LMFDB - Embedded newform 525.2.q.e.299.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("525.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			299.8
Root			$-1.16543 + 2.01859i$ of defining polynomial
Character	$\chi$	$=$	525.299
Dual form			525.2.q.e.374.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16543 - 2.01859i) q^{2} +(-0.437000 - 1.67602i) q^{3} +(-1.71646 - 2.97300i) q^{4} +(-3.89248 - 1.07116i) q^{6} +(-2.39840 - 1.11699i) q^{7} -3.33995 q^{8} +(-2.61806 + 1.46484i) q^{9} +O(q^{10})$	\(q+(1.16543 - 2.01859i) q^{2} +(-0.437000 - 1.67602i) q^{3} +(-1.71646 - 2.97300i) q^{4} +(-3.89248 - 1.07116i) q^{6} +(-2.39840 - 1.11699i) q^{7} -3.33995 q^{8} +(-2.61806 + 1.46484i) q^{9} +(-2.42019 + 1.39730i) q^{11} +(-4.23270 + 4.17602i) q^{12} +3.20486 q^{13} +(-5.04991 + 3.53962i) q^{14} +(-0.459555 + 0.795973i) q^{16} +(0.763780 - 0.440969i) q^{17} +(-0.0942709 + 6.99195i) q^{18} +(-1.90160 - 1.09789i) q^{19} +(-0.823984 + 4.50789i) q^{21} +6.51381i q^{22} +(3.77148 - 6.53240i) q^{23} +(1.45956 + 5.59780i) 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} +(3.39951 + 3.44566i) q^{33} -2.05568i q^{34} +(8.84876 + 5.26916i) q^{36} +(0.352865 + 0.203727i) q^{37} +(-4.43237 + 2.55903i) q^{38} +(-1.40052 - 5.37140i) q^{39} +8.55098 q^{41} +(8.13927 + 6.91692i) 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} +(-1.07284 - 1.08741i) q^{51} +(-5.50102 - 9.52805i) q^{52} +(-3.73427 - 6.46794i) q^{53} +(11.7598 - 2.89748i) 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} +(7.91537 - 0.588936i) q^{63} -12.4147 q^{64} +(10.9173 - 2.84653i) q^{66} +(1.38932 - 0.802125i) q^{67} +(-2.62200 - 1.51381i) q^{68} +(-12.5965 - 3.46641i) q^{69} -6.25869i q^{71} +(8.74419 - 4.89248i) 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} +(4.70850 - 7.67007i) q^{81} +(9.96559 - 17.2609i) q^{82} +0.666893i q^{83} +(14.8163 - 5.28791i) q^{84} +(-0.238319 - 0.137594i) q^{86} +(-13.6641 + 3.56273i) q^{87} +(8.08330 - 4.66689i) q^{88} +(-0.437271 + 0.757376i) q^{89} +(-7.68656 - 3.57978i) q^{91} -25.8944 q^{92} +(10.7125 + 10.8579i) q^{93} +(-5.30832 + 3.06476i) q^{94} +(-5.59470 + 5.51978i) 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} - 8 q^{9}+O(q^{10}) $ 16 * q - 6 * q^4 - 10 * q^6 - 8 * q^9	$ 16 q - 6 q^{4} - 10 q^{6} - 8 q^{9} - 24 q^{14} + 2 q^{16} - 18 q^{19} - 44 q^{21} + 14 q^{24} + 12 q^{26} - 42 q^{31} + 18 q^{36} - 30 q^{39} + 60 q^{41} - 14 q^{46} + 8 q^{49} + 24 q^{51} - 14 q^{54} + 42 q^{56} - 24 q^{59} + 30 q^{61} - 76 q^{64} - 32 q^{66} - 26 q^{69} + 108 q^{74} + 58 q^{79} + 56 q^{81} + 102 q^{84} - 18 q^{86} - 6 q^{89} - 6 q^{91} + 48 q^{94} - 84 q^{96} + 68 q^{99}+O(q^{100}) $ 16 * q - 6 * q^4 - 10 * q^6 - 8 * q^9 - 24 * q^14 + 2 * q^16 - 18 * q^19 - 44 * q^21 + 14 * q^24 + 12 * q^26 - 42 * q^31 + 18 * q^36 - 30 * q^39 + 60 * q^41 - 14 * q^46 + 8 * q^49 + 24 * q^51 - 14 * q^54 + 42 * q^56 - 24 * q^59 + 30 * q^61 - 76 * q^64 - 32 * q^66 - 26 * q^69 + 108 * q^74 + 58 * q^79 + 56 * q^81 + 102 * q^84 - 18 * q^86 - 6 * q^89 - 6 * q^91 + 48 * q^94 - 84 * 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	$-0.525023\pi$
$2$	1.16543	−	2.01859i	0.824085	−	1.42736i	0.902617	−	0.430445i	$-0.141643\pi$
$3$	−0.437000	−	1.67602i	−0.252302	−	0.967649i
$3$	−0.437000	−	1.67602i	−0.252302	−	0.967649i
$4$	−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
$9$	−2.61806	+	1.46484i	−0.872687	+	0.488279i
$10$		0			0
$11$	−2.42019	+	1.39730i	−0.729714	+	0.421301i	−0.818318	−	0.574766i	$-0.805093\pi$
$11$	−2.42019	+	1.39730i	−0.729714	+	0.421301i	0.0886035	+	0.996067i	$0.471760\pi$
$12$	−4.23270	+	4.17602i	−1.22188	+	1.20551i
$13$	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	$-0.632558\pi$
$17$	0.763780	−	0.440969i	0.185244	−	0.106951i	0.589754	+	0.807583i	$0.299225\pi$
$18$	−0.0942709	+	6.99195i	−0.0222199	+	1.64802i
$19$	−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
$21$	−0.823984	+	4.50789i	−0.179808	+	0.983702i
$22$			6.51381i			1.38875i
$23$	3.77148	−	6.53240i	0.786408	−	1.36210i	−0.141746	−	0.989903i	$-0.545272\pi$
$23$	3.77148	−	6.53240i	0.786408	−	1.36210i	0.928154	−	0.372196i	$-0.121395\pi$
$24$	1.45956	+	5.59780i	0.297930	+	1.14265i
$25$		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	−0.990896	−	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
$33$	3.39951	+	3.44566i	0.591779	+	0.599812i
$34$		−	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
$39$	−1.40052	−	5.37140i	−0.224263	−	0.860113i
$40$		0			0
$41$	8.55098			1.33544			0.667720	−	0.744413i	$-0.267270\pi$
$41$	8.55098			1.33544			0.667720	+	0.744413i	$0.267270\pi$
$42$	8.13927	+	6.91692i	1.25592	+	1.06730i
$43$		−	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	0.324621	−	0.945844i	$-0.394763\pi$
