LMFDB - Embedded newform 775.2.bs.b.418.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(182,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("775.182");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.bs (of order $20$, degree $8$, 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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			418.6
Character	$\chi$	$=$	775.418
Dual form			775.2.bs.b.432.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0296108 + 0.186955i) q^{2} +(-0.693043 + 0.109767i) q^{3} +(1.86804 + 0.606962i) q^{4} -0.132818i q^{6} +(-0.0394047 - 0.0773360i) q^{7} +(-0.340657 + 0.668577i) q^{8} +(-2.38491 + 0.774904i) q^{9} +O(q^{10})$	\(q+(-0.0296108 + 0.186955i) q^{2} +(-0.693043 + 0.109767i) q^{3} +(1.86804 + 0.606962i) q^{4} -0.132818i q^{6} +(-0.0394047 - 0.0773360i) q^{7} +(-0.340657 + 0.668577i) q^{8} +(-2.38491 + 0.774904i) q^{9} +(-4.57319 - 1.48592i) q^{11} +(-1.36125 - 0.215601i) q^{12} +(-5.28416 + 0.836929i) q^{13} +(0.0156252 - 0.00507693i) q^{14} +(3.06319 + 2.22554i) q^{16} +(-2.79468 + 5.48486i) q^{17} +(-0.0742534 - 0.468817i) q^{18} +(-3.71362 - 5.11136i) q^{19} +(0.0357981 + 0.0492718i) q^{21} +(0.413217 - 0.810983i) q^{22} +(-0.142255 - 0.0724827i) q^{23} +(0.162702 - 0.500745i) q^{24} -1.01268i q^{26} +(3.44339 - 1.75450i) q^{27} +(-0.0266694 - 0.168384i) q^{28} +(-0.363268 + 0.263930i) q^{29} +(2.91241 + 4.74530i) q^{31} +(-1.56795 + 1.56795i) q^{32} +(3.33252 + 0.527820i) q^{33} +(-0.942672 - 0.684891i) q^{34} -4.92544 q^{36} +(4.15226 + 4.15226i) q^{37} +(1.06556 - 0.542929i) q^{38} +(3.57028 - 1.16006i) q^{39} +(-4.35479 + 3.16394i) q^{41} +(-0.0102716 + 0.00523366i) q^{42} +(0.613991 - 3.87659i) q^{43} +(-7.64100 - 5.55151i) q^{44} +(0.0177633 - 0.0244491i) q^{46} +(8.99268 - 1.42430i) q^{47} +(-2.36721 - 1.20615i) q^{48} +(4.11007 - 5.65702i) q^{49} +(1.33477 - 4.10801i) q^{51} +(-10.3790 - 1.64387i) q^{52} +(-9.20858 - 4.69201i) q^{53} +(0.226051 + 0.695713i) q^{54} +0.0651285 q^{56} +(3.13475 + 3.13475i) q^{57} +(-0.0385864 - 0.0757301i) q^{58} +(-4.50267 + 6.19740i) q^{59} +7.29096i q^{61} +(-0.973398 + 0.403978i) q^{62} +(0.153905 + 0.153905i) q^{63} +(4.20436 + 5.78681i) q^{64} +(-0.197357 + 0.607404i) q^{66} +(-4.22535 + 4.22535i) q^{67} +(-8.54966 + 8.54966i) q^{68} +(0.106545 + 0.0346186i) q^{69} +(0.487541 + 1.50050i) q^{71} +(0.294353 - 1.85847i) q^{72} +(-4.73742 - 9.29771i) q^{73} +(-0.899239 + 0.653335i) q^{74} +(-3.83478 - 11.8022i) q^{76} +(0.0652900 + 0.412225i) q^{77} +(0.111160 + 0.701834i) q^{78} +(-1.35924 - 4.18331i) q^{79} +(3.89235 - 2.82795i) q^{81} +(-0.462566 - 0.907838i) q^{82} +(-2.19708 + 13.8718i) q^{83} +(0.0369660 + 0.113770i) q^{84} +(0.706568 + 0.229578i) q^{86} +(0.222790 - 0.222790i) q^{87} +(2.55134 - 2.55134i) q^{88} +(-2.77006 + 8.52536i) q^{89} +(0.272946 + 0.375677i) q^{91} +(-0.221744 - 0.221744i) q^{92} +(-2.53930 - 2.96901i) q^{93} +1.72340i q^{94} +(0.914547 - 1.25877i) q^{96} +(-3.65452 - 7.17241i) q^{97} +(0.935908 + 0.935908i) q^{98} +12.0581 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 6 q^{2} + 10 q^{3} + 18 q^{7} + 20 q^{8}+O(q^{10}) $ 112 * q + 6 * q^2 + 10 * q^3 + 18 * q^7 + 20 * q^8	$ 112 q + 6 q^{2} + 10 q^{3} + 18 q^{7} + 20 q^{8} - 20 q^{11} - 10 q^{12} + 10 q^{13} - 12 q^{16} + 10 q^{17} - 4 q^{18} + 20 q^{21} - 60 q^{22} + 40 q^{27} + 48 q^{28} - 4 q^{31} - 44 q^{32} + 26 q^{33} - 64 q^{36} + 32 q^{38} - 16 q^{41} - 70 q^{42} + 10 q^{43} - 60 q^{46} - 46 q^{47} - 150 q^{48} + 12 q^{51} + 80 q^{52} - 10 q^{53} - 24 q^{56} + 10 q^{58} + 54 q^{62} + 200 q^{63} - 52 q^{66} + 68 q^{67} + 8 q^{71} + 18 q^{72} - 30 q^{73} - 128 q^{76} + 30 q^{77} - 36 q^{78} + 64 q^{81} + 44 q^{82} - 160 q^{83} - 20 q^{86} - 60 q^{91} - 10 q^{93} - 92 q^{97} - 144 q^{98}+O(q^{100}) $ 112 * q + 6 * q^2 + 10 * q^3 + 18 * q^7 + 20 * q^8 - 20 * q^11 - 10 * q^12 + 10 * q^13 - 12 * q^16 + 10 * q^17 - 4 * q^18 + 20 * q^21 - 60 * q^22 + 40 * q^27 + 48 * q^28 - 4 * q^31 - 44 * q^32 + 26 * q^33 - 64 * q^36 + 32 * q^38 - 16 * q^41 - 70 * q^42 + 10 * q^43 - 60 * q^46 - 46 * q^47 - 150 * q^48 + 12 * q^51 + 80 * q^52 - 10 * q^53 - 24 * q^56 + 10 * q^58 + 54 * q^62 + 200 * q^63 - 52 * q^66 + 68 * q^67 + 8 * q^71 + 18 * q^72 - 30 * q^73 - 128 * q^76 + 30 * q^77 - 36 * q^78 + 64 * q^81 + 44 * q^82 - 160 * q^83 - 20 * q^86 - 60 * q^91 - 10 * q^93 - 92 * q^97 - 144 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.0296108	+	0.186955i	−0.0209380	+	0.132197i	−0.995943	−	0.0899851i	$-0.971318\pi$
$2$	−0.0296108	+	0.186955i	−0.0209380	+	0.132197i	0.975005	+	0.222182i	$0.0713181\pi$
$3$	−0.693043	+	0.109767i	−0.400128	+	0.0633741i	−0.353256	−	0.935527i	$-0.614925\pi$
$3$	−0.693043	+	0.109767i	−0.400128	+	0.0633741i	−0.0468725	+	0.998901i	$0.514925\pi$
$4$	1.86804	+	0.606962i	0.934019	+	0.303481i
$5$		0			0
$5$		0			0
$6$		−	0.132818i		−	0.0542228i
$7$	−0.0394047	−	0.0773360i	−0.0148936	−	0.0292303i	0.883440	−	0.468545i	$-0.155221\pi$
$7$	−0.0394047	−	0.0773360i	−0.0148936	−	0.0292303i	−0.898333	+	0.439314i	$0.855221\pi$
$8$	−0.340657	+	0.668577i	−0.120440	+	0.236378i
$9$	−2.38491	+	0.774904i	−0.794970	+	0.258301i
$10$		0			0
$11$	−4.57319	−	1.48592i	−1.37887	−	0.448022i	−0.476572	−	0.879136i	$-0.658121\pi$
$11$	−4.57319	−	1.48592i	−1.37887	−	0.448022i	−0.902298	+	0.431114i	$0.858121\pi$
$12$	−1.36125	−	0.215601i	−0.392960	−	0.0622388i
$13$	−5.28416	+	0.836929i	−1.46556	+	0.232122i	−0.837670	−	0.546177i	$-0.816083\pi$
$13$	−5.28416	+	0.836929i	−1.46556	+	0.232122i	−0.627894	+	0.778299i	$0.716083\pi$
$14$	0.0156252	−	0.00507693i	0.00417601	−	0.00135687i
$15$		0			0
$16$	3.06319	+	2.22554i	0.765797	+	0.556384i
$17$	−2.79468	+	5.48486i	−0.677809	+	1.33027i	0.253957	+	0.967215i	$0.418268\pi$
$17$	−2.79468	+	5.48486i	−0.677809	+	1.33027i	−0.931766	+	0.363059i	$0.881732\pi$
$18$	−0.0742534	−	0.468817i	−0.0175017	−	0.110501i
$19$	−3.71362	−	5.11136i	−0.851962	−	1.17263i	−0.983427	−	0.181305i	$-0.941968\pi$
$19$	−3.71362	−	5.11136i	−0.851962	−	1.17263i	0.131465	−	0.991321i	$-0.458032\pi$
$20$		0			0
$21$	0.0357981	+	0.0492718i	0.00781178	+	0.0107520i
$22$	0.413217	−	0.810983i	0.0880981	−	0.172902i
$23$	−0.142255	−	0.0724827i	−0.0296623	−	0.0151137i	0.439096	−	0.898440i	$-0.355299\pi$
$23$	−0.142255	−	0.0724827i	−0.0296623	−	0.0151137i	−0.468759	+	0.883326i	$0.655299\pi$
$24$	0.162702	−	0.500745i	0.0332114	−	0.102214i
$25$		0			0
$26$		−	1.01268i		−	0.198604i
$27$	3.44339	−	1.75450i	0.662681	−	0.337653i
$28$	−0.0266694	−	0.168384i	−0.00504004	−	0.0318215i
$29$	−0.363268	+	0.263930i	−0.0674572	+	0.0490105i	−0.621003	−	0.783808i	$-0.713274\pi$
$29$	−0.363268	+	0.263930i	−0.0674572	+	0.0490105i	0.553546	+	0.832819i	$0.313274\pi$
$30$		0			0
$31$	2.91241	+	4.74530i	0.523084	+	0.852281i
$31$	2.91241	+	4.74530i	0.523084	+	0.852281i
$32$	−1.56795	+	1.56795i	−0.277177	+	0.277177i
$33$	3.33252	+	0.527820i	0.580118	+	0.0918816i
$34$	−0.942672	−	0.684891i	−0.161667	−	0.117458i
$35$		0			0
$36$	−4.92544			−0.820907
$37$	4.15226	+	4.15226i	0.682627	+	0.682627i	0.960591	−	0.277964i	$-0.0896596\pi$
$37$	4.15226	+	4.15226i	0.682627	+	0.682627i	−0.277964	+	0.960591i	$0.589660\pi$
$38$	1.06556	−	0.542929i	0.172856	−	0.0880748i
$39$	3.57028	−	1.16006i	0.571703	−	0.185758i
$40$		0			0
$41$	−4.35479	+	3.16394i	−0.680104	+	0.494124i	−0.873392	−	0.487018i	$-0.838085\pi$
$41$	−4.35479	+	3.16394i	−0.680104	+	0.494124i	0.193288	+	0.981142i	$0.438085\pi$
$42$	−0.0102716	+	0.00523366i	−0.00158495	+	0.000807572i
$43$	0.613991	−	3.87659i	0.0936328	−	0.591174i	−0.895604	−	0.444852i	$-0.853256\pi$
$43$	0.613991	−	3.87659i	0.0936328	−	0.591174i	0.989237	−	0.146322i	$-0.0467436\pi$
$44$	−7.64100	−	5.55151i	−1.15192	−	0.836922i
$45$		0			0
$46$	0.0177633	−	0.0244491i	0.00261906	−	0.00360483i
$47$	8.99268	−	1.42430i	1.31172	−	0.207756i	0.538892	−	0.842375i	$-0.318843\pi$
$47$	8.99268	−	1.42430i	1.31172	−	0.207756i	0.772825	+	0.634619i	$0.218843\pi$
$48$	−2.36721	−	1.20615i	−0.341677	−	0.174093i
$49$	4.11007	−	5.65702i	0.587153	−	0.808146i
$50$		0			0
$51$	1.33477	−	4.10801i	0.186905	−	0.575236i
$52$	−10.3790	−	1.64387i	−1.43931	−	0.227964i
$53$	−9.20858	−	4.69201i	−1.26490	−	0.644497i	−0.312662	−	0.949865i	$-0.601221\pi$
$53$	−9.20858	−	4.69201i	−1.26490	−	0.644497i	−0.952235	+	0.305368i	$0.901221\pi$
$54$	0.226051	+	0.695713i	0.0307616	+	0.0946745i
$55$		0			0
$56$	0.0651285			0.00870317
$57$	3.13475	+	3.13475i	0.415208	+	0.415208i
$58$	−0.0385864	−	0.0757301i	−0.00506665	−	0.00994385i
$59$	−4.50267	+	6.19740i	−0.586198	+	0.806833i	−0.994358	−	0.106078i	$-0.966171\pi$
$59$	−4.50267	+	6.19740i	−0.586198	+	0.806833i	0.408160	+	0.912911i	$0.366171\pi$
$60$		0			0
