LMFDB - Embedded newform 975.2.bb.i.874.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(724,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("975.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bb (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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			874.3
Root			$1.35234 - 0.780776i$ of defining polynomial
Character	$\chi$	$=$	975.874
Dual form			975.2.bb.i.724.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35234 - 0.780776i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.219224 - 0.379706i) q^{4} +(0.780776 - 1.35234i) q^{6} +(0.486319 + 0.280776i) q^{7} +2.43845i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.35234 - 0.780776i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.219224 - 0.379706i) q^{4} +(0.780776 - 1.35234i) q^{6} +(0.486319 + 0.280776i) q^{7} +2.43845i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} -0.438447i q^{12} +(3.57071 + 0.500000i) q^{13} +0.876894 q^{14} +(2.34233 + 4.05703i) q^{16} +(-1.35234 - 0.780776i) q^{17} -1.56155i q^{18} +(3.56155 - 6.16879i) q^{19} +0.561553 q^{21} +(2.70469 + 1.56155i) q^{22} +(1.73205 - 1.00000i) q^{23} +(1.21922 + 2.11176i) q^{24} +(5.21922 - 2.11176i) q^{26} -1.00000i q^{27} +(0.213225 - 0.123106i) q^{28} +(3.34233 + 5.78908i) q^{29} +2.56155 q^{31} +(2.11176 + 1.21922i) q^{32} +(1.73205 + 1.00000i) q^{33} -2.43845 q^{34} +(-0.219224 - 0.379706i) q^{36} +(-6.54850 + 3.78078i) q^{37} -11.1231i q^{38} +(3.34233 - 1.35234i) q^{39} +(0.780776 + 1.35234i) q^{41} +(0.759413 - 0.438447i) q^{42} +(-3.95042 - 2.28078i) q^{43} +0.876894 q^{44} +(1.56155 - 2.70469i) q^{46} -8.24621i q^{47} +(4.05703 + 2.34233i) q^{48} +(-3.34233 - 5.78908i) q^{49} -1.56155 q^{51} +(0.972638 - 1.24621i) q^{52} -0.684658i q^{53} +(-0.780776 - 1.35234i) q^{54} +(-0.684658 + 1.18586i) q^{56} -7.12311i q^{57} +(9.03996 + 5.21922i) q^{58} +(-1.43845 + 2.49146i) q^{59} +(-1.93845 + 3.35749i) q^{61} +(3.46410 - 2.00000i) q^{62} +(0.486319 - 0.280776i) q^{63} -5.56155 q^{64} +3.12311 q^{66} +(-3.95042 + 2.28078i) q^{67} +(-0.592932 + 0.342329i) q^{68} +(1.00000 - 1.73205i) q^{69} +(-7.00000 + 12.1244i) q^{71} +(2.11176 + 1.21922i) q^{72} -10.1231i q^{73} +(-5.90388 + 10.2258i) q^{74} +(-1.56155 - 2.70469i) q^{76} +1.12311i q^{77} +(3.46410 - 4.43845i) q^{78} -5.43845 q^{79} +(-0.500000 - 0.866025i) q^{81} +(2.11176 + 1.21922i) q^{82} -0.876894i q^{83} +(0.123106 - 0.213225i) q^{84} -7.12311 q^{86} +(5.78908 + 3.34233i) q^{87} +(-4.22351 + 2.43845i) q^{88} +(2.43845 + 4.22351i) q^{89} +(1.59612 + 1.24573i) q^{91} -0.876894i q^{92} +(2.21837 - 1.28078i) q^{93} +(-6.43845 - 11.1517i) q^{94} +2.43845 q^{96} +(-7.41452 - 4.28078i) q^{97} +(-9.03996 - 5.21922i) q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q + 10 * q^4 - 2 * q^6 + 4 * q^9	$ 8 q + 10 q^{4} - 2 q^{6} + 4 q^{9} + 8 q^{11} + 40 q^{14} - 6 q^{16} + 12 q^{19} - 12 q^{21} + 18 q^{24} + 50 q^{26} + 2 q^{29} + 4 q^{31} - 36 q^{34} - 10 q^{36} + 2 q^{39} - 2 q^{41} + 40 q^{44} - 4 q^{46} - 2 q^{49} + 4 q^{51} + 2 q^{54} + 44 q^{56} - 28 q^{59} - 32 q^{61} - 28 q^{64} - 8 q^{66} + 8 q^{69} - 56 q^{71} - 6 q^{74} + 4 q^{76} - 60 q^{79} - 4 q^{81} - 32 q^{84} - 24 q^{86} + 36 q^{89} + 54 q^{91} - 68 q^{94} + 36 q^{96} + 16 q^{99}+O(q^{100}) $ 8 * q + 10 * q^4 - 2 * q^6 + 4 * q^9 + 8 * q^11 + 40 * q^14 - 6 * q^16 + 12 * q^19 - 12 * q^21 + 18 * q^24 + 50 * q^26 + 2 * q^29 + 4 * q^31 - 36 * q^34 - 10 * q^36 + 2 * q^39 - 2 * q^41 + 40 * q^44 - 4 * q^46 - 2 * q^49 + 4 * q^51 + 2 * q^54 + 44 * q^56 - 28 * q^59 - 32 * q^61 - 28 * q^64 - 8 * q^66 + 8 * q^69 - 56 * q^71 - 6 * q^74 + 4 * q^76 - 60 * q^79 - 4 * q^81 - 32 * q^84 - 24 * q^86 + 36 * q^89 + 54 * q^91 - 68 * q^94 + 36 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.35234	−	0.780776i	0.956252	−	0.552092i	0.0612344	−	0.998123i	$-0.480496\pi$
$2$	1.35234	−	0.780776i	0.956252	−	0.552092i	0.895017	+	0.446031i	$0.147163\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.219224	−	0.379706i	0.109612	−	0.189853i
$5$		0			0
$5$		0			0
$6$	0.780776	−	1.35234i	0.318751	−	0.552092i
$7$	0.486319	+	0.280776i	0.183811	+	0.106124i	0.589082	−	0.808073i	$-0.299489\pi$
$7$	0.486319	+	0.280776i	0.183811	+	0.106124i	−0.405271	+	0.914197i	$0.632823\pi$
$8$			2.43845i			0.862121i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$		−	0.438447i		−	0.126569i
$13$	3.57071	+	0.500000i	0.990338	+	0.138675i
$13$	3.57071	+	0.500000i	0.990338	+	0.138675i
$14$	0.876894			0.234360
$15$		0			0
$16$	2.34233	+	4.05703i	0.585582	+	1.01426i
$17$	−1.35234	−	0.780776i	−0.327992	−	0.189366i	0.326957	−	0.945039i	$-0.393977\pi$
$17$	−1.35234	−	0.780776i	−0.327992	−	0.189366i	−0.654949	+	0.755673i	$0.727310\pi$
$18$		−	1.56155i		−	0.368062i
$19$	3.56155	−	6.16879i	0.817076	−	1.41522i	−0.0907512	−	0.995874i	$-0.528927\pi$
$19$	3.56155	−	6.16879i	0.817076	−	1.41522i	0.907827	−	0.419344i	$-0.137740\pi$
$20$		0			0
$21$	0.561553			0.122541
$22$	2.70469	+	1.56155i	0.576642	+	0.332924i
$23$	1.73205	−	1.00000i	0.361158	−	0.208514i	−0.308431	−	0.951247i	$-0.599804\pi$
$23$	1.73205	−	1.00000i	0.361158	−	0.208514i	0.669588	+	0.742732i	$0.266471\pi$
$24$	1.21922	+	2.11176i	0.248873	+	0.431061i
$25$		0			0
$26$	5.21922	−	2.11176i	1.02357	−	0.414150i
$27$		−	1.00000i		−	0.192450i
$28$	0.213225	−	0.123106i	0.0402958	−	0.0232648i
$29$	3.34233	+	5.78908i	0.620655	+	1.07501i	0.989364	+	0.145461i	$0.0464665\pi$
$29$	3.34233	+	5.78908i	0.620655	+	1.07501i	−0.368709	+	0.929545i	$0.620200\pi$
$30$		0			0
$31$	2.56155			0.460068			0.230034	−	0.973183i	$-0.426116\pi$
$31$	2.56155			0.460068			0.230034	+	0.973183i	$0.426116\pi$
$32$	2.11176	+	1.21922i	0.373309	+	0.215530i
$33$	1.73205	+	1.00000i	0.301511	+	0.174078i
$34$	−2.43845			−0.418190
$35$		0			0
$36$	−0.219224	−	0.379706i	−0.0365373	−	0.0632844i
$37$	−6.54850	+	3.78078i	−1.07657	+	0.621556i	−0.929968	−	0.367640i	$-0.880166\pi$
$37$	−6.54850	+	3.78078i	−1.07657	+	0.621556i	−0.146598	+	0.989196i	$0.546832\pi$
$38$		−	11.1231i		−	1.80441i
$39$	3.34233	−	1.35234i	0.535201	−	0.216548i
$40$		0			0
$41$	0.780776	+	1.35234i	0.121937	+	0.211201i	0.920531	−	0.390669i	$-0.127756\pi$
$41$	0.780776	+	1.35234i	0.121937	+	0.211201i	−0.798595	+	0.601869i	$0.794423\pi$
$42$	0.759413	−	0.438447i	0.117180	−	0.0676539i
$43$	−3.95042	−	2.28078i	−0.602433	−	0.347815i	0.167565	−	0.985861i	$-0.446410\pi$
$43$	−3.95042	−	2.28078i	−0.602433	−	0.347815i	−0.769998	+	0.638046i	$0.779743\pi$
$44$	0.876894			0.132197
$45$		0			0
$46$	1.56155	−	2.70469i	0.230238	−	0.398785i
$47$		−	8.24621i		−	1.20283i	−0.798935	−	0.601417i	$-0.794603\pi$
$47$		−	8.24621i		−	1.20283i	0.798935	−	0.601417i	$-0.205397\pi$
$48$	4.05703	+	2.34233i	0.585582	+	0.338086i
$49$	−3.34233	−	5.78908i	−0.477476	−	0.827012i
$50$		0			0
$51$	−1.56155			−0.218661
$52$	0.972638	−	1.24621i	0.134881	−	0.172818i
$53$		−	0.684658i		−	0.0940451i	−0.998894	−	0.0470225i	$-0.985027\pi$
$53$		−	0.684658i		−	0.0940451i	0.998894	−	0.0470225i	$-0.0149733\pi$
$54$	−0.780776	−	1.35234i	−0.106250	−	0.184031i
$55$		0			0
$56$	−0.684658	+	1.18586i	−0.0914913	+	0.158468i
$57$		−	7.12311i		−	0.943478i
$58$	9.03996	+	5.21922i	1.18700	+	0.685318i
$59$	−1.43845	+	2.49146i	−0.187270	+	0.324361i	−0.944339	−	0.328974i	$-0.893297\pi$
$59$	−1.43845	+	2.49146i	−0.187270	+	0.324361i	0.757069	+	0.653335i	$0.226631\pi$
$60$		0			0
$61$	−1.93845	+	3.35749i	−0.248193	+	0.429882i	−0.963024	−	0.269414i	$-0.913170\pi$
$61$	−1.93845	+	3.35749i	−0.248193	+	0.429882i	0.714832	+	0.699297i	$0.246503\pi$
$62$	3.46410	−	2.00000i	0.439941	−	0.254000i
$63$	0.486319	−	0.280776i	0.0612704	−	0.0353745i
$64$	−5.56155			−0.695194
$65$		0			0
$66$	3.12311			0.384428
$67$	−3.95042	+	2.28078i	−0.482621	+	0.278641i	−0.721508	−	0.692406i	$-0.756551\pi$
$67$	−3.95042	+	2.28078i	−0.482621	+	0.278641i	0.238887	+	0.971047i	$0.423217\pi$
$68$	−0.592932	+	0.342329i	−0.0719035	+	0.0415135i
$69$	1.00000	−	1.73205i	0.120386	−	0.208514i
$70$		0			0
$71$	−7.00000	+	12.1244i	−0.830747	+	1.43890i	0.0666994	+	0.997773i	$0.478753\pi$
