LMFDB - Embedded newform 275.3.f.c.243.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(232,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.232"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			243.5
Character	$\chi$	$=$	275.243
Dual form			275.3.f.c.232.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.925034 + 0.925034i) q^{2} +(-3.86940 - 3.86940i) q^{3} +2.28862i q^{4} +7.15866 q^{6} +(-2.48674 + 2.48674i) q^{7} +(-5.81719 - 5.81719i) q^{8} +20.9446i q^{9} -3.31662 q^{11} +(8.85561 - 8.85561i) q^{12} +(11.1429 + 11.1429i) q^{13} -4.60065i q^{14} +1.60771 q^{16} +(-1.87959 + 1.87959i) q^{17} +(-19.3745 - 19.3745i) q^{18} -32.2173i q^{19} +19.2444 q^{21} +(3.06799 - 3.06799i) q^{22} +(-10.9067 - 10.9067i) q^{23} +45.0181i q^{24} -20.6151 q^{26} +(46.2184 - 46.2184i) q^{27} +(-5.69122 - 5.69122i) q^{28} -15.8039i q^{29} +56.3876 q^{31} +(21.7816 - 21.7816i) q^{32} +(12.8334 + 12.8334i) q^{33} -3.47738i q^{34} -47.9343 q^{36} +(43.0478 - 43.0478i) q^{37} +(29.8021 + 29.8021i) q^{38} -86.2325i q^{39} +41.8566 q^{41} +(-17.8018 + 17.8018i) q^{42} +(-3.70228 - 3.70228i) q^{43} -7.59051i q^{44} +20.1781 q^{46} +(-27.8097 + 27.8097i) q^{47} +(-6.22088 - 6.22088i) q^{48} +36.6322i q^{49} +14.5458 q^{51} +(-25.5018 + 25.5018i) q^{52} +(-14.7508 - 14.7508i) q^{53} +85.5073i q^{54} +28.9317 q^{56} +(-124.662 + 124.662i) q^{57} +(14.6191 + 14.6191i) q^{58} -102.568i q^{59} -34.3345 q^{61} +(-52.1605 + 52.1605i) q^{62} +(-52.0838 - 52.0838i) q^{63} +46.7283i q^{64} -23.7426 q^{66} +(-6.48045 + 6.48045i) q^{67} +(-4.30168 - 4.30168i) q^{68} +84.4048i q^{69} -20.3765 q^{71} +(121.839 - 121.839i) q^{72} +(44.6499 + 44.6499i) q^{73} +79.6413i q^{74} +73.7332 q^{76} +(8.24760 - 8.24760i) q^{77} +(79.7680 + 79.7680i) q^{78} +28.9929i q^{79} -169.174 q^{81} +(-38.7188 + 38.7188i) q^{82} +(99.4392 + 99.4392i) q^{83} +44.0433i q^{84} +6.84948 q^{86} +(-61.1515 + 61.1515i) q^{87} +(19.2934 + 19.2934i) q^{88} -143.090i q^{89} -55.4189 q^{91} +(24.9613 - 24.9613i) q^{92} +(-218.186 - 218.186i) q^{93} -51.4498i q^{94} -168.564 q^{96} +(-4.67226 + 4.67226i) q^{97} +(-33.8860 - 33.8860i) q^{98} -69.4653i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) $ 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.925034	+	0.925034i	−0.462517	+	0.462517i	−0.899480	−	0.436963i	$-0.856054\pi$
$2$	−0.925034	+	0.925034i	−0.462517	+	0.462517i	0.436963	+	0.899480i	$0.356054\pi$
$3$	−3.86940	−	3.86940i	−1.28980	−	1.28980i	−0.934906	−	0.354896i	$-0.884516\pi$
$3$	−3.86940	−	3.86940i	−1.28980	−	1.28980i	−0.354896	−	0.934906i	$-0.615484\pi$
$4$			2.28862i			0.572156i
$5$		0			0
$5$		0			0
$6$	7.15866			1.19311
$7$	−2.48674	+	2.48674i	−0.355249	+	0.355249i	−0.862058	−	0.506809i	$-0.830825\pi$
$7$	−2.48674	+	2.48674i	−0.355249	+	0.355249i	0.506809	+	0.862058i	$0.330825\pi$
$8$	−5.81719	−	5.81719i	−0.727149	−	0.727149i
$9$			20.9446i			2.32718i
$10$		0			0
$11$	−3.31662			−0.301511
$11$	−3.31662			−0.301511
$12$	8.85561	−	8.85561i	0.737968	−	0.737968i
$13$	11.1429	+	11.1429i	0.857143	+	0.857143i	0.991001	−	0.133858i	$-0.0427365\pi$
$13$	11.1429	+	11.1429i	0.857143	+	0.857143i	−0.133858	+	0.991001i	$0.542736\pi$
$14$		−	4.60065i		−	0.328618i
$15$		0			0
$16$	1.60771			0.100482
$17$	−1.87959	+	1.87959i	−0.110564	+	0.110564i	−0.760225	−	0.649660i	$-0.774911\pi$
$17$	−1.87959	+	1.87959i	−0.110564	+	0.110564i	0.649660	+	0.760225i	$0.274911\pi$
$18$	−19.3745	−	19.3745i	−1.07636	−	1.07636i
$19$		−	32.2173i		−	1.69565i	−0.530280	−	0.847823i	$-0.677913\pi$
$19$		−	32.2173i		−	1.69565i	0.530280	−	0.847823i	$-0.322087\pi$
$20$		0			0
$21$	19.2444			0.916402
$22$	3.06799	−	3.06799i	0.139454	−	0.139454i
$23$	−10.9067	−	10.9067i	−0.474204	−	0.474204i	0.429068	−	0.903272i	$-0.358842\pi$
$23$	−10.9067	−	10.9067i	−0.474204	−	0.474204i	−0.903272	+	0.429068i	$0.858842\pi$
$24$			45.0181i			1.87576i
$25$		0			0
$26$	−20.6151			−0.792887
$27$	46.2184	−	46.2184i	1.71179	−	1.71179i
$28$	−5.69122	−	5.69122i	−0.203258	−	0.203258i
$29$		−	15.8039i		−	0.544961i	−0.962161	−	0.272480i	$-0.912156\pi$
$29$		−	15.8039i		−	0.544961i	0.962161	−	0.272480i	$-0.0878440\pi$
$30$		0			0
$31$	56.3876			1.81896			0.909478	−	0.415753i	$-0.136482\pi$
$31$	56.3876			1.81896			0.909478	+	0.415753i	$0.136482\pi$
$32$	21.7816	−	21.7816i	0.680674	−	0.680674i
$33$	12.8334	+	12.8334i	0.388890	+	0.388890i
$34$		−	3.47738i		−	0.102276i
$35$		0			0
$36$	−47.9343			−1.33151
$37$	43.0478	−	43.0478i	1.16345	−	1.16345i	0.179739	−	0.983714i	$-0.442475\pi$
$37$	43.0478	−	43.0478i	1.16345	−	1.16345i	0.983714	−	0.179739i	$-0.0575254\pi$
$38$	29.8021	+	29.8021i	0.784265	+	0.784265i
$39$		−	86.2325i		−	2.21109i
$40$		0			0
$41$	41.8566			1.02089			0.510447	−	0.859909i	$-0.329480\pi$
$41$	41.8566			1.02089			0.510447	+	0.859909i	$0.329480\pi$
$42$	−17.8018	+	17.8018i	−0.423852	+	0.423852i
$43$	−3.70228	−	3.70228i	−0.0860996	−	0.0860996i	0.662745	−	0.748845i	$-0.269391\pi$
$43$	−3.70228	−	3.70228i	−0.0860996	−	0.0860996i	−0.748845	+	0.662745i	$0.769391\pi$
$44$		−	7.59051i		−	0.172511i
$45$		0			0
$46$	20.1781			0.438655
$47$	−27.8097	+	27.8097i	−0.591695	+	0.591695i	−0.938089	−	0.346394i	$-0.887406\pi$
$47$	−27.8097	+	27.8097i	−0.591695	+	0.591695i	0.346394	+	0.938089i	$0.387406\pi$
$48$	−6.22088	−	6.22088i	−0.129602	−	0.129602i
$49$			36.6322i			0.747596i
$50$		0			0
$51$	14.5458			0.285212
$52$	−25.5018	+	25.5018i	−0.490419	+	0.490419i
$53$	−14.7508	−	14.7508i	−0.278317	−	0.278317i	0.554120	−	0.832437i	$-0.313055\pi$
$53$	−14.7508	−	14.7508i	−0.278317	−	0.278317i	−0.832437	+	0.554120i	$0.813055\pi$
$54$			85.5073i			1.58347i
$55$		0			0
$56$	28.9317			0.516638
$57$	−124.662	+	124.662i	−2.18705	+	2.18705i
$58$	14.6191	+	14.6191i	0.252054	+	0.252054i
$59$		−	102.568i		−	1.73845i	−0.494419	−	0.869224i	$-0.664619\pi$
$59$		−	102.568i		−	1.73845i	0.494419	−	0.869224i	$-0.335381\pi$
$60$		0			0
$61$	−34.3345			−0.562860			−0.281430	−	0.959582i	$-0.590809\pi$
$61$	−34.3345			−0.562860			−0.281430	+	0.959582i	$0.590809\pi$
$62$	−52.1605	+	52.1605i	−0.841298	+	0.841298i
$63$	−52.0838	−	52.0838i	−0.826727	−	0.826727i
$64$			46.7283i			0.730129i
$65$		0			0
$66$	−23.7426			−0.359736
$67$	−6.48045	+	6.48045i	−0.0967231	+	0.0967231i	−0.753813	−	0.657090i	$-0.771787\pi$
$67$	−6.48045	+	6.48045i	−0.0967231	+	0.0967231i	0.657090	+	0.753813i	$0.271787\pi$
$68$	−4.30168	−	4.30168i	−0.0632601	−	0.0632601i
$69$			84.4048i			1.22326i
$70$		0			0
$71$	−20.3765			−0.286993			−0.143497	−	0.989651i	$-0.545835\pi$
$71$	−20.3765			−0.286993			−0.143497	+	0.989651i	$0.545835\pi$
$72$	121.839	−	121.839i	1.69220	−	1.69220i
$73$	44.6499	+	44.6499i	0.611643	+	0.611643i	0.943374	−	0.331731i	$-0.107633\pi$
$73$	44.6499	+	44.6499i	0.611643	+	0.611643i	−0.331731	+	0.943374i	$0.607633\pi$
$74$			79.6413i			1.07623i
$75$		0			0
$76$	73.7332			0.970173
$77$	8.24760	−	8.24760i	0.107112	−	0.107112i
$78$	79.7680	+	79.7680i	1.02267	+	1.02267i
$79$			28.9929i			0.366998i	0.983020	+	0.183499i	$0.0587425\pi$
