LMFDB - Embedded newform 756.2.bo.a.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(85,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("756.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bo (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			337.2
Character	$\chi$	$=$	756.337
Dual form			756.2.bo.a.673.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55705 - 0.758672i) q^{3} +(0.267700 + 0.224627i) q^{5} +(-0.939693 - 0.342020i) q^{7} +(1.84883 + 2.36259i) q^{9} +O(q^{10})$	\(q+(-1.55705 - 0.758672i) q^{3} +(0.267700 + 0.224627i) q^{5} +(-0.939693 - 0.342020i) q^{7} +(1.84883 + 2.36259i) q^{9} +(2.50222 - 2.09961i) q^{11} +(-0.614783 + 3.48661i) q^{13} +(-0.246405 - 0.552853i) q^{15} +(-0.234058 + 0.405401i) q^{17} +(-0.287727 - 0.498357i) q^{19} +(1.20367 + 1.24546i) q^{21} +(2.93807 - 1.06937i) q^{23} +(-0.847035 - 4.80377i) q^{25} +(-1.08631 - 5.08133i) q^{27} +(1.33429 + 7.56712i) q^{29} +(10.2776 - 3.74073i) q^{31} +(-5.48900 + 1.37084i) q^{33} +(-0.174729 - 0.302639i) q^{35} +(4.87338 - 8.44094i) q^{37} +(3.60244 - 4.96242i) q^{39} +(0.124862 - 0.708126i) q^{41} +(4.77587 - 4.00743i) q^{43} +(-0.0357677 + 1.04776i) q^{45} +(-3.28173 - 1.19445i) q^{47} +(0.766044 + 0.642788i) q^{49} +(0.672008 - 0.453658i) q^{51} +8.69539 q^{53} +1.14147 q^{55} +(0.0699164 + 0.994260i) q^{57} +(3.77507 + 3.16766i) q^{59} +(-5.86081 - 2.13316i) q^{61} +(-0.929284 - 2.85244i) q^{63} +(-0.947764 + 0.795269i) q^{65} +(0.259855 - 1.47371i) q^{67} +(-5.38604 - 0.563965i) q^{69} +(5.81940 - 10.0795i) q^{71} +(-4.07774 - 7.06284i) q^{73} +(-2.32561 + 8.12236i) q^{75} +(-3.06942 + 1.11718i) q^{77} +(-0.426107 - 2.41658i) q^{79} +(-2.16363 + 8.73606i) q^{81} +(1.94825 + 11.0491i) q^{83} +(-0.153722 + 0.0559501i) q^{85} +(3.66340 - 12.7947i) q^{87} +(7.77990 + 13.4752i) q^{89} +(1.77020 - 3.06607i) q^{91} +(-18.8407 - 1.97278i) q^{93} +(0.0349201 - 0.198042i) q^{95} +(-2.33888 + 1.96255i) q^{97} +(9.58669 + 2.02987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−1.55705	−	0.758672i	−0.898966	−	0.438019i
$3$	−1.55705	−	0.758672i	−0.898966	−	0.438019i
$4$		0			0
$5$	0.267700	+	0.224627i	0.119719	+	0.100456i	0.700682	−	0.713474i	$-0.252879\pi$
$5$	0.267700	+	0.224627i	0.119719	+	0.100456i	−0.580963	+	0.813930i	$0.697324\pi$
$6$		0			0
$7$	−0.939693	−	0.342020i	−0.355170	−	0.129271i
$7$	−0.939693	−	0.342020i	−0.355170	−	0.129271i
$8$		0			0
$9$	1.84883	+	2.36259i	0.616278	+	0.787529i
$10$		0			0
$11$	2.50222	−	2.09961i	0.754447	−	0.633056i	−0.182228	−	0.983256i	$-0.558331\pi$
$11$	2.50222	−	2.09961i	0.754447	−	0.633056i	0.936675	+	0.350200i	$0.113886\pi$
$12$		0			0
$13$	−0.614783	+	3.48661i	−0.170510	+	0.967011i	0.772689	+	0.634784i	$0.218911\pi$
$13$	−0.614783	+	3.48661i	−0.170510	+	0.967011i	−0.943200	+	0.332227i	$0.892200\pi$
$14$		0			0
$15$	−0.246405	−	0.552853i	−0.0636216	−	0.142746i
$16$		0			0
$17$	−0.234058	+	0.405401i	−0.0567675	+	0.0983242i	−0.893013	−	0.450032i	$-0.851413\pi$
$17$	−0.234058	+	0.405401i	−0.0567675	+	0.0983242i	0.836245	+	0.548356i	$0.184746\pi$
$18$		0			0
$19$	−0.287727	−	0.498357i	−0.0660091	−	0.114331i	0.831132	−	0.556075i	$-0.187693\pi$
$19$	−0.287727	−	0.498357i	−0.0660091	−	0.114331i	−0.897141	+	0.441744i	$0.854360\pi$
$20$		0			0
$21$	1.20367	+	1.24546i	0.262663	+	0.271782i
$22$		0			0
$23$	2.93807	−	1.06937i	0.612630	−	0.222979i	−0.0170234	−	0.999855i	$-0.505419\pi$
$23$	2.93807	−	1.06937i	0.612630	−	0.222979i	0.629654	+	0.776876i	$0.283197\pi$
$24$		0			0
$25$	−0.847035	−	4.80377i	−0.169407	−	0.960755i
$26$		0			0
$27$	−1.08631	−	5.08133i	−0.209060	−	0.977903i
$28$		0			0
$29$	1.33429	+	7.56712i	0.247771	+	1.40518i	0.813969	+	0.580909i	$0.197303\pi$
$29$	1.33429	+	7.56712i	0.247771	+	1.40518i	−0.566198	+	0.824269i	$0.691586\pi$
$30$		0			0
$31$	10.2776	−	3.74073i	1.84591	−	0.671854i	0.858682	−	0.512508i	$-0.171284\pi$
$31$	10.2776	−	3.74073i	1.84591	−	0.671854i	0.987223	−	0.159346i	$-0.0509386\pi$
$32$		0			0
$33$	−5.48900	+	1.37084i	−0.955513	+	0.238633i
$34$		0			0
$35$	−0.174729	−	0.302639i	−0.0295346	−	0.0511554i
$36$		0			0
$37$	4.87338	−	8.44094i	0.801179	−	1.38768i	−0.117662	−	0.993054i	$-0.537540\pi$
$37$	4.87338	−	8.44094i	0.801179	−	1.38768i	0.918841	−	0.394629i	$-0.129127\pi$
$38$		0			0
$39$	3.60244	−	4.96242i	0.576852	−	0.794623i
$40$		0			0
$41$	0.124862	−	0.708126i	0.0195001	−	0.110591i	−0.973504	−	0.228670i	$-0.926562\pi$
$41$	0.124862	−	0.708126i	0.0195001	−	0.110591i	0.993004	+	0.118079i	$0.0376736\pi$
$42$		0			0
$43$	4.77587	−	4.00743i	0.728314	−	0.611128i	−0.201358	−	0.979518i	$-0.564535\pi$
$43$	4.77587	−	4.00743i	0.728314	−	0.611128i	0.929671	+	0.368390i	$0.120091\pi$
$44$		0			0
$45$	−0.0357677	+	1.04776i	−0.00533193	+	0.156191i
$46$		0			0
$47$	−3.28173	−	1.19445i	−0.478689	−	0.174229i	0.0913954	−	0.995815i	$-0.470867\pi$
$47$	−3.28173	−	1.19445i	−0.478689	−	0.174229i	−0.570084	+	0.821586i	$0.693089\pi$
$48$		0			0
$49$	0.766044	+	0.642788i	0.109435	+	0.0918268i
$50$		0			0
$51$	0.672008	−	0.453658i	0.0940999	−	0.0635248i
$52$		0			0
$53$	8.69539			1.19440			0.597202	−	0.802091i	$-0.296279\pi$
$53$	8.69539			1.19440			0.597202	+	0.802091i	$0.296279\pi$
$54$		0			0
$55$	1.14147			0.153916
$56$		0			0
$57$	0.0699164	+	0.994260i	0.00926065	+	0.131693i
$58$		0			0
$59$	3.77507	+	3.16766i	0.491472	+	0.412394i	0.854554	−	0.519363i	$-0.173831\pi$
$59$	3.77507	+	3.16766i	0.491472	+	0.412394i	−0.363081	+	0.931757i	$0.618275\pi$
$60$		0			0
$61$	−5.86081	−	2.13316i	−0.750400	−	0.273123i	−0.0616261	−	0.998099i	$-0.519629\pi$
$61$	−5.86081	−	2.13316i	−0.750400	−	0.273123i	−0.688774	+	0.724976i	$0.741851\pi$
$62$		0			0
$63$	−0.929284	−	2.85244i	−0.117079	−	0.359374i
$64$		0			0
$65$	−0.947764	+	0.795269i	−0.117556	+	0.0986409i
$66$		0			0
$67$	0.259855	−	1.47371i	0.0317463	−	0.180042i	−0.964812	−	0.262942i	$-0.915307\pi$
$67$	0.259855	−	1.47371i	0.0317463	−	0.180042i	0.996558	+	0.0829001i	$0.0264182\pi$
$68$		0			0
$69$	−5.38604	−	0.563965i	−0.648403	−	0.0678933i
$70$		0			0
$71$	5.81940	−	10.0795i	0.690635	−	1.19622i	−0.280994	−	0.959709i	$-0.590664\pi$
$71$	5.81940	−	10.0795i	0.690635	−	1.19622i	0.971630	−	0.236506i	$-0.0760024\pi$
$72$		0			0
$73$	−4.07774	−	7.06284i	−0.477263	−	0.826643i	0.522398	−	0.852702i	$-0.325038\pi$
$73$	−4.07774	−	7.06284i	−0.477263	−	0.826643i	−0.999660	+	0.0260586i	$0.991704\pi$
$74$		0			0
$75$	−2.32561	+	8.12236i	−0.268538	+	0.937889i
$76$		0			0
$77$	−3.06942	+	1.11718i	−0.349793	+	0.127314i
$78$		0			0
$79$	−0.426107	−	2.41658i	−0.0479408	−	0.271886i	0.951409	−	0.307929i	$-0.0996358\pi$
$79$	−0.426107	−	2.41658i	−0.0479408	−	0.271886i	−0.999350	+	0.0360428i	$0.988525\pi$
$80$		0			0
