LMFDB - Embedded newform 1216.2.m.a.303.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(303,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("1216.303");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.m (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 304)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			303.5
Character	$\chi$	$=$	1216.303
Dual form			1216.2.m.a.911.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96187 - 1.96187i) q^{3} +(-3.06749 + 3.06749i) q^{5} -1.97168 q^{7} +4.69788i q^{9} +(2.40953 + 2.40953i) q^{11} +(0.283330 - 0.283330i) q^{13} +12.0360 q^{15} +3.37118 q^{17} +(-1.59086 + 4.05822i) q^{19} +(3.86818 + 3.86818i) q^{21} -3.47264 q^{23} -13.8190i q^{25} +(3.33103 - 3.33103i) q^{27} +(-6.28708 + 6.28708i) q^{29} +1.56762 q^{31} -9.45439i q^{33} +(6.04810 - 6.04810i) q^{35} +(-5.57107 - 5.57107i) q^{37} -1.11171 q^{39} +7.27782 q^{41} +(-3.73284 - 3.73284i) q^{43} +(-14.4107 - 14.4107i) q^{45} +0.0227383i q^{47} -3.11249 q^{49} +(-6.61383 - 6.61383i) q^{51} +(-3.97463 - 3.97463i) q^{53} -14.7824 q^{55} +(11.0828 - 4.84066i) q^{57} +(6.88318 - 6.88318i) q^{59} +(2.07562 + 2.07562i) q^{61} -9.26271i q^{63} +1.73822i q^{65} +(-1.41362 - 1.41362i) q^{67} +(6.81287 + 6.81287i) q^{69} -3.61576i q^{71} +6.11638i q^{73} +(-27.1111 + 27.1111i) q^{75} +(-4.75082 - 4.75082i) q^{77} +7.24446 q^{79} +1.02354 q^{81} +(-0.477010 + 0.477010i) q^{83} +(-10.3411 + 10.3411i) q^{85} +24.6689 q^{87} -11.8214 q^{89} +(-0.558635 + 0.558635i) q^{91} +(-3.07548 - 3.07548i) q^{93} +(-7.56862 - 17.3285i) q^{95} -7.89215i q^{97} +(-11.3197 + 11.3197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 4 q^{5} + 8 q^{7} + 4 q^{11} - 8 q^{17} - 6 q^{19} + 8 q^{23} + 8 q^{39} + 4 q^{43} + 4 q^{45} + 44 q^{49} + 8 q^{55} + 28 q^{61} - 32 q^{77} - 52 q^{81} - 36 q^{83} - 56 q^{85} + 120 q^{87} - 16 q^{93}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q - 4 * q^5 + 8 * q^7 + 4 * q^11 - 8 * q^17 - 6 * q^19 + 8 * q^23 + 8 * q^39 + 4 * q^43 + 4 * q^45 + 44 * q^49 + 8 * q^55 + 28 * q^61 - 32 * q^77 - 52 * q^81 - 36 * q^83 - 56 * q^85 + 120 * q^87 - 16 * q^93 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.96187	−	1.96187i	−1.13269	−	1.13269i	−0.989729	−	0.142959i	$-0.954338\pi$
$3$	−1.96187	−	1.96187i	−1.13269	−	1.13269i	−0.142959	−	0.989729i	$-0.545662\pi$
$4$		0			0
$5$	−3.06749	+	3.06749i	−1.37182	+	1.37182i	−0.514083	+	0.857741i	$0.671868\pi$
$5$	−3.06749	+	3.06749i	−1.37182	+	1.37182i	−0.857741	+	0.514083i	$0.828132\pi$
$6$		0			0
$7$	−1.97168			−0.745224			−0.372612	−	0.927987i	$-0.621538\pi$
$7$	−1.97168			−0.745224			−0.372612	+	0.927987i	$0.621538\pi$
$8$		0			0
$9$			4.69788i			1.56596i
$10$		0			0
$11$	2.40953	+	2.40953i	0.726501	+	0.726501i	0.969921	−	0.243420i	$-0.0782693\pi$
$11$	2.40953	+	2.40953i	0.726501	+	0.726501i	−0.243420	+	0.969921i	$0.578269\pi$
$12$		0			0
$13$	0.283330	−	0.283330i	0.0785816	−	0.0785816i	−0.666724	−	0.745305i	$-0.732304\pi$
$13$	0.283330	−	0.283330i	0.0785816	−	0.0785816i	0.745305	+	0.666724i	$0.232304\pi$
$14$		0			0
$15$	12.0360			3.10769
$16$		0			0
$17$	3.37118			0.817632			0.408816	−	0.912617i	$-0.365942\pi$
$17$	3.37118			0.817632			0.408816	+	0.912617i	$0.365942\pi$
$18$		0			0
$19$	−1.59086	+	4.05822i	−0.364968	+	0.931020i
$19$	−1.59086	+	4.05822i	−0.364968	+	0.931020i
$20$		0			0
$21$	3.86818	+	3.86818i	0.844105	+	0.844105i
$22$		0			0
$23$	−3.47264			−0.724095			−0.362048	−	0.932160i	$-0.617922\pi$
$23$	−3.47264			−0.724095			−0.362048	+	0.932160i	$0.617922\pi$
$24$		0			0
$25$		−	13.8190i		−	2.76380i
$26$		0			0
$27$	3.33103	−	3.33103i	0.641057	−	0.641057i
$28$		0			0
$29$	−6.28708	+	6.28708i	−1.16748	+	1.16748i	−0.184682	+	0.982798i	$0.559126\pi$
$29$	−6.28708	+	6.28708i	−1.16748	+	1.16748i	−0.982798	+	0.184682i	$0.940874\pi$
$30$		0			0
$31$	1.56762			0.281553			0.140777	−	0.990041i	$-0.455040\pi$
$31$	1.56762			0.281553			0.140777	+	0.990041i	$0.455040\pi$
$32$		0			0
$33$		−	9.45439i		−	1.64580i
$34$		0			0
$35$	6.04810	−	6.04810i	1.02232	−	1.02232i
$36$		0			0
$37$	−5.57107	−	5.57107i	−0.915878	−	0.915878i	0.0808488	−	0.996726i	$-0.474237\pi$
$37$	−5.57107	−	5.57107i	−0.915878	−	0.915878i	−0.996726	+	0.0808488i	$0.974237\pi$
$38$		0			0
$39$	−1.11171			−0.178017
$40$		0			0
$41$	7.27782			1.13660			0.568302	−	0.822820i	$-0.307600\pi$
$41$	7.27782			1.13660			0.568302	+	0.822820i	$0.307600\pi$
$42$		0			0
$43$	−3.73284	−	3.73284i	−0.569252	−	0.569252i	0.362667	−	0.931919i	$-0.381866\pi$
$43$	−3.73284	−	3.73284i	−0.569252	−	0.569252i	−0.931919	+	0.362667i	$0.881866\pi$
$44$		0			0
$45$	−14.4107	−	14.4107i	−2.14822	−	2.14822i
$46$		0			0
$47$			0.0227383i			0.00331673i	0.999999	+	0.00165836i	$0.000527873\pi$
$47$			0.0227383i			0.00331673i	−0.999999	+	0.00165836i	$0.999472\pi$
$48$		0			0
$49$	−3.11249			−0.444642
$50$		0			0
$51$	−6.61383	−	6.61383i	−0.926121	−	0.926121i
$52$		0			0
$53$	−3.97463	−	3.97463i	−0.545958	−	0.545958i	0.379311	−	0.925269i	$-0.376161\pi$
$53$	−3.97463	−	3.97463i	−0.545958	−	0.545958i	−0.925269	+	0.379311i	$0.876161\pi$
$54$		0			0
$55$	−14.7824			−1.99326
$56$		0			0
$57$	11.0828	−	4.84066i	1.46795	−	0.641161i
$58$		0			0
$59$	6.88318	−	6.88318i	0.896114	−	0.896114i	−0.0989760	−	0.995090i	$-0.531557\pi$
$59$	6.88318	−	6.88318i	0.896114	−	0.896114i	0.995090	+	0.0989760i	$0.0315567\pi$
$60$		0			0
$61$	2.07562	+	2.07562i	0.265756	+	0.265756i	0.827387	−	0.561632i	$-0.189826\pi$
$61$	2.07562	+	2.07562i	0.265756	+	0.265756i	−0.561632	+	0.827387i	$0.689826\pi$
$62$		0			0
$63$		−	9.26271i		−	1.16699i
$64$		0			0
$65$			1.73822i			0.215600i
$66$		0			0
$67$	−1.41362	−	1.41362i	−0.172701	−	0.172701i	0.615464	−	0.788165i	$-0.288969\pi$
$67$	−1.41362	−	1.41362i	−0.172701	−	0.172701i	−0.788165	+	0.615464i	$0.788969\pi$
$68$		0			0
$69$	6.81287	+	6.81287i	0.820174	+	0.820174i
$70$		0			0
$71$		−	3.61576i		−	0.429112i	−0.976712	−	0.214556i	$-0.931170\pi$
$71$		−	3.61576i		−	0.429112i	0.976712	−	0.214556i	$-0.0688304\pi$
$72$		0			0
$73$			6.11638i			0.715869i	0.933747	+	0.357934i	$0.116519\pi$
$73$			6.11638i			0.715869i	−0.933747	+	0.357934i	$0.883481\pi$
