LMFDB - Embedded newform 1456.2.cc.d.673.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.3
Root			$0.500000 - 0.399480i$ of defining polynomial
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.d.225.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.233273 - 0.404040i) q^{3} +3.38938i q^{5} +(-0.866025 - 0.500000i) q^{7} +(1.39117 - 2.40957i) q^{9} +O(q^{10})$	\(q+(-0.233273 - 0.404040i) q^{3} +3.38938i q^{5} +(-0.866025 - 0.500000i) q^{7} +(1.39117 - 2.40957i) q^{9} +(-0.712505 + 0.411365i) q^{11} +(-2.74987 + 2.33200i) q^{13} +(1.36944 - 0.790648i) q^{15} +(2.29065 - 3.96752i) q^{17} +(5.11492 + 2.95310i) q^{19} +0.466545i q^{21} +(3.06527 + 5.30921i) q^{23} -6.48787 q^{25} -2.69772 q^{27} +(3.43406 + 5.94797i) q^{29} -4.28683i q^{31} +(0.332416 + 0.191920i) q^{33} +(1.69469 - 2.93529i) q^{35} +(-8.39253 + 4.84543i) q^{37} +(1.58369 + 0.567065i) q^{39} +(-0.0774019 + 0.0446880i) q^{41} +(-3.67687 + 6.36853i) q^{43} +(8.16695 + 4.71519i) q^{45} +11.1759i q^{47} +(0.500000 + 0.866025i) q^{49} -2.13738 q^{51} -7.01530 q^{53} +(-1.39427 - 2.41495i) q^{55} -2.75551i q^{57} +(-1.50790 - 0.870585i) q^{59} +(-1.18972 + 2.06066i) q^{61} +(-2.40957 + 1.39117i) q^{63} +(-7.90403 - 9.32034i) q^{65} +(-0.252636 + 0.145859i) q^{67} +(1.43009 - 2.47698i) q^{69} +(-9.48158 - 5.47419i) q^{71} +12.7187i q^{73} +(1.51344 + 2.62136i) q^{75} +0.822730 q^{77} -9.95602 q^{79} +(-3.54420 - 6.13873i) q^{81} +3.23553i q^{83} +(13.4474 + 7.76387i) q^{85} +(1.60215 - 2.77500i) q^{87} +(6.96514 - 4.02133i) q^{89} +(3.54746 - 0.644638i) q^{91} +(-1.73205 + 1.00000i) q^{93} +(-10.0092 + 17.3364i) q^{95} +(12.7945 + 7.38693i) q^{97} +2.28911i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 6 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 - 6 * q^9	$ 12 q + 2 q^{3} - 6 q^{9} + 18 q^{11} - 8 q^{13} + 6 q^{15} + 4 q^{17} - 12 q^{19} + 6 q^{23} - 24 q^{25} - 40 q^{27} - 10 q^{29} + 12 q^{33} - 2 q^{35} - 6 q^{37} + 54 q^{39} - 24 q^{41} - 26 q^{43} + 72 q^{45} + 6 q^{49} + 36 q^{51} + 36 q^{53} + 6 q^{55} - 6 q^{59} - 28 q^{61} - 34 q^{65} + 42 q^{67} + 32 q^{69} - 48 q^{71} + 48 q^{75} - 4 q^{77} - 44 q^{79} - 34 q^{81} + 54 q^{85} - 2 q^{87} + 12 q^{89} + 16 q^{91} - 32 q^{95} + 60 q^{97}+O(q^{100}) $ 12 * q + 2 * q^3 - 6 * q^9 + 18 * q^11 - 8 * q^13 + 6 * q^15 + 4 * q^17 - 12 * q^19 + 6 * q^23 - 24 * q^25 - 40 * q^27 - 10 * q^29 + 12 * q^33 - 2 * q^35 - 6 * q^37 + 54 * q^39 - 24 * q^41 - 26 * q^43 + 72 * q^45 + 6 * q^49 + 36 * q^51 + 36 * q^53 + 6 * q^55 - 6 * q^59 - 28 * q^61 - 34 * q^65 + 42 * q^67 + 32 * q^69 - 48 * q^71 + 48 * q^75 - 4 * q^77 - 44 * q^79 - 34 * q^81 + 54 * q^85 - 2 * q^87 + 12 * q^89 + 16 * q^91 - 32 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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
$3$	−0.233273	−	0.404040i	−0.134680	−	0.233273i	0.790795	−	0.612081i	$-0.209667\pi$
$3$	−0.233273	−	0.404040i	−0.134680	−	0.233273i	−0.925475	+	0.378808i	$0.876334\pi$
$4$		0			0
$5$			3.38938i			1.51578i	0.652385	+	0.757888i	$0.273768\pi$
$5$			3.38938i			1.51578i	−0.652385	+	0.757888i	$0.726232\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		0			0
$9$	1.39117	−	2.40957i	0.463723	−	0.803191i
$10$		0			0
$11$	−0.712505	+	0.411365i	−0.214828	+	0.124031i	−0.603553	−	0.797323i	$-0.706249\pi$
$11$	−0.712505	+	0.411365i	−0.214828	+	0.124031i	0.388725	+	0.921354i	$0.372916\pi$
$12$		0			0
$13$	−2.74987	+	2.33200i	−0.762676	+	0.646781i
$13$	−2.74987	+	2.33200i	−0.762676	+	0.646781i
$14$		0			0
$15$	1.36944	−	0.790648i	0.353589	−	0.204145i
$16$		0			0
$17$	2.29065	−	3.96752i	0.555564	−	0.962265i	−0.442296	−	0.896869i	$-0.645836\pi$
$17$	2.29065	−	3.96752i	0.555564	−	0.962265i	0.997859	−	0.0653954i	$-0.0208309\pi$
$18$		0			0
$19$	5.11492	+	2.95310i	1.17344	+	0.677488i	0.954489	−	0.298247i	$-0.0964018\pi$
$19$	5.11492	+	2.95310i	1.17344	+	0.677488i	0.218955	+	0.975735i	$0.429735\pi$
$20$		0			0
$21$			0.466545i			0.101808i
$22$		0			0
$23$	3.06527	+	5.30921i	0.639154	+	1.10705i	0.985619	+	0.168984i	$0.0540485\pi$
$23$	3.06527	+	5.30921i	0.639154	+	1.10705i	−0.346465	+	0.938063i	$0.612618\pi$
$24$		0			0
$25$	−6.48787			−1.29757
$26$		0			0
$27$	−2.69772			−0.519176
$28$		0			0
$29$	3.43406	+	5.94797i	0.637690	+	1.10451i	0.985938	+	0.167109i	$0.0534431\pi$
$29$	3.43406	+	5.94797i	0.637690	+	1.10451i	−0.348249	+	0.937402i	$0.613224\pi$
$30$		0			0
$31$		−	4.28683i		−	0.769938i	−0.922930	−	0.384969i	$-0.874212\pi$
$31$		−	4.28683i		−	0.769938i	0.922930	−	0.384969i	$-0.125788\pi$
$32$		0			0
$33$	0.332416	+	0.191920i	0.0578662	+	0.0334090i
$34$		0			0
$35$	1.69469	−	2.93529i	0.286455	−	0.496154i
$36$		0			0
$37$	−8.39253	+	4.84543i	−1.37972	+	0.796584i	−0.992126	−	0.125245i	$-0.960028\pi$
$37$	−8.39253	+	4.84543i	−1.37972	+	0.796584i	−0.387598	+	0.921829i	$0.626695\pi$
$38$		0			0
$39$	1.58369	+	0.567065i	0.253593	+	0.0908030i
$40$		0			0
$41$	−0.0774019	+	0.0446880i	−0.0120881	+	0.00697909i	−0.506032	−	0.862515i	$-0.668888\pi$
$41$	−0.0774019	+	0.0446880i	−0.0120881	+	0.00697909i	0.493944	+	0.869494i	$0.335555\pi$
$42$		0			0
$43$	−3.67687	+	6.36853i	−0.560718	+	0.971191i	0.436716	+	0.899599i	$0.356141\pi$
$43$	−3.67687	+	6.36853i	−0.560718	+	0.971191i	−0.997434	+	0.0715921i	$0.977192\pi$
$44$		0			0
$45$	8.16695	+	4.71519i	1.21746	+	0.702899i
$46$		0			0
$47$			11.1759i			1.63018i	0.579335	+	0.815089i	$0.303312\pi$
$47$			11.1759i			1.63018i	−0.579335	+	0.815089i	$0.696688\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	−2.13738			−0.299293
$52$		0			0
$53$	−7.01530			−0.963625			−0.481813	−	0.876274i	$-0.660021\pi$
$53$	−7.01530			−0.963625			−0.481813	+	0.876274i	$0.660021\pi$
$54$		0			0
$55$	−1.39427	−	2.41495i	−0.188003	−	0.325632i
$56$		0			0
$57$		−	2.75551i		−	0.364976i
$58$		0			0
$59$	−1.50790	−	0.870585i	−0.196311	−	0.113340i	0.398622	−	0.917115i	$-0.369488\pi$
$59$	−1.50790	−	0.870585i	−0.196311	−	0.113340i	−0.594934	+	0.803775i	$0.702822\pi$
$60$		0			0
$61$	−1.18972	+	2.06066i	−0.152329	+	0.263841i	−0.932083	−	0.362245i	$-0.882011\pi$
$61$	−1.18972	+	2.06066i	−0.152329	+	0.263841i	0.779754	+	0.626085i	$0.215344\pi$
$62$		0			0
$63$	−2.40957	+	1.39117i	−0.303578	+	0.175271i
$64$		0			0
$65$	−7.90403	−	9.32034i	−0.980374	−	1.15605i
$66$		0			0
$67$	−0.252636	+	0.145859i	−0.0308644	+	0.0178196i	−0.515353	−	0.856978i	$-0.672339\pi$
$67$	−0.252636	+	0.145859i	−0.0308644	+	0.0178196i	0.484488	+	0.874798i	$0.339006\pi$
$68$		0			0
$69$	1.43009	−	2.47698i	0.172162	−	0.298194i
$70$		0			0
$71$	−9.48158	−	5.47419i	−1.12526	−	0.649667i	−0.182519	−	0.983202i	$-0.558425\pi$
$71$	−9.48158	−	5.47419i	−1.12526	−	0.649667i	−0.942738	+	0.333535i	$0.891758\pi$
