LMFDB - Embedded newform 525.2.q.f.374.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(299,525)]

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([3, 3, 5]))

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

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

chi := DirichletCharacter("525.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11x^{14} + 85x^{12} + 332x^{10} + 940x^{8} + 1064x^{6} + 880x^{4} + 128x^{2} + 16 $ x^16 + 11x^14 + 85x^12 + 332x^10 + 940x^8 + 1064x^6 + 880x^4 + 128*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			374.8
Root			$-1.16543 - 2.01859i$ of defining polynomial
Character	$\chi$	$=$	525.374
Dual form			525.2.q.f.299.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16543 + 2.01859i) q^{2} +(1.23297 - 1.21646i) q^{3} +(-1.71646 + 2.97300i) q^{4} +(3.89248 + 1.07116i) q^{6} +(2.39840 - 1.11699i) q^{7} -3.33995 q^{8} +(0.0404447 - 2.99973i) q^{9} +O(q^{10})$	\(q+(1.16543 + 2.01859i) q^{2} +(1.23297 - 1.21646i) q^{3} +(-1.71646 + 2.97300i) q^{4} +(3.89248 + 1.07116i) q^{6} +(2.39840 - 1.11699i) q^{7} -3.33995 q^{8} +(0.0404447 - 2.99973i) q^{9} +(2.42019 + 1.39730i) q^{11} +(1.50019 + 5.75363i) q^{12} -3.20486 q^{13} +(5.04991 + 3.53962i) q^{14} +(-0.459555 - 0.795973i) q^{16} +(0.763780 + 0.440969i) q^{17} +(6.10234 - 3.41434i) q^{18} +(-1.90160 + 1.09789i) q^{19} +(1.59840 - 4.29478i) q^{21} +6.51381i q^{22} +(3.77148 + 6.53240i) q^{23} +(-4.11806 + 4.06291i) q^{24} +(-3.73505 - 6.46929i) q^{26} +(-3.59918 - 3.74778i) q^{27} +(-0.795973 + 9.04771i) q^{28} -8.15270i q^{29} +(-7.62645 - 4.40313i) q^{31} +(-2.26878 + 3.92965i) q^{32} +(4.68378 - 1.22124i) q^{33} +2.05568i q^{34} +(8.84876 + 5.26916i) q^{36} +(-0.352865 + 0.203727i) q^{37} +(-4.43237 - 2.55903i) q^{38} +(-3.95151 + 3.89859i) q^{39} -8.55098 q^{41} +(10.5322 - 1.77876i) q^{42} -0.118062i q^{43} +(-8.30832 + 4.79681i) q^{44} +(-8.79081 + 15.2261i) q^{46} +(-2.27740 + 1.31486i) q^{47} +(-1.53489 - 0.422382i) q^{48} +(4.50469 - 5.35796i) q^{49} +(1.47814 - 0.385407i) q^{51} +(5.50102 - 9.52805i) q^{52} +(-3.73427 + 6.46794i) q^{53} +(3.37062 - 11.6330i) q^{54} +(-8.01054 + 3.73067i) q^{56} +(-1.00908 + 3.66689i) q^{57} +(16.4569 - 9.50142i) q^{58} +(-2.04991 + 3.55054i) q^{59} +(10.7004 - 6.17786i) q^{61} -20.5262i q^{62} +(-3.25365 - 7.23974i) q^{63} -12.4147 q^{64} +(7.92380 + 8.03135i) q^{66} +(-1.38932 - 0.802125i) q^{67} +(-2.62200 + 1.51381i) q^{68} +(12.5965 + 3.46641i) q^{69} -6.25869i q^{71} +(-0.135083 + 10.0189i) q^{72} +(-0.110864 + 0.192022i) q^{73} +(-0.822480 - 0.474859i) q^{74} -7.53794i q^{76} +(7.36535 + 0.647967i) q^{77} +(-12.4749 - 3.43292i) q^{78} +(-1.56849 - 2.71671i) q^{79} +(-8.99673 - 0.242646i) q^{81} +(-9.96559 - 17.2609i) q^{82} -0.666893i q^{83} +(10.0248 + 12.1239i) q^{84} +(0.238319 - 0.137594i) q^{86} +(-9.91745 - 10.0521i) q^{87} +(-8.08330 - 4.66689i) q^{88} +(0.437271 + 0.757376i) q^{89} +(-7.68656 + 3.57978i) q^{91} -25.8944 q^{92} +(-14.7594 + 3.84834i) q^{93} +(-5.30832 - 3.06476i) q^{94} +(1.98292 + 7.60504i) q^{96} -6.37221 q^{97} +(16.0654 + 2.84876i) q^{98} +(4.28939 - 7.20339i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9}+O(q^{10}) $ 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9	$ 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9} + 24 q^{14} + 2 q^{16} - 18 q^{19} + 38 q^{21} - 32 q^{24} - 12 q^{26} - 42 q^{31} + 18 q^{36} + 6 q^{39} - 60 q^{41} - 14 q^{46} + 8 q^{49} - 12 q^{51} - 34 q^{54} - 42 q^{56} + 24 q^{59} + 30 q^{61} - 76 q^{64} + 44 q^{66} + 26 q^{69} - 108 q^{74} + 58 q^{79} - 82 q^{81} + 6 q^{84} + 18 q^{86} + 6 q^{89} - 6 q^{91} + 48 q^{94} - 6 q^{96} + 68 q^{99}+O(q^{100}) $ 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9 + 24 * q^14 + 2 * q^16 - 18 * q^19 + 38 * q^21 - 32 * q^24 - 12 * q^26 - 42 * q^31 + 18 * q^36 + 6 * q^39 - 60 * q^41 - 14 * q^46 + 8 * q^49 - 12 * q^51 - 34 * q^54 - 42 * q^56 + 24 * q^59 + 30 * q^61 - 76 * q^64 + 44 * q^66 + 26 * q^69 - 108 * q^74 + 58 * q^79 - 82 * q^81 + 6 * q^84 + 18 * q^86 + 6 * q^89 - 6 * q^91 + 48 * q^94 - 6 * q^96 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.16543	+	2.01859i	0.824085	+	1.42736i	0.902617	+	0.430445i	$0.141643\pi$
$2$	1.16543	+	2.01859i	0.824085	+	1.42736i	−0.0785324	+	0.996912i	$0.525023\pi$
$3$	1.23297	−	1.21646i	0.711857	−	0.702324i
$3$	1.23297	−	1.21646i	0.711857	−	0.702324i
$4$	−1.71646	+	2.97300i	−0.858231	+	1.48650i
$5$		0			0
$5$		0			0
$6$	3.89248	+	1.07116i	1.58910	+	0.437299i
$7$	2.39840	−	1.11699i	0.906512	−	0.422181i
$7$	2.39840	−	1.11699i	0.906512	−	0.422181i
$8$	−3.33995			−1.18085
$9$	0.0404447	−	2.99973i	0.0134816	−	0.999909i
$10$		0			0
$11$	2.42019	+	1.39730i	0.729714	+	0.421301i	0.818318	−	0.574766i	$-0.194907\pi$
$11$	2.42019	+	1.39730i	0.729714	+	0.421301i	−0.0886035	+	0.996067i	$0.528240\pi$
$12$	1.50019	+	5.75363i	0.433066	+	1.66093i
$13$	−3.20486			−0.888869			−0.444434	−	0.895811i	$-0.646595\pi$
$13$	−3.20486			−0.888869			−0.444434	+	0.895811i	$0.646595\pi$
$14$	5.04991	+	3.53962i	1.34964	+	0.946002i
$15$		0			0
$16$	−0.459555	−	0.795973i	−0.114889	−	0.198993i
$17$	0.763780	+	0.440969i	0.185244	+	0.106951i	0.589754	−	0.807583i	$-0.299225\pi$
$17$	0.763780	+	0.440969i	0.185244	+	0.106951i	−0.404510	+	0.914533i	$0.632558\pi$
$18$	6.10234	−	3.41434i	1.43834	−	0.804767i
$19$	−1.90160	+	1.09789i	−0.436257	+	0.251873i	−0.702009	−	0.712168i	$-0.747713\pi$
$19$	−1.90160	+	1.09789i	−0.436257	+	0.251873i	0.265751	+	0.964042i	$0.414380\pi$
$20$		0			0
$21$	1.59840	−	4.29478i	0.348799	−	0.937197i
$22$			6.51381i			1.38875i
$23$	3.77148	+	6.53240i	0.786408	+	1.36210i	0.928154	+	0.372196i	$0.121395\pi$
$23$	3.77148	+	6.53240i	0.786408	+	1.36210i	−0.141746	+	0.989903i	$0.545272\pi$
$24$	−4.11806	+	4.06291i	−0.840596	+	0.829339i
$25$		0			0
$26$	−3.73505	−	6.46929i	−0.732503	−	1.26873i
$27$	−3.59918	−	3.74778i	−0.692663	−	0.721261i
$28$	−0.795973	+	9.04771i	−0.150425	+	1.70986i
$29$		−	8.15270i		−	1.51392i	−0.653462	−	0.756959i	$-0.726684\pi$
$29$		−	8.15270i		−	1.51392i	0.653462	−	0.756959i	$-0.273316\pi$
$30$		0			0
$31$	−7.62645	−	4.40313i	−1.36975	−	0.790826i	−0.378855	−	0.925456i	$-0.623682\pi$
$31$	−7.62645	−	4.40313i	−1.36975	−	0.790826i	−0.990896	+	0.134630i	$0.957015\pi$
$32$	−2.26878	+	3.92965i	−0.401068	+	0.694671i
$33$	4.68378	−	1.22124i	0.815342	−	0.212590i
$34$			2.05568i			0.352545i
$35$		0			0
$36$	8.84876	+	5.26916i	1.47479	+	0.878193i
$37$	−0.352865	+	0.203727i	−0.0580107	+	0.0334925i	−0.528725	−	0.848793i	$-0.677330\pi$
$37$	−0.352865	+	0.203727i	−0.0580107	+	0.0334925i	0.470714	+	0.882286i	$0.343996\pi$
$38$	−4.43237	−	2.55903i	−0.719026	−	0.415130i
$39$	−3.95151	+	3.89859i	−0.632748	+	0.624274i
$40$		0			0
$41$	−8.55098			−1.33544			−0.667720	−	0.744413i	$-0.732730\pi$
$41$	−8.55098			−1.33544			−0.667720	+	0.744413i	$0.732730\pi$
$42$	10.5322	−	1.77876i	1.62515	−	0.274469i
$43$		−	0.118062i		−	0.0180044i	−0.999959	−	0.00900218i	$-0.997134\pi$
$43$		−	0.118062i		−	0.0180044i	0.999959	−	0.00900218i	$-0.00286552\pi$
$44$	−8.30832	+	4.79681i	−1.25253	+	0.723146i
$45$		0			0
$46$	−8.79081	+	15.2261i	−1.29613	+	2.24497i
$47$	−2.27740	+	1.31486i	−0.332194	+	0.191792i	−0.656815	−	0.754052i	$-0.728097\pi$
$47$	−2.27740	+	1.31486i	−0.332194	+	0.191792i	0.324621	+	0.945844i	$0.394763\pi$
$48$	−1.53489	−	0.422382i	−0.221542	−	0.0609656i
$49$	4.50469	−	5.35796i	0.643527	−	0.765424i
$50$		0			0
$51$	1.47814	−	0.385407i	0.206981	−	0.0539677i
$52$	5.50102	−	9.52805i	0.762854	−	1.32130i
$53$	−3.73427	+	6.46794i	−0.512941	+	0.888440i	0.486946	+	0.873432i	$0.338111\pi$
$53$	−3.73427	+	6.46794i	−0.512941	+	0.888440i	−0.999887	+	0.0150081i	$0.995223\pi$
$54$	3.37062	−	11.6330i	0.458683	−	1.58306i
$55$		0			0
$56$	−8.01054	+	3.73067i	−1.07045	+	0.498532i
$57$	−1.00908	+	3.66689i	−0.133656	+	0.485692i
$58$	16.4569	−	9.50142i	2.16090	−	1.24760i
$59$	−2.04991	+	3.55054i	−0.266875	+	0.462241i	−0.968053	−	0.250745i	$-0.919324\pi$
$59$	−2.04991	+	3.55054i	−0.266875	+	0.462241i	0.701178	+	0.712986i	$0.252658\pi$
$60$		0			0
$61$	10.7004	−	6.17786i	1.37004	−	0.790994i	0.379109	−	0.925352i	$-0.376231\pi$
$61$	10.7004	−	6.17786i	1.37004	−	0.790994i	0.990933	+	0.134358i	$0.0428972\pi$
$62$		−	20.5262i		−	2.60683i
$63$	−3.25365	−	7.23974i	−0.409921	−	0.912121i
