LMFDB - Embedded newform 525.2.q.g.299.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(299,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("525.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.6
Character	$\chi$	$=$	525.299
Dual form			525.2.q.g.374.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.846473 + 1.46613i) q^{2} +(-0.0718963 + 1.73056i) q^{3} +(-0.433034 - 0.750036i) q^{4} +(-2.47637 - 1.57028i) q^{6} +(-2.01688 + 1.71236i) q^{7} -1.91969 q^{8} +(-2.98966 - 0.248842i) q^{9} +O(q^{10})$	\(q+(-0.846473 + 1.46613i) q^{2} +(-0.0718963 + 1.73056i) q^{3} +(-0.433034 - 0.750036i) q^{4} +(-2.47637 - 1.57028i) q^{6} +(-2.01688 + 1.71236i) q^{7} -1.91969 q^{8} +(-2.98966 - 0.248842i) q^{9} +(0.399511 - 0.230658i) q^{11} +(1.32911 - 0.695465i) q^{12} +3.38501 q^{13} +(-0.803314 - 4.40649i) q^{14} +(2.49103 - 4.31459i) q^{16} +(-4.76601 + 2.75166i) q^{17} +(2.89550 - 4.17261i) q^{18} +(-3.49334 - 2.01688i) q^{19} +(-2.81833 - 3.61345i) q^{21} +0.780983i q^{22} +(2.25223 - 3.90097i) q^{23} +(0.138018 - 3.32213i) q^{24} +(-2.86532 + 4.96289i) q^{26} +(0.645580 - 5.15589i) q^{27} +(2.15771 + 0.771225i) q^{28} +7.71756i q^{29} +(-3.01611 + 1.74135i) q^{31} +(2.29749 + 3.97938i) q^{32} +(0.370444 + 0.707961i) q^{33} -9.31681i q^{34} +(1.10798 + 2.35011i) q^{36} +(-5.02232 - 2.89964i) q^{37} +(5.91404 - 3.41448i) q^{38} +(-0.243370 + 5.85796i) q^{39} +6.25727 q^{41} +(7.68344 - 1.07337i) q^{42} +8.35453i q^{43} +(-0.346004 - 0.199765i) q^{44} +(3.81290 + 6.60414i) q^{46} +(2.73630 + 1.57980i) q^{47} +(7.28756 + 4.62108i) q^{48} +(1.13564 - 6.90727i) q^{49} +(-4.41924 - 8.44568i) q^{51} +(-1.46582 - 2.53888i) q^{52} +(-5.78238 - 10.0154i) q^{53} +(7.01277 + 5.31083i) q^{54} +(3.87179 - 3.28720i) q^{56} +(3.74149 - 5.90043i) q^{57} +(-11.3150 - 6.53271i) q^{58} +(4.88061 + 8.45346i) q^{59} +(-6.90647 - 3.98746i) q^{61} -5.89604i q^{62} +(6.45591 - 4.61750i) q^{63} +2.18506 q^{64} +(-1.35154 - 0.0561498i) q^{66} +(-0.793481 + 0.458116i) q^{67} +(4.12768 + 2.38312i) q^{68} +(6.58893 + 4.17808i) q^{69} +1.52593i q^{71} +(5.73922 + 0.477698i) q^{72} +(-3.89906 - 6.75338i) q^{73} +(8.50252 - 4.90893i) q^{74} +3.49351i q^{76} +(-0.410798 + 1.14932i) q^{77} +(-8.38256 - 5.31542i) q^{78} +(-3.58521 + 6.20977i) q^{79} +(8.87616 + 1.48790i) q^{81} +(-5.29661 + 9.17399i) q^{82} +17.5632i q^{83} +(-1.48978 + 3.67860i) q^{84} +(-12.2489 - 7.07188i) q^{86} +(-13.3557 - 0.554864i) q^{87} +(-0.766937 + 0.442791i) q^{88} +(-1.35247 + 2.34254i) q^{89} +(-6.82718 + 5.79637i) q^{91} -3.90116 q^{92} +(-2.79667 - 5.34476i) q^{93} +(-4.63241 + 2.67452i) q^{94} +(-7.05172 + 3.68984i) q^{96} +4.44253 q^{97} +(9.16569 + 7.51181i) q^{98} +(-1.25180 + 0.590174i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 28 q^{4} + 14 q^{9}+O(q^{10}) $ 40 * q - 28 * q^4 + 14 * q^9	$ 40 q - 28 q^{4} + 14 q^{9} - 36 q^{16} - 18 q^{21} - 36 q^{24} + 84 q^{31} - 72 q^{36} - 16 q^{46} + 8 q^{49} + 42 q^{51} + 150 q^{54} - 180 q^{61} + 240 q^{64} + 12 q^{66} - 92 q^{79} + 58 q^{81} - 150 q^{84} - 60 q^{91} - 12 q^{94} + 270 q^{96} - 188 q^{99}+O(q^{100}) $ 40 * q - 28 * q^4 + 14 * q^9 - 36 * q^16 - 18 * q^21 - 36 * q^24 + 84 * q^31 - 72 * q^36 - 16 * q^46 + 8 * q^49 + 42 * q^51 + 150 * q^54 - 180 * q^61 + 240 * q^64 + 12 * q^66 - 92 * q^79 + 58 * q^81 - 150 * q^84 - 60 * q^91 - 12 * q^94 + 270 * q^96 - 188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.846473	+	1.46613i	−0.598547	+	1.03671i	0.394489	+	0.918901i	$0.370922\pi$
$2$	−0.846473	+	1.46613i	−0.598547	+	1.03671i	−0.993036	+	0.117813i	$0.962412\pi$
$3$	−0.0718963	+	1.73056i	−0.0415094	+	0.999138i
$3$	−0.0718963	+	1.73056i	−0.0415094	+	0.999138i
$4$	−0.433034	−	0.750036i	−0.216517	−	0.375018i
$5$		0			0
$5$		0			0
$6$	−2.47637	−	1.57028i	−1.01097	−	0.641064i
$7$	−2.01688	+	1.71236i	−0.762310	+	0.647212i
$7$	−2.01688	+	1.71236i	−0.762310	+	0.647212i
$8$	−1.91969			−0.678712
$9$	−2.98966	−	0.248842i	−0.996554	−	0.0829472i
$10$		0			0
$11$	0.399511	−	0.230658i	0.120457	−	0.0695460i	−0.438561	−	0.898702i	$-0.644512\pi$
$11$	0.399511	−	0.230658i	0.120457	−	0.0695460i	0.559018	+	0.829156i	$0.311178\pi$
$12$	1.32911	−	0.695465i	0.383682	−	0.200763i
$13$	3.38501			0.938834			0.469417	−	0.882977i	$-0.344464\pi$
$13$	3.38501			0.938834			0.469417	+	0.882977i	$0.344464\pi$
$14$	−0.803314	−	4.40649i	−0.214695	−	1.17768i
$15$		0			0
$16$	2.49103	−	4.31459i	0.622758	−	1.07865i
$17$	−4.76601	+	2.75166i	−1.15593	+	0.667374i	−0.950324	−	0.311261i	$-0.899249\pi$
$17$	−4.76601	+	2.75166i	−1.15593	+	0.667374i	−0.205602	+	0.978636i	$0.565915\pi$
$18$	2.89550	−	4.17261i	0.682477	−	0.983493i
$19$	−3.49334	−	2.01688i	−0.801428	−	0.462705i	0.0425421	−	0.999095i	$-0.486454\pi$
$19$	−3.49334	−	2.01688i	−0.801428	−	0.462705i	−0.843970	+	0.536390i	$0.819788\pi$
$20$		0			0
$21$	−2.81833	−	3.61345i	−0.615011	−	0.788519i
$22$			0.780983i			0.166506i
$23$	2.25223	−	3.90097i	0.469622	−	0.813409i	−0.529775	−	0.848138i	$-0.677724\pi$
$23$	2.25223	−	3.90097i	0.469622	−	0.813409i	0.999397	+	0.0347292i	$0.0110569\pi$
$24$	0.138018	−	3.32213i	0.0281729	−	0.678127i
$25$		0			0
$26$	−2.86532	+	4.96289i	−0.561936	+	0.973302i
$27$	0.645580	−	5.15589i	0.124242	−	0.992252i
$28$	2.15771	+	0.771225i	0.407769	+	0.145748i
$29$			7.71756i			1.43311i	0.697528	+	0.716557i	$0.254283\pi$
$29$			7.71756i			1.43311i	−0.697528	+	0.716557i	$0.745717\pi$
$30$		0			0
$31$	−3.01611	+	1.74135i	−0.541710	+	0.312756i	−0.745772	−	0.666202i	$-0.767919\pi$
$31$	−3.01611	+	1.74135i	−0.541710	+	0.312756i	0.204062	+	0.978958i	$0.434586\pi$
$32$	2.29749	+	3.97938i	0.406143	+	0.703461i
$33$	0.370444	+	0.707961i	0.0644860	+	0.123240i
$34$		−	9.31681i		−	1.59782i
$35$		0			0
$36$	1.10798	+	2.35011i	0.184664	+	0.391685i
$37$	−5.02232	−	2.89964i	−0.825665	−	0.476698i	0.0267011	−	0.999643i	$-0.491500\pi$
$37$	−5.02232	−	2.89964i	−0.825665	−	0.476698i	−0.852366	+	0.522946i	$0.824833\pi$
$38$	5.91404	−	3.41448i	0.959385	−	0.553901i
$39$	−0.243370	+	5.85796i	−0.0389704	+	0.938025i
$40$		0			0
$41$	6.25727			0.977221			0.488610	−	0.872502i	$-0.337504\pi$
$41$	6.25727			0.977221			0.488610	+	0.872502i	$0.337504\pi$
$42$	7.68344	−	1.07337i	1.18558	−	0.165625i
$43$			8.35453i			1.27405i	0.770842	+	0.637027i	$0.219836\pi$
$43$			8.35453i			1.27405i	−0.770842	+	0.637027i	$0.780164\pi$
$44$	−0.346004	−	0.199765i	−0.0521620	−	0.0301157i
$45$		0			0
$46$	3.81290	+	6.60414i	0.562182	+	0.973727i
$47$	2.73630	+	1.57980i	0.399130	+	0.230438i	0.686109	−	0.727499i	$-0.259317\pi$
$47$	2.73630	+	1.57980i	0.399130	+	0.230438i	−0.286978	+	0.957937i	$0.592651\pi$
$48$	7.28756	+	4.62108i	1.05187	+	0.666995i
$49$	1.13564	−	6.90727i	0.162234	−	0.986752i
$50$		0			0
$51$	−4.41924	−	8.44568i	−0.618817	−	1.18263i
$52$	−1.46582	−	2.53888i	−0.203273	−	0.352080i
$53$	−5.78238	−	10.0154i	−0.794271	−	1.37572i	−0.923301	−	0.384078i	$-0.874519\pi$
$53$	−5.78238	−	10.0154i	−0.794271	−	1.37572i	0.129029	−	0.991641i	$-0.458814\pi$
$54$	7.01277	+	5.31083i	0.954316	+	0.722713i
$55$		0			0
$56$	3.87179	−	3.28720i	0.517389	−	0.439270i
$57$	3.74149	−	5.90043i	0.495573	−	0.781531i
$58$	−11.3150	−	6.53271i	−1.48573	−	0.857786i
$59$	4.88061	+	8.45346i	0.635401	+	1.10055i	0.986430	+	0.164183i	$0.0524986\pi$
$59$	4.88061	+	8.45346i	0.635401	+	1.10055i	−0.351029	+	0.936365i	$0.614168\pi$
$60$		0			0
$61$	−6.90647	−	3.98746i	−0.884283	−	0.510541i	−0.0122151	−	0.999925i	$-0.503888\pi$
$61$	−6.90647	−	3.98746i	−0.884283	−	0.510541i	−0.872068	+	0.489384i	$0.837222\pi$
$62$		−	5.89604i		−	0.748798i
$63$	6.45591	−	4.61750i	0.813368	−	0.581750i
$64$	2.18506			0.273132
$65$		0			0
$66$	−1.35154	−	0.0561498i	−0.166363	−	0.00691156i
$67$	−0.793481	+	0.458116i	−0.0969391	+	0.0559678i	−0.547686	−	0.836684i	$-0.684491\pi$
$67$	−0.793481	+	0.458116i	−0.0969391	+	0.0559678i	0.450747	+	0.892652i	$0.351158\pi$
$68$	4.12768	+	2.38312i	0.500555	+	0.288995i
$69$	6.58893	+	4.17808i	0.793214	+	0.502981i
$70$		0			0
$71$			1.52593i			0.181094i	0.995892	+	0.0905471i	$0.0288616\pi$
$71$			1.52593i			0.181094i	−0.995892	+	0.0905471i	$0.971138\pi$
