LMFDB - Embedded newform 456.2.q.f.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(49,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("456.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.q (of order $3$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.3
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	456.49
Dual form			456.2.q.f.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(1.87939 - 3.25519i) q^{5} +4.75877 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(1.87939 - 3.25519i) q^{5} +4.75877 q^{7} +(-0.500000 - 0.866025i) q^{9} -4.36959 q^{11} +(-0.500000 - 0.866025i) q^{13} +(-1.87939 - 3.25519i) q^{15} +(-3.06418 + 5.30731i) q^{17} +(0.694593 + 4.30320i) q^{19} +(2.37939 - 4.12122i) q^{21} +(1.87939 + 3.25519i) q^{23} +(-4.56418 - 7.90539i) q^{25} -1.00000 q^{27} +(-2.69459 - 4.66717i) q^{29} +7.36959 q^{31} +(-2.18479 + 3.78417i) q^{33} +(8.94356 - 15.4907i) q^{35} -7.12836 q^{37} -1.00000 q^{39} +(1.75877 - 3.04628i) q^{41} +(0.379385 - 0.657115i) q^{43} -3.75877 q^{45} +(3.00000 + 5.19615i) q^{47} +15.6459 q^{49} +(3.06418 + 5.30731i) q^{51} +(-2.57398 - 4.45826i) q^{53} +(-8.21213 + 14.2238i) q^{55} +(4.07398 + 1.55007i) q^{57} +(-4.63816 + 8.03352i) q^{59} +(4.25877 + 7.37641i) q^{61} +(-2.37939 - 4.12122i) q^{63} -3.75877 q^{65} +(-0.684793 - 1.18610i) q^{67} +3.75877 q^{69} +(5.82295 - 10.0856i) q^{71} +(-2.25877 + 3.91231i) q^{73} -9.12836 q^{75} -20.7939 q^{77} +(-7.07398 + 12.2525i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.90673 q^{83} +(11.5175 + 19.9490i) q^{85} -5.38919 q^{87} +(-4.18479 - 7.24827i) q^{89} +(-2.37939 - 4.12122i) q^{91} +(3.68479 - 6.38225i) q^{93} +(15.3131 + 5.82634i) q^{95} +(5.82295 - 10.0856i) q^{97} +(2.18479 + 3.78417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9	$ 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9} - 12 q^{11} - 3 q^{13} + 3 q^{21} - 9 q^{25} - 6 q^{27} - 12 q^{29} + 30 q^{31} - 6 q^{33} + 24 q^{35} - 6 q^{37} - 6 q^{39} - 12 q^{41} - 9 q^{43} + 18 q^{47} + 12 q^{49} + 9 q^{57} + 6 q^{59} + 3 q^{61} - 3 q^{63} + 3 q^{67} - 6 q^{71} + 9 q^{73} - 18 q^{75} - 12 q^{77} - 27 q^{79} - 3 q^{81} - 24 q^{83} + 24 q^{85} - 24 q^{87} - 18 q^{89} - 3 q^{91} + 15 q^{93} + 48 q^{95} - 6 q^{97} + 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9 - 12 * q^11 - 3 * q^13 + 3 * q^21 - 9 * q^25 - 6 * q^27 - 12 * q^29 + 30 * q^31 - 6 * q^33 + 24 * q^35 - 6 * q^37 - 6 * q^39 - 12 * q^41 - 9 * q^43 + 18 * q^47 + 12 * q^49 + 9 * q^57 + 6 * q^59 + 3 * q^61 - 3 * q^63 + 3 * q^67 - 6 * q^71 + 9 * q^73 - 18 * q^75 - 12 * q^77 - 27 * q^79 - 3 * q^81 - 24 * q^83 + 24 * q^85 - 24 * q^87 - 18 * q^89 - 3 * q^91 + 15 * q^93 + 48 * q^95 - 6 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	1.87939	−	3.25519i	0.840487	−	1.45577i	−0.0489972	−	0.998799i	$-0.515603\pi$
$5$	1.87939	−	3.25519i	0.840487	−	1.45577i	0.889484	−	0.456967i	$-0.151064\pi$
$6$		0			0
$7$	4.75877			1.79865			0.899323	−	0.437285i	$-0.144060\pi$
$7$	4.75877			1.79865			0.899323	+	0.437285i	$0.144060\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−4.36959			−1.31748			−0.658740	−	0.752371i	$-0.728910\pi$
$11$	−4.36959			−1.31748			−0.658740	+	0.752371i	$0.728910\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$	−1.87939	−	3.25519i	−0.485255	−	0.840487i
$16$		0			0
$17$	−3.06418	+	5.30731i	−0.743172	+	1.28721i	0.207872	+	0.978156i	$0.433346\pi$
$17$	−3.06418	+	5.30731i	−0.743172	+	1.28721i	−0.951044	+	0.309056i	$0.899987\pi$
$18$		0			0
$19$	0.694593	+	4.30320i	0.159350	+	0.987222i
$19$	0.694593	+	4.30320i	0.159350	+	0.987222i
$20$		0			0
$21$	2.37939	−	4.12122i	0.519224	−	0.899323i
$22$		0			0
$23$	1.87939	+	3.25519i	0.391879	+	0.678754i	0.992697	−	0.120631i	$-0.0384919\pi$
$23$	1.87939	+	3.25519i	0.391879	+	0.678754i	−0.600818	+	0.799385i	$0.705159\pi$
$24$		0			0
$25$	−4.56418	−	7.90539i	−0.912836	−	1.58108i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.69459	−	4.66717i	−0.500373	−	0.866672i	−1.00000		0.000431109i	$-0.999863\pi$
$29$	−2.69459	−	4.66717i	−0.500373	−	0.866672i	0.499627	−	0.866241i	$-0.333471\pi$
$30$		0			0
$31$	7.36959			1.32362			0.661808	−	0.749673i	$-0.269789\pi$
$31$	7.36959			1.32362			0.661808	+	0.749673i	$0.269789\pi$
$32$		0			0
$33$	−2.18479	+	3.78417i	−0.380324	+	0.658740i
$34$		0			0
$35$	8.94356	−	15.4907i	1.51174	−	2.61841i
$36$		0			0
$37$	−7.12836			−1.17189			−0.585947	−	0.810349i	$-0.699277\pi$
$37$	−7.12836			−1.17189			−0.585947	+	0.810349i	$0.699277\pi$
$38$		0			0
$39$	−1.00000			−0.160128
$40$		0			0
$41$	1.75877	−	3.04628i	0.274674	−	0.475749i	−0.695379	−	0.718643i	$-0.744763\pi$
$41$	1.75877	−	3.04628i	0.274674	−	0.475749i	0.970053	+	0.242894i	$0.0780968\pi$
$42$		0			0
$43$	0.379385	−	0.657115i	0.0578557	−	0.100209i	−0.835647	−	0.549267i	$-0.814907\pi$
$43$	0.379385	−	0.657115i	0.0578557	−	0.100209i	0.893503	+	0.449058i	$0.148240\pi$
$44$		0			0
$45$	−3.75877			−0.560324
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	15.6459			2.23513
$50$		0			0
$51$	3.06418	+	5.30731i	0.429071	+	0.743172i
$52$		0			0
$53$	−2.57398	−	4.45826i	−0.353563	−	0.612389i	0.633308	−	0.773900i	$-0.281697\pi$
$53$	−2.57398	−	4.45826i	−0.353563	−	0.612389i	−0.986871	+	0.161511i	$0.948363\pi$
$54$		0			0
$55$	−8.21213	+	14.2238i	−1.10732	+	1.91794i
$56$		0			0
$57$	4.07398	+	1.55007i	0.539612	+	0.205311i
$58$		0			0
$59$	−4.63816	+	8.03352i	−0.603836	+	1.04588i	0.388398	+	0.921492i	$0.373029\pi$
$59$	−4.63816	+	8.03352i	−0.603836	+	1.04588i	−0.992234	+	0.124384i	$0.960305\pi$
$60$		0			0
$61$	4.25877	+	7.37641i	0.545280	+	0.944452i	0.998589	+	0.0530990i	$0.0169099\pi$
$61$	4.25877	+	7.37641i	0.545280	+	0.944452i	−0.453310	+	0.891353i	$0.649757\pi$
$62$		0			0
$63$	−2.37939	−	4.12122i	−0.299774	−	0.519224i
$64$		0			0
$65$	−3.75877			−0.466218
$66$		0			0
$67$	−0.684793	−	1.18610i	−0.0836607	−	0.144905i	0.821159	−	0.570699i	$-0.193328\pi$
$67$	−0.684793	−	1.18610i	−0.0836607	−	0.144905i	−0.904820	+	0.425795i	$0.859995\pi$
$68$		0			0
$69$	3.75877			0.452503
$70$		0			0
$71$	5.82295	−	10.0856i	0.691057	−	1.19695i	−0.280435	−	0.959873i	$-0.590479\pi$
$71$	5.82295	−	10.0856i	0.691057	−	1.19695i	0.971492	−	0.237073i	$-0.0761879\pi$
$72$		0			0
$73$	−2.25877	+	3.91231i	−0.264369	+	0.457901i	−0.967398	−	0.253260i	$-0.918497\pi$
$73$	−2.25877	+	3.91231i	−0.264369	+	0.457901i	0.703029	+	0.711161i	$0.251830\pi$
$74$		0			0
$75$	−9.12836			−1.05405
