LMFDB - Embedded newform 308.2.j.c.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(113,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("308.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 11x^{10} - 18x^{9} + 48x^{8} - 22x^{7} + 80x^{6} + 68x^{5} + 26x^{4} - 24x^{3} + 9x^{2} + 1 $ x^12 - 4x^11 + 11x^10 - 18x^9 + 48x^8 - 22x^7 + 80x^6 + 68x^5 + 26x^4 - 24x^3 + 9x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			169.2
Root			$-0.632917 + 0.459841i$ of defining polynomial
Character	$\chi$	$=$	308.169
Dual form			308.2.j.c.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.153244 - 0.471635i) q^{3} +(-0.489968 + 0.355982i) q^{5} +(0.309017 + 0.951057i) q^{7} +(2.22809 + 1.61881i) q^{9} +O(q^{10})$	\(q+(0.153244 - 0.471635i) q^{3} +(-0.489968 + 0.355982i) q^{5} +(0.309017 + 0.951057i) q^{7} +(2.22809 + 1.61881i) q^{9} +(3.31235 - 0.168355i) q^{11} +(0.540314 + 0.392561i) q^{13} +(0.0928094 + 0.285638i) q^{15} +(4.47905 - 3.25422i) q^{17} +(0.917225 - 2.82293i) q^{19} +0.495906 q^{21} -2.32688 q^{23} +(-1.43174 + 4.40644i) q^{25} +(2.30852 - 1.67724i) q^{27} +(1.81530 + 5.58691i) q^{29} +(-5.67310 - 4.12175i) q^{31} +(0.428194 - 1.58802i) q^{33} +(-0.489968 - 0.355982i) q^{35} +(-2.54331 - 7.82751i) q^{37} +(0.267945 - 0.194674i) q^{39} +(-3.71790 + 11.4425i) q^{41} +2.96660 q^{43} -1.66796 q^{45} +(-0.388716 + 1.19634i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-0.848418 - 2.61116i) q^{51} +(4.12697 + 2.99842i) q^{53} +(-1.56301 + 1.26163i) q^{55} +(-1.19083 - 0.865191i) q^{57} +(-3.59521 - 11.0649i) q^{59} +(-5.14826 + 3.74043i) q^{61} +(-0.851057 + 2.61928i) q^{63} -0.404481 q^{65} -13.4756 q^{67} +(-0.356579 + 1.09744i) q^{69} +(-3.35131 + 2.43487i) q^{71} +(-2.80193 - 8.62345i) q^{73} +(1.85883 + 1.35052i) q^{75} +(1.18369 + 3.09821i) q^{77} +(-5.81466 - 4.22460i) q^{79} +(2.11589 + 6.51204i) q^{81} +(6.26356 - 4.55074i) q^{83} +(-1.03614 + 3.18892i) q^{85} +2.91317 q^{87} -2.56565 q^{89} +(-0.206382 + 0.635178i) q^{91} +(-2.81333 + 2.04400i) q^{93} +(0.555502 + 1.70966i) q^{95} +(-2.93190 - 2.13015i) q^{97} +(7.65276 + 4.98694i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9	$ 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9} + 2 q^{11} - 7 q^{13} - 4 q^{15} + 3 q^{17} - 23 q^{19} - 4 q^{21} - 38 q^{23} + 2 q^{25} - 18 q^{27} + 29 q^{29} + 9 q^{31} - 4 q^{33} + q^{35} + 3 q^{37} + 25 q^{39} - 18 q^{41} + 34 q^{43} + 14 q^{45} + 9 q^{47} - 3 q^{49} + 35 q^{51} + 13 q^{53} + 16 q^{55} + 9 q^{57} - 17 q^{59} - 19 q^{61} - 9 q^{63} + 8 q^{65} - 20 q^{67} - 14 q^{69} + 15 q^{71} + 9 q^{73} - 47 q^{75} - 8 q^{77} - 14 q^{79} - 49 q^{81} + 41 q^{83} - 66 q^{85} + 40 q^{87} + 34 q^{89} + 13 q^{91} - 40 q^{93} + 42 q^{95} - 10 q^{97} - 24 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9 + 2 * q^11 - 7 * q^13 - 4 * q^15 + 3 * q^17 - 23 * q^19 - 4 * q^21 - 38 * q^23 + 2 * q^25 - 18 * q^27 + 29 * q^29 + 9 * q^31 - 4 * q^33 + q^35 + 3 * q^37 + 25 * q^39 - 18 * q^41 + 34 * q^43 + 14 * q^45 + 9 * q^47 - 3 * q^49 + 35 * q^51 + 13 * q^53 + 16 * q^55 + 9 * q^57 - 17 * q^59 - 19 * q^61 - 9 * q^63 + 8 * q^65 - 20 * q^67 - 14 * q^69 + 15 * q^71 + 9 * q^73 - 47 * q^75 - 8 * q^77 - 14 * q^79 - 49 * q^81 + 41 * q^83 - 66 * q^85 + 40 * q^87 + 34 * q^89 + 13 * q^91 - 40 * q^93 + 42 * q^95 - 10 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.153244	−	0.471635i	0.0884752	−	0.272299i	−0.897023	−	0.441983i	$-0.854275\pi$
$3$	0.153244	−	0.471635i	0.0884752	−	0.272299i	0.985498	+	0.169685i	$0.0542750\pi$
$4$		0			0
$5$	−0.489968	+	0.355982i	−0.219120	+	0.159200i	−0.691931	−	0.721964i	$-0.743240\pi$
$5$	−0.489968	+	0.355982i	−0.219120	+	0.159200i	0.472810	+	0.881164i	$0.343240\pi$
$6$		0			0
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$		0			0
$9$	2.22809	+	1.61881i	0.742698	+	0.539602i
$10$		0			0
$11$	3.31235	−	0.168355i	0.998711	−	0.0507609i
$11$	3.31235	−	0.168355i	0.998711	−	0.0507609i
$12$		0			0
$13$	0.540314	+	0.392561i	0.149856	+	0.108877i	0.660187	−	0.751101i	$-0.270477\pi$
$13$	0.540314	+	0.392561i	0.149856	+	0.108877i	−0.510331	+	0.859978i	$0.670477\pi$
$14$		0			0
$15$	0.0928094	+	0.285638i	0.0239633	+	0.0737514i
$16$		0			0
$17$	4.47905	−	3.25422i	1.08633	−	0.789264i	0.107553	−	0.994199i	$-0.465699\pi$
$17$	4.47905	−	3.25422i	1.08633	−	0.789264i	0.978775	+	0.204936i	$0.0656985\pi$
$18$		0			0
$19$	0.917225	−	2.82293i	0.210426	−	0.647624i	−0.789021	−	0.614366i	$-0.789412\pi$
$19$	0.917225	−	2.82293i	0.210426	−	0.647624i	0.999447	−	0.0332579i	$-0.0105883\pi$
$20$		0			0
$21$	0.495906			0.108216
$22$		0			0
$23$	−2.32688			−0.485187			−0.242594	−	0.970128i	$-0.577998\pi$
$23$	−2.32688			−0.485187			−0.242594	+	0.970128i	$0.577998\pi$
$24$		0			0
$25$	−1.43174	+	4.40644i	−0.286348	+	0.881289i
$26$		0			0
$27$	2.30852	−	1.67724i	0.444274	−	0.322784i
$28$		0			0
$29$	1.81530	+	5.58691i	0.337092	+	1.03746i	0.965682	+	0.259726i	$0.0836324\pi$
$29$	1.81530	+	5.58691i	0.337092	+	1.03746i	−0.628590	+	0.777737i	$0.716368\pi$
$30$		0			0
$31$	−5.67310	−	4.12175i	−1.01892	−	0.740288i	−0.0528578	−	0.998602i	$-0.516833\pi$
$31$	−5.67310	−	4.12175i	−1.01892	−	0.740288i	−0.966061	+	0.258314i	$0.916833\pi$
$32$		0			0
$33$	0.428194	−	1.58802i	0.0745390	−	0.276439i
$34$		0			0
$35$	−0.489968	−	0.355982i	−0.0828196	−	0.0601720i
$36$		0			0
$37$	−2.54331	−	7.82751i	−0.418118	−	1.28683i	−0.909432	−	0.415852i	$-0.863483\pi$
$37$	−2.54331	−	7.82751i	−0.418118	−	1.28683i	0.491314	−	0.870982i	$-0.336517\pi$
$38$		0			0
$39$	0.267945	−	0.194674i	0.0429056	−	0.0311727i
$40$		0			0
$41$	−3.71790	+	11.4425i	−0.580639	+	1.78702i	0.0354825	+	0.999370i	$0.488703\pi$
$41$	−3.71790	+	11.4425i	−0.580639	+	1.78702i	−0.616121	+	0.787651i	$0.711297\pi$
$42$		0			0
$43$	2.96660			0.452402			0.226201	−	0.974081i	$-0.427369\pi$
$43$	2.96660			0.452402			0.226201	+	0.974081i	$0.427369\pi$
$44$		0			0
$45$	−1.66796			−0.248645
$46$		0			0
$47$	−0.388716	+	1.19634i	−0.0567000	+	0.174505i	−0.975396	−	0.220461i	$-0.929244\pi$
$47$	−0.388716	+	1.19634i	−0.0567000	+	0.174505i	0.918696	+	0.394966i	$0.129244\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$		0			0
$51$	−0.848418	−	2.61116i	−0.118802	−	0.365636i
$52$		0			0
$53$	4.12697	+	2.99842i	0.566883	+	0.411865i	0.833972	−	0.551807i	$-0.186062\pi$
$53$	4.12697	+	2.99842i	0.566883	+	0.411865i	−0.267089	+	0.963672i	$0.586062\pi$
$54$		0			0
$55$	−1.56301	+	1.26163i	−0.210757	+	0.170118i
$56$		0			0
$57$	−1.19083	−	0.865191i	−0.157730	−	0.114597i
$58$		0			0
$59$	−3.59521	−	11.0649i	−0.468056	−	1.44053i	−0.855098	−	0.518466i	$-0.826503\pi$
$59$	−3.59521	−	11.0649i	−0.468056	−	1.44053i	0.387042	−	0.922062i	$-0.373497\pi$
$60$		0			0
$61$	−5.14826	+	3.74043i	−0.659167	+	0.478913i	−0.866382	−	0.499383i	$-0.833560\pi$
$61$	−5.14826	+	3.74043i	−0.659167	+	0.478913i	0.207214	+	0.978296i	$0.433560\pi$