$61$			7.29096i			0.933512i	0.884386	+	0.466756i	$0.154577\pi$
$61$			7.29096i			0.933512i	−0.884386	+	0.466756i	$0.845423\pi$
$62$	−0.973398	+	0.403978i	−0.123622	+	0.0513052i
$63$	0.153905	+	0.153905i	0.0193902	+	0.0193902i
$64$	4.20436	+	5.78681i	0.525546	+	0.723351i
$65$		0			0
$66$	−0.197357	+	0.607404i	−0.0242930	+	0.0747662i
$67$	−4.22535	+	4.22535i	−0.516209	+	0.516209i	−0.916422	−	0.400213i	$-0.868936\pi$
$67$	−4.22535	+	4.22535i	−0.516209	+	0.516209i	0.400213	+	0.916422i	$0.368936\pi$
$68$	−8.54966	+	8.54966i	−1.03680	+	1.03680i
$69$	0.106545	+	0.0346186i	0.0128265	+	0.00416760i
$70$		0			0
$71$	0.487541	+	1.50050i	0.0578605	+	0.178076i	0.975810	−	0.218622i	$-0.0701560\pi$
$71$	0.487541	+	1.50050i	0.0578605	+	0.178076i	−0.917949	+	0.396698i	$0.870156\pi$
$72$	0.294353	−	1.85847i	0.0346898	−	0.219023i
$73$	−4.73742	−	9.29771i	−0.554473	−	1.08821i	−0.982814	−	0.184597i	$-0.940902\pi$
$73$	−4.73742	−	9.29771i	−0.554473	−	1.08821i	0.428341	−	0.903617i	$-0.359098\pi$
$74$	−0.899239	+	0.653335i	−0.104534	+	0.0759487i
$75$		0			0
$76$	−3.83478	−	11.8022i	−0.439879	−	1.35381i
$77$	0.0652900	+	0.412225i	0.00744049	+	0.0469774i
$78$	0.111160	+	0.701834i	0.0125863	+	0.0794670i
$79$	−1.35924	−	4.18331i	−0.152926	−	0.470659i	0.845018	−	0.534737i	$-0.179589\pi$
$79$	−1.35924	−	4.18331i	−0.152926	−	0.470659i	−0.997945	+	0.0640780i	$0.979589\pi$
$80$		0			0
$81$	3.89235	−	2.82795i	0.432483	−	0.314217i
$82$	−0.462566	−	0.907838i	−0.0510819	−	0.100254i
$83$	−2.19708	+	13.8718i	−0.241161	+	1.52263i	0.508648	+	0.860975i	$0.330145\pi$
$83$	−2.19708	+	13.8718i	−0.241161	+	1.52263i	−0.749809	+	0.661655i	$0.769855\pi$
$84$	0.0369660	+	0.113770i	0.00403332	+	0.0124133i
$85$		0			0
$86$	0.706568	+	0.229578i	0.0761912	+	0.0247560i
$87$	0.222790	−	0.222790i	0.0238855	−	0.0238855i
$88$	2.55134	−	2.55134i	0.271974	−	0.271974i
$89$	−2.77006	+	8.52536i	−0.293626	+	0.903687i	0.690054	+	0.723758i	$0.257587\pi$
$89$	−2.77006	+	8.52536i	−0.293626	+	0.903687i	−0.983680	+	0.179929i	$0.942413\pi$
$90$		0			0
$91$	0.272946	+	0.375677i	0.0286125	+	0.0393817i
$92$	−0.221744	−	0.221744i	−0.0231184	−	0.0231184i
$93$	−2.53930	−	2.96901i	−0.263313	−	0.307872i
$94$			1.72340i			0.177756i
$95$		0			0
$96$	0.914547	−	1.25877i	0.0933405	−	0.128472i
$97$	−3.65452	−	7.17241i	−0.371061	−	0.728248i	0.627677	−	0.778474i	$-0.284006\pi$
$97$	−3.65452	−	7.17241i	−0.371061	−	0.728248i	−0.998738	+	0.0502262i	$0.984006\pi$
$98$	0.935908	+	0.935908i	0.0945410	+	0.0945410i
$99$	12.0581			1.21188
$100$		0			0
$101$	−1.45935	−	4.49142i	−0.145211	−	0.446913i	0.851827	−	0.523823i	$-0.175495\pi$
$101$	−1.45935	−	4.49142i	−0.145211	−	0.446913i	−0.997038	+	0.0769101i	$0.975495\pi$
$102$	0.728490	+	0.371184i	0.0721313	+	0.0367527i
$103$	18.8427	+	2.98439i	1.85662	+	0.294060i	0.981734	−	0.190260i	$-0.0609331\pi$
$103$	18.8427	+	2.98439i	1.85662	+	0.294060i	0.874891	+	0.484321i	$0.160933\pi$
$104$	1.24054	−	3.81797i	0.121644	−	0.374383i
$105$		0			0
$106$	1.14987	−	1.58266i	0.111685	−	0.153722i
$107$	−11.7516	−	5.98775i	−1.13607	−	0.578857i	−0.218266	−	0.975889i	$-0.570040\pi$
$107$	−11.7516	−	5.98775i	−1.13607	−	0.578857i	−0.917805	+	0.397032i	$0.870040\pi$
$108$	7.49730	−	1.18746i	0.721428	−	0.114263i
$109$	1.58068	−	2.17562i	0.151402	−	0.208386i	−0.726579	−	0.687083i	$-0.758891\pi$
$109$	1.58068	−	2.17562i	0.151402	−	0.208386i	0.877980	+	0.478697i	$0.158891\pi$
$110$		0			0
$111$	−3.33348	−	2.42191i	−0.316399	−	0.229878i
$112$	0.0514102	−	0.324591i	0.00485781	−	0.0306710i
$113$	1.49091	−	0.759656i	0.140253	−	0.0714624i	−0.382456	−	0.923974i	$-0.624922\pi$
$113$	1.49091	−	0.759656i	0.140253	−	0.0714624i	0.522709	+	0.852511i	$0.324922\pi$
$114$	−0.678882	+	0.493236i	−0.0635831	+	0.0461958i
$115$		0			0
$116$	−0.838794	+	0.272541i	−0.0778801	+	0.0253048i
$117$	11.9537	−	6.09072i	1.10512	−	0.563088i
$118$	−1.02531	−	1.02531i	−0.0943873	−	0.0943873i
$119$	0.534301			0.0489793
$120$		0			0
$121$	9.80694	+	7.12516i	0.891540	+	0.647742i
$122$	−1.36308	−	0.215891i	−0.123408	−	0.0195459i
$123$	2.67076	−	2.67076i	0.240814	−	0.240814i
$124$	2.56027	+	10.6321i	0.229919	+	0.954793i
$125$		0			0
$126$	−0.0333305	+	0.0242161i	−0.00296932	+	0.00215734i
$127$	0.709362	+	4.47874i	0.0629457	+	0.397424i	0.998965	+	0.0454761i	$0.0144805\pi$
$127$	0.709362	+	4.47874i	0.0629457	+	0.397424i	−0.936020	+	0.351948i	$0.885520\pi$
$128$	−5.15784	+	2.62805i	−0.455893	+	0.232289i
$129$			2.75404i			0.242479i
$130$		0			0
$131$	−2.53508	+	7.80218i	−0.221491	+	0.681679i	0.777138	+	0.629330i	$0.216671\pi$
$131$	−2.53508	+	7.80218i	−0.221491	+	0.681679i	−0.998629	+	0.0523489i	$0.983329\pi$
$132$	5.90491	+	3.00870i	0.513956	+	0.261874i
$133$	−0.248958	+	0.488608i	−0.0215874	+	0.0423677i
$134$	−0.664836	−	0.915068i	−0.0574331	−	0.0790498i
$135$		0			0
$136$	−2.71502	−	3.73691i	−0.232811	−	0.320437i
$137$	−0.146536	−	0.925193i	−0.0125194	−	0.0790446i	0.980638	−	0.195831i	$-0.0627405\pi$
$137$	−0.146536	−	0.925193i	−0.0125194	−	0.0790446i	−0.993157	+	0.116787i	$0.962741\pi$
$138$	−0.00962703	+	0.0188941i	−0.000819507	+	0.00160837i
$139$	−5.88777	−	4.27772i	−0.499394	−	0.362831i	0.309391	−	0.950935i	$-0.399875\pi$
$139$	−5.88777	−	4.27772i	−0.499394	−	0.362831i	−0.808786	+	0.588104i	$0.799875\pi$
$140$		0			0
$141$	−6.07597	+	1.97420i	−0.511689	+	0.166258i
$142$	−0.294963	+	0.0467175i	−0.0247527	+	0.00392044i
$143$	25.4091	+	4.02441i	2.12482	+	0.336538i
$144$	−9.03001	−	2.93403i	−0.752501	−	0.244502i
$145$		0			0
$146$	1.87853	−	0.610373i	0.155469	−	0.0505148i
$147$	−2.22750	+	4.37171i	−0.183721	+	0.360572i
$148$	5.23631	+	10.2768i	0.430422	+	0.844751i
$149$		−	5.73123i		−	0.469521i	−0.972053	−	0.234760i	$-0.924569\pi$
$149$		−	5.73123i		−	0.469521i	0.972053	−	0.234760i	$-0.0754306\pi$
$150$		0			0
$151$	5.88059	+	1.91072i	0.478555	+	0.155492i	0.538355	−	0.842718i	$-0.319046\pi$
$151$	5.88059	+	1.91072i	0.478555	+	0.155492i	−0.0597993	+	0.998210i	$0.519046\pi$
$152$	4.68240	−	0.741620i	0.379793	−	0.0601533i
$153$	2.41481	−	15.2465i	0.195226	−	1.23261i
$154$	−0.0790009			−0.00636608
$155$		0			0
$156$	7.37353			0.590355
$157$	−0.428576	+	2.70592i	−0.0342041	+	0.215956i	−0.998870	−	0.0475187i	$-0.984869\pi$
$157$	−0.428576	+	2.70592i	−0.0342041	+	0.215956i	0.964666	+	0.263475i	$0.0848686\pi$
$158$	0.822340	−	0.130246i	0.0654219	−	0.0103618i
$159$	6.89697	+	2.24096i	0.546965	+	0.177720i
$160$		0			0
$161$			0.0138576i			0.00109213i
$162$	0.413446	+	0.811433i	0.0324834	+	0.0637522i
$163$	−6.29385	+	12.3524i	−0.492972	+	0.967512i	0.501760	+	0.865007i	$0.332686\pi$
$163$	−6.29385	+	12.3524i	−0.492972	+	0.967512i	−0.994732	+	0.102505i	$0.967314\pi$
$164$	−10.0553	+	3.26716i	−0.785187	+	0.255123i
$165$		0			0
$166$	−2.52835	−	0.821511i	−0.196238	−	0.0637616i
$167$	−4.45518	−	0.705632i	−0.344752	−	0.0546034i	−0.0183426	−	0.999832i	$-0.505839\pi$
$167$	−4.45518	−	0.705632i	−0.344752	−	0.0546034i	−0.326410	+	0.945228i	$0.605839\pi$
$168$	−0.0451369	+	0.00714897i	−0.00348238	+	0.000551555i
$169$	14.8582	−	4.82772i	1.14294	−	0.371363i
$170$		0			0
$171$	12.8175	+	9.31243i	0.980176	+	0.712139i
$172$	3.49990	−	6.86894i	0.266865	−	0.523752i
$173$	0.135075	+	0.852828i	0.0102695	+	0.0648393i	0.992291	−	0.123931i	$-0.0395500\pi$
$173$	0.135075	+	0.852828i	0.0102695	+	0.0648393i	−0.982021	+	0.188770i	$0.939550\pi$
$174$	0.0350547	+	0.0482487i	0.00265749	+	0.00365772i
$175$		0			0
$176$	−10.7016	−	14.7295i	−0.806662	−	1.11027i
$177$	2.44027	−	4.78931i	0.183422	−	0.359986i
$178$	−1.51184	−	0.770320i	−0.113317	−	0.0577379i
$179$	1.71863	−	5.28940i	0.128457	−	0.395349i	−0.866058	−	0.499943i	$-0.833354\pi$
$179$	1.71863	−	5.28940i	0.128457	−	0.395349i	0.994515	+	0.104594i	$0.0333544\pi$
$180$		0			0
$181$			8.45724i			0.628622i	0.949320	+	0.314311i	$0.101773\pi$
$181$			8.45724i			0.628622i	−0.949320	+	0.314311i	$0.898227\pi$
$182$	−0.0783170	+	0.0399045i	−0.00580525	+	0.00295792i
$183$	−0.800308	−	5.05295i	−0.0591605	−	0.373525i
$184$	0.0969205	−	0.0704169i	0.00714507	−	0.00519120i
$185$		0			0
$186$	0.630263	−	0.386821i	0.0462131	−	0.0283631i
$187$	20.9307	−	20.9307i	1.53060	−	1.53060i
$188$	17.6632	+	2.79757i	1.28822	+	0.204034i
$189$	−0.271372	−	0.197163i	−0.0197394	−	0.0143415i
$190$		0			0
$191$	8.75756			0.633675			0.316837	−	0.948480i	$-0.397379\pi$
$191$	8.75756			0.633675			0.316837	+	0.948480i	$0.397379\pi$
$192$	−3.54901	−	3.54901i	−0.256127	−	0.256127i
$193$	17.8973	−	9.11913i	1.28828	−	0.656409i	0.330467	−	0.943818i	$-0.392794\pi$
$193$	17.8973	−	9.11913i	1.28828	−	0.656409i	0.957808	+	0.287409i	$0.0927937\pi$
$194$	1.44913	−	0.470852i	0.104042	−	0.0338052i
$195$		0			0
$196$	11.1114	−	8.07288i	0.793669	−	0.576634i
$197$	−8.62117	+	4.39271i	−0.614233	+	0.312967i	−0.733286	−	0.679920i	$-0.762014\pi$
