LMFDB - Embedded newform 690.2.i.d.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (of order $4$, degree $2$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.1
Root			$-0.437016 + 0.437016i$ of defining polynomial
Character	$\chi$	$=$	690.323
Dual form			690.2.i.d.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.70711 - 0.292893i) q^{3} +1.00000i q^{4} -2.23607i q^{5} +(1.00000 + 1.41421i) q^{6} +(0.707107 - 0.707107i) q^{8} +(2.82843 + 1.00000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.70711 - 0.292893i) q^{3} +1.00000i q^{4} -2.23607i q^{5} +(1.00000 + 1.41421i) q^{6} +(0.707107 - 0.707107i) q^{8} +(2.82843 + 1.00000i) q^{9} +(-1.58114 + 1.58114i) q^{10} +2.82843i q^{11} +(0.292893 - 1.70711i) q^{12} +(4.16228 + 4.16228i) q^{13} +(-0.654929 + 3.81721i) q^{15} -1.00000 q^{16} +(-3.65028 - 3.65028i) q^{17} +(-1.29289 - 2.70711i) q^{18} +5.16228i q^{19} +2.23607 q^{20} +(2.00000 - 2.00000i) q^{22} +(0.707107 - 0.707107i) q^{23} +(-1.41421 + 1.00000i) q^{24} -5.00000 q^{25} -5.88635i q^{26} +(-4.53553 - 2.53553i) q^{27} +4.47214 q^{29} +(3.16228 - 2.23607i) q^{30} +10.3246 q^{31} +(0.707107 + 0.707107i) q^{32} +(0.828427 - 4.82843i) q^{33} +5.16228i q^{34} +(-1.00000 + 2.82843i) q^{36} +(5.16228 - 5.16228i) q^{37} +(3.65028 - 3.65028i) q^{38} +(-5.88635 - 8.32456i) q^{39} +(-1.58114 - 1.58114i) q^{40} -6.11584i q^{41} +(-2.83772 - 2.83772i) q^{43} -2.82843 q^{44} +(2.23607 - 6.32456i) q^{45} -1.00000 q^{46} +(8.71478 + 8.71478i) q^{47} +(1.70711 + 0.292893i) q^{48} +7.00000i q^{49} +(3.53553 + 3.53553i) q^{50} +(5.16228 + 7.30056i) q^{51} +(-4.16228 + 4.16228i) q^{52} +(6.70820 - 6.70820i) q^{53} +(1.41421 + 5.00000i) q^{54} +6.32456 q^{55} +(1.51200 - 8.81256i) q^{57} +(-3.16228 - 3.16228i) q^{58} -9.89949 q^{59} +(-3.81721 - 0.654929i) q^{60} +8.00000 q^{61} +(-7.30056 - 7.30056i) q^{62} -1.00000i q^{64} +(9.30714 - 9.30714i) q^{65} +(-4.00000 + 2.82843i) q^{66} +(5.16228 - 5.16228i) q^{67} +(3.65028 - 3.65028i) q^{68} +(-1.41421 + 1.00000i) q^{69} +3.05792i q^{71} +(2.70711 - 1.29289i) q^{72} +(-7.32456 - 7.32456i) q^{73} -7.30056 q^{74} +(8.53553 + 1.46447i) q^{75} -5.16228 q^{76} +(-1.72407 + 10.0486i) q^{78} +3.16228i q^{79} +2.23607i q^{80} +(7.00000 + 5.65685i) q^{81} +(-4.32456 + 4.32456i) q^{82} +(5.88635 - 5.88635i) q^{83} +(-8.16228 + 8.16228i) q^{85} +4.01315i q^{86} +(-7.63441 - 1.30986i) q^{87} +(2.00000 + 2.00000i) q^{88} +0.458991 q^{89} +(-6.05327 + 2.89100i) q^{90} +(0.707107 + 0.707107i) q^{92} +(-17.6251 - 3.02399i) q^{93} -12.3246i q^{94} +11.5432 q^{95} +(-1.00000 - 1.41421i) q^{96} +(1.16228 - 1.16228i) q^{97} +(4.94975 - 4.94975i) q^{98} +(-2.82843 + 8.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 8 q^{6}+O(q^{10}) $ 8 * q - 8 * q^3 + 8 * q^6	$ 8 q - 8 q^{3} + 8 q^{6} + 8 q^{12} + 8 q^{13} - 8 q^{16} - 16 q^{18} + 16 q^{22} - 40 q^{25} - 8 q^{27} + 32 q^{31} - 16 q^{33} - 8 q^{36} + 16 q^{37} - 48 q^{43} - 8 q^{46} + 8 q^{48} + 16 q^{51} - 8 q^{52} + 16 q^{57} + 64 q^{61} - 32 q^{66} + 16 q^{67} + 16 q^{72} - 8 q^{73} + 40 q^{75} - 16 q^{76} + 8 q^{78} + 56 q^{81} + 16 q^{82} - 40 q^{85} + 16 q^{88} - 32 q^{93} - 8 q^{96} - 16 q^{97}+O(q^{100}) $ 8 * q - 8 * q^3 + 8 * q^6 + 8 * q^12 + 8 * q^13 - 8 * q^16 - 16 * q^18 + 16 * q^22 - 40 * q^25 - 8 * q^27 + 32 * q^31 - 16 * q^33 - 8 * q^36 + 16 * q^37 - 48 * q^43 - 8 * q^46 + 8 * q^48 + 16 * q^51 - 8 * q^52 + 16 * q^57 + 64 * q^61 - 32 * q^66 + 16 * q^67 + 16 * q^72 - 8 * q^73 + 40 * q^75 - 16 * q^76 + 8 * q^78 + 56 * q^81 + 16 * q^82 - 40 * q^85 + 16 * q^88 - 32 * q^93 - 8 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.70711	−	0.292893i	−0.985599	−	0.169102i
$3$	−1.70711	−	0.292893i	−0.985599	−	0.169102i
$4$			1.00000i			0.500000i
$5$		−	2.23607i		−	1.00000i
$5$		−	2.23607i		−	1.00000i
$6$	1.00000	+	1.41421i	0.408248	+	0.577350i
$7$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$7$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.82843	+	1.00000i	0.942809	+	0.333333i
$10$	−1.58114	+	1.58114i	−0.500000	+	0.500000i
$11$			2.82843i			0.852803i	0.904534	+	0.426401i	$0.140219\pi$
$11$			2.82843i			0.852803i	−0.904534	+	0.426401i	$0.859781\pi$
$12$	0.292893	−	1.70711i	0.0845510	−	0.492799i
$13$	4.16228	+	4.16228i	1.15441	+	1.15441i	0.985659	+	0.168749i	$0.0539728\pi$
$13$	4.16228	+	4.16228i	1.15441	+	1.15441i	0.168749	+	0.985659i	$0.446027\pi$
$14$		0			0
$15$	−0.654929	+	3.81721i	−0.169102	+	0.985599i
$16$	−1.00000			−0.250000
$17$	−3.65028	−	3.65028i	−0.885323	−	0.885323i	0.108746	−	0.994070i	$-0.465316\pi$
$17$	−3.65028	−	3.65028i	−0.885323	−	0.885323i	−0.994070	+	0.108746i	$0.965316\pi$
$18$	−1.29289	−	2.70711i	−0.304738	−	0.638071i
$19$			5.16228i			1.18431i	0.805825	+	0.592154i	$0.201722\pi$
$19$			5.16228i			1.18431i	−0.805825	+	0.592154i	$0.798278\pi$
$20$	2.23607			0.500000
$21$		0			0
$22$	2.00000	−	2.00000i	0.426401	−	0.426401i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$24$	−1.41421	+	1.00000i	−0.288675	+	0.204124i
$25$	−5.00000			−1.00000
$26$		−	5.88635i		−	1.15441i
$27$	−4.53553	−	2.53553i	−0.872864	−	0.487964i
$28$		0			0
$29$	4.47214			0.830455			0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214			0.830455			0.415227	+	0.909718i	$0.363702\pi$
$30$	3.16228	−	2.23607i	0.577350	−	0.408248i
$31$	10.3246			1.85434			0.927172	−	0.374635i	$-0.122232\pi$
$31$	10.3246			1.85434			0.927172	+	0.374635i	$0.122232\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.828427	−	4.82843i	0.144211	−	0.840521i
$34$			5.16228i			0.885323i
$35$		0			0
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$	5.16228	−	5.16228i	0.848673	−	0.848673i	−0.141294	−	0.989968i	$-0.545126\pi$
$37$	5.16228	−	5.16228i	0.848673	−	0.848673i	0.989968	+	0.141294i	$0.0451264\pi$
$38$	3.65028	−	3.65028i	0.592154	−	0.592154i
$39$	−5.88635	−	8.32456i	−0.942570	−	1.33300i
$40$	−1.58114	−	1.58114i	−0.250000	−	0.250000i
$41$		−	6.11584i		−	0.955134i	−0.878595	−	0.477567i	$-0.841519\pi$
$41$		−	6.11584i		−	0.955134i	0.878595	−	0.477567i	$-0.158481\pi$
$42$		0			0
$43$	−2.83772	−	2.83772i	−0.432749	−	0.432749i	0.456814	−	0.889562i	$-0.348991\pi$
$43$	−2.83772	−	2.83772i	−0.432749	−	0.432749i	−0.889562	+	0.456814i	$0.848991\pi$
$44$	−2.82843			−0.426401
$45$	2.23607	−	6.32456i	0.333333	−	0.942809i
$46$	−1.00000			−0.147442
$47$	8.71478	+	8.71478i	1.27118	+	1.27118i	0.945469	+	0.325712i	$0.105604\pi$
$47$	8.71478	+	8.71478i	1.27118	+	1.27118i	0.325712	+	0.945469i	$0.394396\pi$
$48$	1.70711	+	0.292893i	0.246400	+	0.0422755i
$49$			7.00000i			1.00000i
$50$	3.53553	+	3.53553i	0.500000	+	0.500000i
$51$	5.16228	+	7.30056i	0.722863	+	1.02228i
$52$	−4.16228	+	4.16228i	−0.577204	+	0.577204i
$53$	6.70820	−	6.70820i	0.921443	−	0.921443i	−0.0756888	−	0.997131i	$-0.524116\pi$
$53$	6.70820	−	6.70820i	0.921443	−	0.921443i	0.997131	+	0.0756888i	$0.0241156\pi$
$54$	1.41421	+	5.00000i	0.192450	+	0.680414i
$55$	6.32456			0.852803
$56$		0			0
$57$	1.51200	−	8.81256i	0.200269	−	1.16725i
$58$	−3.16228	−	3.16228i	−0.415227	−	0.415227i
$59$	−9.89949			−1.28880			−0.644402	−	0.764687i	$-0.722894\pi$
$59$	−9.89949			−1.28880			−0.644402	+	0.764687i	$0.722894\pi$
$60$	−3.81721	−	0.654929i	−0.492799	−	0.0845510i
$61$	8.00000			1.02430			0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000			1.02430			0.512148	+	0.858898i	$0.328850\pi$
$62$	−7.30056	−	7.30056i	−0.927172	−	0.927172i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	9.30714	−	9.30714i	1.15441	−	1.15441i
$66$	−4.00000	+	2.82843i	−0.492366	+	0.348155i
$67$	5.16228	−	5.16228i	0.630673	−	0.630673i	−0.317564	−	0.948237i	$-0.602865\pi$
$67$	5.16228	−	5.16228i	0.630673	−	0.630673i	0.948237	+	0.317564i	$0.102865\pi$
$68$	3.65028	−	3.65028i	0.442662	−	0.442662i
$69$	−1.41421	+	1.00000i	−0.170251	+	0.120386i
$70$		0			0
$71$			3.05792i			0.362909i	0.983399	+	0.181454i	$0.0580804\pi$
$71$			3.05792i			0.362909i	−0.983399	+	0.181454i	$0.941920\pi$
