LMFDB - Embedded newform 525.2.i.k.151.3

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			151.3
Root			$-0.276205 + 0.478401i$ of defining polynomial
Character	$\chi$	$=$	525.151
Dual form			525.2.i.k.226.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.776205 + 1.34443i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.204988 + 0.355049i) q^{4} -1.55241 q^{6} +(2.60214 - 0.478401i) q^{7} +2.46837 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.776205 + 1.34443i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.204988 + 0.355049i) q^{4} -1.55241 q^{6} +(2.60214 - 0.478401i) q^{7} +2.46837 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.21538 + 3.83715i) q^{11} +(-0.204988 - 0.355049i) q^{12} +1.73246 q^{13} +(2.66297 + 3.12705i) q^{14} +(2.32594 + 4.02864i) q^{16} +(1.36623 - 2.36638i) q^{17} +(0.776205 - 1.34443i) q^{18} +(0.152578 + 0.264273i) q^{19} +(-0.886763 + 2.49272i) q^{21} -6.87834 q^{22} +(3.51212 + 6.08316i) q^{23} +(-1.23418 + 2.13767i) q^{24} +(1.34474 + 2.32916i) q^{26} +1.00000 q^{27} +(-0.363551 + 1.02195i) q^{28} -7.79430 q^{29} +(2.64243 - 4.57683i) q^{31} +(-1.14243 + 1.97875i) q^{32} +(-2.21538 - 3.83715i) q^{33} +4.24190 q^{34} +0.409975 q^{36} +(1.83703 + 3.18183i) q^{37} +(-0.236864 + 0.410260i) q^{38} +(-0.866230 + 1.50035i) q^{39} -6.71562 q^{41} +(-4.03959 + 0.742674i) q^{42} -9.71562 q^{43} +(-0.908250 - 1.57313i) q^{44} +(-5.45224 + 9.44356i) q^{46} +(-0.908250 - 1.57313i) q^{47} -4.65187 q^{48} +(6.54227 - 2.48973i) q^{49} +(1.36623 + 2.36638i) q^{51} +(-0.355133 + 0.615108i) q^{52} +(0.857566 - 1.48535i) q^{53} +(0.776205 + 1.34443i) q^{54} +(6.42304 - 1.18087i) q^{56} -0.305156 q^{57} +(-6.04998 - 10.4789i) q^{58} +(0.571217 - 0.989377i) q^{59} +(-4.77818 - 8.27604i) q^{61} +8.20428 q^{62} +(-1.71538 - 2.01432i) q^{63} +5.75669 q^{64} +(3.43917 - 5.95682i) q^{66} +(4.19216 - 7.26104i) q^{67} +(0.560120 + 0.970157i) q^{68} -7.02423 q^{69} +10.2888 q^{71} +(-1.23418 - 2.13767i) q^{72} +(6.41022 - 11.1028i) q^{73} +(-2.85183 + 4.93951i) q^{74} -0.125106 q^{76} +(-3.92903 + 11.0446i) q^{77} -2.68949 q^{78} +(-3.35686 - 5.81425i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-5.21270 - 9.02866i) q^{82} +5.09946 q^{83} +(-0.703262 - 0.825821i) q^{84} +(-7.54131 - 13.0619i) q^{86} +(3.89715 - 6.75007i) q^{87} +(-5.46837 + 9.47149i) q^{88} +(-2.03533 - 3.52529i) q^{89} +(4.50810 - 0.828810i) q^{91} -2.87976 q^{92} +(2.64243 + 4.57683i) q^{93} +(1.40998 - 2.44215i) q^{94} +(-1.14243 - 1.97875i) q^{96} -2.87834 q^{97} +(8.42540 + 6.86305i) q^{98} +4.43075 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 $

$2$	0.776205	+	1.34443i	0.548860	+	0.950653i	0.998353	+	0.0573691i	$0.0182712\pi$
$2$	0.776205	+	1.34443i	0.548860	+	0.950653i	−0.449493	+	0.893284i	$0.648395\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.204988	+	0.355049i	−0.102494	+	0.177524i
$5$		0			0
$5$		0			0
$6$	−1.55241			−0.633769
$7$	2.60214	−	0.478401i	0.983516	−	0.180818i
$7$	2.60214	−	0.478401i	0.983516	−	0.180818i
$8$	2.46837			0.872700
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−2.21538	+	3.83715i	−0.667961	+	1.15694i	0.310512	+	0.950569i	$0.399500\pi$
$11$	−2.21538	+	3.83715i	−0.667961	+	1.15694i	−0.978473	+	0.206373i	$0.933834\pi$
$12$	−0.204988	−	0.355049i	−0.0591748	−	0.102494i
$13$	1.73246			0.480498			0.240249	−	0.970711i	$-0.422771\pi$
$13$	1.73246			0.480498			0.240249	+	0.970711i	$0.422771\pi$
$14$	2.66297	+	3.12705i	0.711708	+	0.835739i
$15$		0			0
$16$	2.32594	+	4.02864i	0.581484	+	1.00716i
$17$	1.36623	−	2.36638i	0.331359	−	0.573931i	−0.651419	−	0.758718i	$-0.725826\pi$
$17$	1.36623	−	2.36638i	0.331359	−	0.573931i	0.982779	+	0.184787i	$0.0591594\pi$
$18$	0.776205	−	1.34443i	0.182953	−	0.316884i
$19$	0.152578	+	0.264273i	0.0350038	+	0.0606284i	0.882997	−	0.469379i	$-0.155522\pi$
$19$	0.152578	+	0.264273i	0.0350038	+	0.0606284i	−0.847993	+	0.530008i	$0.822189\pi$
$20$		0			0
$21$	−0.886763	+	2.49272i	−0.193508	+	0.543956i
$22$	−6.87834			−1.46647
$23$	3.51212	+	6.08316i	0.732327	+	1.26843i	0.955886	+	0.293737i	$0.0948989\pi$
$23$	3.51212	+	6.08316i	0.732327	+	1.26843i	−0.223560	+	0.974690i	$0.571768\pi$
$24$	−1.23418	+	2.13767i	−0.251927	+	0.436350i
$25$		0			0
$26$	1.34474	+	2.32916i	0.263726	+	0.456786i
$27$	1.00000			0.192450
$28$	−0.363551	+	1.02195i	−0.0687046	+	0.193131i
$29$	−7.79430			−1.44737			−0.723683	−	0.690132i	$-0.757552\pi$
$29$	−7.79430			−1.44737			−0.723683	+	0.690132i	$0.757552\pi$
$30$		0			0
$31$	2.64243	−	4.57683i	0.474595	−	0.822023i	−0.524982	−	0.851114i	$-0.675928\pi$
$31$	2.64243	−	4.57683i	0.474595	−	0.822023i	0.999577	+	0.0290906i	$0.00926112\pi$
$32$	−1.14243	+	1.97875i	−0.201956	+	0.349798i
$33$	−2.21538	−	3.83715i	−0.385648	−	0.667961i
$34$	4.24190			0.727479
$35$		0			0
$36$	0.409975			0.0683292
$37$	1.83703	+	3.18183i	0.302006	+	0.523090i	0.976590	−	0.215108i	$-0.0690103\pi$
$37$	1.83703	+	3.18183i	0.302006	+	0.523090i	−0.674584	+	0.738198i	$0.735677\pi$
$38$	−0.236864	+	0.410260i	−0.0384244	+	0.0665530i
$39$	−0.866230	+	1.50035i	−0.138708	+	0.240249i
$40$		0			0
$41$	−6.71562			−1.04880			−0.524402	−	0.851471i	$-0.675711\pi$
$41$	−6.71562			−1.04880			−0.524402	+	0.851471i	$0.675711\pi$
$42$	−4.03959	+	0.742674i	−0.623322	+	0.114597i
$43$	−9.71562			−1.48162			−0.740809	−	0.671715i	$-0.765558\pi$
$43$	−9.71562			−1.48162			−0.740809	+	0.671715i	$0.765558\pi$
$44$	−0.908250	−	1.57313i	−0.136924	−	0.237159i
$45$		0			0
$46$	−5.45224	+	9.44356i	−0.803889	+	1.39238i
$47$	−0.908250	−	1.57313i	−0.132482	−	0.229465i	0.792151	−	0.610325i	$-0.208961\pi$
$47$	−0.908250	−	1.57313i	−0.132482	−	0.229465i	−0.924633	+	0.380860i	$0.875628\pi$
$48$	−4.65187			−0.671440
$49$	6.54227	−	2.48973i	0.934609	−	0.355676i
$50$		0			0
$51$	1.36623	+	2.36638i	0.191310	+	0.331359i
$52$	−0.355133	+	0.615108i	−0.0492480	+	0.0853001i
$53$	0.857566	−	1.48535i	0.117796	−	0.204028i	−0.801098	−	0.598533i	$-0.795751\pi$
$53$	0.857566	−	1.48535i	0.117796	−	0.204028i	0.918894	+	0.394505i	$0.129084\pi$
$54$	0.776205	+	1.34443i	0.105628	+	0.182953i
$55$		0			0
$56$	6.42304	−	1.18087i	0.858315	−	0.157800i
$57$	−0.305156			−0.0404189
$58$	−6.04998	−	10.4789i	−0.794401	−	1.37594i
$59$	0.571217	−	0.989377i	0.0743661	−	0.128806i	−0.826444	−	0.563018i	$-0.809640\pi$
$59$	0.571217	−	0.989377i	0.0743661	−	0.128806i	0.900810	+	0.434213i	$0.142973\pi$
$60$		0			0
$61$	−4.77818	−	8.27604i	−0.611783	−	1.05964i	−0.990940	−	0.134307i	$-0.957119\pi$
$61$	−4.77818	−	8.27604i	−0.611783	−	1.05964i	0.379157	−	0.925332i	$-0.376214\pi$
$62$	8.20428			1.04194
$63$	−1.71538	−	2.01432i	−0.216117	−	0.253780i
$64$	5.75669			0.719586
$65$		0			0
$66$	3.43917	−	5.95682i	0.423333	−	0.733234i
$67$	4.19216	−	7.26104i	0.512154	−	0.887078i	−0.487746	−	0.872985i	$-0.662181\pi$
$67$	4.19216	−	7.26104i	0.512154	−	0.887078i	0.999901	−	0.0140921i	$-0.00448580\pi$
$68$	0.560120	+	0.970157i	0.0679245	+	0.117649i
$69$	−7.02423			−0.845618
$70$		0			0
$71$	10.2888			1.22106			0.610529	−	0.791994i	$-0.290957\pi$
$71$	10.2888			1.22106			0.610529	+	0.791994i	$0.290957\pi$
$72$	−1.23418	−	2.13767i	−0.145450	−	0.251927i
$73$	6.41022	−	11.1028i	0.750260	−	1.29949i	−0.197437	−	0.980316i	$-0.563262\pi$
$73$	6.41022	−	11.1028i	0.750260	−	1.29949i	0.947697	−	0.319172i	$-0.103405\pi$
$74$	−2.85183	+	4.93951i	−0.331518	+	0.574206i
$75$		0			0
$76$	−0.125106			−0.0143507
$77$	−3.92903	+	11.0446i	−0.447754	+	1.25865i
$78$	−2.68949			−0.304524
$79$	−3.35686	−	5.81425i	−0.377676	−	0.654154i	0.613048	−	0.790046i	$-0.289943\pi$
$79$	−3.35686	−	5.81425i	−0.377676	−	0.654154i	−0.990724	+	0.135892i	$0.956610\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−5.21270	−	9.02866i	−0.575646	−	0.997049i
$83$	5.09946			0.559739			0.279869	−	0.960038i	$-0.409709\pi$
