LMFDB - Embedded newform 310.2.b.a.249.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(249,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("310.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.b (of order $2$, degree $1$, 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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			249.6
Root			$0.561103 - 0.561103i$ of defining polynomial
Character	$\chi$	$=$	310.249
Dual form			310.2.b.a.249.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -0.370326i q^{3} -1.00000 q^{4} +(1.45220 + 1.70032i) q^{5} +0.370326 q^{6} -4.27844i q^{7} -1.00000i q^{8} +2.86286 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -0.370326i q^{3} -1.00000 q^{4} +(1.45220 + 1.70032i) q^{5} +0.370326 q^{6} -4.27844i q^{7} -1.00000i q^{8} +2.86286 q^{9} +(-1.70032 + 1.45220i) q^{10} +2.81252 q^{11} +0.370326i q^{12} +4.53408i q^{13} +4.27844 q^{14} +(0.629674 - 0.537789i) q^{15} +1.00000 q^{16} +0.197785i q^{17} +2.86286i q^{18} -2.66000 q^{19} +(-1.45220 - 1.70032i) q^{20} -1.58442 q^{21} +2.81252i q^{22} +0.877793i q^{23} -0.370326 q^{24} +(-0.782203 + 4.93844i) q^{25} -4.53408 q^{26} -2.17117i q^{27} +4.27844i q^{28} +7.47252 q^{29} +(0.537789 + 0.629674i) q^{30} -1.00000 q^{31} +1.00000i q^{32} -1.04155i q^{33} -0.197785 q^{34} +(7.27474 - 6.21317i) q^{35} -2.86286 q^{36} -5.87409i q^{37} -2.66000i q^{38} +1.67909 q^{39} +(1.70032 - 1.45220i) q^{40} -8.99908 q^{41} -1.58442i q^{42} +5.71033i q^{43} -2.81252 q^{44} +(4.15746 + 4.86779i) q^{45} -0.877793 q^{46} -10.0873i q^{47} -0.370326i q^{48} -11.3051 q^{49} +(-4.93844 - 0.782203i) q^{50} +0.0732449 q^{51} -4.53408i q^{52} -0.206568i q^{53} +2.17117 q^{54} +(4.08436 + 4.78220i) q^{55} -4.27844 q^{56} +0.985065i q^{57} +7.47252i q^{58} -4.55688 q^{59} +(-0.629674 + 0.537789i) q^{60} -5.96876 q^{61} -1.00000i q^{62} -12.2486i q^{63} -1.00000 q^{64} +(-7.70941 + 6.58442i) q^{65} +1.04155 q^{66} +5.70571i q^{67} -0.197785i q^{68} +0.325070 q^{69} +(6.21317 + 7.27474i) q^{70} -8.06064 q^{71} -2.86286i q^{72} -14.8079i q^{73} +5.87409 q^{74} +(1.82883 + 0.289670i) q^{75} +2.66000 q^{76} -12.0332i q^{77} +1.67909i q^{78} -1.97754 q^{79} +(1.45220 + 1.70032i) q^{80} +7.78454 q^{81} -8.99908i q^{82} -0.554096i q^{83} +1.58442 q^{84} +(-0.336299 + 0.287224i) q^{85} -5.71033 q^{86} -2.76727i q^{87} -2.81252i q^{88} -12.0532 q^{89} +(-4.86779 + 4.15746i) q^{90} +19.3988 q^{91} -0.877793i q^{92} +0.370326i q^{93} +10.0873 q^{94} +(-3.86286 - 4.52285i) q^{95} +0.370326 q^{96} -1.88287i q^{97} -11.3051i q^{98} +8.05186 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9} + 2 q^{10} - 16 q^{11} + 12 q^{14} + 16 q^{15} + 8 q^{16} - 12 q^{19} + 2 q^{20} - 4 q^{21} + 8 q^{24} + 12 q^{25} - 20 q^{26} + 12 q^{29} + 4 q^{30} - 8 q^{31} + 8 q^{34} + 20 q^{35} + 8 q^{36} - 40 q^{39} - 2 q^{40} + 16 q^{44} + 30 q^{45} - 16 q^{46} - 32 q^{49} - 8 q^{50} - 44 q^{51} + 44 q^{54} + 36 q^{55} - 12 q^{56} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 8 q^{64} + 12 q^{65} + 12 q^{66} - 28 q^{69} - 20 q^{70} - 24 q^{71} + 40 q^{74} - 12 q^{75} + 12 q^{76} + 32 q^{79} - 2 q^{80} + 88 q^{81} + 4 q^{84} + 4 q^{85} - 44 q^{86} - 24 q^{89} - 34 q^{90} - 20 q^{91} + 4 q^{94} - 8 q^{96} + 20 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9 + 2 * q^10 - 16 * q^11 + 12 * q^14 + 16 * q^15 + 8 * q^16 - 12 * q^19 + 2 * q^20 - 4 * q^21 + 8 * q^24 + 12 * q^25 - 20 * q^26 + 12 * q^29 + 4 * q^30 - 8 * q^31 + 8 * q^34 + 20 * q^35 + 8 * q^36 - 40 * q^39 - 2 * q^40 + 16 * q^44 + 30 * q^45 - 16 * q^46 - 32 * q^49 - 8 * q^50 - 44 * q^51 + 44 * q^54 + 36 * q^55 - 12 * q^56 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 8 * q^64 + 12 * q^65 + 12 * q^66 - 28 * q^69 - 20 * q^70 - 24 * q^71 + 40 * q^74 - 12 * q^75 + 12 * q^76 + 32 * q^79 - 2 * q^80 + 88 * q^81 + 4 * q^84 + 4 * q^85 - 44 * q^86 - 24 * q^89 - 34 * q^90 - 20 * q^91 + 4 * q^94 - 8 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		−	0.370326i		−	0.213808i	−0.994269	−	0.106904i	$-0.965906\pi$
$3$		−	0.370326i		−	0.213808i	0.994269	−	0.106904i	$-0.0340937\pi$
$4$	−1.00000			−0.500000
$5$	1.45220	+	1.70032i	0.649446	+	0.760408i
$5$	1.45220	+	1.70032i	0.649446	+	0.760408i
$6$	0.370326			0.151185
$7$		−	4.27844i		−	1.61710i	−0.588428	−	0.808549i	$-0.700253\pi$
$7$		−	4.27844i		−	1.61710i	0.588428	−	0.808549i	$-0.299747\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.86286			0.954286
$10$	−1.70032	+	1.45220i	−0.537690	+	0.459227i
$11$	2.81252			0.848008			0.424004	−	0.905660i	$-0.360624\pi$
$11$	2.81252			0.848008			0.424004	+	0.905660i	$0.360624\pi$
$12$			0.370326i			0.106904i
$13$			4.53408i			1.25753i	0.777596	+	0.628764i	$0.216439\pi$
$13$			4.53408i			1.25753i	−0.777596	+	0.628764i	$0.783561\pi$
$14$	4.27844			1.14346
$15$	0.629674	−	0.537789i	0.162581	−	0.138857i
$16$	1.00000			0.250000
$17$			0.197785i			0.0479699i	0.999712	+	0.0239850i	$0.00763538\pi$
$17$			0.197785i			0.0479699i	−0.999712	+	0.0239850i	$0.992365\pi$
$18$			2.86286i			0.674782i
$19$	−2.66000			−0.610245			−0.305122	−	0.952313i	$-0.598697\pi$
$19$	−2.66000			−0.610245			−0.305122	+	0.952313i	$0.598697\pi$
$20$	−1.45220	−	1.70032i	−0.324723	−	0.380204i
$21$	−1.58442			−0.345748
$22$			2.81252i			0.599632i
$23$			0.877793i			0.183033i	0.995804	+	0.0915163i	$0.0291713\pi$
$23$			0.877793i			0.183033i	−0.995804	+	0.0915163i	$0.970829\pi$
$24$	−0.370326			−0.0755925
$25$	−0.782203	+	4.93844i	−0.156441	+	0.987687i
$26$	−4.53408			−0.889207
$27$		−	2.17117i		−	0.417842i
$28$			4.27844i			0.808549i
$29$	7.47252			1.38761			0.693806	−	0.720162i	$-0.255932\pi$
$29$	7.47252			1.38761			0.693806	+	0.720162i	$0.255932\pi$
$30$	0.537789	+	0.629674i	0.0981864	+	0.114962i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$			1.00000i			0.176777i
$33$		−	1.04155i		−	0.181311i
$34$	−0.197785			−0.0339198
$35$	7.27474	−	6.21317i	1.22965	−	1.05022i
$36$	−2.86286			−0.477143
$37$		−	5.87409i		−	0.965694i	−0.875705	−	0.482847i	$-0.839603\pi$
$37$		−	5.87409i		−	0.965694i	0.875705	−	0.482847i	$-0.160397\pi$
$38$		−	2.66000i		−	0.431508i
$39$	1.67909			0.268869
$40$	1.70032	−	1.45220i	0.268845	−	0.229614i
$41$	−8.99908			−1.40542			−0.702710	−	0.711476i	$-0.748027\pi$
$41$	−8.99908			−1.40542			−0.702710	+	0.711476i	$0.748027\pi$
$42$		−	1.58442i		−	0.244481i
$43$			5.71033i			0.870817i	0.900233	+	0.435409i	$0.143396\pi$
$43$			5.71033i			0.870817i	−0.900233	+	0.435409i	$0.856604\pi$
$44$	−2.81252			−0.424004
$45$	4.15746	+	4.86779i	0.619757	+	0.725647i
$46$	−0.877793			−0.129424
$47$		−	10.0873i		−	1.47138i	−0.677319	−	0.735689i	$-0.736858\pi$
$47$		−	10.0873i		−	1.47138i	0.677319	−	0.735689i	$-0.263142\pi$
$48$		−	0.370326i		−	0.0534519i
$49$	−11.3051			−1.61501
$50$	−4.93844	−	0.782203i	−0.698400	−	0.110620i
$51$	0.0732449			0.0102563
$52$		−	4.53408i		−	0.628764i
$53$		−	0.206568i		−	0.0283743i	−0.999899	−	0.0141872i	$-0.995484\pi$
$53$		−	0.206568i		−	0.0283743i	0.999899	−	0.0141872i	$-0.00451607\pi$
$54$	2.17117			0.295459
$55$	4.08436	+	4.78220i	0.550735	+	0.644832i
$56$	−4.27844			−0.571731
$57$			0.985065i			0.130475i
$58$			7.47252i			0.981190i
$59$	−4.55688			−0.593256			−0.296628	−	0.954993i	$-0.595862\pi$
