LMFDB - Embedded newform 891.2.f.f.82.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(82,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("891.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.f (of order $5$, degree $4$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			82.5
Character	$\chi$	$=$	891.82
Dual form			891.2.f.f.163.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0881157 + 0.271192i) q^{2} +(1.55225 - 1.12778i) q^{4} +(0.837045 - 2.57616i) q^{5} +(3.29540 - 2.39425i) q^{7} +(0.904002 + 0.656796i) q^{8} +0.772391 q^{10} +(1.82892 + 2.76678i) q^{11} +(1.19001 + 3.66248i) q^{13} +(0.939677 + 0.682715i) q^{14} +(1.08735 - 3.34653i) q^{16} +(-1.33502 + 4.10876i) q^{17} +(1.31246 + 0.953561i) q^{19} +(-1.60603 - 4.94285i) q^{20} +(-0.589172 + 0.739785i) q^{22} -1.86423 q^{23} +(-1.89087 - 1.37379i) q^{25} +(-0.888377 + 0.645443i) q^{26} +(2.41511 - 7.43295i) q^{28} +(-2.87472 + 2.08860i) q^{29} +(-1.50324 - 4.62650i) q^{31} +3.23818 q^{32} -1.23190 q^{34} +(-3.40956 - 10.4936i) q^{35} +(-6.26542 + 4.55210i) q^{37} +(-0.142950 + 0.439954i) q^{38} +(2.44870 - 1.77909i) q^{40} +(-5.55968 - 4.03935i) q^{41} +0.984991 q^{43} +(5.95925 + 2.23213i) q^{44} +(-0.164268 - 0.505566i) q^{46} +(-4.74598 - 3.44815i) q^{47} +(2.96411 - 9.12259i) q^{49} +(0.205947 - 0.633841i) q^{50} +(5.97766 + 4.34302i) q^{52} +(-0.485721 - 1.49489i) q^{53} +(8.65855 - 2.39567i) q^{55} +4.55158 q^{56} +(-0.819721 - 0.595562i) q^{58} +(-9.19245 + 6.67871i) q^{59} +(-2.65986 + 8.18620i) q^{61} +(1.12221 - 0.815335i) q^{62} +(-1.88937 - 5.81490i) q^{64} +10.4312 q^{65} -1.74056 q^{67} +(2.56148 + 7.88344i) q^{68} +(2.54534 - 1.84929i) q^{70} +(-1.77418 + 5.46036i) q^{71} +(3.27379 - 2.37855i) q^{73} +(-1.78657 - 1.29802i) q^{74} +3.11268 q^{76} +(12.6514 + 4.73875i) q^{77} +(-1.32264 - 4.07066i) q^{79} +(-7.71104 - 5.60240i) q^{80} +(0.605544 - 1.86367i) q^{82} +(-2.00867 + 6.18204i) q^{83} +(9.46735 + 6.87843i) q^{85} +(0.0867932 + 0.267122i) q^{86} +(-0.163863 + 3.70240i) q^{88} +9.26243 q^{89} +(12.6904 + 9.22014i) q^{91} +(-2.89376 + 2.10244i) q^{92} +(0.516917 - 1.59091i) q^{94} +(3.55511 - 2.58294i) q^{95} +(-2.29064 - 7.04988i) q^{97} +2.73516 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 11 q^{4} + 8 q^{5} + 2 q^{7} + 3 q^{8} - 4 q^{10} + 2 q^{11} + 11 q^{13} + 10 q^{14} + 9 q^{16} - 10 q^{17} + 4 q^{19} + 45 q^{20} + 16 q^{22} - 20 q^{23} - 11 q^{25} - 6 q^{26} - 27 q^{28}+ \cdots - 164 q^{98}+O(q^{100}) $ 36 * q + q^2 - 11 * q^4 + 8 * q^5 + 2 * q^7 + 3 * q^8 - 4 * q^10 + 2 * q^11 + 11 * q^13 + 10 * q^14 + 9 * q^16 - 10 * q^17 + 4 * q^19 + 45 * q^20 + 16 * q^22 - 20 * q^23 - 11 * q^25 - 6 * q^26 - 27 * q^28 + 23 * q^29 - 3 * q^31 - 18 * q^32 - 8 * q^34 + 9 * q^35 - 21 * q^37 + q^38 + 25 * q^40 - 10 * q^41 + 8 * q^43 + 19 * q^44 - 9 * q^46 + 34 * q^47 - q^49 + 27 * q^52 + 2 * q^53 + 9 * q^55 - 114 * q^56 - q^58 + 16 * q^59 + 3 * q^61 + 92 * q^62 + 13 * q^64 - 84 * q^65 - 10 * q^67 + 23 * q^68 + 46 * q^70 - 24 * q^71 - 20 * q^73 - 68 * q^74 - 16 * q^76 + 26 * q^77 - 19 * q^79 - 28 * q^80 + 47 * q^82 - 7 * q^83 - 25 * q^85 + 77 * q^86 - 18 * q^88 - 28 * q^89 + 10 * q^91 - 50 * q^92 + 63 * q^94 + 77 * q^95 + 33 * q^97 - 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.0881157	+	0.271192i	0.0623072	+	0.191762i	0.977365	−	0.211562i	$-0.0678549\pi$
$2$	0.0881157	+	0.271192i	0.0623072	+	0.191762i	−0.915057	+	0.403324i	$0.867855\pi$
$3$		0			0
$3$		0			0
$4$	1.55225	−	1.12778i	0.776127	−	0.563889i
$5$	0.837045	−	2.57616i	0.374338	−	1.15209i	−0.569587	−	0.821931i	$-0.692897\pi$
$5$	0.837045	−	2.57616i	0.374338	−	1.15209i	0.943924	−	0.330162i	$-0.107103\pi$
$6$		0			0
$7$	3.29540	−	2.39425i	1.24554	−	0.904940i	0.247588	−	0.968865i	$-0.420362\pi$
$7$	3.29540	−	2.39425i	1.24554	−	0.904940i	0.997955	+	0.0639253i	$0.0203619\pi$
$8$	0.904002	+	0.656796i	0.319613	+	0.232212i
$9$		0			0
$10$	0.772391			0.244251
$11$	1.82892	+	2.76678i	0.551439	+	0.834215i
$11$	1.82892	+	2.76678i	0.551439	+	0.834215i
$12$		0			0
$13$	1.19001	+	3.66248i	0.330050	+	1.01579i	0.969109	+	0.246631i	$0.0793236\pi$
$13$	1.19001	+	3.66248i	0.330050	+	1.01579i	−0.639060	+	0.769157i	$0.720676\pi$
$14$	0.939677	+	0.682715i	0.251139	+	0.182463i
$15$		0			0
$16$	1.08735	−	3.34653i	0.271839	−	0.836633i
$17$	−1.33502	+	4.10876i	−0.323789	+	0.996520i	0.648195	+	0.761474i	$0.275524\pi$
$17$	−1.33502	+	4.10876i	−0.323789	+	0.996520i	−0.971984	+	0.235046i	$0.924476\pi$
$18$		0			0
$19$	1.31246	+	0.953561i	0.301100	+	0.218762i	0.728068	−	0.685505i	$-0.240418\pi$
$19$	1.31246	+	0.953561i	0.301100	+	0.218762i	−0.426968	+	0.904267i	$0.640418\pi$
$20$	−1.60603	−	4.94285i	−0.359119	−	1.10526i
$21$		0			0
$22$	−0.589172	+	0.739785i	−0.125612	+	0.157723i
$23$	−1.86423			−0.388720			−0.194360	−	0.980930i	$-0.562263\pi$
$23$	−1.86423			−0.388720			−0.194360	+	0.980930i	$0.562263\pi$
$24$		0			0
$25$	−1.89087	−	1.37379i	−0.378173	−	0.274759i
$26$	−0.888377	+	0.645443i	−0.174225	+	0.126582i
$27$		0			0
$28$	2.41511	−	7.43295i	0.456413	−	1.40470i
$29$	−2.87472	+	2.08860i	−0.533821	+	0.387844i	−0.821785	−	0.569797i	$-0.807022\pi$
$29$	−2.87472	+	2.08860i	−0.533821	+	0.387844i	0.287964	+	0.957641i	$0.407022\pi$
$30$		0			0
$31$	−1.50324	−	4.62650i	−0.269990	−	0.830944i	−0.990502	−	0.137501i	$-0.956093\pi$
$31$	−1.50324	−	4.62650i	−0.269990	−	0.830944i	0.720512	−	0.693443i	$-0.243907\pi$
$32$	3.23818			0.572435
$33$		0			0
$34$	−1.23190			−0.211269
$35$	−3.40956	−	10.4936i	−0.576321	−	1.77374i
$36$		0			0
$37$	−6.26542	+	4.55210i	−1.03003	+	0.748360i	−0.968314	−	0.249734i	$-0.919657\pi$
$37$	−6.26542	+	4.55210i	−1.03003	+	0.748360i	−0.0617145	+	0.998094i	$0.519657\pi$
$38$	−0.142950	+	0.439954i	−0.0231895	+	0.0713699i
$39$		0			0
$40$	2.44870	−	1.77909i	0.387174	−	0.281298i
$41$	−5.55968	−	4.03935i	−0.868276	−	0.630840i	0.0618474	−	0.998086i	$-0.480301\pi$
$41$	−5.55968	−	4.03935i	−0.868276	−	0.630840i	−0.930124	+	0.367246i	$0.880301\pi$
$42$		0			0
$43$	0.984991			0.150210			0.0751049	−	0.997176i	$-0.476071\pi$
$43$	0.984991			0.150210			0.0751049	+	0.997176i	$0.476071\pi$
$44$	5.95925	+	2.23213i	0.898391	+	0.336506i
$45$		0			0
$46$	−0.164268	−	0.505566i	−0.0242200	−	0.0745416i
$47$	−4.74598	−	3.44815i	−0.692272	−	0.502965i	0.185134	−	0.982713i	$-0.440728\pi$
$47$	−4.74598	−	3.44815i	−0.692272	−	0.502965i	−0.877406	+	0.479748i	$0.840728\pi$
$48$		0			0
$49$	2.96411	−	9.12259i	0.423444	−	1.30323i
$50$	0.205947	−	0.633841i	0.0291254	−	0.0896386i
$51$		0			0
$52$	5.97766	+	4.34302i	0.828952	+	0.602269i
$53$	−0.485721	−	1.49489i	−0.0667189	−	0.205340i	0.912139	−	0.409881i	$-0.134430\pi$
$53$	−0.485721	−	1.49489i	−0.0667189	−	0.205340i	−0.978858	+	0.204541i	$0.934430\pi$
$54$		0			0
$55$	8.65855	−	2.39567i	1.16752	−	0.323032i
$56$	4.55158			0.608230
$57$		0			0
$58$	−0.819721	−	0.595562i	−0.107635	−	0.0782011i
$59$	−9.19245	+	6.67871i	−1.19676	+	0.869494i	−0.993962	−	0.109728i	$-0.965002\pi$
$59$	−9.19245	+	6.67871i	−1.19676	+	0.869494i	−0.202794	+	0.979222i	$0.565002\pi$
$60$		0			0
$61$	−2.65986	+	8.18620i	−0.340560	+	1.04814i	0.623358	+	0.781936i	$0.285768\pi$
$61$	−2.65986	+	8.18620i	−0.340560	+	1.04814i	−0.963918	+	0.266199i	$0.914232\pi$
$62$	1.12221	−	0.815335i	0.142521	−	0.103548i
$63$		0			0
$64$	−1.88937	−	5.81490i	−0.236172	−	0.726862i
$65$	10.4312			1.29383
$66$		0			0
$67$	−1.74056			−0.212644			−0.106322	−	0.994332i	$-0.533907\pi$
$67$	−1.74056			−0.212644			−0.106322	+	0.994332i	$0.533907\pi$
$68$	2.56148	+	7.88344i	0.310626	+	0.956007i
$69$		0			0
$70$	2.54534	−	1.84929i	0.304226	−	0.221033i
