LMFDB - Embedded newform 525.2.t.i.26.8

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			26.8
Root			$1.73056 + 0.0718963i$ of defining polynomial
Character	$\chi$	$=$	525.26
Dual form			525.2.t.i.101.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46613 + 0.846473i) q^{2} +(0.803015 - 1.53466i) q^{3} +(0.433034 + 0.750036i) q^{4} +(2.47637 - 1.57028i) q^{6} +(-1.71236 - 2.01688i) q^{7} -1.91969i q^{8} +(-1.71033 - 2.46470i) q^{9} +O(q^{10})$	\(q+(1.46613 + 0.846473i) q^{2} +(0.803015 - 1.53466i) q^{3} +(0.433034 + 0.750036i) q^{4} +(2.47637 - 1.57028i) q^{6} +(-1.71236 - 2.01688i) q^{7} -1.91969i q^{8} +(-1.71033 - 2.46470i) q^{9} +(-0.399511 + 0.230658i) q^{11} +(1.49878 - 0.0622670i) q^{12} -3.38501i q^{13} +(-0.803314 - 4.40649i) q^{14} +(2.49103 - 4.31459i) q^{16} +(2.75166 + 4.76601i) q^{17} +(-0.421275 - 5.06134i) q^{18} +(3.49334 + 2.01688i) q^{19} +(-4.47027 + 1.00830i) q^{21} -0.780983 q^{22} +(3.90097 + 2.25223i) q^{23} +(-2.94606 - 1.54154i) 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} +(0.0331669 + 0.798334i) q^{33} +9.31681i q^{34} +(1.10798 - 2.35011i) q^{36} +(2.89964 - 5.02232i) q^{37} +(3.41448 + 5.91404i) q^{38} +(-5.19483 - 2.71822i) q^{39} -6.25727 q^{41} +(-7.40752 - 2.30567i) 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} +(9.52380 - 0.395668i) q^{51} +(2.53888 - 1.46582i) q^{52} +(10.0154 - 5.78238i) q^{53} +(-8.10570 - 3.41782i) 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} +(-2.04231 + 7.67001i) q^{63} -2.18506 q^{64} +(-0.627141 + 1.19854i) q^{66} +(-0.458116 - 0.793481i) q^{67} +(-2.38312 + 4.12768i) q^{68} +(6.58893 - 4.17808i) q^{69} -1.52593i q^{71} +(-4.73146 + 3.28331i) 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} +(-3.14952 + 8.43093i) q^{81} +(-9.17399 - 5.29661i) q^{82} -17.5632 q^{83} +(-2.69204 - 2.91624i) q^{84} +(12.2489 + 7.07188i) q^{86} +(11.8438 + 6.19732i) q^{87} +(0.442791 + 0.766937i) q^{88} +(-1.35247 + 2.34254i) q^{89} +(-6.82718 + 5.79637i) q^{91} +3.90116i q^{92} +(0.250394 + 6.02703i) q^{93} +(4.63241 - 2.67452i) q^{94} +(-0.330363 - 7.95189i) 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.46613	+	0.846473i	1.03671	+	0.598547i	0.918901	−	0.394489i	$-0.129078\pi$
$2$	1.46613	+	0.846473i	1.03671	+	0.598547i	0.117813	+	0.993036i	$0.462412\pi$
$3$	0.803015	−	1.53466i	0.463621	−	0.886034i
$3$	0.803015	−	1.53466i	0.463621	−	0.886034i
$4$	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
$9$	−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	$0.355488\pi$
$12$	1.49878	−	0.0622670i	0.432660	−	0.0179749i
$13$		−	3.38501i		−	0.938834i	−0.882977	−	0.469417i	$-0.844464\pi$
$13$		−	3.38501i		−	0.938834i	0.882977	−	0.469417i	$-0.155536\pi$
$14$	−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	0.978636	+	0.205602i	$0.0659152\pi$
$17$	2.75166	+	4.76601i	0.667374	+	1.15593i	−0.311261	+	0.950324i	$0.600751\pi$
$18$	−0.421275	−	5.06134i	−0.0992955	−	1.19297i
$19$	3.49334	+	2.01688i	0.801428	+	0.462705i	0.843970	−	0.536390i	$-0.180212\pi$
$19$	3.49334	+	2.01688i	0.801428	+	0.462705i	−0.0425421	+	0.999095i	$0.513546\pi$
$20$		0			0
$21$	−4.47027	+	1.00830i	−0.975493	+	0.220028i
$22$	−0.780983			−0.166506
$23$	3.90097	+	2.25223i	0.813409	+	0.469622i	0.848138	−	0.529775i	$-0.177724\pi$
$23$	3.90097	+	2.25223i	0.813409	+	0.469622i	−0.0347292	+	0.999397i	$0.511057\pi$
$24$	−2.94606	−	1.54154i	−0.601362	−	0.314665i
$25$		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	−0.745772	−	0.666202i	$-0.767919\pi$
$31$	−3.01611	+	1.74135i	−0.541710	+	0.312756i	0.204062	+	0.978958i	$0.434586\pi$
$32$	3.97938	−	2.29749i	0.703461	−	0.406143i
$33$	0.0331669	+	0.798334i	0.00577362	+	0.138972i
$34$			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	−0.522946	−	0.852366i	$-0.675167\pi$
$37$	2.89964	−	5.02232i	0.476698	−	0.825665i	0.999643	+	0.0267011i	$0.00850024\pi$
$38$	3.41448	+	5.91404i	0.553901	+	0.959385i
$39$	−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	$0.662496\pi$
$42$	−7.40752	−	2.30567i	−1.14300	−	0.355772i
$43$	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	$-0.759317\pi$
$47$	1.57980	−	2.73630i	0.230438	−	0.399130i	0.957937	+	0.286978i	$0.0926508\pi$
$48$	−4.62108	−	7.28756i	−0.666995	−	1.05187i
$49$	−1.13564	+	6.90727i	−0.162234	+	0.986752i
$50$		0			0
$51$	9.52380	−	0.395668i	1.33360	−	0.0554046i
$52$	2.53888	−	1.46582i	0.352080	−	0.203273i
$53$	10.0154	−	5.78238i	1.37572	−	0.794271i	0.384078	−	0.923301i	$-0.374519\pi$
$53$	10.0154	−	5.78238i	1.37572	−	0.794271i	0.991641	+	0.129029i	$0.0411861\pi$
$54$	−8.10570	−	3.41782i	−1.10305	−	0.465106i
$55$		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	0.986430	+	0.164183i	$0.0524986\pi$
$59$	4.88061	+	8.45346i	0.635401	+	1.10055i	−0.351029	+	0.936365i	$0.614168\pi$
$60$		0			0
$61$	−6.90647	−	3.98746i	−0.884283	−	0.510541i	−0.0122151	−	0.999925i	$-0.503888\pi$
$61$	−6.90647	−	3.98746i	−0.884283	−	0.510541i	−0.872068	+	0.489384i	$0.837222\pi$
$62$	−5.89604			−0.748798
$63$	−2.04231	+	7.67001i	−0.257307	+	0.966330i
$64$	−2.18506			−0.273132
$65$		0			0
$66$	−0.627141	+	1.19854i	−0.0771957	+	0.147530i
$67$	−0.458116	−	0.793481i	−0.0559678	−	0.0969391i	0.836684	−	0.547686i	$-0.184491\pi$
$67$	−0.458116	−	0.793481i	−0.0559678	−	0.0969391i	−0.892652	+	0.450747i	$0.851158\pi$
$68$	−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	$-0.0288616\pi$
