LMFDB - Embedded newform 275.2.h.a.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(26,275)]

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([0, 2]))

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

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

chi := DirichletCharacter("275.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 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:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.2
Root			$1.69513 - 1.23158i$ of defining polynomial
Character	$\chi$	$=$	275.251
Dual form			275.2.h.a.126.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.647481 - 1.99274i) q^{2} +(1.54765 - 1.12443i) q^{3} +(-1.93376 - 1.40496i) q^{4} +(-1.23863 - 3.81211i) q^{6} +(-2.48141 - 1.80285i) q^{7} +(-0.661536 + 0.480634i) q^{8} +(0.203814 - 0.627276i) q^{9} +O(q^{10})$	\(q+(0.647481 - 1.99274i) q^{2} +(1.54765 - 1.12443i) q^{3} +(-1.93376 - 1.40496i) q^{4} +(-1.23863 - 3.81211i) q^{6} +(-2.48141 - 1.80285i) q^{7} +(-0.661536 + 0.480634i) q^{8} +(0.203814 - 0.627276i) q^{9} +(1.86337 + 2.74369i) q^{11} -4.57255 q^{12} +(-0.942444 + 2.90055i) q^{13} +(-5.19927 + 3.77749i) q^{14} +(-0.947813 - 2.91707i) q^{16} +(0.143336 + 0.441143i) q^{17} +(-1.11803 - 0.812299i) q^{18} +(6.38769 - 4.64093i) q^{19} -5.86752 q^{21} +(6.67397 - 1.93673i) q^{22} +1.39026 q^{23} +(-0.483384 + 1.48770i) q^{24} +(5.16983 + 3.75610i) q^{26} +(1.38355 + 4.25813i) q^{27} +(2.26552 + 6.97254i) q^{28} +(-3.01085 - 2.18751i) q^{29} +(-3.23741 + 9.96371i) q^{31} -8.06206 q^{32} +(5.96893 + 2.15103i) q^{33} +0.971892 q^{34} +(-1.27542 + 0.926650i) q^{36} +(1.49226 + 1.08419i) q^{37} +(-5.11227 - 15.7340i) q^{38} +(1.80289 + 5.54873i) q^{39} +(3.56585 - 2.59074i) q^{41} +(-3.79911 + 11.6925i) q^{42} +1.31478 q^{43} +(0.251461 - 7.92360i) q^{44} +(0.900166 - 2.77042i) q^{46} +(-2.41102 + 1.75171i) q^{47} +(-4.74692 - 3.44884i) q^{48} +(0.743998 + 2.28979i) q^{49} +(0.717868 + 0.521562i) q^{51} +(5.89760 - 4.28486i) q^{52} +(-1.29421 + 3.98316i) q^{53} +9.38118 q^{54} +2.50805 q^{56} +(4.66749 - 14.3650i) q^{57} +(-6.30862 + 4.58348i) q^{58} +(-2.27740 - 1.65463i) q^{59} +(-0.623402 - 1.91863i) q^{61} +(17.7590 + 12.9026i) q^{62} +(-1.63663 + 1.18908i) q^{63} +(-3.32441 + 10.2315i) q^{64} +(8.15123 - 10.5018i) q^{66} +6.75753 q^{67} +(0.342610 - 1.05444i) q^{68} +(2.15163 - 1.56325i) q^{69} +(-2.01539 - 6.20274i) q^{71} +(0.166660 + 0.512925i) q^{72} +(-7.98970 - 5.80485i) q^{73} +(3.12672 - 2.27169i) q^{74} -18.8726 q^{76} +(0.322676 - 10.1676i) q^{77} +12.2245 q^{78} +(-3.57158 + 10.9922i) q^{79} +(8.53000 + 6.19741i) q^{81} +(-2.85386 - 8.78327i) q^{82} +(-2.75600 - 8.48210i) q^{83} +(11.3464 + 8.24361i) q^{84} +(0.851296 - 2.62002i) q^{86} -7.11945 q^{87} +(-2.55140 - 0.919451i) q^{88} -6.76978 q^{89} +(7.56782 - 5.49835i) q^{91} +(-2.68842 - 1.95325i) q^{92} +(6.19315 + 19.0606i) q^{93} +(1.92961 + 5.93874i) q^{94} +(-12.4772 + 9.06524i) q^{96} +(-4.74475 + 14.6029i) q^{97} +5.04469 q^{98} +(2.10083 - 0.609644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9	$ 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} + 3 q^{11} - 16 q^{12} + 2 q^{13} - 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} - 20 q^{21} + 7 q^{22} - 10 q^{23} + 13 q^{24} + 10 q^{26} - 10 q^{27} + 6 q^{28} - 9 q^{29} - 10 q^{31} - 16 q^{32} - 5 q^{33} + 4 q^{34} - 15 q^{36} - 24 q^{37} + 21 q^{39} + 8 q^{41} - 9 q^{42} + 38 q^{43} - 12 q^{44} + 3 q^{46} - 5 q^{48} + q^{49} + q^{51} + 28 q^{52} - 13 q^{53} + 16 q^{54} + 22 q^{56} + 45 q^{57} - 12 q^{58} - 27 q^{59} + 6 q^{61} + 30 q^{62} - 25 q^{63} - 26 q^{64} + 13 q^{66} + 38 q^{67} - 11 q^{68} - q^{69} - 20 q^{71} + 30 q^{72} - 13 q^{73} + 20 q^{74} - 34 q^{77} + 16 q^{78} + 37 q^{79} + 8 q^{81} - 28 q^{82} - 27 q^{83} + 28 q^{84} - 3 q^{86} - 38 q^{87} + 36 q^{88} - 16 q^{89} + 44 q^{91} - 11 q^{92} + 35 q^{93} + 17 q^{94} - 17 q^{96} - 24 q^{97} - 16 q^{98} - 20 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 + 3 * q^11 - 16 * q^12 + 2 * q^13 - 16 * q^14 + 4 * q^16 + 13 * q^17 + 15 * q^19 - 20 * q^21 + 7 * q^22 - 10 * q^23 + 13 * q^24 + 10 * q^26 - 10 * q^27 + 6 * q^28 - 9 * q^29 - 10 * q^31 - 16 * q^32 - 5 * q^33 + 4 * q^34 - 15 * q^36 - 24 * q^37 + 21 * q^39 + 8 * q^41 - 9 * q^42 + 38 * q^43 - 12 * q^44 + 3 * q^46 - 5 * q^48 + q^49 + q^51 + 28 * q^52 - 13 * q^53 + 16 * q^54 + 22 * q^56 + 45 * q^57 - 12 * q^58 - 27 * q^59 + 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 + 13 * q^66 + 38 * q^67 - 11 * q^68 - q^69 - 20 * q^71 + 30 * q^72 - 13 * q^73 + 20 * q^74 - 34 * q^77 + 16 * q^78 + 37 * q^79 + 8 * q^81 - 28 * q^82 - 27 * q^83 + 28 * q^84 - 3 * q^86 - 38 * q^87 + 36 * q^88 - 16 * q^89 + 44 * q^91 - 11 * q^92 + 35 * q^93 + 17 * q^94 - 17 * q^96 - 24 * q^97 - 16 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.647481	−	1.99274i	0.457839	−	1.40908i	−0.409932	−	0.912116i	$-0.634447\pi$
$2$	0.647481	−	1.99274i	0.457839	−	1.40908i	0.867770	−	0.496966i	$-0.165553\pi$
$3$	1.54765	−	1.12443i	0.893534	−	0.649191i	−0.0432627	−	0.999064i	$-0.513775\pi$
$3$	1.54765	−	1.12443i	0.893534	−	0.649191i	0.936797	+	0.349873i	$0.113775\pi$
$4$	−1.93376	−	1.40496i	−0.966879	−	0.702479i
$5$		0			0
$5$		0			0
$6$	−1.23863	−	3.81211i	−0.505669	−	1.55629i
$7$	−2.48141	−	1.80285i	−0.937883	−	0.681412i	0.0100271	−	0.999950i	$-0.496808\pi$
$7$	−2.48141	−	1.80285i	−0.937883	−	0.681412i	−0.947910	+	0.318538i	$0.896808\pi$
$8$	−0.661536	+	0.480634i	−0.233888	+	0.169930i
$9$	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
$12$	−4.57255			−1.31998
$13$	−0.942444	+	2.90055i	−0.261387	+	0.804467i	0.731117	+	0.682252i	$0.238999\pi$
$13$	−0.942444	+	2.90055i	−0.261387	+	0.804467i	−0.992504	+	0.122214i	$0.961001\pi$
$14$	−5.19927	+	3.77749i	−1.38956	+	1.00958i
$15$		0			0
$16$	−0.947813	−	2.91707i	−0.236953	−	0.729267i
$17$	0.143336	+	0.441143i	0.0347641	+	0.106993i	0.966933	−	0.255031i	$-0.0820858\pi$
$17$	0.143336	+	0.441143i	0.0347641	+	0.106993i	−0.932169	+	0.362024i	$0.882086\pi$
$18$	−1.11803	−	0.812299i	−0.263523	−	0.191461i
$19$	6.38769	−	4.64093i	1.46544	−	1.06470i	0.483533	−	0.875326i	$-0.339353\pi$
$19$	6.38769	−	4.64093i	1.46544	−	1.06470i	0.981904	−	0.189377i	$-0.0606468\pi$
$20$		0			0
$21$	−5.86752			−1.28040
$22$	6.67397	−	1.93673i	1.42290	−	0.412912i
$23$	1.39026			0.289889			0.144944	−	0.989440i	$-0.453700\pi$
$23$	1.39026			0.289889			0.144944	+	0.989440i	$0.453700\pi$
$24$	−0.483384	+	1.48770i	−0.0986703	+	0.303676i
$25$		0			0
$26$	5.16983	+	3.75610i	1.01389	+	0.736632i
$27$	1.38355	+	4.25813i	0.266264	+	0.819477i
$28$	2.26552	+	6.97254i	0.428142	+	1.31769i
$29$	−3.01085	−	2.18751i	−0.559101	−	0.406211i	0.272029	−	0.962289i	$-0.412305\pi$
$29$	−3.01085	−	2.18751i	−0.559101	−	0.406211i	−0.831130	+	0.556078i	$0.812305\pi$
$30$		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	$0.710062\pi$
$32$	−8.06206			−1.42518
$33$	5.96893	+	2.15103i	1.03906	+	0.374447i
$34$	0.971892			0.166678
$35$		0			0
$36$	−1.27542	+	0.926650i	−0.212571	+	0.154442i
$37$	1.49226	+	1.08419i	0.245326	+	0.178240i	0.703653	−	0.710544i	$-0.251551\pi$
$37$	1.49226	+	1.08419i	0.245326	+	0.178240i	−0.458327	+	0.888784i	$0.651551\pi$
$38$	−5.11227	−	15.7340i	−0.829320	−	2.55238i
$39$	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	$0.188158\pi$
$42$	−3.79911	+	11.6925i	−0.586215	+	1.80418i
$43$	1.31478			0.200502			0.100251	−	0.994962i	$-0.468035\pi$
$43$	1.31478			0.200502			0.100251	+	0.994962i	$0.468035\pi$
$44$	0.251461	−	7.92360i	0.0379092	−	1.19453i
$45$		0			0
$46$	0.900166	−	2.77042i	0.132722	−	0.408477i
$47$	−2.41102	+	1.75171i	−0.351683	+	0.255513i	−0.749575	−	0.661920i	$-0.769742\pi$
$47$	−2.41102	+	1.75171i	−0.351683	+	0.255513i	0.397892	+	0.917432i	$0.369742\pi$
$48$	−4.74692	−	3.44884i	−0.685159	−	0.497797i
$49$	0.743998	+	2.28979i	0.106285	+	0.327113i
$50$		0			0
