LMFDB - Embedded newform 525.2.t.i.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

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, 0, 5]))

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

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

chi := DirichletCharacter("525.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 18 x^{16} - 45 x^{15} + 59 x^{14} - 147 x^{13} + 271 x^{12} + \cdots + 59049 $ x^20 - 3x^19 + 8x^18 - 15x^17 + 18x^16 - 45x^15 + 59x^14 - 147x^13 + 271x^12 - 330x^11 + 879x^10 - 990x^9 + 2439x^8 - 3969x^7 + 4779x^6 - 10935x^5 + 13122x^4 - 32805x^3 + 52488x^2 - 59049*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Root			$0.803015 + 1.53466i$ of defining polynomial
Character	$\chi$	$=$	525.101
Dual form			525.2.t.i.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46613 + 0.846473i) q^{2} +(1.73056 - 0.0718963i) q^{3} +(0.433034 - 0.750036i) q^{4} +(-2.47637 + 1.57028i) q^{6} +(-1.71236 + 2.01688i) q^{7} -1.91969i q^{8} +(2.98966 - 0.248842i) q^{9} +O(q^{10})$	\(q+(-1.46613 + 0.846473i) q^{2} +(1.73056 - 0.0718963i) q^{3} +(0.433034 - 0.750036i) q^{4} +(-2.47637 + 1.57028i) q^{6} +(-1.71236 + 2.01688i) q^{7} -1.91969i q^{8} +(2.98966 - 0.248842i) q^{9} +(0.399511 + 0.230658i) q^{11} +(0.695465 - 1.32911i) q^{12} +3.38501i q^{13} +(0.803314 - 4.40649i) q^{14} +(2.49103 + 4.31459i) q^{16} +(-2.75166 + 4.76601i) q^{17} +(-4.17261 + 2.89550i) q^{18} +(3.49334 - 2.01688i) q^{19} +(-2.81833 + 3.61345i) q^{21} -0.780983 q^{22} +(-3.90097 + 2.25223i) q^{23} +(-0.138018 - 3.32213i) q^{24} +(-2.86532 - 4.96289i) q^{26} +(5.15589 - 0.645580i) q^{27} +(0.771225 + 2.15771i) q^{28} +7.71756i q^{29} +(-3.01611 - 1.74135i) q^{31} +(-3.97938 - 2.29749i) q^{32} +(0.707961 + 0.370444i) q^{33} -9.31681i q^{34} +(1.10798 - 2.35011i) q^{36} +(2.89964 + 5.02232i) q^{37} +(-3.41448 + 5.91404i) q^{38} +(0.243370 + 5.85796i) q^{39} +6.25727 q^{41} +(1.07337 - 7.68344i) q^{42} +8.35453 q^{43} +(0.346004 - 0.199765i) q^{44} +(3.81290 - 6.60414i) q^{46} +(-1.57980 - 2.73630i) q^{47} +(4.62108 + 7.28756i) q^{48} +(-1.13564 - 6.90727i) q^{49} +(-4.41924 + 8.44568i) q^{51} +(2.53888 + 1.46582i) q^{52} +(-10.0154 - 5.78238i) q^{53} +(-7.01277 + 5.31083i) q^{54} +(3.87179 + 3.28720i) q^{56} +(5.90043 - 3.74149i) q^{57} +(-6.53271 - 11.3150i) q^{58} +(-4.88061 + 8.45346i) q^{59} +(-6.90647 + 3.98746i) q^{61} +5.89604 q^{62} +(-4.61750 + 6.45591i) q^{63} -2.18506 q^{64} +(-1.35154 + 0.0561498i) q^{66} +(-0.458116 + 0.793481i) q^{67} +(2.38312 + 4.12768i) q^{68} +(-6.58893 + 4.17808i) q^{69} -1.52593i q^{71} +(-0.477698 - 5.73922i) q^{72} +(-6.75338 - 3.89906i) q^{73} +(-8.50252 - 4.90893i) q^{74} -3.49351i q^{76} +(-1.14932 + 0.410798i) q^{77} +(-5.31542 - 8.38256i) q^{78} +(3.58521 + 6.20977i) q^{79} +(8.87616 - 1.48790i) q^{81} +(-9.17399 + 5.29661i) q^{82} +17.5632 q^{83} +(1.48978 + 3.67860i) q^{84} +(-12.2489 + 7.07188i) q^{86} +(0.554864 + 13.3557i) q^{87} +(0.442791 - 0.766937i) q^{88} +(1.35247 + 2.34254i) q^{89} +(-6.82718 - 5.79637i) q^{91} +3.90116i q^{92} +(-5.34476 - 2.79667i) q^{93} +(4.63241 + 2.67452i) q^{94} +(-7.05172 - 3.68984i) q^{96} -4.44253i q^{97} +(7.51181 + 9.16569i) q^{98} +(1.25180 + 0.590174i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) $ 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9	$ 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9} - 21 q^{12} - 18 q^{16} + 14 q^{18} - 9 q^{21} + 20 q^{22} + 18 q^{24} - 10 q^{28} + 42 q^{31} + 12 q^{33} - 36 q^{36} + 24 q^{37} + 33 q^{42} + 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} - 84 q^{52} - 75 q^{54} + 6 q^{57} - 4 q^{58} - 90 q^{61} - 5 q^{63} - 120 q^{64} + 6 q^{66} + 20 q^{67} - 35 q^{72} - 48 q^{73} - 108 q^{78} + 46 q^{79} + 29 q^{81} + 36 q^{82} + 75 q^{84} + 69 q^{87} + 4 q^{88} - 30 q^{91} - 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) $ 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9 - 21 * q^12 - 18 * q^16 + 14 * q^18 - 9 * q^21 + 20 * q^22 + 18 * q^24 - 10 * q^28 + 42 * q^31 + 12 * q^33 - 36 * q^36 + 24 * q^37 + 33 * q^42 + 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 - 84 * q^52 - 75 * q^54 + 6 * q^57 - 4 * q^58 - 90 * q^61 - 5 * q^63 - 120 * q^64 + 6 * q^66 + 20 * q^67 - 35 * q^72 - 48 * q^73 - 108 * q^78 + 46 * q^79 + 29 * q^81 + 36 * q^82 + 75 * q^84 + 69 * q^87 + 4 * q^88 - 30 * q^91 - 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.46613	+	0.846473i	−1.03671	+	0.598547i	−0.918901	−	0.394489i	$-0.870922\pi$
$2$	−1.46613	+	0.846473i	−1.03671	+	0.598547i	−0.117813	+	0.993036i	$0.537588\pi$
$3$	1.73056	−	0.0718963i	0.999138	−	0.0415094i
$3$	1.73056	−	0.0718963i	0.999138	−	0.0415094i
$4$	0.433034	−	0.750036i	0.216517	−	0.375018i
$5$		0			0
$5$		0			0
$6$	−2.47637	+	1.57028i	−1.01097	+	0.641064i
$7$	−1.71236	+	2.01688i	−0.647212	+	0.762310i
$7$	−1.71236	+	2.01688i	−0.647212	+	0.762310i
$8$		−	1.91969i		−	0.678712i
$9$	2.98966	−	0.248842i	0.996554	−	0.0829472i
$10$		0			0
$11$	0.399511	+	0.230658i	0.120457	+	0.0695460i	0.559018	−	0.829156i	$-0.311178\pi$
$11$	0.399511	+	0.230658i	0.120457	+	0.0695460i	−0.438561	+	0.898702i	$0.644512\pi$
$12$	0.695465	−	1.32911i	0.200763	−	0.383682i
$13$			3.38501i			0.938834i	0.882977	+	0.469417i	$0.155536\pi$
$13$			3.38501i			0.938834i	−0.882977	+	0.469417i	$0.844464\pi$
$14$	0.803314	−	4.40649i	0.214695	−	1.17768i
$15$		0			0
$16$	2.49103	+	4.31459i	0.622758	+	1.07865i
$17$	−2.75166	+	4.76601i	−0.667374	+	1.15593i	0.311261	+	0.950324i	$0.399249\pi$
$17$	−2.75166	+	4.76601i	−0.667374	+	1.15593i	−0.978636	+	0.205602i	$0.934085\pi$
$18$	−4.17261	+	2.89550i	−0.983493	+	0.682477i
$19$	3.49334	−	2.01688i	0.801428	−	0.462705i	−0.0425421	−	0.999095i	$-0.513546\pi$
$19$	3.49334	−	2.01688i	0.801428	−	0.462705i	0.843970	+	0.536390i	$0.180212\pi$
$20$		0			0
$21$	−2.81833	+	3.61345i	−0.615011	+	0.788519i
$22$	−0.780983			−0.166506
$23$	−3.90097	+	2.25223i	−0.813409	+	0.469622i	−0.848138	−	0.529775i	$-0.822276\pi$
$23$	−3.90097	+	2.25223i	−0.813409	+	0.469622i	0.0347292	+	0.999397i	$0.488943\pi$
$24$	−0.138018	−	3.32213i	−0.0281729	−	0.678127i
$25$		0			0
$26$	−2.86532	−	4.96289i	−0.561936	−	0.973302i
$27$	5.15589	−	0.645580i	0.992252	−	0.124242i
$28$	0.771225	+	2.15771i	0.145748	+	0.407769i
$29$			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	0.204062	−	0.978958i	$-0.434586\pi$
$31$	−3.01611	−	1.74135i	−0.541710	−	0.312756i	−0.745772	+	0.666202i	$0.767919\pi$
$32$	−3.97938	−	2.29749i	−0.703461	−	0.406143i
$33$	0.707961	+	0.370444i	0.123240	+	0.0644860i
$34$		−	9.31681i		−	1.59782i
$35$		0			0
$36$	1.10798	−	2.35011i	0.184664	−	0.391685i
$37$	2.89964	+	5.02232i	0.476698	+	0.825665i	0.999643	−	0.0267011i	$-0.00850024\pi$
$37$	2.89964	+	5.02232i	0.476698	+	0.825665i	−0.522946	+	0.852366i	$0.675167\pi$
$38$	−3.41448	+	5.91404i	−0.553901	+	0.959385i
$39$	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	$0.337504\pi$
$42$	1.07337	−	7.68344i	0.165625	−	1.18558i
$43$	8.35453			1.27405			0.637027	−	0.770842i	$-0.280164\pi$
$43$	8.35453			1.27405			0.637027	+	0.770842i	$0.280164\pi$
$44$	0.346004	−	0.199765i	0.0521620	−	0.0301157i
$45$		0			0
$46$	3.81290	−	6.60414i	0.562182	−	0.973727i
$47$	−1.57980	−	2.73630i	−0.230438	−	0.399130i	0.727499	−	0.686109i	$-0.240683\pi$
$47$	−1.57980	−	2.73630i	−0.230438	−	0.399130i	−0.957937	+	0.286978i	$0.907349\pi$
$48$	4.62108	+	7.28756i	0.666995	+	1.05187i
$49$	−1.13564	−	6.90727i	−0.162234	−	0.986752i
$50$		0			0
$51$	−4.41924	+	8.44568i	−0.618817	+	1.18263i
$52$	2.53888	+	1.46582i	0.352080	+	0.203273i
$53$	−10.0154	−	5.78238i	−1.37572	−	0.794271i	−0.384078	−	0.923301i	$-0.625481\pi$
$53$	−10.0154	−	5.78238i	−1.37572	−	0.794271i	−0.991641	+	0.129029i	$0.958814\pi$
$54$	−7.01277	+	5.31083i	−0.954316	+	0.722713i
$55$		0			0
$56$	3.87179	+	3.28720i	0.517389	+	0.439270i
$57$	5.90043	−	3.74149i	0.781531	−	0.495573i
$58$	−6.53271	−	11.3150i	−0.857786	−	1.48573i