$47$	−2.27740	−	1.31486i	−0.332194	−	0.191792i	−0.656815	+	0.754052i	$0.728097\pi$
$48$	1.53489	+	0.422382i	0.221542	+	0.0609656i
$49$	4.50469	+	5.35796i	0.643527	+	0.765424i
$50$		0			0
$51$	−1.07284	−	1.08741i	−0.150228	−	0.152267i
$52$	−5.50102	−	9.52805i	−0.762854	−	1.32130i
$53$	−3.73427	−	6.46794i	−0.512941	−	0.888440i	−0.999887	−	0.0150081i	$-0.995223\pi$
$53$	−3.73427	−	6.46794i	−0.512941	−	0.888440i	0.486946	−	0.873432i	$-0.338111\pi$
$54$	11.7598	−	2.89748i	1.60031	−	0.394297i
$55$		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	$-0.0806755\pi$
$59$	2.04991	+	3.55054i	0.266875	+	0.462241i	−0.701178	+	0.712986i	$0.747342\pi$
$60$		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
$63$	7.91537	−	0.588936i	0.997243	−	0.0741989i
$64$	−12.4147			−1.55183
$65$		0			0
$66$	10.9173	−	2.84653i	1.34382	−	0.350384i
$67$	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	$-0.878883\pi$
$71$		−	6.25869i		−	0.742770i	0.928479	−	0.371385i	$-0.121117\pi$
$72$	8.74419	−	4.89248i	1.03051	−	0.576584i
$73$	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
$81$	4.70850	−	7.67007i	0.523167	−	0.852230i
$82$	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	$0.988347\pi$
$84$	14.8163	−	5.28791i	1.61659	−	0.576959i
$85$		0			0
$86$	−0.238319	−	0.137594i	−0.0256986	−	0.0148371i
$87$	−13.6641	+	3.56273i	−1.46494	+	0.381965i
$88$	8.08330	−	4.66689i	0.861682	−	0.497492i
$89$	−0.437271	+	0.757376i	−0.0463506	+	0.0802816i	−0.888270	−	0.459322i	$-0.848092\pi$
$89$	−0.437271	+	0.757376i	−0.0463506	+	0.0802816i	0.841919	+	0.539603i	$0.181426\pi$
$90$		0			0
$91$	−7.68656	−	3.57978i	−0.805770	−	0.375263i
$92$	−25.8944			−2.69968
$93$	10.7125	+	10.8579i	1.11083	+	1.12591i
$94$	−5.30832	+	3.06476i	−0.547511	+	0.316106i
$95$		0			0
$96$	−5.59470	+	5.51978i	−0.571007	+	0.563360i
$97$	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	$-0.989373\pi$
$101$	−5.31267	−	9.20181i	−0.528630	−	0.915614i	0.470813	−	0.882233i	$-0.343961\pi$
$102$	−3.44535	+	0.898330i	−0.341140	+	0.0889479i
$103$	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	$-0.621440\pi$
$107$	6.38846	−	11.0651i	0.617596	−	1.06971i	0.989923	−	0.141606i	$-0.0452265\pi$
$108$	4.96429	−	17.1333i	0.477689	−	1.64865i
$109$	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	$-0.389545\pi$
$113$	7.23027			0.680166			0.340083	+	0.940395i	$0.389545\pi$
$114$	6.22592	+	6.31043i	0.583111	+	0.591026i
$115$		0			0
$116$	−24.2380	+	13.9938i	−2.25044	+	1.29929i
$117$	−8.39053	+	4.69460i	−0.775705	+	0.434016i
$118$	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
$123$	−3.73678	−	14.3316i	−0.336934	−	1.29224i
$124$	26.1810	+	15.1156i	2.35112	+	1.35742i
$125$		0			0
$126$	8.03601	−	16.6642i	0.715905	−	1.48457i
$127$		−	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
$129$	−0.197875	+	0.0515933i	−0.0174219	+	0.00454253i
$130$		0			0
$131$	−4.94673	+	8.56799i	−0.432198	+	0.748589i	−0.997062	−	0.0765948i	$-0.975595\pi$
$131$	−4.94673	+	8.56799i	−0.432198	+	0.748589i	0.564864	+	0.825184i	$0.308929\pi$
$132$	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	$-0.985770\pi$
$137$	−6.29951	−	10.9111i	−0.538203	−	0.932195i	0.460798	−	0.887505i	$-0.347563\pi$
$138$	−21.6777	+	21.3874i	−1.84532	+	1.82061i
$139$			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
$144$	0.0371731	−	2.75708i	0.00309776	−	0.229757i
$145$		0			0
$146$	0.516818			0.0427722
$147$	7.01149	−	9.89136i	0.578298	−	0.815826i
$148$		−	1.39876i		−	0.114977i
$149$	15.3604	+	8.86834i	1.25837	+	0.726523i	0.972758	−	0.231821i	$-0.0744684\pi$
$149$	15.3604	+	8.86834i	1.25837	+	0.726523i	0.285616	+	0.958344i	$0.407802\pi$
$150$		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
$156$	−13.5652	+	13.3836i	−1.08609	+	1.07154i
$157$	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
$159$	−9.20850	+	9.08518i	−0.730282	+	0.720502i
$160$		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	$0.0440988\pi$
$167$			3.56923i			0.276195i	−0.990419	+	0.138098i	$0.955901\pi$
$168$	2.75206	−	15.0561i	0.212326	−	1.16160i
$169$	−2.72886			−0.209912
$170$		0			0
$171$	6.58674	+	0.0888076i	0.503701	+	0.00679128i
$172$	−0.350999	+	0.202650i	−0.0267634	+	0.0154519i
$173$	7.39784	+	4.27114i	0.562447	+	0.324729i	0.754127	−	0.656728i	$-0.228060\pi$
$173$	7.39784	+	4.27114i	0.562447	+	0.324729i	−0.191680	+	0.981457i	$0.561394\pi$
$174$	−8.73285	+	31.7342i	−0.662036	+	2.40576i
$175$		0			0
$176$		−	2.56854i		−	0.193611i
$177$	5.05496	−	4.98727i	0.379954	−	0.374866i
$178$	1.01922	+	1.76534i	0.0763937	+	0.132318i
$179$	1.06480	−	0.614760i	0.0795866	−	0.0459493i	−0.459679	−	0.888085i	$-0.652035\pi$
$179$	1.06480	−	0.614760i	0.0795866	−	0.0459493i	0.539265	+	0.842136i	$0.318702\pi$
