LMFDB - Embedded newform 275.2.z.a.174.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(49,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.z (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.11316496000000000000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 $ x^16 - x^14 + 15x^12 - 59x^10 + 104x^8 - 59x^6 + 15*x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			174.1
Root			$1.23158 - 1.69513i$ of defining polynomial
Character	$\chi$	$=$	275.174
Dual form			275.2.z.a.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99274 - 0.647481i) q^{2} +(1.12443 + 1.54765i) q^{3} +(1.93376 + 1.40496i) q^{4} +(-1.23863 - 3.81211i) q^{6} +(-1.80285 + 2.48141i) q^{7} +(-0.480634 - 0.661536i) q^{8} +(-0.203814 + 0.627276i) q^{9} +(1.86337 + 2.74369i) q^{11} +4.57255i q^{12} +(-2.90055 - 0.942444i) q^{13} +(5.19927 - 3.77749i) q^{14} +(-0.947813 - 2.91707i) q^{16} +(0.441143 - 0.143336i) q^{17} +(0.812299 - 1.11803i) q^{18} +(-6.38769 + 4.64093i) q^{19} -5.86752 q^{21} +(-1.93673 - 6.67397i) q^{22} +1.39026i q^{23} +(0.483384 - 1.48770i) q^{24} +(5.16983 + 3.75610i) q^{26} +(4.25813 - 1.38355i) q^{27} +(-6.97254 + 2.26552i) q^{28} +(3.01085 + 2.18751i) q^{29} +(-3.23741 + 9.96371i) q^{31} +8.06206i q^{32} +(-2.15103 + 5.96893i) q^{33} -0.971892 q^{34} +(-1.27542 + 0.926650i) q^{36} +(1.08419 - 1.49226i) q^{37} +(15.7340 - 5.11227i) q^{38} +(-1.80289 - 5.54873i) q^{39} +(3.56585 - 2.59074i) q^{41} +(11.6925 + 3.79911i) q^{42} +1.31478i q^{43} +(-0.251461 + 7.92360i) q^{44} +(0.900166 - 2.77042i) q^{46} +(1.75171 + 2.41102i) q^{47} +(3.44884 - 4.74692i) q^{48} +(-0.743998 - 2.28979i) q^{49} +(0.717868 + 0.521562i) q^{51} +(-4.28486 - 5.89760i) q^{52} +(-3.98316 - 1.29421i) q^{53} -9.38118 q^{54} +2.50805 q^{56} +(-14.3650 - 4.66749i) q^{57} +(-4.58348 - 6.30862i) q^{58} +(2.27740 + 1.65463i) q^{59} +(-0.623402 - 1.91863i) q^{61} +(12.9026 - 17.7590i) q^{62} +(-1.18908 - 1.63663i) q^{63} +(3.32441 - 10.2315i) q^{64} +(8.15123 - 10.5018i) q^{66} -6.75753i q^{67} +(1.05444 + 0.342610i) q^{68} +(-2.15163 + 1.56325i) q^{69} +(-2.01539 - 6.20274i) q^{71} +(0.512925 - 0.166660i) q^{72} +(5.80485 - 7.98970i) q^{73} +(-3.12672 + 2.27169i) q^{74} -18.8726 q^{76} +(-10.1676 - 0.322676i) q^{77} +12.2245i q^{78} +(3.57158 - 10.9922i) q^{79} +(8.53000 + 6.19741i) q^{81} +(-8.78327 + 2.85386i) q^{82} +(8.48210 - 2.75600i) q^{83} +(-11.3464 - 8.24361i) q^{84} +(0.851296 - 2.62002i) q^{86} +7.11945i q^{87} +(0.919451 - 2.55140i) q^{88} +6.76978 q^{89} +(7.56782 - 5.49835i) q^{91} +(-1.95325 + 2.68842i) q^{92} +(-19.0606 + 6.19315i) q^{93} +(-1.92961 - 5.93874i) q^{94} +(-12.4772 + 9.06524i) q^{96} +(14.6029 + 4.74475i) q^{97} +5.04469i q^{98} +(-2.10083 + 0.609644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9} + 6 q^{11} + 32 q^{14} + 8 q^{16} - 30 q^{19} - 40 q^{21} - 26 q^{24} + 20 q^{26} + 18 q^{29} - 20 q^{31} - 8 q^{34} - 30 q^{36} - 42 q^{39} + 16 q^{41} + 24 q^{44}+ \cdots + 40 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9 + 6 * q^11 + 32 * q^14 + 8 * q^16 - 30 * q^19 - 40 * q^21 - 26 * q^24 + 20 * q^26 + 18 * q^29 - 20 * q^31 - 8 * q^34 - 30 * q^36 - 42 * q^39 + 16 * q^41 + 24 * q^44 + 6 * q^46 - 2 * q^49 + 2 * q^51 - 32 * q^54 + 44 * q^56 + 54 * q^59 + 12 * q^61 + 52 * q^64 + 26 * q^66 + 2 * q^69 - 40 * q^71 - 40 * q^74 - 74 * q^79 + 16 * q^81 - 56 * q^84 - 6 * q^86 + 32 * q^89 + 88 * q^91 - 34 * q^94 - 34 * q^96 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.99274	−	0.647481i	−1.40908	−	0.457839i	−0.496966	−	0.867770i	$-0.665553\pi$
$2$	−1.99274	−	0.647481i	−1.40908	−	0.457839i	−0.912116	+	0.409932i	$0.865553\pi$
$3$	1.12443	+	1.54765i	0.649191	+	0.893534i	0.999064	−	0.0432627i	$-0.0137753\pi$
$3$	1.12443	+	1.54765i	0.649191	+	0.893534i	−0.349873	+	0.936797i	$0.613775\pi$
$4$	1.93376	+	1.40496i	0.966879	+	0.702479i
$5$		0			0
$5$		0			0
$6$	−1.23863	−	3.81211i	−0.505669	−	1.55629i
$7$	−1.80285	+	2.48141i	−0.681412	+	0.937883i	−0.999950	−	0.0100271i	$-0.996808\pi$
$7$	−1.80285	+	2.48141i	−0.681412	+	0.937883i	0.318538	+	0.947910i	$0.396808\pi$
$8$	−0.480634	−	0.661536i	−0.169930	−	0.233888i
$9$	−0.203814	+	0.627276i	−0.0679381	+	0.209092i
$10$		0			0
$11$	1.86337	+	2.74369i	0.561828	+	0.827254i
$11$	1.86337	+	2.74369i	0.561828	+	0.827254i
$12$			4.57255i			1.31998i
$13$	−2.90055	−	0.942444i	−0.804467	−	0.261387i	−0.122214	−	0.992504i	$-0.538999\pi$
$13$	−2.90055	−	0.942444i	−0.804467	−	0.261387i	−0.682252	+	0.731117i	$0.738999\pi$
$14$	5.19927	−	3.77749i	1.38956	−	1.00958i
$15$		0			0
$16$	−0.947813	−	2.91707i	−0.236953	−	0.729267i
$17$	0.441143	−	0.143336i	0.106993	−	0.0347641i	−0.255031	−	0.966933i	$-0.582086\pi$
$17$	0.441143	−	0.143336i	0.106993	−	0.0347641i	0.362024	+	0.932169i	$0.382086\pi$
$18$	0.812299	−	1.11803i	0.191461	−	0.263523i
$19$	−6.38769	+	4.64093i	−1.46544	+	1.06470i	−0.483533	+	0.875326i	$0.660647\pi$
$19$	−6.38769	+	4.64093i	−1.46544	+	1.06470i	−0.981904	+	0.189377i	$0.939353\pi$
$20$		0			0
$21$	−5.86752			−1.28040
$22$	−1.93673	−	6.67397i	−0.412912	−	1.42290i
$23$			1.39026i			0.289889i	0.989440	+	0.144944i	$0.0463003\pi$
$23$			1.39026i			0.289889i	−0.989440	+	0.144944i	$0.953700\pi$
$24$	0.483384	−	1.48770i	0.0986703	−	0.303676i
$25$		0			0
$26$	5.16983	+	3.75610i	1.01389	+	0.736632i
$27$	4.25813	−	1.38355i	0.819477	−	0.266264i
$28$	−6.97254	+	2.26552i	−1.31769	+	0.428142i
$29$	3.01085	+	2.18751i	0.559101	+	0.406211i	0.831130	−	0.556078i	$-0.187695\pi$
$29$	3.01085	+	2.18751i	0.559101	+	0.406211i	−0.272029	+	0.962289i	$0.587695\pi$
$30$		0			0
$31$	−3.23741	+	9.96371i	−0.581456	+	1.78954i	0.0316054	+	0.999500i	$0.489938\pi$
$31$	−3.23741	+	9.96371i	−0.581456	+	1.78954i	−0.613061	+	0.790036i	$0.710062\pi$
$32$			8.06206i			1.42518i
$33$	−2.15103	+	5.96893i	−0.374447	+	1.03906i
$34$	−0.971892			−0.166678
$35$		0			0
$36$	−1.27542	+	0.926650i	−0.212571	+	0.154442i
$37$	1.08419	−	1.49226i	0.178240	−	0.245326i	−0.710544	−	0.703653i	$-0.751551\pi$
$37$	1.08419	−	1.49226i	0.178240	−	0.245326i	0.888784	+	0.458327i	$0.151551\pi$
$38$	15.7340	−	5.11227i	2.55238	−	0.829320i
$39$	−1.80289	−	5.54873i	−0.288694	−	0.888509i
$40$		0			0
$41$	3.56585	−	2.59074i	0.556892	−	0.404605i	−0.273428	−	0.961892i	$-0.588158\pi$
$41$	3.56585	−	2.59074i	0.556892	−	0.404605i	0.830320	+	0.557287i	$0.188158\pi$
$42$	11.6925	+	3.79911i	1.80418	+	0.586215i
$43$			1.31478i			0.200502i	0.994962	+	0.100251i	$0.0319646\pi$
$43$			1.31478i			0.200502i	−0.994962	+	0.100251i	$0.968035\pi$
$44$	−0.251461	+	7.92360i	−0.0379092	+	1.19453i
$45$		0			0
$46$	0.900166	−	2.77042i	0.132722	−	0.408477i
$47$	1.75171	+	2.41102i	0.255513	+	0.351683i	0.917432	−	0.397892i	$-0.130258\pi$
$47$	1.75171	+	2.41102i	0.255513	+	0.351683i	−0.661920	+	0.749575i	$0.730258\pi$
$48$	3.44884	−	4.74692i	0.497797	−	0.685159i
$49$	−0.743998	−	2.28979i	−0.106285	−	0.327113i
$50$		0			0
$51$	0.717868	+	0.521562i	0.100522	+	0.0730333i
$52$	−4.28486	−	5.89760i	−0.594203	−	0.817850i
$53$	−3.98316	−	1.29421i	−0.547129	−	0.177773i	0.0223927	−	0.999749i	$-0.492872\pi$
$53$	−3.98316	−	1.29421i	−0.547129	−	0.177773i	−0.569522	+	0.821976i	$0.692872\pi$
$54$	−9.38118			−1.27662
$55$		0			0
$56$	2.50805			0.335152
$57$	−14.3650	−	4.66749i	−1.90270	−	0.618224i
$58$	−4.58348	−	6.30862i	−0.601841	−	0.828363i
$59$	2.27740	+	1.65463i	0.296493	+	0.215414i	0.726079	−	0.687611i	$-0.241341\pi$
$59$	2.27740	+	1.65463i	0.296493	+	0.215414i	−0.429586	+	0.903026i	$0.641341\pi$
$60$		0			0
$61$	−0.623402	−	1.91863i	−0.0798185	−	0.245656i	0.903182	−	0.429257i	$-0.141225\pi$
$61$	−0.623402	−	1.91863i	−0.0798185	−	0.245656i	−0.983001	+	0.183601i	$0.941225\pi$
$62$	12.9026	−	17.7590i	1.63864	−	2.25539i
$63$	−1.18908	−	1.63663i	−0.149810	−	0.206196i
$64$	3.32441	−	10.2315i	0.415551	−	1.27894i
$65$		0			0
$66$	8.15123	−	10.5018i	1.00335	−	1.29268i
$67$		−	6.75753i		−	0.825564i	−0.910830	−	0.412782i	$-0.864557\pi$
$67$		−	6.75753i		−	0.825564i	0.910830	−	0.412782i	$-0.135443\pi$
$68$	1.05444	+	0.342610i	0.127870	+	0.0415476i
$69$	−2.15163	+	1.56325i	−0.259025	+	0.188193i
$70$		0			0
$71$	−2.01539	−	6.20274i	−0.239183	−	0.736130i	−0.996539	−	0.0831276i	$-0.973509\pi$
$71$	−2.01539	−	6.20274i	−0.239183	−	0.736130i	0.757356	−	0.653003i	$-0.226491\pi$
