LMFDB - Embedded newform 675.2.l.c.526.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			526.2
Root			$0.500000 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	675.526
Dual form			675.2.l.c.376.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.417037 + 2.36514i) q^{2} +(0.210069 - 1.71926i) q^{3} +(-3.54056 + 1.28866i) q^{4} +(4.15390 - 0.220155i) q^{6} +(-0.544891 - 0.198324i) q^{7} +(-2.12277 - 3.67675i) q^{8} +(-2.91174 - 0.722330i) q^{9} +O(q^{10})$	\(q+(0.417037 + 2.36514i) q^{2} +(0.210069 - 1.71926i) q^{3} +(-3.54056 + 1.28866i) q^{4} +(4.15390 - 0.220155i) q^{6} +(-0.544891 - 0.198324i) q^{7} +(-2.12277 - 3.67675i) q^{8} +(-2.91174 - 0.722330i) q^{9} +(-2.36944 + 1.98820i) q^{11} +(1.47178 + 6.35787i) q^{12} +(-0.729623 + 4.13790i) q^{13} +(0.241824 - 1.37145i) q^{14} +(2.03816 - 1.71022i) q^{16} +(-0.995493 + 1.72424i) q^{17} +(0.494102 - 7.18790i) q^{18} +(1.92271 + 3.33023i) q^{19} +(-0.455437 + 0.895151i) q^{21} +(-5.69050 - 4.77489i) q^{22} +(-4.18428 + 1.52295i) q^{23} +(-6.76724 + 2.87724i) q^{24} -10.0910 q^{26} +(-1.85354 + 4.85432i) q^{27} +2.18479 q^{28} +(1.11126 + 6.30229i) q^{29} +(-1.55754 + 0.566898i) q^{31} +(-1.60967 - 1.35067i) q^{32} +(2.92049 + 4.49135i) q^{33} +(-4.49323 - 1.63540i) q^{34} +(11.2400 - 1.19479i) q^{36} +(2.01505 - 3.49016i) q^{37} +(-7.07461 + 5.93630i) q^{38} +(6.96087 + 2.12366i) q^{39} +(-0.190345 + 1.07950i) q^{41} +(-2.30709 - 0.703859i) q^{42} +(5.28657 - 4.43596i) q^{43} +(5.82704 - 10.0927i) q^{44} +(-5.34699 - 9.26126i) q^{46} +(3.37650 + 1.22894i) q^{47} +(-2.51217 - 3.86340i) q^{48} +(-5.10474 - 4.28338i) q^{49} +(2.75531 + 2.07373i) q^{51} +(-2.74906 - 15.5907i) q^{52} -5.40034 q^{53} +(-12.2541 - 2.35945i) q^{54} +(0.427492 + 2.42443i) q^{56} +(6.12946 - 2.60607i) q^{57} +(-14.4423 + 5.25657i) q^{58} +(-7.87850 - 6.61085i) q^{59} +(12.4005 + 4.51341i) q^{61} +(-1.99034 - 3.44738i) q^{62} +(1.44333 + 0.971060i) q^{63} +(5.18386 - 8.97871i) q^{64} +(-9.40470 + 8.78041i) q^{66} +(1.53458 - 8.70304i) q^{67} +(1.30264 - 7.38764i) q^{68} +(1.73937 + 7.51381i) q^{69} +(-0.572473 + 0.991553i) q^{71} +(3.52514 + 12.2391i) q^{72} +(0.0977361 + 0.169284i) q^{73} +(9.09506 + 3.31033i) q^{74} +(-11.0990 - 9.31317i) q^{76} +(1.68539 - 0.613433i) q^{77} +(-2.11980 + 17.3491i) q^{78} +(-1.25166 - 7.09849i) q^{79} +(7.95648 + 4.20647i) q^{81} -2.63255 q^{82} +(2.58744 + 14.6741i) q^{83} +(0.458958 - 3.75624i) q^{84} +(12.6963 + 10.6535i) q^{86} +(11.0687 - 0.586638i) q^{87} +(12.3399 + 4.49135i) q^{88} +(0.776563 + 1.34505i) q^{89} +(1.21821 - 2.11000i) q^{91} +(12.8521 - 10.7842i) q^{92} +(0.647457 + 2.79691i) q^{93} +(-1.49850 + 8.49839i) q^{94} +(-2.66030 + 2.48371i) q^{96} +(-4.05661 + 3.40390i) q^{97} +(8.00191 - 13.8597i) q^{98} +(8.33533 - 4.07760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8	$ 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8} + 3 q^{11} - 12 q^{12} + 6 q^{13} + 15 q^{14} - 9 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{23} - 18 q^{24} - 30 q^{26} + 9 q^{27} + 12 q^{28} - 6 q^{29} + 3 q^{31} + 9 q^{34} + 18 q^{36} + 3 q^{37} - 42 q^{38} + 33 q^{39} + 15 q^{41} - 18 q^{42} - 3 q^{43} + 3 q^{44} - 3 q^{46} + 15 q^{47} + 15 q^{48} + 12 q^{49} - 18 q^{51} - 9 q^{52} + 18 q^{53} - 54 q^{54} - 33 q^{56} + 3 q^{57} - 21 q^{58} - 12 q^{59} + 12 q^{61} + 12 q^{62} - 9 q^{63} + 12 q^{64} - 9 q^{66} + 15 q^{67} - 9 q^{68} + 9 q^{69} + 27 q^{71} - 18 q^{72} - 6 q^{73} + 33 q^{74} - 48 q^{76} - 15 q^{77} - 18 q^{78} - 42 q^{79} + 36 q^{81} + 12 q^{82} - 39 q^{83} + 6 q^{84} + 51 q^{86} - 9 q^{87} + 30 q^{88} + 9 q^{89} + 6 q^{91} + 39 q^{92} + 39 q^{93} - 15 q^{94} - 3 q^{97} + 45 q^{98} - 27 q^{99}+O(q^{100}) $ 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8 + 3 * q^11 - 12 * q^12 + 6 * q^13 + 15 * q^14 - 9 * q^17 - 9 * q^18 - 3 * q^19 - 12 * q^21 - 3 * q^22 + 12 * q^23 - 18 * q^24 - 30 * q^26 + 9 * q^27 + 12 * q^28 - 6 * q^29 + 3 * q^31 + 9 * q^34 + 18 * q^36 + 3 * q^37 - 42 * q^38 + 33 * q^39 + 15 * q^41 - 18 * q^42 - 3 * q^43 + 3 * q^44 - 3 * q^46 + 15 * q^47 + 15 * q^48 + 12 * q^49 - 18 * q^51 - 9 * q^52 + 18 * q^53 - 54 * q^54 - 33 * q^56 + 3 * q^57 - 21 * q^58 - 12 * q^59 + 12 * q^61 + 12 * q^62 - 9 * q^63 + 12 * q^64 - 9 * q^66 + 15 * q^67 - 9 * q^68 + 9 * q^69 + 27 * q^71 - 18 * q^72 - 6 * q^73 + 33 * q^74 - 48 * q^76 - 15 * q^77 - 18 * q^78 - 42 * q^79 + 36 * q^81 + 12 * q^82 - 39 * q^83 + 6 * q^84 + 51 * q^86 - 9 * q^87 + 30 * q^88 + 9 * q^89 + 6 * q^91 + 39 * q^92 + 39 * q^93 - 15 * q^94 - 3 * q^97 + 45 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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 $

$2$	0.417037	+	2.36514i	0.294890	+	1.67240i	0.667650	+	0.744475i	$0.267300\pi$
$2$	0.417037	+	2.36514i	0.294890	+	1.67240i	−0.372760	+	0.927928i	$0.621589\pi$
$3$	0.210069	−	1.71926i	0.121284	−	0.992618i
$3$	0.210069	−	1.71926i	0.121284	−	0.992618i
$4$	−3.54056	+	1.28866i	−1.77028	+	0.644329i
$5$		0			0
$5$		0			0
$6$	4.15390	−	0.220155i	1.69582	−	0.0898778i
$7$	−0.544891	−	0.198324i	−0.205950	−	0.0749595i	0.236986	−	0.971513i	$-0.423841\pi$
$7$	−0.544891	−	0.198324i	−0.205950	−	0.0749595i	−0.442935	+	0.896554i	$0.646063\pi$
$8$	−2.12277	−	3.67675i	−0.750514	−	1.29993i
$9$	−2.91174	−	0.722330i	−0.970581	−	0.240777i
$10$		0			0
$11$	−2.36944	+	1.98820i	−0.714413	+	0.599464i	−0.925834	−	0.377932i	$-0.876635\pi$
$11$	−2.36944	+	1.98820i	−0.714413	+	0.599464i	0.211421	+	0.977395i	$0.432191\pi$
$12$	1.47178	+	6.35787i	0.424867	+	1.83536i
$13$	−0.729623	+	4.13790i	−0.202361	+	1.14765i	0.699178	+	0.714948i	$0.253550\pi$
$13$	−0.729623	+	4.13790i	−0.202361	+	1.14765i	−0.901539	+	0.432699i	$0.857561\pi$
$14$	0.241824	−	1.37145i	0.0646301	−	0.366536i
$15$		0			0
$16$	2.03816	−	1.71022i	0.509540	−	0.427555i
$17$	−0.995493	+	1.72424i	−0.241443	+	0.418191i	−0.961125	−	0.276112i	$-0.910954\pi$
$17$	−0.995493	+	1.72424i	−0.241443	+	0.418191i	0.719683	+	0.694303i	$0.244287\pi$
$18$	0.494102	−	7.18790i	0.116461	−	1.69420i
$19$	1.92271	+	3.33023i	0.441100	+	0.764008i	0.997771	−	0.0667249i	$-0.0212550\pi$
$19$	1.92271	+	3.33023i	0.441100	+	0.764008i	−0.556671	+	0.830733i	$0.687922\pi$
$20$		0			0
$21$	−0.455437	+	0.895151i	−0.0993845	+	0.195338i
$22$	−5.69050	−	4.77489i	−1.21322	−	1.01801i
$23$	−4.18428	+	1.52295i	−0.872482	+	0.317558i	−0.739172	−	0.673517i	$-0.764783\pi$
$23$	−4.18428	+	1.52295i	−0.872482	+	0.317558i	−0.133310	+	0.991074i	$0.542561\pi$
$24$	−6.76724	+	2.87724i	−1.38136	+	0.587314i
$25$		0			0
$26$	−10.0910			−1.97900
$27$	−1.85354	+	4.85432i	−0.356715	+	0.934213i
$28$	2.18479			0.412887
$29$	1.11126	+	6.30229i	0.206356	+	1.17031i	0.895291	+	0.445482i	$0.146968\pi$
$29$	1.11126	+	6.30229i	0.206356	+	1.17031i	−0.688935	+	0.724823i	$0.741921\pi$
$30$		0			0
$31$	−1.55754	+	0.566898i	−0.279743	+	0.101818i	−0.478081	−	0.878316i	$-0.658668\pi$
$31$	−1.55754	+	0.566898i	−0.279743	+	0.101818i	0.198339	+	0.980134i	$0.436445\pi$
$32$	−1.60967	−	1.35067i	−0.284552	−	0.238767i
$33$	2.92049	+	4.49135i	0.508392	+	0.781844i
$34$	−4.49323	−	1.63540i	−0.770582	−	0.280469i
$35$		0			0
$36$	11.2400	−	1.19479i	1.87334	−	0.199132i
$37$	2.01505	−	3.49016i	0.331272	−	0.573779i	−0.651490	−	0.758657i	$-0.725856\pi$
$37$	2.01505	−	3.49016i	0.331272	−	0.573779i	0.982761	+	0.184878i	$0.0591890\pi$
$38$	−7.07461	+	5.93630i	−1.14765	+	0.962996i
$39$	6.96087	+	2.12366i	1.11463	+	0.340058i
$40$		0			0
$41$	−0.190345	+	1.07950i	−0.0297270	+	0.168590i	−0.996057	−	0.0887159i	$-0.971724\pi$
$41$	−0.190345	+	1.07950i	−0.0297270	+	0.168590i	0.966330	+	0.257306i	$0.0828348\pi$
$42$	−2.30709	−	0.703859i	−0.355991	−	0.108608i
$43$	5.28657	−	4.43596i	0.806194	−	0.676477i	−0.143502	−	0.989650i	$-0.545836\pi$
$43$	5.28657	−	4.43596i	0.806194	−	0.676477i	0.949696	+	0.313173i	$0.101392\pi$
$44$	5.82704	−	10.0927i	0.878459	−	1.52154i
$45$		0			0
$46$	−5.34699	−	9.26126i	−0.788370	−	1.36550i
$47$	3.37650	+	1.22894i	0.492513	+	0.179260i	0.576323	−	0.817222i	$-0.304487\pi$
$47$	3.37650	+	1.22894i	0.492513	+	0.179260i	−0.0838106	+	0.996482i	$0.526709\pi$
$48$	−2.51217	−	3.86340i	−0.362600	−	0.557634i
$49$	−5.10474	−	4.28338i	−0.729248	−	0.611912i
$50$		0			0
$51$	2.75531	+	2.07373i	0.385821	+	0.290380i
$52$	−2.74906	−	15.5907i	−0.381226	−	2.16204i
$53$	−5.40034			−0.741793			−0.370897	−	0.928674i	$-0.620950\pi$
$53$	−5.40034			−0.741793			−0.370897	+	0.928674i	$0.620950\pi$
$54$	−12.2541	−	2.35945i	−1.66757	−	0.321081i
$55$		0			0
$56$	0.427492	+	2.42443i	0.0571260	+	0.323978i
$57$	6.12946	−	2.60607i	0.811866	−	0.345182i
$58$	−14.4423	+	5.25657i	−1.89637	+	0.690222i
$59$	−7.87850	−	6.61085i	−1.02569	−	0.860659i	−0.0353615	−	0.999375i	$-0.511258\pi$
$59$	−7.87850	−	6.61085i	−1.02569	−	0.860659i	−0.990332	+	0.138715i	$0.955703\pi$
