LMFDB - Embedded newform 637.2.bb.b.362.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			362.7
Character	$\chi$	$=$	637.362
Dual form			637.2.bb.b.227.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67430 + 1.67430i) q^{2} +(-1.04118 - 0.601128i) q^{3} +3.60653i q^{4} +(-0.825486 - 3.08075i) q^{5} +(-0.736784 - 2.74971i) q^{6} +(-2.68981 + 2.68981i) q^{8} +(-0.777291 - 1.34631i) q^{9} +O(q^{10})$	\(q+(1.67430 + 1.67430i) q^{2} +(-1.04118 - 0.601128i) q^{3} +3.60653i q^{4} +(-0.825486 - 3.08075i) q^{5} +(-0.736784 - 2.74971i) q^{6} +(-2.68981 + 2.68981i) q^{8} +(-0.777291 - 1.34631i) q^{9} +(3.77599 - 6.54020i) q^{10} +(-1.10170 - 4.11159i) q^{11} +(2.16799 - 3.75506i) q^{12} +(-3.48609 - 0.920440i) q^{13} +(-0.992444 + 3.70385i) q^{15} -1.79401 q^{16} +1.44374 q^{17} +(0.952702 - 3.55553i) q^{18} +(2.42397 + 0.649502i) q^{19} +(11.1108 - 2.97714i) q^{20} +(5.03945 - 8.72858i) q^{22} -5.23024i q^{23} +(4.41750 - 1.18367i) q^{24} +(-4.47949 + 2.58624i) q^{25} +(-4.29565 - 7.37783i) q^{26} +5.47577i q^{27} +(1.34350 + 2.32701i) q^{29} +(-7.86299 + 4.53970i) q^{30} +(-5.14250 - 1.37793i) q^{31} +(2.37592 + 2.37592i) q^{32} +(-1.32452 + 4.94318i) q^{33} +(2.41725 + 2.41725i) q^{34} +(4.85550 - 2.80333i) q^{36} +(0.438839 - 0.438839i) q^{37} +(2.97099 + 5.14591i) q^{38} +(3.07635 + 3.05393i) q^{39} +(10.5070 + 6.06624i) q^{40} +(5.04879 + 1.35282i) q^{41} +(-5.46143 - 3.15316i) q^{43} +(14.8286 - 3.97331i) q^{44} +(-3.50600 + 3.50600i) q^{45} +(8.75696 - 8.75696i) q^{46} +(6.39313 - 1.71303i) q^{47} +(1.86789 + 1.07843i) q^{48} +(-11.8301 - 3.16987i) q^{50} +(-1.50320 - 0.867874i) q^{51} +(3.31960 - 12.5727i) q^{52} +(3.79264 + 6.56904i) q^{53} +(-9.16806 + 9.16806i) q^{54} +(-11.7574 + 6.78811i) q^{55} +(-2.13337 - 2.13337i) q^{57} +(-1.64669 + 6.14553i) q^{58} +(-1.43617 - 1.43617i) q^{59} +(-13.3581 - 3.57928i) q^{60} +(4.53851 - 2.62031i) q^{61} +(-6.30300 - 10.9171i) q^{62} +11.5440i q^{64} +(0.0420647 + 11.4996i) q^{65} +(-10.4940 + 6.05870i) q^{66} +(-8.46631 + 2.26854i) q^{67} +5.20691i q^{68} +(-3.14404 + 5.44564i) q^{69} +(8.31929 - 2.22915i) q^{71} +(5.71208 + 1.53055i) q^{72} +(4.09222 - 15.2724i) q^{73} +1.46949 q^{74} +6.21863 q^{75} +(-2.34245 + 8.74214i) q^{76} +(0.0375447 + 10.2639i) q^{78} +(-1.00643 + 1.74319i) q^{79} +(1.48093 + 5.52690i) q^{80} +(0.959764 - 1.66236i) q^{81} +(6.18815 + 10.7182i) q^{82} +(-5.11623 + 5.11623i) q^{83} +(-1.19179 - 4.44782i) q^{85} +(-3.86473 - 14.4234i) q^{86} -3.23046i q^{87} +(14.0227 + 8.09604i) q^{88} +(4.95005 + 4.95005i) q^{89} -11.7402 q^{90} +18.8630 q^{92} +(4.52597 + 4.52597i) q^{93} +(13.5721 + 7.83586i) q^{94} -8.00382i q^{95} +(-1.04554 - 3.90200i) q^{96} +(-1.62618 - 6.06897i) q^{97} +(-4.67912 + 4.67912i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9	$ 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9} - 16 q^{11} - 8 q^{15} - 24 q^{16} + 68 q^{18} + 4 q^{22} + 4 q^{29} - 12 q^{30} - 68 q^{32} - 8 q^{37} - 48 q^{43} + 60 q^{44} + 24 q^{46} - 44 q^{50} - 12 q^{51} - 36 q^{53} - 92 q^{57} - 28 q^{58} - 104 q^{60} - 32 q^{65} - 8 q^{67} + 84 q^{71} + 124 q^{72} + 48 q^{74} + 148 q^{78} + 40 q^{79} + 28 q^{81} + 36 q^{85} - 60 q^{86} + 228 q^{88} + 24 q^{92} - 84 q^{93} - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9 - 16 * q^11 - 8 * q^15 - 24 * q^16 + 68 * q^18 + 4 * q^22 + 4 * q^29 - 12 * q^30 - 68 * q^32 - 8 * q^37 - 48 * q^43 + 60 * q^44 + 24 * q^46 - 44 * q^50 - 12 * q^51 - 36 * q^53 - 92 * q^57 - 28 * q^58 - 104 * q^60 - 32 * q^65 - 8 * q^67 + 84 * q^71 + 124 * q^72 + 48 * q^74 + 148 * q^78 + 40 * q^79 + 28 * q^81 + 36 * q^85 - 60 * q^86 + 228 * q^88 + 24 * q^92 - 84 * q^93 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.67430	+	1.67430i	1.18391	+	1.18391i	0.978724	+	0.205182i	$0.0657786\pi$
$2$	1.67430	+	1.67430i	1.18391	+	1.18391i	0.205182	+	0.978724i	$0.434221\pi$
$3$	−1.04118	−	0.601128i	−0.601128	−	0.347061i	0.168357	−	0.985726i	$-0.446154\pi$
$3$	−1.04118	−	0.601128i	−0.601128	−	0.347061i	−0.769485	+	0.638665i	$0.779487\pi$
$4$			3.60653i			1.80327i
$5$	−0.825486	−	3.08075i	−0.369168	−	1.37776i	−0.861681	−	0.507450i	$-0.830588\pi$
$5$	−0.825486	−	3.08075i	−0.369168	−	1.37776i	0.492513	−	0.870305i	$-0.336078\pi$
$6$	−0.736784	−	2.74971i	−0.300791	−	1.12257i
$7$		0			0
$7$		0			0
$8$	−2.68981	+	2.68981i	−0.950991	+	0.950991i
$9$	−0.777291	−	1.34631i	−0.259097	−	0.448769i
$10$	3.77599	−	6.54020i	1.19407	−	2.06819i
$11$	−1.10170	−	4.11159i	−0.332174	−	1.23969i	−0.906900	−	0.421345i	$-0.861558\pi$
$11$	−1.10170	−	4.11159i	−0.332174	−	1.23969i	0.574726	−	0.818346i	$-0.305109\pi$
$12$	2.16799	−	3.75506i	0.625844	−	1.08399i
$13$	−3.48609	−	0.920440i	−0.966866	−	0.255284i
$13$	−3.48609	−	0.920440i	−0.966866	−	0.255284i
$14$		0			0
$15$	−0.992444	+	3.70385i	−0.256248	+	0.956331i
$16$	−1.79401			−0.448502
$17$	1.44374			0.350159			0.175080	−	0.984554i	$-0.443982\pi$
$17$	1.44374			0.350159			0.175080	+	0.984554i	$0.443982\pi$
$18$	0.952702	−	3.55553i	0.224554	−	0.838047i
$19$	2.42397	+	0.649502i	0.556098	+	0.149006i	0.525913	−	0.850538i	$-0.323724\pi$
$19$	2.42397	+	0.649502i	0.556098	+	0.149006i	0.0301847	+	0.999544i	$0.490390\pi$
$20$	11.1108	−	2.97714i	2.48446	−	0.665709i
$21$		0			0
$22$	5.03945	−	8.72858i	1.07441	−	1.86094i
$23$		−	5.23024i		−	1.09058i	−0.838248	−	0.545290i	$-0.816420\pi$
$23$		−	5.23024i		−	1.09058i	0.838248	−	0.545290i	$-0.183580\pi$
$24$	4.41750	−	1.18367i	0.901719	−	0.241615i
$25$	−4.47949	+	2.58624i	−0.895898	+	0.517247i
$26$	−4.29565	−	7.37783i	−0.842446	−	1.44691i
$27$			5.47577i			1.05381i
$28$		0			0
$29$	1.34350	+	2.32701i	0.249482	+	0.432116i	0.963382	−	0.268132i	$-0.0864063\pi$
$29$	1.34350	+	2.32701i	0.249482	+	0.432116i	−0.713900	+	0.700248i	$0.753073\pi$
$30$	−7.86299	+	4.53970i	−1.43558	+	0.828832i
$31$	−5.14250	−	1.37793i	−0.923620	−	0.247483i	−0.234488	−	0.972119i	$-0.575341\pi$
$31$	−5.14250	−	1.37793i	−0.923620	−	0.247483i	−0.689132	+	0.724636i	$0.742008\pi$
$32$	2.37592	+	2.37592i	0.420007	+	0.420007i
$33$	−1.32452	+	4.94318i	−0.230570	+	0.860497i
$34$	2.41725	+	2.41725i	0.414555	+	0.414555i
$35$		0			0
$36$	4.85550	−	2.80333i	0.809250	−	0.467221i
$37$	0.438839	−	0.438839i	0.0721448	−	0.0721448i	−0.670114	−	0.742258i	$-0.733755\pi$
$37$	0.438839	−	0.438839i	0.0721448	−	0.0721448i	0.742258	+	0.670114i	$0.233755\pi$
$38$	2.97099	+	5.14591i	0.481958	+	0.834776i
$39$	3.07635	+	3.05393i	0.492611	+	0.489020i
$40$	10.5070	+	6.06624i	1.66131	+	0.959157i
$41$	5.04879	+	1.35282i	0.788488	+	0.211275i	0.630524	−	0.776170i	$-0.282840\pi$
$41$	5.04879	+	1.35282i	0.788488	+	0.211275i	0.157965	+	0.987445i	$0.449507\pi$
$42$		0			0
$43$	−5.46143	−	3.15316i	−0.832860	−	0.480852i	0.0219711	−	0.999759i	$-0.493006\pi$
$43$	−5.46143	−	3.15316i	−0.832860	−	0.480852i	−0.854831	+	0.518907i	$0.826339\pi$
$44$	14.8286	−	3.97331i	2.23549	−	0.598998i
$45$	−3.50600	+	3.50600i	−0.522644	+	0.522644i
$46$	8.75696	−	8.75696i	1.29114	−	1.29114i
$47$	6.39313	−	1.71303i	0.932533	−	0.249872i	0.239599	−	0.970872i	$-0.422984\pi$
$47$	6.39313	−	1.71303i	0.932533	−	0.249872i	0.692935	+	0.721000i	$0.256317\pi$
$48$	1.86789	+	1.07843i	0.269607	+	0.155658i
$49$		0			0
$50$	−11.8301	−	3.16987i	−1.67303	−	0.448287i
$51$	−1.50320	−	0.867874i	−0.210490	−	0.121527i
$52$	3.31960	−	12.5727i	0.460345	−	1.74352i
$53$	3.79264	+	6.56904i	0.520959	+	0.902328i	0.999703	+	0.0243730i	$0.00775895\pi$
$53$	3.79264	+	6.56904i	0.520959	+	0.902328i	−0.478744	+	0.877955i	$0.658908\pi$
$54$	−9.16806	+	9.16806i	−1.24761	+	1.24761i
$55$	−11.7574	+	6.78811i	−1.58536	+	0.915309i
$56$		0			0
$57$	−2.13337	−	2.13337i	−0.282571	−	0.282571i
$58$	−1.64669	+	6.14553i	−0.216221	+	0.806947i
$59$	−1.43617	−	1.43617i	−0.186973	−	0.186973i	0.607413	−	0.794386i	$-0.292207\pi$
$59$	−1.43617	−	1.43617i	−0.186973	−	0.186973i	−0.794386	+	0.607413i	$0.792207\pi$
$60$	−13.3581	−	3.57928i	−1.72452	−	0.462083i
$61$	4.53851	−	2.62031i	0.581097	−	0.335496i	−0.180472	−	0.983580i	$-0.557763\pi$
$61$	4.53851	−	2.62031i	0.581097	−	0.335496i	0.761569	+	0.648084i	$0.224429\pi$
$62$	−6.30300	−	10.9171i	−0.800482	−	1.38648i
$63$		0			0
$64$			11.5440i			1.44300i
$65$	0.0420647	+	11.4996i	0.00521748	+	1.42635i
$66$	−10.4940	+	6.05870i	−1.29172	+	0.745775i
$67$	−8.46631	+	2.26854i	−1.03432	+	0.277147i	−0.735760	−	0.677243i	$-0.763175\pi$
$67$	−8.46631	+	2.26854i	−1.03432	+	0.277147i	−0.298565	+	0.954389i	$0.596508\pi$
$68$			5.20691i			0.631430i
$69$	−3.14404	+	5.44564i	−0.378498	+	0.655578i
$70$		0			0
