LMFDB - Embedded newform 475.2.bb.b.257.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(32,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("475.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.bb (of order $36$, degree $12$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			257.3
Character	$\chi$	$=$	475.257
Dual form			475.2.bb.b.268.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.371046 - 0.259809i) q^{2} +(3.02691 + 0.264820i) q^{3} +(-0.613866 - 1.68658i) q^{4} +(-1.05432 - 0.884679i) q^{6} +(1.89781 - 0.508516i) q^{7} +(-0.444888 + 1.66034i) q^{8} +(6.13763 + 1.08223i) q^{9} +O(q^{10})$	\(q+(-0.371046 - 0.259809i) q^{2} +(3.02691 + 0.264820i) q^{3} +(-0.613866 - 1.68658i) q^{4} +(-1.05432 - 0.884679i) q^{6} +(1.89781 - 0.508516i) q^{7} +(-0.444888 + 1.66034i) q^{8} +(6.13763 + 1.08223i) q^{9} +(0.238127 + 0.412449i) q^{11} +(-1.41148 - 5.26770i) q^{12} +(0.364244 + 4.16333i) q^{13} +(-0.836290 - 0.304385i) q^{14} +(-2.15338 + 1.80690i) q^{16} +(0.463388 - 0.661787i) q^{17} +(-1.99617 - 1.99617i) q^{18} +(-2.59888 - 3.49940i) q^{19} +(5.87916 - 1.03665i) q^{21} +(0.0188017 - 0.214905i) q^{22} +(1.97527 - 4.23599i) q^{23} +(-1.78633 + 4.90790i) q^{24} +(0.946520 - 1.63942i) q^{26} +(9.48666 + 2.54194i) q^{27} +(-2.02265 - 2.88865i) q^{28} +(0.693994 - 3.93584i) q^{29} +(-8.78658 - 5.07294i) q^{31} +(4.69320 - 0.410602i) q^{32} +(0.611565 + 1.31151i) q^{33} +(-0.343876 + 0.125161i) q^{34} +(-1.94241 - 11.0160i) q^{36} +(-4.48456 + 4.48456i) q^{37} +(0.0551271 + 1.97365i) q^{38} +12.6985i q^{39} +(4.84667 + 5.77603i) q^{41} +(-2.45077 - 1.14281i) q^{42} +(-0.992873 + 0.462984i) q^{43} +(0.549451 - 0.654810i) q^{44} +(-1.83346 + 1.05855i) q^{46} +(-7.61531 + 5.33230i) q^{47} +(-6.99661 + 4.89908i) q^{48} +(-2.71909 + 1.56987i) q^{49} +(1.57789 - 1.88046i) q^{51} +(6.79821 - 3.17006i) q^{52} +(6.51205 + 3.03662i) q^{53} +(-2.85956 - 3.40789i) q^{54} +3.37725i q^{56} +(-6.93987 - 11.2806i) q^{57} +(-1.28007 + 1.28007i) q^{58} +(0.304047 + 1.72434i) q^{59} +(-3.30814 + 1.20406i) q^{61} +(1.94223 + 4.16512i) q^{62} +(12.1984 - 1.06722i) q^{63} +(3.02080 + 1.74406i) q^{64} +(0.113822 - 0.645519i) q^{66} +(1.74299 + 2.48924i) q^{67} +(-1.40062 - 0.375294i) q^{68} +(7.10075 - 12.2989i) q^{69} +(-0.907322 + 2.49285i) q^{71} +(-4.52744 + 9.70912i) q^{72} +(-0.0344750 + 0.394051i) q^{73} +(2.82911 - 0.498848i) q^{74} +(-4.30667 + 6.53139i) q^{76} +(0.661657 + 0.661657i) q^{77} +(3.29918 - 4.71172i) q^{78} +(3.51787 - 2.95185i) q^{79} +(10.4727 + 3.81176i) q^{81} +(-0.297669 - 3.40238i) q^{82} +(-2.03694 - 7.60197i) q^{83} +(-5.35742 - 9.27933i) q^{84} +(0.488688 + 0.0861690i) q^{86} +(3.14295 - 11.7296i) q^{87} +(-0.790747 + 0.211880i) q^{88} +(-0.225503 - 0.189219i) q^{89} +(2.80839 + 7.71598i) q^{91} +(-8.35690 - 0.731134i) q^{92} +(-25.2528 - 17.6822i) q^{93} +4.21101 q^{94} +14.3146 q^{96} +(-3.38897 - 2.37298i) q^{97} +(1.41677 + 0.123952i) q^{98} +(1.01517 + 2.78917i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{2} + 12 q^{3} - 12 q^{6} + 18 q^{8}+O(q^{10}) $ 96 * q + 12 * q^2 + 12 * q^3 - 12 * q^6 + 18 * q^8	$ 96 q + 12 q^{2} + 12 q^{3} - 12 q^{6} + 18 q^{8} - 12 q^{11} + 18 q^{12} + 12 q^{13} + 12 q^{16} + 30 q^{17} + 24 q^{21} + 24 q^{22} - 48 q^{26} + 18 q^{27} - 36 q^{31} - 18 q^{32} - 90 q^{33} + 24 q^{36} - 54 q^{38} + 12 q^{41} - 24 q^{42} - 48 q^{43} - 36 q^{46} + 24 q^{47} - 60 q^{48} - 96 q^{51} + 30 q^{53} + 66 q^{57} - 120 q^{58} - 48 q^{61} - 60 q^{62} + 126 q^{63} + 72 q^{66} - 108 q^{67} - 18 q^{68} - 24 q^{71} - 48 q^{72} - 6 q^{73} + 60 q^{76} - 168 q^{77} + 138 q^{78} - 120 q^{81} - 60 q^{82} - 180 q^{86} + 6 q^{87} + 198 q^{88} - 24 q^{91} + 72 q^{92} + 90 q^{93} - 192 q^{96} + 72 q^{97} + 90 q^{98}+O(q^{100}) $ 96 * q + 12 * q^2 + 12 * q^3 - 12 * q^6 + 18 * q^8 - 12 * q^11 + 18 * q^12 + 12 * q^13 + 12 * q^16 + 30 * q^17 + 24 * q^21 + 24 * q^22 - 48 * q^26 + 18 * q^27 - 36 * q^31 - 18 * q^32 - 90 * q^33 + 24 * q^36 - 54 * q^38 + 12 * q^41 - 24 * q^42 - 48 * q^43 - 36 * q^46 + 24 * q^47 - 60 * q^48 - 96 * q^51 + 30 * q^53 + 66 * q^57 - 120 * q^58 - 48 * q^61 - 60 * q^62 + 126 * q^63 + 72 * q^66 - 108 * q^67 - 18 * q^68 - 24 * q^71 - 48 * q^72 - 6 * q^73 + 60 * q^76 - 168 * q^77 + 138 * q^78 - 120 * q^81 - 60 * q^82 - 180 * q^86 + 6 * q^87 + 198 * q^88 - 24 * q^91 + 72 * q^92 + 90 * q^93 - 192 * q^96 + 72 * q^97 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	−0.371046	−	0.259809i	−0.262369	−	0.183713i	0.434989	−	0.900436i	$-0.356752\pi$
$2$	−0.371046	−	0.259809i	−0.262369	−	0.183713i	−0.697358	+	0.716723i	$0.745641\pi$
$3$	3.02691	+	0.264820i	1.74759	+	0.152894i	0.915650	−	0.401976i	$-0.131676\pi$
$3$	3.02691	+	0.264820i	1.74759	+	0.152894i	0.831937	+	0.554870i	$0.187232\pi$
$4$	−0.613866	−	1.68658i	−0.306933	−	0.843292i
$5$		0			0
$5$		0			0
$6$	−1.05432	−	0.884679i	−0.430424	−	0.361169i
$7$	1.89781	−	0.508516i	0.717304	−	0.192201i	0.118336	−	0.992974i	$-0.462244\pi$
$7$	1.89781	−	0.508516i	0.717304	−	0.192201i	0.598968	+	0.800773i	$0.295577\pi$
$8$	−0.444888	+	1.66034i	−0.157292	+	0.587020i
$9$	6.13763	+	1.08223i	2.04588	+	0.360744i
$10$		0			0
$11$	0.238127	+	0.412449i	0.0717981	+	0.124358i	0.899689	−	0.436531i	$-0.143793\pi$
$11$	0.238127	+	0.412449i	0.0717981	+	0.124358i	−0.827891	+	0.560889i	$0.810460\pi$
$12$	−1.41148	−	5.26770i	−0.407458	−	1.52065i
$13$	0.364244	+	4.16333i	0.101023	+	1.15470i	0.862343	+	0.506324i	$0.168996\pi$
$13$	0.364244	+	4.16333i	0.101023	+	1.15470i	−0.761320	+	0.648377i	$0.775448\pi$
$14$	−0.836290	−	0.304385i	−0.223508	−	0.0813503i
$15$		0			0
$16$	−2.15338	+	1.80690i	−0.538346	+	0.451726i
$17$	0.463388	−	0.661787i	0.112388	−	0.160507i	−0.759017	−	0.651071i	$-0.774320\pi$
$17$	0.463388	−	0.661787i	0.112388	−	0.160507i	0.871405	+	0.490564i	$0.163209\pi$
$18$	−1.99617	−	1.99617i	−0.470502	−	0.470502i
$19$	−2.59888	−	3.49940i	−0.596224	−	0.802818i
$19$	−2.59888	−	3.49940i	−0.596224	−	0.802818i
$20$		0			0
$21$	5.87916	−	1.03665i	1.28294	−	0.226217i
$22$	0.0188017	−	0.214905i	0.00400854	−	0.0458179i
$23$	1.97527	−	4.23599i	0.411873	−	0.883265i	−0.585489	−	0.810680i	$-0.699098\pi$
$23$	1.97527	−	4.23599i	0.411873	−	0.883265i	0.997362	−	0.0725845i	$-0.0231247\pi$
$24$	−1.78633	+	4.90790i	−0.364633	+	1.00182i
$25$		0			0
$26$	0.946520	−	1.63942i	0.185628	−	0.321517i
$27$	9.48666	+	2.54194i	1.82571	+	0.489197i
$28$	−2.02265	−	2.88865i	−0.382246	−	0.545904i
$29$	0.693994	−	3.93584i	0.128871	−	0.730866i	−0.850061	−	0.526684i	$-0.823435\pi$
$29$	0.693994	−	3.93584i	0.128871	−	0.730866i	0.978933	−	0.204183i	$-0.0654537\pi$
$30$		0			0
$31$	−8.78658	−	5.07294i	−1.57812	−	0.911126i	−0.995122	−	0.0986501i	$-0.968548\pi$
$31$	−8.78658	−	5.07294i	−1.57812	−	0.911126i	−0.582995	−	0.812476i	$-0.698119\pi$
$32$	4.69320	−	0.410602i	0.829649	−	0.0725849i
$33$	0.611565	+	1.31151i	0.106460	+	0.228304i
$34$	−0.343876	+	0.125161i	−0.0589743	+	0.0214649i
$35$		0			0
$36$	−1.94241	−	11.0160i	−0.323736	−	1.83600i
$37$	−4.48456	+	4.48456i	−0.737257	+	0.737257i	−0.972046	−	0.234789i	$-0.924560\pi$
$37$	−4.48456	+	4.48456i	−0.737257	+	0.737257i	0.234789	+	0.972046i	$0.424560\pi$
$38$	0.0551271	+	1.97365i	0.00894280	+	0.320168i
$39$			12.6985i			2.03339i
$40$		0			0
$41$	4.84667	+	5.77603i	0.756922	+	0.902064i	0.997649	−	0.0685283i	$-0.0218304\pi$
$41$	4.84667	+	5.77603i	0.756922	+	0.902064i	−0.240727	+	0.970593i	$0.577386\pi$
$42$	−2.45077	−	1.14281i	−0.378162	−	0.176340i
$43$	−0.992873	+	0.462984i	−0.151412	+	0.0706044i	−0.496847	−	0.867838i	$-0.665509\pi$
$43$	−0.992873	+	0.462984i	−0.151412	+	0.0706044i	0.345435	+	0.938443i	$0.387731\pi$
$44$	0.549451	−	0.654810i	0.0828328	−	0.0987163i
$45$		0			0
$46$	−1.83346	+	1.05855i	−0.270330	+	0.156075i
$47$	−7.61531	+	5.33230i	−1.11081	+	0.777796i	−0.977006	−	0.213212i	$-0.931607\pi$
$47$	−7.61531	+	5.33230i	−1.11081	+	0.777796i	−0.133802	+	0.991008i	$0.542718\pi$
$48$	−6.99661	+	4.89908i	−1.00987	+	0.707121i
$49$	−2.71909	+	1.56987i	−0.388442	+	0.224267i
$50$		0			0
$51$	1.57789	−	1.88046i	0.220949	−	0.263317i
$52$	6.79821	−	3.17006i	0.942742	−	0.439608i
$53$	6.51205	+	3.03662i	0.894499	+	0.417112i	0.814824	−	0.579709i	$-0.196834\pi$
$53$	6.51205	+	3.03662i	0.894499	+	0.417112i	0.0796756	+	0.996821i	$0.474612\pi$
$54$	−2.85956	−	3.40789i	−0.389137	−	0.463756i
$55$		0			0
$56$			3.37725i			0.451304i
$57$	−6.93987	−	11.2806i	−0.919208	−	1.49415i
$58$	−1.28007	+	1.28007i	−0.168081	+	0.168081i
$59$	0.304047	+	1.72434i	0.0395836	+	0.224490i	0.998182	−	0.0602717i	$-0.0191967\pi$
$59$	0.304047	+	1.72434i	0.0395836	+	0.224490i	−0.958598	+	0.284761i	$0.908086\pi$
$60$		0			0
$61$	−3.30814	+	1.20406i	−0.423564	+	0.154165i	−0.545003	−	0.838434i	$-0.683471\pi$