$72$	5.73922	+	0.477698i	0.676373	+	0.0562972i
$73$	−3.89906	−	6.75338i	−0.456351	−	0.790423i	0.542414	−	0.840112i	$-0.317511\pi$
$73$	−3.89906	−	6.75338i	−0.456351	−	0.790423i	−0.998765	+	0.0496883i	$0.984177\pi$
$74$	8.50252	−	4.90893i	0.988398	−	0.570652i
$75$		0			0
$76$			3.49351i			0.400733i
$77$	−0.410798	+	1.14932i	−0.0468148	+	0.130977i
$78$	−8.38256	−	5.31542i	−0.949138	−	0.601853i
$79$	−3.58521	+	6.20977i	−0.403368	+	0.698654i	−0.994130	−	0.108192i	$-0.965494\pi$
$79$	−3.58521	+	6.20977i	−0.403368	+	0.698654i	0.590762	+	0.806846i	$0.298827\pi$
$80$		0			0
$81$	8.87616	+	1.48790i	0.986240	+	0.165323i
$82$	−5.29661	+	9.17399i	−0.584912	+	1.01310i
$83$			17.5632i			1.92781i	0.266250	+	0.963904i	$0.414215\pi$
$83$			17.5632i			1.92781i	−0.266250	+	0.963904i	$0.585785\pi$
$84$	−1.48978	+	3.67860i	−0.162549	+	0.401368i
$85$		0			0
$86$	−12.2489	−	7.07188i	−1.32083	−	0.762581i
$87$	−13.3557	−	0.554864i	−1.43188	−	0.0594877i
$88$	−0.766937	+	0.442791i	−0.0817558	+	0.0472017i
$89$	−1.35247	+	2.34254i	−0.143361	+	0.248309i	−0.928760	−	0.370681i	$-0.879124\pi$
$89$	−1.35247	+	2.34254i	−0.143361	+	0.248309i	0.785399	+	0.618990i	$0.212458\pi$
$90$		0			0
$91$	−6.82718	+	5.79637i	−0.715683	+	0.607625i
$92$	−3.90116			−0.406724
$93$	−2.79667	−	5.34476i	−0.290001	−	0.554225i
$94$	−4.63241	+	2.67452i	−0.477796	+	0.275856i
$95$		0			0
$96$	−7.05172	+	3.68984i	−0.719713	+	0.376593i
$97$	4.44253			0.451070			0.225535	−	0.974235i	$-0.427587\pi$
$97$	4.44253			0.451070			0.225535	+	0.974235i	$0.427587\pi$
$98$	9.16569	+	7.51181i	0.925875	+	0.758808i
$99$	−1.25180	+	0.590174i	−0.125811	+	0.0593148i
$100$		0			0
$101$	1.36822	+	2.36982i	0.136143	+	0.235806i	0.926033	−	0.377442i	$-0.123196\pi$
$101$	1.36822	+	2.36982i	0.136143	+	0.235806i	−0.789891	+	0.613248i	$0.789863\pi$
$102$	16.1233	+	0.669844i	1.59644	+	0.0663245i
$103$	−9.21552	+	15.9618i	−0.908033	+	1.57276i	−0.0912387	+	0.995829i	$0.529083\pi$
$103$	−9.21552	+	15.9618i	−0.908033	+	1.57276i	−0.816794	+	0.576930i	$0.804251\pi$
$104$	−6.49817			−0.637198
$105$		0			0
$106$	19.5785			1.90163
$107$	−3.32647	+	5.76162i	−0.321582	+	0.556997i	−0.980815	−	0.194942i	$-0.937548\pi$
$107$	−3.32647	+	5.76162i	−0.321582	+	0.556997i	0.659232	+	0.751939i	$0.270881\pi$
$108$	−4.14666	+	1.74847i	−0.399013	+	0.168246i
$109$	−3.91662	−	6.78379i	−0.375144	−	0.649769i	0.615204	−	0.788368i	$-0.289073\pi$
$109$	−3.91662	−	6.78379i	−0.375144	−	0.649769i	−0.990349	+	0.138599i	$0.955740\pi$
$110$		0			0
$111$	5.37908	−	8.48295i	0.510560	−	0.805166i
$112$	2.36402	+	12.9676i	0.223379	+	1.22532i
$113$	−17.3914			−1.63604			−0.818022	−	0.575187i	$-0.804929\pi$
$113$	−17.3914			−1.63604			−0.818022	+	0.575187i	$0.804929\pi$
$114$	5.48375	+	10.4801i	0.513600	+	0.981550i
$115$		0			0
$116$	5.78845	−	3.34196i	0.537444	−	0.310293i
$117$	−10.1200	−	0.842332i	−0.935599	−	0.0778736i
$118$	−16.5252			−1.52127
$119$	4.90065	−	13.7109i	0.449242	−	1.25688i
$120$		0			0
$121$	−5.39359	+	9.34198i	−0.490327	+	0.849271i
$122$	11.6923	−	6.75055i	1.05857	−	0.611166i
$123$	−0.449874	+	10.8286i	−0.0405638	+	0.976378i
$124$	2.61216	+	1.50813i	0.234579	+	0.135434i
$125$		0			0
$126$	1.30512	+	13.3738i	0.116269	+	1.19143i
$127$		−	12.5556i		−	1.11413i	−0.830469	−	0.557065i	$-0.811927\pi$
$127$		−	12.5556i		−	1.11413i	0.830469	−	0.557065i	$-0.188073\pi$
$128$	−6.44458	+	11.1623i	−0.569626	+	0.986621i
$129$	−14.4580	−	0.600660i	−1.27296	−	0.0528851i
$130$		0			0
$131$	−3.36275	+	5.82446i	−0.293805	+	0.508886i	−0.974706	−	0.223490i	$-0.928255\pi$
$131$	−3.36275	+	5.82446i	−0.293805	+	0.508886i	0.680901	+	0.732375i	$0.261588\pi$
$132$	0.370582	−	0.584417i	0.0322550	−	0.0508670i
$133$	10.4993	−	1.91405i	0.910405	−	0.165969i
$134$		−	1.55113i		−	0.133997i
$135$		0			0
$136$	9.14924	−	5.28232i	0.784541	−	0.452955i
$137$	−10.1734	−	17.6208i	−0.869171	−	1.50545i	−0.862845	−	0.505468i	$-0.831320\pi$
$137$	−10.1734	−	17.6208i	−0.869171	−	1.50545i	−0.00632592	−	0.999980i	$-0.502014\pi$
$138$	−11.7030	+	6.12363i	−0.996224	+	0.521278i
$139$			9.79157i			0.830510i	0.909705	+	0.415255i	$0.136308\pi$
$139$			9.79157i			0.830510i	−0.909705	+	0.415255i	$0.863692\pi$
$140$		0			0
$141$	−2.93067	+	4.62174i	−0.246807	+	0.389221i
$142$	−2.23721	−	1.29166i	−0.187743	−	0.108393i
$143$	1.35235	−	0.780781i	0.113089	−	0.0652922i
$144$	−8.52099	+	12.2793i	−0.710082	+	1.02327i
$145$		0			0
$146$	13.2018			1.09259
$147$	11.8718	+	2.46189i	0.979168	+	0.203054i
$148$			5.02257i			0.412852i
$149$	−14.1195	−	8.15190i	−1.15671	−	0.667830i	−0.206200	−	0.978510i	$-0.566110\pi$
$149$	−14.1195	−	8.15190i	−1.15671	−	0.667830i	−0.950514	+	0.310680i	$0.899443\pi$
$150$		0			0
$151$	7.54351	+	13.0657i	0.613882	+	1.06328i	0.990580	+	0.136939i	$0.0437263\pi$
$151$	7.54351	+	13.0657i	0.613882	+	1.06328i	−0.376697	+	0.926336i	$0.622940\pi$
$152$	6.70613	+	3.87179i	0.543939	+	0.314043i
$153$	14.9335	−	7.04054i	1.20730	−	0.569194i
$154$	−1.33733	−	1.57515i	−0.107765	−	0.126929i
$155$		0			0
$156$	4.49907	−	2.35416i	0.360214	−	0.188484i
$157$	6.22562	+	10.7831i	0.496858	+	0.860584i	0.999993	−	0.00362372i	$-0.00115347\pi$
$157$	6.22562	+	10.7831i	0.496858	+	0.860584i	−0.503135	+	0.864208i	$0.667820\pi$
$158$	−6.06958	−	10.5128i	−0.482869	−	0.836354i
$159$	17.7479	−	9.28668i	1.40750	−	0.736482i
$160$		0			0
$161$	2.13739	+	11.7244i	0.168450	+	0.924015i
$162$	−9.69489	+	11.7542i	−0.761703	+	0.923495i
$163$	−4.76649	−	2.75193i	−0.373340	−	0.215548i	0.301577	−	0.953442i	$-0.402487\pi$
$163$	−4.76649	−	2.75193i	−0.373340	−	0.215548i	−0.674917	+	0.737894i	$0.735820\pi$
$164$	−2.70961	−	4.69317i	−0.211585	−	0.366475i
$165$		0			0
$166$	−25.7500	−	14.8667i	−1.99858	−	1.15388i
$167$		−	0.799023i		−	0.0618302i	−0.999522	−	0.0309151i	$-0.990158\pi$
$167$		−	0.799023i		−	0.0618302i	0.999522	−	0.0309151i	$-0.00984216\pi$
$168$	5.41032	+	6.93669i	0.417415	+	0.535177i
$169$	−1.54168			−0.118590
$170$		0			0
$171$	9.94203	+	6.89909i	0.760286	+	0.527586i
$172$	6.26620	−	3.61779i	0.477793	−	0.275854i
$173$	12.5737	+	7.25944i	0.955962	+	0.551925i	0.894928	−	0.446211i	$-0.147227\pi$
$173$	12.5737	+	7.25944i	0.955962	+	0.551925i	0.0610338	+	0.998136i	$0.480560\pi$
$174$	12.1187	−	19.1116i	0.918719	−	1.44884i
$175$		0			0
$176$		−	2.29830i		−	0.173241i
$177$	−14.9801	+	7.83840i	−1.12597	+	0.589171i
$178$	−2.28965	−	3.96579i	−0.171617	−	0.297249i
$179$	−2.04442	+	1.18035i	−0.152807	+	0.0882234i	−0.574454	−	0.818537i	$-0.694786\pi$
$179$	−2.04442	+	1.18035i	−0.152807	+	0.0882234i	0.421647	+	0.906760i	$0.361452\pi$
$180$		0			0
$181$			9.70696i			0.721513i	0.932660	+	0.360756i	$0.117481\pi$
$181$			9.70696i			0.721513i	−0.932660	+	0.360756i	$0.882519\pi$
$182$	−2.71923	−	14.9160i	−0.201563	−	1.10565i
$183$	7.39707	−	11.6654i	0.546807	−	0.862329i
$184$	−4.32357	+	7.48865i	−0.318738	+	0.552071i
$185$		0			0
$186$	10.2034	+	0.423903i	0.748152	+	0.0310821i
$187$	−1.26938	+	2.19863i	−0.0928264	+	0.160780i
$188$		−	2.73643i		−	0.199575i
$189$	7.52669	+	11.5043i	0.547486	+	0.836815i
$190$		0			0
$191$	−4.37389	−	2.52527i	−0.316484	−	0.182722i	0.333341	−	0.942807i	$-0.391824\pi$
$191$	−4.37389	−	2.52527i	−0.316484	−	0.182722i	−0.649824	+	0.760085i	$0.725157\pi$
$192$	−0.157098	+	3.78137i	−0.0113375	+	0.272897i
$193$	11.3481	−	6.55182i	0.816853	−	0.471610i	−0.0324769	−	0.999472i	$-0.510340\pi$
$193$	11.3481	−	6.55182i	0.816853	−	0.471610i	0.849330	+	0.527862i	$0.177006\pi$
$194$	−3.76048	+	6.51334i	−0.269987	+	0.467631i
$195$		0			0
$196$	−5.67247	+	2.13931i	−0.405176	+	0.152808i
$197$	21.2925			1.51703			0.758516	−	0.651655i	$-0.225925\pi$
$197$	21.2925			1.51703			0.758516	+	0.651655i	$0.225925\pi$
$198$	0.194341	−	2.33488i	0.0138112	−	0.165932i
$199$	5.78974	−	3.34271i	0.410424	−	0.236958i	−0.280548	−	0.959840i	$-0.590516\pi$
$199$	5.78974	−	3.34271i	0.410424	−	0.236958i	0.690972	+	0.722882i	$0.257183\pi$
$200$		0			0
$201$	−0.735748	−	1.40610i	−0.0518957	−	0.0991787i
$202$	−4.63263			−0.325951
$203$	−13.2153	−	15.5654i	−0.927529	−	1.09248i
$204$	−4.42089	+	6.97185i	−0.309524	+	0.488127i
$205$		0			0
$206$	−15.6014	−	27.0224i	−1.08700	−	1.88274i
