LMFDB - Embedded newform 700.2.p.e.451.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(451,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.451"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.7
Character	$\chi$	$=$	700.451
Dual form			700.2.p.e.551.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.285823 + 1.38503i) q^{2} +(-1.29809 + 2.24836i) q^{3} +(-1.83661 - 0.791746i) q^{4} +(-2.74302 - 2.44053i) q^{6} +(0.603960 + 2.57589i) q^{7} +(1.62154 - 2.31746i) q^{8} +(-1.87009 - 3.23909i) q^{9} +(-3.12008 - 1.80138i) q^{11} +(4.16422 - 3.10161i) q^{12} -0.818282i q^{13} +(-3.74031 + 0.100253i) q^{14} +(2.74628 + 2.90826i) q^{16} +(-6.40537 - 3.69814i) q^{17} +(5.02075 - 1.66432i) q^{18} +(-1.65329 - 2.86358i) q^{19} +(-6.57554 - 1.98583i) q^{21} +(3.38675 - 3.80652i) q^{22} +(2.19550 - 1.26758i) q^{23} +(3.10559 + 6.65408i) q^{24} +(1.13334 + 0.233884i) q^{26} +1.92166 q^{27} +(0.930214 - 5.20910i) q^{28} +2.04334 q^{29} +(0.955727 - 1.65537i) q^{31} +(-4.81297 + 2.97243i) q^{32} +(8.10030 - 4.67671i) q^{33} +(6.95283 - 7.81461i) q^{34} +(0.870092 + 7.42959i) q^{36} +(3.58360 + 6.20697i) q^{37} +(4.43869 - 1.47138i) q^{38} +(1.83980 + 1.06221i) q^{39} -2.65824i q^{41} +(4.62987 - 8.53972i) q^{42} +2.39696i q^{43} +(4.30413 + 5.77873i) q^{44} +(1.12810 + 3.40314i) q^{46} +(0.667376 + 1.15593i) q^{47} +(-10.1037 + 2.39944i) q^{48} +(-6.27046 + 3.11147i) q^{49} +(16.6295 - 9.60106i) q^{51} +(-0.647871 + 1.50287i) q^{52} +(-0.905503 + 1.56838i) q^{53} +(-0.549253 + 2.66155i) q^{54} +(6.94888 + 2.77725i) q^{56} +8.58450 q^{57} +(-0.584034 + 2.83009i) q^{58} +(0.955727 - 1.65537i) q^{59} +(-8.46625 + 4.88799i) q^{61} +(2.01956 + 1.79685i) q^{62} +(7.21411 - 6.77344i) q^{63} +(-2.74124 - 7.51569i) q^{64} +(4.16213 + 12.5559i) q^{66} +(-8.02134 - 4.63112i) q^{67} +(8.83618 + 11.8635i) q^{68} +6.58172i q^{69} -1.38422i q^{71} +(-10.5389 - 0.918444i) q^{72} +(-6.40537 - 3.69814i) q^{73} +(-9.62111 + 3.18929i) q^{74} +(0.769222 + 6.56827i) q^{76} +(2.75576 - 9.12495i) q^{77} +(-1.99704 + 2.24457i) q^{78} +(6.70979 - 3.87390i) q^{79} +(3.11579 - 5.39670i) q^{81} +(3.68173 + 0.759784i) q^{82} -10.4973 q^{83} +(10.5044 + 8.85335i) q^{84} +(-3.31986 - 0.685105i) q^{86} +(-2.65245 + 4.59418i) q^{87} +(-9.23393 + 4.30966i) q^{88} +(9.19133 - 5.30662i) q^{89} +(2.10781 - 0.494210i) q^{91} +(-5.03589 + 0.589761i) q^{92} +(2.48125 + 4.29764i) q^{93} +(-1.79175 + 0.593945i) q^{94} +(-0.435416 - 14.6798i) q^{96} +7.32005i q^{97} +(-2.51724 - 9.57411i) q^{98} +13.4750i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 6 q^{4} - 4 q^{9} - 22 q^{14} + 18 q^{16} - 52 q^{21} + 48 q^{24} - 18 q^{26} - 28 q^{36} + 26 q^{44} - 22 q^{46} - 48 q^{54} - 16 q^{56} + 36 q^{61} - 36 q^{64} - 24 q^{66} - 14 q^{74} + 72 q^{81}+ \cdots + 60 q^{96}+O(q^{100}) $ 32 * q - 6 * q^4 - 4 * q^9 - 22 * q^14 + 18 * q^16 - 52 * q^21 + 48 * q^24 - 18 * q^26 - 28 * q^36 + 26 * q^44 - 22 * q^46 - 48 * q^54 - 16 * q^56 + 36 * q^61 - 36 * q^64 - 24 * q^66 - 14 * q^74 + 72 * q^81 - 56 * q^84 + 8 * q^86 + 108 * q^89 - 30 * q^94 + 60 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	−0.285823	+	1.38503i	−0.202107	+	0.979363i
$2$	−0.285823	+	1.38503i	−0.202107	+	0.979363i
$3$	−1.29809	+	2.24836i	−0.749454	+	1.29809i	0.198630	+	0.980075i	$0.436351\pi$
$3$	−1.29809	+	2.24836i	−0.749454	+	1.29809i	−0.948084	+	0.318019i	$0.896983\pi$
$4$	−1.83661	−	0.791746i	−0.918305	−	0.395873i
$5$		0			0
$5$		0			0
$6$	−2.74302	−	2.44053i	−1.11983	−	0.996342i
$7$	0.603960	+	2.57589i	0.228275	+	0.973597i
$7$	0.603960	+	2.57589i	0.228275	+	0.973597i
$8$	1.62154	−	2.31746i	0.573300	−	0.819346i
$9$	−1.87009	−	3.23909i	−0.623364	−	1.07970i
$10$		0			0
$11$	−3.12008	−	1.80138i	−0.940738	−	0.543136i	−0.0505467	−	0.998722i	$-0.516096\pi$
$11$	−3.12008	−	1.80138i	−0.940738	−	0.543136i	−0.890192	+	0.455586i	$0.849430\pi$
$12$	4.16422	−	3.10161i	1.20211	−	0.895357i
$13$		−	0.818282i		−	0.226951i	−0.993541	−	0.113475i	$-0.963802\pi$
$13$		−	0.818282i		−	0.226951i	0.993541	−	0.113475i	$-0.0361983\pi$
$14$	−3.74031	+	0.100253i	−0.999641	+	0.0267937i
$15$		0			0
$16$	2.74628	+	2.90826i	0.686569	+	0.727064i
$17$	−6.40537	−	3.69814i	−1.55353	−	0.896931i	−0.997850	−	0.0655347i	$-0.979125\pi$
$17$	−6.40537	−	3.69814i	−1.55353	−	0.896931i	−0.555680	−	0.831396i	$-0.687542\pi$
$18$	5.02075	−	1.66432i	1.18340	−	0.392285i
$19$	−1.65329	−	2.86358i	−0.379291	−	0.656951i	0.611668	−	0.791114i	$-0.290499\pi$
$19$	−1.65329	−	2.86358i	−0.379291	−	0.656951i	−0.990959	+	0.134163i	$0.957165\pi$
$20$		0			0
$21$	−6.57554	−	1.98583i	−1.43490	−	0.433344i
$22$	3.38675	−	3.80652i	0.722057	−	0.811553i
$23$	2.19550	−	1.26758i	0.457794	−	0.264308i	−0.253322	−	0.967382i	$-0.581523\pi$
$23$	2.19550	−	1.26758i	0.457794	−	0.264308i	0.711116	+	0.703074i	$0.248190\pi$
$24$	3.10559	+	6.65408i	0.633925	+	1.35826i
$25$		0			0
$26$	1.13334	+	0.233884i	0.222267	+	0.0458684i
$27$	1.92166			0.369823
$28$	0.930214	−	5.20910i	0.175794	−	0.984427i
$29$	2.04334			0.379439			0.189720	−	0.981838i	$-0.439242\pi$
$29$	2.04334			0.379439			0.189720	+	0.981838i	$0.439242\pi$
$30$		0			0
$31$	0.955727	−	1.65537i	0.171654	−	0.297313i	−0.767345	−	0.641235i	$-0.778422\pi$
$31$	0.955727	−	1.65537i	0.171654	−	0.297313i	0.938998	+	0.343922i	$0.111756\pi$
$32$	−4.81297	+	2.97243i	−0.850821	+	0.525456i
$33$	8.10030	−	4.67671i	1.41008	−	0.814111i
$34$	6.95283	−	7.81461i	1.19240	−	1.34019i
$35$		0			0
$36$	0.870092	+	7.42959i	0.145015	+	1.23827i
$37$	3.58360	+	6.20697i	0.589140	+	1.02042i	0.994345	+	0.106195i	$0.0338666\pi$
$37$	3.58360	+	6.20697i	0.589140	+	1.02042i	−0.405206	+	0.914226i	$0.632800\pi$
$38$	4.43869	−	1.47138i	0.720051	−	0.238689i
$39$	1.83980	+	1.06221i	0.294603	+	0.170089i
$40$		0			0
$41$		−	2.65824i		−	0.415147i	−0.978219	−	0.207573i	$-0.933443\pi$
$41$		−	2.65824i		−	0.415147i	0.978219	−	0.207573i	$-0.0665566\pi$
$42$	4.62987	−	8.53972i	0.714405	−	1.31771i
$43$			2.39696i			0.365533i	0.983156	+	0.182766i	$0.0585052\pi$
$43$			2.39696i			0.365533i	−0.983156	+	0.182766i	$0.941495\pi$
$44$	4.30413	+	5.77873i	0.648872	+	0.871177i
$45$		0			0
$46$	1.12810	+	3.40314i	0.166330	+	0.501766i
$47$	0.667376	+	1.15593i	0.0973468	+	0.168610i	0.910586	−	0.413320i	$-0.135631\pi$
$47$	0.667376	+	1.15593i	0.0973468	+	0.168610i	−0.813239	+	0.581930i	$0.802298\pi$
$48$	−10.1037	+	2.39944i	−1.45835	+	0.346330i
$49$	−6.27046	+	3.11147i	−0.895781	+	0.444496i
$50$		0			0
$51$	16.6295	−	9.60106i	2.32860	−	1.34442i
$52$	−0.647871	+	1.50287i	−0.0898436	+	0.208410i
$53$	−0.905503	+	1.56838i	−0.124380	+	0.215433i	−0.921491	−	0.388401i	$-0.873028\pi$
$53$	−0.905503	+	1.56838i	−0.124380	+	0.215433i	0.797110	+	0.603834i	$0.206361\pi$
$54$	−0.549253	+	2.66155i	−0.0747439	+	0.362191i
$55$		0			0
$56$	6.94888	+	2.77725i	0.928583	+	0.371126i
$57$	8.58450			1.13705
$58$	−0.584034	+	2.83009i	−0.0766874	+	0.371609i
$59$	0.955727	−	1.65537i	0.124425	−	0.215510i	−0.797083	−	0.603870i	$-0.793625\pi$
$59$	0.955727	−	1.65537i	0.124425	−	0.215510i	0.921508	+	0.388359i	$0.126958\pi$
$60$		0			0
$61$	−8.46625	+	4.88799i	−1.08399	+	0.625843i	−0.931970	−	0.362534i	$-0.881912\pi$
$61$	−8.46625	+	4.88799i	−1.08399	+	0.625843i	−0.152021	+	0.988377i	$0.548578\pi$
$62$	2.01956	+	1.79685i	0.256485	+	0.228200i
$63$	7.21411	−	6.77344i	0.908892	−	0.853374i
$64$	−2.74124	−	7.51569i	−0.342655	−	0.939461i
$65$		0			0
$66$	4.16213	+	12.5559i	0.512323	+	1.54552i
$67$	−8.02134	−	4.63112i	−0.979963	−	0.565782i	−0.0777041	−	0.996976i	$-0.524759\pi$
$67$	−8.02134	−	4.63112i	−0.979963	−	0.565782i	−0.902259	+	0.431195i	$0.858092\pi$
$68$	8.83618	+	11.8635i	1.07154	+	1.43866i
$69$			6.58172i			0.792346i
$70$		0			0
$71$		−	1.38422i		−	0.164277i	−0.996621	−	0.0821385i	$-0.973825\pi$
$71$		−	1.38422i		−	0.164277i	0.996621	−	0.0821385i	$-0.0261750\pi$
$72$	−10.5389	−	0.918444i	−1.24202	−	0.108240i
$73$	−6.40537	−	3.69814i	−0.749692	−	0.432835i	0.0758908	−	0.997116i	$-0.475820\pi$
$73$	−6.40537	−	3.69814i	−0.749692	−	0.432835i	−0.825583	+	0.564281i	$0.809153\pi$
$74$	−9.62111	+	3.18929i	−1.11843	+	0.370748i
$75$		0			0
$76$	0.769222	+	6.56827i	0.0882358	+	0.753433i
$77$	2.75576	−	9.12495i	0.314048	−	1.03988i
$78$	−1.99704	+	2.24457i	−0.226121	+	0.254147i