$71$	−1.77418	+	5.46036i	−0.210556	+	0.648026i	0.788883	+	0.614543i	$0.210660\pi$
$71$	−1.77418	+	5.46036i	−0.210556	+	0.648026i	−0.999439	+	0.0334822i	$0.989340\pi$
$72$		0			0
$73$	3.27379	−	2.37855i	0.383168	−	0.278388i	−0.379482	−	0.925199i	$-0.623898\pi$
$73$	3.27379	−	2.37855i	0.383168	−	0.278388i	0.762650	+	0.646811i	$0.223898\pi$
$74$	−1.78657	−	1.29802i	−0.207685	−	0.150892i
$75$		0			0
$76$	3.11268			0.357049
$77$	12.6514	+	4.73875i	1.44176	+	0.540031i
$78$		0			0
$79$	−1.32264	−	4.07066i	−0.148808	−	0.457985i	0.848673	−	0.528918i	$-0.177402\pi$
$79$	−1.32264	−	4.07066i	−0.148808	−	0.457985i	−0.997481	+	0.0709332i	$0.977402\pi$
$80$	−7.71104	−	5.60240i	−0.862120	−	0.626367i
$81$		0			0
$82$	0.605544	−	1.86367i	0.0668711	−	0.205808i
$83$	−2.00867	+	6.18204i	−0.220480	+	0.678567i	0.778239	+	0.627968i	$0.216113\pi$
$83$	−2.00867	+	6.18204i	−0.220480	+	0.678567i	−0.998719	+	0.0505994i	$0.983887\pi$
$84$		0			0
$85$	9.46735	+	6.87843i	1.02688	+	0.746071i
$86$	0.0867932	+	0.267122i	0.00935915	+	0.0288045i
$87$		0			0
$88$	−0.163863	+	3.70240i	−0.0174679	+	0.394677i
$89$	9.26243			0.981816			0.490908	−	0.871211i	$-0.336665\pi$
$89$	9.26243			0.981816			0.490908	+	0.871211i	$0.336665\pi$
$90$		0			0
$91$	12.6904	+	9.22014i	1.33032	+	0.966533i
$92$	−2.89376	+	2.10244i	−0.301696	+	0.219195i
$93$		0			0
$94$	0.516917	−	1.59091i	0.0533160	−	0.164090i
$95$	3.55511	−	2.58294i	0.364747	−	0.265004i
$96$		0			0
$97$	−2.29064	−	7.04988i	−0.232580	−	0.715807i	−0.997433	−	0.0716026i	$-0.977189\pi$
$97$	−2.29064	−	7.04988i	−0.232580	−	0.715807i	0.764854	−	0.644204i	$-0.222811\pi$
$98$	2.73516			0.276293
$99$		0			0
$100$	−4.48444			−0.448444
$101$	−4.23897	−	13.0462i	−0.421794	−	1.29815i	−0.906031	−	0.423211i	$-0.860903\pi$
$101$	−4.23897	−	13.0462i	−0.421794	−	1.29815i	0.484238	−	0.874936i	$-0.339097\pi$
$102$		0			0
$103$	−4.10596	+	2.98316i	−0.404572	+	0.293939i	−0.771401	−	0.636350i	$-0.780444\pi$
$103$	−4.10596	+	2.98316i	−0.404572	+	0.293939i	0.366828	+	0.930289i	$0.380444\pi$
$104$	−1.32973	+	4.09248i	−0.130391	+	0.401301i
$105$		0			0
$106$	0.362604	−	0.263447i	0.0352192	−	0.0255883i
$107$	2.24824	+	1.63344i	0.217346	+	0.157911i	0.691131	−	0.722730i	$-0.257113\pi$
$107$	2.24824	+	1.63344i	0.217346	+	0.157911i	−0.473785	+	0.880640i	$0.657113\pi$
$108$		0			0
$109$	−17.3573			−1.66253			−0.831263	−	0.555879i	$-0.812382\pi$
$109$	−17.3573			−1.66253			−0.831263	+	0.555879i	$0.812382\pi$
$110$	1.41264	+	2.13703i	0.134690	+	0.203758i
$111$		0			0
$112$	−4.42916	−	13.6316i	−0.418516	−	1.28806i
$113$	−0.763432	−	0.554666i	−0.0718177	−	0.0521786i	0.551297	−	0.834309i	$-0.314133\pi$
$113$	−0.763432	−	0.554666i	−0.0718177	−	0.0521786i	−0.623115	+	0.782130i	$0.714133\pi$
$114$		0			0
$115$	−1.56045	+	4.80257i	−0.145513	+	0.447842i
$116$	−2.10681	+	6.48408i	−0.195612	+	0.602032i
$117$		0			0
$118$	−2.62121	−	1.90442i	−0.241302	−	0.175316i
$119$	5.43797	+	16.7364i	0.498498	+	1.53422i
$120$		0			0
$121$	−4.31012	+	10.1204i	−0.391829	+	0.920038i
$122$	−2.45441			−0.222212
$123$		0			0
$124$	−7.55108	−	5.48618i	−0.678107	−	0.492673i
$125$	5.83521	−	4.23953i	0.521917	−	0.379195i
$126$		0			0
$127$	0.757216	−	2.33047i	0.0671920	−	0.206796i	−0.911823	−	0.410583i	$-0.865325\pi$
$127$	0.757216	−	2.33047i	0.0671920	−	0.206796i	0.979015	+	0.203787i	$0.0653251\pi$
$128$	6.64996	−	4.83148i	0.587779	−	0.427047i
$129$		0			0
$130$	0.919154	+	2.82886i	0.0806151	+	0.248108i
$131$	3.99737			0.349252			0.174626	−	0.984635i	$-0.444128\pi$
$131$	3.99737			0.349252			0.174626	+	0.984635i	$0.444128\pi$
$132$		0			0
$133$	6.60815			0.572999
$134$	−0.153371	−	0.472027i	−0.0132492	−	0.0407769i
$135$		0			0
$136$	−3.90547	+	2.83749i	−0.334892	+	0.243313i
$137$	0.336599	−	1.03594i	0.0287576	−	0.0885067i	−0.935648	−	0.352936i	$-0.885183\pi$
$137$	0.336599	−	1.03594i	0.0287576	−	0.0885067i	0.964405	+	0.264429i	$0.0851835\pi$
$138$		0			0
$139$	−2.33395	+	1.69572i	−0.197963	+	0.143829i	−0.682351	−	0.731025i	$-0.739042\pi$
$139$	−2.33395	+	1.69572i	−0.197963	+	0.143829i	0.484388	+	0.874853i	$0.339042\pi$
$140$	−17.1269	−	12.4434i	−1.44749	−	1.05166i
$141$		0			0
$142$	−1.63714			−0.137386
$143$	−7.95683	+	9.99087i	−0.665383	+	0.835478i
$144$		0			0
$145$	2.97431	+	9.15398i	0.247003	+	0.760197i
$146$	0.933515	+	0.678238i	0.0772583	+	0.0561314i
$147$		0			0
$148$	−4.59177	+	14.1320i	−0.377441	+	1.16164i
$149$	6.23436	−	19.1874i	0.510739	−	1.57189i	−0.280165	−	0.959952i	$-0.590389\pi$
$149$	6.23436	−	19.1874i	0.510739	−	1.57189i	0.790904	−	0.611940i	$-0.209611\pi$
$150$		0			0
$151$	8.96258	+	6.51169i	0.729364	+	0.529914i	0.889362	−	0.457203i	$-0.151149\pi$
$151$	8.96258	+	6.51169i	0.729364	+	0.529914i	−0.159998	+	0.987117i	$0.551149\pi$
$152$	0.560175	+	1.72404i	0.0454362	+	0.139838i
$153$		0			0
$154$	−0.170330	+	3.84851i	−0.0137255	+	0.310122i
$155$	−13.1769			−1.05839
$156$		0			0
$157$	−0.269228	−	0.195606i	−0.0214867	−	0.0156110i	0.576990	−	0.816751i	$-0.304227\pi$
$157$	−0.269228	−	0.195606i	−0.0214867	−	0.0156110i	−0.598477	+	0.801140i	$0.704227\pi$
$158$	0.987387	−	0.717378i	0.0785523	−	0.0570716i
$159$		0			0
$160$	2.71050	−	8.34207i	0.214284	−	0.659499i
$161$	−6.14339	+	4.46344i	−0.484167	+	0.351768i
$162$		0			0
$163$	4.12168	+	12.6852i	0.322835	+	0.993584i	0.972408	+	0.233285i	$0.0749475\pi$
$163$	4.12168	+	12.6852i	0.322835	+	0.993584i	−0.649574	+	0.760299i	$0.725053\pi$
$164$	−13.1855			−1.02962
$165$		0			0
$166$	−1.85352			−0.143861
$167$	−5.84510	−	17.9894i	−0.452308	−	1.39206i	−0.874267	−	0.485445i	$-0.838658\pi$
$167$	−5.84510	−	17.9894i	−0.452308	−	1.39206i	0.421960	−	0.906615i	$-0.361342\pi$
$168$		0			0
$169$	−1.48039	+	1.07557i	−0.113876	+	0.0827359i
$170$	−1.03115	+	3.17357i	−0.0790860	+	0.243402i
$171$		0			0
$172$	1.52896	−	1.11085i	0.116582	−	0.0847016i
$173$	1.22492	+	0.889958i	0.0931292	+	0.0676623i	0.633375	−	0.773845i	$-0.281669\pi$
$173$	1.22492	+	0.889958i	0.0931292	+	0.0676623i	−0.540246	+	0.841507i	$0.681669\pi$
$174$		0			0
$175$	−9.52036			−0.719671
$176$	11.2478	−	3.11207i	0.847835	−	0.234581i
$177$		0			0
$178$	0.816166	+	2.51190i	0.0611742	+	0.188275i
$179$	−10.6703	−	7.75244i	−0.797537	−	0.579445i	0.112653	−	0.993634i	$-0.464065\pi$
$179$	−10.6703	−	7.75244i	−0.797537	−	0.579445i	−0.910191	+	0.414190i	$0.864065\pi$
$180$		0			0
$181$	0.864886	−	2.66185i	0.0642865	−	0.197853i	−0.913754	−	0.406267i	$-0.866830\pi$
$181$	0.864886	−	2.66185i	0.0642865	−	0.197853i	0.978041	+	0.208414i	$0.0668301\pi$
$182$	−1.38220	+	4.25398i	−0.102456	+	0.315326i
$183$		0			0
$184$	−1.68527	−	1.22442i	−0.124240	−	0.0902656i
$185$	6.48248	+	19.9510i	0.476602	+	1.46683i
$186$		0			0
$187$	−13.8097	+	3.82089i	−1.00986	+	0.279411i
$188$	−11.2557			−0.820907
$189$		0			0
$190$	1.01374	+	0.736522i	0.0735441	+	0.0534329i
$191$	13.5442	−	9.84044i	0.980024	−	0.712029i	0.0223100	−	0.999751i	$-0.492898\pi$
$191$	13.5442	−	9.84044i	0.980024	−	0.712029i	0.957714	+	0.287722i	$0.0928979\pi$
$192$		0			0
$193$	−6.81054	+	20.9607i	−0.490233	+	1.50878i	0.334022	+	0.942565i	$0.391594\pi$
$193$	−6.81054	+	20.9607i	−0.490233	+	1.50878i	−0.824255	+	0.566218i	$0.808406\pi$
$194$	1.71003	−	1.24241i	0.122773	−	0.0891998i
$195$		0			0
$196$	−5.68721	−	17.5034i	−0.406229	−	1.25024i
$197$	18.2247			1.29845			0.649227	−	0.760595i	$-0.275093\pi$
$197$	18.2247			1.29845			0.649227	+	0.760595i	$0.275093\pi$
$198$		0			0
$199$	−25.0958			−1.77899			−0.889497	−	0.456942i	$-0.848945\pi$
$199$	−25.0958			−1.77899			−0.889497	+	0.456942i	$0.848945\pi$
$200$	−0.807044	−	2.48383i	−0.0570666	−	0.175633i
$201$		0			0
$202$	3.16451	−	2.29915i	0.222654	−	0.161768i
