897078	−	0.441872i	$-0.854315\pi$
$811$	−1.87575	+	3.24890i	−0.0658666	+	0.114084i	0.831211	+	0.555956i	$0.187648\pi$
$812$		0			0
$813$	−27.3476	+	47.3674i	−0.959121	+	1.66125i
$814$		0			0
$815$	14.2691	+	24.7147i	0.499823	+	0.865719i
$816$		0			0
$817$	0.114832	+	0.146116i	0.00401747	+	0.00511196i
$818$		0			0
$819$	−33.4863	−	58.0000i	−1.17011	−	2.02668i
$820$		0			0
$821$	−21.9648	+	38.0442i	−0.766577	+	1.32775i	0.172832	+	0.984951i	$0.444708\pi$
$821$	−21.9648	+	38.0442i	−0.766577	+	1.32775i	−0.939409	+	0.342799i	$0.888625\pi$
$822$		0			0
$823$	0.742353	−	1.28579i	0.0258768	−	0.0448199i	−0.852797	−	0.522243i	$-0.825096\pi$
$823$	0.742353	−	1.28579i	0.0258768	−	0.0448199i	0.878674	+	0.477423i	$0.158429\pi$
$824$		0			0
$825$	12.5539			0.437072
$826$		0			0
$827$	8.17913	−	14.1667i	0.284416	−	0.492624i	−0.688051	−	0.725662i	$-0.741534\pi$
$827$	8.17913	−	14.1667i	0.284416	−	0.492624i	0.972467	+	0.233039i	$0.0748669\pi$
$828$		0			0
$829$	9.64908			0.335126			0.167563	−	0.985861i	$-0.446410\pi$
$829$	9.64908			0.335126			0.167563	+	0.985861i	$0.446410\pi$
$830$		0			0
$831$	−30.7363	−	53.2369i	−1.06623	−	1.84677i
$832$		0			0
$833$	−21.3746	−	37.0218i	−0.740585	−	1.28273i
$834$		0			0
$835$	−9.98669			−0.345604
$836$		0			0
$837$	−0.560812			−0.0193845
$838$		0			0
$839$	−15.7488	−	27.2778i	−0.543710	−	0.941733i	−0.998687	−	0.0512302i	$-0.983686\pi$
$839$	−15.7488	−	27.2778i	−0.543710	−	0.941733i	0.454977	−	0.890503i	$-0.349648\pi$
$840$		0			0
$841$	−38.6153	−	66.8836i	−1.33156	−	2.30633i
$842$		0			0
$843$	23.3045			0.802650
$844$		0			0
$845$	11.8642	−	20.5494i	0.408142	−	0.706922i
$846$		0			0
$847$	7.78637			0.267543
$848$		0			0
$849$	25.9025	−	44.8645i	0.888972	−	1.53974i
$850$		0			0
$851$	−14.7966	+	25.6284i	−0.507220	+	0.878530i
$852$		0			0
$853$	17.0899	+	29.6005i	0.585146	+	1.01350i	0.994857	+	0.101287i	$0.0322960\pi$
$853$	17.0899	+	29.6005i	0.585146	+	1.01350i	−0.409712	+	0.912215i	$0.634371\pi$
$854$		0			0
$855$	31.0364	−	4.45232i	1.06142	−	0.152266i
$856$		0			0
$857$	−2.07547	−	3.59482i	−0.0708968	−	0.122797i	0.828398	−	0.560140i	$-0.189253\pi$
$857$	−2.07547	−	3.59482i	−0.0708968	−	0.122797i	−0.899295	+	0.437343i	$0.855919\pi$
$858$		0			0
$859$	−11.4934	+	19.9072i	−0.392150	+	0.679224i	−0.992733	−	0.120338i	$-0.961602\pi$
$859$	−11.4934	+	19.9072i	−0.392150	+	0.679224i	0.600583	+	0.799563i	$0.294935\pi$
$860$		0			0
$861$	7.60832	−	13.1780i	0.259291	−	0.449105i
$862$		0			0
$863$	−34.1539			−1.16261			−0.581307	−	0.813684i	$-0.697458\pi$
$863$	−34.1539			−1.16261			−0.581307	+	0.813684i	$0.697458\pi$
$864$		0			0
$865$	−14.2280	+	24.6435i	−0.483765	+	0.837906i
$866$		0			0
$867$	27.5862			0.936878
$868$		0			0
$869$	−21.6784	−	37.5481i	−0.735389	−	1.27373i
$870$		0			0
$871$	−16.3738	−	28.3602i	−0.554804	−	0.960949i
$872$		0			0
$873$	−1.94405			−0.0657962
$874$		0			0
$875$	45.0137			1.52174
$876$		0			0