$64$	−12.4147			−1.55183
$65$		0			0
$66$	7.92380	+	8.03135i	0.975352	+	0.988591i
$67$	−1.38932	−	0.802125i	−0.169733	−	0.0979952i	0.412727	−	0.910855i	$-0.364576\pi$
$67$	−1.38932	−	0.802125i	−0.169733	−	0.0979952i	−0.582460	+	0.812860i	$0.697910\pi$
$68$	−2.62200	+	1.51381i	−0.317964	+	0.183577i
$69$	12.5965	+	3.46641i	1.51645	+	0.417307i
$70$		0			0
$71$		−	6.25869i		−	0.742770i	−0.928479	−	0.371385i	$-0.878883\pi$
$71$		−	6.25869i		−	0.742770i	0.928479	−	0.371385i	$-0.121117\pi$
$72$	−0.135083	+	10.0189i	−0.0159197	+	1.18074i
$73$	−0.110864	+	0.192022i	−0.0129757	+	0.0224745i	−0.872440	−	0.488721i	$-0.837464\pi$
$73$	−0.110864	+	0.192022i	−0.0129757	+	0.0224745i	0.859465	+	0.511195i	$0.170797\pi$
$74$	−0.822480	−	0.474859i	−0.0956114	−	0.0552012i
$75$		0			0
$76$		−	7.53794i		−	0.864661i
$77$	7.36535	+	0.647967i	0.839359	+	0.0738427i
$78$	−12.4749	−	3.43292i	−1.41250	−	0.388702i
$79$	−1.56849	−	2.71671i	−0.176469	−	0.305654i	0.764199	−	0.644980i	$-0.223134\pi$
$79$	−1.56849	−	2.71671i	−0.176469	−	0.305654i	−0.940669	+	0.339326i	$0.889801\pi$
$80$		0			0
$81$	−8.99673	−	0.242646i	−0.999636	−	0.0269607i
$82$	−9.96559	−	17.2609i	−1.10051	−	1.90615i
$83$		−	0.666893i		−	0.0732010i	−0.999330	−	0.0366005i	$-0.988347\pi$
$83$		−	0.666893i		−	0.0732010i	0.999330	−	0.0366005i	$-0.0116529\pi$
$84$	10.0248	+	12.1239i	1.09379	+	1.32282i
$85$		0			0
$86$	0.238319	−	0.137594i	0.0256986	−	0.0148371i
$87$	−9.91745	−	10.0521i	−1.06326	−	1.07769i
$88$	−8.08330	−	4.66689i	−0.861682	−	0.497492i
$89$	0.437271	+	0.757376i	0.0463506	+	0.0802816i	0.888270	−	0.459322i	$-0.151908\pi$
$89$	0.437271	+	0.757376i	0.0463506	+	0.0802816i	−0.841919	+	0.539603i	$0.818574\pi$
$90$		0			0
$91$	−7.68656	+	3.57978i	−0.805770	+	0.375263i
$92$	−25.8944			−2.69968
$93$	−14.7594	+	3.84834i	−1.53048	+	0.399054i
$94$	−5.30832	−	3.06476i	−0.547511	−	0.316106i
$95$		0			0
$96$	1.98292	+	7.60504i	0.202381	+	0.776186i
$97$	−6.37221			−0.647000			−0.323500	−	0.946228i	$-0.604860\pi$
$97$	−6.37221			−0.647000			−0.323500	+	0.946228i	$0.604860\pi$
$98$	16.0654	+	2.84876i	1.62285	+	0.287768i
$99$	4.28939	−	7.20339i	0.431100	−	0.723968i
$100$		0			0
$101$	5.31267	−	9.20181i	0.528630	−	0.915614i	−0.470813	−	0.882233i	$-0.656039\pi$
$101$	5.31267	−	9.20181i	0.528630	−	0.915614i	0.999443	−	0.0333808i	$-0.0106274\pi$
$102$	2.50065	+	2.53459i	0.247601	+	0.250962i
$103$	−0.501589	−	0.868777i	−0.0494230	−	0.0856031i	0.840256	−	0.542191i	$-0.182405\pi$
$103$	−0.501589	−	0.868777i	−0.0494230	−	0.0856031i	−0.889679	+	0.456587i	$0.849072\pi$
$104$	10.7041			1.04962
$105$		0			0
$106$	−17.4081			−1.69083
$107$	6.38846	+	11.0651i	0.617596	+	1.06971i	0.989923	+	0.141606i	$0.0452265\pi$
$107$	6.38846	+	11.0651i	0.617596	+	1.06971i	−0.372328	+	0.928101i	$0.621440\pi$
$108$	17.3200	−	4.26745i	1.66662	−	0.410635i
$109$	0.00912370	−	0.0158027i	0.000873892	−	0.00151363i	−0.865588	−	0.500757i	$-0.833055\pi$
$109$	0.00912370	−	0.0158027i	0.000873892	−	0.00151363i	0.866462	+	0.499243i	$0.166388\pi$
$110$		0			0
$111$	−0.187247	+	0.680436i	−0.0177727	+	0.0645841i
$112$	−1.99129	−	1.39575i	−0.188159	−	0.131886i
$113$	7.23027			0.680166			0.340083	−	0.940395i	$-0.389545\pi$
$113$	7.23027			0.680166			0.340083	+	0.940395i	$0.389545\pi$
$114$	−8.57796	+	2.23659i	−0.803399	+	0.209476i
$115$		0			0
$116$	24.2380	+	13.9938i	2.25044	+	1.29929i
$117$	−0.129620	+	9.61371i	−0.0119833	+	0.888788i
$118$	−9.55611			−0.879711
$119$	2.32441	+	0.204490i	0.213078	+	0.0187456i
$120$		0			0
$121$	−1.59513	−	2.76284i	−0.145012	−	0.251167i
$122$	24.9411	+	14.3997i	2.25806	+	1.30369i
$123$	−10.5431	+	10.4019i	−0.950642	+	0.937911i
$124$	26.1810	−	15.1156i	2.35112	−	1.35742i
$125$		0			0
$126$	10.8221	−	15.0052i	0.964112	−	1.33677i
$127$		−	6.99561i		−	0.620760i	−0.950613	−	0.310380i	$-0.899544\pi$
$127$		−	6.99561i		−	0.620760i	0.950613	−	0.310380i	$-0.100456\pi$
$128$	−9.93088	−	17.2008i	−0.877774	−	1.52035i
$129$	−0.143618	−	0.145568i	−0.0126449	−	0.0128165i
$130$		0			0
$131$	4.94673	+	8.56799i	0.432198	+	0.748589i	0.997062	−	0.0765948i	$-0.0244048\pi$
$131$	4.94673	+	8.56799i	0.432198	+	0.748589i	−0.564864	+	0.825184i	$0.691071\pi$
$132$	−4.40880	+	16.0211i	−0.383737	+	1.39446i
$133$	−3.33448	+	4.75724i	−0.289136	+	0.412505i
$134$		−	3.73929i		−	0.323025i
$135$		0			0
$136$	−2.55098	−	1.47281i	−0.218745	−	0.126293i
$137$	−6.29951	+	10.9111i	−0.538203	+	0.932195i	0.460798	+	0.887505i	$0.347563\pi$
$137$	−6.29951	+	10.9111i	−0.538203	+	0.932195i	−0.999001	+	0.0446900i	$0.985770\pi$
$138$	7.68316	+	29.4671i	0.654034	+	2.50840i
$139$		−	0.988113i		−	0.0838106i	−0.999122	−	0.0419053i	$-0.986657\pi$
$139$		−	0.988113i		−	0.0838106i	0.999122	−	0.0419053i	$-0.0133428\pi$
$140$		0			0
$141$	−1.20850	+	4.39156i	−0.101774	+	0.369836i
$142$	12.6337	−	7.29408i	1.06020	−	0.612106i
$143$	−7.75637	−	4.47814i	−0.648620	−	0.374481i
$144$	−2.40629	+	1.34635i	−0.200524	+	0.112196i
$145$		0			0
$146$	−0.516818			−0.0427722
$147$	−0.963598	−	12.0860i	−0.0794762	−	0.996837i
$148$		−	1.39876i		−	0.114977i
$149$	−15.3604	+	8.86834i	−1.25837	+	0.726523i	−0.972758	−	0.231821i	$-0.925532\pi$
$149$	−15.3604	+	8.86834i	−1.25837	+	0.726523i	−0.285616	+	0.958344i	$0.592198\pi$
$150$		0			0
$151$	11.2504	−	19.4862i	0.915542	−	1.58576i	0.109435	−	0.993994i	$-0.465096\pi$
$151$	11.2504	−	19.4862i	0.915542	−	1.58576i	0.806106	−	0.591771i	$-0.201571\pi$
$152$	6.35124	−	3.66689i	0.515154	−	0.297424i
$153$	1.35368	−	2.27330i	0.109438	−	0.183785i
$154$	7.27583	+	15.6228i	0.586303	+	1.25892i
$155$		0			0
$156$	−4.80789	−	18.4396i	−0.384939	−	1.47635i
$157$	−5.94600	+	10.2988i	−0.474542	+	0.821931i	−0.999575	−	0.0291509i	$-0.990720\pi$
$157$	−5.94600	+	10.2988i	−0.474542	+	0.821931i	0.525033	+	0.851082i	$0.324053\pi$
$158$	3.65594	−	6.33228i	0.290851	−	0.503769i
$159$	3.26375	+	12.5174i	0.258832	+	0.992693i
$160$		0			0
$161$	16.3421	+	11.4546i	1.28794	+	0.902752i
$162$	−9.99527	−	18.4435i	−0.785302	−	1.44906i
$163$	7.38130	−	4.26159i	0.578148	−	0.333794i	−0.182249	−	0.983252i	$-0.558338\pi$
$163$	7.38130	−	4.26159i	0.578148	−	0.333794i	0.760397	+	0.649459i	$0.225004\pi$
$164$	14.6774	−	25.4221i	1.14611	−	1.98513i
$165$		0			0
$166$	1.34618	−	0.777218i	0.104484	−	0.0603238i
$167$		−	3.56923i		−	0.276195i	−0.990419	−	0.138098i	$-0.955901\pi$
$167$		−	3.56923i		−	0.276195i	0.990419	−	0.138098i	$-0.0440988\pi$
$168$	−5.33856	+	14.3443i	−0.411879	+	1.10669i
$169$	−2.72886			−0.209912
$170$		0			0
$171$	3.21646	+	5.74869i	0.245969	+	0.439613i
$172$	0.350999	+	0.202650i	0.0267634	+	0.0154519i
$173$	7.39784	−	4.27114i	0.562447	−	0.324729i	−0.191680	−	0.981457i	$-0.561394\pi$
$173$	7.39784	−	4.27114i	0.562447	−	0.324729i	0.754127	+	0.656728i	$0.228060\pi$
$174$	8.73285	−	31.7342i	0.662036	−	2.40576i
$175$		0			0
$176$		−	2.56854i		−	0.193611i
$177$	1.79162	+	6.87136i	0.134666	+	0.516483i
$178$	−1.01922	+	1.76534i	−0.0763937	+	0.132318i
$179$	−1.06480	−	0.614760i	−0.0795866	−	0.0459493i	0.459679	−	0.888085i	$-0.347965\pi$
$179$	−1.06480	−	0.614760i	−0.0795866	−	0.0459493i	−0.539265	+	0.842136i	$0.681298\pi$
$180$		0			0
$181$			15.3995i			1.14464i	0.820032	+	0.572318i	$0.193956\pi$
$181$			15.3995i			1.14464i	−0.820032	+	0.572318i	$0.806044\pi$
$182$	−16.1843	−	11.3440i	−1.19966	−	0.840872i
$183$	5.67814	−	20.6337i	0.419740	−	1.52529i
$184$	−12.5965	−	21.8179i	−0.928630	−	1.60843i
$185$		0			0
$186$	−24.9693	−	25.3082i	−1.83084	−	1.85569i
$187$	1.23233	+	2.13445i	0.0901167	+	0.156087i
$188$		−	9.02762i		−	0.658407i
$189$	−12.8185	−	4.96846i	−0.932410	−	0.361402i
$190$		0			0
$191$	−12.5795	+	7.26275i	−0.910218	+	0.525514i	−0.880501	−	0.474044i	$-0.842794\pi$
$191$	−12.5795	+	7.26275i	−0.910218	+	0.525514i	−0.0297166	+	0.999558i	$0.509460\pi$
$192$	−15.3070	+	15.1020i	−1.10468	+	1.08989i
$193$	0.349134	+	0.201572i	0.0251312	+	0.0145095i	0.512513	−	0.858679i	$-0.328715\pi$
$193$	0.349134	+	0.201572i	0.0251312	+	0.0145095i	−0.487382	+	0.873189i	$0.662048\pi$
$194$	−7.42638	−	12.8629i	−0.533183	−	0.923500i
$195$		0			0
$196$	8.19710	+	22.5892i	0.585507	+	1.61351i
$197$	11.6716			0.831564			0.415782	−	0.909464i	$-0.363508\pi$
$197$	11.6716			0.831564			0.415782	+	0.909464i	$0.363508\pi$
$198$	19.5397	+	0.263449i	1.38862	+	0.0187225i