$74$		0			0
$75$	−27.1111	+	27.1111i	−3.13052	+	3.13052i
$76$		0			0
$77$	−4.75082	−	4.75082i	−0.541406	−	0.541406i
$78$		0			0
$79$	7.24446			0.815066			0.407533	−	0.913191i	$-0.366389\pi$
$79$	7.24446			0.815066			0.407533	+	0.913191i	$0.366389\pi$
$80$		0			0
$81$	1.02354			0.113727
$82$		0			0
$83$	−0.477010	+	0.477010i	−0.0523586	+	0.0523586i	−0.732801	−	0.680443i	$-0.761788\pi$
$83$	−0.477010	+	0.477010i	−0.0523586	+	0.0523586i	0.680443	+	0.732801i	$0.261788\pi$
$84$		0			0
$85$	−10.3411	+	10.3411i	−1.12165	+	1.12165i
$86$		0			0
$87$	24.6689			2.64478
$88$		0			0
$89$	−11.8214			−1.25307			−0.626536	−	0.779393i	$-0.715528\pi$
$89$	−11.8214			−1.25307			−0.626536	+	0.779393i	$0.715528\pi$
$90$		0			0
$91$	−0.558635	+	0.558635i	−0.0585609	+	0.0585609i
$92$		0			0
$93$	−3.07548	−	3.07548i	−0.318912	−	0.318912i
$94$		0			0
$95$	−7.56862	−	17.3285i	−0.776524	−	1.77787i
$96$		0			0
$97$		−	7.89215i		−	0.801327i	−0.916225	−	0.400663i	$-0.868780\pi$
$97$		−	7.89215i		−	0.801327i	0.916225	−	0.400663i	$-0.131220\pi$
$98$		0			0
$99$	−11.3197	+	11.3197i	−1.13767	+	1.13767i
$100$		0			0
$101$	−0.219113	+	0.219113i	−0.0218026	+	0.0218026i	−0.717924	−	0.696121i	$-0.754908\pi$
$101$	−0.219113	+	0.219113i	−0.0218026	+	0.0218026i	0.696121	+	0.717924i	$0.254908\pi$
$102$		0			0
$103$		−	10.4281i		−	1.02751i	−0.857938	−	0.513754i	$-0.828255\pi$
$103$		−	10.4281i		−	1.02751i	0.857938	−	0.513754i	$-0.171745\pi$
$104$		0			0
$105$	−23.7312			−2.31593
$106$		0			0
$107$	6.75806	−	6.75806i	0.653326	−	0.653326i	−0.300466	−	0.953793i	$-0.597142\pi$
$107$	6.75806	−	6.75806i	0.653326	−	0.653326i	0.953793	+	0.300466i	$0.0971422\pi$
$108$		0			0
$109$	2.04303	−	2.04303i	0.195686	−	0.195686i	−0.602461	−	0.798148i	$-0.705813\pi$
$109$	2.04303	−	2.04303i	0.195686	−	0.195686i	0.798148	+	0.602461i	$0.205813\pi$
$110$		0			0
$111$			21.8594i			2.07481i
$112$		0			0
$113$			2.80340i			0.263722i	0.991268	+	0.131861i	$0.0420953\pi$
$113$			2.80340i			0.263722i	−0.991268	+	0.131861i	$0.957905\pi$
$114$		0			0
$115$	10.6523	−	10.6523i	0.993331	−	0.993331i
$116$		0			0
$117$	1.33105	+	1.33105i	0.123056	+	0.123056i
$118$		0			0
$119$	−6.64688			−0.609319
$120$		0			0
$121$			0.611687i			0.0556079i
$122$		0			0
$123$	−14.2782	−	14.2782i	−1.28742	−	1.28742i
$124$		0			0
$125$	27.0522	+	27.0522i	2.41962	+	2.41962i
$126$		0			0
$127$	−9.16238			−0.813030			−0.406515	−	0.913644i	$-0.633256\pi$
$127$	−9.16238			−0.813030			−0.406515	+	0.913644i	$0.633256\pi$
$128$		0			0
$129$			14.6467i			1.28957i
$130$		0			0
$131$	10.3848	−	10.3848i	0.907325	−	0.907325i	−0.0887304	−	0.996056i	$-0.528281\pi$
$131$	10.3848	−	10.3848i	0.907325	−	0.907325i	0.996056	+	0.0887304i	$0.0282810\pi$
$132$		0			0
$133$	3.13666	−	8.00150i	0.271983	−	0.693818i
$134$		0			0
$135$			20.4358i			1.75883i
$136$		0			0
$137$		−	8.79209i		−	0.751159i	−0.926790	−	0.375580i	$-0.877444\pi$
$137$		−	8.79209i		−	0.751159i	0.926790	−	0.375580i	$-0.122556\pi$
$138$		0			0
$139$	−1.36950	−	1.36950i	−0.116159	−	0.116159i	0.646638	−	0.762797i	$-0.276175\pi$
$139$	−1.36950	−	1.36950i	−0.116159	−	0.116159i	−0.762797	+	0.646638i	$0.776175\pi$
$140$		0			0
$141$	0.0446097	−	0.0446097i	0.00375681	−	0.00375681i
$142$		0			0
$143$	1.36539			0.114179
$144$		0			0
$145$		−	38.5711i		−	3.20315i
$146$		0			0
$147$	6.10631	+	6.10631i	0.503640	+	0.503640i
$148$		0			0
$149$	13.1672	−	13.1672i	1.07870	−	1.07870i	0.0820697	−	0.996627i	$-0.473847\pi$
$149$	13.1672	−	13.1672i	1.07870	−	1.07870i	0.996627	−	0.0820697i	$-0.0261530\pi$
$150$		0			0
$151$		−	9.50133i		−	0.773207i	−0.922246	−	0.386604i	$-0.873648\pi$
$151$		−	9.50133i		−	0.773207i	0.922246	−	0.386604i	$-0.126352\pi$
$152$		0			0
$153$			15.8374i			1.28038i
$154$		0			0
$155$	−4.80867	+	4.80867i	−0.386241	+	0.386241i
$156$		0			0
$157$	−2.53872	−	2.53872i	−0.202612	−	0.202612i	0.598506	−	0.801118i	$-0.295761\pi$
$157$	−2.53872	−	2.53872i	−0.202612	−	0.202612i	−0.801118	+	0.598506i	$0.795761\pi$
$158$		0			0
$159$			15.5954i			1.23680i
$160$		0			0
$161$	6.84692			0.539613
$162$		0			0
$163$	−12.8620	+	12.8620i	−1.00743	+	1.00743i	−0.00745526	+	0.999972i	$0.502373\pi$
$163$	−12.8620	+	12.8620i	−1.00743	+	1.00743i	−0.999972	+	0.00745526i	$0.997627\pi$
$164$		0			0
$165$	29.0012	+	29.0012i	2.25774	+	2.25774i
$166$		0			0
$167$			7.86509i			0.608619i	0.952573	+	0.304310i	$0.0984257\pi$
$167$			7.86509i			0.608619i	−0.952573	+	0.304310i	$0.901574\pi$
$168$		0			0
$169$			12.8394i			0.987650i
$170$		0			0
$171$	−19.0651	−	7.47366i	−1.45794	−	0.571525i
$172$		0			0
$173$	17.1920	−	17.1920i	1.30708	−	1.30708i	0.383571	−	0.923511i	$-0.374694\pi$
$173$	17.1920	−	17.1920i	1.30708	−	1.30708i	0.923511	−	0.383571i	$-0.125306\pi$
$174$		0			0
$175$			27.2466i			2.05965i
$176$		0			0
$177$	−27.0078			−2.03003
$178$		0			0
$179$	−8.82567	−	8.82567i	−0.659661	−	0.659661i	0.295639	−	0.955300i	$-0.404468\pi$
$179$	−8.82567	−	8.82567i	−0.659661	−	0.659661i	−0.955300	+	0.295639i	$0.904468\pi$
$180$		0			0
$181$	7.44516	+	7.44516i	0.553395	+	0.553395i	0.927419	−	0.374024i	$-0.122022\pi$
$181$	7.44516	+	7.44516i	0.553395	+	0.553395i	−0.374024	+	0.927419i	$0.622022\pi$
$182$		0			0
$183$		−	8.14419i		−	0.602036i
$184$		0			0
$185$	34.1784			2.51284
$186$		0			0
$187$	8.12297	+	8.12297i	0.594011	+	0.594011i
$188$		0			0
$189$	−6.56771	+	6.56771i	−0.477731	+	0.477731i
$190$		0			0
$191$			14.1870i			1.02653i	0.858229	+	0.513267i	$0.171565\pi$
$191$			14.1870i			1.02653i	−0.858229	+	0.513267i	$0.828435\pi$
$192$		0			0
$193$			1.10407i			0.0794728i	0.999210	+	0.0397364i	$0.0126518\pi$
$193$			1.10407i			0.0794728i	−0.999210	+	0.0397364i	$0.987348\pi$
$194$		0			0
$195$	3.41017	−	3.41017i	0.244208	−	0.244208i
$196$		0			0
$197$	5.11692	−	5.11692i	0.364566	−	0.364566i	−0.500925	−	0.865491i	$-0.667007\pi$
$197$	5.11692	−	5.11692i	0.364566	−	0.364566i	0.865491	+	0.500925i	$0.167007\pi$
$198$		0			0
$199$	−9.39942			−0.666307			−0.333154	−	0.942873i	$-0.608113\pi$
$199$	−9.39942			−0.666307			−0.333154	+	0.942873i	$0.608113\pi$
$200$		0			0
$201$			5.54667i			0.391232i
$202$		0			0
$203$	12.3961	−	12.3961i	0.870034	−	0.870034i