$76$		0			0
$77$	−20.7939			−2.36968
$78$		0			0
$79$	−7.07398	+	12.2525i	−0.795885	+	1.37851i	0.126391	+	0.991980i	$0.459661\pi$
$79$	−7.07398	+	12.2525i	−0.795885	+	1.37851i	−0.922276	+	0.386532i	$0.873673\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	4.90673			0.538583			0.269292	−	0.963059i	$-0.413210\pi$
$83$	4.90673			0.538583			0.269292	+	0.963059i	$0.413210\pi$
$84$		0			0
$85$	11.5175	+	19.9490i	1.24925	+	2.16377i
$86$		0			0
$87$	−5.38919			−0.577781
$88$		0			0
$89$	−4.18479	−	7.24827i	−0.443587	−	0.768315i	0.554365	−	0.832273i	$-0.312961\pi$
$89$	−4.18479	−	7.24827i	−0.443587	−	0.768315i	−0.997953	+	0.0639579i	$0.979628\pi$
$90$		0			0
$91$	−2.37939	−	4.12122i	−0.249427	−	0.432021i
$92$		0			0
$93$	3.68479	−	6.38225i	0.382095	−	0.661808i
$94$		0			0
$95$	15.3131	+	5.82634i	1.57110	+	0.597770i
$96$		0			0
$97$	5.82295	−	10.0856i	0.591231	−	1.02404i	−0.402836	−	0.915272i	$-0.631976\pi$
$97$	5.82295	−	10.0856i	0.591231	−	1.02404i	0.994067	−	0.108770i	$-0.0346911\pi$
$98$		0			0
$99$	2.18479	+	3.78417i	0.219580	+	0.380324i
$100$		0			0
$101$	2.06418	+	3.57526i	0.205393	+	0.355752i	0.950258	−	0.311464i	$-0.100819\pi$
$101$	2.06418	+	3.57526i	0.205393	+	0.355752i	−0.744865	+	0.667216i	$0.767486\pi$
$102$		0			0
$103$	−6.75877			−0.665961			−0.332981	−	0.942934i	$-0.608054\pi$
$103$	−6.75877			−0.665961			−0.332981	+	0.942934i	$0.608054\pi$
$104$		0			0
$105$	−8.94356	−	15.4907i	−0.872802	−	1.51174i
$106$		0			0
$107$	−4.12836			−0.399103			−0.199552	−	0.979887i	$-0.563949\pi$
$107$	−4.12836			−0.399103			−0.199552	+	0.979887i	$0.563949\pi$
$108$		0			0
$109$	0.0641778	−	0.111159i	0.00614712	−	0.0106471i	−0.862935	−	0.505314i	$-0.831377\pi$
$109$	0.0641778	−	0.111159i	0.00614712	−	0.0106471i	0.869083	+	0.494667i	$0.164710\pi$
$110$		0			0
$111$	−3.56418	+	6.17334i	−0.338297	+	0.585947i
$112$		0			0
$113$	−2.40879			−0.226600			−0.113300	−	0.993561i	$-0.536142\pi$
$113$	−2.40879			−0.226600			−0.113300	+	0.993561i	$0.536142\pi$
$114$		0			0
$115$	14.1284			1.31748
$116$		0			0
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$		0			0
$119$	−14.5817	+	25.2563i	−1.33670	+	2.31524i
$120$		0			0
$121$	8.09327			0.735752
$122$		0			0
$123$	−1.75877	−	3.04628i	−0.158583	−	0.274674i
$124$		0			0
$125$	−15.5175			−1.38793
$126$		0			0
$127$	−0.241230	−	0.417822i	−0.0214057	−	0.0370757i	0.855124	−	0.518423i	$-0.173481\pi$
$127$	−0.241230	−	0.417822i	−0.0214057	−	0.0370757i	−0.876530	+	0.481348i	$0.840147\pi$
$128$		0			0
$129$	−0.379385	−	0.657115i	−0.0334030	−	0.0578557i
$130$		0			0
$131$	1.69459	−	2.93512i	0.148057	−	0.256443i	−0.782452	−	0.622711i	$-0.786031\pi$
$131$	1.69459	−	2.93512i	0.148057	−	0.256443i	0.930509	+	0.366268i	$0.119365\pi$
$132$		0			0
$133$	3.30541	+	20.4779i	0.286615	+	1.77566i
$134$		0			0
$135$	−1.87939	+	3.25519i	−0.161752	+	0.280162i
$136$		0			0
$137$	9.21213	+	15.9559i	0.787046	+	1.36320i	0.927769	+	0.373154i	$0.121724\pi$
$137$	9.21213	+	15.9559i	0.787046	+	1.36320i	−0.140724	+	0.990049i	$0.544943\pi$
$138$		0			0
$139$	−0.00980018	−	0.0169744i	−0.000831240	−	0.00143975i	0.865609	−	0.500720i	$-0.166931\pi$
$139$	−0.00980018	−	0.0169744i	−0.000831240	−	0.00143975i	−0.866441	+	0.499280i	$0.833598\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$		0			0
$143$	2.18479	+	3.78417i	0.182702	+	0.316448i
$144$		0			0
$145$	−20.2567			−1.68223
$146$		0			0
$147$	7.82295	−	13.5497i	0.645226	−	1.11756i
$148$		0			0
$149$	−3.12061	+	5.40506i	−0.255651	+	0.442800i	−0.965072	−	0.261985i	$-0.915623\pi$
$149$	−3.12061	+	5.40506i	−0.255651	+	0.442800i	0.709421	+	0.704785i	$0.248956\pi$
$150$		0			0
$151$	0.739170			0.0601528			0.0300764	−	0.999548i	$-0.490425\pi$
$151$	0.739170			0.0601528			0.0300764	+	0.999548i	$0.490425\pi$
$152$		0			0
$153$	6.12836			0.495448
$154$		0			0
$155$	13.8503	−	23.9894i	1.11248	−	1.92688i
$156$		0			0
$157$	3.32295	−	5.75552i	0.265200	−	0.459340i	−0.702416	−	0.711767i	$-0.747895\pi$
$157$	3.32295	−	5.75552i	0.265200	−	0.459340i	0.967616	+	0.252427i	$0.0812286\pi$
$158$		0			0
$159$	−5.14796			−0.408259
$160$		0			0
$161$	8.94356	+	15.4907i	0.704852	+	1.22084i
$162$		0			0
$163$	−11.3696			−0.890535			−0.445267	−	0.895398i	$-0.646891\pi$
$163$	−11.3696			−0.890535			−0.445267	+	0.895398i	$0.646891\pi$
$164$		0			0
$165$	8.21213	+	14.2238i	0.639314	+	1.10732i
$166$		0			0
$167$	−1.49020	−	2.58110i	−0.115315	−	0.199732i	0.802591	−	0.596530i	$-0.203454\pi$
$167$	−1.49020	−	2.58110i	−0.115315	−	0.199732i	−0.917906	+	0.396799i	$0.870121\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	3.37939	−	2.75314i	0.258428	−	0.210538i
$172$		0			0
$173$	2.69459	−	4.66717i	0.204866	−	0.354838i	−0.745224	−	0.666814i	$-0.767657\pi$
$173$	2.69459	−	4.66717i	0.204866	−	0.354838i	0.950090	+	0.311976i	$0.100991\pi$
$174$		0			0
$175$	−21.7199	−	37.6199i	−1.64187	−	2.84380i
$176$		0			0
$177$	4.63816	+	8.03352i	0.348625	+	0.603836i
$178$		0			0
$179$	4.24123			0.317004			0.158502	−	0.987359i	$-0.449334\pi$
$179$	4.24123			0.317004			0.158502	+	0.987359i	$0.449334\pi$
$180$		0			0
$181$	−6.30541	−	10.9213i	−0.468677	−	0.811773i	0.530682	−	0.847571i	$-0.321936\pi$
$181$	−6.30541	−	10.9213i	−0.468677	−	0.811773i	−0.999359	+	0.0357984i	$0.988603\pi$
$182$		0			0
$183$	8.51754			0.629635
$184$		0			0
$185$	−13.3969	+	23.2042i	−0.984962	+	1.70600i
$186$		0			0
$187$	13.3892	−	23.1907i	0.979114	−	1.69588i
$188$		0			0
$189$	−4.75877			−0.346150
$190$		0			0
$191$	−22.6263			−1.63718			−0.818591	−	0.574377i	$-0.805244\pi$
$191$	−22.6263			−1.63718			−0.818591	+	0.574377i	$0.805244\pi$
$192$		0			0
$193$	−12.3229	+	21.3440i	−0.887025	+	1.53637i	−0.0436505	+	0.999047i	$0.513899\pi$
$193$	−12.3229	+	21.3440i	−0.887025	+	1.53637i	−0.843375	+	0.537326i	$0.819435\pi$
$194$		0			0
$195$	−1.87939	+	3.25519i	−0.134586	+	0.233109i
$196$		0			0
$197$	22.6655			1.61485			0.807425	−	0.589970i	$-0.200861\pi$
$197$	22.6655			1.61485			0.807425	+	0.589970i	$0.200861\pi$
$198$		0			0
$199$	−6.96110	−	12.0570i	−0.493460	−	0.854697i	0.506512	−	0.862233i	$-0.330935\pi$
$199$	−6.96110	−	12.0570i	−0.493460	−	0.854697i	−0.999972	+	0.00753584i	$0.997601\pi$
$200$		0			0
$201$	−1.36959			−0.0966031
$202$		0			0
$203$	−12.8229	−	22.2100i	−0.899995	−	1.55884i
$204$		0			0
$205$	−6.61081	−	11.4503i	−0.461719	−	0.799721i
$206$		0			0
$207$	1.87939	−	3.25519i	0.130626	−	0.226251i
$208$		0			0
$209$	−3.03508	−	18.8032i	−0.209941	−	1.30064i