$60$		0			0
$61$	12.4005	+	4.51341i	1.58772	+	0.577883i	0.976864	−	0.213860i	$-0.0686036\pi$
$61$	12.4005	+	4.51341i	1.58772	+	0.577883i	0.610855	+	0.791742i	$0.290826\pi$
$62$	−1.99034	−	3.44738i	−0.252774	−	0.437817i
$63$	1.44333	+	0.971060i	0.181842	+	0.122342i
$64$	5.18386	−	8.97871i	0.647982	−	1.12234i
$65$		0			0
$66$	−9.40470	+	8.78041i	−1.15764	+	1.08079i
$67$	1.53458	−	8.70304i	0.187479	−	1.06324i	−0.735250	−	0.677796i	$-0.762935\pi$
$67$	1.53458	−	8.70304i	0.187479	−	1.06324i	0.922729	−	0.385449i	$-0.125954\pi$
$68$	1.30264	−	7.38764i	0.157968	−	0.895883i
$69$	1.73937	+	7.51381i	0.209396	+	0.904556i
$70$		0			0
$71$	−0.572473	+	0.991553i	−0.0679401	+	0.117676i	−0.897994	−	0.440007i	$-0.854976\pi$
$71$	−0.572473	+	0.991553i	−0.0679401	+	0.117676i	0.830054	+	0.557683i	$0.188309\pi$
$72$	3.52514	+	12.2391i	0.415442	+	1.44239i
$73$	0.0977361	+	0.169284i	0.0114391	+	0.0198132i	0.871688	−	0.490061i	$-0.163025\pi$
$73$	0.0977361	+	0.169284i	0.0114391	+	0.0198132i	−0.860249	+	0.509874i	$0.829692\pi$
$74$	9.09506	+	3.31033i	1.05728	+	0.384818i
$75$		0			0
$76$	−11.0990	−	9.31317i	−1.27314	−	1.06829i
$77$	1.68539	−	0.613433i	0.192069	−	0.0699072i
$78$	−2.11980	+	17.3491i	−0.240020	+	1.96439i
$79$	−1.25166	−	7.09849i	−0.140822	−	0.798642i	−0.970627	−	0.240589i	$-0.922659\pi$
$79$	−1.25166	−	7.09849i	−0.140822	−	0.798642i	0.829805	−	0.558054i	$-0.188452\pi$
$80$		0			0
$81$	7.95648	+	4.20647i	0.884053	+	0.467386i
$82$	−2.63255			−0.290717
$83$	2.58744	+	14.6741i	0.284008	+	1.61069i	0.708808	+	0.705402i	$0.249233\pi$
$83$	2.58744	+	14.6741i	0.284008	+	1.61069i	−0.424800	+	0.905287i	$0.639656\pi$
$84$	0.458958	−	3.75624i	0.0500764	−	0.409839i
$85$		0			0
$86$	12.6963	+	10.6535i	1.36908	+	1.14879i
$87$	11.0687	−	0.586638i	1.18669	−	0.0628942i
$88$	12.3399	+	4.49135i	1.31544	+	0.478780i
$89$	0.776563	+	1.34505i	0.0823155	+	0.142575i	0.904244	−	0.427016i	$-0.140435\pi$
$89$	0.776563	+	1.34505i	0.0823155	+	0.142575i	−0.821929	+	0.569590i	$0.807102\pi$
$90$		0			0
$91$	1.21821	−	2.11000i	0.127703	−	0.221189i
$92$	12.8521	−	10.7842i	1.33993	−	1.12433i
$93$	0.647457	+	2.79691i	0.0671381	+	0.290026i
$94$	−1.49850	+	8.49839i	−0.154558	+	0.876542i
$95$		0			0
$96$	−2.66030	+	2.48371i	−0.271516	+	0.253492i
$97$	−4.05661	+	3.40390i	−0.411887	+	0.345614i	−0.825067	−	0.565035i	$-0.808863\pi$
$97$	−4.05661	+	3.40390i	−0.411887	+	0.345614i	0.413180	+	0.910649i	$0.364418\pi$
$98$	8.00191	−	13.8597i	0.808315	−	1.40004i
$99$	8.33533	−	4.07760i	0.837732	−	0.409814i
$100$		0			0
$101$	6.83061	+	2.48614i	0.679671	+	0.247380i	0.658706	−	0.752400i	$-0.271104\pi$
$101$	6.83061	+	2.48614i	0.679671	+	0.247380i	0.0209647	+	0.999780i	$0.493326\pi$
$102$	−3.75558	+	7.38150i	−0.371858	+	0.730878i
$103$	−4.90374	−	4.11472i	−0.483179	−	0.405436i	0.368395	−	0.929669i	$-0.379907\pi$
$103$	−4.90374	−	4.11472i	−0.483179	−	0.405436i	−0.851574	+	0.524234i	$0.824352\pi$
$104$	16.7629	−	6.10118i	1.64373	−	0.598270i
$105$		0			0
$106$	−2.25214	−	12.7725i	−0.218747	−	1.24058i
$107$	5.54365			0.535925			0.267963	−	0.963429i	$-0.413650\pi$
$107$	5.54365			0.535925			0.267963	+	0.963429i	$0.413650\pi$
$108$	0.307026	−	19.5756i	0.0295436	−	1.88366i
$109$	−6.23137			−0.596857			−0.298428	−	0.954432i	$-0.596462\pi$
$109$	−6.23137			−0.596857			−0.298428	+	0.954432i	$0.596462\pi$
$110$		0			0
$111$	−5.57722	−	4.19758i	−0.529366	−	0.398416i
$112$	−1.44975	+	0.527668i	−0.136989	+	0.0498599i
$113$	9.07301	+	7.61316i	0.853517	+	0.716186i	0.960561	−	0.278068i	$-0.0896941\pi$
$113$	9.07301	+	7.61316i	0.853517	+	0.716186i	−0.107044	+	0.994254i	$0.534139\pi$
$114$	8.71992	+	13.4102i	0.816695	+	1.25598i
$115$		0			0
$116$	−12.0560	−	20.8816i	−1.11937	−	1.93881i
$117$	5.11340	−	11.5215i	0.472734	−	1.06516i
$118$	12.3499	−	21.3907i	1.13690	−	1.96917i
$119$	0.884395	−	0.742096i	0.0810724	−	0.0680278i
$120$		0			0
$121$	−0.248809	+	1.41107i	−0.0226190	+	0.128279i
$122$	−5.50336	+	31.2111i	−0.498250	+	2.82572i
$123$	1.81597	+	0.554025i	0.163740	+	0.0499547i
$124$	4.78403	−	4.01427i	0.429618	−	0.360492i
$125$		0			0
$126$	−1.69477	+	3.81863i	−0.150982	+	0.340191i
$127$	5.76469	+	9.98473i	0.511533	+	0.886002i	0.999911	+	0.0133693i	$0.00425570\pi$
$127$	5.76469	+	9.98473i	0.511533	+	0.886002i	−0.488377	+	0.872633i	$0.662411\pi$
$128$	19.4486	+	7.07872i	1.71903	+	0.625676i
$129$	−6.51604	−	10.0209i	−0.573705	−	0.882288i
$130$		0			0
$131$	8.46830	−	3.08221i	0.739879	−	0.269294i	0.0555383	−	0.998457i	$-0.482312\pi$
$131$	8.46830	−	3.08221i	0.739879	−	0.269294i	0.684340	+	0.729163i	$0.260090\pi$
$132$	−16.1280	−	12.1384i	−1.40376	−	1.05651i
$133$	−0.387203	−	2.19594i	−0.0335747	−	0.190412i
$134$	21.2238			1.83346
$135$		0			0
$136$	8.45283			0.724824
$137$	−2.00047	−	11.3452i	−0.170911	−	0.969287i	−0.942758	−	0.333478i	$-0.891778\pi$
$137$	−2.00047	−	11.3452i	−0.170911	−	0.969287i	0.771846	−	0.635809i	$-0.219333\pi$
$138$	−17.0458	+	7.24738i	−1.45103	+	0.616938i
$139$	−1.60108	+	0.582746i	−0.135802	+	0.0494279i	−0.409027	−	0.912522i	$-0.634132\pi$
$139$	−1.60108	+	0.582746i	−0.135802	+	0.0494279i	0.273225	+	0.961950i	$0.411910\pi$
$140$		0			0
$141$	2.82218	−	5.54693i	0.237670	−	0.467136i
$142$	−2.58390	−	0.940462i	−0.216836	−	0.0789219i
$143$	−6.49816	−	11.2551i	−0.543403	−	0.941202i
$144$	−7.16994	+	3.50750i	−0.597495	+	0.292291i
$145$		0			0
$146$	−0.359620	+	0.301757i	−0.0297623	+	0.0249736i
$147$	−8.43662	+	7.87659i	−0.695840	+	0.649650i
$148$	−2.63677	+	14.9538i	−0.216741	+	1.22920i
$149$	−3.75996	+	21.3238i	−0.308028	+	1.74691i	0.300869	+	0.953666i	$0.402723\pi$
$149$	−3.75996	+	21.3238i	−0.308028	+	1.74691i	−0.608897	+	0.793249i	$0.708388\pi$
$150$		0			0
$151$	−3.63222	+	3.04779i	−0.295586	+	0.248026i	−0.778504	−	0.627640i	$-0.784021\pi$
$151$	−3.63222	+	3.04779i	−0.295586	+	0.248026i	0.482918	+	0.875665i	$0.339577\pi$
$152$	8.16296	−	14.1387i	0.662104	−	1.14680i
$153$	4.14409	−	4.30148i	0.335030	−	0.347754i
$154$	2.15373	+	3.73036i	0.173552	+	0.300601i
$155$		0			0
$156$	−27.3821	+	1.45124i	−2.19232	+	0.116192i
$157$	0.160261	+	0.134475i	0.0127902	+	0.0107323i	0.649160	−	0.760652i	$-0.275120\pi$
$157$	0.160261	+	0.134475i	0.0127902	+	0.0107323i	−0.636370	+	0.771384i	$0.719565\pi$
$158$	16.2669	−	5.92067i	1.29412	−	0.471023i
$159$	−1.13444	+	9.28461i	−0.0899673	+	0.736317i
$160$		0			0
$161$	2.58202			0.203491
$162$	−6.63073	+	20.5724i	−0.520960	+	1.61632i
$163$	−5.62384			−0.440493			−0.220247	−	0.975444i	$-0.570686\pi$
$163$	−5.62384			−0.440493			−0.220247	+	0.975444i	$0.570686\pi$
$164$	−0.717181	−	4.06733i	−0.0560024	−	0.317605i
$165$		0			0
$166$	−33.6271	+	12.2393i	−2.60997	+	0.949951i
$167$	−12.7780	−	10.7220i	−0.988791	−	0.829695i	−0.00339914	−	0.999994i	$-0.501082\pi$
$167$	−12.7780	−	10.7220i	−0.988791	−	0.829695i	−0.985392	+	0.170300i	$0.945526\pi$
$168$	4.25804	−	0.225674i	0.328515	−	0.0174111i
$169$	−4.37386	−	1.59195i	−0.336451	−	0.122458i
$170$		0			0
$171$	−3.19291	−	11.0856i	−0.244168	−	0.847738i
$172$	−13.0010	+	22.5183i	−0.991315	+	1.71701i
$173$	−14.5565	+	12.2143i	−1.10671	+	0.928639i	−0.997858	−	0.0654187i	$-0.979162\pi$
$173$	−14.5565	+	12.2143i	−1.10671	+	0.928639i	−0.108851	+	0.994058i	$0.534717\pi$
$174$	6.00355	+	25.9344i	0.455128	+	1.96608i
$175$		0			0
$176$	−1.42905	+	8.10453i	−0.107718	+	0.610902i
$177$	−13.0208	+	12.1565i	−0.978706	+	0.913738i
$178$	−2.85736	+	2.39761i	−0.214168	+	0.179709i
$179$	−8.11761	+	14.0601i	−0.606739	+	1.05090i	0.385035	+	0.922902i	$0.374189\pi$
$179$	−8.11761	+	14.0601i	−0.606739	+	1.05090i	−0.991774	+	0.128001i	$0.959144\pi$
$180$		0			0
$181$	1.49579	+	2.59078i	0.111181	+	0.192571i	0.916247	−	0.400614i	$-0.131203\pi$
$181$	1.49579	+	2.59078i	0.111181	+	0.192571i	−0.805066	+	0.593186i	$0.797870\pi$
$182$	5.49848	+	2.00128i	0.407575	+	0.148345i
$183$	10.3647	−	20.3716i	0.766181	−	1.50591i
$184$	14.4818	+	12.1517i	1.06761	+	0.895833i
$185$		0			0
$186$	−6.34506	+	2.69774i	−0.465242	+	0.197808i
$187$	−1.06938	−	6.06473i	−0.0782005	−	0.443497i
$188$	−13.5384			−0.987388
$189$	1.97271	−	2.27747i	0.143493	−	0.165662i
$190$		0			0
$191$	−0.391371	−	2.21958i	−0.0283186	−	0.160603i	0.967369	−	0.253371i	$-0.0815395\pi$
$191$	−0.391371	−	2.21958i	−0.0283186	−	0.160603i	−0.995688	+	0.0927685i	$0.970428\pi$
$192$	−14.3478	−	10.7986i	−1.03546	−	0.779320i
$193$	−0.827186	+	0.301071i	−0.0595422	+	0.0216716i	−0.371620	−	0.928385i	$-0.621197\pi$
$193$	−0.827186	+	0.301071i	−0.0595422	+	0.0216716i	0.312077	+	0.950057i	$0.398975\pi$
$194$	−9.74245	−	8.17489i	−0.699467	−	0.586923i
$195$		0			0
$196$	23.5934	+	8.58731i	1.68525	+	0.613379i
$197$	10.1383	+	17.5600i	0.722322	+	1.25110i	0.960067	+	0.279771i	$0.0902586\pi$
$197$	10.1383	+	17.5600i	0.722322	+	1.25110i	−0.237744	+	0.971328i	$0.576408\pi$