$61$	−3.30814	+	1.20406i	−0.423564	+	0.154165i	0.121439	+	0.992599i	$0.461249\pi$
$62$	1.94223	+	4.16512i	0.246663	+	0.528971i
$63$	12.1984	−	1.06722i	1.53685	−	0.134457i
$64$	3.02080	+	1.74406i	0.377600	+	0.218008i
$65$		0			0
$66$	0.113822	−	0.645519i	0.0140106	−	0.0794579i
$67$	1.74299	+	2.48924i	0.212940	+	0.304110i	0.911386	−	0.411553i	$-0.135014\pi$
$67$	1.74299	+	2.48924i	0.212940	+	0.304110i	−0.698446	+	0.715663i	$0.746125\pi$
$68$	−1.40062	−	0.375294i	−0.169850	−	0.0455111i
$69$	7.10075	−	12.2989i	0.854830	−	1.48061i
$70$		0			0
$71$	−0.907322	+	2.49285i	−0.107679	+	0.295847i	−0.981816	−	0.189833i	$-0.939205\pi$
$71$	−0.907322	+	2.49285i	−0.107679	+	0.295847i	0.874137	+	0.485679i	$0.161428\pi$
$72$	−4.52744	+	9.70912i	−0.533563	+	1.14423i
$73$	−0.0344750	+	0.394051i	−0.00403499	+	0.0461202i	−0.997945	−	0.0640723i	$-0.979591\pi$
$73$	−0.0344750	+	0.394051i	−0.00403499	+	0.0461202i	0.993910	+	0.110192i	$0.0351467\pi$
$74$	2.82911	−	0.498848i	0.328877	−	0.0579899i
$75$		0			0
$76$	−4.30667	+	6.53139i	−0.494009	+	0.749202i
$77$	0.661657	+	0.661657i	0.0754028	+	0.0754028i
$78$	3.29918	−	4.71172i	0.373559	−	0.533497i
$79$	3.51787	−	2.95185i	0.395792	−	0.332109i	−0.423073	−	0.906096i	$-0.639048\pi$
$79$	3.51787	−	2.95185i	0.395792	−	0.332109i	0.818864	+	0.573987i	$0.194604\pi$
$80$		0			0
$81$	10.4727	+	3.81176i	1.16364	+	0.423529i
$82$	−0.297669	−	3.40238i	−0.0328721	−	0.375730i
$83$	−2.03694	−	7.60197i	−0.223583	−	0.834425i	−0.982967	−	0.183782i	$-0.941166\pi$
$83$	−2.03694	−	7.60197i	−0.223583	−	0.834425i	0.759384	−	0.650643i	$-0.225501\pi$
$84$	−5.35742	−	9.27933i	−0.584543	−	1.01246i
$85$		0			0
$86$	0.488688	+	0.0861690i	0.0526966	+	0.00929184i
$87$	3.14295	−	11.7296i	0.336959	−	1.25755i
$88$	−0.790747	+	0.211880i	−0.0842939	+	0.0225865i
$89$	−0.225503	−	0.189219i	−0.0239032	−	0.0200572i	0.630758	−	0.775980i	$-0.282744\pi$
$89$	−0.225503	−	0.189219i	−0.0239032	−	0.0200572i	−0.654661	+	0.755923i	$0.727189\pi$
$90$		0			0
$91$	2.80839	+	7.71598i	0.294399	+	0.808855i
$92$	−8.35690	−	0.731134i	−0.871267	−	0.0762260i
$93$	−25.2528	−	17.6822i	−2.61859	−	1.83356i
$94$	4.21101			0.434332
$95$		0			0
$96$	14.3146			1.46098
$97$	−3.38897	−	2.37298i	−0.344097	−	0.240940i	0.388734	−	0.921350i	$-0.372913\pi$
$97$	−3.38897	−	2.37298i	−0.344097	−	0.240940i	−0.732831	+	0.680411i	$0.761801\pi$
$98$	1.41677	+	0.123952i	0.143116	+	0.0125210i
$99$	1.01517	+	2.78917i	0.102029	+	0.280322i
$100$		0			0
$101$	7.59390	+	6.37204i	0.755622	+	0.634042i	0.936983	−	0.349375i	$-0.113606\pi$
$101$	7.59390	+	6.37204i	0.755622	+	0.634042i	−0.181361	+	0.983417i	$0.558050\pi$
$102$	−1.07403	+	0.287785i	−0.106345	+	0.0284950i
$103$	−4.43855	+	16.5649i	−0.437344	+	1.63219i	0.298051	+	0.954550i	$0.403663\pi$
$103$	−4.43855	+	16.5649i	−0.437344	+	1.63219i	−0.735395	+	0.677639i	$0.763003\pi$
$104$	−7.07462	−	1.24745i	−0.693723	−	0.122322i
$105$		0			0
$106$	−1.62733	−	2.81861i	−0.158060	−	0.273768i
$107$	0.271946	+	1.01491i	0.0262900	+	0.0981155i	0.977824	−	0.209427i	$-0.0671600\pi$
$107$	0.271946	+	1.01491i	0.0262900	+	0.0981155i	−0.951534	+	0.307543i	$0.900493\pi$
$108$	−1.53634	−	17.5605i	−0.147834	−	1.68976i
$109$	−7.91145	−	2.87953i	−0.757780	−	0.275809i	−0.0659041	−	0.997826i	$-0.520993\pi$
$109$	−7.91145	−	2.87953i	−0.757780	−	0.275809i	−0.691876	+	0.722017i	$0.743215\pi$
$110$		0			0
$111$	−14.7620	+	12.3868i	−1.40114	+	1.17570i
$112$	−3.16787	+	4.52419i	−0.299336	+	0.427496i
$113$	7.71845	+	7.71845i	0.726091	+	0.726091i	0.969839	−	0.243748i	$-0.0783769\pi$
$113$	7.71845	+	7.71845i	0.726091	+	0.726091i	−0.243748	+	0.969839i	$0.578377\pi$
$114$	−0.355798	+	5.98866i	−0.0333235	+	0.560890i
$115$		0			0
$116$	−7.06413	+	1.24560i	−0.655888	+	0.115651i
$117$	−2.27009	+	25.9472i	−0.209870	+	2.39882i
$118$	0.335183	−	0.718802i	0.0308561	−	0.0661711i
$119$	0.542893	−	1.49159i	0.0497669	−	0.136733i
$120$		0			0
$121$	5.38659	−	9.32985i	0.489690	−	0.848168i
$122$	1.54030	+	0.412721i	0.139452	+	0.0373660i
$123$	13.1408	+	18.7670i	1.18487	+	1.69217i
$124$	−3.16214	+	17.9334i	−0.283969	+	1.61047i
$125$		0			0
$126$	−4.80343	−	2.77326i	−0.427924	−	0.247062i
$127$	−10.0117	+	0.875911i	−0.888395	+	0.0777245i	−0.522210	−	0.852817i	$-0.674892\pi$
$127$	−10.0117	+	0.875911i	−0.888395	+	0.0777245i	−0.366186	+	0.930542i	$0.619337\pi$
$128$	−4.64975	−	9.97142i	−0.410984	−	0.881358i
$129$	−3.12794	+	1.13848i	−0.275400	+	0.100237i
$130$		0			0
$131$	−2.04515	−	11.5986i	−0.178686	−	1.01338i	−0.933803	−	0.357787i	$-0.883531\pi$
$131$	−2.04515	−	11.5986i	−0.178686	−	1.01338i	0.755118	−	0.655589i	$-0.227580\pi$
$132$	1.83655	−	1.83655i	0.159851	−	0.159851i
$133$	−6.71168	−	5.31962i	−0.581976	−	0.461270i
$134$		−	1.37647i		−	0.118909i
$135$		0			0
$136$	0.892639	+	1.06381i	0.0765432	+	0.0912206i
$137$	17.0265	+	7.93960i	1.45467	+	0.678325i	0.979477	−	0.201554i	$-0.0645993\pi$
$137$	17.0265	+	7.93960i	1.45467	+	0.678325i	0.475196	+	0.879880i	$0.342377\pi$
$138$	−5.83006	+	2.71860i	−0.496288	+	0.231423i
$139$	−6.70183	+	7.98693i	−0.568441	+	0.677442i	−0.971310	−	0.237816i	$-0.923569\pi$
$139$	−6.70183	+	7.98693i	−0.568441	+	0.677442i	0.402869	+	0.915258i	$0.368013\pi$
$140$		0			0
$141$	−24.4630	+	14.1237i	−2.06015	+	1.18943i
$142$	0.984322	−	0.689230i	0.0826025	−	0.0578389i
$143$	−1.63042	+	1.14164i	−0.136343	+	0.0954684i
$144$	−15.1722	+	8.75966i	−1.26435	+	0.729972i
$145$		0			0
$146$	0.115170	−	0.137254i	0.00953151	−	0.0113592i
$147$	−8.64618	+	4.03178i	−0.713125	+	0.332536i
$148$	10.3165	+	4.81067i	0.848012	+	0.395434i
$149$	−14.5924	−	17.3906i	−1.19546	−	1.42469i	−0.879487	−	0.475922i	$-0.842114\pi$
$149$	−14.5924	−	17.3906i	−1.19546	−	1.42469i	−0.315970	−	0.948769i	$-0.602330\pi$
$150$		0			0
$151$			3.39398i			0.276198i	0.990418	+	0.138099i	$0.0440992\pi$
$151$			3.39398i			0.276198i	−0.990418	+	0.138099i	$0.955901\pi$
$152$	6.96643	−	2.75820i	0.565052	−	0.223719i
$153$	3.56032	−	3.56032i	0.287834	−	0.287834i
$154$	−0.0736005	−	0.417409i	−0.00593090	−	0.0336358i
$155$		0			0
$156$	21.4171	−	7.79518i	1.71474	−	0.624114i
$157$	−5.22244	−	11.1996i	−0.416796	−	0.893823i	−0.996855	−	0.0792479i	$-0.974748\pi$
$157$	−5.22244	−	11.1996i	−0.416796	−	0.893823i	0.580059	−	0.814575i	$-0.303030\pi$
$158$	−2.07221	+	0.181295i	−0.164856	+	0.0144230i
$159$	18.9072	+	10.9161i	1.49944	+	0.865703i
$160$		0			0
$161$	1.59462	−	9.04355i	0.125674	−	0.712732i
$162$	−2.89553	−	4.13524i	−0.227494	−	0.324895i
$163$	−0.770648	−	0.206494i	−0.0603618	−	0.0161739i	0.228512	−	0.973541i	$-0.426614\pi$
$163$	−0.770648	−	0.206494i	−0.0603618	−	0.0161739i	−0.288874	+	0.957367i	$0.593281\pi$
$164$	6.76655	−	11.7200i	0.528379	−	0.915179i
$165$		0			0
$166$	−1.21926	+	3.34989i	−0.0946331	+	0.260002i
$167$	−5.53000	+	11.8591i	−0.427924	+	0.917687i	0.567611	+	0.823297i	$0.307868\pi$
$167$	−5.53000	+	11.8591i	−0.427924	+	0.917687i	−0.995535	+	0.0943898i	$0.969910\pi$
$168$	−0.894364	+	10.2226i	−0.0690017	+	0.788693i
$169$	−4.39817	+	0.775516i	−0.338321	+	0.0596551i
$170$		0			0
$171$	−12.1638	−	24.2906i	−0.930191	−	1.85755i
$172$	1.39035	+	1.39035i	0.106013	+	0.106013i
$173$	6.01038	−	8.58372i	0.456961	−	0.652608i	−0.522875	−	0.852409i	$-0.675141\pi$
$173$	6.01038	−	8.58372i	0.456961	−	0.652608i	0.979836	+	0.199801i	$0.0640296\pi$
$174$	−4.21364	+	3.53567i	−0.319435	+	0.268038i
$175$		0			0
$176$	−1.25803	−	0.457887i	−0.0948279	−	0.0345145i
$177$	0.463684	+	5.29994i	0.0348526	+	0.398368i
$178$	0.0345109	+	0.128796i	0.00258670	+	0.00965370i
$179$	−2.06040	−	3.56872i	−0.154002	−	0.266739i	0.778693	−	0.627405i	$-0.215883\pi$
$179$	−2.06040	−	3.56872i	−0.154002	−	0.266739i	−0.932695	+	0.360666i	$0.882549\pi$
$180$		0			0
$181$	1.86465	+	0.328788i	0.138598	+	0.0244386i	0.242517	−	0.970147i	$-0.422027\pi$
$181$	1.86465	+	0.328788i	0.138598	+	0.0244386i	−0.103919	+	0.994586i	$0.533138\pi$
$182$	0.962641	−	3.59263i	0.0713557	−	0.266303i
$183$	−10.3323	+	2.76853i	−0.763785	+	0.204656i
$184$	6.15443	+	5.16418i	0.453710	+	0.380708i
$185$		0			0
$186$	4.77594	+	13.1218i	0.350189	+	0.962137i
$187$	0.383299	+	0.0335343i	0.0280296	+	0.00245227i
$188$	13.6681	+	9.57054i	0.996852	+	0.698003i
$189$	19.2965			1.40361
$190$		0			0
$191$	−10.2817			−0.743955			−0.371977	−	0.928242i	$-0.621320\pi$
$191$	−10.2817			−0.743955			−0.371977	+	0.928242i	$0.621320\pi$
$192$	8.68183	+	6.07908i	0.626557	+	0.438720i
$193$	−1.83479	−	0.160524i	−0.132071	−	0.0115547i	0.0209284	−	0.999781i	$-0.493338\pi$
$193$	−1.83479	−	0.160524i	−0.132071	−	0.0115547i	−0.153000	+	0.988226i	$0.548893\pi$
$194$	0.640940	+	1.76097i	0.0460168	+	0.126430i
$195$		0			0
$196$	4.31687	+	3.62229i	0.308348	+	0.258735i
$197$	−6.55723	+	1.75700i	−0.467183	+	0.125181i	−0.484728	−	0.874665i	$-0.661082\pi$