$59$	−4.55688			−0.593256			−0.296628	+	0.954993i	$0.595862\pi$
$60$	−0.629674	+	0.537789i	−0.0812906	+	0.0694283i
$61$	−5.96876			−0.764221			−0.382111	−	0.924117i	$-0.624803\pi$
$61$	−5.96876			−0.764221			−0.382111	+	0.924117i	$0.624803\pi$
$62$		−	1.00000i		−	0.127000i
$63$		−	12.2486i		−	1.54318i
$64$	−1.00000			−0.125000
$65$	−7.70941	+	6.58442i	−0.956235	+	0.816697i
$66$	1.04155			0.128206
$67$			5.70571i			0.697063i	0.937297	+	0.348531i	$0.113320\pi$
$67$			5.70571i			0.697063i	−0.937297	+	0.348531i	$0.886680\pi$
$68$		−	0.197785i		−	0.0239850i
$69$	0.325070			0.0391338
$70$	6.21317	+	7.27474i	0.742616	+	0.869497i
$71$	−8.06064			−0.956622			−0.478311	−	0.878190i	$-0.658751\pi$
$71$	−8.06064			−0.956622			−0.478311	+	0.878190i	$0.658751\pi$
$72$		−	2.86286i		−	0.337391i
$73$		−	14.8079i		−	1.73313i	−0.499061	−	0.866567i	$-0.666322\pi$
$73$		−	14.8079i		−	1.73313i	0.499061	−	0.866567i	$-0.333678\pi$
$74$	5.87409			0.682849
$75$	1.82883	+	0.289670i	0.211175	+	0.0334482i
$76$	2.66000			0.305122
$77$		−	12.0332i		−	1.37131i
$78$			1.67909i			0.190119i
$79$	−1.97754			−0.222491			−0.111245	−	0.993793i	$-0.535484\pi$
$79$	−1.97754			−0.222491			−0.111245	+	0.993793i	$0.535484\pi$
$80$	1.45220	+	1.70032i	0.162361	+	0.190102i
$81$	7.78454			0.864948
$82$		−	8.99908i		−	0.993782i
$83$		−	0.554096i		−	0.0608199i	−0.999538	−	0.0304100i	$-0.990319\pi$
$83$		−	0.554096i		−	0.0608199i	0.999538	−	0.0304100i	$-0.00968128\pi$
$84$	1.58442			0.172874
$85$	−0.336299	+	0.287224i	−0.0364767	+	0.0311539i
$86$	−5.71033			−0.615761
$87$		−	2.76727i		−	0.296682i
$88$		−	2.81252i		−	0.299816i
$89$	−12.0532			−1.27764			−0.638820	−	0.769356i	$-0.720577\pi$
$89$	−12.0532			−1.27764			−0.638820	+	0.769356i	$0.720577\pi$
$90$	−4.86779	+	4.15746i	−0.513110	+	0.438234i
$91$	19.3988			2.03355
$92$		−	0.877793i		−	0.0915163i
$93$			0.370326i			0.0384010i
$94$	10.0873			1.04042
$95$	−3.86286	−	4.52285i	−0.396321	−	0.464035i
$96$	0.370326			0.0377962
$97$		−	1.88287i		−	0.191177i	−0.995421	−	0.0955883i	$-0.969527\pi$
$97$		−	1.88287i		−	0.191177i	0.995421	−	0.0955883i	$-0.0304732\pi$
$98$		−	11.3051i		−	1.14198i
$99$	8.05186			0.809242
$100$	0.782203	−	4.93844i	0.0782203	−	0.493844i
$101$	14.8820			1.48081			0.740405	−	0.672161i	$-0.234634\pi$
$101$	14.8820			1.48081			0.740405	+	0.672161i	$0.234634\pi$
$102$			0.0732449i			0.00725233i
$103$			13.0457i			1.28543i	0.766105	+	0.642716i	$0.222192\pi$
$103$			13.0457i			1.28543i	−0.766105	+	0.642716i	$0.777808\pi$
$104$	4.53408			0.444603
$105$	−2.30090	−	2.69402i	−0.224545	−	0.262910i
$106$	0.206568			0.0200637
$107$		−	0.103114i		−	0.00996840i	−0.999988	−	0.00498420i	$-0.998413\pi$
$107$		−	0.103114i		−	0.00996840i	0.999988	−	0.00498420i	$-0.00158653\pi$
$108$			2.17117i			0.208921i
$109$	−10.1413			−0.971360			−0.485680	−	0.874137i	$-0.661428\pi$
$109$	−10.1413			−0.971360			−0.485680	+	0.874137i	$0.661428\pi$
$110$	−4.78220	+	4.08436i	−0.455965	+	0.389429i
$111$	−2.17533			−0.206473
$112$		−	4.27844i		−	0.404275i
$113$			8.91842i			0.838975i	0.907761	+	0.419487i	$0.137790\pi$
$113$			8.91842i			0.838975i	−0.907761	+	0.419487i	$0.862210\pi$
$114$	−0.985065			−0.0922598
$115$	−1.49253	+	1.27474i	−0.139179	+	0.118870i
$116$	−7.47252			−0.693806
$117$			12.9804i			1.20004i
$118$		−	4.55688i		−	0.419495i
$119$	0.846211			0.0775721
$120$	−0.537789	−	0.629674i	−0.0490932	−	0.0574811i
$121$	−3.08971			−0.280882
$122$		−	5.96876i		−	0.540386i
$123$			3.33259i			0.300490i
$124$	1.00000			0.0898027
$125$	−9.53286	+	5.84162i	−0.852645	+	0.522491i
$126$	12.2486			1.09119
$127$			2.56349i			0.227473i	0.993511	+	0.113736i	$0.0362819\pi$
$127$			2.56349i			0.227473i	−0.993511	+	0.113736i	$0.963718\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	2.11468			0.186187
$130$	−6.58442	−	7.70941i	−0.577492	−	0.676160i
$131$	−8.72064			−0.761926			−0.380963	−	0.924590i	$-0.624407\pi$
$131$	−8.72064			−0.761926			−0.380963	+	0.924590i	$0.624407\pi$
$132$			1.04155i			0.0906554i
$133$			11.3806i			0.986826i
$134$	−5.70571			−0.492898
$135$	3.69169	−	3.15298i	0.317730	−	0.271365i
$136$	0.197785			0.0169599
$137$			9.12221i			0.779363i	0.920950	+	0.389681i	$0.127415\pi$
$137$			9.12221i			0.779363i	−0.920950	+	0.389681i	$0.872585\pi$
$138$			0.325070i			0.0276718i
$139$	−16.5407			−1.40296			−0.701481	−	0.712688i	$-0.747478\pi$
$139$	−16.5407			−1.40296			−0.701481	+	0.712688i	$0.747478\pi$
$140$	−7.27474	+	6.21317i	−0.614827	+	0.525109i
$141$	−3.73557			−0.314592
$142$		−	8.06064i		−	0.676434i
$143$			12.7522i			1.06639i
$144$	2.86286			0.238572
$145$	10.8516	+	12.7057i	0.901179	+	1.05515i
$146$	14.8079			1.22551
$147$			4.18656i			0.345301i
$148$			5.87409i			0.482847i
$149$	−14.2426			−1.16680			−0.583399	−	0.812186i	$-0.698277\pi$
$149$	−14.2426			−1.16680			−0.583399	+	0.812186i	$0.698277\pi$
$150$	−0.289670	+	1.82883i	−0.0236515	+	0.149323i
$151$	23.6632			1.92569			0.962843	−	0.270060i	$-0.0870437\pi$
$151$	23.6632			1.92569			0.962843	+	0.270060i	$0.0870437\pi$
$152$			2.66000i			0.215754i
$153$			0.566231i			0.0457770i
$154$	12.0332			0.969665
$155$	−1.45220	−	1.70032i	−0.116644	−	0.136573i
$156$	−1.67909			−0.134435
$157$			14.1970i			1.13304i	0.824047	+	0.566521i	$0.191711\pi$
$157$			14.1970i			1.13304i	−0.824047	+	0.566521i	$0.808289\pi$
$158$		−	1.97754i		−	0.157325i
$159$	−0.0764976			−0.00606666
$160$	−1.70032	+	1.45220i	−0.134422	+	0.114807i
$161$	3.75559			0.295982
$162$			7.78454i			0.611611i
$163$			1.83128i			0.143437i	0.997425	+	0.0717183i	$0.0228483\pi$
$163$			1.83128i			0.143437i	−0.997425	+	0.0717183i	$0.977152\pi$
$164$	8.99908			0.702710
$165$	1.77097	−	1.51255i	0.137870	−	0.117751i
$166$	0.554096			0.0430062
$167$		−	18.6417i		−	1.44254i	−0.692655	−	0.721269i	$-0.743559\pi$
$167$		−	18.6417i		−	1.44254i	0.692655	−	0.721269i	$-0.256441\pi$
$168$			1.58442i			0.122240i
$169$	−7.55791			−0.581378
$170$	−0.287224	−	0.336299i	−0.0220291	−	0.0257929i
$171$	−7.61519			−0.582348
$172$		−	5.71033i		−	0.435409i
$173$		−	12.1139i		−	0.921001i	−0.887659	−	0.460500i	$-0.847670\pi$
$173$		−	12.1139i		−	0.921001i	0.887659	−	0.460500i	$-0.152330\pi$
$174$	2.76727			0.209786
$175$	21.1288	+	3.34661i	1.59719	+	0.252980i
$176$	2.81252			0.212002
$177$			1.68753i			0.126843i
$178$		−	12.0532i		−	0.903428i
$179$	21.6720			1.61984			0.809921	−	0.586539i	$-0.199510\pi$
$179$	21.6720			1.61984			0.809921	+	0.586539i	$0.199510\pi$
$180$	−4.15746	−	4.86779i	−0.309879	−	0.362823i
$181$	24.4151			1.81476			0.907381	−	0.420310i	$-0.138079\pi$
$181$	24.4151			1.81476			0.907381	+	0.420310i	$0.138079\pi$
$182$			19.3988i			1.43794i
$183$			2.21039i			0.163396i
$184$	0.877793			0.0647118
$185$	9.98785	−	8.53038i	0.734321	−	0.627166i
$186$	−0.370326			−0.0271536
$187$			0.556275i			0.0406789i
$188$			10.0873i			0.735689i
$189$	−9.28922			−0.675691
$190$	4.52285	−	3.86286i	0.328122	−	0.280241i
$191$	−14.6035			−1.05667			−0.528336	−	0.849035i	$-0.677184\pi$
$191$	−14.6035			−1.05667			−0.528336	+	0.849035i	$0.677184\pi$
$192$			0.370326i			0.0267260i
$193$			25.0839i			1.80558i	0.430083	+	0.902789i	$0.358484\pi$
$193$			25.0839i			1.80558i	−0.430083	+	0.902789i	$0.641516\pi$
$194$	1.88287			0.135182