$72$	−4.73146	+	3.28331i	−0.557608	+	0.386941i
$73$	−6.75338	+	3.89906i	−0.790423	+	0.456351i	−0.840112	−	0.542414i	$-0.817511\pi$
$73$	−6.75338	+	3.89906i	−0.790423	+	0.456351i	0.0496883	+	0.998765i	$0.484177\pi$
$74$	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	−0.590762	−	0.806846i	$-0.701173\pi$
$79$	3.58521	−	6.20977i	0.403368	−	0.698654i	0.994130	+	0.108192i	$0.0345061\pi$
$80$		0			0
$81$	−3.14952	+	8.43093i	−0.349946	+	0.936770i
$82$	−9.17399	−	5.29661i	−1.01310	−	0.584912i
$83$	−17.5632			−1.92781			−0.963904	−	0.266250i	$-0.914215\pi$
$83$	−17.5632			−1.92781			−0.963904	+	0.266250i	$0.914215\pi$
$84$	−2.69204	−	2.91624i	−0.293725	−	0.318188i
$85$		0			0
$86$	12.2489	+	7.07188i	1.32083	+	0.762581i
$87$	11.8438	+	6.19732i	1.26979	+	0.664422i
$88$	0.442791	+	0.766937i	0.0472017	+	0.0817558i
$89$	−1.35247	+	2.34254i	−0.143361	+	0.248309i	−0.928760	−	0.370681i	$-0.879124\pi$
$89$	−1.35247	+	2.34254i	−0.143361	+	0.248309i	0.785399	+	0.618990i	$0.212458\pi$
$90$		0			0
$91$	−6.82718	+	5.79637i	−0.715683	+	0.607625i
$92$			3.90116i			0.406724i
$93$	0.250394	+	6.02703i	0.0259646	+	0.624974i
$94$	4.63241	−	2.67452i	0.477796	−	0.275856i
$95$		0			0
$96$	−0.330363	−	7.95189i	−0.0337175	−	0.811587i
$97$			4.44253i			0.451070i	0.974235	+	0.225535i	$0.0724130\pi$
$97$			4.44253i			0.451070i	−0.974235	+	0.225535i	$0.927587\pi$
$98$	−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	$-0.210137\pi$
$101$	−1.36822	−	2.36982i	−0.136143	−	0.235806i	−0.926033	+	0.377442i	$0.876804\pi$
$102$	14.2981	+	7.48154i	1.41572	+	0.740782i
$103$	15.9618	+	9.21552i	1.57276	+	0.908033i	0.995829	+	0.0912387i	$0.0290826\pi$
$103$	15.9618	+	9.21552i	1.57276	+	0.908033i	0.576930	+	0.816794i	$0.304251\pi$
$104$	−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	$-0.229119\pi$
$107$	5.76162	+	3.32647i	0.556997	+	0.321582i	−0.194942	+	0.980815i	$0.562452\pi$
$108$	−2.71688	−	3.58755i	−0.261432	−	0.345212i
$109$	3.91662	+	6.78379i	0.375144	+	0.649769i	0.990349	−	0.138599i	$-0.0442599\pi$
$109$	3.91662	+	6.78379i	0.375144	+	0.649769i	−0.615204	+	0.788368i	$0.710927\pi$
$110$		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	$-0.304929\pi$
$114$	11.8179	−	0.490976i	1.10685	−	0.0459842i
$115$		0			0
$116$	−5.78845	+	3.34196i	−0.537444	+	0.310293i
$117$	−8.34305	+	5.78951i	−0.771316	+	0.535240i
$118$			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
$123$	−5.02468	+	9.60275i	−0.453060	+	0.865850i
$124$	−2.61216	−	1.50813i	−0.234579	−	0.135434i
$125$		0			0
$126$	−9.48675	+	9.51650i	−0.845147	+	0.847797i
$127$	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
$129$	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	$0.0717450\pi$
$132$	−0.584417	+	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	−0.505468	+	0.862845i	$0.668680\pi$
$137$	−17.6208	+	10.1734i	−1.50545	+	0.869171i	−0.999980	+	0.00632592i	$0.997986\pi$
$138$	13.1969	−	0.548267i	1.12339	−	0.0466716i
$139$		−	9.79157i		−	0.830510i	−0.909705	−	0.415255i	$-0.863692\pi$
$139$		−	9.79157i		−	0.830510i	0.909705	−	0.415255i	$-0.136308\pi$
$140$		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
$144$	−14.8947	+	1.23974i	−1.24122	+	0.103312i
$145$		0			0
$146$	−13.2018			−1.09259
$147$	9.68834	+	7.28945i	0.799081	+	0.601224i
$148$	5.02257			0.412852
$149$	−14.1195	−	8.15190i	−1.15671	−	0.667830i	−0.206200	−	0.978510i	$-0.566110\pi$
$149$	−14.1195	−	8.15190i	−1.15671	−	0.667830i	−0.950514	+	0.310680i	$0.899443\pi$
$150$		0			0
$151$	7.54351	+	13.0657i	0.613882	+	1.06328i	0.990580	+	0.136939i	$0.0437263\pi$
$151$	7.54351	+	13.0657i	0.613882	+	1.06328i	−0.376697	+	0.926336i	$0.622940\pi$
$152$	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
$156$	−0.210775	−	5.07339i	−0.0168755	−	0.406196i
$157$	−10.7831	+	6.22562i	−0.860584	+	0.496858i	−0.864208	−	0.503135i	$-0.832180\pi$
$157$	−10.7831	+	6.22562i	−0.860584	+	0.496858i	0.00362372	+	0.999993i	$0.498847\pi$
$158$	10.5128	−	6.06958i	0.836354	−	0.482869i
$159$	−0.831464	−	20.0135i	−0.0659394	−	1.58717i
$160$		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	−0.953442	−	0.301577i	$-0.902487\pi$
$163$	−2.75193	+	4.76649i	−0.215548	+	0.373340i	0.737894	+	0.674917i	$0.235820\pi$
$164$	−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	$-0.509842\pi$
$167$	−0.799023			−0.0618302			−0.0309151	+	0.999522i	$0.509842\pi$
$168$	1.93562	+	8.58153i	0.149336	+	0.662079i
$169$	1.54168			0.118590
$170$		0			0
$171$	−1.00377	−	12.0596i	−0.0767601	−	0.922221i
$172$	3.61779	+	6.26620i	0.275854	+	0.477793i
$173$	−7.25944	+	12.5737i	−0.551925	+	0.955962i	0.446211	+	0.894928i	$0.352773\pi$
$173$	−7.25944	+	12.5737i	−0.551925	+	0.955962i	−0.998136	+	0.0610338i	$0.980560\pi$
$174$	12.1187	+	19.1116i	0.918719	+	1.44884i
$175$		0			0
$176$			2.29830i			0.173241i
$177$	16.8924	−	0.701796i	1.26971	−	0.0527502i
$178$	−3.96579	+	2.28965i	−0.297249	+	0.171617i
$179$	−2.04442	+	1.18035i	−0.152807	+	0.0882234i	−0.574454	−	0.818537i	$-0.694786\pi$
$179$	−2.04442	+	1.18035i	−0.152807	+	0.0882234i	0.421647	+	0.906760i	$0.361452\pi$
$180$		0			0
$181$			9.70696i			0.721513i	0.932660	+	0.360756i	$0.117481\pi$
$181$			9.70696i			0.721513i	−0.932660	+	0.360756i	$0.882519\pi$
$182$	−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
$186$	−4.73461	+	9.04839i	−0.347158	+	0.663460i