$197$	−6.55723	+	1.75700i	−0.467183	+	0.125181i	0.0175452	+	0.999846i	$0.494415\pi$
$198$	0.347975	−	1.29866i	0.0247295	−	0.0922917i
$199$	13.7215	+	2.41947i	0.972691	+	0.171512i	0.637341	−	0.770582i	$-0.280034\pi$
$199$	13.7215	+	2.41947i	0.972691	+	0.171512i	0.335350	+	0.942094i	$0.391145\pi$
$200$		0			0
$201$	4.61667	+	7.99630i	0.325634	+	0.564015i
$202$	−1.16217	−	4.33728i	−0.0817701	−	0.305170i
$203$	−0.684368	−	7.82237i	−0.0480332	−	0.549023i
$204$	−4.14016	−	1.50689i	−0.289869	−	0.105504i
$205$		0			0
$206$	5.95062	−	4.99316i	0.414599	−	0.347890i
$207$	16.7078	−	23.8613i	1.16127	−	1.65847i
$208$	−8.30710	−	8.30710i	−0.575994	−	0.575994i
$209$	0.824459	−	1.90521i	0.0570290	−	0.131786i
$210$		0			0
$211$	10.8661	−	1.91599i	0.748053	−	0.131902i	0.213390	−	0.976967i	$-0.431550\pi$
$211$	10.8661	−	1.91599i	0.748053	−	0.131902i	0.534663	+	0.845065i	$0.320438\pi$
$212$	1.12398	−	12.8472i	0.0771955	−	0.882349i
$213$	−3.40654	+	7.30535i	−0.233412	+	0.500554i
$214$	0.162780	−	0.447234i	0.0111274	−	0.0305723i
$215$		0			0
$216$	−8.44100	+	14.6202i	−0.574337	+	0.994781i
$217$	−19.2549	−	5.15934i	−1.30711	−	0.350239i
$218$	2.18738	+	3.12390i	0.148148	+	0.211578i
$219$	−0.208705	+	1.18363i	−0.0141030	+	0.0799821i
$220$		0			0
$221$	2.92403	+	1.68819i	0.196691	+	0.113560i
$222$	8.69556	−	0.760763i	0.583608	−	0.0510590i
$223$	−0.0883919	−	0.189557i	−0.00591916	−	0.0126937i	0.903326	−	0.428955i	$-0.141118\pi$
$223$	−0.0883919	−	0.189557i	−0.00591916	−	0.0126937i	−0.909245	+	0.416261i	$0.863340\pi$
$224$	8.69800	−	3.16581i	0.581159	−	0.211525i
$225$		0			0
$226$	−0.858575	−	4.86922i	−0.0571116	−	0.323896i
$227$	13.3368	−	13.3368i	0.885192	−	0.885192i	−0.108864	−	0.994057i	$-0.534721\pi$
$227$	13.3368	−	13.3368i	0.885192	−	0.885192i	0.994057	+	0.108864i	$0.0347214\pi$
$228$	−14.7655	+	18.6295i	−0.977872	+	1.23377i
$229$			1.82322i			0.120482i	0.998184	+	0.0602408i	$0.0191869\pi$
$229$			1.82322i			0.120482i	−0.998184	+	0.0602408i	$0.980813\pi$
$230$		0			0
$231$	1.82756	+	2.17800i	0.120244	+	0.143302i
$232$	6.22609	+	2.90328i	0.408763	+	0.190609i
$233$	16.4064	−	7.65042i	1.07482	−	0.501195i	0.197104	−	0.980383i	$-0.436846\pi$
$233$	16.4064	−	7.65042i	1.07482	−	0.501195i	0.877713	+	0.479187i	$0.159068\pi$
$234$	7.58362	−	9.03781i	0.495757	−	0.590820i
$235$		0			0
$236$	2.72160	−	1.57131i	0.177161	−	0.102284i
$237$	11.4300	−	8.00337i	0.742458	−	0.519875i
$238$	−0.588965	+	0.412398i	−0.0381769	+	0.0267318i
$239$	26.1511	−	15.0983i	1.69157	−	0.976630i	0.738323	−	0.674448i	$-0.235618\pi$
$239$	26.1511	−	15.0983i	1.69157	−	0.976630i	0.953250	−	0.302183i	$-0.0977152\pi$
$240$		0			0
$241$	14.7560	−	17.5855i	0.950516	−	1.13278i	−0.0405195	−	0.999179i	$-0.512901\pi$
$241$	14.7560	−	17.5855i	0.950516	−	1.13278i	0.991035	−	0.133602i	$-0.0426543\pi$
$242$	−4.42265	+	2.06232i	−0.284299	+	0.132571i
$243$	3.98716	+	1.85924i	0.255776	+	0.119270i
$244$	4.06151	+	4.84032i	0.260011	+	0.309869i
$245$		0			0
$246$		−	10.3775i		−	0.661647i
$247$	13.6226	−	12.0946i	0.866782	−	0.769564i
$248$	12.3319	−	12.3319i	0.783074	−	0.783074i
$249$	−4.15249	−	23.5499i	−0.263153	−	1.49242i
$250$		0			0
$251$	3.28776	−	1.19665i	0.207522	−	0.0755317i	−0.236168	−	0.971712i	$-0.575892\pi$
$251$	3.28776	−	1.19665i	0.207522	−	0.0755317i	0.443689	+	0.896181i	$0.353669\pi$
$252$	−9.28813	−	19.9185i	−0.585097	−	1.25475i
$253$	2.21749	−	0.194006i	0.139413	−	0.0121970i
$254$	3.94237	+	2.27613i	0.247366	+	0.142817i
$255$		0			0
$256$	0.346016	−	1.96236i	0.0216260	−	0.122647i
$257$	2.42456	+	3.46264i	0.151240	+	0.215993i	0.887622	−	0.460573i	$-0.152356\pi$
$257$	2.42456	+	3.46264i	0.151240	+	0.215993i	−0.736382	+	0.676566i	$0.763467\pi$
$258$	1.45640	+	0.390240i	0.0906713	+	0.0242953i
$259$	−6.23036	+	10.7913i	−0.387136	+	0.670539i
$260$		0			0
$261$	8.51896	−	23.4057i	0.527311	−	1.44877i
$262$	−2.25458	+	4.83497i	−0.139289	+	0.298705i
$263$	1.53523	−	17.5477i	0.0946662	−	1.08204i	−0.789148	−	0.614202i	$-0.789478\pi$
$263$	1.53523	−	17.5477i	0.0946662	−	1.08204i	0.883815	−	0.467837i	$-0.154967\pi$
$264$	−2.44963	+	0.431936i	−0.150764	+	0.0265838i
$265$		0			0
$266$	1.10825	+	3.71758i	0.0679514	+	0.227939i
$267$	−0.632467	−	0.632467i	−0.0387063	−	0.0387063i
$268$	3.12836	−	4.46776i	0.191095	−	0.272912i
$269$	−10.0078	+	8.39751i	−0.610184	+	0.512006i	−0.894701	−	0.446666i	$-0.852611\pi$
$269$	−10.0078	+	8.39751i	−0.610184	+	0.512006i	0.284517	+	0.958671i	$0.408167\pi$
$270$		0			0
$271$	−13.0902	−	4.76443i	−0.795171	−	0.289419i	−0.0876870	−	0.996148i	$-0.527948\pi$
$271$	−13.0902	−	4.76443i	−0.795171	−	0.289419i	−0.707484	+	0.706730i	$0.750170\pi$
$272$	0.197933	+	2.26238i	0.0120014	+	0.137177i
$273$	6.45739	+	24.0993i	0.390819	+	1.45856i
$274$	−4.25484	−	7.36959i	−0.257044	−	0.445213i
$275$		0			0
$276$	−25.1020	−	4.42616i	−1.51096	−	0.266423i
$277$	−4.23013	+	15.7870i	−0.254164	+	0.948552i	0.714390	+	0.699748i	$0.246704\pi$
$277$	−4.23013	+	15.7870i	−0.254164	+	0.948552i	−0.968554	+	0.248804i	$0.919962\pi$
$278$	4.56176	−	1.22232i	0.273596	−	0.0733098i
$279$	−48.4387	−	40.6449i	−2.89995	−	2.43335i
$280$		0			0
$281$	9.89365	+	27.1826i	0.590206	+	1.62158i	0.770123	+	0.637895i	$0.220195\pi$
$281$	9.89365	+	27.1826i	0.590206	+	1.62158i	−0.179918	+	0.983682i	$0.557583\pi$
$282$	12.7463	+	1.11516i	0.759034	+	0.0664068i
$283$	−15.7173	−	11.0054i	−0.934297	−	0.654202i	0.00401516	−	0.999992i	$-0.498722\pi$
$283$	−15.7173	−	11.0054i	−0.934297	−	0.654202i	−0.938312	+	0.345790i	$0.887611\pi$
$284$	4.76137			0.282535
$285$		0			0
$286$	0.901569			0.0533109
$287$	12.1352	+	8.49719i	0.716321	+	0.501573i
$288$	29.2495	+	2.55900i	1.72354	+	0.150791i
$289$	5.59111	+	15.3614i	0.328889	+	0.903614i
$290$		0			0
$291$	−9.62968	−	8.08026i	−0.564502	−	0.473673i
$292$	0.685763	−	0.183750i	0.0401312	−	0.0107531i
$293$	0.726601	−	2.71171i	0.0424485	−	0.158420i	−0.941448	−	0.337157i	$-0.890535\pi$
$293$	0.726601	−	2.71171i	0.0424485	−	0.158420i	0.983897	+	0.178737i	$0.0572012\pi$
$294$	4.25562	+	0.750381i	0.248193	+	0.0437631i
$295$		0			0
$296$	−5.45079	−	9.44105i	−0.316821	−	0.548750i
$297$	1.21061	+	4.51806i	0.0702468	+	0.262165i
$298$	0.896228	+	10.2439i	0.0519171	+	0.593415i
$299$	18.3553	+	6.68079i	1.06152	+	0.386360i
$300$		0			0
$301$	−1.64885	+	1.38355i	−0.0950379	+	0.0797463i
$302$	0.881786	−	1.25932i	0.0507411	−	0.0724658i
$303$	21.2986	+	21.2986i	1.22357	+	1.22357i
$304$	11.9195	+	2.83963i	0.683629	+	0.162864i
$305$		0			0
$306$	−2.24604	+	0.396038i	−0.128398	+	0.0226400i
$307$	0.829858	−	9.48532i	0.0473625	−	0.541356i	−0.935035	−	0.354555i	$-0.884632\pi$
$307$	0.829858	−	9.48532i	0.0473625	−	0.541356i	0.982398	−	0.186801i	$-0.0598120\pi$
$308$	0.709770	−	1.52211i	0.0404429	−	0.0867301i
$309$	−17.8218	+	48.9651i	−1.01385	+	2.78553i
$310$		0			0
$311$	11.9740	−	20.7396i	0.678982	−	1.17603i	−0.296305	−	0.955093i	$-0.595755\pi$
$311$	11.9740	−	20.7396i	0.678982	−	1.17603i	0.975288	−	0.220939i	$-0.0709121\pi$
$312$	−21.0839	−	5.64941i	−1.19364	−	0.319835i
$313$	−4.81731	−	6.87983i	−0.272290	−	0.388871i	0.659597	−	0.751620i	$-0.270727\pi$
$313$	−4.81731	−	6.87983i	−0.272290	−	0.388871i	−0.931887	+	0.362749i	$0.881838\pi$
$314$	−0.971983	+	5.51239i	−0.0548521	+	0.311082i
$315$		0			0
$316$	−7.13804	−	4.12115i	−0.401546	−	0.231833i
$317$	3.43949	−	0.300916i	0.193181	−	0.0169011i	0.00984528	−	0.999952i	$-0.496866\pi$
$317$	3.43949	−	0.300916i	0.193181	−	0.0169011i	0.183335	+	0.983050i	$0.441311\pi$
$318$	−4.17935	−	8.96264i	−0.234366	−	0.502600i
$319$	1.78859	−	0.650993i	0.100142	−	0.0364486i
$320$		0			0
$321$	0.554385	+	3.14407i	0.0309427	+	0.175485i
$322$	−2.94127	+	2.94127i	−0.163911	+	0.163911i
$323$	−3.52015	+	0.0983233i	−0.195866	+	0.00547086i
$324$		−	20.0030i		−	1.11128i
$325$		0			0
$326$	0.232296	+	0.276840i	0.0128657	+	0.0153328i
$327$	−23.1847	−	10.8112i	−1.28212	−	0.597861i
$328$	−11.7464	+	5.47745i	−0.648588	+	0.302441i
$329$	−11.7408	+	13.9922i	−0.647293	+	0.771414i
$330$		0			0
$331$	13.8683	−	8.00688i	0.762272	−	0.440098i	−0.0678392	−	0.997696i	$-0.521610\pi$
$331$	13.8683	−	8.00688i	0.762272	−	0.440098i	0.830111	+	0.557599i	$0.188277\pi$
$332$	−11.5710	+	8.10207i	−0.635038	+	0.444659i
$333$	−32.3779	+	22.6713i	−1.77430	+	1.24238i
$334$	5.13299	−	2.96353i	0.280865	−	0.162157i
$335$		0			0
$336$	−10.7870	+	12.8554i	−0.588477	+	0.701319i
$337$	16.6969	−	7.78587i	0.909536	−	0.424123i	0.0892052	−	0.996013i	$-0.471567\pi$
$337$	16.6969	−	7.78587i	0.909536	−	0.424123i	0.820330	+	0.571890i	$0.193790\pi$
$338$	1.83341	+	0.854932i	0.0997242	+	0.0465022i
$339$	21.3191	+	25.4071i	1.15789	+	1.37992i
$340$		0			0
$341$		−	4.83202i		−	0.261668i
$342$	−1.79759	+	12.1732i	−0.0972028	+	0.658252i