$62$		0			0
$63$	−0.851057	+	2.61928i	−0.107223	+	0.329999i
$64$		0			0
$65$	−0.404481			−0.0501697
$66$		0			0
$67$	−13.4756			−1.64631			−0.823154	−	0.567818i	$-0.807788\pi$
$67$	−13.4756			−1.64631			−0.823154	+	0.567818i	$0.807788\pi$
$68$		0			0
$69$	−0.356579	+	1.09744i	−0.0429270	+	0.132116i
$70$		0			0
$71$	−3.35131	+	2.43487i	−0.397728	+	0.288966i	−0.768615	−	0.639712i	$-0.779054\pi$
$71$	−3.35131	+	2.43487i	−0.397728	+	0.288966i	0.370887	+	0.928678i	$0.379054\pi$
$72$		0			0
$73$	−2.80193	−	8.62345i	−0.327941	−	1.00930i	−0.970096	−	0.242723i	$-0.921959\pi$
$73$	−2.80193	−	8.62345i	−0.327941	−	1.00930i	0.642155	−	0.766575i	$-0.278041\pi$
$74$		0			0
$75$	1.85883	+	1.35052i	0.214639	+	0.155944i
$76$		0			0
$77$	1.18369	+	3.09821i	0.134894	+	0.353073i
$78$		0			0
$79$	−5.81466	−	4.22460i	−0.654201	−	0.475305i	0.210499	−	0.977594i	$-0.432491\pi$
$79$	−5.81466	−	4.22460i	−0.654201	−	0.475305i	−0.864700	+	0.502290i	$0.832491\pi$
$80$		0			0
$81$	2.11589	+	6.51204i	0.235099	+	0.723561i
$82$		0			0
$83$	6.26356	−	4.55074i	0.687515	−	0.499509i	−0.188327	−	0.982106i	$-0.560307\pi$
$83$	6.26356	−	4.55074i	0.687515	−	0.499509i	0.875842	+	0.482598i	$0.160307\pi$
$84$		0			0
$85$	−1.03614	+	3.18892i	−0.112386	+	0.345887i
$86$		0			0
$87$	2.91317			0.312324
$88$		0			0
$89$	−2.56565			−0.271958			−0.135979	−	0.990712i	$-0.543418\pi$
$89$	−2.56565			−0.271958			−0.135979	+	0.990712i	$0.543418\pi$
$90$		0			0
$91$	−0.206382	+	0.635178i	−0.0216347	+	0.0665847i
$92$		0			0
$93$	−2.81333	+	2.04400i	−0.291728	+	0.211953i
$94$		0			0
$95$	0.555502	+	1.70966i	0.0569933	+	0.175407i
$96$		0			0
$97$	−2.93190	−	2.13015i	−0.297690	−	0.216284i	0.428907	−	0.903349i	$-0.358899\pi$
$97$	−2.93190	−	2.13015i	−0.297690	−	0.216284i	−0.726596	+	0.687065i	$0.758899\pi$
$98$		0			0
$99$	7.65276	+	4.98694i	0.769131	+	0.501206i
$100$		0			0
$101$	−8.26268	−	6.00319i	−0.822167	−	0.597340i	0.0951652	−	0.995461i	$-0.469662\pi$
$101$	−8.26268	−	6.00319i	−0.822167	−	0.597340i	−0.917332	+	0.398122i	$0.869662\pi$
$102$		0			0
$103$	−5.82358	−	17.9231i	−0.573815	−	1.76602i	−0.640181	−	0.768224i	$-0.721141\pi$
$103$	−5.82358	−	17.9231i	−0.573815	−	1.76602i	0.0663663	−	0.997795i	$-0.478859\pi$
$104$		0			0
$105$	−0.242978	+	0.176534i	−0.0237122	+	0.0172279i
$106$		0			0
$107$	1.85402	−	5.70609i	0.179235	−	0.551628i	−0.820567	−	0.571551i	$-0.806342\pi$
$107$	1.85402	−	5.70609i	0.179235	−	0.551628i	0.999802	+	0.0199225i	$0.00634196\pi$
$108$		0			0
$109$	9.87230			0.945595			0.472797	−	0.881171i	$-0.343244\pi$
$109$	9.87230			0.945595			0.472797	+	0.881171i	$0.343244\pi$
$110$		0			0
$111$	−4.08147			−0.387396
$112$		0			0
$113$	−5.06939	+	15.6020i	−0.476888	+	1.46771i	0.366505	+	0.930416i	$0.380554\pi$
$113$	−5.06939	+	15.6020i	−0.476888	+	1.46771i	−0.843394	+	0.537296i	$0.819446\pi$
$114$		0			0
$115$	1.14009	−	0.828326i	0.106314	−	0.0772418i
$116$		0			0
$117$	0.568391	+	1.74933i	0.0525478	+	0.161725i
$118$		0			0
$119$	4.47905	+	3.25422i	0.410593	+	0.298314i
$120$		0			0
$121$	10.9433	−	1.11530i	0.994847	−	0.101391i
$122$		0			0
$123$	4.82695	+	3.50699i	0.435232	+	0.316214i
$124$		0			0
$125$	−1.80286	−	5.54865i	−0.161253	−	0.496286i
$126$		0			0
$127$	−2.47340	+	1.79703i	−0.219479	+	0.159461i	−0.692092	−	0.721809i	$-0.743311\pi$
$127$	−2.47340	+	1.79703i	−0.219479	+	0.159461i	0.472613	+	0.881270i	$0.343311\pi$
$128$		0			0
$129$	0.454612	−	1.39915i	0.0400264	−	0.123188i
$130$		0			0
$131$	12.0816			1.05558			0.527788	−	0.849376i	$-0.323022\pi$
$131$	12.0816			1.05558			0.527788	+	0.849376i	$0.323022\pi$
$132$		0			0
$133$	2.96820			0.257376
$134$		0			0
$135$	−0.534032	+	1.64358i	−0.0459622	+	0.141457i
$136$		0			0
$137$	2.71843	−	1.97506i	0.232252	−	0.168741i	−0.465573	−	0.885010i	$-0.654152\pi$
$137$	2.71843	−	1.97506i	0.232252	−	0.168741i	0.697824	+	0.716269i	$0.254152\pi$
$138$		0			0
$139$	3.54405	+	10.9075i	0.300603	+	0.925160i	0.981282	+	0.192578i	$0.0616848\pi$
$139$	3.54405	+	10.9075i	0.300603	+	0.925160i	−0.680679	+	0.732582i	$0.738315\pi$
$140$		0			0
$141$	0.504670	+	0.366664i	0.0425009	+	0.0308787i
$142$		0			0
$143$	1.85580	+	1.20934i	0.155190	+	0.101130i
$144$		0			0
$145$	−2.87828	−	2.09119i	−0.239028	−	0.173664i
$146$		0			0
$147$	0.153244	+	0.471635i	0.0126393	+	0.0388998i
$148$		0			0
$149$	10.8289	−	7.86767i	0.887140	−	0.644545i	−0.0479907	−	0.998848i	$-0.515282\pi$
$149$	10.8289	−	7.86767i	0.887140	−	0.644545i	0.935131	+	0.354303i	$0.115282\pi$
$150$		0			0
$151$	−6.33216	+	19.4884i	−0.515304	+	1.58594i	0.267425	+	0.963579i	$0.413827\pi$
$151$	−6.33216	+	19.4884i	−0.515304	+	1.58594i	−0.782729	+	0.622363i	$0.786173\pi$
$152$		0			0
$153$	15.2477			1.23270
$154$		0			0
$155$	4.24690			0.341120
$156$		0			0
$157$	3.65890	−	11.2609i	0.292012	−	0.898720i	−0.692197	−	0.721709i	$-0.743357\pi$
$157$	3.65890	−	11.2609i	0.292012	−	0.898720i	0.984209	−	0.177011i	$-0.0566429\pi$
$158$		0			0
$159$	2.04659	−	1.48694i	0.162305	−	0.117922i
$160$		0			0
$161$	−0.719044	−	2.21299i	−0.0566686	−	0.174408i
$162$		0			0
$163$	−1.87247	−	1.36043i	−0.146664	−	0.106557i	0.512034	−	0.858965i	$-0.328892\pi$
$163$	−1.87247	−	1.36043i	−0.146664	−	0.106557i	−0.658697	+	0.752408i	$0.728892\pi$
$164$		0			0
$165$	0.355506	+	0.930507i	0.0276761	+	0.0724399i
$166$		0			0
$167$	9.39096	+	6.82293i	0.726694	+	0.527974i	0.888516	−	0.458846i	$-0.151737\pi$
$167$	9.39096	+	6.82293i	0.726694	+	0.527974i	−0.161822	+	0.986820i	$0.551737\pi$
$168$		0			0
$169$	−3.87939	−	11.9395i	−0.298414	−	0.918425i
$170$		0			0
$171$	6.61344	−	4.80494i	0.505742	−	0.367443i
$172$		0			0
$173$	−4.04113	+	12.4373i	−0.307242	+	0.945593i	0.671590	+	0.740923i	$0.265612\pi$
$173$	−4.04113	+	12.4373i	−0.307242	+	0.945593i	−0.978831	+	0.204669i	$0.934388\pi$
$174$		0			0
$175$	−4.63321			−0.350238
$176$		0			0
$177$	−5.76954			−0.433665
$178$		0			0
$179$	0.320191	−	0.985447i	0.0239322	−	0.0736558i	−0.938377	−	0.345613i	$-0.887671\pi$
$179$	0.320191	−	0.985447i	0.0239322	−	0.0736558i	0.962309	+	0.271957i	$0.0876710\pi$
$180$		0			0
$181$	−8.50486	+	6.17914i	−0.632161	+	0.459292i	−0.857148	−	0.515070i	$-0.827766\pi$
$181$	−8.50486	+	6.17914i	−0.632161	+	0.459292i	0.224987	+	0.974362i	$0.427766\pi$
$182$		0			0
$183$	0.975181	+	3.00130i	0.0720874	+	0.221862i
$184$		0			0
$185$	4.03260	+	2.92985i	0.296482	+	0.215407i
$186$		0			0
$187$	14.2883	−	11.5332i	1.04486	−	0.843389i
$188$		0			0
$189$	2.30852	+	1.67724i	0.167920	+	0.122001i
$190$		0			0
$191$	2.63870	+	8.12107i	0.190929	+	0.587620i	1.00000		9.12306e-5i	$-2.90396e-5\pi$
$191$	2.63870	+	8.12107i	0.190929	+	0.587620i	−0.809071	+	0.587711i	$0.800029\pi$
$192$		0			0
$193$	11.1751	−	8.11922i	0.804405	−	0.584434i	−0.107798	−	0.994173i	$-0.534380\pi$
$193$	11.1751	−	8.11922i	0.804405	−	0.584434i	0.912203	+	0.409739i	$0.134380\pi$
