LMFDB - Embedded newform 656.2.u.h.529.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(305,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("656.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.u (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 7 x^{18} - 6 x^{17} + 60 x^{16} - 92 x^{15} + 603 x^{14} - 690 x^{13} + 2935 x^{12} + \cdots + 4096 $ x^20 - 2x^19 + 7x^18 - 6x^17 + 60x^16 - 92x^15 + 603x^14 - 690x^13 + 2935x^12 - 3168x^11 + 7811x^10 - 7928x^9 + 15482x^8 - 24314x^7 + 44829x^6 - 45930x^5 + 53273x^4 - 47528x^3 + 33216x^2 - 12800*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 328)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			529.5
Root			$2.35286 - 1.70946i$ of defining polynomial
Character	$\chi$	$=$	656.529
Dual form			656.2.u.h.625.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.90830 q^{3} +(0.0357330 - 0.109975i) q^{5} +(1.92009 + 1.39502i) q^{7} +5.45821 q^{9} +O(q^{10})$	\(q+2.90830 q^{3} +(0.0357330 - 0.109975i) q^{5} +(1.92009 + 1.39502i) q^{7} +5.45821 q^{9} +(-1.21308 - 3.73348i) q^{11} +(1.37428 - 0.998472i) q^{13} +(0.103922 - 0.319840i) q^{15} +(0.473905 + 1.45853i) q^{17} +(-5.61100 - 4.07663i) q^{19} +(5.58419 + 4.05715i) q^{21} +(-3.68664 + 2.67850i) q^{23} +(4.03427 + 2.93107i) q^{25} +7.14920 q^{27} +(-2.72137 + 8.37552i) q^{29} +(0.699881 + 2.15401i) q^{31} +(-3.52800 - 10.8581i) q^{33} +(0.222028 - 0.161313i) q^{35} +(0.395327 - 1.21669i) q^{37} +(3.99682 - 2.90386i) q^{39} +(5.19414 - 3.74446i) q^{41} +(4.73738 - 3.44191i) q^{43} +(0.195038 - 0.600266i) q^{45} +(-7.04288 + 5.11695i) q^{47} +(-0.422480 - 1.30026i) q^{49} +(1.37826 + 4.24184i) q^{51} +(-2.00508 + 6.17101i) q^{53} -0.453937 q^{55} +(-16.3185 - 11.8561i) q^{57} +(-1.62125 + 1.17791i) q^{59} +(-6.64798 - 4.83004i) q^{61} +(10.4802 + 7.61433i) q^{63} +(-0.0606998 - 0.186815i) q^{65} +(0.327972 - 1.00939i) q^{67} +(-10.7219 + 7.78989i) q^{69} +(-4.57540 - 14.0816i) q^{71} -4.43095 q^{73} +(11.7329 + 8.52442i) q^{75} +(2.87908 - 8.86088i) q^{77} +13.2951 q^{79} +4.41740 q^{81} -16.9410 q^{83} +0.177336 q^{85} +(-7.91457 + 24.3585i) q^{87} +(4.31311 + 3.13366i) q^{89} +4.03163 q^{91} +(2.03546 + 6.26451i) q^{93} +(-0.648825 + 0.471399i) q^{95} +(-1.49561 + 4.60301i) q^{97} +(-6.62125 - 20.3781i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	2.90830			1.67911			0.839554	−	0.543277i	$-0.182816\pi$
$3$	2.90830			1.67911			0.839554	+	0.543277i	$0.182816\pi$
$4$		0			0
$5$	0.0357330	−	0.109975i	0.0159803	−	0.0491823i	−0.942748	−	0.333505i	$-0.891769\pi$
$5$	0.0357330	−	0.109975i	0.0159803	−	0.0491823i	0.958729	+	0.284323i	$0.0917686\pi$
$6$		0			0
$7$	1.92009	+	1.39502i	0.725725	+	0.527270i	0.888208	−	0.459442i	$-0.151950\pi$
$7$	1.92009	+	1.39502i	0.725725	+	0.527270i	−0.162483	+	0.986711i	$0.551950\pi$
$8$		0			0
$9$	5.45821			1.81940
$10$		0			0
$11$	−1.21308	−	3.73348i	−0.365758	−	1.12569i	−0.949505	−	0.313751i	$-0.898414\pi$
$11$	−1.21308	−	3.73348i	−0.365758	−	1.12569i	0.583747	−	0.811935i	$-0.301586\pi$
$12$		0			0
$13$	1.37428	−	0.998472i	0.381157	−	0.276926i	−0.380666	−	0.924713i	$-0.624305\pi$
$13$	1.37428	−	0.998472i	0.381157	−	0.276926i	0.761822	+	0.647786i	$0.224305\pi$
$14$		0			0
$15$	0.103922	−	0.319840i	0.0268326	−	0.0825824i
$16$		0			0
$17$	0.473905	+	1.45853i	0.114939	+	0.353745i	0.991934	−	0.126753i	$-0.0404557\pi$
$17$	0.473905	+	1.45853i	0.114939	+	0.353745i	−0.876995	+	0.480499i	$0.840456\pi$
$18$		0			0
$19$	−5.61100	−	4.07663i	−1.28725	−	0.935243i	−0.287505	−	0.957779i	$-0.592826\pi$
$19$	−5.61100	−	4.07663i	−1.28725	−	0.935243i	−0.999746	+	0.0225366i	$0.992826\pi$
$20$		0			0
$21$	5.58419	+	4.05715i	1.21857	+	0.885343i
$22$		0			0
$23$	−3.68664	+	2.67850i	−0.768718	+	0.558506i	−0.901572	−	0.432629i	$-0.857586\pi$
$23$	−3.68664	+	2.67850i	−0.768718	+	0.558506i	0.132854	+	0.991136i	$0.457586\pi$
$24$		0			0
$25$	4.03427	+	2.93107i	0.806853	+	0.586213i
$26$		0			0
$27$	7.14920			1.37586
$28$		0			0
$29$	−2.72137	+	8.37552i	−0.505346	+	1.55530i	0.294842	+	0.955546i	$0.404733\pi$
$29$	−2.72137	+	8.37552i	−0.505346	+	1.55530i	−0.800188	+	0.599749i	$0.795267\pi$
$30$		0			0
$31$	0.699881	+	2.15401i	0.125702	+	0.386872i	0.994028	−	0.109122i	$-0.0348039\pi$
$31$	0.699881	+	2.15401i	0.125702	+	0.386872i	−0.868326	+	0.495994i	$0.834804\pi$
$32$		0			0
$33$	−3.52800	−	10.8581i	−0.614147	−	1.89015i
$34$		0			0
$35$	0.222028	−	0.161313i	0.0375296	−	0.0272669i
$36$		0			0
$37$	0.395327	−	1.21669i	0.0649914	−	0.200023i	−0.913288	−	0.407315i	$-0.866465\pi$
$37$	0.395327	−	1.21669i	0.0649914	−	0.200023i	0.978279	+	0.207292i	$0.0664651\pi$
$38$		0			0
$39$	3.99682	−	2.90386i	0.640003	−	0.464989i
$40$		0			0
$41$	5.19414	−	3.74446i	0.811188	−	0.584786i
$41$	5.19414	−	3.74446i	0.811188	−	0.584786i
$42$		0			0
$43$	4.73738	−	3.44191i	0.722444	−	0.524887i	−0.164720	−	0.986340i	$-0.552672\pi$
$43$	4.73738	−	3.44191i	0.722444	−	0.524887i	0.887164	+	0.461454i	$0.152672\pi$
$44$		0			0
$45$	0.195038	−	0.600266i	0.0290746	−	0.0894824i
$46$		0			0
$47$	−7.04288	+	5.11695i	−1.02731	+	0.746384i	−0.967768	−	0.251842i	$-0.918964\pi$
$47$	−7.04288	+	5.11695i	−1.02731	+	0.746384i	−0.0595413	+	0.998226i	$0.518964\pi$
$48$		0			0
$49$	−0.422480	−	1.30026i	−0.0603543	−	0.185751i
$50$		0			0
$51$	1.37826	+	4.24184i	0.192995	+	0.593976i
$52$		0			0
$53$	−2.00508	+	6.17101i	−0.275419	+	0.847653i	0.713689	+	0.700463i	$0.247023\pi$
$53$	−2.00508	+	6.17101i	−0.275419	+	0.847653i	−0.989108	+	0.147190i	$0.952977\pi$
$54$		0			0
$55$	−0.453937			−0.0612088
$56$		0			0
$57$	−16.3185	−	11.8561i	−2.16143	−	1.57037i
$58$		0			0
$59$	−1.62125	+	1.17791i	−0.211069	+	0.153351i	−0.688297	−	0.725429i	$-0.741642\pi$
$59$	−1.62125	+	1.17791i	−0.211069	+	0.153351i	0.477228	+	0.878779i	$0.341642\pi$
$60$		0			0
$61$	−6.64798	−	4.83004i	−0.851186	−	0.618423i	0.0742865	−	0.997237i	$-0.476332\pi$
$61$	−6.64798	−	4.83004i	−0.851186	−	0.618423i	−0.925473	+	0.378814i	$0.876332\pi$
$62$		0			0
$63$	10.4802	+	7.61433i	1.32038	+	0.959316i
$64$		0			0
$65$	−0.0606998	−	0.186815i	−0.00752889	−	0.0231715i
$66$		0			0
$67$	0.327972	−	1.00939i	0.0400681	−	0.123317i	−0.929022	−	0.370025i	$-0.879349\pi$
$67$	0.327972	−	1.00939i	0.0400681	−	0.123317i	0.969090	+	0.246708i	$0.0793490\pi$
$68$		0			0
$69$	−10.7219	+	7.78989i	−1.29076	+	0.937793i
$70$		0			0
$71$	−4.57540	−	14.0816i	−0.543000	−	1.67118i	−0.725698	−	0.688013i	$-0.758483\pi$
$71$	−4.57540	−	14.0816i	−0.543000	−	1.67118i	0.182698	−	0.983169i	$-0.441517\pi$
$72$		0			0