$79$	6.70979	−	3.87390i	0.754910	−	0.435848i	−0.0725552	−	0.997364i	$-0.523115\pi$
$79$	6.70979	−	3.87390i	0.754910	−	0.435848i	0.827465	+	0.561517i	$0.189782\pi$
$80$		0			0
$81$	3.11579	−	5.39670i	0.346199	−	0.599634i
$82$	3.68173	+	0.759784i	0.406579	+	0.0839041i
$83$	−10.4973			−1.15223			−0.576113	−	0.817370i	$-0.695431\pi$
$83$	−10.4973			−1.15223			−0.576113	+	0.817370i	$0.695431\pi$
$84$	10.5044	+	8.85335i	1.14613	+	0.965980i
$85$		0			0
$86$	−3.31986	−	0.685105i	−0.357989	−	0.0738768i
$87$	−2.65245	+	4.59418i	−0.284372	+	0.492547i
$88$	−9.23393	+	4.30966i	−0.984341	+	0.459411i
$89$	9.19133	−	5.30662i	0.974279	−	0.562500i	0.0737410	−	0.997277i	$-0.476506\pi$
$89$	9.19133	−	5.30662i	0.974279	−	0.562500i	0.900538	+	0.434777i	$0.143173\pi$
$90$		0			0
$91$	2.10781	−	0.494210i	0.220958	−	0.0518073i
$92$	−5.03589	+	0.589761i	−0.525027	+	0.0614868i
$93$	2.48125	+	4.29764i	0.257293	+	0.445645i
$94$	−1.79175	+	0.593945i	−0.184805	+	0.0612607i
$95$		0			0
$96$	−0.435416	−	14.6798i	−0.0444395	−	1.49825i
$97$			7.32005i			0.743239i	0.928385	+	0.371619i	$0.121197\pi$
$97$			7.32005i			0.743239i	−0.928385	+	0.371619i	$0.878803\pi$
$98$	−2.51724	−	9.57411i	−0.254280	−	0.967131i
$99$			13.4750i			1.35428i
$100$		0			0
$101$	−5.50608	−	3.17894i	−0.547875	−	0.316316i	0.200389	−	0.979716i	$-0.435779\pi$
$101$	−5.50608	−	3.17894i	−0.547875	−	0.316316i	−0.748265	+	0.663400i	$0.769113\pi$
$102$	8.54465	+	25.7766i	0.846047	+	2.55226i
$103$	−0.511038	−	0.885144i	−0.0503541	−	0.0872158i	0.839750	−	0.542974i	$-0.182702\pi$
$103$	−0.511038	−	0.885144i	−0.0503541	−	0.0872158i	−0.890104	+	0.455758i	$0.849368\pi$
$104$	−1.89634	−	1.32687i	−0.185951	−	0.130111i
$105$		0			0
$106$	−1.91343	−	1.70243i	−0.185849	−	0.165354i
$107$	6.28003	−	3.62578i	0.607114	−	0.350517i	−0.164721	−	0.986340i	$-0.552672\pi$
$107$	6.28003	−	3.62578i	0.607114	−	0.350517i	0.771835	+	0.635823i	$0.219339\pi$
$108$	−3.52933	−	1.52146i	−0.339610	−	0.146403i
$109$	−3.98588	+	6.90375i	−0.381778	+	0.661259i	−0.991316	−	0.131498i	$-0.958021\pi$
$109$	−3.98588	+	6.90375i	−0.381778	+	0.661259i	0.609538	+	0.792756i	$0.291355\pi$
$110$		0			0
$111$	−18.6074			−1.76613
$112$	−5.83272	+	8.83059i	−0.551140	+	0.834413i
$113$	−7.61610			−0.716462			−0.358231	−	0.933633i	$-0.616620\pi$
$113$	−7.61610			−0.716462			−0.358231	+	0.933633i	$0.616620\pi$
$114$	−2.45365	+	11.8898i	−0.229805	+	1.11358i
$115$		0			0
$116$	−3.75282	−	1.61781i	−0.348441	−	0.150210i
$117$	−2.65049	+	1.53026i	−0.245038	+	0.141473i
$118$	2.01956	+	1.79685i	0.185916	+	0.165414i
$119$	5.65744	−	18.7331i	0.518616	−	1.71726i
$120$		0			0
$121$	0.989917	+	1.71459i	0.0899925	+	0.155872i
$122$	−4.35016	−	13.1231i	−0.393845	−	1.18811i
$123$	5.97668	+	3.45064i	0.538899	+	0.311134i
$124$	−3.06593	+	2.28357i	−0.275328	+	0.205071i
$125$		0			0
$126$	7.31946	+	11.9277i	0.652069	+	1.06261i
$127$		−	8.78136i		−	0.779220i	−0.920980	−	0.389610i	$-0.872610\pi$
$127$		−	8.78136i		−	0.779220i	0.920980	−	0.389610i	$-0.127390\pi$
$128$	11.1930	−	1.64855i	0.989327	−	0.145712i
$129$	−5.38923	−	3.11147i	−0.474495	−	0.273950i
$130$		0			0
$131$	−6.69467	−	11.5955i	−0.584916	−	1.01310i	−0.994886	−	0.101005i	$-0.967794\pi$
$131$	−6.69467	−	11.5955i	−0.584916	−	1.01310i	0.409970	−	0.912099i	$-0.365539\pi$
$132$	−18.5799	+	2.17592i	−1.61717	+	0.189389i
$133$	6.37777	−	5.98819i	0.553023	−	0.519242i
$134$	8.70692	−	9.78611i	0.752164	−	0.845391i
$135$		0			0
$136$	−18.9568	+	8.84752i	−1.62553	+	0.758668i
$137$	2.61208	−	4.52425i	0.223165	−	0.386533i	−0.732602	−	0.680657i	$-0.761694\pi$
$137$	2.61208	−	4.52425i	0.223165	−	0.386533i	0.955767	+	0.294124i	$0.0950278\pi$
$138$	−9.11588	−	1.88121i	−0.775995	−	0.160139i
$139$	−21.9442			−1.86128			−0.930641	−	0.365933i	$-0.880750\pi$
$139$	−21.9442			−1.86128			−0.930641	+	0.365933i	$0.880750\pi$
$140$		0			0
$141$	−3.46527			−0.291828
$142$	1.91719	+	0.395643i	0.160887	+	0.0332016i
$143$	−1.47403	+	2.55310i	−0.123265	+	0.213501i
$144$	4.28433	−	14.3342i	0.357027	−	1.19451i
$145$		0			0
$146$	6.95283	−	7.81461i	0.575421	−	0.646742i
$147$	1.14392	−	18.1373i	0.0943492	−	1.49594i
$148$	−1.66733	−	14.2371i	−0.137054	−	1.17028i
$149$	−11.9749	−	20.7411i	−0.981019	−	1.69917i	−0.658444	−	0.752630i	$-0.728785\pi$
$149$	−11.9749	−	20.7411i	−0.981019	−	1.69917i	−0.322575	−	0.946544i	$-0.604548\pi$
$150$		0			0
$151$	6.06876	+	3.50380i	0.493869	+	0.285135i	0.726178	−	0.687507i	$-0.241295\pi$
$151$	6.06876	+	3.50380i	0.493869	+	0.285135i	−0.232309	+	0.972642i	$0.574628\pi$
$152$	−9.31711	−	0.811968i	−0.755717	−	0.0658593i
$153$			27.6635i			2.23646i
$154$	11.8507	+	6.42492i	0.954953	+	0.517735i
$155$		0			0
$156$	−2.53799	−	3.40751i	−0.203202	−	0.272819i
$157$	−5.56468	−	3.21277i	−0.444110	−	0.256407i	0.261229	−	0.965277i	$-0.415872\pi$
$157$	−5.56468	−	3.21277i	−0.444110	−	0.256407i	−0.705340	+	0.708870i	$0.749205\pi$
$158$	3.44765	+	10.4005i	0.274280	+	0.827419i
$159$	−2.35085	−	4.07180i	−0.186435	−	0.322915i
$160$		0			0
$161$	4.59114	+	4.88982i	0.361832	+	0.385372i
$162$	6.58403	+	5.85796i	0.517290	+	0.460245i
$163$	−16.0033	+	9.23950i	−1.25347	+	0.723693i	−0.971798	−	0.235816i	$-0.924224\pi$
$163$	−16.0033	+	9.23950i	−1.25347	+	0.723693i	−0.281676	+	0.959510i	$0.590890\pi$
$164$	−2.10465	+	4.88214i	−0.164345	+	0.381231i
$165$		0			0
$166$	3.00036	−	14.5390i	0.232873	−	1.12845i
$167$	1.82894			0.141527			0.0707637	−	0.997493i	$-0.477456\pi$
$167$	1.82894			0.141527			0.0707637	+	0.997493i	$0.477456\pi$
$168$	−15.2646	+	12.0185i	−1.17769	+	0.927245i
$169$	12.3304			0.948493
$170$		0			0
$171$	−6.18361	+	10.7103i	−0.472873	+	0.819039i
$172$	1.89778	−	4.40228i	0.144704	−	0.335671i
$173$	−13.2065	+	7.62476i	−1.00407	+	0.579700i	−0.909450	−	0.415814i	$-0.863497\pi$
$173$	−13.2065	+	7.62476i	−1.00407	+	0.579700i	−0.0946193	+	0.995514i	$0.530163\pi$
$174$	−5.60494	−	4.98684i	−0.424909	−	0.378051i
$175$		0			0
$176$	−3.32973	−	14.0211i	−0.250988	−	1.05688i
$177$	2.48125	+	4.29764i	0.186502	+	0.323031i
$178$	4.72273	+	14.2470i	0.353983	+	1.06786i
$179$	10.8572	+	6.26844i	0.811509	+	0.468525i	0.847480	−	0.530828i	$-0.178119\pi$
$179$	10.8572	+	6.26844i	0.811509	+	0.468525i	−0.0359707	+	0.999353i	$0.511452\pi$
$180$		0			0
$181$			8.01839i			0.596002i	0.954566	+	0.298001i	$0.0963199\pi$
$181$			8.01839i			0.596002i	−0.954566	+	0.298001i	$0.903680\pi$
$182$	0.0820350	+	3.06063i	0.00608084	+	0.226869i
$183$		−	25.3803i		−	1.87616i
$184$	0.622535	−	7.14341i	0.0458939	−	0.526619i
$185$		0			0
$186$	−6.66156	+	2.20823i	−0.488449	+	0.161915i
$187$	13.3235	+	23.0770i	0.974310	+	1.68755i
$188$	−0.310508	−	2.65139i	−0.0226461	−	0.193372i
$189$	1.16060	+	4.94998i	0.0844215	+	0.360058i
$190$		0			0
$191$	5.85379	−	3.37969i	0.423565	−	0.244546i	−0.273036	−	0.962004i	$-0.588028\pi$
$191$	5.85379	−	3.37969i	0.423565	−	0.244546i	0.696602	+	0.717458i	$0.254695\pi$
$192$	20.4564	+	3.59276i	1.47631	+	0.259285i
$193$	1.18001	−	2.04384i	0.0849392	−	0.147119i	−0.820426	−	0.571753i	$-0.806264\pi$
$193$	1.18001	−	2.04384i	0.0849392	−	0.147119i	0.905365	+	0.424634i	$0.139597\pi$
$194$	−10.1385	−	2.09224i	−0.727901	−	0.150214i
$195$		0			0
$196$	13.9799	−	0.749953i	0.998564	−	0.0535681i
$197$	−20.3205			−1.44777			−0.723887	−	0.689918i	$-0.757647\pi$
$197$	−20.3205			−1.44777			−0.723887	+	0.689918i	$0.757647\pi$
$198$	−18.6632	−	3.85145i	−1.32634	−	0.273711i
$199$	−5.72909	+	9.92308i	−0.406125	+	0.703429i	−0.994452	−	0.105195i	$-0.966453\pi$
$199$	−5.72909	+	9.92308i	−0.406125	+	0.703429i	0.588327	+	0.808623i	$0.299787\pi$
$200$		0			0
$201$	20.8249	−	12.0233i	1.46888	−	0.848056i
$202$	5.97668	−	6.71746i	0.420518	−	0.472639i
$203$	1.23410	+	5.26343i	0.0866166	+	0.369421i
$204$	−38.1436	+	4.46706i	−2.67058	+	0.312757i
$205$		0			0
$206$	1.37202	−	0.454808i	0.0955929	−	0.0316880i
$207$	−8.21159	−	4.74097i	−0.570745	−	0.329520i
$208$	2.37978	−	2.24723i	0.165008	−	0.155817i
$209$			11.9128i			0.824026i
$210$		0			0
$211$			22.0647i			1.51900i	0.650510	+	0.759498i	$0.274555\pi$
$211$			22.0647i			1.51900i	−0.650510	+	0.759498i	$0.725445\pi$
$212$	2.90481	−	2.16357i	0.199503	−	0.148595i
$213$	3.11224	+	1.79685i	0.213247	+	0.123118i
$214$	3.22683	+	9.73436i	0.220582	+	0.665427i
$215$		0			0
