LMFDB - Embedded newform 124.2.m.a.113.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,2,Mod(9,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([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("124.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	124.m (of order $15$, degree $8$, 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:	$0.990144985064$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			113.3
Character	$\chi$	$=$	124.113
Dual form			124.2.m.a.45.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.25593 + 2.50547i) q^{3} +(-0.443179 - 0.767609i) q^{5} +(-0.381716 - 3.63179i) q^{7} +(-0.874547 + 8.32076i) q^{9} +O(q^{10})$	\(q+(2.25593 + 2.50547i) q^{3} +(-0.443179 - 0.767609i) q^{5} +(-0.381716 - 3.63179i) q^{7} +(-0.874547 + 8.32076i) q^{9} +(-3.63309 - 1.61756i) q^{11} +(-1.31035 + 0.278523i) q^{13} +(0.923437 - 2.84205i) q^{15} +(0.825590 - 0.367577i) q^{17} +(3.79893 + 0.807487i) q^{19} +(8.23820 - 9.14944i) q^{21} +(-1.81873 - 1.32138i) q^{23} +(2.10718 - 3.64975i) q^{25} +(-14.6376 + 10.6349i) q^{27} +(2.23347 + 6.87391i) q^{29} +(-3.89393 - 3.97961i) q^{31} +(-4.14327 - 12.7517i) q^{33} +(-2.61863 + 1.90254i) q^{35} +(0.608032 - 1.05314i) q^{37} +(-3.65389 - 2.65471i) q^{39} +(-3.12630 + 3.47211i) q^{41} +(5.73115 + 1.21819i) q^{43} +(6.77467 - 3.01628i) q^{45} +(-0.483914 + 1.48933i) q^{47} +(-6.19714 + 1.31724i) q^{49} +(2.78343 + 1.23926i) q^{51} +(-1.01096 + 9.61864i) q^{53} +(0.368460 + 3.50566i) q^{55} +(6.54699 + 11.3397i) q^{57} +(-7.47442 - 8.30118i) q^{59} +9.66024 q^{61} +30.5531 q^{63} +(0.794517 + 0.882400i) q^{65} +(-0.0443615 - 0.0768364i) q^{67} +(-0.792246 - 7.53772i) q^{69} +(0.513750 - 4.88801i) q^{71} +(6.21514 + 2.76716i) q^{73} +(13.8980 - 2.95411i) q^{75} +(-4.48781 + 13.8121i) q^{77} +(-5.54678 + 2.46959i) q^{79} +(-35.1156 - 7.46404i) q^{81} +(-4.51115 + 5.01013i) q^{83} +(-0.648040 - 0.470828i) q^{85} +(-12.1838 + 21.1030i) q^{87} +(-5.56554 + 4.04360i) q^{89} +(1.51172 + 4.65259i) q^{91} +(1.18635 - 18.7338i) q^{93} +(-1.06377 - 3.27395i) q^{95} +(1.08436 - 0.787830i) q^{97} +(16.6366 - 28.8154i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{3} + q^{5} - 9 q^{7} + 2 q^{9}+O(q^{10}) $ 24 * q - q^3 + q^5 - 9 * q^7 + 2 * q^9	$ 24 q - q^{3} + q^{5} - 9 q^{7} + 2 q^{9} + 8 q^{11} + 2 q^{13} - q^{15} - q^{17} - q^{19} + 12 q^{21} - 21 q^{23} - 21 q^{25} - 43 q^{27} - 24 q^{29} - 29 q^{31} - 5 q^{33} + 10 q^{35} - 8 q^{37} - 17 q^{39} + 9 q^{41} - 2 q^{43} - 28 q^{45} - 38 q^{47} + 22 q^{49} + 69 q^{51} + 59 q^{53} - q^{55} - 7 q^{57} - 13 q^{59} + 36 q^{61} + 118 q^{63} + 94 q^{65} + 29 q^{67} + 52 q^{69} + 55 q^{71} + 55 q^{73} + 79 q^{75} - 38 q^{77} - 31 q^{79} - 98 q^{81} - 59 q^{83} - 60 q^{85} - 36 q^{87} - 57 q^{89} - 48 q^{91} - 124 q^{93} - 3 q^{95} - 19 q^{97} - 31 q^{99}+O(q^{100}) $ 24 * q - q^3 + q^5 - 9 * q^7 + 2 * q^9 + 8 * q^11 + 2 * q^13 - q^15 - q^17 - q^19 + 12 * q^21 - 21 * q^23 - 21 * q^25 - 43 * q^27 - 24 * q^29 - 29 * q^31 - 5 * q^33 + 10 * q^35 - 8 * q^37 - 17 * q^39 + 9 * q^41 - 2 * q^43 - 28 * q^45 - 38 * q^47 + 22 * q^49 + 69 * q^51 + 59 * q^53 - q^55 - 7 * q^57 - 13 * q^59 + 36 * q^61 + 118 * q^63 + 94 * q^65 + 29 * q^67 + 52 * q^69 + 55 * q^71 + 55 * q^73 + 79 * q^75 - 38 * q^77 - 31 * q^79 - 98 * q^81 - 59 * q^83 - 60 * q^85 - 36 * q^87 - 57 * q^89 - 48 * q^91 - 124 * q^93 - 3 * q^95 - 19 * q^97 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{4}{15}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.25593	+	2.50547i	1.30246	+	1.44653i	0.821967	+	0.569534i	$0.192876\pi$
$3$	2.25593	+	2.50547i	1.30246	+	1.44653i	0.480495	+	0.876997i	$0.340457\pi$
$4$		0			0
$5$	−0.443179	−	0.767609i	−0.198196	−	0.343285i	0.749748	−	0.661724i	$-0.230175\pi$
$5$	−0.443179	−	0.767609i	−0.198196	−	0.343285i	−0.947943	+	0.318439i	$0.896842\pi$
$6$		0			0
$7$	−0.381716	−	3.63179i	−0.144275	−	1.37269i	−0.791864	−	0.610697i	$-0.790889\pi$
$7$	−0.381716	−	3.63179i	−0.144275	−	1.37269i	0.647589	−	0.761990i	$-0.275777\pi$
$8$		0			0
$9$	−0.874547	+	8.32076i	−0.291516	+	2.77359i
$10$		0			0
$11$	−3.63309	−	1.61756i	−1.09542	−	0.487711i	−0.222180	−	0.975006i	$-0.571317\pi$
$11$	−3.63309	−	1.61756i	−1.09542	−	0.487711i	−0.873238	+	0.487294i	$0.837984\pi$
$12$		0			0
$13$	−1.31035	+	0.278523i	−0.363425	+	0.0772485i	−0.386005	−	0.922497i	$-0.626145\pi$
$13$	−1.31035	+	0.278523i	−0.363425	+	0.0772485i	0.0225798	+	0.999745i	$0.492812\pi$
$14$		0			0
$15$	0.923437	−	2.84205i	0.238430	−	0.733813i
$16$		0			0
$17$	0.825590	−	0.367577i	0.200235	−	0.0891504i	−0.304169	−	0.952618i	$-0.598379\pi$
$17$	0.825590	−	0.367577i	0.200235	−	0.0891504i	0.504404	+	0.863468i	$0.331712\pi$
$18$		0			0
$19$	3.79893	+	0.807487i	0.871534	+	0.185250i	0.621906	−	0.783092i	$-0.286358\pi$
$19$	3.79893	+	0.807487i	0.871534	+	0.185250i	0.249628	+	0.968342i	$0.419692\pi$
$20$		0			0
$21$	8.23820	−	9.14944i	1.79772	−	1.99657i
$22$		0			0
$23$	−1.81873	−	1.32138i	−0.379231	−	0.275528i	0.381797	−	0.924246i	$-0.375305\pi$
$23$	−1.81873	−	1.32138i	−0.379231	−	0.275528i	−0.761028	+	0.648719i	$0.775305\pi$
$24$		0			0
$25$	2.10718	−	3.64975i	0.421437	−	0.729950i
$26$		0			0
$27$	−14.6376	+	10.6349i	−2.81702	+	2.04668i
$28$		0			0
$29$	2.23347	+	6.87391i	0.414745	+	1.27645i	0.912479	+	0.409124i	$0.134166\pi$
$29$	2.23347	+	6.87391i	0.414745	+	1.27645i	−0.497734	+	0.867330i	$0.665834\pi$
$30$		0			0
$31$	−3.89393	−	3.97961i	−0.699370	−	0.714760i
$31$	−3.89393	−	3.97961i	−0.699370	−	0.714760i
$32$		0			0
$33$	−4.14327	−	12.7517i	−0.721251	−	2.21978i
$34$		0			0
$35$	−2.61863	+	1.90254i	−0.442628	+	0.321588i
$36$		0			0
$37$	0.608032	−	1.05314i	0.0999599	−	0.173136i	−0.811708	−	0.584064i	$-0.801462\pi$
$37$	0.608032	−	1.05314i	0.0999599	−	0.173136i	0.911668	+	0.410928i	$0.134795\pi$
$38$		0			0
$39$	−3.65389	−	2.65471i	−0.585091	−	0.425093i
$40$		0			0
$41$	−3.12630	+	3.47211i	−0.488246	+	0.542252i	−0.936044	−	0.351883i	$-0.885542\pi$
$41$	−3.12630	+	3.47211i	−0.488246	+	0.542252i	0.447798	+	0.894135i	$0.352208\pi$
$42$		0			0
$43$	5.73115	+	1.21819i	0.873992	+	0.185773i	0.623005	−	0.782218i	$-0.285912\pi$
$43$	5.73115	+	1.21819i	0.873992	+	0.185773i	0.250987	+	0.967991i	$0.419245\pi$
$44$		0			0
$45$	6.77467	−	3.01628i	1.00991	−	0.449640i
$46$		0			0
$47$	−0.483914	+	1.48933i	−0.0705861	+	0.217242i	−0.980126	−	0.198374i	$-0.936434\pi$
$47$	−0.483914	+	1.48933i	−0.0705861	+	0.217242i	0.909540	+	0.415616i	$0.136434\pi$
$48$		0			0
$49$	−6.19714	+	1.31724i	−0.885306	+	0.188178i
$50$		0			0
$51$	2.78343	+	1.23926i	0.389758	+	0.173531i
$52$		0			0
$53$	−1.01096	+	9.61864i	−0.138866	+	1.32122i	0.673983	+	0.738747i	$0.264582\pi$
$53$	−1.01096	+	9.61864i	−0.138866	+	1.32122i	−0.812849	+	0.582475i	$0.802084\pi$
$54$		0			0
$55$	0.368460	+	3.50566i	0.0496831	+	0.472703i
$56$		0			0
$57$	6.54699	+	11.3397i	0.867170	+	1.50198i
$58$		0			0
$59$	−7.47442	−	8.30118i	−0.973086	−	1.08072i	−0.996714	−	0.0810006i	$-0.974188\pi$
$59$	−7.47442	−	8.30118i	−0.973086	−	1.08072i	0.0236281	−	0.999721i	$-0.492478\pi$
$60$		0			0
