LMFDB - Embedded newform 804.2.y.a.73.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			73.5
Character	$\chi$	$=$	804.73
Dual form			804.2.y.a.793.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{3} +(3.28440 + 0.964386i) q^{5} +(2.82322 - 0.544130i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{3} +(3.28440 + 0.964386i) q^{5} +(2.82322 - 0.544130i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(3.20569 - 3.05662i) q^{11} +(-0.0573785 + 1.20452i) q^{13} +(2.24162 - 2.58697i) q^{15} +(-3.61113 + 2.83982i) q^{17} +(-2.42017 - 0.466450i) q^{19} +(0.677848 - 2.79413i) q^{21} +(-3.31801 + 0.316831i) q^{23} +(5.65096 + 3.63165i) q^{25} +(-0.959493 + 0.281733i) q^{27} +(-1.53005 + 2.65013i) q^{29} +(0.147448 + 3.09531i) q^{31} +(-1.44871 - 4.18576i) q^{33} +(9.79731 + 0.935530i) q^{35} +(-0.201366 - 0.348776i) q^{37} +(1.07184 + 0.552570i) q^{39} +(-3.03677 - 1.21574i) q^{41} +(-0.922752 - 6.41788i) q^{43} +(-1.42199 - 3.11372i) q^{45} +(4.55520 + 6.39689i) q^{47} +(1.17589 - 0.470757i) q^{49} +(1.08308 + 4.46450i) q^{51} +(0.789799 - 5.49317i) q^{53} +(13.4765 - 6.94762i) q^{55} +(-1.42967 + 2.00770i) q^{57} +(-8.95399 + 5.75438i) q^{59} +(-4.08854 - 3.89841i) q^{61} +(-2.26004 - 1.77731i) q^{63} +(-1.35008 + 3.90079i) q^{65} +(1.86647 - 7.96971i) q^{67} +(-1.09015 + 3.14978i) q^{69} +(8.74083 + 6.87387i) q^{71} +(-9.92559 - 9.46403i) q^{73} +(5.65096 - 3.63165i) q^{75} +(7.38715 - 10.3738i) q^{77} +(15.4955 - 7.98847i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(0.0958323 + 0.395026i) q^{83} +(-14.5991 + 5.84458i) q^{85} +(1.77504 + 2.49269i) q^{87} +(-4.72554 - 10.3475i) q^{89} +(0.493425 + 3.43185i) q^{91} +(2.87684 + 1.15171i) q^{93} +(-7.49897 - 3.86599i) q^{95} +(-0.299838 - 0.519334i) q^{97} +(-4.40931 - 0.421038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{20}{33}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$		0			0
$5$	3.28440	+	0.964386i	1.46883	+	0.431287i	0.915718	−	0.401822i	$-0.131623\pi$
$5$	3.28440	+	0.964386i	1.46883	+	0.431287i	0.553109	+	0.833109i	$0.313441\pi$
$6$		0			0
$7$	2.82322	−	0.544130i	1.06708	−	0.205662i	0.374661	−	0.927162i	$-0.377759\pi$
$7$	2.82322	−	0.544130i	1.06708	−	0.205662i	0.692414	+	0.721500i	$0.256547\pi$
$8$		0			0
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$		0			0
$11$	3.20569	−	3.05662i	0.966551	−	0.921604i	−0.0304077	−	0.999538i	$-0.509681\pi$
$11$	3.20569	−	3.05662i	0.966551	−	0.921604i	0.996959	+	0.0779332i	$0.0248321\pi$
$12$		0			0
$13$	−0.0573785	+	1.20452i	−0.0159139	+	0.334074i	0.976845	+	0.213949i	$0.0686327\pi$
$13$	−0.0573785	+	1.20452i	−0.0159139	+	0.334074i	−0.992759	+	0.120125i	$0.961670\pi$
$14$		0			0
$15$	2.24162	−	2.58697i	0.578785	−	0.667953i
$16$		0			0
$17$	−3.61113	+	2.83982i	−0.875827	+	0.688758i	−0.951259	−	0.308393i	$-0.900209\pi$
$17$	−3.61113	+	2.83982i	−0.875827	+	0.688758i	0.0754317	+	0.997151i	$0.475967\pi$
$18$		0			0
$19$	−2.42017	−	0.466450i	−0.555226	−	0.107011i	−0.0960828	−	0.995373i	$-0.530631\pi$
$19$	−2.42017	−	0.466450i	−0.555226	−	0.107011i	−0.459143	+	0.888362i	$0.651843\pi$
$20$		0			0
$21$	0.677848	−	2.79413i	0.147919	−	0.609729i
$22$		0			0
$23$	−3.31801	+	0.316831i	−0.691852	+	0.0660639i	−0.435058	−	0.900402i	$-0.643272\pi$
$23$	−3.31801	+	0.316831i	−0.691852	+	0.0660639i	−0.256794	+	0.966466i	$0.582666\pi$
$24$		0			0
$25$	5.65096	+	3.63165i	1.13019	+	0.726330i
$26$		0			0
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$		0			0
$29$	−1.53005	+	2.65013i	−0.284124	+	0.492117i	−0.972396	−	0.233335i	$-0.925036\pi$
$29$	−1.53005	+	2.65013i	−0.284124	+	0.492117i	0.688272	+	0.725452i	$0.258369\pi$
$30$		0			0
$31$	0.147448	+	3.09531i	0.0264824	+	0.555934i	0.972653	+	0.232265i	$0.0746135\pi$
$31$	0.147448	+	3.09531i	0.0264824	+	0.555934i	−0.946170	+	0.323669i	$0.895083\pi$
$32$		0			0
$33$	−1.44871	−	4.18576i	−0.252187	−	0.728647i
$34$		0			0
$35$	9.79731	+	0.935530i	1.65605	+	0.158133i
$36$		0			0
$37$	−0.201366	−	0.348776i	−0.0331044	−	0.0573385i	0.848999	−	0.528395i	$-0.177206\pi$
$37$	−0.201366	−	0.348776i	−0.0331044	−	0.0573385i	−0.882103	+	0.471057i	$0.843873\pi$
$38$		0			0
$39$	1.07184	+	0.552570i	0.171631	+	0.0884820i
$40$		0			0
$41$	−3.03677	−	1.21574i	−0.474264	−	0.189867i	0.122201	−	0.992505i	$-0.461005\pi$
$41$	−3.03677	−	1.21574i	−0.474264	−	0.189867i	−0.596466	+	0.802638i	$0.703429\pi$
$42$		0			0
$43$	−0.922752	−	6.41788i	−0.140718	−	0.978718i	−0.930751	−	0.365653i	$-0.880846\pi$
$43$	−0.922752	−	6.41788i	−0.140718	−	0.978718i	0.790033	−	0.613065i	$-0.210064\pi$
$44$		0			0
$45$	−1.42199	−	3.11372i	−0.211978	−	0.464166i
$46$		0			0
$47$	4.55520	+	6.39689i	0.664445	+	0.933082i	0.999960	−	0.00895265i	$-0.00284976\pi$
$47$	4.55520	+	6.39689i	0.664445	+	0.933082i	−0.335515	+	0.942035i	$0.608910\pi$
$48$		0			0
$49$	1.17589	−	0.470757i	0.167985	−	0.0672510i
$50$		0			0
$51$	1.08308	+	4.46450i	0.151661	+	0.625156i
$52$		0			0
$53$	0.789799	−	5.49317i	0.108487	−	0.754546i	−0.860858	−	0.508845i	$-0.830073\pi$
$53$	0.789799	−	5.49317i	0.108487	−	0.754546i	0.969346	−	0.245701i	$-0.0790181\pi$
$54$		0			0
$55$	13.4765	−	6.94762i	1.81717	−	0.936817i
$56$		0			0
$57$	−1.42967	+	2.00770i	−0.189365	+	0.265926i
$58$		0			0
$59$	−8.95399	+	5.75438i	−1.16571	+	0.749156i	−0.972706	−	0.232042i	$-0.925459\pi$
$59$	−8.95399	+	5.75438i	−1.16571	+	0.749156i	−0.193004	+	0.981198i	$0.561823\pi$
$60$		0			0
$61$	−4.08854	−	3.89841i	−0.523484	−	0.499141i	0.381627	−	0.924316i	$-0.375364\pi$
$61$	−4.08854	−	3.89841i	−0.523484	−	0.499141i	−0.905111	+	0.425176i	$0.860212\pi$
$62$		0			0
$63$	−2.26004	−	1.77731i	−0.284738	−	0.223921i
$64$		0			0
$65$	−1.35008	+	3.90079i	−0.167457	+	0.483834i
$66$		0			0
$67$	1.86647	−	7.96971i	0.228025	−	0.973655i
$67$	1.86647	−	7.96971i	0.228025	−	0.973655i
$68$		0			0
$69$	−1.09015	+	3.14978i	−0.131239	+	0.379189i
$70$		0			0
$71$	8.74083	+	6.87387i	1.03735	+	0.815778i	0.983159	−	0.182753i	$-0.0585008\pi$
$71$	8.74083	+	6.87387i	1.03735	+	0.815778i	0.0541871	+	0.998531i	$0.482743\pi$
$72$		0			0
$73$	−9.92559	−	9.46403i	−1.16170	−	1.10768i	−0.992518	−	0.122097i	$-0.961038\pi$
$73$	−9.92559	−	9.46403i	−1.16170	−	1.10768i	−0.169184	−	0.985584i	$-0.554113\pi$
$74$		0			0
$75$	5.65096	−	3.63165i	0.652516	−	0.419347i
$76$		0			0
$77$	7.38715	−	10.3738i	0.841844	−	1.18220i
$78$		0			0
$79$	15.4955	−	7.98847i	1.74338	−	0.898773i	0.782115	−	0.623134i	$-0.214141\pi$
$79$	15.4955	−	7.98847i	1.74338	−	0.898773i	0.961261	−	0.275639i	$-0.0888896\pi$
$80$		0			0
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$		0			0
$83$	0.0958323	+	0.395026i	0.0105190	+	0.0433598i	0.976829	−	0.214020i	$-0.0686559\pi$
$83$	0.0958323	+	0.395026i	0.0105190	+	0.0433598i	−0.966310	+	0.257380i	$0.917141\pi$