$71$	8.31929	−	2.22915i	0.987318	−	0.264551i	0.271194	−	0.962525i	$-0.412581\pi$
$71$	8.31929	−	2.22915i	0.987318	−	0.264551i	0.716124	+	0.697974i	$0.245915\pi$
$72$	5.71208	+	1.53055i	0.673175	+	0.180377i
$73$	4.09222	−	15.2724i	0.478958	−	1.78749i	−0.126894	−	0.991916i	$-0.540501\pi$
$73$	4.09222	−	15.2724i	0.478958	−	1.78749i	0.605852	−	0.795578i	$-0.292833\pi$
$74$	1.46949			0.170825
$75$	6.21863			0.718066
$76$	−2.34245	+	8.74214i	−0.268697	+	1.00279i
$77$		0			0
$78$	0.0375447	+	10.2639i	0.00425110	+	1.16216i
$79$	−1.00643	+	1.74319i	−0.113233	+	0.196125i	−0.917072	−	0.398722i	$-0.869454\pi$
$79$	−1.00643	+	1.74319i	−0.113233	+	0.196125i	0.803839	+	0.594847i	$0.202787\pi$
$80$	1.48093	+	5.52690i	0.165573	+	0.617926i
$81$	0.959764	−	1.66236i	0.106640	−	0.184707i
$82$	6.18815	+	10.7182i	0.683367	+	1.18363i
$83$	−5.11623	+	5.11623i	−0.561579	+	0.561579i	−0.929756	−	0.368177i	$-0.879982\pi$
$83$	−5.11623	+	5.11623i	−0.561579	+	0.561579i	0.368177	+	0.929756i	$0.379982\pi$
$84$		0			0
$85$	−1.19179	−	4.44782i	−0.129268	−	0.482434i
$86$	−3.86473	−	14.4234i	−0.416744	−	1.55531i
$87$		−	3.23046i		−	0.346342i
$88$	14.0227	+	8.09604i	1.49483	+	0.863040i
$89$	4.95005	+	4.95005i	0.524704	+	0.524704i	0.918988	−	0.394285i	$-0.129008\pi$
$89$	4.95005	+	4.95005i	0.524704	+	0.524704i	−0.394285	+	0.918988i	$0.629008\pi$
$90$	−11.7402			−1.23752
$91$		0			0
$92$	18.8630			1.96661
$93$	4.52597	+	4.52597i	0.469322	+	0.469322i
$94$	13.5721	+	7.83586i	1.39986	+	0.808207i
$95$		−	8.00382i		−	0.821174i
$96$	−1.04554	−	3.90200i	−0.106710	−	0.398246i
$97$	−1.62618	−	6.06897i	−0.165113	−	0.616211i	−0.998026	−	0.0628062i	$-0.979995\pi$
$97$	−1.62618	−	6.06897i	−0.165113	−	0.616211i	0.832913	−	0.553405i	$-0.186672\pi$
$98$		0			0
$99$	−4.67912	+	4.67912i	−0.470270	+	0.470270i
$100$	−9.32734	−	16.1554i	−0.932734	−	1.61554i
$101$	−6.66959	+	11.5521i	−0.663649	+	1.14947i	0.316001	+	0.948759i	$0.397660\pi$
$101$	−6.66959	+	11.5521i	−0.663649	+	1.14947i	−0.979650	+	0.200715i	$0.935674\pi$
$102$	−1.06373	−	3.96988i	−0.105325	−	0.393077i
$103$	−3.08727	+	5.34730i	−0.304197	+	0.526885i	−0.977082	−	0.212862i	$-0.931722\pi$
$103$	−3.08727	+	5.34730i	−0.304197	+	0.526885i	0.672885	+	0.739747i	$0.265055\pi$
$104$	11.8527	−	6.90110i	1.16225	−	0.676708i
$105$		0			0
$106$	−4.64852	+	17.3485i	−0.451504	+	1.68504i
$107$	−8.54705			−0.826275			−0.413137	−	0.910669i	$-0.635567\pi$
$107$	−8.54705			−0.826275			−0.413137	+	0.910669i	$0.635567\pi$
$108$	−19.7485			−1.90030
$109$	1.20834	−	4.50957i	0.115738	−	0.431939i	−0.883603	−	0.468236i	$-0.844890\pi$
$109$	1.20834	−	4.50957i	0.115738	−	0.431939i	0.999341	+	0.0362973i	$0.0115563\pi$
$110$	−31.0506	−	8.31998i	−2.96056	−	0.793279i
$111$	−0.720711	+	0.193114i	−0.0684069	+	0.0183296i
$112$		0			0
$113$	9.80118	−	16.9761i	0.922018	−	1.59698i	0.125729	−	0.992065i	$-0.459873\pi$
$113$	9.80118	−	16.9761i	0.922018	−	1.59698i	0.796289	−	0.604917i	$-0.206794\pi$
$114$		−	7.14378i		−	0.669076i
$115$	−16.1131	+	4.31748i	−1.50255	+	0.402608i
$116$	−8.39245	+	4.84538i	−0.779219	+	0.449883i
$117$	1.47051	+	5.40879i	0.135949	+	0.500043i
$118$		−	4.80915i		−	0.442718i
$119$		0			0
$120$	−7.29317	−	12.6321i	−0.665773	−	1.15315i
$121$	−6.16515	+	3.55945i	−0.560468	+	0.323586i
$122$	11.9860	+	3.21164i	1.08516	+	0.290768i
$123$	−4.44350	−	4.44350i	−0.400657	−	0.400657i
$124$	4.96954	−	18.5466i	0.446278	−	1.66553i
$125$	0.388969	+	0.388969i	0.0347904	+	0.0347904i
$126$		0			0
$127$	1.02476	−	0.591646i	0.0909329	−	0.0525001i	−0.453844	−	0.891081i	$-0.649948\pi$
$127$	1.02476	−	0.591646i	0.0909329	−	0.0525001i	0.544777	+	0.838581i	$0.316614\pi$
$128$	−14.5762	+	14.5762i	−1.28837	+	1.28837i
$129$	3.79090	+	6.56603i	0.333770	+	0.578107i
$130$	−19.1833	+	19.3241i	−1.68248	+	1.69484i
$131$	−8.37536	−	4.83552i	−0.731758	−	0.422481i	0.0873067	−	0.996181i	$-0.472174\pi$
$131$	−8.37536	−	4.83552i	−0.731758	−	0.422481i	−0.819065	+	0.573701i	$0.805507\pi$
$132$	−17.8277	−	4.77693i	−1.55171	−	0.415778i
$133$		0			0
$134$	−17.9733	−	10.3769i	−1.55266	−	0.896428i
$135$	16.8695	−	4.52017i	1.45190	−	0.389034i
$136$	−3.88339	+	3.88339i	−0.332998	+	0.332998i
$137$	4.66367	−	4.66367i	0.398444	−	0.398444i	−0.479240	−	0.877684i	$-0.659088\pi$
$137$	4.66367	−	4.66367i	0.398444	−	0.398444i	0.877684	+	0.479240i	$0.159088\pi$
$138$	−14.3817	+	3.85355i	−1.22425	+	0.328036i
$139$	19.6752	+	11.3595i	1.66883	+	0.963500i	0.968269	+	0.249909i	$0.0804008\pi$
$139$	19.6752	+	11.3595i	1.66883	+	0.963500i	0.700562	+	0.713591i	$0.252933\pi$
$140$		0			0
$141$	−7.68617	−	2.05950i	−0.647292	−	0.173441i
$142$	17.6612	+	10.1967i	1.48210	+	0.855688i
$143$	0.0561397	+	15.3474i	0.00469464	+	1.28341i
$144$	1.39447	+	2.41529i	0.116206	+	0.201274i
$145$	6.05992	−	6.05992i	0.503249	−	0.503249i
$146$	32.4220	−	18.7189i	2.68327	−	1.54918i
$147$		0			0
$148$	1.58269	+	1.58269i	0.130096	+	0.130096i
$149$	3.93148	−	14.6725i	0.322079	−	1.20202i	−0.595137	−	0.803625i	$-0.702902\pi$
$149$	3.93148	−	14.6725i	0.322079	−	1.20202i	0.917216	−	0.398391i	$-0.130431\pi$
$150$	10.4118	+	10.4118i	0.850122	+	0.850122i
$151$	6.94712	+	1.86148i	0.565349	+	0.151485i	0.530163	−	0.847896i	$-0.322131\pi$
$151$	6.94712	+	1.86148i	0.565349	+	0.151485i	0.0351862	+	0.999381i	$0.488798\pi$
$152$	−8.26706	+	4.77299i	−0.670547	+	0.387141i
$153$	−1.12221	−	1.94372i	−0.0907252	−	0.157141i
$154$		0			0
$155$			16.9802i			1.36389i
$156$	−11.0141	+	11.0950i	−0.881833	+	0.888308i
$157$	16.4569	−	9.50142i	1.31341	−	0.758296i	0.330748	−	0.943719i	$-0.392699\pi$
$157$	16.4569	−	9.50142i	1.31341	−	0.758296i	0.982659	+	0.185423i	$0.0593656\pi$
$158$	−4.60369	+	1.23356i	−0.366250	+	0.0981364i
$159$		−	9.11944i		−	0.723219i
$160$	5.35833	−	9.28090i	0.423613	−	0.733720i
$161$		0			0
$162$	4.39021	−	1.17635i	0.344928	−	0.0924231i
$163$	0.979525	+	0.262463i	0.0767223	+	0.0205577i	0.296976	−	0.954885i	$-0.404022\pi$
$163$	0.979525	+	0.262463i	0.0767223	+	0.0205577i	−0.220254	+	0.975443i	$0.570689\pi$
$164$	−4.87899	+	18.2086i	−0.380985	+	1.42185i
$165$	16.3221			1.27067
$166$	−17.1322			−1.32971
$167$	−0.522634	+	1.95050i	−0.0404426	+	0.150934i	−0.983195	−	0.182561i	$-0.941561\pi$
$167$	−0.522634	+	1.95050i	−0.0404426	+	0.150934i	0.942752	+	0.333495i	$0.108228\pi$
$168$		0			0
$169$	11.3056	+	6.41746i	0.869660	+	0.493651i
$170$	5.45155	−	9.44237i	0.418115	−	0.724197i
$171$	−1.00970	−	3.76827i	−0.0772140	−	0.288166i
$172$	11.3720	−	19.6968i	0.867104	−	1.50187i
$173$	1.22524	+	2.12218i	0.0931533	+	0.161346i	0.908836	−	0.417153i	$-0.136972\pi$
$173$	1.22524	+	2.12218i	0.0931533	+	0.161346i	−0.815683	+	0.578499i	$0.803639\pi$
$174$	5.40875	−	5.40875i	0.410037	−	0.410037i
$175$		0			0
$176$	1.97645	+	7.37623i	0.148981	+	0.556004i
$177$	0.631995	+	2.35864i	0.0475037	+	0.177286i
$178$			16.5757i			1.24240i
$179$	6.50355	+	3.75482i	0.486098	+	0.280649i	0.722954	−	0.690896i	$-0.242784\pi$
$179$	6.50355	+	3.75482i	0.486098	+	0.280649i	−0.236856	+	0.971545i	$0.576117\pi$
$180$	−12.6445	−	12.6445i	−0.942465	−	0.942465i
$181$	4.93320			0.366682			0.183341	−	0.983049i	$-0.441309\pi$
$181$	4.93320			0.366682			0.183341	+	0.983049i	$0.441309\pi$
$182$		0			0
$183$	−6.30057			−0.465751
$184$	14.0683	+	14.0683i	1.03713	+	1.03713i
$185$	−1.71421	−	0.989701i	−0.126031	−	0.0727642i
$186$			15.1556i			1.11127i
$187$	−1.59057	−	5.93608i	−0.116314	−	0.434089i
$188$	6.17811	+	23.0570i	0.450585	+	1.68161i
$189$		0			0
$190$	13.4008	−	13.4008i	0.972193	−	0.972193i
$191$	3.04432	+	5.27291i	0.220279	+	0.381534i	0.954893	−	0.296951i	$-0.0959699\pi$
$191$	3.04432	+	5.27291i	0.220279	+	0.381534i	−0.734614	+	0.678486i	$0.762637\pi$
$192$	6.93941	−	12.0194i	0.500809	−	0.867427i
$193$	3.74968	+	13.9940i	0.269908	+	1.00731i	0.959177	+	0.282805i	$0.0912649\pi$
$193$	3.74968	+	13.9940i	0.269908	+	1.00731i	−0.689270	+	0.724505i	$0.742068\pi$
$194$	7.43855	−	12.8840i	0.534057	−	0.925014i
$195$	6.86892	−	11.9985i	0.491894	−	0.859228i
$196$		0			0
$197$	−4.33340	+	16.1725i	−0.308742	+	1.15224i	0.620934	+	0.783863i	$0.286754\pi$
$197$	−4.33340	+	16.1725i	−0.308742	+	1.15224i	−0.929676	+	0.368379i	$0.879913\pi$
$198$	−15.6685			−1.11351
$199$	19.8149			1.40464			0.702322	−	0.711860i	$-0.252147\pi$
$199$	19.8149			1.40464			0.702322	+	0.711860i	$0.252147\pi$
$200$	5.09250	−	19.0055i	0.360094	−	1.34389i
$201$	10.1787	+	2.72737i	0.717948	+	0.192374i
$202$	−30.5084	+	8.17471i	−2.14657	+	0.575171i
$203$		0			0
$204$	3.13002	−	5.42135i	0.219145	−	0.379570i
$205$		−	16.6708i		−	1.16434i
$206$	−14.1220	+	3.78397i	−0.983923	+	0.263641i