$83$	5.09946			0.559739			0.279869	+	0.960038i	$0.409709\pi$
$84$	−0.703262	−	0.825821i	−0.0767322	−	0.0901044i
$85$		0			0
$86$	−7.54131	−	13.0619i	−0.813201	−	1.40850i
$87$	3.89715	−	6.75007i	0.417819	−	0.723683i
$88$	−5.46837	+	9.47149i	−0.582930	+	1.00966i
$89$	−2.03533	−	3.52529i	−0.215744	−	0.373680i	0.737758	−	0.675065i	$-0.235884\pi$
$89$	−2.03533	−	3.52529i	−0.215744	−	0.373680i	−0.953503	+	0.301385i	$0.902551\pi$
$90$		0			0
$91$	4.50810	−	0.828810i	0.472577	−	0.0868829i
$92$	−2.87976			−0.300236
$93$	2.64243	+	4.57683i	0.274008	+	0.474595i
$94$	1.40998	−	2.44215i	0.145428	−	0.251888i
$95$		0			0
$96$	−1.14243	−	1.97875i	−0.116599	−	0.201956i
$97$	−2.87834			−0.292252			−0.146126	−	0.989266i	$-0.546680\pi$
$97$	−2.87834			−0.292252			−0.146126	+	0.989266i	$0.546680\pi$
$98$	8.42540	+	6.86305i	0.851094	+	0.693273i
$99$	4.43075			0.445308
$100$		0			0
$101$	−3.60883	+	6.25068i	−0.359092	+	0.621966i	−0.987809	−	0.155668i	$-0.950247\pi$
$101$	−3.60883	+	6.25068i	−0.359092	+	0.621966i	0.628717	+	0.777634i	$0.283580\pi$
$102$	−2.12095	+	3.67359i	−0.210005	+	0.363740i
$103$	5.63670	+	9.76304i	0.555400	+	0.961981i	0.997872	+	0.0651989i	$0.0207682\pi$
$103$	5.63670	+	9.76304i	0.555400	+	0.961981i	−0.442472	+	0.896782i	$0.645898\pi$
$104$	4.27635			0.419331
$105$		0			0
$106$	2.66259			0.258613
$107$	3.45798	+	5.98940i	0.334296	+	0.579017i	0.983349	−	0.181726i	$-0.0581683\pi$
$107$	3.45798	+	5.98940i	0.334296	+	0.579017i	−0.649054	+	0.760743i	$0.724835\pi$
$108$	−0.204988	+	0.355049i	−0.0197249	+	0.0341646i
$109$	−2.21097	+	3.82952i	−0.211773	+	0.366801i	−0.952269	−	0.305259i	$-0.901257\pi$
$109$	−2.21097	+	3.82952i	−0.211773	+	0.366801i	0.740497	+	0.672060i	$0.234590\pi$
$110$		0			0
$111$	−3.67406			−0.348727
$112$	7.97971	+	9.37035i	0.754012	+	0.885415i
$113$	2.86151			0.269188			0.134594	−	0.990901i	$-0.457027\pi$
$113$	2.86151			0.269188			0.134594	+	0.990901i	$0.457027\pi$
$114$	−0.236864	−	0.410260i	−0.0221843	−	0.0384244i
$115$		0			0
$116$	1.59774	−	2.76736i	0.148346	−	0.256943i
$117$	−0.866230	−	1.50035i	−0.0800830	−	0.138708i
$118$	1.77353			0.163266
$119$	2.42304	−	6.81125i	0.222120	−	0.624387i
$120$		0			0
$121$	−4.31579	−	7.47517i	−0.392345	−	0.679561i
$122$	7.41769	−	12.8478i	0.671566	−	1.16319i
$123$	3.35781	−	5.81590i	0.302764	−	0.524402i
$124$	1.08333	+	1.87639i	0.0972861	+	0.168504i
$125$		0			0
$126$	1.37662	−	3.86972i	0.122639	−	0.344742i
$127$	−13.7325			−1.21856			−0.609279	−	0.792956i	$-0.708541\pi$
$127$	−13.7325			−1.21856			−0.609279	+	0.792956i	$0.708541\pi$
$128$	6.75324	+	11.6970i	0.596908	+	1.03387i
$129$	4.85781	−	8.41398i	0.427706	−	0.740809i
$130$		0			0
$131$	−10.9909	−	19.0368i	−0.960277	−	1.66325i	−0.721801	−	0.692100i	$-0.756686\pi$
$131$	−10.9909	−	19.0368i	−0.960277	−	1.66325i	−0.238476	−	0.971148i	$-0.576648\pi$
$132$	1.81650			0.158106
$133$	0.523458	+	0.614682i	0.0453896	+	0.0532997i
$134$	13.0159			1.12440
$135$		0			0
$136$	3.37236	−	5.84110i	0.289177	−	0.500870i
$137$	1.50095	−	2.59973i	0.128235	−	0.222110i	−0.794758	−	0.606927i	$-0.792402\pi$
$137$	1.50095	−	2.59973i	0.128235	−	0.222110i	0.922993	+	0.384817i	$0.125735\pi$
$138$	−5.45224	−	9.44356i	−0.464126	−	0.803889i
$139$	−21.7364			−1.84366			−0.921829	−	0.387597i	$-0.873305\pi$
$139$	−21.7364			−1.84366			−0.921829	+	0.387597i	$0.873305\pi$
$140$		0			0
$141$	1.81650			0.152977
$142$	7.98622	+	13.8325i	0.670189	+	1.16080i
$143$	−3.83805	+	6.64770i	−0.320954	+	0.555908i
$144$	2.32594	−	4.02864i	0.193828	−	0.335720i
$145$		0			0
$146$	19.9026			1.64715
$147$	−1.11496	+	6.91063i	−0.0919606	+	0.569979i
$148$	−1.50628			−0.123815
$149$	2.60654	+	4.51467i	0.213536	+	0.369856i	0.952819	−	0.303540i	$-0.0981685\pi$
$149$	2.60654	+	4.51467i	0.213536	+	0.369856i	−0.739282	+	0.673396i	$0.764835\pi$
$150$		0			0
$151$	4.85686	−	8.41233i	0.395246	−	0.684585i	−0.597887	−	0.801580i	$-0.703993\pi$
$151$	4.85686	−	8.41233i	0.395246	−	0.684585i	0.993132	+	0.116995i	$0.0373262\pi$
$152$	0.376619	+	0.652324i	0.0305478	+	0.0529104i
$153$	−2.73246			−0.220906
$154$	−17.8984	+	3.29060i	−1.44230	+	0.265164i
$155$		0			0
$156$	−0.355133	−	0.615108i	−0.0284334	−	0.0492480i
$157$	4.73591	−	8.20284i	0.377967	−	0.654658i	−0.612800	−	0.790238i	$-0.709957\pi$
$157$	4.73591	−	8.20284i	0.377967	−	0.654658i	0.990766	+	0.135581i	$0.0432900\pi$
$158$	5.21122	−	9.02610i	0.414582	−	0.718078i
$159$	0.857566	+	1.48535i	0.0680094	+	0.117796i
$160$		0			0
$161$	12.0492	+	14.1490i	0.949610	+	1.11510i
$162$	−1.55241			−0.121969
$163$	−2.69830	−	4.67358i	−0.211347	−	0.366063i	0.740789	−	0.671737i	$-0.234452\pi$
$163$	−2.69830	−	4.67358i	−0.211347	−	0.366063i	−0.952136	+	0.305674i	$0.901118\pi$
$164$	1.37662	−	2.38437i	0.107496	−	0.186188i
$165$		0			0
$166$	3.95823	+	6.85585i	0.307218	+	0.532117i
$167$	−0.312550			−0.0241859			−0.0120929	−	0.999927i	$-0.503849\pi$
$167$	−0.312550			−0.0241859			−0.0120929	+	0.999927i	$0.503849\pi$
$168$	−2.18886	+	6.15295i	−0.168874	+	0.474711i
$169$	−9.99859			−0.769122
$170$		0			0
$171$	0.152578	−	0.264273i	0.0116679	−	0.0202095i
$172$	1.99158	−	3.44952i	0.151857	−	0.263024i
$173$	−4.80737	−	8.32661i	−0.365498	−	0.633061i	0.623358	−	0.781937i	$-0.285768\pi$
$173$	−4.80737	−	8.32661i	−0.365498	−	0.633061i	−0.988856	+	0.148876i	$0.952435\pi$
$174$	12.1000			0.917295
$175$		0			0
$176$	−20.6113			−1.55363
$177$	0.571217	+	0.989377i	0.0429353	+	0.0743661i
$178$	3.15966	−	5.47269i	0.236827	−	0.410196i
$179$	4.42730	−	7.66831i	0.330912	−	0.573157i	−0.651779	−	0.758409i	$-0.725977\pi$
$179$	4.42730	−	7.66831i	0.330912	−	0.573157i	0.982691	+	0.185252i	$0.0593103\pi$
$180$		0			0
$181$	−16.9234			−1.25790			−0.628952	−	0.777445i	$-0.716516\pi$
$181$	−16.9234			−1.25790			−0.628952	+	0.777445i	$0.716516\pi$
$182$	4.61348	+	5.41748i	0.341974	+	0.401571i
$183$	9.55635			0.706426
$184$	8.66920	+	15.0155i	0.639102	+	1.10696i
$185$		0			0
$186$	−4.10214	+	7.10511i	−0.300784	+	0.520972i
$187$	6.05343	+	10.4848i	0.442670	+	0.766728i
$188$	0.744719			0.0543142
$189$	2.60214	−	0.478401i	0.189278	−	0.0347985i
$190$		0			0
$191$	−0.159271	−	0.275865i	−0.0115244	−	0.0199609i	0.860206	−	0.509947i	$-0.170335\pi$
$191$	−0.159271	−	0.275865i	−0.0115244	−	0.0199609i	−0.871730	+	0.489986i	$0.837002\pi$
$192$	−2.87834	+	4.98544i	−0.207727	+	0.359793i
$193$	−1.04667	+	1.81289i	−0.0753410	+	0.130494i	−0.901234	−	0.433332i	$-0.857338\pi$
$193$	−1.04667	+	1.81289i	−0.0753410	+	0.130494i	0.825894	+	0.563826i	$0.190671\pi$
$194$	−2.23418	−	3.86972i	−0.160405	−	0.277830i
$195$		0			0
$196$	−0.457107	+	2.83319i	−0.0326505	+	0.202371i
$197$	−22.5798			−1.60874			−0.804372	−	0.594126i	$-0.797498\pi$
$197$	−22.5798			−1.60874			−0.804372	+	0.594126i	$0.797498\pi$
$198$	3.43917	+	5.95682i	0.244411	+	0.423333i
$199$	3.75204	−	6.49872i	0.265975	−	0.460682i	−0.701844	−	0.712331i	$-0.747639\pi$
$199$	3.75204	−	6.49872i	0.265975	−	0.460682i	0.967819	+	0.251649i	$0.0809728\pi$
$200$		0			0
$201$	4.19216	+	7.26104i	0.295693	+	0.512154i
$202$	−11.2048			−0.788365
$203$	−20.2819	+	3.72880i	−1.42351	+	0.261710i
$204$	−1.12024			−0.0784325
$205$		0			0
$206$	−8.75046	+	15.1562i	−0.609673	+	1.05599i
$207$	3.51212	−	6.08316i	0.244109	−	0.422809i
$208$	4.02959	+	6.97945i	0.279402	+	0.483938i
$209$	−1.35207			−0.0935248
$210$		0			0
$211$	7.67216			0.528173			0.264087	−	0.964499i	$-0.414930\pi$
$211$	7.67216			0.528173			0.264087	+	0.964499i	$0.414930\pi$
$212$	0.351581	+	0.608955i	0.0241467	+	0.0418232i
$213$	−5.14441	+	8.91037i	−0.352489	+	0.610529i
$214$	−5.36820	+	9.29800i	−0.366963	+	0.635598i
$215$		0			0
$216$	2.46837			0.167951
$217$	4.68643	−	13.1737i	0.318135	−	0.894289i
$218$	−6.86467			−0.464934
$219$	6.41022	+	11.1028i	0.433163	+	0.750260i
$220$		0			0
$221$	2.36694	−	4.09966i	0.159217	−	0.275773i