$81$	−2.16363	+	8.73606i	−0.240403	+	0.970673i
$82$		0			0
$83$	1.94825	+	11.0491i	0.213848	+	1.21279i	0.882894	+	0.469572i	$0.155592\pi$
$83$	1.94825	+	11.0491i	0.213848	+	1.21279i	−0.669046	+	0.743221i	$0.733297\pi$
$84$		0			0
$85$	−0.153722	+	0.0559501i	−0.0166734	+	0.00606864i
$86$		0			0
$87$	3.66340	−	12.7947i	0.392758	−	1.37174i
$88$		0			0
$89$	7.77990	+	13.4752i	0.824668	+	1.42837i	0.902173	+	0.431375i	$0.141971\pi$
$89$	7.77990	+	13.4752i	0.824668	+	1.42837i	−0.0775044	+	0.996992i	$0.524695\pi$
$90$		0			0
$91$	1.77020	−	3.06607i	0.185567	−	0.321412i
$92$		0			0
$93$	−18.8407	−	1.97278i	−1.95369	−	0.204568i
$94$		0			0
$95$	0.0349201	−	0.198042i	0.00358272	−	0.0203186i
$96$		0			0
$97$	−2.33888	+	1.96255i	−0.237477	+	0.199267i	−0.753758	−	0.657152i	$-0.771761\pi$
$97$	−2.33888	+	1.96255i	−0.237477	+	0.199267i	0.516280	+	0.856420i	$0.327316\pi$
$98$		0			0
$99$	9.58669	+	2.02987i	0.963499	+	0.204010i
$100$		0			0
$101$	13.3895	+	4.87339i	1.33231	+	0.484920i	0.907382	−	0.420307i	$-0.138078\pi$
$101$	13.3895	+	4.87339i	1.33231	+	0.484920i	0.424926	+	0.905228i	$0.360300\pi$
$102$		0			0
$103$	−4.84091	−	4.06200i	−0.476989	−	0.400241i	0.372347	−	0.928093i	$-0.378553\pi$
$103$	−4.84091	−	4.06200i	−0.476989	−	0.400241i	−0.849336	+	0.527852i	$0.822997\pi$
$104$		0			0
$105$	0.0424584	+	0.603788i	0.00414351	+	0.0589236i
$106$		0			0
$107$	−1.94932			−0.188448			−0.0942239	−	0.995551i	$-0.530037\pi$
$107$	−1.94932			−0.188448			−0.0942239	+	0.995551i	$0.530037\pi$
$108$		0			0
$109$	10.0895			0.966401			0.483201	−	0.875510i	$-0.339474\pi$
$109$	10.0895			0.966401			0.483201	+	0.875510i	$0.339474\pi$
$110$		0			0
$111$	−13.9920	+	9.44571i	−1.32806	+	0.896547i
$112$		0			0
$113$	−8.64097	−	7.25064i	−0.812874	−	0.682083i	0.138418	−	0.990374i	$-0.455798\pi$
$113$	−8.64097	−	7.25064i	−0.812874	−	0.682083i	−0.951292	+	0.308291i	$0.900243\pi$
$114$		0			0
$115$	1.02673	+	0.373700i	0.0957433	+	0.0348477i
$116$		0			0
$117$	−9.37404	+	4.99368i	−0.866631	+	0.461666i
$118$		0			0
$119$	0.358598	−	0.300900i	0.0328726	−	0.0275834i
$120$		0			0
$121$	−0.0573984	+	0.325523i	−0.00521804	+	0.0295930i
$122$		0			0
$123$	−0.731652	+	1.00786i	−0.0659708	+	0.0908758i
$124$		0			0
$125$	1.72595	−	2.98943i	0.154374	−	0.267383i
$126$		0			0
$127$	0.404169	+	0.700041i	0.0358642	+	0.0621186i	0.883400	−	0.468619i	$-0.155248\pi$
$127$	0.404169	+	0.700041i	0.0358642	+	0.0621186i	−0.847536	+	0.530738i	$0.821915\pi$
$128$		0			0
$129$	−10.4766	+	2.61647i	−0.922415	+	0.230367i
$130$		0			0
$131$	−14.0204	+	5.10302i	−1.22497	+	0.445853i	−0.871872	−	0.489733i	$-0.837094\pi$
$131$	−14.0204	+	5.10302i	−1.22497	+	0.445853i	−0.353098	+	0.935586i	$0.614872\pi$
$132$		0			0
$133$	0.0999265	+	0.566711i	0.00866472	+	0.0491401i
$134$		0			0
$135$	0.850600	−	1.60429i	0.0732080	−	0.138075i
$136$		0			0
$137$	0.186425	+	1.05727i	0.0159273	+	0.0903285i	0.991735	−	0.128301i	$-0.0409524\pi$
$137$	0.186425	+	1.05727i	0.0159273	+	0.0903285i	−0.975808	+	0.218630i	$0.929841\pi$
$138$		0			0
$139$	−6.83855	+	2.48903i	−0.580038	+	0.211117i	−0.615342	−	0.788260i	$-0.710982\pi$
$139$	−6.83855	+	2.48903i	−0.580038	+	0.211117i	0.0353041	+	0.999377i	$0.488760\pi$
$140$		0			0
$141$	4.20363	+	4.34958i	0.354009	+	0.366300i
$142$		0			0
$143$	5.78220	+	10.0151i	0.483532	+	0.837501i
$144$		0			0
$145$	−1.34259	+	2.32544i	−0.111496	+	0.193117i
$146$		0			0
$147$	−0.705108	−	1.58203i	−0.0581563	−	0.130484i
$148$		0			0
$149$	−3.73166	+	21.1633i	−0.305710	+	1.73376i	0.314437	+	0.949278i	$0.398184\pi$
$149$	−3.73166	+	21.1633i	−0.305710	+	1.73376i	−0.620146	+	0.784486i	$0.712927\pi$
$150$		0			0
$151$	−14.4140	+	12.0948i	−1.17300	+	0.984261i	−1.00000		0.000661930i	$-0.999789\pi$
$151$	−14.4140	+	12.0948i	−1.17300	+	0.984261i	−0.172996	+	0.984922i	$0.555345\pi$
$152$		0			0
$153$	−1.39053	+	0.196536i	−0.112418	+	0.0158890i
$154$		0			0
$155$	3.59157	+	1.30723i	0.288482	+	0.104999i
$156$		0			0
$157$	7.30854	+	6.13259i	0.583285	+	0.489434i	0.886024	−	0.463640i	$-0.153457\pi$
$157$	7.30854	+	6.13259i	0.583285	+	0.489434i	−0.302739	+	0.953073i	$0.597901\pi$
$158$		0			0
$159$	−13.5392	−	6.59695i	−1.07373	−	0.523172i
$160$		0			0
$161$	−3.12663			−0.246413
$162$		0			0
$163$	−2.43639			−0.190832			−0.0954162	−	0.995437i	$-0.530418\pi$
$163$	−2.43639			−0.190832			−0.0954162	+	0.995437i	$0.530418\pi$
$164$		0			0
$165$	−1.77734	−	0.866004i	−0.138365	−	0.0674183i
$166$		0			0
$167$	−11.5685	−	9.70712i	−0.895197	−	0.751159i	0.0740490	−	0.997255i	$-0.476408\pi$
$167$	−11.5685	−	9.70712i	−0.895197	−	0.751159i	−0.969246	+	0.246095i	$0.920852\pi$
$168$		0			0
$169$	0.437525	+	0.159246i	0.0336558	+	0.0122497i
$170$		0			0
$171$	0.645453	−	1.60116i	0.0493590	−	0.122444i
$172$		0			0
$173$	−17.1035	+	14.3515i	−1.30035	+	1.09113i	−0.310271	+	0.950648i	$0.600420\pi$
$173$	−17.1035	+	14.3515i	−1.30035	+	1.09113i	−0.990084	+	0.140479i	$0.955136\pi$
$174$		0			0
$175$	−0.847035	+	4.80377i	−0.0640298	+	0.363131i
$176$		0			0
$177$	−3.47477	−	7.79626i	−0.261180	−	0.586003i
$178$		0			0
$179$	2.39047	−	4.14042i	0.178672	−	0.309469i	−0.762754	−	0.646689i	$-0.776153\pi$
$179$	2.39047	−	4.14042i	0.178672	−	0.309469i	0.941426	+	0.337220i	$0.109486\pi$
$180$		0			0
$181$	−7.73206	−	13.3923i	−0.574720	−	0.995443i	−0.996072	−	0.0885465i	$-0.971778\pi$
$181$	−7.73206	−	13.3923i	−0.574720	−	0.995443i	0.421353	−	0.906897i	$-0.361556\pi$
$182$		0			0
$183$	7.50723	+	7.76788i	0.554951	+	0.574218i
$184$		0			0
$185$	3.20067	−	1.16495i	0.235318	−	0.0856487i
$186$		0			0
$187$	0.265519	+	1.50583i	0.0194167	+	0.110117i
$188$		0			0
$189$	−0.717123	+	5.14643i	−0.0521630	+	0.374348i
$190$		0			0
$191$	0.442134	+	2.50747i	0.0319917	+	0.181434i	0.996616	−	0.0821930i	$-0.0261924\pi$
$191$	0.442134	+	2.50747i	0.0319917	+	0.181434i	−0.964625	+	0.263627i	$0.915081\pi$
$192$		0			0
$193$	6.59567	−	2.40063i	0.474767	−	0.172801i	−0.0935437	−	0.995615i	$-0.529819\pi$
$193$	6.59567	−	2.40063i	0.474767	−	0.172801i	0.568310	+	0.822814i	$0.307597\pi$
$194$		0			0
$195$	2.07907	−	0.519234i	0.148885	−	0.0371831i
$196$		0			0
$197$	4.75665	+	8.23876i	0.338897	+	0.586987i	0.984226	−	0.176918i	$-0.0566128\pi$
$197$	4.75665	+	8.23876i	0.338897	+	0.586987i	−0.645328	+	0.763905i	$0.723279\pi$
$198$		0			0
$199$	14.0456	−	24.3276i	0.995664	−	1.72454i	0.417270	−	0.908782i	$-0.362987\pi$
$199$	14.0456	−	24.3276i	0.995664	−	1.72454i	0.578393	−	0.815758i	$-0.303680\pi$
$200$		0			0
$201$	−1.52267	+	2.09750i	−0.107401	+	0.147946i
$202$		0			0
$203$	1.33429	−	7.56712i	0.0936486	−	0.531107i
$204$		0			0
$205$	0.192490	−	0.161518i	0.0134441	−	0.0112809i
$206$		0			0
$207$	7.95849	+	4.96436i	0.553153	+	0.345047i
$208$		0			0
