LMFDB - Embedded newform 1216.2.i.o.961.2

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			961.2
Root			$1.77158 + 3.06846i$ of defining polynomial
Character	$\chi$	$=$	1216.961
Dual form			1216.2.i.o.577.2

$q$-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 $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	0.272605	+	0.962126i	$0.412115\pi$
$3$	−1.20711	+	2.09077i	−0.696923	+	1.20711i	−0.969528	+	0.244981i	$0.921218\pi$
$4$		0			0
$5$	1.27158	−	2.20243i	0.568666	−	0.984958i	−0.428032	−	0.903763i	$-0.640793\pi$
$5$	1.27158	−	2.20243i	0.568666	−	0.984958i	0.996698	−	0.0811950i	$-0.0258737\pi$
$6$		0			0
$7$	−5.01077			−1.89389			−0.946947	−	0.321389i	$-0.895850\pi$
$7$	−5.01077			−1.89389			−0.946947	+	0.321389i	$0.895850\pi$
$8$		0			0
$9$	−1.41421	−	2.44949i	−0.471405	−	0.816497i
$10$		0			0
$11$	3.54315			1.06830			0.534150	−	0.845390i	$-0.320632\pi$
$11$	3.54315			1.06830			0.534150	+	0.845390i	$0.320632\pi$
$12$		0			0
$13$	−2.36275	−	4.09240i	−0.655309	−	1.13503i	−0.981816	−	0.189833i	$-0.939205\pi$
$13$	−2.36275	−	4.09240i	−0.655309	−	1.13503i	0.326508	−	0.945195i	$-0.394128\pi$
$14$		0			0
$15$	3.06986	+	5.31715i	0.792633	+	1.37288i
$16$		0			0
$17$	−1.18040	+	2.04452i	−0.286290	+	0.495868i	−0.972921	−	0.231137i	$-0.925755\pi$
$17$	−1.18040	+	2.04452i	−0.286290	+	0.495868i	0.686631	+	0.727006i	$0.259089\pi$
$18$		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	$-0.0379055\pi$
$23$	1.88751	+	3.26926i	0.393573	+	0.681688i	−0.599345	+	0.800491i	$0.704572\pi$
$24$		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	0.729807	+	0.683653i	$0.239610\pi$
$29$	5.15341	+	8.92597i	0.956964	+	1.65751i	0.227157	+	0.973858i	$0.427057\pi$
$30$		0			0
$31$	1.35392			0.243171			0.121586	−	0.992581i	$-0.461202\pi$
$31$	1.35392			0.243171			0.121586	+	0.992581i	$0.461202\pi$
$32$		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	−0.910949	−	0.412518i	$-0.864649\pi$
$41$	−0.628938	+	1.08935i	−0.0982237	+	0.170128i	0.812726	+	0.582646i	$0.197983\pi$
$42$		0			0
$43$	0.0213173	−	0.0369226i	0.00325085	−	0.00563064i	−0.864395	−	0.502813i	$-0.832299\pi$
$43$	0.0213173	−	0.0369226i	0.00325085	−	0.00563064i	0.867646	+	0.497182i	$0.165632\pi$
$44$		0			0
$45$	−7.19312			−1.07229
$46$		0			0
$47$	−1.94092	−	3.36177i	−0.283112	−	0.490364i	0.689038	−	0.724726i	$-0.258033\pi$
$47$	−1.94092	−	3.36177i	−0.283112	−	0.490364i	−0.972150	+	0.234361i	$0.924700\pi$
$48$		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	0.999974	−	0.00719210i	$-0.00228934\pi$
$53$	3.59462	+	6.22606i	0.493759	+	0.855215i	−0.506216	+	0.862407i	$0.668956\pi$
$54$		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	$-0.690323\pi$
$59$	3.33605	−	5.77820i	0.434316	−	0.752258i	0.997240	+	0.0742515i	$0.0236568\pi$
$60$		0			0
$61$	−3.55685	−	6.16065i	−0.455408	−	0.788790i	0.543303	−	0.839536i	$-0.317173\pi$
$61$	−3.55685	−	6.16065i	−0.455408	−	0.788790i	−0.998712	+	0.0507464i	$0.983840\pi$
$62$		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	$-0.0275330\pi$
$67$	3.46498	+	6.00153i	0.423315	+	0.733203i	−0.572946	+	0.819593i	$0.694200\pi$
$68$		0			0
$69$	−9.11370			−1.09716
$70$		0			0
$71$	−2.31737	+	4.01380i	−0.275021	+	0.476350i	−0.970140	−	0.242544i	$-0.922018\pi$