$195$	2.43838	+	2.85499i	0.174616	+	0.204450i
$196$	11.3051			0.807504
$197$		−	11.5672i		−	0.824128i	−0.911155	−	0.412064i	$-0.864808\pi$
$197$		−	11.5672i		−	0.824128i	0.911155	−	0.412064i	$-0.135192\pi$
$198$			8.05186i			0.572221i
$199$	−0.518696			−0.0367694			−0.0183847	−	0.999831i	$-0.505852\pi$
$199$	−0.518696			−0.0367694			−0.0183847	+	0.999831i	$0.505852\pi$
$200$	4.93844	+	0.782203i	0.349200	+	0.0553101i
$201$	2.11297			0.149037
$202$			14.8820i			1.04709i
$203$		−	31.9707i		−	2.24391i
$204$	−0.0732449			−0.00512817
$205$	−13.0685	−	15.3014i	−0.912744	−	1.06869i
$206$	−13.0457			−0.908938
$207$			2.51300i			0.174665i
$208$			4.53408i			0.314382i
$209$	−7.48130			−0.517493
$210$	2.69402	−	2.30090i	0.185905	−	0.158777i
$211$	−20.2626			−1.39493			−0.697467	−	0.716617i	$-0.745690\pi$
$211$	−20.2626			−1.39493			−0.697467	+	0.716617i	$0.745690\pi$
$212$			0.206568i			0.0141872i
$213$			2.98507i			0.204533i
$214$	0.103114			0.00704872
$215$	−9.70941	+	8.29257i	−0.662176	+	0.565548i
$216$	−2.17117			−0.147729
$217$			4.27844i			0.290439i
$218$		−	10.1413i		−	0.686855i
$219$	−5.48375			−0.370557
$220$	−4.08436	−	4.78220i	−0.275368	−	0.322416i
$221$	−0.896774			−0.0603235
$222$		−	2.17533i		−	0.145998i
$223$			19.6166i			1.31363i	0.754054	+	0.656813i	$0.228096\pi$
$223$			19.6166i			1.31363i	−0.754054	+	0.656813i	$0.771904\pi$
$224$	4.27844			0.285865
$225$	−2.23934	+	14.1380i	−0.149289	+	0.942536i
$226$	−8.91842			−0.593245
$227$		−	19.2501i		−	1.27767i	−0.769342	−	0.638837i	$-0.779416\pi$
$227$		−	19.2501i		−	1.27767i	0.769342	−	0.638837i	$-0.220584\pi$
$228$		−	0.985065i		−	0.0652376i
$229$	23.1807			1.53182			0.765911	−	0.642947i	$-0.222288\pi$
$229$	23.1807			1.53182			0.765911	+	0.642947i	$0.222288\pi$
$230$	−1.27474	−	1.49253i	−0.0840536	−	0.0984147i
$231$	−4.45621			−0.293197
$232$		−	7.47252i		−	0.490595i
$233$		−	7.04155i		−	0.461307i	−0.973036	−	0.230654i	$-0.925914\pi$
$233$		−	7.04155i		−	0.461307i	0.973036	−	0.230654i	$-0.0740864\pi$
$234$	−12.9804			−0.848558
$235$	17.1516	−	14.6488i	1.11885	−	0.955580i
$236$	4.55688			0.296628
$237$			0.732335i			0.0475703i
$238$			0.846211i			0.0548517i
$239$	19.9908			1.29309			0.646547	−	0.762874i	$-0.276212\pi$
$239$	19.9908			1.29309			0.646547	+	0.762874i	$0.276212\pi$
$240$	0.629674	−	0.537789i	0.0406453	−	0.0347141i
$241$	−22.7788			−1.46731			−0.733657	−	0.679520i	$-0.762188\pi$
$241$	−22.7788			−1.46731			−0.733657	+	0.679520i	$0.762188\pi$
$242$		−	3.08971i		−	0.198614i
$243$		−	9.39632i		−	0.602774i
$244$	5.96876			0.382111
$245$	−16.4173	−	19.2223i	−1.04886	−	1.22807i
$246$	−3.33259			−0.212478
$247$		−	12.0606i		−	0.767400i
$248$			1.00000i			0.0635001i
$249$	−0.205196			−0.0130038
$250$	−5.84162	−	9.53286i	−0.369457	−	0.602911i
$251$	19.8050			1.25008			0.625040	−	0.780592i	$-0.285083\pi$
$251$	19.8050			1.25008			0.625040	+	0.780592i	$0.285083\pi$
$252$			12.2486i			0.771588i
$253$			2.46881i			0.155213i
$254$	−2.56349			−0.160847
$255$	0.106367	+	0.124540i	0.00666094	+	0.00779900i
$256$	1.00000			0.0625000
$257$			18.8826i			1.17786i	0.808183	+	0.588931i	$0.200451\pi$
$257$			18.8826i			1.17786i	−0.808183	+	0.588931i	$0.799549\pi$
$258$			2.11468i			0.131654i
$259$	−25.1319			−1.56162
$260$	7.70941	−	6.58442i	0.478117	−	0.408348i
$261$	21.3928			1.32418
$262$		−	8.72064i		−	0.538763i
$263$		−	23.5411i		−	1.45161i	−0.687901	−	0.725804i	$-0.741468\pi$
$263$		−	23.5411i		−	1.45161i	0.687901	−	0.725804i	$-0.258532\pi$
$264$	−1.04155			−0.0641030
$265$	0.351233	−	0.299980i	0.0215761	−	0.0184276i
$266$	−11.3806			−0.697792
$267$			4.46362i			0.273169i
$268$		−	5.70571i		−	0.348531i
$269$	0.0792837			0.00483401			0.00241701	−	0.999997i	$-0.499231\pi$
$269$	0.0792837			0.00483401			0.00241701	+	0.999997i	$0.499231\pi$
$270$	3.15298	+	3.69169i	0.191884	+	0.224669i
$271$	−21.3508			−1.29697			−0.648483	−	0.761229i	$-0.724596\pi$
$271$	−21.3508			−1.29697			−0.648483	+	0.761229i	$0.724596\pi$
$272$			0.197785i			0.0119925i
$273$		−	7.18388i		−	0.434788i
$274$	−9.12221			−0.551093
$275$	−2.19996	+	13.8895i	−0.132663	+	0.837567i
$276$	−0.325070			−0.0195669
$277$			1.24396i			0.0747424i	0.999301	+	0.0373712i	$0.0118984\pi$
$277$			1.24396i			0.0747424i	−0.999301	+	0.0373712i	$0.988102\pi$
$278$		−	16.5407i		−	0.992045i
$279$	−2.86286			−0.171395
$280$	−6.21317	−	7.27474i	−0.371308	−	0.434749i
$281$	23.1818			1.38291			0.691456	−	0.722419i	$-0.256970\pi$
$281$	23.1818			1.38291			0.691456	+	0.722419i	$0.256970\pi$
$282$		−	3.73557i		−	0.222450i
$283$		−	19.3182i		−	1.14834i	−0.818734	−	0.574172i	$-0.805324\pi$
$283$		−	19.3182i		−	1.14834i	0.818734	−	0.574172i	$-0.194676\pi$
$284$	8.06064			0.478311
$285$	−1.67493	+	1.43052i	−0.0992143	+	0.0847365i
$286$	−12.7522			−0.754055
$287$			38.5020i			2.27270i
$288$			2.86286i			0.168696i
$289$	16.9609			0.997699
$290$	−12.7057	+	10.8516i	−0.746105	+	0.637230i
$291$	−0.697276			−0.0408750
$292$			14.8079i			0.866567i
$293$			9.55455i			0.558183i	0.960265	+	0.279091i	$0.0900332\pi$
$293$			9.55455i			0.558183i	−0.960265	+	0.279091i	$0.909967\pi$
$294$	−4.18656			−0.244165
$295$	−6.61753	−	7.74818i	−0.385287	−	0.451116i
$296$	−5.87409			−0.341424
$297$		−	6.10647i		−	0.354333i
$298$		−	14.2426i		−	0.825050i
$299$	−3.97999			−0.230169
$300$	−1.82883	−	0.289670i	−0.105588	−	0.0167241i
$301$	24.4313			1.40820
$302$			23.6632i			1.36167i
$303$		−	5.51117i		−	0.316609i
$304$	−2.66000			−0.152561
$305$	−8.66786	−	10.1488i	−0.496320	−	0.581120i
$306$	−0.566231			−0.0323692
$307$			16.8669i			0.962645i	0.876544	+	0.481323i	$0.159843\pi$
$307$			16.8669i			0.962645i	−0.876544	+	0.481323i	$0.840157\pi$
$308$			12.0332i			0.685656i
$309$	4.83116			0.274835
$310$	1.70032	−	1.45220i	0.0965719	−	0.0824797i
$311$	−8.12870			−0.460936			−0.230468	−	0.973080i	$-0.574026\pi$
$311$	−8.12870			−0.460936			−0.230468	+	0.973080i	$0.574026\pi$
$312$		−	1.67909i		−	0.0950597i
$313$		−	8.53362i		−	0.482349i	−0.970482	−	0.241174i	$-0.922467\pi$
$313$		−	8.53362i		−	0.482349i	0.970482	−	0.241174i	$-0.0775325\pi$
$314$	−14.1970			−0.801182
$315$	20.8265	−	17.7874i	1.17344	−	1.00221i
$316$	1.97754			0.111245
$317$		−	22.0588i		−	1.23895i	−0.785018	−	0.619473i	$-0.787346\pi$
$317$		−	22.0588i		−	1.23895i	0.785018	−	0.619473i	$-0.212654\pi$
$318$		−	0.0764976i		−	0.00428977i
$319$	21.0166			1.17671
$320$	−1.45220	−	1.70032i	−0.0811807	−	0.0950510i
$321$	−0.0381858			−0.00213132
$322$			3.75559i			0.209291i
$323$		−	0.526107i		−	0.0292734i
$324$	−7.78454			−0.432474
$325$	−22.3913	−	3.54657i	−1.24205	−	0.196728i
$326$	−1.83128			−0.101425
$327$			3.75559i			0.207684i
$328$			8.99908i			0.496891i
$329$	−43.1577			−2.37936
$330$	1.51255	+	1.77097i	0.0832629	+	0.0974889i
$331$	−35.4100			−1.94631			−0.973156	−	0.230147i	$-0.926079\pi$
$331$	−35.4100			−1.94631			−0.973156	+	0.230147i	$0.926079\pi$
$332$			0.554096i			0.0304100i
$333$		−	16.8167i		−	0.921549i
$334$	18.6417			1.02003
$335$	−9.70155	+	8.28585i	−0.530052	+	0.452704i
$336$	−1.58442			−0.0864371
$337$		−	12.1827i		−	0.663636i	−0.943343	−	0.331818i	$-0.892338\pi$
$337$		−	12.1827i		−	0.663636i	0.943343	−	0.331818i	$-0.107662\pi$
$338$		−	7.55791i		−	0.411096i
$339$	3.30272			0.179379
