LMFDB - Embedded newform 925.2.y.a.193.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [56] 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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.4
Character	$\chi$	$=$	925.193
Dual form			925.2.y.a.532.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.53267 + 0.884889i) q^{2} +(0.223454 + 0.833940i) q^{3} +(0.566056 - 0.980437i) q^{4} +(-1.08043 - 1.08043i) q^{6} +(-0.456178 - 1.70248i) q^{7} -1.53597i q^{8} +(1.95255 - 1.12731i) q^{9} +5.07893i q^{11} +(0.944113 + 0.252974i) q^{12} +(-3.67447 - 2.12146i) q^{13} +(2.20568 + 2.20568i) q^{14} +(2.49127 + 4.31501i) q^{16} +(-0.745779 - 1.29173i) q^{17} +(-1.99508 + 3.45558i) q^{18} +(-1.08710 - 4.05713i) q^{19} +(1.31783 - 0.760851i) q^{21} +(-4.49429 - 7.78434i) q^{22} +7.96415i q^{23} +(1.28091 - 0.343218i) q^{24} +7.50901 q^{26} +(3.20787 + 3.20787i) q^{27} +(-1.92740 - 0.516445i) q^{28} +(4.25340 + 4.25340i) q^{29} +(-6.65235 + 6.65235i) q^{31} +(-4.97623 - 2.87303i) q^{32} +(-4.23553 + 1.13491i) q^{33} +(2.28607 + 1.31986i) q^{34} -2.55247i q^{36} +(-0.273432 + 6.07661i) q^{37} +(5.25628 + 5.25628i) q^{38} +(0.948094 - 3.53833i) q^{39} +(-0.974387 - 0.562562i) q^{41} +(-1.34654 + 2.33227i) q^{42} +11.2292i q^{43} +(4.97957 + 2.87496i) q^{44} +(-7.04738 - 12.2064i) q^{46} +(-0.00582614 + 0.00582614i) q^{47} +(-3.04178 + 3.04178i) q^{48} +(3.37184 - 1.94673i) q^{49} +(0.910577 - 0.910577i) q^{51} +(-4.15991 + 2.40172i) q^{52} +(1.08040 - 4.03209i) q^{53} +(-7.75522 - 2.07801i) q^{54} +(-2.61496 + 0.700676i) q^{56} +(3.14048 - 1.81316i) q^{57} +(-10.2828 - 2.75528i) q^{58} +(-7.84855 - 2.10301i) q^{59} +(3.03813 + 11.3385i) q^{61} +(4.30928 - 16.0825i) q^{62} +(-2.80993 - 2.80993i) q^{63} +0.204149 q^{64} +(5.48741 - 5.48741i) q^{66} +(-8.30053 + 2.22412i) q^{67} -1.68861 q^{68} +(-6.64162 + 1.77962i) q^{69} +(2.01507 - 3.49020i) q^{71} +(-1.73151 - 2.99906i) q^{72} +(2.62998 - 2.62998i) q^{73} +(-4.95804 - 9.55541i) q^{74} +(-4.59312 - 1.23072i) q^{76} +(8.64678 - 2.31690i) q^{77} +(1.67791 + 6.26206i) q^{78} +(0.875572 + 3.26768i) q^{79} +(1.42356 - 2.46567i) q^{81} +1.99122 q^{82} +(1.50332 - 5.61047i) q^{83} -1.72274i q^{84} +(-9.93659 - 17.2107i) q^{86} +(-2.59664 + 4.49752i) q^{87} +7.80109 q^{88} +(-2.17709 + 8.12500i) q^{89} +(-1.93552 + 7.22347i) q^{91} +(7.80835 + 4.50815i) q^{92} +(-7.03415 - 4.06117i) q^{93} +(0.00377408 - 0.0140850i) q^{94} +(1.28398 - 4.79187i) q^{96} -6.00145 q^{97} +(-3.44528 + 5.96740i) q^{98} +(5.72551 + 9.91688i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 36 q^{4} + 8 q^{14} - 72 q^{16} + 16 q^{19} - 36 q^{21} - 4 q^{24} + 8 q^{26} + 24 q^{31} + 60 q^{34} - 24 q^{41} + 24 q^{44} + 12 q^{49} + 84 q^{51} + 28 q^{54} + 104 q^{56} + 4 q^{59} - 24 q^{61}+ \cdots + 120 q^{99}+O(q^{100}) $ 56 * q + 36 * q^4 + 8 * q^14 - 72 * q^16 + 16 * q^19 - 36 * q^21 - 4 * q^24 + 8 * q^26 + 24 * q^31 + 60 * q^34 - 24 * q^41 + 24 * q^44 + 12 * q^49 + 84 * q^51 + 28 * q^54 + 104 * q^56 + 4 * q^59 - 24 * q^61 - 344 * q^64 - 124 * q^66 - 52 * q^69 - 72 * q^71 - 48 * q^74 + 40 * q^76 + 100 * q^79 + 44 * q^81 + 40 * q^86 + 32 * q^89 - 4 * q^91 - 140 * q^94 - 132 * q^96 + 120 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.53267	+	0.884889i	−1.08376	+	0.625711i	−0.931909	−	0.362692i	$-0.881858\pi$
$2$	−1.53267	+	0.884889i	−1.08376	+	0.625711i	−0.151854	+	0.988403i	$0.548524\pi$
$3$	0.223454	+	0.833940i	0.129011	+	0.481476i	0.999951	−	0.00991401i	$-0.00315578\pi$
$3$	0.223454	+	0.833940i	0.129011	+	0.481476i	−0.870940	+	0.491390i	$0.836489\pi$
$4$	0.566056	−	0.980437i	0.283028	−	0.490219i
$5$		0			0
$5$		0			0
$6$	−1.08043	−	1.08043i	−0.441082	−	0.441082i
$7$	−0.456178	−	1.70248i	−0.172419	−	0.643477i	−0.996977	−	0.0776993i	$-0.975243\pi$
$7$	−0.456178	−	1.70248i	−0.172419	−	0.643477i	0.824558	−	0.565778i	$-0.191424\pi$
$8$		−	1.53597i		−	0.543047i
$9$	1.95255	−	1.12731i	0.650850	−	0.375769i
$10$		0			0
$11$			5.07893i			1.53136i	0.643224	+	0.765678i	$0.277596\pi$
$11$			5.07893i			1.53136i	−0.643224	+	0.765678i	$0.722404\pi$
$12$	0.944113	+	0.252974i	0.272542	+	0.0730274i
$13$	−3.67447	−	2.12146i	−1.01911	−	0.588386i	−0.105267	−	0.994444i	$-0.533570\pi$
$13$	−3.67447	−	2.12146i	−1.01911	−	0.588386i	−0.913847	+	0.406058i	$0.866903\pi$
$14$	2.20568	+	2.20568i	0.589492	+	0.589492i
$15$		0			0
$16$	2.49127	+	4.31501i	0.622818	+	1.07875i
$17$	−0.745779	−	1.29173i	−0.180878	−	0.313290i	0.761302	−	0.648398i	$-0.224561\pi$
$17$	−0.745779	−	1.29173i	−0.180878	−	0.313290i	−0.942180	+	0.335108i	$0.891227\pi$
$18$	−1.99508	+	3.45558i	−0.470245	+	0.814488i
$19$	−1.08710	−	4.05713i	−0.249399	−	0.930768i	−0.971121	−	0.238586i	$-0.923316\pi$
$19$	−1.08710	−	4.05713i	−0.249399	−	0.930768i	0.721723	−	0.692182i	$-0.243351\pi$
$20$		0			0
$21$	1.31783	−	0.760851i	0.287575	−	0.166031i
$22$	−4.49429	−	7.78434i	−0.958186	−	1.65963i
$23$			7.96415i			1.66064i	0.557287	+	0.830320i	$0.311842\pi$
$23$			7.96415i			1.66064i	−0.557287	+	0.830320i	$0.688158\pi$
$24$	1.28091	−	0.343218i	0.261464	−	0.0700591i
$25$		0			0
$26$	7.50901			1.47264
$27$	3.20787	+	3.20787i	0.617355	+	0.617355i
$28$	−1.92740	−	0.516445i	−0.364244	−	0.0975989i
$29$	4.25340	+	4.25340i	0.789836	+	0.789836i	0.981467	−	0.191631i	$-0.0613777\pi$
$29$	4.25340	+	4.25340i	0.789836	+	0.789836i	−0.191631	+	0.981467i	$0.561378\pi$
$30$		0			0
$31$	−6.65235	+	6.65235i	−1.19480	+	1.19480i	−0.219094	+	0.975704i	$0.570310\pi$
$31$	−6.65235	+	6.65235i	−1.19480	+	1.19480i	−0.975704	+	0.219094i	$0.929690\pi$
$32$	−4.97623	−	2.87303i	−0.879682	−	0.507885i
$33$	−4.23553	+	1.13491i	−0.737310	+	0.197562i
$34$	2.28607	+	1.31986i	0.392058	+	0.226355i
$35$		0			0
$36$		−	2.55247i		−	0.425412i
$37$	−0.273432	+	6.07661i	−0.0449520	+	0.998989i
$37$	−0.273432	+	6.07661i	−0.0449520	+	0.998989i
$38$	5.25628	+	5.25628i	0.852681	+	0.852681i
$39$	0.948094	−	3.53833i	0.151817	−	0.566587i
$40$		0			0
$41$	−0.974387	−	0.562562i	−0.152174	−	0.0878575i	0.421980	−	0.906605i	$-0.361335\pi$
$41$	−0.974387	−	0.562562i	−0.152174	−	0.0878575i	−0.574153	+	0.818748i	$0.694669\pi$
$42$	−1.34654	+	2.33227i	−0.207775	+	0.359877i
$43$			11.2292i			1.71244i	0.516614	+	0.856218i	$0.327192\pi$
$43$			11.2292i			1.71244i	−0.516614	+	0.856218i	$0.672808\pi$
$44$	4.97957	+	2.87496i	0.750699	+	0.433416i
$45$		0			0
$46$	−7.04738	−	12.2064i	−1.03908	−	1.79974i
$47$	−0.00582614	+	0.00582614i	−0.000849830	+	0.000849830i	−0.707532	−	0.706682i	$-0.750191\pi$
$47$	−0.00582614	+	0.00582614i	−0.000849830	+	0.000849830i	0.706682	+	0.707532i	$0.250191\pi$
$48$	−3.04178	+	3.04178i	−0.439043	+	0.439043i
$49$	3.37184	−	1.94673i	0.481691	−	0.278104i
$50$		0			0
$51$	0.910577	−	0.910577i	0.127506	−	0.127506i
$52$	−4.15991	+	2.40172i	−0.576875	+	0.333059i
$53$	1.08040	−	4.03209i	0.148404	−	0.553850i	−0.851177	−	0.524879i	$-0.824110\pi$
$53$	1.08040	−	4.03209i	0.148404	−	0.553850i	0.999580	−	0.0289707i	$-0.00922294\pi$
$54$	−7.75522	−	2.07801i	−1.05535	−	0.282781i
$55$		0			0
$56$	−2.61496	+	0.700676i	−0.349439	+	0.0936318i
$57$	3.14048	−	1.81316i	0.415967	−	0.240159i
$58$	−10.2828	−	2.75528i	−1.35020	−	0.361786i
$59$	−7.84855	−	2.10301i	−1.02179	−	0.273789i	−0.291245	−	0.956649i	$-0.594069\pi$
$59$	−7.84855	−	2.10301i	−1.02179	−	0.273789i	−0.730550	+	0.682859i	$0.760736\pi$
$60$		0			0
$61$	3.03813	+	11.3385i	0.388993	+	1.45174i	0.831775	+	0.555113i	$0.187325\pi$
$61$	3.03813	+	11.3385i	0.388993	+	1.45174i	−0.442782	+	0.896629i	$0.646008\pi$
$62$	4.30928	−	16.0825i	0.547279	−	2.04247i
$63$	−2.80993	−	2.80993i	−0.354018	−	0.354018i
$64$	0.204149			0.0255186
$65$		0			0
$66$	5.48741	−	5.48741i	0.675453	−	0.675453i
$67$	−8.30053	+	2.22412i	−1.01407	+	0.271720i	−0.727330	−	0.686288i	$-0.759239\pi$
$67$	−8.30053	+	2.22412i	−1.01407	+	0.271720i	−0.286742	+	0.958008i	$0.592572\pi$
$68$	−1.68861			−0.204774
$69$	−6.64162	+	1.77962i	−0.799558	+	0.214241i
$70$		0			0
$71$	2.01507	−	3.49020i	0.239144	−	0.414210i	−0.721325	−	0.692597i	$-0.756466\pi$
$71$	2.01507	−	3.49020i	0.239144	−	0.414210i	0.960469	+	0.278387i	$0.0897998\pi$
$72$	−1.73151	−	2.99906i	−0.204060	−	0.353443i