$187$	−2.19863	−	1.26938i	−0.160780	−	0.0928264i
$188$	2.73643			0.199575
$189$	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	$0.608176\pi$
$192$	−1.75463	+	3.35331i	−0.126630	+	0.242004i
$193$	−6.55182	−	11.3481i	−0.471610	−	0.816853i	0.527862	−	0.849330i	$-0.322994\pi$
$193$	−6.55182	−	11.3481i	−0.471610	−	0.816853i	−0.999472	+	0.0324769i	$0.989660\pi$
$194$	−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	$-0.274075\pi$
$198$	1.33574	+	1.92489i	0.0949270	+	0.136796i
$199$	−5.78974	+	3.34271i	−0.410424	+	0.236958i	−0.690972	−	0.722882i	$-0.742817\pi$
$199$	−5.78974	+	3.34271i	−0.410424	+	0.236958i	0.280548	+	0.959840i	$0.409484\pi$
$200$		0			0
$201$	−1.58559	+	0.0658738i	−0.111839	+	0.00464638i
$202$		−	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
$207$	−1.12090	−	13.4668i	−0.0779076	−	0.936007i
$208$	−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
$213$	−2.34177	−	1.22534i	−0.160456	−	0.0839591i
$214$	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
$219$	0.560657	+	13.4951i	0.0378857	+	0.911915i
$220$		0			0
$221$	16.1330	−	9.31439i	1.08522	−	0.626554i
$222$	−0.705869	−	16.9904i	−0.0473748	−	1.14032i
$223$		−	5.83493i		−	0.390736i	−0.980730	−	0.195368i	$-0.937410\pi$
$223$		−	5.83493i		−	0.390736i	0.980730	−	0.195368i	$-0.0625901\pi$
$224$	−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	$-0.290313\pi$
$227$	−5.70646	−	9.88387i	−0.378751	−	0.656016i	−0.990881	+	0.134741i	$0.956980\pi$
$228$	5.36134	+	2.80534i	0.355063	+	0.185788i
$229$	0.910719	+	0.525804i	0.0601820	+	0.0347461i	0.529789	−	0.848129i	$-0.322271\pi$
$229$	0.910719	+	0.525804i	0.0601820	+	0.0347461i	−0.469607	+	0.882876i	$0.655604\pi$
$230$		0			0
$231$	1.55335	−	1.43393i	0.102203	−	0.0943457i
$232$	14.8153			0.972672
$233$	−3.36441	−	1.94244i	−0.220410	−	0.127254i	0.385730	−	0.922612i	$-0.373950\pi$
$233$	−3.36441	−	1.94244i	−0.220410	−	0.127254i	−0.606140	+	0.795358i	$0.707283\pi$
$234$	−17.1327	+	1.42602i	−1.12000	+	0.0932220i
$235$		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	−0.435511	−	0.900183i	$-0.643432\pi$
$241$	1.96093	−	1.13215i	0.126315	−	0.0729279i	0.561826	+	0.827255i	$0.310099\pi$
$242$	−15.8155	+	9.13106i	−1.01666	+	0.586967i
$243$	10.4095	+	11.6036i	0.667767	+	0.744370i
$244$		−	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
$249$	−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	$0.361875\pi$
$252$	−6.63717	+	1.78957i	−0.418102	+	0.112732i
$253$	−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	−0.379969	−	0.924999i	$-0.624066\pi$
$257$	9.79648	−	16.9680i	0.611088	−	1.05844i	0.991057	−	0.133436i	$-0.0426012\pi$
$258$	20.6889	−	13.1190i	1.28804	−	0.816750i
$259$	−15.0947	+	2.75180i	−0.937937	+	0.170988i
$260$		0			0
$261$	19.0215	−	13.1996i	1.17740	−	0.817035i
$262$	9.86050	−	5.69296i	0.609184	−	0.351712i
$263$	−14.5263	+	8.38678i	−0.895732	+	0.517151i	−0.875813	−	0.482651i	$-0.839674\pi$
$263$	−14.5263	+	8.38678i	−0.895732	+	0.517151i	−0.0199186	+	0.999802i	$0.506341\pi$
$264$	1.53255	−	0.0636701i	0.0943220	−	0.00391863i
$265$		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	0.834466	+	0.551060i	$0.185776\pi$
$269$	14.6703	+	25.4097i	0.894465	+	1.54926i	0.0599988	+	0.998198i	$0.480890\pi$
$270$		0			0
$271$	2.57129	+	1.48454i	0.156195	+	0.0901792i	0.576060	−	0.817407i	$-0.304589\pi$
$271$	2.57129	+	1.48454i	0.156195	+	0.0901792i	−0.419865	+	0.907586i	$0.637923\pi$
$272$	27.4178			1.66245
$273$	3.41310	+	15.1319i	0.206570	+	0.915827i
$274$	−34.4460			−2.08096
$275$		0			0
$276$	5.98694	+	3.13269i	0.360371	+	0.188566i
$277$	6.51269	+	11.2803i	0.391309	+	0.677768i	0.992623	−	0.121246i	$-0.0386889\pi$
$277$	6.51269	+	11.2803i	0.391309	+	0.677768i	−0.601313	+	0.799014i	$0.705356\pi$
$278$	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	$0.803108\pi$
$282$	−0.384577	−	9.25683i	−0.0229012	−	0.551236i
$283$	4.88399	−	2.81977i	0.290323	−	0.167618i	−0.347764	−	0.937582i	$-0.613059\pi$
$283$	4.88399	−	2.81977i	0.290323	−	0.167618i	0.638088	+	0.769964i	$0.279726\pi$
$284$	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
$291$	6.81775	+	3.56741i	0.399663	+	0.209126i
$292$	−5.84888	−	3.37685i	−0.342280	−	0.197615i
$293$	21.5754			1.26045			0.630226	−	0.776412i	$-0.282962\pi$
$293$	21.5754			1.26045			0.630226	+	0.776412i	$0.282962\pi$
$294$	8.03409	+	18.8882i	0.468557	+	1.10158i
$295$		0			0
$296$	−9.64129	−	5.56640i	−0.560389	−	0.323541i
$297$	1.91093	−	1.44716i	0.110883	−	0.0839730i
$298$	−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
$303$	−4.73555	+	0.196739i	−0.272050	+	0.0113024i
$304$	17.4041	−	10.0482i	0.998191	−	0.576306i
$305$		0			0
$306$	22.9632	−	15.9349i	1.31272	−	0.910935i
$307$			22.9288i			1.30861i	0.756229	+	0.654307i	$0.227040\pi$
$307$			22.9288i			1.30861i	−0.756229	+	0.654307i	$0.772960\pi$
$308$	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	$-0.181094\pi$
$311$	−0.799023	−	1.38395i	−0.0453084	−	0.0784765i	−0.887790	+	0.460248i	$0.847760\pi$
$312$	−5.21813	+	9.97245i	−0.295418	+	0.564579i
$313$	−25.0145	−	14.4421i	−1.41390	−	0.816318i	−0.418151	−	0.908378i	$-0.637322\pi$
$313$	−25.0145	−	14.4421i	−1.41390	−	0.816318i	−0.995754	+	0.0920593i	$0.970655\pi$
$314$	−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	$-0.392313\pi$
$317$	−5.68143	−	3.28018i	−0.319101	−	0.184233i	−0.650992	+	0.759085i	$0.725647\pi$
