LMFDB - Embedded newform 425.2.m.a.376.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			376.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	425.376
Dual form			425.2.m.a.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.292893 + 0.292893i) q^{2} +(2.41421 - 1.00000i) q^{3} -1.82843i q^{4} +(1.00000 + 0.414214i) q^{6} +(-0.414214 + 1.00000i) q^{7} +(1.12132 - 1.12132i) q^{8} +(2.70711 - 2.70711i) q^{9} +O(q^{10})$	\(q+(0.292893 + 0.292893i) q^{2} +(2.41421 - 1.00000i) q^{3} -1.82843i q^{4} +(1.00000 + 0.414214i) q^{6} +(-0.414214 + 1.00000i) q^{7} +(1.12132 - 1.12132i) q^{8} +(2.70711 - 2.70711i) q^{9} +(-1.00000 - 0.414214i) q^{11} +(-1.82843 - 4.41421i) q^{12} -1.41421i q^{13} +(-0.414214 + 0.171573i) q^{14} -3.00000 q^{16} +(2.82843 + 3.00000i) q^{17} +1.58579 q^{18} +(3.41421 + 3.41421i) q^{19} +2.82843i q^{21} +(-0.171573 - 0.414214i) q^{22} +(-3.82843 - 1.58579i) q^{23} +(1.58579 - 3.82843i) q^{24} +(0.414214 - 0.414214i) q^{26} +(0.828427 - 2.00000i) q^{27} +(1.82843 + 0.757359i) q^{28} +(-1.70711 - 4.12132i) q^{29} +(-3.00000 + 1.24264i) q^{31} +(-3.12132 - 3.12132i) q^{32} -2.82843 q^{33} +(-0.0502525 + 1.70711i) q^{34} +(-4.94975 - 4.94975i) q^{36} +(3.53553 - 1.46447i) q^{37} +2.00000i q^{38} +(-1.41421 - 3.41421i) q^{39} +(-3.12132 + 7.53553i) q^{41} +(-0.828427 + 0.828427i) q^{42} +(3.41421 - 3.41421i) q^{43} +(-0.757359 + 1.82843i) q^{44} +(-0.656854 - 1.58579i) q^{46} +10.8284i q^{47} +(-7.24264 + 3.00000i) q^{48} +(4.12132 + 4.12132i) q^{49} +(9.82843 + 4.41421i) q^{51} -2.58579 q^{52} +(1.00000 + 1.00000i) q^{53} +(0.828427 - 0.343146i) q^{54} +(0.656854 + 1.58579i) q^{56} +(11.6569 + 4.82843i) q^{57} +(0.707107 - 1.70711i) q^{58} +(-4.24264 + 4.24264i) q^{59} +(3.53553 - 8.53553i) q^{61} +(-1.24264 - 0.514719i) q^{62} +(1.58579 + 3.82843i) q^{63} +4.17157i q^{64} +(-0.828427 - 0.828427i) q^{66} -6.82843 q^{67} +(5.48528 - 5.17157i) q^{68} -10.8284 q^{69} +(12.0711 - 5.00000i) q^{71} -6.07107i q^{72} +(2.05025 + 4.94975i) q^{73} +(1.46447 + 0.606602i) q^{74} +(6.24264 - 6.24264i) q^{76} +(0.828427 - 0.828427i) q^{77} +(0.585786 - 1.41421i) q^{78} +(-3.82843 - 1.58579i) q^{79} +5.82843i q^{81} +(-3.12132 + 1.29289i) q^{82} +(0.242641 + 0.242641i) q^{83} +5.17157 q^{84} +2.00000 q^{86} +(-8.24264 - 8.24264i) q^{87} +(-1.58579 + 0.656854i) q^{88} +9.41421i q^{89} +(1.41421 + 0.585786i) q^{91} +(-2.89949 + 7.00000i) q^{92} +(-6.00000 + 6.00000i) q^{93} +(-3.17157 + 3.17157i) q^{94} +(-10.6569 - 4.41421i) q^{96} +(-2.46447 - 5.94975i) q^{97} +2.41421i q^{98} +(-3.82843 + 1.58579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 4 q^{11} + 4 q^{12} + 4 q^{14} - 12 q^{16} + 12 q^{18} + 8 q^{19} - 12 q^{22} - 4 q^{23} + 12 q^{24} - 4 q^{26} - 8 q^{27} - 4 q^{28} - 4 q^{29} - 12 q^{31} - 4 q^{32} - 20 q^{34} - 4 q^{41} + 8 q^{42} + 8 q^{43} - 20 q^{44} + 20 q^{46} - 12 q^{48} + 8 q^{49} + 28 q^{51} - 16 q^{52} + 4 q^{53} - 8 q^{54} - 20 q^{56} + 24 q^{57} + 12 q^{62} + 12 q^{63} + 8 q^{66} - 16 q^{67} - 12 q^{68} - 32 q^{69} + 20 q^{71} + 28 q^{73} + 20 q^{74} + 8 q^{76} - 8 q^{77} + 8 q^{78} - 4 q^{79} - 4 q^{82} - 16 q^{83} + 32 q^{84} + 8 q^{86} - 16 q^{87} - 12 q^{88} + 28 q^{92} - 24 q^{93} - 24 q^{94} - 20 q^{96} - 24 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 4 * q^11 + 4 * q^12 + 4 * q^14 - 12 * q^16 + 12 * q^18 + 8 * q^19 - 12 * q^22 - 4 * q^23 + 12 * q^24 - 4 * q^26 - 8 * q^27 - 4 * q^28 - 4 * q^29 - 12 * q^31 - 4 * q^32 - 20 * q^34 - 4 * q^41 + 8 * q^42 + 8 * q^43 - 20 * q^44 + 20 * q^46 - 12 * q^48 + 8 * q^49 + 28 * q^51 - 16 * q^52 + 4 * q^53 - 8 * q^54 - 20 * q^56 + 24 * q^57 + 12 * q^62 + 12 * q^63 + 8 * q^66 - 16 * q^67 - 12 * q^68 - 32 * q^69 + 20 * q^71 + 28 * q^73 + 20 * q^74 + 8 * q^76 - 8 * q^77 + 8 * q^78 - 4 * q^79 - 4 * q^82 - 16 * q^83 + 32 * q^84 + 8 * q^86 - 16 * q^87 - 12 * q^88 + 28 * q^92 - 24 * q^93 - 24 * q^94 - 20 * q^96 - 24 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.292893	+	0.292893i	0.207107	+	0.207107i	0.803037	−	0.595930i	$-0.203216\pi$
$2$	0.292893	+	0.292893i	0.207107	+	0.207107i	−0.595930	+	0.803037i	$0.703216\pi$
$3$	2.41421	−	1.00000i	1.39385	−	0.577350i	0.445700	−	0.895182i	$-0.352955\pi$
$3$	2.41421	−	1.00000i	1.39385	−	0.577350i	0.948147	+	0.317832i	$0.102955\pi$
$4$		−	1.82843i		−	0.914214i
$5$		0			0
$5$		0			0
$6$	1.00000	+	0.414214i	0.408248	+	0.169102i
$7$	−0.414214	+	1.00000i	−0.156558	+	0.377964i	−0.982624	−	0.185610i	$-0.940574\pi$
$7$	−0.414214	+	1.00000i	−0.156558	+	0.377964i	0.826066	+	0.563574i	$0.190574\pi$
$8$	1.12132	−	1.12132i	0.396447	−	0.396447i
$9$	2.70711	−	2.70711i	0.902369	−	0.902369i
$10$		0			0
$11$	−1.00000	−	0.414214i	−0.301511	−	0.124890i	0.226799	−	0.973942i	$-0.427174\pi$
$11$	−1.00000	−	0.414214i	−0.301511	−	0.124890i	−0.528310	+	0.849052i	$0.677174\pi$
$12$	−1.82843	−	4.41421i	−0.527821	−	1.27427i
$13$		−	1.41421i		−	0.392232i	−0.980581	−	0.196116i	$-0.937167\pi$
$13$		−	1.41421i		−	0.392232i	0.980581	−	0.196116i	$-0.0628330\pi$
$14$	−0.414214	+	0.171573i	−0.110703	+	0.0458548i
$15$		0			0
$16$	−3.00000			−0.750000
$17$	2.82843	+	3.00000i	0.685994	+	0.727607i
$17$	2.82843	+	3.00000i	0.685994	+	0.727607i
$18$	1.58579			0.373773
$19$	3.41421	+	3.41421i	0.783274	+	0.783274i	0.980382	−	0.197108i	$-0.0631548\pi$
$19$	3.41421	+	3.41421i	0.783274	+	0.783274i	−0.197108	+	0.980382i	$0.563155\pi$
$20$		0			0
$21$			2.82843i			0.617213i
$22$	−0.171573	−	0.414214i	−0.0365795	−	0.0883106i
$23$	−3.82843	−	1.58579i	−0.798282	−	0.330659i	−0.0540140	−	0.998540i	$-0.517202\pi$
$23$	−3.82843	−	1.58579i	−0.798282	−	0.330659i	−0.744268	+	0.667881i	$0.767202\pi$
$24$	1.58579	−	3.82843i	0.323697	−	0.781474i
$25$		0			0
$26$	0.414214	−	0.414214i	0.0812340	−	0.0812340i
$27$	0.828427	−	2.00000i	0.159431	−	0.384900i
$28$	1.82843	+	0.757359i	0.345540	+	0.143127i
$29$	−1.70711	−	4.12132i	−0.317002	−	0.765310i	−0.999410	−	0.0343389i	$-0.989067\pi$
$29$	−1.70711	−	4.12132i	−0.317002	−	0.765310i	0.682408	−	0.730971i	$-0.260933\pi$
$30$		0			0
$31$	−3.00000	+	1.24264i	−0.538816	+	0.223185i	−0.635460	−	0.772134i	$-0.719189\pi$
$31$	−3.00000	+	1.24264i	−0.538816	+	0.223185i	0.0966436	+	0.995319i	$0.469189\pi$
$32$	−3.12132	−	3.12132i	−0.551777	−	0.551777i
$33$	−2.82843			−0.492366
$34$	−0.0502525	+	1.70711i	−0.00861824	+	0.292766i
$35$		0			0
$36$	−4.94975	−	4.94975i	−0.824958	−	0.824958i
$37$	3.53553	−	1.46447i	0.581238	−	0.240757i	−0.0726379	−	0.997358i	$-0.523142\pi$
$37$	3.53553	−	1.46447i	0.581238	−	0.240757i	0.653876	+	0.756602i	$0.273142\pi$
$38$			2.00000i			0.324443i
$39$	−1.41421	−	3.41421i	−0.226455	−	0.546712i
$40$		0			0
$41$	−3.12132	+	7.53553i	−0.487468	+	1.17685i	0.468521	+	0.883452i	$0.344787\pi$
$41$	−3.12132	+	7.53553i	−0.487468	+	1.17685i	−0.955990	+	0.293400i	$0.905213\pi$
$42$	−0.828427	+	0.828427i	−0.127829	+	0.127829i
$43$	3.41421	−	3.41421i	0.520663	−	0.520663i	−0.397109	−	0.917772i	$-0.629986\pi$
$43$	3.41421	−	3.41421i	0.520663	−	0.520663i	0.917772	+	0.397109i	$0.129986\pi$
$44$	−0.757359	+	1.82843i	−0.114176	+	0.275646i
$45$		0			0
$46$	−0.656854	−	1.58579i	−0.0968479	−	0.233811i
$47$			10.8284i			1.57949i	0.613436	+	0.789744i	$0.289787\pi$
$47$			10.8284i			1.57949i	−0.613436	+	0.789744i	$0.710213\pi$
$48$	−7.24264	+	3.00000i	−1.04539	+	0.433013i
$49$	4.12132	+	4.12132i	0.588760	+	0.588760i
$50$		0			0
$51$	9.82843	+	4.41421i	1.37626	+	0.618114i
$52$	−2.58579			−0.358584
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	0.772444	−	0.635083i	$-0.219034\pi$
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	−0.635083	+	0.772444i	$0.719034\pi$
$54$	0.828427	−	0.343146i	0.112735	−	0.0466962i
$55$		0			0
$56$	0.656854	+	1.58579i	0.0877758	+	0.211910i
$57$	11.6569	+	4.82843i	1.54399	+	0.639541i
$58$	0.707107	−	1.70711i	0.0928477	−	0.224154i
$59$	−4.24264	+	4.24264i	−0.552345	+	0.552345i	−0.927117	−	0.374772i	$-0.877721\pi$
$59$	−4.24264	+	4.24264i	−0.552345	+	0.552345i	0.374772	+	0.927117i	$0.377721\pi$
$60$		0			0
$61$	3.53553	−	8.53553i	0.452679	−	1.09286i	−0.518621	−	0.855004i	$-0.673554\pi$
$61$	3.53553	−	8.53553i	0.452679	−	1.09286i	0.971300	−	0.237859i	$-0.0764456\pi$
$62$	−1.24264	−	0.514719i	−0.157816	−	0.0653693i
$63$	1.58579	+	3.82843i	0.199790	+	0.482336i
$64$			4.17157i			0.521447i
$65$		0			0
$66$	−0.828427	−	0.828427i	−0.101972	−	0.101972i
$67$	−6.82843			−0.834225			−0.417113	−	0.908855i	$-0.636958\pi$