$222$	−2.85183	−	4.93951i	−0.191402	−	0.331518i
$223$	6.90208			0.462198			0.231099	−	0.972930i	$-0.425768\pi$
$223$	6.90208			0.462198			0.231099	+	0.972930i	$0.425768\pi$
$224$	−2.02614	+	5.69554i	−0.135377	+	0.380549i
$225$		0			0
$226$	2.22112	+	3.84709i	0.147746	+	0.255904i
$227$	−3.17360	+	5.49684i	−0.210639	+	0.364838i	−0.951915	−	0.306363i	$-0.900888\pi$
$227$	−3.17360	+	5.49684i	−0.210639	+	0.364838i	0.741275	+	0.671201i	$0.234221\pi$
$228$	0.0625532	−	0.108345i	0.00414269	−	0.00717535i
$229$	−3.37834	−	5.85146i	−0.223247	−	0.386676i	0.732545	−	0.680719i	$-0.238332\pi$
$229$	−3.37834	−	5.85146i	−0.223247	−	0.386676i	−0.955792	+	0.294043i	$0.904999\pi$
$230$		0			0
$231$	−7.60041	−	8.92495i	−0.500071	−	0.587219i
$232$	−19.2392			−1.26312
$233$	−3.70601	−	6.41899i	−0.242789	−	0.420522i	0.718719	−	0.695301i	$-0.244729\pi$
$233$	−3.70601	−	6.41899i	−0.242789	−	0.420522i	−0.961508	+	0.274779i	$0.911395\pi$
$234$	1.34474	−	2.32916i	0.0879086	−	0.152262i
$235$		0			0
$236$	0.234185	+	0.405620i	0.0152441	+	0.0264036i
$237$	6.71372			0.436103
$238$	11.0380	−	2.02933i	0.715488	−	0.131542i
$239$	7.36355			0.476309			0.238154	−	0.971227i	$-0.423458\pi$
$239$	7.36355			0.476309			0.238154	+	0.971227i	$0.423458\pi$
$240$		0			0
$241$	−6.84002	+	11.8473i	−0.440605	+	0.763149i	−0.997734	−	0.0672759i	$-0.978569\pi$
$241$	−6.84002	+	11.8473i	−0.440605	+	0.763149i	0.557130	+	0.830425i	$0.311903\pi$
$242$	6.69988	−	11.6045i	0.430684	−	0.745967i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	3.91787			0.250816
$245$		0			0
$246$	10.4254			0.664699
$247$	0.264335	+	0.457842i	0.0168193	+	0.0291318i
$248$	6.52250	−	11.2973i	0.414179	−	0.717380i
$249$	−2.54973	+	4.41626i	−0.161583	+	0.279869i
$250$		0			0
$251$	23.4843			1.48231			0.741157	−	0.671331i	$-0.234277\pi$
$251$	23.4843			1.48231			0.741157	+	0.671331i	$0.234277\pi$
$252$	1.06681	−	0.196132i	0.0672029	−	0.0123552i
$253$	−31.1226			−1.95666
$254$	−10.6592	−	18.4623i	−0.668818	−	1.15843i
$255$		0			0
$256$	−4.72710	+	8.18758i	−0.295444	+	0.511724i
$257$	−7.29871	−	12.6417i	−0.455281	−	0.788570i	0.543423	−	0.839459i	$-0.317128\pi$
$257$	−7.29871	−	12.6417i	−0.455281	−	0.788570i	−0.998704	+	0.0508890i	$0.983795\pi$
$258$	15.0826			0.939003
$259$	6.30241	+	7.40074i	0.391612	+	0.459860i
$260$		0			0
$261$	3.89715	+	6.75007i	0.241228	+	0.417819i
$262$	17.0623	−	29.5528i	1.05411	−	1.82578i
$263$	2.54470	−	4.40755i	0.156913	−	0.271781i	−0.776841	−	0.629697i	$-0.783179\pi$
$263$	2.54470	−	4.40755i	0.156913	−	0.271781i	0.933754	+	0.357916i	$0.116512\pi$
$264$	−5.46837	−	9.47149i	−0.336555	−	0.582930i
$265$		0			0
$266$	−0.420084	+	1.18087i	−0.0257570	+	0.0724038i
$267$	4.07065			0.249120
$268$	1.71868	+	2.97685i	0.104985	+	0.181840i
$269$	−15.2550	+	26.4224i	−0.930112	+	1.61100i	−0.146984	+	0.989139i	$0.546957\pi$
$269$	−15.2550	+	26.4224i	−0.930112	+	1.61100i	−0.783127	+	0.621862i	$0.786377\pi$
$270$		0			0
$271$	9.74401	+	16.8771i	0.591907	+	1.02521i	0.993975	+	0.109603i	$0.0349579\pi$
$271$	9.74401	+	16.8771i	0.591907	+	1.02521i	−0.402069	+	0.915609i	$0.631709\pi$
$272$	12.7110			0.770720
$273$	−1.53628	+	4.31854i	−0.0929799	+	0.261370i
$274$	4.66019			0.281532
$275$		0			0
$276$	1.43988	−	2.49395i	0.0866706	−	0.150118i
$277$	−12.7401	+	22.0665i	−0.765478	+	1.32585i	0.174515	+	0.984655i	$0.444164\pi$
$277$	−12.7401	+	22.0665i	−0.765478	+	1.32585i	−0.939993	+	0.341193i	$0.889169\pi$
$278$	−16.8719	−	29.2230i	−1.01191	−	1.75268i
$279$	−5.28487			−0.316397
$280$		0			0
$281$	−22.1914			−1.32383			−0.661914	−	0.749580i	$-0.730255\pi$
$281$	−22.1914			−1.32383			−0.661914	+	0.749580i	$0.730255\pi$
$282$	1.40998	+	2.44215i	0.0839628	+	0.145428i
$283$	9.06209	−	15.6960i	0.538685	−	0.933031i	−0.460290	−	0.887769i	$-0.652254\pi$
$283$	9.06209	−	15.6960i	0.538685	−	0.933031i	0.998975	−	0.0452618i	$-0.0144122\pi$
$284$	−2.10908	+	3.65303i	−0.125151	+	0.216768i
$285$		0			0
$286$	−11.9165			−0.704635
$287$	−17.4750	+	3.21276i	−1.03152	+	0.189643i
$288$	2.28487			0.134637
$289$	4.76683	+	8.25640i	0.280402	+	0.485670i
$290$		0			0
$291$	1.43917	−	2.49272i	0.0843658	−	0.146126i
$292$	2.62803	+	4.55188i	0.153794	+	0.266379i
$293$	−13.8958			−0.811801			−0.405901	−	0.913917i	$-0.633042\pi$
$293$	−13.8958			−0.811801			−0.405901	+	0.913917i	$0.633042\pi$
$294$	−10.1563	+	3.86508i	−0.592326	+	0.225416i
$295$		0			0
$296$	4.53447	+	7.85394i	0.263561	+	0.456501i
$297$	−2.21538	+	3.83715i	−0.128549	+	0.222654i
$298$	−4.04642	+	7.00861i	−0.234403	+	0.405998i
$299$	6.08460	+	10.5388i	0.351881	+	0.609476i
$300$		0			0
$301$	−25.2814	+	4.64796i	−1.45720	+	0.267904i
$302$	15.0797			0.867737
$303$	−3.60883	−	6.25068i	−0.207322	−	0.359092i
$304$	−0.709774	+	1.22936i	−0.0407083	+	0.0705089i
$305$		0			0
$306$	−2.12095	−	3.67359i	−0.121247	−	0.210005i
$307$	29.8332			1.70267			0.851335	−	0.524622i	$-0.175793\pi$
$307$	29.8332			1.70267			0.851335	+	0.524622i	$0.175793\pi$
$308$	−3.11598	−	3.65901i	−0.177549	−	0.208491i
$309$	−11.2734			−0.641321
$310$		0			0
$311$	−6.75662	+	11.7028i	−0.383133	+	0.663606i	−0.991508	−	0.130044i	$-0.958488\pi$
$311$	−6.75662	+	11.7028i	−0.383133	+	0.663606i	0.608375	+	0.793650i	$0.291822\pi$
$312$	−2.13817	+	3.70343i	−0.121050	+	0.209665i
$313$	14.4928	+	25.1023i	0.819184	+	1.41887i	0.906284	+	0.422669i	$0.138907\pi$
$313$	14.4928	+	25.1023i	0.819184	+	1.41887i	−0.0871001	+	0.996200i	$0.527760\pi$
$314$	14.7041			0.829803
$315$		0			0
$316$	2.75246			0.154838
$317$	−0.579319	−	1.00341i	−0.0325378	−	0.0563571i	0.849298	−	0.527914i	$-0.177026\pi$
$317$	−0.579319	−	1.00341i	−0.0325378	−	0.0563571i	−0.881836	+	0.471557i	$0.843692\pi$
$318$	−1.33129	+	2.30587i	−0.0746552	+	0.129307i
$319$	17.2673	−	29.9079i	0.966785	−	1.67452i
$320$		0			0
$321$	−6.91596			−0.386011
$322$	−9.66969	+	27.1818i	−0.538871	+	1.51478i
$323$	0.833827			0.0463954
$324$	−0.204988	−	0.355049i	−0.0113882	−	0.0197249i
$325$		0			0
$326$	4.18886	−	7.25532i	0.231999	−	0.401835i
$327$	−2.21097	−	3.82952i	−0.122267	−	0.211773i
$328$	−16.5766			−0.915292
$329$	−3.11598	−	3.65901i	−0.171790	−	0.201728i
$330$		0			0
$331$	14.1746	+	24.5511i	0.779104	+	1.34945i	0.932459	+	0.361277i	$0.117659\pi$
$331$	14.1746	+	24.5511i	0.779104	+	1.34945i	−0.153355	+	0.988171i	$0.549008\pi$
$332$	−1.04533	+	1.81056i	−0.0573697	+	0.0993673i
$333$	1.83703	−	3.18183i	0.100669	−	0.174363i
$334$	−0.242603	−	0.420201i	−0.0132746	−	0.0229924i
$335$		0			0
$336$	−12.1048	+	2.22546i	−0.660372	+	0.121409i
$337$	15.9729			0.870101			0.435051	−	0.900406i	$-0.356730\pi$
$337$	15.9729			0.870101			0.435051	+	0.900406i	$0.356730\pi$
$338$	−7.76095	−	13.4424i	−0.422140	−	0.731168i
$339$	−1.43075	+	2.47814i	−0.0777079	+	0.134594i
$340$		0			0
$341$	11.7080	+	20.2788i	0.634023	+	1.09816i
$342$	0.473727			0.0256162
$343$	15.8328	−	9.60845i	0.854891	−	0.518808i
$344$	−23.9817			−1.29301
$345$		0			0
$346$	7.46301	−	12.9263i	0.401214	−	0.694923i
$347$	−6.50599	+	11.2687i	−0.349260	+	0.604935i	−0.986118	−	0.166045i	$-0.946900\pi$
$347$	−6.50599	+	11.2687i	−0.349260	+	0.604935i	0.636859	+	0.770981i	$0.280234\pi$
$348$	1.59774	+	2.76736i	0.0856476	+	0.148346i
$349$	32.0724			1.71680			0.858398	−	0.512984i	$-0.171460\pi$
$349$	32.0724			1.71680			0.858398	+	0.512984i	$0.171460\pi$
$350$		0			0
$351$	1.73246			0.0924718
$352$	−5.06185	−	8.76737i	−0.269797	−	0.467303i
$353$	−6.68445	+	11.5778i	−0.355778	+	0.616225i	−0.987251	−	0.159173i	$-0.949117\pi$
$353$	−6.68445	+	11.5778i	−0.355778	+	0.616225i	0.631473	+	0.775398i	$0.282451\pi$
$354$	−0.886763	+	1.53592i	−0.0471309	+	0.0816331i
$355$		0			0
$356$	1.66887			0.0884498
$357$	4.68720	+	5.50404i	0.248073	+	0.291305i
$358$	13.7460			0.726497
$359$	6.55974	+	11.3618i	0.346210	+	0.599653i	0.985573	−	0.169252i	$-0.0541352\pi$
