LMFDB - Embedded newform 968.2.i.t.729.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(9,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("968.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.i (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.2
Root			$2.51217 + 1.82520i$ of defining polynomial
Character	$\chi$	$=$	968.729
Dual form			968.2.i.t.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.593044 + 1.82520i) q^{3} +(-2.75577 - 2.00218i) q^{5} +(-0.268582 + 0.826612i) q^{7} +(-0.552609 + 0.401494i) q^{9} +O(q^{10})$	\(q+(0.593044 + 1.82520i) q^{3} +(-2.75577 - 2.00218i) q^{5} +(-0.268582 + 0.826612i) q^{7} +(-0.552609 + 0.401494i) q^{9} +(2.26858 - 1.64822i) q^{13} +(2.02009 - 6.21721i) q^{15} +(-5.89879 - 4.28572i) q^{17} +(-0.736068 - 2.26538i) q^{19} -1.66801 q^{21} +7.44651 q^{23} +(2.04043 + 6.27981i) q^{25} +(3.59730 + 2.61359i) q^{27} +(2.26858 - 6.98198i) q^{29} +(2.13773 - 1.55315i) q^{31} +(2.39518 - 1.74020i) q^{35} +(0.318562 - 0.980434i) q^{37} +(4.35371 + 3.16315i) q^{39} +(-0.894141 - 2.75188i) q^{41} -2.18609 q^{43} +2.32673 q^{45} +(-1.21860 - 3.75047i) q^{47} +(5.05197 + 3.67047i) q^{49} +(4.32407 - 13.3081i) q^{51} +(5.75577 - 4.18181i) q^{53} +(3.69826 - 2.68695i) q^{57} +(2.50000 - 7.69421i) q^{59} +(-2.17920 - 1.58328i) q^{61} +(-0.183459 - 0.564628i) q^{63} -9.55172 q^{65} -13.7720 q^{67} +(4.41611 + 13.5914i) q^{69} +(1.56117 + 1.13426i) q^{71} +(-1.54306 + 4.74906i) q^{73} +(-10.2519 + 7.44841i) q^{75} +(10.8853 - 7.90866i) q^{79} +(-3.27021 + 10.0647i) q^{81} +(-0.157432 - 0.114381i) q^{83} +(7.67490 + 23.6209i) q^{85} +14.0889 q^{87} +4.18609 q^{89} +(0.753138 + 2.31792i) q^{91} +(4.10259 + 2.98071i) q^{93} +(-2.50728 + 7.71661i) q^{95} +(-4.03716 + 2.93317i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} + 2 q^{5} + 8 q^{7} + 7 q^{9}+O(q^{10}) $ 8 * q - q^3 + 2 * q^5 + 8 * q^7 + 7 * q^9	$ 8 q - q^{3} + 2 q^{5} + 8 q^{7} + 7 q^{9} + 8 q^{13} - 3 q^{15} - 11 q^{17} + 12 q^{19} + 2 q^{21} - 4 q^{23} + 22 q^{25} + 8 q^{27} + 8 q^{29} + 2 q^{31} + 29 q^{35} - 14 q^{37} + 21 q^{39} + q^{41} - 6 q^{43} + 44 q^{45} - 6 q^{47} - 2 q^{49} + 52 q^{51} + 22 q^{53} + q^{57} + 20 q^{59} - 26 q^{61} + 5 q^{63} + 10 q^{65} - 10 q^{67} + 42 q^{69} + 30 q^{71} - 13 q^{73} - q^{75} + 6 q^{79} - 6 q^{81} + 20 q^{83} + 26 q^{85} + 6 q^{87} + 22 q^{89} - 13 q^{91} + 15 q^{93} + 13 q^{95} - 12 q^{97}+O(q^{100}) $ 8 * q - q^3 + 2 * q^5 + 8 * q^7 + 7 * q^9 + 8 * q^13 - 3 * q^15 - 11 * q^17 + 12 * q^19 + 2 * q^21 - 4 * q^23 + 22 * q^25 + 8 * q^27 + 8 * q^29 + 2 * q^31 + 29 * q^35 - 14 * q^37 + 21 * q^39 + q^41 - 6 * q^43 + 44 * q^45 - 6 * q^47 - 2 * q^49 + 52 * q^51 + 22 * q^53 + q^57 + 20 * q^59 - 26 * q^61 + 5 * q^63 + 10 * q^65 - 10 * q^67 + 42 * q^69 + 30 * q^71 - 13 * q^73 - q^75 + 6 * q^79 - 6 * q^81 + 20 * q^83 + 26 * q^85 + 6 * q^87 + 22 * q^89 - 13 * q^91 + 15 * q^93 + 13 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.593044	+	1.82520i	0.342394	+	1.05378i	0.962964	+	0.269630i	$0.0869013\pi$
$3$	0.593044	+	1.82520i	0.342394	+	1.05378i	−0.620570	+	0.784151i	$0.713099\pi$
$4$		0			0
$5$	−2.75577	−	2.00218i	−1.23242	−	0.895403i	−0.235348	−	0.971911i	$-0.575623\pi$
$5$	−2.75577	−	2.00218i	−1.23242	−	0.895403i	−0.997069	+	0.0765083i	$0.975623\pi$
$6$		0			0
$7$	−0.268582	+	0.826612i	−0.101515	+	0.312430i	−0.988897	−	0.148605i	$-0.952522\pi$
$7$	−0.268582	+	0.826612i	−0.101515	+	0.312430i	0.887382	+	0.461035i	$0.152522\pi$
$8$		0			0
$9$	−0.552609	+	0.401494i	−0.184203	+	0.133831i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	2.26858	−	1.64822i	0.629192	−	0.457134i	−0.226929	−	0.973911i	$-0.572868\pi$
$13$	2.26858	−	1.64822i	0.629192	−	0.457134i	0.856120	+	0.516777i	$0.172868\pi$
$14$		0			0
$15$	2.02009	−	6.21721i	0.521586	−	1.60528i
$16$		0			0
$17$	−5.89879	−	4.28572i	−1.43067	−	1.03944i	−0.989892	−	0.141823i	$-0.954704\pi$
$17$	−5.89879	−	4.28572i	−1.43067	−	1.03944i	−0.440775	−	0.897618i	$-0.645296\pi$
$18$		0			0
$19$	−0.736068	−	2.26538i	−0.168866	−	0.519715i	0.830435	−	0.557116i	$-0.188092\pi$
$19$	−0.736068	−	2.26538i	−0.168866	−	0.519715i	−0.999300	+	0.0374011i	$0.988092\pi$
$20$		0			0
$21$	−1.66801			−0.363990
$22$		0			0
$23$	7.44651			1.55270			0.776352	−	0.630300i	$-0.217068\pi$
$23$	7.44651			1.55270			0.776352	+	0.630300i	$0.217068\pi$
$24$		0			0
$25$	2.04043	+	6.27981i	0.408087	+	1.25596i
$26$		0			0
$27$	3.59730	+	2.61359i	0.692300	+	0.502986i
$28$		0			0
$29$	2.26858	−	6.98198i	0.421265	−	1.29652i	−0.485260	−	0.874370i	$-0.661275\pi$
$29$	2.26858	−	6.98198i	0.421265	−	1.29652i	0.906525	−	0.422151i	$-0.138725\pi$
$30$		0			0
$31$	2.13773	−	1.55315i	0.383948	−	0.278955i	−0.379023	−	0.925387i	$-0.623740\pi$
$31$	2.13773	−	1.55315i	0.383948	−	0.278955i	0.762971	+	0.646433i	$0.223740\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.39518	−	1.74020i	0.404859	−	0.294147i
$36$		0			0
$37$	0.318562	−	0.980434i	0.0523713	−	0.161182i	−0.921450	−	0.388497i	$-0.872994\pi$
$37$	0.318562	−	0.980434i	0.0523713	−	0.161182i	0.973821	+	0.227314i	$0.0729945\pi$
$38$		0			0
$39$	4.35371	+	3.16315i	0.697151	+	0.506510i
$40$		0			0
$41$	−0.894141	−	2.75188i	−0.139641	−	0.429772i	0.856642	−	0.515912i	$-0.172547\pi$
$41$	−0.894141	−	2.75188i	−0.139641	−	0.429772i	−0.996283	+	0.0861400i	$0.972547\pi$
$42$		0			0
$43$	−2.18609			−0.333375			−0.166688	−	0.986010i	$-0.553307\pi$
$43$	−2.18609			−0.333375			−0.166688	+	0.986010i	$0.553307\pi$
$44$		0			0
$45$	2.32673			0.346848
$46$		0			0
$47$	−1.21860	−	3.75047i	−0.177751	−	0.547063i	0.821997	−	0.569492i	$-0.192860\pi$
$47$	−1.21860	−	3.75047i	−0.177751	−	0.547063i	−0.999748	+	0.0224292i	$0.992860\pi$
$48$		0			0
$49$	5.05197	+	3.67047i	0.721710	+	0.524353i
$50$		0			0
$51$	4.32407	−	13.3081i	0.605490	−	1.86351i
$52$		0			0
$53$	5.75577	−	4.18181i	0.790615	−	0.574416i	−0.117531	−	0.993069i	$-0.537498\pi$
$53$	5.75577	−	4.18181i	0.790615	−	0.574416i	0.908146	+	0.418654i	$0.137498\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.69826	−	2.68695i	0.489847	−	0.355895i
$58$		0			0
$59$	2.50000	−	7.69421i	0.325472	−	1.00170i	−0.645755	−	0.763545i	$-0.723457\pi$
$59$	2.50000	−	7.69421i	0.325472	−	1.00170i	0.971227	−	0.238156i	$-0.0765429\pi$
$60$		0			0
$61$	−2.17920	−	1.58328i	−0.279018	−	0.202719i	0.439471	−	0.898257i	$-0.355166\pi$
$61$	−2.17920	−	1.58328i	−0.279018	−	0.202719i	−0.718489	+	0.695538i	$0.755166\pi$
$62$		0			0
$63$	−0.183459	−	0.564628i	−0.0231136	−	0.0711364i
$64$		0			0
$65$	−9.55172			−1.18475
$66$		0			0
$67$	−13.7720			−1.68251			−0.841256	−	0.540637i	$-0.818183\pi$
$67$	−13.7720			−1.68251			−0.841256	+	0.540637i	$0.818183\pi$
$68$		0			0
$69$	4.41611	+	13.5914i	0.531637	+	1.63621i
$70$		0			0