$71$	−2.31737	+	4.01380i	−0.275021	+	0.476350i	0.695120	+	0.718894i	$0.255351\pi$
$72$		0			0
$73$	−0.967622	+	1.67597i	−0.113252	+	0.196157i	−0.917079	−	0.398704i	$-0.869460\pi$
$73$	−0.967622	+	1.67597i	−0.113252	+	0.196157i	0.803828	+	0.594862i	$0.202793\pi$
$74$		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	0.283991	+	0.958827i	$0.408341\pi$
$79$	−6.11839	+	10.5974i	−0.688373	+	1.19230i	−0.972364	+	0.233470i	$0.924992\pi$
$80$		0			0
$81$	4.74264	−	8.21449i	0.526960	−	0.912722i
$82$		0			0
$83$	−4.47840			−0.491568			−0.245784	−	0.969325i	$-0.579045\pi$
$83$	−4.47840			−0.491568			−0.245784	+	0.969325i	$0.579045\pi$
$84$		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	0.940054	−	0.341026i	$-0.110774\pi$
$89$	1.64802	+	2.85446i	0.174690	+	0.302572i	−0.765364	+	0.643598i	$0.777441\pi$
$90$		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	−0.848051	−	0.529914i	$-0.822224\pi$
$97$	0.343663	−	0.595242i	0.0348937	−	0.0604377i	0.882945	+	0.469477i	$0.155557\pi$
$98$		0			0
$99$	−5.01077	−	8.67891i	−0.503602	−	0.872264i
$100$		0			0
$101$	7.22894	+	12.5209i	0.719307	+	1.24588i	0.961275	+	0.275591i	$0.0888737\pi$
$101$	7.22894	+	12.5209i	0.719307	+	1.24588i	−0.241968	+	0.970284i	$0.577793\pi$
$102$		0			0
$103$	12.7432			1.25562			0.627810	−	0.778366i	$-0.283951\pi$
$103$	12.7432			1.25562			0.627810	+	0.778366i	$0.283951\pi$
$104$		0			0
$105$	−15.3824	−	26.6430i	−1.50116	−	2.60009i
$106$		0			0
$107$	12.1942			1.17885			0.589427	−	0.807822i	$-0.299354\pi$
$107$	12.1942			1.17885			0.589427	+	0.807822i	$0.299354\pi$
$108$		0			0
$109$	3.93330	−	6.81267i	0.376742	−	0.652536i	−0.613844	−	0.789427i	$-0.710378\pi$
$109$	3.93330	−	6.81267i	0.376742	−	0.652536i	0.990586	+	0.136891i	$0.0437111\pi$
$110$		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	$-0.151021\pi$
$127$	0.553696	+	0.959029i	0.0491325	+	0.0851001i	−0.840413	+	0.541946i	$0.817688\pi$
$128$		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	$-0.838794\pi$
$131$	−0.196333	+	0.340059i	−0.0171537	+	0.0297111i	0.857321	+	0.514782i	$0.172127\pi$
$132$		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	0.801352	+	0.598193i	$0.204114\pi$
$137$	10.7534	+	18.6255i	0.918726	+	1.59128i	0.117374	+	0.993088i	$0.462552\pi$
$138$		0			0
$139$	−8.87920	−	15.3792i	−0.753124	−	1.30445i	−0.946302	−	0.323285i	$-0.895213\pi$
$139$	−8.87920	−	15.3792i	−0.753124	−	1.30445i	0.193178	−	0.981164i	$-0.438120\pi$
$140$		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	−0.820290	−	0.571948i	$-0.806188\pi$
$149$	1.03971	−	1.80083i	0.0851763	−	0.147530i	0.905466	+	0.424418i	$0.139521\pi$
$150$		0			0
$151$	7.94602			0.646638			0.323319	−	0.946290i	$-0.395201\pi$
$151$	7.94602			0.646638			0.323319	+	0.946290i	$0.395201\pi$
$152$		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	−0.000195692		1.00000i	$0.500062\pi$
$157$	−10.8525	+	18.7971i	−0.866123	+	1.50017i	−0.865928	+	0.500169i	$0.833271\pi$
$158$		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	$-0.644834\pi$
$163$	−11.2216			−0.878940			−0.439470	+	0.898257i	$0.644834\pi$
$164$		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	$-0.118116\pi$
$167$	1.96345	+	3.40079i	0.151936	+	0.263161i	−0.780003	+	0.625776i	$0.784783\pi$
