LMFDB - Embedded newform 425.2.n.a.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(49,425)]

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([4, 3]))

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

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

chi := DirichletCharacter("425.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$425 = 5^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	425.n (of order $8$ , degree $4$ , 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:	$3.39364208590$
Analytic rank:	$1$
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			349.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	425.349
Dual form			425.2.n.a.274.1

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

Character values

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

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

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	0.595930	−	0.803037i	$-0.296784\pi$
$2$	−0.292893	−	0.292893i	−0.207107	−	0.207107i	−0.803037	+	0.595930i	$0.796784\pi$
$3$	−1.00000	+	2.41421i	−0.577350	+	1.39385i	0.317832	+	0.948147i	$0.397045\pi$
$3$	−1.00000	+	2.41421i	−0.577350	+	1.39385i	−0.895182	+	0.445700i	$0.852955\pi$
$4$		−	1.82843i		−	0.914214i
$5$		0			0
$5$		0			0
$6$	1.00000	−	0.414214i	0.408248	−	0.169102i
$7$	−1.00000	+	0.414214i	−0.377964	+	0.156558i	−0.563574	−	0.826066i	$-0.690574\pi$
$7$	−1.00000	+	0.414214i	−0.377964	+	0.156558i	0.185610	+	0.982624i	$0.440574\pi$
$8$	−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	−0.528310	−	0.849052i	$-0.677174\pi$
$11$	−1.00000	+	0.414214i	−0.301511	+	0.124890i	0.226799	+	0.973942i	$0.427174\pi$
$12$	4.41421	+	1.82843i	1.27427	+	0.527821i
$13$	−1.41421			−0.392232			−0.196116	−	0.980581i	$-0.562833\pi$
$13$	−1.41421			−0.392232			−0.196116	+	0.980581i	$0.562833\pi$
$14$	0.414214	+	0.171573i	0.110703	+	0.0458548i
$15$		0			0
$16$	−3.00000			−0.750000
$17$	−3.00000	−	2.82843i	−0.727607	−	0.685994i
$17$	−3.00000	−	2.82843i	−0.727607	−	0.685994i
$18$			1.58579i			0.373773i
$19$	−3.41421	+	3.41421i	−0.783274	+	0.783274i	−0.980382	−	0.197108i	$-0.936845\pi$
$19$	−3.41421	+	3.41421i	−0.783274	+	0.783274i	0.197108	+	0.980382i	$0.436845\pi$
$20$		0			0
$21$		−	2.82843i		−	0.617213i
$22$	0.414214	+	0.171573i	0.0883106	+	0.0365795i
$23$	−1.58579	−	3.82843i	−0.330659	−	0.798282i	−0.998540	−	0.0540140i	$-0.982798\pi$
$23$	−1.58579	−	3.82843i	−0.330659	−	0.798282i	0.667881	−	0.744268i	$-0.267202\pi$
$24$	−1.58579	−	3.82843i	−0.323697	−	0.781474i
$25$		0			0
$26$	0.414214	+	0.414214i	0.0812340	+	0.0812340i
$27$	2.00000	−	0.828427i	0.384900	−	0.159431i
$28$	0.757359	+	1.82843i	0.143127	+	0.345540i
$29$	1.70711	−	4.12132i	0.317002	−	0.765310i	−0.682408	−	0.730971i	$-0.739067\pi$
$29$	1.70711	−	4.12132i	0.317002	−	0.765310i	0.999410	−	0.0343389i	$-0.0109326\pi$
$30$		0			0
$31$	−3.00000	−	1.24264i	−0.538816	−	0.223185i	0.0966436	−	0.995319i	$-0.469189\pi$
$31$	−3.00000	−	1.24264i	−0.538816	−	0.223185i	−0.635460	+	0.772134i	$0.719189\pi$
$32$	3.12132	+	3.12132i	0.551777	+	0.551777i
$33$		−	2.82843i		−	0.492366i
$34$	0.0502525	+	1.70711i	0.00861824	+	0.292766i
$35$		0			0
$36$	−4.94975	+	4.94975i	−0.824958	+	0.824958i
$37$	1.46447	−	3.53553i	0.240757	−	0.581238i	−0.756602	−	0.653876i	$-0.773142\pi$
$37$	1.46447	−	3.53553i	0.240757	−	0.581238i	0.997358	+	0.0726379i	$0.0231417\pi$
$38$	2.00000			0.324443
$39$	1.41421	−	3.41421i	0.226455	−	0.546712i
$40$		0			0
$41$	−3.12132	−	7.53553i	−0.487468	−	1.17685i	−0.955990	−	0.293400i	$-0.905213\pi$
$41$	−3.12132	−	7.53553i	−0.487468	−	1.17685i	0.468521	−	0.883452i	$-0.344787\pi$
$42$	−0.828427	+	0.828427i	−0.127829	+	0.127829i
$43$	−3.41421	+	3.41421i	−0.520663	+	0.520663i	−0.917772	−	0.397109i	$-0.870014\pi$
$43$	−3.41421	+	3.41421i	−0.520663	+	0.520663i	0.397109	+	0.917772i	$0.370014\pi$
$44$	0.757359	+	1.82843i	0.114176	+	0.275646i
$45$		0			0
$46$	−0.656854	+	1.58579i	−0.0968479	+	0.233811i
$47$	−10.8284			−1.57949			−0.789744	−	0.613436i	$-0.789787\pi$
$47$	−10.8284			−1.57949			−0.789744	+	0.613436i	$0.789787\pi$
$48$	3.00000	−	7.24264i	0.433013	−	1.04539i
$49$	−4.12132	+	4.12132i	−0.588760	+	0.588760i
$50$		0			0
$51$	9.82843	−	4.41421i	1.37626	−	0.618114i
$52$			2.58579i			0.358584i
$53$	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
$57$	−4.82843	−	11.6569i	−0.639541	−	1.54399i
$58$	−1.70711	+	0.707107i	−0.224154	+	0.0928477i
$59$	4.24264	+	4.24264i	0.552345	+	0.552345i	0.927117	−	0.374772i	$-0.122279\pi$
$59$	4.24264	+	4.24264i	0.552345	+	0.552345i	−0.374772	+	0.927117i	$0.622279\pi$
$60$		0			0
$61$	3.53553	+	8.53553i	0.452679	+	1.09286i	0.971300	+	0.237859i	$0.0764456\pi$
$61$	3.53553	+	8.53553i	0.452679	+	1.09286i	−0.518621	+	0.855004i	$0.673554\pi$
$62$	0.514719	+	1.24264i	0.0653693	+	0.157816i
$63$	3.82843	+	1.58579i	0.482336	+	0.199790i
$64$			4.17157i			0.521447i
$65$		0			0
$66$	−0.828427	+	0.828427i	−0.101972	+	0.101972i
$67$			6.82843i			0.834225i	0.908855	+	0.417113i	$0.136958\pi$
$67$			6.82843i			0.834225i	−0.908855	+	0.417113i	$0.863042\pi$
$68$	−5.17157	+	5.48528i	−0.627145	+	0.665188i
$69$	10.8284			1.30359
$70$		0			0
$71$	12.0711	+	5.00000i	1.43257	+	0.593391i	0.957985	−	0.286818i	$-0.0925974\pi$
$71$	12.0711	+	5.00000i	1.43257	+	0.593391i	0.474587	+	0.880209i	$0.342597\pi$
$72$	6.07107			0.715482
$73$	4.94975	+	2.05025i	0.579324	+	0.239964i	0.653050	−	0.757315i	$-0.273489\pi$
$73$	4.94975	+	2.05025i	0.579324	+	0.239964i	−0.0737261	+	0.997279i	$0.523489\pi$
$74$	−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
$78$	−1.41421	+	0.585786i	−0.160128	+	0.0663273i
$79$	3.82843	−	1.58579i	0.430732	−	0.178415i	−0.156775	−	0.987634i	$-0.550110\pi$
$79$	3.82843	−	1.58579i	0.430732	−	0.178415i	0.587506	+	0.809219i	$0.300110\pi$
$80$		0			0
$81$		−	5.82843i		−	0.647603i
$82$	−1.29289	+	3.12132i	−0.142776	+	0.344692i
$83$	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
$88$	0.656854	−	1.58579i	0.0700209	−	0.169045i
$89$			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
$92$	−7.00000	+	2.89949i	−0.729800	+	0.302293i
$93$	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
$97$	5.94975	+	2.46447i	0.604105	+	0.250229i	0.663706	−	0.747994i	$-0.268983\pi$
$97$	5.94975	+	2.46447i	0.604105	+	0.250229i	−0.0596005	+	0.998222i	$0.518983\pi$
$98$	2.41421			0.243872
$99$	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	$0.732585\pi$
$102$	−4.17157	−	1.58579i	−0.413047	−	0.157016i
$103$			4.48528i			0.441948i	0.975280	+	0.220974i	$0.0709236\pi$