$72$	2.70711	−	1.29289i	0.319036	−	0.152369i
$73$	−7.32456	−	7.32456i	−0.857274	−	0.857274i	0.133742	−	0.991016i	$-0.457301\pi$
$73$	−7.32456	−	7.32456i	−0.857274	−	0.857274i	−0.991016	+	0.133742i	$0.957301\pi$
$74$	−7.30056			−0.848673
$75$	8.53553	+	1.46447i	0.985599	+	0.169102i
$76$	−5.16228			−0.592154
$77$		0			0
$78$	−1.72407	+	10.0486i	−0.195213	+	1.13778i
$79$			3.16228i			0.355784i	0.984050	+	0.177892i	$0.0569278\pi$
$79$			3.16228i			0.355784i	−0.984050	+	0.177892i	$0.943072\pi$
$80$			2.23607i			0.250000i
$81$	7.00000	+	5.65685i	0.777778	+	0.628539i
$82$	−4.32456	+	4.32456i	−0.477567	+	0.477567i
$83$	5.88635	−	5.88635i	0.646111	−	0.646111i	−0.305940	−	0.952051i	$-0.598971\pi$
$83$	5.88635	−	5.88635i	0.646111	−	0.646111i	0.952051	+	0.305940i	$0.0989707\pi$
$84$		0			0
$85$	−8.16228	+	8.16228i	−0.885323	+	0.885323i
$86$			4.01315i			0.432749i
$87$	−7.63441	−	1.30986i	−0.818495	−	0.140432i
$88$	2.00000	+	2.00000i	0.213201	+	0.213201i
$89$	0.458991			0.0486529			0.0243264	−	0.999704i	$-0.492256\pi$
$89$	0.458991			0.0486529			0.0243264	+	0.999704i	$0.492256\pi$
$90$	−6.05327	+	2.89100i	−0.638071	+	0.304738i
$91$		0			0
$92$	0.707107	+	0.707107i	0.0737210	+	0.0737210i
$93$	−17.6251	−	3.02399i	−1.82764	−	0.313573i
$94$		−	12.3246i		−	1.27118i
$95$	11.5432			1.18431
$96$	−1.00000	−	1.41421i	−0.102062	−	0.144338i
$97$	1.16228	−	1.16228i	0.118011	−	0.118011i	−0.645635	−	0.763646i	$-0.723407\pi$
$97$	1.16228	−	1.16228i	0.118011	−	0.118011i	0.763646	+	0.645635i	$0.223407\pi$
$98$	4.94975	−	4.94975i	0.500000	−	0.500000i
$99$	−2.82843	+	8.00000i	−0.284268	+	0.804030i
$100$		−	5.00000i		−	0.500000i
$101$			1.64371i			0.163555i	0.996651	+	0.0817776i	$0.0260597\pi$
$101$			1.64371i			0.163555i	−0.996651	+	0.0817776i	$0.973940\pi$
$102$	1.51200	−	8.81256i	0.149710	−	0.872573i
$103$	−11.1623	−	11.1623i	−1.09985	−	1.09985i	−0.994427	−	0.105425i	$-0.966380\pi$
$103$	−11.1623	−	11.1623i	−1.09985	−	1.09985i	−0.105425	−	0.994427i	$-0.533620\pi$
$104$	5.88635			0.577204
$105$		0			0
$106$	−9.48683			−0.921443
$107$	10.3585	+	10.3585i	1.00139	+	1.00139i	0.999999	+	0.00139356i	$0.000443584\pi$
$107$	10.3585	+	10.3585i	1.00139	+	1.00139i	0.00139356	+	0.999999i	$0.499556\pi$
$108$	2.53553	−	4.53553i	0.243982	−	0.436432i
$109$		−	14.3246i		−	1.37204i	−0.727581	−	0.686022i	$-0.759355\pi$
$109$		−	14.3246i		−	1.37204i	0.727581	−	0.686022i	$-0.240645\pi$
$110$	−4.47214	−	4.47214i	−0.426401	−	0.426401i
$111$	−10.3246	+	7.30056i	−0.979963	+	0.692939i
$112$		0			0
$113$	−13.7793	+	13.7793i	−1.29624	+	1.29624i	−0.365391	+	0.930854i	$0.619065\pi$
$113$	−13.7793	+	13.7793i	−1.29624	+	1.29624i	−0.930854	+	0.365391i	$0.880935\pi$
$114$	−7.30056	+	5.16228i	−0.683760	+	0.483492i
$115$	−1.58114	−	1.58114i	−0.147442	−	0.147442i
$116$			4.47214i			0.415227i
$117$	7.61042	+	15.9350i	0.703584	+	1.47319i
$118$	7.00000	+	7.00000i	0.644402	+	0.644402i
$119$		0			0
$120$	2.23607	+	3.16228i	0.204124	+	0.288675i
$121$	3.00000			0.272727
$122$	−5.65685	−	5.65685i	−0.512148	−	0.512148i
$123$	−1.79129	+	10.4404i	−0.161515	+	0.941379i
$124$			10.3246i			0.927172i
$125$			11.1803i			1.00000i
$126$		0			0
$127$	−5.16228	+	5.16228i	−0.458078	+	0.458078i	−0.898024	−	0.439946i	$-0.854998\pi$
$127$	−5.16228	+	5.16228i	−0.458078	+	0.458078i	0.439946	+	0.898024i	$0.354998\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	4.01315	+	5.67544i	0.353338	+	0.499695i
$130$	−13.1623			−1.15441
$131$			7.53006i			0.657904i	0.944347	+	0.328952i	$0.106695\pi$
$131$			7.53006i			0.657904i	−0.944347	+	0.328952i	$0.893305\pi$
$132$	4.82843	+	0.828427i	0.420261	+	0.0721053i
$133$		0			0
$134$	−7.30056			−0.630673
$135$	−5.66963	+	10.1418i	−0.487964	+	0.872864i
$136$	−5.16228			−0.442662
$137$	3.65028	+	3.65028i	0.311865	+	0.311865i	0.845632	−	0.533767i	$-0.179224\pi$
$137$	3.65028	+	3.65028i	0.311865	+	0.311865i	−0.533767	+	0.845632i	$0.679224\pi$
$138$	1.70711	+	0.292893i	0.145319	+	0.0249327i
$139$		−	2.32456i		−	0.197166i	−0.995129	−	0.0985831i	$-0.968569\pi$
$139$		−	2.32456i		−	0.197166i	0.995129	−	0.0985831i	$-0.0314310\pi$
$140$		0			0
$141$	−12.3246	−	17.4296i	−1.03791	−	1.46783i
$142$	2.16228	−	2.16228i	0.181454	−	0.181454i
$143$	−11.7727	+	11.7727i	−0.984483	+	0.984483i
$144$	−2.82843	−	1.00000i	−0.235702	−	0.0833333i
$145$		−	10.0000i		−	0.830455i
$146$			10.3585i			0.857274i
$147$	2.05025	−	11.9497i	0.169102	−	0.985599i
$148$	5.16228	+	5.16228i	0.424337	+	0.424337i
$149$	19.0733			1.56254			0.781271	−	0.624192i	$-0.214572\pi$
$149$	19.0733			1.56254			0.781271	+	0.624192i	$0.214572\pi$
$150$	−5.00000	−	7.07107i	−0.408248	−	0.577350i
$151$	2.32456			0.189170			0.0945848	−	0.995517i	$-0.469848\pi$
$151$	2.32456			0.189170			0.0945848	+	0.995517i	$0.469848\pi$
$152$	3.65028	+	3.65028i	0.296077	+	0.296077i
$153$	−6.67427	−	13.9748i	−0.539583	−	1.12980i
$154$		0			0
$155$		−	23.0864i		−	1.85434i
$156$	8.32456	−	5.88635i	0.666498	−	0.471285i
$157$	−9.48683	+	9.48683i	−0.757132	+	0.757132i	−0.975799	−	0.218668i	$-0.929829\pi$
$157$	−9.48683	+	9.48683i	−0.757132	+	0.757132i	0.218668	+	0.975799i	$0.429829\pi$
$158$	2.23607	−	2.23607i	0.177892	−	0.177892i
$159$	−13.4164	+	9.48683i	−1.06399	+	0.752355i
$160$	1.58114	−	1.58114i	0.125000	−	0.125000i
$161$		0			0
$162$	−0.949747	−	8.94975i	−0.0746192	−	0.703159i
$163$	16.6491	+	16.6491i	1.30406	+	1.30406i	0.925631	+	0.378428i	$0.123535\pi$
$163$	16.6491	+	16.6491i	1.30406	+	1.30406i	0.378428	+	0.925631i	$0.376465\pi$
$164$	6.11584			0.477567
$165$	−10.7967	−	1.85242i	−0.840521	−	0.144211i
$166$	−8.32456			−0.646111
$167$	−3.28742	−	3.28742i	−0.254388	−	0.254388i	0.568379	−	0.822767i	$-0.307571\pi$
$167$	−3.28742	−	3.28742i	−0.254388	−	0.254388i	−0.822767	+	0.568379i	$0.807571\pi$
$168$		0			0
$169$			21.6491i			1.66532i
$170$	11.5432			0.885323
$171$	−5.16228	+	14.6011i	−0.394769	+	1.11658i
$172$	2.83772	−	2.83772i	0.216374	−	0.216374i
$173$	0.229495	−	0.229495i	0.0174482	−	0.0174482i	−0.698329	−	0.715777i	$-0.746073\pi$
$173$	0.229495	−	0.229495i	0.0174482	−	0.0174482i	0.715777	+	0.698329i	$0.246073\pi$
$174$	4.47214	+	6.32456i	0.339032	+	0.479463i
$175$		0			0
$176$		−	2.82843i		−	0.213201i
$177$	16.8995	+	2.89949i	1.27024	+	0.217939i
$178$	−0.324555	−	0.324555i	−0.0243264	−	0.0243264i
$179$	−4.70163			−0.351416			−0.175708	−	0.984442i	$-0.556222\pi$
$179$	−4.70163			−0.351416			−0.175708	+	0.984442i	$0.556222\pi$
$180$	6.32456	+	2.23607i	0.471405	+	0.166667i
$181$	9.67544			0.719170			0.359585	−	0.933112i	$-0.382918\pi$
$181$	9.67544			0.719170			0.359585	+	0.933112i	$0.382918\pi$
$182$		0			0
$183$	−13.6569	−	2.34315i	−1.00954	−	0.173210i
$184$		−	1.00000i		−	0.0737210i
$185$	−11.5432	−	11.5432i	−0.848673	−	0.848673i
$186$	10.3246	+	14.6011i	0.757033	+	1.07061i
$187$	10.3246	−	10.3246i	0.755006	−	0.755006i
$188$	−8.71478	+	8.71478i	−0.635590	+	0.635590i
$189$		0			0
$190$	−8.16228	−	8.16228i	−0.592154	−	0.592154i
$191$		−	0.458991i		−	0.0332114i	−0.999862	−	0.0166057i	$-0.994714\pi$
$191$		−	0.458991i		−	0.0332114i	0.999862	−	0.0166057i	$-0.00528600\pi$
$192$	−0.292893	+	1.70711i	−0.0211377	+	0.123200i
$193$	3.00000	+	3.00000i	0.215945	+	0.215945i	0.806787	−	0.590842i	$-0.201204\pi$
$193$	3.00000	+	3.00000i	0.215945	+	0.215945i	−0.590842	+	0.806787i	$0.701204\pi$
$194$	−1.64371			−0.118011
$195$	−18.6143	+	13.1623i	−1.33300	+	0.942570i
$196$	−7.00000			−0.500000
$197$	11.5432	+	11.5432i	0.822419	+	0.822419i	0.986454	−	0.164035i	$-0.0524511\pi$
$197$	11.5432	+	11.5432i	0.822419	+	0.822419i	−0.164035	+	0.986454i	$0.552451\pi$
$198$	7.65685	−	3.65685i	0.544149	−	0.259881i
$199$			8.83772i			0.626490i	0.949672	+	0.313245i	$0.101416\pi$
$199$			8.83772i			0.626490i	−0.949672	+	0.313245i	$0.898584\pi$
$200$	−3.53553	+	3.53553i	−0.250000	+	0.250000i
$201$	−10.3246	+	7.30056i	−0.728238	+	0.514942i
$202$	1.16228	−	1.16228i	0.0817776	−	0.0817776i
$203$		0			0