$359$	6.55974	+	11.3618i	0.346210	+	0.599653i	−0.639363	+	0.768905i	$0.720802\pi$
$360$		0			0
$361$	9.45344	−	16.3738i	0.497549	−	0.861781i
$362$	−13.1360	−	22.7522i	−0.690412	−	1.19583i
$363$	8.63158			0.453041
$364$	−0.629837	+	1.77049i	−0.0330124	+	0.0927990i
$365$		0			0
$366$	7.41769	+	12.8478i	0.387729	+	0.671566i
$367$	−6.56798	+	11.3761i	−0.342846	+	0.593826i	−0.984960	−	0.172783i	$-0.944724\pi$
$367$	−6.56798	+	11.3761i	−0.342846	+	0.593826i	0.642114	+	0.766609i	$0.278057\pi$
$368$	−16.3379	+	28.2981i	−0.851672	+	1.47514i
$369$	3.35781	+	5.81590i	0.174801	+	0.302764i
$370$		0			0
$371$	1.52091	−	4.27534i	0.0789620	−	0.221965i
$372$	−2.16666			−0.112336
$373$	14.8099	+	25.6514i	0.766826	+	1.32818i	0.939276	+	0.343163i	$0.111498\pi$
$373$	14.8099	+	25.6514i	0.766826	+	1.32818i	−0.172450	+	0.985018i	$0.555168\pi$
$374$	−9.39740	+	16.2768i	−0.485928	+	0.841652i
$375$		0			0
$376$	−2.24190	−	3.88308i	−0.115617	−	0.200254i
$377$	−13.5033			−0.695456
$378$	2.66297	+	3.12705i	0.136968	+	0.160838i
$379$	7.47689			0.384062			0.192031	−	0.981389i	$-0.438493\pi$
$379$	7.47689			0.384062			0.192031	+	0.981389i	$0.438493\pi$
$380$		0			0
$381$	6.86623	−	11.8927i	0.351768	−	0.609279i
$382$	0.247253	−	0.428255i	0.0126506	−	0.0219114i
$383$	11.8695	+	20.5586i	0.606505	+	1.05050i	0.991812	+	0.127709i	$0.0407623\pi$
$383$	11.8695	+	20.5586i	0.606505	+	1.05050i	−0.385307	+	0.922789i	$0.625904\pi$
$384$	−13.5065			−0.689250
$385$		0			0
$386$	−3.24972			−0.165406
$387$	4.85781	+	8.41398i	0.246936	+	0.427706i
$388$	0.590025	−	1.02195i	0.0299540	−	0.0518818i
$389$	7.06523	−	12.2373i	0.358221	−	0.620458i	−0.629442	−	0.777047i	$-0.716717\pi$
$389$	7.06523	−	12.2373i	0.358221	−	0.620458i	0.987664	+	0.156589i	$0.0500499\pi$
$390$		0			0
$391$	19.1934			0.970653
$392$	16.1487	−	6.14558i	0.815634	−	0.310398i
$393$	21.9817			1.10883
$394$	−17.5265	−	30.3569i	−0.882975	−	1.52936i
$395$		0			0
$396$	−0.908250	+	1.57313i	−0.0456413	+	0.0790530i
$397$	−5.63479	−	9.75974i	−0.282802	−	0.489827i	0.689272	−	0.724503i	$-0.257931\pi$
$397$	−5.63479	−	9.75974i	−0.282802	−	0.489827i	−0.972074	+	0.234676i	$0.924597\pi$
$398$	11.6494			0.583932
$399$	−0.794059	+	0.145987i	−0.0397527	+	0.00730849i
$400$		0			0
$401$	−11.6484	−	20.1757i	−0.581694	−	1.00752i	−0.995279	−	0.0970583i	$-0.969057\pi$
$401$	−11.6484	−	20.1757i	−0.581694	−	1.00752i	0.413584	−	0.910466i	$-0.364277\pi$
$402$	−6.50796	+	11.2721i	−0.324587	+	0.562202i
$403$	4.57791	−	7.92917i	0.228042	−	0.394980i
$404$	−1.47953	−	2.56262i	−0.0736094	−	0.127495i
$405$		0			0
$406$	−20.7560	−	24.3732i	−1.03010	−	1.20962i
$407$	−16.2789			−0.806914
$408$	3.37236	+	5.84110i	0.166957	+	0.289177i
$409$	−10.3239	+	17.8815i	−0.510484	+	0.884184i	0.489443	+	0.872036i	$0.337200\pi$
$409$	−10.3239	+	17.8815i	−0.510484	+	0.884184i	−0.999926	+	0.0121481i	$0.996133\pi$
$410$		0			0
$411$	1.50095	+	2.59973i	0.0740366	+	0.128235i
$412$	−4.62181			−0.227700
$413$	1.01307	−	2.84777i	0.0498498	−	0.140130i
$414$	10.9045			0.535926
$415$		0			0
$416$	−1.97922	+	3.42811i	−0.0970393	+	0.168077i
$417$	10.8682	−	18.8243i	0.532218	−	0.921829i
$418$	−1.04948	−	1.81776i	−0.0513320	−	0.0889096i
$419$	−5.48254			−0.267839			−0.133920	−	0.990992i	$-0.542756\pi$
$419$	−5.48254			−0.267839			−0.133920	+	0.990992i	$0.542756\pi$
$420$		0			0
$421$	−3.78079			−0.184264			−0.0921322	−	0.995747i	$-0.529368\pi$
$421$	−3.78079			−0.184264			−0.0921322	+	0.995747i	$0.529368\pi$
$422$	5.95517	+	10.3146i	0.289893	+	0.502109i
$423$	−0.908250	+	1.57313i	−0.0441606	+	0.0764884i
$424$	2.11679	−	3.66639i	0.102800	−	0.178055i
$425$		0			0
$426$	−15.9724			−0.773868
$427$	−16.3927	−	19.2495i	−0.793301	−	0.931551i
$428$	−2.83537			−0.137053
$429$	−3.83805	−	6.64770i	−0.185303	−	0.320954i
$430$		0			0
$431$	13.7564	−	23.8267i	0.662621	−	1.14769i	−0.317303	−	0.948324i	$-0.602777\pi$
$431$	13.7564	−	23.8267i	0.662621	−	1.14769i	0.979924	−	0.199369i	$-0.0638894\pi$
$432$	2.32594	+	4.02864i	0.111907	+	0.193828i
$433$	8.75514			0.420745			0.210373	−	0.977621i	$-0.432532\pi$
$433$	8.75514			0.420745			0.210373	+	0.977621i	$0.432532\pi$
$434$	21.3487	−	3.92493i	1.02477	−	0.188403i
$435$		0			0
$436$	−0.906444	−	1.57001i	−0.0434108	−	0.0751897i
$437$	−1.07174	+	1.85631i	−0.0512685	+	0.0887996i
$438$	−9.95129	+	17.2361i	−0.475491	+	0.823574i
$439$	5.30636	+	9.19088i	0.253259	+	0.438657i	0.964421	−	0.264371i	$-0.0851643\pi$
$439$	5.30636	+	9.19088i	0.253259	+	0.438657i	−0.711163	+	0.703028i	$0.751831\pi$
$440$		0			0
$441$	−5.42730	−	4.42090i	−0.258443	−	0.210519i
$442$	7.34891			0.349552
$443$	−9.99278	−	17.3080i	−0.474771	−	0.822328i	0.524811	−	0.851219i	$-0.324136\pi$
$443$	−9.99278	−	17.3080i	−0.474771	−	0.822328i	−0.999583	+	0.0288905i	$0.990803\pi$
$444$	0.753138	−	1.30447i	0.0357423	−	0.0619075i
$445$		0			0
$446$	5.35743	+	9.27934i	0.253682	+	0.439390i
$447$	−5.21309			−0.246571
$448$	14.9797	−	2.75400i	0.707725	−	0.130114i
$449$	3.02578			0.142795			0.0713976	−	0.997448i	$-0.477254\pi$
$449$	3.02578			0.142795			0.0713976	+	0.997448i	$0.477254\pi$
$450$		0			0
$451$	14.8776	−	25.7688i	0.700561	−	1.21341i
$452$	−0.586574	+	1.01598i	−0.0275901	+	0.0477875i
$453$	4.85686	+	8.41233i	0.228195	+	0.395246i
$454$	−9.85346			−0.462446
$455$		0			0
$456$	−0.753238			−0.0352736
$457$	1.14067	+	1.97570i	0.0533584	+	0.0924195i	0.891471	−	0.453078i	$-0.149674\pi$
$457$	1.14067	+	1.97570i	0.0533584	+	0.0924195i	−0.838112	+	0.545497i	$0.816341\pi$
$458$	5.24457	−	9.08387i	0.245063	−	0.424461i
$459$	1.36623	−	2.36638i	0.0637701	−	0.110453i
$460$		0			0
$461$	−24.0678			−1.12095			−0.560475	−	0.828171i	$-0.689381\pi$
$461$	−24.0678			−1.12095			−0.560475	+	0.828171i	$0.689381\pi$
$462$	6.09946	−	17.1458i	0.283773	−	0.797694i
$463$	−11.1290			−0.517211			−0.258605	−	0.965983i	$-0.583263\pi$
$463$	−11.1290			−0.517211			−0.258605	+	0.965983i	$0.583263\pi$
$464$	−18.1290	−	31.4004i	−0.841620	−	1.45773i
$465$		0			0
$466$	5.75324	−	9.96490i	0.266514	−	0.461615i
$467$	14.2883	+	24.7481i	0.661185	+	1.14521i	0.980305	+	0.197491i	$0.0632793\pi$
$467$	14.2883	+	24.7481i	0.661185	+	1.14521i	−0.319120	+	0.947714i	$0.603387\pi$
$468$	0.710265			0.0328320
$469$	7.43491	−	20.8998i	0.343312	−	0.965062i
$470$		0			0
$471$	4.73591	+	8.20284i	0.218219	+	0.377967i
$472$	1.40998	−	2.44215i	0.0648994	−	0.112409i
$473$	21.5238	−	37.2803i	0.989664	−	1.71415i
$474$	5.21122	+	9.02610i	0.239359	+	0.414582i
$475$		0			0
$476$	1.92163	+	2.25652i	0.0880780	+	0.103427i
$477$	−1.71513			−0.0785305
$478$	5.71562	+	9.89975i	0.261427	+	0.452804i
$479$	2.79005	−	4.83250i	0.127480	−	0.220803i	−0.795219	−	0.606322i	$-0.792644\pi$
$479$	2.79005	−	4.83250i	0.127480	−	0.220803i	0.922700	+	0.385519i	$0.125978\pi$
$480$		0			0
$481$	3.18258	+	5.51240i	0.145113	+	0.251344i
$482$	−21.2370			−0.967320
$483$	−18.2780	+	3.36040i	−0.831679	+	0.152903i
$484$	3.53873			0.160852
$485$		0			0
$486$	0.776205	−	1.34443i	0.0352094	−	0.0609844i
$487$	4.17342	−	7.22858i	0.189116	−	0.327558i	−0.755840	−	0.654756i	$-0.772771\pi$
$487$	4.17342	−	7.22858i	0.189116	−	0.327558i	0.944956	+	0.327198i	$0.106105\pi$
$488$	−11.7943	−	20.4283i	−0.533903	−	0.924747i
$489$	5.39659			0.244042
$490$		0			0
$491$	0.557405			0.0251554			0.0125777	−	0.999921i	$-0.495996\pi$
$491$	0.557405			0.0251554			0.0125777	+	0.999921i	$0.495996\pi$
$492$	1.37662	+	2.38437i	0.0620628	+	0.107496i
$493$	−10.6488	+	18.4443i	−0.479598	+	0.830689i
$494$	−0.410357	+	0.710759i	−0.0184628	+	0.0319785i
$495$		0			0
$496$	24.5845			1.10388
$497$	26.7729	−	4.92217i	1.20093	−	0.220790i
$498$	−7.91645			−0.354745
$499$	13.0168	+	22.5458i	0.582713	+	1.00929i	0.995156	+	0.0983057i	$0.0313423\pi$
$499$	13.0168	+	22.5458i	0.582713	+	1.00929i	−0.412443	+	0.910983i	$0.635324\pi$
$500$		0			0
$501$	0.156275	−	0.270676i	0.00698186	−	0.0120929i