$73$	2.62998	−	2.62998i	0.307816	−	0.307816i	−0.536246	−	0.844062i	$-0.680158\pi$
$73$	2.62998	−	2.62998i	0.307816	−	0.307816i	0.844062	+	0.536246i	$0.180158\pi$
$74$	−4.95804	−	9.55541i	−0.576361	−	1.11079i
$75$		0			0
$76$	−4.59312	−	1.23072i	−0.526867	−	0.141174i
$77$	8.64678	−	2.31690i	0.985393	−	0.264035i
$78$	1.67791	+	6.26206i	0.189986	+	0.709039i
$79$	0.875572	+	3.26768i	0.0985095	+	0.367643i	0.997528	−	0.0702678i	$-0.0223854\pi$
$79$	0.875572	+	3.26768i	0.0985095	+	0.367643i	−0.899019	+	0.437910i	$0.855719\pi$
$80$		0			0
$81$	1.42356	−	2.46567i	0.158173	−	0.273964i
$82$	1.99122			0.219894
$83$	1.50332	−	5.61047i	0.165011	−	0.615829i	−0.833028	−	0.553231i	$-0.813395\pi$
$83$	1.50332	−	5.61047i	0.165011	−	0.615829i	0.998039	−	0.0625981i	$-0.0199386\pi$
$84$		−	1.72274i		−	0.187966i
$85$		0			0
$86$	−9.93659	−	17.2107i	−1.07149	−	1.85588i
$87$	−2.59664	+	4.49752i	−0.278389	+	0.482184i
$88$	7.80109			0.831599
$89$	−2.17709	+	8.12500i	−0.230771	+	0.861248i	0.749239	+	0.662299i	$0.230419\pi$
$89$	−2.17709	+	8.12500i	−0.230771	+	0.861248i	−0.980010	+	0.198949i	$0.936247\pi$
$90$		0			0
$91$	−1.93552	+	7.22347i	−0.202898	+	0.757226i
$92$	7.80835	+	4.50815i	0.814076	+	0.470007i
$93$	−7.03415	−	4.06117i	−0.729408	−	0.421124i
$94$	0.00377408	−	0.0140850i	0.000389266	−	0.00145276i
$95$		0			0
$96$	1.28398	−	4.79187i	0.131045	−	0.489068i
$97$	−6.00145			−0.609355			−0.304677	−	0.952456i	$-0.598549\pi$
$97$	−6.00145			−0.609355			−0.304677	+	0.952456i	$0.598549\pi$
$98$	−3.44528	+	5.96740i	−0.348026	+	0.602798i
$99$	5.72551	+	9.91688i	0.575436	+	0.996684i
$100$		0			0
$101$		−	9.27066i		−	0.922465i	−0.887279	−	0.461232i	$-0.847407\pi$
$101$		−	9.27066i		−	0.922465i	0.887279	−	0.461232i	$-0.152593\pi$
$102$	−0.589856	+	2.20137i	−0.0584045	+	0.217969i
$103$	−13.1554			−1.29624			−0.648120	−	0.761539i	$-0.724444\pi$
$103$	−13.1554			−1.29624			−0.648120	+	0.761539i	$0.724444\pi$
$104$	−3.25849	+	5.64387i	−0.319521	+	0.553427i
$105$		0			0
$106$	1.91206	+	7.13590i	0.185716	+	0.693100i
$107$	3.31035	+	12.3544i	0.320024	+	1.19434i	0.919221	+	0.393743i	$0.128820\pi$
$107$	3.31035	+	12.3544i	0.320024	+	1.19434i	−0.599197	+	0.800602i	$0.704513\pi$
$108$	4.96095	−	1.32928i	0.477367	−	0.127910i
$109$	−16.4940	−	4.41956i	−1.57984	−	0.423317i	−0.640964	−	0.767571i	$-0.721465\pi$
$109$	−16.4940	−	4.41956i	−1.57984	−	0.423317i	−0.938876	+	0.344254i	$0.888132\pi$
$110$		0			0
$111$	−5.12863	+	1.12982i	−0.486788	+	0.107237i
$112$	6.20976	−	6.20976i	0.586767	−	0.586767i
$113$	2.77437	+	4.80535i	0.260991	+	0.452050i	0.966506	−	0.256646i	$-0.0826174\pi$
$113$	2.77437	+	4.80535i	0.260991	+	0.452050i	−0.705515	+	0.708695i	$0.749284\pi$
$114$	−3.20889	+	5.55796i	−0.300540	+	0.520550i
$115$		0			0
$116$	6.57785	−	1.76253i	0.610738	−	0.163647i
$117$	−9.56612			−0.884388
$118$	13.8902	−	3.72187i	1.27870	−	0.342626i
$119$	−1.85893	+	1.85893i	−0.170408	+	0.170408i
$120$		0			0
$121$	−14.7956			−1.34505
$122$	−14.6897	−	14.6897i	−1.32995	−	1.32995i
$123$	0.251413	−	0.938287i	0.0226692	−	0.0846025i
$124$	2.75661	+	10.2878i	0.247551	+	0.923873i
$125$		0			0
$126$	6.79317	+	1.82023i	0.605184	+	0.162159i
$127$	9.23310	+	2.47400i	0.819305	+	0.219532i	0.644043	−	0.764990i	$-0.277256\pi$
$127$	9.23310	+	2.47400i	0.819305	+	0.219532i	0.175263	+	0.984522i	$0.443923\pi$
$128$	9.63957	−	5.56541i	0.852026	−	0.491917i
$129$	−9.36448	+	2.50920i	−0.824497	+	0.220923i
$130$		0			0
$131$	14.8890	+	3.98950i	1.30086	+	0.348564i	0.841775	−	0.539829i	$-0.181511\pi$
$131$	14.8890	+	3.98950i	1.30086	+	0.348564i	0.459084	+	0.888393i	$0.348178\pi$
$132$	−1.28484	+	4.79509i	−0.111831	+	0.417359i
$133$	−6.41127	+	3.70155i	−0.555927	+	0.320965i
$134$	10.7539	−	10.7539i	0.928995	−	0.928995i
$135$		0			0
$136$	−1.98405	+	1.14549i	−0.170131	+	0.0982253i
$137$	0.140572	−	0.140572i	0.0120099	−	0.0120099i	−0.701076	−	0.713086i	$-0.747297\pi$
$137$	0.140572	−	0.140572i	0.0120099	−	0.0120099i	0.713086	+	0.701076i	$0.247297\pi$
$138$	8.60467	−	8.60467i	0.732478	−	0.732478i
$139$	−10.7764	−	18.6653i	−0.914042	−	1.58317i	−0.808299	−	0.588773i	$-0.799611\pi$
$139$	−10.7764	−	18.6653i	−0.914042	−	1.58317i	−0.105743	−	0.994393i	$-0.533722\pi$
$140$		0			0
$141$	−0.00616052	−	0.00355678i	−0.000518810	−	0.000299535i
$142$			7.13243i			0.598541i
$143$	10.7747	−	18.6624i	0.901028	−	1.56063i
$144$	9.72868	+	5.61686i	0.810723	+	0.468071i
$145$		0			0
$146$	−1.70366	+	6.35813i	−0.140996	+	0.526203i
$147$	2.37691	+	2.37691i	0.196044	+	0.196044i
$148$	5.80296	+	3.70778i	0.477000	+	0.304778i
$149$			4.45566i			0.365022i	0.983204	+	0.182511i	$0.0584226\pi$
$149$			4.45566i			0.365022i	−0.983204	+	0.182511i	$0.941577\pi$
$150$		0			0
$151$	−3.72564	−	2.15100i	−0.303188	−	0.175046i	0.340686	−	0.940177i	$-0.389341\pi$
$151$	−3.72564	−	2.15100i	−0.303188	−	0.175046i	−0.643874	+	0.765131i	$0.722674\pi$
$152$	−6.23162	+	1.66976i	−0.505451	+	0.135435i
$153$	−2.91235	−	1.68144i	−0.235449	−	0.135937i
$154$	−11.2025	+	11.2025i	−0.902722	+	0.902722i
$155$		0			0
$156$	−2.93244	−	2.93244i	−0.234783	−	0.234783i
$157$	0.322991	+	0.0865452i	0.0257775	+	0.00690706i	0.271685	−	0.962386i	$-0.412419\pi$
$157$	0.322991	+	0.0865452i	0.0257775	+	0.00690706i	−0.245907	+	0.969293i	$0.579086\pi$
$158$	−4.23350	−	4.23350i	−0.336799	−	0.336799i
$159$	3.60394			0.285811
$160$		0			0
$161$	13.5588	−	3.63307i	1.06858	−	0.286326i
$162$			5.03875i			0.395882i
$163$	7.31795	+	12.6751i	0.573186	+	0.992788i	0.996236	+	0.0866815i	$0.0276262\pi$
$163$	7.31795	+	12.6751i	0.573186	+	0.992788i	−0.423050	+	0.906106i	$0.639040\pi$
$164$	−1.10311	+	0.636883i	−0.0861388	+	0.0497322i
$165$		0			0
$166$	2.66054	+	9.92928i	0.206498	+	0.770662i
$167$	−2.87280	+	4.97584i	−0.222304	+	0.385042i	−0.955507	−	0.294968i	$-0.904691\pi$
$167$	−2.87280	+	4.97584i	−0.222304	+	0.385042i	0.733203	+	0.680010i	$0.238024\pi$
$168$	−1.16864	−	2.02415i	−0.0901628	−	0.156167i
$169$	2.50115	+	4.33211i	0.192396	+	0.333239i
$170$		0			0
$171$	−6.69625	−	6.69625i	−0.512075	−	0.512075i
$172$	11.0095	+	6.35635i	0.839468	+	0.484667i
$173$	4.22600	+	1.13235i	0.321297	+	0.0860913i	0.415863	−	0.909427i	$-0.363480\pi$
$173$	4.22600	+	1.13235i	0.321297	+	0.0860913i	−0.0945658	+	0.995519i	$0.530146\pi$
$174$		−	9.19095i		−	0.696764i
$175$		0			0
$176$	−21.9157	+	12.6530i	−1.65195	+	0.953756i
$177$		−	7.01515i		−	0.527291i
$178$	−3.85296	−	14.3794i	−0.288791	−	1.07778i
$179$	3.38955	+	3.38955i	0.253347	+	0.253347i	0.822341	−	0.568995i	$-0.192667\pi$
$179$	3.38955	+	3.38955i	0.253347	+	0.253347i	−0.568995	+	0.822341i	$0.692667\pi$
$180$		0			0
$181$	−6.12297	+	10.6053i	−0.455117	+	0.788285i	−0.998695	−	0.0510735i	$-0.983736\pi$
$181$	−6.12297	+	10.6053i	−0.455117	+	0.788285i	0.543578	+	0.839358i	$0.317069\pi$
$182$	−3.42545	−	12.7839i	−0.253911	−	0.947609i
$183$	−8.77672	+	5.06724i	−0.648794	+	0.374581i
$184$	12.2327			0.901806
$185$		0			0
$186$	14.3747			1.05401
$187$	6.56060	−	3.78776i	0.479758	−	0.276989i
$188$	0.00241424	+	0.00901008i	0.000176077	+	0.000657128i
$189$	3.99798	−	6.92470i	0.290810	−	0.503698i
$190$		0			0
$191$	8.10699	+	8.10699i	0.586601	+	0.586601i	0.936709	−	0.350108i	$-0.113855\pi$
$191$	8.10699	+	8.10699i	0.586601	+	0.586601i	−0.350108	+	0.936709i	$0.613855\pi$
$192$	0.0456178	+	0.170248i	0.00329218	+	0.0122866i
$193$			2.94463i			0.211959i	0.994368	+	0.105980i	$0.0337978\pi$
$193$			2.94463i			0.211959i	−0.994368	+	0.105980i	$0.966202\pi$
$194$	9.19825	−	5.31061i	0.660396	−	0.381280i
$195$		0			0
$196$		−	4.40783i		−	0.314845i
$197$	24.1687	+	6.47599i	1.72195	+	0.461395i	0.978303	−	0.207177i	$-0.0664277\pi$
$197$	24.1687	+	6.47599i	1.72195	+	0.461395i	0.743647	+	0.668573i	$0.233094\pi$
$198$	−17.5507	−	10.1329i	−1.24727	−	0.720112i
$199$	−13.0511	−	13.0511i	−0.925169	−	0.925169i	0.0722195	−	0.997389i	$-0.476992\pi$
$199$	−13.0511	−	13.0511i	−0.925169	−	0.925169i	−0.997389	+	0.0722195i	$0.976992\pi$
$200$		0			0
$201$	−3.70957	−	6.42516i	−0.261653	−	0.453196i
$202$	8.20350	+	14.2089i	0.577196	+	0.999733i
$203$	5.30102	−	9.18163i	0.372059	−	0.644424i
$204$	−0.377326	−	1.40820i	−0.0264181	−	0.0985937i
$205$		0			0