$73$	−4.43095			−0.518603			−0.259302	−	0.965796i	$-0.583492\pi$
$73$	−4.43095			−0.518603			−0.259302	+	0.965796i	$0.583492\pi$
$74$		0			0
$75$	11.7329	+	8.52442i	1.35479	+	0.984315i
$76$		0			0
$77$	2.87908	−	8.86088i	0.328101	−	1.00979i
$78$		0			0
$79$	13.2951			1.49581			0.747905	−	0.663805i	$-0.231060\pi$
$79$	13.2951			1.49581			0.747905	+	0.663805i	$0.231060\pi$
$80$		0			0
$81$	4.41740			0.490823
$82$		0			0
$83$	−16.9410			−1.85951			−0.929757	−	0.368173i	$-0.879983\pi$
$83$	−16.9410			−1.85951			−0.929757	+	0.368173i	$0.879983\pi$
$84$		0			0
$85$	0.177336			0.0192348
$86$		0			0
$87$	−7.91457	+	24.3585i	−0.848530	+	2.61151i
$88$		0			0
$89$	4.31311	+	3.13366i	0.457189	+	0.332167i	0.792427	−	0.609966i	$-0.208817\pi$
$89$	4.31311	+	3.13366i	0.457189	+	0.332167i	−0.335239	+	0.942133i	$0.608817\pi$
$90$		0			0
$91$	4.03163			0.422630
$92$		0			0
$93$	2.03546	+	6.26451i	0.211068	+	0.649600i
$94$		0			0
$95$	−0.648825	+	0.471399i	−0.0665681	+	0.0483645i
$96$		0			0
$97$	−1.49561	+	4.60301i	−0.151856	+	0.467365i	−0.997829	−	0.0658611i	$-0.979021\pi$
$97$	−1.49561	+	4.60301i	−0.151856	+	0.467365i	0.845973	+	0.533226i	$0.179021\pi$
$98$		0			0
$99$	−6.62125	−	20.3781i	−0.665460	−	2.04808i
$100$		0			0
$101$	−0.282688	−	0.205385i	−0.0281285	−	0.0204366i	0.573632	−	0.819113i	$-0.305534\pi$
$101$	−0.282688	−	0.205385i	−0.0281285	−	0.0204366i	−0.601761	+	0.798676i	$0.705534\pi$
$102$		0			0
$103$	−7.60584	−	5.52597i	−0.749426	−	0.544490i	0.146223	−	0.989252i	$-0.453288\pi$
$103$	−7.60584	−	5.52597i	−0.749426	−	0.544490i	−0.895649	+	0.444762i	$0.853288\pi$
$104$		0			0
$105$	0.645725	−	0.469147i	0.0630163	−	0.0457840i
$106$		0			0
$107$	1.57087	+	1.14130i	0.151862	+	0.110334i	0.661122	−	0.750279i	$-0.270081\pi$
$107$	1.57087	+	1.14130i	0.151862	+	0.110334i	−0.509260	+	0.860613i	$0.670081\pi$
$108$		0			0
$109$	17.9007			1.71458			0.857290	−	0.514834i	$-0.172147\pi$
$109$	17.9007			1.71458			0.857290	+	0.514834i	$0.172147\pi$
$110$		0			0
$111$	1.14973	−	3.53850i	0.109128	−	0.335860i
$112$		0			0
$113$	4.35354	+	13.3988i	0.409547	+	1.26046i	0.917039	+	0.398799i	$0.130573\pi$
$113$	4.35354	+	13.3988i	0.409547	+	1.26046i	−0.507492	+	0.861657i	$0.669427\pi$
$114$		0			0
$115$	0.162833	+	0.501150i	0.0151843	+	0.0467324i
$116$		0			0
$117$	7.50110	−	5.44987i	0.693477	−	0.503841i
$118$		0			0
$119$	−1.12475	+	3.46161i	−0.103105	+	0.317325i
$120$		0			0
$121$	−3.56812	+	2.59239i	−0.324374	+	0.235672i
$122$		0			0
$123$	15.1061	−	10.8900i	1.36207	−	0.981918i
$124$		0			0
$125$	0.934252	−	0.678774i	0.0835621	−	0.0607114i
$126$		0			0
$127$	−3.47703	+	10.7012i	−0.308537	+	0.949579i	0.669797	+	0.742544i	$0.266381\pi$
$127$	−3.47703	+	10.7012i	−0.308537	+	0.949579i	−0.978334	+	0.207034i	$0.933619\pi$
$128$		0			0
$129$	13.7777	−	10.0101i	1.21306	−	0.881341i
$130$		0			0
$131$	−6.90065	−	21.2380i	−0.602913	−	1.85557i	−0.510549	−	0.859849i	$-0.670558\pi$
$131$	−6.90065	−	21.2380i	−0.602913	−	1.85557i	−0.0923632	−	0.995725i	$-0.529442\pi$
$132$		0			0
$133$	−5.08660	−	15.6550i	−0.441064	−	1.35746i
$134$		0			0
$135$	0.255463	−	0.786234i	0.0219867	−	0.0676682i
$136$		0			0
$137$	−10.5645			−0.902585			−0.451292	−	0.892376i	$-0.649037\pi$
$137$	−10.5645			−0.902585			−0.451292	+	0.892376i	$0.649037\pi$
$138$		0			0
$139$	16.1770	+	11.7533i	1.37212	+	0.996900i	0.997569	+	0.0696925i	$0.0222018\pi$
$139$	16.1770	+	11.7533i	1.37212	+	0.996900i	0.374547	+	0.927208i	$0.377798\pi$
$140$		0			0
$141$	−20.4828	+	14.8816i	−1.72496	+	1.25326i
$142$		0			0
$143$	−5.39489	−	3.91962i	−0.451143	−	0.327775i
$144$		0			0
$145$	0.823855	+	0.598566i	0.0684174	+	0.0497082i
$146$		0			0
$147$	−1.22870	−	3.78154i	−0.101341	−	0.311897i
$148$		0			0
$149$	3.30387	−	10.1683i	0.270663	−	0.833017i	−0.719671	−	0.694315i	$-0.755707\pi$
$149$	3.30387	−	10.1683i	0.270663	−	0.833017i	0.990334	−	0.138701i	$-0.0442927\pi$
$150$		0			0
$151$	−15.1531	+	11.0094i	−1.23314	+	0.895929i	−0.997122	−	0.0758197i	$-0.975843\pi$
$151$	−15.1531	+	11.0094i	−1.23314	+	0.895929i	−0.236019	+	0.971749i	$0.575843\pi$
$152$		0			0
$153$	2.58667	+	7.96096i	0.209120	+	0.643605i
$154$		0			0
$155$	0.261896			0.0210360
$156$		0			0
$157$	−12.2368	−	8.89057i	−0.976605	−	0.709545i	−0.0196577	−	0.999807i	$-0.506258\pi$
$157$	−12.2368	−	8.89057i	−0.976605	−	0.709545i	−0.956947	+	0.290262i	$0.906258\pi$
$158$		0			0
$159$	−5.83138	+	17.9471i	−0.462458	+	1.42330i
$160$		0			0
$161$	−10.8153			−0.852361
$162$		0			0
$163$	−9.53125			−0.746545			−0.373273	−	0.927722i	$-0.621764\pi$
$163$	−9.53125			−0.746545			−0.373273	+	0.927722i	$0.621764\pi$
$164$		0			0
$165$	−1.32018			−0.102776
$166$		0			0
$167$	9.47660			0.733321			0.366661	−	0.930355i	$-0.380501\pi$
$167$	9.47660			0.733321			0.366661	+	0.930355i	$0.380501\pi$
$168$		0			0
$169$	−3.12552	+	9.61937i	−0.240425	+	0.739952i
$170$		0			0
$171$	−30.6260	−	22.2511i	−2.34203	−	1.70158i
$172$		0			0
$173$	1.22407			0.0930640			0.0465320	−	0.998917i	$-0.485183\pi$
$173$	1.22407			0.0930640			0.0465320	+	0.998917i	$0.485183\pi$
$174$		0			0
$175$	3.65723	+	11.2558i	0.276461	+	0.850859i
$176$		0			0
$177$	−4.71509	+	3.42572i	−0.354408	+	0.257493i
$178$		0			0
$179$	−0.505876	+	1.55693i	−0.0378110	+	0.116370i	−0.968180	−	0.250253i	$-0.919486\pi$
$179$	−0.505876	+	1.55693i	−0.0378110	+	0.116370i	0.930369	+	0.366623i	$0.119486\pi$
$180$		0			0
$181$	2.29655	+	7.06804i	0.170701	+	0.525363i	0.999411	−	0.0343146i	$-0.0109248\pi$
$181$	2.29655	+	7.06804i	0.170701	+	0.525363i	−0.828710	+	0.559678i	$0.810925\pi$
$182$		0			0
$183$	−19.3343	−	14.0472i	−1.42923	−	1.03840i
$184$		0			0
$185$	−0.119679	−	0.0869522i	−0.00879901	−	0.00639285i
$186$		0			0
$187$	4.87050	−	3.53863i	0.356167	−	0.258770i
$188$		0			0
$189$	13.7271	+	9.97331i	0.998499	+	0.725452i
$190$		0			0
$191$	−4.11529			−0.297772			−0.148886	−	0.988854i	$-0.547569\pi$
$191$	−4.11529			−0.297772			−0.148886	+	0.988854i	$0.547569\pi$
$192$		0			0
$193$	−7.12402	+	21.9255i	−0.512799	+	1.57823i	0.274454	+	0.961600i	$0.411503\pi$
$193$	−7.12402	+	21.9255i	−0.512799	+	1.57823i	−0.787252	+	0.616631i	$0.788497\pi$
$194$		0			0
$195$	−0.176533	−	0.543313i	−0.0126418	−	0.0389075i
$196$		0			0
$197$	−5.47503	−	16.8504i	−0.390080	−	1.20054i	−0.932728	−	0.360581i	$-0.882578\pi$
$197$	−5.47503	−	16.8504i	−0.390080	−	1.20054i	0.542648	−	0.839960i	$-0.317422\pi$
$198$		0			0
$199$	−1.49882	+	1.08895i	−0.106248	+	0.0771938i	−0.639641	−	0.768674i	$-0.720917\pi$
$199$	−1.49882	+	1.08895i	−0.106248	+	0.0771938i	0.533393	+	0.845868i	$0.320917\pi$