$103$			4.48528i			0.441948i	−0.975280	+	0.220974i	$0.929076\pi$
$104$	1.58579	−	1.58579i	0.155499	−	0.155499i
$105$		0			0
$106$		−	0.585786i		−	0.0568966i
$107$	−5.82843	−	2.41421i	−0.563455	−	0.233391i	0.0827292	−	0.996572i	$-0.473636\pi$
$107$	−5.82843	−	2.41421i	−0.563455	−	0.233391i	−0.646184	+	0.763181i	$0.723636\pi$
$108$	−1.51472	−	3.65685i	−0.145754	−	0.351881i
$109$	−1.63604	−	3.94975i	−0.156704	−	0.378317i	0.825956	−	0.563735i	$-0.190636\pi$
$109$	−1.63604	−	3.94975i	−0.156704	−	0.378317i	−0.982660	+	0.185418i	$0.940636\pi$
$110$		0			0
$111$	7.07107	+	7.07107i	0.671156	+	0.671156i
$112$	3.00000	−	1.24264i	0.283473	−	0.117419i
$113$	−6.19239	−	14.9497i	−0.582531	−	1.40635i	−0.890511	−	0.454961i	$-0.849653\pi$
$113$	−6.19239	−	14.9497i	−0.582531	−	1.40635i	0.307980	−	0.951393i	$-0.400347\pi$
$114$	−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
$118$		−	2.48528i		−	0.228789i
$119$	4.17157	+	1.58579i	0.382407	+	0.145369i
$120$		0			0
$121$	−6.94975	+	6.94975i	−0.631795	+	0.631795i
$122$	1.46447	−	3.53553i	0.132587	−	0.320092i
$123$	21.3137			1.92179
$124$	−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	−0.920745	−	0.390166i	$-0.872418\pi$
$131$	0.0710678	−	0.171573i	0.00620922	−	0.0149904i	0.926954	+	0.375176i	$0.122418\pi$
$132$	−5.17157			−0.450128
$133$	2.00000	−	4.82843i	0.173422	−	0.418678i
$134$	2.00000	−	2.00000i	0.172774	−	0.172774i
$135$		0			0
$136$	6.53553	−	0.192388i	0.560417	−	0.0164971i
$137$			8.72792i			0.745677i	0.927896	+	0.372838i	$0.121615\pi$
$137$			8.72792i			0.745677i	−0.927896	+	0.372838i	$0.878385\pi$
$138$	−3.17157	−	3.17157i	−0.269982	−	0.269982i
$139$	13.8284	+	5.72792i	1.17291	+	0.485836i	0.882154	−	0.470961i	$-0.156093\pi$
$139$	13.8284	+	5.72792i	1.17291	+	0.485836i	0.290758	+	0.956797i	$0.406093\pi$
$140$		0			0
$141$	10.8284	−	26.1421i	0.911918	−	2.20156i
$142$	−2.07107	−	5.00000i	−0.173800	−	0.419591i
$143$	1.41421	−	0.585786i	0.118262	−	0.0489859i
$144$	8.12132	+	8.12132i	0.676777	+	0.676777i
$145$		0			0
$146$	−0.849242	−	2.05025i	−0.0702838	−	0.169680i
$147$	−5.82843	−	14.0711i	−0.480721	−	1.16056i
$148$	−6.46447	−	2.67767i	−0.531376	−	0.220103i
$149$		−	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	−0.972228	−	0.234035i	$-0.924807\pi$
$151$	−9.07107	+	9.07107i	−0.738193	+	0.738193i	0.234035	+	0.972228i	$0.424807\pi$
$152$		−	7.65685i		−	0.621053i
$153$	0.464466	+	15.7782i	0.0375499	+	1.27559i
$154$	−0.485281			−0.0391051
$155$		0			0
$156$	−6.24264	−	2.58579i	−0.499811	−	0.207029i
$157$	1.65685			0.132231			0.0661157	−	0.997812i	$-0.478939\pi$
$157$	1.65685			0.132231			0.0661157	+	0.997812i	$0.478939\pi$
$158$	−1.58579	−	0.656854i	−0.126158	−	0.0522565i
$159$	−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
$163$	−5.24264	+	2.17157i	−0.410635	+	0.170091i	−0.578431	−	0.815731i	$-0.696335\pi$
$163$	−5.24264	+	2.17157i	−0.410635	+	0.170091i	0.167796	+	0.985822i	$0.446335\pi$
$164$	−13.7782	+	5.70711i	−1.07589	+	0.445650i
$165$		0			0
$166$		−	0.142136i		−	0.0110319i
$167$	−3.82843	+	9.24264i	−0.296253	+	0.715217i	0.703736	+	0.710461i	$0.251514\pi$
$167$	−3.82843	+	9.24264i	−0.296253	+	0.715217i	−0.999989	+	0.00475555i	$0.998486\pi$
$168$	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
$173$	−1.29289	+	3.12132i	−0.0982969	+	0.237310i	−0.965377	−	0.260859i	$-0.915994\pi$
$173$	−1.29289	+	3.12132i	−0.0982969	+	0.237310i	0.867080	+	0.498169i	$0.165994\pi$
$174$		−	4.82843i		−	0.366042i
$175$		0			0
$176$	3.00000	−	1.24264i	0.226134	−	0.0936676i
$177$	−14.4853	+	6.00000i	−1.08878	+	0.450988i
$178$	2.75736	−	2.75736i	0.206673	−	0.206673i
$179$	−4.24264	−	4.24264i	−0.317110	−	0.317110i	0.530546	−	0.847656i	$-0.321987\pi$
$179$	−4.24264	−	4.24264i	−0.317110	−	0.317110i	−0.847656	+	0.530546i	$0.821987\pi$
$180$		0			0
$181$	−11.5355	+	4.77817i	−0.857429	+	0.355159i	−0.767702	−	0.640807i	$-0.778600\pi$
$181$	−11.5355	+	4.77817i	−0.857429	+	0.355159i	−0.0897278	+	0.995966i	$0.528600\pi$
$182$	−0.585786	−	0.242641i	−0.0434214	−	0.0179857i
$183$	−24.1421			−1.78464
$184$	6.07107	+	2.51472i	0.447565	+	0.185388i
$185$		0			0
$186$	−3.51472			−0.257712
$187$	4.17157	+	1.58579i	0.305056	+	0.115964i
$188$			19.7990i			1.44399i
$189$	−1.65685	+	1.65685i	−0.120518	+	0.120518i
$190$		0			0
$191$		−	20.0000i		−	1.44715i	−0.690246	−	0.723575i	$-0.742498\pi$
$191$		−	20.0000i		−	1.44715i	0.690246	−	0.723575i	$-0.257502\pi$
$192$	−10.0711	−	4.17157i	−0.726817	−	0.301057i
$193$	−2.12132	−	5.12132i	−0.152696	−	0.368641i	0.828958	−	0.559310i	$-0.188934\pi$
$193$	−2.12132	−	5.12132i	−0.152696	−	0.368641i	−0.981654	+	0.190670i	$0.938934\pi$
$194$	−1.02082	−	2.46447i	−0.0732903	−	0.176938i
$195$		0			0
$196$	7.53553	+	7.53553i	0.538252	+	0.538252i
$197$	13.7782	−	5.70711i	0.981654	−	0.406615i	0.166616	−	0.986022i	$-0.446716\pi$
$197$	13.7782	−	5.70711i	0.981654	−	0.406615i	0.815038	+	0.579407i	$0.196716\pi$
$198$	−0.656854	−	1.58579i	−0.0466806	−	0.112697i
$199$	0.656854	−	1.58579i	0.0465632	−	0.112413i	−0.898887	−	0.438181i	$-0.855623\pi$
$199$	0.656854	−	1.58579i	0.0465632	−	0.112413i	0.945450	+	0.325768i	$0.105623\pi$
$200$		0			0
$201$	−16.4853	−	6.82843i	−1.16278	−	0.481640i
$202$	3.92893	+	3.92893i	0.276439	+	0.276439i
$203$			4.82843i			0.338889i
$204$	−8.07107	−	17.9706i	−0.565088	−	1.25819i
$205$		0			0
$206$	1.31371	−	1.31371i	0.0915304	−	0.0915304i
$207$	−6.07107	+	14.6569i	−0.421968	+	1.01872i
$208$	4.24264			0.294174
$209$	2.00000	−	4.82843i	0.138343	−	0.333989i
$210$		0			0
$211$	5.72792	+	13.8284i	0.394326	+	0.951988i	0.988986	+	0.148010i	$0.0472869\pi$
$211$	5.72792	+	13.8284i	0.394326	+	0.951988i	−0.594659	+	0.803978i	$0.702713\pi$
$212$	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
$217$	3.51472			0.238595
$218$	−0.677670	+	1.63604i	−0.0458976	+	0.110807i
$219$	−9.89949	+	9.89949i	−0.668946	+	0.668946i
$220$		0			0
$221$	4.24264	+	4.00000i	0.285391	+	0.269069i
$222$		−	4.14214i		−	0.278002i
$223$	−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
$227$	−1.92893	−	4.65685i	−0.128028	−	0.309086i	0.846848	−	0.531835i	$-0.178497\pi$
$227$	−1.92893	−	4.65685i	−0.128028	−	0.309086i	−0.974876	+	0.222748i	$0.928497\pi$
$228$	−21.3137	+	8.82843i	−1.41153	+	0.584677i
$229$	−16.1421	−	16.1421i	−1.06670	−	1.06670i	−0.997610	−	0.0690921i	$-0.977990\pi$
$229$	−16.1421	−	16.1421i	−1.06670	−	1.06670i	−0.0690921	−	0.997610i	$-0.522010\pi$
$230$		0			0
$231$	1.17157	+	2.82843i	0.0770838	+	0.186097i
