LMFDB - Embedded newform 525.2.q.g.299.16

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			299.16
Character	$\chi$	$=$	525.299
Dual form			525.2.q.g.374.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.846473 - 1.46613i) q^{2} +(1.53466 + 0.803015i) q^{3} +(-0.433034 - 0.750036i) q^{4} +(2.47637 - 1.57028i) q^{6} +(-2.01688 + 1.71236i) q^{7} +1.91969 q^{8} +(1.71033 + 2.46470i) q^{9} +O(q^{10})$	\(q+(0.846473 - 1.46613i) q^{2} +(1.53466 + 0.803015i) q^{3} +(-0.433034 - 0.750036i) q^{4} +(2.47637 - 1.57028i) q^{6} +(-2.01688 + 1.71236i) q^{7} +1.91969 q^{8} +(1.71033 + 2.46470i) q^{9} +(-0.399511 + 0.230658i) q^{11} +(-0.0622670 - 1.49878i) q^{12} +3.38501 q^{13} +(0.803314 + 4.40649i) q^{14} +(2.49103 - 4.31459i) q^{16} +(4.76601 - 2.75166i) q^{17} +(5.06134 - 0.421275i) q^{18} +(-3.49334 - 2.01688i) q^{19} +(-4.47027 + 1.00830i) q^{21} +0.780983i q^{22} +(-2.25223 + 3.90097i) q^{23} +(2.94606 + 1.54154i) 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} +(-0.798334 + 0.0331669i) q^{33} -9.31681i q^{34} +(1.10798 - 2.35011i) q^{36} +(-5.02232 - 2.89964i) q^{37} +(-5.91404 + 3.41448i) q^{38} +(5.19483 + 2.71822i) q^{39} -6.25727 q^{41} +(-2.30567 + 7.40752i) 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} +(9.52380 - 0.395668i) q^{51} +(-1.46582 - 2.53888i) q^{52} +(5.78238 + 10.0154i) q^{53} +(8.10570 + 3.41782i) 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} +(-7.67001 - 2.04231i) q^{63} +2.18506 q^{64} +(-0.627141 + 1.19854i) q^{66} +(-0.793481 + 0.458116i) q^{67} +(-4.12768 - 2.38312i) q^{68} +(-6.58893 + 4.17808i) q^{69} -1.52593i q^{71} +(3.28331 + 4.73146i) 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} +(-3.14952 + 8.43093i) q^{81} +(-5.29661 + 9.17399i) q^{82} -17.5632i q^{83} +(2.69204 + 2.91624i) q^{84} +(12.2489 + 7.07188i) q^{86} +(6.19732 - 11.8438i) q^{87} +(-0.766937 + 0.442791i) q^{88} +(1.35247 - 2.34254i) q^{89} +(-6.82718 + 5.79637i) q^{91} +3.90116 q^{92} +(-6.02703 + 0.250394i) q^{93} +(-4.63241 + 2.67452i) q^{94} +(-0.330363 - 7.95189i) 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	$-0.629078\pi$
$2$	0.846473	−	1.46613i	0.598547	−	1.03671i	0.993036	−	0.117813i	$-0.0375883\pi$
$3$	1.53466	+	0.803015i	0.886034	+	0.463621i
$3$	1.53466	+	0.803015i	0.886034	+	0.463621i
$4$	−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
$9$	1.71033	+	2.46470i	0.570111	+	0.821567i
$10$		0			0
$11$	−0.399511	+	0.230658i	−0.120457	+	0.0695460i	−0.559018	−	0.829156i	$-0.688822\pi$
$11$	−0.399511	+	0.230658i	−0.120457	+	0.0695460i	0.438561	+	0.898702i	$0.355488\pi$
$12$	−0.0622670	−	1.49878i	−0.0179749	−	0.432660i
$13$	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	0.205602	−	0.978636i	$-0.434085\pi$
$17$	4.76601	−	2.75166i	1.15593	−	0.667374i	0.950324	+	0.311261i	$0.100751\pi$
$18$	5.06134	−	0.421275i	1.19297	−	0.0992955i
$19$	−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
$21$	−4.47027	+	1.00830i	−0.975493	+	0.220028i
$22$			0.780983i			0.166506i
$23$	−2.25223	+	3.90097i	−0.469622	+	0.813409i	−0.999397	−	0.0347292i	$-0.988943\pi$
$23$	−2.25223	+	3.90097i	−0.469622	+	0.813409i	0.529775	+	0.848138i	$0.322276\pi$
$24$	2.94606	+	1.54154i	0.601362	+	0.314665i
$25$		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	$-0.745717\pi$
$29$		−	7.71756i		−	1.43311i	0.697528	−	0.716557i	$-0.254283\pi$
$30$		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
$33$	−0.798334	+	0.0331669i	−0.138972	+	0.00577362i
$34$		−	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
$39$	5.19483	+	2.71822i	0.831839	+	0.435263i
$40$		0			0
$41$	−6.25727			−0.977221			−0.488610	−	0.872502i	$-0.662496\pi$
$41$	−6.25727			−0.977221			−0.488610	+	0.872502i	$0.662496\pi$
$42$	−2.30567	+	7.40752i	−0.355772	+	1.14300i
$43$			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	0.286978	−	0.957937i	$-0.407349\pi$
$47$	−2.73630	−	1.57980i	−0.399130	−	0.230438i	−0.686109	+	0.727499i	$0.740683\pi$
$48$	7.28756	−	4.62108i	1.05187	−	0.666995i
$49$	1.13564	−	6.90727i	0.162234	−	0.986752i
$50$		0			0
$51$	9.52380	−	0.395668i	1.33360	−	0.0554046i
$52$	−1.46582	−	2.53888i	−0.203273	−	0.352080i
$53$	5.78238	+	10.0154i	0.794271	+	1.37572i	0.923301	+	0.384078i	$0.125481\pi$
$53$	5.78238	+	10.0154i	0.794271	+	1.37572i	−0.129029	+	0.991641i	$0.541186\pi$
$54$	8.10570	+	3.41782i	1.10305	+	0.465106i
$55$		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	$-0.947501\pi$
$59$	−4.88061	−	8.45346i	−0.635401	−	1.10055i	0.351029	−	0.936365i	$-0.385832\pi$
$60$		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
$63$	−7.67001	−	2.04231i	−0.966330	−	0.257307i
$64$	2.18506			0.273132
$65$		0			0