$79$			28.9929i			0.366998i	−0.983020	+	0.183499i	$0.941258\pi$
$80$		0			0
$81$	−169.174			−2.08857
$82$	−38.7188	+	38.7188i	−0.472181	+	0.472181i
$83$	99.4392	+	99.4392i	1.19806	+	1.19806i	0.974746	+	0.223317i	$0.0716885\pi$
$83$	99.4392	+	99.4392i	1.19806	+	1.19806i	0.223317	+	0.974746i	$0.428311\pi$
$84$			44.0433i			0.524325i
$85$		0			0
$86$	6.84948			0.0796451
$87$	−61.1515	+	61.1515i	−0.702891	+	0.702891i
$88$	19.2934	+	19.2934i	0.219244	+	0.219244i
$89$		−	143.090i		−	1.60775i	−0.594799	−	0.803874i	$-0.702768\pi$
$89$		−	143.090i		−	1.60775i	0.594799	−	0.803874i	$-0.297232\pi$
$90$		0			0
$91$	−55.4189			−0.608999
$92$	24.9613	−	24.9613i	0.271318	−	0.271318i
$93$	−218.186	−	218.186i	−2.34609	−	2.34609i
$94$		−	51.4498i		−	0.547338i
$95$		0			0
$96$	−168.564			−1.75587
$97$	−4.67226	+	4.67226i	−0.0481676	+	0.0481676i	−0.730780	−	0.682613i	$-0.760844\pi$
$97$	−4.67226	+	4.67226i	−0.0481676	+	0.0481676i	0.682613	+	0.730780i	$0.260844\pi$
$98$	−33.8860	−	33.8860i	−0.345776	−	0.345776i
$99$		−	69.4653i		−	0.701670i
$100$		0			0
$101$	61.2970			0.606901			0.303450	−	0.952847i	$-0.401861\pi$
$101$	61.2970			0.606901			0.303450	+	0.952847i	$0.401861\pi$
$102$	−13.4554	+	13.4554i	−0.131916	+	0.131916i
$103$	2.50303	+	2.50303i	0.0243013	+	0.0243013i	0.719153	−	0.694852i	$-0.244530\pi$
$103$	2.50303	+	2.50303i	0.0243013	+	0.0243013i	−0.694852	+	0.719153i	$0.744530\pi$
$104$		−	129.640i		−	1.24654i
$105$		0			0
$106$	27.2900			0.257453
$107$	113.682	−	113.682i	1.06245	−	1.06245i	0.0645372	−	0.997915i	$-0.479443\pi$
$107$	113.682	−	113.682i	1.06245	−	1.06245i	0.997915	−	0.0645372i	$-0.0205571\pi$
$108$	105.777	+	105.777i	0.979413	+	0.979413i
$109$			79.9776i			0.733740i	0.930272	+	0.366870i	$0.119571\pi$
$109$			79.9776i			0.733740i	−0.930272	+	0.366870i	$0.880429\pi$
$110$		0			0
$111$	−333.139			−3.00125
$112$	−3.99796	+	3.99796i	−0.0356961	+	0.0356961i
$113$	52.3355	+	52.3355i	0.463146	+	0.463146i	0.899685	−	0.436539i	$-0.143796\pi$
$113$	52.3355	+	52.3355i	0.463146	+	0.463146i	−0.436539	+	0.899685i	$0.643796\pi$
$114$		−	230.633i		−	2.02309i
$115$		0			0
$116$	36.1691			0.311802
$117$	−233.383	+	233.383i	−1.99472	+	1.99472i
$118$	94.8793	+	94.8793i	0.804062	+	0.804062i
$119$		−	9.34814i		−	0.0785558i
$120$		0			0
$121$	11.0000			0.0909091
$122$	31.7606	−	31.7606i	0.260333	−	0.260333i
$123$	−161.960	−	161.960i	−1.31675	−	1.31675i
$124$			129.050i			1.04073i
$125$		0			0
$126$	96.3586			0.764751
$127$	115.361	−	115.361i	0.908353	−	0.908353i	−0.0877867	−	0.996139i	$-0.527979\pi$
$127$	115.361	−	115.361i	0.908353	−	0.908353i	0.996139	+	0.0877867i	$0.0279794\pi$
$128$	43.9011	+	43.9011i	0.342977	+	0.342977i
$129$			28.6513i			0.222103i
$130$		0			0
$131$	−75.4069			−0.575625			−0.287812	−	0.957687i	$-0.592928\pi$
$131$	−75.4069			−0.575625			−0.287812	+	0.957687i	$0.592928\pi$
$132$	−29.3707	+	29.3707i	−0.222506	+	0.222506i
$133$	80.1161	+	80.1161i	0.602377	+	0.602377i
$134$		−	11.9893i		−	0.0894721i
$135$		0			0
$136$	21.8679			0.160794
$137$	−8.03264	+	8.03264i	−0.0586324	+	0.0586324i	−0.735815	−	0.677183i	$-0.763201\pi$
$137$	−8.03264	+	8.03264i	−0.0586324	+	0.0586324i	0.677183	+	0.735815i	$0.263201\pi$
$138$	−78.0773	−	78.0773i	−0.565777	−	0.565777i
$139$			154.718i			1.11308i	0.830821	+	0.556540i	$0.187871\pi$
$139$			154.718i			1.11308i	−0.830821	+	0.556540i	$0.812129\pi$
$140$		0			0
$141$	215.214			1.52634
$142$	18.8490	−	18.8490i	0.132739	−	0.132739i
$143$	−36.9567	−	36.9567i	−0.258438	−	0.258438i
$144$			33.6728i			0.233839i
$145$		0			0
$146$	−82.6054			−0.565791
$147$	141.745	−	141.745i	0.964251	−	0.964251i
$148$	98.5202	+	98.5202i	0.665677	+	0.665677i
$149$		−	80.0369i		−	0.537160i	−0.963257	−	0.268580i	$-0.913446\pi$
$149$		−	80.0369i		−	0.537160i	0.963257	−	0.268580i	$-0.0865544\pi$
$150$		0			0
$151$	206.188			1.36548			0.682742	−	0.730659i	$-0.260787\pi$
$151$	206.188			1.36548			0.682742	+	0.730659i	$0.260787\pi$
$152$	−187.414	+	187.414i	−1.23299	+	1.23299i
$153$	−39.3673	−	39.3673i	−0.257303	−	0.257303i
$154$			15.2586i			0.0990819i
$155$		0			0
$156$	197.354			1.26509
$157$	76.0386	−	76.0386i	0.484322	−	0.484322i	−0.422187	−	0.906509i	$-0.638737\pi$
$157$	76.0386	−	76.0386i	0.484322	−	0.484322i	0.906509	+	0.422187i	$0.138737\pi$
$158$	−26.8194	−	26.8194i	−0.169743	−	0.169743i
$159$			114.154i			0.717947i
$160$		0			0
$161$	54.2443			0.336921
$162$	156.492	−	156.492i	0.966000	−	0.966000i
$163$	−21.8597	−	21.8597i	−0.134108	−	0.134108i	0.636866	−	0.770974i	$-0.280230\pi$
$163$	−21.8597	−	21.8597i	−0.134108	−	0.134108i	−0.770974	+	0.636866i	$0.780230\pi$
$164$			95.7941i			0.584110i
$165$		0			0
$166$	−183.969			−1.10825
$167$	19.5124	−	19.5124i	0.116841	−	0.116841i	−0.646269	−	0.763110i	$-0.723672\pi$
$167$	19.5124	−	19.5124i	0.116841	−	0.116841i	0.763110	+	0.646269i	$0.223672\pi$
$168$	−111.949	−	111.949i	−0.666361	−	0.666361i
$169$			79.3266i			0.469388i
$170$		0			0
$171$	674.777			3.94607
$172$	8.47313	−	8.47313i	0.0492624	−	0.0492624i
$173$	−214.952	−	214.952i	−1.24250	−	1.24250i	−0.958961	−	0.283539i	$-0.908492\pi$
$173$	−214.952	−	214.952i	−1.24250	−	1.24250i	−0.283539	−	0.958961i	$-0.591508\pi$
$174$		−	113.135i		−	0.650198i
$175$		0			0
$176$	−5.33217			−0.0302964
$177$	−396.879	+	396.879i	−2.24225	+	2.24225i
$178$	132.363	+	132.363i	0.743611	+	0.743611i
$179$		−	111.046i		−	0.620370i	−0.950676	−	0.310185i	$-0.899609\pi$
$179$		−	111.046i		−	0.620370i	0.950676	−	0.310185i	$-0.100391\pi$
$180$		0			0
$181$	−126.341			−0.698014			−0.349007	−	0.937120i	$-0.613481\pi$
$181$	−126.341			−0.698014			−0.349007	+	0.937120i	$0.613481\pi$
$182$	51.2644	−	51.2644i	0.281672	−	0.281672i
$183$	132.854	+	132.854i	0.725978	+	0.725978i
$184$			126.893i			0.689633i
$185$		0			0
$186$	403.660			2.17021
$187$	6.23391	−	6.23391i	0.0333364	−	0.0333364i
$188$	−63.6459	−	63.6459i	−0.338542	−	0.338542i
$189$			229.867i			1.21623i
$190$		0			0
$191$	−172.600			−0.903665			−0.451832	−	0.892103i	$-0.649230\pi$
$191$	−172.600			−0.903665			−0.451832	+	0.892103i	$0.649230\pi$
$192$	180.811	−	180.811i	0.941721	−	0.941721i
$193$	51.8757	+	51.8757i	0.268786	+	0.268786i	0.828611	−	0.559825i	$-0.189132\pi$
$193$	51.8757	+	51.8757i	0.268786	+	0.268786i	−0.559825	+	0.828611i	$0.689132\pi$
$194$		−	8.64400i		−	0.0445567i
$195$		0			0
$196$	−83.8373			−0.427741
$197$	117.224	−	117.224i	0.595045	−	0.595045i	−0.343945	−	0.938990i	$-0.611763\pi$
$197$	117.224	−	117.224i	0.595045	−	0.595045i	0.938990	+	0.343945i	$0.111763\pi$
$198$	64.2578	+	64.2578i	0.324534	+	0.324534i
$199$		−	124.111i		−	0.623671i	−0.950136	−	0.311836i	$-0.899056\pi$
$199$		−	124.111i		−	0.623671i	0.950136	−	0.311836i	$-0.100944\pi$
$200$		0			0
$201$	50.1509			0.249507
$202$	−56.7018	+	56.7018i	−0.280702	+	0.280702i
$203$	39.3002	+	39.3002i	0.193597	+	0.193597i
$204$			33.2899i			0.163186i
$205$		0			0
$206$	−4.63078			−0.0224795
$207$	228.436	−	228.436i	1.10356	−	1.10356i
$208$	17.9145	+	17.9145i	0.0861273	+	0.0861273i
$209$			106.853i			0.511256i
$210$		0			0