$209$	−1.76631	−	0.642885i	−0.122178	−	0.0444693i
$210$		0			0
$211$	10.5445	+	8.84786i	0.725911	+	0.609112i	0.929014	−	0.370046i	$-0.120658\pi$
$211$	10.5445	+	8.84786i	0.725911	+	0.609112i	−0.203102	+	0.979158i	$0.565102\pi$
$212$		0			0
$213$	−16.7081	+	11.2793i	−1.14482	+	0.772845i
$214$		0			0
$215$	2.17868			0.148585
$216$		0			0
$217$	−10.9372			−0.742462
$218$		0			0
$219$	0.990872	+	14.0909i	0.0669570	+	0.952174i
$220$		0			0
$221$	−1.26958	−	1.06530i	−0.0854011	−	0.0716601i
$222$		0			0
$223$	−4.39819	−	1.60081i	−0.294525	−	0.107198i	0.190532	−	0.981681i	$-0.438979\pi$
$223$	−4.39819	−	1.60081i	−0.294525	−	0.107198i	−0.485057	+	0.874483i	$0.661201\pi$
$224$		0			0
$225$	9.78330	−	10.8826i	0.652220	−	0.725505i
$226$		0			0
$227$	−15.3808	+	12.9060i	−1.02086	+	0.856600i	−0.989735	−	0.142916i	$-0.954352\pi$
$227$	−15.3808	+	12.9060i	−1.02086	+	0.856600i	−0.0311214	+	0.999516i	$0.509908\pi$
$228$		0			0
$229$	−0.206969	+	1.17378i	−0.0136769	+	0.0775655i	−0.990882	−	0.134731i	$-0.956983\pi$
$229$	−0.206969	+	1.17378i	−0.0136769	+	0.0775655i	0.977205	+	0.212296i	$0.0680942\pi$
$230$		0			0
$231$	5.62683	+	0.589178i	0.370218	+	0.0387650i
$232$		0			0
$233$	5.50011	−	9.52647i	0.360324	−	0.624100i	−0.627690	−	0.778464i	$-0.715999\pi$
$233$	5.50011	−	9.52647i	0.360324	−	0.624100i	0.988014	+	0.154364i	$0.0493327\pi$
$234$		0			0
$235$	−0.610213	−	1.05692i	−0.0398059	−	0.0689458i
$236$		0			0
$237$	−1.16992	+	4.08601i	−0.0759942	+	0.265415i
$238$		0			0
$239$	27.6043	−	10.0471i	1.78557	−	0.649896i	0.786079	−	0.618126i	$-0.212108\pi$
$239$	27.6043	−	10.0471i	1.78557	−	0.649896i	0.999495	−	0.0317703i	$-0.0101145\pi$
$240$		0			0
$241$	−2.76209	−	15.6646i	−0.177922	−	1.00904i	−0.934717	−	0.355392i	$-0.884347\pi$
$241$	−2.76209	−	15.6646i	−0.177922	−	1.00904i	0.756795	−	0.653652i	$-0.226764\pi$
$242$		0			0
$243$	9.99668	−	11.9610i	0.641288	−	0.767301i
$244$		0			0
$245$	0.0606827	+	0.344149i	0.00387688	+	0.0219869i
$246$		0			0
$247$	1.91447	−	0.696809i	0.121815	−	0.0443369i
$248$		0			0
$249$	5.34909	−	18.6821i	0.338985	−	1.18393i
$250$		0			0
$251$	−2.54328	−	4.40509i	−0.160530	−	0.278047i	0.774529	−	0.632539i	$-0.217987\pi$
$251$	−2.54328	−	4.40509i	−0.160530	−	0.278047i	−0.935059	+	0.354492i	$0.884654\pi$
$252$		0			0
$253$	5.10643	−	8.84460i	0.321039	−	0.556055i
$254$		0			0
$255$	0.281800	+	0.0295069i	0.0176470	+	0.00184780i
$256$		0			0
$257$	3.60656	−	20.4538i	0.224971	−	1.27587i	−0.637770	−	0.770227i	$-0.720143\pi$
$257$	3.60656	−	20.4538i	0.224971	−	1.27587i	0.862741	−	0.505647i	$-0.168746\pi$
$258$		0			0
$259$	−7.46645	+	6.26510i	−0.463943	+	0.389294i
$260$		0			0
$261$	−15.4111	+	17.1427i	−0.953922	+	1.06111i
$262$		0			0
$263$	−19.8339	−	7.21894i	−1.22301	−	0.445139i	−0.351811	−	0.936071i	$-0.614434\pi$
$263$	−19.8339	−	7.21894i	−1.22301	−	0.445139i	−0.871198	+	0.490932i	$0.836656\pi$
$264$		0			0
$265$	2.32776	+	1.95322i	0.142993	+	0.119985i
$266$		0			0
$267$	−1.89048	−	26.8840i	−0.115696	−	1.64527i
$268$		0			0
$269$	12.6659			0.772253			0.386127	−	0.922446i	$-0.373813\pi$
$269$	12.6659			0.772253			0.386127	+	0.922446i	$0.373813\pi$
$270$		0			0
$271$	10.6317			0.645831			0.322915	−	0.946428i	$-0.395337\pi$
$271$	10.6317			0.645831			0.322915	+	0.946428i	$0.395337\pi$
$272$		0			0
$273$	−5.08244	+	3.43104i	−0.307603	+	0.207656i
$274$		0			0
$275$	−12.2055	−	10.2416i	−0.736020	−	0.617594i
$276$		0			0
$277$	−18.5867	−	6.76499i	−1.11676	−	0.406469i	−0.283294	−	0.959033i	$-0.591427\pi$
$277$	−18.5867	−	6.76499i	−1.11676	−	0.406469i	−0.833470	+	0.552564i	$0.813649\pi$
$278$		0			0
$279$	27.8393	+	17.3656i	1.66670	+	1.03965i
$280$		0			0
$281$	9.52145	−	7.98945i	0.568002	−	0.476610i	−0.312980	−	0.949760i	$-0.601327\pi$
$281$	9.52145	−	7.98945i	0.568002	−	0.476610i	0.880982	+	0.473149i	$0.156883\pi$
$282$		0			0
$283$	−1.38694	+	7.86575i	−0.0824453	+	0.467570i	0.915433	+	0.402469i	$0.131848\pi$
$283$	−1.38694	+	7.86575i	−0.0824453	+	0.467570i	−0.997879	+	0.0651009i	$0.979263\pi$
$284$		0			0
$285$	−0.204621	+	0.281869i	−0.0121207	+	0.0166965i
$286$		0			0
$287$	−0.359525	+	0.622716i	−0.0212221	+	0.0367578i
$288$		0			0
$289$	8.39043	+	14.5327i	0.493555	+	0.854862i
$290$		0			0
$291$	5.13070	−	1.28136i	0.300767	−	0.0751147i
$292$		0			0
$293$	−8.01176	+	2.91604i	−0.468052	+	0.170357i	−0.565270	−	0.824906i	$-0.691228\pi$
$293$	−8.01176	+	2.91604i	−0.468052	+	0.170357i	0.0972178	+	0.995263i	$0.469006\pi$
$294$		0			0
$295$	0.299045	+	1.69597i	0.0174111	+	0.0987430i
$296$		0			0
$297$	−13.3870	−	10.4338i	−0.776792	−	0.605429i
$298$		0			0
$299$	1.92220	+	10.9013i	0.111164	+	0.630441i
$300$		0			0
$301$	−5.85847	+	2.13231i	−0.337677	+	0.122904i
$302$		0			0
$303$	−17.1509	−	17.7464i	−0.985294	−	1.01950i
$304$		0			0
$305$	−1.08977	−	1.88755i	−0.0624003	−	0.108081i
$306$		0			0
$307$	−13.7838	+	23.8742i	−0.786682	+	1.36257i	0.141307	+	0.989966i	$0.454870\pi$
$307$	−13.7838	+	23.8742i	−0.786682	+	1.36257i	−0.927989	+	0.372608i	$0.878464\pi$
$308$		0			0
$309$	4.45582	+	9.99742i	0.253483	+	0.568733i
$310$		0			0
$311$	1.32027	−	7.48765i	0.0748659	−	0.424586i	−0.924221	−	0.381858i	$-0.875284\pi$
$311$	1.32027	−	7.48765i	0.0748659	−	0.424586i	0.999087	−	0.0427274i	$-0.0136047\pi$
$312$		0			0
$313$	−7.25388	+	6.08673i	−0.410014	+	0.344042i	−0.824349	−	0.566082i	$-0.808459\pi$
$313$	−7.25388	+	6.08673i	−0.410014	+	0.344042i	0.414335	+	0.910124i	$0.364014\pi$
$314$		0			0
$315$	0.391967	−	0.972342i	0.0220848	−	0.0547853i
$316$		0			0
$317$	28.5699	+	10.3986i	1.60464	+	0.584043i	0.980371	−	0.197164i	$-0.0631731\pi$
$317$	28.5699	+	10.3986i	1.60464	+	0.584043i	0.624273	+	0.781206i	$0.285395\pi$
$318$		0			0
$319$	19.2267	+	16.1331i	1.07649	+	0.903280i
$320$		0			0
$321$	3.03519	+	1.47889i	0.169408	+	0.0825438i
$322$		0			0
$323$	0.269379			0.0149887
$324$		0			0
$325$	17.2696			0.957946
$326$		0			0
$327$	−15.7099	−	7.65464i	−0.868762	−	0.423303i
$328$		0			0
$329$	2.67529	+	2.24483i	0.147493	+	0.123762i
$330$		0			0
$331$	−9.20135	−	3.34902i	−0.505752	−	0.184079i	0.0765273	−	0.997067i	$-0.475617\pi$
$331$	−9.20135	−	3.34902i	−0.505752	−	0.184079i	−0.582279	+	0.812989i	$0.697839\pi$
$332$		0			0
$333$	28.9525	−	4.09212i	1.58659	−	0.224247i
$334$		0			0
$335$	0.400598	−	0.336142i	0.0218870	−	0.0183654i
$336$		0			0
$337$	−2.04964	+	11.6241i	−0.111651	+	0.633204i	0.876703	+	0.481032i	$0.159738\pi$
$337$	−2.04964	+	11.6241i	−0.111651	+	0.633204i	−0.988354	+	0.152172i	$0.951373\pi$
$338$		0			0
$339$	7.95361	+	17.8453i	0.431981	+	0.969223i
$340$		0			0
$341$	17.8626	−	30.9390i	0.967316	−	1.67544i
$342$		0			0
$343$	−0.500000	−	0.866025i	−0.0269975	−	0.0467610i
$344$		0			0
$345$	−1.31516	−	1.36082i	−0.0708059	−	0.0732643i
