LMFDB - Embedded newform 960.2.bi.e.737.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(353,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("960.353");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.bi (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.3
Root			$-1.14412 - 1.14412i$ of defining polynomial
Character	$\chi$	$=$	960.737
Dual form			960.2.bi.e.353.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.292893 - 1.70711i) q^{3} +(-1.58114 + 1.58114i) q^{5} +(-2.23607 - 2.23607i) q^{7} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})$	\(q+(-0.292893 - 1.70711i) q^{3} +(-1.58114 + 1.58114i) q^{5} +(-2.23607 - 2.23607i) q^{7} +(-2.82843 + 1.00000i) q^{9} -4.24264 q^{11} +(4.47214 + 4.47214i) q^{13} +(3.16228 + 2.23607i) q^{15} +(2.82843 - 2.82843i) q^{17} +2.00000 q^{19} +(-3.16228 + 4.47214i) q^{21} +(3.16228 + 3.16228i) q^{23} -5.00000i q^{25} +(2.53553 + 4.53553i) q^{27} +9.48683i q^{29} +4.47214 q^{31} +(1.24264 + 7.24264i) q^{33} +7.07107 q^{35} +(6.32456 - 8.94427i) q^{39} +2.82843i q^{41} +(4.00000 + 4.00000i) q^{43} +(2.89100 - 6.05327i) q^{45} +(-3.16228 + 3.16228i) q^{47} +3.00000i q^{49} +(-5.65685 - 4.00000i) q^{51} +(-6.32456 + 6.32456i) q^{53} +(6.70820 - 6.70820i) q^{55} +(-0.585786 - 3.41421i) q^{57} -7.07107i q^{59} -8.94427i q^{61} +(8.56062 + 4.08849i) q^{63} -14.1421 q^{65} +(-6.00000 + 6.00000i) q^{67} +(4.47214 - 6.32456i) q^{69} +6.32456i q^{71} +(-3.00000 + 3.00000i) q^{73} +(-8.53553 + 1.46447i) q^{75} +(9.48683 + 9.48683i) q^{77} +4.47214i q^{79} +(7.00000 - 5.65685i) q^{81} +(-5.65685 + 5.65685i) q^{83} +8.94427i q^{85} +(16.1950 - 2.77863i) q^{87} +8.48528 q^{89} -20.0000i q^{91} +(-1.30986 - 7.63441i) q^{93} +(-3.16228 + 3.16228i) q^{95} +(3.00000 + 3.00000i) q^{97} +(12.0000 - 4.24264i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3}+O(q^{10}) $ 8 * q - 8 * q^3	$ 8 q - 8 q^{3} + 16 q^{19} - 8 q^{27} - 24 q^{33} + 32 q^{43} - 16 q^{57} - 48 q^{67} - 24 q^{73} - 40 q^{75} + 56 q^{81} + 24 q^{97} + 96 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 + 16 * q^19 - 8 * q^27 - 24 * q^33 + 32 * q^43 - 16 * q^57 - 48 * q^67 - 24 * q^73 - 40 * q^75 + 56 * q^81 + 24 * q^97 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.292893	−	1.70711i	−0.169102	−	0.985599i
$3$	−0.292893	−	1.70711i	−0.169102	−	0.985599i
$4$		0			0
$5$	−1.58114	+	1.58114i	−0.707107	+	0.707107i
$5$	−1.58114	+	1.58114i	−0.707107	+	0.707107i
$6$		0			0
$7$	−2.23607	−	2.23607i	−0.845154	−	0.845154i	0.144370	−	0.989524i	$-0.453885\pi$
$7$	−2.23607	−	2.23607i	−0.845154	−	0.845154i	−0.989524	+	0.144370i	$0.953885\pi$
$8$		0			0
$9$	−2.82843	+	1.00000i	−0.942809	+	0.333333i
$10$		0			0
$11$	−4.24264			−1.27920			−0.639602	−	0.768706i	$-0.720901\pi$
$11$	−4.24264			−1.27920			−0.639602	+	0.768706i	$0.720901\pi$
$12$		0			0
$13$	4.47214	+	4.47214i	1.24035	+	1.24035i	0.959857	+	0.280491i	$0.0904971\pi$
$13$	4.47214	+	4.47214i	1.24035	+	1.24035i	0.280491	+	0.959857i	$0.409503\pi$
$14$		0			0
$15$	3.16228	+	2.23607i	0.816497	+	0.577350i
$16$		0			0
$17$	2.82843	−	2.82843i	0.685994	−	0.685994i	−0.275350	−	0.961344i	$-0.588794\pi$
$17$	2.82843	−	2.82843i	0.685994	−	0.685994i	0.961344	+	0.275350i	$0.0887937\pi$
$18$		0			0
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$		0			0
$21$	−3.16228	+	4.47214i	−0.690066	+	0.975900i
$22$		0			0
$23$	3.16228	+	3.16228i	0.659380	+	0.659380i	0.955233	−	0.295853i	$-0.0956039\pi$
$23$	3.16228	+	3.16228i	0.659380	+	0.659380i	−0.295853	+	0.955233i	$0.595604\pi$
$24$		0			0
$25$		−	5.00000i		−	1.00000i
$26$		0			0
$27$	2.53553	+	4.53553i	0.487964	+	0.872864i
$28$		0			0
$29$			9.48683i			1.76166i	0.473432	+	0.880830i	$0.343015\pi$
$29$			9.48683i			1.76166i	−0.473432	+	0.880830i	$0.656985\pi$
$30$		0			0
$31$	4.47214			0.803219			0.401610	−	0.915811i	$-0.368451\pi$
$31$	4.47214			0.803219			0.401610	+	0.915811i	$0.368451\pi$
$32$		0			0
$33$	1.24264	+	7.24264i	0.216316	+	1.26078i
$34$		0			0
$35$	7.07107			1.19523
$36$		0			0
$37$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$37$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$38$		0			0
$39$	6.32456	−	8.94427i	1.01274	−	1.43223i
$40$		0			0
$41$			2.82843i			0.441726i	0.975305	+	0.220863i	$0.0708874\pi$
$41$			2.82843i			0.441726i	−0.975305	+	0.220863i	$0.929113\pi$
$42$		0			0
$43$	4.00000	+	4.00000i	0.609994	+	0.609994i	0.942944	−	0.332950i	$-0.108044\pi$
$43$	4.00000	+	4.00000i	0.609994	+	0.609994i	−0.332950	+	0.942944i	$0.608044\pi$
$44$		0			0
$45$	2.89100	−	6.05327i	0.430964	−	0.902369i
$46$		0			0
$47$	−3.16228	+	3.16228i	−0.461266	+	0.461266i	−0.899070	−	0.437805i	$-0.855756\pi$
$47$	−3.16228	+	3.16228i	−0.461266	+	0.461266i	0.437805	+	0.899070i	$0.355756\pi$
$48$		0			0
$49$			3.00000i			0.428571i
$50$		0			0
$51$	−5.65685	−	4.00000i	−0.792118	−	0.560112i
$52$		0			0
$53$	−6.32456	+	6.32456i	−0.868744	+	0.868744i	−0.992333	−	0.123589i	$-0.960560\pi$
$53$	−6.32456	+	6.32456i	−0.868744	+	0.868744i	0.123589	+	0.992333i	$0.460560\pi$
$54$		0			0
$55$	6.70820	−	6.70820i	0.904534	−	0.904534i
$56$		0			0
$57$	−0.585786	−	3.41421i	−0.0775893	−	0.452224i
$58$		0			0
$59$		−	7.07107i		−	0.920575i	−0.887770	−	0.460287i	$-0.847746\pi$
$59$		−	7.07107i		−	0.920575i	0.887770	−	0.460287i	$-0.152254\pi$
$60$		0			0
$61$		−	8.94427i		−	1.14520i	−0.819836	−	0.572598i	$-0.805935\pi$
$61$		−	8.94427i		−	1.14520i	0.819836	−	0.572598i	$-0.194065\pi$
$62$		0			0
$63$	8.56062	+	4.08849i	1.07854	+	0.515101i
$64$		0			0
$65$	−14.1421			−1.75412
$66$		0			0
$67$	−6.00000	+	6.00000i	−0.733017	+	0.733017i	−0.971216	−	0.238200i	$-0.923443\pi$
$67$	−6.00000	+	6.00000i	−0.733017	+	0.733017i	0.238200	+	0.971216i	$0.423443\pi$
$68$		0			0
$69$	4.47214	−	6.32456i	0.538382	−	0.761387i
$70$		0			0
$71$			6.32456i			0.750587i	0.926906	+	0.375293i	$0.122458\pi$
$71$			6.32456i			0.750587i	−0.926906	+	0.375293i	$0.877542\pi$
$72$		0			0
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	−0.860527	−	0.509404i	$-0.829866\pi$
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	0.509404	+	0.860527i	$0.329866\pi$
$74$		0			0
$75$	−8.53553	+	1.46447i	−0.985599	+	0.169102i
$76$		0			0
$77$	9.48683	+	9.48683i	1.08112	+	1.08112i