$71$	1.56117	+	1.13426i	0.185277	+	0.134611i	0.676557	−	0.736390i	$-0.263471\pi$
$71$	1.56117	+	1.13426i	0.185277	+	0.134611i	−0.491281	+	0.871001i	$0.663471\pi$
$72$		0			0
$73$	−1.54306	+	4.74906i	−0.180602	+	0.555836i	−0.999845	−	0.0176109i	$-0.994394\pi$
$73$	−1.54306	+	4.74906i	−0.180602	+	0.555836i	0.819243	+	0.573447i	$0.194394\pi$
$74$		0			0
$75$	−10.2519	+	7.44841i	−1.18378	+	0.860068i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	10.8853	−	7.90866i	1.22470	−	0.889794i	0.228215	−	0.973611i	$-0.426711\pi$
$79$	10.8853	−	7.90866i	1.22470	−	0.889794i	0.996481	+	0.0838172i	$0.0267112\pi$
$80$		0			0
$81$	−3.27021	+	10.0647i	−0.363356	+	1.11830i
$82$		0			0
$83$	−0.157432	−	0.114381i	−0.0172804	−	0.0125550i	0.579112	−	0.815248i	$-0.303400\pi$
$83$	−0.157432	−	0.114381i	−0.0172804	−	0.0125550i	−0.596392	+	0.802693i	$0.703400\pi$
$84$		0			0
$85$	7.67490	+	23.6209i	0.832460	+	2.56205i
$86$		0			0
$87$	14.0889			1.51049
$88$		0			0
$89$	4.18609			0.443724			0.221862	−	0.975078i	$-0.428786\pi$
$89$	4.18609			0.443724			0.221862	+	0.975078i	$0.428786\pi$
$90$		0			0
$91$	0.753138	+	2.31792i	0.0789503	+	0.242984i
$92$		0			0
$93$	4.10259	+	2.98071i	0.425419	+	0.309085i
$94$		0			0
$95$	−2.50728	+	7.71661i	−0.257241	+	0.791708i
$96$		0			0
$97$	−4.03716	+	2.93317i	−0.409912	+	0.297818i	−0.773566	−	0.633716i	$-0.781529\pi$
$97$	−4.03716	+	2.93317i	−0.409912	+	0.297818i	0.363654	+	0.931534i	$0.381529\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.69074	+	4.86111i	−0.665753	+	0.483698i	−0.868601	−	0.495512i	$-0.834980\pi$
$101$	−6.69074	+	4.86111i	−0.665753	+	0.483698i	0.202848	+	0.979210i	$0.434980\pi$
$102$		0			0
$103$	0.253534	−	0.780296i	0.0249814	−	0.0768849i	−0.937789	−	0.347207i	$-0.887130\pi$
$103$	0.253534	−	0.780296i	0.0249814	−	0.0768849i	0.962770	+	0.270322i	$0.0871302\pi$
$104$		0			0
$105$	4.59666	+	3.33967i	0.448588	+	0.325918i
$106$		0			0
$107$	−3.82911	−	11.7848i	−0.370174	−	1.13928i	−0.946677	−	0.322184i	$-0.895583\pi$
$107$	−3.82911	−	11.7848i	−0.370174	−	1.13928i	0.576503	−	0.817095i	$-0.304417\pi$
$108$		0			0
$109$	7.20439			0.690055			0.345028	−	0.938593i	$-0.387870\pi$
$109$	7.20439			0.690055			0.345028	+	0.938593i	$0.387870\pi$
$110$		0			0
$111$	1.97841			0.187782
$112$		0			0
$113$	0.636108	+	1.95774i	0.0598400	+	0.184169i	0.976508	−	0.215481i	$-0.0691319\pi$
$113$	0.636108	+	1.95774i	0.0598400	+	0.184169i	−0.916668	+	0.399649i	$0.869132\pi$
$114$		0			0
$115$	−20.5208	−	14.9093i	−1.91358	−	1.39030i
$116$		0			0
$117$	−0.591888	+	1.82165i	−0.0547201	+	0.168411i
$118$		0			0
$119$	5.12694	−	3.72494i	0.469986	−	0.341465i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	4.49248	−	3.26397i	0.405073	−	0.294303i
$124$		0			0
$125$	1.68732	−	5.19303i	0.150918	−	0.464479i
$126$		0			0
$127$	6.77161	+	4.91986i	0.600883	+	0.436567i	0.846192	−	0.532878i	$-0.178889\pi$
$127$	6.77161	+	4.91986i	0.600883	+	0.436567i	−0.245309	+	0.969445i	$0.578889\pi$
$128$		0			0
$129$	−1.29645	−	3.99005i	−0.114146	−	0.351304i
$130$		0			0
$131$	−13.3511			−1.16649			−0.583244	−	0.812297i	$-0.698217\pi$
$131$	−13.3511			−1.16649			−0.583244	+	0.812297i	$0.698217\pi$
$132$		0			0
$133$	2.07029			0.179517
$134$		0			0
$135$	−4.68043	−	14.4049i	−0.402828	−	1.23978i
$136$		0			0
$137$	−0.801097	−	0.582031i	−0.0684423	−	0.0497263i	0.553038	−	0.833156i	$-0.313468\pi$
$137$	−0.801097	−	0.582031i	−0.0684423	−	0.0497263i	−0.621480	+	0.783430i	$0.713468\pi$
$138$		0			0
$139$	−1.85248	+	5.70134i	−0.157125	+	0.483581i	−0.998370	−	0.0570730i	$-0.981823\pi$
$139$	−1.85248	+	5.70134i	−0.157125	+	0.483581i	0.841245	+	0.540654i	$0.181823\pi$
$140$		0			0
$141$	6.12268	−	4.44839i	0.515623	−	0.374622i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−20.2309	+	14.6986i	−1.68008	+	1.22065i
$146$		0			0
$147$	−3.70331	+	11.3976i	−0.305444	+	0.940059i
$148$		0			0
$149$	−13.9906	−	10.1647i	−1.14615	−	0.832727i	−0.158187	−	0.987409i	$-0.550565\pi$
$149$	−13.9906	−	10.1647i	−1.14615	−	0.832727i	−0.987964	+	0.154682i	$0.950565\pi$
$150$		0			0
$151$	0.244233	+	0.751672i	0.0198754	+	0.0611702i	0.960502	−	0.278272i	$-0.0897617\pi$
$151$	0.244233	+	0.751672i	0.0198754	+	0.0611702i	−0.940627	+	0.339442i	$0.889762\pi$
$152$		0			0
$153$	4.98042			0.402643
$154$		0			0
$155$	−9.00079			−0.722961
$156$		0			0
$157$	−3.93580	−	12.1132i	−0.314111	−	0.966735i	−0.976119	−	0.217238i	$-0.930295\pi$
$157$	−3.93580	−	12.1132i	−0.314111	−	0.966735i	0.662007	−	0.749497i	$-0.269705\pi$
$158$		0			0
$159$	11.0461	+	8.02544i	0.876010	+	0.636459i
$160$		0			0
$161$	−2.00000	+	6.15537i	−0.157622	+	0.485111i
$162$		0			0
$163$	0.134067	−	0.0974056i	0.0105010	−	0.00762940i	−0.582522	−	0.812815i	$-0.697934\pi$
$163$	0.134067	−	0.0974056i	0.0105010	−	0.00762940i	0.593023	+	0.805185i	$0.297934\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−17.5448	+	12.7471i	−1.35766	+	0.986398i	−0.359071	+	0.933310i	$0.616906\pi$
$167$	−17.5448	+	12.7471i	−1.35766	+	0.986398i	−0.998590	+	0.0530877i	$0.983094\pi$
$168$		0			0
$169$	−1.58739	+	4.88548i	−0.122107	+	0.375806i
$170$		0			0
$171$	1.31630	+	0.956346i	0.100660	+	0.0731336i
$172$		0			0
$173$	−4.04756	−	12.4571i	−0.307731	−	0.947097i	−0.978644	−	0.205562i	$-0.934098\pi$
$173$	−4.04756	−	12.4571i	−0.307731	−	0.947097i	0.670914	−	0.741536i	$-0.265902\pi$
$174$		0			0
$175$	−5.73899			−0.433827
$176$		0			0
$177$	15.5261			1.16701
$178$		0			0
$179$	−3.27323	−	10.0740i	−0.244653	−	0.752964i	−0.995693	−	0.0927080i	$-0.970448\pi$
$179$	−3.27323	−	10.0740i	−0.244653	−	0.752964i	0.751040	−	0.660256i	$-0.229552\pi$
$180$		0			0
$181$	−5.17920	−	3.76291i	−0.384967	−	0.279695i	0.378423	−	0.925633i	$-0.376467\pi$
$181$	−5.17920	−	3.76291i	−0.384967	−	0.279695i	−0.763390	+	0.645938i	$0.776467\pi$
$182$		0			0
$183$	1.59745	−	4.91644i	0.118087	−	0.363434i
$184$		0			0
$185$	−2.84089	+	2.06403i	−0.208866	+	0.151750i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−3.12659	+	2.27160i	−0.227426	+	0.165235i
$190$		0			0
$191$	2.09754	−	6.45557i	0.151773	−	0.467109i	−0.846047	−	0.533109i	$-0.821024\pi$
$191$	2.09754	−	6.45557i	0.151773	−	0.467109i	0.997820	+	0.0659998i	$0.0210237\pi$
$192$		0			0
$193$	−6.58345	−	4.78315i	−0.473887	−	0.344299i	0.325067	−	0.945691i	$-0.394613\pi$
$193$	−6.58345	−	4.78315i	−0.473887	−	0.344299i	−0.798954	+	0.601392i	$0.794613\pi$
$194$		0			0
$195$	−5.66459	−	17.4338i	−0.405650	−	1.24846i
$196$		0			0
$197$	16.4907			1.17492			0.587458	−	0.809255i	$-0.300129\pi$
$197$	16.4907			1.17492			0.587458	+	0.809255i	$0.300129\pi$
$198$		0			0
$199$	3.39781			0.240864			0.120432	−	0.992722i	$-0.461572\pi$
$199$	3.39781			0.240864			0.120432	+	0.992722i	$0.461572\pi$
$200$		0			0
$201$	−8.16737	−	25.1366i	−0.576082	−	1.77300i
$202$		0			0
$203$	5.16208	+	3.75047i	0.362307	+	0.263232i