$340$	0.336299	−	0.287224i	0.0182384	−	0.0155769i
$341$	−2.81252			−0.152307
$342$		−	7.61519i		−	0.411782i
$343$			18.4189i			0.994529i
$344$	5.71033			0.307880
$345$	0.472068	+	0.552724i	0.0254153	+	0.0297576i
$346$	12.1139			0.651246
$347$			29.0561i			1.55981i	0.625895	+	0.779907i	$0.284734\pi$
$347$			29.0561i			1.55981i	−0.625895	+	0.779907i	$0.715266\pi$
$348$			2.76727i			0.148341i
$349$	−6.65014			−0.355974			−0.177987	−	0.984033i	$-0.556958\pi$
$349$	−6.65014			−0.355974			−0.177987	+	0.984033i	$0.556958\pi$
$350$	−3.34661	+	21.1288i	−0.178884	+	1.12938i
$351$	9.84426			0.525448
$352$			2.81252i			0.149908i
$353$		−	4.37414i		−	0.232812i	−0.993202	−	0.116406i	$-0.962863\pi$
$353$		−	4.37414i		−	0.232812i	0.993202	−	0.116406i	$-0.0371374\pi$
$354$	−1.68753			−0.0896913
$355$	−11.7057	−	13.7057i	−0.621274	−	0.727423i
$356$	12.0532			0.638820
$357$		−	0.313374i		−	0.0165855i
$358$			21.6720i			1.14540i
$359$	8.42463			0.444635			0.222318	−	0.974974i	$-0.428638\pi$
$359$	8.42463			0.444635			0.222318	+	0.974974i	$0.428638\pi$
$360$	4.86779	−	4.15746i	0.256555	−	0.219117i
$361$	−11.9244			−0.627601
$362$			24.4151i			1.28323i
$363$			1.14420i			0.0600548i
$364$	−19.3988			−1.01677
$365$	25.1782	−	21.5041i	1.31789	−	1.12558i
$366$	−2.21039			−0.115539
$367$		−	23.0748i		−	1.20449i	−0.798310	−	0.602247i	$-0.794272\pi$
$367$		−	23.0748i		−	1.20449i	0.798310	−	0.602247i	$-0.205728\pi$
$368$			0.877793i			0.0457581i
$369$	−25.7631			−1.34117
$370$	8.53038	+	9.98785i	0.443473	+	0.519244i
$371$	−0.883790			−0.0458841
$372$		−	0.370326i		−	0.0192005i
$373$		−	29.9809i		−	1.55235i	−0.630516	−	0.776176i	$-0.717157\pi$
$373$		−	29.9809i		−	1.55235i	0.630516	−	0.776176i	$-0.282843\pi$
$374$	−0.556275			−0.0287643
$375$	2.16330	+	3.53027i	0.111713	+	0.182302i
$376$	−10.0873			−0.520211
$377$			33.8810i			1.74496i
$378$		−	9.28922i		−	0.477786i
$379$	1.67990			0.0862905			0.0431452	−	0.999069i	$-0.486262\pi$
$379$	1.67990			0.0862905			0.0431452	+	0.999069i	$0.486262\pi$
$380$	3.86286	+	4.52285i	0.198160	+	0.232018i
$381$	0.949325			0.0486354
$382$		−	14.6035i		−	0.747181i
$383$			11.1130i			0.567846i	0.958847	+	0.283923i	$0.0916359\pi$
$383$			11.1130i			0.567846i	−0.958847	+	0.283923i	$0.908364\pi$
$384$	−0.370326			−0.0188981
$385$	20.4604	−	17.4747i	1.04276	−	0.890593i
$386$	−25.0839			−1.27674
$387$			16.3479i			0.831009i
$388$			1.88287i			0.0955883i
$389$	22.1026			1.12065			0.560324	−	0.828273i	$-0.310676\pi$
$389$	22.1026			1.12065			0.560324	+	0.828273i	$0.310676\pi$
$390$	−2.85499	+	2.43838i	−0.144568	+	0.123472i
$391$	−0.173614			−0.00878005
$392$			11.3051i			0.570992i
$393$			3.22948i			0.162906i
$394$	11.5672			0.582747
$395$	−2.87180	−	3.36246i	−0.144496	−	0.169184i
$396$	−8.05186			−0.404621
$397$		−	9.80141i		−	0.491919i	−0.969280	−	0.245959i	$-0.920897\pi$
$397$		−	9.80141i		−	0.491919i	0.969280	−	0.245959i	$-0.0791030\pi$
$398$		−	0.518696i		−	0.0259999i
$399$	4.21454			0.210991
$400$	−0.782203	+	4.93844i	−0.0391101	+	0.246922i
$401$	14.1389			0.706061			0.353030	−	0.935612i	$-0.385151\pi$
$401$	14.1389			0.706061			0.353030	+	0.935612i	$0.385151\pi$
$402$			2.11297i			0.105385i
$403$		−	4.53408i		−	0.225859i
$404$	−14.8820			−0.740405
$405$	11.3047	+	13.2362i	0.561737	+	0.657714i
$406$	31.9707			1.58668
$407$		−	16.5210i		−	0.818916i
$408$		−	0.0732449i		−	0.00362616i
$409$	−9.05312			−0.447648			−0.223824	−	0.974630i	$-0.571854\pi$
$409$	−9.05312			−0.447648			−0.223824	+	0.974630i	$0.571854\pi$
$410$	15.3014	−	13.0685i	0.755680	−	0.645408i
$411$	3.37819			0.166634
$412$		−	13.0457i		−	0.642716i
$413$			19.4964i			0.959353i
$414$	−2.51300			−0.123507
$415$	0.942142	−	0.804661i	0.0462480	−	0.0394992i
$416$	−4.53408			−0.222302
$417$			6.12545i			0.299964i
$418$		−	7.48130i		−	0.365923i
$419$	24.5652			1.20009			0.600044	−	0.799967i	$-0.295150\pi$
$419$	24.5652			1.20009			0.600044	+	0.799967i	$0.295150\pi$
$420$	2.30090	+	2.69402i	0.112272	+	0.131455i
$421$	−1.92431			−0.0937851			−0.0468926	−	0.998900i	$-0.514932\pi$
$421$	−1.92431			−0.0937851			−0.0468926	+	0.998900i	$0.514932\pi$
$422$		−	20.2626i		−	0.986367i
$423$		−	28.8784i		−	1.40412i
$424$	−0.206568			−0.0100318
$425$	−0.976749	−	0.154708i	−0.0473793	−	0.00750444i
$426$	−2.98507			−0.144627
$427$			25.5370i			1.23582i
$428$			0.103114i			0.00498420i
$429$	4.72248			0.228003
$430$	−8.29257	−	9.70941i	−0.399903	−	0.468229i
$431$	22.4711			1.08240			0.541198	−	0.840895i	$-0.317971\pi$
$431$	22.4711			1.08240			0.541198	+	0.840895i	$0.317971\pi$
$432$		−	2.17117i		−	0.104460i
$433$			28.8079i			1.38442i	0.721696	+	0.692210i	$0.243363\pi$
$433$			28.8079i			1.38442i	−0.721696	+	0.692210i	$0.756637\pi$
$434$	−4.27844			−0.205372
$435$	4.70525	−	4.01864i	0.225600	−	0.192679i
$436$	10.1413			0.485680
$437$		−	2.33493i		−	0.111695i
$438$		−	5.48375i		−	0.262024i
$439$	11.3814			0.543207			0.271603	−	0.962409i	$-0.412446\pi$
$439$	11.3814			0.543207			0.271603	+	0.962409i	$0.412446\pi$
$440$	4.78220	−	4.08436i	0.227983	−	0.194714i
$441$	−32.3648			−1.54118
$442$		−	0.896774i		−	0.0426552i
$443$			5.48894i			0.260787i	0.991462	+	0.130394i	$0.0416241\pi$
$443$			5.48894i			0.260787i	−0.991462	+	0.130394i	$0.958376\pi$
$444$	2.17533			0.103236
$445$	−17.5038	−	20.4944i	−0.829758	−	0.971528i
$446$	−19.6166			−0.928873
$447$			5.27439i			0.249470i
$448$			4.27844i			0.202137i
$449$	11.7183			0.553021			0.276511	−	0.961011i	$-0.410822\pi$
$449$	11.7183			0.553021			0.276511	+	0.961011i	$0.410822\pi$
$450$	−14.1380	−	2.23934i	−0.666474	−	0.105563i
$451$	−25.3101			−1.19181
$452$		−	8.91842i		−	0.419487i
$453$		−	8.76311i		−	0.411727i
$454$	19.2501			0.903452
$455$	28.1710	+	32.9843i	1.32068	+	1.54633i
$456$	0.985065			0.0461299
$457$		−	19.6698i		−	0.920116i	−0.887889	−	0.460058i	$-0.847829\pi$
$457$		−	19.6698i		−	0.920116i	0.887889	−	0.460058i	$-0.152171\pi$
$458$			23.1807i			1.08316i
$459$	0.429425			0.0200438
$460$	1.49253	−	1.27474i	0.0695897	−	0.0594348i
$461$	34.0577			1.58623			0.793113	−	0.609074i	$-0.208459\pi$
$461$	34.0577			1.58623			0.793113	+	0.609074i	$0.208459\pi$
$462$		−	4.45621i		−	0.207322i
$463$			16.0140i			0.744234i	0.928186	+	0.372117i	$0.121368\pi$
$463$			16.0140i			0.744234i	−0.928186	+	0.372117i	$0.878632\pi$
$464$	7.47252			0.346903
$465$	−0.629674	+	0.537789i	−0.0292004	+	0.0249394i
$466$	7.04155			0.326194
$467$			31.6506i			1.46462i	0.680973	+	0.732308i	$0.261557\pi$
$467$			31.6506i			1.46462i	−0.680973	+	0.732308i	$0.738443\pi$
$468$		−	12.9804i		−	0.600021i
$469$	24.4115			1.12722
$470$	14.6488	+	17.1516i	0.675697	+	0.791145i
$471$	5.25751			0.242253
$472$			4.55688i			0.209747i
$473$			16.0604i			0.738460i
$474$	−0.732335			−0.0336373
$475$	2.08066	−	13.1362i	0.0954670	−	0.602731i
$476$	−0.846211			−0.0387860
$477$		−	0.591376i		−	0.0270772i
$478$			19.9908i			0.914356i
$479$	−3.25751			−0.148839			−0.0744197	−	0.997227i	$-0.523710\pi$
$479$	−3.25751			−0.148839			−0.0744197	+	0.997227i	$0.523710\pi$
$480$	0.537789	+	0.629674i	0.0245466	+	0.0287406i
$481$	26.6336			1.21439
$482$		−	22.7788i		−	1.03755i
$483$		−	1.39079i		−	0.0632832i
$484$	3.08971			0.140441
$485$	3.20149	−	2.73431i	0.145372	−	0.124159i