$194$		0			0
$195$	−0.0619842	+	0.190768i	−0.00443878	+	0.0136612i
$196$		0			0
$197$	17.0552			1.21514			0.607568	−	0.794268i	$-0.292145\pi$
$197$	17.0552			1.21514			0.607568	+	0.794268i	$0.292145\pi$
$198$		0			0
$199$	−16.3332			−1.15783			−0.578916	−	0.815387i	$-0.696524\pi$
$199$	−16.3332			−1.15783			−0.578916	+	0.815387i	$0.696524\pi$
$200$		0			0
$201$	−2.06505	+	6.35557i	−0.145657	+	0.448288i
$202$		0			0
$203$	−4.75251	+	3.45290i	−0.333561	+	0.242346i
$204$		0			0
$205$	−2.25168	−	6.92997i	−0.157264	−	0.484010i
$206$		0			0
$207$	−5.18450	−	3.76676i	−0.360348	−	0.261808i
$208$		0			0
$209$	2.56292	−	9.50494i	0.177281	−	0.657471i
$210$		0			0
$211$	−0.308056	−	0.223816i	−0.0212075	−	0.0154081i	0.577131	−	0.816652i	$-0.304172\pi$
$211$	−0.308056	−	0.223816i	−0.0212075	−	0.0154081i	−0.598339	+	0.801243i	$0.704172\pi$
$212$		0			0
$213$	0.634804	+	1.95373i	0.0434960	+	0.133867i
$214$		0			0
$215$	−1.45354	+	1.05606i	−0.0991304	+	0.0720224i
$216$		0			0
$217$	2.16693	−	6.66913i	0.147101	−	0.452730i
$218$		0			0
$219$	−4.49650			−0.303845
$220$		0			0
$221$	3.69757			0.248726
$222$		0			0
$223$	−4.03142	+	12.4074i	−0.269964	+	0.830863i	0.720544	+	0.693409i	$0.243892\pi$
$223$	−4.03142	+	12.4074i	−0.269964	+	0.830863i	−0.990508	+	0.137454i	$0.956108\pi$
$224$		0			0
$225$	−10.3232	+	7.50026i	−0.688215	+	0.500018i
$226$		0			0
$227$	−0.575912	−	1.77247i	−0.0382246	−	0.117643i	0.930123	−	0.367247i	$-0.119700\pi$
$227$	−0.575912	−	1.77247i	−0.0382246	−	0.117643i	−0.968348	+	0.249604i	$0.919700\pi$
$228$		0			0
$229$	−10.4035	−	7.55855i	−0.687480	−	0.499483i	0.188351	−	0.982102i	$-0.439686\pi$
$229$	−10.4035	−	7.55855i	−0.687480	−	0.499483i	−0.875831	+	0.482618i	$0.839686\pi$
$230$		0			0
$231$	1.64262	−	0.0834882i	0.108076	−	0.00549312i
$232$		0			0
$233$	−9.08514	−	6.60074i	−0.595187	−	0.432429i	0.248980	−	0.968509i	$-0.419905\pi$
$233$	−9.08514	−	6.60074i	−0.595187	−	0.432429i	−0.844167	+	0.536080i	$0.819905\pi$
$234$		0			0
$235$	−0.235419	−	0.724546i	−0.0153571	−	0.0472642i
$236$		0			0
$237$	−2.88353	+	2.09501i	−0.187305	+	0.136085i
$238$		0			0
$239$	1.29138	−	3.97447i	0.0835326	−	0.257087i	−0.900563	−	0.434725i	$-0.856846\pi$
$239$	1.29138	−	3.97447i	0.0835326	−	0.257087i	0.984096	+	0.177638i	$0.0568456\pi$
$240$		0			0
$241$	0.747047			0.0481216			0.0240608	−	0.999710i	$-0.492340\pi$
$241$	0.747047			0.0481216			0.0240608	+	0.999710i	$0.492340\pi$
$242$		0			0
$243$	11.9560			0.766978
$244$		0			0
$245$	0.187151	−	0.575991i	0.0119566	−	0.0367987i
$246$		0			0
$247$	1.60376	−	1.16520i	0.102045	−	0.0741400i
$248$		0			0
$249$	−1.18644	−	3.65149i	−0.0751876	−	0.231404i
$250$		0			0
$251$	0.190238	+	0.138216i	0.0120077	+	0.00872410i	0.593773	−	0.804633i	$-0.297638\pi$
$251$	0.190238	+	0.138216i	0.0120077	+	0.00872410i	−0.581765	+	0.813357i	$0.697638\pi$
$252$		0			0
$253$	−7.70742	+	0.391740i	−0.484562	+	0.0246285i
$254$		0			0
$255$	1.34523	+	0.977363i	0.0842413	+	0.0612049i
$256$		0			0
$257$	−2.91069	−	8.95818i	−0.181564	−	0.558796i	0.818308	−	0.574779i	$-0.194912\pi$
$257$	−2.91069	−	8.95818i	−0.181564	−	0.558796i	−0.999872	+	0.0159833i	$0.994912\pi$
$258$		0			0
$259$	6.65848	−	4.83767i	0.413738	−	0.300598i
$260$		0			0
$261$	−4.99947	+	15.3868i	−0.309459	+	0.952418i
$262$		0			0
$263$	−15.6464			−0.964797			−0.482399	−	0.875952i	$-0.660234\pi$
$263$	−15.6464			−0.964797			−0.482399	+	0.875952i	$0.660234\pi$
$264$		0			0
$265$	−3.08947			−0.189784
$266$		0			0
$267$	−0.393169	+	1.21005i	−0.0240616	+	0.0740539i
$268$		0			0
$269$	−2.85951	+	2.07756i	−0.174348	+	0.126671i	−0.671537	−	0.740971i	$-0.734365\pi$
$269$	−2.85951	+	2.07756i	−0.174348	+	0.126671i	0.497189	+	0.867642i	$0.334365\pi$
$270$		0			0
$271$	7.42841	+	22.8623i	0.451244	+	1.38879i	0.875489	+	0.483239i	$0.160540\pi$
$271$	7.42841	+	22.8623i	0.451244	+	1.38879i	−0.424245	+	0.905548i	$0.639460\pi$
$272$		0			0
$273$	0.267945	+	0.194674i	0.0162168	+	0.0117822i
$274$		0			0
$275$	−4.00058	+	14.8367i	−0.241244	+	0.894688i
$276$		0			0
$277$	−22.9358	−	16.6639i	−1.37808	−	1.00123i	−0.997057	−	0.0766684i	$-0.975572\pi$
$277$	−22.9358	−	16.6639i	−1.37808	−	1.00123i	−0.381023	−	0.924565i	$-0.624428\pi$
$278$		0			0
$279$	−5.96790	−	18.3673i	−0.357289	−	1.09962i
$280$		0			0
$281$	−7.51781	+	5.46201i	−0.448475	+	0.325836i	−0.788993	−	0.614402i	$-0.789397\pi$
$281$	−7.51781	+	5.46201i	−0.448475	+	0.325836i	0.340518	+	0.940238i	$0.389397\pi$
$282$		0			0
$283$	−1.83203	+	5.63842i	−0.108903	+	0.335169i	−0.990627	−	0.136597i	$-0.956383\pi$
$283$	−1.83203	+	5.63842i	−0.108903	+	0.335169i	0.881724	+	0.471766i	$0.156383\pi$
$284$		0			0
$285$	0.891462			0.0528057
$286$		0			0
$287$	−12.0314			−0.710190
$288$		0			0
$289$	4.21863	−	12.9836i	0.248155	−	0.763742i
$290$		0			0
$291$	−1.45395	+	1.05636i	−0.0852320	+	0.0619247i
$292$		0			0
$293$	−5.73103	−	17.6383i	−0.334810	−	1.03044i	−0.966815	−	0.255476i	$-0.917768\pi$
$293$	−5.73103	−	17.6383i	−0.334810	−	1.03044i	0.632005	−	0.774964i	$-0.282232\pi$
$294$		0			0
$295$	5.70044	+	4.14161i	0.331893	+	0.241134i
$296$		0			0
$297$	7.36424	−	5.94424i	0.427317	−	0.344920i
$298$		0			0
$299$	−1.25724	−	0.913441i	−0.0727083	−	0.0528257i
$300$		0			0
$301$	0.916729	+	2.82140i	0.0528394	+	0.162623i
$302$		0			0
$303$	−4.09752	+	2.97702i	−0.235396	+	0.171025i
$304$		0			0
$305$	1.19095	−	3.66538i	0.0681938	−	0.209879i
$306$		0			0
$307$	−9.50268			−0.542347			−0.271173	−	0.962531i	$-0.587412\pi$
$307$	−9.50268			−0.542347			−0.271173	+	0.962531i	$0.587412\pi$
$308$		0			0
$309$	−9.34561			−0.531653
$310$		0			0
$311$	−10.5496	+	32.4684i	−0.598213	+	1.84111i	−0.0601812	+	0.998187i	$0.519168\pi$
$311$	−10.5496	+	32.4684i	−0.598213	+	1.84111i	−0.538032	+	0.842924i	$0.680832\pi$
$312$		0			0
$313$	−15.3125	+	11.1252i	−0.865513	+	0.628832i	−0.929379	−	0.369127i	$-0.879657\pi$
$313$	−15.3125	+	11.1252i	−0.865513	+	0.628832i	0.0638665	+	0.997958i	$0.479657\pi$
$314$		0			0
$315$	−0.515428	−	1.58632i	−0.0290411	−	0.0893793i
$316$		0			0
$317$	18.9122	+	13.7405i	1.06222	+	0.771745i	0.974497	−	0.224400i	$-0.0720422\pi$
$317$	18.9122	+	13.7405i	1.06222	+	0.771745i	0.0877192	+	0.996145i	$0.472042\pi$
$318$		0			0
$319$	6.95348	+	18.2002i	0.389320	+	1.01901i
$320$		0			0
$321$	−2.40707	−	1.74884i	−0.134350	−	0.0976109i
$322$		0			0
$323$	−5.07813	−	15.6289i	−0.282555	−	0.869614i
$324$		0			0
$325$	−2.50339	+	1.81882i	−0.138863	+	0.100890i
$326$		0			0
$327$	1.51287	−	4.65612i	0.0836617	−	0.257484i
$328$		0			0
$329$	−1.25791			−0.0693509
$330$		0			0
$331$	−13.5260			−0.743455			−0.371727	−	0.928342i	$-0.621234\pi$
$331$	−13.5260			−0.743455			−0.371727	+	0.928342i	$0.621234\pi$
$332$		0			0
$333$	7.00448	−	21.5576i	0.383843	−	1.18135i
$334$		0			0
$335$	6.60262	−	4.79708i	0.360739	−	0.262093i
$336$		0			0
