LMFDB - Embedded newform 525.2.i.h.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(151,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("525.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.4
Root			$1.39083 - 2.40898i$ of defining polynomial
Character	$\chi$	$=$	525.151
Dual form			525.2.i.h.226.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.890827 + 1.54296i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.587145 + 1.01696i) q^{4} +1.78165 q^{6} +(-1.09398 - 2.40898i) q^{7} +1.47113 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.890827 + 1.54296i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.587145 + 1.01696i) q^{4} +1.78165 q^{6} +(-1.09398 - 2.40898i) q^{7} +1.47113 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.03925 - 1.80003i) q^{11} +(0.587145 + 1.01696i) q^{12} +3.13023 q^{13} +(2.74241 - 3.83396i) q^{14} +(2.48481 + 4.30382i) q^{16} +(1.06512 - 1.84483i) q^{17} +(0.890827 - 1.54296i) q^{18} +(3.86880 + 6.70095i) q^{19} +(-2.63323 - 0.257073i) q^{21} +3.70316 q^{22} +(-2.76827 - 4.79479i) q^{23} +(0.735565 - 1.27404i) q^{24} +(2.78849 + 4.82981i) q^{26} -1.00000 q^{27} +(3.09218 + 0.301877i) q^{28} -4.01368 q^{29} +(-1.45594 + 2.52177i) q^{31} +(-2.95594 + 5.11984i) q^{32} +(-1.03925 - 1.80003i) q^{33} +3.79533 q^{34} +1.17429 q^{36} +(-1.75759 - 3.04424i) q^{37} +(-6.89286 + 11.9388i) q^{38} +(1.56512 - 2.71086i) q^{39} +7.99038 q^{41} +(-1.94910 - 4.29197i) q^{42} -4.99038 q^{43} +(1.22038 + 2.11376i) q^{44} +(4.93210 - 8.54266i) q^{46} +(-1.22038 - 2.11376i) q^{47} +4.96962 q^{48} +(-4.60639 + 5.27078i) q^{49} +(-1.06512 - 1.84483i) q^{51} +(-1.83790 + 3.18333i) q^{52} +(-4.95594 + 8.58394i) q^{53} +(-0.890827 - 1.54296i) q^{54} +(-1.60939 - 3.54393i) q^{56} +7.73760 q^{57} +(-3.57549 - 6.19294i) q^{58} +(-1.47797 + 2.55992i) q^{59} +(5.44729 + 9.43499i) q^{61} -5.18797 q^{62} +(-1.53925 + 2.15191i) q^{63} -0.593684 q^{64} +(1.85158 - 3.20703i) q^{66} +(-1.91970 + 3.32501i) q^{67} +(1.25075 + 2.16637i) q^{68} -5.53655 q^{69} -15.0248 q^{71} +(-0.735565 - 1.27404i) q^{72} +(4.27684 - 7.40771i) q^{73} +(3.13142 - 5.42378i) q^{74} -9.08617 q^{76} +(-5.47316 - 0.534324i) q^{77} +5.57699 q^{78} +(-4.05677 - 7.02653i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(7.11804 + 12.3288i) q^{82} -8.75128 q^{83} +(1.80752 - 2.52696i) q^{84} +(-4.44556 - 7.69994i) q^{86} +(-2.00684 + 3.47595i) q^{87} +(1.52887 - 2.64808i) q^{88} +(-0.309330 - 0.535776i) q^{89} +(-3.42443 - 7.54067i) q^{91} +6.50151 q^{92} +(1.45594 + 2.52177i) q^{93} +(2.17429 - 3.76598i) q^{94} +(2.95594 + 5.11984i) q^{96} -0.296842 q^{97} +(-12.2361 - 2.41212i) q^{98} -2.07850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{6} + 2 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^6 + 2 * q^7 + 12 * q^8 - 4 * q^9	$ 8 q - 2 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{6} + 2 q^{7} + 12 q^{8} - 4 q^{9} + 4 q^{12} + 4 q^{13} + 12 q^{14} - 2 q^{17} - 2 q^{18} + 12 q^{19} - 2 q^{21} + 28 q^{22} - 10 q^{23} + 6 q^{24} - 6 q^{26} - 8 q^{27} - 12 q^{28} - 12 q^{29} + 8 q^{31} - 4 q^{32} - 8 q^{34} + 8 q^{36} - 24 q^{37} - 8 q^{38} + 2 q^{39} + 8 q^{41} - 6 q^{42} + 16 q^{43} - 10 q^{44} - 16 q^{46} + 10 q^{47} + 20 q^{49} + 2 q^{51} - 34 q^{52} - 20 q^{53} + 2 q^{54} + 42 q^{56} + 24 q^{57} - 10 q^{58} - 2 q^{59} + 8 q^{61} - 20 q^{62} - 4 q^{63} - 8 q^{64} + 14 q^{66} - 6 q^{67} + 30 q^{68} - 20 q^{69} - 28 q^{71} - 6 q^{72} - 12 q^{73} - 20 q^{74} - 32 q^{76} - 6 q^{77} - 12 q^{78} + 8 q^{79} - 4 q^{81} + 18 q^{82} - 12 q^{83} - 6 q^{84} - 24 q^{86} - 6 q^{87} + 12 q^{88} - 8 q^{89} + 4 q^{91} + 92 q^{92} - 8 q^{93} + 16 q^{94} + 4 q^{96} - 4 q^{97} - 20 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^6 + 2 * q^7 + 12 * q^8 - 4 * q^9 + 4 * q^12 + 4 * q^13 + 12 * q^14 - 2 * q^17 - 2 * q^18 + 12 * q^19 - 2 * q^21 + 28 * q^22 - 10 * q^23 + 6 * q^24 - 6 * q^26 - 8 * q^27 - 12 * q^28 - 12 * q^29 + 8 * q^31 - 4 * q^32 - 8 * q^34 + 8 * q^36 - 24 * q^37 - 8 * q^38 + 2 * q^39 + 8 * q^41 - 6 * q^42 + 16 * q^43 - 10 * q^44 - 16 * q^46 + 10 * q^47 + 20 * q^49 + 2 * q^51 - 34 * q^52 - 20 * q^53 + 2 * q^54 + 42 * q^56 + 24 * q^57 - 10 * q^58 - 2 * q^59 + 8 * q^61 - 20 * q^62 - 4 * q^63 - 8 * q^64 + 14 * q^66 - 6 * q^67 + 30 * q^68 - 20 * q^69 - 28 * q^71 - 6 * q^72 - 12 * q^73 - 20 * q^74 - 32 * q^76 - 6 * q^77 - 12 * q^78 + 8 * q^79 - 4 * q^81 + 18 * q^82 - 12 * q^83 - 6 * q^84 - 24 * q^86 - 6 * q^87 + 12 * q^88 - 8 * q^89 + 4 * q^91 + 92 * q^92 - 8 * q^93 + 16 * q^94 + 4 * q^96 - 4 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.890827	+	1.54296i	0.629910	+	1.09104i	0.987569	+	0.157184i	$0.0502414\pi$
$2$	0.890827	+	1.54296i	0.629910	+	1.09104i	−0.357660	+	0.933852i	$0.616425\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.587145	+	1.01696i	−0.293572	+	0.508482i
$5$		0			0
$5$		0			0
$6$	1.78165			0.727357
$7$	−1.09398	−	2.40898i	−0.413487	−	0.910510i
$7$	−1.09398	−	2.40898i	−0.413487	−	0.910510i
$8$	1.47113			0.520123
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.03925	−	1.80003i	0.313345	−	0.542729i	−0.665739	−	0.746184i	$-0.731884\pi$
$11$	1.03925	−	1.80003i	0.313345	−	0.542729i	0.979084	+	0.203455i	$0.0652171\pi$
$12$	0.587145	+	1.01696i	0.169494	+	0.293572i
$13$	3.13023			0.868170			0.434085	−	0.900872i	$-0.357072\pi$
$13$	3.13023			0.868170			0.434085	+	0.900872i	$0.357072\pi$
$14$	2.74241	−	3.83396i	0.732939	−	1.02467i
$15$		0			0
$16$	2.48481	+	4.30382i	0.621203	+	1.07596i
$17$	1.06512	−	1.84483i	0.258329	−	0.447438i	−0.707466	−	0.706748i	$-0.750162\pi$
$17$	1.06512	−	1.84483i	0.258329	−	0.447438i	0.965794	+	0.259310i	$0.0834950\pi$
$18$	0.890827	−	1.54296i	0.209970	−	0.363678i
$19$	3.86880	+	6.70095i	0.887563	+	1.53730i	0.842747	+	0.538309i	$0.180937\pi$
$19$	3.86880	+	6.70095i	0.887563	+	1.53730i	0.0448157	+	0.998995i	$0.485730\pi$
$20$		0			0
$21$	−2.63323	−	0.257073i	−0.574618	−	0.0560978i
$22$	3.70316			0.789516
$23$	−2.76827	−	4.79479i	−0.577225	−	0.999783i	−0.995796	−	0.0915990i	$-0.970802\pi$
$23$	−2.76827	−	4.79479i	−0.577225	−	0.999783i	0.418571	−	0.908184i	$-0.362531\pi$
$24$	0.735565	−	1.27404i	0.150147	−	0.260062i
$25$		0			0
$26$	2.78849	+	4.82981i	0.546869	+	0.947204i
$27$	−1.00000			−0.192450
$28$	3.09218	+	0.301877i	0.584366	+	0.0570495i
$29$	−4.01368			−0.745322			−0.372661	−	0.927968i	$-0.621555\pi$
$29$	−4.01368			−0.745322			−0.372661	+	0.927968i	$0.621555\pi$
$30$		0			0
$31$	−1.45594	+	2.52177i	−0.261495	+	0.452923i	−0.966639	−	0.256141i	$-0.917549\pi$
$31$	−1.45594	+	2.52177i	−0.261495	+	0.452923i	0.705144	+	0.709064i	$0.250882\pi$
$32$	−2.95594	+	5.11984i	−0.522542	+	0.905069i
$33$	−1.03925	−	1.80003i	−0.180910	−	0.313345i
$34$	3.79533			0.650894
$35$		0			0
$36$	1.17429			0.195715
$37$	−1.75759	−	3.04424i	−0.288947	−	0.500470i	0.684612	−	0.728908i	$-0.259972\pi$
$37$	−1.75759	−	3.04424i	−0.288947	−	0.500470i	−0.973559	+	0.228437i	$0.926638\pi$
$38$	−6.89286	+	11.9388i	−1.11817	+	1.93673i
$39$	1.56512	−	2.71086i	0.250619	−	0.434085i
$40$		0			0
$41$	7.99038			1.24789			0.623944	−	0.781469i	$-0.285529\pi$
$41$	7.99038			1.24789			0.623944	+	0.781469i	$0.285529\pi$
$42$	−1.94910	−	4.29197i	−0.300753	−	0.662266i
$43$	−4.99038			−0.761026			−0.380513	−	0.924776i	$-0.624253\pi$
$43$	−4.99038			−0.761026			−0.380513	+	0.924776i	$0.624253\pi$
$44$	1.22038	+	2.11376i	0.183979	+	0.318661i
$45$		0			0
$46$	4.93210	−	8.54266i	0.727199	−	1.25955i
$47$	−1.22038	−	2.11376i	−0.178010	−	0.308323i	0.763189	−	0.646176i	$-0.223633\pi$
$47$	−1.22038	−	2.11376i	−0.178010	−	0.308323i	−0.941199	+	0.337853i	$0.890299\pi$
$48$	4.96962			0.717303
$49$	−4.60639	+	5.27078i	−0.658056	+	0.752969i
$50$		0			0
$51$	−1.06512	−	1.84483i	−0.149146	−	0.258329i
$52$	−1.83790	+	3.18333i	−0.254871	+	0.441449i
$53$	−4.95594	+	8.58394i	−0.680751	+	1.17910i	0.294001	+	0.955805i	$0.405013\pi$
$53$	−4.95594	+	8.58394i	−0.680751	+	1.17910i	−0.974752	+	0.223290i	$0.928320\pi$
$54$	−0.890827	−	1.54296i	−0.121226	−	0.209970i
$55$		0			0
$56$	−1.60939	−	3.54393i	−0.215064	−	0.473577i
$57$	7.73760			1.02487
$58$	−3.57549	−	6.19294i	−0.469485	−	0.813173i
$59$	−1.47797	+	2.55992i	−0.192415	+	0.333273i	−0.946050	−	0.324020i	$-0.894965\pi$