$61$	9.66024			1.23687			0.618433	−	0.785837i	$-0.287768\pi$
$61$	9.66024			1.23687			0.618433	+	0.785837i	$0.287768\pi$
$62$		0			0
$63$	30.5531			3.84932
$64$		0			0
$65$	0.794517	+	0.882400i	0.0985477	+	0.109448i
$66$		0			0
$67$	−0.0443615	−	0.0768364i	−0.00541962	−	0.00938706i	0.863303	−	0.504686i	$-0.168392\pi$
$67$	−0.0443615	−	0.0768364i	−0.00541962	−	0.00938706i	−0.868722	+	0.495299i	$0.835058\pi$
$68$		0			0
$69$	−0.792246	−	7.53772i	−0.0953752	−	0.907434i
$70$		0			0
$71$	0.513750	−	4.88801i	0.0609709	−	0.580100i	−0.920800	−	0.390034i	$-0.872463\pi$
$71$	0.513750	−	4.88801i	0.0609709	−	0.580100i	0.981771	−	0.190066i	$-0.0608701\pi$
$72$		0			0
$73$	6.21514	+	2.76716i	0.727427	+	0.323871i	0.736824	−	0.676085i	$-0.236325\pi$
$73$	6.21514	+	2.76716i	0.727427	+	0.323871i	−0.00939729	+	0.999956i	$0.502991\pi$
$74$		0			0
$75$	13.8980	−	2.95411i	1.60480	−	0.341111i
$76$		0			0
$77$	−4.48781	+	13.8121i	−0.511433	+	1.57403i
$78$		0			0
$79$	−5.54678	+	2.46959i	−0.624062	+	0.277850i	−0.694306	−	0.719680i	$-0.744289\pi$
$79$	−5.54678	+	2.46959i	−0.624062	+	0.277850i	0.0702447	+	0.997530i	$0.477622\pi$
$80$		0			0
$81$	−35.1156	−	7.46404i	−3.90173	−	0.829338i
$82$		0			0
$83$	−4.51115	+	5.01013i	−0.495163	+	0.549934i	−0.937985	−	0.346676i	$-0.887311\pi$
$83$	−4.51115	+	5.01013i	−0.495163	+	0.549934i	0.442823	+	0.896609i	$0.353977\pi$
$84$		0			0
$85$	−0.648040	−	0.470828i	−0.0702898	−	0.0510685i
$86$		0			0
$87$	−12.1838	+	21.1030i	−1.30624	+	2.26248i
$88$		0			0
$89$	−5.56554	+	4.04360i	−0.589946	+	0.428621i	−0.842296	−	0.539015i	$-0.818797\pi$
$89$	−5.56554	+	4.04360i	−0.589946	+	0.428621i	0.252350	+	0.967636i	$0.418797\pi$
$90$		0			0
$91$	1.51172	+	4.65259i	0.158471	+	0.487724i
$92$		0			0
$93$	1.18635	−	18.7338i	0.123019	−	1.94261i
$94$		0			0
$95$	−1.06377	−	3.27395i	−0.109141	−	0.335901i
$96$		0			0
$97$	1.08436	−	0.787830i	0.110100	−	0.0799920i	−0.531373	−	0.847138i	$-0.678324\pi$
$97$	1.08436	−	0.787830i	0.110100	−	0.0799920i	0.641473	+	0.767146i	$0.278324\pi$
$98$		0			0
$99$	16.6366	−	28.8154i	1.67204	−	2.89606i
$100$		0			0
$101$	−3.43149	−	2.49312i	−0.341446	−	0.248075i	0.403826	−	0.914836i	$-0.367680\pi$
$101$	−3.43149	−	2.49312i	−0.341446	−	0.248075i	−0.745272	+	0.666761i	$0.767680\pi$
$102$		0			0
$103$	−5.03239	+	5.58904i	−0.495856	+	0.550704i	−0.938178	−	0.346152i	$-0.887488\pi$
$103$	−5.03239	+	5.58904i	−0.495856	+	0.550704i	0.442322	+	0.896856i	$0.354155\pi$
$104$		0			0
$105$	−10.6742	−	2.26887i	−1.04169	−	0.221419i
$106$		0			0
$107$	16.0515	−	7.14657i	1.55175	−	0.690885i	0.561158	−	0.827709i	$-0.310356\pi$
$107$	16.0515	−	7.14657i	1.55175	−	0.690885i	0.990595	+	0.136824i	$0.0436894\pi$
$108$		0			0
$109$	−2.52946	+	7.78488i	−0.242278	+	0.745656i	0.753794	+	0.657111i	$0.228222\pi$
$109$	−2.52946	+	7.78488i	−0.242278	+	0.745656i	−0.996072	+	0.0885451i	$0.971778\pi$
$110$		0			0
$111$	4.01029	−	0.852414i	0.380640	−	0.0809076i
$112$		0			0
$113$	4.40318	+	1.96042i	0.414216	+	0.184421i	0.603255	−	0.797549i	$-0.293870\pi$
$113$	4.40318	+	1.96042i	0.414216	+	0.184421i	−0.189038	+	0.981970i	$0.560537\pi$
$114$		0			0
$115$	−0.208283	+	1.98168i	−0.0194225	+	0.184793i
$116$		0			0
$117$	−1.17156	−	11.1467i	−0.108311	−	1.03051i
$118$		0			0
$119$	−1.65010	−	2.85806i	−0.151265	−	0.261998i
$120$		0			0
$121$	3.22241	+	3.57885i	0.292946	+	0.325350i
$122$		0			0
$123$	−15.7520			−1.42031
$124$		0			0
$125$	−8.16724			−0.730500
$126$		0			0
$127$	−8.69144	−	9.65282i	−0.771241	−	0.856549i	0.221706	−	0.975114i	$-0.428838\pi$
$127$	−8.69144	−	9.65282i	−0.771241	−	0.856549i	−0.992946	+	0.118564i	$0.962171\pi$
$128$		0			0
$129$	9.87694	+	17.1074i	0.869616	+	1.50622i
$130$		0			0
$131$	1.28877	+	12.2618i	0.112600	+	1.07132i	0.894240	+	0.447588i	$0.147717\pi$
$131$	1.28877	+	12.2618i	0.112600	+	1.07132i	−0.781640	+	0.623730i	$0.785616\pi$
$132$		0			0
$133$	1.48251	−	14.1051i	0.128550	−	1.22307i
$134$		0			0
$135$	14.6505	+	6.52284i	1.26092	+	0.561396i
$136$		0			0
$137$	3.53102	−	0.750541i	0.301675	−	0.0641231i	−0.0545871	−	0.998509i	$-0.517384\pi$
$137$	3.53102	−	0.750541i	0.301675	−	0.0641231i	0.356262	+	0.934386i	$0.384051\pi$
$138$		0			0
$139$	3.27716	−	10.0861i	0.277965	−	0.855489i	−0.710454	−	0.703743i	$-0.751511\pi$
$139$	3.27716	−	10.0861i	0.277965	−	0.855489i	0.988420	−	0.151746i	$-0.0484894\pi$
$140$		0			0
$141$	−4.82315	+	2.14741i	−0.406183	+	0.180844i
$142$		0			0
$143$	5.21114	+	1.10766i	0.435778	+	0.0926274i
$144$		0			0
$145$	4.28665	−	4.76081i	0.355987	−	0.395364i
$146$		0			0
$147$	−17.2806	−	12.5551i	−1.42528	−	1.03553i
$148$		0			0
$149$	8.04083	−	13.9271i	0.658730	−	1.14095i	−0.322214	−	0.946667i	$-0.604427\pi$
$149$	8.04083	−	13.9271i	0.658730	−	1.14095i	0.980945	−	0.194288i	$-0.0622396\pi$
$150$		0			0
$151$	−1.76497	+	1.28233i	−0.143631	+	0.104354i	−0.657280	−	0.753646i	$-0.728293\pi$
$151$	−1.76497	+	1.28233i	−0.143631	+	0.104354i	0.513649	+	0.858000i	$0.328293\pi$
$152$		0			0
$153$	2.33650	+	7.19100i	0.188895	+	0.581358i
$154$		0			0
$155$	−1.32908	+	4.75270i	−0.106754	+	0.381746i
$156$		0			0
$157$	−4.36683	−	13.4397i	−0.348511	−	1.07261i	−0.959677	−	0.281104i	$-0.909300\pi$
$157$	−4.36683	−	13.4397i	−0.348511	−	1.07261i	0.611167	−	0.791502i	$-0.290700\pi$
$158$		0			0
$159$	−26.3798	+	19.1661i	−2.09206	+	1.51997i
$160$		0			0
$161$	−4.10475	+	7.10963i	−0.323499	+	0.560317i
$162$		0			0
$163$	12.7538	+	9.26615i	0.998952	+	0.725781i	0.961863	−	0.273531i	$-0.0881916\pi$
$163$	12.7538	+	9.26615i	0.998952	+	0.725781i	0.0370888	+	0.999312i	$0.488192\pi$
$164$		0			0
$165$	−7.95209	+	8.83169i	−0.619070	+	0.687546i
$166$		0			0
$167$	17.3850	+	3.69530i	1.34529	+	0.285951i	0.823594	−	0.567179i	$-0.191965\pi$
$167$	17.3850	+	3.69530i	1.34529	+	0.285951i	0.521698	+	0.853130i	$0.325299\pi$
$168$		0			0
$169$	−10.2367	+	4.55765i	−0.787435	+	0.350589i
$170$		0			0
$171$	−10.0412	+	30.9038i	−0.767873	+	2.36327i
$172$		0			0
$173$	6.69691	−	1.42347i	0.509156	−	0.108225i	0.0538317	−	0.998550i	$-0.482857\pi$
$173$	6.69691	−	1.42347i	0.509156	−	0.108225i	0.455325	+	0.890326i	$0.349523\pi$
$174$		0			0
$175$	−14.0595	−	6.25968i	−1.06280	−	0.473187i
$176$		0			0
$177$	3.93655	−	37.4538i	0.295889	−	2.81520i
$178$		0			0
$179$	−2.00391	−	19.0659i	−0.149779	−	1.42505i	−0.768705	−	0.639604i	$-0.779098\pi$
$179$	−2.00391	−	19.0659i	−0.149779	−	1.42505i	0.618925	−	0.785450i	$-0.287568\pi$
$180$		0			0
$181$	5.84705	+	10.1274i	0.434608	+	0.752763i	0.997264	−	0.0739286i	$-0.0235537\pi$
$181$	5.84705	+	10.1274i	0.434608	+	0.752763i	−0.562656	+	0.826691i	$0.690220\pi$
$182$		0			0
$183$	21.7928	+	24.2034i	1.61097	+	1.78917i
$184$		0			0
$185$	−1.07787			−0.0792465
$186$		0			0
$187$	−3.59402			−0.262821
$188$		0			0
$189$	44.2110	+	49.1013i	3.21588	+	3.57160i
$190$		0			0
$191$	−11.6355	−	20.1533i	−0.841915	−	1.45824i	−0.888273	−	0.459316i	$-0.848095\pi$
$191$	−11.6355	−	20.1533i	−0.841915	−	1.45824i	0.0463577	−	0.998925i	$-0.485239\pi$
$192$		0			0
$193$	−0.722563	−	6.87473i	−0.0520112	−	0.494854i	−0.989257	−	0.146185i	$-0.953301\pi$