$337$	−7.58300	−	23.3381i	−0.413072	−	1.27131i	−0.913964	−	0.405796i	$-0.866995\pi$
$337$	−7.58300	−	23.3381i	−0.413072	−	1.27131i	0.500892	−	0.865510i	$-0.333005\pi$
$338$		0			0
$339$	6.58159	+	4.78181i	0.357463	+	0.259712i
$340$		0			0
$341$	−19.4852	−	12.6976i	−1.05518	−	0.687612i
$342$		0			0
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$		0			0
$345$	−0.215956	−	0.664644i	−0.0116267	−	0.0357832i
$346$		0			0
$347$	10.1233	−	7.35501i	0.543447	−	0.394838i	−0.281916	−	0.959439i	$-0.590970\pi$
$347$	10.1233	−	7.35501i	0.543447	−	0.394838i	0.825364	+	0.564601i	$0.190970\pi$
$348$		0			0
$349$	−0.330208	+	1.01628i	−0.0176756	+	0.0544000i	−0.959505	−	0.281691i	$-0.909105\pi$
$349$	−0.330208	+	1.01628i	−0.0176756	+	0.0544000i	0.941830	+	0.336091i	$0.109105\pi$
$350$		0			0
$351$	1.90574			0.101721
$352$		0			0
$353$	6.17258			0.328533			0.164267	−	0.986416i	$-0.447474\pi$
$353$	6.17258			0.328533			0.164267	+	0.986416i	$0.447474\pi$
$354$		0			0
$355$	0.775264	−	2.38602i	0.0411467	−	0.126637i
$356$		0			0
$357$	2.22119	−	1.61379i	0.117558	−	0.0854107i
$358$		0			0
$359$	3.05072	+	9.38914i	0.161011	+	0.495540i	0.998720	−	0.0505762i	$-0.0161058\pi$
$359$	3.05072	+	9.38914i	0.161011	+	0.495540i	−0.837710	+	0.546116i	$0.816106\pi$
$360$		0			0
$361$	8.24370	+	5.98940i	0.433879	+	0.315231i
$362$		0			0
$363$	1.15098	−	5.33216i	0.0604107	−	0.279866i
$364$		0			0
$365$	4.44265	+	3.22777i	0.232539	+	0.168949i
$366$		0			0
$367$	5.86741	+	18.0580i	0.306276	+	0.942621i	0.979198	+	0.202907i	$0.0650390\pi$
$367$	5.86741	+	18.0580i	0.306276	+	0.942621i	−0.672922	+	0.739714i	$0.734961\pi$
$368$		0			0
$369$	−26.8071	+	19.4765i	−1.39552	+	1.01390i
$370$		0			0
$371$	−1.57636	+	4.85155i	−0.0818407	+	0.251880i
$372$		0			0
$373$	11.0416			0.571711			0.285855	−	0.958273i	$-0.407722\pi$
$373$	11.0416			0.571711			0.285855	+	0.958273i	$0.407722\pi$
$374$		0			0
$375$	−2.89321			−0.149405
$376$		0			0
$377$	−1.21237	+	3.73130i	−0.0624404	+	0.192172i
$378$		0			0
$379$	30.5012	−	22.1604i	1.56674	−	1.13830i	0.636544	−	0.771240i	$-0.280363\pi$
$379$	30.5012	−	22.1604i	1.56674	−	1.13830i	0.930196	−	0.367063i	$-0.119637\pi$
$380$		0			0
$381$	0.468510	+	1.44193i	0.0240025	+	0.0738721i
$382$		0			0
$383$	−9.44477	−	6.86203i	−0.482605	−	0.350633i	0.319728	−	0.947509i	$-0.396408\pi$
$383$	−9.44477	−	6.86203i	−0.482605	−	0.350633i	−0.802333	+	0.596876i	$0.796408\pi$
$384$		0			0
$385$	−1.68287	−	1.09665i	−0.0857672	−	0.0558904i
$386$		0			0
$387$	6.60986	+	4.80235i	0.335998	+	0.244117i
$388$		0			0
$389$	2.01485	+	6.20107i	0.102157	+	0.314407i	0.989053	−	0.147563i	$-0.0471429\pi$
$389$	2.01485	+	6.20107i	0.102157	+	0.314407i	−0.886896	+	0.461970i	$0.847143\pi$
$390$		0			0
$391$	−10.4222	+	7.57216i	−0.527072	+	0.382940i
$392$		0			0
$393$	1.85143	−	5.69812i	0.0933923	−	0.287432i
$394$		0			0
$395$	4.35288			0.219017
$396$		0			0
$397$	31.2840			1.57010			0.785049	−	0.619434i	$-0.212638\pi$
$397$	31.2840			1.57010			0.785049	+	0.619434i	$0.212638\pi$
$398$		0			0
$399$	0.454858	−	1.39991i	0.0227714	−	0.0700831i
$400$		0			0
$401$	−8.28927	+	6.02251i	−0.413947	+	0.300750i	−0.775198	−	0.631719i	$-0.782350\pi$
$401$	−8.28927	+	6.02251i	−0.413947	+	0.300750i	0.361251	+	0.932469i	$0.382350\pi$
$402$		0			0
$403$	−1.44722	−	4.45408i	−0.0720911	−	0.221874i
$404$		0			0
$405$	−3.35489	−	2.43747i	−0.166706	−	0.121119i
$406$		0			0
$407$	−9.74214	−	25.4993i	−0.482900	−	1.26395i
$408$		0			0
$409$	24.7392	+	17.9741i	1.22327	+	0.888761i	0.996368	−	0.0851560i	$-0.0271389\pi$
$409$	24.7392	+	17.9741i	1.22327	+	0.888761i	0.226906	+	0.973917i	$0.427139\pi$
$410$		0			0
$411$	−0.514924	−	1.58477i	−0.0253993	−	0.0781711i
$412$		0			0
$413$	9.41237	−	6.83849i	0.463152	−	0.336500i
$414$		0			0
$415$	−1.44896	+	4.45943i	−0.0711265	+	0.218905i
$416$		0			0
$417$	5.68745			0.278516
$418$		0			0
$419$	16.9127			0.826241			0.413121	−	0.910676i	$-0.364439\pi$
$419$	16.9127			0.826241			0.413121	+	0.910676i	$0.364439\pi$
$420$		0			0
$421$	2.81872	−	8.67512i	0.137376	−	0.422800i	−0.858576	−	0.512686i	$-0.828650\pi$
$421$	2.81872	−	8.67512i	0.137376	−	0.422800i	0.995952	+	0.0898866i	$0.0286505\pi$
$422$		0			0
$423$	−2.80274	+	2.03631i	−0.136274	+	0.0990089i
$424$		0			0
$425$	7.92669	+	24.3959i	0.384501	+	1.18337i
$426$		0			0
$427$	−5.14826	−	3.74043i	−0.249142	−	0.181012i
$428$		0			0
$429$	0.854754	−	0.689937i	0.0412679	−	0.0333105i
$430$		0			0
$431$	−23.3163	−	16.9403i	−1.12311	−	0.815986i	−0.138431	−	0.990372i	$-0.544206\pi$
$431$	−23.3163	−	16.9403i	−1.12311	−	0.815986i	−0.984677	+	0.174386i	$0.944206\pi$
$432$		0			0
$433$	5.16127	+	15.8848i	0.248035	+	0.763373i	0.995122	+	0.0986471i	$0.0314515\pi$
$433$	5.16127	+	15.8848i	0.248035	+	0.763373i	−0.747088	+	0.664726i	$0.768549\pi$
$434$		0			0
$435$	−1.42736	+	1.03704i	−0.0684365	+	0.0497220i
$436$		0			0
$437$	−2.13427	+	6.56860i	−0.102096	+	0.314219i
$438$		0			0
$439$	14.2354			0.679420			0.339710	−	0.940530i	$-0.389671\pi$
$439$	14.2354			0.679420			0.339710	+	0.940530i	$0.389671\pi$
$440$		0			0
$441$	−2.75408			−0.131147
$442$		0			0
$443$	−0.814765	+	2.50759i	−0.0387107	+	0.119139i	−0.968544	−	0.248841i	$-0.919950\pi$
$443$	−0.814765	+	2.50759i	−0.0387107	+	0.119139i	0.929834	+	0.367980i	$0.119950\pi$
$444$		0			0
$445$	1.25708	−	0.913326i	0.0595915	−	0.0432958i
$446$		0			0
$447$	−2.05121	−	6.31297i	−0.0970188	−	0.298593i
$448$		0			0
$449$	−28.4872	−	20.6972i	−1.34440	−	0.976761i	−0.999270	−	0.0382041i	$-0.987836\pi$
$449$	−28.4872	−	20.6972i	−1.34440	−	0.976761i	−0.345126	−	0.938556i	$-0.612164\pi$
$450$		0			0
$451$	−10.3886	+	38.5276i	−0.489179	+	1.81419i
$452$		0			0
$453$	8.22104	+	5.97294i	0.386258	+	0.280633i
$454$		0			0
$455$	−0.124992	−	0.384685i	−0.00585970	−	0.0180343i
$456$		0			0
$457$	27.9916	−	20.3371i	1.30939	−	0.951328i	0.309390	−	0.950935i	$-0.399875\pi$
$457$	27.9916	−	20.3371i	1.30939	−	0.951328i	1.00000		0.000392360i	$-0.000124892\pi$
$458$		0			0
$459$	4.88186	−	15.0248i	0.227866	−	0.701299i
$460$		0			0
$461$	−9.43624			−0.439490			−0.219745	−	0.975557i	$-0.570522\pi$
$461$	−9.43624			−0.439490			−0.219745	+	0.975557i	$0.570522\pi$
$462$		0			0
$463$	14.9810			0.696226			0.348113	−	0.937453i	$-0.386823\pi$
$463$	14.9810			0.696226			0.348113	+	0.937453i	$0.386823\pi$
$464$		0			0
$465$	0.650811	−	2.00299i	0.0301806	−	0.0928864i
$466$		0			0
$467$	32.8173	−	23.8432i	1.51860	−	1.10333i	0.556431	−	0.830894i	$-0.312170\pi$
$467$	32.8173	−	23.8432i	1.51860	−	1.10333i	0.962174	−	0.272437i	$-0.0878298\pi$
$468$		0			0
$469$	−4.16419	−	12.8161i	−0.192285	−	0.591791i
$470$		0			0
$471$	−4.75035	−	3.45133i	−0.218884	−	0.159029i
$472$		0			0
$473$	9.82641	−	0.499441i	0.451819	−	0.0229643i
$474$		0			0
$475$	11.1258	+	8.08340i	0.510489	+	0.370892i
$476$		0			0
$477$	4.34142	+	13.3615i	0.198780	+	0.611782i