$59$	−4.88061	+	8.45346i	−0.635401	+	1.10055i	0.351029	+	0.936365i	$0.385832\pi$
$59$	−4.88061	+	8.45346i	−0.635401	+	1.10055i	−0.986430	+	0.164183i	$0.947501\pi$
$60$		0			0
$61$	−6.90647	+	3.98746i	−0.884283	+	0.510541i	−0.872068	−	0.489384i	$-0.837222\pi$
$61$	−6.90647	+	3.98746i	−0.884283	+	0.510541i	−0.0122151	+	0.999925i	$0.503888\pi$
$62$	5.89604			0.748798
$63$	−4.61750	+	6.45591i	−0.581750	+	0.813368i
$64$	−2.18506			−0.273132
$65$		0			0
$66$	−1.35154	+	0.0561498i	−0.166363	+	0.00691156i
$67$	−0.458116	+	0.793481i	−0.0559678	+	0.0969391i	−0.892652	−	0.450747i	$-0.851158\pi$
$67$	−0.458116	+	0.793481i	−0.0559678	+	0.0969391i	0.836684	+	0.547686i	$0.184491\pi$
$68$	2.38312	+	4.12768i	0.288995	+	0.500555i
$69$	−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	$-0.0288616\pi$
$72$	−0.477698	−	5.73922i	−0.0562972	−	0.676373i
$73$	−6.75338	−	3.89906i	−0.790423	−	0.456351i	0.0496883	−	0.998765i	$-0.484177\pi$
$73$	−6.75338	−	3.89906i	−0.790423	−	0.456351i	−0.840112	+	0.542414i	$0.817511\pi$
$74$	−8.50252	−	4.90893i	−0.988398	−	0.570652i
$75$		0			0
$76$		−	3.49351i		−	0.400733i
$77$	−1.14932	+	0.410798i	−0.130977	+	0.0468148i
$78$	−5.31542	−	8.38256i	−0.601853	−	0.949138i
$79$	3.58521	+	6.20977i	0.403368	+	0.698654i	0.994130	−	0.108192i	$-0.0345061\pi$
$79$	3.58521	+	6.20977i	0.403368	+	0.698654i	−0.590762	+	0.806846i	$0.701173\pi$
$80$		0			0
$81$	8.87616	−	1.48790i	0.986240	−	0.165323i
$82$	−9.17399	+	5.29661i	−1.01310	+	0.584912i
$83$	17.5632			1.92781			0.963904	−	0.266250i	$-0.0857848\pi$
$83$	17.5632			1.92781			0.963904	+	0.266250i	$0.0857848\pi$
$84$	1.48978	+	3.67860i	0.162549	+	0.401368i
$85$		0			0
$86$	−12.2489	+	7.07188i	−1.32083	+	0.762581i
$87$	0.554864	+	13.3557i	0.0594877	+	1.43188i
$88$	0.442791	−	0.766937i	0.0472017	−	0.0817558i
$89$	1.35247	+	2.34254i	0.143361	+	0.248309i	0.928760	−	0.370681i	$-0.120876\pi$
$89$	1.35247	+	2.34254i	0.143361	+	0.248309i	−0.785399	+	0.618990i	$0.787542\pi$
$90$		0			0
$91$	−6.82718	−	5.79637i	−0.715683	−	0.607625i
$92$			3.90116i			0.406724i
$93$	−5.34476	−	2.79667i	−0.554225	−	0.290001i
$94$	4.63241	+	2.67452i	0.477796	+	0.275856i
$95$		0			0
$96$	−7.05172	−	3.68984i	−0.719713	−	0.376593i
$97$		−	4.44253i		−	0.451070i	−0.974235	−	0.225535i	$-0.927587\pi$
$97$		−	4.44253i		−	0.451070i	0.974235	−	0.225535i	$-0.0724130\pi$
$98$	7.51181	+	9.16569i	0.758808	+	0.925875i
$99$	1.25180	+	0.590174i	0.125811	+	0.0593148i
$100$		0			0
$101$	1.36822	−	2.36982i	0.136143	−	0.235806i	−0.789891	−	0.613248i	$-0.789863\pi$
$101$	1.36822	−	2.36982i	0.136143	−	0.235806i	0.926033	+	0.377442i	$0.123196\pi$
$102$	−0.669844	−	16.1233i	−0.0663245	−	1.59644i
$103$	15.9618	−	9.21552i	1.57276	−	0.908033i	0.576930	−	0.816794i	$-0.304251\pi$
$103$	15.9618	−	9.21552i	1.57276	−	0.908033i	0.995829	−	0.0912387i	$-0.0290826\pi$
$104$	6.49817			0.637198
$105$		0			0
$106$	19.5785			1.90163
$107$	−5.76162	+	3.32647i	−0.556997	+	0.321582i	−0.751939	−	0.659232i	$-0.770881\pi$
$107$	−5.76162	+	3.32647i	−0.556997	+	0.321582i	0.194942	+	0.980815i	$0.437548\pi$
$108$	1.74847	−	4.14666i	0.168246	−	0.399013i
$109$	3.91662	−	6.78379i	0.375144	−	0.649769i	−0.615204	−	0.788368i	$-0.710927\pi$
$109$	3.91662	−	6.78379i	0.375144	−	0.649769i	0.990349	+	0.138599i	$0.0442599\pi$
$110$		0			0
$111$	5.37908	+	8.48295i	0.510560	+	0.805166i
$112$	−12.9676	−	2.36402i	−1.22532	−	0.223379i
$113$		−	17.3914i		−	1.63604i	−0.575187	−	0.818022i	$-0.695071\pi$
$113$		−	17.3914i		−	1.63604i	0.575187	−	0.818022i	$-0.304929\pi$
$114$	−5.48375	+	10.4801i	−0.513600	+	0.981550i
$115$		0			0
$116$	5.78845	+	3.34196i	0.537444	+	0.310293i
$117$	0.842332	+	10.1200i	0.0778736	+	0.935599i
$118$		−	16.5252i		−	1.52127i
$119$	−4.90065	−	13.7109i	−0.449242	−	1.25688i
$120$		0			0
$121$	−5.39359	−	9.34198i	−0.490327	−	0.849271i
$122$	6.75055	−	11.6923i	0.611166	−	1.05857i
$123$	10.8286	−	0.449874i	0.976378	−	0.0405638i
$124$	−2.61216	+	1.50813i	−0.234579	+	0.135434i
$125$		0			0
$126$	1.30512	−	13.3738i	0.116269	−	1.19143i
$127$	12.5556			1.11413			0.557065	−	0.830469i	$-0.311927\pi$
$127$	12.5556			1.11413			0.557065	+	0.830469i	$0.311927\pi$
$128$	11.1623	−	6.44458i	0.986621	−	0.569626i
$129$	14.4580	−	0.600660i	1.27296	−	0.0528851i
$130$		0			0
$131$	−3.36275	−	5.82446i	−0.293805	−	0.508886i	0.680901	−	0.732375i	$-0.261588\pi$
$131$	−3.36275	−	5.82446i	−0.293805	−	0.508886i	−0.974706	+	0.223490i	$0.928255\pi$
$132$	0.584417	−	0.370582i	0.0508670	−	0.0322550i
$133$	−1.91405	+	10.4993i	−0.165969	+	0.910405i
$134$		−	1.55113i		−	0.133997i
$135$		0			0
$136$	9.14924	+	5.28232i	0.784541	+	0.452955i
$137$	17.6208	+	10.1734i	1.50545	+	0.869171i	0.999980	+	0.00632592i	$0.00201362\pi$
$137$	17.6208	+	10.1734i	1.50545	+	0.869171i	0.505468	+	0.862845i	$0.331320\pi$
$138$	6.12363	−	11.7030i	0.521278	−	0.996224i
$139$			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
$142$	1.29166	+	2.23721i	0.108393	+	0.187743i
$143$	−0.780781	+	1.35235i	−0.0652922	+	0.113089i
$144$	8.52099	+	12.2793i	0.710082	+	1.02327i
$145$		0			0
$146$	13.2018			1.09259
$147$	−2.46189	−	11.8718i	−0.203054	−	0.979168i
$148$	5.02257			0.412852
$149$	14.1195	−	8.15190i	1.15671	−	0.667830i	0.206200	−	0.978510i	$-0.433890\pi$
$149$	14.1195	−	8.15190i	1.15671	−	0.667830i	0.950514	+	0.310680i	$0.100557\pi$
$150$		0			0
$151$	7.54351	−	13.0657i	0.613882	−	1.06328i	−0.376697	−	0.926336i	$-0.622940\pi$
$151$	7.54351	−	13.0657i	0.613882	−	1.06328i	0.990580	−	0.136939i	$-0.0437263\pi$
$152$	−3.87179	−	6.70613i	−0.314043	−	0.543939i
$153$	−7.04054	+	14.9335i	−0.569194	+	1.20730i
$154$	1.33733	−	1.57515i	0.107765	−	0.126929i
$155$		0			0
$156$	4.49907	+	2.35416i	0.360214	+	0.188484i
$157$	−10.7831	−	6.22562i	−0.860584	−	0.496858i	0.00362372	−	0.999993i	$-0.498847\pi$
$157$	−10.7831	−	6.22562i	−0.860584	−	0.496858i	−0.864208	+	0.503135i	$0.832180\pi$
$158$	−10.5128	−	6.06958i	−0.836354	−	0.482869i
$159$	−17.7479	−	9.28668i	−1.40750	−	0.736482i
$160$		0			0
$161$	2.13739	−	11.7244i	0.168450	−	0.924015i
$162$	−11.7542	+	9.69489i	−0.923495	+	0.761703i
$163$	−2.75193	−	4.76649i	−0.215548	−	0.373340i	0.737894	−	0.674917i	$-0.235820\pi$
$163$	−2.75193	−	4.76649i	−0.215548	−	0.373340i	−0.953442	+	0.301577i	$0.902487\pi$
$164$	2.70961	−	4.69317i	0.211585	−	0.366475i
$165$		0			0
$166$	−25.7500	+	14.8667i	−1.99858	+	1.15388i
$167$	0.799023			0.0618302			0.0309151	−	0.999522i	$-0.490158\pi$
$167$	0.799023			0.0618302			0.0309151	+	0.999522i	$0.490158\pi$
$168$	6.93669	+	5.41032i	0.535177	+	0.417415i
$169$	1.54168			0.118590
$170$		0			0
$171$	9.94203	−	6.89909i	0.760286	−	0.527586i
$172$	3.61779	−	6.26620i	0.275854	−	0.477793i
$173$	7.25944	+	12.5737i	0.551925	+	0.955962i	0.998136	+	0.0610338i	$0.0194397\pi$
$173$	7.25944	+	12.5737i	0.551925	+	0.955962i	−0.446211	+	0.894928i	$0.647227\pi$
$174$	−12.1187	−	19.1116i	−0.918719	−	1.44884i
$175$		0			0
$176$			2.29830i			0.173241i
$177$	−7.83840	+	14.9801i	−0.589171	+	1.12597i
$178$	−3.96579	−	2.28965i	−0.297249	−	0.171617i
$179$	2.04442	+	1.18035i	0.152807	+	0.0882234i	0.574454	−	0.818537i	$-0.305214\pi$
$179$	2.04442	+	1.18035i	0.152807	+	0.0882234i	−0.421647	+	0.906760i	$0.638548\pi$
$180$		0			0
$181$		−	9.70696i		−	0.721513i	−0.932660	−	0.360756i	$-0.882519\pi$
$181$		−	9.70696i		−	0.721513i	0.932660	−	0.360756i	$-0.117481\pi$
$182$	14.9160	+	2.71923i	1.10565	+	0.201563i
$183$	−11.6654	+	7.39707i	−0.862329	+	0.546807i
$184$	4.32357	+	7.48865i	0.318738	+	0.552071i
$185$		0			0
$186$	10.2034	−	0.423903i	0.748152	−	0.0310821i
$187$	−2.19863	+	1.26938i	−0.160780	+	0.0928264i
$188$	−2.73643			−0.199575
$189$	−7.52669	+	11.5043i	−0.547486	+	0.836815i
$190$		0			0
$191$	−4.37389	+	2.52527i	−0.316484	+	0.182722i	−0.649824	−	0.760085i	$-0.725157\pi$
$191$	−4.37389	+	2.52527i	−0.316484	+	0.182722i	0.333341	+	0.942807i	$0.391824\pi$
$192$	−3.78137	+	0.157098i	−0.272897	+	0.0113375i
$193$	−6.55182	+	11.3481i	−0.471610	+	0.816853i	−0.999472	−	0.0324769i	$-0.989660\pi$