$207$	−7.70412	+	11.1021i	−0.535474	+	0.771652i
$208$	8.43218	−	14.6050i	0.584666	−	1.01267i
$209$	−1.86084			−0.128717
$210$		0			0
$211$	5.72156			0.393889			0.196944	−	0.980415i	$-0.436898\pi$
$211$	5.72156			0.393889			0.196944	+	0.980415i	$0.436898\pi$
$212$	−5.00793	+	8.67399i	−0.343946	+	0.595732i
$213$	−2.64071	−	0.109709i	−0.180938	−	0.00751711i
$214$	−5.63154	−	9.75412i	−0.384964	−	0.666778i
$215$		0			0
$216$	−1.23931	+	9.89770i	−0.0843245	+	0.673453i
$217$	3.10132	−	8.67678i	0.210531	−	0.589019i
$218$	13.2613			0.898166
$219$	11.9674	−	6.26201i	0.808685	−	0.423148i
$220$		0			0
$221$	−16.1330	+	9.31439i	−1.08522	+	0.626554i
$222$	7.88390	+	15.0670i	0.529132	+	1.01123i
$223$	5.83493			0.390736			0.195368	−	0.980730i	$-0.437410\pi$
$223$	5.83493			0.390736			0.195368	+	0.980730i	$0.437410\pi$
$224$	−11.4479	−	4.09180i	−0.764896	−	0.273395i
$225$		0			0
$226$	14.7213	−	25.4981i	0.979249	−	1.69611i
$227$	9.88387	−	5.70646i	0.656016	−	0.378751i	−0.134741	−	0.990881i	$-0.543020\pi$
$227$	9.88387	−	5.70646i	0.656016	−	0.378751i	0.790757	+	0.612130i	$0.209687\pi$
$228$	−6.04573	−	0.251171i	−0.400388	−	0.0166342i
$229$	−0.910719	−	0.525804i	−0.0601820	−	0.0347461i	0.469607	−	0.882876i	$-0.344396\pi$
$229$	−0.910719	−	0.525804i	−0.0601820	−	0.0347461i	−0.529789	+	0.848129i	$0.677729\pi$
$230$		0			0
$231$	−1.95943	−	0.793541i	−0.128921	−	0.0522112i
$232$		−	14.8153i		−	0.972672i
$233$	−1.94244	+	3.36441i	−0.127254	+	0.220410i	−0.922612	−	0.385730i	$-0.873950\pi$
$233$	−1.94244	+	3.36441i	−0.127254	+	0.220410i	0.795358	+	0.606140i	$0.207283\pi$
$234$	9.80132	−	14.1243i	0.640732	−	0.923337i
$235$		0			0
$236$	4.22694	−	7.32127i	0.275150	−	0.476574i
$237$	−10.4886	−	6.65088i	−0.681308	−	0.432021i
$238$	15.9537	+	18.7909i	1.03413	+	1.21803i
$239$			6.40306i			0.414180i	0.978322	+	0.207090i	$0.0663993\pi$
$239$			6.40306i			0.414180i	−0.978322	+	0.207090i	$0.933601\pi$
$240$		0			0
$241$	1.96093	−	1.13215i	0.126315	−	0.0729279i	−0.435511	−	0.900183i	$-0.643432\pi$
$241$	1.96093	−	1.13215i	0.126315	−	0.0729279i	0.561826	+	0.827255i	$0.310099\pi$
$242$	−9.13106	−	15.8155i	−0.586967	−	1.01666i
$243$	−3.21307	+	15.2537i	−0.206118	+	0.978527i
$244$			6.90681i			0.442163i
$245$		0			0
$246$	−15.4953	−	9.82566i	−0.987945	−	0.626461i
$247$	−11.8250	−	6.82718i	−0.752408	−	0.434403i
$248$	5.79000	−	3.34286i	0.367665	−	0.212272i
$249$	−30.3941	−	1.26273i	−1.92615	−	0.0800221i
$250$		0			0
$251$	−13.3221			−0.840886			−0.420443	−	0.907319i	$-0.638125\pi$
$251$	−13.3221			−0.840886			−0.420443	+	0.907319i	$0.638125\pi$
$252$	−6.25891	−	2.84263i	−0.394274	−	0.179069i
$253$		−	2.07798i		−	0.130641i
$254$	18.4082	+	10.6280i	1.15503	+	0.666859i
$255$		0			0
$256$	−8.72527	−	15.1126i	−0.545329	−	0.944538i
$257$	16.9680	+	9.79648i	1.05844	+	0.611088i	0.924999	−	0.379969i	$-0.124066\pi$
$257$	16.9680	+	9.79648i	1.05844	+	0.611088i	0.133436	+	0.991057i	$0.457399\pi$
$258$	13.1190	−	20.6889i	0.816750	−	1.28804i
$259$	15.0947	−	2.75180i	0.937937	−	0.170988i
$260$		0			0
$261$	1.92045	−	23.0729i	0.118873	−	1.42818i
$262$	−5.69296	−	9.86050i	−0.351712	−	0.609184i
$263$	8.38678	+	14.5263i	0.517151	+	0.895732i	0.999802	+	0.0199186i	$0.00634072\pi$
$263$	8.38678	+	14.5263i	0.517151	+	0.895732i	−0.482651	+	0.875813i	$0.660326\pi$
$264$	−0.711136	−	1.35906i	−0.0437674	−	0.0836446i
$265$		0			0
$266$	−6.08112	+	17.0136i	−0.372858	+	1.04317i
$267$	−3.95666	−	2.50894i	−0.242144	−	0.153545i
$268$	0.687207	+	0.396759i	0.0419779	+	0.0242359i
$269$	14.6703	+	25.4097i	0.894465	+	1.54926i	0.834466	+	0.551060i	$0.185776\pi$
$269$	14.6703	+	25.4097i	0.894465	+	1.54926i	0.0599988	+	0.998198i	$0.480890\pi$
$270$		0			0
$271$	2.57129	+	1.48454i	0.156195	+	0.0901792i	0.576060	−	0.817407i	$-0.304589\pi$
$271$	2.57129	+	1.48454i	0.156195	+	0.0901792i	−0.419865	+	0.907586i	$0.637923\pi$
$272$			27.4178i			1.66245i
$273$	−9.54010	−	12.2316i	−0.577393	−	0.740288i
$274$	34.4460			2.08096
$275$		0			0
$276$	0.280479	−	6.75118i	0.0168829	−	0.406374i
$277$	11.2803	−	6.51269i	0.677768	−	0.391309i	−0.121246	−	0.992623i	$-0.538689\pi$
$277$	11.2803	−	6.51269i	0.677768	−	0.391309i	0.799014	+	0.601313i	$0.205356\pi$
$278$	−14.3558	−	8.28830i	−0.861001	−	0.497099i
$279$	9.45048	−	4.45553i	0.565786	−	0.266745i
$280$		0			0
$281$		−	19.4404i		−	1.15972i	−0.814717	−	0.579859i	$-0.803108\pi$
$281$		−	19.4404i		−	1.15972i	0.814717	−	0.579859i	$-0.196892\pi$
$282$	−4.29536	−	8.20894i	−0.255785	−	0.488835i
$283$	2.81977	+	4.88399i	0.167618	+	0.290323i	0.937582	−	0.347764i	$-0.113059\pi$
$283$	2.81977	+	4.88399i	0.167618	+	0.290323i	−0.769964	+	0.638088i	$0.779726\pi$
$284$	1.14450	−	0.660778i	0.0679136	−	0.0392099i
$285$		0			0
$286$			2.64364i			0.156322i
$287$	−12.6202	+	10.7147i	−0.744945	+	0.632469i
$288$	−5.87850	−	12.4687i	−0.346394	−	0.734725i
$289$	6.64321	−	11.5064i	0.390777	−	0.676846i
$290$		0			0
$291$	−0.319401	+	7.68805i	−0.0187236	+	0.450681i
$292$	−3.37685	+	5.84888i	−0.197615	+	0.342280i
$293$		−	21.5754i		−	1.26045i	−0.776412	−	0.630226i	$-0.782962\pi$
$293$		−	21.5754i		−	1.26045i	0.776412	−	0.630226i	$-0.217038\pi$
$294$	−13.6586	+	15.3217i	−0.796586	+	0.893579i
$295$		0			0
$296$	9.64129	+	5.56640i	0.560389	+	0.323541i
$297$	−0.931331	−	2.20875i	−0.0540413	−	0.128164i
$298$	23.9036	−	13.8007i	1.38470	−	0.799455i
$299$	7.62382	−	13.2049i	0.440897	−	0.763656i
$300$		0			0
$301$	−14.3060	−	16.8501i	−0.824582	−	0.971224i
$302$	−25.5415			−1.46975
$303$	−4.19948	+	2.19740i	−0.241254	+	0.126237i
$304$	−17.4041	+	10.0482i	−0.998191	+	0.576306i
$305$		0			0
$306$	−2.31841	+	27.8541i	−0.132535	+	1.59231i
$307$	22.9288			1.30861			0.654307	−	0.756229i	$-0.272960\pi$
$307$	22.9288			1.30861			0.654307	+	0.756229i	$0.272960\pi$
$308$	1.03992	−	0.189580i	0.0592549	−	0.0108023i
$309$	−26.9602	−	17.0956i	−1.53371	−	0.972534i
$310$		0			0
$311$	0.799023	+	1.38395i	0.0453084	+	0.0784765i	0.887790	−	0.460248i	$-0.152240\pi$
$311$	0.799023	+	1.38395i	0.0453084	+	0.0784765i	−0.842482	+	0.538725i	$0.818906\pi$
$312$	0.467195	−	11.2455i	0.0264497	−	0.636649i
$313$	14.4421	−	25.0145i	0.816318	−	1.41390i	−0.0920593	−	0.995754i	$-0.529345\pi$
$313$	14.4421	−	25.0145i	0.816318	−	1.41390i	0.908378	−	0.418151i	$-0.137322\pi$
$314$	−21.0793			−1.18957
$315$		0			0
$316$	6.21007			0.349344
$317$	3.28018	−	5.68143i	0.184233	−	0.319101i	−0.759085	−	0.650992i	$-0.774353\pi$
$317$	3.28018	−	5.68143i	0.184233	−	0.319101i	0.943318	+	0.331891i	$0.107687\pi$
$318$	−1.40762	+	33.8818i	−0.0789357	+	1.90000i
$319$	1.78012	+	3.08325i	0.0996674	+	0.172629i
$320$		0			0
$321$	−9.73166	−	6.17090i	−0.543168	−	0.344426i
$322$	−18.9988	−	6.79071i	−1.05876	−	0.378432i
$323$	22.1991			1.23519
$324$	−2.72769	−	7.30175i	−0.151538	−	0.405653i
$325$		0			0
$326$	8.06940	−	4.65887i	0.446923	−	0.258031i
$327$	12.0213	−	6.29021i	0.664781	−	0.347849i
$328$	−12.0120			−0.663251
$329$	−8.22399	+	1.49925i	−0.453403	+	0.0826566i
$330$		0			0
$331$	6.76497	−	11.7173i	0.371836	−	0.644040i	−0.618012	−	0.786169i	$-0.712062\pi$
$331$	6.76497	−	11.7173i	0.371836	−	0.644040i	0.989848	+	0.142129i	$0.0453949\pi$
$332$	13.1730	−	7.60544i	0.722963	−	0.417403i
$333$	14.2935	+	9.91871i	0.783279	+	0.543542i
$334$	1.17147	+	0.676351i	0.0641002	+	0.0370083i
$335$		0			0
$336$	−22.6111	+	3.15876i	−1.23354	+	0.172324i
$337$			30.7122i			1.67300i	0.547966	+	0.836501i	$0.315402\pi$
$337$			30.7122i			1.67300i	−0.547966	+	0.836501i	$0.684598\pi$
$338$	1.30499	−	2.26030i	0.0709819	−	0.122944i
$339$	1.25038	−	30.0968i	0.0679111	−	1.63463i
$340$		0			0
$341$	−0.803314	+	1.39138i	−0.0435019	+	0.0753475i
$342$	−18.5307	+	8.73647i	−1.00202	+	0.472414i
$343$	9.53729	+	15.8758i	0.514965	+	0.857211i
$344$		−	16.0381i		−	0.864715i
$345$		0			0
$346$	−21.2866	+	12.2898i	−1.14438	+	0.660706i
$347$	−3.91036	−	6.77295i	−0.209919	−	0.363591i	0.741770	−	0.670655i	$-0.233987\pi$
$347$	−3.91036	−	6.77295i	−0.209919	−	0.363591i	−0.951689	+	0.307064i	$0.900653\pi$
$348$	5.36729	+	10.2575i	0.287717	+	0.549861i
$349$			25.1501i			1.34625i	0.739526	+	0.673127i	$0.235049\pi$