$206$	20.1629	−	11.6411i	1.40482	−	0.811071i
$207$	8.97803	+	15.5504i	0.624016	+	1.08083i
$208$		−	21.1405i		−	1.46583i
$209$	20.6059	−	5.52132i	1.42534	−	0.381918i
$210$		0			0
$211$	16.7927			1.15606			0.578029	−	0.816016i	$-0.303822\pi$
$211$	16.7927			1.15606			0.578029	+	0.816016i	$0.303822\pi$
$212$	−3.34165	−	3.34165i	−0.229505	−	0.229505i
$213$	3.36089	+	0.900547i	0.230284	+	0.0617045i
$214$	−16.0059	−	16.0059i	−1.09414	−	1.09414i
$215$		0			0
$216$	4.92719	−	4.92719i	0.335253	−	0.335253i
$217$	14.3602	+	8.29084i	0.974831	+	0.562819i
$218$	29.1907	−	7.82163i	1.97705	−	0.529748i
$219$	2.78092	+	1.60557i	0.187917	+	0.108494i
$220$		0			0
$221$			6.32855i			0.425704i
$222$	6.86075	−	6.26990i	0.460463	−	0.420808i
$223$	10.7596	+	10.7596i	0.720516	+	0.720516i	0.968710	−	0.248194i	$-0.0798372\pi$
$223$	10.7596	+	10.7596i	0.720516	+	0.720516i	−0.248194	+	0.968710i	$0.579837\pi$
$224$	−2.62123	+	9.78255i	−0.175138	+	0.653624i
$225$		0			0
$226$	−8.50440	−	4.91002i	−0.565704	−	0.326610i
$227$	−1.03285	+	1.78895i	−0.0685526	+	0.118737i	−0.898264	−	0.439455i	$-0.855171\pi$
$227$	−1.03285	+	1.78895i	−0.0685526	+	0.118737i	0.829712	+	0.558192i	$0.188505\pi$
$228$		−	4.10539i		−	0.271886i
$229$	8.25538	+	4.76625i	0.545531	+	0.314962i	0.747317	−	0.664467i	$-0.231341\pi$
$229$	8.25538	+	4.76625i	0.545531	+	0.314962i	−0.201787	+	0.979429i	$0.564675\pi$
$230$		0			0
$231$	3.86431	+	6.69318i	0.254253	+	0.440379i
$232$	6.53309	−	6.53309i	0.428918	−	0.428918i
$233$	6.47501	−	6.47501i	0.424192	−	0.424192i	−0.462452	−	0.886644i	$-0.653030\pi$
$233$	6.47501	−	6.47501i	0.424192	−	0.424192i	0.886644	+	0.462452i	$0.153030\pi$
$234$	14.6617	−	8.46495i	0.958467	−	0.553371i
$235$		0			0
$236$	−6.50459	+	6.50459i	−0.423413	+	0.423413i
$237$	−2.52940	+	1.46035i	−0.164302	+	0.0948599i
$238$	1.20419	−	4.49408i	0.0780558	−	0.291308i
$239$	20.0354	+	5.36847i	1.29598	+	0.347258i	0.839930	−	0.542695i	$-0.182596\pi$
$239$	20.0354	+	5.36847i	1.29598	+	0.347258i	0.456053	+	0.889952i	$0.349263\pi$
$240$		0			0
$241$	−11.5629	+	3.09827i	−0.744832	+	0.199577i	−0.611225	−	0.791457i	$-0.709323\pi$
$241$	−11.5629	+	3.09827i	−0.744832	+	0.199577i	−0.133608	+	0.991034i	$0.542656\pi$
$242$	22.6767	−	13.0924i	1.45772	−	0.841612i
$243$	15.5204	+	4.15868i	0.995635	+	0.266780i
$244$	12.8364	+	3.43951i	0.821767	+	0.220192i
$245$		0			0
$246$	0.444945	+	1.66056i	0.0283687	+	0.105873i
$247$	−4.61248	+	17.2140i	−0.293485	+	1.09530i
$248$	10.2178	+	10.2178i	0.648831	+	0.648831i
$249$	5.01472			0.317795
$250$		0			0
$251$	−12.7774	+	12.7774i	−0.806501	+	0.806501i	−0.984102	−	0.177602i	$-0.943166\pi$
$251$	−12.7774	+	12.7774i	−0.806501	+	0.806501i	0.177602	+	0.984102i	$0.443166\pi$
$252$	−4.34553	+	1.16438i	−0.273743	+	0.0733492i
$253$	−40.4494			−2.54303
$254$	−16.3405	+	4.37843i	−1.02530	+	0.274727i
$255$		0			0
$256$	−10.0537	+	17.4135i	−0.628355	+	1.08834i
$257$	−11.9481	−	20.6947i	−0.745303	−	1.29090i	−0.950053	−	0.312088i	$-0.898972\pi$
$257$	−11.9481	−	20.6947i	−0.745303	−	1.29090i	0.204751	−	0.978814i	$-0.434362\pi$
$258$	12.1323	−	12.1323i	0.755325	−	0.755325i
$259$	10.4701	−	2.30651i	0.650577	−	0.143319i
$260$		0			0
$261$	13.0999	+	3.51010i	0.810861	+	0.217269i
$262$	−26.3502	+	7.06052i	−1.62792	+	0.436201i
$263$	2.09369	+	7.81377i	0.129103	+	0.481818i	0.999953	−	0.00973123i	$-0.00309760\pi$
$263$	2.09369	+	7.81377i	0.129103	+	0.481818i	−0.870850	+	0.491549i	$0.836431\pi$
$264$	1.74318	+	6.50564i	0.107285	+	0.400394i
$265$		0			0
$266$	6.55091	−	11.3465i	0.401662	−	0.695699i
$267$	−7.26224			−0.444442
$268$	−2.51795	+	9.39713i	−0.153808	+	0.574021i
$269$			5.85649i			0.357076i	0.983933	+	0.178538i	$0.0571368\pi$
$269$			5.85649i			0.357076i	−0.983933	+	0.178538i	$0.942863\pi$
$270$		0			0
$271$	−7.08302	−	12.2681i	−0.430263	−	0.745237i	0.566633	−	0.823970i	$-0.308246\pi$
$271$	−7.08302	−	12.2681i	−0.430263	−	0.745237i	−0.996896	+	0.0787334i	$0.974912\pi$
$272$	3.71588	−	6.43609i	0.225308	−	0.390246i
$273$	−6.45645			−0.390762
$274$	−0.0910604	+	0.339842i	−0.00550116	+	0.0205306i
$275$		0			0
$276$	−2.01473	+	7.51906i	−0.121272	+	0.452594i
$277$	17.5165	+	10.1132i	1.05247	+	0.607641i	0.923339	−	0.383987i	$-0.125449\pi$
$277$	17.5165	+	10.1132i	1.05247	+	0.607641i	0.129127	+	0.991628i	$0.458783\pi$
$278$	33.0333	+	19.0718i	1.98121	+	1.14385i
$279$	−5.48982	+	20.4883i	−0.328667	+	1.22660i
$280$		0			0
$281$	3.65016	−	13.6226i	0.217750	−	0.812656i	−0.767430	−	0.641133i	$-0.778465\pi$
$281$	3.65016	−	13.6226i	0.217750	−	0.812656i	0.985180	−	0.171523i	$-0.0548686\pi$
$282$	0.0125894			0.000749689
$283$	15.5011	−	26.8486i	0.921442	−	1.59599i	0.124257	−	0.992250i	$-0.460345\pi$
$283$	15.5011	−	26.8486i	0.921442	−	1.59599i	0.797185	−	0.603735i	$-0.206322\pi$
$284$	−2.28128	−	3.95129i	−0.135369	−	0.234466i
$285$		0			0
$286$			38.1377i			2.25513i
$287$	−0.513258	+	1.91550i	−0.0302966	+	0.113069i
$288$	−12.9551			−0.763388
$289$	7.38763	−	12.7957i	0.434566	−	0.752691i
$290$		0			0
$291$	−1.34104	−	5.00485i	−0.0786134	−	0.293389i
$292$	−1.08981	−	4.06724i	−0.0637765	−	0.238017i
$293$	−29.2669	+	7.84205i	−1.70979	+	0.458137i	−0.975373	−	0.220560i	$-0.929212\pi$
$293$	−29.2669	+	7.84205i	−1.70979	+	0.458137i	−0.734418	+	0.678697i	$0.762545\pi$
$294$	−5.74631	−	1.53972i	−0.335132	−	0.0897983i
$295$		0			0
$296$	9.33349	+	0.419984i	0.542498	+	0.0244111i
$297$	−16.2926	+	16.2926i	−0.945390	+	0.945390i
$298$	−3.94277	−	6.82907i	−0.228398	−	0.395597i
$299$	16.8956	−	29.2640i	0.977097	−	1.69238i
$300$		0			0
$301$	19.1175	−	5.12252i	1.10191	−	0.295257i
$302$	7.61358			0.438113
$303$	7.73118	−	2.07156i	0.444144	−	0.119008i
$304$	14.7983	−	14.7983i	0.848739	−	0.848739i
$305$		0			0
$306$	5.95156			0.340228
$307$	7.31187	+	7.31187i	0.417310	+	0.417310i	0.884276	−	0.466965i	$-0.154653\pi$
$307$	7.31187	+	7.31187i	0.417310	+	0.417310i	−0.466965	+	0.884276i	$0.654653\pi$
$308$	2.62299	−	9.78912i	0.149459	−	0.557787i
$309$	−2.93962	−	10.9708i	−0.167229	−	0.624107i
$310$		0			0
$311$	−8.87440	−	2.37789i	−0.503221	−	0.134838i	−0.00172654	−	0.999999i	$-0.500550\pi$
$311$	−8.87440	−	2.37789i	−0.503221	−	0.134838i	−0.501494	+	0.865161i	$0.667216\pi$
$312$	−5.43477	−	1.45624i	−0.307684	−	0.0824435i
$313$	−1.42040	+	0.820070i	−0.0802859	+	0.0463531i	−0.539606	−	0.841918i	$-0.681427\pi$
$313$	−1.42040	+	0.820070i	−0.0802859	+	0.0463531i	0.459320	+	0.888271i	$0.348093\pi$
$314$	−0.571622	+	0.153166i	−0.0322585	+	0.00864364i
$315$		0			0
$316$	3.69938	+	0.991245i	0.208106	+	0.0557619i
$317$	0.185930	−	0.693899i	0.0104429	−	0.0389733i	−0.960508	−	0.278253i	$-0.910245\pi$
$317$	0.185930	−	0.693899i	0.0104429	−	0.0389733i	0.970951	+	0.239280i	$0.0769113\pi$
$318$	−5.52366	+	3.18909i	−0.309751	+	0.178835i
$319$	−21.6027	+	21.6027i	−1.20952	+	1.20952i
$320$		0			0
$321$	−9.56312	+	5.52127i	−0.533761	+	0.308167i
$322$	−17.5663	+	17.5663i	−0.978934	+	0.978934i
$323$	−4.42996	+	4.42996i	−0.246490	+	0.246490i
$324$	−1.61162	−	2.79141i	−0.0895347	−	0.155079i
$325$		0			0
$326$	−22.4320	−	12.9511i	−1.24240	−	0.717298i
$327$		−	14.7426i		−	0.815267i
$328$	−0.864079	+	1.49663i	−0.0477108	+	0.0826375i
$329$	0.0125767	+	0.00726113i	0.000693373	+	0.000400319i
$330$		0			0
$331$	2.35027	−	8.77134i	0.129183	−	0.482117i	−0.870771	−	0.491688i	$-0.836380\pi$
$331$	2.35027	−	8.77134i	0.129183	−	0.482117i	0.999954	+	0.00957141i	$0.00304672\pi$
$332$	−4.64975	−	4.64975i	−0.255188	−	0.255188i
$333$	6.31631	+	12.1731i	0.346132	+	0.667084i
$334$		−	10.1684i		−	0.556392i
$335$		0			0
$336$	6.56616	+	3.79098i	0.358214	+	0.206815i
$337$	−29.5830	+	7.92675i	−1.61149	+	0.431798i	−0.948486	−	0.316818i	$-0.897386\pi$
$337$	−29.5830	+	7.92675i	−1.61149	+	0.431798i	−0.663005	+	0.748615i	$0.730719\pi$
$338$	−7.66688	−	4.42647i	−0.417023	−	0.240768i
$339$	−3.38743	+	3.38743i	−0.183980	+	0.183980i
$340$		0			0
$341$	−33.7868	−	33.7868i	−1.82966	−	1.82966i
$342$	16.1886	+	4.33772i	0.875378	+	0.234557i
$343$	−13.5765	−	13.5765i	−0.733065	−	0.733065i
$344$	17.2477			0.929934
$345$		0			0
$346$	−7.47909	+	2.00402i	−0.402078	+	0.107737i
$347$		−	15.1256i		−	0.811984i	−0.913877	−	0.405992i	$-0.866926\pi$