$72$		0			0
$73$			12.7187i			1.48861i	0.667841	+	0.744304i	$0.267219\pi$
$73$			12.7187i			1.48861i	−0.667841	+	0.744304i	$0.732781\pi$
$74$		0			0
$75$	1.51344	+	2.62136i	0.174757	+	0.302688i
$76$		0			0
$77$	0.822730			0.0937588
$78$		0			0
$79$	−9.95602			−1.12014			−0.560070	−	0.828445i	$-0.689226\pi$
$79$	−9.95602			−1.12014			−0.560070	+	0.828445i	$0.689226\pi$
$80$		0			0
$81$	−3.54420	−	6.13873i	−0.393800	−	0.682082i
$82$		0			0
$83$			3.23553i			0.355146i	0.984108	+	0.177573i	$0.0568246\pi$
$83$			3.23553i			0.355146i	−0.984108	+	0.177573i	$0.943175\pi$
$84$		0			0
$85$	13.4474	+	7.76387i	1.45858	+	0.842110i
$86$		0			0
$87$	1.60215	−	2.77500i	0.171768	−	0.297511i
$88$		0			0
$89$	6.96514	−	4.02133i	0.738303	−	0.426260i	−0.0831487	−	0.996537i	$-0.526498\pi$
$89$	6.96514	−	4.02133i	0.738303	−	0.426260i	0.821452	+	0.570277i	$0.193164\pi$
$90$		0			0
$91$	3.54746	−	0.644638i	0.371874	−	0.0675764i
$92$		0			0
$93$	−1.73205	+	1.00000i	−0.179605	+	0.103695i
$94$		0			0
$95$	−10.0092	+	17.3364i	−1.02692	+	1.77868i
$96$		0			0
$97$	12.7945	+	7.38693i	1.29909	+	0.750029i	0.980247	−	0.197778i	$-0.0633726\pi$
$97$	12.7945	+	7.38693i	1.29909	+	0.750029i	0.318842	+	0.947808i	$0.396706\pi$
$98$		0			0
$99$			2.28911i			0.230064i
$100$		0			0
$101$	−4.11988	−	7.13584i	−0.409943	−	0.710043i	0.584939	−	0.811077i	$-0.301118\pi$
$101$	−4.11988	−	7.13584i	−0.409943	−	0.710043i	−0.994883	+	0.101034i	$0.967785\pi$
$102$		0			0
$103$	13.3231			1.31277			0.656383	−	0.754428i	$-0.272086\pi$
$103$	13.3231			1.31277			0.656383	+	0.754428i	$0.272086\pi$
$104$		0			0
$105$	−1.58130			−0.154319
$106$		0			0
$107$	−4.51325	−	7.81717i	−0.436312	−	0.755715i	0.561090	−	0.827755i	$-0.310382\pi$
$107$	−4.51325	−	7.81717i	−0.436312	−	0.755715i	−0.997402	+	0.0720404i	$0.977049\pi$
$108$		0			0
$109$			0.397192i			0.0380441i	0.999819	+	0.0190220i	$0.00605527\pi$
$109$			0.397192i			0.0380441i	−0.999819	+	0.0190220i	$0.993945\pi$
$110$		0			0
$111$	3.91549	+	2.26061i	0.371642	+	0.214568i
$112$		0			0
$113$	−2.23661	+	3.87392i	−0.210402	+	0.364428i	−0.951841	−	0.306594i	$-0.900811\pi$
$113$	−2.23661	+	3.87392i	−0.210402	+	0.364428i	0.741438	+	0.671021i	$0.234144\pi$
$114$		0			0
$115$	−17.9949	+	10.3894i	−1.67803	+	0.968813i
$116$		0			0
$117$	1.79360	+	9.87021i	0.165818	+	0.912502i
$118$		0			0
$119$	−3.96752	+	2.29065i	−0.363702	+	0.209983i
$120$		0			0
$121$	−5.16156	+	8.94008i	−0.469232	+	0.812735i
$122$		0			0
$123$	0.0361115	+	0.0208490i	0.00325606	+	0.00187989i
$124$		0			0
$125$		−	5.04295i		−	0.451056i
$126$		0			0
$127$	0.270063	+	0.467763i	0.0239642	+	0.0415073i	0.877759	−	0.479103i	$-0.159038\pi$
$127$	0.270063	+	0.467763i	0.0239642	+	0.0415073i	−0.853795	+	0.520610i	$0.825705\pi$
$128$		0			0
$129$	3.43085			0.302070
$130$		0			0
$131$	7.72615			0.675037			0.337518	−	0.941319i	$-0.390413\pi$
$131$	7.72615			0.675037			0.337518	+	0.941319i	$0.390413\pi$
$132$		0			0
$133$	−2.95310	−	5.11492i	−0.256067	−	0.443520i
$134$		0			0
$135$		−	9.14359i		−	0.786955i
$136$		0			0
$137$	10.8600	+	6.27005i	0.927837	+	0.535687i	0.886127	−	0.463443i	$-0.153386\pi$
$137$	10.8600	+	6.27005i	0.927837	+	0.535687i	0.0417099	+	0.999130i	$0.486719\pi$
$138$		0			0
$139$	6.04868	−	10.4766i	0.513042	−	0.888615i	−0.486843	−	0.873489i	$-0.661852\pi$
$139$	6.04868	−	10.4766i	0.513042	−	0.888615i	0.999886	−	0.0151258i	$-0.00481487\pi$
$140$		0			0
$141$	4.51553	−	2.60704i	0.380276	−	0.219552i
$142$		0			0
$143$	0.999992	−	2.79276i	0.0836235	−	0.233543i
$144$		0			0
$145$	−20.1599	+	11.6393i	−1.67419	+	0.966594i
$146$		0			0
$147$	0.233273	−	0.404040i	0.0192400	−	0.0333246i
$148$		0			0
$149$	14.7292	+	8.50389i	1.20666	+	0.696666i	0.962028	−	0.272950i	$-0.0879992\pi$
$149$	14.7292	+	8.50389i	1.20666	+	0.696666i	0.244633	+	0.969616i	$0.421333\pi$
$150$		0			0
$151$			5.54567i			0.451300i	0.974208	+	0.225650i	$0.0724506\pi$
$151$			5.54567i			0.451300i	−0.974208	+	0.225650i	$0.927549\pi$
$152$		0			0
$153$	−6.37335	−	11.0390i	−0.515255	−	0.892448i
$154$		0			0
$155$	14.5297			1.16705
$156$		0			0
$157$	2.29353			0.183044			0.0915218	−	0.995803i	$-0.470827\pi$
$157$	2.29353			0.183044			0.0915218	+	0.995803i	$0.470827\pi$
$158$		0			0
$159$	1.63648	+	2.83446i	0.129781	+	0.224787i
$160$		0			0
$161$		−	6.13055i		−	0.483155i
$162$		0			0
$163$	20.2269	+	11.6780i	1.58429	+	0.914691i	0.994223	+	0.107337i	$0.0342324\pi$
$163$	20.2269	+	11.6780i	1.58429	+	0.914691i	0.590068	+	0.807354i	$0.299101\pi$
$164$		0			0
$165$	−0.650490	+	1.12668i	−0.0506406	+	0.0877121i
$166$		0			0
$167$	18.8603	−	10.8890i	1.45945	−	0.842614i	0.460467	−	0.887677i	$-0.347682\pi$
$167$	18.8603	−	10.8890i	1.45945	−	0.842614i	0.998984	+	0.0450626i	$0.0143487\pi$
$168$		0			0
$169$	2.12355	−	12.8254i	0.163350	−	0.986568i
$170$		0			0
$171$	14.2314	−	8.21652i	1.08831	−	0.628333i
$172$		0			0
$173$	4.04866	−	7.01249i	0.307814	−	0.533150i	−0.670070	−	0.742298i	$-0.733736\pi$
$173$	4.04866	−	7.01249i	0.307814	−	0.533150i	0.977884	+	0.209148i	$0.0670691\pi$
$174$		0			0
$175$	5.61866	+	3.24394i	0.424731	+	0.245218i
$176$		0			0
$177$			0.812334i			0.0610588i
$178$		0			0
$179$	−4.95442	−	8.58130i	−0.370310	−	0.641397i	0.619303	−	0.785152i	$-0.287415\pi$
$179$	−4.95442	−	8.58130i	−0.370310	−	0.641397i	−0.989613	+	0.143756i	$0.954082\pi$
$180$		0			0
$181$	1.27902			0.0950685			0.0475343	−	0.998870i	$-0.484864\pi$
$181$	1.27902			0.0950685			0.0475343	+	0.998870i	$0.484864\pi$
$182$		0			0
$183$	1.11012			0.0820624
$184$		0			0
$185$	−16.4230	−	28.4454i	−1.20744	−	2.09135i
$186$		0			0
$187$			3.76917i			0.275629i
$188$		0			0
$189$	2.33629	+	1.34886i	0.169940	+	0.0981151i
$190$		0			0
$191$	−5.01710	+	8.68988i	−0.363025	+	0.628777i	−0.988457	−	0.151501i	$-0.951589\pi$
$191$	−5.01710	+	8.68988i	−0.363025	+	0.628777i	0.625432	+	0.780278i	$0.284923\pi$
$192$		0			0
$193$	−13.7336	+	7.92911i	−0.988567	+	0.570750i	−0.904846	−	0.425740i	$-0.860014\pi$
$193$	−13.7336	+	7.92911i	−0.988567	+	0.570750i	−0.0837217	+	0.996489i	$0.526681\pi$
$194$		0			0
$195$	−1.92200	+	5.36772i	−0.137637	+	0.384390i
$196$		0			0
$197$	12.8242	−	7.40403i	0.913683	−	0.527515i	0.0320686	−	0.999486i	$-0.489790\pi$
$197$	12.8242	−	7.40403i	0.913683	−	0.527515i	0.881614	+	0.471971i	$0.156457\pi$
$198$		0			0
$199$	1.27771	−	2.21306i	0.0905747	−	0.156880i	−0.817178	−	0.576385i	$-0.804463\pi$
$199$	1.27771	−	2.21306i	0.0905747	−	0.156880i	0.907753	+	0.419505i	$0.137796\pi$
$200$		0			0
$201$	0.117866	+	0.0680499i	0.00831362	+	0.00479987i
$202$		0			0
$203$		−	6.86813i		−	0.482048i
$204$		0			0
$205$	−0.151464	−	0.262344i	−0.0105787	−	0.0183229i
$206$		0			0
$207$	17.0572			1.18556