$346$		0			0
$347$	−11.8989	+	4.33085i	−0.638767	+	0.232492i	−0.641043	−	0.767505i	$-0.721498\pi$
$347$	−11.8989	+	4.33085i	−0.638767	+	0.232492i	0.00227540	+	0.999997i	$0.499276\pi$
$348$		0			0
$349$	−0.900119	−	5.10483i	−0.0481822	−	0.273255i	0.951193	−	0.308596i	$-0.0998593\pi$
$349$	−0.900119	−	5.10483i	−0.0481822	−	0.273255i	−0.999375	+	0.0353414i	$0.988748\pi$
$350$		0			0
$351$	18.3845	−	0.663609i	0.981290	−	0.0354209i
$352$		0			0
$353$	5.38954	+	30.5656i	0.286856	+	1.62684i	0.698579	+	0.715533i	$0.253816\pi$
$353$	5.38954	+	30.5656i	0.286856	+	1.62684i	−0.411723	+	0.911309i	$0.635073\pi$
$354$		0			0
$355$	3.82198	−	1.39109i	0.202850	−	0.0738313i
$356$		0			0
$357$	−0.786641	+	0.196459i	−0.0416334	+	0.0103977i
$358$		0			0
$359$	0.443957	+	0.768956i	0.0234311	+	0.0405839i	0.877503	−	0.479571i	$-0.159208\pi$
$359$	0.443957	+	0.768956i	0.0234311	+	0.0405839i	−0.854072	+	0.520155i	$0.825874\pi$
$360$		0			0
$361$	9.33443	−	16.1677i	0.491286	−	0.850932i
$362$		0			0
$363$	0.336337	−	0.463310i	0.0176531	−	0.0243175i
$364$		0			0
$365$	0.494896	−	2.80669i	0.0259040	−	0.146909i
$366$		0			0
$367$	8.01479	−	6.72521i	0.418369	−	0.351053i	−0.409173	−	0.912457i	$-0.634183\pi$
$367$	8.01479	−	6.72521i	0.418369	−	0.351053i	0.827542	+	0.561404i	$0.189738\pi$
$368$		0			0
$369$	1.90386	−	1.01421i	0.0991109	−	0.0527977i
$370$		0			0
$371$	−8.17099	−	2.97400i	−0.424217	−	0.154402i
$372$		0			0
$373$	−4.65143	−	3.90301i	−0.240842	−	0.202090i	0.514375	−	0.857565i	$-0.328024\pi$
$373$	−4.65143	−	3.90301i	−0.240842	−	0.202090i	−0.755217	+	0.655475i	$0.772468\pi$
$374$		0			0
$375$	−4.95540	+	3.34528i	−0.255896	+	0.172750i
$376$		0			0
$377$	−27.2039			−1.40107
$378$		0			0
$379$	4.89244			0.251308			0.125654	−	0.992074i	$-0.459897\pi$
$379$	4.89244			0.251308			0.125654	+	0.992074i	$0.459897\pi$
$380$		0			0
$381$	−0.0982113	−	1.39663i	−0.00503152	−	0.0715516i
$382$		0			0
$383$	0.873116	+	0.732632i	0.0446142	+	0.0374357i	0.664822	−	0.747002i	$-0.268507\pi$
$383$	0.873116	+	0.732632i	0.0446142	+	0.0374357i	−0.620208	+	0.784437i	$0.712952\pi$
$384$		0			0
$385$	−1.07263	−	0.390407i	−0.0546665	−	0.0198970i
$386$		0			0
$387$	18.2977	+	3.87433i	0.930124	+	0.196943i
$388$		0			0
$389$	2.84972	−	2.39120i	0.144486	−	0.121239i	−0.567680	−	0.823250i	$-0.692159\pi$
$389$	2.84972	−	2.39120i	0.144486	−	0.121239i	0.712166	+	0.702011i	$0.247714\pi$
$390$		0			0
$391$	−0.254156	+	1.44139i	−0.0128532	+	0.0728943i
$392$		0			0
$393$	25.7021	+	2.69123i	1.29650	+	0.135755i
$394$		0			0
$395$	0.428759	−	0.742633i	0.0215732	−	0.0373659i
$396$		0			0
$397$	−13.3195	−	23.0700i	−0.668485	−	1.15785i	−0.978328	−	0.207063i	$-0.933610\pi$
$397$	−13.3195	−	23.0700i	−0.668485	−	1.15785i	0.309842	−	0.950788i	$-0.399724\pi$
$398$		0			0
$399$	0.274357	−	0.958211i	0.0137350	−	0.0479706i
$400$		0			0
$401$	−32.6562	+	11.8859i	−1.63077	+	0.593553i	−0.985391	−	0.170306i	$-0.945524\pi$
$401$	−32.6562	+	11.8859i	−1.63077	+	0.593553i	−0.645383	+	0.763859i	$0.723302\pi$
$402$		0			0
$403$	6.72398	+	38.1336i	0.334945	+	1.89957i
$404$		0			0
$405$	−2.54156	+	1.85264i	−0.126291	+	0.0920582i
$406$		0			0
$407$	−5.52843	−	31.3533i	−0.274034	−	1.55412i
$408$		0			0
$409$	13.9495	−	5.07719i	0.689757	−	0.251051i	0.0267256	−	0.999643i	$-0.491492\pi$
$409$	13.9495	−	5.07719i	0.689757	−	0.251051i	0.663031	+	0.748592i	$0.269270\pi$
$410$		0			0
$411$	0.511846	−	1.78766i	0.0252475	−	0.0881787i
$412$		0			0
$413$	−2.46400	−	4.26778i	−0.121246	−	0.210004i
$414$		0			0
$415$	−1.96037	+	3.39547i	−0.0962310	+	0.166677i
$416$		0			0
$417$	12.5363	+	1.31266i	0.613908	+	0.0642814i
$418$		0			0
$419$	2.90063	−	16.4503i	0.141705	−	0.803648i	−0.828249	−	0.560360i	$-0.810663\pi$
$419$	2.90063	−	16.4503i	0.141705	−	0.803648i	0.969954	−	0.243288i	$-0.0782261\pi$
$420$		0			0
$421$	−18.5375	+	15.5549i	−0.903465	+	0.758097i	−0.970865	−	0.239629i	$-0.922974\pi$
$421$	−18.5375	+	15.5549i	−0.903465	+	0.758097i	0.0673997	+	0.997726i	$0.478530\pi$
$422$		0			0
$423$	−3.24537	−	9.96170i	−0.157796	−	0.484354i
$424$		0			0
$425$	2.14571	+	0.780975i	0.104082	+	0.0378828i
$426$		0			0
$427$	4.77778	+	4.00903i	0.231213	+	0.194011i
$428$		0			0
$429$	−1.40505	−	19.9808i	−0.0678364	−	0.964681i
$430$		0			0
$431$	−12.4584			−0.600100			−0.300050	−	0.953924i	$-0.597003\pi$
$431$	−12.4584			−0.600100			−0.300050	+	0.953924i	$0.597003\pi$
$432$		0			0
$433$	13.9324			0.669548			0.334774	−	0.942298i	$-0.391340\pi$
$433$	13.9324			0.669548			0.334774	+	0.942298i	$0.391340\pi$
$434$		0			0
$435$	3.85473	−	2.60224i	0.184820	−	0.124768i
$436$		0			0
$437$	−1.37829	−	1.15652i	−0.0659326	−	0.0553240i
$438$		0			0
$439$	−1.29885	−	0.472744i	−0.0619909	−	0.0225628i	0.310839	−	0.950463i	$-0.399390\pi$
$439$	−1.29885	−	0.472744i	−0.0619909	−	0.0225628i	−0.372829	+	0.927900i	$0.621612\pi$
$440$		0			0
$441$	−0.102352	+	2.99825i	−0.00487390	+	0.142774i
$442$		0			0
$443$	−9.71576	+	8.15249i	−0.461610	+	0.387337i	−0.843723	−	0.536779i	$-0.819641\pi$
$443$	−9.71576	+	8.15249i	−0.461610	+	0.387337i	0.382113	+	0.924116i	$0.375196\pi$
$444$		0			0
$445$	−0.944211	+	5.35489i	−0.0447599	+	0.253846i
$446$		0			0
$447$	21.8664	−	30.1213i	1.03424	−	1.42469i
$448$		0			0
$449$	18.4099	−	31.8869i	0.868816	−	1.50483i	0.00560923	−	0.999984i	$-0.498215\pi$
$449$	18.4099	−	31.8869i	0.868816	−	1.50483i	0.863207	−	0.504850i	$-0.168452\pi$
$450$		0			0
$451$	−1.17436	−	2.03405i	−0.0552983	−	0.0957795i
$452$		0			0
$453$	31.6194	−	7.89674i	1.48561	−	0.371021i
$454$		0			0
$455$	1.16260	−	0.423154i	0.0545038	−	0.0198377i
$456$		0			0
$457$	−2.91836	−	16.5509i	−0.136515	−	0.774216i	−0.973793	−	0.227438i	$-0.926965\pi$
$457$	−2.91836	−	16.5509i	−0.136515	−	0.774216i	0.837277	−	0.546778i	$-0.184146\pi$
$458$		0			0
$459$	2.31424	+	0.748938i	0.108019	+	0.0349574i
$460$		0			0
$461$	−1.01372	−	5.74909i	−0.0472137	−	0.267762i	0.952058	−	0.305917i	$-0.0989630\pi$
$461$	−1.01372	−	5.74909i	−0.0472137	−	0.267762i	−0.999272	+	0.0381551i	$0.987852\pi$
$462$		0			0
$463$	−11.8156	+	4.30053i	−0.549118	+	0.199863i	−0.601655	−	0.798756i	$-0.705492\pi$
$463$	−11.8156	+	4.30053i	−0.549118	+	0.199863i	0.0525364	+	0.998619i	$0.483269\pi$
$464$		0			0
$465$	−4.60052	−	4.76025i	−0.213344	−	0.220751i
$466$		0			0
$467$	10.8635	+	18.8161i	0.502702	+	0.870705i	0.999995	+	0.00312268i	$0.000993981\pi$
$467$	10.8635	+	18.8161i	0.502702	+	0.870705i	−0.497293	+	0.867583i	$0.665673\pi$
$468$		0			0
$469$	−0.748221	+	1.29596i	−0.0345496	+	0.0598417i
$470$		0			0
$471$	−6.72716	−	15.0936i	−0.309971	−	0.695474i
$472$		0			0
$473$	3.53623	−	20.0549i	0.162596	−	0.922127i
$474$		0			0
$475$	−2.15028	+	1.80430i	−0.0986617	+	0.0827870i
$476$		0			0