$877$	−16.5778	−	28.7136i	−0.559793	−	0.969590i	−0.997513	−	0.0704791i	$-0.977547\pi$
$877$	−16.5778	−	28.7136i	−0.559793	−	0.969590i	0.437720	−	0.899111i	$-0.355786\pi$
$878$		0			0
$879$	3.09117	+	5.35407i	0.104263	+	0.180588i
$880$		0			0
$881$	−3.44330			−0.116008			−0.0580038	−	0.998316i	$-0.518474\pi$
$881$	−3.44330			−0.116008			−0.0580038	+	0.998316i	$0.518474\pi$
$882$		0			0
$883$	15.4940	−	26.8364i	0.521414	−	0.903116i	−0.478275	−	0.878210i	$-0.658738\pi$
$883$	15.4940	−	26.8364i	0.521414	−	0.903116i	0.999690	−	0.0249063i	$-0.00792873\pi$
$884$		0			0
$885$	40.9647			1.37701
$886$		0			0
$887$	−0.701757	+	1.21548i	−0.0235627	+	0.0408118i	−0.877566	−	0.479455i	$-0.840834\pi$
$887$	−0.701757	+	1.21548i	−0.0235627	+	0.0408118i	0.854004	+	0.520267i	$0.174168\pi$
$888$		0			0
$889$	−2.77444	+	4.80548i	−0.0930519	+	0.161171i
$890$		0			0
$891$	−16.8039	−	29.1052i	−0.562952	−	0.975061i
$892$		0			0
$893$	−6.29370	+	15.7065i	−0.210611	+	0.525597i
$894$		0			0
$895$	−11.0427	−	19.1265i	−0.369116	−	0.639328i
$896$		0			0
$897$	21.5334	−	37.2969i	0.718979	−	1.24531i
$898$		0			0
$899$	−6.97730	+	12.0850i	−0.232706	+	0.403059i
$900$		0			0
$901$	−16.9724			−0.565432
$902$		0			0
$903$	0.257877	−	0.446655i	0.00858160	−	0.0148638i
$904$		0			0
$905$	−23.5815			−0.783875
$906$		0			0
$907$	−2.21238	−	3.83196i	−0.0734610	−	0.127238i	0.826955	−	0.562268i	$-0.190071\pi$
$907$	−2.21238	−	3.83196i	−0.0734610	−	0.127238i	−0.900416	+	0.435030i	$0.856738\pi$
$908$		0			0
$909$	20.4465	+	35.4144i	0.678169	+	1.17462i
$910$		0			0
$911$	48.4423			1.60496			0.802482	−	0.596676i	$-0.203512\pi$
$911$	48.4423			1.60496			0.802482	+	0.596676i	$0.203512\pi$
$912$		0			0
$913$	−15.8676			−0.525142
$914$		0			0
$915$	−21.8380	−	37.8246i	−0.721943	−	1.25044i
$916$		0			0
$917$	0.983782	+	1.70396i	0.0324873	+	0.0562697i
$918$		0			0
$919$	−53.4116			−1.76189			−0.880943	−	0.473222i	$-0.843091\pi$
$919$	−53.4116			−1.76189			−0.880943	+	0.473222i	$0.843091\pi$
$920$		0			0
$921$	−7.45875	+	12.9189i	−0.245774	+	0.425694i
$922$		0			0
$923$	−21.9014			−0.720894
$924$		0			0
$925$	−5.75249	+	9.96360i	−0.189141	+	0.327601i
$926$		0			0
$927$	18.0215	−	31.2142i	0.591905	−	1.02521i
$928$		0			0
$929$	3.13919	+	5.43724i	0.102994	+	0.178390i	0.912917	−	0.408146i	$-0.133825\pi$
$929$	3.13919	+	5.43724i	0.102994	+	0.178390i	−0.809923	+	0.586536i	$0.800491\pi$
$930$		0			0
$931$	−78.1304	+	11.2082i	−2.56062	+	0.367334i
$932$		0			0
$933$	9.91375	+	17.1711i	0.324562	+	0.562157i
$934$		0			0
$935$	−10.6363	+	18.4227i	−0.347846	+	0.602486i
$936$		0			0
$937$	−15.3676	+	26.6175i	−0.502039	+	0.869557i	0.497959	+	0.867201i	$0.334083\pi$
$937$	−15.3676	+	26.6175i	−0.502039	+	0.869557i	−0.999997	+	0.00235571i	$0.999250\pi$
$938$		0			0
$939$	44.8358			1.46316
$940$		0			0
$941$	−6.38384	+	11.0571i	−0.208107	+	0.360452i	−0.951118	−	0.308827i	$-0.900064\pi$
$941$	−6.38384	+	11.0571i	−0.208107	+	0.360452i	0.743011	+	0.669279i	$0.233397\pi$