$349$			25.1501i			1.34625i	−0.739526	+	0.673127i	$0.764951\pi$
$350$		0			0
$351$	2.18530	−	17.4528i	0.116643	−	0.931560i
$352$	1.83575	+	1.05987i	0.0978458	+	0.0564913i
$353$	−10.6252	+	6.13445i	−0.565521	+	0.326504i	−0.755359	−	0.655312i	$-0.772537\pi$
$353$	−10.6252	+	6.13445i	−0.565521	+	0.326504i	0.189837	+	0.981816i	$0.439204\pi$
$354$	1.18810	−	28.5979i	0.0631469	−	1.51996i
$355$		0			0
$356$	2.34265			0.124160
$357$	23.3752	+	9.46662i	1.23714	+	0.501027i
$358$		−	3.99653i		−	0.211223i
$359$	−7.11574	−	4.10828i	−0.375555	−	0.216827i	0.300328	−	0.953836i	$-0.402904\pi$
$359$	−7.11574	−	4.10828i	−0.375555	−	0.216827i	−0.675882	+	0.737010i	$0.736237\pi$
$360$		0			0
$361$	−1.36436	−	2.36315i	−0.0718086	−	0.124376i
$362$	−14.2317	−	8.21668i	−0.748002	−	0.431859i
$363$	−15.7791	−	10.0056i	−0.828186	−	0.525157i
$364$	7.30388	+	2.61061i	0.382827	+	0.136833i
$365$		0			0
$366$	10.8416	+	20.7195i	0.566698	+	1.08303i
$367$	13.9526	+	24.1666i	0.728320	+	1.26149i	0.957593	+	0.288125i	$0.0930318\pi$
$367$	13.9526	+	24.1666i	0.728320	+	1.26149i	−0.229273	+	0.973362i	$0.573635\pi$
$368$	−11.2207	−	19.4349i	−0.584921	−	1.01311i
$369$	−18.7071	−	1.55707i	−0.973853	−	0.0810577i
$370$		0			0
$371$	28.8123	+	10.2983i	1.49586	+	0.534663i
$372$	−2.79771	+	4.41206i	−0.145054	+	0.228755i
$373$	15.6612	+	9.04199i	0.810905	+	0.468176i	0.847270	−	0.531162i	$-0.178245\pi$
$373$	15.6612	+	9.04199i	0.810905	+	0.468176i	−0.0363650	+	0.999339i	$0.511578\pi$
$374$	−2.14900	−	3.72217i	−0.111122	−	0.192469i
$375$		0			0
$376$	−5.25284	−	3.03273i	−0.270895	−	0.156401i
$377$			26.1241i			1.34546i
$378$	−23.2380	+	1.29706i	−1.19523	+	0.0667135i
$379$	−24.7450			−1.27107			−0.635534	−	0.772073i	$-0.719220\pi$
$379$	−24.7450			−1.27107			−0.635534	+	0.772073i	$0.719220\pi$
$380$		0			0
$381$	21.7282	+	0.902702i	1.11317	+	0.0462468i
$382$	7.40476	−	4.27514i	0.378861	−	0.218735i
$383$	11.1972	+	6.46470i	0.572150	+	0.330331i	0.758008	−	0.652246i	$-0.226173\pi$
$383$	11.1972	+	6.46470i	0.572150	+	0.330331i	−0.185858	+	0.982577i	$0.559506\pi$
$384$	−18.8537	−	11.9552i	−0.962126	−	0.610089i
$385$		0			0
$386$			22.1838i			1.12912i
$387$	2.07895	−	24.9772i	0.105679	−	1.26966i
$388$	−1.92376	−	3.33205i	−0.0976642	−	0.169159i
$389$	16.4024	−	9.46992i	0.831634	−	0.480144i	−0.0227777	−	0.999741i	$-0.507251\pi$
$389$	16.4024	−	9.46992i	0.831634	−	0.480144i	0.854412	+	0.519596i	$0.173918\pi$
$390$		0			0
$391$			24.7894i			1.25365i
$392$	−2.18007	+	13.2598i	−0.110110	+	0.669721i
$393$	−9.83780	−	6.23820i	−0.496251	−	0.314675i
$394$	−18.0236	+	31.2177i	−0.908014	+	1.57273i
$395$		0			0
$396$	0.984724	+	0.683331i	0.0494842	+	0.0343387i
$397$	−3.64333	+	6.31044i	−0.182854	+	0.316712i	−0.942851	−	0.333214i	$-0.891867\pi$
$397$	−3.64333	+	6.31044i	−0.182854	+	0.316712i	0.759998	+	0.649926i	$0.225200\pi$
$398$			11.3181i			0.567323i
$399$	2.55751	+	18.3073i	0.128036	+	0.916510i
$400$		0			0
$401$	13.7394	+	7.93243i	0.686111	+	0.396126i	0.802154	−	0.597118i	$-0.203688\pi$
$401$	13.7394	+	7.93243i	0.686111	+	0.396126i	−0.116042	+	0.993244i	$0.537021\pi$
$402$	2.68432	+	0.111521i	0.133882	+	0.00556215i
$403$	−10.2096	+	5.89451i	−0.508576	+	0.293626i
$404$	1.18497	−	2.05242i	0.0589543	−	0.102112i
$405$		0			0
$406$	34.0073	−	6.19963i	1.68776	−	0.307682i
$407$	−2.67530			−0.132610
$408$	8.48356	+	16.2131i	0.419999	+	0.802667i
$409$	22.8109	−	13.1699i	1.12793	−	0.651209i	0.184515	−	0.982830i	$-0.440929\pi$
$409$	22.8109	−	13.1699i	1.12793	−	0.651209i	0.943413	+	0.331620i	$0.107595\pi$
$410$		0			0
$411$	31.2253	−	16.3388i	1.54023	−	0.805932i
$412$	15.9625			0.786417
$413$	−24.3190	−	8.69228i	−1.19666	−	0.427719i
$414$	−9.75590	−	20.6929i	−0.479476	−	1.01700i
$415$		0			0
$416$	7.77705	+	13.4702i	0.381301	+	0.660433i
$417$	−16.9449	−	0.703978i	−0.829794	−	0.0344739i
$418$	1.57515	−	2.72824i	0.0770432	−	0.133443i
$419$	−14.3499			−0.701039			−0.350519	−	0.936555i	$-0.613995\pi$
$419$	−14.3499			−0.701039			−0.350519	+	0.936555i	$0.613995\pi$
$420$		0			0
$421$	−10.0679			−0.490682			−0.245341	−	0.969437i	$-0.578900\pi$
$421$	−10.0679			−0.490682			−0.245341	+	0.969437i	$0.578900\pi$
$422$	−4.84315	+	8.38858i	−0.235761	+	0.408350i
$423$	−7.78749	−	5.40398i	−0.378641	−	0.262751i
$424$	11.1004	+	19.2264i	0.539082	+	0.933717i
$425$		0			0
$426$	2.39613	−	3.77876i	0.116093	−	0.183082i
$427$	20.7575	−	3.78415i	1.00453	−	0.183128i
$428$	5.76190			0.278512
$429$	1.25396	+	2.39646i	0.0605416	+	0.115702i
$430$		0			0
$431$	7.13983	−	4.12218i	0.343914	−	0.198559i	−0.318088	−	0.948061i	$-0.603041\pi$
$431$	7.13983	−	4.12218i	0.343914	−	0.198559i	0.662001	+	0.749503i	$0.269707\pi$
$432$	−20.6374	−	15.6289i	−0.992918	−	0.751946i
$433$	−10.7241			−0.515367			−0.257683	−	0.966229i	$-0.582959\pi$
$433$	−10.7241			−0.515367			−0.257683	+	0.966229i	$0.582959\pi$
$434$	10.0961	+	11.8916i	0.484631	+	0.570816i
$435$		0			0
$436$	−3.39206	+	5.87521i	−0.162450	+	0.281372i
$437$	−15.7356	+	9.08496i	−0.752737	+	0.434593i
$438$	−0.949162	+	22.8465i	−0.0453527	+	1.09165i
$439$	2.74233	+	1.58329i	0.130884	+	0.0755661i	0.564013	−	0.825766i	$-0.309257\pi$
$439$	2.74233	+	1.58329i	0.130884	+	0.0755661i	−0.433128	+	0.901332i	$0.642590\pi$
$440$		0			0
$441$	−5.11399	+	20.3678i	−0.243523	+	0.969895i
$442$		−	31.5375i		−	1.50009i
$443$	−8.72667	+	15.1150i	−0.414617	+	0.718137i	−0.995388	−	0.0959297i	$-0.969418\pi$
$443$	−8.72667	+	15.1150i	−0.414617	+	0.718137i	0.580772	+	0.814067i	$0.302751\pi$
$444$	−8.69184	−	0.361104i	−0.412496	−	0.0171372i
$445$		0			0
$446$	−4.93911	+	8.55480i	−0.233874	+	0.405081i
$447$	15.1225	−	23.8485i	0.715268	−	1.12800i
$448$	−4.40700	+	3.74161i	−0.208211	+	0.176774i
$449$		−	12.2873i		−	0.579876i	−0.957046	−	0.289938i	$-0.906365\pi$
$449$		−	12.2873i		−	0.579876i	0.957046	−	0.289938i	$-0.0936346\pi$
$450$		0			0
$451$	2.49985	−	1.44329i	0.117713	−	0.0679618i
$452$	7.53105	+	13.0442i	0.354231	+	0.613546i
$453$	−23.1534	+	12.1151i	−1.08784	+	0.569217i
$454$			19.3215i			0.906801i
$455$		0			0
$456$	−7.18250	+	11.3270i	−0.336351	+	0.530434i
$457$	4.23430	+	2.44467i	0.198072	+	0.114357i	0.595756	−	0.803165i	$-0.296853\pi$
$457$	4.23430	+	2.44467i	0.198072	+	0.114357i	−0.397684	+	0.917523i	$0.630186\pi$
$458$	1.54180	−	0.890158i	0.0720435	−	0.0415943i
$459$	11.1104	+	26.3494i	0.518589	+	1.22989i
$460$		0			0
$461$	−5.12746			−0.238810			−0.119405	−	0.992846i	$-0.538099\pi$
$461$	−5.12746			−0.238810			−0.119405	+	0.992846i	$0.538099\pi$
$462$	2.82204	−	2.20107i	0.131293	−	0.102403i
$463$			39.9073i			1.85465i	0.374257	+	0.927325i	$0.377898\pi$
$463$			39.9073i			1.85465i	−0.374257	+	0.927325i	$0.622102\pi$
$464$	33.2981	+	19.2247i	1.54583	+	0.892483i
$465$		0			0
$466$	−3.28845	−	5.69577i	−0.152335	−	0.263851i
$467$	−7.90350	−	4.56309i	−0.365730	−	0.211155i	0.305861	−	0.952076i	$-0.401056\pi$
$467$	−7.90350	−	4.56309i	−0.365730	−	0.211155i	−0.671592	+	0.740922i	$0.734389\pi$
$468$	3.75054	+	7.95516i	0.173369	+	0.367727i
$469$	0.815897	−	2.28269i	0.0376746	−	0.105405i
$470$		0			0
$471$	−19.1084	+	9.99853i	−0.880467	+	0.460708i
$472$	−9.36925	−	16.2280i	−0.431254	−	0.746955i
$473$	1.92704	+	3.33773i	0.0886053	+	0.153469i
$474$	18.6294	−	9.74792i	0.855677	−	0.447737i
$475$		0			0
$476$	−12.4058	+	2.26161i	−0.568619	+	0.103661i
$477$	14.7951	+	31.3815i	0.677422	+	1.43686i
$478$	−9.38775	−	5.42002i	−0.429386	−	0.247906i
$479$	6.20210	+	10.7424i	0.283381	+	0.490831i	0.972215	−	0.234088i	$-0.0752105\pi$
$479$	6.20210	+	10.7424i	0.283381	+	0.490831i	−0.688834	+	0.724919i	$0.741877\pi$
$480$		0			0
$481$	−17.0006	−	9.81532i	−0.775162	−	0.447540i
$482$			3.83332i			0.174603i
$483$	−20.4435	+	2.85594i	−0.930211	+	0.129950i
$484$	9.34243			0.424656
$485$		0			0
$486$	−19.6442	−	17.6227i	−0.891081	−	0.799380i
$487$	−12.2665	+	7.08208i	−0.555849	+	0.320920i	−0.751478	−	0.659758i	$-0.770659\pi$
$487$	−12.2665	+	7.08208i	−0.555849	+	0.320920i	0.195628	+	0.980678i	$0.437325\pi$
$488$	13.2583	+	7.65467i	0.600174	+	0.346511i
$489$	5.10507	−	8.05083i	0.230859	−	0.364071i
$490$		0			0
