LMFDB - Embedded newform 196.2.j.a.111.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(27,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

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

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

chi := DirichletCharacter("196.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.j (of order $14$, degree $6$, 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:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.3
Character	$\chi$	$=$	196.111
Dual form			196.2.j.a.83.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35333 - 0.410501i) q^{2} +(-1.57092 - 1.96987i) q^{3} +(1.66298 + 1.11108i) q^{4} +(1.55435 - 1.23956i) q^{5} +(1.31733 + 3.31074i) q^{6} +(2.03422 - 1.69173i) q^{7} +(-1.79445 - 2.18631i) q^{8} +(-0.745040 + 3.26424i) q^{9} +(-2.61238 + 1.03946i) q^{10} +(3.09970 - 0.707487i) q^{11} +(-0.423717 - 5.02127i) q^{12} +(-5.38387 + 1.22883i) q^{13} +(-3.44741 + 1.45442i) q^{14} +(-4.88353 - 1.11463i) q^{15} +(1.53099 + 3.69541i) q^{16} +(2.48020 - 5.15019i) q^{17} +(2.34825 - 4.11173i) q^{18} -7.59495 q^{19} +(3.96210 - 0.334339i) q^{20} +(-6.52809 - 1.34957i) q^{21} +(-4.48533 - 0.314971i) q^{22} +(-0.751225 - 1.55993i) q^{23} +(-1.48781 + 6.96935i) q^{24} +(-0.233088 + 1.02123i) q^{25} +(7.79056 + 0.547072i) q^{26} +(0.790388 - 0.380631i) q^{27} +(5.26251 - 0.553135i) q^{28} +(0.626525 + 0.301719i) q^{29} +(6.15144 + 3.51315i) q^{30} +8.05654 q^{31} +(-0.554962 - 5.62957i) q^{32} +(-6.26305 - 4.99461i) q^{33} +(-5.47067 + 5.95175i) q^{34} +(1.06489 - 5.15108i) q^{35} +(-4.86582 + 4.60055i) q^{36} +(4.24933 + 2.04637i) q^{37} +(10.2784 + 3.11773i) q^{38} +(10.8783 + 8.67513i) q^{39} +(-5.49926 - 1.17398i) q^{40} +(-0.0970188 + 0.0773699i) q^{41} +(8.28063 + 4.50619i) q^{42} +(3.53279 + 2.81730i) q^{43} +(5.94082 + 2.26749i) q^{44} +(2.88814 + 5.99729i) q^{45} +(0.376297 + 2.41948i) q^{46} +(-0.299542 - 1.31238i) q^{47} +(4.87442 - 8.82105i) q^{48} +(1.27607 - 6.88271i) q^{49} +(0.734659 - 1.28637i) q^{50} +(-14.0414 + 3.20486i) q^{51} +(-10.3186 - 3.93840i) q^{52} +(0.183642 - 0.0884374i) q^{53} +(-1.22590 + 0.190662i) q^{54} +(3.94107 - 4.94194i) q^{55} +(-7.34895 - 1.41169i) q^{56} +(11.9311 + 14.9611i) q^{57} +(-0.724037 - 0.665513i) q^{58} +(-1.40598 + 1.76305i) q^{59} +(-6.88275 - 7.27961i) q^{60} +(0.524559 - 1.08926i) q^{61} +(-10.9031 - 3.30722i) q^{62} +(4.00665 + 7.90057i) q^{63} +(-1.55990 + 7.84645i) q^{64} +(-6.84523 + 8.58365i) q^{65} +(6.42565 + 9.33032i) q^{66} -3.71909i q^{67} +(9.84680 - 5.80894i) q^{68} +(-1.89276 + 3.93035i) q^{69} +(-3.55567 + 6.53394i) q^{70} +(-3.42655 - 7.11531i) q^{71} +(8.47357 - 4.22862i) q^{72} +(4.61124 + 1.05248i) q^{73} +(-4.91069 - 4.51376i) q^{74} +(2.37785 - 1.14511i) q^{75} +(-12.6302 - 8.43862i) q^{76} +(5.10859 - 6.68306i) q^{77} +(-11.1607 - 16.2058i) q^{78} +9.99726i q^{79} +(6.96037 + 3.84622i) q^{80} +(7.05839 + 3.39914i) q^{81} +(0.163058 - 0.0648804i) q^{82} +(0.712952 - 3.12364i) q^{83} +(-9.35659 - 9.49754i) q^{84} +(-2.52883 - 11.0795i) q^{85} +(-3.62451 - 5.26294i) q^{86} +(-0.389874 - 1.70815i) q^{87} +(-7.10905 - 5.50736i) q^{88} +(14.8115 + 3.38064i) q^{89} +(-1.44670 - 9.30187i) q^{90} +(-8.87310 + 11.6078i) q^{91} +(0.483945 - 3.42881i) q^{92} +(-12.6562 - 15.8703i) q^{93} +(-0.133355 + 1.89904i) q^{94} +(-11.8052 + 9.41436i) q^{95} +(-10.2177 + 9.93680i) q^{96} -3.30506i q^{97} +(-4.55230 + 8.79071i) q^{98} +10.6453i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26}+ \cdots + 105 q^{98}+O(q^{100}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{11}{14}\right)$

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 $

$2$	−1.35333	−	0.410501i	−0.956945	−	0.290268i
$2$	−1.35333	−	0.410501i	−0.956945	−	0.290268i
$3$	−1.57092	−	1.96987i	−0.906971	−	1.13731i	−0.990043	−	0.140762i	$-0.955045\pi$
$3$	−1.57092	−	1.96987i	−0.906971	−	1.13731i	0.0830725	−	0.996544i	$-0.473527\pi$
$4$	1.66298	+	1.11108i	0.831489	+	0.555541i
$5$	1.55435	−	1.23956i	0.695128	−	0.554346i	−0.210929	−	0.977501i	$-0.567649\pi$
$5$	1.55435	−	1.23956i	0.695128	−	0.554346i	0.906057	+	0.423155i	$0.139078\pi$
$6$	1.31733	+	3.31074i	0.537798	+	1.35160i
$7$	2.03422	−	1.69173i	0.768861	−	0.639415i
$7$	2.03422	−	1.69173i	0.768861	−	0.639415i
$8$	−1.79445	−	2.18631i	−0.634434	−	0.772977i
$9$	−0.745040	+	3.26424i	−0.248347	+	1.08808i
$10$	−2.61238	+	1.03946i	−0.826108	+	0.328705i
$11$	3.09970	−	0.707487i	0.934596	−	0.213315i	0.272004	−	0.962296i	$-0.412314\pi$
$11$	3.09970	−	0.707487i	0.934596	−	0.213315i	0.662592	+	0.748981i	$0.269456\pi$
$12$	−0.423717	−	5.02127i	−0.122316	−	1.44952i
$13$	−5.38387	+	1.22883i	−1.49322	+	0.340817i	−0.889705	−	0.456537i	$-0.849090\pi$
$13$	−5.38387	+	1.22883i	−1.49322	+	0.340817i	−0.603512	+	0.797354i	$0.706233\pi$
$14$	−3.44741	+	1.45442i	−0.921360	+	0.388710i
$15$	−4.88353	−	1.11463i	−1.26092	−	0.287797i
$16$	1.53099	+	3.69541i	0.382748	+	0.923853i
$17$	2.48020	−	5.15019i	0.601537	−	1.24910i	−0.348601	−	0.937271i	$-0.613343\pi$
$17$	2.48020	−	5.15019i	0.601537	−	1.24910i	0.950137	−	0.311832i	$-0.100943\pi$
$18$	2.34825	−	4.11173i	0.553489	−	0.969145i
$19$	−7.59495			−1.74240			−0.871201	−	0.490927i	$-0.836658\pi$
$19$	−7.59495			−1.74240			−0.871201	+	0.490927i	$0.836658\pi$
$20$	3.96210	−	0.334339i	0.885953	−	0.0747605i
$21$	−6.52809	−	1.34957i	−1.42455	−	0.294499i
$22$	−4.48533	−	0.314971i	−0.956276	−	0.0671520i
$23$	−0.751225	−	1.55993i	−0.156641	−	0.325269i	0.807848	−	0.589391i	$-0.200632\pi$
$23$	−0.751225	−	1.55993i	−0.156641	−	0.325269i	−0.964489	+	0.264122i	$0.914918\pi$
$24$	−1.48781	+	6.96935i	−0.303698	+	1.42261i
$25$	−0.233088	+	1.02123i	−0.0466177	+	0.204245i
$26$	7.79056	+	0.547072i	1.52786	+	0.107290i
$27$	0.790388	−	0.380631i	0.152110	−	0.0732524i
$28$	5.26251	−	0.553135i	0.994521	−	0.104533i
$29$	0.626525	+	0.301719i	0.116343	+	0.0560277i	0.491150	−	0.871075i	$-0.336577\pi$
$29$	0.626525	+	0.301719i	0.116343	+	0.0560277i	−0.374807	+	0.927103i	$0.622291\pi$
$30$	6.15144	+	3.51315i	1.12309	+	0.641411i
$31$	8.05654			1.44700			0.723499	−	0.690326i	$-0.242533\pi$
$31$	8.05654			1.44700			0.723499	+	0.690326i	$0.242533\pi$
$32$	−0.554962	−	5.62957i	−0.0981043	−	0.995176i
$33$	−6.26305	−	4.99461i	−1.09026	−	0.869451i
$34$	−5.47067	+	5.95175i	−0.938212	+	1.02072i
$35$	1.06489	−	5.15108i	0.180000	−	0.870691i
$36$	−4.86582	+	4.60055i	−0.810970	+	0.766759i
$37$	4.24933	+	2.04637i	0.698586	+	0.336421i	0.749243	−	0.662295i	$-0.230417\pi$
$37$	4.24933	+	2.04637i	0.698586	+	0.336421i	−0.0506571	+	0.998716i	$0.516132\pi$
$38$	10.2784	+	3.11773i	1.66738	+	0.505763i
$39$	10.8783	+	8.67513i	1.74192	+	1.38913i
$40$	−5.49926	−	1.17398i	−0.869509	−	0.185622i
$41$	−0.0970188	+	0.0773699i	−0.0151518	+	0.0120832i	−0.631036	−	0.775753i	$-0.717370\pi$
$41$	−0.0970188	+	0.0773699i	−0.0151518	+	0.0120832i	0.615885	+	0.787836i	$0.288799\pi$
$42$	8.28063	+	4.50619i	1.27773	+	0.695320i
$43$	3.53279	+	2.81730i	0.538745	+	0.429635i	0.854687	−	0.519144i	$-0.173749\pi$
$43$	3.53279	+	2.81730i	0.538745	+	0.429635i	−0.315942	+	0.948779i	$0.602320\pi$
$44$	5.94082	+	2.26749i	0.895612	+	0.341837i
$45$	2.88814	+	5.99729i	0.430539	+	0.894024i
$46$	0.376297	+	2.41948i	0.0554820	+	0.356732i
$47$	−0.299542	−	1.31238i	−0.0436927	−	0.191430i	0.948372	−	0.317161i	$-0.102730\pi$
$47$	−0.299542	−	1.31238i	−0.0436927	−	0.191430i	−0.992064	+	0.125731i	$0.959872\pi$
$48$	4.87442	−	8.82105i	0.703561	−	1.27321i
$49$	1.27607	−	6.88271i	0.182296	−	0.983244i
$50$	0.734659	−	1.28637i	0.103896	−	0.181920i
$51$	−14.0414	+	3.20486i	−1.96619	+	0.448770i
$52$	−10.3186	−	3.93840i	−1.43093	−	0.546158i
$53$	0.183642	−	0.0884374i	0.0252252	−	0.0121478i	−0.421229	−	0.906954i	$-0.638401\pi$
$53$	0.183642	−	0.0884374i	0.0252252	−	0.0121478i	0.446454	+	0.894807i	$0.352687\pi$
$54$	−1.22590	+	0.190662i	−0.166824	+	0.0259459i
$55$	3.94107	−	4.94194i	0.531413	−	0.666371i
$56$	−7.34895	−	1.41169i	−0.982045	−	0.188646i
$57$	11.9311	+	14.9611i	1.58031	+	1.98164i
$58$	−0.724037	−	0.665513i	−0.0950707	−	0.0873861i
$59$	−1.40598	+	1.76305i	−0.183043	+	0.229529i	−0.864884	−	0.501971i	$-0.832608\pi$
$59$	−1.40598	+	1.76305i	−0.183043	+	0.229529i	0.681841	+	0.731501i	$0.261180\pi$
$60$	−6.88275	−	7.27961i	−0.888559	−	0.939794i
$61$	0.524559	−	1.08926i	0.0671629	−	0.139465i	−0.864685	−	0.502315i	$-0.832482\pi$
$61$	0.524559	−	1.08926i	0.0671629	−	0.139465i	0.931848	+	0.362850i	$0.118196\pi$
$62$	−10.9031	−	3.30722i	−1.38470	−	0.420017i
$63$	4.00665	+	7.90057i	0.504790	+	0.995378i
$64$	−1.55990	+	7.84645i	−0.194987	+	0.980806i
$65$	−6.84523	+	8.58365i	−0.849046	+	1.06467i
$66$	6.42565	+	9.33032i	0.790942	+	1.14848i
$67$		−	3.71909i		−	0.454359i	−0.973853	−	0.227179i	$-0.927050\pi$
$67$		−	3.71909i		−	0.454359i	0.973853	−	0.227179i	$-0.0729504\pi$
$68$	9.84680	−	5.80894i	1.19410	−	0.704438i
$69$	−1.89276	+	3.93035i	−0.227861	+	0.473158i
$70$	−3.55567	+	6.53394i	−0.424983	+	0.780955i
$71$	−3.42655	−	7.11531i	−0.406657	−	0.844432i	−0.999242	−	0.0389243i	$-0.987607\pi$
$71$	−3.42655	−	7.11531i	−0.406657	−	0.844432i	0.592585	−	0.805508i	$-0.298107\pi$
$72$	8.47357	−	4.22862i	0.998619	−	0.498348i