$200$		0			0
$201$	0.953841	−	2.93562i	0.0672787	−	0.207063i
$202$		0			0
$203$	−16.9093	+	12.2853i	−1.18680	+	0.862262i
$204$		0			0
$205$	−0.226194	−	0.705026i	−0.0157981	−	0.0492411i
$206$		0			0
$207$	−20.1225	+	14.6198i	−1.39861	+	1.01615i
$208$		0			0
$209$	−8.41341	+	25.8938i	−0.581968	+	1.79111i
$210$		0			0
$211$	14.1555	−	10.2845i	0.974502	−	0.708017i	0.0180288	−	0.999837i	$-0.494261\pi$
$211$	14.1555	−	10.2845i	0.974502	−	0.708017i	0.956473	+	0.291820i	$0.0942609\pi$
$212$		0			0
$213$	−13.3066	−	40.9536i	−0.911756	−	2.80610i
$214$		0			0
$215$	−0.209243	−	0.643984i	−0.0142703	−	0.0439193i
$216$		0			0
$217$	−1.66107	+	5.11224i	−0.112761	+	0.347041i
$218$		0			0
$219$	−12.8865			−0.870791
$220$		0			0
$221$	2.10758	+	1.53125i	0.141771	+	0.103003i
$222$		0			0
$223$	21.4153	−	15.5591i	1.43408	−	1.04192i	0.444836	−	0.895612i	$-0.353262\pi$
$223$	21.4153	−	15.5591i	1.43408	−	1.04192i	0.989240	−	0.146305i	$-0.0467380\pi$
$224$		0			0
$225$	22.0199	+	15.9984i	1.46799	+	1.06656i
$226$		0			0
$227$	19.0018	+	13.8056i	1.26119	+	0.916310i	0.998816	−	0.0486552i	$-0.0154935\pi$
$227$	19.0018	+	13.8056i	1.26119	+	0.916310i	0.262377	+	0.964965i	$0.415494\pi$
$228$		0			0
$229$	−4.84964	−	14.9257i	−0.320473	−	0.986316i	−0.973443	−	0.228931i	$-0.926477\pi$
$229$	−4.84964	−	14.9257i	−0.320473	−	0.986316i	0.652969	−	0.757384i	$-0.273523\pi$
$230$		0			0
$231$	8.37321	−	25.7701i	0.550917	−	1.69555i
$232$		0			0
$233$	1.12767	−	0.819303i	0.0738764	−	0.0536743i	−0.550234	−	0.835010i	$-0.685462\pi$
$233$	1.12767	−	0.819303i	0.0738764	−	0.0536743i	0.624110	+	0.781336i	$0.285462\pi$
$234$		0			0
$235$	0.311073	+	0.957385i	0.0202922	+	0.0624529i
$236$		0			0
$237$	38.6660			2.51163
$238$		0			0
$239$	−6.79321	−	4.93556i	−0.439416	−	0.319255i	0.345987	−	0.938239i	$-0.387544\pi$
$239$	−6.79321	−	4.93556i	−0.439416	−	0.319255i	−0.785403	+	0.618985i	$0.787544\pi$
$240$		0			0
$241$	7.50627	−	23.1019i	0.483522	−	1.48813i	−0.350589	−	0.936529i	$-0.614019\pi$
$241$	7.50627	−	23.1019i	0.483522	−	1.48813i	0.834111	−	0.551597i	$-0.185981\pi$
$242$		0			0
$243$	−8.60047			−0.551721
$244$		0			0
$245$	−0.158093			−0.0101002
$246$		0			0
$247$	−11.7815			−0.749637
$248$		0			0
$249$	−49.2695			−3.12233
$250$		0			0
$251$	−4.10203	+	12.6247i	−0.258918	+	0.796867i	0.734115	+	0.679026i	$0.237597\pi$
$251$	−4.10203	+	12.6247i	−0.258918	+	0.796867i	−0.993032	+	0.117841i	$0.962403\pi$
$252$		0			0
$253$	14.4723	+	10.5148i	0.909868	+	0.661058i
$254$		0			0
$255$	0.515746			0.0322972
$256$		0			0
$257$	1.91794	+	5.90281i	0.119638	+	0.368207i	0.992886	−	0.119068i	$-0.0379908\pi$
$257$	1.91794	+	5.90281i	0.119638	+	0.368207i	−0.873248	+	0.487275i	$0.837991\pi$
$258$		0			0
$259$	2.45638	−	1.78466i	0.152632	−	0.110894i
$260$		0			0
$261$	−14.8538	+	45.7153i	−0.919428	+	2.82971i
$262$		0			0
$263$	−3.36306	−	10.3504i	−0.207375	−	0.638236i	−0.999607	−	0.0280159i	$-0.991081\pi$
$263$	−3.36306	−	10.3504i	−0.207375	−	0.638236i	0.792232	−	0.610220i	$-0.208919\pi$
$264$		0			0
$265$	0.607009	+	0.441018i	0.0372883	+	0.0270915i
$266$		0			0
$267$	12.5438	+	9.11361i	0.767669	+	0.557744i
$268$		0			0
$269$	14.2261	−	10.3359i	0.867381	−	0.630189i	−0.0625019	−	0.998045i	$-0.519908\pi$
$269$	14.2261	−	10.3359i	0.867381	−	0.630189i	0.929883	+	0.367856i	$0.119908\pi$
$270$		0			0
$271$	18.6967	+	13.5840i	1.13574	+	0.825167i	0.986521	−	0.163636i	$-0.0523224\pi$
$271$	18.6967	+	13.5840i	1.13574	+	0.825167i	0.149224	+	0.988803i	$0.452322\pi$
$272$		0			0
$273$	11.7252			0.709640
$274$		0			0
$275$	6.04919	−	18.6175i	0.364780	−	1.12268i
$276$		0			0
$277$	−3.58803	−	11.0428i	−0.215584	−	0.663499i	−0.999112	−	0.0421422i	$-0.986582\pi$
$277$	−3.58803	−	11.0428i	−0.215584	−	0.663499i	0.783528	−	0.621357i	$-0.213418\pi$
$278$		0			0
$279$	3.82009	+	11.7570i	0.228703	+	0.703876i
$280$		0			0
$281$	19.5657	−	14.2153i	1.16719	−	0.848015i	0.176522	−	0.984297i	$-0.443515\pi$
$281$	19.5657	−	14.2153i	1.16719	−	0.848015i	0.990670	+	0.136282i	$0.0435152\pi$
$282$		0			0
$283$	1.58062	−	4.86464i	0.0939580	−	0.289173i	−0.893023	−	0.450012i	$-0.851420\pi$
$283$	1.58062	−	4.86464i	0.0939580	−	0.289173i	0.986981	+	0.160839i	$0.0514199\pi$
$284$		0			0
$285$	−1.88698	+	1.37097i	−0.111775	+	0.0812092i
$286$		0			0
$287$	15.1968	+	0.0562662i	0.897039	+	0.00332129i
$288$		0			0
$289$	11.8506	−	8.60994i	0.697092	−	0.506467i
$290$		0			0
$291$	−4.34968	+	13.3869i	−0.254983	+	0.784756i
$292$		0			0
$293$	−23.4650	+	17.0483i	−1.37084	+	0.995974i	−0.373170	+	0.927763i	$0.621729\pi$
$293$	−23.4650	+	17.0483i	−1.37084	+	0.995974i	−0.997671	+	0.0682116i	$0.978271\pi$
$294$		0			0
$295$	0.0716083	+	0.220388i	0.00416920	+	0.0128315i
$296$		0			0
$297$	−8.67256	−	26.6914i	−0.503233	−	1.54879i
$298$		0			0
$299$	−2.39207	+	7.36202i	−0.138337	+	0.425757i
$300$		0			0
$301$	13.8977			0.801052
$302$		0			0
$303$	−0.822142	−	0.597321i	−0.0472308	−	0.0343152i
$304$		0			0
$305$	−0.768736	+	0.558519i	−0.0440177	+	0.0319807i
$306$		0			0
$307$	7.17075	+	5.20985i	0.409256	+	0.297342i	0.773301	−	0.634040i	$-0.218604\pi$
$307$	7.17075	+	5.20985i	0.409256	+	0.297342i	−0.364044	+	0.931382i	$0.618604\pi$
$308$		0			0
$309$	−22.1201	−	16.0712i	−1.25837	−	0.914257i
$310$		0			0
$311$	4.48560	+	13.8052i	0.254355	+	0.782824i	0.993956	+	0.109778i	$0.0350141\pi$
$311$	4.48560	+	13.8052i	0.254355	+	0.782824i	−0.739601	+	0.673045i	$0.764986\pi$
$312$		0			0
$313$	7.90647	−	24.3336i	0.446900	−	1.37542i	−0.433487	−	0.901160i	$-0.642717\pi$
$313$	7.90647	−	24.3336i	0.446900	−	1.37542i	0.880387	−	0.474257i	$-0.157283\pi$
$314$		0			0
$315$	1.21188	−	0.880480i	0.0682815	−	0.0496094i
$316$		0			0
$317$	−2.35483	−	7.24741i	−0.132260	−	0.407055i	0.862894	−	0.505386i	$-0.168650\pi$
$317$	−2.35483	−	7.24741i	−0.132260	−	0.407055i	−0.995154	+	0.0983304i	$0.968650\pi$
$318$		0			0
$319$	34.5711			1.93561
$320$		0			0
$321$	4.56856	+	3.31926i	0.254992	+	0.185263i
$322$		0			0
$323$	3.28680	−	10.1157i	0.182883	−	0.562855i
$324$		0			0
$325$	8.47080			0.469875
$326$		0			0
$327$	52.0607			2.87896
$328$		0			0
$329$	−20.6612			−1.13909
$330$		0			0
$331$	35.6457			1.95926			0.979631	−	0.200805i	$-0.0643557\pi$
$331$	35.6457			1.95926			0.979631	+	0.200805i	$0.0643557\pi$
$332$		0			0
$333$	2.15778	−	6.64096i	0.118245	−	0.363922i
$334$		0			0
$335$	−0.0992886	−	0.0721374i	−0.00542472	−	0.00394129i
$336$		0			0
$337$	9.30528			0.506891			0.253445	−	0.967350i	$-0.418436\pi$
$337$	9.30528			0.506891			0.253445	+	0.967350i	$0.418436\pi$