$180$		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
$186$	34.4022	−	8.96994i	2.52249	−	0.657708i
$187$	−1.23233	+	2.13445i	−0.0901167	+	0.156087i
$188$			9.02762i			0.658407i
$189$	−4.44608	−	13.0089i	−0.323405	−	0.946261i
$190$		0			0
$191$	12.5795	+	7.26275i	0.910218	+	0.525514i	0.880501	−	0.474044i	$-0.157206\pi$
$191$	12.5795	+	7.26275i	0.910218	+	0.525514i	0.0297166	+	0.999558i	$0.490540\pi$
$192$	5.42521	+	20.8072i	0.391531	+	1.50163i
$193$	−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	$-0.363508\pi$
$197$	11.6716			0.831564			0.415782	+	0.909464i	$0.363508\pi$
$198$	−9.54168	−	17.0536i	−0.678097	−	1.21194i
$199$	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
$201$	−1.95151	−	1.97800i	−0.137649	−	0.139517i
$202$	−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
$207$	−0.305073	+	22.6268i	−0.0212040	+	1.57267i
$208$	−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
$213$	−10.4897	+	2.73505i	−0.718741	+	0.187402i
$214$	−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
$219$	0.273385	−	0.269724i	0.0184737	−	0.0182263i
$220$		0			0
$221$	2.44781	−	1.41324i	0.164658	−	0.0950651i
$222$	−1.15530	−	1.17098i	−0.0775383	−	0.0785908i
$223$	−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	$-0.655392\pi$
$227$	0.924157	−	0.533562i	0.0613385	−	0.0354138i	0.530356	+	0.847775i	$0.322058\pi$
$228$	12.6337	−	3.29408i	0.836688	−	0.218156i
$229$	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
$231$	−4.30466	−	12.0613i	−0.283226	−	0.793574i
$232$			27.2296i			1.78771i
$233$	8.99983	−	15.5882i	0.589598	−	1.02121i	−0.404687	−	0.914455i	$-0.632619\pi$
$233$	8.99983	−	15.5882i	0.589598	−	1.02121i	0.994285	−	0.106759i	$-0.0340473\pi$
$234$	−0.302125	+	22.4082i	−0.0197506	+	1.46487i
$235$		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	−0.346683	−	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
$243$	−14.9128	−	4.53971i	−0.956655	−	0.291222i
$244$		−	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
$249$	1.11772	−	0.291432i	0.0708328	−	0.0184688i
$250$		0			0
$251$	15.0765			0.951620			0.475810	−	0.879548i	$-0.342155\pi$
$251$	15.0765			0.951620			0.475810	+	0.879548i	$0.342155\pi$
$252$	−15.3373	−	22.5215i	−0.966161	−	1.41872i
$253$			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	$-0.168060\pi$
$257$	13.7781	+	7.95478i	0.859453	+	0.496206i	−0.00437591	+	0.999990i	$0.501393\pi$
$258$	−0.126464	+	0.459555i	−0.00787329	+	0.0286107i
$259$	−0.618753	−	0.882764i	−0.0384475	−	0.0548523i
$260$		0			0
$261$	11.9424	+	21.3443i	0.739215	+	1.32118i
$262$	11.5302	+	19.9708i	0.712336	+	1.23380i
$263$	−4.15187	−	7.19124i	−0.256015	−	0.443431i	0.709156	−	0.705052i	$-0.249076\pi$
$263$	−4.15187	−	7.19124i	−0.256015	−	0.443431i	−0.965171	+	0.261621i	$0.915743\pi$
$264$	−11.3542	−	11.5083i	−0.698802	−	0.708287i
$265$		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	$0.0111615\pi$
$269$	8.69353	+	15.0576i	0.530054	+	0.918080i	−0.469332	+	0.883022i	$0.655505\pi$
$270$		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
$273$	−2.64075	+	14.4472i	−0.159826	+	0.874382i
$274$	−29.3666			−1.77410
$275$		0			0
$276$	11.3158	+	43.3995i	0.681134	+	2.61234i
$277$	−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	$0.115744\pi$
$281$			11.9239i			0.711320i	−0.934616	+	0.355660i	$0.884256\pi$
$282$	7.45632	+	7.55753i	0.444017	+	0.450044i
$283$	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
$291$	−2.78466	−	10.6799i	−0.163239	−	0.626069i
$292$	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	$-0.0280251\pi$
$294$	−11.7952	−	25.6810i	−0.687907	−	1.49775i
$295$		0			0
$296$	−1.17855	−	0.680436i	−0.0685018	−	0.0395495i
$297$	−13.9475	−	4.04121i	−0.809314	−	0.234495i
$298$	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
$303$	−13.1007	+	12.9253i	−0.752618	+	0.742539i
$304$	1.74778	−	1.00908i	0.100242	−	0.0578748i
$305$		0			0
$306$	3.01123	+	5.38189i	0.172141	+	0.307662i
$307$	−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	$-0.885311\pi$
$311$	−13.6359	−	23.6181i	−0.773222	−	1.33926i	0.162567	−	0.986697i	$-0.448023\pi$
$312$	4.67767	+	17.9402i	0.264821	+	1.01566i
$313$	−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	$0.419855\pi$
$317$	−12.7151	+	22.0233i	−0.714153	+	1.23695i	−0.963285	+	0.268480i	$0.913479\pi$
$318$	7.60735	+	29.1763i	0.426599	+	1.63613i
$319$	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
$324$	−30.8851	−	0.832984i	−1.71584	−	0.0462769i
$325$		0			0
$326$	−17.2048	+	9.93319i	−0.952885	+	0.550149i
$327$	0.0224986	−	0.0221973i	0.00124417	−	0.00122751i
$328$	−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
$333$	−1.22225	−	0.0164793i	−0.0669788	−	0.000903061i
$334$	7.20480	+	4.15970i	0.394229	+	0.227608i
$335$		0			0
$336$	−3.20949	−	2.72749i	−0.175092	−	0.148797i