$199$	16.0886	+	9.28875i	1.14049	+	0.658462i	0.946552	−	0.322552i	$-0.104541\pi$
$199$	16.0886	+	9.28875i	1.14049	+	0.658462i	0.193938	+	0.981014i	$0.437874\pi$
$200$		0			0
$201$	−2.68875	+	0.701057i	−0.189650	+	0.0494488i
$202$	24.7662			1.74254
$203$	−9.10645	−	19.5535i	−0.639147	−	1.37239i
$204$	−1.39136	+	5.05605i	−0.0974147	+	0.353994i
$205$		0			0
$206$	1.16913	−	2.02500i	0.0814574	−	0.141088i
$207$	19.7479	−	11.0492i	1.37258	−	0.767974i
$208$	1.47281	+	2.55098i	0.102121	+	0.176879i
$209$	−6.13631			−0.424457
$210$		0			0
$211$	6.98175			0.480644			0.240322	−	0.970693i	$-0.422747\pi$
$211$	6.98175			0.480644			0.240322	+	0.970693i	$0.422747\pi$
$212$	−12.8194	−	22.2039i	−0.880443	−	1.52497i
$213$	−7.61346	−	7.71680i	−0.521666	−	0.528746i
$214$	−14.8906	+	25.7913i	−1.01790	+	1.76306i
$215$		0			0
$216$	12.0211	+	12.5174i	0.817931	+	0.851700i
$217$	−23.2095	−	2.04186i	−1.57557	−	0.138611i
$218$	0.0425322			0.00288064
$219$	0.0968952	+	0.371620i	0.00654757	+	0.0251118i
$220$		0			0
$221$	−2.44781	−	1.41324i	−0.164658	−	0.0950651i
$222$	−1.59174	+	0.415027i	−0.106831	+	0.0278548i
$223$	1.44594			0.0968271			0.0484135	−	0.998827i	$-0.484583\pi$
$223$	1.44594			0.0968271			0.0484135	+	0.998827i	$0.484583\pi$
$224$	−1.05210	+	11.9591i	−0.0702965	+	0.799050i
$225$		0			0
$226$	8.42638	+	14.5949i	0.560514	+	0.970839i
$227$	0.924157	+	0.533562i	0.0613385	+	0.0354138i	0.530356	−	0.847775i	$-0.322058\pi$
$227$	0.924157	+	0.533562i	0.0613385	+	0.0354138i	−0.469017	+	0.883189i	$0.655392\pi$
$228$	−9.16961	−	9.29408i	−0.607272	−	0.615515i
$229$	6.58058	−	3.79930i	0.434857	−	0.251065i	−0.266557	−	0.963819i	$-0.585886\pi$
$229$	6.58058	−	3.79930i	0.434857	−	0.251065i	0.701414	+	0.712755i	$0.252553\pi$
$230$		0			0
$231$	9.86950	−	8.16073i	0.649366	−	0.536937i
$232$			27.2296i			1.78771i
$233$	8.99983	+	15.5882i	0.589598	+	1.02121i	0.994285	+	0.106759i	$0.0340473\pi$
$233$	8.99983	+	15.5882i	0.589598	+	1.02121i	−0.404687	+	0.914455i	$0.632619\pi$
$234$	−19.5572	+	10.9425i	−1.27849	+	0.715332i
$235$		0			0
$236$	−7.03717	−	12.1887i	−0.458081	−	0.793419i
$237$	−5.23868	−	1.44162i	−0.340289	−	0.0936433i
$238$	2.29616	+	4.93034i	0.148838	+	0.319587i
$239$			29.8816i			1.93288i	0.256892	+	0.966440i	$0.417302\pi$
$239$			29.8816i			1.93288i	−0.256892	+	0.966440i	$0.582698\pi$
$240$		0			0
$241$	4.53760	+	2.61978i	0.292292	+	0.168755i	0.638975	−	0.769227i	$-0.279359\pi$
$241$	4.53760	+	2.61978i	0.292292	+	0.168755i	−0.346683	+	0.937982i	$0.612692\pi$
$242$	3.71802	−	6.43980i	0.239004	−	0.413966i
$243$	−11.3879	+	10.6450i	−0.730534	+	0.682877i
$244$			42.4162i			2.71542i
$245$		0			0
$246$	−33.2845	−	9.15948i	−2.12214	−	0.583987i
$247$	6.09437	−	3.51859i	0.387776	−	0.223882i
$248$	25.4719	+	14.7062i	1.61747	+	0.933846i
$249$	−0.811249	−	0.822261i	−0.0514108	−	0.0521087i
$250$		0			0
$251$	−15.0765			−0.951620			−0.475810	−	0.879548i	$-0.657845\pi$
$251$	−15.0765			−0.951620			−0.475810	+	0.879548i	$0.657845\pi$
$252$	27.1085	+	2.75363i	1.70767	+	0.173463i
$253$			21.0795i			1.32526i
$254$	14.1212	−	8.15291i	0.886046	−	0.511559i
$255$		0			0
$256$	10.7329	−	18.5898i	0.670803	−	1.16187i
$257$	13.7781	−	7.95478i	0.859453	−	0.496206i	−0.00437591	−	0.999990i	$-0.501393\pi$
$257$	13.7781	−	7.95478i	0.859453	−	0.496206i	0.863829	+	0.503785i	$0.168060\pi$
$258$	0.126464	−	0.459555i	0.00787329	−	0.0286107i
$259$	−0.618753	+	0.882764i	−0.0384475	+	0.0548523i
$260$		0			0
$261$	−24.4559	−	0.329733i	−1.51378	−	0.0204100i
$262$	−11.5302	+	19.9708i	−0.712336	+	1.23380i
$263$	−4.15187	+	7.19124i	−0.256015	+	0.443431i	−0.965171	−	0.261621i	$-0.915743\pi$
$263$	−4.15187	+	7.19124i	−0.256015	+	0.443431i	0.709156	+	0.705052i	$0.249076\pi$
$264$	−15.6436	+	4.07886i	−0.962796	+	0.251037i
$265$		0			0
$266$	−13.4890	−	1.18670i	−0.827065	−	0.0727611i
$267$	1.46046	+	0.401900i	0.0893788	+	0.0245959i
$268$	4.76943	−	2.75363i	0.291340	−	0.168205i
$269$	−8.69353	+	15.0576i	−0.530054	+	0.918080i	0.469332	+	0.883022i	$0.344495\pi$
$269$	−8.69353	+	15.0576i	−0.530054	+	0.918080i	−0.999385	+	0.0350578i	$0.988838\pi$
$270$		0			0
$271$	−8.82614	+	5.09577i	−0.536150	+	0.309546i	−0.743517	−	0.668717i	$-0.766844\pi$
$271$	−8.82614	+	5.09577i	−0.536150	+	0.309546i	0.207367	+	0.978263i	$0.433510\pi$
$272$		−	0.810598i		−	0.0491497i
$273$	−5.12265	+	13.7642i	−0.310037	+	0.833046i
$274$	−29.3666			−1.77410
$275$		0			0
$276$	−31.9271	+	31.4995i	−1.92179	+	1.89605i
$277$	8.27951	+	4.78018i	0.497468	+	0.287213i	0.727667	−	0.685930i	$-0.240605\pi$
$277$	8.27951	+	4.78018i	0.497468	+	0.287213i	−0.230199	+	0.973143i	$0.573938\pi$
$278$	1.99459	−	1.15158i	0.119628	−	0.0690670i
$279$	−13.5166	+	22.6992i	−0.809220	+	1.35896i
$280$		0			0
$281$			11.9239i			0.711320i	0.934616	+	0.355660i	$0.115744\pi$
$281$			11.9239i			0.711320i	−0.934616	+	0.355660i	$0.884256\pi$
$282$	−10.2732	+	2.67860i	−0.611758	+	0.159508i
$283$	−9.98469	+	17.2940i	−0.593528	+	1.02802i	0.400225	+	0.916417i	$0.368932\pi$
$283$	−9.98469	+	17.2940i	−0.593528	+	1.02802i	−0.993753	+	0.111604i	$0.964401\pi$
$284$	18.6071	+	10.7428i	1.10413	+	0.637468i
$285$		0			0
$286$		−	20.8759i		−	1.23442i
$287$	−20.5087	+	9.55132i	−1.21059	+	0.563797i
$288$	11.6961	+	6.96467i	0.689201	+	0.410397i
$289$	−8.11109	−	14.0488i	−0.477123	−	0.826401i
$290$		0			0
$291$	−7.85677	+	7.75155i	−0.460572	+	0.454404i
$292$	−0.380588	−	0.659198i	−0.0222722	−	0.0385766i
$293$			3.01023i			0.175859i	0.996127	+	0.0879297i	$0.0280251\pi$
$293$			3.01023i			0.175859i	−0.996127	+	0.0879297i	$0.971975\pi$
$294$	23.2736	−	16.0305i	1.35735	−	0.934919i
$295$		0			0
$296$	1.17855	−	0.680436i	0.0685018	−	0.0395495i
$297$	−3.47394	−	14.0995i	−0.201579	−	0.818134i
$298$	−35.8030	−	20.6709i	−2.07401	−	1.19743i
$299$	−12.0871	−	20.9354i	−0.699014	−	1.21073i
$300$		0			0
$301$	−0.131874	−	0.283161i	−0.00760109	−	0.0163212i
$302$	52.4461			3.01793
$303$	−4.64327	−	17.8082i	−0.266749	−	1.02306i
$304$	1.74778	+	1.00908i	0.100242	+	0.0578748i
$305$		0			0
$306$	6.16647	+	0.0831411i	0.352513	+	0.00475286i
$307$	20.3794			1.16311			0.581556	−	0.813507i	$-0.302444\pi$
$307$	20.3794			1.16311			0.581556	+	0.813507i	$0.302444\pi$
$308$	−14.5687	+	20.7850i	−0.830131	+	1.18433i
$309$	−1.67528	−	0.461015i	−0.0953033	−	0.0262263i
$310$		0			0
$311$	13.6359	−	23.6181i	0.773222	−	1.33926i	−0.162567	−	0.986697i	$-0.551977\pi$
$311$	13.6359	−	23.6181i	0.773222	−	1.33926i	0.935789	−	0.352562i	$-0.114689\pi$
$312$	13.1978	−	13.0211i	0.747180	−	0.737173i
$313$	0.315354	+	0.546210i	0.0178249	+	0.0308736i	0.874800	−	0.484484i	$-0.160993\pi$
$313$	0.315354	+	0.546210i	0.0178249	+	0.0308736i	−0.856975	+	0.515357i	$0.827659\pi$
$314$	−27.7186			−1.56425
$315$		0			0
$316$	10.7690			0.605806
$317$	−12.7151	−	22.0233i	−0.714153	−	1.23695i	−0.963285	−	0.268480i	$-0.913479\pi$
$317$	−12.7151	−	22.0233i	−0.714153	−	1.23695i	0.249132	−	0.968470i	$-0.419855\pi$
$318$	−21.4638	+	21.1763i	−1.20363	+	1.18751i
$319$	11.3917	−	19.7311i	0.637815	−	1.10473i
$320$		0			0
$321$	21.3371	+	5.87170i	1.19092	+	0.327726i
$322$	−4.07655	+	46.3376i	−0.227177	+	2.58229i
$323$	−1.93654			−0.107752
$324$	16.1639	−	26.3308i	0.897996	−	1.46282i
$325$		0			0
$326$	17.2048	+	9.93319i	0.952885	+	0.550149i
$327$	−0.00797411	−	0.0305829i	−0.000440969	−	0.00169124i
$328$	28.5598			1.57695
$329$	−3.99346	+	5.69739i	−0.220166	+	0.314107i
$330$		0			0
$331$	−5.74666	−	9.95352i	−0.315865	−	0.547095i	0.663756	−	0.747949i	$-0.268961\pi$
$331$	−5.74666	−	9.95352i	−0.315865	−	0.547095i	−0.979621	+	0.200855i	$0.935628\pi$
$332$	1.98267	+	1.14470i	0.108813	+	0.0628233i
$333$	0.596853	+	1.06674i	0.0327074	+	0.0584569i
$334$	7.20480	−	4.15970i	0.394229	−	0.227608i
$335$		0			0
$336$	−4.15308	+	0.701406i	−0.226569	+	0.0382648i
$337$			16.2041i			0.882694i	0.897336	+	0.441347i	$0.145499\pi$
$337$			16.2041i			0.882694i	−0.897336	+	0.441347i	$0.854501\pi$
$338$	−3.18030	−	5.50843i	−0.172985	−	0.299619i
$339$	8.91472	−	8.79534i	0.484181	−	0.477697i
$340$		0			0
$341$	−12.3050	−	21.3128i	−0.666351	−	1.15415i
$342$	−7.85566	+	13.1924i	−0.424786	+	0.713364i
$343$	4.81930	−	17.8822i	0.260218	−	0.965550i
$344$			0.394322i			0.0212604i
$345$		0			0
$346$	17.2433	+	9.95545i	0.927008	+	0.535208i
$347$	−8.99121	+	15.5732i	−0.482673	+	0.836015i	−0.999802	−	0.0198929i	$-0.993667\pi$