$203$	−4.47270	+	13.7656i	−0.313922	+	0.966153i
$204$		0			0
$205$	−15.0597	+	10.9415i	−1.05181	+	0.764188i
$206$	−1.17081	−	0.850642i	−0.0815741	−	0.0592670i
$207$		0			0
$208$	13.5506			0.939563
$209$	−0.237902	+	5.37528i	−0.0164560	+	0.371816i
$210$		0			0
$211$	2.55558	+	7.86526i	0.175933	+	0.541467i	0.999675	−	0.0254986i	$-0.00811733\pi$
$211$	2.55558	+	7.86526i	0.175933	+	0.541467i	−0.823742	+	0.566965i	$0.808117\pi$
$212$	−2.43987	−	1.77267i	−0.167571	−	0.121747i
$213$		0			0
$214$	−0.244872	+	0.753637i	−0.0167391	+	0.0515176i
$215$	0.824482	−	2.53749i	0.0562292	−	0.173056i
$216$		0			0
$217$	−16.0308	−	11.6470i	−1.08824	−	0.790652i
$218$	−1.52945	−	4.70716i	−0.103587	−	0.318809i
$219$		0			0
$220$	10.7385	−	13.4836i	0.723988	−	0.909064i
$221$	−16.6369			−1.11912
$222$		0			0
$223$	5.94796	+	4.32145i	0.398305	+	0.289385i	0.768850	−	0.639429i	$-0.220829\pi$
$223$	5.94796	+	4.32145i	0.398305	+	0.289385i	−0.370545	+	0.928814i	$0.620829\pi$
$224$	10.6711	−	7.75301i	0.712993	−	0.518020i
$225$		0			0
$226$	0.0831507	−	0.255912i	0.00553110	−	0.0170230i
$227$	15.3237	−	11.1334i	1.01707	−	0.738947i	0.0513921	−	0.998679i	$-0.483634\pi$
$227$	15.3237	−	11.1334i	1.01707	−	0.738947i	0.965681	+	0.259732i	$0.0836342\pi$
$228$		0			0
$229$	−2.42870	−	7.47478i	−0.160493	−	0.493947i	0.838183	−	0.545389i	$-0.183618\pi$
$229$	−2.42870	−	7.47478i	−0.160493	−	0.493947i	−0.998676	+	0.0514422i	$0.983618\pi$
$230$	−1.43992			−0.0949454
$231$		0			0
$232$	−3.97054			−0.260678
$233$	−2.03006	−	6.24789i	−0.132994	−	0.409313i	0.862279	−	0.506434i	$-0.169037\pi$
$233$	−2.03006	−	6.24789i	−0.132994	−	0.409313i	−0.995273	+	0.0971212i	$0.969037\pi$
$234$		0			0
$235$	−12.8556	+	9.34013i	−0.838606	+	0.609283i
$236$	−6.73691	+	20.7341i	−0.438536	+	1.34967i
$237$		0			0
$238$	−4.05960	+	2.94947i	−0.263145	+	0.191186i
$239$	20.6674	+	15.0157i	1.33686	+	0.971287i	0.999553	+	0.0298925i	$0.00951648\pi$
$239$	20.6674	+	15.0157i	1.33686	+	0.971287i	0.337308	+	0.941394i	$0.390484\pi$
$240$		0			0
$241$	−2.98198			−0.192086			−0.0960432	−	0.995377i	$-0.530619\pi$
$241$	−2.98198			−0.192086			−0.0960432	+	0.995377i	$0.530619\pi$
$242$	−3.12437	−	0.277103i	−0.200842	−	0.0178129i
$243$		0			0
$244$	5.10344	+	15.7068i	0.326714	+	1.00552i
$245$	−21.0201	−	15.2720i	−1.34293	−	0.975694i
$246$		0			0
$247$	−1.93055	+	5.94161i	−0.122838	+	0.378056i
$248$	1.67973	−	5.16969i	0.106663	−	0.328276i
$249$		0			0
$250$	1.66390	+	1.20889i	0.105234	+	0.0764572i
$251$	3.60577	+	11.0974i	0.227594	+	0.700463i	0.998018	+	0.0629308i	$0.0200447\pi$
$251$	3.60577	+	11.0974i	0.227594	+	0.700463i	−0.770424	+	0.637532i	$0.779955\pi$
$252$		0			0
$253$	−3.40953	−	5.15792i	−0.214355	−	0.324276i
$254$	0.698728			0.0438421
$255$		0			0
$256$	−7.99667	−	5.80992i	−0.499792	−	0.363120i
$257$	−16.7664	+	12.1815i	−1.04586	+	0.759863i	−0.971421	−	0.237363i	$-0.923717\pi$
$257$	−16.7664	+	12.1815i	−1.04586	+	0.759863i	−0.0744403	+	0.997225i	$0.523717\pi$
$258$		0			0
$259$	−9.74822	+	30.0019i	−0.605725	+	1.86423i
$260$	16.1919	−	11.7641i	1.00418	−	0.729578i
$261$		0			0
$262$	0.352231	+	1.08406i	0.0217609	+	0.0669732i
$263$	9.08545			0.560233			0.280117	−	0.959966i	$-0.409627\pi$
$263$	9.08545			0.560233			0.280117	+	0.959966i	$0.409627\pi$
$264$		0			0
$265$	−4.25766			−0.261546
$266$	0.582281	+	1.79208i	0.0357020	+	0.109879i
$267$		0			0
$268$	−2.70179	+	1.96297i	−0.165038	+	0.119907i
$269$	2.45399	−	7.55261i	0.149623	−	0.460491i	−0.847954	−	0.530070i	$-0.822166\pi$
$269$	2.45399	−	7.55261i	0.149623	−	0.460491i	0.997576	+	0.0695792i	$0.0221656\pi$
$270$		0			0
$271$	−3.01249	+	2.18870i	−0.182995	+	0.132954i	−0.675512	−	0.737349i	$-0.736077\pi$
$271$	−3.01249	+	2.18870i	−0.182995	+	0.132954i	0.492516	+	0.870303i	$0.336077\pi$
$272$	12.2985	+	8.93536i	0.745704	+	0.541786i
$273$		0			0
$274$	0.310600			0.0187640
$275$	0.342746	−	7.74416i	0.0206683	−	0.466991i
$276$		0			0
$277$	−1.20536	−	3.70973i	−0.0724232	−	0.222896i	0.908292	−	0.418336i	$-0.137386\pi$
$277$	−1.20536	−	3.70973i	−0.0724232	−	0.222896i	−0.980716	+	0.195440i	$0.937386\pi$
$278$	−0.665523	−	0.483531i	−0.0399154	−	0.0290003i
$279$		0			0
$280$	3.80987	−	11.7256i	0.227684	−	0.700738i
$281$	0.0122442	−	0.0376838i	0.000730428	−	0.00224803i	−0.950691	−	0.310141i	$-0.899624\pi$
$281$	0.0122442	−	0.0376838i	0.000730428	−	0.00224803i	0.951421	+	0.307893i	$0.0996238\pi$
$282$		0			0
$283$	−5.17275	−	3.75822i	−0.307488	−	0.223403i	0.423330	−	0.905976i	$-0.360861\pi$
$283$	−5.17275	−	3.75822i	−0.307488	−	0.223403i	−0.730818	+	0.682572i	$0.760861\pi$
$284$	3.40410	+	10.4767i	0.201996	+	0.621680i
$285$		0			0
$286$	−3.41057	−	1.27748i	−0.201671	−	0.0755388i
$287$	−27.9925			−1.65235
$288$		0			0
$289$	−1.34634	−	0.978174i	−0.0791965	−	0.0575397i
$290$	−2.22041	+	1.61322i	−0.130387	+	0.0947315i
$291$		0			0
$292$	2.39928	−	7.38421i	0.140407	−	0.432128i
$293$	18.9370	−	13.7585i	1.10631	−	0.803782i	0.124233	−	0.992253i	$-0.460353\pi$
$293$	18.9370	−	13.7585i	1.10631	−	0.803782i	0.982079	+	0.188471i	$0.0603531\pi$
$294$		0			0
$295$	9.51092	+	29.2716i	0.553747	+	1.70426i
$296$	−8.65375			−0.502989
$297$		0			0
$298$	5.75282			0.333252
$299$	−2.21846	−	6.82772i	−0.128297	−	0.394857i
$300$		0			0
$301$	3.24594	−	2.35831i	0.187093	−	0.135931i
$302$	−0.976177	+	3.00436i	−0.0561727	+	0.172882i
$303$		0			0
$304$	4.61824	−	3.35534i	0.264874	−	0.192442i
$305$	18.8625	+	13.7044i	1.08007	+	0.784713i
$306$		0			0
$307$	29.1494			1.66365			0.831823	−	0.555042i	$-0.187298\pi$
$307$	29.1494			1.66365			0.831823	+	0.555042i	$0.187298\pi$
$308$	24.9824	−	6.91218i	1.42350	−	0.393858i
$309$		0			0
$310$	−1.16109	−	3.57347i	−0.0659455	−	0.202959i
$311$	15.9423	+	11.5827i	0.904003	+	0.656797i	0.939491	−	0.342573i	$-0.111299\pi$
$311$	15.9423	+	11.5827i	0.904003	+	0.656797i	−0.0354879	+	0.999370i	$0.511299\pi$
$312$		0			0
$313$	0.413581	−	1.27287i	0.0233770	−	0.0719470i	−0.938687	−	0.344769i	$-0.887957\pi$
$313$	0.413581	−	1.27287i	0.0233770	−	0.0719470i	0.962064	+	0.272822i	$0.0879571\pi$
$314$	0.0293235	−	0.0902485i	0.00165482	−	0.00509302i
$315$		0			0
$316$	−6.64387	−	4.82706i	−0.373747	−	0.271543i
$317$	1.23634	+	3.80507i	0.0694400	+	0.213714i	0.979754	−	0.200203i	$-0.0641602\pi$
$317$	1.23634	+	3.80507i	0.0694400	+	0.213714i	−0.910314	+	0.413917i	$0.864160\pi$
$318$		0			0
$319$	−11.0363	−	4.13382i	−0.617915	−	0.231449i
$320$	−16.5616			−0.925821
$321$		0			0
$322$	−1.75178	−	1.27274i	−0.0976228	−	0.0709271i
$323$	−5.67011	+	4.11958i	−0.315493	+	0.229219i
$324$		0			0
$325$	2.78134	−	8.56008i	0.154281	−	0.474828i
$326$	−3.07695	+	2.23554i	−0.170417	+	0.123815i
$327$		0			0
$328$	−2.37294	−	7.30315i	−0.131024	−	0.403249i
$329$	−23.8956			−1.31741
$330$		0			0
$331$	3.18033			0.174807			0.0874034	−	0.996173i	$-0.472143\pi$
$331$	3.18033			0.174807			0.0874034	+	0.996173i	$0.472143\pi$
$332$	3.85401	+	11.8614i	0.211516	+	0.650980i
$333$		0			0
$334$	4.36353	−	3.17029i	0.238762	−	0.173471i
$335$	−1.45693	+	4.48397i	−0.0796006	+	0.244985i
$336$		0			0
$337$	14.7223	−	10.6964i	0.801977	−	0.582670i	−0.109517	−	0.993985i	$-0.534930\pi$
$337$	14.7223	−	10.6964i	0.801977	−	0.582670i	0.911493	+	0.411315i	$0.134930\pi$
$338$	−0.422131	−	0.306696i	−0.0229609	−	0.0166821i
$339$		0			0
$340$	22.4531			1.21769
$341$	10.0512	−	12.6206i	0.544303	−	0.683445i
$342$		0			0
$343$	−3.26270	−	10.0416i	−0.176169	−	0.542193i
$344$	0.890434	+	0.646938i	0.0480090	+	0.0348806i
$345$		0			0
$346$	−0.133415	+	0.410609i	−0.00717243	+	0.0220745i
$347$	−8.47142	+	26.0724i	−0.454770	+	1.39964i	0.416635	+	0.909074i	$0.363209\pi$