$204$	−7.30056	+	5.16228i	−0.511142	+	0.361432i
$205$	−13.6754			−0.955134
$206$			15.7858i			1.09985i
$207$	2.70711	−	1.29289i	0.188157	−	0.0898623i
$208$	−4.16228	−	4.16228i	−0.288602	−	0.288602i
$209$	−14.6011			−1.00998
$210$		0			0
$211$	14.3246			0.986143			0.493072	−	0.869989i	$-0.335874\pi$
$211$	14.3246			0.986143			0.493072	+	0.869989i	$0.335874\pi$
$212$	6.70820	+	6.70820i	0.460721	+	0.460721i
$213$	0.895645	−	5.22020i	0.0613686	−	0.357682i
$214$		−	14.6491i		−	1.00139i
$215$	−6.34534	+	6.34534i	−0.432749	+	0.432749i
$216$	−5.00000	+	1.41421i	−0.340207	+	0.0962250i
$217$		0			0
$218$	−10.1290	+	10.1290i	−0.686022	+	0.686022i
$219$	10.3585	+	14.6491i	0.699962	+	0.989895i
$220$			6.32456i			0.426401i
$221$		−	30.3870i		−	2.04405i
$222$	12.4628	+	2.13829i	0.836451	+	0.143512i
$223$	13.1623	+	13.1623i	0.881411	+	0.881411i	0.993678	−	0.112267i	$-0.0358111\pi$
$223$	13.1623	+	13.1623i	0.881411	+	0.881411i	−0.112267	+	0.993678i	$0.535811\pi$
$224$		0			0
$225$	−14.1421	−	5.00000i	−0.942809	−	0.333333i
$226$	19.4868			1.29624
$227$	4.24264	+	4.24264i	0.281594	+	0.281594i	0.833744	−	0.552151i	$-0.186193\pi$
$227$	4.24264	+	4.24264i	0.281594	+	0.281594i	−0.552151	+	0.833744i	$0.686193\pi$
$228$	8.81256	+	1.51200i	0.583626	+	0.100134i
$229$		−	25.2982i		−	1.67175i	−0.548917	−	0.835877i	$-0.684960\pi$
$229$		−	25.2982i		−	1.67175i	0.548917	−	0.835877i	$-0.315040\pi$
$230$			2.23607i			0.147442i
$231$		0			0
$232$	3.16228	−	3.16228i	0.207614	−	0.207614i
$233$	5.88635	−	5.88635i	0.385628	−	0.385628i	−0.487497	−	0.873125i	$-0.662090\pi$
$233$	5.88635	−	5.88635i	0.385628	−	0.385628i	0.873125	+	0.487497i	$0.162090\pi$
$234$	5.88635	−	16.6491i	0.384803	−	1.08839i
$235$	19.4868	−	19.4868i	1.27118	−	1.27118i
$236$		−	9.89949i		−	0.644402i
$237$	0.926210	−	5.39835i	0.0601638	−	0.350660i
$238$		0			0
$239$	−6.34534			−0.410446			−0.205223	−	0.978715i	$-0.565792\pi$
$239$	−6.34534			−0.410446			−0.205223	+	0.978715i	$0.565792\pi$
$240$	0.654929	−	3.81721i	0.0422755	−	0.246400i
$241$	8.32456			0.536232			0.268116	−	0.963387i	$-0.413599\pi$
$241$	8.32456			0.536232			0.268116	+	0.963387i	$0.413599\pi$
$242$	−2.12132	−	2.12132i	−0.136364	−	0.136364i
$243$	−10.2929	−	11.7071i	−0.660289	−	0.751011i
$244$			8.00000i			0.512148i
$245$	15.6525			1.00000
$246$	8.64911	−	6.11584i	0.551447	−	0.389932i
$247$	−21.4868	+	21.4868i	−1.36717	+	1.36717i
$248$	7.30056	−	7.30056i	0.463586	−	0.463586i
$249$	−11.7727	+	8.32456i	−0.746064	+	0.527547i
$250$	7.90569	−	7.90569i	0.500000	−	0.500000i
$251$		−	5.65685i		−	0.357057i	−0.983935	−	0.178529i	$-0.942866\pi$
$251$		−	5.65685i		−	0.357057i	0.983935	−	0.178529i	$-0.0571337\pi$
$252$		0			0
$253$	2.00000	+	2.00000i	0.125739	+	0.125739i
$254$	7.30056			0.458078
$255$	16.3246	−	11.5432i	1.02228	−	0.722863i
$256$	1.00000			0.0625000
$257$	−16.4743	−	16.4743i	−1.02764	−	1.02764i	−0.999607	−	0.0280335i	$-0.991075\pi$
$257$	−16.4743	−	16.4743i	−1.02764	−	1.02764i	−0.0280335	−	0.999607i	$-0.508925\pi$
$258$	1.17542	−	6.85087i	0.0731786	−	0.426516i
$259$		0			0
$260$	9.30714	+	9.30714i	0.577204	+	0.577204i
$261$	12.6491	+	4.47214i	0.782960	+	0.276818i
$262$	5.32456	−	5.32456i	0.328952	−	0.328952i
$263$	−17.4296	+	17.4296i	−1.07475	+	1.07475i	−0.0777819	+	0.996970i	$0.524784\pi$
$263$	−17.4296	+	17.4296i	−1.07475	+	1.07475i	−0.996970	+	0.0777819i	$0.975216\pi$
$264$	−2.82843	−	4.00000i	−0.174078	−	0.246183i
$265$	−15.0000	−	15.0000i	−0.921443	−	0.921443i
$266$		0			0
$267$	−0.783546	−	0.134435i	−0.0479522	−	0.00822730i
$268$	5.16228	+	5.16228i	0.315336	+	0.315336i
$269$	−18.6143			−1.13493			−0.567466	−	0.823397i	$-0.692076\pi$
$269$	−18.6143			−1.13493			−0.567466	+	0.823397i	$0.692076\pi$
$270$	11.1803	−	3.16228i	0.680414	−	0.192450i
$271$	−6.97367			−0.423620			−0.211810	−	0.977311i	$-0.567936\pi$
$271$	−6.97367			−0.423620			−0.211810	+	0.977311i	$0.567936\pi$
$272$	3.65028	+	3.65028i	0.221331	+	0.221331i
$273$		0			0
$274$		−	5.16228i		−	0.311865i
$275$		−	14.1421i		−	0.852803i
$276$	−1.00000	−	1.41421i	−0.0601929	−	0.0851257i
$277$	4.16228	−	4.16228i	0.250087	−	0.250087i	−0.570919	−	0.821006i	$-0.693413\pi$
$277$	4.16228	−	4.16228i	0.250087	−	0.250087i	0.821006	+	0.570919i	$0.193413\pi$
$278$	−1.64371	+	1.64371i	−0.0985831	+	0.0985831i
$279$	29.2023	+	10.3246i	1.74829	+	0.618115i
$280$		0			0
$281$			2.10270i			0.125437i	0.998031	+	0.0627183i	$0.0199770\pi$
$281$			2.10270i			0.125437i	−0.998031	+	0.0627183i	$0.980023\pi$
$282$	−3.60978	+	21.0393i	−0.214959	+	1.25287i
$283$	−16.6491	−	16.6491i	−0.989687	−	0.989687i	0.0102605	−	0.999947i	$-0.496734\pi$
$283$	−16.6491	−	16.6491i	−0.989687	−	0.989687i	−0.999947	+	0.0102605i	$0.996734\pi$
$284$	−3.05792			−0.181454
$285$	−19.7055	−	3.38093i	−1.16725	−	0.200269i
$286$	16.6491			0.984483
$287$		0			0
$288$	1.29289	+	2.70711i	0.0761845	+	0.159518i
$289$			9.64911i			0.567595i
$290$	−7.07107	+	7.07107i	−0.415227	+	0.415227i
$291$	−2.32456	+	1.64371i	−0.136268	+	0.0963559i
$292$	7.32456	−	7.32456i	0.428637	−	0.428637i
$293$	−0.133369	+	0.133369i	−0.00779148	+	0.00779148i	−0.710992	−	0.703200i	$-0.751754\pi$
$293$	−0.133369	+	0.133369i	−0.00779148	+	0.00779148i	0.703200	+	0.710992i	$0.251754\pi$
$294$	−9.89949	+	7.00000i	−0.577350	+	0.408248i
$295$			22.1359i			1.28880i
$296$		−	7.30056i		−	0.424337i
$297$	7.17157	−	12.8284i	0.416137	−	0.744381i
$298$	−13.4868	−	13.4868i	−0.781271	−	0.781271i
$299$	5.88635			0.340416
$300$	−1.46447	+	8.53553i	−0.0845510	+	0.492799i
$301$		0			0
$302$	−1.64371	−	1.64371i	−0.0945848	−	0.0945848i
$303$	0.481431	−	2.80599i	0.0276575	−	0.161200i
$304$		−	5.16228i		−	0.296077i
$305$		−	17.8885i		−	1.02430i
$306$	−5.16228	+	14.6011i	−0.295108	+	0.834691i
$307$	2.32456	−	2.32456i	0.132669	−	0.132669i	−0.637654	−	0.770323i	$-0.720095\pi$
$307$	2.32456	−	2.32456i	0.132669	−	0.132669i	0.770323	+	0.637654i	$0.220095\pi$
$308$		0			0
$309$	15.7858	+	22.3246i	0.898025	+	1.27000i
$310$	−16.3246	+	16.3246i	−0.927172	+	0.927172i
$311$		−	26.6033i		−	1.50854i	−0.656567	−	0.754268i	$-0.727992\pi$
$311$		−	26.6033i		−	1.50854i	0.656567	−	0.754268i	$-0.272008\pi$
$312$	−10.0486	−	1.72407i	−0.568891	−	0.0976063i
$313$	−9.16228	−	9.16228i	−0.517883	−	0.517883i	0.399048	−	0.916930i	$-0.369341\pi$
$313$	−9.16228	−	9.16228i	−0.517883	−	0.517883i	−0.916930	+	0.399048i	$0.869341\pi$
$314$	13.4164			0.757132
$315$		0			0
$316$	−3.16228			−0.177892
$317$	2.59893	+	2.59893i	0.145971	+	0.145971i	0.776315	−	0.630345i	$-0.217086\pi$
$317$	2.59893	+	2.59893i	0.145971	+	0.145971i	−0.630345	+	0.776315i	$0.717086\pi$
$318$	16.1950	+	2.77863i	0.908173	+	0.155818i
$319$			12.6491i			0.708214i
$320$	−2.23607			−0.125000
$321$	−14.6491	−	20.7170i	−0.817634	−	1.15631i
$322$		0			0
$323$	18.8438	−	18.8438i	1.04850	−	1.04850i
$324$	−5.65685	+	7.00000i	−0.314270	+	0.388889i
$325$	−20.8114	−	20.8114i	−1.15441	−	1.15441i
$326$		−	23.5454i		−	1.30406i
$327$	−4.19557	+	24.4535i	−0.232015	+	1.35228i
$328$	−4.32456	−	4.32456i	−0.238784	−	0.238784i
$329$		0			0
$330$	6.32456	+	8.94427i	0.348155	+	0.492366i
$331$	2.97367			0.163447			0.0817237	−	0.996655i	$-0.473957\pi$
$331$	2.97367			0.163447			0.0817237	+	0.996655i	$0.473957\pi$
$332$	5.88635	+	5.88635i	0.323055	+	0.323055i
$333$	19.7634	−	9.43885i	1.08303	−	0.517246i
$334$			4.64911i			0.254388i
$335$	−11.5432	−	11.5432i	−0.630673	−	0.630673i
$336$		0			0
$337$	−9.48683	+	9.48683i	−0.516781	+	0.516781i	−0.916596	−	0.399815i	$-0.869074\pi$
$337$	−9.48683	+	9.48683i	−0.516781	+	0.516781i	0.399815	+	0.916596i	$0.369074\pi$
$338$	15.3082	−	15.3082i	0.832658	−	0.832658i
$339$	27.5585	−	19.4868i	1.49677	−	1.05838i
$340$	−8.16228	−	8.16228i	−0.442662	−	0.442662i
$341$			29.2023i			1.58139i
$342$	13.9748	−	6.67427i	0.755673	−	0.360903i
$343$		0			0
$344$	−4.01315			−0.216374
$345$	2.23607	+	3.16228i	0.120386	+	0.170251i
$346$	−0.324555			−0.0174482
$347$	0.955223	+	0.955223i	0.0512791	+	0.0512791i	0.732281	−	0.681002i	$-0.238456\pi$