$71$	−7.00000	+	12.1244i	−0.830747	+	1.43890i	−0.897447	+	0.441123i	$0.854580\pi$
$72$	2.11176	+	1.21922i	0.248873	+	0.143687i
$73$		−	10.1231i		−	1.18482i	−0.805637	−	0.592410i	$-0.798177\pi$
$73$		−	10.1231i		−	1.18482i	0.805637	−	0.592410i	$-0.201823\pi$
$74$	−5.90388	+	10.2258i	−0.686312	+	1.18873i
$75$		0			0
$76$	−1.56155	−	2.70469i	−0.179122	−	0.310249i
$77$			1.12311i			0.127990i
$78$	3.46410	−	4.43845i	0.392232	−	0.502555i
$79$	−5.43845			−0.611873			−0.305937	−	0.952052i	$-0.598970\pi$
$79$	−5.43845			−0.611873			−0.305937	+	0.952052i	$0.598970\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.11176	+	1.21922i	0.233205	+	0.134641i
$83$		−	0.876894i		−	0.0962517i	−0.998841	−	0.0481258i	$-0.984675\pi$
$83$		−	0.876894i		−	0.0962517i	0.998841	−	0.0481258i	$-0.0153248\pi$
$84$	0.123106	−	0.213225i	0.0134319	−	0.0232648i
$85$		0			0
$86$	−7.12311			−0.768104
$87$	5.78908	+	3.34233i	0.620655	+	0.358335i
$88$	−4.22351	+	2.43845i	−0.450228	+	0.259939i
$89$	2.43845	+	4.22351i	0.258475	+	0.447692i	0.965834	−	0.259163i	$-0.0834467\pi$
$89$	2.43845	+	4.22351i	0.258475	+	0.447692i	−0.707359	+	0.706855i	$0.750113\pi$
$90$		0			0
$91$	1.59612	+	1.24573i	0.167319	+	0.130588i
$92$		−	0.876894i		−	0.0914226i
$93$	2.21837	−	1.28078i	0.230034	−	0.132810i
$94$	−6.43845	−	11.1517i	−0.664075	−	1.15021i
$95$		0			0
$96$	2.43845			0.248873
$97$	−7.41452	−	4.28078i	−0.752831	−	0.434647i	0.0738851	−	0.997267i	$-0.476460\pi$
$97$	−7.41452	−	4.28078i	−0.752831	−	0.434647i	−0.826716	+	0.562620i	$0.809794\pi$
$98$	−9.03996	−	5.21922i	−0.913174	−	0.527221i
$99$	2.00000			0.201008
$100$		0			0
$101$	3.78078	+	6.54850i	0.376201	+	0.651600i	0.990506	−	0.137469i	$-0.0438968\pi$
$101$	3.78078	+	6.54850i	0.376201	+	0.651600i	−0.614305	+	0.789069i	$0.710563\pi$
$102$	−2.11176	+	1.21922i	−0.209095	+	0.120721i
$103$		−	3.43845i		−	0.338800i	−0.985547	−	0.169400i	$-0.945817\pi$
$103$		−	3.43845i		−	0.338800i	0.985547	−	0.169400i	$-0.0541830\pi$
$104$	−1.21922	+	8.70700i	−0.119555	+	0.853791i
$105$		0			0
$106$	−0.534565	−	0.925894i	−0.0519216	−	0.0899308i
$107$	7.14143	−	4.12311i	0.690388	−	0.398596i	−0.113369	−	0.993553i	$-0.536164\pi$
$107$	7.14143	−	4.12311i	0.690388	−	0.398596i	0.803757	+	0.594957i	$0.202831\pi$
$108$	−0.379706	−	0.219224i	−0.0365373	−	0.0210948i
$109$	2.80776			0.268935			0.134468	−	0.990918i	$-0.457068\pi$
$109$	2.80776			0.268935			0.134468	+	0.990918i	$0.457068\pi$
$110$		0			0
$111$	−3.78078	+	6.54850i	−0.358855	+	0.621556i
$112$			2.63068i			0.248576i
$113$	−5.02967	−	2.90388i	−0.473152	−	0.273174i	0.244406	−	0.969673i	$-0.421407\pi$
$113$	−5.02967	−	2.90388i	−0.473152	−	0.273174i	−0.717558	+	0.696499i	$0.754740\pi$
$114$	−5.56155	−	9.63289i	−0.520887	−	0.902203i
$115$		0			0
$116$	2.93087			0.272124
$117$	2.21837	−	2.84233i	0.205088	−	0.262773i
$118$			4.49242i			0.413561i
$119$	−0.438447	−	0.759413i	−0.0401924	−	0.0696153i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$			6.05398i			0.548101i
$123$	1.35234	+	0.780776i	0.121937	+	0.0704002i
$124$	0.561553	−	0.972638i	0.0504289	−	0.0873455i
$125$		0			0
$126$	0.438447	−	0.759413i	0.0390600	−	0.0676539i
$127$	−4.70983	+	2.71922i	−0.417930	+	0.241292i	−0.694191	−	0.719791i	$-0.744238\pi$
$127$	−4.70983	+	2.71922i	−0.417930	+	0.241292i	0.276261	+	0.961083i	$0.410905\pi$
$128$	−11.7446	+	6.78078i	−1.03809	+	0.599342i
$129$	−4.56155			−0.401622
$130$		0			0
$131$	7.36932			0.643860			0.321930	−	0.946763i	$-0.395668\pi$
$131$	7.36932			0.643860			0.321930	+	0.946763i	$0.395668\pi$
$132$	0.759413	−	0.438447i	0.0660984	−	0.0381619i
$133$	3.46410	−	2.00000i	0.300376	−	0.173422i
$134$	−3.56155	+	6.16879i	−0.307671	+	0.532902i
$135$		0			0
$136$	1.90388	−	3.29762i	0.163257	−	0.282769i
$137$	−4.81645	−	2.78078i	−0.411497	−	0.237578i	0.279936	−	0.960019i	$-0.409687\pi$
$137$	−4.81645	−	2.78078i	−0.411497	−	0.237578i	−0.691433	+	0.722441i	$0.743020\pi$
$138$		−	3.12311i		−	0.265856i
$139$	−8.96543	+	15.5286i	−0.760438	+	1.31712i	0.182187	+	0.983264i	$0.441682\pi$
$139$	−8.96543	+	15.5286i	−0.760438	+	1.31712i	−0.942625	+	0.333854i	$0.891651\pi$
$140$		0			0
$141$	−4.12311	−	7.14143i	−0.347228	−	0.601417i
$142$			21.8617i			1.83460i
$143$	2.70469	+	6.68466i	0.226177	+	0.558999i
$144$	4.68466			0.390388
$145$		0			0
$146$	−7.90388	−	13.6899i	−0.654130	−	1.13299i
$147$	−5.78908	−	3.34233i	−0.477476	−	0.275671i
$148$			3.31534i			0.272519i
$149$	−1.21922	+	2.11176i	−0.0998827	+	0.173002i	−0.911636	−	0.410999i	$-0.865180\pi$
$149$	−1.21922	+	2.11176i	−0.0998827	+	0.173002i	0.811753	+	0.584001i	$0.198513\pi$
$150$		0			0
$151$	−9.36932			−0.762464			−0.381232	−	0.924479i	$-0.624500\pi$
$151$	−9.36932			−0.762464			−0.381232	+	0.924479i	$0.624500\pi$
$152$	15.0423	+	8.68466i	1.22009	+	0.704419i
$153$	−1.35234	+	0.780776i	−0.109331	+	0.0631220i
$154$	0.876894	+	1.51883i	0.0706622	+	0.122390i
$155$		0			0
$156$	0.219224	−	1.56557i	0.0175519	−	0.125346i
$157$		−	20.3693i		−	1.62565i	−0.582509	−	0.812824i	$-0.697929\pi$
$157$		−	20.3693i		−	1.62565i	0.582509	−	0.812824i	$-0.302071\pi$
$158$	−7.35465	+	4.24621i	−0.585105	+	0.337810i
$159$	−0.342329	−	0.592932i	−0.0271485	−	0.0470225i
$160$		0			0
$161$	1.12311			0.0885131
$162$	−1.35234	−	0.780776i	−0.106250	−	0.0613436i
$163$	4.16365	+	2.40388i	0.326122	+	0.188287i	0.654118	−	0.756393i	$-0.273040\pi$
$163$	4.16365	+	2.40388i	0.326122	+	0.188287i	−0.327996	+	0.944679i	$0.606373\pi$
$164$	0.684658			0.0534628
$165$		0			0
$166$	−0.684658	−	1.18586i	−0.0531398	−	0.0920408i
$167$	−8.87348	+	5.12311i	−0.686650	+	0.396438i	−0.802356	−	0.596846i	$-0.796420\pi$
$167$	−8.87348	+	5.12311i	−0.686650	+	0.396438i	0.115706	+	0.993284i	$0.463087\pi$
$168$			1.36932i			0.105645i
$169$	12.5000	+	3.57071i	0.961538	+	0.274670i
$170$		0			0
$171$	−3.56155	−	6.16879i	−0.272359	−	0.471739i
$172$	−1.73205	+	1.00000i	−0.132068	+	0.0762493i
$173$	−17.5337	−	10.1231i	−1.33307	−	0.769645i	−0.347297	−	0.937755i	$-0.612900\pi$
$173$	−17.5337	−	10.1231i	−1.33307	−	0.769645i	−0.985768	+	0.168110i	$0.946234\pi$
$174$	10.4384			0.791337
$175$		0			0
$176$	−4.68466	+	8.11407i	−0.353119	+	0.611621i
$177$			2.87689i			0.216241i
$178$	6.59524	+	3.80776i	0.494334	+	0.285404i
$179$	−2.43845	−	4.22351i	−0.182258	−	0.315680i	0.760391	−	0.649466i	$-0.225007\pi$
$179$	−2.43845	−	4.22351i	−0.182258	−	0.315680i	−0.942649	+	0.333785i	$0.891674\pi$
$180$		0			0
$181$	−2.68466			−0.199549			−0.0997745	−	0.995010i	$-0.531812\pi$
$181$	−2.68466			−0.199549			−0.0997745	+	0.995010i	$0.531812\pi$
$182$	3.13114	+	0.438447i	0.232095	+	0.0324999i
$183$			3.87689i			0.286588i
$184$	2.43845	+	4.22351i	0.179765	+	0.311362i
$185$		0			0
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$		−	3.12311i		−	0.228384i
$188$	−3.13114	−	1.80776i	−0.228362	−	0.131845i
$189$	0.280776	−	0.486319i	0.0204235	−	0.0353745i
$190$		0			0
$191$	4.56155	−	7.90084i	0.330062	−	0.571685i	−0.652461	−	0.757822i	$-0.726264\pi$
$191$	4.56155	−	7.90084i	0.330062	−	0.571685i	0.982524	+	0.186137i	$0.0595969\pi$
$192$	−4.81645	+	2.78078i	−0.347597	+	0.200685i
$193$	−11.6848	+	6.74621i	−0.841089	+	0.485603i	−0.857634	−	0.514260i	$-0.828067\pi$
$193$	−11.6848	+	6.74621i	−0.841089	+	0.485603i	0.0165453	+	0.999863i	$0.494733\pi$
$194$	−13.3693			−0.959861
$195$		0			0
$196$	−2.93087			−0.209348
$197$	−11.5782	+	6.68466i	−0.824910	+	0.476262i	−0.852107	−	0.523368i	$-0.824675\pi$
$197$	−11.5782	+	6.68466i	−0.824910	+	0.476262i	0.0271965	+	0.999630i	$0.491342\pi$
$198$	2.70469	−	1.56155i	0.192214	−	0.110975i
$199$	11.0885	−	19.2059i	0.786046	−	1.36147i	−0.142327	−	0.989820i	$-0.545458\pi$
$199$	11.0885	−	19.2059i	0.786046	−	1.36147i	0.928372	−	0.371651i	$-0.121208\pi$
$200$		0			0
$201$	−2.28078	+	3.95042i	−0.160874	+	0.278641i
$202$	10.2258	+	5.90388i	0.719486	+	0.415396i
$203$			3.75379i			0.263464i
$204$	−0.342329	+	0.592932i	−0.0239678	+	0.0415135i
$205$		0			0
$206$	−2.68466	−	4.64996i	−0.187049	−	0.323978i
$207$		−	2.00000i		−	0.139010i