$232$	2.70711	+	6.53553i	0.177730	+	0.429079i
$233$	−9.36396	−	3.87868i	−0.613453	−	0.254101i	0.0542508	−	0.998527i	$-0.482723\pi$
$233$	−9.36396	−	3.87868i	−0.613453	−	0.254101i	−0.667704	+	0.744427i	$0.732723\pi$
$234$		−	2.24264i		−	0.146606i
$235$		0			0
$236$	7.75736	−	7.75736i	0.504961	−	0.504961i
$237$			10.8284i			0.703382i
$238$	−0.757359	−	1.68629i	−0.0490923	−	0.109306i
$239$	−9.17157			−0.593260			−0.296630	−	0.954993i	$-0.595863\pi$
$239$	−9.17157			−0.593260			−0.296630	+	0.954993i	$0.595863\pi$
$240$		0			0
$241$	11.3640	+	4.70711i	0.732017	+	0.303211i	0.717381	−	0.696681i	$-0.245341\pi$
$241$	11.3640	+	4.70711i	0.732017	+	0.303211i	0.0146365	+	0.999893i	$0.495341\pi$
$242$	4.07107			0.261698
$243$	20.0711	+	8.31371i	1.28756	+	0.533325i
$244$	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
$248$	4.75736	−	1.97056i	0.302093	−	0.125131i
$249$	−0.828427	+	0.343146i	−0.0524994	+	0.0217460i
$250$		0			0
$251$			3.51472i			0.221847i	0.993829	+	0.110924i	$0.0353809\pi$
$251$			3.51472i			0.221847i	−0.993829	+	0.110924i	$0.964619\pi$
$252$	2.89949	−	7.00000i	0.182651	−	0.440959i
$253$	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	0.0230858	−	0.999733i	$-0.492651\pi$
$257$	−15.6569	−	15.6569i	−0.976648	−	0.976648i	−0.999733	+	0.0230858i	$0.992651\pi$
$258$	−2.00000	+	4.82843i	−0.124515	+	0.300605i
$259$			4.14214i			0.257380i
$260$		0			0
$261$	−15.7782	+	6.53553i	−0.976644	+	0.404539i
$262$	−0.0710678	+	0.0294373i	−0.00439058	+	0.00181864i
$263$	−4.58579	+	4.58579i	−0.282772	+	0.282772i	−0.834213	−	0.551442i	$-0.814078\pi$
$263$	−4.58579	+	4.58579i	−0.282772	+	0.282772i	0.551442	+	0.834213i	$0.314078\pi$
$264$	3.17157	+	3.17157i	0.195197	+	0.195197i
$265$		0			0
$266$	−2.00000	+	0.828427i	−0.122628	+	0.0507941i
$267$	−22.7279	−	9.41421i	−1.39093	−	0.576141i
$268$	12.4853			0.762660
$269$	−5.87868	−	2.43503i	−0.358429	−	0.148466i	0.196200	−	0.980564i	$-0.437140\pi$
$269$	−5.87868	−	2.43503i	−0.358429	−	0.148466i	−0.554629	+	0.832098i	$0.687140\pi$
$270$		0			0
$271$	−6.14214			−0.373108			−0.186554	−	0.982445i	$-0.559732\pi$
$271$	−6.14214			−0.373108			−0.186554	+	0.982445i	$0.559732\pi$
$272$	9.00000	+	8.48528i	0.545705	+	0.514496i
$273$			4.00000i			0.242091i
$274$	2.55635	−	2.55635i	0.154435	−	0.154435i
$275$		0			0
$276$		−	19.7990i		−	1.19176i
$277$	20.3640	+	8.43503i	1.22355	+	0.506812i	0.898537	−	0.438897i	$-0.144631\pi$
$277$	20.3640	+	8.43503i	1.22355	+	0.506812i	0.325015	+	0.945709i	$0.394631\pi$
$278$	−2.37258	−	5.72792i	−0.142298	−	0.343538i
$279$	4.75736	+	11.4853i	0.284816	+	0.687606i
$280$		0			0
$281$	−12.6569	−	12.6569i	−0.755045	−	0.755045i	0.220371	−	0.975416i	$-0.429273\pi$
$281$	−12.6569	−	12.6569i	−0.755045	−	0.755045i	−0.975416	+	0.220371i	$0.929273\pi$
$282$	−10.8284	+	4.48528i	−0.644823	+	0.267095i
$283$	−8.75736	−	21.1421i	−0.520571	−	1.25677i	−0.937549	−	0.347853i	$-0.886911\pi$
$283$	−8.75736	−	21.1421i	−0.520571	−	1.25677i	0.416978	−	0.908917i	$-0.363089\pi$
$284$	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
$288$		−	16.8995i		−	0.995812i
$289$	1.00000	+	16.9706i	0.0588235	+	0.998268i
$290$		0			0
$291$	−11.8995	+	11.8995i	−0.697561	+	0.697561i
$292$	3.74874	−	9.05025i	0.219378	−	0.529626i
$293$	23.6569			1.38205			0.691024	−	0.722832i	$-0.257160\pi$
$293$	23.6569			1.38205			0.691024	+	0.722832i	$0.257160\pi$
$294$	−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
$302$	5.31371			0.305770
$303$	13.4142	−	32.3848i	0.770626	−	1.86046i
$304$	10.2426	−	10.2426i	0.587456	−	0.587456i
$305$		0			0
$306$	4.48528	−	4.75736i	0.256406	−	0.271960i
$307$			2.14214i			0.122258i	0.998130	+	0.0611291i	$0.0194701\pi$
$307$			2.14214i			0.122258i	−0.998130	+	0.0611291i	$0.980530\pi$
$308$	−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	−0.965268	−	0.261261i	$-0.915862\pi$
$311$	−1.72792	+	4.17157i	−0.0979815	+	0.236548i	0.867287	+	0.497809i	$0.165862\pi$
$312$	2.24264	+	5.41421i	0.126965	+	0.306519i
$313$	−11.7782	+	4.87868i	−0.665742	+	0.275759i	−0.689852	−	0.723950i	$-0.742325\pi$
$313$	−11.7782	+	4.87868i	−0.665742	+	0.275759i	0.0241106	+	0.999709i	$0.492325\pi$
$314$	−0.485281	−	0.485281i	−0.0273860	−	0.0273860i
$315$		0			0
$316$	−2.89949	−	7.00000i	−0.163109	−	0.393781i
$317$	−2.22183	−	5.36396i	−0.124790	−	0.301270i	0.849122	−	0.528198i	$-0.177132\pi$
$317$	−2.22183	−	5.36396i	−0.124790	−	0.301270i	−0.973912	+	0.226927i	$0.927132\pi$
$318$	1.41421	+	0.585786i	0.0793052	+	0.0328493i
$319$			4.82843i			0.270340i
$320$		0			0
$321$	11.6569	−	11.6569i	0.650622	−	0.650622i
$322$		−	1.85786i		−	0.103535i
$323$	19.8995	−	0.585786i	1.10724	−	0.0325940i
$324$	−10.6569			−0.592047
$325$		0			0
$326$	2.17157	+	0.899495i	0.120272	+	0.0498184i
$327$	11.1716			0.617789
$328$	11.9497	+	4.94975i	0.659814	+	0.273304i
$329$	10.8284	−	4.48528i	0.596991	−	0.247282i
$330$		0			0
$331$	−12.5858	−	12.5858i	−0.691777	−	0.691777i	0.270845	−	0.962623i	$-0.412697\pi$
$331$	−12.5858	−	12.5858i	−0.691777	−	0.691777i	−0.962623	+	0.270845i	$0.912697\pi$
$332$	0.443651	−	0.443651i	0.0243485	−	0.0243485i
$333$	−13.5355	+	5.60660i	−0.741743	+	0.307240i
$334$	3.82843	−	1.58579i	0.209482	−	0.0867704i
$335$		0			0
$336$			8.48528i			0.462910i
$337$	13.1924	−	31.8492i	0.718635	−	1.73494i	0.0414336	−	0.999141i	$-0.486808\pi$
$337$	13.1924	−	31.8492i	0.718635	−	1.73494i	0.677202	−	0.735798i	$-0.263192\pi$
$338$	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
$343$	5.31371	−	12.8284i	0.286913	−	0.692670i
$344$		−	7.65685i		−	0.412830i
$345$		0			0
$346$	1.29289	−	0.535534i	0.0695064	−	0.0287905i
$347$	3.58579	−	1.48528i	0.192495	−	0.0797341i	−0.284354	−	0.958719i	$-0.591779\pi$
$347$	3.58579	−	1.48528i	0.192495	−	0.0797341i	0.476849	+	0.878985i	$0.341779\pi$
$348$	15.0711	−	15.0711i	0.807894	−	0.807894i
$349$	−3.00000	−	3.00000i	−0.160586	−	0.160586i	0.622240	−	0.782826i	$-0.286223\pi$
$349$	−3.00000	−	3.00000i	−0.160586	−	0.160586i	−0.782826	+	0.622240i	$0.786223\pi$
$350$		0			0
$351$	−2.82843	+	1.17157i	−0.150970	+	0.0625339i
$352$	−4.41421	−	1.82843i	−0.235278	−	0.0974555i
$353$	−14.0000			−0.745145			−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000			−0.745145			−0.372572	+	0.928003i	$0.621524\pi$
$354$	6.00000	+	2.48528i	0.318896	+	0.132091i
$355$		0			0
$356$	17.2132			0.912298
$357$	−8.00000	+	8.48528i	−0.423405	+	0.449089i
$358$			2.48528i			0.131351i
$359$	−16.3848	+	16.3848i	−0.864755	+	0.864755i	−0.991886	−	0.127131i	$-0.959423\pi$
$359$	−16.3848	+	16.3848i	−0.864755	+	0.864755i	0.127131	+	0.991886i	$0.459423\pi$