$193$	−6.55182	+	11.3481i	−0.471610	+	0.816853i	0.527862	+	0.849330i	$0.322994\pi$
$194$	3.76048	+	6.51334i	0.269987	+	0.467631i
$195$		0			0
$196$	−5.67247	−	2.13931i	−0.405176	−	0.152808i
$197$		−	21.2925i		−	1.51703i	−0.651655	−	0.758516i	$-0.725925\pi$
$197$		−	21.2925i		−	1.51703i	0.651655	−	0.758516i	$-0.274075\pi$
$198$	−2.33488	+	0.194341i	−0.165932	+	0.0138112i
$199$	−5.78974	−	3.34271i	−0.410424	−	0.236958i	0.280548	−	0.959840i	$-0.409484\pi$
$199$	−5.78974	−	3.34271i	−0.410424	−	0.236958i	−0.690972	+	0.722882i	$0.742817\pi$
$200$		0			0
$201$	−0.735748	+	1.40610i	−0.0518957	+	0.0991787i
$202$			4.63263i			0.325951i
$203$	−15.5654	−	13.2153i	−1.09248	−	0.927529i
$204$	4.42089	+	6.97185i	0.309524	+	0.488127i
$205$		0			0
$206$	−15.6014	+	27.0224i	−1.08700	+	1.88274i
$207$	−11.1021	+	7.70412i	−0.771652	+	0.535474i
$208$	−14.6050	+	8.43218i	−1.01267	+	0.584666i
$209$	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	$0.436898\pi$
$212$	−8.67399	+	5.00793i	−0.595732	+	0.343946i
$213$	−0.109709	−	2.64071i	−0.00751711	−	0.180938i
$214$	5.63154	−	9.75412i	0.384964	−	0.666778i
$215$		0			0
$216$	−1.23931	−	9.89770i	−0.0843245	−	0.673453i
$217$	8.67678	−	3.10132i	0.589019	−	0.210531i
$218$			13.2613i			0.898166i
$219$	−11.9674	−	6.26201i	−0.808685	−	0.423148i
$220$		0			0
$221$	−16.1330	−	9.31439i	−1.08522	−	0.626554i
$222$	−15.0670	−	7.88390i	−1.01123	−	0.529132i
$223$			5.83493i			0.390736i	0.980730	+	0.195368i	$0.0625901\pi$
$223$			5.83493i			0.390736i	−0.980730	+	0.195368i	$0.937410\pi$
$224$	11.4479	−	4.09180i	0.764896	−	0.273395i
$225$		0			0
$226$	14.7213	+	25.4981i	0.979249	+	1.69611i
$227$	5.70646	−	9.88387i	0.378751	−	0.656016i	−0.612130	−	0.790757i	$-0.709687\pi$
$227$	5.70646	−	9.88387i	0.378751	−	0.656016i	0.990881	+	0.134741i	$0.0430204\pi$
$228$	−0.251171	−	6.04573i	−0.0166342	−	0.400388i
$229$	0.910719	−	0.525804i	0.0601820	−	0.0347461i	−0.469607	−	0.882876i	$-0.655604\pi$
$229$	0.910719	−	0.525804i	0.0601820	−	0.0347461i	0.529789	+	0.848129i	$0.322271\pi$
$230$		0			0
$231$	−1.95943	+	0.793541i	−0.128921	+	0.0522112i
$232$	14.8153			0.972672
$233$	3.36441	−	1.94244i	0.220410	−	0.127254i	−0.385730	−	0.922612i	$-0.626050\pi$
$233$	3.36441	−	1.94244i	0.220410	−	0.127254i	0.606140	+	0.795358i	$0.292717\pi$
$234$	−9.80132	−	14.1243i	−0.640732	−	0.923337i
$235$		0			0
$236$	4.22694	+	7.32127i	0.275150	+	0.476574i
$237$	6.65088	+	10.4886i	0.432021	+	0.681308i
$238$	18.7909	+	15.9537i	1.21803	+	1.03413i
$239$			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	0.561826	−	0.827255i	$-0.310099\pi$
$241$	1.96093	+	1.13215i	0.126315	+	0.0729279i	−0.435511	+	0.900183i	$0.643432\pi$
$242$	15.8155	+	9.13106i	1.01666	+	0.586967i
$243$	15.2537	−	3.21307i	0.978527	−	0.206118i
$244$			6.90681i			0.442163i
$245$		0			0
$246$	−15.4953	+	9.82566i	−0.987945	+	0.626461i
$247$	6.82718	+	11.8250i	0.434403	+	0.752408i
$248$	−3.34286	+	5.79000i	−0.212272	+	0.367665i
$249$	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	$0.638125\pi$
$252$	2.84263	+	6.25891i	0.179069	+	0.394274i
$253$	−2.07798			−0.130641
$254$	−18.4082	+	10.6280i	−1.15503	+	0.666859i
$255$		0			0
$256$	−8.72527	+	15.1126i	−0.545329	+	0.944538i
$257$	−9.79648	−	16.9680i	−0.611088	−	1.05844i	−0.991057	−	0.133436i	$-0.957399\pi$
$257$	−9.79648	−	16.9680i	−0.611088	−	1.05844i	0.379969	−	0.924999i	$-0.375934\pi$
$258$	−20.6889	+	13.1190i	−1.28804	+	0.816750i
$259$	−15.0947	−	2.75180i	−0.937937	−	0.170988i
$260$		0			0
$261$	1.92045	+	23.0729i	0.118873	+	1.42818i
$262$	9.86050	+	5.69296i	0.609184	+	0.351712i
$263$	14.5263	+	8.38678i	0.895732	+	0.517151i	0.875813	−	0.482651i	$-0.160326\pi$
$263$	14.5263	+	8.38678i	0.895732	+	0.517151i	0.0199186	+	0.999802i	$0.493659\pi$
$264$	0.711136	−	1.35906i	0.0437674	−	0.0836446i
$265$		0			0
$266$	−6.08112	−	17.0136i	−0.372858	−	1.04317i
$267$	2.50894	+	3.95666i	0.153545	+	0.242144i
$268$	0.396759	+	0.687207i	0.0242359	+	0.0419779i
$269$	−14.6703	+	25.4097i	−0.894465	+	1.54926i	−0.0599988	+	0.998198i	$0.519110\pi$
$269$	−14.6703	+	25.4097i	−0.894465	+	1.54926i	−0.834466	+	0.551060i	$0.814224\pi$
$270$		0			0
$271$	2.57129	−	1.48454i	0.156195	−	0.0901792i	−0.419865	−	0.907586i	$-0.637923\pi$
$271$	2.57129	−	1.48454i	0.156195	−	0.0901792i	0.576060	+	0.817407i	$0.304589\pi$
$272$	−27.4178			−1.66245
$273$	−12.2316	−	9.54010i	−0.740288	−	0.577393i
$274$	−34.4460			−2.08096
$275$		0			0
$276$	0.280479	+	6.75118i	0.0168829	+	0.406374i
$277$	6.51269	−	11.2803i	0.391309	−	0.677768i	−0.601313	−	0.799014i	$-0.705356\pi$
$277$	6.51269	−	11.2803i	0.391309	−	0.677768i	0.992623	+	0.121246i	$0.0386889\pi$
$278$	−8.28830	−	14.3558i	−0.497099	−	0.861001i
$279$	−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	$0.803108\pi$
$282$	8.20894	+	4.29536i	0.488835	+	0.255785i
$283$	4.88399	+	2.81977i	0.290323	+	0.167618i	0.638088	−	0.769964i	$-0.279726\pi$
$283$	4.88399	+	2.81977i	0.290323	+	0.167618i	−0.347764	+	0.937582i	$0.613059\pi$
$284$	−1.14450	−	0.660778i	−0.0679136	−	0.0392099i
$285$		0			0
$286$		−	2.64364i		−	0.156322i
$287$	−10.7147	+	12.6202i	−0.632469	+	0.744945i
$288$	−12.4687	−	5.87850i	−0.734725	−	0.346394i
$289$	−6.64321	−	11.5064i	−0.390777	−	0.676846i
$290$		0			0
$291$	−0.319401	−	7.68805i	−0.0187236	−	0.450681i
$292$	−5.84888	+	3.37685i	−0.342280	+	0.197615i
$293$	−21.5754			−1.26045			−0.630226	−	0.776412i	$-0.717038\pi$
$293$	−21.5754			−1.26045			−0.630226	+	0.776412i	$0.717038\pi$
$294$	13.6586	+	15.3217i	0.796586	+	0.893579i
$295$		0			0
$296$	9.64129	−	5.56640i	0.560389	−	0.323541i
$297$	2.20875	+	0.931331i	0.128164	+	0.0540413i
$298$	−13.8007	+	23.9036i	−0.799455	+	1.38470i
$299$	−7.62382	−	13.2049i	−0.440897	−	0.763656i
$300$		0			0
$301$	−14.3060	+	16.8501i	−0.824582	+	0.971224i
$302$			25.5415i			1.46975i
$303$	2.19740	−	4.19948i	0.126237	−	0.241254i
$304$	17.4041	+	10.0482i	0.998191	+	0.576306i
$305$		0			0
$306$	−2.31841	−	27.8541i	−0.132535	−	1.59231i
$307$		−	22.9288i		−	1.30861i	−0.756229	−	0.654307i	$-0.772960\pi$
$307$		−	22.9288i		−	1.30861i	0.756229	−	0.654307i	$-0.227040\pi$
$308$	−0.189580	+	1.03992i	−0.0108023	+	0.0592549i
$309$	26.9602	−	17.0956i	1.53371	−	0.972534i
$310$		0			0
$311$	0.799023	−	1.38395i	0.0453084	−	0.0784765i	−0.842482	−	0.538725i	$-0.818906\pi$
$311$	0.799023	−	1.38395i	0.0453084	−	0.0784765i	0.887790	+	0.460248i	$0.152240\pi$
$312$	11.2455	−	0.467195i	0.636649	−	0.0264497i
$313$	−25.0145	+	14.4421i	−1.41390	+	0.816318i	−0.995754	−	0.0920593i	$-0.970655\pi$
$313$	−25.0145	+	14.4421i	−1.41390	+	0.816318i	−0.418151	+	0.908378i	$0.637322\pi$
$314$	21.0793			1.18957
$315$		0			0
$316$	6.21007			0.349344
$317$	5.68143	−	3.28018i	0.319101	−	0.184233i	−0.331891	−	0.943318i	$-0.607687\pi$
$317$	5.68143	−	3.28018i	0.319101	−	0.184233i	0.650992	+	0.759085i	$0.274353\pi$
$318$	33.8818	−	1.40762i	1.90000	−	0.0789357i
$319$	−1.78012	+	3.08325i	−0.0996674	+	0.172629i
$320$		0			0
$321$	−9.73166	+	6.17090i	−0.543168	+	0.344426i
$322$	6.79071	+	18.9988i	0.378432	+	1.05876i
$323$			22.1991i			1.23519i
$324$	2.72769	−	7.30175i	0.151538	−	0.405653i
$325$		0			0
$326$	8.06940	+	4.65887i	0.446923	+	0.258031i
$327$	6.29021	−	12.0213i	0.347849	−	0.664781i
$328$		−	12.0120i		−	0.663251i
$329$	8.22399	+	1.49925i	0.453403	+	0.0826566i
$330$		0			0
$331$	6.76497	+	11.7173i	0.371836	+	0.644040i	0.989848	−	0.142129i	$-0.0453949\pi$
$331$	6.76497	+	11.7173i	0.371836	+	0.644040i	−0.618012	+	0.786169i	$0.712062\pi$
$332$	7.60544	−	13.1730i	0.417403	−	0.722963i
$333$	9.91871	+	14.2935i	0.543542	+	0.783279i
$334$	−1.17147	+	0.676351i	−0.0641002	+	0.0370083i
$335$		0			0
$336$	−22.6111	−	3.15876i	−1.23354	−	0.172324i
$337$	−30.7122			−1.67300			−0.836501	−	0.547966i	$-0.815402\pi$
$337$	−30.7122			−1.67300			−0.836501	+	0.547966i	$0.815402\pi$
$338$	−2.26030	+	1.30499i	−0.122944	+	0.0709819i
$339$	−1.25038	−	30.0968i	−0.0679111	−	1.63463i
$340$		0			0
$341$	−0.803314	−	1.39138i	−0.0435019	−	0.0753475i
$342$	−8.73647	+	18.5307i	−0.472414	+	1.00202i