$84$		0			0
$85$	−14.5991	+	5.84458i	−1.58349	+	0.633934i
$86$		0			0
$87$	1.77504	+	2.49269i	0.190304	+	0.267244i
$88$		0			0
$89$	−4.72554	−	10.3475i	−0.500906	−	1.09683i	−0.976174	−	0.216991i	$-0.930376\pi$
$89$	−4.72554	−	10.3475i	−0.500906	−	1.09683i	0.475267	−	0.879841i	$-0.342351\pi$
$90$		0			0
$91$	0.493425	+	3.43185i	0.0517250	+	0.359755i
$92$		0			0
$93$	2.87684	+	1.15171i	0.298315	+	0.119427i
$94$		0			0
$95$	−7.49897	−	3.86599i	−0.769378	−	0.396642i
$96$		0			0
$97$	−0.299838	−	0.519334i	−0.0304439	−	0.0527304i	0.850402	−	0.526133i	$-0.176359\pi$
$97$	−0.299838	−	0.519334i	−0.0304439	−	0.0527304i	−0.880846	+	0.473403i	$0.843025\pi$
$98$		0			0
$99$	−4.40931	−	0.421038i	−0.443153	−	0.0423160i
$100$		0			0
$101$	5.26621	+	15.2157i	0.524008	+	1.51402i	0.827655	+	0.561236i	$0.189674\pi$
$101$	5.26621	+	15.2157i	0.524008	+	1.51402i	−0.303648	+	0.952784i	$0.598205\pi$
$102$		0			0
$103$	0.203590	+	4.27388i	0.0200603	+	0.421118i	0.986453	+	0.164046i	$0.0524547\pi$
$103$	0.203590	+	4.27388i	0.0200603	+	0.421118i	−0.966392	+	0.257072i	$0.917242\pi$
$104$		0			0
$105$	4.92094	−	8.52332i	0.480234	−	0.831791i
$106$		0			0
$107$	15.4893	−	4.54806i	1.49741	−	0.439678i	0.572509	−	0.819898i	$-0.305970\pi$
$107$	15.4893	−	4.54806i	1.49741	−	0.439678i	0.924896	+	0.380220i	$0.124152\pi$
$108$		0			0
$109$	7.60895	+	4.88997i	0.728805	+	0.468374i	0.851690	−	0.524047i	$-0.175578\pi$
$109$	7.60895	+	4.88997i	0.728805	+	0.468374i	−0.122885	+	0.992421i	$0.539215\pi$
$110$		0			0
$111$	−0.400909	+	0.0382821i	−0.0380526	+	0.00363358i
$112$		0			0
$113$	−4.07051	+	16.7789i	−0.382922	+	1.57842i	0.375603	+	0.926781i	$0.377436\pi$
$113$	−4.07051	+	16.7789i	−0.382922	+	1.57842i	−0.758525	+	0.651644i	$0.774080\pi$
$114$		0			0
$115$	−11.2032	−	2.15924i	−1.04470	−	0.201350i
$116$		0			0
$117$	0.947892	−	0.745431i	0.0876326	−	0.0689151i
$118$		0			0
$119$	−8.64976	+	9.98236i	−0.792923	+	0.915081i
$120$		0			0
$121$	0.410124	−	8.60956i	0.0372840	−	0.782688i
$122$		0			0
$123$	−2.36740	+	2.25731i	−0.213461	+	0.203535i
$124$		0			0
$125$	3.84955	+	4.44262i	0.344314	+	0.397360i
$126$		0			0
$127$	−18.2364	+	3.51478i	−1.61822	+	0.311887i	−0.916338	−	0.400405i	$-0.868869\pi$
$127$	−18.2364	+	3.51478i	−1.61822	+	0.311887i	−0.701884	+	0.712292i	$0.747657\pi$
$128$		0			0
$129$	−6.22124	−	1.82672i	−0.547749	−	0.160834i
$130$		0			0
$131$	−5.39799	+	11.8199i	−0.471625	+	1.03271i	0.513058	+	0.858354i	$0.328513\pi$
$131$	−5.39799	+	11.8199i	−0.471625	+	1.03271i	−0.984682	+	0.174359i	$0.944215\pi$
$132$		0			0
$133$	−7.08648			−0.614476
$134$		0			0
$135$	−3.42305			−0.294610
$136$		0			0
$137$	−6.49143	+	14.2143i	−0.554600	+	1.21441i	0.400000	+	0.916515i	$0.369010\pi$
$137$	−6.49143	+	14.2143i	−0.554600	+	1.21441i	−0.954600	+	0.297890i	$0.903717\pi$
$138$		0			0
$139$	−17.2621	−	5.06862i	−1.46416	−	0.429915i	−0.549961	−	0.835191i	$-0.685357\pi$
$139$	−17.2621	−	5.06862i	−1.46416	−	0.429915i	−0.914194	+	0.405276i	$0.867175\pi$
$140$		0			0
$141$	7.71112	−	1.48620i	0.649393	−	0.125160i
$142$		0			0
$143$	3.49782	+	4.03670i	0.292503	+	0.337566i
$144$		0			0
$145$	−7.58105	+	7.22852i	−0.629572	+	0.600296i
$146$		0			0
$147$	0.0602685	−	1.26519i	0.00497086	−	0.104351i
$148$		0			0
$149$	−6.27673	+	7.24373i	−0.514210	+	0.593430i	−0.952172	−	0.305564i	$-0.901155\pi$
$149$	−6.27673	+	7.24373i	−0.514210	+	0.593430i	0.437962	+	0.898994i	$0.355700\pi$
$150$		0			0
$151$	11.5041	−	9.04692i	0.936190	−	0.736228i	−0.0285058	−	0.999594i	$-0.509075\pi$
$151$	11.5041	−	9.04692i	0.936190	−	0.736228i	0.964696	+	0.263365i	$0.0848325\pi$
$152$		0			0
$153$	4.51098	+	0.869421i	0.364691	+	0.0702885i
$154$		0			0
$155$	−2.50080	+	10.3084i	−0.200869	+	0.827992i
$156$		0			0
$157$	−0.865661	+	0.0826606i	−0.0690873	+	0.00659704i	−0.129542	−	0.991574i	$-0.541351\pi$
$157$	−0.865661	+	0.0826606i	−0.0690873	+	0.00659704i	0.0604551	+	0.998171i	$0.480745\pi$
$158$		0			0
$159$	−4.66867	−	3.00037i	−0.370250	−	0.237945i
$160$		0			0
$161$	−9.19505	+	2.69991i	−0.724671	+	0.212783i
$162$		0			0
$163$	−0.427179	+	0.739895i	−0.0334592	+	0.0579531i	−0.882270	−	0.470744i	$-0.843986\pi$
$163$	−0.427179	+	0.739895i	−0.0334592	+	0.0579531i	0.848811	+	0.528697i	$0.177319\pi$
$164$		0			0
$165$	−0.721436	−	15.1448i	−0.0561637	−	1.17902i
$166$		0			0
$167$	−2.40003	−	6.93444i	−0.185720	−	0.536603i	0.813253	−	0.581910i	$-0.197695\pi$
$167$	−2.40003	−	6.93444i	−0.185720	−	0.536603i	−0.998973	+	0.0453073i	$0.985573\pi$
$168$		0			0
$169$	11.4936	+	1.09750i	0.884120	+	0.0844232i
$170$		0			0
$171$	1.23236	+	2.13451i	0.0942407	+	0.163230i
$172$		0			0
$173$	−8.35556	−	4.30759i	−0.635262	−	0.327500i	0.110338	−	0.993894i	$-0.464807\pi$
$173$	−8.35556	−	4.30759i	−0.635262	−	0.327500i	−0.745600	+	0.666394i	$0.767837\pi$
$174$		0			0
$175$	17.9300	+	7.17807i	1.35538	+	0.542611i
$176$		0			0
$177$	1.51475	+	10.5353i	0.113855	+	0.791881i
$178$		0			0
$179$	1.24553	+	2.72734i	0.0930955	+	0.203851i	0.950451	−	0.310874i	$-0.100622\pi$
$179$	1.24553	+	2.72734i	0.0930955	+	0.203851i	−0.857356	+	0.514724i	$0.827894\pi$
$180$		0			0
$181$	−10.7320	−	15.0710i	−0.797706	−	1.12022i	−0.990300	−	0.138942i	$-0.955630\pi$
$181$	−10.7320	−	15.0710i	−0.797706	−	1.12022i	0.192595	−	0.981278i	$-0.438310\pi$
$182$		0			0
$183$	−5.24456	+	2.09961i	−0.387689	+	0.155207i
$184$		0			0
$185$	−0.325011	−	1.33971i	−0.0238953	−	0.0984978i
$186$		0			0
$187$	−2.89590	+	20.1414i	−0.211769	+	1.47289i
$188$		0			0
$189$	−2.55556	+	1.31748i	−0.185889	+	0.0958326i
$190$		0			0
$191$	−7.58295	+	10.6488i	−0.548683	+	0.770518i	−0.992053	−	0.125821i	$-0.959843\pi$
$191$	−7.58295	+	10.6488i	−0.548683	+	0.770518i	0.443370	+	0.896339i	$0.353783\pi$
$192$		0			0
$193$	4.05447	−	2.60565i	0.291847	−	0.187559i	−0.386522	−	0.922280i	$-0.626324\pi$
$193$	4.05447	−	2.60565i	0.291847	−	0.187559i	0.678369	+	0.734722i	$0.262687\pi$
$194$		0			0
$195$	2.98744	+	2.84852i	0.213935	+	0.203987i
$196$		0			0
$197$	1.54432	+	1.21447i	0.110028	+	0.0865272i	0.671657	−	0.740862i	$-0.265583\pi$
$197$	1.54432	+	1.21447i	0.110028	+	0.0865272i	−0.561629	+	0.827389i	$0.689825\pi$
$198$		0			0
$199$	0.466739	−	1.34855i	0.0330862	−	0.0955964i	−0.927248	−	0.374448i	$-0.877832\pi$
$199$	0.466739	−	1.34855i	0.0330862	−	0.0955964i	0.960334	+	0.278851i	$0.0899536\pi$
$200$		0			0
$201$	−6.47415	−	5.00854i	−0.456651	−	0.353275i
$202$		0			0
$203$	−2.87766	+	8.31444i	−0.201972	+	0.583559i
$204$		0			0
$205$	−8.80153	−	6.92160i	−0.614725	−	0.483425i
$206$		0			0
$207$	2.41228	+	2.30010i	0.167665	+	0.159868i
$208$		0			0
$209$	−9.18408	+	5.90225i	−0.635276	+	0.408267i
$210$		0			0
$211$	9.37720	−	13.1684i	0.645553	−	0.906553i	−0.354036	−	0.935232i	$-0.615191\pi$