$78$		0			0
$79$			4.47214i			0.503155i	0.967837	+	0.251577i	$0.0809493\pi$
$79$			4.47214i			0.503155i	−0.967837	+	0.251577i	$0.919051\pi$
$80$		0			0
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$		0			0
$83$	−5.65685	+	5.65685i	−0.620920	+	0.620920i	−0.945767	−	0.324846i	$-0.894687\pi$
$83$	−5.65685	+	5.65685i	−0.620920	+	0.620920i	0.324846	+	0.945767i	$0.394687\pi$
$84$		0			0
$85$			8.94427i			0.970143i
$86$		0			0
$87$	16.1950	−	2.77863i	1.73629	−	0.297900i
$88$		0			0
$89$	8.48528			0.899438			0.449719	−	0.893170i	$-0.351524\pi$
$89$	8.48528			0.899438			0.449719	+	0.893170i	$0.351524\pi$
$90$		0			0
$91$		−	20.0000i		−	2.09657i
$92$		0			0
$93$	−1.30986	−	7.63441i	−0.135826	−	0.791652i
$94$		0			0
$95$	−3.16228	+	3.16228i	−0.324443	+	0.324443i
$96$		0			0
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	0.842812	−	0.538208i	$-0.180899\pi$
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	−0.538208	+	0.842812i	$0.680899\pi$
$98$		0			0
$99$	12.0000	−	4.24264i	1.20605	−	0.426401i
$100$		0			0
$101$	−3.16228			−0.314658			−0.157329	−	0.987546i	$-0.550288\pi$
$101$	−3.16228			−0.314658			−0.157329	+	0.987546i	$0.550288\pi$
$102$		0			0
$103$	2.23607	−	2.23607i	0.220326	−	0.220326i	−0.588310	−	0.808636i	$-0.700206\pi$
$103$	2.23607	−	2.23607i	0.220326	−	0.220326i	0.808636	+	0.588310i	$0.200206\pi$
$104$		0			0
$105$	−2.07107	−	12.0711i	−0.202116	−	1.17802i
$106$		0			0
$107$	11.3137	+	11.3137i	1.09374	+	1.09374i	0.995126	+	0.0986115i	$0.0314401\pi$
$107$	11.3137	+	11.3137i	1.09374	+	1.09374i	0.0986115	+	0.995126i	$0.468560\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.48528	+	8.48528i	0.798228	+	0.798228i	0.982816	−	0.184588i	$-0.0590950\pi$
$113$	8.48528	+	8.48528i	0.798228	+	0.798228i	−0.184588	+	0.982816i	$0.559095\pi$
$114$		0			0
$115$	−10.0000			−0.932505
$116$		0			0
$117$	−17.1212	−	8.17697i	−1.58286	−	0.755962i
$118$		0			0
$119$	−12.6491			−1.15954
$120$		0			0
$121$	7.00000			0.636364
$122$		0			0
$123$	4.82843	−	0.828427i	0.435365	−	0.0746968i
$124$		0			0
$125$	7.90569	+	7.90569i	0.707107	+	0.707107i
$126$		0			0
$127$	−2.23607	−	2.23607i	−0.198419	−	0.198419i	0.600903	−	0.799322i	$-0.294808\pi$
$127$	−2.23607	−	2.23607i	−0.198419	−	0.198419i	−0.799322	+	0.600903i	$0.794808\pi$
$128$		0			0
$129$	5.65685	−	8.00000i	0.498058	−	0.704361i
$130$		0			0
$131$	−7.07107			−0.617802			−0.308901	−	0.951094i	$-0.599961\pi$
$131$	−7.07107			−0.617802			−0.308901	+	0.951094i	$0.599961\pi$
$132$		0			0
$133$	−4.47214	−	4.47214i	−0.387783	−	0.387783i
$134$		0			0
$135$	−11.1803	−	3.16228i	−0.962250	−	0.272166i
$136$		0			0
$137$	−2.82843	+	2.82843i	−0.241649	+	0.241649i	−0.817532	−	0.575883i	$-0.804658\pi$
$137$	−2.82843	+	2.82843i	−0.241649	+	0.241649i	0.575883	+	0.817532i	$0.304658\pi$
$138$		0			0
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$		0			0
$141$	6.32456	+	4.47214i	0.532624	+	0.376622i
$142$		0			0
$143$	−18.9737	−	18.9737i	−1.58666	−	1.58666i
$144$		0			0
$145$	−15.0000	−	15.0000i	−1.24568	−	1.24568i
$146$		0			0
$147$	5.12132	−	0.878680i	0.422399	−	0.0724723i
$148$		0			0
$149$		−	3.16228i		−	0.259064i	−0.991575	−	0.129532i	$-0.958653\pi$
$149$		−	3.16228i		−	0.259064i	0.991575	−	0.129532i	$-0.0413475\pi$
$150$		0			0
$151$	−17.8885			−1.45575			−0.727875	−	0.685710i	$-0.759492\pi$
$151$	−17.8885			−1.45575			−0.727875	+	0.685710i	$0.759492\pi$
$152$		0			0
$153$	−5.17157	+	10.8284i	−0.418097	+	0.875426i
$154$		0			0
$155$	−7.07107	+	7.07107i	−0.567962	+	0.567962i
$156$		0			0
$157$	8.94427	−	8.94427i	0.713831	−	0.713831i	−0.253504	−	0.967334i	$-0.581583\pi$
$157$	8.94427	−	8.94427i	0.713831	−	0.713831i	0.967334	+	0.253504i	$0.0815830\pi$
$158$		0			0
$159$	12.6491	+	8.94427i	1.00314	+	0.709327i
$160$		0			0
$161$		−	14.1421i		−	1.11456i
$162$		0			0
$163$	12.0000	+	12.0000i	0.939913	+	0.939913i	0.998294	−	0.0583818i	$-0.0185941\pi$
$163$	12.0000	+	12.0000i	0.939913	+	0.939913i	−0.0583818	+	0.998294i	$0.518594\pi$
$164$		0			0
$165$	−13.4164	−	9.48683i	−1.04447	−	0.738549i
$166$		0			0
$167$	−9.48683	+	9.48683i	−0.734113	+	0.734113i	−0.971432	−	0.237319i	$-0.923731\pi$
$167$	−9.48683	+	9.48683i	−0.734113	+	0.734113i	0.237319	+	0.971432i	$0.423731\pi$
$168$		0			0
$169$			27.0000i			2.07692i
$170$		0			0
$171$	−5.65685	+	2.00000i	−0.432590	+	0.152944i
$172$		0			0
$173$	3.16228	−	3.16228i	0.240424	−	0.240424i	−0.576602	−	0.817025i	$-0.695622\pi$
$173$	3.16228	−	3.16228i	0.240424	−	0.240424i	0.817025	+	0.576602i	$0.195622\pi$
$174$		0			0
$175$	−11.1803	+	11.1803i	−0.845154	+	0.845154i
$176$		0			0
$177$	−12.0711	+	2.07107i	−0.907317	+	0.155671i
$178$		0			0
$179$		−	15.5563i		−	1.16274i	−0.813641	−	0.581368i	$-0.802518\pi$
$179$		−	15.5563i		−	1.16274i	0.813641	−	0.581368i	$-0.197482\pi$
$180$		0			0
$181$			17.8885i			1.32964i	0.747001	+	0.664822i	$0.231493\pi$
$181$			17.8885i			1.32964i	−0.747001	+	0.664822i	$0.768507\pi$
$182$		0			0
$183$	−15.2688	+	2.61972i	−1.12870	+	0.193655i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−12.0000	+	12.0000i	−0.877527	+	0.877527i
$188$		0			0
$189$	4.47214	−	15.8114i	0.325300	−	1.15011i
$190$		0			0
$191$		−	12.6491i		−	0.915258i	−0.889143	−	0.457629i	$-0.848699\pi$
$191$		−	12.6491i		−	0.915258i	0.889143	−	0.457629i	$-0.151301\pi$
$192$		0			0
$193$	−3.00000	+	3.00000i	−0.215945	+	0.215945i	−0.806787	−	0.590842i	$-0.798796\pi$
$193$	−3.00000	+	3.00000i	−0.215945	+	0.215945i	0.590842	+	0.806787i	$0.298796\pi$
$194$		0			0
$195$	4.14214	+	24.1421i	0.296624	+	1.72885i
$196$		0			0
$197$	−6.32456	−	6.32456i	−0.450606	−	0.450606i	0.444950	−	0.895556i	$-0.353222\pi$
$197$	−6.32456	−	6.32456i	−0.450606	−	0.450606i	−0.895556	+	0.444950i	$0.853222\pi$
$198$		0			0
$199$			17.8885i			1.26809i	0.773298	+	0.634043i	$0.218606\pi$
$199$			17.8885i			1.26809i	−0.773298	+	0.634043i	$0.781394\pi$
$200$		0			0
$201$	12.0000	+	8.48528i	0.846415	+	0.598506i
$202$		0			0
$203$	21.2132	−	21.2132i	1.48888	−	1.48888i
$204$		0			0
$205$	−4.47214	−	4.47214i	−0.312348	−	0.312348i
$206$		0			0
$207$	−12.1065	−	5.78199i	−0.841463	−	0.401876i
$208$		0			0
$209$	−8.48528			−0.586939
$210$		0			0
$211$		−	14.0000i		−	0.963800i	−0.876226	−	0.481900i	$-0.839947\pi$