$73$	4.61124	+	1.05248i	0.539704	+	0.123184i	0.483679	−	0.875245i	$-0.339300\pi$
$73$	4.61124	+	1.05248i	0.539704	+	0.123184i	0.0560251	+	0.998429i	$0.482157\pi$
$74$	−4.91069	−	4.51376i	−0.570857	−	0.524714i
$75$	2.37785	−	1.14511i	0.274570	−	0.132226i
$76$	−12.6302	−	8.43862i	−1.44879	−	0.967976i
$77$	5.10859	−	6.68306i	0.582178	−	0.761605i
$78$	−11.1607	−	16.2058i	−1.26370	−	1.83495i
$79$			9.99726i			1.12478i	0.826872	+	0.562390i	$0.190118\pi$
$79$			9.99726i			1.12478i	−0.826872	+	0.562390i	$0.809882\pi$
$80$	6.96037	+	3.84622i	0.778193	+	0.430021i
$81$	7.05839	+	3.39914i	0.784266	+	0.377683i
$82$	0.163058	−	0.0648804i	0.0180068	−	0.00716484i
$83$	0.712952	−	3.12364i	0.0782566	−	0.342865i	−0.920609	−	0.390486i	$-0.872307\pi$
$83$	0.712952	−	3.12364i	0.0782566	−	0.342865i	0.998865	+	0.0476215i	$0.0151641\pi$
$84$	−9.35659	−	9.49754i	−1.02089	−	1.03627i
$85$	−2.52883	−	11.0795i	−0.274291	−	1.20175i
$86$	−3.62451	−	5.26294i	−0.390840	−	0.567518i
$87$	−0.389874	−	1.70815i	−0.0417989	−	0.183133i
$88$	−7.10905	−	5.50736i	−0.757827	−	0.587087i
$89$	14.8115	+	3.38064i	1.57002	+	0.358347i	0.916966	−	0.398965i	$-0.130630\pi$
$89$	14.8115	+	3.38064i	1.57002	+	0.358347i	0.653054	+	0.757312i	$0.273488\pi$
$90$	−1.44670	−	9.30187i	−0.152496	−	0.980504i
$91$	−8.87310	+	11.6078i	−0.930153	+	1.21683i
$92$	0.483945	−	3.42881i	0.0504547	−	0.357478i
$93$	−12.6562	−	15.8703i	−1.31238	−	1.64568i
$94$	−0.133355	+	1.89904i	−0.0137545	+	0.195871i
$95$	−11.8052	+	9.41436i	−1.21119	+	0.965893i
$96$	−10.2177	+	9.93680i	−1.04284	+	1.01417i
$97$		−	3.30506i		−	0.335578i	−0.985823	−	0.167789i	$-0.946337\pi$
$97$		−	3.30506i		−	0.335578i	0.985823	−	0.167789i	$-0.0536627\pi$
$98$	−4.55230	+	8.79071i	−0.459851	+	0.887996i
$99$			10.6453i			1.06989i
$100$	−1.52229	+	1.43930i	−0.152229	+	0.143930i
$101$	9.75340	−	7.77807i	0.970499	−	0.773947i	−0.00361730	−	0.999993i	$-0.501151\pi$
$101$	9.75340	−	7.77807i	0.970499	−	0.773947i	0.974117	+	0.226046i	$0.0725800\pi$
$102$	20.3182	+	1.42679i	2.01180	+	0.141273i
$103$	5.67864	+	7.12079i	0.559533	+	0.701632i	0.978471	−	0.206383i	$-0.0661691\pi$
$103$	5.67864	+	7.12079i	0.559533	+	0.701632i	−0.418938	+	0.908015i	$0.637598\pi$
$104$	12.3477	+	9.56573i	1.21079	+	0.937997i
$105$	−11.8198	+	5.99422i	−1.15350	+	0.584976i
$106$	−0.284831	+	0.0442993i	−0.0276653	+	0.00430273i
$107$	8.12037	+	1.85342i	0.785025	+	0.179177i	0.596202	−	0.802834i	$-0.296676\pi$
$107$	8.12037	+	1.85342i	0.785025	+	0.179177i	0.188823	+	0.982011i	$0.439533\pi$
$108$	1.73731	+	0.245205i	0.167173	+	0.0235949i
$109$	−3.41321	−	14.9542i	−0.326926	−	1.43236i	−0.824957	−	0.565196i	$-0.808801\pi$
$109$	−3.41321	−	14.9542i	−0.326926	−	1.43236i	0.498031	−	0.867159i	$-0.334057\pi$
$110$	−7.36221	+	5.07024i	−0.701960	+	0.483429i
$111$	−2.64428	−	11.5853i	−0.250984	−	1.09963i
$112$	9.36602	+	4.92723i	0.885006	+	0.465580i
$113$	−3.52940	+	15.4633i	−0.332018	+	1.45467i	0.483198	+	0.875511i	$0.339475\pi$
$113$	−3.52940	+	15.4633i	−0.332018	+	1.45467i	−0.815217	+	0.579156i	$0.803382\pi$
$114$	−10.0051	−	25.1449i	−0.937061	−	2.35504i
$115$	−3.10129	−	1.49350i	−0.289197	−	0.139270i
$116$	0.706663	+	1.19787i	0.0656121	+	0.111220i
$117$		−	18.4898i		−	1.70938i
$118$	2.62649	−	1.80882i	0.241788	−	0.166515i
$119$	−3.66748	−	14.6724i	−0.336198	−	1.34502i
$120$	6.32631	+	12.6771i	0.577511	+	1.15725i
$121$	−0.803027	+	0.386717i	−0.0730024	+	0.0351561i
$122$	−1.15704	+	1.25879i	−0.104754	+	0.113965i
$123$	0.304818	+	0.0695726i	0.0274845	+	0.00627315i
$124$	13.3979	+	8.95148i	1.20316	+	0.803867i
$125$	5.21657	+	10.8323i	0.466584	+	0.968872i
$126$	−2.17910	−	12.3368i	−0.194130	−	1.09905i
$127$	4.41971	−	9.17762i	0.392186	−	0.814382i	−0.607611	−	0.794234i	$-0.707872\pi$
$127$	4.41971	−	9.17762i	0.392186	−	0.814382i	0.999797	−	0.0201474i	$-0.00641356\pi$
$128$	5.33202	−	9.97845i	0.471289	−	0.881979i
$129$		−	11.3849i		−	1.00238i
$130$	12.7874	−	8.80649i	1.12153	−	0.772380i
$131$	−2.38863	+	2.99525i	−0.208696	+	0.261696i	−0.875152	−	0.483848i	$-0.839239\pi$
$131$	−2.38863	+	2.99525i	−0.208696	+	0.261696i	0.666456	+	0.745544i	$0.267810\pi$
$132$	−4.86588	−	15.2647i	−0.423521	−	1.32862i
$133$	−15.4498	+	12.8486i	−1.33967	+	1.11412i
$134$	−1.52669	+	5.03314i	−0.131886	+	0.434797i
$135$	0.756729	−	1.57136i	0.0651289	−	0.135241i
$136$	−15.7105	+	3.81927i	−1.34716	+	0.327500i
$137$	−6.94284	+	8.70604i	−0.593166	+	0.743807i	−0.984296	−	0.176529i	$-0.943513\pi$
$137$	−6.94284	+	8.70604i	−0.593166	+	0.743807i	0.391129	+	0.920336i	$0.372085\pi$
$138$	4.17492	−	4.54206i	0.355393	−	0.386646i
$139$	8.02974	+	10.0690i	0.681074	+	0.854040i	0.995453	−	0.0952580i	$-0.0303676\pi$
$139$	8.02974	+	10.0690i	0.681074	+	0.854040i	−0.314379	+	0.949298i	$0.601796\pi$
$140$	7.49416	−	7.38294i	0.633372	−	0.623972i
$141$	−2.11466	+	2.65170i	−0.178086	+	0.223313i
$142$	1.71640	+	11.0359i	0.144037	+	0.926115i
$143$	−15.8190	+	7.61804i	−1.32285	+	0.637053i
$144$	−13.2033	+	2.24429i	−1.10028	+	0.187024i
$145$	1.34784	−	0.307635i	0.111932	−	0.0255477i
$146$	−5.80846	−	3.31727i	−0.480711	−	0.274539i
$147$	−15.5627	+	8.29848i	−1.28359	+	0.684447i
$148$	4.79286	+	8.12443i	0.393971	+	0.667824i
$149$	1.60103	+	7.01458i	0.131162	+	0.574657i	0.997207	+	0.0746909i	$0.0237970\pi$
$149$	1.60103	+	7.01458i	0.131162	+	0.574657i	−0.866045	+	0.499966i	$0.833346\pi$
$150$	−3.68807	+	0.573600i	−0.301130	+	0.0468342i
$151$	−2.11679	−	4.39555i	−0.172262	−	0.357705i	0.796908	−	0.604101i	$-0.206468\pi$
$151$	−2.11679	−	4.39555i	−0.172262	−	0.357705i	−0.969169	+	0.246396i	$0.920753\pi$
$152$	13.6288	+	16.6049i	1.10544	+	1.34684i
$153$	14.9636	+	11.9330i	1.20973	+	0.964730i
$154$	−9.65698	+	6.94727i	−0.778182	+	0.559827i
$155$	12.5227	−	9.98653i	1.00585	−	0.802137i
$156$	8.45154	+	26.5132i	0.676665	+	2.12276i
$157$	2.88021	+	2.29689i	0.229866	+	0.183312i	0.731649	−	0.681682i	$-0.238751\pi$
$157$	2.88021	+	2.29689i	0.229866	+	0.183312i	−0.501783	+	0.864993i	$0.667322\pi$
$158$	4.10388	−	13.5295i	0.326487	−	1.07635i
$159$	−0.462698	−	0.222823i	−0.0366943	−	0.0176710i
$160$	−7.84076	−	8.06243i	−0.619867	−	0.637391i
$161$	−4.16715	−	1.90237i	−0.328417	−	0.149928i
$162$	−8.15695	−	7.49762i	−0.640870	−	0.589069i
$163$	12.2208	+	9.74575i	0.957205	+	0.763346i	0.971619	−	0.236550i	$-0.0760168\pi$
$163$	12.2208	+	9.74575i	0.957205	+	0.763346i	−0.0144139	+	0.999896i	$0.504588\pi$
$164$	−0.247304	+	0.0208686i	−0.0193112	+	0.00162956i
$165$	−15.9261			−1.23984
$166$	−2.24711	+	3.93464i	−0.174410	+	0.305387i
$167$	−2.02545	−	0.975404i	−0.156734	−	0.0754790i	0.353872	−	0.935294i	$-0.384865\pi$
$167$	−2.02545	−	0.975404i	−0.156734	−	0.0754790i	−0.510606	+	0.859815i	$0.670579\pi$
$168$	8.76376	+	16.6942i	0.676139	+	1.28798i
$169$	15.7634	−	7.59127i	1.21257	−	0.583944i
$170$	−1.12583	+	16.0323i	−0.0863471	+	1.22962i
$171$	5.65855	−	24.7917i	0.432720	−	1.89587i
$172$	2.74469	+	8.61033i	0.209281	+	0.656532i
$173$	−7.41839	−	15.4044i	−0.564010	−	1.17118i	−0.966717	−	0.255849i	$-0.917645\pi$
$173$	−7.41839	−	15.4044i	−0.564010	−	1.17118i	0.402707	−	0.915329i	$-0.368069\pi$
$174$	−0.173571	+	2.47173i	−0.0131583	+	0.187381i
$175$	1.25349	+	2.47172i	0.0947551	+	0.186845i
$176$	7.36008	+	10.3715i	0.554787	+	0.781783i
$177$	5.68166			0.427060
$178$	−18.6571	−	10.6552i	−1.39841	−	0.798645i
$179$	1.31652	−	2.73379i	0.0984016	−	0.204333i	−0.845957	−	0.533252i	$-0.820970\pi$
$179$	1.31652	−	2.73379i	0.0984016	−	0.204333i	0.944358	+	0.328919i	$0.106684\pi$
$180$	−1.86057	+	13.1823i	−0.138678	+	0.982553i
$181$	5.81694	+	1.32768i	0.432370	+	0.0986855i	0.433166	−	0.901314i	$-0.357396\pi$
$181$	5.81694	+	1.32768i	0.432370	+	0.0986855i	−0.000796483		1.00000i	$0.500254\pi$
$182$	16.7732	−	12.0667i	1.24331	−	0.894443i
$183$	−2.96974	+	0.677824i	−0.219529	+	0.0501062i
$184$	−2.06246	+	4.44163i	−0.152047	+	0.327442i
$185$	9.14156	−	2.08650i	0.672101	−	0.153403i
$186$	10.6131	+	26.6731i	0.778193	+	1.95577i
$187$	4.04419	−	17.7188i	0.295741	−	1.29572i
$188$	0.960029	−	2.51527i	0.0700173	−	0.183445i
$189$	0.963894	−	2.11141i	0.0701130	−	0.153583i
$190$	19.8409	−	7.89463i	1.43941	−	0.572737i
$191$	4.32371	−	3.44805i	0.312853	−	0.249492i	−0.454456	−	0.890769i	$-0.650166\pi$
$191$	4.32371	−	3.44805i	0.312853	−	0.249492i	0.767309	+	0.641277i	$0.221595\pi$
$192$	17.9070	−	9.25334i	1.29232	−	0.667802i
$193$	11.1359	+	13.9639i	0.801578	+	1.00515i	0.999688	+	0.0249671i	$0.00794810\pi$
$193$	11.1359	+	13.9639i	0.801578	+	1.00515i	−0.198110	+	0.980180i	$0.563480\pi$
$194$	−1.35673	+	4.47281i	−0.0974074	+	0.321129i
$195$	27.6620			1.98092
$196$	9.76933	−	10.0280i	0.697809	−	0.716283i
$197$	−0.741517			−0.0528309			−0.0264154	−	0.999651i	$-0.508409\pi$
$197$	−0.741517			−0.0528309			−0.0264154	+	0.999651i	$0.508409\pi$
$198$	4.36989	−	14.4065i	0.310555	−	1.02383i
$199$	−0.0710715	−	0.0891209i	−0.00503813	−	0.00631761i	0.779306	−	0.626644i	$-0.215572\pi$
$199$	−0.0710715	−	0.0891209i	−0.00503813	−	0.00631761i	−0.784344	+	0.620326i	$0.787000\pi$
$200$	2.65098	−	1.32294i	0.187453	−	0.0935458i
$201$	−7.32612	+	5.84239i	−0.516745	+	0.412090i
$202$	−16.3924	+	6.52249i	−1.15337	+	0.458921i
$203$	1.78492	−	0.446153i	0.125276	−	0.0313138i
$204$	−26.9114	−	10.2715i	−1.88417	−	0.719151i