$197$	−8.62117	+	4.39271i	−0.614233	+	0.312967i	0.119053	+	0.992888i	$0.462014\pi$
$198$	−0.357050	+	2.25433i	−0.0253745	+	0.160208i
$199$	10.3681	+	7.53285i	0.734973	+	0.533989i	0.891133	−	0.453742i	$-0.149911\pi$
$199$	10.3681	+	7.53285i	0.734973	+	0.533989i	−0.156160	+	0.987732i	$0.549911\pi$
$200$		0			0
$201$	2.46454	−	3.39215i	0.173835	−	0.239264i
$202$	0.882907	−	0.139839i	0.0621211	−	0.00983902i
$203$	0.0347258	+	0.0176937i	0.00243727	+	0.00124185i
$204$	4.98681	−	6.86375i	0.349146	−	0.480559i
$205$		0			0
$206$	−1.11589	+	3.43437i	−0.0777480	+	0.239284i
$207$	0.395433	+	0.0626305i	0.0274845	+	0.00435312i
$208$	−18.0490	−	9.19643i	−1.25147	−	0.637658i
$209$	9.38802	+	28.8934i	0.649383	+	1.99860i
$210$		0			0
$211$	−4.69679			−0.323340			−0.161670	−	0.986845i	$-0.551688\pi$
$211$	−4.69679			−0.323340			−0.161670	+	0.986845i	$0.551688\pi$
$212$	−14.3541	−	14.3541i	−0.985844	−	0.985844i
$213$	−0.502592	−	0.986393i	−0.0344370	−	0.0675865i
$214$	1.46742	−	2.01972i	0.100310	−	0.138066i
$215$		0			0
$216$			2.89985i			0.197310i
$217$	0.252220	−	0.412221i	0.0171218	−	0.0279834i
$218$	0.359938	+	0.359938i	0.0243781	+	0.0243781i
$219$	4.30382	+	5.92369i	0.290825	+	0.400286i
$220$		0			0
$221$	10.1771	−	31.3219i	0.684585	−	2.10694i
$222$	0.551496	−	0.551496i	0.0370140	−	0.0370140i
$223$	−5.76053	+	5.76053i	−0.385754	+	0.385754i	−0.873170	−	0.487416i	$-0.837940\pi$
$223$	−5.76053	+	5.76053i	−0.385754	+	0.385754i	0.487416	+	0.873170i	$0.337940\pi$
$224$	0.183044	+	0.0594745i	0.0122301	+	0.00397381i
$225$		0			0
$226$	0.0978747	+	0.301227i	0.00651053	+	0.0200373i
$227$	−1.60629	+	10.1417i	−0.106613	+	0.673130i	0.875269	+	0.483637i	$0.160685\pi$
$227$	−1.60629	+	10.1417i	−0.106613	+	0.673130i	−0.981882	+	0.189493i	$0.939315\pi$
$228$	3.95316	+	7.75852i	0.261805	+	0.513820i
$229$	−15.2775	+	11.0998i	−1.00957	+	0.733494i	−0.964118	−	0.265473i	$-0.914472\pi$
$229$	−15.2775	+	11.0998i	−1.00957	+	0.733494i	−0.0454490	+	0.998967i	$0.514472\pi$
$230$		0			0
$231$	−0.0904975	−	0.278523i	−0.00595430	−	0.0183254i
$232$	−0.0527075	−	0.332782i	−0.00346042	−	0.0218482i
$233$	−4.03590	−	25.4817i	−0.264401	−	1.66936i	−0.660251	−	0.751045i	$-0.729550\pi$
$233$	−4.03590	−	25.4817i	−0.264401	−	1.66936i	0.395850	−	0.918315i	$-0.370450\pi$
$234$	0.784734	+	2.41516i	0.0512997	+	0.157884i
$235$		0			0
$236$	−12.1728	+	8.84402i	−0.792379	+	0.575697i
$237$	1.40120	+	2.75001i	0.0910178	+	0.178632i
$238$	−0.0158211	+	0.0998904i	−0.00102553	+	0.00647493i
$239$	3.12536	+	9.61888i	0.202163	+	0.622193i	0.999818	+	0.0190795i	$0.00607357\pi$
$239$	3.12536	+	9.61888i	0.202163	+	0.622193i	−0.797655	+	0.603114i	$0.793926\pi$
$240$		0			0
$241$	−13.5094	−	4.38946i	−0.870215	−	0.282750i	−0.160326	−	0.987064i	$-0.551255\pi$
$241$	−13.5094	−	4.38946i	−0.870215	−	0.282750i	−0.709888	+	0.704314i	$0.751255\pi$
$242$	−1.62248	+	1.62248i	−0.104297	+	0.104297i
$243$	−10.5852	+	10.5852i	−0.679042	+	0.679042i
$244$	−4.42534	+	13.6198i	−0.283303	+	0.871918i
$245$		0			0
$246$	0.420229	+	0.578396i	0.0267928	+	0.0368772i
$247$	23.9012	+	23.9012i	1.52080	+	1.52080i
$248$	−4.16473	+	0.330649i	−0.264461	+	0.0209962i
$249$		−	9.85492i		−	0.624530i
$250$		0			0
$251$	−0.781319	+	1.07539i	−0.0493164	+	0.0678783i	−0.832963	−	0.553329i	$-0.813357\pi$
$251$	−0.781319	+	1.07539i	−0.0493164	+	0.0678783i	0.783647	+	0.621207i	$0.213357\pi$
$252$	0.194085	+	0.380914i	0.0122262	+	0.0239953i
$253$	0.542858	+	0.542858i	0.0341292	+	0.0341292i
$254$	−0.858329			−0.0538563
$255$		0			0
$256$	4.08213	+	12.5635i	0.255133	+	0.785219i
$257$	−11.9807	−	6.10449i	−0.747337	−	0.380787i	0.0384691	−	0.999260i	$-0.487752\pi$
$257$	−11.9807	−	6.10449i	−0.747337	−	0.380787i	−0.785807	+	0.618472i	$0.787752\pi$
$258$	−0.514882	−	0.0815492i	−0.0320551	−	0.00507703i
$259$	0.157501	−	0.484738i	0.00978663	−	0.0301201i
$260$		0			0
$261$	0.661842	−	0.910947i	0.0409670	−	0.0563862i
$262$	−1.38359	−	0.704976i	−0.0854786	−	0.0435535i
$263$	−6.54232	+	1.03620i	−0.403417	+	0.0638949i	−0.354846	−	0.934925i	$-0.615467\pi$
$263$	−6.54232	+	1.03620i	−0.403417	+	0.0638949i	−0.0485708	+	0.998820i	$0.515467\pi$
$264$	−1.48813	+	2.04824i	−0.0915883	+	0.126061i
$265$		0			0
$266$	−0.0839760	−	0.0610121i	−0.00514890	−	0.00374089i
$267$	0.983963	−	6.21250i	0.0602176	−	0.380199i
$268$	−10.4577	+	5.32849i	−0.638808	+	0.325489i
$269$	12.5762	−	9.13717i	0.766787	−	0.557103i	−0.134198	−	0.990955i	$-0.542846\pi$
$269$	12.5762	−	9.13717i	0.766787	−	0.557103i	0.900984	+	0.433851i	$0.142846\pi$
$270$		0			0
$271$	1.82103	−	0.591689i	0.110620	−	0.0359425i	−0.253184	−	0.967418i	$-0.581478\pi$
$271$	1.82103	−	0.591689i	0.110620	−	0.0359425i	0.363804	+	0.931476i	$0.381478\pi$
$272$	−20.7674	+	10.5815i	−1.25921	+	0.641598i
$273$	−0.230400	−	0.230400i	−0.0139444	−	0.0139444i
$274$	0.177309			0.0107116
$275$		0			0
$276$	0.178018	+	0.129338i	0.0107154	+	0.00778522i
$277$	1.76406	+	0.279400i	0.105992	+	0.0167875i	0.209205	−	0.977872i	$-0.432912\pi$
$277$	1.76406	+	0.279400i	0.105992	+	0.0167875i	−0.103213	+	0.994659i	$0.532912\pi$
$278$	0.974084	−	0.974084i	0.0584217	−	0.0584217i
$279$	−10.6230	−	9.06028i	−0.635982	−	0.542425i
$280$		0			0
$281$	−10.0343	+	7.29034i	−0.598596	+	0.434905i	−0.845380	−	0.534165i	$-0.820626\pi$
$281$	−10.0343	+	7.29034i	−0.598596	+	0.434905i	0.246785	+	0.969070i	$0.420626\pi$
$282$	−0.189173	−	1.19439i	−0.0112651	−	0.0711250i
$283$	6.94984	−	3.54112i	0.413125	−	0.210498i	−0.235060	−	0.971981i	$-0.575529\pi$
$283$	6.94984	−	3.54112i	0.413125	−	0.210498i	0.648185	+	0.761483i	$0.275529\pi$
$284$			3.09890i			0.183886i
$285$		0			0
$286$	−1.50477	+	4.63120i	−0.0889789	+	0.273849i
$287$	0.416286	+	0.212108i	0.0245726	+	0.0125203i
$288$	2.52441	−	4.95443i	0.148752	−	0.291943i
$289$	−12.2811	−	16.9035i	−0.722420	−	0.994326i
$290$		0			0
$291$	3.32004	+	4.56964i	0.194624	+	0.267877i
$292$	−3.20632	−	20.2439i	−0.187636	−	1.18468i
$293$	−11.4285	+	22.4296i	−0.667658	+	1.31035i	0.270022	+	0.962854i	$0.412969\pi$
$293$	−11.4285	+	22.4296i	−0.667658	+	1.31035i	−0.937680	+	0.347499i	$0.887031\pi$
$294$	−0.751356	−	0.545892i	−0.0438200	−	0.0318371i
$295$		0			0
$296$	−4.19060	+	1.36161i	−0.243574	+	0.0791419i
$297$	−18.3543	+	2.90704i	−1.06503	+	0.168684i
$298$	1.07148	+	0.169707i	0.0620694	+	0.00983083i
$299$	0.812364	+	0.263953i	0.0469802	+	0.0152648i
$300$		0			0
$301$	−0.323994	+	0.105272i	−0.0186747	+	0.00606778i
$302$	−0.531348	+	1.04283i	−0.0305756	+	0.0600081i
$303$	1.50440	+	2.95255i	0.0864256	+	0.169620i
$304$		−	23.9218i		−	1.37201i
$305$		0			0
$306$	2.77891	+	0.902923i	0.158860	+	0.0516167i
$307$	24.6332	−	3.90151i	1.40589	−	0.222671i	0.593054	−	0.805163i	$-0.297922\pi$
$307$	24.6332	−	3.90151i	1.40589	−	0.222671i	0.812836	+	0.582492i	$0.197922\pi$
$308$	−0.128241	+	0.809680i	−0.00730719	+	0.0461358i
$309$	−13.3864			−0.761524
$310$		0			0
$311$	−1.47644			−0.0837214			−0.0418607	−	0.999123i	$-0.513329\pi$
$311$	−1.47644			−0.0837214			−0.0418607	+	0.999123i	$0.513329\pi$
$312$	−0.440655	+	2.78219i	−0.0249472	+	0.157510i
$313$	2.90446	−	0.460021i	0.164170	−	0.0260019i	−0.0738084	−	0.997272i	$-0.523515\pi$
$313$	2.90446	−	0.460021i	0.164170	−	0.0260019i	0.237978	+	0.971271i	$0.423515\pi$
$314$	−0.493196	−	0.160249i	−0.0278327	−	0.00904339i
$315$		0			0
$316$		−	8.63959i		−	0.486015i
$317$	8.84924	+	17.3676i	0.497023	+	0.975462i	0.994173	+	0.107797i	$0.0343797\pi$
$317$	8.84924	+	17.3676i	0.497023	+	0.975462i	−0.497150	+	0.867664i	$0.665620\pi$
$318$	−0.623185	+	1.22307i	−0.0349465	+	0.0685863i
$319$	2.05347	−	0.667214i	0.114972	−	0.0373568i
$320$		0			0
$321$	8.80162	+	2.85982i	0.491259	+	0.159620i
$322$	−0.00259076		0.000410336i	−0.000144377		2.28671e-5i
$323$	38.4134	−	6.08409i	2.13738	−	0.338528i
$324$	8.98751	−	2.92022i	0.499306	−	0.162234i
$325$		0			0
$326$	−2.12298	−	1.54243i	−0.117581	−	0.0854274i
$327$	−0.856667	+	1.68130i	−0.0473738	+	0.0929763i
$328$	−0.631847	−	3.98933i	−0.0348879	−	0.220274i
$329$	−0.464503	−	0.639334i	−0.0256089	−	0.0352476i
$330$		0			0
$331$	−9.86813	−	13.5823i	−0.542402	−	0.746552i	0.446555	−	0.894756i	$-0.352651\pi$
$331$	−9.86813	−	13.5823i	−0.542402	−	0.746552i	−0.988957	+	0.148204i	$0.952651\pi$
$332$	−12.5239	+	24.5795i	−0.687338	+	1.34898i
$333$	−13.1204	−	6.68516i	−0.718992	−	0.366345i
$334$	0.263843	−	0.812026i	0.0144369	−	0.0444321i
$335$		0			0
$336$			0.230599i			0.0125802i
$337$	−6.97949	+	3.55623i	−0.380197	+	0.193720i	−0.633636	−	0.773631i	$-0.718438\pi$
$337$	−6.97949	+	3.55623i	−0.380197	+	0.193720i	0.253439	+	0.967351i	$0.418438\pi$
$338$	0.462605	+	2.92077i	0.0251624	+	0.158869i
$339$	−0.949877	+	0.690126i	−0.0515903	+	0.0374825i
$340$		0			0