$502$	18.2286	+	31.5729i	0.813583	+	1.40917i
$503$	−5.52409			−0.246307			−0.123154	−	0.992388i	$-0.539301\pi$
$503$	−5.52409			−0.246307			−0.123154	+	0.992388i	$0.539301\pi$
$504$	−4.23418	−	4.97208i	−0.188606	−	0.221474i
$505$		0			0
$506$	−24.1575	−	41.8421i	−1.07393	−	1.86011i
$507$	4.99929	−	8.65903i	0.222026	−	0.384561i
$508$	2.81498	−	4.87569i	0.124895	−	0.216324i
$509$	−11.4446	−	19.8227i	−0.507274	−	0.878625i	−0.999965	−	0.00842016i	$-0.997320\pi$
$509$	−11.4446	−	19.8227i	−0.507274	−	0.878625i	0.492690	−	0.870205i	$-0.336014\pi$
$510$		0			0
$511$	11.3687	−	31.9578i	0.502921	−	1.41373i
$512$	12.3362			0.545186
$513$	0.152578	+	0.264273i	0.00673649	+	0.0116679i
$514$	11.3306	−	19.6251i	0.499771	−	0.865628i
$515$		0			0
$516$	1.99158	+	3.44952i	0.0876745	+	0.151857i
$517$	8.04846			0.353971
$518$	−5.05779	+	14.2176i	−0.222226	+	0.624686i
$519$	9.61475			0.422041
$520$		0			0
$521$	−13.0995	+	22.6889i	−0.573898	+	0.994020i	0.422263	+	0.906474i	$0.361236\pi$
$521$	−13.0995	+	22.6889i	−0.573898	+	0.994020i	−0.996160	+	0.0875466i	$0.972097\pi$
$522$	−6.04998	+	10.4789i	−0.264800	+	0.458648i
$523$	−13.4380	−	23.2753i	−0.587603	−	1.01776i	−0.994545	−	0.104304i	$-0.966738\pi$
$523$	−13.4380	−	23.2753i	−0.587603	−	1.01776i	0.406943	−	0.913454i	$-0.366595\pi$
$524$	9.01197			0.393690
$525$		0			0
$526$	7.90083			0.344493
$527$	−7.22034	−	12.5060i	−0.314523	−	0.544770i
$528$	10.3056	−	17.8499i	0.448496	−	0.776817i
$529$	−13.1699	+	22.8109i	−0.572605	+	0.991780i
$530$		0			0
$531$	−1.14243			−0.0495774
$532$	−0.325545	+	0.0598510i	−0.0141141	+	0.00259487i
$533$	−11.6345			−0.503948
$534$	3.15966	+	5.47269i	0.136732	+	0.236827i
$535$		0			0
$536$	10.3478	−	17.9229i	0.446957	−	0.774153i
$537$	4.42730	+	7.66831i	0.191052	+	0.330912i
$538$	−47.3639			−2.04200
$539$	−4.94013	+	30.6193i	−0.212786	+	1.31887i
$540$		0			0
$541$	9.39222	+	16.2678i	0.403803	+	0.699408i	0.994181	−	0.107719i	$-0.0343547\pi$
$541$	9.39222	+	16.2678i	0.403803	+	0.699408i	−0.590378	+	0.807127i	$0.701021\pi$
$542$	−15.1267	+	26.2002i	−0.649747	+	1.12540i
$543$	8.46168	−	14.6561i	0.363125	−	0.628952i
$544$	3.12166	+	5.40687i	0.133840	+	0.231817i
$545$		0			0
$546$	−6.99842	+	1.28665i	−0.299505	+	0.0550636i
$547$	13.4126			0.573483			0.286742	−	0.958008i	$-0.407428\pi$
$547$	13.4126			0.573483			0.286742	+	0.958008i	$0.407428\pi$
$548$	0.615353	+	1.06582i	0.0262866	+	0.0455297i
$549$	−4.77818	+	8.27604i	−0.203928	+	0.353213i
$550$		0			0
$551$	−1.18924	−	2.05982i	−0.0506633	−	0.0877515i
$552$	−17.3384			−0.737971
$553$	−11.5166	−	13.5236i	−0.489734	−	0.575081i
$554$	−39.5557			−1.68056
$555$		0			0
$556$	4.45569	−	7.71749i	0.188963	−	0.327294i
$557$	20.0922	−	34.8008i	0.851336	−	1.47456i	−0.0286677	−	0.999589i	$-0.509126\pi$
$557$	20.0922	−	34.8008i	0.851336	−	1.47456i	0.880003	−	0.474968i	$-0.157540\pi$
$558$	−4.10214	−	7.10511i	−0.173657	−	0.300784i
$559$	−16.8319			−0.711914
$560$		0			0
$561$	−12.1069			−0.511152
$562$	−17.2251	−	29.8347i	−0.726595	−	1.25850i
$563$	−12.5940	+	21.8134i	−0.530772	+	0.919325i	0.468583	+	0.883420i	$0.344765\pi$
$563$	−12.5940	+	21.8134i	−0.530772	+	0.919325i	−0.999355	+	0.0359052i	$0.988569\pi$
$564$	−0.372360	+	0.644946i	−0.0156792	+	0.0271571i
$565$		0			0
$566$	28.1362			1.18265
$567$	−0.886763	+	2.49272i	−0.0372405	+	0.104684i
$568$	25.3966			1.06562
$569$	5.51757	+	9.55672i	0.231309	+	0.400638i	0.958194	−	0.286121i	$-0.0923659\pi$
$569$	5.51757	+	9.55672i	0.231309	+	0.400638i	−0.726885	+	0.686759i	$0.759033\pi$
$570$		0			0
$571$	−14.3573	+	24.8677i	−0.600836	+	1.04068i	0.391858	+	0.920026i	$0.371832\pi$
$571$	−14.3573	+	24.8677i	−0.600836	+	1.04068i	−0.992695	+	0.120654i	$0.961501\pi$
$572$	−1.57351	−	2.72539i	−0.0657916	−	0.113954i
$573$	0.318541			0.0133073
$574$	−17.8835	−	21.0001i	−0.746442	−	0.876526i
$575$		0			0
$576$	−2.87834	−	4.98544i	−0.119931	−	0.207727i
$577$	−3.43202	+	5.94444i	−0.142877	+	0.247470i	−0.928579	−	0.371135i	$-0.878969\pi$
$577$	−3.43202	+	5.94444i	−0.142877	+	0.247470i	0.785702	+	0.618605i	$0.212302\pi$
$578$	−7.40008	+	12.8173i	−0.307803	+	0.533130i
$579$	−1.04667	−	1.81289i	−0.0434981	−	0.0753410i
$580$		0			0
$581$	13.2695	−	2.43959i	0.550512	−	0.101211i
$582$	4.46837			0.185220
$583$	3.79966	+	6.58121i	0.157366	+	0.272566i
$584$	15.8228	−	27.4059i	0.654752	−	1.13406i
$585$		0			0
$586$	−10.7860	−	18.6819i	−0.445565	−	0.771741i
$587$	−9.03965			−0.373106			−0.186553	−	0.982445i	$-0.559732\pi$
$587$	−9.03965			−0.373106			−0.186553	+	0.982445i	$0.559732\pi$
$588$	−2.22506	−	1.81246i	−0.0917599	−	0.0747446i
$589$	1.61271			0.0664506
$590$		0			0
$591$	11.2899	−	19.5547i	0.464404	−	0.804372i
$592$	−8.54564	+	14.8015i	−0.351224	+	0.608337i
$593$	−2.55399	−	4.42364i	−0.104880	−	0.181657i	0.808809	−	0.588071i	$-0.200112\pi$
$593$	−2.55399	−	4.42364i	−0.104880	−	0.181657i	−0.913689	+	0.406414i	$0.866779\pi$
$594$	−6.87834			−0.282222
$595$		0			0
$596$	−2.13724			−0.0875446
$597$	3.75204	+	6.49872i	0.153561	+	0.265975i
$598$	−9.44578	+	16.3606i	−0.386267	+	0.669034i
$599$	14.9721	−	25.9325i	0.611745	−	1.05957i	−0.379202	−	0.925314i	$-0.623801\pi$
$599$	14.9721	−	25.9325i	0.611745	−	1.05957i	0.990946	−	0.134259i	$-0.0428654\pi$
$600$		0			0
$601$	−12.5387			−0.511466			−0.255733	−	0.966747i	$-0.582317\pi$
$601$	−12.5387			−0.511466			−0.255733	+	0.966747i	$0.582317\pi$
$602$	−25.8724	−	30.3812i	−1.05448	−	1.23825i
$603$	−8.38433			−0.341436
$604$	1.99119	+	3.44884i	0.0810204	+	0.140331i
$605$		0			0
$606$	5.60239	−	9.70362i	0.227581	−	0.394182i
$607$	4.79903	+	8.31216i	0.194786	+	0.337380i	0.946831	−	0.321733i	$-0.104265\pi$
$607$	4.79903	+	8.31216i	0.194786	+	0.337380i	−0.752044	+	0.659113i	$0.770932\pi$
$608$	−0.697242			−0.0282769
$609$	6.91170	−	19.4290i	0.280076	−	0.787304i
$610$		0			0
$611$	−1.57351	−	2.72539i	−0.0636572	−	0.110258i
$612$	0.560120	−	0.970157i	0.0226415	−	0.0392163i
$613$	13.8323	−	23.9583i	0.558682	−	0.967665i	−0.438925	−	0.898524i	$-0.644641\pi$
$613$	13.8323	−	23.9583i	0.558682	−	0.967665i	0.997607	−	0.0691416i	$-0.0220260\pi$
$614$	23.1567	+	40.1085i	0.934527	+	1.61865i
$615$		0			0
$616$	−9.69830	+	27.2622i	−0.390755	+	1.09843i
$617$	20.4155			0.821896			0.410948	−	0.911659i	$-0.365198\pi$
$617$	20.4155			0.821896			0.410948	+	0.911659i	$0.365198\pi$
$618$	−8.75046	−	15.1562i	−0.351995	−	0.609673i
$619$	7.72112	−	13.3734i	0.310338	−	0.537521i	−0.668098	−	0.744074i	$-0.732891\pi$
$619$	7.72112	−	13.3734i	0.310338	−	0.537521i	0.978435	+	0.206553i	$0.0662245\pi$
$620$		0			0
$621$	3.51212	+	6.08316i	0.140936	+	0.244109i
$622$	−20.9781			−0.841145
$623$	−6.98271	−	8.19960i	−0.279756	−	0.328510i
$624$	−8.05918			−0.322625
$625$		0			0
$626$	−22.4988	+	38.9691i	−0.899234	+	1.55752i
$627$	0.676036	−	1.17093i	0.0269983	−	0.0467624i
$628$	1.94161	+	3.36296i	0.0774785	+	0.134197i
$629$	10.0392			0.400290
$630$		0			0
$631$	−38.1722			−1.51961			−0.759805	−	0.650151i	$-0.774705\pi$
$631$	−38.1722			−1.51961			−0.759805	+	0.650151i	$0.774705\pi$
$632$	−8.28597	−	14.3517i	−0.329598	−	0.570881i
$633$	−3.83608	+	6.64428i	−0.152470	+	0.264087i
$634$	0.899340	−	1.55770i	0.0357173	−	0.0618643i
$635$		0			0
$636$	−0.703161			−0.0278822
$637$	11.3342	−	4.31336i	0.449078	−	0.170901i
$638$	53.6119			2.12252
$639$	−5.14441	−	8.91037i	−0.203510	−	0.352489i
$640$		0			0
$641$	8.39007	−	14.5320i	0.331388	−	0.573981i	−0.651396	−	0.758738i	$-0.725816\pi$
$641$	8.39007	−	14.5320i	0.331388	−	0.573981i	0.982784	+	0.184757i	$0.0591498\pi$
$642$	−5.36820	−	9.29800i	−0.211866	−	0.366963i
$643$	14.2002			0.560001			0.280001	−	0.960000i	$-0.409665\pi$
$643$	14.2002			0.560001			0.280001	+	0.960000i	$0.409665\pi$
$644$	−7.49354	+	1.37768i	−0.295287	+	0.0542882i
$645$		0			0
$646$	0.647220	+	1.12102i	0.0254645	+	0.0441059i