$338$		0			0
$339$	12.6614	+	38.9678i	0.687673	+	2.11644i
$340$		0			0
$341$	7.19295	−	5.22598i	0.389520	−	0.283003i
$342$		0			0
$343$	6.13655	−	18.8864i	0.331343	−	1.01977i
$344$		0			0
$345$	0.473568	+	1.45749i	0.0254961	+	0.0784688i
$346$		0			0
$347$	20.0643	+	14.5776i	1.07711	+	0.782565i	0.977176	−	0.212429i	$-0.0681375\pi$
$347$	20.0643	+	14.5776i	1.07711	+	0.782565i	0.0999318	+	0.994994i	$0.468138\pi$
$348$		0			0
$349$	17.2888	+	12.5610i	0.925448	+	0.672377i	0.944874	−	0.327434i	$-0.106184\pi$
$349$	17.2888	+	12.5610i	0.925448	+	0.672377i	−0.0194264	+	0.999811i	$0.506184\pi$
$350$		0			0
$351$	9.82500	−	7.13828i	0.524420	−	0.381013i
$352$		0			0
$353$	−6.31302	−	4.58668i	−0.336008	−	0.244124i	0.406967	−	0.913443i	$-0.366586\pi$
$353$	−6.31302	−	4.58668i	−0.336008	−	0.244124i	−0.742976	+	0.669318i	$0.766586\pi$
$354$		0			0
$355$	−1.71212			−0.0908699
$356$		0			0
$357$	−3.27110	+	10.0674i	−0.173125	+	0.532824i
$358$		0			0
$359$	−2.26176	−	6.96099i	−0.119371	−	0.367387i	0.873462	−	0.486892i	$-0.161869\pi$
$359$	−2.26176	−	6.96099i	−0.119371	−	0.367387i	−0.992834	+	0.119505i	$0.961869\pi$
$360$		0			0
$361$	8.99307	+	27.6778i	0.473319	+	1.45673i
$362$		0			0
$363$	−10.3772	+	7.53945i	−0.544660	+	0.395718i
$364$		0			0
$365$	−0.158331	+	0.487293i	−0.00828744	+	0.0255061i
$366$		0			0
$367$	−10.0505	+	7.30215i	−0.524634	+	0.381169i	−0.818347	−	0.574725i	$-0.805109\pi$
$367$	−10.0505	+	7.30215i	−0.524634	+	0.381169i	0.293713	+	0.955894i	$0.405109\pi$
$368$		0			0
$369$	28.3507	−	20.4380i	1.47588	−	1.06396i
$370$		0			0
$371$	−12.4586	+	9.05173i	−0.646820	+	0.469942i
$372$		0			0
$373$	−0.385680	+	1.18700i	−0.0199697	+	0.0614605i	−0.960545	−	0.278125i	$-0.910287\pi$
$373$	−0.385680	+	1.18700i	−0.0199697	+	0.0614605i	0.940575	+	0.339586i	$0.110287\pi$
$374$		0			0
$375$	2.71709	−	1.97408i	0.140310	−	0.101941i
$376$		0			0
$377$	4.62280	+	14.2275i	0.238086	+	0.732755i
$378$		0			0
$379$	−2.44082	−	7.51208i	−0.125377	−	0.385870i	0.868593	−	0.495527i	$-0.165025\pi$
$379$	−2.44082	−	7.51208i	−0.125377	−	0.385870i	−0.993970	+	0.109657i	$0.965025\pi$
$380$		0			0
$381$	−10.1123	+	31.1223i	−0.518067	+	1.59445i
$382$		0			0
$383$	−21.4243			−1.09473			−0.547364	−	0.836894i	$-0.684369\pi$
$383$	−21.4243			−1.09473			−0.547364	+	0.836894i	$0.684369\pi$
$384$		0			0
$385$	−0.871597	−	0.633253i	−0.0444207	−	0.0322735i
$386$		0			0
$387$	25.8576	−	18.7867i	1.31442	−	0.954980i
$388$		0			0
$389$	10.5196	+	7.64291i	0.533363	+	0.387511i	0.821614	−	0.570044i	$-0.193074\pi$
$389$	10.5196	+	7.64291i	0.533363	+	0.387511i	−0.288251	+	0.957555i	$0.593074\pi$
$390$		0			0
$391$	−5.65379	−	4.10772i	−0.285925	−	0.207736i
$392$		0			0
$393$	−20.0692	−	61.7665i	−1.01235	−	3.11571i
$394$		0			0
$395$	0.475073	−	1.46212i	0.0239035	−	0.0735674i
$396$		0			0
$397$	5.06628	−	3.68087i	0.254270	−	0.184738i	−0.453347	−	0.891334i	$-0.649770\pi$
$397$	5.06628	−	3.68087i	0.254270	−	0.184738i	0.707617	+	0.706596i	$0.249770\pi$
$398$		0			0
$399$	−14.7934	−	45.5293i	−0.740595	−	2.27932i
$400$		0			0
$401$	2.74224			0.136941			0.0684704	−	0.997653i	$-0.478188\pi$
$401$	2.74224			0.136941			0.0684704	+	0.997653i	$0.478188\pi$
$402$		0			0
$403$	3.11255	+	2.26140i	0.155047	+	0.112648i
$404$		0			0
$405$	0.157847	−	0.485804i	0.00784350	−	0.0241398i
$406$		0			0
$407$	−5.02206			−0.248934
$408$		0			0
$409$	30.7127			1.51865			0.759323	−	0.650714i	$-0.225530\pi$
$409$	30.7127			1.51865			0.759323	+	0.650714i	$0.225530\pi$
$410$		0			0
$411$	−30.7247			−1.51554
$412$		0			0
$413$	−4.75616			−0.234035
$414$		0			0
$415$	−0.605353	+	1.86308i	−0.0297156	+	0.0914552i
$416$		0			0
$417$	47.0476	+	34.1821i	2.30393	+	1.67390i
$418$		0			0
$419$	−8.68618			−0.424348			−0.212174	−	0.977232i	$-0.568054\pi$
$419$	−8.68618			−0.424348			−0.212174	+	0.977232i	$0.568054\pi$
$420$		0			0
$421$	−1.90042	−	5.84889i	−0.0926207	−	0.285057i	0.894006	−	0.448056i	$-0.147883\pi$
$421$	−1.90042	−	5.84889i	−0.0926207	−	0.285057i	−0.986626	+	0.162999i	$0.947883\pi$
$422$		0			0
$423$	−38.4415	+	27.9294i	−1.86909	+	1.35797i
$424$		0			0
$425$	−2.36319	+	7.27314i	−0.114631	+	0.352799i
$426$		0			0
$427$	−6.02667	−	18.5482i	−0.291651	−	0.897610i
$428$		0			0
$429$	−15.6900	−	11.3994i	−0.757518	−	0.550369i
$430$		0			0
$431$	7.85638	+	5.70799i	0.378428	+	0.274944i	0.760697	−	0.649107i	$-0.224857\pi$
$431$	7.85638	+	5.70799i	0.378428	+	0.274944i	−0.382269	+	0.924051i	$0.624857\pi$
$432$		0			0
$433$	−19.7332	+	14.3370i	−0.948317	+	0.688992i	−0.950408	−	0.311005i	$-0.899334\pi$
$433$	−19.7332	+	14.3370i	−0.948317	+	0.688992i	0.00209152	+	0.999998i	$0.499334\pi$
$434$		0			0
$435$	2.39602	+	1.74081i	0.114880	+	0.0834654i
$436$		0			0
$437$	31.6050			1.51187
$438$		0			0
$439$	−9.03410	+	27.8041i	−0.431174	+	1.32702i	0.465783	+	0.884899i	$0.345773\pi$
$439$	−9.03410	+	27.8041i	−0.431174	+	1.32702i	−0.896957	+	0.442118i	$0.854227\pi$
$440$		0			0
$441$	−2.30598	−	7.09709i	−0.109809	−	0.337956i
$442$		0			0
$443$	2.84957	+	8.77009i	0.135387	+	0.416680i	0.995650	−	0.0931715i	$-0.0297005\pi$
$443$	2.84957	+	8.77009i	0.135387	+	0.416680i	−0.860263	+	0.509851i	$0.829701\pi$
$444$		0			0
$445$	0.498744	−	0.362359i	0.0236428	−	0.0171775i
$446$		0			0
$447$	9.60864	−	29.5724i	0.454473	−	1.39872i
$448$		0			0
$449$	−5.94930	+	4.32242i	−0.280765	+	0.203987i	−0.719251	−	0.694750i	$-0.755515\pi$
$449$	−5.94930	+	4.32242i	−0.280765	+	0.203987i	0.438486	+	0.898738i	$0.355515\pi$
$450$		0			0
$451$	−20.2808	−	14.8499i	−0.954984	−	0.699253i
$452$		0			0
$453$	−44.0697	+	32.0185i	−2.07058	+	1.50436i
$454$		0			0
$455$	0.144062	−	0.443378i	0.00675375	−	0.0207859i
$456$		0			0
$457$	0.0948054	−	0.0688802i	0.00443481	−	0.00322208i	−0.585566	−	0.810625i	$-0.699128\pi$
$457$	0.0948054	−	0.0688802i	0.00443481	−	0.00322208i	0.590000	+	0.807403i	$0.299128\pi$
$458$		0			0
$459$	3.38804	+	10.4273i	0.158140	+	0.486706i
$460$		0			0
$461$	5.07922	+	15.6322i	0.236563	+	0.728066i	0.996910	+	0.0785493i	$0.0250288\pi$
$461$	5.07922	+	15.6322i	0.236563	+	0.728066i	−0.760347	+	0.649517i	$0.774971\pi$
$462$		0			0
$463$	−7.23732	+	22.2742i	−0.336347	+	1.03517i	0.629708	+	0.776832i	$0.283175\pi$
$463$	−7.23732	+	22.2742i	−0.336347	+	1.03517i	−0.966055	+	0.258337i	$0.916825\pi$
$464$		0			0
$465$	0.761673			0.0353217
$466$		0			0
$467$	−3.37645	−	2.45314i	−0.156244	−	0.113518i	0.506917	−	0.861995i	$-0.330785\pi$
$467$	−3.37645	−	2.45314i	−0.156244	−	0.113518i	−0.663160	+	0.748477i	$0.730785\pi$
$468$		0			0