$66$	−0.627141	+	1.19854i	−0.0771957	+	0.147530i
$67$	−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	$-0.971138\pi$
$71$		−	1.52593i		−	0.181094i	0.995892	−	0.0905471i	$-0.0288616\pi$
$72$	3.28331	+	4.73146i	0.386941	+	0.557608i
$73$	−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
$81$	−3.14952	+	8.43093i	−0.349946	+	0.936770i
$82$	−5.29661	+	9.17399i	−0.584912	+	1.01310i
$83$		−	17.5632i		−	1.92781i	−0.266250	−	0.963904i	$-0.585785\pi$
$83$		−	17.5632i		−	1.92781i	0.266250	−	0.963904i	$-0.414215\pi$
$84$	2.69204	+	2.91624i	0.293725	+	0.318188i
$85$		0			0
$86$	12.2489	+	7.07188i	1.32083	+	0.762581i
$87$	6.19732	−	11.8438i	0.664422	−	1.26979i
$88$	−0.766937	+	0.442791i	−0.0817558	+	0.0472017i
$89$	1.35247	−	2.34254i	0.143361	−	0.248309i	−0.785399	−	0.618990i	$-0.787542\pi$
$89$	1.35247	−	2.34254i	0.143361	−	0.248309i	0.928760	+	0.370681i	$0.120876\pi$
$90$		0			0
$91$	−6.82718	+	5.79637i	−0.715683	+	0.607625i
$92$	3.90116			0.406724
$93$	−6.02703	+	0.250394i	−0.624974	+	0.0259646i
$94$	−4.63241	+	2.67452i	−0.477796	+	0.275856i
$95$		0			0
$96$	−0.330363	−	7.95189i	−0.0337175	−	0.811587i
$97$	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	0.789891	−	0.613248i	$-0.210137\pi$
$101$	−1.36822	−	2.36982i	−0.136143	−	0.235806i	−0.926033	+	0.377442i	$0.876804\pi$
$102$	7.48154	−	14.2981i	0.740782	−	1.41572i
$103$	−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	−0.659232	−	0.751939i	$-0.729119\pi$
$107$	3.32647	−	5.76162i	0.321582	−	0.556997i	0.980815	+	0.194942i	$0.0624520\pi$
$108$	3.58755	−	2.71688i	0.345212	−	0.261432i
$109$	−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	$-0.195071\pi$
$113$	17.3914			1.63604			0.818022	+	0.575187i	$0.195071\pi$
$114$	−11.8179	+	0.490976i	−1.10685	+	0.0459842i
$115$		0			0
$116$	−5.78845	+	3.34196i	−0.537444	+	0.310293i
$117$	5.78951	+	8.34305i	0.535240	+	0.771316i
$118$	−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
$123$	−9.60275	−	5.02468i	−0.865850	−	0.453060i
$124$	2.61216	+	1.50813i	0.234579	+	0.135434i
$125$		0			0
$126$	−9.48675	+	9.51650i	−0.845147	+	0.847797i
$127$		−	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
$129$	−6.70881	+	12.8213i	−0.590678	+	1.12885i
$130$		0			0
$131$	3.36275	−	5.82446i	0.293805	−	0.508886i	−0.680901	−	0.732375i	$-0.738412\pi$
$131$	3.36275	−	5.82446i	0.293805	−	0.508886i	0.974706	+	0.223490i	$0.0717450\pi$
$132$	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	$0.168680\pi$
$137$	10.1734	+	17.6208i	0.869171	+	1.50545i	0.00632592	+	0.999980i	$0.497986\pi$
$138$	0.548267	+	13.1969i	0.0466716	+	1.12339i
$139$			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
$144$	14.8947	−	1.23974i	1.24122	−	0.103312i
$145$		0			0
$146$	−13.2018			−1.09259
$147$	7.28945	−	9.68834i	0.601224	−	0.799081i
$148$			5.02257i			0.412852i
$149$	14.1195	+	8.15190i	1.15671	+	0.667830i	0.950514	−	0.310680i	$-0.100557\pi$
$149$	14.1195	+	8.15190i	1.15671	+	0.667830i	0.206200	+	0.978510i	$0.433890\pi$
$150$		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
$156$	−0.210775	−	5.07339i	−0.0168755	−	0.406196i
$157$	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
$159$	0.831464	+	20.0135i	0.0659394	+	1.58717i
$160$		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	$0.00984216\pi$
$167$			0.799023i			0.0618302i	−0.999522	+	0.0309151i	$0.990158\pi$
$168$	−8.58153	+	1.93562i	−0.662079	+	0.149336i
$169$	−1.54168			−0.118590
$170$		0			0
$171$	−1.00377	−	12.0596i	−0.0767601	−	0.922221i
$172$	6.26620	−	3.61779i	0.477793	−	0.275854i
$173$	−12.5737	−	7.25944i	−0.955962	−	0.551925i	−0.0610338	−	0.998136i	$-0.519440\pi$
$173$	−12.5737	−	7.25944i	−0.955962	−	0.551925i	−0.894928	+	0.446211i	$0.852773\pi$
$174$	−12.1187	−	19.1116i	−0.918719	−	1.44884i
$175$		0			0
$176$			2.29830i			0.173241i
$177$	−0.701796	−	16.8924i	−0.0527502	−	1.26971i
$178$	−2.28965	−	3.96579i	−0.171617	−	0.297249i
$179$	2.04442	−	1.18035i	0.152807	−	0.0882234i	−0.421647	−	0.906760i	$-0.638548\pi$
$179$	2.04442	−	1.18035i	0.152807	−	0.0882234i	0.574454	+	0.818537i	$0.305214\pi$
$180$		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
$186$	−4.73461	+	9.04839i	−0.347158	+	0.663460i
$187$	−1.26938	+	2.19863i	−0.0928264	+	0.160780i
$188$			2.73643i			0.199575i
$189$	−10.1308	−	9.29337i	−0.736908	−	0.675993i
$190$		0			0
$191$	4.37389	+	2.52527i	0.316484	+	0.182722i	0.649824	−	0.760085i	$-0.274843\pi$
$191$	4.37389	+	2.52527i	0.316484	+	0.182722i	−0.333341	+	0.942807i	$0.608176\pi$
$192$	3.35331	+	1.75463i	0.242004	+	0.126630i
$193$	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	$-0.774075\pi$
$197$	−21.2925			−1.51703			−0.758516	+	0.651655i	$0.774075\pi$