$210$		0			0
$211$	1.00980	−	1.74903i	0.0695175	−	0.120408i	−0.829172	−	0.558994i	$-0.811187\pi$
$211$	1.00980	−	1.74903i	0.0695175	−	0.120408i	0.898689	+	0.438586i	$0.144521\pi$
$212$		0			0
$213$	−5.82295	−	10.0856i	−0.398982	−	0.691057i
$214$		0			0
$215$	−1.42602	−	2.46994i	−0.0972539	−	0.168449i
$216$		0			0
$217$	35.0702			2.38072
$218$		0			0
$219$	2.25877	+	3.91231i	0.152634	+	0.264369i
$220$		0			0
$221$	6.12836			0.412238
$222$		0			0
$223$	−14.1827	+	24.5652i	−0.949746	+	1.64501i	−0.203789	+	0.979015i	$0.565325\pi$
$223$	−14.1827	+	24.5652i	−0.949746	+	1.64501i	−0.745958	+	0.665993i	$0.768008\pi$
$224$		0			0
$225$	−4.56418	+	7.90539i	−0.304279	+	0.527026i
$226$		0			0
$227$	20.1830			1.33960			0.669798	−	0.742544i	$-0.266381\pi$
$227$	20.1830			1.33960			0.669798	+	0.742544i	$0.266381\pi$
$228$		0			0
$229$	11.7784			0.778337			0.389168	−	0.921167i	$-0.372762\pi$
$229$	11.7784			0.778337			0.389168	+	0.921167i	$0.372762\pi$
$230$		0			0
$231$	−10.3969	+	18.0080i	−0.684068	+	1.18484i
$232$		0			0
$233$	0.0641778	−	0.111159i	0.00420443	−	0.00728228i	−0.863916	−	0.503637i	$-0.831995\pi$
$233$	0.0641778	−	0.111159i	0.00420443	−	0.00728228i	0.868120	+	0.496354i	$0.165328\pi$
$234$		0			0
$235$	22.5526			1.47117
$236$		0			0
$237$	7.07398	+	12.2525i	0.459504	+	0.795885i
$238$		0			0
$239$	3.10876			0.201089			0.100544	−	0.994933i	$-0.467942\pi$
$239$	3.10876			0.201089			0.100544	+	0.994933i	$0.467942\pi$
$240$		0			0
$241$	−5.64796	−	9.78255i	−0.363817	−	0.630149i	0.624769	−	0.780810i	$-0.285193\pi$
$241$	−5.64796	−	9.78255i	−0.363817	−	0.630149i	−0.988586	+	0.150661i	$0.951860\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	29.4047	−	50.9304i	1.87860	−	3.25382i
$246$		0			0
$247$	3.37939	−	2.75314i	0.215025	−	0.175178i
$248$		0			0
$249$	2.45336	−	4.24935i	0.155476	−	0.269292i
$250$		0			0
$251$	0.758770	+	1.31423i	0.0478932	+	0.0829534i	0.888978	−	0.457950i	$-0.151416\pi$
$251$	0.758770	+	1.31423i	0.0478932	+	0.0829534i	−0.841085	+	0.540903i	$0.818083\pi$
$252$		0			0
$253$	−8.21213	−	14.2238i	−0.516292	−	0.894245i
$254$		0			0
$255$	23.0351			1.44251
$256$		0			0
$257$	6.09152	+	10.5508i	0.379979	+	0.658142i	0.991059	−	0.133427i	$-0.0425980\pi$
$257$	6.09152	+	10.5508i	0.379979	+	0.658142i	−0.611080	+	0.791569i	$0.709265\pi$
$258$		0			0
$259$	−33.9222			−2.10782
$260$		0			0
$261$	−2.69459	+	4.66717i	−0.166791	+	0.288891i
$262$		0			0
$263$	9.69459	−	16.7915i	0.597794	−	1.03541i	−0.395352	−	0.918530i	$-0.629377\pi$
$263$	9.69459	−	16.7915i	0.597794	−	1.03541i	0.993146	−	0.116880i	$-0.0372893\pi$
$264$		0			0
$265$	−19.3500			−1.18866
$266$		0			0
$267$	−8.36959			−0.512210
$268$		0			0
$269$	−11.7023	+	20.2690i	−0.713504	+	1.23582i	0.250030	+	0.968238i	$0.419560\pi$
$269$	−11.7023	+	20.2690i	−0.713504	+	1.23582i	−0.963534	+	0.267587i	$0.913774\pi$
$270$		0			0
$271$	−0.482459	+	0.835644i	−0.0293073	+	0.0507617i	−0.880307	−	0.474404i	$-0.842663\pi$
$271$	−0.482459	+	0.835644i	−0.0293073	+	0.0507617i	0.851000	+	0.525166i	$0.175997\pi$
$272$		0			0
$273$	−4.75877			−0.288014
$274$		0			0
$275$	19.9436	+	34.5433i	1.20264	+	2.08304i
$276$		0			0
$277$	15.3892			0.924647			0.462323	−	0.886711i	$-0.347016\pi$
$277$	15.3892			0.924647			0.462323	+	0.886711i	$0.347016\pi$
$278$		0			0
$279$	−3.68479	−	6.38225i	−0.220603	−	0.382095i
$280$		0			0
$281$	−4.24897	−	7.35943i	−0.253472	−	0.439027i	0.711007	−	0.703185i	$-0.248239\pi$
$281$	−4.24897	−	7.35943i	−0.253472	−	0.439027i	−0.964479	+	0.264158i	$0.914906\pi$
$282$		0			0
$283$	5.51754	−	9.55666i	0.327984	−	0.568085i	−0.654128	−	0.756384i	$-0.726964\pi$
$283$	5.51754	−	9.55666i	0.327984	−	0.568085i	0.982112	+	0.188299i	$0.0602975\pi$
$284$		0			0
$285$	12.7023	−	10.3484i	0.752421	−	0.612987i
$286$		0			0
$287$	8.36959	−	14.4965i	0.494041	−	0.855704i
$288$		0			0
$289$	−10.2784	−	17.8027i	−0.604610	−	1.04722i
$290$		0			0
$291$	−5.82295	−	10.0856i	−0.341347	−	0.591231i
$292$		0			0
$293$	−1.03508			−0.0604701			−0.0302351	−	0.999543i	$-0.509626\pi$
$293$	−1.03508			−0.0604701			−0.0302351	+	0.999543i	$0.509626\pi$
$294$		0			0
$295$	17.4338	+	30.1962i	1.01503	+	1.75809i
$296$		0			0
$297$	4.36959			0.253549
$298$		0			0
$299$	1.87939	−	3.25519i	0.108688	−	0.188253i
$300$		0			0
$301$	1.80541	−	3.12706i	0.104062	−	0.180241i
$302$		0			0
$303$	4.12836			0.237168
$304$		0			0
$305$	32.0155			1.83320
$306$		0			0
$307$	−7.43376	+	12.8757i	−0.424267	+	0.734852i	−0.996352	−	0.0853423i	$-0.972802\pi$
$307$	−7.43376	+	12.8757i	−0.424267	+	0.734852i	0.572084	+	0.820195i	$0.306135\pi$
$308$		0			0
$309$	−3.37939	+	5.85327i	−0.192247	+	0.332981i
$310$		0			0
$311$	−16.0547			−0.910378			−0.455189	−	0.890395i	$-0.650428\pi$
$311$	−16.0547			−0.910378			−0.455189	+	0.890395i	$0.650428\pi$
$312$		0			0
$313$	−17.5817	−	30.4524i	−0.993777	−	1.72127i	−0.593350	−	0.804945i	$-0.702195\pi$
$313$	−17.5817	−	30.4524i	−0.993777	−	1.72127i	−0.400428	−	0.916328i	$-0.631138\pi$
$314$		0			0
$315$	−17.8871			−1.00783
$316$		0			0
$317$	−9.26857	−	16.0536i	−0.520575	−	0.901662i	−0.999714	−	0.0239230i	$-0.992384\pi$
$317$	−9.26857	−	16.0536i	−0.520575	−	0.901662i	0.479139	−	0.877739i	$-0.340949\pi$
$318$		0			0
$319$	11.7743	+	20.3936i	0.659232	+	1.14182i
$320$		0			0
$321$	−2.06418	+	3.57526i	−0.115211	+	0.199552i
$322$		0			0
$323$	−24.9668	−	9.49935i	−1.38919	−	0.528558i
$324$		0			0
$325$	−4.56418	+	7.90539i	−0.253175	+	0.438512i
$326$		0			0
$327$	−0.0641778	−	0.111159i	−0.00354904	−	0.00614712i
$328$		0			0
$329$	14.2763	+	24.7273i	0.787079	+	1.36326i
$330$		0			0
$331$	−8.75877			−0.481426			−0.240713	−	0.970596i	$-0.577381\pi$
$331$	−8.75877			−0.481426			−0.240713	+	0.970596i	$0.577381\pi$
$332$		0			0
$333$	3.56418	+	6.17334i	0.195316	+	0.338297i
$334$		0			0
$335$	−5.14796			−0.281263
$336$		0			0
$337$	10.6925	−	18.5200i	0.582459	−	1.00885i	−0.412728	−	0.910855i	$-0.635424\pi$
$337$	10.6925	−	18.5200i	0.582459	−	1.00885i	0.995187	−	0.0979947i	$-0.0312428\pi$
$338$		0			0
$339$	−1.20439	+	2.08607i	−0.0654136	+	0.113300i
$340$		0			0
$341$	−32.2020			−1.74384
$342$		0			0
$343$	41.1438			2.22156
$344$		0			0
$345$	7.06418	−	12.2355i	0.380323	−	0.658738i
$346$		0			0
$347$	−11.9632	+	20.7208i	−0.642216	+	1.11235i	0.342721	+	0.939437i	$0.388652\pi$
$347$	−11.9632	+	20.7208i	−0.642216	+	1.11235i	−0.984937	+	0.172914i	$0.944682\pi$
$348$		0			0
$349$	−23.0702			−1.23492			−0.617459	−	0.786603i	$-0.711838\pi$