$211$	9.37720	−	13.1684i	0.645553	−	0.906553i	0.999589	+	0.0286794i	$0.00913020\pi$
$212$		0			0
$213$	9.88376	−	5.09543i	0.677224	−	0.349133i
$214$		0			0
$215$	3.15863	−	21.9688i	0.215417	−	1.49826i
$216$		0			0
$217$	2.10053	+	8.65849i	0.142593	+	0.587777i
$218$		0			0
$219$	−12.7320	+	5.09713i	−0.860350	+	0.344432i
$220$		0			0
$221$	−3.21343	−	4.51263i	−0.216159	−	0.303552i
$222$		0			0
$223$	−1.88230	−	4.12165i	−0.126048	−	0.276006i	0.836079	−	0.548610i	$-0.184843\pi$
$223$	−1.88230	−	4.12165i	−0.126048	−	0.276006i	−0.962127	+	0.272603i	$0.912115\pi$
$224$		0			0
$225$	−0.955972	−	6.64893i	−0.0637315	−	0.443262i
$226$		0			0
$227$	10.0703	+	4.03154i	0.668388	+	0.267582i	0.680940	−	0.732339i	$-0.261571\pi$
$227$	10.0703	+	4.03154i	0.668388	+	0.267582i	−0.0125519	+	0.999921i	$0.503996\pi$
$228$		0			0
$229$	−3.24860	−	1.67477i	−0.214673	−	0.110672i	0.347536	−	0.937666i	$-0.387018\pi$
$229$	−3.24860	−	1.67477i	−0.214673	−	0.110672i	−0.562210	+	0.826995i	$0.690049\pi$
$230$		0			0
$231$	−6.36761	−	11.0290i	−0.418958	−	0.725656i
$232$		0			0
$233$	−19.2318	−	1.83641i	−1.25992	−	0.120307i	−0.556357	−	0.830944i	$-0.687801\pi$
$233$	−19.2318	−	1.83641i	−1.25992	−	0.120307i	−0.703560	+	0.710636i	$0.748407\pi$
$234$		0			0
$235$	8.79203	+	25.4029i	0.573529	+	1.65710i
$236$		0			0
$237$	−0.829517	−	17.4137i	−0.0538829	−	1.13114i
$238$		0			0
$239$	8.46938	−	14.6694i	0.547839	−	0.948884i	−0.450584	−	0.892734i	$-0.648784\pi$
$239$	8.46938	−	14.6694i	0.547839	−	0.948884i	0.998422	−	0.0561502i	$-0.0178826\pi$
$240$		0			0
$241$	7.90559	−	2.32129i	0.509244	−	0.149527i	−0.0170096	−	0.999855i	$-0.505415\pi$
$241$	7.90559	−	2.32129i	0.509244	−	0.149527i	0.526253	+	0.850328i	$0.323596\pi$
$242$		0			0
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$		0			0
$245$	4.31610	−	0.412137i	0.275745	−	0.0263305i
$246$		0			0
$247$	0.700716	−	2.88839i	0.0445855	−	0.183784i
$248$		0			0
$249$	0.399139	+	0.0769277i	0.0252944	+	0.00487509i
$250$		0			0
$251$	8.07837	−	6.35290i	0.509902	−	0.400992i	−0.329790	−	0.944054i	$-0.606978\pi$
$251$	8.07837	−	6.35290i	0.509902	−	0.400992i	0.839692	+	0.543063i	$0.182735\pi$
$252$		0			0
$253$	−9.66805	+	11.1575i	−0.607825	+	0.701468i
$254$		0			0
$255$	−0.748250	+	15.7077i	−0.0468573	+	0.983655i
$256$		0			0
$257$	−2.38231	+	2.27152i	−0.148604	+	0.141694i	−0.760735	−	0.649063i	$-0.775161\pi$
$257$	−2.38231	+	2.27152i	−0.148604	+	0.141694i	0.612131	+	0.790757i	$0.290313\pi$
$258$		0			0
$259$	−0.758280	−	0.875102i	−0.0471172	−	0.0543762i
$260$		0			0
$261$	3.00481	−	0.579129i	0.185993	−	0.0358472i
$262$		0			0
$263$	−13.9679	−	4.10134i	−0.861297	−	0.252900i	−0.178888	−	0.983870i	$-0.557250\pi$
$263$	−13.9679	−	4.10134i	−0.861297	−	0.252900i	−0.682410	+	0.730970i	$0.739068\pi$
$264$		0			0
$265$	7.89155	−	17.2801i	0.484774	−	1.06151i
$266$		0			0
$267$	−11.3755			−0.696168
$268$		0			0
$269$	−22.1652			−1.35144			−0.675719	−	0.737160i	$-0.736167\pi$
$269$	−22.1652			−1.35144			−0.675719	+	0.737160i	$0.736167\pi$
$270$		0			0
$271$	−10.9123	+	23.8947i	−0.662878	+	1.45150i	0.216938	+	0.976185i	$0.430393\pi$
$271$	−10.9123	+	23.8947i	−0.662878	+	1.45150i	−0.879816	+	0.475315i	$0.842334\pi$
$272$		0			0
$273$	3.32669	+	0.976806i	0.201341	+	0.0591190i
$274$		0			0
$275$	29.2157	−	5.63087i	1.76178	−	0.339554i
$276$		0			0
$277$	7.25295	+	8.37035i	0.435787	+	0.502925i	0.930581	−	0.366085i	$-0.119302\pi$
$277$	7.25295	+	8.37035i	0.435787	+	0.502925i	−0.494794	+	0.869010i	$0.664757\pi$
$278$		0			0
$279$	2.24272	−	2.13843i	0.134268	−	0.128024i
$280$		0			0
$281$	0.332428	−	6.97852i	0.0198310	−	0.416303i	−0.967023	−	0.254689i	$-0.918027\pi$
$281$	0.332428	−	6.97852i	0.0198310	−	0.416303i	0.986854	−	0.161614i	$-0.0516701\pi$
$282$		0			0
$283$	7.57286	−	8.73954i	0.450160	−	0.519512i	−0.484627	−	0.874721i	$-0.661045\pi$
$283$	7.57286	−	8.73954i	0.450160	−	0.519512i	0.934787	+	0.355209i	$0.115590\pi$
$284$		0			0
$285$	−6.63181	+	5.21532i	−0.392835	+	0.308929i
$286$		0			0
$287$	−9.23499	−	1.77990i	−0.545124	−	0.105064i
$288$		0			0
$289$	0.967755	−	3.98914i	0.0569268	−	0.234655i
$290$		0			0
$291$	−0.596960	+	0.0570028i	−0.0349944	+	0.00334156i
$292$		0			0
$293$	24.1857	+	15.5432i	1.41294	+	0.908042i	0.999996	−	0.00271337i	$-0.000863695\pi$
$293$	24.1857	+	15.5432i	1.41294	+	0.908042i	0.412945	+	0.910756i	$0.364500\pi$
$294$		0			0
$295$	−34.9579	+	10.2646i	−2.03533	+	0.597626i
$296$		0			0
$297$	−2.21469	+	3.83595i	−0.128509	+	0.222584i
$298$		0			0
$299$	−0.191248	−	4.01479i	−0.0110602	−	0.232181i
$300$		0			0
$301$	−6.09729	−	17.6170i	−0.351442	−	1.01543i
$302$		0			0
$303$	16.0284	+	1.53052i	0.920806	+	0.0879263i
$304$		0			0
$305$	−9.66881	−	16.7469i	−0.553634	−	0.958923i
$306$		0			0
$307$	−10.4661	−	5.39567i	−0.597335	−	0.307947i	0.132915	−	0.991127i	$-0.457566\pi$
$307$	−10.4661	−	5.39567i	−0.597335	−	0.307947i	−0.730250	+	0.683180i	$0.760596\pi$
$308$		0			0
$309$	3.97223	+	1.59024i	0.225973	+	0.0904657i
$310$		0			0
$311$	−3.32184	−	23.1039i	−0.188364	−	1.31010i	−0.836243	−	0.548358i	$-0.815253\pi$
$311$	−3.32184	−	23.1039i	−0.188364	−	1.31010i	0.647879	−	0.761743i	$-0.275656\pi$
$312$		0			0
$313$	5.94607	+	13.0201i	0.336092	+	0.735938i	0.999929	−	0.0119390i	$-0.00380039\pi$
$313$	5.94607	+	13.0201i	0.336092	+	0.735938i	−0.663837	+	0.747877i	$0.731073\pi$
$314$		0			0
$315$	−5.70885	−	8.01696i	−0.321657	−	0.451704i
$316$		0			0
$317$	1.34359	−	0.537892i	0.0754635	−	0.0302110i	−0.333624	−	0.942706i	$-0.608271\pi$
$317$	1.34359	−	0.537892i	0.0754635	−	0.0302110i	0.409087	+	0.912495i	$0.365847\pi$
$318$		0			0
$319$	3.19556	+	13.1723i	0.178917	+	0.737506i
$320$		0			0
$321$	2.29742	−	15.9789i	0.128229	−	0.891854i
$322$		0			0
$323$	10.0642	−	5.18845i	0.559987	−	0.288693i
$324$		0			0
$325$	−4.69864	+	6.59832i	−0.260634	+	0.366009i
$326$		0			0
$327$	7.60895	−	4.88997i	0.420776	−	0.270416i
$328$		0			0
$329$	16.3411	+	15.5812i	0.900912	+	0.859018i
$330$		0			0
$331$	27.2753	+	21.4495i	1.49919	+	1.17897i	0.935674	+	0.352866i	$0.114793\pi$
$331$	27.2753	+	21.4495i	1.49919	+	1.17897i	0.563513	+	0.826107i	$0.309450\pi$
$332$		0			0
$333$	−0.131721	+	0.380582i	−0.00721826	+	0.0208558i
$334$		0			0
$335$	13.8161	−	24.3757i	0.754854	−	1.33179i
$336$		0			0
$337$	−2.92200	+	8.44256i	−0.159171	+	0.459896i	−0.996183	−	0.0872896i	$-0.972179\pi$
$337$	−2.92200	+	8.44256i	−0.159171	+	0.459896i	0.837012	+	0.547185i	$0.184301\pi$
$338$		0			0
$339$	13.5717	+	10.6729i	0.737111	+	0.579671i
$340$		0			0
$341$	9.93384	+	9.47190i	0.537948	+	0.512932i
$342$		0			0
$343$	−13.8676	+	8.91217i	−0.748780	+	0.481212i
$344$		0			0
$345$	−6.61809	+	9.29380i	−0.356306	+	0.500362i
$346$		0			0
$347$	19.7871	−	10.2009i	1.06223	−	0.547616i	0.163688	−	0.986512i	$-0.447661\pi$