$51$	0.717868	+	0.521562i	0.100522	+	0.0730333i
$52$	5.89760	−	4.28486i	0.817850	−	0.594203i
$53$	−1.29421	+	3.98316i	−0.177773	+	0.547129i	−0.999749	−	0.0223927i	$-0.992872\pi$
$53$	−1.29421	+	3.98316i	−0.177773	+	0.547129i	0.821976	+	0.569522i	$0.192872\pi$
$54$	9.38118			1.27662
$55$		0			0
$56$	2.50805			0.335152
$57$	4.66749	−	14.3650i	0.618224	−	1.90270i
$58$	−6.30862	+	4.58348i	−0.828363	+	0.601841i
$59$	−2.27740	−	1.65463i	−0.296493	−	0.215414i	0.429586	−	0.903026i	$-0.358659\pi$
$59$	−2.27740	−	1.65463i	−0.296493	−	0.215414i	−0.726079	+	0.687611i	$0.758659\pi$
$60$		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	$0.941225\pi$
$62$	17.7590	+	12.9026i	2.25539	+	1.63864i
$63$	−1.63663	+	1.18908i	−0.206196	+	0.149810i
$64$	−3.32441	+	10.2315i	−0.415551	+	1.27894i
$65$		0			0
$66$	8.15123	−	10.5018i	1.00335	−	1.29268i
$67$	6.75753			0.825564			0.412782	−	0.910830i	$-0.364557\pi$
$67$	6.75753			0.825564			0.412782	+	0.910830i	$0.364557\pi$
$68$	0.342610	−	1.05444i	0.0415476	−	0.127870i
$69$	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	$-0.226491\pi$
$72$	0.166660	+	0.512925i	0.0196410	+	0.0604488i
$73$	−7.98970	−	5.80485i	−0.935123	−	0.679407i	0.0121186	−	0.999927i	$-0.496142\pi$
$73$	−7.98970	−	5.80485i	−0.935123	−	0.679407i	−0.947242	+	0.320520i	$0.896142\pi$
$74$	3.12672	−	2.27169i	0.363474	−	0.264079i
$75$		0			0
$76$	−18.8726			−2.16483
$77$	0.322676	−	10.1676i	0.0367723	−	1.15870i
$78$	12.2245			1.38416
$79$	−3.57158	+	10.9922i	−0.401834	+	1.23672i	0.521677	+	0.853143i	$0.325307\pi$
$79$	−3.57158	+	10.9922i	−0.401834	+	1.23672i	−0.923510	+	0.383573i	$0.874693\pi$
$80$		0			0
$81$	8.53000	+	6.19741i	0.947777	+	0.688601i
$82$	−2.85386	−	8.78327i	−0.315156	−	0.969950i
$83$	−2.75600	−	8.48210i	−0.302510	−	0.931032i	−0.980594	−	0.196047i	$-0.937189\pi$
$83$	−2.75600	−	8.48210i	−0.302510	−	0.931032i	0.678084	−	0.734984i	$-0.262811\pi$
$84$	11.3464	+	8.24361i	1.23799	+	0.899452i
$85$		0			0
$86$	0.851296	−	2.62002i	0.0917976	−	0.282524i
$87$	−7.11945			−0.763285
$88$	−2.55140	−	0.919451i	−0.271980	−	0.0980138i
$89$	−6.76978			−0.717595			−0.358797	−	0.933415i	$-0.616813\pi$
$89$	−6.76978			−0.717595			−0.358797	+	0.933415i	$0.616813\pi$
$90$		0			0
$91$	7.56782	−	5.49835i	0.793324	−	0.576383i
$92$	−2.68842	−	1.95325i	−0.280287	−	0.203641i
$93$	6.19315	+	19.0606i	0.642200	+	1.97649i
$94$	1.92961	+	5.93874i	0.199024	+	0.612534i
$95$		0			0
$96$	−12.4772	+	9.06524i	−1.27345	+	0.925217i
$97$	−4.74475	+	14.6029i	−0.481757	+	1.48269i	0.354867	+	0.934917i	$0.384526\pi$
$97$	−4.74475	+	14.6029i	−0.481757	+	1.48269i	−0.836624	+	0.547778i	$0.815474\pi$
$98$	5.04469			0.509591
$99$	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	$-0.0984027\pi$
$102$	1.50415	−	1.09283i	0.148933	−	0.108206i
$103$	11.2357	+	8.16319i	1.10708	+	0.804343i	0.982202	−	0.187828i	$-0.0601448\pi$
$103$	11.2357	+	8.16319i	1.10708	+	0.804343i	0.124882	+	0.992172i	$0.460145\pi$
$104$	−0.770639	−	2.37178i	−0.0755674	−	0.232573i
$105$		0			0
$106$	7.09944	+	5.15804i	0.689559	+	0.500994i
$107$	−5.92282	+	4.30318i	−0.572580	+	0.416004i	−0.836042	−	0.548666i	$-0.815136\pi$
$107$	−5.92282	+	4.30318i	−0.572580	+	0.416004i	0.263461	+	0.964670i	$0.415136\pi$
$108$	3.30704	−	10.1780i	0.318220	−	0.979380i
$109$	−7.43306			−0.711958			−0.355979	−	0.934494i	$-0.615853\pi$
$109$	−7.43306			−0.711958			−0.355979	+	0.934494i	$0.615853\pi$
$110$		0			0
$111$	3.52859			0.334919
$112$	−2.90712	+	8.94719i	−0.274697	+	0.845430i
$113$	−2.45650	+	1.78475i	−0.231088	+	0.167895i	−0.697304	−	0.716776i	$-0.745617\pi$
$113$	−2.45650	+	1.78475i	−0.231088	+	0.167895i	0.466216	+	0.884671i	$0.345617\pi$
$114$	−25.6037	−	18.6022i	−2.39801	−	1.74226i
$115$		0			0
$116$	2.74890	+	8.46024i	0.255229	+	0.785514i
$117$	1.62736	+	1.18235i	0.150449	+	0.109308i
$118$	−4.77183	+	3.46694i	−0.439282	+	0.319157i
$119$	0.439638	−	1.35307i	0.0403016	−	0.124035i
$120$		0			0
$121$	−4.05569	+	10.2250i	−0.368699	+	0.929549i
$122$	−4.22699			−0.382693
$123$	2.60556	−	8.01910i	0.234936	−	0.723058i
$124$	20.2590	−	14.7190i	1.81931	−	1.32181i
$125$		0			0
$126$	1.30984	+	4.03129i	0.116690	+	0.359136i
$127$	0.139551	+	0.429495i	0.0123832	+	0.0381115i	0.957057	−	0.289899i	$-0.0936218\pi$
$127$	0.139551	+	0.429495i	0.0123832	+	0.0381115i	−0.944674	+	0.328011i	$0.893622\pi$
$128$	5.19153	+	3.77187i	0.458871	+	0.333389i
$129$	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	$0.491252\pi$
$132$	−8.52037	−	12.5457i	−0.741603	−	1.09196i
$133$	−24.2173			−2.09991
$134$	4.37538	−	13.4660i	0.377975	−	1.16329i
$135$		0			0
$136$	−0.306850	−	0.222940i	−0.0263122	−	0.0191169i
$137$	−3.45586	−	10.6360i	−0.295254	−	0.908698i	−0.983136	−	0.182876i	$-0.941459\pi$
$137$	−3.45586	−	10.6360i	−0.295254	−	0.908698i	0.687882	−	0.725823i	$-0.258541\pi$
$138$	−1.72201	−	5.29981i	−0.146588	−	0.451150i
$139$	1.92138	+	1.39596i	0.162969	+	0.118404i	0.666281	−	0.745701i	$-0.267885\pi$
$139$	1.92138	+	1.39596i	0.162969	+	0.118404i	−0.503312	+	0.864105i	$0.667885\pi$
$140$		0			0
$141$	−1.76173	+	5.42205i	−0.148364	+	0.456619i
$142$	−13.6654			−1.14678
$143$	−9.71433	+	2.81902i	−0.812353	+	0.235738i
$144$	−2.02298			−0.168582
$145$		0			0
$146$	−16.7408	+	12.1629i	−1.38548	+	1.00661i
$147$	3.72616	+	2.70721i	0.307328	+	0.223287i
$148$	−1.36243	−	4.19312i	−0.111991	−	0.344672i
$149$	−2.69473	−	8.29354i	−0.220761	−	0.679433i	−0.998694	−	0.0510859i	$-0.983732\pi$
$149$	−2.69473	−	8.29354i	−0.220761	−	0.679433i	0.777933	−	0.628347i	$-0.216268\pi$
$150$		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	$0.461415\pi$
$152$	−1.99510	+	6.14028i	−0.161824	+	0.498043i
$153$	0.305932			0.0247332
$154$	−20.0525	−	7.22633i	−1.61587	−	0.582315i
$155$		0			0
$156$	4.30938	−	13.2629i	0.345026	−	1.06188i
$157$	3.13520	−	2.27786i	0.250216	−	0.181793i	−0.455606	−	0.890181i	$-0.650578\pi$
$157$	3.13520	−	2.27786i	0.250216	−	0.181793i	0.705823	+	0.708389i	$0.250578\pi$
$158$	19.5921	+	14.2345i	1.55866	+	1.13243i
$159$	2.47581	+	7.61977i	0.196345	+	0.604287i
$160$		0			0
$161$	−3.44979	−	2.50642i	−0.271882	−	0.197534i
$162$	17.8729	−	12.9854i	1.40422	−	1.02023i
$163$	3.07046	−	9.44990i	0.240497	−	0.740173i	−0.755848	−	0.654748i	$-0.772775\pi$
$163$	3.07046	−	9.44990i	0.240497	−	0.740173i	0.996345	−	0.0854258i	$-0.0272251\pi$
$164$	−10.5354			−0.822674
$165$		0			0
$166$	−18.6871			−1.45040
$167$	−4.30152	+	13.2387i	−0.332862	+	1.02444i	0.634904	+	0.772591i	$0.281040\pi$
$167$	−4.30152	+	13.2387i	−0.332862	+	1.02444i	−0.967766	+	0.251852i	$0.918960\pi$
$168$	3.88157	−	2.82013i	0.299470	−	0.217577i
$169$	2.99226	+	2.17400i	0.230174	+	0.167231i
$170$		0			0
$171$	−1.60924	−	4.95274i	−0.123062	−	0.378745i
$172$	−2.54247	−	1.84721i	−0.193861	−	0.140848i
$173$	8.76256	−	6.36637i	0.666205	−	0.484026i	−0.202548	−	0.979272i	$-0.564922\pi$
$173$	8.76256	−	6.36637i	0.666205	−	0.484026i	0.868753	+	0.495246i	$0.164922\pi$
$174$	−4.60971	+	14.1872i	−0.349461	+	1.07553i
$175$		0			0
$176$	6.23741	−	8.03609i	0.470162	−	0.605743i
$177$	−5.38513			−0.404771
$178$	−4.38331	+	13.4904i	−0.328543	+	1.01115i
$179$	−18.3918	+	13.3624i	−1.37466	+	0.998752i	−0.377307	+	0.926088i	$0.623150\pi$
$179$	−18.3918	+	13.3624i	−1.37466	+	0.998752i	−0.997356	+	0.0726638i	$0.976850\pi$
$180$		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	$0.871590\pi$
$182$	−6.05677	−	18.6408i	−0.448957	−	1.38175i
$183$	−3.12218	−	2.26840i	−0.230798	−	0.167685i
$184$	−0.919704	+	0.668204i	−0.0678015	+	0.0492607i
$185$		0			0
$186$	41.9927			3.07906
$187$	−0.943272	+	1.21528i	−0.0689789	+	0.0888703i
$188$	7.12340			0.519527
$189$	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	$0.914472\pi$
$192$	6.35959	+	19.5728i	0.458964	+	1.41254i
$193$	0.799036	+	2.45918i	0.0575159	+	0.177016i	0.975687	−	0.219168i	$-0.0703343\pi$
$193$	0.799036	+	2.45918i	0.0575159	+	0.177016i	−0.918171	+	0.396184i	$0.870334\pi$