$72$	0.512925	−	0.166660i	0.0604488	−	0.0196410i
$73$	5.80485	−	7.98970i	0.679407	−	0.935123i	−0.320520	−	0.947242i	$-0.603858\pi$
$73$	5.80485	−	7.98970i	0.679407	−	0.935123i	0.999927	+	0.0121186i	$0.00385757\pi$
$74$	−3.12672	+	2.27169i	−0.363474	+	0.264079i
$75$		0			0
$76$	−18.8726			−2.16483
$77$	−10.1676	−	0.322676i	−1.15870	−	0.0367723i
$78$			12.2245i			1.38416i
$79$	3.57158	−	10.9922i	0.401834	−	1.23672i	−0.521677	−	0.853143i	$-0.674693\pi$
$79$	3.57158	−	10.9922i	0.401834	−	1.23672i	0.923510	−	0.383573i	$-0.125307\pi$
$80$		0			0
$81$	8.53000	+	6.19741i	0.947777	+	0.688601i
$82$	−8.78327	+	2.85386i	−0.969950	+	0.315156i
$83$	8.48210	−	2.75600i	0.931032	−	0.302510i	0.196047	−	0.980594i	$-0.437189\pi$
$83$	8.48210	−	2.75600i	0.931032	−	0.302510i	0.734984	+	0.678084i	$0.237189\pi$
$84$	−11.3464	−	8.24361i	−1.23799	−	0.899452i
$85$		0			0
$86$	0.851296	−	2.62002i	0.0917976	−	0.282524i
$87$			7.11945i			0.763285i
$88$	0.919451	−	2.55140i	0.0980138	−	0.271980i
$89$	6.76978			0.717595			0.358797	−	0.933415i	$-0.383187\pi$
$89$	6.76978			0.717595			0.358797	+	0.933415i	$0.383187\pi$
$90$		0			0
$91$	7.56782	−	5.49835i	0.793324	−	0.576383i
$92$	−1.95325	+	2.68842i	−0.203641	+	0.280287i
$93$	−19.0606	+	6.19315i	−1.97649	+	0.642200i
$94$	−1.92961	−	5.93874i	−0.199024	−	0.612534i
$95$		0			0
$96$	−12.4772	+	9.06524i	−1.27345	+	0.925217i
$97$	14.6029	+	4.74475i	1.48269	+	0.481757i	0.934917	−	0.354867i	$-0.115474\pi$
$97$	14.6029	+	4.74475i	1.48269	+	0.481757i	0.547778	+	0.836624i	$0.315474\pi$
$98$			5.04469i			0.509591i
$99$	−2.10083	+	0.609644i	−0.211142	+	0.0612716i
$100$		0			0
$101$	3.62557	−	11.1584i	0.360758	−	1.11030i	−0.591838	−	0.806057i	$-0.701597\pi$
$101$	3.62557	−	11.1584i	0.360758	−	1.11030i	0.952595	−	0.304241i	$-0.0984027\pi$
$102$	−1.09283	−	1.50415i	−0.108206	−	0.148933i
$103$	−8.16319	+	11.2357i	−0.804343	+	1.10708i	0.187828	+	0.982202i	$0.439855\pi$
$103$	−8.16319	+	11.2357i	−0.804343	+	1.10708i	−0.992172	+	0.124882i	$0.960145\pi$
$104$	0.770639	+	2.37178i	0.0755674	+	0.232573i
$105$		0			0
$106$	7.09944	+	5.15804i	0.689559	+	0.500994i
$107$	4.30318	+	5.92282i	0.416004	+	0.572580i	0.964670	−	0.263461i	$-0.0848642\pi$
$107$	4.30318	+	5.92282i	0.416004	+	0.572580i	−0.548666	+	0.836042i	$0.684864\pi$
$108$	10.1780	+	3.30704i	0.979380	+	0.318220i
$109$	7.43306			0.711958			0.355979	−	0.934494i	$-0.384147\pi$
$109$	7.43306			0.711958			0.355979	+	0.934494i	$0.384147\pi$
$110$		0			0
$111$	3.52859			0.334919
$112$	8.94719	+	2.90712i	0.845430	+	0.274697i
$113$	−1.78475	−	2.45650i	−0.167895	−	0.231088i	0.716776	−	0.697304i	$-0.245617\pi$
$113$	−1.78475	−	2.45650i	−0.167895	−	0.231088i	−0.884671	+	0.466216i	$0.845617\pi$
$114$	25.6037	+	18.6022i	2.39801	+	1.74226i
$115$		0			0
$116$	2.74890	+	8.46024i	0.255229	+	0.785514i
$117$	1.18235	−	1.62736i	0.109308	−	0.150449i
$118$	−3.46694	−	4.77183i	−0.319157	−	0.439282i
$119$	−0.439638	+	1.35307i	−0.0403016	+	0.124035i
$120$		0			0
$121$	−4.05569	+	10.2250i	−0.368699	+	0.929549i
$122$			4.22699i			0.382693i
$123$	8.01910	+	2.60556i	0.723058	+	0.234936i
$124$	−20.2590	+	14.7190i	−1.81931	+	1.32181i
$125$		0			0
$126$	1.30984	+	4.03129i	0.116690	+	0.359136i
$127$	0.429495	−	0.139551i	0.0381115	−	0.0123832i	−0.289899	−	0.957057i	$-0.593622\pi$
$127$	0.429495	−	0.139551i	0.0381115	−	0.0123832i	0.328011	+	0.944674i	$0.393622\pi$
$128$	−3.77187	+	5.19153i	−0.333389	+	0.458871i
$129$	−2.03482	+	1.47838i	−0.179156	+	0.130164i
$130$		0			0
$131$	0.629003			0.0549563			0.0274781	−	0.999622i	$-0.491252\pi$
$131$	0.629003			0.0549563			0.0274781	+	0.999622i	$0.491252\pi$
$132$	−12.5457	+	8.52037i	−1.09196	+	0.741603i
$133$		−	24.2173i		−	2.09991i
$134$	−4.37538	+	13.4660i	−0.377975	+	1.16329i
$135$		0			0
$136$	−0.306850	−	0.222940i	−0.0263122	−	0.0191169i
$137$	−10.6360	+	3.45586i	−0.908698	+	0.295254i	−0.725823	−	0.687882i	$-0.758541\pi$
$137$	−10.6360	+	3.45586i	−0.908698	+	0.295254i	−0.182876	+	0.983136i	$0.558541\pi$
$138$	5.29981	−	1.72201i	0.451150	−	0.146588i
$139$	−1.92138	−	1.39596i	−0.162969	−	0.118404i	0.503312	−	0.864105i	$-0.332115\pi$
$139$	−1.92138	−	1.39596i	−0.162969	−	0.118404i	−0.666281	+	0.745701i	$0.732115\pi$
$140$		0			0
$141$	−1.76173	+	5.42205i	−0.148364	+	0.456619i
$142$			13.6654i			1.14678i
$143$	−2.81902	−	9.71433i	−0.235738	−	0.812353i
$144$	2.02298			0.168582
$145$		0			0
$146$	−16.7408	+	12.1629i	−1.38548	+	1.00661i
$147$	2.70721	−	3.72616i	0.223287	−	0.307328i
$148$	4.19312	−	1.36243i	0.344672	−	0.111991i
$149$	2.69473	+	8.29354i	0.220761	+	0.679433i	0.998694	+	0.0510859i	$0.0162682\pi$
$149$	2.69473	+	8.29354i	0.220761	+	0.679433i	−0.777933	+	0.628347i	$0.783732\pi$
$150$		0			0
$151$	−9.65596	+	7.01547i	−0.785791	+	0.570911i	−0.906711	−	0.421752i	$-0.861415\pi$
$151$	−9.65596	+	7.01547i	−0.785791	+	0.570911i	0.120920	+	0.992662i	$0.461415\pi$
$152$	6.14028	+	1.99510i	0.498043	+	0.161824i
$153$			0.305932i			0.0247332i
$154$	20.0525	+	7.22633i	1.61587	+	0.582315i
$155$		0			0
$156$	4.30938	−	13.2629i	0.345026	−	1.06188i
$157$	−2.27786	−	3.13520i	−0.181793	−	0.250216i	0.708389	−	0.705823i	$-0.249422\pi$
$157$	−2.27786	−	3.13520i	−0.181793	−	0.250216i	−0.890181	+	0.455606i	$0.849422\pi$
$158$	−14.2345	+	19.5921i	−1.13243	+	1.55866i
$159$	−2.47581	−	7.61977i	−0.196345	−	0.604287i
$160$		0			0
$161$	−3.44979	−	2.50642i	−0.271882	−	0.197534i
$162$	−12.9854	−	17.8729i	−1.02023	−	1.40422i
$163$	9.44990	+	3.07046i	0.740173	+	0.240497i	0.654748	−	0.755848i	$-0.272775\pi$
$163$	9.44990	+	3.07046i	0.740173	+	0.240497i	0.0854258	+	0.996345i	$0.472775\pi$
$164$	10.5354			0.822674
$165$		0			0
$166$	−18.6871			−1.45040
$167$	13.2387	+	4.30152i	1.02444	+	0.332862i	0.772591	−	0.634904i	$-0.218960\pi$
$167$	13.2387	+	4.30152i	1.02444	+	0.332862i	0.251852	+	0.967766i	$0.418960\pi$
$168$	2.82013	+	3.88157i	0.217577	+	0.299470i
$169$	−2.99226	−	2.17400i	−0.230174	−	0.167231i
$170$		0			0
$171$	−1.60924	−	4.95274i	−0.123062	−	0.378745i
$172$	−1.84721	+	2.54247i	−0.140848	+	0.193861i
$173$	6.36637	+	8.76256i	0.484026	+	0.666205i	0.979272	−	0.202548i	$-0.0649221\pi$
$173$	6.36637	+	8.76256i	0.484026	+	0.666205i	−0.495246	+	0.868753i	$0.664922\pi$
$174$	4.60971	−	14.1872i	0.349461	−	1.07553i
$175$		0			0
$176$	6.23741	−	8.03609i	0.470162	−	0.605743i
$177$			5.38513i			0.404771i
$178$	−13.4904	−	4.38331i	−1.01115	−	0.328543i
$179$	18.3918	−	13.3624i	1.37466	−	0.998752i	0.377307	−	0.926088i	$-0.376850\pi$
$179$	18.3918	−	13.3624i	1.37466	−	0.998752i	0.997356	−	0.0726638i	$-0.0231500\pi$
$180$		0			0
$181$	0.741120	+	2.28093i	0.0550870	+	0.169540i	0.974815	−	0.223017i	$-0.0715905\pi$
$181$	0.741120	+	2.28093i	0.0550870	+	0.169540i	−0.919728	+	0.392557i	$0.871590\pi$
$182$	−18.6408	+	6.05677i	−1.38175	+	0.448957i
$183$	2.26840	−	3.12218i	0.167685	−	0.230798i
$184$	0.919704	−	0.668204i	0.0678015	−	0.0492607i
$185$		0			0
$186$	41.9927			3.07906
$187$	1.21528	+	0.943272i	0.0888703	+	0.0689789i
$188$			7.12340i			0.519527i
$189$	−4.24360	+	13.0605i	−0.308677	+	0.950009i
$190$		0			0
$191$	−13.9525	−	10.1371i	−1.00957	−	0.733494i	−0.0454496	−	0.998967i	$-0.514472\pi$
$191$	−13.9525	−	10.1371i	−1.00957	−	0.733494i	−0.964118	+	0.265473i	$0.914472\pi$
$192$	19.5728	−	6.35959i	1.41254	−	0.458964i
$193$	−2.45918	+	0.799036i	−0.177016	+	0.0575159i	−0.396184	−	0.918171i	$-0.629666\pi$
$193$	−2.45918	+	0.799036i	−0.177016	+	0.0575159i	0.219168	+	0.975687i	$0.429666\pi$
$194$	−26.0276	−	18.9102i	−1.86867	−	1.35767i
$195$		0			0
$196$	1.77835	−	5.47319i	0.127025	−	0.390942i
$197$			0.144731i			0.0103116i	0.999987	+	0.00515582i	$0.00164116\pi$
$197$			0.144731i			0.0103116i	−0.999987	+	0.00515582i	$0.998359\pi$
$198$	4.58116	+	0.145386i	0.325569	+	0.0103322i
$199$	7.54177			0.534622			0.267311	−	0.963610i	$-0.413865\pi$
$199$	7.54177			0.534622			0.267311	+	0.963610i	$0.413865\pi$
$200$		0			0
$201$	10.4583	−	7.59838i	0.737670	−	0.535948i
$202$	−14.4497	+	19.8882i	−1.01667	+	1.39933i
$203$	−10.8562	+	3.52740i	−0.761957	+	0.247575i
$204$	0.655412	+	2.01715i	0.0458880	+	0.141229i
$205$		0			0
$206$	23.5420	−	17.1043i	1.64025	−	1.19171i
$207$	−0.872075	−	0.283354i	−0.0606134	−	0.0196945i
$208$			9.35435i			0.648607i