$211$	−72.1006			−0.341709			−0.170854	−	0.985296i	$-0.554653\pi$
$211$	−72.1006			−0.341709			−0.170854	+	0.985296i	$0.554653\pi$
$212$	33.7590	−	33.7590i	0.159241	−	0.159241i
$213$	78.8450	+	78.8450i	0.370164	+	0.370164i
$214$			210.320i			0.982805i
$215$		0			0
$216$	−537.723			−2.48946
$217$	−140.222	+	140.222i	−0.646182	+	0.646182i
$218$	−73.9820	−	73.9820i	−0.339367	−	0.339367i
$219$		−	345.537i		−	1.57780i
$220$		0			0
$221$	−41.8881			−0.189539
$222$	308.165	−	308.165i	1.38813	−	1.38813i
$223$	−208.503	−	208.503i	−0.934993	−	0.934993i	0.0630193	−	0.998012i	$-0.479927\pi$
$223$	−208.503	−	208.503i	−0.934993	−	0.934993i	−0.998012	+	0.0630193i	$0.979927\pi$
$224$			108.330i			0.483618i
$225$		0			0
$226$	−96.8243			−0.428426
$227$	96.7721	−	96.7721i	0.426309	−	0.426309i	−0.461060	−	0.887369i	$-0.652531\pi$
$227$	96.7721	−	96.7721i	0.426309	−	0.426309i	0.887369	+	0.461060i	$0.152531\pi$
$228$	−285.304	−	285.304i	−1.25133	−	1.25133i
$229$			24.3833i			0.106477i	0.998582	+	0.0532387i	$0.0169544\pi$
$229$			24.3833i			0.106477i	−0.998582	+	0.0532387i	$0.983046\pi$
$230$		0			0
$231$	−63.8266			−0.276306
$232$	−91.9341	+	91.9341i	−0.396268	+	0.396268i
$233$	6.08298	+	6.08298i	0.0261072	+	0.0261072i	0.720040	−	0.693933i	$-0.244123\pi$
$233$	6.08298	+	6.08298i	0.0261072	+	0.0261072i	−0.693933	+	0.720040i	$0.744123\pi$
$234$		−	431.774i		−	1.84519i
$235$		0			0
$236$	234.740			0.994663
$237$	112.185	−	112.185i	0.473355	−	0.473355i
$238$	8.64735	+	8.64735i	0.0363334	+	0.0363334i
$239$		−	301.659i		−	1.26217i	−0.775713	−	0.631086i	$-0.782609\pi$
$239$		−	301.659i		−	1.26217i	0.775713	−	0.631086i	$-0.217391\pi$
$240$		0			0
$241$	−152.402			−0.632372			−0.316186	−	0.948697i	$-0.602402\pi$
$241$	−152.402			−0.632372			−0.316186	+	0.948697i	$0.602402\pi$
$242$	−10.1754	+	10.1754i	−0.0420470	+	0.0420470i
$243$	238.638	+	238.638i	0.982050	+	0.982050i
$244$		−	78.5787i		−	0.322044i
$245$		0			0
$246$	299.638			1.21804
$247$	358.992	−	358.992i	1.45341	−	1.45341i
$248$	−328.018	−	328.018i	−1.32265	−	1.32265i
$249$		−	769.541i		−	3.09053i
$250$		0			0
$251$	0.830967			0.00331063			0.00165531	−	0.999999i	$-0.499473\pi$
$251$	0.830967			0.00331063			0.00165531	+	0.999999i	$0.499473\pi$
$252$	119.200	−	119.200i	0.473017	−	0.473017i
$253$	36.1734	+	36.1734i	0.142978	+	0.142978i
$254$			213.425i			0.840257i
$255$		0			0
$256$	−268.133			−1.04739
$257$	−213.892	+	213.892i	−0.832265	+	0.832265i	−0.987826	−	0.155561i	$-0.950281\pi$
$257$	−213.892	+	213.892i	−0.832265	+	0.832265i	0.155561	+	0.987826i	$0.450281\pi$
$258$	−26.5034	−	26.5034i	−0.102726	−	0.102726i
$259$			214.098i			0.826632i
$260$		0			0
$261$	331.005			1.26822
$262$	69.7539	−	69.7539i	0.266236	−	0.266236i
$263$	−242.199	−	242.199i	−0.920908	−	0.920908i	0.0761856	−	0.997094i	$-0.475726\pi$
$263$	−242.199	−	242.199i	−0.920908	−	0.920908i	−0.997094	+	0.0761856i	$0.975726\pi$
$264$		−	149.308i		−	0.565562i
$265$		0			0
$266$	−148.220			−0.557219
$267$	−553.672	+	553.672i	−2.07368	+	2.07368i
$268$	−14.8313	−	14.8313i	−0.0553407	−	0.0553407i
$269$			274.273i			1.01960i	0.860292	+	0.509801i	$0.170281\pi$
$269$			274.273i			1.01960i	−0.860292	+	0.509801i	$0.829719\pi$
$270$		0			0
$271$	−224.792			−0.829490			−0.414745	−	0.909938i	$-0.636129\pi$
$271$	−224.792			−0.829490			−0.414745	+	0.909938i	$0.636129\pi$
$272$	−3.02184	+	3.02184i	−0.0111097	+	0.0111097i
$273$	214.438	+	214.438i	0.785487	+	0.785487i
$274$		−	14.8609i		−	0.0542370i
$275$		0			0
$276$	−193.171			−0.699894
$277$	63.8151	−	63.8151i	0.230379	−	0.230379i	−0.582472	−	0.812851i	$-0.697914\pi$
$277$	63.8151	−	63.8151i	0.230379	−	0.230379i	0.812851	+	0.582472i	$0.197914\pi$
$278$	−143.119	−	143.119i	−0.514818	−	0.514818i
$279$			1181.01i			4.23303i
$280$		0			0
$281$	305.190			1.08609			0.543043	−	0.839705i	$-0.317272\pi$
$281$	305.190			1.08609			0.543043	+	0.839705i	$0.317272\pi$
$282$	−199.080	+	199.080i	−0.705958	+	0.705958i
$283$	367.259	+	367.259i	1.29773	+	1.29773i	0.929885	+	0.367849i	$0.119906\pi$
$283$	367.259	+	367.259i	1.29773	+	1.29773i	0.367849	+	0.929885i	$0.380094\pi$
$284$		−	46.6342i		−	0.164205i
$285$		0			0
$286$	68.3724			0.239064
$287$	−104.087	+	104.087i	−0.362672	+	0.362672i
$288$	456.206	+	456.206i	1.58405	+	1.58405i
$289$			281.934i			0.975551i
$290$		0			0
$291$	36.1577			0.124253
$292$	−102.187	+	102.187i	−0.349955	+	0.349955i
$293$	249.733	+	249.733i	0.852332	+	0.852332i	0.990420	−	0.138088i	$-0.0440957\pi$
$293$	249.733	+	249.733i	0.852332	+	0.852332i	−0.138088	+	0.990420i	$0.544096\pi$
$294$			262.238i			0.891965i
$295$		0			0
$296$	−500.834			−1.69201
$297$	−153.289	+	153.289i	−0.516125	+	0.516125i
$298$	74.0368	+	74.0368i	0.248446	+	0.248446i
$299$		−	243.063i		−	0.812921i
$300$		0			0
$301$	18.4133			0.0611736
$302$	−190.731	+	190.731i	−0.631560	+	0.631560i
$303$	−237.183	−	237.183i	−0.782781	−	0.782781i
$304$		−	51.7960i		−	0.170382i
$305$		0			0
$306$	72.8323			0.238014
$307$	282.935	−	282.935i	0.921614	−	0.921614i	−0.0755300	−	0.997144i	$-0.524065\pi$
$307$	282.935	−	282.935i	0.921614	−	0.921614i	0.997144	+	0.0755300i	$0.0240649\pi$
$308$	18.8756	+	18.8756i	0.0612846	+	0.0612846i
$309$		−	19.3705i		−	0.0626876i
$310$		0			0
$311$	−20.6266			−0.0663233			−0.0331617	−	0.999450i	$-0.510558\pi$
$311$	−20.6266			−0.0663233			−0.0331617	+	0.999450i	$0.510558\pi$
$312$	−501.631	+	501.631i	−1.60779	+	1.60779i
$313$	−164.238	−	164.238i	−0.524722	−	0.524722i	0.394272	−	0.918994i	$-0.370997\pi$
$313$	−164.238	−	164.238i	−0.524722	−	0.524722i	−0.918994	+	0.394272i	$0.870997\pi$
$314$			140.677i			0.448015i
$315$		0			0
$316$	−66.3538			−0.209980
$317$	−58.8640	+	58.8640i	−0.185691	+	0.185691i	−0.793830	−	0.608139i	$-0.791916\pi$
$317$	−58.8640	+	58.8640i	−0.185691	+	0.185691i	0.608139	+	0.793830i	$0.291916\pi$
$318$	−105.596	−	105.596i	−0.332063	−	0.332063i
$319$			52.4155i			0.164312i
$320$		0			0
$321$	−879.767			−2.74071
$322$	−50.1778	+	50.1778i	−0.155832	+	0.155832i
$323$	60.5554	+	60.5554i	0.187478	+	0.187478i
$324$		−	387.176i		−	1.19499i
$325$		0			0
$326$	40.4419			0.124055
$327$	309.466	−	309.466i	0.946378	−	0.946378i
$328$	−243.488	−	243.488i	−0.742342	−	0.742342i
$329$		−	138.311i		−	0.420398i
$330$		0			0
$331$	388.432			1.17351			0.586756	−	0.809764i	$-0.300405\pi$
$331$	388.432			1.17351			0.586756	+	0.809764i	$0.300405\pi$
$332$	−227.579	+	227.579i	−0.685479	+	0.685479i
$333$	901.618	+	901.618i	2.70756	+	2.70756i
$334$			36.0992i			0.108081i
$335$		0			0
$336$	30.9395			0.0920817
$337$	77.3541	−	77.3541i	0.229538	−	0.229538i	−0.582962	−	0.812499i	$-0.698106\pi$
$337$	77.3541	−	77.3541i	0.229538	−	0.229538i	0.812499	+	0.582962i	$0.198106\pi$
$338$	−73.3799	−	73.3799i	−0.217100	−	0.217100i
$339$		−	405.014i		−	1.19473i
$340$		0			0
$341$	−187.017			−0.548436
$342$	−624.192	+	624.192i	−1.82512	+	1.82512i
$343$	−212.945	−	212.945i	−0.620832	−	0.620832i
$344$			43.0738i			0.125214i
$345$		0			0
$346$	397.677			1.14935
$347$	−171.192	+	171.192i	−0.493349	+	0.493349i	−0.909360	−	0.416011i	$-0.863428\pi$