$204$		0			0
$205$	−22.3246	+	22.3246i	−1.55922	+	1.55922i
$206$		0			0
$207$		−	16.3141i		−	1.13391i
$208$		0			0
$209$	−13.6116	+	5.94520i	−0.941537	+	0.411238i
$210$		0			0
$211$	−17.8880	−	17.8880i	−1.23146	−	1.23146i	−0.963403	−	0.268055i	$-0.913619\pi$
$211$	−17.8880	−	17.8880i	−1.23146	−	1.23146i	−0.268055	−	0.963403i	$-0.586381\pi$
$212$		0			0
$213$	−7.09366	+	7.09366i	−0.486050	+	0.486050i
$214$		0			0
$215$	22.9009			1.56183
$216$		0			0
$217$	−3.09084			−0.209820
$218$		0			0
$219$	11.9996	−	11.9996i	0.810855	−	0.810855i
$220$		0			0
$221$	0.955158	−	0.955158i	0.0642509	−	0.0642509i
$222$		0			0
$223$	17.0885			1.14433			0.572166	−	0.820138i	$-0.306103\pi$
$223$	17.0885			1.14433			0.572166	+	0.820138i	$0.306103\pi$
$224$		0			0
$225$	64.9200			4.32800
$226$		0			0
$227$	12.4738	+	12.4738i	0.827912	+	0.827912i	0.987228	−	0.159315i	$-0.0509287\pi$
$227$	12.4738	+	12.4738i	0.827912	+	0.827912i	−0.159315	+	0.987228i	$0.550929\pi$
$228$		0			0
$229$	−0.928431	+	0.928431i	−0.0613524	+	0.0613524i	−0.737117	−	0.675765i	$-0.763813\pi$
$229$	−0.928431	+	0.928431i	−0.0613524	+	0.0613524i	0.675765	+	0.737117i	$0.263813\pi$
$230$		0			0
$231$			18.6410i			1.22649i
$232$		0			0
$233$			4.56392i			0.298992i	0.988762	+	0.149496i	$0.0477651\pi$
$233$			4.56392i			0.298992i	−0.988762	+	0.149496i	$0.952235\pi$
$234$		0			0
$235$	−0.0697496	−	0.0697496i	−0.00454996	−	0.00454996i
$236$		0			0
$237$	−14.2127	−	14.2127i	−0.923214	−	0.923214i
$238$		0			0
$239$		−	17.3712i		−	1.12365i	−0.827255	−	0.561826i	$-0.810099\pi$
$239$		−	17.3712i		−	1.12365i	0.827255	−	0.561826i	$-0.189901\pi$
$240$		0			0
$241$		−	22.1998i		−	1.43001i	−0.699118	−	0.715006i	$-0.746424\pi$
$241$		−	22.1998i		−	1.43001i	0.699118	−	0.715006i	$-0.253576\pi$
$242$		0			0
$243$	−12.0011	−	12.0011i	−0.769874	−	0.769874i
$244$		0			0
$245$	9.54754	−	9.54754i	0.609970	−	0.609970i
$246$		0			0
$247$	0.699079	+	1.60055i	0.0444813	+	0.101841i
$248$		0			0
$249$	1.87166			0.118612
$250$		0			0
$251$	7.63703	+	7.63703i	0.482045	+	0.482045i	0.905784	−	0.423739i	$-0.139283\pi$
$251$	7.63703	+	7.63703i	0.482045	+	0.482045i	−0.423739	+	0.905784i	$0.639283\pi$
$252$		0			0
$253$	−8.36743	−	8.36743i	−0.526056	−	0.526056i
$254$		0			0
$255$	40.5757			2.54095
$256$		0			0
$257$			14.0081i			0.873803i	0.899509	+	0.436902i	$0.143924\pi$
$257$			14.0081i			0.873803i	−0.899509	+	0.436902i	$0.856076\pi$
$258$		0			0
$259$	10.9843	+	10.9843i	0.682534	+	0.682534i
$260$		0			0
$261$	−29.5360	−	29.5360i	−1.82823	−	1.82823i
$262$		0			0
$263$	23.6906			1.46083			0.730414	−	0.683005i	$-0.239327\pi$
$263$	23.6906			1.46083			0.730414	+	0.683005i	$0.239327\pi$
$264$		0			0
$265$	24.3843			1.49792
$266$		0			0
$267$	23.1922	+	23.1922i	1.41934	+	1.41934i
$268$		0			0
$269$	−3.14908	+	3.14908i	−0.192003	+	0.192003i	−0.796561	−	0.604558i	$-0.793350\pi$
$269$	−3.14908	+	3.14908i	−0.192003	+	0.192003i	0.604558	+	0.796561i	$0.293350\pi$
$270$		0			0
$271$			13.1346i			0.797873i	0.916979	+	0.398937i	$0.130621\pi$
$271$			13.1346i			0.797873i	−0.916979	+	0.398937i	$0.869379\pi$
$272$		0			0
$273$	2.19194			0.132662
$274$		0			0
$275$	33.2973	−	33.2973i	2.00790	−	2.00790i
$276$		0			0
$277$	9.24323	−	9.24323i	0.555372	−	0.555372i	−0.372615	−	0.927986i	$-0.621539\pi$
$277$	9.24323	−	9.24323i	0.555372	−	0.555372i	0.927986	+	0.372615i	$0.121539\pi$
$278$		0			0
$279$			7.36451i			0.440902i
$280$		0			0
$281$	−21.1029			−1.25889			−0.629447	−	0.777043i	$-0.716719\pi$
$281$	−21.1029			−1.25889			−0.629447	+	0.777043i	$0.716719\pi$
$282$		0			0
$283$	−4.11095	−	4.11095i	−0.244371	−	0.244371i	0.574285	−	0.818655i	$-0.305280\pi$
$283$	−4.11095	−	4.11095i	−0.244371	−	0.244371i	−0.818655	+	0.574285i	$0.805280\pi$
$284$		0			0
$285$	−19.1476	+	48.8450i	−1.13421	+	2.89333i
$286$		0			0
$287$	−14.3495			−0.847025
$288$		0			0
$289$	−5.63513			−0.331478
$290$		0			0
$291$	−15.4834	+	15.4834i	−0.907652	+	0.907652i
$292$		0			0
$293$	−8.24133	−	8.24133i	−0.481464	−	0.481464i	0.424135	−	0.905599i	$-0.360578\pi$
$293$	−8.24133	−	8.24133i	−0.481464	−	0.481464i	−0.905599	+	0.424135i	$0.860578\pi$
$294$		0			0
$295$			42.2282i			2.45862i
$296$		0			0
$297$	16.0524			0.931457
$298$		0			0
$299$	−0.983903	+	0.983903i	−0.0569006	+	0.0569006i
$300$		0			0
$301$	7.35995	+	7.35995i	0.424220	+	0.424220i
$302$		0			0
$303$	0.859745			0.0493911
$304$		0			0
$305$	−12.7339			−0.729140
$306$		0			0
$307$	−4.69111	−	4.69111i	−0.267736	−	0.267736i	0.560451	−	0.828187i	$-0.310628\pi$
$307$	−4.69111	−	4.69111i	−0.267736	−	0.267736i	−0.828187	+	0.560451i	$0.810628\pi$
$308$		0			0
$309$	−20.4585	+	20.4585i	−1.16384	+	1.16384i
$310$		0			0
$311$	−21.7357			−1.23252			−0.616258	−	0.787544i	$-0.711352\pi$
$311$	−21.7357			−1.23252			−0.616258	+	0.787544i	$0.711352\pi$
$312$		0			0
$313$			14.1098i			0.797534i	0.917052	+	0.398767i	$0.130562\pi$
$313$			14.1098i			0.797534i	−0.917052	+	0.398767i	$0.869438\pi$
$314$		0			0
$315$	28.4133	+	28.4133i	1.60091	+	1.60091i
$316$		0			0
$317$	1.71710	−	1.71710i	0.0964419	−	0.0964419i	−0.657240	−	0.753682i	$-0.728276\pi$
$317$	1.71710	−	1.71710i	0.0964419	−	0.0964419i	0.753682	+	0.657240i	$0.228276\pi$
$318$		0			0
$319$	−30.2978			−1.69635
$320$		0			0
$321$	−26.5169			−1.48003
$322$		0			0
$323$	−5.36307	+	13.6810i	−0.298409	+	0.761232i
$324$		0			0
$325$	−3.91534	−	3.91534i	−0.217184	−	0.217184i
$326$		0			0
$327$	−8.01631			−0.443303
$328$		0			0
$329$		−	0.0448326i		−	0.00247170i
$330$		0			0
$331$	4.38508	−	4.38508i	0.241026	−	0.241026i	−0.576249	−	0.817274i	$-0.695484\pi$
$331$	4.38508	−	4.38508i	0.241026	−	0.241026i	0.817274	+	0.576249i	$0.195484\pi$
$332$		0			0
$333$	26.1722	−	26.1722i	1.43423	−	1.43423i
$334$		0			0
$335$	8.67250			0.473830
$336$		0			0
$337$			26.5372i			1.44557i	0.691071	+	0.722787i	$0.257139\pi$
$337$			26.5372i			1.44557i	−0.691071	+	0.722787i	$0.742861\pi$
$338$		0			0
$339$	5.49992	−	5.49992i	0.298715	−	0.298715i
$340$		0			0
$341$	3.77724	+	3.77724i	0.204549	+	0.204549i
$342$		0			0
$343$	19.9386			1.07658
$344$		0			0
$345$	−41.7968			−2.25027
$346$		0			0