$67$	−6.82843			−0.834225			−0.417113	+	0.908855i	$0.636958\pi$
$68$	5.48528	−	5.17157i	0.665188	−	0.627145i
$69$	−10.8284			−1.30359
$70$		0			0
$71$	12.0711	−	5.00000i	1.43257	−	0.593391i	0.474587	−	0.880209i	$-0.342597\pi$
$71$	12.0711	−	5.00000i	1.43257	−	0.593391i	0.957985	+	0.286818i	$0.0925974\pi$
$72$		−	6.07107i		−	0.715482i
$73$	2.05025	+	4.94975i	0.239964	+	0.579324i	0.997279	−	0.0737261i	$-0.0234891\pi$
$73$	2.05025	+	4.94975i	0.239964	+	0.579324i	−0.757315	+	0.653050i	$0.773489\pi$
$74$	1.46447	+	0.606602i	0.170241	+	0.0705160i
$75$		0			0
$76$	6.24264	−	6.24264i	0.716080	−	0.716080i
$77$	0.828427	−	0.828427i	0.0944080	−	0.0944080i
$78$	0.585786	−	1.41421i	0.0663273	−	0.160128i
$79$	−3.82843	−	1.58579i	−0.430732	−	0.178415i	0.156775	−	0.987634i	$-0.449890\pi$
$79$	−3.82843	−	1.58579i	−0.430732	−	0.178415i	−0.587506	+	0.809219i	$0.699890\pi$
$80$		0			0
$81$			5.82843i			0.647603i
$82$	−3.12132	+	1.29289i	−0.344692	+	0.142776i
$83$	0.242641	+	0.242641i	0.0266333	+	0.0266333i	0.720298	−	0.693665i	$-0.244005\pi$
$83$	0.242641	+	0.242641i	0.0266333	+	0.0266333i	−0.693665	+	0.720298i	$0.744005\pi$
$84$	5.17157			0.564265
$85$		0			0
$86$	2.00000			0.215666
$87$	−8.24264	−	8.24264i	−0.883704	−	0.883704i
$88$	−1.58579	+	0.656854i	−0.169045	+	0.0700209i
$89$			9.41421i			0.997905i	0.866629	+	0.498952i	$0.166282\pi$
$89$			9.41421i			0.997905i	−0.866629	+	0.498952i	$0.833718\pi$
$90$		0			0
$91$	1.41421	+	0.585786i	0.148250	+	0.0614071i
$92$	−2.89949	+	7.00000i	−0.302293	+	0.729800i
$93$	−6.00000	+	6.00000i	−0.622171	+	0.622171i
$94$	−3.17157	+	3.17157i	−0.327123	+	0.327123i
$95$		0			0
$96$	−10.6569	−	4.41421i	−1.08766	−	0.450524i
$97$	−2.46447	−	5.94975i	−0.250229	−	0.604105i	0.747994	−	0.663706i	$-0.231017\pi$
$97$	−2.46447	−	5.94975i	−0.250229	−	0.604105i	−0.998222	+	0.0596005i	$0.981017\pi$
$98$			2.41421i			0.243872i
$99$	−3.82843	+	1.58579i	−0.384771	+	0.159378i
$100$		0			0
$101$	−13.4142			−1.33476			−0.667382	−	0.744715i	$-0.732585\pi$
$101$	−13.4142			−1.33476			−0.667382	+	0.744715i	$0.732585\pi$
$102$	1.58579	+	4.17157i	0.157016	+	0.413047i
$103$	4.48528			0.441948			0.220974	−	0.975280i	$-0.429076\pi$
$103$	4.48528			0.441948			0.220974	+	0.975280i	$0.429076\pi$
$104$	−1.58579	−	1.58579i	−0.155499	−	0.155499i
$105$		0			0
$106$			0.585786i			0.0568966i
$107$	2.41421	+	5.82843i	0.233391	+	0.563455i	0.996572	−	0.0827292i	$-0.0263636\pi$
$107$	2.41421	+	5.82843i	0.233391	+	0.563455i	−0.763181	+	0.646184i	$0.776364\pi$
$108$	−3.65685	−	1.51472i	−0.351881	−	0.145754i
$109$	1.63604	−	3.94975i	0.156704	−	0.378317i	−0.825956	−	0.563735i	$-0.809364\pi$
$109$	1.63604	−	3.94975i	0.156704	−	0.378317i	0.982660	+	0.185418i	$0.0593639\pi$
$110$		0			0
$111$	7.07107	−	7.07107i	0.671156	−	0.671156i
$112$	1.24264	−	3.00000i	0.117419	−	0.283473i
$113$	−14.9497	−	6.19239i	−1.40635	−	0.582531i	−0.454961	−	0.890511i	$-0.650347\pi$
$113$	−14.9497	−	6.19239i	−1.40635	−	0.582531i	−0.951393	+	0.307980i	$0.900347\pi$
$114$	2.00000	+	4.82843i	0.187317	+	0.452224i
$115$		0			0
$116$	−7.53553	+	3.12132i	−0.699657	+	0.289807i
$117$	−3.82843	−	3.82843i	−0.353938	−	0.353938i
$118$	−2.48528			−0.228789
$119$	−4.17157	+	1.58579i	−0.382407	+	0.145369i
$120$		0			0
$121$	−6.94975	−	6.94975i	−0.631795	−	0.631795i
$122$	3.53553	−	1.46447i	0.320092	−	0.132587i
$123$			21.3137i			1.92179i
$124$	2.27208	+	5.48528i	0.204039	+	0.492593i
$125$		0			0
$126$	−0.656854	+	1.58579i	−0.0585172	+	0.141273i
$127$	12.2426	−	12.2426i	1.08636	−	1.08636i	0.0904585	−	0.995900i	$-0.471167\pi$
$127$	12.2426	−	12.2426i	1.08636	−	1.08636i	0.995900	−	0.0904585i	$-0.0288332\pi$
$128$	−7.46447	+	7.46447i	−0.659772	+	0.659772i
$129$	4.82843	−	11.6569i	0.425119	−	1.02633i
$130$		0			0
$131$	0.0710678	+	0.171573i	0.00620922	+	0.0149904i	0.926954	−	0.375176i	$-0.122418\pi$
$131$	0.0710678	+	0.171573i	0.00620922	+	0.0149904i	−0.920745	+	0.390166i	$0.872418\pi$
$132$			5.17157i			0.450128i
$133$	−4.82843	+	2.00000i	−0.418678	+	0.173422i
$134$	−2.00000	−	2.00000i	−0.172774	−	0.172774i
$135$		0			0
$136$	6.53553	+	0.192388i	0.560417	+	0.0164971i
$137$	−8.72792			−0.745677			−0.372838	−	0.927896i	$-0.621615\pi$
$137$	−8.72792			−0.745677			−0.372838	+	0.927896i	$0.621615\pi$
$138$	−3.17157	−	3.17157i	−0.269982	−	0.269982i
$139$	−13.8284	+	5.72792i	−1.17291	+	0.485836i	−0.882154	−	0.470961i	$-0.843907\pi$
$139$	−13.8284	+	5.72792i	−1.17291	+	0.485836i	−0.290758	+	0.956797i	$0.593907\pi$
$140$		0			0
$141$	10.8284	+	26.1421i	0.911918	+	2.20156i
$142$	5.00000	+	2.07107i	0.419591	+	0.173800i
$143$	−0.585786	+	1.41421i	−0.0489859	+	0.118262i
$144$	−8.12132	+	8.12132i	−0.676777	+	0.676777i
$145$		0			0
$146$	−0.849242	+	2.05025i	−0.0702838	+	0.169680i
$147$	14.0711	+	5.82843i	1.16056	+	0.480721i
$148$	−2.67767	−	6.46447i	−0.220103	−	0.531376i
$149$		−	16.9706i		−	1.39028i	−0.718873	−	0.695141i	$-0.755342\pi$
$149$		−	16.9706i		−	1.39028i	0.718873	−	0.695141i	$-0.244658\pi$
$150$		0			0
$151$	−9.07107	−	9.07107i	−0.738193	−	0.738193i	0.234035	−	0.972228i	$-0.424807\pi$
$151$	−9.07107	−	9.07107i	−0.738193	−	0.738193i	−0.972228	+	0.234035i	$0.924807\pi$
$152$	7.65685			0.621053
$153$	15.7782	+	0.464466i	1.27559	+	0.0375499i
$154$	0.485281			0.0391051
$155$		0			0
$156$	−6.24264	+	2.58579i	−0.499811	+	0.207029i
$157$		−	1.65685i		−	0.132231i	−0.997812	−	0.0661157i	$-0.978939\pi$
$157$		−	1.65685i		−	0.132231i	0.997812	−	0.0661157i	$-0.0210606\pi$
$158$	−0.656854	−	1.58579i	−0.0522565	−	0.126158i
$159$	3.41421	+	1.41421i	0.270765	+	0.112154i
$160$		0			0
$161$	3.17157	−	3.17157i	0.249955	−	0.249955i
$162$	−1.70711	+	1.70711i	−0.134123	+	0.134123i
$163$	2.17157	−	5.24264i	0.170091	−	0.410635i	−0.815731	−	0.578431i	$-0.803665\pi$
$163$	2.17157	−	5.24264i	0.170091	−	0.410635i	0.985822	+	0.167796i	$0.0536650\pi$
$164$	13.7782	+	5.70711i	1.07589	+	0.445650i
$165$		0			0
$166$			0.142136i			0.0110319i
$167$	−9.24264	+	3.82843i	−0.715217	+	0.296253i	−0.710461	−	0.703736i	$-0.751514\pi$
$167$	−9.24264	+	3.82843i	−0.715217	+	0.296253i	−0.00475555	+	0.999989i	$0.501514\pi$
$168$	3.17157	+	3.17157i	0.244692	+	0.244692i
$169$	11.0000			0.846154
$170$		0			0
$171$	18.4853			1.41360
$172$	−6.24264	−	6.24264i	−0.475997	−	0.475997i
$173$	3.12132	−	1.29289i	0.237310	−	0.0982969i	−0.260859	−	0.965377i	$-0.584006\pi$
$173$	3.12132	−	1.29289i	0.237310	−	0.0982969i	0.498169	+	0.867080i	$0.334006\pi$
$174$		−	4.82843i		−	0.366042i
$175$		0			0
$176$	3.00000	+	1.24264i	0.226134	+	0.0936676i
$177$	−6.00000	+	14.4853i	−0.450988	+	1.08878i
$178$	−2.75736	+	2.75736i	−0.206673	+	0.206673i
$179$	4.24264	−	4.24264i	0.317110	−	0.317110i	−0.530546	−	0.847656i	$-0.678013\pi$
$179$	4.24264	−	4.24264i	0.317110	−	0.317110i	0.847656	+	0.530546i	$0.178013\pi$
$180$		0			0
$181$	−11.5355	−	4.77817i	−0.857429	−	0.355159i	−0.0897278	−	0.995966i	$-0.528600\pi$
$181$	−11.5355	−	4.77817i	−0.857429	−	0.355159i	−0.767702	+	0.640807i	$0.778600\pi$
$182$	0.242641	+	0.585786i	0.0179857	+	0.0434214i
$183$		−	24.1421i		−	1.78464i
$184$	−6.07107	+	2.51472i	−0.447565	+	0.185388i
$185$		0			0
$186$	−3.51472			−0.257712
$187$	−1.58579	−	4.17157i	−0.115964	−	0.305056i
$188$	19.7990			1.44399
$189$	1.65685	+	1.65685i	0.120518	+	0.120518i
$190$		0			0
$191$			20.0000i			1.44715i	0.690246	+	0.723575i	$0.257502\pi$
$191$			20.0000i			1.44715i	−0.690246	+	0.723575i	$0.742498\pi$
$192$	4.17157	+	10.0711i	0.301057	+	0.726817i
$193$	−5.12132	−	2.12132i	−0.368641	−	0.152696i	0.190670	−	0.981654i	$-0.438934\pi$
$193$	−5.12132	−	2.12132i	−0.368641	−	0.152696i	−0.559310	+	0.828958i	$0.688934\pi$
$194$	1.02082	−	2.46447i	0.0732903	−	0.176938i
$195$		0			0
$196$	7.53553	−	7.53553i	0.538252	−	0.538252i
$197$	5.70711	−	13.7782i	0.406615	−	0.981654i	−0.579407	−	0.815038i	$-0.696716\pi$
$197$	5.70711	−	13.7782i	0.406615	−	0.981654i	0.986022	−	0.166616i	$-0.0532841\pi$
$198$	−1.58579	−	0.656854i	−0.112697	−	0.0466806i
$199$	−0.656854	−	1.58579i	−0.0465632	−	0.112413i	0.898887	−	0.438181i	$-0.144377\pi$
$199$	−0.656854	−	1.58579i	−0.0465632	−	0.112413i	−0.945450	+	0.325768i	$0.894377\pi$
$200$		0			0
$201$	−16.4853	+	6.82843i	−1.16278	+	0.481640i
$202$	−3.92893	−	3.92893i	−0.276439	−	0.276439i
$203$	4.82843			0.338889
$204$	8.07107	−	17.9706i	0.565088	−	1.25819i
$205$		0			0
$206$	1.31371	+	1.31371i	0.0915304	+	0.0915304i
$207$	−14.6569	+	6.07107i	−1.01872	+	0.421968i