$198$	−1.92489	+	1.33574i	−0.136796	+	0.0949270i
$199$	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
$201$	−1.58559	+	0.0658738i	−0.111839	+	0.00464638i
$202$	−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
$207$	−13.4668	+	1.12090i	−0.936007	+	0.0779076i
$208$	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
$213$	1.22534	−	2.34177i	0.0839591	−	0.160456i
$214$	−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
$219$	−0.560657	−	13.4951i	−0.0378857	−	0.911915i
$220$		0			0
$221$	16.1330	−	9.31439i	1.08522	−	0.626554i
$222$	−16.9904	+	0.705869i	−1.14032	+	0.0473748i
$223$	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	−0.790757	−	0.612130i	$-0.790313\pi$
$227$	−9.88387	+	5.70646i	−0.656016	+	0.378751i	0.134741	+	0.990881i	$0.456980\pi$
$228$	−2.80534	+	5.36134i	−0.185788	+	0.355063i
$229$	−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
$231$	1.55335	−	1.43393i	0.102203	−	0.0943457i
$232$		−	14.8153i		−	0.972672i
$233$	1.94244	−	3.36441i	0.127254	−	0.220410i	−0.795358	−	0.606140i	$-0.792717\pi$
$233$	1.94244	−	3.36441i	0.127254	−	0.220410i	0.922612	+	0.385730i	$0.126050\pi$
$234$	17.1327	−	1.42602i	1.12000	−	0.0932220i
$235$		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	$-0.933601\pi$
$239$		−	6.40306i		−	0.414180i	0.978322	−	0.207090i	$-0.0663993\pi$
$240$		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
$243$	−11.6036	+	10.4095i	−0.744370	+	0.667767i
$244$			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
$249$	14.1035	−	26.9534i	0.893772	−	1.70810i
$250$		0			0
$251$	13.3221			0.840886			0.420443	−	0.907319i	$-0.361875\pi$
$251$	13.3221			0.840886			0.420443	+	0.907319i	$0.361875\pi$
$252$	1.78957	+	6.63717i	0.112732	+	0.418102i
$253$		−	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	−0.133436	−	0.991057i	$-0.542601\pi$
$257$	−16.9680	−	9.79648i	−1.05844	−	0.611088i	−0.924999	+	0.379969i	$0.875934\pi$
$258$	13.1190	+	20.6889i	0.816750	+	1.28804i
$259$	15.0947	−	2.75180i	0.937937	−	0.170988i
$260$		0			0
$261$	19.0215	−	13.1996i	1.17740	−	0.817035i
$262$	−5.69296	−	9.86050i	−0.351712	−	0.609184i
$263$	−8.38678	−	14.5263i	−0.517151	−	0.895732i	−0.999802	−	0.0199186i	$-0.993659\pi$
$263$	−8.38678	−	14.5263i	−0.517151	−	0.895732i	0.482651	−	0.875813i	$-0.339674\pi$
$264$	−1.53255	+	0.0636701i	−0.0943220	+	0.00391863i
$265$		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	$-0.814224\pi$
$269$	−14.6703	−	25.4097i	−0.894465	−	1.54926i	−0.0599988	−	0.998198i	$-0.519110\pi$
$270$		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
$273$	−15.1319	+	3.41310i	−0.915827	+	0.206570i
$274$	34.4460			2.08096
$275$		0			0
$276$	5.98694	+	3.13269i	0.360371	+	0.188566i
$277$	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	$0.196892\pi$
$281$			19.4404i			1.15972i	−0.814717	+	0.579859i	$0.803108\pi$
$282$	−9.25683	+	0.384577i	−0.551236	+	0.0229012i
$283$	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
$291$	6.81775	+	3.56741i	0.399663	+	0.209126i
$292$	−3.37685	+	5.84888i	−0.197615	+	0.342280i
$293$			21.5754i			1.26045i	0.776412	+	0.630226i	$0.217038\pi$
$293$			21.5754i			1.26045i	−0.776412	+	0.630226i	$0.782962\pi$
$294$	−8.03409	−	18.8882i	−0.468557	−	1.10158i
$295$		0			0
$296$	−9.64129	−	5.56640i	−0.560389	−	0.323541i
$297$	−1.44716	−	1.91093i	−0.0839730	−	0.110883i
$298$	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
$303$	−0.196739	−	4.73555i	−0.0113024	−	0.272050i
$304$	−17.4041	+	10.0482i	−0.998191	+	0.576306i
$305$		0			0
$306$	22.9632	−	15.9349i	1.31272	−	0.910935i
$307$	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	0.842482	−	0.538725i	$-0.181094\pi$
$311$	−0.799023	−	1.38395i	−0.0453084	−	0.0784765i	−0.887790	+	0.460248i	$0.847760\pi$
$312$	9.97245	+	5.21813i	0.564579	+	0.295418i
$313$	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	−0.943318	−	0.331891i	$-0.892313\pi$
$317$	−3.28018	+	5.68143i	−0.184233	+	0.319101i	0.759085	+	0.650992i	$0.225647\pi$
$318$	30.0463	+	15.7219i	1.68491	+	0.881638i
$319$	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
$324$	7.68735	−	1.28862i	0.427075	−	0.0715903i
$325$		0			0
$326$	−8.06940	+	4.65887i	−0.446923	+	0.258031i
$327$	−0.563181	−	13.5559i	−0.0311440	−	0.749642i
$328$	−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
$333$	−1.44310	−	17.3379i	−0.0790815	−	0.950110i
$334$	1.17147	+	0.676351i	0.0641002	+	0.0370083i
$335$		0			0
$336$	−6.78520	+	21.7991i	−0.370163	+	1.18924i
$337$			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
$339$	26.6898	+	13.9655i	1.44959	+	0.758504i
$340$		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	0.951689	−	0.307064i	$-0.0993465\pi$