$347$	19.7871	−	10.2009i	1.06223	−	0.547616i	0.898538	+	0.438897i	$0.144631\pi$
$348$		0			0
$349$	3.33314	−	23.1825i	0.178419	−	1.24093i	−0.682004	−	0.731349i	$-0.738891\pi$
$349$	3.33314	−	23.1825i	0.178419	−	1.24093i	0.860422	−	0.509581i	$-0.170200\pi$
$350$		0			0
$351$	−0.284299	−	1.17190i	−0.0151748	−	0.0625512i
$352$		0			0
$353$	−26.5783	+	10.6403i	−1.41462	+	0.566329i	−0.948040	−	0.318150i	$-0.896938\pi$
$353$	−26.5783	+	10.6403i	−1.41462	+	0.566329i	−0.466580	+	0.884479i	$0.654514\pi$
$354$		0			0
$355$	22.0793	+	31.0060i	1.17185	+	1.64563i
$356$		0			0
$357$	5.48703	+	12.0149i	0.290405	+	0.635897i
$358$		0			0
$359$	−1.43735	−	9.99699i	−0.0758604	−	0.527621i	−0.991948	−	0.126643i	$-0.959580\pi$
$359$	−1.43735	−	9.99699i	−0.0758604	−	0.527621i	0.916088	−	0.400978i	$-0.131329\pi$
$360$		0			0
$361$	−11.9993	−	4.80381i	−0.631543	−	0.252832i
$362$		0			0
$363$	−7.66116	−	3.94960i	−0.402107	−	0.207300i
$364$		0			0
$365$	−23.4726	−	40.6557i	−1.22861	−	2.12802i
$366$		0			0
$367$	−16.9320	−	1.61681i	−0.883844	−	0.0843969i	−0.356746	−	0.934201i	$-0.616114\pi$
$367$	−16.9320	−	1.61681i	−0.883844	−	0.0843969i	−0.527098	+	0.849804i	$0.676720\pi$
$368$		0			0
$369$	1.06987	+	3.09118i	0.0556951	+	0.160920i
$370$		0			0
$371$	−0.759229	−	15.9382i	−0.0394172	−	0.827469i
$372$		0			0
$373$	−16.6266	+	28.7980i	−0.860890	+	1.49111i	0.0101805	+	0.999948i	$0.496759\pi$
$373$	−16.6266	+	28.7980i	−0.860890	+	1.49111i	−0.871071	+	0.491158i	$0.836574\pi$
$374$		0			0
$375$	5.64031	−	1.65614i	0.291264	−	0.0855229i
$376$		0			0
$377$	−3.10435	−	1.99504i	−0.159882	−	0.102750i
$378$		0			0
$379$	18.9662	−	1.81106i	0.974230	−	0.0930277i	0.404217	−	0.914663i	$-0.367544\pi$
$379$	18.9662	−	1.81106i	0.974230	−	0.0930277i	0.570013	+	0.821636i	$0.306938\pi$
$380$		0			0
$381$	−4.37853	+	18.0485i	−0.224319	+	0.924655i
$382$		0			0
$383$	16.4700	+	3.17434i	0.841580	+	0.162201i	0.591783	−	0.806097i	$-0.298424\pi$
$383$	16.4700	+	3.17434i	0.841580	+	0.162201i	0.249796	+	0.968298i	$0.419636\pi$
$384$		0			0
$385$	34.2667	−	26.9476i	1.74639	−	1.37338i
$386$		0			0
$387$	−4.24604	+	4.90019i	−0.215838	+	0.249091i
$388$		0			0
$389$	−0.799214	+	16.7776i	−0.0405218	+	0.850657i	0.883527	+	0.468381i	$0.155163\pi$
$389$	−0.799214	+	16.7776i	−0.0405218	+	0.850657i	−0.924048	+	0.382276i	$0.875140\pi$
$390$		0			0
$391$	11.0820	−	10.5667i	0.560441	−	0.534379i
$392$		0			0
$393$	8.50940	+	9.82037i	0.429242	+	0.495372i
$394$		0			0
$395$	58.5972	−	11.2937i	2.94835	−	0.568247i
$396$		0			0
$397$	25.9362	+	7.61555i	1.30170	+	0.382213i	0.857856	−	0.513891i	$-0.171796\pi$
$397$	25.9362	+	7.61555i	1.30170	+	0.382213i	0.443844	+	0.896104i	$0.353615\pi$
$398$		0			0
$399$	−2.94383	+	6.44609i	−0.147376	+	0.322708i
$400$		0			0
$401$	24.7621			1.23656			0.618280	−	0.785958i	$-0.287830\pi$
$401$	24.7621			1.23656			0.618280	+	0.785958i	$0.287830\pi$
$402$		0			0
$403$	−3.73683			−0.186145
$404$		0			0
$405$	−1.42199	+	3.11372i	−0.0706592	+	0.154722i
$406$		0			0
$407$	−1.71159	−	0.502569i	−0.0848405	−	0.0249114i
$408$		0			0
$409$	13.5454	−	2.61067i	0.669779	−	0.129089i	0.156985	−	0.987601i	$-0.449823\pi$
$409$	13.5454	−	2.61067i	0.669779	−	0.129089i	0.512794	+	0.858512i	$0.328610\pi$
$410$		0			0
$411$	10.2331	+	11.8096i	0.504762	+	0.582526i
$412$		0			0
$413$	−22.1479	+	21.1180i	−1.08983	+	1.03915i
$414$		0			0
$415$	−0.0662063	+	1.38984i	−0.00324994	+	0.0682247i
$416$		0			0
$417$	−11.7815	+	13.5966i	−0.576944	+	0.665829i
$418$		0			0
$419$	−5.68069	+	4.46734i	−0.277520	+	0.218244i	−0.747211	−	0.664587i	$-0.768608\pi$
$419$	−5.68069	+	4.46734i	−0.277520	+	0.218244i	0.469691	+	0.882831i	$0.344365\pi$
$420$		0			0
$421$	26.6573	+	5.13778i	1.29920	+	0.250400i	0.791518	−	0.611146i	$-0.209291\pi$
$421$	26.6573	+	5.13778i	1.29920	+	0.250400i	0.507680	+	0.861546i	$0.330503\pi$
$422$		0			0
$423$	1.85142	−	7.63166i	0.0900192	−	0.371064i
$424$		0			0
$425$	−30.7196	+	2.93336i	−1.49012	+	0.142289i
$426$		0			0
$427$	−13.6641	−	8.78136i	−0.661251	−	0.424960i
$428$		0			0
$429$	5.12496	−	1.50483i	0.247436	−	0.0726536i
$430$		0			0
$431$	1.72122	−	2.98123i	0.0829081	−	0.143601i	−0.821590	−	0.570079i	$-0.806913\pi$
$431$	1.72122	−	2.98123i	0.0829081	−	0.143601i	0.904498	+	0.426478i	$0.140246\pi$
$432$		0			0
$433$	−1.42813	−	29.9801i	−0.0686314	−	1.44075i	−0.726266	−	0.687414i	$-0.758746\pi$
$433$	−1.42813	−	29.9801i	−0.0686314	−	1.44075i	0.657634	−	0.753337i	$-0.271557\pi$
$434$		0			0
$435$	3.42601	+	9.89880i	0.164265	+	0.474611i
$436$		0			0
$437$	8.17794	+	0.780898i	0.391204	+	0.0373554i
$438$		0			0
$439$	−11.4925	−	19.9055i	−0.548505	−	0.950039i	−0.998377	−	0.0569459i	$-0.981864\pi$
$439$	−11.4925	−	19.9055i	−0.548505	−	0.950039i	0.449872	−	0.893093i	$-0.351470\pi$
$440$		0			0
$441$	−1.12582	−	0.580401i	−0.0536106	−	0.0276382i
$442$		0			0
$443$	−15.0979	−	6.04430i	−0.717325	−	0.287174i	−0.0158566	−	0.999874i	$-0.505048\pi$
$443$	−15.0979	−	6.04430i	−0.717325	−	0.287174i	−0.701468	+	0.712701i	$0.747472\pi$
$444$		0			0
$445$	−5.54158	−	38.5425i	−0.262696	−	1.82709i
$446$		0			0
$447$	3.98168	+	8.71867i	0.188327	+	0.412379i
$448$		0			0
$449$	6.68867	+	9.39292i	0.315658	+	0.443279i	0.941672	−	0.336533i	$-0.109254\pi$
$449$	6.68867	+	9.39292i	0.315658	+	0.443279i	−0.626014	+	0.779812i	$0.715315\pi$
$450$		0			0
$451$	−13.4510	+	5.38497i	−0.633383	+	0.253568i
$452$		0			0
$453$	−3.45040	−	14.2227i	−0.162114	−	0.668242i
$454$		0			0
$455$	−1.68902	+	11.7474i	−0.0791825	+	0.550727i
$456$		0			0
$457$	29.3977	−	15.1555i	1.37516	−	0.708947i	0.397203	−	0.917731i	$-0.369981\pi$
$457$	29.3977	−	15.1555i	1.37516	−	0.708947i	0.977962	+	0.208784i	$0.0669506\pi$
$458$		0			0
$459$	2.66478	−	3.74216i	0.124381	−	0.174669i
$460$		0			0
$461$	19.3891	−	12.4606i	0.903042	−	0.580350i	−0.00464909	−	0.999989i	$-0.501480\pi$
$461$	19.3891	−	12.4606i	0.903042	−	0.580350i	0.907691	+	0.419639i	$0.137843\pi$
$462$		0			0
$463$	−9.88884	−	9.42899i	−0.459573	−	0.438202i	0.424586	−	0.905388i	$-0.360420\pi$
$463$	−9.88884	−	9.42899i	−0.459573	−	0.438202i	−0.884159	+	0.467185i	$0.845268\pi$
$464$		0			0
$465$	8.33800	+	6.55708i	0.386665	+	0.304077i
$466$		0			0
$467$	−5.42433	+	15.6726i	−0.251008	+	0.725240i	0.747155	+	0.664650i	$0.231419\pi$
$467$	−5.42433	+	15.6726i	−0.251008	+	0.725240i	−0.998163	+	0.0605899i	$0.980702\pi$
$468$		0			0
$469$	0.932881	−	23.5158i	0.0430764	−	1.08586i
$470$		0			0
$471$	−0.284418	+	0.821772i	−0.0131053	+	0.0378652i
$472$		0			0
$473$	−22.5751	−	17.7532i	−1.03800	−	0.816294i
$474$		0			0
$475$	−11.9823	−	11.4251i	−0.549786	−	0.524220i
$476$		0			0
$477$	−4.66867	+	3.00037i	−0.213764	+	0.137378i
$478$		0			0
$479$	12.0372	−	16.9039i	0.549995	−	0.772360i	−0.442219	−	0.896907i	$-0.645809\pi$