$59$	−1.47797	+	2.55992i	−0.192415	+	0.333273i	0.753635	+	0.657293i	$0.228299\pi$
$60$		0			0
$61$	5.44729	+	9.43499i	0.697454	+	1.20803i	0.969346	+	0.245699i	$0.0790174\pi$
$61$	5.44729	+	9.43499i	0.697454	+	1.20803i	−0.271892	+	0.962328i	$0.587649\pi$
$62$	−5.18797			−0.658873
$63$	−1.53925	+	2.15191i	−0.193927	+	0.271115i
$64$	−0.593684			−0.0742104
$65$		0			0
$66$	1.85158	−	3.20703i	0.227914	−	0.394758i
$67$	−1.91970	+	3.32501i	−0.234528	+	0.406215i	−0.959135	−	0.282947i	$-0.908688\pi$
$67$	−1.91970	+	3.32501i	−0.234528	+	0.406215i	0.724607	+	0.689162i	$0.242021\pi$
$68$	1.25075	+	2.16637i	0.151676	+	0.262711i
$69$	−5.53655			−0.666522
$70$		0			0
$71$	−15.0248			−1.78312			−0.891559	−	0.452905i	$-0.850388\pi$
$71$	−15.0248			−1.78312			−0.891559	+	0.452905i	$0.850388\pi$
$72$	−0.735565	−	1.27404i	−0.0866872	−	0.150147i
$73$	4.27684	−	7.40771i	0.500567	−	0.867007i	−0.499433	−	0.866352i	$-0.666458\pi$
$73$	4.27684	−	7.40771i	0.500567	−	0.867007i	1.00000		0.000654464i	$-0.000208322\pi$
$74$	3.13142	−	5.42378i	0.364021	−	0.630502i
$75$		0			0
$76$	−9.08617			−1.04226
$77$	−5.47316	−	0.534324i	−0.623725	−	0.0608919i
$78$	5.57699			0.631470
$79$	−4.05677	−	7.02653i	−0.456422	−	0.790546i	0.542347	−	0.840155i	$-0.317536\pi$
$79$	−4.05677	−	7.02653i	−0.456422	−	0.790546i	−0.998769	+	0.0496086i	$0.984203\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	7.11804	+	12.3288i	0.786056	+	1.36149i
$83$	−8.75128			−0.960577			−0.480289	−	0.877110i	$-0.659468\pi$
$83$	−8.75128			−0.960577			−0.480289	+	0.877110i	$0.659468\pi$
$84$	1.80752	−	2.52696i	0.197217	−	0.275714i
$85$		0			0
$86$	−4.44556	−	7.69994i	−0.479377	−	0.830306i
$87$	−2.00684	+	3.47595i	−0.215156	+	0.372661i
$88$	1.52887	−	2.64808i	0.162978	−	0.282286i
$89$	−0.309330	−	0.535776i	−0.0327890	−	0.0567921i	0.849165	−	0.528127i	$-0.177106\pi$
$89$	−0.309330	−	0.535776i	−0.0327890	−	0.0567921i	−0.881954	+	0.471335i	$0.843772\pi$
$90$		0			0
$91$	−3.42443	−	7.54067i	−0.358977	−	0.790477i
$92$	6.50151			0.677829
$93$	1.45594	+	2.52177i	0.150974	+	0.261495i
$94$	2.17429	−	3.76598i	0.224261	−	0.388431i
$95$		0			0
$96$	2.95594	+	5.11984i	0.301690	+	0.522542i
$97$	−0.296842			−0.0301397			−0.0150699	−	0.999886i	$-0.504797\pi$
$97$	−0.296842			−0.0301397			−0.0150699	+	0.999886i	$0.504797\pi$
$98$	−12.2361	−	2.41212i	−1.23603	−	0.243660i
$99$	−2.07850			−0.208897
$100$		0			0
$101$	−4.12939	+	7.15232i	−0.410890	+	0.711682i	−0.994987	−	0.100001i	$-0.968115\pi$
$101$	−4.12939	+	7.15232i	−0.410890	+	0.711682i	0.584097	+	0.811684i	$0.301449\pi$
$102$	1.89767	−	3.28686i	0.187897	−	0.325447i
$103$	8.54331	+	14.7974i	0.841797	+	1.45804i	0.888374	+	0.459121i	$0.151836\pi$
$103$	8.54331	+	14.7974i	0.841797	+	1.45804i	−0.0465766	+	0.998915i	$0.514831\pi$
$104$	4.60498			0.451555
$105$		0			0
$106$	−17.6595			−1.71525
$107$	−3.15526	−	5.46507i	−0.305031	−	0.528329i	0.672238	−	0.740336i	$-0.265333\pi$
$107$	−3.15526	−	5.46507i	−0.305031	−	0.528329i	−0.977268	+	0.212007i	$0.932000\pi$
$108$	0.587145	−	1.01696i	0.0564980	−	0.0978574i
$109$	−1.22338	+	2.11895i	−0.117178	+	0.202959i	−0.918648	−	0.395076i	$-0.870718\pi$
$109$	−1.22338	+	2.11895i	−0.117178	+	0.202959i	0.801470	+	0.598035i	$0.204052\pi$
$110$		0			0
$111$	−3.51519			−0.333647
$112$	7.64948	−	10.6942i	0.722808	−	1.01051i
$113$	10.1570			0.955489			0.477745	−	0.878499i	$-0.341454\pi$
$113$	10.1570			0.955489			0.477745	+	0.878499i	$0.341454\pi$
$114$	6.89286	+	11.9388i	0.645575	+	1.11817i
$115$		0			0
$116$	2.35661	−	4.08177i	0.218806	−	0.378983i
$117$	−1.56512	−	2.71086i	−0.144695	−	0.250619i
$118$	−5.26647			−0.484817
$119$	−5.60939	−	0.547624i	−0.514212	−	0.0502006i
$120$		0			0
$121$	3.33993	+	5.78493i	0.303630	+	0.525902i
$122$	−9.70519	+	16.8099i	−0.878667	+	1.52190i
$123$	3.99519	−	6.91987i	0.360234	−	0.623944i
$124$	−1.70970	−	2.96128i	−0.153535	−	0.265931i
$125$		0			0
$126$	−4.69151	−	0.458014i	−0.417953	−	0.0408031i
$127$	8.86977			0.787065			0.393532	−	0.919311i	$-0.371253\pi$
$127$	8.86977			0.787065			0.393532	+	0.919311i	$0.371253\pi$
$128$	5.38302	+	9.32366i	0.475796	+	0.824103i
$129$	−2.49519	+	4.32180i	−0.219689	+	0.380513i
$130$		0			0
$131$	−2.67075	−	4.62588i	−0.233345	−	0.404165i	0.725446	−	0.688279i	$-0.241634\pi$
$131$	−2.67075	−	4.62588i	−0.233345	−	0.404165i	−0.958790	+	0.284115i	$0.908300\pi$
$132$	2.44075			0.212440
$133$	11.9101	−	16.6506i	1.03273	−	1.44379i
$134$	−6.84047			−0.590926
$135$		0			0
$136$	1.56692	−	2.71399i	0.134363	−	0.232723i
$137$	6.55196	−	11.3483i	0.559772	−	0.969553i	−0.437744	−	0.899100i	$-0.644222\pi$
$137$	6.55196	−	11.3483i	0.559772	−	0.969553i	0.997515	−	0.0704529i	$-0.0224444\pi$
$138$	−4.93210	−	8.54266i	−0.419849	−	0.727199i
$139$	0.243164			0.0206249			0.0103125	−	0.999947i	$-0.496717\pi$
$139$	0.243164			0.0206249			0.0103125	+	0.999947i	$0.496717\pi$
$140$		0			0
$141$	−2.44075			−0.205549
$142$	−13.3845	−	23.1827i	−1.12320	−	1.94544i
$143$	3.25309	−	5.63451i	0.272037	−	0.471181i
$144$	2.48481	−	4.30382i	0.207068	−	0.358652i
$145$		0			0
$146$	15.2397			1.26125
$147$	2.26143	+	6.62464i	0.186520	+	0.546391i
$148$	4.12785			0.339307
$149$	−1.16864	−	2.02415i	−0.0957388	−	0.165824i	0.814178	−	0.580615i	$-0.197188\pi$
$149$	−1.16864	−	2.02415i	−0.0957388	−	0.165824i	−0.909917	+	0.414791i	$0.863855\pi$
$150$		0			0
$151$	5.55677	−	9.62460i	0.452203	−	0.783239i	−0.546319	−	0.837577i	$-0.683971\pi$
$151$	5.55677	−	9.62460i	0.452203	−	0.783239i	0.998523	+	0.0543378i	$0.0173048\pi$
$152$	5.69151	+	9.85798i	0.461642	+	0.799588i
$153$	−2.13023			−0.172219
$154$	−4.05120	−	8.92084i	−0.326455	−	0.718862i
$155$		0			0
$156$	1.83790	+	3.18333i	0.147150	+	0.254871i
$157$	−5.65910	+	9.80185i	−0.451645	+	0.782273i	−0.998488	−	0.0549624i	$-0.982496\pi$
$157$	−5.65910	+	9.80185i	−0.451645	+	0.782273i	0.546843	+	0.837235i	$0.315829\pi$
$158$	7.22775	−	12.5188i	0.575009	−	0.995945i
$159$	4.95594	+	8.58394i	0.393032	+	0.680751i
$160$		0			0
$161$	−8.52212	+	11.9142i	−0.671637	+	0.938967i
$162$	−1.78165			−0.139980
$163$	1.05174	+	1.82166i	0.0823783	+	0.142683i	0.904271	−	0.426959i	$-0.140415\pi$
$163$	1.05174	+	1.82166i	0.0823783	+	0.142683i	−0.821893	+	0.569642i	$0.807082\pi$
$164$	−4.69151	+	8.12593i	−0.366345	+	0.634529i
$165$		0			0
$166$	−7.79587	−	13.5028i	−0.605077	−	1.04802i
$167$	−3.58600			−0.277493			−0.138747	−	0.990328i	$-0.544307\pi$
$167$	−3.58600			−0.277493			−0.138747	+	0.990328i	$0.544307\pi$
$168$	−3.87383	−	0.378187i	−0.298872	−	0.0291778i
$169$	−3.20165			−0.246281
$170$		0			0
$171$	3.86880	−	6.70095i	0.295854	−	0.512435i
$172$	2.93007	−	5.07504i	0.223416	−	0.386968i
$173$	−7.77000	−	13.4580i	−0.590742	−	1.02320i	−0.994133	−	0.108168i	$-0.965502\pi$
$173$	−7.77000	−	13.4580i	−0.590742	−	1.02320i	0.403390	−	0.915028i	$-0.367832\pi$
$174$	−7.15099			−0.542115
$175$		0			0
$176$	10.3293			0.778603
$177$	1.47797	+	2.55992i	0.111091	+	0.192415i
$178$	0.551120	−	0.954567i	0.0413082	−	0.0715478i
$179$	−7.86783	+	13.6275i	−0.588069	+	1.01857i	0.406416	+	0.913688i	$0.366778\pi$
$179$	−7.86783	+	13.6275i	−0.588069	+	1.01857i	−0.994485	+	0.104877i	$0.966555\pi$
$180$		0			0
$181$	−4.98692			−0.370675			−0.185337	−	0.982675i	$-0.559338\pi$
$181$	−4.98692			−0.370675			−0.185337	+	0.982675i	$0.559338\pi$
$182$	8.58437	−	12.0012i	0.636315	−	0.889586i
$183$	10.8946			0.805351
$184$	−4.07249	−	7.05376i	−0.300228	−	0.520010i
$185$		0			0
$186$	−2.59398	+	4.49291i	−0.190200	+	0.329436i
$187$	−2.21384	−	3.83448i	−0.161892	−	0.280405i
$188$	2.86615			0.209036
$189$	1.09398	+	2.40898i	0.0795757	+	0.175228i
$190$		0			0
$191$	−5.90421	−	10.2264i	−0.427213	−	0.739955i	0.569411	−	0.822053i	$-0.307171\pi$
$191$	−5.90421	−	10.2264i	−0.427213	−	0.739955i	−0.996624	+	0.0820978i	$0.973838\pi$
$192$	−0.296842	+	0.514145i	−0.0214227	+	0.0371052i
$193$	−12.3690	+	21.4238i	−0.890342	+	1.54212i	−0.0508752	+	0.998705i	$0.516201\pi$
$193$	−12.3690	+	21.4238i	−0.890342	+	1.54212i	−0.839466	+	0.543412i	$0.817132\pi$
$194$	−0.264435	−	0.458014i	−0.0189853	−	0.0328835i
$195$		0			0
$196$	−2.65558	−	7.77925i	−0.189684	−	0.555661i
$197$	19.5526			1.39307			0.696533	−	0.717525i	$-0.254725\pi$
$197$	19.5526			1.39307			0.696533	+	0.717525i	$0.254725\pi$
$198$	−1.85158	−	3.20703i	−0.131586	−	0.227914i
