LMFDB - Embedded newform 275.2.z.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(49,275)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
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			49.1
Root			$1.23158 + 1.69513i$ of defining polynomial
Character	$\chi$	$=$	275.49
Dual form			275.2.z.a.174.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99274 + 0.647481i) q^{2} +(1.12443 - 1.54765i) q^{3} +(1.93376 - 1.40496i) q^{4} +(-1.23863 + 3.81211i) q^{6} +(-1.80285 - 2.48141i) q^{7} +(-0.480634 + 0.661536i) q^{8} +(-0.203814 - 0.627276i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

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	−0.912116	−	0.409932i	$-0.865553\pi$
$2$	−1.99274	+	0.647481i	−1.40908	+	0.457839i	−0.496966	+	0.867770i	$0.665553\pi$
$3$	1.12443	−	1.54765i	0.649191	−	0.893534i	−0.349873	−	0.936797i	$-0.613775\pi$
$3$	1.12443	−	1.54765i	0.649191	−	0.893534i	0.999064	+	0.0432627i	$0.0137753\pi$
$4$	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	0.318538	−	0.947910i	$-0.396808\pi$
$7$	−1.80285	−	2.48141i	−0.681412	−	0.937883i	−0.999950	+	0.0100271i	$0.996808\pi$
$8$	−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	−0.682252	−	0.731117i	$-0.738999\pi$
$13$	−2.90055	+	0.942444i	−0.804467	+	0.261387i	−0.122214	+	0.992504i	$0.538999\pi$
$14$	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	0.362024	−	0.932169i	$-0.382086\pi$
$17$	0.441143	+	0.143336i	0.106993	+	0.0347641i	−0.255031	+	0.966933i	$0.582086\pi$
$18$	0.812299	+	1.11803i	0.191461	+	0.263523i
$19$	−6.38769	−	4.64093i	−1.46544	−	1.06470i	−0.981904	−	0.189377i	$-0.939353\pi$
$19$	−6.38769	−	4.64093i	−1.46544	−	1.06470i	−0.483533	−	0.875326i	$-0.660647\pi$
$20$		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	$-0.953700\pi$
$23$		−	1.39026i		−	0.289889i	0.989440	−	0.144944i	$-0.0463003\pi$
$24$	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	−0.272029	−	0.962289i	$-0.587695\pi$
$29$	3.01085	−	2.18751i	0.559101	−	0.406211i	0.831130	+	0.556078i	$0.187695\pi$
$30$		0			0
$31$	−3.23741	−	9.96371i	−0.581456	−	1.78954i	−0.613061	−	0.790036i	$-0.710062\pi$
$31$	−3.23741	−	9.96371i	−0.581456	−	1.78954i	0.0316054	−	0.999500i	$-0.489938\pi$
$32$		−	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	0.888784	−	0.458327i	$-0.151551\pi$
$37$	1.08419	+	1.49226i	0.178240	+	0.245326i	−0.710544	+	0.703653i	$0.751551\pi$
$38$	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	0.830320	−	0.557287i	$-0.188158\pi$
$41$	3.56585	+	2.59074i	0.556892	+	0.404605i	−0.273428	+	0.961892i	$0.588158\pi$
$42$	11.6925	−	3.79911i	1.80418	−	0.586215i
$43$		−	1.31478i		−	0.200502i	−0.994962	−	0.100251i	$-0.968035\pi$
$43$		−	1.31478i		−	0.200502i	0.994962	−	0.100251i	$-0.0319646\pi$
$44$	−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	−0.661920	−	0.749575i	$-0.730258\pi$
$47$	1.75171	−	2.41102i	0.255513	−	0.351683i	0.917432	+	0.397892i	$0.130258\pi$
$48$	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	−0.569522	−	0.821976i	$-0.692872\pi$
$53$	−3.98316	+	1.29421i	−0.547129	+	0.177773i	0.0223927	+	0.999749i	$0.492872\pi$
$54$	−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	−0.429586	−	0.903026i	$-0.641341\pi$
$59$	2.27740	−	1.65463i	0.296493	−	0.215414i	0.726079	+	0.687611i	$0.241341\pi$
$60$		0			0
$61$	−0.623402	+	1.91863i	−0.0798185	+	0.245656i	−0.983001	−	0.183601i	$-0.941225\pi$
$61$	−0.623402	+	1.91863i	−0.0798185	+	0.245656i	0.903182	+	0.429257i	$0.141225\pi$
$62$	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	$0.135443\pi$
$67$			6.75753i			0.825564i	−0.910830	+	0.412782i	$0.864557\pi$
$68$	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	0.757356	+	0.653003i	$0.226491\pi$
$71$	−2.01539	+	6.20274i	−0.239183	+	0.736130i	−0.996539	+	0.0831276i	$0.973509\pi$
$72$	0.512925	+	0.166660i	0.0604488	+	0.0196410i
