LMFDB - Embedded newform 525.2.q.f.299.1

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			299.1
Root			$1.16543 - 2.01859i$ of defining polynomial
Character	$\chi$	$=$	525.299
Dual form			525.2.q.f.374.1

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

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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	0.0785324	+	0.996912i	$0.474977\pi$
$2$	−1.16543	+	2.01859i	−0.824085	+	1.42736i	−0.902617	+	0.430445i	$0.858357\pi$
$3$	−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	−0.0886035	−	0.996067i	$-0.528240\pi$
$11$	2.42019	−	1.39730i	0.729714	−	0.421301i	0.818318	+	0.574766i	$0.194907\pi$
$12$	−1.50019	+	5.75363i	−0.433066	+	1.66093i
$13$	3.20486			0.888869			0.444434	−	0.895811i	$-0.353405\pi$
$13$	3.20486			0.888869			0.444434	+	0.895811i	$0.353405\pi$
$14$	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	$-0.700775\pi$
$17$	−0.763780	+	0.440969i	−0.185244	+	0.106951i	0.404510	+	0.914533i	$0.367442\pi$
$18$	−6.10234	−	3.41434i	−1.43834	−	0.804767i
$19$	−1.90160	−	1.09789i	−0.436257	−	0.251873i	0.265751	−	0.964042i	$-0.414380\pi$
$19$	−1.90160	−	1.09789i	−0.436257	−	0.251873i	−0.702009	+	0.712168i	$0.747713\pi$
$20$		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	0.141746	+	0.989903i	$0.454728\pi$
$23$	−3.77148	+	6.53240i	−0.786408	+	1.36210i	−0.928154	+	0.372196i	$0.878605\pi$
$24$	−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	$0.273316\pi$
$29$			8.15270i			1.51392i	−0.653462	+	0.756959i	$0.726684\pi$
$30$		0			0
$31$	−7.62645	+	4.40313i	−1.36975	+	0.790826i	−0.990896	−	0.134630i	$-0.957015\pi$
$31$	−7.62645	+	4.40313i	−1.36975	+	0.790826i	−0.378855	+	0.925456i	$0.623682\pi$
$32$	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	$-0.322670\pi$
$37$	0.352865	+	0.203727i	0.0580107	+	0.0334925i	−0.470714	+	0.882286i	$0.656004\pi$
$38$	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	$-0.271903\pi$
$47$	2.27740	+	1.31486i	0.332194	+	0.191792i	−0.324621	+	0.945844i	$0.605237\pi$
$48$	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	0.999887	+	0.0150081i	$0.00477741\pi$
$53$	3.73427	+	6.46794i	0.512941	+	0.888440i	−0.486946	+	0.873432i	$0.661889\pi$
$54$	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	0.701178	−	0.712986i	$-0.252658\pi$
$59$	−2.04991	−	3.55054i	−0.266875	−	0.462241i	−0.968053	+	0.250745i	$0.919324\pi$
$60$		0			0
$61$	10.7004	+	6.17786i	1.37004	+	0.790994i	0.990933	−	0.134358i	$-0.0428972\pi$
$61$	10.7004	+	6.17786i	1.37004	+	0.790994i	0.379109	+	0.925352i	$0.376231\pi$
$62$		−	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	$-0.635424\pi$
$67$	1.38932	−	0.802125i	0.169733	−	0.0979952i	0.582460	+	0.812860i	$0.302090\pi$
$68$	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	$0.121117\pi$
$71$			6.25869i			0.742770i	−0.928479	+	0.371385i	$0.878883\pi$
$72$	0.135083	+	10.0189i	0.0159197	+	1.18074i
$73$	0.110864	+	0.192022i	0.0129757	+	0.0224745i	0.872440	−	0.488721i	$-0.162536\pi$
$73$	0.110864	+	0.192022i	0.0129757	+	0.0224745i	−0.859465	+	0.511195i	$0.829203\pi$
$74$	−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	−0.940669	−	0.339326i	$-0.889801\pi$
$79$	−1.56849	+	2.71671i	−0.176469	+	0.305654i	0.764199	+	0.644980i	$0.223134\pi$