$204$		0			0
$205$	−3.04573	+	9.37378i	−0.212723	+	0.654693i
$206$		0			0
$207$	−4.11501	+	2.98973i	−0.286013	+	0.207801i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	12.9307	−	9.39468i	0.890184	−	0.646756i	−0.0457422	−	0.998953i	$-0.514565\pi$
$211$	12.9307	−	9.39468i	0.890184	−	0.646756i	0.935926	+	0.352197i	$0.114565\pi$
$212$		0			0
$213$	−1.14440	+	3.52211i	−0.0784133	+	0.241331i
$214$		0			0
$215$	6.02435	+	4.37695i	0.410857	+	0.298505i
$216$		0			0
$217$	0.709698	+	2.18422i	0.0481774	+	0.148275i
$218$		0			0
$219$	−9.58310			−0.647566
$220$		0			0
$221$	−20.4457			−1.37533
$222$		0			0
$223$	2.34291	+	7.21074i	0.156893	+	0.482867i	0.998348	−	0.0574606i	$-0.0183004\pi$
$223$	2.34291	+	7.21074i	0.156893	+	0.482867i	−0.841455	+	0.540328i	$0.818300\pi$
$224$		0			0
$225$	−3.64887	−	2.65106i	−0.243258	−	0.176737i
$226$		0			0
$227$	−4.63936	+	14.2785i	−0.307925	+	0.947696i	0.670644	+	0.741779i	$0.266018\pi$
$227$	−4.63936	+	14.2785i	−0.307925	+	0.947696i	−0.978569	+	0.205917i	$0.933982\pi$
$228$		0			0
$229$	−1.94314	+	1.41177i	−0.128406	+	0.0932925i	−0.650134	−	0.759819i	$-0.725287\pi$
$229$	−1.94314	+	1.41177i	−0.128406	+	0.0932925i	0.521728	+	0.853112i	$0.325287\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.05093	−	3.66972i	0.330898	−	0.240411i	−0.409914	−	0.912124i	$-0.634441\pi$
$233$	5.05093	−	3.66972i	0.330898	−	0.240411i	0.740811	+	0.671713i	$0.234441\pi$
$234$		0			0
$235$	−4.15094	+	12.7753i	−0.270778	+	0.833368i
$236$		0			0
$237$	20.8904	+	15.1778i	1.35698	+	0.985901i
$238$		0			0
$239$	5.27183	+	16.2250i	0.341006	+	1.04951i	0.963687	+	0.267034i	$0.0860436\pi$
$239$	5.27183	+	16.2250i	0.341006	+	1.04951i	−0.622681	+	0.782476i	$0.713956\pi$
$240$		0			0
$241$	−0.0166322			−0.00107138			−0.000535688	−	1.00000i	$-0.500171\pi$
$241$	−0.0166322			−0.00107138			−0.000535688		1.00000i	$0.500171\pi$
$242$		0			0
$243$	−6.96990			−0.447119
$244$		0			0
$245$	−6.57310	−	20.2299i	−0.419940	−	1.29244i
$246$		0			0
$247$	−5.40369	−	3.92601i	−0.343828	−	0.249806i
$248$		0			0
$249$	0.115405	−	0.355179i	0.00731347	−	0.0225085i
$250$		0			0
$251$	19.5692	−	14.2178i	1.23520	−	0.897423i	0.237928	−	0.971283i	$-0.423532\pi$
$251$	19.5692	−	14.2178i	1.23520	−	0.897423i	0.997269	+	0.0738602i	$0.0235319\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−38.5614	+	28.0165i	−2.41481	+	1.75446i
$256$		0			0
$257$	−8.93959	+	27.5132i	−0.557636	+	1.71623i	0.131241	+	0.991350i	$0.458104\pi$
$257$	−8.93959	+	27.5132i	−0.557636	+	1.71623i	−0.688878	+	0.724878i	$0.741896\pi$
$258$		0			0
$259$	0.724878	+	0.526655i	0.0450417	+	0.0327247i
$260$		0			0
$261$	1.54958	+	4.76913i	0.0959168	+	0.295202i
$262$		0			0
$263$	17.2531			1.06387			0.531935	−	0.846785i	$-0.321465\pi$
$263$	17.2531			1.06387			0.531935	+	0.846785i	$0.321465\pi$
$264$		0			0
$265$	−24.2343			−1.48870
$266$		0			0
$267$	2.48253	+	7.64046i	0.151929	+	0.467588i
$268$		0			0
$269$	−2.26858	−	1.64822i	−0.138318	−	0.100494i	0.516475	−	0.856302i	$-0.327244\pi$
$269$	−2.26858	−	1.64822i	−0.138318	−	0.100494i	−0.654793	+	0.755809i	$0.727244\pi$
$270$		0			0
$271$	−7.03251	+	21.6439i	−0.427195	+	1.31477i	0.473682	+	0.880696i	$0.342925\pi$
$271$	−7.03251	+	21.6439i	−0.427195	+	1.31477i	−0.900877	+	0.434075i	$0.857075\pi$
$272$		0			0
$273$	−3.78403	+	2.74926i	−0.229020	+	0.166393i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	2.69202	−	1.95587i	0.161748	−	0.117517i	−0.503967	−	0.863723i	$-0.668127\pi$
$277$	2.69202	−	1.95587i	0.161748	−	0.117517i	0.665715	+	0.746206i	$0.268127\pi$
$278$		0			0
$279$	−0.557749	+	1.71657i	−0.0333916	+	0.102769i
$280$		0			0
$281$	7.05093	+	5.12280i	0.420623	+	0.305601i	0.777889	−	0.628402i	$-0.216291\pi$
$281$	7.05093	+	5.12280i	0.420623	+	0.305601i	−0.357265	+	0.934003i	$0.616291\pi$
$282$		0			0
$283$	8.99509	+	27.6840i	0.534702	+	1.64564i	0.744291	+	0.667855i	$0.232787\pi$
$283$	8.99509	+	27.6840i	0.534702	+	1.64564i	−0.209589	+	0.977790i	$0.567213\pi$
$284$		0			0
$285$	−15.5713			−0.922364
$286$		0			0
$287$	2.51489			0.148449
$288$		0			0
$289$	11.1750	+	34.3932i	0.657355	+	2.02313i
$290$		0			0
$291$	−7.74785	−	5.62914i	−0.454187	−	0.329986i
$292$		0			0
$293$	6.78465	−	20.8810i	0.396363	−	1.21988i	−0.531531	−	0.847039i	$-0.678383\pi$
$293$	6.78465	−	20.8810i	0.396363	−	1.21988i	0.927895	−	0.372842i	$-0.121617\pi$
$294$		0			0
$295$	−22.2946	+	16.1980i	−1.29804	+	0.943084i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	16.8930	−	12.2735i	0.976948	−	0.709794i
$300$		0			0
$301$	0.587145	−	1.80705i	0.0338425	−	0.104156i
$302$		0			0
$303$	−12.8404	−	9.32910i	−0.737662	−	0.535943i
$304$		0			0
$305$	2.83536	+	8.72633i	0.162352	+	0.499668i
$306$		0			0
$307$	24.1835			1.38023			0.690113	−	0.723701i	$-0.257561\pi$
$307$	24.1835			1.38023			0.690113	+	0.723701i	$0.257561\pi$
$308$		0			0
$309$	1.57455			0.0895733
$310$		0			0
$311$	−1.10359	−	3.39651i	−0.0625791	−	0.192599i	0.914879	−	0.403728i	$-0.132286\pi$
$311$	−1.10359	−	3.39651i	−0.0625791	−	0.192599i	−0.977458	+	0.211130i	$0.932286\pi$
$312$		0			0
$313$	−7.04548	−	5.11884i	−0.398234	−	0.289334i	0.370587	−	0.928798i	$-0.379156\pi$
$313$	−7.04548	−	5.11884i	−0.398234	−	0.289334i	−0.768821	+	0.639464i	$0.779156\pi$
$314$		0			0
$315$	−0.624918	+	1.92330i	−0.0352101	+	0.108366i
$316$		0			0
$317$	−17.8150	+	12.9434i	−1.00059	+	0.726973i	−0.962215	−	0.272290i	$-0.912219\pi$
$317$	−17.8150	+	12.9434i	−1.00059	+	0.726973i	−0.0383776	+	0.999263i	$0.512219\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	19.2388	−	13.9778i	1.07380	−	0.780165i
$322$		0			0
$323$	−5.36690	+	16.5176i	−0.298622	+	0.919065i
$324$		0			0
$325$	14.9794	+	10.8832i	0.830908	+	0.603690i
$326$		0			0
$327$	4.27252	+	13.1495i	0.236271	+	0.727167i
$328$		0			0
$329$	3.42748			0.188963
$330$		0			0
$331$	−2.07719			−0.114173			−0.0570865	−	0.998369i	$-0.518181\pi$
$331$	−2.07719			−0.114173			−0.0570865	+	0.998369i	$0.518181\pi$
$332$		0			0
$333$	0.217598	+	0.669698i	0.0119243	+	0.0366992i
$334$		0			0
$335$	37.9523	+	27.5740i	2.07356	+	1.50653i
$336$		0			0
$337$	−7.81040	+	24.0379i	−0.425459	+	1.30943i	0.477094	+	0.878852i	$0.341690\pi$
$337$	−7.81040	+	24.0379i	−0.425459	+	1.30943i	−0.902554	+	0.430577i	$0.858310\pi$
$338$		0			0
$339$	−3.19603	+	2.32205i	−0.173584	+	0.126117i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−9.31303	+	6.76631i	−0.502856	+	0.365346i
$344$		0			0
$345$	15.0426	−	46.2965i	0.809869	−	2.49252i
$346$		0			0
$347$	17.0271	+	12.3709i	0.914061	+	0.664105i	0.942039	−	0.335504i	$-0.108907\pi$
$347$	17.0271	+	12.3709i	0.914061	+	0.664105i	−0.0279773	+	0.999609i	$0.508907\pi$
$348$		0			0
$349$	−7.18722	−	22.1200i	−0.384723	−	1.18406i	−0.936681	−	0.350184i	$-0.886119\pi$
