LMFDB - Embedded newform 525.2.i.h.226.2

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			226.2
Root			$-0.276205 - 0.478401i$ of defining polynomial
Character	$\chi$	$=$	525.226
Dual form			525.2.i.h.151.2

$q$-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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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	0.449493	+	0.893284i	$0.351605\pi$
$2$	−0.776205	+	1.34443i	−0.548860	+	0.950653i	−0.998353	+	0.0573691i	$0.981729\pi$
$3$	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	−0.978473	−	0.206373i	$-0.933834\pi$
$11$	−2.21538	−	3.83715i	−0.667961	−	1.15694i	0.310512	−	0.950569i	$-0.399500\pi$
$12$	0.204988	−	0.355049i	0.0591748	−	0.102494i
$13$	−1.73246			−0.480498			−0.240249	−	0.970711i	$-0.577229\pi$
$13$	−1.73246			−0.480498			−0.240249	+	0.970711i	$0.577229\pi$
$14$	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	$-0.274174\pi$
$17$	−1.36623	−	2.36638i	−0.331359	−	0.573931i	−0.982779	+	0.184787i	$0.940841\pi$
$18$	−0.776205	−	1.34443i	−0.182953	−	0.316884i
$19$	0.152578	−	0.264273i	0.0350038	−	0.0606284i	−0.847993	−	0.530008i	$-0.822189\pi$
$19$	0.152578	−	0.264273i	0.0350038	−	0.0606284i	0.882997	+	0.469379i	$0.155522\pi$
$20$		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	0.223560	+	0.974690i	$0.428232\pi$
$23$	−3.51212	+	6.08316i	−0.732327	+	1.26843i	−0.955886	+	0.293737i	$0.905101\pi$
$24$	−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	0.999577	−	0.0290906i	$-0.00926112\pi$
$31$	2.64243	+	4.57683i	0.474595	+	0.822023i	−0.524982	+	0.851114i	$0.675928\pi$
$32$	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	$-0.930990\pi$
$37$	−1.83703	+	3.18183i	−0.302006	+	0.523090i	0.674584	+	0.738198i	$0.264323\pi$
$38$	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	$-0.234442\pi$
$43$	9.71562			1.48162			0.740809	+	0.671715i	$0.234442\pi$
$44$	−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	$-0.791039\pi$
$47$	0.908250	−	1.57313i	0.132482	−	0.229465i	0.924633	+	0.380860i	$0.124372\pi$
$48$	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	$-0.204249\pi$
$53$	−0.857566	−	1.48535i	−0.117796	−	0.204028i	−0.918894	+	0.394505i	$0.870916\pi$
$54$	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	0.900810	−	0.434213i	$-0.142973\pi$
$59$	0.571217	+	0.989377i	0.0743661	+	0.128806i	−0.826444	+	0.563018i	$0.809640\pi$
$60$		0			0
$61$	−4.77818	+	8.27604i	−0.611783	+	1.05964i	0.379157	+	0.925332i	$0.376214\pi$
$61$	−4.77818	+	8.27604i	−0.611783	+	1.05964i	−0.990940	+	0.134307i	$0.957119\pi$
$62$	−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	−0.999901	−	0.0140921i	$-0.995514\pi$
$67$	−4.19216	−	7.26104i	−0.512154	−	0.887078i	0.487746	−	0.872985i	$-0.337819\pi$
$68$	−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	−0.947697	−	0.319172i	$-0.896595\pi$
$73$	−6.41022	−	11.1028i	−0.750260	−	1.29949i	0.197437	−	0.980316i	$-0.436738\pi$
$74$	−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	−0.990724	−	0.135892i	$-0.956610\pi$
$79$	−3.35686	+	5.81425i	−0.377676	+	0.654154i	0.613048	+	0.790046i	$0.289943\pi$
$80$		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	$-0.590291\pi$
$83$	−5.09946			−0.559739			−0.279869	+	0.960038i	$0.590291\pi$
$84$	−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	−0.953503	−	0.301385i	$-0.902551\pi$