$211$		−	14.0000i		−	0.963800i	0.876226	−	0.481900i	$-0.160053\pi$
$212$		0			0
$213$	10.7967	−	1.85242i	0.739777	−	0.126926i
$214$		0			0
$215$	−12.6491			−0.862662
$216$		0			0
$217$	−10.0000	−	10.0000i	−0.678844	−	0.678844i
$218$		0			0
$219$	6.00000	+	4.24264i	0.405442	+	0.286691i
$220$		0			0
$221$	25.2982			1.70174
$222$		0			0
$223$	2.23607	−	2.23607i	0.149738	−	0.149738i	−0.628263	−	0.778001i	$-0.716234\pi$
$223$	2.23607	−	2.23607i	0.149738	−	0.149738i	0.778001	+	0.628263i	$0.216234\pi$
$224$		0			0
$225$	5.00000	+	14.1421i	0.333333	+	0.942809i
$226$		0			0
$227$	−7.07107	−	7.07107i	−0.469323	−	0.469323i	0.432372	−	0.901695i	$-0.357677\pi$
$227$	−7.07107	−	7.07107i	−0.469323	−	0.469323i	−0.901695	+	0.432372i	$0.857677\pi$
$228$		0			0
$229$	−26.8328			−1.77316			−0.886581	−	0.462573i	$-0.846926\pi$
$229$	−26.8328			−1.77316			−0.886581	+	0.462573i	$0.846926\pi$
$230$		0			0
$231$	13.4164	−	18.9737i	0.882735	−	1.24838i
$232$		0			0
$233$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$233$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$234$		0			0
$235$		−	10.0000i		−	0.652328i
$236$		0			0
$237$	7.63441	−	1.30986i	0.495908	−	0.0850844i
$238$		0			0
$239$	−18.9737			−1.22730			−0.613652	−	0.789576i	$-0.710300\pi$
$239$	−18.9737			−1.22730			−0.613652	+	0.789576i	$0.710300\pi$
$240$		0			0
$241$	24.0000			1.54598			0.772988	−	0.634421i	$-0.218761\pi$
$241$	24.0000			1.54598			0.772988	+	0.634421i	$0.218761\pi$
$242$		0			0
$243$	−11.7071	−	10.2929i	−0.751011	−	0.660289i
$244$		0			0
$245$	−4.74342	−	4.74342i	−0.303046	−	0.303046i
$246$		0			0
$247$	8.94427	+	8.94427i	0.569110	+	0.569110i
$248$		0			0
$249$	11.3137	+	8.00000i	0.716977	+	0.506979i
$250$		0			0
$251$	−24.0416			−1.51749			−0.758747	−	0.651385i	$-0.774188\pi$
$251$	−24.0416			−1.51749			−0.758747	+	0.651385i	$0.774188\pi$
$252$		0			0
$253$	−13.4164	−	13.4164i	−0.843482	−	0.843482i
$254$		0			0
$255$	15.2688	−	2.61972i	0.956171	−	0.164053i
$256$		0			0
$257$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$257$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−9.48683	−	26.8328i	−0.587220	−	1.66091i
$262$		0			0
$263$	3.16228	+	3.16228i	0.194994	+	0.194994i	0.797850	−	0.602856i	$-0.205971\pi$
$263$	3.16228	+	3.16228i	0.194994	+	0.194994i	−0.602856	+	0.797850i	$0.705971\pi$
$264$		0			0
$265$		−	20.0000i		−	1.22859i
$266$		0			0
$267$	−2.48528	−	14.4853i	−0.152097	−	0.886485i
$268$		0			0
$269$			3.16228i			0.192807i	0.995342	+	0.0964037i	$0.0307340\pi$
$269$			3.16228i			0.192807i	−0.995342	+	0.0964037i	$0.969266\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$		0			0
$273$	−34.1421	+	5.85786i	−2.06638	+	0.354534i
$274$		0			0
$275$			21.2132i			1.27920i
$276$		0			0
$277$	−8.94427	+	8.94427i	−0.537409	+	0.537409i	−0.922767	−	0.385358i	$-0.874078\pi$
$277$	−8.94427	+	8.94427i	−0.537409	+	0.537409i	0.385358	+	0.922767i	$0.374078\pi$
$278$		0			0
$279$	−12.6491	+	4.47214i	−0.757282	+	0.267740i
$280$		0			0
$281$		−	28.2843i		−	1.68730i	−0.536895	−	0.843649i	$-0.680403\pi$
$281$		−	28.2843i		−	1.68730i	0.536895	−	0.843649i	$-0.319597\pi$
$282$		0			0
$283$	22.0000	+	22.0000i	1.30776	+	1.30776i	0.923026	+	0.384739i	$0.125708\pi$
$283$	22.0000	+	22.0000i	1.30776	+	1.30776i	0.384739	+	0.923026i	$0.374292\pi$
$284$		0			0
$285$	6.32456	+	4.47214i	0.374634	+	0.264906i
$286$		0			0
$287$	6.32456	−	6.32456i	0.373327	−	0.373327i
$288$		0			0
$289$			1.00000i			0.0588235i
$290$		0			0
$291$	4.24264	−	6.00000i	0.248708	−	0.351726i
$292$		0			0
$293$	12.6491	−	12.6491i	0.738969	−	0.738969i	−0.233410	−	0.972379i	$-0.574988\pi$
$293$	12.6491	−	12.6491i	0.738969	−	0.738969i	0.972379	+	0.233410i	$0.0749883\pi$
$294$		0			0
$295$	11.1803	+	11.1803i	0.650945	+	0.650945i
$296$		0			0
$297$	−10.7574	−	19.2426i	−0.624205	−	1.11657i
$298$		0			0
$299$			28.2843i			1.63572i
$300$		0			0
$301$		−	17.8885i		−	1.03108i
$302$		0			0
$303$	0.926210	+	5.39835i	0.0532094	+	0.310127i
$304$		0			0
$305$	14.1421	+	14.1421i	0.809776	+	0.809776i
$306$		0			0
$307$	4.00000	−	4.00000i	0.228292	−	0.228292i	−0.583687	−	0.811979i	$-0.698390\pi$
$307$	4.00000	−	4.00000i	0.228292	−	0.228292i	0.811979	+	0.583687i	$0.198390\pi$
$308$		0			0
$309$	−4.47214	−	3.16228i	−0.254411	−	0.179896i
$310$		0			0
$311$			18.9737i			1.07590i	0.842977	+	0.537949i	$0.180801\pi$
$311$			18.9737i			1.07590i	−0.842977	+	0.537949i	$0.819199\pi$
$312$		0			0
$313$	19.0000	−	19.0000i	1.07394	−	1.07394i	0.0769051	−	0.997038i	$-0.475496\pi$
$313$	19.0000	−	19.0000i	1.07394	−	1.07394i	0.997038	−	0.0769051i	$-0.0245038\pi$
$314$		0			0
$315$	−20.0000	+	7.07107i	−1.12687	+	0.398410i
$316$		0			0
$317$	3.16228	+	3.16228i	0.177611	+	0.177611i	0.790314	−	0.612702i	$-0.209918\pi$
$317$	3.16228	+	3.16228i	0.177611	+	0.177611i	−0.612702	+	0.790314i	$0.709918\pi$
$318$		0			0
$319$		−	40.2492i		−	2.25352i
$320$		0			0
$321$	16.0000	−	22.6274i	0.893033	−	1.26294i
$322$		0			0
$323$	5.65685	−	5.65685i	0.314756	−	0.314756i
$324$		0			0
$325$	22.3607	−	22.3607i	1.24035	−	1.24035i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	14.1421			0.779681
$330$		0			0
$331$		−	6.00000i		−	0.329790i	−0.986311	−	0.164895i	$-0.947272\pi$
$331$		−	6.00000i		−	0.329790i	0.986311	−	0.164895i	$-0.0527285\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	18.9737i		−	1.03664i
$336$		0			0
$337$	11.0000	+	11.0000i	0.599208	+	0.599208i	0.940102	−	0.340894i	$-0.110730\pi$
$337$	11.0000	+	11.0000i	0.599208	+	0.599208i	−0.340894	+	0.940102i	$0.610730\pi$
$338$		0			0
$339$	12.0000	−	16.9706i	0.651751	−	0.921714i
$340$		0			0
$341$	−18.9737			−1.02748
$342$		0			0
$343$	−8.94427	+	8.94427i	−0.482945	+	0.482945i
$344$		0			0
$345$	2.92893	+	17.0711i	0.157688	+	0.919075i
$346$		0			0
$347$	−4.24264	−	4.24264i	−0.227757	−	0.227757i	0.583998	−	0.811755i	$-0.301488\pi$
$347$	−4.24264	−	4.24264i	−0.227757	−	0.227757i	−0.811755	+	0.583998i	$0.801488\pi$
$348$		0			0
$349$	26.8328			1.43633			0.718164	−	0.695874i	$-0.244983\pi$
$349$	26.8328			1.43633			0.718164	+	0.695874i	$0.244983\pi$
$350$		0			0
$351$	−8.94427	+	31.6228i	−0.477410	+	1.68790i
$352$		0			0
$353$	14.1421	+	14.1421i	0.752710	+	0.752710i	0.974984	−	0.222274i	$-0.0713480\pi$
