LMFDB - Embedded newform 700.2.t.e.299.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(199,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("700.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.18
Character	$\chi$	$=$	700.299
Dual form			700.2.t.e.199.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.133142 - 1.40793i) q^{2} +(-1.52103 + 0.878165i) q^{3} +(-1.96455 - 0.374909i) q^{4} +(1.03388 + 2.25842i) q^{6} +(1.72616 - 2.00509i) q^{7} +(-0.789410 + 2.71603i) q^{8} +(0.0423472 - 0.0733475i) q^{9} +O(q^{10})$	\(q+(0.133142 - 1.40793i) q^{2} +(-1.52103 + 0.878165i) q^{3} +(-1.96455 - 0.374909i) q^{4} +(1.03388 + 2.25842i) q^{6} +(1.72616 - 2.00509i) q^{7} +(-0.789410 + 2.71603i) q^{8} +(0.0423472 - 0.0733475i) q^{9} +(-3.59956 + 2.07821i) q^{11} +(3.31736 - 1.15495i) q^{12} +4.90376 q^{13} +(-2.59321 - 2.69727i) q^{14} +(3.71889 + 1.47305i) q^{16} +(0.113880 + 0.197246i) q^{17} +(-0.0976301 - 0.0693876i) q^{18} +(-0.396093 + 0.686053i) q^{19} +(-0.864729 + 4.56564i) q^{21} +(2.44673 + 5.34464i) q^{22} +(2.72379 - 4.71775i) q^{23} +(-1.18441 - 4.82439i) q^{24} +(0.652895 - 6.90416i) q^{26} -5.12024i q^{27} +(-4.14284 + 3.29194i) q^{28} +8.17136 q^{29} +(2.11825 + 3.66891i) q^{31} +(2.56910 - 5.03981i) q^{32} +(3.65002 - 6.32202i) q^{33} +(0.292871 - 0.134074i) q^{34} +(-0.110692 + 0.128218i) q^{36} +(4.47631 + 2.58440i) q^{37} +(0.913180 + 0.649014i) q^{38} +(-7.45874 + 4.30631i) q^{39} -5.46577i q^{41} +(6.31299 + 1.82536i) q^{42} +4.95932 q^{43} +(7.85065 - 2.73323i) q^{44} +(-6.27962 - 4.46305i) q^{46} +(-5.01175 - 2.89353i) q^{47} +(-6.95011 + 1.02524i) q^{48} +(-1.04077 - 6.92220i) q^{49} +(-0.346429 - 0.200011i) q^{51} +(-9.63366 - 1.83846i) q^{52} +(9.38050 - 5.41584i) q^{53} +(-7.20895 - 0.681718i) q^{54} +(4.08324 + 6.27113i) q^{56} -1.39134i q^{57} +(1.08795 - 11.5047i) q^{58} +(-3.93063 - 6.80806i) q^{59} +(11.5731 + 6.68172i) q^{61} +(5.44760 - 2.49386i) q^{62} +(-0.0739705 - 0.211519i) q^{63} +(-6.75366 - 4.28813i) q^{64} +(-8.41501 - 5.98071i) q^{66} +(3.24881 + 5.62711i) q^{67} +(-0.149773 - 0.430194i) q^{68} +9.56776i q^{69} -2.03817i q^{71} +(0.165785 + 0.172918i) q^{72} +(-2.68098 - 4.64359i) q^{73} +(4.23464 - 5.95825i) q^{74} +(1.03535 - 1.19928i) q^{76} +(-2.04641 + 10.8048i) q^{77} +(5.06992 + 11.0748i) q^{78} +(4.42687 + 2.55585i) q^{79} +(4.62346 + 8.00806i) q^{81} +(-7.69544 - 0.727723i) q^{82} +9.52133i q^{83} +(3.41050 - 8.64523i) q^{84} +(0.660292 - 6.98238i) q^{86} +(-12.4289 + 7.17580i) q^{87} +(-2.80295 - 11.4171i) q^{88} +(2.01542 + 1.16361i) q^{89} +(8.46465 - 9.83247i) q^{91} +(-7.11975 + 8.24706i) q^{92} +(-6.44381 - 3.72034i) q^{93} +(-4.74117 + 6.67095i) q^{94} +(0.518122 + 9.92178i) q^{96} -17.7211 q^{97} +(-9.88455 + 0.543702i) q^{98} +0.352025i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 2 q^{4} + 32 q^{9}+O(q^{10}) $ 64 * q - 2 * q^4 + 32 * q^9	$ 64 q - 2 q^{4} + 32 q^{9} + 26 q^{14} + 2 q^{16} + 24 q^{21} + 36 q^{24} - 30 q^{26} - 16 q^{29} - 60 q^{36} - 24 q^{44} + 4 q^{46} - 40 q^{49} - 114 q^{54} - 62 q^{56} - 24 q^{61} - 80 q^{64} - 132 q^{66} + 2 q^{74} - 72 q^{81} - 134 q^{84} + 8 q^{86} + 120 q^{89} - 90 q^{94} + 186 q^{96}+O(q^{100}) $ 64 * q - 2 * q^4 + 32 * q^9 + 26 * q^14 + 2 * q^16 + 24 * q^21 + 36 * q^24 - 30 * q^26 - 16 * q^29 - 60 * q^36 - 24 * q^44 + 4 * q^46 - 40 * q^49 - 114 * q^54 - 62 * q^56 - 24 * q^61 - 80 * q^64 - 132 * q^66 + 2 * q^74 - 72 * q^81 - 134 * q^84 + 8 * q^86 + 120 * q^89 - 90 * q^94 + 186 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.133142	−	1.40793i	0.0941455	−	0.995558i
$2$	0.133142	−	1.40793i	0.0941455	−	0.995558i
$3$	−1.52103	+	0.878165i	−0.878165	+	0.507009i	−0.870053	−	0.492958i	$-0.835915\pi$
$3$	−1.52103	+	0.878165i	−0.878165	+	0.507009i	−0.00811200	+	0.999967i	$0.502582\pi$
$4$	−1.96455	−	0.374909i	−0.982273	−	0.187455i
$5$		0			0
$5$		0			0
$6$	1.03388	+	2.25842i	0.422082	+	0.921997i
$7$	1.72616	−	2.00509i	0.652426	−	0.757853i
$7$	1.72616	−	2.00509i	0.652426	−	0.757853i
$8$	−0.789410	+	2.71603i	−0.279099	+	0.960262i
$9$	0.0423472	−	0.0733475i	0.0141157	−	0.0244492i
$10$		0			0
$11$	−3.59956	+	2.07821i	−1.08531	+	0.626604i	−0.932324	−	0.361625i	$-0.882222\pi$
$11$	−3.59956	+	2.07821i	−1.08531	+	0.626604i	−0.152986	+	0.988228i	$0.548889\pi$
$12$	3.31736	−	1.15495i	0.957639	−	0.333405i
$13$	4.90376			1.36006			0.680029	−	0.733186i	$-0.261967\pi$
$13$	4.90376			1.36006			0.680029	+	0.733186i	$0.261967\pi$
$14$	−2.59321	−	2.69727i	−0.693064	−	0.720876i
$15$		0			0
$16$	3.71889	+	1.47305i	0.929722	+	0.368263i
$17$	0.113880	+	0.197246i	0.0276200	+	0.0478392i	0.879505	−	0.475890i	$-0.157874\pi$
$17$	0.113880	+	0.197246i	0.0276200	+	0.0478392i	−0.851885	+	0.523729i	$0.824541\pi$
$18$	−0.0976301	−	0.0693876i	−0.0230116	−	0.0163548i
$19$	−0.396093	+	0.686053i	−0.0908700	+	0.157391i	−0.907877	−	0.419236i	$-0.862298\pi$
$19$	−0.396093	+	0.686053i	−0.0908700	+	0.157391i	0.817007	+	0.576627i	$0.195631\pi$
$20$		0			0
$21$	−0.864729	+	4.56564i	−0.188699	+	0.996305i
$22$	2.44673	+	5.34464i	0.521644	+	1.13948i
$23$	2.72379	−	4.71775i	0.567950	−	0.983719i	−0.428818	−	0.903391i	$-0.641070\pi$
$23$	2.72379	−	4.71775i	0.567950	−	0.983719i	0.996768	−	0.0803281i	$-0.0255968\pi$
$24$	−1.18441	−	4.82439i	−0.241767	−	0.984774i
$25$		0			0
$26$	0.652895	−	6.90416i	0.128043	−	1.35402i
$27$		−	5.12024i		−	0.985390i
$28$	−4.14284	+	3.29194i	−0.782923	+	0.622118i
$29$	8.17136			1.51738			0.758692	−	0.651449i	$-0.225839\pi$
$29$	8.17136			1.51738			0.758692	+	0.651449i	$0.225839\pi$
$30$		0			0
$31$	2.11825	+	3.66891i	0.380448	+	0.658956i	0.991126	−	0.132923i	$-0.0424364\pi$
$31$	2.11825	+	3.66891i	0.380448	+	0.658956i	−0.610678	+	0.791879i	$0.709103\pi$
$32$	2.56910	−	5.03981i	0.454157	−	0.890922i
$33$	3.65002	−	6.32202i	0.635387	−	1.10052i
$34$	0.292871	−	0.134074i	0.0502270	−	0.0229934i
$35$		0			0
$36$	−0.110692	+	0.128218i	−0.0184486	+	0.0213697i
$37$	4.47631	+	2.58440i	0.735901	+	0.424873i	0.820577	−	0.571536i	$-0.193652\pi$
$37$	4.47631	+	2.58440i	0.735901	+	0.424873i	−0.0846759	+	0.996409i	$0.526986\pi$
$38$	0.913180	+	0.649014i	0.148137	+	0.105284i
$39$	−7.45874	+	4.30631i	−1.19435	+	0.689561i
$40$		0			0
$41$		−	5.46577i		−	0.853610i	−0.904344	−	0.426805i	$-0.859639\pi$
$41$		−	5.46577i		−	0.853610i	0.904344	−	0.426805i	$-0.140361\pi$
$42$	6.31299	+	1.82536i	0.974115	+	0.281659i
$43$	4.95932			0.756289			0.378144	−	0.925747i	$-0.376562\pi$
$43$	4.95932			0.756289			0.378144	+	0.925747i	$0.376562\pi$
$44$	7.85065	−	2.73323i	1.18353	−	0.412050i
$45$		0			0
$46$	−6.27962	−	4.46305i	−0.925880	−	0.658041i
$47$	−5.01175	−	2.89353i	−0.731038	−	0.422065i	0.0877636	−	0.996141i	$-0.472028\pi$
$47$	−5.01175	−	2.89353i	−0.731038	−	0.422065i	−0.818802	+	0.574076i	$0.805361\pi$
$48$	−6.95011	+	1.02524i	−1.00316	+	0.147981i
$49$	−1.04077	−	6.92220i	−0.148682	−	0.988885i
$50$		0			0
$51$	−0.346429	−	0.200011i	−0.0485098	−	0.0280071i
$52$	−9.63366	−	1.83846i	−1.33595	−	0.254949i
$53$	9.38050	−	5.41584i	1.28851	−	0.743922i	0.310123	−	0.950697i	$-0.399630\pi$
$53$	9.38050	−	5.41584i	1.28851	−	0.743922i	0.978389	+	0.206774i	$0.0662966\pi$
$54$	−7.20895	−	0.681718i	−0.981014	−	0.0927700i
$55$		0			0
$56$	4.08324	+	6.27113i	0.545646	+	0.838015i
$57$		−	1.39134i		−	0.184287i
$58$	1.08795	−	11.5047i	0.142855	−	1.51064i
$59$	−3.93063	−	6.80806i	−0.511725	−	0.886334i	−0.999908	−	0.0135921i	$-0.995673\pi$
$59$	−3.93063	−	6.80806i	−0.511725	−	0.886334i	0.488183	−	0.872741i	$-0.337660\pi$
$60$		0			0
$61$	11.5731	+	6.68172i	1.48178	+	0.855507i	0.999786	−	0.0206676i	$-0.00657915\pi$
$61$	11.5731	+	6.68172i	1.48178	+	0.855507i	0.481995	+	0.876174i	$0.339912\pi$
$62$	5.44760	−	2.49386i	0.691846	−	0.316721i
$63$	−0.0739705	−	0.211519i	−0.00931940	−	0.0266489i
$64$	−6.75366	−	4.28813i	−0.844208	−	0.536016i
$65$		0			0
$66$	−8.41501	−	5.98071i	−1.03582	−	0.736174i
$67$	3.24881	+	5.62711i	0.396906	+	0.687461i	0.993342	−	0.115199i	$-0.0367506\pi$
$67$	3.24881	+	5.62711i	0.396906	+	0.687461i	−0.596437	+	0.802660i	$0.703417\pi$
$68$	−0.149773	−	0.430194i	−0.0181627	−	0.0521686i
$69$			9.56776i			1.15182i
$70$		0			0
$71$		−	2.03817i		−	0.241886i	−0.992659	−	0.120943i	$-0.961408\pi$
$71$		−	2.03817i		−	0.241886i	0.992659	−	0.120943i	$-0.0385919\pi$