$207$	−7.04151	+	4.06542i	−0.489419	+	0.282566i
$208$	6.25407	+	1.65128i	0.433642	+	0.114495i
$209$		−	10.6819i		−	0.738885i
$210$		0			0
$211$	−9.56393	−	16.5652i	−0.658408	−	1.14040i	−0.981028	−	0.193868i	$-0.937897\pi$
$211$	−9.56393	−	16.5652i	−0.658408	−	1.14040i	0.322619	−	0.946529i	$-0.395437\pi$
$212$	−23.6915	+	13.6783i	−1.62714	+	0.939428i
$213$	−10.0019	−	2.68000i	−0.685320	−	0.183631i
$214$	−14.3103	−	14.3103i	−0.978232	−	0.978232i
$215$	−5.20577	+	19.4282i	−0.355031	+	1.32499i
$216$	−14.7288	−	14.7288i	−1.00217	−	1.00217i
$217$		0			0
$218$	9.57347	−	5.52725i	0.648397	−	0.374352i
$219$	−13.4414	+	13.4414i	−0.908285	+	0.908285i
$220$	−24.4816	−	42.4033i	−1.65055	−	2.85883i
$221$	−5.03301	−	1.32888i	−0.338557	−	0.0893900i
$222$	−1.53001	−	0.883353i	−0.102688	−	0.0592868i
$223$	0.670621	+	0.179692i	0.0449081	+	0.0120331i	0.281203	−	0.959648i	$-0.409267\pi$
$223$	0.670621	+	0.179692i	0.0449081	+	0.0120331i	−0.236295	+	0.971681i	$0.575933\pi$
$224$		0			0
$225$	6.96374	+	4.02052i	0.464249	+	0.268034i
$226$	44.8332	−	12.0130i	2.98226	−	0.799094i
$227$	3.68514	−	3.68514i	0.244591	−	0.244591i	−0.574155	−	0.818747i	$-0.694669\pi$
$227$	3.68514	−	3.68514i	0.244591	−	0.244591i	0.818747	+	0.574155i	$0.194669\pi$
$228$	7.69406	−	7.69406i	0.509551	−	0.509551i
$229$	1.02319	−	0.274163i	0.0676142	−	0.0181172i	−0.224853	−	0.974393i	$-0.572190\pi$
$229$	1.02319	−	0.274163i	0.0676142	−	0.0181172i	0.292468	+	0.956275i	$0.405524\pi$
$230$	−34.2068	−	19.7493i	−2.25553	−	1.30223i
$231$		0			0
$232$	−9.87299	−	2.64546i	−0.648193	−	0.173683i
$233$	−1.14405	−	0.660517i	−0.0749492	−	0.0432719i	0.462057	−	0.886850i	$-0.347112\pi$
$233$	−1.14405	−	0.660517i	−0.0749492	−	0.0432719i	−0.537006	+	0.843578i	$0.680445\pi$
$234$	−6.59385	+	11.5180i	−0.431054	+	0.752954i
$235$	−10.5549	−	18.2816i	−0.688524	−	1.19256i
$236$	5.17959	−	5.17959i	0.337163	−	0.337163i
$237$	2.09577	−	1.20999i	0.136135	−	0.0785973i
$238$		0			0
$239$	15.2273	+	15.2273i	0.984972	+	0.984972i	0.999889	−	0.0149168i	$-0.00474835\pi$
$239$	15.2273	+	15.2273i	0.984972	+	0.984972i	−0.0149168	+	0.999889i	$0.504748\pi$
$240$	1.78045	−	6.64475i	0.114928	−	0.428917i
$241$	2.48112	+	2.48112i	0.159823	+	0.159823i	0.782488	−	0.622665i	$-0.213950\pi$
$241$	2.48112	+	2.48112i	0.159823	+	0.159823i	−0.622665	+	0.782488i	$0.713950\pi$
$242$	−16.2819	−	4.36271i	−1.04664	−	0.280446i
$243$	12.2279	−	7.05977i	0.784419	−	0.452885i
$244$	9.45024	+	16.3683i	0.604989	+	1.04787i
$245$		0			0
$246$		−	14.8795i		−	0.948680i
$247$	−7.85235	−	4.49534i	−0.499633	−	0.286032i
$248$	17.5387	−	10.1260i	1.11371	−	0.643000i
$249$	8.40244	−	2.25143i	0.532483	−	0.142678i
$250$			1.30250i			0.0823772i
$251$	−8.75834	+	15.1699i	−0.552822	+	0.957515i	0.445248	+	0.895407i	$0.353116\pi$
$251$	−8.75834	+	15.1699i	−0.552822	+	0.957515i	−0.998069	+	0.0621079i	$0.980218\pi$
$252$		0			0
$253$	−21.5046	+	5.76214i	−1.35198	+	0.362262i
$254$	2.70634	+	0.725163i	0.169811	+	0.0455008i
$255$	−1.43283	+	5.34741i	−0.0897276	+	0.334868i
$256$	−25.7218			−1.60761
$257$	6.85118			0.427365			0.213683	−	0.976903i	$-0.431454\pi$
$257$	6.85118			0.427365			0.213683	+	0.976903i	$0.431454\pi$
$258$	−4.64639	+	17.3406i	−0.289272	+	1.07958i
$259$		0			0
$260$	−41.4736	+	0.151708i	−2.57208	+	0.00940850i
$261$	2.08858	−	3.61753i	0.129280	−	0.223920i
$262$	−5.92674	−	22.1189i	−0.366155	−	1.36651i
$263$	−8.70849	+	15.0836i	−0.536989	+	0.930092i	0.462076	+	0.886841i	$0.347105\pi$
$263$	−8.70849	+	15.0836i	−0.536989	+	0.930092i	−0.999064	+	0.0432511i	$0.986228\pi$
$264$	−9.73350	−	16.8589i	−0.599056	−	1.03759i
$265$	17.1068	−	17.1068i	1.05086	−	1.05086i
$266$		0			0
$267$	−2.17830	−	8.12952i	−0.133310	−	0.497518i
$268$	−8.18157	−	30.5340i	−0.499769	−	1.86516i
$269$		−	0.167750i		−	0.0102279i	−0.999987	−	0.00511396i	$-0.998372\pi$
$269$		−	0.167750i		−	0.0102279i	0.999987	−	0.00511396i	$-0.00162783\pi$
$270$	35.8126	+	20.6764i	2.17949	+	1.25833i
$271$	1.76361	+	1.76361i	0.107131	+	0.107131i	0.758641	−	0.651509i	$-0.225864\pi$
$271$	1.76361	+	1.76361i	0.107131	+	0.107131i	−0.651509	+	0.758641i	$0.725864\pi$
$272$	−2.59009			−0.157047
$273$		0			0
$274$	15.6167			0.943441
$275$	15.5686	+	15.5686i	0.938821	+	0.938821i
$276$	−19.6399	−	11.3391i	−1.18218	−	0.682532i
$277$			8.53013i			0.512526i	0.966607	+	0.256263i	$0.0824913\pi$
$277$			8.53013i			0.512526i	−0.966607	+	0.256263i	$0.917509\pi$
$278$	13.9230	+	51.9613i	0.835046	+	3.11643i
$279$	2.14210	+	7.99444i	0.128244	+	0.478614i
$280$		0			0
$281$	15.7936	−	15.7936i	0.942166	−	0.942166i	−0.0562508	−	0.998417i	$-0.517915\pi$
$281$	15.7936	−	15.7936i	0.942166	−	0.942166i	0.998417	+	0.0562508i	$0.0179146\pi$
$282$	−9.42071	−	16.3171i	−0.560995	−	0.971672i
$283$	−4.79048	+	8.29736i	−0.284765	+	0.493227i	−0.972552	−	0.232685i	$-0.925249\pi$
$283$	−4.79048	+	8.29736i	−0.284765	+	0.493227i	0.687787	+	0.725912i	$0.258582\pi$
$284$	8.03949	+	30.0038i	0.477056	+	1.78040i
$285$	−4.81132	+	8.33345i	−0.284998	+	0.493631i
$286$	−25.6021	+	25.7901i	−1.51388	+	1.52500i
$287$		0			0
$288$	1.35194	−	5.04550i	0.0796636	−	0.297309i
$289$	−14.9156			−0.877389
$290$	20.2922			1.19160
$291$	−1.95508	+	7.29645i	−0.114609	+	0.427726i
$292$	55.0802	+	14.7587i	3.22333	+	0.863688i
$293$	14.5286	−	3.89292i	0.848769	−	0.227427i	0.191884	−	0.981418i	$-0.438540\pi$
$293$	14.5286	−	3.89292i	0.848769	−	0.227427i	0.656885	+	0.753991i	$0.271874\pi$
$294$		0			0
$295$	−3.23895	+	5.61003i	−0.188579	+	0.326628i
$296$			2.36079i			0.137218i
$297$	22.5141	−	6.03264i	1.30640	−	0.350049i
$298$	31.1485	−	17.9836i	1.80438	−	1.04176i
$299$	−4.81412	+	18.2331i	−0.278408	+	1.05444i
$300$			22.4277i			1.29486i
$301$		0			0
$302$	8.51488	+	14.7482i	0.489976	+	0.848663i
$303$	13.8885	−	8.01855i	0.797875	−	0.460654i
$304$	−4.34863	−	1.16521i	−0.249411	−	0.0668295i
$305$	−11.8190	−	11.8190i	−0.676755	−	0.676755i
$306$	1.37546	−	5.13328i	0.0786296	−	0.293450i
$307$	−15.7439	−	15.7439i	−0.898552	−	0.898552i	0.0967560	−	0.995308i	$-0.469153\pi$
$307$	−15.7439	−	15.7439i	−0.898552	−	0.898552i	−0.995308	+	0.0967560i	$0.969153\pi$
$308$		0			0
$309$	6.42882	−	3.71168i	0.365723	−	0.211150i
$310$	−28.4299	+	28.4299i	−1.61471	+	1.61471i
$311$	−1.94686	−	3.37206i	−0.110396	−	0.191212i	0.805534	−	0.592550i	$-0.201879\pi$
$311$	−1.94686	−	3.37206i	−0.110396	−	0.191212i	−0.915930	+	0.401338i	$0.868545\pi$
$312$	−16.4893	+	0.0603167i	−0.933522	+	0.00341476i
$313$	−8.63858	−	4.98749i	−0.488282	−	0.281910i	0.235580	−	0.971855i	$-0.424301\pi$
$313$	−8.63858	−	4.98749i	−0.488282	−	0.281910i	−0.723861	+	0.689946i	$0.757634\pi$
$314$	43.4620	+	11.6456i	2.45270	+	0.657199i
$315$		0			0
$316$	−6.28689	−	3.62974i	−0.353665	−	0.204189i
$317$	−14.9972	+	4.01848i	−0.842326	+	0.225701i	−0.654084	−	0.756422i	$-0.726946\pi$
$317$	−14.9972	+	4.01848i	−0.842326	+	0.225701i	−0.188242	+	0.982123i	$0.560279\pi$
$318$	15.2686	−	15.2686i	0.856223	−	0.856223i
$319$	8.08759	−	8.08759i	0.452818	−	0.452818i
$320$	35.5642	−	9.52940i	1.98810	−	0.532710i
$321$	8.89905	+	5.13787i	0.496697	+	0.286768i
$322$		0			0
$323$	3.49959	+	0.937714i	0.194723	+	0.0521758i
$324$	5.99535	+	3.46142i	0.333075	+	0.192301i
$325$	17.9964	−	4.89274i	0.998259	−	0.271400i
$326$	1.20057	+	2.07946i	0.0664936	+	0.115170i
$327$	−3.96893	+	3.96893i	−0.219482	+	0.219482i
$328$	−17.2191	+	9.94146i	−0.950766	+	0.548925i
$329$		0			0
$330$	27.3280	+	27.3280i	1.50436	+	1.50436i
$331$	−3.79022	+	14.1453i	−0.208329	+	0.777495i	0.780080	+	0.625680i	$0.215178\pi$
$331$	−3.79022	+	14.1453i	−0.208329	+	0.777495i	−0.988409	+	0.151815i	$0.951488\pi$
$332$	−18.4518	−	18.4518i	−1.01268	−	1.01268i
$333$	−0.931919	−	0.249707i	−0.0510688	−	0.0136839i
$334$	−4.14075	+	2.39066i	−0.226572	+	0.130811i
$335$	13.9776	+	24.2100i	0.763680	+	1.32273i
$336$		0			0
$337$			11.8235i			0.644066i	0.946728	+	0.322033i	$0.104366\pi$
$337$			11.8235i			0.644066i	−0.946728	+	0.322033i	$0.895634\pi$
$338$	8.18416	+	29.6736i	0.445159	+	1.61403i
$339$	−20.4097	+	11.7835i	−1.10850	+	0.639993i
$340$	16.0412	−	4.29823i	0.869956	−	0.233104i
$341$			22.6619i			1.22721i
$342$	4.61865	−	7.99973i	0.249748	−	0.432576i
$343$		0			0
$344$	23.1716	−	6.20881i	1.24933	−	0.334756i
$345$	19.3720	+	5.19072i	1.04295	+	0.279459i
$346$	−1.50174	+	5.60457i	−0.0807340	+	0.301303i
$347$	−10.0137			−0.537564			−0.268782	−	0.963201i	$-0.586621\pi$
$347$	−10.0137			−0.537564			−0.268782	+	0.963201i	$0.586621\pi$
$348$	11.6508			0.624547
$349$	4.39634	−	16.4073i	0.235330	−	0.878265i	−0.742669	−	0.669658i	$-0.766441\pi$