$216$	3.11603	−	4.45336i	0.212019	−	0.303013i
$217$	4.84127	+	1.46208i	0.328647	+	0.0992522i
$218$	−8.42263	−	7.49381i	−0.570453	−	0.507545i
$219$	16.6295	−	9.60106i	1.12372	−	0.648780i
$220$		0			0
$221$	−3.02612	+	5.24140i	−0.203559	+	0.352575i
$222$	5.31841	−	25.7718i	0.356948	−	1.72969i
$223$	23.5776			1.57887			0.789436	−	0.613833i	$-0.210373\pi$
$223$	23.5776			1.57887			0.789436	+	0.613833i	$0.210373\pi$
$224$	−10.5635	−	10.6025i	−0.705804	−	0.708408i
$225$		0			0
$226$	2.17685	−	10.5485i	0.144802	−	0.701677i
$227$	−10.4634	+	18.1231i	−0.694478	+	1.20287i	0.275879	+	0.961192i	$0.411031\pi$
$227$	−10.4634	+	18.1231i	−0.694478	+	1.20287i	−0.970356	+	0.241678i	$0.922302\pi$
$228$	−15.7664	−	6.79674i	−1.04415	−	0.450125i
$229$	−4.48735	+	2.59077i	−0.296533	+	0.171203i	−0.640884	−	0.767638i	$-0.721432\pi$
$229$	−4.48735	+	2.59077i	−0.296533	+	0.171203i	0.344352	+	0.938841i	$0.388099\pi$
$230$		0			0
$231$	16.9390	+	18.0410i	1.11450	+	1.18701i
$232$	3.31335	−	4.73536i	0.217532	−	0.310892i
$233$	−10.3847	−	17.9868i	−0.680324	−	1.17836i	−0.974882	−	0.222722i	$-0.928506\pi$
$233$	−10.3847	−	17.9868i	−0.680324	−	1.17836i	0.294558	−	0.955634i	$-0.404828\pi$
$234$	−1.36189	−	4.10839i	−0.0890294	−	0.268574i
$235$		0			0
$236$	−3.06593	+	2.28357i	−0.199575	+	0.148648i
$237$			20.1147i			1.30659i
$238$	24.3288	+	13.1901i	1.57700	+	0.854984i
$239$			21.1286i			1.36670i	0.730092	+	0.683349i	$0.239477\pi$
$239$			21.1286i			1.36670i	−0.730092	+	0.683349i	$0.760523\pi$
$240$		0			0
$241$	1.57448	+	0.909029i	0.101421	+	0.0585557i	0.549853	−	0.835262i	$-0.314684\pi$
$241$	1.57448	+	0.909029i	0.101421	+	0.0585557i	−0.448431	+	0.893817i	$0.648017\pi$
$242$	−2.65769	+	0.880996i	−0.170843	+	0.0566326i
$243$	10.9716	+	19.0035i	0.703832	+	1.21907i
$244$	19.4192	−	2.27422i	1.24319	−	0.145592i
$245$		0			0
$246$	−6.48750	+	7.29160i	−0.413628	+	0.464896i
$247$	−2.34322	+	1.35286i	−0.149095	+	0.0860803i
$248$	−2.28650	−	4.89910i	−0.145193	−	0.311093i
$249$	13.6264	−	23.6017i	0.863540	−	1.49570i
$250$		0			0
$251$	14.0187			0.884856			0.442428	−	0.896804i	$-0.354117\pi$
$251$	14.0187			0.884856			0.442428	+	0.896804i	$0.354117\pi$
$252$	−18.6123	+	6.72844i	−1.17247	+	0.423852i
$253$	−9.13352			−0.574220
$254$	12.1624	+	2.50991i	0.763140	+	0.157486i
$255$		0			0
$256$	−0.915918	+	15.9738i	−0.0572449	+	0.998360i
$257$	−15.4780	+	8.93624i	−0.965492	+	0.557427i	−0.897859	−	0.440283i	$-0.854878\pi$
$257$	−15.4780	+	8.93624i	−0.965492	+	0.557427i	−0.0676333	+	0.997710i	$0.521545\pi$
$258$	5.84985	−	6.57491i	0.364196	−	0.409336i
$259$	−13.8242	+	12.9797i	−0.858991	+	0.806521i
$260$		0			0
$261$	−3.82124	−	6.61858i	−0.236529	−	0.409680i
$262$	17.9736	−	5.95805i	1.11041	−	0.368090i
$263$	−18.9629	−	10.9482i	−1.16930	−	0.675097i	−0.215787	−	0.976440i	$-0.569232\pi$
$263$	−18.9629	−	10.9482i	−1.16930	−	0.675097i	−0.953516	+	0.301343i	$0.902565\pi$
$264$	2.29684	−	26.3556i	0.141361	−	1.62207i
$265$		0			0
$266$	6.47091	+	10.5450i	0.396757	+	0.646553i
$267$			27.5539i			1.68627i
$268$	11.0654	+	14.8564i	0.675928	+	0.907501i
$269$	−2.49661	−	1.44142i	−0.152221	−	0.0878847i	0.421955	−	0.906617i	$-0.361344\pi$
$269$	−2.49661	−	1.44142i	−0.152221	−	0.0878847i	−0.574176	+	0.818732i	$0.694677\pi$
$270$		0			0
$271$	−8.47793	−	14.6842i	−0.514997	−	0.892002i	−0.999849	−	0.0174049i	$-0.994460\pi$
$271$	−8.47793	−	14.6842i	−0.514997	−	0.892002i	0.484851	−	0.874597i	$-0.338874\pi$
$272$	−6.83578	−	28.7846i	−0.414480	−	1.74532i
$273$	−1.62497	+	5.38065i	−0.0983476	+	0.325652i
$274$	5.51963	+	4.91094i	0.333453	+	0.296681i
$275$		0			0
$276$	5.21105	−	12.0881i	0.313668	−	0.727616i
$277$	13.4258	−	23.2541i	0.806677	−	1.39720i	−0.108477	−	0.994099i	$-0.534597\pi$
$277$	13.4258	−	23.2541i	0.806677	−	1.39720i	0.915153	−	0.403106i	$-0.132069\pi$
$278$	6.27215	−	30.3933i	0.376179	−	1.82287i
$279$	−7.14919			−0.428011
$280$		0			0
$281$	24.9497			1.48838			0.744188	−	0.667971i	$-0.232837\pi$
$281$	24.9497			1.48838			0.744188	+	0.667971i	$0.232837\pi$
$282$	0.990452	−	4.79950i	0.0589806	−	0.285806i
$283$	−4.91910	+	8.52014i	−0.292410	+	0.506470i	−0.974379	−	0.224912i	$-0.927791\pi$
$283$	−4.91910	+	8.52014i	−0.292410	+	0.506470i	0.681969	+	0.731381i	$0.261124\pi$
$284$	−1.09595	+	2.54228i	−0.0650328	+	0.150857i
$285$		0			0
$286$	−3.11481	−	2.77132i	−0.184183	−	0.163871i
$287$	6.84733	−	1.60547i	0.404185	−	0.0947678i
$288$	18.6287	+	10.0309i	1.09770	+	0.591079i
$289$	18.8525	+	32.6535i	1.10897	+	1.92079i
$290$		0			0
$291$	−16.4581	−	9.50211i	−0.964793	−	0.557024i
$292$	8.83618	+	11.8635i	0.517098	+	0.694257i
$293$		−	23.4039i		−	1.36727i	−0.729823	−	0.683636i	$-0.760398\pi$
$293$		−	23.4039i		−	1.36727i	0.729823	−	0.683636i	$-0.239602\pi$
$294$	24.7937	+	6.76841i	1.44600	+	0.394742i
$295$		0			0
$296$	20.1953	+	1.75999i	1.17383	+	0.102297i
$297$	−5.99571	−	3.46163i	−0.347907	−	0.200864i
$298$	32.1497	−	10.6573i	1.86238	−	0.617358i
$299$	−1.03723	−	1.79654i	−0.0599848	−	0.103897i
$300$		0			0
$301$	−6.17431	+	1.44767i	−0.355881	+	0.0834421i
$302$	−6.58746	+	7.40395i	−0.379066	+	0.426049i
$303$	14.2948	−	8.25311i	0.821215	−	0.474129i
$304$	3.78764	−	12.6724i	0.217236	−	0.726811i
$305$		0			0
$306$	−38.3147	−	7.90685i	−2.19031	−	0.452004i
$307$	−2.18529			−0.124721			−0.0623606	−	0.998054i	$-0.519863\pi$
$307$	−2.18529			−0.124721			−0.0623606	+	0.998054i	$0.519863\pi$
$308$	−12.2859	+	14.5771i	−0.700053	+	0.830608i
$309$	2.65350			0.150952
$310$		0			0
$311$	−14.4501	+	25.0282i	−0.819388	+	1.41922i	0.0867457	+	0.996230i	$0.472353\pi$
$311$	−14.4501	+	25.0282i	−0.819388	+	1.41922i	−0.906134	+	0.422991i	$0.860980\pi$
$312$	5.44492	−	2.54125i	0.308258	−	0.143870i
$313$	5.50189	−	3.17652i	0.310985	−	0.179548i	−0.336382	−	0.941726i	$-0.609203\pi$
$313$	5.50189	−	3.17652i	0.310985	−	0.179548i	0.647367	+	0.762178i	$0.275870\pi$
$314$	6.04030	−	6.78897i	0.340874	−	0.383124i
$315$		0			0
$316$	−15.3904	+	1.80240i	−0.865778	+	0.101393i
$317$	−9.40153	−	16.2839i	−0.528043	−	0.914597i	−0.999466	−	0.0326894i	$-0.989593\pi$
$317$	−9.40153	−	16.2839i	−0.528043	−	0.914597i	0.471423	−	0.881907i	$-0.343741\pi$
$318$	6.31149	−	2.09219i	0.353931	−	0.117324i
$319$	−6.37538	−	3.68083i	−0.356953	−	0.206087i
$320$		0			0
$321$			18.8264i			1.05079i
$322$	−8.08480	+	4.96124i	−0.450548	+	0.276479i
$323$			24.4564i			1.36079i
$324$	−9.99530	+	7.44473i	−0.555295	+	0.413596i
$325$		0			0
$326$	−8.22287	−	24.8059i	−0.455423	−	1.37387i
$327$	−10.3481	−	17.9234i	−0.572250	−	0.991167i
$328$	−6.16035	−	4.31042i	−0.340149	−	0.238003i
$329$	−2.57448	+	2.41723i	−0.141936	+	0.133266i
$330$		0			0
$331$	−11.3353	+	6.54441i	−0.623042	+	0.359713i	−0.778052	−	0.628199i	$-0.783792\pi$
$331$	−11.3353	+	6.54441i	−0.623042	+	0.359713i	0.155010	+	0.987913i	$0.450459\pi$
$332$	19.2794	+	8.31117i	1.05809	+	0.456135i
$333$	13.4033	−	23.2152i	0.734497	−	1.27219i
$334$	−0.522752	+	2.53313i	−0.0286037	+	0.138607i
$335$		0			0
$336$	−12.2830	−	24.5770i	−0.670091	−	1.34079i
$337$	−11.7319			−0.639079			−0.319539	−	0.947573i	$-0.603528\pi$
$337$	−11.7319			−0.639079			−0.319539	+	0.947573i	$0.603528\pi$
$338$	−3.52431	+	17.0780i	−0.191697	+	0.928920i
$339$	9.88640	−	17.1238i	0.536956	−	0.930035i
$340$		0			0
$341$	−5.96388	+	3.44325i	−0.322962	+	0.186462i
$342$	−13.0667	−	11.6257i	−0.706566	−	0.628648i
$343$	−11.8019	−	14.2729i	−0.637245	−	0.770661i
$344$	5.55485	+	3.88675i	0.299498	+	0.209560i
$345$		0			0
$346$	−6.78580	−	20.4707i	−0.364807	−	1.10051i
$347$	3.82065	+	2.20585i	0.205103	+	0.118416i	0.599034	−	0.800724i	$-0.295552\pi$
$347$	3.82065	+	2.20585i	0.205103	+	0.118416i	−0.393930	+	0.919140i	$0.628885\pi$
$348$	8.50894	−	6.33765i	0.456127	−	0.339734i
$349$			18.3479i			0.982142i	0.871120	+	0.491071i	$0.163394\pi$
$349$			18.3479i			0.982142i	−0.871120	+	0.491071i	$0.836606\pi$
$350$		0			0
$351$		−	1.57246i		−	0.0839316i
$352$	20.3713	−	0.604231i	1.08579	−	0.0322056i
$353$	10.1742	+	5.87406i	0.541516	+	0.312645i	0.745693	−	0.666289i	$-0.232118\pi$
$353$	10.1742	+	5.87406i	0.541516	+	0.312645i	−0.204177	+	0.978934i	$0.565452\pi$
$354$	−6.66156	+	2.20823i	−0.354058	+	0.117366i
$355$		0			0
$356$	−21.0824	+	2.46899i	−1.11736	+	0.130856i
$357$	34.7749	+	37.0373i	1.84048	+	1.96022i