$349$	−7.18722	−	22.1200i	−0.384723	−	1.18406i	0.551958	−	0.833872i	$-0.313881\pi$
$350$		0			0
$351$	12.4685			0.665522
$352$		0			0
$353$	−18.6464			−0.992446			−0.496223	−	0.868195i	$-0.665280\pi$
$353$	−18.6464			−0.992446			−0.496223	+	0.868195i	$0.665280\pi$
$354$		0			0
$355$	−2.03123	−	6.25149i	−0.107807	−	0.331795i
$356$		0			0
$357$	9.83927	+	7.14865i	0.520749	+	0.378346i
$358$		0			0
$359$	11.6277	−	35.7863i	0.613685	−	1.88873i	0.194221	−	0.980958i	$-0.437782\pi$
$359$	11.6277	−	35.7863i	0.613685	−	1.88873i	0.419465	−	0.907772i	$-0.362218\pi$
$360$		0			0
$361$	10.7812	−	7.83297i	0.567429	−	0.412261i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	13.7608	−	9.99782i	0.720274	−	0.523310i
$366$		0			0
$367$	−2.64046	+	8.12649i	−0.137831	+	0.424199i	−0.996020	−	0.0891348i	$-0.971590\pi$
$367$	−2.64046	+	8.12649i	−0.137831	+	0.424199i	0.858189	+	0.513334i	$0.171590\pi$
$368$		0			0
$369$	1.59898	+	1.16172i	0.0832393	+	0.0604769i
$370$		0			0
$371$	1.91083	+	5.88094i	0.0992056	+	0.305323i
$372$		0			0
$373$	−18.1461			−0.939569			−0.469785	−	0.882781i	$-0.655668\pi$
$373$	−18.1461			−0.939569			−0.469785	+	0.882781i	$0.655668\pi$
$374$		0			0
$375$	10.4790			0.541132
$376$		0			0
$377$	−6.36138	−	19.5783i	−0.327628	−	1.00833i
$378$		0			0
$379$	−22.7356	−	16.5184i	−1.16785	−	0.848491i	−0.177098	−	0.984193i	$-0.556671\pi$
$379$	−22.7356	−	16.5184i	−1.16785	−	0.848491i	−0.990750	+	0.135702i	$0.956671\pi$
$380$		0			0
$381$	−4.96388	+	15.2772i	−0.254307	+	0.782677i
$382$		0			0
$383$	14.3331	−	10.4136i	0.732388	−	0.532111i	−0.157930	−	0.987450i	$-0.550482\pi$
$383$	14.3331	−	10.4136i	0.732388	−	0.532111i	0.890318	+	0.455339i	$0.150482\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.20805	−	0.877702i	0.0614088	−	0.0446161i
$388$		0			0
$389$	−0.407941	+	1.25551i	−0.0206834	+	0.0636570i	−0.960865	−	0.277015i	$-0.910655\pi$
$389$	−0.407941	+	1.25551i	−0.0206834	+	0.0636570i	0.940182	+	0.340672i	$0.110655\pi$
$390$		0			0
$391$	−43.9254	−	31.9137i	−2.22140	−	1.61394i
$392$		0			0
$393$	−7.91778	−	24.3684i	−0.399399	−	1.22922i
$394$		0			0
$395$	−45.8320			−2.30606
$396$		0			0
$397$	13.7700			0.691096			0.345548	−	0.938401i	$-0.387693\pi$
$397$	13.7700			0.691096			0.345548	+	0.938401i	$0.387693\pi$
$398$		0			0
$399$	1.22777	+	3.77869i	0.0614655	+	0.189171i
$400$		0			0
$401$	13.8985	+	10.0978i	0.694058	+	0.504262i	0.877992	−	0.478676i	$-0.158883\pi$
$401$	13.8985	+	10.0978i	0.694058	+	0.504262i	−0.183934	+	0.982939i	$0.558883\pi$
$402$		0			0
$403$	2.28968	−	7.04692i	0.114057	−	0.351032i
$404$		0			0
$405$	29.1632	−	21.1883i	1.44913	−	1.05286i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	6.83138	−	4.96329i	0.337790	−	0.245419i	−0.405939	−	0.913900i	$-0.633055\pi$
$409$	6.83138	−	4.96329i	0.337790	−	0.245419i	0.743729	+	0.668482i	$0.233055\pi$
$410$		0			0
$411$	0.587238	−	1.80733i	0.0289663	−	0.0891492i
$412$		0			0
$413$	5.68867	+	4.13306i	0.279921	+	0.203374i
$414$		0			0
$415$	0.204835	+	0.630416i	0.0100549	+	0.0309459i
$416$		0			0
$417$	−11.5047			−0.563387
$418$		0			0
$419$	30.9791			1.51343			0.756715	−	0.653745i	$-0.226803\pi$
$419$	30.9791			1.51343			0.756715	+	0.653745i	$0.226803\pi$
$420$		0			0
$421$	7.89793	+	24.3073i	0.384921	+	1.18467i	0.936537	+	0.350568i	$0.114011\pi$
$421$	7.89793	+	24.3073i	0.384921	+	1.18467i	−0.551616	+	0.834098i	$0.685989\pi$
$422$		0			0
$423$	2.17920	+	1.58328i	0.105957	+	0.0769819i
$424$		0			0
$425$	14.8774	−	45.7880i	0.721662	−	2.22105i
$426$		0			0
$427$	1.89406	−	1.37611i	0.0916598	−	0.0665948i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−14.5948	+	10.6038i	−0.703008	+	0.510765i	−0.880910	−	0.473283i	$-0.843069\pi$
$431$	−14.5948	+	10.6038i	−0.703008	+	0.510765i	0.177903	+	0.984048i	$0.443069\pi$
$432$		0			0
$433$	7.81970	−	24.0666i	0.375791	−	1.15656i	−0.567153	−	0.823612i	$-0.691955\pi$
$433$	7.81970	−	24.0666i	0.375791	−	1.15656i	0.942944	−	0.332952i	$-0.108045\pi$
$434$		0			0
$435$	−38.8257	−	28.2085i	−1.86155	−	1.35250i
$436$		0			0
$437$	−5.48113	−	16.8692i	−0.262198	−	0.806963i
$438$		0			0
$439$	28.5630			1.36324			0.681620	−	0.731707i	$-0.261276\pi$
$439$	28.5630			1.36324			0.681620	+	0.731707i	$0.261276\pi$
$440$		0			0
$441$	−4.26544			−0.203116
$442$		0			0
$443$	11.4870	+	35.3535i	0.545765	+	1.67969i	0.719163	+	0.694841i	$0.244525\pi$
$443$	11.4870	+	35.3535i	0.545765	+	1.67969i	−0.173398	+	0.984852i	$0.555475\pi$
$444$		0			0
$445$	−11.5359	−	8.38131i	−0.546853	−	0.397312i
$446$		0			0
$447$	10.2557	−	31.5637i	0.485077	−	1.49291i
$448$		0			0
$449$	−8.44329	+	6.13441i	−0.398463	+	0.289501i	−0.768915	−	0.639351i	$-0.779203\pi$
$449$	−8.44329	+	6.13441i	−0.398463	+	0.289501i	0.370451	+	0.928852i	$0.379203\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−1.22711	+	0.891549i	−0.0576547	+	0.0418886i
$454$		0			0
$455$	2.56542	−	7.89557i	0.120269	−	0.370150i
$456$		0			0
$457$	21.1432	+	15.3614i	0.989036	+	0.718577i	0.959710	−	0.280993i	$-0.0906638\pi$
$457$	21.1432	+	15.3614i	0.989036	+	0.718577i	0.0293262	+	0.999570i	$0.490664\pi$
$458$		0			0
$459$	−10.0186	−	30.8340i	−0.467628	−	1.43921i
$460$		0			0
$461$	−11.1743			−0.520439			−0.260219	−	0.965550i	$-0.583795\pi$
$461$	−11.1743			−0.520439			−0.260219	+	0.965550i	$0.583795\pi$
$462$		0			0
$463$	38.7695			1.80177			0.900885	−	0.434059i	$-0.142919\pi$
$463$	38.7695			1.80177			0.900885	+	0.434059i	$0.142919\pi$
$464$		0			0
$465$	−5.33787	−	16.4283i	−0.247538	−	0.761842i
$466$		0			0
$467$	1.87732	+	1.36395i	0.0868718	+	0.0631161i	0.630373	−	0.776292i	$-0.282902\pi$
$467$	1.87732	+	1.36395i	0.0868718	+	0.0631161i	−0.543502	+	0.839408i	$0.682902\pi$
$468$		0			0
$469$	3.69890	−	11.3841i	0.170799	−	0.525667i
$470$		0			0
$471$	19.7749	−	14.3673i	0.911177	−	0.662009i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	12.7243	−	9.24474i	0.583830	−	0.424178i
$476$		0			0
$477$	−1.50172	+	4.62181i	−0.0687590	+	0.211618i
$478$		0			0
$479$	20.0714	+	14.5827i	0.917087	+	0.666303i	0.942797	−	0.333367i	$-0.108185\pi$
$479$	20.0714	+	14.5827i	0.917087	+	0.666303i	−0.0257104	+	0.999669i	$0.508185\pi$
$480$		0			0
$481$	−0.893288	−	2.74926i	−0.0407304	−	0.125355i
$482$		0			0
$483$	−12.4209			−0.565169
$484$		0			0
$485$	16.9982			0.771850
$486$		0			0
$487$	5.67244	+	17.4580i	0.257043	+	0.791096i	0.993420	+	0.114525i	$0.0365347\pi$
$487$	5.67244	+	17.4580i	0.257043	+	0.791096i	−0.736378	+	0.676571i	$0.763465\pi$
$488$		0			0
$489$	0.257293	+	0.186934i	0.0116352	+	0.00845345i
$490$		0			0
$491$	−6.67667	+	20.5487i	−0.301314	+	0.927349i	0.679713	+	0.733478i	$0.262104\pi$
$491$	−6.67667	+	20.5487i	−0.301314	+	0.927349i	−0.981027	+	0.193871i	$0.937896\pi$
$492$		0			0
$493$	−43.3047	+	31.4627i	−1.95035	+	1.41701i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.35689	+	0.985840i	−0.0608649	+	0.0442210i