$341$	−6.26786	−	26.0288i	−0.339424	−	1.40954i
$342$	−2.12054	+	2.12054i	−0.114666	+	0.114666i
$343$	−1.19954	−	0.189989i	−0.0647691	−	0.0102584i
$344$	2.38264	+	1.73109i	0.128463	+	0.0933339i
$345$		0			0
$346$	−0.163440			−0.00878661
$347$	−8.99045	−	8.99045i	−0.482632	−	0.482632i	0.423339	−	0.905971i	$-0.360858\pi$
$347$	−8.99045	−	8.99045i	−0.482632	−	0.482632i	−0.905971	+	0.423339i	$0.860858\pi$
$348$	0.551404	−	0.280954i	0.0295584	−	0.0150607i
$349$	−22.9814	+	7.46711i	−1.23017	+	0.399705i	−0.850775	−	0.525530i	$-0.823867\pi$
$349$	−22.9814	+	7.46711i	−1.23017	+	0.399705i	−0.379392	+	0.925236i	$0.623867\pi$
$350$		0			0
$351$	−16.7271	+	12.1529i	−0.892825	+	0.648675i
$352$	9.50039	−	4.84069i	0.506372	−	0.258010i
$353$	−4.96495	+	31.3475i	−0.264258	+	1.66846i	0.396634	+	0.917977i	$0.370178\pi$
$353$	−4.96495	+	31.3475i	−0.264258	+	1.66846i	−0.660892	+	0.750481i	$0.729822\pi$
$354$	0.823128	+	0.598037i	0.0437488	+	0.0317853i
$355$		0			0
$356$	−10.3491	+	14.2444i	−0.548504	+	0.754950i
$357$	−0.370293	+	0.0586487i	−0.0195980	+	0.00310402i
$358$	0.937992	+	0.477931i	0.0495744	+	0.0252594i
$359$	−7.36358	+	10.1351i	−0.388635	+	0.534910i	−0.957846	−	0.287281i	$-0.907249\pi$
$359$	−7.36358	+	10.1351i	−0.388635	+	0.534910i	0.569211	+	0.822191i	$0.307249\pi$
$360$		0			0
$361$	−6.46369	+	19.8932i	−0.340194	+	1.04701i
$362$	−1.58113	−	0.250426i	−0.0831022	−	0.0131621i
$363$	−7.57874	−	3.86156i	−0.397781	−	0.202679i
$364$	0.281851	+	0.867447i	0.0147730	+	0.0454666i
$365$		0			0
$366$	0.968373			0.0506177
$367$	5.44698	+	5.44698i	0.284330	+	0.284330i	0.834833	−	0.550503i	$-0.185564\pi$
$367$	5.44698	+	5.44698i	0.284330	+	0.284330i	−0.550503	+	0.834833i	$0.685564\pi$
$368$	−0.274442	−	0.538623i	−0.0143063	−	0.0280777i
$369$	7.93403	−	10.9203i	0.413029	−	0.568486i
$370$		0			0
$371$			0.897043i			0.0465721i
$372$	−2.94143	−	7.08748i	−0.152506	−	0.367469i
$373$	−6.52208	−	6.52208i	−0.337701	−	0.337701i	0.517801	−	0.855501i	$-0.326751\pi$
$373$	−6.52208	−	6.52208i	−0.337701	−	0.337701i	−0.855501	+	0.517801i	$0.826751\pi$
$374$	3.29333	+	4.53287i	0.170294	+	0.234389i
$375$		0			0
$376$	−2.11116	+	6.49749i	−0.108875	+	0.335083i
$377$	1.69868	−	1.69868i	0.0874864	−	0.0874864i
$378$	0.0448962	−	0.0448962i	0.00230921	−	0.00230921i
$379$	−25.7530	−	8.36766i	−1.32284	−	0.429818i	−0.439372	−	0.898305i	$-0.644799\pi$
$379$	−25.7530	−	8.36766i	−1.32284	−	0.429818i	−0.883470	+	0.468487i	$0.844799\pi$
$380$		0			0
$381$	−0.983236	−	3.02609i	−0.0503727	−	0.155031i
$382$	−0.259319	+	1.63727i	−0.0132679	+	0.0837702i
$383$	−7.17114	−	14.0742i	−0.366428	−	0.719156i	0.632014	−	0.774957i	$-0.282229\pi$
$383$	−7.17114	−	14.0742i	−0.366428	−	0.719156i	−0.998442	+	0.0558014i	$0.982229\pi$
$384$	3.28613	−	2.38751i	0.167694	−	0.121837i
$385$		0			0
$386$	1.17492	+	3.61602i	0.0598016	+	0.184051i
$387$	1.53967	+	9.72110i	0.0782658	+	0.494151i
$388$	−2.47341	−	15.6165i	−0.125568	−	0.792807i
$389$	−10.0516	−	30.9357i	−0.509637	−	1.56850i	−0.792833	−	0.609439i	$-0.791395\pi$
$389$	−10.0516	−	30.9357i	−0.509637	−	1.56850i	0.283196	−	0.959062i	$-0.408605\pi$
$390$		0			0
$391$	0.795115	−	0.577685i	0.0402107	−	0.0292148i
$392$	2.38203	+	4.67500i	0.120311	+	0.236123i
$393$	0.900496	−	5.68551i	0.0454240	−	0.286796i
$394$	−0.565960	−	1.74185i	−0.0285127	−	0.0877530i
$395$		0			0
$396$	22.5250	+	7.31881i	1.13192	+	0.367784i
$397$	2.56560	−	2.56560i	0.128764	−	0.128764i	−0.639788	−	0.768552i	$-0.720978\pi$
$397$	2.56560	−	2.56560i	0.128764	−	0.128764i	0.768552	+	0.639788i	$0.220978\pi$
$398$	−1.71531	+	1.71531i	−0.0859809	+	0.0859809i
$399$	0.118905	−	0.365953i	0.00595272	−	0.0183206i
$400$		0			0
$401$	6.24840	+	8.60018i	0.312030	+	0.429473i	0.936013	−	0.351965i	$-0.114486\pi$
$401$	6.24840	+	8.60018i	0.312030	+	0.429473i	−0.623983	+	0.781438i	$0.714486\pi$
$402$	0.561204	+	0.561204i	0.0279903	+	0.0279903i
$403$	−19.3611	−	22.6375i	−0.964446	−	1.12765i
$404$		−	9.27590i		−	0.461493i
$405$		0			0
$406$	−0.00433618	+	0.00596824i	−0.000215201	+	0.000296199i
$407$	−12.8192	−	25.1590i	−0.635422	−	1.24709i
$408$	2.29182	+	2.29182i	0.113462	+	0.113462i
$409$	27.1411			1.34204			0.671020	−	0.741439i	$-0.265856\pi$
$409$	27.1411			1.34204			0.671020	+	0.741439i	$0.265856\pi$
$410$		0			0
$411$	0.203112	+	0.625113i	0.0100188	+	0.0308346i
$412$	33.3874	+	17.0117i	1.64488	+	0.838108i
$413$	0.656709	+	0.104012i	0.0323145	+	0.00511812i
$414$	−0.0234182	+	0.0720739i	−0.00115094	+	0.00354224i
$415$		0			0
$416$	6.97304	−	9.59757i	0.341882	−	0.470560i
$417$	4.55003	+	2.31836i	0.222816	+	0.113530i
$418$	−5.67975	+	0.899585i	−0.277806	+	0.0440001i
$419$	12.4104	−	17.0814i	0.606285	−	0.834480i	−0.389980	−	0.920823i	$-0.627518\pi$
$419$	12.4104	−	17.0814i	0.606285	−	0.834480i	0.996265	+	0.0863430i	$0.0275181\pi$
$420$		0			0
$421$	−8.34200	−	6.06082i	−0.406564	−	0.295386i	0.365645	−	0.930754i	$-0.380848\pi$
$421$	−8.34200	−	6.06082i	−0.406564	−	0.295386i	−0.772209	+	0.635368i	$0.780848\pi$
$422$	0.139076	−	0.878089i	0.00677010	−	0.0427447i
$423$	−20.3430	+	10.3653i	−0.989112	+	0.503978i
$424$	6.27393	−	4.55828i	0.304689	−	0.221370i
$425$		0			0
$426$	0.199294	−	0.0647544i	0.00965580	−	0.00313736i
$427$	0.563854	−	0.287298i	0.0272868	−	0.0139033i
$428$	−18.3181	−	18.3181i	−0.885440	−	0.885440i
$429$	−18.0513			−0.871527
$430$		0			0
$431$	26.6952	+	19.3952i	1.28586	+	0.934234i	0.999713	−	0.0239508i	$-0.00762449\pi$
$431$	26.6952	+	19.3952i	1.28586	+	0.934234i	0.286150	+	0.958185i	$0.407624\pi$
$432$	14.4525	+	2.28904i	0.695344	+	0.110132i
$433$	−20.1332	+	20.1332i	−0.967542	+	0.967542i	−0.999490	−	0.0319476i	$-0.989829\pi$
$433$	−20.1332	+	20.1332i	−0.967542	+	0.967542i	0.0319476	+	0.999490i	$0.489829\pi$
$434$	0.0695985	+	0.0593601i	0.00334083	+	0.00284938i
$435$		0			0
$436$	4.27329	−	3.10472i	0.204653	−	0.148689i
$437$	0.157797	+	0.996291i	0.00754845	+	0.0476591i
$438$	−1.23491	+	0.629216i	−0.0590061	+	0.0300651i
$439$			5.16012i			0.246279i	0.992389	+	0.123139i	$0.0392962\pi$
$439$			5.16012i			0.246279i	−0.992389	+	0.123139i	$0.960704\pi$
$440$		0			0
$441$	−5.41849	+	16.6764i	−0.258023	+	0.794115i
$442$	5.55444	+	2.83013i	0.264198	+	0.134615i
$443$	−6.69351	+	13.1367i	−0.318018	+	0.624146i	−0.993577	−	0.113161i	$-0.963903\pi$
$443$	−6.69351	+	13.1367i	−0.318018	+	0.624146i	0.675559	+	0.737306i	$0.263903\pi$
$444$	−4.75705	−	6.54751i	−0.225760	−	0.310731i
$445$		0			0
$446$	−0.906388	−	1.24754i	−0.0429187	−	0.0590726i
$447$	0.629101	+	3.97199i	0.0297555	+	0.187869i
$448$	0.281857	−	0.553176i	0.0133165	−	0.0261351i
$449$	0.484943	+	0.352332i	0.0228859	+	0.0166276i	0.599169	−	0.800622i	$-0.295498\pi$
$449$	0.484943	+	0.352332i	0.0228859	+	0.0166276i	−0.576284	+	0.817250i	$0.695498\pi$
$450$		0			0
$451$	24.6166	−	7.99843i	1.15915	−	0.376631i
$452$	3.24615	−	0.514140i	0.152686	−	0.0241831i
$453$	−4.28523	−	0.678714i	−0.201338	−	0.0318888i
$454$	−1.84849	−	0.600610i	−0.0867538	−	0.0281880i
$455$		0			0
$456$	−3.16370	+	1.02795i	−0.148154	+	0.0481381i
$457$	−16.1712	+	31.7377i	−0.756456	+	1.48463i	0.114583	+	0.993414i	$0.463447\pi$
$457$	−16.1712	+	31.7377i	−0.756456	+	1.48463i	−0.871039	+	0.491214i	$0.836553\pi$
$458$	−1.62278	−	3.18489i	−0.0758276	−	0.148820i
$459$			23.7898i			1.11041i
$460$		0			0
$461$	−10.4533	−	3.39648i	−0.486858	−	0.158190i	0.0552940	−	0.998470i	$-0.482390\pi$
$461$	−10.4533	−	3.39648i	−0.486858	−	0.158190i	−0.542152	+	0.840280i	$0.682390\pi$
$462$	0.0547510	−	0.00867171i	0.00254725	−	0.000403444i
$463$	1.19930	−	7.57209i	0.0557363	−	0.351905i	−0.944021	−	0.329885i	$-0.892990\pi$
$463$	1.19930	−	7.57209i	0.0557363	−	0.351905i	0.999758	−	0.0220203i	$-0.00700983\pi$
$464$	−1.70014			−0.0789272
$465$		0			0
$466$	4.88344			0.226221
$467$	2.17419	−	13.7273i	0.100609	−	0.635223i	−0.884923	−	0.465737i	$-0.845789\pi$
$467$	2.17419	−	13.7273i	0.100609	−	0.635223i	0.985533	−	0.169486i	$-0.0542107\pi$
$468$	26.0268	−	4.12225i	1.20309	−	0.190551i
$469$	0.493270	+	0.160273i	0.0227771	+	0.00740073i
$470$		0			0
$471$		−	1.92236i		−	0.0885779i
$472$	−2.60957	−	5.12157i	−0.120115	−	0.235739i
$473$	−8.56820	+	16.8160i	−0.393966	+	0.773202i
$474$	−0.555620	+	0.180532i	−0.0255205	+	0.00829210i
$475$		0			0
$476$	0.998094	+	0.324300i	0.0457476	+	0.0148643i
$477$	25.5975	+	4.05425i	1.17203	+	0.185631i
$478$	−1.89085	+	0.299480i	−0.0864852	+	0.0136979i
$479$	−0.0578624	+	0.0188006i	−0.00264380	+	0.000859023i	−0.310339	−	0.950626i	$-0.600442\pi$
$479$	−0.0578624	+	0.0188006i	−0.00264380	+	0.000859023i	0.307695	+	0.951485i	$0.400442\pi$
$480$		0			0
$481$	−25.4164	−	18.4661i	−1.15889	−	0.841981i
$482$	1.22066	−	2.39567i	0.0555994	−	0.109120i
$483$	−0.00152111	−	0.00960392i	−6.92130e−5	−	0.000436994i