$343$	−14.0871	+	14.0871i	−0.760629	+	0.760629i
$344$	−0.326996	−	1.85449i	−0.0176304	−	0.0999872i
$345$		0			0
$346$	−4.46025	+	1.62340i	−0.239785	+	0.0872745i
$347$	5.63123	+	12.0762i	0.302300	+	0.648285i	0.997510	−	0.0705217i	$-0.0224664\pi$
$347$	5.63123	+	12.0762i	0.302300	+	0.648285i	−0.695210	+	0.718807i	$0.744689\pi$
$348$	−21.7124	+	1.89959i	−1.16390	+	0.101828i
$349$	−14.8650	−	8.58233i	−0.795707	−	0.459401i	0.0462610	−	0.998929i	$-0.485269\pi$
$349$	−14.8650	−	8.58233i	−0.795707	−	0.459401i	−0.841968	+	0.539528i	$0.818603\pi$
$350$		0			0
$351$	−7.12749	+	40.4220i	−0.380437	+	2.15757i
$352$	1.28693	+	1.83793i	0.0685937	+	0.0979620i
$353$	−11.2432	−	3.01262i	−0.598417	−	0.160345i	−0.0531199	−	0.998588i	$-0.516917\pi$
$353$	−11.2432	−	3.01262i	−0.598417	−	0.160345i	−0.545297	+	0.838243i	$0.683583\pi$
$354$	1.20492	−	2.08699i	0.0640409	−	0.110922i
$355$		0			0
$356$	−0.180705	+	0.496484i	−0.00957737	+	0.0263136i
$357$	2.03829	−	4.37113i	0.107878	−	0.231345i
$358$	−0.162683	+	1.85947i	−0.00859804	+	0.0982761i
$359$	−20.8766	+	3.68111i	−1.10183	+	0.194282i	−0.694848	−	0.719156i	$-0.744528\pi$
$359$	−20.8766	+	3.68111i	−1.10183	+	0.194282i	−0.406978	+	0.913438i	$0.633417\pi$
$360$		0			0
$361$	−5.49164	+	18.1891i	−0.289034	+	0.957319i
$362$	−0.606448	−	0.606448i	−0.0318742	−	0.0318742i
$363$	18.7755	−	26.8141i	0.985456	−	1.40738i
$364$	11.2897	−	9.47316i	0.591740	−	0.496529i
$365$		0			0
$366$	4.55304	+	1.65717i	0.237991	+	0.0866218i
$367$	0.0284950	+	0.325699i	0.00148743	+	0.0170014i	0.996902	−	0.0786519i	$-0.0250616\pi$
$367$	0.0284950	+	0.325699i	0.00148743	+	0.0170014i	−0.995415	+	0.0956532i	$0.969506\pi$
$368$	3.40050	+	12.6908i	0.177263	+	0.661556i
$369$	23.4961	+	40.6964i	1.22316	+	2.11857i
$370$		0			0
$371$	13.9028	+	2.45144i	0.721797	+	0.127272i
$372$	−14.3207	+	53.4454i	−0.742491	+	2.77102i
$373$	13.8768	−	3.71828i	0.718515	−	0.192525i	0.119006	−	0.992894i	$-0.462029\pi$
$373$	13.8768	−	3.71828i	0.718515	−	0.192525i	0.599509	+	0.800368i	$0.295363\pi$
$374$	−0.133509	−	0.112027i	−0.00690358	−	0.00579279i
$375$		0			0
$376$	−5.46549	−	15.0163i	−0.281861	−	0.774407i
$377$	16.6390	+	1.45572i	0.856951	+	0.0749735i
$378$	−7.15987	−	5.01340i	−0.368264	−	0.257861i
$379$	−9.33155			−0.479330			−0.239665	−	0.970856i	$-0.577038\pi$
$379$	−9.33155			−0.479330			−0.239665	+	0.970856i	$0.577038\pi$
$380$		0			0
$381$	−30.5365			−1.56443
$382$	3.81496	+	2.67127i	0.195191	+	0.136674i
$383$	7.77191	+	0.679954i	0.397126	+	0.0347440i	0.283970	−	0.958833i	$-0.408348\pi$
$383$	7.77191	+	0.679954i	0.397126	+	0.0347440i	0.113156	+	0.993577i	$0.463904\pi$
$384$	−11.4337	−	31.4140i	−0.583476	−	1.60309i
$385$		0			0
$386$	0.639086	+	0.536257i	0.0325286	+	0.0272948i
$387$	−6.59495	+	1.76711i	−0.335240	+	0.0898273i
$388$	−1.92186	+	7.17247i	−0.0975675	+	0.364127i
$389$	−5.11375	−	0.901692i	−0.259277	−	0.0457176i	0.0424983	−	0.999097i	$-0.486468\pi$
$389$	−5.11375	−	0.901692i	−0.259277	−	0.0457176i	−0.301776	+	0.953379i	$0.597579\pi$
$390$		0			0
$391$	−1.88800	−	3.27012i	−0.0954805	−	0.165377i
$392$	−1.39683	−	5.21305i	−0.0705506	−	0.263299i
$393$	−3.11894	−	35.6496i	−0.157330	−	1.79828i
$394$	2.88952	+	1.05170i	0.145572	+	0.0529838i
$395$		0			0
$396$	4.08098	−	3.42435i	0.205077	−	0.172080i
$397$	−4.72039	+	6.74142i	−0.236910	+	0.338342i	−0.919948	−	0.392040i	$-0.871769\pi$
$397$	−4.72039	+	6.74142i	−0.236910	+	0.338342i	0.683038	+	0.730383i	$0.260658\pi$
$398$	−4.46270	−	4.46270i	−0.223695	−	0.223695i
$399$	−18.9069	−	17.8794i	−0.946529	−	0.895090i
$400$		0			0
$401$	1.97650	−	0.348511i	0.0987019	−	0.0174038i	−0.124079	−	0.992272i	$-0.539598\pi$
$401$	1.97650	−	0.348511i	0.0987019	−	0.0174038i	0.222781	+	0.974869i	$0.428487\pi$
$402$	0.364517	−	4.16644i	0.0181804	−	0.207803i
$403$	17.9199	−	38.4293i	0.892652	−	1.91430i
$404$	6.08534	−	16.7193i	0.302757	−	0.831818i
$405$		0			0
$406$	−1.77839	+	3.08026i	−0.0882600	+	0.152871i
$407$	−2.91755	−	0.781755i	−0.144617	−	0.0387501i
$408$	2.42022	+	3.45643i	0.119819	+	0.171119i
$409$	2.66460	−	15.1117i	0.131756	−	0.747224i	−0.845308	−	0.534279i	$-0.820583\pi$
$409$	2.66460	−	15.1117i	0.131756	−	0.747224i	0.977064	−	0.212945i	$-0.0683056\pi$
$410$		0			0
$411$	49.4352	+	28.5414i	2.43846	+	1.40784i
$412$	30.6628	−	2.68264i	1.51065	−	0.132164i
$413$	1.45388	+	3.11785i	0.0715406	+	0.153419i
$414$	−12.3987	+	4.51277i	−0.609364	+	0.221791i
$415$		0			0
$416$	3.41895	+	19.3898i	0.167628	+	0.950663i
$417$	−22.4009	+	22.4009i	−1.09698	+	1.09698i
$418$	−0.800902	+	0.492717i	−0.0391734	+	0.0240996i
$419$			5.33874i			0.260814i	0.991461	+	0.130407i	$0.0416284\pi$
$419$			5.33874i			0.260814i	−0.991461	+	0.130407i	$0.958372\pi$
$420$		0			0
$421$	6.17855	+	7.36331i	0.301124	+	0.358866i	0.895295	−	0.445473i	$-0.146964\pi$
$421$	6.17855	+	7.36331i	0.301124	+	0.358866i	−0.594171	+	0.804338i	$0.702520\pi$
$422$	−4.52961	−	2.11219i	−0.220498	−	0.102820i
$423$	−52.5108	+	24.4862i	−2.55316	+	1.19056i
$424$	−7.93897	+	9.46129i	−0.385550	+	0.459481i
$425$		0			0
$426$	3.16198	−	1.82557i	0.153198	−	0.0884491i
$427$	−5.66592	+	3.96732i	−0.274193	+	0.191992i
$428$	1.54480	−	1.08168i	0.0746707	−	0.0522850i
$429$	−5.23748	+	3.02386i	−0.252868	+	0.145993i
$430$		0			0
$431$	1.69479	−	2.01978i	0.0816354	−	0.0972892i	−0.723681	−	0.690135i	$-0.757551\pi$
$431$	1.69479	−	2.01978i	0.0816354	−	0.0972892i	0.805316	+	0.592846i	$0.201996\pi$
$432$	−25.0215	+	11.6677i	−1.20385	+	0.561363i
$433$	18.5804	+	8.66419i	0.892918	+	0.416375i	0.814242	−	0.580526i	$-0.197153\pi$
$433$	18.5804	+	8.66419i	0.892918	+	0.416375i	0.0786761	+	0.996900i	$0.474931\pi$
$434$	5.80401	+	6.91695i	0.278601	+	0.332024i
$435$		0			0
$436$			15.1110i			0.723684i
$437$	−19.9569	+	4.09655i	−0.954670	+	0.195965i
$438$	0.384956	−	0.384956i	0.0183939	−	0.0183939i
$439$	−6.25393	−	35.4678i	−0.298484	−	1.69279i	−0.652696	−	0.757620i	$-0.726362\pi$
$439$	−6.25393	−	35.4678i	−0.298484	−	1.69279i	0.354212	−	0.935165i	$-0.384749\pi$
$440$		0			0
$441$	−18.3878	+	6.69259i	−0.875607	+	0.318695i
$442$	−0.646341	−	1.38608i	−0.0307433	−	0.0659293i
$443$	−21.6260	+	1.89203i	−1.02748	+	0.0898931i	−0.588414	−	0.808560i	$-0.700247\pi$
$443$	−21.6260	+	1.89203i	−1.02748	+	0.0898931i	−0.439069	+	0.898453i	$0.644692\pi$
$444$	29.9532	+	17.2935i	1.42152	+	0.820712i
$445$		0			0
$446$	−0.0164512	+	0.0932993i	−0.000778986	+	0.00441785i
$447$	−39.5646	−	56.5041i	−1.87134	−	2.67255i
$448$	6.61978	+	1.77377i	0.312755	+	0.0838025i
$449$	−4.13533	+	7.16260i	−0.195158	+	0.338024i	−0.946952	−	0.321374i	$-0.895855\pi$
$449$	−4.13533	+	7.16260i	−0.195158	+	0.338024i	0.751794	+	0.659398i	$0.229189\pi$
$450$		0			0
$451$	−1.22819	+	3.37443i	−0.0578333	+	0.158896i
$452$	8.27972	−	17.7559i	0.389445	−	0.835168i
$453$	−0.898795	+	10.2733i	−0.0422291	+	0.482680i
$454$	−8.41356	+	1.48354i	−0.394868	+	0.0696259i
$455$		0			0
$456$	21.8172	−	6.50396i	1.02168	−	0.304576i
$457$	11.1032	+	11.1032i	0.519384	+	0.519384i	0.917385	−	0.398001i	$-0.130296\pi$
$457$	11.1032	+	11.1032i	0.519384	+	0.519384i	−0.398001	+	0.917385i	$0.630296\pi$
$458$	0.473688	−	0.676497i	0.0221340	−	0.0316106i
$459$	6.07823	−	5.10024i	0.283708	−	0.238059i
$460$		0			0
$461$	−20.8249	−	7.57966i	−0.969914	−	0.353020i	−0.192003	−	0.981394i	$-0.561498\pi$
$461$	−20.8249	−	7.57966i	−0.969914	−	0.353020i	−0.777911	+	0.628374i	$0.783721\pi$
$462$	−0.112244	−	1.28295i	−0.00522205	−	0.0596883i
$463$	1.71716	+	6.40852i	0.0798031	+	0.297829i	0.994279	−	0.106810i	$-0.0340637\pi$
$463$	1.71716	+	6.40852i	0.0798031	+	0.297829i	−0.914476	+	0.404639i	$0.867397\pi$
$464$	5.61724	+	9.72935i	0.260774	+	0.451674i
$465$		0			0
$466$	−8.07516	−	1.42387i	−0.374074	−	0.0659594i
$467$	9.78057	−	36.5016i	0.452591	−	1.68909i	−0.242485	−	0.970155i	$-0.577963\pi$
$467$	9.78057	−	36.5016i	0.452591	−	1.68909i	0.695076	−	0.718936i	$-0.255371\pi$
$468$	45.1557	−	12.0994i	2.08732	−	0.559296i
$469$	4.57368	+	3.83777i	0.211193	+	0.177212i
$470$		0			0
$471$	−12.8420	−	35.2831i	−0.591728	−	1.62576i
$472$	−2.99826	−	0.262314i	−0.138006	−	0.0120740i
$473$	−0.427387	−	0.299260i	−0.0196513	−	0.0137600i
$474$	−6.32040			−0.290306
$475$		0			0
$476$	−2.84895			−0.130581
$477$	36.6823	+	25.6852i	1.67957	+	1.17604i
$478$	−13.6259	−	1.19211i	−0.623235	−	0.0545260i
$479$	−4.30184	−	11.8192i	−0.196556	−	0.540033i	0.801785	−	0.597613i	$-0.203884\pi$
$479$	−4.30184	−	11.8192i	−0.196556	−	0.540033i	−0.998341	+	0.0575797i	$0.981662\pi$
$480$		0			0
$481$	−20.3042	−	17.0372i	−0.925792	−	0.776832i
$482$	−10.0440	+	2.69128i	−0.457492	+	0.122585i
$483$	7.22170	−	26.9517i	0.328599	−	1.22635i
$484$	−19.0422	−	3.35766i	−0.865555	−	0.152621i
$485$		0			0
$486$	−0.996369	−	1.72576i	−0.0451962	−	0.0782822i