$469$	2.03786	−	1.48059i	0.0940998	−	0.0683675i
$470$		0			0
$471$	−35.5884	−	25.8565i	−1.63983	−	1.19140i
$472$		0			0
$473$	−18.5971	−	13.5116i	−0.855097	−	0.621265i
$474$		0			0
$475$	−10.6874	−	32.8924i	−0.490371	−	1.50921i
$476$		0			0
$477$	−10.9442	+	33.6826i	−0.501098	+	1.54222i
$478$		0			0
$479$	25.5560	−	18.5675i	1.16768	−	0.848372i	0.176954	−	0.984219i	$-0.443375\pi$
$479$	25.5560	−	18.5675i	1.16768	−	0.848372i	0.990730	+	0.135847i	$0.0433755\pi$
$480$		0			0
$481$	−0.671543	−	2.06680i	−0.0306197	−	0.0942379i
$482$		0			0
$483$	−31.4540			−1.43121
$484$		0			0
$485$	0.452774	+	0.328959i	0.0205594	+	0.0149373i
$486$		0			0
$487$	−5.93419	+	18.2636i	−0.268904	+	0.827601i	0.721864	+	0.692034i	$0.243285\pi$
$487$	−5.93419	+	18.2636i	−0.268904	+	0.827601i	−0.990768	+	0.135566i	$0.956715\pi$
$488$		0			0
$489$	−27.7197			−1.25353
$490$		0			0
$491$	−0.574075			−0.0259077			−0.0129538	−	0.999916i	$-0.504123\pi$
$491$	−0.574075			−0.0259077			−0.0129538	+	0.999916i	$0.504123\pi$
$492$		0			0
$493$	−13.5056			−0.608262
$494$		0			0
$495$	−2.47768			−0.111363
$496$		0			0
$497$	10.8591	−	33.4208i	0.487095	−	1.49913i
$498$		0			0
$499$	−4.78209	−	3.47439i	−0.214076	−	0.155535i	0.475580	−	0.879672i	$-0.342238\pi$
$499$	−4.78209	−	3.47439i	−0.214076	−	0.155535i	−0.689656	+	0.724137i	$0.742238\pi$
$500$		0			0
$501$	27.5608			1.23133
$502$		0			0
$503$	−3.33460	−	10.2629i	−0.148683	−	0.457598i	0.848784	−	0.528741i	$-0.177336\pi$
$503$	−3.33460	−	10.2629i	−0.148683	−	0.457598i	−0.997466	+	0.0711423i	$0.977336\pi$
$504$		0			0
$505$	−0.0326885	+	0.0237496i	−0.00145462	+	0.00105684i
$506$		0			0
$507$	−9.08996	+	27.9760i	−0.403699	+	1.24246i
$508$		0			0
$509$	−1.90892	−	5.87504i	−0.0846112	−	0.260407i	0.899796	−	0.436311i	$-0.143715\pi$
$509$	−1.90892	−	5.87504i	−0.0846112	−	0.260407i	−0.984407	+	0.175904i	$0.943715\pi$
$510$		0			0
$511$	−8.50780	−	6.18128i	−0.376363	−	0.273444i
$512$		0			0
$513$	−40.1142	−	29.1446i	−1.77108	−	1.28677i
$514$		0			0
$515$	−0.879498	+	0.638993i	−0.0387553	+	0.0281574i
$516$		0			0
$517$	27.6476	+	20.0872i	1.21594	+	0.883433i
$518$		0			0
$519$	3.55995			0.156264
$520$		0			0
$521$	4.76841	−	14.6757i	0.208908	−	0.642952i	−0.790622	−	0.612304i	$-0.790243\pi$
$521$	4.76841	−	14.6757i	0.208908	−	0.642952i	0.999530	−	0.0306481i	$-0.00975711\pi$
$522$		0			0
$523$	−3.30641	−	10.1761i	−0.144579	−	0.444969i	0.852377	−	0.522927i	$-0.175160\pi$
$523$	−3.30641	−	10.1761i	−0.144579	−	0.444969i	−0.996957	+	0.0779580i	$0.975160\pi$
$524$		0			0
$525$	10.6363	+	32.7353i	0.464207	+	1.42868i
$526$		0			0
$527$	−2.81001	+	2.04159i	−0.122406	+	0.0889332i
$528$		0			0
$529$	−0.690432	+	2.12493i	−0.0300188	+	0.0923883i
$530$		0			0
$531$	−8.84914	+	6.42928i	−0.384020	+	0.279007i
$532$		0			0
$533$	3.39946	−	10.3321i	0.147247	−	0.447534i
$534$		0			0
$535$	0.181647	−	0.131974i	0.00785328	−	0.00570574i
$536$		0			0
$537$	−1.47124	+	4.52801i	−0.0634887	+	0.195398i
$538$		0			0
$539$	−4.34199	+	3.15464i	−0.187023	+	0.135880i
$540$		0			0
$541$	−3.07731	−	9.47098i	−0.132304	−	0.407189i	0.862857	−	0.505448i	$-0.168673\pi$
$541$	−3.07731	−	9.47098i	−0.132304	−	0.407189i	−0.995161	+	0.0982586i	$0.968673\pi$
$542$		0			0
$543$	6.67904	+	20.5560i	0.286625	+	0.882142i
$544$		0			0
$545$	0.639648	−	1.96863i	0.0273995	−	0.0843270i
$546$		0			0
$547$	29.8779			1.27749			0.638744	−	0.769420i	$-0.279454\pi$
$547$	29.8779			1.27749			0.638744	+	0.769420i	$0.279454\pi$
$548$		0			0
$549$	−36.2860	−	26.3634i	−1.54865	−	1.12516i
$550$		0			0
$551$	49.4135	−	35.9010i	2.10509	−	1.52943i
$552$		0			0
$553$	25.5277	+	18.5469i	1.08555	+	0.788696i
$554$		0			0
$555$	−0.348064	−	0.252883i	−0.0147745	−	0.0107343i
$556$		0			0
$557$	3.46825	+	10.6742i	0.146954	+	0.452279i	0.997257	−	0.0740147i	$-0.0235812\pi$
$557$	3.46825	+	10.6742i	0.146954	+	0.452279i	−0.850303	+	0.526294i	$0.823581\pi$
$558$		0			0
$559$	3.07384	−	9.46029i	0.130009	−	0.400128i
$560$		0			0
$561$	14.1649	−	10.2914i	0.598042	−	0.434503i
$562$		0			0
$563$	8.00678	+	24.6423i	0.337446	+	1.03855i	0.965505	+	0.260385i	$0.0838496\pi$
$563$	8.00678	+	24.6423i	0.337446	+	1.03855i	−0.628059	+	0.778166i	$0.716150\pi$
$564$		0			0
$565$	1.62910			0.0685368
$566$		0			0
$567$	8.48180	+	6.16239i	0.356202	+	0.258796i
$568$		0			0
$569$	−0.944952	+	2.90826i	−0.0396145	+	0.121921i	−0.968908	−	0.247421i	$-0.920417\pi$
$569$	−0.944952	+	2.90826i	−0.0396145	+	0.121921i	0.929294	+	0.369342i	$0.120417\pi$
$570$		0			0
$571$	−15.8433			−0.663022			−0.331511	−	0.943451i	$-0.607558\pi$
$571$	−15.8433			−0.663022			−0.331511	+	0.943451i	$0.607558\pi$
$572$		0			0
$573$	−11.9685			−0.499991
$574$		0			0
$575$	−22.7238			−0.947647
$576$		0			0
$577$	18.9959			0.790810			0.395405	−	0.918507i	$-0.370604\pi$
$577$	18.9959			0.790810			0.395405	+	0.918507i	$0.370604\pi$
$578$		0			0
$579$	−20.7188	+	63.7659i	−0.861044	+	2.65002i
$580$		0			0
$581$	−32.5282	−	23.6331i	−1.34950	−	0.980466i
$582$		0			0
$583$	25.4717			1.05493
$584$		0			0
$585$	−0.331312	−	1.01967i	−0.0136981	−	0.0421583i
$586$		0			0
$587$	6.23400	−	4.52927i	0.257305	−	0.186943i	−0.451653	−	0.892194i	$-0.649166\pi$
$587$	6.23400	−	4.52927i	0.257305	−	0.186943i	0.708958	+	0.705251i	$0.249166\pi$
$588$		0			0
$589$	4.85407	−	14.9393i	0.200009	−	0.615563i
$590$		0			0
$591$	−15.9230	−	49.0060i	−0.654986	−	2.01584i
$592$		0			0
$593$	9.96100	+	7.23709i	0.409049	+	0.297192i	0.773217	−	0.634142i	$-0.218646\pi$
$593$	9.96100	+	7.23709i	0.409049	+	0.297192i	−0.364168	+	0.931333i	$0.618646\pi$
$594$		0			0
$595$	0.340500	+	0.247388i	0.0139591	+	0.0101419i
$596$		0			0
$597$	−4.35900	+	3.16700i	−0.178402	+	0.129617i
$598$		0			0
$599$	−5.42456	−	3.94118i	−0.221642	−	0.161032i	0.471424	−	0.881907i	$-0.343740\pi$
$599$	−5.42456	−	3.94118i	−0.221642	−	0.161032i	−0.693065	+	0.720875i	$0.743740\pi$
$600$		0			0
$601$	−27.0775			−1.10451			−0.552256	−	0.833674i	$-0.686233\pi$
$601$	−27.0775			−1.10451			−0.552256	+	0.833674i	$0.686233\pi$
$602$		0			0
$603$	1.79014	−	5.50948i	0.0729001	−	0.224363i
$604$		0			0
$605$	0.157598	+	0.485038i	0.00640728	+	0.0197196i
$606$		0			0
$607$	−3.87682	−	11.9316i	−0.157355	−	0.484290i	0.841036	−	0.540978i	$-0.181946\pi$
$607$	−3.87682	−	11.9316i	−0.157355	−	0.484290i	−0.998392	+	0.0566881i	$0.981946\pi$
$608$		0			0
$609$	−49.1774	+	35.7295i	−1.99277	+	1.44783i
$610$		0			0
$611$	−4.56975	+	14.0642i	−0.184872	+	0.568978i
$612$		0			0
$613$	13.8363	−	10.0527i	0.558844	−	0.406024i	−0.272192	−	0.962243i	$-0.587749\pi$