$360$		0			0
$361$		−	4.31371i		−	0.227037i
$362$	4.77817	+	1.97918i	0.251135	+	0.104024i
$363$	−9.82843	−	23.7279i	−0.515859	−	1.24539i
$364$	−1.07107	−	2.58579i	−0.0561392	−	0.135532i
$365$		0			0
$366$	7.07107	+	7.07107i	0.369611	+	0.369611i
$367$	−24.3137	+	10.0711i	−1.26917	+	0.525705i	−0.912710	−	0.408607i	$-0.866015\pi$
$367$	−24.3137	+	10.0711i	−1.26917	+	0.525705i	−0.356455	+	0.934313i	$0.616015\pi$
$368$	4.75736	+	11.4853i	0.247994	+	0.598712i
$369$	−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
$373$			19.5563i			1.01259i	0.862361	+	0.506295i	$0.168985\pi$
$373$			19.5563i			1.01259i	−0.862361	+	0.506295i	$0.831015\pi$
$374$	−0.757359	−	1.68629i	−0.0391621	−	0.0871961i
$375$		0			0
$376$	12.1421	−	12.1421i	0.626183	−	0.626183i
$377$	−2.41421	+	5.82843i	−0.124338	+	0.300179i
$378$	0.970563			0.0499204
$379$	−0.414214	+	1.00000i	−0.0212767	+	0.0513665i	−0.934161	−	0.356852i	$-0.883850\pi$
$379$	−0.414214	+	1.00000i	−0.0212767	+	0.0513665i	0.912884	+	0.408219i	$0.133850\pi$
$380$		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	−0.600426	−	0.799681i	$-0.705002\pi$
$383$	3.89949	−	3.89949i	0.199255	−	0.199255i	0.799681	+	0.600426i	$0.205002\pi$
$384$	10.5563	+	25.4853i	0.538701	+	1.30054i
$385$		0			0
$386$	−0.878680	+	2.12132i	−0.0447236	+	0.107972i
$387$	18.4853			0.939660
$388$	4.50610	−	10.8787i	0.228762	−	0.552281i
$389$	11.4142	−	11.4142i	0.578724	−	0.578724i	−0.355828	−	0.934551i	$-0.615801\pi$
$389$	11.4142	−	11.4142i	0.578724	−	0.578724i	0.934551	+	0.355828i	$0.115801\pi$
$390$		0			0
$391$	−6.07107	+	15.9706i	−0.307027	+	0.807666i
$392$		−	9.24264i		−	0.466824i
$393$	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
$397$	10.4350	+	25.1924i	0.523719	+	1.26437i	0.935577	+	0.353122i	$0.114880\pi$
$397$	10.4350	+	25.1924i	0.523719	+	1.26437i	−0.411858	+	0.911248i	$0.635120\pi$
$398$	−0.656854	+	0.272078i	−0.0329251	+	0.0136380i
$399$	9.65685	+	9.65685i	0.483447	+	0.483447i
$400$		0			0
$401$	6.53553	+	15.7782i	0.326369	+	0.787924i	0.998856	+	0.0478157i	$0.0152260\pi$
$401$	6.53553	+	15.7782i	0.326369	+	0.787924i	−0.672487	+	0.740109i	$0.734774\pi$
$402$	2.82843	+	6.82843i	0.141069	+	0.340571i
$403$	4.24264	+	1.75736i	0.211341	+	0.0875403i
$404$			24.5269i			1.22026i
$405$		0			0
$406$	1.41421	−	1.41421i	0.0701862	−	0.0701862i
$407$			4.14214i			0.205318i
$408$	−6.07107	+	15.9706i	−0.300563	+	0.790661i
$409$	−19.3137			−0.955001			−0.477501	−	0.878631i	$-0.658457\pi$
$409$	−19.3137			−0.955001			−0.477501	+	0.878631i	$0.658457\pi$
$410$		0			0
$411$	−21.0711	−	8.72792i	−1.03936	−	0.430517i
$412$	8.20101			0.404035
$413$	−6.00000	−	2.48528i	−0.295241	−	0.122293i
$414$	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
$418$	−2.00000	+	0.828427i	−0.0978232	+	0.0405197i
$419$	24.8995	−	10.3137i	1.21642	−	0.503858i	0.320150	−	0.947367i	$-0.396267\pi$
$419$	24.8995	−	10.3137i	1.21642	−	0.503858i	0.896270	+	0.443509i	$0.146267\pi$
$420$		0			0
$421$			17.4142i			0.848717i	0.905494	+	0.424358i	$0.139500\pi$
$421$			17.4142i			0.848717i	−0.905494	+	0.424358i	$0.860500\pi$
$422$	2.37258	−	5.72792i	0.115496	−	0.278831i
$423$	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
$428$	−4.41421	+	10.6569i	−0.213369	+	0.515118i
$429$			4.00000i			0.193122i
$430$		0			0
$431$	−36.7990	+	15.2426i	−1.77254	+	0.734212i	−0.778200	+	0.628017i	$0.783867\pi$
$431$	−36.7990	+	15.2426i	−1.77254	+	0.734212i	−0.994345	+	0.106195i	$0.966133\pi$
$432$	−6.00000	+	2.48528i	−0.288675	+	0.119573i
$433$	−10.7279	+	10.7279i	−0.515551	+	0.515551i	−0.916222	−	0.400671i	$-0.868777\pi$
$433$	−10.7279	+	10.7279i	−0.515551	+	0.515551i	0.400671	+	0.916222i	$0.368777\pi$
$434$	−1.02944	−	1.02944i	−0.0494146	−	0.0494146i
$435$		0			0
$436$	−7.22183	+	2.99138i	−0.345863	+	0.143261i
$437$	18.4853	+	7.65685i	0.884271	+	0.366277i
$438$	5.79899			0.277086
$439$	−10.0711	−	4.17157i	−0.480666	−	0.199098i	0.129176	−	0.991622i	$-0.458767\pi$
$439$	−10.0711	−	4.17157i	−0.480666	−	0.199098i	−0.609841	+	0.792523i	$0.708767\pi$
$440$		0			0
$441$	22.3137			1.06256
$442$	−0.0710678	−	2.41421i	−0.00338035	−	0.114832i
$443$		−	15.7990i		−	0.750633i	−0.926897	−	0.375316i	$-0.877534\pi$
$443$		−	15.7990i		−	0.750633i	0.926897	−	0.375316i	$-0.122466\pi$
$444$	12.9289	−	12.9289i	0.613580	−	0.613580i
$445$		0			0
$446$			0.343146i			0.0162484i
$447$	40.9706	+	16.9706i	1.93784	+	0.802680i
$448$	−1.72792	−	4.17157i	−0.0816366	−	0.197088i
$449$	7.19239	+	17.3640i	0.339430	+	0.819456i	0.997771	+	0.0667361i	$0.0212585\pi$
$449$	7.19239	+	17.3640i	0.339430	+	0.819456i	−0.658341	+	0.752720i	$0.728741\pi$
$450$		0			0
$451$	6.24264	+	6.24264i	0.293954	+	0.293954i
$452$	−27.3345	+	11.3223i	−1.28571	+	0.532558i
$453$	−12.8284	−	30.9706i	−0.602732	−	1.45512i
$454$	−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	0.323455	−	0.946244i	$-0.395156\pi$
$457$	−13.3137	−	13.3137i	−0.622789	−	0.622789i	−0.946244	+	0.323455i	$0.895156\pi$
$458$			9.45584i			0.441843i
$459$	−8.34315	−	3.17157i	−0.389425	−	0.148036i
$460$		0			0
$461$	17.0000	−	17.0000i	0.791769	−	0.791769i	−0.190013	−	0.981782i	$-0.560853\pi$
$461$	17.0000	−	17.0000i	0.791769	−	0.791769i	0.981782	+	0.190013i	$0.0608529\pi$
$462$	0.485281	−	1.17157i	0.0225773	−	0.0545065i
$463$	30.6274			1.42338			0.711688	−	0.702495i	$-0.247931\pi$
$463$	30.6274			1.42338			0.711688	+	0.702495i	$0.247931\pi$
$464$	−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
$472$	−9.51472			−0.437950
$473$	2.00000	−	4.82843i	0.0919601	−	0.222011i
$474$	3.17157	−	3.17157i	0.145675	−	0.145675i
$475$		0			0
$476$	2.89949	−	7.62742i	0.132898	−	0.349602i
$477$		−	5.41421i		−	0.247900i
$478$	2.68629	+	2.68629i	0.122868	+	0.122868i
$479$	31.9706	+	13.2426i	1.46077	+	0.605072i	0.964733	−	0.263229i	$-0.0847874\pi$
$479$	31.9706	+	13.2426i	1.46077	+	0.605072i	0.496039	+	0.868300i	$0.334787\pi$
$480$		0			0
$481$	−2.07107	+	5.00000i	−0.0944326	+	0.227980i
$482$	−1.94975	−	4.70711i	−0.0888086	−	0.214403i
$483$	−10.8284	+	4.48528i	−0.492710	+	0.204087i
$484$	12.7071	+	12.7071i	0.577596	+	0.577596i
$485$		0			0
$486$	−3.44365	−	8.31371i	−0.156207	−	0.377117i
$487$	−1.68629	−	4.07107i	−0.0764132	−	0.184478i	0.881057	−	0.473010i	$-0.156833\pi$
$487$	−1.68629	−	4.07107i	−0.0764132	−	0.184478i	−0.957470	+	0.288533i	$0.906833\pi$
$488$	−13.5355	−	5.60660i	−0.612725	−	0.253799i
$489$		−	14.8284i		−	0.670565i
$490$		0			0
$491$	17.7574	−	17.7574i	0.801378	−	0.801378i	−0.181933	−	0.983311i	$-0.558235\pi$