$198$	13.1202	+	18.0137i	0.932413	+	1.28018i
$199$	9.50472	−	16.4627i	0.673772	−	1.16701i	−0.303054	−	0.952973i	$-0.598006\pi$
$199$	9.50472	−	16.4627i	0.673772	−	1.16701i	0.976826	−	0.214034i	$-0.0686603\pi$
$200$		0			0
$201$	−14.6405	−	4.46659i	−1.03266	−	0.315049i
$202$	−3.03144	+	17.1921i	−0.213291	+	1.20963i
$203$	0.644379	−	3.65445i	0.0452265	−	0.256492i
$204$	−12.4277	−	3.79150i	−0.870110	−	0.265458i
$205$		0			0
$206$	7.68684	−	13.3140i	0.535567	−	0.927630i
$207$	13.2836	−	1.41202i	0.923275	−	0.0981420i
$208$	5.58963	+	9.68152i	0.387571	+	0.671293i
$209$	−11.1769	−	4.06806i	−0.773123	−	0.281394i
$210$		0			0
$211$	12.3977	+	10.4029i	0.853494	+	0.716166i	0.960556	−	0.278086i	$-0.0897000\pi$
$211$	12.3977	+	10.4029i	0.853494	+	0.716166i	−0.107062	+	0.994252i	$0.534144\pi$
$212$	19.1202	−	6.95919i	1.31318	−	0.477959i
$213$	1.58448	+	1.19253i	0.108567	+	0.0817107i
$214$	2.31191	+	13.1115i	0.158039	+	0.896283i
$215$		0			0
$216$	21.7828	−	3.48960i	1.48213	−	0.237437i
$217$	0.961120			0.0652451
$218$	−2.59871	−	14.7380i	−0.176007	−	0.998186i
$219$	0.311575	−	0.132473i	0.0210543	−	0.00895168i
$220$		0			0
$221$	−6.40842	−	5.37730i	−0.431077	−	0.361716i
$222$	7.60193	−	14.9414i	0.510208	−	1.00280i
$223$	20.1633	+	7.33883i	1.35023	+	0.491444i	0.913020	−	0.407914i	$-0.133744\pi$
$223$	20.1633	+	7.33883i	1.35023	+	0.491444i	0.437212	+	0.899359i	$0.355966\pi$
$224$	0.609223	+	1.05520i	0.0407054	+	0.0705038i
$225$		0			0
$226$	−14.2224	+	24.6339i	−0.946058	+	1.63862i
$227$	14.6424	−	12.2864i	0.971848	−	0.815477i	−0.0109918	−	0.999940i	$-0.503499\pi$
$227$	14.6424	−	12.2864i	0.971848	−	0.815477i	0.982840	+	0.184462i	$0.0590544\pi$
$228$	−18.3434	+	17.1257i	−1.21482	+	1.13418i
$229$	3.90190	−	22.1288i	0.257845	−	1.46231i	−0.530818	−	0.847486i	$-0.678115\pi$
$229$	3.90190	−	22.1288i	0.257845	−	1.46231i	0.788663	−	0.614826i	$-0.210774\pi$
$230$		0			0
$231$	−0.700605	−	3.02650i	−0.0460964	−	0.199129i
$232$	20.8130	−	17.4642i	1.36644	−	1.14658i
$233$	−8.84074	+	15.3126i	−0.579176	+	1.00316i	0.416398	+	0.909182i	$0.363292\pi$
$233$	−8.84074	+	15.3126i	−0.579176	+	1.00316i	−0.995574	+	0.0939796i	$0.970041\pi$
$234$	29.3823	+	7.28901i	1.92078	+	0.476497i
$235$		0			0
$236$	36.4134	+	13.2534i	2.37031	+	0.862723i
$237$	−12.4671	+	0.660752i	−0.809826	+	0.0429204i
$238$	2.12398	+	1.78223i	0.137677	+	0.115525i
$239$	14.4904	−	5.27406i	0.937303	−	0.341151i	0.172203	−	0.985061i	$-0.444912\pi$
$239$	14.4904	−	5.27406i	0.937303	−	0.341151i	0.765100	+	0.643911i	$0.222689\pi$
$240$		0			0
$241$	2.28373	+	12.9516i	0.147108	+	0.834289i	0.965651	+	0.259844i	$0.0836711\pi$
$241$	2.28373	+	12.9516i	0.147108	+	0.834289i	−0.818543	+	0.574445i	$0.805218\pi$
$242$	−3.44113			−0.221204
$243$	8.90345	−	12.7956i	0.571157	−	0.820841i
$244$	−49.7209			−3.18305
$245$		0			0
$246$	−0.553018	+	4.52605i	−0.0352592	+	0.288571i
$247$	−15.1830	+	5.52617i	−0.966073	+	0.351622i
$248$	5.39065	+	4.52329i	0.342307	+	0.287229i
$249$	25.7722	−	1.36591i	1.63324	−	0.0865612i
$250$		0			0
$251$	−8.70830	−	15.0832i	−0.549663	−	0.952045i	−0.998297	−	0.0583292i	$-0.981423\pi$
$251$	−8.70830	−	15.0832i	−0.549663	−	0.952045i	0.448634	−	0.893716i	$-0.351911\pi$
$252$	−6.36155	−	1.57814i	−0.400740	−	0.0994135i
$253$	6.88646	−	11.9277i	0.432948	−	0.749889i
$254$	−21.2112	+	17.7983i	−1.33091	+	1.11676i
$255$		0			0
$256$	−5.03066	+	28.5303i	−0.314416	+	1.78314i
$257$	−1.94270	+	11.0176i	−0.121182	+	0.687260i	0.862320	+	0.506364i	$0.169011\pi$
$257$	−1.94270	+	11.0176i	−0.121182	+	0.687260i	−0.983502	+	0.180896i	$0.942100\pi$
$258$	20.9833	−	19.5904i	1.30636	−	1.21964i
$259$	−1.79017	+	1.50213i	−0.111236	+	0.0933377i
$260$		0			0
$261$	1.31662	−	19.1533i	0.0814965	−	1.18556i
$262$	10.8214	+	18.7433i	0.668550	+	1.15796i
$263$	−19.4619	−	7.08354i	−1.20007	−	0.436790i	−0.336821	−	0.941569i	$-0.609352\pi$
$263$	−19.4619	−	7.08354i	−1.20007	−	0.436790i	−0.863249	+	0.504779i	$0.831574\pi$
$264$	10.3141	−	20.2720i	0.634786	−	1.24766i
$265$		0			0
$266$	5.03221	−	1.83157i	0.308544	−	0.112301i
$267$	2.47562	−	1.05256i	0.151506	−	0.0644159i
$268$	5.78197	+	32.7912i	0.353190	+	2.00304i
$269$	−28.2449			−1.72212			−0.861060	−	0.508504i	$-0.830199\pi$
$269$	−28.2449			−1.72212			−0.861060	+	0.508504i	$0.830199\pi$
$270$		0			0
$271$	17.2626			1.04863			0.524316	−	0.851524i	$-0.324321\pi$
$271$	17.2626			1.04863			0.524316	+	0.851524i	$0.324321\pi$
$272$	0.919863	+	5.21680i	0.0557749	+	0.316315i
$273$	−3.37175	−	2.53767i	−0.204067	−	0.153587i
$274$	25.9987	−	9.46275i	1.57064	−	0.571666i
$275$		0			0
$276$	−15.8411	−	24.3616i	−0.953520	−	1.46640i
$277$	4.85725	+	1.76789i	0.291844	+	0.106222i	0.483793	−	0.875182i	$-0.339259\pi$
$277$	4.85725	+	1.76789i	0.291844	+	0.106222i	−0.191949	+	0.981405i	$0.561481\pi$
$278$	−2.04598	−	3.54375i	−0.122710	−	0.212540i
$279$	4.94464	−	0.525604i	0.296028	−	0.0314671i
$280$		0			0
$281$	−2.52522	+	2.11891i	−0.150642	+	0.126404i	−0.714994	−	0.699131i	$-0.753571\pi$
$281$	−2.52522	+	2.11891i	−0.150642	+	0.126404i	0.564352	+	0.825534i	$0.309126\pi$
$282$	14.2962	+	4.36156i	0.851326	+	0.259727i
$283$	1.58553	−	8.99200i	0.0942501	−	0.534519i	−0.900724	−	0.434391i	$-0.856964\pi$
$283$	1.58553	−	8.99200i	0.0942501	−	0.534519i	0.994975	−	0.100128i	$-0.0319253\pi$
$284$	0.749103	−	4.24837i	0.0444511	−	0.252095i
$285$		0			0
$286$	23.9099	−	20.0628i	1.41382	−	1.18634i
$287$	0.317809	−	0.550462i	0.0187597	−	0.0324927i
$288$	3.71130	+	5.09551i	0.218691	+	0.300256i
$289$	6.51799	+	11.2895i	0.383411	+	0.664087i
$290$		0			0
$291$	5.00004	+	7.68945i	0.293108	+	0.450764i
$292$	−0.564189	−	0.473411i	−0.0330167	−	0.0277043i
$293$	−2.65598	+	0.966697i	−0.155164	+	0.0564750i	−0.418434	−	0.908247i	$-0.637421\pi$
$293$	−2.65598	+	0.966697i	−0.155164	+	0.0564750i	0.263271	+	0.964722i	$0.415199\pi$
$294$	−22.1476	−	16.6689i	−1.29167	−	0.972151i
$295$		0			0
$296$	−17.1100			−0.994496
$297$	−5.25947	−	15.1872i	−0.305185	−	0.881251i
$298$	−52.0017			−3.01238
$299$	−3.24888	−	18.4253i	−0.187887	−	1.06556i
$300$		0			0
$301$	−3.76036	+	1.36866i	−0.216744	+	0.0788882i
$302$	−8.72321	−	7.31964i	−0.501964	−	0.421198i
$303$	5.70923	−	11.2214i	0.327987	−	0.644650i
$304$	9.61423	+	3.49929i	0.551414	+	0.200698i
$305$		0			0
$306$	11.9018	+	8.00746i	0.680382	+	0.457756i
$307$	3.14723	−	5.45116i	0.179622	−	0.311114i	−0.762129	−	0.647425i	$-0.775846\pi$
$307$	3.14723	−	5.45116i	0.179622	−	0.311114i	0.941751	+	0.336311i	$0.109179\pi$
$308$	−5.17673	+	4.34380i	−0.294972	+	0.247511i
$309$	−8.10442	+	7.56644i	−0.461045	+	0.430440i
$310$		0			0
$311$	−1.28029	+	7.26088i	−0.0725985	+	0.411727i	0.926751	+	0.375675i	$0.122589\pi$
$311$	−1.28029	+	7.26088i	−0.0725985	+	0.411727i	−0.999350	+	0.0360515i	$0.988522\pi$
$312$	−6.96818	−	30.1015i	−0.394496	−	1.70416i
$313$	3.27159	−	2.74519i	0.184921	−	0.155167i	−0.545628	−	0.838028i	$-0.683709\pi$
$313$	3.27159	−	2.74519i	0.184921	−	0.155167i	0.730549	+	0.682860i	$0.239264\pi$
$314$	−0.251217	+	0.435120i	−0.0141770	+	0.0245552i
$315$		0			0
$316$	13.5791	+	23.5197i	0.763883	+	1.32308i
$317$	15.1738	+	5.52279i	0.852243	+	0.310191i	0.730954	−	0.682426i	$-0.239075\pi$
$317$	15.1738	+	5.52279i	0.852243	+	0.310191i	0.121288	+	0.992617i	$0.461297\pi$
$318$	−22.4325	+	1.18891i	−1.25795	+	0.0666708i
$319$	−15.1632	−	12.7235i	−0.848979	−	0.712378i
$320$		0			0
$321$	1.16455	−	9.53101i	0.0649989	−	0.531969i
$322$	1.07680	+	6.10682i	0.0600075	+	0.340320i
$323$	−7.65618			−0.426001
$324$	−33.5911	−	4.64009i	−1.86617	−	0.257783i
$325$		0			0
$326$	−2.34535	−	13.3012i	−0.129897	−	0.736683i
$327$	−1.30902	+	10.7134i	−0.0723890	+	0.592451i
$328$	4.37313	−	1.59169i	0.241465	−	0.0878862i
$329$	−1.59610	−	1.33928i	−0.0879956	−	0.0738371i
$330$		0			0
$331$	−18.0686	−	6.57644i	−0.993142	−	0.361474i	−0.206206	−	0.978509i	$-0.566112\pi$
$331$	−18.0686	−	6.57644i	−0.993142	−	0.361474i	−0.786936	+	0.617035i	$0.788334\pi$
$332$	−28.0708	−	48.6201i	−1.54059	−	2.66838i
$333$	−8.38834	+	8.70693i	−0.459678	+	0.477137i
$334$	20.0301	−	34.6932i	1.09600	−	1.89833i
$335$		0			0
$336$	0.602651	+	2.60336i	0.0328773	+	0.142025i
$337$	5.11615	−	29.0152i	0.278695	−	1.58056i	−0.448281	−	0.893893i	$-0.647964\pi$
$337$	5.11615	−	29.0152i	0.278695	−	1.58056i	0.726976	−	0.686663i	$-0.240925\pi$
$338$	1.94112	−	11.0087i	0.105583	−	0.598792i
$339$	14.9950	−	13.9996i	0.814417	−	0.760355i
$340$		0			0
$341$	2.56339	−	4.43993i	0.138815	−	0.240435i
$342$	24.8874	−	12.1748i	1.34576	−	0.658337i
$343$	3.96154	+	6.86159i	0.213903	+	0.370491i
$344$	−27.5321	−	10.0209i	−1.48443	−	0.540289i
$345$		0			0
$346$	−34.9592	−	29.3342i	−1.87942	−	1.57702i
$347$	10.7097	−	3.89801i	0.574927	−	0.209256i	−0.0381600	−	0.999272i	$-0.512150\pi$