$347$	3.91036	+	6.77295i	0.209919	+	0.363591i	−0.741770	+	0.670655i	$0.766013\pi$
$348$	−11.5669	+	0.480550i	−0.620052	+	0.0257602i
$349$			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	−0.189837	−	0.981816i	$-0.560796\pi$
$353$	10.6252	−	6.13445i	0.565521	−	0.326504i	0.755359	+	0.655312i	$0.227463\pi$
$354$	−25.3605	−	13.2700i	−1.34790	−	0.705292i
$355$		0			0
$356$	−2.34265			−0.124160
$357$	−18.5309	+	17.1062i	−0.980757	+	0.905356i
$358$		−	3.99653i		−	0.211223i
$359$	7.11574	+	4.10828i	0.375555	+	0.216827i	0.675882	−	0.737010i	$-0.263763\pi$
$359$	7.11574	+	4.10828i	0.375555	+	0.216827i	−0.300328	+	0.953836i	$0.597096\pi$
$360$		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
$366$	−23.3644	+	0.970679i	−1.22128	+	0.0507382i
$367$	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
$369$	−10.7020	−	15.4223i	−0.557125	−	0.802853i
$370$		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
$378$	−22.2008	+	6.98655i	−1.14189	+	0.359349i
$379$	−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
$381$	10.0823	−	19.2685i	0.516534	−	0.987157i
$382$	7.40476	−	4.27514i	0.378861	−	0.218735i
$383$	−11.1972	−	6.46470i	−0.572150	−	0.330331i	0.185858	−	0.982577i	$-0.440494\pi$
$383$	−11.1972	−	6.46470i	−0.572150	−	0.330331i	−0.758008	+	0.652246i	$0.773827\pi$
$384$	18.8537	−	11.9552i	0.962126	−	0.610089i
$385$		0			0
$386$		−	22.1838i		−	1.12912i
$387$	−20.5914	+	14.2890i	−1.04672	+	0.726352i
$388$	−1.92376	−	3.33205i	−0.0976642	−	0.169159i
$389$	−16.4024	+	9.46992i	−0.831634	+	0.480144i	−0.854412	−	0.519596i	$-0.826082\pi$
$389$	−16.4024	+	9.46992i	−0.831634	+	0.480144i	0.0227777	+	0.999741i	$0.492749\pi$
$390$		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
$396$	0.0994198	+	1.19446i	0.00499603	+	0.0600239i
$397$	−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
$399$	17.6498	+	5.49369i	0.883596	+	0.275028i
$400$		0			0
$401$	−13.7394	−	7.93243i	−0.686111	−	0.396126i	0.116042	−	0.993244i	$-0.462979\pi$
$401$	−13.7394	−	7.93243i	−0.686111	−	0.396126i	−0.802154	+	0.597118i	$0.796312\pi$
$402$	−1.24558	+	2.38045i	−0.0621240	+	0.118726i
$403$	−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
$408$	18.2827	−	0.759558i	0.905129	−	0.0376037i
$409$	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
$411$	1.46286	+	35.2113i	0.0721575	+	1.73684i
$412$	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
$417$	−7.86278	+	15.0267i	−0.385042	+	0.735860i
$418$	1.57515	−	2.72824i	0.0770432	−	0.133443i
$419$	14.3499			0.701039			0.350519	−	0.936555i	$-0.386005\pi$
$419$	14.3499			0.701039			0.350519	+	0.936555i	$0.386005\pi$
$420$		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
$423$	−0.786241	−	9.44616i	−0.0382284	−	0.459288i
$424$	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
$429$	−2.70237	+	0.112271i	−0.130472	+	0.00542047i
$430$		0			0
$431$	−7.13983	+	4.12218i	−0.343914	+	0.198559i	−0.662001	−	0.749503i	$-0.730293\pi$
$431$	−7.13983	+	4.12218i	−0.343914	+	0.198559i	0.318088	+	0.948061i	$0.396959\pi$
$432$	23.8537	+	10.0581i	1.14766	+	0.483919i
$433$	−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
$438$	−20.2602	−	10.6013i	−0.968071	−	0.506548i
$439$	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
$441$	18.9667	−	9.01472i	0.903175	−	0.429273i
$442$		−	31.5375i		−	1.50009i
$443$	8.72667	−	15.1150i	0.414617	−	0.718137i	−0.580772	−	0.814067i	$-0.697249\pi$
$443$	8.72667	−	15.1150i	0.414617	−	0.718137i	0.995388	+	0.0959297i	$0.0305824\pi$
$444$	−4.03319	+	7.70791i	−0.191407	+	0.365801i
$445$		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	$0.0936346\pi$
$449$			12.2873i			0.579876i	−0.957046	+	0.289938i	$0.906365\pi$
$450$		0			0
$451$	2.49985	−	1.44329i	0.117713	−	0.0679618i
$452$	−7.53105	−	13.0442i	−0.354231	−	0.613546i
$453$	1.08470	+	26.1090i	0.0509637	+	1.22671i
$454$			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
$459$	17.2641	+	22.7966i	0.805818	+	1.06405i
$460$		0			0
$461$	5.12746			0.238810			0.119405	−	0.992846i	$-0.461901\pi$
$461$	5.12746			0.238810			0.119405	+	0.992846i	$0.461901\pi$
$462$	−0.787463	−	3.49121i	−0.0366361	−	0.162426i
$463$			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	0.671592	−	0.740922i	$-0.265611\pi$
$467$	7.90350	+	4.56309i	0.365730	+	0.211155i	−0.305861	+	0.952076i	$0.598944\pi$
$468$	3.75054	−	7.95516i	0.173369	−	0.367727i
$469$	0.815897	−	2.28269i	0.0376746	−	0.105405i
$470$		0			0
$471$	0.895198	+	21.5476i	0.0412486	+	0.992860i
$472$	−9.36925	−	16.2280i	−0.431254	−	0.746955i
$473$	−1.92704	−	3.33773i	−0.0886053	−	0.153469i
$474$	0.872760	+	21.0075i	0.0400872	+	0.964907i