$487$	6.63552	+	24.7641i	0.300684	+	1.12217i	0.936597	+	0.350408i	$0.113957\pi$
$487$	6.63552	+	24.7641i	0.300684	+	1.12217i	−0.635913	+	0.771761i	$0.719376\pi$
$488$	−0.527410	−	6.02832i	−0.0238747	−	0.272889i
$489$	−2.27800	−	0.829124i	−0.103015	−	0.0374943i
$490$		0			0
$491$	26.2335	−	22.0125i	1.18390	−	0.993410i	0.183955	−	0.982935i	$-0.441110\pi$
$491$	26.2335	−	22.0125i	1.18390	−	0.993410i	0.999945	−	0.0104757i	$-0.00333458\pi$
$492$	23.5855	−	33.6835i	1.06331	−	1.51857i
$493$	−2.28310	−	2.28310i	−0.102826	−	0.102826i
$494$	−8.19688	+	0.948404i	−0.368795	+	0.0426707i
$495$		0			0
$496$	28.0872	−	4.95253i	1.26115	−	0.222375i
$497$	−0.454270	+	5.19233i	−0.0203768	+	0.232908i
$498$	−4.57772	+	9.81695i	−0.205132	+	0.439908i
$499$	9.81630	−	26.9701i	0.439438	−	1.20735i	−0.500421	−	0.865782i	$-0.666821\pi$
$499$	9.81630	−	26.9701i	0.439438	−	1.20735i	0.939859	−	0.341563i	$-0.110956\pi$
$500$		0			0
$501$	−19.8794	+	34.4321i	−0.888144	+	1.53831i
$502$	−1.53081	−	0.410179i	−0.0683233	−	0.0183072i
$503$	6.16974	+	8.81131i	0.275095	+	0.392877i	0.932797	−	0.360401i	$-0.117360\pi$
$503$	6.16974	+	8.81131i	0.275095	+	0.392877i	−0.657702	+	0.753278i	$0.728471\pi$
$504$	−3.65496	+	20.7283i	−0.162805	+	0.923312i
$505$		0			0
$506$	−0.873196	−	0.504140i	−0.0388183	−	0.0224118i
$507$	−13.5182	+	1.18269i	−0.600366	+	0.0525252i
$508$	7.62315	+	16.3479i	0.338222	+	0.725320i
$509$	25.8598	−	9.41220i	1.14622	−	0.417188i	0.302061	−	0.953288i	$-0.402325\pi$
$509$	25.8598	−	9.41220i	1.14622	−	0.417188i	0.844154	+	0.536100i	$0.180103\pi$
$510$		0			0
$511$	0.134954	+	0.765364i	0.00597003	+	0.0338577i
$512$	−16.1978	+	16.1978i	−0.715846	+	0.715846i
$513$	−15.7594	−	39.8038i	−0.695795	−	1.75738i
$514$		−	1.91472i		−	0.0844547i
$515$		0			0
$516$	3.84028	+	4.57667i	0.169059	+	0.201476i
$517$	−4.01271	−	1.87116i	−0.176479	−	0.0822935i
$518$	5.11543	−	2.38536i	0.224759	−	0.104807i
$519$	20.4660	−	24.3905i	0.898360	−	1.07062i
$520$		0			0
$521$	29.9147	−	17.2713i	1.31059	−	0.756669i	0.328395	−	0.944540i	$-0.393492\pi$
$521$	29.9147	−	17.2713i	1.31059	−	0.756669i	0.982194	+	0.187871i	$0.0601588\pi$
$522$	−9.24192	+	6.47127i	−0.404508	+	0.283240i
$523$	27.1041	−	18.9785i	1.18518	−	0.829870i	0.196585	−	0.980487i	$-0.437015\pi$
$523$	27.1041	−	18.9785i	1.18518	−	0.829870i	0.988592	+	0.150616i	$0.0481258\pi$
$524$	−18.3066	+	10.5693i	−0.799728	+	0.461723i
$525$		0			0
$526$	−5.12870	+	6.11214i	−0.223622	+	0.266502i
$527$	−7.42880	+	3.46411i	−0.323604	+	0.150899i
$528$	−3.68670	−	1.71914i	−0.160443	−	0.0748158i
$529$	0.742222	+	0.884546i	0.0322705	+	0.0384585i
$530$		0			0
$531$			10.9124i			0.473558i
$532$	−4.85191	+	14.5853i	−0.210357	+	0.632355i
$533$	−22.2822	+	22.2822i	−0.965148	+	0.965148i
$534$	0.0703535	+	0.398995i	0.00304449	+	0.0172662i
$535$		0			0
$536$	−4.90844	+	1.78653i	−0.212012	+	0.0771661i
$537$	−5.29159	−	11.3478i	−0.228349	−	0.489696i
$538$	5.89509	−	0.515753i	0.254155	−	0.0222357i
$539$	−1.29498	−	0.747657i	−0.0557787	−	0.0322039i
$540$		0			0
$541$	−5.47144	+	31.0301i	−0.235235	+	1.33409i	0.606882	+	0.794792i	$0.292420\pi$
$541$	−5.47144	+	31.0301i	−0.235235	+	1.33409i	−0.842117	+	0.539294i	$0.818691\pi$
$542$	3.61921	+	5.16876i	0.155458	+	0.222017i
$543$	5.55706	+	1.48901i	0.238476	+	0.0638995i
$544$	1.90304	−	3.29617i	0.0815924	−	0.141322i
$545$		0			0
$546$	3.86523	−	10.6196i	0.165417	−	0.454478i
$547$	14.6492	−	31.4152i	0.626352	−	1.34322i	−0.295376	−	0.955381i	$-0.595445\pi$
$547$	14.6492	−	31.4152i	0.626352	−	1.34322i	0.921728	−	0.387836i	$-0.126777\pi$
$548$	2.93879	−	33.5905i	0.125539	−	1.43491i
$549$	−21.6072	+	3.80994i	−0.922173	+	0.162604i
$550$		0			0
$551$	−15.5767	+	7.80020i	−0.663589	+	0.332300i
$552$	17.2613	+	17.2613i	0.734690	+	0.734690i
$553$	5.17519	−	7.39093i	0.220071	−	0.314294i
$554$	5.67119	−	4.75869i	0.240946	−	0.202177i
$555$		0			0
$556$	17.5846	+	6.40029i	0.745755	+	0.271433i
$557$	1.53414	+	17.5353i	0.0650037	+	0.742996i	0.956836	+	0.290629i	$0.0938646\pi$
$557$	1.53414	+	17.5353i	0.0650037	+	0.742996i	−0.891832	+	0.452367i	$0.850580\pi$
$558$	7.41307	+	27.6659i	0.313820	+	1.17119i
$559$	−2.28921	−	3.96502i	−0.0968231	−	0.167703i
$560$		0			0
$561$	1.15133	+	0.203011i	0.0486092	+	0.00857111i
$562$	3.39128	−	12.6564i	0.143053	−	0.533879i
$563$	−30.4542	+	8.16017i	−1.28349	+	0.343910i	−0.835184	−	0.549970i	$-0.814639\pi$
$563$	−30.4542	+	8.16017i	−1.28349	+	0.343910i	−0.448306	+	0.893880i	$0.647973\pi$
$564$	38.8378	+	32.5888i	1.63537	+	1.37223i
$565$		0			0
$566$	2.97254	+	8.16699i	0.124945	+	0.343284i
$567$	21.8135	+	1.90844i	0.916083	+	0.0801469i
$568$	−3.73533	−	2.61551i	−0.156731	−	0.109744i
$569$	1.63769			0.0686556			0.0343278	−	0.999411i	$-0.489071\pi$
$569$	1.63769			0.0686556			0.0343278	+	0.999411i	$0.489071\pi$
$570$		0			0
$571$	24.8017			1.03792			0.518959	−	0.854799i	$-0.326320\pi$
$571$	24.8017			1.03792			0.518959	+	0.854799i	$0.326320\pi$
$572$	2.92633	+	2.04904i	0.122356	+	0.0856745i
$573$	−31.1217	−	2.72279i	−1.30013	−	0.113746i
$574$	−2.29508	−	6.30569i	−0.0957949	−	0.263194i
$575$		0			0
$576$	16.6531	+	13.9736i	0.693879	+	0.582234i
$577$	−41.7607	+	11.1898i	−1.73852	+	0.465835i	−0.982118	−	0.188269i	$-0.939712\pi$
$577$	−41.7607	+	11.1898i	−1.73852	+	0.465835i	−0.756404	+	0.654104i	$0.773046\pi$
$578$	1.91648	−	7.15242i	0.0797152	−	0.297501i
$579$	−5.51125	−	0.971781i	−0.229040	−	0.0403858i
$580$		0			0
$581$	−7.73145	−	13.3913i	−0.320755	−	0.555563i
$582$	1.47373	+	5.50002i	0.0610880	+	0.227983i
$583$	0.298248	+	3.40899i	0.0123522	+	0.141186i
$584$	−0.638923	−	0.232549i	−0.0264388	−	0.00962294i
$585$		0			0
$586$	−0.974129	+	0.817392i	−0.0402409	+	0.0337661i
$587$	−16.0679	+	22.9473i	−0.663193	+	0.947138i	0.336792	+	0.941579i	$0.390658\pi$
$587$	−16.0679	+	22.9473i	−0.663193	+	0.947138i	−0.999985	+	0.00555837i	$0.998231\pi$
$588$	12.1075	+	12.1075i	0.499306	+	0.499306i
$589$	5.08303	+	43.9317i	0.209443	+	1.81018i
$590$		0			0
$591$	−20.3134	+	3.58181i	−0.835583	+	0.147336i
$592$	1.55381	−	17.7602i	0.0638613	−	0.729938i
$593$	−17.5629	+	37.6638i	−0.721223	+	1.54667i	0.111985	+	0.993710i	$0.464279\pi$
$593$	−17.5629	+	37.6638i	−0.721223	+	1.54667i	−0.833209	+	0.552959i	$0.813499\pi$
$594$	0.724641	−	1.99094i	0.0297324	−	0.0816891i
$595$		0			0
$596$	−20.3729	+	35.2868i	−0.834505	+	1.44540i
$597$	40.8930	+	10.9573i	1.67364	+	0.448451i
$598$	−5.07493	−	7.24775i	−0.207529	−	0.296383i
$599$	−6.78798	+	38.4965i	−0.277349	+	1.57293i	0.454050	+	0.890976i	$0.349979\pi$
$599$	−6.78798	+	38.4965i	−0.277349	+	1.57293i	−0.731399	+	0.681949i	$0.761132\pi$
$600$		0			0
$601$	−10.8442	−	6.26090i	−0.442344	−	0.255388i	0.262247	−	0.965001i	$-0.415536\pi$
$601$	−10.8442	−	6.26090i	−0.442344	−	0.255388i	−0.704592	+	0.709613i	$0.748870\pi$
$602$	0.971255	−	0.0849738i	0.0395854	−	0.00346327i
$603$	8.00389	+	17.1644i	0.325943	+	0.698988i
$604$	5.72423	−	2.08345i	0.232916	−	0.0847743i
$605$		0			0
$606$	−2.36919	−	13.4363i	−0.0962417	−	0.545814i
$607$	4.99686	−	4.99686i	0.202816	−	0.202816i	−0.598389	−	0.801206i	$-0.704192\pi$
$607$	4.99686	−	4.99686i	0.202816	−	0.202816i	0.801206	+	0.598389i	$0.204192\pi$
$608$	−13.6339	−	15.3563i	−0.552929	−	0.622780i
$609$		−	23.8588i		−	0.966809i
$610$		0			0
$611$	−24.9740	−	29.7628i	−1.01034	−	1.20407i
$612$	−8.19033	−	3.81921i	−0.331074	−	0.154382i
$613$	−41.0827	+	19.1572i	−1.65931	+	0.773750i	−0.659557	+	0.751655i	$0.729256\pi$
$613$	−41.0827	+	19.1572i	−1.65931	+	0.773750i	−0.999756	+	0.0220954i	$0.992966\pi$
$614$	−2.77229	+	3.30388i	−0.111880	+	0.133334i
$615$		0			0
$616$	−1.39294	+	0.804215i	−0.0561232	+	0.0324027i
$617$	0.737938	−	0.516710i	0.0297083	−	0.0208019i	−0.558628	−	0.829418i	$-0.688672\pi$
$617$	0.737938	−	0.516710i	0.0297083	−	0.0208019i	0.588336	+	0.808616i	$0.299783\pi$
$618$	19.3343	−	13.5380i	0.777738	−	0.544578i
$619$	14.0597	−	8.11739i	0.565108	−	0.326266i	−0.190085	−	0.981768i	$-0.560876\pi$
$619$	14.0597	−	8.11739i	0.565108	−	0.326266i	0.755193	+	0.655502i	$0.227543\pi$
$620$		0			0
$621$	29.5064	−	35.1643i	1.18405	−	1.41110i
$622$	−9.83122	+	4.58437i	−0.394196	+	0.183817i
$623$	−0.524181	−	0.244430i	−0.0210009	−	0.00979287i
$624$	−22.9450	−	27.3447i	−0.918534	−	1.09467i
$625$		0			0
$626$			3.80431i			0.152051i
$627$	3.00010	−	5.54856i	0.119813	−	0.221588i
$628$	−15.6831	+	15.6831i	−0.625825	+	0.625825i
$629$	0.889732	+	5.04592i	0.0354759	+	0.201194i
$630$		0			0
$631$	−28.4762	+	10.3645i	−1.13362	+	0.412603i	−0.839604	−	0.543198i	$-0.817213\pi$
$631$	−28.4762	+	10.3645i	−1.13362	+	0.412603i	−0.294013	+	0.955801i	$0.594991\pi$
$632$	3.33602	+	7.15412i	0.132700	+	0.284576i
$633$	33.3981	−	2.92196i	1.32746	−	0.116137i
$634$	−1.35439	−	0.781955i	−0.0537896	−	0.0310554i
