LMFDB - Embedded newform 441.2.u.c.64.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			64.3
Character	$\chi$	$=$	441.64
Dual form			441.2.u.c.379.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.243969 - 1.06890i) q^{2} +(0.718913 + 0.346210i) q^{4} +(2.19062 - 2.74696i) q^{5} +(0.626501 - 2.57050i) q^{7} +(1.91263 - 2.39836i) q^{8} +O(q^{10})$	\(q+(0.243969 - 1.06890i) q^{2} +(0.718913 + 0.346210i) q^{4} +(2.19062 - 2.74696i) q^{5} +(0.626501 - 2.57050i) q^{7} +(1.91263 - 2.39836i) q^{8} +(-2.40177 - 3.01173i) q^{10} +(-0.448609 + 1.96548i) q^{11} +(-1.56617 + 6.86183i) q^{13} +(-2.59476 - 1.29679i) q^{14} +(-1.10198 - 1.38184i) q^{16} +(-3.40512 + 1.63982i) q^{17} +0.124717 q^{19} +(2.52589 - 1.21641i) q^{20} +(1.99146 + 0.959035i) q^{22} +(-4.63107 - 2.23021i) q^{23} +(-1.63433 - 7.16046i) q^{25} +(6.95251 + 3.34815i) q^{26} +(1.34034 - 1.63107i) q^{28} +(-0.781907 + 0.376546i) q^{29} +6.42302 q^{31} +(3.78177 - 1.82120i) q^{32} +(0.922058 + 4.03980i) q^{34} +(-5.68863 - 7.35198i) q^{35} +(4.76417 - 2.29430i) q^{37} +(0.0304271 - 0.133310i) q^{38} +(-2.39834 - 10.5078i) q^{40} +(-4.77254 + 5.98457i) q^{41} +(2.89539 + 3.63071i) q^{43} +(-1.00298 + 1.25770i) q^{44} +(-3.51370 + 4.40605i) q^{46} +(0.715551 - 3.13503i) q^{47} +(-6.21499 - 3.22085i) q^{49} -8.05253 q^{50} +(-3.50158 + 4.39084i) q^{52} +(1.49012 + 0.717602i) q^{53} +(4.41636 + 5.53794i) q^{55} +(-4.96674 - 6.41900i) q^{56} +(0.211729 + 0.927645i) q^{58} +(4.33385 + 5.43448i) q^{59} +(-10.5515 + 5.08132i) q^{61} +(1.56702 - 6.86556i) q^{62} +(-1.81063 - 7.93289i) q^{64} +(15.4183 + 19.3339i) q^{65} -5.05874 q^{67} -3.01571 q^{68} +(-9.24638 + 4.28692i) q^{70} +(3.71799 + 1.79049i) q^{71} +(-1.41231 - 6.18774i) q^{73} +(-1.29007 - 5.65216i) q^{74} +(0.0896606 + 0.0431783i) q^{76} +(4.77123 + 2.38453i) q^{77} +10.1833 q^{79} -6.20987 q^{80} +(5.23255 + 6.56141i) q^{82} +(2.35665 + 10.3251i) q^{83} +(-2.95483 + 12.9460i) q^{85} +(4.58725 - 2.20910i) q^{86} +(3.85592 + 4.83517i) q^{88} +(-1.60829 - 7.04636i) q^{89} +(16.6572 + 8.32479i) q^{91} +(-2.55722 - 3.20665i) q^{92} +(-3.17646 - 1.52970i) q^{94} +(0.273208 - 0.342592i) q^{95} -14.5510 q^{97} +(-4.95903 + 5.85741i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	0.243969	−	1.06890i	0.172512	−	0.755826i	−0.812446	−	0.583036i	$-0.801865\pi$
$2$	0.243969	−	1.06890i	0.172512	−	0.755826i	0.984959	−	0.172790i	$-0.0552782\pi$
$3$		0			0
$3$		0			0
$4$	0.718913	+	0.346210i	0.359457	+	0.173105i
$5$	2.19062	−	2.74696i	0.979677	−	1.22848i	0.00613176	−	0.999981i	$-0.498048\pi$
$5$	2.19062	−	2.74696i	0.979677	−	1.22848i	0.973545	−	0.228495i	$-0.0733804\pi$
$6$		0			0
$7$	0.626501	−	2.57050i	0.236795	−	0.971560i
$7$	0.626501	−	2.57050i	0.236795	−	0.971560i
$8$	1.91263	−	2.39836i	0.676217	−	0.847949i
$9$		0			0
$10$	−2.40177	−	3.01173i	−0.759508	−	0.952392i
$11$	−0.448609	+	1.96548i	−0.135261	+	0.592615i	0.861179	+	0.508302i	$0.169727\pi$
$11$	−0.448609	+	1.96548i	−0.135261	+	0.592615i	−0.996439	+	0.0843131i	$0.973130\pi$
$12$		0			0
$13$	−1.56617	+	6.86183i	−0.434377	+	1.90313i	−0.00503542	+	0.999987i	$0.501603\pi$
$13$	−1.56617	+	6.86183i	−0.434377	+	1.90313i	−0.429341	+	0.903142i	$0.641254\pi$
$14$	−2.59476	−	1.29679i	−0.693480	−	0.346582i
$15$		0			0
$16$	−1.10198	−	1.38184i	−0.275495	−	0.345459i
$17$	−3.40512	+	1.63982i	−0.825864	+	0.397715i	−0.798562	−	0.601912i	$-0.794406\pi$
$17$	−3.40512	+	1.63982i	−0.825864	+	0.397715i	−0.0273016	+	0.999627i	$0.508691\pi$
$18$		0			0
$19$	0.124717			0.0286120			0.0143060	−	0.999898i	$-0.495446\pi$
$19$	0.124717			0.0286120			0.0143060	+	0.999898i	$0.495446\pi$
$20$	2.52589	−	1.21641i	0.564807	−	0.271997i
$21$		0			0
$22$	1.99146	+	0.959035i	0.424580	+	0.204467i
$23$	−4.63107	−	2.23021i	−0.965645	−	0.465030i	−0.116500	−	0.993191i	$-0.537168\pi$
$23$	−4.63107	−	2.23021i	−0.965645	−	0.465030i	−0.849144	+	0.528161i	$0.822882\pi$
$24$		0			0
$25$	−1.63433	−	7.16046i	−0.326865	−	1.43209i
$26$	6.95251	+	3.34815i	1.36350	+	0.656627i
$27$		0			0
$28$	1.34034	−	1.63107i	0.253300	−	0.308243i
$29$	−0.781907	+	0.376546i	−0.145196	+	0.0699229i	−0.505071	−	0.863078i	$-0.668534\pi$
$29$	−0.781907	+	0.376546i	−0.145196	+	0.0699229i	0.359875	+	0.933001i	$0.382819\pi$
$30$		0			0
$31$	6.42302			1.15361			0.576804	−	0.816883i	$-0.304300\pi$
$31$	6.42302			1.15361			0.576804	+	0.816883i	$0.304300\pi$
$32$	3.78177	−	1.82120i	0.668528	−	0.321946i
$33$		0			0
$34$	0.922058	+	4.03980i	0.158132	+	0.692820i
$35$	−5.68863	−	7.35198i	−0.961555	−	1.24271i
$36$		0			0
$37$	4.76417	−	2.29430i	0.783225	−	0.377181i	0.000858683	−	1.00000i	$-0.499727\pi$
$37$	4.76417	−	2.29430i	0.783225	−	0.377181i	0.782367	+	0.622818i	$0.214012\pi$
$38$	0.0304271	−	0.133310i	0.00493593	−	0.0216257i
$39$		0			0
$40$	−2.39834	−	10.5078i	−0.379211	−	1.66143i
$41$	−4.77254	+	5.98457i	−0.745345	+	0.934633i	−0.999470	−	0.0325381i	$-0.989641\pi$
$41$	−4.77254	+	5.98457i	−0.745345	+	0.934633i	0.254125	+	0.967171i	$0.418212\pi$
$42$		0			0
$43$	2.89539	+	3.63071i	0.441543	+	0.553678i	0.951949	−	0.306256i	$-0.0990763\pi$
$43$	2.89539	+	3.63071i	0.441543	+	0.553678i	−0.510406	+	0.859934i	$0.670505\pi$
$44$	−1.00298	+	1.25770i	−0.151205	+	0.189605i
$45$		0			0
$46$	−3.51370	+	4.40605i	−0.518067	+	0.649636i
$47$	0.715551	−	3.13503i	0.104374	−	0.457292i	−0.895550	−	0.444961i	$-0.853218\pi$
$47$	0.715551	−	3.13503i	0.104374	−	0.457292i	0.999924	−	0.0123311i	$-0.00392520\pi$
$48$		0			0
$49$	−6.21499	−	3.22085i	−0.887856	−	0.460121i
$50$	−8.05253			−1.13880
$51$		0			0
$52$	−3.50158	+	4.39084i	−0.485581	+	0.608899i
$53$	1.49012	+	0.717602i	0.204683	+	0.0985702i	0.533417	−	0.845852i	$-0.320908\pi$
$53$	1.49012	+	0.717602i	0.204683	+	0.0985702i	−0.328734	+	0.944423i	$0.606622\pi$
$54$		0			0
$55$	4.41636	+	5.53794i	0.595502	+	0.746736i
$56$	−4.96674	−	6.41900i	−0.663708	−	0.857775i
$57$		0			0
$58$	0.211729	+	0.927645i	0.0278014	+	0.121806i
$59$	4.33385	+	5.43448i	0.564220	+	0.707509i	0.979332	−	0.202261i	$-0.0648290\pi$
$59$	4.33385	+	5.43448i	0.564220	+	0.707509i	−0.415112	+	0.909770i	$0.636258\pi$
$60$		0			0
$61$	−10.5515	+	5.08132i	−1.35098	+	0.650596i	−0.962606	−	0.270907i	$-0.912677\pi$
$61$	−10.5515	+	5.08132i	−1.35098	+	0.650596i	−0.388372	+	0.921503i	$0.626962\pi$
$62$	1.56702	−	6.86556i	0.199012	−	0.871927i
$63$		0			0
$64$	−1.81063	−	7.93289i	−0.226329	−	0.991611i
$65$	15.4183	+	19.3339i	1.91240	+	2.39807i
$66$		0			0
$67$	−5.05874			−0.618024			−0.309012	−	0.951058i	$-0.599998\pi$
$67$	−5.05874			−0.618024			−0.309012	+	0.951058i	$0.599998\pi$
$68$	−3.01571			−0.365709
$69$		0			0
$70$	−9.24638	+	4.28692i	−1.10515	+	0.512385i
$71$	3.71799	+	1.79049i	0.441245	+	0.212492i	0.641297	−	0.767293i	$-0.278397\pi$
$71$	3.71799	+	1.79049i	0.441245	+	0.212492i	−0.200052	+	0.979785i	$0.564111\pi$
$72$		0			0
$73$	−1.41231	−	6.18774i	−0.165299	−	0.724221i	−0.987835	−	0.155508i	$-0.950299\pi$
$73$	−1.41231	−	6.18774i	−0.165299	−	0.724221i	0.822536	−	0.568713i	$-0.192558\pi$
$74$	−1.29007	−	5.65216i	−0.149967	−	0.657050i
$75$		0			0
$76$	0.0896606	+	0.0431783i	0.0102848	+	0.00495289i
$77$	4.77123	+	2.38453i	0.543732	+	0.271742i
$78$		0			0
$79$	10.1833			1.14571			0.572857	−	0.819655i	$-0.305835\pi$
$79$	10.1833			1.14571			0.572857	+	0.819655i	$0.305835\pi$
$80$	−6.20987			−0.694284
$81$		0			0
$82$	5.23255	+	6.56141i	0.577839	+	0.724587i