$89$	−2.03533	+	3.52529i	−0.215744	+	0.373680i	0.737758	+	0.675065i	$0.235884\pi$
$90$		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	$-0.453320\pi$
$97$	2.87834			0.292252			0.146126	+	0.989266i	$0.453320\pi$
$98$	−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	0.628717	−	0.777634i	$-0.283580\pi$
$101$	−3.60883	−	6.25068i	−0.359092	−	0.621966i	−0.987809	+	0.155668i	$0.950247\pi$
$102$	2.12095	+	3.67359i	0.210005	+	0.363740i
$103$	−5.63670	+	9.76304i	−0.555400	+	0.961981i	0.442472	+	0.896782i	$0.354102\pi$
$103$	−5.63670	+	9.76304i	−0.555400	+	0.961981i	−0.997872	+	0.0651989i	$0.979232\pi$
$104$	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	$-0.941832\pi$
$107$	−3.45798	+	5.98940i	−0.334296	+	0.579017i	0.649054	+	0.760743i	$0.275165\pi$
$108$	0.204988	+	0.355049i	0.0197249	+	0.0341646i
$109$	−2.21097	−	3.82952i	−0.211773	−	0.366801i	0.740497	−	0.672060i	$-0.234590\pi$
$109$	−2.21097	−	3.82952i	−0.211773	−	0.366801i	−0.952269	+	0.305259i	$0.901257\pi$
$110$		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	$-0.542973\pi$
$113$	−2.86151			−0.269188			−0.134594	+	0.990901i	$0.542973\pi$
$114$	−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	$-0.291459\pi$
$127$	13.7325			1.21856			0.609279	+	0.792956i	$0.291459\pi$
$128$	−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	−0.238476	+	0.971148i	$0.576648\pi$
$131$	−10.9909	+	19.0368i	−0.960277	+	1.66325i	−0.721801	+	0.692100i	$0.756686\pi$
$132$	−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	$-0.207598\pi$
$137$	−1.50095	−	2.59973i	−0.128235	−	0.222110i	−0.922993	+	0.384817i	$0.874265\pi$
$138$	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	−0.739282	−	0.673396i	$-0.764835\pi$
$149$	2.60654	−	4.51467i	0.213536	−	0.369856i	0.952819	+	0.303540i	$0.0981685\pi$
$150$		0			0
$151$	4.85686	+	8.41233i	0.395246	+	0.684585i	0.993132	−	0.116995i	$-0.0373262\pi$
$151$	4.85686	+	8.41233i	0.395246	+	0.684585i	−0.597887	+	0.801580i	$0.703993\pi$
$152$	−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	$-0.290043\pi$
$157$	−4.73591	−	8.20284i	−0.377967	−	0.654658i	−0.990766	+	0.135581i	$0.956710\pi$
$158$	−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	$-0.765548\pi$
$163$	2.69830	−	4.67358i	0.211347	−	0.366063i	0.952136	+	0.305674i	$0.0988817\pi$
$164$	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	$-0.496151\pi$
$167$	0.312550			0.0241859			0.0120929	+	0.999927i	$0.496151\pi$
$168$	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	$-0.714232\pi$
$173$	4.80737	−	8.32661i	0.365498	−	0.633061i	0.988856	+	0.148876i	$0.0475654\pi$
$174$	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	0.982691	−	0.185252i	$-0.0593103\pi$
$179$	4.42730	+	7.66831i	0.330912	+	0.573157i	−0.651779	+	0.758409i	$0.725977\pi$
$180$		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	−0.871730	−	0.489986i	$-0.837002\pi$
$191$	−0.159271	+	0.275865i	−0.0115244	+	0.0199609i	0.860206	+	0.509947i	$0.170335\pi$
$192$	2.87834	+	4.98544i	0.207727	+	0.359793i
$193$	1.04667	+	1.81289i	0.0753410	+	0.130494i	0.901234	−	0.433332i	$-0.142662\pi$
$193$	1.04667	+	1.81289i	0.0753410	+	0.130494i	−0.825894	+	0.563826i	$0.809329\pi$
$194$	−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	$-0.202502\pi$
$197$	22.5798			1.60874			0.804372	+	0.594126i	$0.202502\pi$