$194$	26.0276	+	18.9102i	1.86867	+	1.35767i
$195$		0			0
$196$	1.77835	−	5.47319i	0.127025	−	0.390942i
$197$	−0.144731			−0.0103116			−0.00515582	−	0.999987i	$-0.501641\pi$
$197$	−0.144731			−0.0103116			−0.00515582	+	0.999987i	$0.501641\pi$
$198$	0.145386	−	4.58116i	0.0103322	−	0.325569i
$199$	−7.54177			−0.534622			−0.267311	−	0.963610i	$-0.586135\pi$
$199$	−7.54177			−0.534622			−0.267311	+	0.963610i	$0.586135\pi$
$200$		0			0
$201$	10.4583	−	7.59838i	0.737670	−	0.535948i
$202$	−19.8882	−	14.4497i	−1.39933	−	1.01667i
$203$	3.52740	+	10.8562i	0.247575	+	0.761957i
$204$	−0.655412	−	2.01715i	−0.0458880	−	0.141229i
$205$		0			0
$206$	23.5420	−	17.1043i	1.64025	−	1.19171i
$207$	0.283354	−	0.872075i	0.0196945	−	0.0606134i
$208$	9.35435			0.648607
$209$	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	$0.124884\pi$
$212$	8.09886	−	5.88416i	0.556232	−	0.404126i
$213$	−10.0937	−	7.33349i	−0.691607	−	0.502482i
$214$	4.74021	+	14.5889i	0.324034	+	0.997275i
$215$		0			0
$216$	−2.96187	−	2.15192i	−0.201529	−	0.146420i
$217$	25.9964	−	18.8875i	1.76475	−	1.28216i
$218$	−4.81277	+	14.8122i	−0.325962	+	1.00321i
$219$	−18.8924			−1.27663
$220$		0			0
$221$	−1.41464			−0.0951591
$222$	2.28469	−	7.03156i	0.153339	−	0.471928i
$223$	6.94111	−	5.04301i	0.464811	−	0.337705i	−0.330605	−	0.943769i	$-0.607253\pi$
$223$	6.94111	−	5.04301i	0.464811	−	0.337705i	0.795415	+	0.606065i	$0.207253\pi$
$224$	20.0052	+	14.5347i	1.33666	+	0.971138i
$225$		0			0
$226$	1.96601	+	6.05076i	0.130777	+	0.402491i
$227$	5.01622	+	3.64450i	0.332938	+	0.241894i	0.741676	−	0.670758i	$-0.234031\pi$
$227$	5.01622	+	3.64450i	0.332938	+	0.241894i	−0.408738	+	0.912652i	$0.634031\pi$
$228$	−29.2081	+	21.2209i	−1.93435	+	1.40539i
$229$	7.15865	−	22.0321i	0.473057	−	1.45592i	−0.375503	−	0.926821i	$-0.622530\pi$
$229$	7.15865	−	22.0321i	0.473057	−	1.45592i	0.848560	−	0.529099i	$-0.177470\pi$
$230$		0			0
$231$	−10.9334	−	16.0987i	−0.719362	−	1.05921i
$232$	3.04318			0.199794
$233$	8.61005	−	26.4990i	0.564063	−	1.73601i	−0.106656	−	0.994296i	$-0.534014\pi$
$233$	8.61005	−	26.4990i	0.564063	−	1.73601i	0.670719	−	0.741711i	$-0.265986\pi$
$234$	3.40980	−	2.47736i	0.222905	−	0.161950i
$235$		0			0
$236$	2.07926	+	6.39931i	0.135348	+	0.416560i
$237$	6.83241	+	21.0280i	0.443813	+	1.36592i
$238$	−2.41166	−	1.75217i	−0.156325	−	0.113576i
$239$	13.1758	−	9.57280i	0.852274	−	0.619213i	−0.0734982	−	0.997295i	$-0.523416\pi$
$239$	13.1758	−	9.57280i	0.852274	−	0.619213i	0.925772	+	0.378082i	$0.123416\pi$
$240$		0			0
$241$	4.39063			0.282826			0.141413	−	0.989951i	$-0.454836\pi$
$241$	4.39063			0.282826			0.141413	+	0.989951i	$0.454836\pi$
$242$	17.7499	+	14.7025i	1.14101	+	0.945111i
$243$	6.73820			0.432256
$244$	−1.49009	+	4.58603i	−0.0953933	+	0.293590i
$245$		0			0
$246$	−14.2930	−	10.3844i	−0.911285	−	0.662087i
$247$	7.44119	+	22.9016i	0.473471	+	1.45720i
$248$	−2.64724	−	8.14736i	−0.168100	−	0.517358i
$249$	−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	$0.126821\pi$
$252$	4.83545			0.304605
$253$	2.59056	+	3.81444i	0.162867	+	0.239812i
$254$	0.946229			0.0593717
$255$		0			0
$256$	−6.52905	+	4.74363i	−0.408066	+	0.296477i
$257$	−17.5012	−	12.7154i	−1.09169	−	0.793162i	−0.112010	−	0.993707i	$-0.535729\pi$
$257$	−17.5012	−	12.7154i	−1.09169	−	0.793162i	−0.979685	+	0.200545i	$0.935729\pi$
$258$	−1.62853	−	5.01209i	−0.101388	−	0.312039i
$259$	−1.74827	−	5.38063i	−0.108632	−	0.334336i
$260$		0			0
$261$	−1.98583	+	1.44279i	−0.122920	+	0.0893064i
$262$	0.407268	−	1.25344i	0.0251611	−	0.0774379i
$263$	−22.1392			−1.36516			−0.682581	−	0.730810i	$-0.739142\pi$
$263$	−22.1392			−1.36516			−0.682581	+	0.730810i	$0.739142\pi$
$264$	−4.98252	+	1.44589i	−0.306653	+	0.0889881i
$265$		0			0
$266$	−15.6803	+	48.2590i	−0.961420	+	2.95895i
$267$	−10.4772	+	7.61215i	−0.641196	+	0.465856i
$268$	−13.0674	−	9.49404i	−0.798220	−	0.579941i
$269$	6.40233	+	19.7044i	0.390357	+	1.20140i	0.932519	+	0.361121i	$0.117606\pi$
$269$	6.40233	+	19.7044i	0.390357	+	1.20140i	−0.542162	+	0.840274i	$0.682394\pi$
$270$		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	$0.695909\pi$
$272$	1.15099	−	0.836242i	0.0697889	−	0.0507046i
$273$	5.52981	−	17.0190i	0.334679	−	1.03004i
$274$	−23.4325			−1.41561
$275$		0			0
$276$	−6.35702			−0.382648
$277$	2.64906	−	8.15298i	0.159167	−	0.489865i	−0.839392	−	0.543526i	$-0.817089\pi$
$277$	2.64906	−	8.15298i	0.159167	−	0.489865i	0.998559	+	0.0536607i	$0.0170889\pi$
$278$	4.02585	−	2.92495i	0.241455	−	0.175427i
$279$	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	$0.967061\pi$
$282$	9.66406	+	7.02135i	0.575487	+	0.418115i
$283$	8.05229	−	5.85033i	0.478659	−	0.347766i	−0.322147	−	0.946690i	$-0.604405\pi$
$283$	8.05229	−	5.85033i	0.478659	−	0.347766i	0.800806	+	0.598924i	$0.204405\pi$
$284$	−4.81731	+	14.8261i	−0.285855	+	0.879770i
$285$		0			0
$286$	−0.672272	+	21.1834i	−0.0397523	+	1.25260i
$287$	−13.5190			−0.798002
$288$	−1.64316	+	5.05714i	−0.0968244	+	0.297995i
$289$	13.5792	−	9.86589i	0.798778	−	0.580346i
$290$		0			0
$291$	9.07670	+	27.9352i	0.532086	+	1.63759i
$292$	7.29457	+	22.4504i	0.426882	+	1.31381i
$293$	17.6535	+	12.8260i	1.03133	+	0.749302i	0.968574	−	0.248727i	$-0.0800122\pi$
$293$	17.6535	+	12.8260i	1.03133	+	0.749302i	0.0627522	+	0.998029i	$0.480012\pi$
$294$	7.80740	−	5.67241i	0.455337	−	0.330822i
$295$		0			0
$296$	−1.50828			−0.0876670
$297$	−9.10492	+	11.7305i	−0.528321	+	0.680673i
$298$	−18.2717			−1.05845
$299$	−1.31024	+	4.03250i	−0.0757731	+	0.233206i
$300$		0			0
$301$	−3.26250	−	2.37035i	−0.188048	−	0.136625i
$302$	7.72797	+	23.7842i	0.444694	+	1.36863i
$303$	−6.93570	−	21.3459i	−0.398446	−	1.22629i
$304$	−19.5922	−	14.2346i	−1.12369	−	0.816410i
$305$		0			0
$306$	0.198085	−	0.609644i	0.0113238	−	0.0348511i
$307$	30.8674			1.76170			0.880849	−	0.473397i	$-0.156972\pi$
$307$	30.8674			1.76170			0.880849	+	0.473397i	$0.156972\pi$
$308$	−14.9090	+	19.2083i	−0.849519	+	1.09449i
$309$	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	$0.114451\pi$
$312$	−3.85959	−	2.80415i	−0.218506	−	0.158754i
$313$	−0.324922	−	1.00001i	−0.0183657	−	0.0565237i	0.941454	−	0.337142i	$-0.109460\pi$
$313$	−0.324922	−	1.00001i	−0.0183657	−	0.0565237i	−0.959819	+	0.280619i	$0.909460\pi$
$314$	−2.50920	−	7.72252i	−0.141602	−	0.435807i
$315$		0			0
$316$	22.3501	−	16.2383i	1.25729	−	0.913476i
$317$	7.36432	−	22.6650i	0.413621	−	1.27300i	−0.499857	−	0.866108i	$-0.666614\pi$
$317$	7.36432	−	22.6650i	0.413621	−	1.27300i	0.913478	−	0.406887i	$-0.133386\pi$
$318$	16.7873			0.941385
$319$	0.391524	−	12.3370i	0.0219211	−	0.690740i
$320$		0			0
$321$	−4.32780	+	13.3196i	−0.241554	+	0.743428i
$322$	−7.22833	+	5.25169i	−0.402819	+	0.292665i
$323$	2.96290	+	2.15267i	0.164860	+	0.119778i
$324$	−7.78786	−	23.9686i	−0.432659	−	1.33159i
$325$		0			0
$326$	−16.8432	−	12.2373i	−0.932856	−	0.677760i
$327$	−11.5038	+	8.35796i	−0.636159	+	0.462196i
$328$	−1.11374	+	3.42773i	−0.0614959	+	0.189265i
$329$	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	$0.250742\pi$
$332$	−6.58755	+	20.2744i	−0.361539	+	1.11270i
$333$	0.984230	−	0.715085i	0.0539354	−	0.0391864i
$334$	23.5962	+	17.1436i	1.29113	+	0.938059i
$335$		0			0
$336$	5.56131	+	17.1159i	0.303394	+	0.933751i
$337$	−19.3292	−	14.0435i	−1.05293	−	0.764996i	−0.0801597	−	0.996782i	$-0.525543\pi$
$337$	−19.3292	−	14.0435i	−1.05293	−	0.764996i	−0.972767	+	0.231786i	$0.925543\pi$
$338$	6.26966	−	4.55518i	0.341025	−	0.247769i
$339$	−1.79496	+	5.52433i	−0.0974890	+	0.300040i
$340$		0			0
$341$	−33.3699	+	9.68365i	−1.80708	+	0.524399i
$342$	−10.9115			−0.590026
$343$	−4.35271	+	13.3963i	−0.235024	+	0.723330i
$344$	−0.869774	+	0.631928i	−0.0468951	+	0.0340713i
$345$		0			0
$346$	−7.01295	−	21.5836i	−0.377018	−	1.16034i
$347$	0.102641	+	0.315895i	0.00551004	+	0.0169582i	0.953774	−	0.300526i	$-0.0971621\pi$
$347$	0.102641	+	0.315895i	0.00551004	+	0.0169582i	−0.948264	+	0.317484i	$0.897162\pi$