$72$	0.165785	+	0.172918i	0.0195379	+	0.0203785i
$73$	−2.68098	−	4.64359i	−0.313785	−	0.543491i	0.665394	−	0.746493i	$-0.268264\pi$
$73$	−2.68098	−	4.64359i	−0.313785	−	0.543491i	−0.979178	+	0.203002i	$0.934930\pi$
$74$	4.23464	−	5.95825i	0.492267	−	0.692633i
$75$		0			0
$76$	1.03535	−	1.19928i	0.118763	−	0.137567i
$77$	−2.04641	+	10.8048i	−0.233210	+	1.23132i
$78$	5.06992	+	11.0748i	0.574055	+	1.25397i
$79$	4.42687	+	2.55585i	0.498062	+	0.287556i	0.727913	−	0.685670i	$-0.240491\pi$
$79$	4.42687	+	2.55585i	0.498062	+	0.287556i	−0.229851	+	0.973226i	$0.573824\pi$
$80$		0			0
$81$	4.62346	+	8.00806i	0.513717	+	0.889784i
$82$	−7.69544	−	0.727723i	−0.849819	−	0.0803635i
$83$			9.52133i			1.04510i	0.852608	+	0.522551i	$0.175020\pi$
$83$			9.52133i			1.04510i	−0.852608	+	0.522551i	$0.824980\pi$
$84$	3.41050	−	8.64523i	0.372116	−	0.943271i
$85$		0			0
$86$	0.660292	−	6.98238i	0.0712012	−	0.752930i
$87$	−12.4289	+	7.17580i	−1.33251	+	0.769327i
$88$	−2.80295	−	11.4171i	−0.298796	−	1.21707i
$89$	2.01542	+	1.16361i	0.213634	+	0.123342i	0.602999	−	0.797742i	$-0.293972\pi$
$89$	2.01542	+	1.16361i	0.213634	+	0.123342i	−0.389365	+	0.921084i	$0.627305\pi$
$90$		0			0
$91$	8.46465	−	9.83247i	0.887336	−	1.03072i
$92$	−7.11975	+	8.24706i	−0.742285	+	0.859816i
$93$	−6.44381	−	3.72034i	−0.668192	−	0.385781i
$94$	−4.74117	+	6.67095i	−0.489014	+	0.688056i
$95$		0			0
$96$	0.518122	+	9.92178i	0.0528806	+	1.01264i
$97$	−17.7211			−1.79931			−0.899654	−	0.436603i	$-0.856181\pi$
$97$	−17.7211			−1.79931			−0.899654	+	0.436603i	$0.856181\pi$
$98$	−9.88455	+	0.543702i	−0.998491	+	0.0549222i
$99$			0.352025i			0.0353799i
$100$		0			0
$101$	−13.3283	+	7.69509i	−1.32621	+	0.765690i	−0.984712	−	0.174191i	$-0.944269\pi$
$101$	−13.3283	+	7.69509i	−1.32621	+	0.765690i	−0.341502	+	0.939881i	$0.610936\pi$
$102$	−0.327726	+	0.461119i	−0.0324497	+	0.0456576i
$103$	9.47127	+	5.46824i	0.933231	+	0.538801i	0.887832	−	0.460167i	$-0.152211\pi$
$103$	9.47127	+	5.46824i	0.933231	+	0.538801i	0.0453993	+	0.998969i	$0.485544\pi$
$104$	−3.87107	+	13.3188i	−0.379590	+	1.30601i
$105$		0			0
$106$	−6.37619	−	13.9282i	−0.619311	−	1.35283i
$107$	−2.36075	+	4.08895i	−0.228223	+	0.395293i	−0.957281	−	0.289158i	$-0.906625\pi$
$107$	−2.36075	+	4.08895i	−0.228223	+	0.395293i	0.729059	+	0.684451i	$0.239958\pi$
$108$	−1.91962	+	10.0589i	−0.184716	+	0.967923i
$109$	4.06945	+	7.04850i	0.389783	+	0.675124i	0.992420	−	0.122891i	$-0.0392167\pi$
$109$	4.06945	+	7.04850i	0.389783	+	0.675124i	−0.602637	+	0.798015i	$0.705883\pi$
$110$		0			0
$111$	−9.07812			−0.861657
$112$	9.37298	−	4.91398i	0.885664	−	0.464328i
$113$			9.50633i			0.894280i	0.894464	+	0.447140i	$0.147557\pi$
$113$			9.50633i			0.894280i	−0.894464	+	0.447140i	$0.852443\pi$
$114$	−1.95891	−	0.185245i	−0.183469	−	0.0173498i
$115$		0			0
$116$	−16.0530	−	3.06352i	−1.49049	−	0.284441i
$117$	0.207660	−	0.359678i	0.0191982	−	0.0332523i
$118$	−10.1086	+	4.62763i	−0.930574	+	0.426008i
$119$	0.592071	+	0.112138i	0.0542750	+	0.0102796i
$120$		0			0
$121$	3.13791	−	5.43502i	0.285265	−	0.494093i
$122$	10.9483	−	15.4045i	0.991210	−	1.39466i
$123$	4.79985	+	8.31358i	0.432788	+	0.749610i
$124$	−2.78588	−	8.00189i	−0.250180	−	0.718591i
$125$		0			0
$126$	−0.307653	+	0.0759834i	−0.0274079	+	0.00676914i
$127$	12.3200			1.09322			0.546612	−	0.837386i	$-0.315917\pi$
$127$	12.3200			1.09322			0.546612	+	0.837386i	$0.315917\pi$
$128$	−6.93659	+	8.93777i	−0.613113	+	0.789995i
$129$	−7.54325	+	4.35510i	−0.664146	+	0.383445i
$130$		0			0
$131$	−8.32817	+	14.4248i	−0.727635	+	1.26030i	0.230245	+	0.973133i	$0.426047\pi$
$131$	−8.32817	+	14.4248i	−0.727635	+	1.26030i	−0.957880	+	0.287169i	$0.907286\pi$
$132$	−9.54082	+	11.0515i	−0.830422	+	0.961908i
$133$	0.691880	+	1.97844i	0.0599936	+	0.171552i
$134$	8.35514	−	3.82491i	0.721774	−	0.330422i
$135$		0			0
$136$	−0.625625	+	0.153594i	−0.0536469	+	0.0131706i
$137$	3.81315	−	2.20153i	0.325780	−	0.188089i	−0.328186	−	0.944613i	$-0.606437\pi$
$137$	3.81315	−	2.20153i	0.325780	−	0.188089i	0.653966	+	0.756524i	$0.273104\pi$
$138$	13.4708	+	1.27387i	1.14671	+	0.108439i
$139$	13.2240			1.12164			0.560822	−	0.827936i	$-0.310485\pi$
$139$	13.2240			1.12164			0.560822	+	0.827936i	$0.310485\pi$
$140$		0			0
$141$	10.1640			0.855963
$142$	−2.86961	−	0.271366i	−0.240812	−	0.0227725i
$143$	−17.6514	+	10.1910i	−1.47608	+	0.852217i
$144$	0.265529	−	0.210391i	0.0221274	−	0.0175326i
$145$		0			0
$146$	−6.89481	+	3.15638i	−0.570619	+	0.261224i
$147$	7.66187	+	9.61487i	0.631940	+	0.793021i
$148$	−7.82501	−	6.75538i	−0.643212	−	0.555289i
$149$	−5.77374	+	10.0004i	−0.473003	+	0.819265i	−0.999523	−	0.0308978i	$-0.990163\pi$
$149$	−5.77374	+	10.0004i	−0.473003	+	0.819265i	0.526520	+	0.850163i	$0.323497\pi$
$150$		0			0
$151$	14.9095	−	8.60802i	1.21332	−	0.700511i	0.249839	−	0.968287i	$-0.419622\pi$
$151$	14.9095	−	8.60802i	1.21332	−	0.700511i	0.963481	+	0.267776i	$0.0862888\pi$
$152$	−1.55066	−	1.61738i	−0.125775	−	0.131187i
$153$	0.0192900			0.00155950
$154$	14.9399	+	4.31978i	1.20389	+	0.348097i
$155$		0			0
$156$	16.2675	−	5.66359i	1.30244	−	0.453450i
$157$	−10.4421	−	18.0862i	−0.833369	−	1.44344i	−0.895352	−	0.445359i	$-0.853076\pi$
$157$	−10.4421	−	18.0862i	−0.833369	−	1.44344i	0.0619833	−	0.998077i	$-0.480257\pi$
$158$	4.18787	−	5.89244i	0.333169	−	0.468777i
$159$	−9.51200	+	16.4753i	−0.754350	+	1.30657i
$160$		0			0
$161$	−4.75782	−	13.6050i	−0.374969	−	1.07223i
$162$	11.8904	−	5.44330i	0.934196	−	0.427666i
$163$	3.60798	−	6.24921i	0.282599	−	0.489476i	−0.689425	−	0.724357i	$-0.742137\pi$
$163$	3.60798	−	6.24921i	0.282599	−	0.489476i	0.972024	+	0.234881i	$0.0754701\pi$
$164$	−2.04917	+	10.7378i	−0.160013	+	0.838478i
$165$		0			0
$166$	13.4054	+	1.26769i	1.04046	+	0.0983916i
$167$		−	14.7801i		−	1.14372i	−0.820351	−	0.571860i	$-0.806222\pi$
$167$		−	14.7801i		−	1.14372i	0.820351	−	0.571860i	$-0.193778\pi$
$168$	−11.7178	−	5.95280i	−0.904049	−	0.459268i
$169$	11.0468			0.849756
$170$		0			0
$171$	0.0335469	+	0.0581049i	0.00256539	+	0.00444339i
$172$	−9.74281	−	1.85929i	−0.742882	−	0.141770i
$173$	9.38545	−	16.2561i	0.713563	−	1.23593i	−0.249949	−	0.968259i	$-0.580414\pi$
$173$	9.38545	−	16.2561i	0.713563	−	1.23593i	0.963511	−	0.267667i	$-0.0862529\pi$
$174$	8.44825	+	18.4544i	0.640460	+	1.39902i
$175$		0			0
$176$	−16.4477	+	2.42627i	−1.23979	+	0.182887i
$177$	11.9572	+	6.90349i	0.898758	+	0.518898i
$178$	1.90661	−	2.68265i	0.142907	−	0.201073i
$179$	11.1064	−	6.41230i	0.830134	−	0.479278i	−0.0237648	−	0.999718i	$-0.507565\pi$
$179$	11.1064	−	6.41230i	0.830134	−	0.479278i	0.853898	+	0.520440i	$0.174232\pi$
$180$		0			0
$181$		−	8.55295i		−	0.635736i	−0.948135	−	0.317868i	$-0.897033\pi$
$181$		−	8.55295i		−	0.635736i	0.948135	−	0.317868i	$-0.102967\pi$
$182$	−12.7165	−	13.2268i	−0.942606	−	0.980433i
$183$	−23.4706			−1.73500
$184$	10.6634	+	11.1222i	0.786114	+	0.819936i
$185$		0			0
$186$	−6.09593	+	8.57712i	−0.446975	+	0.628905i
$187$	−0.819837	−	0.473333i	−0.0599524	−	0.0346135i
$188$	8.76100	+	7.56343i	0.638961	+	0.551620i
$189$	−10.2665	−	8.83833i	−0.746781	−	0.642894i
$190$		0			0
$191$	−0.426822	−	0.246426i	−0.0308837	−	0.0178307i	0.484479	−	0.874803i	$-0.339009\pi$
$191$	−0.426822	−	0.246426i	−0.0308837	−	0.0178307i	−0.515362	+	0.856972i	$0.672343\pi$
$192$	14.0382	+	0.591523i	1.01312	+	0.0426895i
$193$	−23.3615	+	13.4878i	−1.68160	+	0.970870i	−0.720994	+	0.692941i	$0.756314\pi$
$193$	−23.3615	+	13.4878i	−1.68160	+	0.970870i	−0.960602	+	0.277928i	$0.910352\pi$
$194$	−2.35942	+	24.9502i	−0.169397	+	1.79132i
$195$		0			0
$196$	−0.550552	+	13.9892i	−0.0393251	+	0.999226i
$197$		−	2.48025i		−	0.176710i	−0.996089	−	0.0883552i	$-0.971839\pi$
$197$		−	2.48025i		−	0.176710i	0.996089	−	0.0883552i	$-0.0281611\pi$
$198$	0.495628	+	0.0468693i	0.0352227	+	0.00333086i
$199$	−2.76798	−	4.79428i	−0.196217	−	0.339858i	0.751082	−	0.660209i	$-0.229532\pi$
$199$	−2.76798	−	4.79428i	−0.196217	−	0.339858i	−0.947299	+	0.320351i	$0.896199\pi$
$200$		0			0
$201$	−9.88306	−	5.70599i	−0.697097	−	0.402469i
$202$	9.05961	+	19.7899i	0.637432	+	1.39241i
$203$	14.1050	−	16.3843i	0.989980	−	1.14995i
$204$	0.605590	+	0.522810i	0.0423998	+	0.0366040i
$205$		0			0
$206$	8.95993	−	12.6068i	0.624268	−	0.878361i