$205$	−0.0548972	+	0.240520i	−0.00383419	+	0.0167987i
$206$	−4.76196	−	11.9678i	−0.331781	−	0.833838i
$207$	5.65169	−	1.28996i	0.392819	−	0.0896584i
$208$	−12.7837	−	18.0143i	−0.886391	−	1.24907i
$209$	−23.5421	+	5.37333i	−1.62844	+	0.371681i
$210$	18.4567	−	3.26009i	1.27363	−	0.224968i
$211$	16.3523	+	3.73231i	1.12574	+	0.256943i	0.744558	−	0.667558i	$-0.232660\pi$
$211$	16.3523	+	3.73231i	1.12574	+	0.256943i	0.381181	+	0.924500i	$0.375517\pi$
$212$	0.403654	+	0.0569721i	0.0277231	+	0.00391286i
$213$	−8.63341	+	17.9275i	−0.591551	+	1.22837i
$214$	−10.2287	−	5.84170i	−0.699217	−	0.399330i
$215$	8.98340			0.612663
$216$	−2.25049	−	1.04501i	−0.153126	−	0.0711039i
$217$	16.3887	−	13.6295i	1.11254	−	0.925232i
$218$	−1.51955	+	21.6391i	−0.102917	+	1.46558i
$219$	−5.17062	−	10.7369i	−0.349398	−	0.725533i
$220$	12.0448	−	3.83949i	0.812061	−	0.258858i
$221$	−7.02435	+	30.7757i	−0.472509	+	2.07020i
$222$	−1.17722	+	16.7642i	−0.0790100	+	1.12514i
$223$	−14.8371	+	7.14518i	−0.993567	+	0.478477i	−0.858751	−	0.512394i	$-0.828759\pi$
$223$	−14.8371	+	7.14518i	−0.993567	+	0.478477i	−0.134817	+	0.990871i	$0.543045\pi$
$224$	−10.6526	−	10.5129i	−0.711760	−	0.702423i
$225$	−3.15987	−	1.52171i	−0.210658	−	0.101447i
$226$	11.1241	−	19.4781i	0.739967	−	1.29566i
$227$	−17.2029			−1.14179			−0.570897	−	0.821022i	$-0.693404\pi$
$227$	−17.2029			−1.14179			−0.570897	+	0.821022i	$0.693404\pi$
$228$	3.21811	+	38.1363i	0.213124	+	2.52564i
$229$	−16.9479	−	13.5155i	−1.11995	−	0.893130i	−0.124866	−	0.992174i	$-0.539850\pi$
$229$	−16.9479	−	13.5155i	−1.11995	−	0.893130i	−0.995083	+	0.0990437i	$0.968422\pi$
$230$	3.58397	+	3.29428i	0.236320	+	0.217218i
$231$	−21.1899	+	0.435286i	−1.39420	+	0.0286397i
$232$	−0.464618	−	1.91120i	−0.0305037	−	0.125476i
$233$	−20.6657	−	9.95205i	−1.35385	−	0.651981i	−0.390595	−	0.920563i	$-0.627731\pi$
$233$	−20.6657	−	9.95205i	−1.35385	−	0.651981i	−0.963257	+	0.268582i	$0.913445\pi$
$234$	−7.59006	+	25.0226i	−0.496178	+	1.63578i
$235$	−2.09236	−	1.66860i	−0.136490	−	0.108847i
$236$	−4.29701	+	1.36975i	−0.279712	+	0.0891629i
$237$	19.6933	−	15.7049i	1.27922	−	1.02014i
$238$	−1.05975	+	21.3621i	−0.0686931	+	1.38470i
$239$	−5.37585	−	4.28709i	−0.347735	−	0.277309i	0.434010	−	0.900908i	$-0.357098\pi$
$239$	−5.37585	−	4.28709i	−0.347735	−	0.277309i	−0.781744	+	0.623599i	$0.785670\pi$
$240$	−3.35762	−	19.7531i	−0.216733	−	1.27506i
$241$	−0.404203	−	0.839335i	−0.0260370	−	0.0540664i	0.887545	−	0.460722i	$-0.152409\pi$
$241$	−0.404203	−	0.839335i	−0.0260370	−	0.0540664i	−0.913582	+	0.406655i	$0.866695\pi$
$242$	1.24550	−	0.193711i	0.0800640	−	0.0124522i
$243$	−4.97792	−	21.8097i	−0.319334	−	1.39909i
$244$	2.08259	−	1.22858i	0.133324	−	0.0786521i
$245$	−6.54803	−	12.2799i	−0.418338	−	0.784535i
$246$	−0.383958	−	0.219282i	−0.0244802	−	0.0139809i
$247$	40.8902	−	9.33293i	2.60178	−	0.593840i
$248$	−14.4571	−	17.6141i	−0.918024	−	1.11850i
$249$	−7.27317	+	3.50257i	−0.460918	+	0.221967i
$250$	−2.61304	−	16.8011i	−0.165263	−	1.06259i
$251$	−9.29737	+	11.6585i	−0.586845	+	0.735880i	−0.983263	−	0.182190i	$-0.941681\pi$
$251$	−9.29737	+	11.6585i	−0.586845	+	0.735880i	0.396419	+	0.918070i	$0.370253\pi$
$252$	−2.11522	+	17.5902i	−0.133246	+	1.10808i
$253$	−3.43221	−	4.30385i	−0.215781	−	0.270581i
$254$	−9.74872	+	10.6060i	−0.611689	+	0.665480i
$255$	−17.8527	+	22.3866i	−1.11798	+	1.40190i
$256$	−11.3121	+	11.3153i	−0.707008	+	0.707206i
$257$	−8.96630	+	18.6187i	−0.559302	+	1.16140i	0.409211	+	0.912440i	$0.365804\pi$
$257$	−8.96630	+	18.6187i	−0.559302	+	1.16140i	−0.968513	+	0.248963i	$0.919910\pi$
$258$	−4.67351	+	15.4075i	−0.290960	+	0.959227i
$259$	12.1060	−	3.02598i	0.752229	−	0.188025i
$260$	−20.9206	+	6.66880i	−1.29744	+	0.413582i
$261$	−1.45167	+	1.82033i	−0.0898560	+	0.112676i
$262$	4.46215	−	3.07301i	0.275672	−	0.189851i
$263$		−	19.6671i		−	1.21273i	−0.795187	−	0.606364i	$-0.792628\pi$
$263$		−	19.6671i		−	1.21273i	0.795187	−	0.606364i	$-0.207372\pi$
$264$	0.318955	+	22.6555i	0.0196303	+	1.39435i
$265$	0.175822	−	0.365098i	0.0108006	−	0.0224278i
$266$	26.1829	−	11.0462i	1.60538	−	0.677288i
$267$	−16.6083	−	34.4875i	−1.01641	−	2.11060i
$268$	4.13221	−	6.18476i	0.252415	−	0.377794i
$269$	−10.6024	−	2.41992i	−0.646438	−	0.147545i	−0.113283	−	0.993563i	$-0.536137\pi$
$269$	−10.6024	−	2.41992i	−0.646438	−	0.147545i	−0.533155	+	0.846018i	$0.678994\pi$
$270$	−1.66915	+	1.81593i	−0.101581	+	0.110514i
$271$	−12.0661	+	5.81071i	−0.732961	+	0.352975i	−0.762848	−	0.646578i	$-0.776200\pi$
$271$	−12.0661	+	5.81071i	−0.732961	+	0.352975i	0.0298869	+	0.999553i	$0.490485\pi$
$272$	22.8292	+	1.28046i	1.38422	+	0.0776391i
$273$	36.8048	−	0.756047i	2.22753	−	0.0457580i
$274$	12.9698	−	8.93206i	0.783531	−	0.539606i
$275$			3.33041i			0.200831i
$276$	−7.51455	+	4.43307i	−0.452323	+	0.266840i
$277$	−17.1335	−	8.25104i	−1.02945	−	0.495757i	−0.158619	−	0.987340i	$-0.550704\pi$
$277$	−17.1335	−	8.25104i	−1.02945	−	0.495757i	−0.870831	+	0.491583i	$0.836418\pi$
$278$	−6.73353	−	16.9228i	−0.403850	−	1.01496i
$279$	−6.00245	+	26.2984i	−0.359357	+	1.57445i
$280$	−13.1727	+	6.91516i	−0.787222	+	0.413260i
$281$	−5.93480	−	26.0021i	−0.354040	−	1.55115i	−0.767754	−	0.640745i	$-0.778626\pi$
$281$	−5.93480	−	26.0021i	−0.354040	−	1.55115i	0.413713	−	0.910407i	$-0.364232\pi$
$282$	3.95035	−	2.72054i	0.235240	−	0.162006i
$283$	1.45981	+	6.39582i	0.0867764	+	0.380192i	0.999604	−	0.0281538i	$-0.00896281\pi$
$283$	1.45981	+	6.39582i	0.0867764	+	0.380192i	−0.912827	+	0.408346i	$0.866106\pi$
$284$	2.20741	−	15.6398i	0.130986	−	0.928051i
$285$	37.0902	+	8.46559i	2.19703	+	0.501458i
$286$	24.5355	−	3.81596i	1.45081	−	0.225643i
$287$	−0.0664679	+	0.321517i	−0.00392348	+	0.0189786i
$288$	18.7897	+	2.38273i	1.10719	+	0.140404i
$289$	−9.77370	−	12.2558i	−0.574923	−	0.720931i
$290$	−1.95035	−	0.136958i	−0.114528	−	0.00804246i
$291$	−6.51053	+	5.19198i	−0.381654	+	0.304359i
$292$	6.49899	+	6.87372i	0.380324	+	0.402254i
$293$			7.82413i			0.457091i	0.973533	+	0.228545i	$0.0733969\pi$
$293$			7.82413i			0.457091i	−0.973533	+	0.228545i	$0.926603\pi$
$294$	24.4679	−	4.84206i	1.42699	−	0.282395i
$295$			4.48319i			0.261022i
$296$	−3.15122	−	12.9625i	−0.183161	−	0.753428i
$297$	2.18068	−	1.73903i	0.126536	−	0.100909i
$298$	0.712774	−	10.1502i	0.0412899	−	0.587987i
$299$	5.96140	+	7.47535i	0.344756	+	0.432311i
$300$	5.22662	+	0.737690i	0.301759	+	0.0425906i
$301$	11.9526	−	0.245531i	0.688936	−	0.0141522i
$302$	1.06032	+	6.81755i	0.0610147	+	0.392306i
$303$	−30.6436	−	6.99420i	−1.76043	−	0.401807i
$304$	−11.6278	−	28.0665i	−0.666901	−	1.60972i
$305$	−0.534846	−	2.34331i	−0.0306252	−	0.134178i
$306$	−15.3521	−	22.2919i	−0.877618	−	1.27434i
$307$	0.232854	+	1.02020i	0.0132897	+	0.0582258i	0.981138	−	0.193309i	$-0.0619219\pi$
$307$	0.232854	+	1.02020i	0.0132897	+	0.0582258i	−0.967848	+	0.251535i	$0.919065\pi$
$308$	15.9209	−	5.43772i	0.907177	−	0.309843i
$309$	5.10635	−	22.3724i	0.290490	−	1.27272i
$310$	−21.0468	+	8.37444i	−1.19538	+	0.475636i
$311$	16.3645	+	7.88070i	0.927943	+	0.446874i	0.835900	−	0.548881i	$-0.184946\pi$
$311$	16.3645	+	7.88070i	0.927943	+	0.446874i	0.0920426	+	0.995755i	$0.470660\pi$
$312$	−0.553992	−	39.3504i	−0.0313636	−	2.22778i
$313$			25.7343i			1.45459i	0.686326	+	0.727294i	$0.259222\pi$
$313$			25.7343i			1.45459i	−0.686326	+	0.727294i	$0.740778\pi$
$314$	−2.95498	−	4.29077i	−0.166759	−	0.242142i
$315$	16.0209	+	7.31382i	0.902677	+	0.412087i
$316$	−11.1078	+	16.6252i	−0.624861	+	0.935242i
$317$	28.7099	−	13.8260i	1.61251	−	0.776544i	0.612605	−	0.790389i	$-0.290122\pi$
$317$	28.7099	−	13.8260i	1.61251	−	0.776544i	0.999904	+	0.0138453i	$0.00440725\pi$
$318$	0.534711	+	0.491490i	0.0299851	+	0.0275614i
$319$	2.15551	+	0.491980i	0.120685	+	0.0275456i
$320$	7.30147	+	14.1297i	0.408165	+	0.789876i
$321$	−9.10544	−	18.9077i	−0.508216	−	1.05532i
$322$	4.85858	+	4.28514i	0.270758	+	0.238802i
$323$	−18.8370	+	39.1154i	−1.04812	+	2.17644i
$324$	7.96123	+	13.4952i	0.442290	+	0.749731i
$325$		−	5.78458i		−	0.320871i
$326$	−12.5381	−	18.2058i	−0.694418	−	1.00833i
$327$	−24.0960	+	30.2155i	−1.33251	+	1.67092i
$328$	0.343250	+	0.0732767i	0.0189528	+	0.00404603i
$329$	−2.82953	−	2.16292i	−0.155997	−	0.119245i
$330$	21.5532	+	6.53767i	1.18646	+	0.359887i
$331$	−6.28270	+	13.0462i	−0.345328	+	0.717082i	−0.999219	−	0.0395071i	$-0.987421\pi$
$331$	−6.28270	+	13.0462i	−0.345328	+	0.717082i	0.653891	+	0.756589i	$0.273136\pi$
$332$	4.65625	−	4.40241i	0.255545	−	0.241613i
$333$	−9.84577	+	12.3462i	−0.539545	+	0.676568i
$334$	2.34068	+	2.15149i	0.128077	+	0.117724i
$335$	−4.61001	−	5.78078i	−0.251872	−	0.315838i
$336$	−5.00726	−	26.1901i	−0.273168	−	1.42879i
$337$	−19.2318	+	24.1159i	−1.04762	+	1.31368i	−0.0997545	+	0.995012i	$0.531806\pi$
$337$	−19.2318	+	24.1159i	−1.04762	+	1.31368i	−0.947868	+	0.318664i	$0.896766\pi$
$338$	−24.4493	+	3.80255i	−1.32987	+	0.206832i
$339$	36.0052	−	17.3392i	1.95553	−	0.941735i
$340$	8.10489	−	21.2348i	0.439550	−	1.15162i
$341$	24.9729	−	5.69990i	1.35236	−	0.308667i
$342$	−17.8349	+	31.2284i	−0.964399	+	1.68864i
$343$	−9.04790	−	16.1597i	−0.488541	−	0.872541i
$344$	−0.179912	−	12.7793i	−0.00970022	−	0.689013i
$345$	1.92987	+	8.45532i	0.103901	+	0.455219i
