LMFDB - Embedded newform 525.2.q.f.374.1

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			374.1
Root			$1.16543 + 2.01859i$ of defining polynomial
Character	$\chi$	$=$	525.374
Dual form			525.2.q.f.299.1

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

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

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	$-0.858357\pi$
$2$	−1.16543	−	2.01859i	−0.824085	−	1.42736i	0.0785324	−	0.996912i	$-0.474977\pi$
$3$	−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	$-0.353405\pi$
$13$	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	0.404510	−	0.914533i	$-0.367442\pi$
$17$	−0.763780	−	0.440969i	−0.185244	−	0.106951i	−0.589754	+	0.807583i	$0.700775\pi$
$18$	−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	$-0.878605\pi$
$23$	−3.77148	−	6.53240i	−0.786408	−	1.36210i	0.141746	−	0.989903i	$-0.454728\pi$
$24$	−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	−0.470714	−	0.882286i	$-0.656004\pi$
$37$	0.352865	−	0.203727i	0.0580107	−	0.0334925i	0.528725	+	0.848793i	$0.322670\pi$
$38$	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	$0.00286552\pi$
$43$			0.118062i			0.0180044i	−0.999959	+	0.00900218i	$0.997134\pi$
$44$	−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	−0.324621	−	0.945844i	$-0.605237\pi$
$47$	2.27740	−	1.31486i	0.332194	−	0.191792i	0.656815	+	0.754052i	$0.271903\pi$
$48$	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	$-0.661889\pi$
$53$	3.73427	−	6.46794i	0.512941	−	0.888440i	0.999887	−	0.0150081i	$-0.00477741\pi$
$54$	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	0.582460	−	0.812860i	$-0.302090\pi$
$67$	1.38932	+	0.802125i	0.169733	+	0.0979952i	−0.412727	+	0.910855i	$0.635424\pi$
$68$	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	−0.859465	−	0.511195i	$-0.829203\pi$
$73$	0.110864	−	0.192022i	0.0129757	−	0.0224745i	0.872440	+	0.488721i	$0.162536\pi$
$74$	−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	$0.0116529\pi$
$83$			0.666893i			0.0732010i	−0.999330	+	0.0366005i	$0.988347\pi$
$84$	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	$-0.395140\pi$
$97$	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	−0.470813	−	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	0.889679	−	0.456587i	$-0.150928\pi$
$103$	0.501589	+	0.868777i	0.0494230	+	0.0856031i	−0.840256	+	0.542191i	$0.817595\pi$
$104$	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	$-0.954774\pi$
$107$	−6.38846	−	11.0651i	−0.617596	−	1.06971i	0.372328	−	0.928101i	$-0.378560\pi$
$108$	−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	$-0.610455\pi$
$113$	−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	$0.100456\pi$
$127$			6.99561i			0.620760i	−0.950613	+	0.310380i	$0.899544\pi$
$128$	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	$-0.652437\pi$
$137$	6.29951	−	10.9111i	0.538203	−	0.932195i	0.999001	−	0.0446900i	$-0.0142300\pi$
$138$	−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	−0.525033	−	0.851082i	$-0.675947\pi$
$157$	5.94600	−	10.2988i	0.474542	−	0.821931i	0.999575	+	0.0291509i	$0.00928032\pi$
$158$	−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	−0.760397	−	0.649459i	$-0.774996\pi$
$163$	−7.38130	+	4.26159i	−0.578148	+	0.333794i	0.182249	+	0.983252i	$0.441662\pi$
$164$	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	$0.0440988\pi$
$167$			3.56923i			0.276195i	−0.990419	+	0.138098i	$0.955901\pi$
$168$	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	−0.754127	−	0.656728i	$-0.771940\pi$
$173$	−7.39784	+	4.27114i	−0.562447	+	0.324729i	0.191680	+	0.981457i	$0.438606\pi$
$174$	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	0.487382	−	0.873189i	$-0.337952\pi$
$193$	−0.349134	−	0.201572i	−0.0251312	−	0.0145095i	−0.512513	+	0.858679i	$0.671285\pi$
$194$	−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	0.946552	−	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	$-0.515417\pi$