$347$	−171.192	+	171.192i	−0.493349	+	0.493349i	0.416011	+	0.909360i	$0.363428\pi$
$348$	−139.953	−	139.953i	−0.402163	−	0.402163i
$349$			29.9624i			0.0858521i	0.999078	+	0.0429260i	$0.0136680\pi$
$349$			29.9624i			0.0858521i	−0.999078	+	0.0429260i	$0.986332\pi$
$350$		0			0
$351$	1030.01			2.93450
$352$	−72.2413	+	72.2413i	−0.205231	+	0.205231i
$353$	126.771	+	126.771i	0.359125	+	0.359125i	0.863490	−	0.504365i	$-0.168274\pi$
$353$	126.771	+	126.771i	0.359125	+	0.359125i	−0.504365	+	0.863490i	$0.668274\pi$
$354$		−	734.253i		−	2.07416i
$355$		0			0
$356$	327.478			0.919883
$357$	−36.1717	+	36.1717i	−0.101321	+	0.101321i
$358$	102.722	+	102.722i	0.286932	+	0.286932i
$359$			191.615i			0.533745i	0.963732	+	0.266873i	$0.0859903\pi$
$359$			191.615i			0.533745i	−0.963732	+	0.266873i	$0.914010\pi$
$360$		0			0
$361$	−676.952			−1.87521
$362$	116.869	−	116.869i	0.322844	−	0.322844i
$363$	−42.5635	−	42.5635i	−0.117255	−	0.117255i
$364$		−	126.833i		−	0.348442i
$365$		0			0
$366$	−245.789			−0.671555
$367$	−214.617	+	214.617i	−0.584788	+	0.584788i	−0.936215	−	0.351427i	$-0.885697\pi$
$367$	−214.617	+	214.617i	−0.584788	+	0.584788i	0.351427	+	0.936215i	$0.385697\pi$
$368$	−17.5348	−	17.5348i	−0.0476489	−	0.0476489i
$369$			876.670i			2.37580i
$370$		0			0
$371$	73.3629			0.197744
$372$	499.347	−	499.347i	1.34233	−	1.34233i
$373$	118.727	+	118.727i	0.318304	+	0.318304i	0.848115	−	0.529812i	$-0.177737\pi$
$373$	118.727	+	118.727i	0.318304	+	0.318304i	−0.529812	+	0.848115i	$0.677737\pi$
$374$			11.5332i			0.0308373i
$375$		0			0
$376$	323.548			0.860501
$377$	176.100	−	176.100i	0.467109	−	0.467109i
$378$	−212.635	−	212.635i	−0.562526	−	0.562526i
$379$		−	70.6243i		−	0.186344i	−0.995650	−	0.0931719i	$-0.970299\pi$
$379$		−	70.6243i		−	0.186344i	0.995650	−	0.0931719i	$-0.0297006\pi$
$380$		0			0
$381$	−892.755			−2.34319
$382$	159.661	−	159.661i	0.417960	−	0.417960i
$383$	−408.698	−	408.698i	−1.06710	−	1.06710i	−0.997581	−	0.0695164i	$-0.977854\pi$
$383$	−408.698	−	408.698i	−1.06710	−	1.06710i	−0.0695164	−	0.997581i	$-0.522146\pi$
$384$		−	339.742i		−	0.884745i
$385$		0			0
$386$	−95.9735			−0.248636
$387$	77.5428	−	77.5428i	0.200369	−	0.200369i
$388$	−10.6930	−	10.6930i	−0.0275594	−	0.0275594i
$389$		−	601.280i		−	1.54571i	−0.634584	−	0.772854i	$-0.718829\pi$
$389$		−	601.280i		−	1.54571i	0.634584	−	0.772854i	$-0.281171\pi$
$390$		0			0
$391$	41.0003			0.104860
$392$	213.097	−	213.097i	0.543614	−	0.543614i
$393$	291.780	+	291.780i	0.742442	+	0.742442i
$394$			216.872i			0.550437i
$395$		0			0
$396$	158.980			0.401465
$397$	341.609	−	341.609i	0.860477	−	0.860477i	−0.130916	−	0.991393i	$-0.541792\pi$
$397$	341.609	−	341.609i	0.860477	−	0.860477i	0.991393	+	0.130916i	$0.0417919\pi$
$398$	114.807	+	114.807i	0.288459	+	0.288459i
$399$		−	620.003i		−	1.55389i
$400$		0			0
$401$	−210.080			−0.523889			−0.261945	−	0.965083i	$-0.584364\pi$
$401$	−210.080			−0.523889			−0.261945	+	0.965083i	$0.584364\pi$
$402$	−46.3913	+	46.3913i	−0.115401	+	0.115401i
$403$	628.319	+	628.319i	1.55910	+	1.55910i
$404$			140.286i			0.347242i
$405$		0			0
$406$	−72.7080			−0.179084
$407$	−142.773	+	142.773i	−0.350794	+	0.350794i
$408$	−84.6159	−	84.6159i	−0.207392	−	0.207392i
$409$		−	691.981i		−	1.69188i	−0.533275	−	0.845942i	$-0.679039\pi$
$409$		−	691.981i		−	1.69188i	0.533275	−	0.845942i	$-0.320961\pi$
$410$		0			0
$411$	62.1630			0.151248
$412$	−5.72850	+	5.72850i	−0.0139041	+	0.0139041i
$413$	255.061	+	255.061i	0.617582	+	0.617582i
$414$			422.622i			1.02083i
$415$		0			0
$416$	485.418			1.16687
$417$	598.667	−	598.667i	1.43565	−	1.43565i
$418$	−98.8423	−	98.8423i	−0.236465	−	0.236465i
$419$			390.808i			0.932717i	0.884596	+	0.466358i	$0.154434\pi$
$419$			390.808i			0.932717i	−0.884596	+	0.466358i	$0.845566\pi$
$420$		0			0
$421$	−417.581			−0.991879			−0.495939	−	0.868357i	$-0.665176\pi$
$421$	−417.581			−0.991879			−0.495939	+	0.868357i	$0.665176\pi$
$422$	66.6955	−	66.6955i	0.158046	−	0.158046i
$423$	−582.462	−	582.462i	−1.37698	−	1.37698i
$424$			171.616i			0.404756i
$425$		0			0
$426$	−145.869			−0.342415
$427$	85.3811	−	85.3811i	0.199956	−	0.199956i
$428$	260.176	+	260.176i	0.607888	+	0.607888i
$429$			286.001i			0.666668i
$430$		0			0
$431$	−114.444			−0.265532			−0.132766	−	0.991147i	$-0.542386\pi$
$431$	−114.444			−0.265532			−0.132766	+	0.991147i	$0.542386\pi$
$432$	74.3058	−	74.3058i	0.172004	−	0.172004i
$433$	−212.706	−	212.706i	−0.491237	−	0.491237i	0.417459	−	0.908696i	$-0.362921\pi$
$433$	−212.706	−	212.706i	−0.491237	−	0.491237i	−0.908696	+	0.417459i	$0.862921\pi$
$434$		−	259.419i		−	0.597741i
$435$		0			0
$436$	−183.039			−0.419813
$437$	−351.384	+	351.384i	−0.804081	+	0.804081i
$438$	319.634	+	319.634i	0.729758	+	0.729758i
$439$			410.312i			0.934652i	0.884085	+	0.467326i	$0.154783\pi$
$439$			410.312i			0.934652i	−0.884085	+	0.467326i	$0.845217\pi$
$440$		0			0
$441$	−767.246			−1.73979
$442$	38.7479	−	38.7479i	0.0876650	−	0.0876650i
$443$	−226.060	−	226.060i	−0.510293	−	0.510293i	0.404323	−	0.914616i	$-0.367507\pi$
$443$	−226.060	−	226.060i	−0.510293	−	0.510293i	−0.914616	+	0.404323i	$0.867507\pi$
$444$		−	762.429i		−	1.71718i
$445$		0			0
$446$	385.746			0.864901
$447$	−309.695	+	309.695i	−0.692830	+	0.692830i
$448$	−116.201	−	116.201i	−0.259378	−	0.259378i
$449$		−	378.916i		−	0.843912i	−0.906616	−	0.421956i	$-0.861344\pi$
$449$		−	378.916i		−	0.843912i	0.906616	−	0.421956i	$-0.138656\pi$
$450$		0			0
$451$	−138.823			−0.307811
$452$	−119.776	+	119.776i	−0.264992	+	0.264992i
$453$	−797.825	−	797.825i	−1.76120	−	1.76120i
$454$			179.035i			0.394350i
$455$		0			0
$456$	1450.36			3.18062
$457$	360.460	−	360.460i	0.788753	−	0.788753i	−0.192537	−	0.981290i	$-0.561671\pi$
$457$	360.460	−	360.460i	0.788753	−	0.788753i	0.981290	+	0.192537i	$0.0616715\pi$
$458$	−22.5554	−	22.5554i	−0.0492476	−	0.0492476i
$459$			173.744i			0.378527i
$460$		0			0
$461$	−219.012			−0.475081			−0.237540	−	0.971378i	$-0.576341\pi$
$461$	−219.012			−0.475081			−0.237540	+	0.971378i	$0.576341\pi$
$462$	59.0418	−	59.0418i	0.127796	−	0.127796i
$463$	−192.919	−	192.919i	−0.416672	−	0.416672i	0.467383	−	0.884055i	$-0.345197\pi$
$463$	−192.919	−	192.919i	−0.416672	−	0.416672i	−0.884055	+	0.467383i	$0.845197\pi$
$464$		−	25.4080i		−	0.0547586i
$465$		0			0
$466$	−11.2539			−0.0241500
$467$	82.3422	−	82.3422i	0.176322	−	0.176322i	−0.613429	−	0.789750i	$-0.710210\pi$
$467$	82.3422	−	82.3422i	0.176322	−	0.176322i	0.789750	+	0.613429i	$0.210210\pi$
$468$	−534.125	−	534.125i	−1.14129	−	1.14129i
$469$		−	32.2304i		−	0.0687216i
$470$		0			0
$471$	−588.448			−1.24936
$472$	−596.660	+	596.660i	−1.26411	+	1.26411i
$473$	12.2791	+	12.2791i	0.0259600	+	0.0259600i
$474$			207.550i			0.437870i
$475$		0			0
$476$	21.3944			0.0449462
$477$	308.949	−	308.949i	0.647692	−	0.647692i
$478$	279.045	+	279.045i	0.583777	+	0.583777i
$479$			888.420i			1.85474i	0.374147	+	0.927369i	$0.377935\pi$
$479$			888.420i			1.85474i	−0.374147	+	0.927369i	$0.622065\pi$
$480$		0			0