$207$	−0.230690	−	0.399567i	−0.0160341	−	0.0277718i
$208$	18.2365	+	7.22349i	1.26447	+	0.500859i
$209$		−	3.29266i		−	0.227758i
$210$		0			0
$211$			21.7260i			1.49568i	0.663879	+	0.747840i	$0.268909\pi$
$211$			21.7260i			1.49568i	−0.663879	+	0.747840i	$0.731091\pi$
$212$	−20.4589	+	7.12283i	−1.40512	+	0.489198i
$213$	1.78985	+	3.10011i	0.122638	+	0.212416i
$214$	5.44264	+	3.86819i	0.372051	+	0.264424i
$215$		0			0
$216$	13.9067	+	4.04197i	0.946233	+	0.275021i
$217$	11.0129	+	2.08584i	0.747605	+	0.141596i
$218$	10.4656	−	4.79106i	0.708822	−	0.324492i
$219$	8.15568	+	4.70868i	0.551110	+	0.318183i
$220$		0			0
$221$	0.558440	+	0.967246i	0.0375647	+	0.0650640i
$222$	−1.20868	+	12.7814i	−0.0811211	+	0.857830i
$223$		−	24.6124i		−	1.64817i	−0.566467	−	0.824084i	$-0.691690\pi$
$223$		−	24.6124i		−	1.64817i	0.566467	−	0.824084i	$-0.308310\pi$
$224$	−5.67062	−	13.8508i	−0.378884	−	0.925444i
$225$		0			0
$226$	13.3843	+	1.26569i	0.890308	+	0.0841924i
$227$	7.10120	−	4.09988i	0.471323	−	0.272119i	−0.245470	−	0.969404i	$-0.578942\pi$
$227$	7.10120	−	4.09988i	0.471323	−	0.272119i	0.716793	+	0.697286i	$0.245609\pi$
$228$	−0.521626	+	2.73335i	−0.0345455	+	0.181021i
$229$	4.20964	+	2.43044i	0.278181	+	0.160608i	0.632600	−	0.774479i	$-0.281988\pi$
$229$	4.20964	+	2.43044i	0.278181	+	0.160608i	−0.354419	+	0.935087i	$0.615321\pi$
$230$		0			0
$231$	−6.37572	−	18.2314i	−0.419491	−	1.19954i
$232$	−6.45056	+	22.1937i	−0.423500	+	1.45709i
$233$	−18.3238	−	10.5793i	−1.20043	−	0.693071i	−0.239783	−	0.970827i	$-0.577076\pi$
$233$	−18.3238	−	10.5793i	−1.20043	−	0.693071i	−0.960652	+	0.277755i	$0.910410\pi$
$234$	−0.478754	−	0.340260i	−0.0312972	−	0.0222435i
$235$		0			0
$236$	5.16951	+	14.8484i	0.336506	+	0.966547i
$237$	−8.97784			−0.583174
$238$	0.236712	−	0.818665i	0.0153437	−	0.0530662i
$239$		−	2.45963i		−	0.159100i	−0.996831	−	0.0795500i	$-0.974652\pi$
$239$		−	2.45963i		−	0.159100i	0.996831	−	0.0795500i	$-0.0253483\pi$
$240$		0			0
$241$	−1.36901	+	0.790395i	−0.0881854	+	0.0509138i	−0.543444	−	0.839445i	$-0.682880\pi$
$241$	−1.36901	+	0.790395i	−0.0881854	+	0.0509138i	0.455259	+	0.890359i	$0.349547\pi$
$242$	−7.23435	−	5.14159i	−0.465042	−	0.330514i
$243$	−0.762024	−	0.439955i	−0.0488839	−	0.0282231i
$244$	−20.2308	−	17.4654i	−1.29515	−	1.11811i
$245$		0			0
$246$	12.3440	−	5.65098i	0.787026	−	0.360293i
$247$	−1.94234	+	3.36424i	−0.123588	+	0.214061i
$248$	−11.6370	+	2.85695i	−0.738953	+	0.181417i
$249$	−8.36130	−	14.4822i	−0.529876	−	0.917772i
$250$		0			0
$251$	−26.3036			−1.66027			−0.830135	−	0.557562i	$-0.811737\pi$
$251$	−26.3036			−1.66027			−0.830135	+	0.557562i	$0.811737\pi$
$252$	0.0660179	+	0.443271i	0.00415874	+	0.0279235i
$253$			22.6425i			1.42352i
$254$	1.64031	−	17.3457i	0.102922	−	1.08837i
$255$		0			0
$256$	11.6602	+	10.9562i	0.728764	+	0.684765i
$257$	5.99938	−	10.3912i	0.374231	−	0.648187i	−0.615981	−	0.787761i	$-0.711240\pi$
$257$	5.99938	−	10.3912i	0.374231	−	0.648187i	0.990212	+	0.139574i	$0.0445734\pi$
$258$	5.12736	+	11.2002i	0.319216	+	0.697296i
$259$	12.9088	−	4.51433i	0.802112	−	0.280507i
$260$		0			0
$261$	0.346034	−	0.599349i	0.0214190	−	0.0370988i
$262$	19.2003	+	13.6460i	1.18620	+	0.843055i
$263$	4.85628	+	8.41133i	0.299451	+	0.518665i	0.976011	−	0.217723i	$-0.0698631\pi$
$263$	4.85628	+	8.41133i	0.299451	+	0.518665i	−0.676559	+	0.736388i	$0.736530\pi$
$264$	14.2895	+	14.9042i	0.879455	+	0.917293i
$265$		0			0
$266$	2.87762	−	0.710708i	0.176438	−	0.0435763i
$267$	−4.08735			−0.250142
$268$	−4.27279	−	12.2727i	−0.261002	−	0.749676i
$269$	−2.91623	+	1.68369i	−0.177806	+	0.102656i	−0.586261	−	0.810122i	$-0.699401\pi$
$269$	−2.91623	+	1.68369i	−0.177806	+	0.102656i	0.408456	+	0.912778i	$0.366067\pi$
$270$		0			0
$271$	−4.96774	+	8.60437i	−0.301768	+	0.522678i	−0.976537	−	0.215352i	$-0.930910\pi$
$271$	−4.96774	+	8.60437i	−0.301768	+	0.522678i	0.674768	+	0.738030i	$0.264244\pi$
$272$	0.132953	+	0.901287i	0.00806146	+	0.0546485i
$273$	−4.24042	+	22.3888i	−0.256642	+	1.35503i
$274$	−2.59191	−	5.66178i	−0.156583	−	0.342041i
$275$		0			0
$276$	3.58704	−	18.7963i	0.215915	−	1.13141i
$277$	0.347087	−	0.200391i	0.0208544	−	0.0120403i	−0.489537	−	0.871983i	$-0.662834\pi$
$277$	0.347087	−	0.200391i	0.0208544	−	0.0120403i	0.510391	+	0.859942i	$0.329501\pi$
$278$	1.76067	−	18.6185i	0.105598	−	1.11666i
$279$	0.358807			0.0214812
$280$		0			0
$281$	−21.4548			−1.27988			−0.639942	−	0.768423i	$-0.721042\pi$
$281$	−21.4548			−1.27988			−0.639942	+	0.768423i	$0.721042\pi$
$282$	1.35325	−	14.3102i	0.0805850	−	0.852161i
$283$	−17.6896	+	10.2131i	−1.05154	+	0.607106i	−0.923080	−	0.384609i	$-0.874336\pi$
$283$	−17.6896	+	10.2131i	−1.05154	+	0.607106i	−0.128459	+	0.991715i	$0.541003\pi$
$284$	−0.764129	+	4.00408i	−0.0453427	+	0.237598i
$285$		0			0
$286$	11.9981	+	26.2088i	0.709465	+	1.54976i
$287$	−10.9594	−	9.43477i	−0.646911	−	0.556917i
$288$	−0.260864	−	0.401859i	−0.0153715	−	0.0236798i
$289$	8.47406	−	14.6775i	0.498474	−	0.863383i
$290$		0			0
$291$	26.9543	−	15.5621i	1.58009	−	0.912265i
$292$	3.52598	+	10.1277i	0.206342	+	0.592677i
$293$	4.64138			0.271152			0.135576	−	0.990767i	$-0.456711\pi$
$293$	4.64138			0.271152			0.135576	+	0.990767i	$0.456711\pi$
$294$	14.5572	−	9.50725i	0.848993	−	0.554474i
$295$		0			0
$296$	−10.5530	+	10.1177i	−0.613378	+	0.588077i
$297$	10.6409	+	18.4306i	0.617449	+	1.06945i
$298$	13.3112	+	9.46050i	0.771095	+	0.548032i
$299$	13.3568	−	23.1347i	0.772445	−	1.33791i
$300$		0			0
$301$	8.56055	−	9.94388i	0.493422	−	0.573155i
$302$	−10.1344	−	22.1377i	−0.583171	−	1.27388i
$303$	13.5151	−	23.4089i	0.776423	−	1.34480i
$304$	−2.48362	+	1.96789i	−0.142445	+	0.112866i
$305$		0			0
$306$	0.00256831	−	0.0271590i	0.000146820	−	0.00155258i
$307$			6.02430i			0.343825i	0.985112	+	0.171912i	$0.0549946\pi$
$307$			6.02430i			0.343825i	−0.985112	+	0.171912i	$0.945005\pi$
$308$	8.07108	−	20.4592i	0.459892	−	1.16577i
$309$	−19.2081			−1.09271
$310$		0			0
$311$	11.5074	+	19.9313i	0.652522	+	1.13020i	0.982509	+	0.186216i	$0.0596223\pi$
$311$	11.5074	+	19.9313i	0.652522	+	1.13020i	−0.329987	+	0.943986i	$0.607044\pi$
$312$	−5.80806	−	23.6576i	−0.328817	−	1.33935i
$313$	−4.26073	+	7.37980i	−0.240831	+	0.417131i	−0.960951	−	0.276718i	$-0.910753\pi$
$313$	−4.26073	+	7.37980i	−0.240831	+	0.417131i	0.720120	+	0.693849i	$0.244087\pi$
$314$	−26.8544	+	12.2937i	−1.51548	+	0.693774i
$315$		0			0
$316$	−7.73857	−	6.68077i	−0.435329	−	0.375822i
$317$	3.63973	+	2.10140i	0.204428	+	0.118026i	0.598719	−	0.800959i	$-0.295677\pi$
$317$	3.63973	+	2.10140i	0.204428	+	0.118026i	−0.394291	+	0.918985i	$0.629010\pi$
$318$	21.9296	+	15.5858i	1.22975	+	0.874008i
$319$	−29.4133	+	16.9818i	−1.64683	+	0.950799i
$320$		0			0
$321$		−	8.29252i		−	0.462844i
$322$	−19.7884	+	4.88729i	−1.10277	+	0.272358i
$323$	−0.180428			−0.0100393
$324$	−6.08070	−	17.4656i	−0.337817	−	0.970310i
$325$		0			0
$326$	−8.31809	−	5.91182i	−0.460696	−	0.327426i
$327$	−12.3795	−	7.14730i	−0.684587	−	0.395247i
$328$	14.8452	+	4.31474i	0.819690	+	0.238241i
$329$	−14.4528	+	5.05431i	−0.796811	+	0.278653i
$330$		0			0
$331$	−9.27412	−	5.35442i	−0.509752	−	0.294305i	0.222980	−	0.974823i	$-0.428422\pi$
$331$	−9.27412	−	5.35442i	−0.509752	−	0.294305i	−0.732732	+	0.680518i	$0.761755\pi$
$332$	3.56964	−	18.7051i	0.195909	−	1.02658i
$333$	0.379119	−	0.218884i	0.0207756	−	0.0119948i
$334$	−20.8094	−	1.96785i	−1.13864	−	0.107676i
$335$		0			0
$336$	−9.94127	+	15.7053i	−0.542340	+	0.856795i
$337$		−	28.6850i		−	1.56257i	−0.624173	−	0.781286i	$-0.714564\pi$
$337$		−	28.6850i		−	1.56257i	0.624173	−	0.781286i	$-0.285436\pi$
$338$	1.47079	−	15.5532i	0.0800007	−	0.845982i
$339$	−8.34812	−	14.4594i	−0.453408	−	0.785326i
$340$		0			0
$341$	−15.2495	−	8.80432i	−0.825808	−	0.476780i
$342$	0.0862742	−	0.0394955i	0.00466517	−	0.00213567i
$343$	−15.6762	−	9.86195i	−0.846433	−	0.532495i
$344$	−3.91493	+	13.4697i	−0.211079	+	0.726236i
$345$		0			0
$346$	−21.6379	−	15.3784i	−1.16326	−	0.826750i
$347$	11.7072	+	20.2775i	0.628475	+	1.08855i	0.987858	+	0.155361i	$0.0496540\pi$
$347$	11.7072	+	20.2775i	0.628475	+	1.08855i	−0.359383	+	0.933190i	$0.617013\pi$
$348$	27.1073	−	9.43751i	1.45311	−	0.505904i
$349$		−	19.7474i		−	1.05706i	−0.848916	−	0.528528i	$-0.822744\pi$