$193$	−0.722563	−	6.87473i	−0.0520112	−	0.494854i	0.937246	−	0.348669i	$-0.113366\pi$
$194$		0			0
$195$	−0.418448	+	3.98127i	−0.0299657	+	0.285105i
$196$		0			0
$197$	2.40587	+	1.07116i	0.171411	+	0.0763171i	0.490648	−	0.871358i	$-0.336760\pi$
$197$	2.40587	+	1.07116i	0.171411	+	0.0763171i	−0.319237	+	0.947675i	$0.603427\pi$
$198$		0			0
$199$	5.54480	−	1.17858i	0.393060	−	0.0835476i	−0.00714168	−	0.999974i	$-0.502273\pi$
$199$	5.54480	−	1.17858i	0.393060	−	0.0835476i	0.400202	+	0.916427i	$0.368940\pi$
$200$		0			0
$201$	0.0924344	−	0.284484i	0.00651982	−	0.0200660i
$202$		0			0
$203$	24.1120	−	10.7354i	1.69233	−	0.753475i
$204$		0			0
$205$	4.05073	+	0.861010i	0.282915	+	0.0601355i
$206$		0			0
$207$	12.5855	−	13.9776i	0.874751	−	0.971510i
$208$		0			0
$209$	−12.4957	−	9.07865i	−0.864345	−	0.627983i
$210$		0			0
$211$	2.20604	−	3.82097i	0.151870	−	0.263046i	−0.780045	−	0.625723i	$-0.784804\pi$
$211$	2.20604	−	3.82097i	0.151870	−	0.263046i	0.931915	+	0.362677i	$0.118137\pi$
$212$		0			0
$213$	13.4057	−	9.73983i	0.918545	−	0.667362i
$214$		0			0
$215$	−1.60483	−	4.93916i	−0.109449	−	0.336848i
$216$		0			0
$217$	−12.9667	+	15.6610i	−0.880240	+	1.06314i
$218$		0			0
$219$	7.08791	+	21.8143i	0.478956	+	1.47408i
$220$		0			0
$221$	−0.979433	+	0.711600i	−0.0658838	+	0.0478674i
$222$		0			0
$223$	−9.36149	+	16.2146i	−0.626892	+	1.08581i	0.361280	+	0.932457i	$0.382340\pi$
$223$	−9.36149	+	16.2146i	−0.626892	+	1.08581i	−0.988172	+	0.153351i	$0.950993\pi$
$224$		0			0
$225$	28.5259	+	20.7252i	1.90172	+	1.38168i
$226$		0			0
$227$	7.79669	−	8.65910i	0.517485	−	0.574725i	−0.426595	−	0.904443i	$-0.640287\pi$
$227$	7.79669	−	8.65910i	0.517485	−	0.574725i	0.944079	+	0.329718i	$0.106954\pi$
$228$		0			0
$229$	0.0807807	+	0.0171705i	0.00533814	+	0.00113466i	0.210580	−	0.977577i	$-0.432465\pi$
$229$	0.0807807	+	0.0171705i	0.00533814	+	0.00113466i	−0.205242	+	0.978711i	$0.565798\pi$
$230$		0			0
$231$	−44.7298	+	19.9150i	−2.94301	+	1.31031i
$232$		0			0
$233$	5.81414	−	17.8941i	0.380897	−	1.17228i	−0.558517	−	0.829493i	$-0.688629\pi$
$233$	5.81414	−	17.8941i	0.380897	−	1.17228i	0.939413	−	0.342786i	$-0.111371\pi$
$234$		0			0
$235$	1.35769	−	0.288585i	0.0885657	−	0.0188252i
$236$		0			0
$237$	−18.7006	−	8.32605i	−1.21474	−	0.540835i
$238$		0			0
$239$	2.04739	−	19.4796i	0.132435	−	1.26003i	−0.703297	−	0.710896i	$-0.748290\pi$
$239$	2.04739	−	19.4796i	0.132435	−	1.26003i	0.835732	−	0.549137i	$-0.185044\pi$
$240$		0			0
$241$	−0.275552	−	2.62170i	−0.0177499	−	0.168879i	0.982056	−	0.188590i	$-0.0603919\pi$
$241$	−0.275552	−	2.62170i	−0.0177499	−	0.168879i	−0.999806	+	0.0197116i	$0.993725\pi$
$242$		0			0
$243$	−33.3777	−	57.8119i	−2.14118	−	3.70864i
$244$		0			0
$245$	3.75757	+	4.17321i	0.240063	+	0.266617i
$246$		0			0
$247$	−5.20283			−0.331048
$248$		0			0
$249$	−22.7296			−1.44043
$250$		0			0
$251$	9.76262	+	10.8425i	0.616211	+	0.684372i	0.967782	−	0.251790i	$-0.0810191\pi$
$251$	9.76262	+	10.8425i	0.616211	+	0.684372i	−0.351571	+	0.936161i	$0.614352\pi$
$252$		0			0
$253$	4.47019	+	7.74260i	0.281039	+	0.486773i
$254$		0			0
$255$	−0.282289	−	2.68580i	−0.0176776	−	0.168191i
$256$		0			0
$257$	−0.508254	+	4.83571i	−0.0317040	+	0.301643i	0.967167	+	0.254141i	$0.0817928\pi$
$257$	−0.508254	+	4.83571i	−0.0317040	+	0.301643i	−0.998871	+	0.0475022i	$0.984874\pi$
$258$		0			0
$259$	−4.05689	−	1.80624i	−0.252083	−	0.112234i
$260$		0			0
$261$	−59.1494	+	12.5726i	−3.66126	+	0.778224i
$262$		0			0
$263$	2.30319	−	7.08850i	0.142021	−	0.437096i	−0.854595	−	0.519295i	$-0.826194\pi$
$263$	2.30319	−	7.08850i	0.142021	−	0.437096i	0.996616	+	0.0821995i	$0.0261945\pi$
$264$		0			0
$265$	7.83139	−	3.48676i	0.481079	−	0.214190i
$266$		0			0
$267$	−22.6866	−	4.82218i	−1.38840	−	0.295113i
$268$		0			0
$269$	3.64287	−	4.04582i	0.222110	−	0.246678i	−0.621783	−	0.783189i	$-0.713591\pi$
$269$	3.64287	−	4.04582i	0.222110	−	0.246678i	0.843893	+	0.536511i	$0.180258\pi$
$270$		0			0
$271$	15.6854	+	11.3961i	0.952819	+	0.692263i	0.951472	−	0.307736i	$-0.0995713\pi$
$271$	15.6854	+	11.3961i	0.952819	+	0.692263i	0.00134688	+	0.999999i	$0.499571\pi$
$272$		0			0
$273$	−8.24658	+	14.2835i	−0.499106	+	0.864476i
$274$		0			0
$275$	−13.5593	+	9.85138i	−0.817654	+	0.594060i
$276$		0			0
$277$	−6.49583	−	19.9921i	−0.390296	−	1.20121i	−0.932564	−	0.361003i	$-0.882434\pi$
$277$	−6.49583	−	19.9921i	−0.390296	−	1.20121i	0.542268	−	0.840206i	$-0.317566\pi$
$278$		0			0
$279$	36.5188	−	28.9201i	2.18633	−	1.73140i
$280$		0			0
$281$	−1.96495	−	6.04751i	−0.117219	−	0.360764i	0.875184	−	0.483790i	$-0.160740\pi$
$281$	−1.96495	−	6.04751i	−0.117219	−	0.360764i	−0.992403	+	0.123026i	$0.960740\pi$
$282$		0			0
$283$	−10.7187	+	7.78759i	−0.637161	+	0.462924i	−0.858874	−	0.512188i	$-0.828835\pi$
$283$	−10.7187	+	7.78759i	−0.637161	+	0.462924i	0.221713	+	0.975112i	$0.428835\pi$
$284$		0			0
$285$	5.80298	−	10.0511i	0.343739	−	0.595374i
$286$		0			0
$287$	13.8033	+	10.0287i	0.814784	+	0.591975i
$288$		0			0
$289$	−10.8287	+	12.0265i	−0.636984	+	0.707443i
$290$		0			0
$291$	4.42011	+	0.939524i	0.259112	+	0.0550759i
$292$		0			0
$293$	7.31278	−	3.25586i	0.427217	−	0.190209i	−0.181853	−	0.983326i	$-0.558209\pi$
$293$	7.31278	−	3.25586i	0.427217	−	0.190209i	0.609070	+	0.793116i	$0.291543\pi$
$294$		0			0
$295$	−3.05955	+	9.41634i	−0.178134	+	0.548241i
$296$		0			0
$297$	70.3824	−	14.9602i	4.08400	−	0.868081i
$298$		0			0
$299$	2.75121	+	1.22492i	0.159106	+	0.0708387i
$300$		0			0
$301$	2.23655	−	21.2793i	0.128912	−	1.22652i
$302$		0			0
$303$	−1.49477	−	14.2218i	−0.0858723	−	0.817021i
$304$		0			0
$305$	−4.28122	−	7.41529i	−0.245142	−	0.424598i
$306$		0			0
$307$	15.2645	+	16.9529i	0.871190	+	0.967555i	0.999708	−	0.0241524i	$-0.00768870\pi$
$307$	15.2645	+	16.9529i	0.871190	+	0.967555i	−0.128518	+	0.991707i	$0.541022\pi$
$308$		0			0
$309$	−25.3559			−1.44245
$310$		0			0
$311$	−10.5270			−0.596934			−0.298467	−	0.954420i	$-0.596475\pi$
$311$	−10.5270			−0.596934			−0.298467	+	0.954420i	$0.596475\pi$
$312$		0			0
$313$	−3.23906	−	3.59734i	−0.183082	−	0.203334i	0.644616	−	0.764506i	$-0.277017\pi$
$313$	−3.23906	−	3.59734i	−0.183082	−	0.203334i	−0.827699	+	0.561173i	$0.810350\pi$
$314$		0			0
$315$	−13.5405	−	23.4528i	−0.762920	−	1.32142i
$316$		0			0
$317$	3.51636	+	33.4559i	0.197498	+	1.87907i	0.424857	+	0.905260i	$0.360324\pi$
$317$	3.51636	+	33.4559i	0.197498	+	1.87907i	−0.227359	+	0.973811i	$0.573009\pi$
$318$		0			0
$319$	3.00454	−	28.5863i	0.168222	−	1.60053i
$320$		0			0
$321$	54.1165	+	24.0942i	3.02049	+	1.34481i
$322$		0			0
$323$	3.43317	−	0.729743i	0.191027	−	0.0406040i
$324$		0			0
$325$	−1.74461	+	5.36935i	−0.0967734	+	0.297838i
$326$		0			0
$327$	−25.2110	+	11.2247i	−1.39417	+	0.620726i
$328$		0			0
$329$	5.59366	+	1.18897i	0.308388	+	0.0655500i
$330$		0			0
$331$	−16.5970	+	18.4329i	−0.912256	+	1.01316i	0.0875990	+	0.996156i	$0.472081\pi$
$331$	−16.5970	+	18.4329i	−0.912256	+	1.01316i	−0.999855	+	0.0170075i	$0.994586\pi$
$332$		0			0
$333$	8.23119	+	5.98031i	0.451067	+	0.327719i
$334$		0			0
$335$	−0.0393202	+	0.0681046i	−0.00214829	+	0.00372095i
$336$		0			0