$346$	3.71596	+	23.8925i	0.199771	+	1.28447i
$347$	12.5789	+	26.1205i	0.675273	+	1.40222i	0.903490	+	0.428609i	$0.140996\pi$
$347$	12.5789	+	26.1205i	0.675273	+	1.40222i	−0.228217	+	0.973610i	$0.573289\pi$
$348$	1.24954	−	3.27380i	0.0669825	−	0.175494i
$349$	15.1909	+	12.1143i	0.813151	+	0.648466i	0.939128	−	0.343567i	$-0.111635\pi$
$349$	15.1909	+	12.1143i	0.813151	+	0.648466i	−0.125978	+	0.992033i	$0.540207\pi$
$350$	−0.681740	−	3.85960i	−0.0364405	−	0.206304i
$351$	−3.78761	+	3.02052i	−0.202168	+	0.161224i
$352$	−5.70306	−	17.0574i	−0.303974	−	0.909161i
$353$	2.04384	+	1.62991i	0.108783	+	0.0867513i	0.676371	−	0.736562i	$-0.263552\pi$
$353$	2.04384	+	1.62991i	0.108783	+	0.0867513i	−0.567588	+	0.823313i	$0.692123\pi$
$354$	−7.68914	−	2.33233i	−0.408673	−	0.123962i
$355$	−14.1459	−	6.81230i	−0.750786	−	0.361560i
$356$	20.8751	+	22.0788i	1.10638	+	1.17017i
$357$	−23.1415	+	30.2737i	−1.22478	+	1.60225i
$358$	−2.90391	+	3.15927i	−0.153476	+	0.166973i
$359$	3.91208	+	3.11978i	0.206472	+	0.164656i	0.721266	−	0.692658i	$-0.243560\pi$
$359$	3.91208	+	3.11978i	0.206472	+	0.164656i	−0.514795	+	0.857314i	$0.672132\pi$
$360$	7.92931	−	17.0762i	0.417911	−	0.899996i
$361$	38.6833			2.03596
$362$	−7.32719	−	4.18464i	−0.385109	−	0.219940i
$363$	2.02327	+	0.974357i	0.106194	+	0.0511405i
$364$	−27.6530	+	9.44476i	−1.44941	+	0.495040i
$365$	8.47210	−	4.07995i	0.443450	−	0.213554i
$366$	4.29727	+	0.301765i	0.224622	+	0.0157735i
$367$	7.28238	−	31.9062i	0.380137	−	1.66549i	−0.316903	−	0.948458i	$-0.602643\pi$
$367$	7.28238	−	31.9062i	0.380137	−	1.66549i	0.697040	−	0.717032i	$-0.254500\pi$
$368$	4.61448	−	5.16433i	0.240546	−	0.269209i
$369$	−0.180271	−	0.374336i	−0.00938452	−	0.0194872i
$370$	−13.2280	−	0.928903i	−0.687691	−	0.0482914i
$371$	0.223955	−	0.490575i	0.0116272	−	0.0254694i
$372$	−3.41369	−	40.4541i	−0.176992	−	2.09745i
$373$	−14.3401			−0.742504			−0.371252	−	0.928532i	$-0.621071\pi$
$373$	−14.3401			−0.742504			−0.371252	+	0.928532i	$0.621071\pi$
$374$	−12.7467	+	22.3191i	−0.659115	+	1.15409i
$375$	13.1435	−	27.2927i	0.678725	−	1.40939i
$376$	−2.33175	+	3.00989i	−0.120251	+	0.155223i
$377$	−3.74389	−	0.854519i	−0.192820	−	0.0440100i
$378$	−2.17120	+	2.46175i	−0.111674	+	0.126619i
$379$	27.7499	−	6.33372i	1.42541	−	0.325341i	0.560872	−	0.827902i	$-0.310466\pi$
$379$	27.7499	−	6.33372i	1.42541	−	0.325341i	0.864542	+	0.502561i	$0.167609\pi$
$380$	−30.0920	+	2.53929i	−1.54369	+	0.130263i
$381$	−25.0217	+	5.71105i	−1.28190	+	0.292586i
$382$	−7.26682	+	2.89144i	−0.371803	+	0.147939i
$383$	1.61271	−	7.06576i	0.0824058	−	0.361043i	−0.916866	−	0.399195i	$-0.869290\pi$
$383$	1.61271	−	7.06576i	0.0824058	−	0.361043i	0.999272	+	0.0381514i	$0.0121469\pi$
$384$	−28.0324	+	5.17195i	−1.43052	+	0.263930i
$385$	−0.343468	−	16.7202i	−0.0175048	−	0.852141i
$386$	−9.33825	−	23.4690i	−0.475304	−	1.19454i
$387$	−11.8284	+	9.43285i	−0.601272	+	0.479499i
$388$	3.67219	−	5.49624i	0.186427	−	0.279029i
$389$	−15.7635	−	19.7668i	−0.799241	−	1.00222i	−0.999746	−	0.0225239i	$-0.992830\pi$
$389$	−15.7635	−	19.7668i	−0.799241	−	1.00222i	0.200505	−	0.979693i	$-0.435742\pi$
$390$	−37.4357	−	11.3553i	−1.89563	−	0.574996i
$391$	−9.89714			−0.500520
$392$	−17.3376	+	9.56078i	−0.875680	+	0.482892i
$393$	9.65260			0.486909
$394$	1.00351	+	0.304393i	0.0505563	+	0.0153351i
$395$	12.3922	+	15.5393i	0.623517	+	0.781865i
$396$	−11.8278	+	17.7029i	−0.594368	+	0.889602i
$397$	−25.7507	+	20.5355i	−1.29239	+	1.03065i	−0.295225	+	0.955428i	$0.595395\pi$
$397$	−25.7507	+	20.5355i	−1.29239	+	1.03065i	−0.997167	+	0.0752205i	$0.976034\pi$
$398$	0.0595987	+	0.149784i	0.00298741	+	0.00750802i
$399$	49.5805	+	10.2499i	2.48213	+	0.513136i
$400$	−4.13071	+	0.702134i	−0.206536	+	0.0351067i
$401$	3.21728	−	14.0958i	0.160664	−	0.703913i	−0.828850	−	0.559471i	$-0.811004\pi$
$401$	3.21728	−	14.0958i	0.160664	−	0.703913i	0.989513	−	0.144442i	$-0.0461386\pi$
$402$	12.3129	−	4.89927i	0.614113	−	0.244353i
$403$	−43.3754	+	9.90015i	−2.16068	+	0.493161i
$404$	24.8618	−	2.09794i	1.23692	−	0.104377i
$405$	15.1847	−	3.46580i	0.754532	−	0.172217i
$406$	−2.59872	−	0.128919i	−0.128972	−	0.00639815i
$407$	14.6195	+	3.33680i	0.724660	+	0.165399i
$408$	32.2034	+	24.9479i	1.59431	+	1.23510i
$409$	−5.10552	+	10.6017i	−0.252452	+	0.524222i	−0.988225	−	0.153006i	$-0.951105\pi$
$409$	−5.10552	+	10.6017i	−0.252452	+	0.524222i	0.735773	+	0.677228i	$0.236819\pi$
$410$	0.173028	−	0.302967i	0.00854522	−	0.0149625i
$411$	28.0564			1.38392
$412$	1.53167	+	18.1511i	0.0754600	+	0.894243i
$413$	0.122533	+	5.96497i	0.00602945	+	0.293517i
$414$	−8.17810	−	0.574286i	−0.401932	−	0.0282246i
$415$	−2.76375	−	5.73899i	−0.135667	−	0.281716i
$416$	9.90564	+	29.6269i	0.485664	+	1.45258i
$417$	7.22051	−	31.6351i	0.353590	−	1.54918i
$418$	34.0659	+	2.39219i	1.66622	+	0.117006i
$419$	−3.59339	+	1.73049i	−0.175549	+	0.0845398i	−0.519594	−	0.854413i	$-0.673917\pi$
$419$	−3.59339	+	1.73049i	−0.175549	+	0.0845398i	0.344045	+	0.938953i	$0.388203\pi$
$420$	−26.3162	−	3.16452i	−1.28410	−	0.154413i
$421$	1.67069	+	0.804561i	0.0814244	+	0.0392119i	0.474153	−	0.880443i	$-0.342754\pi$
$421$	1.67069	+	0.804561i	0.0814244	+	0.0392119i	−0.392728	+	0.919655i	$0.628469\pi$
$422$	−20.5979	−	11.7637i	−1.00269	−	0.572646i
$423$	4.50708			0.219142
$424$	−0.522888	−	0.242802i	−0.0253937	−	0.0117915i
$425$	4.68140	+	3.73329i	0.227081	+	0.181091i
$426$	19.0430	−	20.7177i	0.922638	−	1.00377i
$427$	−0.775669	−	3.10320i	−0.0375372	−	0.150174i
$428$	11.4447	+	12.1046i	0.553200	+	0.585098i
$429$	39.8570	+	19.1941i	1.92431	+	0.926700i
$430$	−12.1575	−	3.68769i	−0.586285	−	0.177836i
$431$	−4.92721	−	3.92932i	−0.237336	−	0.189269i	0.497598	−	0.867408i	$-0.334215\pi$
$431$	−4.92721	−	3.92932i	−0.237336	−	0.189269i	−0.734934	+	0.678139i	$0.762787\pi$
$432$	2.61666	+	2.33806i	0.125894	+	0.112490i
$433$	−10.8842	+	8.67983i	−0.523059	+	0.417126i	−0.849102	−	0.528229i	$-0.822856\pi$
$433$	−10.8842	+	8.67983i	−0.523059	+	0.417126i	0.326042	+	0.945355i	$0.394285\pi$
$434$	−27.7742	+	11.7176i	−1.33321	+	0.562462i
$435$	−2.72335	−	2.17180i	−0.130575	−	0.104130i
$436$	10.9393	−	28.6609i	0.523897	−	1.37261i
$437$	5.70552	+	11.8476i	0.272932	+	0.566749i
$438$	2.59002	+	16.6531i	0.123756	+	0.795715i
$439$	3.55582	+	15.5791i	0.169710	+	0.743548i	0.986114	+	0.166067i	$0.0531069\pi$
$439$	3.55582	+	15.5791i	0.169710	+	0.743548i	−0.816404	+	0.577481i	$0.804036\pi$
$440$	−17.8767	+	0.251675i	−0.852236	+	0.0119982i
$441$	21.5160	+	9.29329i	1.02457	+	0.442538i
$442$	22.1397	−	38.7660i	1.05308	−	1.84391i
$443$	−32.3858	+	7.39184i	−1.53869	+	0.351197i	−0.906024	−	0.423225i	$-0.860898\pi$
$443$	−32.3858	+	7.39184i	−1.53869	+	0.351197i	−0.632669	+	0.774422i	$0.718041\pi$
$444$	8.47488	−	22.2042i	0.402200	−	1.05376i
$445$	27.2128	−	13.1050i	1.29001	−	0.621237i
$446$	23.0126	−	3.57910i	1.08968	−	0.169475i
$447$	11.3027	−	14.1732i	0.534601	−	0.670368i
$448$	10.1009	+	18.6003i	0.477224	+	0.878782i
$449$	19.8347	+	24.8720i	0.936058	+	1.17378i	0.984576	+	0.174958i	$0.0559789\pi$
$449$	19.8347	+	24.8720i	0.936058	+	1.17378i	−0.0485175	+	0.998822i	$0.515450\pi$
$450$	3.65166	+	3.35650i	0.172141	+	0.158227i
$451$	−0.245991	+	0.308463i	−0.0115833	+	0.0145250i
$452$	−23.0503	+	21.7937i	−1.08420	+	1.02509i
$453$	−5.33337	+	11.0749i	−0.250583	+	0.520342i
$454$	23.2811	+	7.06179i	1.09263	+	0.331426i
$455$	0.596569	+	29.0413i	0.0279676	+	1.36148i
$456$	11.2999	−	52.9319i	0.529164	−	2.47876i
$457$	−11.6251	+	14.5775i	−0.543801	+	0.681905i	−0.975471	−	0.220126i	$-0.929353\pi$
$457$	−11.6251	+	14.5775i	−0.543801	+	0.681905i	0.431670	+	0.902032i	$0.357924\pi$
$458$	17.3879	+	25.2480i	0.812484	+	1.17976i
$459$		−	5.01468i		−	0.234065i
$460$	−3.49798	−	5.92946i	−0.163094	−	0.276462i
$461$	−8.29001	+	17.2144i	−0.386104	+	0.801754i	0.613820	+	0.789446i	$0.289632\pi$
$461$	−8.29001	+	17.2144i	−0.386104	+	0.801754i	−0.999924	+	0.0123080i	$0.996082\pi$
$462$	28.8556	+	8.10941i	1.34248	+	0.377284i
$463$	6.70600	+	13.9251i	0.311654	+	0.647156i	0.996685	−	0.0813576i	$-0.0259256\pi$
$463$	6.70600	+	13.9251i	0.311654	+	0.647156i	−0.685031	+	0.728514i	$0.740211\pi$
$464$	−0.155769	+	2.77720i	−0.00723139	+	0.128928i
$465$	−39.3443	−	8.98009i	−1.82455	−	0.416442i
$466$	23.8820	+	21.9516i	1.10631	+	1.01689i
$467$	−17.9246	+	8.63204i	−0.829452	+	0.399443i	−0.799910	−	0.600120i	$-0.795119\pi$
$467$	−17.9246	+	8.63204i	−0.829452	+	0.399443i	−0.0295426	+	0.999564i	$0.509405\pi$
$468$	20.5436	−	30.7481i	0.949630	−	1.42133i
$469$	−6.29171	−	7.56543i	−0.290524	−	0.349339i
$470$	2.14668	+	3.11707i	0.0990190	+	0.143780i
$471$		−	9.28187i		−	0.427686i
$472$	6.37753	−	0.0897857i	0.293550	−	0.00413272i
$473$	12.9438	+	6.23341i	0.595157	+	0.286612i
$474$	−33.0983	+	13.1697i	−1.52026	+	0.604904i
$475$	1.77030	−	7.75617i	0.0812267	−	0.355878i
$476$	10.2033	−	28.4748i	0.467669	−	1.30514i
$477$	0.151860	+	0.665341i	0.00695318	+	0.0304639i
$478$	5.51541	+	8.00862i	0.252269	+	0.366306i
$479$	7.98484	+	34.9839i	0.364837	+	1.59845i	0.740738	+	0.671794i	$0.234476\pi$
$479$	7.98484	+	34.9839i	0.364837	+	1.59845i	−0.375901	+	0.926660i	$0.622667\pi$
$480$	−3.56473	+	28.1107i	−0.162707	+	1.28307i