$647$	7.24426	−	12.5474i	0.284801	−	0.493290i	−0.687760	−	0.725938i	$-0.741406\pi$
$647$	7.24426	−	12.5474i	0.284801	−	0.493290i	0.972561	+	0.232648i	$0.0747391\pi$
$648$	−1.23418	+	2.13767i	−0.0484834	+	0.0839756i
$649$	2.53092	+	4.38369i	0.0993474	+	0.172075i
$650$		0			0
$651$	9.06554	+	10.6454i	0.355307	+	0.417227i
$652$	2.21247			0.0866469
$653$	5.14166	+	8.90562i	0.201209	+	0.348504i	0.948918	−	0.315522i	$-0.102180\pi$
$653$	5.14166	+	8.90562i	0.201209	+	0.348504i	−0.747709	+	0.664026i	$0.768846\pi$
$654$	3.43233	−	5.94498i	0.134215	−	0.232467i
$655$		0			0
$656$	−15.6201	−	27.0548i	−0.609863	−	1.05631i
$657$	−12.8204			−0.500173
$658$	2.50063	−	7.02935i	0.0974846	−	0.274032i
$659$	14.9773			0.583433			0.291717	−	0.956505i	$-0.405774\pi$
$659$	14.9773			0.583433			0.291717	+	0.956505i	$0.405774\pi$
$660$		0			0
$661$	−1.22323	+	2.11870i	−0.0475782	+	0.0824079i	−0.888834	−	0.458230i	$-0.848484\pi$
$661$	−1.22323	+	2.11870i	−0.0475782	+	0.0824079i	0.841256	+	0.540638i	$0.181817\pi$
$662$	−22.0047	+	38.1133i	−0.855238	+	1.48131i
$663$	2.36694	+	4.09966i	0.0919242	+	0.159217i
$664$	12.5874			0.488484
$665$		0			0
$666$	5.70365			0.221012
$667$	−27.3745	−	47.4140i	−1.05994	−	1.83588i
$668$	0.0640689	−	0.110971i	0.00247890	−	0.00429358i
$669$	−3.45104	+	5.97738i	−0.133425	+	0.231099i
$670$		0			0
$671$	42.3418			1.63459
$672$	−3.91941	−	4.60245i	−0.151195	−	0.177544i
$673$	−17.2596			−0.665310			−0.332655	−	0.943049i	$-0.607945\pi$
$673$	−17.2596			−0.665310			−0.332655	+	0.943049i	$0.607945\pi$
$674$	12.3983	+	21.4744i	0.477564	+	0.827164i
$675$		0			0
$676$	2.04959	−	3.54999i	0.0788302	−	0.136538i
$677$	5.81918	+	10.0791i	0.223649	+	0.387372i	0.955913	−	0.293649i	$-0.0948697\pi$
$677$	5.81918	+	10.0791i	0.223649	+	0.387372i	−0.732264	+	0.681021i	$0.761536\pi$
$678$	−4.44223			−0.170603
$679$	−7.48986	+	1.37700i	−0.287434	+	0.0528445i
$680$		0			0
$681$	−3.17360	−	5.49684i	−0.121613	−	0.210639i
$682$	−18.1756	+	31.4810i	−0.695979	+	1.20547i
$683$	−15.5480	+	26.9299i	−0.594928	+	1.03044i	0.398629	+	0.917112i	$0.369486\pi$
$683$	−15.5480	+	26.9299i	−0.594928	+	1.03044i	−0.993557	+	0.113333i	$0.963847\pi$
$684$	0.0625532	+	0.108345i	0.00239178	+	0.00414269i
$685$		0			0
$686$	25.2073	+	13.8279i	0.962421	+	0.527952i
$687$	6.75669			0.257784
$688$	−22.5979	−	39.1407i	−0.861537	−	1.49223i
$689$	1.48570	−	2.57330i	0.0566006	−	0.0980351i
$690$		0			0
$691$	8.96695	+	15.5312i	0.341119	+	0.590835i	0.984641	−	0.174592i	$-0.0558607\pi$
$691$	8.96695	+	15.5312i	0.341119	+	0.590835i	−0.643522	+	0.765428i	$0.722527\pi$
$692$	3.94181			0.149845
$693$	11.5294	−	2.11968i	0.437967	−	0.0805198i
$694$	−20.1999			−0.766778
$695$		0			0
$696$	9.61961	−	16.6617i	0.364630	−	0.631559i
$697$	−9.17508	+	15.8917i	−0.347531	+	0.601941i
$698$	24.8947	+	43.1190i	0.942280	+	1.63208i
$699$	7.41201			0.280348
$700$		0			0
$701$	7.04488			0.266081			0.133041	−	0.991111i	$-0.457526\pi$
$701$	7.04488			0.266081			0.133041	+	0.991111i	$0.457526\pi$
$702$	1.34474	+	2.32916i	0.0507541	+	0.0879086i
$703$	−0.560582	+	0.970956i	−0.0211427	+	0.0366203i
$704$	−12.7532	+	22.0893i	−0.480656	+	0.832520i
$705$		0			0
$706$	−20.7540			−0.781088
$707$	−6.40036	+	17.9916i	−0.240710	+	0.676644i
$708$	−0.468370			−0.0176024
$709$	12.9622	+	22.4511i	0.486804	+	0.843170i	0.999885	−	0.0151705i	$-0.00482909\pi$
$709$	12.9622	+	22.4511i	0.486804	+	0.843170i	−0.513080	+	0.858341i	$0.671496\pi$
$710$		0			0
$711$	−3.35686	+	5.81425i	−0.125892	+	0.218051i
$712$	−5.02394	−	8.70172i	−0.188280	−	0.326111i
$713$	37.1221			1.39023
$714$	−3.76156	+	10.5739i	−0.140773	+	0.395717i
$715$		0			0
$716$	1.81508	+	3.14382i	0.0678329	+	0.117490i
$717$	−3.68178	+	6.37702i	−0.137498	+	0.238154i
$718$	−10.1834	+	17.6382i	−0.380041	+	0.658251i
$719$	−15.6427	−	27.0940i	−0.583376	−	1.01044i	−0.995076	−	0.0991173i	$-0.968398\pi$
$719$	−15.6427	−	27.0940i	−0.583376	−	1.01044i	0.411700	−	0.911320i	$-0.364935\pi$
$720$		0			0
$721$	19.3381	+	22.7082i	0.720189	+	0.845698i
$722$	29.3512			1.09234
$723$	−6.84002	−	11.8473i	−0.254383	−	0.440605i
$724$	3.46908	−	6.00862i	0.128927	−	0.223309i
$725$		0			0
$726$	6.69988	+	11.6045i	0.248656	+	0.430684i
$727$	22.8312			0.846761			0.423380	−	0.905952i	$-0.360843\pi$
$727$	22.8312			0.846761			0.423380	+	0.905952i	$0.360843\pi$
$728$	11.1277	−	2.04581i	0.412419	−	0.0758227i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−13.2738	+	22.9908i	−0.490948	+	0.850347i
$732$	−1.95893	+	3.39297i	−0.0724043	+	0.125408i
$733$	2.97717	+	5.15661i	0.109964	+	0.190464i	0.915756	−	0.401736i	$-0.131593\pi$
$733$	2.97717	+	5.15661i	0.109964	+	0.190464i	−0.805791	+	0.592200i	$0.798260\pi$
$734$	−20.3924			−0.752696
$735$		0			0
$736$	−16.0494			−0.591590
$737$	18.5745	+	32.1719i	0.684199	+	1.18507i
$738$	−5.21270	+	9.02866i	−0.191882	+	0.332350i
$739$	−20.7539	+	35.9469i	−0.763446	+	1.32233i	0.177618	+	0.984099i	$0.443161\pi$
$739$	−20.7539	+	35.9469i	−0.763446	+	1.32233i	−0.941064	+	0.338228i	$0.890173\pi$
$740$		0			0
$741$	−0.528671			−0.0194212
$742$	6.92842	−	1.27378i	0.254350	−	0.0467620i
$743$	−6.80015			−0.249473			−0.124737	−	0.992190i	$-0.539809\pi$
$743$	−6.80015			−0.249473			−0.124737	+	0.992190i	$0.539809\pi$
$744$	6.52250	+	11.2973i	0.239127	+	0.414179i
$745$		0			0
$746$	−22.9910	+	39.8216i	−0.841760	+	1.45797i
$747$	−2.54973	−	4.41626i	−0.0932898	−	0.161583i
$748$	−4.96351			−0.181484
$749$	11.8635	+	13.9310i	0.433482	+	0.509026i
$750$		0			0
$751$	−11.8056	−	20.4480i	−0.430794	−	0.746157i	0.566148	−	0.824304i	$-0.308433\pi$
$751$	−11.8056	−	20.4480i	−0.430794	−	0.746157i	−0.996942	+	0.0781464i	$0.975100\pi$
$752$	4.22506	−	7.31802i	0.154072	−	0.266861i
$753$	−11.7421	+	20.3380i	−0.427907	+	0.741157i
$754$	−10.4813	−	18.1542i	−0.381708	−	0.661137i
$755$		0			0
$756$	−0.363551	+	1.02195i	−0.0132222	+	0.0371681i
$757$	16.2267			0.589769			0.294884	−	0.955533i	$-0.404719\pi$
$757$	16.2267			0.589769			0.294884	+	0.955533i	$0.404719\pi$
$758$	5.80360	+	10.0521i	0.210796	+	0.365110i
$759$	15.5613	−	26.9530i	0.564840	−	0.978332i
$760$		0			0
$761$	1.27754	+	2.21276i	0.0463108	+	0.0802126i	0.888252	−	0.459357i	$-0.151920\pi$
$761$	1.27754	+	2.21276i	0.0463108	+	0.0802126i	−0.841941	+	0.539570i	$0.818587\pi$
$762$	21.3184			0.772284
$763$	−3.92122	+	11.0227i	−0.141958	+	0.399047i
$764$	0.130594			0.00472473
$765$		0			0
$766$	−18.4264	+	31.9154i	−0.665772	+	1.15315i
$767$	0.989610	−	1.71406i	0.0357328	−	0.0618910i
$768$	−4.72710	−	8.18758i	−0.170575	−	0.295444i
$769$	−45.4525			−1.63906			−0.819530	−	0.573037i	$-0.805765\pi$
$769$	−45.4525			−1.63906			−0.819530	+	0.573037i	$0.805765\pi$
$770$		0			0
$771$	14.5974			0.525713
$772$	−0.429109	−	0.743238i	−0.0154440	−	0.0267497i
$773$	25.7446	−	44.5909i	0.925968	−	1.60382i	0.135970	−	0.990713i	$-0.456585\pi$
$773$	25.7446	−	44.5909i	0.925968	−	1.60382i	0.789997	−	0.613110i	$-0.210082\pi$
$774$	−7.54131	+	13.0619i	−0.271067	+	0.469502i
$775$		0			0
$776$	−7.10482			−0.255048
$777$	−9.56043	+	1.75767i	−0.342979	+	0.0630562i
$778$	21.9363			0.786453
$779$	−1.02466	−	1.77476i	−0.0367121	−	0.0635873i
$780$		0			0
$781$	−22.7936	+	39.4797i	−0.815619	+	1.41269i
$782$	14.8980	+	25.8041i	0.532752	+	0.922754i
$783$	−7.79430			−0.278546
$784$	25.2471	+	20.5655i	0.901683	+	0.734481i
$785$		0			0
$786$	17.0623	+	29.5528i	0.608593	+	1.05411i
$787$	−10.0757	+	17.4517i	−0.359161	+	0.622085i	−0.987821	−	0.155596i	$-0.950270\pi$
$787$	−10.0757	+	17.4517i	−0.359161	+	0.622085i	0.628660	+	0.777680i	$0.283604\pi$
$788$	4.62858	−	8.01693i	0.164886	−	0.285591i
$789$	2.54470	+	4.40755i	0.0905937	+	0.156913i
$790$		0			0
$791$	7.44605	−	1.36895i	0.264751	−	0.0486742i
$792$	10.9367			0.388620
$793$	−8.27800	−	14.3379i	−0.293960	−	0.509154i
$794$	8.74750	−	15.1511i	0.310437	−	0.537693i
$795$		0			0