$223$	−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	0.469017	−	0.883189i	$-0.344608\pi$
$227$	−0.924157	−	0.533562i	−0.0613385	−	0.0354138i	−0.530356	+	0.847775i	$0.677942\pi$
$228$	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	$-0.965953\pi$
$233$	−8.99983	−	15.5882i	−0.589598	−	1.02121i	0.404687	−	0.914455i	$-0.367381\pi$
$234$	−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	−0.863829	−	0.503785i	$-0.831940\pi$
$257$	−13.7781	+	7.95478i	−0.859453	+	0.496206i	0.00437591	+	0.999990i	$0.498607\pi$
$258$	−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	−0.709156	−	0.705052i	$-0.750924\pi$
$263$	4.15187	−	7.19124i	0.256015	−	0.443431i	0.965171	+	0.261621i	$0.0842570\pi$
$264$	−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	0.230199	−	0.973143i	$-0.426062\pi$
$277$	−8.27951	−	4.78018i	−0.497468	−	0.287213i	−0.727667	+	0.685930i	$0.759395\pi$
$278$	−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	$-0.631068\pi$
$283$	9.98469	−	17.2940i	0.593528	−	1.02802i	0.993753	−	0.111604i	$-0.0355988\pi$
$284$	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	$-0.971975\pi$
$293$		−	3.01023i		−	0.175859i	0.996127	−	0.0879297i	$-0.0280251\pi$
$294$	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	−0.162567	−	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	0.856975	−	0.515357i	$-0.172341\pi$
$313$	−0.315354	−	0.546210i	−0.0178249	−	0.0308736i	−0.874800	+	0.484484i	$0.839007\pi$
$314$	−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	$0.0865214\pi$
$317$	12.7151	+	22.0233i	0.714153	+	1.23695i	−0.249132	+	0.968470i	$0.580145\pi$
$318$	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	$-0.854501\pi$
$337$		−	16.2041i		−	0.882694i	0.897336	−	0.441347i	$-0.145499\pi$
$338$	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	−0.517129	−	0.855908i	$-0.672999\pi$
$347$	8.99121	−	15.5732i	0.482673	−	0.836015i	0.999802	+	0.0198929i	$0.00633251\pi$
$348$	−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	0.989384	−	0.145326i	$-0.0464230\pi$
$353$	25.5186	+	14.7332i	1.35822	+	0.784169i	0.368836	+	0.929494i	$0.379756\pi$
$354$	−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	$0.529808\pi$
$367$	−17.4136	+	30.1613i	−0.908984	+	1.57441i	−0.815478	+	0.578788i	$0.803526\pi$
$368$	−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	−0.880146	−	0.474702i	$-0.842556\pi$
$373$	−17.5579	+	10.1371i	−0.909115	+	0.524878i	−0.0289688	+	0.999580i	$0.509222\pi$
$374$	−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	−0.966851	−	0.255339i	$-0.917813\pi$
$383$	−24.0549	+	13.8881i	−1.22915	+	0.709648i	−0.262295	+	0.964988i	$0.584479\pi$
$384$	−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	0.525515	−	0.850784i	$-0.323873\pi$
$397$	−9.44524	−	16.3596i	−0.474043	−	0.821067i	−0.999558	+	0.0297174i	$0.990539\pi$
$398$		−	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	$-0.744907\pi$
$433$	−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	−0.150174	−	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	0.891876	−	0.452281i	$-0.149389\pi$
$443$	1.14186	+	1.97776i	0.0542513	+	0.0939660i	−0.837624	+	0.546247i	$0.816056\pi$
$444$	−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	0.343560	−	0.939131i	$-0.388367\pi$
$457$	28.4033	−	16.3987i	1.32865	−	0.767097i	0.985091	+	0.172033i	$0.0550336\pi$
$458$	−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	$0.323496\pi$
$463$			36.5866i			1.70032i	−0.526522	+	0.850162i	$0.676504\pi$
$464$	−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	$0.733451\pi$
$467$	−35.6023	+	20.5550i	−1.64748	+	0.951171i	−0.978070	+	0.208275i	$0.933215\pi$
$468$	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	0.539341	−	0.842087i	$-0.318673\pi$
$487$	1.75977	+	1.01601i	0.0797430	+	0.0460396i	−0.459598	+	0.888127i	$0.652007\pi$
$488$	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	$-0.876042\pi$