$484$	13.9950	+	19.2625i	0.636138	+	0.875569i
$485$		0			0
$486$	−1.66553	−	2.29240i	−0.0755498	−	0.103985i
$487$	2.00159	−	3.92834i	0.0907006	−	0.178010i	−0.841200	−	0.540725i	$-0.818150\pi$
$487$	2.00159	−	3.92834i	0.0907006	−	0.178010i	0.931900	+	0.362715i	$0.118150\pi$
$488$	−4.87457	−	2.48372i	−0.220661	−	0.112433i
$489$	3.00602	−	9.25157i	0.135937	−	0.418371i
$490$		0			0
$491$		−	19.9221i		−	0.899072i	−0.893262	−	0.449536i	$-0.851589\pi$
$491$		−	19.9221i		−	0.899072i	0.893262	−	0.449536i	$-0.148411\pi$
$492$	6.61012	−	3.36803i	0.298007	−	0.151842i
$493$	−0.432401	−	2.73007i	−0.0194744	−	0.122956i
$494$	−5.17619	+	3.76072i	−0.232888	+	0.169203i
$495$		0			0
$496$	−1.63959	+	21.0174i	−0.0736197	+	0.943710i
$497$	0.0968311	−	0.0968311i	0.00434347	−	0.00434347i
$498$	1.84243	+	0.291812i	0.0825613	+	0.0130764i
$499$	29.7517	+	21.6159i	1.33187	+	0.967660i	0.999701	+	0.0244406i	$0.00778047\pi$
$499$	29.7517	+	21.6159i	1.33187	+	0.967660i	0.332169	+	0.943220i	$0.392220\pi$
$500$		0			0
$501$	3.16509			0.141406
$502$	−0.177915	−	0.177915i	−0.00794074	−	0.00794074i
$503$	−5.99366	+	3.05392i	−0.267244	+	0.136168i	−0.582478	−	0.812846i	$-0.697917\pi$
$503$	−5.99366	+	3.05392i	−0.267244	+	0.136168i	0.315234	+	0.949014i	$0.397917\pi$
$504$	−0.155326	+	0.0504684i	−0.00691876	+	0.00224804i
$505$		0			0
$506$	−0.117565	+	0.0854157i	−0.00522638	+	0.00379719i
$507$	−9.76744	+	4.97676i	−0.433787	+	0.221026i
$508$	−1.39331	+	8.79700i	−0.0618181	+	0.390304i
$509$	3.65345	+	2.65438i	0.161936	+	0.117654i	0.665802	−	0.746128i	$-0.268089\pi$
$509$	3.65345	+	2.65438i	0.161936	+	0.117654i	−0.503866	+	0.863782i	$0.668089\pi$
$510$		0			0
$511$	−0.532371	+	0.732746i	−0.0235507	+	0.0324148i
$512$	−13.9047	+	2.20229i	−0.614507	+	0.0973283i
$513$	−21.7553	−	11.0849i	−0.960520	−	0.489409i
$514$	1.49603	−	2.05910i	0.0659869	−	0.0908231i
$515$		0			0
$516$	−1.67160	+	5.14464i	−0.0735879	+	0.226480i
$517$	−43.2416	−	6.84880i	−1.90177	−	0.301210i
$518$	0.0859606	+	0.0437991i	0.00377689	+	0.00192442i
$519$	−0.187225	−	0.576219i	−0.00821827	−	0.0252932i
$520$		0			0
$521$	−31.6931			−1.38850			−0.694251	−	0.719733i	$-0.744264\pi$
$521$	−31.6931			−1.38850			−0.694251	+	0.719733i	$0.744264\pi$
$522$	0.150709	+	0.150709i	0.00659634	+	0.00659634i
$523$	−0.0522529	−	0.102552i	−0.00228486	−	0.00448429i	0.889861	−	0.456231i	$-0.150801\pi$
$523$	−0.0522529	−	0.102552i	−0.00228486	−	0.00448429i	−0.892146	+	0.451747i	$0.850801\pi$
$524$	−9.47125	+	13.0361i	−0.413754	+	0.569483i
$525$		0			0
$526$		−	1.25380i		−	0.0546685i
$527$	−34.1666	+	2.71257i	−1.48832	+	0.118161i
$528$	9.03346	+	9.03346i	0.393131	+	0.393131i
$529$	−13.5041	−	18.5868i	−0.587134	−	0.808120i
$530$		0			0
$531$	5.93608	−	18.2694i	0.257604	−	0.792824i
$532$	−0.761630	+	0.761630i	−0.0330208	+	0.0330208i
$533$	20.3634	−	20.3634i	0.882038	−	0.882038i
$534$	1.13232	+	0.367914i	0.0490005	+	0.0159212i
$535$		0			0
$536$	−1.38558	−	4.26437i	−0.0598478	−	0.184193i
$537$	−0.610482	+	3.85443i	−0.0263442	+	0.166331i
$538$	1.33585	+	2.62175i	0.0575926	+	0.113032i
$539$	−27.2020	+	19.7634i	−1.17167	+	0.851271i
$540$		0			0
$541$	6.04315	+	18.5989i	0.259815	+	0.799629i	0.992843	+	0.119430i	$0.0381067\pi$
$541$	6.04315	+	18.5989i	0.259815	+	0.799629i	−0.733027	+	0.680199i	$0.761893\pi$
$542$	0.0566972	+	0.357972i	0.00243535	+	0.0153762i
$543$	−0.928328	−	5.86123i	−0.0398383	−	0.251529i
$544$	−4.21808	−	12.9819i	−0.180849	−	0.556595i
$545$		0			0
$546$	0.0498968	−	0.0362522i	0.00213539	−	0.00155145i
$547$	−0.746358	−	1.46481i	−0.0319120	−	0.0626308i	0.874500	−	0.485025i	$-0.161190\pi$
$547$	−0.746358	−	1.46481i	−0.0319120	−	0.0626308i	−0.906412	+	0.422395i	$0.861190\pi$
$548$	0.287822	−	1.81724i	0.0122951	−	0.0776285i
$549$	−5.64980	−	17.3883i	−0.241128	−	0.742114i
$550$		0			0
$551$	2.69808	+	0.876659i	0.114942	+	0.0373469i
$552$	−0.0594406	+	0.0594406i	−0.00252996	+	0.00252996i
$553$	−0.269960	+	0.269960i	−0.0114799	+	0.0114799i
$554$	−0.104471	+	0.321528i	−0.00443853	+	0.0136604i
$555$		0			0
$556$	−8.40217	−	11.5646i	−0.356331	−	0.490448i
$557$	−12.0788	−	12.0788i	−0.511793	−	0.511793i	0.403282	−	0.915076i	$-0.367869\pi$
$557$	−12.0788	−	12.0788i	−0.511793	−	0.511793i	−0.915076	+	0.403282i	$0.867869\pi$
$558$	2.00842	−	1.71774i	0.0850233	−	0.0727178i
$559$			20.9984i			0.888137i
$560$		0			0
$561$	−12.2083	+	16.8033i	−0.515437	+	0.709438i
$562$	−1.06584	−	2.09184i	−0.0449599	−	0.0882388i
$563$	2.42308	+	2.42308i	0.102121	+	0.102121i	0.756321	−	0.654201i	$-0.226995\pi$
$563$	2.42308	+	2.42308i	0.102121	+	0.102121i	−0.654201	+	0.756321i	$0.726995\pi$
$564$	−12.5484			−0.528383
$565$		0			0
$566$	0.456241	+	1.40417i	0.0191772	+	0.0590215i
$567$	−0.372079	−	0.189584i	−0.0156259	−	0.00796178i
$568$	−1.16928	−	0.185196i	−0.0490620	−	0.00777065i
$569$	4.85525	−	14.9429i	0.203543	−	0.626440i	−0.796227	−	0.604997i	$-0.793174\pi$
$569$	4.85525	−	14.9429i	0.203543	−	0.626440i	0.999770	−	0.0214424i	$-0.00682585\pi$
$570$		0			0
$571$	21.0462	−	28.9676i	0.880756	−	1.21226i	−0.0954551	−	0.995434i	$-0.530431\pi$
$571$	21.0462	−	28.9676i	0.880756	−	1.21226i	0.976211	−	0.216823i	$-0.0695694\pi$
$572$	45.0225	+	22.9401i	1.88249	+	0.959174i
$573$	−6.06936	+	0.961293i	−0.253551	+	0.0401586i
$574$	−0.0519813	+	0.0715461i	−0.00216966	+	0.00298628i
$575$		0			0
$576$	−14.5113	−	10.5430i	−0.604636	−	0.439294i
$577$	3.98467	−	25.1582i	0.165884	−	1.04735i	−0.754491	−	0.656311i	$-0.772116\pi$
$577$	3.98467	−	25.1582i	0.165884	−	1.04735i	0.920374	−	0.391038i	$-0.127884\pi$
$578$	3.52386	−	1.79550i	0.146573	−	0.0746829i
$579$	−11.4026	+	8.28448i	−0.473876	+	0.344291i
$580$		0			0
$581$	1.15937	−	0.376701i	0.0480986	−	0.0156282i
$582$	−0.952627	+	0.485388i	−0.0394877	+	0.0201200i
$583$	35.1407	+	35.1407i	1.45538	+	1.45538i
$584$	7.83006			0.324010
$585$		0			0
$586$	−3.85493	−	2.80077i	−0.159246	−	0.115699i
$587$	−21.2521	−	3.36600i	−0.877168	−	0.138930i	−0.298418	−	0.954435i	$-0.596459\pi$
$587$	−21.2521	−	3.36600i	−0.877168	−	0.138930i	−0.578750	+	0.815505i	$0.696459\pi$
$588$	−6.81451	+	6.81451i	−0.281026	+	0.281026i
$589$	13.4394	−	32.5086i	0.553759	−	1.33949i
$590$		0			0
$591$	5.49267	−	3.99066i	0.225938	−	0.164154i
$592$	3.47815	+	21.9602i	0.142951	+	0.902557i
$593$	30.9467	−	15.7681i	1.27083	−	0.647520i	0.317159	−	0.948372i	$-0.397271\pi$
$593$	30.9467	−	15.7681i	1.27083	−	0.647520i	0.953671	+	0.300852i	$0.0972712\pi$
$594$		−	3.51752i		−	0.144326i
$595$		0			0
$596$	3.47864	−	10.7062i	0.142491	−	0.438541i
$597$	−8.01238	−	4.08251i	−0.327925	−	0.167086i
$598$	−0.0734022	+	0.144060i	−0.00300164	+	0.00589105i
$599$	21.6049	+	29.7365i	0.882751	+	1.21500i	0.975651	+	0.219327i	$0.0703862\pi$
$599$	21.6049	+	29.7365i	0.882751	+	1.21500i	−0.0929005	+	0.995675i	$0.529614\pi$
$600$		0			0
$601$	18.6239	+	25.6337i	0.759686	+	1.04562i	0.997240	+	0.0742443i	$0.0236545\pi$
$601$	18.6239	+	25.6337i	0.759686	+	1.04562i	−0.237554	+	0.971374i	$0.576346\pi$
$602$	−0.0100874	−	0.0636896i	−0.000411133	−	0.00259579i
$603$	6.80284	−	13.3513i	0.277033	−	0.543708i
$604$	9.82543	+	7.13859i	0.399791	+	0.290465i
$605$		0			0
$606$	−0.596542	+	0.193828i	−0.0242329	+	0.00787374i
$607$	10.9881	−	1.74034i	0.445993	−	0.0706384i	0.0706014	−	0.997505i	$-0.477508\pi$
$607$	10.9881	−	1.74034i	0.445993	−	0.0706384i	0.375392	+	0.926866i	$0.377508\pi$
$608$	13.8371	+	2.19158i	0.561169	+	0.0888805i
$609$	−0.0260086	−	0.00845071i	−0.00105392	−	0.000342440i
$610$		0			0
$611$	−46.3268	+	15.0525i	−1.87418	+	0.608958i
$612$	13.7650	−	27.0154i	0.556418	−	1.09203i
$613$	6.58033	+	12.9146i	0.265777	+	0.521617i	0.984870	−	0.173298i	$-0.0554422\pi$
$613$	6.58033	+	12.9146i	0.265777	+	0.521617i	−0.719092	+	0.694914i	$0.755442\pi$
$614$			4.72083i			0.190517i
$615$		0			0
$616$	−0.297845	−	0.0967758i	−0.0120005	−	0.00389921i
$617$	−6.82628	+	1.08118i	−0.274816	+	0.0435265i	−0.292321	−	0.956320i	$-0.594428\pi$
$617$	−6.82628	+	1.08118i	−0.274816	+	0.0435265i	0.0175054	+	0.999847i	$0.494428\pi$
$618$	0.396381	−	2.50265i	0.0159448	−	0.100671i
$619$	−33.5305			−1.34770			−0.673852	−	0.738866i	$-0.735362\pi$
$619$	−33.5305			−1.34770			−0.673852	+	0.738866i	$0.735362\pi$
$620$		0			0
$621$	−0.617012			−0.0247598
$622$	0.0437187	−	0.276029i	0.00175296	−	0.0110677i
$623$	0.768471	−	0.121714i	0.0307881	−	0.00487636i
$624$	13.5182	+	4.39233i	0.541161	+	0.175834i
$625$		0			0
$626$			0.556626i			0.0222472i
$627$	−9.67784	−	18.9938i	−0.386496	−	0.758540i
$628$	−2.44299	+	4.79464i	−0.0974859	+	0.191327i
$629$	−34.3788	+	11.1704i	−1.37077	+	0.445391i
$630$		0			0
$631$	−15.2364	−	4.95061i	−0.606552	−	0.197081i	−0.0103916	−	0.999946i	$-0.503308\pi$
$631$	−15.2364	−	4.95061i	−0.606552	−	0.197081i	−0.596161	+	0.802865i	$0.703308\pi$