$349$	−23.0702			−1.23492			−0.617459	+	0.786603i	$0.711838\pi$
$350$		0			0
$351$	0.500000	+	0.866025i	0.0266880	+	0.0462250i
$352$		0			0
$353$	−28.4979			−1.51679			−0.758396	−	0.651794i	$-0.774017\pi$
$353$	−28.4979			−1.51679			−0.758396	+	0.651794i	$0.774017\pi$
$354$		0			0
$355$	−21.8871	−	37.9096i	−1.16165	−	2.01203i
$356$		0			0
$357$	14.5817	+	25.2563i	0.771746	+	1.33670i
$358$		0			0
$359$	−2.48246	+	4.29975i	−0.131019	+	0.226932i	−0.924070	−	0.382224i	$-0.875158\pi$
$359$	−2.48246	+	4.29975i	−0.131019	+	0.226932i	0.793051	+	0.609156i	$0.208492\pi$
$360$		0			0
$361$	−18.0351	+	5.97794i	−0.949215	+	0.314629i
$362$		0			0
$363$	4.04664	−	7.00898i	0.212393	−	0.367876i
$364$		0			0
$365$	8.49020	+	14.7055i	0.444397	+	0.769719i
$366$		0			0
$367$	−9.42396	−	16.3228i	−0.491927	−	0.852042i	0.508030	−	0.861339i	$-0.330374\pi$
$367$	−9.42396	−	16.3228i	−0.491927	−	0.852042i	−0.999957	+	0.00929712i	$0.997041\pi$
$368$		0			0
$369$	−3.51754			−0.183116
$370$		0			0
$371$	−12.2490	−	21.2158i	−0.635935	−	1.10147i
$372$		0			0
$373$	35.9026			1.85897			0.929483	−	0.368864i	$-0.120253\pi$
$373$	35.9026			1.85897			0.929483	+	0.368864i	$0.120253\pi$
$374$		0			0
$375$	−7.75877	+	13.4386i	−0.400661	+	0.693966i
$376$		0			0
$377$	−2.69459	+	4.66717i	−0.138779	+	0.240372i
$378$		0			0
$379$	−12.2763			−0.630592			−0.315296	−	0.948993i	$-0.602104\pi$
$379$	−12.2763			−0.630592			−0.315296	+	0.948993i	$0.602104\pi$
$380$		0			0
$381$	−0.482459			−0.0247171
$382$		0			0
$383$	−7.20439	+	12.4784i	−0.368127	+	0.637615i	−0.989273	−	0.146080i	$-0.953334\pi$
$383$	−7.20439	+	12.4784i	−0.368127	+	0.637615i	0.621145	+	0.783695i	$0.286668\pi$
$384$		0			0
$385$	−39.0797	+	67.6880i	−1.99168	+	3.44970i
$386$		0			0
$387$	−0.758770			−0.0385705
$388$		0			0
$389$	−3.18479	−	5.51622i	−0.161475	−	0.279684i	0.773923	−	0.633280i	$-0.218292\pi$
$389$	−3.18479	−	5.51622i	−0.161475	−	0.279684i	−0.935398	+	0.353597i	$0.884959\pi$
$390$		0			0
$391$	−23.0351			−1.16493
$392$		0			0
$393$	−1.69459	−	2.93512i	−0.0854809	−	0.148057i
$394$		0			0
$395$	26.5895	+	46.0543i	1.33786	+	2.31724i
$396$		0			0
$397$	5.27837	−	9.14241i	0.264914	−	0.458844i	−0.702627	−	0.711558i	$-0.747990\pi$
$397$	5.27837	−	9.14241i	0.264914	−	0.458844i	0.967541	+	0.252714i	$0.0813231\pi$
$398$		0			0
$399$	19.3871	+	7.37641i	0.970570	+	0.369282i
$400$		0			0
$401$	−10.7219	+	18.5709i	−0.535428	+	0.927388i	0.463715	+	0.885985i	$0.346516\pi$
$401$	−10.7219	+	18.5709i	−0.535428	+	0.927388i	−0.999143	+	0.0414036i	$0.986817\pi$
$402$		0			0
$403$	−3.68479	−	6.38225i	−0.183553	−	0.317922i
$404$		0			0
$405$	1.87939	+	3.25519i	0.0933874	+	0.161752i
$406$		0			0
$407$	31.1480			1.54395
$408$		0			0
$409$	−3.32501	−	5.75908i	−0.164411	−	0.284768i	0.772035	−	0.635580i	$-0.219239\pi$
$409$	−3.32501	−	5.75908i	−0.164411	−	0.284768i	−0.936446	+	0.350812i	$0.885906\pi$
$410$		0			0
$411$	18.4243			0.908802
$412$		0			0
$413$	−22.0719	+	38.2297i	−1.08609	+	1.88116i
$414$		0			0
$415$	9.22163	−	15.9723i	0.452672	−	0.784051i
$416$		0			0
$417$	−0.0196004			−0.000959834
$418$		0			0
$419$	5.84793			0.285690			0.142845	−	0.989745i	$-0.454375\pi$
$419$	5.84793			0.285690			0.142845	+	0.989745i	$0.454375\pi$
$420$		0			0
$421$	−0.714193	+	1.23702i	−0.0348076	+	0.0602886i	−0.882904	−	0.469553i	$-0.844415\pi$
$421$	−0.714193	+	1.23702i	−0.0348076	+	0.0602886i	0.848097	+	0.529841i	$0.177749\pi$
$422$		0			0
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$		0			0
$425$	55.9418			2.71358
$426$		0			0
$427$	20.2665	+	35.1026i	0.980765	+	1.69874i
$428$		0			0
$429$	4.36959			0.210966
$430$		0			0
$431$	−0.389185	−	0.674089i	−0.0187464	−	0.0324697i	0.856500	−	0.516147i	$-0.172634\pi$
$431$	−0.389185	−	0.674089i	−0.0187464	−	0.0324697i	−0.875246	+	0.483677i	$0.839301\pi$
$432$		0			0
$433$	−13.3425	−	23.1100i	−0.641202	−	1.11059i	−0.985165	−	0.171611i	$-0.945103\pi$
$433$	−13.3425	−	23.1100i	−0.641202	−	1.11059i	0.343963	−	0.938983i	$-0.388231\pi$
$434$		0			0
$435$	−10.1284	+	17.5428i	−0.485617	+	0.841114i
$436$		0			0
$437$	−12.7023	+	10.3484i	−0.607635	+	0.495031i
$438$		0			0
$439$	14.2665	−	24.7103i	0.680903	−	1.17936i	−0.293802	−	0.955866i	$-0.594921\pi$
$439$	14.2665	−	24.7103i	0.680903	−	1.17936i	0.974706	−	0.223493i	$-0.0717460\pi$
$440$		0			0
$441$	−7.82295	−	13.5497i	−0.372521	−	0.645226i
$442$		0			0
$443$	8.82295	+	15.2818i	0.419191	+	0.726060i	0.995858	−	0.0909191i	$-0.0289805\pi$
$443$	8.82295	+	15.2818i	0.419191	+	0.726060i	−0.576667	+	0.816979i	$0.695647\pi$
$444$		0			0
$445$	−31.4593			−1.49132
$446$		0			0
$447$	3.12061	+	5.40506i	0.147600	+	0.255651i
$448$		0			0
$449$	−1.38919			−0.0655597			−0.0327799	−	0.999463i	$-0.510436\pi$
$449$	−1.38919			−0.0655597			−0.0327799	+	0.999463i	$0.510436\pi$
$450$		0			0
$451$	−7.68510	+	13.3110i	−0.361877	+	0.626790i
$452$		0			0
$453$	0.369585	−	0.640140i	0.0173646	−	0.0300764i
$454$		0			0
$455$	−17.8871			−0.838561
$456$		0			0
$457$	24.6851			1.15472			0.577360	−	0.816490i	$-0.304083\pi$
$457$	24.6851			1.15472			0.577360	+	0.816490i	$0.304083\pi$
$458$		0			0
$459$	3.06418	−	5.30731i	0.143024	−	0.247724i
$460$		0			0
$461$	−0.795607	+	1.37803i	−0.0370551	+	0.0641813i	−0.883958	−	0.467566i	$-0.845131\pi$
$461$	−0.795607	+	1.37803i	−0.0370551	+	0.0641813i	0.846903	+	0.531747i	$0.178464\pi$
$462$		0			0
$463$	−21.7547			−1.01102			−0.505512	−	0.862819i	$-0.668696\pi$
$463$	−21.7547			−1.01102			−0.505512	+	0.862819i	$0.668696\pi$
$464$		0			0
$465$	−13.8503	−	23.9894i	−0.642292	−	1.11248i
$466$		0			0
$467$	15.5175			0.718066			0.359033	−	0.933325i	$-0.383107\pi$
$467$	15.5175			0.718066			0.359033	+	0.933325i	$0.383107\pi$
$468$		0			0
$469$	−3.25877	−	5.64436i	−0.150476	−	0.260632i
$470$		0			0
$471$	−3.32295	−	5.75552i	−0.153113	−	0.265200i
$472$		0			0
$473$	−1.65776	+	2.87132i	−0.0762237	+	0.132023i
$474$		0			0
$475$	30.8482	−	25.1316i	1.41541	−	1.15312i
$476$		0			0
$477$	−2.57398	+	4.45826i	−0.117854	+	0.204130i
$478$		0			0
$479$	5.82295	+	10.0856i	0.266057	+	0.460825i	0.967840	−	0.251566i	$-0.0809456\pi$
$479$	5.82295	+	10.0856i	0.266057	+	0.460825i	−0.701783	+	0.712391i	$0.747612\pi$
$480$		0			0
$481$	3.56418	+	6.17334i	0.162513	+	0.281480i
$482$		0			0
$483$	17.8871			0.813892
$484$		0			0
$485$	−21.8871	−	37.9096i	−0.993843	−	1.72139i
$486$		0			0
$487$	38.5526			1.74699			0.873493	−	0.486837i	$-0.161849\pi$