$337$			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
$339$	−3.15962	−	12.1180i	−0.171607	−	0.658162i
$340$		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	$-0.327001\pi$
$347$	−8.99121	−	15.5732i	−0.482673	−	0.836015i	−0.999802	+	0.0198929i	$0.993667\pi$
$348$	34.0458	+	34.5079i	1.82505	+	1.84982i
$349$			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	−0.989384	−	0.145326i	$-0.953577\pi$
$353$	−25.5186	+	14.7332i	−1.35822	+	0.784169i	−0.368836	+	0.929494i	$0.620244\pi$
$354$	−4.17602	−	16.0162i	−0.221953	−	0.851251i
$355$		0			0
$356$	3.00223			0.159118
$357$	1.35850	+	3.80639i	0.0718992	+	0.201455i
$358$		−	2.86584i		−	0.151465i
$359$	−30.5228	−	17.6224i	−1.61093	−	0.930073i	−0.989154	−	0.146881i	$-0.953077\pi$
$359$	−30.5228	−	17.6224i	−1.61093	−	0.930073i	−0.621779	−	0.783192i	$-0.713590\pi$
$360$		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
$366$	−35.0335	−	35.5090i	−1.83123	−	1.85608i
$367$	−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
$369$	−22.3870	+	12.5258i	−1.16542	+	0.652067i
$370$		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
$378$	−31.4413	−	6.18622i	−1.61716	−	0.318185i
$379$	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
$381$	−11.7248	+	3.05708i	−0.600678	+	0.156619i
$382$	29.3210	−	16.9285i	1.50019	−	0.866137i
$383$	24.0549	+	13.8881i	1.22915	+	0.709648i	0.966851	−	0.255339i	$-0.0821872\pi$
$383$	24.0549	+	13.8881i	1.22915	+	0.709648i	0.262295	+	0.964988i	$0.415521\pi$
$384$	33.1686	+	9.12758i	1.69263	+	0.465790i
$385$		0			0
$386$			0.939675i			0.0478282i
$387$	0.172942	+	0.309095i	0.00879115	+	0.0157122i
$388$	−10.9377	−	18.9446i	−0.555275	−	0.961765i
$389$	−13.4945	+	7.79107i	−0.684200	+	0.395023i	−0.801436	−	0.598081i	$-0.795930\pi$
$389$	−13.4945	+	7.79107i	−0.684200	+	0.395023i	0.117236	+	0.993104i	$0.462597\pi$
$390$		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
$396$	−28.7782	−	0.388011i	−1.44616	−	0.0194983i
$397$	−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
$399$	6.51605	−	7.66756i	0.326211	−	0.383858i
$400$		0			0
$401$	−18.0127	−	10.3996i	−0.899511	−	0.519333i	−0.0224695	−	0.999748i	$-0.507153\pi$
$401$	−18.0127	−	10.3996i	−0.899511	−	0.519333i	−0.877042	+	0.480415i	$0.840486\pi$
$402$	−6.26711	+	1.63407i	−0.312575	+	0.0814999i
$403$	−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
$408$	3.58324	+	3.63187i	0.177397	+	0.179805i
$409$	−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
$411$	−15.5342	+	15.3262i	−0.766248	+	0.755986i
$412$	−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
$417$	1.65609	−	0.431805i	0.0810992	−	0.0211456i
$418$	7.15145	−	12.3867i	0.349789	−	0.605852i
$419$	−3.24500			−0.158528			−0.0792642	−	0.996854i	$-0.525257\pi$
$419$	−3.24500			−0.158528			−0.0792642	+	0.996854i	$0.525257\pi$
$420$		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
$423$	7.88844	+	0.106358i	0.383549	+	0.00517131i
$424$	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
$429$	10.8950	+	11.0429i	0.526014	+	0.533154i
$430$		0			0
$431$	33.1792	−	19.1560i	1.59819	−	0.922714i	0.606351	−	0.795197i	$-0.292633\pi$
$431$	33.1792	−	19.1560i	1.59819	−	0.922714i	0.991836	−	0.127516i	$-0.0407006\pi$
$432$	−4.63716	+	1.14254i	−0.223105	+	0.0549705i
$433$	−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
$438$	−0.225850	−	0.866196i	−0.0107915	−	0.0413885i
$439$	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
$441$	−19.6421	−	7.42885i	−0.935338	−	0.353755i
$442$		−	6.58816i		−	0.313367i
$443$	−1.14186	+	1.97776i	−0.0542513	+	0.0939660i	−0.891876	−	0.452281i	$-0.850611\pi$
$443$	−1.14186	+	1.97776i	−0.0542513	+	0.0939660i	0.837624	+	0.546247i	$0.183944\pi$
$444$	−2.34434	+	0.611256i	−0.111257	+	0.0290089i
$445$		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
$453$	27.7428	−	27.3713i	1.30347	−	1.28601i
$454$		−	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
$459$	4.40164	+	1.27535i	0.205451	+	0.0595284i
$460$		0			0
$461$	−16.5678			−0.771637			−0.385819	−	0.922575i	$-0.626081\pi$
$461$	−16.5678			−0.771637			−0.385819	+	0.922575i	$0.626081\pi$
$462$	−29.3635	−	5.36727i	−1.36612	−	0.249708i
$463$		−	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	$0.0667848\pi$
$467$	35.6023	+	20.5550i	1.64748	+	0.951171i	0.669406	+	0.742896i	$0.266549\pi$
$468$	28.3591	+	16.8869i	1.31090	+	0.780598i
$469$	−4.22812	+	0.371969i	−0.195236	+	0.0171759i
$470$		0			0
$471$	14.6625	−	14.4661i	0.675613	−	0.666565i
$472$	−6.84658	−	11.8586i	−0.315139	−	0.545837i
$473$	0.164968	+	0.285733i	0.00758524	+	0.0131380i
$474$	9.01536	−	8.89463i	0.414089	−	0.408544i
$475$		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	$-0.289843\pi$
$479$	−8.25944	−	14.3058i	−0.377383	−	0.653647i	−0.990681	+	0.136205i	$0.956509\pi$