$347$	10.7097	−	3.89801i	0.574927	−	0.209256i	0.613087	+	0.790015i	$0.289927\pi$
$348$	−38.4336	+	16.3408i	−2.06025	+	0.875961i
$349$	4.89021	+	27.7338i	0.261767	+	1.48456i	0.778085	+	0.628158i	$0.216191\pi$
$349$	4.89021	+	27.7338i	0.261767	+	1.48456i	−0.516318	+	0.856397i	$0.672698\pi$
$350$		0			0
$351$	−18.7343	−	11.2116i	−0.999962	−	0.598431i
$352$	6.49941			0.346419
$353$	−4.97573	−	28.2188i	−0.264831	−	1.50193i	−0.769515	−	0.638629i	$-0.779502\pi$
$353$	−4.97573	−	28.2188i	−0.264831	−	1.50193i	0.504683	−	0.863305i	$-0.331609\pi$
$354$	−34.1819	−	25.7263i	−1.81675	−	1.36734i
$355$		0			0
$356$	−4.48277	−	3.76149i	−0.237586	−	0.199359i
$357$	−1.09007	−	1.67640i	−0.0576929	−	0.0887245i
$358$	−36.6394	−	13.3357i	−1.93645	−	0.704812i
$359$	15.5161	+	26.8747i	0.818909	+	1.41839i	0.906486	+	0.422235i	$0.138754\pi$
$359$	15.5161	+	26.8747i	0.818909	+	1.41839i	−0.0875770	+	0.996158i	$0.527912\pi$
$360$		0			0
$361$	2.10636	−	3.64833i	0.110861	−	0.192017i
$362$	−5.50376	+	4.61820i	−0.289271	+	0.242727i
$363$	2.37373	+	0.724191i	0.124589	+	0.0380102i
$364$	−1.59408	+	9.04045i	−0.0835523	+	0.473848i
$365$		0			0
$366$	52.5040	+	16.0182i	2.74443	+	0.837286i
$367$	−18.4802	+	15.5067i	−0.964660	+	0.809446i	−0.981705	−	0.190409i	$-0.939019\pi$
$367$	−18.4802	+	15.5067i	−0.964660	+	0.809446i	0.0170450	+	0.999855i	$0.494574\pi$
$368$	−5.92365	+	10.2601i	−0.308791	+	0.534843i
$369$	1.33399	−	3.00574i	0.0694449	−	0.156473i
$370$		0			0
$371$	2.94260	+	1.07102i	0.152772	+	0.0556045i
$372$	−5.89662	−	9.06828i	−0.305726	−	0.470169i
$373$	9.64114	+	8.08988i	0.499199	+	0.418878i	0.857309	−	0.514801i	$-0.172134\pi$
$373$	9.64114	+	8.08988i	0.499199	+	0.418878i	−0.358110	+	0.933679i	$0.616579\pi$
$374$	13.8979	−	5.05843i	0.718645	−	0.261565i
$375$		0			0
$376$	−2.64902	−	15.0233i	−0.136613	−	0.774769i
$377$	−26.8890			−1.38486
$378$	6.20922	+	3.71593i	0.319368	+	0.191127i
$379$	−7.70522			−0.395790			−0.197895	−	0.980223i	$-0.563411\pi$
$379$	−7.70522			−0.395790			−0.197895	+	0.980223i	$0.563411\pi$
$380$		0			0
$381$	18.3774	−	7.81354i	0.941502	−	0.400300i
$382$	5.08638	−	1.85129i	0.260242	−	0.0947203i
$383$	13.6828	+	11.4812i	0.699159	+	0.586664i	0.921534	−	0.388297i	$-0.126937\pi$
$383$	13.6828	+	11.4812i	0.699159	+	0.586664i	−0.222376	+	0.974961i	$0.571381\pi$
$384$	16.2557	−	31.9503i	0.829548	−	1.63046i
$385$		0			0
$386$	−1.05704	−	1.83085i	−0.0538020	−	0.0931878i
$387$	−18.5973	+	9.09771i	−0.945356	+	0.462463i
$388$	9.97622	−	17.2793i	0.506466	−	0.877224i
$389$	20.9808	−	17.6050i	1.06377	−	0.892607i	0.0692941	−	0.997596i	$-0.477925\pi$
$389$	20.9808	−	17.6050i	1.06377	−	0.892607i	0.994473	+	0.104989i	$0.0334809\pi$
$390$		0			0
$391$	1.53948	−	8.73081i	0.0778547	−	0.441536i
$392$	−4.91274	+	27.8615i	−0.248131	+	1.40722i
$393$	−3.52020	−	15.2067i	−0.177571	−	0.767078i
$394$	−37.3038	+	31.3016i	−1.87934	+	1.57695i
$395$		0			0
$396$	−24.2571	+	25.1784i	−1.21896	+	1.26526i
$397$	2.10799	+	3.65115i	0.105797	+	0.183246i	0.914064	−	0.405571i	$-0.132927\pi$
$397$	2.10799	+	3.65115i	0.105797	+	0.183246i	−0.808266	+	0.588817i	$0.799594\pi$
$398$	42.9002	+	15.6144i	2.15039	+	0.782680i
$399$	−3.85673	+	0.204405i	−0.193078	+	0.0102331i
$400$		0			0
$401$	−14.2575	+	5.18930i	−0.711985	+	0.259141i	−0.672519	−	0.740080i	$-0.734788\pi$
$401$	−14.2575	+	5.18930i	−0.711985	+	0.259141i	−0.0394656	+	0.999221i	$0.512566\pi$
$402$	4.45848	−	36.4894i	0.222369	−	1.81993i
$403$	−1.20935	−	6.85857i	−0.0602420	−	0.341650i
$404$	−27.3880			−1.36260
$405$		0			0
$406$	8.91200			0.442295
$407$	2.16460	+	12.2760i	0.107295	+	0.608501i
$408$	1.77568	−	14.5326i	0.0879093	−	0.719473i
$409$	−4.42559	+	1.61078i	−0.218831	+	0.0796481i	−0.449109	−	0.893477i	$-0.648259\pi$
$409$	−4.42559	+	1.61078i	−0.218831	+	0.0796481i	0.230278	+	0.973125i	$0.426036\pi$
$410$		0			0
$411$	−19.9257	+	1.05605i	−0.982860	+	0.0520912i
$412$	22.6644	+	8.24918i	1.11660	+	0.406408i
$413$	2.98184	+	5.16469i	0.146727	+	0.254138i
$414$	8.87937	+	30.8287i	0.436397	+	1.51515i
$415$		0			0
$416$	6.76339	−	5.67516i	0.331602	−	0.278248i
$417$	0.665556	+	2.87510i	0.0325924	+	0.140794i
$418$	4.96033	−	28.1314i	0.242618	−	1.37595i
$419$	3.43669	−	19.4905i	0.167894	−	0.952171i	−0.778137	−	0.628094i	$-0.783835\pi$
$419$	3.43669	−	19.4905i	0.167894	−	0.952171i	0.946031	−	0.324077i	$-0.105054\pi$
$420$		0			0
$421$	21.5915	−	18.1174i	1.05231	−	0.882989i	0.0589715	−	0.998260i	$-0.481218\pi$
$421$	21.5915	−	18.1174i	1.05231	−	0.882989i	0.993334	+	0.115270i	$0.0367734\pi$
$422$	−19.4340	+	33.6607i	−0.946032	+	1.63858i
$423$	−8.94379	−	6.01731i	−0.434862	−	0.292572i
$424$	11.4637	+	19.8557i	0.556726	+	0.964278i
$425$		0			0
$426$	−2.15970	+	4.24484i	−0.104638	+	0.205663i
$427$	−5.86180	−	4.91863i	−0.283672	−	0.238029i
$428$	−19.6276	+	7.14387i	−0.948737	+	0.345312i
$429$	−20.7156	+	8.80769i	−1.00016	+	0.425239i
$430$		0			0
$431$	−5.19681			−0.250321			−0.125161	−	0.992136i	$-0.539945\pi$
$431$	−5.19681			−0.250321			−0.125161	+	0.992136i	$0.539945\pi$
$432$	4.52413	+	13.0638i	0.217667	+	0.628534i
$433$	−25.3285			−1.21721			−0.608605	−	0.793473i	$-0.708270\pi$
$433$	−25.3285			−1.21721			−0.608605	+	0.793473i	$0.708270\pi$
$434$	0.400823	+	2.27318i	0.0192401	+	0.109116i
$435$		0			0
$436$	22.0625	−	8.03011i	1.05660	−	0.384572i
$437$	−13.1169	−	11.0064i	−0.627469	−	0.526509i
$438$	0.443254	+	0.681671i	0.0211795	+	0.0325715i
$439$	14.7167	+	5.35646i	0.702392	+	0.255650i	0.668432	−	0.743773i	$-0.266966\pi$
$439$	14.7167	+	5.35646i	0.702392	+	0.255650i	0.0339602	+	0.999423i	$0.489188\pi$
$440$		0			0
$441$	11.7697	+	16.1594i	0.560460	+	0.769496i
$442$	10.0455	−	17.3993i	0.477815	−	0.827600i
$443$	13.9833	−	11.7333i	0.664365	−	0.557468i	−0.247027	−	0.969009i	$-0.579454\pi$
$443$	13.9833	−	11.7333i	0.664365	−	0.557468i	0.911391	+	0.411541i	$0.135009\pi$
$444$	25.1557	+	7.67464i	1.19384	+	0.364222i
$445$		0			0
$446$	−8.94849	+	50.7494i	−0.423723	+	2.40305i
$447$	35.8714	+	10.9439i	1.69666	+	0.517626i
$448$	−4.60534	+	3.86434i	−0.217582	+	0.182573i
$449$	−14.3608	+	24.8737i	−0.677729	+	1.17386i	0.297934	+	0.954586i	$0.403702\pi$
$449$	−14.3608	+	24.8737i	−0.677729	+	1.17386i	−0.975663	+	0.219274i	$0.929631\pi$
$450$		0			0
$451$	−1.69525	−	2.93626i	−0.0798262	−	0.138263i
$452$	−41.9343	−	15.2628i	−1.97242	−	0.717904i
$453$	4.47694	+	6.88499i	0.210345	+	0.323485i
$454$	35.1654	+	29.5073i	1.65039	+	1.38485i
$455$		0			0
$456$	−22.5933	−	17.0044i	−1.05803	−	0.796304i
$457$	6.14505	+	34.8503i	0.287453	+	1.63023i	0.696389	+	0.717665i	$0.254789\pi$
$457$	6.14505	+	34.8503i	0.287453	+	1.63023i	−0.408936	+	0.912563i	$0.634100\pi$
$458$	53.9648			2.52161
$459$	−6.52484	−	8.02840i	−0.304553	−	0.374734i
$460$		0			0
$461$	0.395350	+	2.24214i	0.0184133	+	0.104427i	0.992629	−	0.121190i	$-0.0386712\pi$
$461$	0.395350	+	2.24214i	0.0184133	+	0.104427i	−0.974216	+	0.225617i	$0.927560\pi$
$462$	6.86591	−	2.91919i	0.319431	−	0.135813i
$463$	17.2664	−	6.28446i	0.802438	−	0.292064i	0.0919417	−	0.995764i	$-0.470693\pi$
$463$	17.2664	−	6.28446i	0.802438	−	0.292064i	0.710496	+	0.703701i	$0.248470\pi$
$464$	13.0432	+	10.9446i	0.605517	+	0.508089i
$465$		0			0
$466$	−39.9033	−	14.5236i	−1.84848	−	0.672793i
$467$	2.32935	+	4.03455i	0.107789	+	0.186697i	0.914874	−	0.403738i	$-0.132289\pi$
$467$	2.32935	+	4.03455i	0.107789	+	0.186697i	−0.807085	+	0.590435i	$0.798956\pi$
$468$	−3.25707	+	47.3819i	−0.150558	+	2.19023i
$469$	−2.56220	+	4.43786i	−0.118312	+	0.204922i
$470$		0			0
$471$	0.264864	−	0.247282i	0.0122043	−	0.0113941i
$472$	−7.58218	+	43.0007i	−0.348998	+	1.97927i
$473$	−3.70665	+	21.0215i	−0.170432	+	0.966568i
$474$	−6.76202	−	29.2109i	−0.310590	−	1.34170i
$475$		0			0
$476$	−2.17495	+	3.76712i	−0.0996885	+	0.172666i
$477$	15.7244	+	3.90082i	0.719970	+	0.178606i
$478$	18.5169	+	32.0722i	0.846942	+	1.46695i
$479$	13.3210	+	4.84844i	0.608651	+	0.221531i	0.627913	−	0.778283i	$-0.283909\pi$
$479$	13.3210	+	4.84844i	0.608651	+	0.221531i	−0.0192617	+	0.999814i	$0.506132\pi$
$480$		0			0
$481$	12.9717	+	10.8846i	0.591460	+	0.496294i
$482$	−29.6800	+	10.8026i	−1.35189	+	0.492047i
$483$	0.542402	−	4.43917i	0.0246802	−	0.201989i
$484$	−0.937459	−	5.31660i	−0.0426118	−	0.241663i
$485$		0			0
$486$	33.9765	+	15.7216i	1.54121	+	0.713147i
$487$	21.4338			0.971258			0.485629	−	0.874165i	$-0.338591\pi$
$487$	21.4338			0.971258			0.485629	+	0.874165i	$0.338591\pi$
$488$	−9.72875	−	55.1745i	−0.440400	−	2.49763i
$489$	−1.18140	+	9.66888i	−0.0534246	+	0.437242i
$490$		0			0
$491$	−10.7919	−	9.05550i	−0.487033	−	0.408669i	0.365929	−	0.930643i	$-0.380751\pi$
$491$	−10.7919	−	9.05550i	−0.487033	−	0.408669i	−0.852961	+	0.521974i	$0.825196\pi$
$492$	−7.14348	+	0.378601i	−0.322053	+	0.0170687i
$493$	−11.9729	−	4.35779i	−0.539234	−	0.196265i