$80$		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	−0.841919	−	0.539603i	$-0.818574\pi$
$89$	0.437271	−	0.757376i	0.0463506	−	0.0802816i	0.888270	+	0.459322i	$0.151908\pi$
$90$		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	$-0.395140\pi$
$97$	6.37221			0.647000			0.323500	+	0.946228i	$0.395140\pi$
$98$	−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	0.999443	+	0.0333808i	$0.0106274\pi$
$101$	5.31267	+	9.20181i	0.528630	+	0.915614i	−0.470813	+	0.882233i	$0.656039\pi$
$102$	−2.50065	+	2.53459i	−0.247601	+	0.250962i
$103$	0.501589	−	0.868777i	0.0494230	−	0.0856031i	−0.840256	−	0.542191i	$-0.817595\pi$
$103$	0.501589	−	0.868777i	0.0494230	−	0.0856031i	0.889679	+	0.456587i	$0.150928\pi$
$104$	10.7041			1.04962
$105$		0			0
$106$	−17.4081			−1.69083
$107$	−6.38846	+	11.0651i	−0.617596	+	1.06971i	0.372328	+	0.928101i	$0.378560\pi$
$107$	−6.38846	+	11.0651i	−0.617596	+	1.06971i	−0.989923	+	0.141606i	$0.954774\pi$
$108$	−17.3200	−	4.26745i	−1.66662	−	0.410635i
$109$	0.00912370	+	0.0158027i	0.000873892	+	0.00151363i	0.866462	−	0.499243i	$-0.166388\pi$
$109$	0.00912370	+	0.0158027i	0.000873892	+	0.00151363i	−0.865588	+	0.500757i	$0.833055\pi$
$110$		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	$-0.610455\pi$
$113$	−7.23027			−0.680166			−0.340083	+	0.940395i	$0.610455\pi$
$114$	−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	−0.564864	−	0.825184i	$-0.691071\pi$
$131$	4.94673	−	8.56799i	0.432198	−	0.748589i	0.997062	+	0.0765948i	$0.0244048\pi$
$132$	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	0.999001	+	0.0446900i	$0.0142300\pi$
$137$	6.29951	+	10.9111i	0.538203	+	0.932195i	−0.460798	+	0.887505i	$0.652437\pi$
$138$	−7.68316	+	29.4671i	−0.654034	+	2.50840i
$139$			0.988113i			0.0838106i	0.999122	+	0.0419053i	$0.0133428\pi$
$139$			0.988113i			0.0838106i	−0.999122	+	0.0419053i	$0.986657\pi$
$140$		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	−0.285616	−	0.958344i	$-0.592198\pi$
$149$	−15.3604	−	8.86834i	−1.25837	−	0.726523i	−0.972758	+	0.231821i	$0.925532\pi$
$150$		0			0
$151$	11.2504	+	19.4862i	0.915542	+	1.58576i	0.806106	+	0.591771i	$0.201571\pi$
$151$	11.2504	+	19.4862i	0.915542	+	1.58576i	0.109435	+	0.993994i	$0.465096\pi$
$152$	−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	$-0.00928032\pi$
$157$	5.94600	+	10.2988i	0.474542	+	0.821931i	−0.525033	+	0.851082i	$0.675947\pi$
$158$	−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	$-0.441662\pi$
$163$	−7.38130	−	4.26159i	−0.578148	−	0.333794i	−0.760397	+	0.649459i	$0.774996\pi$
$164$	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	$-0.438606\pi$
$173$	−7.39784	−	4.27114i	−0.562447	−	0.324729i	−0.754127	+	0.656728i	$0.771940\pi$
$174$	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	−0.539265	−	0.842136i	$-0.681298\pi$
$179$	−1.06480	+	0.614760i	−0.0795866	+	0.0459493i	0.459679	+	0.888085i	$0.347965\pi$
$180$		0			0
$181$		−	15.3995i		−	1.14464i	−0.820032	−	0.572318i	$-0.806044\pi$
$181$		−	15.3995i		−	1.14464i	0.820032	−	0.572318i	$-0.193956\pi$
$182$	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	−0.0297166	−	0.999558i	$-0.509460\pi$
$191$	−12.5795	−	7.26275i	−0.910218	−	0.525514i	−0.880501	+	0.474044i	$0.842794\pi$
$192$	15.3070	+	15.1020i	1.10468	+	1.08989i