$358$	−11.7852	+	13.2459i	−0.622868	+	0.700070i
$359$	0.171388	−	0.0989510i	0.00904552	−	0.00522243i	−0.495470	−	0.868625i	$-0.665004\pi$
$359$	0.171388	−	0.0989510i	0.00904552	−	0.00522243i	0.504516	+	0.863402i	$0.331671\pi$
$360$		0			0
$361$	4.03326	−	6.98581i	0.212277	−	0.367674i
$362$	−11.1057	−	2.29184i	−0.583703	−	0.120456i
$363$	−5.14002			−0.269781
$364$	−4.26251	−	0.761178i	−0.223416	−	0.0398966i
$365$		0			0
$366$	35.1524	+	7.25426i	1.83745	+	0.379186i
$367$	3.76412	−	6.51964i	0.196485	−	0.340323i	−0.750901	−	0.660415i	$-0.770381\pi$
$367$	3.76412	−	6.51964i	0.196485	−	0.340323i	0.947386	+	0.320092i	$0.103714\pi$
$368$	9.71590	+	2.90398i	0.506476	+	0.151380i
$369$	−8.61028	+	4.97115i	−0.448233	+	0.258787i
$370$		0			0
$371$	−4.58686	−	1.38524i	−0.238138	−	0.0719182i
$372$	−1.15444	−	9.85761i	−0.0598550	−	0.511093i
$373$	15.5696	+	26.9674i	0.806164	+	1.39632i	0.915503	+	0.402312i	$0.131793\pi$
$373$	15.5696	+	26.9674i	0.806164	+	1.39632i	−0.109339	+	0.994005i	$0.534873\pi$
$374$	−35.7704	+	11.8575i	−1.84964	+	0.613137i
$375$		0			0
$376$	3.76100	+	0.327763i	0.193959	+	0.0169031i
$377$		−	1.67203i		−	0.0861140i
$378$	−7.18760	+	0.192651i	−0.369690	+	0.00990891i
$379$		−	16.3396i		−	0.839307i	−0.907684	−	0.419654i	$-0.862152\pi$
$379$		−	16.3396i		−	0.839307i	0.907684	−	0.419654i	$-0.137848\pi$
$380$		0			0
$381$	19.7437	+	11.3990i	1.01150	+	0.583990i
$382$	3.00782	+	9.07366i	0.153893	+	0.464249i
$383$	−4.42434	−	7.66318i	−0.226073	−	0.391570i	0.730568	−	0.682840i	$-0.239256\pi$
$383$	−4.42434	−	7.66318i	−0.226073	−	0.391570i	−0.956641	+	0.291270i	$0.905922\pi$
$384$	−10.8230	+	27.3058i	−0.552307	+	1.39344i
$385$		0			0
$386$	2.49351	+	2.21853i	0.126916	+	0.112920i
$387$	7.76397	−	4.48253i	0.394665	−	0.227860i
$388$	5.79562	−	13.4441i	0.294228	−	0.682520i
$389$	4.67264	−	8.09325i	0.236912	−	0.410344i	−0.722915	−	0.690937i	$-0.757198\pi$
$389$	4.67264	−	8.09325i	0.236912	−	0.410344i	0.959827	+	0.280594i	$0.0905313\pi$
$390$		0			0
$391$	−18.7507			−0.948263
$392$	−2.95707	+	19.5769i	−0.149354	+	0.988784i
$393$	34.7612			1.75347
$394$	5.80806	−	28.1445i	0.292606	−	1.41790i
$395$		0			0
$396$	10.6687	−	24.7483i	0.536125	−	1.24365i
$397$	17.5826	−	10.1513i	0.882446	−	0.509480i	0.0109817	−	0.999940i	$-0.496504\pi$
$397$	17.5826	−	10.1513i	0.882446	−	0.509480i	0.871464	+	0.490459i	$0.163171\pi$
$398$	−12.1063	−	10.7712i	−0.606831	−	0.539912i
$399$	5.18470	+	22.1128i	0.259559	+	1.10702i
$400$		0			0
$401$	5.54334	+	9.60135i	0.276821	+	0.479469i	0.970593	−	0.240726i	$-0.0773857\pi$
$401$	5.54334	+	9.60135i	0.276821	+	0.479469i	−0.693772	+	0.720195i	$0.744052\pi$
$402$	10.7003	+	32.2796i	0.533684	+	1.60996i
$403$	−1.35456	−	0.782054i	−0.0674753	−	0.0389569i
$404$	7.59561	+	10.1979i	0.377896	+	0.507363i
$405$		0			0
$406$	−7.64274	+	0.204851i	−0.379303	+	0.0101666i
$407$		−	25.8216i		−	1.27993i
$408$	4.71530	−	54.1067i	0.233442	−	2.67868i
$409$	−5.09812	−	2.94340i	−0.252086	−	0.145542i	0.368633	−	0.929575i	$-0.379826\pi$
$409$	−5.09812	−	2.94340i	−0.252086	−	0.145542i	−0.620719	+	0.784033i	$0.713159\pi$
$410$		0			0
$411$	6.78145	+	11.7458i	0.334504	+	0.579378i
$412$	0.237769	+	2.03028i	0.0117140	+	0.100025i
$413$	4.84127	+	1.46208i	0.238223	+	0.0719441i
$414$	8.91343	−	10.0182i	0.438071	−	0.492369i
$415$		0			0
$416$	2.43229	+	3.93837i	0.119253	+	0.193094i
$417$	28.4856	−	49.3385i	1.39495	−	2.41612i
$418$	−16.4996	−	3.40495i	−0.807020	−	0.166542i
$419$	16.7262			0.817126			0.408563	−	0.912730i	$-0.366030\pi$
$419$	16.7262			0.817126			0.408563	+	0.912730i	$0.366030\pi$
$420$		0			0
$421$	−1.18823			−0.0579109			−0.0289555	−	0.999581i	$-0.509218\pi$
$421$	−1.18823			−0.0579109			−0.0289555	+	0.999581i	$0.509218\pi$
$422$	−30.5602	−	6.30659i	−1.48765	−	0.307000i
$423$	2.49611	−	4.32339i	0.121365	−	0.210210i
$424$	2.16635	+	4.64165i	0.105207	+	0.225418i
$425$		0			0
$426$	−3.37824	+	3.79696i	−0.163676	+	0.183963i
$427$	−17.7042	−	18.8560i	−0.856767	−	0.912506i
$428$	−14.4047	+	1.68696i	−0.696276	+	0.0815421i
$429$	−3.82687	−	6.62833i	−0.184763	−	0.320019i
$430$		0			0
$431$	20.8669	+	12.0475i	1.00512	+	0.580307i	0.909760	−	0.415135i	$-0.136266\pi$
$431$	20.8669	+	12.0475i	1.00512	+	0.580307i	0.0953622	+	0.995443i	$0.469599\pi$
$432$	5.27740	+	5.58867i	0.253909	+	0.268885i
$433$		−	14.9805i		−	0.719916i	−0.932968	−	0.359958i	$-0.882791\pi$
$433$		−	14.9805i		−	0.719916i	0.932968	−	0.359958i	$-0.117209\pi$
$434$	−3.40876	+	6.28741i	−0.163626	+	0.301805i
$435$		0			0
$436$	12.7865	−	9.52369i	0.612363	−	0.456102i
$437$	−7.25962	−	4.19134i	−0.347275	−	0.200499i
$438$	8.54465	+	25.7766i	0.408279	+	1.23165i
$439$	8.66266	+	15.0042i	0.413446	+	0.716110i	0.995264	−	0.0972091i	$-0.0309916\pi$
$439$	8.66266	+	15.0042i	0.413446	+	0.716110i	−0.581818	+	0.813319i	$0.697658\pi$
$440$		0			0
$441$	21.8047	+	14.4919i	1.03832	+	0.690090i
$442$	−6.39456	−	5.68938i	−0.304158	−	0.270616i
$443$	21.8520	−	12.6162i	1.03822	−	0.599416i	0.118890	−	0.992907i	$-0.462066\pi$
$443$	21.8520	−	12.6162i	1.03822	−	0.599416i	0.919328	+	0.393492i	$0.128733\pi$
$444$	34.1745	+	14.7323i	1.62185	+	0.699164i
$445$		0			0
$446$	−6.73901	+	32.6556i	−0.319101	+	1.54629i
$447$	62.1779			2.94091
$448$	17.7040	−	11.6003i	0.836436	−	0.548064i
$449$	−7.06145			−0.333251			−0.166625	−	0.986020i	$-0.553287\pi$
$449$	−7.06145			−0.333251			−0.166625	+	0.986020i	$0.553287\pi$
$450$		0			0
$451$	−4.78848	+	8.29390i	−0.225481	+	0.390544i
$452$	13.9878	+	6.03001i	0.657931	+	0.283628i
$453$	−15.7556	+	9.09653i	−0.740265	+	0.427392i
$454$	−22.1103	−	19.6720i	−1.03769	−	0.923255i
$455$		0			0
$456$	13.9201	−	19.8942i	0.651867	−	0.931633i
$457$	9.44078	+	16.3519i	0.441621	+	0.764910i	0.997810	−	0.0661459i	$-0.0210703\pi$
$457$	9.44078	+	16.3519i	0.441621	+	0.764910i	−0.556189	+	0.831056i	$0.687737\pi$
$458$	−2.30571	−	6.95562i	−0.107739	−	0.325015i
$459$	−12.3089	−	7.10656i	−0.574531	−	0.331706i
$460$		0			0
$461$		−	34.6087i		−	1.61189i	−0.591992	−	0.805944i	$-0.701658\pi$
$461$		−	34.6087i		−	1.61189i	0.591992	−	0.805944i	$-0.298342\pi$
$462$	−29.8288	+	18.3044i	−1.38776	+	0.851600i
$463$			15.0235i			0.698202i	0.937085	+	0.349101i	$0.113513\pi$
$463$			15.0235i			0.698202i	−0.937085	+	0.349101i	$0.886487\pi$
$464$	5.61159	+	5.94257i	0.260511	+	0.275877i
$465$		0			0
$466$	27.8804	−	9.24206i	1.29154	−	0.428130i
$467$	−12.7195	−	22.0309i	−0.588590	−	1.01947i	−0.994417	−	0.105518i	$-0.966350\pi$
$467$	−12.7195	−	22.0309i	−0.588590	−	1.01947i	0.405828	−	0.913950i	$-0.366983\pi$
$468$	6.07950	−	0.711981i	0.281025	−	0.0329113i
$469$	7.08472	−	23.4591i	0.327142	−	1.08324i
$470$		0			0
$471$	14.4470	−	8.34096i	0.665681	−	0.384331i
$472$	−2.28650	−	4.89910i	−0.105245	−	0.225499i
$473$	4.31782	−	7.47869i	0.198534	−	0.343871i
$474$	−27.8595	−	5.74925i	−1.27963	−	0.264072i
$475$		0			0
$476$	−25.2223	+	29.9261i	−1.15606	+	1.37166i
$477$	6.77350			0.310137
$478$	−29.2638	−	6.03905i	−1.33849	−	0.276220i
$479$	−10.2844	+	17.8131i	−0.469905	+	0.813900i	−0.999408	−	0.0344084i	$-0.989045\pi$
$479$	−10.2844	+	17.8131i	−0.469905	+	0.813900i	0.529502	+	0.848308i	$0.322379\pi$
$480$		0			0
$481$	5.07906	−	2.93239i	0.231585	−	0.133706i
$482$	−1.70906	+	1.92089i	−0.0778453	+	0.0874939i
$483$	−16.9538	+	3.97510i	−0.771426	+	0.180873i
$484$	−0.460576	−	3.93279i	−0.0209353	−	0.178763i
$485$		0			0
$486$	−29.4563	+	9.76443i	−1.33616	+	0.442924i
$487$	−25.1658	−	14.5295i	−1.14037	−	0.658394i	−0.193849	−	0.981031i	$-0.562097\pi$
$487$	−25.1658	−	14.5295i	−1.14037	−	0.658394i	−0.946522	+	0.322638i	$0.895430\pi$
$488$	−2.40060	+	27.5462i	−0.108670	+	1.24696i
$489$		−	47.9749i		−	2.16950i
$490$		0			0
$491$			9.51815i			0.429548i	0.976664	+	0.214774i	$0.0689015\pi$
$491$			9.51815i			0.429548i	−0.976664	+	0.214774i	$0.931098\pi$
$492$	−8.24481	−	11.0695i	−0.371705	−	0.499051i
$493$	−13.0884	−	7.55657i	−0.589470	−	0.340331i
$494$	−1.20400	−	3.63210i	−0.0541706	−	0.163416i
$495$		0			0
$496$	7.43893	−	1.76660i	0.334018	−	0.0793226i
$497$	3.56561	−	0.836015i	0.159940	−	0.0375004i
$498$	28.7943	+	25.6189i	1.29030	+	1.14801i
$499$	−17.4855	+	10.0953i	−0.782760	+	0.451927i	−0.837407	−	0.546579i	$-0.815930\pi$
$499$	−17.4855	+	10.0953i	−0.782760	+	0.451927i	0.0546477	+	0.998506i	$0.482596\pi$