$347$	−8.99121	+	15.5732i	−0.482673	+	0.836015i	0.517129	+	0.855908i	$0.327001\pi$
$348$	46.9077	−	12.2306i	2.51451	−	0.655627i
$349$		−	6.15422i		−	0.329428i	−0.986341	−	0.164714i	$-0.947330\pi$
$349$		−	6.15422i		−	0.329428i	0.986341	−	0.164714i	$-0.0526701\pi$
$350$		0			0
$351$	11.5349	+	12.0111i	0.615687	+	0.641106i
$352$	−10.9818	+	6.34033i	−0.585330	+	0.337941i
$353$	−25.5186	−	14.7332i	−1.35822	−	0.784169i	−0.368836	−	0.929494i	$-0.620244\pi$
$353$	−25.5186	−	14.7332i	−1.35822	−	0.784169i	−0.989384	+	0.145326i	$0.953577\pi$
$354$	−11.7824	+	11.6246i	−0.626229	+	0.617842i
$355$		0			0
$356$	−3.00223			−0.159118
$357$	3.11469	−	2.57542i	0.164847	−	0.136306i
$358$		−	2.86584i		−	0.151465i
$359$	30.5228	−	17.6224i	1.61093	−	0.930073i	0.621779	−	0.783192i	$-0.286410\pi$
$359$	30.5228	−	17.6224i	1.61093	−	0.930073i	0.989154	−	0.146881i	$-0.0469233\pi$
$360$		0			0
$361$	−7.08928	+	12.2790i	−0.373120	+	0.646262i
$362$	−31.0852	+	17.9471i	−1.63380	+	0.943277i
$363$	−5.32764	−	1.46610i	−0.279628	−	0.0769502i
$364$	2.55098	−	28.9967i	0.133708	−	1.51984i
$365$		0			0
$366$	48.2684	−	12.5854i	2.52303	−	0.657848i
$367$	17.4136	−	30.1613i	0.908984	−	1.57441i	0.0935065	−	0.995619i	$-0.470192\pi$
$367$	17.4136	−	30.1613i	0.908984	−	1.57441i	0.815478	−	0.578788i	$-0.196474\pi$
$368$	3.46641	−	6.00400i	0.180699	−	0.312980i
$369$	−0.345842	+	25.6506i	−0.0180038	+	1.33532i
$370$		0			0
$371$	−1.73169	+	19.6839i	−0.0899048	+	1.02194i
$372$	13.8929	−	50.4853i	0.720314	−	2.61754i
$373$	17.5579	−	10.1371i	0.909115	−	0.524878i	0.0289688	−	0.999580i	$-0.490778\pi$
$373$	17.5579	−	10.1371i	0.909115	−	0.524878i	0.880146	+	0.474702i	$0.157444\pi$
$374$	−2.87239	+	4.97512i	−0.148528	+	0.257257i
$375$		0			0
$376$	7.60641	−	4.39156i	0.392270	−	0.226477i
$377$			26.1283i			1.34568i
$378$	−4.90984	−	31.6657i	−0.252535	−	1.62871i
$379$	9.07202			0.465998			0.232999	−	0.972477i	$-0.425146\pi$
$379$	9.07202			0.465998			0.232999	+	0.972477i	$0.425146\pi$
$380$		0			0
$381$	−8.50989	−	8.62540i	−0.435975	−	0.441893i
$382$	−29.3210	−	16.9285i	−1.50019	−	0.866137i
$383$	24.0549	−	13.8881i	1.22915	−	0.709648i	0.262295	−	0.964988i	$-0.415521\pi$
$383$	24.0549	−	13.8881i	1.22915	−	0.709648i	0.966851	+	0.255339i	$0.0821872\pi$
$384$	−33.1686	−	9.12758i	−1.69263	−	0.465790i
$385$		0			0
$386$			0.939675i			0.0478282i
$387$	−0.354155	−	0.00477499i	−0.0180027	−	0.000242727i
$388$	10.9377	−	18.9446i	0.555275	−	0.961765i
$389$	13.4945	+	7.79107i	0.684200	+	0.395023i	0.801436	−	0.598081i	$-0.204070\pi$
$389$	13.4945	+	7.79107i	0.684200	+	0.395023i	−0.117236	+	0.993104i	$0.537403\pi$
$390$		0			0
$391$			6.65242i			0.336427i
$392$	−15.0454	+	17.8953i	−0.759908	+	0.903850i
$393$	16.5218	+	4.54660i	0.833416	+	0.229345i
$394$	13.6024	+	23.5600i	0.685279	+	1.18694i
$395$		0			0
$396$	14.0531	+	25.1167i	0.706194	+	1.26216i
$397$	9.44524	+	16.3596i	0.474043	+	0.821067i	0.999558	−	0.0297174i	$-0.00946073\pi$
$397$	9.44524	+	16.3596i	0.474043	+	0.821067i	−0.525515	+	0.850784i	$0.676127\pi$
$398$			43.3016i			2.17051i
$399$	1.67568	+	9.92182i	0.0838888	+	0.496712i
$400$		0			0
$401$	18.0127	−	10.3996i	0.899511	−	0.519333i	0.0224695	−	0.999748i	$-0.492847\pi$
$401$	18.0127	−	10.3996i	0.899511	−	0.519333i	0.877042	+	0.480415i	$0.159514\pi$
$402$	−4.54870	−	4.61044i	−0.226869	−	0.229948i
$403$	24.4417	+	14.1114i	1.21753	+	0.702941i
$404$	18.2380	+	31.5891i	0.907373	+	1.57162i
$405$		0			0
$406$	28.8574	−	41.1704i	1.43217	−	2.04325i
$407$	−1.13867			−0.0564416
$408$	−4.93691	+	1.28724i	−0.244414	+	0.0637277i
$409$	−24.9664	−	14.4143i	−1.23451	−	0.712744i	−0.266542	−	0.963823i	$-0.585881\pi$
$409$	−24.9664	−	14.4143i	−1.23451	−	0.712744i	−0.967966	+	0.251080i	$0.919214\pi$
$410$		0			0
$411$	5.50577	+	21.1162i	0.271579	+	1.04158i
$412$	3.44383			0.169665
$413$	−0.950602	+	10.8054i	−0.0467761	+	0.531697i
$414$	45.3187	+	26.9858i	2.22729	+	1.32628i
$415$		0			0
$416$	7.27114	−	12.5940i	0.356497	−	0.617471i
$417$	−1.20200	−	1.21832i	−0.0588622	−	0.0596612i
$418$	−7.15145	−	12.3867i	−0.349789	−	0.605852i
$419$	3.24500			0.158528			0.0792642	−	0.996854i	$-0.474743\pi$
$419$	3.24500			0.158528			0.0792642	+	0.996854i	$0.474743\pi$
$420$		0			0
$421$	27.9322			1.36133			0.680665	−	0.732594i	$-0.261691\pi$
$421$	27.9322			1.36133			0.680665	+	0.732594i	$0.261691\pi$
$422$	8.13675	+	14.0933i	0.396091	+	0.686050i
$423$	3.85211	+	6.88477i	0.187296	+	0.334749i
$424$	12.4722	−	21.6026i	0.605706	−	1.04911i
$425$		0			0
$426$	6.70407	−	24.3618i	0.324813	−	1.18033i
$427$	18.7632	−	26.7692i	0.908016	−	1.29545i
$428$	−43.8622			−2.12016
$429$	−15.0109	+	3.91389i	−0.724732	+	0.188965i
$430$		0			0
$431$	−33.1792	−	19.1560i	−1.59819	−	0.922714i	−0.991836	−	0.127516i	$-0.959299\pi$
$431$	−33.1792	−	19.1560i	−1.59819	−	0.922714i	−0.606351	−	0.795197i	$-0.707367\pi$
$432$	−1.32911	+	4.58717i	−0.0639468	+	0.220700i
$433$	28.9533			1.39140			0.695702	−	0.718330i	$-0.255093\pi$
$433$	28.9533			1.39140			0.695702	+	0.718330i	$0.255093\pi$
$434$	−22.9275	−	49.2301i	−1.10055	−	2.36312i
$435$		0			0
$436$	0.0313210	+	0.0542495i	0.00150000	+	0.00259808i
$437$	−14.3437	−	8.28134i	−0.686153	−	0.396150i
$438$	−0.637223	+	0.628690i	−0.0304477	+	0.0300400i
$439$	13.2197	−	7.63242i	0.630943	−	0.364275i	−0.150174	−	0.988660i	$-0.547983\pi$
$439$	13.2197	−	7.63242i	0.630943	−	0.364275i	0.781117	+	0.624384i	$0.214650\pi$
$440$		0			0
$441$	−15.8902	−	13.7295i	−0.756678	−	0.653787i
$442$		−	6.58816i		−	0.313367i
$443$	−1.14186	−	1.97776i	−0.0542513	−	0.0939660i	0.837624	−	0.546247i	$-0.183944\pi$
$443$	−1.14186	−	1.97776i	−0.0542513	−	0.0939660i	−0.891876	+	0.452281i	$0.850611\pi$
$444$	−1.70153	−	1.72463i	−0.0807512	−	0.0818472i
$445$		0			0
$446$	1.68514	+	2.91875i	0.0797937	+	0.138207i
$447$	−8.15099	+	29.6198i	−0.385528	+	1.40097i
$448$	−29.7754	+	13.8670i	−1.40676	+	0.655155i
$449$		−	10.3113i		−	0.486619i	−0.969949	−	0.243310i	$-0.921767\pi$
$449$		−	10.3113i		−	0.486619i	0.969949	−	0.243310i	$-0.0782331\pi$
$450$		0			0
$451$	−20.6950	−	11.9483i	−0.974489	−	0.562621i
$452$	−12.4105	+	21.4956i	−0.583739	+	1.01107i
$453$	−9.83281	−	37.7116i	−0.461986	−	1.77184i
$454$			2.48732i			0.116736i
$455$		0			0
$456$	3.37028	−	12.2472i	0.157828	−	0.573529i
$457$	−28.4033	+	16.3987i	−1.32865	+	0.767097i	−0.985091	−	0.172033i	$-0.944966\pi$
$457$	−28.4033	+	16.3987i	−1.32865	+	0.767097i	−0.343560	+	0.939131i	$0.611633\pi$
$458$	15.3384	+	8.85564i	0.716718	+	0.413797i
$459$	−1.09633	−	4.44961i	−0.0511724	−	0.207690i
$460$		0			0
$461$	16.5678			0.771637			0.385819	−	0.922575i	$-0.373919\pi$
$461$	16.5678			0.771637			0.385819	+	0.922575i	$0.373919\pi$
$462$	27.9754	+	10.4117i	1.30153	+	0.484395i
$463$		−	36.5866i		−	1.70032i	−0.526522	−	0.850162i	$-0.676504\pi$
$463$		−	36.5866i		−	1.70032i	0.526522	−	0.850162i	$-0.323496\pi$
$464$	−6.48933	+	3.74662i	−0.301260	+	0.173932i
$465$		0			0
$466$	−20.9774	+	36.3339i	−0.971758	+	1.68313i
$467$	35.6023	−	20.5550i	1.64748	−	0.951171i	0.669406	−	0.742896i	$-0.266549\pi$
$467$	35.6023	−	20.5550i	1.64748	−	0.951171i	0.978070	−	0.208275i	$-0.0667848\pi$
$468$	−28.3591	−	16.8869i	−1.31090	−	0.780598i
$469$	−4.22812	−	0.371969i	−0.195236	−	0.0171759i
$470$		0			0
$471$	5.19680	+	19.9312i	0.239456	+	0.918380i
$472$	6.84658	−	11.8586i	0.315139	−	0.545837i
$473$	0.164968	−	0.285733i	0.00758524	−	0.0131380i
$474$	−3.19529	−	12.2548i	−0.146765	−	0.562884i
$475$		0			0
$476$	−4.59771	+	6.55947i	−0.210736	+	0.300653i
$477$	19.2510	+	11.4634i	0.881444	+	0.524872i
$478$	−60.3186	+	34.8250i	−2.75891	+	1.59286i
$479$	8.25944	−	14.3058i	0.377383	−	0.653647i	−0.613297	−	0.789852i	$-0.710157\pi$
$479$	8.25944	−	14.3058i	0.377383	−	0.653647i	0.990681	+	0.136205i	$0.0434906\pi$
$480$		0			0
$481$	1.13088	−	0.652916i	0.0515639	−	0.0297704i
$482$			12.2127i			0.556274i
$483$	34.0835	−	5.75630i	1.55085	−	0.261921i
$484$	10.9519			0.497813
$485$		0			0
$486$	−34.7597	−	10.5814i	−1.57673	−	0.479984i
$487$	−1.75977	−	1.01601i	−0.0797430	−	0.0460396i	0.459598	−	0.888127i	$-0.347993\pi$
$487$	−1.75977	−	1.01601i	−0.0797430	−	0.0460396i	−0.539341	+	0.842087i	$0.681327\pi$
$488$	−35.7386	+	20.6337i	−1.61781	+	0.934044i
$489$	3.91688	−	14.2335i	0.177127	−	0.643661i
$490$		0			0
$491$			5.97889i			0.269824i	0.990858	+	0.134912i	$0.0430751\pi$