$73$	5.80485	+	7.98970i	0.679407	+	0.935123i	0.999927	−	0.0121186i	$-0.00385757\pi$
$73$	5.80485	+	7.98970i	0.679407	+	0.935123i	−0.320520	+	0.947242i	$0.603858\pi$
$74$	−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	0.923510	+	0.383573i	$0.125307\pi$
$79$	3.57158	+	10.9922i	0.401834	+	1.23672i	−0.521677	+	0.853143i	$0.674693\pi$
$80$		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	0.734984	−	0.678084i	$-0.237189\pi$
$83$	8.48210	+	2.75600i	0.931032	+	0.302510i	0.196047	+	0.980594i	$0.437189\pi$
$84$	−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	0.547778	−	0.836624i	$-0.315474\pi$
$97$	14.6029	−	4.74475i	1.48269	−	0.481757i	0.934917	+	0.354867i	$0.115474\pi$
$98$		−	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	0.952595	+	0.304241i	$0.0984027\pi$
$101$	3.62557	+	11.1584i	0.360758	+	1.11030i	−0.591838	+	0.806057i	$0.701597\pi$
$102$	−1.09283	+	1.50415i	−0.108206	+	0.148933i
$103$	−8.16319	−	11.2357i	−0.804343	−	1.10708i	−0.992172	−	0.124882i	$-0.960145\pi$
$103$	−8.16319	−	11.2357i	−0.804343	−	1.10708i	0.187828	−	0.982202i	$-0.439855\pi$
$104$	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	−0.548666	−	0.836042i	$-0.684864\pi$
$107$	4.30318	−	5.92282i	0.416004	−	0.572580i	0.964670	+	0.263461i	$0.0848642\pi$
$108$	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	−0.884671	−	0.466216i	$-0.845617\pi$
$113$	−1.78475	+	2.45650i	−0.167895	+	0.231088i	0.716776	+	0.697304i	$0.245617\pi$
$114$	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	0.328011	−	0.944674i	$-0.393622\pi$
$127$	0.429495	+	0.139551i	0.0381115	+	0.0123832i	−0.289899	+	0.957057i	$0.593622\pi$
$128$	−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	−0.182876	−	0.983136i	$-0.558541\pi$
$137$	−10.6360	−	3.45586i	−0.908698	−	0.295254i	−0.725823	+	0.687882i	$0.758541\pi$
$138$	5.29981	+	1.72201i	0.451150	+	0.146588i
$139$	−1.92138	+	1.39596i	−0.162969	+	0.118404i	−0.666281	−	0.745701i	$-0.732115\pi$
$139$	−1.92138	+	1.39596i	−0.162969	+	0.118404i	0.503312	+	0.864105i	$0.332115\pi$
$140$		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	−0.777933	−	0.628347i	$-0.783732\pi$
$149$	2.69473	−	8.29354i	0.220761	−	0.679433i	0.998694	−	0.0510859i	$-0.0162682\pi$
$150$		0			0
$151$	−9.65596	−	7.01547i	−0.785791	−	0.570911i	0.120920	−	0.992662i	$-0.461415\pi$
$151$	−9.65596	−	7.01547i	−0.785791	−	0.570911i	−0.906711	+	0.421752i	$0.861415\pi$
$152$	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	−0.890181	−	0.455606i	$-0.849422\pi$
$157$	−2.27786	+	3.13520i	−0.181793	+	0.250216i	0.708389	+	0.705823i	$0.249422\pi$
$158$	−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	0.0854258	−	0.996345i	$-0.472775\pi$
$163$	9.44990	−	3.07046i	0.740173	−	0.240497i	0.654748	+	0.755848i	$0.272775\pi$
$164$	10.5354			0.822674
$165$		0			0
$166$	−18.6871			−1.45040
$167$	13.2387	−	4.30152i	1.02444	−	0.332862i	0.251852	−	0.967766i	$-0.418960\pi$
$167$	13.2387	−	4.30152i	1.02444	−	0.332862i	0.772591	+	0.634904i	$0.218960\pi$
$168$	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	−0.495246	−	0.868753i	$-0.664922\pi$
$173$	6.36637	−	8.76256i	0.484026	−	0.666205i	0.979272	+	0.202548i	$0.0649221\pi$
$174$	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	0.997356	+	0.0726638i	$0.0231500\pi$
$179$	18.3918	+	13.3624i	1.37466	+	0.998752i	0.377307	+	0.926088i	$0.376850\pi$
$180$		0			0
$181$	0.741120	−	2.28093i	0.0550870	−	0.169540i	−0.919728	−	0.392557i	$-0.871590\pi$
$181$	0.741120	−	2.28093i	0.0550870	−	0.169540i	0.974815	+	0.223017i	$0.0715905\pi$
$182$	−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	−0.964118	−	0.265473i	$-0.914472\pi$
$191$	−13.9525	+	10.1371i	−1.00957	+	0.733494i	−0.0454496	+	0.998967i	$0.514472\pi$
$192$	19.5728	+	6.35959i	1.41254	+	0.458964i