$942$		0			0
$943$	4.74851			0.154633
$944$		0			0
$945$	2.63919	+	4.57122i	0.0858530	+	0.148702i
$946$		0			0
$947$	−6.17319	−	10.6923i	−0.200602	−	0.347452i	0.748121	−	0.663563i	$-0.230956\pi$
$947$	−6.17319	−	10.6923i	−0.200602	−	0.347452i	−0.948722	+	0.316110i	$0.897623\pi$
$948$		0			0
$949$	9.14499			0.296859
$950$		0			0
$951$	2.76425			0.0896368
$952$		0			0
$953$	21.5010	+	37.2409i	0.696487	+	1.20635i	0.969677	+	0.244391i	$0.0785879\pi$
$953$	21.5010	+	37.2409i	0.696487	+	1.20635i	−0.273190	+	0.961960i	$0.588079\pi$
$954$		0			0
$955$	10.1726	+	17.6195i	0.329178	+	0.570153i
$956$		0			0
$957$	−88.1638			−2.84993
$958$		0			0
$959$	53.8829	−	93.3280i	1.73997	−	3.01372i
$960$		0			0
$961$	−29.1669			−0.940868
$962$		0			0
$963$	17.2451	−	29.8695i	0.555717	−	0.962530i
$964$		0			0
$965$	−27.4075	+	47.4711i	−0.882277	+	1.52815i
$966$		0			0
$967$	1.66155	+	2.87788i	0.0534317	+	0.0925465i	0.891504	−	0.453013i	$-0.149651\pi$
$967$	1.66155	+	2.87788i	0.0534317	+	0.0925465i	−0.838072	+	0.545559i	$0.816317\pi$
$968$		0			0
$969$	−9.24070	+	23.0610i	−0.296854	+	0.740825i
$970$		0			0
$971$	−11.9870	−	20.7622i	−0.384683	−	0.666290i	0.607042	−	0.794669i	$-0.292356\pi$
$971$	−11.9870	−	20.7622i	−0.384683	−	0.666290i	−0.991725	+	0.128379i	$0.959022\pi$
$972$		0			0
$973$	44.4916	−	77.0618i	1.42634	−	2.47049i
$974$		0			0
$975$	8.37158	−	14.5000i	0.268105	−	0.464372i
$976$		0			0
$977$	1.73927			0.0556442			0.0278221	−	0.999613i	$-0.491143\pi$
$977$	1.73927			0.0556442			0.0278221	+	0.999613i	$0.491143\pi$
$978$		0			0
$979$	−5.83920	+	10.1138i	−0.186622	+	0.323238i
$980$		0			0
$981$	−22.2501			−0.710391
$982$		0			0
$983$	−22.3032	−	38.6302i	−0.711360	−	1.23211i	−0.964347	−	0.264643i	$-0.914746\pi$
$983$	−22.3032	−	38.6302i	−0.711360	−	1.23211i	0.252986	−	0.967470i	$-0.418587\pi$
$984$		0			0
$985$	−7.39759	−	12.8130i	−0.235707	−	0.408256i
$986$		0			0
$987$	46.9589			1.49472
$988$		0			0
$989$	0.160946			0.00511779
$990$		0			0
$991$	3.51737	+	6.09227i	0.111733	+	0.193527i	0.916469	−	0.400106i	$-0.131027\pi$
$991$	3.51737	+	6.09227i	0.111733	+	0.193527i	−0.804736	+	0.593633i	$0.797693\pi$
$992$		0			0
$993$	−10.2249	−	17.7101i	−0.324479	−	0.562014i
$994$		0			0
$995$	−13.6220			−0.431846
$996$		0			0
$997$	16.4334	−	28.4635i	0.520451	−	0.901448i	−0.479266	−	0.877670i	$-0.659097\pi$
$997$	16.4334	−	28.4635i	0.520451	−	0.901448i	0.999717	−	0.0237784i	$-0.00756961\pi$
$998$		0			0
$999$	3.24710			0.102734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.i.q.577.4		8
4.3	odd	2		1216.2.i.o.577.2		8
8.3	odd	2		608.2.i.e.577.3	yes	8
8.5	even	2		608.2.i.c.577.1	yes	8
19.11	even	3	inner	1216.2.i.q.961.4		8
76.11	odd	6		1216.2.i.o.961.2		8
152.11	odd	6		608.2.i.e.353.3	yes	8
152.125	even	6		608.2.i.c.353.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
608.2.i.c.353.1	✓	8	152.125	even	6
608.2.i.c.577.1	yes	8	8.5	even	2
608.2.i.e.353.3	yes	8	152.11	odd	6