$348$	13.7673	+	10.0025i	0.738004	+	0.536191i
$349$	−0.988203	+	0.717971i	−0.0528973	+	0.0384321i	−0.613920	−	0.789368i	$-0.710408\pi$
$349$	−0.988203	+	0.717971i	−0.0528973	+	0.0384321i	0.561022	+	0.827801i	$0.310408\pi$
$350$		0			0
$351$	−13.6548			−0.728840
$352$	−15.0226	−	22.1198i	−0.800708	−	1.17899i
$353$	25.7038			1.36808			0.684039	−	0.729446i	$-0.260222\pi$
$353$	25.7038			1.36808			0.684039	+	0.729446i	$0.260222\pi$
$354$	−3.48677	+	10.7312i	−0.185320	+	0.570356i
$355$		0			0
$356$	13.0911	+	9.51125i	0.693828	+	0.504095i
$357$	−0.841026	−	2.58841i	−0.0445118	−	0.136993i
$358$	14.7195	+	45.3019i	0.777949	+	2.39428i
$359$	14.5069	+	10.5399i	0.765643	+	0.556272i	0.900636	−	0.434574i	$-0.143101\pi$
$359$	14.5069	+	10.5399i	0.765643	+	0.556272i	−0.134993	+	0.990847i	$0.543101\pi$
$360$		0			0
$361$	13.3931	−	41.2196i	0.704899	−	2.16945i
$362$	5.02517			0.264117
$363$	5.22057	+	20.3851i	0.274009	+	1.06994i
$364$	−22.3593			−1.17195
$365$		0			0
$366$	−6.54188	+	4.75296i	−0.341950	+	0.248441i
$367$	−6.86929	−	4.99083i	−0.358574	−	0.260519i	0.393883	−	0.919161i	$-0.371131\pi$
$367$	−6.86929	−	4.99083i	−0.358574	−	0.260519i	−0.752457	+	0.658641i	$0.771131\pi$
$368$	−1.31770	−	4.05547i	−0.0686900	−	0.211406i
$369$	−0.898338	−	2.76480i	−0.0467656	−	0.143930i
$370$		0			0
$371$	10.3925	−	7.55058i	0.539551	−	0.392006i
$372$	14.8032	−	45.5596i	0.767511	−	2.36216i
$373$	−35.8450			−1.85598			−0.927991	−	0.372604i	$-0.878465\pi$
$373$	−35.8450			−1.85598			−0.927991	+	0.372604i	$0.878465\pi$
$374$	1.81100	+	2.66657i	0.0936443	+	0.137885i
$375$		0			0
$376$	0.753045	−	2.31763i	0.0388353	−	0.119523i
$377$	9.18254	−	6.67151i	0.472925	−	0.343600i
$378$	−23.2785	−	16.9128i	−1.19732	−	0.869902i
$379$	5.42373	+	16.6925i	0.278598	+	0.857438i	0.988245	+	0.152880i	$0.0488547\pi$
$379$	5.42373	+	16.6925i	0.278598	+	0.857438i	−0.709646	+	0.704558i	$0.751145\pi$
$380$		0			0
$381$	0.698913	+	0.507790i	0.0358064	+	0.0260149i
$382$	−29.2346	+	21.2402i	−1.49577	+	1.08674i
$383$	6.68251	−	20.5666i	0.341460	−	1.05091i	−0.621991	−	0.783024i	$-0.713676\pi$
$383$	6.68251	−	20.5666i	0.341460	−	1.05091i	0.963452	−	0.267882i	$-0.0863238\pi$
$384$	12.2759			0.626450
$385$		0			0
$386$	5.41788			0.275763
$387$	0.267971	−	0.824730i	0.0136217	−	0.0419234i
$388$	29.6916	−	21.5722i	1.50736	−	1.09516i
$389$	−28.9156	−	21.0084i	−1.46608	−	1.06517i	−0.981727	−	0.190295i	$-0.939056\pi$
$389$	−28.9156	−	21.0084i	−1.46608	−	1.06517i	−0.484352	−	0.874873i	$-0.660944\pi$
$390$		0			0
$391$	0.199274	+	0.613302i	0.0100777	+	0.0310160i
$392$	−1.59273	−	1.15719i	−0.0804451	−	0.0584468i
$393$	0.973475	−	0.707271i	0.0491053	−	0.0356771i
$394$	−0.0937106	+	0.288411i	−0.00472107	+	0.0145300i
$395$		0			0
$396$	−4.91903	−	1.77268i	−0.247191	−	0.0890804i
$397$	20.0447			1.00601			0.503007	−	0.864282i	$-0.332227\pi$
$397$	20.0447			1.00601			0.503007	+	0.864282i	$0.332227\pi$
$398$	−4.88315	+	15.0288i	−0.244770	+	0.753326i
$399$	−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	$-0.274745\pi$
$402$	−8.37008	−	25.7605i	−0.417462	−	1.28481i
$403$	−25.8491	−	18.7805i	−1.28764	−	0.935523i
$404$	−22.6880	+	16.4838i	−1.12877	+	0.820099i
$405$		0			0
$406$	23.9176			1.18701
$407$	−0.194050	+	6.11454i	−0.00961869	+	0.303087i
$408$	−0.725576			−0.0359214
$409$	7.26134	−	22.3481i	0.359050	−	1.10504i	−0.594574	−	0.804041i	$-0.702679\pi$
$409$	7.26134	−	22.3481i	0.359050	−	1.10504i	0.953624	−	0.301001i	$-0.0973208\pi$
$410$		0			0
$411$	−17.3079	−	12.5750i	−0.853738	−	0.620277i
$412$	−10.2581	−	31.5713i	−0.505382	−	1.55541i
$413$	2.66812	+	8.21161i	0.131289	+	0.404067i
$414$	−1.55435	−	1.12930i	−0.0763924	−	0.0555023i
$415$		0			0
$416$	7.59804	−	23.3844i	0.372525	−	1.14651i
$417$	4.54328			0.222485
$418$	33.6431	−	43.3447i	1.64554	−	2.12006i
$419$	−10.1128			−0.494043			−0.247022	−	0.969010i	$-0.579452\pi$
$419$	−10.1128			−0.494043			−0.247022	+	0.969010i	$0.579452\pi$
$420$		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	$0.369769\pi$
$422$	3.84593	+	2.79423i	0.187217	+	0.136021i
$423$	0.607404	+	1.86940i	0.0295330	+	0.0908932i
$424$	−1.05828	−	3.25704i	−0.0513945	−	0.158176i
$425$		0			0
$426$	−21.1492	+	15.3658i	−1.02468	+	0.744476i
$427$	−1.91209	+	5.88481i	−0.0925325	+	0.284786i
$428$	17.4991			0.845850
$429$	−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	$0.960564\pi$
$432$	11.1099	−	8.07181i	0.534525	−	0.388355i
$433$	7.39763	+	5.37469i	0.355507	+	0.258291i	0.751176	−	0.660102i	$-0.229487\pi$
$433$	7.39763	+	5.37469i	0.355507	+	0.258291i	−0.395668	+	0.918393i	$0.629487\pi$
$434$	−20.8057	−	64.0334i	−0.998706	−	3.07370i
$435$		0			0
$436$	14.3737	+	10.4431i	0.688377	+	0.500135i
$437$	8.88054	−	6.45209i	0.424814	−	0.308645i
$438$	−12.2325	+	37.6477i	−0.584490	+	1.79888i
$439$	6.46946			0.308770			0.154385	−	0.988011i	$-0.450660\pi$
$439$	6.46946			0.308770			0.154385	+	0.988011i	$0.450660\pi$
$440$		0			0
$441$	1.58797			0.0756176
$442$	−0.915954	+	2.81902i	−0.0435675	+	0.134087i
$443$	−33.0760	+	24.0311i	−1.57149	+	1.14175i	−0.645774	+	0.763529i	$0.723465\pi$
$443$	−33.0760	+	24.0311i	−1.57149	+	1.14175i	−0.925714	+	0.378224i	$0.876535\pi$
$444$	−6.82343	−	4.95751i	−0.323826	−	0.235273i
$445$		0			0
$446$	−5.55518	−	17.0971i	−0.263045	−	0.809571i
$447$	−13.4960	−	9.80542i	−0.638339	−	0.463781i
$448$	26.6950	−	19.3951i	1.26122	−	0.916330i
$449$	−3.75788	+	11.5656i	−0.177345	+	0.545813i	−0.999733	−	0.0231150i	$-0.992642\pi$
$449$	−3.75788	+	11.5656i	−0.177345	+	0.545813i	0.822387	+	0.568928i	$0.192642\pi$
$450$		0			0
$451$	13.7527	+	4.95608i	0.647589	+	0.233373i
$452$	7.25777			0.341377
$453$	−7.05561	+	21.7149i	−0.331501	+	1.02026i
$454$	10.5105	−	7.63629i	0.493280	−	0.358389i
$455$		0			0
$456$	3.81662	+	11.7463i	0.178730	+	0.550073i
$457$	3.06001	+	9.41775i	0.143141	+	0.440544i	0.996767	−	0.0803428i	$-0.0256015\pi$
$457$	3.06001	+	9.41775i	0.143141	+	0.440544i	−0.853626	+	0.520886i	$0.825602\pi$
$458$	−39.2691	−	28.5307i	−1.83493	−	1.33315i
$459$	−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	$0.523187\pi$
$462$	−39.1596	+	11.3638i	−1.82187	+	0.528692i
$463$	24.3518			1.13173			0.565863	−	0.824499i	$-0.308543\pi$
$463$	24.3518			1.13173			0.565863	+	0.824499i	$0.308543\pi$
$464$	−3.52740	+	10.8562i	−0.163755	+	0.503987i
$465$		0			0
$466$	−47.2309	−	34.3152i	−2.18793	−	1.58962i
$467$	−10.2512	−	31.5501i	−0.474371	−	1.45996i	−0.846805	−	0.531904i	$-0.821477\pi$
$467$	−10.2512	−	31.5501i	−0.474371	−	1.45996i	0.372434	−	0.928059i	$-0.378523\pi$
$468$	−1.48577	−	4.57274i	−0.0686799	−	0.211375i
$469$	−16.7682	−	12.1828i	−0.774282	−	0.562549i
$470$		0			0
$471$	2.29089	−	7.05063i	0.105559	−	0.324876i
$472$	2.30185			0.105951
$473$	2.44992	+	3.60735i	0.112648	+	0.165866i
$474$	46.3273			2.12788
$475$		0			0
$476$	−2.75116	+	1.99883i	−0.126099	+	0.0916163i
$477$	2.23476	+	1.62365i	0.102323	+	0.0743418i
$478$	−10.5450	−	32.4543i	−0.482318	−	1.48442i
$479$	−5.34529	−	16.4511i	−0.244232	−	0.751670i	−0.995762	−	0.0919705i	$-0.970683\pi$
$479$	−5.34529	−	16.4511i	−0.244232	−	0.751670i	0.751529	−	0.659700i	$-0.229317\pi$
$480$		0			0
$481$	−4.55111	+	3.30658i	−0.207513	+	0.150767i
$482$	2.84285	−	8.74941i	0.129488	−	0.398524i
$483$	−8.15736			−0.371173
$484$	22.2085	−	14.0747i	1.00948	−	0.639758i
$485$		0			0
$486$	4.36286	−	13.4275i	0.197903	−	0.609084i
$487$	6.18138	−	4.49104i	0.280105	−	0.203508i	−0.438858	−	0.898556i	$-0.644617\pi$
$487$	6.18138	−	4.49104i	0.280105	−	0.203508i	0.718963	+	0.695048i	$0.244617\pi$
$488$	1.33456	+	0.969617i	0.0604128	+	0.0438925i
$489$	−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	$0.456840\pi$
$492$	−16.3050	+	11.8463i	−0.735087	+	0.534072i
$493$	0.533442	−	1.64177i	0.0240250	−	0.0739414i
$494$	50.4551			2.27008
$495$		0			0
$496$	32.1333			1.44283
$497$	−6.18159	+	19.0250i	−0.277282	+	0.853386i