$343$	15.8758	+	9.53729i	0.857211	+	0.514965i
$344$		−	16.0381i		−	0.864715i
$345$		0			0
$346$	−21.2866	−	12.2898i	−1.14438	−	0.660706i
$347$	6.77295	+	3.91036i	0.363591	+	0.209919i	0.670655	−	0.741770i	$-0.266013\pi$
$347$	6.77295	+	3.91036i	0.363591	+	0.209919i	−0.307064	+	0.951689i	$0.599347\pi$
$348$	10.2575	+	5.36729i	0.549861	+	0.287717i
$349$			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
$352$	−1.05987	−	1.83575i	−0.0564913	−	0.0978458i
$353$	6.13445	−	10.6252i	0.326504	−	0.565521i	−0.655312	−	0.755359i	$-0.727463\pi$
$353$	6.13445	−	10.6252i	0.326504	−	0.565521i	0.981816	+	0.189837i	$0.0607960\pi$
$354$	−1.18810	−	28.5979i	−0.0631469	−	1.51996i
$355$		0			0
$356$	2.34265			0.124160
$357$	−9.46662	−	23.3752i	−0.501027	−	1.23714i
$358$	−3.99653			−0.211223
$359$	7.11574	−	4.10828i	0.375555	−	0.216827i	−0.300328	−	0.953836i	$-0.597096\pi$
$359$	7.11574	−	4.10828i	0.375555	−	0.216827i	0.675882	+	0.737010i	$0.263763\pi$
$360$		0			0
$361$	−1.36436	+	2.36315i	−0.0718086	+	0.124376i
$362$	8.21668	+	14.2317i	0.431859	+	0.748002i
$363$	−10.0056	−	15.7791i	−0.525157	−	0.828186i
$364$	−7.30388	+	2.61061i	−0.382827	+	0.136833i
$365$		0			0
$366$	10.8416	−	20.7195i	0.566698	−	1.08303i
$367$	−24.1666	−	13.9526i	−1.26149	−	0.728320i	−0.288125	−	0.957593i	$-0.593032\pi$
$367$	−24.1666	−	13.9526i	−1.26149	−	0.728320i	−0.973362	+	0.229273i	$0.926365\pi$
$368$	−19.4349	−	11.2207i	−1.01311	−	0.584921i
$369$	18.7071	−	1.55707i	0.973853	−	0.0810577i
$370$		0			0
$371$	28.8123	−	10.2983i	1.49586	−	0.534663i
$372$	−4.41206	+	2.79771i	−0.228755	+	0.145054i
$373$	9.04199	+	15.6612i	0.468176	+	0.810905i	0.999339	−	0.0363650i	$-0.0115779\pi$
$373$	9.04199	+	15.6612i	0.468176	+	0.810905i	−0.531162	+	0.847270i	$0.678245\pi$
$374$	2.14900	−	3.72217i	0.111122	−	0.192469i
$375$		0			0
$376$	−5.25284	+	3.03273i	−0.270895	+	0.156401i
$377$	−26.1241			−1.34546
$378$	1.29706	−	23.2380i	0.0667135	−	1.19523i
$379$	24.7450			1.27107			0.635534	−	0.772073i	$-0.280780\pi$
$379$	24.7450			1.27107			0.635534	+	0.772073i	$0.280780\pi$
$380$		0			0
$381$	21.7282	−	0.902702i	1.11317	−	0.0462468i
$382$	4.27514	−	7.40476i	0.218735	−	0.378861i
$383$	6.46470	+	11.1972i	0.330331	+	0.572150i	0.982577	−	0.185858i	$-0.0595063\pi$
$383$	6.46470	+	11.1972i	0.330331	+	0.572150i	−0.652246	+	0.758008i	$0.726173\pi$
$384$	18.8537	−	11.9552i	0.962126	−	0.610089i
$385$		0			0
$386$		−	22.1838i		−	1.12912i
$387$	24.9772	−	2.07895i	1.26966	−	0.105679i
$388$	−3.33205	−	1.92376i	−0.169159	−	0.0976642i
$389$	−16.4024	−	9.46992i	−0.831634	−	0.480144i	0.0227777	−	0.999741i	$-0.492749\pi$
$389$	−16.4024	−	9.46992i	−0.831634	−	0.480144i	−0.854412	+	0.519596i	$0.826082\pi$
$390$		0			0
$391$		−	24.7894i		−	1.25365i
$392$	−13.2598	+	2.18007i	−0.669721	+	0.110110i
$393$	−6.23820	−	9.83780i	−0.314675	−	0.496251i
$394$	18.0236	+	31.2177i	0.908014	+	1.57273i
$395$		0			0
$396$	0.984724	−	0.683331i	0.0494842	−	0.0343387i
$397$	−6.31044	+	3.64333i	−0.316712	+	0.182854i	−0.649926	−	0.759998i	$-0.725200\pi$
$397$	−6.31044	+	3.64333i	−0.316712	+	0.182854i	0.333214	+	0.942851i	$0.391867\pi$
$398$	11.3181			0.567323
$399$	−2.55751	+	18.3073i	−0.128036	+	0.916510i
$400$		0			0
$401$	13.7394	−	7.93243i	0.686111	−	0.396126i	−0.116042	−	0.993244i	$-0.537021\pi$
$401$	13.7394	−	7.93243i	0.686111	−	0.396126i	0.802154	+	0.597118i	$0.203688\pi$
$402$	−0.111521	−	2.68432i	−0.00556215	−	0.133882i
$403$	5.89451	−	10.2096i	0.293626	−	0.508576i
$404$	−1.18497	−	2.05242i	−0.0589543	−	0.102112i
$405$		0			0
$406$	34.0073	+	6.19963i	1.68776	+	0.307682i
$407$			2.67530i			0.132610i
$408$	16.2131	+	8.48356i	0.802667	+	0.419999i
$409$	−22.8109	−	13.1699i	−1.12793	−	0.651209i	−0.184515	−	0.982830i	$-0.559071\pi$
$409$	−22.8109	−	13.1699i	−1.12793	−	0.651209i	−0.943413	+	0.331620i	$0.892405\pi$
$410$		0			0
$411$	31.2253	+	16.3388i	1.54023	+	0.805932i
$412$		−	15.9625i		−	0.786417i
$413$	−8.69228	−	24.3190i	−0.427719	−	1.19666i
$414$	9.75590	−	20.6929i	0.479476	−	1.01700i
$415$		0			0
$416$	7.77705	−	13.4702i	0.381301	−	0.660433i
$417$	0.703978	+	16.9449i	0.0344739	+	0.829794i
$418$	−2.72824	+	1.57515i	−0.133443	+	0.0770432i
$419$	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	$0.578900\pi$
$422$	−8.38858	+	4.84315i	−0.408350	+	0.235761i
$423$	−5.40398	−	7.78749i	−0.262751	−	0.378641i
$424$	−11.1004	+	19.2264i	−0.539082	+	0.933717i
$425$		0			0
$426$	2.39613	+	3.77876i	0.116093	+	0.183082i
$427$	3.78415	−	20.7575i	0.183128	−	1.00453i
$428$			5.76190i			0.278512i
$429$	−1.25396	+	2.39646i	−0.0605416	+	0.115702i
$430$		0			0
$431$	7.13983	+	4.12218i	0.343914	+	0.198559i	0.662001	−	0.749503i	$-0.269707\pi$
$431$	7.13983	+	4.12218i	0.343914	+	0.198559i	−0.318088	+	0.948061i	$0.603041\pi$
$432$	15.6289	+	20.6374i	0.751946	+	0.992918i
$433$		−	10.7241i		−	0.515367i	−0.966229	−	0.257683i	$-0.917041\pi$
$433$		−	10.7241i		−	0.515367i	0.966229	−	0.257683i	$-0.0829591\pi$
$434$	−10.0961	+	11.8916i	−0.484631	+	0.570816i
$435$		0			0
$436$	−3.39206	−	5.87521i	−0.162450	−	0.281372i
$437$	−9.08496	+	15.7356i	−0.434593	+	0.752737i
$438$	22.8465	−	0.949162i	1.09165	−	0.0453527i
$439$	−2.74233	+	1.58329i	−0.130884	+	0.0755661i	−0.564013	−	0.825766i	$-0.690743\pi$
$439$	−2.74233	+	1.58329i	−0.130884	+	0.0755661i	0.433128	+	0.901332i	$0.357410\pi$
$440$		0			0
$441$	−5.11399	−	20.3678i	−0.243523	−	0.969895i
$442$	31.5375			1.50009
$443$	15.1150	−	8.72667i	0.718137	−	0.414617i	−0.0959297	−	0.995388i	$-0.530582\pi$
$443$	15.1150	−	8.72667i	0.718137	−	0.414617i	0.814067	+	0.580772i	$0.197249\pi$
$444$	8.69184	−	0.361104i	0.412496	−	0.0171372i
$445$		0			0
$446$	−4.93911	−	8.55480i	−0.233874	−	0.405081i
$447$	23.8485	−	15.1225i	1.12800	−	0.715268i
$448$	3.74161	−	4.40700i	0.176774	−	0.208211i
$449$		−	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
$452$	−13.0442	−	7.53105i	−0.613546	−	0.354231i
$453$	12.1151	−	23.1534i	0.569217	−	1.08784i
$454$			19.3215i			0.906801i
$455$		0			0
$456$	−7.18250	−	11.3270i	−0.336351	−	0.530434i
$457$	−2.44467	−	4.23430i	−0.114357	−	0.198072i	0.803165	−	0.595756i	$-0.203147\pi$
$457$	−2.44467	−	4.23430i	−0.114357	−	0.198072i	−0.917523	+	0.397684i	$0.869814\pi$
$458$	−0.890158	+	1.54180i	−0.0415943	+	0.0720435i
$459$	−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	$0.538099\pi$
$462$	2.20107	−	2.82204i	0.102403	−	0.131293i
$463$	39.9073			1.85465			0.927325	−	0.374257i	$-0.122102\pi$
$463$	39.9073			1.85465			0.927325	+	0.374257i	$0.122102\pi$
$464$	−33.2981	+	19.2247i	−1.54583	+	0.892483i
$465$		0			0
$466$	−3.28845	+	5.69577i	−0.152335	+	0.263851i
$467$	4.56309	+	7.90350i	0.211155	+	0.365730i	0.952076	−	0.305861i	$-0.0989443\pi$
$467$	4.56309	+	7.90350i	0.211155	+	0.365730i	−0.740922	+	0.671592i	$0.765611\pi$
$468$	7.95516	+	3.75054i	0.367727	+	0.173369i
$469$	−0.815897	−	2.28269i	−0.0376746	−	0.105405i
$470$		0			0
$471$	−19.1084	−	9.99853i	−0.880467	−	0.460708i
$472$	16.2280	+	9.36925i	0.746955	+	0.431254i
$473$	3.33773	+	1.92704i	0.153469	+	0.0886053i
$474$	−18.6294	−	9.74792i	−0.855677	−	0.447737i
$475$		0			0
$476$	−12.4058	−	2.26161i	−0.568619	−	0.103661i
$477$	−31.3815	−	14.7951i	−1.43686	−	0.677422i
$478$	−5.42002	−	9.38775i	−0.247906	−	0.429386i
$479$	−6.20210	+	10.7424i	−0.283381	+	0.490831i	−0.972215	−	0.234088i	$-0.924790\pi$
$479$	−6.20210	+	10.7424i	−0.283381	+	0.490831i	0.688834	+	0.724919i	$0.258123\pi$
$480$		0			0
$481$	−17.0006	+	9.81532i	−0.775162	+	0.447540i
$482$	−3.83332			−0.174603
$483$	2.85594	−	20.4435i	0.129950	−	0.930211i
$484$	−9.34243			−0.424656
$485$		0			0
$486$	−19.6442	+	17.6227i	−0.891081	+	0.799380i
$487$	−7.08208	+	12.2665i	−0.320920	+	0.555849i	−0.980678	−	0.195628i	$-0.937325\pi$
$487$	−7.08208	+	12.2665i	−0.320920	+	0.555849i	0.659758	+	0.751478i	$0.270659\pi$
$488$	7.65467	+	13.2583i	0.346511	+	0.600174i
$489$	−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	$0.741926\pi$
$492$	4.35171	−	8.31662i	0.196190	−	0.374942i