$491$		−	32.1216i		−	1.44963i	−0.688946	−	0.724813i	$-0.741926\pi$
$491$		−	32.1216i		−	1.44963i	0.688946	−	0.724813i	$-0.258074\pi$
$492$	8.31662	−	4.35171i	0.374942	−	0.196190i
$493$	−21.2361	−	36.7819i	−0.956424	−	1.65658i
$494$	20.0191	−	11.5580i	0.900703	−	0.520021i
$495$		0			0
$496$			17.3511i			0.779086i
$497$	−2.61294	−	3.07762i	−0.117206	−	0.138050i
$498$	27.5791	−	43.4929i	1.23585	−	1.94897i
$499$	13.3589	−	23.1383i	0.598027	−	1.03581i	−0.395085	−	0.918644i	$-0.629285\pi$
$499$	13.3589	−	23.1383i	0.598027	−	1.03581i	0.993112	−	0.117168i	$-0.0373817\pi$
$500$		0			0
$501$	1.38276	+	0.0574468i	0.0617769	+	0.00256653i
$502$	11.2768	−	19.5320i	0.503310	−	0.871758i
$503$		−	9.55539i		−	0.426054i	−0.977046	−	0.213027i	$-0.931668\pi$
$503$		−	9.55539i		−	0.426054i	0.977046	−	0.213027i	$-0.0683322\pi$
$504$	−12.3933	+	8.86415i	−0.552042	+	0.394841i
$505$		0			0
$506$	3.04659	+	1.75895i	0.135438	+	0.0781950i
$507$	0.110841	−	2.66796i	0.00492261	−	0.118488i
$508$	−9.41716	+	5.43700i	−0.417819	+	0.241228i
$509$	−9.10071	+	15.7629i	−0.403382	+	0.698678i	−0.994132	−	0.108177i	$-0.965499\pi$
$509$	−9.10071	+	15.7629i	−0.403382	+	0.698678i	0.590750	+	0.806855i	$0.298832\pi$
$510$		0			0
$511$	19.4282	+	6.94417i	0.859452	+	0.307192i
$512$	3.76451			0.166369
$513$	−12.6541	+	16.7092i	−0.558691	+	0.737731i
$514$	−28.7259	+	16.5849i	−1.26705	+	0.731530i
$515$		0			0
$516$	5.81028	+	11.1041i	0.255783	+	0.488832i
$517$	1.45758			0.0641042
$518$	−8.74273	+	24.4601i	−0.384133	+	1.07472i
$519$	−13.4669	+	21.2376i	−0.591130	+	0.932228i
$520$		0			0
$521$	1.93741	+	3.35569i	0.0848794	+	0.147015i	0.905340	−	0.424688i	$-0.139616\pi$
$521$	1.93741	+	3.35569i	0.0848794	+	0.147015i	−0.820460	+	0.571703i	$0.806283\pi$
$522$	32.2024	+	22.3462i	1.40946	+	0.978067i
$523$	9.42099	−	16.3176i	0.411951	−	0.713520i	−0.583152	−	0.812363i	$-0.698181\pi$
$523$	9.42099	−	16.3176i	0.411951	−	0.713520i	0.995103	+	0.0988429i	$0.0315141\pi$
$524$	5.82474			0.254455
$525$		0			0
$526$	−28.3967			−1.23816
$527$	9.58321	−	16.5986i	0.417451	−	0.723047i
$528$	3.97735	+	0.165240i	0.173092	+	0.00719113i
$529$	1.35494	+	2.34682i	0.0589104	+	0.102036i
$530$		0			0
$531$	−12.4878	−	26.4875i	−0.541924	−	1.14946i
$532$	−5.98216	−	7.04601i	−0.259359	−	0.305483i
$533$	21.1809			0.917448
$534$	7.02765	−	3.67725i	0.304116	−	0.159130i
$535$		0			0
$536$	1.52324	−	0.879440i	0.0657937	−	0.0379860i
$537$	−1.89568	−	3.62286i	−0.0818044	−	0.156338i
$538$	−49.6721			−2.14152
$539$	−1.13952	−	3.02147i	−0.0490824	−	0.130144i
$540$		0			0
$541$	−11.0977	+	19.2218i	−0.477128	+	0.826410i	−0.999656	−	0.0262117i	$-0.991656\pi$
$541$	−11.0977	+	19.2218i	−0.477128	+	0.826410i	0.522528	+	0.852622i	$0.324989\pi$
$542$	−4.35306	+	2.51324i	−0.186980	+	0.107953i
$543$	−16.7985	−	0.697895i	−0.720891	−	0.0299495i
$544$	−21.8997	−	12.6438i	−0.938944	−	0.542099i
$545$		0			0
$546$	26.0086	−	3.63338i	1.11306	−	0.155494i
$547$			1.23468i			0.0527911i	0.999652	+	0.0263956i	$0.00840295\pi$
$547$			1.23468i			0.0527911i	−0.999652	+	0.0263956i	$0.991597\pi$
$548$	−8.81083	+	15.2608i	−0.376380	+	0.651910i
$549$	19.6558	+	13.6398i	0.838888	+	0.582131i
$550$		0			0
$551$	15.5654	−	26.9601i	0.663109	−	1.14854i
$552$	−12.6487	−	8.02060i	−0.538364	−	0.341379i
$553$	−3.40242	−	18.6636i	−0.144685	−	0.793656i
$554$			22.0513i			0.936868i
$555$		0			0
$556$	7.34403	−	4.24008i	0.311456	−	0.179819i
$557$	−1.15681	−	2.00365i	−0.0490155	−	0.0848973i	0.840477	−	0.541848i	$-0.182275\pi$
$557$	−1.15681	−	2.00365i	−0.0490155	−	0.0848973i	−0.889492	+	0.456950i	$0.848942\pi$
$558$	−1.46718	+	17.6272i	−0.0621106	+	0.746217i
$559$			28.2802i			1.19612i
$560$		0			0
$561$	−3.71360	−	2.35481i	−0.156788	−	0.0994203i
$562$	28.5023	+	16.4558i	1.20230	+	0.694146i
$563$	15.7239	−	9.07818i	0.662682	−	0.382600i	−0.130616	−	0.991433i	$-0.541696\pi$
$563$	15.7239	−	9.07818i	0.662682	−	0.382600i	0.793298	+	0.608833i	$0.208362\pi$
$564$	4.73555	+	0.196739i	0.199403	+	0.00828422i
$565$		0			0
$566$	−9.54745			−0.401309
$567$	−20.4500	+	12.1983i	−0.858819	+	0.512279i
$568$		−	2.92930i		−	0.122911i
$569$	−12.9811	−	7.49465i	−0.544197	−	0.314192i	0.202581	−	0.979265i	$-0.435067\pi$
$569$	−12.9811	−	7.49465i	−0.544197	−	0.314192i	−0.746778	+	0.665073i	$0.768400\pi$
$570$		0			0
$571$	−11.6375	−	20.1568i	−0.487015	−	0.843535i	0.512873	−	0.858464i	$-0.328581\pi$
$571$	−11.6375	−	20.1568i	−0.487015	−	0.843535i	−0.999889	+	0.0149293i	$0.995248\pi$
$572$	−1.17123	−	0.676208i	−0.0489715	−	0.0282737i
$573$	4.68459	−	7.38771i	0.195701	−	0.308626i
$574$	−5.02655	−	27.5726i	−0.209804	−	1.15086i
$575$		0			0
$576$	−6.53258	−	0.543733i	−0.272191	−	0.0226555i
$577$	−13.3341	−	23.0953i	−0.555105	−	0.961471i	−0.997895	−	0.0648455i	$-0.979345\pi$
$577$	−13.3341	−	23.0953i	−0.555105	−	0.961471i	0.442790	−	0.896625i	$-0.353989\pi$
$578$	11.2466	+	19.4797i	0.467797	+	0.810248i
$579$	10.5224	+	20.1096i	0.437297	+	0.835725i
$580$		0			0
$581$	−30.0745	−	35.4229i	−1.24770	−	1.46959i
$582$	−11.0013	−	6.97601i	−0.456021	−	0.289165i
$583$	−4.62026	−	2.66751i	−0.191351	−	0.110477i
$584$	7.48499	+	12.9644i	0.309731	+	0.536470i
$585$		0			0
$586$	31.6325	+	18.2630i	1.30673	+	0.754439i
$587$		−	45.9722i		−	1.89748i	−0.316065	−	0.948738i	$-0.602362\pi$
$587$		−	45.9722i		−	1.89748i	0.316065	−	0.948738i	$-0.397638\pi$
$588$	−3.29437	−	9.97034i	−0.135857	−	0.411170i
$589$	14.0484			0.578856
$590$		0			0
$591$	−1.53086	+	36.8480i	−0.0629710	+	1.51572i
$592$	−25.0215	+	14.4462i	−1.02838	+	0.593735i
$593$	−2.68984	−	1.55298i	−0.110458	−	0.0637732i	0.443753	−	0.896149i	$-0.353647\pi$
$593$	−2.68984	−	1.55298i	−0.110458	−	0.0637732i	−0.554211	+	0.832376i	$0.686980\pi$
$594$	4.02666	+	0.504187i	0.165216	+	0.0206871i
$595$		0			0
$596$			14.1202i			0.578385i
$597$	5.36849	+	10.2598i	0.219718	+	0.419906i
$598$	12.9067	+	22.3551i	0.527795	+	0.914168i
$599$	7.34708	−	4.24184i	0.300193	−	0.173317i	−0.342336	−	0.939577i	$-0.611218\pi$
$599$	7.34708	−	4.24184i	0.300193	−	0.173317i	0.642530	+	0.766261i	$0.277885\pi$
$600$		0			0
$601$		−	2.63388i		−	0.107438i	−0.998556	−	0.0537191i	$-0.982892\pi$
$601$		−	2.63388i		−	0.107438i	0.998556	−	0.0537191i	$-0.0171076\pi$
$602$	36.8141	−	6.71131i	1.50043	−	0.273533i
$603$	2.48624	−	1.17216i	0.101247	−	0.0477341i
$604$	6.53319	−	11.3158i	0.265832	−	0.460434i
$605$		0			0
$606$	0.333069	−	8.01704i	0.0135300	−	0.325670i
$607$	−15.1355	+	26.2154i	−0.614330	+	1.06405i	0.376171	+	0.926550i	$0.377240\pi$
$607$	−15.1355	+	26.2154i	−0.614330	+	1.06405i	−0.990502	+	0.137501i	$0.956093\pi$
$608$		−	18.5351i		−	0.751698i
$609$	27.8870	−	21.7507i	1.13004	−	0.881381i
$610$		0			0
$611$	9.26241	+	5.34766i	0.374717	+	0.216343i
$612$	−11.7474	−	8.15185i	−0.474859	−	0.329519i
$613$	15.6207	−	9.01861i	0.630914	−	0.364258i	−0.150192	−	0.988657i	$-0.547989\pi$
$613$	15.6207	−	9.01861i	0.630914	−	0.364258i	0.781106	+	0.624399i	$0.214656\pi$
$614$	−19.4086	+	33.6167i	−0.783267	+	1.35666i
$615$		0			0
$616$	0.788604	−	2.20633i	0.0317738	−	0.0888956i
$617$	11.2586			0.453254			0.226627	−	0.973982i	$-0.427230\pi$
$617$	11.2586			0.453254			0.226627	+	0.973982i	$0.427230\pi$
$618$	47.8855	−	25.0563i	1.92624	−	1.00791i
$619$	5.23950	−	3.02503i	0.210593	−	0.121586i	−0.390994	−	0.920393i	$-0.627869\pi$
$619$	5.23950	−	3.02503i	0.210593	−	0.121586i	0.601587	+	0.798807i	$0.294535\pi$
$620$		0			0
$621$	−18.6590	−	14.1306i	−0.748760	−	0.567043i
$622$	−2.70540			−0.108477
$623$	−1.28351	−	7.04054i	−0.0514227	−	0.282073i
$624$	24.6685	+	15.6424i	0.987530	+	0.626198i
$625$		0			0
$626$	24.4498	+	42.3482i	0.977209	+	1.69258i
$627$	0.133788	−	3.22029i	0.00534296	−	0.128606i
$628$	5.39180	−	9.33888i	0.215156	−	0.372662i
$629$	31.9152			1.27254
$630$		0			0
$631$	47.3970			1.88684			0.943422	−	0.331594i	$-0.107586\pi$
$631$	47.3970			1.88684			0.943422	+	0.331594i	$0.107586\pi$
$632$	6.88249	−	11.9208i	0.273771	−	0.474185i
$633$	−0.411359	+	9.90150i	−0.0163501	+	0.393549i
$634$	5.55316	+	9.61836i	0.220544	+	0.381994i
$635$		0			0
$636$	−14.6508	−	9.29014i	−0.580942	−	0.368378i
$637$	3.84415	−	23.3812i	0.152311	−	0.926397i