$481$	959.351			1.99449
$482$	140.977	−	140.977i	0.292483	−	0.292483i
$483$	−209.893	−	209.893i	−0.434561	−	0.434561i
$484$			25.1749i			0.0520142i
$485$		0			0
$486$	−441.497			−0.908430
$487$	124.471	−	124.471i	0.255587	−	0.255587i	−0.567669	−	0.823257i	$-0.692155\pi$
$487$	124.471	−	124.471i	0.255587	−	0.255587i	0.823257	+	0.567669i	$0.192155\pi$
$488$	199.730	+	199.730i	0.409283	+	0.409283i
$489$			169.168i			0.345946i
$490$		0			0
$491$	970.147			1.97586			0.987929	−	0.154906i	$-0.0495074\pi$
$491$	970.147			1.97586			0.987929	+	0.154906i	$0.0495074\pi$
$492$	370.666	−	370.666i	0.753386	−	0.753386i
$493$	29.7049	+	29.7049i	0.0602533	+	0.0602533i
$494$			664.161i			1.34445i
$495$		0			0
$496$	90.6549			0.182772
$497$	50.6712	−	50.6712i	0.101954	−	0.101954i
$498$	711.852	+	711.852i	1.42942	+	1.42942i
$499$			581.566i			1.16546i	0.812665	+	0.582732i	$0.198016\pi$
$499$			581.566i			1.16546i	−0.812665	+	0.582732i	$0.801984\pi$
$500$		0			0
$501$	−151.003			−0.301402
$502$	−0.768673	+	0.768673i	−0.00153122	+	0.00153122i
$503$	337.601	+	337.601i	0.671176	+	0.671176i	0.957987	−	0.286811i	$-0.0925953\pi$
$503$	337.601	+	337.601i	0.671176	+	0.671176i	−0.286811	+	0.957987i	$0.592595\pi$
$504$			605.963i			1.20231i
$505$		0			0
$506$	−66.9232			−0.132259
$507$	306.947	−	306.947i	0.605418	−	0.605418i
$508$	264.017	+	264.017i	0.519719	+	0.519719i
$509$			368.994i			0.724939i	0.931996	+	0.362470i	$0.118066\pi$
$509$			368.994i			0.724939i	−0.931996	+	0.362470i	$0.881934\pi$
$510$		0			0
$511$	−222.066			−0.434571
$512$	72.4279	−	72.4279i	0.141461	−	0.141461i
$513$	−1489.03	−	1489.03i	−2.90260	−	2.90260i
$514$		−	395.715i		−	0.769873i
$515$		0			0
$516$	−65.5720			−0.127077
$517$	92.2342	−	92.2342i	0.178403	−	0.178403i
$518$	−198.048	−	198.048i	−0.382331	−	0.382331i
$519$			1663.48i			3.20516i
$520$		0			0
$521$	533.075			1.02318			0.511589	−	0.859231i	$-0.329057\pi$
$521$	533.075			1.02318			0.511589	+	0.859231i	$0.329057\pi$
$522$	−306.191	+	306.191i	−0.586573	+	0.586573i
$523$	−311.717	−	311.717i	−0.596018	−	0.596018i	0.343233	−	0.939250i	$-0.388478\pi$
$523$	−311.717	−	311.717i	−0.596018	−	0.596018i	−0.939250	+	0.343233i	$0.888478\pi$
$524$		−	172.578i		−	0.329347i
$525$		0			0
$526$	448.084			0.851871
$527$	−105.986	+	105.986i	−0.201112	+	0.201112i
$528$	20.6323	+	20.6323i	0.0390764	+	0.0390764i
$529$		−	291.088i		−	0.550262i
$530$		0			0
$531$	2148.25			4.04567
$532$	−183.356	+	183.356i	−0.344653	+	0.344653i
$533$	466.403	+	466.403i	0.875052	+	0.875052i
$534$		−	1024.33i		−	1.91822i
$535$		0			0
$536$	75.3960			0.140664
$537$	−429.683	+	429.683i	−0.800154	+	0.800154i
$538$	−253.712	−	253.712i	−0.471584	−	0.471584i
$539$		−	121.495i		−	0.225409i
$540$		0			0
$541$	1005.97			1.85947			0.929736	−	0.368227i	$-0.120035\pi$
$541$	1005.97			1.85947			0.929736	+	0.368227i	$0.120035\pi$
$542$	207.940	−	207.940i	0.383653	−	0.383653i
$543$	488.863	+	488.863i	0.900300	+	0.900300i
$544$			81.8811i			0.150517i
$545$		0			0
$546$	−396.725			−0.726603
$547$	−5.81163	+	5.81163i	−0.0106245	+	0.0106245i	−0.712399	−	0.701775i	$-0.752391\pi$
$547$	−5.81163	+	5.81163i	−0.0106245	+	0.0106245i	0.701775	+	0.712399i	$0.252391\pi$
$548$	−18.3837	−	18.3837i	−0.0335469	−	0.0335469i
$549$		−	719.121i		−	1.30988i
$550$		0			0
$551$	−509.157			−0.924060
$552$	490.999	−	490.999i	0.889490	−	0.889490i
$553$	−72.0979	−	72.0979i	−0.130376	−	0.130376i
$554$			118.062i			0.213109i
$555$		0			0
$556$	−354.091			−0.636855
$557$	−647.706	+	647.706i	−1.16285	+	1.16285i	−0.178998	+	0.983850i	$0.557285\pi$
$557$	−647.706	+	647.706i	−1.16285	+	1.16285i	−0.983850	+	0.178998i	$0.942715\pi$
$558$	−1092.48	−	1092.48i	−1.95785	−	1.95785i
$559$		−	82.5081i		−	0.147599i
$560$		0			0
$561$	−48.2430			−0.0859947
$562$	−282.311	+	282.311i	−0.502334	+	0.502334i
$563$	175.680	+	175.680i	0.312042	+	0.312042i	0.845700	−	0.533658i	$-0.179183\pi$
$563$	175.680	+	175.680i	0.312042	+	0.312042i	−0.533658	+	0.845700i	$0.679183\pi$
$564$			492.543i			0.873304i
$565$		0			0
$566$	−679.454			−1.20045
$567$	420.693	−	420.693i	0.741964	−	0.741964i
$568$	118.534	+	118.534i	0.208687	+	0.208687i
$569$		−	731.096i		−	1.28488i	−0.766336	−	0.642440i	$-0.777922\pi$
$569$		−	731.096i		−	1.28488i	0.766336	−	0.642440i	$-0.222078\pi$
$570$		0			0
$571$	135.547			0.237385			0.118693	−	0.992931i	$-0.462130\pi$
$571$	135.547			0.237385			0.118693	+	0.992931i	$0.462130\pi$
$572$	84.5799	−	84.5799i	0.147867	−	0.147867i
$573$	667.859	+	667.859i	1.16555	+	1.16555i
$574$		−	192.568i		−	0.335484i
$575$		0			0
$576$	−978.704			−1.69914
$577$	232.635	−	232.635i	0.403180	−	0.403180i	−0.476172	−	0.879352i	$-0.657976\pi$
$577$	232.635	−	232.635i	0.403180	−	0.403180i	0.879352	+	0.476172i	$0.157976\pi$
$578$	−260.799	−	260.799i	−0.451209	−	0.451209i
$579$		−	401.456i		−	0.693361i
$580$		0			0
$581$	−494.560			−0.851222
$582$	−33.4471	+	33.4471i	−0.0574693	+	0.0574693i
$583$	48.9228	+	48.9228i	0.0839157	+	0.0839157i
$584$		−	519.475i		−	0.889511i
$585$		0			0
$586$	−462.024			−0.788436
$587$	344.731	−	344.731i	0.587275	−	0.587275i	−0.349617	−	0.936893i	$-0.613688\pi$
$587$	344.731	−	344.731i	0.587275	−	0.587275i	0.936893	+	0.349617i	$0.113688\pi$
$588$	324.401	+	324.401i	0.551702	+	0.551702i
$589$		−	1816.65i		−	3.08430i
$590$		0			0
$591$	−907.173			−1.53498
$592$	69.2083	−	69.2083i	0.116906	−	0.116906i
$593$	497.299	+	497.299i	0.838616	+	0.838616i	0.988677	−	0.150060i	$-0.0479468\pi$
$593$	497.299	+	497.299i	0.838616	+	0.838616i	−0.150060	+	0.988677i	$0.547947\pi$
$594$		−	283.595i		−	0.477433i
$595$		0			0
$596$	183.174			0.307339
$597$	−480.234	+	480.234i	−0.804412	+	0.804412i
$598$	224.842	+	224.842i	0.375990	+	0.375990i
$599$			282.743i			0.472025i	0.971750	+	0.236012i	$0.0758406\pi$
$599$			282.743i			0.472025i	−0.971750	+	0.236012i	$0.924159\pi$
$600$		0			0
$601$	755.637			1.25730			0.628650	−	0.777689i	$-0.283608\pi$
$601$	755.637			1.25730			0.628650	+	0.777689i	$0.283608\pi$
$602$	−17.0329	+	17.0329i	−0.0282939	+	0.0282939i
$603$	−135.730	−	135.730i	−0.225092	−	0.225092i
$604$			471.887i			0.781270i
$605$		0			0
$606$	438.804			0.724100
$607$	−171.655	+	171.655i	−0.282792	+	0.282792i	−0.834221	−	0.551430i	$-0.814083\pi$
$607$	−171.655	+	171.655i	−0.282792	+	0.282792i	0.551430	+	0.834221i	$0.314083\pi$
$608$	−701.743	−	701.743i	−1.15418	−	1.15418i
$609$		−	304.136i		−	0.499403i
$610$		0			0
$611$	−619.759			−1.01433
$612$	90.0970	−	90.0970i	0.147217	−	0.147217i
$613$	15.8263	+	15.8263i	0.0258178	+	0.0258178i	0.719898	−	0.694080i	$-0.244189\pi$
$613$	15.8263	+	15.8263i	0.0258178	+	0.0258178i	−0.694080	+	0.719898i	$0.744189\pi$
$614$			523.450i			0.852524i
$615$		0			0
$616$	−95.9557			−0.155772
$617$	85.3768	−	85.3768i	0.138374	−	0.138374i	−0.634527	−	0.772901i	$-0.718805\pi$
$617$	85.3768	−	85.3768i	0.138374	−	0.138374i	0.772901	+	0.634527i	$0.218805\pi$
$618$	17.9184	+	17.9184i	0.0289941	+	0.0289941i
$619$		−	833.509i		−	1.34654i	−0.739396	−	0.673270i	$-0.764889\pi$