$491$			5.97889i			0.269824i	−0.990858	+	0.134912i	$0.956925\pi$
$492$	−12.8281	−	49.1992i	−0.578334	−	2.21807i
$493$	3.59509	−	6.22687i	0.161915	−	0.280444i
$494$	14.2051	+	8.20134i	0.639120	+	0.368996i
$495$		0			0
$496$			8.09393i			0.363428i
$497$	−6.99087	−	15.0109i	−0.313583	−	0.673330i
$498$	0.714349	−	2.59587i	0.0320108	−	0.116323i
$499$	4.24155	+	7.34658i	0.189878	+	0.328878i	0.945209	−	0.326465i	$-0.105857\pi$
$499$	4.24155	+	7.34658i	0.189878	+	0.328878i	−0.755331	+	0.655343i	$0.772524\pi$
$500$		0			0
$501$	−4.34183	−	4.40077i	−0.193979	−	0.196612i
$502$	−17.5706	−	30.4332i	−0.784216	−	1.35830i
$503$			17.0296i			0.759312i	0.925128	+	0.379656i	$0.123958\pi$
$503$			17.0296i			0.759312i	−0.925128	+	0.379656i	$0.876042\pi$
$504$	10.8670	+	24.1803i	0.484055	+	1.07708i
$505$		0			0
$506$	−42.5508	+	24.5667i	−1.89161	+	1.09212i
$507$	−3.36461	+	3.31955i	−0.149427	+	0.147426i
$508$	20.7979	+	12.0077i	0.922759	+	0.532755i
$509$	−6.43409	−	11.1442i	−0.285186	−	0.493956i	0.687468	−	0.726214i	$-0.258722\pi$
$509$	−6.43409	−	11.1442i	−0.285186	−	0.493956i	−0.972654	+	0.232258i	$0.925389\pi$
$510$		0			0
$511$	−0.0514110	+	0.584381i	−0.00227429	+	0.0258515i
$512$	10.3101			0.455646
$513$	10.9589	+	3.17528i	0.483846	+	0.140192i
$514$	32.1148	+	18.5415i	1.41652	+	0.817831i
$515$		0			0
$516$	0.679288	−	0.177116i	0.0299040	−	0.00779708i
$517$	−7.34899			−0.323208
$518$	−2.50305	−	0.220206i	−0.109978	−	0.00967530i
$519$	3.92565	−	14.2654i	0.172317	−	0.626181i
$520$		0			0
$521$	−8.32724	+	14.4232i	−0.364823	+	0.631892i	−0.988748	−	0.149592i	$-0.952204\pi$
$521$	−8.32724	+	14.4232i	−0.364823	+	0.631892i	0.623925	+	0.781485i	$0.285537\pi$
$522$	−27.8361	−	49.7506i	−1.21835	−	2.17752i
$523$	18.1827	+	31.4934i	0.795075	+	1.37711i	0.922791	+	0.385300i	$0.125902\pi$
$523$	18.1827	+	31.4934i	0.795075	+	1.37711i	−0.127716	+	0.991811i	$0.540765\pi$
$524$	−33.9635			−1.48370
$525$		0			0
$526$	−19.3549			−0.843912
$527$	−3.88329	−	6.72605i	−0.169159	−	0.292991i
$528$	−3.12453	−	3.16694i	−0.135978	−	0.137823i
$529$	−16.9482	+	29.3551i	−0.736876	+	1.27631i
$530$		0			0
$531$	10.5678	+	6.29276i	0.458602	+	0.273083i
$532$	−8.41977	−	18.0790i	−0.365043	−	0.783826i
$533$	27.4047			1.18703
$534$	0.890797	+	3.41645i	0.0385485	+	0.147844i
$535$		0			0
$536$	4.64026	+	2.67906i	0.200429	+	0.115718i
$537$	−2.06070	+	0.537300i	−0.0889256	+	0.0231862i
$538$	−40.5268			−1.74724
$539$	18.3889	−	6.67290i	0.792064	−	0.287422i
$540$		0			0
$541$	−1.89575	−	3.28353i	−0.0815046	−	0.141170i	0.822392	−	0.568922i	$-0.192639\pi$
$541$	−1.89575	−	3.28353i	−0.0815046	−	0.141170i	−0.903896	+	0.427751i	$0.859306\pi$
$542$	−20.5725	−	11.8775i	−0.883665	−	0.510184i
$543$	18.7329	+	18.9872i	0.803906	+	0.814818i
$544$	−3.46571	+	2.00093i	−0.148591	+	0.0857890i
$545$		0			0
$546$	−33.7543	+	5.70069i	−1.44455	+	0.243967i
$547$			10.9382i			0.467684i	0.972275	+	0.233842i	$0.0751299\pi$
$547$			10.9382i			0.467684i	−0.972275	+	0.233842i	$0.924870\pi$
$548$	−21.6257	−	37.4568i	−0.923805	−	1.60008i
$549$	−18.0991	−	32.3480i	−0.772452	−	1.38058i
$550$		0			0
$551$	8.95077	+	15.5032i	0.381316	+	0.660458i
$552$	−42.0718	−	11.5776i	−1.79069	−	0.492776i
$553$	−6.79641	−	4.76379i	−0.289013	−	0.202577i
$554$			22.2839i			0.946752i
$555$		0			0
$556$	2.93766	+	1.69606i	0.124584	+	0.0719288i
$557$	4.86622	−	8.42853i	0.206188	−	0.357128i	−0.744322	−	0.667820i	$-0.767227\pi$
$557$	4.86622	−	8.42853i	0.206188	−	0.357128i	0.950511	+	0.310692i	$0.100561\pi$
$558$	−61.5730	−	0.830175i	−2.60659	−	0.0351441i
$559$			0.378374i			0.0160035i
$560$		0			0
$561$	4.11591	+	1.13265i	0.173774	+	0.0478203i
$562$	−24.0694	+	13.8965i	−1.01531	+	0.586187i
$563$	0.407265	+	0.235135i	0.0171642	+	0.00990975i	0.508558	−	0.861028i	$-0.330179\pi$
$563$	0.407265	+	0.235135i	0.0171642	+	0.00990975i	−0.491393	+	0.870938i	$0.663512\pi$
$564$	−10.9818	−	11.1308i	−0.462415	−	0.468692i
$565$		0			0
$566$	−46.5459			−1.95647
$567$	−21.8488	+	9.46725i	−0.917564	+	0.397587i
$568$			20.9037i			0.877100i
$569$	5.38387	−	3.10838i	0.225703	−	0.130310i	−0.382885	−	0.923796i	$-0.625069\pi$
$569$	5.38387	−	3.10838i	0.225703	−	0.130310i	0.608588	+	0.793486i	$0.291736\pi$
$570$		0			0
$571$	−5.31121	+	9.19928i	−0.222267	+	0.384978i	−0.955496	−	0.295004i	$-0.904679\pi$
$571$	−5.31121	+	9.19928i	−0.222267	+	0.384978i	0.733229	+	0.679982i	$0.238012\pi$
$572$	26.6270	−	15.3731i	1.11333	−	0.642782i
$573$	−6.67528	+	24.2572i	−0.278864	+	1.01336i
$574$	−43.1817	−	30.2672i	−1.80237	−	1.26333i
$575$		0			0
$576$	−0.502107	+	37.2406i	−0.0209211	+	1.55169i
$577$	−1.48330	+	2.56914i	−0.0617504	+	0.106955i	−0.895248	−	0.445568i	$-0.853002\pi$
$577$	−1.48330	+	2.56914i	−0.0617504	+	0.106955i	0.833497	+	0.552523i	$0.186335\pi$
$578$	18.9058	−	32.7459i	0.786380	−	1.36205i
$579$	0.675677	−	0.176174i	0.0280802	−	0.00732155i
$580$		0			0
$581$	−0.744909	−	1.59948i	−0.0309040	−	0.0663576i
$582$	−24.8037	−	6.82566i	−1.02815	−	0.282933i
$583$	−18.0753	+	10.4358i	−0.748601	+	0.432205i
$584$	0.370280	−	0.641344i	0.0153223	−	0.0265390i
$585$		0			0
$586$	−6.07641	+	3.50821i	−0.251014	+	0.144923i
$587$		−	18.8819i		−	0.779341i	−0.920954	−	0.389670i	$-0.872589\pi$
$587$		−	18.8819i		−	0.779341i	0.920954	−	0.389670i	$-0.127411\pi$
$588$	37.5856	+	17.8804i	1.55001	+	0.737375i
$589$	19.3366			0.796751
$590$		0			0
$591$	14.3907	−	14.1980i	0.591955	−	0.584027i
$592$	0.324322	+	0.187247i	0.0133296	+	0.00769582i
$593$	−26.2357	+	15.1472i	−1.07737	+	0.622020i	−0.930186	−	0.367088i	$-0.880355\pi$
$593$	−26.2357	+	15.1472i	−1.07737	+	0.622020i	−0.147185	+	0.989109i	$0.547021\pi$
$594$	24.4123	−	23.4444i	1.00165	−	0.961936i
$595$		0			0
$596$		−	60.8887i		−	2.49410i
$597$	31.1362	−	8.11836i	1.27432	−	0.332262i
$598$	28.1733	−	48.7976i	1.15209	−	1.99548i
$599$	−6.29024	−	3.63167i	−0.257012	−	0.148386i	0.365959	−	0.930631i	$-0.380741\pi$
$599$	−6.29024	−	3.63167i	−0.257012	−	0.148386i	−0.622971	+	0.782245i	$0.714075\pi$
$600$		0			0
$601$			45.3302i			1.84906i	0.381110	+	0.924530i	$0.375542\pi$
$601$			45.3302i			1.84906i	−0.381110	+	0.924530i	$0.624458\pi$
$602$	0.417896	−	0.596204i	0.0170322	−	0.0242995i
$603$	−2.46235	+	4.13515i	−0.100275	+	0.168396i
$604$	38.6216	+	66.8946i	1.57149	+	2.72190i
$605$		0			0
$606$	30.5360	−	30.1271i	1.24044	−	1.22383i
$607$	−13.0117	−	22.5370i	−0.528130	−	0.914748i	−0.999462	−	0.0327925i	$-0.989560\pi$
$607$	−13.0117	−	22.5370i	−0.528130	−	0.914748i	0.471332	−	0.881956i	$-0.343773\pi$
$608$		−	9.96351i		−	0.404073i
$609$	−35.0141	−	13.0313i	−1.41884	−	0.528054i
$610$		0			0
$611$	7.29877	−	4.21394i	0.295276	−	0.170478i
$612$	4.43498	+	7.92651i	0.179273	+	0.320410i
$613$	−22.2611	−	12.8525i	−0.899118	−	0.519106i	−0.0222040	−	0.999753i	$-0.507068\pi$
$613$	−22.2611	−	12.8525i	−0.899118	−	0.519106i	−0.876914	+	0.480648i	$0.840402\pi$
$614$	23.7507	+	41.1375i	0.958502	+	1.66017i
$615$		0			0
$616$	−24.5999	−	2.16417i	−0.991157	−	0.0871971i
$617$	8.88258			0.357599			0.178800	−	0.983886i	$-0.442779\pi$
$617$	8.88258			0.357599			0.178800	+	0.983886i	$0.442779\pi$
$618$	−1.02182	−	3.91898i	−0.0411037	−	0.157644i
$619$	26.4112	+	15.2485i	1.06156	+	0.612890i	0.925863	−	0.377861i	$-0.123340\pi$
$619$	26.4112	+	15.2485i	1.06156	+	0.612890i	0.135694	+	0.990751i	$0.456673\pi$
$620$		0			0
$621$	10.9077	−	37.6460i	0.437713	−	1.51068i
$622$	63.5669			2.54880
$623$	1.89473	+	1.32807i	0.0759108	+	0.0532079i
$624$	4.91911	+	1.35368i	0.196922	+	0.0541904i
$625$		0			0
$626$	−0.735048	+	1.27314i	−0.0293784	+	0.0508849i
$627$	−7.56590	+	7.46458i	−0.302153	+	0.298107i
$628$	−20.4121	−	35.3549i	−0.814533	−	1.41081i
$629$	−0.359349			−0.0143282
$630$		0			0
$631$	44.3335			1.76489			0.882445	−	0.470416i	$-0.155896\pi$
$631$	44.3335			1.76489			0.882445	+	0.470416i	$0.155896\pi$
$632$	5.23868	+	9.07367i	0.208384	+	0.360931i
$633$	8.60831	−	8.49303i	0.342150	−	0.337568i
$634$	29.6372	−	51.3332i	1.17705	−	2.03870i
$635$		0			0
$636$	−42.8163	−	11.7825i	−1.69778	−	0.467206i
$637$	−14.4369	+	17.1715i	−0.572011	+	0.680361i
$638$	53.1052			2.10245
$639$	−18.7744	−	0.253131i	−0.742703	−	0.0100137i
$640$		0			0
$641$	6.03197	+	3.48256i	0.238249	+	0.137553i	0.614371	−	0.789017i	$-0.289410\pi$
$641$	6.03197	+	3.48256i	0.238249	+	0.137553i	−0.376123	+	0.926570i	$0.622743\pi$