$638$	−6.02728			−0.238622
$639$	0.379714	−	4.56201i	0.0150213	−	0.180470i
$640$		0			0
$641$	−2.08690	+	1.20488i	−0.0824278	+	0.0475897i	−0.540647	−	0.841249i	$-0.681821\pi$
$641$	−2.08690	+	1.20488i	−0.0824278	+	0.0475897i	0.458220	+	0.888839i	$0.348487\pi$
$642$	17.2850	−	9.04442i	0.682183	−	0.356955i
$643$	−30.1631			−1.18952			−0.594759	−	0.803904i	$-0.702753\pi$
$643$	−30.1631			−1.18952			−0.594759	+	0.803904i	$0.702753\pi$
$644$	7.86819	−	6.68020i	0.310050	−	0.263237i
$645$		0			0
$646$	−18.7909	+	32.5468i	−0.739319	+	1.28054i
$647$	−12.1065	+	6.98967i	−0.475954	+	0.274792i	−0.718729	−	0.695291i	$-0.755276\pi$
$647$	−12.1065	+	6.98967i	−0.475954	+	0.274792i	0.242775	+	0.970083i	$0.421942\pi$
$648$	−17.0394	−	2.85631i	−0.669373	−	0.112206i
$649$	3.89972	+	2.25150i	0.153077	+	0.0883792i
$650$		0			0
$651$	14.7927	+	5.99085i	0.579772	+	0.234800i
$652$			4.76671i			0.186679i
$653$	3.42169	−	5.92653i	0.133901	−	0.231923i	−0.791276	−	0.611459i	$-0.790583\pi$
$653$	3.42169	−	5.92653i	0.133901	−	0.231923i	0.925177	+	0.379536i	$0.123916\pi$
$654$	−0.953435	+	22.9494i	−0.0372823	+	0.897391i
$655$		0			0
$656$	15.5870	−	26.9975i	0.608572	−	1.05408i
$657$	9.97636	+	21.1606i	0.389215	+	0.825552i
$658$	4.76328	−	13.3266i	0.185692	−	0.519523i
$659$		−	10.0735i		−	0.392409i	−0.980563	−	0.196204i	$-0.937138\pi$
$659$		−	10.0735i		−	0.392409i	0.980563	−	0.196204i	$-0.0628616\pi$
$660$		0			0
$661$	−8.84503	+	5.10668i	−0.344032	+	0.198627i	−0.662053	−	0.749457i	$-0.730315\pi$
$661$	−8.84503	+	5.10668i	−0.344032	+	0.198627i	0.318022	+	0.948083i	$0.396981\pi$
$662$	11.4527	+	19.8367i	0.445123	+	0.770976i
$663$	−14.9592	−	28.5888i	−0.580967	−	1.11030i
$664$		−	33.7158i		−	1.30843i
$665$		0			0
$666$	−26.6412	+	12.5603i	−1.03233	+	0.486701i
$667$	30.1060	+	17.3817i	1.16571	+	0.673022i
$668$	−0.599296	+	0.346004i	−0.0231875	+	0.0133873i
$669$	−0.419510	+	10.0977i	−0.0162192	+	0.390399i
$670$		0			0
$671$	−3.67895			−0.142024
$672$	7.90416	−	19.5171i	0.304909	−	0.752888i
$673$			19.1004i			0.736266i	0.929773	+	0.368133i	$0.120003\pi$
$673$			19.1004i			0.736266i	−0.929773	+	0.368133i	$0.879997\pi$
$674$	−45.0282	−	25.9971i	−1.73442	−	1.00137i
$675$		0			0
$676$	0.667597	+	1.15631i	0.0256768	+	0.0444735i
$677$	3.44314	+	1.98790i	0.132331	+	0.0764011i	0.564704	−	0.825294i	$-0.308990\pi$
$677$	3.44314	+	1.98790i	0.132331	+	0.0764011i	−0.432373	+	0.901695i	$0.642324\pi$
$678$	43.0675	+	27.3094i	1.65400	+	1.04881i
$679$	−8.96006	+	7.60721i	−0.343855	+	0.291938i
$680$		0			0
$681$	9.16474	+	17.5149i	0.351194	+	0.671172i
$682$	−1.35997	−	2.35553i	−0.0520759	−	0.0901981i
$683$	5.32313	+	9.21993i	0.203684	+	0.352791i	0.949713	−	0.313123i	$-0.101375\pi$
$683$	5.32313	+	9.21993i	0.203684	+	0.352791i	−0.746029	+	0.665914i	$0.768042\pi$
$684$	0.869331	−	10.4444i	0.0332397	−	0.399352i
$685$		0			0
$686$	−31.3491	+	0.544533i	−1.19691	+	0.0207904i
$687$	0.975412	−	1.53825i	0.0372143	−	0.0586879i
$688$	36.0464	+	20.8114i	1.37426	+	0.793427i
$689$	−19.5735	−	33.9022i	−0.745689	−	1.29157i
$690$		0			0
$691$	14.3020	+	8.25729i	0.544076	+	0.314122i	0.746729	−	0.665128i	$-0.231623\pi$
$691$	14.3020	+	8.25729i	0.544076	+	0.314122i	−0.202653	+	0.979251i	$0.564956\pi$
$692$		−	12.5743i		−	0.478004i
$693$	1.51415	−	3.33385i	0.0575176	−	0.126642i
$694$	13.2401			0.502586
$695$		0			0
$696$	25.6387	+	1.06517i	0.971834	+	0.0403750i
$697$	−29.8222	+	17.2178i	−1.12960	+	0.652172i
$698$	−36.8735	−	21.2889i	−1.39568	−	0.805797i
$699$	−5.68265	−	3.60340i	−0.214938	−	0.136293i
$700$		0			0
$701$			19.5702i			0.739158i	0.929199	+	0.369579i	$0.120498\pi$
$701$			19.5702i			0.739158i	−0.929199	+	0.369579i	$0.879502\pi$
$702$	23.7383	+	17.9772i	0.895945	+	0.678507i
$703$	11.6965	+	20.2589i	0.441141	+	0.764078i
$704$	0.872955	−	0.504001i	0.0329007	−	0.0189952i
$705$		0			0
$706$		−	20.7706i		−	0.781712i
$707$	−6.81752	−	2.43677i	−0.256399	−	0.0916441i
$708$	12.3660	+	7.84133i	0.464742	+	0.294695i
$709$	14.1418	−	24.4943i	0.531106	−	0.919903i	−0.468235	−	0.883604i	$-0.655110\pi$
$709$	14.1418	−	24.4943i	0.531106	−	0.919903i	0.999341	−	0.0362991i	$-0.0115569\pi$
$710$		0			0
$711$	12.2638	−	17.6730i	0.459929	−	0.662788i
$712$	2.59631	−	4.49694i	0.0973009	−	0.168530i
$713$			15.6877i			0.587509i
$714$	−33.6658	+	26.2579i	−1.25991	+	0.982676i
$715$		0			0
$716$	1.77061	+	1.02226i	0.0661707	+	0.0382037i
$717$	−11.0809	−	0.460357i	−0.413823	−	0.0171923i
$718$	12.0466	−	6.95509i	0.449574	−	0.259562i
$719$	9.75873	−	16.9026i	0.363939	−	0.630361i	−0.624666	−	0.780892i	$-0.714765\pi$
$719$	9.75873	−	16.9026i	0.363939	−	0.630361i	0.988605	+	0.150531i	$0.0480983\pi$
$720$		0			0
$721$	−8.74566	−	47.9733i	−0.325705	−	1.78662i
$722$	4.61959			0.171923
$723$	1.81826	+	3.47491i	0.0676218	+	0.129233i
$724$	7.28057	−	4.20344i	0.270580	−	0.156220i
$725$		0			0
$726$	28.0261	−	14.6648i	1.04015	−	0.544260i
$727$	−26.5060			−0.983052			−0.491526	−	0.870863i	$-0.663561\pi$
$727$	−26.5060			−0.983052			−0.491526	+	0.870863i	$0.663561\pi$
$728$	13.1061	−	11.1272i	0.485743	−	0.412402i
$729$	−26.1665	−	6.65709i	−0.969128	−	0.246559i
$730$		0			0
$731$	−22.9888	−	39.8177i	−0.850271	−	1.47271i
$732$	−11.9526	−	0.496574i	−0.441782	−	0.0183539i
$733$	0.106580	−	0.184602i	0.00393663	−	0.00681844i	−0.864050	−	0.503405i	$-0.832080\pi$
$733$	0.106580	−	0.184602i	0.00393663	−	0.00681844i	0.867987	+	0.496587i	$0.165414\pi$
$734$	−47.2420			−1.74373
$735$		0			0
$736$	20.6979			0.762935
$737$	−0.211336	+	0.366045i	−0.00778467	+	0.0134835i
$738$	18.1179	−	26.1091i	0.666930	−	0.961090i
$739$	−23.2265	−	40.2296i	−0.854402	−	1.47987i	−0.877198	−	0.480128i	$-0.840590\pi$
$739$	−23.2265	−	40.2296i	−0.854402	−	1.47987i	0.0227959	−	0.999740i	$-0.492743\pi$
$740$		0			0
$741$	12.6650	−	19.9730i	0.465261	−	0.733728i
$742$	−39.4876	+	33.5255i	−1.44964	+	1.23076i
$743$	−28.0937			−1.03066			−0.515330	−	0.856992i	$-0.672330\pi$
$743$	−28.0937			−1.03066			−0.515330	+	0.856992i	$0.672330\pi$
$744$	5.36873	+	10.2603i	0.196827	+	0.376159i
$745$		0			0
$746$	−26.5135	+	15.3076i	−0.970729	+	0.560451i
$747$	4.37044	−	52.5079i	0.159906	−	1.92116i
$748$	2.19874			0.0803939
$749$	−3.15687	−	17.3166i	−0.115349	−	0.632736i
$750$		0			0
$751$	−12.4832	+	21.6215i	−0.455518	+	0.788981i	−0.998718	−	0.0506227i	$-0.983879\pi$
$751$	−12.4832	+	21.6215i	−0.455518	+	0.788981i	0.543199	+	0.839604i	$0.317213\pi$
$752$	13.6324	−	7.87068i	0.497123	−	0.287014i
$753$	0.957813	−	23.0547i	0.0349046	−	0.840161i
$754$	−38.3014	−	22.1133i	−1.39485	−	0.805319i
$755$		0			0
$756$	5.36933	−	10.6270i	0.195281	−	0.386502i
$757$		−	6.25577i		−	0.227370i	−0.993517	−	0.113685i	$-0.963735\pi$
$757$		−	6.25577i		−	0.227370i	0.993517	−	0.113685i	$-0.0362655\pi$
$758$	20.9460	−	36.2796i	0.760794	−	1.31773i
$759$	3.59606	+	0.149399i	0.130529	+	0.00542284i
$760$		0			0
$761$	−26.3374	+	45.6178i	−0.954731	+	1.65364i	−0.219750	+	0.975556i	$0.570524\pi$
$761$	−26.3374	+	45.6178i	−0.954731	+	1.65364i	−0.734982	+	0.678087i	$0.762809\pi$
$762$	−19.7158	+	31.0924i	−0.714229	+	1.12636i
$763$	19.5157	+	6.97543i	0.706514	+	0.252528i
$764$			4.37410i			0.158249i
$765$		0			0
$766$	−18.9563	+	10.9444i	−0.684917	+	0.395437i
$767$	16.5209	+	28.6151i	0.596536	+	1.03323i
$768$	26.7806	−	14.0130i	0.966360	−	0.505652i
$769$		−	5.37059i		−	0.193669i	−0.995301	−	0.0968343i	$-0.969128\pi$
$769$		−	5.37059i		−	0.193669i	0.995301	−	0.0968343i	$-0.0308717\pi$
$770$		0			0
$771$	−18.1733	+	28.6598i	−0.654496	+	1.03216i
$772$	−9.82820	−	5.67432i	−0.353725	−	0.204223i
$773$	−2.12434	+	1.22649i	−0.0764073	+	0.0441138i	−0.537717	−	0.843125i	$-0.680713\pi$
$773$	−2.12434	+	1.22649i	−0.0764073	+	0.0441138i	0.461310	+	0.887239i	$0.347380\pi$
$774$	34.8602	+	24.1906i	1.25302	+	0.869512i
$775$		0			0
$776$	−8.52826			−0.306147
$777$	3.67689	+	26.3201i	0.131908	+	0.944227i
$778$			32.0641i			1.14956i
$779$	−21.8588	−	12.6202i	−0.783172	−	0.452165i
$780$		0			0
$781$	0.351967	+	0.609625i	0.0125944	+	0.0218141i
$782$	−36.3446	−	20.9836i	−1.29968	−	0.750371i
$783$	39.7909	+	4.98230i	1.42201	+	0.178053i