$337$	4.83875	−	3.51556i	0.263584	−	0.191505i	−0.448142	−	0.893963i	$-0.647914\pi$
$337$	4.83875	−	3.51556i	0.263584	−	0.191505i	0.711725	+	0.702458i	$0.247914\pi$
$338$		0			0
$339$	5.02150	+	15.4546i	0.272731	+	0.839379i
$340$		0			0
$341$	7.70974	+	20.7569i	0.417506	+	1.12405i
$342$		0			0
$343$	−0.749764	−	2.30754i	−0.0404835	−	0.124595i
$344$		0			0
$345$	−5.43491	+	3.94870i	−0.292606	+	0.212591i
$346$		0			0
$347$	−15.1552	+	26.2496i	−0.813576	+	1.40915i	0.0967703	+	0.995307i	$0.469149\pi$
$347$	−15.1552	+	26.2496i	−0.813576	+	1.40915i	−0.910346	+	0.413848i	$0.864185\pi$
$348$		0			0
$349$	−24.4184	−	17.7410i	−1.30708	−	0.949653i	−0.307087	−	0.951682i	$-0.599354\pi$
$349$	−24.4184	−	17.7410i	−1.30708	−	0.949653i	−0.999998	+	0.00202904i	$0.999354\pi$
$350$		0			0
$351$	16.2184	−	18.0123i	0.865672	−	0.961427i
$352$		0			0
$353$	13.3079	+	2.82869i	0.708309	+	0.150556i	0.547960	−	0.836505i	$-0.315405\pi$
$353$	13.3079	+	2.82869i	0.708309	+	0.150556i	0.160349	+	0.987060i	$0.448738\pi$
$354$		0			0
$355$	−3.97976	+	1.77190i	−0.211224	+	0.0940429i
$356$		0			0
$357$	3.43825	−	10.5819i	0.181972	−	0.560051i
$358$		0			0
$359$	−25.6097	+	5.44351i	−1.35163	+	0.287297i	−0.826121	−	0.563493i	$-0.809457\pi$
$359$	−25.6097	+	5.44351i	−1.35163	+	0.287297i	−0.525506	+	0.850790i	$0.676124\pi$
$360$		0			0
$361$	−3.57754	−	1.59282i	−0.188292	−	0.0838328i
$362$		0			0
$363$	−1.69715	+	16.1473i	−0.0890772	+	0.847513i
$364$		0			0
$365$	−0.630325	−	5.99714i	−0.0329927	−	0.313905i
$366$		0			0
$367$	15.0492	+	26.0660i	0.785562	+	1.36063i	0.928663	+	0.370926i	$0.120960\pi$
$367$	15.0492	+	26.0660i	0.785562	+	1.36063i	−0.143100	+	0.989708i	$0.545707\pi$
$368$		0			0
$369$	−26.1565	−	29.0497i	−1.36165	−	1.51227i
$370$		0			0
$371$	35.3188			1.83366
$372$		0			0
$373$	6.45719			0.334341			0.167170	−	0.985928i	$-0.446537\pi$
$373$	6.45719			0.334341			0.167170	+	0.985928i	$0.446537\pi$
$374$		0			0
$375$	−18.4247	−	20.4627i	−0.951449	−	1.05669i
$376$		0			0
$377$	−4.84117	−	8.38515i	−0.249333	−	0.431857i
$378$		0			0
$379$	3.42011	+	32.5402i	0.175679	+	1.67148i	0.626927	+	0.779078i	$0.284312\pi$
$379$	3.42011	+	32.5402i	0.175679	+	1.67148i	−0.451248	+	0.892399i	$0.649021\pi$
$380$		0			0
$381$	4.57752	−	43.5522i	0.234514	−	2.23125i
$382$		0			0
$383$	−3.97133	−	1.76815i	−0.202926	−	0.0903483i	0.302757	−	0.953068i	$-0.402093\pi$
$383$	−3.97133	−	1.76815i	−0.202926	−	0.0903483i	−0.505683	+	0.862719i	$0.668759\pi$
$384$		0			0
$385$	12.5912	−	2.67633i	0.641705	−	0.136399i
$386$		0			0
$387$	−15.1484	+	46.6221i	−0.770039	+	2.36994i
$388$		0			0
$389$	27.6863	−	12.3267i	1.40375	−	0.624990i	0.441527	−	0.897248i	$-0.354437\pi$
$389$	27.6863	−	12.3267i	1.40375	−	0.624990i	0.962224	+	0.272258i	$0.0877704\pi$
$390$		0			0
$391$	−1.98723	−	0.422400i	−0.100499	−	0.0213617i
$392$		0			0
$393$	−27.8141	+	30.8907i	−1.40304	+	1.55823i
$394$		0			0
$395$	4.35390	+	3.16329i	0.219068	+	0.159162i
$396$		0			0
$397$	−11.9889	+	20.7655i	−0.601708	+	1.04219i	0.390855	+	0.920452i	$0.372180\pi$
$397$	−11.9889	+	20.7655i	−0.601708	+	1.04219i	−0.992562	+	0.121736i	$0.961154\pi$
$398$		0			0
$399$	38.6844	−	28.1058i	1.93664	−	1.40705i
$400$		0			0
$401$	0.361704	+	1.11321i	0.0180626	+	0.0555911i	0.959682	−	0.281089i	$-0.0906958\pi$
$401$	0.361704	+	1.11321i	0.0180626	+	0.0555911i	−0.941619	+	0.336681i	$0.890696\pi$
$402$		0			0
$403$	6.21082	+	4.13013i	0.309383	+	0.205737i
$404$		0			0
$405$	9.83303	+	30.2629i	0.488607	+	1.50378i
$406$		0			0
$407$	−3.91255	+	2.84264i	−0.193938	+	0.140904i
$408$		0			0
$409$	6.00233	−	10.3963i	0.296796	−	0.514066i	−0.678605	−	0.734503i	$-0.737415\pi$
$409$	6.00233	−	10.3963i	0.296796	−	0.514066i	0.975401	+	0.220437i	$0.0707485\pi$
$410$		0			0
$411$	9.84620	+	7.15368i	0.485677	+	0.352865i
$412$		0			0
$413$	−27.2950	+	30.3142i	−1.34310	+	1.49166i
$414$		0			0
$415$	5.84507	+	1.24241i	0.286923	+	0.0609874i
$416$		0			0
$417$	32.6633	−	14.5427i	1.59953	−	0.712157i
$418$		0			0
$419$	2.58499	−	7.95578i	0.126285	−	0.388665i	−0.867848	−	0.496830i	$-0.834497\pi$
$419$	2.58499	−	7.95578i	0.126285	−	0.388665i	0.994133	+	0.108165i	$0.0344974\pi$
$420$		0			0
$421$	−24.2251	+	5.14921i	−1.18066	+	0.250957i	−0.756108	−	0.654446i	$-0.772902\pi$
$421$	−24.2251	+	5.14921i	−1.18066	+	0.250957i	−0.424552	+	0.905404i	$0.639568\pi$
$422$		0			0
$423$	−11.9692	−	5.32902i	−0.581961	−	0.259106i
$424$		0			0
$425$	0.398109	−	3.78775i	0.0193111	−	0.183733i
$426$		0			0
$427$	−3.68747	−	35.0839i	−0.178449	−	1.69783i
$428$		0			0
$429$	8.98077	+	15.5551i	0.433596	+	0.751010i
$430$		0			0
$431$	−11.2802	−	12.5279i	−0.543347	−	0.603448i	0.407463	−	0.913222i	$-0.366413\pi$
$431$	−11.2802	−	12.5279i	−0.543347	−	0.603448i	−0.950810	+	0.309774i	$0.899747\pi$
$432$		0			0
$433$	20.9872			1.00858			0.504291	−	0.863534i	$-0.331754\pi$
$433$	20.9872			1.00858			0.504291	+	0.863534i	$0.331754\pi$
$434$		0			0
$435$	21.5984			1.03557
$436$		0			0
$437$	−5.84222	−	6.48844i	−0.279471	−	0.310384i
$438$		0			0
$439$	2.69322	+	4.66479i	0.128540	+	0.222638i	0.923111	−	0.384533i	$-0.125637\pi$
$439$	2.69322	+	4.66479i	0.128540	+	0.222638i	−0.794571	+	0.607171i	$0.792304\pi$
$440$		0			0
$441$	−5.54077	−	52.7169i	−0.263846	−	2.51033i
$442$		0			0
$443$	0.376152	−	3.57885i	0.0178715	−	0.170036i	−0.981946	−	0.189164i	$-0.939422\pi$
$443$	0.376152	−	3.57885i	0.0178715	−	0.170036i	0.999817	+	0.0191276i	$0.00608889\pi$
$444$		0			0
$445$	5.57044	+	2.48012i	0.264064	+	0.117569i
$446$		0			0
$447$	53.0335	−	11.2726i	2.50840	−	0.533177i
$448$		0			0
$449$	−0.278944	+	0.858502i	−0.0131642	+	0.0405152i	−0.957423	−	0.288689i	$-0.906781\pi$
$449$	−0.278944	+	0.858502i	−0.0131642	+	0.0405152i	0.944259	+	0.329204i	$0.106781\pi$
$450$		0			0
$451$	16.9744	−	7.55751i	0.799295	−	0.355869i
$452$		0			0
$453$	−7.19448	−	1.52923i	−0.338026	−	0.0718497i
$454$		0			0
$455$	2.90141	−	3.22234i	0.136020	−	0.151066i
$456$		0			0
$457$	−19.6729	−	14.2932i	−0.920262	−	0.668609i	0.0233274	−	0.999728i	$-0.492574\pi$
$457$	−19.6729	−	14.2932i	−0.920262	−	0.668609i	−0.943589	+	0.331119i	$0.892574\pi$
$458$		0			0
$459$	−8.17557	+	14.1605i	−0.381603	+	0.660956i
$460$		0			0
$461$	−28.4674	+	20.6828i	−1.32586	+	0.963294i	−0.326022	+	0.945362i	$0.605708\pi$
$461$	−28.4674	+	20.6828i	−1.32586	+	0.963294i	−0.999839	+	0.0179322i	$0.994292\pi$
$462$		0			0
$463$	8.14627	+	25.0716i	0.378589	+	1.16518i	0.941025	+	0.338337i	$0.109864\pi$
$463$	8.14627	+	25.0716i	0.378589	+	1.16518i	−0.562436	+	0.826841i	$0.690136\pi$
$464$		0			0
$465$	−14.9060	+	7.39180i	−0.691251	+	0.342786i
$466$		0			0
$467$	−4.33874	−	13.3533i	−0.200773	−	0.617916i	−0.999861	−	0.0167012i	$-0.994684\pi$
$467$	−4.33874	−	13.3533i	−0.200773	−	0.617916i	0.799087	−	0.601215i	$-0.205316\pi$
$468$		0			0
$469$	−0.262120	+	0.190441i	−0.0121036	+	0.00879376i
$470$		0			0
$471$	23.8215	−	41.2600i	1.09764	−	1.90116i
$472$		0			0
$473$	−18.8513	−	13.6963i	−0.866782	−	0.629754i
$474$		0			0
$475$	10.9522	−	12.1636i	0.502520	−	0.558105i
$476$		0			0
$477$	−79.1502	−	16.8239i	−3.62404	−	0.770314i