$493$	−36.7819	−	21.2361i	−1.65658	−	0.956424i
$494$	−20.0191	−	11.5580i	−0.900703	−	0.520021i
$495$		0			0
$496$		−	17.3511i		−	0.779086i
$497$	3.07762	+	2.61294i	0.138050	+	0.117206i
$498$	−43.4929	+	27.5791i	−1.94897	+	1.23585i
$499$	−13.3589	−	23.1383i	−0.598027	−	1.03581i	−0.993112	−	0.117168i	$-0.962618\pi$
$499$	−13.3589	−	23.1383i	−0.598027	−	1.03581i	0.395085	−	0.918644i	$-0.370715\pi$
$500$		0			0
$501$	1.38276	−	0.0574468i	0.0617769	−	0.00256653i
$502$	19.5320	−	11.2768i	0.871758	−	0.503310i
$503$	−9.55539			−0.426054			−0.213027	−	0.977046i	$-0.568332\pi$
$503$	−9.55539			−0.426054			−0.213027	+	0.977046i	$0.568332\pi$
$504$	12.3933	+	8.86415i	0.552042	+	0.394841i
$505$		0			0
$506$	3.04659	−	1.75895i	0.135438	−	0.0781950i
$507$	2.66796	−	0.110841i	0.118488	−	0.00492261i
$508$	5.43700	−	9.41716i	0.241228	−	0.417819i
$509$	9.10071	+	15.7629i	0.403382	+	0.698678i	0.994132	−	0.108177i	$-0.0345013\pi$
$509$	9.10071	+	15.7629i	0.403382	+	0.698678i	−0.590750	+	0.806855i	$0.701168\pi$
$510$		0			0
$511$	19.4282	−	6.94417i	0.859452	−	0.307192i
$512$		−	3.76451i		−	0.166369i
$513$	16.7092	−	12.6541i	0.737731	−	0.558691i
$514$	28.7259	+	16.5849i	1.26705	+	0.731530i
$515$		0			0
$516$	5.81028	−	11.1041i	0.255783	−	0.488832i
$517$		−	1.45758i		−	0.0641042i
$518$	24.4601	−	8.74273i	1.07472	−	0.384133i
$519$	13.4669	+	21.2376i	0.591130	+	0.932228i
$520$		0			0
$521$	1.93741	−	3.35569i	0.0848794	−	0.147015i	−0.820460	−	0.571703i	$-0.806283\pi$
$521$	1.93741	−	3.35569i	0.0848794	−	0.147015i	0.905340	+	0.424688i	$0.139616\pi$
$522$	−22.3462	−	32.2024i	−0.978067	−	1.40946i
$523$	−16.3176	+	9.42099i	−0.713520	+	0.411951i	−0.812363	−	0.583152i	$-0.801819\pi$
$523$	−16.3176	+	9.42099i	−0.713520	+	0.411951i	0.0988429	+	0.995103i	$0.468486\pi$
$524$	−5.82474			−0.254455
$525$		0			0
$526$	−28.3967			−1.23816
$527$	16.5986	−	9.58321i	0.723047	−	0.417451i
$528$	0.165240	+	3.97735i	0.00719113	+	0.173092i
$529$	−1.35494	+	2.34682i	−0.0589104	+	0.102036i
$530$		0			0
$531$	−12.4878	+	26.4875i	−0.541924	+	1.14946i
$532$	7.04601	+	5.98216i	0.305483	+	0.259359i
$533$			21.1809i			0.917448i
$534$	−7.02765	−	3.67725i	−0.304116	−	0.159130i
$535$		0			0
$536$	1.52324	+	0.879440i	0.0657937	+	0.0379860i
$537$	3.62286	+	1.89568i	0.156338	+	0.0818044i
$538$		−	49.6721i		−	2.14152i
$539$	1.13952	−	3.02147i	0.0490824	−	0.130144i
$540$		0			0
$541$	−11.0977	−	19.2218i	−0.477128	−	0.826410i	0.522528	−	0.852622i	$-0.324989\pi$
$541$	−11.0977	−	19.2218i	−0.477128	−	0.826410i	−0.999656	+	0.0262117i	$0.991656\pi$
$542$	−2.51324	+	4.35306i	−0.107953	+	0.186980i
$543$	−0.697895	−	16.7985i	−0.0299495	−	0.720891i
$544$	21.8997	−	12.6438i	0.938944	−	0.542099i
$545$		0			0
$546$	26.0086	+	3.63338i	1.11306	+	0.155494i
$547$	−1.23468			−0.0527911			−0.0263956	−	0.999652i	$-0.508403\pi$
$547$	−1.23468			−0.0527911			−0.0263956	+	0.999652i	$0.508403\pi$
$548$	15.2608	−	8.81083i	0.651910	−	0.376380i
$549$	−19.6558	+	13.6398i	−0.838888	+	0.582131i
$550$		0			0
$551$	15.5654	+	26.9601i	0.663109	+	1.14854i
$552$	8.02060	+	12.6487i	0.341379	+	0.538364i
$553$	−18.6636	−	3.40242i	−0.793656	−	0.144685i
$554$			22.0513i			0.936868i
$555$		0			0
$556$	7.34403	+	4.24008i	0.311456	+	0.179819i
$557$	2.00365	+	1.15681i	0.0848973	+	0.0490155i	0.541848	−	0.840477i	$-0.317725\pi$
$557$	2.00365	+	1.15681i	0.0848973	+	0.0490155i	−0.456950	+	0.889492i	$0.651058\pi$
$558$	17.6272	−	1.46718i	0.746217	−	0.0621106i
$559$			28.2802i			1.19612i
$560$		0			0
$561$	−3.71360	+	2.35481i	−0.156788	+	0.0994203i
$562$	−16.4558	−	28.5023i	−0.694146	−	1.20230i
$563$	−9.07818	+	15.7239i	−0.382600	+	0.662682i	−0.991433	−	0.130616i	$-0.958304\pi$
$563$	−9.07818	+	15.7239i	−0.382600	+	0.662682i	0.608833	+	0.793298i	$0.291638\pi$
$564$	−4.73555	+	0.196739i	−0.199403	+	0.00828422i
$565$		0			0
$566$	−9.54745			−0.401309
$567$	−12.1983	+	20.4500i	−0.512279	+	0.858819i
$568$	−2.92930			−0.122911
$569$	12.9811	−	7.49465i	0.544197	−	0.314192i	−0.202581	−	0.979265i	$-0.564933\pi$
$569$	12.9811	−	7.49465i	0.544197	−	0.314192i	0.746778	+	0.665073i	$0.231600\pi$
$570$		0			0
$571$	−11.6375	+	20.1568i	−0.487015	+	0.843535i	−0.999889	−	0.0149293i	$-0.995248\pi$
$571$	−11.6375	+	20.1568i	−0.487015	+	0.843535i	0.512873	+	0.858464i	$0.328581\pi$
$572$	0.676208	+	1.17123i	0.0282737	+	0.0489715i
$573$	−7.38771	+	4.68459i	−0.308626	+	0.195701i
$574$	5.02655	−	27.5726i	0.209804	−	1.15086i
$575$		0			0
$576$	−6.53258	+	0.543733i	−0.272191	+	0.0226555i
$577$	23.0953	+	13.3341i	0.961471	+	0.555105i	0.896625	−	0.442790i	$-0.146011\pi$
$577$	23.0953	+	13.3341i	0.961471	+	0.555105i	0.0648455	+	0.997895i	$0.479345\pi$
$578$	19.4797	+	11.2466i	0.810248	+	0.467797i
$579$	−10.5224	+	20.1096i	−0.437297	+	0.835725i
$580$		0			0
$581$	−30.0745	+	35.4229i	−1.24770	+	1.46959i
$582$	6.97601	+	11.0013i	0.289165	+	0.456021i
$583$	−2.66751	−	4.62026i	−0.110477	−	0.191351i
$584$	−7.48499	+	12.9644i	−0.309731	+	0.536470i
$585$		0			0
$586$	31.6325	−	18.2630i	1.30673	−	0.754439i
$587$	45.9722			1.89748			0.948738	−	0.316065i	$-0.102362\pi$
$587$	45.9722			1.89748			0.948738	+	0.316065i	$0.102362\pi$
$588$	−9.97034	−	3.29437i	−0.411170	−	0.135857i
$589$	−14.0484			−0.578856
$590$		0			0
$591$	−1.53086	−	36.8480i	−0.0629710	−	1.51572i
$592$	−14.4462	+	25.0215i	−0.593735	+	1.02838i
$593$	−1.55298	−	2.68984i	−0.0637732	−	0.110458i	0.832376	−	0.554211i	$-0.186980\pi$
$593$	−1.55298	−	2.68984i	−0.0637732	−	0.110458i	−0.896149	+	0.443753i	$0.853647\pi$
$594$	−4.02666	+	0.504187i	−0.165216	+	0.0206871i
$595$		0			0
$596$		−	14.1202i		−	0.578385i
$597$	−10.2598	−	5.36849i	−0.419906	−	0.219718i
$598$	22.3551	+	12.9067i	0.914168	+	0.527795i
$599$	−7.34708	−	4.24184i	−0.300193	−	0.173317i	0.342336	−	0.939577i	$-0.388782\pi$
$599$	−7.34708	−	4.24184i	−0.300193	−	0.173317i	−0.642530	+	0.766261i	$0.722115\pi$
$600$		0			0
$601$			2.63388i			0.107438i	0.998556	+	0.0537191i	$0.0171076\pi$
$601$			2.63388i			0.107438i	−0.998556	+	0.0537191i	$0.982892\pi$
$602$	6.71131	−	36.8141i	0.273533	−	1.50043i
$603$	−1.17216	+	2.48624i	−0.0477341	+	0.101247i
$604$	−6.53319	−	11.3158i	−0.265832	−	0.460434i
$605$		0			0
$606$	0.333069	+	8.01704i	0.0135300	+	0.325670i
$607$	−26.2154	+	15.1355i	−1.06405	+	0.614330i	−0.926550	−	0.376171i	$-0.877240\pi$
$607$	−26.2154	+	15.1355i	−1.06405	+	0.614330i	−0.137501	+	0.990502i	$0.543907\pi$
$608$	−18.5351			−0.751698
$609$	−27.8870	−	21.7507i	−1.13004	−	0.881381i
$610$		0			0
$611$	9.26241	−	5.34766i	0.374717	−	0.216343i
$612$	8.15185	+	11.7474i	0.329519	+	0.474859i
$613$	−9.01861	+	15.6207i	−0.364258	+	0.630914i	−0.988657	−	0.150192i	$-0.952011\pi$
$613$	−9.01861	+	15.6207i	−0.364258	+	0.630914i	0.624399	+	0.781106i	$0.285344\pi$
$614$	19.4086	+	33.6167i	0.783267	+	1.35666i
$615$		0			0
$616$	0.788604	+	2.20633i	0.0317738	+	0.0888956i
$617$		−	11.2586i		−	0.453254i	−0.973982	−	0.226627i	$-0.927230\pi$
$617$		−	11.2586i		−	0.453254i	0.973982	−	0.226627i	$-0.0727699\pi$
$618$	−25.0563	+	47.8855i	−1.00791	+	1.92624i
$619$	−5.23950	−	3.02503i	−0.210593	−	0.121586i	0.390994	−	0.920393i	$-0.372131\pi$
$619$	−5.23950	−	3.02503i	−0.210593	−	0.121586i	−0.601587	+	0.798807i	$0.705465\pi$
$620$		0			0
$621$	−18.6590	+	14.1306i	−0.748760	+	0.567043i
$622$			2.70540i			0.108477i
$623$	−7.04054	−	1.28351i	−0.282073	−	0.0514227i
$624$	−24.6685	+	15.6424i	−0.987530	+	0.626198i
$625$		0			0
$626$	24.4498	−	42.3482i	0.977209	−	1.69258i
$627$	3.22029	−	0.133788i	0.128606	−	0.00534296i
$628$	−9.33888	+	5.39180i	−0.372662	+	0.215156i
$629$	−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	$0.107586\pi$
$632$	11.9208	−	6.88249i	0.474185	−	0.273771i
$633$	9.90150	−	0.411359i	0.393549	−	0.0163501i
$634$	−5.55316	+	9.61836i	−0.220544	+	0.381994i
$635$		0			0
$636$	−14.6508	+	9.29014i	−0.580942	+	0.368378i
$637$	23.3812	−	3.84415i	0.926397	−	0.152311i
$638$		−	6.02728i		−	0.238622i
$639$	−0.379714	−	4.56201i	−0.0150213	−	0.180470i