$349$		−	19.7474i		−	1.05706i	0.848916	−	0.528528i	$-0.177256\pi$
$350$		0			0
$351$		−	25.1084i		−	1.34019i
$352$	1.22616	+	23.4803i	0.0653543	+	1.25150i
$353$	10.7803	+	18.6720i	0.573776	+	0.993809i	0.996173	+	0.0873982i	$0.0278552\pi$
$353$	10.7803	+	18.6720i	0.573776	+	0.993809i	−0.422398	+	0.906411i	$0.638811\pi$
$354$	11.3116	−	15.9158i	0.601207	−	0.845914i
$355$		0			0
$356$	−3.52315	−	3.04156i	−0.186726	−	0.161202i
$357$	−0.999030	+	0.349371i	−0.0528743	+	0.0184907i
$358$	−7.54936	−	16.4908i	−0.398996	−	0.871568i
$359$	−6.74629	−	3.89497i	−0.356056	−	0.205569i	0.311294	−	0.950314i	$-0.399238\pi$
$359$	−6.74629	−	3.89497i	−0.356056	−	0.205569i	−0.667349	+	0.744745i	$0.732571\pi$
$360$		0			0
$361$	9.18622	+	15.9110i	0.483485	+	0.837421i
$362$	−12.0420	−	1.13876i	−0.632912	−	0.0598516i
$363$			11.0224i			0.578526i
$364$	−20.3155	+	16.1429i	−1.06482	+	0.846117i
$365$		0			0
$366$	−3.12492	+	33.0450i	−0.163342	+	1.72729i
$367$	4.79223	−	2.76679i	0.250152	−	0.144425i	−0.369682	−	0.929158i	$-0.620533\pi$
$367$	4.79223	−	2.76679i	0.250152	−	0.144425i	0.619834	+	0.784733i	$0.287200\pi$
$368$	17.0790	−	13.5325i	0.890303	−	0.705429i
$369$	−0.400901	−	0.231460i	−0.0208701	−	0.0120493i
$370$		0			0
$371$	5.33297	−	28.1573i	0.276874	−	1.46186i
$372$	11.2644	+	9.72462i	0.584031	+	0.504198i
$373$	8.20453	+	4.73689i	0.424814	+	0.245267i	0.697135	−	0.716940i	$-0.254458\pi$
$373$	8.20453	+	4.73689i	0.424814	+	0.245267i	−0.272321	+	0.962207i	$0.587791\pi$
$374$	−0.775576	+	1.09125i	−0.0401041	+	0.0564274i
$375$		0			0
$376$	11.8153	−	11.3279i	0.609325	−	0.584191i
$377$	40.0704			2.06373
$378$	−13.8107	+	13.2778i	−0.710344	+	0.682938i
$379$		−	23.6212i		−	1.21334i	−0.794954	−	0.606670i	$-0.792505\pi$
$379$		−	23.6212i		−	1.21334i	0.794954	−	0.606670i	$-0.207495\pi$
$380$		0			0
$381$	−18.7390	+	10.8190i	−0.960030	+	0.554274i
$382$	−0.403778	+	0.568127i	−0.0206591	+	0.0290679i
$383$	−14.6082	−	8.43407i	−0.746446	−	0.430961i	0.0779625	−	0.996956i	$-0.475159\pi$
$383$	−14.6082	−	8.43407i	−0.746446	−	0.430961i	−0.824408	+	0.565996i	$0.808492\pi$
$384$	2.70189	−	19.6861i	0.137880	−	1.00460i
$385$		0			0
$386$	15.8795	+	34.6872i	0.808243	+	1.76553i
$387$	0.210013	−	0.363754i	0.0106756	−	0.0184906i
$388$	34.8140	+	6.64382i	1.76741	+	0.337289i
$389$	−5.17328	−	8.96039i	−0.262296	−	0.454310i	0.704556	−	0.709649i	$-0.251146\pi$
$389$	−5.17328	−	8.96039i	−0.262296	−	0.454310i	−0.966852	+	0.255339i	$0.917813\pi$
$390$		0			0
$391$	1.24074			0.0627471
$392$	19.6225	+	2.63768i	0.991086	+	0.133223i
$393$		−	29.2540i		−	1.47567i
$394$	−3.49202	−	0.330225i	−0.175926	−	0.0166365i
$395$		0			0
$396$	0.131978	−	0.691570i	0.00663212	−	0.0347527i
$397$	−1.29257	+	2.23880i	−0.0648724	+	0.112362i	−0.896637	−	0.442766i	$-0.853997\pi$
$397$	−1.29257	+	2.23880i	−0.0648724	+	0.112362i	0.831765	+	0.555128i	$0.187331\pi$
$398$	−7.11856	+	3.25881i	−0.356821	+	0.163349i
$399$	−2.78976	−	2.40167i	−0.139663	−	0.120234i
$400$		0			0
$401$	−3.98844	+	6.90819i	−0.199173	+	0.344978i	−0.948261	−	0.317493i	$-0.897159\pi$
$401$	−3.98844	+	6.90819i	−0.199173	+	0.344978i	0.749087	+	0.662471i	$0.230492\pi$
$402$	−9.34949	+	13.1550i	−0.466310	+	0.656111i
$403$	10.3874	+	17.9914i	0.517431	+	0.896217i
$404$	29.0690	−	10.1205i	1.44624	−	0.503512i
$405$		0			0
$406$	−21.1900	−	22.0404i	−1.05164	−	1.09385i
$407$	−21.4837			−1.06491
$408$	0.816711	−	0.783022i	0.0404332	−	0.0387654i
$409$	5.63217	−	3.25173i	0.278493	−	0.160788i	−0.354248	−	0.935151i	$-0.615263\pi$
$409$	5.63217	−	3.25173i	0.278493	−	0.160788i	0.632741	+	0.774364i	$0.281930\pi$
$410$		0			0
$411$	−3.86661	+	6.69716i	−0.190726	+	0.330346i
$412$	−16.5566	−	14.2935i	−0.815688	−	0.704189i
$413$	−20.4357	−	3.87049i	−1.00557	−	0.190455i
$414$	−0.593278	+	0.271597i	−0.0291580	+	0.0133483i
$415$		0			0
$416$	12.5982	−	24.7140i	0.617679	−	1.21170i
$417$	−20.1140	+	11.6128i	−0.984989	+	0.568684i
$418$	−4.63584	−	0.438390i	−0.226746	−	0.0214424i
$419$	−29.4385			−1.43817			−0.719083	−	0.694924i	$-0.755438\pi$
$419$	−29.4385			−1.43817			−0.719083	+	0.694924i	$0.755438\pi$
$420$		0			0
$421$	−11.3233			−0.551863			−0.275932	−	0.961177i	$-0.588986\pi$
$421$	−11.3233			−0.551863			−0.275932	+	0.961177i	$0.588986\pi$
$422$	30.5887	+	2.89264i	1.48904	+	0.140811i
$423$	−0.424467	+	0.245066i	−0.0206383	+	0.0119155i
$424$	7.30452	+	29.7531i	0.354739	+	1.44494i
$425$		0			0
$426$	4.60305	−	2.10723i	0.223018	−	0.102096i
$427$	33.3744	−	11.6714i	1.61510	−	0.564817i
$428$	6.17079	−	7.14785i	0.298277	−	0.345505i
$429$	17.8988	−	31.0017i	0.864163	−	1.49677i
$430$		0			0
$431$	28.5918	−	16.5075i	1.37722	−	0.795136i	0.385393	−	0.922753i	$-0.374066\pi$
$431$	28.5918	−	16.5075i	1.37722	−	0.795136i	0.991824	+	0.127616i	$0.0407325\pi$
$432$	7.54238	−	19.0416i	0.362883	−	0.916139i
$433$	18.9367			0.910041			0.455021	−	0.890481i	$-0.349632\pi$
$433$	18.9367			0.910041			0.455021	+	0.890481i	$0.349632\pi$
$434$	4.40300	−	15.2277i	0.211351	−	0.730954i
$435$		0			0
$436$	−5.35208	−	15.3728i	−0.256318	−	0.736223i
$437$	2.15775	+	3.73734i	0.103219	+	0.178781i
$438$	7.71537	−	10.8557i	0.368654	−	0.518706i
$439$	−12.1486	+	21.0420i	−0.579820	+	1.00428i	0.415680	+	0.909511i	$0.363544\pi$
$439$	−12.1486	+	21.0420i	−0.579820	+	1.00428i	−0.995500	+	0.0947665i	$0.969790\pi$
$440$		0			0
$441$	−0.551800	−	0.216798i	−0.0262762	−	0.0103237i
$442$	1.43617	−	0.657465i	0.0683116	−	0.0312724i
$443$	7.50299	−	12.9956i	0.356478	−	0.617438i	−0.630892	−	0.775871i	$-0.717311\pi$
$443$	7.50299	−	12.9956i	0.356478	−	0.617438i	0.987370	+	0.158433i	$0.0506442\pi$
$444$	17.8344	+	3.40347i	0.846382	+	0.161522i
$445$		0			0
$446$	−34.6526	−	3.27694i	−1.64085	−	0.155168i
$447$		−	20.2812i		−	0.959267i
$448$	−20.2560	+	6.13973i	−0.957004	+	0.290075i
$449$	−10.9965			−0.518957			−0.259479	−	0.965749i	$-0.583551\pi$
$449$	−10.9965			−0.518957			−0.259479	+	0.965749i	$0.583551\pi$
$450$		0			0
$451$	11.3590	+	19.6744i	0.534875	+	0.926431i
$452$	3.56401	−	18.6756i	0.167637	−	0.878428i
$453$	−15.1185	+	26.1861i	−0.710330	+	1.23033i
$454$	−4.82689	−	10.5439i	−0.226537	−	0.494848i
$455$		0			0
$456$	3.77892	+	1.09834i	0.176964	+	0.0514344i
$457$	−14.3732	−	8.29835i	−0.672348	−	0.388180i	0.124618	−	0.992205i	$-0.460230\pi$
$457$	−14.3732	−	8.29835i	−0.672348	−	0.388180i	−0.796966	+	0.604024i	$0.793563\pi$
$458$	3.98237	−	5.60330i	0.186084	−	0.261825i
$459$	1.00995	−	0.583093i	0.0471403	−	0.0272164i
$460$		0			0
$461$		−	6.62872i		−	0.308730i	−0.988014	−	0.154365i	$-0.950667\pi$
$461$		−	6.62872i		−	0.308730i	0.988014	−	0.154365i	$-0.0493332\pi$
$462$	−26.5175	+	6.54921i	−1.23370	+	0.304697i
$463$	2.10944			0.0980341			0.0490170	−	0.998798i	$-0.484391\pi$
$463$	2.10944			0.0980341			0.0490170	+	0.998798i	$0.484391\pi$
$464$	30.3884	+	12.0369i	1.41074	+	0.558797i
$465$		0			0
$466$	−17.3346	+	24.3902i	−0.803009	+	1.12985i
$467$	9.85173	+	5.68790i	0.455883	+	0.263204i	0.710312	−	0.703887i	$-0.248554\pi$
$467$	9.85173	+	5.68790i	0.455883	+	0.263204i	−0.254428	+	0.967092i	$0.581887\pi$
$468$	−0.542805	+	0.628751i	−0.0250912	+	0.0290640i
$469$	16.8908	+	3.19911i	0.779946	+	0.147721i
$470$		0			0
$471$	31.7653	+	18.3397i	1.46367	+	0.845050i
$472$	21.5938	−	5.30138i	0.993935	−	0.244016i
$473$	−17.8514	+	10.3065i	−0.820807	+	0.473893i
$474$	−1.19533	+	12.6402i	−0.0549031	+	0.580583i
$475$		0			0
$476$	−1.12111	−	0.442272i	−0.0513859	−	0.0202715i
$477$		−	0.917382i		−	0.0420040i
$478$	−3.46299	−	0.327479i	−0.158393	−	0.0149786i
$479$	5.01824	+	8.69185i	0.229289	+	0.397141i	0.957598	−	0.288109i	$-0.0930265\pi$
$479$	5.01824	+	8.69185i	0.229289	+	0.397141i	−0.728308	+	0.685250i	$0.759693\pi$
$480$		0			0
$481$	21.9507	+	12.6733i	1.00087	+	0.577851i
$482$	0.930551	+	2.03270i	0.0423855	+	0.0925870i
$483$	19.1842	+	16.5155i	0.872913	+	0.751479i
$484$	−8.20221	+	9.50092i	−0.372828	+	0.431860i
$485$		0			0
$486$	−0.720884	+	1.01430i	−0.0326999	+	0.0460097i
$487$	13.0973	+	22.6852i	0.593495	+	1.02796i	0.993757	+	0.111563i	$0.0355856\pi$
$487$	13.0973	+	22.6852i	0.593495	+	1.02796i	−0.400262	+	0.916401i	$0.631081\pi$
$488$	−27.2837	+	26.1582i	−1.23507	+	1.18413i
$489$			12.6736i			0.573120i
$490$		0			0
$491$			26.0472i			1.17549i	0.809045	+	0.587747i	$0.199985\pi$