$318$	15.7219	−	30.0463i	0.881638	−	1.68491i
$319$	−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
$324$	−7.68735	+	1.28862i	−0.427075	+	0.0715903i
$325$		0			0
$326$	−8.06940	+	4.65887i	−0.446923	+	0.258031i
$327$	13.5559	−	0.563181i	0.749642	−	0.0311440i
$328$			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	−0.618012	−	0.786169i	$-0.712062\pi$
$331$	6.76497	−	11.7173i	0.371836	−	0.644040i	0.989848	+	0.142129i	$0.0453949\pi$
$332$	−7.60544	−	13.1730i	−0.417403	−	0.722963i
$333$	−17.3379	+	1.44310i	−0.950110	+	0.0790815i
$334$	−1.17147	−	0.676351i	−0.0641002	−	0.0370083i
$335$		0			0
$336$	−6.78520	+	21.7991i	−0.370163	+	1.18924i
$337$	−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
$339$	−26.6898	−	13.9655i	−1.44959	−	0.758504i
$340$		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	$-0.733987\pi$
$347$	−6.77295	+	3.91036i	−0.363591	+	0.209919i	0.307064	+	0.951689i	$0.400653\pi$
$348$	0.480550	+	11.5669i	0.0257602	+	0.620052i
$349$		−	25.1501i		−	1.34625i	−0.739526	−	0.673127i	$-0.764951\pi$
$349$		−	25.1501i		−	1.34625i	0.739526	−	0.673127i	$-0.235049\pi$
$350$		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	$-0.272537\pi$
$353$	−6.13445	−	10.6252i	−0.326504	−	0.565521i	−0.981816	+	0.189837i	$0.939204\pi$
$354$	25.3605	+	13.2700i	1.34790	+	0.705292i
$355$		0			0
$356$	−2.34265			−0.124160
$357$	−17.1062	−	18.5309i	−0.905356	−	0.980757i
$358$	−3.99653			−0.211223
$359$	−7.11574	−	4.10828i	−0.375555	−	0.216827i	0.300328	−	0.953836i	$-0.402904\pi$
$359$	−7.11574	−	4.10828i	−0.375555	−	0.216827i	−0.675882	+	0.737010i	$0.736237\pi$
$360$		0			0
$361$	−1.36436	−	2.36315i	−0.0718086	−	0.124376i
$362$	−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
$366$	−23.3644	+	0.970679i	−1.22128	+	0.0507382i
$367$	−24.1666	+	13.9526i	−1.26149	+	0.728320i	−0.973362	−	0.229273i	$-0.926365\pi$
$367$	−24.1666	+	13.9526i	−1.26149	+	0.728320i	−0.288125	+	0.957593i	$0.593032\pi$
$368$	19.4349	−	11.2207i	1.01311	−	0.584921i
$369$	10.7020	+	15.4223i	0.557125	+	0.802853i
$370$		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	−0.531162	−	0.847270i	$-0.678245\pi$
$373$	9.04199	−	15.6612i	0.468176	−	0.810905i	0.999339	+	0.0363650i	$0.0115779\pi$
$374$	−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
$378$	6.98655	+	22.2008i	0.359349	+	1.14189i
$379$	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
$381$	10.0823	−	19.2685i	0.516534	−	0.987157i
$382$	4.27514	+	7.40476i	0.218735	+	0.378861i
$383$	−6.46470	+	11.1972i	−0.330331	+	0.572150i	−0.982577	−	0.185858i	$-0.940494\pi$
$383$	−6.46470	+	11.1972i	−0.330331	+	0.572150i	0.652246	+	0.758008i	$0.273827\pi$
$384$	−18.8537	+	11.9552i	−0.962126	+	0.610089i
$385$		0			0
$386$		−	22.1838i		−	1.12912i
$387$	−14.2890	−	20.5914i	−0.726352	−	1.04672i
$388$	−3.33205	+	1.92376i	−0.169159	+	0.0976642i
$389$	16.4024	−	9.46992i	0.831634	−	0.480144i	−0.0227777	−	0.999741i	$-0.507251\pi$
$389$	16.4024	−	9.46992i	0.831634	−	0.480144i	0.854412	+	0.519596i	$0.173918\pi$
$390$		0			0
$391$			24.7894i			1.25365i
$392$	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
$396$	0.0994198	+	1.19446i	0.00499603	+	0.0600239i
$397$	−6.31044	−	3.64333i	−0.316712	−	0.182854i	0.333214	−	0.942851i	$-0.391867\pi$
$397$	−6.31044	−	3.64333i	−0.316712	−	0.182854i	−0.649926	+	0.759998i	$0.725200\pi$
$398$	−11.3181			−0.567323
$399$	−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	$0.796312\pi$
$402$	−2.38045	−	1.24558i	−0.118726	−	0.0621240i
$403$	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
$408$	−0.759558	−	18.2827i	−0.0376037	−	0.905129i
$409$	−22.8109	+	13.1699i	−1.12793	+	0.651209i	−0.943413	−	0.331620i	$-0.892405\pi$
$409$	−22.8109	+	13.1699i	−1.12793	+	0.651209i	−0.184515	+	0.982830i	$0.559071\pi$
$410$		0			0
$411$	1.46286	+	35.2113i	0.0721575	+	1.73684i
$412$			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
$417$	−15.0267	−	7.86278i	−0.735860	−	0.385042i
$418$	−2.72824	−	1.57515i	−0.133443	−	0.0770432i
$419$	−14.3499			−0.701039			−0.350519	−	0.936555i	$-0.613995\pi$
$419$	−14.3499			−0.701039			−0.350519	+	0.936555i	$0.613995\pi$
$420$		0			0
$421$	−10.0679			−0.490682			−0.245341	−	0.969437i	$-0.578900\pi$
$421$	−10.0679			−0.490682			−0.245341	+	0.969437i	$0.578900\pi$
$422$	8.38858	+	4.84315i	0.408350	+	0.235761i
$423$	−9.44616	+	0.786241i	−0.459288	+	0.0382284i
$424$	−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
$429$	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	$0.396959\pi$
$432$	−10.0581	+	23.8537i	−0.483919	+	1.14766i
$433$			10.7241i			0.515367i	0.966229	+	0.257683i	$0.0829591\pi$
$433$			10.7241i			0.515367i	−0.966229	+	0.257683i	$0.917041\pi$
$434$	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
$438$	−10.6013	+	20.2602i	−0.506548	+	0.968071i
$439$	−2.74233	−	1.58329i	−0.130884	−	0.0755661i	0.433128	−	0.901332i	$-0.357410\pi$
$439$	−2.74233	−	1.58329i	−0.130884	−	0.0755661i	−0.564013	+	0.825766i	$0.690743\pi$
$440$		0			0
$441$	18.9667	−	9.01472i	0.903175	−	0.429273i
$442$	31.5375			1.50009
$443$	−15.1150	−	8.72667i	−0.718137	−	0.414617i	0.0959297	−	0.995388i	$-0.469418\pi$
$443$	−15.1150	−	8.72667i	−0.718137	−	0.414617i	−0.814067	+	0.580772i	$0.802751\pi$
$444$	4.03319	−	7.70791i	0.191407	−	0.365801i
$445$		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
$453$	26.1090	−	1.08470i	1.22671	−	0.0509637i