$640$		0			0
$641$	−2.08690	−	1.20488i	−0.0824278	−	0.0475897i	0.458220	−	0.888839i	$-0.348487\pi$
$641$	−2.08690	−	1.20488i	−0.0824278	−	0.0475897i	−0.540647	+	0.841249i	$0.681821\pi$
$642$	9.04442	−	17.2850i	0.356955	−	0.682183i
$643$		−	30.1631i		−	1.18952i	−0.803904	−	0.594759i	$-0.797247\pi$
$643$		−	30.1631i		−	1.18952i	0.803904	−	0.594759i	$-0.202753\pi$
$644$	−7.86819	−	6.68020i	−0.310050	−	0.263237i
$645$		0			0
$646$	−18.7909	−	32.5468i	−0.739319	−	1.28054i
$647$	−6.98967	+	12.1065i	−0.274792	+	0.475954i	−0.970083	−	0.242775i	$-0.921942\pi$
$647$	−6.98967	+	12.1065i	−0.274792	+	0.475954i	0.695291	+	0.718729i	$0.255276\pi$
$648$	−2.85631	−	17.0394i	−0.112206	−	0.669373i
$649$	−3.89972	+	2.25150i	−0.153077	+	0.0883792i
$650$		0			0
$651$	14.7927	−	5.99085i	0.579772	−	0.234800i
$652$	−4.76671			−0.186679
$653$	−5.92653	+	3.42169i	−0.231923	+	0.133901i	−0.611459	−	0.791276i	$-0.709417\pi$
$653$	−5.92653	+	3.42169i	−0.231923	+	0.133901i	0.379536	+	0.925177i	$0.376084\pi$
$654$	0.953435	+	22.9494i	0.0372823	+	0.897391i
$655$		0			0
$656$	15.5870	+	26.9975i	0.608572	+	1.05408i
$657$	−21.1606	−	9.97636i	−0.825552	−	0.389215i
$658$	−13.3266	+	4.76328i	−0.519523	+	0.185692i
$659$		−	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	0.318022	−	0.948083i	$-0.396981\pi$
$661$	−8.84503	−	5.10668i	−0.344032	−	0.198627i	−0.662053	+	0.749457i	$0.730315\pi$
$662$	−19.8367	−	11.4527i	−0.770976	−	0.445123i
$663$	−28.5888	−	14.9592i	−1.11030	−	0.580967i
$664$		−	33.7158i		−	1.30843i
$665$		0			0
$666$	−26.6412	−	12.5603i	−1.03233	−	0.486701i
$667$	−17.3817	−	30.1060i	−0.673022	−	1.16571i
$668$	0.346004	−	0.599296i	0.0133873	−	0.0231875i
$669$	0.419510	+	10.0977i	0.0162192	+	0.390399i
$670$		0			0
$671$	−3.67895			−0.142024
$672$	19.5171	−	7.90416i	0.752888	−	0.304909i
$673$	19.1004			0.736266			0.368133	−	0.929773i	$-0.379997\pi$
$673$	19.1004			0.736266			0.368133	+	0.929773i	$0.379997\pi$
$674$	45.0282	−	25.9971i	1.73442	−	1.00137i
$675$		0			0
$676$	0.667597	−	1.15631i	0.0256768	−	0.0444735i
$677$	−1.98790	−	3.44314i	−0.0764011	−	0.132331i	0.825294	−	0.564704i	$-0.191010\pi$
$677$	−1.98790	−	3.44314i	−0.0764011	−	0.132331i	−0.901695	+	0.432373i	$0.857676\pi$
$678$	27.3094	+	43.0675i	1.04881	+	1.65400i
$679$	8.96006	+	7.60721i	0.343855	+	0.291938i
$680$		0			0
$681$	9.16474	−	17.5149i	0.351194	−	0.671172i
$682$	2.35553	+	1.35997i	0.0901981	+	0.0520759i
$683$	9.21993	+	5.32313i	0.352791	+	0.203684i	0.665914	−	0.746029i	$-0.268042\pi$
$683$	9.21993	+	5.32313i	0.352791	+	0.203684i	−0.313123	+	0.949713i	$0.601375\pi$
$684$	−0.869331	−	10.4444i	−0.0332397	−	0.399352i
$685$		0			0
$686$	−31.3491	−	0.544533i	−1.19691	−	0.0207904i
$687$	1.53825	−	0.975412i	0.0586879	−	0.0372143i
$688$	20.8114	+	36.0464i	0.793427	+	1.37426i
$689$	19.5735	−	33.9022i	0.745689	−	1.29157i
$690$		0			0
$691$	14.3020	−	8.25729i	0.544076	−	0.314122i	−0.202653	−	0.979251i	$-0.564956\pi$
$691$	14.3020	−	8.25729i	0.544076	−	0.314122i	0.746729	+	0.665128i	$0.231623\pi$
$692$	12.5743			0.478004
$693$	−3.33385	+	1.51415i	−0.126642	+	0.0575176i
$694$	−13.2401			−0.502586
$695$		0			0
$696$	25.6387	−	1.06517i	0.971834	−	0.0403750i
$697$	−17.2178	+	29.8222i	−0.652172	+	1.12960i
$698$	−21.2889	−	36.8735i	−0.805797	−	1.39568i
$699$	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	$-0.120498\pi$
$702$	−17.9772	−	23.7383i	−0.678507	−	0.895945i
$703$	20.2589	+	11.6965i	0.764078	+	0.441141i
$704$	−0.872955	−	0.504001i	−0.0329007	−	0.0189952i
$705$		0			0
$706$			20.7706i			0.781712i
$707$	2.43677	+	6.81752i	0.0916441	+	0.256399i
$708$	7.84133	+	12.3660i	0.294695	+	0.464742i
$709$	−14.1418	−	24.4943i	−0.531106	−	0.919903i	−0.999341	−	0.0362991i	$-0.988443\pi$
$709$	−14.1418	−	24.4943i	−0.531106	−	0.919903i	0.468235	−	0.883604i	$-0.344890\pi$
$710$		0			0
$711$	12.2638	+	17.6730i	0.459929	+	0.662788i
$712$	4.49694	−	2.59631i	0.168530	−	0.0973009i
$713$	15.6877			0.587509
$714$	33.6658	+	26.2579i	1.25991	+	0.982676i
$715$		0			0
$716$	1.77061	−	1.02226i	0.0661707	−	0.0382037i
$717$	0.460357	+	11.0809i	0.0171923	+	0.413823i
$718$	−6.95509	+	12.0466i	−0.259562	+	0.449574i
$719$	−9.75873	−	16.9026i	−0.363939	−	0.630361i	0.624666	−	0.780892i	$-0.285235\pi$
$719$	−9.75873	−	16.9026i	−0.363939	−	0.630361i	−0.988605	+	0.150531i	$0.951902\pi$
$720$		0			0
$721$	−8.74566	+	47.9733i	−0.325705	+	1.78662i
$722$		−	4.61959i		−	0.171923i
$723$	3.47491	+	1.81826i	0.129233	+	0.0676218i
$724$	−7.28057	−	4.20344i	−0.270580	−	0.156220i
$725$		0			0
$726$	28.0261	+	14.6648i	1.04015	+	0.544260i
$727$			26.5060i			0.983052i	0.870863	+	0.491526i	$0.163561\pi$
$727$			26.5060i			0.983052i	−0.870863	+	0.491526i	$0.836439\pi$
$728$	−11.1272	+	13.1061i	−0.412402	+	0.485743i
$729$	26.1665	−	6.65709i	0.969128	−	0.246559i
$730$		0			0
$731$	−22.9888	+	39.8177i	−0.850271	+	1.47271i
$732$	0.496574	+	11.9526i	0.0183539	+	0.441782i
$733$	−0.184602	+	0.106580i	−0.00681844	+	0.00393663i	−0.503405	−	0.864050i	$-0.667920\pi$
$733$	−0.184602	+	0.106580i	−0.00681844	+	0.00393663i	0.496587	+	0.867987i	$0.334586\pi$
$734$	47.2420			1.74373
$735$		0			0
$736$	20.6979			0.762935
$737$	−0.366045	+	0.211336i	−0.0134835	+	0.00778467i
$738$	−26.1091	+	18.1179i	−0.961090	+	0.666930i
$739$	23.2265	−	40.2296i	0.854402	−	1.47987i	−0.0227959	−	0.999740i	$-0.507257\pi$
$739$	23.2265	−	40.2296i	0.854402	−	1.47987i	0.877198	−	0.480128i	$-0.159410\pi$
$740$		0			0
$741$	12.6650	+	19.9730i	0.465261	+	0.733728i
$742$	−33.5255	+	39.4876i	−1.23076	+	1.44964i
$743$		−	28.0937i		−	1.03066i	−0.856992	−	0.515330i	$-0.827670\pi$
$743$		−	28.0937i		−	1.03066i	0.856992	−	0.515330i	$-0.172330\pi$
$744$	−5.36873	+	10.2603i	−0.196827	+	0.376159i
$745$		0			0
$746$	−26.5135	−	15.3076i	−0.970729	−	0.560451i
$747$	52.5079	−	4.37044i	1.92116	−	0.159906i
$748$			2.19874i			0.0803939i
$749$	3.15687	−	17.3166i	0.115349	−	0.632736i
$750$		0			0
$751$	−12.4832	−	21.6215i	−0.455518	−	0.788981i	0.543199	−	0.839604i	$-0.317213\pi$
$751$	−12.4832	−	21.6215i	−0.455518	−	0.788981i	−0.998718	+	0.0506227i	$0.983879\pi$
$752$	7.87068	−	13.6324i	0.287014	−	0.497123i
$753$	−23.0547	+	0.957813i	−0.840161	+	0.0349046i
$754$	38.3014	−	22.1133i	1.39485	−	0.805319i
$755$		0			0
$756$	5.36933	+	10.6270i	0.195281	+	0.386502i
$757$	6.25577			0.227370			0.113685	−	0.993517i	$-0.463735\pi$
$757$	6.25577			0.227370			0.113685	+	0.993517i	$0.463735\pi$
$758$	−36.2796	+	20.9460i	−1.31773	+	0.760794i
$759$	−3.59606	+	0.149399i	−0.130529	+	0.00542284i
$760$		0			0
$761$	−26.3374	−	45.6178i	−0.954731	−	1.65364i	−0.734982	−	0.678087i	$-0.762809\pi$
$761$	−26.3374	−	45.6178i	−0.954731	−	1.65364i	−0.219750	−	0.975556i	$-0.570524\pi$
$762$	−31.0924	+	19.7158i	−1.12636	+	0.714229i
$763$	6.97543	+	19.5157i	0.252528	+	0.706514i
$764$			4.37410i			0.158249i
$765$		0			0
$766$	−18.9563	−	10.9444i	−0.684917	−	0.395437i
$767$	−28.6151	−	16.5209i	−1.03323	−	0.596536i
$768$	−14.0130	+	26.7806i	−0.505652	+	0.966360i
$769$		−	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
$772$	5.67432	+	9.82820i	0.204223	+	0.353725i
$773$	1.22649	−	2.12434i	0.0441138	−	0.0764073i	−0.843125	−	0.537717i	$-0.819287\pi$
$773$	1.22649	−	2.12434i	0.0441138	−	0.0764073i	0.887239	+	0.461310i	$0.152620\pi$
$774$	−34.8602	+	24.1906i	−1.25302	+	0.869512i
$775$		0			0
$776$	−8.52826			−0.306147
$777$	−26.3201	−	3.67689i	−0.944227	−	0.131908i
$778$	32.0641			1.14956
$779$	21.8588	−	12.6202i	0.783172	−	0.452165i
$780$		0			0
$781$	0.351967	−	0.609625i	0.0125944	−	0.0218141i
$782$	20.9836	+	36.3446i	0.750371	+	1.29968i
$783$	4.98230	+	39.7909i	0.178053	+	1.42201i
$784$	26.9731	−	22.1060i	0.963326	−	0.789501i
$785$		0			0
$786$	17.4735	+	9.14307i	0.623258	+	0.326122i
$787$	−35.6885	−	20.6048i	−1.27216	−	0.734481i	−0.296764	−	0.954951i	$-0.595908\pi$
$787$	−35.6885	−	20.6048i	−1.27216	−	0.734481i	−0.975394	+	0.220470i	$0.929241\pi$
$788$	−15.9702	−	9.22039i	−0.568914	−	0.328463i
$789$	25.7416	+	13.4694i	0.916426	+	0.479524i