$491$	17.7574	−	17.7574i	0.801378	−	0.801378i	0.983311	+	0.181933i	$0.0582353\pi$
$492$		−	38.9706i		−	1.75693i
$493$	−16.7782	+	7.53553i	−0.755651	+	0.339383i
$494$	−2.82843			−0.127257
$495$		0			0
$496$	9.00000	+	3.72792i	0.404112	+	0.167389i
$497$	−14.1421			−0.634361
$498$	0.343146	+	0.142136i	0.0153767	+	0.00636925i
$499$	−34.2132	+	14.1716i	−1.53159	+	0.634407i	−0.979873	−	0.199622i	$-0.936028\pi$
$499$	−34.2132	+	14.1716i	−1.53159	+	0.634407i	−0.551720	+	0.834029i	$0.686028\pi$
$500$		0			0
$501$	−18.4853	−	18.4853i	−0.825861	−	0.825861i
$502$	1.02944	−	1.02944i	0.0459460	−	0.0459460i
$503$	13.8284	−	5.72792i	0.616579	−	0.255395i	−0.0524595	−	0.998623i	$-0.516706\pi$
$503$	13.8284	−	5.72792i	0.616579	−	0.255395i	0.669039	+	0.743228i	$0.266706\pi$
$504$	−6.07107	+	2.51472i	−0.270427	+	0.112014i
$505$		0			0
$506$		−	1.85786i		−	0.0825921i
$507$	11.0000	−	26.5563i	0.488527	−	1.17941i
$508$	−22.3848	−	22.3848i	−0.993164	−	0.993164i
$509$	3.02944			0.134277			0.0671387	−	0.997744i	$-0.478613\pi$
$509$	3.02944			0.134277			0.0671387	+	0.997744i	$0.478613\pi$
$510$		0			0
$511$	−5.79899			−0.256532
$512$	−16.0919	−	16.0919i	−0.711167	−	0.711167i
$513$	−4.00000	+	9.65685i	−0.176604	+	0.426361i
$514$			9.17157i			0.404541i
$515$		0			0
$516$	−21.3137	+	8.82843i	−0.938284	+	0.388650i
$517$	10.8284	−	4.48528i	0.476234	−	0.197262i
$518$	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	−0.318732	−	0.947845i	$-0.603257\pi$
$521$	2.87868	−	1.19239i	0.126117	−	0.0522395i	0.444850	+	0.895605i	$0.353257\pi$
$522$	6.53553	+	2.70711i	0.286053	+	0.118487i
$523$	6.82843			0.298586			0.149293	−	0.988793i	$-0.452300\pi$
$523$	6.82843			0.298586			0.149293	+	0.988793i	$0.452300\pi$
$524$	−0.313708	−	0.129942i	−0.0137044	−	0.00567656i
$525$		0			0
$526$	2.68629			0.117128
$527$	5.48528	+	12.2132i	0.238943	+	0.532015i
$528$			8.48528i			0.369274i
$529$	4.12132	−	4.12132i	0.179188	−	0.179188i
$530$		0			0
$531$		−	22.9706i		−	0.996838i
$532$	−8.82843	−	3.65685i	−0.382761	−	0.158545i
$533$	4.41421	+	10.6569i	0.191201	+	0.461600i
$534$	3.89949	+	9.41421i	0.168748	+	0.407393i
$535$		0			0
$536$	−7.65685	−	7.65685i	−0.330726	−	0.330726i
$537$	14.4853	−	6.00000i	0.625086	−	0.258919i
$538$	1.00862	+	2.43503i	0.0434848	+	0.104982i
$539$	2.41421	−	5.82843i	0.103988	−	0.251048i
$540$		0			0
$541$	−16.9497	−	7.02082i	−0.728727	−	0.301848i	−0.0126980	−	0.999919i	$-0.504042\pi$
$541$	−16.9497	−	7.02082i	−0.728727	−	0.301848i	−0.716029	+	0.698071i	$0.754042\pi$
$542$	1.79899	+	1.79899i	0.0772732	+	0.0772732i
$543$		−	32.6274i		−	1.40018i
$544$	−0.535534	−	18.1924i	−0.0229608	−	0.779992i
$545$		0			0
$546$	1.17157	−	1.17157i	0.0501387	−	0.0501387i
$547$	−9.48528	+	22.8995i	−0.405561	+	0.979112i	0.580730	+	0.814096i	$0.302767\pi$
$547$	−9.48528	+	22.8995i	−0.405561	+	0.979112i	−0.986291	+	0.165015i	$0.947233\pi$
$548$	15.9584			0.681708
$549$	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
$557$	28.2426			1.19668			0.598340	−	0.801243i	$-0.295827\pi$
$557$	28.2426			1.19668			0.598340	+	0.801243i	$0.295827\pi$
$558$	1.97056	−	4.75736i	0.0834206	−	0.201395i
$559$	4.82843	−	4.82843i	0.204221	−	0.204221i
$560$		0			0
$561$	−8.00000	+	8.48528i	−0.337760	+	0.358249i
$562$			7.41421i			0.312750i
$563$	−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
$567$	2.41421	+	5.82843i	0.101387	+	0.244771i
$568$	−19.1421	+	7.92893i	−0.803186	+	0.332691i
$569$	−25.4853	−	25.4853i	−1.06840	−	1.06840i	−0.997482	−	0.0709163i	$-0.977408\pi$
$569$	−25.4853	−	25.4853i	−1.06840	−	1.06840i	−0.0709163	−	0.997482i	$-0.522592\pi$
$570$		0			0
$571$	−18.0711	−	43.6274i	−0.756251	−	1.82575i	−0.520295	−	0.853987i	$-0.674178\pi$
$571$	−18.0711	−	43.6274i	−0.756251	−	1.82575i	−0.235956	−	0.971764i	$-0.575822\pi$
$572$	−1.07107	−	2.58579i	−0.0447836	−	0.108117i
$573$	48.2843	+	20.0000i	2.01710	+	0.835512i
$574$		−	3.65685i		−	0.152634i
$575$		0			0
$576$	11.2929	−	11.2929i	0.470537	−	0.470537i
$577$		−	12.9289i		−	0.538238i	−0.963107	−	0.269119i	$-0.913267\pi$
$577$		−	12.9289i		−	0.538238i	0.963107	−	0.269119i	$-0.0867326\pi$
$578$	4.67767	−	5.26346i	0.194565	−	0.218931i
$579$	14.4853			0.601988
$580$		0			0
$581$	−0.343146	−	0.142136i	−0.0142361	−	0.00589678i
$582$	6.97056			0.288939
$583$	−1.41421	−	0.585786i	−0.0585707	−	0.0242608i
$584$	−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	$0.0949093\pi$
$588$	−25.7279	+	10.6569i	−1.06100	+	0.439481i
$589$	14.4853	−	6.00000i	0.596856	−	0.247226i
$590$		0			0
$591$			38.9706i			1.60303i
$592$	−4.39340	+	10.6066i	−0.180568	+	0.435929i
$593$	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
$598$	0.928932	−	2.24264i	0.0379869	−	0.0917084i
$599$			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	−0.731242	−	0.682118i	$-0.761059\pi$
$601$	−18.7782	+	7.77817i	−0.765978	+	0.317278i	−0.0347358	+	0.999397i	$0.511059\pi$
$602$	−2.00000	+	0.828427i	−0.0815139	+	0.0337642i
$603$	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
$607$	−31.7279	−	13.1421i	−1.28780	−	0.533423i	−0.369469	−	0.929243i	$-0.620460\pi$
$607$	−31.7279	−	13.1421i	−1.28780	−	0.533423i	−0.918328	+	0.395820i	$0.870460\pi$
$608$	−21.3137			−0.864385
$609$	−11.6569	−	4.82843i	−0.472360	−	0.195658i
$610$		0			0
$611$	15.3137			0.619526
$612$	28.8492	−	0.849242i	1.16616	−	0.0343286i
$613$			17.3137i			0.699294i	0.936881	+	0.349647i	$0.113698\pi$
$613$			17.3137i			0.699294i	−0.936881	+	0.349647i	$0.886302\pi$
$614$	0.627417	−	0.627417i	0.0253205	−	0.0253205i
$615$		0			0
$616$			1.85786i			0.0748555i
$617$	−3.12132	−	1.29289i	−0.125660	−	0.0520499i	0.318968	−	0.947766i	$-0.396664\pi$
$617$	−3.12132	−	1.29289i	−0.125660	−	0.0520499i	−0.444627	+	0.895716i	$0.646664\pi$
$618$	1.85786	+	4.48528i	0.0747343	+	0.180424i
$619$	−3.68629	−	8.89949i	−0.148165	−	0.357701i	0.832320	−	0.554295i	$-0.187012\pi$
$619$	−3.68629	−	8.89949i	−0.148165	−	0.357701i	−0.980485	+	0.196594i	$0.937012\pi$
$620$		0			0
$621$	−6.34315	−	6.34315i	−0.254542	−	0.254542i
$622$	1.72792	−	0.715729i	0.0692834	−	0.0286981i
$623$	−3.89949	−	9.41421i	−0.156230	−	0.377173i
$624$	−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
$628$		−	3.02944i		−	0.120888i
$629$	−14.3934	+	6.46447i	−0.573902	+	0.257755i
$630$		0			0
$631$	4.72792	−	4.72792i	0.188216	−	0.188216i	−0.606709	−	0.794924i	$-0.707511\pi$
$631$	4.72792	−	4.72792i	0.188216	−	0.188216i	0.794924	+	0.606709i	$0.207511\pi$
$632$	−2.51472	+	6.07107i	−0.100030	+	0.241494i
$633$	−39.1127			−1.55459