$198$	−3.43917	+	5.95682i	−0.244411	+	0.423333i
$199$	3.75204	+	6.49872i	0.265975	+	0.460682i	0.967819	−	0.251649i	$-0.0809728\pi$
$199$	3.75204	+	6.49872i	0.265975	+	0.460682i	−0.701844	+	0.712331i	$0.747639\pi$
$200$		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	$-0.574232\pi$
$223$	−6.90208			−0.462198			−0.231099	+	0.972930i	$0.574232\pi$
$224$	−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	$-0.0991121\pi$
$227$	3.17360	+	5.49684i	0.210639	+	0.364838i	−0.741275	+	0.671201i	$0.765779\pi$
$228$	−0.0625532	−	0.108345i	−0.00414269	−	0.00717535i
$229$	−3.37834	+	5.85146i	−0.223247	+	0.386676i	−0.955792	−	0.294043i	$-0.904999\pi$
$229$	−3.37834	+	5.85146i	−0.223247	+	0.386676i	0.732545	+	0.680719i	$0.238332\pi$
$230$		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	$-0.755271\pi$
$233$	3.70601	−	6.41899i	0.242789	−	0.420522i	0.961508	+	0.274779i	$0.0886046\pi$
$234$	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	0.557130	−	0.830425i	$-0.311903\pi$
$241$	−6.84002	−	11.8473i	−0.440605	−	0.763149i	−0.997734	+	0.0672759i	$0.978569\pi$
$242$	−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	$-0.682872\pi$
$257$	7.29871	−	12.6417i	0.455281	−	0.788570i	0.998704	+	0.0508890i	$0.0162055\pi$
$258$	−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	$-0.216821\pi$
$263$	−2.54470	−	4.40755i	−0.156913	−	0.271781i	−0.933754	+	0.357916i	$0.883488\pi$
$264$	−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	−0.783127	−	0.621862i	$-0.786377\pi$
$269$	−15.2550	−	26.4224i	−0.930112	−	1.61100i	−0.146984	−	0.989139i	$-0.546957\pi$
$270$		0			0
$271$	9.74401	−	16.8771i	0.591907	−	1.02521i	−0.402069	−	0.915609i	$-0.631709\pi$
$271$	9.74401	−	16.8771i	0.591907	−	1.02521i	0.993975	−	0.109603i	$-0.0349579\pi$
$272$	−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	0.939993	+	0.341193i	$0.110831\pi$
$277$	12.7401	+	22.0665i	0.765478	+	1.32585i	−0.174515	+	0.984655i	$0.555836\pi$
$278$	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	−0.998975	−	0.0452618i	$-0.985588\pi$
$283$	−9.06209	−	15.6960i	−0.538685	−	0.933031i	0.460290	−	0.887769i	$-0.347746\pi$
$284$	−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	$-0.366958\pi$
$293$	13.8958			0.811801			0.405901	+	0.913917i	$0.366958\pi$
$294$	−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	$-0.824207\pi$
$307$	−29.8332			−1.70267			−0.851335	+	0.524622i	$0.824207\pi$
$308$	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	0.608375	−	0.793650i	$-0.291822\pi$
$311$	−6.75662	−	11.7028i	−0.383133	−	0.663606i	−0.991508	+	0.130044i	$0.958488\pi$
$312$	2.13817	+	3.70343i	0.121050	+	0.209665i
$313$	−14.4928	+	25.1023i	−0.819184	+	1.41887i	0.0871001	+	0.996200i	$0.472240\pi$
$313$	−14.4928	+	25.1023i	−0.819184	+	1.41887i	−0.906284	+	0.422669i	$0.861093\pi$
$314$	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	$-0.822974\pi$
$317$	0.579319	−	1.00341i	0.0325378	−	0.0563571i	0.881836	+	0.471557i	$0.156308\pi$
$318$	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	−0.153355	−	0.988171i	$-0.549008\pi$
$331$	14.1746	−	24.5511i	0.779104	−	1.34945i	0.932459	−	0.361277i	$-0.117659\pi$
$332$	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	$-0.643270\pi$
$337$	−15.9729			−0.870101			−0.435051	+	0.900406i	$0.643270\pi$
$338$	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	$-0.0530998\pi$