$349$	4.39634	−	16.4073i	0.235330	−	0.878265i	0.978000	−	0.208607i	$-0.0668928\pi$
$350$		0			0
$351$	5.04012	−	19.0890i	0.269022	−	1.01890i
$352$	7.15125	−	12.3863i	0.381163	−	0.660194i
$353$	9.33817	+	34.8505i	0.497021	+	1.85491i	0.518405	+	0.855135i	$0.326526\pi$
$353$	9.33817	+	34.8505i	0.497021	+	1.85491i	−0.0213843	+	0.999771i	$0.506807\pi$
$354$	−2.89091	+	5.00721i	−0.153650	+	0.266130i
$355$	−13.7349	−	23.7896i	−0.728973	−	1.26262i
$356$	−17.8525	+	17.8525i	−0.946181	+	0.946181i
$357$		0			0
$358$	4.60217	+	17.1755i	0.243232	+	0.907756i
$359$	−0.896679	−	3.34645i	−0.0473249	−	0.176619i	0.938218	−	0.346045i	$-0.112475\pi$
$359$	−0.896679	−	3.34645i	−0.0473249	−	0.176619i	−0.985543	+	0.169426i	$0.945809\pi$
$360$		−	18.8609i		−	0.994059i
$361$	−11.0007	−	6.35125i	−0.578984	−	0.334276i
$362$	8.25963	+	8.25963i	0.434117	+	0.434117i
$363$	8.55873			0.449217
$364$		0			0
$365$	−50.4284			−2.63954
$366$	−10.5490	−	10.5490i	−0.551406	−	0.551406i
$367$	−10.9829	−	6.34099i	−0.573303	−	0.330997i	0.185164	−	0.982708i	$-0.440718\pi$
$367$	−10.9829	−	6.34099i	−0.573303	−	0.330997i	−0.758468	+	0.651711i	$0.774052\pi$
$368$			9.38309i			0.489128i
$369$	−2.10307	−	7.84876i	−0.109481	−	0.408590i
$370$	−1.21305	−	4.52715i	−0.0630633	−	0.235355i
$371$		0			0
$372$	−16.3231	+	16.3231i	−0.846312	+	0.846312i
$373$	−15.0192	−	26.0141i	−0.777667	−	1.34696i	−0.933283	−	0.359141i	$-0.883070\pi$
$373$	−15.0192	−	26.0141i	−0.777667	−	1.34696i	0.155617	−	0.987818i	$-0.450264\pi$
$374$	7.27567	−	12.6018i	0.376216	−	0.651625i
$375$	−0.171168	−	0.638808i	−0.00883908	−	0.0329879i
$376$	−12.5886	+	21.8040i	−0.649206	+	1.12446i
$377$	−2.54169	−	9.34878i	−0.130904	−	0.481487i
$378$		0			0
$379$	3.10882	−	11.6023i	0.159689	−	0.595969i	−0.838969	−	0.544180i	$-0.816841\pi$
$379$	3.10882	−	11.6023i	0.159689	−	0.595969i	0.998658	−	0.0517891i	$-0.0164924\pi$
$380$	28.8660			1.48080
$381$	−1.42262			−0.0728830
$382$	−3.73133	+	13.9255i	−0.190911	+	0.712490i
$383$	5.52856	+	1.48137i	0.282496	+	0.0756947i	0.397285	−	0.917695i	$-0.369952\pi$
$383$	5.52856	+	1.48137i	0.282496	+	0.0756947i	−0.114789	+	0.993390i	$0.536619\pi$
$384$	23.9387	−	6.41436i	1.22162	−	0.327331i
$385$		0			0
$386$	−17.1520	+	29.7082i	−0.873015	+	1.51211i
$387$			9.80368i			0.498349i
$388$	21.8879	−	5.86486i	1.11119	−	0.297743i
$389$	−14.2446	+	8.22413i	−0.722231	+	0.416980i	−0.815573	−	0.578654i	$-0.803578\pi$
$389$	−14.2446	+	8.22413i	−0.722231	+	0.416980i	0.0933424	+	0.995634i	$0.470245\pi$
$390$	31.5896	−	8.58837i	1.59960	−	0.434889i
$391$		−	7.55112i		−	0.381877i
$392$		0			0
$393$	5.81352	+	10.0693i	0.293253	+	0.507930i
$394$	−34.3329	+	19.8221i	−1.72967	+	0.998624i
$395$	6.20115	+	1.66159i	0.312014	+	0.0836038i
$396$	−16.8754	−	16.8754i	−0.848021	−	0.848021i
$397$	2.92375	−	10.9116i	0.146739	−	0.547636i	−0.852933	−	0.522020i	$-0.825179\pi$
$397$	2.92375	−	10.9116i	0.146739	−	0.547636i	0.999672	−	0.0256162i	$-0.00815477\pi$
$398$	33.1761	+	33.1761i	1.66297	+	1.66297i
$399$		0			0
$400$	8.03625	−	4.63973i	0.401812	−	0.231987i
$401$	17.1175	−	17.1175i	0.854808	−	0.854808i	−0.135913	−	0.990721i	$-0.543397\pi$
$401$	17.1175	−	17.1175i	0.854808	−	0.854808i	0.990721	+	0.135913i	$0.0433967\pi$
$402$	12.4757	+	21.6085i	0.622231	+	1.07774i
$403$	16.6589	+	9.53694i	0.829838	+	0.475069i
$404$	−41.6629	−	24.0541i	−2.07281	−	1.19674i
$405$	−5.91359	−	1.58454i	−0.293849	−	0.0787366i
$406$		0			0
$407$	−2.28780	−	1.32086i	−0.113402	−	0.0654726i
$408$	6.37774	−	1.70891i	0.315745	−	0.0846037i
$409$	−0.255125	+	0.255125i	−0.0126151	+	0.0126151i	−0.713386	−	0.700771i	$-0.752839\pi$
$409$	−0.255125	+	0.255125i	−0.0126151	+	0.0126151i	0.700771	+	0.713386i	$0.252839\pi$
$410$	27.9119	−	27.9119i	1.37847	−	1.37847i
$411$	−7.65920	+	2.05228i	−0.377800	+	0.101231i
$412$	−19.2852	−	11.1343i	−0.950114	−	0.548549i
$413$		0			0
$414$	−18.5963	−	4.98286i	−0.913957	−	0.244894i
$415$	19.9852	+	11.5385i	0.981036	+	0.566401i
$416$	−6.09576	−	10.4695i	−0.298869	−	0.513311i
$417$	−13.6570	−	23.6547i	−0.668787	−	1.15837i
$418$	17.8847	−	17.8847i	0.874770	−	0.874770i
$419$	−15.9181	+	9.19033i	−0.777651	+	0.448977i	−0.835597	−	0.549343i	$-0.814878\pi$
$419$	−15.9181	+	9.19033i	−0.777651	+	0.448977i	0.0579460	+	0.998320i	$0.481545\pi$
$420$		0			0
$421$	20.7439	+	20.7439i	1.01099	+	1.01099i	0.999939	+	0.0110561i	$0.00351933\pi$
$421$	20.7439	+	20.7439i	1.01099	+	1.01099i	0.0110561	+	0.999939i	$0.496481\pi$
$422$	11.7222	−	43.7479i	0.570629	−	2.12962i
$423$	−7.27559	−	7.27559i	−0.353751	−	0.353751i
$424$	−27.8710	−	7.46800i	−1.35353	−	0.362678i
$425$	−6.46724	+	3.73386i	−0.313707	+	0.181119i
$426$	−12.2590	−	21.2333i	−0.593952	−	1.02876i
$427$		0			0
$428$		−	30.8252i		−	1.48999i
$429$	9.16729	−	16.0132i	0.442601	−	0.773125i
$430$	−41.2445	+	23.8125i	−1.98899	+	1.14834i
$431$	9.32194	−	2.49781i	0.449022	−	0.120315i	−0.0272197	−	0.999629i	$-0.508665\pi$
$431$	9.32194	−	2.49781i	0.449022	−	0.120315i	0.476242	+	0.879314i	$0.341999\pi$
$432$		−	9.82358i		−	0.472637i
$433$	13.6960	−	23.7221i	0.658186	−	1.14001i	−0.322899	−	0.946433i	$-0.604657\pi$
$433$	13.6960	−	23.7221i	0.658186	−	1.14001i	0.981085	−	0.193578i	$-0.0620093\pi$
$434$		0			0
$435$	−9.95227	+	2.66670i	−0.477175	+	0.127859i
$436$	16.2639	+	4.35791i	0.778901	+	0.208706i
$437$	3.39705	−	12.6780i	0.162503	−	0.606469i
$438$	−45.0097			−2.15065
$439$	−34.5915			−1.65096			−0.825481	−	0.564429i	$-0.809096\pi$
$439$	−34.5915			−1.65096			−0.825481	+	0.564429i	$0.809096\pi$
$440$	13.3663	−	49.8838i	0.637214	−	2.37812i
$441$		0			0
$442$	−6.20181	−	10.6517i	−0.294990	−	0.506649i
$443$	−3.98607	+	6.90408i	−0.189384	+	0.328023i	−0.945045	−	0.326940i	$-0.893982\pi$
$443$	−3.98607	+	6.90408i	−0.189384	+	0.328023i	0.755661	+	0.654963i	$0.227316\pi$
$444$	−0.696472	−	2.59927i	−0.0330531	−	0.123356i
$445$	11.1637	−	19.3361i	0.529209	−	0.916617i
$446$	0.821959	+	1.42368i	0.0389209	+	0.0674130i
$447$	−12.9134	+	12.9134i	−0.610784	+	0.610784i
$448$		0			0
$449$	−5.25579	−	19.6149i	−0.248036	−	0.925683i	−0.971833	−	0.235670i	$-0.924271\pi$
$449$	−5.25579	−	19.6149i	−0.248036	−	0.925683i	0.723797	−	0.690013i	$-0.242395\pi$
$450$	4.92782	+	18.3909i	0.232300	+	0.866955i
$451$		−	22.2489i		−	1.04766i
$452$	61.2250	+	35.3483i	2.87978	+	1.66264i
$453$	−6.11425	−	6.11425i	−0.287272	−	0.287272i
$454$	12.3400			0.579146
$455$		0			0
$456$	11.4767			0.537446
$457$	0.993775	+	0.993775i	0.0464868	+	0.0464868i	0.729968	−	0.683481i	$-0.239535\pi$
$457$	0.993775	+	0.993775i	0.0464868	+	0.0464868i	−0.683481	+	0.729968i	$0.739535\pi$
$458$	2.17215	+	1.25409i	0.101498	+	0.0585998i
$459$			7.90561i			0.369002i
$460$	−15.5711	−	58.1123i	−0.726009	−	2.70950i
$461$	−4.89285	−	18.2604i	−0.227883	−	0.850469i	−0.981229	−	0.192846i	$-0.938228\pi$
$461$	−4.89285	−	18.2604i	−0.227883	−	0.850469i	0.753347	−	0.657624i	$-0.228438\pi$
$462$		0			0
$463$	22.4573	−	22.4573i	1.04368	−	1.04368i	0.0446754	−	0.999002i	$-0.485775\pi$
$463$	22.4573	−	22.4573i	1.04368	−	1.04368i	0.999002	−	0.0446754i	$-0.0142253\pi$
$464$	−2.41026	−	4.17468i	−0.111893	−	0.193805i
$465$	10.2073	−	17.6795i	0.473352	−	0.819869i
$466$	−0.809576	−	3.02138i	−0.0375029	−	0.139963i
$467$	14.1945	−	24.5855i	0.656841	−	1.13768i	−0.324588	−	0.945855i	$-0.605226\pi$
$467$	14.1945	−	24.5855i	0.656841	−	1.13768i	0.981429	−	0.191826i	$-0.0614410\pi$
$468$	−19.5070	+	5.30343i	−0.901711	+	0.245151i
$469$		0			0
$470$	12.9368	−	48.2807i	0.596729	−	2.22702i
$471$	−22.8463			−1.05270
$472$	7.72605			0.355620
$473$	−6.94764	+	25.9290i	−0.319453	+	1.19221i
$474$	5.53481	+	1.48305i	0.254222	+	0.0681187i
$475$	−12.5379	+	3.35953i	−0.575280	+	0.154146i
$476$		0			0
$477$	5.89597	−	10.2121i	0.269958	−	0.467581i
$478$			50.9900i			2.33223i
$479$	−3.37834	+	0.905222i	−0.154360	+	0.0413607i	−0.335172	−	0.942157i	$-0.608794\pi$
$479$	−3.37834	+	0.905222i	−0.154360	+	0.0413607i	0.180811	+	0.983518i	$0.442128\pi$
$480$	−11.1580	+	6.44208i	−0.509291	+	0.294039i
$481$	−1.93376	+	1.12591i	−0.0881717	+	0.0513369i
$482$			8.30825i			0.378430i
$483$		0			0
$484$	−12.8373	−	22.2348i	−0.583512	−	1.01067i
$485$	−17.3546	+	10.0197i	−0.788033	+	0.454971i
$486$	32.2933	+	8.65295i	1.46485	+	0.392506i
$487$	17.1904	+	17.1904i	0.778973	+	0.778973i	0.979656	−	0.200683i	$-0.0643161\pi$
$487$	17.1904	+	17.1904i	0.778973	+	0.778973i	−0.200683	+	0.979656i	$0.564316\pi$
$488$	−5.15960	+	19.2559i	−0.233564	+	0.871672i
$489$	−0.862092	−	0.862092i	−0.0389851	−	0.0389851i
$490$		0			0