$478$		0			0
$479$	16.7583	−	12.1756i	0.765705	−	0.556318i	−0.134950	−	0.990852i	$-0.543087\pi$
$479$	16.7583	−	12.1756i	0.765705	−	0.556318i	0.900655	+	0.434535i	$0.143087\pi$
$480$		0			0
$481$	1.69859	−	5.22772i	0.0774490	−	0.238364i
$482$		0			0
$483$	−1.15391			−0.0525048
$484$		0			0
$485$	2.19483			0.0996622
$486$		0			0
$487$	2.03922	−	6.27607i	0.0924059	−	0.284396i	−0.894163	−	0.447741i	$-0.852228\pi$
$487$	2.03922	−	6.27607i	0.0924059	−	0.284396i	0.986569	+	0.163345i	$0.0522285\pi$
$488$		0			0
$489$	−0.928572	+	0.674647i	−0.0419915	+	0.0305086i
$490$		0			0
$491$	9.86575	+	30.3637i	0.445235	+	1.37029i	0.882226	+	0.470827i	$0.156044\pi$
$491$	9.86575	+	30.3637i	0.445235	+	1.37029i	−0.436990	+	0.899466i	$0.643956\pi$
$492$		0			0
$493$	26.3118	+	19.1167i	1.18503	+	0.860971i
$494$		0			0
$495$	−5.52487	+	0.280809i	−0.248324	+	0.0126214i
$496$		0			0
$497$	−3.35131	−	2.43487i	−0.150327	−	0.109219i
$498$		0			0
$499$	9.46933	+	29.1436i	0.423905	+	1.30465i	0.904039	+	0.427451i	$0.140588\pi$
$499$	9.46933	+	29.1436i	0.423905	+	1.30465i	−0.480133	+	0.877195i	$0.659412\pi$
$500$		0			0
$501$	4.65704	−	3.38353i	0.208061	−	0.151165i
$502$		0			0
$503$	12.8823	−	39.6477i	0.574395	−	1.76781i	−0.0638362	−	0.997960i	$-0.520334\pi$
$503$	12.8823	−	39.6477i	0.574395	−	1.76781i	0.638231	−	0.769845i	$-0.279666\pi$
$504$		0			0
$505$	6.18547			0.275250
$506$		0			0
$507$	−6.22559			−0.276488
$508$		0			0
$509$	−8.37807	+	25.7850i	−0.371351	+	1.14290i	0.574556	+	0.818465i	$0.305175\pi$
$509$	−8.37807	+	25.7850i	−0.371351	+	1.14290i	−0.945907	+	0.324437i	$0.894825\pi$
$510$		0			0
$511$	7.33554	−	5.32958i	0.324505	−	0.235767i
$512$		0			0
$513$	−2.61729	−	8.05518i	−0.115556	−	0.355645i
$514$		0			0
$515$	9.23369	+	6.70867i	0.406885	+	0.295619i
$516$		0			0
$517$	−1.08615	+	4.02815i	−0.0477689	+	0.177158i
$518$		0			0
$519$	5.24660	+	3.81188i	0.230300	+	0.167323i
$520$		0			0
$521$	7.92004	+	24.3754i	0.346983	+	1.06791i	0.960513	+	0.278234i	$0.0897490\pi$
$521$	7.92004	+	24.3754i	0.346983	+	1.06791i	−0.613530	+	0.789671i	$0.710251\pi$
$522$		0			0
$523$	−29.2151	+	21.2260i	−1.27749	+	0.928148i	−0.999474	−	0.0324292i	$-0.989676\pi$
$523$	−29.2151	+	21.2260i	−1.27749	+	0.928148i	−0.278012	+	0.960577i	$0.589676\pi$
$524$		0			0
$525$	−0.710009	+	2.18518i	−0.0309873	+	0.0953692i
$526$		0			0
$527$	−38.8231			−1.69116
$528$		0			0
$529$	−17.5857			−0.764594
$530$		0			0
$531$	9.90147	−	30.4736i	0.429687	−	1.32244i
$532$		0			0
$533$	−6.50073	+	4.72305i	−0.281578	+	0.204578i
$534$		0			0
$535$	1.12286	+	3.45580i	0.0485453	+	0.149407i
$536$		0			0
$537$	−0.415704	−	0.302027i	−0.0179390	−	0.0130334i
$538$		0			0
$539$	−2.58079	+	2.08315i	−0.111163	+	0.0897277i
$540$		0			0
$541$	20.6470	+	15.0010i	0.887686	+	0.644942i	0.935274	−	0.353926i	$-0.115153\pi$
$541$	20.6470	+	15.0010i	0.887686	+	0.644942i	−0.0475877	+	0.998867i	$0.515153\pi$
$542$		0			0
$543$	1.61099	+	4.95810i	0.0691340	+	0.212773i
$544$		0			0
$545$	−4.83711	+	3.51436i	−0.207199	+	0.150539i
$546$		0			0
$547$	3.70274	−	11.3959i	0.158318	−	0.487252i	−0.840164	−	0.542332i	$-0.817541\pi$
$547$	3.70274	−	11.3959i	0.158318	−	0.487252i	0.998482	+	0.0550802i	$0.0175415\pi$
$548$		0			0
$549$	−17.5258			−0.747985
$550$		0			0
$551$	17.4365			0.742819
$552$		0			0
$553$	2.22100	−	6.83555i	0.0944467	−	0.290677i
$554$		0			0
$555$	1.99979	−	1.45293i	0.0848864	−	0.0616736i
$556$		0			0
$557$	−7.64564	−	23.5309i	−0.323956	−	0.997034i	−0.971910	−	0.235355i	$-0.924375\pi$
$557$	−7.64564	−	23.5309i	−0.323956	−	0.997034i	0.647953	−	0.761680i	$-0.275625\pi$
$558$		0			0
$559$	1.60290	+	1.16457i	0.0677953	+	0.0492561i
$560$		0			0
$561$	−3.24986	−	8.50625i	−0.137209	−	0.359134i
$562$		0			0
$563$	−6.35686	−	4.61853i	−0.267910	−	0.194648i	0.445717	−	0.895174i	$-0.352949\pi$
$563$	−6.35686	−	4.61853i	−0.267910	−	0.194648i	−0.713627	+	0.700526i	$0.752949\pi$
$564$		0			0
$565$	−3.07019	−	9.44908i	−0.129164	−	0.397526i
$566$		0			0
$567$	−5.53948	+	4.02466i	−0.232636	+	0.169020i
$568$		0			0
$569$	−2.20741	+	6.79371i	−0.0925394	+	0.284807i	−0.986605	−	0.163130i	$-0.947841\pi$
$569$	−2.20741	+	6.79371i	−0.0925394	+	0.284807i	0.894065	+	0.447937i	$0.147841\pi$
$570$		0			0
$571$	−32.4959			−1.35991			−0.679956	−	0.733253i	$-0.738001\pi$
$571$	−32.4959			−1.35991			−0.679956	+	0.733253i	$0.738001\pi$
$572$		0			0
$573$	4.23455			0.176901
$574$		0			0
$575$	3.33148	−	10.2532i	0.138932	−	0.427590i
$576$		0			0
$577$	−20.6634	+	15.0128i	−0.860227	+	0.624991i	−0.927947	−	0.372713i	$-0.878428\pi$
$577$	−20.6634	+	15.0128i	−0.860227	+	0.624991i	0.0677198	+	0.997704i	$0.478428\pi$
$578$		0			0
$579$	−2.11679	−	6.51481i	−0.0879708	−	0.270746i
$580$		0			0
$581$	6.26356	+	4.55074i	0.259856	+	0.188797i
$582$		0			0
$583$	14.1748	+	9.23702i	0.587059	+	0.382558i
$584$		0			0
$585$	−0.901223	−	0.654777i	−0.0372610	−	0.0270717i
$586$		0			0
$587$	−7.71834	−	23.7546i	−0.318570	−	0.980458i	−0.974260	−	0.225428i	$-0.927622\pi$
$587$	−7.71834	−	23.7546i	−0.318570	−	0.980458i	0.655690	−	0.755030i	$-0.272378\pi$
$588$		0			0
$589$	−16.8389	+	12.2342i	−0.693835	+	0.504101i
$590$		0			0
$591$	2.61360	−	8.04385i	0.107509	−	0.330880i
$592$		0			0
$593$	6.90728			0.283648			0.141824	−	0.989892i	$-0.454703\pi$
$593$	6.90728			0.283648			0.141824	+	0.989892i	$0.454703\pi$
$594$		0			0
$595$	−3.35303			−0.137461
$596$		0			0
$597$	−2.50296	+	7.70333i	−0.102439	+	0.315276i
$598$		0			0
$599$	11.0294	−	8.01332i	0.450649	−	0.327416i	−0.339203	−	0.940713i	$-0.610157\pi$
$599$	11.0294	−	8.01332i	0.450649	−	0.327416i	0.789852	+	0.613298i	$0.210157\pi$
$600$		0			0
$601$	13.0487	+	40.1599i	0.532270	+	1.63816i	0.749476	+	0.662031i	$0.230306\pi$
$601$	13.0487	+	40.1599i	0.532270	+	1.63816i	−0.217206	+	0.976126i	$0.569694\pi$
$602$		0			0
$603$	−30.0250	−	21.8144i	−1.22271	−	0.888351i
$604$		0			0
$605$	−4.96484	+	4.44209i	−0.201850	+	0.180596i
$606$		0			0
$607$	36.1839	+	26.2892i	1.46866	+	1.06704i	0.981000	+	0.194010i	$0.0621495\pi$
$607$	36.1839	+	26.2892i	1.46866	+	1.06704i	0.487660	+	0.873034i	$0.337851\pi$
$608$		0			0
$609$	0.900218	+	2.77059i	0.0364787	+	0.112270i
$610$		0			0
$611$	−0.679667	+	0.493807i	−0.0274964	+	0.0199773i
$612$		0			0
$613$	7.57207	−	23.3044i	0.305833	−	0.941258i	−0.673532	−	0.739158i	$-0.735224\pi$
$613$	7.57207	−	23.3044i	0.305833	−	0.941258i	0.979365	−	0.202100i	$-0.0647765\pi$
$614$		0			0
$615$	−3.61347			−0.145709
$616$		0			0
$617$	29.7119			1.19616			0.598078	−	0.801438i	$-0.295931\pi$
$617$	29.7119			1.19616			0.598078	+	0.801438i	$0.295931\pi$
$618$		0			0
$619$	3.84304	−	11.8277i	0.154465	−	0.475394i	−0.843642	−	0.536907i	$-0.819593\pi$
$619$	3.84304	−	11.8277i	0.154465	−	0.475394i	0.998106	+	0.0615133i	$0.0195926\pi$
$620$		0			0
$621$	−5.37163	+	3.90272i	−0.215556	+	0.156611i