$347$	−15.9182	−	15.9182i	−0.854536	−	0.854536i	0.136152	−	0.990688i	$-0.456526\pi$
$347$	−15.9182	−	15.9182i	−0.854536	−	0.854536i	−0.990688	+	0.136152i	$0.956526\pi$
$348$		0			0
$349$	9.28048	+	9.28048i	0.496773	+	0.496773i	0.910432	−	0.413659i	$-0.135749\pi$
$349$	9.28048	+	9.28048i	0.496773	+	0.496773i	−0.413659	+	0.910432i	$0.635749\pi$
$350$		0			0
$351$		−	1.88756i		−	0.100751i
$352$		0			0
$353$	3.56073			0.189519			0.0947593	−	0.995500i	$-0.469792\pi$
$353$	3.56073			0.189519			0.0947593	+	0.995500i	$0.469792\pi$
$354$		0			0
$355$	11.0913	+	11.0913i	0.588666	+	0.588666i
$356$		0			0
$357$	13.0403	+	13.0403i	0.690167	+	0.690167i
$358$		0			0
$359$	−1.99352			−0.105214			−0.0526070	−	0.998615i	$-0.516753\pi$
$359$	−1.99352			−0.105214			−0.0526070	+	0.998615i	$0.516753\pi$
$360$		0			0
$361$	−13.9383	−	12.9121i	−0.733597	−	0.679584i
$362$		0			0
$363$	1.20005	−	1.20005i	0.0629863	−	0.0629863i
$364$		0			0
$365$	−18.7619	−	18.7619i	−0.982045	−	0.982045i
$366$		0			0
$367$		−	0.994011i		−	0.0518869i	−0.999663	−	0.0259435i	$-0.991741\pi$
$367$		−	0.994011i		−	0.0518869i	0.999663	−	0.0259435i	$-0.00825899\pi$
$368$		0			0
$369$			34.1904i			1.77988i
$370$		0			0
$371$	7.83669	+	7.83669i	0.406861	+	0.406861i
$372$		0			0
$373$	−19.5869	−	19.5869i	−1.01417	−	1.01417i	−0.999898	−	0.0142735i	$-0.995456\pi$
$373$	−19.5869	−	19.5869i	−1.01417	−	1.01417i	−0.0142735	−	0.999898i	$-0.504544\pi$
$374$		0			0
$375$		−	106.146i		−	5.48135i
$376$		0			0
$377$			3.56264i			0.183485i
$378$		0			0
$379$	−12.0558	+	12.0558i	−0.619264	+	0.619264i	−0.945343	−	0.326079i	$-0.894272\pi$
$379$	−12.0558	+	12.0558i	−0.619264	+	0.619264i	0.326079	+	0.945343i	$0.394272\pi$
$380$		0			0
$381$	17.9754	+	17.9754i	0.920909	+	0.920909i
$382$		0			0
$383$	−28.3361			−1.44791			−0.723954	−	0.689848i	$-0.757677\pi$
$383$	−28.3361			−1.44791			−0.723954	+	0.689848i	$0.757677\pi$
$384$		0			0
$385$	29.1462			1.48543
$386$		0			0
$387$	17.5364	−	17.5364i	0.891427	−	0.891427i
$388$		0			0
$389$	−10.5559	+	10.5559i	−0.535206	+	0.535206i	−0.922117	−	0.386911i	$-0.873542\pi$
$389$	−10.5559	+	10.5559i	−0.535206	+	0.535206i	0.386911	+	0.922117i	$0.373542\pi$
$390$		0			0
$391$	−11.7069			−0.592043
$392$		0			0
$393$	−40.7473			−2.05543
$394$		0			0
$395$	−22.2223	+	22.2223i	−1.11813	+	1.11813i
$396$		0			0
$397$	15.7916	+	15.7916i	0.792558	+	0.792558i	0.981909	−	0.189351i	$-0.0606385\pi$
$397$	15.7916	+	15.7916i	0.792558	+	0.792558i	−0.189351	+	0.981909i	$0.560639\pi$
$398$		0			0
$399$	−21.8516	+	9.54421i	−1.09395	+	0.477808i
$400$		0			0
$401$		−	19.7805i		−	0.987793i	−0.869521	−	0.493897i	$-0.835572\pi$
$401$		−	19.7805i		−	0.987793i	0.869521	−	0.493897i	$-0.164428\pi$
$402$		0			0
$403$	0.444155	−	0.444155i	0.0221249	−	0.0221249i
$404$		0			0
$405$	−3.13970	+	3.13970i	−0.156013	+	0.156013i
$406$		0			0
$407$		−	26.8473i		−	1.33077i
$408$		0			0
$409$	−2.52435			−0.124821			−0.0624105	−	0.998051i	$-0.519879\pi$
$409$	−2.52435			−0.124821			−0.0624105	+	0.998051i	$0.519879\pi$
$410$		0			0
$411$	−17.2490	+	17.2490i	−0.850828	+	0.850828i
$412$		0			0
$413$	−13.5714	+	13.5714i	−0.667805	+	0.667805i
$414$		0			0
$415$		−	2.92644i		−	0.143654i
$416$		0			0
$417$			5.37357i			0.263145i
$418$		0			0
$419$	−16.8455	+	16.8455i	−0.822957	+	0.822957i	−0.986531	−	0.163574i	$-0.947698\pi$
$419$	−16.8455	+	16.8455i	−0.822957	+	0.822957i	0.163574	+	0.986531i	$0.447698\pi$
$420$		0			0
$421$	−23.6174	−	23.6174i	−1.15104	−	1.15104i	−0.986344	−	0.164698i	$-0.947335\pi$
$421$	−23.6174	−	23.6174i	−1.15104	−	1.15104i	−0.164698	−	0.986344i	$-0.552665\pi$
$422$		0			0
$423$	−0.106822			−0.00519386
$424$		0			0
$425$		−	46.5863i		−	2.25977i
$426$		0			0
$427$	−4.09245	−	4.09245i	−0.198047	−	0.198047i
$428$		0			0
$429$	−2.67871	−	2.67871i	−0.129329	−	0.129329i
$430$		0			0
$431$	27.2068			1.31051			0.655253	−	0.755409i	$-0.272562\pi$
$431$	27.2068			1.31051			0.655253	+	0.755409i	$0.272562\pi$
$432$		0			0
$433$			21.1651i			1.01713i	0.861024	+	0.508564i	$0.169823\pi$
$433$			21.1651i			1.01713i	−0.861024	+	0.508564i	$0.830177\pi$
$434$		0			0
$435$	−75.6715	+	75.6715i	−3.62817	+	3.62817i
$436$		0			0
$437$	5.52447	−	14.0927i	0.264271	−	0.674147i
$438$		0			0
$439$			36.9150i			1.76186i	0.473249	+	0.880929i	$0.343081\pi$
$439$			36.9150i			1.76186i	−0.473249	+	0.880929i	$0.656919\pi$
$440$		0			0
$441$		−	14.6221i		−	0.696292i
$442$		0			0
$443$	2.68182	+	2.68182i	0.127417	+	0.127417i	0.767940	−	0.640522i	$-0.221282\pi$
$443$	2.68182	+	2.68182i	0.127417	+	0.127417i	−0.640522	+	0.767940i	$0.721282\pi$
$444$		0			0
$445$	36.2622	−	36.2622i	1.71899	−	1.71899i
$446$		0			0
$447$	−51.6646			−2.44365
$448$		0			0
$449$			30.7631i			1.45180i	0.687799	+	0.725901i	$0.258577\pi$
$449$			30.7631i			1.45180i	−0.687799	+	0.725901i	$0.741423\pi$
$450$		0			0
$451$	17.5361	+	17.5361i	0.825744	+	0.825744i
$452$		0			0
$453$	−18.6404	+	18.6404i	−0.875802	+	0.875802i
$454$		0			0
$455$		−	3.42722i		−	0.160670i
$456$		0			0
$457$		−	10.8846i		−	0.509161i	−0.967052	−	0.254581i	$-0.918063\pi$
$457$		−	10.8846i		−	0.509161i	0.967052	−	0.254581i	$-0.0819374\pi$
$458$		0			0
$459$	11.2295	−	11.2295i	0.524149	−	0.524149i
$460$		0			0
$461$	−13.6547	−	13.6547i	−0.635963	−	0.635963i	0.313594	−	0.949557i	$-0.398467\pi$
$461$	−13.6547	−	13.6547i	−0.635963	−	0.635963i	−0.949557	+	0.313594i	$0.898467\pi$
$462$		0			0
$463$		−	32.9847i		−	1.53293i	−0.642287	−	0.766464i	$-0.722014\pi$
$463$		−	32.9847i		−	1.53293i	0.642287	−	0.766464i	$-0.277986\pi$
$464$		0			0
$465$	18.8680			0.874982
$466$		0			0
$467$	12.6894	−	12.6894i	0.587194	−	0.587194i	−0.349677	−	0.936870i	$-0.613709\pi$
$467$	12.6894	−	12.6894i	0.587194	−	0.587194i	0.936870	+	0.349677i	$0.113709\pi$
$468$		0			0
$469$	2.78719	+	2.78719i	0.128701	+	0.128701i
$470$		0			0
$471$			9.96130i			0.458993i
$472$		0			0
$473$		−	17.9888i		−	0.827125i
$474$		0			0
$475$	56.0806	+	21.9840i	2.57315	+	1.00870i
$476$		0			0
$477$	18.6724	−	18.6724i	0.854949	−	0.854949i
$478$		0			0
$479$		−	25.4874i		−	1.16455i	−0.812993	−	0.582274i	$-0.802163\pi$
$479$		−	25.4874i		−	1.16455i	0.812993	−	0.582274i	$-0.197837\pi$