$494$	−19.4020	−	33.6053i	−0.872938	−	1.51197i
$495$		0			0
$496$	−2.20500	+	3.81917i	−0.0990073	+	0.171486i
$497$	0.508585	−	0.426753i	0.0228131	−	0.0191425i
$498$	13.9785	+	60.3850i	0.626392	+	2.70592i
$499$	2.58898	−	14.6828i	0.115899	−	0.657294i	−0.870403	−	0.492340i	$-0.836142\pi$
$499$	2.58898	−	14.6828i	0.115899	−	0.657294i	0.986301	−	0.164953i	$-0.0527473\pi$
$500$		0			0
$501$	−21.1182	+	19.7164i	−0.943494	+	0.880864i
$502$	32.0422	−	26.8866i	1.43011	−	1.20001i
$503$	−7.93153	+	13.7378i	−0.353650	+	0.612539i	−0.986886	−	0.161420i	$-0.948393\pi$
$503$	−7.93153	+	13.7378i	−0.353650	+	0.612539i	0.633236	+	0.773958i	$0.281726\pi$
$504$	0.506490	−	7.36810i	0.0225608	−	0.328201i
$505$		0			0
$506$	31.0826	+	11.3131i	1.38179	+	0.502930i
$507$	−3.65580	+	7.18540i	−0.162360	+	0.319115i
$508$	−33.2771	−	27.9228i	−1.47643	−	1.23888i
$509$	−31.8807	+	11.6036i	−1.41309	+	0.514321i	−0.932034	−	0.362371i	$-0.881967\pi$
$509$	−31.8807	+	11.6036i	−1.41309	+	0.514321i	−0.481052	+	0.876692i	$0.659745\pi$
$510$		0			0
$511$	−0.0196825	−	0.111625i	−0.000870700	−	0.00493799i
$512$	−28.1824			−1.24550
$513$	−19.7298	+	3.16072i	−0.871093	+	0.139549i
$514$	−26.8683			−1.18511
$515$		0			0
$516$	35.9839	+	27.0825i	1.58410	+	1.19224i
$517$	−10.4438	+	3.80123i	−0.459317	+	0.167178i
$518$	−4.29930	−	3.60754i	−0.188900	−	0.158506i
$519$	17.9418	+	27.5923i	0.787558	+	1.21117i
$520$		0			0
$521$	21.3899	+	37.0484i	0.937108	+	1.62312i	0.770831	+	0.637040i	$0.219841\pi$
$521$	21.3899	+	37.0484i	0.937108	+	1.62312i	0.166277	+	0.986079i	$0.446825\pi$
$522$	45.8493	−	4.87367i	2.00677	−	0.213315i
$523$	−1.38893	+	2.40569i	−0.0607335	+	0.105193i	−0.894793	−	0.446480i	$-0.852677\pi$
$523$	−1.38893	+	2.40569i	−0.0607335	+	0.105193i	0.834060	+	0.551674i	$0.186011\pi$
$524$	−26.0106	+	21.8255i	−1.13628	+	0.953451i
$525$		0			0
$526$	8.63721	−	48.9840i	0.376600	−	2.13581i
$527$	0.573049	−	3.24992i	0.0249624	−	0.141569i
$528$	13.6336	+	4.15942i	0.593327	+	0.181016i
$529$	−2.43023	+	2.03920i	−0.105662	+	0.0886609i
$530$		0			0
$531$	18.1650	+	24.9400i	0.788292	+	1.08230i
$532$	4.20073	+	7.27587i	0.182125	+	0.315449i
$533$	−4.32799	−	1.57526i	−0.187466	−	0.0682321i
$534$	3.52188	+	5.41622i	0.152407	+	0.234383i
$535$		0			0
$536$	−35.2565	+	12.8323i	−1.52285	+	0.554271i
$537$	22.4678	+	16.9099i	0.969557	+	0.729717i
$538$	−11.7792	−	66.8029i	−0.507835	−	2.88008i
$539$	20.6116			0.887803
$540$		0			0
$541$	−3.59390			−0.154514			−0.0772570	−	0.997011i	$-0.524616\pi$
$541$	−3.59390			−0.154514			−0.0772570	+	0.997011i	$0.524616\pi$
$542$	7.19917	+	40.8285i	0.309231	+	1.75373i
$543$	4.76846	−	2.02741i	0.204634	−	0.0870047i
$544$	3.93130	−	1.43088i	0.168553	−	0.0613483i
$545$		0			0
$546$	4.59580	−	9.03294i	0.196682	−	0.386574i
$547$	−37.1985	−	13.5392i	−1.59049	−	0.578892i	−0.613042	−	0.790051i	$-0.710054\pi$
$547$	−37.1985	−	13.5392i	−1.59049	−	0.578892i	−0.977452	+	0.211158i	$0.932276\pi$
$548$	21.7029	+	37.5905i	0.927101	+	1.60579i
$549$	−32.8468	−	22.0991i	−1.40187	−	0.943167i
$550$		0			0
$551$	−18.8514	+	15.8182i	−0.803099	+	0.673880i
$552$	23.9341	−	22.3453i	1.01870	−	0.951081i
$553$	−0.725786	+	4.11614i	−0.0308636	+	0.175036i
$554$	−2.15566	+	12.2253i	−0.0915850	+	0.519405i
$555$		0			0
$556$	4.91776	−	4.12649i	0.208560	−	0.175002i
$557$	−5.71731	+	9.90267i	−0.242250	+	0.419590i	−0.961355	−	0.275312i	$-0.911219\pi$
$557$	−5.71731	+	9.90267i	−0.242250	+	0.419590i	0.719105	+	0.694902i	$0.244552\pi$
$558$	3.30522	+	11.4756i	0.139921	+	0.485799i
$559$	14.4983	+	25.1119i	0.613214	+	1.06212i
$560$		0			0
$561$	−10.6515	+	0.564526i	−0.449707	+	0.0238343i
$562$	−6.06462	−	5.08882i	−0.255821	−	0.214659i
$563$	13.6357	−	4.96298i	0.574676	−	0.209165i	−0.0383005	−	0.999266i	$-0.512194\pi$
$563$	13.6357	−	4.96298i	0.574676	−	0.209165i	0.612976	+	0.790101i	$0.289972\pi$
$564$	−2.84400	+	23.2761i	−0.119754	+	0.980099i
$565$		0			0
$566$	21.9285			0.921725
$567$	−3.50117	−	3.87003i	−0.147035	−	0.162526i
$568$	4.86093			0.203960
$569$	−0.225601	−	1.27945i	−0.00945767	−	0.0536371i	0.979714	−	0.200402i	$-0.0642249\pi$
$569$	−0.225601	−	1.27945i	−0.00945767	−	0.0536371i	−0.989171	+	0.146765i	$0.953114\pi$
$570$		0			0
$571$	−15.0890	+	5.49193i	−0.631453	+	0.229830i	−0.637864	−	0.770149i	$-0.720182\pi$
$571$	−15.0890	+	5.49193i	−0.631453	+	0.229830i	0.00641065	+	0.999979i	$0.497959\pi$
$572$	37.5111	+	31.4756i	1.56842	+	1.31606i
$573$	−3.89825	+	0.206606i	−0.162852	+	0.00863108i
$574$	1.43445	+	0.522099i	0.0598730	+	0.0217920i
$575$		0			0
$576$	−21.5796	+	22.3992i	−0.899152	+	0.933301i
$577$	−4.23017	+	7.32686i	−0.176104	+	0.305021i	−0.940543	−	0.339675i	$-0.889683\pi$
$577$	−4.23017	+	7.32686i	−0.176104	+	0.305021i	0.764439	+	0.644696i	$0.223016\pi$
$578$	−23.9829	+	20.1241i	−0.997558	+	0.837050i
$579$	0.343854	+	1.48540i	0.0142901	+	0.0617310i
$580$		0			0
$581$	1.50035	−	8.50893i	0.0622452	−	0.353010i
$582$	−16.1014	+	15.0326i	−0.667424	+	0.623120i
$583$	12.7958	−	10.7369i	0.529947	−	0.444678i
$584$	0.414943	−	0.718703i	0.0171705	−	0.0297401i
$585$		0			0
$586$	−3.39401	−	5.87860i	−0.140205	−	0.242843i
$587$	−17.2764	−	6.28811i	−0.713075	−	0.259538i	−0.0400919	−	0.999196i	$-0.512765\pi$
$587$	−17.2764	−	6.28811i	−0.713075	−	0.259538i	−0.672983	+	0.739658i	$0.734987\pi$
$588$	19.7201	−	38.7594i	0.813244	−	1.59841i
$589$	−4.88260	−	4.09699i	−0.201184	−	0.168814i
$590$		0			0
$591$	32.3200	−	13.7416i	1.32947	−	0.565252i
$592$	−1.86196	−	10.5597i	−0.0765260	−	0.434001i
$593$	−13.5128			−0.554905			−0.277452	−	0.960739i	$-0.589490\pi$
$593$	−13.5128			−0.554905			−0.277452	+	0.960739i	$0.589490\pi$
$594$	33.7264	−	18.7730i	1.38381	−	0.770265i
$595$		0			0
$596$	−14.1667	−	80.3435i	−0.580292	−	3.29100i
$597$	−26.3070	−	19.7994i	−1.07667	−	0.810337i
$598$	42.2234	−	15.3681i	1.72664	−	0.628447i
$599$	8.44772	+	7.08848i	0.345165	+	0.289627i	0.798845	−	0.601537i	$-0.205445\pi$
$599$	8.44772	+	7.08848i	0.345165	+	0.289627i	−0.453680	+	0.891164i	$0.649889\pi$
$600$		0			0
$601$	−24.2421	−	8.82341i	−0.988856	−	0.359914i	−0.203579	−	0.979058i	$-0.565257\pi$
$601$	−24.2421	−	8.82341i	−0.988856	−	0.359914i	−0.785277	+	0.619144i	$0.787480\pi$
$602$	−4.80528	−	8.32298i	−0.195848	−	0.339219i
$603$	−10.7548	+	24.2325i	−0.437968	+	0.986824i
$604$	8.93252	−	15.4716i	0.363459	−	0.629529i
$605$		0			0
$606$	28.9210	+	8.82338i	1.17484	+	0.358425i
$607$	2.56823	−	14.5652i	0.104241	−	0.591182i	−0.887279	−	0.461233i	$-0.847407\pi$
$607$	2.56823	−	14.5652i	0.104241	−	0.591182i	0.991521	−	0.129950i	$-0.0414816\pi$
$608$	1.40312	−	7.95752i	0.0569042	−	0.322720i
$609$	−6.14761	−	1.87555i	−0.249114	−	0.0760009i
$610$		0			0
$611$	−7.54882	+	13.0749i	−0.305393	+	0.528956i
$612$	−9.12926	+	20.5700i	−0.369029	+	0.831492i
$613$	18.1370	+	31.4141i	0.732545	+	1.26880i	0.955792	+	0.294043i	$0.0950009\pi$
$613$	18.1370	+	31.4141i	0.732545	+	1.26880i	−0.223248	+	0.974762i	$0.571666\pi$
$614$	14.2053	+	5.17029i	0.573277	+	0.208656i
$615$		0			0
$616$	−5.83316	−	4.89460i	−0.235025	−	0.197209i
$617$	−37.9387	+	13.8086i	−1.52736	+	0.555912i	−0.962972	−	0.269601i	$-0.913108\pi$
$617$	−37.9387	+	13.8086i	−1.52736	+	0.555912i	−0.564383	+	0.825513i	$0.690886\pi$
$618$	−21.2755	−	16.0126i	−0.855826	−	0.644120i
$619$	−1.19701	−	6.78858i	−0.0481119	−	0.272856i	0.951256	−	0.308402i	$-0.0997941\pi$
$619$	−1.19701	−	6.78858i	−0.0481119	−	0.272856i	−0.999368	+	0.0355458i	$0.988683\pi$
$620$		0			0
$621$	0.362848	−	23.1347i	0.0145606	−	0.928362i
$622$	−17.7069			−0.709981
$623$	−0.156387	−	0.886916i	−0.00626552	−	0.0355335i
$624$	17.8193	−	7.57626i	0.713343	−	0.303293i
$625$		0			0
$626$	7.85711	+	6.59290i	0.314033	+	0.263505i
$627$	−9.34200	+	18.3615i	−0.373083	+	0.733287i
$628$	−0.740705	−	0.269595i	−0.0295574	−	0.0107580i
$629$	4.01193	+	6.94887i	0.159966	+	0.277070i
$630$		0			0
$631$	−14.9095	+	25.8241i	−0.593539	+	1.02804i	0.400212	+	0.916423i	$0.368936\pi$
$631$	−14.9095	+	25.8241i	−0.593539	+	1.02804i	−0.993751	+	0.111617i	$0.964397\pi$
$632$	−23.4424	+	19.6705i	−0.932489	+	0.782451i
$633$	20.4897	−	19.1296i	0.814394	−	0.760334i
$634$	−6.73414	+	38.1912i	−0.267447	+	1.51677i
$635$		0			0
$636$	−7.94811	−	34.3346i	−0.315163	−	1.36146i
$637$	21.4487	−	17.9976i	0.849830	−	0.713092i
$638$	23.7691	−	41.1693i	0.941028	−	1.62991i
$639$	2.38312	−	2.47363i	0.0942749	−	0.0978554i
$640$		0			0
$641$	−40.2947	−	14.6661i	−1.59155	−	0.579275i	−0.613872	−	0.789406i	$-0.710389\pi$
$641$	−40.2947	−	14.6661i	−1.59155	−	0.579275i	−0.977673	+	0.210131i	$0.932611\pi$
$642$	23.0278	−	1.22046i	0.908834	−	0.0481678i
$643$	20.9998	+	17.6209i	0.828150	+	0.694901i	0.954866	−	0.297038i	$-0.0959989\pi$
$643$	20.9998	+	17.6209i	0.828150	+	0.694901i	−0.126715	+	0.991939i	$0.540443\pi$