$480$		0			0
$481$	1.13088	+	0.652916i	0.0515639	+	0.0297704i
$482$		−	12.2127i		−	0.556274i
$483$	26.3397	+	22.3840i	1.19850	+	1.01851i
$484$	10.9519			0.497813
$485$		0			0
$486$	−26.5436	+	24.8120i	−1.20404	+	1.12550i
$487$	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	$0.0430751\pi$
$491$			5.97889i			0.269824i	−0.990858	+	0.134912i	$0.956925\pi$
$492$	−36.1938	+	35.7091i	−1.63174	+	1.60989i
$493$	−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
$501$	5.98209	−	1.55975i	0.267260	−	0.0696846i
$502$	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	$-0.123958\pi$
$504$	−26.4369	+	1.96701i	−1.17759	+	0.0876177i
$505$		0			0
$506$	42.5508	+	24.5667i	1.89161	+	1.09212i
$507$	1.19251	+	4.57361i	0.0529612	+	0.203121i
$508$	−20.7979	+	12.0077i	−0.922759	+	0.532755i
$509$	6.43409	−	11.1442i	0.285186	−	0.493956i	−0.687468	−	0.726214i	$-0.741278\pi$
$509$	6.43409	−	11.1442i	0.285186	−	0.493956i	0.972654	+	0.232258i	$0.0746113\pi$
$510$		0			0
$511$	−0.0514110	−	0.584381i	−0.00227429	−	0.0258515i
$512$	10.3101			0.455646
$513$	−2.72956	−	11.0783i	−0.120513	−	0.489119i
$514$	32.1148	−	18.5415i	1.41652	−	0.817831i
$515$		0			0
$516$	0.493031	+	0.499723i	0.0217045	+	0.0219991i
$517$	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	$-0.0477961\pi$
$521$	8.32724	+	14.4232i	0.364823	+	0.631892i	−0.623925	+	0.781485i	$0.714463\pi$
$522$	57.0033	+	0.768563i	2.49497	+	0.0336391i
$523$	−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
$528$	−4.30491	+	1.12245i	−0.187347	+	0.0488484i
$529$	−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
$534$	2.51334	−	2.47968i	0.108763	−	0.107306i
$535$		0			0
$536$	−4.64026	+	2.67906i	−0.200429	+	0.115718i
$537$	−1.49566	−	1.51597i	−0.0645427	−	0.0654188i
$538$	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
$543$	−25.8098	+	6.72958i	−1.10761	+	0.288794i
$544$	−3.46571	−	2.00093i	−0.148591	−	0.0857890i
$545$		0			0
$546$	26.0852	+	22.1678i	1.11634	+	0.948693i
$547$			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
$549$	−37.0638	−	0.499723i	−1.58184	−	0.0213277i
$550$		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	$-0.100561\pi$
$557$	4.86622	+	8.42853i	0.206188	+	0.357128i	−0.744322	+	0.667820i	$0.767227\pi$
$558$	−30.0675	−	53.7389i	−1.27286	−	2.27495i
$559$		−	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	$-0.663512\pi$
$563$	0.407265	−	0.235135i	0.0171642	−	0.00990975i	0.508558	+	0.861028i	$0.330179\pi$
$564$	15.1304	−	3.94507i	0.637107	−	0.166117i
$565$		0			0
$566$	46.5459			1.95647
$567$	−19.8602	+	13.1366i	−0.834052	+	0.551686i
$568$			20.9037i			0.877100i
$569$	−5.38387	−	3.10838i	−0.225703	−	0.130310i	0.382885	−	0.923796i	$-0.374931\pi$
$569$	−5.38387	−	3.10838i	−0.225703	−	0.130310i	−0.608588	+	0.793486i	$0.708264\pi$
$570$		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
$576$	32.5024	−	18.1855i	1.35427	−	0.757728i
$577$	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
$579$	0.490410	+	0.497067i	0.0203807	+	0.0206574i
$580$		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	$0.872589\pi$
$588$	−41.4419	−	3.86701i	−1.70904	−	0.159473i
$589$	19.3366			0.796751
$590$		0			0
$591$	−5.10047	−	19.5617i	−0.209805	−	0.804661i
$592$	−0.324322	+	0.187247i	−0.0133296	+	0.00769582i
$593$	−26.2357	−	15.1472i	−1.07737	−	0.622020i	−0.147185	−	0.989109i	$-0.547021\pi$
$593$	−26.2357	−	15.1472i	−1.07737	−	0.622020i	−0.930186	+	0.367088i	$0.880355\pi$
$594$	−24.4123	+	23.4444i	−1.00165	+	0.961936i
$595$		0			0
$596$		−	60.8887i		−	2.49410i
$597$	−22.5988	−	22.9056i	−0.924907	−	0.937462i
$598$	−28.1733	−	48.7976i	−1.15209	−	1.99548i
$599$	6.29024	−	3.63167i	0.257012	−	0.148386i	−0.365959	−	0.930631i	$-0.619259\pi$
$599$	6.29024	−	3.63167i	0.257012	−	0.148386i	0.622971	+	0.782245i	$0.285925\pi$
$600$		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
$606$	10.8228	+	41.5085i	0.439647	+	1.68617i
$607$	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
$609$	36.7515	+	6.71769i	1.48924	+	0.272215i
$610$		0			0
$611$	−7.29877	−	4.21394i	−0.295276	−	0.170478i
$612$	9.08204	+	0.122451i	0.367120	+	0.00494980i
$613$	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	$-0.442779\pi$
$617$	8.88258			0.357599			0.178800	+	0.983886i	$0.442779\pi$
$618$	−2.88302	+	2.84441i	−0.115972	+	0.114419i
$619$	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
$621$	38.0563	−	9.37661i	1.52715	−	0.376271i
$622$	−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
$627$	−2.68157	−	10.2846i	−0.107091	−	0.410726i
$628$	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
$633$	−3.05102	−	11.7015i	−0.121267	−	0.465094i
$634$	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
$639$	9.16797	+	16.3857i	0.362679	+	0.648206i