$208$	6.33527	+	15.6577i	0.439272	+	1.08566i
$209$	14.2462			0.985431
$210$		0			0
$211$	−9.84233	−	17.0474i	−0.677574	−	1.17359i	−0.975709	−	0.219069i	$-0.929698\pi$
$211$	−9.84233	−	17.0474i	−0.677574	−	1.17359i	0.298136	−	0.954524i	$-0.403635\pi$
$212$	−0.259969	−	0.150093i	−0.0178548	−	0.0103084i
$213$			14.0000i			0.959264i
$214$	6.43845	−	11.1517i	0.440123	−	0.762316i
$215$		0			0
$216$	2.43845			0.165915
$217$	1.24573	+	0.719224i	0.0845658	+	0.0488241i
$218$	3.79706	−	2.19224i	0.257170	−	0.148477i
$219$	−5.06155	−	8.76687i	−0.342028	−	0.592410i
$220$		0			0
$221$	−4.43845	−	3.46410i	−0.298562	−	0.233021i
$222$			11.8078i			0.792485i
$223$	6.92820	−	4.00000i	0.463947	−	0.267860i	−0.249756	−	0.968309i	$-0.580350\pi$
$223$	6.92820	−	4.00000i	0.463947	−	0.267860i	0.713702	+	0.700449i	$0.247017\pi$
$224$	0.684658	+	1.18586i	0.0457457	+	0.0792338i
$225$		0			0
$226$	−9.06913			−0.603270
$227$	6.16879	+	3.56155i	0.409437	+	0.236389i	0.690548	−	0.723287i	$-0.257370\pi$
$227$	6.16879	+	3.56155i	0.409437	+	0.236389i	−0.281111	+	0.959675i	$0.590703\pi$
$228$	−2.70469	−	1.56155i	−0.179122	−	0.103416i
$229$	16.2462			1.07358			0.536790	−	0.843716i	$-0.319637\pi$
$229$	16.2462			1.07358			0.536790	+	0.843716i	$0.319637\pi$
$230$		0			0
$231$	0.561553	+	0.972638i	0.0369475	+	0.0639949i
$232$	−14.1164	+	8.15009i	−0.926785	+	0.535080i
$233$			26.0000i			1.70332i	0.524097	+	0.851658i	$0.324403\pi$
$233$			26.0000i			1.70332i	−0.524097	+	0.851658i	$0.675597\pi$
$234$	0.780776	−	5.57586i	0.0510410	−	0.364505i
$235$		0			0
$236$	0.630683	+	1.09238i	0.0410540	+	0.0711076i
$237$	−4.70983	+	2.71922i	−0.305937	+	0.176633i
$238$	−1.18586	−	0.684658i	−0.0768681	−	0.0443798i
$239$	25.3693			1.64100			0.820502	−	0.571643i	$-0.193694\pi$
$239$	25.3693			1.64100			0.820502	+	0.571643i	$0.193694\pi$
$240$		0			0
$241$	8.90388	−	15.4220i	0.573549	−	0.993417i	−0.422648	−	0.906294i	$-0.638899\pi$
$241$	8.90388	−	15.4220i	0.573549	−	0.993417i	0.996198	−	0.0871229i	$-0.0277673\pi$
$242$		−	10.9309i		−	0.702663i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	0.849907	+	1.47208i	0.0544097	+	0.0942404i
$245$		0			0
$246$	2.43845			0.155470
$247$	15.8017	−	20.2462i	1.00544	−	1.28824i
$248$			6.24621i			0.396635i
$249$	−0.438447	−	0.759413i	−0.0277855	−	0.0481258i
$250$		0			0
$251$	−9.36932	+	16.2281i	−0.591386	+	1.02431i	0.402660	+	0.915350i	$0.368086\pi$
$251$	−9.36932	+	16.2281i	−0.591386	+	1.02431i	−0.994046	+	0.108961i	$0.965248\pi$
$252$		−	0.246211i		−	0.0155099i
$253$	3.46410	+	2.00000i	0.217786	+	0.125739i
$254$	−4.24621	+	7.35465i	−0.266431	+	0.461472i
$255$		0			0
$256$	−5.02699	+	8.70700i	−0.314187	+	0.544187i
$257$	−25.2681	+	14.5885i	−1.57618	+	0.910008i	−0.580795	+	0.814050i	$0.697258\pi$
$257$	−25.2681	+	14.5885i	−1.57618	+	0.910008i	−0.995385	+	0.0959583i	$0.969408\pi$
$258$	−6.16879	+	3.56155i	−0.384052	+	0.221733i
$259$	−4.24621			−0.263847
$260$		0			0
$261$	6.68466			0.413770
$262$	9.96585	−	5.75379i	0.615693	−	0.355470i
$263$	8.11407	−	4.68466i	0.500335	−	0.288868i	−0.228517	−	0.973540i	$-0.573388\pi$
$263$	8.11407	−	4.68466i	0.500335	−	0.288868i	0.728852	+	0.684672i	$0.240054\pi$
$264$	−2.43845	+	4.22351i	−0.150076	+	0.259939i
$265$		0			0
$266$	3.12311	−	5.40938i	0.191490	−	0.331670i
$267$	4.22351	+	2.43845i	0.258475	+	0.149231i
$268$			2.00000i			0.122169i
$269$	−10.6847	+	18.5064i	−0.651455	+	1.12835i	0.331315	+	0.943520i	$0.392508\pi$
$269$	−10.6847	+	18.5064i	−0.651455	+	1.12835i	−0.982770	+	0.184833i	$0.940826\pi$
$270$		0			0
$271$	14.9654	+	25.9209i	0.909085	+	1.57458i	0.815337	+	0.578986i	$0.196551\pi$
$271$	14.9654	+	25.9209i	0.909085	+	1.57458i	0.0937481	+	0.995596i	$0.470115\pi$
$272$		−	7.31534i		−	0.443558i
$273$	2.00514	+	0.280776i	0.121357	+	0.0169934i
$274$	−8.68466			−0.524659
$275$		0			0
$276$	−0.438447	−	0.759413i	−0.0263914	−	0.0457113i
$277$	4.60322	+	2.65767i	0.276581	+	0.159684i	0.631874	−	0.775071i	$-0.282286\pi$
$277$	4.60322	+	2.65767i	0.276581	+	0.159684i	−0.355294	+	0.934755i	$0.615619\pi$
$278$			28.0000i			1.67933i
$279$	1.28078	−	2.21837i	0.0766781	−	0.132810i
$280$		0			0
$281$	17.8078			1.06232			0.531161	−	0.847271i	$-0.321756\pi$
$281$	17.8078			1.06232			0.531161	+	0.847271i	$0.321756\pi$
$282$	−11.1517	−	6.43845i	−0.664075	−	0.383404i
$283$	−11.8513	+	6.84233i	−0.704484	+	0.406734i	−0.809015	−	0.587787i	$-0.799999\pi$
$283$	−11.8513	+	6.84233i	−0.704484	+	0.406734i	0.104531	+	0.994522i	$0.466666\pi$
$284$	3.06913	+	5.31589i	0.182119	+	0.315440i
$285$		0			0
$286$	8.87689	+	6.92820i	0.524902	+	0.409673i
$287$			0.876894i			0.0517614i
$288$	2.11176	−	1.21922i	0.124436	−	0.0718434i
$289$	−7.28078	−	12.6107i	−0.428281	−	0.741804i
$290$		0			0
$291$	−8.56155			−0.501887
$292$	−3.84381	−	2.21922i	−0.224942	−	0.129870i
$293$	−17.7002	−	10.2192i	−1.03406	−	0.597013i	−0.115913	−	0.993259i	$-0.536979\pi$
$293$	−17.7002	−	10.2192i	−1.03406	−	0.597013i	−0.918144	+	0.396246i	$0.870313\pi$
$294$	−10.4384			−0.608783
$295$		0			0
$296$	−9.21922	−	15.9682i	−0.535856	−	0.928131i
$297$	1.73205	−	1.00000i	0.100504	−	0.0580259i
$298$			3.80776i			0.220578i
$299$	6.68466	−	2.70469i	0.386584	−	0.156416i
$300$		0			0
$301$	−1.28078	−	2.21837i	−0.0738227	−	0.127865i
$302$	−12.6705	+	7.31534i	−0.729108	+	0.420951i
$303$	6.54850	+	3.78078i	0.376201	+	0.217200i
$304$	33.3693			1.91386
$305$		0			0
$306$	−1.21922	+	2.11176i	−0.0696984	+	0.120721i
$307$		−	30.8078i		−	1.75829i	−0.476553	−	0.879146i	$-0.658114\pi$
$307$		−	30.8078i		−	1.75829i	0.476553	−	0.879146i	$-0.341886\pi$
$308$	0.426450	+	0.246211i	0.0242993	+	0.0140292i
$309$	−1.71922	−	2.97778i	−0.0978032	−	0.169400i
$310$		0			0
$311$	−19.1231			−1.08437			−0.542186	−	0.840259i	$-0.682403\pi$
$311$	−19.1231			−1.08437			−0.542186	+	0.840259i	$0.682403\pi$
$312$	3.29762	+	8.15009i	0.186691	+	0.461408i
$313$		−	13.6847i		−	0.773503i	−0.922184	−	0.386751i	$-0.873597\pi$
$313$		−	13.6847i		−	0.773503i	0.922184	−	0.386751i	$-0.126403\pi$
$314$	−15.9039	−	27.5463i	−0.897508	−	1.55453i
$315$		0			0
$316$	−1.19224	+	2.06501i	−0.0670685	+	0.116166i
$317$		−	14.0540i		−	0.789350i	−0.918821	−	0.394675i	$-0.870857\pi$
$317$		−	14.0540i		−	0.789350i	0.918821	−	0.394675i	$-0.129143\pi$
$318$	−0.925894	−	0.534565i	−0.0519216	−	0.0299769i
$319$	−6.68466	+	11.5782i	−0.374269	+	0.648253i
$320$		0			0
$321$	4.12311	−	7.14143i	0.230129	−	0.398596i
$322$	1.51883	−	0.876894i	0.0846408	−	0.0488674i
$323$	−9.63289	+	5.56155i	−0.535988	+	0.309453i
$324$	−0.438447			−0.0243582
$325$		0			0
$326$	7.50758			0.415806
$327$	2.43160	−	1.40388i	0.134468	−	0.0776349i
$328$	−3.29762	+	1.90388i	−0.182081	+	0.105124i
$329$	2.31534	−	4.01029i	0.127649	−	0.221094i
$330$		0			0
$331$	1.59612	−	2.76456i	0.0877306	−	0.151954i	−0.818821	−	0.574049i	$-0.805372\pi$
$331$	1.59612	−	2.76456i	0.0877306	−	0.151954i	0.906552	+	0.422095i	$0.138705\pi$
$332$	−0.332962	−	0.192236i	−0.0182737	−	0.0105503i
$333$			7.56155i			0.414371i
$334$	−8.00000	+	13.8564i	−0.437741	+	0.758189i
$335$		0			0
$336$	1.31534	+	2.27824i	0.0717578	+	0.124288i
$337$			6.12311i			0.333547i	0.985995	+	0.166773i	$0.0533348\pi$
$337$			6.12311i			0.333547i	−0.985995	+	0.166773i	$0.946665\pi$
$338$	19.6922	−	4.93087i	1.07112	−	0.268204i
$339$	−5.80776			−0.315434
$340$		0			0
$341$	2.56155	+	4.43674i	0.138716	+	0.240263i
$342$	−9.63289	−	5.56155i	−0.520887	−	0.300734i
$343$		−	7.68466i		−	0.414933i
$344$	5.56155	−	9.63289i	0.299859	−	0.519371i
$345$		0			0
$346$	−31.6155			−1.69966
$347$	23.9157	+	13.8078i	1.28386	+	0.741240i	0.977553	−	0.210692i	$-0.0675716\pi$
$347$	23.9157	+	13.8078i	1.28386	+	0.741240i	0.306312	+	0.951931i	$0.400905\pi$
$348$	2.53821	−	1.46543i	0.136062	−	0.0785556i
$349$	3.40388	+	5.89570i	0.182206	+	0.315589i	0.942631	−	0.333836i	$-0.108343\pi$
$349$	3.40388	+	5.89570i	0.182206	+	0.315589i	−0.760426	+	0.649425i	$0.775010\pi$
$350$		0			0
$351$	0.500000	−	3.57071i	0.0266880	−	0.190591i
$352$			4.87689i			0.259939i
$353$	4.60322	−	2.65767i	0.245005	−	0.141454i	−0.372470	−	0.928044i	$-0.621489\pi$