$209$	−24.6359	−	8.87809i	−1.70410	−	0.614110i
$210$		0			0
$211$	−0.701101	+	2.15777i	−0.0482658	+	0.148547i	−0.972285	−	0.233800i	$-0.924884\pi$
$211$	−0.701101	+	2.15777i	−0.0482658	+	0.148547i	0.924019	+	0.382347i	$0.124884\pi$
$212$	−5.88416	−	8.09886i	−0.404126	−	0.556232i
$213$	7.33349	−	10.0937i	0.502482	−	0.691607i
$214$	−4.74021	−	14.5889i	−0.324034	−	0.997275i
$215$		0			0
$216$	−2.96187	−	2.15192i	−0.201529	−	0.146420i
$217$	−18.8875	−	25.9964i	−1.28216	−	1.76475i
$218$	−14.8122	−	4.81277i	−1.00321	−	0.325962i
$219$	18.8924			1.27663
$220$		0			0
$221$	−1.41464			−0.0951591
$222$	−7.03156	−	2.28469i	−0.471928	−	0.153339i
$223$	5.04301	+	6.94111i	0.337705	+	0.464811i	0.943769	−	0.330605i	$-0.107253\pi$
$223$	5.04301	+	6.94111i	0.337705	+	0.464811i	−0.606065	+	0.795415i	$0.707253\pi$
$224$	−20.0052	−	14.5347i	−1.33666	−	0.971138i
$225$		0			0
$226$	1.96601	+	6.05076i	0.130777	+	0.402491i
$227$	3.64450	−	5.01622i	0.241894	−	0.332938i	−0.670758	−	0.741676i	$-0.734031\pi$
$227$	3.64450	−	5.01622i	0.241894	−	0.332938i	0.912652	+	0.408738i	$0.134031\pi$
$228$	−21.2209	−	29.2081i	−1.40539	−	1.93435i
$229$	−7.15865	+	22.0321i	−0.473057	+	1.45592i	0.375503	+	0.926821i	$0.377470\pi$
$229$	−7.15865	+	22.0321i	−0.473057	+	1.45592i	−0.848560	+	0.529099i	$0.822530\pi$
$230$		0			0
$231$	−10.9334	−	16.0987i	−0.719362	−	1.05921i
$232$		−	3.04318i		−	0.199794i
$233$	26.4990	+	8.61005i	1.73601	+	0.564063i	0.994296	−	0.106656i	$-0.0340144\pi$
$233$	26.4990	+	8.61005i	1.73601	+	0.564063i	0.741711	+	0.670719i	$0.234014\pi$
$234$	−3.40980	+	2.47736i	−0.222905	+	0.161950i
$235$		0			0
$236$	2.07926	+	6.39931i	0.135348	+	0.416560i
$237$	21.0280	−	6.83241i	1.36592	−	0.443813i
$238$	1.75217	−	2.41166i	0.113576	−	0.156325i
$239$	−13.1758	+	9.57280i	−0.852274	+	0.619213i	−0.925772	−	0.378082i	$-0.876584\pi$
$239$	−13.1758	+	9.57280i	−0.852274	+	0.619213i	0.0734982	+	0.997295i	$0.476584\pi$
$240$		0			0
$241$	4.39063			0.282826			0.141413	−	0.989951i	$-0.454836\pi$
$241$	4.39063			0.282826			0.141413	+	0.989951i	$0.454836\pi$
$242$	14.7025	−	17.7499i	0.945111	−	1.14101i
$243$			6.73820i			0.432256i
$244$	1.49009	−	4.58603i	0.0953933	−	0.293590i
$245$		0			0
$246$	−14.2930	−	10.3844i	−0.911285	−	0.662087i
$247$	22.9016	−	7.44119i	1.45720	−	0.473471i
$248$	8.14736	−	2.64724i	0.517358	−	0.168100i
$249$	13.8029	+	10.0284i	0.874721	+	0.635522i
$250$		0			0
$251$	−0.824050	+	2.53616i	−0.0520136	+	0.160081i	−0.973689	−	0.227880i	$-0.926821\pi$
$251$	−0.824050	+	2.53616i	−0.0520136	+	0.160081i	0.921676	+	0.387961i	$0.126821\pi$
$252$		−	4.83545i		−	0.304605i
$253$	−3.81444	+	2.59056i	−0.239812	+	0.162867i
$254$	−0.946229			−0.0593717
$255$		0			0
$256$	−6.52905	+	4.74363i	−0.408066	+	0.296477i
$257$	−12.7154	+	17.5012i	−0.793162	+	1.09169i	0.200545	+	0.979685i	$0.435729\pi$
$257$	−12.7154	+	17.5012i	−0.793162	+	1.09169i	−0.993707	+	0.112010i	$0.964271\pi$
$258$	5.01209	−	1.62853i	0.312039	−	0.101388i
$259$	1.74827	+	5.38063i	0.108632	+	0.334336i
$260$		0			0
$261$	−1.98583	+	1.44279i	−0.122920	+	0.0893064i
$262$	−1.25344	−	0.407268i	−0.0774379	−	0.0251611i
$263$		−	22.1392i		−	1.36516i	−0.730810	−	0.682581i	$-0.760858\pi$
$263$		−	22.1392i		−	1.36516i	0.730810	−	0.682581i	$-0.239142\pi$
$264$	4.98252	−	1.44589i	0.306653	−	0.0889881i
$265$		0			0
$266$	−15.6803	+	48.2590i	−0.961420	+	2.95895i
$267$	7.61215	+	10.4772i	0.465856	+	0.641196i
$268$	9.49404	−	13.0674i	0.579941	−	0.798220i
$269$	−6.40233	−	19.7044i	−0.390357	−	1.20140i	−0.932519	−	0.361121i	$-0.882394\pi$
$269$	−6.40233	−	19.7044i	−0.390357	−	1.20140i	0.542162	−	0.840274i	$-0.317606\pi$
$270$		0			0
$271$	0.342305	+	0.248699i	0.0207935	+	0.0151074i	0.598133	−	0.801396i	$-0.295909\pi$
$271$	0.342305	+	0.248699i	0.0207935	+	0.0151074i	−0.577340	+	0.816504i	$0.695909\pi$
$272$	−0.836242	−	1.15099i	−0.0507046	−	0.0697889i
$273$	17.0190	+	5.52981i	1.03004	+	0.334679i
$274$	23.4325			1.41561
$275$		0			0
$276$	−6.35702			−0.382648
$277$	−8.15298	−	2.64906i	−0.489865	−	0.159167i	0.0536607	−	0.998559i	$-0.482911\pi$
$277$	−8.15298	−	2.64906i	−0.489865	−	0.159167i	−0.543526	+	0.839392i	$0.682911\pi$
$278$	2.92495	+	4.02585i	0.175427	+	0.241455i
$279$	−5.59017	−	4.06150i	−0.334675	−	0.243155i
$280$		0			0
$281$	−2.16654	−	6.66793i	−0.129245	−	0.397776i	0.865405	−	0.501072i	$-0.167061\pi$
$281$	−2.16654	−	6.66793i	−0.129245	−	0.397776i	−0.994651	+	0.103297i	$0.967061\pi$
$282$	7.02135	−	9.66406i	0.418115	−	0.575487i
$283$	5.85033	+	8.05229i	0.347766	+	0.478659i	0.946690	−	0.322147i	$-0.104405\pi$
$283$	5.85033	+	8.05229i	0.347766	+	0.478659i	−0.598924	+	0.800806i	$0.704405\pi$
$284$	4.81731	−	14.8261i	0.285855	−	0.879770i
$285$		0			0
$286$	−0.672272	+	21.1834i	−0.0397523	+	1.25260i
$287$			13.5190i			0.798002i
$288$	−5.05714	−	1.64316i	−0.297995	−	0.0968244i
$289$	−13.5792	+	9.86589i	−0.798778	+	0.580346i
$290$		0			0
$291$	9.07670	+	27.9352i	0.532086	+	1.63759i
$292$	22.4504	−	7.29457i	1.31381	−	0.426882i
$293$	−12.8260	+	17.6535i	−0.749302	+	1.03133i	0.248727	+	0.968574i	$0.419988\pi$
$293$	−12.8260	+	17.6535i	−0.749302	+	1.03133i	−0.998029	+	0.0627522i	$0.980012\pi$
$294$	−7.80740	+	5.67241i	−0.455337	+	0.330822i
$295$		0			0
$296$	−1.50828			−0.0876670
$297$	11.7305	+	9.10492i	0.680673	+	0.528321i
$298$		−	18.2717i		−	1.05845i
$299$	1.31024	−	4.03250i	0.0757731	−	0.233206i
$300$		0			0
$301$	−3.26250	−	2.37035i	−0.188048	−	0.136625i
$302$	23.7842	−	7.72797i	1.36863	−	0.444694i
$303$	21.3459	−	6.93570i	1.22629	−	0.398446i
$304$	19.5922	+	14.2346i	1.12369	+	0.816410i
$305$		0			0
$306$	0.198085	−	0.609644i	0.0113238	−	0.0348511i
$307$		−	30.8674i		−	1.76170i	−0.473397	−	0.880849i	$-0.656972\pi$
$307$		−	30.8674i		−	1.76170i	0.473397	−	0.880849i	$-0.343028\pi$
$308$	−19.2083	−	14.9090i	−1.09449	−	0.849519i
$309$	−26.5678			−1.51139
$310$		0			0
$311$	15.7071	−	11.4119i	0.890667	−	0.647107i	−0.0453850	−	0.998970i	$-0.514451\pi$
$311$	15.7071	−	11.4119i	0.890667	−	0.647107i	0.936052	+	0.351862i	$0.114451\pi$
$312$	−2.80415	+	3.85959i	−0.158754	+	0.218506i
$313$	1.00001	−	0.324922i	0.0565237	−	0.0183657i	−0.280619	−	0.959819i	$-0.590540\pi$
$313$	1.00001	−	0.324922i	0.0565237	−	0.0183657i	0.337142	+	0.941454i	$0.390540\pi$
$314$	2.50920	+	7.72252i	0.141602	+	0.435807i
$315$		0			0
$316$	22.3501	−	16.2383i	1.25729	−	0.913476i
$317$	−22.6650	−	7.36432i	−1.27300	−	0.413621i	−0.406887	−	0.913478i	$-0.633386\pi$
$317$	−22.6650	−	7.36432i	−1.27300	−	0.413621i	−0.866108	+	0.499857i	$0.833386\pi$
$318$			16.7873i			0.941385i
$319$	−0.391524	+	12.3370i	−0.0219211	+	0.690740i
$320$		0			0
$321$	−4.32780	+	13.3196i	−0.241554	+	0.743428i
$322$	5.25169	+	7.22833i	0.292665	+	0.402819i
$323$	−2.15267	+	2.96290i	−0.119778	+	0.164860i
$324$	7.78786	+	23.9686i	0.432659	+	1.33159i
$325$		0			0
$326$	−16.8432	−	12.2373i	−0.932856	−	0.677760i
$327$	8.35796	+	11.5038i	0.462196	+	0.636159i
$328$	−3.42773	−	1.11374i	−0.189265	−	0.0614959i
$329$	−9.14077			−0.503947
$330$		0			0
$331$	25.6693			1.41091			0.705457	−	0.708753i	$-0.250742\pi$
$331$	25.6693			1.41091			0.705457	+	0.708753i	$0.250742\pi$
$332$	20.2744	+	6.58755i	1.11270	+	0.361539i
$333$	0.715085	+	0.984230i	0.0391864	+	0.0539354i
$334$	−23.5962	−	17.1436i	−1.29113	−	0.938059i
$335$		0			0
$336$	5.56131	+	17.1159i	0.303394	+	0.933751i
$337$	−14.0435	+	19.3292i	−0.764996	+	1.05293i	0.231786	+	0.972767i	$0.425543\pi$
$337$	−14.0435	+	19.3292i	−0.764996	+	1.05293i	−0.996782	+	0.0801597i	$0.974457\pi$
$338$	4.55518	+	6.26966i	0.247769	+	0.341025i
$339$	1.79496	−	5.52433i	0.0974890	−	0.300040i
$340$		0			0
$341$	−33.3699	+	9.68365i	−1.80708	+	0.524399i
$342$			10.9115i			0.590026i
$343$	−13.3963	−	4.35271i	−0.723330	−	0.235024i
$344$	0.869774	−	0.631928i	0.0468951	−	0.0340713i
$345$		0			0
$346$	−7.01295	−	21.5836i	−0.377018	−	1.16034i
$347$	0.315895	−	0.102641i	0.0169582	−	0.00551004i	−0.300526	−	0.953774i	$-0.597162\pi$
$347$	0.315895	−	0.102641i	0.0169582	−	0.00551004i	0.317484	+	0.948264i	$0.397162\pi$
$348$	−10.0025	+	13.7673i	−0.536191	+	0.738004i
$349$	0.988203	−	0.717971i	0.0528973	−	0.0384321i	−0.561022	−	0.827801i	$-0.689592\pi$
$349$	0.988203	−	0.717971i	0.0528973	−	0.0384321i	0.613920	+	0.789368i	$0.289592\pi$