$475$		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	0.688834	−	0.724919i	$-0.258123\pi$
$479$	−6.20210	−	10.7424i	−0.283381	−	0.490831i	−0.972215	+	0.234088i	$0.924790\pi$
$480$		0			0
$481$	−17.0006	−	9.81532i	−0.775162	−	0.447540i
$482$		−	3.83332i		−	0.174603i
$483$	6.13473	−	19.7093i	0.279140	−	0.896805i
$484$	9.34243			0.424656
$485$		0			0
$486$	5.43955	+	25.8237i	0.246743	+	1.17139i
$487$	−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	$0.258074\pi$
$491$			32.1216i			1.44963i	−0.688946	+	0.724813i	$0.741926\pi$
$492$	0.389621	+	9.37826i	0.0175655	+	0.422805i
$493$	−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
$501$	−0.641627	+	1.22622i	−0.0286658	+	0.0547837i
$502$	11.2768	−	19.5320i	0.503310	−	0.871758i
$503$			9.55539i			0.426054i	0.977046	+	0.213027i	$0.0683322\pi$
$503$			9.55539i			0.426054i	−0.977046	+	0.213027i	$0.931668\pi$
$504$	−14.7240	−	3.92059i	−0.655860	−	0.174637i
$505$		0			0
$506$	−3.04659	−	1.75895i	−0.135438	−	0.0781950i
$507$	−2.36594	−	1.23799i	−0.105075	−	0.0549810i
$508$	−9.41716	+	5.43700i	−0.417819	+	0.241228i
$509$	9.10071	−	15.7629i	0.403382	−	0.698678i	−0.590750	−	0.806855i	$-0.701168\pi$
$509$	9.10071	−	15.7629i	0.403382	−	0.698678i	0.994132	+	0.108177i	$0.0345013\pi$
$510$		0			0
$511$	19.4282	+	6.94417i	0.859452	+	0.307192i
$512$	−3.76451			−0.166369
$513$	8.14360	−	19.3134i	0.359549	−	0.852706i
$514$	−28.7259	+	16.5849i	−1.26705	+	0.731530i
$515$		0			0
$516$	12.5216	−	0.520212i	0.551232	−	0.0229010i
$517$	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	0.820460	−	0.571703i	$-0.193717\pi$
$521$	−1.93741	−	3.35569i	−0.0848794	−	0.147015i	−0.905340	+	0.424688i	$0.860384\pi$
$522$	−3.25122	−	39.0612i	−0.142302	−	1.70966i
$523$	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
$528$	−1.84557	+	3.52711i	−0.0803183	+	0.153498i
$529$	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
$534$	−0.329235	−	7.92475i	−0.0142474	−	0.342937i
$535$		0			0
$536$	−1.52324	+	0.879440i	−0.0657937	+	0.0379860i
$537$	4.08532	−	0.169725i	0.176295	−	0.00732419i
$538$	−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
$543$	−7.79483	+	14.8968i	−0.334508	+	0.639285i
$544$	−21.8997	−	12.6438i	−0.938944	−	0.542099i
$545$		0			0
$546$	−7.80472	+	25.0746i	−0.334011	+	1.07309i
$547$			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
$549$	−1.98449	−	23.8423i	−0.0846959	−	1.01756i
$550$		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	0.889492	−	0.456950i	$-0.151058\pi$
$557$	1.15681	+	2.00365i	0.0490155	+	0.0848973i	−0.840477	+	0.541848i	$0.817725\pi$
$558$	−14.5320	+	10.0842i	−0.615188	+	0.426898i
$559$			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	−0.793298	−	0.608833i	$-0.791638\pi$
$563$	−15.7239	+	9.07818i	−0.662682	+	0.382600i	0.130616	+	0.991433i	$0.458304\pi$
$564$	−2.19740	+	4.19948i	−0.0925270	+	0.176830i
$565$		0			0
$566$	9.54745			0.401309
$567$	−8.08459	−	22.3973i	−0.339521	−	0.940599i
$568$		−	2.92930i		−	0.122911i
$569$	12.9811	+	7.49465i	0.544197	+	0.314192i	0.746778	−	0.665073i	$-0.231600\pi$
$569$	12.9811	+	7.49465i	0.544197	+	0.314192i	−0.202581	+	0.979265i	$0.564933\pi$
$570$		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
$576$	3.73718	+	5.38551i	0.155716	+	0.224396i
$577$	−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
$579$	22.6766	−	0.942104i	0.942408	−	0.0391525i
$580$		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	$0.397638\pi$
$587$			45.9722i			1.89748i	−0.316065	+	0.948738i	$0.602362\pi$
$588$	−10.4232	−	1.27197i	−0.429845	−	0.0524553i
$589$	14.0484			0.578856
$590$		0			0
$591$	−32.6767	−	17.0982i	−1.34414	−	0.703327i
$592$	−25.0215	+	14.4462i	−1.02838	+	0.593735i
$593$	2.68984	+	1.55298i	0.110458	+	0.0637732i	0.554211	−	0.832376i	$-0.313020\pi$
$593$	2.68984	+	1.55298i	0.110458	+	0.0637732i	−0.443753	+	0.896149i	$0.646353\pi$
$594$	−4.02666	+	0.504187i	−0.165216	+	0.0206871i
$595$		0			0
$596$		−	14.1202i		−	0.578385i
$597$	11.5695	−	0.480657i	0.473508	−	0.0196720i
$598$	12.9067	+	22.3551i	0.527795	+	0.914168i
$599$	−7.34708	+	4.24184i	−0.300193	+	0.173317i	−0.642530	−	0.766261i	$-0.722115\pi$
$599$	−7.34708	+	4.24184i	−0.300193	+	0.173317i	0.342336	+	0.939577i	$0.388782\pi$
$600$		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
$606$	−7.10949	−	3.72007i	−0.288803	−	0.151118i
$607$	−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
$609$	7.78159	+	34.4996i	0.315326	+	1.39799i
$610$		0			0
$611$	−9.26241	−	5.34766i	−0.374717	−	0.216343i
$612$	−1.18604	−	14.2494i	−0.0479427	−	0.575999i
$613$	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	$-0.572770\pi$
$617$	−11.2586			−0.453254			−0.226627	+	0.973982i	$0.572770\pi$