$83$	2.35665	+	10.3251i	0.258676	+	1.13333i	0.922669	+	0.385593i	$0.126003\pi$
$83$	2.35665	+	10.3251i	0.258676	+	1.13333i	−0.663993	+	0.747739i	$0.731140\pi$
$84$		0			0
$85$	−2.95483	+	12.9460i	−0.320496	+	1.40419i
$86$	4.58725	−	2.20910i	0.494656	−	0.238214i
$87$		0			0
$88$	3.85592	+	4.83517i	0.411042	+	0.515431i
$89$	−1.60829	−	7.04636i	−0.170478	−	0.746913i	−0.985803	−	0.167909i	$-0.946299\pi$
$89$	−1.60829	−	7.04636i	−0.170478	−	0.746913i	0.815325	−	0.579004i	$-0.196559\pi$
$90$		0			0
$91$	16.6572	+	8.32479i	1.74615	+	0.872675i
$92$	−2.55722	−	3.20665i	−0.266608	−	0.334316i
$93$		0			0
$94$	−3.17646	−	1.52970i	−0.327627	−	0.157777i
$95$	0.273208	−	0.342592i	0.0280305	−	0.0351492i
$96$		0			0
$97$	−14.5510			−1.47743			−0.738716	−	0.674017i	$-0.764568\pi$
$97$	−14.5510			−1.47743			−0.738716	+	0.674017i	$0.764568\pi$
$98$	−4.95903	+	5.85741i	−0.500938	+	0.591688i
$99$		0			0
$100$	1.30408	−	5.71357i	0.130408	−	0.571357i
$101$	−8.66336	+	10.8635i	−0.862036	+	1.08096i	0.133909	+	0.990994i	$0.457247\pi$
$101$	−8.66336	+	10.8635i	−0.862036	+	1.08096i	−0.995945	+	0.0899654i	$0.971324\pi$
$102$		0			0
$103$	3.17382	−	3.97985i	0.312726	−	0.392146i	−0.600483	−	0.799637i	$-0.705025\pi$
$103$	3.17382	−	3.97985i	0.312726	−	0.392146i	0.913209	+	0.407492i	$0.133596\pi$
$104$	13.4617	+	16.8804i	1.32002	+	1.65526i
$105$		0			0
$106$	1.13059	−	1.41771i	0.109812	−	0.137700i
$107$	−3.18118	−	13.9376i	−0.307536	−	1.34740i	−0.858474	−	0.512857i	$-0.828587\pi$
$107$	−3.18118	−	13.9376i	−0.307536	−	1.34740i	0.550938	−	0.834546i	$-0.314270\pi$
$108$		0			0
$109$	1.12219	−	4.91664i	0.107486	−	0.470929i	−0.892323	−	0.451398i	$-0.850926\pi$
$109$	1.12219	−	4.91664i	0.107486	−	0.470929i	0.999809	−	0.0195310i	$-0.00621730\pi$
$110$	6.99696	−	3.36956i	0.667134	−	0.321275i
$111$		0			0
$112$	−4.24241	+	1.96692i	−0.400870	+	0.185856i
$113$	−2.11436	−	9.26363i	−0.198903	−	0.871449i	−0.971591	−	0.236664i	$-0.923946\pi$
$113$	−2.11436	−	9.26363i	−0.198903	−	0.871449i	0.772689	−	0.634785i	$-0.218911\pi$
$114$		0			0
$115$	−16.2712	+	7.83580i	−1.51730	+	0.730692i
$116$	−0.692487			−0.0642958
$117$		0			0
$118$	6.86624	−	3.30661i	0.632089	−	0.304398i
$119$	2.08185	+	9.78024i	0.190843	+	0.896553i
$120$		0			0
$121$	6.24879	+	3.00926i	0.568071	+	0.273569i
$122$	2.85718	+	12.5181i	0.258677	+	1.13334i
$123$		0			0
$124$	4.61759	+	2.22371i	0.414672	+	0.199695i
$125$	−7.42193	−	3.57422i	−0.663838	−	0.319688i
$126$		0			0
$127$	11.4770	−	5.52704i	1.01842	−	0.490445i	0.151270	−	0.988492i	$-0.451664\pi$
$127$	11.4770	−	5.52704i	1.01842	−	0.490445i	0.867150	+	0.498047i	$0.165949\pi$
$128$	−0.526310			−0.0465196
$129$		0			0
$130$	24.4276	−	11.7637i	2.14244	−	1.03174i
$131$	9.55332	+	11.9795i	0.834677	+	1.04665i	0.998192	+	0.0601110i	$0.0191455\pi$
$131$	9.55332	+	11.9795i	0.834677	+	1.04665i	−0.163515	+	0.986541i	$0.552283\pi$
$132$		0			0
$133$	0.0781353	−	0.320585i	0.00677519	−	0.0277983i
$134$	−1.23418	+	5.40728i	−0.106617	+	0.467118i
$135$		0			0
$136$	−2.57986	+	11.3031i	−0.221221	+	0.969232i
$137$	−2.20703	−	2.76752i	−0.188559	−	0.236445i	0.678562	−	0.734543i	$-0.262603\pi$
$137$	−2.20703	−	2.76752i	−0.188559	−	0.236445i	−0.867121	+	0.498098i	$0.834032\pi$
$138$		0			0
$139$	5.95746	−	7.47042i	0.505305	−	0.633633i	−0.462112	−	0.886822i	$-0.652908\pi$
$139$	5.95746	−	7.47042i	0.505305	−	0.633633i	0.967417	+	0.253189i	$0.0814795\pi$
$140$	−1.54430	−	7.25490i	−0.130517	−	0.613151i
$141$		0			0
$142$	2.82093	−	3.53734i	0.236727	−	0.296847i
$143$	−12.7842	−	6.15655i	−1.06907	−	0.514837i
$144$		0			0
$145$	−0.678507	+	2.97273i	−0.0563470	+	0.246872i
$146$	−6.95864			−0.575901
$147$		0			0
$148$	4.21934			0.346827
$149$	−3.71309	+	16.2681i	−0.304188	+	1.33274i	0.559550	+	0.828796i	$0.310974\pi$
$149$	−3.71309	+	16.2681i	−0.304188	+	1.33274i	−0.863739	+	0.503940i	$0.831883\pi$
$150$		0			0
$151$	−0.668927	−	0.322138i	−0.0544365	−	0.0262152i	0.406467	−	0.913665i	$-0.366760\pi$
$151$	−0.668927	−	0.322138i	−0.0544365	−	0.0262152i	−0.460904	+	0.887450i	$0.652475\pi$
$152$	0.238537	−	0.299116i	0.0193479	−	0.0242615i
$153$		0			0
$154$	3.71285	−	4.51821i	0.299190	−	0.364088i
$155$	14.0704	−	17.6437i	1.13016	−	1.41718i
$156$		0			0
$157$	−4.38425	−	5.49767i	−0.349901	−	0.438762i	0.575471	−	0.817822i	$-0.304819\pi$
$157$	−4.38425	−	5.49767i	−0.349901	−	0.438762i	−0.925372	+	0.379060i	$0.876247\pi$
$158$	2.48442	−	10.8850i	0.197650	−	0.865961i
$159$		0			0
$160$	3.28167	−	14.3779i	0.259439	−	1.13667i
$161$	−8.63413	+	10.5070i	−0.680464	+	0.828064i
$162$		0			0
$163$	3.04788	+	3.82192i	0.238729	+	0.299356i	0.886734	−	0.462279i	$-0.152968\pi$
$163$	3.04788	+	3.82192i	0.238729	+	0.299356i	−0.648006	+	0.761635i	$0.724397\pi$
$164$	−5.50296	+	2.65009i	−0.429709	+	0.206937i
$165$		0			0
$166$	11.6115			0.901227
$167$	−2.02338	+	0.974406i	−0.156573	+	0.0754018i	−0.510529	−	0.859860i	$-0.670551\pi$
$167$	−2.02338	+	0.974406i	−0.156573	+	0.0754018i	0.353956	+	0.935262i	$0.384836\pi$
$168$		0			0
$169$	−32.9192	−	15.8531i	−2.53225	−	1.21947i
$170$	13.1170	+	6.31683i	1.00603	+	0.484479i
$171$		0			0
$172$	0.824547	+	3.61258i	0.0628711	+	0.275456i
$173$	−16.4173	−	7.90615i	−1.24818	−	0.601093i	−0.311159	−	0.950358i	$-0.600717\pi$
$173$	−16.4173	−	7.90615i	−1.24818	−	0.601093i	−0.937024	+	0.349265i	$0.886431\pi$
$174$		0			0
$175$	−19.4299	−	0.284990i	−1.46876	−	0.0215432i
$176$	3.21033	−	1.54602i	0.241988	−	0.116535i
$177$		0			0
$178$	−7.92422			−0.593946
$179$	−4.06987	+	1.95994i	−0.304196	+	0.146493i	−0.579755	−	0.814791i	$-0.696852\pi$
$179$	−4.06987	+	1.95994i	−0.304196	+	0.146493i	0.275558	+	0.961284i	$0.411137\pi$
$180$		0			0
$181$	2.25472	+	9.87857i	0.167592	+	0.734268i	0.986955	+	0.160994i	$0.0514699\pi$
$181$	2.25472	+	9.87857i	0.167592	+	0.734268i	−0.819363	+	0.573274i	$0.805673\pi$
$182$	12.9622	−	15.7738i	0.960822	−	1.16923i
$183$		0			0
$184$	−14.2064	+	6.84142i	−1.04731	+	0.504356i
$185$	4.13416	−	18.1129i	0.303949	−	1.33169i
$186$		0			0
$187$	−1.69547	−	7.42835i	−0.123985	−	0.543215i
$188$	1.59980	−	2.00609i	0.116677	−	0.146309i
$189$		0			0
$190$	−0.299542	−	0.375614i	−0.0217310	−	0.0272499i
$191$	0.195519	−	0.245173i	0.0141473	−	0.0177401i	−0.774708	−	0.632320i	$-0.782103\pi$
$191$	0.195519	−	0.245173i	0.0141473	−	0.0177401i	0.788855	+	0.614580i	$0.210674\pi$
$192$		0			0
$193$	−8.32223	+	10.4357i	−0.599047	+	0.751181i	−0.985229	−	0.171241i	$-0.945222\pi$
$193$	−8.32223	+	10.4357i	−0.599047	+	0.751181i	0.386182	+	0.922423i	$0.373794\pi$
$194$	−3.55000	+	15.5536i	−0.254875	+	1.11668i
$195$		0			0
$196$	−3.35295	−	4.46721i	−0.239496	−	0.319086i
$197$	23.2608			1.65727			0.828633	−	0.559792i	$-0.189119\pi$
$197$	23.2608			1.65727			0.828633	+	0.559792i	$0.189119\pi$
$198$		0			0
$199$	−8.99075	+	11.2740i	−0.637337	+	0.799195i	−0.990667	−	0.136303i	$-0.956478\pi$
$199$	−8.99075	+	11.2740i	−0.637337	+	0.799195i	0.353330	+	0.935499i	$0.385049\pi$
$200$	−20.2992	−	9.77559i	−1.43537	−	0.691239i
$201$		0			0
$202$	9.49840	+	11.9106i	0.668305	+	0.838028i
$203$	0.478049	+	2.24580i	0.0335524	+	0.157624i
$204$		0			0
$205$	5.98452	+	26.2199i	0.417977	+	1.83128i
$206$	−3.47974	−	4.36346i	−0.242445	−	0.304016i
$207$		0			0
$208$	11.2078	−	5.39740i	0.777122	−	0.374242i
$209$	−0.0559491	+	0.245129i	−0.00387008	+	0.0169559i
$210$		0			0
$211$	−1.36359	−	5.97427i	−0.0938733	−	0.411286i	0.906056	−	0.423157i	$-0.139078\pi$