$478$		0			0
$479$	−19.3205	+	8.60206i	−0.882778	+	0.393038i	−0.797500	−	0.603319i	$-0.793845\pi$
$479$	−19.3205	+	8.60206i	−0.882778	+	0.393038i	−0.0852781	+	0.996357i	$0.527178\pi$
$480$		0			0
$481$	−0.503410	+	1.54934i	−0.0229535	+	0.0706436i
$482$		0			0
$483$	−27.0730	+	5.75454i	−1.23186	+	0.261841i
$484$		0			0
$485$	−1.08531	−	0.483211i	−0.0492814	−	0.0219415i
$486$		0			0
$487$	−0.0639837	+	0.608765i	−0.00289938	+	0.0275858i	−0.995876	−	0.0907255i	$-0.971081\pi$
$487$	−0.0639837	+	0.608765i	−0.00289938	+	0.0275858i	0.992977	+	0.118311i	$0.0377481\pi$
$488$		0			0
$489$	5.55559	+	52.8579i	0.251233	+	2.39032i
$490$		0			0
$491$	−4.33134	−	7.50209i	−0.195470	−	0.338565i	0.751584	−	0.659637i	$-0.229290\pi$
$491$	−4.33134	−	7.50209i	−0.195470	−	0.338565i	−0.947055	+	0.321072i	$0.895957\pi$
$492$		0			0
$493$	4.37062	+	4.85407i	0.196843	+	0.218616i
$494$		0			0
$495$	−29.4920			−1.32557
$496$		0			0
$497$	−17.9483			−0.805092
$498$		0			0
$499$	−18.5592	−	20.6121i	−0.830826	−	0.922726i	0.167175	−	0.985927i	$-0.446536\pi$
$499$	−18.5592	−	20.6121i	−0.830826	−	0.922726i	−0.998001	+	0.0632016i	$0.979869\pi$
$500$		0			0
$501$	29.9610	+	51.8939i	1.33856	+	2.31845i
$502$		0			0
$503$	0.0216011	+	0.205521i	0.000963146	+	0.00916372i	0.994993	−	0.0999455i	$-0.0318668\pi$
$503$	0.0216011	+	0.205521i	0.000963146	+	0.00916372i	−0.994030	+	0.109109i	$0.965200\pi$
$504$		0			0
$505$	−0.392979	+	3.73894i	−0.0174873	+	0.166381i
$506$		0			0
$507$	−34.5122	−	15.3658i	−1.53274	−	0.682421i
$508$		0			0
$509$	−25.4498	+	5.40953i	−1.12804	+	0.239773i	−0.733888	−	0.679270i	$-0.762296\pi$
$509$	−25.4498	+	5.40953i	−1.12804	+	0.239773i	−0.394156	+	0.919043i	$0.628963\pi$
$510$		0			0
$511$	7.67731	−	23.6283i	0.339624	−	1.04526i
$512$		0			0
$513$	−64.1949	+	28.5814i	−2.83427	+	1.26190i
$514$		0			0
$515$	6.52045	+	1.38596i	0.287325	+	0.0610729i
$516$		0			0
$517$	4.16718	−	4.62812i	0.183272	−	0.203545i
$518$		0			0
$519$	18.6742	+	13.5676i	0.819707	+	0.595552i
$520$		0			0
$521$	20.5739	−	35.6351i	0.901360	−	1.56120i	0.0756289	−	0.997136i	$-0.475904\pi$
$521$	20.5739	−	35.6351i	0.901360	−	1.56120i	0.825731	−	0.564065i	$-0.190763\pi$
$522$		0			0
$523$	7.04258	−	5.11673i	0.307950	−	0.223739i	−0.423066	−	0.906099i	$-0.639046\pi$
$523$	7.04258	−	5.11673i	0.307950	−	0.223739i	0.731017	+	0.682360i	$0.239046\pi$
$524$		0			0
$525$	−16.0338	−	49.3469i	−0.699772	−	2.15368i
$526$		0			0
$527$	−4.67760	−	1.85422i	−0.203760	−	0.0807709i
$528$		0			0
$529$	−5.54567	−	17.0678i	−0.241116	−	0.742079i
$530$		0			0
$531$	75.6088	−	54.9330i	3.28114	−	2.38389i
$532$		0			0
$533$	3.12948	−	5.42042i	0.135553	−	0.234784i
$534$		0			0
$535$	−12.5995	−	9.15404i	−0.544722	−	0.395764i
$536$		0			0
$537$	43.2483	−	48.0321i	1.86630	−	2.07274i
$538$		0			0
$539$	24.6455	+	5.23856i	1.06156	+	0.225641i
$540$		0			0
$541$	25.6333	−	11.4127i	1.10206	−	0.490670i	0.226616	−	0.973984i	$-0.427234\pi$
$541$	25.6333	−	11.4127i	1.10206	−	0.490670i	0.875447	+	0.483314i	$0.160567\pi$
$542$		0			0
$543$	−12.1833	+	37.4963i	−0.522835	+	1.60912i
$544$		0			0
$545$	7.09675	−	1.50846i	0.303991	−	0.0646154i
$546$		0			0
$547$	25.1828	+	11.2121i	1.07674	+	0.479396i	0.866973	−	0.498356i	$-0.166063\pi$
$547$	25.1828	+	11.2121i	1.07674	+	0.479396i	0.209768	+	0.977751i	$0.432729\pi$
$548$		0			0
$549$	−8.44833	+	80.3805i	−0.360566	+	3.43056i
$550$		0			0
$551$	2.93420	+	27.9170i	0.125001	+	1.18930i
$552$		0			0
$553$	11.0863	+	19.2020i	0.471438	+	0.816554i
$554$		0			0
$555$	−2.43160	−	2.70057i	−0.103216	−	0.114633i
$556$		0			0
$557$	−6.52194			−0.276344			−0.138172	−	0.990408i	$-0.544123\pi$
$557$	−6.52194			−0.276344			−0.138172	+	0.990408i	$0.544123\pi$
$558$		0			0
$559$	−7.84910			−0.331982
$560$		0			0
$561$	−8.10786	−	9.00469i	−0.342314	−	0.380178i
$562$		0			0
$563$	2.73806	+	4.74246i	0.115395	+	0.199871i	0.917938	−	0.396724i	$-0.129853\pi$
$563$	2.73806	+	4.74246i	0.115395	+	0.199871i	−0.802542	+	0.596595i	$0.796520\pi$
$564$		0			0
$565$	−0.446561	−	4.24874i	−0.0187869	−	0.178746i
$566$		0			0
$567$	−13.7036	+	130.381i	−0.575499	+	5.47550i
$568$		0			0
$569$	−22.7646	−	10.1354i	−0.954340	−	0.424900i	−0.130328	−	0.991471i	$-0.541603\pi$
$569$	−22.7646	−	10.1354i	−0.954340	−	0.424900i	−0.824013	+	0.566571i	$0.808270\pi$
$570$		0			0
$571$	−3.11385	+	0.661870i	−0.130311	+	0.0276984i	−0.272605	−	0.962126i	$-0.587885\pi$
$571$	−3.11385	+	0.661870i	−0.130311	+	0.0276984i	0.142295	+	0.989824i	$0.454552\pi$
$572$		0			0
$573$	24.2445	−	74.6168i	1.01283	−	3.11716i
$574$		0			0
$575$	−8.65512	+	3.85351i	−0.360943	+	0.160702i
$576$		0			0
$577$	22.9023	+	4.86804i	0.953437	+	0.202659i	0.658266	−	0.752785i	$-0.271290\pi$
$577$	22.9023	+	4.86804i	0.953437	+	0.202659i	0.295171	+	0.955444i	$0.404623\pi$
$578$		0			0
$579$	15.5943	−	17.3193i	0.648079	−	0.719764i
$580$		0			0
$581$	19.9177	+	14.4711i	0.826326	+	0.600361i
$582$		0			0
$583$	19.2316	−	33.3101i	0.796491	−	1.37956i
$584$		0			0
$585$	−8.03708	+	5.83928i	−0.332292	+	0.241425i
$586$		0			0
$587$	2.41979	+	7.44735i	0.0998754	+	0.307385i	0.988494	−	0.151263i	$-0.0483340\pi$
$587$	2.41979	+	7.44735i	0.0998754	+	0.307385i	−0.888618	+	0.458648i	$0.848334\pi$
$588$		0			0
$589$	−11.5793	−	18.2626i	−0.477115	−	0.752496i
$590$		0			0
$591$	2.74372	+	8.44429i	0.112861	+	0.347352i
$592$		0			0
$593$	−27.5969	+	20.0503i	−1.13327	+	0.823369i	−0.986167	−	0.165753i	$-0.946995\pi$
$593$	−27.5969	+	20.0503i	−1.13327	+	0.823369i	−0.147102	+	0.989121i	$0.546995\pi$
$594$		0			0
$595$	−1.46258	+	2.53327i	−0.0599600	+	0.103854i
$596$		0			0
$597$	15.4616	+	11.2335i	0.632801	+	0.459757i
$598$		0			0
$599$	−10.7002	+	11.8838i	−0.437198	+	0.485558i	−0.920968	−	0.389637i	$-0.872600\pi$
$599$	−10.7002	+	11.8838i	−0.437198	+	0.485558i	0.483770	+	0.875195i	$0.339267\pi$
$600$		0			0
$601$	14.8167	+	3.14939i	0.604385	+	0.128466i	0.499933	−	0.866064i	$-0.333358\pi$
$601$	14.8167	+	3.14939i	0.604385	+	0.128466i	0.104452	+	0.994530i	$0.466691\pi$
$602$		0			0
$603$	0.678133	−	0.301924i	0.0276157	−	0.0122953i
$604$		0			0
$605$	1.31905	−	4.05962i	0.0536271	−	0.165047i
$606$		0			0
$607$	−10.9648	+	2.33065i	−0.445049	+	0.0945982i	−0.424985	−	0.905201i	$-0.639721\pi$
$607$	−10.9648	+	2.33065i	−0.445049	+	0.0945982i	−0.0200647	+	0.999799i	$0.506387\pi$
$608$		0			0
$609$	81.2922	+	36.1936i	3.29413	+	1.46664i
$610$		0			0
$611$	0.219282	−	2.08633i	0.00887120	−	0.0844038i
$612$		0			0
$613$	−0.507185	−	4.82554i	−0.0204850	−	0.194902i	0.979493	−	0.201476i	$-0.0645739\pi$
$613$	−0.507185	−	4.82554i	−0.0204850	−	0.194902i	−0.999978	+	0.00657456i	$0.997907\pi$
$614$		0			0
$615$	6.98095	+	12.0914i	0.281499	+	0.487570i
$616$		0			0
$617$	4.61741	+	5.12815i	0.185890	+	0.206451i	0.828886	−	0.559418i	$-0.188975\pi$
$617$	4.61741	+	5.12815i	0.185890	+	0.206451i	−0.642996	+	0.765870i	$0.722309\pi$
$618$		0			0
$619$	−21.5547			−0.866358			−0.433179	−	0.901308i	$-0.642608\pi$
$619$	−21.5547			−0.866358			−0.433179	+	0.901308i	$0.642608\pi$
$620$		0			0
$621$	40.6747			1.63222
$622$		0			0
$623$	16.8100	+	18.6693i	0.673477	+	0.747972i