$790$		0			0
$791$	35.0764	+	29.7803i	1.24717	+	1.05887i
$792$	1.13295	−	2.40307i	0.0402576	−	0.0853893i
$793$	−13.4976	−	23.3785i	−0.479314	−	0.830196i
$794$	6.16797	−	10.6832i	0.218893	−	0.379134i
$795$		0			0
$796$	−5.01431	+	2.89501i	−0.177727	+	0.102611i
$797$	36.9407			1.30851			0.654253	−	0.756276i	$-0.272983\pi$
$797$	36.9407			1.30851			0.654253	+	0.756276i	$0.272983\pi$
$798$	−11.7469	−	29.0058i	−0.415837	−	1.02679i
$799$	17.3883			0.615154
$800$		0			0
$801$	4.62634	+	6.66685i	0.163464	+	0.235562i
$802$	−13.4292	+	23.2600i	−0.474200	+	0.821339i
$803$	−1.79870	−	3.11544i	−0.0634748	−	0.109942i
$804$	0.736023	+	1.16073i	0.0259575	+	0.0409357i
$805$		0			0
$806$			19.9582i			0.702997i
$807$	−23.5610	+	45.0277i	−0.829385	+	1.58505i
$808$	−4.54931	−	2.62655i	−0.160044	−	0.0924016i
$809$	45.9461	+	26.5270i	1.61538	+	0.932640i	0.988094	+	0.153850i	$0.0491672\pi$
$809$	45.9461	+	26.5270i	1.61538	+	0.932640i	0.627285	+	0.778790i	$0.284166\pi$
$810$		0			0
$811$			19.0686i			0.669590i	0.942291	+	0.334795i	$0.108667\pi$
$811$			19.0686i			0.669590i	−0.942291	+	0.334795i	$0.891333\pi$
$812$	−16.6523	+	5.95198i	−0.584380	+	0.208873i
$813$	4.34304	−	2.75394i	0.152317	−	0.0965850i
$814$	−2.26457	−	3.92235i	−0.0793731	−	0.137478i
$815$		0			0
$816$	−47.4481	+	1.97124i	−1.66102	+	0.0690072i
$817$	29.1852	−	16.8501i	1.02106	−	0.589511i
$818$	44.5918			1.55912
$819$	−21.8533	−	15.6303i	−0.763617	−	0.546167i
$820$		0			0
$821$	9.46302	−	5.46348i	0.330262	−	0.190677i	−0.325696	−	0.945475i	$-0.605598\pi$
$821$	9.46302	−	5.46348i	0.330262	−	0.190677i	0.655957	+	0.754798i	$0.272265\pi$
$822$	−59.6108	+	2.47654i	−2.07916	+	0.0863793i
$823$	20.9937	−	36.3622i	0.731794	−	1.26750i	−0.224321	−	0.974515i	$-0.572016\pi$
$823$	20.9937	−	36.3622i	0.731794	−	1.26750i	0.956116	−	0.292990i	$-0.0946502\pi$
$824$	−17.6909	−	30.6416i	−0.616293	−	1.06745i
$825$		0			0
$826$	33.3294	+	28.2971i	1.15968	+	0.984584i
$827$			22.1128i			0.768937i	0.923138	+	0.384468i	$0.125615\pi$
$827$			22.1128i			0.768937i	−0.923138	+	0.384468i	$0.874385\pi$
$828$	0.970771	+	11.6632i	0.0337366	+	0.405323i
$829$	27.1141	+	15.6543i	0.941711	+	0.543697i	0.890496	−	0.454990i	$-0.150357\pi$
$829$	27.1141	+	15.6543i	0.941711	+	0.543697i	0.0512148	+	0.998688i	$0.483691\pi$
$830$		0			0
$831$	10.4596	−	19.9895i	0.362838	−	0.693427i
$832$		−	7.39645i		−	0.256426i
$833$	36.0450	+	13.5940i	1.24888	+	0.471003i
$834$	−15.3755	−	24.2476i	−0.532410	−	0.839625i
$835$		0			0
$836$	0.805806	−	1.39570i	0.0278694	−	0.0482712i
$837$	−16.6749	−	7.03109i	−0.576370	−	0.243030i
$838$	−21.0389	+	12.1468i	−0.726777	+	0.419605i
$839$	−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
$842$	14.7610	−	8.52225i	0.508696	−	0.293696i
$843$	1.39769	+	33.6428i	0.0481391	+	1.15872i
$844$	2.47763	−	4.29138i	0.0852835	−	0.147715i
$845$		0			0
$846$	14.5149	+	6.84318i	0.499031	+	0.235273i
$847$	28.0775	+	5.11859i	0.964753	+	0.175877i
$848$		−	57.6164i		−	1.97855i
$849$	8.65476	+	4.52864i	0.297031	+	0.155423i
$850$		0			0
$851$	−22.6228	−	13.0613i	−0.775501	−	0.447736i
$852$	−2.02813	−	1.06123i	−0.0694826	−	0.0363571i
$853$			48.3400i			1.65513i	0.561370	+	0.827565i	$0.310274\pi$
$853$			48.3400i			1.65513i	−0.561370	+	0.827565i	$0.689726\pi$
$854$	12.0226	+	33.6365i	0.411405	+	1.15102i
$855$		0			0
$856$	6.38579	+	11.0605i	0.218262	+	0.378041i
$857$	−16.8218	+	29.1362i	−0.574622	+	0.995274i	0.421461	+	0.906847i	$0.361517\pi$
$857$	−16.8218	+	29.1362i	−0.574622	+	0.995274i	−0.996083	+	0.0884274i	$0.971816\pi$
$858$	−0.190068	−	4.57497i	−0.00648881	−	0.156187i
$859$	22.6082	−	13.0528i	0.771382	−	0.445357i	−0.0619856	−	0.998077i	$-0.519743\pi$
$859$	22.6082	−	13.0528i	0.771382	−	0.445357i	0.833367	+	0.552720i	$0.186410\pi$
$860$		0			0
$861$	−17.6351	+	22.6103i	−0.601001	+	0.770557i
$862$	−13.9573			−0.475387
$863$	−34.0767	+	19.6742i	−1.15998	+	0.669718i	−0.951300	−	0.308265i	$-0.900252\pi$
$863$	−34.0767	+	19.6742i	−1.15998	+	0.669718i	−0.208685	+	0.977983i	$0.566918\pi$
$864$	−22.0005	−	9.27662i	−0.748471	−	0.315597i
$865$		0			0
$866$	9.07765	+	15.7230i	0.308471	+	0.534288i
$867$	−12.3237	−	19.4348i	−0.418536	−	0.660042i
$868$	1.43124	−	7.85088i	0.0485793	−	0.266476i
$869$			3.30783i			0.112211i
$870$		0			0
$871$	−2.68594	−	1.55073i	−0.0910097	−	0.0525445i
$872$	−13.0227	−	7.51869i	−0.441006	−	0.254615i
$873$	−1.10548	−	13.2817i	−0.0374150	−	0.449516i
$874$		−	30.7607i		−	1.04050i
$875$		0			0
$876$	−9.87904	+	6.26435i	−0.333782	+	0.211653i
$877$	13.2655	+	22.9766i	0.447945	+	0.775864i	0.998252	−	0.0590984i	$-0.0188226\pi$
$877$	13.2655	+	22.9766i	0.447945	+	0.775864i	−0.550307	+	0.834963i	$0.685489\pi$
$878$	2.68042	−	4.64262i	0.0904597	−	0.156681i
$879$	−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	$0.571406\pi$
$882$	24.7386	+	25.5331i	0.832991	+	0.859743i
$883$	27.3728			0.921169			0.460584	−	0.887616i	$-0.347640\pi$
$883$	27.3728			0.921169			0.460584	+	0.887616i	$0.347640\pi$
$884$	−13.9723	+	8.06689i	−0.469938	+	0.271319i
$885$		0			0
$886$	−14.7738	+	25.5889i	−0.496335	+	0.859677i
$887$	−16.4606	−	28.5105i	−0.552692	−	0.957290i	−0.998079	−	0.0619524i	$-0.980267\pi$
$887$	−16.4606	−	28.5105i	−0.552692	−	0.957290i	0.445387	−	0.895338i	$-0.353066\pi$
$888$	16.2846	−	10.3262i	0.546476	−	0.346523i
$889$	−21.4997	+	25.3232i	−0.721078	+	0.849313i
$890$		0			0
$891$	3.88932	+	1.45292i	0.130297	+	0.0486747i
$892$	4.37641	+	2.52672i	0.146533	+	0.0846009i
$893$	−11.0376	−	6.37256i	−0.369359	−	0.213250i
$894$	−22.1644	+	42.3587i	−0.741288	+	1.41669i
$895$		0			0
$896$	−6.11599	+	33.5486i	−0.204321	+	1.12078i
$897$	−14.1429	−	22.3036i	−0.472216	−	0.744697i
$898$	10.4009	+	18.0149i	0.347083	+	0.601165i
$899$	13.4390	−	23.2770i	0.448216	−	0.776333i
$900$		0			0
$901$	55.1178	−	31.8223i	1.83624	−	1.06015i
$902$	−4.88682			−0.162713
$903$	−23.5458	+	30.1886i	−0.783557	+	1.00461i
$904$	−33.3860			−1.11040
$905$		0			0
$906$	1.83634	+	44.2011i	0.0610083	+	1.46848i
$907$	10.4117	−	18.0335i	0.345714	−	0.598793i	−0.639770	−	0.768567i	$-0.720970\pi$
$907$	10.4117	−	18.0335i	0.345714	−	0.598793i	0.985483	+	0.169773i	$0.0543035\pi$
$908$	−4.94217	−	8.56010i	−0.164012	−	0.284077i
$909$	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	$-0.312853\pi$
$912$	30.8412	+	16.1378i	1.02125	+	0.534375i
$913$	7.01668	+	4.05108i	0.232218	+	0.134071i
$914$	7.16844	+	4.13870i	0.237111	+	0.136896i
$915$		0			0
$916$		−	0.910763i		−	0.0300925i
$917$	17.5055	+	3.19130i	0.578083	+	0.105386i
$918$	−6.01475	−	48.0365i	−0.198516	−	1.58544i
$919$	9.88707	+	17.1249i	0.326144	+	0.564899i	0.981743	−	0.190211i	$-0.0609171\pi$
$919$	9.88707	+	17.1249i	0.326144	+	0.564899i	−0.655599	+	0.755109i	$0.727584\pi$
$920$		0			0
$921$	−1.64849	−	39.6796i	−0.0543197	−	1.30749i
$922$	7.51755	−	4.34026i	0.247577	−	0.142939i
$923$	5.16529			0.170017
$924$	−0.253313	+	1.81327i	−0.00833338	+	0.0596522i
$925$		0			0
$926$	−58.5095	+	33.7805i	−1.92274	+	1.11009i
$927$	45.4270	−	31.5232i	1.49202	−	1.03536i
$928$	17.7310	−	30.7111i	0.582050	−	1.00814i
$929$	1.84133	+	3.18927i	0.0604119	+	0.104637i	0.894650	−	0.446769i	$-0.147425\pi$
$929$	1.84133	+	3.18927i	0.0604119	+	0.104637i	−0.834238	+	0.551405i	$0.814092\pi$
$930$		0			0
$931$	−17.8983	−	21.8390i	−0.586594	−	0.715745i
$932$		−	3.36457i		−	0.110210i
$933$	1.28325	−	2.45245i	0.0420119	−	0.0802896i
$934$	−13.3802	−	7.72506i	−0.437814	−	0.252772i
$935$		0			0
$936$	19.4273	−	1.61701i	0.635002	−	0.0528538i
$937$			36.7871i			1.20178i	0.799331	+	0.600891i	$0.205187\pi$
$937$			36.7871i			1.20178i	−0.799331	+	0.600891i	$0.794813\pi$
$938$	3.12845	+	2.65610i	0.102148	+	0.0867247i
$939$	−42.2507	+	26.7914i	−1.37880	+	0.874305i
$940$		0			0
$941$	−10.1072	+	17.5061i	−0.329484	+	0.570684i	−0.982410	−	0.186739i	$-0.940208\pi$
$941$	−10.1072	+	17.5061i	−0.329484	+	0.570684i	0.652925	+	0.757422i	$0.273542\pi$
$942$	36.4789	−	1.51552i	1.18855	−	0.0493784i
$943$	−24.4094	+	14.0928i	−0.794880	+	0.458924i