$487$	38.5526			1.74699			0.873493	+	0.486837i	$0.161849\pi$
$488$		0			0
$489$	−5.68479	+	9.84635i	−0.257075	+	0.445267i
$490$		0			0
$491$	−3.82295	+	6.62154i	−0.172527	+	0.298826i	−0.939303	−	0.343089i	$-0.888527\pi$
$491$	−3.82295	+	6.62154i	−0.172527	+	0.298826i	0.766776	+	0.641915i	$0.221860\pi$
$492$		0			0
$493$	33.0268			1.48745
$494$		0			0
$495$	16.4243			0.738216
$496$		0			0
$497$	27.7101	−	47.9953i	1.24297	−	2.15288i
$498$		0			0
$499$	−15.3152	+	26.5267i	−0.685603	+	1.18750i	0.287644	+	0.957737i	$0.407128\pi$
$499$	−15.3152	+	26.5267i	−0.685603	+	1.18750i	−0.973247	+	0.229762i	$0.926205\pi$
$500$		0			0
$501$	−2.98040			−0.133154
$502$		0			0
$503$	2.69459	+	4.66717i	0.120146	+	0.208099i	0.919825	−	0.392329i	$-0.128330\pi$
$503$	2.69459	+	4.66717i	0.120146	+	0.208099i	−0.799679	+	0.600428i	$0.794997\pi$
$504$		0			0
$505$	15.5175			0.690522
$506$		0			0
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$		0			0
$509$	1.12836	+	1.95437i	0.0500135	+	0.0866259i	0.889948	−	0.456061i	$-0.150740\pi$
$509$	1.12836	+	1.95437i	0.0500135	+	0.0866259i	−0.839935	+	0.542687i	$0.817407\pi$
$510$		0			0
$511$	−10.7490	+	18.6178i	−0.475506	+	0.823601i
$512$		0			0
$513$	−0.694593	−	4.30320i	−0.0306670	−	0.189991i
$514$		0			0
$515$	−12.7023	+	22.0011i	−0.559732	+	0.969484i
$516$		0			0
$517$	−13.1088	−	22.7050i	−0.576522	−	0.998566i
$518$		0			0
$519$	−2.69459	−	4.66717i	−0.118279	−	0.204866i
$520$		0			0
$521$	37.2763			1.63310			0.816552	−	0.577271i	$-0.195882\pi$
$521$	37.2763			1.63310			0.816552	+	0.577271i	$0.195882\pi$
$522$		0			0
$523$	0.186852	+	0.323637i	0.00817046	+	0.0141517i	0.870082	−	0.492907i	$-0.164066\pi$
$523$	0.186852	+	0.323637i	0.00817046	+	0.0141517i	−0.861911	+	0.507059i	$0.830733\pi$
$524$		0			0
$525$	−43.4397			−1.89587
$526$		0			0
$527$	−22.5817	+	39.1127i	−0.983675	+	1.70378i
$528$		0			0
$529$	4.43582	−	7.68307i	0.192862	−	0.334046i
$530$		0			0
$531$	9.27631			0.402558
$532$		0			0
$533$	−3.51754			−0.152362
$534$		0			0
$535$	−7.75877	+	13.4386i	−0.335441	+	0.581001i
$536$		0			0
$537$	2.12061	−	3.67301i	0.0915113	−	0.158502i
$538$		0			0
$539$	−68.3661			−2.94474
$540$		0			0
$541$	9.54458	+	16.5317i	0.410353	+	0.710753i	0.994928	−	0.100587i	$-0.0320720\pi$
$541$	9.54458	+	16.5317i	0.410353	+	0.710753i	−0.584575	+	0.811340i	$0.698739\pi$
$542$		0			0
$543$	−12.6108			−0.541182
$544$		0			0
$545$	−0.241230	−	0.417822i	−0.0103331	−	0.0178975i
$546$		0			0
$547$	−21.8773	−	37.8926i	−0.935407	−	1.62017i	−0.773907	−	0.633300i	$-0.781700\pi$
$547$	−21.8773	−	37.8926i	−0.935407	−	1.62017i	−0.161500	−	0.986873i	$-0.551633\pi$
$548$		0			0
$549$	4.25877	−	7.37641i	0.181760	−	0.314817i
$550$		0			0
$551$	18.2121	−	14.8372i	0.775863	−	0.632084i
$552$		0			0
$553$	−33.6634	+	58.3068i	−1.43151	+	2.47946i
$554$		0			0
$555$	13.3969	+	23.2042i	0.568668	+	0.984962i
$556$		0			0
$557$	−15.9513	−	27.6285i	−0.675878	−	1.17066i	−0.976211	−	0.216821i	$-0.930431\pi$
$557$	−15.9513	−	27.6285i	−0.675878	−	1.17066i	0.300333	−	0.953834i	$-0.402902\pi$
$558$		0			0
$559$	−0.758770			−0.0320926
$560$		0			0
$561$	−13.3892	−	23.1907i	−0.565292	−	0.979114i
$562$		0			0
$563$	−3.87164			−0.163170			−0.0815852	−	0.996666i	$-0.525998\pi$
$563$	−3.87164			−0.163170			−0.0815852	+	0.996666i	$0.525998\pi$
$564$		0			0
$565$	−4.52704	+	7.84106i	−0.190454	+	0.329876i
$566$		0			0
$567$	−2.37939	+	4.12122i	−0.0999248	+	0.173075i
$568$		0			0
$569$	−32.9959			−1.38326			−0.691630	−	0.722252i	$-0.743107\pi$
$569$	−32.9959			−1.38326			−0.691630	+	0.722252i	$0.743107\pi$
$570$		0			0
$571$	−24.1789			−1.01186			−0.505928	−	0.862576i	$-0.668850\pi$
$571$	−24.1789			−1.01186			−0.505928	+	0.862576i	$0.668850\pi$
$572$		0			0
$573$	−11.3131	+	19.5949i	−0.472614	+	0.818591i
$574$		0			0
$575$	17.1557	−	29.7145i	0.715442	−	1.23918i
$576$		0			0
$577$	−3.16344			−0.131696			−0.0658478	−	0.997830i	$-0.520975\pi$
$577$	−3.16344			−0.131696			−0.0658478	+	0.997830i	$0.520975\pi$
$578$		0			0
$579$	12.3229	+	21.3440i	0.512124	+	0.887025i
$580$		0			0
$581$	23.3500			0.968721
$582$		0			0
$583$	11.2472	+	19.4807i	0.465812	+	0.806810i
$584$		0			0
$585$	1.87939	+	3.25519i	0.0777030	+	0.134586i
$586$		0			0
$587$	3.00774	−	5.20956i	0.124143	−	0.215022i	−0.797255	−	0.603643i	$-0.793715\pi$
$587$	3.00774	−	5.20956i	0.124143	−	0.215022i	0.921398	+	0.388621i	$0.127049\pi$
$588$		0			0
$589$	5.11886	+	31.7128i	0.210919	+	1.30670i
$590$		0			0
$591$	11.3327	−	19.6289i	0.466167	−	0.807425i
$592$		0			0
$593$	−11.4611	−	19.8512i	−0.470651	−	0.815192i	0.528785	−	0.848756i	$-0.322648\pi$
$593$	−11.4611	−	19.8512i	−0.470651	−	0.815192i	−0.999437	+	0.0335639i	$0.989314\pi$
$594$		0			0
$595$	54.8093	+	94.9326i	2.24696	+	3.89186i
$596$		0			0
$597$	−13.9222			−0.569798
$598$		0			0
$599$	−17.2199	−	29.8257i	−0.703585	−	1.21864i	−0.967200	−	0.254017i	$-0.918248\pi$
$599$	−17.2199	−	29.8257i	−0.703585	−	1.21864i	0.263615	−	0.964628i	$-0.415085\pi$
$600$		0			0
$601$	24.1634			0.985647			0.492824	−	0.870129i	$-0.335965\pi$
$601$	24.1634			0.985647			0.492824	+	0.870129i	$0.335965\pi$
$602$		0			0
$603$	−0.684793	+	1.18610i	−0.0278869	+	0.0483015i
$604$		0			0
$605$	15.2104	−	26.3451i	0.618390	−	1.07108i
$606$		0			0
$607$	−6.84793			−0.277949			−0.138974	−	0.990296i	$-0.544381\pi$
$607$	−6.84793			−0.277949			−0.138974	+	0.990296i	$0.544381\pi$
$608$		0			0
$609$	−25.6459			−1.03922
$610$		0			0
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$		0			0
$613$	−8.47296	+	14.6756i	−0.342220	+	0.592742i	−0.984845	−	0.173439i	$-0.944512\pi$
$613$	−8.47296	+	14.6756i	−0.342220	+	0.592742i	0.642625	+	0.766181i	$0.277845\pi$
$614$		0			0
$615$	−13.2216			−0.533148
$616$		0			0
$617$	−21.1361	−	36.6088i	−0.850907	−	1.47381i	−0.880391	−	0.474249i	$-0.842720\pi$
$617$	−21.1361	−	36.6088i	−0.850907	−	1.47381i	0.0294834	−	0.999565i	$-0.490614\pi$
$618$		0			0
$619$	4.59121			0.184536			0.0922682	−	0.995734i	$-0.470588\pi$
$619$	4.59121			0.184536			0.0922682	+	0.995734i	$0.470588\pi$
$620$		0			0
$621$	−1.87939	−	3.25519i	−0.0754171	−	0.130626i
$622$		0			0
$623$	−19.9145	−	34.4929i	−0.797856	−	1.38193i
$624$		0			0
$625$	−6.34255	+	10.9856i	−0.253702	+	0.439425i
$626$		0			0
$627$	−17.8016	−	6.77314i	−0.710927	−	0.270493i
$628$		0			0
$629$	21.8425	−	37.8324i	0.870919	−	1.50848i
$630$		0			0
$631$	18.7841	+	32.5349i	0.747781	+	1.29520i	0.948884	+	0.315625i	$0.102214\pi$