$635$		0			0
$636$	6.80440	−	38.5897i	0.269812	−	1.53018i
$637$	−7.52630	−	10.7487i	−0.298203	−	0.425878i
$638$	−0.832782	−	0.223143i	−0.0329702	−	0.00883433i
$639$	−8.26665	+	14.3183i	−0.327024	+	0.566422i
$640$		0			0
$641$	−10.4710	+	28.7688i	−0.413580	+	1.13630i	0.541694	+	0.840576i	$0.317783\pi$
$641$	−10.4710	+	28.7688i	−0.413580	+	1.13630i	−0.955273	+	0.295725i	$0.904439\pi$
$642$	0.611156	−	1.31063i	0.0241204	−	0.0517264i
$643$	0.116664	−	1.33347i	0.00460077	−	0.0525870i	−0.993547	−	0.113419i	$-0.963820\pi$
$643$	0.116664	−	1.33347i	0.00460077	−	0.0525870i	0.998148	+	0.0608319i	$0.0193753\pi$
$644$	−16.2316	+	2.86207i	−0.639614	+	0.112781i
$645$		0			0
$646$	1.33168	+	0.878084i	0.0523943	+	0.0345478i
$647$	3.23855	+	3.23855i	0.127320	+	0.127320i	0.767896	−	0.640575i	$-0.221304\pi$
$647$	3.23855	+	3.23855i	0.127320	+	0.127320i	−0.640575	+	0.767896i	$0.721304\pi$
$648$	−10.9880	+	15.6925i	−0.431650	+	0.616460i
$649$	−0.638799	+	0.536016i	−0.0250751	+	0.0210405i
$650$		0			0
$651$	−56.9166	−	20.7160i	−2.23074	−	0.811922i
$652$	0.124804	+	1.42652i	0.00488772	+	0.0558669i
$653$	−0.186959	−	0.697739i	−0.00731626	−	0.0273047i	0.962171	−	0.272446i	$-0.0878325\pi$
$653$	−0.186959	−	0.697739i	−0.00731626	−	0.0273047i	−0.969487	+	0.245141i	$0.921166\pi$
$654$	5.79373	+	10.0350i	0.226553	+	0.392401i
$655$		0			0
$656$	−20.8735	−	3.68056i	−0.814972	−	0.143702i
$657$	−0.638049	+	2.38123i	−0.0248927	+	0.0929006i
$658$	7.99168	−	2.14136i	0.311548	−	0.0834791i
$659$	1.32005	+	1.10766i	0.0514220	+	0.0431482i	0.668136	−	0.744039i	$-0.267092\pi$
$659$	1.32005	+	1.10766i	0.0514220	+	0.0431482i	−0.616714	+	0.787187i	$0.711537\pi$
$660$		0			0
$661$	−12.2612	−	33.6874i	−0.476905	−	1.31029i	−0.912106	−	0.409954i	$-0.865545\pi$
$661$	−12.2612	−	33.6874i	−0.476905	−	1.31029i	0.435201	−	0.900333i	$-0.356677\pi$
$662$	−7.22603	−	0.632196i	−0.280848	−	0.0245710i
$663$	8.40370	+	5.88434i	0.326373	+	0.228529i
$664$	13.5281			0.524992
$665$		0			0
$666$	17.9039			0.693762
$667$	−15.3013	−	10.7141i	−0.592470	−	0.414852i
$668$	23.3961	+	2.04689i	0.905222	+	0.0791966i
$669$	−0.217356	−	0.597180i	−0.00840346	−	0.0230883i
$670$		0			0
$671$	−1.28437	−	1.07772i	−0.0495826	−	0.0416048i
$672$	27.1664	−	7.27922i	1.04797	−	0.280802i
$673$	3.39184	−	12.6585i	0.130746	−	0.487950i	−0.869233	−	0.494402i	$-0.835387\pi$
$673$	3.39184	−	12.6585i	0.130746	−	0.487950i	0.999979	+	0.00645186i	$0.00205370\pi$
$674$	−8.21813	−	1.44908i	−0.316551	−	0.0558164i
$675$		0			0
$676$	4.00786	+	6.94182i	0.154148	+	0.266993i
$677$	−1.89938	−	7.08859i	−0.0729992	−	0.272437i	0.919773	−	0.392451i	$-0.128373\pi$
$677$	−1.89938	−	7.08859i	−0.0729992	−	0.272437i	−0.992772	+	0.120014i	$0.961706\pi$
$678$	−1.30936	−	14.9661i	−0.0502857	−	0.574768i
$679$	−7.63830	−	2.78012i	−0.293131	−	0.106691i
$680$		0			0
$681$	43.9011	−	36.8374i	1.68229	−	1.41161i
$682$	−1.25540	+	1.79290i	−0.0480718	+	0.0686537i
$683$	29.0355	+	29.0355i	1.11101	+	1.11101i	0.993014	+	0.117997i	$0.0376472\pi$
$683$	29.0355	+	29.0355i	1.11101	+	1.11101i	0.117997	+	0.993014i	$0.462353\pi$
$684$	−33.5012	+	35.4265i	−1.28095	+	1.35457i
$685$		0			0
$686$	8.88688	−	1.56700i	0.339303	−	0.0598282i
$687$	−0.482825	+	5.51872i	−0.0184209	+	0.210552i
$688$	1.30147	−	2.79101i	0.0496180	−	0.106406i
$689$	−10.2705	+	28.2179i	−0.391274	+	1.07502i
$690$		0			0
$691$	7.26116	−	12.5767i	0.276228	−	0.478440i	−0.694217	−	0.719766i	$-0.744249\pi$
$691$	7.26116	−	12.5767i	0.276228	−	0.478440i	0.970444	+	0.241326i	$0.0775823\pi$
$692$	−18.1667	−	4.86776i	−0.690595	−	0.185044i
$693$	3.34494	+	4.77707i	0.127064	+	0.181466i
$694$	1.04806	−	5.94387i	0.0397840	−	0.225626i
$695$		0			0
$696$	18.0770	+	10.4368i	0.685206	+	0.395604i
$697$	6.06839	−	0.530916i	0.229857	−	0.0201099i
$698$	3.28584	+	7.04650i	0.124371	+	0.266714i
$699$	51.6866	−	18.8124i	1.95497	−	0.711550i
$700$		0			0
$701$	6.45153	+	36.5885i	0.243671	+	1.38193i	0.823559	+	0.567231i	$0.191985\pi$
$701$	6.45153	+	36.5885i	0.243671	+	1.38193i	−0.579888	+	0.814696i	$0.696904\pi$
$702$	13.1466	−	13.1466i	0.496187	−	0.496187i
$703$	27.3481	+	4.03845i	1.03145	+	0.152313i
$704$			1.66123i			0.0626101i
$705$		0			0
$706$	3.38905	+	4.03891i	0.127549	+	0.152006i
$707$	17.6521	+	8.23129i	0.663874	+	0.309569i
$708$	8.65414	−	4.03549i	0.325243	−	0.151663i
$709$	14.2659	−	17.0015i	0.535768	−	0.638503i	−0.428466	−	0.903558i	$-0.640946\pi$
$709$	14.2659	−	17.0015i	0.535768	−	0.638503i	0.964233	+	0.265055i	$0.0853901\pi$
$710$		0			0
$711$	24.7860	−	14.3102i	0.929548	−	0.536675i
$712$	0.414492	−	0.290231i	0.0155338	−	0.0108769i
$713$	−38.8448	+	27.1994i	−1.45475	+	1.01863i
$714$	−1.89196	+	1.09232i	−0.0708047	+	0.0408791i
$715$		0			0
$716$	−4.75414	+	5.66576i	−0.177670	+	0.211739i
$717$	83.1553	−	38.7760i	3.10549	−	1.44812i
$718$	8.70256	+	4.05807i	0.324777	+	0.151446i
$719$	−16.1088	−	19.1978i	−0.600758	−	0.715956i	0.376877	−	0.926263i	$-0.376998\pi$
$719$	−16.1088	−	19.1978i	−0.600758	−	0.715956i	−0.977635	+	0.210308i	$0.932553\pi$
$720$		0			0
$721$			33.6941i			1.25483i
$722$	6.76333	−	5.32219i	0.251705	−	0.198072i
$723$	49.3220	−	49.3220i	1.83430	−	1.83430i
$724$	−0.590117	−	3.34672i	−0.0219315	−	0.124380i
$725$		0			0
$726$	−13.9331	+	5.07124i	−0.517106	+	0.188211i
$727$	−8.02156	−	17.2023i	−0.297503	−	0.637998i	0.699561	−	0.714573i	$-0.253379\pi$
$727$	−8.02156	−	17.2023i	−0.297503	−	0.637998i	−0.997064	+	0.0765756i	$0.975601\pi$
$728$	−14.0606	+	1.23014i	−0.521121	+	0.0455922i
$729$	−17.3787	−	10.0336i	−0.643656	−	0.371615i
$730$		0			0
$731$	−0.153689	+	0.871612i	−0.00568438	+	0.0322377i
$732$	11.0120	+	15.7268i	0.407015	+	0.581278i
$733$	35.7038	+	9.56681i	1.31875	+	0.353358i	0.848510	−	0.529180i	$-0.177500\pi$
$733$	35.7038	+	9.56681i	1.31875	+	0.353358i	0.470241	+	0.882538i	$0.344167\pi$
$734$	0.0740466	−	0.128252i	0.00273311	−	0.00473388i
$735$		0			0
$736$	7.53105	−	20.6914i	0.277598	−	0.762695i
$737$	−0.611632	+	1.31165i	−0.0225298	+	0.0483153i
$738$	1.85517	−	21.2047i	0.0682898	−	0.780556i
$739$	−22.2479	+	3.92291i	−0.818404	+	0.144307i	−0.567150	−	0.823615i	$-0.691954\pi$
$739$	−22.2479	+	3.92291i	−0.818404	+	0.144307i	−0.251254	+	0.967921i	$0.580843\pi$
$740$		0			0
$741$	44.4372	−	33.0019i	1.63244	−	1.21235i
$742$	−4.52166	−	4.52166i	−0.165996	−	0.165996i
$743$	−8.12048	+	11.5972i	−0.297912	+	0.425462i	−0.940003	−	0.341166i	$-0.889178\pi$
$743$	−8.12048	+	11.5972i	−0.297912	+	0.425462i	0.642091	+	0.766628i	$0.278067\pi$
$744$	40.5932	−	34.0617i	1.48822	−	1.24876i
$745$		0			0
$746$	−6.11498	−	2.22567i	−0.223885	−	0.0814876i
$747$	−4.27492	−	48.8626i	−0.156411	−	1.78779i
$748$	−0.178736	−	0.667051i	−0.00653523	−	0.0243898i
$749$	1.03220	+	1.78782i	0.0377158	+	0.0653257i
$750$		0			0
$751$	−3.03316	−	0.534827i	−0.110681	−	0.0195161i	0.118033	−	0.993010i	$-0.462341\pi$
$751$	−3.03316	−	0.534827i	−0.110681	−	0.0195161i	−0.228715	+	0.973494i	$0.573452\pi$
$752$	6.76374	−	25.2426i	0.246648	−	0.920504i
$753$	10.2687	−	2.75148i	0.374210	−	0.100269i
$754$	−5.79561	−	4.86309i	−0.211064	−	0.177103i
$755$		0			0
$756$	−11.8455	−	32.5451i	−0.430815	−	1.18365i
$757$	−12.0991	−	1.05854i	−0.439750	−	0.0384731i	−0.134869	−	0.990864i	$-0.543061\pi$
$757$	−12.0991	−	1.05854i	−0.439750	−	0.0384731i	−0.304881	+	0.952390i	$0.598617\pi$
$758$	3.46243	+	2.42442i	0.125761	+	0.0880589i
$759$	6.76353			0.245501
$760$		0			0
$761$	−42.4931			−1.54037			−0.770187	−	0.637819i	$-0.779837\pi$
$761$	−42.4931			−1.54037			−0.770187	+	0.637819i	$0.779837\pi$
$762$	11.3304	+	7.93366i	0.410458	+	0.287406i
$763$	−16.4787	−	1.44170i	−0.596569	−	0.0521930i
$764$	6.31156	+	17.3409i	0.228344	+	0.627371i
$765$		0			0
$766$	−2.70708	−	2.27151i	−0.0978106	−	0.0820728i
$767$	−7.06825	+	1.89393i	−0.255220	+	0.0683859i
$768$	1.56703	−	5.84824i	0.0565454	−	0.211030i
$769$	35.2926	+	6.22304i	1.27268	+	0.224408i	0.768871	−	0.639404i	$-0.220819\pi$
$769$	35.2926	+	6.22304i	1.27268	+	0.224408i	0.503813	+	0.863813i	$0.331930\pi$
$770$		0			0
$771$	6.42196	+	11.1232i	0.231281	+	0.400591i
$772$	0.855581	+	3.19307i	0.0307930	+	0.114921i
$773$	0.848094	+	9.69376i	0.0305038	+	0.348660i	0.996074	+	0.0885194i	$0.0282135\pi$
$773$	0.848094	+	9.69376i	0.0305038	+	0.348660i	−0.965571	+	0.260141i	$0.916231\pi$
$774$	2.90614	+	1.05775i	0.104459	+	0.0380199i
$775$		0			0
$776$	5.44767	−	4.57114i	0.195560	−	0.164094i
$777$	−21.7165	+	31.0144i	−0.779076	+	1.11264i
$778$	1.66317	+	1.66317i	0.0596274	+	0.0596274i
$779$	7.61675	−	31.9716i	0.272899	−	1.14550i
$780$		0			0
$781$	−1.24423	+	0.219391i	−0.0445220	+	0.00785044i
$782$	−0.149071	+	1.70388i	−0.00533075	+	0.0609308i
$783$	16.5884	−	35.5738i	0.592819	−	1.27131i
$784$	3.01865	−	8.29367i	0.107809	−	0.296202i
$785$		0			0