$500$		0			0
$501$	−2.37413	+	4.11211i	−0.106068	+	0.183716i
$502$	−4.00688	+	19.4164i	−0.178836	+	0.866595i
$503$	13.3134			0.593616			0.296808	−	0.954937i	$-0.404078\pi$
$503$	13.3134			0.593616			0.296808	+	0.954937i	$0.404078\pi$
$504$	−3.99925	−	27.7018i	−0.178141	−	1.23394i
$505$		0			0
$506$	2.61057	−	12.6502i	0.116054	−	0.562370i
$507$	−16.0060	+	27.7233i	−0.710853	+	1.23123i
$508$	−6.95261	+	16.1279i	−0.308472	+	0.715562i
$509$	−12.4294	+	7.17613i	−0.550925	+	0.318077i	−0.749495	−	0.662010i	$-0.769704\pi$
$509$	−12.4294	+	7.17613i	−0.550925	+	0.318077i	0.198570	+	0.980087i	$0.436370\pi$
$510$		0			0
$511$	5.65744	−	18.7331i	0.250270	−	0.828703i
$512$	−21.8623	−	5.83424i	−0.966188	−	0.257839i
$513$	−3.17706	−	5.50282i	−0.140270	−	0.242956i
$514$	−7.95298	−	23.9917i	−0.350791	−	1.05823i
$515$		0			0
$516$	7.43442	+	9.98147i	0.327282	+	0.439410i
$517$		−	4.80879i		−	0.211490i
$518$	−14.0260	−	22.8568i	−0.616269	−	1.00427i
$519$		−	39.5906i		−	1.73783i
$520$		0			0
$521$	−31.9571	−	18.4505i	−1.40007	−	0.808330i	−0.405669	−	0.914020i	$-0.632961\pi$
$521$	−31.9571	−	18.4505i	−1.40007	−	0.808330i	−0.994399	+	0.105690i	$0.966295\pi$
$522$	10.2591	−	3.40079i	0.449030	−	0.148848i
$523$	−9.07509	−	15.7185i	−0.396826	−	0.687323i	0.596506	−	0.802608i	$-0.296555\pi$
$523$	−9.07509	−	15.7185i	−0.396826	−	0.687323i	−0.993332	+	0.115285i	$0.963222\pi$
$524$	3.11481	+	26.5969i	0.136071	+	1.16189i
$525$		0			0
$526$	20.5837	−	23.1349i	0.897490	−	1.00873i
$527$	−12.2436	+	7.06883i	−0.533338	+	0.307923i
$528$	35.8467	+	10.7142i	1.56003	+	0.466276i
$529$	−8.28651	+	14.3526i	−0.360283	+	0.624028i
$530$		0			0
$531$	−7.14919			−0.310248
$532$	−16.4546	+	5.94841i	−0.713397	+	0.257896i
$533$	−2.17519			−0.0942178
$534$	−38.1630	−	7.87554i	−1.65147	−	0.340808i
$535$		0			0
$536$	−23.7393	+	11.0796i	−1.02538	+	0.478566i
$537$	−28.1874	+	16.2740i	−1.21638	+	0.702276i
$538$	2.70999	−	3.04588i	0.116836	−	0.131317i
$539$	25.1693	+	1.58743i	1.08412	+	0.0683756i
$540$		0			0
$541$	9.37629	+	16.2402i	0.403118	+	0.698221i	0.994100	−	0.108463i	$-0.0345930\pi$
$541$	9.37629	+	16.2402i	0.403118	+	0.698221i	−0.590982	+	0.806685i	$0.701260\pi$
$542$	22.7612	−	7.54509i	0.977678	−	0.324090i
$543$	−18.0283	−	10.4086i	−0.773667	−	0.446677i
$544$	41.8213	−	1.24046i	1.79307	−	0.0531842i
$545$		0			0
$546$	−6.98790	−	3.78854i	−0.299055	−	0.162135i
$547$			34.1580i			1.46049i	0.683185	+	0.730246i	$0.260594\pi$
$547$			34.1580i			1.46049i	−0.683185	+	0.730246i	$0.739406\pi$
$548$	−8.37943	+	6.24119i	−0.357952	+	0.266610i
$549$	31.6653	+	18.2820i	1.35144	+	0.780256i
$550$		0			0
$551$	−3.37824	−	5.85128i	−0.143918	−	0.249273i
$552$	15.2529	+	10.6725i	0.649206	+	0.454252i
$553$	14.0312	+	14.9440i	0.596667	+	0.635485i
$554$	28.3702	+	25.2416i	1.20534	+	1.07241i
$555$		0			0
$556$	40.3029	+	17.3742i	1.70923	+	0.736831i
$557$	−20.2183	+	35.0192i	−0.856679	+	1.48381i	0.0184005	+	0.999831i	$0.494143\pi$
$557$	−20.2183	+	35.0192i	−0.856679	+	1.48381i	−0.875079	+	0.483980i	$0.839191\pi$
$558$	2.04340	−	9.90183i	0.0865041	−	0.419178i
$559$	1.96139			0.0829579
$560$		0			0
$561$	−69.1805			−2.92080
$562$	−7.13120	+	34.5561i	−0.300811	+	1.45766i
$563$	−0.159465	+	0.276201i	−0.00672065	+	0.0116405i	−0.869366	−	0.494168i	$-0.835473\pi$
$563$	−0.159465	+	0.276201i	−0.00672065	+	0.0116405i	0.862646	+	0.505809i	$0.168806\pi$
$564$	6.36435	+	2.74361i	0.267987	+	0.115527i
$565$		0			0
$566$	−10.3946	−	9.24835i	−0.436920	−	0.388737i
$567$	15.7831	+	4.76655i	0.662830	+	0.200176i
$568$	−3.20788	−	2.24457i	−0.134600	−	0.0941800i
$569$	15.3058	+	26.5104i	0.641651	+	1.11137i	0.985064	+	0.172188i	$0.0550836\pi$
$569$	15.3058	+	26.5104i	0.641651	+	1.11137i	−0.343413	+	0.939184i	$0.611583\pi$
$570$		0			0
$571$	7.35081	+	4.24399i	0.307622	+	0.177606i	0.645862	−	0.763454i	$-0.276498\pi$
$571$	7.35081	+	4.24399i	0.307622	+	0.177606i	−0.338240	+	0.941060i	$0.609832\pi$
$572$	4.72864	−	3.52200i	0.197714	−	0.147262i
$573$			17.5486i			0.733103i
$574$	0.266495	+	9.94264i	0.0111233	+	0.414998i
$575$		0			0
$576$	−19.2177	+	22.9342i	−0.800735	+	0.955591i
$577$	−2.91419	−	1.68251i	−0.121319	−	0.0700438i	0.438112	−	0.898920i	$-0.355647\pi$
$577$	−2.91419	−	1.68251i	−0.121319	−	0.0700438i	−0.559432	+	0.828876i	$0.688981\pi$
$578$	−50.6145	+	16.7781i	−2.10529	+	0.697879i
$579$	3.06354	+	5.30620i	0.127316	+	0.220518i
$580$		0			0
$581$	−6.33993	−	27.0399i	−0.263025	−	1.12180i
$582$	17.8648	−	20.0791i	0.740520	−	0.832305i
$583$	5.65048	−	3.26230i	0.234019	−	0.135111i
$584$	−18.9568	+	8.84752i	−0.784439	+	0.366113i
$585$		0			0
$586$	32.4151	+	6.68938i	1.33906	+	0.276336i
$587$	−2.02359			−0.0835225			−0.0417613	−	0.999128i	$-0.513297\pi$
$587$	−2.02359			−0.0835225			−0.0417613	+	0.999128i	$0.513297\pi$
$588$	−16.4610	+	32.4054i	−0.678842	+	1.33638i
$589$	−6.32038			−0.260427
$590$		0			0
$591$	26.3779	−	45.6878i	1.08504	−	1.87935i
$592$	−8.20992	+	27.4681i	−0.337426	+	1.12893i
$593$	−23.2318	+	13.4129i	−0.954016	+	0.550802i	−0.894326	−	0.447415i	$-0.852345\pi$
$593$	−23.2318	+	13.4129i	−0.954016	+	0.550802i	−0.0596901	+	0.998217i	$0.519011\pi$
$594$	6.50817	−	7.31483i	0.267033	−	0.300131i
$595$		0			0
$596$	5.57151	+	47.5743i	0.228218	+	1.94872i
$597$	−14.8738	−	25.7622i	−0.608744	−	1.05438i
$598$	2.78473	−	0.923107i	0.113876	−	0.0377487i
$599$	−32.0964	−	18.5309i	−1.31143	−	0.757152i	−0.329093	−	0.944297i	$-0.606743\pi$
$599$	−32.0964	−	18.5309i	−1.31143	−	0.757152i	−0.982332	+	0.187146i	$0.940076\pi$
$600$		0			0
$601$		−	1.27911i		−	0.0521761i	−0.999660	−	0.0260880i	$-0.991695\pi$
$601$		−	1.27911i		−	0.0521761i	0.999660	−	0.0260880i	$-0.00830503\pi$
$602$	−0.240301	−	8.96537i	−0.00979396	−	0.365401i
$603$			34.6425i			1.41075i
$604$	−8.37184	−	11.2400i	−0.340645	−	0.457351i
$605$		0			0
$606$	7.34501	+	22.1576i	0.298371	+	0.900093i
$607$	11.3045	+	19.5800i	0.458836	+	0.794727i	0.998900	−	0.0468970i	$-0.0149333\pi$
$607$	11.3045	+	19.5800i	0.458836	+	0.794727i	−0.540064	+	0.841624i	$0.681600\pi$
$608$	16.4690	+	8.86805i	0.667907	+	0.359647i
$609$	−13.4361	−	4.05773i	−0.544458	−	0.164428i
$610$		0			0
$611$	0.945877	−	0.546102i	0.0382661	−	0.0220929i
$612$	21.9024	−	50.8070i	0.885353	−	2.05375i
$613$	1.50973	−	2.61492i	0.0609773	−	0.105616i	−0.833925	−	0.551877i	$-0.813912\pi$
$613$	1.50973	−	2.61492i	0.0609773	−	0.105616i	0.894903	+	0.446262i	$0.147245\pi$
$614$	0.624606	−	3.02669i	0.0252071	−	0.122147i
$615$		0			0
$616$	−16.6781	−	21.1828i	−0.671982	−	0.853479i
$617$	14.3344			0.577081			0.288540	−	0.957468i	$-0.406830\pi$
$617$	14.3344			0.577081			0.288540	+	0.957468i	$0.406830\pi$
$618$	−0.758431	+	3.67517i	−0.0305086	+	0.147837i
$619$	−10.8987	+	18.8771i	−0.438055	+	0.758733i	−0.997539	−	0.0701078i	$-0.977666\pi$
$619$	−10.8987	+	18.8771i	−0.438055	+	0.758733i	0.559485	+	0.828841i	$0.310999\pi$
$620$		0			0
$621$	4.21901	−	2.43584i	0.169303	−	0.0977471i
$622$	−30.5347	−	27.1674i	−1.22433	−	1.08931i
$623$	19.2205	+	20.4709i	0.770052	+	0.820150i
$624$	1.96342	+	8.26771i	0.0785997	+	0.330973i
$625$		0			0
$626$	2.82701	+	8.52821i	0.112990	+	0.340856i
$627$	−26.7843	−	15.4639i	−1.06966	−	0.617570i
$628$	7.67646	+	10.3064i	0.306324	+	0.411271i
$629$		−	53.0106i		−	2.11367i
$630$		0			0
$631$		−	15.1512i		−	0.603160i	−0.953441	−	0.301580i	$-0.902486\pi$
$631$		−	15.1512i		−	0.603160i	0.953441	−	0.301580i	$-0.0975140\pi$
$632$	1.90256	−	21.8313i	0.0756797	−	0.868404i
$633$	−49.6094	−	28.6420i	−1.97180	−	1.13842i
$634$	25.2409	−	8.36708i	1.00244	−	0.332299i
$635$		0			0
$636$	1.09378	+	9.33959i	0.0433710	+	0.370339i
$637$	2.54606	+	5.13101i	0.100879	+	0.203298i
$638$	6.92029	−	7.77803i	0.273977	−	0.307935i
$639$	−4.48363	+	2.58863i	−0.177370	+	0.102404i
$640$		0			0
$641$	−14.9960	+	25.9739i	−0.592308	+	1.02591i	0.401613	+	0.915809i	$0.368450\pi$
$641$	−14.9960	+	25.9739i	−0.592308	+	1.02591i	−0.993921	+	0.110098i	$0.964884\pi$
$642$	−26.0751	−	5.38101i	−1.02910	−	0.212372i
$643$	1.63196			0.0643583			0.0321792	−	0.999482i	$-0.489755\pi$
$643$	1.63196			0.0643583			0.0321792	+	0.999482i	$0.489755\pi$
$644$	−4.56063	−	12.6157i	−0.179714	−	0.497129i
$645$		0			0
$646$	−33.8728	−	6.99020i	−1.33271	−	0.275026i
$647$	−16.3832	+	28.3765i	−0.644090	+	1.11560i	0.340421	+	0.940273i	$0.389430\pi$