$168$		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	−0.571102	−	0.820879i	$-0.693484\pi$
$173$	5.59462	−	9.69016i	0.425351	−	0.736729i	0.996453	+	0.0841497i	$0.0268174\pi$
$174$		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	$-0.394789\pi$
$179$	8.68425			0.649092			0.324546	+	0.945870i	$0.394789\pi$
$180$		0			0
$181$	−4.63627	−	8.03025i	−0.344611	−	0.596884i	0.640672	−	0.767815i	$-0.278656\pi$
$181$	−4.63627	−	8.03025i	−0.344611	−	0.596884i	−0.985283	+	0.170931i	$0.945323\pi$
$182$		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	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$		0			0
$193$	10.7770	−	18.6662i	0.775743	−	1.34363i	−0.158633	−	0.987338i	$-0.550709\pi$
$193$	10.7770	−	18.6662i	0.775743	−	1.34363i	0.934376	−	0.356288i	$-0.115958\pi$
$194$		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	$-0.105866\pi$
$199$	2.67817	+	4.63873i	0.189851	+	0.328831i	−0.755350	+	0.655322i	$0.772533\pi$
$200$		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	$-0.752089\pi$
$211$	3.66740	−	6.35212i	0.252474	−	0.437298i	0.964206	+	0.265153i	$0.0854224\pi$
$212$		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	$-0.713636\pi$
$223$	5.48407	−	9.49869i	0.367240	−	0.636079i	0.989133	+	0.147023i	$0.0469693\pi$
$224$		0			0
$225$	−2.07553	+	3.59492i	−0.138369	+	0.239662i
$226$		0			0
$227$	20.8646			1.38483			0.692417	−	0.721497i	$-0.256546\pi$
$227$	20.8646			1.38483			0.692417	+	0.721497i	$0.256546\pi$
$228$		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	−0.950801	−	0.309801i	$-0.899737\pi$
$233$	−3.16132	+	5.47556i	−0.207105	+	0.358716i	0.743697	+	0.668517i	$0.233071\pi$
$234$		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	$-0.661992\pi$
$239$	−15.0648			−0.974458			−0.487229	+	0.873274i	$0.661992\pi$
$240$		0			0
$241$	−8.46814	−	14.6672i	−0.545481	−	0.944800i	−0.998576	−	0.0533385i	$-0.983014\pi$
$241$	−8.46814	−	14.6672i	−0.545481	−	0.944800i	0.453096	−	0.891462i	$-0.350320\pi$
$242$		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	0.998676	+	0.0514458i	$0.0163829\pi$
$251$	8.61686	+	14.9248i	0.543891	+	0.942047i	−0.454785	+	0.890601i	$0.650284\pi$
$252$		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	0.673652	−	0.739049i	$-0.264725\pi$
$257$	−4.86081	−	8.41916i	−0.303209	−	0.525173i	−0.976861	+	0.213876i	$0.931391\pi$
$258$		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	$-0.702991\pi$
$263$	6.45667	−	11.1833i	0.398135	−	0.689591i	0.993496	+	0.113868i	$0.0363241\pi$
$264$		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	−0.174413	−	0.984673i	$-0.555803\pi$
$269$	12.5559	−	21.7474i	0.765545	−	1.32596i	0.939958	−	0.341290i	$-0.110864\pi$
$270$		0			0
$271$	−11.3277	+	19.6202i	−0.688111	+	1.19184i	0.284338	+	0.958724i	$0.408226\pi$
$271$	−11.3277	+	19.6202i	−0.688111	+	1.19184i	−0.972448	+	0.233119i	$0.925107\pi$
$272$		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	0.973315	−	0.229475i	$-0.0737009\pi$
$281$	4.82652	+	8.35978i	0.287926	+	0.498703i	−0.685388	+	0.728178i	$0.740368\pi$
$282$		0			0
$283$	10.7292	−	18.5835i	0.637783	−	1.10467i	−0.348135	−	0.937444i	$-0.613185\pi$
$283$	10.7292	−	18.5835i	0.637783	−	1.10467i	0.985918	−	0.167228i	$-0.0534817\pi$