$193$	−0.349134	+	0.201572i	−0.0251312	+	0.0145095i	−0.512513	−	0.858679i	$-0.671285\pi$
$193$	−0.349134	+	0.201572i	−0.0251312	+	0.0145095i	0.487382	+	0.873189i	$0.337952\pi$
$194$	−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	$-0.636492\pi$
$197$	−11.6716			−0.831564			−0.415782	+	0.909464i	$0.636492\pi$
$198$	−19.5397	+	0.263449i	−1.38862	+	0.0187225i
$199$	16.0886	−	9.28875i	1.14049	−	0.658462i	0.193938	−	0.981014i	$-0.437874\pi$
$199$	16.0886	−	9.28875i	1.14049	−	0.658462i	0.946552	+	0.322552i	$0.104541\pi$
$200$		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	$-0.515417\pi$
$223$	−1.44594			−0.0968271			−0.0484135	+	0.998827i	$0.515417\pi$
$224$	−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	$-0.677942\pi$
$227$	−0.924157	+	0.533562i	−0.0613385	+	0.0354138i	0.469017	+	0.883189i	$0.344608\pi$
$228$	9.16961	−	9.29408i	0.607272	−	0.615515i
$229$	6.58058	+	3.79930i	0.434857	+	0.251065i	0.701414	−	0.712755i	$-0.252553\pi$
$229$	6.58058	+	3.79930i	0.434857	+	0.251065i	−0.266557	+	0.963819i	$0.585886\pi$
$230$		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	0.404687	+	0.914455i	$0.367381\pi$
$233$	−8.99983	+	15.5882i	−0.589598	+	1.02121i	−0.994285	+	0.106759i	$0.965953\pi$
$234$	−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	$-0.582698\pi$
$239$		−	29.8816i		−	1.93288i	0.256892	−	0.966440i	$-0.417302\pi$
$240$		0			0
$241$	4.53760	−	2.61978i	0.292292	−	0.168755i	−0.346683	−	0.937982i	$-0.612692\pi$
$241$	4.53760	−	2.61978i	0.292292	−	0.168755i	0.638975	+	0.769227i	$0.279359\pi$
$242$	−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	$-0.498607\pi$
$257$	−13.7781	−	7.95478i	−0.859453	−	0.496206i	−0.863829	+	0.503785i	$0.831940\pi$
$258$	−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	$-0.0842570\pi$
$263$	4.15187	+	7.19124i	0.256015	+	0.443431i	−0.709156	+	0.705052i	$0.750924\pi$
$264$	−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	−0.999385	−	0.0350578i	$-0.988838\pi$
$269$	−8.69353	−	15.0576i	−0.530054	−	0.918080i	0.469332	−	0.883022i	$-0.344495\pi$
$270$		0			0
$271$	−8.82614	−	5.09577i	−0.536150	−	0.309546i	0.207367	−	0.978263i	$-0.433510\pi$
$271$	−8.82614	−	5.09577i	−0.536150	−	0.309546i	−0.743517	+	0.668717i	$0.766844\pi$
$272$		−	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	$-0.759395\pi$
$277$	−8.27951	+	4.78018i	−0.497468	+	0.287213i	0.230199	+	0.973143i	$0.426062\pi$
$278$	−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	$-0.884256\pi$
$281$		−	11.9239i		−	0.711320i	0.934616	−	0.355660i	$-0.115744\pi$
$282$	10.2732	+	2.67860i	0.611758	+	0.159508i
$283$	9.98469	+	17.2940i	0.593528	+	1.02802i	0.993753	+	0.111604i	$0.0355988\pi$
$283$	9.98469	+	17.2940i	0.593528	+	1.02802i	−0.400225	+	0.916417i	$0.631068\pi$
$284$	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	$-0.697556\pi$
$307$	−20.3794			−1.16311			−0.581556	+	0.813507i	$0.697556\pi$
$308$	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	0.935789	+	0.352562i	$0.114689\pi$
$311$	13.6359	+	23.6181i	0.773222	+	1.33926i	−0.162567	+	0.986697i	$0.551977\pi$
$312$	−13.1978	−	13.0211i	−0.747180	−	0.737173i
$313$	−0.315354	+	0.546210i	−0.0178249	+	0.0308736i	−0.874800	−	0.484484i	$-0.839007\pi$
$313$	−0.315354	+	0.546210i	−0.0178249	+	0.0308736i	0.856975	+	0.515357i	$0.172341\pi$
$314$	−27.7186			−1.56425