$619$		−	833.509i		−	1.34654i	0.739396	−	0.673270i	$-0.235111\pi$
$620$		0			0
$621$	−1008.18			−1.62348
$622$	19.0803	−	19.0803i	0.0306757	−	0.0306757i
$623$	355.827	+	355.827i	0.571151	+	0.571151i
$624$		−	138.637i		−	0.222174i
$625$		0			0
$626$	303.851			0.485386
$627$	413.456	−	413.456i	0.659419	−	0.659419i
$628$	174.024	+	174.024i	0.277108	+	0.277108i
$629$			161.825i			0.257273i
$630$		0			0
$631$	581.183			0.921051			0.460526	−	0.887646i	$-0.347661\pi$
$631$	581.183			0.921051			0.460526	+	0.887646i	$0.347661\pi$
$632$	168.657	−	168.657i	0.266862	−	0.266862i
$633$	278.986	+	278.986i	0.440737	+	0.440737i
$634$		−	108.902i		−	0.171770i
$635$		0			0
$636$	−261.254			−0.410778
$637$	−408.188	+	408.188i	−0.640797	+	0.640797i
$638$	−48.4861	−	48.4861i	−0.0759970	−	0.0759970i
$639$		−	426.778i		−	0.667884i
$640$		0			0
$641$	109.559			0.170918			0.0854592	−	0.996342i	$-0.472764\pi$
$641$	109.559			0.170918			0.0854592	+	0.996342i	$0.472764\pi$
$642$	813.814	−	813.814i	1.26762	−	1.26762i
$643$	572.874	+	572.874i	0.890940	+	0.890940i	0.994612	−	0.103672i	$-0.0330591\pi$
$643$	572.874	+	572.874i	0.890940	+	0.890940i	−0.103672	+	0.994612i	$0.533059\pi$
$644$			124.145i			0.192771i
$645$		0			0
$646$	−112.032			−0.173424
$647$	−389.176	+	389.176i	−0.601509	+	0.601509i	−0.940713	−	0.339204i	$-0.889842\pi$
$647$	−389.176	+	389.176i	−0.601509	+	0.601509i	0.339204	+	0.940713i	$0.389842\pi$
$648$	984.120	+	984.120i	1.51870	+	1.51870i
$649$			340.181i			0.524162i
$650$		0			0
$651$	1085.15			1.66689
$652$	50.0285	−	50.0285i	0.0767308	−	0.0767308i
$653$	365.630	+	365.630i	0.559923	+	0.559923i	0.929285	−	0.369362i	$-0.120424\pi$
$653$	365.630	+	365.630i	0.559923	+	0.559923i	−0.369362	+	0.929285i	$0.620424\pi$
$654$			572.533i			0.875432i
$655$		0			0
$656$	67.2933			0.102581
$657$	−935.174	+	935.174i	−1.42340	+	1.42340i
$658$	127.942	+	127.942i	0.194441	+	0.194441i
$659$			472.236i			0.716595i	0.933607	+	0.358298i	$0.116643\pi$
$659$			472.236i			0.716595i	−0.933607	+	0.358298i	$0.883357\pi$
$660$		0			0
$661$	−240.373			−0.363651			−0.181825	−	0.983331i	$-0.558201\pi$
$661$	−240.373			−0.363651			−0.181825	+	0.983331i	$0.558201\pi$
$662$	−359.313	+	359.313i	−0.542769	+	0.542769i
$663$	162.082	+	162.082i	0.244468	+	0.244468i
$664$		−	1156.91i		−	1.74234i
$665$		0			0
$666$	−1668.05			−2.50459
$667$	−172.368	+	172.368i	−0.258422	+	0.258422i
$668$	44.6565	+	44.6565i	0.0668510	+	0.0668510i
$669$			1613.57i			2.41191i
$670$		0			0
$671$	113.875			0.169709
$672$	419.174	−	419.174i	0.623771	−	0.623771i
$673$	−243.135	−	243.135i	−0.361270	−	0.361270i	0.503010	−	0.864280i	$-0.332226\pi$
$673$	−243.135	−	243.135i	−0.361270	−	0.361270i	−0.864280	+	0.503010i	$0.832226\pi$
$674$			143.110i			0.212330i
$675$		0			0
$676$	−181.549			−0.268563
$677$	471.912	−	471.912i	0.697064	−	0.697064i	−0.266712	−	0.963776i	$-0.585937\pi$
$677$	471.912	−	471.912i	0.697064	−	0.697064i	0.963776	+	0.266712i	$0.0859374\pi$
$678$	374.652	+	374.652i	0.552584	+	0.552584i
$679$		−	23.2374i		−	0.0342230i
$680$		0			0
$681$	−748.901			−1.09971
$682$	172.997	−	172.997i	0.253661	−	0.253661i
$683$	30.4808	+	30.4808i	0.0446278	+	0.0446278i	0.729069	−	0.684441i	$-0.239954\pi$
$683$	30.4808	+	30.4808i	0.0446278	+	0.0446278i	−0.684441	+	0.729069i	$0.739954\pi$
$684$			1544.31i			2.25776i
$685$		0			0
$686$	393.964			0.574291
$687$	94.3489	−	94.3489i	0.137335	−	0.137335i
$688$	−5.95219	−	5.95219i	−0.00865145	−	0.00865145i
$689$		−	328.732i		−	0.477115i
$690$		0			0
$691$	121.709			0.176134			0.0880671	−	0.996115i	$-0.471931\pi$
$691$	121.709			0.176134			0.0880671	+	0.996115i	$0.471931\pi$
$692$	491.945	−	491.945i	0.710903	−	0.710903i
$693$	172.743	+	172.743i	0.249268	+	0.249268i
$694$		−	316.717i		−	0.456365i
$695$		0			0
$696$	711.460			1.02221
$697$	−78.6735	+	78.6735i	−0.112874	+	0.112874i
$698$	−27.7162	−	27.7162i	−0.0397080	−	0.0397080i
$699$		−	47.0750i		−	0.0673462i
$700$		0			0
$701$	930.403			1.32725			0.663625	−	0.748065i	$-0.269017\pi$
$701$	930.403			1.32725			0.663625	+	0.748065i	$0.269017\pi$
$702$	−952.795	+	952.795i	−1.35726	+	1.35726i
$703$	−1386.88	−	1386.88i	−1.97280	−	1.97280i
$704$		−	154.980i		−	0.220142i
$705$		0			0
$706$	−234.535			−0.332203
$707$	−152.430	+	152.430i	−0.215601	+	0.215601i
$708$	−908.306	−	908.306i	−1.28292	−	1.28292i
$709$		−	1012.74i		−	1.42841i	−0.699935	−	0.714206i	$-0.746788\pi$
$709$		−	1012.74i		−	1.42841i	0.699935	−	0.714206i	$-0.253212\pi$
$710$		0			0
$711$	−607.244			−0.854070
$712$	−832.380	+	832.380i	−1.16907	+	1.16907i
$713$	−615.002	−	615.002i	−0.862555	−	0.862555i
$714$		−	66.9202i		−	0.0937258i
$715$		0			0
$716$	254.143			0.354948
$717$	−1167.24	+	1167.24i	−1.62795	+	1.62795i
$718$	−177.250	−	177.250i	−0.246866	−	0.246866i
$719$		−	1241.19i		−	1.72627i	−0.504973	−	0.863135i	$-0.668498\pi$
$719$		−	1241.19i		−	1.72627i	0.504973	−	0.863135i	$-0.331502\pi$
$720$		0			0
$721$	−12.4488			−0.0172660
$722$	626.204	−	626.204i	0.867318	−	0.867318i
$723$	589.704	+	589.704i	0.815635	+	0.815635i
$724$		−	289.146i		−	0.399373i
$725$		0			0
$726$	78.7453			0.108465
$727$	−251.623	+	251.623i	−0.346112	+	0.346112i	−0.858659	−	0.512547i	$-0.828702\pi$
$727$	−251.623	+	251.623i	−0.346112	+	0.346112i	0.512547	+	0.858659i	$0.328702\pi$
$728$	322.382	+	322.382i	0.442833	+	0.442833i
$729$		−	324.206i		−	0.444727i
$730$		0			0
$731$	13.9176			0.0190391
$732$	−304.053	+	304.053i	−0.415373	+	0.415373i
$733$	−458.627	−	458.627i	−0.625685	−	0.625685i	0.321294	−	0.946979i	$-0.395882\pi$
$733$	−458.627	−	458.627i	−0.625685	−	0.625685i	−0.946979	+	0.321294i	$0.895882\pi$
$734$		−	397.057i		−	0.540949i
$735$		0			0
$736$	−475.130			−0.645557
$737$	21.4932	−	21.4932i	0.0291631	−	0.0291631i
$738$	−810.949	−	810.949i	−1.09885	−	1.09885i
$739$			912.068i			1.23419i	0.786888	+	0.617096i	$0.211691\pi$
$739$			912.068i			1.23419i	−0.786888	+	0.617096i	$0.788309\pi$
$740$		0			0
$741$	−2778.17			−3.74922
$742$	−67.8632	+	67.8632i	−0.0914598	+	0.0914598i
$743$	623.884	+	623.884i	0.839682	+	0.839682i	0.988817	−	0.149134i	$-0.0476487\pi$
$743$	623.884	+	623.884i	0.839682	+	0.839682i	−0.149134	+	0.988817i	$0.547649\pi$
$744$			2538.47i			3.41192i
$745$		0			0
$746$	−219.654			−0.294442
$747$	−2082.71	+	2082.71i	−2.78810	+	2.78810i
$748$	14.2671	+	14.2671i	0.0190736	+	0.0190736i
$749$			565.398i			0.754871i
$750$		0			0
$751$	−776.710			−1.03423			−0.517117	−	0.855915i	$-0.672995\pi$
$751$	−776.710			−1.03423			−0.517117	+	0.855915i	$0.672995\pi$
$752$	−44.7099	+	44.7099i	−0.0594546	+	0.0594546i
$753$	−3.21535	−	3.21535i	−0.00427005	−	0.00427005i
$754$			325.797i			0.432092i
$755$		0			0
$756$	−526.079			−0.695871
$757$	−490.116	+	490.116i	−0.647445	+	0.647445i	−0.952375	−	0.304930i	$-0.901367\pi$
$757$	−490.116	+	490.116i	−0.647445	+	0.647445i	0.304930	+	0.952375i	$0.401367\pi$
$758$	65.3299	+	65.3299i	0.0861872	+	0.0861872i
$759$		−	279.939i		−	0.368826i
$760$		0			0
$761$	60.1820			0.0790828			0.0395414	−	0.999218i	$-0.487410\pi$
$761$	60.1820			0.0790828			0.0395414	+	0.999218i	$0.487410\pi$