$786$	−8.10482	+	14.0380i	−0.289089	+	0.500717i
$787$	29.8799	+	8.00629i	1.06510	+	0.285393i	0.748479	−	0.663158i	$-0.230784\pi$
$787$	29.8799	+	8.00629i	1.06510	+	0.285393i	0.316623	+	0.948551i	$0.397451\pi$
$788$	6.98859	+	9.98075i	0.248958	+	0.355549i
$789$	9.29400	−	52.7089i	0.330875	−	1.87649i
$790$		0			0
$791$	18.5731	+	10.7232i	0.660383	+	0.381272i
$792$	−5.08262	+	0.444672i	−0.180603	+	0.0158007i
$793$	−6.21789	−	13.3343i	−0.220804	−	0.473515i
$794$	3.50296	−	1.27497i	0.124316	−	0.0452471i
$795$		0			0
$796$	−4.34252	−	24.6277i	−0.153917	−	0.872905i
$797$	18.1021	−	18.1021i	0.641208	−	0.641208i	−0.309644	−	0.950852i	$-0.600210\pi$
$797$	18.1021	−	18.1021i	0.641208	−	0.641208i	0.950852	+	0.309644i	$0.100210\pi$
$798$	2.37009	+	11.5463i	0.0839005	+	0.408733i
$799$			7.51064i			0.265707i
$800$		0			0
$801$	−1.17927	−	1.40540i	−0.0416676	−	0.0496575i
$802$	−0.823919	−	0.384200i	−0.0290936	−	0.0135666i
$803$	−0.170735	+	0.0796151i	−0.00602511	+	0.00280956i
$804$	10.6524	−	12.6950i	0.375682	−	0.447720i
$805$		0			0
$806$	−16.6333	+	9.60327i	−0.585885	+	0.338261i
$807$	−32.5165	+	22.7683i	−1.14463	+	0.801481i
$808$	−13.9582	+	9.77365i	−0.491049	+	0.343836i
$809$	23.1968	−	13.3927i	0.815557	−	0.470862i	−0.0333247	−	0.999445i	$-0.510610\pi$
$809$	23.1968	−	13.3927i	0.815557	−	0.470862i	0.848882	+	0.528582i	$0.177276\pi$
$810$		0			0
$811$	−19.0809	+	22.7397i	−0.670020	+	0.798499i	−0.988787	−	0.149334i	$-0.952287\pi$
$811$	−19.0809	+	22.7397i	−0.670020	+	0.798499i	0.318767	+	0.947833i	$0.396731\pi$
$812$	−12.7730	+	5.95613i	−0.448243	+	0.209019i
$813$	−38.3610	−	17.8880i	−1.34538	−	0.627361i
$814$	0.879437	+	1.04807i	0.0308242	+	0.0367349i
$815$		0			0
$816$			6.90044i			0.241564i
$817$	4.20053	+	2.27122i	0.146958	+	0.0794600i
$818$	−4.91483	+	4.91483i	−0.171843	+	0.171843i
$819$	8.88639	+	50.3972i	0.310516	+	1.76102i
$820$		0			0
$821$	36.7112	−	13.3618i	1.28123	−	0.466329i	0.390390	−	0.920649i	$-0.372340\pi$
$821$	36.7112	−	13.3618i	1.28123	−	0.466329i	0.890838	+	0.454320i	$0.150118\pi$
$822$	−10.9274	−	23.4339i	−0.381137	−	0.817350i
$823$	2.29311	−	0.200621i	0.0799326	−	0.00699320i	−0.0471193	−	0.998889i	$-0.515004\pi$
$823$	2.29311	−	0.200621i	0.0799326	−	0.00699320i	0.127052	+	0.991896i	$0.459449\pi$
$824$	−25.5288	−	14.7391i	−0.889338	−	0.513459i
$825$		0			0
$826$	0.270590	−	1.53459i	0.00941505	−	0.0533954i
$827$	2.29730	+	3.28088i	0.0798848	+	0.114087i	0.857106	−	0.515140i	$-0.172260\pi$
$827$	2.29730	+	3.28088i	0.0798848	+	0.114087i	−0.777221	+	0.629228i	$0.783371\pi$
$828$	−50.5004	−	13.5315i	−1.75501	−	0.470253i
$829$	−14.2569	+	24.6936i	−0.495161	+	0.857645i	−0.999984	−	0.00557813i	$-0.998224\pi$
$829$	−14.2569	+	24.6936i	−0.495161	+	0.857645i	0.504823	+	0.863223i	$0.331558\pi$
$830$		0			0
$831$	−16.9849	+	46.6658i	−0.589201	+	1.61882i
$832$	−6.16079	+	13.2119i	−0.213587	+	0.458039i
$833$	−0.221077	+	2.52692i	−0.00765986	+	0.0875526i
$834$	14.1317	−	2.49180i	0.489342	−	0.0862842i
$835$		0			0
$836$	−3.71940	−	0.220977i	−0.128638	−	0.00764264i
$837$	−70.4602	−	70.4602i	−2.43546	−	2.43546i
$838$	1.38705	−	1.98091i	0.0479149	−	0.0684295i
$839$	−5.48743	+	4.60450i	−0.189447	+	0.158965i	−0.732578	−	0.680683i	$-0.761683\pi$
$839$	−5.48743	+	4.60450i	−0.189447	+	0.158965i	0.543131	+	0.839648i	$0.317239\pi$
$840$		0			0
$841$	12.2419	+	4.45569i	0.422135	+	0.153645i
$842$	−0.379470	−	4.33736i	−0.0130774	−	0.149475i
$843$	22.7487	+	84.8993i	0.783507	+	2.92409i
$844$	−9.90180	−	17.1504i	−0.340834	−	0.590342i
$845$		0			0
$846$	25.8456	+	4.55728i	0.888591	+	0.156683i
$847$	5.47834	−	20.4454i	0.188238	−	0.702513i
$848$	−19.5098	+	5.22764i	−0.669970	+	0.179518i
$849$	−44.6604	−	37.4745i	−1.53274	−	1.28612i
$850$		0			0
$851$	10.1383	+	27.8548i	0.347537	+	0.954850i
$852$	14.4122	+	1.26091i	0.493755	+	0.0431980i
$853$	14.1091	+	9.87932i	0.483087	+	0.338261i	0.789617	−	0.613600i	$-0.210279\pi$
$853$	14.1091	+	9.87932i	0.483087	+	0.338261i	−0.306530	+	0.951861i	$0.599168\pi$
$854$	3.13306			0.107211
$855$		0			0
$856$	−1.80609			−0.0617310
$857$	−40.4277	−	28.3078i	−1.38098	−	0.966975i	−0.999085	−	0.0427711i	$-0.986381\pi$
$857$	−40.4277	−	28.3078i	−1.38098	−	0.966975i	−0.381899	−	0.924204i	$-0.624730\pi$
$858$	2.72897	+	0.238754i	0.0931655	+	0.00815092i
$859$	9.95294	+	27.3455i	0.339590	+	0.933016i	0.985511	+	0.169611i	$0.0542513\pi$
$859$	9.95294	+	27.3455i	0.339590	+	0.933016i	−0.645921	+	0.763404i	$0.723527\pi$
$860$		0			0
$861$	34.4821	+	28.9339i	1.17515	+	0.986064i
$862$	−1.15360	+	0.309107i	−0.0392918	+	0.0105282i
$863$	3.59381	−	13.4123i	0.122335	−	0.456560i	−0.877396	−	0.479767i	$-0.840721\pi$
$863$	3.59381	−	13.4123i	0.122335	−	0.456560i	0.999731	+	0.0232074i	$0.00738782\pi$
$864$	45.5665	+	8.03461i	1.55020	+	0.273343i
$865$		0			0
$866$	−4.64315	−	8.04217i	−0.157781	−	0.273284i
$867$	12.8558	+	47.9784i	0.436605	+	1.62943i
$868$	3.11828	+	35.6422i	0.105841	+	1.20977i
$869$	2.05519	+	0.748027i	0.0697174	+	0.0253751i
$870$		0			0
$871$	−9.72868	+	8.16333i	−0.329644	+	0.276604i
$872$	8.30073	−	11.8547i	0.281098	−	0.401450i
$873$	−18.2321	−	18.2321i	−0.617064	−	0.617064i
$874$	8.46925	+	3.66498i	0.286477	+	0.123970i
$875$		0			0
$876$	2.12440	−	0.374590i	0.0717769	−	0.0126562i
$877$	−2.10737	+	24.0873i	−0.0711608	+	0.813372i	0.873821	+	0.486248i	$0.161635\pi$
$877$	−2.10737	+	24.0873i	−0.0711608	+	0.813372i	−0.944982	+	0.327124i	$0.893921\pi$
$878$	−6.89436	+	14.7850i	−0.232673	+	0.498969i
$879$	2.91747	−	8.01569i	0.0984039	−	0.270363i
$880$		0			0
$881$	−11.2657	+	19.5128i	−0.379552	+	0.657403i	−0.990997	−	0.133884i	$-0.957255\pi$
$881$	−11.2657	+	19.5128i	−0.379552	+	0.657403i	0.611445	+	0.791287i	$0.290588\pi$
$882$	8.56149	+	2.29404i	0.288280	+	0.0772445i
$883$	−10.7621	−	15.3698i	−0.362172	−	0.517236i	0.596170	−	0.802858i	$-0.296689\pi$
$883$	−10.7621	−	15.3698i	−0.362172	−	0.517236i	−0.958342	+	0.285623i	$0.907800\pi$
$884$	1.05231	−	5.96794i	0.0353930	−	0.200723i
$885$		0			0
$886$	8.51580	+	4.91660i	0.286094	+	0.165176i
$887$	41.7992	−	3.65695i	1.40348	−	0.122788i	0.639877	−	0.768477i	$-0.278985\pi$
$887$	41.7992	−	3.65695i	1.40348	−	0.122788i	0.763601	+	0.645689i	$0.223430\pi$
$888$	−13.9989	−	30.0207i	−0.469771	−	1.00743i
$889$	−18.5549	+	6.75343i	−0.622311	+	0.226503i
$890$		0			0
$891$	0.921686	+	5.22714i	0.0308776	+	0.175116i
$892$	−0.265443	+	0.265443i	−0.00888768	+	0.00888768i
$893$	38.4511	+	12.7910i	1.28672	+	0.428036i
$894$			31.2448i			1.04498i
$895$		0			0
$896$	−13.8950	−	16.5594i	−0.464198	−	0.553210i
$897$	53.7907	+	25.0830i	1.79602	+	0.837497i
$898$	3.39530	−	1.58326i	0.113303	−	0.0528339i
$899$	−26.0641	+	31.0620i	−0.869286	+	1.03597i
$900$		0			0
$901$	5.02721	−	2.90246i	0.167481	−	0.0966949i
$902$	1.33242	−	0.932973i	0.0443648	−	0.0310646i
$903$	−5.35730	+	3.75122i	−0.178280	+	0.124833i
$904$	−16.2491	+	9.38144i	−0.540438	+	0.312022i
$905$		0			0
$906$	3.00258	−	3.57834i	0.0997541	−	0.118882i
$907$	−38.1030	+	17.7677i	−1.26519	+	0.589967i	−0.935234	−	0.354030i	$-0.884811\pi$
$907$	−38.1030	+	17.7677i	−1.26519	+	0.589967i	−0.329954	+	0.943997i	$0.607033\pi$
$908$	−30.6806	−	14.3066i	−1.01817	−	0.474781i
$909$	39.7126	+	47.3276i	1.31718	+	1.56976i
$910$		0			0
$911$		−	43.1012i		−	1.42801i	−0.700142	−	0.714003i	$-0.746880\pi$
$911$		−	43.1012i		−	1.42801i	0.700142	−	0.714003i	$-0.253120\pi$
$912$	35.3272	+	11.7518i	1.16980	+	0.389142i
$913$	2.65037	−	2.65037i	0.0877145	−	0.0877145i
$914$	−1.23508	−	7.00448i	−0.0408528	−	0.231688i
$915$		0			0
$916$	3.07501	−	1.11921i	0.101601	−	0.0369798i
$917$	−9.77939	−	20.9720i	−0.322944	−	0.692555i
$918$	−3.58039	+	0.313244i	−0.118170	+	0.0103386i
$919$	−5.67097	−	3.27413i	−0.187068	−	0.108004i	0.403541	−	0.914961i	$-0.367779\pi$
$919$	−5.67097	−	3.27413i	−0.187068	−	0.108004i	−0.590609	+	0.806958i	$0.701113\pi$
$920$		0			0
$921$	5.02381	−	28.4914i	0.165540	−	0.938825i
$922$	5.75774	+	8.22291i	0.189621	+	0.270807i
$923$	−10.7090	−	2.86948i	−0.352492	−	0.0944501i
$924$	2.55150	−	4.41932i	0.0839381	−	0.145385i
$925$		0			0
$926$	1.02785	−	2.82399i	0.0337771	−	0.0928019i
$927$	−45.1693	+	96.8658i	−1.48355	+	3.18149i
$928$	1.64099	−	18.7566i	0.0538682	−	0.615717i
$929$	28.0269	−	4.94190i	0.919533	−	0.162138i	0.306204	−	0.951966i	$-0.400941\pi$
$929$	28.0269	−	4.94190i	0.919533	−	0.162138i	0.613329	+	0.789827i	$0.289830\pi$
$930$		0			0
$931$	12.5602	+	5.43530i	0.411644	+	0.178135i
$932$	−22.9744	−	22.9744i	−0.752551	−	0.752551i
$933$	41.7364	−	59.6058i	1.36639	−	1.95141i
$934$	−13.1125	+	11.0027i	−0.429053	+	0.360018i
$935$		0			0
$936$	−42.0714	−	15.3127i	−1.37515	−	0.500512i
$937$	2.75156	+	31.4504i	0.0898895	+	1.02744i	0.898464	+	0.439047i	$0.144684\pi$