$454$		−	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	−0.917523	−	0.397684i	$-0.869814\pi$
$457$	−2.44467	+	4.23430i	−0.114357	+	0.198072i	0.803165	+	0.595756i	$0.203147\pi$
$458$	0.890158	+	1.54180i	0.0415943	+	0.0720435i
$459$	−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	$0.461901\pi$
$462$	3.49121	−	0.787463i	0.162426	−	0.0366361i
$463$	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	$-0.901056\pi$
$467$	−4.56309	+	7.90350i	−0.211155	+	0.365730i	0.740922	+	0.671592i	$0.234389\pi$
$468$	−7.95516	−	3.75054i	−0.367727	−	0.173369i
$469$	−0.815897	+	2.28269i	−0.0376746	+	0.105405i
$470$		0			0
$471$	0.895198	+	21.5476i	0.0412486	+	0.992860i
$472$	16.2280	−	9.36925i	0.746955	−	0.431254i
$473$	−3.33773	+	1.92704i	−0.153469	+	0.0886053i
$474$	−0.872760	−	21.0075i	−0.0400872	−	0.964907i
$475$		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	$-0.0752105\pi$
$479$	6.20210	+	10.7424i	0.283381	+	0.490831i	−0.688834	+	0.724919i	$0.741877\pi$
$480$		0			0
$481$	−17.0006	−	9.81532i	−0.775162	−	0.447540i
$482$	3.83332			0.174603
$483$	−19.7093	−	6.13473i	−0.896805	−	0.279140i
$484$	−9.34243			−0.424656
$485$		0			0
$486$	5.43955	+	25.8237i	0.246743	+	1.17139i
$487$	−7.08208	−	12.2665i	−0.320920	−	0.555849i	0.659758	−	0.751478i	$-0.270659\pi$
$487$	−7.08208	−	12.2665i	−0.320920	−	0.555849i	−0.980678	+	0.195628i	$0.937325\pi$
$488$	−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	$0.741926\pi$
$492$	−9.37826	+	0.389621i	−0.422805	+	0.0175655i
$493$	−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	0.395085	+	0.918644i	$0.370715\pi$
$499$	−13.3589	+	23.1383i	−0.598027	+	1.03581i	−0.993112	+	0.117168i	$0.962618\pi$
$500$		0			0
$501$	−0.641627	+	1.22622i	−0.0286658	+	0.0547837i
$502$	19.5320	+	11.2768i	0.871758	+	0.503310i
$503$	9.55539			0.426054			0.213027	−	0.977046i	$-0.431668\pi$
$503$	9.55539			0.426054			0.213027	+	0.977046i	$0.431668\pi$
$504$	14.7240	+	3.92059i	0.655860	+	0.174637i
$505$		0			0
$506$	−3.04659	−	1.75895i	−0.135438	−	0.0781950i
$507$	1.23799	−	2.36594i	0.0549810	−	0.105075i
$508$	5.43700	+	9.41716i	0.241228	+	0.417819i
$509$	−9.10071	+	15.7629i	−0.403382	+	0.698678i	−0.994132	−	0.108177i	$-0.965499\pi$
$509$	−9.10071	+	15.7629i	−0.403382	+	0.698678i	0.590750	+	0.806855i	$0.298832\pi$
$510$		0			0
$511$	19.4282	+	6.94417i	0.859452	+	0.307192i
$512$		−	3.76451i		−	0.166369i
$513$	−19.3134	−	8.14360i	−0.852706	−	0.359549i
$514$	28.7259	−	16.5849i	1.26705	−	0.731530i
$515$		0			0
$516$	12.5216	−	0.520212i	0.551232	−	0.0229010i
$517$			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	$-0.193717\pi$
$521$	−1.93741	−	3.35569i	−0.0848794	−	0.147015i	−0.905340	+	0.424688i	$0.860384\pi$
$522$	39.0612	−	3.25122i	1.70966	−	0.142302i
$523$	−16.3176	−	9.42099i	−0.713520	−	0.411951i	0.0988429	−	0.995103i	$-0.468486\pi$
$523$	−16.3176	−	9.42099i	−0.713520	−	0.411951i	−0.812363	+	0.583152i	$0.801819\pi$
$524$	5.82474			0.254455
$525$		0			0
$526$	−28.3967			−1.23816
$527$	−16.5986	−	9.58321i	−0.723047	−	0.417451i
$528$	3.52711	+	1.84557i	0.153498	+	0.0803183i
$529$	−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
$534$	0.329235	+	7.92475i	0.0142474	+	0.342937i
$535$		0			0
$536$	−1.52324	+	0.879440i	−0.0657937	+	0.0379860i
$537$	0.169725	+	4.08532i	0.00732419	+	0.176295i
$538$			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	−0.999656	−	0.0262117i	$-0.991656\pi$
$541$	−11.0977	+	19.2218i	−0.477128	+	0.826410i	0.522528	+	0.852622i	$0.324989\pi$
$542$	2.51324	+	4.35306i	0.107953	+	0.186980i
$543$	14.8968	+	7.79483i	0.639285	+	0.334508i
$544$	21.8997	+	12.6438i	0.938944	+	0.542099i
$545$		0			0
$546$	−7.80472	+	25.0746i	−0.334011	+	1.07309i
$547$	−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
$549$	1.98449	+	23.8423i	0.0846959	+	1.01756i
$550$		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	$-0.682275\pi$
$557$	−2.00365	+	1.15681i	−0.0848973	+	0.0490155i	0.456950	+	0.889492i	$0.348942\pi$
$558$	10.0842	+	14.5320i	0.426898	+	0.615188i
$559$		−	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	$-0.0416956\pi$
$563$	9.07818	+	15.7239i	0.382600	+	0.662682i	−0.608833	+	0.793298i	$0.708362\pi$
$564$	2.19740	−	4.19948i	0.0925270	−	0.176830i
$565$		0			0
$566$	9.54745			0.401309
$567$	22.3973	−	8.08459i	0.940599	−	0.339521i
$568$	−2.92930			−0.122911
$569$	−12.9811	−	7.49465i	−0.544197	−	0.314192i	0.202581	−	0.979265i	$-0.435067\pi$
$569$	−12.9811	−	7.49465i	−0.544197	−	0.314192i	−0.746778	+	0.665073i	$0.768400\pi$
$570$		0			0
$571$	−11.6375	−	20.1568i	−0.487015	−	0.843535i	0.512873	−	0.858464i	$-0.328581\pi$
$571$	−11.6375	−	20.1568i	−0.487015	−	0.843535i	−0.999889	+	0.0149293i	$0.995248\pi$
$572$	−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
$576$	3.73718	+	5.38551i	0.155716	+	0.224396i
$577$	23.0953	−	13.3341i	0.961471	−	0.555105i	0.0648455	−	0.997895i	$-0.479345\pi$
$577$	23.0953	−	13.3341i	0.961471	−	0.555105i	0.896625	+	0.442790i	$0.146011\pi$
$578$	−19.4797	+	11.2466i	−0.810248	+	0.467797i
$579$	−22.6766	+	0.942104i	−0.942408	+	0.0391525i
$580$		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	$-0.897638\pi$
$587$	−45.9722			−1.89748			−0.948738	+	0.316065i	$0.897638\pi$
$588$	−1.27197	+	10.4232i	−0.0524553	+	0.429845i
$589$	−14.0484			−0.578856
$590$		0			0
$591$	−32.6767	−	17.0982i	−1.34414	−	0.703327i