$498$	−28.9210	+	21.0124i	−1.29598	+	0.941587i
$499$	30.3206	+	22.0292i	1.35734	+	0.986162i	0.998609	+	0.0527188i	$0.0167887\pi$
$499$	30.3206	+	22.0292i	1.35734	+	0.986162i	0.358726	+	0.933443i	$0.383211\pi$
$500$		0			0
$501$	8.22879	+	25.3256i	0.367635	+	1.13147i
$502$	4.52037	+	3.28424i	0.201754	+	0.146583i
$503$	6.85800	−	4.98263i	0.305783	−	0.222164i	−0.424302	−	0.905521i	$-0.639480\pi$
$503$	6.85800	−	4.98263i	0.305783	−	0.222164i	0.730085	+	0.683356i	$0.239480\pi$
$504$	0.511176	−	1.57324i	0.0227696	−	0.0700776i
$505$		0			0
$506$	9.27854	−	2.69255i	0.412481	−	0.119699i
$507$	7.07548			0.314233
$508$	0.333563	−	1.02660i	0.0147995	−	0.0455481i
$509$	1.37309	−	0.997609i	0.0608612	−	0.0442183i	−0.556939	−	0.830554i	$-0.688024\pi$
$509$	1.37309	−	0.997609i	0.0608612	−	0.0442183i	0.617800	+	0.786335i	$0.288024\pi$
$510$		0			0
$511$	9.36041	+	28.8084i	0.414080	+	1.27441i
$512$	9.19138	+	28.2882i	0.406206	+	1.25017i
$513$	28.5994	+	20.7787i	1.26269	+	0.917400i
$514$	−36.6701	+	26.6424i	−1.61745	+	1.17515i
$515$		0			0
$516$	−6.01190			−0.264659
$517$	−9.29877	−	3.35101i	−0.408959	−	0.147377i
$518$	−11.8542			−0.520843
$519$	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	$0.398087\pi$
$522$	1.58932	+	4.89143i	0.0695627	+	0.214092i
$523$	5.58759	+	17.1968i	0.244328	+	0.751965i	0.995746	+	0.0921382i	$0.0293702\pi$
$523$	5.58759	+	17.1968i	0.244328	+	0.751965i	−0.751418	+	0.659826i	$0.770630\pi$
$524$	−1.21634	−	0.883723i	−0.0531361	−	0.0386056i
$525$		0			0
$526$	−14.3347	+	44.1177i	−0.625023	+	1.92362i
$527$	−4.85946			−0.211681
$528$	0.617278	−	19.4506i	0.0268636	−	0.846477i
$529$	−21.0672			−0.915965
$530$		0			0
$531$	−1.50208	+	1.09132i	−0.0651846	+	0.0473594i
$532$	46.8305	+	34.0244i	2.03036	+	1.47514i
$533$	4.15394	+	12.7845i	0.179927	+	0.553759i
$534$	8.38525	+	25.8071i	0.362865	+	1.11678i
$535$		0			0
$536$	−4.47035	+	3.24790i	−0.193090	+	0.140288i
$537$	−13.4388	+	41.3605i	−0.579929	+	1.78484i
$538$	43.4111			1.87159
$539$	−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	$0.0187019\pi$
$542$	0.717229	−	0.521098i	0.0308076	−	0.0223831i
$543$	3.71174	+	2.69674i	0.159286	+	0.115728i
$544$	−1.15558	−	3.55652i	−0.0495452	−	0.152485i
$545$		0			0
$546$	−30.3340	−	22.0390i	−1.29818	−	0.943181i
$547$	−17.6017	+	12.7884i	−0.752593	+	0.546791i	−0.896629	−	0.442782i	$-0.853992\pi$
$547$	−17.6017	+	12.7884i	−0.752593	+	0.546791i	0.144037	+	0.989572i	$0.453992\pi$
$548$	−8.26039	+	25.4229i	−0.352866	+	1.08601i
$549$	−1.33057			−0.0567874
$550$		0			0
$551$	−29.3845			−1.25182
$552$	−0.672028	+	2.06829i	−0.0286034	+	0.0880322i
$553$	28.6797	−	20.8370i	1.21959	−	0.886081i
$554$	−14.5316	−	10.5578i	−0.617388	−	0.448558i
$555$		0			0
$556$	−1.75421	−	5.39891i	−0.0743952	−	0.228965i
$557$	3.91104	+	2.84154i	0.165716	+	0.120400i	0.667552	−	0.744563i	$-0.267342\pi$
$557$	3.91104	+	2.84154i	0.165716	+	0.120400i	−0.501836	+	0.864963i	$0.667342\pi$
$558$	11.7130	−	8.51003i	0.495853	−	0.360258i
$559$	−1.23911	+	3.81358i	−0.0524086	+	0.161297i
$560$		0			0
$561$	−0.0933499	+	2.94147i	−0.00394124	+	0.124189i
$562$	−14.6903			−0.619672
$563$	−1.47463	+	4.53843i	−0.0621481	+	0.191272i	−0.977310	−	0.211815i	$-0.932063\pi$
$563$	−1.47463	+	4.53843i	−0.0621481	+	0.191272i	0.915162	+	0.403087i	$0.132063\pi$
$564$	11.0245	−	8.00978i	0.464216	−	0.337272i
$565$		0			0
$566$	−6.44449	−	19.8341i	−0.270882	−	0.833690i
$567$	−9.99341	−	30.7566i	−0.419684	−	1.29165i
$568$	4.31450	+	3.13467i	0.181032	+	0.131528i
$569$	−28.8971	+	20.9949i	−1.21143	+	0.880154i	−0.995360	−	0.0962246i	$-0.969323\pi$
$569$	−28.8971	+	20.9949i	−1.21143	+	0.880154i	−0.216068	+	0.976378i	$0.569323\pi$
$570$		0			0
$571$	−33.9838			−1.42218			−0.711090	−	0.703101i	$-0.751798\pi$
$571$	−33.9838			−1.42218			−0.711090	+	0.703101i	$0.751798\pi$
$572$	22.7458	+	8.19692i	0.951048	+	0.342731i
$573$	−32.9920			−1.37826
$574$	−8.75331	+	26.9399i	−0.365356	+	1.12445i
$575$		0			0
$576$	5.74040	+	4.17065i	0.239183	+	0.173777i
$577$	6.38364	+	19.6468i	0.265755	+	0.817909i	0.991519	+	0.129965i	$0.0414864\pi$
$577$	6.38364	+	19.6468i	0.265755	+	0.817909i	−0.725764	+	0.687944i	$0.758514\pi$
$578$	−10.8679	−	33.4479i	−0.452044	−	1.39125i
$579$	4.00181	+	2.90748i	0.166309	+	0.120831i
$580$		0			0
$581$	−8.45317	+	26.0162i	−0.350697	+	1.07933i
$582$	61.5447			2.55111
$583$	−13.3402	+	3.87120i	−0.552493	+	0.160329i
$584$	8.07548			0.334166
$585$		0			0
$586$	36.9892	−	26.8742i	1.52801	−	1.11016i
$587$	10.8085	+	7.85284i	0.446115	+	0.324121i	0.788060	−	0.615599i	$-0.211086\pi$
$587$	10.8085	+	7.85284i	0.446115	+	0.324121i	−0.341945	+	0.939720i	$0.611086\pi$
$588$	−3.40197	−	10.4702i	−0.140295	−	0.431783i
$589$	25.5614	+	78.6698i	1.05324	+	3.24153i
$590$		0			0
$591$	−0.223992	+	0.162740i	−0.00921381	+	0.00669423i
$592$	1.74827	−	5.38063i	0.0718535	−	0.221142i
$593$	−20.8062			−0.854410			−0.427205	−	0.904155i	$-0.640502\pi$
$593$	−20.8062			−0.854410			−0.427205	+	0.904155i	$0.640502\pi$
$594$	17.4806	+	25.7391i	0.717238	+	1.05609i
$595$		0			0
$596$	−6.44111	+	19.8237i	−0.263838	+	0.812010i
$597$	−11.6720	+	8.48020i	−0.477703	+	0.347071i
$598$	7.18739	+	5.22194i	0.293914	+	0.213541i
$599$	−4.40214	−	13.5484i	−0.179867	−	0.553573i	0.819956	−	0.572427i	$-0.193998\pi$
$599$	−4.40214	−	13.5484i	−0.179867	−	0.553573i	−0.999822	+	0.0188544i	$0.993998\pi$
$600$		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	$0.560932\pi$
$602$	−6.83590	+	4.96657i	−0.278611	+	0.202422i
$603$	1.37728	−	4.23884i	0.0560872	−	0.172619i
$604$	28.5287			1.16082
$605$		0			0
$606$	−47.0276			−1.91037
$607$	−5.53818	+	17.0448i	−0.224788	+	0.691825i	0.773525	+	0.633765i	$0.218492\pi$
$607$	−5.53818	+	17.0448i	−0.224788	+	0.691825i	−0.998313	+	0.0580601i	$0.981508\pi$
$608$	−51.4980	+	37.4155i	−2.08852	+	1.51740i
$609$	17.6662	+	12.8353i	0.715872	+	0.520111i
$610$		0			0
$611$	−2.80866	−	8.64416i	−0.113626	−	0.349705i
$612$	−0.591599	−	0.429822i	−0.0239140	−	0.0173745i
$613$	−22.8158	+	16.5766i	−0.921521	+	0.669524i	−0.943902	−	0.330225i	$-0.892875\pi$
$613$	−22.8158	+	16.5766i	−0.921521	+	0.669524i	0.0223811	+	0.999750i	$0.492875\pi$
$614$	19.9861	−	61.5109i	0.806573	−	2.48238i
$615$		0			0
$616$	4.67342	+	6.88131i	0.188298	+	0.277256i
$617$	4.72930			0.190394			0.0951972	−	0.995458i	$-0.469652\pi$
$617$	4.72930			0.190394			0.0951972	+	0.995458i	$0.469652\pi$
$618$	17.2022	−	52.9428i	0.691972	−	2.12967i
$619$	24.3170	−	17.6673i	0.977383	−	0.710110i	0.0202609	−	0.999795i	$-0.493550\pi$
$619$	24.3170	−	17.6673i	0.977383	−	0.710110i	0.957122	+	0.289684i	$0.0935503\pi$
$620$		0			0
$621$	1.92349	+	5.91989i	0.0771870	+	0.237557i
$622$	−12.5709	−	38.6891i	−0.504046	−	1.55129i
$623$	16.7986	+	12.2049i	0.673020	+	0.488978i
$624$	14.4772	−	10.5183i	0.579553	−	0.421070i
$625$		0			0
$626$	−2.20314			−0.0880551
$627$	48.1105	−	13.9613i	1.92135	−	0.557560i
$628$	−9.26301			−0.369634
$629$	−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	$0.482624\pi$
$632$	−2.92049	−	8.98834i	−0.116171	−	0.357537i
$633$	1.34120	+	4.12780i	0.0533081	+	0.164065i
$634$	−40.3973	−	29.3504i	−1.60438	−	1.16565i
$635$		0			0
$636$	5.91783	−	18.2132i	0.234657	−	0.722201i
$637$	−7.34282			−0.290933
$638$	−24.3310	−	8.76819i	−0.963272	−	0.347136i
$639$	−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	$0.177854\pi$
$642$	23.7404	+	17.2484i	0.936958	+	0.680740i
$643$	11.2015	+	34.4747i	0.441745	+	1.35955i	0.886015	+	0.463657i	$0.153463\pi$
$643$	11.2015	+	34.4747i	0.441745	+	1.35955i	−0.444270	+	0.895893i	$0.646537\pi$
$644$	3.14965	+	9.69362i	0.124114	+	0.381982i
$645$		0			0
$646$	6.20815	−	4.51048i	0.244256	−	0.177463i
$647$	10.8007	−	33.2412i	0.424620	−	1.30685i	−0.478737	−	0.877958i	$-0.658905\pi$
$647$	10.8007	−	33.2412i	0.424620	−	1.30685i	0.903357	−	0.428889i	$-0.141095\pi$
$648$	−8.62158			−0.338688
$649$	0.296148	−	9.33168i	0.0116248	−	0.366301i