$211$	−1.36359	−	5.97427i	−0.0938733	−	0.411286i	−0.999930	+	0.0118714i	$0.996221\pi$
$212$	0.822822	+	1.03179i	0.0565117	+	0.0708634i
$213$		0			0
$214$	−15.6740			−1.07146
$215$	16.3161			1.11275
$216$		0			0
$217$	4.02403	−	16.5104i	0.273169	−	1.12080i
$218$	−4.98161	−	2.39902i	−0.337397	−	0.162482i
$219$		0			0
$220$	1.25769	+	5.51029i	0.0847933	+	0.371504i
$221$	−5.91918	−	25.9336i	−0.398167	−	1.74448i
$222$		0			0
$223$	−9.86850	−	4.75242i	−0.660844	−	0.318246i	0.0732302	−	0.997315i	$-0.476669\pi$
$223$	−9.86850	−	4.75242i	−0.660844	−	0.318246i	−0.734074	+	0.679069i	$0.762384\pi$
$224$	−2.31213	−	10.8620i	−0.154486	−	0.725751i
$225$		0			0
$226$	−10.4177			−0.692977
$227$	−9.08467			−0.602971			−0.301485	−	0.953471i	$-0.597482\pi$
$227$	−9.08467			−0.602971			−0.301485	+	0.953471i	$0.597482\pi$
$228$		0			0
$229$	2.61298	+	3.27657i	0.172671	+	0.216522i	0.860635	−	0.509222i	$-0.170067\pi$
$229$	2.61298	+	3.27657i	0.172671	+	0.216522i	−0.687964	+	0.725744i	$0.741495\pi$
$230$	4.40601	+	19.3040i	0.290524	+	1.27287i
$231$		0			0
$232$	−0.592403	+	2.59549i	−0.0388932	+	0.170402i
$233$	10.4625	−	5.03849i	0.685424	−	0.330083i	−0.0585568	−	0.998284i	$-0.518650\pi$
$233$	10.4625	−	5.03849i	0.685424	−	0.330083i	0.743980	+	0.668201i	$0.232936\pi$
$234$		0			0
$235$	−7.04430	−	8.83327i	−0.459519	−	0.576219i
$236$	1.23419	+	5.40734i	0.0803390	+	0.351988i
$237$		0			0
$238$	10.9620	+	0.160786i	0.710561	+	0.0104222i
$239$	−2.35597	−	2.95430i	−0.152395	−	0.191098i	0.699773	−	0.714365i	$-0.253284\pi$
$239$	−2.35597	−	2.95430i	−0.152395	−	0.191098i	−0.852169	+	0.523267i	$0.824713\pi$
$240$		0			0
$241$	23.2734	+	11.2079i	1.49917	+	0.721963i	0.990309	−	0.138884i	$-0.0443516\pi$
$241$	23.2734	+	11.2079i	1.49917	+	0.721963i	0.508863	+	0.860847i	$0.330066\pi$
$242$	4.74110	−	5.94516i	0.304770	−	0.382169i
$243$		0			0
$244$	−9.34479			−0.598239
$245$	−22.4622	+	10.0166i	−1.43506	+	0.639939i
$246$		0			0
$247$	−0.195328	+	0.855786i	−0.0124284	+	0.0544524i
$248$	12.2849	−	15.4047i	0.780089	−	0.978201i
$249$		0			0
$250$	−5.63120	+	7.06130i	−0.356148	+	0.446596i
$251$	−14.8973	−	18.6807i	−0.940312	−	1.17911i	−0.983657	−	0.180054i	$-0.942373\pi$
$251$	−14.8973	−	18.6807i	−0.940312	−	1.17911i	0.0433449	−	0.999060i	$-0.486199\pi$
$252$		0			0
$253$	6.46097	−	8.10180i	0.406198	−	0.509356i
$254$	−3.10781	−	13.6162i	−0.195001	−	0.854356i
$255$		0			0
$256$	3.49286	−	15.3032i	0.218304	−	0.956451i
$257$	2.67552	−	1.28846i	0.166894	−	0.0803720i	−0.348572	−	0.937282i	$-0.613333\pi$
$257$	2.67552	−	1.28846i	0.166894	−	0.0803720i	0.515466	+	0.856910i	$0.327619\pi$
$258$		0			0
$259$	−2.91276	−	13.6837i	−0.180990	−	0.850265i
$260$	4.39080	+	19.2373i	0.272306	+	1.19305i
$261$		0			0
$262$	15.1356	−	7.28891i	0.935079	−	0.450310i
$263$	−6.30252			−0.388630			−0.194315	−	0.980939i	$-0.562248\pi$
$263$	−6.30252			−0.388630			−0.194315	+	0.980939i	$0.562248\pi$
$264$		0			0
$265$	5.23550	−	2.52129i	0.321614	−	0.154881i
$266$	−0.323611	−	0.161732i	−0.0198419	−	0.00991641i
$267$		0			0
$268$	−3.63680	−	1.75139i	−0.222153	−	0.106983i
$269$	0.720241	+	3.15558i	0.0439139	+	0.192399i	0.992127	−	0.125235i	$-0.0399686\pi$
$269$	0.720241	+	3.15558i	0.0439139	+	0.192399i	−0.948213	+	0.317635i	$0.897111\pi$
$270$		0			0
$271$	4.96691	+	2.39194i	0.301718	+	0.145300i	0.578617	−	0.815599i	$-0.303592\pi$
$271$	4.96691	+	2.39194i	0.301718	+	0.145300i	−0.276899	+	0.960899i	$0.589307\pi$
$272$	6.01834	+	2.89828i	0.364915	+	0.175734i
$273$		0			0
$274$	−3.49665	+	1.68390i	−0.211240	+	0.101728i
$275$	14.8069			0.892891
$276$		0			0
$277$	−1.31662	+	0.634048i	−0.0791077	+	0.0380963i	−0.473019	−	0.881052i	$-0.656836\pi$
$277$	−1.31662	+	0.634048i	−0.0791077	+	0.0380963i	0.393912	+	0.919148i	$0.371122\pi$
$278$	−6.53169	−	8.19048i	−0.391745	−	0.491232i
$279$		0			0
$280$	−28.5130	−	0.418216i	−1.70398	−	0.0249932i
$281$	1.20007	−	5.25787i	0.0715904	−	0.313658i	−0.926436	−	0.376452i	$-0.877144\pi$
$281$	1.20007	−	5.25787i	0.0715904	−	0.313658i	0.998027	+	0.0627940i	$0.0200011\pi$
$282$		0			0
$283$	5.89452	−	25.8256i	0.350393	−	1.53517i	−0.425884	−	0.904778i	$-0.640037\pi$
$283$	5.89452	−	25.8256i	0.350393	−	1.53517i	0.776276	−	0.630393i	$-0.217106\pi$
$284$	2.05303	+	2.57442i	0.121825	+	0.152763i
$285$		0			0
$286$	−9.69969	+	12.1630i	−0.573555	+	0.719215i
$287$	12.3934	+	16.0172i	0.731558	+	0.945464i
$288$		0			0
$289$	−1.69347	+	2.12354i	−0.0996159	+	0.124914i
$290$	3.01202	+	1.45051i	0.176872	+	0.0851770i
$291$		0			0
$292$	1.12693	−	4.93741i	0.0659486	−	0.288940i
$293$	−0.659144			−0.0385076			−0.0192538	−	0.999815i	$-0.506129\pi$
$293$	−0.659144			−0.0385076			−0.0192538	+	0.999815i	$0.506129\pi$
$294$		0			0
$295$	24.4221			1.42191
$296$	3.60953	−	15.8144i	0.209799	−	0.919192i
$297$		0			0
$298$	16.4831	+	7.93785i	0.954841	+	0.459827i
$299$	22.5563	−	28.2847i	1.30447	−	1.63575i
$300$		0			0
$301$	11.1467	−	5.16798i	0.642486	−	0.297877i
$302$	−0.507531	+	0.636423i	−0.0292051	+	0.0366220i
$303$		0			0
$304$	−0.137435	−	0.172338i	−0.00788245	−	0.00988429i
$305$	−9.15614	+	40.1157i	−0.524279	+	2.29702i
$306$		0			0
$307$	7.73998	−	33.9111i	0.441744	−	1.93541i	0.102407	−	0.994743i	$-0.467346\pi$
$307$	7.73998	−	33.9111i	0.441744	−	1.93541i	0.339337	−	0.940665i	$-0.389797\pi$
$308$	2.60455	+	3.36612i	0.148408	+	0.191802i
$309$		0			0
$310$	−15.4266	−	19.3444i	−0.876174	−	1.09869i
$311$	4.91998	−	2.36934i	0.278986	−	0.134353i	−0.289159	−	0.957281i	$-0.593376\pi$
$311$	4.91998	−	2.36934i	0.278986	−	0.134353i	0.568145	+	0.822928i	$0.307661\pi$
$312$		0			0
$313$	2.78805			0.157590			0.0787949	−	0.996891i	$-0.474893\pi$
$313$	2.78805			0.157590			0.0787949	+	0.996891i	$0.474893\pi$
$314$	−6.94608	+	3.34506i	−0.391990	+	0.188772i
$315$		0			0
$316$	7.32093	+	3.52557i	0.411835	+	0.198329i
$317$	11.8511	+	5.70717i	0.665622	+	0.320547i	0.736008	−	0.676973i	$-0.236709\pi$
$317$	11.8511	+	5.70717i	0.665622	+	0.320547i	−0.0703855	+	0.997520i	$0.522423\pi$
$318$		0			0
$319$	−0.389325	−	1.70575i	−0.0217980	−	0.0955034i
$320$	−25.7577	−	12.4043i	−1.43990	−	0.693419i
$321$		0			0
$322$	9.12442	+	11.7924i	0.508484	+	0.657164i
$323$	−0.424676	+	0.204513i	−0.0236296	+	0.0113794i
$324$		0			0
$325$	51.6935			2.86744
$326$	4.82884	−	2.32545i	0.267445	−	0.128795i
$327$		0			0
$328$	5.22507	+	22.8925i	0.288506	+	1.26403i
$329$	−7.61033	−	3.80343i	−0.419571	−	0.209690i
$330$		0			0
$331$	−29.4211	+	14.1685i	−1.61713	+	0.778770i	−0.999967	−	0.00806449i	$-0.997433\pi$
$331$	−29.4211	+	14.1685i	−1.61713	+	0.778770i	−0.617164	+	0.786834i	$0.711719\pi$
$332$	−1.88045	+	8.23878i	−0.103203	+	0.452162i
$333$		0			0
$334$	0.547901	+	2.40051i	0.0299798	+	0.131350i
$335$	−11.0818	+	13.8961i	−0.605463	+	0.759227i
$336$		0			0
$337$	−0.136854	−	0.171610i	−0.00745492	−	0.00934817i	0.778090	−	0.628153i	$-0.216189\pi$
$337$	−0.136854	−	0.171610i	−0.00745492	−	0.00934817i	−0.785545	+	0.618805i	$0.787617\pi$
$338$	−24.9766	+	31.3197i	−1.35855	+	1.70357i
$339$		0			0
$340$	−6.60629	+	8.28403i	−0.358276	+	0.449264i
$341$	−2.88142	+	12.6243i	−0.156038	+	0.683646i
$342$		0			0
$343$	−12.1729	+	13.9578i	−0.657276	+	0.753650i
$344$	14.2456			0.768069
$345$		0			0
$346$	−12.4562	+	15.6196i	−0.669649	+	0.839713i
$347$	−5.80838	−	2.79717i	−0.311810	−	0.150160i	0.271433	−	0.962457i	$-0.412502\pi$
$347$	−5.80838	−	2.79717i	−0.311810	−	0.150160i	−0.583244	+	0.812297i	$0.698217\pi$