$347$	−8.47142	+	26.0724i	−0.454770	+	1.39964i	−0.871405	+	0.490564i	$0.836791\pi$
$348$		0			0
$349$	−18.5310	−	13.4635i	−0.991940	−	0.720686i	−0.0315945	−	0.999501i	$-0.510059\pi$
$349$	−18.5310	−	13.4635i	−0.991940	−	0.720686i	−0.960345	+	0.278815i	$0.910059\pi$
$350$	−0.838893	−	2.58185i	−0.0448407	−	0.138006i
$351$		0			0
$352$	5.92237	+	8.95933i	0.315663	+	0.477534i
$353$	−29.7047			−1.58102			−0.790511	−	0.612448i	$-0.790185\pi$
$353$	−29.7047			−1.58102			−0.790511	+	0.612448i	$0.790185\pi$
$354$		0			0
$355$	12.5817	+	9.14113i	0.667767	+	0.485161i
$356$	14.3776	−	10.4460i	0.762013	−	0.553635i
$357$		0			0
$358$	1.16218	−	3.57682i	0.0614231	−	0.189041i
$359$	29.8183	−	21.6643i	1.57375	−	1.14340i	0.650299	−	0.759678i	$-0.274644\pi$
$359$	29.8183	−	21.6643i	1.57375	−	1.14340i	0.923450	−	0.383718i	$-0.125356\pi$
$360$		0			0
$361$	−5.05804	−	15.5670i	−0.266213	−	0.819318i
$362$	0.798082			0.0419462
$363$		0			0
$364$	30.0970			1.57751
$365$	−3.38721	−	10.4247i	−0.177294	−	0.545656i
$366$		0			0
$367$	20.1127	−	14.6127i	1.04987	−	0.762777i	0.0776846	−	0.996978i	$-0.475247\pi$
$367$	20.1127	−	14.6127i	1.04987	−	0.762777i	0.972188	+	0.234201i	$0.0752473\pi$
$368$	−2.02708	+	6.23872i	−0.105669	+	0.325216i
$369$		0			0
$370$	−4.83936	+	3.51600i	−0.251586	+	0.182788i
$371$	−5.17979	−	3.76334i	−0.268921	−	0.195383i
$372$		0			0
$373$	18.2790			0.946453			0.473227	−	0.880941i	$-0.343089\pi$
$373$	18.2790			0.946453			0.473227	+	0.880941i	$0.343089\pi$
$374$	−2.25304	−	3.40839i	−0.116502	−	0.176244i
$375$		0			0
$376$	−2.02564	−	6.23428i	−0.104464	−	0.321508i
$377$	−11.0704	−	8.04312i	−0.570155	−	0.414242i
$378$		0			0
$379$	−9.72145	+	29.9196i	−0.499357	+	1.53686i	0.310697	+	0.950509i	$0.399438\pi$
$379$	−9.72145	+	29.9196i	−0.499357	+	1.53686i	−0.810054	+	0.586355i	$0.800562\pi$
$380$	2.60545	−	8.01876i	0.133657	−	0.411354i
$381$		0			0
$382$	3.86211	+	2.80598i	0.197603	+	0.143567i
$383$	−3.84163	−	11.8233i	−0.196298	−	0.604143i	−0.999959	−	0.00905578i	$-0.997117\pi$
$383$	−3.84163	−	11.8233i	−0.196298	−	0.604143i	0.803661	−	0.595087i	$-0.202883\pi$
$384$		0			0
$385$	22.7975	−	28.6254i	1.16187	−	1.45888i
$386$	−6.28449			−0.319872
$387$		0			0
$388$	−11.5064	−	8.35986i	−0.584147	−	0.424408i
$389$	−5.92175	+	4.30240i	−0.300244	+	0.218140i	−0.727699	−	0.685896i	$-0.759410\pi$
$389$	−5.92175	+	4.30240i	−0.300244	+	0.218140i	0.427455	+	0.904037i	$0.359410\pi$
$390$		0			0
$391$	2.48878	−	7.65969i	0.125863	−	0.387367i
$392$	8.67124	−	6.30003i	0.437964	−	0.318199i
$393$		0			0
$394$	1.60588	+	4.94239i	0.0809030	+	0.248994i
$395$	−11.5938			−0.583346
$396$		0			0
$397$	34.2087			1.71688			0.858442	−	0.512911i	$-0.171433\pi$
$397$	34.2087			1.71688			0.858442	+	0.512911i	$0.171433\pi$
$398$	−2.21133	−	6.80578i	−0.110844	−	0.341143i
$399$		0			0
$400$	−6.65349	+	4.83404i	−0.332675	+	0.241702i
$401$	2.31014	−	7.10988i	0.115363	−	0.355051i	−0.876660	−	0.481111i	$-0.840233\pi$
$401$	2.31014	−	7.10988i	0.115363	−	0.355051i	0.992023	+	0.126061i	$0.0402334\pi$
$402$		0			0
$403$	15.1556	−	11.0112i	0.754953	−	0.548505i
$404$	−21.2932	−	15.4704i	−1.05938	−	0.769682i
$405$		0			0
$406$	−4.12723			−0.204831
$407$	−24.0536	−	9.00962i	−1.19229	−	0.446590i
$408$		0			0
$409$	0.744792	+	2.29224i	0.0368276	+	0.113344i	0.967780	−	0.251796i	$-0.0810212\pi$
$409$	0.744792	+	2.29224i	0.0368276	+	0.113344i	−0.930953	+	0.365140i	$0.881021\pi$
$410$	−4.29425	−	3.11995i	−0.212078	−	0.154084i
$411$		0			0
$412$	−3.00915	+	9.26122i	−0.148250	+	0.456268i
$413$	−14.3023	+	44.0180i	−0.703771	+	2.16598i
$414$		0			0
$415$	14.2446	+	10.3493i	0.699239	+	0.508027i
$416$	3.85347	+	11.8598i	0.188932	+	0.581473i
$417$		0			0
$418$	−1.47870	+	0.409129i	−0.0723254	+	0.0200112i
$419$	−11.2018			−0.547242			−0.273621	−	0.961838i	$-0.588221\pi$
$419$	−11.2018			−0.547242			−0.273621	+	0.961838i	$0.588221\pi$
$420$		0			0
$421$	5.58615	+	4.05858i	0.272252	+	0.197803i	0.715531	−	0.698581i	$-0.246185\pi$
$421$	5.58615	+	4.05858i	0.272252	+	0.197803i	−0.443279	+	0.896384i	$0.646185\pi$
$422$	−1.90781	+	1.38611i	−0.0928708	+	0.0674746i
$423$		0			0
$424$	0.542748	−	1.67041i	0.0263582	−	0.0811222i
$425$	8.16893	−	5.93507i	0.396251	−	0.287893i
$426$		0			0
$427$	10.8345	+	33.3451i	0.524318	+	1.61368i
$428$	5.33200			0.257732
$429$		0			0
$430$	0.760798			0.0366890
$431$	−9.01729	−	27.7524i	−0.434348	−	1.33678i	−0.893754	−	0.448558i	$-0.851938\pi$
$431$	−9.01729	−	27.7524i	−0.434348	−	1.33678i	0.459406	−	0.888226i	$-0.348062\pi$
$432$		0			0
$433$	29.5582	−	21.4753i	1.42048	−	1.03204i	0.428785	−	0.903407i	$-0.358942\pi$
$433$	29.5582	−	21.4753i	1.42048	−	1.03204i	0.991693	−	0.128630i	$-0.0410581\pi$
$434$	1.74602	−	5.37370i	0.0838117	−	0.257946i
$435$		0			0
$436$	−26.9429	+	19.5752i	−1.29033	+	0.937480i
$437$	−2.44674	−	1.77766i	−0.117043	−	0.0850370i
$438$		0			0
$439$	−21.4975			−1.02602			−0.513009	−	0.858383i	$-0.671469\pi$
$439$	−21.4975			−1.02602			−0.513009	+	0.858383i	$0.671469\pi$
$440$	9.40081	+	3.52121i	0.448166	+	0.167867i
$441$		0			0
$442$	−1.46597	−	4.51180i	−0.0697293	−	0.214605i
$443$	27.0576	+	19.6585i	1.28554	+	0.934002i	0.999705	−	0.0242753i	$-0.00772784\pi$
$443$	27.0576	+	19.6585i	1.28554	+	0.934002i	0.285839	+	0.958278i	$0.407728\pi$
$444$		0			0
$445$	7.75307	−	23.8615i	0.367531	−	1.13114i
$446$	−0.647834	+	1.99383i	−0.0306758	+	0.0944105i
$447$		0			0
$448$	−20.1485	−	14.6388i	−0.951929	−	0.691617i
$449$	12.2165	+	37.5984i	0.576530	+	1.77438i	0.630908	+	0.775858i	$0.282682\pi$
$449$	12.2165	+	37.5984i	0.576530	+	1.77438i	−0.0543777	+	0.998520i	$0.517318\pi$
$450$		0			0
$451$	1.00777	−	22.7700i	0.0474540	−	1.07220i
$452$	−1.81058			−0.0851625
$453$		0			0
$454$	4.36954	+	3.17466i	0.205073	+	0.148994i
$455$	34.3750	−	24.9749i	1.61152	−	1.17084i
$456$		0			0
$457$	11.5919	−	35.6763i	0.542248	−	1.66887i	−0.185196	−	0.982702i	$-0.559292\pi$
$457$	11.5919	−	35.6763i	0.542248	−	1.66887i	0.727444	−	0.686167i	$-0.240708\pi$
$458$	1.81309	−	1.31729i	0.0847204	−	0.0615529i
$459$		0			0
$460$	2.99402	+	9.21464i	0.139597	+	0.429635i
$461$	19.3653			0.901932			0.450966	−	0.892541i	$-0.351080\pi$
$461$	19.3653			0.901932			0.450966	+	0.892541i	$0.351080\pi$
$462$		0			0
$463$	−14.3493			−0.666867			−0.333434	−	0.942774i	$-0.608207\pi$
$463$	−14.3493			−0.666867			−0.333434	+	0.942774i	$0.608207\pi$
$464$	3.86375	+	11.8914i	0.179370	+	0.552044i
$465$		0			0
$466$	1.51550	−	1.10107i	0.0702041	−	0.0510063i
$467$	−6.89755	+	21.2285i	−0.319180	+	0.982336i	0.654819	+	0.755786i	$0.272745\pi$
$467$	−6.89755	+	21.2285i	−0.319180	+	0.982336i	−0.973999	+	0.226551i	$0.927255\pi$
$468$		0			0
$469$	−5.73585	+	4.16734i	−0.264857	+	0.192430i
$470$	−3.66575	−	2.66332i	−0.169088	−	0.122850i
$471$		0			0
$472$	−12.6965			−0.584406
$473$	1.80147	+	2.72525i	0.0828316	+	0.125307i
$474$		0			0
$475$	−1.17170	−	3.60611i	−0.0537611	−	0.165460i
$476$	27.3160	+	19.8462i	1.25203	+	0.909651i
$477$		0			0
$478$	−2.25103	+	6.92795i	−0.102960	+	0.316877i
$479$	−7.18824	+	22.1231i	−0.328439	+	1.01083i	0.641425	+	0.767186i	$0.278343\pi$
$479$	−7.18824	+	22.1231i	−0.328439	+	1.01083i	−0.969864	+	0.243646i	$0.921657\pi$
$480$		0			0
$481$	−24.1279	−	17.5299i	−1.10014	−	0.799296i
$482$	−0.262760	−	0.808691i	−0.0119684	−	0.0368349i
$483$		0			0
$484$	4.72319	+	20.5703i	0.214690	+	0.935014i
$485$	−20.0790			−0.911740
$486$		0			0
$487$	−0.219083	−	0.159173i	−0.00992760	−	0.00721282i	0.582810	−	0.812608i	$-0.301953\pi$
$487$	−0.219083	−	0.159173i	−0.00992760	−	0.00721282i	−0.592738	+	0.805395i	$0.701953\pi$
$488$	−7.78118	+	5.65336i	−0.352237	+	0.255915i