$631$	18.7841	+	32.5349i	0.747781	+	1.29520i	−0.201103	+	0.979570i	$0.564452\pi$
$632$		0			0
$633$	−1.00980	−	1.74903i	−0.0401360	−	0.0695175i
$634$		0			0
$635$	−1.81345			−0.0719647
$636$		0			0
$637$	−7.82295	−	13.5497i	−0.309956	−	0.536860i
$638$		0			0
$639$	−11.6459			−0.460705
$640$		0			0
$641$	2.75877	−	4.77833i	0.108965	−	0.188733i	−0.806386	−	0.591389i	$-0.798580\pi$
$641$	2.75877	−	4.77833i	0.108965	−	0.188733i	0.915351	+	0.402656i	$0.131913\pi$
$642$		0			0
$643$	17.5915	−	30.4694i	0.693742	−	1.20160i	−0.276861	−	0.960910i	$-0.589294\pi$
$643$	17.5915	−	30.4694i	0.693742	−	1.20160i	0.970603	−	0.240686i	$-0.0773724\pi$
$644$		0			0
$645$	−2.85204			−0.112299
$646$		0			0
$647$	−3.57573			−0.140577			−0.0702883	−	0.997527i	$-0.522392\pi$
$647$	−3.57573			−0.140577			−0.0702883	+	0.997527i	$0.522392\pi$
$648$		0			0
$649$	20.2668	−	35.1032i	0.795542	−	1.37792i
$650$		0			0
$651$	17.5351	−	30.3717i	0.687254	−	1.19036i
$652$		0			0
$653$	32.6418			1.27737			0.638686	−	0.769468i	$-0.279478\pi$
$653$	32.6418			1.27737			0.638686	+	0.769468i	$0.279478\pi$
$654$		0			0
$655$	−6.36959	−	11.0324i	−0.248880	−	0.431073i
$656$		0			0
$657$	4.51754			0.176246
$658$		0			0
$659$	−24.4807	−	42.4018i	−0.953633	−	1.65174i	−0.737466	−	0.675384i	$-0.763978\pi$
$659$	−24.4807	−	42.4018i	−0.953633	−	1.65174i	−0.216167	−	0.976356i	$-0.569355\pi$
$660$		0			0
$661$	−17.7392	−	30.7251i	−0.689974	−	1.19507i	−0.971846	−	0.235618i	$-0.924289\pi$
$661$	−17.7392	−	30.7251i	−0.689974	−	1.19507i	0.281872	−	0.959452i	$-0.409045\pi$
$662$		0			0
$663$	3.06418	−	5.30731i	0.119003	−	0.206119i
$664$		0			0
$665$	72.8718	+	27.7262i	2.82585	+	1.07518i
$666$		0			0
$667$	10.1284	−	17.5428i	0.392171	−	0.679261i
$668$		0			0
$669$	14.1827	+	24.5652i	0.548336	+	0.949746i
$670$		0			0
$671$	−18.6091	−	32.2318i	−0.718395	−	1.24430i
$672$		0			0
$673$	2.68510			0.103503			0.0517514	−	0.998660i	$-0.483520\pi$
$673$	2.68510			0.103503			0.0517514	+	0.998660i	$0.483520\pi$
$674$		0			0
$675$	4.56418	+	7.90539i	0.175675	+	0.304279i
$676$		0			0
$677$	18.3351			0.704676			0.352338	−	0.935873i	$-0.385387\pi$
$677$	18.3351			0.704676			0.352338	+	0.935873i	$0.385387\pi$
$678$		0			0
$679$	27.7101	−	47.9953i	1.06342	−	1.84189i
$680$		0			0
$681$	10.0915	−	17.4790i	0.386708	−	0.669798i
$682$		0			0
$683$	4.07367			0.155875			0.0779374	−	0.996958i	$-0.475167\pi$
$683$	4.07367			0.155875			0.0779374	+	0.996958i	$0.475167\pi$
$684$		0			0
$685$	69.2526			2.64601
$686$		0			0
$687$	5.88919	−	10.2004i	0.224686	−	0.389168i
$688$		0			0
$689$	−2.57398	+	4.45826i	−0.0980608	+	0.169846i
$690$		0			0
$691$	43.5485			1.65666			0.828332	−	0.560238i	$-0.189290\pi$
$691$	43.5485			1.65666			0.828332	+	0.560238i	$0.189290\pi$
$692$		0			0
$693$	10.3969	+	18.0080i	0.394947	+	0.684068i
$694$		0			0
$695$	−0.0736733			−0.00279459
$696$		0			0
$697$	10.7784	+	18.6687i	0.408260	+	0.707127i
$698$		0			0
$699$	−0.0641778	−	0.111159i	−0.00242743	−	0.00420443i
$700$		0			0
$701$	−15.6536	+	27.1129i	−0.591230	+	1.02404i	0.402837	+	0.915272i	$0.368024\pi$
$701$	−15.6536	+	27.1129i	−0.591230	+	1.02404i	−0.994067	+	0.108768i	$0.965309\pi$
$702$		0			0
$703$	−4.95130	−	30.6747i	−0.186742	−	1.15692i
$704$		0			0
$705$	11.2763	−	19.5311i	0.424690	−	0.735585i
$706$		0			0
$707$	9.82295	+	17.0138i	0.369430	+	0.639872i
$708$		0			0
$709$	−11.9047	−	20.6195i	−0.447089	−	0.774381i	0.551106	−	0.834435i	$-0.314206\pi$
$709$	−11.9047	−	20.6195i	−0.447089	−	0.774381i	−0.998195	+	0.0600541i	$0.980873\pi$
$710$		0			0
$711$	14.1480			0.530590
$712$		0			0
$713$	13.8503	+	23.9894i	0.518697	+	0.898410i
$714$		0			0
$715$	16.4243			0.614233
$716$		0			0
$717$	1.55438	−	2.69226i	0.0580493	−	0.100544i
$718$		0			0
$719$	−15.8949	+	27.5307i	−0.592779	+	1.02672i	0.401078	+	0.916044i	$0.368636\pi$
$719$	−15.8949	+	27.5307i	−0.592779	+	1.02672i	−0.993856	+	0.110678i	$0.964698\pi$
$720$		0			0
$721$	−32.1634			−1.19783
$722$		0			0
$723$	−11.2959			−0.420099
$724$		0			0
$725$	−24.5972	+	42.6036i	−0.913517	+	1.58226i
$726$		0			0
$727$	3.22193	−	5.58055i	0.119495	−	0.206971i	−0.800073	−	0.599903i	$-0.795206\pi$
$727$	3.22193	−	5.58055i	0.119495	−	0.206971i	0.919568	+	0.392932i	$0.128539\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	2.32501	+	4.02703i	0.0859935	+	0.148945i
$732$		0			0
$733$	−33.9728			−1.25481			−0.627406	−	0.778692i	$-0.715884\pi$
$733$	−33.9728			−1.25481			−0.627406	+	0.778692i	$0.715884\pi$
$734$		0			0
$735$	−29.4047	−	50.9304i	−1.08461	−	1.87860i
$736$		0			0
$737$	2.99226	+	5.18274i	0.110221	+	0.190909i
$738$		0			0
$739$	−11.4632	+	19.8548i	−0.421679	+	0.730370i	−0.996104	−	0.0881876i	$-0.971893\pi$
$739$	−11.4632	+	19.8548i	−0.421679	+	0.730370i	0.574425	+	0.818557i	$0.305226\pi$
$740$		0			0
$741$	−0.694593	−	4.30320i	−0.0255165	−	0.158082i
$742$		0			0
$743$	3.98276	−	6.89835i	0.146113	−	0.253076i	−0.783674	−	0.621172i	$-0.786657\pi$
$743$	3.98276	−	6.89835i	0.146113	−	0.253076i	0.929788	+	0.368096i	$0.119990\pi$
$744$		0			0
$745$	11.7297	+	20.3164i	0.429742	+	0.744335i
$746$		0			0
$747$	−2.45336	−	4.24935i	−0.0897639	−	0.155476i
$748$		0			0
$749$	−19.6459			−0.717845
$750$		0			0
$751$	11.3794	+	19.7097i	0.415240	+	0.719216i	0.995454	−	0.0952479i	$-0.0303644\pi$
$751$	11.3794	+	19.7097i	0.415240	+	0.719216i	−0.580214	+	0.814464i	$0.697031\pi$
$752$		0			0
$753$	1.51754			0.0553023
$754$		0			0
$755$	1.38919	−	2.40614i	0.0505576	−	0.0875684i
$756$		0			0
$757$	−2.38713	+	4.13462i	−0.0867616	+	0.150275i	−0.906140	−	0.422977i	$-0.860985\pi$
$757$	−2.38713	+	4.13462i	−0.0867616	+	0.150275i	0.819379	+	0.573252i	$0.194318\pi$
$758$		0			0
$759$	−16.4243			−0.596163
$760$		0			0
$761$	28.2222			1.02306			0.511528	−	0.859267i	$-0.329080\pi$
$761$	28.2222			1.02306			0.511528	+	0.859267i	$0.329080\pi$
$762$		0			0
$763$	0.305407	−	0.528981i	0.0110565	−	0.0191504i
$764$		0			0
$765$	11.5175	−	19.9490i	0.416418	−	0.721256i
$766$		0			0
$767$	9.27631			0.334948
$768$		0			0
$769$	−12.1108	−	20.9765i	−0.436727	−	0.756434i	0.560708	−	0.828014i	$-0.310529\pi$
$769$	−12.1108	−	20.9765i	−0.436727	−	0.756434i	−0.997435	+	0.0715802i	$0.977196\pi$
$770$		0			0
$771$	12.1830			0.438761
$772$		0			0
$773$	−11.9804	−	20.7507i	−0.430905	−	0.746349i	0.566046	−	0.824373i	$-0.308472\pi$
$773$	−11.9804	−	20.7507i	−0.430905	−	0.746349i	−0.996951	+	0.0780239i	$0.975139\pi$
$774$		0			0
$775$	−33.6361	−	58.2594i	−1.20824	−	2.09274i
$776$		0			0