$647$	−16.3832	+	28.3765i	−0.644090	+	1.11560i	−0.984511	+	0.175323i	$0.943903\pi$
$648$	−7.45428	−	15.9717i	−0.292832	−	0.627426i
$649$	−5.96388	+	3.44325i	−0.234103	+	0.135159i
$650$		0			0
$651$	−9.57170	+	8.98703i	−0.375145	+	0.352229i
$652$	36.7071	−	4.29883i	1.43756	−	0.168355i
$653$	11.2646	+	19.5109i	0.440819	+	0.763521i	0.997750	−	0.0670377i	$-0.0213548\pi$
$653$	11.2646	+	19.5109i	0.440819	+	0.763521i	−0.556932	+	0.830558i	$0.688021\pi$
$654$	27.7822	−	9.20948i	1.08637	−	0.360119i
$655$		0			0
$656$	7.73083	−	7.30025i	0.301838	−	0.285027i
$657$			27.6635i			1.07925i
$658$	−2.61208	−	4.25663i	−0.101830	−	0.165941i
$659$		−	19.2525i		−	0.749969i	−0.927031	−	0.374985i	$-0.877648\pi$
$659$		−	19.2525i		−	0.749969i	0.927031	−	0.374985i	$-0.122352\pi$
$660$		0			0
$661$	30.1079	+	17.3828i	1.17106	+	0.676113i	0.953930	−	0.300030i	$-0.0969966\pi$
$661$	30.1079	+	17.3828i	1.17106	+	0.676113i	0.217132	+	0.976142i	$0.430330\pi$
$662$	−5.82433	−	17.5702i	−0.226369	−	0.682885i
$663$	−7.85638	−	13.6077i	−0.305117	−	0.528477i
$664$	−17.0217	+	24.3270i	−0.660570	+	0.944071i
$665$		0			0
$666$	28.3228	+	25.1994i	1.09749	+	0.976458i
$667$	4.48617	−	2.59009i	0.173705	−	0.100289i
$668$	−3.35904	−	1.44805i	−0.129965	−	0.0560268i
$669$	−30.6059	+	53.0110i	−1.18329	+	2.04952i
$670$		0			0
$671$	35.2205			1.35967
$672$	37.5506	−	9.98759i	1.44855	−	0.385280i
$673$	−42.6368			−1.64353			−0.821764	−	0.569827i	$-0.807010\pi$
$673$	−42.6368			−1.64353			−0.821764	+	0.569827i	$0.807010\pi$
$674$	3.35325	−	16.2491i	0.129162	−	0.625890i
$675$		0			0
$676$	−22.6462	−	9.76255i	−0.871007	−	0.375483i
$677$	−1.54611	+	0.892648i	−0.0594219	+	0.0343073i	−0.529417	−	0.848362i	$-0.677589\pi$
$677$	−1.54611	+	0.892648i	−0.0594219	+	0.0343073i	0.469995	+	0.882669i	$0.344256\pi$
$678$	20.8911	+	18.5873i	0.802319	+	0.713842i
$679$	−18.8557	+	4.42102i	−0.723615	+	0.169663i
$680$		0			0
$681$	−27.1648	−	47.0509i	−1.04096	−	1.80299i
$682$	−3.06439	−	9.24431i	−0.117341	−	0.353983i
$683$	7.45237	+	4.30263i	0.285157	+	0.164636i	0.635756	−	0.771890i	$-0.280689\pi$
$683$	7.45237	+	4.30263i	0.285157	+	0.164636i	−0.350599	+	0.936526i	$0.614022\pi$
$684$	19.8367	−	14.7749i	0.758477	−	0.564931i
$685$		0			0
$686$	23.1416	−	12.2665i	0.883549	−	0.468338i
$687$		−	13.4523i		−	0.513236i
$688$	−6.97097	+	6.58271i	−0.265766	+	0.250963i
$689$	1.28338	+	0.740957i	0.0488927	+	0.0282282i
$690$		0			0
$691$	−20.1511	−	34.9027i	−0.766583	−	1.32776i	−0.939405	−	0.342808i	$-0.888622\pi$
$691$	−20.1511	−	34.9027i	−0.766583	−	1.32776i	0.172822	−	0.984953i	$-0.444711\pi$
$692$	30.2920	−	3.54755i	1.15153	−	0.134858i
$693$	−34.7101	+	8.13834i	−1.31853	+	0.309150i
$694$	−4.14720	+	4.66123i	−0.157426	+	0.176938i
$695$		0			0
$696$	6.34578	+	13.5966i	0.240536	+	0.515377i
$697$	−9.83053	+	17.0270i	−0.372358	+	0.644943i
$698$	−25.4124	−	5.24425i	−0.961874	−	0.198498i
$699$	53.9212			2.03949
$700$		0			0
$701$	37.3051			1.40899			0.704497	−	0.709707i	$-0.251172\pi$
$701$	37.3051			1.40899			0.704497	+	0.709707i	$0.251172\pi$
$702$	2.17790	+	0.449444i	0.0821995	+	0.0169632i
$703$	11.8495	−	20.5239i	0.446911	−	0.774072i
$704$	−4.98570	+	28.3875i	−0.187906	+	1.06990i
$705$		0			0
$706$	−11.0438	+	12.4126i	−0.415637	+	0.467154i
$707$	4.86315	−	16.1030i	0.182898	−	0.605617i
$708$	−1.15444	−	9.85761i	−0.0433866	−	0.370472i
$709$	−4.02866	−	6.97784i	−0.151299	−	0.262058i	0.780406	−	0.625273i	$-0.215012\pi$
$709$	−4.02866	−	6.97784i	−0.151299	−	0.262058i	−0.931705	+	0.363215i	$0.881679\pi$
$710$		0			0
$711$	−25.0958	−	14.4891i	−0.941168	−	0.543383i
$712$	2.60620	−	29.9054i	0.0976714	−	1.12075i
$713$		−	4.84582i		−	0.181477i
$714$	−61.2371	+	37.5782i	−2.29174	+	1.40633i
$715$		0			0
$716$	−14.9775	−	20.1089i	−0.559737	−	0.751503i
$717$	−47.5049	−	27.4269i	−1.77410	−	1.02428i
$718$	0.0880634	+	0.265660i	0.00328650	+	0.00991434i
$719$	−5.87241	−	10.1713i	−0.219004	−	0.379326i	0.735500	−	0.677525i	$-0.236947\pi$
$719$	−5.87241	−	10.1713i	−0.219004	−	0.379326i	−0.954504	+	0.298199i	$0.903614\pi$
$720$		0			0
$721$	1.97139	−	1.85097i	0.0734184	−	0.0689338i
$722$	8.52275	+	7.58289i	0.317184	+	0.282206i
$723$	−4.08766	+	2.36001i	−0.152022	+	0.0877697i
$724$	6.34853	−	14.7267i	0.235941	−	0.547312i
$725$		0			0
$726$	1.46913	−	7.11908i	0.0545247	−	0.264214i
$727$	33.3549			1.23706			0.618532	−	0.785760i	$-0.287728\pi$
$727$	33.3549			1.23706			0.618532	+	0.785760i	$0.287728\pi$
$728$	2.27258	−	5.68614i	0.0842273	−	0.210742i
$729$	−38.2742			−1.41756
$730$		0			0
$731$	8.86429	−	15.3534i	0.327857	−	0.567866i
$732$	−20.0947	+	46.6137i	−0.742722	+	1.72289i
$733$	9.95934	−	5.75003i	0.367856	−	0.212382i	−0.304665	−	0.952460i	$-0.598545\pi$
$733$	9.95934	−	5.75003i	0.367856	−	0.212382i	0.672522	+	0.740077i	$0.265211\pi$
$734$	7.95403	+	7.07688i	0.293588	+	0.261212i
$735$		0			0
$736$	−6.79912	+	12.6268i	−0.250619	+	0.465429i
$737$	16.6848	+	28.8989i	0.614593	+	1.06451i
$738$	−4.42417	−	13.3463i	−0.162856	−	0.491286i
$739$	9.70301	+	5.60203i	0.356931	+	0.206074i	0.667734	−	0.744400i	$-0.267265\pi$
$739$	9.70301	+	5.60203i	0.356931	+	0.206074i	−0.310803	+	0.950474i	$0.600598\pi$
$740$		0			0
$741$		−	7.02455i		−	0.258053i
$742$	3.22963	−	5.95700i	0.118564	−	0.218688i
$743$		−	43.7950i		−	1.60668i	−0.595520	−	0.803341i	$-0.703054\pi$
$743$		−	43.7950i		−	1.60668i	0.595520	−	0.803341i	$-0.296946\pi$
$744$	13.9830	+	1.21859i	0.512643	+	0.0446759i
$745$		0			0
$746$	−41.8007	+	13.8565i	−1.53043	+	0.507322i
$747$	19.6309	+	34.0017i	0.718256	+	1.24406i
$748$	−6.19898	−	52.9322i	−0.226657	−	1.93539i
$749$	13.1325	+	13.9869i	0.479852	+	0.511069i
$750$		0			0
$751$	−44.5322	+	25.7107i	−1.62500	+	0.938196i	−0.639450	+	0.768832i	$0.720838\pi$
$751$	−44.5322	+	25.7107i	−1.62500	+	0.938196i	−0.985554	+	0.169364i	$0.945829\pi$
$752$	−1.52894	+	5.11541i	−0.0557547	+	0.186540i
$753$	−18.1976	+	31.5192i	−0.663159	+	1.14862i
$754$	2.31581	+	0.477905i	0.0843369	+	0.0174043i
$755$		0			0
$756$	1.78755	−	10.0101i	0.0650126	−	0.364064i
$757$	−18.1453			−0.659502			−0.329751	−	0.944068i	$-0.606965\pi$
$757$	−18.1453			−0.659502			−0.329751	+	0.944068i	$0.606965\pi$
$758$	22.6308	+	4.67022i	0.821987	+	0.169630i
$759$	11.8562	−	20.5355i	0.430352	−	0.745391i
$760$		0			0
$761$	−28.4860	+	16.4464i	−1.03262	+	0.596181i	−0.917733	−	0.397198i	$-0.869983\pi$
$761$	−28.4860	+	16.4464i	−1.03262	+	0.596181i	−0.114883	+	0.993379i	$0.536649\pi$
$762$	−21.4312	+	24.0875i	−0.776370	+	0.872598i
$763$	−20.1906	−	6.09762i	−0.730950	−	0.220749i
$764$	−13.4270	+	1.57246i	−0.485771	+	0.0568895i
$765$		0			0
$766$	11.8783	−	3.93753i	0.429181	−	0.142269i
$767$	−1.35456	−	0.782054i	−0.0489102	−	0.0282383i
$768$	−34.7259	−	22.7948i	−1.25306	−	0.822535i
$769$			20.8502i			0.751876i	0.926645	+	0.375938i	$0.122679\pi$
$769$			20.8502i			0.751876i	−0.926645	+	0.375938i	$0.877321\pi$
$770$		0			0
$771$		−	46.4003i		−	1.67107i
$772$	−3.78543	+	2.81947i	−0.136241	+	0.101475i
$773$	7.52368	+	4.34380i	0.270608	+	0.156236i	0.629164	−	0.777273i	$-0.283397\pi$
$773$	7.52368	+	4.34380i	0.270608	+	0.156236i	−0.358556	+	0.933508i	$0.616731\pi$
$774$	3.98932	+	12.0345i	0.143393	+	0.432572i
$775$		0			0
$776$	16.9639	+	11.8697i	0.608970	+	0.426099i
$777$	−11.2381	−	47.9306i	−0.403165	−	1.71950i
$778$	9.87384	+	8.78497i	0.353994	+	0.314957i
$779$	−7.61208	+	4.39484i	−0.272731	+	0.157461i
$780$		0			0
$781$	−2.49351	+	4.31888i	−0.0892247	+	0.154542i
$782$	5.35937	−	25.9703i	0.191651	−	0.928694i
$783$	3.92660			0.140325
$784$	−26.2694	−	9.69115i	−0.938193	−	0.346113i
$785$		0			0
$786$	−9.93555	+	48.1453i	−0.354389	+	1.71729i
$787$	18.6062	−	32.2270i	0.663241	−	1.14877i	−0.316518	−	0.948586i	$-0.602514\pi$
$787$	18.6062	−	32.2270i	0.663241	−	1.14877i	0.979759	−	0.200180i	$-0.0641528\pi$
$788$	37.3208	+	16.0887i	1.32950	+	0.573135i
$789$	49.2312	−	28.4237i	1.75268	−	1.01191i
$790$		0			0
$791$	−4.59982	−	19.6183i	−0.163551	−	0.697545i
$792$	31.2277	+	21.8501i	1.10963	+	0.776411i
$793$	3.99976	+	6.92778i	0.142036	+	0.246013i
$794$	9.03437	+	27.2539i	0.320618	+	0.967205i
$795$		0			0
$796$	18.3787	−	13.6889i	0.651415	−	0.485189i
$797$			21.3900i			0.757671i	0.925464	+	0.378835i	$0.123675\pi$