$762$	825.829	−	825.829i	1.08377	−	1.08377i
$763$	−198.884	−	198.884i	−0.260660	−	0.260660i
$764$		−	395.016i		−	0.517037i
$765$		0			0
$766$	756.120			0.987101
$767$	1142.91	−	1142.91i	1.49010	−	1.49010i
$768$	1037.52	+	1037.52i	1.35093	+	1.35093i
$769$			637.781i			0.829363i	0.909967	+	0.414682i	$0.136107\pi$
$769$			637.781i			0.829363i	−0.909967	+	0.414682i	$0.863893\pi$
$770$		0			0
$771$	1655.27			2.14691
$772$	−118.724	+	118.724i	−0.153787	+	0.153787i
$773$	−173.796	−	173.796i	−0.224833	−	0.224833i	0.585697	−	0.810530i	$-0.300821\pi$
$773$	−173.796	−	173.796i	−0.224833	−	0.224833i	−0.810530	+	0.585697i	$0.800821\pi$
$774$			143.459i			0.185348i
$775$		0			0
$776$	54.3589			0.0700501
$777$	828.430	−	828.430i	1.06619	−	1.06619i
$778$	556.205	+	556.205i	0.714916	+	0.714916i
$779$		−	1348.51i		−	1.73107i
$780$		0			0
$781$	67.5813			0.0865317
$782$	−37.9267	+	37.9267i	−0.0484996	+	0.0484996i
$783$	−730.430	−	730.430i	−0.932860	−	0.932860i
$784$			58.8939i			0.0751198i
$785$		0			0
$786$	−539.812			−0.686784
$787$	−812.907	+	812.907i	−1.03292	+	1.03292i	−0.0334795	+	0.999439i	$0.510659\pi$
$787$	−812.907	+	812.907i	−1.03292	+	1.03292i	−0.999439	+	0.0334795i	$0.989341\pi$
$788$	268.281	+	268.281i	0.340459	+	0.340459i
$789$			1874.33i			2.37558i
$790$		0			0
$791$	−260.290			−0.329064
$792$	−404.093	+	404.093i	−0.510219	+	0.510219i
$793$	−382.584	−	382.584i	−0.482452	−	0.482452i
$794$			632.001i			0.795971i
$795$		0			0
$796$	284.042			0.356837
$797$	−971.779	+	971.779i	−1.21930	+	1.21930i	−0.251417	+	0.967879i	$0.580897\pi$
$797$	−971.779	+	971.779i	−1.21930	+	1.21930i	−0.967879	+	0.251417i	$0.919103\pi$
$798$	573.524	+	573.524i	0.718702	+	0.718702i
$799$		−	104.542i		−	0.130841i
$800$		0			0
$801$	2996.95			3.74151
$802$	194.331	−	194.331i	0.242308	−	0.242308i
$803$	−148.087	−	148.087i	−0.184417	−	0.184417i
$804$			114.777i			0.142757i
$805$		0			0
$806$	−1162.43			−1.44223
$807$	1061.27	−	1061.27i	1.31508	−	1.31508i
$808$	−356.576	−	356.576i	−0.441307	−	0.441307i
$809$			17.3877i			0.0214928i	0.999942	+	0.0107464i	$0.00342076\pi$
$809$			17.3877i			0.0214928i	−0.999942	+	0.0107464i	$0.996579\pi$
$810$		0			0
$811$	−852.035			−1.05060			−0.525299	−	0.850918i	$-0.676046\pi$
$811$	−852.035			−1.05060			−0.525299	+	0.850918i	$0.676046\pi$
$812$	−89.9433	+	89.9433i	−0.110768	+	0.110768i
$813$	869.810	+	869.810i	1.06988	+	1.06988i
$814$		−	264.140i		−	0.324497i
$815$		0			0
$816$	23.3855			0.0286586
$817$	−119.277	+	119.277i	−0.145994	+	0.145994i
$818$	640.106	+	640.106i	0.782525	+	0.782525i
$819$		−	1160.73i		−	1.41725i
$820$		0			0
$821$	632.202			0.770039			0.385020	−	0.922908i	$-0.374195\pi$
$821$	632.202			0.770039			0.385020	+	0.922908i	$0.374195\pi$
$822$	−57.5029	+	57.5029i	−0.0699549	+	0.0699549i
$823$	−783.340	−	783.340i	−0.951810	−	0.951810i	0.0470806	−	0.998891i	$-0.485008\pi$
$823$	−783.340	−	783.340i	−0.951810	−	0.951810i	−0.998891	+	0.0470806i	$0.985008\pi$
$824$		−	29.1212i		−	0.0353413i
$825$		0			0
$826$	−471.881			−0.571285
$827$	−841.100	+	841.100i	−1.01705	+	1.01705i	−0.0171980	+	0.999852i	$0.505475\pi$
$827$	−841.100	+	841.100i	−1.01705	+	1.01705i	−0.999852	+	0.0171980i	$0.994525\pi$
$828$	522.804	+	522.804i	0.631406	+	0.631406i
$829$			57.3663i			0.0691994i	0.999401	+	0.0345997i	$0.0110156\pi$
$829$			57.3663i			0.0691994i	−0.999401	+	0.0345997i	$0.988984\pi$
$830$		0			0
$831$	−493.853			−0.594287
$832$	−520.686	+	520.686i	−0.625825	+	0.625825i
$833$	−68.8537	−	68.8537i	−0.0826575	−	0.0826575i
$834$			1107.57i			1.32803i
$835$		0			0
$836$	−244.545			−0.292518
$837$	2606.15	−	2606.15i	3.11368	−	3.11368i
$838$	−361.511	−	361.511i	−0.431397	−	0.431397i
$839$			1356.86i			1.61724i	0.588333	+	0.808619i	$0.299785\pi$
$839$			1356.86i			1.61724i	−0.588333	+	0.808619i	$0.700215\pi$
$840$		0			0
$841$	591.238			0.703018
$842$	386.277	−	386.277i	0.458761	−	0.458761i
$843$	−1180.90	−	1180.90i	−1.40084	−	1.40084i
$844$		−	165.011i		−	0.195511i
$845$		0			0
$846$	1077.59			1.27375
$847$	−27.3542	+	27.3542i	−0.0322954	+	0.0322954i
$848$	−23.7150	−	23.7150i	−0.0279658	−	0.0279658i
$849$		−	2842.15i		−	3.34764i
$850$		0			0
$851$	−939.017			−1.10343
$852$	−180.447	+	180.447i	−0.211792	+	0.211792i
$853$	306.457	+	306.457i	0.359269	+	0.359269i	0.863544	−	0.504274i	$-0.168240\pi$
$853$	306.457	+	306.457i	0.359269	+	0.359269i	−0.504274	+	0.863544i	$0.668240\pi$
$854$			157.961i			0.184966i
$855$		0			0
$856$	−1322.62			−1.54512
$857$	698.176	−	698.176i	0.814674	−	0.814674i	−0.170656	−	0.985331i	$-0.554589\pi$
$857$	698.176	−	698.176i	0.814674	−	0.814674i	0.985331	+	0.170656i	$0.0545888\pi$
$858$	−264.560	−	264.560i	−0.308346	−	0.308346i
$859$			126.063i			0.146755i	0.997304	+	0.0733776i	$0.0233778\pi$
$859$			126.063i			0.146755i	−0.997304	+	0.0733776i	$0.976622\pi$
$860$		0			0
$861$	805.507			0.935549
$862$	105.865	−	105.865i	0.122813	−	0.122813i
$863$	−828.692	−	828.692i	−0.960245	−	0.960245i	0.0389942	−	0.999239i	$-0.487585\pi$
$863$	−828.692	−	828.692i	−0.960245	−	0.960245i	−0.999239	+	0.0389942i	$0.987585\pi$
$864$		−	2013.42i		−	2.33035i
$865$		0			0
$866$	393.520			0.454411
$867$	1090.92	−	1090.92i	1.25827	−	1.25827i
$868$	−320.914	−	320.914i	−0.369717	−	0.369717i
$869$		−	96.1585i		−	0.110654i
$870$		0			0
$871$	−144.421			−0.165811
$872$	465.245	−	465.245i	0.533538	−	0.533538i
$873$	−97.8586	−	97.8586i	−0.112095	−	0.112095i
$874$		−	650.084i		−	0.743803i
$875$		0			0
$876$	790.805			0.902745
$877$	601.057	−	601.057i	0.685356	−	0.685356i	−0.275846	−	0.961202i	$-0.588958\pi$
$877$	601.057	−	601.057i	0.685356	−	0.685356i	0.961202	+	0.275846i	$0.0889579\pi$
$878$	−379.553	−	379.553i	−0.432293	−	0.432293i
$879$		−	1932.64i		−	2.19868i
$880$		0			0
$881$	179.995			0.204307			0.102154	−	0.994769i	$-0.467427\pi$
$881$	179.995			0.204307			0.102154	+	0.994769i	$0.467427\pi$
$882$	709.729	−	709.729i	0.804682	−	0.804682i
$883$	−688.177	−	688.177i	−0.779362	−	0.779362i	0.200360	−	0.979722i	$-0.435789\pi$
$883$	−688.177	−	688.177i	−0.779362	−	0.779362i	−0.979722	+	0.200360i	$0.935789\pi$
$884$		−	95.8661i		−	0.108446i
$885$		0			0
$886$	418.226			0.472038
$887$	342.387	−	342.387i	0.386005	−	0.386005i	−0.487255	−	0.873260i	$-0.662002\pi$
$887$	342.387	−	342.387i	0.386005	−	0.386005i	0.873260	+	0.487255i	$0.162002\pi$
$888$	1937.93	+	1937.93i	2.18235	+	2.18235i
$889$			573.745i			0.645383i
$890$		0			0
$891$	561.088			0.629728
$892$	477.186	−	477.186i	0.534962	−	0.534962i
$893$	895.952	+	895.952i	1.00331	+	1.00331i
$894$		−	572.957i		−	0.640891i
$895$		0			0
$896$	−218.342			−0.243685
$897$	−940.510	+	940.510i	−1.04851	+	1.04851i
$898$	350.511	+	350.511i	0.390324	+	0.390324i
$899$		−	891.142i		−	0.991259i
$900$		0			0
$901$	55.4510			0.0615439
$902$	128.416	−	128.416i	0.142368	−	0.142368i
$903$	−71.2484	−	71.2484i	−0.0789018	−	0.0789018i
$904$		−	608.891i		−	0.673552i
$905$		0			0
$906$	1476.03			1.62917
$907$	826.608	−	826.608i	0.911365	−	0.911365i	−0.0850144	−	0.996380i	$-0.527094\pi$