$199$	11.1201	−	19.2605i	0.788281	−	1.36534i	−0.138738	−	0.990329i	$-0.544305\pi$
$199$	11.1201	−	19.2605i	0.788281	−	1.36534i	0.927019	−	0.375014i	$-0.122362\pi$
$200$		0			0
$201$	1.91970	+	3.32501i	0.135405	+	0.234528i
$202$	−14.7143			−1.03529
$203$	4.39091	+	9.66889i	0.308181	+	0.678623i
$204$	2.50151			0.175141
$205$		0			0
$206$	−15.2212	+	26.3639i	−1.06051	+	1.83686i
$207$	−2.76827	+	4.79479i	−0.192408	+	0.333261i
$208$	7.77804	+	13.4720i	0.539310	+	0.934112i
$209$	16.0826			1.11245
$210$		0			0
$211$	23.6191			1.62601			0.813003	−	0.582259i	$-0.197831\pi$
$211$	23.6191			1.62601			0.813003	+	0.582259i	$0.197831\pi$
$212$	−5.81971	−	10.0800i	−0.399699	−	0.692299i
$213$	−7.51241	+	13.0119i	−0.514742	+	0.891559i
$214$	5.62158	−	9.73687i	0.384283	−	0.665598i
$215$		0			0
$216$	−1.47113			−0.100098
$217$	7.66767	+	0.748566i	0.520515	+	0.0508159i
$218$	−4.35927			−0.295247
$219$	−4.27684	−	7.40771i	−0.289002	−	0.500567i
$220$		0			0
$221$	3.33406	−	5.77476i	0.224273	−	0.388452i
$222$	−3.13142	−	5.42378i	−0.210167	−	0.364021i
$223$	−25.1420			−1.68363			−0.841815	−	0.539765i	$-0.818513\pi$
$223$	−25.1420			−1.68363			−0.841815	+	0.539765i	$0.818513\pi$
$224$	15.5674	+	1.51978i	1.04014	+	0.101545i
$225$		0			0
$226$	9.04812	+	15.6718i	0.601872	+	1.04247i
$227$	−11.8351	+	20.4990i	−0.785524	+	1.36057i	0.143161	+	0.989699i	$0.454273\pi$
$227$	−11.8351	+	20.4990i	−0.785524	+	1.36057i	−0.928685	+	0.370869i	$0.879060\pi$
$228$	−4.54309	+	7.86886i	−0.300873	+	0.521128i
$229$	−0.203158	−	0.351880i	−0.0134251	−	0.0232529i	0.859235	−	0.511581i	$-0.170940\pi$
$229$	−0.203158	−	0.351880i	−0.0134251	−	0.0232529i	−0.872660	+	0.488328i	$0.837607\pi$
$230$		0			0
$231$	−3.19932	+	4.47273i	−0.210500	+	0.294284i
$232$	−5.90465			−0.387659
$233$	3.58264	+	6.20531i	0.234706	+	0.406523i	0.959187	−	0.282772i	$-0.0912538\pi$
$233$	3.58264	+	6.20531i	0.234706	+	0.406523i	−0.724481	+	0.689295i	$0.757920\pi$
$234$	2.78849	−	4.82981i	0.182290	−	0.315735i
$235$		0			0
$236$	−1.73557	−	3.00609i	−0.112976	−	0.195680i
$237$	−8.11354			−0.527031
$238$	−4.15204	−	9.14289i	−0.269137	−	0.592646i
$239$	10.0922			0.652809			0.326404	−	0.945230i	$-0.394163\pi$
$239$	10.0922			0.652809			0.326404	+	0.945230i	$0.394163\pi$
$240$		0			0
$241$	2.30338	−	3.98957i	0.148374	−	0.256991i	−0.782253	−	0.622961i	$-0.785929\pi$
$241$	2.30338	−	3.98957i	0.148374	−	0.256991i	0.930627	+	0.365970i	$0.119263\pi$
$242$	−5.95060	+	10.3067i	−0.382519	+	0.662542i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−12.7934			−0.819013
$245$		0			0
$246$	14.2361			0.907660
$247$	12.1102	+	20.9755i	0.770556	+	1.33464i
$248$	−2.14188	+	3.70985i	−0.136010	+	0.235576i
$249$	−4.37564	+	7.57883i	−0.277295	+	0.480289i
$250$		0			0
$251$	−0.311597			−0.0196678			−0.00983390	−	0.999952i	$-0.503130\pi$
$251$	−0.311597			−0.0196678			−0.00983390	+	0.999952i	$0.503130\pi$
$252$	−1.28465	−	2.82884i	−0.0809256	−	0.178200i
$253$	−11.5077			−0.723482
$254$	7.90143	+	13.6857i	0.495780	+	0.858715i
$255$		0			0
$256$	−10.1844	+	17.6398i	−0.636522	+	1.10249i
$257$	1.25106	+	2.16689i	0.0780387	+	0.135167i	0.902404	−	0.430892i	$-0.141801\pi$
$257$	1.25106	+	2.16689i	0.0780387	+	0.135167i	−0.824365	+	0.566059i	$0.808468\pi$
$258$	−8.89113			−0.553537
$259$	−5.41075	+	7.56437i	−0.336207	+	0.470027i
$260$		0			0
$261$	2.00684	+	3.47595i	0.124220	+	0.215156i
$262$	4.75835	−	8.24171i	0.293972	−	0.509174i
$263$	2.31255	−	4.00546i	0.142598	−	0.246987i	−0.785876	−	0.618384i	$-0.787788\pi$
$263$	2.31255	−	4.00546i	0.142598	−	0.246987i	0.928474	+	0.371397i	$0.121121\pi$
$264$	−1.52887	−	2.64808i	−0.0940954	−	0.162978i
$265$		0			0
$266$	36.3010	+	3.54393i	2.22576	+	0.217292i
$267$	−0.618661			−0.0378614
$268$	−2.25428	−	3.90452i	−0.137702	−	0.238507i
$269$	−6.01165	+	10.4125i	−0.366537	+	0.634860i	−0.989022	−	0.147772i	$-0.952790\pi$
$269$	−6.01165	+	10.4125i	−0.366537	+	0.634860i	0.622485	+	0.782632i	$0.286123\pi$
$270$		0			0
$271$	2.73467	+	4.73660i	0.166120	+	0.287728i	0.937052	−	0.349189i	$-0.113543\pi$
$271$	2.73467	+	4.73660i	0.166120	+	0.287728i	−0.770933	+	0.636917i	$0.780210\pi$
$272$	10.5864			0.641898
$273$	−8.24263	−	0.804697i	−0.498867	−	0.0487024i
$274$	23.3466			1.41042
$275$		0			0
$276$	3.25075	−	5.63047i	0.195672	−	0.338915i
$277$	−14.9050	+	25.8162i	−0.895553	+	1.55114i	−0.0624333	+	0.998049i	$0.519886\pi$
$277$	−14.9050	+	25.8162i	−0.895553	+	1.55114i	−0.833119	+	0.553093i	$0.813447\pi$
$278$	0.216617	+	0.375192i	0.0129918	+	0.0225025i
$279$	2.91188			0.174330
$280$		0			0
$281$	7.78511			0.464421			0.232210	−	0.972666i	$-0.425404\pi$
$281$	7.78511			0.464421			0.232210	+	0.972666i	$0.425404\pi$
$282$	−2.17429	−	3.76598i	−0.129477	−	0.224261i
$283$	1.30722	−	2.26417i	0.0777062	−	0.134591i	−0.824554	−	0.565784i	$-0.808574\pi$
$283$	1.30722	−	2.26417i	0.0777062	−	0.134591i	0.902260	+	0.431193i	$0.141907\pi$
$284$	8.82174	−	15.2797i	0.523474	−	0.906683i
$285$		0			0
$286$	11.5917			0.685434
$287$	−8.74136	−	19.2487i	−0.515986	−	1.13621i
$288$	5.91188			0.348361
$289$	6.23106	+	10.7925i	0.366533	+	0.634853i
$290$		0			0
$291$	−0.148421	+	0.257073i	−0.00870059	+	0.0150699i
$292$	5.02225	+	8.69879i	0.293905	+	0.509058i
$293$	12.7559			0.745210			0.372605	−	0.927990i	$-0.378465\pi$
$293$	12.7559			0.745210			0.372605	+	0.927990i	$0.378465\pi$
$294$	−8.20700	+	9.39071i	−0.478642	+	0.547677i
$295$		0			0
$296$	−2.58565	−	4.47848i	−0.150288	−	0.260306i
$297$	−1.03925	+	1.80003i	−0.0603033	+	0.104448i
$298$	2.08211	−	3.60633i	0.120614	−	0.208909i
$299$	−8.66534	−	15.0088i	−0.501129	−	0.867982i
$300$		0			0
$301$	5.45940	+	12.0217i	0.314675	+	0.692922i
$302$	19.8005			1.13939
$303$	4.12939	+	7.15232i	0.237227	+	0.410890i
$304$	−19.2265	+	33.3012i	−1.10271	+	1.90996i
$305$		0			0
$306$	−1.89767	−	3.28686i	−0.108482	−	0.187897i
$307$	13.1919			0.752900			0.376450	−	0.926437i	$-0.377145\pi$
$307$	13.1919			0.752900			0.376450	+	0.926437i	$0.377145\pi$
$308$	3.75693	−	5.25228i	0.214071	−	0.299277i
$309$	17.0866			0.972024
$310$		0			0
$311$	7.14113	−	12.3688i	0.404937	−	0.701371i	−0.589378	−	0.807858i	$-0.700627\pi$
$311$	7.14113	−	12.3688i	0.404937	−	0.701371i	0.994314	+	0.106487i	$0.0339603\pi$
$312$	2.30249	−	3.98803i	0.130353	−	0.225778i
$313$	2.38572	+	4.13218i	0.134849	+	0.233565i	0.925540	−	0.378651i	$-0.123612\pi$
$313$	2.38572	+	4.13218i	0.134849	+	0.233565i	−0.790691	+	0.612215i	$0.790279\pi$
$314$	−20.1651			−1.13798
$315$		0			0
$316$	9.52764			0.535971
$317$	−9.40240	−	16.2854i	−0.528091	−	0.914681i	−0.999464	−	0.0327466i	$-0.989575\pi$
$317$	−9.40240	−	16.2854i	−0.528091	−	0.914681i	0.471372	−	0.881934i	$-0.343759\pi$
$318$	−8.82977	+	15.2936i	−0.495149	+	0.857623i
$319$	−4.17121	+	7.22474i	−0.233543	+	0.404508i
$320$		0			0
$321$	−6.31052			−0.352219
$322$	−25.9748	−	2.53582i	−1.44752	−	0.141316i
$323$	16.4829			0.917131
$324$	−0.587145	−	1.01696i	−0.0326191	−	0.0564980i
$325$		0			0
$326$	−1.87383	+	3.24557i	−0.103782	+	0.179755i
$327$	1.22338	+	2.11895i	0.0676530	+	0.117178i
$328$	11.7549			0.649055
$329$	−3.75693	+	5.25228i	−0.207126	+	0.289568i
$330$		0			0
$331$	−8.88708	−	15.3929i	−0.488478	−	0.846069i	0.511434	−	0.859322i	$-0.329114\pi$
$331$	−8.88708	−	15.3929i	−0.488478	−	0.846069i	−0.999912	+	0.0132538i	$0.995781\pi$
$332$	5.13826	−	8.89973i	0.281999	−	0.488436i
$333$	−1.75759	+	3.04424i	−0.0963156	+	0.166823i
$334$	−3.19451	−	5.53305i	−0.174796	−	0.302755i
$335$		0			0
$336$	−5.43669	−	11.9717i	−0.296596	−	0.653112i
$337$	−3.86675			−0.210635			−0.105318	−	0.994439i	$-0.533586\pi$
$337$	−3.86675			−0.210635			−0.105318	+	0.994439i	$0.533586\pi$
$338$	−2.85212	−	4.94001i	−0.155135	−	0.268701i
$339$	5.07850	−	8.79621i	0.275826	−	0.477745i
$340$		0			0
$341$	3.02617	+	5.24148i	0.163876	+	0.283842i
$342$	13.7857			0.745446
$343$	17.7365	+	5.33057i	0.957683	+	0.287824i
$344$	−7.34150			−0.395827
$345$		0			0
$346$	13.8435	−	23.9776i	0.744229	−	1.28904i
$347$	5.13623	−	8.89622i	0.275727	−	0.477574i	−0.694591	−	0.719405i	$-0.744415\pi$
$347$	5.13623	−	8.89622i	0.275727	−	0.477574i	0.970318	+	0.241831i	$0.0777479\pi$
$348$	−2.35661	−	4.08177i	−0.126328	−	0.218806i
$349$	23.6180			1.26424			0.632122	−	0.774869i	$-0.282184\pi$
$349$	23.6180			1.26424			0.632122	+	0.774869i	$0.282184\pi$