$284$		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	$-0.889755\pi$
$307$	−3.08952	+	5.35120i	−0.176328	+	0.305409i	0.764292	+	0.644870i	$0.223089\pi$
$308$		0			0
$309$	−15.3824	+	26.6430i	−0.875071	+	1.51567i
$310$		0			0
$311$	−8.21282			−0.465706			−0.232853	−	0.972512i	$-0.574806\pi$
$311$	−8.21282			−0.465706			−0.232853	+	0.972512i	$0.574806\pi$
$312$		0			0
$313$	9.28579	+	16.0835i	0.524864	+	0.909091i	0.999581	+	0.0289525i	$0.00921717\pi$
$313$	9.28579	+	16.0835i	0.524864	+	0.909091i	−0.474717	+	0.880139i	$0.657449\pi$
$314$		0			0
$315$	36.0431			2.03080
$316$		0			0
$317$	0.572494	+	0.991589i	0.0321545	+	0.0556932i	0.881655	−	0.471895i	$-0.156430\pi$
$317$	0.572494	+	0.991589i	0.0321545	+	0.0556932i	−0.849500	+	0.527588i	$0.823096\pi$
$318$		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	$-0.425213\pi$
$331$	8.47062			0.465587			0.232794	+	0.972526i	$0.425213\pi$
$332$		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	−0.993413	−	0.114589i	$-0.963445\pi$
$337$	−7.29657	+	12.6380i	−0.397469	+	0.688437i	0.595944	+	0.803026i	$0.296778\pi$
$338$		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	$-0.669820\pi$
$347$	9.15370	−	15.8547i	0.491396	−	0.851123i	0.999951	+	0.00990637i	$0.00315335\pi$
$348$		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	−0.0593669	−	0.998236i	$-0.518908\pi$
$359$	15.8175	−	27.3967i	0.834814	−	1.44594i	0.894181	−	0.447705i	$-0.147758\pi$
$360$		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	$-0.219092\pi$
$367$	−3.14092	−	5.44024i	−0.163955	−	0.283978i	−0.936284	+	0.351245i	$0.885758\pi$
$368$		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	$-0.689526\pi$
$379$	−21.8372			−1.12170			−0.560852	+	0.827916i	$0.689526\pi$
$380$		0			0
$381$	−2.67348			−0.136966
$382$		0			0
$383$	−1.27960	+	2.21633i	−0.0653845	+	0.113249i	−0.896865	−	0.442305i	$-0.854161\pi$
$383$	−1.27960	+	2.21633i	−0.0653845	+	0.113249i	0.831480	+	0.555555i	$0.187494\pi$
$384$		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	0.753882	−	0.657010i	$-0.228179\pi$
$389$	−3.78774	−	6.56055i	−0.192046	−	0.332633i	−0.945928	+	0.324376i	$0.894846\pi$
$390$		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	−0.999800	−	0.0199755i	$-0.993641\pi$
$397$	−9.61576	+	16.6550i	−0.482601	+	0.835889i	0.517199	+	0.855865i	$0.326975\pi$
$398$		0			0
$399$	32.5824	−	41.4588i	1.63116	−	2.07554i
$400$		0			0
$401$	−16.5270	+	28.6257i	−0.825321	+	1.42950i	0.0763524	+	0.997081i	$0.475673\pi$
$401$	−16.5270	+	28.6257i	−0.825321	+	1.42950i	−0.901674	+	0.432417i	$0.857661\pi$
$402$		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	0.999898	+	0.0142685i	$0.00454196\pi$
$409$	10.3607	+	17.9453i	0.512306	+	0.887340i	−0.487592	+	0.873071i	$0.662125\pi$
$410$		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	$-0.706870\pi$
$419$	−24.7725			−1.21021			−0.605107	+	0.796144i	$0.706870\pi$
$420$		0			0
$421$	4.71765	−	8.17121i	0.229924	−	0.398240i	−0.727861	−	0.685724i	$-0.759485\pi$
$421$	4.71765	−	8.17121i	0.229924	−	0.398240i	0.957785	+	0.287484i	$0.0928188\pi$
$422$		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	0.998394	+	0.0566502i	$0.0180420\pi$
$431$	11.3821	+	19.7144i	0.548258	+	0.949610i	−0.450137	+	0.892960i	$0.648625\pi$
$432$		0			0