$644$	−9.14178	+	3.32734i	−0.360237	+	0.131115i
$645$		0			0
$646$	−3.19291	−	18.1079i	−0.125623	−	0.712446i
$647$	16.1623			0.635407			0.317703	−	0.948190i	$-0.397088\pi$
$647$	16.1623			0.635407			0.317703	+	0.948190i	$0.397088\pi$
$648$	−1.42365	−	38.1834i	−0.0559261	−	1.49999i
$649$	31.8113			1.24870
$650$		0			0
$651$	0.201902	−	1.65242i	0.00791316	−	0.0647634i
$652$	19.9116	−	7.24721i	0.779797	−	0.283823i
$653$	−24.7021	−	20.7275i	−0.966668	−	0.811130i	0.0153573	−	0.999882i	$-0.495111\pi$
$653$	−24.7021	−	20.7275i	−0.966668	−	0.811130i	−0.982025	+	0.188752i	$0.939556\pi$
$654$	−25.8845	+	1.37187i	−1.01216	+	0.0536442i
$655$		0			0
$656$	1.45823	+	2.52573i	0.0569344	+	0.0986133i
$657$	−0.162303	−	0.563508i	−0.00633206	−	0.0219846i
$658$	2.50195	−	4.33351i	0.0975363	−	0.168938i
$659$	21.3103	−	17.8814i	0.830130	−	0.696562i	−0.125191	−	0.992133i	$-0.539954\pi$
$659$	21.3103	−	17.8814i	0.830130	−	0.696562i	0.955321	+	0.295571i	$0.0955098\pi$
$660$		0			0
$661$	5.34639	−	30.3209i	0.207950	−	1.17934i	−0.684779	−	0.728751i	$-0.740101\pi$
$661$	5.34639	−	30.3209i	0.207950	−	1.17934i	0.892729	−	0.450594i	$-0.148788\pi$
$662$	8.01889	−	45.4774i	0.311663	−	1.76753i
$663$	−10.5912	+	9.88816i	−0.411329	+	0.384024i
$664$	48.4604	−	40.6631i	1.88063	−	1.57803i
$665$		0			0
$666$	−24.0913	−	16.2085i	−0.933519	−	0.628065i
$667$	−14.2479	−	24.6781i	−0.551682	−	0.955540i
$668$	59.0583	+	21.4955i	2.28503	+	0.831684i
$669$	16.8531	−	33.1243i	0.651577	−	1.28066i
$670$		0			0
$671$	−38.3557	+	13.9603i	−1.48071	+	0.538933i
$672$	1.94216	−	0.825749i	0.0749203	−	0.0318540i
$673$	4.53753	+	25.7336i	0.174909	+	0.991959i	0.938249	+	0.345961i	$0.112447\pi$
$673$	4.53753	+	25.7336i	0.174909	+	0.991959i	−0.763340	+	0.645997i	$0.776442\pi$
$674$	70.7584			2.72551
$675$		0			0
$676$	17.5374			0.674515
$677$	−3.15944	−	17.9181i	−0.121427	−	0.688648i	−0.983366	−	0.181635i	$-0.941861\pi$
$677$	−3.15944	−	17.9181i	−0.121427	−	0.688648i	0.861939	−	0.507012i	$-0.169250\pi$
$678$	39.3645	+	29.6269i	1.51178	+	1.13781i
$679$	2.88549	−	1.05023i	0.110735	−	0.0403042i
$680$		0			0
$681$	−18.0477	−	27.7551i	−0.691588	−	1.06358i
$682$	11.5701	+	4.21116i	0.443040	+	0.161253i
$683$	11.7486	+	20.3491i	0.449546	+	0.778636i	0.998356	−	0.0573104i	$-0.0182525\pi$
$683$	11.7486	+	20.3491i	0.449546	+	0.778636i	−0.548811	+	0.835947i	$0.684919\pi$
$684$	25.5903	+	35.1347i	0.978468	+	1.34341i
$685$		0			0
$686$	−14.5765	+	12.2311i	−0.556533	+	0.466987i
$687$	−37.2256	−	11.3570i	−1.42024	−	0.433296i
$688$	3.18841	−	18.0824i	0.121557	−	0.689384i
$689$	3.94021	−	22.3460i	0.150110	−	0.851317i
$690$		0			0
$691$	−34.1180	+	28.6284i	−1.29791	+	1.08908i	−0.307409	+	0.951577i	$0.599462\pi$
$691$	−34.1180	+	28.6284i	−1.29791	+	1.08908i	−0.990502	+	0.137499i	$0.956094\pi$
$692$	35.7980	−	62.0039i	1.36084	−	2.35704i
$693$	−5.35054	+	0.568750i	−0.203250	+	0.0216050i
$694$	13.6857	+	23.7043i	0.519501	+	0.899802i
$695$		0			0
$696$	−25.6534	−	39.4517i	−0.972388	−	1.49541i
$697$	−1.67184	−	1.40284i	−0.0633254	−	0.0531363i
$698$	−63.5547	+	23.1320i	−2.40558	+	0.875560i
$699$	24.4692	+	18.4163i	0.925512	+	0.696567i
$700$		0			0
$701$	−25.2567			−0.953934			−0.476967	−	0.878921i	$-0.658264\pi$
$701$	−25.2567			−0.953934			−0.476967	+	0.878921i	$0.658264\pi$
$702$	18.7041	−	48.9848i	0.705939	−	1.84881i
$703$	15.4974			0.584496
$704$	5.56859	+	31.5810i	0.209874	+	1.19025i
$705$		0			0
$706$	64.6662	−	23.5366i	2.43374	−	0.885810i
$707$	−3.22888	−	2.70935i	−0.121434	−	0.101896i
$708$	30.4355	−	59.8202i	1.14383	−	2.24818i
$709$	14.7382	+	5.36425i	0.553503	+	0.201459i	0.603602	−	0.797286i	$-0.293731\pi$
$709$	14.7382	+	5.36425i	0.553503	+	0.201459i	−0.0500991	+	0.998744i	$0.515954\pi$
$710$		0			0
$711$	−1.48295	+	21.5731i	−0.0556150	+	0.809053i
$712$	3.29694	−	5.71046i	0.123558	−	0.214009i
$713$	5.65382	−	4.74412i	0.211737	−	0.177669i
$714$	3.51031	−	3.27730i	0.131370	−	0.122650i
$715$		0			0
$716$	10.6222	−	60.2415i	0.396970	−	2.25133i
$717$	−6.02352	−	26.0207i	−0.224953	−	0.971760i
$718$	−57.0915	+	47.9055i	−2.13064	+	1.78782i
$719$	26.5804	−	46.0385i	0.991280	−	1.71695i	0.381523	−	0.924359i	$-0.375400\pi$
$719$	26.5804	−	46.0385i	0.991280	−	1.71695i	0.609757	−	0.792588i	$-0.291267\pi$
$720$		0			0
$721$	1.85595	+	3.21461i	0.0691194	+	0.119718i
$722$	9.50721	+	3.46034i	0.353822	+	0.128781i
$723$	22.7471	−	1.20558i	0.845972	−	0.0448361i
$724$	−8.63457	−	7.24526i	−0.320901	−	0.269268i
$725$		0			0
$726$	−0.722875	+	5.91621i	−0.0268284	+	0.219571i
$727$	−0.0814709	−	0.462044i	−0.00302159	−	0.0171363i	0.983260	−	0.182210i	$-0.0583250\pi$
$727$	−0.0814709	−	0.462044i	−0.00302159	−	0.0171363i	−0.986281	+	0.165073i	$0.947214\pi$
$728$	−10.3440			−0.383372
$729$	−20.1288	−	17.9954i	−0.745509	−	0.666495i
$730$		0			0
$731$	2.38593	+	13.5313i	0.0882469	+	0.500473i
$732$	−10.4448	+	85.4834i	−0.386052	+	3.15956i
$733$	−43.6076	+	15.8719i	−1.61068	+	0.586241i	−0.981575	−	0.191075i	$-0.938803\pi$
$733$	−43.6076	+	15.8719i	−1.61068	+	0.586241i	−0.629109	+	0.777317i	$0.716580\pi$
$734$	−44.3825	−	37.2413i	−1.63819	−	1.37460i
$735$		0			0
$736$	8.79230	+	3.20014i	0.324088	+	0.117959i
$737$	13.6672	+	23.6724i	0.503439	+	0.871983i
$738$	7.66531	+	1.90157i	0.282164	+	0.0699977i
$739$	−12.9047	+	22.3515i	−0.474706	+	0.822214i	−0.999580	−	0.0289653i	$-0.990779\pi$
$739$	−12.9047	+	22.3515i	−0.474706	+	0.822214i	0.524875	+	0.851179i	$0.324112\pi$
$740$		0			0
$741$	6.31146	+	27.2645i	0.231857	+	1.00159i
$742$	−1.30593	+	7.40629i	−0.0479422	+	0.271894i
$743$	−6.02726	+	34.1823i	−0.221119	+	1.25403i	0.648848	+	0.760918i	$0.275251\pi$
$743$	−6.02726	+	34.1823i	−0.221119	+	1.25403i	−0.869967	+	0.493110i	$0.835860\pi$
$744$	8.90915	−	8.31775i	0.326625	−	0.304944i
$745$		0			0
$746$	−15.1129	+	26.1764i	−0.553324	+	0.958385i
$747$	3.06557	−	44.5961i	0.112163	−	1.63169i
$748$	11.6015	+	20.0945i	0.424195	+	0.734727i
$749$	−3.02069	−	1.09944i	−0.110374	−	0.0401727i
$750$		0			0
$751$	18.3742	+	15.4178i	0.670485	+	0.562604i	0.913209	−	0.407492i	$-0.133596\pi$
$751$	18.3742	+	15.4178i	0.670485	+	0.562604i	−0.242724	+	0.970095i	$0.578041\pi$
$752$	8.98361	−	3.26977i	0.327599	−	0.119236i
$753$	−27.7614	+	11.8034i	−1.01168	+	0.430138i
$754$	−11.2137	−	63.5962i	−0.408380	−	2.31604i
$755$		0			0
$756$	−4.04961	+	10.6057i	−0.147283	+	0.385725i
$757$	8.78780			0.319398			0.159699	−	0.987166i	$-0.448948\pi$
$757$	8.78780			0.319398			0.159699	+	0.987166i	$0.448948\pi$
$758$	−3.21336	−	18.2239i	−0.116715	−	0.661921i
$759$	−19.0603	−	14.3453i	−0.691843	−	0.520701i
$760$		0			0
$761$	10.5361	+	8.84082i	0.381933	+	0.320479i	0.813461	−	0.581620i	$-0.197581\pi$
$761$	10.5361	+	8.84082i	0.381933	+	0.320479i	−0.431528	+	0.902100i	$0.642025\pi$
$762$	26.1441	+	40.2065i	0.947102	+	1.45653i
$763$	3.39542	+	1.23583i	0.122922	+	0.0447401i
$764$	4.24595	+	7.35420i	0.153613	+	0.266066i
$765$		0			0
$766$	−21.4484	+	37.1498i	−0.774963	+	1.34228i
$767$	33.1034	−	27.7770i	1.19529	−	1.00297i
$768$	47.9943	+	14.6424i	1.73185	+	0.528361i
$769$	−5.44525	+	30.8815i	−0.196361	+	1.11362i	0.714107	+	0.700036i	$0.246833\pi$
$769$	−5.44525	+	30.8815i	−0.196361	+	1.11362i	−0.910468	+	0.413580i	$0.864278\pi$
$770$		0			0
$771$	18.5341	+	5.65448i	0.667489	+	0.203641i
$772$	2.54072	−	2.13192i	0.0914426	−	0.0767295i
$773$	14.0607	−	24.3539i	0.505729	−	0.875948i	−0.494249	−	0.869320i	$-0.664557\pi$
$773$	14.0607	−	24.3539i	0.505729	−	0.875948i	0.999978	−	0.00662776i	$-0.00210970\pi$
$774$	−29.2731	−	40.1911i	−1.05220	−	1.44464i
$775$		0			0
$776$	21.1266	+	7.68945i	0.758400	+	0.276035i
$777$	2.20650	+	3.39332i	0.0791576	+	0.121735i
$778$	50.3879	+	42.2804i	1.80649	+	1.51583i
$779$	−3.96098	+	1.44168i	−0.141917	+	0.0516535i
$780$		0			0
$781$	−0.614960	−	3.48761i	−0.0220050	−	0.124797i
$782$	21.2916			0.761385
$783$	−32.6531	−	6.28714i	−1.16693	−	0.224684i
$784$	−17.7298			−0.633207
$785$		0			0
$786$	34.4979	−	14.6675i	1.23050	−	0.523173i
$787$	−34.0170	+	12.3812i	−1.21258	+	0.441342i	−0.867597	−	0.497269i	$-0.834336\pi$
$787$	−34.0170	+	12.3812i	−1.21258	+	0.441342i	−0.344979	+	0.938610i	$0.612114\pi$
$788$	−58.5240	−	49.1075i	−2.08483	−	1.74938i
$789$	−16.2668	+	31.9721i	−0.579114	+	1.13824i
$790$		0			0
$791$	−3.43393	−	5.94775i	−0.122097	−	0.211478i
$792$	−32.6863	−	21.9911i	−1.16146	−	0.781421i
$793$	−27.7237	+	48.0189i	−0.984498	+	1.70520i
$794$	−7.75636	+	6.50836i	−0.275263	+	0.230973i
$795$		0			0
$796$	−12.4373	+	70.5354i	−0.440828	+	2.50006i
$797$	5.14000	−	29.1504i	0.182068	−	1.03256i	−0.747596	−	0.664153i	$-0.768792\pi$
$797$	5.14000	−	29.1504i	0.182068	−	1.03256i	0.929665	−	0.368407i	$-0.120097\pi$
$798$	−2.09185	−	9.03645i	−0.0740506	−	0.319887i
$799$	−5.48028	+	4.59850i	−0.193878	+	0.162683i
$800$		0			0