$353$	4.60322	−	2.65767i	0.245005	−	0.141454i	0.617475	+	0.786591i	$0.288156\pi$
$354$	2.24621	+	3.89055i	0.119385	+	0.206781i
$355$		0			0
$356$	2.13826			0.113328
$357$	−0.759413	−	0.438447i	−0.0401924	−	0.0232051i
$358$	−6.59524	−	3.80776i	−0.348569	−	0.201247i
$359$	9.36932			0.494494			0.247247	−	0.968953i	$-0.420474\pi$
$359$	9.36932			0.494494			0.247247	+	0.968953i	$0.420474\pi$
$360$		0			0
$361$	−15.8693	−	27.4865i	−0.835227	−	1.44666i
$362$	−3.63058	+	2.09612i	−0.190819	+	0.110170i
$363$		−	7.00000i		−	0.367405i
$364$	0.822919	−	0.332962i	0.0431327	−	0.0174520i
$365$		0			0
$366$	3.02699	+	5.24290i	0.158223	+	0.274051i
$367$	14.7692	−	8.52699i	0.770945	−	0.445105i	−0.0622668	−	0.998060i	$-0.519833\pi$
$367$	14.7692	−	8.52699i	0.770945	−	0.445105i	0.833212	+	0.552954i	$0.186500\pi$
$368$	8.11407	+	4.68466i	0.422975	+	0.244205i
$369$	1.56155			0.0812912
$370$		0			0
$371$	0.192236	−	0.332962i	0.00998039	−	0.0172865i
$372$		−	1.12311i		−	0.0582303i
$373$	−24.5685	−	14.1847i	−1.27211	−	0.734454i	−0.296726	−	0.954963i	$-0.595895\pi$
$373$	−24.5685	−	14.1847i	−1.27211	−	0.734454i	−0.975385	+	0.220509i	$0.929228\pi$
$374$	−2.43845	−	4.22351i	−0.126089	−	0.218393i
$375$		0			0
$376$	20.1080			1.03699
$377$	9.03996	+	22.3423i	0.465582	+	1.15069i
$378$		−	0.876894i		−	0.0451026i
$379$	11.8423	+	20.5115i	0.608300	+	1.05361i	0.991521	+	0.129949i	$0.0414814\pi$
$379$	11.8423	+	20.5115i	0.608300	+	1.05361i	−0.383221	+	0.923657i	$0.625185\pi$
$380$		0			0
$381$	−2.71922	+	4.70983i	−0.139310	+	0.241292i
$382$		−	14.2462i		−	0.728900i
$383$	19.6922	+	11.3693i	1.00623	+	0.580945i	0.910085	−	0.414423i	$-0.136016\pi$
$383$	19.6922	+	11.3693i	1.00623	+	0.580945i	0.0961417	+	0.995368i	$0.469350\pi$
$384$	−6.78078	+	11.7446i	−0.346030	+	0.599342i
$385$		0			0
$386$	−10.5346	+	18.2464i	−0.536195	+	0.928717i
$387$	−3.95042	+	2.28078i	−0.200811	+	0.115938i
$388$	−3.25088	+	1.87689i	−0.165038	+	0.0952849i
$389$	−34.0540			−1.72661			−0.863303	−	0.504687i	$-0.831608\pi$
$389$	−34.0540			−1.72661			−0.863303	+	0.504687i	$0.831608\pi$
$390$		0			0
$391$	−3.12311			−0.157942
$392$	14.1164	−	8.15009i	0.712985	−	0.411642i
$393$	6.38202	−	3.68466i	0.321930	−	0.185866i
$394$	−10.4384	+	18.0799i	−0.525881	+	0.910853i
$395$		0			0
$396$	0.438447	−	0.759413i	0.0220328	−	0.0381619i
$397$	21.6974	+	12.5270i	1.08896	+	0.628711i	0.933299	−	0.359099i	$-0.116916\pi$
$397$	21.6974	+	12.5270i	1.08896	+	0.628711i	0.155661	+	0.987811i	$0.450249\pi$
$398$		−	34.6307i		−	1.73588i
$399$	2.00000	−	3.46410i	0.100125	−	0.173422i
$400$		0			0
$401$	−7.21922	−	12.5041i	−0.360511	−	0.624423i	0.627534	−	0.778589i	$-0.284064\pi$
$401$	−7.21922	−	12.5041i	−0.360511	−	0.624423i	−0.988045	+	0.154166i	$0.950731\pi$
$402$			7.12311i			0.355268i
$403$	9.14657	+	1.28078i	0.455623	+	0.0638000i
$404$	3.31534			0.164944
$405$		0			0
$406$	2.93087	+	5.07642i	0.145457	+	0.251938i
$407$	−13.0970	−	7.56155i	−0.649194	−	0.374812i
$408$		−	3.80776i		−	0.188512i
$409$	3.18466	−	5.51599i	0.157471	−	0.272748i	−0.776485	−	0.630136i	$-0.782999\pi$
$409$	3.18466	−	5.51599i	0.157471	−	0.272748i	0.933956	+	0.357388i	$0.116333\pi$
$410$		0			0
$411$	−5.56155			−0.274331
$412$	−1.30560	−	0.753789i	−0.0643223	−	0.0371365i
$413$	−1.39909	+	0.807764i	−0.0688446	+	0.0397475i
$414$	−1.56155	−	2.70469i	−0.0767461	−	0.132928i
$415$		0			0
$416$	6.93087	+	5.40938i	0.339814	+	0.265217i
$417$			17.9309i			0.878078i
$418$	19.2658	−	11.1231i	0.942320	−	0.544049i
$419$	−17.1231	−	29.6581i	−0.836518	−	1.44889i	−0.892788	−	0.450477i	$-0.851254\pi$
$419$	−17.1231	−	29.6581i	−0.836518	−	1.44889i	0.0562697	−	0.998416i	$-0.482079\pi$
$420$		0			0
$421$	31.2462			1.52285			0.761424	−	0.648255i	$-0.224501\pi$
$421$	31.2462			1.52285			0.761424	+	0.648255i	$0.224501\pi$
$422$	−26.6204	−	15.3693i	−1.29586	−	0.748167i
$423$	−7.14143	−	4.12311i	−0.347228	−	0.200472i
$424$	1.66950			0.0810783
$425$		0			0
$426$	10.9309	+	18.9328i	0.529602	+	0.917298i
$427$	−1.88541	+	1.08854i	−0.0912413	+	0.0526782i
$428$		−	3.61553i		−	0.174763i
$429$	5.68466	+	4.43674i	0.274458	+	0.214208i
$430$		0			0
$431$	5.56155	+	9.63289i	0.267891	+	0.464000i	0.968317	−	0.249725i	$-0.0803401\pi$
$431$	5.56155	+	9.63289i	0.267891	+	0.464000i	−0.700426	+	0.713725i	$0.747007\pi$
$432$	4.05703	−	2.34233i	0.195194	−	0.112695i
$433$	−7.58100	−	4.37689i	−0.364320	−	0.210340i	0.306654	−	0.951821i	$-0.400790\pi$
$433$	−7.58100	−	4.37689i	−0.364320	−	0.210340i	−0.670974	+	0.741481i	$0.734124\pi$
$434$	2.24621			0.107822
$435$		0			0
$436$	0.615528	−	1.06613i	0.0294785	−	0.0510582i
$437$		−	14.2462i		−	0.681489i
$438$	−13.6899	−	7.90388i	−0.654130	−	0.377662i
$439$	−6.84233	−	11.8513i	−0.326567	−	0.565630i	0.655262	−	0.755402i	$-0.272558\pi$
$439$	−6.84233	−	11.8513i	−0.326567	−	0.565630i	−0.981828	+	0.189772i	$0.939225\pi$
$440$		0			0
$441$	−6.68466			−0.318317
$442$	−8.70700	−	1.21922i	−0.414150	−	0.0579926i
$443$		−	34.7386i		−	1.65048i	−0.564781	−	0.825241i	$-0.691039\pi$
$443$		−	34.7386i		−	1.65048i	0.564781	−	0.825241i	$-0.308961\pi$
$444$	1.65767	+	2.87117i	0.0786696	+	0.136260i
$445$		0			0
$446$	6.24621	−	10.8188i	0.295767	−	0.512283i
$447$			2.43845i			0.115335i
$448$	−2.70469	−	1.56155i	−0.127785	−	0.0737764i
$449$	−4.12311	+	7.14143i	−0.194581	+	0.337025i	−0.946763	−	0.321931i	$-0.895668\pi$
$449$	−4.12311	+	7.14143i	−0.194581	+	0.337025i	0.752182	+	0.658956i	$0.229002\pi$
$450$		0			0
$451$	−1.56155	+	2.70469i	−0.0735307	+	0.127359i
$452$	−2.20525	+	1.27320i	−0.103726	+	0.0598862i
$453$	−8.11407	+	4.68466i	−0.381232	+	0.220104i
$454$	11.1231			0.522033
$455$		0			0
$456$	17.3693			0.813393
$457$	−10.9254	+	6.30776i	−0.511067	+	0.295065i	−0.733272	−	0.679935i	$-0.762008\pi$
$457$	−10.9254	+	6.30776i	−0.511067	+	0.295065i	0.222205	+	0.975000i	$0.428675\pi$
$458$	21.9705	−	12.6847i	1.02661	−	0.592715i
$459$	−0.780776	+	1.35234i	−0.0364435	+	0.0631220i
$460$		0			0
$461$	8.09612	−	14.0229i	0.377074	−	0.653111i	−0.613561	−	0.789647i	$-0.710264\pi$
$461$	8.09612	−	14.0229i	0.377074	−	0.653111i	0.990635	+	0.136536i	$0.0435970\pi$
$462$	1.51883	+	0.876894i	0.0706622	+	0.0407968i
$463$		−	14.3153i		−	0.665290i	−0.943052	−	0.332645i	$-0.892059\pi$
$463$		−	14.3153i		−	0.665290i	0.943052	−	0.332645i	$-0.107941\pi$
$464$	−15.6577	+	27.1199i	−0.726889	+	1.25901i
$465$		0			0
$466$	20.3002	+	35.1610i	0.940388	+	1.62880i
$467$			26.0000i			1.20314i	0.798821	+	0.601568i	$0.205457\pi$
$467$			26.0000i			1.20314i	−0.798821	+	0.601568i	$0.794543\pi$
$468$	−0.592932	−	1.46543i	−0.0274083	−	0.0677397i
$469$	−2.56155			−0.118282
$470$		0			0
$471$	−10.1847	−	17.6403i	−0.469284	−	0.812824i
$472$	−6.07530	−	3.50758i	−0.279638	−	0.161449i
$473$		−	9.12311i		−	0.419481i
$474$	−4.24621	+	7.35465i	−0.195035	+	0.337810i
$475$		0			0
$476$	−0.384472			−0.0176222
$477$	−0.592932	−	0.342329i	−0.0271485	−	0.0156742i
$478$	34.3081	−	19.8078i	1.56921	−	0.905986i
$479$	5.12311	+	8.87348i	0.234081	+	0.405440i	0.959005	−	0.283389i	$-0.0914587\pi$
$479$	5.12311	+	8.87348i	0.234081	+	0.405440i	−0.724924	+	0.688828i	$0.758125\pi$
$480$		0			0
$481$	−25.2732	+	10.2258i	−1.15236	+	0.466257i
$482$		−	27.8078i		−	1.26661i
$483$	0.972638	−	0.561553i	0.0442566	−	0.0255515i
$484$	−1.53457	−	2.65794i	−0.0697530	−	0.120816i
$485$		0			0
$486$	−1.56155			−0.0708335
$487$	6.16879	+	3.56155i	0.279535	+	0.161389i	0.633213	−	0.773978i	$-0.281736\pi$
$487$	6.16879	+	3.56155i	0.279535	+	0.161389i	−0.353678	+	0.935367i	$0.615069\pi$
$488$	−8.18706	−	4.72680i	−0.370611	−	0.213972i
$489$	4.80776			0.217415
$490$		0			0
$491$	18.1231	+	31.3901i	0.817884	+	1.41662i	0.907238	+	0.420617i	$0.138186\pi$
$491$	18.1231	+	31.3901i	0.817884	+	1.41662i	−0.0893539	+	0.996000i	$0.528480\pi$
$492$	0.592932	−	0.342329i	0.0267314	−	0.0154334i
$493$		−	10.4384i		−	0.470124i
$494$	5.56155	−	39.7174i	0.250226	−	1.78697i
$495$		0			0
$496$	6.00000	+	10.3923i	0.269408	+	0.466628i
$497$	−6.80847	+	3.93087i	−0.305401	+	0.176324i
$498$	−1.18586	−	0.684658i	−0.0531398	−	0.0306803i