$350$		0			0
$351$	−3.13023			−0.167079
$352$	6.14391	+	10.6416i	0.327472	+	0.567197i
$353$	2.88880	−	5.00354i	0.153755	−	0.266312i	−0.778850	−	0.627210i	$-0.784197\pi$
$353$	2.88880	−	5.00354i	0.153755	−	0.266312i	0.932605	+	0.360899i	$0.117530\pi$
$354$	−2.63323	+	4.56089i	−0.139955	+	0.242409i
$355$		0			0
$356$	0.726487			0.0385037
$357$	−3.27895	+	4.58407i	−0.173541	+	0.242615i
$358$	−28.0355			−1.48172
$359$	−15.6527	−	27.1113i	−0.826118	−	1.43088i	−0.901062	−	0.433691i	$-0.857211\pi$
$359$	−15.6527	−	27.1113i	−0.826118	−	1.43088i	0.0749437	−	0.997188i	$-0.476122\pi$
$360$		0			0
$361$	−20.4352	+	35.3948i	−1.07554	+	1.86288i
$362$	−4.44248	−	7.69461i	−0.233492	−	0.404420i
$363$	6.67986			0.350602
$364$	9.67923	+	0.944946i	0.507329	+	0.0495286i
$365$		0			0
$366$	9.70519	+	16.8099i	0.507298	+	0.878667i
$367$	8.27595	−	14.3344i	0.432001	−	0.748248i	−0.565044	−	0.825061i	$-0.691141\pi$
$367$	8.27595	−	14.3344i	0.432001	−	0.748248i	0.997046	+	0.0768125i	$0.0244743\pi$
$368$	13.7573	−	23.8283i	0.717148	−	1.24214i
$369$	−3.99519	−	6.91987i	−0.207981	−	0.360234i
$370$		0			0
$371$	26.1003	+	2.54807i	1.35506	+	0.132289i
$372$	−3.41939			−0.177287
$373$	−16.0713	−	27.8363i	−0.832140	−	1.44131i	−0.896338	−	0.443371i	$-0.853782\pi$
$373$	−16.0713	−	27.8363i	−0.832140	−	1.44131i	0.0641985	−	0.997937i	$-0.479551\pi$
$374$	3.94429	−	6.83171i	0.203954	−	0.353260i
$375$		0			0
$376$	−1.79533	−	3.10961i	−0.0925873	−	0.160366i
$377$	−12.5638			−0.647066
$378$	−2.74241	+	3.83396i	−0.141054	+	0.197198i
$379$	−4.98800			−0.256216			−0.128108	−	0.991760i	$-0.540890\pi$
$379$	−4.98800			−0.256216			−0.128108	+	0.991760i	$0.540890\pi$
$380$		0			0
$381$	4.43488	−	7.68144i	0.227206	−	0.393532i
$382$	10.5192	−	18.2199i	0.538212	−	0.932210i
$383$	−13.2284	−	22.9123i	−0.675940	−	1.17076i	−0.976193	−	0.216903i	$-0.930404\pi$
$383$	−13.2284	−	22.9123i	−0.675940	−	1.17076i	0.300253	−	0.953860i	$-0.402929\pi$
$384$	10.7660			0.549402
$385$		0			0
$386$	−44.0746			−2.24334
$387$	2.49519	+	4.32180i	0.126838	+	0.219689i
$388$	0.174289	−	0.301877i	0.00884818	−	0.0153255i
$389$	6.38580	−	11.0605i	0.323773	−	0.560791i	−0.657491	−	0.753463i	$-0.728382\pi$
$389$	6.38580	−	11.0605i	0.323773	−	0.560791i	0.981263	+	0.192672i	$0.0617154\pi$
$390$		0			0
$391$	−11.7941			−0.596455
$392$	−6.77661	+	7.75401i	−0.342270	+	0.391637i
$393$	−5.34150			−0.269443
$394$	17.4180	+	30.1688i	0.877506	+	1.51988i
$395$		0			0
$396$	1.22038	−	2.11376i	0.0613263	−	0.106220i
$397$	7.56061	+	13.0954i	0.379456	+	0.657237i	0.990983	−	0.133986i	$-0.0427778\pi$
$397$	7.56061	+	13.0954i	0.379456	+	0.657237i	−0.611527	+	0.791223i	$0.709444\pi$
$398$	39.6242			1.98618
$399$	−8.46481	−	18.6397i	−0.423771	−	0.933154i
$400$		0			0
$401$	−6.18029	−	10.7046i	−0.308629	−	0.534561i	0.669434	−	0.742872i	$-0.266537\pi$
$401$	−6.18029	−	10.7046i	−0.308629	−	0.534561i	−0.978063	+	0.208311i	$0.933203\pi$
$402$	−3.42023	+	5.92402i	−0.170586	+	0.295463i
$403$	−4.55744	+	7.89371i	−0.227022	+	0.393214i
$404$	−4.84910	−	8.39889i	−0.241252	−	0.417860i
$405$		0			0
$406$	−11.0071	+	15.3883i	−0.546275	+	0.763708i
$407$	−7.30630			−0.362160
$408$	−1.56692	−	2.71399i	−0.0775743	−	0.134363i
$409$	5.26435	−	9.11813i	0.260306	−	0.450863i	−0.706017	−	0.708194i	$-0.749510\pi$
$409$	5.26435	−	9.11813i	0.260306	−	0.450863i	0.966323	+	0.257332i	$0.0828434\pi$
$410$		0			0
$411$	−6.55196	−	11.3483i	−0.323184	−	0.559772i
$412$	−20.0646			−0.988513
$413$	7.78368	+	0.759892i	0.383010	+	0.0373918i
$414$	−9.86421			−0.484799
$415$		0			0
$416$	−9.25278	+	16.0263i	−0.453655	+	0.785754i
$417$	0.121582	−	0.210587i	0.00595391	−	0.0103125i
$418$	14.3268	+	24.8147i	0.700745	+	1.21373i
$419$	13.3110			0.650283			0.325142	−	0.945665i	$-0.394588\pi$
$419$	13.3110			0.650283			0.325142	+	0.945665i	$0.394588\pi$
$420$		0			0
$421$	19.1520			0.933413			0.466707	−	0.884412i	$-0.345440\pi$
$421$	19.1520			0.933413			0.466707	+	0.884412i	$0.345440\pi$
$422$	21.0405	+	36.4433i	1.02424	+	1.77403i
$423$	−1.22038	+	2.11376i	−0.0593368	+	0.102774i
$424$	−7.29084	+	12.6281i	−0.354074	+	0.613275i
$425$		0			0
$426$	−26.7690			−1.29696
$427$	16.7695	−	23.4442i	0.811531	−	1.13454i
$428$	7.41038			0.358194
$429$	−3.25309	−	5.63451i	−0.157060	−	0.272037i
$430$		0			0
$431$	−5.44818	+	9.43653i	−0.262430	+	0.454542i	−0.966887	−	0.255205i	$-0.917857\pi$
$431$	−5.44818	+	9.43653i	−0.262430	+	0.454542i	0.704457	+	0.709746i	$0.251190\pi$
$432$	−2.48481	−	4.30382i	−0.119551	−	0.207068i
$433$	19.4869			0.936482			0.468241	−	0.883601i	$-0.344888\pi$
$433$	19.4869			0.936482			0.468241	+	0.883601i	$0.344888\pi$
$434$	5.67556	+	12.4977i	0.272436	+	0.599910i
$435$		0			0
$436$	−1.43660	−	2.48826i	−0.0688006	−	0.119166i
$437$	21.4198	−	37.1002i	1.02465	−	1.77474i
$438$	7.61985	−	13.1980i	0.364091	−	0.630624i
$439$	−6.76549	−	11.7182i	−0.322899	−	0.559278i	0.658186	−	0.752856i	$-0.271324\pi$
$439$	−6.76549	−	11.7182i	−0.322899	−	0.559278i	−0.981085	+	0.193578i	$0.937991\pi$
$440$		0			0
$441$	6.86783	+	1.35386i	0.327039	+	0.0644697i
$442$	11.8803			0.565087
$443$	−14.4332	−	24.9990i	−0.685740	−	1.18774i	−0.973204	−	0.229945i	$-0.926145\pi$
$443$	−14.4332	−	24.9990i	−0.685740	−	1.18774i	0.287463	−	0.957792i	$-0.407188\pi$
$444$	2.06392	−	3.57482i	0.0979495	−	0.169653i
$445$		0			0
$446$	−22.3971	−	38.7930i	−1.06054	−	1.83690i
$447$	−2.33728			−0.110550
$448$	0.649481	+	1.43017i	0.0306851	+	0.0675693i
$449$	23.4298			1.10572			0.552860	−	0.833274i	$-0.313536\pi$
$449$	23.4298			1.10572			0.552860	+	0.833274i	$0.313536\pi$
$450$		0			0
$451$	8.30398	−	14.3829i	0.391019	−	0.677265i
$452$	−5.96362	+	10.3293i	−0.280505	+	0.485849i
$453$	−5.55677	−	9.62460i	−0.261080	−	0.452203i
$454$	−42.1722			−1.97924
$455$		0			0
$456$	11.3830			0.533059
$457$	−15.1438	−	26.2298i	−0.708396	−	1.22698i	−0.965452	−	0.260582i	$-0.916086\pi$
$457$	−15.1438	−	26.2298i	−0.708396	−	1.22698i	0.257056	−	0.966397i	$-0.417248\pi$
$458$	0.361958	−	0.626929i	0.0169132	−	0.0292945i
$459$	−1.06512	+	1.84483i	−0.0497153	+	0.0861095i
$460$		0			0
$461$	−7.02196			−0.327045			−0.163523	−	0.986540i	$-0.552286\pi$
$461$	−7.02196			−0.327045			−0.163523	+	0.986540i	$0.552286\pi$
$462$	−9.75128	−	0.951980i	−0.453670	−	0.0442901i
$463$	2.97324			0.138178			0.0690891	−	0.997610i	$-0.477991\pi$
$463$	2.97324			0.138178			0.0690891	+	0.997610i	$0.477991\pi$
$464$	−9.97324	−	17.2742i	−0.462996	−	0.801933i
$465$		0			0
$466$	−6.38302	+	11.0557i	−0.295687	+	0.512146i
$467$	−11.8774	−	20.5723i	−0.549623	−	0.951974i	−0.998300	−	0.0582807i	$-0.981438\pi$
$467$	−11.8774	−	20.5723i	−0.549623	−	0.951974i	0.448678	−	0.893694i	$-0.351895\pi$
$468$	3.67580			0.169914
$469$	10.1100	+	0.987002i	0.466837	+	0.0455755i
$470$		0			0
$471$	5.65910	+	9.80185i	0.260758	+	0.451645i
$472$	−2.17429	+	3.76598i	−0.100080	+	0.173343i
$473$	−5.18624	+	8.98283i	−0.238464	+	0.413031i
$474$	−7.22775	−	12.5188i	−0.331982	−	0.575009i
$475$		0			0
$476$	3.85044	−	5.38302i	0.176485	−	0.246730i
$477$	9.91188			0.453834
$478$	8.99038	+	15.5718i	0.411210	+	0.712237i
$479$	3.27211	−	5.66747i	0.149507	−	0.258953i	−0.781539	−	0.623857i	$-0.785565\pi$
$479$	3.27211	−	5.66747i	0.149507	−	0.258953i	0.931045	+	0.364904i	$0.118898\pi$
$480$		0			0
$481$	−5.50168	−	9.52918i	−0.250855	−	0.434493i
$482$	8.20765			0.373848
$483$	6.05690	+	13.3374i	0.275598	+	0.606875i
$484$	−7.84408			−0.356549
$485$		0			0
$486$	−0.890827	+	1.54296i	−0.0404087	+	0.0699900i
$487$	−8.16346	+	14.1395i	−0.369922	+	0.640723i	−0.989553	−	0.144170i	$-0.953949\pi$
$487$	−8.16346	+	14.1395i	−0.369922	+	0.640723i	0.619631	+	0.784893i	$0.287282\pi$
$488$	8.01368	+	13.8801i	0.362762	+	0.628323i
$489$	2.10347			0.0951223
$490$		0			0
$491$	24.9009			1.12376			0.561882	−	0.827218i	$-0.310078\pi$
$491$	24.9009			1.12376			0.561882	+	0.827218i	$0.310078\pi$
$492$	4.69151	+	8.12593i	0.211510	+	0.366345i
$493$	−4.27503	+	7.40458i	−0.192538	+	0.333485i
$494$	−21.5762	+	37.3711i	−0.970761	+	1.68141i
$495$		0			0
$496$	−14.4710			−0.649766
$497$	16.4369	+	36.1945i	0.737297	+	1.62355i
$498$	−15.5917			−0.698683
$499$	6.10197	+	10.5689i	0.273161	+	0.473130i	0.969670	−	0.244419i	$-0.0785973\pi$
$499$	6.10197	+	10.5689i	0.273161	+	0.473130i	−0.696508	+	0.717549i	$0.745264\pi$