$477$	16.0763	+	20.5436i	0.736085	+	0.940627i
$478$		0			0
$479$	−4.46900	−	1.62658i	−0.204194	−	0.0743205i	0.237898	−	0.971290i	$-0.423541\pi$
$479$	−4.46900	−	1.62658i	−0.204194	−	0.0743205i	−0.442092	+	0.896970i	$0.645764\pi$
$480$		0			0
$481$	26.4342	+	22.1809i	1.20530	+	1.01136i
$482$		0			0
$483$	4.86833	+	2.37209i	0.221517	+	0.107934i
$484$		0			0
$485$	−1.06696			−0.0484483
$486$		0			0
$487$	−37.3165			−1.69097			−0.845486	−	0.533998i	$-0.820689\pi$
$487$	−37.3165			−1.69097			−0.845486	+	0.533998i	$0.820689\pi$
$488$		0			0
$489$	3.79358	+	1.84842i	0.171552	+	0.0835883i
$490$		0			0
$491$	−23.2373	−	19.4984i	−1.04868	−	0.879950i	−0.0557291	−	0.998446i	$-0.517748\pi$
$491$	−23.2373	−	19.4984i	−1.04868	−	0.879950i	−0.992955	+	0.118496i	$0.962193\pi$
$492$		0			0
$493$	−3.38002	−	1.23023i	−0.152228	−	0.0554066i
$494$		0			0
$495$	2.11039	+	2.69683i	0.0948552	+	0.121213i
$496$		0			0
$497$	−8.91583	+	7.48127i	−0.399930	+	0.335581i
$498$		0			0
$499$	−1.67458	+	9.49703i	−0.0749646	+	0.425145i	0.924110	+	0.382127i	$0.124808\pi$
$499$	−1.67458	+	9.49703i	−0.0749646	+	0.425145i	−0.999074	+	0.0430180i	$0.986303\pi$
$500$		0			0
$501$	10.6482	+	23.8912i	0.475729	+	1.06738i
$502$		0			0
$503$	12.5107	−	21.6691i	0.557823	−	0.966177i	−0.439855	−	0.898069i	$-0.644970\pi$
$503$	12.5107	−	21.6691i	0.557823	−	0.966177i	0.997678	−	0.0681083i	$-0.0216964\pi$
$504$		0			0
$505$	2.48968	+	4.31226i	0.110789	+	0.191893i
$506$		0			0
$507$	−0.560435	−	0.579893i	−0.0248898	−	0.0257540i
$508$		0			0
$509$	−2.75403	+	1.00239i	−0.122070	+	0.0444300i	−0.402333	−	0.915493i	$-0.631801\pi$
$509$	−2.75403	+	1.00239i	−0.122070	+	0.0444300i	0.280263	+	0.959923i	$0.409578\pi$
$510$		0			0
$511$	1.41618	+	8.03157i	0.0626482	+	0.355296i
$512$		0			0
$513$	−2.21976	+	2.00340i	−0.0980048	+	0.0884525i
$514$		0			0
$515$	−0.383475	−	2.17480i	−0.0168979	−	0.0958330i
$516$		0			0
$517$	−10.7195	+	3.90157i	−0.471442	+	0.171591i
$518$		0			0
$519$	37.5192	−	9.37017i	1.64691	−	0.411305i
$520$		0			0
$521$	17.2621	+	29.8989i	0.756268	+	1.30989i	0.944741	+	0.327817i	$0.106313\pi$
$521$	17.2621	+	29.8989i	0.756268	+	1.30989i	−0.188473	+	0.982078i	$0.560354\pi$
$522$		0			0
$523$	5.22824	−	9.05558i	0.228615	−	0.395973i	−0.728783	−	0.684745i	$-0.759914\pi$
$523$	5.22824	−	9.05558i	0.228615	−	0.395973i	0.957398	+	0.288772i	$0.0932470\pi$
$524$		0			0
$525$	4.96337	−	6.83711i	0.216619	−	0.298396i
$526$		0			0
$527$	−0.889055	+	5.04208i	−0.0387279	+	0.219637i
$528$		0			0
$529$	−10.1303	+	8.50034i	−0.440448	+	0.369580i
$530$		0			0
$531$	−0.504391	+	14.7754i	−0.0218887	+	0.641198i
$532$		0			0
$533$	2.39220	+	0.870688i	0.103618	+	0.0377137i
$534$		0			0
$535$	−0.521833	−	0.437870i	−0.0225608	−	0.0189308i
$536$		0			0
$537$	−6.86331	+	4.63327i	−0.296174	+	0.199940i
$538$		0			0
$539$	3.26641			0.140694
$540$		0			0
$541$	2.32842			0.100107			0.0500533	−	0.998747i	$-0.484061\pi$
$541$	2.32842			0.100107			0.0500533	+	0.998747i	$0.484061\pi$
$542$		0			0
$543$	1.87886	+	26.7187i	0.0806295	+	1.14661i
$544$		0			0
$545$	2.70097	+	2.26638i	0.115697	+	0.0970811i
$546$		0			0
$547$	10.1926	+	3.70982i	0.435806	+	0.158620i	0.550600	−	0.834769i	$-0.314399\pi$
$547$	10.1926	+	3.70982i	0.435806	+	0.158620i	−0.114795	+	0.993389i	$0.536621\pi$
$548$		0			0
$549$	−5.79589	−	17.7905i	−0.247363	−	0.759282i
$550$		0			0
$551$	3.38722	−	2.84221i	0.144300	−	0.121082i
$552$		0			0
$553$	−0.426107	+	2.41658i	−0.0181199	+	0.102763i
$554$		0			0
$555$	−5.86743	−	0.614370i	−0.249058	−	0.0260786i
$556$		0			0
$557$	19.2109	−	33.2742i	0.813991	−	1.40987i	−0.0960600	−	0.995376i	$-0.530624\pi$
$557$	19.2109	−	33.2742i	0.813991	−	1.40987i	0.910051	−	0.414497i	$-0.136043\pi$
$558$		0			0
$559$	11.0362	+	19.1153i	0.466782	+	0.808491i
$560$		0			0
$561$	0.729006	−	2.54610i	0.0307786	−	0.107497i
$562$		0			0
$563$	7.50669	−	2.73221i	0.316369	−	0.115149i	−0.178955	−	0.983857i	$-0.557272\pi$
$563$	7.50669	−	2.73221i	0.316369	−	0.115149i	0.495324	+	0.868708i	$0.335049\pi$
$564$		0			0
$565$	−0.684500	−	3.88199i	−0.0287971	−	0.163317i
$566$		0			0
$567$	5.02105	−	7.46921i	0.210864	−	0.313677i
$568$		0			0
$569$	1.20085	+	6.81039i	0.0503425	+	0.285506i	0.999578	−	0.0290610i	$-0.00925171\pi$
$569$	1.20085	+	6.81039i	0.0503425	+	0.285506i	−0.949235	+	0.314567i	$0.898141\pi$
$570$		0			0
$571$	−33.2240	+	12.0925i	−1.39038	+	0.506057i	−0.925308	−	0.379217i	$-0.876193\pi$
$571$	−33.2240	+	12.0925i	−1.39038	+	0.506057i	−0.465071	+	0.885273i	$0.653971\pi$
$572$		0			0
$573$	1.21392	−	4.23969i	0.0507121	−	0.177116i
$574$		0			0
$575$	−7.62566	−	13.2080i	−0.318012	−	0.550813i
$576$		0			0
$577$	13.1679	−	22.8074i	0.548185	−	0.949485i	−0.450214	−	0.892921i	$-0.648652\pi$
$577$	13.1679	−	22.8074i	0.548185	−	0.949485i	0.998399	−	0.0565640i	$-0.0180145\pi$
$578$		0			0
$579$	−12.0911	−	1.26604i	−0.502489	−	0.0526149i
$580$		0			0
$581$	1.94825	−	11.0491i	0.0808270	−	0.458393i
$582$		0			0
$583$	21.7578	−	18.2569i	0.901114	−	0.756125i
$584$		0			0
$585$	−3.63115	−	0.768855i	−0.150130	−	0.0317882i
$586$		0			0
$587$	−9.49129	−	3.45455i	−0.391748	−	0.142584i	0.138634	−	0.990344i	$-0.455729\pi$
$587$	−9.49129	−	3.45455i	−0.391748	−	0.142584i	−0.530381	+	0.847759i	$0.677951\pi$
$588$		0			0
$589$	−4.82135	−	4.04559i	−0.198660	−	0.166696i
$590$		0			0
$591$	−1.15585	−	16.4369i	−0.0475451	−	0.676125i
$592$		0			0
$593$	−28.8800			−1.18596			−0.592980	−	0.805217i	$-0.702049\pi$
$593$	−28.8800			−1.18596			−0.592980	+	0.805217i	$0.702049\pi$
$594$		0			0
$595$	0.163587			0.00670641
$596$		0			0
$597$	−40.3264	+	27.2235i	−1.65045	+	1.11418i
$598$		0			0
$599$	−34.4240	−	28.8851i	−1.40653	−	1.18022i	−0.958114	−	0.286388i	$-0.907545\pi$
$599$	−34.4240	−	28.8851i	−1.40653	−	1.18022i	−0.448412	−	0.893827i	$-0.648010\pi$
$600$		0			0
$601$	−25.0378	−	9.11300i	−1.02131	−	0.371727i	−0.223545	−	0.974694i	$-0.571763\pi$
$601$	−25.0378	−	9.11300i	−1.02131	−	0.371727i	−0.797767	+	0.602966i	$0.793985\pi$
$602$		0			0
$603$	3.96219	−	2.11071i	0.161353	−	0.0859549i
$604$		0			0
$605$	−0.0884868	+	0.0742493i	−0.00359750	+	0.00301866i
$606$		0			0
$607$	−0.532309	+	3.01887i	−0.0216058	+	0.122532i	−0.993703	−	0.112046i	$-0.964260\pi$
$607$	−0.532309	+	3.01887i	−0.0216058	+	0.122532i	0.972097	+	0.234578i	$0.0753708\pi$
$608$		0			0
$609$	−7.81851	+	10.7701i	−0.316822	+	0.436427i
$610$		0			0
$611$	6.18213	−	10.7078i	0.250102	−	0.433190i
$612$		0			0
$613$	4.56554	+	7.90775i	0.184400	+	0.319391i	0.943374	−	0.331730i	$-0.107632\pi$
$613$	4.56554	+	7.90775i	0.184400	+	0.319391i	−0.758974	+	0.651121i	$0.774299\pi$
$614$		0			0
$615$	−0.422256	+	0.105456i	−0.0170270	+	0.00425239i
$616$		0			0