$489$		0			0
$490$	2.28945	−	7.04621i	0.103427	−	0.318315i
$491$	3.40318	−	2.47255i	0.153583	−	0.111585i	−0.508340	−	0.861157i	$-0.669741\pi$
$491$	3.40318	−	2.47255i	0.153583	−	0.111585i	0.661923	+	0.749572i	$0.269741\pi$
$492$		0			0
$493$	−4.74377	−	14.5998i	−0.213649	−	0.657544i
$494$	−1.78143			−0.0801504
$495$		0			0
$496$	−17.1173			−0.768589
$497$	7.22682	+	22.2419i	0.324167	+	0.997685i
$498$		0			0
$499$	12.4299	−	9.03087i	0.556440	−	0.404277i	−0.273714	−	0.961811i	$-0.588252\pi$
$499$	12.4299	−	9.03087i	0.556440	−	0.404277i	0.830154	+	0.557534i	$0.188252\pi$
$500$	4.27647	−	13.1616i	0.191250	−	0.588606i
$501$		0			0
$502$	−2.69181	+	1.95571i	−0.120141	+	0.0872878i
$503$	−3.16786	−	2.30159i	−0.141248	−	0.102623i	0.514917	−	0.857240i	$-0.327823\pi$
$503$	−3.16786	−	2.30159i	−0.141248	−	0.102623i	−0.656165	+	0.754617i	$0.727823\pi$
$504$		0			0
$505$	−37.1573			−1.65348
$506$	1.09836	−	1.37913i	0.0488279	−	0.0613099i
$507$		0			0
$508$	−1.45286	−	4.47145i	−0.0644604	−	0.198389i
$509$	−23.0969	−	16.7809i	−1.02375	−	0.743801i	−0.0567047	−	0.998391i	$-0.518059\pi$
$509$	−23.0969	−	16.7809i	−1.02375	−	0.743801i	−0.967049	+	0.254590i	$0.918059\pi$
$510$		0			0
$511$	5.09361	−	15.6765i	0.225328	−	0.693488i
$512$	5.95109	−	18.3156i	0.263004	−	0.809442i
$513$		0			0
$514$	−4.78092	−	3.47354i	−0.210877	−	0.153211i
$515$	4.24821	+	13.0746i	0.187198	+	0.576138i
$516$		0			0
$517$	0.860274	−	19.4375i	0.0378348	−	0.854858i
$518$	−8.99526			−0.395229
$519$		0			0
$520$	9.42984	+	6.85118i	0.413526	+	0.300444i
$521$	11.5485	−	8.39049i	0.505950	−	0.367594i	−0.305335	−	0.952245i	$-0.598768\pi$
$521$	11.5485	−	8.39049i	0.505950	−	0.367594i	0.811285	+	0.584651i	$0.198768\pi$
$522$		0			0
$523$	−10.2462	+	31.5345i	−0.448034	+	1.37891i	0.431088	+	0.902310i	$0.358130\pi$
$523$	−10.2462	+	31.5345i	−0.448034	+	1.37891i	−0.879122	+	0.476597i	$0.841870\pi$
$524$	6.20494	−	4.50815i	0.271064	−	0.196939i
$525$		0			0
$526$	0.800571	+	2.46390i	0.0349066	+	0.107431i
$527$	21.0160			0.915472
$528$		0			0
$529$	−19.5246			−0.848897
$530$	−0.375166	−	1.15464i	−0.0162962	−	0.0501545i
$531$		0			0
$532$	10.2575	−	7.45252i	0.444720	−	0.323108i
$533$	8.17793	−	25.1691i	0.354225	−	1.09019i
$534$		0			0
$535$	6.08988	−	4.42456i	0.263289	−	0.191290i
$536$	−1.57347	−	1.14320i	−0.0679637	−	0.0493785i
$537$		0			0
$538$	2.26444			0.0976271
$539$	30.6613	−	8.48344i	1.32068	−	0.365407i
$540$		0			0
$541$	−8.79490	−	27.0679i	−0.378122	−	1.16374i	−0.941348	−	0.337437i	$-0.890440\pi$
$541$	−8.79490	−	27.0679i	−0.378122	−	1.16374i	0.563226	−	0.826303i	$-0.309560\pi$
$542$	−0.859005	−	0.624104i	−0.0368974	−	0.0268076i
$543$		0			0
$544$	−4.32303	+	13.3049i	−0.185348	+	0.570443i
$545$	−14.5288	+	44.7151i	−0.622346	+	1.91539i
$546$		0			0
$547$	24.8745	+	18.0724i	1.06356	+	0.772721i	0.974744	−	0.223327i	$-0.0716919\pi$
$547$	24.8745	+	18.0724i	1.06356	+	0.772721i	0.0888154	+	0.996048i	$0.471692\pi$
$548$	−0.645829	−	1.98766i	−0.0275884	−	0.0849085i
$549$		0			0
$550$	2.13036	−	0.589432i	0.0908388	−	0.0251335i
$551$	−5.76457			−0.245579
$552$		0			0
$553$	−14.1048	−	10.2477i	−0.599796	−	0.435778i
$554$	0.899837	−	0.653770i	0.0382304	−	0.0277760i
$555$		0			0
$556$	−1.71050	+	5.26436i	−0.0725412	+	0.223259i
$557$	5.90145	−	4.28765i	0.250052	−	0.181674i	−0.455698	−	0.890135i	$-0.650610\pi$
$557$	5.90145	−	4.28765i	0.250052	−	0.181674i	0.705750	+	0.708461i	$0.250610\pi$
$558$		0			0
$559$	1.17215	+	3.60751i	0.0495767	+	0.152581i
$560$	−38.8245			−1.64063
$561$		0			0
$562$	0.0112985			0.000476597
$563$	−11.3018	−	34.7834i	−0.476315	−	1.46595i	−0.844176	−	0.536065i	$-0.819910\pi$
$563$	−11.3018	−	34.7834i	−0.476315	−	1.46595i	0.367862	−	0.929881i	$-0.380090\pi$
$564$		0			0
$565$	−2.06793	+	1.50244i	−0.0869987	+	0.0632082i
$566$	0.563400	−	1.73397i	0.0236815	−	0.0728841i
$567$		0			0
$568$	−5.19020	+	3.77090i	−0.217776	+	0.158224i
$569$	−0.122553	−	0.0890399i	−0.00513769	−	0.00373275i	0.585213	−	0.810879i	$-0.301011\pi$
$569$	−0.122553	−	0.0890399i	−0.00513769	−	0.00373275i	−0.590351	+	0.807147i	$0.701011\pi$
$570$		0			0
$571$	43.2254			1.80893			0.904463	−	0.426552i	$-0.140272\pi$
$571$	43.2254			1.80893			0.904463	+	0.426552i	$0.140272\pi$
$572$	−1.08353	+	24.4819i	−0.0453048	+	1.02364i
$573$		0			0
$574$	−2.46658	−	7.59136i	−0.102953	−	0.316857i
$575$	3.52502	+	2.56108i	0.147003	+	0.106804i
$576$		0			0
$577$	9.00017	−	27.6997i	0.374682	−	1.15315i	−0.569011	−	0.822330i	$-0.692674\pi$
$577$	9.00017	−	27.6997i	0.374682	−	1.15315i	0.943693	−	0.330822i	$-0.107326\pi$
$578$	0.146639	−	0.451310i	0.00609940	−	0.0187720i
$579$		0			0
$580$	14.9405	+	10.8549i	0.620372	+	0.450727i
$581$	8.18198	+	25.1815i	0.339446	+	1.04471i
$582$		0			0
$583$	3.24770	−	4.07792i	0.134506	−	0.168890i
$584$	4.52173			0.187111
$585$		0			0
$586$	5.39985	+	3.92322i	0.223066	+	0.162067i
$587$	18.3605	−	13.3397i	0.757821	−	0.550589i	−0.140420	−	0.990092i	$-0.544845\pi$
$587$	18.3605	−	13.3397i	0.757821	−	0.550589i	0.898241	+	0.439503i	$0.144845\pi$
$588$		0			0
$589$	2.43870	−	7.50554i	0.100485	−	0.309261i
$590$	−7.10017	+	5.15857i	−0.292309	+	0.212375i
$591$		0			0
$592$	8.42100	+	25.9172i	0.346101	+	1.06519i
$593$	−22.9308			−0.941656			−0.470828	−	0.882225i	$-0.656045\pi$
$593$	−22.9308			−0.941656			−0.470828	+	0.882225i	$0.656045\pi$
$594$		0			0
$595$	47.6673			1.95417
$596$	−11.9618	−	36.8147i	−0.489975	−	1.50799i
$597$		0			0
$598$	1.65614	−	1.20326i	0.0677247	−	0.0492049i
$599$	−3.86293	+	11.8889i	−0.157835	+	0.485766i	−0.998437	−	0.0558871i	$-0.982201\pi$
$599$	−3.86293	+	11.8889i	−0.157835	+	0.485766i	0.840602	+	0.541653i	$0.182201\pi$
$600$		0			0
$601$	−18.1858	+	13.2127i	−0.741812	+	0.538958i	−0.893278	−	0.449504i	$-0.851601\pi$
$601$	−18.1858	+	13.2127i	−0.741812	+	0.538958i	0.151466	+	0.988462i	$0.451601\pi$
$602$	0.925574	+	0.672469i	0.0377236	+	0.0274078i
$603$		0			0
$604$	21.2559			0.864892
$605$	22.4640	+	19.5748i	0.913293	+	0.795829i
$606$		0			0
$607$	8.25222	+	25.3977i	0.334947	+	1.03086i	0.966748	+	0.255731i	$0.0823161\pi$
$607$	8.25222	+	25.3977i	0.334947	+	1.03086i	−0.631801	+	0.775131i	$0.717684\pi$
$608$	4.25000	+	3.08780i	0.172360	+	0.125227i
$609$		0			0
$610$	−2.05445	+	6.32295i	−0.0831822	+	0.256009i
$611$	6.98102	−	21.4854i	0.282422	−	0.869205i
$612$		0			0
$613$	35.1797	+	25.5595i	1.42089	+	1.03234i	0.991623	+	0.129163i	$0.0412289\pi$
$613$	35.1797	+	25.5595i	1.42089	+	1.03234i	0.429269	+	0.903176i	$0.358771\pi$
$614$	2.56852	+	7.90510i	0.103657	+	0.319024i
$615$		0			0
$616$	8.32446	+	12.5932i	0.335402	+	0.507395i
$617$	41.4255			1.66773			0.833864	−	0.551969i	$-0.186123\pi$
$617$	41.4255			1.66773			0.833864	+	0.551969i	$0.186123\pi$
$618$		0			0
$619$	−7.20976	−	5.23820i	−0.289785	−	0.210541i	0.433389	−	0.901207i	$-0.357318\pi$
$619$	−7.20976	−	5.23820i	−0.289785	−	0.210541i	−0.723174	+	0.690666i	$0.757318\pi$
$620$	−20.4539	+	14.8606i	−0.821446	+	0.596816i
$621$		0			0
$622$	−1.73638	+	5.34404i	−0.0696227	+	0.214277i
$623$	30.5234	−	22.1765i	1.22289	−	0.888485i
$624$		0			0
$625$	−9.64859	−	29.6953i	−0.385944	−	1.18781i
$626$	0.381636			0.0152532
$627$		0			0
$628$	−0.638510			−0.0254793
$629$	−10.3390	−	31.8202i	−0.412244	−	1.26876i
$630$		0			0
$631$	4.58752	−	3.33303i	0.182626	−	0.132686i	−0.492716	−	0.870190i	$-0.663996\pi$
$631$	4.58752	−	3.33303i	0.182626	−	0.132686i	0.675342	+	0.737504i	$0.263996\pi$
$632$	1.47793	−	4.54859i	0.0587888	−	0.180933i
$633$		0			0
$634$	−0.922965	+	0.670573i	−0.0366556	+	0.0266319i
$635$	−5.36984	−	3.90142i	−0.213096	−	0.154823i
$636$		0			0
$637$	36.9386			1.46356