$624$		0			0
$625$	−6.91637	−	11.9795i	−0.276655	−	0.479180i
$626$		0			0
$627$	−5.44317	−	51.7883i	−0.217379	−	2.06823i
$628$		0			0
$629$	0.114875	−	1.09296i	0.00458037	−	0.0435793i
$630$		0			0
$631$	−24.5781	−	10.9429i	−0.978440	−	0.435629i	−0.145721	−	0.989326i	$-0.546550\pi$
$631$	−24.5781	−	10.9429i	−0.978440	−	0.435629i	−0.832719	+	0.553696i	$0.813217\pi$
$632$		0			0
$633$	14.5500	−	3.09269i	0.578310	−	0.122924i
$634$		0			0
$635$	−3.55773	+	10.9496i	−0.141184	+	0.434520i
$636$		0			0
$637$	7.75354	−	3.45210i	0.307206	−	0.136777i
$638$		0			0
$639$	40.2226	+	8.54958i	1.59118	+	0.338216i
$640$		0			0
$641$	25.9302	−	28.7984i	1.02418	−	1.13747i	0.0337537	−	0.999430i	$-0.489254\pi$
$641$	25.9302	−	28.7984i	1.02418	−	1.13747i	0.990427	−	0.138038i	$-0.0440795\pi$
$642$		0			0
$643$	−39.9231	−	29.0058i	−1.57441	−	1.14388i	−0.922770	−	0.385352i	$-0.874080\pi$
$643$	−39.9231	−	29.0058i	−1.57441	−	1.14388i	−0.651643	−	0.758526i	$-0.725920\pi$
$644$		0			0
$645$	8.75451	−	15.1633i	0.344709	−	0.597053i
$646$		0			0
$647$	−23.9855	+	17.4265i	−0.942966	+	0.685105i	−0.949133	−	0.314876i	$-0.898037\pi$
$647$	−23.9855	+	17.4265i	−0.942966	+	0.685105i	0.00616717	+	0.999981i	$0.498037\pi$
$648$		0			0
$649$	13.7276	+	42.2492i	0.538855	+	1.65843i
$650$		0			0
$651$	−68.4902	+	2.84243i	−2.68434	+	0.111403i
$652$		0			0
$653$	−4.20545	−	12.9431i	−0.164572	−	0.506501i	0.834432	−	0.551110i	$-0.185796\pi$
$653$	−4.20545	−	12.9431i	−0.164572	−	0.506501i	−0.999005	+	0.0446094i	$0.985796\pi$
$654$		0			0
$655$	8.84111	−	6.42345i	0.345451	−	0.250985i
$656$		0			0
$657$	−28.4603	+	49.2946i	−1.11034	+	1.92317i
$658$		0			0
$659$	−31.6145	−	22.9693i	−1.23153	−	0.894756i	−0.234522	−	0.972111i	$-0.575353\pi$
$659$	−31.6145	−	22.9693i	−1.23153	−	0.894756i	−0.997004	+	0.0773550i	$0.975353\pi$
$660$		0			0
$661$	−14.5709	+	16.1826i	−0.566742	+	0.629431i	−0.956586	−	0.291450i	$-0.905862\pi$
$661$	−14.5709	+	16.1826i	−0.566742	+	0.629431i	0.389844	+	0.920881i	$0.372529\pi$
$662$		0			0
$663$	−3.99242	−	0.848616i	−0.155053	−	0.0329575i
$664$		0			0
$665$	−11.4842	+	5.11312i	−0.445340	+	0.198278i
$666$		0			0
$667$	5.02100	−	15.4531i	0.194414	−	0.598345i
$668$		0			0
$669$	−61.7440	+	13.1241i	−2.38716	+	0.507406i
$670$		0			0
$671$	−35.0965	−	15.6260i	−1.35489	−	0.603234i
$672$		0			0
$673$	−1.50734	+	14.3414i	−0.0581038	+	0.552821i	0.926286	+	0.376821i	$0.122983\pi$
$673$	−1.50734	+	14.3414i	−0.0581038	+	0.552821i	−0.984390	+	0.176000i	$0.943684\pi$
$674$		0			0
$675$	7.97041	+	75.8334i	0.306781	+	2.91883i
$676$		0			0
$677$	20.8524	+	36.1175i	0.801425	+	1.38811i	0.918678	+	0.395006i	$0.129258\pi$
$677$	20.8524	+	36.1175i	0.801425	+	1.38811i	−0.117254	+	0.993102i	$0.537409\pi$
$678$		0			0
$679$	−3.27515	−	3.63742i	−0.125689	−	0.139591i
$680$		0			0
$681$	39.2839			1.50536
$682$		0			0
$683$	5.73929			0.219608			0.109804	−	0.993953i	$-0.464978\pi$
$683$	5.73929			0.219608			0.109804	+	0.993953i	$0.464978\pi$
$684$		0			0
$685$	−2.14100	−	2.37782i	−0.0818033	−	0.0908518i
$686$		0			0
$687$	0.139216	+	0.241129i	0.00531141	+	0.00919963i
$688$		0			0
$689$	−1.35431	−	12.8854i	−0.0515949	−	0.490893i
$690$		0			0
$691$	0.201002	−	1.91241i	0.00764649	−	0.0727515i	−0.990033	−	0.140834i	$-0.955022\pi$
$691$	0.201002	−	1.91241i	0.00764649	−	0.0727515i	0.997680	+	0.0680828i	$0.0216882\pi$
$692$		0			0
$693$	−111.002	−	49.4213i	−4.21662	−	1.87736i
$694$		0			0
$695$	−9.19453	+	1.95436i	−0.348768	+	0.0741330i
$696$		0			0
$697$	−1.30478	+	4.01569i	−0.0494220	+	0.152105i
$698$		0			0
$699$	57.9493	−	25.8007i	2.19184	−	0.975872i
$700$		0			0
$701$	37.3533	+	7.93969i	1.41082	+	0.299878i	0.849441	−	0.527684i	$-0.176939\pi$
$701$	37.3533	+	7.93969i	1.41082	+	0.299878i	0.561374	+	0.827562i	$0.310273\pi$
$702$		0			0
$703$	3.16027	−	3.50984i	0.119192	−	0.132376i
$704$		0			0
$705$	3.78589	+	2.75061i	0.142585	+	0.103594i
$706$		0			0
$707$	−7.74464	+	13.4141i	−0.291267	+	0.504489i
$708$		0			0
$709$	23.2396	−	16.8846i	0.872783	−	0.634114i	−0.0585493	−	0.998285i	$-0.518647\pi$
$709$	23.2396	−	16.8846i	0.872783	−	0.634114i	0.931332	+	0.364171i	$0.118647\pi$
$710$		0			0
$711$	−15.6979	−	48.3132i	−0.588717	−	1.81189i
$712$		0			0
$713$	1.82340	+	12.3832i	0.0682869	+	0.463755i
$714$		0			0
$715$	−1.45922	−	4.49101i	−0.0545717	−	0.167954i
$716$		0			0
$717$	53.4244	−	38.8151i	1.99517	−	1.44958i
$718$		0			0
$719$	−22.4508	+	38.8860i	−0.837274	+	1.45020i	0.0548905	+	0.998492i	$0.482519\pi$
$719$	−22.4508	+	38.8860i	−0.837274	+	1.45020i	−0.892165	+	0.451710i	$0.850814\pi$
$720$		0			0
$721$	22.2191	+	16.1432i	0.827484	+	0.601202i
$722$		0			0
$723$	5.94696	−	6.60477i	0.221170	−	0.245634i
$724$		0			0
$725$	29.7944	+	6.33299i	1.10654	+	0.235201i
$726$		0			0
$727$	24.5168	−	10.9156i	0.909278	−	0.404837i	0.101848	−	0.994800i	$-0.467524\pi$
$727$	24.5168	−	10.9156i	0.909278	−	0.404837i	0.807430	+	0.589963i	$0.200858\pi$
$728$		0			0
$729$	36.2667	−	111.618i	1.34321	−	4.13398i
$730$		0			0
$731$	5.17936	−	1.10091i	0.191566	−	0.0407185i
$732$		0			0
$733$	9.30950	+	4.14485i	0.343854	+	0.153094i	0.571396	−	0.820675i	$-0.306402\pi$
$733$	9.30950	+	4.14485i	0.343854	+	0.153094i	−0.227542	+	0.973768i	$0.573069\pi$
$734$		0			0
$735$	−1.97900	+	18.8289i	−0.0729966	+	0.694516i
$736$		0			0
$737$	0.0368822	+	0.350911i	0.00135857	+	0.0129260i
$738$		0			0
$739$	9.94744	+	17.2295i	0.365922	+	0.633796i	0.988924	−	0.148425i	$-0.0474202\pi$
$739$	9.94744	+	17.2295i	0.365922	+	0.633796i	−0.623001	+	0.782221i	$0.714087\pi$
$740$		0			0
$741$	−11.7372	−	13.0355i	−0.431178	−	0.478871i
$742$		0			0
$743$	47.3605			1.73749			0.868745	−	0.495260i	$-0.164927\pi$
$743$	47.3605			1.73749			0.868745	+	0.495260i	$0.164927\pi$
$744$		0			0
$745$	−14.2541			−0.522231
$746$		0			0
$747$	−37.7429	−	41.9177i	−1.38094	−	1.53369i
$748$		0			0
$749$	−32.0819	−	55.5675i	−1.17225	−	2.03039i
$750$		0			0
$751$	−0.530325	−	5.04570i	−0.0193518	−	0.184120i	0.980576	−	0.196140i	$-0.0628406\pi$
$751$	−0.530325	−	5.04570i	−0.0193518	−	0.184120i	−0.999928	+	0.0120195i	$0.996174\pi$
$752$		0			0
$753$	−5.14168	+	48.9198i	−0.187373	+	1.78274i
$754$		0			0
$755$	1.76652	+	0.786507i	0.0642904	+	0.0286239i
$756$		0			0
$757$	16.1310	−	3.42875i	0.586291	−	0.124620i	0.0947906	−	0.995497i	$-0.469782\pi$
$757$	16.1310	−	3.42875i	0.586291	−	0.124620i	0.491501	+	0.870877i	$0.336448\pi$
$758$		0			0
$759$	−9.31437	+	28.6667i	−0.338090	+	1.04054i
$760$		0			0
$761$	−24.3149	+	10.8257i	−0.881415	+	0.392431i	−0.796986	−	0.603998i	$-0.793573\pi$
$761$	−24.3149	+	10.8257i	−0.881415	+	0.392431i	−0.0844296	+	0.996429i	$0.526907\pi$
$762$		0			0
$763$	29.2386	+	6.21485i	1.05851	+	0.224993i
$764$		0			0
$765$	4.48439	−	4.98042i	0.162133	−	0.180067i
$766$		0			0
$767$	12.1062	+	8.79564i	0.437128	+	0.317592i
$768$		0			0
$769$	−15.3503	+	26.5874i	−0.553545	+	0.958768i	0.444470	+	0.895794i	$0.353392\pi$
$769$	−15.3503	+	26.5874i	−0.553545	+	0.958768i	−0.998015	+	0.0629742i	$0.979941\pi$
$770$		0			0
$771$	−13.2623	+	9.63562i	−0.477630	+	0.347018i
$772$		0			0