$479$	12.0372	−	16.9039i	0.549995	−	0.772360i	0.992214	+	0.124548i	$0.0397480\pi$
$480$		0			0
$481$	0.431663	−	0.222538i	0.0196821	−	0.0101468i
$482$		0			0
$483$	−1.36384	+	9.48569i	−0.0620567	+	0.431614i
$484$		0			0
$485$	−0.483948	−	1.99486i	−0.0219749	−	0.0905819i
$486$		0			0
$487$	−2.93417	+	1.17467i	−0.132960	+	0.0532292i	−0.437188	−	0.899370i	$-0.644026\pi$
$487$	−2.93417	+	1.17467i	−0.132960	+	0.0532292i	0.304228	+	0.952599i	$0.401601\pi$
$488$		0			0
$489$	0.495576	+	0.695939i	0.0224107	+	0.0314715i
$490$		0			0
$491$	−2.84309	−	6.22549i	−0.128307	−	0.280952i	0.834566	−	0.550908i	$-0.185718\pi$
$491$	−2.84309	−	6.22549i	−0.128307	−	0.280952i	−0.962873	+	0.269955i	$0.912991\pi$
$492$		0			0
$493$	−2.00068	−	13.9150i	−0.0901062	−	0.626702i
$494$		0			0
$495$	−14.0759	−	5.63514i	−0.632664	−	0.253281i
$496$		0			0
$497$	28.4175	+	14.6503i	1.27470	+	0.657154i
$498$		0			0
$499$	11.4884	+	19.8985i	0.514291	+	0.890778i	0.999863	+	0.0165809i	$0.00527809\pi$
$499$	11.4884	+	19.8985i	0.514291	+	0.890778i	−0.485572	+	0.874197i	$0.661389\pi$
$500$		0			0
$501$	−7.30480	−	0.697524i	−0.326354	−	0.0311631i
$502$		0			0
$503$	−5.28553	−	15.2715i	−0.235670	−	0.680924i	−0.999375	−	0.0353581i	$-0.988743\pi$
$503$	−5.28553	−	15.2715i	−0.235670	−	0.680924i	0.763705	−	0.645566i	$-0.223378\pi$
$504$		0			0
$505$	2.62250	+	55.0531i	0.116700	+	2.44983i
$506$		0			0
$507$	5.77292	−	9.99899i	0.256384	−	0.444071i
$508$		0			0
$509$	36.4035	−	10.6890i	1.61356	−	0.473783i	0.654281	−	0.756251i	$-0.272971\pi$
$509$	36.4035	−	10.6890i	1.61356	−	0.473783i	0.959277	+	0.282468i	$0.0911532\pi$
$510$		0			0
$511$	−33.1717	−	21.3182i	−1.46743	−	0.943061i
$512$		0			0
$513$	2.45355	−	0.234286i	0.108327	−	0.0103440i
$514$		0			0
$515$	−3.45300	+	14.2335i	−0.152157	+	0.627201i
$516$		0			0
$517$	34.1554	+	6.58291i	1.50215	+	0.289516i
$518$		0			0
$519$	−7.38935	+	5.81105i	−0.324356	+	0.255077i
$520$		0			0
$521$	−2.73711	+	3.15879i	−0.119915	+	0.138389i	−0.812533	−	0.582916i	$-0.801912\pi$
$521$	−2.73711	+	3.15879i	−0.119915	+	0.138389i	0.692618	+	0.721305i	$0.256457\pi$
$522$		0			0
$523$	0.681719	−	14.3110i	0.0298095	−	0.625778i	−0.933692	−	0.358076i	$-0.883433\pi$
$523$	0.681719	−	14.3110i	0.0298095	−	0.625778i	0.963502	−	0.267702i	$-0.0862643\pi$
$524$		0			0
$525$	13.9778	−	13.3278i	0.610040	−	0.581672i
$526$		0			0
$527$	−9.32258	−	10.7588i	−0.406098	−	0.468662i
$528$		0			0
$529$	−11.6756	+	2.25028i	−0.507634	+	0.0978384i
$530$		0			0
$531$	10.2125	+	2.99866i	0.443184	+	0.130131i
$532$		0			0
$533$	1.63863	−	3.58810i	0.0709770	−	0.155418i
$534$		0			0
$535$	55.2590			2.38906
$536$		0			0
$537$	2.99828			0.129386
$538$		0			0
$539$	2.33063	−	5.10336i	0.100387	−	0.219817i
$540$		0			0
$541$	−8.46806	−	2.48645i	−0.364070	−	0.106901i	0.0945806	−	0.995517i	$-0.469849\pi$
$541$	−8.46806	−	2.48645i	−0.364070	−	0.106901i	−0.458651	+	0.888617i	$0.651667\pi$
$542$		0			0
$543$	−18.1673	+	3.50147i	−0.779635	+	0.150262i
$544$		0			0
$545$	20.2750	+	23.3986i	0.868485	+	1.00228i
$546$		0			0
$547$	−19.1764	+	18.2847i	−0.819926	+	0.781798i	−0.978652	−	0.205525i	$-0.934110\pi$
$547$	−19.1764	+	18.2847i	−0.819926	+	0.781798i	0.158726	+	0.987323i	$0.449261\pi$
$548$		0			0
$549$	−0.268801	+	5.64283i	−0.0114721	+	0.240830i
$550$		0			0
$551$	4.93915	−	5.70008i	0.210415	−	0.242832i
$552$		0			0
$553$	39.4003	−	30.9847i	1.67547	−	1.31760i
$554$		0			0
$555$	−1.35366	−	0.260897i	−0.0574597	−	0.0110745i
$556$		0			0
$557$	9.34820	−	38.5338i	0.396096	−	1.63273i	−0.329177	−	0.944268i	$-0.606771\pi$
$557$	9.34820	−	38.5338i	0.396096	−	1.63273i	0.725273	−	0.688462i	$-0.241714\pi$
$558$		0			0
$559$	7.78343	−	0.743227i	0.329204	−	0.0314352i
$560$		0			0
$561$	17.1183	+	11.0012i	0.722734	+	0.464473i
$562$		0			0
$563$	−0.389152	+	0.114265i	−0.0164008	+	0.00481571i	−0.289923	−	0.957050i	$-0.593630\pi$
$563$	−0.389152	+	0.114265i	−0.0164008	+	0.00481571i	0.273522	+	0.961866i	$0.411811\pi$
$564$		0			0
$565$	−29.5505	+	51.1830i	−1.24320	+	2.15328i
$566$		0			0
$567$	0.136806	+	2.87192i	0.00574532	+	0.120609i
$568$		0			0
$569$	6.77849	+	19.5851i	0.284169	+	0.821052i	0.993257	+	0.115932i	$0.0369856\pi$
$569$	6.77849	+	19.5851i	0.284169	+	0.821052i	−0.709088	+	0.705120i	$0.750893\pi$
$570$		0			0
$571$	32.0018	+	3.05580i	1.33923	+	0.127881i	0.739954	−	0.672658i	$-0.234847\pi$
$571$	32.0018	+	3.05580i	1.33923	+	0.127881i	0.599281	+	0.800539i	$0.295453\pi$
$572$		0			0
$573$	6.53639	+	11.3214i	0.273061	+	0.472956i
$574$		0			0
$575$	−19.9005	−	10.2594i	−0.829909	−	0.427848i
$576$		0			0
$577$	−8.18675	−	3.27748i	−0.340819	−	0.136443i	0.194938	−	0.980816i	$-0.437549\pi$
$577$	−8.18675	−	3.27748i	−0.340819	−	0.136443i	−0.535757	+	0.844372i	$0.679974\pi$
$578$		0			0
$579$	−0.685895	−	4.77050i	−0.0285048	−	0.198255i
$580$		0			0
$581$	0.485501	+	1.06310i	0.0201420	+	0.0441048i
$582$		0			0
$583$	−14.2587	−	20.0235i	−0.590534	−	0.829289i
$584$		0			0
$585$	3.83214	−	1.53416i	0.158439	−	0.0634295i
$586$		0			0
$587$	−6.13319	−	25.2813i	−0.253144	−	1.04347i	−0.946455	−	0.322835i	$-0.895364\pi$
$587$	−6.13319	−	25.2813i	−0.253144	−	1.04347i	0.693312	−	0.720638i	$-0.256151\pi$
$588$		0			0
$589$	1.08696	−	7.55996i	0.0447873	−	0.311503i
$590$		0			0
$591$	1.74625	−	0.900256i	0.0718312	−	0.0370316i
$592$		0			0
$593$	−11.3867	+	15.9904i	−0.467598	+	0.656649i	−0.979277	−	0.202528i	$-0.935084\pi$
$593$	−11.3867	+	15.9904i	−0.467598	+	0.656649i	0.511679	+	0.859177i	$0.329024\pi$
$594$		0			0
$595$	−38.0361	+	24.4443i	−1.55933	+	1.00212i
$596$		0			0
$597$	−1.03280	−	0.984770i	−0.0422696	−	0.0403039i
$598$		0			0
$599$	−20.7033	−	16.2813i	−0.845914	−	0.665234i	0.0980866	−	0.995178i	$-0.468728\pi$
$599$	−20.7033	−	16.2813i	−0.845914	−	0.665234i	−0.944001	+	0.329944i	$0.892970\pi$
$600$		0			0
$601$	−0.800214	+	2.31207i	−0.0326414	+	0.0943111i	−0.960144	−	0.279505i	$-0.909830\pi$
$601$	−0.800214	+	2.31207i	−0.0326414	+	0.0943111i	0.927503	+	0.373816i	$0.121951\pi$
$602$		0			0
$603$	−7.24538	+	3.80847i	−0.295055	+	0.155093i
$604$		0			0
$605$	9.64995	−	27.8817i	0.392326	−	1.13355i
$606$		0			0
$607$	−21.9605	−	17.2699i	−0.891349	−	0.700964i	0.0635238	−	0.997980i	$-0.479766\pi$
$607$	−21.9605	−	17.2699i	−0.891349	−	0.700964i	−0.954873	+	0.297016i	$0.904009\pi$
$608$		0			0
$609$	6.36766	+	6.07155i	0.258031	+	0.246032i
$610$		0			0
$611$	−7.96657	+	5.11980i	−0.322293	+	0.207125i
$612$		0			0
$613$	−22.8608	+	32.1036i	−0.923340	+	1.29665i	0.0314916	+	0.999504i	$0.489974\pi$
$613$	−22.8608	+	32.1036i	−0.923340	+	1.29665i	−0.954832	+	0.297146i	$0.903965\pi$
$614$		0			0
$615$	−9.95239	+	5.13082i	−0.401319	+	0.206894i
$616$		0			0
$617$	−2.72330	+	18.9410i	−0.109636	+	0.762536i	0.858627	+	0.512601i	$0.171318\pi$