$348$		0			0
$349$	−4.44544	−	5.57441i	−0.237959	−	0.298391i	0.648485	−	0.761228i	$-0.275403\pi$
$349$	−4.44544	−	5.57441i	−0.237959	−	0.298391i	−0.886444	+	0.462837i	$0.846832\pi$
$350$	−5.04492	+	20.6991i	−0.269662	+	1.10641i
$351$		0			0
$352$	1.88301	+	8.25001i	0.100365	+	0.439727i
$353$	10.9943	+	13.7864i	0.585165	+	0.733774i	0.982984	−	0.183690i	$-0.0588043\pi$
$353$	10.9943	+	13.7864i	0.585165	+	0.733774i	−0.397819	+	0.917464i	$0.630233\pi$
$354$		0			0
$355$	13.0631	−	6.29087i	0.693319	−	0.333885i
$356$	1.28331	−	5.62253i	0.0680150	−	0.297993i
$357$		0			0
$358$	1.10206	+	4.82844i	0.0582457	+	0.255191i
$359$	−18.5877	−	23.3082i	−0.981019	−	1.23016i	−0.973146	−	0.230190i	$-0.926065\pi$
$359$	−18.5877	−	23.3082i	−0.981019	−	1.23016i	−0.00787335	−	0.999969i	$-0.502506\pi$
$360$		0			0
$361$	−18.9844			−0.999181
$362$	11.1093			0.583891
$363$		0			0
$364$	9.09292	+	11.7517i	0.476599	+	0.615956i
$365$	−20.0913	−	9.67546i	−1.05163	−	0.506437i
$366$		0			0
$367$	2.09078	+	9.16031i	0.109138	+	0.478164i	0.999727	+	0.0233559i	$0.00743510\pi$
$367$	2.09078	+	9.16031i	0.109138	+	0.478164i	−0.890589	+	0.454808i	$0.849708\pi$
$368$	2.02156	+	8.85702i	0.105381	+	0.461704i
$369$		0			0
$370$	−18.3523	−	8.83800i	−0.954090	−	0.459466i
$371$	2.77816	−	3.38077i	0.144235	−	0.175521i
$372$		0			0
$373$	−11.5591			−0.598509			−0.299255	−	0.954173i	$-0.596738\pi$
$373$	−11.5591			−0.598509			−0.299255	+	0.954173i	$0.596738\pi$
$374$	−8.35380			−0.431965
$375$		0			0
$376$	−6.15036	−	7.71231i	−0.317181	−	0.397732i
$377$	−1.35920	−	5.95505i	−0.0700024	−	0.306700i
$378$		0			0
$379$	1.54209	−	6.75632i	0.0792117	−	0.347049i	−0.919755	−	0.392492i	$-0.871613\pi$
$379$	1.54209	−	6.75632i	0.0792117	−	0.347049i	0.998967	+	0.0454434i	$0.0144701\pi$
$380$	0.315021	−	0.151706i	0.0161603	−	0.00778237i
$381$		0			0
$382$	−0.214365	−	0.268805i	−0.0109679	−	0.0137533i
$383$	−1.05533	−	4.62368i	−0.0539246	−	0.236259i	0.940782	−	0.339011i	$-0.110092\pi$
$383$	−1.05533	−	4.62368i	−0.0539246	−	0.236259i	−0.994707	+	0.102752i	$0.967235\pi$
$384$		0			0
$385$	17.0022	−	7.88275i	0.866510	−	0.401742i
$386$	9.12439	+	11.4416i	0.464419	+	0.582363i
$387$		0			0
$388$	−10.4609	−	5.03771i	−0.531073	−	0.255751i
$389$	−4.19291	+	5.25774i	−0.212589	+	0.266578i	−0.876680	−	0.481073i	$-0.840247\pi$
$389$	−4.19291	+	5.25774i	−0.212589	+	0.266578i	0.664091	+	0.747651i	$0.268819\pi$
$390$		0			0
$391$	19.4265			0.982441
$392$	−19.6117	+	8.74551i	−0.990543	+	0.441715i
$393$		0			0
$394$	5.67493	−	24.8635i	0.285899	−	1.25260i
$395$	22.3079	−	27.9732i	1.12243	−	1.40748i
$396$		0			0
$397$	10.2348	−	12.8341i	0.513671	−	0.644124i	−0.455580	−	0.890195i	$-0.650568\pi$
$397$	10.2348	−	12.8341i	0.513671	−	0.644124i	0.969252	+	0.246071i	$0.0791396\pi$
$398$	9.85735	+	12.3607i	0.494104	+	0.619587i
$399$		0			0
$400$	−8.09359	+	10.1490i	−0.404679	+	0.507452i
$401$	−6.50280	−	28.4906i	−0.324735	−	1.42276i	−0.829020	−	0.559218i	$-0.811101\pi$
$401$	−6.50280	−	28.4906i	−0.324735	−	1.42276i	0.504286	−	0.863537i	$-0.331756\pi$
$402$		0			0
$403$	−10.0595	+	44.0737i	−0.501101	+	2.19547i
$404$	−9.98926	+	4.81057i	−0.496984	+	0.239335i
$405$		0			0
$406$	2.51717	+	0.0369207i	0.124925	+	0.00183235i
$407$	2.37217	+	10.3931i	0.117584	+	0.515169i
$408$		0			0
$409$	−13.5023	+	6.50238i	−0.667648	+	0.321522i	−0.736826	−	0.676082i	$-0.763676\pi$
$409$	−13.5023	+	6.50238i	−0.667648	+	0.321522i	0.0691785	+	0.997604i	$0.477962\pi$
$410$	29.4865			1.45623
$411$		0			0
$412$	3.65957	−	1.76235i	0.180294	−	0.0868249i
$413$	16.6845	−	7.73548i	0.820992	−	0.380638i
$414$		0			0
$415$	33.5252	+	16.1449i	1.64569	+	0.792522i
$416$	6.57391	+	28.8022i	0.322312	+	1.41214i
$417$		0			0
$418$	0.248368	+	0.119608i	0.0121481	+	0.00585021i
$419$	−18.3943	−	8.85823i	−0.898621	−	0.432753i	−0.0732302	−	0.997315i	$-0.523331\pi$
$419$	−18.3943	−	8.85823i	−0.898621	−	0.432753i	−0.825391	+	0.564562i	$0.809045\pi$
$420$		0			0
$421$	16.4271	−	7.91089i	0.800610	−	0.385553i	0.0115991	−	0.999933i	$-0.496308\pi$
$421$	16.4271	−	7.91089i	0.800610	−	0.385553i	0.789011	+	0.614379i	$0.210594\pi$
$422$	−6.71857			−0.327055
$423$		0			0
$424$	4.57111	−	2.20133i	0.221993	−	0.106906i
$425$	17.3070	+	21.7022i	0.839511	+	1.05271i
$426$		0			0
$427$	6.45105	+	30.3061i	0.312188	+	1.46661i
$428$	2.53837	−	11.1213i	0.122697	−	0.537569i
$429$		0			0
$430$	3.98063	−	17.4403i	0.191963	−	0.841045i
$431$	16.6445	+	20.8715i	0.801737	+	1.00535i	0.999684	+	0.0251335i	$0.00800110\pi$
$431$	16.6445	+	20.8715i	0.801737	+	1.00535i	−0.197947	+	0.980213i	$0.563427\pi$
$432$		0			0
$433$	−4.63434	+	5.81128i	−0.222712	+	0.279272i	−0.880617	−	0.473829i	$-0.842872\pi$
$433$	−4.63434	+	5.81128i	−0.222712	+	0.279272i	0.657905	+	0.753101i	$0.271443\pi$
$434$	−16.6662	−	8.32931i	−0.800004	−	0.399820i
$435$		0			0
$436$	2.50895	−	3.14612i	0.120157	−	0.150672i
$437$	−0.577573	−	0.278144i	−0.0276290	−	0.0133054i
$438$		0			0
$439$	−3.85169	+	16.8754i	−0.183831	+	0.805417i	0.795953	+	0.605359i	$0.206970\pi$
$439$	−3.85169	+	16.8754i	−0.183831	+	0.805417i	−0.979784	+	0.200059i	$0.935887\pi$
$440$	21.7289			1.03588
$441$		0			0
$442$	−29.1645			−1.38722
$443$	−5.78115	+	25.3289i	−0.274671	+	1.20341i	0.629760	+	0.776790i	$0.283153\pi$
$443$	−5.78115	+	25.3289i	−0.274671	+	1.20341i	−0.904430	+	0.426621i	$0.859704\pi$
$444$		0			0
$445$	−22.8792	−	11.0180i	−1.08458	−	0.522305i
$446$	−7.48747	+	9.38899i	−0.354542	+	0.444582i
$447$		0			0
$448$	−21.5259	−	0.315733i	−1.01700	−	0.0149170i
$449$	−10.8125	+	13.5585i	−0.510275	+	0.639865i	−0.968512	−	0.248965i	$-0.919910\pi$
$449$	−10.8125	+	13.5585i	−0.510275	+	0.639865i	0.458237	+	0.888830i	$0.348481\pi$
$450$		0			0
$451$	−9.62157	−	12.0651i	−0.453062	−	0.568122i
$452$	1.68712	−	7.39176i	0.0793555	−	0.347679i
$453$		0			0
$454$	−2.21638	+	9.71059i	−0.104020	+	0.455741i
$455$	59.3574	−	27.5200i	2.78272	−	1.29016i
$456$		0			0
$457$	−20.4846	−	25.6869i	−0.958230	−	1.20158i	−0.979425	−	0.201807i	$-0.935319\pi$
$457$	−20.4846	−	25.6869i	−0.958230	−	1.20158i	0.0211952	−	0.999775i	$-0.493253\pi$
$458$	4.13981	−	1.99363i	0.193441	−	0.0931562i
$459$		0			0
$460$	−14.4104			−0.671889
$461$	11.3541	−	5.46784i	0.528813	−	0.254663i	−0.150373	−	0.988629i	$-0.548047\pi$
$461$	11.3541	−	5.46784i	0.528813	−	0.254663i	0.679186	+	0.733966i	$0.262333\pi$
$462$		0			0
$463$	−19.8756	−	9.57160i	−0.923699	−	0.444830i	−0.0893084	−	0.996004i	$-0.528466\pi$
$463$	−19.8756	−	9.57160i	−0.923699	−	0.444830i	−0.834390	+	0.551174i	$0.814180\pi$
$464$	1.38197	+	0.665522i	0.0641563	+	0.0308961i
$465$		0			0
$466$	−2.83310	−	12.4126i	−0.131241	−	0.575004i
$467$	29.1053	+	14.0164i	1.34683	+	0.648600i	0.961660	−	0.274244i	$-0.0884277\pi$
$467$	29.1053	+	14.0164i	1.34683	+	0.648600i	0.385172	+	0.922845i	$0.374142\pi$
$468$		0			0
$469$	−3.16931	+	13.0035i	−0.146345	+	0.600447i
$470$	−11.1605	+	5.37460i	−0.514794	+	0.247912i
$471$		0			0
$472$	21.3229			0.981467
$473$	−8.43499	+	4.06208i	−0.387841	+	0.186774i
$474$		0			0
$475$	−0.203828	−	0.893030i	−0.00935228	−	0.0409750i
$476$	−1.88935	+	7.75190i	−0.0865981	+	0.355308i
$477$		0			0
$478$	−3.73263	+	1.79754i	−0.170727	+	0.0822176i
$479$	1.88027	−	8.23799i	0.0859116	−	0.376404i	−0.913634	−	0.406537i	$-0.866736\pi$
$479$	1.88027	−	8.23799i	0.0859116	−	0.376404i	0.999546	+	0.0301337i	$0.00959330\pi$
$480$		0			0