$773$	4.93072	+	15.1752i	0.177346	+	0.545814i	0.999733	−	0.0231144i	$-0.00735819\pi$
$773$	4.93072	+	15.1752i	0.177346	+	0.545814i	−0.822387	+	0.568928i	$0.807358\pi$
$774$		0			0
$775$	−22.7298	+	5.82608i	−0.816479	+	0.209279i
$776$		0			0
$777$	−4.62658	−	14.2392i	−0.165978	−	0.510827i
$778$		0			0
$779$	−14.6803	+	10.6658i	−0.525975	+	0.382143i
$780$		0			0
$781$	−9.77312	+	16.9275i	−0.349710	+	0.605715i
$782$		0			0
$783$	−105.796	−	76.8652i	−3.78084	−	2.74694i
$784$		0			0
$785$	−8.38116	+	9.30822i	−0.299136	+	0.332225i
$786$		0			0
$787$	−0.648655	−	0.137876i	−0.0231220	−	0.00491474i	0.196336	−	0.980537i	$-0.437096\pi$
$787$	−0.648655	−	0.137876i	−0.0231220	−	0.00491474i	−0.219458	+	0.975622i	$0.570429\pi$
$788$		0			0
$789$	22.9559	−	10.2206i	0.817250	−	0.363863i
$790$		0			0
$791$	5.43907	−	16.7397i	0.193391	−	0.595197i
$792$		0			0
$793$	−12.6583	+	2.69060i	−0.449509	+	0.0955461i
$794$		0			0
$795$	26.4031	+	11.7554i	0.936420	+	0.416921i
$796$		0			0
$797$	−4.54381	+	43.2314i	−0.160950	+	1.53134i	0.554211	+	0.832376i	$0.313020\pi$
$797$	−4.54381	+	43.2314i	−0.160950	+	1.53134i	−0.715161	+	0.698960i	$0.753647\pi$
$798$		0			0
$799$	0.147929	+	1.40745i	0.00523337	+	0.0497922i
$800$		0			0
$801$	−28.7785	−	49.8458i	−1.01684	−	1.76122i
$802$		0			0
$803$	−18.1041	−	20.1067i	−0.638880	−	0.709548i
$804$		0			0
$805$	7.27656			0.256465
$806$		0			0
$807$	18.3547			0.646118
$808$		0			0
$809$	−33.1824	−	36.8528i	−1.16663	−	1.29567i	−0.947418	−	0.319998i	$-0.896318\pi$
$809$	−33.1824	−	36.8528i	−1.16663	−	1.29567i	−0.219213	−	0.975677i	$-0.570349\pi$
$810$		0			0
$811$	18.4836	+	32.0146i	0.649048	+	1.12418i	0.983351	+	0.181718i	$0.0581658\pi$
$811$	18.4836	+	32.0146i	0.649048	+	1.12418i	−0.334303	+	0.942466i	$0.608501\pi$
$812$		0			0
$813$	6.83262	+	65.0080i	0.239630	+	2.27993i
$814$		0			0
$815$	1.46058	−	13.8965i	0.0511618	−	0.486772i
$816$		0			0
$817$	20.7885	+	9.25566i	0.727299	+	0.323814i
$818$		0			0
$819$	−40.0352	+	8.50974i	−1.39894	+	0.297354i
$820$		0			0
$821$	−1.48393	+	4.56706i	−0.0517894	+	0.159391i	−0.973606	−	0.228234i	$-0.926705\pi$
$821$	−1.48393	+	4.56706i	−0.0517894	+	0.159391i	0.921817	+	0.387626i	$0.126705\pi$
$822$		0			0
$823$	−29.0078	+	12.9151i	−1.01115	+	0.450192i	−0.844346	−	0.535799i	$-0.820011\pi$
$823$	−29.0078	+	12.9151i	−1.01115	+	0.450192i	−0.166802	+	0.985990i	$0.553344\pi$
$824$		0			0
$825$	−55.2711	−	11.7482i	−1.92429	−	0.409021i
$826$		0			0
$827$	7.51349	−	8.34458i	0.261270	−	0.290169i	−0.598210	−	0.801339i	$-0.704121\pi$
$827$	7.51349	−	8.34458i	0.261270	−	0.290169i	0.859480	+	0.511170i	$0.170788\pi$
$828$		0			0
$829$	−14.9149	−	10.8363i	−0.518015	−	0.376360i	0.297841	−	0.954616i	$-0.403734\pi$
$829$	−14.9149	−	10.8363i	−0.518015	−	0.376360i	−0.815855	+	0.578256i	$0.803734\pi$
$830$		0			0
$831$	35.4354	−	61.3759i	1.22924	−	2.12911i
$832$		0			0
$833$	−4.63211	+	3.36543i	−0.160493	+	0.116605i
$834$		0			0
$835$	−4.86813	−	14.9826i	−0.168469	−	0.518493i
$836$		0			0
$837$	99.3206	+	16.8408i	3.43302	+	0.582102i
$838$		0			0
$839$	1.93245	+	5.94745i	0.0667154	+	0.205329i	0.978857	−	0.204547i	$-0.0655721\pi$
$839$	1.93245	+	5.94745i	0.0667154	+	0.205329i	−0.912141	+	0.409876i	$0.865572\pi$
$840$		0			0
$841$	−18.8008	+	13.6596i	−0.648303	+	0.471020i
$842$		0			0
$843$	10.7190	−	18.5659i	0.369183	−	0.639443i
$844$		0			0
$845$	8.03517	+	5.83789i	0.276418	+	0.200830i
$846$		0			0
$847$	11.7676	−	13.0692i	0.404339	−	0.449064i
$848$		0			0
$849$	−43.6922	−	9.28706i	−1.49951	−	0.318731i
$850$		0			0
$851$	−2.49745	+	1.11194i	−0.0856115	+	0.0381167i
$852$		0			0
$853$	−12.4453	+	38.3026i	−0.426118	+	1.31146i	0.475802	+	0.879552i	$0.342158\pi$
$853$	−12.4453	+	38.3026i	−0.426118	+	1.31146i	−0.901920	+	0.431903i	$0.857842\pi$
$854$		0			0
$855$	28.1721	−	5.98816i	0.963466	−	0.204791i
$856$		0			0
$857$	−43.5928	−	19.4088i	−1.48910	−	0.662990i	−0.508869	−	0.860844i	$-0.669936\pi$
$857$	−43.5928	−	19.4088i	−1.48910	−	0.662990i	−0.980232	+	0.197853i	$0.936603\pi$
$858$		0			0
$859$	2.42018	−	23.0264i	0.0825753	−	0.785652i	−0.872365	−	0.488855i	$-0.837415\pi$
$859$	2.42018	−	23.0264i	0.0825753	−	0.785652i	0.954941	−	0.296797i	$-0.0959185\pi$
$860$		0			0
$861$	6.01278	+	57.2078i	0.204915	+	1.94964i
$862$		0			0
$863$	−12.4890	−	21.6316i	−0.425131	−	0.736349i	0.571301	−	0.820740i	$-0.306439\pi$
$863$	−12.4890	−	21.6316i	−0.425131	−	0.736349i	−0.996433	+	0.0843913i	$0.973105\pi$
$864$		0			0
$865$	−4.06060	−	4.50975i	−0.138065	−	0.153336i
$866$		0			0
$867$	−54.5609			−1.85299
$868$		0			0
$869$	24.1466			0.819118
$870$		0			0
$871$	0.0795298	+	0.0883268i	0.00269476	+	0.00299284i
$872$		0			0
$873$	5.60702	+	9.71165i	0.189769	+	0.328690i
$874$		0			0
$875$	3.11757	+	29.6617i	0.105393	+	1.00275i
$876$		0			0
$877$	0.152679	−	1.45264i	0.00515561	−	0.0490523i	−0.991642	−	0.129023i	$-0.958816\pi$
$877$	0.152679	−	1.45264i	0.00515561	−	0.0490523i	0.996797	+	0.0799705i	$0.0254826\pi$
$878$		0			0
$879$	24.6546	+	10.9769i	0.831578	+	0.370243i
$880$		0			0
$881$	35.1807	−	7.47789i	1.18527	−	0.251937i	0.427228	−	0.904144i	$-0.359490\pi$
$881$	35.1807	−	7.47789i	1.18527	−	0.251937i	0.758040	+	0.652208i	$0.226157\pi$
$882$		0			0
$883$	−10.8926	+	33.5239i	−0.366564	+	1.12817i	0.582431	+	0.812880i	$0.302102\pi$
$883$	−10.8926	+	33.5239i	−0.366564	+	1.12817i	−0.948996	+	0.315289i	$0.897898\pi$
$884$		0			0
$885$	−30.4945	+	13.5770i	−1.02506	+	0.456386i
$886$		0			0
$887$	28.4207	+	6.04100i	0.954273	+	0.202837i	0.658635	−	0.752463i	$-0.271134\pi$
$887$	28.4207	+	6.04100i	0.954273	+	0.202837i	0.295638	+	0.955300i	$0.404468\pi$
$888$		0			0
$889$	−31.7393	+	35.2501i	−1.06450	+	1.18225i
$890$		0			0
$891$	115.504	+	83.9189i	3.86954	+	2.81139i
$892$		0			0
$893$	−3.04097	+	5.26712i	−0.101762	+	0.176257i
$894$		0			0
$895$	−13.7471	+	9.98784i	−0.459514	+	0.333857i
$896$		0			0
$897$	3.13755	+	9.65638i	0.104760	+	0.322417i
$898$		0			0
$899$	18.6586	−	35.6549i	0.622298	−	1.18916i
$900$		0			0
$901$	2.70095	+	8.31266i	0.0899816	+	0.276935i
$902$		0			0
$903$	58.3601	−	42.4011i	1.94210	−	1.41102i
$904$		0			0
$905$	5.18258	−	8.97650i	0.172275	−	0.298389i
$906$		0			0
$907$	−17.0245	−	12.3690i	−0.565288	−	0.410706i	0.268103	−	0.963390i	$-0.413603\pi$
$907$	−17.0245	−	12.3690i	−0.565288	−	0.410706i	−0.833390	+	0.552685i	$0.813603\pi$
$908$		0			0
$909$	23.7457	−	26.3722i	0.787594	−	0.874712i
$910$		0			0
$911$	21.6264	+	4.59684i	0.716516	+	0.152300i	0.551722	−	0.834028i	$-0.313971\pi$
$911$	21.6264	+	4.59684i	0.716516	+	0.152300i	0.164793	+	0.986328i	$0.447304\pi$
$912$		0			0
$913$	24.4936	−	10.9052i	0.810619	−	0.360911i
$914$		0			0
$915$	8.92062	−	27.4548i	0.294906	−	0.907629i
$916$		0			0
$917$	44.0403	−	9.36105i	1.45434	−	0.309129i
$918$		0			0
$919$	46.2060	+	20.5722i	1.52419	+	0.678615i	0.986385	−	0.164452i	$-0.0525855\pi$
$919$	46.2060	+	20.5722i	1.52419	+	0.678615i	0.537809	+	0.843067i	$0.319252\pi$
$920$		0			0
$921$	−8.03935	+	76.4893i	−0.264906	+	2.52041i
$922$		0			0
$923$	0.688232	+	6.54809i	0.0226534	+	0.215533i
$924$		0			0