$622$		0			0
$623$	−0.792829	−	2.44008i	−0.0317640	−	0.0977596i
$624$		0			0
$625$	−15.8832	−	11.5398i	−0.635326	−	0.461592i
$626$		0			0
$627$	−4.09011	−	2.66533i	−0.163343	−	0.106443i
$628$		0			0
$629$	−36.8640	−	26.7833i	−1.46987	−	1.06792i
$630$		0			0
$631$	−7.57381	−	23.3098i	−0.301509	−	0.927948i	−0.980957	−	0.194225i	$-0.937781\pi$
$631$	−7.57381	−	23.3098i	−0.301509	−	0.927948i	0.679448	−	0.733723i	$-0.262219\pi$
$632$		0			0
$633$	−0.152767	+	0.110992i	−0.00607195	+	0.00441153i
$634$		0			0
$635$	0.572175	−	1.76097i	0.0227061	−	0.0698821i
$636$		0			0
$637$	−0.667865			−0.0264618
$638$		0			0
$639$	−11.4086			−0.451318
$640$		0			0
$641$	5.16605	−	15.8995i	0.204047	−	0.627991i	−0.795705	−	0.605685i	$-0.792899\pi$
$641$	5.16605	−	15.8995i	0.204047	−	0.627991i	0.999751	−	0.0223059i	$-0.00710079\pi$
$642$		0			0
$643$	−31.2039	+	22.6710i	−1.23056	+	0.894056i	−0.996932	−	0.0782690i	$-0.975061\pi$
$643$	−31.2039	+	22.6710i	−1.23056	+	0.894056i	−0.233631	+	0.972325i	$0.575061\pi$
$644$		0			0
$645$	0.275328	+	0.847373i	0.0108410	+	0.0333653i
$646$		0			0
$647$	−8.86217	−	6.43874i	−0.348408	−	0.253133i	0.399793	−	0.916605i	$-0.369082\pi$
$647$	−8.86217	−	6.43874i	−0.348408	−	0.253133i	−0.748201	+	0.663472i	$0.769082\pi$
$648$		0			0
$649$	−13.7714	−	36.0456i	−0.540575	−	1.41491i
$650$		0			0
$651$	−2.81333	−	2.04400i	−0.110263	−	0.0801107i
$652$		0			0
$653$	14.6929	+	45.2202i	0.574978	+	1.76960i	0.636253	+	0.771480i	$0.280483\pi$
$653$	14.6929	+	45.2202i	0.574978	+	1.76960i	−0.0612747	+	0.998121i	$0.519517\pi$
$654$		0			0
$655$	−5.91960	+	4.30084i	−0.231298	+	0.168048i
$656$		0			0
$657$	7.71672	−	23.7496i	0.301058	−	0.926561i
$658$		0			0
$659$	−36.2764			−1.41313			−0.706564	−	0.707649i	$-0.749756\pi$
$659$	−36.2764			−1.41313			−0.706564	+	0.707649i	$0.749756\pi$
$660$		0			0
$661$	23.1692			0.901179			0.450590	−	0.892731i	$-0.351214\pi$
$661$	23.1692			0.901179			0.450590	+	0.892731i	$0.351214\pi$
$662$		0			0
$663$	0.566629	−	1.74391i	0.0220061	−	0.0677277i
$664$		0			0
$665$	−1.45432	+	1.05663i	−0.0563962	+	0.0409743i
$666$		0			0
$667$	−4.22397	−	13.0000i	−0.163553	−	0.503364i
$668$		0			0
$669$	5.23399	+	3.80272i	0.202358	+	0.147022i
$670$		0			0
$671$	−16.4231	+	13.2563i	−0.634007	+	0.511756i
$672$		0			0
$673$	−1.30176	−	0.945782i	−0.0501790	−	0.0364572i	0.562413	−	0.826856i	$-0.309873\pi$
$673$	−1.30176	−	0.945782i	−0.0501790	−	0.0364572i	−0.612592	+	0.790399i	$0.709873\pi$
$674$		0			0
$675$	4.08545	+	12.5737i	0.157249	+	0.483963i
$676$		0			0
$677$	−37.5881	+	27.3093i	−1.44463	+	1.04958i	−0.457577	+	0.889170i	$0.651283\pi$
$677$	−37.5881	+	27.3093i	−1.44463	+	1.04958i	−0.987050	+	0.160413i	$0.948717\pi$
$678$		0			0
$679$	1.11989	−	3.44666i	0.0429773	−	0.132271i
$680$		0			0
$681$	−0.924216			−0.0354160
$682$		0			0
$683$	−27.5679			−1.05486			−0.527428	−	0.849600i	$-0.676843\pi$
$683$	−27.5679			−1.05486			−0.527428	+	0.849600i	$0.676843\pi$
$684$		0			0
$685$	−0.628859	+	1.93543i	−0.0240275	+	0.0739489i
$686$		0			0
$687$	−5.15914	+	3.74834i	−0.196834	+	0.143008i
$688$		0			0
$689$	1.05280	+	3.24018i	0.0401084	+	0.123441i
$690$		0			0
$691$	−32.1894	−	23.3869i	−1.22454	−	0.889681i	−0.228072	−	0.973644i	$-0.573242\pi$
$691$	−32.1894	−	23.3869i	−1.22454	−	0.889681i	−0.996469	+	0.0839635i	$0.973242\pi$
$692$		0			0
$693$	−2.37803	+	8.81926i	−0.0903338	+	0.335016i
$694$		0			0
$695$	−5.61934	−	4.08269i	−0.213154	−	0.154865i
$696$		0			0
$697$	20.5838	+	63.3504i	0.779667	+	2.39957i
$698$		0			0
$699$	−4.50538	+	3.27335i	−0.170409	+	0.123809i
$700$		0			0
$701$	−2.30867	+	7.10534i	−0.0871971	+	0.268365i	−0.985142	−	0.171743i	$-0.945060\pi$
$701$	−2.30867	+	7.10534i	−0.0871971	+	0.268365i	0.897945	+	0.440108i	$0.145060\pi$
$702$		0			0
$703$	−24.4293			−0.921368
$704$		0			0
$705$	−0.377798			−0.0142287
$706$		0			0
$707$	3.15606	−	9.71336i	0.118696	−	0.365309i
$708$		0			0
$709$	17.2543	−	12.5360i	0.647999	−	0.470799i	−0.214590	−	0.976704i	$-0.568842\pi$
$709$	17.2543	−	12.5360i	0.647999	−	0.470799i	0.862589	+	0.505906i	$0.168842\pi$
$710$		0			0
$711$	−6.11681	−	18.8256i	−0.229398	−	0.706016i
$712$		0			0
$713$	13.2006	+	9.59079i	0.494366	+	0.359178i
$714$		0			0
$715$	−1.33978	+	0.0680964i	−0.0501051	+	0.00254666i
$716$		0			0
$717$	−1.67660	−	1.21812i	−0.0626138	−	0.0454916i
$718$		0			0
$719$	−7.43942	−	22.8962i	−0.277444	−	0.853883i	−0.988562	−	0.150812i	$-0.951811\pi$
$719$	−7.43942	−	22.8962i	−0.277444	−	0.853883i	0.711119	−	0.703072i	$-0.248189\pi$
$720$		0			0
$721$	15.2463	−	11.0771i	0.567803	−	0.412533i
$722$		0			0
$723$	0.114480	−	0.352334i	0.00425756	−	0.0131034i
$724$		0			0
$725$	−27.2174			−1.01083
$726$		0			0
$727$	22.5715			0.837129			0.418565	−	0.908187i	$-0.362533\pi$
$727$	22.5715			0.837129			0.418565	+	0.908187i	$0.362533\pi$
$728$		0			0
$729$	−4.51549	+	13.8973i	−0.167241	+	0.514713i
$730$		0			0
$731$	13.2875	−	9.65396i	0.491457	−	0.357064i
$732$		0			0
$733$	3.50520	+	10.7879i	0.129468	+	0.398461i	0.994689	−	0.102930i	$-0.0328219\pi$
$733$	3.50520	+	10.7879i	0.129468	+	0.398461i	−0.865221	+	0.501391i	$0.832822\pi$
$734$		0			0
$735$	−0.242978	−	0.176534i	−0.00896238	−	0.00651155i
$736$		0			0
$737$	−44.6359	+	2.26868i	−1.64419	+	0.0835680i
$738$		0			0
$739$	36.9382	+	26.8372i	1.35879	+	0.987221i	0.998521	+	0.0543739i	$0.0173163\pi$
$739$	36.9382	+	26.8372i	1.35879	+	0.987221i	0.360273	+	0.932847i	$0.382684\pi$
$740$		0			0
$741$	−0.303784	−	0.934950i	−0.0111598	−	0.0343463i
$742$		0			0
$743$	−8.19175	+	5.95165i	−0.300526	+	0.218345i	−0.727821	−	0.685767i	$-0.759467\pi$
$743$	−8.19175	+	5.95165i	−0.300526	+	0.218345i	0.427295	+	0.904112i	$0.359467\pi$
$744$		0			0
$745$	−2.50507	+	7.70981i	−0.0917786	+	0.282466i
$746$		0			0
$747$	21.3226			0.780152
$748$		0			0
$749$	5.99974			0.219226
$750$		0			0
$751$	10.9427	−	33.6780i	0.399303	−	1.22893i	−0.526256	−	0.850326i	$-0.676405\pi$
$751$	10.9427	−	33.6780i	0.399303	−	1.22893i	0.925559	−	0.378603i	$-0.123595\pi$
$752$		0			0
$753$	0.0943401	−	0.0685421i	0.00343795	−	0.00249781i
$754$		0			0
$755$	−3.83497	−	11.8028i	−0.139569	−	0.429548i
$756$		0			0
$757$	8.03197	+	5.83557i	0.291927	+	0.212097i	0.724103	−	0.689692i	$-0.242254\pi$
$757$	8.03197	+	5.83557i	0.291927	+	0.212097i	−0.432176	+	0.901789i	$0.642254\pi$
$758$		0			0
$759$	−0.996354	+	3.69512i	−0.0361654	+	0.134124i
$760$		0			0
$761$	−5.68843	−	4.13289i	−0.206206	−	0.149817i	0.479890	−	0.877329i	$-0.340677\pi$
$761$	−5.68843	−	4.13289i	−0.206206	−	0.149817i	−0.686095	+	0.727512i	$0.740677\pi$
$762$		0			0
$763$	3.05071	+	9.38911i	0.110443	+	0.339909i
$764$		0			0
$765$	−7.47087	+	5.42791i	−0.270110	+	0.196246i
$766$		0			0
$767$	2.40111	−	7.38987i	0.0866992	−	0.266833i
$768$		0			0
$769$	9.56002			0.344743			0.172371	−	0.985032i	$-0.444857\pi$