$592$	−14.4462	−	25.0215i	−0.593735	−	1.02838i
$593$	1.55298	−	2.68984i	0.0637732	−	0.110458i	−0.832376	−	0.554211i	$-0.813020\pi$
$593$	1.55298	−	2.68984i	0.0637732	−	0.110458i	0.896149	+	0.443753i	$0.146353\pi$
$594$	4.02666	−	0.504187i	0.165216	−	0.0206871i
$595$		0			0
$596$		−	14.1202i		−	0.578385i
$597$	0.480657	+	11.5695i	0.0196720	+	0.473508i
$598$	22.3551	−	12.9067i	0.914168	−	0.527795i
$599$	7.34708	−	4.24184i	0.300193	−	0.173317i	−0.342336	−	0.939577i	$-0.611218\pi$
$599$	7.34708	−	4.24184i	0.300193	−	0.173317i	0.642530	+	0.766261i	$0.277885\pi$
$600$		0			0
$601$		−	2.63388i		−	0.107438i	−0.998556	−	0.0537191i	$-0.982892\pi$
$601$		−	2.63388i		−	0.107438i	0.998556	−	0.0537191i	$-0.0171076\pi$
$602$	−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
$606$	−7.10949	−	3.72007i	−0.288803	−	0.151118i
$607$	−26.2154	−	15.1355i	−1.06405	−	0.614330i	−0.137501	−	0.990502i	$-0.543907\pi$
$607$	−26.2154	−	15.1355i	−1.06405	−	0.614330i	−0.926550	+	0.376171i	$0.877240\pi$
$608$	18.5351			0.751698
$609$	−7.78159	−	34.4996i	−0.315326	−	1.39799i
$610$		0			0
$611$	−9.26241	−	5.34766i	−0.374717	−	0.216343i
$612$	14.2494	−	1.18604i	0.575999	−	0.0479427i
$613$	−9.01861	−	15.6207i	−0.364258	−	0.630914i	0.624399	−	0.781106i	$-0.285344\pi$
$613$	−9.01861	−	15.6207i	−0.364258	−	0.630914i	−0.988657	+	0.150192i	$0.952011\pi$
$614$	−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	$-0.0727699\pi$
$618$	53.9982	−	2.24336i	2.17213	−	0.0902414i
$619$	−5.23950	+	3.02503i	−0.210593	+	0.121586i	−0.601587	−	0.798807i	$-0.705465\pi$
$619$	−5.23950	+	3.02503i	−0.210593	+	0.121586i	0.390994	+	0.920393i	$0.372131\pi$
$620$		0			0
$621$	−21.5670	−	9.09385i	−0.865454	−	0.364924i
$622$		−	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
$627$	−1.49428	+	2.85575i	−0.0596759	+	0.114048i
$628$	−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
$633$	4.59450	−	8.78063i	0.182615	−	0.348999i
$634$	−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
$639$	−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	$0.318179\pi$
$642$	19.4914	−	0.809774i	0.769265	−	0.0319592i
$643$			30.1631i			1.18952i	0.803904	+	0.594759i	$0.202753\pi$
$643$			30.1631i			1.18952i	−0.803904	+	0.594759i	$0.797247\pi$
$644$	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	$-0.0780576\pi$
$647$	6.98967	+	12.1065i	0.274792	+	0.475954i	−0.695291	+	0.718729i	$0.744724\pi$
$648$	16.1847	+	6.04609i	0.635797	+	0.237513i
$649$	−3.89972	−	2.25150i	−0.153077	−	0.0883792i
$650$		0			0
$651$	11.7270	−	10.8255i	0.459619	−	0.424283i
$652$	−4.76671			−0.186679
$653$	5.92653	+	3.42169i	0.231923	+	0.133901i	0.611459	−	0.791276i	$-0.290583\pi$
$653$	5.92653	+	3.42169i	0.231923	+	0.133901i	−0.379536	+	0.925177i	$0.623916\pi$
$654$	20.3515	+	10.6490i	0.795805	+	0.416408i
$655$		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	−0.662053	−	0.749457i	$-0.730315\pi$
$661$	−8.84503	+	5.10668i	−0.344032	+	0.198627i	0.318022	+	0.948083i	$0.396981\pi$
$662$	19.8367	−	11.4527i	0.770976	−	0.445123i
$663$	−1.33934	−	32.2382i	−0.0520157	−	1.25203i
$664$			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
$669$	−8.95461	−	4.68554i	−0.346205	−	0.181153i
$670$		0			0
$671$	3.67895			0.142024
$672$	−15.4723	+	14.2828i	−0.596858	+	0.550972i
$673$	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	$-0.808990\pi$
$677$	1.98790	−	3.44314i	0.0764011	−	0.132331i	0.901695	+	0.432373i	$0.142324\pi$
$678$	−27.3094	−	43.0675i	−1.04881	−	1.65400i
$679$	8.96006	−	7.60721i	0.343855	−	0.291938i
$680$		0			0
$681$	−19.7507	+	0.820547i	−0.756849	+	0.0314434i
$682$	2.35553	−	1.35997i	0.0901981	−	0.0520759i
$683$	−9.21993	+	5.32313i	−0.352791	+	0.203684i	−0.665914	−	0.746029i	$-0.731958\pi$
$683$	−9.21993	+	5.32313i	−0.352791	+	0.203684i	0.313123	+	0.949713i	$0.398625\pi$
$684$	8.61047	−	5.97507i	0.329229	−	0.228463i
$685$		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	0.746729	−	0.665128i	$-0.231623\pi$
$691$	14.3020	+	8.25729i	0.544076	+	0.314122i	−0.202653	+	0.979251i	$0.564956\pi$
$692$	−12.5743			−0.478004
$693$	−0.953223	−	3.53533i	−0.0362099	−	0.134296i
$694$	−13.2401			−0.502586
$695$		0			0
$696$	11.8969	−	22.7364i	0.450951	−	0.861820i
$697$	−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	$-0.120498\pi$
$702$	−11.5694	+	27.4379i	−0.436657	+	1.03558i
$703$	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	0.468235	+	0.883604i	$0.344890\pi$
$709$	−14.1418	+	24.4943i	−0.531106	+	0.919903i	−0.999341	+	0.0362991i	$0.988443\pi$
$710$		0			0
$711$	−21.4372	+	1.78430i	−0.803956	+	0.0669165i
$712$	4.49694	+	2.59631i	0.168530	+	0.0973009i
$713$	−15.6877			−0.587509
$714$	−9.39411	−	41.6487i	−0.351566	−	1.55866i
$715$		0			0
$716$	−1.77061	−	1.02226i	−0.0661707	−	0.0382037i
$717$	9.82650	+	5.14176i	0.366977	+	0.192022i
$718$	−6.95509	−	12.0466i	−0.259562	−	0.449574i
$719$	9.75873	−	16.9026i	0.363939	−	0.630361i	−0.624666	−	0.780892i	$-0.714765\pi$
$719$	9.75873	−	16.9026i	0.363939	−	0.630361i	0.988605	+	0.150531i	$0.0480983\pi$
$720$		0			0
$721$	−8.74566	−	47.9733i	−0.325705	−	1.78662i
$722$		−	4.61959i		−	0.171923i
$723$	−0.162794	−	3.91849i	−0.00605438	−	0.145730i
$724$	−7.28057	+	4.20344i	−0.270580	+	0.156220i
$725$		0			0
$726$	1.31298	+	31.6037i	0.0487293	+	1.17292i
$727$		−	26.5060i		−	0.983052i	−0.870863	−	0.491526i	$-0.836439\pi$