$353$	14.1421	+	14.1421i	0.752710	+	0.752710i	−0.222274	+	0.974984i	$0.571348\pi$
$354$		0			0
$355$	−10.0000	−	10.0000i	−0.530745	−	0.530745i
$356$		0			0
$357$	3.70484	+	21.5934i	0.196081	+	1.14284i
$358$		0			0
$359$	18.9737			1.00139			0.500696	−	0.865623i	$-0.333077\pi$
$359$	18.9737			1.00139			0.500696	+	0.865623i	$0.333077\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$		0			0
$363$	−2.05025	−	11.9497i	−0.107610	−	0.627199i
$364$		0			0
$365$		−	9.48683i		−	0.496564i
$366$		0			0
$367$	6.70820	+	6.70820i	0.350165	+	0.350165i	0.860171	−	0.510006i	$-0.170357\pi$
$367$	6.70820	+	6.70820i	0.350165	+	0.350165i	−0.510006	+	0.860171i	$0.670357\pi$
$368$		0			0
$369$	−2.82843	−	8.00000i	−0.147242	−	0.416463i
$370$		0			0
$371$	28.2843			1.46845
$372$		0			0
$373$	8.94427	+	8.94427i	0.463117	+	0.463117i	0.899676	−	0.436559i	$-0.143803\pi$
$373$	8.94427	+	8.94427i	0.463117	+	0.463117i	−0.436559	+	0.899676i	$0.643803\pi$
$374$		0			0
$375$	11.1803	−	15.8114i	0.577350	−	0.816497i
$376$		0			0
$377$	−42.4264	+	42.4264i	−2.18507	+	2.18507i
$378$		0			0
$379$	−2.00000			−0.102733			−0.0513665	−	0.998680i	$-0.516358\pi$
$379$	−2.00000			−0.102733			−0.0513665	+	0.998680i	$0.516358\pi$
$380$		0			0
$381$	−3.16228	+	4.47214i	−0.162008	+	0.229114i
$382$		0			0
$383$	22.1359	+	22.1359i	1.13109	+	1.13109i	0.989996	+	0.141098i	$0.0450634\pi$
$383$	22.1359	+	22.1359i	1.13109	+	1.13109i	0.141098	+	0.989996i	$0.454937\pi$
$384$		0			0
$385$	−30.0000			−1.52894
$386$		0			0
$387$	−15.3137	−	7.31371i	−0.778440	−	0.371777i
$388$		0			0
$389$			3.16228i			0.160334i	0.996781	+	0.0801669i	$0.0255453\pi$
$389$			3.16228i			0.160334i	−0.996781	+	0.0801669i	$0.974455\pi$
$390$		0			0
$391$	17.8885			0.904663
$392$		0			0
$393$	2.07107	+	12.0711i	0.104472	+	0.608905i
$394$		0			0
$395$	−7.07107	−	7.07107i	−0.355784	−	0.355784i
$396$		0			0
$397$	−13.4164	+	13.4164i	−0.673350	+	0.673350i	−0.958487	−	0.285137i	$-0.907961\pi$
$397$	−13.4164	+	13.4164i	−0.673350	+	0.673350i	0.285137	+	0.958487i	$0.407961\pi$
$398$		0			0
$399$	−6.32456	+	8.94427i	−0.316624	+	0.447774i
$400$		0			0
$401$		−	2.82843i		−	0.141245i	−0.997503	−	0.0706225i	$-0.977501\pi$
$401$		−	2.82843i		−	0.141245i	0.997503	−	0.0706225i	$-0.0224986\pi$
$402$		0			0
$403$	20.0000	+	20.0000i	0.996271	+	0.996271i
$404$		0			0
$405$	−2.12370	+	20.0122i	−0.105527	+	0.994416i
$406$		0			0
$407$		0			0
$408$		0			0
$409$			28.0000i			1.38451i	0.721653	+	0.692255i	$0.243383\pi$
$409$			28.0000i			1.38451i	−0.721653	+	0.692255i	$0.756617\pi$
$410$		0			0
$411$	5.65685	+	4.00000i	0.279032	+	0.197305i
$412$		0			0
$413$	−15.8114	+	15.8114i	−0.778028	+	0.778028i
$414$		0			0
$415$		−	17.8885i		−	0.878114i
$416$		0			0
$417$	−0.585786	−	3.41421i	−0.0286861	−	0.167195i
$418$		0			0
$419$			1.41421i			0.0690889i	0.999403	+	0.0345444i	$0.0109980\pi$
$419$			1.41421i			0.0690889i	−0.999403	+	0.0345444i	$0.989002\pi$
$420$		0			0
$421$			17.8885i			0.871834i	0.899987	+	0.435917i	$0.143576\pi$
$421$			17.8885i			0.871834i	−0.899987	+	0.435917i	$0.856424\pi$
$422$		0			0
$423$	5.78199	−	12.1065i	0.281130	−	0.588641i
$424$		0			0
$425$	−14.1421	−	14.1421i	−0.685994	−	0.685994i
$426$		0			0
$427$	−20.0000	+	20.0000i	−0.967868	+	0.967868i
$428$		0			0
$429$	−26.8328	+	37.9473i	−1.29550	+	1.83211i
$430$		0			0
$431$		−	31.6228i		−	1.52322i	−0.648038	−	0.761608i	$-0.724410\pi$
$431$		−	31.6228i		−	1.52322i	0.648038	−	0.761608i	$-0.275590\pi$
$432$		0			0
$433$	3.00000	−	3.00000i	0.144171	−	0.144171i	−0.631337	−	0.775508i	$-0.717494\pi$
$433$	3.00000	−	3.00000i	0.144171	−	0.144171i	0.775508	+	0.631337i	$0.217494\pi$
$434$		0			0
$435$	−21.2132	+	30.0000i	−1.01710	+	1.43839i
$436$		0			0
$437$	6.32456	+	6.32456i	0.302545	+	0.302545i
$438$		0			0
$439$		−	17.8885i		−	0.853774i	−0.904305	−	0.426887i	$-0.859610\pi$
$439$		−	17.8885i		−	0.853774i	0.904305	−	0.426887i	$-0.140390\pi$
$440$		0			0
$441$	−3.00000	−	8.48528i	−0.142857	−	0.404061i
$442$		0			0
$443$	12.7279	−	12.7279i	0.604722	−	0.604722i	−0.336840	−	0.941562i	$-0.609358\pi$
$443$	12.7279	−	12.7279i	0.604722	−	0.604722i	0.941562	+	0.336840i	$0.109358\pi$
$444$		0			0
$445$	−13.4164	+	13.4164i	−0.635999	+	0.635999i
$446$		0			0
$447$	−5.39835	+	0.926210i	−0.255333	+	0.0438082i
$448$		0			0
$449$	5.65685			0.266963			0.133482	−	0.991051i	$-0.457384\pi$
$449$	5.65685			0.266963			0.133482	+	0.991051i	$0.457384\pi$
$450$		0			0
$451$		−	12.0000i		−	0.565058i
$452$		0			0
$453$	5.23943	+	30.5377i	0.246170	+	1.43478i
$454$		0			0
$455$	31.6228	+	31.6228i	1.48250	+	1.48250i
$456$		0			0
$457$	−1.00000	−	1.00000i	−0.0467780	−	0.0467780i	0.683331	−	0.730109i	$-0.260531\pi$
$457$	−1.00000	−	1.00000i	−0.0467780	−	0.0467780i	−0.730109	+	0.683331i	$0.760531\pi$
$458$		0			0
$459$	20.0000	+	5.65685i	0.933520	+	0.264039i
$460$		0			0
$461$	−28.4605			−1.32554			−0.662769	−	0.748824i	$-0.730619\pi$
$461$	−28.4605			−1.32554			−0.662769	+	0.748824i	$0.730619\pi$
$462$		0			0
$463$	−11.1803	+	11.1803i	−0.519594	+	0.519594i	−0.917449	−	0.397854i	$-0.869755\pi$
$463$	−11.1803	+	11.1803i	−0.519594	+	0.519594i	0.397854	+	0.917449i	$0.369755\pi$
$464$		0			0
$465$	14.1421	+	10.0000i	0.655826	+	0.463739i
$466$		0			0
$467$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$467$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$468$		0			0
$469$	26.8328			1.23902
$470$		0			0
$471$	−17.8885	−	12.6491i	−0.824261	−	0.582840i
$472$		0			0
$473$	−16.9706	−	16.9706i	−0.780307	−	0.780307i
$474$		0			0
$475$		−	10.0000i		−	0.458831i
$476$		0			0
$477$	11.5640	−	24.2131i	0.529479	−	1.10864i
$478$		0			0
$479$	31.6228			1.44488			0.722441	−	0.691433i	$-0.243020\pi$
$479$	31.6228			1.44488			0.722441	+	0.691433i	$0.243020\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−24.1421	+	4.14214i	−1.09851	+	0.188474i
$484$		0			0
$485$	−9.48683			−0.430775
$486$		0			0
$487$	−24.5967	−	24.5967i	−1.11459	−	1.11459i	−0.992522	−	0.122063i	$-0.961049\pi$
$487$	−24.5967	−	24.5967i	−1.11459	−	1.11459i	−0.122063	−	0.992522i	$-0.538951\pi$
$488$		0			0
$489$	16.9706	−	24.0000i	0.767435	−	1.08532i
$490$		0			0
$491$	7.07107			0.319113			0.159556	−	0.987189i	$-0.448994\pi$