$640$		0			0
$641$	−6.03197	+	3.48256i	−0.238249	+	0.137553i	−0.614371	−	0.789017i	$-0.710590\pi$
$641$	−6.03197	+	3.48256i	−0.238249	+	0.137553i	0.376123	+	0.926570i	$0.377257\pi$
$642$	−36.7195	+	36.2277i	−1.44920	+	1.42979i
$643$	−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	$-0.729884\pi$
$647$	−8.69245	+	5.01859i	−0.341735	+	0.197301i	0.319304	+	0.947652i	$0.396551\pi$
$648$	−15.7261	+	25.6176i	−0.617781	+	1.00636i
$649$	−9.92232	−	5.72866i	−0.389485	−	0.224869i
$650$		0			0
$651$	−13.5648	−	38.0073i	−0.531645	−	1.48962i
$652$			29.2594i			1.14589i
$653$	19.8000	−	34.2946i	0.774833	−	1.34205i	−0.160055	−	0.987108i	$-0.551167\pi$
$653$	19.8000	−	34.2946i	0.774833	−	1.34205i	0.934888	−	0.354942i	$-0.115500\pi$
$654$	−0.0185866	−	0.0712847i	−0.000726792	−	0.00278745i
$655$		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	−0.562991	−	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
$663$	−3.43831	−	3.48498i	−0.133533	−	0.135346i
$664$		−	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
$669$	0.631874	+	2.42341i	0.0244297	+	0.0936946i
$670$		0			0
$671$	−34.5292			−1.33299
$672$	19.5839	−	6.98946i	0.755464	−	0.269624i
$673$			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	−0.114370	−	0.993438i	$-0.536485\pi$
$677$	−26.8492	−	15.5014i	−1.03190	−	0.595766i	−0.917528	+	0.397672i	$0.869818\pi$
$678$	−28.1436	−	7.74478i	−1.08085	−	0.297436i
$679$	−15.2831	−	7.11767i	−0.586513	−	0.273151i
$680$		0			0
$681$	−1.29812	−	1.31574i	−0.0497439	−	0.0504191i
$682$	−28.6812	−	49.6772i	−1.09826	−	1.90224i
$683$	9.55050	+	16.5419i	0.365440	+	0.632960i	0.988847	−	0.148937i	$-0.0475853\pi$
$683$	9.55050	+	16.5419i	0.365440	+	0.632960i	−0.623407	+	0.781898i	$0.714252\pi$
$684$	−11.0419	−	19.7348i	−0.422196	−	0.754579i
$685$		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
$693$	−18.3338	+	12.4855i	−0.696443	+	0.474283i
$694$	−41.9145			−1.59105
$695$		0			0
$696$	45.6372	−	11.8993i	1.72987	−	0.451043i
$697$	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	$0.864360\pi$
$702$	37.6886	−	9.28603i	1.42247	−	0.350479i
$703$	−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
$711$	0.126874	−	9.41011i	0.00475816	−	0.352907i
$712$	1.46046	−	2.52959i	0.0547331	−	0.0948005i
$713$			66.4253i			2.48765i
$714$	9.26675	+	1.69384i	0.346800	+	0.0633905i
$715$		0			0
$716$	−3.65536	−	2.11042i	−0.136607	−	0.0788703i
$717$	50.0821	−	13.0583i	1.87035	−	0.487669i
$718$	−71.1445	+	41.0753i	−2.65509	+	1.53292i
$719$	11.1296	−	19.2770i	0.415064	−	0.718912i	−0.580371	−	0.814352i	$-0.697093\pi$
$719$	11.1296	−	19.2770i	0.415064	−	0.718912i	0.995435	+	0.0954404i	$0.0304259\pi$
$720$		0			0
$721$	−2.17342	+	1.52341i	−0.0809425	+	0.0567348i
$722$	−33.0483			−1.22993
$723$	−6.37373	−	6.46025i	−0.237042	−	0.240259i
$724$	−45.7827	+	26.4327i	−1.70150	+	0.982362i
$725$		0			0
$726$	9.16844	−	9.04566i	0.340273	−	0.335716i
$727$	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
$732$	−71.0903	+	18.5359i	−2.62757	+	0.685106i
$733$	−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
$738$	−0.806109	+	59.7881i	−0.0296733	+	2.20083i
$739$	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	$-0.551759\pi$
$743$	−8.82565			−0.323782			−0.161891	+	0.986809i	$0.551759\pi$
$744$	−35.7791	−	36.2647i	−1.31173	−	1.32953i
$745$		0			0
$746$	−40.9251	+	23.6281i	−1.49838	+	0.865087i
$747$	−0.976890	−	1.74597i	−0.0357425	−	0.0638816i
$748$	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
$753$	−6.58843	−	25.2685i	−0.240096	−	0.920834i
$754$	−52.7422	−	30.4507i	−1.92076	−	1.10895i
$755$		0			0
$756$	−31.0440	+	35.5475i	−1.12906	+	1.29285i
$757$			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
$759$	35.3296	−	9.21174i	1.28238	−	0.334365i
$760$		0			0
$761$	0.915074	−	1.58495i	0.0331714	−	0.0574545i	−0.848963	−	0.528452i	$-0.822773\pi$
$761$	0.915074	−	1.58495i	0.0331714	−	0.0574545i	0.882135	+	0.470998i	$0.156106\pi$
$762$	−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
$768$	26.4666	−	26.1122i	0.955032	−	0.942243i
$769$		−	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	−0.999997	−	0.00246461i	$-0.999215\pi$
$773$	−41.6448	+	24.0437i	−1.49786	+	0.864790i	−0.497864	+	0.867255i	$0.665882\pi$
$774$	0.825487	+	0.0111299i	0.0296715	+	0.000400054i
$775$		0			0
$776$	−21.2828			−0.764010
$777$	−1.20913	+	1.42281i	−0.0433774	+	0.0510430i
$778$			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
$786$	28.4327	−	28.0520i	1.01416	−	1.00058i
$787$	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
$789$	−10.2383	+	10.1012i	−0.364492	+	0.359611i
$790$		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	$0.979664\pi$
$798$	−7.88362	−	22.0892i	−0.279077	−	0.781950i
$799$	−2.31925			−0.0820491
$800$		0			0