$503$		−	17.0296i		−	0.759312i	0.925128	−	0.379656i	$-0.123958\pi$
$504$	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	$-0.874098\pi$
$523$	−18.1827	−	31.4934i	−0.795075	−	1.37711i	0.127716	−	0.991811i	$-0.459235\pi$
$524$	−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	$-0.924870\pi$
$547$		−	10.9382i		−	0.467684i	0.972275	−	0.233842i	$-0.0751299\pi$
$548$	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	−0.950511	−	0.310692i	$-0.899439\pi$
$557$	−4.86622	+	8.42853i	−0.206188	+	0.357128i	0.744322	+	0.667820i	$0.232773\pi$
$558$	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	0.491393	−	0.870938i	$-0.336488\pi$
$563$	−0.407265	−	0.235135i	−0.0171642	−	0.00990975i	−0.508558	+	0.861028i	$0.669821\pi$
$564$	−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	−0.833497	−	0.552523i	$-0.813665\pi$
$577$	1.48330	−	2.56914i	0.0617504	−	0.106955i	0.895248	+	0.445568i	$0.146998\pi$
$578$	−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	$0.127411\pi$
$587$			18.8819i			0.779341i	−0.920954	+	0.389670i	$0.872589\pi$
$588$	−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	0.147185	−	0.989109i	$-0.452979\pi$
$593$	26.2357	−	15.1472i	1.07737	−	0.622020i	0.930186	+	0.367088i	$0.119645\pi$
$594$	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	$0.0104401\pi$
$607$	13.0117	+	22.5370i	0.528130	+	0.914748i	−0.471332	+	0.881956i	$0.656227\pi$
$608$			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	0.876914	−	0.480648i	$-0.159598\pi$
$613$	22.2611	+	12.8525i	0.899118	+	0.519106i	0.0222040	+	0.999753i	$0.492932\pi$
$614$	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	0.925863	−	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	$-0.670545\pi$
$643$	−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	0.661039	−	0.750351i	$-0.270116\pi$
$647$	8.69245	+	5.01859i	0.341735	+	0.197301i	−0.319304	+	0.947652i	$0.603449\pi$
$648$	−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	$-0.884500\pi$
$653$	−19.8000	−	34.2946i	−0.774833	−	1.34205i	0.160055	−	0.987108i	$-0.448833\pi$
$654$	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	$-0.993355\pi$
$673$		−	1.08304i		−	0.0417483i	0.999782	−	0.0208741i	$-0.00664493\pi$
$674$	−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	0.114370	−	0.993438i	$-0.463515\pi$
$677$	26.8492	−	15.5014i	1.03190	−	0.595766i	0.917528	+	0.397672i	$0.130182\pi$
$678$	−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	−0.988847	−	0.148937i	$-0.952415\pi$
$683$	−9.55050	+	16.5419i	−0.365440	+	0.632960i	0.623407	+	0.781898i	$0.285748\pi$
$684$	−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	$-0.198358\pi$
$727$	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	0.516495	−	0.856290i	$-0.327237\pi$
$733$	−13.0854	−	22.6647i	−0.483322	−	0.837138i	−0.999817	+	0.0191524i	$0.993903\pi$
$734$	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	$-0.448241\pi$
$743$	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	−0.971748	−	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	$-0.782336\pi$
$757$		−	34.7636i		−	1.26351i	0.775170	−	0.631753i	$-0.217664\pi$
$758$	−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	0.999997	−	0.00246461i	$-0.000784510\pi$
$773$	41.6448	+	24.0437i	1.49786	+	0.864790i	0.497864	+	0.867255i	$0.334118\pi$
$774$	−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	$-0.652654\pi$
$787$	15.0823	−	26.1234i	0.537627	−	0.931197i	0.999031	−	0.0440072i	$-0.0140125\pi$
$788$	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	$0.0203358\pi$
$797$			3.60475i			0.127687i	−0.997960	+	0.0638435i	$0.979664\pi$
$798$	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	0.808689	−	0.588237i	$-0.200178\pi$
$823$	20.1850	+	11.6538i	0.703605	+	0.406227i	−0.105084	+	0.994463i	$0.533511\pi$
$824$	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	−0.0247149	−	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	$-0.596031\pi$