$801$	−1.28958	−	4.47736i	−0.0455652	−	0.158200i
$802$	−18.2193	−	31.5568i	−0.643346	−	1.11431i
$803$	−0.568149	−	0.206789i	−0.0200495	−	0.00729744i
$804$	57.5913	−	3.05231i	2.03109	−	0.107647i
$805$		0			0
$806$	15.7171	−	5.72055i	0.553611	−	0.201498i
$807$	−5.93338	+	48.5604i	−0.208865	+	1.70941i
$808$	−5.35892	−	30.3920i	−0.188526	−	1.06919i
$809$	−5.75943			−0.202491			−0.101245	−	0.994861i	$-0.532283\pi$
$809$	−5.75943			−0.202491			−0.101245	+	0.994861i	$0.532283\pi$
$810$		0			0
$811$	12.4896			0.438569			0.219284	−	0.975661i	$-0.429628\pi$
$811$	12.4896			0.438569			0.219284	+	0.975661i	$0.429628\pi$
$812$	2.42788	+	13.7692i	0.0852019	+	0.483204i
$813$	3.62635	−	29.6791i	0.127182	−	1.04089i
$814$	−28.1318	+	10.2391i	−0.986018	+	0.358881i
$815$		0			0
$816$	9.16230	−	0.485598i	0.320744	−	0.0169993i
$817$	24.9373	+	9.07644i	0.872446	+	0.317544i
$818$	−5.65535	−	9.79536i	−0.197735	−	0.342487i
$819$	−5.07123	+	5.26384i	−0.177203	+	0.183933i
$820$		0			0
$821$	32.9911	−	27.6828i	1.15140	−	0.966136i	0.151644	−	0.988435i	$-0.451543\pi$
$821$	32.9911	−	27.6828i	1.15140	−	0.966136i	0.999751	+	0.0222995i	$0.00709873\pi$
$822$	−10.8074	−	46.6865i	−0.376953	−	1.62838i
$823$	−1.78581	+	10.1279i	−0.0622496	+	0.353035i	0.937734	+	0.347353i	$0.112920\pi$
$823$	−1.78581	+	10.1279i	−0.0622496	+	0.353035i	−0.999984	+	0.00568141i	$0.998192\pi$
$824$	−4.71930	+	26.7645i	−0.164404	+	0.932384i
$825$		0			0
$826$	−10.9717	+	9.20632i	−0.381753	+	0.320329i
$827$	3.04731	−	5.27810i	0.105965	−	0.183538i	−0.808167	−	0.588954i	$-0.799540\pi$
$827$	3.04731	−	5.27810i	0.105965	−	0.183538i	0.914132	+	0.405416i	$0.132873\pi$
$828$	−45.2118	+	22.1174i	−1.57122	+	0.768632i
$829$	16.8489	+	29.1832i	0.585188	+	1.01358i	0.994852	+	0.101339i	$0.0323126\pi$
$829$	16.8489	+	29.1832i	0.585188	+	1.01358i	−0.409664	+	0.912236i	$0.634354\pi$
$830$		0			0
$831$	4.05984	−	7.97952i	0.140834	−	0.276806i
$832$	33.3707	+	28.0014i	1.15692	+	0.970772i
$833$	12.4673	−	4.53774i	0.431967	−	0.157223i
$834$	−6.52244	+	2.77315i	−0.225853	+	0.0960264i
$835$		0			0
$836$	44.8148			1.54995
$837$	0.135065	−	8.61156i	0.00466853	−	0.297659i
$838$	47.5308			1.64192
$839$	−7.33250	−	41.5847i	−0.253146	−	1.43566i	−0.800787	−	0.598950i	$-0.795585\pi$
$839$	−7.33250	−	41.5847i	−0.253146	−	1.43566i	0.547641	−	0.836714i	$-0.315526\pi$
$840$		0			0
$841$	−11.2328	+	4.08841i	−0.387339	+	0.140980i
$842$	51.8546	+	43.5112i	1.78703	+	1.49949i
$843$	3.11250	+	4.78664i	0.107200	+	0.164861i
$844$	−57.3007	−	20.8557i	−1.97237	−	0.717884i
$845$		0			0
$846$	10.5019	−	23.6627i	0.361062	−	0.813541i
$847$	0.415423	−	0.719533i	0.0142741	−	0.0247235i
$848$	−11.0068	+	9.23576i	−0.377973	+	0.317157i
$849$	−15.1266	−	4.61489i	−0.519142	−	0.158383i
$850$		0			0
$851$	−3.11616	+	17.6726i	−0.106821	+	0.605810i
$852$	−7.14672	−	2.18036i	−0.244842	−	0.0746979i
$853$	27.3705	−	22.9665i	0.937147	−	0.786359i	−0.0399399	−	0.999202i	$-0.512717\pi$
$853$	27.3705	−	22.9665i	0.937147	−	0.786359i	0.977086	+	0.212843i	$0.0682722\pi$
$854$	9.18865	−	15.9152i	0.314429	−	0.544607i
$855$		0			0
$856$	−11.7679	−	20.3826i	−0.402219	−	0.696664i
$857$	7.43170	+	2.70492i	0.253862	+	0.0923983i	0.465817	−	0.884881i	$-0.345761\pi$
$857$	7.43170	+	2.70492i	0.253862	+	0.0923983i	−0.211954	+	0.977280i	$0.567983\pi$
$858$	−29.4706	−	45.3221i	−1.00611	−	1.54727i
$859$	−34.2569	−	28.7449i	−1.16883	−	0.980764i	−0.168841	−	0.985643i	$-0.554002\pi$
$859$	−34.2569	−	28.7449i	−1.16883	−	0.980764i	−0.999988	+	0.00487963i	$0.998447\pi$
$860$		0			0
$861$	−0.879627	−	0.662033i	−0.0299776	−	0.0225620i
$862$	−2.16726	−	12.2911i	−0.0738172	−	0.418638i
$863$	22.9170			0.780103			0.390052	−	0.920793i	$-0.372457\pi$
$863$	22.9170			0.780103			0.390052	+	0.920793i	$0.372457\pi$
$864$	9.54017	−	5.31030i	0.324563	−	0.180660i
$865$		0			0
$866$	−10.5629	−	59.9053i	−0.358943	−	2.03567i
$867$	20.7788	−	8.83457i	0.705686	−	0.300038i
$868$	−3.40290	+	1.23856i	−0.115502	+	0.0420393i
$869$	17.0789	+	14.3309i	0.579362	+	0.486143i
$870$		0			0
$871$	34.8926	+	12.6999i	1.18229	+	0.430319i
$872$	13.2278	+	22.9112i	0.447950	+	0.775871i
$873$	14.2706	−	6.98108i	0.482985	−	0.236274i
$874$	20.5614	−	35.6134i	0.695501	−	1.20464i
$875$		0			0
$876$	−0.932438	+	0.870542i	−0.0315041	+	0.0294129i
$877$	3.84416	−	21.8013i	0.129808	−	0.736178i	−0.848527	−	0.529152i	$-0.822510\pi$
$877$	3.84416	−	21.8013i	0.129808	−	0.736178i	0.978335	−	0.207026i	$-0.0663786\pi$
$878$	−6.53132	+	37.0409i	−0.220421	+	1.25007i
$879$	1.10407	+	4.76940i	0.0372393	+	0.160868i
$880$		0			0
$881$	−4.93202	+	8.54251i	−0.166164	+	0.287804i	−0.937068	−	0.349147i	$-0.886471\pi$
$881$	−4.93202	+	8.54251i	−0.166164	+	0.287804i	0.770904	+	0.636951i	$0.219805\pi$
$882$	−33.3108	+	34.5759i	−1.12163	+	1.16423i
$883$	23.7865	+	41.1995i	0.800481	+	1.38647i	0.919300	+	0.393558i	$0.128756\pi$
$883$	23.7865	+	41.1995i	0.800481	+	1.38647i	−0.118819	+	0.992916i	$0.537911\pi$
$884$	29.6189	+	10.7804i	0.996191	+	0.362584i
$885$		0			0
$886$	33.5825	+	28.1791i	1.12823	+	0.946694i
$887$	12.5517	−	4.56846i	0.421446	−	0.153394i	−0.122587	−	0.992458i	$-0.539119\pi$
$887$	12.5517	−	4.56846i	0.421446	−	0.153394i	0.544033	+	0.839064i	$0.316897\pi$
$888$	−3.59428	+	29.4165i	−0.120616	+	0.987155i
$889$	−1.16091	−	6.58387i	−0.0389358	−	0.220816i
$890$		0			0
$891$	−27.2157	+	5.85205i	−0.911760	+	0.196051i
$892$	−80.8465			−2.70694
$893$	2.39936	+	13.6074i	0.0802914	+	0.455355i
$894$	−10.9240	+	89.4048i	−0.365352	+	2.99014i
$895$		0			0
$896$	−9.19350	−	7.71427i	−0.307133	−	0.257716i
$897$	−32.3605	+	1.71509i	−1.08048	+	0.0572652i
$898$	−64.8186	−	23.5920i	−2.16302	−	0.787276i
$899$	−5.30359	−	9.18609i	−0.176885	−	0.306373i
$900$		0			0
$901$	5.37600	−	9.31150i	0.179100	−	0.310211i
$902$	6.23767	−	5.23403i	0.207692	−	0.174274i
$903$	1.56315	+	6.75257i	0.0520184	+	0.224712i
$904$	8.73176	−	49.5203i	0.290414	−	1.64702i
$905$		0			0
$906$	−14.4169	+	13.4599i	−0.478969	+	0.447174i
$907$	−28.3135	+	23.7578i	−0.940134	+	0.788866i	−0.977609	−	0.210431i	$-0.932513\pi$
$907$	−28.3135	+	23.7578i	−0.940134	+	0.788866i	0.0374746	+	0.999298i	$0.488069\pi$
$908$	−36.0092	+	62.3697i	−1.19501	+	2.06981i
$909$	−18.0932	−	12.1729i	−0.600112	−	0.403751i
$910$		0			0
$911$	45.4916	+	16.5576i	1.50720	+	0.548577i	0.957914	−	0.287056i	$-0.0926766\pi$
$911$	45.4916	+	16.5576i	1.50720	+	0.548577i	0.549288	+	0.835633i	$0.314899\pi$
$912$	8.03587	−	15.7943i	0.266094	−	0.523002i
$913$	−35.3057	−	29.6250i	−1.16845	−	0.980445i
$914$	−79.8629	+	29.0677i	−2.64163	+	0.961475i
$915$		0			0
$916$	14.7015	+	83.3765i	0.485752	+	2.75484i
$917$	−5.22558			−0.172564
$918$	16.2671	−	18.7803i	0.536896	−	0.619841i
$919$	8.93459			0.294725			0.147363	−	0.989083i	$-0.452922\pi$
$919$	8.93459			0.294725			0.147363	+	0.989083i	$0.452922\pi$
$920$		0			0
$921$	−8.71086	−	6.55604i	−0.287032	−	0.216029i
$922$	−5.13809	+	1.87011i	−0.169214	+	0.0615889i
$923$	−3.68526	−	3.09230i	−0.121302	−	0.101784i
$924$	6.38066	+	9.81267i	0.209908	+	0.322813i
$925$		0			0
$926$	22.0643	+	38.2165i	0.725079	+	1.25587i
$927$	11.3062	+	15.5231i	0.371345	+	0.509846i
$928$	6.72355	−	11.6455i	0.220711	−	0.382283i
$929$	−4.78330	+	4.01366i	−0.156935	+	0.131684i	−0.717874	−	0.696173i	$-0.754885\pi$
$929$	−4.78330	+	4.01366i	−0.156935	+	0.131684i	0.560939	+	0.827857i	$0.310440\pi$
$930$		0			0
$931$	4.44973	−	25.2357i	0.145834	−	0.827066i
$932$	11.5684	−	65.6079i	0.378937	−	2.14906i
$933$	12.2144	+	3.72644i	0.399882	+	0.121998i
$934$	−8.57084	+	7.19179i	−0.280446	+	0.235322i
$935$		0			0
$936$	−53.2162	+	5.65676i	−1.73943	+	0.184897i
$937$	22.9212	+	39.7006i	0.748802	+	1.29696i	0.948397	+	0.317085i	$0.102704\pi$
$937$	22.9212	+	39.7006i	0.748802	+	1.29696i	−0.199595	+	0.979878i	$0.563963\pi$
$938$	−11.5647	−	4.20920i	−0.377600	−	0.137435i
$939$	−4.03244	−	6.20140i	−0.131594	−	0.202375i
$940$		0			0
$941$	4.09014	−	1.48869i	0.133335	−	0.0485298i	−0.274491	−	0.961590i	$-0.588509\pi$
$941$	4.09014	−	1.48869i	0.133335	−	0.0485298i	0.407826	+	0.913060i	$0.366287\pi$
$942$	0.695313	+	0.523313i	0.0226545	+	0.0170505i
$943$	−0.847573	−	4.80683i	−0.0276008	−	0.156532i
$944$	−27.3637			−0.890612
$945$		0			0
$946$	−51.2644			−1.66675
$947$	−0.350202	−	1.98610i	−0.0113800	−	0.0645395i	0.978589	−	0.205825i	$-0.0659877\pi$
$947$	−0.350202	−	1.98610i	−0.0113800	−	0.0645395i	−0.989969	+	0.141285i	$0.954877\pi$
$948$	43.2891	−	18.4053i	1.40596	−	0.597776i
$949$	−0.771790	+	0.280909i	−0.0250534	+	0.00911868i
$950$		0			0
$951$	12.6827	−	24.9275i	0.411264	−	0.808331i
$952$	−4.60587	−	1.67640i	−0.149277	−	0.0543325i
$953$	−17.8644	−	30.9420i	−0.578684	−	1.00231i	−0.995631	−	0.0933786i	$-0.970233\pi$
$953$	−17.8644	−	30.9420i	−0.578684	−	1.00231i	0.416947	−	0.908931i	$-0.363100\pi$