$650$		0			0
$651$	18.9955	−	58.4623i	0.744494	−	2.29132i
$652$	−19.2142	+	13.9600i	−0.752488	+	0.546714i
$653$	−24.1000	−	17.5097i	−0.943106	−	0.685207i	0.00605995	−	0.999982i	$-0.498071\pi$
$653$	−24.1000	−	17.5097i	−0.943106	−	0.685207i	−0.949166	+	0.314775i	$0.898071\pi$
$654$	9.20681	+	28.3356i	0.360015	+	1.10801i
$655$		0			0
$656$	−10.9371	−	7.94628i	−0.427023	−	0.310250i
$657$	−5.26966	+	3.82863i	−0.205589	+	0.149369i
$658$	5.91848	−	18.2152i	0.230726	−	0.710103i
$659$	−7.30532			−0.284575			−0.142287	−	0.989825i	$-0.545446\pi$
$659$	−7.30532			−0.284575			−0.142287	+	0.989825i	$0.545446\pi$
$660$		0			0
$661$	−22.7352			−0.884296			−0.442148	−	0.896942i	$-0.645783\pi$
$661$	−22.7352			−0.884296			−0.442148	+	0.896942i	$0.645783\pi$
$662$	16.6204	−	51.1524i	0.645971	−	1.98809i
$663$	−2.18937	+	1.59067i	−0.0850279	+	0.0617764i
$664$	5.89998	+	4.28658i	0.228964	+	0.166352i
$665$		0			0
$666$	−0.787710	−	2.42432i	−0.0305231	−	0.0939405i
$667$	−4.18586	−	3.04120i	−0.162077	−	0.117756i
$668$	26.9179	−	19.5570i	1.04149	−	0.756684i
$669$	5.07186	−	15.6096i	0.196090	−	0.603502i
$670$		0			0
$671$	4.10251	−	5.28555i	0.158376	−	0.204046i
$672$	47.3043			1.82480
$673$	5.48354	−	16.8766i	0.211375	−	0.650546i	−0.788016	−	0.615655i	$-0.788892\pi$
$673$	5.48354	−	16.8766i	0.211375	−	0.650546i	0.999391	−	0.0348910i	$-0.0111084\pi$
$674$	−40.5003	+	29.4252i	−1.56001	+	1.13342i
$675$		0			0
$676$	−2.73192	−	8.40799i	−0.105074	−	0.323384i
$677$	−2.52224	−	7.76267i	−0.0969377	−	0.298344i	0.890816	−	0.454364i	$-0.150133\pi$
$677$	−2.52224	−	7.76267i	−0.0969377	−	0.298344i	−0.987754	+	0.156020i	$0.950133\pi$
$678$	9.84636	+	7.15380i	0.378147	+	0.274740i
$679$	38.1004	−	27.6815i	1.46216	−	1.06232i
$680$		0			0
$681$	11.8613			0.454527
$682$	−2.30933	+	72.7675i	−0.0884289	+	2.78641i
$683$	6.19100			0.236892			0.118446	−	0.992960i	$-0.462209\pi$
$683$	6.19100			0.236892			0.118446	+	0.992960i	$0.462209\pi$
$684$	−3.84650	+	11.8383i	−0.147075	+	0.452649i
$685$		0			0
$686$	23.8770	+	17.3477i	0.911628	+	0.662336i
$687$	−13.6945	−	42.1473i	−0.522477	−	1.60802i
$688$	−1.24617	−	3.83530i	−0.0475096	−	0.146220i
$689$	−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	$-0.0482162\pi$
$692$	−25.8892			−0.984158
$693$	−6.31212	−	2.27471i	−0.239778	−	0.0864090i
$694$	0.695956			0.0264181
$695$		0			0
$696$	4.70977	−	3.42185i	0.178523	−	0.129705i
$697$	1.65400	+	1.20170i	0.0626497	+	0.0455177i
$698$	0.790889	+	2.43411i	0.0299356	+	0.0921323i
$699$	−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	$0.548178\pi$
$702$	−8.84124	+	27.2105i	−0.333691	+	1.02700i
$703$	14.5637			0.549282
$704$	−34.2667	+	9.94389i	−1.29147	+	0.374775i
$705$		0			0
$706$	16.6428	−	51.2211i	0.626358	−	1.92773i
$707$	−29.1133	+	21.1521i	−1.09492	+	0.795505i
$708$	10.4135	+	7.56588i	0.391365	+	0.284343i
$709$	5.64072	+	17.3603i	0.211842	+	0.651981i	0.999363	+	0.0356939i	$0.0113641\pi$
$709$	5.64072	+	17.3603i	0.211842	+	0.651981i	−0.787521	+	0.616288i	$0.788636\pi$
$710$		0			0
$711$	6.16719	+	4.48073i	0.231288	+	0.168040i
$712$	4.47845	−	3.25378i	0.167837	−	0.121941i
$713$	−4.50083	+	13.8521i	−0.168557	+	0.518766i
$714$	−5.70259			−0.213414
$715$		0			0
$716$	54.3388			2.03074
$717$	9.62758	−	29.6306i	0.359549	−	1.10658i
$718$	30.3961	−	22.0841i	1.13437	−	0.824171i
$719$	−7.74544	−	5.62739i	−0.288856	−	0.209866i	0.433915	−	0.900954i	$-0.357132\pi$
$719$	−7.74544	−	5.62739i	−0.288856	−	0.209866i	−0.722771	+	0.691088i	$0.757132\pi$
$720$		0			0
$721$	−13.1633	−	40.5124i	−0.490226	−	1.50876i
$722$	−73.4684	−	53.3779i	−2.73421	−	1.98652i
$723$	6.79515	−	4.93697i	0.252714	−	0.183608i
$724$	1.77147	−	5.45202i	0.0658361	−	0.202623i
$725$		0			0
$726$	44.0025	+	2.79572i	1.63309	+	0.103759i
$727$	14.0175			0.519882			0.259941	−	0.965625i	$-0.416297\pi$
$727$	14.0175			0.519882			0.259941	+	0.965625i	$0.416297\pi$
$728$	−2.36369	+	7.27470i	−0.0876043	+	0.269618i
$729$	−15.1616	+	11.0156i	−0.561542	+	0.407984i
$730$		0			0
$731$	0.188455	+	0.580006i	0.00697027	+	0.0214523i
$732$	2.85054	+	8.77306i	0.105359	+	0.324262i
$733$	7.51392	+	5.45918i	0.277533	+	0.201640i	0.717841	−	0.696207i	$-0.245131\pi$
$733$	7.51392	+	5.45918i	0.277533	+	0.201640i	−0.440308	+	0.897847i	$0.645131\pi$
$734$	−14.3932	+	10.4573i	−0.531262	+	0.385984i
$735$		0			0
$736$	−11.2083			−0.413145
$737$	12.5918	+	18.5406i	0.463824	+	0.682951i
$738$	−6.09119			−0.224220
$739$	−12.0389	+	37.0519i	−0.442857	+	1.36298i	0.441959	+	0.897035i	$0.354284\pi$
$739$	−12.0389	+	37.0519i	−0.442857	+	1.36298i	−0.884816	+	0.465940i	$0.845716\pi$
$740$		0			0
$741$	37.2676	+	27.0765i	1.36906	+	0.994681i
$742$	−8.31742	−	25.5984i	−0.305342	−	0.939747i
$743$	−14.1930	−	43.6817i	−0.520692	−	1.60252i	−0.772681	−	0.634795i	$-0.781085\pi$
$743$	−14.1930	−	43.6817i	−0.520692	−	1.60252i	0.251989	−	0.967730i	$-0.418915\pi$
$744$	−13.2581	−	9.63260i	−0.486067	−	0.353148i
$745$		0			0
$746$	−23.2089	+	71.4298i	−0.849740	+	2.61523i
$747$	−5.88233			−0.215223
$748$	3.53148	−	1.02481i	0.129124	−	0.0374706i
$749$	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	$0.439079\pi$
$752$	7.39504	+	5.37281i	0.269669	+	0.195926i
$753$	1.57640	+	4.85167i	0.0574474	+	0.176805i
$754$	−7.34907	−	22.6181i	−0.267637	−	0.823703i
$755$		0			0
$756$	−26.5555	+	19.2937i	−0.965815	+	0.701705i
$757$	2.01541	−	6.20281i	0.0732515	−	0.225445i	−0.907727	−	0.419561i	$-0.862184\pi$
$757$	2.01541	−	6.20281i	0.0732515	−	0.225445i	0.980979	+	0.194116i	$0.0621839\pi$
$758$	36.7757			1.33575
$759$	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	$0.137976\pi$
$762$	1.46443	−	1.06397i	0.0530507	−	0.0385436i
$763$	18.4444	+	13.4007i	0.667733	+	0.485137i
$764$	12.7386	+	39.2054i	0.460866	+	1.41840i
$765$		0			0
$766$	−36.6572	−	26.6330i	−1.32448	−	0.962291i
$767$	6.94565	−	5.04631i	0.250793	−	0.182212i
$768$	−4.77078	+	14.6829i	−0.172151	+	0.529825i
$769$	12.5950			0.454188			0.227094	−	0.973873i	$-0.427078\pi$
$769$	12.5950			0.454188			0.227094	+	0.973873i	$0.427078\pi$
$770$		0			0
$771$	−41.3832			−1.49038
$772$	1.90990	−	5.87807i	0.0687389	−	0.211557i
$773$	17.7537	−	12.8988i	0.638557	−	0.463939i	−0.220797	−	0.975320i	$-0.570866\pi$
$773$	17.7537	−	12.8988i	0.638557	−	0.463939i	0.859354	+	0.511381i	$0.170866\pi$
$774$	−1.46997	−	1.06799i	−0.0528369	−	0.0383883i
$775$		0			0
$776$	−3.87980	−	11.9408i	−0.139277	−	0.428650i
$777$	−8.75585	−	6.36150i	−0.314114	−	0.228217i
$778$	−60.5867	+	44.0188i	−2.17214	+	1.57815i
$779$	10.7541	−	33.0977i	0.385305	−	1.18585i
$780$		0			0
$781$	13.2630	−	17.0876i	0.474587	−	0.611444i
$782$	1.35118			0.0483181
$783$	5.14904	−	15.8471i	0.184012	−	0.566330i
$784$	5.97430	−	4.34059i	0.213368	−	0.155021i
$785$		0			0
$786$	−0.779102	−	2.39783i	−0.0277897	−	0.0855278i
$787$	−5.16981	−	15.9110i	−0.184284	−	0.567167i	0.815652	−	0.578543i	$-0.196379\pi$
$787$	−5.16981	−	15.9110i	−0.184284	−	0.567167i	−0.999935	+	0.0113766i	$0.996379\pi$
$788$	0.279875	+	0.203341i	0.00997012	+	0.00724372i
$789$	−34.2637	+	24.8940i	−1.21982	+	0.886250i
$790$		0			0
$791$	9.31320			0.331139
$792$	−1.09676	+	1.41303i	−0.0389717	+	0.0502100i
$793$	6.15261			0.218486
$794$	12.9786	−	39.9439i	0.460592	−	1.41756i
$795$		0			0
$796$	14.5840	+	10.5959i	0.516915	+	0.375560i
$797$	3.63735	+	11.1946i	0.128842	+	0.396533i	0.994581	−	0.103961i	$-0.0331516\pi$
$797$	3.63735	+	11.1946i	0.128842	+	0.396533i	−0.865740	+	0.500494i	$0.833152\pi$
$798$	29.9963	+	92.3192i	1.06186	+	3.26807i
$799$	−1.11834	−	0.812521i	−0.0395640	−	0.0287449i
$800$		0			0
$801$	−1.37978	+	4.24652i	−0.0487521	+	0.150043i
$802$	−43.7889			−1.54624
$803$	1.03896	−	32.7379i	0.0366641	−	1.15529i
$804$	−30.8992			−1.08973
$805$		0			0
$806$	−54.1615	+	39.3507i	−1.90776	+	1.38607i
$807$	32.0647	+	23.2964i	1.12873	+	0.820072i
$808$	2.96464	+	9.12422i	0.104296	+	0.320989i
$809$	0.369567	+	1.13741i	0.0129933	+	0.0399893i	0.957343	−	0.288954i	$-0.0933075\pi$