$853$	−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	−0.385752	−	0.922602i	$-0.626058\pi$
$857$	−40.3294	−	23.2842i	−1.37763	−	0.795372i	−0.991873	+	0.127230i	$0.959391\pi$
$858$	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	0.885553	−	0.464539i	$-0.153780\pi$
$863$	1.18901	+	2.05942i	0.0404742	+	0.0701034i	−0.845079	+	0.534642i	$0.820446\pi$
$864$	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	−0.786953	−	0.617012i	$-0.788343\pi$
$877$	−19.1332	+	11.0465i	−0.646082	+	0.373015i	0.140872	+	0.990028i	$0.455009\pi$
$878$	−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	$0.0200513\pi$
$883$			3.74124i			0.125903i	−0.998017	+	0.0629514i	$0.979949\pi$
$884$	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	−0.0429963	−	0.999075i	$-0.513690\pi$
$887$	23.8478	−	13.7685i	0.800730	−	0.462302i	0.843726	+	0.536773i	$0.180357\pi$
$888$	−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	−0.173928	−	0.984758i	$-0.555646\pi$
$907$	−33.5412	−	19.3650i	−1.11372	−	0.643005i	−0.939790	+	0.341754i	$0.888979\pi$
$908$	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	$-0.440432\pi$
$937$	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	0.287129	+	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	0.959950	−	0.280172i	$-0.0903917\pi$
$947$	7.30370	+	12.6504i	0.237338	+	0.411082i	−0.722611	+	0.691255i	$0.757058\pi$
$948$	−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	$0.00209731\pi$
$967$			0.409782i			0.0131777i	−0.999978	+	0.00658885i	$0.997903\pi$
$968$	−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	−0.998094	−	0.0617045i	$-0.980346\pi$
$977$	−13.9284	+	24.1247i	−0.445610	+	0.771818i	0.552485	+	0.833523i	$0.313680\pi$
$978$	−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	0.509104	−	0.860705i	$-0.329977\pi$
$983$	0.572640	+	0.330614i	0.0182644	+	0.0105449i	−0.490840	+	0.871250i	$0.663310\pi$
$984$	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	−0.909786	−	0.415078i	$-0.863754\pi$
$997$	−3.01307	+	5.21879i	−0.0954249	+	0.165281i	0.814361	+	0.580359i	$0.197088\pi$
$998$	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.374.1		16
3.2	odd	2		525.2.q.e.374.8		16
5.2	odd	4		525.2.t.g.101.4		8
5.3	odd	4		105.2.s.c.101.1	yes	8
5.4	even	2	inner	525.2.q.f.374.8		16
7.5	odd	6		525.2.q.e.299.1		16
15.2	even	4		525.2.t.f.101.1		8
15.8	even	4		105.2.s.d.101.4	yes	8
15.14	odd	2		525.2.q.e.374.1		16
21.5	even	6	inner	525.2.q.f.299.8		16
35.3	even	12		735.2.b.c.146.1		8
35.12	even	12		525.2.t.f.26.1		8
35.13	even	4		735.2.s.k.521.1		8
35.18	odd	12		735.2.b.d.146.1		8
35.19	odd	6		525.2.q.e.299.8		16
35.23	odd	12		735.2.s.l.656.4		8
35.33	even	12		105.2.s.d.26.4	yes	8
105.23	even	12		735.2.s.k.656.1		8
105.38	odd	12		735.2.b.d.146.8		8
105.47	odd	12		525.2.t.g.26.4		8
105.53	even	12		735.2.b.c.146.8		8
105.68	odd	12		105.2.s.c.26.1	✓	8
105.83	odd	4		735.2.s.l.521.4		8
105.89	even	6	inner	525.2.q.f.299.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.1	✓	8	105.68	odd	12
105.2.s.c.101.1	yes	8	5.3	odd	4
105.2.s.d.26.4	yes	8	35.33	even	12
105.2.s.d.101.4	yes	8	15.8	even	4
525.2.q.e.299.1		16	7.5	odd	6
525.2.q.e.299.8		16	35.19	odd	6
525.2.q.e.374.1		16	15.14	odd	2
525.2.q.e.374.8		16	3.2	odd	2
525.2.q.f.299.1		16	105.89	even	6	inner
525.2.q.f.299.8		16	21.5	even	6	inner
525.2.q.f.374.1		16	1.1	even	1	trivial
525.2.q.f.374.8		16	5.4	even	2	inner
525.2.t.f.26.1		8	35.12	even	12
525.2.t.f.101.1		8	15.2	even	4
525.2.t.g.26.4		8	105.47	odd	12
525.2.t.g.101.4		8	5.2	odd	4
735.2.b.c.146.1		8	35.3	even	12
735.2.b.c.146.8		8	105.53	even	12
735.2.b.d.146.1		8	35.18	odd	12
735.2.b.d.146.8		8	105.38	odd	12
735.2.s.k.521.1		8	35.13	even	4
735.2.s.k.656.1		8	105.23	even	12
735.2.s.l.521.4		8	105.83	odd	4
735.2.s.l.656.4		8	35.23	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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