$347$	0.955223	+	0.955223i	0.0512791	+	0.0512791i	−0.681002	+	0.732281i	$0.738456\pi$
$348$	1.30986	−	7.63441i	0.0702158	−	0.409248i
$349$		−	14.0000i		−	0.749403i	−0.927146	−	0.374701i	$-0.877745\pi$
$349$		−	14.0000i		−	0.749403i	0.927146	−	0.374701i	$-0.122255\pi$
$350$		0			0
$351$	−8.32456	−	29.4317i	−0.444332	−	1.57095i
$352$	−2.00000	+	2.00000i	−0.106600	+	0.106600i
$353$	−17.6590	+	17.6590i	−0.939896	+	0.939896i	−0.998293	−	0.0583971i	$-0.981401\pi$
$353$	−17.6590	+	17.6590i	−0.939896	+	0.939896i	0.0583971	+	0.998293i	$0.481401\pi$
$354$	−9.89949	−	14.0000i	−0.526152	−	0.744092i
$355$	6.83772			0.362909
$356$			0.458991i			0.0243264i
$357$		0			0
$358$	3.32456	+	3.32456i	0.175708	+	0.175708i
$359$	−19.7990			−1.04495			−0.522475	−	0.852654i	$-0.674991\pi$
$359$	−19.7990			−1.04495			−0.522475	+	0.852654i	$0.674991\pi$
$360$	−2.89100	−	6.05327i	−0.152369	−	0.319036i
$361$	−7.64911			−0.402585
$362$	−6.84157	−	6.84157i	−0.359585	−	0.359585i
$363$	−5.12132	−	0.878680i	−0.268800	−	0.0461187i
$364$		0			0
$365$	−16.3782	+	16.3782i	−0.857274	+	0.857274i
$366$	8.00000	+	11.3137i	0.418167	+	0.591377i
$367$	1.48683	−	1.48683i	0.0776120	−	0.0776120i	−0.667235	−	0.744847i	$-0.732522\pi$
$367$	1.48683	−	1.48683i	0.0776120	−	0.0776120i	0.744847	+	0.667235i	$0.232522\pi$
$368$	−0.707107	+	0.707107i	−0.0368605	+	0.0368605i
$369$	6.11584	−	17.2982i	0.318378	−	0.900509i
$370$			16.3246i			0.848673i
$371$		0			0
$372$	3.02399	−	17.6251i	0.156787	−	0.913820i
$373$	13.4868	+	13.4868i	0.698322	+	0.698322i	0.964048	−	0.265727i	$-0.0856119\pi$
$373$	13.4868	+	13.4868i	0.698322	+	0.698322i	−0.265727	+	0.964048i	$0.585612\pi$
$374$	−14.6011			−0.755006
$375$	3.27465	−	19.0860i	0.169102	−	0.985599i
$376$	12.3246			0.635590
$377$	18.6143	+	18.6143i	0.958684	+	0.958684i
$378$		0			0
$379$			3.48683i			0.179107i	0.995982	+	0.0895533i	$0.0285439\pi$
$379$			3.48683i			0.179107i	−0.995982	+	0.0895533i	$0.971456\pi$
$380$			11.5432i			0.592154i
$381$	10.3246	−	7.30056i	0.528943	−	0.374019i
$382$	−0.324555	+	0.324555i	−0.0166057	+	0.0166057i
$383$	−6.84157	+	6.84157i	−0.349588	+	0.349588i	−0.859956	−	0.510368i	$-0.829509\pi$
$383$	−6.84157	+	6.84157i	−0.349588	+	0.349588i	0.510368	+	0.859956i	$0.329509\pi$
$384$	1.41421	−	1.00000i	0.0721688	−	0.0510310i
$385$		0			0
$386$		−	4.24264i		−	0.215945i
$387$	−5.18857	−	10.8640i	−0.263750	−	0.552249i
$388$	1.16228	+	1.16228i	0.0590057	+	0.0590057i
$389$	12.4984			0.633695			0.316848	−	0.948476i	$-0.397376\pi$
$389$	12.4984			0.633695			0.316848	+	0.948476i	$0.397376\pi$
$390$	22.4694	+	3.85514i	1.13778	+	0.195213i
$391$	−5.16228			−0.261068
$392$	4.94975	+	4.94975i	0.250000	+	0.250000i
$393$	2.20550	−	12.8546i	0.111253	−	0.648429i
$394$		−	16.3246i		−	0.822419i
$395$	7.07107			0.355784
$396$	−8.00000	−	2.82843i	−0.402015	−	0.142134i
$397$	6.81139	−	6.81139i	0.341854	−	0.341854i	−0.515210	−	0.857064i	$-0.672286\pi$
$397$	6.81139	−	6.81139i	0.341854	−	0.341854i	0.857064	+	0.515210i	$0.172286\pi$
$398$	6.24921	−	6.24921i	0.313245	−	0.313245i
$399$		0			0
$400$	5.00000			0.250000
$401$		−	19.7990i		−	0.988714i	−0.869259	−	0.494357i	$-0.835403\pi$
$401$		−	19.7990i		−	0.988714i	0.869259	−	0.494357i	$-0.164597\pi$
$402$	12.4628	+	2.13829i	0.621590	+	0.106648i
$403$	42.9737	+	42.9737i	2.14067	+	2.14067i
$404$	−1.64371			−0.0817776
$405$	12.6491	−	15.6525i	0.628539	−	0.777778i
$406$		0			0
$407$	14.6011	+	14.6011i	0.723751	+	0.723751i
$408$	8.81256	+	1.51200i	0.436287	+	0.0748550i
$409$			20.0000i			0.988936i	0.869196	+	0.494468i	$0.164637\pi$
$409$			20.0000i			0.988936i	−0.869196	+	0.494468i	$0.835363\pi$
$410$	9.67000	+	9.67000i	0.477567	+	0.477567i
$411$	−5.16228	−	7.30056i	−0.254636	−	0.360110i
$412$	11.1623	−	11.1623i	0.549926	−	0.549926i
$413$		0			0
$414$	−2.82843	−	1.00000i	−0.139010	−	0.0491473i
$415$	−13.1623	−	13.1623i	−0.646111	−	0.646111i
$416$			5.88635i			0.288602i
$417$	−0.680846	+	3.96826i	−0.0333412	+	0.194327i
$418$	10.3246	+	10.3246i	0.504991	+	0.504991i
$419$	−26.3738			−1.28845			−0.644223	−	0.764838i	$-0.722819\pi$
$419$	−26.3738			−1.28845			−0.644223	+	0.764838i	$0.722819\pi$
$420$		0			0
$421$	11.3509			0.553208			0.276604	−	0.960984i	$-0.410791\pi$
$421$	11.3509			0.553208			0.276604	+	0.960984i	$0.410791\pi$
$422$	−10.1290	−	10.1290i	−0.493072	−	0.493072i
$423$	15.9343	+	33.3639i	0.774754	+	1.62221i
$424$		−	9.48683i		−	0.460721i
$425$	18.2514	+	18.2514i	0.885323	+	0.885323i
$426$	−4.32456	+	3.05792i	−0.209525	+	0.148157i
$427$		0			0
$428$	−10.3585	+	10.3585i	−0.500696	+	0.500696i
$429$	23.5454	−	16.6491i	1.13678	−	0.803827i
$430$	8.97367			0.432749
$431$		−	6.11584i		−	0.294590i	−0.989093	−	0.147295i	$-0.952943\pi$
$431$		−	6.11584i		−	0.294590i	0.989093	−	0.147295i	$-0.0470566\pi$
$432$	4.53553	+	2.53553i	0.218216	+	0.121991i
$433$	16.1359	+	16.1359i	0.775444	+	0.775444i	0.979052	−	0.203608i	$-0.0652669\pi$
$433$	16.1359	+	16.1359i	0.775444	+	0.775444i	−0.203608	+	0.979052i	$0.565267\pi$
$434$		0			0
$435$	−2.92893	+	17.0711i	−0.140432	+	0.818495i
$436$	14.3246			0.686022
$437$	3.65028	+	3.65028i	0.174617	+	0.174617i
$438$	3.03393	−	17.6830i	0.144967	−	0.844928i
$439$		−	11.3509i		−	0.541748i	−0.962615	−	0.270874i	$-0.912687\pi$
$439$		−	11.3509i		−	0.541748i	0.962615	−	0.270874i	$-0.0873127\pi$
$440$	4.47214	−	4.47214i	0.213201	−	0.213201i
$441$	−7.00000	+	19.7990i	−0.333333	+	0.942809i
$442$	−21.4868	+	21.4868i	−1.02202	+	1.02202i
$443$	−11.3137	+	11.3137i	−0.537531	+	0.537531i	−0.922803	−	0.385272i	$-0.874107\pi$
$443$	−11.3137	+	11.3137i	−0.537531	+	0.537531i	0.385272	+	0.922803i	$0.374107\pi$
$444$	−7.30056	−	10.3246i	−0.346469	−	0.489982i
$445$		−	1.02633i		−	0.0486529i
$446$		−	18.6143i		−	0.881411i
$447$	−32.5601	−	5.58643i	−1.54004	−	0.264229i
$448$		0			0
$449$	5.65685			0.266963			0.133482	−	0.991051i	$-0.457384\pi$
$449$	5.65685			0.266963			0.133482	+	0.991051i	$0.457384\pi$
$450$	6.46447	+	13.5355i	0.304738	+	0.638071i
$451$	17.2982			0.814541
$452$	−13.7793	−	13.7793i	−0.648122	−	0.648122i
$453$	−3.96826	−	0.680846i	−0.186445	−	0.0319890i
$454$		−	6.00000i		−	0.281594i
$455$		0			0
$456$	−5.16228	−	7.30056i	−0.241746	−	0.341880i
$457$	−19.1623	+	19.1623i	−0.896374	+	0.896374i	−0.995113	−	0.0987397i	$-0.968519\pi$
$457$	−19.1623	+	19.1623i	−0.896374	+	0.896374i	0.0987397	+	0.995113i	$0.468519\pi$
$458$	−17.8885	+	17.8885i	−0.835877	+	0.835877i
$459$	7.30056	+	25.8114i	0.340761	+	1.20477i
$460$	1.58114	−	1.58114i	0.0737210	−	0.0737210i
$461$			4.01315i			0.186911i	0.995623	+	0.0934554i	$0.0297913\pi$
$461$			4.01315i			0.186911i	−0.995623	+	0.0934554i	$0.970209\pi$
$462$		0			0
$463$	−26.1359	−	26.1359i	−1.21464	−	1.21464i	−0.969483	−	0.245157i	$-0.921161\pi$
$463$	−26.1359	−	26.1359i	−1.21464	−	1.21464i	−0.245157	−	0.969483i	$-0.578839\pi$
$464$	−4.47214			−0.207614
$465$	−6.76185	+	39.4110i	−0.313573	+	1.82764i
$466$	−8.32456			−0.385628
$467$	4.70163	+	4.70163i	0.217566	+	0.217566i	0.807472	−	0.589906i	$-0.200835\pi$
$467$	4.70163	+	4.70163i	0.217566	+	0.217566i	−0.589906	+	0.807472i	$0.700835\pi$
$468$	−15.9350	+	7.61042i	−0.736595	+	0.351792i
$469$		0			0
$470$	−27.5585			−1.27118
$471$	18.9737	−	13.4164i	0.874260	−	0.618195i
$472$	−7.00000	+	7.00000i	−0.322201	+	0.322201i
$473$	8.02629	−	8.02629i	0.369049	−	0.369049i
$474$	−4.47214	+	3.16228i	−0.205412	+	0.145248i
$475$		−	25.8114i		−	1.18431i
$476$		0			0
$477$	25.6819	−	12.2655i	1.17589	−	0.561597i
$478$	4.48683	+	4.48683i	0.205223	+	0.205223i
$479$	28.2843			1.29234			0.646171	−	0.763193i	$-0.276369\pi$
$479$	28.2843			1.29234			0.646171	+	0.763193i	$0.276369\pi$
$480$	−3.16228	+	2.23607i	−0.144338	+	0.102062i
$481$	42.9737			1.95943
$482$	−5.88635	−	5.88635i	−0.268116	−	0.268116i
$483$		0			0
$484$			3.00000i			0.136364i
$485$	−2.59893	−	2.59893i	−0.118011	−	0.118011i
$486$	−1.00000	+	15.5563i	−0.0453609	+	0.705650i