$491$	7.07107			0.319113			0.159556	+	0.987189i	$0.448994\pi$
$492$		0			0
$493$	26.8328	+	26.8328i	1.20849	+	1.20849i
$494$		0			0
$495$	−12.2655	+	25.6819i	−0.551292	+	1.15431i
$496$		0			0
$497$	14.1421	−	14.1421i	0.634361	−	0.634361i
$498$		0			0
$499$	−26.0000			−1.16392			−0.581960	−	0.813217i	$-0.697714\pi$
$499$	−26.0000			−1.16392			−0.581960	+	0.813217i	$0.697714\pi$
$500$		0			0
$501$	18.9737	+	13.4164i	0.847681	+	0.599401i
$502$		0			0
$503$	9.48683	+	9.48683i	0.422997	+	0.422997i	0.886234	−	0.463237i	$-0.153312\pi$
$503$	9.48683	+	9.48683i	0.422997	+	0.422997i	−0.463237	+	0.886234i	$0.653312\pi$
$504$		0			0
$505$	5.00000	−	5.00000i	0.222497	−	0.222497i
$506$		0			0
$507$	46.0919	−	7.90812i	2.04701	−	0.351212i
$508$		0			0
$509$		−	15.8114i		−	0.700827i	−0.936595	−	0.350414i	$-0.886041\pi$
$509$		−	15.8114i		−	0.700827i	0.936595	−	0.350414i	$-0.113959\pi$
$510$		0			0
$511$	13.4164			0.593507
$512$		0			0
$513$	5.07107	+	9.07107i	0.223893	+	0.400497i
$514$		0			0
$515$			7.07107i			0.311588i
$516$		0			0
$517$	13.4164	−	13.4164i	0.590053	−	0.590053i
$518$		0			0
$519$	−6.32456	−	4.47214i	−0.277617	−	0.196305i
$520$		0			0
$521$			11.3137i			0.495663i	0.968803	+	0.247831i	$0.0797179\pi$
$521$			11.3137i			0.495663i	−0.968803	+	0.247831i	$0.920282\pi$
$522$		0			0
$523$	−2.00000	−	2.00000i	−0.0874539	−	0.0874539i	0.662027	−	0.749480i	$-0.269697\pi$
$523$	−2.00000	−	2.00000i	−0.0874539	−	0.0874539i	−0.749480	+	0.662027i	$0.769697\pi$
$524$		0			0
$525$	22.3607	+	15.8114i	0.975900	+	0.690066i
$526$		0			0
$527$	12.6491	−	12.6491i	0.551004	−	0.551004i
$528$		0			0
$529$		−	3.00000i		−	0.130435i
$530$		0			0
$531$	7.07107	+	20.0000i	0.306858	+	0.867926i
$532$		0			0
$533$	−12.6491	+	12.6491i	−0.547894	+	0.547894i
$534$		0			0
$535$	−35.7771			−1.54678
$536$		0			0
$537$	−26.5563	+	4.55635i	−1.14599	+	0.196621i
$538$		0			0
$539$		−	12.7279i		−	0.548230i
$540$		0			0
$541$			26.8328i			1.15363i	0.816874	+	0.576816i	$0.195705\pi$
$541$			26.8328i			1.15363i	−0.816874	+	0.576816i	$0.804295\pi$
$542$		0			0
$543$	30.5377	−	5.23943i	1.31050	−	0.224846i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	16.0000	−	16.0000i	0.684111	−	0.684111i	−0.276813	−	0.960924i	$-0.589278\pi$
$547$	16.0000	−	16.0000i	0.684111	−	0.684111i	0.960924	+	0.276813i	$0.0892783\pi$
$548$		0			0
$549$	8.94427	+	25.2982i	0.381732	+	1.07970i
$550$		0			0
$551$			18.9737i			0.808305i
$552$		0			0
$553$	10.0000	−	10.0000i	0.425243	−	0.425243i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−25.2982	−	25.2982i	−1.07192	−	1.07192i	−0.997205	−	0.0747151i	$-0.976195\pi$
$557$	−25.2982	−	25.2982i	−1.07192	−	1.07192i	−0.0747151	−	0.997205i	$-0.523805\pi$
$558$		0			0
$559$			35.7771i			1.51321i
$560$		0			0
$561$	24.0000	+	16.9706i	1.01328	+	0.716498i
$562$		0			0
$563$	−21.2132	+	21.2132i	−0.894030	+	0.894030i	−0.994900	−	0.100870i	$-0.967837\pi$
$563$	−21.2132	+	21.2132i	−0.894030	+	0.894030i	0.100870	+	0.994900i	$0.467837\pi$
$564$		0			0
$565$	−26.8328			−1.12887
$566$		0			0
$567$	−28.3016	−	3.00337i	−1.18855	−	0.126129i
$568$		0			0
$569$	36.7696			1.54146			0.770730	−	0.637162i	$-0.219892\pi$
$569$	36.7696			1.54146			0.770730	+	0.637162i	$0.219892\pi$
$570$		0			0
$571$		−	18.0000i		−	0.753277i	−0.926360	−	0.376638i	$-0.877080\pi$
$571$		−	18.0000i		−	0.753277i	0.926360	−	0.376638i	$-0.122920\pi$
$572$		0			0
$573$	−21.5934	+	3.70484i	−0.902076	+	0.154772i
$574$		0			0
$575$	15.8114	−	15.8114i	0.659380	−	0.659380i
$576$		0			0
$577$	21.0000	+	21.0000i	0.874241	+	0.874241i	0.992931	−	0.118690i	$-0.0378694\pi$
$577$	21.0000	+	21.0000i	0.874241	+	0.874241i	−0.118690	+	0.992931i	$0.537869\pi$
$578$		0			0
$579$	6.00000	+	4.24264i	0.249351	+	0.176318i
$580$		0			0
$581$	25.2982			1.04955
$582$		0			0
$583$	26.8328	−	26.8328i	1.11130	−	1.11130i
$584$		0			0
$585$	40.0000	−	14.1421i	1.65380	−	0.584705i
$586$		0			0
$587$	−11.3137	−	11.3137i	−0.466967	−	0.466967i	0.433964	−	0.900930i	$-0.357115\pi$
$587$	−11.3137	−	11.3137i	−0.466967	−	0.466967i	−0.900930	+	0.433964i	$0.857115\pi$
$588$		0			0
$589$	8.94427			0.368542
$590$		0			0
$591$	−8.94427	+	12.6491i	−0.367918	+	0.520315i
$592$		0			0
$593$	−22.6274	−	22.6274i	−0.929197	−	0.929197i	0.0684574	−	0.997654i	$-0.478192\pi$
$593$	−22.6274	−	22.6274i	−0.929197	−	0.929197i	−0.997654	+	0.0684574i	$0.978192\pi$
$594$		0			0
$595$	20.0000	−	20.0000i	0.819920	−	0.819920i
$596$		0			0
$597$	30.5377	−	5.23943i	1.24982	−	0.214436i
$598$		0			0
$599$	44.2719			1.80890			0.904450	−	0.426579i	$-0.140282\pi$
$599$	44.2719			1.80890			0.904450	+	0.426579i	$0.140282\pi$
$600$		0			0
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$	10.9706	−	22.9706i	0.446756	−	0.935434i
$604$		0			0
$605$	−11.0680	+	11.0680i	−0.449977	+	0.449977i
$606$		0			0
$607$	20.1246	+	20.1246i	0.816833	+	0.816833i	0.985648	−	0.168815i	$-0.0539940\pi$
$607$	20.1246	+	20.1246i	0.816833	+	0.816833i	−0.168815	+	0.985648i	$0.553994\pi$
$608$		0			0
$609$	−42.4264	−	30.0000i	−1.71920	−	1.21566i
$610$		0			0
$611$	−28.2843			−1.14426
$612$		0			0
$613$	−22.3607	−	22.3607i	−0.903139	−	0.903139i	0.0925671	−	0.995706i	$-0.470493\pi$
$613$	−22.3607	−	22.3607i	−0.903139	−	0.903139i	−0.995706	+	0.0925671i	$0.970493\pi$
$614$		0			0
$615$	−6.32456	+	8.94427i	−0.255031	+	0.360668i
$616$		0			0
$617$	28.2843	−	28.2843i	1.13868	−	1.13868i	0.149995	−	0.988687i	$-0.452074\pi$
$617$	28.2843	−	28.2843i	1.13868	−	1.13868i	0.988687	−	0.149995i	$-0.0479258\pi$
$618$		0			0
$619$	−34.0000			−1.36658			−0.683288	−	0.730149i	$-0.739451\pi$
$619$	−34.0000			−1.36658			−0.683288	+	0.730149i	$0.739451\pi$
$620$		0			0
$621$	−6.32456	+	22.3607i	−0.253796	+	0.897303i
$622$		0			0
$623$	−18.9737	−	18.9737i	−0.760164	−	0.760164i
$624$		0			0
$625$	−25.0000			−1.00000
$626$		0			0
$627$	2.48528	+	14.4853i	0.0992526	+	0.578486i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	40.2492			1.60230			0.801148	−	0.598466i	$-0.204223\pi$
$631$	40.2492			1.60230			0.801148	+	0.598466i	$0.204223\pi$
$632$		0			0
$633$	−23.8995	+	4.10051i	−0.949920	+	0.162980i
$634$		0			0
$635$	7.07107			0.280607
$636$		0			0
$637$	−13.4164	+	13.4164i	−0.531577	+	0.531577i