$784$	−26.9731	−	22.1060i	−0.963326	−	0.789501i
$785$		0			0
$786$	17.4735	−	9.14307i	0.623258	−	0.326122i
$787$	20.6048	+	35.6885i	0.734481	+	1.27216i	0.954951	+	0.296764i	$0.0959076\pi$
$787$	20.6048	+	35.6885i	0.734481	+	1.27216i	−0.220470	+	0.975394i	$0.570759\pi$
$788$	−9.22039	−	15.9702i	−0.328463	−	0.568914i
$789$	−25.7416	+	13.4694i	−0.916426	+	0.479524i
$790$		0			0
$791$	35.0764	−	29.7803i	1.24717	−	1.05887i
$792$	2.40307	−	1.13295i	0.0853893	−	0.0402576i
$793$	−23.3785	−	13.4976i	−0.830196	−	0.479314i
$794$	−6.16797	−	10.6832i	−0.218893	−	0.379134i
$795$		0			0
$796$	−5.01431	−	2.89501i	−0.177727	−	0.102611i
$797$		−	36.9407i		−	1.30851i	−0.756276	−	0.654253i	$-0.772983\pi$
$797$		−	36.9407i		−	1.30851i	0.756276	−	0.654253i	$-0.227017\pi$
$798$	−29.0058	−	11.7469i	−1.02679	−	0.415837i
$799$	−17.3883			−0.615154
$800$		0			0
$801$	4.62634	−	6.66685i	0.163464	−	0.235562i
$802$	−23.2600	+	13.4292i	−0.821339	+	0.474200i
$803$	−3.11544	−	1.79870i	−0.109942	−	0.0634748i
$804$	−0.736023	+	1.16073i	−0.0259575	+	0.0409357i
$805$		0			0
$806$		−	19.9582i		−	0.702997i
$807$	−45.0277	+	23.5610i	−1.58505	+	0.829385i
$808$	−2.62655	−	4.54931i	−0.0924016	−	0.160044i
$809$	−45.9461	+	26.5270i	−1.61538	+	0.932640i	−0.627285	+	0.778790i	$0.715834\pi$
$809$	−45.9461	+	26.5270i	−1.61538	+	0.932640i	−0.988094	+	0.153850i	$0.950833\pi$
$810$		0			0
$811$		−	19.0686i		−	0.669590i	−0.942291	−	0.334795i	$-0.891333\pi$
$811$		−	19.0686i		−	0.669590i	0.942291	−	0.334795i	$-0.108667\pi$
$812$	−5.95198	+	16.6523i	−0.208873	+	0.584380i
$813$	−2.75394	+	4.34304i	−0.0965850	+	0.152317i
$814$	2.26457	−	3.92235i	0.0793731	−	0.137478i
$815$		0			0
$816$	−47.4481	−	1.97124i	−1.66102	−	0.0690072i
$817$	16.8501	−	29.1852i	0.589511	−	1.02106i
$818$			44.5918i			1.55912i
$819$	21.8533	−	15.6303i	0.763617	−	0.546167i
$820$		0			0
$821$	9.46302	+	5.46348i	0.330262	+	0.190677i	0.655957	−	0.754798i	$-0.272265\pi$
$821$	9.46302	+	5.46348i	0.330262	+	0.190677i	−0.325696	+	0.945475i	$0.605598\pi$
$822$	−2.47654	+	59.6108i	−0.0863793	+	2.07916i
$823$	−36.3622	+	20.9937i	−1.26750	+	0.731794i	−0.974515	−	0.224321i	$-0.927984\pi$
$823$	−36.3622	+	20.9937i	−1.26750	+	0.731794i	−0.292990	+	0.956116i	$0.594650\pi$
$824$	17.6909	−	30.6416i	0.616293	−	1.06745i
$825$		0			0
$826$	33.3294	−	28.2971i	1.15968	−	0.984584i
$827$	−22.1128			−0.768937			−0.384468	−	0.923138i	$-0.625615\pi$
$827$	−22.1128			−0.768937			−0.384468	+	0.923138i	$0.625615\pi$
$828$	11.6632	+	0.970771i	0.405323	+	0.0337366i
$829$	−27.1141	+	15.6543i	−0.941711	+	0.543697i	−0.890496	−	0.454990i	$-0.849643\pi$
$829$	−27.1141	+	15.6543i	−0.941711	+	0.543697i	−0.0512148	+	0.998688i	$0.516309\pi$
$830$		0			0
$831$	10.4596	+	19.9895i	0.362838	+	0.693427i
$832$	7.39645			0.256426
$833$	13.5940	+	36.0450i	0.471003	+	1.24888i
$834$	15.3755	−	24.2476i	0.532410	−	0.839625i
$835$		0			0
$836$	0.805806	+	1.39570i	0.0278694	+	0.0482712i
$837$	7.03109	+	16.6749i	0.243030	+	0.576370i
$838$	12.1468	−	21.0389i	0.419605	−	0.726777i
$839$	8.65688			0.298869			0.149434	−	0.988772i	$-0.452255\pi$
$839$	8.65688			0.298869			0.149434	+	0.988772i	$0.452255\pi$
$840$		0			0
$841$	−30.5607			−1.05382
$842$	8.52225	−	14.7610i	0.293696	−	0.508696i
$843$	33.6428	+	1.39769i	1.15872	+	0.0481391i
$844$	−2.47763	−	4.29138i	−0.0852835	−	0.147715i
$845$		0			0
$846$	14.5149	−	6.84318i	0.499031	−	0.235273i
$847$	−5.11859	−	28.0775i	−0.175877	−	0.964753i
$848$	−57.6164			−1.97855
$849$	−8.65476	+	4.52864i	−0.297031	+	0.155423i
$850$		0			0
$851$	−22.6228	+	13.0613i	−0.775501	+	0.447736i
$852$	1.06123	+	2.02813i	0.0363571	+	0.0694826i
$853$	48.3400			1.65513			0.827565	−	0.561370i	$-0.189726\pi$
$853$	48.3400			1.65513			0.827565	+	0.561370i	$0.189726\pi$
$854$	−12.0226	+	33.6365i	−0.411405	+	1.15102i
$855$		0			0
$856$	6.38579	−	11.0605i	0.218262	−	0.378041i
$857$	−29.1362	+	16.8218i	−0.995274	+	0.574622i	−0.906847	−	0.421461i	$-0.861517\pi$
$857$	−29.1362	+	16.8218i	−0.995274	+	0.574622i	−0.0884274	+	0.996083i	$0.528184\pi$
$858$	−4.57497	−	0.190068i	−0.156187	−	0.00648881i
$859$	−22.6082	−	13.0528i	−0.771382	−	0.445357i	0.0619856	−	0.998077i	$-0.480257\pi$
$859$	−22.6082	−	13.0528i	−0.771382	−	0.445357i	−0.833367	+	0.552720i	$0.813590\pi$
$860$		0			0
$861$	−17.6351	−	22.6103i	−0.601001	−	0.770557i
$862$			13.9573i			0.475387i
$863$	19.6742	−	34.0767i	0.669718	−	1.15998i	−0.308265	−	0.951300i	$-0.599748\pi$
$863$	19.6742	−	34.0767i	0.669718	−	1.15998i	0.977983	−	0.208685i	$-0.0669182\pi$
$864$	22.0005	−	9.27662i	0.748471	−	0.315597i
$865$		0			0
$866$	9.07765	−	15.7230i	0.308471	−	0.534288i
$867$	19.4348	+	12.3237i	0.660042	+	0.418536i
$868$	−7.85088	+	1.43124i	−0.266476	+	0.0485793i
$869$			3.30783i			0.112211i
$870$		0			0
$871$	−2.68594	+	1.55073i	−0.0910097	+	0.0525445i
$872$	7.51869	+	13.0227i	0.254615	+	0.441006i
$873$	−13.2817	−	1.10548i	−0.449516	−	0.0374150i
$874$		−	30.7607i		−	1.04050i
$875$		0			0
$876$	−9.87904	−	6.26435i	−0.333782	−	0.211653i
$877$	−22.9766	−	13.2655i	−0.775864	−	0.447945i	0.0590984	−	0.998252i	$-0.481177\pi$
$877$	−22.9766	−	13.2655i	−0.775864	−	0.447945i	−0.834963	+	0.550307i	$0.814511\pi$
$878$	−4.64262	+	2.68042i	−0.156681	+	0.0904597i
$879$	37.3376	+	1.55120i	1.25936	+	0.0523205i
$880$		0			0
$881$	−13.2055			−0.444904			−0.222452	−	0.974944i	$-0.571406\pi$
$881$	−13.2055			−0.444904			−0.222452	+	0.974944i	$0.571406\pi$
$882$	−25.5331	−	24.7386i	−0.859743	−	0.832991i
$883$			27.3728i			0.921169i	0.887616	+	0.460584i	$0.152360\pi$
$883$			27.3728i			0.921169i	−0.887616	+	0.460584i	$0.847640\pi$
$884$	13.9723	+	8.06689i	0.469938	+	0.271319i
$885$		0			0
$886$	−14.7738	−	25.5889i	−0.496335	−	0.859677i
$887$	28.5105	+	16.4606i	0.957290	+	0.552692i	0.895338	−	0.445387i	$-0.146934\pi$
$887$	28.5105	+	16.4606i	0.957290	+	0.552692i	0.0619524	+	0.998079i	$0.480267\pi$
$888$	−10.3262	+	16.2846i	−0.346523	+	0.546476i
$889$	21.4997	+	25.3232i	0.721078	+	0.849313i
$890$		0			0
$891$	3.88932	−	1.45292i	0.130297	−	0.0486747i
$892$	−2.52672	−	4.37641i	−0.0846009	−	0.146533i
$893$	−6.37256	−	11.0376i	−0.213250	−	0.369359i
$894$	22.1644	+	42.3587i	0.741288	+	1.41669i
$895$		0			0
$896$	−6.11599	−	33.5486i	−0.204321	−	1.12078i
$897$	22.3036	+	14.1429i	0.744697	+	0.472216i
$898$	18.0149	+	10.4009i	0.601165	+	0.347083i
$899$	−13.4390	−	23.2770i	−0.448216	−	0.776333i
$900$		0			0
$901$	55.1178	+	31.8223i	1.83624	+	1.06015i
$902$			4.88682i			0.162713i
$903$	30.1886	−	23.5458i	1.00461	−	0.783557i
$904$	33.3860			1.11040
$905$		0			0
$906$	1.83634	−	44.2011i	0.0610083	−	1.46848i
$907$	18.0335	−	10.4117i	0.598793	−	0.345714i	−0.169773	−	0.985483i	$-0.554304\pi$
$907$	18.0335	−	10.4117i	0.598793	−	0.345714i	0.768567	+	0.639770i	$0.220970\pi$
$908$	−8.56010	−	4.94217i	−0.284077	−	0.164012i
$909$	−3.50079	−	7.42543i	−0.116114	−	0.246286i
$910$		0			0
$911$			50.2293i			1.66417i	0.554648	+	0.832085i	$0.312853\pi$
$911$			50.2293i			1.66417i	−0.554648	+	0.832085i	$0.687147\pi$
$912$	−16.1378	−	30.8412i	−0.534375	−	1.02125i
$913$	4.05108	+	7.01668i	0.134071	+	0.232218i
$914$	−7.16844	+	4.13870i	−0.237111	+	0.136896i
$915$		0			0
$916$			0.910763i			0.0300925i
$917$	−3.19130	−	17.5055i	−0.105386	−	0.578083i
$918$	−48.0365	−	6.01475i	−1.58544	−	0.198516i
$919$	−9.88707	+	17.1249i	−0.326144	+	0.564899i	−0.981743	−	0.190211i	$-0.939083\pi$
$919$	−9.88707	+	17.1249i	−0.326144	+	0.564899i	0.655599	+	0.755109i	$0.272416\pi$
$920$		0			0
$921$	−1.64849	+	39.6796i	−0.0543197	+	1.30749i
$922$	4.34026	−	7.51755i	0.142939	−	0.247577i
$923$			5.16529i			0.170017i
$924$	0.253313	+	1.81327i	0.00833338	+	0.0596522i
$925$		0			0
$926$	−58.5095	−	33.7805i	−1.92274	−	1.11009i
$927$	31.5232	−	45.4270i	1.03536	−	1.49202i
$928$	−30.7111	+	17.7310i	−1.00814	+	0.582050i
$929$	−1.84133	+	3.18927i	−0.0604119	+	0.104637i	−0.894650	−	0.446769i	$-0.852575\pi$
$929$	−1.84133	+	3.18927i	−0.0604119	+	0.104637i	0.834238	+	0.551405i	$0.185908\pi$
$930$		0			0
$931$	−17.8983	+	21.8390i	−0.586594	+	0.715745i
$932$	3.36457			0.110210
$933$	−2.45245	+	1.28325i	−0.0802896	+	0.0420119i