$796$	1.53824	+	2.66431i	0.0545216	+	0.0944341i
$797$	−13.0702			−0.462971			−0.231486	−	0.972838i	$-0.574359\pi$
$797$	−13.0702			−0.462971			−0.231486	+	0.972838i	$0.574359\pi$
$798$	−0.812621	−	0.954238i	−0.0287665	−	0.0337797i
$799$	−4.96351			−0.175596
$800$		0			0
$801$	−2.03533	+	3.52529i	−0.0719148	+	0.124560i
$802$	18.0831	−	31.3209i	0.638537	−	1.10598i
$803$	28.4021	+	49.1939i	1.00229	+	1.73602i
$804$	−3.43737			−0.121227
$805$		0			0
$806$	14.2136			0.500652
$807$	−15.2550	−	26.4224i	−0.537000	−	0.930112i
$808$	−8.90793	+	15.4290i	−0.313380	+	0.542790i
$809$	0.868598	−	1.50446i	0.0305383	−	0.0528938i	−0.850352	−	0.526214i	$-0.823611\pi$
$809$	0.868598	−	1.50446i	0.0305383	−	0.0528938i	0.880891	+	0.473320i	$0.156945\pi$
$810$		0			0
$811$	−27.9004			−0.979715			−0.489858	−	0.871802i	$-0.662951\pi$
$811$	−27.9004			−0.979715			−0.489858	+	0.871802i	$0.662951\pi$
$812$	2.83363	−	7.96541i	0.0994408	−	0.279531i
$813$	−19.4880			−0.683475
$814$	−12.6357	−	21.8857i	−0.442883	−	0.767095i
$815$		0			0
$816$	−6.35552	+	11.0081i	−0.222488	+	0.385360i
$817$	−1.48239	−	2.56758i	−0.0518623	−	0.0898282i
$818$	−32.0538			−1.12074
$819$	−2.97182	−	3.48973i	−0.103844	−	0.121941i
$820$		0			0
$821$	−8.46799	−	14.6670i	−0.295535	−	0.511881i	0.679574	−	0.733607i	$-0.262165\pi$
$821$	−8.46799	−	14.6670i	−0.295535	−	0.511881i	−0.975109	+	0.221725i	$0.928831\pi$
$822$	−2.33009	+	4.03584i	−0.0812714	+	0.140766i
$823$	−4.94516	+	8.56526i	−0.172377	+	0.298566i	−0.939251	−	0.343232i	$-0.888478\pi$
$823$	−4.94516	+	8.56526i	−0.172377	+	0.298566i	0.766873	+	0.641799i	$0.221812\pi$
$824$	13.9134	+	24.0988i	0.484698	+	0.839521i
$825$		0			0
$826$	4.61496	−	0.848456i	0.160575	−	0.0295216i
$827$	35.3201			1.22820			0.614101	−	0.789228i	$-0.289519\pi$
$827$	35.3201			1.22820			0.614101	+	0.789228i	$0.289519\pi$
$828$	1.43988	+	2.49395i	0.0500393	+	0.0866706i
$829$	−4.64975	+	8.05361i	−0.161493	+	0.279713i	−0.935404	−	0.353580i	$-0.884964\pi$
$829$	−4.64975	+	8.05361i	−0.161493	+	0.279713i	0.773912	+	0.633294i	$0.218297\pi$
$830$		0			0
$831$	−12.7401	−	22.0665i	−0.441949	−	0.765478i
$832$	9.97323			0.345760
$833$	3.04659	−	18.8830i	0.105558	−	0.654258i
$834$	33.7438			1.16845
$835$		0			0
$836$	0.277158	−	0.480052i	0.00958571	−	0.0166029i
$837$	2.64243	−	4.57683i	0.0913359	−	0.158198i
$838$	−4.25557	−	7.37086i	−0.147006	−	0.254622i
$839$	−7.93405			−0.273914			−0.136957	−	0.990577i	$-0.543732\pi$
$839$	−7.93405			−0.273914			−0.136957	+	0.990577i	$0.543732\pi$
$840$		0			0
$841$	31.7512			1.09487
$842$	−2.93467	−	5.08299i	−0.101135	−	0.175171i
$843$	11.0957	−	19.2183i	0.382156	−	0.661914i
$844$	−1.57270	+	2.72399i	−0.0541345	+	0.0937636i
$845$		0			0
$846$	−2.81995			−0.0969519
$847$	−14.8064	−	17.3868i	−0.508755	−	0.597416i
$848$	7.97857			0.273985
$849$	9.06209	+	15.6960i	0.311010	+	0.538685i
$850$		0			0
$851$	−12.9037	+	22.3499i	−0.442334	+	0.766146i
$852$	−2.10908	−	3.65303i	−0.0722558	−	0.125151i
$853$	30.0757			1.02977			0.514887	−	0.857258i	$-0.327834\pi$
$853$	30.0757			1.02977			0.514887	+	0.857258i	$0.327834\pi$
$854$	13.1555	−	36.9804i	0.450170	−	1.26544i
$855$		0			0
$856$	8.53557	+	14.7840i	0.291740	+	0.505308i
$857$	−23.5686	+	40.8221i	−0.805090	+	1.39446i	0.111141	+	0.993805i	$0.464550\pi$
$857$	−23.5686	+	40.8221i	−0.805090	+	1.39446i	−0.916230	+	0.400652i	$0.868784\pi$
$858$	5.95823	−	10.3199i	0.203410	−	0.352317i
$859$	16.3183	+	28.2642i	0.556774	+	0.964361i	0.997763	+	0.0668485i	$0.0212944\pi$
$859$	16.3183	+	28.2642i	0.556774	+	0.964361i	−0.440989	+	0.897512i	$0.645372\pi$
$860$		0			0
$861$	5.95517	−	16.7402i	0.202951	−	0.570503i
$862$	42.7110			1.45474
$863$	18.7051	+	32.3982i	0.636728	+	1.10285i	0.986146	+	0.165879i	$0.0530461\pi$
$863$	18.7051	+	32.3982i	0.636728	+	1.10285i	−0.349418	+	0.936967i	$0.613621\pi$
$864$	−1.14243	+	1.97875i	−0.0388664	+	0.0673186i
$865$		0			0
$866$	6.79578	+	11.7706i	0.230930	+	0.399983i
$867$	−9.53367			−0.323780
$868$	3.71665	+	4.36435i	0.126151	+	0.148136i
$869$	29.7468			1.00909
$870$		0			0
$871$	7.26275	−	12.5795i	0.246089	−	0.426239i
$872$	−5.45750	+	9.45266i	−0.184814	+	0.320108i
$873$	1.43917	+	2.49272i	0.0487086	+	0.0843658i
$874$	−3.32757			−0.112557
$875$		0			0
$876$	−5.25606			−0.177586
$877$	16.7828	+	29.0687i	0.566716	+	0.981581i	0.996888	+	0.0788336i	$0.0251196\pi$
$877$	16.7828	+	29.0687i	0.566716	+	0.981581i	−0.430172	+	0.902747i	$0.641547\pi$
$878$	−8.23764	+	14.2680i	−0.278007	+	0.481522i
$879$	6.94790	−	12.0341i	0.234347	−	0.405901i
$880$		0			0
$881$	−12.1952			−0.410867			−0.205433	−	0.978671i	$-0.565860\pi$
$881$	−12.1952			−0.410867			−0.205433	+	0.978671i	$0.565860\pi$
$882$	1.73088	−	10.7281i	0.0582817	−	0.361235i
$883$	11.0408			0.371552			0.185776	−	0.982592i	$-0.440520\pi$
$883$	11.0408			0.371552			0.185776	+	0.982592i	$0.440520\pi$
$884$	0.970385	+	1.68076i	0.0326376	+	0.0565300i
$885$		0			0
$886$	15.5129	−	26.8691i	0.521166	−	0.902685i
$887$	0.780464	+	1.35180i	0.0262054	+	0.0453891i	0.878831	−	0.477134i	$-0.158324\pi$
$887$	0.780464	+	1.35180i	0.0262054	+	0.0453891i	−0.852625	+	0.522523i	$0.824991\pi$
$888$	−9.06895			−0.304334
$889$	−35.7338	+	6.56962i	−1.19847	+	0.220338i
$890$		0			0
$891$	−2.21538	−	3.83715i	−0.0742179	−	0.128549i
$892$	−1.41484	+	2.45058i	−0.0473724	+	0.0820514i
$893$	0.277158	−	0.480052i	0.00927474	−	0.0160643i
$894$	−4.04642	−	7.00861i	−0.135333	−	0.234403i
$895$		0			0
$896$	23.1687	+	27.2064i	0.774012	+	0.908900i
$897$	−12.1692			−0.406318
$898$	2.34862	+	4.06793i	0.0783745	+	0.135749i
$899$	−20.5959	+	35.6732i	−0.686913	+	1.18977i
$900$		0			0
$901$	−2.34326	−	4.05865i	−0.0780654	−	0.135213i
$902$	46.1924			1.53804
$903$	8.61545	−	24.2183i	0.286704	−	0.805935i
$904$	7.06326			0.234921
$905$		0			0
$906$	−7.53983	+	13.0594i	−0.250494	+	0.433869i
$907$	−8.70390	+	15.0756i	−0.289008	+	0.500577i	−0.973573	−	0.228375i	$-0.926659\pi$
$907$	−8.70390	+	15.0756i	−0.289008	+	0.500577i	0.684565	+	0.728952i	$0.259992\pi$
$908$	−1.30110	−	2.25357i	−0.0431785	−	0.0747873i
$909$	7.21767			0.239395
$910$		0			0
$911$	−18.3203			−0.606978			−0.303489	−	0.952835i	$-0.598152\pi$
$911$	−18.3203			−0.606978			−0.303489	+	0.952835i	$0.598152\pi$
$912$	−0.709774	−	1.22936i	−0.0235030	−	0.0407083i
$913$	−11.2972	+	19.5674i	−0.373884	+	0.647586i
$914$	−1.77079	+	3.06710i	−0.0585726	+	0.101451i
$915$		0			0
$916$	2.77007			0.0915258
$917$	−37.7070	−	44.2783i	−1.24519	−	1.46220i
$918$	4.24190			0.140003
$919$	−11.2963	−	19.5658i	−0.372632	−	0.645417i	0.617338	−	0.786698i	$-0.288211\pi$
$919$	−11.2963	−	19.5658i	−0.372632	−	0.645417i	−0.989970	+	0.141281i	$0.954878\pi$
$920$		0			0
$921$	−14.9166	+	25.8363i	−0.491519	+	0.851335i
$922$	−18.6816	−	32.3574i	−0.615244	−	1.06563i
$923$	17.8249			0.586715
$924$	4.72678	−	0.869014i	0.155500	−	0.0285885i
$925$		0			0
$926$	−8.63842	−	14.9622i	−0.283876	−	0.491688i
$927$	5.63670	−	9.76304i	0.185133	−	0.320660i
$928$	8.90448	−	15.4230i	0.292304	−	0.506285i
$929$	−19.3356	−	33.4903i	−0.634381	−	1.09878i	−0.986646	−	0.162880i	$-0.947922\pi$
$929$	−19.3356	−	33.4903i	−0.634381	−	1.09878i	0.352265	−	0.935900i	$-0.385412\pi$
$930$		0			0
$931$	1.65618	+	1.34907i	0.0542790	+	0.0442139i
$932$	3.03874			0.0995372
$933$	−6.75662	−	11.7028i	−0.221202	−	0.383133i
$934$	−22.1813	+	38.4192i	−0.725795	+	1.25711i
$935$		0			0
$936$	−2.13817	−	3.70343i	−0.0698884	−	0.121050i
$937$	−46.7921			−1.52863			−0.764316	−	0.644842i	$-0.776923\pi$
$937$	−46.7921			−1.52863			−0.764316	+	0.644842i	$0.776923\pi$
$938$	33.8692	−	6.22682i	1.10587	−	0.203313i
$939$	−28.9857			−0.945912
$940$		0			0
$941$	20.9461	−	36.2797i	0.682824	−	1.18268i	−0.291292	−	0.956634i	$-0.594085\pi$
$941$	20.9461	−	36.2797i	0.682824	−	1.18268i	0.974116	−	0.226051i	$-0.0725815\pi$