$491$	−5.24444	+	3.02788i	−0.236678	+	0.136646i	−0.613649	−	0.789579i	$-0.710299\pi$
$491$	−5.24444	+	3.02788i	−0.236678	+	0.136646i	0.376971	+	0.926225i	$0.376966\pi$
$492$	16.0256	−	16.0256i	0.722491	−	0.722491i
$493$	1.93967	+	3.35961i	0.0873584	+	0.151309i
$494$	−5.62063	−	20.6737i	−0.252884	−	0.930153i
$495$	18.2778	+	10.5527i	0.821525	+	0.474308i
$496$	9.22569	+	2.47202i	0.414246	+	0.110997i
$497$		0			0
$498$	17.8377	+	10.2986i	0.799328	+	0.461492i
$499$	−17.6712	+	4.73497i	−0.791070	+	0.211967i	−0.631660	−	0.775246i	$-0.717626\pi$
$499$	−17.6712	+	4.73497i	−0.791070	+	0.211967i	−0.159410	+	0.987212i	$0.550959\pi$
$500$	−1.40283	+	1.40283i	−0.0627364	+	0.0627364i
$501$	1.71665	−	1.71665i	0.0766945	−	0.0766945i
$502$	−40.0629	+	10.7348i	−1.78810	+	0.479119i
$503$	−7.01237	−	4.04859i	−0.312666	−	0.180518i	0.335453	−	0.942057i	$-0.391111\pi$
$503$	−7.01237	−	4.04859i	−0.312666	−	0.180518i	−0.648119	+	0.761539i	$0.724444\pi$
$504$		0			0
$505$	41.0947	+	11.0113i	1.82869	+	0.489996i
$506$	−45.6526	−	26.3575i	−2.02950	−	1.17173i
$507$	−7.91347	−	13.4779i	−0.351450	−	0.598573i
$508$	2.13379	+	3.69583i	0.0946717	+	0.163976i
$509$	11.4221	−	11.4221i	0.506275	−	0.506275i	−0.407106	−	0.913381i	$-0.633462\pi$
$509$	11.4221	−	11.4221i	0.506275	−	0.506275i	0.913381	+	0.407106i	$0.133462\pi$
$510$	−11.3521	+	6.55416i	−0.502681	+	0.290223i
$511$		0			0
$512$	−13.9135	−	13.9135i	−0.614896	−	0.614896i
$513$	−3.55652	+	13.2731i	−0.157024	+	0.586023i
$514$	11.4709	+	11.4709i	0.505960	+	0.505960i
$515$	19.0222	+	5.09699i	0.838219	+	0.224600i
$516$	−23.6806	+	13.6720i	−1.04248	+	0.601876i
$517$	−14.0866	−	24.3987i	−0.619527	−	1.07305i
$518$		0			0
$519$		−	2.94610i		−	0.129320i
$520$	−31.0448	−	30.8185i	−1.36141	−	1.35148i
$521$	28.0133	−	16.1735i	1.22729	−	0.708574i	0.260825	−	0.965386i	$-0.416005\pi$
$521$	28.0133	−	16.1735i	1.22729	−	0.708574i	0.966461	+	0.256812i	$0.0826721\pi$
$522$	9.55373	−	2.55991i	0.418155	−	0.112044i
$523$		−	21.3161i		−	0.932086i	−0.884762	−	0.466043i	$-0.845679\pi$
$523$		−	21.3161i		−	0.932086i	0.884762	−	0.466043i	$-0.154321\pi$
$524$	17.4394	−	30.2060i	0.761845	−	1.31956i
$525$		0			0
$526$	−39.8349	+	10.6737i	−1.73688	+	0.465397i
$527$	−7.42445	−	1.98937i	−0.323414	−	0.0866585i
$528$	2.37620	−	8.86811i	0.103411	−	0.385935i
$529$	−4.35538			−0.189364
$530$	57.2838			2.48825
$531$	−0.817205	+	3.04985i	−0.0354637	+	0.132352i
$532$		0			0
$533$	−16.3553	−	9.36315i	−0.708428	−	0.405563i
$534$	9.96410	−	17.2583i	0.431189	−	0.746841i
$535$	7.05547	+	26.3314i	0.305034	+	1.13840i
$536$	16.6708	−	28.8747i	0.720070	−	1.24720i
$537$	−4.51426	−	7.81892i	−0.194805	−	0.337411i
$538$	0.280864	−	0.280864i	0.0121089	−	0.0121089i
$539$		0			0
$540$	16.3021	+	60.8404i	0.701532	+	2.61815i
$541$	4.79305	+	17.8879i	0.206069	+	0.769061i	0.989121	+	0.147104i	$0.0469953\pi$
$541$	4.79305	+	17.8879i	0.206069	+	0.769061i	−0.783052	+	0.621957i	$0.786338\pi$
$542$			5.90560i			0.253667i
$543$	−5.13637	−	2.96548i	−0.220423	−	0.127261i
$544$	3.43021	+	3.43021i	0.147069	+	0.147069i
$545$	−14.8904			−0.637833
$546$		0			0
$547$	−35.0943			−1.50053			−0.750263	−	0.661140i	$-0.770073\pi$
$547$	−35.0943			−1.50053			−0.750263	+	0.661140i	$0.770073\pi$
$548$	16.8197	+	16.8197i	0.718501	+	0.718501i
$549$	−7.05549	−	4.07349i	−0.301121	−	0.173852i
$550$			52.1328i			2.22295i
$551$	1.74521	+	6.51323i	0.0743486	+	0.277473i
$552$	−6.19086	−	23.1046i	−0.263500	−	0.983397i
$553$		0			0
$554$	−14.2820	+	14.2820i	−0.606782	+	0.606782i
$555$	1.18987	+	2.06092i	0.0505073	+	0.0874812i
$556$	−40.9684	+	70.9594i	−1.73745	+	3.00935i
$557$	−2.45464	−	9.16086i	−0.104007	−	0.388158i	0.894224	−	0.447620i	$-0.147728\pi$
$557$	−2.45464	−	9.16086i	−0.104007	−	0.388158i	−0.998231	+	0.0594618i	$0.981062\pi$
$558$	−9.79854	+	16.9716i	−0.414805	+	0.718464i
$559$	16.1367	+	16.0191i	0.682510	+	0.677535i
$560$		0			0
$561$	−1.91227	+	7.13668i	−0.0807360	+	0.301311i
$562$	52.8862			2.23087
$563$	−31.6702			−1.33474			−0.667369	−	0.744727i	$-0.732580\pi$
$563$	−31.6702			−1.33474			−0.667369	+	0.744727i	$0.732580\pi$
$564$	7.42767	−	27.7204i	0.312761	−	1.16724i
$565$	−60.3901	−	16.1815i	−2.54063	−	0.680760i
$566$	−21.9129	+	5.87155i	−0.921069	+	0.246800i
$567$		0			0
$568$	−16.3813	+	28.3733i	−0.687345	+	1.19052i
$569$		−	6.99573i		−	0.293276i	−0.989190	−	0.146638i	$-0.953155\pi$
$569$		−	6.99573i		−	0.293276i	0.989190	−	0.146638i	$-0.0468453\pi$
$570$	−22.0082	+	5.89708i	−0.921823	+	0.247002i
$571$	13.2500	−	7.64990i	0.554496	−	0.320139i	−0.196437	−	0.980516i	$-0.562937\pi$
$571$	13.2500	−	7.64990i	0.554496	−	0.320139i	0.750933	+	0.660378i	$0.229604\pi$
$572$	−55.3509	+	0.202470i	−2.31434	+	0.00846568i
$573$		−	7.32009i		−	0.305801i
$574$		0			0
$575$	13.5266	+	23.4288i	0.564099	+	0.977049i
$576$	15.5418	−	8.97304i	0.647574	−	0.373877i
$577$	−40.3714	−	10.8175i	−1.68068	−	0.450338i	−0.712725	−	0.701444i	$-0.752539\pi$
$577$	−40.3714	−	10.8175i	−1.68068	−	0.450338i	−0.967960	+	0.251106i	$0.919206\pi$
$578$	−24.9731	−	24.9731i	−1.03875	−	1.03875i
$579$	4.50807	−	16.8244i	0.187349	−	0.699196i
$580$	21.8553	+	21.8553i	0.907491	+	0.907491i
$581$		0			0
$582$	−15.4898	+	8.94304i	−0.642073	+	0.370701i
$583$	22.8309	−	22.8309i	0.945558	−	0.945558i
$584$	30.0724	+	52.0870i	1.24441	+	2.15538i
$585$	15.4493	−	8.99515i	0.638749	−	0.371904i
$586$	30.8431	+	17.8073i	1.27412	+	0.735611i
$587$	−0.941084	−	0.252163i	−0.0388427	−	0.0104079i	0.239345	−	0.970934i	$-0.423067\pi$
$587$	−0.941084	−	0.252163i	−0.0388427	−	0.0104079i	−0.278188	+	0.960527i	$0.589734\pi$
$588$		0			0
$589$	−11.5703	−	6.68012i	−0.476746	−	0.275250i
$590$	−14.8158	+	3.96988i	−0.609957	+	0.163437i
$591$	14.2336	−	14.2336i	0.585492	−	0.585492i
$592$	−0.787282	+	0.787282i	−0.0323571	+	0.0323571i
$593$	−38.1404	+	10.2197i	−1.56624	+	0.419673i	−0.934632	−	0.355616i	$-0.884271\pi$
$593$	−38.1404	+	10.2197i	−1.56624	+	0.419673i	−0.631608	+	0.775288i	$0.717605\pi$
$594$	47.7957	+	27.5949i	1.96108	+	1.13223i
$595$		0			0
$596$	52.9167	+	14.1790i	2.16755	+	0.580794i
$597$	−20.6310	−	11.9113i	−0.844370	−	0.487497i
$598$	−38.5878	+	22.4673i	−1.57797	+	0.918755i
$599$	−8.27438	−	14.3316i	−0.338082	−	0.585575i	0.645990	−	0.763346i	$-0.276445\pi$
$599$	−8.27438	−	14.3316i	−0.338082	−	0.585575i	−0.984072	+	0.177771i	$0.943111\pi$
$600$	−16.7269	+	16.7269i	−0.682874	+	0.682874i
$601$	9.99562	−	5.77097i	0.407730	−	0.235403i	−0.282084	−	0.959390i	$-0.591026\pi$
$601$	9.99562	−	5.77097i	0.407730	−	0.235403i	0.689814	+	0.723987i	$0.257692\pi$
$602$		0			0
$603$	9.63495	+	9.63495i	0.392365	+	0.392365i
$604$	−6.71347	+	25.0550i	−0.273167	+	1.01947i
$605$	16.0550	+	16.0550i	0.652730	+	0.652730i
$606$	36.6789	+	9.82809i	1.48998	+	0.399239i
$607$	−18.5137	+	10.6889i	−0.751447	+	0.433848i	−0.826216	−	0.563353i	$-0.809511\pi$
$607$	−18.5137	+	10.6889i	−0.751447	+	0.433848i	0.0747696	+	0.997201i	$0.476178\pi$
$608$	4.21600	+	7.30232i	0.170981	+	0.296148i
$609$		0			0
$610$		−	39.5770i		−	1.60243i
$611$	−23.8637	+	0.0872919i	−0.965423	+	0.00353145i
$612$	7.01010	−	4.04728i	0.283366	−	0.163602i
$613$	−30.1473	+	8.07793i	−1.21764	+	0.326265i	−0.809754	−	0.586770i	$-0.800399\pi$
$613$	−30.1473	+	8.07793i	−1.21764	+	0.326265i	−0.407882	+	0.913034i	$0.633733\pi$
$614$		−	52.7199i		−	2.12760i
$615$	−10.0213	+	17.3574i	−0.404097	+	0.699917i
$616$		0			0
$617$	26.9421	−	7.21911i	1.08465	−	0.290630i	0.328149	−	0.944626i	$-0.393575\pi$
$617$	26.9421	−	7.21911i	1.08465	−	0.290630i	0.756498	+	0.653996i	$0.226909\pi$
$618$	16.9782	+	4.54929i	0.682963	+	0.182999i
$619$	−12.4597	+	46.5004i	−0.500799	+	1.86901i	−0.00603119	+	0.999982i	$0.501920\pi$
$619$	−12.4597	+	46.5004i	−0.500799	+	1.86901i	−0.494768	+	0.869025i	$0.664747\pi$
$620$	−61.2397			−2.45945
$621$	28.6396			1.14927
$622$	2.38621	−	8.90546i	0.0956783	−	0.357076i
$623$		0			0
$624$	−5.51901	−	5.47878i	−0.220937	−	0.219327i
$625$	−12.0539	+	20.8781i	−0.482158	+	0.835122i
$626$	−6.11301	−	22.8141i	−0.244325	−	0.911834i
$627$	−6.42121	+	11.1219i	−0.256438	+	0.444164i
$628$	34.2672	+	59.3525i	1.36741	+	2.36842i
$629$	0.633571	−	0.633571i	0.0252621	−	0.0252621i
$630$		0			0
$631$	−2.94853	−	11.0041i	−0.117379	−	0.438064i	0.882075	−	0.471109i	$-0.156146\pi$
$631$	−2.94853	−	11.0041i	−0.117379	−	0.438064i	−0.999454	+	0.0330448i	$0.989480\pi$
$632$	−1.98175	−	7.39598i	−0.0788296	−	0.294196i
$633$			22.9966i			0.914032i
$634$	−31.8379	−	18.3816i	−1.26444	−	0.730026i
$635$	−2.66864	−	2.66864i	−0.105902	−	0.105902i
$636$	32.8896			1.30416
$637$		0			0