$934$	13.3802	−	7.72506i	0.437814	−	0.252772i
$935$		0			0
$936$	19.4273	+	1.61701i	0.635002	+	0.0528538i
$937$	−36.7871			−1.20178			−0.600891	−	0.799331i	$-0.705187\pi$
$937$	−36.7871			−1.20178			−0.600891	+	0.799331i	$0.705187\pi$
$938$	2.65610	+	3.12845i	0.0867247	+	0.102148i
$939$	42.2507	+	26.7914i	1.37880	+	0.874305i
$940$		0			0
$941$	−10.1072	−	17.5061i	−0.329484	−	0.570684i	0.652925	−	0.757422i	$-0.273542\pi$
$941$	−10.1072	−	17.5061i	−0.329484	−	0.570684i	−0.982410	+	0.186739i	$0.940208\pi$
$942$	1.51552	−	36.4789i	0.0493784	−	1.18855i
$943$	14.0928	−	24.4094i	0.458924	−	0.794880i
$944$	48.6310			1.58280
$945$		0			0
$946$	−6.52474			−0.212138
$947$	4.91182	−	8.50752i	0.159613	−	0.276457i	−0.775116	−	0.631819i	$-0.782309\pi$
$947$	4.91182	−	8.50752i	0.159613	−	0.276457i	0.934729	+	0.355361i	$0.115642\pi$
$948$	−0.446481	+	10.7469i	−0.0145010	+	0.349043i
$949$	−13.1984	−	22.8603i	−0.428438	−	0.742076i
$950$		0			0
$951$	9.59621	+	6.08501i	0.311179	+	0.197320i
$952$	−9.40772	+	26.3206i	−0.304906	+	0.853057i
$953$	24.7365			0.801294			0.400647	−	0.916232i	$-0.368785\pi$
$953$	24.7365			0.801294			0.400647	+	0.916232i	$0.368785\pi$
$954$	−58.5332	−	4.87195i	−1.89508	−	0.157735i
$955$		0			0
$956$	4.80253	−	2.77274i	0.155325	−	0.0896769i
$957$	−5.46373	+	2.85892i	−0.176617	+	0.0924158i
$958$	−20.9996			−0.678468
$959$	50.6917	+	18.1186i	1.63692	+	0.585081i
$960$		0			0
$961$	−9.43537	+	16.3425i	−0.304367	+	0.527179i
$962$	28.7812	−	16.6168i	0.927942	−	0.535748i
$963$	11.3788	−	16.3975i	0.366676	−	0.528403i
$964$	−1.69830	−	0.980514i	−0.0546986	−	0.0315802i
$965$		0			0
$966$	13.1177	−	32.3904i	0.422054	−	1.04214i
$967$		−	14.0157i		−	0.450713i	−0.974276	−	0.225357i	$-0.927645\pi$
$967$		−	14.0157i		−	0.450713i	0.974276	−	0.225357i	$-0.0723547\pi$
$968$	10.3540	−	17.9337i	0.332791	−	0.576410i
$969$	−1.59603	+	38.4168i	−0.0512719	+	1.23412i
$970$		0			0
$971$	0.0308306	−	0.0534003i	0.000989403	−	0.00171370i	−0.865530	−	0.500857i	$-0.833018\pi$
$971$	0.0308306	−	0.0534003i	0.000989403	−	0.00171370i	0.866520	+	0.499143i	$0.166352\pi$
$972$	12.8322	−	4.19546i	0.411593	−	0.134569i
$973$	−16.7667	−	19.7485i	−0.537516	−	0.633106i
$974$		−	23.9792i		−	0.768342i
$975$		0			0
$976$	−34.4085	+	19.8657i	−1.10139	+	0.635887i
$977$	9.53996	+	16.5237i	0.305210	+	0.528640i	0.977308	−	0.211822i	$-0.0679399\pi$
$977$	9.53996	+	16.5237i	0.305210	+	0.528640i	−0.672098	+	0.740462i	$0.734607\pi$
$978$	7.48229	+	14.2995i	0.239257	+	0.457248i
$979$			1.24783i			0.0398808i
$980$		0			0
$981$	10.0213	+	21.2558i	0.319955	+	0.678647i
$982$	47.0945	+	27.1900i	1.50285	+	0.867669i
$983$	−7.05465	+	4.07300i	−0.225008	+	0.129909i	−0.608267	−	0.793732i	$-0.708135\pi$
$983$	−7.05465	+	4.07300i	−0.225008	+	0.129909i	0.383259	+	0.923641i	$0.374802\pi$
$984$	0.863618	−	20.7875i	0.0275311	−	0.662680i
$985$		0			0
$986$	71.9030			2.28986
$987$	−2.00327	−	14.3399i	−0.0637649	−	0.456444i
$988$			11.8256i			0.376222i
$989$	32.5908	+	18.8163i	1.03633	+	0.598324i
$990$		0			0
$991$	−5.21862	−	9.03891i	−0.165775	−	0.287130i	0.771155	−	0.636647i	$-0.219679\pi$
$991$	−5.21862	−	9.03891i	−0.165775	−	0.287130i	−0.936930	+	0.349517i	$0.886346\pi$
$992$	−13.8590	−	8.00150i	−0.440024	−	0.254048i
$993$	19.7910	+	12.5496i	0.628050	+	0.398250i
$994$	6.72398	−	1.22580i	0.213272	−	0.0388800i
$995$		0			0
$996$	12.2146	+	23.3435i	0.387033	+	0.739666i
$997$	−6.74411	−	11.6811i	−0.213588	−	0.369945i	0.739247	−	0.673435i	$-0.235182\pi$
$997$	−6.74411	−	11.6811i	−0.213588	−	0.369945i	−0.952835	+	0.303489i	$0.901848\pi$
$998$	22.6159	+	39.1719i	0.715894	+	1.23996i
$999$	−18.1925	+	24.0226i	−0.575587	+	0.760042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.q.g.299.6		40
3.2	odd	2	inner	525.2.q.g.299.16		40
5.2	odd	4		525.2.t.i.26.3	yes	20
5.3	odd	4		525.2.t.h.26.8	yes	20
5.4	even	2	inner	525.2.q.g.299.15		40
7.3	odd	6	inner	525.2.q.g.374.5		40
15.2	even	4		525.2.t.i.26.8	yes	20
15.8	even	4		525.2.t.h.26.3	✓	20
15.14	odd	2	inner	525.2.q.g.299.5		40
21.17	even	6	inner	525.2.q.g.374.15		40
35.3	even	12		525.2.t.h.101.3	yes	20
35.17	even	12		525.2.t.i.101.8	yes	20
35.24	odd	6	inner	525.2.q.g.374.16		40
105.17	odd	12		525.2.t.i.101.3	yes	20
105.38	odd	12		525.2.t.h.101.8	yes	20
105.59	even	6	inner	525.2.q.g.374.6		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.5		40	15.14	odd	2	inner
525.2.q.g.299.6		40	1.1	even	1	trivial
525.2.q.g.299.15		40	5.4	even	2	inner
525.2.q.g.299.16		40	3.2	odd	2	inner
525.2.q.g.374.5		40	7.3	odd	6	inner
525.2.q.g.374.6		40	105.59	even	6	inner
525.2.q.g.374.15		40	21.17	even	6	inner
525.2.q.g.374.16		40	35.24	odd	6	inner
525.2.t.h.26.3	✓	20	15.8	even	4
525.2.t.h.26.8	yes	20	5.3	odd	4
525.2.t.h.101.3	yes	20	35.3	even	12
525.2.t.h.101.8	yes	20	105.38	odd	12
525.2.t.i.26.3	yes	20	5.2	odd	4
525.2.t.i.26.8	yes	20	15.2	even	4
525.2.t.i.101.3	yes	20	105.17	odd	12
525.2.t.i.101.8	yes	20	35.17	even	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.846473 + 1.46613i) q^{2} +(-0.0718963 + 1.73056i) q^{3} +(-0.433034 - 0.750036i) q^{4} +(-2.47637 - 1.57028i) q^{6} +(-2.01688 + 1.71236i) q^{7} -1.91969 q^{8} +(-2.98966 - 0.248842i) q^{9} +O(q^{10})\)	\(q+(-0.846473 + 1.46613i) q^{2} +(-0.0718963 + 1.73056i) q^{3} +(-0.433034 - 0.750036i) q^{4} +(-2.47637 - 1.57028i) q^{6} +(-2.01688 + 1.71236i) q^{7} -1.91969 q^{8} +(-2.98966 - 0.248842i) q^{9} +(0.399511 - 0.230658i) q^{11} +(1.32911 - 0.695465i) q^{12} +3.38501 q^{13} +(-0.803314 - 4.40649i) q^{14} +(2.49103 - 4.31459i) q^{16} +(-4.76601 + 2.75166i) q^{17} +(2.89550 - 4.17261i) q^{18} +(-3.49334 - 2.01688i) q^{19} +(-2.81833 - 3.61345i) q^{21} +0.780983i q^{22} +(2.25223 - 3.90097i) q^{23} +(0.138018 - 3.32213i) q^{24} +(-2.86532 + 4.96289i) q^{26} +(0.645580 - 5.15589i) q^{27} +(2.15771 + 0.771225i) q^{28} +7.71756i q^{29} +(-3.01611 + 1.74135i) q^{31} +(2.29749 + 3.97938i) q^{32} +(0.370444 + 0.707961i) q^{33} -9.31681i q^{34} +(1.10798 + 2.35011i) q^{36} +(-5.02232 - 2.89964i) q^{37} +(5.91404 - 3.41448i) q^{38} +(-0.243370 + 5.85796i) q^{39} +6.25727 q^{41} +(7.68344 - 1.07337i) q^{42} +8.35453i q^{43} +(-0.346004 - 0.199765i) q^{44} +(3.81290 + 6.60414i) q^{46} +(2.73630 + 1.57980i) q^{47} +(7.28756 + 4.62108i) q^{48} +(1.13564 - 6.90727i) q^{49} +(-4.41924 - 8.44568i) q^{51} +(-1.46582 - 2.53888i) q^{52} +(-5.78238 - 10.0154i) q^{53} +(7.01277 + 5.31083i) q^{54} +(3.87179 - 3.28720i) q^{56} +(3.74149 - 5.90043i) q^{57} +(-11.3150 - 6.53271i) q^{58} +(4.88061 + 8.45346i) q^{59} +(-6.90647 - 3.98746i) q^{61} -5.89604i q^{62} +(6.45591 - 4.61750i) q^{63} +2.18506 q^{64} +(-1.35154 - 0.0561498i) q^{66} +(-0.793481 + 0.458116i) q^{67} +(4.12768 + 2.38312i) q^{68} +(6.58893 + 4.17808i) q^{69} +1.52593i q^{71} +(5.73922 + 0.477698i) q^{72} +(-3.89906 - 6.75338i) q^{73} +(8.50252 - 4.90893i) q^{74} +3.49351i q^{76} +(-0.410798 + 1.14932i) q^{77} +(-8.38256 - 5.31542i) q^{78} +(-3.58521 + 6.20977i) q^{79} +(8.87616 + 1.48790i) q^{81} +(-5.29661 + 9.17399i) q^{82} +17.5632i q^{83} +(-1.48978 + 3.67860i) q^{84} +(-12.2489 - 7.07188i) q^{86} +(-13.3557 - 0.554864i) q^{87} +(-0.766937 + 0.442791i) q^{88} +(-1.35247 + 2.34254i) q^{89} +(-6.82718 + 5.79637i) q^{91} -3.90116 q^{92} +(-2.79667 - 5.34476i) q^{93} +(-4.63241 + 2.67452i) q^{94} +(-7.05172 + 3.68984i) q^{96} +4.44253 q^{97} +(9.16569 + 7.51181i) q^{98} +(-1.25180 + 0.590174i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 28 q^{4} + 14 q^{9}+O(q^{10}) \) 40 * q - 28 * q^4 + 14 * q^9	\( 40 q - 28 q^{4} + 14 q^{9} - 36 q^{16} - 18 q^{21} - 36 q^{24} + 84 q^{31} - 72 q^{36} - 16 q^{46} + 8 q^{49} + 42 q^{51} + 150 q^{54} - 180 q^{61} + 240 q^{64} + 12 q^{66} - 92 q^{79} + 58 q^{81} - 150 q^{84} - 60 q^{91} - 12 q^{94} + 270 q^{96} - 188 q^{99}+O(q^{100}) \) 40 * q - 28 * q^4 + 14 * q^9 - 36 * q^16 - 18 * q^21 - 36 * q^24 + 84 * q^31 - 72 * q^36 - 16 * q^46 + 8 * q^49 + 42 * q^51 + 150 * q^54 - 180 * q^61 + 240 * q^64 + 12 * q^66 - 92 * q^79 + 58 * q^81 - 150 * q^84 - 60 * q^91 - 12 * q^94 + 270 * q^96 - 188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more