$618$	2.24336	+	53.9982i	0.0902414	+	2.17213i
$619$	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
$621$	−21.5670	−	9.09385i	−0.865454	−	0.364924i
$622$	−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
$627$	2.85575	+	1.49428i	0.114048	+	0.0596759i
$628$	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
$633$	8.78063	+	4.59450i	0.348999	+	0.182615i
$634$	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
$639$	3.76096	−	2.60984i	0.148781	−	0.103244i
$640$		0			0
$641$	2.08690	−	1.20488i	0.0824278	−	0.0475897i	−0.458220	−	0.888839i	$-0.651513\pi$
$641$	2.08690	−	1.20488i	0.0824278	−	0.0475897i	0.540647	+	0.841249i	$0.318179\pi$
$642$	−0.809774	−	19.4914i	−0.0319592	−	0.769265i
$643$	−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	−0.242775	−	0.970083i	$-0.578058\pi$
$647$	12.1065	−	6.98967i	0.475954	−	0.274792i	0.718729	+	0.695291i	$0.244724\pi$
$648$	−6.04609	+	16.1847i	−0.237513	+	0.635797i
$649$	3.89972	+	2.25150i	0.153077	+	0.0883792i
$650$		0			0
$651$	11.7270	−	10.8255i	0.459619	−	0.424283i
$652$			4.76671i			0.186679i
$653$	−3.42169	+	5.92653i	−0.133901	+	0.231923i	−0.925177	−	0.379536i	$-0.876084\pi$
$653$	−3.42169	+	5.92653i	−0.133901	+	0.231923i	0.791276	+	0.611459i	$0.209417\pi$
$654$	−20.3515	−	10.6490i	−0.795805	−	0.416408i
$655$		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	$0.0628616\pi$
$659$			10.0735i			0.392409i	−0.980563	+	0.196204i	$0.937138\pi$
$660$		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
$663$	32.2382	−	1.33934i	1.25203	−	0.0520157i
$664$		−	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
$669$	8.95461	+	4.68554i	0.346205	+	0.181153i
$670$		0			0
$671$	3.67895			0.142024
$672$	14.2828	+	15.4723i	0.550972	+	0.596858i
$673$			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	0.432373	−	0.901695i	$-0.357676\pi$
$677$	−3.44314	−	1.98790i	−0.132331	−	0.0764011i	−0.564704	+	0.825294i	$0.691010\pi$
$678$	43.0675	−	27.3094i	1.65400	−	1.04881i
$679$	−8.96006	+	7.60721i	−0.343855	+	0.291938i
$680$		0			0
$681$	−19.7507	+	0.820547i	−0.756849	+	0.0314434i
$682$	−1.35997	−	2.35553i	−0.0520759	−	0.0901981i
$683$	−5.32313	−	9.21993i	−0.203684	−	0.352791i	0.746029	−	0.665914i	$-0.231958\pi$
$683$	−5.32313	−	9.21993i	−0.203684	−	0.352791i	−0.949713	+	0.313123i	$0.898625\pi$
$684$	−8.61047	+	5.97507i	−0.329229	+	0.228463i
$685$		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
$693$	3.53533	−	0.953223i	0.134296	−	0.0362099i
$694$	13.2401			0.502586
$695$		0			0
$696$	11.8969	−	22.7364i	0.450951	−	0.861820i
$697$	−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	$-0.879502\pi$
$701$		−	19.5702i		−	0.739158i	0.929199	−	0.369579i	$-0.120498\pi$
$702$	27.4379	+	11.5694i	1.03558	+	0.436657i
$703$	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
$711$	−21.4372	+	1.78430i	−0.803956	+	0.0669165i
$712$	2.59631	−	4.49694i	0.0973009	−	0.168530i
$713$		−	15.6877i		−	0.587509i
$714$	9.39411	+	41.6487i	0.351566	+	1.55866i
$715$		0			0
$716$	−1.77061	−	1.02226i	−0.0661707	−	0.0382037i
$717$	5.14176	−	9.82650i	0.192022	−	0.366977i
$718$	12.0466	−	6.95509i	0.449574	−	0.259562i
$719$	−9.75873	+	16.9026i	−0.363939	+	0.630361i	−0.988605	−	0.150531i	$-0.951902\pi$
$719$	−9.75873	+	16.9026i	−0.363939	+	0.630361i	0.624666	+	0.780892i	$0.285235\pi$
$720$		0			0
$721$	−8.74566	−	47.9733i	−0.325705	−	1.78662i
$722$	−4.61959			−0.171923
$723$	3.91849	−	0.162794i	0.145730	−	0.00605438i
$724$	7.28057	−	4.20344i	0.270580	−	0.156220i
$725$		0			0
$726$	1.31298	+	31.6037i	0.0487293	+	1.17292i
$727$	−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
$732$	−5.54627	+	10.5996i	−0.204996	+	0.391771i
$733$	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
$738$	−31.6701	+	2.63603i	−1.16579	+	0.0970337i
$739$	−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	$-0.327670\pi$
$743$	28.0937			1.03066			0.515330	+	0.856992i	$0.327670\pi$
$744$	−11.5700	+	0.480678i	−0.424177	+	0.0176225i
$745$		0			0
$746$	26.5135	−	15.3076i	0.970729	−	0.560451i
$747$	43.2880	−	30.0389i	1.58382	−	1.09907i
$748$	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
$753$	20.4449	+	10.6979i	0.745053	+	0.389852i
$754$	−38.3014	−	22.1133i	−1.39485	−	0.805319i
$755$		0			0
$756$	−2.58338	+	11.6228i	−0.0939566	+	0.422718i
$757$		−	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
$759$	1.66865	−	3.18898i	0.0605680	−	0.115753i
$760$		0			0
$761$	26.3374	−	45.6178i	0.954731	−	1.65364i	0.219750	−	0.975556i	$-0.429476\pi$
$761$	26.3374	−	45.6178i	0.954731	−	1.65364i	0.734982	−	0.678087i	$-0.237191\pi$
$762$	−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
$768$	−1.25463	−	30.1992i	−0.0452725	−	1.08972i