$480$		0			0
$481$	−3.15690			−0.143942
$482$		0			0
$483$	−13.4328	−	13.4328i	−0.611213	−	0.611213i
$484$		0			0
$485$	24.2091	+	24.2091i	1.09928	+	1.09928i
$486$		0			0
$487$		−	13.9190i		−	0.630732i	−0.948970	−	0.315366i	$-0.897873\pi$
$487$		−	13.9190i		−	0.630732i	0.948970	−	0.315366i	$-0.102127\pi$
$488$		0			0
$489$	50.4671			2.28220
$490$		0			0
$491$	12.0480	+	12.0480i	0.543717	+	0.543717i	0.924616	−	0.380900i	$-0.124386\pi$
$491$	12.0480	+	12.0480i	0.543717	+	0.543717i	−0.380900	+	0.924616i	$0.624386\pi$
$492$		0			0
$493$	−21.1949	+	21.1949i	−0.954569	+	0.954569i
$494$		0			0
$495$		−	69.4461i		−	3.12137i
$496$		0			0
$497$			7.12911i			0.319784i
$498$		0			0
$499$	15.3835	−	15.3835i	0.688662	−	0.688662i	−0.273274	−	0.961936i	$-0.588107\pi$
$499$	15.3835	−	15.3835i	0.688662	−	0.688662i	0.961936	+	0.273274i	$0.0881066\pi$
$500$		0			0
$501$	15.4303	−	15.4303i	0.689375	−	0.689375i
$502$		0			0
$503$	16.3820			0.730436			0.365218	−	0.930922i	$-0.380995\pi$
$503$	16.3820			0.730436			0.365218	+	0.930922i	$0.380995\pi$
$504$		0			0
$505$		−	1.34426i		−	0.0598186i
$506$		0			0
$507$	25.1894	−	25.1894i	1.11870	−	1.11870i
$508$		0			0
$509$	14.5621	−	14.5621i	0.645453	−	0.645453i	−0.306438	−	0.951891i	$-0.599137\pi$
$509$	14.5621	−	14.5621i	0.645453	−	0.645453i	0.951891	+	0.306438i	$0.0991372\pi$
$510$		0			0
$511$		−	12.0595i		−	0.533482i
$512$		0			0
$513$	8.21887	+	18.8173i	0.362872	+	0.830802i
$514$		0			0
$515$	31.9880	+	31.9880i	1.40956	+	1.40956i
$516$		0			0
$517$	−0.0547887	+	0.0547887i	−0.00240960	+	0.00240960i
$518$		0			0
$519$	−67.4569			−2.96103
$520$		0			0
$521$	27.5768			1.20816			0.604082	−	0.796922i	$-0.293540\pi$
$521$	27.5768			1.20816			0.604082	+	0.796922i	$0.293540\pi$
$522$		0			0
$523$	4.27047	−	4.27047i	0.186735	−	0.186735i	−0.607548	−	0.794283i	$-0.707847\pi$
$523$	4.27047	−	4.27047i	0.186735	−	0.186735i	0.794283	+	0.607548i	$0.207847\pi$
$524$		0			0
$525$	53.4543	−	53.4543i	2.33294	−	2.33294i
$526$		0			0
$527$	5.28474			0.230207
$528$		0			0
$529$	−10.9408			−0.475686
$530$		0			0
$531$	32.3364	+	32.3364i	1.40328	+	1.40328i
$532$		0			0
$533$	2.06203	−	2.06203i	0.0893162	−	0.0893162i
$534$		0			0
$535$			41.4606i			1.79250i
$536$		0			0
$537$			34.6297i			1.49438i
$538$		0			0
$539$	−7.49965	−	7.49965i	−0.323033	−	0.323033i
$540$		0			0
$541$	−9.91814	−	9.91814i	−0.426414	−	0.426414i	0.460991	−	0.887405i	$-0.347494\pi$
$541$	−9.91814	−	9.91814i	−0.426414	−	0.426414i	−0.887405	+	0.460991i	$0.847494\pi$
$542$		0			0
$543$		−	29.2129i		−	1.25365i
$544$		0			0
$545$			12.5339i			0.536895i
$546$		0			0
$547$	−4.55774	−	4.55774i	−0.194875	−	0.194875i	0.602924	−	0.797799i	$-0.294002\pi$
$547$	−4.55774	−	4.55774i	−0.194875	−	0.194875i	−0.797799	+	0.602924i	$0.794002\pi$
$548$		0			0
$549$	−9.75101	+	9.75101i	−0.416163	+	0.416163i
$550$		0			0
$551$	−15.5125	−	35.5162i	−0.660855	−	1.51304i
$552$		0			0
$553$	−14.2837			−0.607406
$554$		0			0
$555$	−67.0536	−	67.0536i	−2.84627	−	2.84627i
$556$		0			0
$557$	−0.433432	−	0.433432i	−0.0183651	−	0.0183651i	0.697865	−	0.716230i	$-0.254134\pi$
$557$	−0.433432	−	0.433432i	−0.0183651	−	0.0183651i	−0.716230	+	0.697865i	$0.754134\pi$
$558$		0			0
$559$	−2.11525			−0.0894656
$560$		0			0
$561$		−	31.8725i		−	1.34566i
$562$		0			0
$563$	−23.2442	−	23.2442i	−0.979626	−	0.979626i	0.0201710	−	0.999797i	$-0.493579\pi$
$563$	−23.2442	−	23.2442i	−0.979626	−	0.979626i	−0.999797	+	0.0201710i	$0.993579\pi$
$564$		0			0
$565$	−8.59941	−	8.59941i	−0.361780	−	0.361780i
$566$		0			0
$567$	−2.01809			−0.0847518
$568$		0			0
$569$	−15.7971			−0.662248			−0.331124	−	0.943587i	$-0.607428\pi$
$569$	−15.7971			−0.662248			−0.331124	+	0.943587i	$0.607428\pi$
$570$		0			0
$571$	−2.55691	−	2.55691i	−0.107003	−	0.107003i	0.651578	−	0.758582i	$-0.274107\pi$
$571$	−2.55691	−	2.55691i	−0.107003	−	0.107003i	−0.758582	+	0.651578i	$0.774107\pi$
$572$		0			0
$573$	27.8330	−	27.8330i	1.16274	−	1.16274i
$574$		0			0
$575$			47.9884i			2.00125i
$576$		0			0
$577$	10.7687			0.448307			0.224153	−	0.974554i	$-0.428038\pi$
$577$	10.7687			0.448307			0.224153	+	0.974554i	$0.428038\pi$
$578$		0			0
$579$	2.16605	−	2.16605i	0.0900178	−	0.0900178i
$580$		0			0
$581$	0.940509	−	0.940509i	0.0390189	−	0.0390189i
$582$		0			0
$583$		−	19.1540i		−	0.793278i
$584$		0			0
$585$	−8.16598			−0.337622
$586$		0			0
$587$	8.58004	+	8.58004i	0.354136	+	0.354136i	0.861646	−	0.507510i	$-0.169434\pi$
$587$	8.58004	+	8.58004i	0.354136	+	0.354136i	−0.507510	+	0.861646i	$0.669434\pi$
$588$		0			0
$589$	−2.49386	+	6.36176i	−0.102758	+	0.262132i
$590$		0			0
$591$	−20.0775			−0.825878
$592$		0			0
$593$	10.1128			0.415283			0.207641	−	0.978205i	$-0.433421\pi$
$593$	10.1128			0.415283			0.207641	+	0.978205i	$0.433421\pi$
$594$		0			0
$595$	20.3892	−	20.3892i	0.835878	−	0.835878i
$596$		0			0
$597$	18.4405	+	18.4405i	0.754718	+	0.754718i
$598$		0			0
$599$			35.6436i			1.45636i	0.685388	+	0.728179i	$0.259633\pi$
$599$			35.6436i			1.45636i	−0.685388	+	0.728179i	$0.740367\pi$
$600$		0			0
$601$	33.4257			1.36346			0.681731	−	0.731603i	$-0.261228\pi$
$601$	33.4257			1.36346			0.681731	+	0.731603i	$0.261228\pi$
$602$		0			0
$603$	6.64100	−	6.64100i	0.270443	−	0.270443i
$604$		0			0
$605$	−1.87634	−	1.87634i	−0.0762842	−	0.0762842i
$606$		0			0
$607$	−31.9197			−1.29558			−0.647791	−	0.761818i	$-0.724307\pi$
$607$	−31.9197			−1.29558			−0.647791	+	0.761818i	$0.724307\pi$
$608$		0			0
$609$	−48.6390			−1.97095
$610$		0			0
$611$	0.00644245	+	0.00644245i	0.000260634	+	0.000260634i
$612$		0			0
$613$	5.35841	−	5.35841i	0.216424	−	0.216424i	−0.590565	−	0.806990i	$-0.701095\pi$
$613$	5.35841	−	5.35841i	0.216424	−	0.216424i	0.806990	+	0.590565i	$0.201095\pi$
$614$		0			0
$615$	87.5962			3.53222
$616$		0			0
$617$		−	46.8728i		−	1.88703i	−0.331332	−	0.943514i	$-0.607498\pi$
$617$		−	46.8728i		−	1.88703i	0.331332	−	0.943514i	$-0.392502\pi$
$618$		0			0
$619$	−8.55781	−	8.55781i	−0.343967	−	0.343967i	0.513889	−	0.857857i	$-0.328204\pi$
$619$	−8.55781	−	8.55781i	−0.343967	−	0.343967i	−0.857857	+	0.513889i	$0.828204\pi$
$620$		0			0