$777$	−16.9611	+	29.3775i	−0.608476	+	1.05391i
$778$		0			0
$779$	14.3304	+	5.45242i	0.513439	+	0.195353i
$780$		0			0
$781$	−25.4439	+	44.0701i	−0.910453	+	1.57695i
$782$		0			0
$783$	2.69459	+	4.66717i	0.0962969	+	0.166791i
$784$		0			0
$785$	−12.4902	−	21.6337i	−0.445794	−	0.772138i
$786$		0			0
$787$	−28.8871			−1.02971			−0.514857	−	0.857276i	$-0.672155\pi$
$787$	−28.8871			−1.02971			−0.514857	+	0.857276i	$0.672155\pi$
$788$		0			0
$789$	−9.69459	−	16.7915i	−0.345137	−	0.597794i
$790$		0			0
$791$	−11.4629			−0.407572
$792$		0			0
$793$	4.25877	−	7.37641i	0.151233	−	0.261944i
$794$		0			0
$795$	−9.67499	+	16.7576i	−0.343137	+	0.594330i
$796$		0			0
$797$	−7.61493			−0.269735			−0.134867	−	0.990864i	$-0.543061\pi$
$797$	−7.61493			−0.269735			−0.134867	+	0.990864i	$0.543061\pi$
$798$		0			0
$799$	−36.7701			−1.30083
$800$		0			0
$801$	−4.18479	+	7.24827i	−0.147862	+	0.256105i
$802$		0			0
$803$	9.86989	−	17.0952i	0.348301	−	0.603275i
$804$		0			0
$805$	67.2336			2.36967
$806$		0			0
$807$	11.7023	+	20.2690i	0.411942	+	0.713504i
$808$		0			0
$809$	22.5681			0.793452			0.396726	−	0.917937i	$-0.370146\pi$
$809$	22.5681			0.793452			0.396726	+	0.917937i	$0.370146\pi$
$810$		0			0
$811$	12.3696	+	21.4247i	0.434355	+	0.752325i	0.997243	−	0.0742086i	$-0.0236431\pi$
$811$	12.3696	+	21.4247i	0.434355	+	0.752325i	−0.562888	+	0.826533i	$0.690310\pi$
$812$		0			0
$813$	0.482459	+	0.835644i	0.0169206	+	0.0293073i
$814$		0			0
$815$	−21.3678	+	37.0102i	−0.748482	+	1.29641i
$816$		0			0
$817$	3.09121	+	1.17614i	0.108148	+	0.0411481i
$818$		0			0
$819$	−2.37939	+	4.12122i	−0.0831424	+	0.144007i
$820$		0			0
$821$	9.30541	+	16.1174i	0.324761	+	0.562502i	0.981464	−	0.191647i	$-0.0613828\pi$
$821$	9.30541	+	16.1174i	0.324761	+	0.562502i	−0.656703	+	0.754149i	$0.728049\pi$
$822$		0			0
$823$	10.9804	+	19.0186i	0.382753	+	0.662947i	0.991455	−	0.130452i	$-0.0416428\pi$
$823$	10.9804	+	19.0186i	0.382753	+	0.662947i	−0.608702	+	0.793399i	$0.708309\pi$
$824$		0			0
$825$	39.8871			1.38869
$826$		0			0
$827$	12.9513	+	22.4323i	0.450361	+	0.780048i	0.998408	−	0.0563993i	$-0.0179620\pi$
$827$	12.9513	+	22.4323i	0.450361	+	0.780048i	−0.548047	+	0.836447i	$0.684629\pi$
$828$		0			0
$829$	−43.0310			−1.49453			−0.747264	−	0.664528i	$-0.768633\pi$
$829$	−43.0310			−1.49453			−0.747264	+	0.664528i	$0.768633\pi$
$830$		0			0
$831$	7.69459	−	13.3274i	0.266922	−	0.462323i
$832$		0			0
$833$	−47.9418	+	83.0376i	−1.66109	+	2.87708i
$834$		0			0
$835$	−11.2026			−0.387683
$836$		0			0
$837$	−7.36959			−0.254730
$838$		0			0
$839$	−4.16519	+	7.21432i	−0.143798	+	0.249066i	−0.928924	−	0.370270i	$-0.879265\pi$
$839$	−4.16519	+	7.21432i	−0.143798	+	0.249066i	0.785126	+	0.619337i	$0.212598\pi$
$840$		0			0
$841$	−0.0216598	+	0.0375158i	−0.000746888	+	0.00129365i
$842$		0			0
$843$	−8.49794			−0.292685
$844$		0			0
$845$	−22.5526	−	39.0623i	−0.775834	−	1.34378i
$846$		0			0
$847$	38.5140			1.32336
$848$		0			0
$849$	−5.51754	−	9.55666i	−0.189362	−	0.327984i
$850$		0			0
$851$	−13.3969	−	23.2042i	−0.459241	−	0.795428i
$852$		0			0
$853$	21.6925	−	37.5726i	0.742738	−	1.28646i	−0.208506	−	0.978021i	$-0.566860\pi$
$853$	21.6925	−	37.5726i	0.742738	−	1.28646i	0.951244	−	0.308439i	$-0.0998066\pi$
$854$		0			0
$855$	−2.61081	−	16.1747i	−0.0892880	−	0.553165i
$856$		0			0
$857$	−17.2567	+	29.8895i	−0.589478	+	1.02101i	0.404823	+	0.914395i	$0.367333\pi$
$857$	−17.2567	+	29.8895i	−0.589478	+	1.02101i	−0.994301	+	0.106611i	$0.966000\pi$
$858$		0			0
$859$	9.08946	+	15.7434i	0.310128	+	0.537158i	0.978390	−	0.206768i	$-0.0662946\pi$
$859$	9.08946	+	15.7434i	0.310128	+	0.537158i	−0.668262	+	0.743926i	$0.732961\pi$
$860$		0			0
$861$	−8.36959	−	14.4965i	−0.285235	−	0.494041i
$862$		0			0
$863$	44.3269			1.50890			0.754452	−	0.656355i	$-0.227903\pi$
$863$	44.3269			1.50890			0.754452	+	0.656355i	$0.227903\pi$
$864$		0			0
$865$	−10.1284	−	17.5428i	−0.344374	−	0.596474i
$866$		0			0
$867$	−20.5567			−0.698144
$868$		0			0
$869$	30.9103	−	53.5383i	1.04856	−	1.81616i
$870$		0			0
$871$	−0.684793	+	1.18610i	−0.0232033	+	0.0401893i
$872$		0			0
$873$	−11.6459			−0.394154
$874$		0			0
$875$	−73.8444			−2.49640
$876$		0			0
$877$	−5.95336	+	10.3115i	−0.201031	+	0.348196i	−0.948861	−	0.315695i	$-0.897762\pi$
$877$	−5.95336	+	10.3115i	−0.201031	+	0.348196i	0.747830	+	0.663890i	$0.231096\pi$
$878$		0			0
$879$	−0.517541	+	0.896407i	−0.0174562	+	0.0302351i
$880$		0			0
$881$	28.9804			0.976374			0.488187	−	0.872739i	$-0.337658\pi$
$881$	28.9804			0.976374			0.488187	+	0.872739i	$0.337658\pi$
$882$		0			0
$883$	−2.23143	−	3.86495i	−0.0750936	−	0.130066i	0.826033	−	0.563621i	$-0.190592\pi$
$883$	−2.23143	−	3.86495i	−0.0750936	−	0.130066i	−0.901127	+	0.433555i	$0.857259\pi$
$884$		0			0
$885$	34.8675			1.17206
$886$		0			0
$887$	14.1557	+	24.5184i	0.475302	+	0.823247i	0.999600	−	0.0282880i	$-0.00900555\pi$
$887$	14.1557	+	24.5184i	0.475302	+	0.823247i	−0.524298	+	0.851535i	$0.675672\pi$
$888$		0			0
$889$	−1.14796	−	1.98832i	−0.0385012	−	0.0666860i
$890$		0			0
$891$	2.18479	−	3.78417i	0.0731933	−	0.126775i
$892$		0			0
$893$	−20.2763	+	16.5188i	−0.678521	+	0.552781i
$894$		0			0
$895$	7.97090	−	13.8060i	0.266438	−	0.461484i
$896$		0			0
$897$	−1.87939	−	3.25519i	−0.0627508	−	0.108688i
$898$		0			0
$899$	−19.8580	−	34.3951i	−0.662302	−	1.14714i
$900$		0			0
$901$	31.5485			1.05103
$902$		0			0
$903$	−1.80541	−	3.12706i	−0.0600802	−	0.104062i
$904$		0			0
$905$	−47.4012			−1.57567
$906$		0			0
$907$	−10.2567	+	17.7651i	−0.340569	+	0.589882i	−0.984538	−	0.175169i	$-0.943953\pi$
$907$	−10.2567	+	17.7651i	−0.340569	+	0.589882i	0.643970	+	0.765051i	$0.277286\pi$
$908$		0			0
$909$	2.06418	−	3.57526i	0.0684645	−	0.118584i
$910$		0			0
$911$	21.9608			0.727594			0.363797	−	0.931478i	$-0.381480\pi$
$911$	21.9608			0.727594			0.363797	+	0.931478i	$0.381480\pi$
$912$		0			0
$913$	−21.4404			−0.709572
$914$		0			0
$915$	16.0077	−	27.7262i	0.529200	−	0.916601i
$916$		0			0
$917$	8.06418	−	13.9676i	0.266303	−	0.461250i
$918$		0			0
$919$	−22.0898			−0.728674			−0.364337	−	0.931267i	$-0.618704\pi$
$919$	−22.0898			−0.728674			−0.364337	+	0.931267i	$0.618704\pi$
$920$		0			0
$921$	7.43376	+	12.8757i	0.244951	+	0.424267i
$922$		0			0
$923$	−11.6459			−0.383329
$924$		0			0
$925$	32.5351	+	56.3524i	1.06975	+	1.85286i
$926$		0			0
$927$	3.37939	+	5.85327i	0.110994	+	0.192247i
$928$		0			0