$809$	0.369567	+	1.13741i	0.0129933	+	0.0399893i	−0.944350	+	0.328943i	$0.893307\pi$
$810$		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	$0.516535\pi$
$812$	8.43138	−	25.9491i	0.295884	−	0.910636i
$813$	0.809412			0.0283873
$814$	12.0591	+	4.34575i	0.422670	+	0.152318i
$815$		0			0
$816$	0.841026	−	2.58841i	0.0294418	−	0.0906126i
$817$	8.39841	−	6.10181i	0.293823	−	0.213475i
$818$	−39.8324	−	28.9400i	−1.39271	−	1.01186i
$819$	−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	$0.730552\pi$
$822$	−36.2652	+	26.3482i	−1.26490	+	0.919000i
$823$	−13.2028	+	40.6341i	−0.460222	+	1.41642i	0.404672	+	0.914462i	$0.367386\pi$
$823$	−13.2028	+	40.6341i	−0.460222	+	1.41642i	−0.864894	+	0.501955i	$0.832614\pi$
$824$	−11.3563			−0.395616
$825$		0			0
$826$	18.0912			0.629473
$827$	−10.0186	+	30.8340i	−0.348380	+	1.07220i	0.611369	+	0.791345i	$0.290619\pi$
$827$	−10.0186	+	30.8340i	−0.348380	+	1.07220i	−0.959749	+	0.280858i	$0.909381\pi$
$828$	−1.77317	+	1.28828i	−0.0616218	+	0.0447709i
$829$	2.35544	+	1.71133i	0.0818079	+	0.0594369i	0.627937	−	0.778264i	$-0.283899\pi$
$829$	2.35544	+	1.71133i	0.0818079	+	0.0594369i	−0.546130	+	0.837701i	$0.683899\pi$
$830$		0			0
$831$	−5.06765	−	15.5966i	−0.175795	−	0.541041i
$832$	−26.5438	−	19.2852i	−0.920241	−	0.668594i
$833$	−0.903483	+	0.656419i	−0.0313038	+	0.0227436i
$834$	2.94169	−	9.05359i	0.101862	−	0.313500i
$835$		0			0
$836$	−35.1666	−	51.7805i	−1.21626	−	1.79087i
$837$	−46.9059			−1.62130
$838$	−6.54786	+	20.1522i	−0.226192	+	0.696147i
$839$	16.8652	−	12.2533i	0.582250	−	0.423030i	−0.257284	−	0.966336i	$-0.582828\pi$
$839$	16.8652	−	12.2533i	0.582250	−	0.423030i	0.839535	+	0.543306i	$0.182828\pi$
$840$		0			0
$841$	−4.68147	−	14.4081i	−0.161430	−	0.496830i
$842$	5.77737	+	17.7809i	0.199101	+	0.612771i
$843$	−10.8507	−	7.88348i	−0.373717	−	0.271521i
$844$	4.38733	−	3.18758i	0.151018	−	0.109721i
$845$		0			0
$846$	4.11851			0.141597
$847$	28.4980	−	18.0607i	0.979203	−	0.620572i
$848$	12.8458			0.441127
$849$	5.88380	−	18.1085i	0.201932	−	0.621482i
$850$		0			0
$851$	2.07462	+	1.50730i	0.0711171	+	0.0516696i
$852$	9.21549	+	28.3624i	0.315718	+	0.971679i
$853$	−10.6768	−	32.8599i	−0.365567	−	1.12510i	−0.949625	−	0.313388i	$-0.898536\pi$
$853$	−10.6768	−	32.8599i	−0.365567	−	1.12510i	0.584058	−	0.811712i	$-0.301464\pi$
$854$	10.4889	+	7.62061i	0.358922	+	0.260772i
$855$		0			0
$856$	1.84990	−	5.69341i	0.0632283	−	0.194597i
$857$	−33.2969			−1.13740			−0.568699	−	0.822545i	$-0.692553\pi$
$857$	−33.2969			−1.13740			−0.568699	+	0.822545i	$0.692553\pi$
$858$	22.7789	+	33.5404i	0.777658	+	1.14505i
$859$	−16.7665			−0.572067			−0.286034	−	0.958220i	$-0.592337\pi$
$859$	−16.7665			−0.572067			−0.286034	+	0.958220i	$0.592337\pi$
$860$		0			0
$861$	−20.9227	+	15.2012i	−0.713043	+	0.518056i
$862$	29.8550	+	21.6909i	1.01687	+	0.738796i
$863$	0.458628	+	1.41151i	0.0156119	+	0.0480484i	0.958559	−	0.284894i	$-0.0919585\pi$
$863$	0.458628	+	1.41151i	0.0156119	+	0.0480484i	−0.942947	+	0.332943i	$0.891958\pi$
$864$	−11.1543	−	34.3293i	−0.379476	−	1.16791i
$865$		0			0
$866$	15.5002	−	11.2616i	0.526719	−	0.382683i
$867$	9.92234	−	30.5378i	0.336980	−	1.03712i
$868$	−76.8068			−2.60699
$869$	−36.8143	+	10.6832i	−1.24884	+	0.362403i
$870$		0			0
$871$	−6.36860	+	19.6005i	−0.215792	+	0.664138i
$872$	4.91723	−	3.57258i	0.166518	−	0.120983i
$873$	8.19297	+	5.95254i	0.277290	+	0.201463i
$874$	−7.10737	−	21.8742i	−0.240410	−	0.739907i
$875$		0			0
$876$	36.5333	+	26.5430i	1.23435	+	0.896805i
$877$	−20.1134	+	14.6132i	−0.679180	+	0.493453i	−0.873086	−	0.487567i	$-0.837885\pi$
$877$	−20.1134	+	14.6132i	−0.679180	+	0.493453i	0.193905	+	0.981020i	$0.437885\pi$
$878$	4.18885	−	12.8920i	0.141367	−	0.435083i
$879$	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	$0.314326\pi$
$882$	1.02818	−	3.16441i	0.0346206	−	0.106551i
$883$	38.5268	−	27.9914i	1.29653	−	0.941985i	0.296615	−	0.954997i	$-0.404142\pi$
$883$	38.5268	−	27.9914i	1.29653	−	0.941985i	0.999915	+	0.0130124i	$0.00414210\pi$
$884$	2.73557	+	1.98751i	0.0920073	+	0.0668472i
$885$		0			0
$886$	26.4717	+	81.4717i	0.889336	+	2.73709i
$887$	47.8097	+	34.7358i	1.60529	+	1.16631i	0.876267	+	0.481826i	$0.160026\pi$
$887$	47.8097	+	34.7358i	1.60529	+	1.16631i	0.729025	+	0.684487i	$0.239974\pi$
$888$	−2.33428	+	1.69596i	−0.0783335	+	0.0569126i
$889$	0.428030	−	1.31734i	0.0143557	−	0.0441822i
$890$		0			0
$891$	−1.10922	+	34.9518i	−0.0371603	+	1.17093i
$892$	−20.5076			−0.686646
$893$	−7.27130	+	22.3787i	−0.243325	+	0.748876i
$894$	−28.2781	+	20.5452i	−0.945761	+	0.687136i
$895$		0			0
$896$	−6.08220	−	18.7191i	−0.203192	−	0.625360i
$897$	2.50648	+	7.71417i	0.0836891	+	0.257569i
$898$	20.6140	+	14.9770i	0.687900	+	0.499788i
$899$	31.5431	−	22.9174i	1.05202	−	0.764338i
$900$		0			0
$901$	−1.94265			−0.0647190
$902$	18.7808	−	24.1966i	0.625332	−	0.805659i
$903$	−7.71450			−0.256722
$904$	0.767250	−	2.36135i	0.0255183	−	0.0785374i
$905$		0			0
$906$	38.7039	+	28.1200i	1.28585	+	0.934225i
$907$	−10.7098	−	32.9613i	−0.355612	−	1.09446i	−0.955654	−	0.294493i	$-0.904849\pi$
$907$	−10.7098	−	32.9613i	−0.355612	−	1.09446i	0.600041	−	0.799969i	$-0.295151\pi$
$908$	−4.57979	−	14.0952i	−0.151986	−	0.467764i
$909$	−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	$0.153981\pi$
$912$	−46.3277			−1.53406
$913$	18.1368	−	23.3669i	0.600241	−	0.773332i
$914$	20.7484			0.686298
$915$		0			0
$916$	−44.7972	+	32.5471i	−1.48014	+	1.07539i
$917$	−1.56081	−	1.13400i	−0.0515426	−	0.0374479i
$918$	1.34466	+	4.13844i	0.0443804	+	0.136589i
$919$	−11.1644	−	34.3606i	−0.368281	−	1.13345i	−0.947901	−	0.318565i	$-0.896799\pi$
$919$	−11.1644	−	34.3606i	−0.368281	−	1.13345i	0.579620	−	0.814887i	$-0.303201\pi$
$920$		0			0
$921$	47.7719	−	34.7083i	1.57414	−	1.14368i
$922$	−2.02357	+	6.22790i	−0.0666427	+	0.205105i
$923$	19.8907			0.654711
$924$	−1.47545	+	46.4918i	−0.0485389	+	1.52947i
$925$		0			0
$926$	15.7674	−	48.5269i	0.518148	−	1.59469i
$927$	7.41057	−	5.38409i	0.243395	−	0.176837i
$928$	24.2737	+	17.6359i	0.796823	+	0.578926i
$929$	8.69078	+	26.7475i	0.285135	+	0.877556i	0.986358	+	0.164614i	$0.0526379\pi$
$929$	8.69078	+	26.7475i	0.285135	+	0.877556i	−0.701223	+	0.712942i	$0.747362\pi$
$930$		0			0
$931$	15.3792	+	11.1736i	0.504033	+	0.366201i
$932$	−53.8797	+	39.1459i	−1.76489	+	1.28227i
$933$	11.4772	−	35.3231i	0.375745	−	1.15643i
$934$	−69.5087			−2.27439
$935$		0			0
$936$	−1.64483			−0.0537630
$937$	−0.0263183	+	0.0809993i	−0.000859781	+	0.00264613i	−0.951485	−	0.307694i	$-0.900443\pi$
$937$	−0.0263183	+	0.0809993i	−0.000859781	+	0.00264613i	0.950626	+	0.310340i	$0.100443\pi$
$938$	−35.1342	+	25.5265i	−1.14717	+	0.833471i
$939$	−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	$-0.338703\pi$
$942$	−12.5668	−	9.13031i	−0.409448	−	0.297482i
$943$	4.95744	−	3.60179i	0.161437	−	0.117291i
$944$	−2.66812	+	8.21161i	−0.0868398	+	0.267265i
$945$		0			0
$946$	8.77481	−	2.54638i	0.285294	−	0.0827898i
$947$	−8.92463			−0.290012			−0.145006	−	0.989431i	$-0.546320\pi$
$947$	−8.92463			−0.290012			−0.145006	+	0.989431i	$0.546320\pi$
$948$	16.3312	−	50.2623i	0.530413	−	1.63244i
$949$	24.3671	−	17.7037i	0.790989	−	0.574687i
$950$		0			0
$951$	−14.0879	−	43.3581i	−0.456832	−	1.40598i
$952$	0.359493	+	1.10641i	0.0116512	+	0.0358589i
$953$	4.25853	+	3.09400i	0.137947	+	0.100225i	0.654619	−	0.755959i	$-0.272829\pi$
$953$	4.25853	+	3.09400i	0.137947	+	0.100225i	−0.516672	+	0.856184i	$0.672829\pi$
$954$	4.68249	−	3.40202i	0.151601	−	0.110145i
$955$		0			0
$956$	−38.9283			−1.25903
$957$	−13.2662	−	19.5336i	−0.428834	−	0.631431i
$958$	−36.2438			−1.17098
$959$	−10.5998	+	32.6227i	−0.342284	+	1.05344i
$960$		0			0
$961$	−63.7153	−	46.2919i	−2.05533	−	1.49329i
$962$	3.64240	+	11.2101i	0.117436	+	0.361429i
$963$	1.49213	+	4.59229i	0.0480831	+	0.147984i