$347$		−	15.1256i		−	0.811984i	0.913877	−	0.405992i	$-0.133074\pi$
$348$	2.93969	+	5.09169i	0.157584	+	0.272943i
$349$	−9.49147	+	5.47990i	−0.508067	+	0.293332i	−0.732039	−	0.681263i	$-0.761431\pi$
$349$	−9.49147	+	5.47990i	−0.508067	+	0.293332i	0.223972	+	0.974596i	$0.428098\pi$
$350$		0			0
$351$	−4.98187	−	18.5926i	−0.265912	−	0.992398i
$352$	14.5919	−	25.2739i	0.777752	−	1.34711i
$353$	−15.0422	−	26.0539i	−0.800618	−	1.38671i	−0.919210	−	0.393768i	$-0.871171\pi$
$353$	−15.0422	−	26.0539i	−0.800618	−	1.38671i	0.118592	−	0.992943i	$-0.462162\pi$
$354$	6.20763	+	10.7519i	0.329932	+	0.571458i
$355$		0			0
$356$	6.73370	+	6.73370i	0.356885	+	0.356885i
$357$	−1.96562	−	1.13485i	−0.104032	−	0.0600628i
$358$	−8.19443	−	2.19569i	−0.433089	−	0.116046i
$359$			13.7760i			0.727068i	0.931581	+	0.363534i	$0.118430\pi$
$359$			13.7760i			0.727068i	−0.931581	+	0.363534i	$0.881570\pi$
$360$		0			0
$361$	1.17601	−	0.678970i	0.0618953	−	0.0357353i
$362$		−	21.6726i		−	1.13909i
$363$	−3.30612	−	12.3386i	−0.173526	−	0.647609i
$364$	5.98655	+	5.98655i	0.313780	+	0.313780i
$365$		0			0
$366$	8.96789	−	15.5328i	0.468759	−	0.811915i
$367$	1.80899	+	6.75123i	0.0944283	+	0.352411i	0.996932	−	0.0782705i	$-0.0249398\pi$
$367$	1.80899	+	6.75123i	0.0944283	+	0.352411i	−0.902504	+	0.430682i	$0.858273\pi$
$368$	−34.3654	+	19.8409i	−1.79142	+	1.03428i
$369$	−2.53672			−0.132056
$370$		0			0
$371$	−7.35741			−0.381978
$372$	−7.96345	+	4.59770i	−0.412885	+	0.238380i
$373$	5.90026	+	22.0201i	0.305504	+	1.14016i	0.932511	+	0.361142i	$0.117613\pi$
$373$	5.90026	+	22.0201i	0.305504	+	1.14016i	−0.627007	+	0.779014i	$0.715720\pi$
$374$	−6.70350	+	11.6108i	−0.346630	+	0.600380i
$375$		0			0
$376$	0.00894877	+	0.00894877i	0.000461498	+	0.000461498i
$377$	−6.60558	−	24.6524i	−0.340205	−	1.26966i
$378$			14.1511i			0.727852i
$379$	−9.69628	+	5.59815i	−0.498064	+	0.287558i	−0.727914	−	0.685669i	$-0.759510\pi$
$379$	−9.69628	+	5.59815i	−0.498064	+	0.287558i	0.229849	+	0.973226i	$0.426177\pi$
$380$		0			0
$381$			8.25268i			0.422798i
$382$	−19.5991	−	5.25158i	−1.00278	−	0.268694i
$383$	17.3869	+	10.0383i	0.888430	+	0.512935i	0.873429	−	0.486952i	$-0.161891\pi$
$383$	17.3869	+	10.0383i	0.888430	+	0.512935i	0.0150011	+	0.999887i	$0.495225\pi$
$384$	6.79522	+	6.79522i	0.346767	+	0.346767i
$385$		0			0
$386$	−2.60567	−	4.51315i	−0.132625	−	0.229713i
$387$	12.6587	+	21.9256i	0.643480	+	1.11454i
$388$	−3.39715	+	5.88404i	−0.172464	+	0.298717i
$389$	−3.05764	−	11.4113i	−0.155028	−	0.578574i	−0.999103	−	0.0423478i	$-0.986516\pi$
$389$	−3.05764	−	11.4113i	−0.155028	−	0.578574i	0.844075	−	0.536226i	$-0.180150\pi$
$390$		0			0
$391$	10.2875	−	5.93950i	0.520262	−	0.300373i
$392$	−2.99012	−	5.17904i	−0.151024	−	0.261581i
$393$			13.3080i			0.671300i
$394$	−42.7733	+	11.4611i	−2.15489	+	0.577400i
$395$		0			0
$396$	12.9638			0.651457
$397$	−2.69155	−	2.69155i	−0.135085	−	0.135085i	0.636331	−	0.771416i	$-0.280451\pi$
$397$	−2.69155	−	2.69155i	−0.135085	−	0.135085i	−0.771416	+	0.636331i	$0.780451\pi$
$398$	31.5519	+	8.45430i	1.58155	+	0.423776i
$399$	−4.51949	−	4.51949i	−0.226257	−	0.226257i
$400$		0			0
$401$	10.9226	−	10.9226i	0.545449	−	0.545449i	−0.379672	−	0.925121i	$-0.623963\pi$
$401$	10.9226	−	10.9226i	0.545449	−	0.545449i	0.925121	+	0.379672i	$0.123963\pi$
$402$	11.3711	+	6.56511i	0.567139	+	0.327438i
$403$	38.5565	−	10.3312i	1.92064	−	0.514633i
$404$	−9.08930	−	5.24771i	−0.452209	−	0.261083i
$405$		0			0
$406$			18.7632i			0.931204i
$407$	−30.8627	−	1.38874i	−1.52981	−	0.0688375i
$408$	−1.39862	−	1.39862i	−0.0692419	−	0.0692419i
$409$	6.66691	−	24.8813i	0.329658	−	1.23030i	−0.579888	−	0.814696i	$-0.696904\pi$
$409$	6.66691	−	24.8813i	0.329658	−	1.23030i	0.909546	−	0.415603i	$-0.136429\pi$
$410$		0			0
$411$	0.148640	+	0.0858175i	0.00733188	+	0.00423306i
$412$	−7.44668	+	12.8980i	−0.366872	+	0.635440i
$413$			14.3214i			0.704708i
$414$	−27.5208	−	15.8891i	−1.35257	−	0.780907i
$415$		0			0
$416$	12.1900	+	21.1137i	0.597664	+	1.03518i
$417$	13.1577	−	13.1577i	0.644335	−	0.644335i
$418$	−26.6963	+	26.6963i	−1.30576	+	1.30576i
$419$	−27.9140	+	16.1161i	−1.36369	+	0.787325i	−0.990113	−	0.140275i	$-0.955201\pi$
$419$	−27.9140	+	16.1161i	−1.36369	+	0.787325i	−0.373575	+	0.927600i	$0.621868\pi$
$420$		0			0
$421$	24.8345	−	24.8345i	1.21036	−	1.21036i	0.239450	−	0.970909i	$-0.423033\pi$
$421$	24.8345	−	24.8345i	1.21036	−	1.21036i	0.970909	−	0.239450i	$-0.0769672\pi$
$422$	−25.7377	+	14.8597i	−1.25289	+	0.723358i
$423$	−0.00480799	+	0.0179437i	−0.000233773	+	0.000872452i
$424$	−6.19317	−	1.65945i	−0.300767	−	0.0805902i
$425$		0			0
$426$	−5.94802	+	1.59377i	−0.288183	+	0.0772183i
$427$	17.9176	−	10.3447i	0.867093	−	0.500617i
$428$	13.9866	+	3.74769i	0.676066	+	0.181151i
$429$	17.9710	+	4.81530i	0.867646	+	0.232485i
$430$		0			0
$431$	4.49781	+	16.7861i	0.216652	+	0.808557i	0.985578	+	0.169219i	$0.0541246\pi$
$431$	4.49781	+	16.7861i	0.216652	+	0.808557i	−0.768926	+	0.639337i	$0.779209\pi$
$432$	−5.85032	+	21.8337i	−0.281474	+	1.05047i
$433$	−1.46291	−	1.46291i	−0.0703030	−	0.0703030i	0.671081	−	0.741384i	$-0.265830\pi$
$433$	−1.46291	−	1.46291i	−0.0703030	−	0.0703030i	−0.741384	+	0.671081i	$0.765830\pi$
$434$	−29.3459			−1.40865
$435$		0			0
$436$	−13.6696	+	13.6696i	−0.654656	+	0.654656i
$437$	32.3115	−	8.65785i	1.54567	−	0.414161i
$438$	−5.68299			−0.271544
$439$	−10.9636	+	2.93768i	−0.523262	+	0.140208i	−0.510775	−	0.859714i	$-0.670642\pi$
$439$	−10.9636	+	2.93768i	−0.523262	+	0.140208i	−0.0124870	+	0.999922i	$0.503975\pi$
$440$		0			0
$441$	4.38912	−	7.60218i	0.209006	−	0.362009i
$442$	−5.60006	−	9.69959i	−0.266368	−	0.461363i
$443$	−11.3049	+	11.3049i	−0.537112	+	0.537112i	−0.922680	−	0.385567i	$-0.874006\pi$
$443$	−11.3049	+	11.3049i	−0.537112	+	0.537112i	0.385567	+	0.922680i	$0.374006\pi$
$444$	−1.79538	+	5.66784i	−0.0852049	+	0.268984i
$445$		0			0
$446$	−26.0120	−	6.96989i	−1.23170	−	0.330034i
$447$	−3.71576	+	0.995634i	−0.175749	+	0.0470919i
$448$	−0.0931283	−	0.347560i	−0.00439990	−	0.0164206i
$449$	1.16501	+	4.34789i	0.0549804	+	0.205190i	0.987952	−	0.154760i	$-0.0494605\pi$
$449$	1.16501	+	4.34789i	0.0549804	+	0.205190i	−0.932972	+	0.359950i	$0.882794\pi$
$450$		0			0
$451$	2.85722	−	4.94884i	0.134541	−	0.233032i
$452$	6.28179			0.295471
$453$	0.961298	−	3.58761i	0.0451657	−	0.168561i
$454$		−	3.65582i		−	0.171576i
$455$		0			0
$456$	−2.78496	−	4.82369i	−0.130418	−	0.225890i
$457$	−1.69554	+	2.93677i	−0.0793142	+	0.137376i	−0.902954	−	0.429737i	$-0.858606\pi$
$457$	−1.69554	+	2.93677i	−0.0793142	+	0.137376i	0.823640	+	0.567113i	$0.191940\pi$
$458$	−16.8704			−0.788301
$459$	1.75133	−	6.53606i	0.0817452	−	0.305077i
$460$		0			0
$461$	−2.88225	+	10.7567i	−0.134240	+	0.500989i	0.865760	+	0.500459i	$0.166835\pi$
$461$	−2.88225	+	10.7567i	−0.134240	+	0.500989i	−1.00000		0.000529983i	$0.999831\pi$
$462$	−11.8454	−	6.83897i	−0.551100	−	0.318178i
$463$	−4.87143	−	2.81252i	−0.226395	−	0.130709i	0.382513	−	0.923950i	$-0.375059\pi$
$463$	−4.87143	−	2.81252i	−0.226395	−	0.130709i	−0.608908	+	0.793241i	$0.708392\pi$
$464$	−7.75708	+	28.9498i	−0.360114	+	1.34396i
$465$		0			0
$466$	−4.19440	+	15.6537i	−0.194302	+	0.725144i
$467$	24.0241			1.11170			0.555852	−	0.831281i	$-0.312392\pi$
$467$	24.0241			1.11170			0.555852	+	0.831281i	$0.312392\pi$
$468$	−5.41496	+	9.37898i	−0.250306	+	0.433543i
$469$	7.57305	+	13.1169i	0.349691	+	0.605682i
$470$		0			0
$471$			0.288694i			0.0133023i
$472$	−3.23017	+	12.0551i	−0.148680	+	0.554883i
$473$	−57.0323			−2.62235
$474$	2.58449	−	4.47647i	0.118710	−	0.205611i
$475$		0			0
$476$	0.770308	+	2.87483i	0.0353070	+	0.131767i
$477$	−2.43587	−	9.09080i	−0.111531	−	0.416239i
$478$	−35.4582	+	9.50100i	−1.62182	+	0.434566i
$479$	−1.13540	−	0.304230i	−0.0518778	−	0.0139006i	0.232787	−	0.972528i	$-0.425216\pi$
$479$	−1.13540	−	0.304230i	−0.0518778	−	0.0139006i	−0.284665	+	0.958627i	$0.591882\pi$
$480$		0			0
$481$	13.8960	−	21.7483i	0.633602	−	0.991635i
$482$	14.9805	−	14.9805i	0.682344	−	0.682344i
$483$	6.05953	+	10.4954i	0.275718	+	0.477558i
$484$	−8.37511	+	14.5061i	−0.380687	+	0.659369i