$907$	826.608	−	826.608i	0.911365	−	0.911365i	0.996380	+	0.0850144i	$0.0270936\pi$
$908$	221.475	+	221.475i	0.243915	+	0.243915i
$909$			1283.84i			1.41236i
$910$		0			0
$911$	−826.053			−0.906754			−0.453377	−	0.891319i	$-0.649781\pi$
$911$	−826.053			−0.906754			−0.453377	+	0.891319i	$0.649781\pi$
$912$	−200.420	+	200.420i	−0.219758	+	0.219758i
$913$	−329.803	−	329.803i	−0.361230	−	0.361230i
$914$			666.876i			0.729623i
$915$		0			0
$916$	−55.8042			−0.0609216
$917$	187.518	−	187.518i	0.204490	−	0.204490i
$918$	−160.719	−	160.719i	−0.175075	−	0.175075i
$919$			319.750i			0.347933i	0.984752	+	0.173966i	$0.0556584\pi$
$919$			319.750i			0.347933i	−0.984752	+	0.173966i	$0.944342\pi$
$920$		0			0
$921$	−2189.58			−2.37740
$922$	202.594	−	202.594i	0.219733	−	0.219733i
$923$	−227.053	−	227.053i	−0.245994	−	0.245994i
$924$		−	146.075i		−	0.158090i
$925$		0			0
$926$	356.913			0.385435
$927$	−52.4249	+	52.4249i	−0.0565533	+	0.0565533i
$928$	−344.233	−	344.233i	−0.370941	−	0.370941i
$929$			756.667i			0.814496i	0.913318	+	0.407248i	$0.133512\pi$
$929$			756.667i			0.814496i	−0.913318	+	0.407248i	$0.866488\pi$
$930$		0			0
$931$	1180.19			1.26766
$932$	−13.9216	+	13.9216i	−0.0149374	+	0.0149374i
$933$	79.8125	+	79.8125i	0.0855440	+	0.0855440i
$934$			152.339i			0.163104i
$935$		0			0
$936$	2715.26			2.90092
$937$	−422.038	+	422.038i	−0.450414	+	0.450414i	−0.895492	−	0.445078i	$-0.853176\pi$
$937$	−422.038	+	422.038i	−0.450414	+	0.450414i	0.445078	+	0.895492i	$0.353176\pi$
$938$	29.8142	+	29.8142i	0.0317849	+	0.0317849i
$939$			1271.01i			1.35357i
$940$		0			0
$941$	−1091.44			−1.15987			−0.579937	−	0.814661i	$-0.696923\pi$
$941$	−1091.44			−1.15987			−0.579937	+	0.814661i	$0.696923\pi$
$942$	544.335	−	544.335i	0.577850	−	0.577850i
$943$	−456.517	−	456.517i	−0.484111	−	0.484111i
$944$		−	164.900i		−	0.174682i
$945$		0			0
$946$	−22.7171			−0.0240139
$947$	681.095	−	681.095i	0.719213	−	0.719213i	−0.249231	−	0.968444i	$-0.580178\pi$
$947$	681.095	−	681.095i	0.719213	−	0.719213i	0.968444	+	0.249231i	$0.0801778\pi$
$948$	256.750	+	256.750i	0.270833	+	0.270833i
$949$			995.056i			1.04853i
$950$		0			0
$951$	455.537			0.479008
$952$	−54.3799	+	54.3799i	−0.0571218	+	0.0571218i
$953$	402.146	+	402.146i	0.421979	+	0.421979i	0.885885	−	0.463905i	$-0.153552\pi$
$953$	402.146	+	402.146i	0.421979	+	0.421979i	−0.463905	+	0.885885i	$0.653552\pi$
$954$			571.577i			0.599137i
$955$		0			0
$956$	690.385			0.722160
$957$	202.817	−	202.817i	0.211930	−	0.211930i
$958$	−821.819	−	821.819i	−0.857848	−	0.857848i
$959$		−	39.9502i		−	0.0416582i
$960$		0			0
$961$	2218.56			2.30860
$962$	−887.432	+	887.432i	−0.922487	+	0.922487i
$963$	2381.03	+	2381.03i	2.47251	+	2.47251i
$964$		−	348.790i		−	0.361816i
$965$		0			0
$966$	388.316			0.401984
$967$	−568.231	+	568.231i	−0.587623	+	0.587623i	−0.936987	−	0.349364i	$-0.886398\pi$
$967$	−568.231	+	568.231i	−0.587623	+	0.587623i	0.349364	+	0.936987i	$0.386398\pi$
$968$	−63.9891	−	63.9891i	−0.0661045	−	0.0661045i
$969$		−	468.627i		−	0.483619i
$970$		0			0
$971$	−1823.88			−1.87835			−0.939176	−	0.343436i	$-0.888409\pi$
$971$	−1823.88			−1.87835			−0.939176	+	0.343436i	$0.888409\pi$
$972$	−546.153	+	546.153i	−0.561886	+	0.561886i
$973$	−384.744	−	384.744i	−0.395421	−	0.395421i
$974$			230.280i			0.236427i
$975$		0			0
$976$	−55.1999			−0.0565572
$977$	61.1157	−	61.1157i	0.0625544	−	0.0625544i	−0.675137	−	0.737692i	$-0.735916\pi$
$977$	61.1157	−	61.1157i	0.0625544	−	0.0625544i	0.737692	+	0.675137i	$0.235916\pi$
$978$	−156.486	−	156.486i	−0.160006	−	0.160006i
$979$			474.575i			0.484754i
$980$		0			0
$981$	−1675.10			−1.70754
$982$	−897.419	+	897.419i	−0.913868	+	0.913868i
$983$	55.5500	+	55.5500i	0.0565107	+	0.0565107i	0.734797	−	0.678287i	$-0.237277\pi$
$983$	55.5500	+	55.5500i	0.0565107	+	0.0565107i	−0.678287	+	0.734797i	$0.737277\pi$
$984$			1884.31i			1.91495i
$985$		0			0
$986$	−54.9560			−0.0557363
$987$	−535.182	+	535.182i	−0.542231	+	0.542231i
$988$	821.599	+	821.599i	0.831577	+	0.831577i
$989$			80.7593i			0.0816575i
$990$		0			0
$991$	−491.094			−0.495554			−0.247777	−	0.968817i	$-0.579700\pi$
$991$	−491.094			−0.495554			−0.247777	+	0.968817i	$0.579700\pi$
$992$	1228.21	−	1228.21i	1.23812	−	1.23812i
$993$	−1503.00	−	1503.00i	−1.51360	−	1.51360i
$994$			93.7452i			0.0943111i
$995$		0			0
$996$	1761.19			1.76826
$997$	175.640	−	175.640i	0.176169	−	0.176169i	−0.613515	−	0.789683i	$-0.710245\pi$
$997$	175.640	−	175.640i	0.176169	−	0.176169i	0.789683	+	0.613515i	$0.210245\pi$
$998$	−537.969	−	537.969i	−0.539047	−	0.539047i
$999$		−	3979.20i		−	3.98318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.f.c.243.5	yes	24
5.2	odd	4	inner	275.3.f.c.232.5	✓	24
5.3	odd	4	inner	275.3.f.c.232.8	yes	24
5.4	even	2	inner	275.3.f.c.243.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.f.c.232.5	✓	24	5.2	odd	4	inner
275.3.f.c.232.8	yes	24	5.3	odd	4	inner
275.3.f.c.243.5	yes	24	1.1	even	1	trivial
275.3.f.c.243.8	yes	24	5.4	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.925034 + 0.925034i) q^{2} +(-3.86940 - 3.86940i) q^{3} +2.28862i q^{4} +7.15866 q^{6} +(-2.48674 + 2.48674i) q^{7} +(-5.81719 - 5.81719i) q^{8} +20.9446i q^{9} -3.31662 q^{11} +(8.85561 - 8.85561i) q^{12} +(11.1429 + 11.1429i) q^{13} -4.60065i q^{14} +1.60771 q^{16} +(-1.87959 + 1.87959i) q^{17} +(-19.3745 - 19.3745i) q^{18} -32.2173i q^{19} +19.2444 q^{21} +(3.06799 - 3.06799i) q^{22} +(-10.9067 - 10.9067i) q^{23} +45.0181i q^{24} -20.6151 q^{26} +(46.2184 - 46.2184i) q^{27} +(-5.69122 - 5.69122i) q^{28} -15.8039i q^{29} +56.3876 q^{31} +(21.7816 - 21.7816i) q^{32} +(12.8334 + 12.8334i) q^{33} -3.47738i q^{34} -47.9343 q^{36} +(43.0478 - 43.0478i) q^{37} +(29.8021 + 29.8021i) q^{38} -86.2325i q^{39} +41.8566 q^{41} +(-17.8018 + 17.8018i) q^{42} +(-3.70228 - 3.70228i) q^{43} -7.59051i q^{44} +20.1781 q^{46} +(-27.8097 + 27.8097i) q^{47} +(-6.22088 - 6.22088i) q^{48} +36.6322i q^{49} +14.5458 q^{51} +(-25.5018 + 25.5018i) q^{52} +(-14.7508 - 14.7508i) q^{53} +85.5073i q^{54} +28.9317 q^{56} +(-124.662 + 124.662i) q^{57} +(14.6191 + 14.6191i) q^{58} -102.568i q^{59} -34.3345 q^{61} +(-52.1605 + 52.1605i) q^{62} +(-52.0838 - 52.0838i) q^{63} +46.7283i q^{64} -23.7426 q^{66} +(-6.48045 + 6.48045i) q^{67} +(-4.30168 - 4.30168i) q^{68} +84.4048i q^{69} -20.3765 q^{71} +(121.839 - 121.839i) q^{72} +(44.6499 + 44.6499i) q^{73} +79.6413i q^{74} +73.7332 q^{76} +(8.24760 - 8.24760i) q^{77} +(79.7680 + 79.7680i) q^{78} +28.9929i q^{79} -169.174 q^{81} +(-38.7188 + 38.7188i) q^{82} +(99.4392 + 99.4392i) q^{83} +44.0433i q^{84} +6.84948 q^{86} +(-61.1515 + 61.1515i) q^{87} +(19.2934 + 19.2934i) q^{88} -143.090i q^{89} -55.4189 q^{91} +(24.9613 - 24.9613i) q^{92} +(-218.186 - 218.186i) q^{93} -51.4498i q^{94} -168.564 q^{96} +(-4.67226 + 4.67226i) q^{97} +(-33.8860 - 33.8860i) q^{98} -69.4653i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) \) 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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