$801$	0.0353705	−	2.62339i	0.00124976	−	0.0926928i
$802$	−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
$807$	21.4378	−	21.1507i	0.754645	−	0.744539i
$808$	17.7440	+	30.7335i	0.624232	+	1.08120i
$809$	−18.7612	+	10.8318i	−0.659607	+	0.380824i	−0.792127	−	0.610356i	$-0.791026\pi$
$809$	−18.7612	+	10.8318i	−0.659607	+	0.380824i	0.132520	+	0.991180i	$0.457693\pi$
$810$		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
$816$	1.35858	−	0.354231i	0.0475597	−	0.0124006i
$817$	−0.129620	+	0.224508i	−0.00453481	+	0.00785453i
$818$			67.1957i			2.34944i
$819$	25.3677	−	1.88746i	0.886419	−	0.0659531i
$820$		0			0
$821$	−12.2722	−	7.08534i	−0.428302	−	0.247280i	0.270321	−	0.962770i	$-0.412870\pi$
$821$	−12.2722	−	7.08534i	−0.428302	−	0.247280i	−0.698623	+	0.715490i	$0.746203\pi$
$822$	12.8332	+	49.2189i	0.447609	+	1.71670i
$823$	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	$-0.688393\pi$
$827$	−32.0877			−1.11580			−0.557900	+	0.829908i	$0.688393\pi$
$828$	67.7932	−	37.9311i	2.35598	−	1.31820i
$829$	−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
$831$	11.6298	+	11.7877i	0.403434	+	0.408910i
$832$	−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
$837$	−43.9510	−	12.7346i	−1.51917	−	0.440172i
$838$	−3.78182	+	6.55031i	−0.130641	+	0.226277i
$839$	28.6277			0.988337			0.494168	−	0.869366i	$-0.335473\pi$
$839$	28.6277			0.988337			0.494168	+	0.869366i	$0.335473\pi$
$840$		0			0
$841$	−37.4666			−1.29195
$842$	32.5530	−	56.3835i	1.12185	−	1.94310i
$843$	19.9846	−	5.21074i	0.688307	−	0.179467i
$844$	−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
$849$	24.6217	−	24.2920i	0.845015	−	0.833698i
$850$		0			0
$851$	2.66165	−	1.53670i	0.0912401	−	0.0526775i
$852$	26.1364	+	26.4912i	0.895419	+	0.907573i
$853$	−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	$-0.373942\pi$
$857$	40.3294	−	23.2842i	1.37763	−	0.795372i	0.991873	+	0.127230i	$0.0406087\pi$
$858$	34.9883	−	9.12275i	1.19448	−	0.311446i
$859$	−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
$861$	−7.04587	+	38.5469i	−0.240123	+	1.31367i
$862$		−	89.3002i		−	3.04158i
$863$	−1.18901	+	2.05942i	−0.0404742	+	0.0701034i	−0.885553	−	0.464539i	$-0.846220\pi$
$863$	−1.18901	+	2.05942i	−0.0404742	+	0.0701034i	0.845079	+	0.534642i	$0.179554\pi$
$864$	6.56170	−	22.6464i	0.223234	−	0.770448i
$865$		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
$873$	−16.6829	+	9.33426i	−0.564629	+	0.315917i
$874$			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
$879$	−5.04519	+	1.31547i	−0.170170	+	0.0443697i
$880$		0			0
$881$	33.5633			1.13078			0.565388	−	0.824825i	$-0.308727\pi$
$881$	33.5633			1.13078			0.565388	+	0.824825i	$0.308727\pi$
$882$	−37.8873	+	30.9915i	−1.27573	+	1.04354i
$883$		−	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	0.0429963	−	0.999075i	$-0.486310\pi$
$887$	−23.8478	−	13.7685i	−0.800730	−	0.462302i	−0.843726	+	0.536773i	$0.819643\pi$
$888$	−0.625396	+	2.27262i	−0.0209869	+	0.0762641i
$889$	−7.81399	+	16.7783i	−0.262073	+	0.562726i
$890$		0			0
$891$	−0.678096	+	25.1422i	−0.0227171	+	0.842295i
$892$	2.48189	+	4.29877i	0.0831000	+	0.143933i
$893$	2.88714	+	5.00068i	0.0966146	+	0.167341i
$894$	−50.2907	−	50.9733i	−1.68197	−	1.70480i
$895$		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
$903$	0.532212	+	0.0972815i	0.0177109	+	0.00323733i
$904$	−24.1487			−0.803174
$905$		0			0
$906$	−22.9189	−	87.9005i	−0.761431	−	2.92030i
$907$	−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	$-0.873310\pi$
$911$		−	23.3967i		−	0.775167i	0.921835	−	0.387583i	$-0.126690\pi$
$912$	−2.45502	−	2.48834i	−0.0812938	−	0.0823973i
$913$	−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
$921$	8.90578	+	34.1561i	0.293455	+	1.12548i
$922$	−19.3086	+	33.4434i	−0.635894	+	1.10140i
$923$		−	20.0583i		−	0.660225i
$924$	−28.4694	+	33.5005i	−0.936574	+	1.10208i
$925$		0			0
$926$	−73.8532	−	42.6392i	−2.42697	−	1.40121i
$927$	−0.0405732	+	3.00926i	−0.00133260	+	0.0988370i
$928$	−32.0373	+	18.4967i	−1.05168	+	0.607185i
$929$	6.27980	−	10.8769i	0.206034	−	0.356861i	−0.744428	−	0.667703i	$-0.767278\pi$
$929$	6.27980	−	10.8769i	0.206034	−	0.356861i	0.950462	+	0.310842i	$0.100611\pi$
$930$		0			0
$931$	−2.68366	−	15.1344i	−0.0879535	−	0.496009i
$932$	−61.7914			−2.02405
$933$	−33.6254	+	33.1751i	−1.10085	+	1.08610i
$934$	82.9840	−	47.9108i	2.71532	−	1.56769i
$935$		0			0
$936$	28.0239	−	15.6797i	0.915990	−	0.512508i
$937$	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	$0.0739658\pi$
$941$	21.0434	+	36.4482i	0.685994	+	1.18818i	−0.287129	+	0.957892i	$0.592701\pi$
$942$	−12.1130	−	46.4568i	−0.394664	−	1.51365i
$943$	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	$-0.909608\pi$
$947$	−7.30370	+	12.6504i	−0.237338	+	0.411082i	0.722611	+	0.691255i	$0.242942\pi$