$485$		0			0
$486$	−27.4677	+	7.35994i	−1.24596	+	0.333854i
$487$	−40.1900			−1.82118			−0.910592	−	0.413306i	$-0.864374\pi$
$487$	−40.1900			−1.82118			−0.910592	+	0.413306i	$0.864374\pi$
$488$	17.4155	−	4.66648i	0.788365	−	0.211242i
$489$	−8.93503	+	8.93503i	−0.404056	+	0.404056i
$490$		0			0
$491$	1.98284			0.0894844			0.0447422	−	0.998999i	$-0.485753\pi$
$491$	1.98284			0.0894844			0.0447422	+	0.998999i	$0.485753\pi$
$492$	−0.777618	−	0.777618i	−0.0350577	−	0.0350577i
$493$	2.32214	−	8.66633i	0.104584	−	0.390312i
$494$	−8.16307	−	30.4650i	−0.367274	−	1.37068i
$495$		0			0
$496$	−45.2778	−	12.1321i	−2.03303	−	0.544750i
$497$	−6.86122	−	1.83846i	−0.307768	−	0.0824661i
$498$	−7.68592	+	4.43747i	−0.344414	+	0.198848i
$499$	13.7849	−	3.69365i	0.617096	−	0.165350i	0.0632887	−	0.997995i	$-0.479841\pi$
$499$	13.7849	−	3.69365i	0.617096	−	0.165350i	0.553807	+	0.832645i	$0.313174\pi$
$500$		0			0
$501$	−4.79149	−	1.28388i	−0.214068	−	0.0573593i
$502$	8.27697	−	30.8901i	0.369419	−	1.37869i
$503$	−12.9393	+	7.47052i	−0.576936	+	0.333094i	−0.759915	−	0.650023i	$-0.774759\pi$
$503$	−12.9393	+	7.47052i	−0.576936	+	0.333094i	0.182979	+	0.983117i	$0.441426\pi$
$504$	−4.31597	+	4.31597i	−0.192248	+	0.192248i
$505$		0			0
$506$	61.9956	−	35.7932i	2.75604	−	1.59120i
$507$	−3.05383	+	3.05383i	−0.135626	+	0.135626i
$508$	7.65205	−	7.65205i	0.339505	−	0.339505i
$509$	14.2610	+	24.7007i	0.632106	+	1.09484i	0.987120	+	0.159979i	$0.0511427\pi$
$509$	14.2610	+	24.7007i	0.632106	+	1.09484i	−0.355014	+	0.934861i	$0.615524\pi$
$510$		0			0
$511$	−5.67723	−	3.27775i	−0.251146	−	0.144999i
$512$		−	13.3239i		−	0.588840i
$513$	9.52745	−	16.5020i	0.420647	−	0.728582i
$514$	36.6251	+	21.1455i	1.61546	+	0.932688i
$515$		0			0
$516$	−2.84070	+	10.6016i	−0.125055	+	0.466711i
$517$	−0.0295906	−	0.0295906i	−0.00130139	−	0.00130139i
$518$	−14.0062	+	12.7999i	−0.615395	+	0.562397i
$519$			3.77726i			0.165803i
$520$		0			0
$521$	20.2281	+	11.6787i	0.886208	+	0.511652i	0.872700	−	0.488256i	$-0.162367\pi$
$521$	20.2281	+	11.6787i	0.886208	+	0.511652i	0.0135077	+	0.999909i	$0.495700\pi$
$522$	−23.1838	+	6.21209i	−1.01473	+	0.271896i
$523$	22.7748	+	13.1491i	0.995874	+	0.574968i	0.907025	−	0.421077i	$-0.138348\pi$
$523$	22.7748	+	13.1491i	0.995874	+	0.574968i	0.0888492	+	0.996045i	$0.471681\pi$
$524$	12.3395	−	12.3395i	0.539052	−	0.539052i
$525$		0			0
$526$	−10.1233	−	10.1233i	−0.441395	−	0.441395i
$527$	13.5542	+	3.63184i	0.590431	+	0.158205i
$528$	−15.4490	−	15.4490i	−0.672331	−	0.672331i
$529$	−40.4277			−1.75772
$530$		0			0
$531$	−17.6954	+	4.74148i	−0.767917	+	0.205763i
$532$			8.38112i			0.363368i
$533$	2.38690	+	4.13424i	0.103388	+	0.179074i
$534$	11.1306	−	6.42627i	0.481670	−	0.278092i
$535$		0			0
$536$	3.41618	+	12.7494i	0.147557	+	0.550689i
$537$	−2.06927	+	3.58409i	−0.0892957	+	0.154665i
$538$	−5.18234	−	8.97607i	−0.223426	−	0.386986i
$539$	9.88731	+	17.1253i	0.425877	+	0.737640i
$540$		0			0
$541$	14.4954	+	14.4954i	0.623204	+	0.623204i	0.946349	−	0.323145i	$-0.104740\pi$
$541$	14.4954	+	14.4954i	0.623204	+	0.623204i	−0.323145	+	0.946349i	$0.604740\pi$
$542$	21.7119	+	12.5354i	0.932605	+	0.538440i
$543$	−10.2124	−	2.73640i	−0.438255	−	0.117430i
$544$			8.57058i			0.367461i
$545$		0			0
$546$	9.89561	−	5.71324i	0.423493	−	0.244504i
$547$		−	35.8869i		−	1.53441i	−0.641400	−	0.767207i	$-0.721646\pi$
$547$		−	35.8869i		−	1.53441i	0.641400	−	0.767207i	$-0.278354\pi$
$548$	−0.0582505	−	0.217394i	−0.00248834	−	0.00928661i
$549$	18.7140	+	18.7140i	0.798696	+	0.798696i
$550$		0			0
$551$	12.6327	−	21.8804i	0.538170	−	0.932138i
$552$	2.73344	+	10.2013i	0.116343	+	0.434198i
$553$	5.16374	−	2.98129i	0.219585	−	0.126777i
$554$	−35.7961			−1.52083
$555$		0			0
$556$	−24.4001			−1.03480
$557$	7.91255	−	4.56831i	0.335265	−	0.193566i	−0.322911	−	0.946429i	$-0.604661\pi$
$557$	7.91255	−	4.56831i	0.335265	−	0.193566i	0.658176	+	0.752864i	$0.271328\pi$
$558$	−9.71576	−	36.2597i	−0.411301	−	1.53500i
$559$	23.8222	−	41.2613i	1.00757	−	1.74517i
$560$		0			0
$561$	4.62476	+	4.62476i	0.195257	+	0.195257i
$562$	6.45997	+	24.1089i	0.272498	+	1.01697i
$563$			25.2123i			1.06257i	0.847193	+	0.531286i	$0.178291\pi$
$563$			25.2123i			1.06257i	−0.847193	+	0.531286i	$0.821709\pi$
$564$	−0.00697440	+	0.00402667i	−0.000293675	+	0.000169553i
$565$		0			0
$566$			54.8668i			2.30623i
$567$	−4.84715	−	1.29879i	−0.203561	−	0.0545441i
$568$	−5.36083	−	3.09508i	−0.224936	−	0.129867i
$569$	−29.7457	−	29.7457i	−1.24700	−	1.24700i	−0.957037	−	0.289966i	$-0.906356\pi$
$569$	−29.7457	−	29.7457i	−1.24700	−	1.24700i	−0.289966	−	0.957037i	$-0.593644\pi$
$570$		0			0
$571$	−12.0676	−	20.9018i	−0.505015	−	0.874712i	−0.999983	−	0.00580103i	$-0.998153\pi$
$571$	−12.0676	−	20.9018i	−0.505015	−	0.874712i	0.494968	−	0.868911i	$-0.335180\pi$
$572$	−12.1982	−	21.1279i	−0.510032	−	0.883401i
$573$	−4.94921	+	8.57229i	−0.206756	+	0.358112i
$574$	−0.908352	−	3.39001i	−0.0379139	−	0.141496i
$575$		0			0
$576$	0.398611	−	0.230138i	0.0166088	−	0.00958910i
$577$	4.49827	+	7.79123i	0.187265	+	0.324353i	0.944338	−	0.328978i	$-0.106704\pi$
$577$	4.49827	+	7.79123i	0.187265	+	0.324353i	−0.757072	+	0.653331i	$0.773371\pi$
$578$			26.1489i			1.08765i
$579$	−2.45565	+	0.657988i	−0.102053	+	0.0273451i
$580$		0			0
$581$	−10.2375			−0.424723
$582$	6.48411	+	6.48411i	0.268775	+	0.268775i
$583$	20.4787	+	5.48725i	0.848142	+	0.227259i
$584$	−4.03957	−	4.03957i	−0.167158	−	0.167158i
$585$		0			0
$586$	37.9173	−	37.9173i	1.56635	−	1.56635i
$587$	−11.8890	−	6.86411i	−0.490711	−	0.283312i	0.234159	−	0.972198i	$-0.424767\pi$
$587$	−11.8890	−	6.86411i	−0.490711	−	0.283312i	−0.724869	+	0.688886i	$0.758100\pi$
$588$	3.67587	−	0.984946i	0.151590	−	0.0406185i
$589$	34.2212	+	19.7576i	1.41006	+	0.814099i
$590$		0			0
$591$			21.6024i			0.888602i
$592$	−26.9019	+	13.9586i	−1.10566	+	0.573697i
$593$	29.2800	+	29.2800i	1.20239	+	1.20239i	0.973439	+	0.228948i	$0.0735285\pi$
$593$	29.2800	+	29.2800i	1.20239	+	1.20239i	0.228948	+	0.973439i	$0.426472\pi$
$594$	10.5540	−	39.3882i	0.433038	−	1.61612i
$595$		0			0
$596$	4.36850	+	2.52215i	0.178941	+	0.103311i
$597$	7.96753	−	13.8002i	0.326089	−	0.564803i
$598$			59.8028i			2.44552i
$599$	13.6676	+	7.89098i	0.558442	+	0.322417i	0.752520	−	0.658569i	$-0.228838\pi$
$599$	13.6676	+	7.89098i	0.558442	+	0.322417i	−0.194078	+	0.980986i	$0.562171\pi$
$600$		0			0
$601$	−14.0555	−	24.3449i	−0.573338	−	0.993050i	−0.996220	−	0.0868653i	$-0.972315\pi$
$601$	−14.0555	−	24.3449i	−0.573338	−	0.993050i	0.422882	−	0.906185i	$-0.361018\pi$
$602$	−24.7680	+	24.7680i	−1.00947	+	1.00947i
$603$	−13.6999	+	13.6999i	−0.557905	+	0.557905i
$604$	−4.21784	+	2.43517i	−0.171622	+	0.0990857i
$605$		0			0
$606$	−10.0163	+	10.0163i	−0.406883	+	0.406883i
$607$	−20.9733	+	12.1090i	−0.851282	+	0.491488i	−0.861083	−	0.508464i	$-0.830213\pi$
$607$	−20.9733	+	12.1090i	−0.851282	+	0.491488i	0.00980151	+	0.999952i	$0.496880\pi$
$608$	−6.24656	+	23.3125i	−0.253331	+	0.945446i
$609$	8.84147	+	2.36906i	0.358274	+	0.0959993i
$610$		0			0
$611$	0.0337679	−	0.00904807i	0.00136610	−	0.000366046i
$612$	−3.29710	+	1.90358i	−0.133277	+	0.0769477i
$613$	−35.9689	−	9.63784i	−1.45277	−	0.389269i	−0.555784	−	0.831327i	$-0.687582\pi$
$613$	−35.9689	−	9.63784i	−1.45277	−	0.389269i	−0.896987	+	0.442058i	$0.854249\pi$
$614$	−17.6769	−	4.73651i	−0.713381	−	0.191150i
$615$		0			0
$616$	−3.55869	−	13.2812i	−0.143384	−	0.535115i
$617$	10.6716	−	39.8269i	0.429621	−	1.60337i	−0.323998	−	0.946058i	$-0.605027\pi$
$617$	10.6716	−	39.8269i	0.429621	−	1.60337i	0.753619	−	0.657311i	$-0.228306\pi$
$618$	14.2134	+	14.2134i	0.571747	+	0.571747i
$619$	13.6890			0.550207			0.275104	−	0.961415i	$-0.411288\pi$
$619$	13.6890			0.550207			0.275104	+	0.961415i	$0.411288\pi$
$620$		0			0
$621$	−25.5480	+	25.5480i	−1.02520	+	1.02520i
$622$	15.7057	−	4.20833i	0.629742	−	0.168739i
$623$	14.8258			0.593983
$624$	17.6299	−	4.72392i	0.705761	−	0.189108i
$625$		0			0
$626$	1.45134	−	2.51380i	0.0580073	−	0.100472i
$627$	9.20891	+	15.9503i	0.367768	+	0.636994i
$628$	0.267683	−	0.267683i	0.0106817	−	0.0106817i
$629$	8.05325	−	4.17861i	0.321104	−	0.166612i