$193$	−2.45918	−	0.799036i	−0.177016	−	0.0575159i	0.219168	−	0.975687i	$-0.429666\pi$
$193$	−2.45918	−	0.799036i	−0.177016	−	0.0575159i	−0.396184	+	0.918171i	$0.629666\pi$
$194$	−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	$-0.998359\pi$
$197$		−	0.144731i		−	0.0103116i	0.999987	−	0.00515582i	$-0.00164116\pi$
$198$	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	0.924019	−	0.382347i	$-0.124884\pi$
$211$	−0.701101	−	2.15777i	−0.0482658	−	0.148547i	−0.972285	+	0.233800i	$0.924884\pi$
$212$	−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	−0.606065	−	0.795415i	$-0.707253\pi$
$223$	5.04301	−	6.94111i	0.337705	−	0.464811i	0.943769	+	0.330605i	$0.107253\pi$
$224$	−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	0.912652	−	0.408738i	$-0.134031\pi$
$227$	3.64450	+	5.01622i	0.241894	+	0.332938i	−0.670758	+	0.741676i	$0.734031\pi$
$228$	−21.2209	+	29.2081i	−1.40539	+	1.93435i
$229$	−7.15865	−	22.0321i	−0.473057	−	1.45592i	−0.848560	−	0.529099i	$-0.822530\pi$
$229$	−7.15865	−	22.0321i	−0.473057	−	1.45592i	0.375503	−	0.926821i	$-0.377470\pi$
$230$		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	0.741711	−	0.670719i	$-0.234014\pi$
$233$	26.4990	−	8.61005i	1.73601	−	0.564063i	0.994296	+	0.106656i	$0.0340144\pi$
$234$	−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	0.0734982	−	0.997295i	$-0.476584\pi$
$239$	−13.1758	−	9.57280i	−0.852274	−	0.619213i	−0.925772	+	0.378082i	$0.876584\pi$
$240$		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	0.921676	−	0.387961i	$-0.126821\pi$
$251$	−0.824050	−	2.53616i	−0.0520136	−	0.160081i	−0.973689	+	0.227880i	$0.926821\pi$
$252$			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	−0.993707	−	0.112010i	$-0.964271\pi$
$257$	−12.7154	−	17.5012i	−0.793162	−	1.09169i	0.200545	−	0.979685i	$-0.435729\pi$
$258$	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	$0.239142\pi$
$263$			22.1392i			1.36516i	−0.730810	+	0.682581i	$0.760858\pi$
$264$	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	0.542162	+	0.840274i	$0.317606\pi$
$269$	−6.40233	+	19.7044i	−0.390357	+	1.20140i	−0.932519	+	0.361121i	$0.882394\pi$
$270$		0			0
$271$	0.342305	−	0.248699i	0.0207935	−	0.0151074i	−0.577340	−	0.816504i	$-0.695909\pi$
$271$	0.342305	−	0.248699i	0.0207935	−	0.0151074i	0.598133	+	0.801396i	$0.295909\pi$
$272$	−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	−0.543526	−	0.839392i	$-0.682911\pi$
$277$	−8.15298	+	2.64906i	−0.489865	+	0.159167i	0.0536607	+	0.998559i	$0.482911\pi$
$278$	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	−0.994651	−	0.103297i	$-0.967061\pi$
$281$	−2.16654	+	6.66793i	−0.129245	+	0.397776i	0.865405	+	0.501072i	$0.167061\pi$
$282$	7.02135	+	9.66406i	0.418115	+	0.575487i
$283$	5.85033	−	8.05229i	0.347766	−	0.478659i	−0.598924	−	0.800806i	$-0.704405\pi$
$283$	5.85033	−	8.05229i	0.347766	−	0.478659i	0.946690	+	0.322147i	$0.104405\pi$
$284$	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	−0.998029	−	0.0627522i	$-0.980012\pi$
$293$	−12.8260	−	17.6535i	−0.749302	−	1.03133i	0.248727	−	0.968574i	$-0.419988\pi$
$294$	−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	$0.343028\pi$
$307$			30.8674i			1.76170i	−0.473397	+	0.880849i	$0.656972\pi$
$308$	−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	0.936052	−	0.351862i	$-0.114451\pi$
$311$	15.7071	+	11.4119i	0.890667	+	0.647107i	−0.0453850	+	0.998970i	$0.514451\pi$
$312$	−2.80415	−	3.85959i	−0.158754	−	0.218506i
$313$	1.00001	+	0.324922i	0.0565237	+	0.0183657i	0.337142	−	0.941454i	$-0.390540\pi$
$313$	1.00001	+	0.324922i	0.0565237	+	0.0183657i	−0.280619	+	0.959819i	$0.590540\pi$
$314$	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	−0.866108	−	0.499857i	$-0.833386\pi$
$317$	−22.6650	+	7.36432i	−1.27300	+	0.413621i	−0.406887	+	0.913478i	$0.633386\pi$