$487$	−23.1623	+	23.1623i	−1.04958	+	1.04958i	−0.0508781	+	0.998705i	$0.516202\pi$
$487$	−23.1623	+	23.1623i	−1.04958	+	1.04958i	−0.998705	+	0.0508781i	$0.983798\pi$
$488$	5.65685	−	5.65685i	0.256074	−	0.256074i
$489$	−23.5454	−	33.2982i	−1.06476	−	1.50580i
$490$	−11.0680	−	11.0680i	−0.500000	−	0.500000i
$491$			9.89949i			0.446758i	0.974732	+	0.223379i	$0.0717087\pi$
$491$			9.89949i			0.446758i	−0.974732	+	0.223379i	$0.928291\pi$
$492$	−10.4404	−	1.79129i	−0.470690	−	0.0807576i
$493$	−16.3246	−	16.3246i	−0.735221	−	0.735221i
$494$	30.3870			1.36717
$495$	17.8885	+	6.32456i	0.804030	+	0.284268i
$496$	−10.3246			−0.463586
$497$		0			0
$498$	14.2109	+	2.43821i	0.636806	+	0.109259i
$499$		−	15.3509i		−	0.687200i	−0.939116	−	0.343600i	$-0.888354\pi$
$499$		−	15.3509i		−	0.687200i	0.939116	−	0.343600i	$-0.111646\pi$
$500$	−11.1803			−0.500000
$501$	4.64911	+	6.57484i	0.207707	+	0.293742i
$502$	−4.00000	+	4.00000i	−0.178529	+	0.178529i
$503$	15.7858	−	15.7858i	0.703856	−	0.703856i	−0.261380	−	0.965236i	$-0.584178\pi$
$503$	15.7858	−	15.7858i	0.703856	−	0.703856i	0.965236	+	0.261380i	$0.0841776\pi$
$504$		0			0
$505$	3.67544			0.163555
$506$		−	2.82843i		−	0.125739i
$507$	6.34088	−	36.9573i	0.281608	−	1.64133i
$508$	−5.16228	−	5.16228i	−0.229039	−	0.229039i
$509$	−27.0996			−1.20117			−0.600583	−	0.799562i	$-0.705065\pi$
$509$	−27.0996			−1.20117			−0.600583	+	0.799562i	$0.705065\pi$
$510$	−19.7055	−	3.38093i	−0.872573	−	0.149710i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	13.0891	−	23.4137i	0.577899	−	1.03374i
$514$			23.2982i			1.02764i
$515$	−24.9596	+	24.9596i	−1.09985	+	1.09985i
$516$	−5.67544	+	4.01315i	−0.249848	+	0.176669i
$517$	−24.6491	+	24.6491i	−1.08407	+	1.08407i
$518$		0			0
$519$	−0.458991	+	0.324555i	−0.0201474	+	0.0142464i
$520$		−	13.1623i		−	0.577204i
$521$			9.40326i			0.411964i	0.978556	+	0.205982i	$0.0660389\pi$
$521$			9.40326i			0.411964i	−0.978556	+	0.205982i	$0.933961\pi$
$522$	−5.78199	−	12.1065i	−0.253071	−	0.529889i
$523$	−21.2982	−	21.2982i	−0.931306	−	0.931306i	0.0664815	−	0.997788i	$-0.478823\pi$
$523$	−21.2982	−	21.2982i	−0.931306	−	0.931306i	−0.997788	+	0.0664815i	$0.978823\pi$
$524$	−7.53006			−0.328952
$525$		0			0
$526$	24.6491			1.07475
$527$	−37.6875	−	37.6875i	−1.64169	−	1.64169i
$528$	−0.828427	+	4.82843i	−0.0360527	+	0.210130i
$529$		−	1.00000i		−	0.0434783i
$530$			21.2132i			0.921443i
$531$	−28.0000	−	9.89949i	−1.21510	−	0.429601i
$532$		0			0
$533$	25.4558	−	25.4558i	1.10262	−	1.10262i
$534$	0.458991	+	0.649111i	0.0198625	+	0.0280898i
$535$	23.1623	−	23.1623i	1.00139	−	1.00139i
$536$		−	7.30056i		−	0.315336i
$537$	8.02619	+	1.37708i	0.346356	+	0.0594252i
$538$	13.1623	+	13.1623i	0.567466	+	0.567466i
$539$	−19.7990			−0.852803
$540$	−10.1418	−	5.66963i	−0.436432	−	0.243982i
$541$	26.3246			1.13178			0.565891	−	0.824480i	$-0.308532\pi$
$541$	26.3246			1.13178			0.565891	+	0.824480i	$0.308532\pi$
$542$	4.93113	+	4.93113i	0.211810	+	0.211810i
$543$	−16.5170	−	2.83387i	−0.708813	−	0.121613i
$544$		−	5.16228i		−	0.221331i
$545$	−32.0307			−1.37204
$546$		0			0
$547$	6.32456	−	6.32456i	0.270418	−	0.270418i	−0.558850	−	0.829269i	$-0.688757\pi$
$547$	6.32456	−	6.32456i	0.270418	−	0.270418i	0.829269	+	0.558850i	$0.188757\pi$
$548$	−3.65028	+	3.65028i	−0.155932	+	0.155932i
$549$	22.6274	+	8.00000i	0.965715	+	0.341432i
$550$	−10.0000	+	10.0000i	−0.426401	+	0.426401i
$551$			23.0864i			0.983514i
$552$	−0.292893	+	1.70711i	−0.0124664	+	0.0726593i
$553$		0			0
$554$	−5.88635			−0.250087
$555$	16.3246	+	23.0864i	0.692939	+	0.979963i
$556$	2.32456			0.0985831
$557$	22.0351	+	22.0351i	0.933655	+	0.933655i	0.997932	−	0.0642767i	$-0.0204740\pi$
$557$	22.0351	+	22.0351i	0.933655	+	0.933655i	−0.0642767	+	0.997932i	$0.520474\pi$
$558$	−13.3485	−	27.9497i	−0.565089	−	1.18320i
$559$		−	23.6228i		−	0.999137i
$560$		0			0
$561$	−20.6491	+	14.6011i	−0.871806	+	0.616460i
$562$	1.48683	−	1.48683i	0.0627183	−	0.0627183i
$563$	−3.05792	+	3.05792i	−0.128876	+	0.128876i	−0.768603	−	0.639727i	$-0.779048\pi$
$563$	−3.05792	+	3.05792i	−0.128876	+	0.128876i	0.639727	+	0.768603i	$0.279048\pi$
$564$	17.4296	−	12.3246i	0.733917	−	0.518957i
$565$	30.8114	+	30.8114i	1.29624	+	1.29624i
$566$			23.5454i			0.989687i
$567$		0			0
$568$	2.16228	+	2.16228i	0.0907272	+	0.0907272i
$569$	−1.18472			−0.0496660			−0.0248330	−	0.999692i	$-0.507905\pi$
$569$	−1.18472			−0.0496660			−0.0248330	+	0.999692i	$0.507905\pi$
$570$	11.5432	+	16.3246i	0.483492	+	0.683760i
$571$	−17.1623			−0.718219			−0.359109	−	0.933295i	$-0.616920\pi$
$571$	−17.1623			−0.718219			−0.359109	+	0.933295i	$0.616920\pi$
$572$	−11.7727	−	11.7727i	−0.492241	−	0.492241i
$573$	−0.134435	+	0.783546i	−0.00561611	+	0.0327331i
$574$		0			0
$575$	−3.53553	+	3.53553i	−0.147442	+	0.147442i
$576$	1.00000	−	2.82843i	0.0416667	−	0.117851i
$577$	−19.3246	+	19.3246i	−0.804492	+	0.804492i	−0.983794	−	0.179302i	$-0.942616\pi$
$577$	−19.3246	+	19.3246i	−0.804492	+	0.804492i	0.179302	+	0.983794i	$0.442616\pi$
$578$	6.82295	−	6.82295i	0.283797	−	0.283797i
$579$	−4.24264	−	6.00000i	−0.176318	−	0.249351i
$580$	10.0000			0.415227
$581$		0			0
$582$	2.80599	+	0.481431i	0.116312	+	0.0199560i
$583$	18.9737	+	18.9737i	0.785809	+	0.785809i
$584$	−10.3585			−0.428637
$585$	35.6317	−	17.0174i	1.47319	−	0.703584i
$586$	0.188612			0.00779148
$587$	−7.07107	−	7.07107i	−0.291854	−	0.291854i	0.545958	−	0.837812i	$-0.316166\pi$
$587$	−7.07107	−	7.07107i	−0.291854	−	0.291854i	−0.837812	+	0.545958i	$0.816166\pi$
$588$	11.9497	+	2.05025i	0.492799	+	0.0845510i
$589$			53.2982i			2.19611i
$590$	15.6525	−	15.6525i	0.644402	−	0.644402i
$591$	−16.3246	−	23.0864i	−0.671502	−	0.949648i
$592$	−5.16228	+	5.16228i	−0.212168	+	0.212168i
$593$	−7.98905	+	7.98905i	−0.328071	+	0.328071i	−0.851853	−	0.523782i	$-0.824521\pi$
$593$	−7.98905	+	7.98905i	−0.328071	+	0.328071i	0.523782	+	0.851853i	$0.324521\pi$
$594$	−14.1421	+	4.00000i	−0.580259	+	0.164122i
$595$		0			0
$596$			19.0733i			0.781271i
$597$	2.58851	−	15.0869i	0.105941	−	0.617467i
$598$	−4.16228	−	4.16228i	−0.170208	−	0.170208i
$599$	8.25579			0.337322			0.168661	−	0.985674i	$-0.446056\pi$
$599$	8.25579			0.337322			0.168661	+	0.985674i	$0.446056\pi$
$600$	7.07107	−	5.00000i	0.288675	−	0.204124i
$601$	−34.6491			−1.41337			−0.706683	−	0.707530i	$-0.749809\pi$
$601$	−34.6491			−1.41337			−0.706683	+	0.707530i	$0.749809\pi$
$602$		0			0
$603$	19.7634	−	9.43885i	0.804828	−	0.384380i
$604$			2.32456i			0.0945848i
$605$		−	6.70820i		−	0.272727i
$606$	−2.32456	+	1.64371i	−0.0944286	+	0.0667711i
$607$	0.837722	−	0.837722i	0.0340021	−	0.0340021i	−0.689901	−	0.723903i	$-0.742346\pi$
$607$	0.837722	−	0.837722i	0.0340021	−	0.0340021i	0.723903	+	0.689901i	$0.242346\pi$
$608$	−3.65028	+	3.65028i	−0.148038	+	0.148038i
$609$		0			0
$610$	−12.6491	+	12.6491i	−0.512148	+	0.512148i
$611$			72.5466i			2.93492i
$612$	13.9748	−	6.67427i	0.564899	−	0.269792i
$613$	−26.4605	−	26.4605i	−1.06873	−	1.06873i	−0.997457	−	0.0712726i	$-0.977294\pi$
$613$	−26.4605	−	26.4605i	−1.06873	−	1.06873i	−0.0712726	−	0.997457i	$-0.522706\pi$
$614$	−3.28742			−0.132669
$615$	23.3454	+	4.00545i	0.941379	+	0.161515i
$616$		0			0
$617$	−7.66343	−	7.66343i	−0.308518	−	0.308518i	0.535817	−	0.844334i	$-0.320004\pi$
$617$	−7.66343	−	7.66343i	−0.308518	−	0.308518i	−0.844334	+	0.535817i	$0.820004\pi$
$618$	4.62357	−	26.9481i	0.185987	−	1.08401i
$619$		−	18.4605i		−	0.741990i	−0.928635	−	0.370995i	$-0.879017\pi$
$619$		−	18.4605i		−	0.741990i	0.928635	−	0.370995i	$-0.120983\pi$
$620$	23.0864			0.927172
$621$	−5.00000	+	1.41421i	−0.200643	+	0.0567504i
$622$	−18.8114	+	18.8114i	−0.754268	+	0.754268i
$623$		0			0
$624$	5.88635	+	8.32456i	0.235643	+	0.333249i
$625$	25.0000			1.00000
$626$			12.9574i			0.517883i
$627$	24.9257	+	4.27657i	0.995436	+	0.170790i
$628$	−9.48683	−	9.48683i	−0.378566	−	0.378566i
$629$	−37.6875			−1.50270
$630$		0			0