$208$			4.24264i			0.294174i
$209$	−2.00000	−	4.82843i	−0.138343	−	0.333989i
$210$		0			0
$211$	5.72792	−	13.8284i	0.394326	−	0.951988i	−0.594659	−	0.803978i	$-0.702713\pi$
$211$	5.72792	−	13.8284i	0.394326	−	0.951988i	0.988986	−	0.148010i	$-0.0472869\pi$
$212$	1.82843	−	1.82843i	0.125577	−	0.125577i
$213$	24.1421	−	24.1421i	1.65419	−	1.65419i
$214$	−1.00000	+	2.41421i	−0.0683586	+	0.165032i
$215$		0			0
$216$	−1.31371	−	3.17157i	−0.0893865	−	0.215798i
$217$		−	3.51472i		−	0.238595i
$218$	1.63604	−	0.677670i	0.110807	−	0.0458976i
$219$	9.89949	+	9.89949i	0.668946	+	0.668946i
$220$		0			0
$221$	4.24264	−	4.00000i	0.285391	−	0.269069i
$222$	4.14214			0.278002
$223$	−0.585786	−	0.585786i	−0.0392272	−	0.0392272i	0.687221	−	0.726448i	$-0.258830\pi$
$223$	−0.585786	−	0.585786i	−0.0392272	−	0.0392272i	−0.726448	+	0.687221i	$0.758830\pi$
$224$	4.41421	−	1.82843i	0.294937	−	0.122167i
$225$		0			0
$226$	−2.56497	−	6.19239i	−0.170619	−	0.411912i
$227$	4.65685	+	1.92893i	0.309086	+	0.128028i	0.531835	−	0.846848i	$-0.321503\pi$
$227$	4.65685	+	1.92893i	0.309086	+	0.128028i	−0.222748	+	0.974876i	$0.571503\pi$
$228$	8.82843	−	21.3137i	0.584677	−	1.41153i
$229$	16.1421	−	16.1421i	1.06670	−	1.06670i	0.0690921	−	0.997610i	$-0.477990\pi$
$229$	16.1421	−	16.1421i	1.06670	−	1.06670i	0.997610	−	0.0690921i	$-0.0220102\pi$
$230$		0			0
$231$	1.17157	−	2.82843i	0.0770838	−	0.186097i
$232$	−6.53553	−	2.70711i	−0.429079	−	0.177730i
$233$	−3.87868	−	9.36396i	−0.254101	−	0.613453i	0.744427	−	0.667704i	$-0.232723\pi$
$233$	−3.87868	−	9.36396i	−0.254101	−	0.613453i	−0.998527	+	0.0542508i	$0.982723\pi$
$234$		−	2.24264i		−	0.146606i
$235$		0			0
$236$	7.75736	+	7.75736i	0.504961	+	0.504961i
$237$	−10.8284			−0.703382
$238$	−1.68629	−	0.757359i	−0.109306	−	0.0490923i
$239$	9.17157			0.593260			0.296630	−	0.954993i	$-0.404137\pi$
$239$	9.17157			0.593260			0.296630	+	0.954993i	$0.404137\pi$
$240$		0			0
$241$	11.3640	−	4.70711i	0.732017	−	0.303211i	0.0146365	−	0.999893i	$-0.495341\pi$
$241$	11.3640	−	4.70711i	0.732017	−	0.303211i	0.717381	+	0.696681i	$0.245341\pi$
$242$		−	4.07107i		−	0.261698i
$243$	8.31371	+	20.0711i	0.533325	+	1.28756i
$244$	−15.6066	−	6.46447i	−0.999110	−	0.413845i
$245$		0			0
$246$	−6.24264	+	6.24264i	−0.398016	+	0.398016i
$247$	4.82843	−	4.82843i	0.307225	−	0.307225i
$248$	−1.97056	+	4.75736i	−0.125131	+	0.302093i
$249$	0.828427	+	0.343146i	0.0524994	+	0.0217460i
$250$		0			0
$251$		−	3.51472i		−	0.221847i	−0.993829	−	0.110924i	$-0.964619\pi$
$251$		−	3.51472i		−	0.221847i	0.993829	−	0.110924i	$-0.0353809\pi$
$252$	7.00000	−	2.89949i	0.440959	−	0.182651i
$253$	3.17157	+	3.17157i	0.199395	+	0.199395i
$254$	7.17157			0.449985
$255$		0			0
$256$	3.97056			0.248160
$257$	15.6569	+	15.6569i	0.976648	+	0.976648i	0.999733	−	0.0230858i	$-0.00734908\pi$
$257$	15.6569	+	15.6569i	0.976648	+	0.976648i	−0.0230858	+	0.999733i	$0.507349\pi$
$258$	4.82843	−	2.00000i	0.300605	−	0.124515i
$259$			4.14214i			0.257380i
$260$		0			0
$261$	−15.7782	−	6.53553i	−0.976644	−	0.404539i
$262$	−0.0294373	+	0.0710678i	−0.00181864	+	0.00439058i
$263$	4.58579	−	4.58579i	0.282772	−	0.282772i	−0.551442	−	0.834213i	$-0.685922\pi$
$263$	4.58579	−	4.58579i	0.282772	−	0.282772i	0.834213	+	0.551442i	$0.185922\pi$
$264$	−3.17157	+	3.17157i	−0.195197	+	0.195197i
$265$		0			0
$266$	−2.00000	−	0.828427i	−0.122628	−	0.0507941i
$267$	9.41421	+	22.7279i	0.576141	+	1.39093i
$268$			12.4853i			0.762660i
$269$	5.87868	−	2.43503i	0.358429	−	0.148466i	−0.196200	−	0.980564i	$-0.562860\pi$
$269$	5.87868	−	2.43503i	0.358429	−	0.148466i	0.554629	+	0.832098i	$0.312860\pi$
$270$		0			0
$271$	−6.14214			−0.373108			−0.186554	−	0.982445i	$-0.559732\pi$
$271$	−6.14214			−0.373108			−0.186554	+	0.982445i	$0.559732\pi$
$272$	−8.48528	−	9.00000i	−0.514496	−	0.545705i
$273$	4.00000			0.242091
$274$	−2.55635	−	2.55635i	−0.154435	−	0.154435i
$275$		0			0
$276$			19.7990i			1.19176i
$277$	−8.43503	−	20.3640i	−0.506812	−	1.22355i	−0.945709	−	0.325015i	$-0.894631\pi$
$277$	−8.43503	−	20.3640i	−0.506812	−	1.22355i	0.438897	−	0.898537i	$-0.355369\pi$
$278$	−5.72792	−	2.37258i	−0.343538	−	0.142298i
$279$	−4.75736	+	11.4853i	−0.284816	+	0.687606i
$280$		0			0
$281$	−12.6569	+	12.6569i	−0.755045	+	0.755045i	−0.975416	−	0.220371i	$-0.929273\pi$
$281$	−12.6569	+	12.6569i	−0.755045	+	0.755045i	0.220371	+	0.975416i	$0.429273\pi$
$282$	−4.48528	+	10.8284i	−0.267095	+	0.644823i
$283$	−21.1421	−	8.75736i	−1.25677	−	0.520571i	−0.347853	−	0.937549i	$-0.613089\pi$
$283$	−21.1421	−	8.75736i	−1.25677	−	0.520571i	−0.908917	+	0.416978i	$0.863089\pi$
$284$	−9.14214	−	22.0711i	−0.542486	−	1.30968i
$285$		0			0
$286$	−0.585786	+	0.242641i	−0.0346383	+	0.0143476i
$287$	−6.24264	−	6.24264i	−0.368491	−	0.368491i
$288$	−16.8995			−0.995812
$289$	−1.00000	+	16.9706i	−0.0588235	+	0.998268i
$290$		0			0
$291$	−11.8995	−	11.8995i	−0.697561	−	0.697561i
$292$	9.05025	−	3.74874i	0.529626	−	0.219378i
$293$			23.6569i			1.38205i	0.722832	+	0.691024i	$0.242840\pi$
$293$			23.6569i			1.38205i	−0.722832	+	0.691024i	$0.757160\pi$
$294$	2.41421	+	5.82843i	0.140800	+	0.339921i
$295$		0			0
$296$	2.32233	−	5.60660i	0.134983	−	0.325877i
$297$	−1.65685	+	1.65685i	−0.0961404	+	0.0961404i
$298$	4.97056	−	4.97056i	0.287937	−	0.287937i
$299$	−2.24264	+	5.41421i	−0.129695	+	0.313112i
$300$		0			0
$301$	2.00000	+	4.82843i	0.115278	+	0.278306i
$302$		−	5.31371i		−	0.305770i
$303$	−32.3848	+	13.4142i	−1.86046	+	0.770626i
$304$	−10.2426	−	10.2426i	−0.587456	−	0.587456i
$305$		0			0
$306$	4.48528	+	4.75736i	0.256406	+	0.271960i
$307$	−2.14214			−0.122258			−0.0611291	−	0.998130i	$-0.519470\pi$
$307$	−2.14214			−0.122258			−0.0611291	+	0.998130i	$0.519470\pi$
$308$	−1.51472	−	1.51472i	−0.0863091	−	0.0863091i
$309$	10.8284	−	4.48528i	0.616008	−	0.255159i
$310$		0			0
$311$	−1.72792	−	4.17157i	−0.0979815	−	0.236548i	0.867287	−	0.497809i	$-0.165862\pi$
$311$	−1.72792	−	4.17157i	−0.0979815	−	0.236548i	−0.965268	+	0.261261i	$0.915862\pi$
$312$	−5.41421	−	2.24264i	−0.306519	−	0.126965i
$313$	4.87868	−	11.7782i	0.275759	−	0.665742i	−0.723950	−	0.689852i	$-0.757675\pi$
$313$	4.87868	−	11.7782i	0.275759	−	0.665742i	0.999709	+	0.0241106i	$0.00767540\pi$
$314$	0.485281	−	0.485281i	0.0273860	−	0.0273860i
$315$		0			0
$316$	−2.89949	+	7.00000i	−0.163109	+	0.393781i
$317$	5.36396	+	2.22183i	0.301270	+	0.124790i	0.528198	−	0.849122i	$-0.322868\pi$
$317$	5.36396	+	2.22183i	0.301270	+	0.124790i	−0.226927	+	0.973912i	$0.572868\pi$
$318$	0.585786	+	1.41421i	0.0328493	+	0.0793052i
$319$			4.82843i			0.270340i
$320$		0			0
$321$	11.6569	+	11.6569i	0.650622	+	0.650622i
$322$	1.85786			0.103535
$323$	−0.585786	+	19.8995i	−0.0325940	+	1.10724i
$324$	10.6569			0.592047
$325$		0			0
$326$	2.17157	−	0.899495i	0.120272	−	0.0498184i
$327$		−	11.1716i		−	0.617789i
$328$	4.94975	+	11.9497i	0.273304	+	0.659814i
$329$	−10.8284	−	4.48528i	−0.596991	−	0.247282i
$330$		0			0
$331$	−12.5858	+	12.5858i	−0.691777	+	0.691777i	−0.962623	−	0.270845i	$-0.912697\pi$
$331$	−12.5858	+	12.5858i	−0.691777	+	0.691777i	0.270845	+	0.962623i	$0.412697\pi$
$332$	0.443651	−	0.443651i	0.0243485	−	0.0243485i
$333$	5.60660	−	13.5355i	0.307240	−	0.741743i
$334$	−3.82843	−	1.58579i	−0.209482	−	0.0867704i
$335$		0			0
$336$		−	8.48528i		−	0.462910i
$337$	31.8492	−	13.1924i	1.73494	−	0.718635i	0.735798	−	0.677202i	$-0.236808\pi$
$337$	31.8492	−	13.1924i	1.73494	−	0.718635i	0.999141	−	0.0414336i	$-0.0131925\pi$
$338$	3.22183	+	3.22183i	0.175244	+	0.175244i
$339$	−42.2843			−2.29657
$340$		0			0
$341$	3.51472			0.190333
$342$	5.41421	+	5.41421i	0.292767	+	0.292767i
$343$	−12.8284	+	5.31371i	−0.692670	+	0.286913i
$344$		−	7.65685i		−	0.412830i
$345$		0			0
$346$	1.29289	+	0.535534i	0.0695064	+	0.0287905i
$347$	1.48528	−	3.58579i	0.0797341	−	0.192495i	−0.878985	−	0.476849i	$-0.841779\pi$
$347$	1.48528	−	3.58579i	0.0797341	−	0.192495i	0.958719	+	0.284354i	$0.0917790\pi$
$348$	−15.0711	+	15.0711i	−0.807894	+	0.807894i
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	−0.622240	−	0.782826i	$-0.713777\pi$
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	0.782826	+	0.622240i	$0.213777\pi$
$350$		0			0
$351$	−2.82843	−	1.17157i	−0.150970	−	0.0625339i
$352$	1.82843	+	4.41421i	0.0974555	+	0.235278i
$353$		−	14.0000i		−	0.745145i	−0.928003	−	0.372572i	$-0.878476\pi$
$353$		−	14.0000i		−	0.745145i	0.928003	−	0.372572i	$-0.121524\pi$