$942$	−7.35207	+	12.7342i	−0.239543	+	0.414901i
$943$	−23.5860	−	40.8522i	−0.768067	−	1.33033i
$944$	5.31446			0.172971
$945$		0			0
$946$	66.8274			2.17275
$947$	−28.0573	−	48.5967i	−0.911740	−	1.57918i	−0.811605	−	0.584206i	$-0.801406\pi$
$947$	−28.0573	−	48.5967i	−0.911740	−	1.57918i	−0.100134	−	0.994974i	$-0.531927\pi$
$948$	−1.37623	+	2.38370i	−0.0446978	+	0.0774189i
$949$	11.1054	−	19.2352i	0.360498	−	0.624401i
$950$		0			0
$951$	1.15864			0.0375714
$952$	5.98097	−	16.8127i	0.193844	−	0.544903i
$953$	17.7705			0.575643			0.287821	−	0.957684i	$-0.407069\pi$
$953$	17.7705			0.575643			0.287821	+	0.957684i	$0.407069\pi$
$954$	−1.33129	−	2.30587i	−0.0431022	−	0.0746552i
$955$		0			0
$956$	−1.50944	+	2.61442i	−0.0488187	+	0.0845564i
$957$	17.2673	+	29.9079i	0.558173	+	0.966785i
$958$	8.66259			0.279875
$959$	2.66198	−	7.48291i	0.0859598	−	0.241636i
$960$		0			0
$961$	1.53508	+	2.65884i	0.0495188	+	0.0857690i
$962$	−4.94067	+	8.55750i	−0.159294	+	0.275905i
$963$	3.45798	−	5.98940i	0.111432	−	0.193006i
$964$	−2.80424	−	4.85708i	−0.0903185	−	0.156436i
$965$		0			0
$966$	−18.7053	−	21.9651i	−0.601833	−	0.706716i
$967$	−22.5942			−0.726579			−0.363290	−	0.931676i	$-0.618346\pi$
$967$	−22.5942			−0.726579			−0.363290	+	0.931676i	$0.618346\pi$
$968$	−10.6530	−	18.4515i	−0.342399	−	0.593053i
$969$	−0.416913	+	0.722115i	−0.0133932	+	0.0231977i
$970$		0			0
$971$	−20.5244	−	35.5493i	−0.658660	−	1.14083i	−0.980963	−	0.194196i	$-0.937790\pi$
$971$	−20.5244	−	35.5493i	−0.658660	−	1.14083i	0.322303	−	0.946637i	$-0.395543\pi$
$972$	0.409975			0.0131500
$973$	−56.5612	+	10.3987i	−1.81327	+	0.333367i
$974$	12.9577			0.415192
$975$		0			0
$976$	22.2275	−	38.4991i	0.711484	−	1.23233i
$977$	9.73668	−	16.8644i	0.311504	−	0.539541i	−0.667184	−	0.744893i	$-0.732501\pi$
$977$	9.73668	−	16.8644i	0.311504	−	0.539541i	0.978688	+	0.205352i	$0.0658339\pi$
$978$	4.18886	+	7.25532i	0.133945	+	0.231999i
$979$	18.0361			0.576435
$980$		0			0
$981$	4.42195			0.141182
$982$	0.432661	+	0.749390i	0.0138068	+	0.0239140i
$983$	−25.8636	+	44.7970i	−0.824920	+	1.42880i	0.0770602	+	0.997026i	$0.475447\pi$
$983$	−25.8636	+	44.7970i	−0.824920	+	1.42880i	−0.901980	+	0.431777i	$0.857887\pi$
$984$	8.28832	−	14.3558i	0.264222	−	0.457646i
$985$		0			0
$986$	−33.0626			−1.05293
$987$	4.72678	−	0.869014i	0.150455	−	0.0276610i
$988$	−0.216742			−0.00689548
$989$	−34.1224	−	59.1017i	−1.08503	−	1.87932i
$990$		0			0
$991$	−17.9749	+	31.1335i	−0.570992	+	0.988988i	0.425472	+	0.904972i	$0.360108\pi$
$991$	−17.9749	+	31.1335i	−0.570992	+	0.988988i	−0.996464	+	0.0840162i	$0.973225\pi$
$992$	6.03762	+	10.4575i	0.191694	+	0.332025i
$993$	−28.3491			−0.899632
$994$	27.3988	+	32.1736i	0.869036	+	1.02048i
$995$		0			0
$996$	−1.04533	−	1.81056i	−0.0331224	−	0.0573697i
$997$	−28.0300	+	48.5493i	−0.887718	+	1.53757i	−0.0451513	+	0.998980i	$0.514377\pi$
$997$	−28.0300	+	48.5493i	−0.887718	+	1.53757i	−0.842567	+	0.538592i	$0.818956\pi$
$998$	−20.2075	+	35.0003i	−0.639656	+	1.10792i
$999$	1.83703	+	3.18183i	0.0581211	+	0.100669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.i.k.151.3		8
5.2	odd	4		105.2.q.a.4.3	✓	16
5.3	odd	4		105.2.q.a.4.6	yes	16
5.4	even	2		525.2.i.h.151.2		8
7.2	even	3	inner	525.2.i.k.226.3		8
7.3	odd	6		3675.2.a.bn.1.2		4
7.4	even	3		3675.2.a.bp.1.2		4
15.2	even	4		315.2.bf.b.109.6		16
15.8	even	4		315.2.bf.b.109.3		16
20.3	even	4		1680.2.di.d.529.8		16
20.7	even	4		1680.2.di.d.529.1		16
35.2	odd	12		105.2.q.a.79.6	yes	16
35.3	even	12		735.2.d.e.589.6		8
35.4	even	6		3675.2.a.bz.1.3		4
35.9	even	6		525.2.i.h.226.2		8
35.12	even	12		735.2.q.g.79.6		16
35.13	even	4		735.2.q.g.214.6		16
35.17	even	12		735.2.d.e.589.3		8
35.18	odd	12		735.2.d.d.589.6		8
35.23	odd	12		105.2.q.a.79.3	yes	16
35.24	odd	6		3675.2.a.cb.1.3		4
35.27	even	4		735.2.q.g.214.3		16
35.32	odd	12		735.2.d.d.589.3		8
35.33	even	12		735.2.q.g.79.3		16
105.2	even	12		315.2.bf.b.289.3		16
105.17	odd	12		2205.2.d.o.1324.6		8
105.23	even	12		315.2.bf.b.289.6		16
105.32	even	12		2205.2.d.s.1324.6		8
105.38	odd	12		2205.2.d.o.1324.3		8
105.53	even	12		2205.2.d.s.1324.3		8
140.23	even	12		1680.2.di.d.289.1		16
140.107	even	12		1680.2.di.d.289.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.3	✓	16	5.2	odd	4
105.2.q.a.4.6	yes	16	5.3	odd	4
105.2.q.a.79.3	yes	16	35.23	odd	12
105.2.q.a.79.6	yes	16	35.2	odd	12
315.2.bf.b.109.3		16	15.8	even	4
315.2.bf.b.109.6		16	15.2	even	4
315.2.bf.b.289.3		16	105.2	even	12
315.2.bf.b.289.6		16	105.23	even	12
525.2.i.h.151.2		8	5.4	even	2
525.2.i.h.226.2		8	35.9	even	6
525.2.i.k.151.3		8	1.1	even	1	trivial
525.2.i.k.226.3		8	7.2	even	3	inner
735.2.d.d.589.3		8	35.32	odd	12
735.2.d.d.589.6		8	35.18	odd	12
735.2.d.e.589.3		8	35.17	even	12
735.2.d.e.589.6		8	35.3	even	12
735.2.q.g.79.3		16	35.33	even	12
735.2.q.g.79.6		16	35.12	even	12
735.2.q.g.214.3		16	35.27	even	4
735.2.q.g.214.6		16	35.13	even	4
1680.2.di.d.289.1		16	140.23	even	12
1680.2.di.d.289.8		16	140.107	even	12
1680.2.di.d.529.1		16	20.7	even	4
1680.2.di.d.529.8		16	20.3	even	4
2205.2.d.o.1324.3		8	105.38	odd	12
2205.2.d.o.1324.6		8	105.17	odd	12
2205.2.d.s.1324.3		8	105.53	even	12
2205.2.d.s.1324.6		8	105.32	even	12
3675.2.a.bn.1.2		4	7.3	odd	6
3675.2.a.bp.1.2		4	7.4	even	3
3675.2.a.bz.1.3		4	35.4	even	6
3675.2.a.cb.1.3		4	35.24	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)

\(f(q)\)	\(=\)	\(q+(0.776205 + 1.34443i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.204988 + 0.355049i) q^{4} -1.55241 q^{6} +(2.60214 - 0.478401i) q^{7} +2.46837 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.776205 + 1.34443i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.204988 + 0.355049i) q^{4} -1.55241 q^{6} +(2.60214 - 0.478401i) q^{7} +2.46837 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.21538 + 3.83715i) q^{11} +(-0.204988 - 0.355049i) q^{12} +1.73246 q^{13} +(2.66297 + 3.12705i) q^{14} +(2.32594 + 4.02864i) q^{16} +(1.36623 - 2.36638i) q^{17} +(0.776205 - 1.34443i) q^{18} +(0.152578 + 0.264273i) q^{19} +(-0.886763 + 2.49272i) q^{21} -6.87834 q^{22} +(3.51212 + 6.08316i) q^{23} +(-1.23418 + 2.13767i) q^{24} +(1.34474 + 2.32916i) q^{26} +1.00000 q^{27} +(-0.363551 + 1.02195i) q^{28} -7.79430 q^{29} +(2.64243 - 4.57683i) q^{31} +(-1.14243 + 1.97875i) q^{32} +(-2.21538 - 3.83715i) q^{33} +4.24190 q^{34} +0.409975 q^{36} +(1.83703 + 3.18183i) q^{37} +(-0.236864 + 0.410260i) q^{38} +(-0.866230 + 1.50035i) q^{39} -6.71562 q^{41} +(-4.03959 + 0.742674i) q^{42} -9.71562 q^{43} +(-0.908250 - 1.57313i) q^{44} +(-5.45224 + 9.44356i) q^{46} +(-0.908250 - 1.57313i) q^{47} -4.65187 q^{48} +(6.54227 - 2.48973i) q^{49} +(1.36623 + 2.36638i) q^{51} +(-0.355133 + 0.615108i) q^{52} +(0.857566 - 1.48535i) q^{53} +(0.776205 + 1.34443i) q^{54} +(6.42304 - 1.18087i) q^{56} -0.305156 q^{57} +(-6.04998 - 10.4789i) q^{58} +(0.571217 - 0.989377i) q^{59} +(-4.77818 - 8.27604i) q^{61} +8.20428 q^{62} +(-1.71538 - 2.01432i) q^{63} +5.75669 q^{64} +(3.43917 - 5.95682i) q^{66} +(4.19216 - 7.26104i) q^{67} +(0.560120 + 0.970157i) q^{68} -7.02423 q^{69} +10.2888 q^{71} +(-1.23418 - 2.13767i) q^{72} +(6.41022 - 11.1028i) q^{73} +(-2.85183 + 4.93951i) q^{74} -0.125106 q^{76} +(-3.92903 + 11.0446i) q^{77} -2.68949 q^{78} +(-3.35686 - 5.81425i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-5.21270 - 9.02866i) q^{82} +5.09946 q^{83} +(-0.703262 - 0.825821i) q^{84} +(-7.54131 - 13.0619i) q^{86} +(3.89715 - 6.75007i) q^{87} +(-5.46837 + 9.47149i) q^{88} +(-2.03533 - 3.52529i) q^{89} +(4.50810 - 0.828810i) q^{91} -2.87976 q^{92} +(2.64243 + 4.57683i) q^{93} +(1.40998 - 2.44215i) q^{94} +(-1.14243 - 1.97875i) q^{96} -2.87834 q^{97} +(8.42540 + 6.86305i) q^{98} +4.43075 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

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