$481$	8.28164	+	36.2842i	0.377610	+	1.65442i
$482$	17.6581	−	22.1425i	0.804304	−	1.00857i
$483$		0			0
$484$	3.45050	+	4.32679i	0.156841	+	0.196672i
$485$	−31.8758	+	39.9710i	−1.44741	+	1.81499i
$486$		0			0
$487$	7.30311	−	9.15781i	0.330935	−	0.414980i	−0.588328	−	0.808622i	$-0.700214\pi$
$487$	7.30311	−	9.15781i	0.330935	−	0.414980i	0.919264	+	0.393642i	$0.128785\pi$
$488$	−7.99421	+	35.0249i	−0.361881	+	1.58550i
$489$		0			0
$490$	5.22668	+	26.4536i	0.236117	+	1.19505i
$491$	−20.7969			−0.938552			−0.469276	−	0.883052i	$-0.655485\pi$
$491$	−20.7969			−0.938552			−0.469276	+	0.883052i	$0.655485\pi$
$492$		0			0
$493$	2.04502	−	2.56437i	0.0921031	−	0.115494i
$494$	0.867095	+	0.417571i	0.0390125	+	0.0187874i
$495$		0			0
$496$	−7.07802	−	8.87556i	−0.317813	−	0.398524i
$497$	6.93180	−	8.43538i	0.310934	−	0.378378i
$498$		0			0
$499$	−7.28402	−	31.9134i	−0.326077	−	1.42864i	−0.826539	−	0.562880i	$-0.809693\pi$
$499$	−7.28402	−	31.9134i	−0.326077	−	1.42864i	0.500461	−	0.865759i	$-0.333164\pi$
$500$	−4.09830	−	5.13910i	−0.183281	−	0.229828i
$501$		0			0
$502$	−23.6023	+	11.3662i	−1.05342	+	0.507300i
$503$	5.44622	−	23.8614i	0.242835	−	1.06393i	−0.695588	−	0.718440i	$-0.744856\pi$
$503$	5.44622	−	23.8614i	0.242835	−	1.06393i	0.938423	−	0.345488i	$-0.112287\pi$
$504$		0			0
$505$	10.8634	+	47.5957i	0.483415	+	2.11798i
$506$	−7.08373	−	8.88271i	−0.314910	−	0.394885i
$507$		0			0
$508$	10.1645			0.450976
$509$	−27.0468			−1.19883			−0.599415	−	0.800439i	$-0.704600\pi$
$509$	−27.0468			−1.19883			−0.599415	+	0.800439i	$0.704600\pi$
$510$		0			0
$511$	−16.7904	−	0.246275i	−0.742765	−	0.0108946i
$512$	−16.4538	−	7.92374i	−0.727163	−	0.350183i
$513$		0			0
$514$	−0.724492	−	3.17421i	−0.0319560	−	0.140008i
$515$	−3.97981	−	17.4367i	−0.175371	−	0.768353i
$516$		0			0
$517$	5.84085	+	2.81281i	0.256880	+	0.123707i
$518$	−15.3371	−	0.224959i	−0.673875	−	0.00988412i
$519$		0			0
$520$	75.8591			3.32664
$521$	1.11367			0.0487910			0.0243955	−	0.999702i	$-0.492234\pi$
$521$	1.11367			0.0487910			0.0243955	+	0.999702i	$0.492234\pi$
$522$		0			0
$523$	−5.48200	−	6.87421i	−0.239711	−	0.300588i	0.647394	−	0.762155i	$-0.275859\pi$
$523$	−5.48200	−	6.87421i	−0.239711	−	0.300588i	−0.887105	+	0.461567i	$0.847287\pi$
$524$	2.72058	+	11.9197i	0.118849	+	0.520713i
$525$		0			0
$526$	−1.53762	+	6.73675i	−0.0670434	+	0.293736i
$527$	−21.8712	+	10.5326i	−0.952723	+	0.458807i
$528$		0			0
$529$	2.13272	+	2.67435i	0.0927271	+	0.116276i
$530$	−1.41770	−	6.21134i	−0.0615809	−	0.269803i
$531$		0			0
$532$	0.167162	−	0.203422i	0.00724741	−	0.00881945i
$533$	−33.5905	−	42.1212i	−1.45497	−	1.82447i
$534$		0			0
$535$	−45.2549	−	21.7936i	−1.95654	−	0.942219i
$536$	−9.67550	+	12.1327i	−0.417918	+	0.524053i
$537$		0			0
$538$	3.54872			0.152996
$539$	9.11862	−	10.7706i	0.392767	−	0.463921i
$540$		0			0
$541$	−6.86039	+	30.0573i	−0.294951	+	1.29227i	0.582591	+	0.812766i	$0.302039\pi$
$541$	−6.86039	+	30.0573i	−0.294951	+	1.29227i	−0.877542	+	0.479500i	$0.840818\pi$
$542$	3.76852	−	4.72557i	0.161872	−	0.202981i
$543$		0			0
$544$	−9.89094	+	12.4028i	−0.424071	+	0.531768i
$545$	−11.0475	−	13.8531i	−0.473223	−	0.593403i
$546$		0			0
$547$	24.6249	−	30.8786i	1.05288	−	1.32027i	0.107540	−	0.994201i	$-0.465703\pi$
$547$	24.6249	−	30.8786i	1.05288	−	1.32027i	0.945344	−	0.326074i	$-0.105726\pi$
$548$	−0.628515	−	2.75370i	−0.0268488	−	0.117632i
$549$		0			0
$550$	3.61243	−	15.8271i	0.154035	−	0.674870i
$551$	−0.0975170	+	0.0469617i	−0.00415436	+	0.00200064i
$552$		0			0
$553$	6.37987	−	26.1763i	0.271300	−	1.11313i
$554$	0.356520	+	1.56202i	0.0151471	+	0.0663638i
$555$		0			0
$556$	6.86923	−	3.30805i	0.291320	−	0.140292i
$557$	12.2479			0.518961			0.259481	−	0.965748i	$-0.416449\pi$
$557$	12.2479			0.518961			0.259481	+	0.965748i	$0.416449\pi$
$558$		0			0
$559$	−29.4480	+	14.1814i	−1.24552	+	0.599809i
$560$	−3.89049	+	15.9625i	−0.164403	+	0.674538i
$561$		0			0
$562$	−5.32735	−	2.56552i	−0.224721	−	0.108220i
$563$	7.70851	+	33.7732i	0.324875	+	1.42337i	0.828762	+	0.559601i	$0.189046\pi$
$563$	7.70851	+	33.7732i	0.324875	+	1.42337i	−0.503887	+	0.863770i	$0.668097\pi$
$564$		0			0
$565$	−30.0786	−	14.4851i	−1.26541	−	0.609392i
$566$	−26.1668	−	12.6013i	−1.09987	−	0.529672i
$567$		0			0
$568$	11.4054	−	5.49255i	0.478560	−	0.230462i
$569$	6.77357			0.283963			0.141981	−	0.989869i	$-0.454653\pi$
$569$	6.77357			0.283963			0.141981	+	0.989869i	$0.454653\pi$
$570$		0			0
$571$	13.9033	−	6.69546i	0.581834	−	0.280196i	−0.119726	−	0.992807i	$-0.538202\pi$
$571$	13.9033	−	6.69546i	0.581834	−	0.280196i	0.701560	+	0.712611i	$0.252487\pi$
$572$	−7.05928	−	8.85205i	−0.295163	−	0.370123i
$573$		0			0
$574$	20.1443	−	9.33957i	0.840809	−	0.389826i
$575$	−8.40060	+	36.8055i	−0.350329	+	1.53489i
$576$		0			0
$577$	−2.40365	+	10.5311i	−0.100065	+	0.438414i	0.899932	+	0.436030i	$0.143616\pi$
$577$	−2.40365	+	10.5311i	−0.100065	+	0.438414i	−0.999997	+	0.00238386i	$0.999241\pi$
$578$	1.85670	+	2.32823i	0.0772285	+	0.0968415i
$579$		0			0
$580$	−1.51698	+	1.90223i	−0.0629891	+	0.0789859i
$581$	28.0173	+	0.410946i	1.16235	+	0.0170489i
$582$		0			0
$583$	−2.07891	+	2.60687i	−0.0860997	+	0.107966i
$584$	−17.5417	−	8.44763i	−0.725880	−	0.349565i
$585$		0			0
$586$	−0.160811	+	0.704558i	−0.00664304	+	0.0291050i
$587$	35.5021			1.46533			0.732664	−	0.680591i	$-0.238277\pi$
$587$	35.5021			1.46533			0.732664	+	0.680591i	$0.238277\pi$
$588$		0			0
$589$	0.801059			0.0330070
$590$	5.95825	−	26.1048i	0.245297	−	1.07472i
$591$		0			0
$592$	−8.42037	−	4.05504i	−0.346075	−	0.166661i
$593$	−15.7548	+	19.7559i	−0.646972	+	0.811277i	−0.991856	−	0.127368i	$-0.959347\pi$
$593$	−15.7548	+	19.7559i	−0.646972	+	0.811277i	0.344883	+	0.938646i	$0.387918\pi$
$594$		0			0
$595$	31.4264	+	15.7061i	1.28836	+	0.643886i
$596$	−8.30158	+	10.4099i	−0.340046	+	0.426404i
$597$		0			0
$598$	−24.7305	−	31.0111i	−1.01130	−	1.26814i
$599$	−1.63084	+	7.14517i	−0.0666343	+	0.291944i	−0.997255	−	0.0740407i	$-0.976411\pi$
$599$	−1.63084	+	7.14517i	−0.0666343	+	0.291944i	0.930621	+	0.365984i	$0.119268\pi$
$600$		0			0
$601$	5.85306	−	25.6439i	0.238751	−	1.04604i	−0.703386	−	0.710808i	$-0.748329\pi$
$601$	5.85306	−	25.6439i	0.238751	−	1.04604i	0.942137	−	0.335229i	$-0.108814\pi$
$602$	−2.80459	−	13.1755i	−0.114307	−	0.536995i
$603$		0			0
$604$	−0.369373	−	0.463178i	−0.0150296	−	0.0188465i
$605$	21.9550	−	10.5730i	0.892599	−	0.429853i
$606$		0			0
$607$	1.83838			0.0746173			0.0373087	−	0.999304i	$-0.488122\pi$
$607$	1.83838			0.0746173			0.0373087	+	0.999304i	$0.488122\pi$
$608$	0.471650	−	0.227135i	0.0191279	−	0.00921153i
$609$		0			0
$610$	40.6458	+	19.5740i	1.64570	+	0.792528i
$611$	20.3914	+	9.81998i	0.824948	+	0.397274i
$612$		0			0
$613$	8.54209	+	37.4254i	0.345012	+	1.51160i	0.788342	+	0.615237i	$0.210940\pi$
$613$	8.54209	+	37.4254i	0.345012	+	1.51160i	−0.443330	+	0.896358i	$0.646203\pi$
$614$	−34.3592	−	16.5465i	−1.38662	−	0.667763i
$615$		0			0
$616$	14.8446	−	6.88242i	0.598104	−	0.277300i
$617$	18.7643	−	9.03639i	0.755420	−	0.363791i	−0.0162049	−	0.999869i	$-0.505158\pi$
$617$	18.7643	−	9.03639i	0.755420	−	0.363791i	0.771625	+	0.636077i	$0.219444\pi$
$618$		0			0
$619$	2.40019			0.0964718			0.0482359	−	0.998836i	$-0.484640\pi$
$619$	2.40019			0.0964718			0.0482359	+	0.998836i	$0.484640\pi$
$620$	16.2238	−	7.81299i	0.651565	−	0.313777i
$621$		0			0