$491$			26.0472i			1.17549i	−0.809045	+	0.587747i	$0.800015\pi$
$492$	−6.31269	−	18.1319i	−0.284598	−	0.817450i
$493$	0.930555	+	1.61177i	0.0419101	+	0.0725904i
$494$	4.47801	+	3.18261i	0.201475	+	0.143192i
$495$		0			0
$496$	2.47302	+	16.7645i	0.111042	+	0.752750i
$497$	−4.08671	−	3.51820i	−0.183314	−	0.157813i
$498$	−21.5032	+	9.84396i	−0.963581	+	0.441118i
$499$	15.0374	+	8.68187i	0.673169	+	0.388654i	0.797276	−	0.603615i	$-0.206273\pi$
$499$	15.0374	+	8.68187i	0.673169	+	0.388654i	−0.124108	+	0.992269i	$0.539607\pi$
$500$		0			0
$501$	12.9794	+	22.4810i	0.579876	+	1.00437i
$502$	−3.50211	+	37.0337i	−0.156307	+	1.65290i
$503$		−	31.7491i		−	1.41562i	−0.706403	−	0.707810i	$-0.749683\pi$
$503$		−	31.7491i		−	1.41562i	0.706403	−	0.707810i	$-0.250317\pi$
$504$	0.632886	−	0.0339308i	0.0281910	−	0.00151140i
$505$		0			0
$506$	31.8791	+	3.01466i	1.41720	+	0.134018i
$507$	−16.8025	+	9.70093i	−0.746226	+	0.430834i
$508$	−24.2032	−	4.61888i	−1.07384	−	0.204930i
$509$	8.90601	+	5.14189i	0.394752	+	0.227910i	0.684217	−	0.729278i	$-0.260144\pi$
$509$	8.90601	+	5.14189i	0.394752	+	0.227910i	−0.289465	+	0.957189i	$0.593477\pi$
$510$		0			0
$511$	−13.9386	−	2.63996i	−0.616607	−	0.116785i
$512$	16.9781	−	14.9581i	0.750333	−	0.661060i
$513$	3.51276	+	2.02809i	0.155092	+	0.0895424i
$514$	−13.8314	−	9.83023i	−0.610076	−	0.433593i
$515$		0			0
$516$	16.4518	−	5.72776i	0.724252	−	0.252150i
$517$	24.0535			1.05787
$518$	−4.63718	−	18.7757i	−0.203746	−	0.824958i
$519$			32.9679i			1.44713i
$520$		0			0
$521$	13.7812	−	7.95657i	0.603764	−	0.348584i	−0.166757	−	0.985998i	$-0.553329\pi$
$521$	13.7812	−	7.95657i	0.603764	−	0.348584i	0.770521	+	0.637415i	$0.219996\pi$
$522$	−0.797771	−	0.566991i	−0.0349175	−	0.0248165i
$523$	2.03784	+	1.17655i	0.0891087	+	0.0514470i	0.543892	−	0.839155i	$-0.316950\pi$
$523$	2.03784	+	1.17655i	0.0891087	+	0.0514470i	−0.454783	+	0.890602i	$0.650283\pi$
$524$	21.7691	−	25.2159i	0.950986	−	1.10156i
$525$		0			0
$526$	12.4892	−	5.71742i	0.544553	−	0.249291i
$527$	−0.482452	+	0.835631i	−0.0210159	+	0.0364007i
$528$	22.8867	−	18.1342i	0.996015	−	0.789190i
$529$	−3.33811	−	5.78178i	−0.145135	−	0.251382i
$530$		0			0
$531$	−0.665805			−0.0288935
$532$	−0.617496	−	4.14612i	−0.0267719	−	0.179757i
$533$		−	26.8028i		−	1.16096i
$534$	−0.544197	+	5.75471i	−0.0235497	+	0.249031i
$535$		0			0
$536$	−17.8481	+	4.38179i	−0.770919	+	0.189264i
$537$	−11.2621	+	19.5066i	−0.485996	+	0.841770i
$538$	1.98225	+	4.33003i	0.0854607	+	0.186681i
$539$	18.1321	+	22.7539i	0.781005	+	0.980082i
$540$		0			0
$541$	23.1217	−	40.0480i	0.994081	−	1.72180i	0.402955	−	0.915220i	$-0.367983\pi$
$541$	23.1217	−	40.0480i	0.994081	−	1.72180i	0.591126	−	0.806579i	$-0.298683\pi$
$542$	11.4530	+	8.13984i	0.491947	+	0.349636i
$543$	7.51090	+	13.0093i	0.322324	+	0.558281i
$544$	1.28665	−	0.0671899i	0.0551648	−	0.00288074i
$545$		0			0
$546$	30.9573	+	8.95111i	1.32485	+	0.383072i
$547$	0.635487			0.0271715			0.0135857	−	0.999908i	$-0.495675\pi$
$547$	0.635487			0.0271715			0.0135857	+	0.999908i	$0.495675\pi$
$548$	−8.31649	+	2.89541i	−0.355263	+	0.123686i
$549$	0.980175	−	0.565904i	0.0418329	−	0.0241522i
$550$		0			0
$551$	−3.23662	+	5.60599i	−0.137885	+	0.238823i
$552$	−25.9864	−	7.55289i	−1.10605	−	0.321472i
$553$	12.7662	−	4.46447i	0.542873	−	0.189848i
$554$	−0.235925	−	0.515355i	−0.0100235	−	0.0218953i
$555$		0			0
$556$	−25.9792	−	4.95780i	−1.10176	−	0.210257i
$557$	−26.4995	+	15.2995i	−1.12282	+	0.648260i	−0.942119	−	0.335279i	$-0.891170\pi$
$557$	−26.4995	+	15.2995i	−1.12282	+	0.648260i	−0.180700	+	0.983538i	$0.557836\pi$
$558$	0.0477722	−	0.505176i	0.00202236	−	0.0213858i
$559$	24.3193			1.02860
$560$		0			0
$561$	1.66266			0.0701975
$562$	−2.85653	+	30.2069i	−0.120495	+	1.27420i
$563$	−8.81511	+	5.08940i	−0.371512	+	0.214493i	−0.674119	−	0.738623i	$-0.735477\pi$
$563$	−8.81511	+	5.08940i	−0.371512	+	0.214493i	0.302607	+	0.953116i	$0.402143\pi$
$564$	−19.9676	−	3.81058i	−0.840789	−	0.160454i
$565$		0			0
$566$	12.0241	+	26.2656i	0.505412	+	1.10402i
$567$	24.0377	+	4.55272i	1.00949	+	0.191196i
$568$	5.53574	+	1.60895i	0.232274	+	0.0675101i
$569$	−19.6151	+	33.9744i	−0.822308	+	1.42428i	0.0816516	+	0.996661i	$0.473981\pi$
$569$	−19.6151	+	33.9744i	−0.822308	+	1.42428i	−0.903959	+	0.427618i	$0.859353\pi$
$570$		0			0
$571$	−19.0886	+	11.0208i	−0.798833	+	0.461206i	−0.843063	−	0.537815i	$-0.819250\pi$
$571$	−19.0886	+	11.0208i	−0.798833	+	0.461206i	0.0442302	+	0.999021i	$0.485917\pi$
$572$	38.4977	−	13.4031i	1.60967	−	0.560411i
$573$	0.865610			0.0361614
$574$	−14.7427	+	14.1739i	−0.615347	+	0.591606i
$575$		0			0
$576$	−0.600522	+	0.313774i	−0.0250218	+	0.0130739i
$577$	−20.6789	−	35.8168i	−0.860872	−	1.49107i	−0.871088	−	0.491127i	$-0.836585\pi$
$577$	−20.6789	−	35.8168i	−0.860872	−	1.49107i	0.0102160	−	0.999948i	$-0.496748\pi$
$578$	−19.5367	−	13.8851i	−0.812619	−	0.577544i
$579$	23.6889	−	41.0305i	0.984479	−	1.70517i
$580$		0			0
$581$	19.0911	+	16.4353i	0.792033	+	0.681851i
$582$	−18.3216	−	40.0218i	−0.759455	−	1.65896i
$583$	−22.5105	+	38.9893i	−0.932289	+	1.61477i
$584$	14.7285	−	3.61593i	0.609471	−	0.149628i
$585$		0			0
$586$	0.617962	−	6.53475i	0.0255278	−	0.269948i
$587$			0.600496i			0.0247851i	0.999923	+	0.0123926i	$0.00394478\pi$
$587$			0.600496i			0.0247851i	−0.999923	+	0.0123926i	$0.996055\pi$
$588$	−11.4474	−	21.7614i	−0.472083	−	0.897424i
$589$	−3.35609			−0.138285
$590$		0			0
$591$	2.17807	+	3.77252i	0.0895938	+	0.155181i
$592$	12.8399	+	16.2049i	0.527718	+	0.666019i
$593$	18.0379	−	31.2425i	0.740727	−	1.28298i	−0.211437	−	0.977392i	$-0.567814\pi$
$593$	18.0379	−	31.2425i	0.740727	−	1.28298i	0.952165	−	0.305586i	$-0.0988522\pi$
$594$	27.3658	−	12.5278i	1.12283	−	0.514023i
$595$		0			0
$596$	15.0920	−	17.4816i	0.618193	−	0.716076i
$597$	8.42034	+	4.86149i	0.344622	+	0.198967i
$598$	−30.7937	−	21.8857i	−1.25925	−	0.894973i
$599$	−4.57779	+	2.64299i	−0.187043	+	0.107989i	−0.590598	−	0.806966i	$-0.701108\pi$
$599$	−4.57779	+	2.64299i	−0.187043	+	0.107989i	0.403554	+	0.914956i	$0.367775\pi$
$600$		0			0
$601$			34.2340i			1.39643i	0.715886	+	0.698217i	$0.246023\pi$
$601$			34.2340i			1.39643i	−0.715886	+	0.698217i	$0.753977\pi$
$602$	−12.8605	−	13.3766i	−0.524156	−	0.545191i
$603$	0.550313			0.0224105
$604$	−32.5177	+	11.3211i	−1.32313	+	0.460651i
$605$		0			0
$606$	−31.1587	−	22.1451i	−1.26573	−	0.899581i
$607$	−26.3130	−	15.1918i	−1.06801	−	0.616618i	−0.140375	−	0.990098i	$-0.544831\pi$
$607$	−26.3130	−	15.1918i	−1.06801	−	0.616618i	−0.927638	+	0.373481i	$0.878164\pi$
$608$	2.43998	+	3.75877i	0.0989542	+	0.152438i
$609$	−7.06601	+	37.3075i	−0.286329	+	1.51178i
$610$		0			0
$611$	−24.5764	−	14.1892i	−0.994254	−	0.574033i
$612$	−0.0378961	−	0.00723200i	−0.00153186	−	0.000292336i
$613$	2.20790	−	1.27473i	0.0891763	−	0.0514859i	−0.454749	−	0.890620i	$-0.650271\pi$
$613$	2.20790	−	1.27473i	0.0891763	−	0.0514859i	0.543925	+	0.839134i	$0.316938\pi$
$614$	8.48181	+	0.802086i	0.342298	+	0.0323696i
$615$		0			0
$616$	−27.7306	−	14.0875i	−1.11730	−	0.567602i
$617$			30.0546i			1.20995i	0.796243	+	0.604976i	$0.206817\pi$
$617$			30.0546i			1.20995i	−0.796243	+	0.604976i	$0.793183\pi$
$618$	−2.55740	+	27.0436i	−0.102874	+	1.08785i
$619$	−5.95465	−	10.3137i	−0.239337	−	0.414545i	0.721187	−	0.692741i	$-0.243597\pi$
$619$	−5.95465	−	10.3137i	−0.239337	−	0.414545i	−0.960524	+	0.278196i	$0.910264\pi$
$620$		0			0
$621$	−24.1560	−	13.9465i	−0.969347	−	0.559653i
$622$	29.5941	−	13.5479i	1.18661	−	0.543220i
$623$	5.81207	−	2.03254i	0.232856	−	0.0814320i
$624$	−34.0816	+	5.02754i	−1.36436	+	0.201263i
$625$		0			0
$626$	9.82298	+	6.98138i	0.392605	+	0.279032i
$627$	2.89150	+	5.00822i	0.115475	+	0.200009i
$628$	13.7333	+	39.4460i	0.548017	+	1.57407i
$629$			1.17725i			0.0469399i
$630$		0			0
$631$		−	25.8722i		−	1.02996i	−0.857203	−	0.514979i	$-0.827800\pi$
$631$		−	25.8722i		−	1.02996i	0.857203	−	0.514979i	$-0.172200\pi$
$632$	−10.4364	+	10.0059i	−0.415137	+	0.398013i
$633$	−19.0790	−	33.0458i	−0.758323	−	1.31345i
$634$	3.44323	−	4.84471i	0.136748	−	0.192408i
$635$		0			0
$636$	24.8635	−	28.8003i	0.985901	−	1.14201i
$637$	−5.10369	−	33.9448i	−0.202215	−	1.34494i
$638$	19.9931	+	43.6730i	0.791534	+	1.72903i
$639$	−0.149495	−	0.0863108i	−0.00591392	−	0.00341440i