$315$		0			0
$316$	10.7690			0.605806
$317$	12.7151	−	22.0233i	0.714153	−	1.23695i	−0.249132	−	0.968470i	$-0.580145\pi$
$317$	12.7151	−	22.0233i	0.714153	−	1.23695i	0.963285	−	0.268480i	$-0.0865214\pi$
$318$	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	−0.979621	−	0.200855i	$-0.935628\pi$
$331$	−5.74666	+	9.95352i	−0.315865	+	0.547095i	0.663756	+	0.747949i	$0.268961\pi$
$332$	−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	$-0.00633251\pi$
$347$	8.99121	+	15.5732i	0.482673	+	0.836015i	−0.517129	+	0.855908i	$0.672999\pi$
$348$	−46.9077	−	12.2306i	−2.51451	−	0.655627i
$349$			6.15422i			0.329428i	0.986341	+	0.164714i	$0.0526701\pi$
$349$			6.15422i			0.329428i	−0.986341	+	0.164714i	$0.947330\pi$
$350$		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	$-0.379756\pi$
$353$	25.5186	−	14.7332i	1.35822	−	0.784169i	0.989384	+	0.145326i	$0.0464230\pi$
$354$	−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	0.989154	+	0.146881i	$0.0469233\pi$
$359$	30.5228	+	17.6224i	1.61093	+	0.930073i	0.621779	+	0.783192i	$0.286410\pi$
$360$		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	−0.815478	−	0.578788i	$-0.803526\pi$
$367$	−17.4136	−	30.1613i	−0.908984	−	1.57441i	−0.0935065	−	0.995619i	$-0.529808\pi$
$368$	−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	$-0.509222\pi$
$373$	−17.5579	−	10.1371i	−0.909115	−	0.524878i	−0.880146	+	0.474702i	$0.842556\pi$
$374$	−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	$-0.584479\pi$
$383$	−24.0549	−	13.8881i	−1.22915	−	0.709648i	−0.966851	+	0.255339i	$0.917813\pi$
$384$	−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	−0.117236	−	0.993104i	$-0.537403\pi$
$389$	13.4945	−	7.79107i	0.684200	−	0.395023i	0.801436	+	0.598081i	$0.204070\pi$
$390$		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	$-0.990539\pi$
$397$	−9.44524	+	16.3596i	−0.474043	+	0.821067i	0.525515	+	0.850784i	$0.323873\pi$
$398$			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	0.877042	−	0.480415i	$-0.159514\pi$
$401$	18.0127	+	10.3996i	0.899511	+	0.519333i	0.0224695	+	0.999748i	$0.492847\pi$
$402$	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	−0.967966	−	0.251080i	$-0.919214\pi$
$409$	−24.9664	+	14.4143i	−1.23451	+	0.712744i	−0.266542	+	0.963823i	$0.585881\pi$
$410$		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	−0.606351	+	0.795197i	$0.707367\pi$
$431$	−33.1792	+	19.1560i	−1.59819	+	0.922714i	−0.991836	+	0.127516i	$0.959299\pi$
$432$	1.32911	+	4.58717i	0.0639468	+	0.220700i
$433$	−28.9533			−1.39140			−0.695702	−	0.718330i	$-0.744907\pi$
$433$	−28.9533			−1.39140			−0.695702	+	0.718330i	$0.744907\pi$
$434$	−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	0.781117	−	0.624384i	$-0.214650\pi$
$439$	13.2197	+	7.63242i	0.630943	+	0.364275i	−0.150174	+	0.988660i	$0.547983\pi$
$440$		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	$-0.816056\pi$
$443$	1.14186	−	1.97776i	0.0542513	−	0.0939660i	0.891876	+	0.452281i	$0.149389\pi$
$444$	−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	$0.0782331\pi$
$449$			10.3113i			0.486619i	−0.969949	+	0.243310i	$0.921767\pi$
$450$		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	$-0.0550336\pi$
$457$	28.4033	+	16.3987i	1.32865	+	0.767097i	0.343560	+	0.939131i	$0.388367\pi$