$937$	2.75156	+	31.4504i	0.0898895	+	1.02744i	−0.808574	+	0.588394i	$0.799760\pi$
$938$	−0.699956	−	2.61227i	−0.0228544	−	0.0852936i
$939$	−12.7596	−	22.1003i	−0.416395	−	0.721217i
$940$		0			0
$941$	−39.5313	−	6.97043i	−1.28868	−	0.227229i	−0.513020	−	0.858377i	$-0.671473\pi$
$941$	−39.5313	−	6.97043i	−1.28868	−	0.227229i	−0.775663	+	0.631147i	$0.782584\pi$
$942$	−4.40190	+	16.4281i	−0.143422	+	0.535256i
$943$	34.0407	−	9.12118i	1.10852	−	0.297026i
$944$	−3.77044	−	3.16378i	−0.122718	−	0.102972i
$945$		0			0
$946$	0.0808298	+	0.222078i	0.00262800	+	0.00722038i
$947$	6.90626	+	0.604220i	0.224423	+	0.0196345i	0.198813	−	0.980037i	$-0.436291\pi$
$947$	6.90626	+	0.604220i	0.224423	+	0.0196345i	0.0256106	+	0.999672i	$0.491847\pi$
$948$	−20.5148	−	14.3646i	−0.666291	−	0.466542i
$949$	−1.65312			−0.0536626
$950$		0			0
$951$	10.4907			0.340184
$952$	2.23502	+	1.56498i	0.0724374	+	0.0507212i
$953$	12.1246	+	1.06076i	0.392754	+	0.0343615i	0.281822	−	0.959467i	$-0.409061\pi$
$953$	12.1246	+	1.06076i	0.392754	+	0.0343615i	0.110931	+	0.993828i	$0.464617\pi$
$954$	−6.93755	−	19.0608i	−0.224612	−	0.617115i
$955$		0			0
$956$	−41.5179	−	34.8376i	−1.34278	−	1.12673i
$957$	5.58630	−	1.49684i	0.180579	−	0.0483861i
$958$	−1.47456	+	5.50312i	−0.0476407	+	0.177798i
$959$	36.3505	+	6.40957i	1.17382	+	0.206976i
$960$		0			0
$961$	35.9694	+	62.3007i	1.16030	+	2.00970i
$962$	3.10736	+	11.5968i	0.100185	+	0.373896i
$963$	0.570731	+	6.52348i	0.0183915	+	0.210216i
$964$	−38.7176	−	14.0920i	−1.24701	−	0.453874i
$965$		0			0
$966$	−9.68188	+	8.12406i	−0.311509	+	0.261387i
$967$	6.10838	−	8.72367i	0.196432	−	0.280534i	−0.708837	−	0.705372i	$-0.750780\pi$
$967$	6.10838	−	8.72367i	0.196432	−	0.280534i	0.905269	+	0.424838i	$0.139669\pi$
$968$	13.0943	+	13.0943i	0.420868	+	0.420868i
$969$	−10.6812	−	0.634592i	−0.343130	−	0.0203860i
$970$		0			0
$971$	2.17846	−	0.384122i	0.0699102	−	0.0123270i	−0.138584	−	0.990351i	$-0.544255\pi$
$971$	2.17846	−	0.384122i	0.0699102	−	0.0123270i	0.208494	+	0.978024i	$0.433144\pi$
$972$	0.688186	−	7.86600i	0.0220736	−	0.252302i
$973$	−8.65730	+	18.5656i	−0.277540	+	0.595187i
$974$	3.97185	−	10.9126i	0.127266	−	0.349662i
$975$		0			0
$976$	4.94806	−	8.57030i	0.158384	−	0.274329i
$977$	22.3268	+	5.98245i	0.714298	+	0.191396i	0.597626	−	0.801775i	$-0.296111\pi$
$977$	22.3268	+	5.98245i	0.714298	+	0.191396i	0.116672	+	0.993171i	$0.462777\pi$
$978$	0.629828	+	0.899487i	0.0201397	+	0.0287624i
$979$	0.0243448	−	0.138066i	0.000778064	−	0.00441262i
$980$		0			0
$981$	−45.4413	−	26.2355i	−1.45083	−	0.837636i
$982$	−15.4529	+	1.35195i	−0.493121	+	0.0431425i
$983$	5.81504	+	12.4704i	0.185471	+	0.397744i	0.976955	−	0.213446i	$-0.0684689\pi$
$983$	5.81504	+	12.4704i	0.185471	+	0.397744i	−0.791484	+	0.611190i	$0.790691\pi$
$984$	−37.0059	+	13.4691i	−1.17971	+	0.429378i
$985$		0			0
$986$	0.253964	+	1.44030i	0.00808787	+	0.0458686i
$987$	−39.2439	+	39.2439i	−1.24915	+	1.24915i
$988$	−28.7610	−	15.5511i	−0.915011	−	0.494746i
$989$			5.12032i			0.162817i
$990$		0			0
$991$	−23.8389	−	28.4101i	−0.757267	−	0.902476i	0.240405	−	0.970673i	$-0.422720\pi$
$991$	−23.8389	−	28.4101i	−0.757267	−	0.902476i	−0.997672	+	0.0681968i	$0.978275\pi$
$992$	−43.3202	−	20.2005i	−1.37542	−	0.641367i
$993$	44.0985	−	20.5635i	1.39942	−	0.652562i
$994$	1.51757	−	1.80857i	0.0481344	−	0.0573643i
$995$		0			0
$996$	−37.1698	+	21.4600i	−1.17777	+	0.679986i
$997$	12.5743	−	8.80465i	0.398234	−	0.278846i	−0.357256	−	0.934006i	$-0.616288\pi$
$997$	12.5743	−	8.80465i	0.398234	−	0.278846i	0.755490	+	0.655160i	$0.227399\pi$
$998$	−10.6494	+	7.45676i	−0.337099	+	0.236040i
$999$	−53.9430	+	31.1440i	−1.70668	+	0.985353i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.bb.b.257.3		96
5.2	odd	4		95.2.r.a.48.6	yes	96
5.3	odd	4	inner	475.2.bb.b.143.3		96
5.4	even	2		95.2.r.a.67.6	yes	96
15.2	even	4		855.2.dl.a.523.3		96
15.14	odd	2		855.2.dl.a.352.3		96
19.2	odd	18	inner	475.2.bb.b.382.3		96
95.2	even	36		95.2.r.a.78.6	yes	96
95.59	odd	18		95.2.r.a.2.6	✓	96
95.78	even	36	inner	475.2.bb.b.268.3		96
285.2	odd	36		855.2.dl.a.838.3		96
285.59	even	18		855.2.dl.a.667.3		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.2.6	✓	96	95.59	odd	18
95.2.r.a.48.6	yes	96	5.2	odd	4
95.2.r.a.67.6	yes	96	5.4	even	2
95.2.r.a.78.6	yes	96	95.2	even	36
475.2.bb.b.143.3		96	5.3	odd	4	inner
475.2.bb.b.257.3		96	1.1	even	1	trivial
475.2.bb.b.268.3		96	95.78	even	36	inner
475.2.bb.b.382.3		96	19.2	odd	18	inner
855.2.dl.a.352.3		96	15.14	odd	2
855.2.dl.a.523.3		96	15.2	even	4
855.2.dl.a.667.3		96	285.59	even	18
855.2.dl.a.838.3		96	285.2	odd	36

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.371046 - 0.259809i) q^{2} +(3.02691 + 0.264820i) q^{3} +(-0.613866 - 1.68658i) q^{4} +(-1.05432 - 0.884679i) q^{6} +(1.89781 - 0.508516i) q^{7} +(-0.444888 + 1.66034i) q^{8} +(6.13763 + 1.08223i) q^{9} +O(q^{10})\)	\(q+(-0.371046 - 0.259809i) q^{2} +(3.02691 + 0.264820i) q^{3} +(-0.613866 - 1.68658i) q^{4} +(-1.05432 - 0.884679i) q^{6} +(1.89781 - 0.508516i) q^{7} +(-0.444888 + 1.66034i) q^{8} +(6.13763 + 1.08223i) q^{9} +(0.238127 + 0.412449i) q^{11} +(-1.41148 - 5.26770i) q^{12} +(0.364244 + 4.16333i) q^{13} +(-0.836290 - 0.304385i) q^{14} +(-2.15338 + 1.80690i) q^{16} +(0.463388 - 0.661787i) q^{17} +(-1.99617 - 1.99617i) q^{18} +(-2.59888 - 3.49940i) q^{19} +(5.87916 - 1.03665i) q^{21} +(0.0188017 - 0.214905i) q^{22} +(1.97527 - 4.23599i) q^{23} +(-1.78633 + 4.90790i) q^{24} +(0.946520 - 1.63942i) q^{26} +(9.48666 + 2.54194i) q^{27} +(-2.02265 - 2.88865i) q^{28} +(0.693994 - 3.93584i) q^{29} +(-8.78658 - 5.07294i) q^{31} +(4.69320 - 0.410602i) q^{32} +(0.611565 + 1.31151i) q^{33} +(-0.343876 + 0.125161i) q^{34} +(-1.94241 - 11.0160i) q^{36} +(-4.48456 + 4.48456i) q^{37} +(0.0551271 + 1.97365i) q^{38} +12.6985i q^{39} +(4.84667 + 5.77603i) q^{41} +(-2.45077 - 1.14281i) q^{42} +(-0.992873 + 0.462984i) q^{43} +(0.549451 - 0.654810i) q^{44} +(-1.83346 + 1.05855i) q^{46} +(-7.61531 + 5.33230i) q^{47} +(-6.99661 + 4.89908i) q^{48} +(-2.71909 + 1.56987i) q^{49} +(1.57789 - 1.88046i) q^{51} +(6.79821 - 3.17006i) q^{52} +(6.51205 + 3.03662i) q^{53} +(-2.85956 - 3.40789i) q^{54} +3.37725i q^{56} +(-6.93987 - 11.2806i) q^{57} +(-1.28007 + 1.28007i) q^{58} +(0.304047 + 1.72434i) q^{59} +(-3.30814 + 1.20406i) q^{61} +(1.94223 + 4.16512i) q^{62} +(12.1984 - 1.06722i) q^{63} +(3.02080 + 1.74406i) q^{64} +(0.113822 - 0.645519i) q^{66} +(1.74299 + 2.48924i) q^{67} +(-1.40062 - 0.375294i) q^{68} +(7.10075 - 12.2989i) q^{69} +(-0.907322 + 2.49285i) q^{71} +(-4.52744 + 9.70912i) q^{72} +(-0.0344750 + 0.394051i) q^{73} +(2.82911 - 0.498848i) q^{74} +(-4.30667 + 6.53139i) q^{76} +(0.661657 + 0.661657i) q^{77} +(3.29918 - 4.71172i) q^{78} +(3.51787 - 2.95185i) q^{79} +(10.4727 + 3.81176i) q^{81} +(-0.297669 - 3.40238i) q^{82} +(-2.03694 - 7.60197i) q^{83} +(-5.35742 - 9.27933i) q^{84} +(0.488688 + 0.0861690i) q^{86} +(3.14295 - 11.7296i) q^{87} +(-0.790747 + 0.211880i) q^{88} +(-0.225503 - 0.189219i) q^{89} +(2.80839 + 7.71598i) q^{91} +(-8.35690 - 0.731134i) q^{92} +(-25.2528 - 17.6822i) q^{93} +4.21101 q^{94} +14.3146 q^{96} +(-3.38897 - 2.37298i) q^{97} +(1.41677 + 0.123952i) q^{98} +(1.01517 + 2.78917i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{2} + 12 q^{3} - 12 q^{6} + 18 q^{8}+O(q^{10}) \) 96 * q + 12 * q^2 + 12 * q^3 - 12 * q^6 + 18 * q^8	\( 96 q + 12 q^{2} + 12 q^{3} - 12 q^{6} + 18 q^{8} - 12 q^{11} + 18 q^{12} + 12 q^{13} + 12 q^{16} + 30 q^{17} + 24 q^{21} + 24 q^{22} - 48 q^{26} + 18 q^{27} - 36 q^{31} - 18 q^{32} - 90 q^{33} + 24 q^{36} - 54 q^{38} + 12 q^{41} - 24 q^{42} - 48 q^{43} - 36 q^{46} + 24 q^{47} - 60 q^{48} - 96 q^{51} + 30 q^{53} + 66 q^{57} - 120 q^{58} - 48 q^{61} - 60 q^{62} + 126 q^{63} + 72 q^{66} - 108 q^{67} - 18 q^{68} - 24 q^{71} - 48 q^{72} - 6 q^{73} + 60 q^{76} - 168 q^{77} + 138 q^{78} - 120 q^{81} - 60 q^{82} - 180 q^{86} + 6 q^{87} + 198 q^{88} - 24 q^{91} + 72 q^{92} + 90 q^{93} - 192 q^{96} + 72 q^{97} + 90 q^{98}+O(q^{100}) \) 96 * q + 12 * q^2 + 12 * q^3 - 12 * q^6 + 18 * q^8 - 12 * q^11 + 18 * q^12 + 12 * q^13 + 12 * q^16 + 30 * q^17 + 24 * q^21 + 24 * q^22 - 48 * q^26 + 18 * q^27 - 36 * q^31 - 18 * q^32 - 90 * q^33 + 24 * q^36 - 54 * q^38 + 12 * q^41 - 24 * q^42 - 48 * q^43 - 36 * q^46 + 24 * q^47 - 60 * q^48 - 96 * q^51 + 30 * q^53 + 66 * q^57 - 120 * q^58 - 48 * q^61 - 60 * q^62 + 126 * q^63 + 72 * q^66 - 108 * q^67 - 18 * q^68 - 24 * q^71 - 48 * q^72 - 6 * q^73 + 60 * q^76 - 168 * q^77 + 138 * q^78 - 120 * q^81 - 60 * q^82 - 180 * q^86 + 6 * q^87 + 198 * q^88 - 24 * q^91 + 72 * q^92 + 90 * q^93 - 192 * q^96 + 72 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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