$640$		0			0
$641$	−17.7104	−	30.6754i	−0.699520	−	1.21160i	−0.968633	−	0.248496i	$-0.920064\pi$
$641$	−17.7104	−	30.6754i	−0.699520	−	1.21160i	0.269113	−	0.963109i	$-0.413270\pi$
$642$	−11.6753	−	1.10408i	−0.460788	−	0.0435746i
$643$			23.1771i			0.914017i	0.889462	+	0.457008i	$0.151079\pi$
$643$			23.1771i			0.914017i	−0.889462	+	0.457008i	$0.848921\pi$
$644$	4.24631	+	28.5115i	0.167328	+	1.12351i
$645$		0			0
$646$	−0.0240226	+	0.254031i	−0.000945155	+	0.00999471i
$647$	−28.8793	+	16.6735i	−1.13536	+	0.655501i	−0.945278	−	0.326267i	$-0.894209\pi$
$647$	−28.8793	+	16.6735i	−1.13536	+	0.655501i	−0.190083	+	0.981768i	$0.560876\pi$
$648$	−25.3999	+	6.23581i	−0.997804	+	0.244966i
$649$	28.2971	+	16.3374i	1.11076	+	0.641298i
$650$		0			0
$651$	−18.5826	+	6.49854i	−0.728311	+	0.254698i
$652$	−9.43093	+	10.9242i	−0.369344	+	0.427824i
$653$	9.86500	+	5.69556i	0.386047	+	0.222884i	0.680446	−	0.732798i	$-0.261786\pi$
$653$	9.86500	+	5.69556i	0.386047	+	0.222884i	−0.294399	+	0.955683i	$0.595119\pi$
$654$	−11.7111	+	16.4779i	−0.457942	+	0.644336i
$655$		0			0
$656$	8.05137	−	20.3266i	0.314353	−	0.793620i
$657$	−0.454128			−0.0177172
$658$	5.19185	+	21.0216i	0.202399	+	0.819506i
$659$		−	9.33865i		−	0.363782i	−0.983319	−	0.181891i	$-0.941778\pi$
$659$		−	9.33865i		−	0.363782i	0.983319	−	0.181891i	$-0.0582218\pi$
$660$		0			0
$661$	−8.88871	+	5.13190i	−0.345731	+	0.199608i	−0.662803	−	0.748793i	$-0.730633\pi$
$661$	−8.88871	+	5.13190i	−0.345731	+	0.199608i	0.317072	+	0.948401i	$0.397300\pi$
$662$	−8.77343	+	12.3444i	−0.340989	+	0.479780i
$663$	−1.69880	−	0.980805i	−0.0659761	−	0.0380913i
$664$	−25.8602	−	7.51624i	−1.00357	−	0.291687i
$665$		0			0
$666$	−0.257698	−	0.562916i	−0.00998558	−	0.0218125i
$667$	22.2571	−	38.5505i	0.861799	−	1.49268i
$668$	−5.54120	+	29.0362i	−0.214396	+	1.12345i
$669$	21.6137	+	37.4361i	0.835636	+	1.44736i
$670$		0			0
$671$	−55.5441			−2.14425
$672$	20.7884	+	16.0877i	0.801931	+	0.620595i
$673$		−	14.1636i		−	0.545967i	−0.962019	−	0.272983i	$-0.911990\pi$
$673$		−	14.1636i		−	0.545967i	0.962019	−	0.272983i	$-0.0880104\pi$
$674$	−40.3865	−	3.81917i	−1.55563	−	0.147109i
$675$		0			0
$676$	−21.7020	−	4.14156i	−0.834692	−	0.159291i
$677$	−7.78573	+	13.4853i	−0.299230	+	0.518281i	−0.975960	−	0.217950i	$-0.930063\pi$
$677$	−7.78573	+	13.4853i	−0.299230	+	0.518281i	0.676730	+	0.736231i	$0.263396\pi$
$678$	−21.4693	+	9.82845i	−0.824524	+	0.377459i
$679$	−30.5894	+	35.5325i	−1.17392	+	1.36361i
$680$		0			0
$681$	−7.20074	+	12.4720i	−0.275933	+	0.477930i
$682$	−14.4262	+	20.2981i	−0.552409	+	0.777253i
$683$	0.0471556	+	0.0816759i	0.00180436	+	0.00312524i	0.866926	−	0.498437i	$-0.166092\pi$
$683$	0.0471556	+	0.0816759i	0.00180436	+	0.00312524i	−0.865122	+	0.501562i	$0.832759\pi$
$684$	−0.0441203	−	0.126727i	−0.00168698	−	0.00484552i
$685$		0			0
$686$	−15.9721	+	20.7579i	−0.609818	+	0.792542i
$687$	−8.53730			−0.325718
$688$	18.4431	+	7.30534i	0.703138	+	0.278513i
$689$	45.9997	−	26.5579i	1.75245	−	1.01178i
$690$		0			0
$691$	−3.68824	+	6.38822i	−0.140307	+	0.243019i	−0.927612	−	0.373544i	$-0.878142\pi$
$691$	−3.68824	+	6.38822i	−0.140307	+	0.243019i	0.787305	+	0.616564i	$0.211476\pi$
$692$	−24.5327	+	28.4171i	−0.932594	+	1.08026i
$693$	0.705843	+	0.607651i	0.0268127	+	0.0230827i
$694$	30.1080	−	13.7832i	1.14288	−	0.523202i
$695$		0			0
$696$	−9.67825	−	39.4218i	−0.366853	−	1.49428i
$697$	1.07810	−	0.622442i	0.0408360	−	0.0235767i
$698$	−27.8031	−	2.62921i	−1.05236	−	0.0995171i
$699$	37.1614			1.40557
$700$		0			0
$701$	3.40837			0.128732			0.0643661	−	0.997926i	$-0.479497\pi$
$701$	3.40837			0.128732			0.0643661	+	0.997926i	$0.479497\pi$
$702$	−35.3509	−	3.34298i	−1.33423	−	0.126173i
$703$	−3.54607	+	2.04733i	−0.133743	+	0.0772163i
$704$	33.2219	+	1.39986i	1.25210	+	0.0527592i
$705$		0			0
$706$	27.7242	−	12.6919i	1.04341	−	0.477665i
$707$	−7.57735	+	40.0073i	−0.284976	+	1.50463i
$708$	−20.9023	−	18.0451i	−0.785556	−	0.678176i
$709$	−13.4643	+	23.3209i	−0.505663	+	0.875834i	0.494315	+	0.869283i	$0.335419\pi$
$709$	−13.4643	+	23.3209i	−0.505663	+	0.875834i	−0.999979	+	0.00655175i	$0.997914\pi$
$710$		0			0
$711$	0.374931	−	0.216466i	0.0140610	−	0.00811813i
$712$	−4.75138	+	4.55539i	−0.178066	+	0.170721i
$713$	23.0787			0.864303
$714$	0.358879	+	1.45308i	0.0134307	+	0.0543803i
$715$		0			0
$716$	−24.2231	+	8.43336i	−0.905261	+	0.315169i
$717$	2.15996	+	3.74116i	0.0806651	+	0.139716i
$718$	−6.38207	+	8.97974i	−0.238177	+	0.335121i
$719$	−0.995916	+	1.72498i	−0.0371414	+	0.0643308i	−0.883999	−	0.467490i	$-0.845159\pi$
$719$	−0.995916	+	1.72498i	−0.0371414	+	0.0643308i	0.846857	+	0.531820i	$0.178492\pi$
$720$		0			0
$721$	27.3132	−	9.55171i	1.01720	−	0.355724i
$722$	23.6247	−	10.8152i	0.879220	−	0.402498i
$723$	1.38820	−	2.40442i	0.0516275	−	0.0894215i
$724$	−3.20658	+	16.8027i	−0.119172	+	0.624466i
$725$		0			0
$726$	15.5188	+	1.46754i	0.575957	+	0.0544656i
$727$		−	26.2307i		−	0.972843i	−0.873724	−	0.486422i	$-0.838302\pi$
$727$		−	26.2307i		−	0.972843i	0.873724	−	0.486422i	$-0.161698\pi$
$728$	20.0232	+	30.7521i	0.742110	+	1.13975i
$729$	−26.1953			−0.970197
$730$		0			0
$731$	0.564767	+	0.978205i	0.0208887	+	0.0361802i
$732$	46.1091	+	8.79935i	1.70424	+	0.325233i
$733$	1.54402	−	2.67432i	0.0570296	−	0.0987782i	−0.836101	−	0.548575i	$-0.815170\pi$
$733$	1.54402	−	2.67432i	0.0570296	−	0.0987782i	0.893131	+	0.449797i	$0.148504\pi$
$734$	−3.25741	−	7.11551i	−0.120233	−	0.262638i
$735$		0			0
$736$	−16.7789	−	25.8478i	−0.618478	−	0.952762i
$737$	−23.3886	−	13.5034i	−0.861531	−	0.497405i
$738$	−0.379257	+	0.533624i	−0.0139606	+	0.0196430i
$739$	10.1238	−	5.84500i	0.372411	−	0.215012i	−0.302100	−	0.953276i	$-0.597688\pi$
$739$	10.1238	−	5.84500i	0.372411	−	0.215012i	0.674511	+	0.738264i	$0.264354\pi$
$740$		0			0
$741$		−	6.82279i		−	0.250642i
$742$	−38.9336	−	11.2574i	−1.42930	−	0.413272i
$743$	12.3264			0.452214			0.226107	−	0.974103i	$-0.427400\pi$
$743$	12.3264			0.452214			0.226107	+	0.974103i	$0.427400\pi$
$744$	15.1914	−	14.5647i	0.556943	−	0.533969i
$745$		0			0
$746$	7.76158	−	10.9207i	0.284172	−	0.399837i
$747$	0.698366	+	0.403202i	0.0255519	+	0.0147524i
$748$	1.43315	+	1.23725i	0.0524012	+	0.0452383i
$749$	4.12367	+	11.7917i	0.150676	+	0.430859i
$750$		0			0
$751$	−23.8338	−	13.7605i	−0.869709	−	0.502127i	−0.00245756	−	0.999997i	$-0.500782\pi$
$751$	−23.8338	−	13.7605i	−0.869709	−	0.502127i	−0.867252	+	0.497870i	$0.834116\pi$
$752$	−14.3758	−	18.1433i	−0.524231	−	0.661618i
$753$	40.0085	−	23.0989i	1.45799	−	0.841772i
$754$	5.33504	−	56.4164i	0.194291	−	2.05456i
$755$		0			0
$756$	16.8555	+	21.2123i	0.613029	+	0.771485i
$757$			20.5776i			0.747904i	0.927448	+	0.373952i	$0.121998\pi$
$757$			20.5776i			0.747904i	−0.927448	+	0.373952i	$0.878002\pi$
$758$	−33.2571	−	3.14497i	−1.20795	−	0.114230i
$759$	−19.8838	−	34.4398i	−0.721737	−	1.25008i
$760$		0			0
$761$	2.16571	+	1.25037i	0.0785069	+	0.0453260i	0.538740	−	0.842472i	$-0.318901\pi$
$761$	2.16571	+	1.25037i	0.0785069	+	0.0453260i	−0.460233	+	0.887798i	$0.652234\pi$
$762$	12.7375	+	27.8238i	0.461429	+	1.00795i
$763$	21.1574	+	4.00719i	0.765949	+	0.145070i
$764$	0.746124	+	0.644134i	0.0269938	+	0.0233040i
$765$		0			0
$766$	−13.8196	+	19.4445i	−0.499321	+	0.702557i
$767$	−19.2749	−	33.3851i	−0.695975	−	1.20546i
$768$	−27.3569	−	6.42512i	−0.987157	−	0.231846i
$769$			36.2043i			1.30556i	0.757548	+	0.652779i	$0.226397\pi$
$769$			36.2043i			1.30556i	−0.757548	+	0.652779i	$0.773603\pi$
$770$		0			0
$771$			21.0738i			0.758953i
$772$	50.9514	−	17.7389i	1.83378	−	0.638436i
$773$	−5.61812	−	9.73087i	−0.202070	−	0.349995i	0.747125	−	0.664683i	$-0.231433\pi$
$773$	−5.61812	−	9.73087i	−0.202070	−	0.349995i	−0.949195	+	0.314688i	$0.898100\pi$
$774$	−0.484179	−	0.344115i	−0.0174034	−	0.0123690i
$775$		0			0
$776$	13.9892	−	48.1312i	0.502185	−	1.72781i
$777$	−15.6702	+	18.2024i	−0.562167	+	0.653009i
$778$	−13.3044	+	6.09063i	−0.476986	+	0.218360i
$779$	3.74981	+	2.16495i	0.134351	+	0.0775675i
$780$		0			0
$781$	4.23574	+	7.33653i	0.151567	+	0.262522i
$782$	0.165195	−	1.74688i	0.00590735	−	0.0624684i
$783$		−	41.8393i		−	1.49522i
$784$	6.32625	−	27.2760i	0.225938	−	0.974142i
$785$		0			0
$786$	−41.1877	−	3.89493i	−1.46912	−	0.138928i