608.2.i.e.577.3	yes	8	8.3	odd	2
1216.2.i.o.577.2		8	4.3	odd	2
1216.2.i.o.961.2		8	76.11	odd	6
1216.2.i.q.577.4		8	1.1	even	1	trivial
1216.2.i.q.961.4		8	19.11	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.20711 + 2.09077i) q^{3} +(1.27158 + 2.20243i) q^{5} +5.01077 q^{7} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(1.20711 + 2.09077i) q^{3} +(1.27158 + 2.20243i) q^{5} +5.01077 q^{7} +(-1.41421 + 2.44949i) q^{9} -3.54315 q^{11} +(-2.36275 + 4.09240i) q^{13} +(-3.06986 + 5.31715i) q^{15} +(-1.18040 - 2.04452i) q^{17} +(-4.31473 + 0.618970i) q^{19} +(6.04854 + 10.4764i) q^{21} +(-1.88751 + 3.26926i) q^{23} +(-0.733811 + 1.27100i) q^{25} +0.414214 q^{27} +(5.15341 - 8.92597i) q^{29} -1.35392 q^{31} +(-4.27696 - 7.40792i) q^{33} +(6.37158 + 11.0359i) q^{35} +7.83920 q^{37} -11.4084 q^{39} +(-0.628938 - 1.08935i) q^{41} +(-0.0213173 - 0.0369226i) q^{43} -7.19312 q^{45} +(1.94092 - 3.36177i) q^{47} +18.1079 q^{49} +(2.84974 - 4.93590i) q^{51} +(3.59462 - 6.22606i) q^{53} +(-4.50539 - 7.80356i) q^{55} +(-6.50246 - 8.27394i) q^{57} +(-3.33605 - 5.77820i) q^{59} +(-3.55685 + 6.16065i) q^{61} +(-7.08630 + 12.2738i) q^{63} -12.0177 q^{65} +(-3.46498 + 6.00153i) q^{67} -9.11370 q^{69} +(2.31737 + 4.01380i) q^{71} +(-0.967622 - 1.67597i) q^{73} -3.54315 q^{75} -17.7539 q^{77} +(6.11839 + 10.5974i) q^{79} +(4.74264 + 8.21449i) q^{81} +4.47840 q^{83} +(3.00194 - 5.19952i) q^{85} +24.8829 q^{87} +(1.64802 - 2.85446i) q^{89} +(-11.8392 + 20.5061i) q^{91} +(-1.63433 - 2.83073i) q^{93} +(-6.84974 - 8.71584i) q^{95} +(0.343663 + 0.595242i) q^{97} +(5.01077 - 8.67891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 2 q^{5} + 8 q^{7}+O(q^{10}) \) 8 * q + 4 * q^3 - 2 * q^5 + 8 * q^7	\( 8 q + 4 q^{3} - 2 q^{5} + 8 q^{7} - 4 q^{11} - 2 q^{13} - 2 q^{15} - 2 q^{17} + 2 q^{19} + 8 q^{21} - 2 q^{23} - 2 q^{25} - 8 q^{27} + 10 q^{29} - 24 q^{31} - 6 q^{33} + 4 q^{35} + 8 q^{37} + 12 q^{39} + 8 q^{41} - 18 q^{43} - 16 q^{45} + 6 q^{47} + 32 q^{49} + 18 q^{51} + 10 q^{53} - 20 q^{55} + 10 q^{57} - 8 q^{59} - 18 q^{61} - 8 q^{63} - 36 q^{65} + 4 q^{67} - 52 q^{69} + 6 q^{71} - 4 q^{75} - 16 q^{77} - 14 q^{79} + 4 q^{81} - 4 q^{83} + 22 q^{85} + 60 q^{87} - 2 q^{89} - 40 q^{91} + 16 q^{93} - 50 q^{95} - 12 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 2 * q^5 + 8 * q^7 - 4 * q^11 - 2 * q^13 - 2 * q^15 - 2 * q^17 + 2 * q^19 + 8 * q^21 - 2 * q^23 - 2 * q^25 - 8 * q^27 + 10 * q^29 - 24 * q^31 - 6 * q^33 + 4 * q^35 + 8 * q^37 + 12 * q^39 + 8 * q^41 - 18 * q^43 - 16 * q^45 + 6 * q^47 + 32 * q^49 + 18 * q^51 + 10 * q^53 - 20 * q^55 + 10 * q^57 - 8 * q^59 - 18 * q^61 - 8 * q^63 - 36 * q^65 + 4 * q^67 - 52 * q^69 + 6 * q^71 - 4 * q^75 - 16 * q^77 - 14 * q^79 + 4 * q^81 - 4 * q^83 + 22 * q^85 + 60 * q^87 - 2 * q^89 - 40 * q^91 + 16 * q^93 - 50 * q^95 - 12 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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