$208$		0			0
$209$	−4.85921			−0.336119
$210$		0			0
$211$	−4.31824	−	7.47942i	−0.297280	−	0.514904i	0.678233	−	0.734847i	$-0.262746\pi$
$211$	−4.31824	−	7.47942i	−0.297280	−	0.514904i	−0.975513	+	0.219943i	$0.929413\pi$
$212$		0			0
$213$			5.10792i			0.349989i
$214$		0			0
$215$	−21.5853	−	12.4623i	−1.47211	−	0.849922i
$216$		0			0
$217$	−2.14342	+	3.71251i	−0.145505	+	0.252021i
$218$		0			0
$219$	5.13885	−	2.96692i	0.347251	−	0.200486i
$220$		0			0
$221$	2.95328	+	16.2519i	0.198659	+	1.09322i
$222$		0			0
$223$	17.2579	−	9.96384i	1.15567	−	0.667228i	0.205410	−	0.978676i	$-0.434147\pi$
$223$	17.2579	−	9.96384i	1.15567	−	0.667228i	0.950263	+	0.311448i	$0.100814\pi$
$224$		0			0
$225$	−9.02572	+	15.6330i	−0.601715	+	1.04220i
$226$		0			0
$227$	−0.305381	−	0.176312i	−0.0202689	−	0.0117022i	0.489831	−	0.871817i	$-0.337058\pi$
$227$	−0.305381	−	0.176312i	−0.0202689	−	0.0117022i	−0.510100	+	0.860115i	$0.670392\pi$
$228$		0			0
$229$			8.31317i			0.549350i	0.961537	+	0.274675i	$0.0885702\pi$
$229$			8.31317i			0.549350i	−0.961537	+	0.274675i	$0.911430\pi$
$230$		0			0
$231$	−0.191920	−	0.332416i	−0.0126274	−	0.0218714i
$232$		0			0
$233$	−15.3798			−1.00756			−0.503781	−	0.863831i	$-0.668058\pi$
$233$	−15.3798			−1.00756			−0.503781	+	0.863831i	$0.668058\pi$
$234$		0			0
$235$	−37.8795			−2.47098
$236$		0			0
$237$	2.32247	+	4.02263i	0.150860	+	0.261298i
$238$		0			0
$239$			2.88606i			0.186684i	0.995634	+	0.0933418i	$0.0297549\pi$
$239$			2.88606i			0.186684i	−0.995634	+	0.0933418i	$0.970245\pi$
$240$		0			0
$241$	−5.42777	−	3.13372i	−0.349633	−	0.201861i	0.314891	−	0.949128i	$-0.398032\pi$
$241$	−5.42777	−	3.13372i	−0.349633	−	0.201861i	−0.664524	+	0.747267i	$0.731366\pi$
$242$		0			0
$243$	−5.70011	+	9.87288i	−0.365662	+	0.633345i
$244$		0			0
$245$	−2.93529	+	1.69469i	−0.187529	+	0.108270i
$246$		0			0
$247$	−20.9520	+	3.80736i	−1.33314	+	0.242257i
$248$		0			0
$249$	1.30728	−	0.754761i	0.0828458	−	0.0478310i
$250$		0			0
$251$	−8.63325	+	14.9532i	−0.544926	+	0.943839i	0.453686	+	0.891162i	$0.350109\pi$
$251$	−8.63325	+	14.9532i	−0.544926	+	0.943839i	−0.998612	+	0.0526775i	$0.983224\pi$
$252$		0			0
$253$	−4.36805	−	2.52189i	−0.274617	−	0.158550i
$254$		0			0
$255$		−	7.24439i		−	0.453661i
$256$		0			0
$257$	−5.59655	−	9.69351i	−0.349103	−	0.604664i	0.636987	−	0.770874i	$-0.280180\pi$
$257$	−5.59655	−	9.69351i	−0.349103	−	0.604664i	−0.986090	+	0.166210i	$0.946847\pi$
$258$		0			0
$259$	9.69086			0.602161
$260$		0			0
$261$	19.1094			1.18284
$262$		0			0
$263$	−14.2913	−	24.7533i	−0.881240	−	1.52635i	−0.849963	−	0.526842i	$-0.823376\pi$
$263$	−14.2913	−	24.7533i	−0.881240	−	1.52635i	−0.0312773	−	0.999511i	$-0.509957\pi$
$264$		0			0
$265$		−	23.7775i		−	1.46064i
$266$		0			0
$267$	−3.24955	−	1.87613i	−0.198869	−	0.114817i
$268$		0			0
$269$	9.18769	−	15.9135i	0.560183	−	0.970266i	−0.437297	−	0.899317i	$-0.644064\pi$
$269$	9.18769	−	15.9135i	0.560183	−	0.970266i	0.997480	−	0.0709485i	$-0.0226026\pi$
$270$		0			0
$271$	−17.6518	+	10.1913i	−1.07227	+	0.619075i	−0.928801	−	0.370580i	$-0.879159\pi$
$271$	−17.6518	+	10.1913i	−1.07227	+	0.619075i	−0.143468	+	0.989655i	$0.545826\pi$
$272$		0			0
$273$	−1.08798	−	1.28294i	−0.0658477	−	0.0776469i
$274$		0			0
$275$	4.62264	−	2.66888i	0.278756	−	0.160940i
$276$		0			0
$277$	3.61609	−	6.26326i	0.217270	−	0.376323i	−0.736702	−	0.676217i	$-0.763618\pi$
$277$	3.61609	−	6.26326i	0.217270	−	0.376323i	0.953972	+	0.299894i	$0.0969514\pi$
$278$		0			0
$279$	−10.3294	−	5.96370i	−0.618407	−	0.357038i
$280$		0			0
$281$		−	12.4585i		−	0.743215i	−0.928390	−	0.371607i	$-0.878807\pi$
$281$		−	12.4585i		−	0.743215i	0.928390	−	0.371607i	$-0.121193\pi$
$282$		0			0
$283$	−6.53035	−	11.3109i	−0.388189	−	0.672363i	0.604017	−	0.796972i	$-0.293566\pi$
$283$	−6.53035	−	11.3109i	−0.388189	−	0.672363i	−0.992206	+	0.124608i	$0.960233\pi$
$284$		0			0
$285$	9.33946			0.553222
$286$		0			0
$287$	0.0893760			0.00527570
$288$		0			0
$289$	−1.99414	−	3.45395i	−0.117302	−	0.203174i
$290$		0			0
$291$		−	6.89267i		−	0.404056i
$292$		0			0
$293$	−12.6078	−	7.27909i	−0.736553	−	0.425249i	0.0842617	−	0.996444i	$-0.473147\pi$
$293$	−12.6078	−	7.27909i	−0.736553	−	0.425249i	−0.820815	+	0.571195i	$0.806480\pi$
$294$		0			0
$295$	2.95074	−	5.11083i	0.171799	−	0.297564i
$296$		0			0
$297$	1.92214	−	1.10975i	0.111534	−	0.0643941i
$298$		0			0
$299$	−20.8102	−	7.45140i	−1.20348	−	0.430926i
$300$		0			0
$301$	6.36853	−	3.67687i	0.367076	−	0.211931i
$302$		0			0
$303$	−1.92211	+	3.32919i	−0.110422	+	0.191257i
$304$		0			0
$305$	−6.98436	−	4.03242i	−0.399923	−	0.230896i
$306$		0			0
$307$		−	3.24267i		−	0.185069i	−0.995709	−	0.0925345i	$-0.970503\pi$
$307$		−	3.24267i		−	0.185069i	0.995709	−	0.0925345i	$-0.0294968\pi$
$308$		0			0
$309$	−3.10792	−	5.38307i	−0.176803	−	0.306232i
$310$		0			0
$311$	10.2709			0.582408			0.291204	−	0.956661i	$-0.405944\pi$
$311$	10.2709			0.582408			0.291204	+	0.956661i	$0.405944\pi$
$312$		0			0
$313$	−6.13382			−0.346704			−0.173352	−	0.984860i	$-0.555460\pi$
$313$	−6.13382			−0.346704			−0.173352	+	0.984860i	$0.555460\pi$
$314$		0			0
$315$	−4.71519	−	8.16695i	−0.265671	−	0.460156i
$316$		0			0
$317$		−	5.04487i		−	0.283348i	−0.989913	−	0.141674i	$-0.954752\pi$
$317$		−	5.04487i		−	0.283348i	0.989913	−	0.141674i	$-0.0452485\pi$
$318$		0			0
$319$	−4.89358	−	2.82531i	−0.273988	−	0.158187i
$320$		0			0
$321$	−2.10563	+	3.64706i	−0.117525	+	0.203559i
$322$		0			0
$323$	23.4330	−	13.5290i	1.30385	−	0.752776i
$324$		0			0
$325$	17.8408	−	15.1297i	0.989629	−	0.839246i
$326$		0			0
$327$	0.160481	−	0.0926539i	0.00887463	−	0.00512377i
$328$		0			0
$329$	5.58797	−	9.67865i	0.308075	−	0.533601i
$330$		0			0
$331$	19.9943	+	11.5437i	1.09898	+	0.634499i	0.935954	−	0.352122i	$-0.114540\pi$
$331$	19.9943	+	11.5437i	1.09898	+	0.634499i	0.163030	+	0.986621i	$0.447873\pi$
$332$		0			0
$333$			26.9632i			1.47758i
$334$		0			0
$335$	−0.494372	−	0.856278i	−0.0270104	−	0.0467834i
$336$		0			0
$337$	29.1429			1.58751			0.793757	−	0.608235i	$-0.208122\pi$
$337$	29.1429			1.58751			0.793757	+	0.608235i	$0.208122\pi$
$338$		0			0
$339$	2.08696			0.113348
$340$		0			0
$341$	1.76345	+	3.05439i	0.0954963	+	0.165405i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	8.39543	+	4.84711i	0.451995	+	0.260959i
$346$		0			0
$347$	−14.5541	+	25.2085i	−0.781306	+	1.35326i	0.149875	+	0.988705i	$0.452113\pi$
$347$	−14.5541	+	25.2085i	−0.781306	+	1.35326i	−0.931181	+	0.364557i	$0.881221\pi$
$348$		0			0
$349$	22.3263	−	12.8901i	1.19510	−	0.689992i	0.235642	−	0.971840i	$-0.424281\pi$
$349$	22.3263	−	12.8901i	1.19510	−	0.689992i	0.959459	+	0.281848i	$0.0909475\pi$