$631$	−27.8114			−1.10715			−0.553577	−	0.832798i	$-0.686738\pi$
$631$	−27.8114			−1.10715			−0.553577	+	0.832798i	$0.686738\pi$
$632$	2.23607	+	2.23607i	0.0889460	+	0.0889460i
$633$	−24.4535	−	4.19557i	−0.971941	−	0.166759i
$634$		−	3.67544i		−	0.145971i
$635$	11.5432	+	11.5432i	0.458078	+	0.458078i
$636$	−9.48683	−	13.4164i	−0.376177	−	0.531995i
$637$	−29.1359	+	29.1359i	−1.15441	+	1.15441i
$638$	8.94427	−	8.94427i	0.354107	−	0.354107i
$639$	−3.05792	+	8.64911i	−0.120970	+	0.342154i
$640$	1.58114	+	1.58114i	0.0625000	+	0.0625000i
$641$		−	10.8547i		−	0.428736i	−0.976753	−	0.214368i	$-0.931231\pi$
$641$		−	10.8547i		−	0.428736i	0.976753	−	0.214368i	$-0.0687691\pi$
$642$	−4.29063	+	25.0076i	−0.169337	+	0.986971i
$643$	−5.16228	−	5.16228i	−0.203580	−	0.203580i	0.597952	−	0.801532i	$-0.295981\pi$
$643$	−5.16228	−	5.16228i	−0.203580	−	0.203580i	−0.801532	+	0.597952i	$0.795981\pi$
$644$		0			0
$645$	12.6907	−	8.97367i	0.499695	−	0.353338i
$646$	−26.6491			−1.04850
$647$	−19.5695	−	19.5695i	−0.769356	−	0.769356i	0.208637	−	0.977993i	$-0.433097\pi$
$647$	−19.5695	−	19.5695i	−0.769356	−	0.769356i	−0.977993	+	0.208637i	$0.933097\pi$
$648$	8.94975	−	0.949747i	0.351579	−	0.0373096i
$649$		−	28.0000i		−	1.09910i
$650$			29.4317i			1.15441i
$651$		0			0
$652$	−16.6491	+	16.6491i	−0.652029	+	0.652029i
$653$	−17.6590	+	17.6590i	−0.691052	+	0.691052i	−0.962463	−	0.271411i	$-0.912510\pi$
$653$	−17.6590	+	17.6590i	−0.691052	+	0.691052i	0.271411	+	0.962463i	$0.412510\pi$
$654$	20.2580	−	14.3246i	0.792150	−	0.560134i
$655$	16.8377			0.657904
$656$			6.11584i			0.238784i
$657$	−13.3924	−	28.0415i	−0.522488	−	1.09400i
$658$		0			0
$659$	8.94427			0.348419			0.174210	−	0.984709i	$-0.444263\pi$
$659$	8.94427			0.348419			0.174210	+	0.984709i	$0.444263\pi$
$660$	1.85242	−	10.7967i	0.0721053	−	0.420261i
$661$	−32.6491			−1.26990			−0.634952	−	0.772552i	$-0.718980\pi$
$661$	−32.6491			−1.26990			−0.634952	+	0.772552i	$0.718980\pi$
$662$	−2.10270	−	2.10270i	−0.0817237	−	0.0817237i
$663$	−8.90014	+	51.8738i	−0.345653	+	2.01461i
$664$		−	8.32456i		−	0.323055i
$665$		0			0
$666$	−20.6491	−	7.30056i	−0.800137	−	0.282891i
$667$	3.16228	−	3.16228i	0.122444	−	0.122444i
$668$	3.28742	−	3.28742i	0.127194	−	0.127194i
$669$	−18.6143	−	26.3246i	−0.719669	−	1.01777i
$670$			16.3246i			0.630673i
$671$			22.6274i			0.873522i
$672$		0			0
$673$	31.3246	+	31.3246i	1.20747	+	1.20747i	0.971843	+	0.235630i	$0.0757154\pi$
$673$	31.3246	+	31.3246i	1.20747	+	1.20747i	0.235630	+	0.971843i	$0.424285\pi$
$674$	13.4164			0.516781
$675$	22.6777	+	12.6777i	0.872864	+	0.487964i
$676$	−21.6491			−0.832658
$677$	25.7815	+	25.7815i	0.990862	+	0.990862i	0.999959	−	0.00909639i	$-0.00289551\pi$
$677$	25.7815	+	25.7815i	0.990862	+	0.990862i	−0.00909639	+	0.999959i	$0.502896\pi$
$678$	−33.2661	−	5.70756i	−1.27758	−	0.219198i
$679$		0			0
$680$			11.5432i			0.442662i
$681$	−6.00000	−	8.48528i	−0.229920	−	0.325157i
$682$	20.6491	−	20.6491i	0.790695	−	0.790695i
$683$	−31.0755	+	31.0755i	−1.18907	+	1.18907i	−0.211744	+	0.977325i	$0.567914\pi$
$683$	−31.0755	+	31.0755i	−1.18907	+	1.18907i	−0.977325	+	0.211744i	$0.932086\pi$
$684$	−14.6011	−	5.16228i	−0.558288	−	0.197385i
$685$	8.16228	−	8.16228i	0.311865	−	0.311865i
$686$		0			0
$687$	−7.40968	+	43.1868i	−0.282697	+	1.64768i
$688$	2.83772	+	2.83772i	0.108187	+	0.108187i
$689$	55.8428			2.12744
$690$	0.654929	−	3.81721i	0.0249327	−	0.145319i
$691$	−12.6491			−0.481195			−0.240597	−	0.970625i	$-0.577343\pi$
$691$	−12.6491			−0.481195			−0.240597	+	0.970625i	$0.577343\pi$
$692$	0.229495	+	0.229495i	0.00872410	+	0.00872410i
$693$		0			0
$694$		−	1.35089i		−	0.0512791i
$695$	−5.19786			−0.197166
$696$	−6.32456	+	4.47214i	−0.239732	+	0.169516i
$697$	−22.3246	+	22.3246i	−0.845603	+	0.845603i
$698$	−9.89949	+	9.89949i	−0.374701	+	0.374701i
$699$	−11.7727	+	8.32456i	−0.445284	+	0.314864i
$700$		0			0
$701$		−	25.9148i		−	0.978790i	−0.872062	−	0.489395i	$-0.837218\pi$
$701$		−	25.9148i		−	0.978790i	0.872062	−	0.489395i	$-0.162782\pi$
$702$	−14.9250	+	26.6977i	−0.563309	+	1.00764i
$703$	26.6491	+	26.6491i	1.00509	+	1.00509i
$704$	2.82843			0.106600
$705$	−38.9737	+	27.5585i	−1.46783	+	1.03791i
$706$	24.9737			0.939896
$707$		0			0
$708$	−2.89949	+	16.8995i	−0.108970	+	0.635122i
$709$			25.9473i			0.974473i	0.873270	+	0.487236i	$0.161995\pi$
$709$			25.9473i			0.974473i	−0.873270	+	0.487236i	$0.838005\pi$
$710$	−4.83500	−	4.83500i	−0.181454	−	0.181454i
$711$	−3.16228	+	8.94427i	−0.118595	+	0.335436i
$712$	0.324555	−	0.324555i	0.0121632	−	0.0121632i
$713$	7.30056	−	7.30056i	0.273408	−	0.273408i
$714$		0			0
$715$	26.3246	+	26.3246i	0.984483	+	0.984483i
$716$		−	4.70163i		−	0.175708i
$717$	10.8322	+	1.85851i	0.404535	+	0.0694072i
$718$	14.0000	+	14.0000i	0.522475	+	0.522475i
$719$	30.3497			1.13185			0.565927	−	0.824455i	$-0.308518\pi$
$719$	30.3497			1.13185			0.565927	+	0.824455i	$0.308518\pi$
$720$	−2.23607	+	6.32456i	−0.0833333	+	0.235702i
$721$		0			0
$722$	5.40874	+	5.40874i	0.201292	+	0.201292i
$723$	−14.2109	−	2.43821i	−0.528509	−	0.0906778i
$724$			9.67544i			0.359585i
$725$	−22.3607			−0.830455
$726$	3.00000	+	4.24264i	0.111340	+	0.157459i
$727$	13.6754	−	13.6754i	0.507194	−	0.507194i	−0.406470	−	0.913664i	$-0.633240\pi$
$727$	13.6754	−	13.6754i	0.507194	−	0.507194i	0.913664	+	0.406470i	$0.133240\pi$
$728$		0			0
$729$	14.1421	+	23.0000i	0.523783	+	0.851852i
$730$	23.1623			0.857274
$731$			20.7170i			0.766245i
$732$	2.34315	−	13.6569i	0.0866052	−	0.504772i
$733$	−33.8114	−	33.8114i	−1.24885	−	1.24885i	−0.956227	−	0.292625i	$-0.905471\pi$
$733$	−33.8114	−	33.8114i	−1.24885	−	1.24885i	−0.292625	−	0.956227i	$-0.594529\pi$
$734$	−2.10270			−0.0776120
$735$	−26.7204	−	4.58450i	−0.985599	−	0.169102i
$736$	1.00000			0.0368605
$737$	14.6011	+	14.6011i	0.537839	+	0.537839i
$738$	−16.5562	+	7.90713i	−0.609444	+	0.291066i
$739$		−	52.2719i		−	1.92285i	−0.275063	−	0.961426i	$-0.588699\pi$
$739$		−	52.2719i		−	1.92285i	0.275063	−	0.961426i	$-0.411301\pi$
$740$	11.5432	−	11.5432i	0.424337	−	0.424337i
$741$	42.9737	−	30.3870i	1.57868	−	1.11629i
$742$		0			0
$743$	16.2448	−	16.2448i	0.595965	−	0.595965i	−0.343271	−	0.939236i	$-0.611535\pi$
$743$	16.2448	−	16.2448i	0.595965	−	0.595965i	0.939236	+	0.343271i	$0.111535\pi$
$744$	−14.6011	+	10.3246i	−0.535303	+	0.378517i
$745$		−	42.6491i		−	1.56254i
$746$		−	19.0733i		−	0.698322i
$747$	22.5355	−	10.7628i	0.824529	−	0.393789i
$748$	10.3246	+	10.3246i	0.377503	+	0.377503i
$749$		0			0
$750$	−15.8114	+	11.1803i	−0.577350	+	0.408248i
$751$	−28.4605			−1.03854			−0.519269	−	0.854611i	$-0.673796\pi$
$751$	−28.4605			−1.03854			−0.519269	+	0.854611i	$0.673796\pi$
$752$	−8.71478	−	8.71478i	−0.317795	−	0.317795i
$753$	−1.65685	+	9.65685i	−0.0603791	+	0.351915i
$754$		−	26.3246i		−	0.958684i
$755$		−	5.19786i		−	0.189170i
$756$		0			0
$757$	9.48683	−	9.48683i	0.344805	−	0.344805i	−0.513365	−	0.858170i	$-0.671601\pi$
$757$	9.48683	−	9.48683i	0.344805	−	0.344805i	0.858170	+	0.513365i	$0.171601\pi$
$758$	2.46556	−	2.46556i	0.0895533	−	0.0895533i
$759$	−2.82843	−	4.00000i	−0.102665	−	0.145191i
$760$	8.16228	−	8.16228i	0.296077	−	0.296077i
$761$		−	21.1760i		−	0.767628i	−0.923410	−	0.383814i	$-0.874610\pi$
$761$		−	21.1760i		−	0.767628i	0.923410	−	0.383814i	$-0.125390\pi$
$762$	−12.4628	−	2.13829i	−0.451481	−	0.0774619i
$763$		0			0
$764$	0.458991			0.0166057
$765$	−31.2487	+	14.9241i	−1.12980	+	0.539583i
$766$	9.67544			0.349588
$767$	−41.2044	−	41.2044i	−1.48781	−	1.48781i
$768$	−1.70711	−	0.292893i	−0.0615999	−	0.0105689i
$769$		−	3.67544i		−	0.132540i	−0.997802	−	0.0662700i	$-0.978890\pi$
$769$		−	3.67544i		−	0.132540i	0.997802	−	0.0662700i	$-0.0211099\pi$
$770$		0			0
$771$	23.2982	+	32.9487i	0.839065	+	1.18662i
$772$	−3.00000	+	3.00000i	−0.107972	+	0.107972i
$773$	−17.5629	+	17.5629i	−0.631694	+	0.631694i	−0.948493	−	0.316798i	$-0.897392\pi$
$773$	−17.5629	+	17.5629i	−0.631694	+	0.631694i	0.316798	+	0.948493i	$0.397392\pi$