$630$		0			0
$631$	8.04532	+	2.15574i	0.320279	+	0.0858185i	0.415377	−	0.909649i	$-0.363650\pi$
$631$	8.04532	+	2.15574i	0.320279	+	0.0858185i	−0.0950978	+	0.995468i	$0.530316\pi$
$632$	5.01905	−	1.34485i	0.199647	−	0.0534953i
$633$	3.75239	+	14.0041i	0.149144	+	0.556614i
$634$	0.329054	+	1.22805i	0.0130684	+	0.0487720i
$635$		0			0
$636$	2.04003	−	3.53344i	0.0808925	−	0.140110i
$637$	−16.5196			−0.654531
$638$	13.9939	−	52.2259i	0.554023	−	2.06764i
$639$		−	9.08638i		−	0.359452i
$640$		0			0
$641$	1.42182	+	2.46266i	0.0561585	+	0.0972694i	0.892738	−	0.450576i	$-0.148781\pi$
$641$	1.42182	+	2.46266i	0.0561585	+	0.0972694i	−0.836579	+	0.547846i	$0.815448\pi$
$642$	9.77142	−	16.9246i	0.385647	−	0.667960i
$643$	28.1328			1.10945			0.554724	−	0.832035i	$-0.312824\pi$
$643$	28.1328			1.10945			0.554724	+	0.832035i	$0.312824\pi$
$644$	4.11304	−	15.3501i	0.162077	−	0.604878i
$645$		0			0
$646$	2.86966	−	10.7097i	0.112905	−	0.421368i
$647$	−35.5702	−	20.5365i	−1.39841	−	0.807372i	−0.404183	−	0.914678i	$-0.632444\pi$
$647$	−35.5702	−	20.5365i	−1.39841	−	0.807372i	−0.994226	+	0.107306i	$0.965777\pi$
$648$	−3.78720	−	2.18654i	−0.148775	−	0.0858954i
$649$	10.6811	−	39.8623i	0.419268	−	1.56473i
$650$		0			0
$651$	−3.70524	+	13.8281i	−0.145220	+	0.541967i
$652$	16.5695			0.648911
$653$	21.4609	−	37.1713i	0.839829	−	1.45463i	−0.0502088	−	0.998739i	$-0.515989\pi$
$653$	21.4609	−	37.1713i	0.839829	−	1.45463i	0.890038	−	0.455887i	$-0.150678\pi$
$654$	13.0455	+	22.5956i	0.510121	+	0.883556i
$655$		0			0
$656$		−	5.60599i		−	0.218877i
$657$	2.17038	−	8.09996i	0.0846745	−	0.316009i
$658$	−0.0257012			−0.00100194
$659$	3.90506	−	6.76375i	0.152119	−	0.263478i	−0.779887	−	0.625920i	$-0.784724\pi$
$659$	3.90506	−	6.76375i	0.152119	−	0.263478i	0.932006	+	0.362442i	$0.118057\pi$
$660$		0			0
$661$	12.7002	+	47.3979i	0.493982	+	1.84356i	0.535660	+	0.844434i	$0.320063\pi$
$661$	12.7002	+	47.3979i	0.493982	+	1.84356i	−0.0416782	+	0.999131i	$0.513270\pi$
$662$	4.15946	+	15.5233i	0.161662	+	0.603331i
$663$	−5.27763	+	1.41414i	−0.204966	+	0.0549206i
$664$	−8.61751	−	2.30906i	−0.334424	−	0.0896087i
$665$		0			0
$666$	−20.4527	−	13.0682i	−0.792526	−	0.506383i
$667$	−33.8747	+	33.8747i	−1.31163	+	1.31163i
$668$	3.25233	+	5.63320i	0.125836	+	0.217955i
$669$	−6.56859	+	11.3771i	−0.253956	+	0.439865i
$670$		0			0
$671$	−57.5873	+	15.4305i	−2.22313	+	0.595687i
$672$	−8.74379			−0.337299
$673$	−7.24213	+	1.94052i	−0.279164	+	0.0748017i	−0.395684	−	0.918387i	$-0.629493\pi$
$673$	−7.24213	+	1.94052i	−0.279164	+	0.0748017i	0.116521	+	0.993188i	$0.462826\pi$
$674$	38.3268	−	38.3268i	1.47629	−	1.47629i
$675$		0			0
$676$	5.66315			0.217814
$677$	−30.5875	−	30.5875i	−1.17557	−	1.17557i	−0.980860	−	0.194715i	$-0.937622\pi$
$677$	−30.5875	−	30.5875i	−1.17557	−	1.17557i	−0.194715	−	0.980860i	$-0.562378\pi$
$678$	2.19432	−	8.18933i	0.0842725	−	0.314509i
$679$	2.73773	+	10.2173i	0.105064	+	0.392106i
$680$		0			0
$681$	−1.72267	−	0.461588i	−0.0660128	−	0.0176881i
$682$	81.6817	+	21.8866i	3.12775	+	0.838079i
$683$	34.7149	−	20.0426i	1.32833	−	0.766911i	0.343287	−	0.939231i	$-0.388460\pi$
$683$	34.7149	−	20.0426i	1.32833	−	0.766911i	0.985041	+	0.172320i	$0.0551263\pi$
$684$	−10.3557	+	2.77480i	−0.395960	+	0.106097i
$685$		0			0
$686$	32.8221	+	8.79466i	1.25315	+	0.335782i
$687$	−2.13007	+	7.94953i	−0.0812672	+	0.303293i
$688$	−48.4541	+	27.9750i	−1.84730	+	1.06654i
$689$	−12.5238	+	12.5238i	−0.477118	+	0.477118i
$690$		0			0
$691$	28.5744	−	16.4974i	1.08702	−	0.627592i	0.154240	−	0.988033i	$-0.450707\pi$
$691$	28.5744	−	16.4974i	1.08702	−	0.627592i	0.932782	+	0.360441i	$0.117374\pi$
$692$	3.50236	−	3.50236i	0.133140	−	0.133140i
$693$	14.2714	−	14.2714i	0.542127	−	0.542127i
$694$	13.3845	+	23.1826i	0.508067	+	0.879998i
$695$		0			0
$696$	6.90805	+	3.98836i	0.261849	+	0.151179i
$697$			1.67819i			0.0635660i
$698$	9.69821	−	16.7978i	0.367083	−	0.635806i
$699$	6.84663	+	3.95290i	0.258963	+	0.149513i
$700$		0			0
$701$	−1.13499	+	4.23585i	−0.0428680	+	0.159986i	−0.984042	−	0.177937i	$-0.943058\pi$
$701$	−1.13499	+	4.23585i	−0.0428680	+	0.159986i	0.941174	+	0.337923i	$0.109724\pi$
$702$	24.0879	+	24.0879i	0.909140	+	0.909140i
$703$	24.9508	−	5.49656i	0.941038	−	0.207307i
$704$			1.03686i			0.0390781i
$705$		0			0
$706$	46.1097	+	26.6214i	1.73536	+	1.00191i
$707$	−15.7831	+	4.22907i	−0.593585	+	0.159051i
$708$	−6.87791	−	3.97097i	−0.258488	−	0.149238i
$709$	7.54090	−	7.54090i	0.283205	−	0.283205i	−0.551181	−	0.834386i	$-0.685823\pi$
$709$	7.54090	−	7.54090i	0.283205	−	0.283205i	0.834386	+	0.551181i	$0.185823\pi$
$710$		0			0
$711$	5.39327	+	5.39327i	0.202264	+	0.202264i
$712$	12.4797	+	3.34394i	0.467698	+	0.125319i
$713$	−52.9803	−	52.9803i	−1.98413	−	1.98413i
$714$	4.01688			0.150328
$715$		0			0
$716$	5.24191	−	1.40457i	0.195899	−	0.0524911i
$717$			17.9079i			0.668784i
$718$	−12.1902	−	21.1141i	−0.454934	−	0.787969i
$719$	19.9831	−	11.5373i	0.745245	−	0.430268i	−0.0787281	−	0.996896i	$-0.525086\pi$
$719$	19.9831	−	11.5373i	0.745245	−	0.430268i	0.823973	+	0.566629i	$0.191753\pi$
$720$		0			0
$721$	6.00120	+	22.3968i	0.223497	+	0.834100i
$722$	−1.20163	+	2.08128i	−0.0447199	+	0.0774571i
$723$	−5.16755	−	8.95045i	−0.192183	−	0.332871i
$724$	6.93188	+	12.0064i	0.257621	+	0.446213i
$725$		0			0
$726$	15.9855	+	15.9855i	0.593277	+	0.593277i
$727$	15.0509	+	8.68964i	0.558207	+	0.322281i	0.752425	−	0.658677i	$-0.228884\pi$
$727$	15.0509	+	8.68964i	0.558207	+	0.322281i	−0.194219	+	0.980958i	$0.562217\pi$
$728$	11.0950	+	2.97291i	0.411209	+	0.110183i
$729$			5.33104i			0.197446i
$730$		0			0
$731$	14.5051	−	8.37450i	0.536489	−	0.309742i
$732$			11.4734i			0.424068i
$733$	−8.68494	−	32.4126i	−0.320786	−	1.19719i	−0.918481	−	0.395465i	$-0.870584\pi$
$733$	−8.68494	−	32.4126i	−0.320786	−	1.19719i	0.597696	−	0.801723i	$-0.296083\pi$
$734$	−8.74667	−	8.74667i	−0.322845	−	0.322845i
$735$		0			0
$736$	22.8812	−	39.6314i	0.843413	−	1.46083i
$737$	−11.2962	−	42.1578i	−0.416099	−	1.55290i
$738$	3.88796	−	2.24471i	0.143118	−	0.0826291i
$739$	21.1980			0.779781			0.389891	−	0.920861i	$-0.372513\pi$
$739$	21.1980			0.779781			0.389891	+	0.920861i	$0.372513\pi$
$740$		0			0
$741$	−15.3861			−0.565224
$742$	11.2765	−	6.51049i	0.413973	−	0.239008i
$743$	−5.93426	−	22.1470i	−0.217707	−	0.812493i	−0.985196	−	0.171431i	$-0.945161\pi$
$743$	−5.93426	−	22.1470i	−0.217707	−	0.812493i	0.767489	−	0.641062i	$-0.221506\pi$
$744$	−6.23784	+	10.8042i	−0.228690	+	0.396103i
$745$		0			0
$746$	−28.5285	−	28.5285i	−1.04450	−	1.04450i
$747$	−3.38941	−	12.6494i	−0.124012	−	0.462819i
$748$		−	8.57634i		−	0.313582i
$749$	19.5230	−	11.2716i	0.713355	−	0.411856i
$750$		0			0
$751$		−	9.63421i		−	0.351557i	−0.984430	−	0.175779i	$-0.943756\pi$
$751$		−	9.63421i		−	0.351557i	0.984430	−	0.175779i	$-0.0562443\pi$
$752$	−0.0396544	−	0.0106254i	−0.00144605	−	0.000387467i
$753$	−13.5107	−	7.80042i	−0.492358	−	0.284263i
$754$	31.9388	+	31.9388i	1.16314	+	1.16314i
$755$		0			0
$756$	−4.52615	−	7.83953i	−0.164615	−	0.285121i
$757$	−10.4032	−	18.0188i	−0.378110	−	0.654906i	0.612677	−	0.790333i	$-0.290093\pi$
$757$	−10.4032	−	18.0188i	−0.378110	−	0.654906i	−0.990787	+	0.135427i	$0.956759\pi$
$758$	9.90748	−	17.1603i	0.359856	−	0.623289i
$759$	−9.03856	−	33.7324i	−0.328079	−	1.22441i
$760$		0			0
$761$	13.9463	−	8.05189i	0.505552	−	0.291881i	−0.225451	−	0.974254i	$-0.572386\pi$
$761$	13.9463	−	8.05189i	0.505552	−	0.291881i	0.731003	+	0.682374i	$0.239052\pi$
$762$	−7.30270	−	12.6487i	−0.264549	−	0.458212i
$763$			30.0968i			1.08958i
$764$	12.5374	−	3.35939i	0.453587	−	0.121538i
$765$		0			0
$766$	−35.5312			−1.28380
$767$	24.3778	+	24.3778i	0.880232	+	0.880232i
$768$	−16.7683	−	4.49306i	−0.605075	−	0.162129i
$769$	−28.5069	−	28.5069i	−1.02798	−	1.02798i	−0.999597	−	0.0283867i	$-0.990963\pi$
$769$	−28.5069	−	28.5069i	−1.02798	−	1.02798i	−0.0283867	−	0.999597i	$-0.509037\pi$
$770$		0			0
$771$	14.5883	−	14.5883i	0.525386	−	0.525386i
$772$	2.88702	+	1.66682i	0.103906	+	0.0599903i
$773$	17.3557	−	4.65045i	0.624241	−	0.167265i	0.0671861	−	0.997740i	$-0.478598\pi$