$481$	−25.3925	−	5.79568i	−1.15780	−	0.264260i
$482$	0.202470	+	1.30182i	0.00922224	+	0.0592962i
$483$	2.79883	+	11.1972i	0.127351	+	0.509491i
$484$	−1.76509	−	0.249126i	−0.0802314	−	0.0113239i
$485$	−4.09680	−	5.13722i	−0.186026	−	0.233269i
$486$	−2.21615	+	31.5591i	−0.100527	+	1.43155i
$487$	7.89951	−	6.29965i	0.357961	−	0.285464i	−0.427952	−	0.903801i	$-0.640765\pi$
$487$	7.89951	−	6.29965i	0.357961	−	0.285464i	0.785913	+	0.618337i	$0.212193\pi$
$488$	−3.32275	+	0.807771i	−0.150414	+	0.0365661i
$489$		−	39.3831i		−	1.78097i
$490$	3.82069	+	19.3067i	0.172601	+	0.872187i
$491$		−	16.2149i		−	0.731767i	−0.930661	−	0.365884i	$-0.880767\pi$
$491$		−	16.2149i		−	0.731767i	0.930661	−	0.365884i	$-0.119233\pi$
$492$	0.429604	+	0.454375i	0.0193680	+	0.0204848i
$493$	3.10781	−	2.47840i	0.139969	−	0.111621i
$494$	−59.1690	−	4.15499i	−2.66214	−	0.186942i
$495$	13.1954	+	16.5465i	0.593089	+	0.743710i
$496$	12.3345	+	29.7722i	0.553836	+	1.33681i
$497$	−19.0076	−	8.67727i	−0.852606	−	0.389229i
$498$	11.2808	−	1.75448i	0.505503	−	0.0786201i
$499$	−3.88726	−	0.887242i	−0.174018	−	0.0397184i	0.134624	−	0.990897i	$-0.457017\pi$
$499$	−3.88726	−	0.887242i	−0.174018	−	0.0397184i	−0.308642	+	0.951178i	$0.599874\pi$
$500$	−3.36056	+	23.8099i	−0.150289	+	1.06481i
$501$	1.26040	+	5.52215i	0.0563103	+	0.246712i
$502$	17.3682	−	11.9612i	0.775181	−	0.533855i
$503$	−7.57203	−	33.1752i	−0.337620	−	1.47921i	−0.804002	−	0.594627i	$-0.797300\pi$
$503$	−7.57203	−	33.1752i	−0.337620	−	1.47921i	0.466382	−	0.884584i	$-0.345557\pi$
$504$	10.0834	−	22.9369i	0.449149	−	1.02169i
$505$	5.51887	−	24.1797i	0.245586	−	1.07598i
$506$	2.87816	+	7.23344i	0.127950	+	0.321566i
$507$	−39.7169	−	19.1267i	−1.76389	−	0.849445i
$508$	17.5470	−	10.3515i	0.778521	−	0.459274i
$509$		−	7.63685i		−	0.338498i	−0.985573	−	0.169249i	$-0.945866\pi$
$509$		−	7.63685i		−	0.338498i	0.985573	−	0.169249i	$-0.0541341\pi$
$510$	33.3502	−	22.9678i	1.47677	−	1.01703i
$511$	11.1608	−	5.66000i	0.493724	−	0.250384i
$512$	19.9539	−	10.6696i	0.881847	−	0.471536i
$513$	−6.00296	+	2.89087i	−0.265037	+	0.127635i
$514$	19.7773	−	21.5165i	0.872340	−	0.949052i
$515$	17.6532	+	4.02923i	0.777894	+	0.177549i
$516$	12.6496	−	18.9328i	0.556866	−	0.833472i
$517$	−1.85698	−	3.85606i	−0.0816700	−	0.169589i
$518$	−17.6255	−	0.874379i	−0.774420	−	0.0384180i
$519$	−18.6911	+	38.8124i	−0.820447	+	1.70368i
$520$	31.0499	−	0.437134i	1.36163	−	0.0191696i
$521$		−	9.54407i		−	0.418133i	−0.977901	−	0.209067i	$-0.932957\pi$
$521$		−	9.54407i		−	0.418133i	0.977901	−	0.209067i	$-0.0670426\pi$
$522$	2.71183	−	1.86759i	0.118693	−	0.0817423i
$523$	−11.9118	+	14.9370i	−0.520868	+	0.653148i	−0.970793	−	0.239918i	$-0.922879\pi$
$523$	−11.9118	+	14.9370i	−0.520868	+	0.653148i	0.449925	+	0.893066i	$0.351451\pi$
$524$	−7.30021	+	2.32707i	−0.318911	+	0.101658i
$525$	2.89983	−	6.35209i	0.126559	−	0.277228i
$526$	−8.07337	+	26.6160i	−0.352016	+	1.16051i
$527$	19.9818	−	41.4927i	0.870422	−	1.80745i
$528$	8.86847	−	30.7912i	0.385951	−	1.34002i
$529$	12.4712	−	15.6384i	0.542226	−	0.679931i
$530$	−0.387817	+	0.421921i	−0.0168457	+	0.0183271i
$531$	−4.70749	−	5.90300i	−0.204288	−	0.256169i
$532$	−39.9685	+	4.20103i	−1.73286	+	0.182138i
$533$	0.427262	−	0.535770i	0.0185068	−	0.0232068i
$534$	8.31930	+	53.4906i	0.360011	+	2.31476i
$535$	14.9193	−	7.18477i	0.645019	−	0.310625i
$536$	−8.13108	+	6.67372i	−0.351209	+	0.288261i
$537$	−7.45337	+	1.70118i	−0.321637	+	0.0734115i
$538$	13.3551	+	7.62722i	0.575778	+	0.328833i
$539$	−0.913981	−	22.2372i	−0.0393680	−	0.957822i
$540$	3.00434	−	1.77236i	0.129286	−	0.0762700i
$541$	3.95174	+	17.3137i	0.169899	+	0.744374i	0.986038	+	0.166520i	$0.0532529\pi$
$541$	3.95174	+	17.3137i	0.169899	+	0.744374i	−0.816140	+	0.577855i	$0.803890\pi$
$542$	18.7146	−	2.91065i	0.803861	−	0.125023i
$543$	−6.52259	−	13.5443i	−0.279911	−	0.581241i
$544$	−30.3697	−	11.1043i	−1.30209	−	0.476092i
$545$	−23.8419	−	19.0133i	−1.02128	−	0.814440i
$546$	−50.1192	−	14.0852i	−2.14490	−	0.602792i
$547$	−12.9729	+	10.3455i	−0.554681	+	0.442343i	−0.860284	−	0.509816i	$-0.829714\pi$
$547$	−12.9729	+	10.3455i	−0.554681	+	0.442343i	0.305603	+	0.952159i	$0.401142\pi$
$548$	−21.2189	+	6.76389i	−0.906427	+	0.288939i
$549$	3.16478	+	2.52383i	0.135069	+	0.107714i
$550$	1.36714	−	4.50713i	0.0582949	−	0.192185i
$551$	−4.75843	−	2.29154i	−0.202716	−	0.0976228i
$552$	11.9894	−	2.91466i	0.510303	−	0.124056i
$553$	16.9127	+	20.3366i	0.719201	+	0.864799i
$554$	19.8001	+	18.1996i	0.841225	+	0.773229i
$555$	−18.4708	−	14.7300i	−0.784041	−	0.625252i
$556$	2.16582	+	25.6662i	0.0918514	+	1.08849i
$557$	11.9318			0.505565			0.252782	−	0.967523i	$-0.418654\pi$
$557$	11.9318			0.505565			0.252782	+	0.967523i	$0.418654\pi$
$558$	18.9188	−	33.1263i	0.800897	−	1.40235i
$559$	−22.4821	−	10.8268i	−0.950890	−	0.457925i
$560$	20.6657	−	3.95104i	0.873284	−	0.166962i
$561$	−41.2568	+	19.8682i	−1.74186	+	0.838837i
$562$	−2.64215	+	37.6255i	−0.111452	+	1.58713i
$563$	2.67570	−	11.7230i	0.112768	−	0.494067i	−0.886728	−	0.462292i	$-0.847027\pi$
$563$	2.67570	−	11.7230i	0.112768	−	0.494067i	0.999495	−	0.0317744i	$-0.0101158\pi$
$564$	−6.46289	+	2.06016i	−0.272137	+	0.0867483i
$565$	13.6817	+	28.4104i	0.575594	+	1.19523i
$566$	0.649900	−	9.25488i	0.0273173	−	0.389012i
$567$	20.1087	−	5.02633i	0.844488	−	0.211086i
$568$	−9.40749	+	20.2596i	−0.394730	+	0.850073i
$569$	−17.3784			−0.728542			−0.364271	−	0.931293i	$-0.618682\pi$
$569$	−17.3784			−0.728542			−0.364271	+	0.931293i	$0.618682\pi$
$570$	−46.7199	−	26.6822i	−1.95688	−	1.11760i
$571$	−5.16552	+	10.7263i	−0.216170	+	0.448882i	−0.980651	−	0.195765i	$-0.937281\pi$
$571$	−5.16552	+	10.7263i	−0.216170	+	0.448882i	0.764481	+	0.644647i	$0.222995\pi$
$572$	−34.7710	−	4.90760i	−1.45385	−	0.205197i
$573$	−13.5844	−	3.10055i	−0.567497	−	0.129528i
$574$	0.221936	−	0.407832i	0.00926342	−	0.0170226i
$575$	1.76815	−	0.403568i	0.0737369	−	0.0168300i
$576$	−24.4505	−	10.9378i	−1.01877	−	0.455741i
$577$	−0.105405	+	0.0240579i	−0.00438805	+	0.00100154i	−0.224714	−	0.974425i	$-0.572145\pi$
$577$	−0.105405	+	0.0240579i	−0.00438805	+	0.00100154i	0.220326	+	0.975426i	$0.429288\pi$
$578$	8.19596	+	20.5982i	0.340907	+	0.856774i
$579$	10.0136	−	43.8725i	0.416151	−	1.82328i
$580$	2.58323	+	0.985968i	0.107263	+	0.0409401i
$581$	−3.83408	−	7.56029i	−0.159064	−	0.313654i
$582$	10.9422	−	4.35385i	0.453568	−	0.180473i
$583$	0.506668	−	0.404054i	0.0209841	−	0.0167342i
$584$	−5.97358	−	11.9702i	−0.247188	−	0.495331i
$585$	−22.9191	−	28.7396i	−0.947587	−	1.18824i
$586$	3.21181	−	10.5886i	0.132679	−	0.437411i
$587$	−24.1166			−0.995398			−0.497699	−	0.867350i	$-0.665822\pi$
$587$	−24.1166			−0.995398			−0.497699	+	0.867350i	$0.665822\pi$
$588$	−35.1006	−	3.49119i	−1.44753	−	0.143974i
$589$	−61.1890			−2.52125
$590$	1.84035	−	6.06722i	0.0757662	−	0.249783i
$591$	1.16486	+	1.46069i	0.0479161	+	0.0600849i
$592$	−1.05648	+	18.8360i	−0.0434212	+	0.774156i
$593$	21.5334	−	17.1723i	0.884272	−	0.705183i	−0.0720804	−	0.997399i	$-0.522964\pi$
$593$	21.5334	−	17.1723i	0.884272	−	0.705183i	0.956353	+	0.292215i	$0.0943924\pi$
$594$	−3.66504	+	1.45831i	−0.150378	+	0.0598350i
$595$	−23.8878	−	18.2601i	−0.979306	−	0.748590i
$596$	−5.13129	+	13.4440i	−0.210186	+	0.550687i
$597$	−0.0639090	+	0.280004i	−0.00261562	+	0.0114598i
$598$	−4.99907	−	12.5637i	−0.204427	−	0.513770i
$599$	−19.1491	+	4.37067i	−0.782412	+	0.178581i	−0.595027	−	0.803706i	$-0.702859\pi$
$599$	−19.1491	+	4.37067i	−0.782412	+	0.178581i	−0.187386	+	0.982286i	$0.560001\pi$
$600$	−6.77050	−	3.14387i	−0.276405	−	0.128348i
$601$	4.09575	−	0.934828i	0.167069	−	0.0381324i	−0.138168	−	0.990409i	$-0.544121\pi$
$601$	4.09575	−	0.934828i	0.167069	−	0.0381324i	0.305237	+	0.952276i	$0.401264\pi$
$602$	−16.2765	−	4.57426i	−0.663382	−	0.186433i
$603$	12.1400	+	2.77087i	0.494378	+	0.112839i
$604$	1.36365	−	9.66163i	0.0554861	−	0.393126i
$605$	−0.768829	+	1.59649i	−0.0312574	+	0.0649066i
$606$	38.5996	+	22.0447i	1.56800	+	0.895503i
$607$	−24.0326			−0.975454			−0.487727	−	0.872996i	$-0.662174\pi$
$607$	−24.0326			−0.975454			−0.487727	+	0.872996i	$0.662174\pi$
$608$	4.21491	+	42.7563i	0.170937	+	1.73400i
$609$	−3.68282	−	2.81518i	−0.149236	−	0.114077i
$610$	−0.238111	+	3.39082i	−0.00964085	+	0.137290i
$611$	3.22539	+	6.69759i	0.130485	+	0.270955i
$612$	11.6255	+	36.4702i	0.469933	+	1.47422i
$613$	4.83674	−	21.1911i	0.195354	−	0.855902i	−0.778304	−	0.627888i	$-0.783920\pi$
$613$	4.83674	−	21.1911i	0.195354	−	0.855902i	0.973658	−	0.228014i	$-0.0732233\pi$
$614$	0.103666	−	1.47625i	0.00418360	−	0.0595765i
$615$	0.560033	−	0.269698i	0.0225827	−	0.0108753i
$616$	−23.7783	+	0.823457i	−0.958057	+	0.0331780i
$617$	31.4055	+	15.1241i	1.26434	+	0.608873i	0.941318	−	0.337520i	$-0.109588\pi$
$617$	31.4055	+	15.1241i	1.26434	+	0.608873i	0.323019	+	0.946393i	$0.395302\pi$
$618$	−16.0944	+	28.1809i	−0.647413	+	1.13360i
$619$	7.51453			0.302034			0.151017	−	0.988531i	$-0.451745\pi$
$619$	7.51453			0.302034			0.151017	+	0.988531i	$0.451745\pi$
$620$	31.9208	−	2.69362i	1.28197	−	0.108178i
$621$	−1.18752	−	0.947014i	−0.0476534	−	0.0380024i
$622$	−18.9114	−	17.3828i	−0.758278	−	0.696986i
$623$	35.8490	−	18.1802i	1.43626	−	0.728376i