$632$	3.25990	+	0.516317i	0.129672	+	0.0205380i
$633$	3.25507	−	0.515553i	0.129378	−	0.0204914i
$634$	−3.50900	+	1.14014i	−0.139360	+	0.0452809i
$635$		0			0
$636$	11.5236	+	8.37240i	0.456941	+	0.331987i
$637$	−16.9837	+	33.3325i	−0.672921	+	1.32068i
$638$	0.0639342	+	0.403665i	0.00253118	+	0.0159812i
$639$	−2.32548	−	3.20075i	−0.0919947	−	0.126620i
$640$		0			0
$641$	9.66011	+	13.2960i	0.381551	+	0.525161i	0.955995	−	0.293384i	$-0.0947814\pi$
$641$	9.66011	+	13.2960i	0.381551	+	0.525161i	−0.574443	+	0.818544i	$0.694781\pi$
$642$	−0.795282	+	1.56083i	−0.0313873	+	0.0616010i
$643$	39.0128	+	19.8780i	1.53851	+	0.783912i	0.998337	−	0.0576395i	$-0.0183574\pi$
$643$	39.0128	+	19.8780i	1.53851	+	0.783912i	0.540177	+	0.841552i	$0.318357\pi$
$644$	−0.00841105	+	0.0258866i	−0.000331442	+	0.00102007i
$645$		0			0
$646$			7.36175i			0.289644i
$647$	22.1017	−	11.2614i	0.868909	−	0.442731i	0.0380902	−	0.999274i	$-0.487873\pi$
$647$	22.1017	−	11.2614i	0.868909	−	0.442731i	0.830819	+	0.556543i	$0.187873\pi$
$648$	0.564750	+	3.56569i	0.0221855	+	0.140074i
$649$	29.8004	−	21.6513i	1.16977	−	0.849887i
$650$		0			0
$651$	−0.129551	+	0.313372i	−0.00507751	+	0.0122820i
$652$	−19.2546	+	19.2546i	−0.754067	+	0.754067i
$653$	21.1187	+	3.34487i	0.826437	+	0.130895i	0.555304	−	0.831647i	$-0.312602\pi$
$653$	21.1187	+	3.34487i	0.826437	+	0.130895i	0.271133	+	0.962542i	$0.412602\pi$
$654$	−0.288962	−	0.209943i	−0.0112993	−	0.00820943i
$655$		0			0
$656$	−20.3810			−0.795744
$657$	18.5032	+	18.5032i	0.721877	+	0.721877i
$658$	0.133281	−	0.0679102i	0.00519584	−	0.00264741i
$659$	−3.82083	+	1.24146i	−0.148839	+	0.0483606i	−0.382489	−	0.923960i	$-0.624933\pi$
$659$	−3.82083	+	1.24146i	−0.148839	+	0.0483606i	0.233650	+	0.972321i	$0.424933\pi$
$660$		0			0
$661$	1.57891	−	1.14715i	0.0614127	−	0.0446189i	−0.556655	−	0.830744i	$-0.687916\pi$
$661$	1.57891	−	1.14715i	0.0614127	−	0.0446189i	0.618068	+	0.786125i	$0.287916\pi$
$662$	2.83149	−	1.44272i	0.110049	−	0.0560728i
$663$	−3.61504	+	22.8245i	−0.140397	+	0.886430i
$664$	−8.52592	−	6.19444i	−0.330870	−	0.240391i
$665$		0			0
$666$	1.63833	−	2.25497i	0.0634841	−	0.0873783i
$667$	0.0708072	−	0.0112148i	0.00274167	−	0.000434237i
$668$	−7.89416	−	4.02227i	−0.305434	−	0.155626i
$669$	3.35998	−	4.62461i	0.129904	−	0.178798i
$670$		0			0
$671$	10.8338	−	33.3430i	0.418234	−	1.28719i
$672$	−0.133385	−	0.0211262i	−0.00514545	−	0.000814960i
$673$	−36.7630	−	18.7317i	−1.41711	−	0.722053i	−0.433297	−	0.901251i	$-0.642650\pi$
$673$	−36.7630	−	18.7317i	−1.41711	−	0.722053i	−0.983813	+	0.179198i	$0.942650\pi$
$674$	−0.458187	−	1.41016i	−0.0176487	−	0.0543172i
$675$		0			0
$676$	30.6859			1.18023
$677$	12.4000	+	12.4000i	0.476572	+	0.476572i	0.904034	−	0.427461i	$-0.140592\pi$
$677$	12.4000	+	12.4000i	0.476572	+	0.476572i	−0.427461	+	0.904034i	$0.640592\pi$
$678$	−0.100896	−	0.198020i	−0.00387489	−	0.00760491i
$679$	−0.410680	+	0.565253i	−0.0157605	+	0.0216924i
$680$		0			0
$681$		−	7.20497i		−	0.276095i
$682$	5.05182	−	0.401077i	0.193444	−	0.0153580i
$683$	3.74664	+	3.74664i	0.143361	+	0.143361i	0.775145	−	0.631784i	$-0.217677\pi$
$683$	3.74664	+	3.74664i	0.143361	+	0.143361i	−0.631784	+	0.775145i	$0.717677\pi$
$684$	18.2912	+	25.1757i	0.699382	+	0.962616i
$685$		0			0
$686$	0.0710388	−	0.218635i	0.00271227	−	0.00834752i
$687$	9.36958	−	9.36958i	0.357472	−	0.357472i
$688$	10.5083	−	10.5083i	0.400624	−	0.400624i
$689$	52.5866	+	17.0864i	2.00339	+	0.650940i
$690$		0			0
$691$	13.5458	+	41.6897i	0.515307	+	1.58595i	0.782724	+	0.622369i	$0.213830\pi$
$691$	13.5458	+	41.6897i	0.515307	+	1.58595i	−0.267417	+	0.963581i	$0.586170\pi$
$692$	−0.265310	+	1.67510i	−0.0100856	+	0.0636778i
$693$	−0.475146	−	0.932526i	−0.0180493	−	0.0354237i
$694$	1.94703	−	1.41460i	0.0739081	−	0.0536974i
$695$		0			0
$696$	0.0730571	+	0.224847i	0.00276922	+	0.00852279i
$697$	−5.18354	−	32.7276i	−0.196341	−	1.23965i
$698$	−0.715518	−	4.51761i	−0.0270828	−	0.170994i
$699$	5.59410	+	17.2169i	0.211588	+	0.651202i
$700$		0			0
$701$	40.8000	−	29.6430i	1.54100	−	1.11960i	0.591289	−	0.806460i	$-0.298619\pi$
$701$	40.8000	−	29.6430i	1.54100	−	1.11960i	0.949707	−	0.313139i	$-0.101381\pi$
$702$	−1.77675	−	3.48707i	−0.0670592	−	0.131611i
$703$	5.80378	−	36.6436i	0.218894	−	1.38204i
$704$	−10.6286	−	32.7116i	−0.400582	−	1.23286i
$705$		0			0
$706$	−5.71356	−	1.85645i	−0.215033	−	0.0698684i
$707$	−0.289843	+	0.289843i	−0.0109007	+	0.0109007i
$708$	7.46545	−	7.46545i	0.280569	−	0.280569i
$709$	−0.248780	+	0.765667i	−0.00934314	+	0.0287552i	−0.955619	−	0.294604i	$-0.904812\pi$
$709$	−0.248780	+	0.765667i	−0.00934314	+	0.0287552i	0.946276	+	0.323359i	$0.104812\pi$
$710$		0			0
$711$	6.48333	+	8.92354i	0.243144	+	0.334659i
$712$	−4.75622	−	4.75622i	−0.178247	−	0.178247i
$713$	−0.0703532	−	0.886144i	−0.00263475	−	0.0331863i
$714$		−	0.0709649i		−	0.00265580i
$715$		0			0
$716$	6.42094	−	8.83766i	0.239962	−	0.330279i
$717$	−3.22185	−	6.32323i	−0.120322	−	0.236145i
$718$	−1.67677	−	1.67677i	−0.0625765	−	0.0625765i
$719$	−14.4497			−0.538884			−0.269442	−	0.963017i	$-0.586839\pi$
$719$	−14.4497			−0.538884			−0.269442	+	0.963017i	$0.586839\pi$
$720$		0			0
$721$	−0.511689	−	1.57482i	−0.0190563	−	0.0586493i
$722$	−3.52774	−	1.79747i	−0.131289	−	0.0668950i
$723$	9.84439	+	1.55920i	0.366117	+	0.0579872i
$724$	−5.13323	+	15.7984i	−0.190775	+	0.587145i
$725$		0			0
$726$	0.946352	−	1.30254i	0.0351224	−	0.0483418i
$727$	−31.3661	−	15.9818i	−1.16331	−	0.592734i	−0.237743	−	0.971328i	$-0.576408\pi$
$727$	−31.3661	−	15.9818i	−1.16331	−	0.592734i	−0.925563	+	0.378594i	$0.876408\pi$
$728$	−0.344150	+	0.0545080i	−0.0127550	+	0.00202020i
$729$	−2.30976	+	3.17912i	−0.0855468	+	0.117745i
$730$		0			0
$731$	19.5466	+	14.2015i	0.722958	+	0.525260i
$732$	1.57194	−	9.92485i	0.0581007	−	0.366833i
$733$	−8.91679	+	4.54333i	−0.329349	+	0.167812i	−0.610844	−	0.791751i	$-0.709170\pi$
$733$	−8.91679	+	4.54333i	−0.329349	+	0.167812i	0.281495	+	0.959563i	$0.409170\pi$
$734$	−1.17963	+	0.857052i	−0.0435410	+	0.0316344i
$735$		0			0
$736$	0.336699	−	0.109400i	0.0124109	−	0.00403254i
$737$	25.6019	−	13.0448i	0.943057	−	0.480512i
$738$	1.80667	+	1.80667i	0.0665043	+	0.0665043i
$739$	32.2294			1.18558			0.592788	−	0.805359i	$-0.298027\pi$
$739$	32.2294			1.18558			0.592788	+	0.805359i	$0.298027\pi$
$740$		0			0
$741$	−19.1881	−	13.9410i	−0.704893	−	0.512135i
$742$	−0.167707	−	0.0265622i	−0.00615671	−	0.000975128i
$743$	−32.5904	+	32.5904i	−1.19563	+	1.19563i	−0.220163	+	0.975463i	$0.570659\pi$
$743$	−32.5904	+	32.5904i	−1.19563	+	1.19563i	−0.975463	+	0.220163i	$0.929341\pi$
$744$	2.85004	−	0.686304i	0.104488	−	0.0251611i
$745$		0			0
$746$	1.41246	−	1.02621i	0.0517139	−	0.0375724i
$747$	−5.50949	−	34.7856i	−0.201582	−	1.27274i
$748$	51.8034	−	26.3951i	1.89412	−	0.965102i
$749$			1.14477i			0.0418289i
$750$		0			0
$751$	9.54227	−	29.3681i	0.348202	−	1.07166i	−0.611645	−	0.791132i	$-0.709492\pi$
$751$	9.54227	−	29.3681i	0.348202	−	1.07166i	0.959847	−	0.280524i	$-0.0905081\pi$
$752$	30.7161	+	15.6506i	1.12010	+	0.570720i
$753$	0.423445	−	0.831057i	0.0154312	−	0.0302854i
$754$	0.267278	+	0.367876i	0.00973368	+	0.0133973i
$755$		0			0
$756$	−0.387262	−	0.533020i	−0.0140846	−	0.0193858i
$757$	−5.65030	−	35.6746i	−0.205364	−	1.29662i	−0.847816	−	0.530290i	$-0.822083\pi$
$757$	−5.65030	−	35.6746i	−0.205364	−	1.29662i	0.642453	−	0.766325i	$-0.277917\pi$
$758$	2.32695	−	4.56689i	0.0845185	−	0.165877i
$759$	−0.435811	−	0.316635i	−0.0158189	−	0.0114931i
$760$		0			0
$761$	−25.1374	+	8.16764i	−0.911230	+	0.296077i	−0.726864	−	0.686781i	$-0.759023\pi$
$761$	−25.1374	+	8.16764i	−0.911230	+	0.296077i	−0.184366	+	0.982858i	$0.559023\pi$
$762$	0.594858	−	0.0942163i	0.0215494	−	0.00341310i
$763$	−0.230540	−	0.0365139i	−0.00834611	−	0.00132189i
$764$	16.3595	+	5.31551i	0.591864	+	0.192308i
$765$		0			0
$766$	2.84358	−	0.923936i	0.102743	−	0.0333832i
$767$	18.6061	−	36.5165i	0.671827	−	1.31853i
$768$	−4.20815	−	8.25896i	−0.151849	−	0.298020i
$769$			33.2932i			1.20059i	0.799780	+	0.600293i	$0.204949\pi$
$769$			33.2932i			1.20059i	−0.799780	+	0.600293i	$0.795051\pi$
$770$		0			0
$771$	8.97323	+	2.91558i	0.323163	+	0.105002i
$772$	38.9678	−	6.17189i	1.40248	−	0.222131i
$773$	−2.18234	+	13.7787i	−0.0784932	+	0.495587i	0.916853	+	0.399225i	$0.130721\pi$
$773$	−2.18234	+	13.7787i	−0.0784932	+	0.495587i	−0.995346	+	0.0963621i	$0.969279\pi$
$774$	−1.86300			−0.0669642
$775$		0			0
$776$	6.04024			0.216832
$777$	−0.0559465	+	0.353232i	−0.00200707	+	0.0126721i
$778$	6.08123	−	0.963172i	0.218023	−	0.0345314i
$779$	32.3440	+	10.5092i	1.15885	+	0.376532i
$780$		0			0
$781$		−	7.58651i		−	0.271467i