$727$		−	26.5060i		−	0.983052i	0.870863	−	0.491526i	$-0.163561\pi$
$728$	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
$732$	−10.5996	−	5.54627i	−0.391771	−	0.204996i
$733$	−0.184602	−	0.106580i	−0.00681844	−	0.00393663i	0.496587	−	0.867987i	$-0.334586\pi$
$733$	−0.184602	−	0.106580i	−0.00681844	−	0.00393663i	−0.503405	+	0.864050i	$0.667920\pi$
$734$	−47.2420			−1.74373
$735$		0			0
$736$	20.6979			0.762935
$737$	0.366045	+	0.211336i	0.0134835	+	0.00778467i
$738$	2.63603	+	31.6701i	0.0970337	+	1.16579i
$739$	23.2265	+	40.2296i	0.854402	+	1.47987i	0.877198	+	0.480128i	$0.159410\pi$
$739$	23.2265	+	40.2296i	0.854402	+	1.47987i	−0.0227959	+	0.999740i	$0.507257\pi$
$740$		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	$-0.172330\pi$
$744$	11.5700	−	0.480678i	0.424177	−	0.0176225i
$745$		0			0
$746$	26.5135	−	15.3076i	0.970729	−	0.560451i
$747$	30.0389	+	43.2880i	1.09907	+	1.58382i
$748$		−	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	−0.998718	−	0.0506227i	$-0.983879\pi$
$751$	−12.4832	+	21.6215i	−0.455518	+	0.788981i	0.543199	+	0.839604i	$0.317213\pi$
$752$	−7.87068	−	13.6324i	−0.287014	−	0.497123i
$753$	10.6979	−	20.4449i	0.389852	−	0.745053i
$754$	38.3014	+	22.1133i	1.39485	+	0.805319i
$755$		0			0
$756$	−2.58338	+	11.6228i	−0.0939566	+	0.422718i
$757$	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
$759$	−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	$-0.237191\pi$
$762$	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
$768$	−30.1992	+	1.25463i	−1.08972	+	0.0452725i
$769$			5.37059i			0.193669i	0.995301	+	0.0968343i	$0.0308717\pi$
$769$			5.37059i			0.193669i	−0.995301	+	0.0968343i	$0.969128\pi$
$770$		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	$-0.180713\pi$
$773$	−1.22649	−	2.12434i	−0.0441138	−	0.0764073i	−0.887239	+	0.461310i	$0.847380\pi$
$774$	−3.51956	−	42.2851i	−0.126508	−	1.51991i
$775$		0			0
$776$	8.52826			0.306147
$777$	−7.89819	+	25.3749i	−0.283346	+	0.910318i
$778$	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
$786$	−0.818606	−	19.7040i	−0.0291987	−	0.702818i
$787$	−35.6885	+	20.6048i	−1.27216	+	0.734481i	−0.975394	−	0.220470i	$-0.929241\pi$
$787$	−35.6885	+	20.6048i	−1.27216	+	0.734481i	−0.296764	+	0.954951i	$0.595908\pi$
$788$	15.9702	−	9.22039i	0.568914	−	0.328463i
$789$	1.20596	+	29.0276i	0.0429332	+	1.03341i
$790$		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	$-0.727017\pi$
$797$	−36.9407			−1.30851			−0.654253	+	0.756276i	$0.727017\pi$
$798$	−21.2267	−	22.9946i	−0.751419	−	0.814000i
$799$	17.3883			0.615154
$800$		0			0
$801$	8.08683	−	0.673099i	0.285734	−	0.0237828i
$802$	−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
$807$	50.7756	−	2.10948i	1.78739	−	0.0742573i
$808$	−4.54931	+	2.62655i	−0.160044	+	0.0924016i
$809$	−45.9461	+	26.5270i	−1.61538	+	0.932640i	−0.627285	+	0.778790i	$0.715834\pi$
$809$	−45.9461	+	26.5270i	−1.61538	+	0.932640i	−0.988094	+	0.153850i	$0.950833\pi$
$810$		0			0
$811$		−	19.0686i		−	0.669590i	−0.942291	−	0.334795i	$-0.891333\pi$
$811$		−	19.0686i		−	0.669590i	0.942291	−	0.334795i	$-0.108667\pi$
$812$	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
$816$	22.0169	−	42.0769i	0.770747	−	1.47299i
$817$	29.1852	+	16.8501i	1.02106	+	0.589511i
$818$	−44.5918			−1.55912
$819$	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	$0.727735\pi$
$822$	−27.6606	+	52.8627i	−0.964776	+	1.84380i
$823$	20.9937	+	36.3622i	0.731794	+	1.26750i	0.956116	+	0.292990i	$0.0946502\pi$
$823$	20.9937	+	36.3622i	0.731794	+	1.26750i	−0.224321	+	0.974515i	$0.572016\pi$
$824$	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	$0.874385\pi$
$828$	9.61520	−	6.67229i	0.334151	−	0.231878i
$829$	27.1141	−	15.6543i	0.941711	−	0.543697i	0.0512148	−	0.998688i	$-0.483691\pi$
$829$	27.1141	−	15.6543i	0.941711	−	0.543697i	0.890496	+	0.454990i	$0.150357\pi$
$830$		0			0
$831$	22.5412	−	0.936477i	0.781944	−	0.0324860i
$832$			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
$837$	14.4266	−	10.9254i	0.498655	−	0.377636i
$838$	−21.0389	−	12.1468i	−0.726777	−	0.419605i
$839$	8.65688			0.298869			0.149434	−	0.988772i	$-0.452255\pi$
$839$	8.65688			0.298869			0.149434	+	0.988772i	$0.452255\pi$
$840$		0			0
$841$	−30.5607			−1.05382
$842$	−14.7610	−	8.52225i	−0.508696	−	0.293696i
$843$	29.8343	+	15.6109i	1.02755	+	0.537669i
$844$	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
$849$	−0.405463	−	9.75956i	−0.0139154	−	0.334947i
$850$		0			0
$851$	22.6228	−	13.0613i	0.775501	−	0.447736i
$852$	−0.0950150	−	2.28703i	−0.00325516	−	0.0783523i
$853$		−	48.3400i		−	1.65513i	−0.561370	−	0.827565i	$-0.689726\pi$
$853$		−	48.3400i		−	1.65513i	0.561370	−	0.827565i	$-0.310274\pi$
$854$	−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	0.996083	+	0.0884274i	$0.0281841\pi$
$857$	16.8218	+	29.1362i	0.574622	+	0.995274i	−0.421461	+	0.906847i	$0.638483\pi$
$858$	4.05708	+	2.12288i	0.138506	+	0.0724740i
$859$	22.6082	+	13.0528i	0.771382	+	0.445357i	0.833367	−	0.552720i	$-0.186410\pi$
$859$	22.6082	+	13.0528i	0.771382	+	0.445357i	−0.0619856	+	0.998077i	$0.519743\pi$
$860$		0			0
$861$	27.9717	−	6.30918i	0.953272	−	0.215016i
$862$	−13.9573			−0.475387
$863$	34.0767	+	19.6742i	1.15998	+	0.669718i	0.951300	−	0.308265i	$-0.0997485\pi$
$863$	34.0767	+	19.6742i	1.15998	+	0.669718i	0.208685	+	0.977983i	$0.433082\pi$