$624$	−15.4036	+	53.4813i	−0.616639	+	2.14096i
$625$	16.8169	+	8.09858i	0.672675	+	0.323943i
$626$	10.5640	−	34.8269i	0.422220	−	1.39196i
$627$	47.5675	+	37.9338i	1.89966	+	1.51493i
$628$	2.23769	+	7.01983i	0.0892936	+	0.280122i
$629$	21.0784	−	16.8095i	0.840450	−	0.670237i
$630$	−18.6792	−	16.4746i	−0.744197	−	0.656363i
$631$	−35.8624	−	28.5993i	−1.42766	−	1.13852i	−0.968157	−	0.250343i	$-0.919457\pi$
$631$	−35.8624	−	28.5993i	−1.42766	−	1.13852i	−0.459502	−	0.888177i	$-0.651972\pi$
$632$	21.8571	−	17.9396i	0.869429	−	0.713598i
$633$	−18.3360	−	38.0751i	−0.728790	−	1.51335i
$634$	−44.5294	+	6.92558i	−1.76849	+	0.275050i
$635$	−4.50638	−	19.7437i	−0.178830	−	0.783506i
$636$	−0.521881	−	0.884645i	−0.0206939	−	0.0350785i
$637$	1.58749	+	38.6237i	0.0628987	+	1.53033i
$638$	−2.71514	−	1.55065i	−0.107493	−	0.0613906i
$639$	25.7790	−	5.88388i	1.01980	−	0.232763i
$640$	−4.08100	−	22.1194i	−0.161316	−	0.874345i
$641$	−29.0858	+	14.0070i	−1.14882	+	0.553243i	−0.908679	−	0.417495i	$-0.862908\pi$
$641$	−29.0858	+	14.0070i	−1.14882	+	0.553243i	−0.240141	+	0.970738i	$0.577194\pi$
$642$	4.56102	+	29.3260i	0.180009	+	1.15740i
$643$	29.4902	−	36.9796i	1.16298	−	1.45833i	0.299395	−	0.954129i	$-0.403215\pi$
$643$	29.4902	−	36.9796i	1.16298	−	1.45833i	0.863585	−	0.504203i	$-0.168214\pi$
$644$	−4.81618	−	7.79365i	−0.189784	−	0.307113i
$645$	−14.1122	−	17.6961i	−0.555668	−	0.696785i
$646$	41.5495	−	45.2033i	1.63474	−	1.77850i
$647$	−29.9412	+	37.5451i	−1.17711	+	1.47605i	−0.330522	+	0.943798i	$0.607225\pi$
$647$	−29.9412	+	37.5451i	−1.17711	+	1.47605i	−0.846587	+	0.532250i	$0.821347\pi$
$648$	−5.23436	−	21.5314i	−0.205625	−	0.845834i
$649$	−3.11080	+	6.45964i	−0.122110	+	0.253563i
$650$	−2.37458	+	7.82842i	−0.0931385	+	0.307056i
$651$	−52.5938	−	10.8728i	−2.06131	−	0.426140i
$652$	9.49456	+	29.7853i	0.371836	+	1.16648i
$653$	20.8002	−	26.0826i	0.813974	−	1.02069i	−0.185303	−	0.982681i	$-0.559327\pi$
$653$	20.8002	−	26.0826i	0.813974	−	1.02069i	0.999277	−	0.0380098i	$-0.0121018\pi$
$654$	45.0132	−	30.9999i	1.76016	−	1.21219i
$655$			7.61651i			0.297602i
$656$	−0.434449	−	0.240072i	−0.0169624	−	0.00937322i
$657$	−6.87111	+	14.2680i	−0.268068	+	0.556648i
$658$	2.94139	+	4.08865i	0.114667	+	0.159392i
$659$	−8.96210	−	18.6100i	−0.349114	−	0.724943i	0.650282	−	0.759693i	$-0.274651\pi$
$659$	−8.96210	−	18.6100i	−0.349114	−	0.724943i	−0.999396	+	0.0347503i	$0.988936\pi$
$660$	−26.4847	−	17.6952i	−1.03092	−	0.688784i
$661$	40.9935	+	9.35649i	1.59446	+	0.363925i	0.925313	−	0.379204i	$-0.123802\pi$
$661$	40.9935	+	9.35649i	1.59446	+	0.363925i	0.669148	+	0.743129i	$0.266659\pi$
$662$	13.8580	−	15.0766i	0.538606	−	0.585970i
$663$	71.6588	−	34.5091i	2.78300	−	1.34022i
$664$	−8.10861	+	4.04649i	−0.314675	+	0.157034i
$665$	−8.08781	+	39.1222i	−0.313632	+	1.51709i
$666$	18.3926	−	12.6667i	0.712701	−	0.490826i
$667$		−	1.20400i		−	0.0466189i
$668$	−2.28452	−	3.87251i	−0.0883908	−	0.149832i
$669$	37.3830	+	18.0027i	1.44531	+	0.696025i
$670$	3.86584	+	9.71568i	0.149350	+	0.375350i
$671$	0.855342	−	3.74750i	0.0330201	−	0.144671i
$672$	−3.97463	+	37.4993i	−0.153325	+	1.44657i
$673$	−11.3173	−	49.5842i	−0.436248	−	1.91133i	−0.410970	−	0.911649i	$-0.634810\pi$
$673$	−11.3173	−	49.5842i	−0.436248	−	1.91133i	−0.0252786	−	0.999680i	$-0.508047\pi$
$674$	35.9265	−	24.7420i	1.38384	−	0.953026i
$675$	0.204480	+	0.895886i	0.00787045	+	0.0344827i
$676$	34.6488	+	4.89036i	1.33265	+	0.188091i
$677$	5.35324	+	1.22184i	0.205742	+	0.0469592i	0.324150	−	0.946006i	$-0.394922\pi$
$677$	5.35324	+	1.22184i	0.205742	+	0.0469592i	−0.118408	+	0.992965i	$0.537779\pi$
$678$	−55.8444	+	8.68539i	−2.14469	+	0.333560i
$679$	−5.59127	−	6.72320i	−0.214573	−	0.258013i
$680$	−19.6855	+	25.4105i	−0.754903	+	0.974449i
$681$	27.0243	+	33.8874i	1.03557	+	1.29857i
$682$	−36.1363	−	2.53758i	−1.38373	−	0.0971688i
$683$	−4.85165	+	3.86906i	−0.185643	+	0.148045i	−0.711902	−	0.702279i	$-0.752166\pi$
$683$	−4.85165	+	3.86906i	−0.185643	+	0.148045i	0.526259	+	0.850325i	$0.323594\pi$
$684$	36.9557	−	34.9410i	1.41304	−	1.33600i
$685$			22.1383i			0.845860i
$686$	5.61119	+	25.5835i	0.214236	+	0.976782i
$687$			54.6170i			2.08377i
$688$	−5.00243	+	17.3684i	−0.190716	+	0.662163i
$689$	−0.880031	+	0.701801i	−0.0335265	+	0.0267365i
$690$	0.859172	−	12.2350i	0.0327081	−	0.465779i
$691$	26.3182	+	33.0019i	1.00119	+	1.25545i	0.966664	+	0.256049i	$0.0824207\pi$
$691$	26.3182	+	33.0019i	1.00119	+	1.25545i	0.0345260	+	0.999404i	$0.489008\pi$
$692$	4.77899	−	33.8597i	0.181670	−	1.28715i
$693$	18.0090	+	21.6548i	0.684104	+	0.822597i
$694$	−6.30094	−	40.5131i	−0.239180	−	1.53786i
$695$	24.9621	+	5.69744i	0.946867	+	0.216116i
$696$	−3.03493	+	3.91757i	−0.115039	+	0.148495i
$697$	0.157844	+	0.691558i	0.00597875	+	0.0261946i
$698$	−15.5853	−	22.6305i	−0.589912	−	0.856578i
$699$	12.8598	+	56.3425i	0.486403	+	2.13107i
$700$	−0.661754	+	5.50315i	−0.0250120	+	0.208000i
$701$	−4.75445	+	20.8306i	−0.179573	+	0.786761i	0.802254	+	0.596983i	$0.203634\pi$
$701$	−4.75445	+	20.8306i	−0.179573	+	0.786761i	−0.981827	+	0.189778i	$0.939223\pi$
$702$	6.36580	−	2.53293i	0.240262	−	0.0955992i
$703$	−32.2735	−	15.5421i	−1.21722	−	0.586181i
$704$	0.716038	+	25.4253i	0.0269867	+	0.958251i
$705$			6.74291i			0.253953i
$706$	−2.09690	−	3.04480i	−0.0789180	−	0.114592i
$707$	6.68209	−	32.3224i	0.251306	−	1.21561i
$708$	9.44848	+	6.31280i	0.355096	+	0.237249i
$709$	6.71673	−	3.23461i	0.252252	−	0.121478i	−0.303485	−	0.952836i	$-0.598150\pi$
$709$	6.71673	−	3.23461i	0.252252	−	0.121478i	0.555737	+	0.831358i	$0.312436\pi$
$710$	16.3475	+	15.0262i	0.613512	+	0.563922i
$711$	−32.6334	−	7.44836i	−1.22385	−	0.279335i
$712$	−19.1874	−	38.4490i	−0.719080	−	1.44094i
$713$	−6.05227	−	12.5677i	−0.226659	−	0.470663i
$714$	43.7453	−	31.4705i	1.63713	−	1.17776i
$715$	−15.1454	+	31.4497i	−0.566405	+	1.17615i
$716$	5.22682	−	3.08347i	0.195335	−	0.115235i
$717$			17.3244i			0.646992i
$718$	−4.01364	−	5.82799i	−0.149788	−	0.217499i
$719$	18.2757	−	22.9170i	0.681569	−	0.854660i	−0.313929	−	0.949447i	$-0.601645\pi$
$719$	18.2757	−	22.9170i	0.681569	−	0.854660i	0.995498	+	0.0947862i	$0.0302167\pi$
$720$	−17.7407	+	19.8547i	−0.661158	+	0.739941i
$721$	23.5981	+	4.87848i	0.878838	+	0.181684i
$722$	−52.3511	−	15.8795i	−1.94831	−	0.590975i
$723$	−1.01841	+	2.11476i	−0.0378752	+	0.0786486i
$724$	8.19828	+	8.67099i	0.304687	+	0.322255i
$725$	−0.454159	+	0.569497i	−0.0168670	+	0.0211506i
$726$	−2.33817	−	2.14918i	−0.0867777	−	0.0797635i
$727$	17.3818	+	21.7961i	0.644654	+	0.808371i	0.991576	−	0.129523i	$-0.0413446\pi$
$727$	17.3818	+	21.7961i	0.644654	+	0.808371i	−0.346922	+	0.937894i	$0.612773\pi$
$728$	41.3006	−	1.43026i	1.53070	−	0.0530090i
$729$	−20.4887	+	25.6921i	−0.758842	+	0.951557i
$730$	−13.1403	+	2.04369i	−0.486345	+	0.0756405i
$731$	23.2717	−	11.2070i	0.860733	−	0.414507i
$732$	−5.69173	−	2.17242i	−0.210372	−	0.0802949i
$733$	21.3762	−	4.87897i	0.789546	−	0.180209i	0.191311	−	0.981529i	$-0.438726\pi$
$733$	21.3762	−	4.87897i	0.789546	−	0.180209i	0.598235	+	0.801321i	$0.295869\pi$
$734$	−22.9530	+	40.1900i	−0.847209	+	1.48344i
$735$	−13.9034	+	32.1895i	−0.512836	+	1.18733i
$736$	−8.36485	+	5.09477i	−0.308333	+	0.187796i
$737$	−2.63121	−	11.5281i	−0.0969218	−	0.424642i
$738$	0.0902997	+	0.580600i	0.00332398	+	0.0213722i
$739$	−5.76368	−	11.9684i	−0.212021	−	0.440265i	0.767652	−	0.640866i	$-0.221425\pi$
$739$	−5.76368	−	11.9684i	−0.212021	−	0.440265i	−0.979673	+	0.200601i	$0.935710\pi$
$740$	17.5205	+	6.68722i	0.644066	+	0.245827i
$741$	−82.6200	−	65.8872i	−3.03512	−	2.42043i
$742$	−0.504466	+	0.571973i	−0.0185195	+	0.0209978i
$743$	−19.9125	+	15.8797i	−0.730517	+	0.582568i	−0.916524	−	0.399981i	$-0.869017\pi$
$743$	−19.9125	+	15.8797i	−0.730517	+	0.582568i	0.186006	+	0.982549i	$0.440445\pi$
$744$	−11.9866	+	56.1489i	−0.439450	+	2.05852i
$745$	11.1835	+	8.91857i	0.409733	+	0.326751i
$746$	19.4069	+	5.88663i	0.710535	+	0.215525i
$747$	9.66513	+	4.65448i	0.353629	+	0.170299i
$748$	26.4124	−	24.9725i	0.965733	−	0.913085i
$749$	19.6541	−	9.96724i	0.718144	−	0.364195i
$750$	−28.9910	+	31.5405i	−1.05860	+	1.15169i
$751$	−9.84532	−	7.85138i	−0.359261	−	0.286501i	0.427180	−	0.904167i	$-0.359507\pi$
$751$	−9.84532	−	7.85138i	−0.359261	−	0.286501i	−0.786441	+	0.617666i	$0.788078\pi$
$752$	4.39118	−	3.11617i	0.160130	−	0.113635i
$753$	37.5712			1.36917
$754$	4.71592	+	2.69331i	0.171744	+	0.0980847i
$755$	−8.73876	−	4.20836i	−0.318036	−	0.153158i
$756$	3.94889	−	2.44027i	0.143620	−	0.0887516i
$757$	−6.17722	+	2.97479i	−0.224515	+	0.108121i	−0.542760	−	0.839888i	$-0.682621\pi$
$757$	−6.17722	+	2.97479i	−0.224515	+	0.108121i	0.318245	+	0.948008i	$0.396906\pi$
$758$	−40.1546	−	2.81975i	−1.45848	−	0.102418i
$759$	−3.08631	+	13.5220i	−0.112026	+	0.490818i
$760$	41.7666	+	8.91630i	1.51503	+	0.323428i
$761$	−10.8210	−	22.4700i	−0.392261	−	0.814538i	−0.999795	−	0.0202447i	$-0.993555\pi$
$761$	−10.8210	−	22.4700i	−0.392261	−	0.814538i	0.607534	−	0.794294i	$-0.292159\pi$
$762$	36.2069	+	2.54254i	1.31164	+	0.0921064i
$763$	−32.2418	−	24.6459i	−1.16723	−	0.892242i
$764$	11.0213	−	0.930025i	0.398737	−	0.0336471i
$765$	38.0503			1.37571
$766$	−5.08302	+	8.90025i	−0.183657	+	0.321579i