$638$		0			0
$639$	−6.32456	−	17.8885i	−0.250196	−	0.707660i
$640$		0			0
$641$			28.2843i			1.11716i	0.829450	+	0.558581i	$0.188654\pi$
$641$			28.2843i			1.11716i	−0.829450	+	0.558581i	$0.811346\pi$
$642$		0			0
$643$	−4.00000	−	4.00000i	−0.157745	−	0.157745i	0.623822	−	0.781567i	$-0.285579\pi$
$643$	−4.00000	−	4.00000i	−0.157745	−	0.157745i	−0.781567	+	0.623822i	$0.785579\pi$
$644$		0			0
$645$	3.70484	+	21.5934i	0.145878	+	0.850239i
$646$		0			0
$647$	15.8114	−	15.8114i	0.621610	−	0.621610i	−0.324333	−	0.945943i	$-0.605140\pi$
$647$	15.8114	−	15.8114i	0.621610	−	0.621610i	0.945943	+	0.324333i	$0.105140\pi$
$648$		0			0
$649$			30.0000i			1.17760i
$650$		0			0
$651$	−14.1421	+	20.0000i	−0.554274	+	0.783862i
$652$		0			0
$653$	28.4605	−	28.4605i	1.11375	−	1.11375i	0.121106	−	0.992640i	$-0.461356\pi$
$653$	28.4605	−	28.4605i	1.11375	−	1.11375i	0.992640	−	0.121106i	$-0.0386440\pi$
$654$		0			0
$655$	11.1803	−	11.1803i	0.436852	−	0.436852i
$656$		0			0
$657$	5.48528	−	11.4853i	0.214001	−	0.448084i
$658$		0			0
$659$		−	26.8701i		−	1.04671i	−0.852115	−	0.523354i	$-0.824680\pi$
$659$		−	26.8701i		−	1.04671i	0.852115	−	0.523354i	$-0.175320\pi$
$660$		0			0
$661$		−	44.7214i		−	1.73946i	−0.493528	−	0.869730i	$-0.664293\pi$
$661$		−	44.7214i		−	1.73946i	0.493528	−	0.869730i	$-0.335707\pi$
$662$		0			0
$663$	−7.40968	−	43.1868i	−0.287768	−	1.67723i
$664$		0			0
$665$	14.1421			0.548408
$666$		0			0
$667$	−30.0000	+	30.0000i	−1.16160	+	1.16160i
$668$		0			0
$669$	−4.47214	−	3.16228i	−0.172903	−	0.122261i
$670$		0			0
$671$			37.9473i			1.46494i
$672$		0			0
$673$	9.00000	−	9.00000i	0.346925	−	0.346925i	−0.512038	−	0.858963i	$-0.671109\pi$
$673$	9.00000	−	9.00000i	0.346925	−	0.346925i	0.858963	+	0.512038i	$0.171109\pi$
$674$		0			0
$675$	22.6777	−	12.6777i	0.872864	−	0.487964i
$676$		0			0
$677$	−15.8114	−	15.8114i	−0.607681	−	0.607681i	0.334658	−	0.942339i	$-0.391379\pi$
$677$	−15.8114	−	15.8114i	−0.607681	−	0.607681i	−0.942339	+	0.334658i	$0.891379\pi$
$678$		0			0
$679$		−	13.4164i		−	0.514874i
$680$		0			0
$681$	−10.0000	+	14.1421i	−0.383201	+	0.541928i
$682$		0			0
$683$	−33.9411	+	33.9411i	−1.29872	+	1.29872i	−0.369484	+	0.929237i	$0.620466\pi$
$683$	−33.9411	+	33.9411i	−1.29872	+	1.29872i	−0.929237	+	0.369484i	$0.879534\pi$
$684$		0			0
$685$		−	8.94427i		−	0.341743i
$686$		0			0
$687$	7.85915	+	45.8065i	0.299845	+	1.74763i
$688$		0			0
$689$	−56.5685			−2.15509
$690$		0			0
$691$			34.0000i			1.29342i	0.762736	+	0.646710i	$0.223856\pi$
$691$			34.0000i			1.29342i	−0.762736	+	0.646710i	$0.776144\pi$
$692$		0			0
$693$	−36.3196	−	17.3460i	−1.37967	−	0.658919i
$694$		0			0
$695$	−3.16228	+	3.16228i	−0.119952	+	0.119952i
$696$		0			0
$697$	8.00000	+	8.00000i	0.303022	+	0.303022i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−28.4605			−1.07494			−0.537469	−	0.843283i	$-0.680620\pi$
$701$	−28.4605			−1.07494			−0.537469	+	0.843283i	$0.680620\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−17.0711	+	2.92893i	−0.642934	+	0.110310i
$706$		0			0
$707$	7.07107	+	7.07107i	0.265935	+	0.265935i
$708$		0			0
$709$	17.8885			0.671818			0.335909	−	0.941894i	$-0.390956\pi$
$709$	17.8885			0.671818			0.335909	+	0.941894i	$0.390956\pi$
$710$		0			0
$711$	−4.47214	−	12.6491i	−0.167718	−	0.474379i
$712$		0			0
$713$	14.1421	+	14.1421i	0.529627	+	0.529627i
$714$		0			0
$715$	60.0000			2.24387
$716$		0			0
$717$	5.55726	+	32.3901i	0.207540	+	1.20963i
$718$		0			0
$719$	−25.2982			−0.943464			−0.471732	−	0.881742i	$-0.656371\pi$
$719$	−25.2982			−0.943464			−0.471732	+	0.881742i	$0.656371\pi$
$720$		0			0
$721$	−10.0000			−0.372419
$722$		0			0
$723$	−7.02944	−	40.9706i	−0.261428	−	1.52371i
$724$		0			0
$725$	47.4342			1.76166
$726$		0			0
$727$	11.1803	+	11.1803i	0.414656	+	0.414656i	0.883357	−	0.468701i	$-0.155278\pi$
$727$	11.1803	+	11.1803i	0.414656	+	0.414656i	−0.468701	+	0.883357i	$0.655278\pi$
$728$		0			0
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$		0			0
$731$	22.6274			0.836905
$732$		0			0
$733$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$733$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$734$		0			0
$735$	−6.70820	+	9.48683i	−0.247436	+	0.349927i
$736$		0			0
$737$	25.4558	−	25.4558i	0.937678	−	0.937678i
$738$		0			0
$739$	−6.00000			−0.220714			−0.110357	−	0.993892i	$-0.535199\pi$
$739$	−6.00000			−0.220714			−0.110357	+	0.993892i	$0.535199\pi$
$740$		0			0
$741$	12.6491	−	17.8885i	0.464677	−	0.657152i
$742$		0			0
$743$	28.4605	+	28.4605i	1.04411	+	1.04411i	0.998981	+	0.0451335i	$0.0143713\pi$
$743$	28.4605	+	28.4605i	1.04411	+	1.04411i	0.0451335	+	0.998981i	$0.485629\pi$
$744$		0			0
$745$	5.00000	+	5.00000i	0.183186	+	0.183186i
$746$		0			0
$747$	10.3431	−	21.6569i	0.378436	−	0.792383i
$748$		0			0
$749$		−	50.5964i		−	1.84875i
$750$		0			0
$751$	−40.2492			−1.46872			−0.734358	−	0.678763i	$-0.762516\pi$
$751$	−40.2492			−1.46872			−0.734358	+	0.678763i	$0.762516\pi$
$752$		0			0
$753$	7.04163	+	41.0416i	0.256611	+	1.49564i
$754$		0			0
$755$	28.2843	−	28.2843i	1.02937	−	1.02937i
$756$		0			0
$757$	17.8885	−	17.8885i	0.650170	−	0.650170i	−0.302864	−	0.953034i	$-0.597943\pi$
$757$	17.8885	−	17.8885i	0.650170	−	0.650170i	0.953034	+	0.302864i	$0.0979427\pi$
$758$		0			0
$759$	−18.9737	+	26.8328i	−0.688700	+	0.973970i
$760$		0			0
$761$			39.5980i			1.43543i	0.696339	+	0.717713i	$0.254811\pi$
$761$			39.5980i			1.43543i	−0.696339	+	0.717713i	$0.745189\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−8.94427	−	25.2982i	−0.323381	−	0.914659i
$766$		0			0
$767$	31.6228	−	31.6228i	1.14183	−	1.14183i
$768$		0			0
$769$		−	42.0000i		−	1.51456i	−0.653091	−	0.757279i	$-0.726528\pi$
$769$		−	42.0000i		−	1.51456i	0.653091	−	0.757279i	$-0.273472\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	9.48683	−	9.48683i	0.341218	−	0.341218i	−0.515607	−	0.856825i	$-0.672434\pi$
$773$	9.48683	−	9.48683i	0.341218	−	0.341218i	0.856825	+	0.515607i	$0.172434\pi$
$774$		0			0
$775$		−	22.3607i		−	0.803219i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			5.65685i			0.202678i
$780$		0			0
$781$		−	26.8328i		−	0.960154i
$782$		0			0
$783$	−43.0279	+	24.0542i	−1.53769	+	0.859627i