$350$		0			0
$351$	−13.6548			−0.728840
$352$	−22.1198	+	15.0226i	−1.17899	+	0.800708i
$353$			25.7038i			1.36808i	0.729446	+	0.684039i	$0.239778\pi$
$353$			25.7038i			1.36808i	−0.729446	+	0.684039i	$0.760222\pi$
$354$	3.48677	−	10.7312i	0.185320	−	0.570356i
$355$		0			0
$356$	13.0911	+	9.51125i	0.693828	+	0.504095i
$357$	−2.58841	+	0.841026i	−0.136993	+	0.0445118i
$358$	−45.3019	+	14.7195i	−2.39428	+	0.777949i
$359$	−14.5069	−	10.5399i	−0.765643	−	0.556272i	0.134993	−	0.990847i	$-0.456899\pi$
$359$	−14.5069	−	10.5399i	−0.765643	−	0.556272i	−0.900636	+	0.434574i	$0.856899\pi$
$360$		0			0
$361$	13.3931	−	41.2196i	0.704899	−	2.16945i
$362$		−	5.02517i		−	0.264117i
$363$	−20.3851	+	5.22057i	−1.06994	+	0.274009i
$364$	22.3593			1.17195
$365$		0			0
$366$	−6.54188	+	4.75296i	−0.341950	+	0.248441i
$367$	−4.99083	+	6.86929i	−0.260519	+	0.358574i	−0.919161	−	0.393883i	$-0.871131\pi$
$367$	−4.99083	+	6.86929i	−0.260519	+	0.358574i	0.658641	+	0.752457i	$0.271131\pi$
$368$	4.05547	−	1.31770i	0.211406	−	0.0686900i
$369$	0.898338	+	2.76480i	0.0467656	+	0.143930i
$370$		0			0
$371$	10.3925	−	7.55058i	0.539551	−	0.392006i
$372$	−45.5596	−	14.8032i	−2.36216	−	0.767511i
$373$		−	35.8450i		−	1.85598i	−0.372604	−	0.927991i	$-0.621535\pi$
$373$		−	35.8450i		−	1.85598i	0.372604	−	0.927991i	$-0.378465\pi$
$374$	−1.81100	−	2.66657i	−0.0936443	−	0.137885i
$375$		0			0
$376$	0.753045	−	2.31763i	0.0388353	−	0.119523i
$377$	−6.67151	−	9.18254i	−0.343600	−	0.472925i
$378$	16.9128	−	23.2785i	0.869902	−	1.19732i
$379$	−5.42373	−	16.6925i	−0.278598	−	0.857438i	−0.988245	−	0.152880i	$-0.951145\pi$
$379$	−5.42373	−	16.6925i	−0.278598	−	0.857438i	0.709646	−	0.704558i	$-0.248855\pi$
$380$		0			0
$381$	0.698913	+	0.507790i	0.0358064	+	0.0260149i
$382$	21.2402	+	29.2346i	1.08674	+	1.49577i
$383$	20.5666	+	6.68251i	1.05091	+	0.341460i	0.783024	−	0.621991i	$-0.213676\pi$
$383$	20.5666	+	6.68251i	1.05091	+	0.341460i	0.267882	+	0.963452i	$0.413676\pi$
$384$	−12.2759			−0.626450
$385$		0			0
$386$	5.41788			0.275763
$387$	−0.824730	−	0.267971i	−0.0419234	−	0.0136217i
$388$	21.5722	+	29.6916i	1.09516	+	1.50736i
$389$	28.9156	+	21.0084i	1.46608	+	1.06517i	0.981727	+	0.190295i	$0.0609444\pi$
$389$	28.9156	+	21.0084i	1.46608	+	1.06517i	0.484352	+	0.874873i	$0.339056\pi$
$390$		0			0
$391$	0.199274	+	0.613302i	0.0100777	+	0.0310160i
$392$	−1.15719	+	1.59273i	−0.0584468	+	0.0804451i
$393$	0.707271	+	0.973475i	0.0356771	+	0.0491053i
$394$	0.0937106	−	0.288411i	0.00472107	−	0.0145300i
$395$		0			0
$396$	−4.91903	−	1.77268i	−0.247191	−	0.0890804i
$397$		−	20.0447i		−	1.00601i	−0.864282	−	0.503007i	$-0.832227\pi$
$397$		−	20.0447i		−	1.00601i	0.864282	−	0.503007i	$-0.167773\pi$
$398$	−15.0288	−	4.88315i	−0.753326	−	0.244770i
$399$	37.4799	−	27.2307i	1.87634	−	1.36324i
$400$		0			0
$401$	−6.45805	−	19.8758i	−0.322500	−	0.992551i	−0.972557	−	0.232666i	$-0.925255\pi$
$401$	−6.45805	−	19.8758i	−0.322500	−	0.992551i	0.650057	−	0.759885i	$-0.274745\pi$
$402$	−25.7605	+	8.37008i	−1.28481	+	0.417462i
$403$	18.7805	−	25.8491i	0.935523	−	1.28764i
$404$	22.6880	−	16.4838i	1.12877	−	0.820099i
$405$		0			0
$406$	23.9176			1.18701
$407$	6.11454	+	0.194050i	0.303087	+	0.00961869i
$408$		−	0.725576i		−	0.0359214i
$409$	−7.26134	+	22.3481i	−0.359050	+	1.10504i	0.594574	+	0.804041i	$0.297321\pi$
$409$	−7.26134	+	22.3481i	−0.359050	+	1.10504i	−0.953624	+	0.301001i	$0.902679\pi$
$410$		0			0
$411$	−17.3079	−	12.5750i	−0.853738	−	0.620277i
$412$	−31.5713	+	10.2581i	−1.55541	+	0.505382i
$413$	−8.21161	+	2.66812i	−0.404067	+	0.131289i
$414$	1.55435	+	1.12930i	0.0763924	+	0.0555023i
$415$		0			0
$416$	7.59804	−	23.3844i	0.372525	−	1.14651i
$417$		−	4.54328i		−	0.222485i
$418$	43.3447	+	33.6431i	2.12006	+	1.64554i
$419$	10.1128			0.494043			0.247022	−	0.969010i	$-0.420548\pi$
$419$	10.1128			0.494043			0.247022	+	0.969010i	$0.420548\pi$
$420$		0			0
$421$	−7.21872	+	5.24471i	−0.351819	+	0.255611i	−0.749632	−	0.661855i	$-0.769769\pi$
$421$	−7.21872	+	5.24471i	−0.351819	+	0.255611i	0.397813	+	0.917467i	$0.369769\pi$
$422$	2.79423	−	3.84593i	0.136021	−	0.187217i
$423$	−1.86940	+	0.607404i	−0.0908932	+	0.0295330i
$424$	1.05828	+	3.25704i	0.0513945	+	0.158176i
$425$		0			0
$426$	−21.1492	+	15.3658i	−1.02468	+	0.744476i
$427$	5.88481	+	1.91209i	0.284786	+	0.0925325i
$428$			17.4991i			0.845850i
$429$	11.8646	−	15.2859i	0.572826	−	0.738012i
$430$		0			0
$431$	−5.44248	+	16.7502i	−0.262155	+	0.806831i	0.730180	+	0.683255i	$0.239436\pi$
$431$	−5.44248	+	16.7502i	−0.262155	+	0.806831i	−0.992335	+	0.123576i	$0.960564\pi$
$432$	−8.07181	−	11.1099i	−0.388355	−	0.534525i
$433$	−5.37469	+	7.39763i	−0.258291	+	0.355507i	−0.918393	−	0.395668i	$-0.870513\pi$
$433$	−5.37469	+	7.39763i	−0.258291	+	0.355507i	0.660102	+	0.751176i	$0.270513\pi$
$434$	20.8057	+	64.0334i	0.998706	+	3.07370i
$435$		0			0
$436$	14.3737	+	10.4431i	0.688377	+	0.500135i
$437$	−6.45209	−	8.88054i	−0.308645	−	0.424814i
$438$	−37.6477	−	12.2325i	−1.79888	−	0.584490i
$439$	−6.46946			−0.308770			−0.154385	−	0.988011i	$-0.549340\pi$
$439$	−6.46946			−0.308770			−0.154385	+	0.988011i	$0.549340\pi$
$440$		0			0
$441$	1.58797			0.0756176
$442$	2.81902	+	0.915954i	0.134087	+	0.0435675i
$443$	−24.0311	−	33.0760i	−1.14175	−	1.57149i	−0.763529	−	0.645774i	$-0.776535\pi$
$443$	−24.0311	−	33.0760i	−1.14175	−	1.57149i	−0.378224	−	0.925714i	$-0.623465\pi$
$444$	6.82343	+	4.95751i	0.323826	+	0.235273i
$445$		0			0
$446$	−5.55518	−	17.0971i	−0.263045	−	0.809571i
$447$	−9.80542	+	13.4960i	−0.463781	+	0.638339i
$448$	19.3951	+	26.6950i	0.916330	+	1.26122i
$449$	3.75788	−	11.5656i	0.177345	−	0.545813i	−0.822387	−	0.568928i	$-0.807358\pi$
$449$	3.75788	−	11.5656i	0.177345	−	0.545813i	0.999733	+	0.0231150i	$0.00735838\pi$
$450$		0			0
$451$	13.7527	+	4.95608i	0.647589	+	0.233373i
$452$		−	7.25777i		−	0.341377i
$453$	−21.7149	−	7.05561i	−1.02026	−	0.331501i
$454$	−10.5105	+	7.63629i	−0.493280	+	0.358389i
$455$		0			0
$456$	3.81662	+	11.7463i	0.178730	+	0.550073i
$457$	9.41775	−	3.06001i	0.440544	−	0.143141i	−0.0803428	−	0.996767i	$-0.525602\pi$
$457$	9.41775	−	3.06001i	0.440544	−	0.143141i	0.520886	+	0.853626i	$0.325602\pi$
$458$	28.5307	−	39.2691i	1.33315	−	1.83493i
$459$	1.68013	−	1.22069i	0.0784218	−	0.0569767i
$460$		0			0
$461$	−3.12529			−0.145559			−0.0727796	−	0.997348i	$-0.523187\pi$
$461$	−3.12529			−0.145559			−0.0727796	+	0.997348i	$0.523187\pi$
$462$	11.3638	+	39.1596i	0.528692	+	1.82187i
$463$			24.3518i			1.13173i	0.824499	+	0.565863i	$0.191457\pi$
$463$			24.3518i			1.13173i	−0.824499	+	0.565863i	$0.808543\pi$
$464$	3.52740	−	10.8562i	0.163755	−	0.503987i
$465$		0			0
$466$	−47.2309	−	34.3152i	−2.18793	−	1.58962i
$467$	−31.5501	+	10.2512i	−1.45996	+	0.474371i	−0.928059	−	0.372434i	$-0.878523\pi$
$467$	−31.5501	+	10.2512i	−1.45996	+	0.474371i	−0.531904	+	0.846805i	$0.678523\pi$
$468$	4.57274	−	1.48577i	0.211375	−	0.0686799i
$469$	16.7682	+	12.1828i	0.774282	+	0.562549i
$470$		0			0
$471$	2.29089	−	7.05063i	0.105559	−	0.324876i
$472$		−	2.30185i		−	0.105951i
$473$	−3.60735	+	2.44992i	−0.165866	+	0.112648i
$474$	−46.3273			−2.12788
$475$		0			0
$476$	−2.75116	+	1.99883i	−0.126099	+	0.0916163i
$477$	1.62365	−	2.23476i	0.0743418	−	0.102323i
$478$	32.4543	−	10.5450i	1.48442	−	0.482318i
$479$	5.34529	+	16.4511i	0.244232	+	0.751670i	0.995762	+	0.0919705i	$0.0293165\pi$
$479$	5.34529	+	16.4511i	0.244232	+	0.751670i	−0.751529	+	0.659700i	$0.770683\pi$
$480$		0			0
$481$	−4.55111	+	3.30658i	−0.207513	+	0.150767i
$482$	−8.74941	−	2.84285i	−0.398524	−	0.129488i
$483$		−	8.15736i		−	0.371173i
$484$	−22.2085	+	14.0747i	−1.00948	+	0.639758i
$485$		0			0
$486$	4.36286	−	13.4275i	0.197903	−	0.609084i
$487$	−4.49104	−	6.18138i	−0.203508	−	0.280105i	0.695048	−	0.718963i	$-0.255383\pi$
$487$	−4.49104	−	6.18138i	−0.203508	−	0.280105i	−0.898556	+	0.438858i	$0.855383\pi$
$488$	−0.969617	+	1.33456i	−0.0438925	+	0.0604128i
$489$	5.87378	+	18.0776i	0.265621	+	0.817499i
$490$		0			0
$491$	24.8015	+	18.0193i	1.11928	+	0.813201i	0.984099	−	0.177620i	$-0.0568399\pi$
$491$	24.8015	+	18.0193i	1.11928	+	0.813201i	0.135176	+	0.990822i	$0.456840\pi$
$492$	11.8463	+	16.3050i	0.534072	+	0.735087i