$787$	−33.2271	+	19.1837i	−1.18442	+	0.683825i	−0.957033	−	0.289980i	$-0.906351\pi$
$787$	−33.2271	+	19.1837i	−1.18442	+	0.683825i	−0.227387	+	0.973805i	$0.573018\pi$
$788$	−0.929868	+	4.87257i	−0.0331252	+	0.173578i
$789$	−14.7731	−	8.52923i	−0.525935	−	0.303649i
$790$		0			0
$791$	19.0610	+	16.4094i	0.677733	+	0.583451i
$792$	−0.956112	−	0.277892i	−0.0339740	−	0.00987448i
$793$	56.7516	+	32.7655i	2.01531	+	1.16354i
$794$	2.97999	+	2.11793i	0.105756	+	0.0751626i
$795$		0			0
$796$	3.64041	+	10.4563i	0.129031	+	0.370615i
$797$	35.5238			1.25832			0.629159	−	0.777276i	$-0.283399\pi$
$797$	35.5238			1.25832			0.629159	+	0.777276i	$0.283399\pi$
$798$	−3.75282	+	3.60803i	−0.132848	+	0.127723i
$799$		−	1.31806i		−	0.0466297i
$800$		0			0
$801$	0.170695	−	0.0985508i	0.00603121	−	0.00348212i
$802$	9.19523	+	6.53523i	0.324695	+	0.230767i
$803$	19.3007	+	11.1433i	0.681107	+	0.393237i
$804$	17.2765	+	14.9149i	0.609295	+	0.526009i
$805$		0			0
$806$	26.7137	−	12.2293i	0.940951	−	0.430758i
$807$	2.95711	−	5.12186i	0.104095	−	0.180298i
$808$	−10.3786	−	42.2746i	−0.365119	−	1.48722i
$809$	−1.74646	−	3.02495i	−0.0614022	−	0.106352i	0.833690	−	0.552232i	$-0.186224\pi$
$809$	−1.74646	−	3.02495i	−0.0614022	−	0.106352i	−0.895092	+	0.445881i	$0.852891\pi$
$810$		0			0
$811$	16.6986			0.586367			0.293184	−	0.956056i	$-0.405285\pi$
$811$	16.6986			0.586367			0.293184	+	0.956056i	$0.405285\pi$
$812$	−33.8527	+	26.8996i	−1.18800	+	0.943992i
$813$		−	17.4500i		−	0.611997i
$814$	−2.86038	+	30.2476i	−0.100256	+	1.06018i
$815$		0			0
$816$	−0.993703	−	1.25413i	−0.0347866	−	0.0439032i
$817$	−1.96435	+	3.40235i	−0.0687239	+	0.119033i
$818$	−3.82834	−	8.36265i	−0.133855	−	0.292393i
$819$	−0.362733	−	1.03724i	−0.0126749	−	0.0362440i
$820$		0			0
$821$	−14.5330	+	25.1719i	−0.507206	+	0.878506i	0.492760	+	0.870165i	$0.335988\pi$
$821$	−14.5330	+	25.1719i	−0.507206	+	0.878506i	−0.999965	+	0.00834036i	$0.997345\pi$
$822$	8.91434	+	6.33559i	0.310923	+	0.220979i
$823$	−1.47377	−	2.55264i	−0.0513724	−	0.0889796i	0.839196	−	0.543830i	$-0.183026\pi$
$823$	−1.47377	−	2.55264i	−0.0513724	−	0.0889796i	−0.890568	+	0.454850i	$0.849693\pi$
$824$	−22.3286	+	21.4076i	−0.777854	+	0.745768i
$825$		0			0
$826$	−8.17023	+	28.2567i	−0.284279	+	0.983176i
$827$	−17.2803			−0.600896			−0.300448	−	0.953798i	$-0.597136\pi$
$827$	−17.2803			−0.600896			−0.300448	+	0.953798i	$0.597136\pi$
$828$	0.303400	+	0.871456i	0.0105439	+	0.0302852i
$829$	1.71627	−	0.990889i	0.0596085	−	0.0344150i	−0.469900	−	0.882720i	$-0.655710\pi$
$829$	1.71627	−	0.990889i	0.0596085	−	0.0344150i	0.529508	+	0.848305i	$0.322377\pi$
$830$		0			0
$831$	−0.351952	+	0.609599i	−0.0122091	+	0.0211468i
$832$	−33.1183	−	21.0279i	−1.14817	−	0.729012i
$833$	1.24685	−	0.993588i	0.0432009	−	0.0344258i
$834$	13.6721	+	29.8654i	0.473426	+	1.03415i
$835$		0			0
$836$	−1.23445	+	6.46858i	−0.0426943	+	0.223720i
$837$	18.7857	−	10.8459i	0.649328	−	0.374890i
$838$	−3.91950	+	41.4475i	−0.135397	+	1.43178i
$839$	−28.7538			−0.992693			−0.496346	−	0.868125i	$-0.665325\pi$
$839$	−28.7538			−0.992693			−0.496346	+	0.868125i	$0.665325\pi$
$840$		0			0
$841$	37.7712			1.30245
$842$	−1.50760	+	15.9424i	−0.0519554	+	0.549412i
$843$	32.6333	−	18.8408i	1.12395	−	0.648913i
$844$	8.14528	−	42.6817i	0.280372	−	1.46917i
$845$		0			0
$846$	0.288522	+	0.630249i	0.00991959	+	0.0216684i
$847$	−5.48118	−	15.6735i	−0.188336	−	0.538547i
$848$	42.8628	−	6.32290i	1.47192	−	0.217129i
$849$	17.9376	−	31.0688i	0.615616	−	1.06628i
$850$		0			0
$851$	24.3851	−	14.0788i	0.835911	−	0.482613i
$852$	−2.35398	−	6.76134i	−0.0806461	−	0.231640i
$853$	−54.2406			−1.85716			−0.928582	−	0.371127i	$-0.878972\pi$
$853$	−54.2406			−1.85716			−0.928582	+	0.371127i	$0.878972\pi$
$854$	−11.9890	−	48.5428i	−0.410254	−	1.66110i
$855$		0			0
$856$	−9.24210	−	9.63974i	−0.315889	−	0.329479i
$857$	−2.48284	−	4.30041i	−0.0848123	−	0.146899i	0.820499	−	0.571648i	$-0.193696\pi$
$857$	−2.48284	−	4.30041i	−0.0848123	−	0.146899i	−0.905311	+	0.424749i	$0.860362\pi$
$858$	−41.2652	−	29.3279i	−1.40877	−	1.00124i
$859$	−17.3837	+	30.1095i	−0.593125	+	1.02732i	0.400684	+	0.916216i	$0.368772\pi$
$859$	−17.3837	+	30.1095i	−0.593125	+	1.02732i	−0.993809	+	0.111106i	$0.964561\pi$
$860$		0			0
$861$	24.9548	+	4.72641i	0.850456	+	0.161076i
$862$	−19.4346	−	42.4531i	−0.661946	−	1.44596i
$863$	−16.4912	+	28.5637i	−0.561369	+	0.972319i	0.436009	+	0.899942i	$0.356392\pi$
$863$	−16.4912	+	28.5637i	−0.561369	+	0.972319i	−0.997377	+	0.0723765i	$0.976942\pi$
$864$	−25.8051	−	13.1544i	−0.877906	−	0.447522i
$865$		0			0
$866$	2.52127	−	26.6616i	0.0856762	−	0.905999i
$867$			29.7665i			1.01092i
$868$	−20.8534	−	8.22657i	−0.707810	−	0.279228i
$869$	−21.2464			−0.720735
$870$		0			0
$871$	15.9314	+	27.5940i	0.539815	+	0.934986i
$872$	−22.3564	+	5.48861i	−0.757084	+	0.185868i
$873$	−0.750440	+	1.29980i	−0.0253986	+	0.0439916i
$874$	5.54920	−	2.54037i	0.187705	−	0.0859294i
$875$		0			0
$876$	−14.2569	−	12.3081i	−0.481695	−	0.415851i
$877$	−27.3489	−	15.7899i	−0.923507	−	0.533187i	−0.0387545	−	0.999249i	$-0.512339\pi$
$877$	−27.3489	−	15.7899i	−0.923507	−	0.533187i	−0.884752	+	0.466062i	$0.845672\pi$
$878$	28.0082	+	19.9059i	0.945230	+	0.671793i
$879$	−7.05966	+	4.07590i	−0.238116	+	0.137477i
$880$		0			0
$881$			31.0031i			1.04452i	0.852786	+	0.522261i	$0.174911\pi$
$881$			31.0031i			1.04452i	−0.852786	+	0.522261i	$0.825089\pi$
$882$	−0.378704	+	0.748032i	−0.0127516	+	0.0251875i
$883$	−1.05418			−0.0354759			−0.0177380	−	0.999843i	$-0.505646\pi$
$883$	−1.05418			−0.0354759			−0.0177380	+	0.999843i	$0.505646\pi$
$884$	−0.734452	−	2.10956i	−0.0247023	−	0.0709523i
$885$		0			0
$886$	−17.2979	−	12.2940i	−0.581135	−	0.413023i
$887$	17.0213	+	9.82722i	0.571518	+	0.329966i	0.757755	−	0.652539i	$-0.226296\pi$
$887$	17.0213	+	9.82722i	0.571518	+	0.329966i	−0.186238	+	0.982505i	$0.559629\pi$
$888$	7.16636	−	24.6565i	0.240487	−	0.827417i
$889$	21.2662	−	24.7027i	0.713247	−	0.828502i
$890$		0			0
$891$	−33.2848	−	19.2170i	−1.11508	−	0.643794i
$892$	−9.22742	+	48.3522i	−0.308957	+	1.61895i
$893$	3.97023	−	2.29222i	0.132859	−	0.0767061i
$894$	−28.5545	−	2.70027i	−0.955006	−	0.0903106i
$895$		0			0
$896$	5.94741	+	29.3365i	0.198689	+	0.980063i
$897$			46.9180i			1.56655i
$898$	−1.46410	+	15.4823i	−0.0488575	+	0.516652i
$899$	17.3090	+	29.9800i	0.577286	+	0.999889i
$900$		0			0
$901$	2.13650	+	1.23351i	0.0711773	+	0.0410942i
$902$	29.2126	−	13.3732i	0.972673	−	0.445280i
$903$	−4.28846	+	22.6425i	−0.142711	+	0.753494i
$904$	−25.8195	−	7.50439i	−0.858744	−	0.249592i
$905$		0			0
$906$	34.8553	+	24.7723i	1.15799	+	0.823005i
$907$	6.43706	+	11.1493i	0.213739	+	0.370207i	0.952882	−	0.303342i	$-0.0981025\pi$
$907$	6.43706	+	11.1493i	0.213739	+	0.370207i	−0.739143	+	0.673549i	$0.764769\pi$
$908$	−15.4877	+	5.39210i	−0.513978	+	0.178943i
$909$			1.30346i			0.0432331i
$910$		0			0
$911$		−	15.4628i		−	0.512306i	−0.966636	−	0.256153i	$-0.917545\pi$
$911$		−	15.4628i		−	0.512306i	0.966636	−	0.256153i	$-0.0824551\pi$
$912$	2.04952	−	5.17423i	0.0678663	−	0.171336i
$913$	−19.7873	−	34.2727i	−0.654865	−	1.13426i
$914$	−13.5972	+	19.1316i	−0.449755	+	0.632817i
$915$		0			0
$916$	−7.35885	−	6.35294i	−0.243143	−	0.209907i
$917$	14.5473	+	41.5982i	0.480395	+	1.37369i
$918$	−0.686489	−	1.49957i	−0.0226575	−	0.0494932i
$919$	−13.7399	−	7.93272i	−0.453236	−	0.261676i	0.255960	−	0.966687i	$-0.417609\pi$
$919$	−13.7399	−	7.93272i	−0.453236	−	0.261676i	−0.709196	+	0.705011i	$0.750942\pi$
$920$		0			0
$921$	−5.29033	−	9.16312i	−0.174322	−	0.301935i
$922$	−9.33279	−	0.882559i	−0.307359	−	0.0290655i
$923$		−	9.99469i		−	0.328979i
$924$	5.69027	+	38.2068i	0.187196	+	1.25691i
$925$		0			0
$926$	0.280855	−	2.96995i	0.00922946	−	0.0975987i
$927$	0.802163	−	0.463129i	0.0263465	−	0.0152112i
$928$	20.9930	−	41.1822i	0.689130	−	1.35187i
$929$	−0.835215	−	0.482212i	−0.0274025	−	0.0158209i	0.486236	−	0.873827i	$-0.338369\pi$
$929$	−0.835215	−	0.482212i	−0.0274025	−	0.0158209i	−0.513639	+	0.858007i	$0.671703\pi$
$930$		0			0
$931$	5.16124	+	2.02781i	0.169153	+	0.0664588i
$932$	32.0318	+	27.6533i	1.04924	+	0.905813i
$933$	−35.0060	−	20.2107i	−1.14604	−	0.661669i
$934$	9.31985	−	13.1133i	0.304955	−	0.429079i
$935$		0			0
$936$	0.812969	+	0.847946i	0.0265727	+	0.0277160i