$318$		−	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	−0.996782	−	0.0801597i	$-0.974457\pi$
$337$	−14.0435	−	19.3292i	−0.764996	−	1.05293i	0.231786	−	0.972767i	$-0.425543\pi$
$338$	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	0.317484	−	0.948264i	$-0.397162\pi$
$347$	0.315895	+	0.102641i	0.0169582	+	0.00551004i	−0.300526	+	0.953774i	$0.597162\pi$
$348$	−10.0025	−	13.7673i	−0.536191	−	0.738004i
$349$	0.988203	+	0.717971i	0.0528973	+	0.0384321i	0.613920	−	0.789368i	$-0.289592\pi$
$349$	0.988203	+	0.717971i	0.0528973	+	0.0384321i	−0.561022	+	0.827801i	$0.689592\pi$
$350$		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	$-0.760222\pi$
$353$		−	25.7038i		−	1.36808i	0.729446	−	0.684039i	$-0.239778\pi$
$354$	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	−0.900636	−	0.434574i	$-0.856899\pi$
$359$	−14.5069	+	10.5399i	−0.765643	+	0.556272i	0.134993	+	0.990847i	$0.456899\pi$
$360$		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	0.658641	−	0.752457i	$-0.271131\pi$
$367$	−4.99083	−	6.86929i	−0.260519	−	0.358574i	−0.919161	+	0.393883i	$0.871131\pi$
$368$	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	$0.378465\pi$
$373$			35.8450i			1.85598i	−0.372604	+	0.927991i	$0.621535\pi$
$374$	−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	0.709646	+	0.704558i	$0.248855\pi$
$379$	−5.42373	+	16.6925i	−0.278598	+	0.857438i	−0.988245	+	0.152880i	$0.951145\pi$
$380$		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	0.267882	−	0.963452i	$-0.413676\pi$
$383$	20.5666	−	6.68251i	1.05091	−	0.341460i	0.783024	+	0.621991i	$0.213676\pi$
$384$	−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	0.484352	−	0.874873i	$-0.339056\pi$
$389$	28.9156	−	21.0084i	1.46608	−	1.06517i	0.981727	−	0.190295i	$-0.0609444\pi$
$390$		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	$0.167773\pi$
$397$			20.0447i			1.00601i	−0.864282	+	0.503007i	$0.832227\pi$
$398$	−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	0.650057	+	0.759885i	$0.274745\pi$
$401$	−6.45805	+	19.8758i	−0.322500	+	0.992551i	−0.972557	+	0.232666i	$0.925255\pi$
$402$	−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	−0.953624	−	0.301001i	$-0.902679\pi$
$409$	−7.26134	−	22.3481i	−0.359050	−	1.10504i	0.594574	−	0.804041i	$-0.297321\pi$
$410$		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	0.397813	−	0.917467i	$-0.369769\pi$
$421$	−7.21872	−	5.24471i	−0.351819	−	0.255611i	−0.749632	+	0.661855i	$0.769769\pi$
$422$	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	−0.992335	−	0.123576i	$-0.960564\pi$
$431$	−5.44248	−	16.7502i	−0.262155	−	0.806831i	0.730180	−	0.683255i	$-0.239436\pi$
$432$	−8.07181	+	11.1099i	−0.388355	+	0.534525i
$433$	−5.37469	−	7.39763i	−0.258291	−	0.355507i	0.660102	−	0.751176i	$-0.270513\pi$
$433$	−5.37469	−	7.39763i	−0.258291	−	0.355507i	−0.918393	+	0.395668i	$0.870513\pi$
$434$	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	−0.378224	+	0.925714i	$0.623465\pi$
$443$	−24.0311	+	33.0760i	−1.14175	+	1.57149i	−0.763529	+	0.645774i	$0.776535\pi$
$444$	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	0.999733	−	0.0231150i	$-0.00735838\pi$
$449$	3.75788	+	11.5656i	0.177345	+	0.545813i	−0.822387	+	0.568928i	$0.807358\pi$
$450$		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	0.520886	−	0.853626i	$-0.325602\pi$
$457$	9.41775	+	3.06001i	0.440544	+	0.143141i	−0.0803428	+	0.996767i	$0.525602\pi$
$458$	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	$-0.808543\pi$
$463$		−	24.3518i		−	1.13173i	0.824499	−	0.565863i	$-0.191457\pi$
$464$	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	−0.531904	−	0.846805i	$-0.678523\pi$
$467$	−31.5501	−	10.2512i	−1.45996	−	0.474371i	−0.928059	+	0.372434i	$0.878523\pi$
$468$	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	−0.751529	−	0.659700i	$-0.770683\pi$