$347$	6.50599	+	11.2687i	0.349260	+	0.604935i	−0.636859	+	0.770981i	$0.719766\pi$
$348$	−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	$-0.0508827\pi$
$353$	6.68445	+	11.5778i	0.355778	+	0.616225i	−0.631473	+	0.775398i	$0.717549\pi$
$354$	−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	−0.639363	−	0.768905i	$-0.720802\pi$
$359$	6.55974	−	11.3618i	0.346210	−	0.599653i	0.985573	+	0.169252i	$0.0541352\pi$
$360$		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	$-0.0552759\pi$
$367$	6.56798	+	11.3761i	0.342846	+	0.593826i	−0.642114	+	0.766609i	$0.721943\pi$
$368$	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	0.172450	+	0.985018i	$0.444832\pi$
$373$	−14.8099	+	25.6514i	−0.766826	+	1.32818i	−0.939276	+	0.343163i	$0.888502\pi$
$374$	−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	0.385307	+	0.922789i	$0.374096\pi$
$383$	−11.8695	+	20.5586i	−0.606505	+	1.05050i	−0.991812	+	0.127709i	$0.959238\pi$
$384$	−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	0.987664	−	0.156589i	$-0.0500499\pi$
$389$	7.06523	+	12.2373i	0.358221	+	0.620458i	−0.629442	+	0.777047i	$0.716717\pi$
$390$		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	$-0.742069\pi$
$397$	5.63479	−	9.75974i	0.282802	−	0.489827i	0.972074	+	0.234676i	$0.0754028\pi$
$398$	−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	0.413584	+	0.910466i	$0.364277\pi$
$401$	−11.6484	+	20.1757i	−0.581694	+	1.00752i	−0.995279	+	0.0970583i	$0.969057\pi$
$402$	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	−0.999926	−	0.0121481i	$-0.996133\pi$
$409$	−10.3239	−	17.8815i	−0.510484	−	0.884184i	0.489443	−	0.872036i	$-0.337200\pi$
$410$		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	0.979924	+	0.199369i	$0.0638894\pi$
$431$	13.7564	+	23.8267i	0.662621	+	1.14769i	−0.317303	+	0.948324i	$0.602777\pi$
$432$	−2.32594	+	4.02864i	−0.111907	+	0.193828i
$433$	−8.75514			−0.420745			−0.210373	−	0.977621i	$-0.567468\pi$
$433$	−8.75514			−0.420745			−0.210373	+	0.977621i	$0.567468\pi$
$434$	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	−0.711163	−	0.703028i	$-0.751831\pi$
$439$	5.30636	−	9.19088i	0.253259	−	0.438657i	0.964421	+	0.264371i	$0.0851643\pi$
$440$		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	$-0.675864\pi$
$443$	9.99278	−	17.3080i	0.474771	−	0.822328i	0.999583	+	0.0288905i	$0.00919742\pi$
$444$	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	$-0.850326\pi$
$457$	−1.14067	+	1.97570i	−0.0533584	+	0.0924195i	0.838112	+	0.545497i	$0.183659\pi$
$458$	−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	$-0.416737\pi$
$463$	11.1290			0.517211			0.258605	+	0.965983i	$0.416737\pi$
$464$	−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	0.319120	+	0.947714i	$0.396613\pi$
$467$	−14.2883	+	24.7481i	−0.661185	+	1.14521i	−0.980305	+	0.197491i	$0.936721\pi$
$468$	−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	0.922700	−	0.385519i	$-0.125978\pi$
$479$	2.79005	+	4.83250i	0.127480	+	0.220803i	−0.795219	+	0.606322i	$0.792644\pi$
$480$		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	$-0.227229\pi$
$487$	−4.17342	−	7.22858i	−0.189116	−	0.327558i	−0.944956	+	0.327198i	$0.893895\pi$
$488$	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	−0.412443	−	0.910983i	$-0.635324\pi$