$642$	13.0144	+	49.9139i	0.513637	+	1.96994i
$643$	25.8907			1.02103			0.510514	−	0.859869i	$-0.329455\pi$
$643$	25.8907			1.02103			0.510514	+	0.859869i	$0.329455\pi$
$644$	−62.1053	+	28.9237i	−2.44729	+	1.13975i
$645$		0			0
$646$	−2.25691	−	3.90908i	−0.0887968	−	0.153801i
$647$	−8.69245	−	5.01859i	−0.341735	−	0.197301i	0.319304	−	0.947652i	$-0.396551\pi$
$647$	−8.69245	−	5.01859i	−0.341735	−	0.197301i	−0.661039	+	0.750351i	$0.729884\pi$
$648$	30.0486	+	0.810424i	1.18042	+	0.0318365i
$649$	−9.92232	+	5.72866i	−0.389485	+	0.224869i
$650$		0			0
$651$	−31.1006	+	25.7159i	−1.21893	+	1.00789i
$652$			29.2594i			1.14589i
$653$	19.8000	+	34.2946i	0.774833	+	1.34205i	0.934888	+	0.354942i	$0.115500\pi$
$653$	19.8000	+	34.2946i	0.774833	+	1.34205i	−0.160055	+	0.987108i	$0.551167\pi$
$654$	0.0524410	−	0.0517388i	0.00205061	−	0.00202315i
$655$		0			0
$656$	3.92965	+	6.80635i	0.153427	+	0.265744i
$657$	0.571531	+	0.340329i	0.0222975	+	0.0132775i
$658$	−16.1548	−	1.42122i	−0.629779	−	0.0554048i
$659$		−	17.9364i		−	0.698705i	−0.936991	−	0.349352i	$-0.886402\pi$
$659$		−	17.9364i		−	0.698705i	0.936991	−	0.349352i	$-0.113598\pi$
$660$		0			0
$661$	−3.31012	−	1.91110i	−0.128749	−	0.0743332i	0.434242	−	0.900796i	$-0.357016\pi$
$661$	−3.31012	−	1.91110i	−0.128749	−	0.0743332i	−0.562991	+	0.826463i	$0.690350\pi$
$662$	13.3947	−	23.2003i	0.520599	−	0.901705i
$663$	−4.73724	+	1.23517i	−0.183979	+	0.0479702i
$664$			2.22739i			0.0864393i
$665$		0			0
$666$	−1.45771	+	2.44801i	−0.0564852	+	0.0948585i
$667$	53.2567	−	30.7478i	2.06211	−	1.19056i
$668$	10.6113	+	6.12645i	0.410564	+	0.237039i
$669$	1.78280	−	1.75893i	0.0689271	−	0.0680040i
$670$		0			0
$671$	34.5292			1.33299
$672$	13.2506	+	16.0251i	0.511151	+	0.618181i
$673$			1.08304i			0.0417483i	0.999782	+	0.0208741i	$0.00664493\pi$
$673$			1.08304i			0.0417483i	−0.999782	+	0.0208741i	$0.993355\pi$
$674$	−32.7094	+	18.8848i	−1.25992	+	0.727415i
$675$		0			0
$676$	4.68398	−	8.11288i	0.180153	−	0.312034i
$677$	−26.8492	+	15.5014i	−1.03190	+	0.595766i	−0.917528	−	0.397672i	$-0.869818\pi$
$677$	−26.8492	+	15.5014i	−1.03190	+	0.595766i	−0.114370	+	0.993438i	$0.536485\pi$
$678$	28.1436	+	7.74478i	1.08085	+	0.297436i
$679$	−15.2831	+	7.11767i	−0.586513	+	0.273151i
$680$		0			0
$681$	1.78852	−	0.466333i	0.0685362	−	0.0178699i
$682$	28.6812	−	49.6772i	1.09826	−	1.90224i
$683$	9.55050	−	16.5419i	0.365440	−	0.632960i	−0.623407	−	0.781898i	$-0.714252\pi$
$683$	9.55050	−	16.5419i	0.365440	−	0.632960i	0.988847	+	0.148937i	$0.0475853\pi$
$684$	−22.6118	−	0.304869i	−0.864583	−	0.0116570i
$685$		0			0
$686$	41.7134	−	11.1124i	1.59263	−	0.424272i
$687$	3.49198	−	12.6894i	0.133227	−	0.484133i
$688$	−0.0939745	+	0.0542562i	−0.00358275	+	0.00206850i
$689$	11.9678	−	20.7289i	0.455937	−	0.789707i
$690$		0			0
$691$	−14.5775	+	8.41632i	−0.554554	+	0.320172i	−0.750957	−	0.660351i	$-0.770407\pi$
$691$	−14.5775	+	8.41632i	−0.554554	+	0.320172i	0.196403	+	0.980523i	$0.437074\pi$
$692$			29.3250i			1.11477i
$693$	2.24161	−	22.0678i	0.0851519	−	0.838288i
$694$	−41.9145			−1.59105
$695$		0			0
$696$	33.1237	+	33.5733i	1.25555	+	1.27259i
$697$	−6.53107	−	3.77072i	−0.247382	−	0.142826i
$698$	12.4228	−	7.17232i	0.470211	−	0.271476i
$699$	30.0589	+	8.27184i	1.13693	+	0.312870i
$700$		0			0
$701$			21.8878i			0.826691i	0.910574	+	0.413345i	$0.135640\pi$
$701$			21.8878i			0.826691i	−0.910574	+	0.413345i	$0.864360\pi$
$702$	−10.8024	+	37.2823i	−0.407709	+	1.40713i
$703$	0.447339	−	0.774814i	0.0168717	−	0.0292227i
$704$	−30.0458	−	17.3470i	−1.13240	−	0.653789i
$705$		0			0
$706$		−	68.6821i		−	2.58489i
$707$	2.46364	−	28.0038i	0.0926547	−	1.05319i
$708$	−23.5038	−	6.46794i	−0.883326	−	0.243080i
$709$	−5.41030	−	9.37091i	−0.203188	−	0.351932i	0.746366	−	0.665536i	$-0.231797\pi$
$709$	−5.41030	−	9.37091i	−0.203188	−	0.351932i	−0.949554	+	0.313604i	$0.898464\pi$
$710$		0			0
$711$	−8.21283	+	4.59518i	−0.308005	+	0.172333i
$712$	−1.46046	−	2.52959i	−0.0547331	−	0.0948005i
$713$		−	66.4253i		−	2.48765i
$714$	8.82867	+	3.28579i	0.330405	+	0.122968i
$715$		0			0
$716$	3.65536	−	2.11042i	0.136607	−	0.0788703i
$717$	36.3498	+	36.8432i	1.35751	+	1.37593i
$718$	71.1445	+	41.0753i	2.65509	+	1.53292i
$719$	−11.1296	−	19.2770i	−0.415064	−	0.718912i	0.580371	−	0.814352i	$-0.302907\pi$
$719$	−11.1296	−	19.2770i	−0.415064	−	0.718912i	−0.995435	+	0.0954404i	$0.969574\pi$
$720$		0			0
$721$	−2.17342	−	1.52341i	−0.0809425	−	0.0567348i
$722$	−33.0483			−1.22993
$723$	8.78160	−	2.28969i	0.326591	−	0.0851545i
$724$	−45.7827	−	26.4327i	−1.70150	−	0.982362i
$725$		0			0
$726$	−3.24955	−	12.4629i	−0.120602	−	0.462543i
$727$	−43.7899			−1.62408			−0.812038	−	0.583604i	$-0.801642\pi$
$727$	−43.7899			−1.62408			−0.812038	+	0.583604i	$0.801642\pi$
$728$	25.6727	−	11.9563i	0.951493	−	0.443129i
$729$	−1.09174	+	26.9779i	−0.0404349	+	0.999182i
$730$		0			0
$731$	0.0520618	−	0.0901738i	0.00192558	−	0.00333520i
$732$	51.5977	+	52.2981i	1.90711	+	1.93299i
$733$	13.0854	+	22.6647i	0.483322	+	0.837138i	0.999817	−	0.0191524i	$-0.00609676\pi$
$733$	13.0854	+	22.6647i	0.483322	+	0.837138i	−0.516495	+	0.856290i	$0.672763\pi$
$734$	81.1776			2.99632
$735$		0			0
$736$	−34.2267			−1.26161
$737$	−2.24161	−	3.88259i	−0.0825709	−	0.143017i
$738$	−52.1811	+	29.1959i	−1.92081	+	1.07472i
$739$	20.1777	−	34.9489i	0.742250	−	1.28561i	−0.209219	−	0.977869i	$-0.567092\pi$
$739$	20.1777	−	34.9489i	0.742250	−	1.28561i	0.951469	−	0.307746i	$-0.0995746\pi$
$740$		0			0
$741$	3.23397	−	11.7519i	0.118803	−	0.431716i
$742$	−41.7517	+	19.4446i	−1.53275	+	0.713835i
$743$	−8.82565			−0.323782			−0.161891	−	0.986809i	$-0.551759\pi$
$743$	−8.82565			−0.323782			−0.161891	+	0.986809i	$0.551759\pi$
$744$	49.2957	−	12.8532i	1.80727	−	0.471222i
$745$		0			0
$746$	40.9251	+	23.6281i	1.49838	+	0.865087i
$747$	−2.00050	−	0.0269722i	−0.0731943	−	0.000986863i
$748$	−8.46097			−0.309364
$749$	27.6817	+	19.4029i	1.01147	+	0.708965i
$750$		0			0
$751$	−18.9165	−	32.7644i	−0.690274	−	1.19559i	−0.971748	−	0.236020i	$-0.924157\pi$
$751$	−18.9165	−	32.7644i	−0.690274	−	1.19559i	0.281475	−	0.959569i	$-0.409176\pi$
$752$	2.09319	+	1.20850i	0.0763307	+	0.0440695i
$753$	−18.5889	+	18.3400i	−0.677418	+	0.668346i
$754$	−52.7422	+	30.4507i	−1.92076	+	1.10895i
$755$		0			0
$756$	36.7737	−	29.5813i	1.33745	−	1.07586i
$757$			34.7636i			1.26351i	0.775170	+	0.631753i	$0.217664\pi$
$757$			34.7636i			1.26351i	−0.775170	+	0.631753i	$0.782336\pi$
$758$	10.5728	+	18.3127i	0.384022	+	0.665146i
$759$	25.6424	+	25.9905i	0.930760	+	0.943394i
$760$		0			0
$761$	−0.915074	−	1.58495i	−0.0331714	−	0.0574545i	0.848963	−	0.528452i	$-0.177227\pi$
$761$	−0.915074	−	1.58495i	−0.0331714	−	0.0574545i	−0.882135	+	0.470998i	$0.843894\pi$
$762$	7.49342	−	27.2303i	0.271458	−	0.986448i
$763$	0.00423093	−	0.0480923i	0.000153170	−	0.00174106i
$764$		−	49.8649i		−	1.80405i
$765$		0			0
$766$	56.0686	+	32.3712i	2.02584	+	1.16962i
$767$	6.56967	−	11.3790i	0.237217	−	0.410872i
$768$	−9.38051	−	35.9769i	−0.338490	−	1.29820i
$769$			23.5601i			0.849598i	0.905288	+	0.424799i	$0.139655\pi$
$769$			23.5601i			0.849598i	−0.905288	+	0.424799i	$0.860345\pi$
$770$		0			0
$771$	7.31132	−	26.5685i	0.263311	−	0.956842i
$772$	−1.19855	+	0.691982i	−0.0431367	+	0.0249050i
$773$	−41.6448	−	24.0437i	−1.49786	−	0.864790i	−0.497864	−	0.867255i	$-0.665882\pi$
$773$	−41.6448	−	24.0437i	−1.49786	−	0.864790i	−0.999997	+	0.00246461i	$0.999215\pi$
$774$	−0.403105	−	0.720458i	−0.0144893	−	0.0258963i
$775$		0			0
$776$	21.2828			0.764010
$777$	0.310942	+	1.84111i	0.0111550	+	0.0660496i
$778$			36.3198i			1.30213i
$779$	16.2606	−	9.38804i	0.582595	−	0.336361i
$780$		0			0
$781$	8.74525	−	15.1472i	0.312930	−	0.542010i
$782$	−13.4285	+	7.75294i	−0.480202	+	0.277245i
$783$	−30.5546	+	29.3431i	−1.09193	+	1.04864i
$784$	−6.33495	−	1.12333i	−0.226248	−	0.0401189i
$785$		0			0
$786$	10.0774	+	38.6495i	0.359447	+	1.37858i
$787$	−15.0823	+	26.1234i	−0.537627	+	0.931197i	0.461404	+	0.887190i	$0.347346\pi$
$787$	−15.0823	+	26.1234i	−0.537627	+	0.931197i	−0.999031	+	0.0440072i	$0.985988\pi$
$788$	−20.0338	+	34.6995i	−0.713673	+	1.23612i
$789$	3.62873	+	13.9172i	0.129186	+	0.495465i
$790$		0			0
$791$	17.3411	−	8.07610i	0.616579	−	0.287153i