$499$	−4.49242			−0.201108			−0.100554	−	0.994932i	$-0.532062\pi$
$499$	−4.49242			−0.201108			−0.100554	+	0.994932i	$0.532062\pi$
$500$		0			0
$501$	−5.12311	+	8.87348i	−0.228883	+	0.396438i
$502$			29.2614i			1.30600i
$503$	24.4619	+	14.1231i	1.09070	+	0.629718i	0.933764	−	0.357890i	$-0.116504\pi$
$503$	24.4619	+	14.1231i	1.09070	+	0.629718i	0.156940	+	0.987608i	$0.449837\pi$
$504$	0.684658	+	1.18586i	0.0304971	+	0.0528225i
$505$		0			0
$506$	6.24621			0.277678
$507$	12.6107	−	3.15767i	0.560060	−	0.140237i
$508$			2.38447i			0.105794i
$509$	−6.90388	−	11.9579i	−0.306009	−	0.530023i	0.671476	−	0.741026i	$-0.265660\pi$
$509$	−6.90388	−	11.9579i	−0.306009	−	0.530023i	−0.977486	+	0.211003i	$0.932327\pi$
$510$		0			0
$511$	2.84233	−	4.92306i	0.125737	−	0.217783i
$512$		−	11.4233i		−	0.504843i
$513$	−6.16879	−	3.56155i	−0.272359	−	0.157246i
$514$	−22.7808	+	39.4575i	−1.00482	+	1.74039i
$515$		0			0
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$	14.2829	−	8.24621i	0.628159	−	0.362668i
$518$	−5.74234	+	3.31534i	−0.252304	+	0.145668i
$519$	−20.2462			−0.888710
$520$		0			0
$521$	−9.06913			−0.397326			−0.198663	−	0.980068i	$-0.563660\pi$
$521$	−9.06913			−0.397326			−0.198663	+	0.980068i	$0.563660\pi$
$522$	9.03996	−	5.21922i	0.395668	−	0.228439i
$523$	29.3251	−	16.9309i	1.28230	−	0.740335i	0.305030	−	0.952343i	$-0.401333\pi$
$523$	29.3251	−	16.9309i	1.28230	−	0.740335i	0.977268	+	0.212007i	$0.0680001\pi$
$524$	1.61553	−	2.79818i	0.0705747	−	0.122239i
$525$		0			0
$526$	7.31534	−	12.6705i	0.318964	−	0.552462i
$527$	−3.46410	−	2.00000i	−0.150899	−	0.0871214i
$528$			9.36932i			0.407747i
$529$	−9.50000	+	16.4545i	−0.413043	+	0.715412i
$530$		0			0
$531$	1.43845	+	2.49146i	0.0624233	+	0.108120i
$532$		−	1.75379i		−	0.0760364i
$533$	2.11176	+	5.21922i	0.0914704	+	0.226070i
$534$	7.61553			0.329556
$535$		0			0
$536$	−5.56155	−	9.63289i	−0.240222	−	0.416078i
$537$	−4.22351	−	2.43845i	−0.182258	−	0.105227i
$538$			33.3693i			1.43865i
$539$	6.68466	−	11.5782i	0.287929	−	0.498707i
$540$		0			0
$541$	19.7386			0.848630			0.424315	−	0.905515i	$-0.360515\pi$
$541$	19.7386			0.848630			0.424315	+	0.905515i	$0.360515\pi$
$542$	40.4768	+	23.3693i	1.73863	+	1.00380i
$543$	−2.32498	+	1.34233i	−0.0997745	+	0.0576049i
$544$	−1.90388	−	3.29762i	−0.0816283	−	0.141384i
$545$		0			0
$546$	2.93087	−	1.18586i	0.125430	−	0.0507503i
$547$		−	3.93087i		−	0.168072i	−0.996463	−	0.0840359i	$-0.973219\pi$
$547$		−	3.93087i		−	0.168072i	0.996463	−	0.0840359i	$-0.0267811\pi$
$548$	−2.11176	+	1.21922i	−0.0902098	+	0.0520827i
$549$	1.93845	+	3.35749i	0.0827309	+	0.143294i
$550$		0			0
$551$	47.6155			2.02849
$552$	4.22351	+	2.43845i	0.179765	+	0.103787i
$553$	−2.64482	−	1.52699i	−0.112469	−	0.0649341i
$554$	8.30019			0.352641
$555$		0			0
$556$	3.93087	+	6.80847i	0.166706	+	0.288743i
$557$	37.1792	−	21.4654i	1.57533	−	0.909520i	0.579837	−	0.814733i	$-0.303116\pi$
$557$	37.1792	−	21.4654i	1.57533	−	0.909520i	0.995498	−	0.0947869i	$-0.0302170\pi$
$558$		−	4.00000i		−	0.169334i
$559$	−12.9654	−	10.1192i	−0.548379	−	0.427997i
$560$		0			0
$561$	−1.56155	−	2.70469i	−0.0659288	−	0.114192i
$562$	24.0822	−	13.9039i	1.01585	−	0.586500i
$563$	20.2384	+	11.6847i	0.852948	+	0.492450i	0.861644	−	0.507513i	$-0.169435\pi$
$563$	20.2384	+	11.6847i	0.852948	+	0.492450i	−0.00869657	+	0.999962i	$0.502768\pi$
$564$	−3.61553			−0.152241
$565$		0			0
$566$	−10.6847	+	18.5064i	−0.449110	+	0.777881i
$567$		−	0.561553i		−	0.0235830i
$568$	−29.5646	−	17.0691i	−1.24050	−	0.716205i
$569$	−4.36932	−	7.56788i	−0.183171	−	0.317262i	0.759787	−	0.650171i	$-0.225303\pi$
$569$	−4.36932	−	7.56788i	−0.183171	−	0.317262i	−0.942959	+	0.332910i	$0.891970\pi$
$570$		0			0
$571$	−5.36932			−0.224699			−0.112349	−	0.993669i	$-0.535838\pi$
$571$	−5.36932			−0.224699			−0.112349	+	0.993669i	$0.535838\pi$
$572$	3.13114	+	0.438447i	0.130920	+	0.0183324i
$573$		−	9.12311i		−	0.381123i
$574$	0.684658	+	1.18586i	0.0285771	+	0.0494970i
$575$		0			0
$576$	−2.78078	+	4.81645i	−0.115866	+	0.200685i
$577$			17.3153i			0.720847i	0.932789	+	0.360424i	$0.117368\pi$
$577$			17.3153i			0.720847i	−0.932789	+	0.360424i	$0.882632\pi$
$578$	−19.6922	−	11.3693i	−0.819089	−	0.472901i
$579$	−6.74621	+	11.6848i	−0.280363	+	0.485603i
$580$		0			0
$581$	0.246211	−	0.426450i	0.0102146	−	0.0176921i
$582$	−11.5782	+	6.68466i	−0.479931	+	0.277088i
$583$	1.18586	−	0.684658i	0.0491134	−	0.0283557i
$584$	24.6847			1.02146
$585$		0			0
$586$	−31.9157			−1.31843
$587$	−34.0948	+	19.6847i	−1.40724	+	0.812473i	−0.995122	−	0.0986556i	$-0.968546\pi$
$587$	−34.0948	+	19.6847i	−1.40724	+	0.812473i	−0.412123	+	0.911128i	$0.635212\pi$
$588$	−2.53821	+	1.46543i	−0.104674	+	0.0604335i
$589$	9.12311	−	15.8017i	0.375911	−	0.651097i
$590$		0			0
$591$	−6.68466	+	11.5782i	−0.274970	+	0.476262i
$592$	−30.6775	−	17.7116i	−1.26084	−	0.727944i
$593$		−	17.4233i		−	0.715489i	−0.933820	−	0.357744i	$-0.883546\pi$
$593$		−	17.4233i		−	0.715489i	0.933820	−	0.357744i	$-0.116454\pi$
$594$	1.56155	−	2.70469i	0.0640713	−	0.110975i
$595$		0			0
$596$	0.534565	+	0.925894i	0.0218966	+	0.0379261i
$597$		−	22.1771i		−	0.907648i
$598$	6.92820	−	8.87689i	0.283315	−	0.363003i
$599$	41.6155			1.70036			0.850182	−	0.526489i	$-0.176492\pi$
$599$	41.6155			1.70036			0.850182	+	0.526489i	$0.176492\pi$
$600$		0			0
$601$	3.53457	+	6.12205i	0.144178	+	0.249723i	0.929066	−	0.369914i	$-0.120613\pi$
$601$	3.53457	+	6.12205i	0.144178	+	0.249723i	−0.784888	+	0.619638i	$0.787280\pi$
$602$	−3.46410	−	2.00000i	−0.141186	−	0.0815139i
$603$			4.56155i			0.185761i
$604$	−2.05398	+	3.55759i	−0.0835751	+	0.144756i
$605$		0			0
$606$	11.8078			0.479658
$607$	−13.8564	−	8.00000i	−0.562414	−	0.324710i	0.191700	−	0.981454i	$-0.438600\pi$
$607$	−13.8564	−	8.00000i	−0.562414	−	0.324710i	−0.754114	+	0.656744i	$0.771933\pi$
$608$	15.0423	−	8.68466i	0.610045	−	0.352209i
$609$	1.87689	+	3.25088i	0.0760556	+	0.131732i
$610$		0			0
$611$	4.12311	−	29.4449i	0.166803	−	1.19121i
$612$			0.684658i			0.0276757i
$613$	−30.1912	+	17.4309i	−1.21941	+	0.704026i	−0.964792	−	0.263016i	$-0.915283\pi$
$613$	−30.1912	+	17.4309i	−1.21941	+	0.704026i	−0.254618	+	0.967042i	$0.581950\pi$
$614$	−24.0540	−	41.6627i	−0.970739	−	1.68137i
$615$		0			0
$616$	−2.73863			−0.110343
$617$	8.49377	+	4.90388i	0.341946	+	0.197423i	0.661132	−	0.750269i	$-0.270076\pi$
$617$	8.49377	+	4.90388i	0.341946	+	0.197423i	−0.319186	+	0.947692i	$0.603409\pi$
$618$	−4.64996	−	2.68466i	−0.187049	−	0.107993i
$619$	−29.3002			−1.17767			−0.588837	−	0.808252i	$-0.700414\pi$
$619$	−29.3002			−1.17767			−0.588837	+	0.808252i	$0.700414\pi$
$620$		0			0
$621$	−1.00000	−	1.73205i	−0.0401286	−	0.0695048i
$622$	−25.8610	+	14.9309i	−1.03693	+	0.598673i
$623$			2.73863i			0.109721i
$624$	13.3153	+	10.3923i	0.533040	+	0.416025i
$625$		0			0
$626$	−10.6847	−	18.5064i	−0.427045	−	0.739663i
$627$	12.3376	−	7.12311i	0.492716	−	0.284469i
$628$	−7.73436	−	4.46543i	−0.308635	−	0.178190i
$629$	11.8078			0.470806
$630$		0			0
$631$	9.28078	−	16.0748i	0.369462	−	0.639927i	−0.620020	−	0.784586i	$-0.712875\pi$
$631$	9.28078	−	16.0748i	0.369462	−	0.639927i	0.989481	+	0.144660i	$0.0462087\pi$
$632$		−	13.2614i		−	0.527509i
$633$	−17.0474	−	9.84233i	−0.677574	−	0.391197i
$634$	−10.9730	−	19.0058i	−0.435794	−	0.754817i
$635$		0			0
$636$	−0.300187			−0.0119032
$637$	−9.03996	−	22.3423i	−0.358176	−	0.885235i
$638$			20.8769i			0.826524i
$639$	7.00000	+	12.1244i	0.276916	+	0.479632i
$640$		0			0
$641$	9.58854	−	16.6078i	0.378725	−	0.655970i	−0.612152	−	0.790740i	$-0.709696\pi$
$641$	9.58854	−	16.6078i	0.378725	−	0.655970i	0.990877	+	0.134770i	$0.0430294\pi$
$642$		−	12.8769i		−	0.508210i
$643$	27.3200	+	15.7732i	1.07739	+	0.622034i	0.930192	−	0.367072i	$-0.119640\pi$
$643$	27.3200	+	15.7732i	1.07739	+	0.622034i	0.147202	+	0.989106i	$0.452973\pi$
$644$	0.246211	−	0.426450i	0.00970208	−	0.0168045i
$645$		0			0
$646$	−8.68466	+	15.0423i	−0.341693	+	0.591830i
$647$	5.52911	−	3.19224i	0.217372	−	0.125500i	−0.387361	−	0.921928i	$-0.626613\pi$