$769$		−	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	−0.461310	−	0.887239i	$-0.652620\pi$
$773$	2.12434	−	1.22649i	0.0764073	−	0.0441138i	0.537717	+	0.843125i	$0.319287\pi$
$774$	3.51956	+	42.2851i	0.126508	+	1.51991i
$775$		0			0
$776$	8.52826			0.306147
$777$	25.3749	+	7.89819i	0.910318	+	0.283346i
$778$			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
$786$	−0.818606	−	19.7040i	−0.0291987	−	0.702818i
$787$	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
$789$	−1.20596	−	29.0276i	−0.0429332	−	1.03341i
$790$		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	$0.227017\pi$
$797$			36.9407i			1.30851i	−0.756276	+	0.654253i	$0.772983\pi$
$798$	22.9946	−	21.2267i	0.814000	−	0.751419i
$799$	−17.3883			−0.615154
$800$		0			0
$801$	8.08683	−	0.673099i	0.285734	−	0.0237828i
$802$	−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
$807$	−2.10948	−	50.7756i	−0.0742573	−	1.78739i
$808$	−2.62655	−	4.54931i	−0.0924016	−	0.160044i
$809$	45.9461	−	26.5270i	1.61538	−	0.932640i	0.627285	−	0.778790i	$-0.284166\pi$
$809$	45.9461	−	26.5270i	1.61538	−	0.932640i	0.988094	−	0.153850i	$-0.0491672\pi$
$810$		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
$816$	22.0169	−	42.0769i	0.770747	−	1.47299i
$817$	16.8501	−	29.1852i	0.589511	−	1.02106i
$818$		−	44.5918i		−	1.55912i
$819$	−25.9631	−	6.91324i	−0.907223	−	0.241568i
$820$		0			0
$821$	−9.46302	−	5.46348i	−0.330262	−	0.190677i	0.325696	−	0.945475i	$-0.394402\pi$
$821$	−9.46302	−	5.46348i	−0.330262	−	0.190677i	−0.655957	+	0.754798i	$0.727735\pi$
$822$	52.8627	+	27.6606i	1.84380	+	0.964776i
$823$	−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	$-0.374385\pi$
$827$	22.1128			0.768937			0.384468	+	0.923138i	$0.374385\pi$
$828$	6.67229	+	9.61520i	0.231878	+	0.334151i
$829$	−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
$831$	22.5412	−	0.936477i	0.781944	−	0.0324860i
$832$	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
$837$	−10.9254	−	14.4266i	−0.377636	−	0.498655i
$838$	12.1468	−	21.0389i	0.419605	−	0.726777i
$839$	−8.65688			−0.298869			−0.149434	−	0.988772i	$-0.547745\pi$
$839$	−8.65688			−0.298869			−0.149434	+	0.988772i	$0.547745\pi$
$840$		0			0
$841$	−30.5607			−1.05382
$842$	−8.52225	+	14.7610i	−0.293696	+	0.508696i
$843$	−15.6109	+	29.8343i	−0.537669	+	1.02755i
$844$	−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
$849$	0.405463	+	9.75956i	0.0139154	+	0.334947i
$850$		0			0
$851$	22.6228	−	13.0613i	0.775501	−	0.447736i
$852$	−2.28703	+	0.0950150i	−0.0783523	+	0.00325516i
$853$	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	0.0884274	−	0.996083i	$-0.471816\pi$
$857$	29.1362	−	16.8218i	0.995274	−	0.574622i	0.906847	+	0.421461i	$0.138483\pi$
$858$	−2.12288	+	4.05708i	−0.0724740	+	0.138506i
$859$	−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
$861$	27.9717	−	6.30918i	0.953272	−	0.215016i
$862$			13.9573i			0.475387i
$863$	−19.6742	+	34.0767i	−0.669718	+	1.15998i	0.308265	+	0.951300i	$0.400252\pi$
$863$	−19.6742	+	34.0767i	−0.669718	+	1.15998i	−0.977983	+	0.208685i	$0.933082\pi$
$864$	19.0340	−	14.4146i	0.647550	−	0.490396i
$865$		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
$873$	7.59820	+	10.9495i	0.257160	+	0.370585i
$874$		−	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
$879$	−17.3254	+	33.1109i	−0.584371	+	1.11680i
$880$		0			0
$881$	13.2055			0.444904			0.222452	−	0.974944i	$-0.428594\pi$
$881$	13.2055			0.444904			0.222452	+	0.974944i	$0.428594\pi$
$882$	2.83798	−	35.4384i	0.0955598	−	1.19327i
$883$			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	−0.0619524	−	0.998079i	$-0.519733\pi$
$887$	−28.5105	−	16.4606i	−0.957290	−	0.552692i	−0.895338	+	0.445387i	$0.853066\pi$
$888$	−10.3262	−	16.2846i	−0.346523	−	0.546476i
$889$	21.4997	+	25.3232i	0.721078	+	0.849313i
$890$		0			0
$891$	−0.686394	−	4.09471i	−0.0229951	−	0.137178i
$892$	−2.52672	−	4.37641i	−0.0846009	−	0.146533i
$893$	6.37256	+	11.0376i	0.213250	+	0.369359i
$894$	47.7659	−	1.98444i	1.59753	−	0.0663697i
$895$		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
$903$	−8.42384	−	37.3470i	−0.280328	−	1.24283i
$904$	33.3860			1.11040
$905$		0			0
$906$	39.1974	+	20.5102i	1.30225	+	0.681406i
$907$	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	$-0.687147\pi$
$911$		−	50.2293i		−	1.66417i	0.554648	−	0.832085i	$-0.312853\pi$
$912$	−34.7781	+	1.44486i	−1.15162	+	0.0478442i
$913$	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
$921$	35.1878	+	18.4121i	1.15948	+	0.606701i
$922$	4.34026	−	7.51755i	0.142939	−	0.247577i
$923$		−	5.16529i		−	0.170017i
$924$	−1.74815	−	0.544131i	−0.0575100	−	0.0179006i
$925$		0			0