$622$	−1.33226	−	5.83700i	−0.0534187	−	0.234043i
$623$	−19.1203	−	0.280449i	−0.766039	−	0.0112359i
$624$		0			0
$625$	7.00940	−	3.37555i	0.280376	−	0.135022i
$626$	0.680198	−	2.98014i	0.0271862	−	0.119110i
$627$		0			0
$628$	−1.24854	−	5.47022i	−0.0498222	−	0.218286i
$629$	−12.4604	+	15.6248i	−0.496827	+	0.623001i
$630$		0			0
$631$	−22.2400	−	27.8880i	−0.885359	−	1.11020i	−0.993244	−	0.116041i	$-0.962979\pi$
$631$	−22.2400	−	27.8880i	−0.885359	−	1.11020i	0.107886	−	0.994163i	$-0.465592\pi$
$632$	19.4770	−	24.4233i	0.774751	−	0.971508i
$633$		0			0
$634$	8.99169	−	11.2752i	0.357106	−	0.447796i
$635$	9.95929	−	43.6345i	0.395223	−	1.73158i
$636$		0			0
$637$	31.8347	−	37.6018i	1.26133	−	1.48984i
$638$	−1.91825			−0.0759444
$639$		0			0
$640$	−1.15295	+	1.44575i	−0.0455742	+	0.0571483i
$641$	13.7503	+	6.62181i	0.543105	+	0.261546i	0.685260	−	0.728299i	$-0.259689\pi$
$641$	13.7503	+	6.62181i	0.543105	+	0.261546i	−0.142154	+	0.989844i	$0.545403\pi$
$642$		0			0
$643$	−25.5225	−	32.0043i	−1.00651	−	1.26212i	−0.964797	−	0.262995i	$-0.915290\pi$
$643$	−25.5225	−	32.0043i	−1.00651	−	1.26212i	−0.0417137	−	0.999130i	$-0.513282\pi$
$644$	−9.84480	+	4.56437i	−0.387940	+	0.179861i
$645$		0			0
$646$	0.114996	+	0.503831i	0.00452447	+	0.0198230i
$647$	8.45485	+	10.6020i	0.332395	+	0.416810i	0.919741	−	0.392526i	$-0.128399\pi$
$647$	8.45485	+	10.6020i	0.332395	+	0.416810i	−0.587346	+	0.809336i	$0.699827\pi$
$648$		0			0
$649$	−12.6256	+	6.08016i	−0.495597	+	0.238667i
$650$	12.6116	−	55.2551i	0.494668	−	2.16728i
$651$		0			0
$652$	0.867973	+	3.80284i	0.0339924	+	0.148931i
$653$	4.76420	+	5.97412i	0.186438	+	0.233785i	0.866263	−	0.499589i	$-0.166516\pi$
$653$	4.76420	+	5.97412i	0.186438	+	0.233785i	−0.679825	+	0.733374i	$0.737944\pi$
$654$		0			0
$655$	53.8348			2.10350
$656$	13.5289			0.528216
$657$		0			0
$658$	−5.92217	+	7.20675i	−0.230870	+	0.280948i
$659$	13.9465	+	6.71628i	0.543279	+	0.261629i	0.685333	−	0.728230i	$-0.259657\pi$
$659$	13.9465	+	6.71628i	0.543279	+	0.261629i	−0.142055	+	0.989859i	$0.545371\pi$
$660$		0			0
$661$	−4.35405	−	19.0763i	−0.169353	−	0.741983i	−0.986258	−	0.165211i	$-0.947169\pi$
$661$	−4.35405	−	19.0763i	−0.169353	−	0.741983i	0.816905	−	0.576772i	$-0.195688\pi$
$662$	7.96682	+	34.9049i	0.309639	+	1.35662i
$663$		0			0
$664$	29.2708	+	14.0961i	1.13593	+	0.547034i
$665$	−0.709469	−	0.916916i	−0.0275120	−	0.0355565i
$666$		0			0
$667$	4.46084			0.172724
$668$	−1.79198			−0.0693338
$669$		0			0
$670$	12.1500	+	15.2356i	0.469394	+	0.588601i
$671$	−5.25377	−	23.0183i	−0.202819	−	0.888610i
$672$		0			0
$673$	−1.47132	+	6.44625i	−0.0567150	+	0.248485i	−0.995336	−	0.0964642i	$-0.969247\pi$
$673$	−1.47132	+	6.44625i	−0.0567150	+	0.248485i	0.938621	+	0.344949i	$0.112104\pi$
$674$	−0.216822	+	0.104416i	−0.00835166	+	0.00402195i
$675$		0			0
$676$	−18.1776	−	22.7940i	−0.699138	−	0.876691i
$677$	−5.82545	−	25.5230i	−0.223890	−	0.980927i	−0.954519	−	0.298152i	$-0.903630\pi$
$677$	−5.82545	−	25.5230i	−0.223890	−	0.980927i	0.730628	−	0.682775i	$-0.239227\pi$
$678$		0			0
$679$	−9.11623	+	37.4035i	−0.349849	+	1.43541i
$680$	25.3976	+	31.8476i	0.973954	+	1.22130i
$681$		0			0
$682$	12.7912	+	6.15990i	0.489799	+	0.235875i
$683$	24.2021	−	30.3485i	0.926068	−	1.16125i	−0.0605436	−	0.998166i	$-0.519283\pi$
$683$	24.2021	−	30.3485i	0.926068	−	1.16125i	0.986612	−	0.163087i	$-0.0521452\pi$
$684$		0			0
$685$	−12.4370			−0.475194
$686$	11.9497	+	16.4169i	0.456240	+	0.626800i
$687$		0			0
$688$	1.82639	−	8.00192i	0.0696303	−	0.305070i
$689$	−7.25783	+	9.10103i	−0.276501	+	0.346722i
$690$		0			0
$691$	4.62329	−	5.79742i	0.175878	−	0.220544i	−0.686077	−	0.727529i	$-0.740669\pi$
$691$	4.62329	−	5.79742i	0.175878	−	0.220544i	0.861955	+	0.506985i	$0.169240\pi$
$692$	−9.06541	−	11.3677i	−0.344615	−	0.432134i
$693$		0			0
$694$	−4.40696	+	5.52615i	−0.167286	+	0.209770i
$695$	−7.47035	−	32.7298i	−0.283367	−	1.24151i
$696$		0			0
$697$	6.43745	−	28.2043i	0.243836	−	1.06831i
$698$	−7.04303	+	3.39174i	−0.266583	+	0.128379i
$699$		0			0
$700$	−13.8697	−	6.93171i	−0.524227	−	0.261994i
$701$	−7.51537	−	32.9270i	−0.283851	−	1.24363i	−0.892810	−	0.450433i	$-0.851270\pi$
$701$	−7.51537	−	32.9270i	−0.283851	−	1.24363i	0.608959	−	0.793202i	$-0.291587\pi$
$702$		0			0
$703$	0.594173	−	0.286139i	0.0224097	−	0.0107919i
$704$	16.4042			0.618258
$705$		0			0
$706$	17.4185	−	8.38830i	0.655554	−	0.315698i
$707$	22.4971	+	29.0752i	0.846090	+	1.09349i
$708$		0			0
$709$	14.4500	+	6.95873i	0.542679	+	0.261341i	0.685079	−	0.728469i	$-0.259768\pi$
$709$	14.4500	+	6.95873i	0.542679	+	0.261341i	−0.142400	+	0.989809i	$0.545482\pi$
$710$	−3.53731	−	15.4980i	−0.132753	−	0.581628i
$711$		0			0
$712$	−19.9758	−	9.61983i	−0.748624	−	0.360518i
$713$	−29.7454	−	14.3246i	−1.11398	−	0.536462i
$714$		0			0
$715$	−44.9172	+	21.6310i	−1.67981	+	0.808953i
$716$	−3.60443			−0.134704
$717$		0			0
$718$	−29.4489	+	14.1819i	−1.09902	+	0.529262i
$719$	−10.0457	−	12.5969i	−0.374641	−	0.469785i	0.558391	−	0.829578i	$-0.311419\pi$
$719$	−10.0457	−	12.5969i	−0.374641	−	0.469785i	−0.933032	+	0.359793i	$0.882847\pi$
$720$		0			0
$721$	−8.24181	−	10.6517i	−0.306941	−	0.396690i
$722$	−4.63162	+	20.2925i	−0.172371	+	0.755207i
$723$		0			0
$724$	−1.79912	+	7.88244i	−0.0668636	+	0.292949i
$725$	3.97413	+	4.98341i	0.147596	+	0.185079i
$726$		0			0
$727$	−13.1736	+	16.5192i	−0.488583	+	0.612664i	−0.963611	−	0.267307i	$-0.913866\pi$
$727$	−13.1736	+	16.5192i	−0.488583	+	0.612664i	0.475029	+	0.879970i	$0.342438\pi$
$728$	51.8249	−	24.0277i	1.92076	−	0.890525i
$729$		0			0
$730$	−15.2438	+	19.1151i	−0.564197	+	0.707480i
$731$	−15.8129	−	7.61508i	−0.584861	−	0.281654i
$732$		0			0
$733$	2.14769	−	9.40964i	0.0793267	−	0.347553i	−0.919652	−	0.392734i	$-0.871529\pi$
$733$	2.14769	−	9.40964i	0.0793267	−	0.347553i	0.998979	+	0.0451811i	$0.0143865\pi$
$734$	10.3015			0.380237
$735$		0			0
$736$	−21.5753			−0.795276
$737$	2.26939	−	9.94287i	0.0835942	−	0.366250i
$738$		0			0
$739$	42.5906	+	20.5105i	1.56672	+	0.754492i	0.997697	−	0.0678302i	$-0.0216076\pi$
$739$	42.5906	+	20.5105i	1.56672	+	0.754492i	0.569022	+	0.822322i	$0.307322\pi$
$740$	9.24298	−	11.5903i	0.339779	−	0.426069i
$741$		0			0
$742$	−2.93592	−	3.79438i	−0.107781	−	0.139296i
$743$	−21.1720	+	26.5489i	−0.776727	+	0.973985i	−1.00000		0.000771328i	$-0.999754\pi$
$743$	−21.1720	+	26.5489i	−0.776727	+	0.973985i	0.223273	+	0.974756i	$0.428326\pi$
$744$		0			0
$745$	36.5538	+	45.8370i	1.33923	+	1.67934i
$746$	−2.82007	+	12.3556i	−0.103250	+	0.452369i
$747$		0			0
$748$	1.35287	−	5.92733i	0.0494660	−	0.216725i
$749$	−37.8198	−	0.554725i	−1.38191	−	0.0202692i
$750$		0			0
$751$	−4.15544	−	5.21076i	−0.151634	−	0.190143i	0.700212	−	0.713935i	$-0.253089\pi$
$751$	−4.15544	−	5.21076i	−0.151634	−	0.190143i	−0.851847	+	0.523791i	$0.824517\pi$
$752$	−5.12063	+	2.46596i	−0.186730	+	0.0899245i
$753$		0			0
$754$	−6.69695			−0.243888
$755$	−2.35027	+	1.13183i	−0.0855349	+	0.0411914i
$756$		0			0
$757$	−15.1149	−	7.27897i	−0.549362	−	0.264559i	0.138547	−	0.990356i	$-0.455757\pi$
$757$	−15.1149	−	7.27897i	−0.549362	−	0.264559i	−0.687909	+	0.725797i	$0.741471\pi$
$758$	−6.84561	−	3.29667i	−0.248644	−	0.119740i
$759$		0			0
$760$	−0.299114	−	1.31050i	−0.0108500	−	0.0475369i
$761$	38.3304	+	18.4589i	1.38947	+	0.669136i	0.970997	−	0.239091i	$-0.0768495\pi$
$761$	38.3304	+	18.4589i	1.38947	+	0.669136i	0.418478	+	0.908227i	$0.362564\pi$