$792$	−14.3263	+	24.0589i	−0.509064	+	0.854897i
$793$	−34.2932	+	19.7992i	−1.21779	+	0.703090i
$794$	−22.0156	+	38.1321i	−0.781303	+	1.35326i
$795$		0			0
$796$	−55.2309	+	31.8876i	−1.95761	+	1.13022i
$797$		−	3.60475i		−	0.127687i	−0.997960	−	0.0638435i	$-0.979664\pi$
$797$		−	3.60475i		−	0.127687i	0.997960	−	0.0638435i	$-0.0203358\pi$
$798$	−18.0752	+	14.9457i	−0.639854	+	0.529072i
$799$	−2.31925			−0.0820491
$800$		0			0
$801$	2.28961	−	1.28106i	0.0808992	−	0.0452641i
$802$	41.9851	+	24.2401i	1.48255	+	0.855948i
$803$	−0.536624	+	0.309820i	−0.0189371	+	0.0109333i
$804$	2.53089	−	9.19699i	0.0892578	−	0.324353i
$805$		0			0
$806$			65.7836i			2.31713i
$807$	7.59814	+	29.1410i	0.267467	+	1.02581i
$808$	−17.7440	+	30.7335i	−0.624232	+	1.08120i
$809$	18.7612	+	10.8318i	0.659607	+	0.380824i	0.792127	−	0.610356i	$-0.208974\pi$
$809$	18.7612	+	10.8318i	0.659607	+	0.380824i	−0.132520	+	0.991180i	$0.542307\pi$
$810$		0			0
$811$		−	27.6526i		−	0.971015i	−0.874232	−	0.485508i	$-0.838635\pi$
$811$		−	27.6526i		−	0.971015i	0.874232	−	0.485508i	$-0.161365\pi$
$812$	73.7633	+	6.48933i	2.58858	+	0.227731i
$813$	−4.68358	+	17.0196i	−0.164260	+	0.596904i
$814$	−1.32704	−	2.29850i	−0.0465126	−	0.0805623i
$815$		0			0
$816$	−0.986061	−	0.999446i	−0.0345190	−	0.0349876i
$817$	0.129620	+	0.224508i	0.00453481	+	0.00785453i
$818$		−	67.1957i		−	2.34944i
$819$	10.4275	+	23.2024i	0.364366	+	0.810756i
$820$		0			0
$821$	12.2722	−	7.08534i	0.428302	−	0.247280i	−0.270321	−	0.962770i	$-0.587130\pi$
$821$	12.2722	−	7.08534i	0.428302	−	0.247280i	0.698623	+	0.715490i	$0.253797\pi$
$822$	−36.2082	+	35.7233i	−1.26291	+	1.24599i
$823$	−20.1850	−	11.6538i	−0.703605	−	0.406227i	0.105084	−	0.994463i	$-0.466489\pi$
$823$	−20.1850	−	11.6538i	−0.703605	−	0.406227i	−0.808689	+	0.588237i	$0.799822\pi$
$824$	1.67528	+	2.90167i	0.0583611	+	0.101084i
$825$		0			0
$826$	−22.9194	+	10.6740i	−0.797468	+	0.371397i
$827$	−32.0877			−1.11580			−0.557900	−	0.829908i	$-0.688393\pi$
$827$	−32.0877			−1.11580			−0.557900	+	0.829908i	$0.688393\pi$
$828$	−1.04729	+	77.6762i	−0.0363959	+	2.69943i
$829$	−25.9947	−	15.0080i	−0.902833	−	0.521251i	−0.0247149	−	0.999695i	$-0.507868\pi$
$829$	−25.9947	−	15.0080i	−0.902833	−	0.521251i	−0.878118	+	0.478444i	$0.841201\pi$
$830$		0			0
$831$	16.0233	−	4.17788i	0.555843	−	0.144929i
$832$	39.7873			1.37938
$833$	5.80329	−	2.10588i	0.201072	−	0.0729645i
$834$	1.05843	−	3.84621i	0.0366503	−	0.133183i
$835$		0			0
$836$	10.5327	−	18.2432i	0.364282	−	0.630956i
$837$	10.9470	+	44.4299i	0.378384	+	1.53572i
$838$	3.78182	+	6.55031i	0.130641	+	0.226277i
$839$	−28.6277			−0.988337			−0.494168	−	0.869366i	$-0.664527\pi$
$839$	−28.6277			−0.988337			−0.494168	+	0.869366i	$0.664527\pi$
$840$		0			0
$841$	−37.4666			−1.29195
$842$	32.5530	+	56.3835i	1.12185	+	1.94310i
$843$	14.5049	+	14.7018i	0.499577	+	0.506358i
$844$	−11.9839	+	20.7567i	−0.412503	+	0.714476i
$845$		0			0
$846$	−9.40813	+	15.7995i	−0.323458	+	0.543200i
$847$	−6.91181	−	4.84468i	−0.237493	−	0.166465i
$848$	6.86441			0.235725
$849$	8.72661	+	33.4690i	0.299497	+	1.14865i
$850$		0			0
$851$	−2.66165	−	1.53670i	−0.0912401	−	0.0526775i
$852$	36.0102	−	9.38921i	1.23369	−	0.321669i
$853$	17.3563			0.594269			0.297135	−	0.954836i	$-0.403969\pi$
$853$	17.3563			0.594269			0.297135	+	0.954836i	$0.403969\pi$
$854$	75.9031	+	6.67758i	2.59735	+	0.228502i
$855$		0			0
$856$	−21.3371	−	36.9569i	−0.729287	−	1.26316i
$857$	40.3294	+	23.2842i	1.37763	+	0.795372i	0.991873	−	0.127230i	$-0.0406087\pi$
$857$	40.3294	+	23.2842i	1.37763	+	0.795372i	0.385752	+	0.922602i	$0.373942\pi$
$858$	−25.3947	−	25.7394i	−0.866960	−	0.878728i
$859$	−31.5359	+	18.2072i	−1.07599	+	0.621223i	−0.929812	−	0.368035i	$-0.880031\pi$
$859$	−31.5359	+	18.2072i	−1.07599	+	0.621223i	−0.146178	+	0.989258i	$0.546697\pi$
$860$		0			0
$861$	−13.6679	+	36.7246i	−0.465800	+	1.25157i
$862$		−	89.3002i		−	3.04158i
$863$	−1.18901	−	2.05942i	−0.0404742	−	0.0701034i	0.845079	−	0.534642i	$-0.179554\pi$
$863$	−1.18901	−	2.05942i	−0.0404742	−	0.0701034i	−0.885553	+	0.464539i	$0.846220\pi$
$864$	22.8933	−	5.64063i	0.778844	−	0.191898i
$865$		0			0
$866$	33.7430	+	58.4447i	1.14664	+	1.98603i
$867$	−27.0906	−	7.45499i	−0.920045	−	0.253185i
$868$	45.9087	−	65.4971i	1.55824	−	2.22312i
$869$		−	8.76660i		−	0.297387i
$870$		0			0
$871$	4.45259	+	2.57070i	0.150870	+	0.0871049i
$872$	−0.0304727	+	0.0527802i	−0.00103193	+	0.00178736i
$873$	−0.257722	+	19.1149i	−0.00872257	+	0.646942i
$874$		−	38.6054i		−	1.30585i
$875$		0			0
$876$	−1.27114	−	0.349803i	−0.0429480	−	0.0118187i
$877$	19.1332	−	11.0465i	0.646082	−	0.373015i	−0.140872	−	0.990028i	$-0.544991\pi$
$877$	19.1332	−	11.0465i	0.646082	−	0.373015i	0.786953	+	0.617012i	$0.211657\pi$
$878$	30.8134	+	17.7901i	1.03990	+	0.600387i
$879$	3.66183	+	3.71153i	0.123510	+	0.125187i
$880$		0			0
$881$	−33.5633			−1.13078			−0.565388	−	0.824825i	$-0.691273\pi$
$881$	−33.5633			−1.13078			−0.565388	+	0.824825i	$0.691273\pi$
$882$	9.19527	−	48.0767i	0.309621	−	1.61883i
$883$		−	3.74124i		−	0.125903i	−0.998017	−	0.0629514i	$-0.979949\pi$
$883$		−	3.74124i		−	0.125903i	0.998017	−	0.0629514i	$-0.0200513\pi$
$884$	8.40314	−	4.85156i	0.282628	−	0.163176i
$885$		0			0
$886$	2.66151	−	4.60988i	0.0894153	−	0.154872i
$887$	−23.8478	+	13.7685i	−0.800730	+	0.462302i	−0.843726	−	0.536773i	$-0.819643\pi$
$887$	−23.8478	+	13.7685i	−0.800730	+	0.462302i	0.0429963	+	0.999075i	$0.486310\pi$
$888$	0.625396	−	2.27262i	0.0209869	−	0.0762641i
$889$	−7.81399	−	16.7783i	−0.262073	−	0.562726i
$890$		0			0
$891$	−21.4347	−	13.1583i	−0.718090	−	0.440821i
$892$	−2.48189	+	4.29877i	−0.0831000	+	0.143933i
$893$	2.88714	−	5.00068i	0.0966146	−	0.167341i
$894$	−69.2895	+	18.0663i	−2.31739	+	0.604229i
$895$		0			0
$896$	−43.0313	−	30.1618i	−1.43758	−	1.00764i
$897$	−40.3702	−	11.1094i	−1.34792	−	0.370931i
$898$	20.8142	−	12.0171i	0.694579	−	0.401015i
$899$	−35.8974	+	62.1762i	−1.19725	+	2.07369i
$900$		0			0
$901$	−5.70432	+	3.29339i	−0.190038	+	0.109719i
$902$		−	55.6995i		−	1.85459i
$903$	−0.507052	−	0.188711i	−0.0168736	−	0.00627990i
$904$	−24.1487			−0.803174
$905$		0			0
$906$	64.6646	−	63.7987i	2.14834	−	2.11957i
$907$	33.5412	+	19.3650i	1.11372	+	0.643005i	0.939790	−	0.341754i	$-0.111021\pi$
$907$	33.5412	+	19.3650i	1.11372	+	0.643005i	0.173928	+	0.984758i	$0.444354\pi$
$908$	−3.17256	+	1.83168i	−0.105285	+	0.0607864i
$909$	−27.3880	−	16.3087i	−0.908404	−	0.540926i
$910$		0			0
$911$		−	23.3967i		−	0.775167i	−0.921835	−	0.387583i	$-0.873310\pi$
$911$		−	23.3967i		−	0.775167i	0.921835	−	0.387583i	$-0.126690\pi$
$912$	3.38248	−	0.881938i	0.112005	−	0.0292039i
$913$	0.931847	−	1.61401i	0.0308396	−	0.0534158i
$914$	−66.2043	−	38.2231i	−2.18984	−	1.26431i
$915$		0			0
$916$			26.0854i			0.861886i
$917$	21.4346	+	15.0241i	0.707833	+	0.496139i
$918$	7.70422	−	7.39876i	0.254277	−	0.244195i
$919$	−4.32329	−	7.48816i	−0.142612	−	0.247012i	0.785867	−	0.618395i	$-0.212217\pi$
$919$	−4.32329	−	7.48816i	−0.142612	−	0.247012i	−0.928480	+	0.371383i	$0.878884\pi$
$920$		0			0
$921$	25.1272	−	24.7907i	0.827969	−	0.816881i
$922$	19.3086	+	33.4434i	0.635894	+	1.10140i
$923$			20.0583i			0.660225i
$924$	7.32123	+	43.3496i	0.240851	+	1.42610i
$925$		0			0
$926$	73.8532	−	42.6392i	2.42697	−	1.40121i
$927$	−2.62638	+	1.46949i	−0.0862616	+	0.0482644i
$928$	32.0373	+	18.4967i	1.05168	+	0.607185i
$929$	−6.27980	−	10.8769i	−0.206034	−	0.356861i	0.744428	−	0.667703i	$-0.232722\pi$
$929$	−6.27980	−	10.8769i	−0.206034	−	0.356861i	−0.950462	+	0.310842i	$0.899389\pi$
$930$		0			0
$931$	−2.68366	+	15.1344i	−0.0879535	+	0.496009i
$932$	−61.7914			−2.02405
$933$	−11.9178	−	45.7080i	−0.390171	−	1.49641i
$934$	82.9840	+	47.9108i	2.71532	+	1.56769i
$935$		0			0
$936$	0.432922	−	32.1093i	0.0141505	−	1.04952i
$937$	−11.3901			−0.372097			−0.186048	−	0.982541i	$-0.559568\pi$
$937$	−11.3901			−0.372097			−0.186048	+	0.982541i	$0.559568\pi$
$938$	−4.17673	−	8.96833i	−0.136375	−	0.292826i
$939$	1.05327	+	0.289846i	0.0343720	+	0.00945875i
$940$		0			0
$941$	−21.0434	+	36.4482i	−0.685994	+	1.18818i	0.287129	+	0.957892i	$0.407299\pi$
$941$	−21.0434	+	36.4482i	−0.685994	+	1.18818i	−0.973123	+	0.230285i	$0.926034\pi$
$942$	−34.1763	+	33.7186i	−1.11352	+	1.09861i
$943$	−32.2499	−	55.8584i	−1.05020	−	1.81900i