$493$	1.64177	+	0.533442i	0.0739414	+	0.0240250i
$494$	−50.4551			−2.27008
$495$		0			0
$496$	32.1333			1.44283
$497$	19.0250	+	6.18159i	0.853386	+	0.277282i
$498$	−21.0124	−	28.9210i	−0.941587	−	1.29598i
$499$	−30.3206	−	22.0292i	−1.35734	−	0.986162i	−0.998609	−	0.0527188i	$-0.983211\pi$
$499$	−30.3206	−	22.0292i	−1.35734	−	0.986162i	−0.358726	−	0.933443i	$-0.616789\pi$
$500$		0			0
$501$	8.22879	+	25.3256i	0.367635	+	1.13147i
$502$	3.28424	−	4.52037i	0.146583	−	0.201754i
$503$	4.98263	+	6.85800i	0.222164	+	0.305783i	0.905521	−	0.424302i	$-0.139480\pi$
$503$	4.98263	+	6.85800i	0.222164	+	0.305783i	−0.683356	+	0.730085i	$0.739480\pi$
$504$	−0.511176	+	1.57324i	−0.0227696	+	0.0700776i
$505$		0			0
$506$	9.27854	−	2.69255i	0.412481	−	0.119699i
$507$		−	7.07548i		−	0.314233i
$508$	1.02660	+	0.333563i	0.0455481	+	0.0147995i
$509$	−1.37309	+	0.997609i	−0.0608612	+	0.0442183i	−0.617800	−	0.786335i	$-0.711976\pi$
$509$	−1.37309	+	0.997609i	−0.0608612	+	0.0442183i	0.556939	+	0.830554i	$0.311976\pi$
$510$		0			0
$511$	9.36041	+	28.8084i	0.414080	+	1.27441i
$512$	28.2882	−	9.19138i	1.25017	−	0.406206i
$513$	−20.7787	+	28.5994i	−0.917400	+	1.26269i
$514$	36.6701	−	26.6424i	1.61745	−	1.17515i
$515$		0			0
$516$	−6.01190			−0.264659
$517$	−3.35101	+	9.29877i	−0.147377	+	0.408959i
$518$		−	11.8542i		−	0.520843i
$519$	−6.40280	+	19.7058i	−0.281052	+	0.864988i
$520$		0			0
$521$	30.0088	+	21.8027i	1.31471	+	0.955192i	0.999982	+	0.00601047i	$0.00191320\pi$
$521$	30.0088	+	21.8027i	1.31471	+	0.955192i	0.314728	+	0.949182i	$0.398087\pi$
$522$	4.89143	−	1.58932i	0.214092	−	0.0695627i
$523$	−17.1968	+	5.58759i	−0.751965	+	0.244328i	−0.659826	−	0.751418i	$-0.729370\pi$
$523$	−17.1968	+	5.58759i	−0.751965	+	0.244328i	−0.0921382	+	0.995746i	$0.529370\pi$
$524$	1.21634	+	0.883723i	0.0531361	+	0.0386056i
$525$		0			0
$526$	−14.3347	+	44.1177i	−0.625023	+	1.92362i
$527$			4.85946i			0.211681i
$528$	19.4506	+	0.617278i	0.846477	+	0.0268636i
$529$	21.0672			0.915965
$530$		0			0
$531$	−1.50208	+	1.09132i	−0.0651846	+	0.0473594i
$532$	34.0244	−	46.8305i	1.47514	−	2.03036i
$533$	−12.7845	+	4.15394i	−0.553759	+	0.179927i
$534$	−8.38525	−	25.8071i	−0.362865	−	1.11678i
$535$		0			0
$536$	−4.47035	+	3.24790i	−0.193090	+	0.140288i
$537$	41.3605	+	13.4388i	1.78484	+	0.579929i
$538$			43.4111i			1.87159i
$539$	4.89614	−	6.30803i	0.210892	−	0.271706i
$540$		0			0
$541$	3.63169	−	11.1772i	0.156139	−	0.480545i	−0.842136	−	0.539265i	$-0.818702\pi$
$541$	3.63169	−	11.1772i	0.156139	−	0.480545i	0.998274	+	0.0587201i	$0.0187019\pi$
$542$	−0.521098	−	0.717229i	−0.0223831	−	0.0308076i
$543$	−2.69674	+	3.71174i	−0.115728	+	0.159286i
$544$	1.15558	+	3.55652i	0.0495452	+	0.152485i
$545$		0			0
$546$	−30.3340	−	22.0390i	−1.29818	−	0.943181i
$547$	12.7884	+	17.6017i	0.546791	+	0.752593i	0.989572	−	0.144037i	$-0.0460083\pi$
$547$	12.7884	+	17.6017i	0.546791	+	0.752593i	−0.442782	+	0.896629i	$0.646008\pi$
$548$	−25.4229	−	8.26039i	−1.08601	−	0.352866i
$549$	1.33057			0.0567874
$550$		0			0
$551$	−29.3845			−1.25182
$552$	2.06829	+	0.672028i	0.0880322	+	0.0286034i
$553$	20.8370	+	28.6797i	0.886081	+	1.21959i
$554$	14.5316	+	10.5578i	0.617388	+	0.448558i
$555$		0			0
$556$	−1.75421	−	5.39891i	−0.0743952	−	0.228965i
$557$	2.84154	−	3.91104i	0.120400	−	0.165716i	−0.744563	−	0.667552i	$-0.767342\pi$
$557$	2.84154	−	3.91104i	0.120400	−	0.165716i	0.864963	+	0.501836i	$0.167342\pi$
$558$	8.51003	+	11.7130i	0.360258	+	0.495853i
$559$	1.23911	−	3.81358i	0.0524086	−	0.161297i
$560$		0			0
$561$	−0.0933499	+	2.94147i	−0.00394124	+	0.124189i
$562$			14.6903i			0.619672i
$563$	−4.53843	−	1.47463i	−0.191272	−	0.0621481i	0.211815	−	0.977310i	$-0.432063\pi$
$563$	−4.53843	−	1.47463i	−0.191272	−	0.0621481i	−0.403087	+	0.915162i	$0.632063\pi$
$564$	−11.0245	+	8.00978i	−0.464216	+	0.337272i
$565$		0			0
$566$	−6.44449	−	19.8341i	−0.270882	−	0.833690i
$567$	−30.7566	+	9.99341i	−1.29165	+	0.419684i
$568$	−3.13467	+	4.31450i	−0.131528	+	0.181032i
$569$	28.8971	−	20.9949i	1.21143	−	0.880154i	0.216068	−	0.976378i	$-0.430677\pi$
$569$	28.8971	−	20.9949i	1.21143	−	0.880154i	0.995360	+	0.0962246i	$0.0306767\pi$
$570$		0			0
$571$	−33.9838			−1.42218			−0.711090	−	0.703101i	$-0.751798\pi$
$571$	−33.9838			−1.42218			−0.711090	+	0.703101i	$0.751798\pi$
$572$	8.19692	−	22.7458i	0.342731	−	0.951048i
$573$		−	32.9920i		−	1.37826i
$574$	8.75331	−	26.9399i	0.365356	−	1.12445i
$575$		0			0
$576$	5.74040	+	4.17065i	0.239183	+	0.173777i
$577$	19.6468	−	6.38364i	0.817909	−	0.265755i	0.129965	−	0.991519i	$-0.458514\pi$
$577$	19.6468	−	6.38364i	0.817909	−	0.265755i	0.687944	+	0.725764i	$0.258514\pi$
$578$	33.4479	−	10.8679i	1.39125	−	0.452044i
$579$	−4.00181	−	2.90748i	−0.166309	−	0.120831i
$580$		0			0
$581$	−8.45317	+	26.0162i	−0.350697	+	1.07933i
$582$		−	61.5447i		−	2.55111i
$583$	−3.87120	−	13.3402i	−0.160329	−	0.552493i
$584$	−8.07548			−0.334166
$585$		0			0
$586$	36.9892	−	26.8742i	1.52801	−	1.11016i
$587$	7.85284	−	10.8085i	0.324121	−	0.446115i	−0.615599	−	0.788060i	$-0.711086\pi$
$587$	7.85284	−	10.8085i	0.324121	−	0.446115i	0.939720	+	0.341945i	$0.111086\pi$
$588$	10.4702	−	3.40197i	0.431783	−	0.140295i
$589$	−25.5614	−	78.6698i	−1.05324	−	3.24153i
$590$		0			0
$591$	−0.223992	+	0.162740i	−0.00921381	+	0.00669423i
$592$	−5.38063	−	1.74827i	−0.221142	−	0.0718535i
$593$		−	20.8062i		−	0.854410i	−0.904155	−	0.427205i	$-0.859498\pi$
$593$		−	20.8062i		−	0.854410i	0.904155	−	0.427205i	$-0.140502\pi$
$594$	−17.4806	−	25.7391i	−0.717238	−	1.05609i
$595$		0			0
$596$	−6.44111	+	19.8237i	−0.263838	+	0.812010i
$597$	8.48020	+	11.6720i	0.347071	+	0.477703i
$598$	−5.22194	+	7.18739i	−0.213541	+	0.293914i
$599$	4.40214	+	13.5484i	0.179867	+	0.553573i	0.999822	−	0.0188544i	$-0.00600189\pi$
$599$	4.40214	+	13.5484i	0.179867	+	0.553573i	−0.819956	+	0.572427i	$0.806002\pi$
$600$		0			0
$601$	16.7840	+	12.1943i	0.684634	+	0.497416i	0.874892	−	0.484318i	$-0.160932\pi$
$601$	16.7840	+	12.1943i	0.684634	+	0.497416i	−0.190257	+	0.981734i	$0.560932\pi$
$602$	4.96657	+	6.83590i	0.202422	+	0.278611i
$603$	4.23884	+	1.37728i	0.172619	+	0.0560872i
$604$	−28.5287			−1.16082
$605$		0			0
$606$	−47.0276			−1.91037
$607$	17.0448	+	5.53818i	0.691825	+	0.224788i	0.633765	−	0.773525i	$-0.281508\pi$
$607$	17.0448	+	5.53818i	0.691825	+	0.224788i	0.0580601	+	0.998313i	$0.481508\pi$
$608$	−37.4155	−	51.4980i	−1.51740	−	2.08852i
$609$	−17.6662	−	12.8353i	−0.715872	−	0.520111i
$610$		0			0
$611$	−2.80866	−	8.64416i	−0.113626	−	0.349705i
$612$	−0.429822	+	0.591599i	−0.0173745	+	0.0239140i
$613$	−16.5766	−	22.8158i	−0.669524	−	0.921521i	0.330225	−	0.943902i	$-0.392875\pi$
$613$	−16.5766	−	22.8158i	−0.669524	−	0.921521i	−0.999750	+	0.0223811i	$0.992875\pi$
$614$	−19.9861	+	61.5109i	−0.806573	+	2.48238i
$615$		0			0
$616$	4.67342	+	6.88131i	0.188298	+	0.277256i
$617$		−	4.72930i		−	0.190394i	−0.995458	−	0.0951972i	$-0.969652\pi$
$617$		−	4.72930i		−	0.190394i	0.995458	−	0.0951972i	$-0.0303482\pi$
$618$	52.9428	+	17.2022i	2.12967	+	0.691972i
$619$	−24.3170	+	17.6673i	−0.977383	+	0.710110i	−0.957122	−	0.289684i	$-0.906450\pi$
$619$	−24.3170	+	17.6673i	−0.977383	+	0.710110i	−0.0202609	+	0.999795i	$0.506450\pi$
$620$		0			0
$621$	1.92349	+	5.91989i	0.0771870	+	0.237557i
$622$	−38.6891	+	12.5709i	−1.55129	+	0.504046i
$623$	−12.2049	+	16.7986i	−0.488978	+	0.673020i
$624$	−14.4772	+	10.5183i	−0.579553	+	0.421070i
$625$		0			0
$626$	−2.20314			−0.0880551
$627$	−13.9613	−	48.1105i	−0.557560	−	1.92135i
$628$		−	9.26301i		−	0.369634i
$629$	0.264388	−	0.813702i	0.0105418	−	0.0324444i
$630$		0			0
$631$	25.6487	+	18.6349i	1.02106	+	0.741843i	0.966500	−	0.256667i	$-0.0826244\pi$
$631$	25.6487	+	18.6349i	1.02106	+	0.741843i	0.0545601	+	0.998510i	$0.482624\pi$
$632$	−8.98834	+	2.92049i	−0.357537	+	0.116171i
$633$	−4.12780	+	1.34120i	−0.164065	+	0.0533081i
$634$	40.3973	+	29.3504i	1.60438	+	1.16565i
$635$		0			0
$636$	5.91783	−	18.2132i	0.234657	−	0.722201i
$637$			7.34282i			0.290933i
$638$	8.76819	−	24.3310i	0.347136	−	0.963272i
$639$	4.30160			0.170169
$640$		0			0
$641$	15.3368	−	11.1428i	0.605768	−	0.440116i	−0.242154	−	0.970238i	$-0.577854\pi$
$641$	15.3368	−	11.1428i	0.605768	−	0.440116i	0.847921	+	0.530122i	$0.177854\pi$