$354$	−6.00000	+	2.48528i	−0.318896	+	0.132091i
$355$		0			0
$356$	17.2132			0.912298
$357$	−8.48528	+	8.00000i	−0.449089	+	0.423405i
$358$	2.48528			0.131351
$359$	16.3848	+	16.3848i	0.864755	+	0.864755i	0.991886	−	0.127131i	$-0.0405767\pi$
$359$	16.3848	+	16.3848i	0.864755	+	0.864755i	−0.127131	+	0.991886i	$0.540577\pi$
$360$		0			0
$361$			4.31371i			0.227037i
$362$	−1.97918	−	4.77817i	−0.104024	−	0.251135i
$363$	−23.7279	−	9.82843i	−1.24539	−	0.515859i
$364$	1.07107	−	2.58579i	0.0561392	−	0.135532i
$365$		0			0
$366$	7.07107	−	7.07107i	0.369611	−	0.369611i
$367$	−10.0711	+	24.3137i	−0.525705	+	1.26917i	0.408607	+	0.912710i	$0.366015\pi$
$367$	−10.0711	+	24.3137i	−0.525705	+	1.26917i	−0.934313	+	0.356455i	$0.883985\pi$
$368$	11.4853	+	4.75736i	0.598712	+	0.247994i
$369$	11.9497	+	28.8492i	0.622079	+	1.50183i
$370$		0			0
$371$	−1.41421	+	0.585786i	−0.0734223	+	0.0304125i
$372$	10.9706	+	10.9706i	0.568797	+	0.568797i
$373$	19.5563			1.01259			0.506295	−	0.862361i	$-0.331015\pi$
$373$	19.5563			1.01259			0.506295	+	0.862361i	$0.331015\pi$
$374$	0.757359	−	1.68629i	0.0391621	−	0.0871961i
$375$		0			0
$376$	12.1421	+	12.1421i	0.626183	+	0.626183i
$377$	−5.82843	+	2.41421i	−0.300179	+	0.124338i
$378$			0.970563i			0.0499204i
$379$	0.414214	+	1.00000i	0.0212767	+	0.0513665i	0.934161	−	0.356852i	$-0.116150\pi$
$379$	0.414214	+	1.00000i	0.0212767	+	0.0513665i	−0.912884	+	0.408219i	$0.866150\pi$
$380$		0			0
$381$	17.3137	−	41.7990i	0.887008	−	2.14143i
$382$	−5.85786	+	5.85786i	−0.299714	+	0.299714i
$383$	−3.89949	+	3.89949i	−0.199255	+	0.199255i	−0.799681	−	0.600426i	$-0.794998\pi$
$383$	−3.89949	+	3.89949i	−0.199255	+	0.199255i	0.600426	+	0.799681i	$0.294998\pi$
$384$	−10.5563	+	25.4853i	−0.538701	+	1.30054i
$385$		0			0
$386$	−0.878680	−	2.12132i	−0.0447236	−	0.107972i
$387$		−	18.4853i		−	0.939660i
$388$	−10.8787	+	4.50610i	−0.552281	+	0.228762i
$389$	−11.4142	−	11.4142i	−0.578724	−	0.578724i	0.355828	−	0.934551i	$-0.384199\pi$
$389$	−11.4142	−	11.4142i	−0.578724	−	0.578724i	−0.934551	+	0.355828i	$0.884199\pi$
$390$		0			0
$391$	−6.07107	−	15.9706i	−0.307027	−	0.807666i
$392$	9.24264			0.466824
$393$	0.343146	+	0.343146i	0.0173094	+	0.0173094i
$394$	5.70711	−	2.36396i	0.287520	−	0.119095i
$395$		0			0
$396$	2.89949	+	7.00000i	0.145705	+	0.351763i
$397$	−25.1924	−	10.4350i	−1.26437	−	0.523719i	−0.353122	−	0.935577i	$-0.614880\pi$
$397$	−25.1924	−	10.4350i	−1.26437	−	0.523719i	−0.911248	+	0.411858i	$0.864880\pi$
$398$	0.272078	−	0.656854i	0.0136380	−	0.0329251i
$399$	−9.65685	+	9.65685i	−0.483447	+	0.483447i
$400$		0			0
$401$	6.53553	−	15.7782i	0.326369	−	0.787924i	−0.672487	−	0.740109i	$-0.734774\pi$
$401$	6.53553	−	15.7782i	0.326369	−	0.787924i	0.998856	−	0.0478157i	$-0.0152260\pi$
$402$	−6.82843	−	2.82843i	−0.340571	−	0.141069i
$403$	1.75736	+	4.24264i	0.0875403	+	0.211341i
$404$			24.5269i			1.22026i
$405$		0			0
$406$	1.41421	+	1.41421i	0.0701862	+	0.0701862i
$407$	−4.14214			−0.205318
$408$	15.9706	−	6.07107i	0.790661	−	0.300563i
$409$	19.3137			0.955001			0.477501	−	0.878631i	$-0.341543\pi$
$409$	19.3137			0.955001			0.477501	+	0.878631i	$0.341543\pi$
$410$		0			0
$411$	−21.0711	+	8.72792i	−1.03936	+	0.430517i
$412$		−	8.20101i		−	0.404035i
$413$	−2.48528	−	6.00000i	−0.122293	−	0.295241i
$414$	−6.07107	−	2.51472i	−0.298377	−	0.123592i
$415$		0			0
$416$	−4.41421	+	4.41421i	−0.216425	+	0.216425i
$417$	−27.6569	+	27.6569i	−1.35436	+	1.35436i
$418$	0.828427	−	2.00000i	0.0405197	−	0.0978232i
$419$	−24.8995	−	10.3137i	−1.21642	−	0.503858i	−0.320150	−	0.947367i	$-0.603733\pi$
$419$	−24.8995	−	10.3137i	−1.21642	−	0.503858i	−0.896270	+	0.443509i	$0.853733\pi$
$420$		0			0
$421$		−	17.4142i		−	0.848717i	−0.905494	−	0.424358i	$-0.860500\pi$
$421$		−	17.4142i		−	0.848717i	0.905494	−	0.424358i	$-0.139500\pi$
$422$	5.72792	−	2.37258i	0.278831	−	0.115496i
$423$	29.3137	+	29.3137i	1.42528	+	1.42528i
$424$	2.24264			0.108912
$425$		0			0
$426$	14.1421			0.685189
$427$	7.07107	+	7.07107i	0.342193	+	0.342193i
$428$	10.6569	−	4.41421i	0.515118	−	0.213369i
$429$			4.00000i			0.193122i
$430$		0			0
$431$	−36.7990	−	15.2426i	−1.77254	−	0.734212i	−0.994345	−	0.106195i	$-0.966133\pi$
$431$	−36.7990	−	15.2426i	−1.77254	−	0.734212i	−0.778200	−	0.628017i	$-0.783867\pi$
$432$	−2.48528	+	6.00000i	−0.119573	+	0.288675i
$433$	10.7279	−	10.7279i	0.515551	−	0.515551i	−0.400671	−	0.916222i	$-0.631223\pi$
$433$	10.7279	−	10.7279i	0.515551	−	0.515551i	0.916222	+	0.400671i	$0.131223\pi$
$434$	1.02944	−	1.02944i	0.0494146	−	0.0494146i
$435$		0			0
$436$	−7.22183	−	2.99138i	−0.345863	−	0.143261i
$437$	−7.65685	−	18.4853i	−0.366277	−	0.884271i
$438$			5.79899i			0.277086i
$439$	10.0711	−	4.17157i	0.480666	−	0.199098i	−0.129176	−	0.991622i	$-0.541233\pi$
$439$	10.0711	−	4.17157i	0.480666	−	0.199098i	0.609841	+	0.792523i	$0.291233\pi$
$440$		0			0
$441$	22.3137			1.06256
$442$	2.41421	+	0.0710678i	0.114832	+	0.00338035i
$443$	−15.7990			−0.750633			−0.375316	−	0.926897i	$-0.622466\pi$
$443$	−15.7990			−0.750633			−0.375316	+	0.926897i	$0.622466\pi$
$444$	−12.9289	−	12.9289i	−0.613580	−	0.613580i
$445$		0			0
$446$		−	0.343146i		−	0.0162484i
$447$	−16.9706	−	40.9706i	−0.802680	−	1.93784i
$448$	−4.17157	−	1.72792i	−0.197088	−	0.0816366i
$449$	−7.19239	+	17.3640i	−0.339430	+	0.819456i	0.658341	+	0.752720i	$0.271259\pi$
$449$	−7.19239	+	17.3640i	−0.339430	+	0.819456i	−0.997771	+	0.0667361i	$0.978741\pi$
$450$		0			0
$451$	6.24264	−	6.24264i	0.293954	−	0.293954i
$452$	−11.3223	+	27.3345i	−0.532558	+	1.28571i
$453$	−30.9706	−	12.8284i	−1.45512	−	0.602732i
$454$	0.798990	+	1.92893i	0.0374985	+	0.0905293i
$455$		0			0
$456$	18.4853	−	7.65685i	0.865653	−	0.358565i
$457$	13.3137	+	13.3137i	0.622789	+	0.622789i	0.946244	−	0.323455i	$-0.104844\pi$
$457$	13.3137	+	13.3137i	0.622789	+	0.622789i	−0.323455	+	0.946244i	$0.604844\pi$
$458$	9.45584			0.441843
$459$	8.34315	−	3.17157i	0.389425	−	0.148036i
$460$		0			0
$461$	17.0000	+	17.0000i	0.791769	+	0.791769i	0.981782	−	0.190013i	$-0.0608529\pi$
$461$	17.0000	+	17.0000i	0.791769	+	0.791769i	−0.190013	+	0.981782i	$0.560853\pi$
$462$	1.17157	−	0.485281i	0.0545065	−	0.0225773i
$463$			30.6274i			1.42338i	0.702495	+	0.711688i	$0.252069\pi$
$463$			30.6274i			1.42338i	−0.702495	+	0.711688i	$0.747931\pi$
$464$	5.12132	+	12.3640i	0.237751	+	0.573982i
$465$		0			0
$466$	1.60660	−	3.87868i	0.0744244	−	0.179676i
$467$	−8.92893	+	8.92893i	−0.413182	+	0.413182i	−0.882845	−	0.469664i	$-0.844375\pi$
$467$	−8.92893	+	8.92893i	−0.413182	+	0.413182i	0.469664	+	0.882845i	$0.344375\pi$
$468$	−7.00000	+	7.00000i	−0.323575	+	0.323575i
$469$	2.82843	−	6.82843i	0.130605	−	0.315307i
$470$		0			0
$471$	−1.65685	−	4.00000i	−0.0763438	−	0.184310i
$472$			9.51472i			0.437950i
$473$	−4.82843	+	2.00000i	−0.222011	+	0.0919601i
$474$	−3.17157	−	3.17157i	−0.145675	−	0.145675i
$475$		0			0
$476$	2.89949	+	7.62742i	0.132898	+	0.349602i
$477$	5.41421			0.247900
$478$	2.68629	+	2.68629i	0.122868	+	0.122868i
$479$	−31.9706	+	13.2426i	−1.46077	+	0.605072i	−0.964733	−	0.263229i	$-0.915213\pi$
$479$	−31.9706	+	13.2426i	−1.46077	+	0.605072i	−0.496039	+	0.868300i	$0.665213\pi$
$480$		0			0
$481$	−2.07107	−	5.00000i	−0.0944326	−	0.227980i
$482$	4.70711	+	1.94975i	0.214403	+	0.0888086i
$483$	4.48528	−	10.8284i	0.204087	−	0.492710i
$484$	−12.7071	+	12.7071i	−0.577596	+	0.577596i
$485$		0			0
$486$	−3.44365	+	8.31371i	−0.156207	+	0.377117i
$487$	4.07107	+	1.68629i	0.184478	+	0.0764132i	0.473010	−	0.881057i	$-0.343167\pi$
$487$	4.07107	+	1.68629i	0.184478	+	0.0764132i	−0.288533	+	0.957470i	$0.593167\pi$
$488$	−5.60660	−	13.5355i	−0.253799	−	0.612725i
$489$		−	14.8284i		−	0.670565i
$490$		0			0
$491$	17.7574	+	17.7574i	0.801378	+	0.801378i	0.983311	−	0.181933i	$-0.0582353\pi$
$491$	17.7574	+	17.7574i	0.801378	+	0.801378i	−0.181933	+	0.983311i	$0.558235\pi$
$492$	38.9706			1.75693
$493$	7.53553	−	16.7782i	0.339383	−	0.755651i
$494$	2.82843			0.127257
$495$		0			0
$496$	9.00000	−	3.72792i	0.404112	−	0.167389i
$497$			14.1421i			0.634361i
$498$	0.142136	+	0.343146i	0.00636925	+	0.0153767i
$499$	34.2132	+	14.1716i	1.53159	+	0.634407i	0.979873	−	0.199622i	$-0.0639715\pi$
$499$	34.2132	+	14.1716i	1.53159	+	0.634407i	0.551720	+	0.834029i	$0.313972\pi$
$500$		0			0
$501$	−18.4853	+	18.4853i	−0.825861	+	0.825861i
$502$	1.02944	−	1.02944i	0.0459460	−	0.0459460i