$774$	−4.01315	+	11.3509i	−0.144250	+	0.407999i
$775$	−51.6228			−1.85434
$776$		−	1.64371i		−	0.0590057i
$777$		0			0
$778$	−8.83772	−	8.83772i	−0.316848	−	0.316848i
$779$	31.5717			1.13117
$780$	−13.1623	−	18.6143i	−0.471285	−	0.666498i
$781$	−8.64911			−0.309490
$782$	3.65028	+	3.65028i	0.130534	+	0.130534i
$783$	−20.2835	−	11.3393i	−0.724874	−	0.405232i
$784$		−	7.00000i		−	0.250000i
$785$	21.2132	+	21.2132i	0.757132	+	0.757132i
$786$	−10.6491	+	7.53006i	−0.379841	+	0.268588i
$787$	8.13594	−	8.13594i	0.290015	−	0.290015i	−0.547071	−	0.837086i	$-0.684257\pi$
$787$	8.13594	−	8.13594i	0.290015	−	0.290015i	0.837086	+	0.547071i	$0.184257\pi$
$788$	−11.5432	+	11.5432i	−0.411210	+	0.411210i
$789$	34.8591	−	24.6491i	1.24102	−	0.877532i
$790$	−5.00000	−	5.00000i	−0.177892	−	0.177892i
$791$		0			0
$792$	3.65685	+	7.65685i	0.129941	+	0.272074i
$793$	33.2982	+	33.2982i	1.18245	+	1.18245i
$794$	−9.63276			−0.341854
$795$	21.2132	+	30.0000i	0.752355	+	1.06399i
$796$	−8.83772			−0.313245
$797$	11.9061	+	11.9061i	0.421735	+	0.421735i	0.885801	−	0.464066i	$-0.153610\pi$
$797$	11.9061	+	11.9061i	0.421735	+	0.421735i	−0.464066	+	0.885801i	$0.653610\pi$
$798$		0			0
$799$		−	63.6228i		−	2.25081i
$800$	−3.53553	−	3.53553i	−0.125000	−	0.125000i
$801$	1.29822	+	0.458991i	0.0458704	+	0.0162176i
$802$	−14.0000	+	14.0000i	−0.494357	+	0.494357i
$803$	20.7170	−	20.7170i	0.731086	−	0.731086i
$804$	−7.30056	−	10.3246i	−0.257471	−	0.364119i
$805$		0			0
$806$		−	60.7739i		−	2.14067i
$807$	31.7765	+	5.45199i	1.11859	+	0.191919i
$808$	1.16228	+	1.16228i	0.0408888	+	0.0408888i
$809$	−40.0570			−1.40833			−0.704164	−	0.710037i	$-0.748678\pi$
$809$	−40.0570			−1.40833			−0.704164	+	0.710037i	$0.748678\pi$
$810$	−20.0122	+	2.12370i	−0.703159	+	0.0746192i
$811$	−27.3509			−0.960420			−0.480210	−	0.877154i	$-0.659439\pi$
$811$	−27.3509			−0.960420			−0.480210	+	0.877154i	$0.659439\pi$
$812$		0			0
$813$	11.9048	+	2.04254i	0.417519	+	0.0716350i
$814$		−	20.6491i		−	0.723751i
$815$	37.2285	−	37.2285i	1.30406	−	1.30406i
$816$	−5.16228	−	7.30056i	−0.180716	−	0.255571i
$817$	14.6491	−	14.6491i	0.512508	−	0.512508i
$818$	14.1421	−	14.1421i	0.494468	−	0.494468i
$819$		0			0
$820$		−	13.6754i		−	0.477567i
$821$		−	0.266737i		−	0.00930919i	−0.999989	−	0.00465460i	$-0.998518\pi$
$821$		−	0.266737i		−	0.00930919i	0.999989	−	0.00465460i	$-0.00148161\pi$
$822$	−1.51200	+	8.81256i	−0.0527369	+	0.307373i
$823$	−31.8114	−	31.8114i	−1.10888	−	1.10888i	−0.993299	−	0.115577i	$-0.963128\pi$
$823$	−31.8114	−	31.8114i	−1.10888	−	1.10888i	−0.115577	−	0.993299i	$-0.536872\pi$
$824$	−15.7858			−0.549926
$825$	−4.14214	+	24.1421i	−0.144211	+	0.840521i
$826$		0			0
$827$	−12.2689	−	12.2689i	−0.426633	−	0.426633i	0.460847	−	0.887480i	$-0.347546\pi$
$827$	−12.2689	−	12.2689i	−0.426633	−	0.426633i	−0.887480	+	0.460847i	$0.847546\pi$
$828$	1.29289	+	2.70711i	0.0449311	+	0.0940785i
$829$			29.6754i			1.03067i	0.856989	+	0.515335i	$0.172333\pi$
$829$			29.6754i			1.03067i	−0.856989	+	0.515335i	$0.827667\pi$
$830$			18.6143i			0.646111i
$831$	−8.32456	+	5.88635i	−0.288776	+	0.204195i
$832$	4.16228	−	4.16228i	0.144301	−	0.144301i
$833$	25.5520	−	25.5520i	0.885323	−	0.885323i
$834$	3.28742	−	2.32456i	0.113834	−	0.0804928i
$835$	−7.35089	+	7.35089i	−0.254388	+	0.254388i
$836$		−	14.6011i		−	0.504991i
$837$	−46.8274	−	26.1783i	−1.61859	−	0.904853i
$838$	18.6491	+	18.6491i	0.644223	+	0.644223i
$839$	−15.0601			−0.519933			−0.259966	−	0.965618i	$-0.583712\pi$
$839$	−15.0601			−0.519933			−0.259966	+	0.965618i	$0.583712\pi$
$840$		0			0
$841$	−9.00000			−0.310345
$842$	−8.02629	−	8.02629i	−0.276604	−	0.276604i
$843$	0.615866	−	3.58953i	0.0212116	−	0.123630i
$844$			14.3246i			0.493072i
$845$	48.4089			1.66532
$846$	12.3246	−	34.8591i	0.423727	−	1.19848i
$847$		0			0
$848$	−6.70820	+	6.70820i	−0.230361	+	0.230361i
$849$	23.5454	+	33.2982i	0.808076	+	1.14279i
$850$		−	25.8114i		−	0.885323i
$851$		−	7.30056i		−	0.250260i
$852$	5.22020	+	0.895645i	0.178841	+	0.0306843i
$853$	17.8377	+	17.8377i	0.610752	+	0.610752i	0.943142	−	0.332390i	$-0.107855\pi$
$853$	17.8377	+	17.8377i	0.610752	+	0.610752i	−0.332390	+	0.943142i	$0.607855\pi$
$854$		0			0
$855$	32.6491	+	11.5432i	1.11658	+	0.394769i
$856$	14.6491			0.500696
$857$	7.07107	+	7.07107i	0.241543	+	0.241543i	0.817488	−	0.575945i	$-0.195366\pi$
$857$	7.07107	+	7.07107i	0.241543	+	0.241543i	−0.575945	+	0.817488i	$0.695366\pi$
$858$	−28.4218	−	4.87641i	−0.970305	−	0.166478i
$859$			17.6754i			0.603078i	0.953454	+	0.301539i	$0.0975004\pi$
$859$			17.6754i			0.603078i	−0.953454	+	0.301539i	$0.902500\pi$
$860$	−6.34534	−	6.34534i	−0.216374	−	0.216374i
$861$		0			0
$862$	−4.32456	+	4.32456i	−0.147295	+	0.147295i
$863$	11.3137	−	11.3137i	0.385123	−	0.385123i	−0.487821	−	0.872944i	$-0.662208\pi$
$863$	11.3137	−	11.3137i	0.385123	−	0.385123i	0.872944	+	0.487821i	$0.162208\pi$
$864$	−1.41421	−	5.00000i	−0.0481125	−	0.170103i
$865$	−0.513167	−	0.513167i	−0.0174482	−	0.0174482i
$866$		−	22.8197i		−	0.775444i
$867$	2.82616	−	16.4721i	0.0959814	−	0.559421i
$868$		0			0
$869$	−8.94427			−0.303414
$870$	14.1421	−	10.0000i	0.479463	−	0.339032i
$871$	42.9737			1.45611
$872$	−10.1290	−	10.1290i	−0.343011	−	0.343011i
$873$	4.44970	−	2.12514i	0.150599	−	0.0719251i
$874$		−	5.16228i		−	0.174617i
$875$		0			0
$876$	−14.6491	+	10.3585i	−0.494948	+	0.349981i
$877$	30.8114	−	30.8114i	1.04043	−	1.04043i	0.0412790	−	0.999148i	$-0.486857\pi$
$877$	30.8114	−	30.8114i	1.04043	−	1.04043i	0.999148	−	0.0412790i	$-0.0131432\pi$
$878$	−8.02629	+	8.02629i	−0.270874	+	0.270874i
$879$	0.266737	−	0.188612i	0.00899682	−	0.00636171i
$880$	−6.32456			−0.213201
$881$		−	34.5924i		−	1.16545i	−0.812671	−	0.582723i	$-0.801987\pi$
$881$		−	34.5924i		−	1.16545i	0.812671	−	0.582723i	$-0.198013\pi$
$882$	18.9497	−	9.05025i	0.638071	−	0.304738i
$883$	−22.3246	−	22.3246i	−0.751281	−	0.751281i	0.223437	−	0.974718i	$-0.428272\pi$
$883$	−22.3246	−	22.3246i	−0.751281	−	0.751281i	−0.974718	+	0.223437i	$0.928272\pi$
$884$	30.3870			1.02202
$885$	6.48347	−	37.7884i	0.217939	−	1.27024i
$886$	16.0000			0.537531
$887$	−13.6831	−	13.6831i	−0.459435	−	0.459435i	0.439035	−	0.898470i	$-0.355320\pi$
$887$	−13.6831	−	13.6831i	−0.459435	−	0.459435i	−0.898470	+	0.439035i	$0.855320\pi$
$888$	−2.13829	+	12.4628i	−0.0717562	+	0.418226i
$889$		0			0
$890$	−0.725728	+	0.725728i	−0.0243264	+	0.0243264i
$891$	−16.0000	+	19.7990i	−0.536020	+	0.663291i
$892$	−13.1623	+	13.1623i	−0.440706	+	0.440706i
$893$	−44.9881	+	44.9881i	−1.50547	+	1.50547i
$894$	19.0733	+	26.9737i	0.637905	+	0.902134i
$895$			10.5132i			0.351416i
$896$		0			0
$897$	−10.0486	−	1.72407i	−0.335514	−	0.0575651i
$898$	−4.00000	−	4.00000i	−0.133482	−	0.133482i
$899$	46.1728			1.53995
$900$	5.00000	−	14.1421i	0.166667	−	0.471405i
$901$	−48.9737			−1.63155
$902$	−12.2317	−	12.2317i	−0.407271	−	0.407271i
$903$		0			0
$904$			19.4868i			0.648122i
$905$		−	21.6350i		−	0.719170i
$906$	2.32456	+	3.28742i	0.0772282	+	0.109217i
$907$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$907$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$908$	−4.24264	+	4.24264i	−0.140797	+	0.140797i
$909$	−1.64371	+	4.64911i	−0.0545184	+	0.154201i
$910$		0			0
$911$			3.28742i			0.108917i	0.998516	+	0.0544585i	$0.0173433\pi$
$911$			3.28742i			0.108917i	−0.998516	+	0.0544585i	$0.982657\pi$
$912$	−1.51200	+	8.81256i	−0.0500672	+	0.291813i
$913$	16.6491	+	16.6491i	0.551005	+	0.551005i
$914$	27.0996			0.896374
$915$	−5.23943	+	30.5377i	−0.173210	+	1.00954i
$916$	25.2982			0.835877
$917$		0			0
$918$	13.0891	−	23.4137i	0.432006	−	0.772767i
$919$		−	18.1359i		−	0.598250i	−0.954214	−	0.299125i	$-0.903305\pi$
$919$		−	18.1359i		−	0.598250i	0.954214	−	0.299125i	$-0.0966947\pi$
$920$	−2.23607			−0.0737210
$921$	−4.64911	+	3.28742i	−0.153193	+	0.108324i
$922$	2.83772	−	2.83772i	0.0934554	−	0.0934554i