$944$	−48.6310			−1.58280
$945$		0			0
$946$	−6.52474			−0.212138
$947$	8.50752	−	4.91182i	0.276457	−	0.159613i	−0.355361	−	0.934729i	$-0.615642\pi$
$947$	8.50752	−	4.91182i	0.276457	−	0.159613i	0.631819	+	0.775116i	$0.282309\pi$
$948$	10.7469	−	0.446481i	0.349043	−	0.0145010i
$949$	13.1984	−	22.8603i	0.428438	−	0.742076i
$950$		0			0
$951$	9.59621	−	6.08501i	0.311179	−	0.197320i
$952$	−26.3206	+	9.40772i	−0.853057	+	0.304906i
$953$			24.7365i			0.801294i	0.916232	+	0.400647i	$0.131215\pi$
$953$			24.7365i			0.801294i	−0.916232	+	0.400647i	$0.868785\pi$
$954$	58.5332	−	4.87195i	1.89508	−	0.157735i
$955$		0			0
$956$	4.80253	+	2.77274i	0.155325	+	0.0896769i
$957$	−2.85892	+	5.46373i	−0.0924158	+	0.176617i
$958$		−	20.9996i		−	0.678468i
$959$	−50.6917	+	18.1186i	−1.63692	+	0.585081i
$960$		0			0
$961$	−9.43537	−	16.3425i	−0.304367	−	0.527179i
$962$	16.6168	−	28.7812i	0.535748	−	0.927942i
$963$	−16.3975	+	11.3788i	−0.528403	+	0.366676i
$964$	1.69830	−	0.980514i	0.0546986	−	0.0315802i
$965$		0			0
$966$	13.1177	+	32.3904i	0.422054	+	1.04214i
$967$	14.0157			0.450713			0.225357	−	0.974276i	$-0.427645\pi$
$967$	14.0157			0.450713			0.225357	+	0.974276i	$0.427645\pi$
$968$	−17.9337	+	10.3540i	−0.576410	+	0.332791i
$969$	1.59603	+	38.4168i	0.0512719	+	1.23412i
$970$		0			0
$971$	0.0308306	+	0.0534003i	0.000989403	+	0.00171370i	0.866520	−	0.499143i	$-0.166352\pi$
$971$	0.0308306	+	0.0534003i	0.000989403	+	0.00171370i	−0.865530	+	0.500857i	$0.833018\pi$
$972$	4.19546	−	12.8322i	0.134569	−	0.411593i
$973$	−19.7485	−	16.7667i	−0.633106	−	0.537516i
$974$		−	23.9792i		−	0.768342i
$975$		0			0
$976$	−34.4085	−	19.8657i	−1.10139	−	0.635887i
$977$	−16.5237	−	9.53996i	−0.528640	−	0.305210i	0.211822	−	0.977308i	$-0.432060\pi$
$977$	−16.5237	−	9.53996i	−0.528640	−	0.305210i	−0.740462	+	0.672098i	$0.765393\pi$
$978$	14.2995	+	7.48229i	0.457248	+	0.239257i
$979$			1.24783i			0.0398808i
$980$		0			0
$981$	10.0213	−	21.2558i	0.319955	−	0.678647i
$982$	−27.1900	−	47.0945i	−0.867669	−	1.50285i
$983$	4.07300	−	7.05465i	0.129909	−	0.225008i	−0.793732	−	0.608267i	$-0.791865\pi$
$983$	4.07300	−	7.05465i	0.129909	−	0.225008i	0.923641	+	0.383259i	$0.125198\pi$
$984$	−0.863618	−	20.7875i	−0.0275311	−	0.662680i
$985$		0			0
$986$	71.9030			2.28986
$987$	14.3399	+	2.00327i	0.456444	+	0.0637649i
$988$	11.8256			0.376222
$989$	−32.5908	+	18.8163i	−1.03633	+	0.598324i
$990$		0			0
$991$	−5.21862	+	9.03891i	−0.165775	+	0.287130i	−0.936930	−	0.349517i	$-0.886346\pi$
$991$	−5.21862	+	9.03891i	−0.165775	+	0.287130i	0.771155	+	0.636647i	$0.219679\pi$
$992$	8.00150	+	13.8590i	0.254048	+	0.440024i
$993$	12.5496	+	19.7910i	0.398250	+	0.628050i
$994$	−6.72398	−	1.22580i	−0.213272	−	0.0388800i
$995$		0			0
$996$	12.2146	−	23.3435i	0.387033	−	0.739666i
$997$	11.6811	+	6.74411i	0.369945	+	0.213588i	0.673435	−	0.739247i	$-0.264818\pi$
$997$	11.6811	+	6.74411i	0.369945	+	0.213588i	−0.303489	+	0.952835i	$0.598152\pi$
$998$	39.1719	+	22.6159i	1.23996	+	0.715894i
$999$	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.t.i.101.3	yes	20
3.2	odd	2	inner	525.2.t.i.101.8	yes	20
5.2	odd	4		525.2.q.g.374.6		40
5.3	odd	4		525.2.q.g.374.15		40
5.4	even	2		525.2.t.h.101.8	yes	20
7.5	odd	6	inner	525.2.t.i.26.8	yes	20
15.2	even	4		525.2.q.g.374.16		40
15.8	even	4		525.2.q.g.374.5		40
15.14	odd	2		525.2.t.h.101.3	yes	20
21.5	even	6	inner	525.2.t.i.26.3	yes	20
35.12	even	12		525.2.q.g.299.5		40
35.19	odd	6		525.2.t.h.26.3	✓	20
35.33	even	12		525.2.q.g.299.16		40
105.47	odd	12		525.2.q.g.299.15		40
105.68	odd	12		525.2.q.g.299.6		40
105.89	even	6		525.2.t.h.26.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.5		40	35.12	even	12
525.2.q.g.299.6		40	105.68	odd	12
525.2.q.g.299.15		40	105.47	odd	12
525.2.q.g.299.16		40	35.33	even	12
525.2.q.g.374.5		40	15.8	even	4
525.2.q.g.374.6		40	5.2	odd	4
525.2.q.g.374.15		40	5.3	odd	4
525.2.q.g.374.16		40	15.2	even	4
525.2.t.h.26.3	✓	20	35.19	odd	6
525.2.t.h.26.8	yes	20	105.89	even	6
525.2.t.h.101.3	yes	20	15.14	odd	2
525.2.t.h.101.8	yes	20	5.4	even	2
525.2.t.i.26.3	yes	20	21.5	even	6	inner
525.2.t.i.26.8	yes	20	7.5	odd	6	inner
525.2.t.i.101.3	yes	20	1.1	even	1	trivial
525.2.t.i.101.8	yes	20	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46613 + 0.846473i) q^{2} +(1.73056 - 0.0718963i) q^{3} +(0.433034 - 0.750036i) q^{4} +(-2.47637 + 1.57028i) q^{6} +(-1.71236 + 2.01688i) q^{7} -1.91969i q^{8} +(2.98966 - 0.248842i) q^{9} +O(q^{10})\)	\(q+(-1.46613 + 0.846473i) q^{2} +(1.73056 - 0.0718963i) q^{3} +(0.433034 - 0.750036i) q^{4} +(-2.47637 + 1.57028i) q^{6} +(-1.71236 + 2.01688i) q^{7} -1.91969i q^{8} +(2.98966 - 0.248842i) q^{9} +(0.399511 + 0.230658i) q^{11} +(0.695465 - 1.32911i) q^{12} +3.38501i q^{13} +(0.803314 - 4.40649i) q^{14} +(2.49103 + 4.31459i) q^{16} +(-2.75166 + 4.76601i) q^{17} +(-4.17261 + 2.89550i) q^{18} +(3.49334 - 2.01688i) q^{19} +(-2.81833 + 3.61345i) q^{21} -0.780983 q^{22} +(-3.90097 + 2.25223i) q^{23} +(-0.138018 - 3.32213i) q^{24} +(-2.86532 - 4.96289i) q^{26} +(5.15589 - 0.645580i) q^{27} +(0.771225 + 2.15771i) q^{28} +7.71756i q^{29} +(-3.01611 - 1.74135i) q^{31} +(-3.97938 - 2.29749i) q^{32} +(0.707961 + 0.370444i) q^{33} -9.31681i q^{34} +(1.10798 - 2.35011i) q^{36} +(2.89964 + 5.02232i) q^{37} +(-3.41448 + 5.91404i) q^{38} +(0.243370 + 5.85796i) q^{39} +6.25727 q^{41} +(1.07337 - 7.68344i) q^{42} +8.35453 q^{43} +(0.346004 - 0.199765i) q^{44} +(3.81290 - 6.60414i) q^{46} +(-1.57980 - 2.73630i) q^{47} +(4.62108 + 7.28756i) q^{48} +(-1.13564 - 6.90727i) q^{49} +(-4.41924 + 8.44568i) q^{51} +(2.53888 + 1.46582i) q^{52} +(-10.0154 - 5.78238i) q^{53} +(-7.01277 + 5.31083i) q^{54} +(3.87179 + 3.28720i) q^{56} +(5.90043 - 3.74149i) q^{57} +(-6.53271 - 11.3150i) q^{58} +(-4.88061 + 8.45346i) q^{59} +(-6.90647 + 3.98746i) q^{61} +5.89604 q^{62} +(-4.61750 + 6.45591i) q^{63} -2.18506 q^{64} +(-1.35154 + 0.0561498i) q^{66} +(-0.458116 + 0.793481i) q^{67} +(2.38312 + 4.12768i) q^{68} +(-6.58893 + 4.17808i) q^{69} -1.52593i q^{71} +(-0.477698 - 5.73922i) q^{72} +(-6.75338 - 3.89906i) q^{73} +(-8.50252 - 4.90893i) q^{74} -3.49351i q^{76} +(-1.14932 + 0.410798i) q^{77} +(-5.31542 - 8.38256i) q^{78} +(3.58521 + 6.20977i) q^{79} +(8.87616 - 1.48790i) q^{81} +(-9.17399 + 5.29661i) q^{82} +17.5632 q^{83} +(1.48978 + 3.67860i) q^{84} +(-12.2489 + 7.07188i) q^{86} +(0.554864 + 13.3557i) q^{87} +(0.442791 - 0.766937i) q^{88} +(1.35247 + 2.34254i) q^{89} +(-6.82718 - 5.79637i) q^{91} +3.90116i q^{92} +(-5.34476 - 2.79667i) q^{93} +(4.63241 + 2.67452i) q^{94} +(-7.05172 - 3.68984i) q^{96} -4.44253i q^{97} +(7.51181 + 9.16569i) q^{98} +(1.25180 + 0.590174i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) \) 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9	\( 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9} - 21 q^{12} - 18 q^{16} + 14 q^{18} - 9 q^{21} + 20 q^{22} + 18 q^{24} - 10 q^{28} + 42 q^{31} + 12 q^{33} - 36 q^{36} + 24 q^{37} + 33 q^{42} + 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} - 84 q^{52} - 75 q^{54} + 6 q^{57} - 4 q^{58} - 90 q^{61} - 5 q^{63} - 120 q^{64} + 6 q^{66} + 20 q^{67} - 35 q^{72} - 48 q^{73} - 108 q^{78} + 46 q^{79} + 29 q^{81} + 36 q^{82} + 75 q^{84} + 69 q^{87} + 4 q^{88} - 30 q^{91} - 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) \) 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9 - 21 * q^12 - 18 * q^16 + 14 * q^18 - 9 * q^21 + 20 * q^22 + 18 * q^24 - 10 * q^28 + 42 * q^31 + 12 * q^33 - 36 * q^36 + 24 * q^37 + 33 * q^42 + 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 - 84 * q^52 - 75 * q^54 + 6 * q^57 - 4 * q^58 - 90 * q^61 - 5 * q^63 - 120 * q^64 + 6 * q^66 + 20 * q^67 - 35 * q^72 - 48 * q^73 - 108 * q^78 + 46 * q^79 + 29 * q^81 + 36 * q^82 + 75 * q^84 + 69 * q^87 + 4 * q^88 - 30 * q^91 - 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * q^99

Introduction

L-functions

Modular forms

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