$782$	0.0844573	+	0.165757i	0.00302019	+	0.00592745i
$783$	−0.787812	+	1.54617i	−0.0281541	+	0.0552555i
$784$	25.1798	−	8.18142i	0.899280	−	0.292194i
$785$		0			0
$786$	1.03627	+	0.336705i	0.0369626	+	0.0120099i
$787$	0.777735	+	0.123181i	0.0277233	+	0.00439093i	0.170281	−	0.985396i	$-0.445533\pi$
$787$	0.777735	+	0.123181i	0.0277233	+	0.00439093i	−0.142557	+	0.989787i	$0.545533\pi$
$788$	−18.7709	+	2.97302i	−0.668685	+	0.105909i
$789$	4.42036	−	1.43626i	0.157369	−	0.0511323i
$790$		0			0
$791$	−0.117498	−	0.0853669i	−0.00417773	−	0.00303530i
$792$	−4.10767	+	8.06176i	−0.145960	+	0.286462i
$793$	−6.10202	−	38.5267i	−0.216689	−	1.36812i
$794$	0.403684	+	0.555623i	0.0143262	+	0.0197183i
$795$		0			0
$796$	14.7958	+	20.3647i	0.524423	+	0.721807i
$797$	−17.1477	+	33.6544i	−0.607404	+	1.19210i	0.358580	+	0.933499i	$0.383261\pi$
$797$	−17.1477	+	33.6544i	−0.607404	+	1.19210i	−0.965985	+	0.258599i	$0.916739\pi$
$798$	0.0648961	+	0.0330662i	0.00229730	+	0.00117053i
$799$	−17.3195	+	53.3041i	−0.612721	+	1.88576i
$800$		0			0
$801$		−	22.4788i		−	0.794248i
$802$	−1.79287	+	0.913513i	−0.0633085	+	0.0322573i
$803$	7.84947	+	49.5596i	0.277002	+	1.74892i
$804$	6.66277	−	4.84078i	0.234978	−	0.170721i
$805$		0			0
$806$	4.80549	−	2.94935i	0.169266	−	0.103886i
$807$	−7.71291	+	7.71291i	−0.271507	+	0.271507i
$808$	3.49999	+	0.554344i	0.123129	+	0.0195018i
$809$	−29.7848	−	21.6399i	−1.04718	−	0.760819i	−0.0755037	−	0.997146i	$-0.524056\pi$
$809$	−29.7848	−	21.6399i	−1.04718	−	0.760819i	−0.971674	+	0.236327i	$0.924056\pi$
$810$		0			0
$811$	−2.80659			−0.0985528			−0.0492764	−	0.998785i	$-0.515692\pi$
$811$	−2.80659			−0.0985528			−0.0492764	+	0.998785i	$0.515692\pi$
$812$	0.0541296	+	0.0541296i	0.00189958	+	0.00189958i
$813$	−1.19710	+	0.609955i	−0.0419843	+	0.0213921i
$814$	5.08320	−	1.65163i	0.178166	−	0.0578896i
$815$		0			0
$816$	13.2312	−	9.61301i	0.463184	−	0.336523i
$817$	−22.0947	+	11.2578i	−0.772997	+	0.393862i
$818$	−0.803670	+	5.07417i	−0.0280997	+	0.177414i
$819$	−0.942065	−	0.684450i	−0.0329184	−	0.0239166i
$820$		0			0
$821$	26.5833	−	36.5887i	0.927762	−	1.27695i	−0.0329643	−	0.999457i	$-0.510495\pi$
$821$	26.5833	−	36.5887i	0.927762	−	1.27695i	0.960726	−	0.277498i	$-0.0895052\pi$
$822$	−0.122883	+	0.0194627i	−0.00428602	+	0.000678839i
$823$	−10.2832	−	5.23956i	−0.358450	−	0.182639i	0.265486	−	0.964115i	$-0.414468\pi$
$823$	−10.2832	−	5.23956i	−0.358450	−	0.182639i	−0.623936	+	0.781475i	$0.714468\pi$
$824$	−8.41418	+	11.5811i	−0.293122	+	0.403448i
$825$		0			0
$826$	−0.0388914	+	0.119695i	−0.00135320	+	0.00416473i
$827$	26.7495	+	4.23670i	0.930170	+	0.147325i	0.603091	−	0.797672i	$-0.293936\pi$
$827$	26.7495	+	4.23670i	0.930170	+	0.147325i	0.327079	+	0.944997i	$0.393936\pi$
$828$	0.700670	+	0.357009i	0.0243500	+	0.0124069i
$829$	−14.2574	−	43.8799i	−0.495181	−	1.52401i	−0.816674	−	0.577099i	$-0.804185\pi$
$829$	−14.2574	−	43.8799i	−0.495181	−	1.52401i	0.321493	−	0.946912i	$-0.395815\pi$
$830$		0			0
$831$	−1.25324			−0.0434744
$832$	−27.0597	−	27.0597i	−0.938127	−	0.938127i
$833$	19.5417	+	38.3527i	0.677079	+	1.32884i
$834$	−0.568159	+	0.782004i	−0.0196737	+	0.0270786i
$835$		0			0
$836$			59.6720i			2.06380i
$837$	18.3542	+	11.2301i	0.634413	+	0.388170i
$838$	2.82598	+	2.82598i	0.0976217	+	0.0976217i
$839$	11.4208	+	15.7194i	0.394290	+	0.542694i	0.959299	−	0.282391i	$-0.0911275\pi$
$839$	11.4208	+	15.7194i	0.394290	+	0.542694i	−0.565009	+	0.825084i	$0.691127\pi$
$840$		0			0
$841$	−8.89919	+	27.3889i	−0.306869	+	0.944444i
$842$	1.38012	−	1.38012i	0.0475619	−	0.0475619i
$843$	6.15395	−	6.15395i	0.211953	−	0.211953i
$844$	−8.77377	−	2.85077i	−0.302006	−	0.0981276i
$845$		0			0
$846$	−1.33547	−	4.11016i	−0.0459145	−	0.141310i
$847$	0.164592	−	1.03919i	0.00565546	−	0.0357072i
$848$	−17.7654	−	34.8665i	−0.610066	−	1.19732i
$849$	−4.42784	+	3.21701i	−0.151963	+	0.110408i
$850$		0			0
$851$	−0.289714	−	0.891648i	−0.00993127	−	0.0305653i
$852$	−0.340158	−	2.14767i	−0.0116536	−	0.0735781i
$853$	8.44786	+	53.3377i	0.289249	+	1.82625i	0.521098	+	0.853497i	$0.325522\pi$
$853$	8.44786	+	53.3377i	0.289249	+	1.82625i	−0.231849	+	0.972752i	$0.574478\pi$
$854$	0.0370157	+	0.113923i	0.00126665	+	0.00389835i
$855$		0			0
$856$	8.00653	−	5.81709i	0.273658	−	0.198824i
$857$	13.0264	+	25.5657i	0.444972	+	0.873307i	0.999163	+	0.0409171i	$0.0130279\pi$
$857$	13.0264	+	25.5657i	0.444972	+	0.873307i	−0.554190	+	0.832390i	$0.686972\pi$
$858$	0.534515	−	3.37479i	0.0182480	−	0.115214i
$859$	−10.4191	−	32.0666i	−0.355494	−	1.09410i	−0.955723	−	0.294269i	$-0.904924\pi$
$859$	−10.4191	−	32.0666i	−0.355494	−	1.09410i	0.600229	−	0.799828i	$-0.295076\pi$
$860$		0			0
$861$	−0.311786	−	0.101305i	−0.0106256	−	0.00345248i
$862$	−4.41650	+	4.41650i	−0.150427	+	0.150427i
$863$	19.4909	−	19.4909i	0.663477	−	0.663477i	−0.292721	−	0.956198i	$-0.594561\pi$
$863$	19.4909	−	19.4909i	0.663477	−	0.663477i	0.956198	+	0.292721i	$0.0945606\pi$
$864$	−2.64811	+	8.15003i	−0.0900904	+	0.277270i
$865$		0			0
$866$	−3.16786	−	4.36018i	−0.107648	−	0.148165i
$867$	10.3668	+	10.3668i	0.352075	+	0.352075i
$868$	0.721360	−	0.616956i	0.0244845	−	0.0209409i
$869$			21.1508i			0.717492i
$870$		0			0
$871$	18.7911	−	25.8638i	0.636713	−	0.876360i
$872$	0.916099	+	1.79794i	0.0310230	+	0.0608861i
$873$	14.2736	+	14.2736i	0.483090	+	0.483090i
$874$	−0.190934			−0.00645845
$875$		0			0
$876$	4.44423	+	13.6779i	0.150157	+	0.462135i
$877$	−4.36454	−	2.22384i	−0.147380	−	0.0750939i	0.378745	−	0.925501i	$-0.376356\pi$
$877$	−4.36454	−	2.22384i	−0.147380	−	0.0750939i	−0.526125	+	0.850407i	$0.676356\pi$
$878$	−0.964711	−	0.152795i	−0.0325574	−	0.00515659i
$879$	5.45838	−	16.7992i	0.184107	−	0.566622i
$880$		0			0
$881$	−31.2510	+	43.0133i	−1.05287	+	1.44915i	−0.166579	+	0.986028i	$0.553272\pi$
$881$	−31.2510	+	43.0133i	−1.05287	+	1.44915i	−0.886293	+	0.463125i	$0.846728\pi$
$882$	−2.95730	−	1.50682i	−0.0995774	−	0.0507372i
$883$	−15.3227	+	2.42688i	−0.515650	+	0.0816709i	−0.408835	−	0.912608i	$-0.634065\pi$
$883$	−15.3227	+	2.42688i	−0.515650	+	0.0816709i	−0.106814	+	0.994279i	$0.534065\pi$
$884$	38.0224	−	52.3333i	1.27883	−	1.76016i
$885$		0			0
$886$	−2.25779	−	1.64038i	−0.0758518	−	0.0551095i
$887$	0.985897	−	6.22471i	0.0331032	−	0.209005i	−0.965593	−	0.260059i	$-0.916258\pi$
$887$	0.985897	−	6.22471i	0.0331032	−	0.209005i	0.998696	+	0.0510537i	$0.0162580\pi$
$888$	2.75480	−	1.40364i	0.0924452	−	0.0471032i
$889$	0.318416	−	0.231342i	0.0106793	−	0.00775898i
$890$		0			0
$891$	−22.0026	+	7.14907i	−0.737114	+	0.239503i
$892$	−14.2573	+	7.26446i	−0.477370	+	0.243232i
$893$	−40.6755	−	40.6755i	−1.36115	−	1.36115i
$894$	−0.761213			−0.0254588
$895$		0			0
$896$	0.406486	+	0.295329i	0.0135797	+	0.00986625i
$897$	−0.591976	−	0.0937598i	−0.0197655	−	0.00313055i
$898$	−0.0802299	+	0.0802299i	−0.00267730	+	0.00267730i
$899$	−2.31041	−	0.955146i	−0.0770565	−	0.0318559i
$900$		0			0
$901$	51.4700	−	37.3952i	1.71472	−	1.24581i
$902$	0.766431	+	4.83905i	0.0255194	+	0.161123i
$903$	0.212986	−	0.108522i	0.00708774	−	0.00361138i
$904$			1.25557i			0.0417596i
$905$		0			0
$906$	0.253778	−	0.781050i	0.00843122	−	0.0259486i
$907$	18.3781	+	9.36409i	0.610233	+	0.310929i	0.731659	−	0.681671i	$-0.238747\pi$
$907$	18.3781	+	9.36409i	0.610233	+	0.310929i	−0.121425	+	0.992601i	$0.538747\pi$
$908$	−9.15626	+	17.9702i	−0.303861	+	0.596361i
$909$	6.96084	+	9.58077i	0.230876	+	0.317774i
$910$		0			0
$911$	−15.3879	−	21.1797i	−0.509825	−	0.701714i	0.474065	−	0.880490i	$-0.342786\pi$
$911$	−15.3879	−	21.1797i	−0.509825	−	0.701714i	−0.983890	+	0.178776i	$0.942786\pi$
$912$	2.62583	+	16.5789i	0.0869500	+	0.548981i
$913$	30.6601	−	60.1738i	1.01470	−	1.99146i
$914$	−5.45469	−	3.96307i	−0.180425	−	0.131087i
$915$		0			0
$916$	−35.2761	+	11.4619i	−1.16556	+	0.378712i
$917$	0.703283	−	0.111389i	0.0232245	−	0.00367839i
$918$	−4.44763	−	0.704435i	−0.146794	−	0.0232498i
$919$	−45.6491	−	14.8323i	−1.50582	−	0.489272i	−0.564114	−	0.825697i	$-0.690782\pi$
$919$	−45.6491	−	14.8323i	−1.50582	−	0.489272i	−0.941710	+	0.336425i	$0.890782\pi$
$920$		0			0
$921$	−16.6436	+	5.40783i	−0.548425	+	0.178194i
$922$	0.944520	−	1.85373i	0.0311061	−	0.0610492i
$923$	−3.83206	−	7.52084i	−0.126134	−	0.247551i
$924$		−	0.575219i		−	0.0189233i
$925$		0			0
$926$	1.38013	+	0.448432i	0.0453539	+	0.0147364i
$927$	−47.2507	+	7.48378i	−1.55192	+	0.245800i
$928$	0.155758	−	0.983415i	0.00511300	−	0.0322822i
$929$	−23.1044			−0.758032			−0.379016	−	0.925390i	$-0.623737\pi$
$929$	−23.1044			−0.758032			−0.379016	+	0.925390i	$0.623737\pi$
$930$		0			0
$931$	−44.1783			−1.44789
$932$	7.92720	−	50.0504i	0.259664	−	1.63945i
$933$	1.02324	−	0.162065i	0.0334993	−	0.00530577i