$621$	−11.5675	+	11.5675i	−0.464186	+	0.464186i
$622$		0			0
$623$	23.3081			0.933818
$624$		0			0
$625$	−96.8696			−3.87478
$626$		0			0
$627$	38.3680	+	15.0406i	1.53227	+	0.600663i
$628$		0			0
$629$	−18.7811	−	18.7811i	−0.748851	−	0.748851i
$630$		0			0
$631$	−43.3565			−1.72599			−0.862997	−	0.505210i	$-0.831415\pi$
$631$	−43.3565			−1.72599			−0.862997	+	0.505210i	$0.831415\pi$
$632$		0			0
$633$			70.1878i			2.78972i
$634$		0			0
$635$	28.1055	−	28.1055i	1.11533	−	1.11533i
$636$		0			0
$637$	−0.881863	+	0.881863i	−0.0349407	+	0.0349407i
$638$		0			0
$639$	16.9864			0.671973
$640$		0			0
$641$		−	36.9181i		−	1.45818i	−0.684420	−	0.729088i	$-0.739944\pi$
$641$		−	36.9181i		−	1.45818i	0.684420	−	0.729088i	$-0.260056\pi$
$642$		0			0
$643$	25.0873	−	25.0873i	0.989345	−	0.989345i	−0.0105987	−	0.999944i	$-0.503374\pi$
$643$	25.0873	−	25.0873i	0.989345	−	0.989345i	0.999944	+	0.0105987i	$0.00337374\pi$
$644$		0			0
$645$	−44.9286	−	44.9286i	−1.76906	−	1.76906i
$646$		0			0
$647$	3.74333			0.147166			0.0735828	−	0.997289i	$-0.476557\pi$
$647$	3.74333			0.147166			0.0735828	+	0.997289i	$0.476557\pi$
$648$		0			0
$649$	33.1705			1.30206
$650$		0			0
$651$	6.06384	+	6.06384i	0.237661	+	0.237661i
$652$		0			0
$653$	22.2848	+	22.2848i	0.872073	+	0.872073i	0.992698	−	0.120625i	$-0.0384900\pi$
$653$	22.2848	+	22.2848i	0.872073	+	0.872073i	−0.120625	+	0.992698i	$0.538490\pi$
$654$		0			0
$655$			63.7106i			2.48938i
$656$		0			0
$657$	−28.7341			−1.12102
$658$		0			0
$659$	−11.3228	−	11.3228i	−0.441074	−	0.441074i	0.451299	−	0.892373i	$-0.350961\pi$
$659$	−11.3228	−	11.3228i	−0.441074	−	0.441074i	−0.892373	+	0.451299i	$0.850961\pi$
$660$		0			0
$661$	2.14571	+	2.14571i	0.0834583	+	0.0834583i	0.747604	−	0.664145i	$-0.231204\pi$
$661$	2.14571	+	2.14571i	0.0834583	+	0.0834583i	−0.664145	+	0.747604i	$0.731204\pi$
$662$		0			0
$663$	−3.74779			−0.145552
$664$		0			0
$665$	14.9229	+	34.1662i	0.578684	+	1.32491i
$666$		0			0
$667$	21.8327	−	21.8327i	0.845367	−	0.845367i
$668$		0			0
$669$	−33.5255	−	33.5255i	−1.29617	−	1.29617i
$670$		0			0
$671$			10.0025i			0.386144i
$672$		0			0
$673$			1.49471i			0.0576167i	0.999585	+	0.0288083i	$0.00917125\pi$
$673$			1.49471i			0.0576167i	−0.999585	+	0.0288083i	$0.990829\pi$
$674$		0			0
$675$	−46.0315	−	46.0315i	−1.77175	−	1.77175i
$676$		0			0
$677$	3.08165	+	3.08165i	0.118438	+	0.118438i	0.763841	−	0.645404i	$-0.223311\pi$
$677$	3.08165	+	3.08165i	0.118438	+	0.118438i	−0.645404	+	0.763841i	$0.723311\pi$
$678$		0			0
$679$			15.5608i			0.597167i
$680$		0			0
$681$		−	48.9438i		−	1.87553i
$682$		0			0
$683$	−18.2706	+	18.2706i	−0.699106	+	0.699106i	−0.964218	−	0.265112i	$-0.914591\pi$
$683$	−18.2706	+	18.2706i	−0.699106	+	0.699106i	0.265112	+	0.964218i	$0.414591\pi$
$684$		0			0
$685$	26.9697	+	26.9697i	1.03046	+	1.03046i
$686$		0			0
$687$	3.64292			0.138986
$688$		0			0
$689$	−2.25227			−0.0858046
$690$		0			0
$691$	−18.4458	+	18.4458i	−0.701712	+	0.701712i	−0.964778	−	0.263066i	$-0.915266\pi$
$691$	−18.4458	+	18.4458i	−0.701712	+	0.701712i	0.263066	+	0.964778i	$0.415266\pi$
$692$		0			0
$693$	22.3188	−	22.3188i	0.847821	−	0.847821i
$694$		0			0
$695$	8.40186			0.318701
$696$		0			0
$697$	24.5349			0.929324
$698$		0			0
$699$	8.95382	−	8.95382i	0.338665	−	0.338665i
$700$		0			0
$701$	24.7360	+	24.7360i	0.934266	+	0.934266i	0.997969	−	0.0637026i	$-0.0202909\pi$
$701$	24.7360	+	24.7360i	0.934266	+	0.934266i	−0.0637026	+	0.997969i	$0.520291\pi$
$702$		0			0
$703$	31.4714	−	13.7459i	1.18697	−	0.518435i
$704$		0			0
$705$			0.273680i			0.0103074i
$706$		0			0
$707$	0.432021	−	0.432021i	0.0162478	−	0.0162478i
$708$		0			0
$709$	−6.98219	+	6.98219i	−0.262222	+	0.262222i	−0.825956	−	0.563734i	$-0.809364\pi$
$709$	−6.98219	+	6.98219i	−0.262222	+	0.262222i	0.563734	+	0.825956i	$0.309364\pi$
$710$		0			0
$711$			34.0336i			1.27636i
$712$		0			0
$713$	−5.44379			−0.203871
$714$		0			0
$715$	−4.18831	+	4.18831i	−0.156634	+	0.156634i
$716$		0			0
$717$	−34.0802	+	34.0802i	−1.27275	+	1.27275i
$718$		0			0
$719$			30.9143i			1.15291i	0.817129	+	0.576455i	$0.195564\pi$
$719$			30.9143i			1.15291i	−0.817129	+	0.576455i	$0.804436\pi$
$720$		0			0
$721$			20.5608i			0.765723i
$722$		0			0
$723$	−43.5531	+	43.5531i	−1.61976	+	1.61976i
$724$		0			0
$725$	86.8811	+	86.8811i	3.22668	+	3.22668i
$726$		0			0
$727$	−37.9913			−1.40902			−0.704510	−	0.709694i	$-0.748833\pi$
$727$	−37.9913			−1.40902			−0.704510	+	0.709694i	$0.748833\pi$
$728$		0			0
$729$			44.0188i			1.63033i
$730$		0			0
$731$	−12.5841	−	12.5841i	−0.465439	−	0.465439i
$732$		0			0
$733$	−24.6552	−	24.6552i	−0.910660	−	0.910660i	0.0856642	−	0.996324i	$-0.472699\pi$
$733$	−24.6552	−	24.6552i	−0.910660	−	0.910660i	−0.996324	+	0.0856642i	$0.972699\pi$
$734$		0			0
$735$	−37.4621			−1.38181
$736$		0			0
$737$		−	6.81230i		−	0.250934i
$738$		0			0
$739$	−10.1897	+	10.1897i	−0.374834	+	0.374834i	−0.869234	−	0.494400i	$-0.835388\pi$
$739$	−10.1897	+	10.1897i	−0.374834	+	0.374834i	0.494400	+	0.869234i	$0.335388\pi$
$740$		0			0
$741$	1.76858	−	4.51159i	0.0649704	−	0.165737i
$742$		0			0
$743$		−	4.34278i		−	0.159321i	−0.996822	−	0.0796605i	$-0.974616\pi$
$743$		−	4.34278i		−	0.159321i	0.996822	−	0.0796605i	$-0.0253836\pi$
$744$		0			0
$745$			80.7803i			2.95956i
$746$		0			0
$747$	−2.24094	−	2.24094i	−0.0819915	−	0.0819915i
$748$		0			0
$749$	−13.3247	+	13.3247i	−0.486874	+	0.486874i
$750$		0			0
$751$	18.9926			0.693049			0.346524	−	0.938041i	$-0.387362\pi$
$751$	18.9926			0.693049			0.346524	+	0.938041i	$0.387362\pi$
$752$		0			0
$753$		−	29.9658i		−	1.09201i
$754$		0			0
$755$	29.1452	+	29.1452i	1.06070	+	1.06070i
$756$		0			0
$757$	12.3994	−	12.3994i	0.450664	−	0.450664i	−0.444911	−	0.895575i	$-0.646765\pi$
$757$	12.3994	−	12.3994i	0.450664	−	0.450664i	0.895575	+	0.444911i	$0.146765\pi$
$758$		0			0
$759$			32.8317i			1.19171i
$760$		0			0
$761$		−	18.6209i		−	0.675006i	−0.941324	−	0.337503i	$-0.890418\pi$
$761$		−	18.6209i		−	0.675006i	0.941324	−	0.337503i	$-0.109582\pi$
$762$		0			0
$763$	−4.02819	+	4.02819i	−0.145830	+	0.145830i
$764$		0			0
$765$	−48.5811	−	48.5811i	−1.75645	−	1.75645i
$766$		0			0