$638$	27.0820			1.07219
$639$	−9.46763	−	9.46763i	−0.374534	−	0.374534i
$640$	56.9382	+	32.8733i	2.25068	+	1.29943i
$641$			19.5260i			0.771232i	0.922659	+	0.385616i	$0.126011\pi$
$641$			19.5260i			0.771232i	−0.922659	+	0.385616i	$0.873989\pi$
$642$	6.29733	+	23.5020i	0.248536	+	0.927548i
$643$	9.35047	+	34.8964i	0.368747	+	1.37618i	0.862270	+	0.506449i	$0.169042\pi$
$643$	9.35047	+	34.8964i	0.368747	+	1.37618i	−0.493524	+	0.869732i	$0.664291\pi$
$644$		0			0
$645$	17.0990	−	17.0990i	0.673272	−	0.673272i
$646$	4.28935	+	7.42937i	0.168762	+	0.292304i
$647$	−2.89695	+	5.01767i	−0.113891	+	0.197265i	−0.917336	−	0.398114i	$-0.869665\pi$
$647$	−2.89695	+	5.01767i	−0.113891	+	0.197265i	0.803445	+	0.595379i	$0.202998\pi$
$648$	1.88985	+	7.05301i	0.0742403	+	0.277069i
$649$	−4.32272	+	7.48717i	−0.169682	+	0.293897i
$650$	38.3231	+	21.9393i	1.50316	+	0.860532i
$651$		0			0
$652$	−0.946581	+	3.53269i	−0.0370710	+	0.138351i
$653$	36.2070			1.41689			0.708445	−	0.705766i	$-0.249397\pi$
$653$	36.2070			1.41689			0.708445	+	0.705766i	$0.249397\pi$
$654$	−13.2903			−0.519693
$655$	−7.98330	+	29.7941i	−0.311933	+	1.16415i
$656$	−9.05757	−	2.42697i	−0.353639	−	0.0947573i
$657$	−23.7421	+	6.36168i	−0.926269	+	0.248193i
$658$		0			0
$659$	−10.3685	+	17.9588i	−0.403901	+	0.699576i	−0.994193	−	0.107613i	$-0.965679\pi$
$659$	−10.3685	+	17.9588i	−0.403901	+	0.699576i	0.590292	+	0.807190i	$0.299013\pi$
$660$			58.8662i			2.29136i
$661$	32.7827	−	8.78410i	1.27510	−	0.341662i	0.443117	−	0.896464i	$-0.353872\pi$
$661$	32.7827	−	8.78410i	1.27510	−	0.341662i	0.831983	+	0.554801i	$0.187206\pi$
$662$	−30.0293	+	17.3374i	−1.16712	+	0.673838i
$663$	4.44146	+	4.40909i	0.172492	+	0.171235i
$664$		−	27.5234i		−	1.06811i
$665$		0			0
$666$	−1.14222	−	1.97839i	−0.0442603	−	0.0766611i
$667$	12.1708	−	7.02683i	0.471257	−	0.272080i
$668$	−7.03452	−	1.88490i	−0.272174	−	0.0729288i
$669$	−0.590221	−	0.590221i	−0.0228193	−	0.0228193i
$670$	−17.1320	+	63.9374i	−0.661866	+	2.47012i
$671$	−15.7737	−	15.7737i	−0.608937	−	0.608937i
$672$		0			0
$673$	−35.7571	+	20.6444i	−1.37834	+	0.795783i	−0.991959	−	0.126558i	$-0.959607\pi$
$673$	−35.7571	+	20.6444i	−1.37834	+	0.795783i	−0.386377	+	0.922341i	$0.626274\pi$
$674$	−19.7960	+	19.7960i	−0.762514	+	0.762514i
$675$	−14.1616	−	24.5287i	−0.545082	−	0.944109i
$676$	−23.1448	+	40.7739i	−0.890184	+	1.56823i
$677$	39.1750	+	22.6177i	1.50562	+	0.869268i	0.999979	+	0.00652270i	$0.00207626\pi$
$677$	39.1750	+	22.6177i	1.50562	+	0.869268i	0.505638	+	0.862746i	$0.331257\pi$
$678$	−53.9009	−	14.4427i	−2.07005	−	0.554669i
$679$		0			0
$680$	15.1695	+	8.75810i	0.581723	+	0.335858i
$681$	−6.05215	+	1.62167i	−0.231919	+	0.0621425i
$682$	−37.9427	+	37.9427i	−1.45290	+	1.45290i
$683$	30.7528	−	30.7528i	1.17672	−	1.17672i	0.196147	−	0.980574i	$-0.437157\pi$
$683$	30.7528	−	30.7528i	1.17672	−	1.17672i	0.980574	−	0.196147i	$-0.0628431\pi$
$684$	13.5904	−	3.64153i	0.519641	−	0.139237i
$685$	−18.2174	−	10.5178i	−0.696051	−	0.401866i
$686$		0			0
$687$	−1.23013	−	0.329613i	−0.0469325	−	0.0125755i
$688$	9.79785	+	5.65679i	0.373539	+	0.215663i
$689$	−7.17506	−	26.3911i	−0.273348	−	1.00542i
$690$	23.7437	+	41.1253i	0.903907	+	1.56561i
$691$	−15.2248	+	15.2248i	−0.579179	+	0.579179i	−0.934677	−	0.355498i	$-0.884311\pi$
$691$	−15.2248	+	15.2248i	−0.579179	+	0.579179i	0.355498	+	0.934677i	$0.384311\pi$
$692$	−7.65370	+	4.41887i	−0.290950	+	0.167980i
$693$		0			0
$694$	−16.7659	−	16.7659i	−0.636425	−	0.636425i
$695$	18.7542	−	69.9917i	0.711388	−	2.65494i
$696$	8.68934	+	8.68934i	0.329368	+	0.329368i
$697$	7.28916	+	1.95312i	0.276096	+	0.0739798i
$698$	34.8315	−	20.1100i	1.31839	−	0.761174i
$699$	0.794111	+	1.37544i	0.0300360	+	0.0520239i
$700$		0			0
$701$			8.77295i			0.331350i	0.986180	+	0.165675i	$0.0529803\pi$
$701$			8.77295i			0.331350i	−0.986180	+	0.165675i	$0.947020\pi$
$702$	40.3993	−	23.5220i	1.52477	−	0.887780i
$703$	1.34876	−	0.778708i	0.0508695	−	0.0293695i
$704$	47.4642	−	12.7180i	1.78887	−	0.479327i
$705$			25.3793i			0.955840i
$706$	−42.7152	+	73.9850i	−1.60761	+	2.78446i
$707$		0			0
$708$	−8.50651	+	2.27931i	−0.319694	+	0.0856618i
$709$	40.9718	+	10.9783i	1.53873	+	0.412300i	0.925854	−	0.377881i	$-0.123347\pi$
$709$	40.9718	+	10.9783i	1.53873	+	0.412300i	0.612872	+	0.790182i	$0.290014\pi$
$710$	16.8345	−	62.8270i	0.631786	−	2.35786i
$711$	3.12917			0.117353
$712$	−26.6294			−0.997978
$713$	−7.20689	+	26.8965i	−0.269900	+	1.00728i
$714$		0			0
$715$	47.2352	−	12.8420i	1.76650	−	0.480264i
$716$	−13.5419	+	23.4553i	−0.506084	+	0.876564i
$717$	−6.70086	−	25.0080i	−0.250248	−	0.933939i
$718$	4.10165	−	7.10426i	0.153072	−	0.265129i
$719$	−2.80010	−	4.84991i	−0.104426	−	0.180871i	0.809078	−	0.587702i	$-0.199967\pi$
$719$	−2.80010	−	4.84991i	−0.104426	−	0.180871i	−0.913504	+	0.406831i	$0.866634\pi$
$720$	6.28980	−	6.28980i	0.234407	−	0.234407i
$721$		0			0
$722$	−7.78453	−	29.0523i	−0.289710	−	1.08121i
$723$	−1.09183	−	4.07477i	−0.0406056	−	0.151542i
$724$			17.7917i			0.661225i
$725$	−12.0364	−	6.94923i	−0.447021	−	0.258088i
$726$	14.3299	+	14.3299i	0.531831	+	0.531831i
$727$	−32.0200			−1.18756			−0.593778	−	0.804629i	$-0.702364\pi$
$727$	−32.0200			−1.18756			−0.593778	+	0.804629i	$0.702364\pi$
$728$		0			0
$729$	−22.7339			−0.841996
$730$	−84.4321	−	84.4321i	−3.12497	−	3.12497i
$731$	−7.88490	−	4.55235i	−0.291633	−	0.168375i
$732$		−	22.7232i		−	0.839873i
$733$	−0.237044	−	0.884660i	−0.00875542	−	0.0326757i	0.961410	−	0.275120i	$-0.0887175\pi$
$733$	−0.237044	−	0.884660i	−0.00875542	−	0.0326757i	−0.970165	+	0.242444i	$0.922051\pi$
$734$	−7.77195	−	29.0053i	−0.286868	−	1.07061i
$735$		0			0
$736$	12.4266	−	12.4266i	0.458051	−	0.458051i
$737$	18.6546	+	32.3108i	0.687152	+	1.19018i
$738$	9.61998	−	16.6623i	0.354116	−	0.613348i
$739$	2.27016	+	8.47234i	0.0835090	+	0.311660i	0.995028	−	0.0995988i	$-0.0317559\pi$
$739$	2.27016	+	8.47234i	0.0835090	+	0.311660i	−0.911519	+	0.411259i	$0.865089\pi$
$740$	3.56939	−	6.18236i	0.131213	−	0.227268i
$741$	5.47347	+	9.40074i	0.201073	+	0.345345i
$742$		0			0
$743$	−9.56609	+	35.7011i	−0.350946	+	1.30975i	0.534564	+	0.845128i	$0.320476\pi$
$743$	−9.56609	+	35.7011i	−0.350946	+	1.30975i	−0.885510	+	0.464620i	$0.846191\pi$
$744$	−24.3480			−0.892642
$745$	−48.4476			−1.77498
$746$	18.4086	−	68.7019i	0.673988	−	2.51536i
$747$	10.8648	+	2.91122i	0.397523	+	0.106516i
$748$	21.4087	−	5.73643i	0.782778	−	0.209745i
$749$		0			0
$750$	0.782967	−	1.35614i	0.0285899	−	0.0495192i
$751$		−	12.4140i		−	0.452992i	−0.974012	−	0.226496i	$-0.927273\pi$
$751$		−	12.4140i		−	0.452992i	0.974012	−	0.226496i	$-0.0727270\pi$
$752$	−11.4693	+	3.07320i	−0.418243	+	0.112068i
$753$	18.2381	−	10.5298i	0.664633	−	0.383726i
$754$	11.3971	−	19.9082i	0.415057	−	0.725012i
$755$		−	22.9390i		−	0.834835i
$756$		0			0
$757$	11.7793	+	20.4023i	0.428124	+	0.741533i	0.996707	−	0.0810934i	$-0.0258412\pi$
$757$	11.7793	+	20.4023i	0.428124	+	0.741533i	−0.568582	+	0.822626i	$0.692508\pi$
$758$	24.6307	−	14.2206i	0.894628	−	0.516514i
$759$	25.8540	+	6.92756i	0.938441	+	0.251454i
$760$	21.5287	+	21.5287i	0.780930	+	0.780930i
$761$	3.50579	−	13.0838i	0.127085	−	0.474286i	−0.872821	−	0.488041i	$-0.837712\pi$
$761$	3.50579	−	13.0838i	0.127085	−	0.474286i	0.999905	+	0.0137545i	$0.00437834\pi$
$762$	−2.38189	−	2.38189i	−0.0862866	−	0.0862866i
$763$		0			0
$764$	−19.0169	+	10.9794i	−0.688008	+	0.397222i
$765$	−5.06176	+	5.06176i	−0.183008	+	0.183008i
$766$	6.77619	+	11.7367i	0.244834	+	0.424064i
$767$	3.68470	+	6.32852i	0.133047	+	0.228510i
$768$	26.7812	+	15.4621i	0.966382	+	0.557941i
$769$	−29.8604	−	8.00107i	−1.07679	−	0.288526i	−0.323512	−	0.946224i	$-0.604864\pi$
$769$	−29.8604	−	8.00107i	−1.07679	−	0.288526i	−0.753282	+	0.657698i	$0.771530\pi$
$770$		0			0
$771$	−7.13334	−	4.11844i	−0.256901	−	0.148322i
$772$	−50.4698	+	13.5233i	−1.81645	+	0.486716i
$773$	−14.1285	+	14.1285i	−0.508166	+	0.508166i	−0.913963	−	0.405797i	$-0.866994\pi$
$773$	−14.1285	+	14.1285i	−0.508166	+	0.508166i	0.405797	+	0.913963i	$0.366994\pi$
$774$	−16.4143	+	16.4143i	−0.589998	+	0.589998i
$775$	26.5994	−	7.12729i	0.955480	−	0.256020i
$776$	20.6985	+	11.9503i	0.743032	+	0.428990i
$777$		0			0
$778$	−37.6193	−	10.0801i	−1.34872	−	0.361388i
$779$	11.3595	+	6.55839i	0.406995	+	0.234979i
$780$	43.2728	+	24.7730i	1.54942	+	0.887015i
$781$	−18.3307	−	31.7497i	−0.655923	−	1.13609i
$782$	12.6428	−	12.6428i	0.452106	−	0.452106i
$783$	−12.7422	+	7.35671i	−0.455369	+	0.262907i
$784$		0			0
$785$	−42.8565	−	42.8565i	−1.52961	−	1.52961i