$458$	−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	−0.978070	−	0.208275i	$-0.933215\pi$
$467$	−35.6023	−	20.5550i	−1.64748	−	0.951171i	−0.669406	−	0.742896i	$-0.733451\pi$
$468$	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	0.990681	−	0.136205i	$-0.0434906\pi$
$479$	8.25944	+	14.3058i	0.377383	+	0.653647i	−0.613297	+	0.789852i	$0.710157\pi$
$480$		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	$-0.652007\pi$
$487$	1.75977	−	1.01601i	0.0797430	−	0.0460396i	0.539341	+	0.842087i	$0.318673\pi$
$488$	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	$-0.956925\pi$
$491$		−	5.97889i		−	0.269824i	0.990858	−	0.134912i	$-0.0430751\pi$
$492$	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	−0.755331	−	0.655343i	$-0.772524\pi$
$499$	4.24155	−	7.34658i	0.189878	−	0.328878i	0.945209	+	0.326465i	$0.105857\pi$
$500$		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	−0.972654	−	0.232258i	$-0.925389\pi$
$509$	−6.43409	+	11.1442i	−0.285186	+	0.493956i	0.687468	+	0.726214i	$0.258722\pi$
$510$		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	0.623925	−	0.781485i	$-0.285537\pi$
$521$	−8.32724	−	14.4232i	−0.364823	−	0.631892i	−0.988748	+	0.149592i	$0.952204\pi$
$522$	27.8361	−	49.7506i	1.21835	−	2.17752i
$523$	−18.1827	+	31.4934i	−0.795075	+	1.37711i	0.127716	+	0.991811i	$0.459235\pi$
$523$	−18.1827	+	31.4934i	−0.795075	+	1.37711i	−0.922791	+	0.385300i	$0.874098\pi$
$524$	−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	−0.903896	−	0.427751i	$-0.859306\pi$
$541$	−1.89575	+	3.28353i	−0.0815046	+	0.141170i	0.822392	+	0.568922i	$0.192639\pi$
$542$	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	$-0.232773\pi$
$557$	−4.86622	−	8.42853i	−0.206188	−	0.357128i	−0.950511	+	0.310692i	$0.899439\pi$
$558$	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	$-0.669821\pi$
$563$	−0.407265	+	0.235135i	−0.0171642	+	0.00990975i	0.491393	+	0.870938i	$0.336488\pi$
$564$	−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	0.608588	−	0.793486i	$-0.291736\pi$
$569$	5.38387	+	3.10838i	0.225703	+	0.130310i	−0.382885	+	0.923796i	$0.625069\pi$
$570$		0			0
$571$	−5.31121	−	9.19928i	−0.222267	−	0.384978i	0.733229	−	0.679982i	$-0.238012\pi$
$571$	−5.31121	−	9.19928i	−0.222267	−	0.384978i	−0.955496	+	0.295004i	$0.904679\pi$
$572$	−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	$-0.146998\pi$
$577$	1.48330	+	2.56914i	0.0617504	+	0.106955i	−0.833497	+	0.552523i	$0.813665\pi$
$578$	−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	$-0.119645\pi$
$593$	26.2357	+	15.1472i	1.07737	+	0.622020i	0.147185	+	0.989109i	$0.452979\pi$
$594$	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	−0.622971	−	0.782245i	$-0.714075\pi$
$599$	−6.29024	+	3.63167i	−0.257012	+	0.148386i	0.365959	+	0.930631i	$0.380741\pi$
$600$		0			0
$601$		−	45.3302i		−	1.84906i	−0.381110	−	0.924530i	$-0.624458\pi$
$601$		−	45.3302i		−	1.84906i	0.381110	−	0.924530i	$-0.375542\pi$
$602$	−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	−0.471332	−	0.881956i	$-0.656227\pi$
$607$	13.0117	−	22.5370i	0.528130	−	0.914748i	0.999462	−	0.0327925i	$-0.0104401\pi$
$608$		−	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	$-0.492932\pi$
$613$	22.2611	−	12.8525i	0.899118	−	0.519106i	0.876914	+	0.480648i	$0.159598\pi$