$647$	5.52911	−	3.19224i	0.217372	−	0.125500i	0.604733	+	0.796428i	$0.293280\pi$
$648$	2.11176	−	1.21922i	0.0829577	−	0.0478956i
$649$	−5.75379			−0.225856
$650$		0			0
$651$	1.43845			0.0563772
$652$	1.82554	−	1.05398i	0.0714936	−	0.0412769i
$653$	20.0252	−	11.5616i	0.783647	−	0.452439i	−0.0540745	−	0.998537i	$-0.517221\pi$
$653$	20.0252	−	11.5616i	0.783647	−	0.452439i	0.837721	+	0.546098i	$0.183888\pi$
$654$	2.19224	−	3.79706i	0.0857232	−	0.148477i
$655$		0			0
$656$	−3.65767	+	6.33527i	−0.142808	+	0.247351i
$657$	−8.76687	−	5.06155i	−0.342028	−	0.197470i
$658$		−	7.23106i		−	0.281896i
$659$	−1.12311	+	1.94528i	−0.0437500	+	0.0757772i	−0.887071	−	0.461633i	$-0.847264\pi$
$659$	−1.12311	+	1.94528i	−0.0437500	+	0.0757772i	0.843321	+	0.537410i	$0.180597\pi$
$660$		0			0
$661$	−2.81534	−	4.87631i	−0.109504	−	0.189667i	0.806065	−	0.591827i	$-0.201593\pi$
$661$	−2.81534	−	4.87631i	−0.109504	−	0.189667i	−0.915569	+	0.402160i	$0.868260\pi$
$662$		−	4.98485i		−	0.193742i
$663$	−5.57586	−	0.780776i	−0.216548	−	0.0303228i
$664$	2.13826			0.0829806
$665$		0			0
$666$	5.90388	+	10.2258i	0.228771	+	0.396243i
$667$	11.5782	+	6.68466i	0.448308	+	0.258831i
$668$			4.49242i			0.173817i
$669$	4.00000	−	6.92820i	0.154649	−	0.267860i
$670$		0			0
$671$	−7.75379			−0.299332
$672$	1.18586	+	0.684658i	0.0457457	+	0.0264113i
$673$	−20.1318	+	11.6231i	−0.776024	+	0.448038i	−0.835019	−	0.550220i	$-0.814544\pi$
$673$	−20.1318	+	11.6231i	−0.776024	+	0.448038i	0.0589952	+	0.998258i	$0.481210\pi$
$674$	4.78078	+	8.28055i	0.184149	+	0.318955i
$675$		0			0
$676$	4.09612	−	3.96355i	0.157543	−	0.152444i
$677$			15.6155i			0.600153i	0.953915	+	0.300077i	$0.0970123\pi$
$677$			15.6155i			0.600153i	−0.953915	+	0.300077i	$0.902988\pi$
$678$	−7.85410	+	4.53457i	−0.301635	+	0.174149i
$679$	−2.40388	−	4.16365i	−0.0922525	−	0.159786i
$680$		0			0
$681$	7.12311			0.272958
$682$	6.92820	+	4.00000i	0.265295	+	0.153168i
$683$	33.0025	+	19.0540i	1.26280	+	0.729080i	0.973616	−	0.228192i	$-0.0732815\pi$
$683$	33.0025	+	19.0540i	1.26280	+	0.729080i	0.289188	+	0.957272i	$0.406615\pi$
$684$	−3.12311			−0.119415
$685$		0			0
$686$	−6.00000	−	10.3923i	−0.229081	−	0.396780i
$687$	14.0696	−	8.12311i	0.536790	−	0.309916i
$688$		−	21.3693i		−	0.814698i
$689$	0.342329	−	2.44472i	0.0130417	−	0.0931364i
$690$		0			0
$691$	25.6501	+	44.4273i	0.975776	+	1.69009i	0.677352	+	0.735659i	$0.263128\pi$
$691$	25.6501	+	44.4273i	0.975776	+	1.69009i	0.298424	+	0.954433i	$0.403539\pi$
$692$	−7.68762	+	4.43845i	−0.292239	+	0.168724i
$693$	0.972638	+	0.561553i	0.0369475	+	0.0213316i
$694$	43.1231			1.63693
$695$		0			0
$696$	−8.15009	+	14.1164i	−0.308928	+	0.535080i
$697$		−	2.43845i		−	0.0923628i
$698$	9.20644	+	5.31534i	0.348469	+	0.201189i
$699$	13.0000	+	22.5167i	0.491705	+	0.851658i
$700$		0			0
$701$	−5.36932			−0.202796			−0.101398	−	0.994846i	$-0.532332\pi$
$701$	−5.36932			−0.202796			−0.101398	+	0.994846i	$0.532332\pi$
$702$	−2.11176	−	5.21922i	−0.0797031	−	0.196987i
$703$			53.8617i			2.03143i
$704$	−5.56155	−	9.63289i	−0.209609	−	0.363053i
$705$		0			0
$706$	4.15009	−	7.18817i	0.156191	−	0.270530i
$707$			4.24621i			0.159695i
$708$	1.09238	+	0.630683i	0.0410540	+	0.0237025i
$709$	−3.74621	+	6.48863i	−0.140692	+	0.243686i	−0.927757	−	0.373184i	$-0.878266\pi$
$709$	−3.74621	+	6.48863i	−0.140692	+	0.243686i	0.787065	+	0.616869i	$0.211599\pi$
$710$		0			0
$711$	−2.71922	+	4.70983i	−0.101979	+	0.176633i
$712$	−10.2988	+	5.94602i	−0.385964	+	0.222837i
$713$	4.43674	−	2.56155i	0.166157	−	0.0959309i
$714$	−1.36932			−0.0512454
$715$		0			0
$716$	−2.13826			−0.0799106
$717$	21.9705	−	12.6847i	0.820502	−	0.473717i
$718$	12.6705	−	7.31534i	0.472860	−	0.273006i
$719$	−11.6847	+	20.2384i	−0.435764	+	0.754766i	−0.997358	−	0.0726475i	$-0.976855\pi$
$719$	−11.6847	+	20.2384i	−0.435764	+	0.754766i	0.561593	+	0.827413i	$0.310189\pi$
$720$		0			0
$721$	0.965435	−	1.67218i	0.0359547	−	0.0622753i
$722$	−42.9216	−	24.7808i	−1.59738	−	0.922245i
$723$		−	17.8078i		−	0.662278i
$724$	−0.588540	+	1.01938i	−0.0218729	+	0.0378850i
$725$		0			0
$726$	−5.46543	−	9.46641i	−0.202841	−	0.351331i
$727$			38.6695i			1.43417i	0.696984	+	0.717086i	$0.254525\pi$
$727$			38.6695i			1.43417i	−0.696984	+	0.717086i	$0.745475\pi$
$728$	−3.03765	+	3.89205i	−0.112583	+	0.144249i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	3.56155	+	6.16879i	0.131729	+	0.228161i
$732$	1.47208	+	0.849907i	0.0544097	+	0.0314135i
$733$			20.5076i			0.757465i	0.925506	+	0.378732i	$0.123640\pi$
$733$			20.5076i			0.757465i	−0.925506	+	0.378732i	$0.876360\pi$
$734$	13.3153	−	23.0628i	0.491478	−	0.851265i
$735$		0			0
$736$	4.87689			0.179765
$737$	−7.90084	−	4.56155i	−0.291031	−	0.168027i
$738$	2.11176	−	1.21922i	0.0777349	−	0.0448802i
$739$	5.12311	+	8.87348i	0.188456	+	0.326416i	0.944736	−	0.327833i	$-0.106318\pi$
$739$	5.12311	+	8.87348i	0.188456	+	0.326416i	−0.756279	+	0.654249i	$0.772985\pi$
$740$		0			0
$741$	3.56155	−	25.4346i	0.130837	−	0.934362i
$742$		−	0.600373i		−	0.0220404i
$743$	−10.9385	+	6.31534i	−0.401294	+	0.231687i	−0.687042	−	0.726617i	$-0.741091\pi$
$743$	−10.9385	+	6.31534i	−0.401294	+	0.231687i	0.285748	+	0.958305i	$0.407758\pi$
$744$	3.12311	+	5.40938i	0.114499	+	0.198317i
$745$		0			0
$746$	−44.3002			−1.62195
$747$	−0.759413	−	0.438447i	−0.0277855	−	0.0160419i
$748$	−1.18586	−	0.684658i	−0.0433595	−	0.0250336i
$749$	4.63068			0.169201
$750$		0			0
$751$	−22.0540	−	38.1986i	−0.804761	−	1.39389i	−0.916452	−	0.400144i	$-0.868960\pi$
$751$	−22.0540	−	38.1986i	−0.804761	−	1.39389i	0.111691	−	0.993743i	$-0.464373\pi$
$752$	33.4552	−	19.3153i	1.21998	−	0.704358i
$753$			18.7386i			0.682874i
$754$	29.6695	+	23.1563i	1.08050	+	0.843304i
$755$		0			0
$756$	−0.123106	−	0.213225i	−0.00447731	−	0.00775493i
$757$	−25.9808	+	15.0000i	−0.944287	+	0.545184i	−0.891302	−	0.453411i	$-0.850207\pi$
$757$	−25.9808	+	15.0000i	−0.944287	+	0.545184i	−0.0529853	+	0.998595i	$0.516874\pi$
$758$	32.0298	+	18.4924i	1.16338	+	0.671675i
$759$	4.00000			0.145191
$760$		0			0
$761$	−4.68466	+	8.11407i	−0.169819	+	0.294135i	−0.938356	−	0.345670i	$-0.887652\pi$
$761$	−4.68466	+	8.11407i	−0.169819	+	0.294135i	0.768537	+	0.639805i	$0.220985\pi$
$762$			8.49242i			0.307648i
$763$	1.36547	+	0.788354i	0.0494333	+	0.0285403i
$764$	−2.00000	−	3.46410i	−0.0723575	−	0.125327i
$765$		0			0
$766$	35.5076			1.28294
$767$	−6.38202	+	8.17708i	−0.230441	+	0.295257i
$768$			10.0540i			0.362792i
$769$	−9.00000	−	15.5885i	−0.324548	−	0.562134i	0.656873	−	0.754002i	$-0.271879\pi$
$769$	−9.00000	−	15.5885i	−0.324548	−	0.562134i	−0.981421	+	0.191867i	$0.938546\pi$
$770$		0			0
$771$	−14.5885	+	25.2681i	−0.525393	+	0.910008i
$772$			5.91571i			0.212911i
$773$	20.9978	+	12.1231i	0.755240	+	0.436038i	0.827584	−	0.561342i	$-0.189715\pi$
$773$	20.9978	+	12.1231i	0.755240	+	0.436038i	−0.0723444	+	0.997380i	$0.523048\pi$
$774$	−3.56155	+	6.16879i	−0.128017	+	0.221733i
$775$		0			0
$776$	10.4384	−	18.0799i	0.374718	−	0.649031i
$777$	−3.67733	+	2.12311i	−0.131923	+	0.0761660i
$778$	−46.0527	+	26.5885i	−1.65107	+	0.953245i
$779$	11.1231			0.398527
$780$		0			0
$781$	−28.0000			−1.00192
$782$	−4.22351	+	2.43845i	−0.151033	+	0.0871987i
$783$	5.78908	−	3.34233i	0.206885	−	0.119445i
$784$	15.6577	−	27.1199i	0.559203	−	0.968567i
$785$		0			0
$786$	5.75379	−	9.96585i	0.205231	−	0.355470i
$787$	38.2585	+	22.0885i	1.36377	+	0.787371i	0.990123	−	0.140201i	$-0.0447748\pi$
$787$	38.2585	+	22.0885i	1.36377	+	0.787371i	0.373644	+	0.927572i	$0.378108\pi$
$788$			5.86174i			0.208816i
$789$	4.68466	−	8.11407i	0.166778	−	0.288868i
$790$		0			0
$791$	−1.63068	−	2.82443i	−0.0579804	−	0.100425i
$792$			4.87689i			0.173293i
$793$	−8.60039	+	11.0194i	−0.305409	+	0.391311i
$794$	39.1231			1.38843
$795$		0			0
$796$	−4.86174	−	8.42078i	−0.172320	−	0.298467i
$797$	−0.332962	−	0.192236i	−0.0117941	−	0.00680935i	0.494091	−	0.869410i	$-0.335501\pi$
$797$	−0.332962	−	0.192236i	−0.0117941	−	0.00680935i	−0.505885	+	0.862601i	$0.668834\pi$
$798$		−	6.24621i		−	0.221113i