$786$	−7.12546	+	26.5926i	−0.254157	+	0.948526i
$787$	−35.0682	−	35.0682i	−1.25005	−	1.25005i	−0.955698	−	0.294350i	$-0.904897\pi$
$787$	−35.0682	−	35.0682i	−1.25005	−	1.25005i	−0.294350	−	0.955698i	$-0.595103\pi$
$788$	−58.3266	−	15.6286i	−2.07780	−	0.556744i
$789$	18.1343	−	10.4698i	0.645597	−	0.372736i
$790$	7.60056	+	13.1646i	0.270416	+	0.468374i
$791$		0			0
$792$		−	25.1719i		−	0.894445i
$793$	−18.2335	+	4.95720i	−0.647490	+	0.176035i
$794$	23.1644	−	13.3740i	0.822075	−	0.474625i
$795$	−28.0948	+	7.52797i	−0.996418	+	0.266990i
$796$			71.4632i			2.53295i
$797$	3.67854	−	6.37141i	0.130300	−	0.225687i	−0.793492	−	0.608581i	$-0.791739\pi$
$797$	3.67854	−	6.37141i	0.130300	−	0.225687i	0.923792	+	0.382894i	$0.125072\pi$
$798$		0			0
$799$	9.23003	−	2.47318i	0.326535	−	0.0874948i
$800$	−16.7876	−	4.49822i	−0.593531	−	0.159036i
$801$	2.81666	−	10.5119i	0.0995217	−	0.371420i
$802$	57.3196			2.02402
$803$	−67.3020			−2.37504
$804$	−9.83634	+	36.7097i	−0.346901	+	1.29465i
$805$		0			0
$806$	11.9243	+	43.8596i	0.420014	+	1.54489i
$807$	−0.100839	+	0.174659i	−0.00354972	+	0.00614829i
$808$	−13.1329	−	49.0128i	−0.462015	−	1.72426i
$809$	−20.3898	+	35.3162i	−0.716867	+	1.24165i	0.245368	+	0.969430i	$0.421091\pi$
$809$	−20.3898	+	35.3162i	−0.716867	+	1.24165i	−0.962235	+	0.272220i	$0.912242\pi$
$810$	−7.24811	−	12.5541i	−0.254673	−	0.441106i
$811$	2.15658	−	2.15658i	0.0757278	−	0.0757278i	−0.668228	−	0.743956i	$-0.732947\pi$
$811$	2.15658	−	2.15658i	0.0757278	−	0.0757278i	0.743956	+	0.668228i	$0.232947\pi$
$812$		0			0
$813$	−0.776086	−	2.89639i	−0.0272185	−	0.101581i
$814$	−1.61894	−	6.04195i	−0.0567437	−	0.211770i
$815$		−	3.23434i		−	0.113294i
$816$	2.69676	+	1.55697i	0.0944054	+	0.0545050i
$817$	−11.1904	−	11.1904i	−0.391501	−	0.391501i
$818$	−0.854311			−0.0298703
$819$		0			0
$820$	60.1238			2.09961
$821$	26.4192	+	26.4192i	0.922036	+	0.922036i	0.997173	−	0.0751375i	$-0.0239396\pi$
$821$	26.4192	+	26.4192i	0.922036	+	0.922036i	−0.0751375	+	0.997173i	$0.523940\pi$
$822$	−16.2599	−	9.38764i	−0.567128	−	0.327432i
$823$		−	36.8214i		−	1.28351i	−0.766908	−	0.641757i	$-0.778206\pi$
$823$		−	36.8214i		−	1.28351i	0.766908	−	0.641757i	$-0.221794\pi$
$824$	−6.07906	−	22.6874i	−0.211774	−	0.790352i
$825$	−6.85105	−	25.5685i	−0.238523	−	0.890179i
$826$		0			0
$827$	−16.2525	+	16.2525i	−0.565154	+	0.565154i	−0.930767	−	0.365613i	$-0.880859\pi$
$827$	−16.2525	+	16.2525i	−0.565154	+	0.565154i	0.365613	+	0.930767i	$0.380859\pi$
$828$	−14.6621	−	25.3954i	−0.509542	−	0.882552i
$829$	6.86086	−	11.8834i	0.238287	−	0.412726i	−0.721936	−	0.691960i	$-0.756747\pi$
$829$	6.86086	−	11.8834i	0.238287	−	0.412726i	0.960223	+	0.279234i	$0.0900806\pi$
$830$	14.1424	+	52.7800i	0.490888	+	1.83202i
$831$	5.12770	−	8.88143i	0.177878	−	0.308093i
$832$	10.6256	−	40.2434i	0.368375	−	1.39519i
$833$		0			0
$834$	16.7390	−	62.4708i	0.579624	−	2.16319i
$835$	6.44042			0.222880
$836$	38.5247			1.33241
$837$	7.54522	−	28.1591i	0.260801	−	0.973322i
$838$	−42.0390	−	11.2643i	−1.45221	−	0.389119i
$839$	4.02716	−	1.07907i	0.139033	−	0.0372537i	−0.188631	−	0.982048i	$-0.560405\pi$
$839$	4.02716	−	1.07907i	0.139033	−	0.0372537i	0.327664	+	0.944794i	$0.393738\pi$
$840$		0			0
$841$	10.8900	−	18.8620i	0.375517	−	0.650415i
$842$			69.4628i			2.39385i
$843$	−25.9380	+	6.95006i	−0.893351	+	0.239373i
$844$	59.7430	−	34.4926i	2.05644	−	1.18729i
$845$	10.4380	−	40.1272i	0.359079	−	1.38042i
$846$		−	24.3630i		−	0.837617i
$847$		0			0
$848$	−6.80403	−	11.7849i	−0.233651	−	0.404696i
$849$	9.97555	−	5.75939i	0.342360	−	0.197662i
$850$	−17.0796	−	4.57648i	−0.585827	−	0.156972i
$851$	−2.29523	−	2.29523i	−0.0786796	−	0.0786796i
$852$	9.66552	−	36.0722i	0.331135	−	1.23581i
$853$	3.44436	+	3.44436i	0.117933	+	0.117933i	0.763610	−	0.645678i	$-0.223425\pi$
$853$	3.44436	+	3.44436i	0.117933	+	0.117933i	−0.645678	+	0.763610i	$0.723425\pi$
$854$		0			0
$855$	−10.7756	+	6.22130i	−0.368518	+	0.212764i
$856$	22.9899	−	22.9899i	0.785780	−	0.785780i
$857$	24.3123	+	42.1101i	0.830491	+	1.43845i	0.897650	+	0.440710i	$0.145273\pi$
$857$	24.3123	+	42.1101i	0.830491	+	1.43845i	−0.0671586	+	0.997742i	$0.521393\pi$
$858$	42.1596	−	11.4621i	1.43930	−	0.391309i
$859$	−21.7355	−	12.5490i	−0.741606	−	0.428167i	0.0810468	−	0.996710i	$-0.474174\pi$
$859$	−21.7355	−	12.5490i	−0.741606	−	0.428167i	−0.822653	+	0.568544i	$0.807507\pi$
$860$	−70.0684	−	18.7748i	−2.38931	−	0.640214i
$861$		0			0
$862$	19.7898	+	11.4256i	0.674042	+	0.389158i
$863$	−50.2112	+	13.4540i	−1.70921	+	0.457981i	−0.975230	−	0.221192i	$-0.929005\pi$
$863$	−50.2112	+	13.4540i	−1.70921	+	0.457981i	−0.733978	+	0.679173i	$0.762338\pi$
$864$	−13.0100	+	13.0100i	−0.442608	+	0.442608i
$865$	5.52649	−	5.52649i	0.187906	−	0.187906i
$866$	62.6489	−	16.7867i	2.12890	−	0.570436i
$867$	15.5299	+	8.96618i	0.527423	+	0.304508i
$868$		0			0
$869$	8.27609	+	2.21757i	0.280747	+	0.0752259i
$870$	−21.1279	−	12.1982i	−0.716302	−	0.413557i
$871$	31.6023	−	0.115599i	1.07080	−	0.00391693i
$872$	8.87970	+	15.3801i	0.300705	+	0.520836i
$873$	−6.90669	+	6.90669i	−0.233756	+	0.233756i
$874$	26.9143	−	15.5390i	0.910390	−	0.525614i
$875$		0			0
$876$	−48.4768	−	48.4768i	−1.63788	−	1.63788i
$877$	−8.66346	+	32.3325i	−0.292544	+	1.09179i	0.650604	+	0.759417i	$0.274516\pi$
$877$	−8.66346	+	32.3325i	−0.292544	+	1.09179i	−0.943148	+	0.332373i	$0.892151\pi$
$878$	−57.9164	−	57.9164i	−1.95458	−	1.95458i
$879$	−17.4671	−	4.68029i	−0.589150	−	0.157862i
$880$	21.0928	−	12.1779i	0.711038	−	0.410518i
$881$	26.0483	+	45.1170i	0.877590	+	1.52003i	0.853978	+	0.520309i	$0.174183\pi$
$881$	26.0483	+	45.1170i	0.877590	+	1.52003i	0.0236116	+	0.999721i	$0.492483\pi$
$882$		0			0
$883$			22.4598i			0.755831i	0.925840	+	0.377916i	$0.123359\pi$
$883$			22.4598i			0.755831i	−0.925840	+	0.377916i	$0.876641\pi$
$884$	4.79264	−	18.1517i	0.161194	−	0.610508i
$885$	6.74468	−	3.89404i	0.226720	−	0.130897i
$886$	−18.2333	+	4.88561i	−0.612561	+	0.164135i
$887$		−	11.9811i		−	0.402285i	−0.979562	−	0.201142i	$-0.935535\pi$
$887$		−	11.9811i		−	0.402285i	0.979562	−	0.201142i	$-0.0644654\pi$
$888$	1.41914	−	2.45801i	0.0476231	−	0.0824856i
$889$		0			0
$890$	51.0656	−	13.6830i	1.71172	−	0.458655i
$891$	−7.89231	−	2.11474i	−0.264402	−	0.0708464i
$892$	−0.648066	+	2.41861i	−0.0216989	+	0.0809812i
$893$	16.6094			0.555812
$894$	−43.2418			−1.44622
$895$	6.19911	−	23.1354i	0.207213	−	0.773330i
$896$		0			0
$897$	15.9728	−	16.0901i	0.533315	−	0.537231i
$898$	24.0414	−	41.6409i	0.802271	−	1.38957i
$899$	−3.70250	−	13.8179i	−0.123485	−	0.460853i
$900$	−14.5001	+	25.1149i	−0.483337	+	0.837165i
$901$	5.47560	+	9.48401i	0.182419	+	0.315958i
$902$	37.2513	−	37.2513i	1.24033	−	1.24033i
$903$		0			0
$904$	19.2993	+	72.0259i	0.641885	+	2.39555i
$905$	−4.07228	−	15.1980i	−0.135367	−	0.505198i
$906$		−	20.4741i		−	0.680207i
$907$	0.460660	+	0.265962i	0.0152959	+	0.00883112i	0.507628	−	0.861576i	$-0.330522\pi$
$907$	0.460660	+	0.265962i	0.0152959	+	0.00883112i	−0.492333	+	0.870407i	$0.663856\pi$
$908$	13.2906	+	13.2906i	0.441063	+	0.441063i
$909$	20.7368			0.687798
$910$		0			0
$911$	2.16430			0.0717065			0.0358532	−	0.999357i	$-0.488585\pi$
$911$	2.16430			0.0717065			0.0358532	+	0.999357i	$0.488585\pi$
$912$	3.82728	+	3.82728i	0.126734	+	0.126734i
$913$	26.6724	+	15.3993i	0.882727	+	0.509642i
$914$			3.32774i			0.110072i
$915$	5.20103	+	19.4105i	0.171941	+	0.641691i
$916$	0.988776	+	3.69016i	0.0326701	+	0.121926i
$917$		0			0
$918$	−13.2363	+	13.2363i	−0.436864	+	0.436864i
$919$	12.9020	+	22.3470i	0.425599	+	0.737158i	0.996476	−	0.0838769i	$-0.0267302\pi$
$919$	12.9020	+	22.3470i	0.425599	+	0.737158i	−0.570878	+	0.821035i	$0.693397\pi$
$920$	31.7279	−	54.9543i	1.04604	−	1.81179i
$921$	6.92820	+	25.8564i	0.228292	+	0.851997i
$922$	22.3812	−	38.7653i	0.737084	−	1.27667i
$923$	−31.0535	+	0.113592i	−1.02214	+	0.00373892i
$924$		0			0
$925$	−0.830835	+	3.10072i	−0.0273177	+	0.101951i
$926$	75.2002			2.47123
$927$	9.59881			0.315266
$928$	−2.33674	+	8.72084i	−0.0767073	+	0.286276i
$929$	20.0699	+	5.37770i	0.658470	+	0.176437i	0.572556	−	0.819866i	$-0.305952\pi$
$929$	20.0699	+	5.37770i	0.658470	+	0.176437i	0.0859148	+	0.996302i	$0.472619\pi$
$930$	46.6908	−	12.5108i	1.53105	−	0.410244i
$931$		0			0
$932$	2.38218	−	4.12605i	0.0780308	−	0.135153i
$933$			4.68125i			0.153257i
$934$	64.9291	−	17.3977i	2.12455	−	0.569270i
$935$	−16.9746	+	9.80029i	−0.555129	+	0.320504i
$936$	−18.5040	−	10.5932i	−0.604822	−	0.346251i