$433$	1.50831	+	2.61247i	0.0724849	+	0.125547i	0.899990	−	0.435911i	$-0.143574\pi$
$433$	1.50831	+	2.61247i	0.0724849	+	0.125547i	−0.827505	+	0.561458i	$0.810240\pi$
$434$		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	0.102667	+	0.994716i	$0.467263\pi$
$439$	−16.9738	+	29.3995i	−0.810116	+	1.40316i	−0.912782	+	0.408446i	$0.866071\pi$
$440$		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	$-0.245301\pi$
$443$	−5.14681	−	8.91454i	−0.244532	−	0.423543i	−0.962000	+	0.273049i	$0.911968\pi$
$444$		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	−0.941597	−	0.336741i	$-0.890675\pi$
$461$	−3.84700	+	6.66319i	−0.179172	+	0.310336i	0.762425	+	0.647077i	$0.224009\pi$
$462$		0			0
$463$	2.88045			0.133866			0.0669328	−	0.997757i	$-0.478679\pi$
$463$	2.88045			0.133866			0.0669328	+	0.997757i	$0.478679\pi$
$464$		0			0
$465$	4.15634	+	7.19899i	0.192746	+	0.333845i
$466$		0			0
$467$	−13.2431			−0.612818			−0.306409	−	0.951900i	$-0.599127\pi$
$467$	−13.2431			−0.612818			−0.306409	+	0.951900i	$0.599127\pi$
$468$		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	$-0.0732973\pi$
$479$	6.32814	+	10.9607i	0.289140	+	0.500805i	−0.684465	+	0.729046i	$0.739964\pi$
$480$		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	$-0.514534\pi$
$487$	−2.01459			−0.0912896			−0.0456448	+	0.998958i	$0.514534\pi$
$488$		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	$-0.698444\pi$
$491$	9.11151	−	15.7816i	0.411197	−	0.712213i	0.995021	+	0.0996666i	$0.0317776\pi$
$492$		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	0.360799	−	0.932643i	$-0.382504\pi$
$499$	22.0723	−	38.2304i	0.988093	−	1.71143i	0.627293	−	0.778783i	$-0.284163\pi$
$500$		0			0
$501$	−9.48036			−0.423551
$502$		0			0
$503$	−3.27432	−	5.67130i	−0.145995	−	0.252871i	0.783749	−	0.621078i	$-0.213305\pi$
$503$	−3.27432	−	5.67130i	−0.145995	−	0.252871i	−0.929744	+	0.368207i	$0.879972\pi$
$504$		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	0.922724	−	0.385462i	$-0.125958\pi$
$509$	2.87747	+	4.98392i	0.127542	+	0.220908i	−0.795182	+	0.606371i	$0.792625\pi$
$510$		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	$-0.0824167\pi$
$523$	5.98257	+	10.3621i	0.261600	+	0.453104i	−0.705068	+	0.709140i	$0.749083\pi$
$524$		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	0.984968	+	0.172735i	$0.0552605\pi$
$541$	14.9343	+	25.8670i	0.642077	+	1.11211i	−0.342891	+	0.939375i	$0.611406\pi$
$542$		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	$-0.207309\pi$
$547$	−2.97811	−	5.15823i	−0.127335	−	0.220550i	−0.922643	+	0.385655i	$0.873976\pi$
$548$		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	0.898708	−	0.438547i	$-0.144507\pi$
$557$	1.64171	+	2.84353i	0.0695616	+	0.120484i	−0.829147	+	0.559031i	$0.811173\pi$
$558$		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	$-0.151508\pi$
$563$	42.1804			1.77769			0.888846	+	0.458206i	$0.151508\pi$
$564$		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	$-0.610260\pi$
$571$	−16.2254			−0.679010			−0.339505	+	0.940604i	$0.610260\pi$
$572$		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	0.0207917	+	0.999784i	$0.493381\pi$
$587$	−20.7257	+	35.8980i	−0.855442	+	1.48167i	−0.876234	+	0.481886i	$0.839952\pi$