$799$	−6.43845	+	11.1517i	−0.227776	+	0.394519i
$800$		0			0
$801$	4.87689			0.172317
$802$	−19.5258	−	11.2732i	−0.689478	−	0.398070i
$803$	17.5337	−	10.1231i	0.618752	−	0.357237i
$804$	1.00000	+	1.73205i	0.0352673	+	0.0610847i
$805$		0			0
$806$	13.3693	−	5.40938i	0.470914	−	0.190537i
$807$			21.3693i			0.752236i
$808$	−15.9682	+	9.21922i	−0.561758	+	0.324331i
$809$	−8.15009	−	14.1164i	−0.286542	−	0.496305i	0.686440	−	0.727187i	$-0.259172\pi$
$809$	−8.15009	−	14.1164i	−0.286542	−	0.496305i	−0.972982	+	0.230881i	$0.925839\pi$
$810$		0			0
$811$	2.56155			0.0899483			0.0449741	−	0.998988i	$-0.485679\pi$
$811$	2.56155			0.0899483			0.0449741	+	0.998988i	$0.485679\pi$
$812$	1.42534	+	0.822919i	0.0500195	+	0.0288788i
$813$	25.9209	+	14.9654i	0.909085	+	0.524861i
$814$	−23.6155			−0.827724
$815$		0			0
$816$	−3.65767	−	6.33527i	−0.128044	−	0.221779i
$817$	−28.1393	+	16.2462i	−0.984468	+	0.568383i
$818$		−	9.94602i		−	0.347755i
$819$	1.87689	−	0.759413i	0.0655840	−	0.0265360i
$820$		0			0
$821$	−3.24621	−	5.62260i	−0.113294	−	0.196230i	0.803803	−	0.594896i	$-0.202807\pi$
$821$	−3.24621	−	5.62260i	−0.113294	−	0.196230i	−0.917096	+	0.398666i	$0.869473\pi$
$822$	−7.52113	+	4.34233i	−0.262330	+	0.151456i
$823$	−6.92820	−	4.00000i	−0.241502	−	0.139431i	0.374365	−	0.927281i	$-0.377861\pi$
$823$	−6.92820	−	4.00000i	−0.241502	−	0.139431i	−0.615867	+	0.787850i	$0.711194\pi$
$824$	8.38447			0.292087
$825$		0			0
$826$	−1.26137	+	2.18475i	−0.0438885	+	0.0760172i
$827$			14.7386i			0.512513i	0.966609	+	0.256256i	$0.0824891\pi$
$827$			14.7386i			0.512513i	−0.966609	+	0.256256i	$0.917511\pi$
$828$	−0.759413	−	0.438447i	−0.0263914	−	0.0152371i
$829$	6.74621	+	11.6848i	0.234306	+	0.405829i	0.959071	−	0.283167i	$-0.0913850\pi$
$829$	6.74621	+	11.6848i	0.234306	+	0.405829i	−0.724765	+	0.688996i	$0.758052\pi$
$830$		0			0
$831$	5.31534			0.184387
$832$	−19.8587	−	2.78078i	−0.688477	−	0.0964061i
$833$			10.4384i			0.361671i
$834$	14.0000	+	24.2487i	0.484780	+	0.839664i
$835$		0			0
$836$	3.12311	−	5.40938i	0.108015	−	0.187087i
$837$		−	2.56155i		−	0.0885402i
$838$	−46.3127	−	26.7386i	−1.59984	−	0.923671i
$839$	10.8078	−	18.7196i	0.373125	−	0.646272i	−0.616919	−	0.787027i	$-0.711619\pi$
$839$	10.8078	−	18.7196i	0.373125	−	0.646272i	0.990045	+	0.140754i	$0.0449528\pi$
$840$		0			0
$841$	−7.84233	+	13.5833i	−0.270425	+	0.468390i
$842$	42.2556	−	24.3963i	1.45623	−	0.840752i
$843$	15.4220	−	8.90388i	0.531161	−	0.306666i
$844$	−8.63068			−0.297080
$845$		0			0
$846$	−12.8769			−0.442717
$847$	3.40423	−	1.96543i	0.116971	−	0.0675331i
$848$	2.77768	−	1.60370i	0.0953860	−	0.0550711i
$849$	−6.84233	+	11.8513i	−0.234828	+	0.406734i
$850$		0			0
$851$	−7.56155	+	13.0970i	−0.259207	+	0.448959i
$852$	5.31589	+	3.06913i	0.182119	+	0.105147i
$853$			2.12311i			0.0726938i	0.999339	+	0.0363469i	$0.0115721\pi$
$853$			2.12311i			0.0726938i	−0.999339	+	0.0363469i	$0.988428\pi$
$854$	−1.69981	+	2.94416i	−0.0581664	+	0.100747i
$855$		0			0
$856$	10.0540	+	17.4140i	0.343638	+	0.595198i
$857$		−	35.5616i		−	1.21476i	−0.794412	−	0.607380i	$-0.792221\pi$
$857$		−	35.5616i		−	1.21476i	0.794412	−	0.607380i	$-0.207779\pi$
$858$	11.1517	+	1.56155i	0.380713	+	0.0533105i
$859$	−24.5616			−0.838029			−0.419015	−	0.907979i	$-0.637624\pi$
$859$	−24.5616			−0.838029			−0.419015	+	0.907979i	$0.637624\pi$
$860$		0			0
$861$	0.438447	+	0.759413i	0.0149422	+	0.0258807i
$862$	15.0423	+	8.68466i	0.512342	+	0.295801i
$863$			30.4924i			1.03797i	0.854782	+	0.518987i	$0.173691\pi$
$863$			30.4924i			1.03797i	−0.854782	+	0.518987i	$0.826309\pi$
$864$	1.21922	−	2.11176i	0.0414788	−	0.0718434i
$865$		0			0
$866$	−13.6695			−0.464509
$867$	−12.6107	−	7.28078i	−0.428281	−	0.247268i
$868$	0.546188	−	0.315342i	0.0185388	−	0.0107034i
$869$	−5.43845	−	9.41967i	−0.184487	−	0.319540i
$870$		0			0
$871$	−15.2462	+	6.16879i	−0.516598	+	0.209021i
$872$			6.84658i			0.231855i
$873$	−7.41452	+	4.28078i	−0.250944	+	0.144882i
$874$	−11.1231	−	19.2658i	−0.376245	−	0.651675i
$875$		0			0
$876$	−4.43845			−0.149961
$877$	20.4049	+	11.7808i	0.689025	+	0.397809i	0.803247	−	0.595647i	$-0.203104\pi$
$877$	20.4049	+	11.7808i	0.689025	+	0.397809i	−0.114222	+	0.993455i	$0.536437\pi$
$878$	−18.5064	−	10.6847i	−0.624560	−	0.360590i
$879$	−20.4384			−0.689372
$880$		0			0
$881$	4.53457	+	7.85410i	0.152773	+	0.264611i	0.932246	−	0.361825i	$-0.117846\pi$
$881$	4.53457	+	7.85410i	0.152773	+	0.264611i	−0.779473	+	0.626436i	$0.784513\pi$
$882$	−9.03996	+	5.21922i	−0.304391	+	0.175740i
$883$			8.80776i			0.296405i	0.988957	+	0.148202i	$0.0473487\pi$
$883$			8.80776i			0.296405i	−0.988957	+	0.148202i	$0.952651\pi$
$884$	−2.28835	+	0.925894i	−0.0769657	+	0.0311412i
$885$		0			0
$886$	−27.1231	−	46.9786i	−0.911219	−	1.57828i
$887$	−21.3308	+	12.3153i	−0.716218	+	0.413509i	−0.813359	−	0.581762i	$-0.802364\pi$
$887$	−21.3308	+	12.3153i	−0.716218	+	0.413509i	0.0971410	+	0.995271i	$0.469030\pi$
$888$	−15.9682	−	9.21922i	−0.535856	−	0.309377i
$889$	−3.05398			−0.102427
$890$		0			0
$891$	1.00000	−	1.73205i	0.0335013	−	0.0580259i
$892$		−	3.50758i		−	0.117442i
$893$	−50.8691	−	29.3693i	−1.70227	−	0.982807i
$894$	1.90388	+	3.29762i	0.0636753	+	0.110289i
$895$		0			0
$896$	−7.61553			−0.254417
$897$	4.43674	−	5.68466i	0.148138	−	0.189805i
$898$			12.8769i			0.429708i
$899$	8.56155	+	14.8290i	0.285544	+	0.494576i
$900$		0			0
$901$	−0.534565	+	0.925894i	−0.0178089	+	0.0308460i
$902$			4.87689i			0.162383i
$903$	−2.21837	−	1.28078i	−0.0738227	−	0.0426216i
$904$	7.08096	−	12.2646i	0.235509	−	0.407914i
$905$		0			0
$906$	−7.31534	+	12.6705i	−0.243036	+	0.420951i
$907$	−24.2487	+	14.0000i	−0.805165	+	0.464862i	−0.845274	−	0.534333i	$-0.820563\pi$
$907$	−24.2487	+	14.0000i	−0.805165	+	0.464862i	0.0401089	+	0.999195i	$0.487230\pi$
$908$	2.70469	−	1.56155i	0.0897583	−	0.0518220i
$909$	7.56155			0.250801
$910$		0			0
$911$	38.7386			1.28347			0.641734	−	0.766927i	$-0.278215\pi$
$911$	38.7386			1.28347			0.641734	+	0.766927i	$0.278215\pi$
$912$	28.8987	−	16.6847i	0.956931	−	0.552484i
$913$	1.51883	−	0.876894i	0.0502658	−	0.0290210i
$914$	−9.84991	+	17.0605i	−0.325806	+	0.564312i
$915$		0			0
$916$	3.56155	−	6.16879i	0.117677	−	0.203823i
$917$	3.58384	+	2.06913i	0.118349	+	0.0683287i
$918$			2.43845i			0.0804807i
$919$	5.75379	−	9.96585i	0.189800	−	0.328743i	−0.755383	−	0.655283i	$-0.772549\pi$
$919$	5.75379	−	9.96585i	0.189800	−	0.328743i	0.945183	+	0.326540i	$0.105883\pi$
$920$		0			0
$921$	−15.4039	−	26.6803i	−0.507575	−	0.879146i
$922$		−	25.2850i		−	0.832718i
$923$	−31.0572	+	39.7926i	−1.02226	+	1.30979i
$924$	0.492423			0.0161995
$925$		0			0
$926$	−11.1771	−	19.3593i	−0.367302	−	0.636185i
$927$	−2.97778	−	1.71922i	−0.0978032	−	0.0564667i
$928$			16.3002i			0.535080i
$929$	−3.90388	+	6.76172i	−0.128082	+	0.221845i	−0.922934	−	0.384959i	$-0.874215\pi$
$929$	−3.90388	+	6.76172i	−0.128082	+	0.221845i	0.794851	+	0.606804i	$0.207549\pi$
$930$		0			0
$931$	−47.6155			−1.56054
$932$	9.87237	+	5.69981i	0.323380	+	0.186704i
$933$	−16.5611	+	9.56155i	−0.542186	+	0.313031i
$934$	20.3002	+	35.1610i	0.664242	+	1.15050i
$935$		0			0
$936$	6.93087	+	5.40938i	0.226543	+	0.176811i
$937$			7.56155i			0.247025i	0.992343	+	0.123513i	$0.0394159\pi$
$937$			7.56155i			0.247025i	−0.992343	+	0.123513i	$0.960584\pi$
$938$	−3.46410	+	2.00000i	−0.113107	+	0.0653023i
$939$	−6.84233	−	11.8513i	−0.223291	−	0.386751i
$940$		0			0
$941$	30.4924			0.994025			0.497012	−	0.867744i	$-0.334430\pi$
$941$	30.4924			0.994025			0.497012	+	0.867744i	$0.334430\pi$
$942$	−27.5463	−	15.9039i	−0.897508	−	0.518176i
$943$	2.70469	+	1.56155i	0.0880768	+	0.0508512i
$944$	−13.4773			−0.438648
$945$		0			0
$946$	−7.12311	−	12.3376i	−0.231592	−	0.401129i
$947$	33.5486	−	19.3693i	1.09018	−	0.629418i	0.156559	−	0.987669i	$-0.449960\pi$
$947$	33.5486	−	19.3693i	1.09018	−	0.629418i	0.933626	+	0.358250i	$0.116627\pi$
$948$			2.38447i			0.0774440i
$949$	5.06155	−	36.1467i	0.164305	−	1.17337i
$950$		0			0
$951$	−7.02699	−	12.1711i	−0.227866	−	0.394675i
$952$	1.85179	−	1.06913i	0.0600168	−	0.0346507i