$929$	−26.2645	+	45.4914i	−0.861709	+	1.49252i	0.00856978	+	0.999963i	$0.497272\pi$
$929$	−26.2645	+	45.4914i	−0.861709	+	1.49252i	−0.870278	+	0.492560i	$0.836061\pi$
$930$		0			0
$931$	10.8675	+	67.3274i	0.356169	+	2.20657i
$932$		0			0
$933$	−8.02734	+	13.9038i	−0.262803	+	0.455189i
$934$		0			0
$935$	−50.3269	−	87.1687i	−1.64586	−	2.85072i
$936$		0			0
$937$	12.9688	+	22.4627i	0.423674	+	0.733824i	0.996296	−	0.0859953i	$-0.0274070\pi$
$937$	12.9688	+	22.4627i	0.423674	+	0.733824i	−0.572622	+	0.819820i	$0.694074\pi$
$938$		0			0
$939$	−35.1634			−1.14752
$940$		0			0
$941$	−8.90673	−	15.4269i	−0.290351	−	0.502903i	0.683542	−	0.729911i	$-0.260439\pi$
$941$	−8.90673	−	15.4269i	−0.290351	−	0.502903i	−0.973893	+	0.227009i	$0.927105\pi$
$942$		0			0
$943$	13.2216			0.430555
$944$		0			0
$945$	−8.94356	+	15.4907i	−0.290934	+	0.503913i
$946$		0			0
$947$	17.0446	−	29.5221i	0.553874	−	0.959339i	−0.444116	−	0.895969i	$-0.646482\pi$
$947$	17.0446	−	29.5221i	0.553874	−	0.959339i	0.997990	−	0.0633691i	$-0.0201845\pi$
$948$		0			0
$949$	4.51754			0.146646
$950$		0			0
$951$	−18.5371			−0.601108
$952$		0			0
$953$	6.34224	−	10.9851i	0.205445	−	0.355842i	−0.744829	−	0.667255i	$-0.767469\pi$
$953$	6.34224	−	10.9851i	0.205445	−	0.355842i	0.950275	+	0.311413i	$0.100802\pi$
$954$		0			0
$955$	−42.5235	+	73.6529i	−1.37603	+	2.38335i
$956$		0			0
$957$	23.5485			0.761215
$958$		0			0
$959$	43.8384	+	75.9304i	1.41562	+	2.45192i
$960$		0			0
$961$	23.3108			0.751961
$962$		0			0
$963$	2.06418	+	3.57526i	0.0665172	+	0.115211i
$964$		0			0
$965$	46.3191	+	80.2271i	1.49107	+	2.58260i
$966$		0			0
$967$	23.6266	−	40.9225i	0.759780	−	1.31598i	−0.183182	−	0.983079i	$-0.558640\pi$
$967$	23.6266	−	40.9225i	0.759780	−	1.31598i	0.942962	−	0.332899i	$-0.108027\pi$
$968$		0			0
$969$	−20.7101	+	16.8722i	−0.665303	+	0.542013i
$970$		0			0
$971$	17.6810	−	30.6244i	0.567410	−	0.982782i	−0.429411	−	0.903109i	$-0.641279\pi$
$971$	17.6810	−	30.6244i	0.567410	−	0.982782i	0.996821	−	0.0796733i	$-0.0253877\pi$
$972$		0			0
$973$	−0.0466368	−	0.0807773i	−0.00149511	−	0.00258960i
$974$		0			0
$975$	4.56418	+	7.90539i	0.146171	+	0.253175i
$976$		0			0
$977$	45.0660			1.44179			0.720895	−	0.693044i	$-0.243731\pi$
$977$	45.0660			1.44179			0.720895	+	0.693044i	$0.243731\pi$
$978$		0			0
$979$	18.2858	+	31.6719i	0.584417	+	1.01224i
$980$		0			0
$981$	−0.128356			−0.00409808
$982$		0			0
$983$	13.0915	−	22.6752i	0.417555	−	0.723226i	−0.578138	−	0.815939i	$-0.696221\pi$
$983$	13.0915	−	22.6752i	0.417555	−	0.723226i	0.995693	+	0.0927130i	$0.0295539\pi$
$984$		0			0
$985$	42.5972	−	73.7805i	1.35726	−	2.35084i
$986$		0			0
$987$	28.5526			0.908840
$988$		0			0
$989$	2.85204			0.0906897
$990$		0			0
$991$	10.6070	−	18.3719i	0.336942	−	0.583601i	−0.646914	−	0.762563i	$-0.723941\pi$
$991$	10.6070	−	18.3719i	0.336942	−	0.583601i	0.983856	+	0.178962i	$0.0572739\pi$
$992$		0			0
$993$	−4.37939	+	7.58532i	−0.138976	+	0.240713i
$994$		0			0
$995$	−52.3304			−1.65898
$996$		0			0
$997$	27.1364	+	47.0016i	0.859418	+	1.48856i	0.872485	+	0.488642i	$0.162507\pi$
$997$	27.1364	+	47.0016i	0.859418	+	1.48856i	−0.0130661	+	0.999915i	$0.504159\pi$
$998$		0			0
$999$	7.12836			0.225531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.q.f.49.3	✓	6
3.2	odd	2		1368.2.s.j.505.1		6
4.3	odd	2		912.2.q.k.49.3		6
12.11	even	2		2736.2.s.x.1873.1		6
19.7	even	3	inner	456.2.q.f.121.3	yes	6
19.8	odd	6		8664.2.a.z.1.1		3
19.11	even	3		8664.2.a.x.1.1		3
57.26	odd	6		1368.2.s.j.577.1		6
76.7	odd	6		912.2.q.k.577.3		6
228.83	even	6		2736.2.s.x.577.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.q.f.49.3	✓	6	1.1	even	1	trivial
456.2.q.f.121.3	yes	6	19.7	even	3	inner
912.2.q.k.49.3		6	4.3	odd	2
912.2.q.k.577.3		6	76.7	odd	6
1368.2.s.j.505.1		6	3.2	odd	2
1368.2.s.j.577.1		6	57.26	odd	6
2736.2.s.x.577.1		6	228.83	even	6
2736.2.s.x.1873.1		6	12.11	even	2
8664.2.a.x.1.1		3	19.11	even	3
8664.2.a.z.1.1		3	19.8	odd	6

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.87939 - 3.25519i) q^{5} +4.75877 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.87939 - 3.25519i) q^{5} +4.75877 q^{7} +(-0.500000 - 0.866025i) q^{9} -4.36959 q^{11} +(-0.500000 - 0.866025i) q^{13} +(-1.87939 - 3.25519i) q^{15} +(-3.06418 + 5.30731i) q^{17} +(0.694593 + 4.30320i) q^{19} +(2.37939 - 4.12122i) q^{21} +(1.87939 + 3.25519i) q^{23} +(-4.56418 - 7.90539i) q^{25} -1.00000 q^{27} +(-2.69459 - 4.66717i) q^{29} +7.36959 q^{31} +(-2.18479 + 3.78417i) q^{33} +(8.94356 - 15.4907i) q^{35} -7.12836 q^{37} -1.00000 q^{39} +(1.75877 - 3.04628i) q^{41} +(0.379385 - 0.657115i) q^{43} -3.75877 q^{45} +(3.00000 + 5.19615i) q^{47} +15.6459 q^{49} +(3.06418 + 5.30731i) q^{51} +(-2.57398 - 4.45826i) q^{53} +(-8.21213 + 14.2238i) q^{55} +(4.07398 + 1.55007i) q^{57} +(-4.63816 + 8.03352i) q^{59} +(4.25877 + 7.37641i) q^{61} +(-2.37939 - 4.12122i) q^{63} -3.75877 q^{65} +(-0.684793 - 1.18610i) q^{67} +3.75877 q^{69} +(5.82295 - 10.0856i) q^{71} +(-2.25877 + 3.91231i) q^{73} -9.12836 q^{75} -20.7939 q^{77} +(-7.07398 + 12.2525i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.90673 q^{83} +(11.5175 + 19.9490i) q^{85} -5.38919 q^{87} +(-4.18479 - 7.24827i) q^{89} +(-2.37939 - 4.12122i) q^{91} +(3.68479 - 6.38225i) q^{93} +(15.3131 + 5.82634i) q^{95} +(5.82295 - 10.0856i) q^{97} +(2.18479 + 3.78417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9	\( 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9} - 12 q^{11} - 3 q^{13} + 3 q^{21} - 9 q^{25} - 6 q^{27} - 12 q^{29} + 30 q^{31} - 6 q^{33} + 24 q^{35} - 6 q^{37} - 6 q^{39} - 12 q^{41} - 9 q^{43} + 18 q^{47} + 12 q^{49} + 9 q^{57} + 6 q^{59} + 3 q^{61} - 3 q^{63} + 3 q^{67} - 6 q^{71} + 9 q^{73} - 18 q^{75} - 12 q^{77} - 27 q^{79} - 3 q^{81} - 24 q^{83} + 24 q^{85} - 24 q^{87} - 18 q^{89} - 3 q^{91} + 15 q^{93} + 48 q^{95} - 6 q^{97} + 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9 - 12 * q^11 - 3 * q^13 + 3 * q^21 - 9 * q^25 - 6 * q^27 - 12 * q^29 + 30 * q^31 - 6 * q^33 + 24 * q^35 - 6 * q^37 - 6 * q^39 - 12 * q^41 - 9 * q^43 + 18 * q^47 + 12 * q^49 + 9 * q^57 + 6 * q^59 + 3 * q^61 - 3 * q^63 + 3 * q^67 - 6 * q^71 + 9 * q^73 - 18 * q^75 - 12 * q^77 - 27 * q^79 - 3 * q^81 - 24 * q^83 + 24 * q^85 - 24 * q^87 - 18 * q^89 - 3 * q^91 + 15 * q^93 + 48 * q^95 - 6 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

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Database

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