$617$	−2.72330	+	18.9410i	−0.109636	+	0.762536i	−0.968263	+	0.249934i	$0.919591\pi$
$618$		0			0
$619$	11.2781	+	46.4888i	0.453304	+	1.86854i	0.494148	+	0.869378i	$0.335480\pi$
$619$	11.2781	+	46.4888i	0.453304	+	1.86854i	−0.0408441	+	0.999166i	$0.513005\pi$
$620$		0			0
$621$	3.09434	−	1.23879i	0.124172	−	0.0497108i
$622$		0			0
$623$	−18.9716	−	26.6419i	−0.760081	−	1.06738i
$624$		0			0
$625$	−5.59329	−	12.2476i	−0.223732	−	0.489904i
$626$		0			0
$627$	1.55367	+	10.8060i	0.0620476	+	0.431551i
$628$		0			0
$629$	1.71762	+	0.687632i	0.0684861	+	0.0274177i
$630$		0			0
$631$	−28.7833	−	14.8388i	−1.14584	−	0.590724i	−0.222589	−	0.974912i	$-0.571451\pi$
$631$	−28.7833	−	14.8388i	−1.14584	−	0.590724i	−0.923255	+	0.384189i	$0.874481\pi$
$632$		0			0
$633$	−8.08300	−	14.0002i	−0.321270	−	0.556457i
$634$		0			0
$635$	−63.2853	−	6.04301i	−2.51140	−	0.239810i
$636$		0			0
$637$	0.499566	+	1.44340i	0.0197935	+	0.0571897i
$638$		0			0
$639$	−0.529106	−	11.1073i	−0.0209311	−	0.439398i
$640$		0			0
$641$	3.55540	−	6.15813i	0.140430	−	0.243232i	−0.787229	−	0.616661i	$-0.788485\pi$
$641$	3.55540	−	6.15813i	0.140430	−	0.243232i	0.927659	+	0.373430i	$0.121818\pi$
$642$		0			0
$643$	−37.3118	+	10.9557i	−1.47143	+	0.432052i	−0.916565	−	0.399887i	$-0.869049\pi$
$643$	−37.3118	+	10.9557i	−1.47143	+	0.432052i	−0.554868	+	0.831938i	$0.687231\pi$
$644$		0			0
$645$	−18.6714	−	11.9993i	−0.735184	−	0.472474i
$646$		0			0
$647$	16.9751	−	1.62092i	0.667359	−	0.0637251i	0.244123	−	0.969744i	$-0.421500\pi$
$647$	16.9751	−	1.62092i	0.667359	−	0.0637251i	0.423236	+	0.906019i	$0.360894\pi$
$648$		0			0
$649$	−11.1148	+	45.8156i	−0.436292	+	1.79842i
$650$		0			0
$651$	8.74863	+	1.68616i	0.342886	+	0.0660859i
$652$		0			0
$653$	−21.5640	+	16.9581i	−0.843864	+	0.663622i	−0.943489	−	0.331403i	$-0.892478\pi$
$653$	−21.5640	+	16.9581i	−0.843864	+	0.663622i	0.0996256	+	0.995025i	$0.468235\pi$
$654$		0			0
$655$	−29.1281	+	33.6157i	−1.13813	+	1.31347i
$656$		0			0
$657$	−0.652558	+	13.6989i	−0.0254587	+	0.534444i
$658$		0			0
$659$	6.98951	−	6.66449i	0.272273	−	0.259612i	−0.541624	−	0.840621i	$-0.682190\pi$
$659$	6.98951	−	6.66449i	0.272273	−	0.259612i	0.813897	+	0.581009i	$0.197342\pi$
$660$		0			0
$661$	10.5398	+	12.1636i	0.409952	+	0.473110i	0.922750	−	0.385399i	$-0.125936\pi$
$661$	10.5398	+	12.1636i	0.409952	+	0.473110i	−0.512798	+	0.858510i	$0.671391\pi$
$662$		0			0
$663$	−5.43974	+	1.04842i	−0.211262	+	0.0407174i
$664$		0			0
$665$	−23.2748	−	6.83410i	−0.902559	−	0.265015i
$666$		0			0
$667$	4.23708	−	9.27792i	0.164060	−	0.359242i
$668$		0			0
$669$	−4.53112			−0.175183
$670$		0			0
$671$	−25.0225			−0.965984
$672$		0			0
$673$	16.5779	−	36.3006i	0.639033	−	1.39929i	−0.261801	−	0.965122i	$-0.584316\pi$
$673$	16.5779	−	36.3006i	0.639033	−	1.39929i	0.900834	−	0.434164i	$-0.142956\pi$
$674$		0			0
$675$	−6.44521	−	1.89248i	−0.248076	−	0.0728417i
$676$		0			0
$677$	28.9586	−	5.58131i	1.11297	−	0.214507i	0.400559	−	0.916271i	$-0.368816\pi$
$677$	28.9586	−	5.58131i	1.11297	−	0.214507i	0.712410	+	0.701764i	$0.247604\pi$
$678$		0			0
$679$	−1.12909	−	1.30304i	−0.0433306	−	0.0500062i
$680$		0			0
$681$	7.85056	−	7.48550i	0.300834	−	0.286845i
$682$		0			0
$683$	0.424902	−	8.91979i	0.0162584	−	0.341306i	−0.976052	−	0.217535i	$-0.930198\pi$
$683$	0.424902	−	8.91979i	0.0162584	−	0.341306i	0.992311	−	0.123771i	$-0.0394987\pi$
$684$		0			0
$685$	−35.0285	+	40.4250i	−1.33837	+	1.54456i
$686$		0			0
$687$	−2.87294	+	2.25930i	−0.109609	+	0.0861978i
$688$		0			0
$689$	6.57133	+	1.26652i	0.250348	+	0.0482506i
$690$		0			0
$691$	−5.81711	+	23.9784i	−0.221293	+	0.912183i	0.747490	+	0.664273i	$0.231259\pi$
$691$	−5.81711	+	23.9784i	−0.221293	+	0.912183i	−0.968783	+	0.247910i	$0.920256\pi$
$692$		0			0
$693$	−12.6775	+	1.21056i	−0.481580	+	0.0459853i
$694$		0			0
$695$	−51.8076	−	33.2947i	−1.96517	−	1.26294i
$696$		0			0
$697$	14.4187	−	4.23370i	0.546146	−	0.160363i
$698$		0			0
$699$	−9.65963	+	16.7310i	−0.365361	+	0.632824i
$700$		0			0
$701$	0.0197384	+	0.414360i	0.000745510	+	0.0156502i	0.999209	−	0.0397554i	$-0.0126579\pi$
$701$	0.0197384	+	0.414360i	0.000745510	+	0.0156502i	−0.998464	+	0.0554055i	$0.982355\pi$
$702$		0			0
$703$	0.324654	+	0.938027i	0.0122446	+	0.0353783i
$704$		0			0
$705$	26.7596	+	2.55523i	1.00783	+	0.0962357i
$706$		0			0
$707$	23.1470	+	40.0918i	0.870532	+	1.50781i
$708$		0			0
$709$	42.3550	+	21.8355i	1.59068	+	0.820051i	0.999913	+	0.0132066i	$0.00420393\pi$
$709$	42.3550	+	21.8355i	1.59068	+	0.820051i	0.590764	+	0.806844i	$0.298826\pi$
$710$		0			0
$711$	−16.1847	−	6.47936i	−0.606972	−	0.242995i
$712$		0			0
$713$	−1.46992	−	10.2235i	−0.0550490	−	0.382874i
$714$		0			0
$715$	7.59530	+	16.6314i	0.284048	+	0.621979i
$716$		0			0
$717$	−9.82545	−	13.7979i	−0.366938	−	0.515292i
$718$		0			0
$719$	6.72624	−	2.69278i	0.250846	−	0.100424i	−0.242832	−	0.970068i	$-0.578076\pi$
$719$	6.72624	−	2.69278i	0.250846	−	0.100424i	0.493678	+	0.869645i	$0.335652\pi$
$720$		0			0
$721$	2.90033	+	11.9553i	0.108014	+	0.445239i
$722$		0			0
$723$	1.17258	−	8.15547i	0.0436087	−	0.303305i
$724$		0			0
$725$	−18.2706	+	9.41915i	−0.678553	+	0.349819i
$726$		0			0
$727$	6.90869	−	9.70189i	0.256229	−	0.359823i	−0.666345	−	0.745644i	$-0.732142\pi$
$727$	6.90869	−	9.70189i	0.256229	−	0.359823i	0.922574	+	0.385820i	$0.126082\pi$
$728$		0			0
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$		0			0
$731$	21.5578	+	20.5554i	0.797345	+	0.760267i
$732$		0			0
$733$	−15.7037	−	12.3495i	−0.580029	−	0.456140i	0.284533	−	0.958666i	$-0.408162\pi$
$733$	−15.7037	−	12.3495i	−0.580029	−	0.456140i	−0.864562	+	0.502526i	$0.832404\pi$
$734$		0			0
$735$	1.41808	−	4.09727i	0.0523066	−	0.151130i
$736$		0			0
$737$	−18.3770	−	31.2535i	−0.676927	−	1.15124i
$738$		0			0
$739$	−13.5433	+	39.1308i	−0.498198	+	1.43945i	0.363292	+	0.931675i	$0.381653\pi$
$739$	−13.5433	+	39.1308i	−0.498198	+	1.43945i	−0.861490	+	0.507774i	$0.830468\pi$
$740$		0			0
$741$	−2.33628	−	1.83727i	−0.0858255	−	0.0674939i
$742$		0			0
$743$	−4.58248	−	4.36939i	−0.168115	−	0.160297i	0.601351	−	0.798985i	$-0.294629\pi$
$743$	−4.58248	−	4.36939i	−0.168115	−	0.160297i	−0.769466	+	0.638687i	$0.779478\pi$
$744$		0			0
$745$	−27.6010	+	17.7381i	−1.01122	+	0.649874i
$746$		0			0
$747$	0.235784	−	0.331112i	0.00862689	−	0.0121148i
$748$		0			0
$749$	41.2548	−	21.2683i	1.50742	−	0.777129i
$750$		0			0
$751$	4.40514	−	30.6384i	0.160746	−	1.11801i	−0.736487	−	0.676452i	$-0.763517\pi$
$751$	4.40514	−	30.6384i	0.160746	−	1.11801i	0.897232	−	0.441559i	$-0.145574\pi$
$752$		0			0
$753$	−2.42293	−	9.98743i	−0.0882963	−	0.363962i
$754$		0			0
$755$	46.5088	−	18.6193i	1.69263	−	0.677626i
$756$		0			0