$500$		0			0
$501$	−1.79300	+	3.10557i	−0.0801054	+	0.138747i
$502$	−0.277579	−	0.480780i	−0.0123889	−	0.0214583i
$503$	−27.8165			−1.24028			−0.620139	−	0.784492i	$-0.712924\pi$
$503$	−27.8165			−1.24028			−0.620139	+	0.784492i	$0.712924\pi$
$504$	−2.26443	+	3.16574i	−0.100866	+	0.141013i
$505$		0			0
$506$	−10.2514	−	17.7559i	−0.455728	−	0.789345i
$507$	−1.60083	+	2.77271i	−0.0710952	+	0.123140i
$508$	−5.20784	+	9.02024i	−0.231060	+	0.400208i
$509$	13.9099	+	24.0927i	0.616547	+	1.06789i	0.990111	+	0.140287i	$0.0448025\pi$
$509$	13.9099	+	24.0927i	0.616547	+	1.06789i	−0.373563	+	0.927605i	$0.621864\pi$
$510$		0			0
$511$	−22.5238	−	2.19892i	−0.996396	−	0.0972744i
$512$	−14.7579			−0.652214
$513$	−3.86880	−	6.70095i	−0.170812	−	0.295854i
$514$	−2.22895	+	3.86065i	−0.0983146	+	0.170286i
$515$		0			0
$516$	−2.93007	−	5.07504i	−0.128989	−	0.223416i
$517$	−5.07310			−0.223115
$518$	−16.4915	−	1.61001i	−0.724596	−	0.0707396i
$519$	−15.5400			−0.682131
$520$		0			0
$521$	−16.7513	+	29.0141i	−0.733887	+	1.27113i	0.221323	+	0.975200i	$0.428962\pi$
$521$	−16.7513	+	29.0141i	−0.733887	+	1.27113i	−0.955210	+	0.295929i	$0.904371\pi$
$522$	−3.57549	+	6.19294i	−0.156495	+	0.271058i
$523$	−6.39790	−	11.0815i	−0.279761	−	0.484560i	0.691564	−	0.722315i	$-0.256922\pi$
$523$	−6.39790	−	11.0815i	−0.279761	−	0.484560i	−0.971325	+	0.237755i	$0.923588\pi$
$524$	6.27247			0.274014
$525$		0			0
$526$	8.24034			0.359296
$527$	3.10149	+	5.37195i	0.135103	+	0.234006i
$528$	5.16467	−	8.94547i	0.224763	−	0.389302i
$529$	−3.82668	+	6.62801i	−0.166377	+	0.288174i
$530$		0			0
$531$	2.95594			0.128277
$532$	9.94014	+	21.8884i	0.430960	+	0.948984i
$533$	25.0117			1.08338
$534$	−0.551120	−	0.954567i	−0.0238493	−	0.0413082i
$535$		0			0
$536$	−2.82412	+	4.89153i	−0.121984	+	0.211282i
$537$	7.86783	+	13.6275i	0.339522	+	0.588069i
$538$	−21.4214			−0.923540
$539$	4.70038	+	13.7693i	0.202460	+	0.593085i
$540$		0			0
$541$	−12.6283	−	21.8728i	−0.542933	−	0.940387i	−0.998734	−	0.0503053i	$-0.983981\pi$
$541$	−12.6283	−	21.8728i	−0.542933	−	0.940387i	0.455801	−	0.890082i	$-0.349353\pi$
$542$	−4.87224	+	8.43897i	−0.209281	+	0.362485i
$543$	−2.49346	+	4.31880i	−0.107005	+	0.185337i
$544$	6.29684	+	10.9064i	0.269975	+	0.467610i
$545$		0			0
$546$	−6.10114	−	13.4349i	−0.261105	−	0.574959i
$547$	−38.8743			−1.66214			−0.831072	−	0.556165i	$-0.812272\pi$
$547$	−38.8743			−1.66214			−0.831072	+	0.556165i	$0.812272\pi$
$548$	7.69389	+	13.3262i	0.328667	+	0.569268i
$549$	5.44729	−	9.43499i	0.232485	−	0.402676i
$550$		0			0
$551$	−15.5281	−	26.8955i	−0.661520	−	1.14579i
$552$	−8.14499			−0.346674
$553$	−12.4887	+	17.4596i	−0.531075	+	0.742458i
$554$	−53.1110			−2.25647
$555$		0			0
$556$	−0.142773	+	0.247290i	−0.00605491	+	0.0104874i
$557$	0.681888	−	1.18106i	0.0288925	−	0.0500433i	−0.851218	−	0.524813i	$-0.824135\pi$
$557$	0.681888	−	1.18106i	0.0288925	−	0.0500433i	0.880110	+	0.474770i	$0.157469\pi$
$558$	2.59398	+	4.49291i	0.109812	+	0.190200i
$559$	−15.6210			−0.660700
$560$		0			0
$561$	−4.42768			−0.186937
$562$	6.93519	+	12.0121i	0.292543	+	0.506700i
$563$	−5.28722	+	9.15774i	−0.222830	+	0.385953i	−0.955666	−	0.294452i	$-0.904863\pi$
$563$	−5.28722	+	9.15774i	−0.222830	+	0.385953i	0.732836	+	0.680405i	$0.238196\pi$
$564$	1.43308	−	2.48216i	0.0603434	−	0.104518i
$565$		0			0
$566$	4.65803			0.195791
$567$	2.63323	+	0.257073i	0.110585	+	0.0107960i
$568$	−22.1035			−0.927441
$569$	−18.9932	−	32.8973i	−0.796238	−	1.37913i	−0.922050	−	0.387071i	$-0.873487\pi$
$569$	−18.9932	−	32.8973i	−0.796238	−	1.37913i	0.125811	−	0.992054i	$-0.459847\pi$
$570$		0			0
$571$	7.84550	−	13.5888i	0.328324	−	0.568674i	−0.653856	−	0.756619i	$-0.726850\pi$
$571$	7.84550	−	13.5888i	0.328324	−	0.568674i	0.982179	+	0.187946i	$0.0601829\pi$
$572$	3.82006	+	6.61654i	0.159725	+	0.276652i
$573$	−11.8084			−0.493304
$574$	21.9129	−	30.6348i	0.914625	−	1.27867i
$575$		0			0
$576$	0.296842	+	0.514145i	0.0123684	+	0.0214227i
$577$	1.72405	−	2.98614i	0.0717730	−	0.124315i	−0.827905	−	0.560868i	$-0.810468\pi$
$577$	1.72405	−	2.98614i	0.0717730	−	0.124315i	0.899678	+	0.436553i	$0.143801\pi$
$578$	−11.1016	+	19.2285i	−0.461765	+	0.799800i
$579$	12.3690	+	21.4238i	0.514039	+	0.890342i
$580$		0			0
$581$	9.57377	+	21.0817i	0.397187	+	0.874615i
$582$	−0.528869			−0.0219223
$583$	10.3009	+	17.8417i	0.426620	+	0.738927i
$584$	6.29180	−	10.8977i	0.260356	−	0.450950i
$585$		0			0
$586$	11.3633	+	19.6819i	0.469415	+	0.813051i
$587$	10.5983			0.437441			0.218720	−	0.975788i	$-0.429812\pi$
$587$	10.5983			0.437441			0.218720	+	0.975788i	$0.429812\pi$
$588$	−8.06481	−	1.58983i	−0.332587	−	0.0655634i
$589$	−22.5310			−0.928373
$590$		0			0
$591$	9.77631	−	16.9331i	0.402144	−	0.696533i
$592$	8.73458	−	15.1287i	0.358989	−	0.621787i
$593$	0.117206	+	0.203007i	0.00481307	+	0.00833648i	0.868422	−	0.495826i	$-0.165135\pi$
$593$	0.117206	+	0.203007i	0.00481307	+	0.00833648i	−0.863609	+	0.504162i	$0.831801\pi$
$594$	−3.70316			−0.151942
$595$		0			0
$596$	2.74464			0.112425
$597$	−11.1201	−	19.2605i	−0.455114	−	0.788281i
$598$	15.4386	−	26.7405i	0.631333	−	1.09350i
$599$	12.9145	−	22.3686i	0.527673	−	0.913956i	−0.471807	−	0.881702i	$-0.656398\pi$
$599$	12.9145	−	22.3686i	0.527673	−	0.913956i	0.999480	−	0.0322543i	$-0.0102687\pi$
$600$		0			0
$601$	−1.15592			−0.0471508			−0.0235754	−	0.999722i	$-0.507505\pi$
$601$	−1.15592			−0.0471508			−0.0235754	+	0.999722i	$0.507505\pi$
$602$	−13.6856	+	19.1329i	−0.557785	+	0.779799i
$603$	3.83939			0.156352
$604$	6.52525	+	11.3021i	0.265509	+	0.459875i
$605$		0			0
$606$	−7.35715	+	12.7430i	−0.298864	+	0.517647i
$607$	−11.6056	−	20.1014i	−0.471055	−	0.815891i	0.528397	−	0.848997i	$-0.322793\pi$
$607$	−11.6056	−	20.1014i	−0.471055	−	0.815891i	−0.999452	+	0.0331064i	$0.989460\pi$
$608$	−45.7438			−1.85516
$609$	10.5690	+	1.03181i	0.428276	+	0.0418109i
$610$		0			0
$611$	−3.82006	−	6.61654i	−0.154543	−	0.267677i
$612$	1.25075	−	2.16637i	0.0505587	−	0.0875703i
$613$	−3.16572	+	5.48319i	−0.127862	+	0.221464i	−0.922848	−	0.385164i	$-0.874145\pi$
$613$	−3.16572	+	5.48319i	−0.127862	+	0.221464i	0.794986	+	0.606628i	$0.207478\pi$
$614$	11.7517	+	20.3545i	0.474259	+	0.821440i
$615$		0			0
$616$	−8.05174	−	0.786061i	−0.324414	−	0.0316713i
$617$	−25.9546			−1.04489			−0.522447	−	0.852672i	$-0.674981\pi$
$617$	−25.9546			−1.04489			−0.522447	+	0.852672i	$0.674981\pi$
$618$	15.2212	+	26.3639i	0.612287	+	1.06051i
$619$	14.5481	−	25.1981i	0.584738	−	1.01280i	−0.410170	−	0.912009i	$-0.634531\pi$
$619$	14.5481	−	25.1981i	0.584738	−	1.01280i	0.994908	−	0.100787i	$-0.0321361\pi$
$620$		0			0
$621$	2.76827	+	4.79479i	0.111087	+	0.192408i
$622$	25.4460			1.02029
$623$	−0.952272	+	1.33130i	−0.0381520	+	0.0533375i
$624$	15.5561			0.622741
$625$		0			0
$626$	−4.25052	+	7.36211i	−0.169885	+	0.294249i
$627$	8.04128	−	13.9279i	0.321138	−	0.556227i
$628$	−6.64542	−	11.5102i	−0.265181	−	0.459307i
$629$	−7.48816			−0.298573
$630$		0			0
$631$	−37.3609			−1.48731			−0.743657	−	0.668561i	$-0.766911\pi$
$631$	−37.3609			−1.48731			−0.743657	+	0.668561i	$0.766911\pi$
$632$	−5.96804	−	10.3369i	−0.237396	−	0.411181i
$633$	11.8096	−	20.4547i	0.469388	−	0.813003i
$634$	16.7518	−	29.0150i	0.665300	−	1.15233i
$635$		0			0
$636$	−11.6394			−0.461533
$637$	−14.4191	+	16.4988i	−0.571305	+	0.653705i
$638$	−14.8633			−0.588443
$639$	7.51241	+	13.0119i	0.297186	+	0.514742i
$640$		0			0
$641$	13.9268	−	24.1219i	0.550074	−	0.952756i	−0.448195	−	0.893936i	$-0.647933\pi$
$641$	13.9268	−	24.1219i	0.550074	−	0.952756i	0.998269	−	0.0588199i	$-0.0187338\pi$
$642$	−5.62158	−	9.73687i	−0.221866	−	0.384283i
$643$	20.3104			0.800963			0.400481	−	0.916305i	$-0.368843\pi$
$643$	20.3104			0.800963			0.400481	+	0.916305i	$0.368843\pi$
$644$	−7.11255	−	15.6620i	−0.280274	−	0.617170i
$645$		0			0
$646$	14.6834	+	25.4324i	0.577710	+	1.00062i
$647$	11.2165	−	19.4275i	0.440964	−	0.763773i	−0.556797	−	0.830649i	$-0.687970\pi$
$647$	11.2165	−	19.4275i	0.440964	−	0.763773i	0.997761	+	0.0668759i	$0.0213031\pi$
$648$	−0.735565	+	1.27404i	−0.0288957	+	0.0500489i
$649$	3.07196	+	5.32078i	0.120585	+	0.208859i
$650$		0			0
$651$	4.48211	−	6.26611i	0.175668	−	0.245588i
$652$	−2.47008			−0.0967360