$479$	5.34529	−	16.4511i	0.244232	−	0.751670i	0.995762	−	0.0919705i	$-0.0293165\pi$
$480$		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	−0.898556	−	0.438858i	$-0.855383\pi$
$487$	−4.49104	+	6.18138i	−0.203508	+	0.280105i	0.695048	+	0.718963i	$0.255383\pi$
$488$	−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	0.135176	−	0.990822i	$-0.456840\pi$
$491$	24.8015	−	18.0193i	1.11928	−	0.813201i	0.984099	+	0.177620i	$0.0568399\pi$
$492$	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	−0.358726	+	0.933443i	$0.616789\pi$
$499$	−30.3206	+	22.0292i	−1.35734	+	0.986162i	−0.998609	+	0.0527188i	$0.983211\pi$
$500$		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	−0.683356	−	0.730085i	$-0.739480\pi$
$503$	4.98263	−	6.85800i	0.222164	−	0.305783i	0.905521	+	0.424302i	$0.139480\pi$
$504$	−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	0.556939	−	0.830554i	$-0.311976\pi$
$509$	−1.37309	−	0.997609i	−0.0608612	−	0.0442183i	−0.617800	+	0.786335i	$0.711976\pi$
$510$		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	0.314728	−	0.949182i	$-0.398087\pi$
$521$	30.0088	−	21.8027i	1.31471	−	0.955192i	0.999982	−	0.00601047i	$-0.00191320\pi$
$522$	4.89143	+	1.58932i	0.214092	+	0.0695627i
$523$	−17.1968	−	5.58759i	−0.751965	−	0.244328i	−0.0921382	−	0.995746i	$-0.529370\pi$
$523$	−17.1968	−	5.58759i	−0.751965	−	0.244328i	−0.659826	+	0.751418i	$0.729370\pi$
$524$	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	0.998274	−	0.0587201i	$-0.0187019\pi$
$541$	3.63169	+	11.1772i	0.156139	+	0.480545i	−0.842136	+	0.539265i	$0.818702\pi$
$542$	−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	−0.442782	−	0.896629i	$-0.646008\pi$
$547$	12.7884	−	17.6017i	0.546791	−	0.752593i	0.989572	+	0.144037i	$0.0460083\pi$
$548$	−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	0.864963	−	0.501836i	$-0.167342\pi$
$557$	2.84154	+	3.91104i	0.120400	+	0.165716i	−0.744563	+	0.667552i	$0.767342\pi$
$558$	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	−0.403087	−	0.915162i	$-0.632063\pi$
$563$	−4.53843	+	1.47463i	−0.191272	+	0.0621481i	0.211815	+	0.977310i	$0.432063\pi$
$564$	−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	0.995360	−	0.0962246i	$-0.0306767\pi$
$569$	28.8971	+	20.9949i	1.21143	+	0.880154i	0.216068	+	0.976378i	$0.430677\pi$
$570$		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	0.687944	−	0.725764i	$-0.258514\pi$
$577$	19.6468	+	6.38364i	0.817909	+	0.265755i	0.129965	+	0.991519i	$0.458514\pi$
$578$	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	0.939720	−	0.341945i	$-0.111086\pi$
$587$	7.85284	+	10.8085i	0.324121	+	0.446115i	−0.615599	+	0.788060i	$0.711086\pi$
$588$	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	$0.140502\pi$
$593$			20.8062i			0.854410i	−0.904155	+	0.427205i	$0.859498\pi$
$594$	−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	−0.819956	−	0.572427i	$-0.806002\pi$
$599$	4.40214	−	13.5484i	0.179867	−	0.553573i	0.999822	+	0.0188544i	$0.00600189\pi$
$600$		0			0
$601$	16.7840	−	12.1943i	0.684634	−	0.497416i	−0.190257	−	0.981734i	$-0.560932\pi$
$601$	16.7840	−	12.1943i	0.684634	−	0.497416i	0.874892	+	0.484318i	$0.160932\pi$
$602$	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	0.0580601	−	0.998313i	$-0.481508\pi$
$607$	17.0448	−	5.53818i	0.691825	−	0.224788i	0.633765	+	0.773525i	$0.281508\pi$
$608$	−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	−0.999750	−	0.0223811i	$-0.992875\pi$
$613$	−16.5766	+	22.8158i	−0.669524	+	0.921521i	0.330225	+	0.943902i	$0.392875\pi$
$614$	−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	$0.0303482\pi$
$617$			4.72930i			0.190394i	−0.995458	+	0.0951972i	$0.969652\pi$
$618$	52.9428	−	17.2022i	2.12967	−	0.691972i
$619$	−24.3170	−	17.6673i	−0.977383	−	0.710110i	−0.0202609	−	0.999795i	$-0.506450\pi$