$784$		0			0
$785$			28.2843i			1.00951i
$786$		0			0
$787$	−2.00000	+	2.00000i	−0.0712923	+	0.0712923i	−0.741854	−	0.670562i	$-0.766053\pi$
$787$	−2.00000	+	2.00000i	−0.0712923	+	0.0712923i	0.670562	+	0.741854i	$0.266053\pi$
$788$		0			0
$789$	4.47214	−	6.32456i	0.159212	−	0.225160i
$790$		0			0
$791$		−	37.9473i		−	1.34925i
$792$		0			0
$793$	40.0000	−	40.0000i	1.42044	−	1.42044i
$794$		0			0
$795$	−34.1421	+	5.85786i	−1.21090	+	0.207757i
$796$		0			0
$797$	−3.16228	−	3.16228i	−0.112014	−	0.112014i	0.648878	−	0.760892i	$-0.275238\pi$
$797$	−3.16228	−	3.16228i	−0.112014	−	0.112014i	−0.760892	+	0.648878i	$0.775238\pi$
$798$		0			0
$799$			17.8885i			0.632851i
$800$		0			0
$801$	−24.0000	+	8.48528i	−0.847998	+	0.299813i
$802$		0			0
$803$	12.7279	−	12.7279i	0.449159	−	0.449159i
$804$		0			0
$805$	22.3607	+	22.3607i	0.788110	+	0.788110i
$806$		0			0
$807$	5.39835	−	0.926210i	0.190031	−	0.0326041i
$808$		0			0
$809$	−28.2843			−0.994422			−0.497211	−	0.867630i	$-0.665643\pi$
$809$	−28.2843			−0.994422			−0.497211	+	0.867630i	$0.665643\pi$
$810$		0			0
$811$			18.0000i			0.632065i	0.948748	+	0.316033i	$0.102351\pi$
$811$			18.0000i			0.632065i	−0.948748	+	0.316033i	$0.897649\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−37.9473			−1.32924
$816$		0			0
$817$	8.00000	+	8.00000i	0.279885	+	0.279885i
$818$		0			0
$819$	20.0000	+	56.5685i	0.698857	+	1.97666i
$820$		0			0
$821$	28.4605			0.993278			0.496639	−	0.867957i	$-0.334567\pi$
$821$	28.4605			0.993278			0.496639	+	0.867957i	$0.334567\pi$
$822$		0			0
$823$	−20.1246	+	20.1246i	−0.701500	+	0.701500i	−0.964732	−	0.263233i	$-0.915211\pi$
$823$	−20.1246	+	20.1246i	−0.701500	+	0.701500i	0.263233	+	0.964732i	$0.415211\pi$
$824$		0			0
$825$	36.2132	−	6.21320i	1.26078	−	0.216316i
$826$		0			0
$827$	24.0416	+	24.0416i	0.836009	+	0.836009i	0.988331	−	0.152322i	$-0.0486749\pi$
$827$	24.0416	+	24.0416i	0.836009	+	0.836009i	−0.152322	+	0.988331i	$0.548675\pi$
$828$		0			0
$829$	−53.6656			−1.86388			−0.931942	−	0.362607i	$-0.881887\pi$
$829$	−53.6656			−1.86388			−0.931942	+	0.362607i	$0.881887\pi$
$830$		0			0
$831$	17.8885	+	12.6491i	0.620547	+	0.438793i
$832$		0			0
$833$	8.48528	+	8.48528i	0.293998	+	0.293998i
$834$		0			0
$835$		−	30.0000i		−	1.03819i
$836$		0			0
$837$	11.3393	+	20.2835i	0.391942	+	0.701101i
$838$		0			0
$839$	−18.9737			−0.655044			−0.327522	−	0.944844i	$-0.606214\pi$
$839$	−18.9737			−0.655044			−0.327522	+	0.944844i	$0.606214\pi$
$840$		0			0
$841$	−61.0000			−2.10345
$842$		0			0
$843$	−48.2843	+	8.28427i	−1.66300	+	0.285325i
$844$		0			0
$845$	−42.6907	−	42.6907i	−1.46861	−	1.46861i
$846$		0			0
$847$	−15.6525	−	15.6525i	−0.537825	−	0.537825i
$848$		0			0
$849$	31.1127	−	44.0000i	1.06779	−	1.51008i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−13.4164	−	13.4164i	−0.459369	−	0.459369i	0.439079	−	0.898448i	$-0.355305\pi$
$853$	−13.4164	−	13.4164i	−0.459369	−	0.459369i	−0.898448	+	0.439079i	$0.855305\pi$
$854$		0			0
$855$	5.78199	−	12.1065i	0.197740	−	0.414035i
$856$		0			0
$857$	16.9706	−	16.9706i	0.579703	−	0.579703i	−0.355118	−	0.934821i	$-0.615559\pi$
$857$	16.9706	−	16.9706i	0.579703	−	0.579703i	0.934821	+	0.355118i	$0.115559\pi$
$858$		0			0
$859$	18.0000			0.614152			0.307076	−	0.951685i	$-0.400649\pi$
$859$	18.0000			0.614152			0.307076	+	0.951685i	$0.400649\pi$
$860$		0			0
$861$	−12.6491	−	8.94427i	−0.431081	−	0.304820i
$862$		0			0
$863$	−15.8114	−	15.8114i	−0.538226	−	0.538226i	0.384782	−	0.923008i	$-0.374277\pi$
$863$	−15.8114	−	15.8114i	−0.538226	−	0.538226i	−0.923008	+	0.384782i	$0.874277\pi$
$864$		0			0
$865$			10.0000i			0.340010i
$866$		0			0
$867$	1.70711	−	0.292893i	0.0579764	−	0.00994718i
$868$		0			0
$869$		−	18.9737i		−	0.643638i
$870$		0			0
$871$	−53.6656			−1.81839
$872$		0			0
$873$	−11.4853	−	5.48528i	−0.388718	−	0.185649i
$874$		0			0
$875$		−	35.3553i		−	1.19523i
$876$		0			0
$877$	−17.8885	+	17.8885i	−0.604053	+	0.604053i	−0.941386	−	0.337332i	$-0.890475\pi$
$877$	−17.8885	+	17.8885i	−0.604053	+	0.604053i	0.337332	+	0.941386i	$0.390475\pi$
$878$		0			0
$879$	−25.2982	−	17.8885i	−0.853288	−	0.603366i
$880$		0			0
$881$		−	42.4264i		−	1.42938i	−0.699440	−	0.714691i	$-0.746567\pi$
$881$		−	42.4264i		−	1.42938i	0.699440	−	0.714691i	$-0.253433\pi$
$882$		0			0
$883$	12.0000	+	12.0000i	0.403832	+	0.403832i	0.879581	−	0.475749i	$-0.157823\pi$
$883$	12.0000	+	12.0000i	0.403832	+	0.403832i	−0.475749	+	0.879581i	$0.657823\pi$
$884$		0			0
$885$	15.8114	−	22.3607i	0.531494	−	0.751646i
$886$		0			0
$887$	−34.7851	+	34.7851i	−1.16797	+	1.16797i	−0.185283	+	0.982685i	$0.559320\pi$
$887$	−34.7851	+	34.7851i	−1.16797	+	1.16797i	−0.982685	+	0.185283i	$0.940680\pi$
$888$		0			0
$889$			10.0000i			0.335389i
$890$		0			0
$891$	−29.6985	+	24.0000i	−0.994937	+	0.804030i
$892$		0			0
$893$	−6.32456	+	6.32456i	−0.211643	+	0.211643i
$894$		0			0
$895$	24.5967	+	24.5967i	0.822179	+	0.822179i
$896$		0			0
$897$	48.2843	−	8.28427i	1.61216	−	0.276604i
$898$		0			0
$899$			42.4264i			1.41500i
$900$		0			0
$901$			35.7771i			1.19191i
$902$		0			0
$903$	−30.5377	+	5.23943i	−1.01623	+	0.174357i
$904$		0			0
$905$	−28.2843	−	28.2843i	−0.940201	−	0.940201i
$906$		0			0
$907$	22.0000	−	22.0000i	0.730498	−	0.730498i	−0.240220	−	0.970718i	$-0.577220\pi$
$907$	22.0000	−	22.0000i	0.730498	−	0.730498i	0.970718	+	0.240220i	$0.0772197\pi$
$908$		0			0
$909$	8.94427	−	3.16228i	0.296663	−	0.104886i
$910$		0			0
$911$		−	56.9210i		−	1.88588i	−0.332967	−	0.942938i	$-0.608050\pi$
$911$		−	56.9210i		−	1.88588i	0.332967	−	0.942938i	$-0.391950\pi$
$912$		0			0
$913$	24.0000	−	24.0000i	0.794284	−	0.794284i
$914$		0			0
$915$	20.0000	−	28.2843i	0.661180	−	0.935049i
$916$		0			0
$917$	15.8114	+	15.8114i	0.522138	+	0.522138i
$918$		0			0
$919$			13.4164i			0.442566i	0.975210	+	0.221283i	$0.0710245\pi$
$919$			13.4164i			0.442566i	−0.975210	+	0.221283i	$0.928975\pi$
$920$		0			0
$921$	−8.00000	−	5.65685i	−0.263609	−	0.186400i
$922$		0			0
$923$	−28.2843	+	28.2843i	−0.930988	+	0.930988i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−4.08849	+	8.56062i	−0.134284	+	0.281168i
$928$		0			0
$929$	−28.2843			−0.927977			−0.463988	−	0.885841i	$-0.653582\pi$