$653$	9.90257	+	17.1517i	0.387517	+	0.671200i	0.992115	−	0.125331i	$-0.0399994\pi$
$653$	9.90257	+	17.1517i	0.387517	+	0.671200i	−0.604598	+	0.796531i	$0.706666\pi$
$654$	−2.17964	+	3.77524i	−0.0852305	+	0.147624i
$655$		0			0
$656$	19.8546	+	34.3892i	0.775192	+	1.34267i
$657$	−8.55369			−0.333711
$658$	−11.4508	−	1.11790i	−0.446399	−	0.0435803i
$659$	38.3567			1.49416			0.747082	−	0.664731i	$-0.231454\pi$
$659$	38.3567			1.49416			0.747082	+	0.664731i	$0.231454\pi$
$660$		0			0
$661$	−1.48746	+	2.57635i	−0.0578554	+	0.100209i	−0.893503	−	0.449058i	$-0.851760\pi$
$661$	−1.48746	+	2.57635i	−0.0578554	+	0.100209i	0.835647	+	0.549267i	$0.185093\pi$
$662$	15.8337	−	27.4248i	0.615394	−	1.06589i
$663$	−3.33406	−	5.77476i	−0.129484	−	0.224273i
$664$	−12.8743			−0.499619
$665$		0			0
$666$	−6.26285			−0.242680
$667$	11.1110	+	19.2448i	0.430218	+	0.745160i
$668$	2.10550	−	3.64684i	0.0814644	−	0.141100i
$669$	−12.5710	+	21.7736i	−0.486022	+	0.841815i
$670$		0			0
$671$	22.6443			0.874175
$672$	9.09985	−	12.7218i	0.351035	−	0.490756i
$673$	22.8397			0.880407			0.440203	−	0.897898i	$-0.354906\pi$
$673$	22.8397			0.880407			0.440203	+	0.897898i	$0.354906\pi$
$674$	−3.44461	−	5.96624i	−0.132681	−	0.229811i
$675$		0			0
$676$	1.87983	−	3.25596i	0.0723012	−	0.125229i
$677$	3.59805	+	6.23200i	0.138284	+	0.239515i	0.926847	−	0.375439i	$-0.122508\pi$
$677$	3.59805	+	6.23200i	0.138284	+	0.239515i	−0.788563	+	0.614954i	$0.789175\pi$
$678$	18.0962			0.694982
$679$	0.324740	+	0.715087i	0.0124624	+	0.0274425i
$680$		0			0
$681$	11.8351	+	20.4990i	0.453523	+	0.785524i
$682$	−5.39159	+	9.33850i	−0.206454	+	0.357590i
$683$	−2.27721	+	3.94425i	−0.0871351	+	0.150922i	−0.906299	−	0.422637i	$-0.861105\pi$
$683$	−2.27721	+	3.94425i	−0.0871351	+	0.150922i	0.819164	+	0.573559i	$0.194438\pi$
$684$	4.54309	+	7.86886i	0.173709	+	0.300873i
$685$		0			0
$686$	7.57535	+	32.1153i	0.289228	+	1.22617i
$687$	−0.406316			−0.0155019
$688$	−12.4002	−	21.4777i	−0.472751	−	0.818830i
$689$	−15.5132	+	26.8697i	−0.591008	+	1.02366i
$690$		0			0
$691$	−1.76948	−	3.06483i	−0.0673142	−	0.116592i	0.830404	−	0.557162i	$-0.188110\pi$
$691$	−1.76948	−	3.06483i	−0.0673142	−	0.116592i	−0.897718	+	0.440570i	$0.854776\pi$
$692$	18.2485			0.693702
$693$	2.27384	+	5.00706i	0.0863761	+	0.190202i
$694$	18.3020			0.694734
$695$		0			0
$696$	−2.95232	+	5.11358i	−0.111908	+	0.193830i
$697$	8.51068	−	14.7409i	0.322365	−	0.558353i
$698$	21.0396	+	36.4416i	0.796360	+	1.37934i
$699$	7.16527			0.271015
$700$		0			0
$701$	−16.8111			−0.634948			−0.317474	−	0.948267i	$-0.602835\pi$
$701$	−16.8111			−0.634948			−0.317474	+	0.948267i	$0.602835\pi$
$702$	−2.78849	−	4.82981i	−0.105245	−	0.182290i
$703$	13.5996	−	23.5551i	0.512917	−	0.888398i
$704$	−0.616984	+	1.06865i	−0.0232535	+	0.0402762i
$705$		0			0
$706$	10.2937			0.387407
$707$	21.7473	+	2.12311i	0.817892	+	0.0798477i
$708$	−3.47113			−0.130453
$709$	−15.9088	−	27.5549i	−0.597468	−	1.03484i	−0.993194	−	0.116476i	$-0.962840\pi$
$709$	−15.9088	−	27.5549i	−0.597468	−	1.03484i	0.395726	−	0.918369i	$-0.370493\pi$
$710$		0			0
$711$	−4.05677	+	7.02653i	−0.152141	+	0.263515i
$712$	−0.455066	−	0.788197i	−0.0170543	−	0.0295389i
$713$	16.1218			0.603766
$714$	−9.99400	−	0.975676i	−0.374016	−	0.0365138i
$715$		0			0
$716$	−9.23910	−	16.0026i	−0.345282	−	0.598045i
$717$	5.04609	−	8.74008i	0.188450	−	0.326404i
$718$	27.8877	−	48.3029i	1.04076	−	1.80265i
$719$	−7.64037	−	13.2335i	−0.284938	−	0.493527i	0.687656	−	0.726036i	$-0.258640\pi$
$719$	−7.64037	−	13.2335i	−0.284938	−	0.493527i	−0.972594	+	0.232510i	$0.925306\pi$
$720$		0			0
$721$	26.3005	−	36.7689i	0.979483	−	1.36934i
$722$	−72.8169			−2.70996
$723$	−2.30338	−	3.98957i	−0.0856637	−	0.148374i
$724$	2.92804	−	5.07152i	0.108820	−	0.188482i
$725$		0			0
$726$	5.95060	+	10.3067i	0.220847	+	0.382519i
$727$	19.1829			0.711453			0.355726	−	0.934590i	$-0.384234\pi$
$727$	19.1829			0.711453			0.355726	+	0.934590i	$0.384234\pi$
$728$	−5.03778	−	11.0933i	−0.186713	−	0.411146i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−5.31533	+	9.20643i	−0.196595	+	0.340512i
$732$	−6.39670	+	11.0794i	−0.236429	+	0.409507i
$733$	−24.3609	−	42.1943i	−0.899790	−	1.55848i	−0.827762	−	0.561080i	$-0.810386\pi$
$733$	−24.3609	−	42.1943i	−0.899790	−	1.55848i	−0.0720283	−	0.997403i	$-0.522947\pi$
$734$	29.4898			1.08849
$735$		0			0
$736$	32.7314			1.20650
$737$	3.99008	+	6.91102i	0.146976	+	0.254571i
$738$	7.11804	−	12.3288i	0.262019	−	0.453830i
$739$	4.74202	−	8.21343i	0.174438	−	0.302136i	−0.765529	−	0.643402i	$-0.777522\pi$
$739$	4.74202	−	8.21343i	0.174438	−	0.302136i	0.939967	+	0.341266i	$0.110856\pi$
$740$		0			0
$741$	24.2205			0.889761
$742$	19.3193	+	42.5415i	0.709233	+	1.56175i
$743$	−30.2032			−1.10805			−0.554023	−	0.832501i	$-0.686908\pi$
$743$	−30.2032			−1.10805			−0.554023	+	0.832501i	$0.686908\pi$
$744$	2.14188	+	3.70985i	0.0785252	+	0.136010i
$745$		0			0
$746$	28.6335	−	49.5946i	1.04835	−	1.81579i
$747$	4.37564	+	7.57883i	0.160096	+	0.277295i
$748$	5.19937			0.190108
$749$	−9.71346	+	13.5797i	−0.354922	+	0.496191i
$750$		0			0
$751$	3.66467	+	6.34739i	0.133726	+	0.231620i	0.925110	−	0.379699i	$-0.123973\pi$
$751$	3.66467	+	6.34739i	0.133726	+	0.231620i	−0.791384	+	0.611319i	$0.790639\pi$
$752$	6.06481	−	10.5046i	0.221161	−	0.383062i
$753$	−0.155798	+	0.269851i	−0.00567760	+	0.00983390i
$754$	−11.1921	−	19.3853i	−0.407593	−	0.705972i
$755$		0			0
$756$	−3.09218	−	0.301877i	−0.112461	−	0.0109792i
$757$	14.1603			0.514666			0.257333	−	0.966323i	$-0.417156\pi$
$757$	14.1603			0.514666			0.257333	+	0.966323i	$0.417156\pi$
$758$	−4.44344	−	7.69626i	−0.161393	−	0.279541i
$759$	−5.75384	+	9.96595i	−0.208851	+	0.361741i
$760$		0			0
$761$	11.9592	+	20.7139i	0.433519	+	0.750878i	0.997173	−	0.0751333i	$-0.0239382\pi$
$761$	11.9592	+	20.7139i	0.433519	+	0.750878i	−0.563654	+	0.826011i	$0.690605\pi$
$762$	15.8029			0.572477
$763$	6.44288	+	0.628994i	0.233248	+	0.0227711i
$764$	13.8665			0.501672
$765$		0			0
$766$	23.5684	−	40.8217i	0.851562	−	1.47495i
$767$	−4.62639	+	8.01315i	−0.167049	+	0.289338i
$768$	10.1844	+	17.6398i	0.367496	+	0.636522i
$769$	14.1358			0.509750			0.254875	−	0.966974i	$-0.417966\pi$
$769$	14.1358			0.509750			0.254875	+	0.966974i	$0.417966\pi$
$770$		0			0
$771$	2.50211			0.0901113
$772$	−14.5248	−	25.1577i	−0.522759	−	0.905445i
$773$	−3.37986	+	5.85409i	−0.121565	+	0.210557i	−0.920385	−	0.391013i	$-0.872125\pi$
$773$	−3.37986	+	5.85409i	−0.121565	+	0.210557i	0.798820	+	0.601570i	$0.205458\pi$
$774$	−4.44556	+	7.69994i	−0.159792	+	0.276769i
$775$		0			0
$776$	−0.436693			−0.0156764
$777$	3.84556	+	8.46803i	0.137959	+	0.303789i
$778$	22.7545			0.815790
$779$	30.9132	+	53.5432i	1.10758	+	1.91838i
$780$		0			0
$781$	−15.6145	+	27.0451i	−0.558731	+	0.967750i
$782$	−10.5065	−	18.1978i	−0.375713	−	0.650753i
$783$	4.01368			0.143437
$784$	−34.1305	−	6.72819i	−1.21895	−	0.240293i
$785$		0			0
$786$	−4.75835	−	8.24171i	−0.169725	−	0.293972i
$787$	−7.68754	+	13.3152i	−0.274031	+	0.474636i	−0.969890	−	0.243543i	$-0.921690\pi$
$787$	−7.68754	+	13.3152i	−0.274031	+	0.474636i	0.695859	+	0.718178i	$0.255024\pi$
$788$	−11.4802	+	19.8843i	−0.408966	+	0.708349i
$789$	−2.31255	−	4.00546i	−0.0823291	−	0.142598i
$790$		0			0
$791$	−11.1116	−	24.4680i	−0.395083	−	0.869982i
$792$	−3.05774			−0.108652
$793$	17.0513	+	29.5337i	0.605509	+	1.04877i
$794$	−13.4704	+	23.3314i	−0.478046	+	0.828000i
$795$		0			0
$796$	13.0582	+	22.6174i	0.462835	+	0.801654i
$797$	−9.46785			−0.335369			−0.167684	−	0.985841i	$-0.553629\pi$
$797$	−9.46785			−0.335369			−0.167684	+	0.985841i	$0.553629\pi$
$798$	21.2196	−	29.6656i	0.751167	−	1.05015i
$799$	−5.19937			−0.183941
$800$		0			0
$801$	−0.309330	+	0.535776i	−0.0109297	+	0.0189307i
$802$	11.0111	−	19.0718i	0.388817	−	0.673450i
$803$	−8.88940	−	15.3969i	−0.313700	−	0.543344i
$804$	−4.50856			−0.159004
$805$		0			0
$806$	−16.2395			−0.572014
$807$	6.01165	+	10.4125i	0.211620	+	0.366537i
$808$	−6.07488	+	10.5220i	−0.213713	+	0.370163i
$809$	−2.81872	+	4.88217i	−0.0991011	+	0.171648i	−0.911313	−	0.411715i	$-0.864930\pi$
$809$	−2.81872	+	4.88217i	−0.0991011	+	0.171648i	0.812212	+	0.583363i	$0.198263\pi$
$810$		0			0
$811$	24.3625			0.855485			0.427742	−	0.903901i	$-0.359309\pi$