$773$	17.3557	−	4.65045i	0.624241	−	0.167265i	0.557055	+	0.830476i	$0.311931\pi$
$774$	−38.8034	−	22.4032i	−1.39476	−	0.805265i
$775$		0			0
$776$			9.21804i			0.330908i
$777$	4.26306	+	8.21600i	0.152936	+	0.294747i
$778$	14.7840	+	14.7840i	0.530034	+	0.530034i
$779$	−1.22313	+	4.56477i	−0.0438231	+	0.163550i
$780$		0			0
$781$	17.7265	+	10.2344i	0.634303	+	0.366215i
$782$	−10.5116	+	18.2066i	−0.375894	+	0.651067i
$783$			27.2887i			0.975218i
$784$	16.8003	+	9.69967i	0.600012	+	0.346417i
$785$		0			0
$786$	−11.7761	−	20.3968i	−0.420040	−	0.727530i
$787$	17.0724	−	17.0724i	0.608565	−	0.608565i	−0.334006	−	0.942571i	$-0.608400\pi$
$787$	17.0724	−	17.0724i	0.608565	−	0.608565i	0.942571	+	0.334006i	$0.108400\pi$
$788$	20.0301	−	20.0301i	0.713544	−	0.713544i
$789$	−6.04837	+	3.49203i	−0.215328	+	0.124320i
$790$		0			0
$791$	6.91541	−	6.91541i	0.245884	−	0.245884i
$792$	15.2320	−	8.79421i	0.541246	−	0.312489i
$793$	12.8905	−	48.1081i	0.457756	−	1.70837i
$794$	6.50699	+	1.74354i	0.230924	+	0.0618760i
$795$		0			0
$796$	−20.1835	+	5.40814i	−0.715384	+	0.191687i
$797$	−13.5326	+	7.81304i	−0.479349	+	0.276752i	−0.720145	−	0.693824i	$-0.755925\pi$
$797$	−13.5326	+	7.81304i	−0.479349	+	0.276752i	0.240796	+	0.970576i	$0.422591\pi$
$798$	10.9261	+	2.92765i	0.386781	+	0.103638i
$799$	0.0118708	+	0.00318077i	0.000419959	+	0.000112528i
$800$		0			0
$801$	4.90849	+	18.3187i	0.173433	+	0.647260i
$802$	−7.07548	+	26.4061i	−0.249844	+	0.932430i
$803$	13.3575	+	13.3575i	0.471375	+	0.471375i
$804$	−8.39929			−0.296220
$805$		0			0
$806$	−49.9525	+	49.9525i	−1.75950	+	1.75950i
$807$	−4.88396	+	1.30865i	−0.171924	+	0.0460668i
$808$	−14.2395			−0.500942
$809$	7.31600	−	1.96032i	0.257217	−	0.0689210i	−0.127906	−	0.991786i	$-0.540826\pi$
$809$	7.31600	−	1.96032i	0.257217	−	0.0689210i	0.385123	+	0.922865i	$0.374159\pi$
$810$		0			0
$811$	−15.7426	+	27.2670i	−0.552799	+	0.957475i	0.445272	+	0.895395i	$0.353107\pi$
$811$	−15.7426	+	27.2670i	−0.552799	+	0.957475i	−0.998071	+	0.0620803i	$0.980227\pi$
$812$	−6.00134	−	10.3946i	−0.210606	−	0.364780i
$813$	8.64818	−	8.64818i	0.303305	−	0.303305i
$814$	48.5313	−	25.1816i	1.70102	−	0.882614i
$815$		0			0
$816$	6.19765	+	1.66065i	0.216961	+	0.0581345i
$817$	45.5583	−	12.2073i	1.59388	−	0.427079i
$818$	11.7989	+	44.0343i	0.412541	+	1.53962i
$819$	4.36386	+	16.2861i	0.152485	+	0.569084i
$820$		0			0
$821$	−10.1275	+	17.5414i	−0.353453	+	0.612199i	−0.986852	−	0.161627i	$-0.948326\pi$
$821$	−10.1275	+	17.5414i	−0.353453	+	0.612199i	0.633399	+	0.773826i	$0.281659\pi$
$822$	−0.303756			−0.0105947
$823$	−2.51580	+	9.38910i	−0.0876953	+	0.327283i	−0.995811	−	0.0914361i	$-0.970854\pi$
$823$	−2.51580	+	9.38910i	−0.0876953	+	0.327283i	0.908116	+	0.418720i	$0.137521\pi$
$824$			20.2063i			0.703919i
$825$		0			0
$826$	−12.6728	−	21.9500i	−0.440943	−	0.763737i
$827$	11.9888	−	20.7652i	0.416890	−	0.722075i	−0.578735	−	0.815516i	$-0.696453\pi$
$827$	11.9888	−	20.7652i	0.416890	−	0.722075i	0.995625	+	0.0934408i	$0.0297866\pi$
$828$	20.3283			0.706456
$829$	−4.86508	+	18.1567i	−0.168971	+	0.630610i	0.828529	+	0.559946i	$0.189178\pi$
$829$	−4.86508	+	18.1567i	−0.168971	+	0.630610i	−0.997500	+	0.0706633i	$0.977488\pi$
$830$		0			0
$831$	−4.51965	+	16.8676i	−0.156785	+	0.585129i
$832$	−0.750139	−	0.433093i	−0.0260064	−	0.0150148i
$833$	−5.02929	−	2.90366i	−0.174255	−	0.100606i
$834$	−8.52333	+	31.8095i	−0.295139	+	1.10147i
$835$		0			0
$836$	6.25075	−	23.3281i	0.216187	−	0.806820i
$837$	−42.6798			−1.47523
$838$	28.5220	−	49.4015i	0.985276	−	1.70655i
$839$	−3.59689	−	6.23000i	−0.124179	−	0.215084i	0.797233	−	0.603672i	$-0.206296\pi$
$839$	−3.59689	−	6.23000i	−0.124179	−	0.215084i	−0.921412	+	0.388588i	$0.872963\pi$
$840$		0			0
$841$			7.18276i			0.247681i
$842$	−16.0874	+	60.0389i	−0.554407	+	2.06908i
$843$	12.1761			0.419366
$844$	9.50561	−	16.4642i	0.327197	−	0.566721i
$845$		0			0
$846$	−0.00850908	−	0.0317563i	−0.000292548	−	0.00109180i
$847$	6.74941	+	25.1891i	0.231913	+	0.865509i
$848$	20.0901	−	5.38312i	0.689896	−	0.184857i
$849$	25.8539	+	6.92754i	0.887304	+	0.237752i
$850$		0			0
$851$	−48.3951	−	2.17765i	−1.65896	−	0.0746490i
$852$	2.78538	−	2.78538i	0.0954255	−	0.0954255i
$853$	15.8619	+	27.4736i	0.543100	+	0.940677i	0.998724	+	0.0505044i	$0.0160829\pi$
$853$	15.8619	+	27.4736i	0.543100	+	0.940677i	−0.455624	+	0.890172i	$0.650584\pi$
$854$	−18.3079	+	31.7102i	−0.626482	+	1.08510i
$855$		0			0
$856$	18.9760	−	5.08460i	0.648586	−	0.173788i
$857$	43.1899			1.47534			0.737669	−	0.675162i	$-0.235926\pi$
$857$	43.1899			1.47534			0.737669	+	0.675162i	$0.235926\pi$
$858$	−31.8046	+	8.52202i	−1.08579	+	0.290937i
$859$	−26.5424	+	26.5424i	−0.905616	+	0.905616i	−0.995915	−	0.0902990i	$-0.971218\pi$
$859$	−26.5424	+	26.5424i	−0.905616	+	0.905616i	0.0902990	+	0.995915i	$0.471218\pi$
$860$		0			0
$861$	−1.71210			−0.0583484
$862$	−21.7475	−	21.7475i	−0.740722	−	0.740722i
$863$	3.13402	−	11.6963i	0.106683	−	0.398147i	−0.891847	−	0.452336i	$-0.850591\pi$
$863$	3.13402	−	11.6963i	0.106683	−	0.398147i	0.998531	+	0.0541891i	$0.0172574\pi$
$864$	−6.74680	−	25.1794i	−0.229531	−	0.856621i
$865$		0			0
$866$	3.53668	+	0.947650i	0.120181	+	0.0322025i
$867$	12.3217	+	3.30158i	0.418466	+	0.112128i
$868$	16.2573	−	9.38615i	0.551809	−	0.318587i
$869$	−16.5963	+	4.44697i	−0.562991	+	0.150853i
$870$		0			0
$871$	35.2184	+	9.43675i	1.19333	+	0.319752i
$872$	−6.78831	+	25.3343i	−0.229881	+	0.857928i
$873$	−11.7181	+	6.76547i	−0.396599	+	0.228976i
$874$	−41.8618	+	41.8618i	−1.41600	+	1.41600i
$875$		0			0
$876$	3.14831	−	1.81768i	0.106372	−	0.0614137i
$877$	0.910508	−	0.910508i	0.0307457	−	0.0307457i	−0.691567	−	0.722312i	$-0.743079\pi$
$877$	0.910508	−	0.910508i	0.0307457	−	0.0307457i	0.722312	+	0.691567i	$0.243079\pi$
$878$	14.2040	−	14.2040i	0.479363	−	0.479363i
$879$	−13.0796	−	22.6545i	−0.441164	−	0.764118i
$880$		0			0
$881$	−3.54878	−	2.04889i	−0.119561	−	0.0690288i	0.439027	−	0.898474i	$-0.355323\pi$
$881$	−3.54878	−	2.04889i	−0.119561	−	0.0690288i	−0.558588	+	0.829445i	$0.688657\pi$
$882$			15.5355i			0.523109i
$883$	15.0734	−	26.1079i	0.507261	−	0.878601i	−0.492704	−	0.870197i	$-0.663991\pi$
$883$	15.0734	−	26.1079i	0.507261	−	0.878601i	0.999965	−	0.00840425i	$-0.00267519\pi$
$884$	6.20475	+	3.58231i	0.208688	+	0.120486i
$885$		0			0
$886$	7.32313	−	27.3303i	0.246025	−	0.918179i
$887$	39.0222	+	39.0222i	1.31024	+	1.31024i	0.921238	+	0.388998i	$0.127179\pi$
$887$	39.0222	+	39.0222i	1.31024	+	1.31024i	0.388998	+	0.921238i	$0.372821\pi$
$888$	1.73536	+	7.87742i	0.0582349	+	0.264349i
$889$		−	16.8478i		−	0.565056i
$890$		0			0
$891$	12.5230	+	7.23014i	0.419536	+	0.242219i
$892$	16.6396	−	4.45858i	0.557136	−	0.149284i
$893$	0.0299710	+	0.0173038i	0.00100294	+	0.000579048i
$894$	4.81401	−	4.81401i	0.161005	−	0.161005i
$895$		0			0
$896$	−13.8724	−	13.8724i	−0.463443	−	0.463443i
$897$	28.1798	+	7.55076i	0.940897	+	0.252113i
$898$	−5.63298	−	5.63298i	−0.187975	−	0.187975i
$899$	−56.5902			−1.88739
$900$		0			0
$901$	−6.01410	+	1.61147i	−0.200359	+	0.0536860i
$902$			10.1133i			0.336735i
$903$	8.54375	+	14.7982i	0.284318	+	0.492453i
$904$	7.38088	−	4.26135i	0.245484	−	0.141730i
$905$		0			0
$906$	1.70128	+	6.34927i	0.0565213	+	0.210941i
$907$	22.7521	−	39.4078i	0.755471	−	1.30851i	−0.189669	−	0.981848i	$-0.560742\pi$
$907$	22.7521	−	39.4078i	0.755471	−	1.30851i	0.945140	−	0.326665i	$-0.105925\pi$
$908$	1.16930	+	2.02529i	0.0388046	+	0.0672115i
$909$	−10.4509	−	18.1014i	−0.346633	−	0.600387i
$910$		0			0
$911$	33.0804	+	33.0804i	1.09600	+	1.09600i	0.994873	+	0.101129i	$0.0322453\pi$
$911$	33.0804	+	33.0804i	1.09600	+	1.09600i	0.101129	+	0.994873i	$0.467755\pi$
$912$	15.6476	+	9.03415i	0.518144	+	0.299151i
$913$	28.4952	+	7.63526i	0.943053	+	0.252690i
$914$		−	6.00147i		−	0.198511i
$915$		0			0
$916$	9.34601	−	5.39592i	0.308801	−	0.178286i
$917$		−	27.1682i		−	0.897172i
$918$	3.09947	+	11.5674i	0.102298	+	0.381780i
$919$	13.7077	+	13.7077i	0.452175	+	0.452175i	0.896076	−	0.443901i	$-0.146406\pi$
$919$	13.7077	+	13.7077i	0.452175	+	0.452175i	−0.443901	+	0.896076i	$0.646406\pi$
$920$		0			0