$614$	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	$-0.557221\pi$
$617$	−8.88258			−0.357599			−0.178800	+	0.983886i	$0.557221\pi$
$618$	1.02182	−	3.91898i	0.0411037	−	0.157644i
$619$	26.4112	−	15.2485i	1.06156	−	0.612890i	0.135694	−	0.990751i	$-0.456673\pi$
$619$	26.4112	−	15.2485i	1.06156	−	0.612890i	0.925863	+	0.377861i	$0.123340\pi$
$620$		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	−0.376123	−	0.926570i	$-0.622743\pi$
$641$	6.03197	−	3.48256i	0.238249	−	0.137553i	0.614371	+	0.789017i	$0.289410\pi$
$642$	−13.0144	+	49.9139i	−0.513637	+	1.96994i
$643$	−25.8907			−1.02103			−0.510514	−	0.859869i	$-0.670545\pi$
$643$	−25.8907			−1.02103			−0.510514	+	0.859869i	$0.670545\pi$
$644$	−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	$-0.603449\pi$
$647$	8.69245	−	5.01859i	0.341735	−	0.197301i	0.661039	+	0.750351i	$0.270116\pi$
$648$	−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	0.160055	+	0.987108i	$0.448833\pi$
$653$	−19.8000	+	34.2946i	−0.774833	+	1.34205i	−0.934888	+	0.354942i	$0.884500\pi$
$654$	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	$0.113598\pi$
$659$			17.9364i			0.698705i	−0.936991	+	0.349352i	$0.886402\pi$
$660$		0			0
$661$	−3.31012	+	1.91110i	−0.128749	+	0.0743332i	−0.562991	−	0.826463i	$-0.690350\pi$
$661$	−3.31012	+	1.91110i	−0.128749	+	0.0743332i	0.434242	+	0.900796i	$0.357016\pi$
$662$	−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	$-0.130182\pi$
$677$	26.8492	+	15.5014i	1.03190	+	0.595766i	0.114370	+	0.993438i	$0.463515\pi$
$678$	−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	$-0.285748\pi$
$683$	−9.55050	−	16.5419i	−0.365440	−	0.632960i	−0.988847	+	0.148937i	$0.952415\pi$
$684$	−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	0.196403	−	0.980523i	$-0.437074\pi$
$691$	−14.5775	−	8.41632i	−0.554554	−	0.320172i	−0.750957	+	0.660351i	$0.770407\pi$
$692$			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	$-0.864360\pi$
$701$		−	21.8878i		−	0.826691i	0.910574	−	0.413345i	$-0.135640\pi$
$702$	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	−0.949554	−	0.313604i	$-0.898464\pi$
$709$	−5.41030	+	9.37091i	−0.203188	+	0.351932i	0.746366	+	0.665536i	$0.231797\pi$
$710$		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	−0.995435	−	0.0954404i	$-0.969574\pi$
$719$	−11.1296	+	19.2770i	−0.415064	+	0.718912i	0.580371	+	0.814352i	$0.302907\pi$
$720$		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	$-0.198358\pi$
$727$	43.7899			1.62408			0.812038	+	0.583604i	$0.198358\pi$
$728$	−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	$-0.993903\pi$
$733$	−13.0854	+	22.6647i	−0.483322	+	0.837138i	0.516495	+	0.856290i	$0.327237\pi$
$734$	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	0.951469	+	0.307746i	$0.0995746\pi$
$739$	20.1777	+	34.9489i	0.742250	+	1.28561i	−0.209219	+	0.977869i	$0.567092\pi$
$740$		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	$-0.448241\pi$
$743$	8.82565			0.323782			0.161891	+	0.986809i	$0.448241\pi$
$744$	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	0.281475	+	0.959569i	$0.409176\pi$
$751$	−18.9165	+	32.7644i	−0.690274	+	1.19559i	−0.971748	+	0.236020i	$0.924157\pi$
$752$	−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	−0.882135	−	0.470998i	$-0.843894\pi$