$350$		0			0
$351$	7.41837	−	6.29108i	0.395963	−	0.335793i
$352$		0			0
$353$	−8.58906	+	4.95890i	−0.457149	+	0.263935i	−0.710845	−	0.703349i	$-0.751687\pi$
$353$	−8.58906	+	4.95890i	−0.457149	+	0.263935i	0.253695	+	0.967284i	$0.418354\pi$
$354$		0			0
$355$	18.5541	−	32.1367i	0.984750	−	1.70564i
$356$		0			0
$357$	1.85103	+	1.06869i	0.0979667	+	0.0565611i
$358$		0			0
$359$		−	25.2683i		−	1.33361i	−0.745233	−	0.666804i	$-0.767662\pi$
$359$		−	25.2683i		−	1.33361i	0.745233	−	0.666804i	$-0.232338\pi$
$360$		0			0
$361$	7.94164	+	13.7553i	0.417981	+	0.723964i
$362$		0			0
$363$	4.81620			0.252785
$364$		0			0
$365$	−43.1084			−2.25640
$366$		0			0
$367$	17.8919	+	30.9897i	0.933950	+	1.61765i	0.776496	+	0.630122i	$0.216995\pi$
$367$	17.8919	+	30.9897i	0.933950	+	1.61765i	0.157454	+	0.987526i	$0.449671\pi$
$368$		0			0
$369$			0.248674i			0.0129455i
$370$		0			0
$371$	6.07543	+	3.50765i	0.315420	+	0.182108i
$372$		0			0
$373$	11.6652	−	20.2047i	0.604000	−	1.04616i	−0.388209	−	0.921572i	$-0.626906\pi$
$373$	11.6652	−	20.2047i	0.604000	−	1.04616i	0.992209	−	0.124587i	$-0.0397607\pi$
$374$		0			0
$375$	−2.03755	+	1.17638i	−0.105219	+	0.0607481i
$376$		0			0
$377$	−23.3139	−	8.34790i	−1.20073	−	0.429939i
$378$		0			0
$379$	−21.0502	+	12.1533i	−1.08127	+	0.624274i	−0.931240	−	0.364407i	$-0.881272\pi$
$379$	−21.0502	+	12.1533i	−1.08127	+	0.624274i	−0.150034	+	0.988681i	$0.547938\pi$
$380$		0			0
$381$	0.125997	−	0.218233i	0.00645501	−	0.0111804i
$382$		0			0
$383$	−4.25348	−	2.45575i	−0.217343	−	0.125483i	0.387376	−	0.921922i	$-0.373381\pi$
$383$	−4.25348	−	2.45575i	−0.217343	−	0.125483i	−0.604719	+	0.796439i	$0.706715\pi$
$384$		0			0
$385$			2.78854i			0.142117i
$386$		0			0
$387$	10.2303	+	17.7194i	0.520035	+	0.900727i
$388$		0			0
$389$	−5.14522			−0.260873			−0.130437	−	0.991457i	$-0.541638\pi$
$389$	−5.14522			−0.260873			−0.130437	+	0.991457i	$0.541638\pi$
$390$		0			0
$391$	28.0858			1.42036
$392$		0			0
$393$	−1.80230	−	3.12167i	−0.0909139	−	0.157467i
$394$		0			0
$395$		−	33.7447i		−	1.69788i
$396$		0			0
$397$	−10.6954	−	6.17498i	−0.536786	−	0.309913i	0.206990	−	0.978343i	$-0.433633\pi$
$397$	−10.6954	−	6.17498i	−0.536786	−	0.309913i	−0.743775	+	0.668430i	$0.766967\pi$
$398$		0			0
$399$	−1.37776	+	2.38634i	−0.0689740	+	0.119467i
$400$		0			0
$401$	28.1366	−	16.2447i	1.40508	−	0.811221i	0.410169	−	0.912010i	$-0.365470\pi$
$401$	28.1366	−	16.2447i	1.40508	−	0.811221i	0.994908	+	0.100788i	$0.0321365\pi$
$402$		0			0
$403$	9.99689	+	11.7882i	0.497981	+	0.587213i
$404$		0			0
$405$	20.8065	−	12.0126i	1.03388	−	0.596912i
$406$		0			0
$407$	3.98648	−	6.90479i	0.197603	−	0.342258i
$408$		0			0
$409$	3.26348	+	1.88417i	0.161369	+	0.0931662i	0.578510	−	0.815676i	$-0.303635\pi$
$409$	3.26348	+	1.88417i	0.161369	+	0.0931662i	−0.417141	+	0.908842i	$0.636968\pi$
$410$		0			0
$411$		−	5.85052i		−	0.288585i
$412$		0			0
$413$	0.870585	+	1.50790i	0.0428387	+	0.0741988i
$414$		0			0
$415$	−10.9664			−0.538321
$416$		0			0
$417$	−5.64396			−0.276386
$418$		0			0
$419$	−5.26504	−	9.11931i	−0.257214	−	0.445508i	0.708281	−	0.705931i	$-0.249471\pi$
$419$	−5.26504	−	9.11931i	−0.257214	−	0.445508i	−0.965495	+	0.260423i	$0.916138\pi$
$420$		0			0
$421$		−	24.9973i		−	1.21830i	−0.793057	−	0.609148i	$-0.791512\pi$
$421$		−	24.9973i		−	1.21830i	0.793057	−	0.609148i	$-0.208488\pi$
$422$		0			0
$423$	26.9293	+	15.5476i	1.30935	+	0.755951i
$424$		0			0
$425$	−14.8614	+	25.7408i	−0.720885	+	1.24861i
$426$		0			0
$427$	2.06066	−	1.18972i	0.0997225	−	0.0575748i
$428$		0			0
$429$	−1.36166	+	0.247438i	−0.0657415	+	0.0119464i
$430$		0			0
$431$	−10.3736	+	5.98919i	−0.499678	+	0.288489i	−0.728581	−	0.684960i	$-0.759820\pi$
$431$	−10.3736	+	5.98919i	−0.499678	+	0.288489i	0.228902	+	0.973449i	$0.426486\pi$
$432$		0			0
$433$	3.98475	−	6.90179i	0.191495	−	0.331679i	−0.754251	−	0.656586i	$-0.772000\pi$
$433$	3.98475	−	6.90179i	0.191495	−	0.331679i	0.945746	+	0.324907i	$0.105333\pi$
$434$		0			0
$435$	9.40551	+	5.43027i	0.450960	+	0.260362i
$436$		0			0
$437$			36.2083i			1.73208i
$438$		0			0
$439$	−2.17827	−	3.77288i	−0.103963	−	0.180070i	0.809351	−	0.587325i	$-0.199819\pi$
$439$	−2.17827	−	3.77288i	−0.103963	−	0.180070i	−0.913314	+	0.407256i	$0.866486\pi$
$440$		0			0
$441$	2.78234			0.132492
$442$		0			0
$443$	11.4823			0.545542			0.272771	−	0.962079i	$-0.412060\pi$
$443$	11.4823			0.545542			0.272771	+	0.962079i	$0.412060\pi$
$444$		0			0
$445$	13.6298	+	23.6075i	0.646114	+	1.11910i
$446$		0			0
$447$		−	7.93490i		−	0.375308i
$448$		0			0
$449$	−25.5692	−	14.7624i	−1.20669	−	0.696680i	−0.244652	−	0.969611i	$-0.578674\pi$
$449$	−25.5692	−	14.7624i	−1.20669	−	0.696680i	−0.962034	+	0.272931i	$0.912007\pi$
$450$		0			0
$451$	0.0367662	−	0.0636809i	0.00173125	−	0.00299861i
$452$		0			0
$453$	2.24067	−	1.29365i	0.105276	−	0.0607810i
$454$		0			0
$455$	2.18492	+	12.0237i	0.102431	+	0.563678i
$456$		0			0
$457$	−14.3744	+	8.29907i	−0.672407	+	0.388214i	−0.796988	−	0.603995i	$-0.793575\pi$
$457$	−14.3744	+	8.29907i	−0.672407	+	0.388214i	0.124581	+	0.992209i	$0.460241\pi$
$458$		0			0
$459$	−6.17953	+	10.7033i	−0.288436	+	0.499585i
$460$		0			0
$461$	22.8996	+	13.2211i	1.06654	+	0.615769i	0.927235	−	0.374481i	$-0.122179\pi$
$461$	22.8996	+	13.2211i	1.06654	+	0.615769i	0.139308	+	0.990249i	$0.455512\pi$
$462$		0			0
$463$			10.4717i			0.486663i	0.969943	+	0.243331i	$0.0782403\pi$
$463$			10.4717i			0.486663i	−0.969943	+	0.243331i	$0.921760\pi$
$464$		0			0
$465$	−3.38938	−	5.87057i	−0.157179	−	0.272241i
$466$		0			0
$467$	−27.9010			−1.29110			−0.645551	−	0.763717i	$-0.723372\pi$
$467$	−27.9010			−1.29110			−0.645551	+	0.763717i	$0.723372\pi$
$468$		0			0
$469$	0.291719			0.0134703
$470$		0			0
$471$	−0.535017	−	0.926677i	−0.0246523	−	0.0426990i
$472$		0			0
$473$		−	6.05015i		−	0.278186i
$474$		0			0
$475$	−33.1850	−	19.1594i	−1.52263	−	0.879091i
$476$		0			0
$477$	−9.75946	+	16.9039i	−0.446855	+	0.773975i
$478$		0			0
$479$	5.95941	−	3.44067i	0.272292	−	0.157208i	−0.357637	−	0.933861i	$-0.616417\pi$
$479$	5.95941	−	3.44067i	0.272292	−	0.157208i	0.629929	+	0.776653i	$0.283084\pi$
$480$		0			0
$481$	11.7788	−	32.8957i	0.537067	−	1.49991i
$482$		0			0
$483$	−2.47698	+	1.43009i	−0.112707	+	0.0650712i
$484$		0			0
$485$	−25.0371	+	43.3655i	−1.13688	+	1.96913i
$486$		0			0
$487$	35.3392	+	20.4031i	1.60137	+	0.924553i	0.991213	+	0.132275i	$0.0422282\pi$
$487$	35.3392	+	20.4031i	1.60137	+	0.924553i	0.610160	+	0.792278i	$0.291105\pi$
$488$		0			0
$489$		−	10.8966i		−	0.492762i
$490$		0			0
$491$	−3.36353	−	5.82581i	−0.151794	−	0.262915i	0.780093	−	0.625664i	$-0.215172\pi$