$503$	−5.72792	+	13.8284i	−0.255395	+	0.616579i	−0.998623	−	0.0524595i	$-0.983294\pi$
$503$	−5.72792	+	13.8284i	−0.255395	+	0.616579i	0.743228	+	0.669039i	$0.233294\pi$
$504$	6.07107	+	2.51472i	0.270427	+	0.112014i
$505$		0			0
$506$			1.85786i			0.0825921i
$507$	26.5563	−	11.0000i	1.17941	−	0.488527i
$508$	−22.3848	−	22.3848i	−0.993164	−	0.993164i
$509$	−3.02944			−0.134277			−0.0671387	−	0.997744i	$-0.521387\pi$
$509$	−3.02944			−0.134277			−0.0671387	+	0.997744i	$0.521387\pi$
$510$		0			0
$511$	−5.79899			−0.256532
$512$	16.0919	+	16.0919i	0.711167	+	0.711167i
$513$	9.65685	−	4.00000i	0.426361	−	0.176604i
$514$			9.17157i			0.404541i
$515$		0			0
$516$	−21.3137	−	8.82843i	−0.938284	−	0.388650i
$517$	4.48528	−	10.8284i	0.197262	−	0.476234i
$518$	−1.21320	+	1.21320i	−0.0533051	+	0.0533051i
$519$	6.24264	−	6.24264i	0.274022	−	0.274022i
$520$		0			0
$521$	2.87868	+	1.19239i	0.126117	+	0.0522395i	0.444850	−	0.895605i	$-0.353257\pi$
$521$	2.87868	+	1.19239i	0.126117	+	0.0522395i	−0.318732	+	0.947845i	$0.603257\pi$
$522$	−2.70711	−	6.53553i	−0.118487	−	0.286053i
$523$			6.82843i			0.298586i	0.988793	+	0.149293i	$0.0476998\pi$
$523$			6.82843i			0.298586i	−0.988793	+	0.149293i	$0.952300\pi$
$524$	0.313708	−	0.129942i	0.0137044	−	0.00567656i
$525$		0			0
$526$	2.68629			0.117128
$527$	−12.2132	−	5.48528i	−0.532015	−	0.238943i
$528$	8.48528			0.369274
$529$	−4.12132	−	4.12132i	−0.179188	−	0.179188i
$530$		0			0
$531$			22.9706i			0.996838i
$532$	3.65685	+	8.82843i	0.158545	+	0.382761i
$533$	10.6569	+	4.41421i	0.461600	+	0.191201i
$534$	−3.89949	+	9.41421i	−0.168748	+	0.407393i
$535$		0			0
$536$	−7.65685	+	7.65685i	−0.330726	+	0.330726i
$537$	6.00000	−	14.4853i	0.258919	−	0.625086i
$538$	2.43503	+	1.00862i	0.104982	+	0.0434848i
$539$	−2.41421	−	5.82843i	−0.103988	−	0.251048i
$540$		0			0
$541$	−16.9497	+	7.02082i	−0.728727	+	0.301848i	−0.716029	−	0.698071i	$-0.754042\pi$
$541$	−16.9497	+	7.02082i	−0.728727	+	0.301848i	−0.0126980	+	0.999919i	$0.504042\pi$
$542$	−1.79899	−	1.79899i	−0.0772732	−	0.0772732i
$543$	−32.6274			−1.40018
$544$	0.535534	−	18.1924i	0.0229608	−	0.779992i
$545$		0			0
$546$	1.17157	+	1.17157i	0.0501387	+	0.0501387i
$547$	−22.8995	+	9.48528i	−0.979112	+	0.405561i	−0.814096	−	0.580730i	$-0.802767\pi$
$547$	−22.8995	+	9.48528i	−0.979112	+	0.405561i	−0.165015	+	0.986291i	$0.552767\pi$
$548$			15.9584i			0.681708i
$549$	−13.5355	−	32.6777i	−0.577683	−	1.39465i
$550$		0			0
$551$	8.24264	−	19.8995i	0.351148	−	0.847747i
$552$	−12.1421	+	12.1421i	−0.516804	+	0.516804i
$553$	3.17157	−	3.17157i	0.134869	−	0.134869i
$554$	3.49390	−	8.43503i	0.148442	−	0.358370i
$555$		0			0
$556$	10.4731	+	25.2843i	0.444158	+	1.07229i
$557$		−	28.2426i		−	1.19668i	−0.801243	−	0.598340i	$-0.795827\pi$
$557$		−	28.2426i		−	1.19668i	0.801243	−	0.598340i	$-0.204173\pi$
$558$	−4.75736	+	1.97056i	−0.201395	+	0.0834206i
$559$	−4.82843	−	4.82843i	−0.204221	−	0.204221i
$560$		0			0
$561$	−8.00000	−	8.48528i	−0.337760	−	0.358249i
$562$	−7.41421			−0.312750
$563$	−27.4142	−	27.4142i	−1.15537	−	1.15537i	−0.985459	−	0.169912i	$-0.945652\pi$
$563$	−27.4142	−	27.4142i	−1.15537	−	1.15537i	−0.169912	−	0.985459i	$-0.554348\pi$
$564$	47.7990	−	19.7990i	2.01270	−	0.833688i
$565$		0			0
$566$	−3.62742	−	8.75736i	−0.152472	−	0.368099i
$567$	−5.82843	−	2.41421i	−0.244771	−	0.101387i
$568$	7.92893	−	19.1421i	0.332691	−	0.803186i
$569$	25.4853	−	25.4853i	1.06840	−	1.06840i	0.0709163	−	0.997482i	$-0.477408\pi$
$569$	25.4853	−	25.4853i	1.06840	−	1.06840i	0.997482	−	0.0709163i	$-0.0225923\pi$
$570$		0			0
$571$	−18.0711	+	43.6274i	−0.756251	+	1.82575i	−0.235956	+	0.971764i	$0.575822\pi$
$571$	−18.0711	+	43.6274i	−0.756251	+	1.82575i	−0.520295	+	0.853987i	$0.674178\pi$
$572$	2.58579	+	1.07107i	0.108117	+	0.0447836i
$573$	20.0000	+	48.2843i	0.835512	+	2.01710i
$574$		−	3.65685i		−	0.152634i
$575$		0			0
$576$	11.2929	+	11.2929i	0.470537	+	0.470537i
$577$	12.9289			0.538238			0.269119	−	0.963107i	$-0.413267\pi$
$577$	12.9289			0.538238			0.269119	+	0.963107i	$0.413267\pi$
$578$	−5.26346	+	4.67767i	−0.218931	+	0.194565i
$579$	−14.4853			−0.601988
$580$		0			0
$581$	−0.343146	+	0.142136i	−0.0142361	+	0.00589678i
$582$		−	6.97056i		−	0.288939i
$583$	−0.585786	−	1.41421i	−0.0242608	−	0.0585707i
$584$	7.84924	+	3.25126i	0.324804	+	0.134538i
$585$		0			0
$586$	−6.92893	+	6.92893i	−0.286232	+	0.286232i
$587$	16.0416	−	16.0416i	0.662109	−	0.662109i	−0.293768	−	0.955877i	$-0.594909\pi$
$587$	16.0416	−	16.0416i	0.662109	−	0.662109i	0.955877	+	0.293768i	$0.0949093\pi$
$588$	10.6569	−	25.7279i	0.439481	−	1.06100i
$589$	−14.4853	−	6.00000i	−0.596856	−	0.247226i
$590$		0			0
$591$		−	38.9706i		−	1.60303i
$592$	−10.6066	+	4.39340i	−0.435929	+	0.180568i
$593$	19.1421	+	19.1421i	0.786073	+	0.786073i	0.980848	−	0.194775i	$-0.0623976\pi$
$593$	19.1421	+	19.1421i	0.786073	+	0.786073i	−0.194775	+	0.980848i	$0.562398\pi$
$594$	−0.970563			−0.0398227
$595$		0			0
$596$	−31.0294			−1.27102
$597$	−3.17157	−	3.17157i	−0.129804	−	0.129804i
$598$	−2.24264	+	0.928932i	−0.0917084	+	0.0379869i
$599$			34.6274i			1.41484i	0.706794	+	0.707419i	$0.250141\pi$
$599$			34.6274i			1.41484i	−0.706794	+	0.707419i	$0.749859\pi$
$600$		0			0
$601$	−18.7782	−	7.77817i	−0.765978	−	0.317278i	−0.0347358	−	0.999397i	$-0.511059\pi$
$601$	−18.7782	−	7.77817i	−0.765978	−	0.317278i	−0.731242	+	0.682118i	$0.761059\pi$
$602$	−0.828427	+	2.00000i	−0.0337642	+	0.0815139i
$603$	−18.4853	+	18.4853i	−0.752779	+	0.752779i
$604$	−16.5858	+	16.5858i	−0.674866	+	0.674866i
$605$		0			0
$606$	−13.4142	−	5.55635i	−0.544915	−	0.225711i
$607$	13.1421	+	31.7279i	0.533423	+	1.28780i	0.929243	+	0.369469i	$0.120460\pi$
$607$	13.1421	+	31.7279i	0.533423	+	1.28780i	−0.395820	+	0.918328i	$0.629540\pi$
$608$		−	21.3137i		−	0.864385i
$609$	11.6569	−	4.82843i	0.472360	−	0.195658i
$610$		0			0
$611$	15.3137			0.619526
$612$	0.849242	−	28.8492i	0.0343286	−	1.16616i
$613$	17.3137			0.699294			0.349647	−	0.936881i	$-0.386302\pi$
$613$	17.3137			0.699294			0.349647	+	0.936881i	$0.386302\pi$
$614$	−0.627417	−	0.627417i	−0.0253205	−	0.0253205i
$615$		0			0
$616$		−	1.85786i		−	0.0748555i
$617$	1.29289	+	3.12132i	0.0520499	+	0.125660i	0.947766	−	0.318968i	$-0.103336\pi$
$617$	1.29289	+	3.12132i	0.0520499	+	0.125660i	−0.895716	+	0.444627i	$0.853336\pi$
$618$	4.48528	+	1.85786i	0.180424	+	0.0747343i
$619$	3.68629	−	8.89949i	0.148165	−	0.357701i	−0.832320	−	0.554295i	$-0.812988\pi$
$619$	3.68629	−	8.89949i	0.148165	−	0.357701i	0.980485	+	0.196594i	$0.0629880\pi$
$620$		0			0
$621$	−6.34315	+	6.34315i	−0.254542	+	0.254542i
$622$	0.715729	−	1.72792i	0.0286981	−	0.0692834i
$623$	−9.41421	−	3.89949i	−0.377173	−	0.156230i
$624$	4.24264	+	10.2426i	0.169842	+	0.410034i
$625$		0			0
$626$	4.87868	−	2.02082i	0.194991	−	0.0807680i
$627$	−9.65685	−	9.65685i	−0.385658	−	0.385658i
$628$	−3.02944			−0.120888
$629$	14.3934	+	6.46447i	0.573902	+	0.257755i
$630$		0			0
$631$	4.72792	+	4.72792i	0.188216	+	0.188216i	0.794924	−	0.606709i	$-0.207511\pi$
$631$	4.72792	+	4.72792i	0.188216	+	0.188216i	−0.606709	+	0.794924i	$0.707511\pi$
$632$	−6.07107	+	2.51472i	−0.241494	+	0.100030i
$633$		−	39.1127i		−	1.55459i
$634$	0.920310	+	2.22183i	0.0365502	+	0.0882400i
$635$		0			0
$636$	2.58579	−	6.24264i	0.102533	−	0.247537i
$637$	5.82843	−	5.82843i	0.230931	−	0.230931i
$638$	−1.41421	+	1.41421i	−0.0559893	+	0.0559893i
$639$	19.1421	−	46.2132i	0.757251	−	1.82817i
$640$		0			0
$641$	−5.73654	−	13.8492i	−0.226580	−	0.547012i	0.769177	−	0.639036i	$-0.220666\pi$
$641$	−5.73654	−	13.8492i	−0.226580	−	0.547012i	−0.995757	+	0.0920237i	$0.970666\pi$
$642$			6.82843i			0.269497i
$643$	37.0416	−	15.3431i	1.46078	−	0.605075i	0.496044	−	0.868297i	$-0.334785\pi$
$643$	37.0416	−	15.3431i	1.46078	−	0.605075i	0.964735	+	0.263223i	$0.0847854\pi$
$644$	−5.79899	−	5.79899i	−0.228512	−	0.228512i
$645$		0			0
$646$	−6.00000	+	5.65685i	−0.236067	+	0.222566i
$647$	−2.82843			−0.111197			−0.0555985	−	0.998453i	$-0.517707\pi$
$647$	−2.82843			−0.111197			−0.0555985	+	0.998453i	$0.517707\pi$
$648$	6.53553	+	6.53553i	0.256740	+	0.256740i
$649$	6.00000	−	2.48528i	0.235521	−	0.0975558i
$650$		0			0
$651$	−3.51472	−	8.48528i	−0.137753	−	0.332564i
$652$	−9.58579	−	3.97056i	−0.375408	−	0.155499i
$653$	6.77817	−	16.3640i	0.265250	−	0.640371i	−0.733997	−	0.679152i	$-0.762348\pi$
$653$	6.77817	−	16.3640i	0.265250	−	0.640371i	0.999248	+	0.0387812i	$0.0123475\pi$