$762$		0			0
$763$	−11.9352	−	5.96488i	−0.432083	−	0.215943i
$764$	0.225443	−	0.108568i	0.00815623	−	0.00392784i
$765$		0			0
$766$	−5.19972			−0.187873
$767$	−44.0780	+	21.2269i	−1.59157	+	0.766458i
$768$		0			0
$769$	5.65073	+	24.7575i	0.203771	+	0.892777i	0.968616	+	0.248563i	$0.0799583\pi$
$769$	5.65073	+	24.7575i	0.203771	+	0.892777i	−0.764845	+	0.644214i	$0.777185\pi$
$770$	−4.27786	−	20.0967i	−0.154163	−	0.724237i
$771$		0			0
$772$	−9.59592	+	4.62115i	−0.345365	+	0.166319i
$773$	8.10062	−	35.4911i	0.291359	−	1.27653i	−0.591276	−	0.806469i	$-0.701376\pi$
$773$	8.10062	−	35.4911i	0.291359	−	1.27653i	0.882635	−	0.470058i	$-0.155767\pi$
$774$		0			0
$775$	−10.4973	−	45.9917i	−0.377075	−	1.65207i
$776$	−27.8307	+	34.8986i	−0.999064	+	1.25279i
$777$		0			0
$778$	4.59706	+	5.76453i	0.164812	+	0.206668i
$779$	−0.595216	+	0.746377i	−0.0213258	+	0.0267417i
$780$		0			0
$781$	−5.18711	+	6.50442i	−0.185609	+	0.232747i
$782$	4.73947	−	20.7650i	0.169483	−	0.742554i
$783$		0			0
$784$	2.39810	+	12.1374i	0.0856463	+	0.433479i
$785$	−24.7061			−0.881798
$786$		0			0
$787$	−5.87103	+	7.36204i	−0.209280	+	0.262428i	−0.875382	−	0.483432i	$-0.839390\pi$
$787$	−5.87103	+	7.36204i	−0.209280	+	0.262428i	0.666102	+	0.745860i	$0.267961\pi$
$788$	16.7225	+	8.05314i	0.595715	+	0.286881i
$789$		0			0
$790$	−24.4581	−	30.6694i	−0.870179	−	1.09117i
$791$	−25.1369	−	0.368697i	−0.893764	−	0.0131094i
$792$		0			0
$793$	−18.3418	−	80.3606i	−0.651336	−	2.85369i
$794$	−11.2213	−	14.0711i	−0.398231	−	0.499365i
$795$		0			0
$796$	−10.3668	+	4.99236i	−0.367440	+	0.176950i
$797$	6.81923	−	29.8770i	0.241550	−	1.05830i	−0.698057	−	0.716042i	$-0.745952\pi$
$797$	6.81923	−	29.8770i	0.241550	−	1.05830i	0.939607	−	0.342256i	$-0.111191\pi$
$798$		0			0
$799$	2.70436	+	11.8486i	0.0956732	+	0.419172i
$800$	−19.2213	−	24.1027i	−0.679575	−	0.852160i
$801$		0			0
$802$	−32.0401			−1.13138
$803$	12.7955			0.451543
$804$		0			0
$805$	9.94803	+	46.7344i	0.350622	+	1.64717i
$806$	44.6561	+	21.5052i	1.57294	+	0.757490i
$807$		0			0
$808$	9.48482	+	41.5557i	0.333675	+	1.46193i
$809$	11.7234	+	51.3636i	0.412173	+	1.80585i	0.573799	+	0.818996i	$0.305469\pi$
$809$	11.7234	+	51.3636i	0.412173	+	1.80585i	−0.161625	+	0.986852i	$0.551674\pi$
$810$		0			0
$811$	39.2935	+	18.9227i	1.37978	+	0.664467i	0.968953	−	0.247246i	$-0.0795256\pi$
$811$	39.2935	+	18.9227i	1.37978	+	0.664467i	0.410827	+	0.911713i	$0.365240\pi$
$812$	−0.433844	+	1.78004i	−0.0152249	+	0.0624672i
$813$		0			0
$814$	11.6880			0.409663
$815$	17.1754			0.601629
$816$		0			0
$817$	0.361104	+	0.452810i	0.0126334	+	0.0158418i
$818$	3.65624	+	16.0190i	0.127837	+	0.560092i
$819$		0			0
$820$	−4.77525	+	20.9217i	−0.166759	+	0.730618i
$821$	−26.3448	+	12.6870i	−0.919438	+	0.442778i	−0.832871	−	0.553468i	$-0.813304\pi$
$821$	−26.3448	+	12.6870i	−0.919438	+	0.442778i	−0.0865677	+	0.996246i	$0.527590\pi$
$822$		0			0
$823$	−3.84590	−	4.82261i	−0.134060	−	0.168106i	0.710270	−	0.703929i	$-0.248573\pi$
$823$	−3.84590	−	4.82261i	−0.134060	−	0.168106i	−0.844330	+	0.535823i	$0.820001\pi$
$824$	−3.47477	−	15.2239i	−0.121049	−	0.530351i
$825$		0			0
$826$	−4.19794	−	19.7213i	−0.146065	−	0.686192i
$827$	23.9644	+	30.0504i	0.833323	+	1.04495i	0.998278	+	0.0586525i	$0.0186804\pi$
$827$	23.9644	+	30.0504i	0.833323	+	1.04495i	−0.164956	+	0.986301i	$0.552748\pi$
$828$		0			0
$829$	2.21915	+	1.06869i	0.0770743	+	0.0371170i	0.472024	−	0.881586i	$-0.343524\pi$
$829$	2.21915	+	1.06869i	0.0770743	+	0.0371170i	−0.394950	+	0.918703i	$0.629238\pi$
$830$	25.4364	−	31.8963i	0.882911	−	1.10714i
$831$		0			0
$832$	57.2699			1.98548
$833$	26.4444	+	0.775919i	0.916245	+	0.0268840i
$834$		0			0
$835$	−1.75580	+	7.69268i	−0.0607621	+	0.266216i
$836$	−0.125089	+	0.156856i	−0.00432628	+	0.00542499i
$837$		0			0
$838$	−13.9562	+	17.5005i	−0.482109	+	0.604546i
$839$	18.7782	+	23.5471i	0.648295	+	0.812936i	0.992013	−	0.126137i	$-0.0402580\pi$
$839$	18.7782	+	23.5471i	0.648295	+	0.812936i	−0.343718	+	0.939073i	$0.611687\pi$
$840$		0			0
$841$	−17.6116	+	22.0843i	−0.607297	+	0.761526i
$842$	−4.44823	−	19.4890i	−0.153296	−	0.671634i
$843$		0			0
$844$	1.08805	−	4.76707i	0.0374523	−	0.164089i
$845$	−115.661	+	55.6996i	−3.97887	+	1.91612i
$846$		0			0
$847$	11.6502	−	14.1772i	0.400305	−	0.487135i
$848$	−0.650466	−	2.84988i	−0.0223371	−	0.0978652i
$849$		0			0
$850$	27.4199	−	13.2047i	0.940494	−	0.452918i
$851$	−27.1800			−0.931718
$852$		0			0
$853$	8.38048	−	4.03582i	0.286942	−	0.138184i	−0.284876	−	0.958564i	$-0.591953\pi$
$853$	8.38048	−	4.03582i	0.286942	−	0.138184i	0.571818	+	0.820380i	$0.306238\pi$
$854$	33.9680	+	0.498228i	1.16236	+	0.0170490i
$855$		0			0
$856$	−39.5119	−	19.0279i	−1.35049	−	0.650362i
$857$	−9.93878	−	43.5446i	−0.339502	−	1.48746i	−0.800110	−	0.599853i	$-0.795226\pi$
$857$	−9.93878	−	43.5446i	−0.339502	−	1.48746i	0.460608	−	0.887603i	$-0.347631\pi$
$858$		0			0
$859$	−0.751695	−	0.361997i	−0.0256475	−	0.0123512i	0.421016	−	0.907053i	$-0.361674\pi$
$859$	−0.751695	−	0.361997i	−0.0256475	−	0.0123512i	−0.446664	+	0.894702i	$0.647388\pi$
$860$	11.7299	+	5.64880i	0.399985	+	0.192623i
$861$		0			0
$862$	26.3703	−	12.6993i	0.898176	−	0.432539i
$863$	−21.0739			−0.717363			−0.358681	−	0.933460i	$-0.616774\pi$
$863$	−21.0739			−0.717363			−0.358681	+	0.933460i	$0.616774\pi$
$864$		0			0
$865$	−57.6819	+	27.7782i	−1.96124	+	0.944486i
$866$	5.08104	+	6.37142i	0.172661	+	0.216510i
$867$		0			0
$868$	8.60900	−	10.4764i	0.292208	−	0.355591i
$869$	−4.56833	+	20.0152i	−0.154970	+	0.678968i
$870$		0			0
$871$	7.92284	−	34.7122i	0.268455	−	1.17618i
$872$	−9.64555	−	12.0951i	−0.326640	−	0.409593i
$873$		0			0
$874$	−0.438218	+	0.549508i	−0.0148230	+	0.0185874i
$875$	−13.8374	+	16.8389i	−0.467789	+	0.569258i
$876$		0			0
$877$	−33.6693	+	42.2200i	−1.13693	+	1.42567i	−0.247329	+	0.968931i	$0.579553\pi$
$877$	−33.6693	+	42.2200i	−1.13693	+	1.42567i	−0.889602	+	0.456736i	$0.849018\pi$
$878$	17.0984	+	8.23414i	0.577042	+	0.277889i
$879$		0			0
$880$	2.78580	−	12.2054i	0.0939093	−	0.411443i
$881$	49.7824			1.67721			0.838605	−	0.544740i	$-0.183372\pi$
$881$	49.7824			1.67721			0.838605	+	0.544740i	$0.183372\pi$
$882$		0			0
$883$	11.2363			0.378131			0.189066	−	0.981964i	$-0.439454\pi$
$883$	11.2363			0.378131			0.189066	+	0.981964i	$0.439454\pi$
$884$	4.72311	−	20.6933i	0.158855	−	0.695991i
$885$		0			0
$886$	25.6636	+	12.3589i	0.862185	+	0.415207i
$887$	−24.5682	+	30.8075i	−0.824918	+	1.03441i	0.173849	+	0.984772i	$0.444380\pi$
$887$	−24.5682	+	30.8075i	−0.824918	+	1.03441i	−0.998767	+	0.0496425i	$0.984192\pi$
$888$		0			0
$889$	−7.01691	−	32.9644i	−0.235340	−	1.10559i
$890$	−17.3590	+	21.7675i	−0.581875	+	0.729648i
$891$		0			0
$892$	−5.44926	−	6.83315i	−0.182455	−	0.228791i
$893$	0.0892413	−	0.390992i	0.00298635	−	0.0130840i
$894$		0			0
$895$	−3.53167	+	15.4732i	−0.118051	+	0.517214i
$896$	−0.329734	+	1.35288i	−0.0110156	+	0.0451966i
$897$		0			0
$898$	11.8547	+	14.8654i	0.395598	+	0.496064i
$899$	−5.02220	+	2.41856i	−0.167500	+	0.0806636i
$900$		0			0
$901$	−6.25077			−0.208243
$902$	−15.2437	+	7.34098i	−0.507560	+	0.244428i
$903$		0			0
$904$	−26.2615	−	12.6469i	−0.873446	−	0.420629i
$905$	32.0752	+	15.4466i	1.06622	+	0.513463i
$906$		0			0
$907$	9.53217	+	41.7631i	0.316510	+	1.38672i	0.843627	+	0.536930i	$0.180416\pi$