$499$	13.0168	−	22.5458i	0.582713	−	1.00929i	0.995156	−	0.0983057i	$-0.0313423\pi$
$500$		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	$-0.460699\pi$
$503$	5.52409			0.246307			0.123154	+	0.992388i	$0.460699\pi$
$504$	−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	0.492690	+	0.870205i	$0.336014\pi$
$509$	−11.4446	+	19.8227i	−0.507274	+	0.878625i	−0.999965	+	0.00842016i	$0.997320\pi$
$510$		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	−0.996160	−	0.0875466i	$-0.972097\pi$
$521$	−13.0995	−	22.6889i	−0.573898	−	0.994020i	0.422263	−	0.906474i	$-0.361236\pi$
$522$	6.04998	+	10.4789i	0.264800	+	0.458648i
$523$	13.4380	−	23.2753i	0.587603	−	1.01776i	−0.406943	−	0.913454i	$-0.633405\pi$
$523$	13.4380	−	23.2753i	0.587603	−	1.01776i	0.994545	−	0.104304i	$-0.0332616\pi$
$524$	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	−0.590378	−	0.807127i	$-0.701021\pi$
$541$	9.39222	−	16.2678i	0.403803	−	0.699408i	0.994181	+	0.107719i	$0.0343547\pi$
$542$	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	$-0.592572\pi$
$547$	−13.4126			−0.573483			−0.286742	+	0.958008i	$0.592572\pi$
$548$	−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	−0.880003	−	0.474968i	$-0.842460\pi$
$557$	−20.0922	−	34.8008i	−0.851336	−	1.47456i	0.0286677	−	0.999589i	$-0.490874\pi$
$558$	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	0.999355	+	0.0359052i	$0.0114315\pi$
$563$	12.5940	+	21.8134i	0.530772	+	0.919325i	−0.468583	+	0.883420i	$0.655235\pi$
$564$	−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	−0.726885	−	0.686759i	$-0.759033\pi$
$569$	5.51757	−	9.55672i	0.231309	−	0.400638i	0.958194	+	0.286121i	$0.0923659\pi$
$570$		0			0
$571$	−14.3573	−	24.8677i	−0.600836	−	1.04068i	−0.992695	−	0.120654i	$-0.961501\pi$
$571$	−14.3573	−	24.8677i	−0.600836	−	1.04068i	0.391858	−	0.920026i	$-0.371832\pi$
$572$	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	$-0.121031\pi$
$577$	3.43202	+	5.94444i	0.142877	+	0.247470i	−0.785702	+	0.618605i	$0.787698\pi$
$578$	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	$-0.440268\pi$
$587$	9.03965			0.373106			0.186553	+	0.982445i	$0.440268\pi$
$588$	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	$-0.799888\pi$
$593$	2.55399	−	4.42364i	0.104880	−	0.181657i	0.913689	+	0.406414i	$0.133221\pi$
$594$	−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	0.990946	+	0.134259i	$0.0428654\pi$
$599$	14.9721	+	25.9325i	0.611745	+	1.05957i	−0.379202	+	0.925314i	$0.623801\pi$
$600$		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	$-0.895735\pi$
$607$	−4.79903	+	8.31216i	−0.194786	+	0.337380i	0.752044	+	0.659113i	$0.229068\pi$
$608$	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	−0.997607	−	0.0691416i	$-0.977974\pi$
$613$	−13.8323	−	23.9583i	−0.558682	−	0.967665i	0.438925	−	0.898524i	$-0.355359\pi$
$614$	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	$-0.634802\pi$
$617$	−20.4155			−0.821896			−0.410948	+	0.911659i	$0.634802\pi$
$618$	8.75046	−	15.1562i	0.351995	−	0.609673i
$619$	7.72112	+	13.3734i	0.310338	+	0.537521i	0.978435	−	0.206553i	$-0.0662245\pi$
$619$	7.72112	+	13.3734i	0.310338	+	0.537521i	−0.668098	+	0.744074i	$0.732891\pi$
$620$		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	0.982784	−	0.184757i	$-0.0591498\pi$
$641$	8.39007	+	14.5320i	0.331388	+	0.573981i	−0.651396	+	0.758738i	$0.725816\pi$