$613$	13.8363	−	10.0527i	0.558844	−	0.406024i	0.831036	+	0.556219i	$0.187749\pi$
$614$		0			0
$615$	−0.657841	−	2.05043i	−0.0265267	−	0.0826812i
$616$		0			0
$617$	−33.5372	+	24.3662i	−1.35016	+	0.980947i	−0.351155	+	0.936318i	$0.614211\pi$
$617$	−33.5372	+	24.3662i	−1.35016	+	0.980947i	−0.999004	+	0.0446298i	$0.985789\pi$
$618$		0			0
$619$	−8.31512	+	25.5913i	−0.334213	+	1.02860i	0.632896	+	0.774237i	$0.281866\pi$
$619$	−8.31512	+	25.5913i	−0.334213	+	1.02860i	−0.967108	+	0.254364i	$0.918134\pi$
$620$		0			0
$621$	−26.3566	+	19.1492i	−1.05765	+	0.768429i
$622$		0			0
$623$	3.91001	+	12.0338i	0.156651	+	0.482123i
$624$		0			0
$625$	7.66350	+	23.5858i	0.306540	+	0.943433i
$626$		0			0
$627$	−24.4687	+	75.3070i	−0.977187	+	3.00747i
$628$		0			0
$629$	1.96193			0.0782272
$630$		0			0
$631$	−23.1442	−	16.8152i	−0.921356	−	0.669404i	0.0225055	−	0.999747i	$-0.492836\pi$
$631$	−23.1442	−	16.8152i	−0.921356	−	0.669404i	−0.943861	+	0.330343i	$0.892836\pi$
$632$		0			0
$633$	41.1683	−	29.9105i	1.63629	−	1.18884i
$634$		0			0
$635$	1.05262	+	0.764774i	0.0417720	+	0.0303491i
$636$		0			0
$637$	−1.87888	−	1.36509i	−0.0744439	−	0.0540866i
$638$		0			0
$639$	−24.9735	−	76.8605i	−0.987936	−	3.04055i
$640$		0			0
$641$	8.22063	−	25.3005i	0.324695	−	0.999309i	−0.646883	−	0.762590i	$-0.723928\pi$
$641$	8.22063	−	25.3005i	0.324695	−	0.999309i	0.971578	−	0.236720i	$-0.0760723\pi$
$642$		0			0
$643$	14.0101	−	10.1790i	0.552506	−	0.401419i	−0.276203	−	0.961099i	$-0.589076\pi$
$643$	14.0101	−	10.1790i	0.552506	−	0.401419i	0.828709	+	0.559680i	$0.189076\pi$
$644$		0			0
$645$	−0.608541	−	1.87290i	−0.0239613	−	0.0737453i
$646$		0			0
$647$	15.5571			0.611611			0.305806	−	0.952094i	$-0.401074\pi$
$647$	15.5571			0.611611			0.305806	+	0.952094i	$0.401074\pi$
$648$		0			0
$649$	6.36442	+	4.62402i	0.249825	+	0.181509i
$650$		0			0
$651$	−4.83088	+	14.8679i	−0.189337	+	0.582720i
$652$		0			0
$653$	−32.2386			−1.26160			−0.630798	−	0.775947i	$-0.717272\pi$
$653$	−32.2386			−1.26160			−0.630798	+	0.775947i	$0.717272\pi$
$654$		0			0
$655$	−2.58223			−0.100896
$656$		0			0
$657$	−24.1850			−0.943548
$658$		0			0
$659$	3.35951			0.130868			0.0654340	−	0.997857i	$-0.479157\pi$
$659$	3.35951			0.130868			0.0654340	+	0.997857i	$0.479157\pi$
$660$		0			0
$661$	−13.8362	+	42.5836i	−0.538167	+	1.65631i	0.198536	+	0.980094i	$0.436381\pi$
$661$	−13.8362	+	42.5836i	−0.538167	+	1.65631i	−0.736704	+	0.676215i	$0.763619\pi$
$662$		0			0
$663$	6.12947	+	4.45332i	0.238049	+	0.172953i
$664$		0			0
$665$	−1.90341			−0.0738112
$666$		0			0
$667$	−12.4011	−	38.1668i	−0.480174	−	1.47782i
$668$		0			0
$669$	62.2821	−	45.2506i	2.40797	−	1.74949i
$670$		0			0
$671$	−9.96832	+	30.6793i	−0.384823	+	1.18436i
$672$		0			0
$673$	4.32012	+	13.2960i	0.166528	+	0.512521i	0.999146	−	0.0413272i	$-0.0131586\pi$
$673$	4.32012	+	13.2960i	0.166528	+	0.512521i	−0.832617	+	0.553849i	$0.813159\pi$
$674$		0			0
$675$	28.8418	+	20.9548i	1.11012	+	0.806550i
$676$		0			0
$677$	12.1716	+	8.84322i	0.467794	+	0.339873i	0.796581	−	0.604532i	$-0.206640\pi$
$677$	12.1716	+	8.84322i	0.467794	+	0.339873i	−0.328787	+	0.944404i	$0.606640\pi$
$678$		0			0
$679$	−9.29302	+	6.75177i	−0.356633	+	0.259109i
$680$		0			0
$681$	55.2629	+	40.1508i	2.11768	+	1.53858i
$682$		0			0
$683$	24.9593			0.955040			0.477520	−	0.878621i	$-0.341536\pi$
$683$	24.9593			0.955040			0.477520	+	0.878621i	$0.341536\pi$
$684$		0			0
$685$	−0.377501	+	1.16183i	−0.0144236	+	0.0443912i
$686$		0			0
$687$	−14.1042	−	43.4083i	−0.538109	−	1.65613i
$688$		0			0
$689$	3.40604	+	10.4827i	0.129760	+	0.399359i
$690$		0			0
$691$	5.95289	−	4.32503i	0.226459	−	0.164532i	−0.468770	−	0.883320i	$-0.655303\pi$
$691$	5.95289	−	4.32503i	0.226459	−	0.164532i	0.695229	+	0.718788i	$0.255303\pi$
$692$		0			0
$693$	15.7146	−	48.3645i	0.596948	−	1.83722i
$694$		0			0
$695$	1.87062	−	1.35909i	0.0709567	−	0.0515531i
$696$		0			0
$697$	7.92293	+	5.80128i	0.300102	+	0.219739i
$698$		0			0
$699$	3.27961	−	2.38278i	0.124046	−	0.0901249i
$700$		0			0
$701$	13.0465	−	40.1530i	0.492760	−	1.51656i	−0.327660	−	0.944796i	$-0.606260\pi$
$701$	13.0465	−	40.1530i	0.492760	−	1.51656i	0.820419	−	0.571762i	$-0.193740\pi$
$702$		0			0
$703$	−7.17818	+	5.21525i	−0.270730	+	0.196697i
$704$		0			0
$705$	0.904694	+	2.78436i	0.0340728	+	0.104865i
$706$		0			0
$707$	−0.256269	−	0.788714i	−0.00963797	−	0.0296626i
$708$		0			0
$709$	10.4178	−	32.0627i	0.391249	−	1.20414i	−0.540596	−	0.841283i	$-0.681801\pi$
$709$	10.4178	−	32.0627i	0.391249	−	1.20414i	0.931845	−	0.362858i	$-0.118199\pi$
$710$		0			0
$711$	72.5672			2.72148
$712$		0			0
$713$	−8.34974	−	6.06644i	−0.312700	−	0.227190i
$714$		0			0
$715$	−0.623836	+	0.453243i	−0.0233301	+	0.0169503i
$716$		0			0
$717$	−19.7567	−	14.3541i	−0.737827	−	0.536063i
$718$		0			0
$719$	26.6788	+	19.3833i	0.994953	+	0.722876i	0.961000	−	0.276548i	$-0.0891904\pi$
$719$	26.6788	+	19.3833i	0.994953	+	0.722876i	0.0339527	+	0.999423i	$0.489190\pi$
$720$		0			0
$721$	−6.89502	−	21.2207i	−0.256784	−	0.790299i
$722$		0			0
$723$	21.8305	−	67.1874i	0.811885	−	2.49872i
$724$		0			0
$725$	−35.5280	+	25.8126i	−1.31948	+	0.958655i
$726$		0			0
$727$	13.1176	+	40.3718i	0.486505	+	1.49731i	0.829790	+	0.558076i	$0.188460\pi$
$727$	13.1176	+	40.3718i	0.486505	+	1.49731i	−0.343285	+	0.939231i	$0.611540\pi$
$728$		0			0
$729$	−38.2650			−1.41722
$730$		0			0
$731$	7.26520	+	5.27848i	0.268713	+	0.195231i
$732$		0			0
$733$	15.8306	−	48.7215i	0.584715	−	1.79957i	−0.0156962	−	0.999877i	$-0.504996\pi$
$733$	15.8306	−	48.7215i	0.584715	−	1.79957i	0.600411	−	0.799691i	$-0.295004\pi$
$734$		0			0
$735$	−0.459780			−0.0169593
$736$		0			0
$737$	−4.16641			−0.153472
$738$		0			0
$739$	12.1785			0.447993			0.223996	−	0.974590i	$-0.428090\pi$
$739$	12.1785			0.447993			0.223996	+	0.974590i	$0.428090\pi$
$740$		0			0
$741$	−34.2641			−1.25872
$742$		0			0
$743$	13.8241	−	42.5461i	0.507156	−	1.56087i	−0.289959	−	0.957039i	$-0.593642\pi$
$743$	13.8241	−	42.5461i	0.507156	−	1.56087i	0.797115	−	0.603828i	$-0.206358\pi$
$744$		0			0
$745$	−1.00020	−	0.726686i	−0.0366444	−	0.0266237i
$746$		0			0
$747$	−92.4674			−3.38321
$748$		0			0
$749$	1.42406	+	4.38281i	0.0520340	+	0.160144i
$750$		0			0
$751$	−9.46852	+	6.87928i	−0.345511	+	0.251029i	−0.746984	−	0.664843i	$-0.768499\pi$
$751$	−9.46852	+	6.87928i	−0.345511	+	0.251029i	0.401472	+	0.915871i	$0.368499\pi$
$752$		0			0
$753$	−11.9299	+	36.7165i	−0.434751	+	1.33803i
$754$		0			0
$755$	0.669288	+	2.05986i	0.0243579	+	0.0749659i
$756$		0			0