$654$	3.27208	−	3.27208i	0.127948	−	0.127948i
$655$		0			0
$656$	9.36396	−	22.6066i	0.365601	−	0.882640i
$657$	18.9497	+	7.84924i	0.739300	+	0.306228i
$658$	−1.85786	−	4.48528i	−0.0724271	−	0.174854i
$659$		−	8.48528i		−	0.330540i	−0.986248	−	0.165270i	$-0.947151\pi$
$659$		−	8.48528i		−	0.330540i	0.986248	−	0.165270i	$-0.0528495\pi$
$660$		0			0
$661$	29.1421	+	29.1421i	1.13350	+	1.13350i	0.989591	+	0.143906i	$0.0459664\pi$
$661$	29.1421	+	29.1421i	1.13350	+	1.13350i	0.143906	+	0.989591i	$0.454034\pi$
$662$	−7.37258			−0.286544
$663$	6.24264	−	13.8995i	0.242444	−	0.539812i
$664$	0.544156			0.0211173
$665$		0			0
$666$	5.60660	−	2.32233i	0.217251	−	0.0899885i
$667$			18.4853i			0.715753i
$668$	7.00000	+	16.8995i	0.270838	+	0.653861i
$669$	−2.00000	−	0.828427i	−0.0773245	−	0.0320288i
$670$		0			0
$671$	−7.07107	+	7.07107i	−0.272976	+	0.272976i
$672$	8.82843	−	8.82843i	0.340564	−	0.340564i
$673$	0.121320	−	0.292893i	0.00467656	−	0.0112902i	−0.921524	−	0.388321i	$-0.873055\pi$
$673$	0.121320	−	0.292893i	0.00467656	−	0.0112902i	0.926201	+	0.377031i	$0.123055\pi$
$674$	13.1924	+	5.46447i	0.508152	+	0.210483i
$675$		0			0
$676$		−	20.1127i		−	0.773565i
$677$	−40.5772	+	16.8076i	−1.55951	+	0.645969i	−0.985004	−	0.172533i	$-0.944805\pi$
$677$	−40.5772	+	16.8076i	−1.55951	+	0.645969i	−0.574503	+	0.818502i	$0.694805\pi$
$678$	−12.3848	−	12.3848i	−0.475634	−	0.475634i
$679$	6.97056			0.267506
$680$		0			0
$681$	13.1716			0.504736
$682$	1.02944	+	1.02944i	0.0394192	+	0.0394192i
$683$	28.8995	−	11.9706i	1.10581	−	0.458041i	0.246316	−	0.969190i	$-0.420780\pi$
$683$	28.8995	−	11.9706i	1.10581	−	0.458041i	0.859492	+	0.511149i	$0.170780\pi$
$684$		−	33.7990i		−	1.29234i
$685$		0			0
$686$	−5.31371	−	2.20101i	−0.202878	−	0.0840350i
$687$	22.8284	−	55.1127i	0.870959	−	2.10268i
$688$	−10.2426	+	10.2426i	−0.390497	+	0.390497i
$689$	1.41421	−	1.41421i	0.0538772	−	0.0538772i
$690$		0			0
$691$	37.6274	+	15.5858i	1.43141	+	0.592911i	0.957700	−	0.287767i	$-0.0929130\pi$
$691$	37.6274	+	15.5858i	1.43141	+	0.592911i	0.473714	+	0.880679i	$0.342913\pi$
$692$	−2.36396	−	5.70711i	−0.0898643	−	0.216952i
$693$		−	4.48528i		−	0.170382i
$694$	1.48528	−	0.615224i	0.0563805	−	0.0233536i
$695$		0			0
$696$	−18.4853			−0.700683
$697$	−31.4350	+	11.9497i	−1.19069	+	0.452629i
$698$	1.75736			0.0665170
$699$	−18.7279	−	18.7279i	−0.708355	−	0.708355i
$700$		0			0
$701$		−	21.6985i		−	0.819540i	−0.912189	−	0.409770i	$-0.865609\pi$
$701$		−	21.6985i		−	0.819540i	0.912189	−	0.409770i	$-0.134391\pi$
$702$	−0.485281	−	1.17157i	−0.0183158	−	0.0442182i
$703$	17.0711	+	7.07107i	0.643848	+	0.266690i
$704$	1.72792	−	4.17157i	0.0651235	−	0.157222i
$705$		0			0
$706$	4.10051	−	4.10051i	0.154325	−	0.154325i
$707$	5.55635	−	13.4142i	0.208968	−	0.504493i
$708$	26.4853	+	10.9706i	0.995378	+	0.412299i
$709$	−4.43503	−	10.7071i	−0.166561	−	0.402114i	0.818456	−	0.574569i	$-0.194830\pi$
$709$	−4.43503	−	10.7071i	−0.166561	−	0.402114i	−0.985017	+	0.172455i	$0.944830\pi$
$710$		0			0
$711$	−14.6569	+	6.07107i	−0.549675	+	0.227683i
$712$	10.5563	+	10.5563i	0.395616	+	0.395616i
$713$	13.4558			0.503925
$714$	−4.82843	−	0.142136i	−0.180699	−	0.00531929i
$715$		0			0
$716$	−7.75736	−	7.75736i	−0.289906	−	0.289906i
$717$	22.1421	−	9.17157i	0.826913	−	0.342519i
$718$			9.59798i			0.358193i
$719$	5.38478	+	13.0000i	0.200818	+	0.484818i	0.991920	−	0.126867i	$-0.0404920\pi$
$719$	5.38478	+	13.0000i	0.200818	+	0.484818i	−0.791102	+	0.611685i	$0.790492\pi$
$720$		0			0
$721$	−1.85786	+	4.48528i	−0.0691905	+	0.167041i
$722$	−1.26346	+	1.26346i	−0.0470210	+	0.0470210i
$723$	22.7279	−	22.7279i	0.845261	−	0.845261i
$724$	−8.73654	+	21.0919i	−0.324691	+	0.783874i
$725$		0			0
$726$	−4.07107	−	9.82843i	−0.151091	−	0.364767i
$727$			19.1127i			0.708851i	0.935084	+	0.354425i	$0.115324\pi$
$727$			19.1127i			0.708851i	−0.935084	+	0.354425i	$0.884676\pi$
$728$	2.24264	−	0.928932i	0.0831178	−	0.0344285i
$729$	27.7782	+	27.7782i	1.02882	+	1.02882i
$730$		0			0
$731$	19.8995	+	0.585786i	0.736009	+	0.0216661i
$732$	−44.1421			−1.63154
$733$	8.51472	+	8.51472i	0.314498	+	0.314498i	0.846649	−	0.532151i	$-0.178616\pi$
$733$	8.51472	+	8.51472i	0.314498	+	0.314498i	−0.532151	+	0.846649i	$0.678616\pi$
$734$	−10.0711	+	4.17157i	−0.371730	+	0.153976i
$735$		0			0
$736$	7.00000	+	16.8995i	0.258023	+	0.622924i
$737$	6.82843	+	2.82843i	0.251528	+	0.104186i
$738$	−4.94975	+	11.9497i	−0.182203	+	0.439876i
$739$	24.2426	−	24.2426i	0.891780	−	0.891780i	−0.102911	−	0.994691i	$-0.532816\pi$
$739$	24.2426	−	24.2426i	0.891780	−	0.891780i	0.994691	+	0.102911i	$0.0328156\pi$
$740$		0			0
$741$	6.82843	−	16.4853i	0.250849	−	0.605602i
$742$	−0.585786	−	0.242641i	−0.0215049	−	0.00890762i
$743$	−18.8579	−	45.5269i	−0.691828	−	1.67022i	−0.741065	−	0.671433i	$-0.765679\pi$
$743$	−18.8579	−	45.5269i	−0.691828	−	1.67022i	0.0492371	−	0.998787i	$-0.484321\pi$
$744$			13.4558i			0.493315i
$745$		0			0
$746$	5.72792	+	5.72792i	0.209714	+	0.209714i
$747$	1.31371			0.0480661
$748$	−7.62742	+	2.89949i	−0.278886	+	0.106016i
$749$	−6.82843			−0.249505
$750$		0			0
$751$	−24.2132	+	10.0294i	−0.883552	+	0.365979i	−0.777873	−	0.628421i	$-0.783702\pi$
$751$	−24.2132	+	10.0294i	−0.883552	+	0.365979i	−0.105679	+	0.994400i	$0.533702\pi$
$752$		−	32.4853i		−	1.18462i
$753$	−3.51472	−	8.48528i	−0.128083	−	0.309221i
$754$	−2.41421	−	1.00000i	−0.0879205	−	0.0364179i
$755$		0			0
$756$	3.02944	−	3.02944i	0.110180	−	0.110180i
$757$	−37.7990	+	37.7990i	−1.37383	+	1.37383i	−0.519136	+	0.854692i	$0.673746\pi$
$757$	−37.7990	+	37.7990i	−1.37383	+	1.37383i	−0.854692	+	0.519136i	$0.826254\pi$
$758$	−0.171573	+	0.414214i	−0.00623181	+	0.0150449i
$759$	10.8284	+	4.48528i	0.393047	+	0.162805i
$760$		0			0
$761$			21.6985i			0.786569i	0.919417	+	0.393285i	$0.128661\pi$
$761$			21.6985i			0.786569i	−0.919417	+	0.393285i	$0.871339\pi$
$762$	17.3137	−	7.17157i	0.627209	−	0.259799i
$763$	3.27208	+	3.27208i	0.118457	+	0.118457i
$764$	36.5685			1.32300
$765$		0			0
$766$	−2.28427			−0.0825341
$767$	6.00000	+	6.00000i	0.216647	+	0.216647i
$768$	9.58579	−	3.97056i	0.345897	−	0.143275i
$769$		−	12.7279i		−	0.458981i	−0.973311	−	0.229490i	$-0.926294\pi$
$769$		−	12.7279i		−	0.458981i	0.973311	−	0.229490i	$-0.0737059\pi$
$770$		0			0
$771$	53.4558	+	22.1421i	1.92517	+	0.797430i
$772$	−3.87868	+	9.36396i	−0.139597	+	0.337016i
$773$	3.41421	−	3.41421i	0.122801	−	0.122801i	−0.643036	−	0.765836i	$-0.722325\pi$
$773$	3.41421	−	3.41421i	0.122801	−	0.122801i	0.765836	+	0.643036i	$0.222325\pi$
$774$	5.41421	−	5.41421i	0.194610	−	0.194610i
$775$		0			0
$776$	−9.43503	−	3.90812i	−0.338698	−	0.140293i
$777$	4.14214	+	10.0000i	0.148598	+	0.358748i
$778$		−	6.68629i		−	0.239715i
$779$	−36.3848	+	15.0711i	−1.30362	+	0.539977i
$780$		0			0
$781$	−14.1421			−0.506045
$782$	2.89949	−	6.45584i	0.103686	−	0.230861i
$783$	−9.65685			−0.345108
$784$	−12.3640	−	12.3640i	−0.441570	−	0.441570i
$785$		0			0
$786$			0.201010i			0.00716979i
$787$	19.0000	+	45.8701i	0.677277	+	1.63509i	0.768955	+	0.639302i	$0.220777\pi$
$787$	19.0000	+	45.8701i	0.677277	+	1.63509i	−0.0916786	+	0.995789i	$0.529223\pi$
$788$	−25.1924	−	10.4350i	−0.897442	−	0.371733i
$789$	6.48528	−	15.6569i	0.230882	−	0.557399i
$790$		0			0
$791$	12.3848	−	12.3848i	0.440352	−	0.440352i
$792$	−2.51472	+	6.07107i	−0.0893566	+	0.215726i
$793$	−12.0711	−	5.00000i	−0.428656	−	0.177555i
$794$	−4.32233	−	10.4350i	−0.153394	−	0.370325i
$795$		0			0
$796$	−2.89949	+	1.20101i	−0.102770	+	0.0425687i
$797$	12.1716	+	12.1716i	0.431139	+	0.431139i	0.889016	−	0.457877i	$-0.151390\pi$
$797$	12.1716	+	12.1716i	0.431139	+	0.431139i	−0.457877	+	0.889016i	$0.651390\pi$
$798$	−5.65685			−0.200250
$799$	−32.4853	+	30.6274i	−1.14925	+	1.08352i
$800$		0			0
$801$	25.4853	+	25.4853i	0.900478	+	0.900478i
$802$	6.53553	−	2.70711i	0.230778	−	0.0955913i
$803$		−	5.79899i		−	0.204642i
$804$	12.4853	+	30.1421i	0.440322	+	1.06303i
$805$		0			0
$806$	−0.727922	+	1.75736i	−0.0256400	+	0.0619003i
$807$	11.7574	−	11.7574i	0.413879	−	0.413879i
$808$	−15.0416	+	15.0416i	−0.529163	+	0.529163i
$809$	−11.3934	+	27.5061i	−0.400571	+	0.967063i	0.586957	+	0.809618i	$0.300326\pi$
$809$	−11.3934	+	27.5061i	−0.400571	+	0.967063i	−0.987528	+	0.157445i	$0.949674\pi$
$810$		0			0
$811$	16.9411	+	40.8995i	0.594883	+	1.43618i	0.878736	+	0.477308i	$0.158387\pi$
$811$	16.9411	+	40.8995i	0.594883	+	1.43618i	−0.283853	+	0.958868i	$0.591613\pi$