$642$	5.36820	−	9.29800i	0.211866	−	0.366963i
$643$	−14.2002			−0.560001			−0.280001	−	0.960000i	$-0.590335\pi$
$643$	−14.2002			−0.560001			−0.280001	+	0.960000i	$0.590335\pi$
$644$	−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	$-0.258594\pi$
$647$	−7.24426	−	12.5474i	−0.284801	−	0.493290i	−0.972561	+	0.232648i	$0.925261\pi$
$648$	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	$-0.897820\pi$
$653$	−5.14166	+	8.90562i	−0.201209	+	0.348504i	0.747709	+	0.664026i	$0.231154\pi$
$654$	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	0.841256	−	0.540638i	$-0.181817\pi$
$661$	−1.22323	−	2.11870i	−0.0475782	−	0.0824079i	−0.888834	+	0.458230i	$0.848484\pi$
$662$	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	$-0.392055\pi$
$673$	17.2596			0.665310			0.332655	+	0.943049i	$0.392055\pi$
$674$	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	$-0.905130\pi$
$677$	−5.81918	+	10.0791i	−0.223649	+	0.387372i	0.732264	+	0.681021i	$0.238464\pi$
$678$	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	0.993557	+	0.113333i	$0.0361526\pi$
$683$	15.5480	+	26.9299i	0.594928	+	1.03044i	−0.398629	+	0.917112i	$0.630514\pi$
$684$	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	−0.643522	−	0.765428i	$-0.722527\pi$
$691$	8.96695	−	15.5312i	0.341119	−	0.590835i	0.984641	+	0.174592i	$0.0558607\pi$
$692$	−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	−0.513080	−	0.858341i	$-0.671496\pi$
$709$	12.9622	−	22.4511i	0.486804	−	0.843170i	0.999885	+	0.0151705i	$0.00482909\pi$
$710$		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	0.411700	+	0.911320i	$0.364935\pi$
$719$	−15.6427	+	27.0940i	−0.583376	+	1.01044i	−0.995076	+	0.0991173i	$0.968398\pi$
$720$		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	$-0.639157\pi$
$727$	−22.8312			−0.846761			−0.423380	+	0.905952i	$0.639157\pi$
$728$	−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	$-0.868407\pi$
$733$	−2.97717	+	5.15661i	−0.109964	+	0.190464i	0.805791	+	0.592200i	$0.201740\pi$
$734$	−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	−0.941064	−	0.338228i	$-0.890173\pi$
$739$	−20.7539	−	35.9469i	−0.763446	−	1.32233i	0.177618	−	0.984099i	$-0.443161\pi$
$740$		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	$-0.460191\pi$
$743$	6.80015			0.249473			0.124737	+	0.992190i	$0.460191\pi$
$744$	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	−0.996942	−	0.0781464i	$-0.975100\pi$
$751$	−11.8056	+	20.4480i	−0.430794	+	0.746157i	0.566148	+	0.824304i	$0.308433\pi$
$752$	−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	$-0.595281\pi$
$757$	−16.2267			−0.589769			−0.294884	+	0.955533i	$0.595281\pi$
$758$	−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	−0.841941	−	0.539570i	$-0.818587\pi$
$761$	1.27754	−	2.21276i	0.0463108	−	0.0802126i	0.888252	+	0.459357i	$0.151920\pi$
$762$	−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	−0.789997	−	0.613110i	$-0.789918\pi$
$773$	−25.7446	−	44.5909i	−0.925968	−	1.60382i	−0.135970	−	0.990713i	$-0.543415\pi$
$774$	−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	$-0.0497297\pi$
$787$	10.0757	+	17.4517i	0.359161	+	0.622085i	−0.628660	+	0.777680i	$0.716396\pi$
$788$	−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	$-0.425641\pi$
$797$	13.0702			0.462971			0.231486	+	0.972838i	$0.425641\pi$