$486$	9.39632			0.426226
$487$			40.0906i			1.81668i	0.418234	+	0.908340i	$0.362649\pi$
$487$			40.0906i			1.81668i	−0.418234	+	0.908340i	$0.637351\pi$
$488$			5.96876i			0.270193i
$489$	0.678169			0.0306679
$490$	19.2223	−	16.4173i	0.868373	−	0.741656i
$491$	−28.6488			−1.29290			−0.646450	−	0.762956i	$-0.723747\pi$
$491$	−28.6488			−1.29290			−0.646450	+	0.762956i	$0.723747\pi$
$492$		−	3.33259i		−	0.150245i
$493$			1.47795i			0.0665636i
$494$	12.0606			0.542634
$495$	11.6929	+	13.6908i	0.525559	+	0.615354i
$496$	−1.00000			−0.0449013
$497$			34.4870i			1.54695i
$498$		−	0.205196i		−	0.00919506i
$499$	18.5438			0.830135			0.415068	−	0.909791i	$-0.363758\pi$
$499$	18.5438			0.830135			0.415068	+	0.909791i	$0.363758\pi$
$500$	9.53286	−	5.84162i	0.426322	−	0.261245i
$501$	−6.90350			−0.308426
$502$			19.8050i			0.883940i
$503$		−	38.4488i		−	1.71435i	−0.515027	−	0.857174i	$-0.672218\pi$
$503$		−	38.4488i		−	1.71435i	0.515027	−	0.857174i	$-0.327782\pi$
$504$	−12.2486			−0.545595
$505$	21.6116	+	25.3041i	0.961705	+	1.12602i
$506$	−2.46881			−0.109752
$507$			2.79889i			0.124303i
$508$		−	2.56349i		−	0.113736i
$509$	38.6820			1.71455			0.857274	−	0.514860i	$-0.172156\pi$
$509$	38.6820			1.71455			0.857274	+	0.514860i	$0.172156\pi$
$510$	−0.124540	+	0.106367i	−0.00551473	+	0.00470999i
$511$	−63.3547			−2.80265
$512$			1.00000i			0.0441942i
$513$			5.77530i			0.254986i
$514$	−18.8826			−0.832874
$515$	−22.1819	+	18.9450i	−0.977453	+	0.834818i
$516$	−2.11468			−0.0930937
$517$		−	28.3707i		−	1.24774i
$518$		−	25.1319i		−	1.10423i
$519$	−4.48608			−0.196917
$520$	6.58442	+	7.70941i	0.288746	+	0.338080i
$521$	−11.4945			−0.503584			−0.251792	−	0.967781i	$-0.581020\pi$
$521$	−11.4945			−0.503584			−0.251792	+	0.967781i	$0.581020\pi$
$522$			21.3928i			0.936336i
$523$			7.48837i			0.327444i	0.986507	+	0.163722i	$0.0523500\pi$
$523$			7.48837i			0.327444i	−0.986507	+	0.163722i	$0.947650\pi$
$524$	8.72064			0.380963
$525$	1.23934	−	7.82455i	0.0540890	−	0.341491i
$526$	23.5411			1.02644
$527$		−	0.197785i		−	0.00861565i
$528$		−	1.04155i		−	0.0453277i
$529$	22.2295			0.966499
$530$	0.299980	+	0.351233i	0.0130303	+	0.0152566i
$531$	−13.0457			−0.566136
$532$		−	11.3806i		−	0.493413i
$533$		−	40.8026i		−	1.76736i
$534$	−4.46362			−0.193160
$535$	0.175327	−	0.149743i	0.00758005	−	0.00647393i
$536$	5.70571			0.246449
$537$		−	8.02571i		−	0.346335i
$538$			0.0792837i			0.00341816i
$539$	−31.7958			−1.36954
$540$	−3.69169	+	3.15298i	−0.158865	+	0.135683i
$541$	14.3075			0.615128			0.307564	−	0.951527i	$-0.400486\pi$
$541$	14.3075			0.615128			0.307564	+	0.951527i	$0.400486\pi$
$542$		−	21.3508i		−	0.917094i
$543$		−	9.04155i		−	0.388010i
$544$	−0.197785			−0.00847996
$545$	−14.7272	−	17.2435i	−0.630846	−	0.738630i
$546$	7.18388			0.307442
$547$		−	11.8919i		−	0.508462i	−0.967144	−	0.254231i	$-0.918178\pi$
$547$		−	11.8919i		−	0.508462i	0.967144	−	0.254231i	$-0.0818223\pi$
$548$		−	9.12221i		−	0.389681i
$549$	−17.0877			−0.729286
$550$	−13.8895	−	2.19996i	−0.592249	−	0.0938068i
$551$	−19.8769			−0.846783
$552$		−	0.325070i		−	0.0138359i
$553$			8.46080i			0.359790i
$554$	−1.24396			−0.0528508
$555$	−3.15902	−	3.69876i	−0.134093	−	0.157004i
$556$	16.5407			0.701481
$557$			10.9703i			0.464826i	0.972617	+	0.232413i	$0.0746621\pi$
$557$			10.9703i			0.464826i	−0.972617	+	0.232413i	$0.925338\pi$
$558$		−	2.86286i		−	0.121194i
$559$	−25.8911			−1.09508
$560$	7.27474	−	6.21317i	0.307414	−	0.262554i
$561$	0.206003			0.00869746
$562$			23.1818i			0.977866i
$563$		−	3.76635i		−	0.158733i	−0.996846	−	0.0793663i	$-0.974710\pi$
$563$		−	3.76635i		−	0.158733i	0.996846	−	0.0793663i	$-0.0252897\pi$
$564$	3.73557			0.157296
$565$	−15.1642	+	12.9514i	−0.637963	+	0.544869i
$566$	19.3182			0.812003
$567$		−	33.3057i		−	1.39871i
$568$			8.06064i			0.338217i
$569$	13.3107			0.558015			0.279008	−	0.960289i	$-0.409995\pi$
$569$	13.3107			0.558015			0.279008	+	0.960289i	$0.409995\pi$
$570$	−1.43052	−	1.67493i	−0.0599178	−	0.0701551i
$571$	−14.6540			−0.613249			−0.306625	−	0.951831i	$-0.599200\pi$
$571$	−14.6540			−0.613249			−0.306625	+	0.951831i	$0.599200\pi$
$572$		−	12.7522i		−	0.533197i
$573$			5.40806i			0.225925i
$574$	−38.5020			−1.60704
$575$	−4.33493	−	0.686612i	−0.180779	−	0.0286337i
$576$	−2.86286			−0.119286
$577$		−	1.56856i		−	0.0653002i	−0.999467	−	0.0326501i	$-0.989605\pi$
$577$		−	1.56856i		−	0.0653002i	0.999467	−	0.0326501i	$-0.0103947\pi$
$578$			16.9609i			0.705480i
$579$	9.28922			0.386047
$580$	−10.8516	−	12.7057i	−0.450589	−	0.527576i
$581$	−2.37067			−0.0983518
$582$		−	0.697276i		−	0.0289030i
$583$		−	0.580978i		−	0.0240617i
$584$	−14.8079			−0.612755
$585$	−22.0710	+	18.8503i	−0.912522	+	0.779362i
$586$	−9.55455			−0.394695
$587$			27.8374i			1.14897i	0.818514	+	0.574487i	$0.194798\pi$
$587$			27.8374i			1.14897i	−0.818514	+	0.574487i	$0.805202\pi$
$588$		−	4.18656i		−	0.172651i
$589$	2.66000			0.109603
$590$	7.74818	−	6.61753i	0.318987	−	0.272439i
$591$	−4.28363			−0.176205
$592$		−	5.87409i		−	0.241424i
$593$			7.78777i			0.319806i	0.987133	+	0.159903i	$0.0511181\pi$
$593$			7.78777i			0.319806i	−0.987133	+	0.159903i	$0.948882\pi$
$594$	6.10647			0.250551
$595$	1.22887	+	1.43883i	0.0503789	+	0.0589864i
$596$	14.2426			0.583399
$597$			0.192087i			0.00786158i
$598$		−	3.97999i		−	0.162754i
$599$	−20.4329			−0.834868			−0.417434	−	0.908707i	$-0.637070\pi$
$599$	−20.4329			−0.834868			−0.417434	+	0.908707i	$0.637070\pi$
$600$	0.289670	−	1.82883i	0.0118257	−	0.0746617i
$601$	2.23121			0.0910128			0.0455064	−	0.998964i	$-0.485510\pi$
$601$	2.23121			0.0910128			0.0455064	+	0.998964i	$0.485510\pi$
$602$			24.4313i			0.995746i
$603$			16.3346i			0.665197i
$604$	−23.6632			−0.962843
$605$	−4.48689	−	5.25350i	−0.182418	−	0.213585i
$606$	5.51117			0.223876
$607$			21.3582i			0.866902i	0.901177	+	0.433451i	$0.142704\pi$
$607$			21.3582i			0.866902i	−0.901177	+	0.433451i	$0.857296\pi$
$608$		−	2.66000i		−	0.107877i
$609$	−11.8396			−0.479765
$610$	10.1488	−	8.66786i	0.410914	−	0.350951i
$611$	45.7365			1.85030
$612$		−	0.566231i		−	0.0228885i
$613$			25.5373i			1.03144i	0.856756	+	0.515721i	$0.172476\pi$
$613$			25.5373i			1.03144i	−0.856756	+	0.515721i	$0.827524\pi$
$614$	−16.8669			−0.680693
$615$	−5.66649	+	4.83961i	−0.228495	+	0.195152i
$616$	−12.0332			−0.484832
$617$		−	7.64751i		−	0.307877i	−0.988080	−	0.153939i	$-0.950804\pi$
$617$		−	7.64751i		−	0.307877i	0.988080	−	0.153939i	$-0.0491958\pi$
$618$			4.83116i			0.194338i
$619$	−19.5972			−0.787676			−0.393838	−	0.919180i	$-0.628853\pi$
$619$	−19.5972			−0.787676			−0.393838	+	0.919180i	$0.628853\pi$
$620$	1.45220	+	1.70032i	0.0583219	+	0.0682867i
$621$	1.90584			0.0764786
$622$		−	8.12870i		−	0.325931i
$623$			51.5690i			2.06607i
$624$	1.67909			0.0672173
$625$	−23.7763	−	7.72572i	−0.951053	−	0.309029i
$626$	8.53362			0.341072
$627$			2.77052i			0.110644i
$628$		−	14.1970i		−	0.566521i
$629$	1.16181			0.0463243
$630$	17.7874	+	20.8265i	0.708668	+	0.829749i
$631$	17.5038			0.696814			0.348407	−	0.937343i	$-0.386723\pi$
$631$	17.5038			0.696814			0.348407	+	0.937343i	$0.386723\pi$
$632$			1.97754i			0.0786624i
$633$			7.50376i			0.298248i
$634$	22.0588			0.876067