$812$		−	8.82843i		−	0.309817i
$813$	−14.8284	+	6.14214i	−0.520056	+	0.215414i
$814$	−1.21320	−	1.21320i	−0.0425228	−	0.0425228i
$815$		0			0
$816$	−29.4853	−	13.2426i	−1.03219	−	0.463585i
$817$	23.3137			0.815643
$818$	5.65685	+	5.65685i	0.197787	+	0.197787i
$819$	5.41421	−	2.24264i	0.189188	−	0.0783642i
$820$		0			0
$821$	−5.50610	−	13.2929i	−0.192164	−	0.463925i	0.798204	−	0.602388i	$-0.205784\pi$
$821$	−5.50610	−	13.2929i	−0.192164	−	0.463925i	−0.990368	+	0.138463i	$0.955784\pi$
$822$	−8.72792	−	3.61522i	−0.304421	−	0.126095i
$823$	−9.00000	+	21.7279i	−0.313720	+	0.757388i	0.685840	+	0.727752i	$0.259435\pi$
$823$	−9.00000	+	21.7279i	−0.313720	+	0.757388i	−0.999561	+	0.0296358i	$0.990565\pi$
$824$	5.02944	−	5.02944i	0.175209	−	0.175209i
$825$		0			0
$826$	1.02944	−	2.48528i	0.0358187	−	0.0864740i
$827$	32.0711	+	13.2843i	1.11522	+	0.461939i	0.862732	−	0.505661i	$-0.168751\pi$
$827$	32.0711	+	13.2843i	1.11522	+	0.461939i	0.252488	+	0.967600i	$0.418751\pi$
$828$	11.1005	+	26.7990i	0.385769	+	0.931329i
$829$			13.9411i			0.484195i	0.970252	+	0.242098i	$0.0778354\pi$
$829$			13.9411i			0.484195i	−0.970252	+	0.242098i	$0.922165\pi$
$830$		0			0
$831$	−40.7279	−	40.7279i	−1.41284	−	1.41284i
$832$	5.89949			0.204528
$833$	−0.707107	+	24.0208i	−0.0244998	+	0.832272i
$834$	−16.2010			−0.560995
$835$		0			0
$836$	−8.82843	+	3.65685i	−0.305338	+	0.126475i
$837$			7.02944i			0.242973i
$838$	−4.27208	−	10.3137i	−0.147576	−	0.356281i
$839$	−3.58579	−	1.48528i	−0.123795	−	0.0512776i	0.319926	−	0.947443i	$-0.396342\pi$
$839$	−3.58579	−	1.48528i	−0.123795	−	0.0512776i	−0.443721	+	0.896165i	$0.646342\pi$
$840$		0			0
$841$	6.43503	−	6.43503i	0.221898	−	0.221898i
$842$	5.10051	−	5.10051i	0.175775	−	0.175775i
$843$	−17.8995	+	43.2132i	−0.616491	+	1.48834i
$844$	−25.2843	−	10.4731i	−0.870321	−	0.360499i
$845$		0			0
$846$			17.1716i			0.590371i
$847$	9.82843	−	4.07107i	0.337709	−	0.139884i
$848$	−3.00000	−	3.00000i	−0.103020	−	0.103020i
$849$	−59.7990			−2.05230
$850$		0			0
$851$	−15.8579			−0.543601
$852$	−44.1421	−	44.1421i	−1.51228	−	1.51228i
$853$	−39.3345	+	16.2929i	−1.34679	+	0.557858i	−0.935397	−	0.353601i	$-0.884957\pi$
$853$	−39.3345	+	16.2929i	−1.34679	+	0.557858i	−0.411392	+	0.911459i	$0.634957\pi$
$854$			4.14214i			0.141741i
$855$		0			0
$856$	9.24264	+	3.82843i	0.315907	+	0.130853i
$857$	1.46447	−	3.53553i	0.0500252	−	0.120772i	−0.896891	−	0.442251i	$-0.854180\pi$
$857$	1.46447	−	3.53553i	0.0500252	−	0.120772i	0.946917	+	0.321479i	$0.104180\pi$
$858$	−1.17157	+	1.17157i	−0.0399968	+	0.0399968i
$859$	−0.727922	+	0.727922i	−0.0248364	+	0.0248364i	−0.719416	−	0.694580i	$-0.755590\pi$
$859$	−0.727922	+	0.727922i	−0.0248364	+	0.0248364i	0.694580	+	0.719416i	$0.255590\pi$
$860$		0			0
$861$	−21.3137	−	8.82843i	−0.726369	−	0.300872i
$862$	−6.31371	−	15.2426i	−0.215046	−	0.519166i
$863$			34.6274i			1.17873i	0.807867	+	0.589365i	$0.200622\pi$
$863$			34.6274i			1.17873i	−0.807867	+	0.589365i	$0.799378\pi$
$864$	−8.82843	+	3.65685i	−0.300349	+	0.124409i
$865$		0			0
$866$	6.28427			0.213548
$867$	14.5563	+	41.9706i	0.494360	+	1.42540i
$868$	−6.42641			−0.218126
$869$	3.17157	+	3.17157i	0.107588	+	0.107588i
$870$		0			0
$871$			9.65685i			0.327210i
$872$	−2.59441	−	6.26346i	−0.0878578	−	0.212107i
$873$	−22.7782	−	9.43503i	−0.770924	−	0.319327i
$874$	3.17157	−	7.65685i	0.107280	−	0.258997i
$875$		0			0
$876$	18.1005	−	18.1005i	0.611559	−	0.611559i
$877$	14.4056	−	34.7782i	0.486442	−	1.17438i	−0.470056	−	0.882637i	$-0.655766\pi$
$877$	14.4056	−	34.7782i	0.486442	−	1.17438i	0.956498	−	0.291739i	$-0.0942338\pi$
$878$	4.17157	+	1.72792i	0.140784	+	0.0583145i
$879$	23.6569	+	57.1127i	0.797926	+	1.92636i
$880$		0			0
$881$	17.1213	−	7.09188i	0.576832	−	0.238932i	−0.0751422	−	0.997173i	$-0.523941\pi$
$881$	17.1213	−	7.09188i	0.576832	−	0.238932i	0.651974	+	0.758241i	$0.273941\pi$
$882$	6.53553	+	6.53553i	0.220063	+	0.220063i
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$	−7.31371	−	7.75736i	−0.245987	−	0.260908i
$885$		0			0
$886$	−4.62742	−	4.62742i	−0.155461	−	0.155461i
$887$	−45.1421	+	18.6985i	−1.51572	+	0.627834i	−0.976729	−	0.214475i	$-0.931196\pi$
$887$	−45.1421	+	18.6985i	−1.51572	+	0.627834i	−0.538995	+	0.842309i	$0.681196\pi$
$888$		−	15.8579i		−	0.532155i
$889$	7.17157	+	17.3137i	0.240527	+	0.580683i
$890$		0			0
$891$	2.41421	−	5.82843i	0.0808792	−	0.195260i
$892$	−1.07107	+	1.07107i	−0.0358620	+	0.0358620i
$893$	−36.9706	+	36.9706i	−1.23717	+	1.23717i
$894$	7.02944	−	16.9706i	0.235100	−	0.567581i
$895$		0			0
$896$	−4.37258	−	10.5563i	−0.146078	−	0.352663i
$897$			15.3137i			0.511310i
$898$	−7.19239	+	2.97918i	−0.240013	+	0.0994167i
$899$	10.2426	+	10.2426i	0.341611	+	0.341611i
$900$		0			0
$901$	−0.171573	+	5.82843i	−0.00571592	+	0.194173i
$902$	3.65685			0.121760
$903$	9.65685	+	9.65685i	0.321360	+	0.321360i
$904$	−23.7071	+	9.81981i	−0.788487	+	0.326602i
$905$		0			0
$906$	−5.31371	−	12.8284i	−0.176536	−	0.426196i
$907$	23.1421	+	9.58579i	0.768422	+	0.318291i	0.732233	−	0.681054i	$-0.238478\pi$
$907$	23.1421	+	9.58579i	0.768422	+	0.318291i	0.0361889	+	0.999345i	$0.488478\pi$
$908$	3.52691	−	8.51472i	0.117045	−	0.282571i
$909$	−36.3137	+	36.3137i	−1.20445	+	1.20445i
$910$		0			0
$911$	−3.24264	+	7.82843i	−0.107433	+	0.259367i	−0.968449	−	0.249211i	$-0.919829\pi$
$911$	−3.24264	+	7.82843i	−0.107433	+	0.259367i	0.861016	+	0.508578i	$0.169829\pi$
$912$	−34.9706	−	14.4853i	−1.15799	−	0.479656i
$913$	−0.142136	−	0.343146i	−0.00470400	−	0.0113565i
$914$			7.79899i			0.257968i
$915$		0			0
$916$	−29.5147	−	29.5147i	−0.975194	−	0.975194i
$917$	−0.201010			−0.00663794
$918$	3.37258	+	1.51472i	0.111312	+	0.0499932i
$919$	−3.31371			−0.109309			−0.0546546	−	0.998505i	$-0.517406\pi$
$919$	−3.31371			−0.109309			−0.0546546	+	0.998505i	$0.517406\pi$
$920$		0			0
$921$	−5.17157	+	2.14214i	−0.170409	+	0.0705858i
$922$			9.95837i			0.327961i
$923$	−7.07107	−	17.0711i	−0.232747	−	0.561901i
$924$	−5.17157	−	2.14214i	−0.170132	−	0.0704711i
$925$		0			0
$926$	−8.97056	+	8.97056i	−0.294791	+	0.294791i
$927$	12.1421	−	12.1421i	0.398800	−	0.398800i
$928$	−7.53553	+	18.1924i	−0.247366	+	0.597194i
$929$	19.3640	+	8.02082i	0.635311	+	0.263154i	0.677008	−	0.735976i	$-0.263276\pi$
$929$	19.3640	+	8.02082i	0.635311	+	0.263154i	−0.0416968	+	0.999130i	$0.513276\pi$
$930$		0			0
$931$			28.1421i			0.922321i
$932$	−17.1213	+	7.09188i	−0.560827	+	0.232302i
$933$	−8.34315	−	8.34315i	−0.273142	−	0.273142i
$934$	−5.23045			−0.171145
$935$		0			0
$936$	−8.58579			−0.280635
$937$	−2.51472	−	2.51472i	−0.0821523	−	0.0821523i	0.664837	−	0.746989i	$-0.268501\pi$
$937$	−2.51472	−	2.51472i	−0.0821523	−	0.0821523i	−0.746989	+	0.664837i	$0.768501\pi$
$938$	2.82843	−	1.17157i	0.0923514	−	0.0382532i
$939$		−	33.3137i		−	1.08715i
$940$		0			0
$941$	17.2635	+	7.15076i	0.562773	+	0.233108i	0.645888	−	0.763432i	$-0.276487\pi$
$941$	17.2635	+	7.15076i	0.562773	+	0.233108i	−0.0831158	+	0.996540i	$0.526487\pi$
$942$	0.686292	−	1.65685i	0.0223606	−	0.0539832i
$943$	23.8995	−	23.8995i	0.778275	−	0.778275i
$944$	12.7279	−	12.7279i	0.414259	−	0.414259i
$945$		0			0
$946$	−2.00000	−	0.828427i	−0.0650256	−	0.0269345i
$947$	−5.68629	−	13.7279i	−0.184780	−	0.446098i	0.804161	−	0.594412i	$-0.202615\pi$
$947$	−5.68629	−	13.7279i	−0.184780	−	0.446098i	−0.988940	+	0.148315i	$0.952615\pi$
$948$			19.7990i			0.643041i
$949$	7.00000	−	2.89949i	0.227230	−	0.0941216i
$950$		0			0
$951$	15.1716			0.491972
$952$	−2.89949	+	6.45584i	−0.0939732	+	0.209235i
$953$	9.69848			0.314165			0.157082	−	0.987586i	$-0.449791\pi$
$953$	9.69848			0.314165			0.157082	+	0.987586i	$0.449791\pi$
$954$	1.58579	+	1.58579i	0.0513417	+	0.0513417i
$955$		0			0
$956$		−	16.7696i		−	0.542366i
$957$	4.82843	+	11.6569i	0.156081	+	0.376813i
$958$	−13.2426	−	5.48528i	−0.427850	−	0.177221i
$959$	3.61522	−	8.72792i	0.116742	−	0.281839i
$960$		0			0
$961$	−14.4645	+	14.4645i	−0.466596	+	0.466596i
$962$	0.857864	−	2.07107i	0.0276587	−	0.0667739i
$963$	22.3137	+	9.24264i	0.719049	+	0.297840i
$964$	−8.60660	−	20.7782i	−0.277200	−	0.669220i
$965$		0			0
$966$	4.48528	−	1.85786i	0.144312	−	0.0597758i
$967$	−22.8701	−	22.8701i	−0.735451	−	0.735451i	0.236243	−	0.971694i	$-0.424084\pi$
$967$	−22.8701	−	22.8701i	−0.735451	−	0.735451i	−0.971694	+	0.236243i	$0.924084\pi$
$968$	−15.5858			−0.500946