$642$	17.2484	−	23.7404i	0.680740	−	0.936958i
$643$	−34.4747	+	11.2015i	−1.35955	+	0.441745i	−0.895893	−	0.444270i	$-0.853463\pi$
$643$	−34.4747	+	11.2015i	−1.35955	+	0.441745i	−0.463657	+	0.886015i	$0.653463\pi$
$644$	−3.14965	−	9.69362i	−0.124114	−	0.381982i
$645$		0			0
$646$	6.20815	−	4.51048i	0.244256	−	0.177463i
$647$	−33.2412	−	10.8007i	−1.30685	−	0.424620i	−0.428889	−	0.903357i	$-0.641095\pi$
$647$	−33.2412	−	10.8007i	−1.30685	−	0.424620i	−0.877958	+	0.478737i	$0.841095\pi$
$648$		−	8.62158i		−	0.338688i
$649$	−0.296148	+	9.33168i	−0.0116248	+	0.366301i
$650$		0			0
$651$	18.9955	−	58.4623i	0.744494	−	2.29132i
$652$	13.9600	+	19.2142i	0.546714	+	0.752488i
$653$	17.5097	−	24.1000i	0.685207	−	0.943106i	−0.314775	−	0.949166i	$-0.601929\pi$
$653$	17.5097	−	24.1000i	0.685207	−	0.943106i	0.999982	+	0.00605995i	$0.00192895\pi$
$654$	−9.20681	−	28.3356i	−0.360015	−	1.10801i
$655$		0			0
$656$	−10.9371	−	7.94628i	−0.427023	−	0.310250i
$657$	3.82863	+	5.26966i	0.149369	+	0.205589i
$658$	18.2152	+	5.91848i	0.710103	+	0.230726i
$659$	7.30532			0.284575			0.142287	−	0.989825i	$-0.454554\pi$
$659$	7.30532			0.284575			0.142287	+	0.989825i	$0.454554\pi$
$660$		0			0
$661$	−22.7352			−0.884296			−0.442148	−	0.896942i	$-0.645783\pi$
$661$	−22.7352			−0.884296			−0.442148	+	0.896942i	$0.645783\pi$
$662$	−51.1524	−	16.6204i	−1.98809	−	0.645971i
$663$	−1.59067	−	2.18937i	−0.0617764	−	0.0850279i
$664$	−5.89998	−	4.28658i	−0.228964	−	0.166352i
$665$		0			0
$666$	−0.787710	−	2.42432i	−0.0305231	−	0.0939405i
$667$	−3.04120	+	4.18586i	−0.117756	+	0.162077i
$668$	19.5570	+	26.9179i	0.756684	+	1.04149i
$669$	−5.07186	+	15.6096i	−0.196090	+	0.603502i
$670$		0			0
$671$	4.10251	−	5.28555i	0.158376	−	0.204046i
$672$		−	47.3043i		−	1.82480i
$673$	16.8766	+	5.48354i	0.650546	+	0.211375i	0.615655	−	0.788016i	$-0.288892\pi$
$673$	16.8766	+	5.48354i	0.650546	+	0.211375i	0.0348910	+	0.999391i	$0.488892\pi$
$674$	40.5003	−	29.4252i	1.56001	−	1.13342i
$675$		0			0
$676$	−2.73192	−	8.40799i	−0.105074	−	0.323384i
$677$	−7.76267	+	2.52224i	−0.298344	+	0.0969377i	−0.454364	−	0.890816i	$-0.650133\pi$
$677$	−7.76267	+	2.52224i	−0.298344	+	0.0969377i	0.156020	+	0.987754i	$0.450133\pi$
$678$	−7.15380	+	9.84636i	−0.274740	+	0.378147i
$679$	−38.1004	+	27.6815i	−1.46216	+	1.06232i
$680$		0			0
$681$	11.8613			0.454527
$682$	72.7675	+	2.30933i	2.78641	+	0.0884289i
$683$			6.19100i			0.236892i	0.992960	+	0.118446i	$0.0377913\pi$
$683$			6.19100i			0.236892i	−0.992960	+	0.118446i	$0.962209\pi$
$684$	3.84650	−	11.8383i	0.147075	−	0.452649i
$685$		0			0
$686$	23.8770	+	17.3477i	0.911628	+	0.662336i
$687$	−42.1473	+	13.6945i	−1.60802	+	0.522477i
$688$	3.83530	−	1.24617i	0.146220	−	0.0475096i
$689$	10.3336	+	7.50781i	0.393680	+	0.286025i
$690$		0			0
$691$	7.29438	−	22.4498i	0.277491	−	0.854030i	−0.711058	−	0.703133i	$-0.751784\pi$
$691$	7.29438	−	22.4498i	0.277491	−	0.854030i	0.988549	−	0.150897i	$-0.0482162\pi$
$692$			25.8892i			0.984158i
$693$	2.27471	−	6.31212i	0.0864090	−	0.239778i
$694$	−0.695956			−0.0264181
$695$		0			0
$696$	4.70977	−	3.42185i	0.178523	−	0.129705i
$697$	1.20170	−	1.65400i	0.0455177	−	0.0626497i
$698$	−2.43411	+	0.790889i	−0.0921323	+	0.0299356i
$699$	16.4710	+	50.6925i	0.622990	+	1.91737i
$700$		0			0
$701$	−30.1184	+	21.8823i	−1.13756	+	0.826483i	−0.986777	−	0.162084i	$-0.948178\pi$
$701$	−30.1184	+	21.8823i	−1.13756	+	0.826483i	−0.150779	+	0.988567i	$0.548178\pi$
$702$	27.2105	+	8.84124i	1.02700	+	0.333691i
$703$			14.5637i			0.549282i
$704$	34.2667	−	9.94389i	1.29147	−	0.374775i
$705$		0			0
$706$	16.6428	−	51.2211i	0.626358	−	1.92773i
$707$	21.1521	+	29.1133i	0.795505	+	1.09492i
$708$	−7.56588	+	10.4135i	−0.284343	+	0.391365i
$709$	−5.64072	−	17.3603i	−0.211842	−	0.651981i	−0.999363	−	0.0356939i	$-0.988636\pi$
$709$	−5.64072	−	17.3603i	−0.211842	−	0.651981i	0.787521	−	0.616288i	$-0.211364\pi$
$710$		0			0
$711$	6.16719	+	4.48073i	0.231288	+	0.168040i
$712$	−3.25378	−	4.47845i	−0.121941	−	0.167837i
$713$	−13.8521	−	4.50083i	−0.518766	−	0.168557i
$714$	5.70259			0.213414
$715$		0			0
$716$	54.3388			2.03074
$717$	−29.6306	−	9.62758i	−1.10658	−	0.359549i
$718$	22.0841	+	30.3961i	0.824171	+	1.13437i
$719$	7.74544	+	5.62739i	0.288856	+	0.209866i	0.722771	−	0.691088i	$-0.242868\pi$
$719$	7.74544	+	5.62739i	0.288856	+	0.209866i	−0.433915	+	0.900954i	$0.642868\pi$
$720$		0			0
$721$	−13.1633	−	40.5124i	−0.490226	−	1.50876i
$722$	−53.3779	+	73.4684i	−1.98652	+	2.73421i
$723$	4.93697	+	6.79515i	0.183608	+	0.252714i
$724$	−1.77147	+	5.45202i	−0.0658361	+	0.202623i
$725$		0			0
$726$	44.0025	+	2.79572i	1.63309	+	0.103759i
$727$		−	14.0175i		−	0.519882i	−0.965625	−	0.259941i	$-0.916297\pi$
$727$		−	14.0175i		−	0.519882i	0.965625	−	0.259941i	$-0.0837031\pi$
$728$	−7.27470	−	2.36369i	−0.269618	−	0.0876043i
$729$	15.1616	−	11.0156i	0.561542	−	0.407984i
$730$		0			0
$731$	0.188455	+	0.580006i	0.00697027	+	0.0214523i
$732$	8.77306	−	2.85054i	0.324262	−	0.105359i
$733$	−5.45918	+	7.51392i	−0.201640	+	0.277533i	−0.897847	−	0.440308i	$-0.854869\pi$
$733$	−5.45918	+	7.51392i	−0.201640	+	0.277533i	0.696207	+	0.717841i	$0.254869\pi$
$734$	14.3932	−	10.4573i	0.531262	−	0.385984i
$735$		0			0
$736$	−11.2083			−0.413145
$737$	18.5406	−	12.5918i	0.682951	−	0.463824i
$738$		−	6.09119i		−	0.224220i
$739$	12.0389	−	37.0519i	0.442857	−	1.36298i	−0.441959	−	0.897035i	$-0.645716\pi$
$739$	12.0389	−	37.0519i	0.442857	−	1.36298i	0.884816	−	0.465940i	$-0.154284\pi$
$740$		0			0
$741$	37.2676	+	27.0765i	1.36906	+	0.994681i
$742$	−25.5984	+	8.31742i	−0.939747	+	0.305342i
$743$	43.6817	−	14.1930i	1.60252	−	0.520692i	0.634795	−	0.772681i	$-0.281085\pi$
$743$	43.6817	−	14.1930i	1.60252	−	0.520692i	0.967730	+	0.251989i	$0.0810846\pi$
$744$	13.2581	+	9.63260i	0.486067	+	0.353148i
$745$		0			0
$746$	−23.2089	+	71.4298i	−0.849740	+	2.61523i
$747$			5.88233i			0.215223i
$748$	1.02481	+	3.53148i	0.0374706	+	0.129124i
$749$	−22.4549			−0.820483
$750$		0			0
$751$	−18.7634	+	13.6324i	−0.684686	+	0.497453i	−0.874909	−	0.484288i	$-0.839079\pi$
$751$	−18.7634	+	13.6324i	−0.684686	+	0.497453i	0.190223	+	0.981741i	$0.439079\pi$
$752$	5.37281	−	7.39504i	0.195926	−	0.269669i
$753$	−4.85167	+	1.57640i	−0.176805	+	0.0574474i
$754$	7.34907	+	22.6181i	0.267637	+	0.823703i
$755$		0			0
$756$	−26.5555	+	19.2937i	−0.965815	+	0.701705i
$757$	−6.20281	−	2.01541i	−0.225445	−	0.0732515i	0.194116	−	0.980979i	$-0.437816\pi$
$757$	−6.20281	−	2.01541i	−0.225445	−	0.0732515i	−0.419561	+	0.907727i	$0.637816\pi$
$758$			36.7757i			1.33575i
$759$	−8.29835	−	2.99049i	−0.301211	−	0.108548i
$760$		0			0
$761$	−2.02926	+	6.24542i	−0.0735606	+	0.226396i	−0.981076	−	0.193622i	$-0.937976\pi$
$761$	−2.02926	+	6.24542i	−0.0735606	+	0.226396i	0.907516	+	0.420018i	$0.137976\pi$
$762$	−1.06397	−	1.46443i	−0.0385436	−	0.0530507i
$763$	−13.4007	+	18.4444i	−0.485137	+	0.667733i
$764$	−12.7386	−	39.2054i	−0.460866	−	1.41840i
$765$		0			0
$766$	−36.6572	−	26.6330i	−1.32448	−	0.962291i
$767$	−5.04631	−	6.94565i	−0.182212	−	0.250793i
$768$	−14.6829	−	4.77078i	−0.529825	−	0.172151i
$769$	−12.5950			−0.454188			−0.227094	−	0.973873i	$-0.572922\pi$
$769$	−12.5950			−0.454188			−0.227094	+	0.973873i	$0.572922\pi$
$770$		0			0
$771$	−41.3832			−1.49038
$772$	−5.87807	−	1.90990i	−0.211557	−	0.0687389i
$773$	12.8988	+	17.7537i	0.463939	+	0.638557i	0.975320	−	0.220797i	$-0.0708660\pi$
$773$	12.8988	+	17.7537i	0.463939	+	0.638557i	−0.511381	+	0.859354i	$0.670866\pi$
$774$	1.46997	+	1.06799i	0.0528369	+	0.0383883i
$775$		0			0
$776$	−3.87980	−	11.9408i	−0.139277	−	0.428650i
$777$	−6.36150	+	8.75585i	−0.228217	+	0.314114i
$778$	−44.0188	−	60.5867i	−1.57815	−	2.17214i
$779$	−10.7541	+	33.0977i	−0.385305	+	1.18585i
$780$		0			0
$781$	13.2630	−	17.0876i	0.474587	−	0.611444i
$782$		−	1.35118i		−	0.0483181i
$783$	15.8471	+	5.14904i	0.566330	+	0.184012i
$784$	−5.97430	+	4.34059i	−0.213368	+	0.155021i
$785$		0			0
$786$	−0.779102	−	2.39783i	−0.0277897	−	0.0855278i
$787$	−15.9110	+	5.16981i	−0.567167	+	0.184284i	−0.578543	−	0.815652i	$-0.696379\pi$
$787$	−15.9110	+	5.16981i	−0.567167	+	0.184284i	0.0113766	+	0.999935i	$0.496379\pi$
$788$	−0.203341	+	0.279875i	−0.00724372	+	0.00997012i