$767$		−	3.90043i		−	0.140836i
$768$		0			0
$769$	41.5054			1.49672			0.748361	−	0.663292i	$-0.230841\pi$
$769$	41.5054			1.49672			0.748361	+	0.663292i	$0.230841\pi$
$770$		0			0
$771$	27.4822	−	27.4822i	0.989746	−	0.989746i
$772$		0			0
$773$	−20.2128	−	20.2128i	−0.727003	−	0.727003i	0.243019	−	0.970022i	$-0.421862\pi$
$773$	−20.2128	−	20.2128i	−0.727003	−	0.727003i	−0.970022	+	0.243019i	$0.921862\pi$
$774$		0			0
$775$		−	21.6630i		−	0.778157i
$776$		0			0
$777$		−	43.0997i		−	1.54619i
$778$		0			0
$779$	−11.5780	+	29.5350i	−0.414824	+	1.05820i
$780$		0			0
$781$	8.71229	−	8.71229i	0.311750	−	0.311750i
$782$		0			0
$783$			41.8849i			1.49684i
$784$		0			0
$785$	15.5750			0.555896
$786$		0			0
$787$	−34.9721	−	34.9721i	−1.24662	−	1.24662i	−0.957202	−	0.289420i	$-0.906538\pi$
$787$	−34.9721	−	34.9721i	−1.24662	−	1.24662i	−0.289420	−	0.957202i	$-0.593462\pi$
$788$		0			0
$789$	−46.4780	−	46.4780i	−1.65466	−	1.65466i
$790$		0			0
$791$		−	5.52741i		−	0.196532i
$792$		0			0
$793$	1.17617			0.0417670
$794$		0			0
$795$	−47.8389	−	47.8389i	−1.69667	−	1.69667i
$796$		0			0
$797$	0.792356	−	0.792356i	0.0280667	−	0.0280667i	−0.692934	−	0.721001i	$-0.743682\pi$
$797$	0.792356	−	0.792356i	0.0280667	−	0.0280667i	0.721001	+	0.692934i	$0.243682\pi$
$798$		0			0
$799$			0.0766550i			0.00271186i
$800$		0			0
$801$		−	55.5358i		−	1.96226i
$802$		0			0
$803$	−14.7376	+	14.7376i	−0.520079	+	0.520079i
$804$		0			0
$805$	−21.0029	+	21.0029i	−0.740254	+	0.740254i
$806$		0			0
$807$	12.3562			0.434958
$808$		0			0
$809$		−	12.8181i		−	0.450662i	−0.974282	−	0.225331i	$-0.927654\pi$
$809$		−	12.8181i		−	0.450662i	0.974282	−	0.225331i	$-0.0723463\pi$
$810$		0			0
$811$	25.1956	−	25.1956i	0.884736	−	0.884736i	−0.109276	−	0.994012i	$-0.534853\pi$
$811$	25.1956	−	25.1956i	0.884736	−	0.884736i	0.994012	+	0.109276i	$0.0348531\pi$
$812$		0			0
$813$	25.7685	−	25.7685i	0.903741	−	0.903741i
$814$		0			0
$815$		−	78.9080i		−	2.76403i
$816$		0			0
$817$	21.0871	−	9.21027i	0.737744	−	0.322227i
$818$		0			0
$819$	−2.62440	−	2.62440i	−0.0917041	−	0.0917041i
$820$		0			0
$821$	7.30455	−	7.30455i	0.254930	−	0.254930i	−0.568058	−	0.822989i	$-0.692305\pi$
$821$	7.30455	−	7.30455i	0.254930	−	0.254930i	0.822989	+	0.568058i	$0.192305\pi$
$822$		0			0
$823$	8.95159			0.312033			0.156016	−	0.987754i	$-0.450135\pi$
$823$	8.95159			0.312033			0.156016	+	0.987754i	$0.450135\pi$
$824$		0			0
$825$	−130.650			−4.54865
$826$		0			0
$827$	−37.1550	+	37.1550i	−1.29201	+	1.29201i	−0.358462	+	0.933544i	$0.616699\pi$
$827$	−37.1550	+	37.1550i	−1.29201	+	1.29201i	−0.933544	+	0.358462i	$0.883301\pi$
$828$		0			0
$829$	−34.6202	+	34.6202i	−1.20241	+	1.20241i	−0.228980	+	0.973431i	$0.573539\pi$
$829$	−34.6202	+	34.6202i	−1.20241	+	1.20241i	−0.973431	+	0.228980i	$0.926461\pi$
$830$		0			0
$831$	−36.2681			−1.25812
$832$		0			0
$833$	−10.4928			−0.363553
$834$		0			0
$835$	−24.1261	−	24.1261i	−0.834918	−	0.834918i
$836$		0			0
$837$	5.22180	−	5.22180i	0.180492	−	0.180492i
$838$		0			0
$839$		−	38.8966i		−	1.34286i	−0.741069	−	0.671429i	$-0.765681\pi$
$839$		−	38.8966i		−	1.34286i	0.741069	−	0.671429i	$-0.234319\pi$
$840$		0			0
$841$		−	50.0546i		−	1.72602i
$842$		0			0
$843$	41.4012	+	41.4012i	1.42593	+	1.42593i
$844$		0			0
$845$	−39.3849	−	39.3849i	−1.35488	−	1.35488i
$846$		0			0
$847$		−	1.20605i		−	0.0414403i
$848$		0			0
$849$			16.1303i			0.553591i
$850$		0			0
$851$	19.3463	+	19.3463i	0.663183	+	0.663183i
$852$		0			0
$853$	6.98168	−	6.98168i	0.239048	−	0.239048i	−0.577408	−	0.816456i	$-0.695936\pi$
$853$	6.98168	−	6.98168i	0.239048	−	0.239048i	0.816456	+	0.577408i	$0.195936\pi$
$854$		0			0
$855$	81.4073	−	35.5565i	2.78407	−	1.21601i
$856$		0			0
$857$	−5.73913			−0.196045			−0.0980225	−	0.995184i	$-0.531252\pi$
$857$	−5.73913			−0.196045			−0.0980225	+	0.995184i	$0.531252\pi$
$858$		0			0
$859$	22.8096	+	22.8096i	0.778253	+	0.778253i	0.979534	−	0.201280i	$-0.0645102\pi$
$859$	22.8096	+	22.8096i	0.778253	+	0.778253i	−0.201280	+	0.979534i	$0.564510\pi$
$860$		0			0
$861$	28.1519	+	28.1519i	0.959414	+	0.959414i
$862$		0			0
$863$	−26.5805			−0.904812			−0.452406	−	0.891812i	$-0.649434\pi$
$863$	−26.5805			−0.904812			−0.452406	+	0.891812i	$0.649434\pi$
$864$		0			0
$865$			105.472i			3.58617i
$866$		0			0
$867$	11.0554	+	11.0554i	0.375461	+	0.375461i
$868$		0			0
$869$	17.4558	+	17.4558i	0.592146	+	0.592146i
$870$		0			0
$871$	−0.801040			−0.0271422
$872$		0			0
$873$	37.0764			1.25485
$874$		0			0
$875$	−53.3381	−	53.3381i	−1.80316	−	1.80316i
$876$		0			0
$877$	−4.70057	+	4.70057i	−0.158727	+	0.158727i	−0.782002	−	0.623276i	$-0.785802\pi$
$877$	−4.70057	+	4.70057i	−0.158727	+	0.158727i	0.623276	+	0.782002i	$0.285802\pi$
$878$		0			0
$879$			32.3369i			1.09070i
$880$		0			0
$881$	42.9256			1.44620			0.723099	−	0.690744i	$-0.242717\pi$
$881$	42.9256			1.44620			0.723099	+	0.690744i	$0.242717\pi$
$882$		0			0
$883$	3.21289	−	3.21289i	0.108123	−	0.108123i	−0.650976	−	0.759098i	$-0.725640\pi$
$883$	3.21289	−	3.21289i	0.108123	−	0.108123i	0.759098	+	0.650976i	$0.225640\pi$
$884$		0			0
$885$	82.8463	−	82.8463i	2.78485	−	2.78485i
$886$		0			0
$887$		−	3.19152i		−	0.107161i	−0.998564	−	0.0535804i	$-0.982937\pi$
$887$		−	3.19152i		−	0.107161i	0.998564	−	0.0535804i	$-0.0170633\pi$
$888$		0			0
$889$	18.0653			0.605889
$890$		0			0
$891$	2.46625	+	2.46625i	0.0826226	+	0.0826226i
$892$		0			0
$893$	−0.0922772	−	0.0361734i	−0.00308794	−	0.00121050i
$894$		0			0
$895$	54.1453			1.80988
$896$		0			0
$897$	3.86058			0.128901
$898$		0			0
$899$	−9.85576	+	9.85576i	−0.328708	+	0.328708i
$900$		0			0
$901$	−13.3992	−	13.3992i	−0.446393	−	0.446393i
$902$		0			0
$903$		−	28.8785i		−	0.961018i
$904$		0			0
$905$	−45.6759			−1.51832
$906$		0			0
$907$	−2.28293	+	2.28293i	−0.0758035	+	0.0758035i	−0.743992	−	0.668189i	$-0.767070\pi$
$907$	−2.28293	+	2.28293i	−0.0758035	+	0.0758035i	0.668189	+	0.743992i	$0.267070\pi$
$908$		0			0
$909$	−1.02937	−	1.02937i	−0.0341420	−	0.0341420i
$910$		0			0
$911$	−31.5176			−1.04422			−0.522112	−	0.852877i	$-0.674856\pi$
$911$	−31.5176			−1.04422			−0.522112	+	0.852877i	$0.674856\pi$