$923$	−12.7279	+	12.7279i	−0.418945	+	0.418945i
$924$		0			0
$925$	−25.8114	+	25.8114i	−0.848673	+	0.848673i
$926$			36.9618i			1.21464i
$927$	−20.4094	−	42.7340i	−0.670333	−	1.40357i
$928$	3.16228	+	3.16228i	0.103807	+	0.103807i
$929$	2.36944			0.0777387			0.0388693	−	0.999244i	$-0.487624\pi$
$929$	2.36944			0.0777387			0.0388693	+	0.999244i	$0.487624\pi$
$930$	32.6491	−	23.0864i	1.07061	−	0.757033i
$931$	−36.1359			−1.18431
$932$	5.88635	+	5.88635i	0.192814	+	0.192814i
$933$	−7.79193	+	45.4147i	−0.255096	+	1.48681i
$934$		−	6.64911i		−	0.217566i
$935$	−23.0864	−	23.0864i	−0.755006	−	0.755006i
$936$	16.6491	+	5.88635i	0.544193	+	0.192401i
$937$	29.8114	−	29.8114i	0.973896	−	0.973896i	−0.0257722	−	0.999668i	$-0.508204\pi$
$937$	29.8114	−	29.8114i	0.973896	−	0.973896i	0.999668	+	0.0257722i	$0.00820447\pi$
$938$		0			0
$939$	12.9574	+	18.3246i	0.422849	+	0.597999i
$940$	19.4868	+	19.4868i	0.635590	+	0.635590i
$941$			11.5804i			0.377512i	0.982024	+	0.188756i	$0.0604455\pi$
$941$			11.5804i			0.377512i	−0.982024	+	0.188756i	$0.939555\pi$
$942$	−22.9032	−	3.92957i	−0.746228	−	0.128032i
$943$	−4.32456	−	4.32456i	−0.140827	−	0.140827i
$944$	9.89949			0.322201
$945$		0			0
$946$	−11.3509			−0.369049
$947$	18.3475	+	18.3475i	0.596215	+	0.596215i	0.939303	−	0.343088i	$-0.111473\pi$
$947$	18.3475	+	18.3475i	0.596215	+	0.596215i	−0.343088	+	0.939303i	$0.611473\pi$
$948$	5.39835	+	0.926210i	0.175330	+	0.0300819i
$949$		−	60.9737i		−	1.97929i
$950$	−18.2514	+	18.2514i	−0.592154	+	0.592154i
$951$	−3.67544	−	5.19786i	−0.119184	−	0.168552i
$952$		0			0
$953$	16.3410	−	16.3410i	0.529336	−	0.529336i	−0.391039	−	0.920374i	$-0.627884\pi$
$953$	16.3410	−	16.3410i	0.529336	−	0.529336i	0.920374	+	0.391039i	$0.127884\pi$
$954$	−26.8328	−	9.48683i	−0.868744	−	0.307148i
$955$	−1.02633			−0.0332114
$956$		−	6.34534i		−	0.205223i
$957$	3.70484	−	21.5934i	0.119760	−	0.698015i
$958$	−20.0000	−	20.0000i	−0.646171	−	0.646171i
$959$		0			0
$960$	3.81721	+	0.654929i	0.123200	+	0.0211377i
$961$	75.5964			2.43859
$962$	−30.3870	−	30.3870i	−0.979715	−	0.979715i
$963$	18.9397	+	39.6567i	0.610324	+	1.27792i
$964$			8.32456i			0.268116i
$965$	6.70820	−	6.70820i	0.215945	−	0.215945i
$966$		0			0
$967$	35.1623	−	35.1623i	1.13074	−	1.13074i	0.140689	−	0.990054i	$-0.455068\pi$
$967$	35.1623	−	35.1623i	1.13074	−	1.13074i	0.990054	−	0.140689i	$-0.0449317\pi$
$968$	2.12132	−	2.12132i	0.0681818	−	0.0681818i
$969$	−37.6875	+	26.6491i	−1.21070	+	0.856093i
$970$			3.67544i			0.118011i
$971$		−	46.6318i		−	1.49649i	−0.663425	−	0.748243i	$-0.730898\pi$
$971$		−	46.6318i		−	1.49649i	0.663425	−	0.748243i	$-0.269102\pi$
$972$	11.7071	−	10.2929i	0.375506	−	0.330145i
$973$		0			0
$974$	32.7564			1.04958
$975$	29.4317	+	41.6228i	0.942570	+	1.33300i
$976$	−8.00000			−0.256074
$977$	−22.7235	−	22.7235i	−0.726991	−	0.726991i	0.243029	−	0.970019i	$-0.421859\pi$
$977$	−22.7235	−	22.7235i	−0.726991	−	0.726991i	−0.970019	+	0.243029i	$0.921859\pi$
$978$	−6.89629	+	40.1945i	−0.220519	+	1.28528i
$979$			1.29822i			0.0414913i
$980$			15.6525i			0.500000i
$981$	14.3246	−	40.5160i	0.457348	−	1.29358i
$982$	7.00000	−	7.00000i	0.223379	−	0.223379i
$983$	−14.1421	+	14.1421i	−0.451064	+	0.451064i	−0.895708	−	0.444644i	$-0.853330\pi$
$983$	−14.1421	+	14.1421i	−0.451064	+	0.451064i	0.444644	+	0.895708i	$0.353330\pi$
$984$	6.11584	+	8.64911i	0.194966	+	0.275724i
$985$	25.8114	−	25.8114i	0.822419	−	0.822419i
$986$			23.0864i			0.735221i
$987$		0			0
$988$	−21.4868	−	21.4868i	−0.683587	−	0.683587i
$989$	−4.01315			−0.127611
$990$	−8.17697	−	17.1212i	−0.259881	−	0.544149i
$991$	25.2982			0.803624			0.401812	−	0.915722i	$-0.368380\pi$
$991$	25.2982			0.803624			0.401812	+	0.915722i	$0.368380\pi$
$992$	7.30056	+	7.30056i	0.231793	+	0.231793i
$993$	−5.07637	−	0.870967i	−0.161094	−	0.0276393i
$994$		0			0
$995$	19.7617			0.626490
$996$	−8.32456	−	11.7727i	−0.263774	−	0.373032i
$997$	−19.4605	+	19.4605i	−0.616320	+	0.616320i	−0.944586	−	0.328265i	$-0.893536\pi$
$997$	−19.4605	+	19.4605i	−0.616320	+	0.616320i	0.328265	+	0.944586i	$0.393536\pi$
$998$	−10.8547	+	10.8547i	−0.343600	+	0.343600i
$999$	−36.5028	+	10.3246i	−1.15490	+	0.326654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.d.323.1	yes	8
3.2	odd	2	inner	690.2.i.d.323.4	yes	8
5.2	odd	4	inner	690.2.i.d.47.3	yes	8
15.2	even	4	inner	690.2.i.d.47.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.d.47.2	✓	8	15.2	even	4	inner
690.2.i.d.47.3	yes	8	5.2	odd	4	inner
690.2.i.d.323.1	yes	8	1.1	even	1	trivial
690.2.i.d.323.4	yes	8	3.2	odd	2	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.70711 - 0.292893i) q^{3} +1.00000i q^{4} -2.23607i q^{5} +(1.00000 + 1.41421i) q^{6} +(0.707107 - 0.707107i) q^{8} +(2.82843 + 1.00000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.70711 - 0.292893i) q^{3} +1.00000i q^{4} -2.23607i q^{5} +(1.00000 + 1.41421i) q^{6} +(0.707107 - 0.707107i) q^{8} +(2.82843 + 1.00000i) q^{9} +(-1.58114 + 1.58114i) q^{10} +2.82843i q^{11} +(0.292893 - 1.70711i) q^{12} +(4.16228 + 4.16228i) q^{13} +(-0.654929 + 3.81721i) q^{15} -1.00000 q^{16} +(-3.65028 - 3.65028i) q^{17} +(-1.29289 - 2.70711i) q^{18} +5.16228i q^{19} +2.23607 q^{20} +(2.00000 - 2.00000i) q^{22} +(0.707107 - 0.707107i) q^{23} +(-1.41421 + 1.00000i) q^{24} -5.00000 q^{25} -5.88635i q^{26} +(-4.53553 - 2.53553i) q^{27} +4.47214 q^{29} +(3.16228 - 2.23607i) q^{30} +10.3246 q^{31} +(0.707107 + 0.707107i) q^{32} +(0.828427 - 4.82843i) q^{33} +5.16228i q^{34} +(-1.00000 + 2.82843i) q^{36} +(5.16228 - 5.16228i) q^{37} +(3.65028 - 3.65028i) q^{38} +(-5.88635 - 8.32456i) q^{39} +(-1.58114 - 1.58114i) q^{40} -6.11584i q^{41} +(-2.83772 - 2.83772i) q^{43} -2.82843 q^{44} +(2.23607 - 6.32456i) q^{45} -1.00000 q^{46} +(8.71478 + 8.71478i) q^{47} +(1.70711 + 0.292893i) q^{48} +7.00000i q^{49} +(3.53553 + 3.53553i) q^{50} +(5.16228 + 7.30056i) q^{51} +(-4.16228 + 4.16228i) q^{52} +(6.70820 - 6.70820i) q^{53} +(1.41421 + 5.00000i) q^{54} +6.32456 q^{55} +(1.51200 - 8.81256i) q^{57} +(-3.16228 - 3.16228i) q^{58} -9.89949 q^{59} +(-3.81721 - 0.654929i) q^{60} +8.00000 q^{61} +(-7.30056 - 7.30056i) q^{62} -1.00000i q^{64} +(9.30714 - 9.30714i) q^{65} +(-4.00000 + 2.82843i) q^{66} +(5.16228 - 5.16228i) q^{67} +(3.65028 - 3.65028i) q^{68} +(-1.41421 + 1.00000i) q^{69} +3.05792i q^{71} +(2.70711 - 1.29289i) q^{72} +(-7.32456 - 7.32456i) q^{73} -7.30056 q^{74} +(8.53553 + 1.46447i) q^{75} -5.16228 q^{76} +(-1.72407 + 10.0486i) q^{78} +3.16228i q^{79} +2.23607i q^{80} +(7.00000 + 5.65685i) q^{81} +(-4.32456 + 4.32456i) q^{82} +(5.88635 - 5.88635i) q^{83} +(-8.16228 + 8.16228i) q^{85} +4.01315i q^{86} +(-7.63441 - 1.30986i) q^{87} +(2.00000 + 2.00000i) q^{88} +0.458991 q^{89} +(-6.05327 + 2.89100i) q^{90} +(0.707107 + 0.707107i) q^{92} +(-17.6251 - 3.02399i) q^{93} -12.3246i q^{94} +11.5432 q^{95} +(-1.00000 - 1.41421i) q^{96} +(1.16228 - 1.16228i) q^{97} +(4.94975 - 4.94975i) q^{98} +(-2.82843 + 8.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 8 q^{6}+O(q^{10}) \) 8 * q - 8 * q^3 + 8 * q^6	\( 8 q - 8 q^{3} + 8 q^{6} + 8 q^{12} + 8 q^{13} - 8 q^{16} - 16 q^{18} + 16 q^{22} - 40 q^{25} - 8 q^{27} + 32 q^{31} - 16 q^{33} - 8 q^{36} + 16 q^{37} - 48 q^{43} - 8 q^{46} + 8 q^{48} + 16 q^{51} - 8 q^{52} + 16 q^{57} + 64 q^{61} - 32 q^{66} + 16 q^{67} + 16 q^{72} - 8 q^{73} + 40 q^{75} - 16 q^{76} + 8 q^{78} + 56 q^{81} + 16 q^{82} - 40 q^{85} + 16 q^{88} - 32 q^{93} - 8 q^{96} - 16 q^{97}+O(q^{100}) \) 8 * q - 8 * q^3 + 8 * q^6 + 8 * q^12 + 8 * q^13 - 8 * q^16 - 16 * q^18 + 16 * q^22 - 40 * q^25 - 8 * q^27 + 32 * q^31 - 16 * q^33 - 8 * q^36 + 16 * q^37 - 48 * q^43 - 8 * q^46 + 8 * q^48 + 16 * q^51 - 8 * q^52 + 16 * q^57 + 64 * q^61 - 32 * q^66 + 16 * q^67 + 16 * q^72 - 8 * q^73 + 40 * q^75 - 16 * q^76 + 8 * q^78 + 56 * q^81 + 16 * q^82 - 40 * q^85 + 16 * q^88 - 32 * q^93 - 8 * q^96 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more