$769$	9.56002			0.344743			0.172371	+	0.985032i	$0.444857\pi$
$770$		0			0
$771$	−4.67104			−0.168223
$772$		0			0
$773$	5.39682	−	16.6097i	0.194110	−	0.597410i	−0.805876	−	0.592085i	$-0.798305\pi$
$773$	5.39682	−	16.6097i	0.194110	−	0.597410i	0.999986	−	0.00532499i	$-0.00169501\pi$
$774$		0			0
$775$	26.2847	−	19.0969i	0.944173	−	0.685982i
$776$		0			0
$777$	−1.26125	−	3.88171i	−0.0452469	−	0.139256i
$778$		0			0
$779$	28.8913	+	20.9907i	1.03514	+	0.752071i
$780$		0			0
$781$	−10.6908	+	8.62936i	−0.382547	+	0.308783i
$782$		0			0
$783$	13.5612	+	9.85280i	0.484638	+	0.352110i
$784$		0			0
$785$	2.21595	+	6.81999i	0.0790906	+	0.243416i
$786$		0			0
$787$	−13.9431	+	10.1303i	−0.497019	+	0.361106i	−0.807877	−	0.589351i	$-0.799384\pi$
$787$	−13.9431	+	10.1303i	−0.497019	+	0.361106i	0.310858	+	0.950456i	$0.399384\pi$
$788$		0			0
$789$	−2.39771	+	7.37938i	−0.0853606	+	0.262713i
$790$		0			0
$791$	−16.4049			−0.583291
$792$		0			0
$793$	−4.25003			−0.150923
$794$		0			0
$795$	−0.473441	+	1.45710i	−0.0167912	+	0.0516780i
$796$		0			0
$797$	29.8828	−	21.7112i	1.05850	−	0.769049i	0.0846934	−	0.996407i	$-0.473009\pi$
$797$	29.8828	−	21.7112i	1.05850	−	0.769049i	0.973811	+	0.227358i	$0.0730089\pi$
$798$		0			0
$799$	2.15209	+	6.62345i	0.0761354	+	0.234321i
$800$		0			0
$801$	−5.71651	−	4.15329i	−0.201983	−	0.146749i
$802$		0			0
$803$	−10.7328	−	28.0921i	−0.378751	−	0.991350i
$804$		0			0
$805$	1.14009	+	0.828326i	0.0401830	+	0.0291947i
$806$		0			0
$807$	0.541647	+	1.66702i	0.0190669	+	0.0586819i
$808$		0			0
$809$	30.5026	−	22.1614i	1.07241	−	0.779155i	0.0960699	−	0.995375i	$-0.469373\pi$
$809$	30.5026	−	22.1614i	1.07241	−	0.779155i	0.976345	+	0.216220i	$0.0693728\pi$
$810$		0			0
$811$	−7.64651	+	23.5335i	−0.268505	+	0.826374i	0.722360	+	0.691517i	$0.243057\pi$
$811$	−7.64651	+	23.5335i	−0.268505	+	0.826374i	−0.990865	+	0.134857i	$0.956943\pi$
$812$		0			0
$813$	11.9210			0.418089
$814$		0			0
$815$	1.40174			0.0491009
$816$		0			0
$817$	2.72104	−	8.37450i	0.0951971	−	0.292986i
$818$		0			0
$819$	−1.48807	+	1.08114i	−0.0519973	+	0.0377782i
$820$		0			0
$821$	−10.8566	−	33.4130i	−0.378896	−	1.16612i	−0.940812	−	0.338929i	$-0.889935\pi$
$821$	−10.8566	−	33.4130i	−0.378896	−	1.16612i	0.561916	−	0.827195i	$-0.310065\pi$
$822$		0			0
$823$	15.7432	+	11.4381i	0.548772	+	0.398706i	0.827333	−	0.561712i	$-0.189857\pi$
$823$	15.7432	+	11.4381i	0.548772	+	0.398706i	−0.278560	+	0.960419i	$0.589857\pi$
$824$		0			0
$825$	6.38445	+	4.16044i	0.222278	+	0.144848i
$826$		0			0
$827$	16.9712	+	12.3303i	0.590147	+	0.428767i	0.842368	−	0.538903i	$-0.181161\pi$
$827$	16.9712	+	12.3303i	0.590147	+	0.428767i	−0.252221	+	0.967670i	$0.581161\pi$
$828$		0			0
$829$	−0.481373	−	1.48151i	−0.0167188	−	0.0514551i	0.942349	−	0.334631i	$-0.108612\pi$
$829$	−0.481373	−	1.48151i	−0.0167188	−	0.0514551i	−0.959068	+	0.283176i	$0.908612\pi$
$830$		0			0
$831$	−11.3740	+	8.26371i	−0.394561	+	0.286665i
$832$		0			0
$833$	−1.71084	+	5.26543i	−0.0592772	+	0.182436i
$834$		0			0
$835$	−7.03011			−0.243287
$836$		0			0
$837$	−20.0096			−0.691633
$838$		0			0
$839$	−4.53264	+	13.9500i	−0.156484	+	0.481608i	−0.998308	−	0.0581436i	$-0.981482\pi$
$839$	−4.53264	+	13.9500i	−0.156484	+	0.481608i	0.841824	+	0.539752i	$0.181482\pi$
$840$		0			0
$841$	−4.45678	+	3.23804i	−0.153682	+	0.111657i
$842$		0			0
$843$	1.42402	+	4.38268i	0.0490458	+	0.150948i
$844$		0			0
$845$	6.15103	+	4.46899i	0.211602	+	0.153738i
$846$		0			0
$847$	4.44238	+	10.0631i	0.152642	+	0.345771i
$848$		0			0
$849$	2.37853	+	1.72810i	0.0816309	+	0.0593083i
$850$		0			0
$851$	5.91797	+	18.2136i	0.202865	+	0.624356i
$852$		0			0
$853$	−44.2596	+	32.1565i	−1.51542	+	1.10102i	−0.551719	+	0.834030i	$0.686028\pi$
$853$	−44.2596	+	32.1565i	−1.51542	+	1.10102i	−0.963700	+	0.266986i	$0.913972\pi$
$854$		0			0
$855$	−1.52990	+	4.70853i	−0.0523213	+	0.161028i
$856$		0			0
$857$	−24.9330			−0.851696			−0.425848	−	0.904795i	$-0.640024\pi$
$857$	−24.9330			−0.851696			−0.425848	+	0.904795i	$0.640024\pi$
$858$		0			0
$859$	25.3304			0.864263			0.432132	−	0.901811i	$-0.357762\pi$
$859$	25.3304			0.864263			0.432132	+	0.901811i	$0.357762\pi$
$860$		0			0
$861$	−1.84373	+	5.67442i	−0.0628342	+	0.193384i
$862$		0			0
$863$	35.0373	−	25.4561i	1.19268	−	0.866536i	0.199139	−	0.979971i	$-0.436185\pi$
$863$	35.0373	−	25.4561i	1.19268	−	0.866536i	0.993545	+	0.113435i	$0.0361853\pi$
$864$		0			0
$865$	−2.44744	−	7.53246i	−0.0832156	−	0.256111i
$866$		0			0
$867$	−5.47705	−	3.97931i	−0.186010	−	0.135144i
$868$		0			0
$869$	−19.9714	−	13.0144i	−0.677484	−	0.441484i
$870$		0			0
$871$	−7.28107	−	5.29001i	−0.246710	−	0.179245i
$872$		0			0
$873$	−3.08425	−	9.49236i	−0.104386	−	0.321268i
$874$		0			0
$875$	4.71996	−	3.42925i	0.159564	−	0.115930i
$876$		0			0
$877$	9.92800	−	30.5553i	0.335245	−	1.03178i	−0.631356	−	0.775493i	$-0.717502\pi$
$877$	9.92800	−	30.5553i	0.335245	−	1.03178i	0.966601	−	0.256285i	$-0.0824985\pi$
$878$		0			0
$879$	−9.19708			−0.310210
$880$		0			0
$881$	54.1285			1.82364			0.911819	−	0.410593i	$-0.134678\pi$
$881$	54.1285			1.82364			0.911819	+	0.410593i	$0.134678\pi$
$882$		0			0
$883$	4.80953	−	14.8022i	0.161854	−	0.498134i	−0.836937	−	0.547299i	$-0.815656\pi$
$883$	4.80953	−	14.8022i	0.161854	−	0.498134i	0.998791	+	0.0491649i	$0.0156560\pi$
$884$		0			0
$885$	2.82689	−	2.05385i	0.0950248	−	0.0690395i
$886$		0			0
$887$	16.8227	+	51.7751i	0.564852	+	1.73844i	0.668389	+	0.743811i	$0.266984\pi$
$887$	16.8227	+	51.7751i	0.564852	+	1.73844i	−0.103537	+	0.994626i	$0.533016\pi$
$888$		0			0
$889$	−2.47340	−	1.79703i	−0.0829552	−	0.0602705i
$890$		0			0
$891$	8.10491	+	21.2139i	0.271525	+	0.710694i
$892$		0			0
$893$	3.02065	+	2.19463i	0.101082	+	0.0734406i
$894$		0			0
$895$	0.193918	+	0.596820i	0.00648198	+	0.0199495i
$896$		0			0
$897$	−0.623475	+	0.452981i	−0.0208172	+	0.0151246i
$898$		0			0
$899$	12.7295	−	39.1773i	0.424552	−	1.30664i
$900$		0			0
$901$	28.2424			0.940891
$902$		0			0
$903$	1.47116			0.0489570
$904$		0			0
$905$	1.96744	−	6.05516i	0.0653999	−	0.201280i
$906$		0			0
$907$	−16.6000	+	12.0606i	−0.551193	+	0.400465i	−0.828225	−	0.560396i	$-0.810649\pi$
$907$	−16.6000	+	12.0606i	−0.551193	+	0.400465i	0.277032	+	0.960861i	$0.410649\pi$
$908$		0			0
$909$	−8.69204	−	26.7513i	−0.288297	−	0.887286i
$910$		0			0
$911$	26.5252	+	19.2717i	0.878819	+	0.638499i	0.932939	−	0.360035i	$-0.117235\pi$
$911$	26.5252	+	19.2717i	0.878819	+	0.638499i	−0.0541201	+	0.998534i	$0.517235\pi$
$912$		0			0
$913$	19.9810	−	16.1281i	0.661273	−	0.533764i
$914$		0			0
$915$	−1.54622	−	1.12339i	−0.0511163	−	0.0371382i
$916$		0			0
$917$	3.73343	+	11.4903i	0.123289	+	0.379443i
$918$		0			0
$919$	18.3830	−	13.3560i	0.606400	−	0.440575i	−0.241745	−	0.970340i	$-0.577720\pi$
$919$	18.3830	−	13.3560i	0.606400	−	0.440575i	0.848145	+	0.529764i	$0.177720\pi$