$498$		0			0
$499$	9.53603	−	29.3489i	0.426892	−	1.31384i	−0.474280	−	0.880374i	$-0.657292\pi$
$499$	9.53603	−	29.3489i	0.426892	−	1.31384i	0.901171	−	0.433463i	$-0.142708\pi$
$500$		0			0
$501$	−33.6708	−	24.4633i	−1.50430	−	1.09294i
$502$		0			0
$503$	1.00363	+	3.08887i	0.0447498	+	0.137726i	0.970935	−	0.239343i	$-0.0769320\pi$
$503$	1.00363	+	3.08887i	0.0447498	+	0.137726i	−0.926185	+	0.377069i	$0.876932\pi$
$504$		0			0
$505$	28.1709			1.25359
$506$		0			0
$507$	−9.85838			−0.437826
$508$		0			0
$509$	−1.43932	−	4.42977i	−0.0637967	−	0.196346i	0.914078	−	0.405539i	$-0.132916\pi$
$509$	−1.43932	−	4.42977i	−0.0637967	−	0.196346i	−0.977874	+	0.209193i	$0.932916\pi$
$510$		0			0
$511$	−3.51119	−	2.55103i	−0.155326	−	0.112851i
$512$		0			0
$513$	3.27293	−	10.0730i	0.144503	−	0.444736i
$514$		0			0
$515$	−2.26097	+	1.64269i	−0.0996304	+	0.0723857i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	20.3364	−	14.7752i	0.892668	−	0.648561i
$520$		0			0
$521$	13.0989	−	40.3144i	0.573875	−	1.76621i	−0.0661029	−	0.997813i	$-0.521057\pi$
$521$	13.0989	−	40.3144i	0.573875	−	1.76621i	0.639978	−	0.768393i	$-0.278943\pi$
$522$		0			0
$523$	0.244545	+	0.177672i	0.0106932	+	0.00776907i	0.593119	−	0.805115i	$-0.297896\pi$
$523$	0.244545	+	0.177672i	0.0106932	+	0.00776907i	−0.582426	+	0.812884i	$0.697896\pi$
$524$		0			0
$525$	−3.40347	−	10.4748i	−0.148540	−	0.457158i
$526$		0			0
$527$	−19.2664			−0.839259
$528$		0			0
$529$	32.4504			1.41089
$530$		0			0
$531$	1.70766	+	5.25563i	0.0741060	+	0.228075i
$532$		0			0
$533$	−6.56414	−	4.76913i	−0.284325	−	0.206574i
$534$		0			0
$535$	−13.0432	+	40.1427i	−0.563905	+	1.73552i
$536$		0			0
$537$	16.4459	−	11.9486i	0.709691	−	0.515621i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	13.6638	−	9.92735i	0.587454	−	0.426810i	−0.253950	−	0.967217i	$-0.581730\pi$
$541$	13.6638	−	9.92735i	0.587454	−	0.426810i	0.841404	+	0.540407i	$0.181730\pi$
$542$		0			0
$543$	3.79658	−	11.6847i	0.162927	−	0.501437i
$544$		0			0
$545$	−19.8536	−	14.4245i	−0.850435	−	0.617877i
$546$		0			0
$547$	5.38371	+	16.5694i	0.230191	+	0.708455i	0.997723	+	0.0674442i	$0.0214845\pi$
$547$	5.38371	+	16.5694i	0.230191	+	0.708455i	−0.767532	+	0.641010i	$0.778516\pi$
$548$		0			0
$549$	1.83993			0.0785262
$550$		0			0
$551$	−17.4867			−0.744958
$552$		0			0
$553$	3.61378	+	11.1221i	0.153674	+	0.472959i
$554$		0			0
$555$	−5.45204	−	3.96114i	−0.231426	−	0.168141i
$556$		0			0
$557$	−6.37301	+	19.6141i	−0.270033	+	0.831076i	0.720458	+	0.693499i	$0.243932\pi$
$557$	−6.37301	+	19.6141i	−0.270033	+	0.831076i	−0.990491	+	0.137578i	$0.956068\pi$
$558$		0			0
$559$	−4.95932	+	3.60316i	−0.209757	+	0.152397i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	15.8749	−	11.5338i	0.669049	−	0.486092i	−0.200658	−	0.979661i	$-0.564308\pi$
$563$	15.8749	−	11.5338i	0.669049	−	0.486092i	0.869707	+	0.493569i	$0.164308\pi$
$564$		0			0
$565$	2.16678	−	6.66868i	0.0911573	−	0.280553i
$566$		0			0
$567$	−7.44125	−	5.40638i	−0.312503	−	0.227047i
$568$		0			0
$569$	10.4279	+	32.0939i	0.437162	+	1.34545i	0.890855	+	0.454288i	$0.150106\pi$
$569$	10.4279	+	32.0939i	0.437162	+	1.34545i	−0.453693	+	0.891158i	$0.649894\pi$
$570$		0			0
$571$	−19.8373			−0.830164			−0.415082	−	0.909784i	$-0.636247\pi$
$571$	−19.8373			−0.830164			−0.415082	+	0.909784i	$0.636247\pi$
$572$		0			0
$573$	13.0267			0.544197
$574$		0			0
$575$	15.1941	+	46.7627i	0.633638	+	1.95014i
$576$		0			0
$577$	−25.6695	−	18.6500i	−1.06863	−	0.776408i	−0.0929675	−	0.995669i	$-0.529635\pi$
$577$	−25.6695	−	18.6500i	−1.06863	−	0.776408i	−0.975666	+	0.219261i	$0.929635\pi$
$578$		0			0
$579$	4.82595	−	14.8527i	0.200560	−	0.617259i
$580$		0			0
$581$	0.136832	−	0.0994145i	0.00567676	−	0.00412441i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	5.27837	−	3.83496i	0.218234	−	0.158556i
$586$		0			0
$587$	−5.94326	+	18.2915i	−0.245304	+	0.754969i	0.750282	+	0.661118i	$0.229918\pi$
$587$	−5.94326	+	18.2915i	−0.245304	+	0.754969i	−0.995586	+	0.0938512i	$0.970082\pi$
$588$		0			0
$589$	−5.09201	−	3.69956i	−0.209813	−	0.152438i
$590$		0			0
$591$	9.77973	+	30.0989i	0.402284	+	1.23810i
$592$		0			0
$593$	36.8924			1.51499			0.757495	−	0.652841i	$-0.226423\pi$
$593$	36.8924			1.51499			0.757495	+	0.652841i	$0.226423\pi$
$594$		0			0
$595$	−21.5867			−0.884967
$596$		0			0
$597$	2.01505	+	6.20168i	0.0824705	+	0.253818i
$598$		0			0
$599$	3.31133	+	2.40583i	0.135297	+	0.0982994i	0.653375	−	0.757034i	$-0.273352\pi$
$599$	3.31133	+	2.40583i	0.135297	+	0.0982994i	−0.518078	+	0.855333i	$0.673352\pi$
$600$		0			0
$601$	6.93959	−	21.3579i	0.283072	−	0.871205i	−0.703898	−	0.710301i	$-0.748559\pi$
$601$	6.93959	−	21.3579i	0.283072	−	0.871205i	0.986970	−	0.160904i	$-0.0514411\pi$
$602$		0			0
$603$	7.61051	−	5.52936i	0.309924	−	0.225173i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.5132	+	8.36480i	−0.467305	+	0.339517i	−0.796390	−	0.604783i	$-0.793260\pi$
$607$	−11.5132	+	8.36480i	−0.467305	+	0.339517i	0.329085	+	0.944300i	$0.393260\pi$
$608$		0			0
$609$	−3.78403	+	11.6460i	−0.153337	+	0.471921i
$610$		0			0
$611$	−8.94611	−	6.49973i	−0.361921	−	0.262951i
$612$		0			0
$613$	4.73717	+	14.5795i	0.191332	+	0.588860i	1.00000		0.000594352i	$0.000189188\pi$
$613$	4.73717	+	14.5795i	0.191332	+	0.588860i	−0.808667	+	0.588266i	$0.799811\pi$
$614$		0			0
$615$	−18.9153			−0.762738
$616$		0			0
$617$	12.4466			0.501080			0.250540	−	0.968106i	$-0.419392\pi$
$617$	12.4466			0.501080			0.250540	+	0.968106i	$0.419392\pi$
$618$		0			0
$619$	10.0208	+	30.8410i	0.402771	+	1.23960i	0.922742	+	0.385419i	$0.125943\pi$
$619$	10.0208	+	30.8410i	0.402771	+	1.23960i	−0.519970	+	0.854184i	$0.674057\pi$
$620$		0			0
$621$	26.7873	+	19.4621i	1.07494	+	0.780988i
$622$		0			0
$623$	−1.12431	+	3.46027i	−0.0450445	+	0.138633i
$624$		0			0
$625$	11.6624	−	8.47323i	0.466496	−	0.338929i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−6.08100	+	4.41811i	−0.242465	+	0.176161i
$630$		0			0
$631$	−5.15077	+	15.8524i	−0.205049	+	0.631076i	0.794662	+	0.607052i	$0.207648\pi$
$631$	−5.15077	+	15.8524i	−0.205049	+	0.631076i	−0.999711	+	0.0240244i	$0.992352\pi$
$632$		0			0
$633$	24.8156	+	18.0296i	0.986333	+	0.716613i
$634$		0			0
$635$	−8.81052	−	27.1160i	−0.349635	−	1.07606i
$636$		0			0
$637$	17.5106			0.693793
$638$		0			0
$639$	−1.31811			−0.0521438
$640$		0			0
$641$	−5.65838	−	17.4147i	−0.223492	−	0.687839i	−0.998441	−	0.0558148i	$-0.982224\pi$
$641$	−5.65838	−	17.4147i	−0.223492	−	0.687839i	0.774949	−	0.632024i	$-0.217776\pi$
$642$		0			0
$643$	−4.14366	−	3.01055i	−0.163410	−	0.118724i	0.503075	−	0.864243i	$-0.332202\pi$
$643$	−4.14366	−	3.01055i	−0.163410	−	0.118724i	−0.666485	+	0.745518i	$0.732202\pi$