$635$	−4.35876	+	3.72271i	−0.172972	+	0.147731i
$636$	0.0764976			0.00303333
$637$		−	51.2581i		−	2.03092i
$638$			21.0166i			0.832057i
$639$	−23.0765			−0.912892
$640$	1.70032	−	1.45220i	0.0672112	−	0.0574034i
$641$	18.9832			0.749792			0.374896	−	0.927067i	$-0.377678\pi$
$641$	18.9832			0.749792			0.374896	+	0.927067i	$0.377678\pi$
$642$		−	0.0381858i		−	0.00150707i
$643$			7.85904i			0.309930i	0.987920	+	0.154965i	$0.0495265\pi$
$643$			7.85904i			0.309930i	−0.987920	+	0.154965i	$0.950473\pi$
$644$	−3.75559			−0.147991
$645$	3.07095	+	3.59565i	0.120919	+	0.141578i
$646$	0.526107			0.0206994
$647$		−	42.4505i		−	1.66890i	−0.551082	−	0.834451i	$-0.685785\pi$
$647$		−	42.4505i		−	1.66890i	0.551082	−	0.834451i	$-0.314215\pi$
$648$		−	7.78454i		−	0.305805i
$649$	−12.8163			−0.503085
$650$	3.54657	−	22.3913i	0.139108	−	0.878258i
$651$	1.58442			0.0620982
$652$		−	1.83128i		−	0.0717183i
$653$		−	20.0881i		−	0.786107i	−0.919516	−	0.393053i	$-0.871419\pi$
$653$		−	20.0881i		−	0.786107i	0.919516	−	0.393053i	$-0.128581\pi$
$654$	−3.75559			−0.146855
$655$	−12.6642	−	14.8279i	−0.494829	−	0.579374i
$656$	−8.99908			−0.351355
$657$		−	42.3929i		−	1.65391i
$658$		−	43.1577i		−	1.68246i
$659$	43.1928			1.68255			0.841276	−	0.540605i	$-0.181805\pi$
$659$	43.1928			1.68255			0.841276	+	0.540605i	$0.181805\pi$
$660$	−1.77097	+	1.51255i	−0.0689351	+	0.0588757i
$661$	10.7458			0.417965			0.208982	−	0.977919i	$-0.432985\pi$
$661$	10.7458			0.417965			0.208982	+	0.977919i	$0.432985\pi$
$662$		−	35.4100i		−	1.37625i
$663$			0.332099i			0.0128976i
$664$	−0.554096			−0.0215031
$665$	−19.3508	+	16.5270i	−0.750391	+	0.640890i
$666$	16.8167			0.651633
$667$			6.55933i			0.253978i
$668$			18.6417i			0.721269i
$669$	7.26454			0.280863
$670$	−8.28585	−	9.70155i	−0.320110	−	0.374803i
$671$	−16.7873			−0.648066
$672$		−	1.58442i		−	0.0611202i
$673$			48.3880i			1.86522i	0.360884	+	0.932611i	$0.382475\pi$
$673$			48.3880i			1.86522i	−0.360884	+	0.932611i	$0.617525\pi$
$674$	12.1827			0.469262
$675$	10.7222	+	1.69829i	0.412697	+	0.0653674i
$676$	7.55791			0.290689
$677$		−	17.4893i		−	0.672168i	−0.941832	−	0.336084i	$-0.890897\pi$
$677$		−	17.4893i		−	0.672168i	0.941832	−	0.336084i	$-0.109103\pi$
$678$			3.30272i			0.126840i
$679$	−8.05575			−0.309151
$680$	0.287224	+	0.336299i	0.0110145	+	0.0128965i
$681$	−7.12881			−0.273177
$682$		−	2.81252i		−	0.107697i
$683$			10.4920i			0.401463i	0.979646	+	0.200732i	$0.0643320\pi$
$683$			10.4920i			0.401463i	−0.979646	+	0.200732i	$0.935668\pi$
$684$	7.61519			0.291174
$685$	−15.5107	+	13.2473i	−0.592634	+	0.506154i
$686$	−18.4189			−0.703238
$687$		−	8.58440i		−	0.327515i
$688$			5.71033i			0.217704i
$689$	0.936598			0.0356815
$690$	−0.552724	+	0.472068i	−0.0210418	+	0.0179713i
$691$	2.24999			0.0855935			0.0427967	−	0.999084i	$-0.486373\pi$
$691$	2.24999			0.0855935			0.0427967	+	0.999084i	$0.486373\pi$
$692$			12.1139i			0.460500i
$693$		−	34.4494i		−	1.30862i
$694$	−29.0561			−1.10296
$695$	−24.0205	−	28.1245i	−0.911148	−	1.06682i
$696$	−2.76727			−0.104893
$697$		−	1.77988i		−	0.0674179i
$698$		−	6.65014i		−	0.251711i
$699$	−2.60767			−0.0986311
$700$	−21.1288	−	3.34661i	−0.798594	−	0.126490i
$701$	−12.1951			−0.460604			−0.230302	−	0.973119i	$-0.573971\pi$
$701$	−12.1951			−0.460604			−0.230302	+	0.973119i	$0.573971\pi$
$702$			9.84426i			0.371548i
$703$			15.6250i			0.589310i
$704$	−2.81252			−0.106001
$705$	−5.42482	−	6.35169i	−0.204310	−	0.239218i
$706$	4.37414			0.164623
$707$		−	63.6716i		−	2.39462i
$708$		−	1.68753i		−	0.0634213i
$709$	10.6764			0.400961			0.200481	−	0.979698i	$-0.435750\pi$
$709$	10.6764			0.400961			0.200481	+	0.979698i	$0.435750\pi$
$710$	13.7057	−	11.7057i	0.514366	−	0.439307i
$711$	−5.66142			−0.212320
$712$			12.0532i			0.451714i
$713$		−	0.877793i		−	0.0328736i
$714$	0.313374			0.0117277
$715$	−21.6829	+	18.5188i	−0.810895	+	0.692565i
$716$	−21.6720			−0.809921
$717$		−	7.40309i		−	0.276474i
$718$			8.42463i			0.314404i
$719$	5.49146			0.204797			0.102398	−	0.994743i	$-0.467348\pi$
$719$	5.49146			0.204797			0.102398	+	0.994743i	$0.467348\pi$
$720$	4.15746	+	4.86779i	0.154939	+	0.181412i
$721$	55.8153			2.07867
$722$		−	11.9244i		−	0.443781i
$723$			8.43559i			0.313723i
$724$	−24.4151			−0.907381
$725$	−5.84503	+	36.9026i	−0.217079	+	1.37053i
$726$	−1.14420			−0.0424652
$727$		−	27.0989i		−	1.00504i	−0.864564	−	0.502522i	$-0.832406\pi$
$727$		−	27.0989i		−	1.00504i	0.864564	−	0.502522i	$-0.167594\pi$
$728$		−	19.3988i		−	0.718968i
$729$	19.8739			0.736071
$730$	21.5041	+	25.1782i	0.795903	+	0.931888i
$731$	−1.12942			−0.0417730
$732$		−	2.21039i		−	0.0816982i
$733$		−	42.3891i		−	1.56568i	−0.622226	−	0.782838i	$-0.713771\pi$
$733$		−	42.3891i		−	1.56568i	0.622226	−	0.782838i	$-0.286229\pi$
$734$	23.0748			0.851705
$735$	−7.11850	+	6.07974i	−0.262570	+	0.224254i
$736$	−0.877793			−0.0323559
$737$			16.0474i			0.591115i
$738$		−	25.7631i		−	0.948353i
$739$	2.05370			0.0755465			0.0377733	−	0.999286i	$-0.487974\pi$
$739$	2.05370			0.0755465			0.0377733	+	0.999286i	$0.487974\pi$
$740$	−9.98785	+	8.53038i	−0.367161	+	0.313583i
$741$	−4.46637			−0.164076
$742$		−	0.883790i		−	0.0324450i
$743$			39.0597i			1.43296i	0.697606	+	0.716481i	$0.254248\pi$
$743$			39.0597i			1.43296i	−0.697606	+	0.716481i	$0.745752\pi$
$744$	0.370326			0.0135768
$745$	−20.6831	−	24.2170i	−0.757771	−	0.887242i
$746$	29.9809			1.09768
$747$		−	1.58630i		−	0.0580396i
$748$		−	0.556275i		−	0.0203394i
$749$	−0.441167			−0.0161199
$750$	−3.53027	+	2.16330i	−0.128907	+	0.0789927i
$751$	−6.86549			−0.250525			−0.125263	−	0.992124i	$-0.539977\pi$
$751$	−6.86549			−0.250525			−0.125263	+	0.992124i	$0.539977\pi$
$752$		−	10.0873i		−	0.367845i
$753$		−	7.33431i		−	0.267277i
$754$	−33.8810			−1.23387
$755$	34.3639	+	40.2352i	1.25063	+	1.46431i
$756$	9.28922			0.337846
$757$			11.3406i			0.412180i	0.978533	+	0.206090i	$0.0660740\pi$
$757$			11.3406i			0.412180i	−0.978533	+	0.206090i	$0.933926\pi$
$758$			1.67990i			0.0610166i
$759$	0.914266			0.0331858
$760$	−4.52285	+	3.86286i	−0.164061	+	0.140121i
$761$	4.58423			0.166178			0.0830891	−	0.996542i	$-0.473521\pi$
$761$	4.58423			0.166178			0.0830891	+	0.996542i	$0.473521\pi$
$762$			0.949325i			0.0343904i
$763$			43.3890i			1.57079i
$764$	14.6035			0.528336
$765$	−0.962775	+	0.822283i	−0.0348092	+	0.0297297i
$766$	−11.1130			−0.401527
$767$		−	20.6613i		−	0.746036i
$768$		−	0.370326i		−	0.0133630i
$769$	−11.5710			−0.417261			−0.208631	−	0.977995i	$-0.566901\pi$
$769$	−11.5710			−0.417261			−0.208631	+	0.977995i	$0.566901\pi$
$770$	17.4747	+	20.4604i	0.629744	+	0.737341i
$771$	6.99270			0.251836
$772$		−	25.0839i		−	0.902789i
$773$		−	30.6711i		−	1.10316i	−0.834121	−	0.551581i	$-0.814025\pi$
$773$		−	30.6711i		−	1.10316i	0.834121	−	0.551581i	$-0.185975\pi$
$774$	−16.3479			−0.587612
$775$	0.782203	−	4.93844i	0.0280976	−	0.177394i
$776$	−1.88287			−0.0675911
$777$			9.30701i			0.333887i
$778$			22.1026i			0.792418i
$779$	23.9375			0.857651
$780$	−2.43838	−	2.85499i	−0.0873080	−	0.102225i
$781$	−22.6708			−0.811224
$782$		−	0.173614i		−	0.00620844i
$783$		−	16.2241i		−	0.579802i
$784$	−11.3051			−0.403752
$785$	−24.1395	+	20.6169i	−0.861574	+	0.735849i