$757$	6.65102	+	9.34005i	0.241735	+	0.339470i	0.917563	−	0.397590i	$-0.130153\pi$
$757$	6.65102	+	9.34005i	0.241735	+	0.339470i	−0.675828	+	0.737059i	$0.736214\pi$
$758$		0			0
$759$	6.13299	+	13.4294i	0.222613	+	0.487455i
$760$		0			0
$761$	−4.44735	−	30.9320i	−0.161216	−	1.12128i	−0.896345	−	0.443357i	$-0.853787\pi$
$761$	−4.44735	−	30.9320i	−0.161216	−	1.12128i	0.735129	−	0.677927i	$-0.237122\pi$
$762$		0			0
$763$	24.1425	+	9.66519i	0.874016	+	0.349903i
$764$		0			0
$765$	13.9774	+	7.20585i	0.505354	+	0.260528i
$766$		0			0
$767$	−6.41751	−	11.1155i	−0.231723	−	0.401356i
$768$		0			0
$769$	34.6017	+	3.30407i	1.24777	+	0.119148i	0.697957	−	0.716140i	$-0.254093\pi$
$769$	34.6017	+	3.30407i	1.24777	+	0.119148i	0.549814	+	0.835287i	$0.314699\pi$
$770$		0			0
$771$	1.07661	+	3.11065i	0.0387730	+	0.112027i
$772$		0			0
$773$	2.10356	+	44.1592i	0.0756598	+	1.58830i	0.643689	+	0.765287i	$0.277403\pi$
$773$	2.10356	+	44.1592i	0.0756598	+	1.58830i	−0.568030	+	0.823008i	$0.692294\pi$
$774$		0			0
$775$	−10.4079	+	18.0269i	−0.373861	+	0.647546i
$776$		0			0
$777$	−1.11102	+	0.326225i	−0.0398577	+	0.0117033i
$778$		0			0
$779$	6.78244	+	4.35881i	0.243006	+	0.156171i
$780$		0			0
$781$	49.0311	−	4.68191i	1.75447	−	0.167532i
$782$		0			0
$783$	0.721448	−	2.97385i	0.0257824	−	0.106277i
$784$		0			0
$785$	−2.92289	−	0.563341i	−0.104322	−	0.0201065i
$786$		0			0
$787$	32.2497	−	25.3614i	1.14958	−	0.904038i	0.153126	−	0.988207i	$-0.451066\pi$
$787$	32.2497	−	25.3614i	1.14958	−	0.904038i	0.996451	+	0.0841691i	$0.0268236\pi$
$788$		0			0
$789$	−9.53319	+	11.0019i	−0.339390	+	0.391677i
$790$		0			0
$791$	−2.36204	+	49.5853i	−0.0839844	+	1.76305i
$792$		0			0
$793$	4.93032	−	4.70105i	0.175081	−	0.166939i
$794$		0			0
$795$	−12.4403	−	14.3568i	−0.441210	−	0.509184i
$796$		0			0
$797$	−22.4747	+	4.33163i	−0.796093	+	0.153434i	−0.571051	−	0.820915i	$-0.693464\pi$
$797$	−22.4747	+	4.33163i	−0.796093	+	0.153434i	−0.225042	+	0.974349i	$0.572252\pi$
$798$		0			0
$799$	−34.6155	−	10.1640i	−1.22461	−	0.359577i
$800$		0			0
$801$	−4.72554	+	10.3475i	−0.166969	+	0.365611i
$802$		0			0
$803$	−60.7462			−2.14369
$804$		0			0
$805$	−32.8039			−1.15619
$806$		0			0
$807$	−9.20777	+	20.1622i	−0.324129	+	0.709743i
$808$		0			0
$809$	12.0127	+	3.52725i	0.422345	+	0.124012i	0.485997	−	0.873961i	$-0.338457\pi$
$809$	12.0127	+	3.52725i	0.422345	+	0.124012i	−0.0636521	+	0.997972i	$0.520275\pi$
$810$		0			0
$811$	50.8322	−	9.79711i	1.78496	−	0.344023i	0.813562	−	0.581478i	$-0.197525\pi$
$811$	50.8322	−	9.79711i	1.78496	−	0.344023i	0.971399	+	0.237455i	$0.0763132\pi$
$812$		0			0
$813$	17.2022	+	19.8524i	0.603309	+	0.696255i
$814$		0			0
$815$	−2.11657	+	2.01814i	−0.0741402	+	0.0706925i
$816$		0			0
$817$	−0.760403	+	15.9628i	−0.0266031	+	0.558468i
$818$		0			0
$819$	2.27049	−	2.62029i	0.0793374	−	0.0915603i
$820$		0			0
$821$	27.3217	−	21.4860i	0.953533	−	0.749867i	−0.0147063	−	0.999892i	$-0.504681\pi$
$821$	27.3217	−	21.4860i	0.953533	−	0.749867i	0.968239	+	0.250025i	$0.0804389\pi$
$822$		0			0
$823$	−48.3577	−	9.32018i	−1.68564	−	0.324881i	−0.745718	−	0.666262i	$-0.767893\pi$
$823$	−48.3577	−	9.32018i	−1.68564	−	0.324881i	−0.939925	+	0.341381i	$0.889106\pi$
$824$		0			0
$825$	7.01464	−	28.9147i	0.244218	−	1.00668i
$826$		0			0
$827$	−50.3532	+	4.80815i	−1.75095	+	0.167196i	−0.920721	−	0.390222i	$-0.872398\pi$
$827$	−50.3532	+	4.80815i	−1.75095	+	0.167196i	−0.830232	+	0.557418i	$0.811792\pi$
$828$		0			0
$829$	−38.1259	−	24.5020i	−1.32417	−	0.850990i	−0.328546	−	0.944488i	$-0.606559\pi$
$829$	−38.1259	−	24.5020i	−1.32417	−	0.850990i	−0.995619	+	0.0934984i	$0.970195\pi$
$830$		0			0
$831$	10.6269	−	3.12034i	0.368644	−	0.108244i
$832$		0			0
$833$	−2.90944	+	5.03930i	−0.100806	+	0.174601i
$834$		0			0
$835$	−1.19518	−	25.0900i	−0.0413611	−	0.868276i
$836$		0			0
$837$	−1.01352	−	2.92839i	−0.0350325	−	0.101220i
$838$		0			0
$839$	25.5050	+	2.43543i	0.880529	+	0.0840803i	0.525519	−	0.850782i	$-0.323871\pi$
$839$	25.5050	+	2.43543i	0.880529	+	0.0840803i	0.355010	+	0.934862i	$0.384477\pi$
$840$		0			0
$841$	9.81787	+	17.0051i	0.338547	+	0.586381i
$842$		0			0
$843$	−6.20979	−	3.20137i	−0.213876	−	0.110261i
$844$		0			0
$845$	36.6910	+	14.6889i	1.26221	+	0.505312i
$846$		0			0
$847$	−3.52686	−	24.5298i	−0.121184	−	0.842854i
$848$		0			0
$849$	−4.80389	−	10.5190i	−0.164869	−	0.361013i
$850$		0			0
$851$	0.778637	+	1.09344i	0.0266913	+	0.0374827i
$852$		0			0
$853$	−11.4985	+	4.60331i	−0.393702	+	0.157614i	−0.560062	−	0.828451i	$-0.689223\pi$
$853$	−11.4985	+	4.60331i	−0.393702	+	0.157614i	0.166360	+	0.986065i	$0.446799\pi$
$854$		0			0
$855$	1.98906	+	8.19903i	0.0680245	+	0.280401i
$856$		0			0
$857$	−6.42160	+	44.6632i	−0.219358	+	1.52567i	0.521061	+	0.853519i	$0.325536\pi$
$857$	−6.42160	+	44.6632i	−0.219358	+	1.52567i	−0.740419	+	0.672146i	$0.765373\pi$
$858$		0			0
$859$	36.2181	−	18.6717i	1.23574	−	0.637071i	0.288469	−	0.957489i	$-0.406854\pi$
$859$	36.2181	−	18.6717i	1.23574	−	0.637071i	0.947276	+	0.320419i	$0.103824\pi$
$860$		0			0
$861$	−5.45541	+	7.66105i	−0.185920	+	0.261088i
$862$		0			0
$863$	32.7622	−	21.0550i	1.11524	−	0.716720i	0.152810	−	0.988256i	$-0.451168\pi$
$863$	32.7622	−	21.0550i	1.11524	−	0.716720i	0.962428	+	0.271536i	$0.0875315\pi$
$864$		0			0
$865$	−23.2888	−	22.2058i	−0.791843	−	0.755021i
$866$		0			0
$867$	−3.22663	−	2.53745i	−0.109582	−	0.0861763i
$868$		0			0
$869$	25.2559	−	72.9722i	0.856749	−	2.47541i
$870$		0			0
$871$	9.49260	+	2.70549i	0.321644	+	0.0916721i
$872$		0			0
$873$	−0.196135	+	0.566694i	−0.00663815	+	0.0191797i
$874$		0			0
$875$	13.2855	+	10.4478i	0.449131	+	0.353200i
$876$		0			0
$877$	10.1785	+	9.70520i	0.343704	+	0.327721i	0.842194	−	0.539174i	$-0.181264\pi$
$877$	10.1785	+	9.70520i	0.343704	+	0.327721i	−0.498490	+	0.866895i	$0.666112\pi$
$878$		0			0
$879$	24.1857	−	15.5432i	0.815762	−	0.524259i
$880$		0			0
$881$	−21.5061	+	30.2011i	−0.724558	+	1.01750i	0.273888	+	0.961762i	$0.411690\pi$
$881$	−21.5061	+	30.2011i	−0.724558	+	1.01750i	−0.998445	+	0.0557375i	$0.982249\pi$
$882$		0			0
$883$	24.2980	−	12.5265i	0.817692	−	0.421550i	0.00197340	−	0.999998i	$-0.499372\pi$
$883$	24.2980	−	12.5265i	0.817692	−	0.421550i	0.815719	+	0.578448i	$0.196342\pi$
$884$		0			0
$885$	−5.18506	+	36.0629i	−0.174294	+	1.21224i
$886$		0			0
$887$	−6.63700	−	27.3581i	−0.222848	−	0.918594i	−0.967849	−	0.251531i	$-0.919066\pi$
$887$	−6.63700	−	27.3581i	−0.222848	−	0.918594i	0.745001	−	0.667063i	$-0.232449\pi$
$888$		0			0
$889$	−49.5729	+	19.8460i	−1.66262	+	0.665613i
$890$		0			0
$891$	2.56929	+	3.60806i	0.0860744	+	0.120875i
$892$		0			0
$893$	−8.04055	−	17.6064i	−0.269067	−	0.589174i
$894$		0			0
$895$	1.46062	+	10.1588i	0.0488231	+	0.339572i
$896$		0			0
$897$	−3.73143	−	1.49384i	−0.124589	−	0.0498778i