$588$		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	−0.971629	−	0.236512i	$-0.923996\pi$
$593$	−16.8182	−	29.1299i	−0.690640	−	1.19622i	0.280989	−	0.959711i	$-0.409338\pi$
$594$		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	$-0.257171\pi$
$599$	−6.86539	−	11.8912i	−0.280512	−	0.485861i	−0.971511	+	0.236995i	$0.923838\pi$
$600$		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	$-0.681202\pi$
$607$	−26.5597			−1.07802			−0.539012	+	0.842298i	$0.681202\pi$
$608$		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	−0.736099	−	0.676874i	$-0.763334\pi$
$613$	5.40092	−	9.35467i	0.218141	−	0.377832i	0.954240	+	0.299043i	$0.0966673\pi$
$614$		0			0
$615$	−7.72300			−0.311421
$616$		0			0
$617$	6.03869	+	10.4593i	0.243108	+	0.421076i	0.961598	−	0.274461i	$-0.0884996\pi$
$617$	6.03869	+	10.4593i	0.243108	+	0.421076i	−0.718490	+	0.695538i	$0.755166\pi$
$618$		0			0
$619$	24.3647			0.979300			0.489650	−	0.871919i	$-0.337125\pi$
$619$	24.3647			0.979300			0.489650	+	0.871919i	$0.337125\pi$
$620$		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	$-0.0737269\pi$
$631$	7.23066	+	12.5239i	0.287848	+	0.498567i	−0.685448	+	0.728122i	$0.740394\pi$
$632$		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	−0.537203	−	0.843453i	$-0.680519\pi$
$641$	11.6931	−	20.2531i	0.461850	−	0.799948i	0.999053	+	0.0435047i	$0.0138523\pi$
$642$		0			0
$643$	−18.2668	+	31.6391i	−0.720373	+	1.24772i	0.240477	+	0.970655i	$0.422696\pi$
$643$	−18.2668	+	31.6391i	−0.720373	+	1.24772i	−0.960850	+	0.277068i	$0.910637\pi$
$644$		0			0
$645$	0.261764			0.0103069
$646$		0			0
$647$	−32.4841			−1.27708			−0.638541	−	0.769587i	$-0.720462\pi$
$647$	−32.4841			−1.27708			−0.638541	+	0.769587i	$0.720462\pi$
$648$		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	0.997719	+	0.0675087i	$0.0215050\pi$
$659$	14.3071	+	24.7805i	0.557324	+	0.965313i	−0.440395	+	0.897804i	$0.645162\pi$
$660$		0			0
$661$	22.9613	+	39.7702i	0.893092	+	1.54688i	0.836148	+	0.548503i	$0.184802\pi$
$661$	22.9613	+	39.7702i	0.893092	+	1.54688i	0.0569438	+	0.998377i	$0.481864\pi$
$662$		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	$-0.403652\pi$
$683$	15.5805			0.596172			0.298086	+	0.954539i	$0.403652\pi$
$684$		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	$-0.558802\pi$
$691$	−9.65685			−0.367364			−0.183682	+	0.982986i	$0.558802\pi$
$692$		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	−0.0202505	+	0.999795i	$0.506446\pi$
$701$	−23.1926	+	40.1708i	−0.875973	+	1.51723i	−0.855723	+	0.517435i	$0.826887\pi$
$702$		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	0.979754	−	0.200204i	$-0.0641605\pi$
$709$	8.42734	+	14.5966i	0.316495	+	0.548186i	−0.663259	+	0.748390i	$0.730827\pi$
$710$		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	−0.381772	−	0.924257i	$-0.624686\pi$
$719$	16.3444	−	28.3093i	0.609544	−	1.05576i	0.991316	−	0.131504i	$-0.0419806\pi$
$720$		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	$-0.952843\pi$
$727$	−9.88710	+	17.1250i	−0.366692	+	0.635130i	0.622354	+	0.782736i	$0.286176\pi$
$728$		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	$-0.982070\pi$
$739$	−12.2453	+	21.2094i	−0.450450	+	0.780202i	0.547964	+	0.836502i	$0.315403\pi$
$740$		0			0
$741$	49.2240	+	7.06143i	1.80829	+	0.259408i