$638$	0.148586	−	3.35722i	0.00588257	−	0.132914i
$639$		0			0
$640$	−6.88034	−	21.1755i	−0.271970	−	0.837036i
$641$	−21.6964	−	15.7633i	−0.856955	−	0.622615i	0.0700995	−	0.997540i	$-0.477668\pi$
$641$	−21.6964	−	15.7633i	−0.856955	−	0.622615i	−0.927055	+	0.374925i	$0.877668\pi$
$642$		0			0
$643$	4.36902	−	13.4465i	0.172297	−	0.530277i	−0.827202	−	0.561904i	$-0.810069\pi$
$643$	4.36902	−	13.4465i	0.172297	−	0.530277i	0.999500	+	0.0316272i	$0.0100689\pi$
$644$	−4.50234	+	13.8568i	−0.177417	+	0.546033i
$645$		0			0
$646$	−1.61682	−	1.17469i	−0.0636130	−	0.0462176i
$647$	−0.393698	−	1.21168i	−0.0154779	−	0.0476360i	0.943019	−	0.332738i	$-0.107973\pi$
$647$	−0.393698	−	1.21168i	−0.0154779	−	0.0476360i	−0.958497	+	0.285102i	$0.907973\pi$
$648$		0			0
$649$	−35.2907	−	13.2187i	−1.38528	−	0.518878i
$650$	2.56651			0.100667
$651$		0			0
$652$	20.7040	+	15.0423i	0.810832	+	0.589104i
$653$	3.90620	−	2.83802i	0.152861	−	0.111060i	−0.508726	−	0.860929i	$-0.669883\pi$
$653$	3.90620	−	2.83802i	0.152861	−	0.111060i	0.661587	+	0.749868i	$0.269883\pi$
$654$		0			0
$655$	3.34598	−	10.2979i	0.130738	−	0.402371i
$656$	−19.5632	+	14.2135i	−0.763813	+	0.554942i
$657$		0			0
$658$	−2.10558	−	6.48030i	−0.0820840	−	0.252628i
$659$	−22.1777			−0.863921			−0.431961	−	0.901892i	$-0.642178\pi$
$659$	−22.1777			−0.863921			−0.431961	+	0.901892i	$0.642178\pi$
$660$		0			0
$661$	−27.3975			−1.06564			−0.532820	−	0.846229i	$-0.678868\pi$
$661$	−27.3975			−1.06564			−0.532820	+	0.846229i	$0.678868\pi$
$662$	0.280237	+	0.862481i	0.0108917	+	0.0335213i
$663$		0			0
$664$	−5.87618	+	4.26930i	−0.228040	+	0.165681i
$665$	5.53132	−	17.0236i	0.214495	−	0.660148i
$666$		0			0
$667$	5.35915	−	3.89365i	0.207507	−	0.150763i
$668$	−29.3611	−	21.3321i	−1.13602	−	0.825363i
$669$		0			0
$670$	−1.34440			−0.0519385
$671$	−27.5141	+	7.61265i	−1.06217	+	0.293883i
$672$		0			0
$673$	10.8909	+	33.5186i	0.419812	+	1.29205i	0.907876	+	0.419239i	$0.137703\pi$
$673$	10.8909	+	33.5186i	0.419812	+	1.29205i	−0.488064	+	0.872808i	$0.662297\pi$
$674$	4.19805	+	3.05006i	0.161703	+	0.117484i
$675$		0			0
$676$	−1.08494	+	3.33910i	−0.0417285	+	0.128427i
$677$	−13.6122	+	41.8940i	−0.523159	+	1.61012i	0.244769	+	0.969581i	$0.421288\pi$
$677$	−13.6122	+	41.8940i	−0.523159	+	1.61012i	−0.767928	+	0.640536i	$0.778712\pi$
$678$		0			0
$679$	−24.4277	−	17.7478i	−0.937450	−	0.681098i
$680$	4.04078	+	12.4362i	0.154957	+	0.476908i
$681$		0			0
$682$	4.30828	+	1.61373i	0.164973	+	0.0617929i
$683$	42.2845			1.61797			0.808985	−	0.587829i	$-0.200017\pi$
$683$	42.2845			1.61797			0.808985	+	0.587829i	$0.200017\pi$
$684$		0			0
$685$	−2.38701	−	1.73426i	−0.0912029	−	0.0662628i
$686$	2.43570	−	1.76964i	0.0929954	−	0.0675651i
$687$		0			0
$688$	1.07103	−	3.29631i	0.0408328	−	0.125670i
$689$	4.89701	−	3.55788i	0.186561	−	0.135545i
$690$		0			0
$691$	−2.61641	−	8.05248i	−0.0995329	−	0.306331i	0.888876	−	0.458149i	$-0.151487\pi$
$691$	−2.61641	−	8.05248i	−0.0995329	−	0.306331i	−0.988408	+	0.151818i	$0.951487\pi$
$692$	2.90507			0.110434
$693$		0			0
$694$	−7.81709			−0.296733
$695$	2.41481	+	7.43203i	0.0915990	+	0.281913i
$696$		0			0
$697$	24.0190	−	17.4508i	0.909783	−	0.660996i
$698$	2.01834	−	6.21180i	0.0763952	−	0.235120i
$699$		0			0
$700$	−14.7780	+	10.7368i	−0.558556	+	0.405815i
$701$	−35.2342	−	25.5991i	−1.33078	−	0.966865i	−0.999730	−	0.0232503i	$-0.992599\pi$
$701$	−35.2342	−	25.5991i	−1.33078	−	0.966865i	−0.331046	−	0.943615i	$-0.607401\pi$
$702$		0			0
$703$	−12.5638			−0.473854
$704$	12.6330	−	15.8624i	0.476125	−	0.597839i
$705$		0			0
$706$	−2.61745	−	8.05569i	−0.0985091	−	0.303180i
$707$	−45.2050	−	32.8433i	−1.70011	−	1.23520i
$708$		0			0
$709$	−1.86253	+	5.73229i	−0.0699489	+	0.215281i	−0.979920	−	0.199391i	$-0.936104\pi$
$709$	−1.86253	+	5.73229i	−0.0699489	+	0.215281i	0.909971	+	0.414672i	$0.136104\pi$
$710$	−1.37036	+	4.21753i	−0.0514287	+	0.158281i
$711$		0			0
$712$	8.37326	+	6.08353i	0.313801	+	0.227990i
$713$	2.80239	+	8.62488i	0.104950	+	0.323004i
$714$		0			0
$715$	19.0778	+	28.8609i	0.713471	+	1.07933i
$716$	−25.3061			−0.945732
$717$		0			0
$718$	8.50264	+	6.17753i	0.317316	+	0.230543i
$719$	−32.6897	+	23.7504i	−1.21912	+	0.885741i	−0.996027	−	0.0890560i	$-0.971615\pi$
$719$	−32.6897	+	23.7504i	−1.21912	+	0.885741i	−0.223092	+	0.974797i	$0.571615\pi$
$720$		0			0
$721$	−6.38836	+	19.6614i	−0.237915	+	0.732227i
$722$	3.77597	−	2.74340i	0.140527	−	0.102099i
$723$		0			0
$724$	−1.65945	−	5.10726i	−0.0616729	−	0.189810i
$725$	8.30501			0.308441
$726$		0			0
$727$	18.7206			0.694310			0.347155	−	0.937808i	$-0.387148\pi$
$727$	18.7206			0.694310			0.347155	+	0.937808i	$0.387148\pi$
$728$	5.41643	+	16.6700i	0.200746	+	0.617833i
$729$		0			0
$730$	2.52864	−	1.83717i	0.0935893	−	0.0679966i
$731$	−1.31498	+	4.04709i	−0.0486363	+	0.149687i
$732$		0			0
$733$	−0.456440	+	0.331623i	−0.0168590	+	0.0122488i	−0.596183	−	0.802849i	$-0.703317\pi$
$733$	−0.456440	+	0.331623i	−0.0168590	+	0.0122488i	0.579324	+	0.815097i	$0.303317\pi$
$734$	5.73510	+	4.16679i	0.211686	+	0.153799i
$735$		0			0
$736$	−6.03673			−0.222517
$737$	−3.18335	−	4.81575i	−0.117260	−	0.177391i
$738$		0			0
$739$	0.602004	+	1.85278i	0.0221451	+	0.0681555i	0.961518	−	0.274741i	$-0.0885921\pi$
$739$	0.602004	+	1.85278i	0.0221451	+	0.0681555i	−0.939373	+	0.342896i	$0.888592\pi$
$740$	32.5628	+	23.6582i	1.19703	+	0.869694i
$741$		0			0
$742$	0.564167	−	1.73633i	0.0207112	−	0.0637426i
$743$	−8.42464	+	25.9284i	−0.309070	+	0.951220i	0.669057	+	0.743211i	$0.266698\pi$
$743$	−8.42464	+	25.9284i	−0.309070	+	0.951220i	−0.978127	+	0.208009i	$0.933302\pi$
$744$		0			0
$745$	−44.2113	−	32.1214i	−1.61978	−	1.17684i
$746$	1.61067	+	4.95714i	0.0589709	+	0.181494i
$747$		0			0
$748$	−17.1270	+	21.5052i	−0.626224	+	0.786308i
$749$	11.3197			0.413613
$750$		0			0
$751$	−24.5183	−	17.8136i	−0.894685	−	0.650027i	0.0424105	−	0.999100i	$-0.486496\pi$
$751$	−24.5183	−	17.8136i	−0.894685	−	0.650027i	−0.937095	+	0.349074i	$0.886496\pi$
$752$	−16.6999	+	12.1332i	−0.608983	+	0.442452i
$753$		0			0
$754$	1.20576	−	3.71093i	0.0439110	−	0.135144i
$755$	24.2772	−	17.6384i	0.883539	−	0.641929i
$756$		0			0
$757$	3.43224	+	10.5634i	0.124747	+	0.383931i	0.993855	−	0.110691i	$-0.0353064\pi$
$757$	3.43224	+	10.5634i	0.124747	+	0.383931i	−0.869108	+	0.494622i	$0.835306\pi$
$758$	−8.97056			−0.325826
$759$		0			0
$760$	4.91030			0.178115
$761$	−10.3029	−	31.7091i	−0.373481	−	1.14945i	−0.944498	−	0.328517i	$-0.893451\pi$
$761$	−10.3029	−	31.7091i	−0.373481	−	1.14945i	0.571017	−	0.820938i	$-0.306549\pi$
$762$		0			0
$763$	−57.1992	+	41.5576i	−2.07075	+	1.50449i
$764$	9.92620	−	30.5497i	0.359117	−	1.10525i
$765$		0			0
$766$	2.86788	−	2.08364i	0.103621	−	0.0752849i
$767$	−35.3997	−	25.7194i	−1.27821	−	0.928674i
$768$		0			0
$769$	−51.9401			−1.87301			−0.936504	−	0.350656i	$-0.885959\pi$
$769$	−51.9401			−1.87301			−0.936504	+	0.350656i	$0.885959\pi$
$770$	9.77180	+	3.66017i	0.352151	+	0.131903i
$771$		0			0
$772$	13.0673	+	40.2171i	0.470303	+	1.44744i
$773$	6.24784	+	4.53932i	0.224719	+	0.163268i	0.694448	−	0.719542i	$-0.255648\pi$
$773$	6.24784	+	4.53932i	0.224719	+	0.163268i	−0.469729	+	0.882811i	$0.655648\pi$
$774$		0			0
$775$	−3.51343	+	10.8132i	−0.126206	+	0.388423i
$776$	2.55959	−	7.87759i	0.0918838	−	0.282789i
$777$		0			0
$778$	−1.68858	−	1.22682i	−0.0605384	−	0.0439837i
$779$	−3.44512	−	10.6030i	−0.123434	−	0.379891i
$780$		0			0
$781$	−18.3524	+	5.07779i	−0.656702	+	0.181698i
$782$	2.29655			0.0821244
$783$		0			0
$784$	−27.3060	−	19.8390i	−0.975215	−	0.708535i
$785$	−0.729267	+	0.529844i	−0.0260287	+	0.0189109i