$634$	−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	−0.995757	−	0.0920237i	$-0.970666\pi$
$641$	−5.73654	+	13.8492i	−0.226580	+	0.547012i	0.769177	+	0.639036i	$0.220666\pi$
$642$	−6.82843			−0.269497
$643$	−15.3431	+	37.0416i	−0.605075	+	1.46078i	0.263223	+	0.964735i	$0.415215\pi$
$643$	−15.3431	+	37.0416i	−0.605075	+	1.46078i	−0.868297	+	0.496044i	$0.834785\pi$
$644$	5.79899	−	5.79899i	0.228512	−	0.228512i
$645$		0			0
$646$	−6.00000	−	5.65685i	−0.236067	−	0.222566i
$647$			2.82843i			0.111197i	0.998453	+	0.0555985i	$0.0177067\pi$
$647$			2.82843i			0.111197i	−0.998453	+	0.0555985i	$0.982293\pi$
$648$	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
$652$	3.97056	+	9.58579i	0.155499	+	0.375408i
$653$	−16.3640	+	6.77817i	−0.640371	+	0.265250i	−0.679152	−	0.733997i	$-0.737652\pi$
$653$	−16.3640	+	6.77817i	−0.640371	+	0.265250i	0.0387812	+	0.999248i	$0.487652\pi$
$654$	−3.27208	−	3.27208i	−0.127948	−	0.127948i
$655$		0			0
$656$	9.36396	+	22.6066i	0.365601	+	0.882640i
$657$	−7.84924	−	18.9497i	−0.306228	−	0.739300i
$658$	−4.48528	−	1.85786i	−0.174854	−	0.0724271i
$659$		−	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	0.143906	−	0.989591i	$-0.454034\pi$
$661$	29.1421	−	29.1421i	1.13350	−	1.13350i	0.989591	−	0.143906i	$-0.0459664\pi$
$662$			7.37258i			0.286544i
$663$	−13.8995	+	6.24264i	−0.539812	+	0.242444i
$664$	−0.544156			−0.0211173
$665$		0			0
$666$	5.60660	+	2.32233i	0.217251	+	0.0899885i
$667$	−18.4853			−0.715753
$668$	16.8995	+	7.00000i	0.653861	+	0.270838i
$669$	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
$673$	−0.292893	+	0.121320i	−0.0112902	+	0.00467656i	−0.388321	−	0.921524i	$-0.626945\pi$
$673$	−0.292893	+	0.121320i	−0.0112902	+	0.00467656i	0.377031	+	0.926201i	$0.376945\pi$
$674$	−13.1924	+	5.46447i	−0.508152	+	0.210483i
$675$		0			0
$676$			20.1127i			0.773565i
$677$	−16.8076	+	40.5772i	−0.645969	+	1.55951i	0.172533	+	0.985004i	$0.444805\pi$
$677$	−16.8076	+	40.5772i	−0.645969	+	1.55951i	−0.818502	+	0.574503i	$0.805195\pi$
$678$	−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
$683$	−11.9706	+	28.8995i	−0.458041	+	1.10581i	0.511149	+	0.859492i	$0.329220\pi$
$683$	−11.9706	+	28.8995i	−0.458041	+	1.10581i	−0.969190	+	0.246316i	$0.920780\pi$
$684$		−	33.7990i		−	1.29234i
$685$		0			0
$686$	−5.31371	+	2.20101i	−0.202878	+	0.0840350i
$687$	55.1127	−	22.8284i	2.10268	−	0.870959i
$688$	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	0.473714	−	0.880679i	$-0.342913\pi$
$691$	37.6274	−	15.5858i	1.43141	−	0.592911i	0.957700	+	0.287767i	$0.0929130\pi$
$692$	5.70711	+	2.36396i	0.216952	+	0.0898643i
$693$	−4.48528			−0.170382
$694$	−1.48528	−	0.615224i	−0.0563805	−	0.0233536i
$695$		0			0
$696$	−18.4853			−0.700683
$697$	−11.9497	+	31.4350i	−0.452629	+	1.19069i
$698$			1.75736i			0.0665170i
$699$	18.7279	−	18.7279i	0.708355	−	0.708355i
$700$		0			0
$701$			21.6985i			0.819540i	0.912189	+	0.409770i	$0.134391\pi$
$701$			21.6985i			0.819540i	−0.912189	+	0.409770i	$0.865609\pi$
$702$	1.17157	+	0.485281i	0.0442182	+	0.0183158i
$703$	7.07107	+	17.0711i	0.266690	+	0.643848i
$704$	−1.72792	−	4.17157i	−0.0651235	−	0.157222i
$705$		0			0
$706$	4.10051	+	4.10051i	0.154325	+	0.154325i
$707$	13.4142	−	5.55635i	0.504493	−	0.208968i
$708$	10.9706	+	26.4853i	0.412299	+	0.995378i
$709$	4.43503	−	10.7071i	0.166561	−	0.402114i	−0.818456	−	0.574569i	$-0.805170\pi$
$709$	4.43503	−	10.7071i	0.166561	−	0.402114i	0.985017	+	0.172455i	$0.0551699\pi$
$710$		0			0
$711$	−14.6569	−	6.07107i	−0.549675	−	0.227683i
$712$	−10.5563	−	10.5563i	−0.395616	−	0.395616i
$713$			13.4558i			0.503925i
$714$	4.82843	−	0.142136i	0.180699	−	0.00531929i
$715$		0			0
$716$	−7.75736	+	7.75736i	−0.289906	+	0.289906i
$717$	9.17157	−	22.1421i	0.342519	−	0.826913i
$718$	9.59798			0.358193
$719$	−5.38478	+	13.0000i	−0.200818	+	0.484818i	−0.991920	−	0.126867i	$-0.959508\pi$
$719$	−5.38478	+	13.0000i	−0.200818	+	0.484818i	0.791102	+	0.611685i	$0.209508\pi$
$720$		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
$727$	−19.1127			−0.708851			−0.354425	−	0.935084i	$-0.615324\pi$
$727$	−19.1127			−0.708851			−0.354425	+	0.935084i	$0.615324\pi$
$728$	−0.928932	+	2.24264i	−0.0344285	+	0.0831178i
$729$	−27.7782	+	27.7782i	−1.02882	+	1.02882i
$730$		0			0
$731$	19.8995	−	0.585786i	0.736009	−	0.0216661i
$732$			44.1421i			1.63154i
$733$	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
$737$	−2.82843	−	6.82843i	−0.104186	−	0.251528i
$738$	11.9497	−	4.94975i	0.439876	−	0.182203i
$739$	−24.2426	−	24.2426i	−0.891780	−	0.891780i	0.102911	−	0.994691i	$-0.467184\pi$
$739$	−24.2426	−	24.2426i	−0.891780	−	0.891780i	−0.994691	+	0.102911i	$0.967184\pi$
$740$		0			0
$741$	6.82843	+	16.4853i	0.250849	+	0.605602i
$742$	0.242641	+	0.585786i	0.00890762	+	0.0215049i
$743$	−45.5269	−	18.8579i	−1.67022	−	0.691828i	−0.671433	−	0.741065i	$-0.734321\pi$
$743$	−45.5269	−	18.8579i	−1.67022	−	0.691828i	−0.998787	+	0.0492371i	$0.984321\pi$
$744$			13.4558i			0.493315i
$745$		0			0
$746$	5.72792	−	5.72792i	0.209714	−	0.209714i
$747$		−	1.31371i		−	0.0480661i
$748$	2.89949	−	7.62742i	0.106016	−	0.278886i
$749$	6.82843			0.249505
$750$		0			0
$751$	−24.2132	−	10.0294i	−0.883552	−	0.365979i	−0.105679	−	0.994400i	$-0.533702\pi$
$751$	−24.2132	−	10.0294i	−0.883552	−	0.365979i	−0.777873	+	0.628421i	$0.783702\pi$
$752$	32.4853			1.18462
$753$	−8.48528	−	3.51472i	−0.309221	−	0.128083i
$754$	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	$0.826254\pi$
$758$	0.414214	−	0.171573i	0.0150449	−	0.00623181i
$759$	−10.8284	+	4.48528i	−0.393047	+	0.162805i
$760$		0			0
$761$		−	21.6985i		−	0.786569i	−0.919417	−	0.393285i	$-0.871339\pi$
$761$		−	21.6985i		−	0.786569i	0.919417	−	0.393285i	$-0.128661\pi$
$762$	7.17157	−	17.3137i	0.259799	−	0.627209i
$763$	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
$768$	−3.97056	+	9.58579i	−0.143275	+	0.345897i
$769$		−	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
$772$	−9.36396	+	3.87868i	−0.337016	+	0.139597i
$773$	−3.41421	+	3.41421i	−0.122801	+	0.122801i	−0.765836	−	0.643036i	$-0.777675\pi$
$773$	−3.41421	+	3.41421i	−0.122801	+	0.122801i	0.643036	+	0.765836i	$0.277675\pi$
$774$	−5.41421	−	5.41421i	−0.194610	−	0.194610i
$775$		0			0
$776$	−9.43503	+	3.90812i	−0.338698	+	0.140293i
$777$	−10.0000	−	4.14214i	−0.358748	−	0.148598i
$778$	−6.68629			−0.239715
$779$	36.3848	+	15.0711i	1.30362	+	0.539977i
$780$		0			0
$781$	−14.1421			−0.506045
$782$	6.45584	−	2.89949i	0.230861	−	0.103686i