$786$	−3.22948			−0.115192
$787$		−	10.4710i		−	0.373251i	−0.982431	−	0.186625i	$-0.940245\pi$
$787$		−	10.4710i		−	0.373251i	0.982431	−	0.186625i	$-0.0597550\pi$
$788$			11.5672i			0.412064i
$789$	−8.71790			−0.310365
$790$	3.36246	−	2.87180i	0.119631	−	0.102174i
$791$	38.1570			1.35671
$792$		−	8.05186i		−	0.286110i
$793$		−	27.0629i		−	0.961030i
$794$	9.80141			0.347839
$795$	−0.111090	−	0.130071i	−0.00393996	−	0.00461313i
$796$	0.518696			0.0183847
$797$			32.9860i			1.16842i	0.811601	+	0.584212i	$0.198596\pi$
$797$			32.9860i			1.16842i	−0.811601	+	0.584212i	$0.801404\pi$
$798$			4.21454i			0.149193i
$799$	1.99511			0.0705819
$800$	−4.93844	−	0.782203i	−0.174600	−	0.0276550i
$801$	−34.5067			−1.21923
$802$			14.1389i			0.499260i
$803$		−	41.6476i		−	1.46971i
$804$	−2.11297			−0.0745187
$805$	5.45388	+	6.38571i	0.192224	+	0.225067i
$806$	4.53408			0.159706
$807$		−	0.0293608i		−	0.00103355i
$808$		−	14.8820i		−	0.523545i
$809$	−36.6076			−1.28705			−0.643527	−	0.765423i	$-0.722530\pi$
$809$	−36.6076			−1.28705			−0.643527	+	0.765423i	$0.722530\pi$
$810$	−13.2362	+	11.3047i	−0.465074	+	0.397208i
$811$	−41.2334			−1.44790			−0.723951	−	0.689851i	$-0.757676\pi$
$811$	−41.2334			−1.44790			−0.723951	+	0.689851i	$0.757676\pi$
$812$			31.9707i			1.12195i
$813$			7.90674i			0.277302i
$814$	16.5210			0.579061
$815$	−3.11376	+	2.65939i	−0.109070	+	0.0931543i
$816$	0.0732449			0.00256408
$817$		−	15.1895i		−	0.531412i
$818$		−	9.05312i		−	0.316535i
$819$	55.5360			1.94059
$820$	13.0685	+	15.3014i	0.456372	+	0.534346i
$821$	1.51560			0.0528947			0.0264474	−	0.999650i	$-0.491581\pi$
$821$	1.51560			0.0528947			0.0264474	+	0.999650i	$0.491581\pi$
$822$			3.37819i			0.117828i
$823$			9.48975i			0.330792i	0.986227	+	0.165396i	$0.0528902\pi$
$823$			9.48975i			0.330792i	−0.986227	+	0.165396i	$0.947110\pi$
$824$	13.0457			0.454469
$825$	5.14363	+	0.814704i	0.179078	+	0.0283643i
$826$	−19.4964			−0.678365
$827$		−	20.3371i		−	0.707190i	−0.935399	−	0.353595i	$-0.884959\pi$
$827$		−	20.3371i		−	0.707190i	0.935399	−	0.353595i	$-0.115041\pi$
$828$		−	2.51300i		−	0.0873327i
$829$	8.76509			0.304424			0.152212	−	0.988348i	$-0.451360\pi$
$829$	8.76509			0.304424			0.152212	+	0.988348i	$0.451360\pi$
$830$	0.804661	+	0.942142i	0.0279302	+	0.0327022i
$831$	0.460671			0.0159805
$832$		−	4.53408i		−	0.157191i
$833$		−	2.23597i		−	0.0774718i
$834$	−6.12545			−0.212107
$835$	31.6969	−	27.0716i	1.09692	−	0.936850i
$836$	7.48130			0.258746
$837$			2.17117i			0.0750466i
$838$			24.5652i			0.848591i
$839$	1.47196			0.0508175			0.0254088	−	0.999677i	$-0.491911\pi$
$839$	1.47196			0.0508175			0.0254088	+	0.999677i	$0.491911\pi$
$840$	−2.69402	+	2.30090i	−0.0929526	+	0.0793886i
$841$	26.8386			0.925468
$842$		−	1.92431i		−	0.0663161i
$843$		−	8.58483i		−	0.295677i
$844$	20.2626			0.697467
$845$	−10.9756	−	12.8509i	−0.377573	−	0.442084i
$846$	28.8784			0.992860
$847$			13.2191i			0.454214i
$848$		−	0.206568i		−	0.00709359i
$849$	−7.15401			−0.245525
$850$	0.154708	−	0.976749i	0.00530644	−	0.0335022i
$851$	5.15623			0.176753
$852$		−	2.98507i		−	0.102267i
$853$		−	32.0816i		−	1.09845i	−0.835674	−	0.549226i	$-0.814923\pi$
$853$		−	32.0816i		−	1.09845i	0.835674	−	0.549226i	$-0.185077\pi$
$854$	−25.5370			−0.873858
$855$	−11.0588	−	12.9483i	−0.378204	−	0.442822i
$856$	−0.103114			−0.00352436
$857$			37.1503i			1.26903i	0.772910	+	0.634516i	$0.218800\pi$
$857$			37.1503i			1.26903i	−0.772910	+	0.634516i	$0.781200\pi$
$858$			4.72248i			0.161223i
$859$	−8.95811			−0.305647			−0.152823	−	0.988254i	$-0.548837\pi$
$859$	−8.95811			−0.305647			−0.152823	+	0.988254i	$0.548837\pi$
$860$	9.70941	−	8.29257i	0.331088	−	0.282774i
$861$	14.2583			0.485922
$862$			22.4711i			0.765370i
$863$		−	5.40970i		−	0.184148i	−0.995752	−	0.0920741i	$-0.970650\pi$
$863$		−	5.40970i		−	0.184148i	0.995752	−	0.0920741i	$-0.0293497\pi$
$864$	2.17117			0.0738647
$865$	20.5975	−	17.5918i	0.700336	−	0.598140i
$866$	−28.8079			−0.978932
$867$		−	6.28105i		−	0.213316i
$868$		−	4.27844i		−	0.145220i
$869$	−5.56189			−0.188674
$870$	4.01864	+	4.70525i	0.136245	+	0.159523i
$871$	−25.8701			−0.876576
$872$			10.1413i			0.343428i
$873$		−	5.39039i		−	0.182437i
$874$	2.33493			0.0789801
$875$	24.9930	+	40.7858i	0.844919	+	1.37881i
$876$	5.48375			0.185279
$877$		−	17.6725i		−	0.596757i	−0.954448	−	0.298379i	$-0.903554\pi$
$877$		−	17.6725i		−	0.596757i	0.954448	−	0.298379i	$-0.0964458\pi$
$878$			11.3814i			0.384105i
$879$	3.53830			0.119344
$880$	4.08436	+	4.78220i	0.137684	+	0.161208i
$881$	2.64487			0.0891081			0.0445540	−	0.999007i	$-0.485813\pi$
$881$	2.64487			0.0891081			0.0445540	+	0.999007i	$0.485813\pi$
$882$		−	32.3648i		−	1.08978i
$883$			36.2706i			1.22060i	0.792170	+	0.610301i	$0.208951\pi$
$883$			36.2706i			1.22060i	−0.792170	+	0.610301i	$0.791049\pi$
$884$	0.896774			0.0301618
$885$	−2.86935	+	2.45064i	−0.0964522	+	0.0823774i
$886$	−5.48894			−0.184405
$887$		−	26.9316i		−	0.904276i	−0.891948	−	0.452138i	$-0.850662\pi$
$887$		−	26.9316i		−	0.904276i	0.891948	−	0.452138i	$-0.149338\pi$
$888$			2.17533i			0.0729992i
$889$	10.9677			0.367846
$890$	20.4944	−	17.5038i	0.686974	−	0.586727i
$891$	21.8942			0.733483
$892$		−	19.6166i		−	0.656813i
$893$			26.8321i			0.897901i
$894$	−5.27439			−0.176402
$895$	31.4722	+	36.8495i	1.05200	+	1.23174i
$896$	−4.27844			−0.142933
$897$			1.47389i			0.0492118i
$898$			11.7183i			0.391045i
$899$	−7.47252			−0.249223
$900$	2.23934	−	14.1380i	0.0746445	−	0.471268i
$901$	0.0408561			0.00136111
$902$		−	25.3101i		−	0.842735i
$903$		−	9.04755i		−	0.301084i
$904$	8.91842			0.296622
$905$	35.4557	+	41.5136i	1.17859	+	1.37996i
$906$	8.76311			0.291135
$907$		−	21.5247i		−	0.714715i	−0.933968	−	0.357358i	$-0.883678\pi$
$907$		−	21.5247i		−	0.714715i	0.933968	−	0.357358i	$-0.116322\pi$
$908$			19.2501i			0.638837i
$909$	42.6049			1.41312
$910$	−32.9843	+	28.1710i	−1.09342	+	0.933861i
$911$	48.7212			1.61421			0.807103	−	0.590410i	$-0.201034\pi$
$911$	48.7212			1.61421			0.807103	+	0.590410i	$0.201034\pi$
$912$			0.985065i			0.0326188i
$913$		−	1.55841i		−	0.0515758i
$914$	19.6698			0.650620
$915$	−3.75837	+	3.20993i	−0.124248	+	0.106117i
$916$	−23.1807			−0.765911
$917$			37.3107i			1.23211i
$918$			0.429425i			0.0141731i
$919$	25.3406			0.835910			0.417955	−	0.908468i	$-0.362747\pi$
$919$	25.3406			0.835910			0.417955	+	0.908468i	$0.362747\pi$
$920$	1.27474	+	1.49253i	0.0420268	+	0.0492073i
$921$	6.24625			0.205821
$922$			34.0577i			1.12163i
$923$		−	36.5476i		−	1.20298i
$924$	4.45621			0.146599
$925$	29.0088	+	4.59473i	0.953804	+	0.151074i
$926$	−16.0140			−0.526253
$927$			37.3480i			1.22667i
$928$			7.47252i			0.245298i
$929$	−42.3414			−1.38918			−0.694588	−	0.719408i	$-0.744413\pi$
$929$	−42.3414			−1.38918			−0.694588	+	0.719408i	$0.744413\pi$
$930$	−0.537789	−	0.629674i	−0.0176348	−	0.0206478i
$931$	30.0714			0.985551
$932$			7.04155i			0.230654i
$933$			3.01027i			0.0985517i
$934$	−31.6506			−1.03564
$935$	−0.945848	+	0.807825i	−0.0309325	+	0.0264187i
$936$	12.9804			0.424279
$937$			17.1119i			0.559022i	0.960142	+	0.279511i	$0.0901724\pi$
$937$			17.1119i			0.559022i	−0.960142	+	0.279511i	$0.909828\pi$
$938$			24.4115i			0.797064i