$921$	−4.46380	+	7.73152i	−0.147087	+	0.254762i
$922$	−5.10093	−	19.0369i	−0.167990	−	0.626948i
$923$	−14.8086	+	8.54974i	−0.487431	+	0.281418i
$924$	8.74966			0.287843
$925$		0			0
$926$	9.95508			0.327144
$927$	−25.6866	+	14.8302i	−0.843658	+	0.487086i
$928$	−8.94576	−	33.3860i	−0.293659	−	1.09595i
$929$	−8.91466	+	15.4406i	−0.292481	+	0.506591i	−0.974396	−	0.224840i	$-0.927814\pi$
$929$	−8.91466	+	15.4406i	−0.292481	+	0.506591i	0.681915	+	0.731431i	$0.261147\pi$
$930$		0			0
$931$	−11.5637	−	11.5637i	−0.378984	−	0.378984i
$932$	−2.68312	−	10.0135i	−0.0878886	−	0.328005i
$933$		−	7.93207i		−	0.259684i
$934$	−36.8211	+	21.2587i	−1.20482	+	0.695605i
$935$		0			0
$936$			14.6933i			0.480264i
$937$	33.5237	+	8.98266i	1.09517	+	0.293451i	0.760797	−	0.648989i	$-0.224808\pi$
$937$	33.5237	+	8.98266i	1.09517	+	0.293451i	0.334375	+	0.942440i	$0.391475\pi$
$938$	−23.2140	−	13.4026i	−0.757964	−	0.437611i
$939$	−1.00128	−	1.00128i	−0.0326757	−	0.0326757i
$940$		0			0
$941$	−9.76125	−	16.9070i	−0.318208	−	0.551152i	0.661907	−	0.749586i	$-0.269748\pi$
$941$	−9.76125	−	16.9070i	−0.318208	−	0.551152i	−0.980114	+	0.198435i	$0.936414\pi$
$942$	−0.255462	−	0.442473i	−0.00832341	−	0.0144166i
$943$	4.48033	−	7.76016i	0.145900	−	0.252706i
$944$	−10.4784	−	39.1058i	−0.341042	−	1.27279i
$945$		0			0
$946$	87.4119	−	50.4673i	2.84200	−	1.64083i
$947$	7.82396	+	13.5515i	0.254245	+	0.440364i	0.964690	−	0.263388i	$-0.0848399\pi$
$947$	7.82396	+	13.5515i	0.254245	+	0.440364i	−0.710446	+	0.703752i	$0.751507\pi$
$948$			3.30656i			0.107392i
$949$	−15.2432	+	4.08439i	−0.494814	+	0.132585i
$950$		0			0
$951$	0.620217			0.0201119
$952$	2.85527	+	2.85527i	0.0925397	+	0.0925397i
$953$	7.24920	+	1.94242i	0.234825	+	0.0629211i	0.374312	−	0.927303i	$-0.377879\pi$
$953$	7.24920	+	1.94242i	0.234825	+	0.0629211i	−0.139488	+	0.990224i	$0.544546\pi$
$954$	11.7777	+	11.7777i	0.381318	+	0.381318i
$955$		0			0
$956$	16.6046	−	16.6046i	0.537031	−	0.537031i
$957$	−22.8426	−	13.1882i	−0.738396	−	0.426313i
$958$	2.00941	−	0.538419i	0.0649210	−	0.0173955i
$959$	−0.303448	−	0.175196i	−0.00979883	−	0.00565736i
$960$		0			0
$961$		−	57.5075i		−	1.85508i
$962$	−2.05320	+	45.6293i	−0.0661980	+	1.47115i
$963$	20.3908	+	20.3908i	0.657085	+	0.657085i
$964$	−3.50759	+	13.0905i	−0.112972	+	0.421616i
$965$		0			0
$966$	−18.5745	−	10.7240i	−0.597626	−	0.345040i
$967$	−5.47930	+	9.49043i	−0.176203	+	0.305192i	−0.940577	−	0.339581i	$-0.889715\pi$
$967$	−5.47930	+	9.49043i	−0.176203	+	0.305192i	0.764374	+	0.644773i	$0.223048\pi$
$968$			22.7255i			0.730426i
$969$	−4.68422	−	2.70443i	−0.150479	−	0.0868789i
$970$		0			0
$971$	21.6891	+	37.5666i	0.696035	+	1.20557i	0.969831	+	0.243780i	$0.0783875\pi$
$971$	21.6891	+	37.5666i	0.696035	+	1.20557i	−0.273795	+	0.961788i	$0.588279\pi$
$972$	12.8627	−	12.8627i	0.412573	−	0.412573i
$973$	−26.8613	+	26.8613i	−0.861133	+	0.861133i
$974$	61.5982	−	35.5637i	1.97373	−	1.13953i
$975$		0			0
$976$	−41.3568	+	41.3568i	−1.32380	+	1.32380i
$977$	−12.0799	+	6.97431i	−0.386469	+	0.223128i	−0.680629	−	0.732628i	$-0.738293\pi$
$977$	−12.0799	+	6.97431i	−0.386469	+	0.223128i	0.294160	+	0.955756i	$0.404960\pi$
$978$	5.78796	−	21.6010i	0.185079	−	0.690723i
$979$	−41.2663	−	11.0573i	−1.31888	−	0.353392i
$980$		0			0
$981$	−37.1876	+	9.96439i	−1.18731	+	0.318138i
$982$	−3.03905	+	1.75459i	−0.0969799	+	0.0559913i
$983$	−16.2097	−	4.34336i	−0.517008	−	0.138532i	−0.00912552	−	0.999958i	$-0.502905\pi$
$983$	−16.2097	−	4.34336i	−0.517008	−	0.138532i	−0.507882	+	0.861427i	$0.669571\pi$
$984$	−1.44118	−	0.386163i	−0.0459432	−	0.0123104i
$985$		0			0
$986$	4.10966	+	15.3375i	0.130878	+	0.488444i
$987$	−0.00324505	+	0.0121107i	−0.000103291	+	0.000385488i
$988$	14.2663	+	14.2663i	0.453873	+	0.453873i
$989$	−89.4310			−2.84374
$990$		0			0
$991$	7.28810	−	7.28810i	0.231514	−	0.231514i	−0.581810	−	0.813325i	$-0.697655\pi$
$991$	7.28810	−	7.28810i	0.231514	−	0.231514i	0.813325	+	0.581810i	$0.197655\pi$
$992$	52.2160	−	13.9912i	1.65786	−	0.444222i
$993$	7.83995			0.248793
$994$	12.1428	−	3.25366i	0.385147	−	0.103200i
$995$		0			0
$996$	2.83861	−	4.91662i	0.0899448	−	0.155789i
$997$	−25.7984	−	44.6841i	−0.817044	−	1.41516i	−0.907851	−	0.419292i	$-0.862278\pi$
$997$	−25.7984	−	44.6841i	−0.817044	−	1.41516i	0.0908077	−	0.995868i	$-0.471055\pi$
$998$	−17.8592	+	17.8592i	−0.565324	+	0.565324i
$999$	−20.3701	+	18.6159i	−0.644482	+	0.588980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.a.193.4	yes	56
5.2	odd	4		925.2.t.a.82.4	✓	56
5.3	odd	4		925.2.t.a.82.11	yes	56
5.4	even	2	inner	925.2.y.a.193.11	yes	56
37.14	odd	12		925.2.t.a.643.4	yes	56
185.14	odd	12		925.2.t.a.643.11	yes	56
185.88	even	12	inner	925.2.y.a.532.11	yes	56
185.162	even	12	inner	925.2.y.a.532.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.t.a.82.4	✓	56	5.2	odd	4
925.2.t.a.82.11	yes	56	5.3	odd	4
925.2.t.a.643.4	yes	56	37.14	odd	12
925.2.t.a.643.11	yes	56	185.14	odd	12
925.2.y.a.193.4	yes	56	1.1	even	1	trivial
925.2.y.a.193.11	yes	56	5.4	even	2	inner
925.2.y.a.532.4	yes	56	185.162	even	12	inner
925.2.y.a.532.11	yes	56	185.88	even	12	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53267 + 0.884889i) q^{2} +(0.223454 + 0.833940i) q^{3} +(0.566056 - 0.980437i) q^{4} +(-1.08043 - 1.08043i) q^{6} +(-0.456178 - 1.70248i) q^{7} -1.53597i q^{8} +(1.95255 - 1.12731i) q^{9} +5.07893i q^{11} +(0.944113 + 0.252974i) q^{12} +(-3.67447 - 2.12146i) q^{13} +(2.20568 + 2.20568i) q^{14} +(2.49127 + 4.31501i) q^{16} +(-0.745779 - 1.29173i) q^{17} +(-1.99508 + 3.45558i) q^{18} +(-1.08710 - 4.05713i) q^{19} +(1.31783 - 0.760851i) q^{21} +(-4.49429 - 7.78434i) q^{22} +7.96415i q^{23} +(1.28091 - 0.343218i) q^{24} +7.50901 q^{26} +(3.20787 + 3.20787i) q^{27} +(-1.92740 - 0.516445i) q^{28} +(4.25340 + 4.25340i) q^{29} +(-6.65235 + 6.65235i) q^{31} +(-4.97623 - 2.87303i) q^{32} +(-4.23553 + 1.13491i) q^{33} +(2.28607 + 1.31986i) q^{34} -2.55247i q^{36} +(-0.273432 + 6.07661i) q^{37} +(5.25628 + 5.25628i) q^{38} +(0.948094 - 3.53833i) q^{39} +(-0.974387 - 0.562562i) q^{41} +(-1.34654 + 2.33227i) q^{42} +11.2292i q^{43} +(4.97957 + 2.87496i) q^{44} +(-7.04738 - 12.2064i) q^{46} +(-0.00582614 + 0.00582614i) q^{47} +(-3.04178 + 3.04178i) q^{48} +(3.37184 - 1.94673i) q^{49} +(0.910577 - 0.910577i) q^{51} +(-4.15991 + 2.40172i) q^{52} +(1.08040 - 4.03209i) q^{53} +(-7.75522 - 2.07801i) q^{54} +(-2.61496 + 0.700676i) q^{56} +(3.14048 - 1.81316i) q^{57} +(-10.2828 - 2.75528i) q^{58} +(-7.84855 - 2.10301i) q^{59} +(3.03813 + 11.3385i) q^{61} +(4.30928 - 16.0825i) q^{62} +(-2.80993 - 2.80993i) q^{63} +0.204149 q^{64} +(5.48741 - 5.48741i) q^{66} +(-8.30053 + 2.22412i) q^{67} -1.68861 q^{68} +(-6.64162 + 1.77962i) q^{69} +(2.01507 - 3.49020i) q^{71} +(-1.73151 - 2.99906i) q^{72} +(2.62998 - 2.62998i) q^{73} +(-4.95804 - 9.55541i) q^{74} +(-4.59312 - 1.23072i) q^{76} +(8.64678 - 2.31690i) q^{77} +(1.67791 + 6.26206i) q^{78} +(0.875572 + 3.26768i) q^{79} +(1.42356 - 2.46567i) q^{81} +1.99122 q^{82} +(1.50332 - 5.61047i) q^{83} -1.72274i q^{84} +(-9.93659 - 17.2107i) q^{86} +(-2.59664 + 4.49752i) q^{87} +7.80109 q^{88} +(-2.17709 + 8.12500i) q^{89} +(-1.93552 + 7.22347i) q^{91} +(7.80835 + 4.50815i) q^{92} +(-7.03415 - 4.06117i) q^{93} +(0.00377408 - 0.0140850i) q^{94} +(1.28398 - 4.79187i) q^{96} -6.00145 q^{97} +(-3.44528 + 5.96740i) q^{98} +(5.72551 + 9.91688i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 36 q^{4} + 8 q^{14} - 72 q^{16} + 16 q^{19} - 36 q^{21} - 4 q^{24} + 8 q^{26} + 24 q^{31} + 60 q^{34} - 24 q^{41} + 24 q^{44} + 12 q^{49} + 84 q^{51} + 28 q^{54} + 104 q^{56} + 4 q^{59} - 24 q^{61}+ \cdots + 120 q^{99}+O(q^{100}) \) 56 * q + 36 * q^4 + 8 * q^14 - 72 * q^16 + 16 * q^19 - 36 * q^21 - 4 * q^24 + 8 * q^26 + 24 * q^31 + 60 * q^34 - 24 * q^41 + 24 * q^44 + 12 * q^49 + 84 * q^51 + 28 * q^54 + 104 * q^56 + 4 * q^59 - 24 * q^61 - 344 * q^64 - 124 * q^66 - 52 * q^69 - 72 * q^71 - 48 * q^74 + 40 * q^76 + 100 * q^79 + 44 * q^81 + 40 * q^86 + 32 * q^89 - 4 * q^91 - 140 * q^94 - 132 * q^96 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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