$811$	24.3625			0.855485			0.427742	+	0.903901i	$0.359309\pi$
$812$	−12.4110	−	1.21164i	−0.435541	−	0.0425202i
$813$	5.46935			0.191818
$814$	−6.50865	−	11.2733i	−0.228128	−	0.395129i
$815$		0			0
$816$	5.29322	−	9.16813i	0.185300	−	0.320949i
$817$	−19.3068	−	33.4403i	−0.675458	−	1.16993i
$818$	18.7585			0.655876
$819$	−4.81820	+	6.73598i	−0.168362	+	0.235374i
$820$		0			0
$821$	15.8731	+	27.4930i	0.553974	+	0.959512i	0.997983	+	0.0634890i	$0.0202228\pi$
$821$	15.8731	+	27.4930i	0.553974	+	0.959512i	−0.444008	+	0.896023i	$0.646444\pi$
$822$	11.6733	−	20.2188i	0.407154	−	0.705211i
$823$	1.98781	−	3.44299i	0.0692908	−	0.120015i	−0.829299	−	0.558806i	$-0.811260\pi$
$823$	1.98781	−	3.44299i	0.0692908	−	0.120015i	0.898589	+	0.438791i	$0.144593\pi$
$824$	12.5683	+	21.7690i	0.437838	+	0.758358i
$825$		0			0
$826$	5.76143	+	12.6868i	0.200466	+	0.441431i
$827$	6.80348			0.236580			0.118290	−	0.992979i	$-0.462259\pi$
$827$	6.80348			0.236580			0.118290	+	0.992979i	$0.462259\pi$
$828$	−3.25075	−	5.63047i	−0.112972	−	0.195672i
$829$	−11.5303	+	19.9710i	−0.400463	+	0.693623i	−0.993782	−	0.111345i	$-0.964484\pi$
$829$	−11.5303	+	19.9710i	−0.400463	+	0.693623i	0.593319	+	0.804968i	$0.297817\pi$
$830$		0			0
$831$	14.9050	+	25.8162i	0.517048	+	0.895553i
$832$	−1.85837			−0.0644273
$833$	4.81738	+	14.1120i	0.166912	+	0.488953i
$834$	0.433235			0.0150017
$835$		0			0
$836$	−9.44278	+	16.3554i	−0.326586	+	0.565663i
$837$	1.45594	−	2.52177i	0.0503247	−	0.0871650i
$838$	11.8578	+	20.5383i	0.409620	+	0.709482i
$839$	−35.0723			−1.21083			−0.605415	−	0.795910i	$-0.706993\pi$
$839$	−35.0723			−1.21083			−0.605415	+	0.795910i	$0.706993\pi$
$840$		0			0
$841$	−12.8904			−0.444495
$842$	17.0611	+	29.5508i	0.587966	+	1.01839i
$843$	3.89256	−	6.74210i	0.134067	−	0.232210i
$844$	−13.8678	+	24.0198i	−0.477350	+	0.826795i
$845$		0			0
$846$	−4.34858			−0.149507
$847$	10.2820	−	14.3745i	0.353292	−	0.493912i
$848$	−49.2583			−1.69154
$849$	−1.30722	−	2.26417i	−0.0448637	−	0.0777062i
$850$		0			0
$851$	−9.73100	+	16.8546i	−0.333575	+	0.577768i
$852$	−8.82174	−	15.2797i	−0.302228	−	0.523474i
$853$	−12.3125			−0.421571			−0.210785	−	0.977532i	$-0.567602\pi$
$853$	−12.3125			−0.421571			−0.210785	+	0.977532i	$0.567602\pi$
$854$	51.1120	+	4.98987i	1.74902	+	0.170750i
$855$		0			0
$856$	−4.64180	−	8.03984i	−0.158654	−	0.274796i
$857$	−16.6249	+	28.7952i	−0.567896	+	0.983624i	0.428878	+	0.903362i	$0.358909\pi$
$857$	−16.6249	+	28.7952i	−0.567896	+	0.983624i	−0.996774	+	0.0802617i	$0.974424\pi$
$858$	5.79587	−	10.0387i	0.197868	−	0.342717i
$859$	1.50697	+	2.61015i	0.0514172	+	0.0890573i	0.890588	−	0.454810i	$-0.150293\pi$
$859$	1.50697	+	2.61015i	0.0514172	+	0.0890573i	−0.839171	+	0.543867i	$0.816959\pi$
$860$		0			0
$861$	−21.0405	−	2.05411i	−0.717059	−	0.0700038i
$862$	−19.4136			−0.661228
$863$	11.1180	+	19.2569i	0.378460	+	0.655513i	0.990838	−	0.135052i	$-0.0431203\pi$
$863$	11.1180	+	19.2569i	0.378460	+	0.655513i	−0.612378	+	0.790565i	$0.709787\pi$
$864$	2.95594	−	5.11984i	0.100563	−	0.174181i
$865$		0			0
$866$	17.3595	+	30.0675i	0.589899	+	1.02174i
$867$	12.4621			0.423236
$868$	−5.26329	+	7.35823i	−0.178648	+	0.249755i
$869$	−16.8639			−0.572070
$870$		0			0
$871$	−6.00909	+	10.4081i	−0.203610	+	0.352663i
$872$	−1.79975	+	3.11726i	−0.0609472	+	0.105564i
$873$	0.148421	+	0.257073i	0.00502329	+	0.00870059i
$874$	76.3253			2.58174
$875$		0			0
$876$	10.0445			0.339372
$877$	7.16105	+	12.4033i	0.241812	+	0.418830i	0.961230	−	0.275747i	$-0.0889251\pi$
$877$	7.16105	+	12.4033i	0.241812	+	0.418830i	−0.719419	+	0.694577i	$0.755592\pi$
$878$	12.0538	−	20.8777i	0.406795	−	0.704589i
$879$	6.37797	−	11.0470i	0.215124	−	0.372605i
$880$		0			0
$881$	49.9929			1.68431			0.842153	−	0.539239i	$-0.181288\pi$
$881$	49.9929			1.68431			0.842153	+	0.539239i	$0.181288\pi$
$882$	4.02909	+	11.8028i	0.135667	+	0.397422i
$883$	44.3095			1.49113			0.745566	−	0.666432i	$-0.232179\pi$
$883$	44.3095			1.49113			0.745566	+	0.666432i	$0.232179\pi$
$884$	3.91515	+	6.78124i	0.131681	+	0.228078i
$885$		0			0
$886$	25.7149	−	44.5395i	0.863909	−	1.49633i
$887$	5.14926	+	8.91878i	0.172895	+	0.299463i	0.939431	−	0.342738i	$-0.111354\pi$
$887$	5.14926	+	8.91878i	0.172895	+	0.299463i	−0.766536	+	0.642202i	$0.778021\pi$
$888$	−5.17130			−0.173538
$889$	−9.70339	−	21.3671i	−0.325441	−	0.716630i
$890$		0			0
$891$	1.03925	+	1.80003i	0.0348161	+	0.0603033i
$892$	14.7620	−	25.5685i	0.494267	−	0.856096i
$893$	9.44278	−	16.3554i	0.315991	−	0.547312i
$894$	−2.08211	−	3.60633i	−0.0696363	−	0.120614i
$895$		0			0
$896$	16.5716	−	23.1675i	0.553618	−	0.773973i
$897$	−17.3307			−0.578654
$898$	20.8719	+	36.1512i	0.696504	+	1.20638i
$899$	5.84369	−	10.1216i	0.194898	−	0.337573i
$900$		0			0
$901$	10.5573	+	18.2858i	0.351715	+	0.609188i
$902$	29.5896			0.985227
$903$	13.1408	+	1.28289i	0.437299	+	0.0426919i
$904$	14.9423			0.496972
$905$		0			0
$906$	9.90023	−	17.1477i	0.328913	−	0.569694i
$907$	−14.7140	+	25.4854i	−0.488570	+	0.846228i	−0.999914	−	0.0131487i	$-0.995815\pi$
$907$	−14.7140	+	25.4854i	−0.488570	+	0.846228i	0.511344	+	0.859376i	$0.329148\pi$
$908$	−13.8979	−	24.0718i	−0.461216	−	0.798850i
$909$	8.25879			0.273927
$910$		0			0
$911$	−24.8078			−0.821918			−0.410959	−	0.911654i	$-0.634806\pi$
$911$	−24.8078			−0.821918			−0.410959	+	0.911654i	$0.634806\pi$
$912$	19.2265	+	33.3012i	0.636652	+	1.10271i
$913$	−9.09474	+	15.7526i	−0.300992	+	0.521334i
$914$	26.9810	−	46.7324i	0.892451	−	1.54577i
$915$		0			0
$916$	0.477133			0.0157649
$917$	−8.22189	+	11.4944i	−0.271511	+	0.379580i
$918$	−3.79533			−0.125265
$919$	−6.50466	−	11.2664i	−0.214569	−	0.371645i	0.738570	−	0.674177i	$-0.235501\pi$
$919$	−6.50466	−	11.2664i	−0.214569	−	0.371645i	−0.953139	+	0.302532i	$0.902168\pi$
$920$		0			0
$921$	6.59594	−	11.4245i	0.217343	−	0.376450i
$922$	−6.25535	−	10.8346i	−0.206009	−	0.356818i
$923$	−47.0312			−1.54805
$924$	−2.67015	−	5.87973i	−0.0878414	−	0.193429i
$925$		0			0
$926$	2.64864	+	4.58758i	0.0870398	+	0.150757i
$927$	8.54331	−	14.7974i	0.280599	−	0.486012i
$928$	11.8642	−	20.5494i	0.389462	−	0.674568i
$929$	−12.4592	−	21.5800i	−0.408775	−	0.708018i	0.585978	−	0.810327i	$-0.300710\pi$
$929$	−12.4592	−	21.5800i	−0.408775	−	0.708018i	−0.994753	+	0.102309i	$0.967377\pi$
$930$		0			0
$931$	−53.1405	−	10.4756i	−1.74161	−	0.343326i
$932$	−8.41410			−0.275613
$933$	−7.14113	−	12.3688i	−0.233790	−	0.404937i
$934$	21.1615	−	36.6528i	0.692425	−	1.19932i
$935$		0			0
$936$	−2.30249	−	3.98803i	−0.0752592	−	0.130353i
$937$	55.1260			1.80089			0.900444	−	0.434973i	$-0.143242\pi$
$937$	55.1260			1.80089			0.900444	+	0.434973i	$0.143242\pi$
$938$	7.48337	+	16.4786i	0.244341	+	0.538044i
$939$	4.77143			0.155710
$940$		0			0
$941$	−6.82233	+	11.8166i	−0.222402	+	0.385211i	−0.955537	−	0.294872i	$-0.904723\pi$
$941$	−6.82233	+	11.8166i	−0.222402	+	0.385211i	0.733135	+	0.680083i	$0.238056\pi$
$942$	−10.0826	+	17.4635i	−0.328507	+	0.568992i
$943$	−22.1196	−	38.3122i	−0.720312	−	1.24762i
$944$	−14.6899			−0.478116
$945$		0			0
$946$	−18.4802			−0.600842
$947$	−0.446544	−	0.773437i	−0.0145107	−	0.0251333i	0.858679	−	0.512514i	$-0.171286\pi$
$947$	−0.446544	−	0.773437i	−0.0145107	−	0.0251333i	−0.873190	+	0.487381i	$0.837952\pi$
$948$	4.76382	−	8.25117i	0.154722	−	0.267986i
$949$	13.3875	−	23.1878i	0.434577	−	0.752709i
$950$		0			0
$951$	−18.8048			−0.609787
$952$	−8.25215	−	0.805627i	−0.267454	−	0.0261105i
$953$	−34.5636			−1.11963			−0.559813	−	0.828619i	$-0.689127\pi$
$953$	−34.5636			−1.11963			−0.559813	+	0.828619i	$0.689127\pi$
$954$	8.82977	+	15.2936i	0.285874	+	0.495149i
$955$		0			0
$956$	−5.92557	+	10.2634i	−0.191646	+	0.331941i
$957$	4.17121	+	7.22474i	0.134836	+	0.233543i
$958$	11.6595			0.376703
$959$	−34.5057	−	3.36866i	−1.11425	−	0.108780i
$960$		0			0
$961$	11.2605	+	19.5037i	0.363241	+	0.629151i
$962$	9.80208	−	16.9777i	0.316032	−	0.547383i
$963$	−3.15526	+	5.46507i	−0.101677	+	0.176110i
$964$	2.70483	+	4.68491i	0.0871169	+	0.150891i
$965$		0			0
$966$	−15.1835	+	21.2269i	−0.488520	+	0.682964i
$967$	−22.1811			−0.713296			−0.356648	−	0.934239i	$-0.616080\pi$
$967$	−22.1811			−0.713296			−0.356648	+	0.934239i	$0.616080\pi$
$968$	4.91347	+	8.51038i	0.157925	+	0.273534i
$969$	8.24144	−	14.2746i	0.264753	−	0.458566i