$929$	−28.2843			−0.927977			−0.463988	+	0.885841i	$0.653582\pi$
$930$		0			0
$931$			6.00000i			0.196642i
$932$		0			0
$933$	32.3901	−	5.55726i	1.06040	−	0.181936i
$934$		0			0
$935$		−	37.9473i		−	1.24101i
$936$		0			0
$937$	21.0000	+	21.0000i	0.686040	+	0.686040i	0.961354	−	0.275314i	$-0.0887819\pi$
$937$	21.0000	+	21.0000i	0.686040	+	0.686040i	−0.275314	+	0.961354i	$0.588782\pi$
$938$		0			0
$939$	−38.0000	−	26.8701i	−1.24008	−	0.876871i
$940$		0			0
$941$	28.4605			0.927786			0.463893	−	0.885891i	$-0.346452\pi$
$941$	28.4605			0.927786			0.463893	+	0.885891i	$0.346452\pi$
$942$		0			0
$943$	−8.94427	+	8.94427i	−0.291266	+	0.291266i
$944$		0			0
$945$	17.9289	+	32.0711i	0.583228	+	1.04327i
$946$		0			0
$947$	−7.07107	−	7.07107i	−0.229779	−	0.229779i	0.582821	−	0.812600i	$-0.301949\pi$
$947$	−7.07107	−	7.07107i	−0.229779	−	0.229779i	−0.812600	+	0.582821i	$0.801949\pi$
$948$		0			0
$949$	−26.8328			−0.871030
$950$		0			0
$951$	4.47214	−	6.32456i	0.145019	−	0.205088i
$952$		0			0
$953$	−5.65685	−	5.65685i	−0.183243	−	0.183243i	0.609524	−	0.792768i	$-0.291361\pi$
$953$	−5.65685	−	5.65685i	−0.183243	−	0.183243i	−0.792768	+	0.609524i	$0.791361\pi$
$954$		0			0
$955$	20.0000	+	20.0000i	0.647185	+	0.647185i
$956$		0			0
$957$	−68.7097	+	11.7887i	−2.22107	+	0.381075i
$958$		0			0
$959$	12.6491			0.408461
$960$		0			0
$961$	−11.0000			−0.354839
$962$		0			0
$963$	−43.3137	−	20.6863i	−1.39576	−	0.666606i
$964$		0			0
$965$		−	9.48683i		−	0.305392i
$966$		0			0
$967$	6.70820	+	6.70820i	0.215721	+	0.215721i	0.806693	−	0.590971i	$-0.201255\pi$
$967$	6.70820	+	6.70820i	0.215721	+	0.215721i	−0.590971	+	0.806693i	$0.701255\pi$
$968$		0			0
$969$	−11.3137	−	8.00000i	−0.363449	−	0.256997i
$970$		0			0
$971$	52.3259			1.67922			0.839609	−	0.543191i	$-0.182784\pi$
$971$	52.3259			1.67922			0.839609	+	0.543191i	$0.182784\pi$
$972$		0			0
$973$	−4.47214	−	4.47214i	−0.143370	−	0.143370i
$974$		0			0
$975$	−44.7214	−	31.6228i	−1.43223	−	1.01274i
$976$		0			0
$977$	−16.9706	+	16.9706i	−0.542936	+	0.542936i	−0.924389	−	0.381452i	$-0.875424\pi$
$977$	−16.9706	+	16.9706i	−0.542936	+	0.542936i	0.381452	+	0.924389i	$0.375424\pi$
$978$		0			0
$979$	−36.0000			−1.15056
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22.1359	−	22.1359i	−0.706027	−	0.706027i	0.259670	−	0.965697i	$-0.416386\pi$
$983$	−22.1359	−	22.1359i	−0.706027	−	0.706027i	−0.965697	+	0.259670i	$0.916386\pi$
$984$		0			0
$985$	20.0000			0.637253
$986$		0			0
$987$	−4.14214	−	24.1421i	−0.131846	−	0.768453i
$988$		0			0
$989$			25.2982i			0.804437i
$990$		0			0
$991$		0			0			−	1.00000i	$-0.5\pi$
$991$		0			0				1.00000i	$0.5\pi$
$992$		0			0
$993$	−10.2426	+	1.75736i	−0.325040	+	0.0557681i
$994$		0			0
$995$	−28.2843	−	28.2843i	−0.896672	−	0.896672i
$996$		0			0
$997$	4.47214	−	4.47214i	0.141634	−	0.141634i	−0.632735	−	0.774369i	$-0.718068\pi$
$997$	4.47214	−	4.47214i	0.141634	−	0.141634i	0.774369	+	0.632735i	$0.218068\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.bi.e.737.3	yes	8
3.2	odd	2	inner	960.2.bi.e.737.2	yes	8
4.3	odd	2		960.2.bi.f.737.1	yes	8
5.3	odd	4		960.2.bi.f.353.3	yes	8
8.3	odd	2	inner	960.2.bi.e.737.4	yes	8
8.5	even	2		960.2.bi.f.737.2	yes	8
12.11	even	2		960.2.bi.f.737.4	yes	8
15.8	even	4		960.2.bi.f.353.2	yes	8
20.3	even	4	inner	960.2.bi.e.353.1	✓	8
24.5	odd	2		960.2.bi.f.737.3	yes	8
24.11	even	2	inner	960.2.bi.e.737.1	yes	8
40.3	even	4		960.2.bi.f.353.4	yes	8
40.13	odd	4	inner	960.2.bi.e.353.2	yes	8
60.23	odd	4	inner	960.2.bi.e.353.4	yes	8
120.53	even	4	inner	960.2.bi.e.353.3	yes	8
120.83	odd	4		960.2.bi.f.353.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.bi.e.353.1	✓	8	20.3	even	4	inner
960.2.bi.e.353.2	yes	8	40.13	odd	4	inner
960.2.bi.e.353.3	yes	8	120.53	even	4	inner
960.2.bi.e.353.4	yes	8	60.23	odd	4	inner
960.2.bi.e.737.1	yes	8	24.11	even	2	inner
960.2.bi.e.737.2	yes	8	3.2	odd	2	inner
960.2.bi.e.737.3	yes	8	1.1	even	1	trivial
960.2.bi.e.737.4	yes	8	8.3	odd	2	inner
960.2.bi.f.353.1	yes	8	120.83	odd	4
960.2.bi.f.353.2	yes	8	15.8	even	4
960.2.bi.f.353.3	yes	8	5.3	odd	4
960.2.bi.f.353.4	yes	8	40.3	even	4
960.2.bi.f.737.1	yes	8	4.3	odd	2
960.2.bi.f.737.2	yes	8	8.5	even	2
960.2.bi.f.737.3	yes	8	24.5	odd	2
960.2.bi.f.737.4	yes	8	12.11	even	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.bi (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.292893 - 1.70711i) q^{3} +(-1.58114 + 1.58114i) q^{5} +(-2.23607 - 2.23607i) q^{7} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})\)	\(q+(-0.292893 - 1.70711i) q^{3} +(-1.58114 + 1.58114i) q^{5} +(-2.23607 - 2.23607i) q^{7} +(-2.82843 + 1.00000i) q^{9} -4.24264 q^{11} +(4.47214 + 4.47214i) q^{13} +(3.16228 + 2.23607i) q^{15} +(2.82843 - 2.82843i) q^{17} +2.00000 q^{19} +(-3.16228 + 4.47214i) q^{21} +(3.16228 + 3.16228i) q^{23} -5.00000i q^{25} +(2.53553 + 4.53553i) q^{27} +9.48683i q^{29} +4.47214 q^{31} +(1.24264 + 7.24264i) q^{33} +7.07107 q^{35} +(6.32456 - 8.94427i) q^{39} +2.82843i q^{41} +(4.00000 + 4.00000i) q^{43} +(2.89100 - 6.05327i) q^{45} +(-3.16228 + 3.16228i) q^{47} +3.00000i q^{49} +(-5.65685 - 4.00000i) q^{51} +(-6.32456 + 6.32456i) q^{53} +(6.70820 - 6.70820i) q^{55} +(-0.585786 - 3.41421i) q^{57} -7.07107i q^{59} -8.94427i q^{61} +(8.56062 + 4.08849i) q^{63} -14.1421 q^{65} +(-6.00000 + 6.00000i) q^{67} +(4.47214 - 6.32456i) q^{69} +6.32456i q^{71} +(-3.00000 + 3.00000i) q^{73} +(-8.53553 + 1.46447i) q^{75} +(9.48683 + 9.48683i) q^{77} +4.47214i q^{79} +(7.00000 - 5.65685i) q^{81} +(-5.65685 + 5.65685i) q^{83} +8.94427i q^{85} +(16.1950 - 2.77863i) q^{87} +8.48528 q^{89} -20.0000i q^{91} +(-1.30986 - 7.63441i) q^{93} +(-3.16228 + 3.16228i) q^{95} +(3.00000 + 3.00000i) q^{97} +(12.0000 - 4.24264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3}+O(q^{10}) \) 8 * q - 8 * q^3	\( 8 q - 8 q^{3} + 16 q^{19} - 8 q^{27} - 24 q^{33} + 32 q^{43} - 16 q^{57} - 48 q^{67} - 24 q^{73} - 40 q^{75} + 56 q^{81} + 24 q^{97} + 96 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 + 16 * q^19 - 8 * q^27 - 24 * q^33 + 32 * q^43 - 16 * q^57 - 48 * q^67 - 24 * q^73 - 40 * q^75 + 56 * q^81 + 24 * q^97 + 96 * q^99

Introduction

L-functions

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