$954$	−2.66832	+	38.8171i	−0.0863900	+	1.25675i
$955$		0			0
$956$	−44.5075	+	37.3462i	−1.43948	+	1.20786i
$957$	−25.0604	+	23.3968i	−0.810086	+	0.756312i
$958$	−5.91188	+	33.5279i	−0.191004	+	1.08324i
$959$	−1.15999	+	6.57865i	−0.0374581	+	0.212436i
$960$		0			0
$961$	−21.6428	+	18.1605i	−0.698155	+	0.585822i
$962$	−20.3338	+	35.2191i	−0.655587	+	1.13551i
$963$	−16.1417	−	4.00434i	−0.520159	−	0.129038i
$964$	−24.7759	−	42.9131i	−0.797978	−	1.38214i
$965$		0			0
$966$	10.7254	−	0.568443i	0.345085	−	0.0182894i
$967$	0.531112	+	0.445656i	0.0170794	+	0.0143313i	0.651287	−	0.758831i	$-0.274229\pi$
$967$	0.531112	+	0.445656i	0.0170794	+	0.0143313i	−0.634208	+	0.773163i	$0.718674\pi$
$968$	5.71631	−	2.08057i	0.183729	−	0.0668719i
$969$	−1.60833	+	13.1630i	−0.0516670	+	0.422857i
$970$		0			0
$971$	47.4942			1.52416			0.762081	−	0.647482i	$-0.224178\pi$
$971$	47.4942			1.52416			0.762081	+	0.647482i	$0.224178\pi$
$972$	−15.0340	+	56.7772i	−0.482216	+	1.82113i
$973$	0.987988			0.0316734
$974$	8.93869	+	50.6938i	0.286414	+	1.62434i
$975$		0			0
$976$	32.9931	−	12.0085i	1.05608	−	0.384383i
$977$	9.65470	+	8.10126i	0.308881	+	0.259182i	0.784029	−	0.620724i	$-0.213161\pi$
$977$	9.65470	+	8.10126i	0.308881	+	0.259182i	−0.475148	+	0.879906i	$0.657606\pi$
$978$	−23.3609	+	1.23812i	−0.746999	+	0.0395906i
$979$	−4.51423	−	1.64305i	−0.144276	−	0.0525120i
$980$		0			0
$981$	18.1441	+	4.50110i	0.579298	+	0.143709i
$982$	16.9168	−	29.3008i	0.539838	−	0.935027i
$983$	−8.84400	+	7.42100i	−0.282080	+	0.236693i	−0.772839	−	0.634602i	$-0.781164\pi$
$983$	−8.84400	+	7.42100i	−0.282080	+	0.236693i	0.490759	+	0.871295i	$0.336720\pi$
$984$	−1.81787	−	7.85292i	−0.0579517	−	0.250342i
$985$		0			0
$986$	5.31361	−	30.1350i	0.169220	−	0.959693i
$987$	−2.63787	+	2.46277i	−0.0839644	+	0.0783908i
$988$	46.6351	−	39.1315i	1.48366	−	1.24494i
$989$	−15.3647	+	26.6125i	−0.488569	+	0.846227i
$990$		0			0
$991$	−9.34676	−	16.1891i	−0.296910	−	0.514263i	0.678518	−	0.734584i	$-0.262623\pi$
$991$	−9.34676	−	16.1891i	−0.296910	−	0.514263i	−0.975427	+	0.220322i	$0.929289\pi$
$992$	3.27281	+	1.19121i	0.103912	+	0.0378209i
$993$	−15.1023	+	29.6832i	−0.479257	+	0.941969i
$994$	1.22143	+	1.02490i	0.0387413	+	0.0325079i
$995$		0			0
$996$	−89.4877	+	38.0476i	−2.83553	+	1.20558i
$997$	−0.583250	−	3.30778i	−0.0184717	−	0.104758i	0.974178	−	0.225782i	$-0.0724936\pi$
$997$	−0.583250	−	3.30778i	−0.0184717	−	0.104758i	−0.992650	+	0.121023i	$0.961382\pi$
$998$	35.8066			1.13344
$999$	13.2074	+	16.2508i	0.417863	+	0.514154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.c.526.2		12
5.2	odd	4		675.2.u.b.499.1		24
5.3	odd	4		675.2.u.b.499.4		24
5.4	even	2		27.2.e.a.13.1	✓	12
15.14	odd	2		81.2.e.a.10.2		12
20.19	odd	2		432.2.u.c.337.1		12
27.25	even	9	inner	675.2.l.c.376.2		12
45.4	even	6		243.2.e.d.190.2		12
45.14	odd	6		243.2.e.a.190.1		12
45.29	odd	6		243.2.e.b.109.2		12
45.34	even	6		243.2.e.c.109.1		12
135.4	even	18		729.2.c.e.487.6		12
135.14	odd	18		729.2.c.b.244.1		12
135.29	odd	18		81.2.e.a.73.2		12
135.34	even	18		243.2.e.c.136.1		12
135.49	even	18		729.2.a.a.1.1		6
135.52	odd	36		675.2.u.b.349.4		24
135.59	odd	18		729.2.a.d.1.6		6
135.74	odd	18		243.2.e.b.136.2		12
135.79	even	18		27.2.e.a.25.1	yes	12
135.94	even	18		729.2.c.e.244.6		12
135.104	odd	18		729.2.c.b.487.1		12
135.119	odd	18		243.2.e.a.55.1		12
135.124	even	18		243.2.e.d.55.2		12
135.133	odd	36		675.2.u.b.349.1		24
540.79	odd	18		432.2.u.c.241.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.1	✓	12	5.4	even	2
27.2.e.a.25.1	yes	12	135.79	even	18
81.2.e.a.10.2		12	15.14	odd	2
81.2.e.a.73.2		12	135.29	odd	18
243.2.e.a.55.1		12	135.119	odd	18
243.2.e.a.190.1		12	45.14	odd	6
243.2.e.b.109.2		12	45.29	odd	6
243.2.e.b.136.2		12	135.74	odd	18
243.2.e.c.109.1		12	45.34	even	6
243.2.e.c.136.1		12	135.34	even	18
243.2.e.d.55.2		12	135.124	even	18
243.2.e.d.190.2		12	45.4	even	6
432.2.u.c.241.1		12	540.79	odd	18
432.2.u.c.337.1		12	20.19	odd	2
675.2.l.c.376.2		12	27.25	even	9	inner
675.2.l.c.526.2		12	1.1	even	1	trivial
675.2.u.b.349.1		24	135.133	odd	36
675.2.u.b.349.4		24	135.52	odd	36
675.2.u.b.499.1		24	5.2	odd	4
675.2.u.b.499.4		24	5.3	odd	4
729.2.a.a.1.1		6	135.49	even	18
729.2.a.d.1.6		6	135.59	odd	18
729.2.c.b.244.1		12	135.14	odd	18
729.2.c.b.487.1		12	135.104	odd	18
729.2.c.e.244.6		12	135.94	even	18
729.2.c.e.487.6		12	135.4	even	18

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.417037 + 2.36514i) q^{2} +(0.210069 - 1.71926i) q^{3} +(-3.54056 + 1.28866i) q^{4} +(4.15390 - 0.220155i) q^{6} +(-0.544891 - 0.198324i) q^{7} +(-2.12277 - 3.67675i) q^{8} +(-2.91174 - 0.722330i) q^{9} +O(q^{10})\)	\(q+(0.417037 + 2.36514i) q^{2} +(0.210069 - 1.71926i) q^{3} +(-3.54056 + 1.28866i) q^{4} +(4.15390 - 0.220155i) q^{6} +(-0.544891 - 0.198324i) q^{7} +(-2.12277 - 3.67675i) q^{8} +(-2.91174 - 0.722330i) q^{9} +(-2.36944 + 1.98820i) q^{11} +(1.47178 + 6.35787i) q^{12} +(-0.729623 + 4.13790i) q^{13} +(0.241824 - 1.37145i) q^{14} +(2.03816 - 1.71022i) q^{16} +(-0.995493 + 1.72424i) q^{17} +(0.494102 - 7.18790i) q^{18} +(1.92271 + 3.33023i) q^{19} +(-0.455437 + 0.895151i) q^{21} +(-5.69050 - 4.77489i) q^{22} +(-4.18428 + 1.52295i) q^{23} +(-6.76724 + 2.87724i) q^{24} -10.0910 q^{26} +(-1.85354 + 4.85432i) q^{27} +2.18479 q^{28} +(1.11126 + 6.30229i) q^{29} +(-1.55754 + 0.566898i) q^{31} +(-1.60967 - 1.35067i) q^{32} +(2.92049 + 4.49135i) q^{33} +(-4.49323 - 1.63540i) q^{34} +(11.2400 - 1.19479i) q^{36} +(2.01505 - 3.49016i) q^{37} +(-7.07461 + 5.93630i) q^{38} +(6.96087 + 2.12366i) q^{39} +(-0.190345 + 1.07950i) q^{41} +(-2.30709 - 0.703859i) q^{42} +(5.28657 - 4.43596i) q^{43} +(5.82704 - 10.0927i) q^{44} +(-5.34699 - 9.26126i) q^{46} +(3.37650 + 1.22894i) q^{47} +(-2.51217 - 3.86340i) q^{48} +(-5.10474 - 4.28338i) q^{49} +(2.75531 + 2.07373i) q^{51} +(-2.74906 - 15.5907i) q^{52} -5.40034 q^{53} +(-12.2541 - 2.35945i) q^{54} +(0.427492 + 2.42443i) q^{56} +(6.12946 - 2.60607i) q^{57} +(-14.4423 + 5.25657i) q^{58} +(-7.87850 - 6.61085i) q^{59} +(12.4005 + 4.51341i) q^{61} +(-1.99034 - 3.44738i) q^{62} +(1.44333 + 0.971060i) q^{63} +(5.18386 - 8.97871i) q^{64} +(-9.40470 + 8.78041i) q^{66} +(1.53458 - 8.70304i) q^{67} +(1.30264 - 7.38764i) q^{68} +(1.73937 + 7.51381i) q^{69} +(-0.572473 + 0.991553i) q^{71} +(3.52514 + 12.2391i) q^{72} +(0.0977361 + 0.169284i) q^{73} +(9.09506 + 3.31033i) q^{74} +(-11.0990 - 9.31317i) q^{76} +(1.68539 - 0.613433i) q^{77} +(-2.11980 + 17.3491i) q^{78} +(-1.25166 - 7.09849i) q^{79} +(7.95648 + 4.20647i) q^{81} -2.63255 q^{82} +(2.58744 + 14.6741i) q^{83} +(0.458958 - 3.75624i) q^{84} +(12.6963 + 10.6535i) q^{86} +(11.0687 - 0.586638i) q^{87} +(12.3399 + 4.49135i) q^{88} +(0.776563 + 1.34505i) q^{89} +(1.21821 - 2.11000i) q^{91} +(12.8521 - 10.7842i) q^{92} +(0.647457 + 2.79691i) q^{93} +(-1.49850 + 8.49839i) q^{94} +(-2.66030 + 2.48371i) q^{96} +(-4.05661 + 3.40390i) q^{97} +(8.00191 - 13.8597i) q^{98} +(8.33533 - 4.07760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8	\( 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8} + 3 q^{11} - 12 q^{12} + 6 q^{13} + 15 q^{14} - 9 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{23} - 18 q^{24} - 30 q^{26} + 9 q^{27} + 12 q^{28} - 6 q^{29} + 3 q^{31} + 9 q^{34} + 18 q^{36} + 3 q^{37} - 42 q^{38} + 33 q^{39} + 15 q^{41} - 18 q^{42} - 3 q^{43} + 3 q^{44} - 3 q^{46} + 15 q^{47} + 15 q^{48} + 12 q^{49} - 18 q^{51} - 9 q^{52} + 18 q^{53} - 54 q^{54} - 33 q^{56} + 3 q^{57} - 21 q^{58} - 12 q^{59} + 12 q^{61} + 12 q^{62} - 9 q^{63} + 12 q^{64} - 9 q^{66} + 15 q^{67} - 9 q^{68} + 9 q^{69} + 27 q^{71} - 18 q^{72} - 6 q^{73} + 33 q^{74} - 48 q^{76} - 15 q^{77} - 18 q^{78} - 42 q^{79} + 36 q^{81} + 12 q^{82} - 39 q^{83} + 6 q^{84} + 51 q^{86} - 9 q^{87} + 30 q^{88} + 9 q^{89} + 6 q^{91} + 39 q^{92} + 39 q^{93} - 15 q^{94} - 3 q^{97} + 45 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8 + 3 * q^11 - 12 * q^12 + 6 * q^13 + 15 * q^14 - 9 * q^17 - 9 * q^18 - 3 * q^19 - 12 * q^21 - 3 * q^22 + 12 * q^23 - 18 * q^24 - 30 * q^26 + 9 * q^27 + 12 * q^28 - 6 * q^29 + 3 * q^31 + 9 * q^34 + 18 * q^36 + 3 * q^37 - 42 * q^38 + 33 * q^39 + 15 * q^41 - 18 * q^42 - 3 * q^43 + 3 * q^44 - 3 * q^46 + 15 * q^47 + 15 * q^48 + 12 * q^49 - 18 * q^51 - 9 * q^52 + 18 * q^53 - 54 * q^54 - 33 * q^56 + 3 * q^57 - 21 * q^58 - 12 * q^59 + 12 * q^61 + 12 * q^62 - 9 * q^63 + 12 * q^64 - 9 * q^66 + 15 * q^67 - 9 * q^68 + 9 * q^69 + 27 * q^71 - 18 * q^72 - 6 * q^73 + 33 * q^74 - 48 * q^76 - 15 * q^77 - 18 * q^78 - 42 * q^79 + 36 * q^81 + 12 * q^82 - 39 * q^83 + 6 * q^84 + 51 * q^86 - 9 * q^87 + 30 * q^88 + 9 * q^89 + 6 * q^91 + 39 * q^92 + 39 * q^93 - 15 * q^94 - 3 * q^97 + 45 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more