$617$	−36.6763	+	13.3491i	−1.47653	+	0.537414i	−0.949866	−	0.312658i	$-0.898781\pi$
$617$	−36.6763	+	13.3491i	−1.47653	+	0.537414i	−0.526667	+	0.850072i	$0.676558\pi$
$618$		0			0
$619$	4.50979	+	25.5763i	0.181264	+	1.02800i	0.930663	+	0.365879i	$0.119231\pi$
$619$	4.50979	+	25.5763i	0.181264	+	1.02800i	−0.749399	+	0.662119i	$0.769657\pi$
$620$		0			0
$621$	−8.62548	−	13.7677i	−0.346128	−	0.552477i
$622$		0			0
$623$	−2.70193	−	15.3234i	−0.108251	−	0.613920i
$624$		0			0
$625$	−21.7850	+	7.92909i	−0.871400	+	0.317164i
$626$		0			0
$627$	2.26250	+	2.34106i	0.0903557	+	0.0934928i
$628$		0			0
$629$	2.28131	+	3.95135i	0.0909618	+	0.157550i
$630$		0			0
$631$	−19.3202	+	33.4635i	−0.769123	+	1.33216i	0.168916	+	0.985631i	$0.445973\pi$
$631$	−19.3202	+	33.4635i	−0.769123	+	1.33216i	−0.938039	+	0.346530i	$0.887360\pi$
$632$		0			0
$633$	−9.70569	−	21.7764i	−0.385766	−	0.865534i
$634$		0			0
$635$	−0.0490521	+	0.278188i	−0.00194657	+	0.0110396i
$636$		0			0
$637$	−2.71210	+	2.27572i	−0.107457	+	0.0901674i
$638$		0			0
$639$	34.5728	−	4.88648i	1.36768	−	0.193306i
$640$		0			0
$641$	11.1711	+	4.06595i	0.441232	+	0.160595i	0.553077	−	0.833130i	$-0.313454\pi$
$641$	11.1711	+	4.06595i	0.441232	+	0.160595i	−0.111844	+	0.993726i	$0.535676\pi$
$642$		0			0
$643$	−0.934361	−	0.784022i	−0.0368476	−	0.0309188i	0.624178	−	0.781282i	$-0.285434\pi$
$643$	−0.934361	−	0.784022i	−0.0368476	−	0.0309188i	−0.661025	+	0.750363i	$0.729878\pi$
$644$		0			0
$645$	−3.39232	−	1.65290i	−0.133573	−	0.0650830i
$646$		0			0
$647$	−5.59932			−0.220132			−0.110066	−	0.993924i	$-0.535106\pi$
$647$	−5.59932			−0.220132			−0.110066	+	0.993924i	$0.535106\pi$
$648$		0			0
$649$	16.0969			0.631859
$650$		0			0
$651$	17.0297	+	8.29771i	0.667448	+	0.325213i
$652$		0			0
$653$	31.7523	+	26.6433i	1.24256	+	1.04263i	0.997319	+	0.0731733i	$0.0233126\pi$
$653$	31.7523	+	26.6433i	1.24256	+	1.04263i	0.245244	+	0.969461i	$0.421132\pi$
$654$		0			0
$655$	−4.89955	−	1.78329i	−0.191441	−	0.0696789i
$656$		0			0
$657$	9.14752	−	22.6920i	0.356879	−	0.885300i
$658$		0			0
$659$	−20.5510	+	17.2443i	−0.800553	+	0.671744i	−0.948333	−	0.317276i	$-0.897232\pi$
$659$	−20.5510	+	17.2443i	−0.800553	+	0.671744i	0.147780	+	0.989020i	$0.452787\pi$
$660$		0			0
$661$	4.31609	−	24.4778i	0.167877	−	0.952075i	−0.778172	−	0.628051i	$-0.783853\pi$
$661$	4.31609	−	24.4778i	0.167877	−	0.952075i	0.946049	−	0.324024i	$-0.105036\pi$
$662$		0			0
$663$	1.16859	+	2.62193i	0.0453842	+	0.101827i
$664$		0			0
$665$	−0.100548	+	0.174155i	−0.00389910	+	0.00675344i
$666$		0			0
$667$	12.0123	+	20.8059i	0.465117	+	0.805607i
$668$		0			0
$669$	5.63373	+	5.82933i	0.217813	+	0.225375i
$670$		0			0
$671$	−19.1438	+	6.96779i	−0.739040	+	0.268988i
$672$		0			0
$673$	1.37367	+	7.79047i	0.0529511	+	0.300301i	0.999770	−	0.0214677i	$-0.00683392\pi$
$673$	1.37367	+	7.79047i	0.0529511	+	0.300301i	−0.946818	+	0.321768i	$0.895723\pi$
$674$		0			0
$675$	−23.4894	+	9.52244i	−0.904109	+	0.366519i
$676$		0			0
$677$	−2.19986	−	12.4760i	−0.0845474	−	0.479492i	−0.997453	−	0.0713221i	$-0.977278\pi$
$677$	−2.19986	−	12.4760i	−0.0845474	−	0.479492i	0.912906	−	0.408170i	$-0.133833\pi$
$678$		0			0
$679$	2.86906	−	1.04425i	0.110105	−	0.0400748i
$680$		0			0
$681$	33.7401	−	8.42637i	1.29292	−	0.322899i
$682$		0			0
$683$	12.2937	+	21.2932i	0.470404	+	0.814763i	0.999427	−	0.0338442i	$-0.0107750\pi$
$683$	12.2937	+	21.2932i	0.470404	+	0.814763i	−0.529023	+	0.848607i	$0.677442\pi$
$684$		0			0
$685$	−0.187585	+	0.324907i	−0.00716725	+	0.0124140i
$686$		0			0
$687$	1.21277	−	1.67062i	0.0462702	−	0.0637379i
$688$		0			0
$689$	−5.34578	+	30.3174i	−0.203658	+	1.15500i
$690$		0			0
$691$	−29.4338	+	24.6979i	−1.11971	+	0.939552i	−0.998590	−	0.0530853i	$-0.983094\pi$
$691$	−29.4338	+	24.6979i	−1.11971	+	0.939552i	−0.121125	+	0.992637i	$0.538650\pi$
$692$		0			0
$693$	−8.31429	−	5.18630i	−0.315834	−	0.197011i
$694$		0			0
$695$	−2.38978	−	0.869810i	−0.0906497	−	0.0329938i
$696$		0			0
$697$	0.257850	+	0.216362i	0.00976677	+	0.00819529i
$698$		0			0
$699$	−15.7914	+	10.6605i	−0.597287	+	0.403215i
$700$		0			0
$701$	−22.6533			−0.855604			−0.427802	−	0.903873i	$-0.640712\pi$
$701$	−22.6533			−0.855604			−0.427802	+	0.903873i	$0.640712\pi$
$702$		0			0
$703$	−5.60881			−0.211540
$704$		0			0
$705$	0.148279	+	2.10863i	0.00558451	+	0.0794157i
$706$		0			0
$707$	−10.9152	−	9.15898i	−0.410510	−	0.344459i
$708$		0			0
$709$	27.3220	+	9.94439i	1.02610	+	0.373469i	0.799594	−	0.600541i	$-0.205048\pi$
$709$	27.3220	+	9.94439i	1.02610	+	0.373469i	0.226504	+	0.974010i	$0.427270\pi$
$710$		0			0
$711$	4.92157	−	5.47456i	0.184573	−	0.205312i
$712$		0			0
$713$	26.1960	−	21.9811i	0.981048	−	0.823197i
$714$		0			0
$715$	−0.701759	+	3.97987i	−0.0262443	+	0.148839i
$716$		0			0
$717$	−50.6039	−	5.29866i	−1.88984	−	0.197882i
$718$		0			0
$719$	−19.8801	+	34.4334i	−0.741404	+	1.28415i	0.210452	+	0.977604i	$0.432506\pi$
$719$	−19.8801	+	34.4334i	−0.741404	+	1.28415i	−0.951856	+	0.306545i	$0.900827\pi$
$720$		0			0
$721$	3.15968	+	5.47272i	0.117673	+	0.203815i
$722$		0			0
$723$	−7.58356	+	26.4861i	−0.282035	+	0.985029i
$724$		0			0
$725$	35.2205	−	12.8192i	1.30806	−	0.476094i
$726$		0			0
$727$	1.71229	+	9.71087i	0.0635053	+	0.360156i	0.999956	+	0.00935773i	$0.00297870\pi$
$727$	1.71229	+	9.71087i	0.0635053	+	0.360156i	−0.936451	+	0.350799i	$0.885910\pi$
$728$		0			0
$729$	−24.6399	+	11.0398i	−0.912588	+	0.408880i
$730$		0			0
$731$	0.506784	+	2.87412i	0.0187441	+	0.106303i
$732$		0			0
$733$	15.6341	−	5.69034i	0.577458	−	0.210178i	−0.0367461	−	0.999325i	$-0.511699\pi$
$733$	15.6341	−	5.69034i	0.577458	−	0.210178i	0.614204	+	0.789147i	$0.289477\pi$
$734$		0			0
$735$	0.166610	−	0.581896i	0.00614549	−	0.0214636i
$736$		0			0
$737$	−2.44400	−	4.23313i	−0.0900259	−	0.155929i
$738$		0			0
$739$	−14.1829	+	24.5655i	−0.521726	+	0.903656i	0.477955	+	0.878385i	$0.341378\pi$
$739$	−14.1829	+	24.5655i	−0.521726	+	0.903656i	−0.999681	+	0.0252715i	$0.991955\pi$
$740$		0			0
$741$	−3.50958	−	0.367483i	−0.128928	−	0.0134998i
$742$		0			0
$743$	−4.51408	+	25.6006i	−0.165605	+	0.939195i	0.782832	+	0.622233i	$0.213774\pi$
$743$	−4.51408	+	25.6006i	−0.165605	+	0.939195i	−0.948438	+	0.316963i	$0.897337\pi$
$744$		0			0
$745$	−5.75282	+	4.82719i	−0.210767	+	0.176854i
$746$		0			0
$747$	−22.5024	+	25.0308i	−0.823320	+	0.915830i
$748$		0			0
$749$	1.83176	+	0.666706i	0.0669311	+	0.0243609i
$750$		0			0
$751$	−23.2187	−	19.4828i	−0.847264	−	0.710939i	0.111921	−	0.993717i	$-0.464300\pi$
$751$	−23.2187	−	19.4828i	−0.847264	−	0.710939i	−0.959185	+	0.282778i	$0.908744\pi$
$752$		0			0
$753$	0.618006	+	8.78847i	0.0225214	+	0.320270i
$754$		0			0
$755$	−6.57545			−0.239305
$756$		0			0