$761$	−0.915074	+	1.58495i	−0.0331714	+	0.0574545i	0.848963	+	0.528452i	$0.177227\pi$
$762$	−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	$-0.860345\pi$
$769$		−	23.5601i		−	0.849598i	0.905288	−	0.424799i	$-0.139655\pi$
$770$		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	$-0.334118\pi$
$773$	41.6448	−	24.0437i	1.49786	−	0.864790i	0.999997	+	0.00246461i	$0.000784510\pi$
$774$	−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	0.999031	+	0.0440072i	$0.0140125\pi$
$787$	15.0823	+	26.1234i	0.537627	+	0.931197i	−0.461404	+	0.887190i	$0.652654\pi$
$788$	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	−0.132520	−	0.991180i	$-0.542307\pi$
$809$	18.7612	−	10.8318i	0.659607	−	0.380824i	0.792127	+	0.610356i	$0.208974\pi$
$810$		0			0
$811$			27.6526i			0.971015i	0.874232	+	0.485508i	$0.161365\pi$
$811$			27.6526i			0.971015i	−0.874232	+	0.485508i	$0.838635\pi$
$812$	−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	0.698623	−	0.715490i	$-0.253797\pi$
$821$	12.2722	+	7.08534i	0.428302	+	0.247280i	−0.270321	+	0.962770i	$0.587130\pi$
$822$	36.2082	+	35.7233i	1.26291	+	1.24599i
$823$	20.1850	−	11.6538i	0.703605	−	0.406227i	−0.105084	−	0.994463i	$-0.533511\pi$
$823$	20.1850	−	11.6538i	0.703605	−	0.406227i	0.808689	+	0.588237i	$0.200178\pi$
$824$	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	$-0.311607\pi$
$827$	32.0877			1.11580			0.557900	+	0.829908i	$0.311607\pi$
$828$	1.04729	+	77.6762i	0.0363959	+	2.69943i
$829$	−25.9947	+	15.0080i	−0.902833	+	0.521251i	−0.878118	−	0.478444i	$-0.841201\pi$
$829$	−25.9947	+	15.0080i	−0.902833	+	0.521251i	−0.0247149	+	0.999695i	$0.507868\pi$
$830$		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	$-0.596031\pi$
$853$	−17.3563			−0.594269			−0.297135	+	0.954836i	$0.596031\pi$
$854$	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	$-0.959391\pi$
$857$	−40.3294	+	23.2842i	−1.37763	+	0.795372i	−0.385752	+	0.922602i	$0.626058\pi$
$858$	25.3947	−	25.7394i	0.866960	−	0.878728i
$859$	−31.5359	−	18.2072i	−1.07599	−	0.621223i	−0.146178	−	0.989258i	$-0.546697\pi$
$859$	−31.5359	−	18.2072i	−1.07599	−	0.621223i	−0.929812	+	0.368035i	$0.880031\pi$
$860$		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	$-0.820446\pi$
$863$	1.18901	−	2.05942i	0.0404742	−	0.0701034i	0.885553	+	0.464539i	$0.153780\pi$
$864$	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	$-0.455009\pi$
$877$	−19.1332	−	11.0465i	−0.646082	−	0.373015i	−0.786953	+	0.617012i	$0.788343\pi$
$878$	−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	$-0.180357\pi$
$887$	23.8478	+	13.7685i	0.800730	+	0.462302i	−0.0429963	+	0.999075i	$0.513690\pi$
$888$	−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	$-0.888979\pi$
$907$	−33.5412	+	19.3650i	−1.11372	+	0.643005i	−0.173928	+	0.984758i	$0.555646\pi$
$908$	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	$0.126690\pi$
$911$			23.3967i			0.775167i	−0.921835	+	0.387583i	$0.873310\pi$
$912$	−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	−0.928480	−	0.371383i	$-0.878884\pi$
$919$	−4.32329	+	7.48816i	−0.142612	+	0.247012i	0.785867	+	0.618395i	$0.212217\pi$
$920$		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	−0.950462	−	0.310842i	$-0.899389\pi$
$929$	−6.27980	+	10.8769i	−0.206034	+	0.356861i	0.744428	+	0.667703i	$0.232722\pi$