$767$	5.40314	−	11.2197i	0.195096	−	0.405121i
$768$	40.0601	+	4.50801i	1.44554	+	0.162669i
$769$	24.8463	+	5.67101i	0.895981	+	0.204502i	0.645627	−	0.763653i	$-0.276596\pi$
$769$	24.8463	+	5.67101i	0.895981	+	0.204502i	0.250354	+	0.968154i	$0.419453\pi$
$770$	−6.39884	+	22.7689i	−0.230598	+	0.820533i
$771$	50.7618	−	11.5860i	1.82814	−	0.417261i
$772$	3.00363	+	35.5946i	0.108103	+	1.28108i
$773$	−28.6502	+	6.53922i	−1.03048	+	0.235199i	−0.704145	−	0.710056i	$-0.748669\pi$
$773$	−28.6502	+	6.53922i	−1.03048	+	0.235199i	−0.326331	+	0.945256i	$0.605812\pi$
$774$	19.8799	−	7.91014i	0.714568	−	0.284324i
$775$	−1.87789	+	8.22756i	−0.0674557	+	0.295543i
$776$	−7.22587	+	5.93076i	−0.259394	+	0.212902i
$777$	−24.9783	−	19.0937i	−0.896092	−	0.684981i
$778$	13.2188	+	33.2218i	0.473919	+	1.19106i
$779$	0.736853	−	0.587621i	0.0264005	−	0.0210537i
$780$	46.0013	+	30.7347i	1.64711	+	1.10048i
$781$	−15.6553	−	19.6311i	−0.560191	−	0.702457i
$782$	13.3940	+	4.06278i	0.478970	+	0.145285i
$783$	0.610041			0.0218011
$784$	27.3881	−	5.82176i	0.978146	−	0.207920i
$785$	7.32398			0.261404
$786$	−13.0631	−	3.96240i	−0.465946	−	0.141334i
$787$	13.1058	+	16.4341i	0.467170	+	0.585813i	0.958476	−	0.285175i	$-0.0920516\pi$
$787$	13.1058	+	16.4341i	0.467170	+	0.585813i	−0.491306	+	0.870987i	$0.663480\pi$
$788$	−1.23313	−	0.823886i	−0.0439283	−	0.0293497i
$789$	−38.7417	+	30.8955i	−1.37924	+	1.09991i
$790$	−10.3917	−	26.1167i	−0.369721	−	0.929189i
$791$	18.9803	+	37.4266i	0.674860	+	1.33074i
$792$	23.2739	−	19.1024i	0.827001	−	0.678775i
$793$	−1.48564	+	6.50902i	−0.0527567	+	0.231142i
$794$	43.2790	−	17.2205i	1.53591	−	0.611134i
$795$	−0.995397	+	0.227193i	−0.0353031	+	0.00805770i
$796$	−0.0191698	−	0.227172i	−0.000679455	−	0.00805191i
$797$	8.41635	−	1.92098i	0.298122	−	0.0680445i	−0.0708435	−	0.997487i	$-0.522569\pi$
$797$	8.41635	−	1.92098i	0.298122	−	0.0680445i	0.368966	+	0.929443i	$0.379712\pi$
$798$	−62.8910	−	34.2243i	−2.22632	−	1.21153i
$799$	−7.50191	−	1.71226i	−0.265399	−	0.0605755i
$800$	5.87842	+	0.745445i	0.207834	+	0.0263555i
$801$	−22.0704	+	45.8296i	−0.779819	+	1.61931i
$802$	−10.1404	+	17.7556i	−0.358070	+	0.626971i
$803$	15.0381			0.530683
$804$	−18.6746	+	1.57584i	−0.658601	+	0.0555756i
$805$	−8.83531	+	2.20845i	−0.311404	+	0.0778377i
$806$	62.7650	+	4.40751i	2.21080	+	0.155248i
$807$	11.8885	+	24.6868i	0.418496	+	0.869017i
$808$	−34.5073	−	7.36658i	−1.21396	−	0.259155i
$809$	1.48072	−	6.48745i	0.0520593	−	0.228087i	−0.942205	−	0.335037i	$-0.891251\pi$
$809$	1.48072	−	6.48745i	0.0520593	−	0.228087i	0.994264	+	0.106950i	$0.0341085\pi$
$810$	−21.9725	−	1.54296i	−0.772035	−	0.0542141i
$811$	−6.44504	+	3.10377i	−0.226316	+	0.108988i	−0.543606	−	0.839341i	$-0.682941\pi$
$811$	−6.44504	+	3.10377i	−0.226316	+	0.108988i	0.317290	+	0.948329i	$0.397227\pi$
$812$	3.46399	+	1.24125i	0.121562	+	0.0435592i
$813$	30.4012	+	14.6404i	1.06622	+	0.513462i
$814$	−18.4151	−	10.5171i	−0.645450	−	0.368623i
$815$	31.0758			1.08854
$816$	−33.3405	−	46.9821i	−1.16715	−	1.64470i
$817$	−26.8314	−	21.3973i	−0.938710	−	0.748597i
$818$	11.2614	−	12.2518i	0.393747	−	0.428373i
$819$	−31.2797	−	37.6122i	−1.09300	−	1.31428i
$820$	−0.358531	+	0.338985i	−0.0125204	+	0.0118379i
$821$	−5.60033	−	2.69698i	−0.195453	−	0.0941251i	0.333597	−	0.942716i	$-0.391737\pi$
$821$	−5.60033	−	2.69698i	−0.195453	−	0.0941251i	−0.529050	+	0.848591i	$0.677452\pi$
$822$	−37.9695	−	11.5172i	−1.32434	−	0.401708i
$823$	−0.911381	−	0.726802i	−0.0317687	−	0.0253347i	0.607477	−	0.794337i	$-0.292182\pi$
$823$	−0.911381	−	0.726802i	−0.0317687	−	0.0253347i	−0.639245	+	0.769003i	$0.720753\pi$
$824$	5.37821	−	25.1932i	0.187359	−	0.877645i
$825$	6.56048	−	5.23181i	0.228407	−	0.182148i
$826$	2.28280	−	8.12284i	0.0794287	−	0.282630i
$827$	17.4505	+	13.9163i	0.606812	+	0.483916i	0.878033	−	0.478601i	$-0.158856\pi$
$827$	17.4505	+	13.9163i	0.606812	+	0.483916i	−0.271221	+	0.962517i	$0.587427\pi$
$828$	10.8319	+	4.13431i	0.376434	+	0.143677i
$829$	9.40692	+	19.5337i	0.326716	+	0.678432i	0.998030	−	0.0627408i	$-0.0199841\pi$
$829$	9.40692	+	19.5337i	0.326716	+	0.678432i	−0.671314	+	0.741173i	$0.734270\pi$
$830$	1.38439	+	8.90124i	0.0480530	+	0.308967i
$831$	10.6618	+	46.7124i	0.369854	+	1.62044i
$832$	−1.24369	−	44.1611i	−0.0431170	−	1.53101i
$833$	−32.2823	−	23.6425i	−1.11852	−	0.819164i
$834$	−22.7579	+	39.8486i	−0.788043	+	1.37984i
$835$	−4.35733	+	0.994531i	−0.150792	+	0.0344172i
$836$	−45.1202	−	17.2215i	−1.56052	−	0.595617i
$837$	6.36779	−	3.06657i	0.220103	−	0.105996i
$838$	5.57340	−	0.866821i	0.192530	−	0.0299438i
$839$	−10.9224	+	13.6962i	−0.377083	+	0.472847i	−0.933769	−	0.357876i	$-0.883501\pi$
$839$	−10.9224	+	13.6962i	−0.377083	+	0.472847i	0.556686	+	0.830723i	$0.312072\pi$
$840$	34.3153	+	15.0854i	1.18399	+	0.520497i
$841$	−17.7797	−	22.2950i	−0.613093	−	0.768795i
$842$	−1.93071	−	1.77465i	−0.0665367	−	0.0611585i
$843$	−41.8976	+	52.5379i	−1.44303	+	1.80950i
$844$	23.0466	+	24.3755i	0.793298	+	0.839039i
$845$	15.0921	−	31.3392i	0.519186	−	1.07810i
$846$	−6.09955	−	1.85016i	−0.209707	−	0.0636098i
$847$	−0.979307	+	2.14517i	−0.0336494	+	0.0737090i
$848$	0.607968	+	0.543236i	0.0208777	+	0.0186548i
$849$	10.3057	−	12.9230i	0.353691	−	0.443515i
$850$	−4.80294	−	6.97408i	−0.164740	−	0.239209i
$851$		−	8.16597i		−	0.279926i
$852$	−34.2760	+	20.2205i	−1.17428	+	0.692744i
$853$	3.86264	−	8.02085i	0.132254	−	0.274629i	−0.824316	−	0.566129i	$-0.808440\pi$
$853$	3.86264	−	8.02085i	0.132254	−	0.274629i	0.956571	+	0.291501i	$0.0941546\pi$
$854$	−0.224135	+	4.51805i	−0.00766974	+	0.154605i
$855$	−21.9353	−	45.5492i	−0.750172	−	1.55775i
$856$	−10.5194	−	21.0795i	−0.359547	−	0.720483i
$857$	7.42901	+	1.69562i	0.253770	+	0.0579214i	0.347513	−	0.937675i	$-0.387026\pi$
$857$	7.42901	+	1.69562i	0.253770	+	0.0579214i	−0.0937432	+	0.995596i	$0.529883\pi$
$858$	−46.0603	−	42.3372i	−1.57247	−	1.44537i
$859$	−24.6355	+	11.8638i	−0.840553	+	0.404789i	−0.804062	−	0.594545i	$-0.797332\pi$
$859$	−24.6355	+	11.8638i	−0.840553	+	0.404789i	−0.0364908	+	0.999334i	$0.511618\pi$
$860$	14.9392	+	9.98130i	0.509423	+	0.340360i
$861$	0.737763	−	0.374144i	0.0251429	−	0.0127508i
$862$	5.05513	+	7.34028i	0.172178	+	0.250011i
$863$		−	13.1810i		−	0.448686i	−0.974510	−	0.224343i	$-0.927976\pi$
$863$		−	13.1810i		−	0.448686i	0.974510	−	0.224343i	$-0.0720237\pi$
$864$	−2.58142	−	4.23831i	−0.0878217	−	0.144190i
$865$	−30.6255	−	14.7484i	−1.04130	−	0.501462i
$866$	18.2929	−	7.27867i	0.621618	−	0.247339i
$867$	−8.78871	+	38.5059i	−0.298480	+	1.30773i
$868$	42.3976	−	4.45636i	1.43907	−	0.151259i
$869$	7.07293	+	30.9885i	0.239933	+	1.05121i
$870$	2.79405	+	4.05708i	0.0947272	+	0.137548i
$871$	4.57014	+	20.0231i	0.154853	+	0.678456i
$872$	−26.5697	+	34.2969i	−0.899765	+	1.16144i
$873$	10.7885	+	2.46240i	0.365135	+	0.0833396i
$874$	−2.85796	−	18.3758i	−0.0966719	−	0.621571i
$875$	28.9370	+	13.2102i	0.978250	+	0.446587i
$876$	3.33096	−	23.6002i	0.112543	−	0.797378i
$877$	30.3485	+	38.0558i	1.02480	+	1.28505i	0.957842	+	0.287296i	$0.0927564\pi$
$877$	30.3485	+	38.0558i	1.02480	+	1.28505i	0.0669533	+	0.997756i	$0.478672\pi$
$878$	1.58304	−	22.5432i	0.0534249	−	0.760796i
$879$	15.4125	−	12.2911i	0.519852	−	0.414568i
$880$	24.2962	+	6.99778i	0.819026	+	0.235895i
$881$			8.25388i			0.278080i	0.990287	+	0.139040i	$0.0444017\pi$
$881$			8.25388i			0.278080i	−0.990287	+	0.139040i	$0.955598\pi$
$882$	−25.3033	−	21.4092i	−0.852007	−	0.720885i
$883$		−	30.8246i		−	1.03733i	−0.854977	−	0.518666i	$-0.826429\pi$
$883$		−	30.8246i		−	1.03733i	0.854977	−	0.518666i	$-0.173571\pi$
$884$	−45.8757	+	43.3747i	−1.54297	+	1.45885i
$885$	8.83131	−	7.04274i	0.296861	−	0.236739i
$886$	46.8628	+	3.29082i	1.57439	+	0.110557i
$887$	−5.90129	−	7.39998i	−0.198146	−	0.248467i	0.672825	−	0.739802i	$-0.265081\pi$
$887$	−5.90129	−	7.39998i	−0.198146	−	0.248467i	−0.870971	+	0.491335i	$0.836509\pi$
$888$	−20.5841	+	26.5705i	−0.690757	+	0.891648i
$889$	−6.53545	−	26.1462i	−0.219192	−	0.876916i
$890$	−42.2074	+	6.56445i	−1.41480	+	0.220041i
$891$	24.2838	+	5.54262i	0.813537	+	0.185685i
$892$	−32.6127	−	4.60298i	−1.09195	−	0.154119i
$893$	2.27501	+	9.96745i	0.0761301	+	0.333548i
$894$	−21.1144	+	14.5411i	−0.706170	+	0.486328i
$895$	−1.34234	−	5.88118i	−0.0448695	−	0.196586i
$896$	−6.03440	−	29.3187i	−0.201595	−	0.979469i
$897$	5.36061	−	23.4864i	0.178986	−	0.784187i
$898$	−16.6329	−	41.8020i	−0.555046	−	1.39495i
$899$	5.04763	+	2.43081i	0.168348	+	0.0810720i
$900$	−3.56404	−	6.04144i	−0.118801	−	0.201381i
$901$		−	1.16513i		−	0.0388162i
$902$	0.459531	−	0.316472i	0.0153007	−	0.0105374i
$903$	−19.2602	−	23.1593i	−0.640940	−	0.770695i
$904$	40.1409	−	20.0318i	1.33507	−	0.666248i
$905$	10.6873	−	5.14673i	0.355258	−	0.171083i
$906$	11.7640	−	12.7985i	0.390833	−	0.425202i
$907$	5.79066	+	1.32168i	0.192276	+	0.0438857i	0.317574	−	0.948233i	$-0.397132\pi$
$907$	5.79066	+	1.32168i	0.192276	+	0.0438857i	−0.125299	+	0.992119i	$0.539989\pi$
$908$	−28.6080	−	19.1138i	−0.949389	−	0.634314i
$909$	18.1228	+	37.6324i	0.601095	+	1.24819i
$910$	11.1141	−	39.5472i	0.368430	−	1.31098i
$911$	19.4905	−	40.4725i	0.645750	−	1.34091i	−0.278983	−	0.960296i	$-0.589997\pi$