$757$	1.23881			0.0450252			0.0225126	−	0.999747i	$-0.492833\pi$
$757$	1.23881			0.0450252			0.0225126	+	0.999747i	$0.492833\pi$
$758$		0			0
$759$	−14.6611	+	9.89742i	−0.532166	+	0.359253i
$760$		0			0
$761$	12.6131	+	10.5837i	0.457226	+	0.383658i	0.842109	−	0.539307i	$-0.181314\pi$
$761$	12.6131	+	10.5837i	0.457226	+	0.383658i	−0.384883	+	0.922965i	$0.625758\pi$
$762$		0			0
$763$	−9.48105	−	3.45082i	−0.343237	−	0.124928i
$764$		0			0
$765$	−0.416392	−	0.259738i	−0.0150547	−	0.00939084i
$766$		0			0
$767$	−13.3652	+	11.2148i	−0.482591	+	0.404942i
$768$		0			0
$769$	−8.28998	+	47.0148i	−0.298944	+	1.69540i	0.351780	+	0.936083i	$0.385577\pi$
$769$	−8.28998	+	47.0148i	−0.298944	+	1.69540i	−0.650724	+	0.759314i	$0.725534\pi$
$770$		0			0
$771$	−21.1333	+	29.1115i	−0.761099	+	1.04843i
$772$		0			0
$773$	−8.15126	+	14.1184i	−0.293180	+	0.507803i	−0.974560	−	0.224127i	$-0.928047\pi$
$773$	−8.15126	+	14.1184i	−0.293180	+	0.507803i	0.681380	+	0.731930i	$0.261380\pi$
$774$		0			0
$775$	−26.6751	−	46.2026i	−0.958197	−	1.65965i
$776$		0			0
$777$	16.3788	−	4.09051i	0.587587	−	0.146746i
$778$		0			0
$779$	−0.388826	+	0.141521i	−0.0139311	+	0.00507052i
$780$		0			0
$781$	−6.60160	−	37.4396i	−0.236224	−	1.33969i
$782$		0			0
$783$	37.0016	−	15.0002i	1.32233	−	0.536062i
$784$		0			0
$785$	0.578950	+	3.28339i	0.0206636	+	0.117189i
$786$		0			0
$787$	50.3092	−	18.3110i	1.79333	−	0.652718i	0.794353	−	0.607457i	$-0.207810\pi$
$787$	50.3092	−	18.3110i	1.79333	−	0.652718i	0.998975	−	0.0452615i	$-0.0144121\pi$
$788$		0			0
$789$	25.4056	+	26.2877i	0.904464	+	0.935866i
$790$		0			0
$791$	5.63999	+	9.76876i	0.200535	+	0.347337i
$792$		0			0
$793$	11.0406	−	19.1229i	0.392064	−	0.679075i
$794$		0			0
$795$	−2.14259	−	4.80727i	−0.0759898	−	0.170496i
$796$		0			0
$797$	−1.03074	+	5.84560i	−0.0365106	+	0.207062i	−0.997606	−	0.0691550i	$-0.977970\pi$
$797$	−1.03074	+	5.84560i	−0.0365106	+	0.207062i	0.961095	+	0.276217i	$0.0890808\pi$
$798$		0			0
$799$	1.25235	−	1.05084i	0.0443048	−	0.0371762i
$800$		0			0
$801$	−17.4525	+	43.2941i	−0.616655	+	1.52972i
$802$		0			0
$803$	−25.0326	−	9.11112i	−0.883381	−	0.321525i
$804$		0			0
$805$	−0.837000	−	0.702326i	−0.0295004	−	0.0247537i
$806$		0			0
$807$	−19.7215	−	9.60926i	−0.694229	−	0.338262i
$808$		0			0
$809$	−15.5649			−0.547234			−0.273617	−	0.961839i	$-0.588220\pi$
$809$	−15.5649			−0.547234			−0.273617	+	0.961839i	$0.588220\pi$
$810$		0			0
$811$	−20.0542			−0.704200			−0.352100	−	0.935962i	$-0.614532\pi$
$811$	−20.0542			−0.704200			−0.352100	+	0.935962i	$0.614532\pi$
$812$		0			0
$813$	−16.5542	−	8.06598i	−0.580580	−	0.282886i
$814$		0			0
$815$	−0.652221	−	0.547278i	−0.0228463	−	0.0191703i
$816$		0			0
$817$	−3.37128	−	1.22705i	−0.117946	−	0.0429289i
$818$		0			0
$819$	10.5167	−	1.48641i	0.367482	−	0.0519395i
$820$		0			0
$821$	22.5337	−	18.9080i	0.786432	−	0.659895i	−0.158427	−	0.987371i	$-0.550642\pi$
$821$	22.5337	−	18.9080i	0.786432	−	0.659895i	0.944860	+	0.327475i	$0.106198\pi$
$822$		0			0
$823$	−3.92092	+	22.2366i	−0.136675	+	0.775120i	0.837004	+	0.547196i	$0.184305\pi$
$823$	−3.92092	+	22.2366i	−0.136675	+	0.775120i	−0.973679	+	0.227924i	$0.926806\pi$
$824$		0			0
$825$	11.2346	+	25.2068i	0.391139	+	0.877587i
$826$		0			0
$827$	−3.60189	+	6.23866i	−0.125250	+	0.216939i	−0.921831	−	0.387593i	$-0.873307\pi$
$827$	−3.60189	+	6.23866i	−0.125250	+	0.216939i	0.796581	+	0.604532i	$0.206640\pi$
$828$		0			0
$829$	−13.8480	−	23.9854i	−0.480959	−	0.833046i	0.518802	−	0.854894i	$-0.326378\pi$
$829$	−13.8480	−	23.9854i	−0.480959	−	0.833046i	−0.999761	+	0.0218486i	$0.993045\pi$
$830$		0			0
$831$	23.8080	+	24.6346i	0.825891	+	0.854566i
$832$		0			0
$833$	−0.439886	+	0.160105i	−0.0152411	+	0.00554732i
$834$		0			0
$835$	−0.916405	−	5.19719i	−0.0317135	−	0.179856i
$836$		0			0
$837$	−30.1725	−	48.1601i	−1.04291	−	1.66466i
$838$		0			0
$839$	3.48252	+	19.7503i	0.120230	+	0.681857i	0.984027	+	0.178018i	$0.0569686\pi$
$839$	3.48252	+	19.7503i	0.120230	+	0.681857i	−0.863797	+	0.503839i	$0.831920\pi$
$840$		0			0
$841$	−28.2298	+	10.2748i	−0.973443	+	0.354304i
$842$		0			0
$843$	−20.8868	+	5.21634i	−0.719379	+	0.179660i
$844$		0			0
$845$	0.0813546	+	0.140910i	0.00279868	+	0.00484746i
$846$		0			0
$847$	0.165272	−	0.286260i	0.00567882	−	0.00983601i
$848$		0			0
$849$	8.12707	−	11.1952i	0.278920	−	0.384217i
$850$		0			0
$851$	5.29185	−	30.0115i	0.181402	−	1.02878i
$852$		0			0
$853$	−5.46252	+	4.58360i	−0.187033	+	0.156939i	−0.731497	−	0.681845i	$-0.761178\pi$
$853$	−5.46252	+	4.58360i	−0.187033	+	0.156939i	0.544463	+	0.838785i	$0.316733\pi$
$854$		0			0
$855$	0.532452	−	0.283644i	0.0182095	−	0.00970043i
$856$		0			0
$857$	−50.6619	−	18.4394i	−1.73058	−	0.629878i	−0.731905	−	0.681407i	$-0.761369\pi$
$857$	−50.6619	−	18.4394i	−1.73058	−	0.629878i	−0.998672	+	0.0515281i	$0.983591\pi$
$858$		0			0
$859$	15.8404	+	13.2917i	0.540468	+	0.453506i	0.871698	−	0.490044i	$-0.163019\pi$
$859$	15.8404	+	13.2917i	0.540468	+	0.453506i	−0.331230	+	0.943550i	$0.607464\pi$
$860$		0			0
$861$	1.03224	−	0.696841i	0.0351785	−	0.0237483i
$862$		0			0
$863$	−53.8614			−1.83346			−0.916732	−	0.399503i	$-0.869183\pi$
$863$	−53.8614			−1.83346			−0.916732	+	0.399503i	$0.869183\pi$
$864$		0			0
$865$	−7.80235			−0.265288
$866$		0			0
$867$	−2.03884	−	28.9937i	−0.0692426	−	0.984678i
$868$		0			0
$869$	−6.14008	−	5.15214i	−0.208288	−	0.174774i
$870$		0			0
$871$	4.97849	+	1.81202i	0.168690	+	0.0613980i
$872$		0			0
$873$	−8.96091	−	1.89737i	−0.303281	−	0.0642163i
$874$		0			0
$875$	−2.64431	+	2.21884i	−0.0893940	+	0.0750105i
$876$		0			0
$877$	8.02708	−	45.5238i	0.271055	−	1.53723i	−0.480165	−	0.877178i	$-0.659423\pi$
$877$	8.02708	−	45.5238i	0.271055	−	1.53723i	0.751220	−	0.660052i	$-0.229466\pi$
$878$		0			0
$879$	14.6871	+	1.53786i	0.495382	+	0.0518708i
$880$		0			0
$881$	19.0333	−	32.9666i	0.641248	−	1.11067i	−0.343906	−	0.939004i	$-0.611750\pi$
$881$	19.0333	−	32.9666i	0.641248	−	1.11067i	0.985154	−	0.171670i	$-0.0549164\pi$
$882$		0			0
$883$	−8.46771	−	14.6665i	−0.284961	−	0.493567i	0.687639	−	0.726053i	$-0.258647\pi$
$883$	−8.46771	−	14.6665i	−0.284961	−	0.493567i	−0.972600	+	0.232486i	$0.925314\pi$
$884$		0			0
$885$	0.821053	−	2.86759i	0.0275994	−	0.0963929i
$886$		0			0
$887$	40.5602	−	14.7627i	1.36188	−	0.495683i	0.445243	−	0.895410i	$-0.353117\pi$
$887$	40.5602	−	14.7627i	1.36188	−	0.495683i	0.916634	+	0.399727i	$0.130895\pi$
$888$		0			0
$889$	−0.140366	−	0.796057i	−0.00470773	−	0.0266989i
$890$		0			0
$891$	12.9285	+	26.4023i	0.433120	+	0.884510i
$892$		0			0
$893$	0.348977	+	1.97915i	0.0116781	+	0.0662297i
$894$		0			0
$895$	1.56998	−	0.571426i	0.0524786	−	0.0191007i
$896$		0			0