$926$	58.5095	+	33.7805i	1.92274	+	1.11009i
$927$	−55.1026	+	4.58641i	−1.80981	+	0.150637i
$928$	−30.7111	+	17.7310i	−1.00814	+	0.582050i
$929$	1.84133	−	3.18927i	0.0604119	−	0.104637i	−0.834238	−	0.551405i	$-0.814092\pi$
$929$	1.84133	−	3.18927i	0.0604119	−	0.104637i	0.894650	+	0.446769i	$0.147425\pi$
$930$		0			0
$931$	−17.8983	+	21.8390i	−0.586594	+	0.715745i
$932$	−3.36457			−0.110210
$933$	−0.114894	−	2.76551i	−0.00376145	−	0.0905387i
$934$	13.3802	−	7.72506i	0.437814	−	0.252772i
$935$		0			0
$936$	11.1140	+	16.0161i	0.363274	+	0.523501i
$937$	−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	0.982410	−	0.186739i	$-0.0597917\pi$
$941$	10.1072	+	17.5061i	0.329484	+	0.570684i	−0.652925	+	0.757422i	$0.726458\pi$
$942$	32.3494	+	16.9270i	1.05400	+	0.551511i
$943$	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	−0.934729	−	0.355361i	$-0.884358\pi$
$947$	−4.91182	+	8.50752i	−0.159613	+	0.276457i	0.775116	+	0.631819i	$0.217691\pi$
$948$	9.53032	+	4.98678i	0.309530	+	0.161963i
$949$	−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	$-0.631215\pi$
$953$	−24.7365			−0.801294			−0.400647	+	0.916232i	$0.631215\pi$
$954$	33.4858	+	48.2552i	1.08414	+	1.56232i
$955$		0			0
$956$	−4.80253	+	2.77274i	−0.155325	+	0.0896769i
$957$	0.255968	+	6.16119i	0.00827426	+	0.199163i
$958$	−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
$963$	19.8901	−	1.65553i	0.640948	−	0.0533487i
$964$	−1.69830	−	0.980514i	−0.0546986	−	0.0315802i
$965$		0			0
$966$	−23.7036	−	25.6778i	−0.762652	−	0.826168i
$967$		−	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
$969$	−34.0679	−	17.8262i	−1.09442	−	0.572660i
$970$		0			0
$971$	−0.0308306	+	0.0534003i	−0.000989403	+	0.00171370i	−0.866520	−	0.499143i	$-0.833648\pi$
$971$	−0.0308306	+	0.0534003i	−0.000989403	+	0.00171370i	0.865530	+	0.500857i	$0.166982\pi$
$972$	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	0.672098	−	0.740462i	$-0.265393\pi$
$977$	−9.53996	−	16.5237i	−0.305210	−	0.528640i	−0.977308	+	0.211822i	$0.932060\pi$
$978$	−16.1249	+	0.669912i	−0.515617	+	0.0214214i
$979$			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	−0.383259	−	0.923641i	$-0.625198\pi$
$983$	7.05465	−	4.07300i	0.225008	−	0.129909i	0.608267	+	0.793732i	$0.291865\pi$
$984$	−18.4343	−	9.64581i	−0.587663	−	0.307497i
$985$		0			0
$986$	−71.9030			−2.28986
$987$	13.8249	+	4.30315i	0.440052	+	0.136971i
$988$			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
$996$	−26.3233	+	1.09361i	−0.834086	+	0.0346522i
$997$	−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
$999$	11.7079	−	27.7665i	0.370422	−	0.878494i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.846473 - 1.46613i) q^{2} +(1.53466 + 0.803015i) q^{3} +(-0.433034 - 0.750036i) q^{4} +(2.47637 - 1.57028i) q^{6} +(-2.01688 + 1.71236i) q^{7} +1.91969 q^{8} +(1.71033 + 2.46470i) q^{9} +O(q^{10})\)	\(q+(0.846473 - 1.46613i) q^{2} +(1.53466 + 0.803015i) q^{3} +(-0.433034 - 0.750036i) q^{4} +(2.47637 - 1.57028i) q^{6} +(-2.01688 + 1.71236i) q^{7} +1.91969 q^{8} +(1.71033 + 2.46470i) q^{9} +(-0.399511 + 0.230658i) q^{11} +(-0.0622670 - 1.49878i) q^{12} +3.38501 q^{13} +(0.803314 + 4.40649i) q^{14} +(2.49103 - 4.31459i) q^{16} +(4.76601 - 2.75166i) q^{17} +(5.06134 - 0.421275i) q^{18} +(-3.49334 - 2.01688i) q^{19} +(-4.47027 + 1.00830i) q^{21} +0.780983i q^{22} +(-2.25223 + 3.90097i) q^{23} +(2.94606 + 1.54154i) 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} +(-0.798334 + 0.0331669i) q^{33} -9.31681i q^{34} +(1.10798 - 2.35011i) q^{36} +(-5.02232 - 2.89964i) q^{37} +(-5.91404 + 3.41448i) q^{38} +(5.19483 + 2.71822i) q^{39} -6.25727 q^{41} +(-2.30567 + 7.40752i) 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} +(9.52380 - 0.395668i) q^{51} +(-1.46582 - 2.53888i) q^{52} +(5.78238 + 10.0154i) q^{53} +(8.10570 + 3.41782i) 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} +(-7.67001 - 2.04231i) q^{63} +2.18506 q^{64} +(-0.627141 + 1.19854i) q^{66} +(-0.793481 + 0.458116i) q^{67} +(-4.12768 - 2.38312i) q^{68} +(-6.58893 + 4.17808i) q^{69} -1.52593i q^{71} +(3.28331 + 4.73146i) 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} +(-3.14952 + 8.43093i) q^{81} +(-5.29661 + 9.17399i) q^{82} -17.5632i q^{83} +(2.69204 + 2.91624i) q^{84} +(12.2489 + 7.07188i) q^{86} +(6.19732 - 11.8438i) q^{87} +(-0.766937 + 0.442791i) q^{88} +(1.35247 - 2.34254i) q^{89} +(-6.82718 + 5.79637i) q^{91} +3.90116 q^{92} +(-6.02703 + 0.250394i) q^{93} +(-4.63241 + 2.67452i) q^{94} +(-0.330363 - 7.95189i) 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

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Database

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