$898$		0			0
$899$	−8.42858	−	4.34523i	−0.281109	−	0.144922i
$900$		0			0
$901$	12.7476	+	22.0795i	0.424683	+	0.735573i
$902$		0			0
$903$	−18.5579	−	1.77206i	−0.617567	−	0.0589705i
$904$		0			0
$905$	−20.7140	−	59.8491i	−0.688555	−	1.98945i
$906$		0			0
$907$	0.599634	+	12.5879i	0.0199105	+	0.417973i	0.986716	+	0.162458i	$0.0519421\pi$
$907$	0.599634	+	12.5879i	0.0199105	+	0.417973i	−0.966805	+	0.255515i	$0.917755\pi$
$908$		0			0
$909$	8.05064	−	13.9441i	0.267023	−	0.462497i
$910$		0			0
$911$	14.3399	−	4.21058i	0.475102	−	0.139503i	−0.0354103	−	0.999373i	$-0.511274\pi$
$911$	14.3399	−	4.21058i	0.475102	−	0.139503i	0.510513	+	0.859870i	$0.329456\pi$
$912$		0			0
$913$	1.51465	+	0.973407i	0.0501277	+	0.0322151i
$914$		0			0
$915$	−19.2500	+	1.83816i	−0.636387	+	0.0607676i
$916$		0			0
$917$	−8.80810	+	36.3075i	−0.290869	+	1.19898i
$918$		0			0
$919$	5.94855	+	1.14649i	0.196225	+	0.0378192i	0.286416	−	0.958105i	$-0.407536\pi$
$919$	5.94855	+	1.14649i	0.196225	+	0.0378192i	−0.0901918	+	0.995924i	$0.528748\pi$
$920$		0			0
$921$	−9.25587	+	7.27890i	−0.304991	+	0.239848i
$922$		0			0
$923$	−8.78126	+	10.1341i	−0.289039	+	0.333568i
$924$		0			0
$925$	0.128722	−	2.70221i	0.00423236	−	0.0888481i
$926$		0			0
$927$	3.09666	−	2.95266i	0.101708	−	0.0969781i
$928$		0			0
$929$	−30.2592	−	34.9209i	−0.992771	−	1.14572i	−0.989325	−	0.145725i	$-0.953448\pi$
$929$	−30.2592	−	34.9209i	−0.992771	−	1.14572i	−0.00344621	−	0.999994i	$-0.501097\pi$
$930$		0			0
$931$	−3.06545	+	0.590818i	−0.100466	+	0.0193633i
$932$		0			0
$933$	−22.3960	−	6.57605i	−0.733211	−	0.215290i
$934$		0			0
$935$	−28.9354	+	63.3596i	−0.946288	+	2.07208i
$936$		0			0
$937$	19.8521			0.648541			0.324271	−	0.945964i	$-0.394881\pi$
$937$	19.8521			0.648541			0.324271	+	0.945964i	$0.394881\pi$
$938$		0			0
$939$	14.3136			0.467106
$940$		0			0
$941$	−23.2927	+	51.0039i	−0.759320	+	1.66268i	−0.0104662	+	0.999945i	$0.503332\pi$
$941$	−23.2927	+	51.0039i	−0.759320	+	1.66268i	−0.748854	+	0.662735i	$0.769396\pi$
$942$		0			0
$943$	10.4612	+	3.07169i	0.340664	+	0.100028i
$944$		0			0
$945$	−9.66402	+	1.86259i	−0.314371	+	0.0605900i
$946$		0			0
$947$	14.8370	+	17.1228i	0.482138	+	0.556417i	0.943748	−	0.330666i	$-0.107273\pi$
$947$	14.8370	+	17.1228i	0.482138	+	0.556417i	−0.461610	+	0.887083i	$0.652728\pi$
$948$		0			0
$949$	11.9691	−	11.4126i	0.388535	−	0.370467i
$950$		0			0
$951$	0.0688634	−	1.44562i	0.00223305	−	0.0468775i
$952$		0			0
$953$	−31.3479	+	36.1774i	−1.01546	+	1.17190i	−0.0304233	+	0.999537i	$0.509686\pi$
$953$	−31.3479	+	36.1774i	−1.01546	+	1.17190i	−0.985034	+	0.172363i	$0.944860\pi$
$954$		0			0
$955$	−35.1749	+	27.6619i	−1.13823	+	0.895117i
$956$		0			0
$957$	13.3094	+	2.56518i	0.430232	+	0.0829204i
$958$		0			0
$959$	−10.5923	+	43.6621i	−0.342043	+	1.40992i
$960$		0			0
$961$	21.3004	−	2.03394i	0.687111	−	0.0656111i
$962$		0			0
$963$	−13.5805	−	8.72767i	−0.437626	−	0.281245i
$964$		0			0
$965$	15.8293	−	4.64792i	0.509565	−	0.149622i
$966$		0			0
$967$	16.1540	−	27.9795i	0.519476	−	0.899759i	−0.480268	−	0.877122i	$-0.659460\pi$
$967$	16.1540	−	27.9795i	0.519476	−	0.899759i	0.999744	−	0.0226370i	$-0.00720620\pi$
$968$		0			0
$969$	−0.538765	−	11.3101i	−0.0173076	−	0.363332i
$970$		0			0
$971$	−2.45360	−	7.08922i	−0.0787399	−	0.227504i	0.898760	−	0.438442i	$-0.144469\pi$
$971$	−2.45360	−	7.08922i	−0.0787399	−	0.227504i	−0.977499	+	0.210938i	$0.932348\pi$
$972$		0			0
$973$	−51.4927	−	4.91696i	−1.65078	−	0.157630i
$974$		0			0
$975$	4.05016	+	7.01508i	0.129709	+	0.224662i
$976$		0			0
$977$	42.4840	+	21.9020i	1.35918	+	0.700707i	0.974928	−	0.222520i	$-0.0714283\pi$
$977$	42.4840	+	21.9020i	1.35918	+	0.700707i	0.384254	+	0.923227i	$0.374459\pi$
$978$		0			0
$979$	−46.7769	−	18.7267i	−1.49500	−	0.598506i
$980$		0			0
$981$	−1.28721	−	8.95271i	−0.0410973	−	0.285838i
$982$		0			0
$983$	21.1461	+	46.3035i	0.674456	+	1.47685i	0.868413	+	0.495842i	$0.165141\pi$
$983$	21.1461	+	46.3035i	0.674456	+	1.47685i	−0.193957	+	0.981010i	$0.562132\pi$
$984$		0			0
$985$	3.90095	+	5.47811i	0.124295	+	0.174547i
$986$		0			0
$987$	20.9615	−	8.39170i	0.667211	−	0.267111i
$988$		0			0
$989$	5.09508	+	21.0022i	0.162014	+	0.667832i
$990$		0			0
$991$	−2.80195	+	19.4880i	−0.0890068	+	0.619056i	0.895677	+	0.444705i	$0.146692\pi$
$991$	−2.80195	+	19.4880i	−0.0890068	+	0.619056i	−0.984684	+	0.174350i	$0.944217\pi$
$992$		0			0
$993$	30.8418	−	15.9000i	0.978734	−	0.504572i
$994$		0			0
$995$	2.83348	−	3.97907i	0.0898274	−	0.126145i
$996$		0			0
$997$	11.9295	−	7.66663i	0.377811	−	0.242805i	−0.337928	−	0.941172i	$-0.609726\pi$
$997$	11.9295	−	7.66663i	0.377811	−	0.242805i	0.715740	+	0.698367i	$0.246090\pi$
$998$		0			0
$999$	0.291471	+	0.277917i	0.00922174	+	0.00879291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.a.73.5	✓	100
67.56	even	33	inner	804.2.y.a.793.5	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.a.73.5	✓	100	1.1	even	1	trivial
804.2.y.a.793.5	yes	100	67.56	even	33	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{3} +(3.28440 + 0.964386i) q^{5} +(2.82322 - 0.544130i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{3} +(3.28440 + 0.964386i) q^{5} +(2.82322 - 0.544130i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(3.20569 - 3.05662i) q^{11} +(-0.0573785 + 1.20452i) q^{13} +(2.24162 - 2.58697i) q^{15} +(-3.61113 + 2.83982i) q^{17} +(-2.42017 - 0.466450i) q^{19} +(0.677848 - 2.79413i) q^{21} +(-3.31801 + 0.316831i) q^{23} +(5.65096 + 3.63165i) q^{25} +(-0.959493 + 0.281733i) q^{27} +(-1.53005 + 2.65013i) q^{29} +(0.147448 + 3.09531i) q^{31} +(-1.44871 - 4.18576i) q^{33} +(9.79731 + 0.935530i) q^{35} +(-0.201366 - 0.348776i) q^{37} +(1.07184 + 0.552570i) q^{39} +(-3.03677 - 1.21574i) q^{41} +(-0.922752 - 6.41788i) q^{43} +(-1.42199 - 3.11372i) q^{45} +(4.55520 + 6.39689i) q^{47} +(1.17589 - 0.470757i) q^{49} +(1.08308 + 4.46450i) q^{51} +(0.789799 - 5.49317i) q^{53} +(13.4765 - 6.94762i) q^{55} +(-1.42967 + 2.00770i) q^{57} +(-8.95399 + 5.75438i) q^{59} +(-4.08854 - 3.89841i) q^{61} +(-2.26004 - 1.77731i) q^{63} +(-1.35008 + 3.90079i) q^{65} +(1.86647 - 7.96971i) q^{67} +(-1.09015 + 3.14978i) q^{69} +(8.74083 + 6.87387i) q^{71} +(-9.92559 - 9.46403i) q^{73} +(5.65096 - 3.63165i) q^{75} +(7.38715 - 10.3738i) q^{77} +(15.4955 - 7.98847i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(0.0958323 + 0.395026i) q^{83} +(-14.5991 + 5.84458i) q^{85} +(1.77504 + 2.49269i) q^{87} +(-4.72554 - 10.3475i) q^{89} +(0.493425 + 3.43185i) q^{91} +(2.87684 + 1.15171i) q^{93} +(-7.49897 - 3.86599i) q^{95} +(-0.299838 - 0.519334i) q^{97} +(-4.40931 - 0.421038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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