$930$		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	$-0.440432\pi$
$937$	11.3901			0.372097			0.186048	+	0.982541i	$0.440432\pi$
$938$	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	−0.973123	−	0.230285i	$-0.926034\pi$
$941$	−21.0434	−	36.4482i	−0.685994	−	1.18818i	0.287129	−	0.957892i	$-0.407299\pi$
$942$	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	$-0.757058\pi$
$947$	7.30370	−	12.6504i	0.237338	−	0.411082i	0.959950	+	0.280172i	$0.0903917\pi$
$948$	−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	$-0.345052\pi$
$953$	28.8817			0.935570			0.467785	+	0.883842i	$0.345052\pi$
$954$	−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	−0.905391	−	0.424579i	$-0.860422\pi$
$971$	−2.64865	+	4.58759i	−0.0849991	+	0.147223i	0.820392	+	0.571802i	$0.193755\pi$
$972$	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	$-0.313680\pi$
$977$	−13.9284	−	24.1247i	−0.445610	−	0.771818i	−0.998094	+	0.0617045i	$0.980346\pi$
$978$	−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	$-0.663310\pi$
$983$	0.572640	−	0.330614i	0.0182644	−	0.0105449i	0.509104	+	0.860705i	$0.329977\pi$
$984$	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	0.916380	+	0.400309i	$0.131097\pi$
$991$	25.3374	+	43.8856i	0.804868	+	1.39407i	−0.111513	+	0.993763i	$0.535570\pi$
$992$	−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	$-0.197088\pi$
$997$	−3.01307	−	5.21879i	−0.0954249	−	0.165281i	−0.909786	+	0.415078i	$0.863754\pi$
$998$	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.299.1		16
3.2	odd	2		525.2.q.e.299.8		16
5.2	odd	4		105.2.s.c.26.1	✓	8
5.3	odd	4		525.2.t.g.26.4		8
5.4	even	2	inner	525.2.q.f.299.8		16
7.3	odd	6		525.2.q.e.374.1		16
15.2	even	4		105.2.s.d.26.4	yes	8
15.8	even	4		525.2.t.f.26.1		8
15.14	odd	2		525.2.q.e.299.1		16
21.17	even	6	inner	525.2.q.f.374.8		16
35.2	odd	12		735.2.b.d.146.8		8
35.3	even	12		525.2.t.f.101.1		8
35.12	even	12		735.2.b.c.146.8		8
35.17	even	12		105.2.s.d.101.4	yes	8
35.24	odd	6		525.2.q.e.374.8		16
35.27	even	4		735.2.s.k.656.1		8
35.32	odd	12		735.2.s.l.521.4		8
105.2	even	12		735.2.b.c.146.1		8
105.17	odd	12		105.2.s.c.101.1	yes	8
105.32	even	12		735.2.s.k.521.1		8
105.38	odd	12		525.2.t.g.101.4		8
105.47	odd	12		735.2.b.d.146.1		8
105.59	even	6	inner	525.2.q.f.374.1		16
105.62	odd	4		735.2.s.l.656.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.1	✓	8	5.2	odd	4
105.2.s.c.101.1	yes	8	105.17	odd	12
105.2.s.d.26.4	yes	8	15.2	even	4
105.2.s.d.101.4	yes	8	35.17	even	12
525.2.q.e.299.1		16	15.14	odd	2
525.2.q.e.299.8		16	3.2	odd	2
525.2.q.e.374.1		16	7.3	odd	6
525.2.q.e.374.8		16	35.24	odd	6
525.2.q.f.299.1		16	1.1	even	1	trivial
525.2.q.f.299.8		16	5.4	even	2	inner
525.2.q.f.374.1		16	105.59	even	6	inner
525.2.q.f.374.8		16	21.17	even	6	inner
525.2.t.f.26.1		8	15.8	even	4
525.2.t.f.101.1		8	35.3	even	12
525.2.t.g.26.4		8	5.3	odd	4
525.2.t.g.101.4		8	105.38	odd	12
735.2.b.c.146.1		8	105.2	even	12
735.2.b.c.146.8		8	35.12	even	12
735.2.b.d.146.1		8	105.47	odd	12
735.2.b.d.146.8		8	35.2	odd	12
735.2.s.k.521.1		8	105.32	even	12
735.2.s.k.656.1		8	35.27	even	4
735.2.s.l.521.4		8	35.32	odd	12
735.2.s.l.656.4		8	105.62	odd	4

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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more