$934$	2.50201	+	0.812952i	0.0818683	+	0.0266006i
$935$		0			0
$936$			10.0668i			0.329044i
$937$	−5.05821	−	9.92729i	−0.165244	−	0.324311i	0.793505	−	0.608564i	$-0.208254\pi$
$937$	−5.05821	−	9.92729i	−0.165244	−	0.324311i	−0.958749	+	0.284254i	$0.908254\pi$
$938$	−0.0445701	+	0.0874737i	−0.00145526	+	0.00285612i
$939$	−1.96242	+	0.637628i	−0.0640411	+	0.0208082i
$940$		0			0
$941$	−36.9335	−	12.0004i	−1.20400	−	0.391203i	−0.362768	−	0.931880i	$-0.618168\pi$
$941$	−36.9335	−	12.0004i	−1.20400	−	0.391203i	−0.841230	+	0.540677i	$0.818168\pi$
$942$	0.359396	+	0.0569228i	0.0117098	+	0.00185464i
$943$	0.848823	−	0.134440i	0.0276415	−	0.00437798i
$944$	−27.5851	+	8.96293i	−0.897818	+	0.291719i
$945$		0			0
$946$	−2.89014	−	2.09981i	−0.0939664	−	0.0682706i
$947$	9.73448	−	19.1050i	0.316328	−	0.620829i	−0.677022	−	0.735963i	$-0.736730\pi$
$947$	9.73448	−	19.1050i	0.316328	−	0.620829i	0.993350	+	0.115134i	$0.0367298\pi$
$948$	0.948343	+	5.98760i	0.0308007	+	0.194468i
$949$	32.8148	+	45.1657i	1.06521	+	1.46614i
$950$		0			0
$951$	−8.03929	−	11.0651i	−0.260692	−	0.358811i
$952$	−0.182013	+	0.357221i	−0.00589908	+	0.0115776i
$953$	31.2019	+	15.8982i	1.01073	+	0.514992i	0.879267	−	0.476329i	$-0.158033\pi$
$953$	31.2019	+	15.8982i	1.01073	+	0.514992i	0.131462	+	0.991321i	$0.458033\pi$
$954$	−1.51593	+	4.66554i	−0.0490799	+	0.151052i
$955$		0			0
$956$			19.8654i			0.642493i
$957$	−1.34991	+	0.687812i	−0.0436363	+	0.0222338i
$958$	−0.00180153	−	0.0113744i	−5.82046e−5	−	0.000367490i
$959$	−0.0657765	+	0.0477895i	−0.00212404	+	0.00154320i
$960$		0			0
$961$	−14.0358	+	27.6405i	−0.452767	+	0.891629i
$962$	4.20493	−	4.20493i	0.135572	−	0.135572i
$963$	32.6665	+	5.17386i	1.05266	+	0.166725i
$964$	−22.5718	−	16.3994i	−0.726988	−	0.528188i
$965$		0			0
$966$	0.00184055			5.92186e−5
$967$	6.97723	+	6.97723i	0.224373	+	0.224373i	0.810337	−	0.585964i	$-0.199284\pi$
$967$	6.97723	+	6.97723i	0.224373	+	0.224373i	−0.585964	+	0.810337i	$0.699284\pi$
$968$	−8.10452	+	4.12946i	−0.260489	+	0.132726i
$969$	−25.9543	+	8.43307i	−0.833773	+	0.270909i
$970$		0			0
$971$	33.0317	−	23.9990i	1.06004	−	0.770163i	0.0859429	−	0.996300i	$-0.472610\pi$
$971$	33.0317	−	23.9990i	1.06004	−	0.770163i	0.974095	+	0.226137i	$0.0726097\pi$
$972$	−26.1984	+	13.3488i	−0.840315	+	0.428162i
$973$	−0.0988159	+	0.623899i	−0.00316789	+	0.0200013i
$974$	0.675155	+	0.490529i	0.0216334	+	0.0157176i
$975$		0			0
$976$	−16.2263	+	22.3336i	−0.519391	+	0.714881i
$977$	−24.9383	+	3.94984i	−0.797847	+	0.126367i	−0.542031	−	0.840359i	$-0.682344\pi$
$977$	−24.9383	+	3.94984i	−0.797847	+	0.126367i	−0.255817	+	0.966725i	$0.582344\pi$
$978$	1.64062	+	0.835938i	0.0524613	+	0.0267303i
$979$	25.3360	−	34.8720i	0.809743	−	1.11452i
$980$		0			0
$981$	−2.08388	+	6.41353i	−0.0665333	+	0.204768i
$982$	3.72454	+	0.589910i	0.118855	+	0.0188248i
$983$	23.0314	+	11.7351i	0.734587	+	0.374291i	0.780916	−	0.624636i	$-0.214752\pi$
$983$	23.0314	+	11.7351i	0.734587	+	0.374291i	−0.0463296	+	0.998926i	$0.514752\pi$
$984$	0.875794	+	2.69542i	0.0279193	+	0.0859268i
$985$		0			0
$986$	0.523206			0.0166623
$987$	0.392098	+	0.392098i	0.0124806	+	0.0124806i
$988$	30.1412	+	59.1555i	0.958920	+	1.88199i
$989$	−0.368329	+	0.506961i	−0.0117122	+	0.0161204i
$990$		0			0
$991$		−	23.8829i		−	0.758665i	−0.925261	−	0.379332i	$-0.876154\pi$
$991$		−	23.8829i		−	0.758665i	0.925261	−	0.379332i	$-0.123846\pi$
$992$	−12.0069	−	2.87389i	−0.381220	−	0.0912460i
$993$	8.32993	+	8.32993i	0.264342	+	0.264342i
$994$	0.0152358	+	0.0209703i	0.000483252	+	0.000665139i
$995$		0			0
$996$	5.98157	−	18.4094i	0.189533	−	0.583323i
$997$	−25.0885	+	25.0885i	−0.794559	+	0.794559i	−0.982232	−	0.187672i	$-0.939906\pi$
$997$	−25.0885	+	25.0885i	−0.794559	+	0.794559i	0.187672	+	0.982232i	$0.439906\pi$
$998$	−4.92218	+	4.92218i	−0.155809	+	0.155809i
$999$	21.5830	+	7.01274i	0.682856	+	0.221873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.bs.b.418.6		112
5.2	odd	4	inner	775.2.bs.b.232.6		112
5.3	odd	4		155.2.r.a.77.9	✓	112
5.4	even	2		155.2.r.a.108.9	yes	112
31.29	odd	10	inner	775.2.bs.b.618.6		112
155.29	odd	10		155.2.r.a.153.9	yes	112
155.122	even	20	inner	775.2.bs.b.432.6		112
155.153	even	20		155.2.r.a.122.9	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.r.a.77.9	✓	112	5.3	odd	4
155.2.r.a.108.9	yes	112	5.4	even	2
155.2.r.a.122.9	yes	112	155.153	even	20
155.2.r.a.153.9	yes	112	155.29	odd	10
775.2.bs.b.232.6		112	5.2	odd	4	inner
775.2.bs.b.418.6		112	1.1	even	1	trivial
775.2.bs.b.432.6		112	155.122	even	20	inner
775.2.bs.b.618.6		112	31.29	odd	10	inner

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.bs (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0296108 + 0.186955i) q^{2} +(-0.693043 + 0.109767i) q^{3} +(1.86804 + 0.606962i) q^{4} -0.132818i q^{6} +(-0.0394047 - 0.0773360i) q^{7} +(-0.340657 + 0.668577i) q^{8} +(-2.38491 + 0.774904i) q^{9} +O(q^{10})\)	\(q+(-0.0296108 + 0.186955i) q^{2} +(-0.693043 + 0.109767i) q^{3} +(1.86804 + 0.606962i) q^{4} -0.132818i q^{6} +(-0.0394047 - 0.0773360i) q^{7} +(-0.340657 + 0.668577i) q^{8} +(-2.38491 + 0.774904i) q^{9} +(-4.57319 - 1.48592i) q^{11} +(-1.36125 - 0.215601i) q^{12} +(-5.28416 + 0.836929i) q^{13} +(0.0156252 - 0.00507693i) q^{14} +(3.06319 + 2.22554i) q^{16} +(-2.79468 + 5.48486i) q^{17} +(-0.0742534 - 0.468817i) q^{18} +(-3.71362 - 5.11136i) q^{19} +(0.0357981 + 0.0492718i) q^{21} +(0.413217 - 0.810983i) q^{22} +(-0.142255 - 0.0724827i) q^{23} +(0.162702 - 0.500745i) q^{24} -1.01268i q^{26} +(3.44339 - 1.75450i) q^{27} +(-0.0266694 - 0.168384i) q^{28} +(-0.363268 + 0.263930i) q^{29} +(2.91241 + 4.74530i) q^{31} +(-1.56795 + 1.56795i) q^{32} +(3.33252 + 0.527820i) q^{33} +(-0.942672 - 0.684891i) q^{34} -4.92544 q^{36} +(4.15226 + 4.15226i) q^{37} +(1.06556 - 0.542929i) q^{38} +(3.57028 - 1.16006i) q^{39} +(-4.35479 + 3.16394i) q^{41} +(-0.0102716 + 0.00523366i) q^{42} +(0.613991 - 3.87659i) q^{43} +(-7.64100 - 5.55151i) q^{44} +(0.0177633 - 0.0244491i) q^{46} +(8.99268 - 1.42430i) q^{47} +(-2.36721 - 1.20615i) q^{48} +(4.11007 - 5.65702i) q^{49} +(1.33477 - 4.10801i) q^{51} +(-10.3790 - 1.64387i) q^{52} +(-9.20858 - 4.69201i) q^{53} +(0.226051 + 0.695713i) q^{54} +0.0651285 q^{56} +(3.13475 + 3.13475i) q^{57} +(-0.0385864 - 0.0757301i) q^{58} +(-4.50267 + 6.19740i) q^{59} +7.29096i q^{61} +(-0.973398 + 0.403978i) q^{62} +(0.153905 + 0.153905i) q^{63} +(4.20436 + 5.78681i) q^{64} +(-0.197357 + 0.607404i) q^{66} +(-4.22535 + 4.22535i) q^{67} +(-8.54966 + 8.54966i) q^{68} +(0.106545 + 0.0346186i) q^{69} +(0.487541 + 1.50050i) q^{71} +(0.294353 - 1.85847i) q^{72} +(-4.73742 - 9.29771i) q^{73} +(-0.899239 + 0.653335i) q^{74} +(-3.83478 - 11.8022i) q^{76} +(0.0652900 + 0.412225i) q^{77} +(0.111160 + 0.701834i) q^{78} +(-1.35924 - 4.18331i) q^{79} +(3.89235 - 2.82795i) q^{81} +(-0.462566 - 0.907838i) q^{82} +(-2.19708 + 13.8718i) q^{83} +(0.0369660 + 0.113770i) q^{84} +(0.706568 + 0.229578i) q^{86} +(0.222790 - 0.222790i) q^{87} +(2.55134 - 2.55134i) q^{88} +(-2.77006 + 8.52536i) q^{89} +(0.272946 + 0.375677i) q^{91} +(-0.221744 - 0.221744i) q^{92} +(-2.53930 - 2.96901i) q^{93} +1.72340i q^{94} +(0.914547 - 1.25877i) q^{96} +(-3.65452 - 7.17241i) q^{97} +(0.935908 + 0.935908i) q^{98} +12.0581 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 6 q^{2} + 10 q^{3} + 18 q^{7} + 20 q^{8}+O(q^{10}) \) 112 * q + 6 * q^2 + 10 * q^3 + 18 * q^7 + 20 * q^8	\( 112 q + 6 q^{2} + 10 q^{3} + 18 q^{7} + 20 q^{8} - 20 q^{11} - 10 q^{12} + 10 q^{13} - 12 q^{16} + 10 q^{17} - 4 q^{18} + 20 q^{21} - 60 q^{22} + 40 q^{27} + 48 q^{28} - 4 q^{31} - 44 q^{32} + 26 q^{33} - 64 q^{36} + 32 q^{38} - 16 q^{41} - 70 q^{42} + 10 q^{43} - 60 q^{46} - 46 q^{47} - 150 q^{48} + 12 q^{51} + 80 q^{52} - 10 q^{53} - 24 q^{56} + 10 q^{58} + 54 q^{62} + 200 q^{63} - 52 q^{66} + 68 q^{67} + 8 q^{71} + 18 q^{72} - 30 q^{73} - 128 q^{76} + 30 q^{77} - 36 q^{78} + 64 q^{81} + 44 q^{82} - 160 q^{83} - 20 q^{86} - 60 q^{91} - 10 q^{93} - 92 q^{97} - 144 q^{98}+O(q^{100}) \) 112 * q + 6 * q^2 + 10 * q^3 + 18 * q^7 + 20 * q^8 - 20 * q^11 - 10 * q^12 + 10 * q^13 - 12 * q^16 + 10 * q^17 - 4 * q^18 + 20 * q^21 - 60 * q^22 + 40 * q^27 + 48 * q^28 - 4 * q^31 - 44 * q^32 + 26 * q^33 - 64 * q^36 + 32 * q^38 - 16 * q^41 - 70 * q^42 + 10 * q^43 - 60 * q^46 - 46 * q^47 - 150 * q^48 + 12 * q^51 + 80 * q^52 - 10 * q^53 - 24 * q^56 + 10 * q^58 + 54 * q^62 + 200 * q^63 - 52 * q^66 + 68 * q^67 + 8 * q^71 + 18 * q^72 - 30 * q^73 - 128 * q^76 + 30 * q^77 - 36 * q^78 + 64 * q^81 + 44 * q^82 - 160 * q^83 - 20 * q^86 - 60 * q^91 - 10 * q^93 - 92 * q^97 - 144 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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