$491$	−3.36353	−	5.82581i	−0.151794	−	0.262915i	−0.931887	+	0.362749i	$0.881838\pi$
$492$		0			0
$493$	31.4649			1.41711
$494$		0			0
$495$	−7.75866			−0.348726
$496$		0			0
$497$	5.47419	+	9.48158i	0.245551	+	0.425307i
$498$		0			0
$499$			1.16200i			0.0520184i	0.999662	+	0.0260092i	$0.00827993\pi$
$499$			1.16200i			0.0520184i	−0.999662	+	0.0260092i	$0.991720\pi$
$500$		0			0
$501$	−8.79916	−	5.08020i	−0.393118	−	0.226967i
$502$		0			0
$503$	4.97527	−	8.61741i	0.221836	−	0.384231i	−0.733529	−	0.679658i	$-0.762128\pi$
$503$	4.97527	−	8.61741i	0.221836	−	0.384231i	0.955366	+	0.295426i	$0.0954617\pi$
$504$		0			0
$505$	24.1861	−	13.9638i	1.07627	−	0.621382i
$506$		0			0
$507$	−5.67733	+	2.13381i	−0.252139	+	0.0947659i
$508$		0			0
$509$	−0.0452068	+	0.0261002i	−0.00200376	+	0.00115687i	−0.501002	−	0.865446i	$-0.667035\pi$
$509$	−0.0452068	+	0.0261002i	−0.00200376	+	0.00115687i	0.498998	+	0.866603i	$0.333702\pi$
$510$		0			0
$511$	6.35934	−	11.0147i	0.281321	−	0.487262i
$512$		0			0
$513$	−13.7986	−	7.96664i	−0.609225	−	0.351736i
$514$		0			0
$515$			45.1570i			1.98986i
$516$		0			0
$517$	−4.59739	−	7.96292i	−0.202193	−	0.350209i
$518$		0			0
$519$	−3.77777			−0.165826
$520$		0			0
$521$	26.0984			1.14339			0.571695	−	0.820466i	$-0.306286\pi$
$521$	26.0984			1.14339			0.571695	+	0.820466i	$0.306286\pi$
$522$		0			0
$523$	−9.76606	−	16.9153i	−0.427040	−	0.739655i	0.569568	−	0.821944i	$-0.307110\pi$
$523$	−9.76606	−	16.9153i	−0.427040	−	0.739655i	−0.996609	+	0.0822887i	$0.973777\pi$
$524$		0			0
$525$		−	3.02688i		−	0.132104i
$526$		0			0
$527$	−17.0081	−	9.81962i	−0.740884	−	0.427750i
$528$		0			0
$529$	−7.29180	+	12.6298i	−0.317035	+	0.549120i
$530$		0			0
$531$	−4.19548	+	2.42226i	−0.182068	+	0.105117i
$532$		0			0
$533$	0.108633	−	0.303387i	0.00470540	−	0.0131412i
$534$		0			0
$535$	26.4953	−	15.2971i	1.14549	−	0.661351i
$536$		0			0
$537$	−2.31146	+	4.00356i	−0.0997468	+	0.172766i
$538$		0			0
$539$	−0.712505	−	0.411365i	−0.0306898	−	0.0177188i
$540$		0			0
$541$			32.8802i			1.41363i	0.707399	+	0.706814i	$0.249868\pi$
$541$			32.8802i			1.41363i	−0.707399	+	0.706814i	$0.750132\pi$
$542$		0			0
$543$	−0.298359	−	0.516774i	−0.0128038	−	0.0221769i
$544$		0			0
$545$	−1.34623			−0.0576662
$546$		0			0
$547$	39.0180			1.66829			0.834144	−	0.551546i	$-0.185962\pi$
$547$	39.0180			1.66829			0.834144	+	0.551546i	$0.185962\pi$
$548$		0			0
$549$	3.31021	+	5.73346i	0.141276	+	0.244698i
$550$		0			0
$551$			40.5646i			1.72811i
$552$		0			0
$553$	8.62217	+	4.97801i	0.366652	+	0.211687i
$554$		0			0
$555$	−7.66206	+	13.2711i	−0.325236	+	0.563326i
$556$		0			0
$557$	−25.5903	+	14.7746i	−1.08430	+	0.626020i	−0.932053	−	0.362323i	$-0.881984\pi$
$557$	−25.5903	+	14.7746i	−1.08430	+	0.626020i	−0.152245	+	0.988343i	$0.548650\pi$
$558$		0			0
$559$	−4.74050	−	26.0871i	−0.200502	−	1.10337i
$560$		0			0
$561$	1.52290	−	0.879244i	0.0642967	−	0.0371217i
$562$		0			0
$563$	13.5662	−	23.4973i	0.571745	−	0.990292i	−0.424642	−	0.905362i	$-0.639600\pi$
$563$	13.5662	−	23.4973i	0.571745	−	0.990292i	0.996387	−	0.0849304i	$-0.0270668\pi$
$564$		0			0
$565$	−13.1302	−	7.58071i	−0.552390	−	0.318923i
$566$		0			0
$567$			7.08840i			0.297685i
$568$		0			0
$569$	21.2297	+	36.7709i	0.889996	+	1.54152i	0.839879	+	0.542774i	$0.182626\pi$
$569$	21.2297	+	36.7709i	0.889996	+	1.54152i	0.0501168	+	0.998743i	$0.484041\pi$
$570$		0			0
$571$	11.2678			0.471543			0.235771	−	0.971809i	$-0.424238\pi$
$571$	11.2678			0.471543			0.235771	+	0.971809i	$0.424238\pi$
$572$		0			0
$573$	4.68141			0.195569
$574$		0			0
$575$	−19.8871	−	34.4455i	−0.829349	−	1.43647i
$576$		0			0
$577$		−	22.8987i		−	0.953286i	−0.879097	−	0.476643i	$-0.841853\pi$
$577$		−	22.8987i		−	0.953286i	0.879097	−	0.476643i	$-0.158147\pi$
$578$		0			0
$579$	6.40735	+	3.69929i	0.266280	+	0.153737i
$580$		0			0
$581$	1.61777	−	2.80205i	0.0671163	−	0.116249i
$582$		0			0
$583$	4.99844	−	2.88585i	0.207014	−	0.119520i
$584$		0			0
$585$	−33.4539	+	6.07918i	−1.38315	+	0.251343i
$586$		0			0
$587$	−31.0054	+	17.9010i	−1.27973	+	0.738852i	−0.976798	−	0.214161i	$-0.931298\pi$
$587$	−31.0054	+	17.9010i	−1.27973	+	0.738852i	−0.302931	+	0.953013i	$0.597965\pi$
$588$		0			0
$589$	12.6595	−	21.9268i	0.521624	−	0.903479i
$590$		0			0
$591$	−5.98304	−	3.45431i	−0.246110	−	0.142091i
$592$		0			0
$593$		−	14.6093i		−	0.599931i	−0.953950	−	0.299965i	$-0.903025\pi$
$593$		−	14.6093i		−	0.599931i	0.953950	−	0.299965i	$-0.0969752\pi$
$594$		0			0
$595$	−7.76387	−	13.4474i	−0.318288	−	0.551290i
$596$		0			0
$597$	−1.19222			−0.0487944
$598$		0			0
$599$	37.5729			1.53519			0.767594	−	0.640936i	$-0.221454\pi$
$599$	37.5729			1.53519			0.767594	+	0.640936i	$0.221454\pi$
$600$		0			0
$601$	2.72579	+	4.72121i	0.111187	+	0.192582i	0.916249	−	0.400609i	$-0.131201\pi$
$601$	2.72579	+	4.72121i	0.111187	+	0.192582i	−0.805062	+	0.593191i	$0.797868\pi$
$602$		0			0
$603$			0.811659i			0.0330533i
$604$		0			0
$605$	−30.3013	−	17.4945i	−1.23192	−	0.711251i
$606$		0			0
$607$	−19.9693	+	34.5879i	−0.810531	+	1.40388i	0.101962	+	0.994788i	$0.467488\pi$
$607$	−19.9693	+	34.5879i	−0.810531	+	1.40388i	−0.912493	+	0.409092i	$0.865845\pi$
$608$		0			0
$609$	−2.77500	+	1.60215i	−0.112449	+	0.0649222i
$610$		0			0
$611$	−26.0623	−	30.7324i	−1.05437	−	1.24330i
$612$		0			0
$613$	14.4238	−	8.32758i	0.582572	−	0.336348i	−0.179583	−	0.983743i	$-0.557475\pi$
$613$	14.4238	−	8.32758i	0.582572	−	0.336348i	0.762155	+	0.647395i	$0.224142\pi$
$614$		0			0
$615$	−0.0706650	+	0.122395i	−0.00284949	+	0.00493546i
$616$		0			0
$617$	−23.3525	−	13.4826i	−0.940137	−	0.542788i	−0.0501339	−	0.998743i	$-0.515965\pi$
$617$	−23.3525	−	13.4826i	−0.940137	−	0.542788i	−0.890003	+	0.455954i	$0.849298\pi$
$618$		0			0
$619$			12.7533i			0.512597i	0.966598	+	0.256298i	$0.0825029\pi$
$619$			12.7533i			0.512597i	−0.966598	+	0.256298i	$0.917497\pi$
$620$		0			0
$621$	−8.26925	−	14.3228i	−0.331833	−	0.574752i
$622$		0			0
$623$	−8.04265			−0.322222
$624$		0			0
$625$	−15.3469			−0.613875
$626$		0			0
$627$	1.13352	+	1.96332i	0.0452685	+	0.0784073i
$628$		0			0
$629$			44.3967i			1.77021i
$630$		0			0
$631$	−32.5218	−	18.7764i	−1.29467	−	0.747479i	−0.315193	−	0.949028i	$-0.602069\pi$
$631$	−32.5218	−	18.7764i	−1.29467	−	0.747479i	−0.979478	+	0.201549i	$0.935402\pi$
$632$		0			0
$633$	−2.01465	+	3.48948i	−0.0800753	+	0.138695i
$634$		0			0
$635$	−1.58543	+	0.915346i	−0.0629157	+	0.0363244i
$636$		0			0
$637$	−3.39451	−	1.21546i	−0.134495	−	0.0481581i
$638$		0			0
$639$	−26.3809	+	15.2310i	−1.04361	+	0.602531i
$640$		0			0
$641$	0.988115	−	1.71147i	0.0390282	−	0.0675988i	−0.845851	−	0.533418i	$-0.820907\pi$
$641$	0.988115	−	1.71147i	0.0390282	−	0.0675988i	0.884880	+	0.465820i	$0.154240\pi$