$797$			21.3900i			0.757671i	−0.925464	+	0.378835i	$0.876325\pi$
$798$	−32.1087	+	0.860619i	−1.13664	+	0.0304656i
$799$		−	9.87221i		−	0.349254i
$800$		0			0
$801$	−34.3773	−	19.8477i	−1.21466	−	0.701285i
$802$	−14.8826	+	4.93341i	−0.525522	+	0.174205i
$803$	13.3235	+	23.0770i	0.470176	+	0.814368i
$804$	−47.7666	+	5.59403i	−1.68460	+	0.197286i
$805$		0			0
$806$	1.47033	−	1.65257i	0.0517902	−	0.0582094i
$807$	6.48166	−	3.74219i	0.228165	−	0.131731i
$808$	−16.2954	+	7.60536i	−0.573269	+	0.267556i
$809$	12.1707	−	21.0803i	0.427900	−	0.741144i	−0.568787	−	0.822485i	$-0.692587\pi$
$809$	12.1707	−	21.0803i	0.427900	−	0.741144i	0.996686	+	0.0813411i	$0.0259203\pi$
$810$		0			0
$811$	31.3778			1.10183			0.550913	−	0.834563i	$-0.314280\pi$
$811$	31.3778			1.10183			0.550913	+	0.834563i	$0.314280\pi$
$812$	1.90075	−	10.6440i	0.0667031	−	0.373530i
$813$	44.0206			1.54387
$814$	35.7637	+	7.38041i	1.25352	+	0.258683i
$815$		0			0
$816$	73.5917	+	21.9958i	2.57622	+	0.770006i
$817$	6.86389	−	3.96287i	0.240137	−	0.138643i
$818$	5.53386	−	6.21976i	0.193487	−	0.217469i
$819$	−5.54259	−	5.90317i	−0.193674	−	0.206274i
$820$		0			0
$821$	−0.0785681	−	0.136084i	−0.00274204	−	0.00474936i	0.864651	−	0.502373i	$-0.167539\pi$
$821$	−0.0785681	−	0.136084i	−0.00274204	−	0.00474936i	−0.867393	+	0.497623i	$0.834206\pi$
$822$	−18.2066	+	6.03528i	−0.635027	+	0.210505i
$823$	16.1904	+	9.34753i	0.564362	+	0.325835i	0.754894	−	0.655846i	$-0.227688\pi$
$823$	16.1904	+	9.34753i	0.564362	+	0.325835i	−0.190532	+	0.981681i	$0.561021\pi$
$824$	−2.87995	−	0.250982i	−0.100328	−	0.00874338i
$825$		0			0
$826$	−3.40876	+	6.28741i	−0.118606	+	0.218767i
$827$			35.2960i			1.22736i	0.789554	+	0.613681i	$0.210312\pi$
$827$			35.2960i			1.22736i	−0.789554	+	0.613681i	$0.789688\pi$
$828$	11.3279	+	15.2088i	0.393670	+	0.528542i
$829$	14.2590	+	8.23245i	0.495237	+	0.285925i	0.726744	−	0.686908i	$-0.241033\pi$
$829$	14.2590	+	8.23245i	0.495237	+	0.285925i	−0.231508	+	0.972833i	$0.574366\pi$
$830$		0			0
$831$	34.8558	+	60.3720i	1.20913	+	2.09428i
$832$	−6.14996	+	2.24311i	−0.213211	+	0.0777659i
$833$	51.6713	+	3.25893i	1.79030	+	0.112915i
$834$	60.1934	+	53.5555i	2.08433	+	1.85447i
$835$		0			0
$836$	9.43191	−	21.8792i	0.326209	−	0.756707i
$837$	1.83658	−	3.18105i	0.0634814	−	0.109953i
$838$	−4.78072	+	23.1662i	−0.165147	+	0.800264i
$839$	54.8000			1.89191			0.945953	−	0.324303i	$-0.105130\pi$
$839$	54.8000			1.89191			0.945953	+	0.324303i	$0.105130\pi$
$840$		0			0
$841$	−24.8248			−0.856026
$842$	0.339624	−	1.64574i	0.0117042	−	0.0567158i
$843$	−32.3871	+	56.0960i	−1.11547	+	1.93205i
$844$	17.4696	−	40.5243i	0.601329	−	1.39490i
$845$		0			0
$846$	5.27458	+	4.69291i	0.181344	+	0.161346i
$847$	−3.81872	+	3.58546i	−0.131213	+	0.123198i
$848$	−7.04801	+	1.67376i	−0.242030	+	0.0574773i
$849$	−12.7709	−	22.1199i	−0.438297	−	0.759152i
$850$		0			0
$851$	15.7356	+	9.08496i	0.539410	+	0.311428i
$852$	−4.29332	−	5.76422i	−0.147087	−	0.197479i
$853$			38.9225i			1.33268i	0.745648	+	0.666340i	$0.232140\pi$
$853$			38.9225i			1.33268i	−0.745648	+	0.666340i	$0.767860\pi$
$854$	31.1764	−	19.1314i	1.06683	−	0.654662i
$855$		0			0
$856$	1.78070	−	20.4331i	0.0608631	−	0.698388i
$857$	−25.4206	−	14.6766i	−0.868350	−	0.501342i	−0.00155047	−	0.999999i	$-0.500494\pi$
$857$	−25.4206	−	14.6766i	−0.868350	−	0.501342i	−0.866800	+	0.498657i	$0.833827\pi$
$858$	10.2742	−	3.40580i	0.350757	−	0.116272i
$859$	−23.6874	−	41.0277i	−0.808202	−	1.39985i	−0.914108	−	0.405471i	$-0.867107\pi$
$859$	−23.6874	−	41.0277i	−0.808202	−	1.39985i	0.105905	−	0.994376i	$-0.466226\pi$
$860$		0			0
$861$	−5.27880	+	17.4793i	−0.179901	+	0.595694i
$862$	−22.6504	+	25.4578i	−0.771474	+	0.867095i
$863$	−20.5257	+	11.8505i	−0.698704	+	0.403397i	−0.806865	−	0.590737i	$-0.798837\pi$
$863$	−20.5257	+	11.8505i	−0.698704	+	0.403397i	0.108161	+	0.994133i	$0.465504\pi$
$864$	−9.24887	+	5.71198i	−0.314653	+	0.194326i
$865$		0			0
$866$	20.7484	+	4.28176i	0.705060	+	0.145500i
$867$	−97.8892			−3.32449
$868$	−7.73394	−	6.51832i	−0.262507	−	0.221246i
$869$	−27.9134			−0.946897
$870$		0			0
$871$	−3.78957	+	6.56372i	−0.128405	+	0.222403i
$872$	9.53591	+	20.4318i	0.322927	+	0.691908i
$873$	23.7103	−	13.6892i	0.802474	−	0.463308i
$874$	7.88009	−	8.85680i	0.266548	−	0.299586i
$875$		0			0
$876$	−38.1436	+	4.46706i	−1.28875	+	0.150928i
$877$	16.6020	+	28.7555i	0.560610	+	0.971004i	0.997443	+	0.0714621i	$0.0227665\pi$
$877$	16.6020	+	28.7555i	0.560610	+	0.971004i	−0.436834	+	0.899542i	$0.643900\pi$
$878$	−23.2572	+	7.70951i	−0.784893	+	0.260183i
$879$	52.6205	+	30.3805i	1.77485	+	1.02471i
$880$		0			0
$881$			19.2043i			0.647008i	0.946227	+	0.323504i	$0.104861\pi$
$881$			19.2043i			0.647008i	−0.946227	+	0.323504i	$0.895139\pi$
$882$	−26.3040	+	26.0580i	−0.885700	+	0.877420i
$883$			8.57526i			0.288581i	0.989535	+	0.144290i	$0.0460899\pi$
$883$			8.57526i			0.288581i	−0.989535	+	0.144290i	$0.953910\pi$
$884$	9.70767	−	7.23049i	0.326504	−	0.243188i
$885$		0			0
$886$	11.2281	+	33.8716i	0.377214	+	1.13794i
$887$	−7.37543	−	12.7746i	−0.247643	−	0.428930i	0.715229	−	0.698891i	$-0.246323\pi$
$887$	−7.37543	−	12.7746i	−0.247643	−	0.428930i	−0.962871	+	0.269961i	$0.912989\pi$
$888$	−30.1725	+	43.1219i	−1.01252	+	1.44707i
$889$	22.6199	−	5.30359i	0.758646	−	0.177877i
$890$		0			0
$891$	−19.4430	+	11.2254i	−0.651365	+	0.376066i
$892$	−43.3028	−	18.6674i	−1.44989	−	0.625032i
$893$	2.20673	−	3.82218i	0.0738455	−	0.127904i
$894$	−17.7719	+	86.1182i	−0.594380	+	2.88022i
$895$		0			0
$896$	11.0066	+	27.8362i	0.367704	+	0.929943i
$897$	5.38571			0.179824
$898$	2.01832	−	9.78032i	0.0673524	−	0.326373i
$899$	1.95288	−	3.38248i	0.0651321	−	0.112812i
$900$		0			0
$901$	11.6002	−	6.69736i	0.386457	−	0.223121i
$902$	−10.1186	−	9.00277i	−0.336914	−	0.299760i
$903$	4.75995	−	15.7613i	0.158401	−	0.524503i
$904$	−12.3498	+	17.6500i	−0.410747	+	0.587030i
$905$		0			0
$906$	−8.09563	−	24.4220i	−0.268959	−	0.811367i
$907$	41.2134	+	23.7946i	1.36847	+	0.790085i	0.990732	−	0.135828i	$-0.0433695\pi$
$907$	41.2134	+	23.7946i	1.36847	+	0.790085i	0.377736	+	0.925914i	$0.376703\pi$
$908$	33.5660	−	25.0007i	1.11393	−	0.829678i
$909$			23.7796i			0.788720i
$910$		0			0
$911$		−	34.7074i		−	1.14991i	−0.818186	−	0.574954i	$-0.805020\pi$
$911$		−	34.7074i		−	1.14991i	0.818186	−	0.574954i	$-0.194980\pi$
$912$	23.5754	+	24.9659i	0.780660	+	0.826705i
$913$	32.7523	+	18.9095i	1.08394	+	0.625814i
$914$	−25.3463	+	8.40200i	−0.838380	+	0.277914i
$915$		0			0
$916$	10.2928	−	1.20540i	0.340082	−	0.0398276i
$917$	25.8255	−	24.2480i	0.852833	−	0.800739i
$918$	13.3610	−	15.0170i	0.440977	−	0.495635i
$919$	−44.9270	+	25.9386i	−1.48200	+	0.855635i	−0.999792	−	0.0204194i	$-0.993500\pi$
$919$	−44.9270	+	25.9386i	−1.48200	+	0.855635i	−0.482212	+	0.876055i	$0.660167\pi$
$920$		0			0
$921$	2.83671	−	4.91333i	0.0934729	−	0.161900i
$922$	47.9340	+	9.89195i	1.57862	+	0.325774i
$923$	−1.13269			−0.0372828
$924$	−16.8264	−	46.5456i	−0.553549	−	1.53124i
$925$		0			0
$926$	−20.8080	−	4.29406i	−0.683794	−	0.141112i
$927$	−1.91138	+	3.31060i	−0.0627778	+	0.108734i
$928$	−9.83454	+	6.07369i	−0.322835	+	0.199379i
$929$	−37.9198	+	21.8930i	−1.24411	+	0.718286i	−0.969928	−	0.243393i	$-0.921740\pi$
$929$	−37.9198	+	21.8930i	−1.24411	+	0.718286i	−0.274180	+	0.961678i	$0.588406\pi$
$930$		0			0
$931$	19.2769	+	12.8118i	0.631774	+	0.419891i
$932$	4.83166	+	41.2568i	0.158266	+	1.35141i
$933$	−37.5151	−	64.9780i	−1.22819	−	2.12728i
$934$	34.1489	−	11.3200i	1.11739	−	0.370402i
$935$		0			0
$936$	−0.751546	+	8.62379i	−0.0245651	+	0.281877i
$937$		−	14.2224i		−	0.464624i	−0.972641	−	0.232312i	$-0.925371\pi$
$937$		−	14.2224i		−	0.464624i	0.972641	−	0.232312i	$-0.0746290\pi$
$938$	30.4666	+	16.5177i	0.994771	+	0.539322i
$939$			16.4937i			0.538251i
$940$		0			0
$941$	4.80070	+	2.77169i	0.156498	+	0.0903544i	0.576204	−	0.817306i	$-0.304533\pi$
$941$	4.80070	+	2.77169i	0.156498	+	0.0903544i	−0.419706	+	0.907660i	$0.637867\pi$
$942$	7.42320	+	22.3935i	0.241861	+	0.729619i
$943$	−3.36951	−	5.83617i	−0.109726	−	0.190052i
$944$	7.43893	−	1.76660i	0.242116	−	0.0574979i
$945$		0			0
$946$	9.12407	+	8.11789i	0.296649	+	0.263935i
$947$	51.5945	−	29.7881i	1.67660	−	0.967983i	0.712791	−	0.701377i	$-0.247431\pi$