$897$	5.27757	−	18.4323i	0.176213	−	0.615436i
$898$		0			0
$899$	42.0197	+	72.7803i	1.40144	+	2.42736i
$900$		0			0
$901$	−2.03523	+	3.52512i	−0.0678033	+	0.117439i
$902$		0			0
$903$	10.7397	+	1.12454i	0.357394	+	0.0374223i
$904$		0			0
$905$	0.938405	−	5.32196i	0.0311936	−	0.176908i
$906$		0			0
$907$	8.70519	−	7.30452i	0.289051	−	0.242543i	−0.486719	−	0.873559i	$-0.661806\pi$
$907$	8.70519	−	7.30452i	0.289051	−	0.242543i	0.775770	+	0.631016i	$0.217362\pi$
$908$		0			0
$909$	13.2412	+	40.6440i	0.439183	+	1.34808i
$910$		0			0
$911$	14.9228	+	5.43145i	0.494414	+	0.179952i	0.577180	−	0.816617i	$-0.304153\pi$
$911$	14.9228	+	5.43145i	0.494414	+	0.179952i	−0.0827661	+	0.996569i	$0.526375\pi$
$912$		0			0
$913$	28.0737	+	23.5566i	0.929104	+	0.779610i
$914$		0			0
$915$	0.264811	+	3.76579i	0.00875437	+	0.124493i
$916$		0			0
$917$	14.9202			0.492709
$918$		0			0
$919$	−2.29548			−0.0757208			−0.0378604	−	0.999283i	$-0.512054\pi$
$919$	−2.29548			−0.0757208			−0.0378604	+	0.999283i	$0.512054\pi$
$920$		0			0
$921$	39.5748	−	26.7161i	1.30403	−	0.880324i
$922$		0			0
$923$	31.5656	+	26.4867i	1.03899	+	0.871819i
$924$		0			0
$925$	−44.6763	−	16.2608i	−1.46895	−	0.534653i
$926$		0			0
$927$	0.646798	−	18.9470i	0.0212436	−	0.622302i
$928$		0			0
$929$	6.21352	−	5.21377i	0.203859	−	0.171058i	−0.535142	−	0.844762i	$-0.679742\pi$
$929$	6.21352	−	5.21377i	0.203859	−	0.171058i	0.739002	+	0.673704i	$0.235298\pi$
$930$		0			0
$931$	0.0999265	−	0.566711i	0.00327496	−	0.0185732i
$932$		0			0
$933$	−7.73641	+	10.6570i	−0.253279	+	0.348895i
$934$		0			0
$935$	−0.267171	+	0.462754i	−0.00873744	+	0.0151337i
$936$		0			0
$937$	22.8699	+	39.6118i	0.747126	+	1.29406i	0.949195	+	0.314688i	$0.101900\pi$
$937$	22.8699	+	39.6118i	0.747126	+	1.29406i	−0.202069	+	0.979371i	$0.564767\pi$
$938$		0			0
$939$	15.9125	−	3.97405i	0.519285	−	0.129688i
$940$		0			0
$941$	24.6058	−	8.95579i	0.802127	−	0.291950i	0.0917594	−	0.995781i	$-0.470751\pi$
$941$	24.6058	−	8.95579i	0.802127	−	0.291950i	0.710368	+	0.703831i	$0.248529\pi$
$942$		0			0
$943$	−0.390397	−	2.21405i	−0.0127131	−	0.0720994i
$944$		0			0
$945$	−1.34800	+	1.21661i	−0.0438505	+	0.0395765i
$946$		0			0
$947$	5.52659	+	31.3429i	0.179590	+	1.01851i	0.932711	+	0.360624i	$0.117436\pi$
$947$	5.52659	+	31.3429i	0.179590	+	1.01851i	−0.753121	+	0.657882i	$0.771453\pi$
$948$		0			0
$949$	27.1323	−	9.87535i	0.880752	−	0.320567i
$950$		0			0
$951$	−36.5957	−	37.8663i	−1.18670	−	1.22790i
$952$		0			0
$953$	−16.5330	−	28.6360i	−0.535556	−	0.927609i	−0.999136	−	0.0415547i	$-0.986769\pi$
$953$	−16.5330	−	28.6360i	−0.535556	−	0.927609i	0.463581	−	0.886055i	$-0.346564\pi$
$954$		0			0
$955$	−0.444885	+	0.770564i	−0.0143962	+	0.0249349i
$956$		0			0
$957$	−17.6972	−	39.7068i	−0.572071	−	1.28354i
$958$		0			0
$959$	0.186425	−	1.05727i	0.00601997	−	0.0341409i
$960$		0			0
$961$	67.8879	−	56.9647i	2.18993	−	1.83757i
$962$		0			0
$963$	−3.60397	−	4.60543i	−0.116136	−	0.148408i
$964$		0			0
$965$	2.30491	+	0.838918i	0.0741976	+	0.0270057i
$966$		0			0
$967$	−34.5631	−	29.0018i	−1.11147	−	0.932636i	−0.113330	−	0.993557i	$-0.536152\pi$
$967$	−34.5631	−	29.0018i	−1.11147	−	0.932636i	−0.998143	+	0.0609210i	$0.980596\pi$
$968$		0			0
$969$	−0.419438	−	0.204371i	−0.0134743	−	0.00656533i
$970$		0			0
$971$	29.0097			0.930966			0.465483	−	0.885057i	$-0.345881\pi$
$971$	29.0097			0.930966			0.465483	+	0.885057i	$0.345881\pi$
$972$		0			0
$973$	7.27743			0.233304
$974$		0			0
$975$	−26.8897	−	13.1020i	−0.861160	−	0.419599i
$976$		0			0
$977$	5.48881	+	4.60565i	0.175602	+	0.147348i	0.726353	−	0.687322i	$-0.241214\pi$
$977$	5.48881	+	4.60565i	0.175602	+	0.147348i	−0.550750	+	0.834670i	$0.685658\pi$
$978$		0			0
$979$	47.7597	+	17.3831i	1.52641	+	0.555566i
$980$		0			0
$981$	18.6539	+	23.8374i	0.595572	+	0.761069i
$982$		0			0
$983$	13.7229	−	11.5149i	0.437693	−	0.367268i	−0.397152	−	0.917753i	$-0.630002\pi$
$983$	13.7229	−	11.5149i	0.437693	−	0.367268i	0.834845	+	0.550485i	$0.185557\pi$
$984$		0			0
$985$	−0.577293	+	3.27399i	−0.0183941	+	0.104318i
$986$		0			0
$987$	−2.46248	−	5.52499i	−0.0783815	−	0.175862i
$988$		0			0
$989$	9.74642	−	16.8813i	0.309918	−	0.536794i
$990$		0			0
$991$	13.5362	+	23.4454i	0.429992	+	0.744767i	0.996872	−	0.0790328i	$-0.0251832\pi$
$991$	13.5362	+	23.4454i	0.429992	+	0.744767i	−0.566880	+	0.823800i	$0.691850\pi$
$992$		0			0
$993$	11.7862	+	12.1954i	0.374024	+	0.387010i
$994$		0			0
$995$	9.22465	−	3.35750i	0.292441	−	0.106440i
$996$		0			0
$997$	−3.91651	−	22.2116i	−0.124037	−	0.703449i	−0.981875	−	0.189529i	$-0.939304\pi$
$997$	−3.91651	−	22.2116i	−0.124037	−	0.703449i	0.857838	−	0.513920i	$-0.171807\pi$
$998$		0			0
$999$	−48.1852	−	15.5938i	−1.52451	−	0.493366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.a.337.2	✓	54
27.25	even	9	inner	756.2.bo.a.673.2	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.a.337.2	✓	54	1.1	even	1	trivial
756.2.bo.a.673.2	yes	54	27.25	even	9	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55705 - 0.758672i) q^{3} +(0.267700 + 0.224627i) q^{5} +(-0.939693 - 0.342020i) q^{7} +(1.84883 + 2.36259i) q^{9} +O(q^{10})\)	\(q+(-1.55705 - 0.758672i) q^{3} +(0.267700 + 0.224627i) q^{5} +(-0.939693 - 0.342020i) q^{7} +(1.84883 + 2.36259i) q^{9} +(2.50222 - 2.09961i) q^{11} +(-0.614783 + 3.48661i) q^{13} +(-0.246405 - 0.552853i) q^{15} +(-0.234058 + 0.405401i) q^{17} +(-0.287727 - 0.498357i) q^{19} +(1.20367 + 1.24546i) q^{21} +(2.93807 - 1.06937i) q^{23} +(-0.847035 - 4.80377i) q^{25} +(-1.08631 - 5.08133i) q^{27} +(1.33429 + 7.56712i) q^{29} +(10.2776 - 3.74073i) q^{31} +(-5.48900 + 1.37084i) q^{33} +(-0.174729 - 0.302639i) q^{35} +(4.87338 - 8.44094i) q^{37} +(3.60244 - 4.96242i) q^{39} +(0.124862 - 0.708126i) q^{41} +(4.77587 - 4.00743i) q^{43} +(-0.0357677 + 1.04776i) q^{45} +(-3.28173 - 1.19445i) q^{47} +(0.766044 + 0.642788i) q^{49} +(0.672008 - 0.453658i) q^{51} +8.69539 q^{53} +1.14147 q^{55} +(0.0699164 + 0.994260i) q^{57} +(3.77507 + 3.16766i) q^{59} +(-5.86081 - 2.13316i) q^{61} +(-0.929284 - 2.85244i) q^{63} +(-0.947764 + 0.795269i) q^{65} +(0.259855 - 1.47371i) q^{67} +(-5.38604 - 0.563965i) q^{69} +(5.81940 - 10.0795i) q^{71} +(-4.07774 - 7.06284i) q^{73} +(-2.32561 + 8.12236i) q^{75} +(-3.06942 + 1.11718i) q^{77} +(-0.426107 - 2.41658i) q^{79} +(-2.16363 + 8.73606i) q^{81} +(1.94825 + 11.0491i) q^{83} +(-0.153722 + 0.0559501i) q^{85} +(3.66340 - 12.7947i) q^{87} +(7.77990 + 13.4752i) q^{89} +(1.77020 - 3.06607i) q^{91} +(-18.8407 - 1.97278i) q^{93} +(0.0349201 - 0.198042i) q^{95} +(-2.33888 + 1.96255i) q^{97} +(9.58669 + 2.02987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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