$644$		0			0
$645$	−4.41611	+	13.5914i	−0.173884	+	0.535160i
$646$		0			0
$647$	−31.8809	+	23.1628i	−1.25337	+	0.910624i	−0.998412	−	0.0563293i	$-0.982060\pi$
$647$	−31.8809	+	23.1628i	−1.25337	+	0.910624i	−0.254954	+	0.966953i	$0.582060\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−3.56577	+	2.59068i	−0.139753	+	0.101537i
$652$		0			0
$653$	−0.937086	+	2.88405i	−0.0366710	+	0.112862i	−0.967716	−	0.252042i	$-0.918898\pi$
$653$	−0.937086	+	2.88405i	−0.0366710	+	0.112862i	0.931045	+	0.364903i	$0.118898\pi$
$654$		0			0
$655$	36.7925	+	26.7313i	1.43760	+	1.04448i
$656$		0			0
$657$	−1.05401	−	3.24391i	−0.0411208	−	0.126557i
$658$		0			0
$659$	1.09096			0.0424978			0.0212489	−	0.999774i	$-0.493236\pi$
$659$	1.09096			0.0424978			0.0212489	+	0.999774i	$0.493236\pi$
$660$		0			0
$661$	−46.1346			−1.79443			−0.897214	−	0.441596i	$-0.854412\pi$
$661$	−46.1346			−1.79443			−0.897214	+	0.441596i	$0.854412\pi$
$662$		0			0
$663$	−12.1252	−	37.3176i	−0.470904	−	1.44929i
$664$		0			0
$665$	−5.70523	−	4.14509i	−0.221239	−	0.160740i
$666$		0			0
$667$	16.8930	−	51.9913i	0.654100	−	2.01311i
$668$		0			0
$669$	−11.7716	+	8.55257i	−0.455117	+	0.330662i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	15.9856	−	11.6142i	0.616200	−	0.447695i	−0.235392	−	0.971900i	$-0.575637\pi$
$673$	15.9856	−	11.6142i	0.616200	−	0.447695i	0.851592	+	0.524205i	$0.175637\pi$
$674$		0			0
$675$	−9.07280	+	27.9232i	−0.349212	+	1.07477i
$676$		0			0
$677$	20.5396	+	14.9229i	0.789400	+	0.573533i	0.907785	−	0.419435i	$-0.137772\pi$
$677$	20.5396	+	14.9229i	0.789400	+	0.573533i	−0.118385	+	0.992968i	$0.537772\pi$
$678$		0			0
$679$	−1.34028	−	4.12497i	−0.0514353	−	0.158302i
$680$		0			0
$681$	−28.8124			−1.10410
$682$		0			0
$683$	−3.69756			−0.141483			−0.0707416	−	0.997495i	$-0.522537\pi$
$683$	−3.69756			−0.141483			−0.0707416	+	0.997495i	$0.522537\pi$
$684$		0			0
$685$	1.04230	+	3.20788i	0.0398244	+	0.122567i
$686$		0			0
$687$	−3.72913	−	2.70937i	−0.142275	−	0.103369i
$688$		0			0
$689$	6.16488	−	18.9736i	0.234863	−	0.722835i
$690$		0			0
$691$	−2.06904	+	1.50324i	−0.0787099	+	0.0571861i	−0.626444	−	0.779466i	$-0.715490\pi$
$691$	−2.06904	+	1.50324i	−0.0787099	+	0.0571861i	0.547734	+	0.836652i	$0.315490\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	16.5201	−	12.0026i	0.626644	−	0.455283i
$696$		0			0
$697$	−6.51945	+	20.0648i	−0.246942	+	0.760009i
$698$		0			0
$699$	9.69340	+	7.04267i	0.366638	+	0.266378i
$700$		0			0
$701$	−11.4258	−	35.1650i	−0.431546	−	1.32816i	−0.896585	−	0.442872i	$-0.853960\pi$
$701$	−11.4258	−	35.1650i	−0.431546	−	1.32816i	0.465039	−	0.885290i	$-0.346040\pi$
$702$		0			0
$703$	−2.45554			−0.0926126
$704$		0			0
$705$	−25.7792			−0.970900
$706$		0			0
$707$	−2.22123	−	6.83625i	−0.0835380	−	0.257104i
$708$		0			0
$709$	27.1043	+	19.6924i	1.01792	+	0.739564i	0.965856	−	0.259080i	$-0.0834192\pi$
$709$	27.1043	+	19.6924i	1.01792	+	0.739564i	0.0520667	+	0.998644i	$0.483419\pi$
$710$		0			0
$711$	−2.84006	+	8.74080i	−0.106510	+	0.327806i
$712$		0			0
$713$	15.9186	−	11.5656i	0.596158	−	0.433134i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−26.4875	+	19.2443i	−0.989195	+	0.718692i
$718$		0			0
$719$	9.28688	−	28.5821i	0.346342	−	1.06593i	−0.614519	−	0.788902i	$-0.710650\pi$
$719$	9.28688	−	28.5821i	0.346342	−	1.06593i	0.960861	−	0.277030i	$-0.0893501\pi$
$720$		0			0
$721$	0.576907	+	0.419148i	0.0214851	+	0.0156099i
$722$		0			0
$723$	−0.00986364	−	0.0303572i	−0.000366833	−	0.00112899i
$724$		0			0
$725$	48.4744			1.80029
$726$		0			0
$727$	22.4183			0.831449			0.415725	−	0.909491i	$-0.363528\pi$
$727$	22.4183			0.831449			0.415725	+	0.909491i	$0.363528\pi$
$728$		0			0
$729$	5.67716	+	17.4725i	0.210265	+	0.647130i
$730$		0			0
$731$	12.8953	+	9.36897i	0.476949	+	0.346524i
$732$		0			0
$733$	−7.58178	+	23.3343i	−0.280039	+	0.861873i	0.707802	+	0.706410i	$0.249687\pi$
$733$	−7.58178	+	23.3343i	−0.280039	+	0.861873i	−0.987842	+	0.155462i	$0.950313\pi$
$734$		0			0
$735$	33.0256	−	23.9945i	1.21817	−	0.885049i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	2.72982	−	1.98333i	0.100418	−	0.0729581i	−0.536443	−	0.843937i	$-0.680232\pi$
$739$	2.72982	−	1.98333i	0.100418	−	0.0729581i	0.636861	+	0.770978i	$0.280232\pi$
$740$		0			0
$741$	3.96113	−	12.1911i	0.145516	−	0.447852i
$742$		0			0
$743$	−4.93978	−	3.58896i	−0.181223	−	0.131666i	0.493475	−	0.869760i	$-0.335726\pi$
$743$	−4.93978	−	3.58896i	−0.181223	−	0.131666i	−0.674698	+	0.738094i	$0.735726\pi$
$744$		0			0
$745$	18.2031	+	56.0233i	0.666909	+	2.05253i
$746$		0			0
$747$	0.132922			0.00486336
$748$		0			0
$749$	10.7699			0.393523
$750$		0			0
$751$	−15.4851	−	47.6581i	−0.565058	−	1.73907i	−0.667778	−	0.744360i	$-0.732755\pi$
$751$	−15.4851	−	47.6581i	−0.565058	−	1.73907i	0.102720	−	0.994710i	$-0.467245\pi$
$752$		0			0
$753$	37.5558	+	27.2859i	1.36861	+	0.994354i
$754$		0			0
$755$	0.831934	−	2.56043i	0.0302772	−	0.0931836i
$756$		0			0
$757$	−4.93452	+	3.58514i	−0.179348	+	0.130304i	−0.673837	−	0.738880i	$-0.735355\pi$
$757$	−4.93452	+	3.58514i	−0.179348	+	0.130304i	0.494489	+	0.869184i	$0.335355\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−35.6531	+	25.9035i	−1.29243	+	0.939002i	−0.999851	−	0.0172412i	$-0.994512\pi$
$761$	−35.6531	+	25.9035i	−1.29243	+	0.939002i	−0.292574	+	0.956243i	$0.594512\pi$
$762$		0			0
$763$	−1.93497	+	5.95523i	−0.0700507	+	0.215594i
$764$		0			0
$765$	−13.7249	−	9.97171i	−0.496224	−	0.360528i
$766$		0			0
$767$	−7.01031	−	21.5755i	−0.253127	−	0.779046i
$768$		0			0
$769$	−53.7688			−1.93895			−0.969476	−	0.245185i	$-0.921151\pi$
$769$	−53.7688			−1.93895			−0.969476	+	0.245185i	$0.921151\pi$
$770$		0			0
$771$	−55.5188			−1.99946
$772$		0			0
$773$	−9.76477	−	30.0529i	−0.351214	−	1.08093i	−0.958172	−	0.286192i	$-0.907610\pi$
$773$	−9.76477	−	30.0529i	−0.351214	−	1.08093i	0.606958	−	0.794734i	$-0.292390\pi$
$774$		0			0
$775$	14.1154	+	10.2555i	0.507041	+	0.368387i
$776$		0			0
$777$	−0.531366	+	1.63538i	−0.0190627	+	0.0586688i
$778$		0			0
$779$	−5.57592	+	4.05114i	−0.199778	+	0.145147i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	26.4088	−	19.1871i	0.943774	−	0.685692i
$784$		0			0
$785$	−13.4066	+	41.2612i	−0.478502	+	1.47268i
$786$		0			0
$787$	−0.0177776	−	0.0129162i	−0.000633704	−	0.000460413i	0.587468	−	0.809247i	$-0.300125\pi$
$787$	−0.0177776	−	0.0129162i	−0.000633704	−	0.000460413i	−0.588102	+	0.808787i	$0.700125\pi$
$788$		0			0
$789$	10.2318	+	31.4904i	0.364263	+	1.12109i
$790$		0			0
$791$	−1.78914			−0.0636144
$792$		0			0
$793$	−7.55331			−0.268226
$794$		0			0
$795$	−14.3720	−	44.2325i	−0.509722	−	1.56876i
$796$		0			0
$797$	6.10556	+	4.43595i	0.216270	+	0.157129i	0.690646	−	0.723193i	$-0.257326\pi$