$911$	19.4905	−	40.4725i	0.645750	−	1.34091i	0.924733	−	0.380617i	$-0.124288\pi$
$912$	−37.0210	+	66.9955i	−1.22589	+	2.21844i
$913$		−	10.1868i		−	0.337133i
$914$	21.7167	−	14.9559i	0.718323	−	0.494698i
$915$	−3.77582	+	4.73473i	−0.124825	+	0.156525i
$916$	−13.1672	−	41.3065i	−0.435055	−	1.36481i
$917$	0.208172	+	10.1339i	0.00687444	+	0.334651i
$918$	−2.05853	+	6.78650i	−0.0679417	+	0.223988i
$919$	−10.7240	+	22.2687i	−0.353753	+	0.734576i	−0.999582	−	0.0289062i	$-0.990798\pi$
$919$	−10.7240	+	22.2687i	−0.353753	+	0.734576i	0.645829	+	0.763482i	$0.276512\pi$
$920$	2.29985	+	9.46040i	0.0758239	+	0.311900i
$921$	1.64387	−	2.06134i	0.0541672	−	0.0679235i
$922$	18.2856	−	19.8936i	0.602204	−	0.655161i
$923$	27.1917	+	34.0973i	0.895024	+	1.12232i
$924$	−35.7221	−	22.8199i	−1.17517	−	0.750720i
$925$	−3.08028	+	3.86255i	−0.101279	+	0.127000i
$926$	−3.35911	−	21.5981i	−0.110387	−	0.709757i
$927$	−27.4747	+	13.2311i	−0.902389	+	0.434568i
$928$	1.35085	−	3.69451i	0.0443437	−	0.121278i
$929$	−37.5830	+	8.57808i	−1.23306	+	0.281438i	−0.788906	−	0.614514i	$-0.789352\pi$
$929$	−37.5830	+	8.57808i	−1.23306	+	0.281438i	−0.444152	+	0.895951i	$0.646495\pi$
$930$	49.5594	+	28.3039i	1.62512	+	0.928120i
$931$	−9.69171	+	52.2738i	−0.317633	+	1.71321i
$932$	−23.3090	−	39.5113i	−0.763511	−	1.29424i
$933$	−10.1833	−	44.6158i	−0.333385	−	1.46066i
$934$	27.8013	−	4.32389i	0.909686	−	0.141482i
$935$	−15.6773	−	32.5542i	−0.512702	−	1.06464i
$936$	−40.4243	+	33.1789i	−1.32131	+	1.08449i
$937$	−24.7847	−	19.7651i	−0.809680	−	0.645699i	0.128553	−	0.991703i	$-0.458967\pi$
$937$	−24.7847	−	19.7651i	−0.809680	−	0.645699i	−0.938233	+	0.346004i	$0.887538\pi$
$938$	5.40911	+	12.8212i	0.176614	+	0.418628i
$939$	50.6933	−	40.4265i	1.65431	−	1.31927i
$940$	−1.62559	−	5.09963i	−0.0530210	−	0.166332i
$941$	26.6795	+	21.2762i	0.869726	+	0.693584i	0.953009	−	0.302942i	$-0.0979690\pi$
$941$	26.6795	+	21.2762i	0.869726	+	0.693584i	−0.0832825	+	0.996526i	$0.526540\pi$
$942$	−3.81022	+	12.5614i	−0.124144	+	0.409272i
$943$	0.193575	+	0.0932208i	0.00630367	+	0.00303569i
$944$	−8.66773	−	2.49647i	−0.282111	−	0.0812533i
$945$	−1.11898	−	4.47668i	−0.0364004	−	0.145626i
$946$	−14.9584	−	13.7493i	−0.486338	−	0.447027i
$947$	−2.24304	−	1.78877i	−0.0728891	−	0.0581271i	0.586368	−	0.810045i	$-0.300557\pi$
$947$	−2.24304	−	1.78877i	−0.0728891	−	0.0581271i	−0.659257	+	0.751918i	$0.729129\pi$
$948$	50.1990	−	4.23600i	1.63039	−	0.137579i
$949$	−26.1196			−0.847879
$950$	−5.57970	+	9.76991i	−0.181029	+	0.316978i
$951$	−72.3363	−	34.8353i	−2.34567	−	1.12961i
$952$	−25.4974	+	34.3472i	−0.826374	+	1.11320i
$953$	−4.56657	+	2.19914i	−0.147926	+	0.0712373i	−0.506382	−	0.862309i	$-0.669017\pi$
$953$	−4.56657	+	2.19914i	−0.147926	+	0.0712373i	0.358456	+	0.933546i	$0.383303\pi$
$954$	0.0676074	−	0.962761i	0.00218887	−	0.0311705i
$955$	2.44653	−	10.7190i	0.0791680	−	0.346858i
$956$	−4.17660	−	13.1024i	−0.135081	−	0.423760i
$957$	−2.41699	−	5.01893i	−0.0781301	−	0.162239i
$958$	3.55482	−	50.6223i	0.114851	−	1.63553i
$959$	0.605075	+	29.4554i	0.0195389	+	0.951164i
$960$	16.3637	−	36.5796i	0.528137	−	1.18060i
$961$	33.9078			1.09380
$962$	31.9852	+	18.2671i	1.03124	+	0.588954i
$963$	−12.1000	+	25.1259i	−0.389917	+	0.809671i
$964$	0.260391	−	1.84490i	0.00838661	−	0.0594202i
$965$	34.6182	+	7.90137i	1.11440	+	0.254354i
$966$	0.808742	−	16.3024i	0.0260208	−	0.524521i
$967$	−37.6110	+	8.58447i	−1.20949	+	0.276058i	−0.779282	−	0.626673i	$-0.784416\pi$
$967$	−37.6110	+	8.58447i	−1.20949	+	0.276058i	−0.430206	+	0.902731i	$0.641559\pi$
$968$	2.28647	+	1.06172i	0.0734901	+	0.0341250i
$969$	106.644	−	24.3407i	3.42589	−	0.781937i
$970$	3.43547	+	8.63407i	0.110306	+	0.277223i
$971$	−8.98727	+	39.3758i	−0.288415	+	1.26363i	0.598285	+	0.801284i	$0.295849\pi$
$971$	−8.98727	+	39.3758i	−0.288415	+	1.26363i	−0.886700	+	0.462345i	$0.847008\pi$
$972$	15.9542	−	41.8000i	0.511731	−	1.34073i
$973$	33.3683	+	6.89829i	1.06974	+	0.221149i
$974$	−13.2766	+	5.28272i	−0.425410	+	0.169269i
$975$	−11.3949	+	9.08711i	−0.364928	+	0.291021i
$976$	4.82835	+	0.270815i	0.154552	+	0.00866858i
$977$	26.7715	+	33.5704i	0.856495	+	1.07401i	0.996478	+	0.0838571i	$0.0267239\pi$
$977$	26.7715	+	33.5704i	0.856495	+	1.07401i	−0.139983	+	0.990154i	$0.544705\pi$
$978$	−16.1668	+	53.2982i	−0.516958	+	1.70429i
$979$	48.3031			1.54378
$980$	2.75477	−	27.6966i	0.0879979	−	0.884736i
$981$	51.3571			1.63971
$982$	−6.65622	+	21.9440i	−0.212409	+	0.700261i
$983$	−16.5231	−	20.7193i	−0.527004	−	0.660842i	0.445076	−	0.895493i	$-0.353177\pi$
$983$	−16.5231	−	20.7193i	−0.527004	−	0.660842i	−0.972080	+	0.234651i	$0.924605\pi$
$984$	−0.394873	−	0.791270i	−0.0125881	−	0.0252248i
$985$	−1.15258	+	0.919151i	−0.0367242	+	0.0292866i
$986$	−5.22327	+	2.07832i	−0.166343	+	0.0661872i
$987$	0.184295	+	8.97157i	0.00586617	+	0.285568i
$988$	78.3692	+	29.9120i	2.49326	+	0.951626i
$989$	1.74089	−	7.62735i	0.0553571	−	0.242535i
$990$	−11.0653	−	27.8095i	−0.351679	−	0.883845i
$991$	−14.9149	+	3.40423i	−0.473788	+	0.108139i	−0.452746	−	0.891640i	$-0.649556\pi$
$991$	−14.9149	+	3.40423i	−0.473788	+	0.108139i	−0.0210420	+	0.999779i	$0.506698\pi$
$992$	−4.47107	−	45.3548i	−0.141957	−	1.44002i
$993$	35.5689	−	8.11836i	1.12874	−	0.257628i
$994$	22.1614	+	19.5458i	0.702917	+	0.619955i
$995$	−0.220940	−	0.0504282i	−0.00700428	−	0.00159868i
$996$	−15.9868	−	2.25638i	−0.506560	−	0.0714963i
$997$	−1.70545	+	3.54141i	−0.0540123	+	0.112158i	−0.926228	−	0.376964i	$-0.876968\pi$
$997$	−1.70545	+	3.54141i	−0.0540123	+	0.112158i	0.872216	+	0.489121i	$0.162682\pi$
$998$	4.89652	+	2.79645i	0.154997	+	0.0885202i
$999$	4.13753			0.130906

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.2.j.a.111.3	yes	156
4.3	odd	2	inner	196.2.j.a.111.21	yes	156
49.34	odd	14	inner	196.2.j.a.83.21	yes	156
196.83	even	14	inner	196.2.j.a.83.3	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.j.a.83.3	✓	156	196.83	even	14	inner
196.2.j.a.83.21	yes	156	49.34	odd	14	inner
196.2.j.a.111.3	yes	156	1.1	even	1	trivial
196.2.j.a.111.21	yes	156	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35333 - 0.410501i) q^{2} +(-1.57092 - 1.96987i) q^{3} +(1.66298 + 1.11108i) q^{4} +(1.55435 - 1.23956i) q^{5} +(1.31733 + 3.31074i) q^{6} +(2.03422 - 1.69173i) q^{7} +(-1.79445 - 2.18631i) q^{8} +(-0.745040 + 3.26424i) q^{9} +(-2.61238 + 1.03946i) q^{10} +(3.09970 - 0.707487i) q^{11} +(-0.423717 - 5.02127i) q^{12} +(-5.38387 + 1.22883i) q^{13} +(-3.44741 + 1.45442i) q^{14} +(-4.88353 - 1.11463i) q^{15} +(1.53099 + 3.69541i) q^{16} +(2.48020 - 5.15019i) q^{17} +(2.34825 - 4.11173i) q^{18} -7.59495 q^{19} +(3.96210 - 0.334339i) q^{20} +(-6.52809 - 1.34957i) q^{21} +(-4.48533 - 0.314971i) q^{22} +(-0.751225 - 1.55993i) q^{23} +(-1.48781 + 6.96935i) q^{24} +(-0.233088 + 1.02123i) q^{25} +(7.79056 + 0.547072i) q^{26} +(0.790388 - 0.380631i) q^{27} +(5.26251 - 0.553135i) q^{28} +(0.626525 + 0.301719i) q^{29} +(6.15144 + 3.51315i) q^{30} +8.05654 q^{31} +(-0.554962 - 5.62957i) q^{32} +(-6.26305 - 4.99461i) q^{33} +(-5.47067 + 5.95175i) q^{34} +(1.06489 - 5.15108i) q^{35} +(-4.86582 + 4.60055i) q^{36} +(4.24933 + 2.04637i) q^{37} +(10.2784 + 3.11773i) q^{38} +(10.8783 + 8.67513i) q^{39} +(-5.49926 - 1.17398i) q^{40} +(-0.0970188 + 0.0773699i) q^{41} +(8.28063 + 4.50619i) q^{42} +(3.53279 + 2.81730i) q^{43} +(5.94082 + 2.26749i) q^{44} +(2.88814 + 5.99729i) q^{45} +(0.376297 + 2.41948i) q^{46} +(-0.299542 - 1.31238i) q^{47} +(4.87442 - 8.82105i) q^{48} +(1.27607 - 6.88271i) q^{49} +(0.734659 - 1.28637i) q^{50} +(-14.0414 + 3.20486i) q^{51} +(-10.3186 - 3.93840i) q^{52} +(0.183642 - 0.0884374i) q^{53} +(-1.22590 + 0.190662i) q^{54} +(3.94107 - 4.94194i) q^{55} +(-7.34895 - 1.41169i) q^{56} +(11.9311 + 14.9611i) q^{57} +(-0.724037 - 0.665513i) q^{58} +(-1.40598 + 1.76305i) q^{59} +(-6.88275 - 7.27961i) q^{60} +(0.524559 - 1.08926i) q^{61} +(-10.9031 - 3.30722i) q^{62} +(4.00665 + 7.90057i) q^{63} +(-1.55990 + 7.84645i) q^{64} +(-6.84523 + 8.58365i) q^{65} +(6.42565 + 9.33032i) q^{66} -3.71909i q^{67} +(9.84680 - 5.80894i) q^{68} +(-1.89276 + 3.93035i) q^{69} +(-3.55567 + 6.53394i) q^{70} +(-3.42655 - 7.11531i) q^{71} +(8.47357 - 4.22862i) q^{72} +(4.61124 + 1.05248i) q^{73} +(-4.91069 - 4.51376i) q^{74} +(2.37785 - 1.14511i) q^{75} +(-12.6302 - 8.43862i) q^{76} +(5.10859 - 6.68306i) q^{77} +(-11.1607 - 16.2058i) q^{78} +9.99726i q^{79} +(6.96037 + 3.84622i) q^{80} +(7.05839 + 3.39914i) q^{81} +(0.163058 - 0.0648804i) q^{82} +(0.712952 - 3.12364i) q^{83} +(-9.35659 - 9.49754i) q^{84} +(-2.52883 - 11.0795i) q^{85} +(-3.62451 - 5.26294i) q^{86} +(-0.389874 - 1.70815i) q^{87} +(-7.10905 - 5.50736i) q^{88} +(14.8115 + 3.38064i) q^{89} +(-1.44670 - 9.30187i) q^{90} +(-8.87310 + 11.6078i) q^{91} +(0.483945 - 3.42881i) q^{92} +(-12.6562 - 15.8703i) q^{93} +(-0.133355 + 1.89904i) q^{94} +(-11.8052 + 9.41436i) q^{95} +(-10.2177 + 9.93680i) q^{96} -3.30506i q^{97} +(-4.55230 + 8.79071i) q^{98} +10.6453i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26}+ \cdots + 105 q^{98}+O(q^{100}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Introduction

L-functions

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