$757$	32.5633	+	23.6586i	1.18353	+	0.859886i	0.992566	−	0.121711i	$-0.0388380\pi$
$757$	32.5633	+	23.6586i	1.18353	+	0.859886i	0.190966	+	0.981597i	$0.438838\pi$
$758$		0			0
$759$	42.0899	+	30.5801i	1.52777	+	1.10999i
$760$		0			0
$761$	−15.1788	+	11.0280i	−0.550231	+	0.399766i	−0.827871	−	0.560919i	$-0.810448\pi$
$761$	−15.1788	+	11.0280i	−0.550231	+	0.399766i	0.277640	+	0.960685i	$0.410448\pi$
$762$		0			0
$763$	34.3710	+	24.9720i	1.24431	+	0.904046i
$764$		0			0
$765$	0.967936			0.0349958
$766$		0			0
$767$	−1.05195	+	3.23755i	−0.0379835	+	0.116901i
$768$		0			0
$769$	−12.4026	−	38.1712i	−0.447248	−	1.37649i	−0.879999	−	0.474975i	$-0.842457\pi$
$769$	−12.4026	−	38.1712i	−0.447248	−	1.37649i	0.432751	−	0.901513i	$-0.357543\pi$
$770$		0			0
$771$	5.57794	+	17.1671i	0.200885	+	0.618259i
$772$		0			0
$773$	−0.166254	+	0.120791i	−0.00597974	+	0.00434453i	−0.590771	−	0.806839i	$-0.701176\pi$
$773$	−0.166254	+	0.120791i	−0.00597974	+	0.00434453i	0.584791	+	0.811184i	$0.301176\pi$
$774$		0			0
$775$	−3.49005	+	10.7413i	−0.125366	+	0.385837i
$776$		0			0
$777$	7.14388	−	5.19033i	0.256285	−	0.186202i
$778$		0			0
$779$	−44.4090	−	0.164425i	−1.59112	−	0.00589112i
$780$		0			0
$781$	−47.0232	+	34.1643i	−1.68262	+	1.22250i
$782$		0			0
$783$	−19.4556	+	59.8783i	−0.695288	+	2.13988i
$784$		0			0
$785$	−1.41500	+	1.02806i	−0.0505035	+	0.0366930i
$786$		0			0
$787$	−5.74933	−	17.6946i	−0.204941	−	0.630745i	−0.999716	−	0.0238399i	$-0.992411\pi$
$787$	−5.74933	−	17.6946i	−0.204941	−	0.630745i	0.794774	−	0.606905i	$-0.207589\pi$
$788$		0			0
$789$	−9.78080	−	30.1022i	−0.348206	−	1.07167i
$790$		0			0
$791$	−10.3325	+	31.8002i	−0.367382	+	1.13068i
$792$		0			0
$793$	−13.9588			−0.495693
$794$		0			0
$795$	1.76536	+	1.28261i	0.0626110	+	0.0454896i
$796$		0			0
$797$	10.1704	−	7.38923i	0.360254	−	0.261740i	−0.392904	−	0.919580i	$-0.628529\pi$
$797$	10.1704	−	7.38923i	0.360254	−	0.261740i	0.753158	+	0.657840i	$0.228529\pi$
$798$		0			0
$799$	−10.8009	−	7.84730i	−0.382108	−	0.277618i
$800$		0			0
$801$	23.5418	+	17.1041i	0.831810	+	0.604345i
$802$		0			0
$803$	5.37510	+	16.5429i	0.189683	+	0.583785i
$804$		0			0
$805$	−0.386462	+	1.18941i	−0.0136210	+	0.0419211i
$806$		0			0
$807$	41.3738	−	30.0598i	1.45643	−	1.05816i
$808$		0			0
$809$	5.25001	+	16.1579i	0.184580	+	0.568080i	0.999941	−	0.0108734i	$-0.00346119\pi$
$809$	5.25001	+	16.1579i	0.184580	+	0.568080i	−0.815360	+	0.578954i	$0.803461\pi$
$810$		0			0
$811$	−35.0730			−1.23158			−0.615790	−	0.787911i	$-0.711163\pi$
$811$	−35.0730			−1.23158			−0.615790	+	0.787911i	$0.711163\pi$
$812$		0			0
$813$	54.3757	+	39.5062i	1.90704	+	1.38554i
$814$		0			0
$815$	−0.340581	+	1.04820i	−0.0119300	+	0.0367168i
$816$		0			0
$817$	−40.6128			−1.42086
$818$		0			0
$819$	22.0055			0.768933
$820$		0			0
$821$	−44.8979			−1.56695			−0.783474	−	0.621424i	$-0.786554\pi$
$821$	−44.8979			−1.56695			−0.783474	+	0.621424i	$0.786554\pi$
$822$		0			0
$823$	−48.8882			−1.70413			−0.852067	−	0.523432i	$-0.824651\pi$
$823$	−48.8882			−1.70413			−0.852067	+	0.523432i	$0.824651\pi$
$824$		0			0
$825$	17.5928	−	54.1452i	0.612504	−	1.88509i
$826$		0			0
$827$	27.3953	+	19.9038i	0.952627	+	0.692124i	0.951427	−	0.307876i	$-0.0996181\pi$
$827$	27.3953	+	19.9038i	0.952627	+	0.692124i	0.00119990	+	0.999999i	$0.499618\pi$
$828$		0			0
$829$	−38.7065			−1.34433			−0.672166	−	0.740400i	$-0.734636\pi$
$829$	−38.7065			−1.34433			−0.672166	+	0.740400i	$0.734636\pi$
$830$		0			0
$831$	−10.4351	−	32.1158i	−0.361989	−	1.11409i
$832$		0			0
$833$	1.69625	−	1.23240i	0.0587716	−	0.0427001i
$834$		0			0
$835$	0.338628	−	1.04219i	0.0117187	−	0.0360664i
$836$		0			0
$837$	5.00359	+	15.3995i	0.172949	+	0.532283i
$838$		0			0
$839$	−0.190437	−	0.138360i	−0.00657461	−	0.00477673i	0.584493	−	0.811399i	$-0.301293\pi$
$839$	−0.190437	−	0.138360i	−0.00657461	−	0.00477673i	−0.591068	+	0.806622i	$0.701293\pi$
$840$		0			0
$841$	−39.2820	−	28.5401i	−1.35455	−	0.984140i
$842$		0			0
$843$	56.9030	−	41.3424i	1.95984	−	1.42391i
$844$		0			0
$845$	0.946206	+	0.687459i	0.0325505	+	0.0236493i
$846$		0			0
$847$	−10.4675			−0.359669
$848$		0			0
$849$	4.59691	−	14.1478i	0.157766	−	0.485552i
$850$		0			0
$851$	1.80148	+	5.54439i	0.0617540	+	0.190059i
$852$		0			0
$853$	1.14823	+	3.53389i	0.0393146	+	0.120998i	0.968788	−	0.247892i	$-0.0797379\pi$
$853$	1.14823	+	3.53389i	0.0393146	+	0.120998i	−0.929473	+	0.368890i	$0.879738\pi$
$854$		0			0
$855$	−3.54142	+	2.57299i	−0.121114	+	0.0879945i
$856$		0			0
$857$	−12.5794	+	38.7153i	−0.429703	+	1.32249i	0.468715	+	0.883350i	$0.344717\pi$
$857$	−12.5794	+	38.7153i	−0.429703	+	1.32249i	−0.898418	+	0.439141i	$0.855283\pi$
$858$		0			0
$859$	−11.5980	+	8.42646i	−0.395719	+	0.287507i	−0.767795	−	0.640695i	$-0.778646\pi$
$859$	−11.5980	+	8.42646i	−0.395719	+	0.287507i	0.372076	+	0.928202i	$0.378646\pi$
$860$		0			0
$861$	44.1968	+	0.163639i	1.50622	+	0.00557680i
$862$		0			0
$863$	3.26212	−	2.37007i	0.111044	−	0.0806782i	−0.530877	−	0.847449i	$-0.678138\pi$
$863$	3.26212	−	2.37007i	0.111044	−	0.0806782i	0.641921	+	0.766770i	$0.278138\pi$
$864$		0			0
$865$	0.0437396	−	0.134617i	0.00148719	−	0.00457710i
$866$		0			0
$867$	34.4650	−	25.0403i	1.17049	−	0.850413i
$868$		0			0
$869$	−16.1280	−	49.6368i	−0.547104	−	1.68381i
$870$		0			0
$871$	−0.557127	−	1.71466i	−0.0188775	−	0.0580990i
$872$		0			0
$873$	−8.16335	+	25.1242i	−0.276287	+	0.850325i
$874$		0			0
$875$	2.74075			0.0926543
$876$		0			0
$877$	−16.4330	−	11.9393i	−0.554904	−	0.403162i	0.274686	−	0.961534i	$-0.411426\pi$
$877$	−16.4330	−	11.9393i	−0.554904	−	0.403162i	−0.829590	+	0.558372i	$0.811426\pi$
$878$		0			0
$879$	−68.2433	+	49.5817i	−2.30179	+	1.67235i
$880$		0			0
$881$	−10.2682	−	7.46031i	−0.345946	−	0.251344i	0.401221	−	0.915981i	$-0.368586\pi$
$881$	−10.2682	−	7.46031i	−0.345946	−	0.251344i	−0.747166	+	0.664637i	$0.768586\pi$
$882$		0			0
$883$	−23.3797	−	16.9864i	−0.786790	−	0.571636i	0.120219	−	0.992747i	$-0.461640\pi$
$883$	−23.3797	−	16.9864i	−0.786790	−	0.571636i	−0.907009	+	0.421111i	$0.861640\pi$
$884$		0			0
$885$	0.208258	+	0.640954i	0.00700053	+	0.0215454i
$886$		0			0
$887$	−4.00621	+	12.3298i	−0.134515	+	0.413996i	−0.995514	−	0.0946111i	$-0.969839\pi$
$887$	−4.00621	+	12.3298i	−0.134515	+	0.413996i	0.860999	+	0.508607i	$0.169839\pi$
$888$		0			0
$889$	−21.6047	+	15.6967i	−0.724597	+	0.526451i
$890$		0			0
$891$	−5.35867	−	16.4923i	−0.179522	−	0.552513i
$892$		0			0
$893$	60.3775			2.02046
$894$		0			0
$895$	0.153147	+	0.111268i	0.00511913	+	0.00371926i