$937$			37.2049i			1.21543i	0.794154	+	0.607716i	$0.207914\pi$
$937$			37.2049i			1.21543i	−0.794154	+	0.607716i	$0.792086\pi$
$938$		0			0
$939$	5.99623	+	10.3858i	0.195680	+	0.338927i
$940$	65.9331	−	38.0665i	2.15050	−	1.24159i
$941$	43.0912	+	11.5462i	1.40473	+	0.376397i	0.880042	−	0.474897i	$-0.157515\pi$
$941$	43.0912	+	11.5462i	1.40473	+	0.376397i	0.524690	+	0.851293i	$0.324181\pi$
$942$	−38.2514	−	38.2514i	−1.24630	−	1.24630i
$943$	7.07556	−	26.4064i	0.230412	−	0.859910i
$944$	2.57650	+	2.57650i	0.0838580	+	0.0838580i
$945$		0			0
$946$	−55.0452	+	31.7803i	−1.78967	+	1.03327i
$947$	5.54665	−	5.54665i	0.180242	−	0.180242i	−0.611219	−	0.791461i	$-0.709321\pi$
$947$	5.54665	−	5.54665i	0.180242	−	0.180242i	0.791461	+	0.611219i	$0.209321\pi$
$948$	4.36387	+	7.55844i	0.141732	+	0.245487i
$949$	−28.3231	+	49.4741i	−0.919407	+	1.60600i
$950$	−26.6170	−	15.3674i	−0.863571	−	0.498583i
$951$	18.0304	+	4.83124i	0.584677	+	0.156664i
$952$		0			0
$953$	28.7075	+	16.5743i	0.929926	+	0.536893i	0.886788	−	0.462176i	$-0.152931\pi$
$953$	28.7075	+	16.5743i	0.929926	+	0.536893i	0.0431379	+	0.999069i	$0.486265\pi$
$954$	26.9697	−	7.22651i	0.873176	−	0.233967i
$955$	13.7315	−	13.7315i	0.444341	−	0.444341i
$956$	−54.9177	+	54.9177i	−1.77617	+	1.77617i
$957$	−13.2823	+	3.55899i	−0.429357	+	0.115046i
$958$	−7.17194	−	4.14072i	−0.231715	−	0.133781i
$959$		0			0
$960$	−42.7573	−	11.4568i	−1.37998	−	0.369766i
$961$	−2.30019	−	1.32801i	−0.0741995	−	0.0428391i
$962$	−5.12278	−	1.35258i	−0.165165	−	0.0436089i
$963$	6.64355	+	11.5070i	0.214085	+	0.370807i
$964$	−8.94823	+	8.94823i	−0.288203	+	0.288203i
$965$	40.0168	−	23.1037i	1.28818	−	0.743734i
$966$		0			0
$967$	−21.9068	−	21.9068i	−0.704477	−	0.704477i	0.260892	−	0.965368i	$-0.415984\pi$
$967$	−21.9068	−	21.9068i	−0.704477	−	0.704477i	−0.965368	+	0.260892i	$0.915984\pi$
$968$	7.00883	−	26.1573i	0.225272	−	0.840728i
$969$	−3.08004	−	3.08004i	−0.0989450	−	0.0989450i
$970$	−45.8327	−	12.2808i	−1.47160	−	0.394314i
$971$	17.9328	−	10.3535i	0.575490	−	0.332259i	−0.183849	−	0.982954i	$-0.558856\pi$
$971$	17.9328	−	10.3535i	0.575490	−	0.332259i	0.759339	+	0.650695i	$0.225522\pi$
$972$	25.4613	+	44.1003i	0.816672	+	1.41452i
$973$		0			0
$974$			57.5638i			1.84446i
$975$	−21.6787	−	5.72387i	−0.694273	−	0.183311i
$976$	−8.14213	+	4.70086i	−0.260623	+	0.150471i
$977$	17.2815	−	4.63057i	0.552885	−	0.148145i	0.0284497	−	0.999595i	$-0.490943\pi$
$977$	17.2815	−	4.63057i	0.552885	−	0.148145i	0.524436	+	0.851450i	$0.324276\pi$
$978$		−	2.88679i		−	0.0923095i
$979$	14.8991	−	25.8060i	0.476177	−	0.824763i
$980$		0			0
$981$	−7.01050	+	1.87846i	−0.223828	+	0.0599746i
$982$	−13.8503	−	3.71118i	−0.441981	−	0.118429i
$983$	−11.5896	+	43.2530i	−0.369651	+	1.37955i	0.491355	+	0.870959i	$0.336502\pi$
$983$	−11.5896	+	43.2530i	−0.369651	+	1.37955i	−0.861006	+	0.508596i	$0.830165\pi$
$984$	23.9043			0.762042
$985$	53.4006			1.70148
$986$	−2.37740	+	8.87257i	−0.0757117	+	0.282560i
$987$		0			0
$988$	16.2126	−	28.3198i	0.515791	−	0.900971i
$989$	−16.4918	+	28.5646i	−0.524407	+	0.908300i
$990$	12.9341	+	48.2707i	0.411073	+	1.53414i
$991$	12.5780	−	21.7857i	0.399553	−	0.692045i	−0.594118	−	0.804378i	$-0.702499\pi$
$991$	12.5780	−	21.7857i	0.399553	−	0.692045i	0.993671	+	0.112332i	$0.0358322\pi$
$992$	−8.94431	−	15.4920i	−0.283982	−	0.491871i
$993$	12.4494	−	12.4494i	0.395071	−	0.395071i
$994$		0			0
$995$	−16.3569	−	61.0449i	−0.518550	−	1.93525i
$996$	8.11985	+	30.3037i	0.257287	+	0.960209i
$997$		−	11.9322i		−	0.377897i	−0.981987	−	0.188948i	$-0.939492\pi$
$997$		−	11.9322i		−	0.377897i	0.981987	−	0.188948i	$-0.0605079\pi$
$998$	−37.5145	−	21.6590i	−1.18750	−	0.685604i
$999$	2.40298	+	2.40298i	0.0760271	+	0.0760271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.b.362.7		32
7.2	even	3		91.2.bc.a.76.8	yes	32
7.3	odd	6		637.2.x.b.570.1		32
7.4	even	3		637.2.x.b.570.2		32
7.5	odd	6		91.2.bc.a.76.7	yes	32
7.6	odd	2	inner	637.2.bb.b.362.8		32
13.6	odd	12		637.2.x.b.19.2		32
21.2	odd	6		819.2.fm.g.622.2		32
21.5	even	6		819.2.fm.g.622.1		32
91.6	even	12		637.2.x.b.19.1		32
91.19	even	12		91.2.bc.a.6.8	yes	32
91.32	odd	12	inner	637.2.bb.b.227.8		32
91.45	even	12	inner	637.2.bb.b.227.7		32
91.58	odd	12		91.2.bc.a.6.7	✓	32
273.110	odd	12		819.2.fm.g.370.2		32
273.149	even	12		819.2.fm.g.370.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.7	✓	32	91.58	odd	12
91.2.bc.a.6.8	yes	32	91.19	even	12
91.2.bc.a.76.7	yes	32	7.5	odd	6
91.2.bc.a.76.8	yes	32	7.2	even	3
637.2.x.b.19.1		32	91.6	even	12
637.2.x.b.19.2		32	13.6	odd	12
637.2.x.b.570.1		32	7.3	odd	6
637.2.x.b.570.2		32	7.4	even	3
637.2.bb.b.227.7		32	91.45	even	12	inner
637.2.bb.b.227.8		32	91.32	odd	12	inner
637.2.bb.b.362.7		32	1.1	even	1	trivial
637.2.bb.b.362.8		32	7.6	odd	2	inner
819.2.fm.g.370.1		32	273.149	even	12
819.2.fm.g.370.2		32	273.110	odd	12
819.2.fm.g.622.1		32	21.5	even	6
819.2.fm.g.622.2		32	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.67430 + 1.67430i) q^{2} +(-1.04118 - 0.601128i) q^{3} +3.60653i q^{4} +(-0.825486 - 3.08075i) q^{5} +(-0.736784 - 2.74971i) q^{6} +(-2.68981 + 2.68981i) q^{8} +(-0.777291 - 1.34631i) q^{9} +O(q^{10})\)	\(q+(1.67430 + 1.67430i) q^{2} +(-1.04118 - 0.601128i) q^{3} +3.60653i q^{4} +(-0.825486 - 3.08075i) q^{5} +(-0.736784 - 2.74971i) q^{6} +(-2.68981 + 2.68981i) q^{8} +(-0.777291 - 1.34631i) q^{9} +(3.77599 - 6.54020i) q^{10} +(-1.10170 - 4.11159i) q^{11} +(2.16799 - 3.75506i) q^{12} +(-3.48609 - 0.920440i) q^{13} +(-0.992444 + 3.70385i) q^{15} -1.79401 q^{16} +1.44374 q^{17} +(0.952702 - 3.55553i) q^{18} +(2.42397 + 0.649502i) q^{19} +(11.1108 - 2.97714i) q^{20} +(5.03945 - 8.72858i) q^{22} -5.23024i q^{23} +(4.41750 - 1.18367i) q^{24} +(-4.47949 + 2.58624i) q^{25} +(-4.29565 - 7.37783i) q^{26} +5.47577i q^{27} +(1.34350 + 2.32701i) q^{29} +(-7.86299 + 4.53970i) q^{30} +(-5.14250 - 1.37793i) q^{31} +(2.37592 + 2.37592i) q^{32} +(-1.32452 + 4.94318i) q^{33} +(2.41725 + 2.41725i) q^{34} +(4.85550 - 2.80333i) q^{36} +(0.438839 - 0.438839i) q^{37} +(2.97099 + 5.14591i) q^{38} +(3.07635 + 3.05393i) q^{39} +(10.5070 + 6.06624i) q^{40} +(5.04879 + 1.35282i) q^{41} +(-5.46143 - 3.15316i) q^{43} +(14.8286 - 3.97331i) q^{44} +(-3.50600 + 3.50600i) q^{45} +(8.75696 - 8.75696i) q^{46} +(6.39313 - 1.71303i) q^{47} +(1.86789 + 1.07843i) q^{48} +(-11.8301 - 3.16987i) q^{50} +(-1.50320 - 0.867874i) q^{51} +(3.31960 - 12.5727i) q^{52} +(3.79264 + 6.56904i) q^{53} +(-9.16806 + 9.16806i) q^{54} +(-11.7574 + 6.78811i) q^{55} +(-2.13337 - 2.13337i) q^{57} +(-1.64669 + 6.14553i) q^{58} +(-1.43617 - 1.43617i) q^{59} +(-13.3581 - 3.57928i) q^{60} +(4.53851 - 2.62031i) q^{61} +(-6.30300 - 10.9171i) q^{62} +11.5440i q^{64} +(0.0420647 + 11.4996i) q^{65} +(-10.4940 + 6.05870i) q^{66} +(-8.46631 + 2.26854i) q^{67} +5.20691i q^{68} +(-3.14404 + 5.44564i) q^{69} +(8.31929 - 2.22915i) q^{71} +(5.71208 + 1.53055i) q^{72} +(4.09222 - 15.2724i) q^{73} +1.46949 q^{74} +6.21863 q^{75} +(-2.34245 + 8.74214i) q^{76} +(0.0375447 + 10.2639i) q^{78} +(-1.00643 + 1.74319i) q^{79} +(1.48093 + 5.52690i) q^{80} +(0.959764 - 1.66236i) q^{81} +(6.18815 + 10.7182i) q^{82} +(-5.11623 + 5.11623i) q^{83} +(-1.19179 - 4.44782i) q^{85} +(-3.86473 - 14.4234i) q^{86} -3.23046i q^{87} +(14.0227 + 8.09604i) q^{88} +(4.95005 + 4.95005i) q^{89} -11.7402 q^{90} +18.8630 q^{92} +(4.52597 + 4.52597i) q^{93} +(13.5721 + 7.83586i) q^{94} -8.00382i q^{95} +(-1.04554 - 3.90200i) q^{96} +(-1.62618 - 6.06897i) q^{97} +(-4.67912 + 4.67912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9	\( 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9} - 16 q^{11} - 8 q^{15} - 24 q^{16} + 68 q^{18} + 4 q^{22} + 4 q^{29} - 12 q^{30} - 68 q^{32} - 8 q^{37} - 48 q^{43} + 60 q^{44} + 24 q^{46} - 44 q^{50} - 12 q^{51} - 36 q^{53} - 92 q^{57} - 28 q^{58} - 104 q^{60} - 32 q^{65} - 8 q^{67} + 84 q^{71} + 124 q^{72} + 48 q^{74} + 148 q^{78} + 40 q^{79} + 28 q^{81} + 36 q^{85} - 60 q^{86} + 228 q^{88} + 24 q^{92} - 84 q^{93} - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9 - 16 * q^11 - 8 * q^15 - 24 * q^16 + 68 * q^18 + 4 * q^22 + 4 * q^29 - 12 * q^30 - 68 * q^32 - 8 * q^37 - 48 * q^43 + 60 * q^44 + 24 * q^46 - 44 * q^50 - 12 * q^51 - 36 * q^53 - 92 * q^57 - 28 * q^58 - 104 * q^60 - 32 * q^65 - 8 * q^67 + 84 * q^71 + 124 * q^72 + 48 * q^74 + 148 * q^78 + 40 * q^79 + 28 * q^81 + 36 * q^85 - 60 * q^86 + 228 * q^88 + 24 * q^92 - 84 * q^93 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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