$944$	3.76818			0.122644
$945$		0			0
$946$	0.769036			0.0250035
$947$	−7.30370	−	12.6504i	−0.237338	−	0.411082i	0.722611	−	0.691255i	$-0.242942\pi$
$947$	−7.30370	−	12.6504i	−0.237338	−	0.411082i	−0.959950	+	0.280172i	$0.909608\pi$
$948$	13.2779	−	13.1001i	0.431247	−	0.425472i
$949$	0.355304	−	0.615405i	0.0115337	−	0.0199769i
$950$		0			0
$951$	−42.4679	−	11.6866i	−1.37711	−	0.378965i
$952$	−7.76340	−	0.682986i	−0.251613	−	0.0221357i
$953$	−28.8817			−0.935570			−0.467785	−	0.883842i	$-0.654948\pi$
$953$	−28.8817			−0.935570			−0.467785	+	0.883842i	$0.654948\pi$
$954$	−0.704066	+	52.2196i	−0.0227950	+	1.69067i
$955$		0			0
$956$	−88.8379	−	51.2906i	−2.87322	−	1.65886i
$957$	−9.95637	−	38.1855i	−0.321844	−	1.23436i
$958$	38.5032			1.24398
$959$	−2.92127	+	33.2056i	−0.0943326	+	1.07226i
$960$		0			0
$961$	23.2751	+	40.3137i	0.750811	+	1.30044i
$962$	2.63594	+	1.52186i	0.0849860	+	0.0490667i
$963$	33.4508	−	18.7161i	1.07794	−	0.603118i
$964$	−15.5772	+	8.99352i	−0.501709	+	0.289662i
$965$		0			0
$966$	51.3416	+	62.0920i	1.65189	+	1.99778i
$967$		−	0.409782i		−	0.0131777i	−0.999978	−	0.00658885i	$-0.997903\pi$
$967$		−	0.409782i		−	0.0131777i	0.999978	−	0.00658885i	$-0.00209731\pi$
$968$	5.32764	+	9.22774i	0.171237	+	0.296591i
$969$	−2.38770	+	2.35573i	−0.0767041	+	0.0756768i
$970$		0			0
$971$	−2.64865	−	4.58759i	−0.0849991	−	0.147223i	0.820392	−	0.571802i	$-0.193755\pi$
$971$	−2.64865	−	4.58759i	−0.0849991	−	0.147223i	−0.905391	+	0.424579i	$0.860422\pi$
$972$	−12.1007	−	52.1279i	−0.388129	−	1.67200i
$973$	−1.10371	−	2.36989i	−0.0353832	−	0.0759753i
$974$		−	4.73634i		−	0.151762i
$975$		0			0
$976$	−9.83482	−	5.67814i	−0.314805	−	0.181753i
$977$	13.9284	−	24.1247i	0.445610	−	0.771818i	−0.552485	−	0.833523i	$-0.686320\pi$
$977$	13.9284	−	24.1247i	0.445610	−	0.771818i	0.998094	+	0.0617045i	$0.0196536\pi$
$978$	33.2964	−	8.68160i	1.06470	−	0.277607i
$979$			2.44399i			0.0781102i
$980$		0			0
$981$	−0.0470348	−	0.0280077i	−0.00150171	−	0.000894219i
$982$	−12.0689	+	6.96799i	−0.385134	+	0.222357i
$983$	−0.572640	−	0.330614i	−0.0182644	−	0.0105449i	0.490840	−	0.871250i	$-0.336690\pi$
$983$	−0.572640	−	0.330614i	−0.0182644	−	0.0105449i	−0.509104	+	0.860705i	$0.670023\pi$
$984$	35.2135	−	34.7419i	1.12257	−	1.10753i
$985$		0			0
$986$	16.7593			0.533725
$987$	2.00683	+	11.8826i	0.0638782	+	0.378228i
$988$			24.1581i			0.768571i
$989$	0.771231	−	0.445270i	0.0245237	−	0.0141588i
$990$		0			0
$991$	25.3374	−	43.8856i	0.804868	−	1.39407i	−0.111513	−	0.993763i	$-0.535570\pi$
$991$	25.3374	−	43.8856i	0.804868	−	1.39407i	0.916380	−	0.400309i	$-0.131097\pi$
$992$	34.6055	−	19.9795i	1.09873	−	0.634350i
$993$	−19.1935	−	5.28182i	−0.609089	−	0.167614i
$994$	22.1534	−	31.6058i	0.702663	−	1.00248i
$995$		0			0
$996$	3.83706	−	1.00046i	0.121582	−	0.0317009i
$997$	3.01307	−	5.21879i	0.0954249	−	0.165281i	−0.814361	−	0.580359i	$-0.802912\pi$
$997$	3.01307	−	5.21879i	0.0954249	−	0.165281i	0.909786	+	0.415078i	$0.136246\pi$
$998$	−9.88647	+	17.1239i	−0.312951	+	0.542047i
$999$	2.03355	+	0.589211i	0.0643387	+	0.0186418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.q.f.374.8		16
3.2	odd	2		525.2.q.e.374.1		16
5.2	odd	4		105.2.s.c.101.1	yes	8
5.3	odd	4		525.2.t.g.101.4		8
5.4	even	2	inner	525.2.q.f.374.1		16
7.5	odd	6		525.2.q.e.299.8		16
15.2	even	4		105.2.s.d.101.4	yes	8
15.8	even	4		525.2.t.f.101.1		8
15.14	odd	2		525.2.q.e.374.8		16
21.5	even	6	inner	525.2.q.f.299.1		16
35.2	odd	12		735.2.s.l.656.4		8
35.12	even	12		105.2.s.d.26.4	yes	8
35.17	even	12		735.2.b.c.146.1		8
35.19	odd	6		525.2.q.e.299.1		16
35.27	even	4		735.2.s.k.521.1		8
35.32	odd	12		735.2.b.d.146.1		8
35.33	even	12		525.2.t.f.26.1		8
105.2	even	12		735.2.s.k.656.1		8
105.17	odd	12		735.2.b.d.146.8		8
105.32	even	12		735.2.b.c.146.8		8
105.47	odd	12		105.2.s.c.26.1	✓	8
105.62	odd	4		735.2.s.l.521.4		8
105.68	odd	12		525.2.t.g.26.4		8
105.89	even	6	inner	525.2.q.f.299.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.1	✓	8	105.47	odd	12
105.2.s.c.101.1	yes	8	5.2	odd	4
105.2.s.d.26.4	yes	8	35.12	even	12
105.2.s.d.101.4	yes	8	15.2	even	4
525.2.q.e.299.1		16	35.19	odd	6
525.2.q.e.299.8		16	7.5	odd	6
525.2.q.e.374.1		16	3.2	odd	2
525.2.q.e.374.8		16	15.14	odd	2
525.2.q.f.299.1		16	21.5	even	6	inner
525.2.q.f.299.8		16	105.89	even	6	inner
525.2.q.f.374.1		16	5.4	even	2	inner
525.2.q.f.374.8		16	1.1	even	1	trivial
525.2.t.f.26.1		8	35.33	even	12
525.2.t.f.101.1		8	15.8	even	4
525.2.t.g.26.4		8	105.68	odd	12
525.2.t.g.101.4		8	5.3	odd	4
735.2.b.c.146.1		8	35.17	even	12
735.2.b.c.146.8		8	105.32	even	12
735.2.b.d.146.1		8	35.32	odd	12
735.2.b.d.146.8		8	105.17	odd	12
735.2.s.k.521.1		8	35.27	even	4
735.2.s.k.656.1		8	105.2	even	12
735.2.s.l.521.4		8	105.62	odd	4
735.2.s.l.656.4		8	35.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.16543 + 2.01859i) q^{2} +(1.23297 - 1.21646i) q^{3} +(-1.71646 + 2.97300i) q^{4} +(3.89248 + 1.07116i) q^{6} +(2.39840 - 1.11699i) q^{7} -3.33995 q^{8} +(0.0404447 - 2.99973i) q^{9} +O(q^{10})\)	\(q+(1.16543 + 2.01859i) q^{2} +(1.23297 - 1.21646i) q^{3} +(-1.71646 + 2.97300i) q^{4} +(3.89248 + 1.07116i) q^{6} +(2.39840 - 1.11699i) q^{7} -3.33995 q^{8} +(0.0404447 - 2.99973i) q^{9} +(2.42019 + 1.39730i) q^{11} +(1.50019 + 5.75363i) q^{12} -3.20486 q^{13} +(5.04991 + 3.53962i) q^{14} +(-0.459555 - 0.795973i) q^{16} +(0.763780 + 0.440969i) q^{17} +(6.10234 - 3.41434i) q^{18} +(-1.90160 + 1.09789i) q^{19} +(1.59840 - 4.29478i) q^{21} +6.51381i q^{22} +(3.77148 + 6.53240i) q^{23} +(-4.11806 + 4.06291i) q^{24} +(-3.73505 - 6.46929i) q^{26} +(-3.59918 - 3.74778i) q^{27} +(-0.795973 + 9.04771i) q^{28} -8.15270i q^{29} +(-7.62645 - 4.40313i) q^{31} +(-2.26878 + 3.92965i) q^{32} +(4.68378 - 1.22124i) q^{33} +2.05568i q^{34} +(8.84876 + 5.26916i) q^{36} +(-0.352865 + 0.203727i) q^{37} +(-4.43237 - 2.55903i) q^{38} +(-3.95151 + 3.89859i) q^{39} -8.55098 q^{41} +(10.5322 - 1.77876i) q^{42} -0.118062i q^{43} +(-8.30832 + 4.79681i) q^{44} +(-8.79081 + 15.2261i) q^{46} +(-2.27740 + 1.31486i) q^{47} +(-1.53489 - 0.422382i) q^{48} +(4.50469 - 5.35796i) q^{49} +(1.47814 - 0.385407i) q^{51} +(5.50102 - 9.52805i) q^{52} +(-3.73427 + 6.46794i) q^{53} +(3.37062 - 11.6330i) q^{54} +(-8.01054 + 3.73067i) q^{56} +(-1.00908 + 3.66689i) q^{57} +(16.4569 - 9.50142i) q^{58} +(-2.04991 + 3.55054i) q^{59} +(10.7004 - 6.17786i) q^{61} -20.5262i q^{62} +(-3.25365 - 7.23974i) q^{63} -12.4147 q^{64} +(7.92380 + 8.03135i) q^{66} +(-1.38932 - 0.802125i) q^{67} +(-2.62200 + 1.51381i) q^{68} +(12.5965 + 3.46641i) q^{69} -6.25869i q^{71} +(-0.135083 + 10.0189i) q^{72} +(-0.110864 + 0.192022i) q^{73} +(-0.822480 - 0.474859i) q^{74} -7.53794i q^{76} +(7.36535 + 0.647967i) q^{77} +(-12.4749 - 3.43292i) q^{78} +(-1.56849 - 2.71671i) q^{79} +(-8.99673 - 0.242646i) q^{81} +(-9.96559 - 17.2609i) q^{82} -0.666893i q^{83} +(10.0248 + 12.1239i) q^{84} +(0.238319 - 0.137594i) q^{86} +(-9.91745 - 10.0521i) q^{87} +(-8.08330 - 4.66689i) q^{88} +(0.437271 + 0.757376i) q^{89} +(-7.68656 + 3.57978i) q^{91} -25.8944 q^{92} +(-14.7594 + 3.84834i) q^{93} +(-5.30832 - 3.06476i) q^{94} +(1.98292 + 7.60504i) q^{96} -6.37221 q^{97} +(16.0654 + 2.84876i) q^{98} +(4.28939 - 7.20339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9}+O(q^{10}) \) 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9	\( 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9} + 24 q^{14} + 2 q^{16} - 18 q^{19} + 38 q^{21} - 32 q^{24} - 12 q^{26} - 42 q^{31} + 18 q^{36} + 6 q^{39} - 60 q^{41} - 14 q^{46} + 8 q^{49} - 12 q^{51} - 34 q^{54} - 42 q^{56} + 24 q^{59} + 30 q^{61} - 76 q^{64} + 44 q^{66} + 26 q^{69} - 108 q^{74} + 58 q^{79} - 82 q^{81} + 6 q^{84} + 18 q^{86} + 6 q^{89} - 6 q^{91} + 48 q^{94} - 6 q^{96} + 68 q^{99}+O(q^{100}) \) 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9 + 24 * q^14 + 2 * q^16 - 18 * q^19 + 38 * q^21 - 32 * q^24 - 12 * q^26 - 42 * q^31 + 18 * q^36 + 6 * q^39 - 60 * q^41 - 14 * q^46 + 8 * q^49 - 12 * q^51 - 34 * q^54 - 42 * q^56 + 24 * q^59 + 30 * q^61 - 76 * q^64 + 44 * q^66 + 26 * q^69 - 108 * q^74 + 58 * q^79 - 82 * q^81 + 6 * q^84 + 18 * q^86 + 6 * q^89 - 6 * q^91 + 48 * q^94 - 6 * q^96 + 68 * q^99

Introduction

L-functions

Modular forms

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