$742$		0			0
$743$	19.3753	−	33.5590i	0.710810	−	1.23116i	−0.253743	−	0.967272i	$-0.581662\pi$
$743$	19.3753	−	33.5590i	0.710810	−	1.23116i	0.964553	−	0.263888i	$-0.0850050\pi$
$744$		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	$-0.0193883\pi$
$751$	12.2321	+	21.1866i	0.446356	+	0.773110i	−0.551790	+	0.833983i	$0.686055\pi$
$752$		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	0.0400479	−	0.999198i	$-0.487249\pi$
$757$	24.3593	−	42.1916i	0.885355	−	1.53348i	0.845307	−	0.534281i	$-0.179418\pi$
$758$		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	0.999916	+	0.0129442i	$0.00412039\pi$
$769$	14.1751	+	24.5520i	0.511168	+	0.885369i	−0.488748	+	0.872425i	$0.662546\pi$
$770$		0			0
$771$	23.4700			0.845253
$772$		0			0
$773$	−7.24499	−	12.5487i	−0.260584	−	0.451345i	0.705813	−	0.708398i	$-0.250582\pi$
$773$	−7.24499	−	12.5487i	−0.260584	−	0.451345i	−0.966397	+	0.257053i	$0.917249\pi$
$774$		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	$-0.469485\pi$
$787$	5.37054			0.191439			0.0957196	+	0.995408i	$0.469485\pi$
$788$		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	$-0.145685\pi$
$811$	1.87575	+	3.24890i	0.0658666	+	0.114084i	−0.831211	+	0.555956i	$0.812352\pi$
$812$		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	−0.939409	−	0.342799i	$-0.888625\pi$
$821$	−21.9648	−	38.0442i	−0.766577	−	1.32775i	0.172832	−	0.984951i	$-0.444708\pi$
$822$		0			0
$823$	−0.742353	−	1.28579i	−0.0258768	−	0.0448199i	0.852797	−	0.522243i	$-0.174904\pi$
$823$	−0.742353	−	1.28579i	−0.0258768	−	0.0448199i	−0.878674	+	0.477423i	$0.841571\pi$
$824$		0			0
$825$	12.5539			0.437072
$826$		0			0
$827$	−8.17913	−	14.1667i	−0.284416	−	0.492624i	0.688051	−	0.725662i	$-0.258466\pi$
$827$	−8.17913	−	14.1667i	−0.284416	−	0.492624i	−0.972467	+	0.233039i	$0.925133\pi$
$828$		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	−0.454977	−	0.890503i	$-0.650352\pi$
$839$	15.7488	−	27.2778i	0.543710	−	0.941733i	0.998687	−	0.0512302i	$-0.0163142\pi$
$840$		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	−0.409712	−	0.912215i	$-0.634371\pi$
$853$	17.0899	−	29.6005i	0.585146	−	1.01350i	0.994857	−	0.101287i	$-0.0322960\pi$
$854$		0			0
$855$	−31.0364	−	4.45232i	−1.06142	−	0.152266i
$856$		0			0
$857$	−2.07547	+	3.59482i	−0.0708968	+	0.122797i	−0.899295	−	0.437343i	$-0.855919\pi$
$857$	−2.07547	+	3.59482i	−0.0708968	+	0.122797i	0.828398	+	0.560140i	$0.189253\pi$
$858$		0			0
$859$	11.4934	+	19.9072i	0.392150	+	0.679224i	0.992733	−	0.120338i	$-0.0383980\pi$
$859$	11.4934	+	19.9072i	0.392150	+	0.679224i	−0.600583	+	0.799563i	$0.705065\pi$
$860$		0			0
$861$	7.60832	+	13.1780i	0.259291	+	0.449105i
$862$		0			0
$863$	34.1539			1.16261			0.581307	−	0.813684i	$-0.302542\pi$
$863$	34.1539			1.16261			0.581307	+	0.813684i	$0.302542\pi$
$864$		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	0.437720	+	0.899111i	$0.355786\pi$
$877$	−16.5778	+	28.7136i	−0.559793	+	0.969590i	−0.997513	+	0.0704791i	$0.977547\pi$
$878$		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	−0.999690	−	0.0249063i	$-0.992071\pi$
$883$	−15.4940	−	26.8364i	−0.521414	−	0.903116i	0.478275	−	0.878210i	$-0.341262\pi$
$884$		0			0
$885$	40.9647			1.37701
$886$		0			0