$797$	6.10556	+	4.43595i	0.216270	+	0.157129i	−0.474376	+	0.880322i	$0.657326\pi$
$798$		0			0
$799$	−8.88520	+	27.3458i	−0.314336	+	0.967426i
$800$		0			0
$801$	−2.31327	+	1.68069i	−0.0817354	+	0.0593843i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	17.8357	−	12.9584i	0.628626	−	0.456723i
$806$		0			0
$807$	1.66297	−	5.11809i	0.0585392	−	0.180165i
$808$		0			0
$809$	−36.7300	−	26.6859i	−1.29136	−	0.938227i	−0.291527	−	0.956563i	$-0.594163\pi$
$809$	−36.7300	−	26.6859i	−1.29136	−	0.938227i	−0.999832	+	0.0183355i	$0.994163\pi$
$810$		0			0
$811$	4.36175	+	13.4241i	0.153162	+	0.471383i	0.997970	−	0.0636860i	$-0.0202856\pi$
$811$	4.36175	+	13.4241i	0.153162	+	0.471383i	−0.844808	+	0.535069i	$0.820286\pi$
$812$		0			0
$813$	−43.6750			−1.53175
$814$		0			0
$815$	−0.564482			−0.0197729
$816$		0			0
$817$	1.60911	+	4.95233i	0.0562956	+	0.173260i
$818$		0			0
$819$	−1.34682	−	0.978524i	−0.0470618	−	0.0341924i
$820$		0			0
$821$	0.111375	−	0.342777i	0.00388701	−	0.0119630i	−0.949094	−	0.314992i	$-0.897998\pi$
$821$	0.111375	−	0.342777i	0.00388701	−	0.0119630i	0.952981	+	0.303029i	$0.0979980\pi$
$822$		0			0
$823$	9.23641	−	6.71065i	0.321961	−	0.233918i	−0.415051	−	0.909798i	$-0.636236\pi$
$823$	9.23641	−	6.71065i	0.321961	−	0.233918i	0.737012	+	0.675880i	$0.236236\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−31.7097	+	23.0384i	−1.10265	+	0.801124i	−0.981491	−	0.191509i	$-0.938662\pi$
$827$	−31.7097	+	23.0384i	−1.10265	+	0.801124i	−0.121162	+	0.992633i	$0.538662\pi$
$828$		0			0
$829$	−9.15682	+	28.1818i	−0.318030	+	0.978795i	0.656460	+	0.754361i	$0.272053\pi$
$829$	−9.15682	+	28.1818i	−0.318030	+	0.978795i	−0.974489	+	0.224434i	$0.927947\pi$
$830$		0			0
$831$	5.16634	+	3.75356i	0.179218	+	0.130210i
$832$		0			0
$833$	−14.0699	−	43.3027i	−0.487493	−	1.50035i
$834$		0			0
$835$	73.8715			2.55643
$836$		0			0
$837$	11.7494			0.406118
$838$		0			0
$839$	−8.64726	−	26.6135i	−0.298537	−	0.918801i	−0.982011	−	0.188826i	$-0.939532\pi$
$839$	−8.64726	−	26.6135i	−0.298537	−	0.918801i	0.683474	−	0.729975i	$-0.260468\pi$
$840$		0			0
$841$	−20.1401	−	14.6326i	−0.694485	−	0.504573i
$842$		0			0
$843$	−5.16863	+	15.9074i	−0.178017	+	0.547881i
$844$		0			0
$845$	14.1561	−	10.2850i	0.486985	−	0.353815i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−45.1945	+	32.8357i	−1.55107	+	1.12692i
$850$		0			0
$851$	2.37218	−	7.30081i	0.0813171	−	0.250268i
$852$		0			0
$853$	33.0517	+	24.0135i	1.13167	+	0.822206i	0.985937	−	0.167118i	$-0.0534459\pi$
$853$	33.0517	+	24.0135i	1.13167	+	0.822206i	0.145733	+	0.989324i	$0.453446\pi$
$854$		0			0
$855$	−1.71263	−	5.27093i	−0.0585707	−	0.180262i
$856$		0			0
$857$	28.8702			0.986189			0.493094	−	0.869976i	$-0.335866\pi$
$857$	28.8702			0.986189			0.493094	+	0.869976i	$0.335866\pi$
$858$		0			0
$859$	−8.76432			−0.299035			−0.149517	−	0.988759i	$-0.547772\pi$
$859$	−8.76432			−0.299035			−0.149517	+	0.988759i	$0.547772\pi$
$860$		0			0
$861$	1.49144	+	4.59018i	0.0508281	+	0.156433i
$862$		0			0
$863$	−29.8527	−	21.6892i	−1.01620	−	0.738310i	−0.0506971	−	0.998714i	$-0.516144\pi$
$863$	−29.8527	−	21.6892i	−1.01620	−	0.738310i	−0.965500	+	0.260404i	$0.916144\pi$
$864$		0			0
$865$	−13.7873	+	42.4329i	−0.468781	+	1.44276i
$866$		0			0
$867$	−56.1473	+	40.7934i	−1.90686	+	1.38542i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−31.2428	+	22.6992i	−1.05862	+	0.769134i
$872$		0			0
$873$	1.05332	−	3.24180i	0.0356496	−	0.109718i
$874$		0			0
$875$	3.83943	+	2.78951i	0.129797	+	0.0943027i
$876$		0			0
$877$	−7.70254	−	23.7060i	−0.260096	−	0.800494i	−0.992783	−	0.119927i	$-0.961734\pi$
$877$	−7.70254	−	23.7060i	−0.260096	−	0.800494i	0.732686	−	0.680566i	$-0.238266\pi$
$878$		0			0
$879$	42.1356			1.42120
$880$		0			0
$881$	25.1252			0.846491			0.423245	−	0.906015i	$-0.360891\pi$
$881$	25.1252			0.846491			0.423245	+	0.906015i	$0.360891\pi$
$882$		0			0
$883$	−1.41149	−	4.34411i	−0.0475003	−	0.146191i	0.924493	−	0.381198i	$-0.124489\pi$
$883$	−1.41149	−	4.34411i	−0.0475003	−	0.146191i	−0.971994	+	0.235007i	$0.924489\pi$
$884$		0			0
$885$	−42.7863	−	31.0861i	−1.43825	−	1.04495i
$886$		0			0
$887$	−0.939055	+	2.89011i	−0.0315304	+	0.0970405i	−0.965583	−	0.260094i	$-0.916246\pi$
$887$	−0.939055	+	2.89011i	−0.0315304	+	0.0970405i	0.934053	+	0.357135i	$0.116246\pi$
$888$		0			0
$889$	−5.88555	+	4.27610i	−0.197395	+	0.143416i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−7.59929	+	5.52121i	−0.254300	+	0.184760i
$894$		0			0
$895$	−11.1497	+	34.3151i	−0.372692	+	1.14703i
$896$		0			0
$897$	32.4199	+	23.5544i	1.08247	+	0.786460i
$898$		0			0
$899$	−5.99446	−	18.4491i	−0.199927	−	0.615311i
$900$		0			0
$901$	−51.8741			−1.72818
$902$		0			0
$903$	3.64643			0.121345
$904$		0			0
$905$	6.73865	+	20.7394i	0.224000	+	0.689402i
$906$		0			0
$907$	11.3564	+	8.25088i	0.377082	+	0.273966i	0.760142	−	0.649758i	$-0.225130\pi$
$907$	11.3564	+	8.25088i	0.377082	+	0.273966i	−0.383060	+	0.923724i	$0.625130\pi$
$908$		0			0
$909$	1.74566	−	5.37259i	0.0578998	−	0.178197i
$910$		0			0
$911$	24.3274	−	17.6749i	0.806002	−	0.585595i	−0.106667	−	0.994295i	$-0.534018\pi$
$911$	24.3274	−	17.6749i	0.806002	−	0.585595i	0.912669	+	0.408700i	$0.134018\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−14.2458	+	10.3502i	−0.470952	+	0.342167i
$916$		0			0
$917$	3.58586	−	11.0362i	0.118416	−	0.364446i
$918$		0			0
$919$	31.1669	+	22.6441i	1.02810	+	0.746960i	0.967928	−	0.251228i	$-0.0808345\pi$
$919$	31.1669	+	22.6441i	1.02810	+	0.746960i	0.0601738	+	0.998188i	$0.480834\pi$
$920$		0			0
$921$	14.3419	+	44.1398i	0.472582	+	1.45446i
$922$		0			0
$923$	5.41115			0.178110
$924$		0			0
$925$	6.80695			0.223811
$926$		0			0
$927$	0.173179	+	0.532991i	0.00568796	+	0.0175057i
$928$		0			0
$929$	−25.0900	−	18.2290i	−0.823177	−	0.598073i	0.0944435	−	0.995530i	$-0.469893\pi$
$929$	−25.0900	−	18.2290i	−0.823177	−	0.598073i	−0.917621	+	0.397457i	$0.869893\pi$
$930$		0			0
$931$	4.59643	−	14.1464i	0.150642	−	0.463628i
$932$		0			0
$933$	5.54484	−	4.02856i	0.181530	−	0.131889i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	28.1717	−	20.4679i	0.920329	−	0.668658i	−0.0232768	−	0.999729i	$-0.507410\pi$
$937$	28.1717	−	20.4679i	0.920329	−	0.668658i	0.943606	+	0.331071i	$0.107410\pi$
$938$		0			0
$939$	5.16464	−	15.8951i	0.168542	−	0.518718i
$940$		0			0
$941$	−27.6033	−	20.0550i	−0.899843	−	0.653774i	0.0385828	−	0.999255i	$-0.487716\pi$
$941$	−27.6033	−	20.0550i	−0.899843	−	0.653774i	−0.938426	+	0.345481i	$0.887716\pi$
$942$		0			0
$943$	−6.65822	−	20.4919i	−0.216822	−	0.667308i
$944$		0			0
$945$	13.1643			0.428236
$946$		0			0
$947$	14.3465			0.466198			0.233099	−	0.972453i	$-0.425113\pi$
$947$	14.3465			0.466198			0.233099	+	0.972453i	$0.425113\pi$
$948$		0			0
$949$	4.32694	+	13.3170i	0.140458	+	0.432287i