$864$	−19.0340	+	14.4146i	−0.647550	+	0.490396i
$865$		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
$873$	10.9495	−	7.59820i	0.370585	−	0.257160i
$874$			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	−0.550307	−	0.834963i	$-0.685489\pi$
$877$	13.2655	−	22.9766i	0.447945	−	0.775864i	0.998252	+	0.0590984i	$0.0188226\pi$
$878$	−2.68042	−	4.64262i	−0.0904597	−	0.156681i
$879$	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	$0.428594\pi$
$882$	35.4384	+	2.83798i	1.19327	+	0.0955598i
$883$	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	−0.445387	−	0.895338i	$-0.646934\pi$
$887$	16.4606	−	28.5105i	0.552692	−	0.957290i	0.998079	−	0.0619524i	$-0.0197327\pi$
$888$	−16.2846	+	10.3262i	−0.546476	+	0.346523i
$889$	−21.4997	−	25.3232i	−0.721078	−	0.849313i
$890$		0			0
$891$	−0.686394	−	4.09471i	−0.0229951	−	0.137178i
$892$	4.37641	−	2.52672i	0.146533	−	0.0846009i
$893$	11.0376	−	6.37256i	0.369359	−	0.213250i
$894$	−47.7659	+	1.98444i	−1.59753	+	0.0663697i
$895$		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
$903$	−37.3470	+	8.42384i	−1.24283	+	0.280328i
$904$	−33.3860			−1.11040
$905$		0			0
$906$	39.1974	+	20.5102i	1.30225	+	0.681406i
$907$	10.4117	+	18.0335i	0.345714	+	0.598793i	0.985483	−	0.169773i	$-0.0543035\pi$
$907$	10.4117	+	18.0335i	0.345714	+	0.598793i	−0.639770	+	0.768567i	$0.720970\pi$
$908$	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	$-0.312853\pi$
$912$	−1.44486	−	34.7781i	−0.0478442	−	1.15162i
$913$	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	−0.655599	−	0.755109i	$-0.727584\pi$
$919$	9.88707	−	17.1249i	0.326144	−	0.564899i	0.981743	+	0.190211i	$0.0609171\pi$
$920$		0			0
$921$	35.1878	+	18.4121i	1.15948	+	0.606701i
$922$	7.51755	+	4.34026i	0.247577	+	0.142939i
$923$	−5.16529			−0.170017
$924$	1.74815	+	0.544131i	0.0575100	+	0.0179006i
$925$		0			0
$926$	58.5095	+	33.7805i	1.92274	+	1.11009i
$927$	−4.58641	−	55.1026i	−0.150637	−	1.80981i
$928$	17.7310	+	30.7111i	0.582050	+	1.00814i
$929$	−1.84133	+	3.18927i	−0.0604119	+	0.104637i	−0.894650	−	0.446769i	$-0.852575\pi$
$929$	−1.84133	+	3.18927i	−0.0604119	+	0.104637i	0.834238	+	0.551405i	$0.185908\pi$
$930$		0			0
$931$	−17.8983	+	21.8390i	−0.586594	+	0.715745i
$932$		−	3.36457i		−	0.110210i
$933$	−2.76551	+	0.114894i	−0.0905387	+	0.00376145i
$934$	−13.3802	+	7.72506i	−0.437814	+	0.252772i
$935$		0			0
$936$	11.1140	+	16.0161i	0.363274	+	0.523501i
$937$		−	36.7871i		−	1.20178i	−0.799331	−	0.600891i	$-0.794813\pi$
$937$		−	36.7871i		−	1.20178i	0.799331	−	0.600891i	$-0.205187\pi$
$938$	−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	$-0.0597917\pi$
$941$	10.1072	+	17.5061i	0.329484	+	0.570684i	−0.652925	+	0.757422i	$0.726458\pi$
$942$	−16.9270	+	32.3494i	−0.551511	+	1.05400i
$943$	−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	$-0.384358\pi$
$947$	−8.50752	−	4.91182i	−0.276457	−	0.159613i	−0.631819	+	0.775116i	$0.717691\pi$
$948$	4.98678	−	9.53032i	0.161963	−	0.309530i
$949$	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	$0.868785\pi$
$954$	−33.4858	−	48.2552i	−1.08414	−	1.56232i
$955$		0			0
$956$	−4.80253	+	2.77274i	−0.155325	+	0.0896769i
$957$	−6.16119	+	0.255968i	−0.199163	+	0.00827426i
$958$			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
$963$	−1.65553	−	19.8901i	−0.0533487	−	0.640948i
$964$	1.69830	+	0.980514i	0.0546986	+	0.0315802i
$965$		0			0
$966$	−23.7036	−	25.6778i	−0.762652	−	0.826168i
$967$	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
$969$	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	$0.166982\pi$
$972$	−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	$-0.567940\pi$
$977$	16.5237	−	9.53996i	0.528640	−	0.305210i	0.740462	+	0.672098i	$0.234607\pi$
$978$	0.669912	+	16.1249i	0.0214214	+	0.515617i
$979$		−	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	$-0.208135\pi$
$983$	−4.07300	−	7.05465i	−0.129909	−	0.225008i	−0.923641	+	0.383259i	$0.874802\pi$
$984$	18.4343	+	9.64581i	0.587663	+	0.307497i
$985$		0			0
$986$	−71.9030			−2.28986
$987$	−4.30315	+	13.8249i	−0.136971	+	0.440052i
$988$	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	0.771155	−	0.636647i	$-0.219679\pi$
$991$	−5.21862	−	9.03891i	−0.165775	−	0.287130i	−0.936930	+	0.349517i	$0.886346\pi$
$992$	−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
$996$	−26.3233	+	1.09361i	−0.834086	+	0.0346522i
$997$	11.6811	−	6.74411i	0.369945	−	0.213588i	−0.303489	−	0.952835i	$-0.598152\pi$
$997$	11.6811	−	6.74411i	0.369945	−	0.213588i	0.673435	+	0.739247i	$0.264818\pi$
$998$	−39.1719	+	22.6159i	−1.23996	+	0.715894i
$999$	−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.t.i.26.8	yes	20
3.2	odd	2	inner	525.2.t.i.26.3	yes	20
5.2	odd	4		525.2.q.g.299.5		40
5.3	odd	4		525.2.q.g.299.16		40
5.4	even	2		525.2.t.h.26.3	✓	20
7.3	odd	6	inner	525.2.t.i.101.3	yes	20
15.2	even	4		525.2.q.g.299.15		40
15.8	even	4		525.2.q.g.299.6		40
15.14	odd	2		525.2.t.h.26.8	yes	20
21.17	even	6	inner	525.2.t.i.101.8	yes	20
35.3	even	12		525.2.q.g.374.15		40
35.17	even	12		525.2.q.g.374.6		40
35.24	odd	6		525.2.t.h.101.8	yes	20
105.17	odd	12		525.2.q.g.374.16		40
105.38	odd	12		525.2.q.g.374.5		40
105.59	even	6		525.2.t.h.101.3	yes	20

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

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

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