$619$	−24.3170	−	17.6673i	−0.977383	−	0.710110i	−0.957122	+	0.289684i	$0.906450\pi$
$620$		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	0.0545601	−	0.998510i	$-0.482624\pi$
$631$	25.6487	−	18.6349i	1.02106	−	0.741843i	0.966500	+	0.256667i	$0.0826244\pi$
$632$	−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	0.847921	−	0.530122i	$-0.177854\pi$
$641$	15.3368	+	11.1428i	0.605768	+	0.440116i	−0.242154	+	0.970238i	$0.577854\pi$
$642$	17.2484	+	23.7404i	0.680740	+	0.936958i
$643$	−34.4747	−	11.2015i	−1.35955	−	0.441745i	−0.463657	−	0.886015i	$-0.653463\pi$
$643$	−34.4747	−	11.2015i	−1.35955	−	0.441745i	−0.895893	+	0.444270i	$0.853463\pi$
$644$	−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	−0.877958	−	0.478737i	$-0.841095\pi$
$647$	−33.2412	+	10.8007i	−1.30685	+	0.424620i	−0.428889	+	0.903357i	$0.641095\pi$
$648$			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	0.999982	−	0.00605995i	$-0.00192895\pi$
$653$	17.5097	+	24.1000i	0.685207	+	0.943106i	−0.314775	+	0.949166i	$0.601929\pi$
$654$	−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	0.0348910	−	0.999391i	$-0.488892\pi$
$673$	16.8766	−	5.48354i	0.650546	−	0.211375i	0.615655	+	0.788016i	$0.288892\pi$
$674$	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	0.156020	−	0.987754i	$-0.450133\pi$
$677$	−7.76267	−	2.52224i	−0.298344	−	0.0969377i	−0.454364	+	0.890816i	$0.650133\pi$
$678$	−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	$-0.962209\pi$
$683$		−	6.19100i		−	0.236892i	0.992960	−	0.118446i	$-0.0377913\pi$
$684$	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	0.988549	+	0.150897i	$0.0482162\pi$
$691$	7.29438	+	22.4498i	0.277491	+	0.854030i	−0.711058	+	0.703133i	$0.751784\pi$
$692$		−	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	−0.150779	−	0.988567i	$-0.548178\pi$
$701$	−30.1184	−	21.8823i	−1.13756	−	0.826483i	−0.986777	+	0.162084i	$0.948178\pi$
$702$	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	0.787521	+	0.616288i	$0.211364\pi$
$709$	−5.64072	+	17.3603i	−0.211842	+	0.651981i	−0.999363	+	0.0356939i	$0.988636\pi$
$710$		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	−0.433915	−	0.900954i	$-0.642868\pi$
$719$	7.74544	−	5.62739i	0.288856	−	0.209866i	0.722771	+	0.691088i	$0.242868\pi$
$720$		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	$0.0837031\pi$
$727$			14.0175i			0.519882i	−0.965625	+	0.259941i	$0.916297\pi$
$728$	−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	0.696207	−	0.717841i	$-0.254869\pi$
$733$	−5.45918	−	7.51392i	−0.201640	−	0.277533i	−0.897847	+	0.440308i	$0.854869\pi$
$734$	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	0.884816	+	0.465940i	$0.154284\pi$
$739$	12.0389	+	37.0519i	0.442857	+	1.36298i	−0.441959	+	0.897035i	$0.645716\pi$
$740$		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	0.967730	−	0.251989i	$-0.0810846\pi$
$743$	43.6817	+	14.1930i	1.60252	+	0.520692i	0.634795	+	0.772681i	$0.281085\pi$
$744$	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	0.190223	−	0.981741i	$-0.439079\pi$
$751$	−18.7634	−	13.6324i	−0.684686	−	0.497453i	−0.874909	+	0.484288i	$0.839079\pi$
$752$	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	−0.419561	−	0.907727i	$-0.637816\pi$
$757$	−6.20281	+	2.01541i	−0.225445	+	0.0732515i	0.194116	+	0.980979i	$0.437816\pi$
$758$		−	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	0.907516	−	0.420018i	$-0.137976\pi$
$761$	−2.02926	−	6.24542i	−0.0735606	−	0.226396i	−0.981076	+	0.193622i	$0.937976\pi$
$762$	−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	−0.511381	−	0.859354i	$-0.670866\pi$
$773$	12.8988	−	17.7537i	0.463939	−	0.638557i	0.975320	+	0.220797i	$0.0708660\pi$
$774$	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	0.0113766	−	0.999935i	$-0.496379\pi$
$787$	−15.9110	−	5.16981i	−0.567167	−	0.184284i	−0.578543	+	0.815652i	$0.696379\pi$