$887$	0.701757	+	1.21548i	0.0235627	+	0.0408118i	0.877566	−	0.479455i	$-0.159166\pi$
$887$	0.701757	+	1.21548i	0.0235627	+	0.0408118i	−0.854004	+	0.520267i	$0.825832\pi$
$888$		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	$-0.809929\pi$
$907$	2.21238	−	3.83196i	0.0734610	−	0.127238i	0.900416	+	0.435030i	$0.143262\pi$
$908$		0			0
$909$	20.4465	−	35.4144i	0.678169	−	1.17462i
$910$		0			0
$911$	−48.4423			−1.60496			−0.802482	−	0.596676i	$-0.796488\pi$
$911$	−48.4423			−1.60496			−0.802482	+	0.596676i	$0.796488\pi$
$912$		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	$-0.156909\pi$
$919$	53.4116			1.76189			0.880943	+	0.473222i	$0.156909\pi$
$920$		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	−0.809923	−	0.586536i	$-0.800491\pi$
$929$	3.13919	−	5.43724i	0.102994	−	0.178390i	0.912917	+	0.408146i	$0.133825\pi$
$930$		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	−0.999997	−	0.00235571i	$-0.999250\pi$
$937$	−15.3676	−	26.6175i	−0.502039	−	0.869557i	0.497959	−	0.867201i	$-0.334083\pi$
$938$		0			0
$939$	−44.8358			−1.46316
$940$		0			0
$941$	−6.38384	−	11.0571i	−0.208107	−	0.360452i	0.743011	−	0.669279i	$-0.233397\pi$
$941$	−6.38384	−	11.0571i	−0.208107	−	0.360452i	−0.951118	+	0.308827i	$0.900064\pi$
$942$		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	$-0.769044\pi$
$947$	6.17319	−	10.6923i	0.200602	−	0.347452i	0.948722	+	0.316110i	$0.102377\pi$
$948$		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	−0.273190	−	0.961960i	$-0.588079\pi$
$953$	21.5010	−	37.2409i	0.696487	−	1.20635i	0.969677	−	0.244391i	$-0.0785879\pi$
$954$		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	$-0.850349\pi$
$967$	−1.66155	+	2.87788i	−0.0534317	+	0.0925465i	0.838072	+	0.545559i	$0.183683\pi$
$968$		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	$-0.707644\pi$
$971$	11.9870	−	20.7622i	0.384683	−	0.666290i	0.991725	+	0.128379i	$0.0409775\pi$
$972$		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	−0.252986	−	0.967470i	$-0.581413\pi$
$983$	22.3032	−	38.6302i	0.711360	−	1.23211i	0.964347	−	0.264643i	$-0.0852540\pi$
$984$		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	$-0.868973\pi$
$991$	−3.51737	+	6.09227i	−0.111733	+	0.193527i	0.804736	+	0.593633i	$0.202307\pi$
$992$		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	0.999717	+	0.0237784i	$0.00756961\pi$
$997$	16.4334	+	28.4635i	0.520451	+	0.901448i	−0.479266	+	0.877670i	$0.659097\pi$
$998$		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.o.961.2		8
4.3	odd	2		1216.2.i.q.961.4		8
8.3	odd	2		608.2.i.c.353.1	✓	8
8.5	even	2		608.2.i.e.353.3	yes	8
19.7	even	3	inner	1216.2.i.o.577.2		8
76.7	odd	6		1216.2.i.q.577.4		8
152.45	even	6		608.2.i.e.577.3	yes	8
152.83	odd	6		608.2.i.c.577.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
608.2.i.c.353.1	✓	8	8.3	odd	2
608.2.i.c.577.1	yes	8	152.83	odd	6
608.2.i.e.353.3	yes	8	8.5	even	2
608.2.i.e.577.3	yes	8	152.45	even	6
1216.2.i.o.577.2		8	19.7	even	3	inner
1216.2.i.o.961.2		8	1.1	even	1	trivial
1216.2.i.q.577.4		8	76.7	odd	6
1216.2.i.q.961.4		8	4.3	odd	2

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

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Database

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