$925$	−2.56247	−	4.43833i	−0.0842536	−	0.145931i
$926$		0			0
$927$	−42.1040	−	46.7612i	−1.38288	−	1.53584i
$928$		0			0
$929$	50.2008			1.64704			0.823518	−	0.567290i	$-0.192008\pi$
$929$	50.2008			1.64704			0.823518	+	0.567290i	$0.192008\pi$
$930$		0			0
$931$	−24.6062			−0.806434
$932$		0			0
$933$	−23.7483	−	26.3751i	−0.777484	−	0.863484i
$934$		0			0
$935$	1.59279	+	2.75880i	0.0520900	+	0.0902225i
$936$		0			0
$937$	−1.36539	−	12.9908i	−0.0446054	−	0.424392i	−0.993923	−	0.110075i	$-0.964891\pi$
$937$	−1.36539	−	12.9908i	−0.0446054	−	0.424392i	0.949318	−	0.314318i	$-0.101776\pi$
$938$		0			0
$939$	1.70592	−	16.2307i	0.0556705	−	0.529669i
$940$		0			0
$941$	25.4165	+	11.3162i	0.828555	+	0.368896i	0.776787	−	0.629763i	$-0.216848\pi$
$941$	25.4165	+	11.3162i	0.828555	+	0.368896i	0.0517672	+	0.998659i	$0.483515\pi$
$942$		0			0
$943$	10.2739	−	2.18378i	0.334563	−	0.0711136i
$944$		0			0
$945$	18.0972	−	55.6975i	0.588702	−	1.81184i
$946$		0			0
$947$	−33.6180	+	14.9677i	−1.09244	+	0.486385i	−0.872244	−	0.489071i	$-0.837336\pi$
$947$	−33.6180	+	14.9677i	−1.09244	+	0.486385i	−0.220194	+	0.975456i	$0.570669\pi$
$948$		0			0
$949$	−8.91472	−	1.89488i	−0.289384	−	0.0615105i
$950$		0			0
$951$	−75.8900	+	84.2844i	−2.46090	+	2.73311i
$952$		0			0
$953$	38.4071	+	27.9044i	1.24413	+	0.903912i	0.997866	−	0.0652908i	$-0.0207975\pi$
$953$	38.4071	+	27.9044i	1.24413	+	0.903912i	0.246262	+	0.969203i	$0.420797\pi$
$954$		0			0
$955$	−10.3132	+	17.8630i	−0.333728	+	0.578034i
$956$		0			0
$957$	78.4000	−	56.9610i	2.53431	−	1.84129i
$958$		0			0
$959$	−4.07365	−	12.5374i	−0.131545	−	0.404854i
$960$		0			0
$961$	−0.674660	+	30.9927i	−0.0217632	+	0.999763i
$962$		0			0
$963$	45.4271	+	139.810i	1.46387	+	4.50532i
$964$		0			0
$965$	−4.95688	+	3.60138i	−0.159568	+	0.115933i
$966$		0			0
$967$	6.67947	−	11.5692i	0.214797	−	0.372040i	−0.738413	−	0.674349i	$-0.764424\pi$
$967$	6.67947	−	11.5692i	0.214797	−	0.372040i	0.953210	+	0.302309i	$0.0977576\pi$
$968$		0			0
$969$	9.57335	+	6.95545i	0.307540	+	0.223441i
$970$		0			0
$971$	−26.0065	+	28.8831i	−0.834587	+	0.926903i	−0.998221	−	0.0596181i	$-0.981012\pi$
$971$	−26.0065	+	28.8831i	−0.834587	+	0.926903i	0.163634	+	0.986521i	$0.447678\pi$
$972$		0			0
$973$	−37.8814	−	8.05194i	−1.21442	−	0.258133i
$974$		0			0
$975$	−17.3884	+	7.74183i	−0.556875	+	0.247937i
$976$		0			0
$977$	17.1553	−	52.7986i	0.548847	−	1.68918i	−0.162815	−	0.986657i	$-0.552057\pi$
$977$	17.1553	−	52.7986i	0.548847	−	1.68918i	0.711663	−	0.702522i	$-0.247943\pi$
$978$		0			0
$979$	26.7608	−	5.68819i	0.855280	−	0.181795i
$980$		0			0
$981$	−62.5640	−	27.8553i	−1.99751	−	0.889350i
$982$		0			0
$983$	5.92393	−	56.3624i	0.188944	−	1.79768i	−0.331155	−	0.943576i	$-0.607438\pi$
$983$	5.92393	−	56.3624i	0.188944	−	1.79768i	0.520099	−	0.854106i	$-0.325895\pi$
$984$		0			0
$985$	−0.243998	−	2.32148i	−0.00777442	−	0.0739687i
$986$		0			0
$987$	9.64000	+	16.6970i	0.306844	+	0.531470i
$988$		0			0
$989$	−8.81370	−	9.78861i	−0.280259	−	0.311260i
$990$		0			0
$991$	−5.02468			−0.159614			−0.0798071	−	0.996810i	$-0.525430\pi$
$991$	−5.02468			−0.159614			−0.0798071	+	0.996810i	$0.525430\pi$
$992$		0			0
$993$	−83.6248			−2.65375
$994$		0			0
$995$	−3.36203	−	3.73391i	−0.106584	−	0.118373i
$996$		0			0
$997$	−24.6232	−	42.6487i	−0.779825	−	1.35070i	−0.932042	−	0.362349i	$-0.881975\pi$
$997$	−24.6232	−	42.6487i	−0.779825	−	1.35070i	0.152217	−	0.988347i	$-0.451359\pi$
$998$		0			0
$999$	2.29988	+	21.8819i	0.0727649	+	0.692312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.2.m.a.113.3	yes	24
4.3	odd	2		496.2.bg.d.113.1		24
31.13	odd	30		3844.2.a.m.1.1		12
31.14	even	15	inner	124.2.m.a.45.3	✓	24
31.18	even	15		3844.2.a.n.1.12		12
124.107	odd	30		496.2.bg.d.417.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.2.m.a.45.3	✓	24	31.14	even	15	inner
124.2.m.a.113.3	yes	24	1.1	even	1	trivial
496.2.bg.d.113.1		24	4.3	odd	2
496.2.bg.d.417.1		24	124.107	odd	30
3844.2.a.m.1.1		12	31.13	odd	30
3844.2.a.n.1.12		12	31.18	even	15

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	124.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.25593 + 2.50547i) q^{3} +(-0.443179 - 0.767609i) q^{5} +(-0.381716 - 3.63179i) q^{7} +(-0.874547 + 8.32076i) q^{9} +O(q^{10})\)	\(q+(2.25593 + 2.50547i) q^{3} +(-0.443179 - 0.767609i) q^{5} +(-0.381716 - 3.63179i) q^{7} +(-0.874547 + 8.32076i) q^{9} +(-3.63309 - 1.61756i) q^{11} +(-1.31035 + 0.278523i) q^{13} +(0.923437 - 2.84205i) q^{15} +(0.825590 - 0.367577i) q^{17} +(3.79893 + 0.807487i) q^{19} +(8.23820 - 9.14944i) q^{21} +(-1.81873 - 1.32138i) q^{23} +(2.10718 - 3.64975i) q^{25} +(-14.6376 + 10.6349i) q^{27} +(2.23347 + 6.87391i) q^{29} +(-3.89393 - 3.97961i) q^{31} +(-4.14327 - 12.7517i) q^{33} +(-2.61863 + 1.90254i) q^{35} +(0.608032 - 1.05314i) q^{37} +(-3.65389 - 2.65471i) q^{39} +(-3.12630 + 3.47211i) q^{41} +(5.73115 + 1.21819i) q^{43} +(6.77467 - 3.01628i) q^{45} +(-0.483914 + 1.48933i) q^{47} +(-6.19714 + 1.31724i) q^{49} +(2.78343 + 1.23926i) q^{51} +(-1.01096 + 9.61864i) q^{53} +(0.368460 + 3.50566i) q^{55} +(6.54699 + 11.3397i) q^{57} +(-7.47442 - 8.30118i) q^{59} +9.66024 q^{61} +30.5531 q^{63} +(0.794517 + 0.882400i) q^{65} +(-0.0443615 - 0.0768364i) q^{67} +(-0.792246 - 7.53772i) q^{69} +(0.513750 - 4.88801i) q^{71} +(6.21514 + 2.76716i) q^{73} +(13.8980 - 2.95411i) q^{75} +(-4.48781 + 13.8121i) q^{77} +(-5.54678 + 2.46959i) q^{79} +(-35.1156 - 7.46404i) q^{81} +(-4.51115 + 5.01013i) q^{83} +(-0.648040 - 0.470828i) q^{85} +(-12.1838 + 21.1030i) q^{87} +(-5.56554 + 4.04360i) q^{89} +(1.51172 + 4.65259i) q^{91} +(1.18635 - 18.7338i) q^{93} +(-1.06377 - 3.27395i) q^{95} +(1.08436 - 0.787830i) q^{97} +(16.6366 - 28.8154i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{3} + q^{5} - 9 q^{7} + 2 q^{9}+O(q^{10}) \) 24 * q - q^3 + q^5 - 9 * q^7 + 2 * q^9	\( 24 q - q^{3} + q^{5} - 9 q^{7} + 2 q^{9} + 8 q^{11} + 2 q^{13} - q^{15} - q^{17} - q^{19} + 12 q^{21} - 21 q^{23} - 21 q^{25} - 43 q^{27} - 24 q^{29} - 29 q^{31} - 5 q^{33} + 10 q^{35} - 8 q^{37} - 17 q^{39} + 9 q^{41} - 2 q^{43} - 28 q^{45} - 38 q^{47} + 22 q^{49} + 69 q^{51} + 59 q^{53} - q^{55} - 7 q^{57} - 13 q^{59} + 36 q^{61} + 118 q^{63} + 94 q^{65} + 29 q^{67} + 52 q^{69} + 55 q^{71} + 55 q^{73} + 79 q^{75} - 38 q^{77} - 31 q^{79} - 98 q^{81} - 59 q^{83} - 60 q^{85} - 36 q^{87} - 57 q^{89} - 48 q^{91} - 124 q^{93} - 3 q^{95} - 19 q^{97} - 31 q^{99}+O(q^{100}) \) 24 * q - q^3 + q^5 - 9 * q^7 + 2 * q^9 + 8 * q^11 + 2 * q^13 - q^15 - q^17 - q^19 + 12 * q^21 - 21 * q^23 - 21 * q^25 - 43 * q^27 - 24 * q^29 - 29 * q^31 - 5 * q^33 + 10 * q^35 - 8 * q^37 - 17 * q^39 + 9 * q^41 - 2 * q^43 - 28 * q^45 - 38 * q^47 + 22 * q^49 + 69 * q^51 + 59 * q^53 - q^55 - 7 * q^57 - 13 * q^59 + 36 * q^61 + 118 * q^63 + 94 * q^65 + 29 * q^67 + 52 * q^69 + 55 * q^71 + 55 * q^73 + 79 * q^75 - 38 * q^77 - 31 * q^79 - 98 * q^81 - 59 * q^83 - 60 * q^85 - 36 * q^87 - 57 * q^89 - 48 * q^91 - 124 * q^93 - 3 * q^95 - 19 * q^97 - 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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