$788$	−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	0.500494	−	0.865740i	$-0.333152\pi$
$797$	11.1946	+	3.63735i	0.396533	+	0.128842i	−0.103961	+	0.994581i	$0.533152\pi$
$798$	−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	−0.957343	−	0.288954i	$-0.906693\pi$
$809$	−0.369567	+	1.13741i	−0.0129933	+	0.0399893i	0.944350	+	0.328943i	$0.106693\pi$
$810$		0			0
$811$	−28.9833	−	21.0576i	−1.01774	−	0.739431i	−0.0519216	−	0.998651i	$-0.516535\pi$
$811$	−28.9833	−	21.0576i	−1.01774	−	0.739431i	−0.965818	+	0.259220i	$0.916535\pi$
$812$	−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	−0.662613	−	0.748962i	$-0.730552\pi$
$821$	−4.44312	+	3.22811i	−0.155066	+	0.112662i	0.507547	+	0.861624i	$0.330552\pi$
$822$	26.3482	−	36.2652i	0.919000	−	1.26490i
$823$	−40.6341	+	13.2028i	−1.41642	+	0.460222i	−0.914462	−	0.404672i	$-0.867386\pi$
$823$	−40.6341	+	13.2028i	−1.41642	+	0.460222i	−0.501955	+	0.864894i	$0.667386\pi$
$824$	11.3563			0.395616
$825$		0			0
$826$	18.0912			0.629473
$827$	30.8340	−	10.0186i	1.07220	−	0.348380i	0.280858	−	0.959749i	$-0.409381\pi$
$827$	30.8340	−	10.0186i	1.07220	−	0.348380i	0.791345	+	0.611369i	$0.209381\pi$
$828$	−1.28828	+	1.77317i	−0.0447709	+	0.0616218i
$829$	−2.35544	+	1.71133i	−0.0818079	+	0.0594369i	−0.627937	−	0.778264i	$-0.716101\pi$
$829$	−2.35544	+	1.71133i	−0.0818079	+	0.0594369i	0.546130	+	0.837701i	$0.316101\pi$
$830$		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	0.257284	−	0.966336i	$-0.417172\pi$
$839$	−16.8652	−	12.2533i	−0.582250	−	0.423030i	−0.839535	+	0.543306i	$0.817172\pi$
$840$		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	0.811712	−	0.584058i	$-0.198536\pi$
$853$	32.8599	+	10.6768i	1.12510	+	0.365567i	0.313388	+	0.949625i	$0.398536\pi$
$854$	−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	$-0.807447\pi$
$857$		−	33.2969i		−	1.13740i	0.822545	−	0.568699i	$-0.192553\pi$
$858$	−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	0.284894	−	0.958559i	$-0.408042\pi$
$863$	−1.41151	−	0.458628i	−0.0480484	−	0.0156119i	−0.332943	+	0.942947i	$0.608042\pi$
$864$	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	−0.487567	−	0.873086i	$-0.662115\pi$
$877$	14.6132	−	20.1134i	0.493453	−	0.679180i	0.981020	+	0.193905i	$0.0621155\pi$
$878$	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	−0.0130124	−	0.999915i	$-0.504142\pi$
$883$	27.9914	−	38.5268i	0.941985	−	1.29653i	0.954997	−	0.296615i	$-0.0958579\pi$
$884$	−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	0.684487	+	0.729025i	$0.260026\pi$
$887$	34.7358	+	47.8097i	1.16631	+	1.60529i	0.481826	+	0.876267i	$0.339974\pi$
$888$	−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	−0.294493	−	0.955654i	$-0.595151\pi$
$907$	−32.9613	−	10.7098i	−1.09446	−	0.355612i	−0.799969	+	0.600041i	$0.795151\pi$
$908$	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	0.885258	−	0.465099i	$-0.153981\pi$
$911$	−3.14834	−	9.68961i	−0.104309	−	0.321031i	−0.989568	+	0.144069i	$0.953981\pi$
$912$		−	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	−0.579620	−	0.814887i	$-0.696799\pi$
$919$	11.1644	−	34.3606i	0.368281	−	1.13345i	0.947901	−	0.318565i	$-0.103201\pi$
$920$		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	0.701223	+	0.712942i	$0.252638\pi$
$929$	−8.69078	+	26.7475i	−0.285135	+	0.877556i	−0.986358	+	0.164614i	$0.947362\pi$
$930$		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	−0.307694	−	0.951485i	$-0.599557\pi$
$937$	0.0809993	−	0.0263183i	0.00264613	−	0.000859781i	0.310340	+	0.950626i	$0.399557\pi$
$938$	−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	0.485320	+	0.874337i	$0.338703\pi$
$941$	−12.9217	+	39.7688i	−0.421234	+	1.29643i	−0.906554	+	0.422089i	$0.861297\pi$
$942$	−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	$-0.953680\pi$