$789$	34.2637	−	24.8940i	1.21982	−	0.886250i
$790$		0			0
$791$	9.31320			0.331139
$792$	1.41303	+	1.09676i	0.0502100	+	0.0389717i
$793$			6.15261i			0.218486i
$794$	−12.9786	+	39.9439i	−0.460592	+	1.41756i
$795$		0			0
$796$	14.5840	+	10.5959i	0.516915	+	0.375560i
$797$	11.1946	−	3.63735i	0.396533	−	0.128842i	−0.103961	−	0.994581i	$-0.533152\pi$
$797$	11.1946	−	3.63735i	0.396533	−	0.128842i	0.500494	+	0.865740i	$0.333152\pi$
$798$	−92.3192	+	29.9963i	−3.26807	+	1.06186i
$799$	1.11834	+	0.812521i	0.0395640	+	0.0287449i
$800$		0			0
$801$	−1.37978	+	4.24652i	−0.0487521	+	0.150043i
$802$			43.7889i			1.54624i
$803$	32.7379	+	1.03896i	1.15529	+	0.0366641i
$804$	30.8992			1.08973
$805$		0			0
$806$	−54.1615	+	39.3507i	−1.90776	+	1.38607i
$807$	23.2964	−	32.0647i	0.820072	−	1.12873i
$808$	−9.12422	+	2.96464i	−0.320989	+	0.104296i
$809$	−0.369567	−	1.13741i	−0.0129933	−	0.0399893i	0.944350	−	0.328943i	$-0.106693\pi$
$809$	−0.369567	−	1.13741i	−0.0129933	−	0.0399893i	−0.957343	+	0.288954i	$0.906693\pi$
$810$		0			0
$811$	−28.9833	+	21.0576i	−1.01774	+	0.739431i	−0.965818	−	0.259220i	$-0.916535\pi$
$811$	−28.9833	+	21.0576i	−1.01774	+	0.739431i	−0.0519216	+	0.998651i	$0.516535\pi$
$812$	−25.9491	−	8.43138i	−0.910636	−	0.295884i
$813$			0.809412i			0.0283873i
$814$	−12.0591	−	4.34575i	−0.422670	−	0.152318i
$815$		0			0
$816$	0.841026	−	2.58841i	0.0294418	−	0.0906126i
$817$	−6.10181	−	8.39841i	−0.213475	−	0.293823i
$818$	28.9400	−	39.8324i	1.01186	−	1.39271i
$819$	1.90655	+	5.86776i	0.0666202	+	0.205036i
$820$		0			0
$821$	−4.44312	−	3.22811i	−0.155066	−	0.112662i	0.507547	−	0.861624i	$-0.330552\pi$
$821$	−4.44312	−	3.22811i	−0.155066	−	0.112662i	−0.662613	+	0.748962i	$0.730552\pi$
$822$	26.3482	+	36.2652i	0.919000	+	1.26490i
$823$	−40.6341	−	13.2028i	−1.41642	−	0.460222i	−0.501955	−	0.864894i	$-0.667386\pi$
$823$	−40.6341	−	13.2028i	−1.41642	−	0.460222i	−0.914462	+	0.404672i	$0.867386\pi$
$824$	11.3563			0.395616
$825$		0			0
$826$	18.0912			0.629473
$827$	30.8340	+	10.0186i	1.07220	+	0.348380i	0.791345	−	0.611369i	$-0.209381\pi$
$827$	30.8340	+	10.0186i	1.07220	+	0.348380i	0.280858	+	0.959749i	$0.409381\pi$
$828$	−1.28828	−	1.77317i	−0.0447709	−	0.0616218i
$829$	−2.35544	−	1.71133i	−0.0818079	−	0.0594369i	0.546130	−	0.837701i	$-0.316101\pi$
$829$	−2.35544	−	1.71133i	−0.0818079	−	0.0594369i	−0.627937	+	0.778264i	$0.716101\pi$
$830$		0			0
$831$	−5.06765	−	15.5966i	−0.175795	−	0.541041i
$832$	−19.2852	+	26.5438i	−0.668594	+	0.920241i
$833$	−0.656419	−	0.903483i	−0.0227436	−	0.0313038i
$834$	−2.94169	+	9.05359i	−0.101862	+	0.313500i
$835$		0			0
$836$	−35.1666	−	51.7805i	−1.21626	−	1.79087i
$837$			46.9059i			1.62130i
$838$	−20.1522	−	6.54786i	−0.696147	−	0.226192i
$839$	−16.8652	+	12.2533i	−0.582250	+	0.423030i	−0.839535	−	0.543306i	$-0.817172\pi$
$839$	−16.8652	+	12.2533i	−0.582250	+	0.423030i	0.257284	+	0.966336i	$0.417172\pi$
$840$		0			0
$841$	−4.68147	−	14.4081i	−0.161430	−	0.496830i
$842$	17.7809	−	5.77737i	0.612771	−	0.199101i
$843$	7.88348	−	10.8507i	0.271521	−	0.373717i
$844$	−4.38733	+	3.18758i	−0.151018	+	0.109721i
$845$		0			0
$846$	4.11851			0.141597
$847$	−18.0607	−	28.4980i	−0.620572	−	0.979203i
$848$			12.8458i			0.441127i
$849$	−5.88380	+	18.1085i	−0.201932	+	0.621482i
$850$		0			0
$851$	2.07462	+	1.50730i	0.0711171	+	0.0516696i
$852$	28.3624	−	9.21549i	0.971679	−	0.315718i
$853$	32.8599	−	10.6768i	1.12510	−	0.365567i	0.313388	−	0.949625i	$-0.398536\pi$
$853$	32.8599	−	10.6768i	1.12510	−	0.365567i	0.811712	+	0.584058i	$0.198536\pi$
$854$	−10.4889	−	7.62061i	−0.358922	−	0.260772i
$855$		0			0
$856$	1.84990	−	5.69341i	0.0632283	−	0.194597i
$857$			33.2969i			1.13740i	0.822545	+	0.568699i	$0.192553\pi$
$857$			33.2969i			1.13740i	−0.822545	+	0.568699i	$0.807447\pi$
$858$	−33.5404	+	22.7789i	−1.14505	+	0.777658i
$859$	16.7665			0.572067			0.286034	−	0.958220i	$-0.407663\pi$
$859$	16.7665			0.572067			0.286034	+	0.958220i	$0.407663\pi$
$860$		0			0
$861$	−20.9227	+	15.2012i	−0.713043	+	0.518056i
$862$	21.6909	−	29.8550i	0.738796	−	1.01687i
$863$	−1.41151	+	0.458628i	−0.0480484	+	0.0156119i	−0.332943	−	0.942947i	$-0.608042\pi$
$863$	−1.41151	+	0.458628i	−0.0480484	+	0.0156119i	0.284894	+	0.958559i	$0.408042\pi$
$864$	11.1543	+	34.3293i	0.379476	+	1.16791i
$865$		0			0
$866$	15.5002	−	11.2616i	0.526719	−	0.382683i
$867$	−30.5378	−	9.92234i	−1.03712	−	0.336980i
$868$		−	76.8068i		−	2.60699i
$869$	36.8143	−	10.6832i	1.24884	−	0.362403i
$870$		0			0
$871$	−6.36860	+	19.6005i	−0.215792	+	0.664138i
$872$	−3.57258	−	4.91723i	−0.120983	−	0.166518i
$873$	−5.95254	+	8.19297i	−0.201463	+	0.277290i
$874$	7.10737	+	21.8742i	0.240410	+	0.739907i
$875$		0			0
$876$	36.5333	+	26.5430i	1.23435	+	0.896805i
$877$	14.6132	+	20.1134i	0.493453	+	0.679180i	0.981020	−	0.193905i	$-0.0621155\pi$
$877$	14.6132	+	20.1134i	0.493453	+	0.679180i	−0.487567	+	0.873086i	$0.662115\pi$
$878$	12.8920	+	4.18885i	0.435083	+	0.141367i
$879$	−41.7433			−1.40797
$880$		0			0
$881$	32.6968			1.10158			0.550792	−	0.834643i	$-0.314326\pi$
$881$	32.6968			1.10158			0.550792	+	0.834643i	$0.314326\pi$
$882$	−3.16441	−	1.02818i	−0.106551	−	0.0346206i
$883$	27.9914	+	38.5268i	0.941985	+	1.29653i	0.954997	+	0.296615i	$0.0958579\pi$
$883$	27.9914	+	38.5268i	0.941985	+	1.29653i	−0.0130124	+	0.999915i	$0.504142\pi$
$884$	−2.73557	−	1.98751i	−0.0920073	−	0.0668472i
$885$		0			0
$886$	26.4717	+	81.4717i	0.889336	+	2.73709i
$887$	34.7358	−	47.8097i	1.16631	−	1.60529i	0.481826	−	0.876267i	$-0.339974\pi$
$887$	34.7358	−	47.8097i	1.16631	−	1.60529i	0.684487	−	0.729025i	$-0.260026\pi$
$888$	−1.69596	−	2.33428i	−0.0569126	−	0.0783335i
$889$	−0.428030	+	1.31734i	−0.0143557	+	0.0441822i
$890$		0			0
$891$	−1.10922	+	34.9518i	−0.0371603	+	1.17093i
$892$			20.5076i			0.686646i
$893$	−22.3787	−	7.27130i	−0.748876	−	0.243325i
$894$	28.2781	−	20.5452i	0.945761	−	0.687136i
$895$		0			0
$896$	−6.08220	−	18.7191i	−0.203192	−	0.625360i
$897$	7.71417	−	2.50648i	0.257569	−	0.0836891i
$898$	−14.9770	+	20.6140i	−0.499788	+	0.687900i
$899$	−31.5431	+	22.9174i	−1.05202	+	0.764338i
$900$		0			0
$901$	−1.94265			−0.0647190
$902$	−24.1966	−	18.7808i	−0.805659	−	0.625332i
$903$		−	7.71450i		−	0.256722i
$904$	−0.767250	+	2.36135i	−0.0255183	+	0.0785374i
$905$		0			0
$906$	38.7039	+	28.1200i	1.28585	+	0.934225i
$907$	−32.9613	+	10.7098i	−1.09446	+	0.355612i	−0.799969	−	0.600041i	$-0.795151\pi$
$907$	−32.9613	+	10.7098i	−1.09446	+	0.355612i	−0.294493	+	0.955654i	$0.595151\pi$
$908$	14.0952	−	4.57979i	0.467764	−	0.151986i
$909$	6.26043	+	4.54847i	0.207645	+	0.150863i
$910$		0			0
$911$	−3.14834	+	9.68961i	−0.104309	+	0.321031i	−0.989568	−	0.144069i	$-0.953981\pi$
$911$	−3.14834	+	9.68961i	−0.104309	+	0.321031i	0.885258	+	0.465099i	$0.153981\pi$
$912$			46.3277i			1.53406i
$913$	23.3669	+	18.1368i	0.773332	+	0.600241i
$914$	−20.7484			−0.686298
$915$		0			0
$916$	−44.7972	+	32.5471i	−1.48014	+	1.07539i
$917$	−1.13400	+	1.56081i	−0.0374479	+	0.0515426i
$918$	−4.13844	+	1.34466i	−0.136589	+	0.0443804i
$919$	11.1644	+	34.3606i	0.368281	+	1.13345i	0.947901	+	0.318565i	$0.103201\pi$
$919$	11.1644	+	34.3606i	0.368281	+	1.13345i	−0.579620	+	0.814887i	$0.696799\pi$
$920$		0			0
$921$	47.7719	−	34.7083i	1.57414	−	1.14368i
$922$	6.22790	+	2.02357i	0.205105	+	0.0666427i
$923$			19.8907i			0.654711i
$924$	1.47545	−	46.4918i	0.0485389	−	1.52947i
$925$		0			0
$926$	15.7674	−	48.5269i	0.518148	−	1.59469i
$927$	−5.38409	−	7.41057i	−0.176837	−	0.243395i
$928$	−17.6359	+	24.2737i	−0.578926	+	0.796823i
$929$	−8.69078	−	26.7475i	−0.285135	−	0.877556i	−0.986358	−	0.164614i	$-0.947362\pi$
$929$	−8.69078	−	26.7475i	−0.285135	−	0.877556i	0.701223	−	0.712942i	$-0.252638\pi$
$930$		0			0
$931$	15.3792	+	11.1736i	0.504033	+	0.366201i
$932$	39.1459	+	53.8797i	1.28227	+	1.76489i
$933$	35.3231	+	11.4772i	1.15643	+	0.375745i
$934$	69.5087			2.27439
$935$		0			0
$936$	−1.64483			−0.0537630
$937$	0.0809993	+	0.0263183i	0.00264613	+	0.000859781i	0.310340	−	0.950626i	$-0.399557\pi$
$937$	0.0809993	+	0.0263183i	0.00264613	+	0.000859781i	−0.307694	+	0.951485i	$0.599557\pi$
$938$	−25.5265	−	35.1342i	−0.833471	−	1.14717i
$939$	1.62730	+	1.18231i	0.0531050	+	0.0385831i
$940$		0			0