$912$		0			0
$913$	−2.29874			−0.0760772
$914$		0			0
$915$	24.9822	+	24.9822i	0.825887	+	0.825887i
$916$		0			0
$917$	−20.4755	+	20.4755i	−0.676160	+	0.676160i
$918$		0			0
$919$	−5.00086			−0.164963			−0.0824815	−	0.996593i	$-0.526285\pi$
$919$	−5.00086			−0.164963			−0.0824815	+	0.996593i	$0.526285\pi$
$920$		0			0
$921$			18.4067i			0.606522i
$922$		0			0
$923$	−1.02445	−	1.02445i	−0.0337203	−	0.0337203i
$924$		0			0
$925$	−76.9865	+	76.9865i	−2.53130	+	2.53130i
$926$		0			0
$927$	48.9898			1.60904
$928$		0			0
$929$	−53.9392			−1.76969			−0.884843	−	0.465889i	$-0.845735\pi$
$929$	−53.9392			−1.76969			−0.884843	+	0.465889i	$0.845735\pi$
$930$		0			0
$931$	4.95153	−	12.6312i	0.162280	−	0.413970i
$932$		0			0
$933$	42.6426	+	42.6426i	1.39605	+	1.39605i
$934$		0			0
$935$	−49.8343			−1.62975
$936$		0			0
$937$		−	28.6384i		−	0.935574i	−0.883841	−	0.467787i	$-0.845051\pi$
$937$		−	28.6384i		−	0.935574i	0.883841	−	0.467787i	$-0.154949\pi$
$938$		0			0
$939$	27.6816	−	27.6816i	0.903356	−	0.903356i
$940$		0			0
$941$	7.68798	−	7.68798i	0.250621	−	0.250621i	−0.570604	−	0.821225i	$-0.693291\pi$
$941$	7.68798	−	7.68798i	0.250621	−	0.250621i	0.821225	+	0.570604i	$0.193291\pi$
$942$		0			0
$943$	−25.2732			−0.823010
$944$		0			0
$945$		−	40.2928i		−	1.31072i
$946$		0			0
$947$	14.8820	−	14.8820i	0.483599	−	0.483599i	−0.422680	−	0.906279i	$-0.638911\pi$
$947$	14.8820	−	14.8820i	0.483599	−	0.483599i	0.906279	+	0.422680i	$0.138911\pi$
$948$		0			0
$949$	1.73296	+	1.73296i	0.0562541	+	0.0562541i
$950$		0			0
$951$	−6.73746			−0.218477
$952$		0			0
$953$	−37.2259			−1.20587			−0.602933	−	0.797792i	$-0.706001\pi$
$953$	−37.2259			−1.20587			−0.602933	+	0.797792i	$0.706001\pi$
$954$		0			0
$955$	−43.5184	−	43.5184i	−1.40822	−	1.40822i
$956$		0			0
$957$	59.4404	+	59.4404i	1.92144	+	1.92144i
$958$		0			0
$959$			17.3352i			0.559781i
$960$		0			0
$961$	−28.5426			−0.920728
$962$		0			0
$963$	31.7486	+	31.7486i	1.02308	+	1.02308i
$964$		0			0
$965$	−3.38673	−	3.38673i	−0.109023	−	0.109023i
$966$		0			0
$967$	11.4725			0.368929			0.184465	−	0.982839i	$-0.440945\pi$
$967$	11.4725			0.368929			0.184465	+	0.982839i	$0.440945\pi$
$968$		0			0
$969$	37.3620	−	16.3187i	1.20024	−	0.524233i
$970$		0			0
$971$	−12.8634	+	12.8634i	−0.412808	+	0.412808i	−0.882715	−	0.469908i	$-0.844287\pi$
$971$	−12.8634	+	12.8634i	−0.412808	+	0.412808i	0.469908	+	0.882715i	$0.344287\pi$
$972$		0			0
$973$	2.70021	+	2.70021i	0.0865648	+	0.0865648i
$974$		0			0
$975$			15.3628i			0.492003i
$976$		0			0
$977$			4.12323i			0.131914i	0.997822	+	0.0659569i	$0.0210100\pi$
$977$			4.12323i			0.131914i	−0.997822	+	0.0659569i	$0.978990\pi$
$978$		0			0
$979$	−28.4842	−	28.4842i	−0.910358	−	0.910358i
$980$		0			0
$981$	9.59790	+	9.59790i	0.306437	+	0.306437i
$982$		0			0
$983$			43.7990i			1.39697i	0.715624	+	0.698485i	$0.246142\pi$
$983$			43.7990i			1.39697i	−0.715624	+	0.698485i	$0.753858\pi$
$984$		0			0
$985$			31.3922i			1.00024i
$986$		0			0
$987$	−0.0879559	+	0.0879559i	−0.00279967	+	0.00279967i
$988$		0			0
$989$	12.9628	+	12.9628i	0.412193	+	0.412193i
$990$		0			0
$991$	−3.63673			−0.115525			−0.0577623	−	0.998330i	$-0.518397\pi$
$991$	−3.63673			−0.115525			−0.0577623	+	0.998330i	$0.518397\pi$
$992$		0			0
$993$	−17.2059			−0.546014
$994$		0			0
$995$	28.8326	−	28.8326i	0.914056	−	0.914056i
$996$		0			0
$997$	−36.6874	+	36.6874i	−1.16190	+	1.16190i	−0.177842	+	0.984059i	$0.556911\pi$
$997$	−36.6874	+	36.6874i	−1.16190	+	1.16190i	−0.984059	+	0.177842i	$0.943089\pi$
$998$		0			0
$999$	−37.1148			−1.17426

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.m.a.303.5		76
4.3	odd	2		304.2.m.a.227.32	yes	76
16.5	even	4		304.2.m.a.75.7	✓	76
16.11	odd	4	inner	1216.2.m.a.911.34		76
19.18	odd	2	inner	1216.2.m.a.303.34		76
76.75	even	2		304.2.m.a.227.7	yes	76
304.37	odd	4		304.2.m.a.75.32	yes	76
304.75	even	4	inner	1216.2.m.a.911.5		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.m.a.75.7	✓	76	16.5	even	4
304.2.m.a.75.32	yes	76	304.37	odd	4
304.2.m.a.227.7	yes	76	76.75	even	2
304.2.m.a.227.32	yes	76	4.3	odd	2
1216.2.m.a.303.5		76	1.1	even	1	trivial
1216.2.m.a.303.34		76	19.18	odd	2	inner
1216.2.m.a.911.5		76	304.75	even	4	inner
1216.2.m.a.911.34		76	16.11	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.m (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.96187 - 1.96187i) q^{3} +(-3.06749 + 3.06749i) q^{5} -1.97168 q^{7} +4.69788i q^{9} +(2.40953 + 2.40953i) q^{11} +(0.283330 - 0.283330i) q^{13} +12.0360 q^{15} +3.37118 q^{17} +(-1.59086 + 4.05822i) q^{19} +(3.86818 + 3.86818i) q^{21} -3.47264 q^{23} -13.8190i q^{25} +(3.33103 - 3.33103i) q^{27} +(-6.28708 + 6.28708i) q^{29} +1.56762 q^{31} -9.45439i q^{33} +(6.04810 - 6.04810i) q^{35} +(-5.57107 - 5.57107i) q^{37} -1.11171 q^{39} +7.27782 q^{41} +(-3.73284 - 3.73284i) q^{43} +(-14.4107 - 14.4107i) q^{45} +0.0227383i q^{47} -3.11249 q^{49} +(-6.61383 - 6.61383i) q^{51} +(-3.97463 - 3.97463i) q^{53} -14.7824 q^{55} +(11.0828 - 4.84066i) q^{57} +(6.88318 - 6.88318i) q^{59} +(2.07562 + 2.07562i) q^{61} -9.26271i q^{63} +1.73822i q^{65} +(-1.41362 - 1.41362i) q^{67} +(6.81287 + 6.81287i) q^{69} -3.61576i q^{71} +6.11638i q^{73} +(-27.1111 + 27.1111i) q^{75} +(-4.75082 - 4.75082i) q^{77} +7.24446 q^{79} +1.02354 q^{81} +(-0.477010 + 0.477010i) q^{83} +(-10.3411 + 10.3411i) q^{85} +24.6689 q^{87} -11.8214 q^{89} +(-0.558635 + 0.558635i) q^{91} +(-3.07548 - 3.07548i) q^{93} +(-7.56862 - 17.3285i) q^{95} -7.89215i q^{97} +(-11.3197 + 11.3197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 4 q^{5} + 8 q^{7} + 4 q^{11} - 8 q^{17} - 6 q^{19} + 8 q^{23} + 8 q^{39} + 4 q^{43} + 4 q^{45} + 44 q^{49} + 8 q^{55} + 28 q^{61} - 32 q^{77} - 52 q^{81} - 36 q^{83} - 56 q^{85} + 120 q^{87} - 16 q^{93}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q - 4 * q^5 + 8 * q^7 + 4 * q^11 - 8 * q^17 - 6 * q^19 + 8 * q^23 + 8 * q^39 + 4 * q^43 + 4 * q^45 + 44 * q^49 + 8 * q^55 + 28 * q^61 - 32 * q^77 - 52 * q^81 - 36 * q^83 - 56 * q^85 + 120 * q^87 - 16 * q^93 - 76 * q^99

Introduction

L-functions

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