$964$	−8.49043	−	6.16866i	−0.273458	−	0.198679i
$965$		0			0
$966$	−5.28174	+	16.2555i	−0.169937	+	0.523013i
$967$	18.5421			0.596275			0.298138	−	0.954523i	$-0.403635\pi$
$967$	18.5421			0.596275			0.298138	+	0.954523i	$0.403635\pi$
$968$	−2.23151	−	8.71353i	−0.0717235	−	0.280063i
$969$	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	$0.172932\pi$
$972$	−13.0301	−	9.46689i	−0.417939	−	0.303651i
$973$	−2.25101	−	6.92790i	−0.0721641	−	0.222098i
$974$	−4.94715	−	15.2258i	−0.158517	−	0.487865i
$975$		0			0
$976$	−5.00592	+	3.63701i	−0.160236	+	0.116418i
$977$	−15.1609	+	46.6606i	−0.485041	+	1.49280i	0.346880	+	0.937910i	$0.387241\pi$
$977$	−15.1609	+	46.6606i	−0.485041	+	1.49280i	−0.831921	+	0.554894i	$0.812759\pi$
$978$	−39.8272			−1.27353
$979$	−12.6146	−	18.5742i	−0.403165	−	0.593634i
$980$		0			0
$981$	−1.51496	+	4.66258i	−0.0483691	+	0.148865i
$982$	51.9664	−	37.7558i	1.65831	−	1.20484i
$983$	39.7546	+	28.8834i	1.26798	+	0.921239i	0.999120	−	0.0419415i	$-0.0133543\pi$
$983$	39.7546	+	28.8834i	1.26798	+	0.921239i	0.268856	+	0.963180i	$0.413354\pi$
$984$	2.13058	+	6.55724i	0.0679203	+	0.209037i
$985$		0			0
$986$	−2.92622	−	2.12603i	−0.0931899	−	0.0677064i
$987$	14.1467	−	10.2782i	0.450294	−	0.327158i
$988$	17.7863	−	54.7408i	0.565859	−	1.74154i
$989$	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	$0.336350\pi$
$992$	26.1002	−	80.3281i	0.828681	−	2.55042i
$993$	39.7271	−	28.8634i	1.26070	−	0.915952i
$994$	33.9094	+	24.6366i	1.07554	+	0.781426i
$995$		0			0
$996$	12.6020	+	38.7849i	0.399309	+	1.22895i
$997$	18.5216	+	13.4567i	0.586584	+	0.426178i	0.841092	−	0.540892i	$-0.181913\pi$
$997$	18.5216	+	13.4567i	0.586584	+	0.426178i	−0.254507	+	0.967071i	$0.581913\pi$
$998$	63.5305	−	46.1576i	2.01102	−	1.46109i
$999$	−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.h.a.251.2		8
5.2	odd	4		275.2.z.a.174.4		16
5.3	odd	4		275.2.z.a.174.1		16
5.4	even	2		55.2.g.b.31.1	yes	8
11.4	even	5		3025.2.a.bd.1.4		4
11.5	even	5	inner	275.2.h.a.126.2		8
11.7	odd	10		3025.2.a.w.1.1		4
15.14	odd	2		495.2.n.e.361.2		8
20.19	odd	2		880.2.bo.h.801.2		8
55.4	even	10		605.2.a.j.1.1		4
55.9	even	10		605.2.g.m.366.2		8
55.14	even	10		605.2.g.m.81.2		8
55.19	odd	10		605.2.g.e.81.1		8
55.24	odd	10		605.2.g.e.366.1		8
55.27	odd	20		275.2.z.a.49.1		16
55.29	odd	10		605.2.a.k.1.4		4
55.38	odd	20		275.2.z.a.49.4		16
55.39	odd	10		605.2.g.k.511.2		8
55.49	even	10		55.2.g.b.16.1	✓	8
55.54	odd	2		605.2.g.k.251.2		8
165.29	even	10		5445.2.a.bi.1.1		4
165.59	odd	10		5445.2.a.bp.1.4		4
165.104	odd	10		495.2.n.e.181.2		8
220.59	odd	10		9680.2.a.cn.1.1		4
220.139	even	10		9680.2.a.cm.1.1		4
220.159	odd	10		880.2.bo.h.401.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.1	✓	8	55.49	even	10
55.2.g.b.31.1	yes	8	5.4	even	2
275.2.h.a.126.2		8	11.5	even	5	inner
275.2.h.a.251.2		8	1.1	even	1	trivial
275.2.z.a.49.1		16	55.27	odd	20
275.2.z.a.49.4		16	55.38	odd	20
275.2.z.a.174.1		16	5.3	odd	4
275.2.z.a.174.4		16	5.2	odd	4
495.2.n.e.181.2		8	165.104	odd	10
495.2.n.e.361.2		8	15.14	odd	2
605.2.a.j.1.1		4	55.4	even	10
605.2.a.k.1.4		4	55.29	odd	10
605.2.g.e.81.1		8	55.19	odd	10
605.2.g.e.366.1		8	55.24	odd	10
605.2.g.k.251.2		8	55.54	odd	2
605.2.g.k.511.2		8	55.39	odd	10
605.2.g.m.81.2		8	55.14	even	10
605.2.g.m.366.2		8	55.9	even	10
880.2.bo.h.401.2		8	220.159	odd	10
880.2.bo.h.801.2		8	20.19	odd	2
3025.2.a.w.1.1		4	11.7	odd	10
3025.2.a.bd.1.4		4	11.4	even	5
5445.2.a.bi.1.1		4	165.29	even	10
5445.2.a.bp.1.4		4	165.59	odd	10
9680.2.a.cm.1.1		4	220.139	even	10
9680.2.a.cn.1.1		4	220.59	odd	10

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.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.647481 - 1.99274i) q^{2} +(1.54765 - 1.12443i) q^{3} +(-1.93376 - 1.40496i) q^{4} +(-1.23863 - 3.81211i) q^{6} +(-2.48141 - 1.80285i) q^{7} +(-0.661536 + 0.480634i) q^{8} +(0.203814 - 0.627276i) q^{9} +O(q^{10})\)	\(q+(0.647481 - 1.99274i) q^{2} +(1.54765 - 1.12443i) q^{3} +(-1.93376 - 1.40496i) q^{4} +(-1.23863 - 3.81211i) q^{6} +(-2.48141 - 1.80285i) q^{7} +(-0.661536 + 0.480634i) q^{8} +(0.203814 - 0.627276i) q^{9} +(1.86337 + 2.74369i) q^{11} -4.57255 q^{12} +(-0.942444 + 2.90055i) q^{13} +(-5.19927 + 3.77749i) q^{14} +(-0.947813 - 2.91707i) q^{16} +(0.143336 + 0.441143i) q^{17} +(-1.11803 - 0.812299i) q^{18} +(6.38769 - 4.64093i) q^{19} -5.86752 q^{21} +(6.67397 - 1.93673i) q^{22} +1.39026 q^{23} +(-0.483384 + 1.48770i) q^{24} +(5.16983 + 3.75610i) q^{26} +(1.38355 + 4.25813i) q^{27} +(2.26552 + 6.97254i) q^{28} +(-3.01085 - 2.18751i) q^{29} +(-3.23741 + 9.96371i) q^{31} -8.06206 q^{32} +(5.96893 + 2.15103i) q^{33} +0.971892 q^{34} +(-1.27542 + 0.926650i) q^{36} +(1.49226 + 1.08419i) q^{37} +(-5.11227 - 15.7340i) q^{38} +(1.80289 + 5.54873i) q^{39} +(3.56585 - 2.59074i) q^{41} +(-3.79911 + 11.6925i) q^{42} +1.31478 q^{43} +(0.251461 - 7.92360i) q^{44} +(0.900166 - 2.77042i) q^{46} +(-2.41102 + 1.75171i) q^{47} +(-4.74692 - 3.44884i) q^{48} +(0.743998 + 2.28979i) q^{49} +(0.717868 + 0.521562i) q^{51} +(5.89760 - 4.28486i) q^{52} +(-1.29421 + 3.98316i) q^{53} +9.38118 q^{54} +2.50805 q^{56} +(4.66749 - 14.3650i) q^{57} +(-6.30862 + 4.58348i) q^{58} +(-2.27740 - 1.65463i) q^{59} +(-0.623402 - 1.91863i) q^{61} +(17.7590 + 12.9026i) q^{62} +(-1.63663 + 1.18908i) q^{63} +(-3.32441 + 10.2315i) q^{64} +(8.15123 - 10.5018i) q^{66} +6.75753 q^{67} +(0.342610 - 1.05444i) q^{68} +(2.15163 - 1.56325i) q^{69} +(-2.01539 - 6.20274i) q^{71} +(0.166660 + 0.512925i) q^{72} +(-7.98970 - 5.80485i) q^{73} +(3.12672 - 2.27169i) q^{74} -18.8726 q^{76} +(0.322676 - 10.1676i) q^{77} +12.2245 q^{78} +(-3.57158 + 10.9922i) q^{79} +(8.53000 + 6.19741i) q^{81} +(-2.85386 - 8.78327i) q^{82} +(-2.75600 - 8.48210i) q^{83} +(11.3464 + 8.24361i) q^{84} +(0.851296 - 2.62002i) q^{86} -7.11945 q^{87} +(-2.55140 - 0.919451i) q^{88} -6.76978 q^{89} +(7.56782 - 5.49835i) q^{91} +(-2.68842 - 1.95325i) q^{92} +(6.19315 + 19.0606i) q^{93} +(1.92961 + 5.93874i) q^{94} +(-12.4772 + 9.06524i) q^{96} +(-4.74475 + 14.6029i) q^{97} +5.04469 q^{98} +(2.10083 - 0.609644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9	\( 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} + 3 q^{11} - 16 q^{12} + 2 q^{13} - 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} - 20 q^{21} + 7 q^{22} - 10 q^{23} + 13 q^{24} + 10 q^{26} - 10 q^{27} + 6 q^{28} - 9 q^{29} - 10 q^{31} - 16 q^{32} - 5 q^{33} + 4 q^{34} - 15 q^{36} - 24 q^{37} + 21 q^{39} + 8 q^{41} - 9 q^{42} + 38 q^{43} - 12 q^{44} + 3 q^{46} - 5 q^{48} + q^{49} + q^{51} + 28 q^{52} - 13 q^{53} + 16 q^{54} + 22 q^{56} + 45 q^{57} - 12 q^{58} - 27 q^{59} + 6 q^{61} + 30 q^{62} - 25 q^{63} - 26 q^{64} + 13 q^{66} + 38 q^{67} - 11 q^{68} - q^{69} - 20 q^{71} + 30 q^{72} - 13 q^{73} + 20 q^{74} - 34 q^{77} + 16 q^{78} + 37 q^{79} + 8 q^{81} - 28 q^{82} - 27 q^{83} + 28 q^{84} - 3 q^{86} - 38 q^{87} + 36 q^{88} - 16 q^{89} + 44 q^{91} - 11 q^{92} + 35 q^{93} + 17 q^{94} - 17 q^{96} - 24 q^{97} - 16 q^{98} - 20 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 + 3 * q^11 - 16 * q^12 + 2 * q^13 - 16 * q^14 + 4 * q^16 + 13 * q^17 + 15 * q^19 - 20 * q^21 + 7 * q^22 - 10 * q^23 + 13 * q^24 + 10 * q^26 - 10 * q^27 + 6 * q^28 - 9 * q^29 - 10 * q^31 - 16 * q^32 - 5 * q^33 + 4 * q^34 - 15 * q^36 - 24 * q^37 + 21 * q^39 + 8 * q^41 - 9 * q^42 + 38 * q^43 - 12 * q^44 + 3 * q^46 - 5 * q^48 + q^49 + q^51 + 28 * q^52 - 13 * q^53 + 16 * q^54 + 22 * q^56 + 45 * q^57 - 12 * q^58 - 27 * q^59 + 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 + 13 * q^66 + 38 * q^67 - 11 * q^68 - q^69 - 20 * q^71 + 30 * q^72 - 13 * q^73 + 20 * q^74 - 34 * q^77 + 16 * q^78 + 37 * q^79 + 8 * q^81 - 28 * q^82 - 27 * q^83 + 28 * q^84 - 3 * q^86 - 38 * q^87 + 36 * q^88 - 16 * q^89 + 44 * q^91 - 11 * q^92 + 35 * q^93 + 17 * q^94 - 17 * q^96 - 24 * q^97 - 16 * q^98 - 20 * q^99

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