$798$	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	0.880891	−	0.473320i	$-0.156945\pi$
$809$	0.868598	+	1.50446i	0.0305383	+	0.0528938i	−0.850352	+	0.526214i	$0.823611\pi$
$810$		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	−0.975109	−	0.221725i	$-0.928831\pi$
$821$	−8.46799	+	14.6670i	−0.295535	+	0.511881i	0.679574	+	0.733607i	$0.262165\pi$
$822$	2.33009	+	4.03584i	0.0812714	+	0.140766i
$823$	4.94516	+	8.56526i	0.172377	+	0.298566i	0.939251	−	0.343232i	$-0.111522\pi$
$823$	4.94516	+	8.56526i	0.172377	+	0.298566i	−0.766873	+	0.641799i	$0.778188\pi$
$824$	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	$-0.710481\pi$
$827$	−35.3201			−1.22820			−0.614101	+	0.789228i	$0.710481\pi$
$828$	−1.43988	+	2.49395i	−0.0500393	+	0.0866706i
$829$	−4.64975	−	8.05361i	−0.161493	−	0.279713i	0.773912	−	0.633294i	$-0.218297\pi$
$829$	−4.64975	−	8.05361i	−0.161493	−	0.279713i	−0.935404	+	0.353580i	$0.884964\pi$
$830$		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	$-0.672166\pi$
$853$	−30.0757			−1.02977			−0.514887	+	0.857258i	$0.672166\pi$
$854$	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	0.916230	+	0.400652i	$0.131216\pi$
$857$	23.5686	+	40.8221i	0.805090	+	1.39446i	−0.111141	+	0.993805i	$0.535450\pi$
$858$	−5.95823	−	10.3199i	−0.203410	−	0.352317i
$859$	16.3183	−	28.2642i	0.556774	−	0.964361i	−0.440989	−	0.897512i	$-0.645372\pi$
$859$	16.3183	−	28.2642i	0.556774	−	0.964361i	0.997763	−	0.0668485i	$-0.0212944\pi$
$860$		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	0.349418	+	0.936967i	$0.386379\pi$
$863$	−18.7051	+	32.3982i	−0.636728	+	1.10285i	−0.986146	+	0.165879i	$0.946954\pi$
$864$	−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	0.430172	+	0.902747i	$0.358453\pi$
$877$	−16.7828	+	29.0687i	−0.566716	+	0.981581i	−0.996888	+	0.0788336i	$0.974880\pi$
$878$	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	$-0.559480\pi$
$883$	−11.0408			−0.371552			−0.185776	+	0.982592i	$0.559480\pi$
$884$	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	$-0.841676\pi$
$887$	−0.780464	+	1.35180i	−0.0262054	+	0.0453891i	0.852625	+	0.522523i	$0.175009\pi$
$888$	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	$-0.0733412\pi$
$907$	8.70390	+	15.0756i	0.289008	+	0.500577i	−0.684565	+	0.728952i	$0.740008\pi$
$908$	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	−0.989970	−	0.141281i	$-0.954878\pi$
$919$	−11.2963	+	19.5658i	−0.372632	+	0.645417i	0.617338	+	0.786698i	$0.288211\pi$
$920$		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	0.352265	+	0.935900i	$0.385412\pi$
$929$	−19.3356	+	33.4903i	−0.634381	+	1.09878i	−0.986646	+	0.162880i	$0.947922\pi$
$930$		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	$-0.223077\pi$
$937$	46.7921			1.52863			0.764316	+	0.644842i	$0.223077\pi$
$938$	−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	0.974116	+	0.226051i	$0.0725815\pi$
$941$	20.9461	+	36.2797i	0.682824	+	1.18268i	−0.291292	+	0.956634i	$0.594085\pi$
$942$	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	0.100134	−	0.994974i	$-0.468073\pi$
$947$	28.0573	−	48.5967i	0.911740	−	1.57918i	0.811605	−	0.584206i	$-0.198594\pi$
$948$	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	$-0.592931\pi$
$953$	−17.7705			−0.575643			−0.287821	+	0.957684i	$0.592931\pi$
$954$	−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	$-0.381654\pi$