$920$		0			0
$921$	−1.45622	+	4.48180i	−0.0479842	+	0.147680i
$922$		0			0
$923$	−2.76660			−0.0910637
$924$		0			0
$925$	38.1328			1.25380
$926$		0			0
$927$	16.0386	−	49.3617i	0.526776	−	1.62125i
$928$		0			0
$929$	−33.0824	+	24.0358i	−1.08540	+	0.788588i	−0.978616	−	0.205695i	$-0.934055\pi$
$929$	−33.0824	+	24.0358i	−1.08540	+	0.788588i	−0.106782	+	0.994283i	$0.534055\pi$
$930$		0			0
$931$	0.917225	+	2.82293i	0.0300608	+	0.0925177i
$932$		0			0
$933$	13.6966	+	9.95113i	0.448405	+	0.325785i
$934$		0			0
$935$	−2.89520	+	10.7373i	−0.0946831	+	0.351146i
$936$		0			0
$937$	11.8584	+	8.61563i	0.387397	+	0.281460i	0.764388	−	0.644757i	$-0.223041\pi$
$937$	11.8584	+	8.61563i	0.387397	+	0.281460i	−0.376991	+	0.926217i	$0.623041\pi$
$938$		0			0
$939$	2.90048	+	8.92676i	0.0946536	+	0.291314i
$940$		0			0
$941$	31.5496	−	22.9221i	1.02849	−	0.747240i	0.0604827	−	0.998169i	$-0.480736\pi$
$941$	31.5496	−	22.9221i	1.02849	−	0.747240i	0.968006	+	0.250929i	$0.0807360\pi$
$942$		0			0
$943$	8.65109	−	26.6253i	0.281718	−	0.867040i
$944$		0			0
$945$	−1.72816			−0.0562172
$946$		0			0
$947$	−33.3858			−1.08489			−0.542446	−	0.840091i	$-0.682502\pi$
$947$	−33.3858			−1.08489			−0.542446	+	0.840091i	$0.682502\pi$
$948$		0			0
$949$	1.87131	−	5.75930i	0.0607453	−	0.186955i
$950$		0			0
$951$	9.37870	−	6.81402i	0.304125	−	0.220960i
$952$		0			0
$953$	6.10845	+	18.7999i	0.197872	+	0.608987i	0.999931	+	0.0117427i	$0.00373790\pi$
$953$	6.10845	+	18.7999i	0.197872	+	0.608987i	−0.802059	+	0.597245i	$0.796262\pi$
$954$		0			0
$955$	−4.18383	−	3.03973i	−0.135386	−	0.0983635i
$956$		0			0
$957$	9.64942	−	0.490445i	0.311922	−	0.0158538i
$958$		0			0
$959$	2.71843	+	1.97506i	0.0877828	+	0.0637780i
$960$		0			0
$961$	5.61573	+	17.2834i	0.181152	+	0.557530i
$962$		0			0
$963$	13.3680	−	9.71241i	0.430777	−	0.312978i
$964$		0			0
$965$	−2.58516	+	7.95631i	−0.0832193	+	0.256123i
$966$		0			0
$967$	41.7836			1.34367			0.671836	−	0.740700i	$-0.265506\pi$
$967$	41.7836			1.34367			0.671836	+	0.740700i	$0.265506\pi$
$968$		0			0
$969$	−8.14932			−0.261794
$970$		0			0
$971$	−13.5352	+	41.6571i	−0.434366	+	1.33684i	0.459370	+	0.888245i	$0.348075\pi$
$971$	−13.5352	+	41.6571i	−0.434366	+	1.33684i	−0.893735	+	0.448595i	$0.851925\pi$
$972$		0			0
$973$	−9.27845	+	6.74119i	−0.297453	+	0.216113i
$974$		0			0
$975$	0.474191	+	1.45941i	0.0151863	+	0.0467385i
$976$		0			0
$977$	13.3225	+	9.67934i	0.426224	+	0.309670i	0.780137	−	0.625609i	$-0.215149\pi$
$977$	13.3225	+	9.67934i	0.426224	+	0.309670i	−0.353913	+	0.935278i	$0.615149\pi$
$978$		0			0
$979$	−8.49832	+	0.431939i	−0.271608	+	0.0138048i
$980$		0			0
$981$	21.9964	+	15.9813i	0.702292	+	0.510245i
$982$		0			0
$983$	9.37477	+	28.8526i	0.299009	+	0.920254i	0.981845	+	0.189683i	$0.0607460\pi$
$983$	9.37477	+	28.8526i	0.299009	+	0.920254i	−0.682837	+	0.730571i	$0.739254\pi$
$984$		0			0
$985$	−8.35651	+	6.07136i	−0.266261	+	0.193450i
$986$		0			0
$987$	−0.192767	+	0.593275i	−0.00613583	+	0.0188841i
$988$		0			0
$989$	−6.90290			−0.219500
$990$		0			0
$991$	27.8600			0.885002			0.442501	−	0.896768i	$-0.354091\pi$
$991$	27.8600			0.885002			0.442501	+	0.896768i	$0.354091\pi$
$992$		0			0
$993$	−2.07277	+	6.37932i	−0.0657773	+	0.202442i
$994$		0			0
$995$	8.00276	−	5.81434i	0.253704	−	0.184327i
$996$		0			0
$997$	−15.3247	−	47.1647i	−0.485339	−	1.49372i	−0.831489	−	0.555542i	$-0.812511\pi$
$997$	−15.3247	−	47.1647i	−0.485339	−	1.49372i	0.346149	−	0.938180i	$-0.387489\pi$
$998$		0			0
$999$	−18.9999	−	13.8042i	−0.601129	−	0.436746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.j.c.169.2	yes	12
11.3	even	5	inner	308.2.j.c.113.2	✓	12
11.5	even	5		3388.2.a.u.1.4		6
11.6	odd	10		3388.2.a.t.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.j.c.113.2	✓	12	11.3	even	5	inner
308.2.j.c.169.2	yes	12	1.1	even	1	trivial
3388.2.a.t.1.4		6	11.6	odd	10
3388.2.a.u.1.4		6	11.5	even	5

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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.153244 - 0.471635i) q^{3} +(-0.489968 + 0.355982i) q^{5} +(0.309017 + 0.951057i) q^{7} +(2.22809 + 1.61881i) q^{9} +O(q^{10})\)	\(q+(0.153244 - 0.471635i) q^{3} +(-0.489968 + 0.355982i) q^{5} +(0.309017 + 0.951057i) q^{7} +(2.22809 + 1.61881i) q^{9} +(3.31235 - 0.168355i) q^{11} +(0.540314 + 0.392561i) q^{13} +(0.0928094 + 0.285638i) q^{15} +(4.47905 - 3.25422i) q^{17} +(0.917225 - 2.82293i) q^{19} +0.495906 q^{21} -2.32688 q^{23} +(-1.43174 + 4.40644i) q^{25} +(2.30852 - 1.67724i) q^{27} +(1.81530 + 5.58691i) q^{29} +(-5.67310 - 4.12175i) q^{31} +(0.428194 - 1.58802i) q^{33} +(-0.489968 - 0.355982i) q^{35} +(-2.54331 - 7.82751i) q^{37} +(0.267945 - 0.194674i) q^{39} +(-3.71790 + 11.4425i) q^{41} +2.96660 q^{43} -1.66796 q^{45} +(-0.388716 + 1.19634i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-0.848418 - 2.61116i) q^{51} +(4.12697 + 2.99842i) q^{53} +(-1.56301 + 1.26163i) q^{55} +(-1.19083 - 0.865191i) q^{57} +(-3.59521 - 11.0649i) q^{59} +(-5.14826 + 3.74043i) q^{61} +(-0.851057 + 2.61928i) q^{63} -0.404481 q^{65} -13.4756 q^{67} +(-0.356579 + 1.09744i) q^{69} +(-3.35131 + 2.43487i) q^{71} +(-2.80193 - 8.62345i) q^{73} +(1.85883 + 1.35052i) q^{75} +(1.18369 + 3.09821i) q^{77} +(-5.81466 - 4.22460i) q^{79} +(2.11589 + 6.51204i) q^{81} +(6.26356 - 4.55074i) q^{83} +(-1.03614 + 3.18892i) q^{85} +2.91317 q^{87} -2.56565 q^{89} +(-0.206382 + 0.635178i) q^{91} +(-2.81333 + 2.04400i) q^{93} +(0.555502 + 1.70966i) q^{95} +(-2.93190 - 2.13015i) q^{97} +(7.65276 + 4.98694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9	\( 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9} + 2 q^{11} - 7 q^{13} - 4 q^{15} + 3 q^{17} - 23 q^{19} - 4 q^{21} - 38 q^{23} + 2 q^{25} - 18 q^{27} + 29 q^{29} + 9 q^{31} - 4 q^{33} + q^{35} + 3 q^{37} + 25 q^{39} - 18 q^{41} + 34 q^{43} + 14 q^{45} + 9 q^{47} - 3 q^{49} + 35 q^{51} + 13 q^{53} + 16 q^{55} + 9 q^{57} - 17 q^{59} - 19 q^{61} - 9 q^{63} + 8 q^{65} - 20 q^{67} - 14 q^{69} + 15 q^{71} + 9 q^{73} - 47 q^{75} - 8 q^{77} - 14 q^{79} - 49 q^{81} + 41 q^{83} - 66 q^{85} + 40 q^{87} + 34 q^{89} + 13 q^{91} - 40 q^{93} + 42 q^{95} - 10 q^{97} - 24 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9 + 2 * q^11 - 7 * q^13 - 4 * q^15 + 3 * q^17 - 23 * q^19 - 4 * q^21 - 38 * q^23 + 2 * q^25 - 18 * q^27 + 29 * q^29 + 9 * q^31 - 4 * q^33 + q^35 + 3 * q^37 + 25 * q^39 - 18 * q^41 + 34 * q^43 + 14 * q^45 + 9 * q^47 - 3 * q^49 + 35 * q^51 + 13 * q^53 + 16 * q^55 + 9 * q^57 - 17 * q^59 - 19 * q^61 - 9 * q^63 + 8 * q^65 - 20 * q^67 - 14 * q^69 + 15 * q^71 + 9 * q^73 - 47 * q^75 - 8 * q^77 - 14 * q^79 - 49 * q^81 + 41 * q^83 - 66 * q^85 + 40 * q^87 + 34 * q^89 + 13 * q^91 - 40 * q^93 + 42 * q^95 - 10 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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