$786$		0			0
$787$	−6.08959	+	18.7418i	−0.217070	+	0.668074i	0.781930	+	0.623367i	$0.214236\pi$
$787$	−6.08959	+	18.7418i	−0.217070	+	0.668074i	−0.999000	+	0.0447073i	$0.985764\pi$
$788$	28.2893	−	20.5534i	1.00776	−	0.732184i
$789$		0			0
$790$	−1.02159	−	3.14414i	−0.0363467	−	0.111864i
$791$	−3.84382			−0.136670
$792$		0			0
$793$	−33.1470			−1.17709
$794$	3.01432	+	9.27712i	0.106974	+	0.329233i
$795$		0			0
$796$	−38.9550	+	28.3025i	−1.38072	+	1.00315i
$797$	4.33420	−	13.3393i	0.153525	−	0.472502i	−0.844483	−	0.535582i	$-0.820092\pi$
$797$	4.33420	−	13.3393i	0.153525	−	0.472502i	0.998008	+	0.0630799i	$0.0200923\pi$
$798$		0			0
$799$	20.5036	−	14.8967i	0.725365	−	0.527008i
$800$	−6.12297	−	4.44860i	−0.216480	−	0.157282i
$801$		0			0
$802$	2.13170			0.0752731
$803$	12.5684	+	4.70768i	0.443529	+	0.166130i
$804$		0			0
$805$	6.35623	+	19.5625i	0.224028	+	0.689486i
$806$	4.32159	+	3.13982i	0.152221	+	0.110595i
$807$		0			0
$808$	4.73666	−	14.5779i	0.166635	−	0.512850i
$809$	−6.46767	+	19.9055i	−0.227391	+	0.699839i	0.770649	+	0.637260i	$0.219932\pi$
$809$	−6.46767	+	19.9055i	−0.227391	+	0.699839i	−0.998040	+	0.0625783i	$0.980068\pi$
$810$		0			0
$811$	−1.57186	−	1.14203i	−0.0551956	−	0.0401019i	0.559845	−	0.828597i	$-0.310861\pi$
$811$	−1.57186	−	1.14203i	−0.0551956	−	0.0401019i	−0.615041	+	0.788495i	$0.710861\pi$
$812$	8.58173	+	26.4118i	0.301160	+	0.926874i
$813$		0			0
$814$	0.323842	−	7.31703i	0.0113506	−	0.256462i
$815$	36.1292			1.26555
$816$		0			0
$817$	1.29276	+	0.939249i	0.0452281	+	0.0328601i
$818$	−0.556008	+	0.403964i	−0.0194404	+	0.0141243i
$819$		0			0
$820$	−11.0369	+	33.9680i	−0.385424	+	1.18621i
$821$	−8.77117	+	6.37263i	−0.306116	+	0.222406i	−0.730228	−	0.683203i	$-0.760586\pi$
$821$	−8.77117	+	6.37263i	−0.306116	+	0.222406i	0.424112	+	0.905610i	$0.360586\pi$
$822$		0			0
$823$	14.7302	+	45.3348i	0.513461	+	1.58027i	0.786065	+	0.618144i	$0.212115\pi$
$823$	14.7302	+	45.3348i	0.513461	+	1.58027i	−0.272604	+	0.962126i	$0.587885\pi$
$824$	−5.67112			−0.197563
$825$		0			0
$826$	−13.1976			−0.459203
$827$	11.5619	+	35.5838i	0.402046	+	1.23737i	0.923337	+	0.383991i	$0.125451\pi$
$827$	11.5619	+	35.5838i	0.402046	+	1.23737i	−0.521291	+	0.853379i	$0.674549\pi$
$828$		0			0
$829$	−8.66207	+	6.29336i	−0.300846	+	0.218578i	−0.727959	−	0.685621i	$-0.759531\pi$
$829$	−8.66207	+	6.29336i	−0.300846	+	0.218578i	0.427113	+	0.904198i	$0.359531\pi$
$830$	−1.55148	+	4.77496i	−0.0538526	+	0.165741i
$831$		0			0
$832$	19.0486	−	13.8396i	0.660390	−	0.479801i
$833$	33.5254	+	24.3576i	1.16159	+	0.843941i
$834$		0			0
$835$	−51.2361			−1.77310
$836$	5.69284	+	8.61209i	0.196891	+	0.297856i
$837$		0			0
$838$	−0.987051	−	3.03783i	−0.0340971	−	0.104940i
$839$	−12.4277	−	9.02927i	−0.429053	−	0.311725i	0.352217	−	0.935918i	$-0.385428\pi$
$839$	−12.4277	−	9.02927i	−0.429053	−	0.311725i	−0.781270	+	0.624193i	$0.785428\pi$
$840$		0			0
$841$	−5.05976	+	15.5724i	−0.174475	+	0.536978i
$842$	−0.608427	+	1.87255i	−0.0209678	+	0.0645322i
$843$		0			0
$844$	12.8372	+	9.32675i	0.441874	+	0.321040i
$845$	1.53168	+	4.71402i	0.0526913	+	0.162167i
$846$		0			0
$847$	10.0272	+	43.6703i	0.344539	+	1.50053i
$848$	−5.53087			−0.189931
$849$		0			0
$850$	2.32936	+	1.69238i	0.0798963	+	0.0580480i
$851$	11.6802	−	8.48617i	0.400393	−	0.290902i
$852$		0			0
$853$	12.8132	−	39.4348i	0.438714	−	1.35022i	−0.450518	−	0.892767i	$-0.648761\pi$
$853$	12.8132	−	39.4348i	0.438714	−	1.35022i	0.889232	−	0.457456i	$-0.151239\pi$
$854$	−8.08825	+	5.87646i	−0.276774	+	0.201088i
$855$		0			0
$856$	0.959576	+	2.95327i	0.0327976	+	0.100941i
$857$	18.4055			0.628719			0.314359	−	0.949304i	$-0.398210\pi$
$857$	18.4055			0.628719			0.314359	+	0.949304i	$0.398210\pi$
$858$		0			0
$859$	−15.0485			−0.513449			−0.256725	−	0.966485i	$-0.582643\pi$
$859$	−15.0485			−0.513449			−0.256725	+	0.966485i	$0.582643\pi$
$860$	−1.58192	−	4.86866i	−0.0539432	−	0.166020i
$861$		0			0
$862$	6.73166	−	4.89084i	0.229281	−	0.166583i
$863$	−4.45906	+	13.7236i	−0.151788	+	0.467155i	−0.997821	−	0.0659746i	$-0.978984\pi$
$863$	−4.45906	+	13.7236i	−0.151788	+	0.467155i	0.846033	+	0.533130i	$0.178984\pi$
$864$		0			0
$865$	3.31799	−	2.41066i	0.112815	−	0.0819649i
$866$	8.42848	+	6.12365i	0.286411	+	0.208090i
$867$		0			0
$868$	−38.0191			−1.29045
$869$	8.84362	−	11.1044i	0.299999	−	0.376689i
$870$		0			0
$871$	−2.07129	−	6.37477i	−0.0701830	−	0.216001i
$872$	−15.6910	−	11.4002i	−0.531365	−	0.386059i
$873$		0			0
$874$	0.266492	−	0.820177i	0.00901421	−	0.0277429i
$875$	9.07885	−	27.9418i	0.306921	−	0.944607i
$876$		0			0
$877$	19.4774	+	14.1511i	0.657704	+	0.477850i	0.865887	−	0.500240i	$-0.166755\pi$
$877$	19.4774	+	14.1511i	0.657704	+	0.477850i	−0.208183	+	0.978090i	$0.566755\pi$
$878$	−1.89426	−	5.82994i	−0.0639283	−	0.196751i
$879$		0			0
$880$	1.39773	−	31.5811i	0.0471176	−	1.06460i
$881$	−10.0956			−0.340129			−0.170064	−	0.985433i	$-0.554398\pi$
$881$	−10.0956			−0.340129			−0.170064	+	0.985433i	$0.554398\pi$
$882$		0			0
$883$	−41.0332	−	29.8124i	−1.38088	−	1.00327i	−0.996798	−	0.0799659i	$-0.974519\pi$
$883$	−41.0332	−	29.8124i	−1.38088	−	1.00327i	−0.384079	−	0.923300i	$-0.625481\pi$
$884$	−25.8247	+	18.7628i	−0.868579	+	0.631060i
$885$		0			0
$886$	−2.94703	+	9.07002i	−0.0990074	+	0.304713i
$887$	2.08136	−	1.51220i	0.0698854	−	0.0507747i	−0.552294	−	0.833649i	$-0.686247\pi$
$887$	2.08136	−	1.51220i	0.0698854	−	0.0507747i	0.622179	+	0.782875i	$0.286247\pi$
$888$		0			0
$889$	−3.08439	−	9.49279i	−0.103447	−	0.318378i
$890$	7.15422			0.239810
$891$		0			0
$892$	14.1064			0.472316
$893$	−2.94090	−	9.05115i	−0.0984134	−	0.302885i
$894$		0			0
$895$	−28.9031	+	20.9993i	−0.966123	+	0.701929i
$896$	10.3465	−	31.8433i	0.345653	−	1.06381i
$897$		0			0
$898$	−9.11993	+	6.62602i	−0.304336	+	0.221113i
$899$	13.9843	+	10.1602i	0.466403	+	0.338862i
$900$		0			0
$901$	6.79061			0.226228
$902$	6.26386	−	1.73310i	0.208564	−	0.0577059i
$903$		0			0
$904$	−0.325842	−	1.00284i	−0.0108373	−	0.0333539i
$905$	−6.13339	−	4.45617i	−0.203881	−	0.148128i
$906$		0			0
$907$	3.18129	−	9.79100i	0.105633	−	0.325105i	−0.884246	−	0.467022i	$-0.845327\pi$
$907$	3.18129	−	9.79100i	0.105633	−	0.325105i	0.989878	+	0.141917i	$0.0453268\pi$
$908$	11.2304	−	34.5636i	0.372693	−	1.14703i
$909$		0			0
$910$	9.80197	+	7.12155i	0.324932	+	0.236077i
$911$	−4.82145	−	14.8389i	−0.159742	−	0.491635i	0.838869	−	0.544334i	$-0.183218\pi$
$911$	−4.82145	−	14.8389i	−0.159742	−	0.491635i	−0.998610	+	0.0526992i	$0.983218\pi$
$912$		0			0
$913$	−20.7780	+	5.74891i	−0.687652	+	0.190261i
$914$	10.6966			0.353811
$915$		0			0
$916$	−12.1999	−	8.86371i	−0.403094	−	0.292865i
$917$	13.1729	−	9.57070i	0.435009	−	0.316052i
$918$		0			0
$919$	3.46483	−	10.6637i	0.114294	−	0.351761i	−0.877505	−	0.479568i	$-0.840794\pi$
$919$	3.46483	−	10.6637i	0.114294	−	0.351761i	0.991799	+	0.127806i	$0.0407935\pi$
$920$	−4.56495	+	3.31663i	−0.150502	+	0.109346i
$921$		0			0
$922$	1.70639	+	5.25172i	0.0561968	+	0.172956i
$923$	−22.1097			−0.727751
$924$		0			0
$925$	18.1007			0.595148
$926$	−1.26440	−	3.89141i	−0.0415506	−	0.127880i
$927$		0			0
$928$	−9.30886	+	6.76328i	−0.305578	+	0.222016i
$929$	7.27040	−	22.3760i	0.238534	−	0.734132i	−0.758099	−	0.652140i	$-0.773872\pi$
$929$	7.27040	−	22.3760i	0.238534	−	0.734132i	0.996633	−	0.0819927i	$-0.0261284\pi$
$930$		0			0
$931$	12.5892	−	9.14661i	0.412595	−	0.299768i
$932$	−10.1974	−	7.40884i	−0.334027	−	0.242685i
$933$		0			0
$934$	−6.36478			−0.208262
$935$	−1.71609	+	38.7741i	−0.0561221	+	1.26805i
$936$		0			0
$937$	5.76486	+	17.7424i	0.188330	+	0.579619i	0.999990	−	0.00451068i	$-0.00143580\pi$