$948$	−4.70607	−	18.0491i	−0.152846	−	0.586207i
$949$	0.355304	+	0.615405i	0.0115337	+	0.0199769i
$950$		0			0
$951$	42.4679	+	11.6866i	1.37711	+	0.378965i
$952$	7.76340	−	0.682986i	0.251613	−	0.0221357i
$953$	−28.8817			−0.935570			−0.467785	−	0.883842i	$-0.654948\pi$
$953$	−28.8817			−0.935570			−0.467785	+	0.883842i	$0.654948\pi$
$954$	45.5756	−	25.5001i	1.47556	−	0.825596i
$955$		0			0
$956$	88.8379	−	51.2906i	2.87322	−	1.65886i
$957$	28.0914	−	27.7152i	0.908066	−	0.895906i
$958$	−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
$963$	−0.516758	+	38.3273i	−0.0166523	+	1.23508i
$964$	−15.5772	−	8.99352i	−0.501709	−	0.289662i
$965$		0			0
$966$	75.8811	−	27.0819i	2.44144	−	0.871346i
$967$		−	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
$969$	0.846268	+	3.24567i	0.0271860	+	0.104266i
$970$		0			0
$971$	2.64865	−	4.58759i	0.0849991	−	0.147223i	−0.820392	−	0.571802i	$-0.806245\pi$
$971$	2.64865	−	4.58759i	0.0849991	−	0.147223i	0.905391	+	0.424579i	$0.139578\pi$
$972$	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	$-0.0196536\pi$
$977$	13.9284	+	24.1247i	0.445610	+	0.771818i	−0.552485	+	0.833523i	$0.686320\pi$
$978$	24.1667	+	24.4947i	0.772765	+	0.783255i
$979$		−	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	$-0.670023\pi$
$983$	−0.572640	+	0.330614i	−0.0182644	+	0.0105449i	0.490840	+	0.871250i	$0.336690\pi$
$984$	12.4806	+	47.8667i	0.397868	+	1.52594i
$985$		0			0
$986$	−16.7593			−0.533725
$987$	7.80378	−	9.18286i	0.248397	−	0.292294i
$988$			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
$996$	−2.78496	−	2.82276i	−0.0882447	−	0.0894425i
$997$	−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
$999$	0.506503	+	2.05571i	0.0160250	+	0.0650398i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.16543 - 2.01859i) q^{2} +(-0.437000 - 1.67602i) q^{3} +(-1.71646 - 2.97300i) q^{4} +(-3.89248 - 1.07116i) q^{6} +(-2.39840 - 1.11699i) q^{7} -3.33995 q^{8} +(-2.61806 + 1.46484i) q^{9} +O(q^{10})\)	\(q+(1.16543 - 2.01859i) q^{2} +(-0.437000 - 1.67602i) q^{3} +(-1.71646 - 2.97300i) q^{4} +(-3.89248 - 1.07116i) q^{6} +(-2.39840 - 1.11699i) q^{7} -3.33995 q^{8} +(-2.61806 + 1.46484i) q^{9} +(-2.42019 + 1.39730i) q^{11} +(-4.23270 + 4.17602i) q^{12} +3.20486 q^{13} +(-5.04991 + 3.53962i) q^{14} +(-0.459555 + 0.795973i) q^{16} +(0.763780 - 0.440969i) q^{17} +(-0.0942709 + 6.99195i) q^{18} +(-1.90160 - 1.09789i) q^{19} +(-0.823984 + 4.50789i) q^{21} +6.51381i q^{22} +(3.77148 - 6.53240i) q^{23} +(1.45956 + 5.59780i) 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} +(3.39951 + 3.44566i) q^{33} -2.05568i q^{34} +(8.84876 + 5.26916i) q^{36} +(0.352865 + 0.203727i) q^{37} +(-4.43237 + 2.55903i) q^{38} +(-1.40052 - 5.37140i) q^{39} +8.55098 q^{41} +(8.13927 + 6.91692i) 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} +(-1.07284 - 1.08741i) q^{51} +(-5.50102 - 9.52805i) q^{52} +(-3.73427 - 6.46794i) q^{53} +(11.7598 - 2.89748i) 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} +(7.91537 - 0.588936i) q^{63} -12.4147 q^{64} +(10.9173 - 2.84653i) q^{66} +(1.38932 - 0.802125i) q^{67} +(-2.62200 - 1.51381i) q^{68} +(-12.5965 - 3.46641i) q^{69} -6.25869i q^{71} +(8.74419 - 4.89248i) 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} +(4.70850 - 7.67007i) q^{81} +(9.96559 - 17.2609i) q^{82} +0.666893i q^{83} +(14.8163 - 5.28791i) q^{84} +(-0.238319 - 0.137594i) q^{86} +(-13.6641 + 3.56273i) q^{87} +(8.08330 - 4.66689i) q^{88} +(-0.437271 + 0.757376i) q^{89} +(-7.68656 - 3.57978i) q^{91} -25.8944 q^{92} +(10.7125 + 10.8579i) q^{93} +(-5.30832 + 3.06476i) q^{94} +(-5.59470 + 5.51978i) q^{96} +6.37221 q^{97} +(16.0654 - 2.84876i) q^{98} +(4.28939 - 7.20339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} - 10 q^{6} - 8 q^{9}+O(q^{10}) \) 16 * q - 6 * q^4 - 10 * q^6 - 8 * q^9	\( 16 q - 6 q^{4} - 10 q^{6} - 8 q^{9} - 24 q^{14} + 2 q^{16} - 18 q^{19} - 44 q^{21} + 14 q^{24} + 12 q^{26} - 42 q^{31} + 18 q^{36} - 30 q^{39} + 60 q^{41} - 14 q^{46} + 8 q^{49} + 24 q^{51} - 14 q^{54} + 42 q^{56} - 24 q^{59} + 30 q^{61} - 76 q^{64} - 32 q^{66} - 26 q^{69} + 108 q^{74} + 58 q^{79} + 56 q^{81} + 102 q^{84} - 18 q^{86} - 6 q^{89} - 6 q^{91} + 48 q^{94} - 84 q^{96} + 68 q^{99}+O(q^{100}) \) 16 * q - 6 * q^4 - 10 * q^6 - 8 * q^9 - 24 * q^14 + 2 * q^16 - 18 * q^19 - 44 * q^21 + 14 * q^24 + 12 * q^26 - 42 * q^31 + 18 * q^36 - 30 * q^39 + 60 * q^41 - 14 * q^46 + 8 * q^49 + 24 * q^51 - 14 * q^54 + 42 * q^56 - 24 * q^59 + 30 * q^61 - 76 * q^64 - 32 * q^66 - 26 * q^69 + 108 * q^74 + 58 * q^79 + 56 * q^81 + 102 * q^84 - 18 * q^86 - 6 * q^89 - 6 * q^91 + 48 * q^94 - 84 * q^96 + 68 * q^99

Introduction

L-functions

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