$941$	−12.9217	−	39.7688i	−0.421234	−	1.29643i	−0.906554	−	0.422089i	$-0.861297\pi$
$941$	−12.9217	−	39.7688i	−0.421234	−	1.29643i	0.485320	−	0.874337i	$-0.338703\pi$
$942$	−9.13031	+	12.5668i	−0.297482	+	0.409448i
$943$	3.60179	+	4.95744i	0.117291	+	0.161437i
$944$	2.66812	−	8.21161i	0.0868398	−	0.267265i
$945$		0			0
$946$	8.77481	−	2.54638i	0.285294	−	0.0827898i
$947$			8.92463i			0.290012i	0.989431	+	0.145006i	$0.0463201\pi$
$947$			8.92463i			0.290012i	−0.989431	+	0.145006i	$0.953680\pi$
$948$	50.2623	+	16.3312i	1.63244	+	0.530413i
$949$	−24.3671	+	17.7037i	−0.790989	+	0.574687i
$950$		0			0
$951$	−14.0879	−	43.3581i	−0.456832	−	1.40598i
$952$	1.10641	−	0.359493i	0.0358589	−	0.0116512i
$953$	−3.09400	+	4.25853i	−0.100225	+	0.137947i	−0.856184	−	0.516672i	$-0.827171\pi$
$953$	−3.09400	+	4.25853i	−0.100225	+	0.137947i	0.755959	+	0.654619i	$0.227171\pi$
$954$	−4.68249	+	3.40202i	−0.151601	+	0.110145i
$955$		0			0
$956$	−38.9283			−1.25903
$957$	−19.5336	+	13.2662i	−0.631431	+	0.428834i
$958$		−	36.2438i		−	1.17098i
$959$	10.5998	−	32.6227i	0.342284	−	1.05344i
$960$		0			0
$961$	−63.7153	−	46.2919i	−2.05533	−	1.49329i
$962$	11.2101	−	3.64240i	0.361429	−	0.117436i
$963$	−4.59229	+	1.49213i	−0.147984	+	0.0480831i
$964$	8.49043	+	6.16866i	0.273458	+	0.198679i
$965$		0			0
$966$	−5.28174	+	16.2555i	−0.169937	+	0.523013i
$967$		−	18.5421i		−	0.596275i	−0.954523	−	0.298138i	$-0.903635\pi$
$967$		−	18.5421i		−	0.596275i	0.954523	−	0.298138i	$-0.0963654\pi$
$968$	8.71353	−	2.23151i	0.280063	−	0.0717235i
$969$	−7.00606			−0.225067
$970$		0			0
$971$	19.5968	−	14.2379i	0.628893	−	0.456917i	−0.227124	−	0.973866i	$-0.572932\pi$
$971$	19.5968	−	14.2379i	0.628893	−	0.456917i	0.856016	+	0.516949i	$0.172932\pi$
$972$	−9.46689	+	13.0301i	−0.303651	+	0.417939i
$973$	6.92790	−	2.25101i	0.222098	−	0.0721641i
$974$	4.94715	+	15.2258i	0.158517	+	0.487865i
$975$		0			0
$976$	−5.00592	+	3.63701i	−0.160236	+	0.116418i
$977$	46.6606	+	15.1609i	1.49280	+	0.485041i	0.937910	−	0.346880i	$-0.112759\pi$
$977$	46.6606	+	15.1609i	1.49280	+	0.485041i	0.554894	+	0.831921i	$0.312759\pi$
$978$		−	39.8272i		−	1.27353i
$979$	12.6146	+	18.5742i	0.403165	+	0.593634i
$980$		0			0
$981$	−1.51496	+	4.66258i	−0.0483691	+	0.148865i
$982$	−37.7558	−	51.9664i	−1.20484	−	1.65831i
$983$	−28.8834	+	39.7546i	−0.921239	+	1.26798i	0.0419415	+	0.999120i	$0.486646\pi$
$983$	−28.8834	+	39.7546i	−0.921239	+	1.26798i	−0.963180	+	0.268856i	$0.913354\pi$
$984$	−2.13058	−	6.55724i	−0.0679203	−	0.209037i
$985$		0			0
$986$	−2.92622	−	2.12603i	−0.0931899	−	0.0677064i
$987$	−10.2782	−	14.1467i	−0.327158	−	0.450294i
$988$	54.7408	+	17.7863i	1.74154	+	0.565859i
$989$	−1.82788			−0.0581233
$990$		0			0
$991$	30.9620			0.983541			0.491771	−	0.870725i	$-0.336350\pi$
$991$	30.9620			0.983541			0.491771	+	0.870725i	$0.336350\pi$
$992$	−80.3281	−	26.1002i	−2.55042	−	0.828681i
$993$	28.8634	+	39.7271i	0.915952	+	1.26070i
$994$	−33.9094	−	24.6366i	−1.07554	−	0.781426i
$995$		0			0
$996$	12.6020	+	38.7849i	0.399309	+	1.22895i
$997$	13.4567	−	18.5216i	0.426178	−	0.586584i	−0.540892	−	0.841092i	$-0.681913\pi$
$997$	13.4567	−	18.5216i	0.426178	−	0.586584i	0.967071	+	0.254507i	$0.0819134\pi$
$998$	46.1576	+	63.5305i	1.46109	+	2.01102i
$999$	2.55200	−	7.85426i	0.0807418	−	0.248498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.z.a.174.1		16
5.2	odd	4		275.2.h.a.251.2		8
5.3	odd	4		55.2.g.b.31.1	yes	8
5.4	even	2	inner	275.2.z.a.174.4		16
11.5	even	5	inner	275.2.z.a.49.4		16
15.8	even	4		495.2.n.e.361.2		8
20.3	even	4		880.2.bo.h.801.2		8
55.3	odd	20		605.2.g.m.81.2		8
55.7	even	20		3025.2.a.w.1.1		4
55.8	even	20		605.2.g.e.81.1		8
55.13	even	20		605.2.g.e.366.1		8
55.18	even	20		605.2.a.k.1.4		4
55.27	odd	20		275.2.h.a.126.2		8
55.28	even	20		605.2.g.k.511.2		8
55.37	odd	20		3025.2.a.bd.1.4		4
55.38	odd	20		55.2.g.b.16.1	✓	8
55.43	even	4		605.2.g.k.251.2		8
55.48	odd	20		605.2.a.j.1.1		4
55.49	even	10	inner	275.2.z.a.49.1		16
55.53	odd	20		605.2.g.m.366.2		8
165.38	even	20		495.2.n.e.181.2		8
165.128	odd	20		5445.2.a.bi.1.1		4
165.158	even	20		5445.2.a.bp.1.4		4
220.103	even	20		9680.2.a.cn.1.1		4
220.183	odd	20		9680.2.a.cm.1.1		4
220.203	even	20		880.2.bo.h.401.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.1	✓	8	55.38	odd	20
55.2.g.b.31.1	yes	8	5.3	odd	4
275.2.h.a.126.2		8	55.27	odd	20
275.2.h.a.251.2		8	5.2	odd	4
275.2.z.a.49.1		16	55.49	even	10	inner
275.2.z.a.49.4		16	11.5	even	5	inner
275.2.z.a.174.1		16	1.1	even	1	trivial
275.2.z.a.174.4		16	5.4	even	2	inner
495.2.n.e.181.2		8	165.38	even	20
495.2.n.e.361.2		8	15.8	even	4
605.2.a.j.1.1		4	55.48	odd	20
605.2.a.k.1.4		4	55.18	even	20
605.2.g.e.81.1		8	55.8	even	20
605.2.g.e.366.1		8	55.13	even	20
605.2.g.k.251.2		8	55.43	even	4
605.2.g.k.511.2		8	55.28	even	20
605.2.g.m.81.2		8	55.3	odd	20
605.2.g.m.366.2		8	55.53	odd	20
880.2.bo.h.401.2		8	220.203	even	20
880.2.bo.h.801.2		8	20.3	even	4
3025.2.a.w.1.1		4	55.7	even	20
3025.2.a.bd.1.4		4	55.37	odd	20
5445.2.a.bi.1.1		4	165.128	odd	20
5445.2.a.bp.1.4		4	165.158	even	20
9680.2.a.cm.1.1		4	220.183	odd	20
9680.2.a.cn.1.1		4	220.103	even	20

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.z (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.99274 - 0.647481i) q^{2} +(1.12443 + 1.54765i) q^{3} +(1.93376 + 1.40496i) q^{4} +(-1.23863 - 3.81211i) q^{6} +(-1.80285 + 2.48141i) q^{7} +(-0.480634 - 0.661536i) q^{8} +(-0.203814 + 0.627276i) q^{9} +(1.86337 + 2.74369i) q^{11} +4.57255i q^{12} +(-2.90055 - 0.942444i) q^{13} +(5.19927 - 3.77749i) q^{14} +(-0.947813 - 2.91707i) q^{16} +(0.441143 - 0.143336i) q^{17} +(0.812299 - 1.11803i) q^{18} +(-6.38769 + 4.64093i) q^{19} -5.86752 q^{21} +(-1.93673 - 6.67397i) q^{22} +1.39026i q^{23} +(0.483384 - 1.48770i) q^{24} +(5.16983 + 3.75610i) q^{26} +(4.25813 - 1.38355i) q^{27} +(-6.97254 + 2.26552i) q^{28} +(3.01085 + 2.18751i) q^{29} +(-3.23741 + 9.96371i) q^{31} +8.06206i q^{32} +(-2.15103 + 5.96893i) q^{33} -0.971892 q^{34} +(-1.27542 + 0.926650i) q^{36} +(1.08419 - 1.49226i) q^{37} +(15.7340 - 5.11227i) q^{38} +(-1.80289 - 5.54873i) q^{39} +(3.56585 - 2.59074i) q^{41} +(11.6925 + 3.79911i) q^{42} +1.31478i q^{43} +(-0.251461 + 7.92360i) q^{44} +(0.900166 - 2.77042i) q^{46} +(1.75171 + 2.41102i) q^{47} +(3.44884 - 4.74692i) q^{48} +(-0.743998 - 2.28979i) q^{49} +(0.717868 + 0.521562i) q^{51} +(-4.28486 - 5.89760i) q^{52} +(-3.98316 - 1.29421i) q^{53} -9.38118 q^{54} +2.50805 q^{56} +(-14.3650 - 4.66749i) q^{57} +(-4.58348 - 6.30862i) q^{58} +(2.27740 + 1.65463i) q^{59} +(-0.623402 - 1.91863i) q^{61} +(12.9026 - 17.7590i) q^{62} +(-1.18908 - 1.63663i) q^{63} +(3.32441 - 10.2315i) q^{64} +(8.15123 - 10.5018i) q^{66} -6.75753i q^{67} +(1.05444 + 0.342610i) q^{68} +(-2.15163 + 1.56325i) q^{69} +(-2.01539 - 6.20274i) q^{71} +(0.512925 - 0.166660i) q^{72} +(5.80485 - 7.98970i) q^{73} +(-3.12672 + 2.27169i) q^{74} -18.8726 q^{76} +(-10.1676 - 0.322676i) q^{77} +12.2245i q^{78} +(3.57158 - 10.9922i) q^{79} +(8.53000 + 6.19741i) q^{81} +(-8.78327 + 2.85386i) q^{82} +(8.48210 - 2.75600i) q^{83} +(-11.3464 - 8.24361i) q^{84} +(0.851296 - 2.62002i) q^{86} +7.11945i q^{87} +(0.919451 - 2.55140i) q^{88} +6.76978 q^{89} +(7.56782 - 5.49835i) q^{91} +(-1.95325 + 2.68842i) q^{92} +(-19.0606 + 6.19315i) q^{93} +(-1.92961 - 5.93874i) q^{94} +(-12.4772 + 9.06524i) q^{96} +(14.6029 + 4.74475i) q^{97} +5.04469i q^{98} +(-2.10083 + 0.609644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9} + 6 q^{11} + 32 q^{14} + 8 q^{16} - 30 q^{19} - 40 q^{21} - 26 q^{24} + 20 q^{26} + 18 q^{29} - 20 q^{31} - 8 q^{34} - 30 q^{36} - 42 q^{39} + 16 q^{41} + 24 q^{44}+ \cdots + 40 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9 + 6 * q^11 + 32 * q^14 + 8 * q^16 - 30 * q^19 - 40 * q^21 - 26 * q^24 + 20 * q^26 + 18 * q^29 - 20 * q^31 - 8 * q^34 - 30 * q^36 - 42 * q^39 + 16 * q^41 + 24 * q^44 + 6 * q^46 - 2 * q^49 + 2 * q^51 - 32 * q^54 + 44 * q^56 + 54 * q^59 + 12 * q^61 + 52 * q^64 + 26 * q^66 + 2 * q^69 - 40 * q^71 - 40 * q^74 - 74 * q^79 + 16 * q^81 - 56 * q^84 - 6 * q^86 + 32 * q^89 + 88 * q^91 - 34 * q^94 - 34 * q^96 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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