$947$		−	8.92463i		−	0.290012i	0.989431	−	0.145006i	$-0.0463201\pi$
$948$	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	0.755959	−	0.654619i	$-0.227171\pi$
$953$	−3.09400	−	4.25853i	−0.100225	−	0.137947i	−0.856184	+	0.516672i	$0.827171\pi$
$954$	−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	$0.0963654\pi$
$967$			18.5421i			0.596275i	−0.954523	+	0.298138i	$0.903635\pi$
$968$	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	0.856016	−	0.516949i	$-0.172932\pi$
$971$	19.5968	+	14.2379i	0.628893	+	0.456917i	−0.227124	+	0.973866i	$0.572932\pi$
$972$	−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	0.554894	−	0.831921i	$-0.312759\pi$
$977$	46.6606	−	15.1609i	1.49280	−	0.485041i	0.937910	+	0.346880i	$0.112759\pi$
$978$			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	−0.963180	−	0.268856i	$-0.913354\pi$
$983$	−28.8834	−	39.7546i	−0.921239	−	1.26798i	0.0419415	−	0.999120i	$-0.486646\pi$
$984$	−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	0.967071	−	0.254507i	$-0.0819134\pi$
$997$	13.4567	+	18.5216i	0.426178	+	0.586584i	−0.540892	+	0.841092i	$0.681913\pi$
$998$	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.49.1		16
5.2	odd	4		55.2.g.b.16.1	✓	8
5.3	odd	4		275.2.h.a.126.2		8
5.4	even	2	inner	275.2.z.a.49.4		16
11.9	even	5	inner	275.2.z.a.174.4		16
15.2	even	4		495.2.n.e.181.2		8
20.7	even	4		880.2.bo.h.401.2		8
55.2	even	20		605.2.g.k.251.2		8
55.3	odd	20		3025.2.a.bd.1.4		4
55.7	even	20		605.2.g.e.366.1		8
55.8	even	20		3025.2.a.w.1.1		4
55.9	even	10	inner	275.2.z.a.174.1		16
55.17	even	20		605.2.g.e.81.1		8
55.27	odd	20		605.2.g.m.81.2		8
55.32	even	4		605.2.g.k.511.2		8
55.37	odd	20		605.2.g.m.366.2		8
55.42	odd	20		55.2.g.b.31.1	yes	8
55.47	odd	20		605.2.a.j.1.1		4
55.52	even	20		605.2.a.k.1.4		4
55.53	odd	20		275.2.h.a.251.2		8
165.47	even	20		5445.2.a.bp.1.4		4
165.107	odd	20		5445.2.a.bi.1.1		4
165.152	even	20		495.2.n.e.361.2		8
220.47	even	20		9680.2.a.cn.1.1		4
220.107	odd	20		9680.2.a.cm.1.1		4
220.207	even	20		880.2.bo.h.801.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.1	✓	8	5.2	odd	4
55.2.g.b.31.1	yes	8	55.42	odd	20
275.2.h.a.126.2		8	5.3	odd	4
275.2.h.a.251.2		8	55.53	odd	20
275.2.z.a.49.1		16	1.1	even	1	trivial
275.2.z.a.49.4		16	5.4	even	2	inner
275.2.z.a.174.1		16	55.9	even	10	inner
275.2.z.a.174.4		16	11.9	even	5	inner
495.2.n.e.181.2		8	15.2	even	4
495.2.n.e.361.2		8	165.152	even	20
605.2.a.j.1.1		4	55.47	odd	20
605.2.a.k.1.4		4	55.52	even	20
605.2.g.e.81.1		8	55.17	even	20
605.2.g.e.366.1		8	55.7	even	20
605.2.g.k.251.2		8	55.2	even	20
605.2.g.k.511.2		8	55.32	even	4
605.2.g.m.81.2		8	55.27	odd	20
605.2.g.m.366.2		8	55.37	odd	20
880.2.bo.h.401.2		8	20.7	even	4
880.2.bo.h.801.2		8	220.207	even	20
3025.2.a.w.1.1		4	55.8	even	20
3025.2.a.bd.1.4		4	55.3	odd	20
5445.2.a.bi.1.1		4	165.107	odd	20
5445.2.a.bp.1.4		4	165.47	even	20
9680.2.a.cm.1.1		4	220.107	odd	20
9680.2.a.cn.1.1		4	220.47	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.99274 + 0.647481i) q^{2} +(1.12443 - 1.54765i) q^{3} +(1.93376 - 1.40496i) q^{4} +(-1.23863 + 3.81211i) q^{6} +(-1.80285 - 2.48141i) q^{7} +(-0.480634 + 0.661536i) q^{8} +(-0.203814 - 0.627276i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9	\( 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9} + 6 q^{11} + 32 q^{14} + 8 q^{16} - 30 q^{19} - 40 q^{21} - 26 q^{24} + 20 q^{26} + 18 q^{29} - 20 q^{31} - 8 q^{34} - 30 q^{36} - 42 q^{39} + 16 q^{41} + 24 q^{44} + 6 q^{46} - 2 q^{49} + 2 q^{51} - 32 q^{54} + 44 q^{56} + 54 q^{59} + 12 q^{61} + 52 q^{64} + 26 q^{66} + 2 q^{69} - 40 q^{71} - 40 q^{74} - 74 q^{79} + 16 q^{81} - 56 q^{84} - 6 q^{86} + 32 q^{89} + 88 q^{91} - 34 q^{94} - 34 q^{96} + 40 q^{99}+O(q^{100}) \) 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

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