$907$	9.53217	+	41.7631i	0.316510	+	1.38672i	−0.527117	+	0.849793i	$0.676727\pi$
$908$	−6.53109	−	3.14520i	−0.216742	−	0.104377i
$909$		0			0
$910$	−14.9347	−	70.1611i	−0.495081	−	2.32582i
$911$	30.5676	−	14.7206i	1.01275	−	0.487714i	0.147503	−	0.989062i	$-0.452876\pi$
$911$	30.5676	−	14.7206i	1.01275	−	0.487714i	0.865246	+	0.501347i	$0.167162\pi$
$912$		0			0
$913$	−21.3511			−0.706619
$914$	−32.4543	+	15.6292i	−1.07349	+	0.516967i
$915$		0			0
$916$	0.744122	+	3.26021i	0.0245865	+	0.107720i
$917$	36.7785	−	17.0517i	1.21453	−	0.563096i
$918$		0			0
$919$	12.7567	−	6.14332i	0.420806	−	0.202649i	−0.211484	−	0.977381i	$-0.567830\pi$
$919$	12.7567	−	6.14332i	0.420806	−	0.202649i	0.632290	+	0.774732i	$0.282115\pi$
$920$	−12.3277	+	54.0112i	−0.406433	+	1.78070i
$921$		0			0
$922$	−3.07452	−	13.4704i	−0.101254	−	0.443623i
$923$	−18.1091	+	22.7080i	−0.596067	+	0.747444i
$924$		0			0
$925$	−24.2145	−	30.3640i	−0.796167	−	0.998362i
$926$	−15.0801	+	18.9099i	−0.495563	+	0.621417i
$927$		0			0
$928$	−2.27122	+	2.84802i	−0.0745565	+	0.0934909i
$929$	−4.17010	+	18.2704i	−0.136817	+	0.599432i	0.859306	+	0.511461i	$0.170896\pi$
$929$	−4.17010	+	18.2704i	−0.136817	+	0.599432i	−0.996123	+	0.0879713i	$0.971962\pi$
$930$		0			0
$931$	−0.775114	−	0.401694i	−0.0254033	−	0.0131650i
$932$	9.26603			0.303519
$933$		0			0
$934$	22.0829	−	27.6911i	0.722574	−	0.906079i
$935$	−24.1195	−	11.6153i	−0.788792	−	0.379862i
$936$		0			0
$937$	20.7494	+	26.0190i	0.677855	+	0.850003i	0.995155	−	0.0983225i	$-0.0313477\pi$
$937$	20.7494	+	26.0190i	0.677855	+	0.850003i	−0.317300	+	0.948325i	$0.602776\pi$
$938$	13.1262	+	6.56013i	0.428587	+	0.214196i
$939$		0			0
$940$	−2.00607	−	8.78916i	−0.0654307	−	0.286671i
$941$	−19.3118	−	24.2162i	−0.629546	−	0.789426i	0.360106	−	0.932911i	$-0.382741\pi$
$941$	−19.3118	−	24.2162i	−0.629546	−	0.789426i	−0.989652	+	0.143485i	$0.954169\pi$
$942$		0			0
$943$	35.4488	−	17.0712i	1.15437	−	0.555916i
$944$	2.73375	−	11.9774i	0.0889761	−	0.389830i
$945$		0			0
$946$	2.28407	+	10.0072i	0.0742616	+	0.325361i
$947$	22.6726	+	28.4305i	0.736759	+	0.923866i	0.999155	−	0.0410937i	$-0.0130842\pi$
$947$	22.6726	+	28.4305i	0.736759	+	0.923866i	−0.262396	+	0.964960i	$0.584513\pi$
$948$		0			0
$949$	44.6712			1.45009
$950$	−1.00429			−0.0325834
$951$		0			0
$952$	27.4384	+	13.7129i	0.889283	+	0.444439i
$953$	−32.1364	−	15.4761i	−1.04100	−	0.501319i	−0.166346	−	0.986068i	$-0.553197\pi$
$953$	−32.1364	−	15.4761i	−1.04100	−	0.501319i	−0.874653	+	0.484749i	$0.838911\pi$
$954$		0			0
$955$	−0.245171	−	1.07417i	−0.00793355	−	0.0347592i
$956$	−0.670932	−	2.93955i	−0.0216995	−	0.0950717i
$957$		0			0
$958$	−8.34686	−	4.01963i	−0.269675	−	0.129869i
$959$	−8.49663	+	3.93931i	−0.274371	+	0.127207i
$960$		0			0
$961$	10.2551			0.330811
$962$	40.8046			1.31559
$963$		0			0
$964$	12.8513	+	16.1150i	0.413912	+	0.519029i
$965$	10.4357	+	45.7216i	0.335935	+	1.47183i
$966$		0			0
$967$	−9.61212	+	42.1135i	−0.309105	+	1.35428i	0.546851	+	0.837230i	$0.315826\pi$
$967$	−9.61212	+	42.1135i	−0.309105	+	1.35428i	−0.855956	+	0.517048i	$0.827031\pi$
$968$	19.1689	−	9.23126i	0.616112	−	0.296704i
$969$		0			0
$970$	34.9483	+	43.8237i	1.12212	+	1.40710i
$971$	−9.18009	−	40.2206i	−0.294603	−	1.29074i	−0.878042	−	0.478584i	$-0.841150\pi$
$971$	−9.18009	−	40.2206i	−0.294603	−	1.29074i	0.583439	−	0.812157i	$-0.301707\pi$
$972$		0			0
$973$	−15.4704	−	19.9939i	−0.495958	−	0.640975i
$974$	−8.00704	−	10.0405i	−0.256562	−	0.321719i
$975$		0			0
$976$	18.6490	+	8.98091i	0.596941	+	0.287472i
$977$	−36.2716	+	45.4832i	−1.16043	+	1.45514i	−0.294025	+	0.955798i	$0.594995\pi$
$977$	−36.2716	+	45.4832i	−1.16043	+	1.45514i	−0.866407	+	0.499338i	$0.833577\pi$
$978$		0			0
$979$	14.5710			0.465691
$980$	−19.6163	−	0.575570i	−0.626619	−	0.0183859i
$981$		0			0
$982$	−5.07381	+	22.2298i	−0.161912	+	0.709382i
$983$	−0.398901	+	0.500206i	−0.0127230	+	0.0159541i	−0.788152	−	0.615480i	$-0.788962\pi$
$983$	−0.398901	+	0.500206i	−0.0127230	+	0.0159541i	0.775429	+	0.631434i	$0.217533\pi$
$984$		0			0
$985$	50.9558	−	63.8965i	1.62359	−	2.03591i
$986$	−2.24214	−	2.81155i	−0.0714042	−	0.0895380i
$987$		0			0
$988$	−0.436706	+	0.547611i	−0.0138935	+	0.0174218i
$989$	−5.31154	−	23.2714i	−0.168897	−	0.739987i
$990$		0			0
$991$	−2.64422	+	11.5851i	−0.0839965	+	0.368013i	−0.999404	−	0.0345152i	$-0.989011\pi$
$991$	−2.64422	+	11.5851i	−0.0839965	+	0.368013i	0.915408	+	0.402528i	$0.131868\pi$
$992$	24.2904	−	11.6976i	0.771220	−	0.371400i
$993$		0			0
$994$	−7.32542	−	9.46737i	−0.232348	−	0.300287i
$995$	11.2739	+	49.3944i	0.357408	+	1.56591i
$996$		0			0
$997$	−50.2047	+	24.1773i	−1.59000	+	0.765703i	−0.999156	−	0.0410848i	$-0.986919\pi$
$997$	−50.2047	+	24.1773i	−1.59000	+	0.765703i	−0.590842	+	0.806787i	$0.701204\pi$
$998$	−35.8893			−1.13605
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.c.64.3		24
3.2	odd	2		147.2.i.a.64.2	✓	24
49.36	even	7	inner	441.2.u.c.379.3		24
147.92	odd	14		7203.2.a.a.1.9		12
147.104	even	14		7203.2.a.b.1.9		12
147.134	odd	14		147.2.i.a.85.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.a.64.2	✓	24	3.2	odd	2
147.2.i.a.85.2	yes	24	147.134	odd	14
441.2.u.c.64.3		24	1.1	even	1	trivial
441.2.u.c.379.3		24	49.36	even	7	inner
7203.2.a.a.1.9		12	147.92	odd	14
7203.2.a.b.1.9		12	147.104	even	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.243969 - 1.06890i) q^{2} +(0.718913 + 0.346210i) q^{4} +(2.19062 - 2.74696i) q^{5} +(0.626501 - 2.57050i) q^{7} +(1.91263 - 2.39836i) q^{8} +O(q^{10})\)	\(q+(0.243969 - 1.06890i) q^{2} +(0.718913 + 0.346210i) q^{4} +(2.19062 - 2.74696i) q^{5} +(0.626501 - 2.57050i) q^{7} +(1.91263 - 2.39836i) q^{8} +(-2.40177 - 3.01173i) q^{10} +(-0.448609 + 1.96548i) q^{11} +(-1.56617 + 6.86183i) q^{13} +(-2.59476 - 1.29679i) q^{14} +(-1.10198 - 1.38184i) q^{16} +(-3.40512 + 1.63982i) q^{17} +0.124717 q^{19} +(2.52589 - 1.21641i) q^{20} +(1.99146 + 0.959035i) q^{22} +(-4.63107 - 2.23021i) q^{23} +(-1.63433 - 7.16046i) q^{25} +(6.95251 + 3.34815i) q^{26} +(1.34034 - 1.63107i) q^{28} +(-0.781907 + 0.376546i) q^{29} +6.42302 q^{31} +(3.78177 - 1.82120i) q^{32} +(0.922058 + 4.03980i) q^{34} +(-5.68863 - 7.35198i) q^{35} +(4.76417 - 2.29430i) q^{37} +(0.0304271 - 0.133310i) q^{38} +(-2.39834 - 10.5078i) q^{40} +(-4.77254 + 5.98457i) q^{41} +(2.89539 + 3.63071i) q^{43} +(-1.00298 + 1.25770i) q^{44} +(-3.51370 + 4.40605i) q^{46} +(0.715551 - 3.13503i) q^{47} +(-6.21499 - 3.22085i) q^{49} -8.05253 q^{50} +(-3.50158 + 4.39084i) q^{52} +(1.49012 + 0.717602i) q^{53} +(4.41636 + 5.53794i) q^{55} +(-4.96674 - 6.41900i) q^{56} +(0.211729 + 0.927645i) q^{58} +(4.33385 + 5.43448i) q^{59} +(-10.5515 + 5.08132i) q^{61} +(1.56702 - 6.86556i) q^{62} +(-1.81063 - 7.93289i) q^{64} +(15.4183 + 19.3339i) q^{65} -5.05874 q^{67} -3.01571 q^{68} +(-9.24638 + 4.28692i) q^{70} +(3.71799 + 1.79049i) q^{71} +(-1.41231 - 6.18774i) q^{73} +(-1.29007 - 5.65216i) q^{74} +(0.0896606 + 0.0431783i) q^{76} +(4.77123 + 2.38453i) q^{77} +10.1833 q^{79} -6.20987 q^{80} +(5.23255 + 6.56141i) q^{82} +(2.35665 + 10.3251i) q^{83} +(-2.95483 + 12.9460i) q^{85} +(4.58725 - 2.20910i) q^{86} +(3.85592 + 4.83517i) q^{88} +(-1.60829 - 7.04636i) q^{89} +(16.6572 + 8.32479i) q^{91} +(-2.55722 - 3.20665i) q^{92} +(-3.17646 - 1.52970i) q^{94} +(0.273208 - 0.342592i) q^{95} -14.5510 q^{97} +(-4.95903 + 5.85741i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more