$783$		−	9.65685i		−	0.345108i
$784$	12.3640	−	12.3640i	0.441570	−	0.441570i
$785$		0			0
$786$		−	0.201010i		−	0.00716979i
$787$	−45.8701	−	19.0000i	−1.63509	−	0.677277i	−0.639302	−	0.768955i	$-0.720777\pi$
$787$	−45.8701	−	19.0000i	−1.63509	−	0.677277i	−0.995789	+	0.0916786i	$0.970777\pi$
$788$	−10.4350	−	25.1924i	−0.371733	−	0.897442i
$789$	−6.48528	−	15.6569i	−0.230882	−	0.557399i
$790$		0			0
$791$	12.3848	+	12.3848i	0.440352	+	0.440352i
$792$	−6.07107	+	2.51472i	−0.215726	+	0.0893566i
$793$	−5.00000	−	12.0711i	−0.177555	−	0.428656i
$794$	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	0.457877	−	0.889016i	$-0.348610\pi$
$797$	−12.1716	−	12.1716i	−0.431139	−	0.431139i	−0.889016	+	0.457877i	$0.848610\pi$
$798$		−	5.65685i		−	0.200250i
$799$	32.4853	+	30.6274i	1.14925	+	1.08352i
$800$		0			0
$801$	25.4853	−	25.4853i	0.900478	−	0.900478i
$802$	2.70711	−	6.53553i	0.0955913	−	0.230778i
$803$	−5.79899			−0.204642
$804$	−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	0.987528	+	0.157445i	$0.0503257\pi$
$809$	11.3934	+	27.5061i	0.400571	+	0.967063i	−0.586957	+	0.809618i	$0.699674\pi$
$810$		0			0
$811$	16.9411	−	40.8995i	0.594883	−	1.43618i	−0.283853	−	0.958868i	$-0.591613\pi$
$811$	16.9411	−	40.8995i	0.594883	−	1.43618i	0.878736	−	0.477308i	$-0.158387\pi$
$812$	8.82843			0.309817
$813$	6.14214	−	14.8284i	0.215414	−	0.520056i
$814$	1.21320	−	1.21320i	0.0425228	−	0.0425228i
$815$		0			0
$816$	−29.4853	+	13.2426i	−1.03219	+	0.463585i
$817$		−	23.3137i		−	0.815643i
$818$	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	−0.990368	−	0.138463i	$-0.955784\pi$
$821$	−5.50610	+	13.2929i	−0.192164	+	0.463925i	0.798204	+	0.602388i	$0.205784\pi$
$822$	3.61522	+	8.72792i	0.126095	+	0.304421i
$823$	21.7279	−	9.00000i	0.757388	−	0.313720i	0.0296358	−	0.999561i	$-0.490565\pi$
$823$	21.7279	−	9.00000i	0.757388	−	0.313720i	0.727752	+	0.685840i	$0.240565\pi$
$824$	−5.02944	−	5.02944i	−0.175209	−	0.175209i
$825$		0			0
$826$	1.02944	+	2.48528i	0.0358187	+	0.0864740i
$827$	−13.2843	−	32.0711i	−0.461939	−	1.11522i	−0.967600	−	0.252488i	$-0.918751\pi$
$827$	−13.2843	−	32.0711i	−0.461939	−	1.11522i	0.505661	−	0.862732i	$-0.331249\pi$
$828$	26.7990	+	11.1005i	0.931329	+	0.385769i
$829$			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
$832$		−	5.89949i		−	0.204528i
$833$	24.0208	−	0.707107i	0.832272	−	0.0244998i
$834$	16.2010			0.560995
$835$		0			0
$836$	−8.82843	−	3.65685i	−0.305338	−	0.126475i
$837$	−7.02944			−0.242973
$838$	−10.3137	−	4.27208i	−0.356281	−	0.147576i
$839$	3.58579	−	1.48528i	0.123795	−	0.0512776i	−0.319926	−	0.947443i	$-0.603658\pi$
$839$	3.58579	−	1.48528i	0.123795	−	0.0512776i	0.443721	+	0.896165i	$0.353658\pi$
$840$		0			0
$841$	6.43503	+	6.43503i	0.221898	+	0.221898i
$842$	5.10051	−	5.10051i	0.175775	−	0.175775i
$843$	43.2132	−	17.8995i	1.48834	−	0.616491i
$844$	25.2843	−	10.4731i	0.870321	−	0.360499i
$845$		0			0
$846$		−	17.1716i		−	0.590371i
$847$	4.07107	−	9.82843i	0.139884	−	0.337709i
$848$	−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
$853$	16.2929	−	39.3345i	0.557858	−	1.34679i	−0.353601	−	0.935397i	$-0.615043\pi$
$853$	16.2929	−	39.3345i	0.557858	−	1.34679i	0.911459	−	0.411392i	$-0.134957\pi$
$854$			4.14214i			0.141741i
$855$		0			0
$856$	9.24264	−	3.82843i	0.315907	−	0.130853i
$857$	3.53553	−	1.46447i	0.120772	−	0.0500252i	−0.321479	−	0.946917i	$-0.604180\pi$
$857$	3.53553	−	1.46447i	0.120772	−	0.0500252i	0.442251	+	0.896891i	$0.354180\pi$
$858$	1.17157	−	1.17157i	0.0399968	−	0.0399968i
$859$	0.727922	+	0.727922i	0.0248364	+	0.0248364i	0.719416	−	0.694580i	$-0.244410\pi$
$859$	0.727922	+	0.727922i	0.0248364	+	0.0248364i	−0.694580	+	0.719416i	$0.744410\pi$
$860$		0			0
$861$	−21.3137	+	8.82843i	−0.726369	+	0.300872i
$862$	15.2426	+	6.31371i	0.519166	+	0.215046i
$863$	34.6274			1.17873			0.589365	−	0.807867i	$-0.299378\pi$
$863$	34.6274			1.17873			0.589365	+	0.807867i	$0.299378\pi$
$864$	8.82843	+	3.65685i	0.300349	+	0.124409i
$865$		0			0
$866$	6.28427			0.213548
$867$	−41.9706	−	14.5563i	−1.42540	−	0.494360i
$868$		−	6.42641i		−	0.218126i
$869$	−3.17157	+	3.17157i	−0.107588	+	0.107588i
$870$		0			0
$871$		−	9.65685i		−	0.327210i
$872$	6.26346	+	2.59441i	0.212107	+	0.0878578i
$873$	−9.43503	−	22.7782i	−0.319327	−	0.770924i
$874$	−3.17157	−	7.65685i	−0.107280	−	0.258997i
$875$		0			0
$876$	18.1005	+	18.1005i	0.611559	+	0.611559i
$877$	34.7782	−	14.4056i	1.17438	−	0.486442i	0.291739	−	0.956498i	$-0.405766\pi$
$877$	34.7782	−	14.4056i	1.17438	−	0.486442i	0.882637	+	0.470056i	$0.155766\pi$
$878$	1.72792	+	4.17157i	0.0583145	+	0.140784i
$879$	−23.6569	+	57.1127i	−0.797926	+	1.92636i
$880$		0			0
$881$	17.1213	+	7.09188i	0.576832	+	0.238932i	0.651974	−	0.758241i	$-0.273941\pi$
$881$	17.1213	+	7.09188i	0.576832	+	0.238932i	−0.0751422	+	0.997173i	$0.523941\pi$
$882$	−6.53553	−	6.53553i	−0.220063	−	0.220063i
$883$		−	8.00000i		−	0.269221i	−0.990899	−	0.134611i	$-0.957022\pi$
$883$		−	8.00000i		−	0.269221i	0.990899	−	0.134611i	$-0.0429784\pi$
$884$	7.31371	−	7.75736i	0.245987	−	0.260908i
$885$		0			0
$886$	−4.62742	+	4.62742i	−0.155461	+	0.155461i
$887$	−18.6985	+	45.1421i	−0.627834	+	1.51572i	0.214475	+	0.976729i	$0.431196\pi$
$887$	−18.6985	+	45.1421i	−0.627834	+	1.51572i	−0.842309	+	0.538995i	$0.818804\pi$
$888$	−15.8579			−0.532155
$889$	−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
$897$	−15.3137			−0.511310
$898$	2.97918	−	7.19239i	0.0994167	−	0.240013i
$899$	−10.2426	+	10.2426i	−0.341611	+	0.341611i
$900$		0			0
$901$	−0.171573	−	5.82843i	−0.00571592	−	0.194173i
$902$		−	3.65685i		−	0.121760i
$903$	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
$907$	−9.58579	−	23.1421i	−0.318291	−	0.768422i	−0.999345	−	0.0361889i	$-0.988478\pi$
$907$	−9.58579	−	23.1421i	−0.318291	−	0.768422i	0.681054	−	0.732233i	$-0.261522\pi$
$908$	−8.51472	+	3.52691i	−0.282571	+	0.117045i
$909$	36.3137	+	36.3137i	1.20445	+	1.20445i
$910$		0			0
$911$	−3.24264	−	7.82843i	−0.107433	−	0.259367i	0.861016	−	0.508578i	$-0.169829\pi$
$911$	−3.24264	−	7.82843i	−0.107433	−	0.259367i	−0.968449	+	0.249211i	$0.919829\pi$
$912$	14.4853	+	34.9706i	0.479656	+	1.15799i
$913$	−0.343146	−	0.142136i	−0.0113565	−	0.00470400i
$914$			7.79899i			0.257968i
$915$		0			0
$916$	−29.5147	+	29.5147i	−0.975194	+	0.975194i
$917$			0.201010i			0.00663794i
$918$	1.51472	+	3.37258i	0.0499932	+	0.111312i
$919$	3.31371			0.109309			0.0546546	−	0.998505i	$-0.482594\pi$
$919$	3.31371			0.109309			0.0546546	+	0.998505i	$0.482594\pi$