$967$	22.5942			0.726579			0.363290	+	0.931676i	$0.381654\pi$
$968$	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	0.322303	+	0.946637i	$0.395543\pi$
$971$	−20.5244	+	35.5493i	−0.658660	+	1.14083i	−0.980963	+	0.194196i	$0.937790\pi$
$972$	−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	$-0.267499\pi$
$977$	−9.73668	−	16.8644i	−0.311504	−	0.539541i	−0.978688	+	0.205352i	$0.934166\pi$
$978$	−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	0.901980	+	0.431777i	$0.142113\pi$
$983$	25.8636	+	44.7970i	0.824920	+	1.42880i	−0.0770602	+	0.997026i	$0.524553\pi$
$984$	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	−0.996464	−	0.0840162i	$-0.973225\pi$
$991$	−17.9749	−	31.1335i	−0.570992	−	0.988988i	0.425472	−	0.904972i	$-0.360108\pi$
$992$	−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	0.842567	+	0.538592i	$0.181044\pi$
$997$	28.0300	+	48.5493i	0.887718	+	1.53757i	0.0451513	+	0.998980i	$0.485623\pi$
$998$	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.h.226.2		8
5.2	odd	4		105.2.q.a.79.3	yes	16
5.3	odd	4		105.2.q.a.79.6	yes	16
5.4	even	2		525.2.i.k.226.3		8
7.2	even	3		3675.2.a.bz.1.3		4
7.4	even	3	inner	525.2.i.h.151.2		8
7.5	odd	6		3675.2.a.cb.1.3		4
15.2	even	4		315.2.bf.b.289.6		16
15.8	even	4		315.2.bf.b.289.3		16
20.3	even	4		1680.2.di.d.289.8		16
20.7	even	4		1680.2.di.d.289.1		16
35.2	odd	12		735.2.d.d.589.6		8
35.3	even	12		735.2.q.g.214.3		16
35.4	even	6		525.2.i.k.151.3		8
35.9	even	6		3675.2.a.bp.1.2		4
35.12	even	12		735.2.d.e.589.6		8
35.13	even	4		735.2.q.g.79.6		16
35.17	even	12		735.2.q.g.214.6		16
35.18	odd	12		105.2.q.a.4.3	✓	16
35.19	odd	6		3675.2.a.bn.1.2		4
35.23	odd	12		735.2.d.d.589.3		8
35.27	even	4		735.2.q.g.79.3		16
35.32	odd	12		105.2.q.a.4.6	yes	16
35.33	even	12		735.2.d.e.589.3		8
105.2	even	12		2205.2.d.s.1324.3		8
105.23	even	12		2205.2.d.s.1324.6		8
105.32	even	12		315.2.bf.b.109.3		16
105.47	odd	12		2205.2.d.o.1324.3		8
105.53	even	12		315.2.bf.b.109.6		16
105.68	odd	12		2205.2.d.o.1324.6		8
140.67	even	12		1680.2.di.d.529.8		16
140.123	even	12		1680.2.di.d.529.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.3	✓	16	35.18	odd	12
105.2.q.a.4.6	yes	16	35.32	odd	12
105.2.q.a.79.3	yes	16	5.2	odd	4
105.2.q.a.79.6	yes	16	5.3	odd	4
315.2.bf.b.109.3		16	105.32	even	12
315.2.bf.b.109.6		16	105.53	even	12
315.2.bf.b.289.3		16	15.8	even	4
315.2.bf.b.289.6		16	15.2	even	4
525.2.i.h.151.2		8	7.4	even	3	inner
525.2.i.h.226.2		8	1.1	even	1	trivial
525.2.i.k.151.3		8	35.4	even	6
525.2.i.k.226.3		8	5.4	even	2
735.2.d.d.589.3		8	35.23	odd	12
735.2.d.d.589.6		8	35.2	odd	12
735.2.d.e.589.3		8	35.33	even	12
735.2.d.e.589.6		8	35.12	even	12
735.2.q.g.79.3		16	35.27	even	4
735.2.q.g.79.6		16	35.13	even	4
735.2.q.g.214.3		16	35.3	even	12
735.2.q.g.214.6		16	35.17	even	12
1680.2.di.d.289.1		16	20.7	even	4
1680.2.di.d.289.8		16	20.3	even	4
1680.2.di.d.529.1		16	140.123	even	12
1680.2.di.d.529.8		16	140.67	even	12
2205.2.d.o.1324.3		8	105.47	odd	12
2205.2.d.o.1324.6		8	105.68	odd	12
2205.2.d.s.1324.3		8	105.2	even	12
2205.2.d.s.1324.6		8	105.23	even	12
3675.2.a.bn.1.2		4	35.19	odd	6
3675.2.a.bp.1.2		4	35.9	even	6
3675.2.a.bz.1.3		4	7.2	even	3
3675.2.a.cb.1.3		4	7.5	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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