$642$		0			0
$643$	33.8360	+	19.5352i	1.33436	+	0.770394i	0.985965	−	0.166953i	$-0.0533929\pi$
$643$	33.8360	+	19.5352i	1.33436	+	0.770394i	0.348397	+	0.937347i	$0.386726\pi$
$644$		0			0
$645$			11.6284i			0.457870i
$646$		0			0
$647$	−6.05254	−	10.4833i	−0.237950	−	0.412141i	0.722176	−	0.691709i	$-0.243142\pi$
$647$	−6.05254	−	10.4833i	−0.237950	−	0.412141i	−0.960126	+	0.279568i	$0.909809\pi$
$648$		0			0
$649$	1.43251			0.0562311
$650$		0			0
$651$	2.00000			0.0783862
$652$		0			0
$653$	−20.1232	−	34.8544i	−0.787481	−	1.36396i	−0.927505	−	0.373810i	$-0.878051\pi$
$653$	−20.1232	−	34.8544i	−0.787481	−	1.36396i	0.140024	−	0.990148i	$-0.455282\pi$
$654$		0			0
$655$			26.1868i			1.02320i
$656$		0			0
$657$	30.6466	+	17.6938i	1.19564	+	0.690301i
$658$		0			0
$659$	−1.81164	+	3.13785i	−0.0705714	+	0.122233i	−0.899152	−	0.437637i	$-0.855816\pi$
$659$	−1.81164	+	3.13785i	−0.0705714	+	0.122233i	0.828580	+	0.559870i	$0.189149\pi$
$660$		0			0
$661$	−20.4698	+	11.8182i	−0.796182	+	0.459676i	−0.842135	−	0.539268i	$-0.818701\pi$
$661$	−20.4698	+	11.8182i	−0.796182	+	0.459676i	0.0459521	+	0.998944i	$0.485368\pi$
$662$		0			0
$663$	5.87752	−	4.98437i	0.228264	−	0.193577i
$664$		0			0
$665$	17.3364	−	10.0092i	0.672277	−	0.388139i
$666$		0			0
$667$	−21.0527	+	36.4643i	−0.815163	+	1.41190i
$668$		0			0
$669$	−8.05157	−	4.64858i	−0.311292	−	0.179724i
$670$		0			0
$671$		−	1.95764i		−	0.0755740i
$672$		0			0
$673$	23.4355	+	40.5914i	0.903372	+	1.56469i	0.823088	+	0.567913i	$0.192249\pi$
$673$	23.4355	+	40.5914i	0.903372	+	1.56469i	0.0802832	+	0.996772i	$0.474418\pi$
$674$		0			0
$675$	17.5025			0.673670
$676$		0			0
$677$	−13.7304			−0.527704			−0.263852	−	0.964563i	$-0.584993\pi$
$677$	−13.7304			−0.527704			−0.263852	+	0.964563i	$0.584993\pi$
$678$		0			0
$679$	−7.38693	−	12.7945i	−0.283484	−	0.491009i
$680$		0			0
$681$			0.164515i			0.00630423i
$682$		0			0
$683$	−3.03610	−	1.75289i	−0.116173	−	0.0670725i	0.440788	−	0.897611i	$-0.354699\pi$
$683$	−3.03610	−	1.75289i	−0.116173	−	0.0670725i	−0.556961	+	0.830539i	$0.688033\pi$
$684$		0			0
$685$	−21.2516	+	36.8088i	−0.811981	+	1.40639i
$686$		0			0
$687$	3.35885	−	1.93923i	0.128148	−	0.0739864i
$688$		0			0
$689$	19.2911	−	16.3597i	0.734934	−	0.623254i
$690$		0			0
$691$	27.5196	−	15.8885i	1.04690	−	0.604426i	0.125117	−	0.992142i	$-0.460069\pi$
$691$	27.5196	−	15.8885i	1.04690	−	0.604426i	0.921779	+	0.387716i	$0.126736\pi$
$692$		0			0
$693$	1.14456	−	1.98243i	0.0434781	−	0.0753062i
$694$		0			0
$695$	35.5092	+	20.5012i	1.34694	+	0.777656i
$696$		0			0
$697$			0.409458i			0.0155093i
$698$		0			0
$699$	3.58768	+	6.21404i	0.135698	+	0.235037i
$700$		0			0
$701$	−31.6828			−1.19664			−0.598322	−	0.801256i	$-0.704166\pi$
$701$	−31.6828			−1.19664			−0.598322	+	0.801256i	$0.704166\pi$
$702$		0			0
$703$	−57.2362			−2.15870
$704$		0			0
$705$	8.83624	+	15.3048i	0.332792	+	0.576413i
$706$		0			0
$707$			8.23976i			0.309888i
$708$		0			0
$709$	−30.5835	−	17.6574i	−1.14859	−	0.663137i	−0.200044	−	0.979787i	$-0.564108\pi$
$709$	−30.5835	−	17.6574i	−1.14859	−	0.663137i	−0.948542	+	0.316650i	$0.897442\pi$
$710$		0			0
$711$	−13.8505	+	23.9898i	−0.519434	+	0.899687i
$712$		0			0
$713$	22.7597	−	13.1403i	0.852357	−	0.492108i
$714$		0			0
$715$	9.46572	+	3.38935i	0.353998	+	0.126754i
$716$		0			0
$717$	1.16608	−	0.673238i	0.0435481	−	0.0251425i
$718$		0			0
$719$	0.609778	−	1.05617i	0.0227409	−	0.0393884i	−0.854431	−	0.519565i	$-0.826094\pi$
$719$	0.609778	−	1.05617i	0.0227409	−	0.0393884i	0.877172	+	0.480177i	$0.159427\pi$
$720$		0			0
$721$	−11.5382	−	6.66156i	−0.429703	−	0.248089i
$722$		0			0
$723$			2.92404i			0.108746i
$724$		0			0
$725$	−22.2798	−	38.5897i	−0.827450	−	1.43318i
$726$		0			0
$727$	−5.75380			−0.213397			−0.106698	−	0.994291i	$-0.534028\pi$
$727$	−5.75380			−0.213397			−0.106698	+	0.994291i	$0.534028\pi$
$728$		0			0
$729$	−15.9465			−0.590611
$730$		0			0
$731$	16.8448	+	29.1761i	0.623029	+	1.07912i
$732$		0			0
$733$			35.2258i			1.30110i	0.759466	+	0.650548i	$0.225461\pi$
$733$			35.2258i			1.30110i	−0.759466	+	0.650548i	$0.774539\pi$
$734$		0			0
$735$	1.36944	+	0.790648i	0.0505127	+	0.0291635i
$736$		0			0
$737$	0.120003	−	0.207851i	0.00442036	−	0.00765629i
$738$		0			0
$739$	25.4199	−	14.6762i	0.935088	−	0.539873i	0.0466705	−	0.998910i	$-0.485139\pi$
$739$	25.4199	−	14.6762i	0.935088	−	0.539873i	0.888417	+	0.459037i	$0.151806\pi$
$740$		0			0
$741$	6.42585	+	7.57729i	0.236060	+	0.278359i
$742$		0			0
$743$	12.9763	−	7.49190i	0.476056	−	0.274851i	−0.242715	−	0.970098i	$-0.578038\pi$
$743$	12.9763	−	7.49190i	0.476056	−	0.274851i	0.718771	+	0.695246i	$0.244705\pi$
$744$		0			0
$745$	−28.8229	+	49.9227i	−1.05599	+	1.82903i
$746$		0			0
$747$	7.79626	+	4.50117i	0.285250	+	0.164689i
$748$		0			0
$749$			9.02649i			0.329821i
$750$		0			0
$751$	−21.9195	−	37.9657i	−0.799855	−	1.38539i	−0.919710	−	0.392598i	$-0.871576\pi$
$751$	−21.9195	−	37.9657i	−0.799855	−	1.38539i	0.119856	−	0.992791i	$-0.461757\pi$
$752$		0			0
$753$	8.05560			0.293562
$754$		0			0
$755$	−18.7963			−0.684069
$756$		0			0
$757$	18.1798	+	31.4884i	0.660758	+	1.14447i	0.980417	+	0.196933i	$0.0630983\pi$
$757$	18.1798	+	31.4884i	0.660758	+	1.14447i	−0.319659	+	0.947533i	$0.603568\pi$
$758$		0			0
$759$			2.35315i			0.0854140i
$760$		0			0
$761$	−15.7906	−	9.11673i	−0.572410	−	0.330481i	0.185701	−	0.982606i	$-0.440544\pi$
$761$	−15.7906	−	9.11673i	−0.572410	−	0.330481i	−0.758111	+	0.652125i	$0.773878\pi$
$762$		0			0
$763$	0.198596	−	0.343978i	0.00718965	−	0.0124528i
$764$		0			0
$765$	37.4152	−	21.6017i	1.35275	−	0.781011i
$766$		0			0
$767$	6.17672	−	1.12242i	0.223029	−	0.0405284i
$768$		0			0
$769$	−5.66870	+	3.27283i	−0.204419	+	0.118021i	−0.598715	−	0.800962i	$-0.704322\pi$
$769$	−5.66870	+	3.27283i	−0.204419	+	0.118021i	0.394296	+	0.918983i	$0.370988\pi$
$770$		0			0
$771$	−2.61104	+	4.52246i	−0.0940344	+	0.162872i
$772$		0			0
$773$	38.6651	+	22.3233i	1.39069	+	0.802913i	0.993391	−	0.114778i	$-0.0366158\pi$
$773$	38.6651	+	22.3233i	1.39069	+	0.802913i	0.397295	+	0.917691i	$0.369949\pi$
$774$		0			0
$775$			27.8124i			0.999051i
$776$		0			0
$777$	−2.26061	−	3.91549i	−0.0810990	−	0.140468i
$778$		0			0
$779$	−0.527873			−0.0189130
$780$		0			0
$781$	9.00757			0.322316
$782$		0			0
$783$	−9.26414	−	16.0460i	−0.331073	−	0.573436i
$784$		0			0
$785$			7.77363i			0.277453i
$786$		0			0
$787$	−21.6962	−	12.5263i	−0.773385	−	0.446514i	0.0606960	−	0.998156i	$-0.480668\pi$
$787$	−21.6962	−	12.5263i	−0.773385	−	0.446514i	−0.834081	+	0.551642i	$0.814001\pi$
$788$		0			0
$789$	−6.66754	+	11.5485i	−0.237371	+	0.411138i
$790$		0			0