$920$		0			0
$921$	−5.17157	−	2.14214i	−0.170409	−	0.0705858i
$922$	−9.95837			−0.327961
$923$	−17.0711	−	7.07107i	−0.561901	−	0.232747i
$924$	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
$928$	18.1924	−	7.53553i	0.597194	−	0.247366i
$929$	−19.3640	+	8.02082i	−0.635311	+	0.263154i	−0.677008	−	0.735976i	$-0.736724\pi$
$929$	−19.3640	+	8.02082i	−0.635311	+	0.263154i	0.0416968	+	0.999130i	$0.486724\pi$
$930$		0			0
$931$		−	28.1421i		−	0.922321i
$932$	−7.09188	+	17.1213i	−0.232302	+	0.560827i
$933$	−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	0.746989	−	0.664837i	$-0.231499\pi$
$937$	2.51472	+	2.51472i	0.0821523	+	0.0821523i	−0.664837	+	0.746989i	$0.731499\pi$
$938$	−1.17157	+	2.82843i	−0.0382532	+	0.0923514i
$939$		−	33.3137i		−	1.08715i
$940$		0			0
$941$	17.2635	−	7.15076i	0.562773	−	0.233108i	−0.0831158	−	0.996540i	$-0.526487\pi$
$941$	17.2635	−	7.15076i	0.562773	−	0.233108i	0.645888	+	0.763432i	$0.276487\pi$
$942$	1.65685	−	0.686292i	0.0539832	−	0.0223606i
$943$	−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
$947$	13.7279	+	5.68629i	0.446098	+	0.184780i	0.594412	−	0.804161i	$-0.297385\pi$
$947$	13.7279	+	5.68629i	0.446098	+	0.184780i	−0.148315	+	0.988940i	$0.547385\pi$
$948$	19.7990			0.643041
$949$	−7.00000	−	2.89949i	−0.227230	−	0.0941216i
$950$		0			0
$951$	15.1716			0.491972
$952$	−6.45584	+	2.89949i	−0.209235	+	0.0939732i
$953$			9.69848i			0.314165i	0.987586	+	0.157082i	$0.0502088\pi$
$953$			9.69848i			0.314165i	−0.987586	+	0.157082i	$0.949791\pi$
$954$	−1.58579	+	1.58579i	−0.0513417	+	0.0513417i
$955$		0			0
$956$			16.7696i			0.542366i
$957$	−11.6569	−	4.82843i	−0.376813	−	0.156081i
$958$	−5.48528	−	13.2426i	−0.177221	−	0.427850i
$959$	−3.61522	−	8.72792i	−0.116742	−	0.281839i
$960$		0			0
$961$	−14.4645	−	14.4645i	−0.466596	−	0.466596i
$962$	2.07107	−	0.857864i	0.0667739	−	0.0276587i
$963$	9.24264	+	22.3137i	0.297840	+	0.719049i
$964$	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	0.971694	−	0.236243i	$-0.0759160\pi$
$967$	22.8701	+	22.8701i	0.735451	+	0.735451i	−0.236243	+	0.971694i	$0.575916\pi$
$968$		−	15.5858i		−	0.500946i
$969$	−18.4853	+	48.6274i	−0.593833	+	1.56214i
$970$		0			0
$971$	−39.4142	+	39.4142i	−1.26486	+	1.26486i	−0.316155	+	0.948708i	$0.602392\pi$
$971$	−39.4142	+	39.4142i	−1.26486	+	1.26486i	−0.948708	+	0.316155i	$0.897608\pi$
$972$	15.2010	−	36.6985i	0.487573	−	1.17710i
$973$	−16.2010			−0.519381
$974$	−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
$982$	−10.4020			−0.331942
$983$	−9.00000	+	21.7279i	−0.287055	+	0.693013i	−0.999966	−	0.00824183i	$-0.997377\pi$
$983$	−9.00000	+	21.7279i	−0.287055	+	0.693013i	0.712911	+	0.701255i	$0.247377\pi$
$984$	−23.8995	+	23.8995i	−0.761888	+	0.761888i
$985$		0			0
$986$	7.12132	+	2.70711i	0.226789	+	0.0862118i
$987$			30.6274i			0.974881i
$988$	−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	−0.600139	−	0.799896i	$-0.704888\pi$
$991$	12.2721	−	29.6274i	0.389835	−	0.941146i	0.989974	−	0.141250i	$-0.0451121\pi$
$992$	−5.48528	−	13.2426i	−0.174158	−	0.420454i
$993$	42.9706	−	17.7990i	1.36363	−	0.564834i
$994$	4.14214	+	4.14214i	0.131381	+	0.131381i
$995$		0			0
$996$	0.627417	+	1.51472i	0.0198805	+	0.0479957i
$997$	−2.94975	−	7.12132i	−0.0934194	−	0.225534i	0.870262	−	0.492589i	$-0.163950\pi$
$997$	−2.94975	−	7.12132i	−0.0934194	−	0.225534i	−0.963681	+	0.267055i	$0.913950\pi$
$998$	14.1716	+	5.87006i	0.448593	+	0.185813i
$999$		−	8.28427i		−	0.262103i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.a.349.1		4
5.2	odd	4		425.2.m.a.26.1		4
5.3	odd	4		17.2.d.a.9.1	yes	4
5.4	even	2		425.2.n.b.349.1		4
15.8	even	4		153.2.l.c.145.1		4
17.2	even	8		425.2.n.b.274.1		4
20.3	even	4		272.2.v.d.145.1		4
35.3	even	12		833.2.v.a.128.1		8
35.13	even	4		833.2.l.a.638.1		4
35.18	odd	12		833.2.v.b.128.1		8
35.23	odd	12		833.2.v.b.655.1		8
35.33	even	12		833.2.v.a.655.1		8
85.2	odd	8		425.2.m.a.376.1		4
85.3	even	16		289.2.c.c.251.3		8
85.8	odd	8		289.2.d.c.134.1		4
85.13	odd	4		289.2.d.c.110.1		4
85.19	even	8	inner	425.2.n.a.274.1		4
85.23	even	16		289.2.a.f.1.1		4
85.28	even	16		289.2.a.f.1.2		4
85.33	odd	4		289.2.d.a.179.1		4
85.38	odd	4		289.2.d.b.110.1		4
85.43	odd	8		289.2.d.b.134.1		4
85.48	even	16		289.2.c.c.251.4		8
85.53	odd	8		17.2.d.a.2.1	✓	4
85.57	even	16		7225.2.a.u.1.4		4
85.58	even	16		289.2.b.b.288.4		4
85.62	even	16		7225.2.a.u.1.3		4
85.63	even	16		289.2.c.c.38.1		8
85.73	even	16		289.2.c.c.38.2		8
85.78	even	16		289.2.b.b.288.3		4
85.83	odd	8		289.2.d.a.155.1		4
255.23	odd	16		2601.2.a.bb.1.4		4
255.53	even	8		153.2.l.c.19.1		4
255.113	odd	16		2601.2.a.bb.1.3		4
340.23	odd	16		4624.2.a.bp.1.4		4
340.223	even	8		272.2.v.d.257.1		4
340.283	odd	16		4624.2.a.bp.1.1		4
595.53	odd	24		833.2.v.b.716.1		8
595.138	even	24		833.2.v.a.410.1		8
595.223	even	8		833.2.l.a.393.1		4
595.478	odd	24		833.2.v.b.410.1		8
595.563	even	24		833.2.v.a.716.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.2.1	✓	4	85.53	odd	8
17.2.d.a.9.1	yes	4	5.3	odd	4
153.2.l.c.19.1		4	255.53	even	8
153.2.l.c.145.1		4	15.8	even	4
272.2.v.d.145.1		4	20.3	even	4
272.2.v.d.257.1		4	340.223	even	8
289.2.a.f.1.1		4	85.23	even	16
289.2.a.f.1.2		4	85.28	even	16
289.2.b.b.288.3		4	85.78	even	16
289.2.b.b.288.4		4	85.58	even	16
289.2.c.c.38.1		8	85.63	even	16
289.2.c.c.38.2		8	85.73	even	16
289.2.c.c.251.3		8	85.3	even	16
289.2.c.c.251.4		8	85.48	even	16
289.2.d.a.155.1		4	85.83	odd	8
289.2.d.a.179.1		4	85.33	odd	4
289.2.d.b.110.1		4	85.38	odd	4
289.2.d.b.134.1		4	85.43	odd	8
289.2.d.c.110.1		4	85.13	odd	4
289.2.d.c.134.1		4	85.8	odd	8
425.2.m.a.26.1		4	5.2	odd	4
425.2.m.a.376.1		4	85.2	odd	8
425.2.n.a.274.1		4	85.19	even	8	inner
425.2.n.a.349.1		4	1.1	even	1	trivial
425.2.n.b.274.1		4	17.2	even	8
425.2.n.b.349.1		4	5.4	even	2
833.2.l.a.393.1		4	595.223	even	8
833.2.l.a.638.1		4	35.13	even	4
833.2.v.a.128.1		8	35.3	even	12
833.2.v.a.410.1		8	595.138	even	24
833.2.v.a.655.1		8	35.33	even	12
833.2.v.a.716.1		8	595.563	even	24
833.2.v.b.128.1		8	35.18	odd	12
833.2.v.b.410.1		8	595.478	odd	24
833.2.v.b.655.1		8	35.23	odd	12
833.2.v.b.716.1		8	595.53	odd	24
2601.2.a.bb.1.3		4	255.113	odd	16
2601.2.a.bb.1.4		4	255.23	odd	16
4624.2.a.bp.1.1		4	340.283	odd	16
4624.2.a.bp.1.4		4	340.23	odd	16
7225.2.a.u.1.3		4	85.62	even	16
7225.2.a.u.1.4		4	85.57	even	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	425.2.n.a.349.1

Level	$425$
Weight	$2$
Character	425.349
Analytic conductor	$3.394$
Analytic rank	$1$
Dimension	$4$
Inner twists	$2$