$953$	−26.8337	−	15.4924i	−0.869228	−	0.501849i	−0.00213612	−	0.999998i	$-0.500680\pi$
$953$	−26.8337	−	15.4924i	−0.869228	−	0.501849i	−0.867091	+	0.498149i	$0.834013\pi$
$954$	−1.06913			−0.0346144
$955$		0			0
$956$	5.56155	−	9.63289i	0.179873	−	0.311550i
$957$			13.3693i			0.432169i
$958$	13.8564	+	8.00000i	0.447680	+	0.258468i
$959$	−1.56155	−	2.70469i	−0.0504252	−	0.0873390i
$960$		0			0
$961$	−24.4384			−0.788337
$962$	−26.1940	+	33.5616i	−0.844528	+	1.08207i
$963$		−	8.24621i		−	0.265730i
$964$	−3.90388	−	6.76172i	−0.125736	−	0.217780i
$965$		0			0
$966$	0.876894	−	1.51883i	0.0282136	−	0.0488674i
$967$			0.876894i			0.0281990i	0.999901	+	0.0140995i	$0.00448816\pi$
$967$			0.876894i			0.0281990i	−0.999901	+	0.0140995i	$0.995512\pi$
$968$	14.7823	+	8.53457i	0.475121	+	0.274311i
$969$	−5.56155	+	9.63289i	−0.178663	+	0.309453i
$970$		0			0
$971$	6.49242	−	11.2452i	0.208352	−	0.360876i	−0.742844	−	0.669465i	$-0.766523\pi$
$971$	6.49242	−	11.2452i	0.208352	−	0.360876i	0.951195	+	0.308589i	$0.0998568\pi$
$972$	−0.379706	+	0.219224i	−0.0121791	+	0.00703160i
$973$	−8.72012	+	5.03457i	−0.279554	+	0.161401i
$974$	11.1231			0.356407
$975$		0			0
$976$	−18.1619			−0.581349
$977$	−52.9809	+	30.5885i	−1.69501	+	0.978614i	−0.744652	+	0.667453i	$0.767385\pi$
$977$	−52.9809	+	30.5885i	−1.69501	+	0.978614i	−0.950357	+	0.311162i	$0.899282\pi$
$978$	6.50175	−	3.75379i	0.207903	−	0.120033i
$979$	−4.87689	+	8.44703i	−0.155866	+	0.269968i
$980$		0			0
$981$	1.40388	−	2.43160i	0.0448225	−	0.0776349i
$982$	49.0174	+	28.3002i	1.56421	+	0.903095i
$983$			13.6155i			0.434268i	0.976142	+	0.217134i	$0.0696708\pi$
$983$			13.6155i			0.434268i	−0.976142	+	0.217134i	$0.930329\pi$
$984$	−1.90388	+	3.29762i	−0.0606935	+	0.105124i
$985$		0			0
$986$	−8.15009	−	14.1164i	−0.259552	−	0.449557i
$987$		−	4.63068i		−	0.147396i
$988$	−4.22351	−	10.4384i	−0.134368	−	0.332091i
$989$	−9.12311			−0.290098
$990$		0			0
$991$	25.1771	+	43.6080i	0.799776	+	1.38525i	0.919762	+	0.392478i	$0.128382\pi$
$991$	25.1771	+	43.6080i	0.799776	+	1.38525i	−0.119985	+	0.992776i	$0.538285\pi$
$992$	5.40938	+	3.12311i	0.171748	+	0.0991587i
$993$		−	3.19224i		−	0.101303i
$994$	−6.13826	+	10.6318i	−0.194694	+	0.337220i
$995$		0			0
$996$	−0.384472			−0.0121825
$997$	−17.8536	−	10.3078i	−0.565428	−	0.326450i	0.189893	−	0.981805i	$-0.439186\pi$
$997$	−17.8536	−	10.3078i	−0.565428	−	0.326450i	−0.755321	+	0.655355i	$0.772519\pi$
$998$	−6.07530	+	3.50758i	−0.192310	+	0.111030i
$999$	3.78078	+	6.54850i	0.119618	+	0.207185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bb.i.874.3		8
5.2	odd	4		39.2.e.b.16.2	✓	4
5.3	odd	4		975.2.i.k.601.1		4
5.4	even	2	inner	975.2.bb.i.874.2		8
13.9	even	3	inner	975.2.bb.i.724.2		8
15.2	even	4		117.2.g.c.55.1		4
20.7	even	4		624.2.q.h.289.1		4
60.47	odd	4		1872.2.t.r.289.2		4
65.2	even	12		507.2.b.d.337.3		4
65.7	even	12		507.2.j.g.316.3		8
65.9	even	6	inner	975.2.bb.i.724.3		8
65.12	odd	4		507.2.e.g.484.1		4
65.17	odd	12		507.2.e.g.22.1		4
65.22	odd	12		39.2.e.b.22.2	yes	4
65.32	even	12		507.2.j.g.316.2		8
65.37	even	12		507.2.b.d.337.2		4
65.42	odd	12		507.2.a.g.1.1		2
65.47	even	4		507.2.j.g.361.2		8
65.48	odd	12		975.2.i.k.451.1		4
65.57	even	4		507.2.j.g.361.3		8
65.62	odd	12		507.2.a.d.1.2		2
195.2	odd	12		1521.2.b.h.1351.2		4
195.62	even	12		1521.2.a.m.1.1		2
195.107	even	12		1521.2.a.g.1.2		2
195.152	even	12		117.2.g.c.100.1		4
195.167	odd	12		1521.2.b.h.1351.3		4
260.87	even	12		624.2.q.h.529.1		4
260.107	even	12		8112.2.a.bk.1.1		2
260.127	even	12		8112.2.a.bo.1.2		2
780.347	odd	12		1872.2.t.r.1153.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.b.16.2	✓	4	5.2	odd	4
39.2.e.b.22.2	yes	4	65.22	odd	12
117.2.g.c.55.1		4	15.2	even	4
117.2.g.c.100.1		4	195.152	even	12
507.2.a.d.1.2		2	65.62	odd	12
507.2.a.g.1.1		2	65.42	odd	12
507.2.b.d.337.2		4	65.37	even	12
507.2.b.d.337.3		4	65.2	even	12
507.2.e.g.22.1		4	65.17	odd	12
507.2.e.g.484.1		4	65.12	odd	4
507.2.j.g.316.2		8	65.32	even	12
507.2.j.g.316.3		8	65.7	even	12
507.2.j.g.361.2		8	65.47	even	4
507.2.j.g.361.3		8	65.57	even	4
624.2.q.h.289.1		4	20.7	even	4
624.2.q.h.529.1		4	260.87	even	12
975.2.i.k.451.1		4	65.48	odd	12
975.2.i.k.601.1		4	5.3	odd	4
975.2.bb.i.724.2		8	13.9	even	3	inner
975.2.bb.i.724.3		8	65.9	even	6	inner
975.2.bb.i.874.2		8	5.4	even	2	inner
975.2.bb.i.874.3		8	1.1	even	1	trivial
1521.2.a.g.1.2		2	195.107	even	12
1521.2.a.m.1.1		2	195.62	even	12
1521.2.b.h.1351.2		4	195.2	odd	12
1521.2.b.h.1351.3		4	195.167	odd	12
1872.2.t.r.289.2		4	60.47	odd	4
1872.2.t.r.1153.2		4	780.347	odd	12
8112.2.a.bk.1.1		2	260.107	even	12
8112.2.a.bo.1.2		2	260.127	even	12

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35234 - 0.780776i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.219224 - 0.379706i) q^{4} +(0.780776 - 1.35234i) q^{6} +(0.486319 + 0.280776i) q^{7} +2.43845i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.35234 - 0.780776i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.219224 - 0.379706i) q^{4} +(0.780776 - 1.35234i) q^{6} +(0.486319 + 0.280776i) q^{7} +2.43845i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} -0.438447i q^{12} +(3.57071 + 0.500000i) q^{13} +0.876894 q^{14} +(2.34233 + 4.05703i) q^{16} +(-1.35234 - 0.780776i) q^{17} -1.56155i q^{18} +(3.56155 - 6.16879i) q^{19} +0.561553 q^{21} +(2.70469 + 1.56155i) q^{22} +(1.73205 - 1.00000i) q^{23} +(1.21922 + 2.11176i) q^{24} +(5.21922 - 2.11176i) q^{26} -1.00000i q^{27} +(0.213225 - 0.123106i) q^{28} +(3.34233 + 5.78908i) q^{29} +2.56155 q^{31} +(2.11176 + 1.21922i) q^{32} +(1.73205 + 1.00000i) q^{33} -2.43845 q^{34} +(-0.219224 - 0.379706i) q^{36} +(-6.54850 + 3.78078i) q^{37} -11.1231i q^{38} +(3.34233 - 1.35234i) q^{39} +(0.780776 + 1.35234i) q^{41} +(0.759413 - 0.438447i) q^{42} +(-3.95042 - 2.28078i) q^{43} +0.876894 q^{44} +(1.56155 - 2.70469i) q^{46} -8.24621i q^{47} +(4.05703 + 2.34233i) q^{48} +(-3.34233 - 5.78908i) q^{49} -1.56155 q^{51} +(0.972638 - 1.24621i) q^{52} -0.684658i q^{53} +(-0.780776 - 1.35234i) q^{54} +(-0.684658 + 1.18586i) q^{56} -7.12311i q^{57} +(9.03996 + 5.21922i) q^{58} +(-1.43845 + 2.49146i) q^{59} +(-1.93845 + 3.35749i) q^{61} +(3.46410 - 2.00000i) q^{62} +(0.486319 - 0.280776i) q^{63} -5.56155 q^{64} +3.12311 q^{66} +(-3.95042 + 2.28078i) q^{67} +(-0.592932 + 0.342329i) q^{68} +(1.00000 - 1.73205i) q^{69} +(-7.00000 + 12.1244i) q^{71} +(2.11176 + 1.21922i) q^{72} -10.1231i q^{73} +(-5.90388 + 10.2258i) q^{74} +(-1.56155 - 2.70469i) q^{76} +1.12311i q^{77} +(3.46410 - 4.43845i) q^{78} -5.43845 q^{79} +(-0.500000 - 0.866025i) q^{81} +(2.11176 + 1.21922i) q^{82} -0.876894i q^{83} +(0.123106 - 0.213225i) q^{84} -7.12311 q^{86} +(5.78908 + 3.34233i) q^{87} +(-4.22351 + 2.43845i) q^{88} +(2.43845 + 4.22351i) q^{89} +(1.59612 + 1.24573i) q^{91} -0.876894i q^{92} +(2.21837 - 1.28078i) q^{93} +(-6.43845 - 11.1517i) q^{94} +2.43845 q^{96} +(-7.41452 - 4.28078i) q^{97} +(-9.03996 - 5.21922i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q + 10 * q^4 - 2 * q^6 + 4 * q^9	\( 8 q + 10 q^{4} - 2 q^{6} + 4 q^{9} + 8 q^{11} + 40 q^{14} - 6 q^{16} + 12 q^{19} - 12 q^{21} + 18 q^{24} + 50 q^{26} + 2 q^{29} + 4 q^{31} - 36 q^{34} - 10 q^{36} + 2 q^{39} - 2 q^{41} + 40 q^{44} - 4 q^{46} - 2 q^{49} + 4 q^{51} + 2 q^{54} + 44 q^{56} - 28 q^{59} - 32 q^{61} - 28 q^{64} - 8 q^{66} + 8 q^{69} - 56 q^{71} - 6 q^{74} + 4 q^{76} - 60 q^{79} - 4 q^{81} - 32 q^{84} - 24 q^{86} + 36 q^{89} + 54 q^{91} - 68 q^{94} + 36 q^{96} + 16 q^{99}+O(q^{100}) \) 8 * q + 10 * q^4 - 2 * q^6 + 4 * q^9 + 8 * q^11 + 40 * q^14 - 6 * q^16 + 12 * q^19 - 12 * q^21 + 18 * q^24 + 50 * q^26 + 2 * q^29 + 4 * q^31 - 36 * q^34 - 10 * q^36 + 2 * q^39 - 2 * q^41 + 40 * q^44 - 4 * q^46 - 2 * q^49 + 4 * q^51 + 2 * q^54 + 44 * q^56 - 28 * q^59 - 32 * q^61 - 28 * q^64 - 8 * q^66 + 8 * q^69 - 56 * q^71 - 6 * q^74 + 4 * q^76 - 60 * q^79 - 4 * q^81 - 32 * q^84 - 24 * q^86 + 36 * q^89 + 54 * q^91 - 68 * q^94 + 36 * q^96 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more