$969$	18.4853	+	48.6274i	0.593833	+	1.56214i
$970$		0			0
$971$	−39.4142	−	39.4142i	−1.26486	−	1.26486i	−0.948708	−	0.316155i	$-0.897608\pi$
$971$	−39.4142	−	39.4142i	−1.26486	−	1.26486i	−0.316155	−	0.948708i	$-0.602392\pi$
$972$	36.6985	−	15.2010i	1.17710	−	0.487573i
$973$		−	16.2010i		−	0.519381i
$974$	0.698485	+	1.68629i	0.0223809	+	0.0540323i
$975$		0			0
$976$	−10.6066	+	25.6066i	−0.339509	+	0.819647i
$977$	−1.14214	+	1.14214i	−0.0365402	+	0.0365402i	−0.725141	−	0.688601i	$-0.758225\pi$
$977$	−1.14214	+	1.14214i	−0.0365402	+	0.0365402i	0.688601	+	0.725141i	$0.258225\pi$
$978$	4.34315	−	4.34315i	0.138878	−	0.138878i
$979$	3.89949	−	9.41421i	0.124628	−	0.300880i
$980$		0			0
$981$	−6.26346	−	15.1213i	−0.199977	−	0.482787i
$982$			10.4020i			0.331942i
$983$	21.7279	−	9.00000i	0.693013	−	0.287055i	−0.00824183	−	0.999966i	$-0.502623\pi$
$983$	21.7279	−	9.00000i	0.693013	−	0.287055i	0.701255	+	0.712911i	$0.252623\pi$
$984$	23.8995	+	23.8995i	0.761888	+	0.761888i
$985$		0			0
$986$	7.12132	−	2.70711i	0.226789	−	0.0862118i
$987$	−30.6274			−0.974881
$988$	−8.82843	−	8.82843i	−0.280870	−	0.280870i
$989$	−18.4853	+	7.65685i	−0.587798	+	0.243474i
$990$		0			0
$991$	12.2721	+	29.6274i	0.389835	+	0.941146i	0.989974	+	0.141250i	$0.0451121\pi$
$991$	12.2721	+	29.6274i	0.389835	+	0.941146i	−0.600139	+	0.799896i	$0.704888\pi$
$992$	13.2426	+	5.48528i	0.420454	+	0.174158i
$993$	−17.7990	+	42.9706i	−0.564834	+	1.36363i
$994$	−4.14214	+	4.14214i	−0.131381	+	0.131381i
$995$		0			0
$996$	0.627417	−	1.51472i	0.0198805	−	0.0479957i
$997$	7.12132	+	2.94975i	0.225534	+	0.0934194i	0.492589	−	0.870262i	$-0.336050\pi$
$997$	7.12132	+	2.94975i	0.225534	+	0.0934194i	−0.267055	+	0.963681i	$0.586050\pi$
$998$	5.87006	+	14.1716i	0.185813	+	0.448593i
$999$		−	8.28427i		−	0.262103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.a.376.1		4
5.2	odd	4		425.2.n.a.274.1		4
5.3	odd	4		425.2.n.b.274.1		4
5.4	even	2		17.2.d.a.2.1	✓	4
15.14	odd	2		153.2.l.c.19.1		4
17.3	odd	16		7225.2.a.u.1.4		4
17.9	even	8	inner	425.2.m.a.26.1		4
17.14	odd	16		7225.2.a.u.1.3		4
20.19	odd	2		272.2.v.d.257.1		4
35.4	even	6		833.2.v.b.716.1		8
35.9	even	6		833.2.v.b.410.1		8
35.19	odd	6		833.2.v.a.410.1		8
35.24	odd	6		833.2.v.a.716.1		8
35.34	odd	2		833.2.l.a.393.1		4
85.4	even	4		289.2.d.c.134.1		4
85.9	even	8		17.2.d.a.9.1	yes	4
85.14	odd	16		289.2.a.f.1.2		4
85.19	even	8		289.2.d.b.110.1		4
85.24	odd	16		289.2.c.c.251.4		8
85.29	odd	16		289.2.b.b.288.4		4
85.39	odd	16		289.2.b.b.288.3		4
85.43	odd	8		425.2.n.a.349.1		4
85.44	odd	16		289.2.c.c.251.3		8
85.49	even	8		289.2.d.c.110.1		4
85.54	odd	16		289.2.a.f.1.1		4
85.59	even	8		289.2.d.a.179.1		4
85.64	even	4		289.2.d.b.134.1		4
85.74	odd	16		289.2.c.c.38.1		8
85.77	odd	8		425.2.n.b.349.1		4
85.79	odd	16		289.2.c.c.38.2		8
85.84	even	2		289.2.d.a.155.1		4
255.14	even	16		2601.2.a.bb.1.3		4
255.179	odd	8		153.2.l.c.145.1		4
255.224	even	16		2601.2.a.bb.1.4		4
340.99	even	16		4624.2.a.bp.1.1		4
340.139	even	16		4624.2.a.bp.1.4		4
340.179	odd	8		272.2.v.d.145.1		4
595.9	even	24		833.2.v.b.655.1		8
595.94	odd	24		833.2.v.a.128.1		8
595.179	even	24		833.2.v.b.128.1		8
595.264	odd	24		833.2.v.a.655.1		8
595.349	odd	8		833.2.l.a.638.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.2.1	✓	4	5.4	even	2
17.2.d.a.9.1	yes	4	85.9	even	8
153.2.l.c.19.1		4	15.14	odd	2
153.2.l.c.145.1		4	255.179	odd	8
272.2.v.d.145.1		4	340.179	odd	8
272.2.v.d.257.1		4	20.19	odd	2
289.2.a.f.1.1		4	85.54	odd	16
289.2.a.f.1.2		4	85.14	odd	16
289.2.b.b.288.3		4	85.39	odd	16
289.2.b.b.288.4		4	85.29	odd	16
289.2.c.c.38.1		8	85.74	odd	16
289.2.c.c.38.2		8	85.79	odd	16
289.2.c.c.251.3		8	85.44	odd	16
289.2.c.c.251.4		8	85.24	odd	16
289.2.d.a.155.1		4	85.84	even	2
289.2.d.a.179.1		4	85.59	even	8
289.2.d.b.110.1		4	85.19	even	8
289.2.d.b.134.1		4	85.64	even	4
289.2.d.c.110.1		4	85.49	even	8
289.2.d.c.134.1		4	85.4	even	4
425.2.m.a.26.1		4	17.9	even	8	inner
425.2.m.a.376.1		4	1.1	even	1	trivial
425.2.n.a.274.1		4	5.2	odd	4
425.2.n.a.349.1		4	85.43	odd	8
425.2.n.b.274.1		4	5.3	odd	4
425.2.n.b.349.1		4	85.77	odd	8
833.2.l.a.393.1		4	35.34	odd	2
833.2.l.a.638.1		4	595.349	odd	8
833.2.v.a.128.1		8	595.94	odd	24
833.2.v.a.410.1		8	35.19	odd	6
833.2.v.a.655.1		8	595.264	odd	24
833.2.v.a.716.1		8	35.24	odd	6
833.2.v.b.128.1		8	595.179	even	24
833.2.v.b.410.1		8	35.9	even	6
833.2.v.b.655.1		8	595.9	even	24
833.2.v.b.716.1		8	35.4	even	6
2601.2.a.bb.1.3		4	255.14	even	16
2601.2.a.bb.1.4		4	255.224	even	16
4624.2.a.bp.1.1		4	340.99	even	16
4624.2.a.bp.1.4		4	340.139	even	16
7225.2.a.u.1.3		4	17.14	odd	16
7225.2.a.u.1.4		4	17.3	odd	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.292893 + 0.292893i) q^{2} +(2.41421 - 1.00000i) q^{3} -1.82843i q^{4} +(1.00000 + 0.414214i) q^{6} +(-0.414214 + 1.00000i) q^{7} +(1.12132 - 1.12132i) q^{8} +(2.70711 - 2.70711i) q^{9} +O(q^{10})\)	\(q+(0.292893 + 0.292893i) q^{2} +(2.41421 - 1.00000i) q^{3} -1.82843i q^{4} +(1.00000 + 0.414214i) q^{6} +(-0.414214 + 1.00000i) q^{7} +(1.12132 - 1.12132i) q^{8} +(2.70711 - 2.70711i) q^{9} +(-1.00000 - 0.414214i) q^{11} +(-1.82843 - 4.41421i) q^{12} -1.41421i q^{13} +(-0.414214 + 0.171573i) q^{14} -3.00000 q^{16} +(2.82843 + 3.00000i) q^{17} +1.58579 q^{18} +(3.41421 + 3.41421i) q^{19} +2.82843i q^{21} +(-0.171573 - 0.414214i) q^{22} +(-3.82843 - 1.58579i) q^{23} +(1.58579 - 3.82843i) q^{24} +(0.414214 - 0.414214i) q^{26} +(0.828427 - 2.00000i) q^{27} +(1.82843 + 0.757359i) q^{28} +(-1.70711 - 4.12132i) q^{29} +(-3.00000 + 1.24264i) q^{31} +(-3.12132 - 3.12132i) q^{32} -2.82843 q^{33} +(-0.0502525 + 1.70711i) q^{34} +(-4.94975 - 4.94975i) q^{36} +(3.53553 - 1.46447i) q^{37} +2.00000i q^{38} +(-1.41421 - 3.41421i) q^{39} +(-3.12132 + 7.53553i) q^{41} +(-0.828427 + 0.828427i) q^{42} +(3.41421 - 3.41421i) q^{43} +(-0.757359 + 1.82843i) q^{44} +(-0.656854 - 1.58579i) q^{46} +10.8284i q^{47} +(-7.24264 + 3.00000i) q^{48} +(4.12132 + 4.12132i) q^{49} +(9.82843 + 4.41421i) q^{51} -2.58579 q^{52} +(1.00000 + 1.00000i) q^{53} +(0.828427 - 0.343146i) q^{54} +(0.656854 + 1.58579i) q^{56} +(11.6569 + 4.82843i) q^{57} +(0.707107 - 1.70711i) q^{58} +(-4.24264 + 4.24264i) q^{59} +(3.53553 - 8.53553i) q^{61} +(-1.24264 - 0.514719i) q^{62} +(1.58579 + 3.82843i) q^{63} +4.17157i q^{64} +(-0.828427 - 0.828427i) q^{66} -6.82843 q^{67} +(5.48528 - 5.17157i) q^{68} -10.8284 q^{69} +(12.0711 - 5.00000i) q^{71} -6.07107i q^{72} +(2.05025 + 4.94975i) q^{73} +(1.46447 + 0.606602i) q^{74} +(6.24264 - 6.24264i) q^{76} +(0.828427 - 0.828427i) q^{77} +(0.585786 - 1.41421i) q^{78} +(-3.82843 - 1.58579i) q^{79} +5.82843i q^{81} +(-3.12132 + 1.29289i) q^{82} +(0.242641 + 0.242641i) q^{83} +5.17157 q^{84} +2.00000 q^{86} +(-8.24264 - 8.24264i) q^{87} +(-1.58579 + 0.656854i) q^{88} +9.41421i q^{89} +(1.41421 + 0.585786i) q^{91} +(-2.89949 + 7.00000i) q^{92} +(-6.00000 + 6.00000i) q^{93} +(-3.17157 + 3.17157i) q^{94} +(-10.6569 - 4.41421i) q^{96} +(-2.46447 - 5.94975i) q^{97} +2.41421i q^{98} +(-3.82843 + 1.58579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 4 q^{11} + 4 q^{12} + 4 q^{14} - 12 q^{16} + 12 q^{18} + 8 q^{19} - 12 q^{22} - 4 q^{23} + 12 q^{24} - 4 q^{26} - 8 q^{27} - 4 q^{28} - 4 q^{29} - 12 q^{31} - 4 q^{32} - 20 q^{34} - 4 q^{41} + 8 q^{42} + 8 q^{43} - 20 q^{44} + 20 q^{46} - 12 q^{48} + 8 q^{49} + 28 q^{51} - 16 q^{52} + 4 q^{53} - 8 q^{54} - 20 q^{56} + 24 q^{57} + 12 q^{62} + 12 q^{63} + 8 q^{66} - 16 q^{67} - 12 q^{68} - 32 q^{69} + 20 q^{71} + 28 q^{73} + 20 q^{74} + 8 q^{76} - 8 q^{77} + 8 q^{78} - 4 q^{79} - 4 q^{82} - 16 q^{83} + 32 q^{84} + 8 q^{86} - 16 q^{87} - 12 q^{88} + 28 q^{92} - 24 q^{93} - 24 q^{94} - 20 q^{96} - 24 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 4 * q^11 + 4 * q^12 + 4 * q^14 - 12 * q^16 + 12 * q^18 + 8 * q^19 - 12 * q^22 - 4 * q^23 + 12 * q^24 - 4 * q^26 - 8 * q^27 - 4 * q^28 - 4 * q^29 - 12 * q^31 - 4 * q^32 - 20 * q^34 - 4 * q^41 + 8 * q^42 + 8 * q^43 - 20 * q^44 + 20 * q^46 - 12 * q^48 + 8 * q^49 + 28 * q^51 - 16 * q^52 + 4 * q^53 - 8 * q^54 - 20 * q^56 + 24 * q^57 + 12 * q^62 + 12 * q^63 + 8 * q^66 - 16 * q^67 - 12 * q^68 - 32 * q^69 + 20 * q^71 + 28 * q^73 + 20 * q^74 + 8 * q^76 - 8 * q^77 + 8 * q^78 - 4 * q^79 - 4 * q^82 - 16 * q^83 + 32 * q^84 + 8 * q^86 - 16 * q^87 - 12 * q^88 + 28 * q^92 - 24 * q^93 - 24 * q^94 - 20 * q^96 - 24 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more