$791$	3.87392	−	2.23661i	0.137741	−	0.0795246i
$792$		0			0
$793$	−1.53388	−	8.44099i	−0.0544698	−	0.299748i
$794$		0			0
$795$	−9.60705	+	5.54663i	−0.340727	+	0.196719i
$796$		0			0
$797$	13.9132	−	24.0984i	0.492831	−	0.853608i	−0.507135	−	0.861867i	$-0.669295\pi$
$797$	13.9132	−	24.0984i	0.492831	−	0.853608i	0.999966	+	0.00825861i	$0.00262883\pi$
$798$		0			0
$799$	44.3408	+	25.6002i	1.56866	+	0.905668i
$800$		0			0
$801$		−	22.3774i		−	0.790665i
$802$		0			0
$803$	−5.23202	−	9.06213i	−0.184634	−	0.319795i
$804$		0			0
$805$	20.7787			0.732354
$806$		0			0
$807$	−8.57294			−0.301782
$808$		0			0
$809$	−3.74825	−	6.49216i	−0.131781	−	0.228252i	0.792582	−	0.609765i	$-0.208736\pi$
$809$	−3.74825	−	6.49216i	−0.131781	−	0.228252i	−0.924363	+	0.381513i	$0.875403\pi$
$810$		0			0
$811$			9.88726i			0.347189i	0.984817	+	0.173594i	$0.0555381\pi$
$811$			9.88726i			0.347189i	−0.984817	+	0.173594i	$0.944462\pi$
$812$		0			0
$813$	8.23535	+	4.75468i	0.288826	+	0.166754i
$814$		0			0
$815$	−39.5811	+	68.5565i	−1.38647	+	2.40143i
$816$		0			0
$817$	−37.6138	+	21.7164i	−1.31594	+	0.759759i
$818$		0			0
$819$	3.38180	−	9.44465i	0.118170	−	0.330023i
$820$		0			0
$821$	12.4426	−	7.18376i	0.434251	−	0.250715i	−0.266905	−	0.963723i	$-0.586001\pi$
$821$	12.4426	−	7.18376i	0.434251	−	0.250715i	0.701156	+	0.713008i	$0.252668\pi$
$822$		0			0
$823$	−5.94343	+	10.2943i	−0.207175	+	0.358837i	−0.950823	−	0.309733i	$-0.899760\pi$
$823$	−5.94343	+	10.2943i	−0.207175	+	0.358837i	0.743649	+	0.668571i	$0.233094\pi$
$824$		0			0
$825$	−2.15667	−	1.24515i	−0.0750856	−	0.0433507i
$826$		0			0
$827$		−	29.0884i		−	1.01150i	−0.862679	−	0.505752i	$-0.831215\pi$
$827$		−	29.0884i		−	1.01150i	0.862679	−	0.505752i	$-0.168785\pi$
$828$		0			0
$829$	−24.8143	−	42.9796i	−0.861836	−	1.49274i	−0.870155	−	0.492779i	$-0.835981\pi$
$829$	−24.8143	−	42.9796i	−0.861836	−	1.49274i	0.00831865	−	0.999965i	$-0.497352\pi$
$830$		0			0
$831$	−3.37414			−0.117048
$832$		0			0
$833$	4.58130			0.158733
$834$		0			0
$835$	36.9068	+	63.9245i	1.27721	+	2.21220i
$836$		0			0
$837$			11.5647i			0.399734i
$838$		0			0
$839$	3.99837	+	2.30846i	0.138039	+	0.0796969i	0.567429	−	0.823422i	$-0.307938\pi$
$839$	3.99837	+	2.30846i	0.138039	+	0.0796969i	−0.429390	+	0.903119i	$0.641271\pi$
$840$		0			0
$841$	−9.08559	+	15.7367i	−0.313296	+	0.542645i
$842$		0			0
$843$	−5.03375	+	2.90624i	−0.173372	+	0.100096i
$844$		0			0
$845$	43.4701	+	7.19750i	1.49542	+	0.247602i
$846$		0			0
$847$	8.94008	−	5.16156i	0.307185	−	0.177353i
$848$		0			0
$849$	−3.04670	+	5.27705i	−0.104563	+	0.181108i
$850$		0			0
$851$	−51.4508	−	29.7051i	−1.76371	−	1.01828i
$852$		0			0
$853$		−	37.8266i		−	1.29516i	−0.761999	−	0.647579i	$-0.775782\pi$
$853$		−	37.8266i		−	1.29516i	0.761999	−	0.647579i	$-0.224218\pi$
$854$		0			0
$855$	27.8489	+	48.2357i	0.952412	+	1.64963i
$856$		0			0
$857$	30.1652			1.03042			0.515211	−	0.857063i	$-0.327713\pi$
$857$	30.1652			1.03042			0.515211	+	0.857063i	$0.327713\pi$
$858$		0			0
$859$	−10.6316			−0.362745			−0.181372	−	0.983414i	$-0.558054\pi$
$859$	−10.6316			−0.362745			−0.181372	+	0.983414i	$0.558054\pi$
$860$		0			0
$861$	−0.0208490	−	0.0361115i	−0.000710531	−	0.00123068i
$862$		0			0
$863$		−	23.8352i		−	0.811360i	−0.914015	−	0.405680i	$-0.867035\pi$
$863$		−	23.8352i		−	0.811360i	0.914015	−	0.405680i	$-0.132965\pi$
$864$		0			0
$865$	23.7680	+	13.7224i	0.808135	+	0.466577i
$866$		0			0
$867$	−0.930356	+	1.61142i	−0.0315965	+	0.0547268i
$868$		0			0
$869$	7.09372	−	4.09556i	0.240638	−	0.138932i
$870$		0			0
$871$	0.354571	−	0.990241i	0.0120142	−	0.0335530i
$872$		0			0
$873$	35.5987	−	20.5529i	1.20483	−	0.695611i
$874$		0			0
$875$	−2.52148	+	4.36733i	−0.0852415	+	0.147643i
$876$		0			0
$877$	24.6164	+	14.2123i	0.831236	+	0.479915i	0.854276	−	0.519820i	$-0.174001\pi$
$877$	24.6164	+	14.2123i	0.831236	+	0.479915i	−0.0230394	+	0.999735i	$0.507334\pi$
$878$		0			0
$879$			6.79205i			0.229090i
$880$		0			0
$881$	27.5915	+	47.7898i	0.929580	+	1.61008i	0.784025	+	0.620729i	$0.213163\pi$
$881$	27.5915	+	47.7898i	0.929580	+	1.61008i	0.145555	+	0.989350i	$0.453503\pi$
$882$		0			0
$883$	−9.18216			−0.309004			−0.154502	−	0.987992i	$-0.549377\pi$
$883$	−9.18216			−0.309004			−0.154502	+	0.987992i	$0.549377\pi$
$884$		0			0
$885$	−2.75331			−0.0925514
$886$		0			0
$887$	16.7857	+	29.0737i	0.563610	+	0.976201i	0.997178	+	0.0750798i	$0.0239211\pi$
$887$	16.7857	+	29.0737i	0.563610	+	0.976201i	−0.433568	+	0.901121i	$0.642746\pi$
$888$		0			0
$889$		−	0.540127i		−	0.0181153i
$890$		0			0
$891$	5.05052	+	2.91592i	0.169199	+	0.0976870i
$892$		0			0
$893$	−33.0037	+	57.1641i	−1.10443	+	1.91292i
$894$		0			0
$895$	29.0853	−	16.7924i	0.972213	−	0.561307i
$896$		0			0
$897$	1.84378	+	10.1463i	0.0615619	+	0.338777i
$898$		0			0
$899$	25.4980	−	14.7213i	0.850405	−	0.490981i
$900$		0			0
$901$	−16.0696	+	27.8333i	−0.535355	+	0.927263i
$902$		0			0
$903$	−2.97120	−	1.71543i	−0.0988755	−	0.0570858i
$904$		0			0
$905$			4.33507i			0.144103i
$906$		0			0
$907$	−5.51747	−	9.55654i	−0.183205	−	0.317320i	0.759765	−	0.650197i	$-0.225314\pi$
$907$	−5.51747	−	9.55654i	−0.183205	−	0.317320i	−0.942970	+	0.332878i	$0.891980\pi$
$908$		0			0
$909$	−22.9258			−0.760400
$910$		0			0
$911$	−59.9931			−1.98766			−0.993830	−	0.110917i	$-0.964621\pi$
$911$	−59.9931			−1.98766			−0.993830	+	0.110917i	$0.964621\pi$
$912$		0			0
$913$	−1.33099	−	2.30533i	−0.0440492	−	0.0762954i
$914$		0			0
$915$			3.76261i			0.124388i
$916$		0			0
$917$	−6.69104	−	3.86307i	−0.220958	−	0.127570i
$918$		0			0
$919$	17.8268	−	30.8770i	0.588053	−	1.01854i	−0.406434	−	0.913680i	$-0.633228\pi$
$919$	17.8268	−	30.8770i	0.588053	−	1.01854i	0.994487	−	0.104858i	$-0.0334388\pi$
$920$		0			0
$921$	−1.31017	+	0.756426i	−0.0431715	+	0.0249251i
$922$		0			0
$923$	38.8389	−	7.05774i	1.27840	−	0.232308i
$924$		0			0
$925$	54.4497	−	31.4365i	1.79029	−	1.03363i
$926$		0			0
$927$	18.5347	−	32.1030i	0.608759	−	1.05440i
$928$		0			0
$929$	25.1409	+	14.5151i	0.824846	+	0.476225i	0.852085	−	0.523404i	$-0.175338\pi$
$929$	25.1409	+	14.5151i	0.824846	+	0.476225i	−0.0272389	+	0.999629i	$0.508671\pi$
$930$		0			0
$931$			5.90621i			0.193568i
$932$		0			0
$933$	−2.39591	−	4.14985i	−0.0784387	−	0.135860i
$934$		0			0
$935$	−12.7751			−0.417792
$936$		0			0
$937$	38.2635			1.25001			0.625006	−	0.780620i	$-0.285096\pi$
$937$	38.2635			1.25001			0.625006	+	0.780620i	$0.285096\pi$
$938$		0			0
$939$	1.43085	+	2.47831i	0.0466941	+	0.0808765i
$940$		0			0
$941$			4.14746i			0.135203i	0.997712	+	0.0676017i	$0.0215347\pi$
$941$			4.14746i			0.135203i	−0.997712	+	0.0676017i	$0.978465\pi$
$942$		0			0