$896$		0			0
$897$	−6.95685	+	21.4110i	−0.232282	+	0.714891i
$898$		0			0
$899$	−19.9456			−0.665223
$900$		0			0
$901$	−9.95081			−0.331510
$902$		0			0
$903$	40.4188			1.34505
$904$		0			0
$905$	0.859370			0.0285664
$906$		0			0
$907$	−10.0778	+	31.0163i	−0.334628	+	1.02988i	0.632277	+	0.774742i	$0.282120\pi$
$907$	−10.0778	+	31.0163i	−0.334628	+	1.02988i	−0.966905	+	0.255137i	$0.917880\pi$
$908$		0			0
$909$	−1.54297	−	1.12103i	−0.0511771	−	0.0371823i
$910$		0			0
$911$	15.5415			0.514913			0.257456	−	0.966290i	$-0.417116\pi$
$911$	15.5415			0.514913			0.257456	+	0.966290i	$0.417116\pi$
$912$		0			0
$913$	20.5508	+	63.2488i	0.680132	+	2.09323i
$914$		0			0
$915$	−2.23571	+	1.62434i	−0.0739104	+	0.0536991i
$916$		0			0
$917$	16.3777	−	50.4054i	0.540840	−	1.66453i
$918$		0			0
$919$	−5.16735	−	15.9035i	−0.170455	−	0.524607i	0.828942	−	0.559335i	$-0.188943\pi$
$919$	−5.16735	−	15.9035i	−0.170455	−	0.524607i	−0.999397	+	0.0347281i	$0.988943\pi$
$920$		0			0
$921$	20.8547	+	15.1518i	0.687185	+	0.499269i
$922$		0			0
$923$	−20.3480	−	14.7837i	−0.669763	−	0.486611i
$924$		0			0
$925$	5.16106	−	3.74973i	0.169695	−	0.123290i
$926$		0			0
$927$	−41.5143	−	30.1619i	−1.36351	−	0.990646i
$928$		0			0
$929$	2.36456			0.0775786			0.0387893	−	0.999247i	$-0.487650\pi$
$929$	2.36456			0.0775786			0.0387893	+	0.999247i	$0.487650\pi$
$930$		0			0
$931$	−2.93014	+	9.01805i	−0.0960315	+	0.295555i
$932$		0			0
$933$	13.0455	+	40.1498i	0.427089	+	1.31445i
$934$		0			0
$935$	−0.215123	−	0.662080i	−0.00703527	−	0.0216523i
$936$		0			0
$937$	5.07744	−	3.68897i	0.165873	−	0.120514i	−0.501752	−	0.865011i	$-0.667311\pi$
$937$	5.07744	−	3.68897i	0.165873	−	0.120514i	0.667625	+	0.744498i	$0.267311\pi$
$938$		0			0
$939$	22.9944	−	70.7694i	0.750393	−	2.30947i
$940$		0			0
$941$	−21.4042	+	15.5511i	−0.697757	+	0.506950i	−0.879201	−	0.476451i	$-0.841923\pi$
$941$	−21.4042	+	15.5511i	−0.697757	+	0.506950i	0.181444	+	0.983401i	$0.441923\pi$
$942$		0			0
$943$	−9.11939	+	27.7170i	−0.296968	+	0.902589i
$944$		0			0
$945$	1.58733	−	1.15326i	0.0516357	−	0.0375155i
$946$		0			0
$947$	−6.95459	+	21.4040i	−0.225994	+	0.695538i	0.772195	+	0.635385i	$0.219159\pi$
$947$	−6.95459	+	21.4040i	−0.225994	+	0.695538i	−0.998189	+	0.0601524i	$0.980841\pi$
$948$		0			0
$949$	−6.08936	+	4.42418i	−0.197669	+	0.143615i
$950$		0			0
$951$	−6.84855	−	21.0777i	−0.222079	−	0.683490i
$952$		0			0
$953$	−9.94994	−	30.6228i	−0.322310	−	0.991969i	−0.972640	−	0.232317i	$-0.925369\pi$
$953$	−9.94994	−	30.6228i	−0.322310	−	0.991969i	0.650330	−	0.759652i	$-0.274631\pi$
$954$		0			0
$955$	−0.147052	+	0.452579i	−0.00475848	+	0.0146451i
$956$		0			0
$957$	100.543			3.25010
$958$		0			0
$959$	−20.2847	−	14.7377i	−0.655028	−	0.475906i
$960$		0			0
$961$	20.9296	−	15.2062i	0.675148	−	0.490524i
$962$		0			0
$963$	8.57414	+	6.22948i	0.276298	+	0.200742i
$964$		0			0
$965$	2.15669	+	1.56693i	0.0694264	+	0.0504412i
$966$		0			0
$967$	−1.77169	−	5.45270i	−0.0569737	−	0.175347i	0.918520	−	0.395375i	$-0.129385\pi$
$967$	−1.77169	−	5.45270i	−0.0569737	−	0.175347i	−0.975494	+	0.220028i	$0.929385\pi$
$968$		0			0
$969$	9.55901	−	29.4196i	0.307080	−	0.945094i
$970$		0			0
$971$	12.9721	−	9.42479i	0.416295	−	0.302456i	−0.359850	−	0.933010i	$-0.617172\pi$
$971$	12.9721	−	9.42479i	0.416295	−	0.302456i	0.776145	+	0.630554i	$0.217172\pi$
$972$		0			0
$973$	14.6651	+	45.1346i	0.470143	+	1.44695i
$974$		0			0
$975$	24.6356			0.788971
$976$		0			0
$977$	32.4954	+	23.6093i	1.03962	+	0.755327i	0.970211	−	0.242261i	$-0.0778891\pi$
$977$	32.4954	+	23.6093i	1.03962	+	0.755327i	0.0694077	+	0.997588i	$0.477889\pi$
$978$		0			0
$979$	6.46729	−	19.9043i	0.206696	−	0.636144i
$980$		0			0
$981$	97.7059			3.11951
$982$		0			0
$983$	11.0911			0.353752			0.176876	−	0.984233i	$-0.443401\pi$
$983$	11.0911			0.353752			0.176876	+	0.984233i	$0.443401\pi$
$984$		0			0
$985$	−2.04876			−0.0652790
$986$		0			0
$987$	−60.0890			−1.91265
$988$		0			0
$989$	−8.24588	+	25.3782i	−0.262204	+	0.806980i
$990$		0			0
$991$	−18.8704	−	13.7101i	−0.599437	−	0.435516i	0.246242	−	0.969208i	$-0.420804\pi$
$991$	−18.8704	−	13.7101i	−0.599437	−	0.435516i	−0.845679	+	0.533692i	$0.820804\pi$
$992$		0			0
$993$	103.668			3.28981
$994$		0			0
$995$	0.0662004	+	0.203744i	0.00209869	+	0.00645911i
$996$		0			0
$997$	−30.4518	+	22.1245i	−0.964418	+	0.700691i	−0.954173	−	0.299257i	$-0.903261\pi$
$997$	−30.4518	+	22.1245i	−0.964418	+	0.700691i	−0.0102454	+	0.999948i	$0.503261\pi$
$998$		0			0
$999$	2.82627	−	8.69838i	0.0894193	−	0.275204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.u.h.529.5		20
4.3	odd	2		328.2.m.c.201.1	✓	20
41.10	even	5	inner	656.2.u.h.625.5		20
164.51	odd	10		328.2.m.c.297.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
328.2.m.c.201.1	✓	20	4.3	odd	2
328.2.m.c.297.1	yes	20	164.51	odd	10
656.2.u.h.529.5		20	1.1	even	1	trivial
656.2.u.h.625.5		20	41.10	even	5	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:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+2.90830 q^{3} +(0.0357330 - 0.109975i) q^{5} +(1.92009 + 1.39502i) q^{7} +5.45821 q^{9} +O(q^{10})\)	\(q+2.90830 q^{3} +(0.0357330 - 0.109975i) q^{5} +(1.92009 + 1.39502i) q^{7} +5.45821 q^{9} +(-1.21308 - 3.73348i) q^{11} +(1.37428 - 0.998472i) q^{13} +(0.103922 - 0.319840i) q^{15} +(0.473905 + 1.45853i) q^{17} +(-5.61100 - 4.07663i) q^{19} +(5.58419 + 4.05715i) q^{21} +(-3.68664 + 2.67850i) q^{23} +(4.03427 + 2.93107i) q^{25} +7.14920 q^{27} +(-2.72137 + 8.37552i) q^{29} +(0.699881 + 2.15401i) q^{31} +(-3.52800 - 10.8581i) q^{33} +(0.222028 - 0.161313i) q^{35} +(0.395327 - 1.21669i) q^{37} +(3.99682 - 2.90386i) q^{39} +(5.19414 - 3.74446i) q^{41} +(4.73738 - 3.44191i) q^{43} +(0.195038 - 0.600266i) q^{45} +(-7.04288 + 5.11695i) q^{47} +(-0.422480 - 1.30026i) q^{49} +(1.37826 + 4.24184i) q^{51} +(-2.00508 + 6.17101i) q^{53} -0.453937 q^{55} +(-16.3185 - 11.8561i) q^{57} +(-1.62125 + 1.17791i) q^{59} +(-6.64798 - 4.83004i) q^{61} +(10.4802 + 7.61433i) q^{63} +(-0.0606998 - 0.186815i) q^{65} +(0.327972 - 1.00939i) q^{67} +(-10.7219 + 7.78989i) q^{69} +(-4.57540 - 14.0816i) q^{71} -4.43095 q^{73} +(11.7329 + 8.52442i) q^{75} +(2.87908 - 8.86088i) q^{77} +13.2951 q^{79} +4.41740 q^{81} -16.9410 q^{83} +0.177336 q^{85} +(-7.91457 + 24.3585i) q^{87} +(4.31311 + 3.13366i) q^{89} +4.03163 q^{91} +(2.03546 + 6.26451i) q^{93} +(-0.648825 + 0.471399i) q^{95} +(-1.49561 + 4.60301i) q^{97} +(-6.62125 - 20.3781i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more