$937$	5.76486	+	17.7424i	0.188330	+	0.579619i	−0.811660	+	0.584130i	$0.801436\pi$
$938$	−1.63557	−	1.18831i	−0.0534032	−	0.0387997i
$939$		0			0
$940$	−9.42153	+	28.9965i	−0.307296	+	0.945761i
$941$	−10.0408	+	30.9023i	−0.327320	+	1.00739i	0.643063	+	0.765814i	$0.277663\pi$
$941$	−10.0408	+	30.9023i	−0.327320	+	1.00739i	−0.970383	+	0.241574i	$0.922337\pi$
$942$		0			0
$943$	10.3646	+	7.53029i	0.337516	+	0.245220i
$944$	12.3551	+	38.0250i	0.402123	+	1.23761i
$945$		0			0
$946$	−0.580329	+	0.728681i	−0.0188681	+	0.0236915i
$947$	−3.84273			−0.124872			−0.0624360	−	0.998049i	$-0.519887\pi$
$947$	−3.84273			−0.124872			−0.0624360	+	0.998049i	$0.519887\pi$
$948$		0			0
$949$	12.6072	+	9.15968i	0.409247	+	0.297336i
$950$	0.874704	−	0.635510i	0.0283792	−	0.0206187i
$951$		0			0
$952$	−6.07643	+	18.7013i	−0.196938	+	0.606114i
$953$	−15.4434	+	11.2203i	−0.500262	+	0.363461i	−0.809117	−	0.587648i	$-0.800054\pi$
$953$	−15.4434	+	11.2203i	−0.500262	+	0.363461i	0.308855	+	0.951109i	$0.400054\pi$
$954$		0			0
$955$	−14.0134	−	43.1289i	−0.453464	−	1.39562i
$956$	49.0154			1.58527
$957$		0			0
$958$	−6.63302			−0.214303
$959$	−1.37108	−	4.21975i	−0.0442745	−	0.136263i
$960$		0			0
$961$	5.93476	−	4.31185i	0.191444	−	0.139092i
$962$	2.62793	−	8.08795i	0.0847280	−	0.260766i
$963$		0			0
$964$	−4.62879	+	3.36302i	−0.149083	+	0.108315i
$965$	48.2973	+	35.0901i	1.55475	+	1.12959i
$966$		0			0
$967$	26.5627			0.854198			0.427099	−	0.904205i	$-0.359536\pi$
$967$	26.5627			0.854198			0.427099	+	0.904205i	$0.359536\pi$
$968$	−10.5434	+	6.31801i	−0.338878	+	0.203069i
$969$		0			0
$970$	−1.76927	−	5.44526i	−0.0568079	−	0.174837i
$971$	41.3472	+	30.0405i	1.32689	+	0.964045i	0.999819	+	0.0190472i	$0.00606329\pi$
$971$	41.3472	+	30.0405i	1.32689	+	0.964045i	0.327076	+	0.944998i	$0.393937\pi$
$972$		0			0
$973$	−3.63134	+	11.1761i	−0.116415	+	0.358290i
$974$	0.0238619	−	0.0734393i	0.000764584	−	0.00235315i
$975$		0			0
$976$	24.5032	+	17.8026i	0.784328	+	0.569847i
$977$	−6.54331	−	20.1382i	−0.209339	−	0.644279i	−0.999507	−	0.0313890i	$-0.990007\pi$
$977$	−6.54331	−	20.1382i	−0.209339	−	0.644279i	0.790168	−	0.612890i	$-0.209993\pi$
$978$		0			0
$979$	16.9402	+	25.6271i	0.541412	+	0.819046i
$980$	−49.8521			−1.59247
$981$		0			0
$982$	0.970410	+	0.705044i	0.0309670	+	0.0224989i
$983$	−41.1267	+	29.8803i	−1.31174	+	0.953034i	−0.311743	+	0.950166i	$0.600913\pi$
$983$	−41.1267	+	29.8803i	−1.31174	+	0.953034i	−0.999996	+	0.00286753i	$0.999087\pi$
$984$		0			0
$985$	15.2549	−	46.9496i	0.486060	−	1.49594i
$986$	3.54136	−	2.57295i	0.112780	−	0.0819394i
$987$		0			0
$988$	3.70412	+	11.4001i	0.117844	+	0.362686i
$989$	−1.83625			−0.0583895
$990$		0			0
$991$	−13.1480			−0.417662			−0.208831	−	0.977952i	$-0.566966\pi$
$991$	−13.1480			−0.417662			−0.208831	+	0.977952i	$0.566966\pi$
$992$	−4.86777	−	14.9815i	−0.154552	−	0.475662i
$993$		0			0
$994$	−5.39503	+	3.91972i	−0.171120	+	0.124326i
$995$	−21.0063	+	64.6507i	−0.665944	+	2.04957i
$996$		0			0
$997$	30.1024	−	21.8707i	0.953354	−	0.692652i	0.00175626	−	0.999998i	$-0.499441\pi$
$997$	30.1024	−	21.8707i	0.953354	−	0.692652i	0.951598	+	0.307346i	$0.0994410\pi$
$998$	3.54437	+	2.57514i	0.112195	+	0.0815146i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.f.f.82.5		36
3.2	odd	2		891.2.f.e.82.5		36
9.2	odd	6		297.2.n.b.280.5		72
9.4	even	3		99.2.m.b.16.5	✓	72
9.5	odd	6		297.2.n.b.181.5		72
9.7	even	3		99.2.m.b.49.5	yes	72
11.3	even	5		9801.2.a.cm.1.10		18
11.8	odd	10		9801.2.a.co.1.9		18
11.9	even	5	inner	891.2.f.f.163.5		36
33.8	even	10		9801.2.a.cn.1.10		18
33.14	odd	10		9801.2.a.cp.1.9		18
33.20	odd	10		891.2.f.e.163.5		36
99.20	odd	30		297.2.n.b.64.5		72
99.25	even	15		1089.2.e.p.364.9		36
99.31	even	15		99.2.m.b.97.5	yes	72
99.52	odd	30		1089.2.e.o.364.10		36
99.58	even	15		1089.2.e.p.727.9		36
99.85	odd	30		1089.2.e.o.727.10		36
99.86	odd	30		297.2.n.b.262.5		72
99.97	even	15		99.2.m.b.31.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.5	✓	72	9.4	even	3
99.2.m.b.31.5	yes	72	99.97	even	15
99.2.m.b.49.5	yes	72	9.7	even	3
99.2.m.b.97.5	yes	72	99.31	even	15
297.2.n.b.64.5		72	99.20	odd	30
297.2.n.b.181.5		72	9.5	odd	6
297.2.n.b.262.5		72	99.86	odd	30
297.2.n.b.280.5		72	9.2	odd	6
891.2.f.e.82.5		36	3.2	odd	2
891.2.f.e.163.5		36	33.20	odd	10
891.2.f.f.82.5		36	1.1	even	1	trivial
891.2.f.f.163.5		36	11.9	even	5	inner
1089.2.e.o.364.10		36	99.52	odd	30
1089.2.e.o.727.10		36	99.85	odd	30
1089.2.e.p.364.9		36	99.25	even	15
1089.2.e.p.727.9		36	99.58	even	15
9801.2.a.cm.1.10		18	11.3	even	5
9801.2.a.cn.1.10		18	33.8	even	10
9801.2.a.co.1.9		18	11.8	odd	10
9801.2.a.cp.1.9		18	33.14	odd	10

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0881157 + 0.271192i) q^{2} +(1.55225 - 1.12778i) q^{4} +(0.837045 - 2.57616i) q^{5} +(3.29540 - 2.39425i) q^{7} +(0.904002 + 0.656796i) q^{8} +0.772391 q^{10} +(1.82892 + 2.76678i) q^{11} +(1.19001 + 3.66248i) q^{13} +(0.939677 + 0.682715i) q^{14} +(1.08735 - 3.34653i) q^{16} +(-1.33502 + 4.10876i) q^{17} +(1.31246 + 0.953561i) q^{19} +(-1.60603 - 4.94285i) q^{20} +(-0.589172 + 0.739785i) q^{22} -1.86423 q^{23} +(-1.89087 - 1.37379i) q^{25} +(-0.888377 + 0.645443i) q^{26} +(2.41511 - 7.43295i) q^{28} +(-2.87472 + 2.08860i) q^{29} +(-1.50324 - 4.62650i) q^{31} +3.23818 q^{32} -1.23190 q^{34} +(-3.40956 - 10.4936i) q^{35} +(-6.26542 + 4.55210i) q^{37} +(-0.142950 + 0.439954i) q^{38} +(2.44870 - 1.77909i) q^{40} +(-5.55968 - 4.03935i) q^{41} +0.984991 q^{43} +(5.95925 + 2.23213i) q^{44} +(-0.164268 - 0.505566i) q^{46} +(-4.74598 - 3.44815i) q^{47} +(2.96411 - 9.12259i) q^{49} +(0.205947 - 0.633841i) q^{50} +(5.97766 + 4.34302i) q^{52} +(-0.485721 - 1.49489i) q^{53} +(8.65855 - 2.39567i) q^{55} +4.55158 q^{56} +(-0.819721 - 0.595562i) q^{58} +(-9.19245 + 6.67871i) q^{59} +(-2.65986 + 8.18620i) q^{61} +(1.12221 - 0.815335i) q^{62} +(-1.88937 - 5.81490i) q^{64} +10.4312 q^{65} -1.74056 q^{67} +(2.56148 + 7.88344i) q^{68} +(2.54534 - 1.84929i) q^{70} +(-1.77418 + 5.46036i) q^{71} +(3.27379 - 2.37855i) q^{73} +(-1.78657 - 1.29802i) q^{74} +3.11268 q^{76} +(12.6514 + 4.73875i) q^{77} +(-1.32264 - 4.07066i) q^{79} +(-7.71104 - 5.60240i) q^{80} +(0.605544 - 1.86367i) q^{82} +(-2.00867 + 6.18204i) q^{83} +(9.46735 + 6.87843i) q^{85} +(0.0867932 + 0.267122i) q^{86} +(-0.163863 + 3.70240i) q^{88} +9.26243 q^{89} +(12.6904 + 9.22014i) q^{91} +(-2.89376 + 2.10244i) q^{92} +(0.516917 - 1.59091i) q^{94} +(3.55511 - 2.58294i) q^{95} +(-2.29064 - 7.04988i) q^{97} +2.73516 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 11 q^{4} + 8 q^{5} + 2 q^{7} + 3 q^{8} - 4 q^{10} + 2 q^{11} + 11 q^{13} + 10 q^{14} + 9 q^{16} - 10 q^{17} + 4 q^{19} + 45 q^{20} + 16 q^{22} - 20 q^{23} - 11 q^{25} - 6 q^{26} - 27 q^{28}+ \cdots - 164 q^{98}+O(q^{100}) \) 36 * q + q^2 - 11 * q^4 + 8 * q^5 + 2 * q^7 + 3 * q^8 - 4 * q^10 + 2 * q^11 + 11 * q^13 + 10 * q^14 + 9 * q^16 - 10 * q^17 + 4 * q^19 + 45 * q^20 + 16 * q^22 - 20 * q^23 - 11 * q^25 - 6 * q^26 - 27 * q^28 + 23 * q^29 - 3 * q^31 - 18 * q^32 - 8 * q^34 + 9 * q^35 - 21 * q^37 + q^38 + 25 * q^40 - 10 * q^41 + 8 * q^43 + 19 * q^44 - 9 * q^46 + 34 * q^47 - q^49 + 27 * q^52 + 2 * q^53 + 9 * q^55 - 114 * q^56 - q^58 + 16 * q^59 + 3 * q^61 + 92 * q^62 + 13 * q^64 - 84 * q^65 - 10 * q^67 + 23 * q^68 + 46 * q^70 - 24 * q^71 - 20 * q^73 - 68 * q^74 - 16 * q^76 + 26 * q^77 - 19 * q^79 - 28 * q^80 + 47 * q^82 - 7 * q^83 - 25 * q^85 + 77 * q^86 - 18 * q^88 - 28 * q^89 + 10 * q^91 - 50 * q^92 + 63 * q^94 + 77 * q^95 + 33 * q^97 - 164 * q^98

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