$947$	51.5945	−	29.7881i	1.67660	−	0.967983i	0.963805	−	0.266607i	$-0.0859024\pi$
$948$	15.9257	−	36.9429i	0.517244	−	1.19985i
$949$	−3.02612	+	5.24140i	−0.0982321	+	0.170143i
$950$		0			0
$951$	48.8163			1.58298
$952$	−34.2394	−	43.4872i	−1.10971	−	1.40943i
$953$	−12.2577			−0.397065			−0.198532	−	0.980094i	$-0.563617\pi$
$953$	−12.2577			−0.397065			−0.198532	+	0.980094i	$0.563617\pi$
$954$	−1.93602	+	9.38149i	−0.0626809	+	0.303737i
$955$		0			0
$956$	16.7285	−	38.8051i	0.541039	−	1.25505i
$957$	16.5517	−	9.55612i	0.535040	−	0.308906i
$958$	−21.7321	−	19.3355i	−0.702133	−	0.624703i
$959$	13.2316	+	3.99597i	0.427270	+	0.129037i
$960$		0			0
$961$	13.6732	+	23.6826i	0.441070	+	0.763956i
$962$	2.60974	+	7.87279i	0.0841414	+	0.253829i
$963$	−23.4885	−	13.5611i	−0.756906	−	0.437000i
$964$	−2.17200	−	2.91612i	−0.0699553	−	0.0939220i
$965$		0			0
$966$	−0.659836	−	24.6177i	−0.0212299	−	0.792062i
$967$		−	53.4551i		−	1.71900i	−0.511137	−	0.859499i	$-0.670775\pi$
$967$		−	53.4551i		−	1.71900i	0.511137	−	0.859499i	$-0.329225\pi$
$968$	5.57867	+	0.486170i	0.179305	+	0.0156261i
$969$	−54.9869	−	31.7467i	−1.76643	−	1.01985i
$970$		0			0
$971$	11.1284	+	19.2749i	0.357126	+	0.618561i	0.987479	−	0.157748i	$-0.0504232\pi$
$971$	11.1284	+	19.2749i	0.357126	+	0.618561i	−0.630353	+	0.776308i	$0.717090\pi$
$972$	−5.10475	−	43.5887i	−0.163735	−	1.39811i
$973$	−13.2534	−	56.5259i	−0.424885	−	1.81214i
$974$	27.3167	−	30.7025i	0.875284	−	0.983772i
$975$		0			0
$976$	−37.4662	−	11.1982i	−1.19926	−	0.358447i
$977$	15.8974	−	27.5351i	0.508603	−	0.880926i	−0.491347	−	0.870964i	$-0.663495\pi$
$977$	15.8974	−	27.5351i	0.508603	−	0.880926i	0.999950	−	0.00996251i	$-0.00317122\pi$
$978$	66.4466	+	13.7123i	2.12473	+	0.438472i
$979$	−38.2369			−1.22206
$980$		0			0
$981$	29.8158			0.951947
$982$	−13.1829	−	2.72051i	−0.420684	−	0.0868148i
$983$	10.2927	−	17.8275i	0.328287	−	0.568609i	−0.653885	−	0.756594i	$-0.726862\pi$
$983$	10.2927	−	17.8275i	0.328287	−	0.568609i	0.982172	+	0.187985i	$0.0601955\pi$
$984$	17.6881	−	8.25538i	0.563877	−	0.263172i
$985$		0			0
$986$	14.2070	−	15.9679i	0.452444	−	0.508522i
$987$	−2.09288	−	8.92616i	−0.0666172	−	0.284123i
$988$	5.37470	−	0.629440i	0.170992	−	0.0200252i
$989$	3.03832	+	5.26253i	0.0966131	+	0.167339i
$990$		0			0
$991$	−32.2836	−	18.6390i	−1.02552	−	0.592086i	−0.109824	−	0.993951i	$-0.535029\pi$
$991$	−32.2836	−	18.6390i	−1.02552	−	0.592086i	−0.915699	+	0.401865i	$0.868362\pi$
$992$	0.320577	+	10.8081i	0.0101783	+	0.343156i
$993$		−	33.9810i		−	1.07836i
$994$	0.138772	+	5.17743i	0.00440158	+	0.164218i
$995$		0			0
$996$	−43.7130	+	32.5584i	−1.38510	+	1.03165i
$997$	10.9485	+	6.32111i	0.346742	+	0.200191i	0.663249	−	0.748399i	$-0.269177\pi$
$997$	10.9485	+	6.32111i	0.346742	+	0.200191i	−0.316508	+	0.948590i	$0.602510\pi$
$998$	−8.98449	−	27.1034i	−0.284399	−	0.857944i
$999$	6.88644	+	11.9277i	0.217877	+	0.377375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.p.e.451.7		32
4.3	odd	2	inner	700.2.p.e.451.15		32
5.2	odd	4		140.2.s.b.59.2	yes	32
5.3	odd	4		140.2.s.b.59.15	yes	32
5.4	even	2	inner	700.2.p.e.451.10		32
7.5	odd	6	inner	700.2.p.e.551.15		32
20.3	even	4		140.2.s.b.59.10	yes	32
20.7	even	4		140.2.s.b.59.7	yes	32
20.19	odd	2	inner	700.2.p.e.451.2		32
28.19	even	6	inner	700.2.p.e.551.7		32
35.2	odd	12		980.2.s.e.19.10		32
35.3	even	12		980.2.c.d.979.7		32
35.12	even	12		140.2.s.b.19.10	yes	32
35.13	even	4		980.2.s.e.619.15		32
35.17	even	12		980.2.c.d.979.26		32
35.18	odd	12		980.2.c.d.979.8		32
35.19	odd	6	inner	700.2.p.e.551.2		32
35.23	odd	12		980.2.s.e.19.7		32
35.27	even	4		980.2.s.e.619.2		32
35.32	odd	12		980.2.c.d.979.25		32
35.33	even	12		140.2.s.b.19.7	yes	32
140.3	odd	12		980.2.c.d.979.28		32
140.19	even	6	inner	700.2.p.e.551.10		32
140.23	even	12		980.2.s.e.19.2		32
140.27	odd	4		980.2.s.e.619.7		32
140.47	odd	12		140.2.s.b.19.15	yes	32
140.67	even	12		980.2.c.d.979.6		32
140.83	odd	4		980.2.s.e.619.10		32
140.87	odd	12		980.2.c.d.979.5		32
140.103	odd	12		140.2.s.b.19.2	✓	32
140.107	even	12		980.2.s.e.19.15		32
140.123	even	12		980.2.c.d.979.27		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.2	✓	32	140.103	odd	12
140.2.s.b.19.7	yes	32	35.33	even	12
140.2.s.b.19.10	yes	32	35.12	even	12
140.2.s.b.19.15	yes	32	140.47	odd	12
140.2.s.b.59.2	yes	32	5.2	odd	4
140.2.s.b.59.7	yes	32	20.7	even	4
140.2.s.b.59.10	yes	32	20.3	even	4
140.2.s.b.59.15	yes	32	5.3	odd	4
700.2.p.e.451.2		32	20.19	odd	2	inner
700.2.p.e.451.7		32	1.1	even	1	trivial
700.2.p.e.451.10		32	5.4	even	2	inner
700.2.p.e.451.15		32	4.3	odd	2	inner
700.2.p.e.551.2		32	35.19	odd	6	inner
700.2.p.e.551.7		32	28.19	even	6	inner
700.2.p.e.551.10		32	140.19	even	6	inner
700.2.p.e.551.15		32	7.5	odd	6	inner
980.2.c.d.979.5		32	140.87	odd	12
980.2.c.d.979.6		32	140.67	even	12
980.2.c.d.979.7		32	35.3	even	12
980.2.c.d.979.8		32	35.18	odd	12
980.2.c.d.979.25		32	35.32	odd	12
980.2.c.d.979.26		32	35.17	even	12
980.2.c.d.979.27		32	140.123	even	12
980.2.c.d.979.28		32	140.3	odd	12
980.2.s.e.19.2		32	140.23	even	12
980.2.s.e.19.7		32	35.23	odd	12
980.2.s.e.19.10		32	35.2	odd	12
980.2.s.e.19.15		32	140.107	even	12
980.2.s.e.619.2		32	35.27	even	4
980.2.s.e.619.7		32	140.27	odd	4
980.2.s.e.619.10		32	140.83	odd	4
980.2.s.e.619.15		32	35.13	even	4

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.285823 + 1.38503i) q^{2} +(-1.29809 + 2.24836i) q^{3} +(-1.83661 - 0.791746i) q^{4} +(-2.74302 - 2.44053i) q^{6} +(0.603960 + 2.57589i) q^{7} +(1.62154 - 2.31746i) q^{8} +(-1.87009 - 3.23909i) q^{9} +(-3.12008 - 1.80138i) q^{11} +(4.16422 - 3.10161i) q^{12} -0.818282i q^{13} +(-3.74031 + 0.100253i) q^{14} +(2.74628 + 2.90826i) q^{16} +(-6.40537 - 3.69814i) q^{17} +(5.02075 - 1.66432i) q^{18} +(-1.65329 - 2.86358i) q^{19} +(-6.57554 - 1.98583i) q^{21} +(3.38675 - 3.80652i) q^{22} +(2.19550 - 1.26758i) q^{23} +(3.10559 + 6.65408i) q^{24} +(1.13334 + 0.233884i) q^{26} +1.92166 q^{27} +(0.930214 - 5.20910i) q^{28} +2.04334 q^{29} +(0.955727 - 1.65537i) q^{31} +(-4.81297 + 2.97243i) q^{32} +(8.10030 - 4.67671i) q^{33} +(6.95283 - 7.81461i) q^{34} +(0.870092 + 7.42959i) q^{36} +(3.58360 + 6.20697i) q^{37} +(4.43869 - 1.47138i) q^{38} +(1.83980 + 1.06221i) q^{39} -2.65824i q^{41} +(4.62987 - 8.53972i) q^{42} +2.39696i q^{43} +(4.30413 + 5.77873i) q^{44} +(1.12810 + 3.40314i) q^{46} +(0.667376 + 1.15593i) q^{47} +(-10.1037 + 2.39944i) q^{48} +(-6.27046 + 3.11147i) q^{49} +(16.6295 - 9.60106i) q^{51} +(-0.647871 + 1.50287i) q^{52} +(-0.905503 + 1.56838i) q^{53} +(-0.549253 + 2.66155i) q^{54} +(6.94888 + 2.77725i) q^{56} +8.58450 q^{57} +(-0.584034 + 2.83009i) q^{58} +(0.955727 - 1.65537i) q^{59} +(-8.46625 + 4.88799i) q^{61} +(2.01956 + 1.79685i) q^{62} +(7.21411 - 6.77344i) q^{63} +(-2.74124 - 7.51569i) q^{64} +(4.16213 + 12.5559i) q^{66} +(-8.02134 - 4.63112i) q^{67} +(8.83618 + 11.8635i) q^{68} +6.58172i q^{69} -1.38422i q^{71} +(-10.5389 - 0.918444i) q^{72} +(-6.40537 - 3.69814i) q^{73} +(-9.62111 + 3.18929i) q^{74} +(0.769222 + 6.56827i) q^{76} +(2.75576 - 9.12495i) q^{77} +(-1.99704 + 2.24457i) q^{78} +(6.70979 - 3.87390i) q^{79} +(3.11579 - 5.39670i) q^{81} +(3.68173 + 0.759784i) q^{82} -10.4973 q^{83} +(10.5044 + 8.85335i) q^{84} +(-3.31986 - 0.685105i) q^{86} +(-2.65245 + 4.59418i) q^{87} +(-9.23393 + 4.30966i) q^{88} +(9.19133 - 5.30662i) q^{89} +(2.10781 - 0.494210i) q^{91} +(-5.03589 + 0.589761i) q^{92} +(2.48125 + 4.29764i) q^{93} +(-1.79175 + 0.593945i) q^{94} +(-0.435416 - 14.6798i) q^{96} +7.32005i q^{97} +(-2.51724 - 9.57411i) q^{98} +13.4750i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 6 q^{4} - 4 q^{9} - 22 q^{14} + 18 q^{16} - 52 q^{21} + 48 q^{24} - 18 q^{26} - 28 q^{36} + 26 q^{44} - 22 q^{46} - 48 q^{54} - 16 q^{56} + 36 q^{61} - 36 q^{64} - 24 q^{66} - 14 q^{74} + 72 q^{81}+ \cdots + 60 q^{96}+O(q^{100}) \) 32 * q - 6 * q^4 - 4 * q^9 - 22 * q^14 + 18 * q^16 - 52 * q^21 + 48 * q^24 - 18 * q^26 - 28 * q^36 + 26 * q^44 - 22 * q^46 - 48 * q^54 - 16 * q^56 + 36 * q^61 - 36 * q^64 - 24 * q^66 - 14 * q^74 + 72 * q^81 - 56 * q^84 + 8 * q^86 + 108 * q^89 - 30 * q^94 + 60 * q^96

Introduction

L-functions

Modular forms

Varieties

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