$950$		0			0
$951$	−34.1894	−	24.8401i	−1.10867	−	0.805494i
$952$		0			0
$953$	−11.2647	+	34.6693i	−0.364901	+	1.12305i	0.585143	+	0.810930i	$0.301038\pi$
$953$	−11.2647	+	34.6693i	−0.364901	+	1.12305i	−0.950043	+	0.312118i	$0.898962\pi$
$954$		0			0
$955$	−18.7056	+	13.5904i	−0.605298	+	0.439775i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.696274	−	0.505873i	0.0224839	−	0.0163355i
$960$		0			0
$961$	−7.42191	+	22.8423i	−0.239416	+	0.736848i
$962$		0			0
$963$	6.84753	+	4.97502i	0.220659	+	0.160318i
$964$		0			0
$965$	8.56570	+	26.3625i	0.275740	+	0.848639i
$966$		0			0
$967$	48.0950			1.54663			0.773315	−	0.634022i	$-0.218597\pi$
$967$	48.0950			1.54663			0.773315	+	0.634022i	$0.218597\pi$
$968$		0			0
$969$	−33.3308			−1.07074
$970$		0			0
$971$	−7.33814	−	22.5845i	−0.235492	−	0.724770i	−0.997056	−	0.0766802i	$-0.975568\pi$
$971$	−7.33814	−	22.5845i	−0.235492	−	0.724770i	0.761564	−	0.648090i	$-0.224432\pi$
$972$		0			0
$973$	−4.21525	−	3.06256i	−0.135135	−	0.0981811i
$974$		0			0
$975$	−10.9806	+	33.7947i	−0.351659	+	1.08230i
$976$		0			0
$977$	−21.8349	+	15.8640i	−0.698559	+	0.507533i	−0.879463	−	0.475968i	$-0.842098\pi$
$977$	−21.8349	+	15.8640i	−0.698559	+	0.507533i	0.180903	+	0.983501i	$0.442098\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−3.98121	+	2.89252i	−0.127110	+	0.0923510i
$982$		0			0
$983$	7.36651	−	22.6718i	0.234955	−	0.723118i	−0.762172	−	0.647374i	$-0.775867\pi$
$983$	7.36651	−	22.6718i	0.234955	−	0.723118i	0.997127	−	0.0757433i	$-0.0241329\pi$
$984$		0			0
$985$	−45.4446	−	33.0175i	−1.44799	−	1.05202i
$986$		0			0
$987$	2.03265	+	6.25584i	0.0646998	+	0.199126i
$988$		0			0
$989$	−16.2787			−0.517633
$990$		0			0
$991$	−10.6048			−0.336871			−0.168436	−	0.985713i	$-0.553872\pi$
$991$	−10.6048			−0.336871			−0.168436	+	0.985713i	$0.553872\pi$
$992$		0			0
$993$	−1.23187	−	3.79130i	−0.0390921	−	0.120313i
$994$		0			0
$995$	−9.36356	−	6.80303i	−0.296845	−	0.215670i
$996$		0			0
$997$	−0.833876	+	2.56641i	−0.0264091	+	0.0812789i	−0.963392	−	0.268095i	$-0.913606\pi$
$997$	−0.833876	+	2.56641i	−0.0264091	+	0.0812789i	0.936983	+	0.349374i	$0.113606\pi$
$998$		0			0
$999$	3.70842	−	2.69432i	0.117329	−	0.0852446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.i.t.729.2		8
11.2	odd	10		968.2.a.n.1.3		4
11.3	even	5		968.2.i.p.753.1		8
11.4	even	5	inner	968.2.i.t.81.2		8
11.5	even	5		968.2.i.p.9.1		8
11.6	odd	10		88.2.i.b.9.1	✓	8
11.7	odd	10		968.2.i.s.81.2		8
11.8	odd	10		88.2.i.b.49.1	yes	8
11.9	even	5		968.2.a.m.1.3		4
11.10	odd	2		968.2.i.s.729.2		8
33.2	even	10		8712.2.a.ce.1.1		4
33.8	even	10		792.2.r.g.577.1		8
33.17	even	10		792.2.r.g.361.1		8
33.20	odd	10		8712.2.a.cd.1.1		4
44.19	even	10		176.2.m.d.49.2		8
44.31	odd	10		1936.2.a.bc.1.2		4
44.35	even	10		1936.2.a.bb.1.2		4
44.39	even	10		176.2.m.d.97.2		8
88.13	odd	10		7744.2.a.di.1.2		4
88.19	even	10		704.2.m.i.577.1		8
88.35	even	10		7744.2.a.dr.1.3		4
88.53	even	10		7744.2.a.dh.1.2		4
88.61	odd	10		704.2.m.l.449.2		8
88.75	odd	10		7744.2.a.ds.1.3		4
88.83	even	10		704.2.m.i.449.1		8
88.85	odd	10		704.2.m.l.577.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.i.b.9.1	✓	8	11.6	odd	10
88.2.i.b.49.1	yes	8	11.8	odd	10
176.2.m.d.49.2		8	44.19	even	10
176.2.m.d.97.2		8	44.39	even	10
704.2.m.i.449.1		8	88.83	even	10
704.2.m.i.577.1		8	88.19	even	10
704.2.m.l.449.2		8	88.61	odd	10
704.2.m.l.577.2		8	88.85	odd	10
792.2.r.g.361.1		8	33.17	even	10
792.2.r.g.577.1		8	33.8	even	10
968.2.a.m.1.3		4	11.9	even	5
968.2.a.n.1.3		4	11.2	odd	10
968.2.i.p.9.1		8	11.5	even	5
968.2.i.p.753.1		8	11.3	even	5
968.2.i.s.81.2		8	11.7	odd	10
968.2.i.s.729.2		8	11.10	odd	2
968.2.i.t.81.2		8	11.4	even	5	inner
968.2.i.t.729.2		8	1.1	even	1	trivial
1936.2.a.bb.1.2		4	44.35	even	10
1936.2.a.bc.1.2		4	44.31	odd	10
7744.2.a.dh.1.2		4	88.53	even	10
7744.2.a.di.1.2		4	88.13	odd	10
7744.2.a.dr.1.3		4	88.35	even	10
7744.2.a.ds.1.3		4	88.75	odd	10
8712.2.a.cd.1.1		4	33.20	odd	10
8712.2.a.ce.1.1		4	33.2	even	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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.593044 + 1.82520i) q^{3} +(-2.75577 - 2.00218i) q^{5} +(-0.268582 + 0.826612i) q^{7} +(-0.552609 + 0.401494i) q^{9} +O(q^{10})\)	\(q+(0.593044 + 1.82520i) q^{3} +(-2.75577 - 2.00218i) q^{5} +(-0.268582 + 0.826612i) q^{7} +(-0.552609 + 0.401494i) q^{9} +(2.26858 - 1.64822i) q^{13} +(2.02009 - 6.21721i) q^{15} +(-5.89879 - 4.28572i) q^{17} +(-0.736068 - 2.26538i) q^{19} -1.66801 q^{21} +7.44651 q^{23} +(2.04043 + 6.27981i) q^{25} +(3.59730 + 2.61359i) q^{27} +(2.26858 - 6.98198i) q^{29} +(2.13773 - 1.55315i) q^{31} +(2.39518 - 1.74020i) q^{35} +(0.318562 - 0.980434i) q^{37} +(4.35371 + 3.16315i) q^{39} +(-0.894141 - 2.75188i) q^{41} -2.18609 q^{43} +2.32673 q^{45} +(-1.21860 - 3.75047i) q^{47} +(5.05197 + 3.67047i) q^{49} +(4.32407 - 13.3081i) q^{51} +(5.75577 - 4.18181i) q^{53} +(3.69826 - 2.68695i) q^{57} +(2.50000 - 7.69421i) q^{59} +(-2.17920 - 1.58328i) q^{61} +(-0.183459 - 0.564628i) q^{63} -9.55172 q^{65} -13.7720 q^{67} +(4.41611 + 13.5914i) q^{69} +(1.56117 + 1.13426i) q^{71} +(-1.54306 + 4.74906i) q^{73} +(-10.2519 + 7.44841i) q^{75} +(10.8853 - 7.90866i) q^{79} +(-3.27021 + 10.0647i) q^{81} +(-0.157432 - 0.114381i) q^{83} +(7.67490 + 23.6209i) q^{85} +14.0889 q^{87} +4.18609 q^{89} +(0.753138 + 2.31792i) q^{91} +(4.10259 + 2.98071i) q^{93} +(-2.50728 + 7.71661i) q^{95} +(-4.03716 + 2.93317i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} + 2 q^{5} + 8 q^{7} + 7 q^{9}+O(q^{10}) \) 8 * q - q^3 + 2 * q^5 + 8 * q^7 + 7 * q^9	\( 8 q - q^{3} + 2 q^{5} + 8 q^{7} + 7 q^{9} + 8 q^{13} - 3 q^{15} - 11 q^{17} + 12 q^{19} + 2 q^{21} - 4 q^{23} + 22 q^{25} + 8 q^{27} + 8 q^{29} + 2 q^{31} + 29 q^{35} - 14 q^{37} + 21 q^{39} + q^{41} - 6 q^{43} + 44 q^{45} - 6 q^{47} - 2 q^{49} + 52 q^{51} + 22 q^{53} + q^{57} + 20 q^{59} - 26 q^{61} + 5 q^{63} + 10 q^{65} - 10 q^{67} + 42 q^{69} + 30 q^{71} - 13 q^{73} - q^{75} + 6 q^{79} - 6 q^{81} + 20 q^{83} + 26 q^{85} + 6 q^{87} + 22 q^{89} - 13 q^{91} + 15 q^{93} + 13 q^{95} - 12 q^{97}+O(q^{100}) \) 8 * q - q^3 + 2 * q^5 + 8 * q^7 + 7 * q^9 + 8 * q^13 - 3 * q^15 - 11 * q^17 + 12 * q^19 + 2 * q^21 - 4 * q^23 + 22 * q^25 + 8 * q^27 + 8 * q^29 + 2 * q^31 + 29 * q^35 - 14 * q^37 + 21 * q^39 + q^41 - 6 * q^43 + 44 * q^45 - 6 * q^47 - 2 * q^49 + 52 * q^51 + 22 * q^53 + q^57 + 20 * q^59 - 26 * q^61 + 5 * q^63 + 10 * q^65 - 10 * q^67 + 42 * q^69 + 30 * q^71 - 13 * q^73 - q^75 + 6 * q^79 - 6 * q^81 + 20 * q^83 + 26 * q^85 + 6 * q^87 + 22 * q^89 - 13 * q^91 + 15 * q^93 + 13 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

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Database

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