$943$	−0.474516	−	0.273962i	−0.0154524	−	0.00892142i
$944$		0			0
$945$	−4.57179	+	7.91858i	−0.148720	+	0.257591i
$946$		0			0
$947$	−0.872884	+	0.503960i	−0.0283649	+	0.0163765i	−0.514115	−	0.857721i	$-0.671880\pi$
$947$	−0.872884	+	0.503960i	−0.0283649	+	0.0163765i	0.485750	+	0.874098i	$0.338546\pi$
$948$		0			0
$949$	−29.6600	−	34.9747i	−0.962803	−	1.13533i
$950$		0			0
$951$	−2.03833	+	1.17683i	−0.0660973	+	0.0381613i
$952$		0			0
$953$	8.25146	−	14.2919i	0.267291	−	0.462962i	−0.700870	−	0.713289i	$-0.747205\pi$
$953$	8.25146	−	14.2919i	0.267291	−	0.462962i	0.968161	+	0.250327i	$0.0805382\pi$
$954$		0			0
$955$	−29.4533	−	17.0048i	−0.953085	−	0.550264i
$956$		0			0
$957$			2.63627i			0.0852184i
$958$		0			0
$959$	−6.27005	−	10.8600i	−0.202471	−	0.350689i
$960$		0			0
$961$	12.6231			0.407196
$962$		0			0
$963$	−25.1147			−0.809311
$964$		0			0
$965$	−26.8747	−	46.5484i	−0.865128	−	1.49845i
$966$		0			0
$967$			37.7765i			1.21481i	0.794392	+	0.607406i	$0.207790\pi$
$967$			37.7765i			1.21481i	−0.794392	+	0.607406i	$0.792210\pi$
$968$		0			0
$969$	−10.9325	−	6.31191i	−0.351204	−	0.202768i
$970$		0			0
$971$	−24.1561	+	41.8396i	−0.775206	+	1.34270i	0.159473	+	0.987202i	$0.449021\pi$
$971$	−24.1561	+	41.8396i	−0.775206	+	1.34270i	−0.934679	+	0.355494i	$0.884313\pi$
$972$		0			0
$973$	−10.4766	+	6.04868i	−0.335865	+	0.193912i
$974$		0			0
$975$	−10.2748	−	3.67904i	−0.329056	−	0.117824i
$976$		0			0
$977$	−14.1198	+	8.15206i	−0.451732	+	0.260807i	−0.708561	−	0.705649i	$-0.750655\pi$
$977$	−14.1198	+	8.15206i	−0.451732	+	0.260807i	0.256830	+	0.966457i	$0.417322\pi$
$978$		0			0
$979$	−3.30847	+	5.73043i	−0.105739	+	0.183145i
$980$		0			0
$981$	0.957062	+	0.552560i	0.0305567	+	0.0176419i
$982$		0			0
$983$		−	29.5121i		−	0.941291i	−0.882322	−	0.470645i	$-0.844021\pi$
$983$		−	29.5121i		−	0.941291i	0.882322	−	0.470645i	$-0.155979\pi$
$984$		0			0
$985$	25.0950	+	43.4659i	0.799594	+	1.38494i
$986$		0			0
$987$	−5.21408			−0.165966
$988$		0			0
$989$	−45.0825			−1.43354
$990$		0			0
$991$	2.19622	+	3.80397i	0.0697653	+	0.120837i	0.898798	−	0.438363i	$-0.144442\pi$
$991$	2.19622	+	3.80397i	0.0697653	+	0.120837i	−0.829033	+	0.559200i	$0.811108\pi$
$992$		0			0
$993$		−	10.7713i		−	0.341817i
$994$		0			0
$995$	7.50091	+	4.33065i	0.237795	+	0.137291i
$996$		0			0
$997$	−23.1669	+	40.1263i	−0.733704	+	1.27081i	0.221586	+	0.975141i	$0.428877\pi$
$997$	−23.1669	+	40.1263i	−0.733704	+	1.27081i	−0.955290	+	0.295671i	$0.904457\pi$
$998$		0			0
$999$	22.6407	−	13.0716i	0.716320	−	0.413567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.d.673.3		12
4.3	odd	2		182.2.m.b.127.5	yes	12
12.11	even	2		1638.2.bj.g.127.1		12
13.4	even	6	inner	1456.2.cc.d.225.3		12
28.3	even	6		1274.2.o.e.569.5		12
28.11	odd	6		1274.2.o.d.569.5		12
28.19	even	6		1274.2.v.d.361.2		12
28.23	odd	6		1274.2.v.e.361.2		12
28.27	even	2		1274.2.m.c.491.5		12
52.3	odd	6		2366.2.d.r.337.9		12
52.11	even	12		2366.2.a.bf.1.3		6
52.15	even	12		2366.2.a.bh.1.3		6
52.23	odd	6		2366.2.d.r.337.3		12
52.43	odd	6		182.2.m.b.43.5	✓	12
156.95	even	6		1638.2.bj.g.1135.3		12
364.95	odd	6		1274.2.v.e.667.2		12
364.199	even	6		1274.2.v.d.667.2		12
364.251	even	6		1274.2.m.c.589.5		12
364.303	odd	6		1274.2.o.d.459.2		12
364.355	even	6		1274.2.o.e.459.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.5	✓	12	52.43	odd	6
182.2.m.b.127.5	yes	12	4.3	odd	2
1274.2.m.c.491.5		12	28.27	even	2
1274.2.m.c.589.5		12	364.251	even	6
1274.2.o.d.459.2		12	364.303	odd	6
1274.2.o.d.569.5		12	28.11	odd	6
1274.2.o.e.459.2		12	364.355	even	6
1274.2.o.e.569.5		12	28.3	even	6
1274.2.v.d.361.2		12	28.19	even	6
1274.2.v.d.667.2		12	364.199	even	6
1274.2.v.e.361.2		12	28.23	odd	6
1274.2.v.e.667.2		12	364.95	odd	6
1456.2.cc.d.225.3		12	13.4	even	6	inner
1456.2.cc.d.673.3		12	1.1	even	1	trivial
1638.2.bj.g.127.1		12	12.11	even	2
1638.2.bj.g.1135.3		12	156.95	even	6
2366.2.a.bf.1.3		6	52.11	even	12
2366.2.a.bh.1.3		6	52.15	even	12
2366.2.d.r.337.3		12	52.23	odd	6
2366.2.d.r.337.9		12	52.3	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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.233273 - 0.404040i) q^{3} +3.38938i q^{5} +(-0.866025 - 0.500000i) q^{7} +(1.39117 - 2.40957i) q^{9} +O(q^{10})\)	\(q+(-0.233273 - 0.404040i) q^{3} +3.38938i q^{5} +(-0.866025 - 0.500000i) q^{7} +(1.39117 - 2.40957i) q^{9} +(-0.712505 + 0.411365i) q^{11} +(-2.74987 + 2.33200i) q^{13} +(1.36944 - 0.790648i) q^{15} +(2.29065 - 3.96752i) q^{17} +(5.11492 + 2.95310i) q^{19} +0.466545i q^{21} +(3.06527 + 5.30921i) q^{23} -6.48787 q^{25} -2.69772 q^{27} +(3.43406 + 5.94797i) q^{29} -4.28683i q^{31} +(0.332416 + 0.191920i) q^{33} +(1.69469 - 2.93529i) q^{35} +(-8.39253 + 4.84543i) q^{37} +(1.58369 + 0.567065i) q^{39} +(-0.0774019 + 0.0446880i) q^{41} +(-3.67687 + 6.36853i) q^{43} +(8.16695 + 4.71519i) q^{45} +11.1759i q^{47} +(0.500000 + 0.866025i) q^{49} -2.13738 q^{51} -7.01530 q^{53} +(-1.39427 - 2.41495i) q^{55} -2.75551i q^{57} +(-1.50790 - 0.870585i) q^{59} +(-1.18972 + 2.06066i) q^{61} +(-2.40957 + 1.39117i) q^{63} +(-7.90403 - 9.32034i) q^{65} +(-0.252636 + 0.145859i) q^{67} +(1.43009 - 2.47698i) q^{69} +(-9.48158 - 5.47419i) q^{71} +12.7187i q^{73} +(1.51344 + 2.62136i) q^{75} +0.822730 q^{77} -9.95602 q^{79} +(-3.54420 - 6.13873i) q^{81} +3.23553i q^{83} +(13.4474 + 7.76387i) q^{85} +(1.60215 - 2.77500i) q^{87} +(6.96514 - 4.02133i) q^{89} +(3.54746 - 0.644638i) q^{91} +(-1.73205 + 1.00000i) q^{93} +(-10.0092 + 17.3364i) q^{95} +(12.7945 + 7.38693i) q^{97} +2.28911i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 6 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 - 6 * q^9	\( 12 q + 2 q^{3} - 6 q^{9} + 18 q^{11} - 8 q^{13} + 6 q^{15} + 4 q^{17} - 12 q^{19} + 6 q^{23} - 24 q^{25} - 40 q^{27} - 10 q^{29} + 12 q^{33} - 2 q^{35} - 6 q^{37} + 54 q^{39} - 24 q^{41} - 26 q^{43} + 72 q^{45} + 6 q^{49} + 36 q^{51} + 36 q^{53} + 6 q^{55} - 6 q^{59} - 28 q^{61} - 34 q^{65} + 42 q^{67} + 32 q^{69} - 48 q^{71} + 48 q^{75} - 4 q^{77} - 44 q^{79} - 34 q^{81} + 54 q^{85} - 2 q^{87} + 12 q^{89} + 16 q^{91} - 32 q^{95} + 60 q^{97}+O(q^{100}) \) 12 * q + 2 * q^3 - 6 * q^9 + 18 * q^11 - 8 * q^13 + 6 * q^15 + 4 * q^17 - 12 * q^19 + 6 * q^23 - 24 * q^25 - 40 * q^27 - 10 * q^29 + 12 * q^33 - 2 * q^35 - 6 * q^37 + 54 * q^39 - 24 * q^41 - 26 * q^43 + 72 * q^45 + 6 * q^49 + 36 * q^51 + 36 * q^53 + 6 * q^55 - 6 * q^59 - 28 * q^61 - 34 * q^65 + 42 * q^67 + 32 * q^69 - 48 * q^71 + 48 * q^75 - 4 * q^77 - 44 * q^79 - 34 * q^81 + 54 * q^85 - 2 * q^87 + 12 * q^89 + 16 * q^91 - 32 * q^95 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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