$937$	−24.0110			−0.784404			−0.392202	−	0.919879i	$-0.628287\pi$
$937$	−24.0110			−0.784404			−0.392202	+	0.919879i	$0.628287\pi$
$938$	6.75300	−	23.3552i	0.220493	−	0.762574i
$939$		−	14.9665i		−	0.488413i
$940$		0			0
$941$	2.18480	−	1.26140i	0.0712225	−	0.0411203i	−0.463966	−	0.885853i	$-0.653574\pi$
$941$	2.18480	−	1.26140i	0.0712225	−	0.0411203i	0.535188	+	0.844733i	$0.320241\pi$
$942$	30.0504	−	42.2817i	0.979095	−	1.37761i
$943$	−25.7861	−	14.8876i	−0.839713	−	0.484808i
$944$	−4.58895	−	31.1084i	−0.149358	−	1.01249i
$945$		0			0
$946$	12.1341	+	26.5058i	0.394513	+	0.861777i
$947$	9.84254	−	17.0478i	0.319840	−	0.553978i	−0.660615	−	0.750725i	$-0.729704\pi$
$947$	9.84254	−	17.0478i	0.319840	−	0.553978i	0.980454	+	0.196747i	$0.0630377\pi$
$948$	17.6374	+	3.36588i	0.572836	+	0.109319i
$949$	−13.1469	−	22.7710i	−0.426765	−	0.739179i
$950$		0			0
$951$	−7.38150			−0.239362
$952$	−0.771956	+	1.51956i	−0.0250192	+	0.0492492i
$953$			26.9765i			0.873856i	0.899496	+	0.436928i	$0.143934\pi$
$953$			26.9765i			0.873856i	−0.899496	+	0.436928i	$0.856066\pi$
$954$	−1.29161	−	0.122142i	−0.0418175	−	0.00395449i
$955$		0			0
$956$	−0.922137	+	4.83205i	−0.0298240	+	0.156280i
$957$	29.8257	−	51.6595i	0.964126	−	1.66992i
$958$	12.9057	−	5.90810i	0.416963	−	0.190882i
$959$	2.16784	−	11.4459i	0.0700033	−	0.369607i
$960$		0			0
$961$	6.52607	−	11.3035i	0.210518	−	0.364629i
$962$	20.7657	−	29.2178i	0.669512	−	0.942020i
$963$	0.199943	+	0.346311i	0.00644306	+	0.0111597i
$964$	2.98580	−	1.03952i	0.0961662	−	0.0334806i
$965$		0			0
$966$	25.8069	−	24.8112i	0.830322	−	0.798287i
$967$	22.8186			0.733797			0.366898	−	0.930261i	$-0.380420\pi$
$967$	22.8186			0.733797			0.366898	+	0.930261i	$0.380420\pi$
$968$	12.2846	+	12.8131i	0.394842	+	0.411829i
$969$	0.274436	−	0.158446i	0.00881616	−	0.00509001i
$970$		0			0
$971$	12.7360	−	22.0594i	0.408718	−	0.707921i	−0.586028	−	0.810291i	$-0.699309\pi$
$971$	12.7360	−	22.0594i	0.408718	−	0.707921i	0.994746	+	0.102370i	$0.0326425\pi$
$972$	1.33209	+	1.15000i	0.0427268	+	0.0368863i
$973$	22.8267	−	26.5153i	0.731790	−	0.850042i
$974$	33.6830	−	15.4198i	1.07927	−	0.494081i
$975$		0			0
$976$	33.1964	+	41.8963i	1.06259	+	1.34107i
$977$	−10.5694	+	6.10223i	−0.338144	+	0.195228i	−0.659451	−	0.751748i	$-0.729211\pi$
$977$	−10.5694	+	6.10223i	−0.338144	+	0.195228i	0.321307	+	0.946975i	$0.395878\pi$
$978$	17.8436	+	1.68739i	0.570575	+	0.0539567i
$979$	−9.67286			−0.309146
$980$		0			0
$981$	0.689320			0.0220083
$982$	36.6727	+	3.46797i	1.17027	+	0.110667i
$983$	−6.42315	+	3.70841i	−0.204867	+	0.118280i	−0.598923	−	0.800806i	$-0.704405\pi$
$983$	−6.42315	+	3.70841i	−0.204867	+	0.118280i	0.394057	+	0.919086i	$0.371071\pi$
$984$	−26.3690	+	6.47372i	−0.840613	+	0.206375i
$985$		0			0
$986$	2.39316	−	1.09556i	0.0762137	−	0.0348899i
$987$	17.5446	−	20.3797i	0.558452	−	0.648694i
$988$	5.07711	−	5.88100i	0.161524	−	0.187099i
$989$	13.5082	−	23.3968i	0.429535	−	0.743976i
$990$		0			0
$991$	22.8598	−	13.1981i	0.726164	−	0.419251i	−0.0908531	−	0.995864i	$-0.528959\pi$
$991$	22.8598	−	13.1981i	0.726164	−	0.419251i	0.817017	+	0.576613i	$0.195626\pi$
$992$	23.9326	−	1.24978i	0.759861	−	0.0396805i
$993$	18.8082			0.596862
$994$	−5.49750	+	5.28540i	−0.174370	+	0.167643i
$995$		0			0
$996$	10.9967	+	31.5857i	0.348442	+	1.00083i
$997$	−4.15834	−	7.20245i	−0.131696	−	0.228104i	0.792635	−	0.609697i	$-0.208709\pi$
$997$	−4.15834	−	7.20245i	−0.131696	−	0.228104i	−0.924330	+	0.381593i	$0.875376\pi$
$998$	14.2256	−	20.0158i	0.450304	−	0.633589i
$999$	13.2327	−	22.9198i	0.418665	−	0.725150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.t.e.299.18		64
4.3	odd	2	inner	700.2.t.e.299.7		64
5.2	odd	4		700.2.p.d.551.16	yes	32
5.3	odd	4		700.2.p.f.551.1	yes	32
5.4	even	2	inner	700.2.t.e.299.15		64
7.3	odd	6	inner	700.2.t.e.199.26		64
20.3	even	4		700.2.p.f.551.11	yes	32
20.7	even	4		700.2.p.d.551.6	yes	32
20.19	odd	2	inner	700.2.t.e.299.26		64
28.3	even	6	inner	700.2.t.e.199.15		64
35.3	even	12		700.2.p.f.451.11	yes	32
35.17	even	12		700.2.p.d.451.6	✓	32
35.24	odd	6	inner	700.2.t.e.199.7		64
140.3	odd	12		700.2.p.f.451.1	yes	32
140.59	even	6	inner	700.2.t.e.199.18		64
140.87	odd	12		700.2.p.d.451.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.p.d.451.6	✓	32	35.17	even	12
700.2.p.d.451.16	yes	32	140.87	odd	12
700.2.p.d.551.6	yes	32	20.7	even	4
700.2.p.d.551.16	yes	32	5.2	odd	4
700.2.p.f.451.1	yes	32	140.3	odd	12
700.2.p.f.451.11	yes	32	35.3	even	12
700.2.p.f.551.1	yes	32	5.3	odd	4
700.2.p.f.551.11	yes	32	20.3	even	4
700.2.t.e.199.7		64	35.24	odd	6	inner
700.2.t.e.199.15		64	28.3	even	6	inner
700.2.t.e.199.18		64	140.59	even	6	inner
700.2.t.e.199.26		64	7.3	odd	6	inner
700.2.t.e.299.7		64	4.3	odd	2	inner
700.2.t.e.299.15		64	5.4	even	2	inner
700.2.t.e.299.18		64	1.1	even	1	trivial
700.2.t.e.299.26		64	20.19	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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.133142 - 1.40793i) q^{2} +(-1.52103 + 0.878165i) q^{3} +(-1.96455 - 0.374909i) q^{4} +(1.03388 + 2.25842i) q^{6} +(1.72616 - 2.00509i) q^{7} +(-0.789410 + 2.71603i) q^{8} +(0.0423472 - 0.0733475i) q^{9} +O(q^{10})\)	\(q+(0.133142 - 1.40793i) q^{2} +(-1.52103 + 0.878165i) q^{3} +(-1.96455 - 0.374909i) q^{4} +(1.03388 + 2.25842i) q^{6} +(1.72616 - 2.00509i) q^{7} +(-0.789410 + 2.71603i) q^{8} +(0.0423472 - 0.0733475i) q^{9} +(-3.59956 + 2.07821i) q^{11} +(3.31736 - 1.15495i) q^{12} +4.90376 q^{13} +(-2.59321 - 2.69727i) q^{14} +(3.71889 + 1.47305i) q^{16} +(0.113880 + 0.197246i) q^{17} +(-0.0976301 - 0.0693876i) q^{18} +(-0.396093 + 0.686053i) q^{19} +(-0.864729 + 4.56564i) q^{21} +(2.44673 + 5.34464i) q^{22} +(2.72379 - 4.71775i) q^{23} +(-1.18441 - 4.82439i) q^{24} +(0.652895 - 6.90416i) q^{26} -5.12024i q^{27} +(-4.14284 + 3.29194i) q^{28} +8.17136 q^{29} +(2.11825 + 3.66891i) q^{31} +(2.56910 - 5.03981i) q^{32} +(3.65002 - 6.32202i) q^{33} +(0.292871 - 0.134074i) q^{34} +(-0.110692 + 0.128218i) q^{36} +(4.47631 + 2.58440i) q^{37} +(0.913180 + 0.649014i) q^{38} +(-7.45874 + 4.30631i) q^{39} -5.46577i q^{41} +(6.31299 + 1.82536i) q^{42} +4.95932 q^{43} +(7.85065 - 2.73323i) q^{44} +(-6.27962 - 4.46305i) q^{46} +(-5.01175 - 2.89353i) q^{47} +(-6.95011 + 1.02524i) q^{48} +(-1.04077 - 6.92220i) q^{49} +(-0.346429 - 0.200011i) q^{51} +(-9.63366 - 1.83846i) q^{52} +(9.38050 - 5.41584i) q^{53} +(-7.20895 - 0.681718i) q^{54} +(4.08324 + 6.27113i) q^{56} -1.39134i q^{57} +(1.08795 - 11.5047i) q^{58} +(-3.93063 - 6.80806i) q^{59} +(11.5731 + 6.68172i) q^{61} +(5.44760 - 2.49386i) q^{62} +(-0.0739705 - 0.211519i) q^{63} +(-6.75366 - 4.28813i) q^{64} +(-8.41501 - 5.98071i) q^{66} +(3.24881 + 5.62711i) q^{67} +(-0.149773 - 0.430194i) q^{68} +9.56776i q^{69} -2.03817i q^{71} +(0.165785 + 0.172918i) q^{72} +(-2.68098 - 4.64359i) q^{73} +(4.23464 - 5.95825i) q^{74} +(1.03535 - 1.19928i) q^{76} +(-2.04641 + 10.8048i) q^{77} +(5.06992 + 11.0748i) q^{78} +(4.42687 + 2.55585i) q^{79} +(4.62346 + 8.00806i) q^{81} +(-7.69544 - 0.727723i) q^{82} +9.52133i q^{83} +(3.41050 - 8.64523i) q^{84} +(0.660292 - 6.98238i) q^{86} +(-12.4289 + 7.17580i) q^{87} +(-2.80295 - 11.4171i) q^{88} +(2.01542 + 1.16361i) q^{89} +(8.46465 - 9.83247i) q^{91} +(-7.11975 + 8.24706i) q^{92} +(-6.44381 - 3.72034i) q^{93} +(-4.74117 + 6.67095i) q^{94} +(0.518122 + 9.92178i) q^{96} -17.7211 q^{97} +(-9.88455 + 0.543702i) q^{98} +0.352025i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 2 q^{4} + 32 q^{9}+O(q^{10}) \) 64 * q - 2 * q^4 + 32 * q^9	\( 64 q - 2 q^{4} + 32 q^{9} + 26 q^{14} + 2 q^{16} + 24 q^{21} + 36 q^{24} - 30 q^{26} - 16 q^{29} - 60 q^{36} - 24 q^{44} + 4 q^{46} - 40 q^{49} - 114 q^{54} - 62 q^{56} - 24 q^{61} - 80 q^{64} - 132 q^{66} + 2 q^{74} - 72 q^{81} - 134 q^{84} + 8 q^{86} + 120 q^{89} - 90 q^{94} + 186 q^{96}+O(q^{100}) \) 64 * q - 2 * q^4 + 32 * q^9 + 26 * q^14 + 2 * q^16 + 24 * q^21 + 36 * q^24 - 30 * q^26 - 16 * q^29 - 60 * q^36 - 24 * q^44 + 4 * q^46 - 40 * q^49 - 114 * q^54 - 62 * q^56 - 24 * q^61 - 80 * q^64 - 132 * q^66 + 2 * q^74 - 72 * q^81 - 134 * q^84 + 8 * q^86 + 120 * q^89 - 90 * q^94 + 186 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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