$939$	−3.16022			−0.103130
$940$	−17.1516	+	14.6488i	−0.559424	+	0.477790i
$941$	10.0045			0.326137			0.163069	−	0.986615i	$-0.447861\pi$
$941$	10.0045			0.326137			0.163069	+	0.986615i	$0.447861\pi$
$942$			5.25751i			0.171299i
$943$		−	7.89933i		−	0.257238i
$944$	−4.55688			−0.148314
$945$	−13.4898	−	15.7947i	−0.438825	−	0.513801i
$946$	−16.0604			−0.522170
$947$		−	41.7436i		−	1.35648i	−0.734839	−	0.678242i	$-0.762742\pi$
$947$		−	41.7436i		−	1.35648i	0.734839	−	0.678242i	$-0.237258\pi$
$948$		−	0.732335i		−	0.0237851i
$949$	67.1403			2.17946
$950$	13.1362	+	2.08066i	0.426195	+	0.0675054i
$951$	−8.16895			−0.264896
$952$		−	0.846211i		−	0.0274259i
$953$		−	16.7473i		−	0.542497i	−0.962509	−	0.271248i	$-0.912564\pi$
$953$		−	16.7473i		−	0.542497i	0.962509	−	0.271248i	$-0.0874365\pi$
$954$	0.591376			0.0191465
$955$	−21.2073	−	24.8307i	−0.686252	−	0.803503i
$956$	−19.9908			−0.646547
$957$		−	7.78301i		−	0.251589i
$958$		−	3.25751i		−	0.105245i
$959$	39.0288			1.26031
$960$	−0.629674	+	0.537789i	−0.0203226	+	0.0173571i
$961$	1.00000			0.0322581
$962$			26.6336i			0.858702i
$963$		−	0.295201i		−	0.00951271i
$964$	22.7788			0.733657
$965$	−42.6507	+	36.4270i	−1.37298	+	1.17263i
$966$	1.39079			0.0447480
$967$		−	2.16792i		−	0.0697155i	−0.999392	−	0.0348577i	$-0.988902\pi$
$967$		−	2.16792i		−	0.0697155i	0.999392	−	0.0348577i	$-0.0110978\pi$
$968$			3.08971i			0.0993069i
$969$	−0.194831			−0.00625888
$970$	2.73431	+	3.20149i	0.0877935	+	0.102794i
$971$	−28.7397			−0.922301			−0.461151	−	0.887322i	$-0.652563\pi$
$971$	−28.7397			−0.922301			−0.461151	+	0.887322i	$0.652563\pi$
$972$			9.39632i			0.301387i
$973$			70.7684i			2.26873i
$974$	−40.0906			−1.28459
$975$	−1.31339	+	8.29207i	−0.0420621	+	0.265559i
$976$	−5.96876			−0.191055
$977$		−	2.81612i		−	0.0900956i	−0.998985	−	0.0450478i	$-0.985656\pi$
$977$		−	2.81612i		−	0.0900956i	0.998985	−	0.0450478i	$-0.0143440\pi$
$978$			0.678169i			0.0216855i
$979$	−33.9000			−1.08345
$980$	16.4173	+	19.2223i	0.524430	+	0.614033i
$981$	−29.0331			−0.926956
$982$		−	28.6488i		−	0.914219i
$983$			8.69493i			0.277325i	0.990340	+	0.138663i	$0.0442804\pi$
$983$			8.69493i			0.277325i	−0.990340	+	0.138663i	$0.955720\pi$
$984$	3.33259			0.106239
$985$	19.6680	−	16.7979i	0.626674	−	0.535227i
$986$	−1.47795			−0.0470676
$987$			15.9824i			0.508726i
$988$			12.0606i			0.383700i
$989$	−5.01249			−0.159388
$990$	−13.6908	+	11.6929i	−0.435121	+	0.371626i
$991$	−57.3615			−1.82215			−0.911073	−	0.412244i	$-0.864745\pi$
$991$	−57.3615			−1.82215			−0.911073	+	0.412244i	$0.864745\pi$
$992$		−	1.00000i		−	0.0317500i
$993$			13.1133i			0.416137i
$994$	−34.4870			−1.09386
$995$	−0.753253	−	0.881952i	−0.0238797	−	0.0279597i
$996$	0.205196			0.00650189
$997$			43.3782i			1.37380i	0.726751	+	0.686901i	$0.241029\pi$
$997$			43.3782i			1.37380i	−0.726751	+	0.686901i	$0.758971\pi$
$998$			18.5438i			0.586994i
$999$	−12.7536			−0.403507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.b.a.249.6	yes	8
3.2	odd	2		2790.2.d.m.559.2		8
4.3	odd	2		2480.2.d.d.1489.5		8
5.2	odd	4		1550.2.a.o.1.2		4
5.3	odd	4		1550.2.a.p.1.3		4
5.4	even	2	inner	310.2.b.a.249.3	✓	8
15.14	odd	2		2790.2.d.m.559.6		8
20.19	odd	2		2480.2.d.d.1489.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.b.a.249.3	✓	8	5.4	even	2	inner
310.2.b.a.249.6	yes	8	1.1	even	1	trivial
1550.2.a.o.1.2		4	5.2	odd	4
1550.2.a.p.1.3		4	5.3	odd	4
2480.2.d.d.1489.4		8	20.19	odd	2
2480.2.d.d.1489.5		8	4.3	odd	2
2790.2.d.m.559.2		8	3.2	odd	2
2790.2.d.m.559.6		8	15.14	odd	2

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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.370326i q^{3} -1.00000 q^{4} +(1.45220 + 1.70032i) q^{5} +0.370326 q^{6} -4.27844i q^{7} -1.00000i q^{8} +2.86286 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -0.370326i q^{3} -1.00000 q^{4} +(1.45220 + 1.70032i) q^{5} +0.370326 q^{6} -4.27844i q^{7} -1.00000i q^{8} +2.86286 q^{9} +(-1.70032 + 1.45220i) q^{10} +2.81252 q^{11} +0.370326i q^{12} +4.53408i q^{13} +4.27844 q^{14} +(0.629674 - 0.537789i) q^{15} +1.00000 q^{16} +0.197785i q^{17} +2.86286i q^{18} -2.66000 q^{19} +(-1.45220 - 1.70032i) q^{20} -1.58442 q^{21} +2.81252i q^{22} +0.877793i q^{23} -0.370326 q^{24} +(-0.782203 + 4.93844i) q^{25} -4.53408 q^{26} -2.17117i q^{27} +4.27844i q^{28} +7.47252 q^{29} +(0.537789 + 0.629674i) q^{30} -1.00000 q^{31} +1.00000i q^{32} -1.04155i q^{33} -0.197785 q^{34} +(7.27474 - 6.21317i) q^{35} -2.86286 q^{36} -5.87409i q^{37} -2.66000i q^{38} +1.67909 q^{39} +(1.70032 - 1.45220i) q^{40} -8.99908 q^{41} -1.58442i q^{42} +5.71033i q^{43} -2.81252 q^{44} +(4.15746 + 4.86779i) q^{45} -0.877793 q^{46} -10.0873i q^{47} -0.370326i q^{48} -11.3051 q^{49} +(-4.93844 - 0.782203i) q^{50} +0.0732449 q^{51} -4.53408i q^{52} -0.206568i q^{53} +2.17117 q^{54} +(4.08436 + 4.78220i) q^{55} -4.27844 q^{56} +0.985065i q^{57} +7.47252i q^{58} -4.55688 q^{59} +(-0.629674 + 0.537789i) q^{60} -5.96876 q^{61} -1.00000i q^{62} -12.2486i q^{63} -1.00000 q^{64} +(-7.70941 + 6.58442i) q^{65} +1.04155 q^{66} +5.70571i q^{67} -0.197785i q^{68} +0.325070 q^{69} +(6.21317 + 7.27474i) q^{70} -8.06064 q^{71} -2.86286i q^{72} -14.8079i q^{73} +5.87409 q^{74} +(1.82883 + 0.289670i) q^{75} +2.66000 q^{76} -12.0332i q^{77} +1.67909i q^{78} -1.97754 q^{79} +(1.45220 + 1.70032i) q^{80} +7.78454 q^{81} -8.99908i q^{82} -0.554096i q^{83} +1.58442 q^{84} +(-0.336299 + 0.287224i) q^{85} -5.71033 q^{86} -2.76727i q^{87} -2.81252i q^{88} -12.0532 q^{89} +(-4.86779 + 4.15746i) q^{90} +19.3988 q^{91} -0.877793i q^{92} +0.370326i q^{93} +10.0873 q^{94} +(-3.86286 - 4.52285i) q^{95} +0.370326 q^{96} -1.88287i q^{97} -11.3051i q^{98} +8.05186 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9} + 2 q^{10} - 16 q^{11} + 12 q^{14} + 16 q^{15} + 8 q^{16} - 12 q^{19} + 2 q^{20} - 4 q^{21} + 8 q^{24} + 12 q^{25} - 20 q^{26} + 12 q^{29} + 4 q^{30} - 8 q^{31} + 8 q^{34} + 20 q^{35} + 8 q^{36} - 40 q^{39} - 2 q^{40} + 16 q^{44} + 30 q^{45} - 16 q^{46} - 32 q^{49} - 8 q^{50} - 44 q^{51} + 44 q^{54} + 36 q^{55} - 12 q^{56} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 8 q^{64} + 12 q^{65} + 12 q^{66} - 28 q^{69} - 20 q^{70} - 24 q^{71} + 40 q^{74} - 12 q^{75} + 12 q^{76} + 32 q^{79} - 2 q^{80} + 88 q^{81} + 4 q^{84} + 4 q^{85} - 44 q^{86} - 24 q^{89} - 34 q^{90} - 20 q^{91} + 4 q^{94} - 8 q^{96} + 20 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9 + 2 * q^10 - 16 * q^11 + 12 * q^14 + 16 * q^15 + 8 * q^16 - 12 * q^19 + 2 * q^20 - 4 * q^21 + 8 * q^24 + 12 * q^25 - 20 * q^26 + 12 * q^29 + 4 * q^30 - 8 * q^31 + 8 * q^34 + 20 * q^35 + 8 * q^36 - 40 * q^39 - 2 * q^40 + 16 * q^44 + 30 * q^45 - 16 * q^46 - 32 * q^49 - 8 * q^50 - 44 * q^51 + 44 * q^54 + 36 * q^55 - 12 * q^56 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 8 * q^64 + 12 * q^65 + 12 * q^66 - 28 * q^69 - 20 * q^70 - 24 * q^71 + 40 * q^74 - 12 * q^75 + 12 * q^76 + 32 * q^79 - 2 * q^80 + 88 * q^81 + 4 * q^84 + 4 * q^85 - 44 * q^86 - 24 * q^89 - 34 * q^90 - 20 * q^91 + 4 * q^94 - 8 * q^96 + 20 * q^99

Introduction

L-functions

Modular forms

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Database

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