$970$		0			0
$971$	−0.0379659	−	0.0657589i	−0.00121839	−	0.00211031i	0.865416	−	0.501055i	$-0.167054\pi$
$971$	−0.0379659	−	0.0657589i	−0.00121839	−	0.00211031i	−0.866634	+	0.498944i	$0.833721\pi$
$972$	−1.17429			−0.0376653
$973$	−0.266018	−	0.585779i	−0.00852815	−	0.0187792i
$974$	−29.0889			−0.932069
$975$		0			0
$976$	−27.0710	+	46.8883i	−0.866521	+	1.50086i
$977$	−21.6057	+	37.4222i	−0.691228	+	1.19724i	0.280207	+	0.959940i	$0.409597\pi$
$977$	−21.6057	+	37.4222i	−0.691228	+	1.19724i	−0.971436	+	0.237303i	$0.923737\pi$
$978$	1.87383	+	3.24557i	0.0599185	+	0.103782i
$979$	−1.28588			−0.0410970
$980$		0			0
$981$	2.44676			0.0781189
$982$	22.1824	+	38.4211i	0.707869	+	1.22607i
$983$	−9.16040	+	15.8663i	−0.292171	+	0.506055i	−0.974323	−	0.225155i	$-0.927711\pi$
$983$	−9.16040	+	15.8663i	−0.292171	+	0.506055i	0.682152	+	0.731211i	$0.261044\pi$
$984$	5.87745	−	10.1800i	0.187366	−	0.324528i
$985$		0			0
$986$	−15.2333			−0.485126
$987$	2.67015	+	5.87973i	0.0849918	+	0.187154i
$988$	−28.4418			−0.904855
$989$	13.8147	+	23.9278i	0.439283	+	0.760861i
$990$		0			0
$991$	15.7888	−	27.3470i	0.501548	−	0.868706i	−0.498450	−	0.866918i	$-0.666097\pi$
$991$	15.7888	−	27.3470i	0.501548	−	0.868706i	0.999998	−	0.00178831i	$-0.000569236\pi$
$992$	−8.60736	−	14.9084i	−0.273284	−	0.473342i
$993$	−17.7742			−0.564046
$994$	−41.2041	+	57.6045i	−1.30692	+	1.82710i
$995$		0			0
$996$	−5.13826	−	8.89973i	−0.162812	−	0.281999i
$997$	19.8657	−	34.4085i	0.629154	−	1.08973i	−0.358568	−	0.933504i	$-0.616735\pi$
$997$	19.8657	−	34.4085i	0.629154	−	1.08973i	0.987722	−	0.156223i	$-0.0499319\pi$
$998$	−10.8716	+	18.8301i	−0.344134	+	0.596058i
$999$	1.75759	+	3.04424i	0.0556078	+	0.0963156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.i.h.151.4		8
5.2	odd	4		105.2.q.a.4.2	✓	16
5.3	odd	4		105.2.q.a.4.7	yes	16
5.4	even	2		525.2.i.k.151.1		8
7.2	even	3	inner	525.2.i.h.226.4		8
7.3	odd	6		3675.2.a.cb.1.1		4
7.4	even	3		3675.2.a.bz.1.1		4
15.2	even	4		315.2.bf.b.109.7		16
15.8	even	4		315.2.bf.b.109.2		16
20.3	even	4		1680.2.di.d.529.2		16
20.7	even	4		1680.2.di.d.529.6		16
35.2	odd	12		105.2.q.a.79.7	yes	16
35.3	even	12		735.2.d.e.589.7		8
35.4	even	6		3675.2.a.bp.1.4		4
35.9	even	6		525.2.i.k.226.1		8
35.12	even	12		735.2.q.g.79.7		16
35.13	even	4		735.2.q.g.214.7		16
35.17	even	12		735.2.d.e.589.2		8
35.18	odd	12		735.2.d.d.589.7		8
35.23	odd	12		105.2.q.a.79.2	yes	16
35.24	odd	6		3675.2.a.bn.1.4		4
35.27	even	4		735.2.q.g.214.2		16
35.32	odd	12		735.2.d.d.589.2		8
35.33	even	12		735.2.q.g.79.2		16
105.2	even	12		315.2.bf.b.289.2		16
105.17	odd	12		2205.2.d.o.1324.7		8
105.23	even	12		315.2.bf.b.289.7		16
105.32	even	12		2205.2.d.s.1324.7		8
105.38	odd	12		2205.2.d.o.1324.2		8
105.53	even	12		2205.2.d.s.1324.2		8
140.23	even	12		1680.2.di.d.289.6		16
140.107	even	12		1680.2.di.d.289.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.2	✓	16	5.2	odd	4
105.2.q.a.4.7	yes	16	5.3	odd	4
105.2.q.a.79.2	yes	16	35.23	odd	12
105.2.q.a.79.7	yes	16	35.2	odd	12
315.2.bf.b.109.2		16	15.8	even	4
315.2.bf.b.109.7		16	15.2	even	4
315.2.bf.b.289.2		16	105.2	even	12
315.2.bf.b.289.7		16	105.23	even	12
525.2.i.h.151.4		8	1.1	even	1	trivial
525.2.i.h.226.4		8	7.2	even	3	inner
525.2.i.k.151.1		8	5.4	even	2
525.2.i.k.226.1		8	35.9	even	6
735.2.d.d.589.2		8	35.32	odd	12
735.2.d.d.589.7		8	35.18	odd	12
735.2.d.e.589.2		8	35.17	even	12
735.2.d.e.589.7		8	35.3	even	12
735.2.q.g.79.2		16	35.33	even	12
735.2.q.g.79.7		16	35.12	even	12
735.2.q.g.214.2		16	35.27	even	4
735.2.q.g.214.7		16	35.13	even	4
1680.2.di.d.289.2		16	140.107	even	12
1680.2.di.d.289.6		16	140.23	even	12
1680.2.di.d.529.2		16	20.3	even	4
1680.2.di.d.529.6		16	20.7	even	4
2205.2.d.o.1324.2		8	105.38	odd	12
2205.2.d.o.1324.7		8	105.17	odd	12
2205.2.d.s.1324.2		8	105.53	even	12
2205.2.d.s.1324.7		8	105.32	even	12
3675.2.a.bn.1.4		4	35.24	odd	6
3675.2.a.bp.1.4		4	35.4	even	6
3675.2.a.bz.1.1		4	7.4	even	3
3675.2.a.cb.1.1		4	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.890827 + 1.54296i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.587145 + 1.01696i) q^{4} +1.78165 q^{6} +(-1.09398 - 2.40898i) q^{7} +1.47113 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.890827 + 1.54296i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.587145 + 1.01696i) q^{4} +1.78165 q^{6} +(-1.09398 - 2.40898i) q^{7} +1.47113 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.03925 - 1.80003i) q^{11} +(0.587145 + 1.01696i) q^{12} +3.13023 q^{13} +(2.74241 - 3.83396i) q^{14} +(2.48481 + 4.30382i) q^{16} +(1.06512 - 1.84483i) q^{17} +(0.890827 - 1.54296i) q^{18} +(3.86880 + 6.70095i) q^{19} +(-2.63323 - 0.257073i) q^{21} +3.70316 q^{22} +(-2.76827 - 4.79479i) q^{23} +(0.735565 - 1.27404i) q^{24} +(2.78849 + 4.82981i) q^{26} -1.00000 q^{27} +(3.09218 + 0.301877i) q^{28} -4.01368 q^{29} +(-1.45594 + 2.52177i) q^{31} +(-2.95594 + 5.11984i) q^{32} +(-1.03925 - 1.80003i) q^{33} +3.79533 q^{34} +1.17429 q^{36} +(-1.75759 - 3.04424i) q^{37} +(-6.89286 + 11.9388i) q^{38} +(1.56512 - 2.71086i) q^{39} +7.99038 q^{41} +(-1.94910 - 4.29197i) q^{42} -4.99038 q^{43} +(1.22038 + 2.11376i) q^{44} +(4.93210 - 8.54266i) q^{46} +(-1.22038 - 2.11376i) q^{47} +4.96962 q^{48} +(-4.60639 + 5.27078i) q^{49} +(-1.06512 - 1.84483i) q^{51} +(-1.83790 + 3.18333i) q^{52} +(-4.95594 + 8.58394i) q^{53} +(-0.890827 - 1.54296i) q^{54} +(-1.60939 - 3.54393i) q^{56} +7.73760 q^{57} +(-3.57549 - 6.19294i) q^{58} +(-1.47797 + 2.55992i) q^{59} +(5.44729 + 9.43499i) q^{61} -5.18797 q^{62} +(-1.53925 + 2.15191i) q^{63} -0.593684 q^{64} +(1.85158 - 3.20703i) q^{66} +(-1.91970 + 3.32501i) q^{67} +(1.25075 + 2.16637i) q^{68} -5.53655 q^{69} -15.0248 q^{71} +(-0.735565 - 1.27404i) q^{72} +(4.27684 - 7.40771i) q^{73} +(3.13142 - 5.42378i) q^{74} -9.08617 q^{76} +(-5.47316 - 0.534324i) q^{77} +5.57699 q^{78} +(-4.05677 - 7.02653i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(7.11804 + 12.3288i) q^{82} -8.75128 q^{83} +(1.80752 - 2.52696i) q^{84} +(-4.44556 - 7.69994i) q^{86} +(-2.00684 + 3.47595i) q^{87} +(1.52887 - 2.64808i) q^{88} +(-0.309330 - 0.535776i) q^{89} +(-3.42443 - 7.54067i) q^{91} +6.50151 q^{92} +(1.45594 + 2.52177i) q^{93} +(2.17429 - 3.76598i) q^{94} +(2.95594 + 5.11984i) q^{96} -0.296842 q^{97} +(-12.2361 - 2.41212i) q^{98} -2.07850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{6} + 2 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^6 + 2 * q^7 + 12 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{6} + 2 q^{7} + 12 q^{8} - 4 q^{9} + 4 q^{12} + 4 q^{13} + 12 q^{14} - 2 q^{17} - 2 q^{18} + 12 q^{19} - 2 q^{21} + 28 q^{22} - 10 q^{23} + 6 q^{24} - 6 q^{26} - 8 q^{27} - 12 q^{28} - 12 q^{29} + 8 q^{31} - 4 q^{32} - 8 q^{34} + 8 q^{36} - 24 q^{37} - 8 q^{38} + 2 q^{39} + 8 q^{41} - 6 q^{42} + 16 q^{43} - 10 q^{44} - 16 q^{46} + 10 q^{47} + 20 q^{49} + 2 q^{51} - 34 q^{52} - 20 q^{53} + 2 q^{54} + 42 q^{56} + 24 q^{57} - 10 q^{58} - 2 q^{59} + 8 q^{61} - 20 q^{62} - 4 q^{63} - 8 q^{64} + 14 q^{66} - 6 q^{67} + 30 q^{68} - 20 q^{69} - 28 q^{71} - 6 q^{72} - 12 q^{73} - 20 q^{74} - 32 q^{76} - 6 q^{77} - 12 q^{78} + 8 q^{79} - 4 q^{81} + 18 q^{82} - 12 q^{83} - 6 q^{84} - 24 q^{86} - 6 q^{87} + 12 q^{88} - 8 q^{89} + 4 q^{91} + 92 q^{92} - 8 q^{93} + 16 q^{94} + 4 q^{96} - 4 q^{97} - 20 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^6 + 2 * q^7 + 12 * q^8 - 4 * q^9 + 4 * q^12 + 4 * q^13 + 12 * q^14 - 2 * q^17 - 2 * q^18 + 12 * q^19 - 2 * q^21 + 28 * q^22 - 10 * q^23 + 6 * q^24 - 6 * q^26 - 8 * q^27 - 12 * q^28 - 12 * q^29 + 8 * q^31 - 4 * q^32 - 8 * q^34 + 8 * q^36 - 24 * q^37 - 8 * q^38 + 2 * q^39 + 8 * q^41 - 6 * q^42 + 16 * q^43 - 10 * q^44 - 16 * q^46 + 10 * q^47 + 20 * q^49 + 2 * q^51 - 34 * q^52 - 20 * q^53 + 2 * q^54 + 42 * q^56 + 24 * q^57 - 10 * q^58 - 2 * q^59 + 8 * q^61 - 20 * q^62 - 4 * q^63 - 8 * q^64 + 14 * q^66 - 6 * q^67 + 30 * q^68 - 20 * q^69 - 28 * q^71 - 6 * q^72 - 12 * q^73 - 20 * q^74 - 32 * q^76 - 6 * q^77 - 12 * q^78 + 8 * q^79 - 4 * q^81 + 18 * q^82 - 12 * q^83 - 6 * q^84 - 24 * q^86 - 6 * q^87 + 12 * q^88 - 8 * q^89 + 4 * q^91 + 92 * q^92 - 8 * q^93 + 16 * q^94 + 4 * q^96 - 4 * q^97 - 20 * q^98

Introduction

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